8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 1, 0, 0, 0, 2] 
dist 0=[52.085428146517959383  ,52.085428146517959383  ] 
dist 1=[51.554480311124536418  ,52.893884466309606522  ] 
dist 2=[51.028877240932711597  ,53.670800126142597936  ] 
dist 3=[49.866700034259728996  ,54.075810059487734419  ] 
dist 4=[48.110544874071503082  ,54.285886455549246353  ] 
dist 5=[46.102853391017835108  ,54.302150660105105724  ] 
dist 6=[43.936018089237382249  ,54.182448682601517654  ] 
dist 7=[41.232885071752456919  ,54.088196734359632743  ] 
dist 8=[37.083311539256385581  ,53.774851782807709795  ] 
dist 9=[32.892383959669889510  ,53.610644861789703676  ] 
dist 10=[30.023970511842373799  ,51.321533941804155976  ] 
dist 11=[27.568470679544631268  ,50.875315245067418533  ] 
dist 12=[25.026292283275372960  ,50.260481822838733325  ] 
dist 13=[22.614959604175617130  ,49.593978784619996440  ] 
dist 14=[20.681744158171502429  ,44.966416151676656695  ] 
dist 15=[18.722667889161750263  ,42.066620391116630267  ] 
dist 16=[16.207541956411754462  ,35.915147453198799546  ] 
dist 17=[13.761526712998261239  ,35.688029566276074503  ] 
dist 18=[12.078190061553880279  ,28.322868681530486476  ] 
dist 19=[10.624535970544378998  ,27.370097221550504532  ] 
dist 20=[9.0955183135520886535 ,25.455611227614122824  ] 
dist 21=[7.6255691706701061014 ,24.955674842524619987  ] 
dist 22=[6.4073112335109585274 ,23.144084206950049359  ] 
dist 23=[5.1321938454082926497 ,22.751748515051015903  ] 
dist 24=[3.4339411942613581563 ,22.091650524072613406  ] 
dist 25=[1.7942977940564266388 ,21.925348048220698517  ] 
dist 26=[.7531725149119522389 ,10.032725237668991201  ] 
dist 27=[-.05748671618908912222,9.7421248553202252322 ] 
dist 28=[-2.1163425134958516661 ,8.8127398543556315918 ] 
dist 29=[-4.4078740506505534276 ,7.2464026000834761486 ] 
dist 30=[-6.4960009827272939239 ,6.9831633786930605504 ] 
dist 31=[-8.0323514505355410000 ,5.9645490311881116001 ] 
dist 32=[-9.4637890510449597304 ,-1.9026747167991692588 ] 
dist 33=[-11.132891508758875938  ,-2.4393355895762349590 ] 
dist 34=[-12.676233535456324751  ,-2.4911832344032353185 ] 
dist 35=[-13.605367720364892321  ,-2.4608417041318226030 ] 
dist 36=[-14.265820208050737193  ,-2.3143415506940918998 ] 
dist 37=[-14.735999340367954298  ,-2.1076818098306808487 ] 
dist 38=[-15.087607728372842693  ,-1.8370018737445281507 ] 
dist 39=[-15.274367241255854792  ,-1.4695304581948654897 ] 
dist 40=[-15.377042793313056354  ,-.87652055513616620992] 
dist 41=[-15.392504284920416893  ,-.27070308090361627338] 
dist 42=[-9.6492341878766953236 ,.14798419475134030245] 
dist 43=[-9.6274710370499976533 ,.5082307069463430579 ] 
dist 44=[-9.6047105982697716732 ,.88105823444526422848] 
dist 45=[-9.5860010543035099811 ,1.2317920168373460839 ] 
dist 46=[-9.5674051772415157077 ,1.5039232964202807205 ] 
dist 47=[-9.5447277446337346374 ,1.7695115598656224252 ] 
dist 48=[-3.8516254841995682621 ,2.0940730015093418647 ] 
dist 49=[-3.3873990323540153637 ,2.3974517331188157844 ] 
dist 50=[-2.2985612318227654995 ,2.5784954413119613016 ] 
dist 51=[-2.1297081413602668345 ,2.7034646022070098915 ] 
dist 52=[-.68845694361003042642,2.7830999891514217275 ] 
dist 53=[-.43549605676024011105,2.8382997854405615123 ] 
dist 54=[-.07624323949797371256,2.8659477193088353734 ] 
dist 55=[.01755425693171568178,3.2725628352590221022 ] 
dist 56=[.68527273538973275124,3.6897524768827164870 ] 
dist 57=[.29467795697632462283,4.2138965910007063046 ] 
dist 58=[.02899517837718498865,4.7117092552755252580 ] 
dist 59=[-.19571444135995739184,5.0238116155586079604 ] 
dist 60=[-.42286788477794462107,5.2611065001363569908 ] 
dist 61=[-.63393333506289328541,5.4600934288447437786 ] 
dist 62=[-.79447871209618383753,5.6207281254321036382 ] 
dist 63=[-.9486699294894877972 ,5.7048543755914610900 ] 
dist 64=[-1.1344207061732676413 ,5.7499315874843165724 ] 
dist 65=[-1.3081554085064604792 ,5.7546804132259515821 ] 
dist 66=[-1.4144151917013412640 ,5.7357425385751920073 ] 
dist 67=[-1.4916438891373466027 ,5.7218972123489735289 ] 
dist 68=[-1.5495441928049640175 ,5.6384154512714498030 ] 
dist 69=[-1.5928923462058600428 ,5.6262019750722288344 ] 
dist 70=[-1.6120282986692293640 ,5.3176419631384396446 ] 
dist 71=[-1.7687167930061364067 ,5.2431725225850209672 ] 
dist 72=[-2.3094677940529865833 ,5.1942269573119323118 ] 
dist 73=[-3.1027529229570341393 ,5.1824277912552146855 ] 
dist 74=[-3.8857772772788875590 ,1.6023622002990315788 ] 
dist 75=[-4.3856078274917005523 ,1.5599198069235511537 ] 
dist 76=[-4.7740935797694964765 ,1.3928295279896671452 ] 
dist 77=[-5.1126759126605367936 ,1.3599020077745123994 ] 
dist 78=[-5.3937297082295915719 ,1.2857759565632063368 ] 
dist 79=[-5.5526008309556765381 ,1.2671866511626920021 ] 
dist 80=[-5.6527245590507777069 ,.81390855334771319464] 
dist 81=[-5.6993293025519276954 ,.9429151312643620857 ] 
dist 82=[-5.7191827190875618606 ,1.0260848129876231104 ] 
dist 83=[-5.7991528619869992876 ,1.0915552446895840228 ] 
dist 84=[-5.9085189861637806397 ,1.1499497393492904372 ] 
dist 85=[-5.9966123913785062404 ,1.1993376914854325453 ] 
dist 86=[-6.0644854274274723081 ,1.2288815736595628811 ] 
dist 87=[-6.0931367047215230153 ,1.2496021042974057106 ] 
dist 88=[-6.0986632798782457400 ,1.2638052221445249733 ] 
dist 89=[-6.0854245922020133098 ,1.2719465217939606128 ] 
dist 90=[-3.1263257473546539339 ,1.2725215288965648720 ] 
dist 91=[-2.8749962509428095189 ,1.2622582966403893429 ] 
dist 92=[-2.2821851879083945938 ,1.6340942305082531709 ] 
dist 93=[-2.1773302862961307583 ,2.2321714123931292797 ] 
dist 94=[-1.6400025735606551572 ,2.7726274912922462312 ] 
dist 95=[-1.6357160431967327918 ,3.1591251994256908472 ] 
dist 96=[-.9759893035412958885 ,3.5068143166365363361 ] 
dist 97=[-.9158976562894871662 ,3.8923379486574937404 ] 
dist 98=[-.24505035489330155935,4.2471536515767900065 ] 
dist 99=[-.14807878213994070226,4.4722821121398620253 ] 
dist 100=[.01936846422062819820,4.6454483303183739189 ] 
dist 101=[.09178273172440145134,4.7929146220466879977 ] 
dist 102=[.29889015661913730038,4.9125845780216242914 ] 
dist 103=[.15312151052252348155,4.9748396047122038875 ] 
dist 104=[-.06082885858182862041,5.0070360333071537496 ] 
dist 105=[-.27441152297574878475,5.0067815624961605245 ] 
dist 106=[-.41871428233843339867,3.5148718951288547621 ] 
dist 107=[-.5399541647376528245 ,3.6790734128428340130 ] 
dist 108=[-.66147762415559770212,3.7913657370873265815 ] 
dist 109=[-.77392984406202753081,3.8624842284698821816 ] 
dist 110=[-.85895953677819540204,3.9096537785990947574 ] 
dist 111=[-.9402116257052148669 ,3.9263265943916783468 ] 
dist 112=[-1.0408934458318907357 ,3.9239418037354632811 ] 
dist 113=[-1.1351965716071763056 ,3.9175195502819874946 ] 
dist 114=[-1.1917231329485654916 ,3.5666239698194503649 ] 
dist 115=[-1.2314394342092121938 ,3.5077227731444070782 ] 
dist 116=[-1.2586460753713541338 ,3.3920926297993664321 ] 
dist 117=[-1.2773438023059206369 ,3.3569716936456118659 ] 
dist 118=[-1.2830930639475255259 ,3.2074195862920838653 ] 
dist 119=[-1.2826639992989504494 ,3.1705940949249557177 ] 
dist 120=[-1.2791859736093539445 ,3.0769093456908651433 ] 
dist 121=[-1.1875142475452607662 ,3.0441292325409087306 ] 
dist 122=[-1.1719684859459262179 ,1.0023610913673149911 ] 
dist 123=[-1.1282377962085593729 ,.81721614599868301213] 
dist 124=[-1.2829840477801834167 ,.67988138295396053736] 
dist 125=[-1.6814122865414948239 ,.76043336520164887179] 
dist 126=[-2.0453764408362075807 ,.81319916386875350247] 
dist 127=[-2.3126444058939677582 ,.85570510655438693867] 
dist 128=[-2.5603598998610234339 ,.89531125887279958186] 
dist 129=[-2.8462837605336699473 ,.92949783340276366274] 
dist 130=[-3.1088054828685955836 ,.95037421998739051275] 
dist 131=[-3.2631128995296620637 ,.96549506739001436275] 
dist 132=[-3.3677670476867038776 ,.97670997493971616438] 
dist 133=[-3.4320990237717008193 ,.98454998226327283905] 
dist 134=[-3.4749552863447972770 ,.98620056467761442165] 
dist 135=[-3.4938848929883321078 ,.98362841407605912604] 
dist 136=[-3.4989307211341430229 ,.98125721651856239485] 
dist 137=[-3.4918151206498628507 ,.52899406189075534427] 
dist 138=[-.88895884849742549403,.66420371793641773824] 
dist 139=[-.7330308605223116872 ,.77583420668599862581] 
dist 140=[-.38076877648605621605,.88451742641327121378] 
dist 141=[-.31484675910617618099,.98302742787651708773] 
dist 142=[-.08719821461603188446,1.0540521906796555785 ] 
dist 143=[-.15668008385471417556,1.1185714582599819194 ] 
dist 144=[-.24536634028242886856,1.1911162677659038035 ] 
dist 145=[-.33082121396996142486,1.2563906133853334553 ] 
dist 146=[-.38740629504708778866,1.4208454705437418323 ] 
dist 147=[-.43366798358633420696,1.5643535590841729177 ] 
dist 148=[-.47792157827844116736,1.6907996824224635953 ] 
dist 149=[-.51748320467822608626,1.8271077945306019716 ] 
dist 150=[-.54501868442083869366,1.9594390543263581787 ] 
dist 151=[-.56900960102240577076,2.0700243726961319364 ] 
dist 152=[-.63990060192547281345,2.1859736217368034366 ] 
dist 153=[-1.0095025248183988448 ,2.3397393985485575113 ] 
dist 154=[-1.3799090365525723197 ,2.4852035212676684776 ] 
dist 155=[-1.6242410534484539197 ,2.5680188174995502282 ] 
dist 156=[-1.8229313541242477595 ,2.6209279066285290160 ] 
dist 157=[-2.0111839531888386246 ,2.6470032429361196909 ] 
dist 158=[-2.1782289098363523447 ,2.6594472013828493028 ] 
dist 159=[-2.2922789398895036105 ,2.6579344722725004800 ] 
dist 160=[-2.3892975532367915924 ,2.6474998848304664320 ] 
dist 161=[-2.4883662986098483278 ,2.6392140282841149669 ] 
dist 162=[-2.5730316043677602554 ,2.3746308185077066561 ] 
dist 163=[-2.6125651575418721740 ,2.3312038889924353761 ] 
dist 164=[-2.6309453914427314049 ,2.2396572310522692793 ] 
dist 165=[-2.6311987886129456232 ,2.2110936130082286541 ] 
dist 166=[-2.5841276530057406600 ,2.0829344796384140391 ] 
dist 167=[-2.5664617996113644451 ,2.0552244979468739967 ] 
dist 168=[-2.5509045289885521605 ,1.9724126473018750173 ] 
dist 169=[-2.5369838914380665050 ,1.9589588717266697473 ] 
dist 170=[-.94588418102400704547,.72687994711162472872] 
dist 171=[-1.2101707066121813347 ,.81904021994780092396] 
dist 172=[-1.4879727506161998920 ,.90192799443823130496] 
dist 173=[-1.7601324160503215636 ,.97250091638075929919] 
dist 174=[-2.0079121076547815588 ,1.0155108677195704969 ] 
dist 175=[-2.1884055913826251600 ,1.0465628487425739242 ] 
dist 176=[-2.3542325069087728765 ,1.0694097726881772051 ] 
dist 177=[-2.5434764828206668578 ,1.0868297234323368268 ] 
dist 178=[-2.7152578325489137454 ,1.0962215651084591281 ] 
dist 179=[-2.8113855122907096371 ,1.1046320737521040099 ] 
dist 180=[-2.8705469195668584962 ,1.1210734731246209928 ] 
dist 181=[-2.8947799060926433106 ,1.1310370282020321372 ] 
dist 182=[-2.9048528805128964763 ,1.1335957917823394278 ] 
dist 183=[-2.9074910569462266725 ,1.1312193946247919802 ] 
dist 184=[-2.9051985959316078129 ,1.1287555938265767128 ] 
dist 185=[-2.8955779470686385099 ,.23471591535813114365] 
dist 186=[-2.5317403494669114692 ,.39920571561235181704] 
dist 187=[-2.6333810764251578089 ,.55179094058114291446] 
dist 188=[-2.7005599647698386510 ,.70762268430899748208] 
dist 189=[-2.7383067817498400932 ,.99432499301173511752] 
dist 190=[-2.7607401928274598890 ,1.2610444108361161198 ] 
dist 191=[-2.7667940710051541546 ,1.4649834845938780543 ] 
dist 192=[-2.7620115551773040082 ,1.6620197658153198405 ] 
dist 193=[-2.7556541308812901309 ,1.9011927313737714712 ] 
dist 194=[-2.4708336191158220107 ,2.1258900705590999974 ] 
dist 195=[-2.4245951005448991433 ,2.2651517610003483094 ] 
dist 196=[-2.3339485409976306249 ,2.3685278108759540660 ] 
dist 197=[-2.3069594909763362002 ,2.4499959862498907226 ] 
dist 198=[-2.1943192065201263124 ,2.5113172674151841633 ] 
dist 199=[-2.1666935489114483523 ,2.5342761295831675686 ] 
dist 200=[-2.2357470439985645091 ,2.5422488908665251367 ] 
dist 201=[-2.4583483729326920613 ,2.5437567490257675039 ] 
dist 202=[-2.5910321708158927679 ,2.4511378412610010500 ] 
dist 203=[-2.6832784050011174384 ,2.4315056709945336305 ] 
dist 204=[-2.7444777126586039379 ,2.4249792465509470175 ] 
dist 205=[-2.7873861704187034865 ,2.4371469976845228888 ] 
dist 206=[-2.8066253779283942718 ,2.4382866167962248911 ] 
dist 207=[-2.8122101284886490072 ,2.4326305034529813384 ] 
dist 208=[-2.8081372931175658246 ,2.4132870734544680967 ] 
dist 209=[-2.5436577925878369103 ,2.4013567198073189383 ] 
dist 210=[-2.4997626228192893582 ,2.4423567227466202011 ] 
dist 211=[-2.4202493538068177512 ,2.5600897732285615795 ] 
dist 212=[-2.3974108381811025088 ,2.6387496815935775555 ] 
dist 213=[-2.3091196169621738631 ,2.6846493317469844125 ] 
dist 214=[-2.2835087449506297926 ,2.7146919303624702599 ] 
dist 215=[-2.2334998582815557162 ,2.7300620124397577055 ] 
dist 216=[-2.2166011577279236794 ,2.7376247743293840503 ] 
dist 217=[-.54450871364639422424,2.7365158684420606431 ] 
dist 218=[-.97961060136519175782,2.6320490798329582868 ] 
dist 219=[-1.2899326404891172968 ,2.6325984395610757619 ] 
dist 220=[-1.5462725984078370586 ,2.6151693656777882395 ] 
dist 221=[-1.7960520129334633095 ,2.6061404907174991224 ] 
dist 222=[-2.0225723725981227038 ,2.4999735103804446364 ] 
dist 223=[-2.1860754917528010330 ,2.4707636001555936738 ] 
dist 224=[-2.3347787235489729391 ,2.4373648228563059504 ] 
dist 225=[-2.5022279856225038432 ,2.4202449831699254196 ] 
dist 226=[-2.6530042553736468200 ,1.9569565713034838485 ] 
dist 227=[-2.7351583686782852508 ,1.8907528258802050079 ] 
dist 228=[-2.7828064236421985521 ,1.7556883812641891129 ] 
dist 229=[-2.7958524574271637440 ,1.7176967603670977161 ] 
dist 230=[-2.7966956753899652836 ,1.5662554284805244815 ] 
dist 231=[-2.7956346041564048851 ,1.5329972171559191335 ] 
dist 232=[-2.7929809763518239215 ,1.4571629155349626235 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 1, 2, 0, 1] 
dist 0=[59.993779764821706359  ,59.993779764821706359  ] 
dist 1=[59.900050552151788994  ,59.959200074440512983  ] 
dist 2=[59.553592809798991725  ,59.993779764821706359  ] 
dist 3=[58.905393990822480606  ,59.609880503357632130  ] 
dist 4=[57.606870802727677348  ,59.503851977766046681  ] 
dist 5=[56.125004554545607169  ,59.433795318582775637  ] 
dist 6=[54.744491472159972787  ,59.393430362440776210  ] 
dist 7=[53.170783139648802756  ,54.602161111666156562  ] 
dist 8=[50.917178102982379137  ,54.300315216256967961  ] 
dist 9=[48.392230416461282925  ,53.136158928981476186  ] 
dist 10=[45.734731467770715463  ,52.819659917824708738  ] 
dist 11=[42.464289364198559819  ,52.191442957210473295  ] 
dist 12=[37.491215009087335943  ,51.984322244829119411  ] 
dist 13=[32.481848259661963270  ,51.122799402937259512  ] 
dist 14=[29.066474462527888275  ,49.943716275491993881  ] 
dist 15=[24.710433198204889626  ,36.709795340905355872  ] 
dist 16=[20.634431843344638277  ,35.596529833366923407  ] 
dist 17=[17.215669384577895067  ,33.446257052495835302  ] 
dist 18=[13.789061249147583390  ,32.898879535560826600  ] 
dist 19=[10.609477913681514681  ,31.030892030970939175  ] 
dist 20=[8.1769182214715626239 ,30.579583049127572424  ] 
dist 21=[5.8187257237675241255 ,30.109414415095199287  ] 
dist 22=[2.9355410870454417882 ,29.985502334479607704  ] 
dist 23=[.20085224637526915567,9.1259503252240237304 ] 
dist 24=[-1.5646142325081621992 ,7.4319673549871030218 ] 
dist 25=[-2.9652369179482168759 ,5.2178338675295037162 ] 
dist 26=[-4.2432049372960812540 ,4.9034311997683562691 ] 
dist 27=[-5.3538573928932460858 ,4.4176290975878346792 ] 
dist 28=[-6.0868592893071213198 ,4.3259914391497045588 ] 
dist 29=[-7.0323955027794286394 ,-.01277729010008877298] 
dist 30=[-9.3291339314293789432 ,-.80172444068572482556] 
dist 31=[-11.490598413137692512  ,-3.8880990671758258698 ] 
dist 32=[-12.853102163864360476  ,-4.0589426376660494031 ] 
dist 33=[-13.895162036464297216  ,-5.2033671025382712176 ] 
dist 34=[-14.776748544122775940  ,-5.3740583778643639856 ] 
dist 35=[-15.490970078889376777  ,-5.6804939050451313977 ] 
dist 36=[-15.864593279517899528  ,-5.7320526692286517738 ] 
dist 37=[-16.061674410425571824  ,-5.9075518350674704939 ] 
dist 38=[-16.097393294639259134  ,-5.8550661314849288479 ] 
dist 39=[-6.6982222140262074314 ,-4.9019570139429161774 ] 
dist 40=[-6.5276084413794781814 ,-3.8398993631497235882 ] 
dist 41=[-6.5374647593400802065 ,-2.8924564571476321644 ] 
dist 42=[-6.5252594517132587312 ,-1.8566644057947544492 ] 
dist 43=[-6.4824034239571645408 ,-.84552450467743135974] 
dist 44=[-6.4546100454259463089 ,.00381732079014261815] 
dist 45=[-4.9968218522341074920 ,.89635038888878067922] 
dist 46=[-4.9293479739268421940 ,2.0801046782081087797 ] 
dist 47=[-2.7383504716568243128 ,3.3631682202092917641 ] 
dist 48=[-2.6495615696222120002 ,4.4526032082582234452 ] 
dist 49=[-1.7696603616200828913 ,5.3496834221867437240 ] 
dist 50=[-1.6091350799141072163 ,6.2183894306957905016 ] 
dist 51=[-1.4157811399300786753 ,7.0019967578649857446 ] 
dist 52=[-1.3791740738342982699 ,7.5594340265734042813 ] 
dist 53=[-.09673738463165343044,8.0576834767934605973 ] 
dist 54=[.05602416033715624027,8.6050155085596471582 ] 
dist 55=[.38029937505278988246,9.0898755502866547579 ] 
dist 56=[.44891128746554697048,9.3388204090985972356 ] 
dist 57=[.76453652682334485592,9.4742364750609581083 ] 
dist 58=[.81926371030464661974,9.5060233121572207129 ] 
dist 59=[.90818423212620335108,9.3933116655211715175 ] 
dist 60=[.92615432860836389148,9.3619275672193494433 ] 
dist 61=[1.4255665476149827298 ,8.9517039102337738441 ] 
dist 62=[0                     ,8.1191962809388797634 ] 
dist 63=[.82428659926660041294,4.3188104612366584032 ] 
dist 64=[.56170972546762194261,4.3227599096138028567 ] 
dist 65=[.28576489144981786826,4.3092439396038623469 ] 
dist 66=[-.08014328729986847420,4.2937029579362724380 ] 
dist 67=[-.47568694714833793981,4.1714834656097898466 ] 
dist 68=[-.87000624128294775369,4.1357386429872374889 ] 
dist 69=[-1.3390273257525782245 ,4.0799762023934277502 ] 
dist 70=[-2.0328422444035492525 ,4.0588131019725063725 ] 
dist 71=[-2.7193136667737796673 ,2.2858476081931852195 ] 
dist 72=[-3.1590582768628177232 ,2.2771907269190097596 ] 
dist 73=[-3.5025570769568229728 ,2.2270026095794520170 ] 
dist 74=[-3.8048682818987392586 ,2.2139132836486221945 ] 
dist 75=[-4.0579188538299180946 ,2.1695016965377600710 ] 
dist 76=[-4.2048083172755180222 ,2.1603868624775341357 ] 
dist 77=[-4.3023240445181744311 ,1.3171335237918853977 ] 
dist 78=[-4.3583381435433928758 ,1.2352348703694719253 ] 
dist 79=[-4.3928096330571631272 ,1.0391598612042333927 ] 
dist 80=[-4.4043270219555156432 ,1.0053695757265614144 ] 
dist 81=[-4.4431267190907075981 ,.7220911197531767421 ] 
dist 82=[-4.5027491067826555766 ,.66849954994581949061] 
dist 83=[-4.5508142398963834180 ,.5920279794094149337 ] 
dist 84=[-4.5754479876911294941 ,.56943016353507619354] 
dist 85=[-4.5877335842564402032 ,.23104914184240433656] 
dist 86=[-4.5865073948145515963 ,.21921499624302389414] 
dist 87=[-2.0942114949093772176 ,.22048185164981895282] 
dist 88=[-2.1212582614741973309 ,.23960282759795379656] 
dist 89=[-2.1435539303084284856 ,.63818957510129922896] 
dist 90=[-2.1501219476027599727 ,1.0848054663397363996 ] 
dist 91=[-2.1477324493423905112 ,1.4929354641886803403 ] 
dist 92=[-2.1433588134887718663 ,1.7925466574728698750 ] 
dist 93=[-1.4562916333177306999 ,2.0699840776633657769 ] 
dist 94=[-1.4571160676159391403 ,2.3895889691608996309 ] 
dist 95=[-1.4473831930357273615 ,2.6871249827793289136 ] 
dist 96=[-1.4442636690373450173 ,2.8764837882308722624 ] 
dist 97=[-1.3833714442120278825 ,3.0227925045725146062 ] 
dist 98=[-1.3672237195204410972 ,3.1485403182553493449 ] 
dist 99=[-1.3537602549322920103 ,3.2514385820300863020 ] 
dist 100=[-1.3459612325132006135 ,3.3065725148076151357 ] 
dist 101=[-1.0850587973422737584 ,3.3373228737028504296 ] 
dist 102=[-1.0487743668670364639 ,3.3429344844600705778 ] 
dist 103=[-.97793932273438946524,2.3396864324064639260 ] 
dist 104=[-.95894494563693834542,2.4271633415736377088 ] 
dist 105=[-.8890813630351194024 ,2.4815590026602923056 ] 
dist 106=[-.87225229970302932465,2.5052766091971652345 ] 
dist 107=[-.8432064781298669594 ,2.5165075755965129312 ] 
dist 108=[-.83522814114711736775,2.5210394012532957627 ] 
dist 109=[-.03024043378253237030,2.5216056884383801488 ] 
dist 110=[.03843660634995396554,2.5169738055713253135 ] 
dist 111=[.18659352688491473725,2.1756615649883208142 ] 
dist 112=[.21762064534266642541,2.1250346003148453888 ] 
dist 113=[.37305320156423376094,2.0337621564858051381 ] 
dist 114=[.39933161438397309393,2.0094993326596198254 ] 
dist 115=[.45320195755332633093,1.9253473111978457745 ] 
dist 116=[.46393997353521726947,1.9002341702017517689 ] 
dist 117=[.50379464400771228484,1.8707832901766398036 ] 
dist 118=[.4465841315965836601 ,1.8568587051092616819 ] 
dist 119=[.02164374928886871804,1.2246037916348730640 ] 
dist 120=[-.26640839057205970268,1.2547203620497670412 ] 
dist 121=[-.50945528303600942732,1.2762571074011463180 ] 
dist 122=[-.75475394038993788306,1.2837139979677530784 ] 
dist 123=[-.98283784135921691779,1.2847766571063760238 ] 
dist 124=[-1.1571712946745146083 ,1.2817090658978567215 ] 
dist 125=[-1.3255924413944462610 ,.07619973291523146250] 
dist 126=[-1.5300785366276703936 ,.01357915594464426391] 
dist 127=[-1.7223010632791641601 ,-.12296742238116904018] 
dist 128=[-1.8417710403553296444 ,-.15053463839027615265] 
dist 129=[-1.9308772845854773097 ,-.29877782629061668149] 
dist 130=[-2.0018984947459175747 ,-.32322671967108079386] 
dist 131=[-2.0558957296962491752 ,-.37635494463499265666] 
dist 132=[-2.0770485838364818299 ,-.37645661214912450836] 
dist 133=[-2.0851530152680895905 ,-.36436869304805158271] 
dist 134=[-2.0870647431300819850 ,-.34186316589013928198] 
dist 135=[-.87471045314935528699,-.13458487913536488304] 
dist 136=[-.92081895551831468653,.02483306134555423406] 
dist 137=[-.96239586428316405874,.16331761040722890888] 
dist 138=[-.9920496157982392846 ,.30940682168497595968] 
dist 139=[-1.0186845462861372246 ,.44918997755011751942] 
dist 140=[-1.0482172590389198270 ,.56251424707989432986] 
dist 141=[-1.0735832168596678160 ,.6781728263027019046 ] 
dist 142=[-1.0835861959811251170 ,.82728448242452621558] 
dist 143=[-1.0870484340374485036 ,.97179615831655435542] 
dist 144=[-1.0862958062912027709 ,1.0691010588564829559 ] 
dist 145=[-1.0582173935530699988 ,1.1505024703213338072 ] 
dist 146=[-1.0489657699624284101 ,1.2315454100264843062 ] 
dist 147=[-1.0416338611841156109 ,1.3062370666975619449 ] 
dist 148=[-1.0355075444225846768 ,1.3622970111682081998 ] 
dist 149=[-.85418771423596204925,1.4155243031015051498 ] 
dist 150=[-.82813181885853559834,1.4789280396810764834 ] 
dist 151=[-.77726342651865028968,1.5358324031219152314 ] 
dist 152=[-.76334740588368990514,1.5631189004758248928 ] 
dist 153=[-.7108344431209794291 ,1.5767073028645307604 ] 
dist 154=[-.81686591000217472908,1.5789064251132147759 ] 
dist 155=[-.92686698795450067   ,1.5521945618233433569 ] 
dist 156=[-1.0100542705057082689 ,1.5438209520635432199 ] 
dist 157=[-1.0894957672791655156 ,1.5375047576363264094 ] 
dist 158=[-1.1845475253095988682 ,1.5323748725135817396 ] 
dist 159=[-1.2730494975518312317 ,1.2658235863981298181 ] 
dist 160=[-1.3263517883263338256 ,1.2279907262742819840 ] 
dist 161=[-1.3640496490810310510 ,1.1570006547327544262 ] 
dist 162=[-1.3902771734061974884 ,1.1381771371964895834 ] 
dist 163=[-1.4074892674550751973 ,1.0715551454364777473 ] 
dist 164=[-1.4108935782726711491 ,1.0536895781371559338 ] 
dist 165=[-1.4060484531177240965 ,1.0298195127824847551 ] 
dist 166=[-1.4038012116697315748 ,1.0206094818761208301 ] 
dist 167=[-.24099791266816304036,1.0230830458926221344 ] 
dist 168=[-.42316299937778559131,1.0438938106703723839 ] 
dist 169=[-.57611270136339952547,1.0580144706263884876 ] 
dist 170=[-.72924261649569937522,1.0622120446535314976 ] 
dist 171=[-.87082563139121048324,1.0615434834211758821 ] 
dist 172=[-.97768749047947353447,1.0587507066792911946 ] 
dist 173=[-1.0796219660360245919 ,.98077850200990305845] 
dist 174=[-1.2015404956353514400 ,.98358850300901680166] 
dist 175=[-1.3152206345427997844 ,.98533023546492772806] 
dist 176=[-1.3842726355232384604 ,.98379805105075483894] 
dist 177=[-1.4338916782752928621 ,.95722581696207410318] 
dist 178=[-1.4700051520272953115 ,.94860067636647650111] 
dist 179=[-1.4957152443843388345 ,.94008838572221299428] 
dist 180=[-1.5038063244467761712 ,.9345393530120195435 ] 
dist 181=[-1.5045621118277006629 ,.77388053948736284922] 
dist 182=[-1.5009923178206479082 ,.75062541100706206227] 
dist 183=[-1.4174815450525423120 ,.70417787812060048339] 
dist 184=[-1.4156279575519130025 ,.69118851138842936858] 
dist 185=[-1.4101997947202152519 ,.64024473071604423473] 
dist 186=[-1.4067645587788337093 ,.6284956226670034046 ] 
dist 187=[-1.3526613859534097501 ,.61228218748224910492] 
dist 188=[-1.3375084148615128872 ,.71635372966193699633] 
dist 189=[-1.3228336102652865179 ,.81946438492612924602] 
dist 190=[-1.3137706342602232353 ,.94825038561816447216] 
dist 191=[-1.0627013435259532445 ,1.0710813771289038986 ] 
dist 192=[-1.0270803746779503093 ,1.1504251105228860415 ] 
dist 193=[-.9816226712237221627 ,1.2131298059468631651 ] 
dist 194=[-.97602374551404426777,1.2695499413301932488 ] 
dist 195=[-.9707722409869739091 ,1.3176426142400256542 ] 
dist 196=[-.96598185448269812963,1.3471116297116900595 ] 
dist 197=[-.93258044449249628959,1.3686074877140161266 ] 
dist 198=[-.97293072964178556744,1.3848814619894464769 ] 
dist 199=[-1.0000307122721497063 ,1.3949909124447711972 ] 
dist 200=[-1.0161391587920230176 ,1.3963584717123024186 ] 
dist 201=[-1.0263825074296378285 ,1.4016702304128522499 ] 
dist 202=[-1.0300721936947116711 ,1.4013055456002688077 ] 
dist 203=[-1.0296669372740415365 ,1.3744549290080832696 ] 
dist 204=[-1.0275304657724486315 ,1.3645094607851980693 ] 
dist 205=[-.96962911346975396631,1.3558416723187722844 ] 
dist 206=[-.96362734711832416094,1.3485943990503035968 ] 
dist 207=[-.9413395278548312122 ,1.3327624902013401857 ] 
dist 208=[-.93708283016460643617,1.3905175054608480236 ] 
dist 209=[-.87378569592845924548,1.4297874568547754179 ] 
dist 210=[-.85887728576784899589,1.4541030382600963949 ] 
dist 211=[-.84533319682245247471,1.4698360594349023784 ] 
dist 212=[-.83958484381646358043,1.4748496616261735858 ] 
dist 213=[-.63090910299925029956,1.4730914361896255204 ] 
dist 214=[-.60265480691201976567,1.4703545305723343359 ] 
dist 215=[-.54701760457819988267,1.3821864049366002540 ] 
dist 216=[-.53225685092193229462,1.3711316952350560916 ] 
dist 217=[-.57562691155985214227,1.3326676282861861980 ] 
dist 218=[-.71716333189098393658,1.3263610032209813689 ] 
dist 219=[-.84742508702043053368,1.2249901575814774234 ] 
dist 220=[-.94472816455175788629,1.2017632849264960004 ] 
dist 221=[-1.0365554615077202475 ,1.1822707739420303813 ] 
dist 222=[-1.1449599657189598435 ,1.1760058394307713950 ] 
dist 223=[-1.2452848894190421244 ,.85608275156387946925] 
dist 224=[-1.3048617949175505628 ,.81360063027281678603] 
dist 225=[-1.3460148222373381386 ,.73099899810080825745] 
dist 226=[-1.3760576044948171108 ,.70951053608465406793] 
dist 227=[-1.4033204091729855802 ,.63389523187624473535] 
dist 228=[-1.4117948907078837268 ,.615647612507803302  ] 
dist 229=[-1.4134033465434467492 ,.5921025116286866922 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 1, 1, 2, 0, 2] 
dist 0=[47.441283040124802036  ,47.441283040124802036  ] 
dist 1=[47.112871688617686871  ,47.964134143997923256  ] 
dist 2=[46.324176580133655919  ,48.507449771838580108  ] 
dist 3=[45.057403314432943097  ,48.762660292842854435  ] 
dist 4=[42.992997810722886488  ,48.866306197696467127  ] 
dist 5=[40.858553300863947612  ,48.864647821394149078  ] 
dist 6=[39.311965912001624338  ,48.577793346210572847  ] 
dist 7=[37.895598373502867250  ,48.201484445446133239  ] 
dist 8=[36.281120641224177143  ,47.056232390520667268  ] 
dist 9=[34.656978610986159360  ,46.923190699845965845  ] 
dist 10=[33.201872850001185223  ,46.391913090431935582  ] 
dist 11=[31.587149611263863985  ,46.224615796840067564  ] 
dist 12=[29.325209300439427657  ,45.844697679671085655  ] 
dist 13=[27.035543052845742476  ,45.698600231533817881  ] 
dist 14=[25.309929565200004858  ,44.991753165860228444  ] 
dist 15=[23.660823179960641526  ,44.177629613317999604  ] 
dist 16=[21.676553928636963441  ,28.974872683623244507  ] 
dist 17=[19.619106962391860382  ,28.577841716760171312  ] 
dist 18=[17.677409904340820413  ,24.794030374489077879  ] 
dist 19=[15.440272994478683009  ,24.166459557391424367  ] 
dist 20=[12.202055905314160952  ,24.041856834802430029  ] 
dist 21=[8.9912631497073743570 ,22.711506401805161306  ] 
dist 22=[6.8636049585265309836 ,17.025599303286323684  ] 
dist 23=[5.1125680958660109825 ,16.763783300674476485  ] 
dist 24=[3.4066232812406219685 ,14.819174544210079356  ] 
dist 25=[1.8507102966036591624 ,14.422502849395457314  ] 
dist 26=[.69906323436131494192,14.125068624615423295  ] 
dist 27=[-.38279233753871135227,13.072572344027920704  ] 
dist 28=[-1.6600899499982584875 ,11.033699689185010394  ] 
dist 29=[-2.8535283972065179345 ,10.858320623297547522  ] 
dist 30=[-4.5296252171841054960 ,4.3945942109631543703 ] 
dist 31=[-7.1836350056905761408 ,2.1366605618160452558 ] 
dist 32=[-9.7614211562558543384 ,-1.8039498393534710443 ] 
dist 33=[-11.370068967453792643  ,-2.1224704510226795764 ] 
dist 34=[-12.586380961159967202  ,-3.1345217788836402021 ] 
dist 35=[-13.596312071714425609  ,-2.9279157507354296156 ] 
dist 36=[-14.408356629510388067  ,-2.4805014887440432291 ] 
dist 37=[-14.833676806736016807  ,-1.9905807602561964282 ] 
dist 38=[-15.067637260269428913  ,-1.6141840534992746844 ] 
dist 39=[-15.116568454384076059  ,-1.2513106365435262452 ] 
dist 40=[-14.928679989699372708  ,-.81484019089670533815] 
dist 41=[-14.856889087025435737  ,-.36671898742647237954] 
dist 42=[-14.782716610925393878  ,.04286120736915395236] 
dist 43=[-14.714463654734357184  ,.50143493371333357065] 
dist 44=[-14.592440312561675363  ,1.1451948078815809706 ] 
dist 45=[-14.510715444833099040  ,1.7915413708311442437 ] 
dist 46=[-14.410043825580503330  ,2.2605210062755448261 ] 
dist 47=[-14.348439953889783185  ,2.6885625899794609952 ] 
dist 48=[-5.6592272735677377451 ,3.1716680823980985783 ] 
dist 49=[-4.9285693878444576818 ,3.6523510510289454455 ] 
dist 50=[-3.2228153496105011854 ,4.0707673766417601455 ] 
dist 51=[-3.0576174798419219834 ,4.5231780898846434811 ] 
dist 52=[-3.0224387589296872002 ,5.1395205933603728005 ] 
dist 53=[-.31095604349250392625,5.7435217242969745201 ] 
dist 54=[.28134646739118950311,6.1467030773757143663 ] 
dist 55=[.43226577175432484175,6.4795455526982784849 ] 
dist 56=[1.8856675385294026596 ,6.8029124729920033829 ] 
dist 57=[1.8133480655836449280 ,7.0950504459218093926 ] 
dist 58=[1.6801186972027673948 ,7.3032953349258207236 ] 
dist 59=[1.4696217205592326724 ,7.4897806615316703390 ] 
dist 60=[1.1630517687728144632 ,7.7684780807556005166 ] 
dist 61=[.64654284990061009798,7.9249304682086189983 ] 
dist 62=[.11441205162925590371,8.0071507511521149172 ] 
dist 63=[-.25451154203541412211,8.0162241317330752260 ] 
dist 64=[-.57355941872175645096,3.8676506584812993638 ] 
dist 65=[-.90680305721678961051,3.8273529081147545772 ] 
dist 66=[-1.2226854265152389685 ,3.7155268371912328033 ] 
dist 67=[-1.4725097462628205437 ,3.6856209033320046816 ] 
dist 68=[-1.7212311853723760160 ,3.6735094611448511925 ] 
dist 69=[-2.0327389592559891595 ,3.4586069590835775617 ] 
dist 70=[-2.3290646057958543920 ,2.9538183359615203183 ] 
dist 71=[-2.5172320779235825094 ,2.9207521281306488970 ] 
dist 72=[-2.6618270002725036449 ,2.2584612354329742852 ] 
dist 73=[-2.7843403617859793337 ,2.2005194616503334632 ] 
dist 74=[-2.8829795176540033442 ,1.9924681425831435970 ] 
dist 75=[-2.9323361887363833721 ,1.9444730928049648286 ] 
dist 76=[-2.9549331485229784949 ,1.8887779307452129369 ] 
dist 77=[-2.9564547359140927427 ,1.8726517224311994643 ] 
dist 78=[-1.5872657942423149561 ,1.4520156803428566233 ] 
dist 79=[-1.7196144709420361535 ,1.4276071326473004196 ] 
dist 80=[-1.8595827968969577967 ,.64524080407906308129] 
dist 81=[-2.2409570718024585338 ,.55621774357662575315] 
dist 82=[-2.5455849403318567414 ,.38290061087172947476] 
dist 83=[-2.8258076874974041936 ,.3405557875552874365 ] 
dist 84=[-3.0694950710562964762 ,.20405227379594051437] 
dist 85=[-3.2282670675061295100 ,.1726330929144911707 ] 
dist 86=[-3.3556051533028220314 ,.1578540223472398791 ] 
dist 87=[-3.4738228862439375870 ,.17296238500896335696] 
dist 88=[-3.5726494255277810074 ,.20134325202197422002] 
dist 89=[-3.6225673180623369122 ,.2424448489936419691 ] 
dist 90=[-3.6464674336046064132 ,.30048801498725982354] 
dist 91=[-3.6477831642703749487 ,.39654668582053895943] 
dist 92=[-3.6231576731999194821 ,.50948747835404372472] 
dist 93=[-3.6088583811128471850 ,.63494117597766791373] 
dist 94=[-3.5640102148332700815 ,.79351061864633076186] 
dist 95=[-3.5416061548901856419 ,1.0386526184632877039 ] 
dist 96=[-2.1326449991007115738 ,1.2842853871295707474 ] 
dist 97=[-2.1091859570190505540 ,1.4448302985807166603 ] 
dist 98=[-1.8482642424106677818 ,1.5737934923573629633 ] 
dist 99=[-1.7955662023157568028 ,1.6933971159747516409 ] 
dist 100=[-1.7397368653092977519 ,1.7978934070717299300 ] 
dist 101=[-1.7230957696797070851 ,1.8665763465866554091 ] 
dist 102=[-1.1419474723210755148 ,1.9222629990369561219 ] 
dist 103=[-1.0669664784791562492 ,1.9749167245808262198 ] 
dist 104=[-.92452943317341147208,2.0171334752856997224 ] 
dist 105=[-.87374713170747941457,2.0311745950929537063 ] 
dist 106=[-.74596688338834980485,2.1338698712608013538 ] 
dist 107=[-.71649973351719670773,2.2183927730570736233 ] 
dist 108=[-.71068831812543116251,2.2845224299915704222 ] 
dist 109=[-.62690412868136597899,2.3142955026358464506 ] 
dist 110=[-.34759182629143884747,2.3264081948669617654 ] 
dist 111=[-.60718474705988796306,2.3247296617358689484 ] 
dist 112=[-1.1022343984623920569 ,2.2226570107036516508 ] 
dist 113=[-1.4250920552143429644 ,2.2204960143283405713 ] 
dist 114=[-1.6835439637453290240 ,2.1201060410480367688 ] 
dist 115=[-1.9215419667787723180 ,2.0990898743857631977 ] 
dist 116=[-2.1280346209695092575 ,2.0842642117343678656 ] 
dist 117=[-2.2607385911549388348 ,2.0740453540050955273 ] 
dist 118=[-2.3646972011656071316 ,2.0218496839907631811 ] 
dist 119=[-2.4564457261259857232 ,2.0839433479424184066 ] 
dist 120=[-2.5345581699279341478 ,2.1221398907878905682 ] 
dist 121=[-2.5840979523023988692 ,2.1377026078768134610 ] 
dist 122=[-2.6221012016246581636 ,2.1436625795430752869 ] 
dist 123=[-2.6542010291147357168 ,2.1435321320971743976 ] 
dist 124=[-2.6800014453384727261 ,2.1389097833669055219 ] 
dist 125=[-2.6928820162859005140 ,2.1322793976977392740 ] 
dist 126=[-2.6987749118243209063 ,1.9258135416264030374 ] 
dist 127=[-2.6967119781712420965 ,1.8975156177438380601 ] 
dist 128=[-1.8607681913932348496 ,1.8132129523387370479 ] 
dist 129=[-2.0355427081658514488 ,1.8009969544101512849 ] 
dist 130=[-2.1649464223848005967 ,1.6185241138670722455 ] 
dist 131=[-2.2664116390472062336 ,1.5791660125567621080 ] 
dist 132=[-2.3461112667252672083 ,1.5457335250439358850 ] 
dist 133=[-2.3886280912277225801 ,1.5386553219228133458 ] 
dist 134=[-2.4120948851100382459 ,1.0403926639948464146 ] 
dist 135=[-2.4157390261621764383 ,.97586869176727699188] 
dist 136=[-2.2676579875243473059 ,.85093791632999130363] 
dist 137=[-2.2398712480740141170 ,.81904757209083901958] 
dist 138=[-2.2052129217375027842 ,.71012032920249114303] 
dist 139=[-2.1893454825499301288 ,.68370022860744503063] 
dist 140=[-2.1579010503836716688 ,.65736478983890598588] 
dist 141=[-2.1440531190156211868 ,.65150709676551120725] 
dist 142=[-2.1334762157927132086 ,.22502612877387121752] 
dist 143=[-2.1246093959268499935 ,.39864828918507888685] 
dist 144=[-.53901401910581319062,.54709638617419451944] 
dist 145=[-.40905341313087419165,.7000162477481438717 ] 
dist 146=[-.11141715535102623077,.84412695044922354294] 
dist 147=[-.06073801076291763453,.95741797767061279803] 
dist 148=[.31079818806754031429,1.0698527082255212783 ] 
dist 149=[.37484183573340056418,1.2105505080464507721 ] 
dist 150=[.4835189621513101687 ,1.3448831956561936432 ] 
dist 151=[.50683863716558020802,1.4319147713172553300 ] 
dist 152=[.6175251096156405861 ,1.5009932655050178737 ] 
dist 153=[.51569014310274536507,1.5636706735064084029 ] 
dist 154=[.39395278195046975818,1.6174789598735134569 ] 
dist 155=[.25575938175258992102,1.6511606373843942908 ] 
dist 156=[.07903497009657913626,1.6765856709256319325 ] 
dist 157=[-.19648891998348162836,1.6974458017746806915 ] 
dist 158=[-.4746881847155084504 ,1.7114611356777756618 ] 
dist 159=[-.66209076924943859535,1.7132582638392655344 ] 
dist 160=[-.81887203919056843764,1.7031731774984243044 ] 
dist 161=[-.9748545913353624841 ,1.6992245452197165826 ] 
dist 162=[-1.1183837590702366498 ,1.6261076378774495136 ] 
dist 163=[-1.2254606218558082605 ,1.6063383227510017436 ] 
dist 164=[-1.3263433430941548576 ,1.5892088419231011139 ] 
dist 165=[-1.4451500220020973394 ,1.5784384947133201983 ] 
dist 166=[-1.5548892621072072588 ,1.2557143265792502648 ] 
dist 167=[-1.6195815685585035320 ,1.2105238076913964114 ] 
dist 168=[-1.6636617089000479845 ,1.1216013967416805396 ] 
dist 169=[-1.6911327676755265156 ,1.0975535116861366912 ] 
dist 170=[-1.7084773648441999844 ,1.0077979039367464518 ] 
dist 171=[-1.7121399401721257927 ,.98653943156742274994] 
dist 172=[-1.7087512753470682258 ,.94765087534342843352] 
dist 173=[-1.7036338068057280585 ,.93693047779270139204] 
dist 174=[-1.5601083561264200012 ,.4503939929363101728 ] 
dist 175=[-1.5373896205412465719 ,.5505610815183781495 ] 
dist 176=[-1.4702309452020229828 ,.65231882161010712158] 
dist 177=[-1.4965731566160521532 ,.72146517588394913721] 
dist 178=[-1.5709317619612358760 ,.7799086130728743091 ] 
dist 179=[-1.6249249854323220947 ,.83895775827544459844] 
dist 180=[-1.6657747435099797593 ,.893816372968862671  ] 
dist 181=[-1.6876658566797956596 ,.93553776955956387206] 
dist 182=[-1.6998864542586092955 ,.97559052015742974661] 
dist 183=[-1.7021256218289318402 ,1.0237898315708978697 ] 
dist 184=[-1.5559034431265134711 ,1.0687726408735816703 ] 
dist 185=[-1.5337925625554832630 ,1.0959899440903402619 ] 
dist 186=[-1.5964756193335520931 ,1.1153789052962094391 ] 
dist 187=[-1.6523753717277633511 ,1.1291233168074347957 ] 
dist 188=[-1.7039753873560687463 ,1.1381641962261640573 ] 
dist 189=[-1.7632153400520024082 ,1.1387835359773486596 ] 
dist 190=[-1.8149246328213282502 ,1.1351772906108667579 ] 
dist 191=[-1.8364663068453472459 ,1.1310536380810986222 ] 
dist 192=[-1.8456071234012395744 ,.82683730896647390013] 
dist 193=[-1.8478187131091950068 ,.96538917610630844177] 
dist 194=[-1.7957857964245733605 ,1.0941250793484490234 ] 
dist 195=[-1.7825634623613166429 ,1.1923084762425590965 ] 
dist 196=[-1.7748692558782013786 ,1.2869278780170047515 ] 
dist 197=[-1.7727042966091512971 ,1.4014355374517135774 ] 
dist 198=[-1.4147922959269998097 ,1.5088136274880404549 ] 
dist 199=[-1.3657564203836534742 ,1.5749746462379333461 ] 
dist 200=[-1.2758955238637375285 ,1.6236099228779911202 ] 
dist 201=[-1.2529324052192711116 ,1.6610344863100576252 ] 
dist 202=[-1.1770765517100595092 ,1.6953776590329124907 ] 
dist 203=[-1.1553636620110901097 ,1.7109562249886722739 ] 
dist 204=[-1.1390170625271956967 ,1.7156060305708481166 ] 
dist 205=[-1.1347515170151302299 ,1.7143966804806883805 ] 
dist 206=[.30257116659272951746,1.6882848942535119781 ] 
dist 207=[.12357734265971031222,1.6796116000676000477 ] 
dist 208=[-.06029249899603551597,1.6572761259456242331 ] 
dist 209=[-.18931369599114459545,1.6782516022523276207 ] 
dist 210=[-.30286658023038455219,1.6870348582033479278 ] 
dist 211=[-.42500083058898835757,1.6860298838648120004 ] 
dist 212=[-.54331005845946293247,1.6567872540853556898 ] 
dist 213=[-.64159800397235007539,1.6450920104359470756 ] 
dist 214=[-.74405462961759843692,1.6302186130605087524 ] 
dist 215=[-.87900476844090490844,1.6220383182732664989 ] 
dist 216=[-1.0111144738630163723 ,1.3777064336113395868 ] 
dist 217=[-1.1022353578450547731 ,1.3412964793438054160 ] 
dist 218=[-1.1807959845456127310 ,1.2663057281312393497 ] 
dist 219=[-1.2627752651201700568 ,1.2444767260693963220 ] 
dist 220=[-1.3407009883373302845 ,1.1537493606227490514 ] 
dist 221=[-1.4030843579981373782 ,1.1339020479065623393 ] 
dist 222=[-1.4660518391682709137 ,1.0835394649243443009 ] 
dist 223=[-1.5463126461010783276 ,1.0701585184183842650 ] 
dist 224=[-1.6205833625372735945 ,-.25988698668654527387] 
dist 225=[-1.6596424414982577124 ,-.2989031138270008464 ] 
dist 226=[-1.6807319389045182414 ,-.43237641589927928231] 
dist 227=[-1.6851403620062933908 ,-.45912053863065300097] 
dist 228=[-1.6763387586307439556 ,-.48364000579409620859] 
dist 229=[-1.6709218042782370946 ,-.47703621567898820697] 
dist 230=[-1.7359718931929360148 ,-.45778444421664623259] 
dist 231=[-1.7980194712926729914 ,-.4231756221430853754 ] 
dist 232=[-1.8378538668375909163 ,-.37067993460860674946] 
dist 233=[-1.8577930552053927794 ,-.28003425750883672609] 
dist 234=[-1.8680957558511135305 ,-.17177751091578195563] 
dist 235=[-1.8694672546454108191 ,-.04898886735456730573] 
dist 236=[-1.8645570284311393670 ,.10799080797062660344] 
dist 237=[-1.8444630032979722639 ,.35271775324449796286] 
dist 238=[-1.1595569271944751106 ,.59972935935924650345] 
dist 239=[-1.1482799963570447769 ,.76582793857335250518] 
dist 240=[-.14503704480310555539,.90449094153893939702] 
dist 241=[-.05791372808895720680,1.0419958029710654998 ] 
dist 242=[.13022163940695166207,1.1682551868654753312 ] 
dist 243=[.17062469722934320953,1.2620325984070704577 ] 
dist 244=[.36924653837305686235,1.3499899234944187016 ] 
dist 245=[.40321406484093250053,1.4530182458548497687 ] 
dist 246=[.47356156589478282656,1.5479149094591833357 ] 
dist 247=[.48774517367730960308,1.6034152189585833309 ] 
dist 248=[.54283340053254008582,1.6406881406886854149 ] 
dist 249=[.54167195389201633608,1.6628318566345422774 ] 
dist 250=[.52066042507073965989,1.6756447617516894210 ] 
dist 251=[.46706581338060035233,1.6761221814604610417 ] 
dist 252=[.39661979185948951133,1.6701865712422536458 ] 
dist 253=[.30834811330784311787,1.6609694367140372628 ] 
dist 254=[.19009848101510693246,1.5324906260049041708 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 0, 1, 1, 2] 
dist 0=[63.316692139018241735  ,63.316692139018241735  ] 
dist 1=[62.801292952190554438  ,63.563116119268290540  ] 
dist 2=[61.783023326017113610  ,63.584505328162581940  ] 
dist 3=[60.577848778784484672  ,63.323430387897560683  ] 
dist 4=[59.316091019378470738  ,63.171552571466421576  ] 
dist 5=[57.768890351236788698  ,62.760752753929968018  ] 
dist 6=[55.423719204057324800  ,62.558621077472483274  ] 
dist 7=[52.739174484615640176  ,61.485534240815223688  ] 
dist 8=[49.836651036874326840  ,59.849795605314642243  ] 
dist 9=[46.212291923036660120  ,57.568295660663045566  ] 
dist 10=[40.645067119470432521  ,57.370251226532443654  ] 
dist 11=[35.022753814715570150  ,56.773151641731661167  ] 
dist 12=[31.178304403997293427  ,56.679772027928811639  ] 
dist 13=[27.891741979682923300  ,55.006143476740039867  ] 
dist 14=[24.497096598620162306  ,51.914032057586771746  ] 
dist 15=[21.283100640092425022  ,39.967665901368381244  ] 
dist 16=[18.717712997692964151  ,39.746318156230442878  ] 
dist 17=[16.129282656424916472  ,30.326514532302566574  ] 
dist 18=[12.822779925972094347  ,29.133202450611161749  ] 
dist 19=[9.6177533879750570600 ,26.749090399413646546  ] 
dist 20=[7.4343127251164580454 ,26.136978741224846525  ] 
dist 21=[5.5737748999680733163 ,23.981569521171466208  ] 
dist 22=[3.6579854544920312498 ,23.509610163646837913  ] 
dist 23=[1.4916655770799296736 ,22.875410865484953441  ] 
dist 24=[-.68194298525622672146,22.674393144218841417  ] 
dist 25=[-2.4695653391754870784 ,5.0471776998363383267 ] 
dist 26=[-4.2072356774463730722 ,3.7752509977306401559 ] 
dist 27=[-5.7896392906125742541 ,.8646088581893983388 ] 
dist 28=[-6.9577790149150116266 ,.6164473349055268149 ] 
dist 29=[-8.0540136375038269328 ,-.13550098429784834762] 
dist 30=[-9.3506116395407014063 ,-.92671185332480091361] 
dist 31=[-10.545902850561646710  ,-5.4315545653015366277 ] 
dist 32=[-12.186352497684960663  ,-5.6737573392002601442 ] 
dist 33=[-14.021991696352085440  ,-7.2345911448903968652 ] 
dist 34=[-15.166078847739887144  ,-7.4511994610275657897 ] 
dist 35=[-16.026303610522009834  ,-7.3897325311472095925 ] 
dist 36=[-16.728226331681852243  ,-6.8695186110493727454 ] 
dist 37=[-17.277992418651764060  ,-5.8075519476668357057 ] 
dist 38=[-17.530591540357434742  ,-4.4995917171899536616 ] 
dist 39=[-17.633027159407821028  ,-2.7648574404623458642 ] 
dist 40=[-17.625989419872605709  ,0                     ] 
dist 41=[-10.171087295311666817  ,.0410269594811769709 ] 
dist 42=[-10.046893926917302489  ,1.4668064760493688539 ] 
dist 43=[-9.5543614398391403683 ,2.6708038558298839572 ] 
dist 44=[-9.4281675939391735681 ,3.8844530499145333080 ] 
dist 45=[-9.1688985317569802362 ,5.0097776436891265309 ] 
dist 46=[-9.0852877738142884402 ,5.8615667618789406596 ] 
dist 47=[-2.0741221966194514534 ,6.6756050143608932456 ] 
dist 48=[-1.4608257705236065383 ,7.6505635544928956468 ] 
dist 49=[-1.0556163197815797082 ,8.5597895736128026188 ] 
dist 50=[-.9721212231222961289 ,9.1116424559233690391 ] 
dist 51=[.37683854493824703413,9.5077654517057237645 ] 
dist 52=[.5508119386920179301 ,9.7956349213508801466 ] 
dist 53=[.90570597780829342568,9.9985367231548955436 ] 
dist 54=[.99003996303025102821,10.055428380766784212  ] 
dist 55=[1.2802861307667913295 ,10.056460768865787908  ] 
dist 56=[1.3367806143481369326 ,10.036477935577962042  ] 
dist 57=[1.3739970141156782282 ,9.4202315578602191528 ] 
dist 58=[1.3422252986797680374 ,9.3016746026997053237 ] 
dist 59=[1.2912717214575651709 ,8.9687019916806426133 ] 
dist 60=[1.2384667805551952455 ,8.8794481405463147956 ] 
dist 61=[1.1750132935153571097 ,8.1817778907388661382 ] 
dist 62=[1.0813644757853088507 ,7.7460257962792643516 ] 
dist 63=[.4327940040505436179 ,1.9244197143533547034 ] 
dist 64=[-.19681206722015878379,1.8141576191025855689 ] 
dist 65=[-.72150321170888838565,1.6811760074158988959 ] 
dist 66=[-1.2400645720214626714 ,1.6496785178496517301 ] 
dist 67=[-1.7150291016934462418 ,1.3777188020522904232 ] 
dist 68=[-2.0657795808094094807 ,1.4253694355468108894 ] 
dist 69=[-2.3928836586198226346 ,1.4795224831083545117 ] 
dist 70=[-2.7735602818748069195 ,1.5566244426825565527 ] 
dist 71=[-3.1244431382034735178 ,1.6423038112608313966 ] 
dist 72=[-3.3326406662363943072 ,1.7306147601665326277 ] 
dist 73=[-3.4764436686120435395 ,1.8373987460992590768 ] 
dist 74=[-3.5702452147503263307 ,1.9966758232196273224 ] 
dist 75=[-3.6362175259899394268 ,2.1523362666271760688 ] 
dist 76=[-3.6689412616601979526 ,2.2446683498696686363 ] 
dist 77=[-3.6837583787434226322 ,2.3077506239535201566 ] 
dist 78=[-3.6783114339146973198 ,2.3467500077413874434 ] 
dist 79=[-3.1243196332583401072 ,2.3723036227212239577 ] 
dist 80=[-3.0559616485525182032 ,2.3817843531145445633 ] 
dist 81=[-2.8679540026695848570 ,2.3810830526786508222 ] 
dist 82=[-2.8389566231153358796 ,2.3762917349694162880 ] 
dist 83=[-2.5211223377641236756 ,2.1325083647374265458 ] 
dist 84=[-2.5526113781997217726 ,2.0917495619797065990 ] 
dist 85=[-2.5663459289024663210 ,2.0170623093662362466 ] 
dist 86=[-2.5655925210412327498 ,1.9953011902730291917 ] 
dist 87=[-2.5191094906404063764 ,1.9086730288166152708 ] 
dist 88=[-2.5017433732329679982 ,1.8862613307036529355 ] 
dist 89=[-2.4865549434204089880 ,2.0495643230123633452 ] 
dist 90=[-2.4741249872662210001 ,2.2041193497152984107 ] 
dist 91=[-2.0927363422122817336 ,2.3413863383541991550 ] 
dist 92=[-2.0408998666650280485 ,2.4357373449570756956 ] 
dist 93=[-1.9092623901760434774 ,2.5169515013570553855 ] 
dist 94=[-1.8835673140534419585 ,2.6018695089304072975 ] 
dist 95=[-1.6618871940376258647 ,2.6742301752084849104 ] 
dist 96=[-1.6164561898426046327 ,2.7053320347251600574 ] 
dist 97=[-1.5524620846093642138 ,2.7179252214880482616 ] 
dist 98=[-1.5315464297156941725 ,2.7162946100485262826 ] 
dist 99=[-1.0837757521794336210 ,2.6588542143453228591 ] 
dist 100=[-1.0238014429183169259 ,2.6813751922149385886 ] 
dist 101=[-.8920913213475548826 ,2.7155478583753341852 ] 
dist 102=[-.8583664593570833078 ,2.7261160300102854609 ] 
dist 103=[-.7013150777124605334 ,2.7240382915998711423 ] 
dist 104=[-.67176864478269920383,2.7170660954504778128 ] 
dist 105=[-.60227871582315814463,2.6876090168424933495 ] 
dist 106=[-.5877050516417467806 ,2.6704138240942660716 ] 
dist 107=[.1288600899512136837 ,2.4124195591354853605 ] 
dist 108=[-.0468478743110478731 ,2.4110333749226095833 ] 
dist 109=[-.3096200908752559546 ,2.4047648826746477741 ] 
dist 110=[-.5721710153130112042 ,2.3977049598977488901 ] 
dist 111=[-.8144069275753483661 ,1.9413866417869918262 ] 
dist 112=[-.9961105426882492231 ,1.8881408211055387652 ] 
dist 113=[-1.1682490706975218437 ,1.7540278435289162563 ] 
dist 114=[-1.3723226267294266502 ,1.7283449804679727226 ] 
dist 115=[-1.5623646863227427725 ,1.5063884121740870600 ] 
dist 116=[-1.6818659104124947195 ,1.4612126177817945030 ] 
dist 117=[-1.8450016824090726528 ,1.3980998375900336309 ] 
dist 118=[-2.0349699547999397040 ,1.3690147951551553360 ] 
dist 119=[-2.2095496962325899705 ,.68693291646503860068] 
dist 120=[-2.3112505414615477336 ,.604983045125720847  ] 
dist 121=[-2.3790989528193968237 ,.38336065596205285353] 
dist 122=[-2.4185330123756111027 ,.12291925113220136655] 
dist 123=[-2.4442352805744042115 ,-.4662739807581236243 ] 
dist 124=[-2.4572714151328294529 ,-.3453845763199166395 ] 
dist 125=[-2.4635381130646452829 ,-.1836575104838923953 ] 
dist 126=[-2.4622385566378245798 ,.0760224478158711403 ] 
dist 127=[-1.3543589522357815093 ,.3396299720232251720 ] 
dist 128=[-1.3227136347972449185 ,.5170377504098419238 ] 
dist 129=[-1.2740217271339561084 ,.6652430175154054322 ] 
dist 130=[-1.3239203455927392868 ,.8123068590707942514 ] 
dist 131=[-1.4165538379606082778 ,.9473573548992245916 ] 
dist 132=[-1.4795508259914512422 ,1.0476204033715924780 ] 
dist 133=[-1.5329035555828410362 ,1.1416007232459405183 ] 
dist 134=[-1.5870323402405745022 ,1.2515823240387984486 ] 
dist 135=[-1.6374801701419818996 ,1.3528320641189310812 ] 
dist 136=[-1.6761312193865393818 ,1.4119654143819820084 ] 
dist 137=[-1.7134942569885961448 ,1.4515875391993173191 ] 
dist 138=[-1.7587836342910697093 ,1.4749680940599207486 ] 
dist 139=[-1.7992018306090195615 ,1.4893664270162407083 ] 
dist 140=[-1.8171206716139501949 ,1.4931351928022945965 ] 
dist 141=[-1.8230487810135015135 ,1.5605565758257993169 ] 
dist 142=[-1.8216210947129233258 ,1.7299907935183348164 ] 
dist 143=[-1.7923741216177373006 ,1.8776374971711379750 ] 
dist 144=[-1.7810169898909006909 ,1.9739256055498726744 ] 
dist 145=[-1.7561475711891975174 ,2.0510734441287266114 ] 
dist 146=[-1.7455522822176490463 ,2.1223275388098378341 ] 
dist 147=[-1.5254853636413734579 ,2.1817148825686722298 ] 
dist 148=[-1.4906687536048882068 ,2.2114974589548924989 ] 
dist 149=[-1.4108838045035945044 ,2.2253278911955167164 ] 
dist 150=[-1.3853787436528126558 ,2.2256420357855153454 ] 
dist 151=[-1.2682152879977232729 ,2.2083934750329125438 ] 
dist 152=[-1.2427565811014862898 ,2.1990078348028853640 ] 
dist 153=[-1.2736334530063083591 ,2.1684742001122355916 ] 
dist 154=[-1.3008981237464744208 ,2.1532550893205341433 ] 
dist 155=[-1.3195108868863255201 ,1.3818613844309748039 ] 
dist 156=[-1.3274538571589455789 ,1.3026980047032741361 ] 
dist 157=[-1.3290984494471478776 ,1.1206946326248366602 ] 
dist 158=[-1.3267730120259165777 ,1.0810552432034664345 ] 
dist 159=[-1.1902702553745538489 ,.83965640773240661697] 
dist 160=[-1.3193018921497322594 ,.79410691345643583048] 
dist 161=[-1.4538893203640108669 ,.70574936498241337068] 
dist 162=[-1.6130217583965176135 ,.68304164555335583397] 
dist 163=[-1.7603680176369516380 ,.39341191132866001137] 
dist 164=[-1.8479160443466310850 ,.35142515087030044786] 
dist 165=[-1.9084397863560991888 ,.26450161129406334805] 
dist 166=[-1.9479276123705684161 ,.24167723301302249323] 
dist 167=[-1.9746075932356395222 ,.1575762365675622730 ] 
dist 168=[-1.9840095287503504133 ,.1405902780772786746 ] 
dist 169=[-1.9831980894207615117 ,.1100976960349774980 ] 
dist 170=[-1.9795736672987544860 ,.1031790649264738769 ] 
dist 171=[-1.8018004934643235034 ,.0867841703632427877 ] 
dist 172=[-1.9185743668597313128 ,.2219802104634250233 ] 
dist 173=[-2.0454295466825893239 ,.40472069986801122409] 
dist 174=[-2.1556795319137233888 ,.59225486319840323411] 
dist 175=[-2.2468413724121787894 ,.76849306170245364605] 
dist 176=[-2.2975098225583544981 ,.90615164793765764155] 
dist 177=[-2.3282343089458530817 ,1.0419059401624235919 ] 
dist 178=[-2.3397948756349284355 ,1.2105462713533243943 ] 
dist 179=[-2.3409703558680615058 ,1.3708641777289831995 ] 
dist 180=[-2.3357928591384672407 ,1.4734038059943137384 ] 
dist 181=[-2.3152232265942816712 ,1.5532549537666876312 ] 
dist 182=[-2.3025433313478738700 ,1.6230213586177193198 ] 
dist 183=[-2.2215534475544115805 ,1.6809721003514440873 ] 
dist 184=[-2.1990184346283837211 ,1.7136670136771567209 ] 
dist 185=[-2.1532476027621723886 ,1.7341345498045332661 ] 
dist 186=[-2.1370497789447795357 ,1.7432878327328402859 ] 
dist 187=[-.9733748055442518509 ,1.7446387538577083846 ] 
dist 188=[-.9548076929379960076 ,1.8202477150576739216 ] 
dist 189=[-.9149730205927556797 ,1.9269867956652058038 ] 
dist 190=[-.9023841936261725879 ,2.0172155054109738101 ] 
dist 191=[-.4636692108765001772 ,2.0899403687898229719 ] 
dist 192=[-.6228993279483552364 ,2.1268155373061697274 ] 
dist 193=[-.7541426948395640848 ,2.1445543871910848166 ] 
dist 194=[-.8814936429252861512 ,2.1473198995155563124 ] 
dist 195=[-.9965853694619497045 ,2.2502306857303683125 ] 
dist 196=[-1.0789008643756078226 ,2.3367559878610836867 ] 
dist 197=[-1.1529695461927731995 ,2.3973699940056049602 ] 
dist 198=[-1.2351479804229738384 ,2.4384723733658563897 ] 
dist 199=[-1.3087864751627759374 ,2.4645352473727636554 ] 
dist 200=[-1.3487708384125315636 ,2.4692236967166746893 ] 
dist 201=[-1.3717587270244523152 ,2.4581299287093494257 ] 
dist 202=[-1.3775603560268358526 ,2.4539438400412751223 ] 
dist 203=[-1.3772541385497848567 ,2.0202648804075470222 ] 
dist 204=[-1.3758646517223221071 ,2.0117423308546063669 ] 
dist 205=[-1.3734176751942371779 ,1.9779048916203807996 ] 
dist 206=[-1.3983925616329824533 ,1.9674403004594124467 ] 
dist 207=[-1.5804620315450572482 ,1.8605769378139806976 ] 
dist 208=[-1.7104388570959157412 ,1.8338129999646517290 ] 
dist 209=[-1.8271607657945959364 ,1.8005362210152545905 ] 
dist 210=[-1.9563272290081062844 ,1.7858398238927251481 ] 
dist 211=[-2.0720961444687439943 ,1.4094865543077779139 ] 
dist 212=[-2.1353446881483823770 ,1.3564111389123673917 ] 
dist 213=[-2.1722386177826084924 ,1.2458443998538818082 ] 
dist 214=[-2.1828178151763690887 ,1.2145815625963405475 ] 
dist 215=[-2.1911076212552837870 ,1.0881412525068036024 ] 
dist 216=[-2.1985449468061845120 ,1.0616434044643572648 ] 
dist 217=[-2.1962747156477363591 ,1.0848609183771215290 ] 
dist 218=[-2.1892458136122098083 ,1.1176911797574340794 ] 
dist 219=[-1.7315221491339457814 ,1.1419078361525740340 ] 
dist 220=[-1.7171720797238356486 ,1.1526445554300619881 ] 
dist 221=[-1.6986748531392928938 ,1.1558283110335767021 ] 
dist 222=[-1.6892175682725447230 ,1.1550109107409402366 ] 
dist 223=[.06924825935267088298,1.0691372888030327300 ] 
dist 224=[.03960223481248429899,1.1244038293088248793 ] 
dist 225=[-.00404154687582859324,1.2194319512450607422 ] 
dist 226=[-.07819968569839090438,1.3062252404730126671 ] 
dist 227=[-.15852504519322481368,1.3810870889190477515 ] 
dist 228=[-.22678329370326601793,1.4284932151091598394 ] 
dist 229=[-.29927384771286035504,1.4648687847004371374 ] 
dist 230=[-.39649109737640168593,1.4957043279255382029 ] 
dist 231=[-.50216101663526989401,1.5189464280990614100 ] 
dist 232=[-.60838767381470134806,1.5637548429152534379 ] 
dist 233=[-.73536781595078039151,1.6083972002784260416 ] 
dist 234=[-.92386856407078711729,1.6444377517541250677 ] 
dist 235=[-1.1105261765289700781 ,1.6721882099566704457 ] 
dist 236=[-1.2301500402124382701 ,1.6837430800861400032 ] 
dist 237=[-1.3235721893222268130 ,1.6856458964957830954 ] 
dist 238=[-1.4056541302790505532 ,1.6837153410652911631 ] 
dist 239=[-1.4741563040491496440 ,1.3230645795885748134 ] 
dist 240=[-1.5133792000338661259 ,1.3332347209002349599 ] 
dist 241=[-1.5386625299822882867 ,1.3356188108469553125 ] 
dist 242=[-1.5515294232119120480 ,1.3332090683654021644 ] 
dist 243=[-1.5572639975670201071 ,1.3050280878904170109 ] 
dist 244=[-1.5551345890685135242 ,1.2951809372439296165 ] 
dist 245=[-1.5465105860965004209 ,1.2766087518818354555 ] 
dist 246=[-1.5398772813332792736 ,1.2694720032828942651 ] 
dist 247=[-1.5085035428948548154 ,1.0899189945402556434 ] 
dist 248=[-1.5349363399111373775 ,1.0624619828057852222 ] 
dist 249=[-1.5482861169023606824 ,1.0014420977465180406 ] 
dist 250=[-1.5498973228712095453 ,.9825817890452322791 ] 
dist 251=[-1.5402010169567923518 ,.8983649461567248214 ] 
dist 252=[-1.5335149149806924163 ,.8806069528058009552 ] 
dist 253=[-1.5166189772605359367 ,.8357247971337178014 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 0, 2, 2, 0, 0, 1] 
dist 0=[52.279688896511932168  ,52.279688896511932168  ] 
dist 1=[51.788688684493868384  ,53.100869527237746334  ] 
dist 2=[50.649508262410304796  ,53.957416492333488173  ] 
dist 3=[48.837671620350098211  ,54.365554684896714356  ] 
dist 4=[45.927624353861073545  ,54.558215646361682089  ] 
dist 5=[42.941916753473875575  ,54.561705826183199019  ] 
dist 6=[40.827818728884491428  ,54.122615991938603723  ] 
dist 7=[38.943334787429525112  ,53.685672283519889470  ] 
dist 8=[36.874244380104688583  ,52.990418778869036910  ] 
dist 9=[34.839150287976218618  ,52.842702661902048623  ] 
dist 10=[33.090160690622013303  ,52.233579103580396343  ] 
dist 11=[31.211095503033728756  ,52.037387749667326216  ] 
dist 12=[28.656086060415498477  ,51.538644224609300200  ] 
dist 13=[26.105238704546827092  ,51.334883296349239590  ] 
dist 14=[24.242538476186912673  ,50.290422199219502628  ] 
dist 15=[22.520985769205108104  ,49.206813098899734506  ] 
dist 16=[20.533504352630912757  ,30.863118309541069471  ] 
dist 17=[18.517506267519349439  ,30.333353757172350667  ] 
dist 18=[16.681592249509243341  ,25.460789733547983687  ] 
dist 19=[14.617510694030814686  ,24.555111175960384367  ] 
dist 20=[11.689198537477358623  ,23.393599325933974610  ] 
dist 21=[8.8009401454194152723 ,23.072404702415684773  ] 
dist 22=[6.8967441939483066918 ,15.685134334013841857  ] 
dist 23=[5.3392323028522523854 ,14.757362291044499517  ] 
dist 24=[3.3098641961808664612 ,12.784108608915779499  ] 
dist 25=[1.1445278436140573088 ,12.311693937017389861  ] 
dist 26=[-.72908610484766324121,10.265945480543355522  ] 
dist 27=[-2.7040582476382151652 ,9.8955682086892048215 ] 
dist 28=[-4.6035326677097854603 ,9.1100091647544182891 ] 
dist 29=[-6.1762340793352422920 ,8.9317694310371571318 ] 
dist 30=[-7.8195476759196692496 ,.45074155771566512851] 
dist 31=[-10.002381629157129892  ,-.32214255083456668079] 
dist 32=[-12.094083081680240990  ,-1.8980456618613289237 ] 
dist 33=[-13.373529445603292999  ,-2.2787567581023763433 ] 
dist 34=[-14.312275250059610879  ,-2.6248956010651574134 ] 
dist 35=[-15.042228399115854298  ,-2.5754732704589330288 ] 
dist 36=[-15.603277780776635896  ,-2.3862950843166945734 ] 
dist 37=[-15.866751533085782537  ,-2.1646540753157613898 ] 
dist 38=[-15.985690354973602404  ,-1.9855054203509614576 ] 
dist 39=[-16.359098348584611082  ,-1.8060968480559920320 ] 
dist 40=[-16.648576107313751828  ,-1.5827503846850200410 ] 
dist 41=[-16.749145299092966016  ,-1.3508030600271773429 ] 
dist 42=[-16.770595094598400819  ,-1.1367736447530053877 ] 
dist 43=[-16.743930866466669152  ,-.530915168644320464  ] 
dist 44=[-16.677543291512506268  ,.73954868109316848487] 
dist 45=[-16.621135804830092734  ,2.7098858134457544357 ] 
dist 46=[-13.726365176255361865  ,4.6928276506731651775 ] 
dist 47=[-13.608505595162334785  ,6.0137251278027963152 ] 
dist 48=[-5.5246459860027558681 ,7.1019398161640502851 ] 
dist 49=[-4.7880907220510506616 ,8.1564498083434039499 ] 
dist 50=[-3.1195845386851795181 ,9.1082766647884622710 ] 
dist 51=[-2.8016275106891814112 ,9.7867990428446592526 ] 
dist 52=[-1.6745769737241690357 ,10.395147131704250113  ] 
dist 53=[-.38563542449542234444,11.067054120753738184  ] 
dist 54=[.2928605426745021067 ,11.665392573976981693  ] 
dist 55=[.4484627446704085040 ,11.980183045926612524  ] 
dist 56=[1.6236295659840368373 ,12.148018734456686724  ] 
dist 57=[1.9856795271754648943 ,12.183331416751517736  ] 
dist 58=[2.0410643240291102896 ,12.116096516834118268  ] 
dist 59=[2.1430213360349012527 ,12.061737087740512447  ] 
dist 60=[2.1612576874987988942 ,11.989312571053889931  ] 
dist 61=[2.1275824844884065952 ,11.781240587726212327  ] 
dist 62=[2.0295818299028760670 ,10.054079605521725422  ] 
dist 63=[1.8724847513979452508 ,9.5268267698300214016 ] 
dist 64=[1.2589260801980414019 ,2.6118925578581623348 ] 
dist 65=[.84051947389333375702,2.6113352016286731102 ] 
dist 66=[.48535294991465384318,2.6066742932642101343 ] 
dist 67=[.12406938427680352534,2.5756716802689743312 ] 
dist 68=[-.21323777027067548966,2.5665182650496162230 ] 
dist 69=[-.47277931854001345208,1.6513944075101910248 ] 
dist 70=[-.72503228247665929609,1.5626426443002972797 ] 
dist 71=[-1.0333280219997117106 ,1.3421188502259428762 ] 
dist 72=[-1.3241977513242531057 ,1.3090083695341881523 ] 
dist 73=[-1.5069396208483465122 ,.96930040617240102295] 
dist 74=[-1.6456549220152541237 ,.90497582990373407953] 
dist 75=[-1.7608450403820262706 ,.82968761821809805448] 
dist 76=[-1.8525017350209106091 ,.81238248715101890104] 
dist 77=[-1.8973356297352949337 ,.23998334586694406165] 
dist 78=[-1.9204431965121738726 ,.16967438412180253769] 
dist 79=[-1.9252280780778069977 ,.02152155680821644126] 
dist 80=[-1.8871254409799085237 ,-.01455213121874203034] 
dist 81=[-1.8759311035342306166 ,-.15914987736235166225] 
dist 82=[-1.8388722830823821620 ,-.18613837443089518257] 
dist 83=[-1.8254271310385550078 ,-.22397607504520317178] 
dist 84=[-1.7936208321686820099 ,-.08035721045464736268] 
dist 85=[-1.7023692763514578055 ,.04497118440597894541] 
dist 86=[-1.6614780065052758071 ,.18067417772398599324] 
dist 87=[-1.6487382958690290160 ,.36573210801529647431] 
dist 88=[-1.6200825385647406367 ,.54943106482869864181] 
dist 89=[-1.5558942802309032689 ,.67973944967815502632] 
dist 90=[-1.5384292571552697636 ,.79580211036334437068] 
dist 91=[-1.5064526218503471842 ,.92269820008512811117] 
dist 92=[-1.4960592468986082674 ,1.0468709691448367144 ] 
dist 93=[-1.2545064316332930848 ,1.1521021974597925834 ] 
dist 94=[-1.2188192816440960976 ,1.2637175584946001275 ] 
dist 95=[-1.1373766259225208439 ,1.4134279856726540684 ] 
dist 96=[-1.1139422657316194101 ,1.5563270720283735235 ] 
dist 97=[-1.0007785814475773566 ,1.6407660663722861002 ] 
dist 98=[-.97733562666327868428,1.6987312228355519235 ] 
dist 99=[-.92509691207746006758,1.7359374978416739799 ] 
dist 100=[-.90890010025950420795,1.7614491148006290263 ] 
dist 101=[-.28453145182773098301,1.7727158807475551499 ] 
dist 102=[-.22097184639165244125,1.7757732739034757192 ] 
dist 103=[-.09220538841796748679,1.8445593623126432375 ] 
dist 104=[-.09993496618508987776,1.9307662389592466218 ] 
dist 105=[-.1513933422652426822 ,1.9772592386006525748 ] 
dist 106=[-.1937668665167437355 ,2.0036238656123282081 ] 
dist 107=[-.23756101367748093295,2.0094758303444106870 ] 
dist 108=[-.29469119063023793565,2.0070191623915302072 ] 
dist 109=[-.35027053583609720416,2.0002118530685525908 ] 
dist 110=[-.38787827842154021089,1.9889195537866102678 ] 
dist 111=[-.41949732723054503566,1.9819759201304371906 ] 
dist 112=[-.45118241893641985825,1.4955613058360709749 ] 
dist 113=[-.48046804698042468732,1.4420937853232022127 ] 
dist 114=[-.50251488598228867854,1.3038728747021352830 ] 
dist 115=[-.63747731890970902481,1.2571153964272021470 ] 
dist 116=[-.80295795051404623147,1.0312341971807107993 ] 
dist 117=[-.92700082495889455401,-.23828640381456675279] 
dist 118=[-1.0444778800038262537 ,-.27386796742918673097] 
dist 119=[-1.1837507111978395174 ,-.34204576560930071265] 
dist 120=[-1.3129316976555065174 ,-.3631514499992760898 ] 
dist 121=[-1.3901264074966525276 ,-.41904722304507323029] 
dist 122=[-1.4440358765712502322 ,-.43013759120726253826] 
dist 123=[-1.4802720561316925977 ,-.43055442661762746318] 
dist 124=[-1.5061737715929994126 ,-.41596534204788557353] 
dist 125=[-1.5188351618421762124 ,-.3602768293819887729 ] 
dist 126=[-1.5242265283420872282 ,-.27599703780239099498] 
dist 127=[-1.5220699330850263601 ,-.13582914976070231021] 
dist 128=[-.71402145161909486398,.00750582744073546385] 
dist 129=[-.72192699026177024861,.10442809499961794521] 
dist 130=[-.72339652170318382741,.18587070720032274695] 
dist 131=[-.72003398209375772081,.26743345140859781076] 
dist 132=[-.71895509202271319743,.34279588086312878748] 
dist 133=[-.67941254704713654169,.39949713233992634719] 
dist 134=[-.67170055345186487994,.45337601242187497639] 
dist 135=[-.64928853246125338954,.51747939842336203845] 
dist 136=[-.64392392091714398809,.57702756046679030848] 
dist 137=[-.59460302492981941649,.61272924135752153905] 
dist 138=[-.58335942249303466335,.63780568931181164578] 
dist 139=[-.56825964048847447573,.65495149299998882888] 
dist 140=[-.56253886235563521057,.66717607818877032812] 
dist 141=[-.42632970354107585143,.70238095291753623286] 
dist 142=[-.40748272695090388761,.72535902112015713144] 
dist 143=[-.36714739276562294517,.73971990075445500087] 
dist 144=[-.35568185431095538525,.74607434780347134119] 
dist 145=[-.30853362690304034744,.74863453377175342248] 
dist 146=[-.29923635553651125139,.74785216645066964429] 
dist 147=[-.27533401827508535956,.74449174995068091884] 
dist 148=[-.2711711431326795186 ,.74225095601209865879] 
dist 149=[-.22853667315304549368,.56037095325972018078] 
dist 150=[-.27567568868163409206,.539964589921198665  ] 
dist 151=[-.33571101232300788332,.49161225263490876442] 
dist 152=[-.39348003736911950076,.4805456617145061858 ] 
dist 153=[-.4315762177051973965 ,.40993974316751645425] 
dist 154=[-.46254742458177037188,.39588035624355369139] 
dist 155=[-.49188406075232271634,.36968704323234798531] 
dist 156=[-.51792417443228871248,.36286839142719552531] 
dist 157=[-.53574161038560914234,.25175841149358678674] 
dist 158=[-.55095572994261614868,.23636929267111759747] 
dist 159=[-.56661044540650038228,.20048802465619156706] 
dist 160=[-.57965925661719637082,.1928883475363495422 ] 
dist 161=[-.5844734541327810201 ,.13842985219852995538] 
dist 162=[-.58586949685391190233,.12821630964306116236] 
dist 163=[-.58527056299809078876,.11399477752245015677] 
dist 164=[-.58158837224875100543,.10972027178520419751] 
dist 165=[-.56282924605129868169,.02959936686284101128] 
dist 166=[-.59991625269857669714,.07803275922409750155] 
dist 167=[-.6541295679396864899 ,.13053656457467704198] 
dist 168=[-.7036927950002966703 ,.18468056250957458361] 
dist 169=[-.74647535897193955774,.23572725423091012113] 
dist 170=[-.77362551187323962199,.27586936576436394967] 
dist 171=[-.79452609986519822145,.31570777140698833592] 
dist 172=[-.81236544203150105733,.36554233494136154537] 
dist 173=[-.82601954466513422114,.41308151906243031166] 
dist 174=[-.83021581989433435606,.44375883478202707084] 
dist 175=[-.83035127740306403764,.46795567408489178938] 
dist 176=[-.82780413306728051398,.48963062840267542779] 
dist 177=[-.80488664162339695672,.50802197880029188216] 
dist 178=[-.79747100437151540023,.51911363573549562907] 
dist 179=[-.78712505028300793651,.52698086241050352633] 
dist 180=[-.78246374867671730856,.53250321078479758892] 
dist 181=[-.57356378642223363107,.5690962448660676054 ] 
dist 182=[-.55954243230596555908,.60882424639079260326] 
dist 183=[-.55411610702782956971,.65213705913673205803] 
dist 184=[-.42322811556761141012,.69093941989652276328] 
dist 185=[-.40503284786711406241,.7126652866606904691 ] 
dist 186=[-.36629184490587413486,.72604549652084302276] 
dist 187=[-.35528232038525095838,.73153755996087337372] 
dist 188=[-.31010567207493387232,.73342326264698373768] 
dist 189=[-.30109200497498507978,.76013485966088525469] 
dist 190=[-.27813902310554474469,.78889749133707419397] 
dist 191=[-.27379338573101319645,.80955064346773605234] 
dist 192=[-.07515083582211383948,.82453555942251177828] 
dist 193=[-.14638509943763639964,.83472847440851253943] 
dist 194=[-.20630531721104425385,.83655591070302457273] 
dist 195=[-.26643984603869600546,.83463962706722271067] 
dist 196=[-.32210014745157844637,.83228699093546540542] 
dist 197=[-.36416371931034122007,.65599544038188106934] 
dist 198=[-.40431961063192874254,.65319734872572147796] 
dist 199=[-.45236680067565758594,.64223109527831287661] 
dist 200=[-.49713580426034572461,.63870550989972873294] 
dist 201=[-.5242084239519846723 ,.60426952854420795817] 
dist 202=[-.56425635969684405483,.59562027145869282485] 
dist 203=[-.6015302761577205032 ,.58446364528722200031] 
dist 204=[-.64231237567997863608,.57971873569115372794] 
dist 205=[-.67875199611184268564,.45875125785644799439] 
dist 206=[-.69869428218191125676,.44165598017124534022] 
dist 207=[-.7103691605325874525 ,.40573415365305637827] 
dist 208=[-.71381200280503302061,.39550338154435584365] 
dist 209=[-.7145000547198157466 ,.35365013213081725821] 
dist 210=[-.71943476927230913609,.34501420988884698896] 
dist 211=[-.72035665500564704426,.32348667575468339076] 
dist 212=[-.71946031974012363565,.3185409490329038326 ] 
dist 213=[-.74608417849772151239,.2645317691507537696 ] 
dist 214=[-.7668928840061526301 ,.30356938002601569697] 
dist 215=[-.78503462673095133765,.35226718826005058997] 
dist 216=[-.79909943319562148635,.39865610466578266713] 
dist 217=[-.8036360125496982125 ,.42847881447789386789] 
dist 218=[-.80410823443865986726,.45187436957390444612] 
dist 219=[-.80195033856940249772,.47261202147554487863] 
dist 220=[-.77964746420218385133,.49005145764154252274] 
dist 221=[-.77243230032765324515,.50028366352040602502] 
dist 222=[-.7631721634162125197 ,.50719568075476707435] 
dist 223=[-.75861043584250100038,.51138422763576194572] 
dist 224=[-.26514659047048407265,.51330946193347822217] 
dist 225=[-.3083882246969782254 ,.55387139875443788883] 
dist 226=[-.35073182002202507865,.59719389272669155931] 
dist 227=[-.40052839125162566839,.63561470563686353016] 
dist 228=[-.47351635480038901567,.66794292851245574913] 
dist 229=[-.54541757045605525145,.68694867661079089174] 
dist 230=[-.59087672894030624335,.69983514215940179762] 
dist 231=[-.62567047758198247076,.7077401761172739508 ] 
dist 232=[-.65500394341803434303,.7348326539651986658 ] 
dist 233=[-.67858012259699308139,.76224323218074325033] 
dist 234=[-.69039541643277307799,.78205911699220136771] 
dist 235=[-.69604501795490516088,.79669055701584471068] 
dist 236=[-.69678234640436321046,.8068682828088746682 ] 
dist 237=[-.68938787803666375494,.80890844094444335654] 
dist 238=[-.68599161579849462487,.807656694509234305  ] 
dist 239=[-.67672809720316806865,.80469569908422918486] 
dist 240=[-.67232184908092905383,.62800562427287051134] 
dist 241=[-.64669798012093835056,.62548788541475833453] 
dist 242=[-.63996325816668315485,.61547789414790297826] 
dist 243=[-.62411882342694063791,.61207478875587907927] 
dist 244=[-.61822135433100880878,.58004864731544860421] 
dist 245=[-.54942229205359592794,.57193407332003806057] 
dist 246=[-.58468120676402802157,.56115480210092762871] 
dist 247=[-.62296276283868262199,.55668755598736586894] 
dist 248=[-.6570816864543548964 ,.44278923779405535641] 
dist 249=[-.67572675256228816102,.42663030235562938364] 
dist 250=[-.68660617369585286434,.39249332998925173199] 
dist 251=[-.68973089439592269797,.38271038642614879141] 
dist 252=[-.68974703256768182624,.34232860302498949417] 
dist 253=[-.68821949838848807913,.33406745584448764012] 
dist 254=[-.68526849480212198254,.31292398485541699428] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 0, 0, 2, 0, 2] 
dist 0=[59.029280377059583590  ,59.029280377059583590  ] 
dist 1=[58.778152579008672611  ,59.101083288716455054  ] 
dist 2=[58.197281225072343874  ,59.136930491999878116  ] 
dist 3=[57.011171778152834723  ,59.057261122606528554  ] 
dist 4=[55.698238738185436997  ,58.981450976860271612  ] 
dist 5=[54.610851916011636941  ,58.527502206271055277  ] 
dist 6=[52.930537439677669489  ,58.393740407131598059  ] 
dist 7=[51.172038142348430742  ,58.166704267525720716  ] 
dist 8=[49.261097425765531028  ,56.441972327419400073  ] 
dist 9=[46.636497244880282198  ,52.458688153538903339  ] 
dist 10=[43.746118316926499839  ,51.647269344871723206  ] 
dist 11=[40.773622963711518131  ,50.235974484316303273  ] 
dist 12=[37.164024283589516643  ,49.878245035427398353  ] 
dist 13=[31.729040352414230310  ,48.809586335666479995  ] 
dist 14=[26.276371030217824817  ,48.506005235087472841  ] 
dist 15=[22.596139554899893025  ,48.184827737842858007  ] 
dist 16=[19.500498252511122727  ,46.361347252131987216  ] 
dist 17=[16.382703504051773178  ,35.726953714439117474  ] 
dist 18=[13.480325856517508499  ,35.208344188261343874  ] 
dist 19=[11.244010385104111765  ,34.999392387453471061  ] 
dist 20=[9.0520154101414270596 ,17.083071467524471074  ] 
dist 21=[6.3432987079917644793 ,12.159218502844962798  ] 
dist 22=[3.7587976775310107199 ,10.125162976690095830  ] 
dist 23=[1.9574851396860980930 ,8.7786825261337756112 ] 
dist 24=[-.82952798979285797722,8.5287810650269497997 ] 
dist 25=[-2.9242053178151983458 ,1.7807352572576082186 ] 
dist 26=[-4.9185352577215123016 ,.93358749042215890604] 
dist 27=[-7.3047106078746705146 ,.13647102805897428574] 
dist 28=[-9.5387797698553125107 ,-1.0011630738959364453 ] 
dist 29=[-10.925578997574768529  ,-1.7619716682737508229 ] 
dist 30=[-11.960871501288820337  ,-2.7122780732422804616 ] 
dist 31=[-12.791015403330586154  ,-2.9552640761170109410 ] 
dist 32=[-13.447118564138256712  ,-3.2724945136754220946 ] 
dist 33=[-13.787364903230941703  ,-5.8875697585274662791 ] 
dist 34=[-13.962571994826864464  ,-6.1294357836601147248 ] 
dist 35=[-13.990729612247002199  ,-5.4761005648717359046 ] 
dist 36=[-7.5500312957635461272 ,-4.6532725015185528586 ] 
dist 37=[-7.2196218338937034161 ,-4.0450600877082794858 ] 
dist 38=[-6.3827481389662048502 ,-3.4813112590718252855 ] 
dist 39=[-6.3011404871086576261 ,-2.8350508175533888526 ] 
dist 40=[-6.2711067537764968475 ,-2.1883370240326697018 ] 
dist 41=[-5.4827871156094976810 ,-1.6223694742580945674 ] 
dist 42=[-5.3648647094643623089 ,-1.0085561376501412715 ] 
dist 43=[-5.1806703853036273607 ,-.17055203657634825452] 
dist 44=[-5.0846723329398697682 ,.66174884318585485808] 
dist 45=[-5.0552157966223611759 ,1.2530173487932345808 ] 
dist 46=[-4.4877530046347513368 ,1.7806677508731411733 ] 
dist 47=[-4.3162478501762604944 ,2.3593786257180709947 ] 
dist 48=[-4.2693282334627270293 ,2.9271403870550618602 ] 
dist 49=[-2.4615185205446203546 ,3.4113208812014015049 ] 
dist 50=[-2.2689048267319924200 ,3.9279011754253789615 ] 
dist 51=[-1.6560412297080928019 ,4.6253409336197016666 ] 
dist 52=[.48240228292294702354,5.2940596170833561451 ] 
dist 53=[.53634556713312043389,5.6960623550226472757 ] 
dist 54=[1.0953117991003267658 ,5.9810332146518866038 ] 
dist 55=[1.1767193811925790799 ,6.1824530002021741502 ] 
dist 56=[1.2641591661255856375 ,6.3309074835893048286 ] 
dist 57=[1.2571637436251670422 ,6.4042959484188151318 ] 
dist 58=[1.2111142596842921737 ,6.4372140118015709148 ] 
dist 59=[1.1110256092240741787 ,6.4322331073614781009 ] 
dist 60=[.95273191537042569169,5.8469209012084871897 ] 
dist 61=[.67442466949859948878,5.7493785073004251772 ] 
dist 62=[.38668038500914017753,5.5769614591363083513 ] 
dist 63=[.19069685612542429328,5.2622889270219616515 ] 
dist 64=[.02489868333308560027,5.0629124691473895024 ] 
dist 65=[-.19618895369645958308,5.0654896979497180784 ] 
dist 66=[-.66426661607184012198,5.0437415651577032150 ] 
dist 67=[-1.6018421897994046204 ,5.0248985535193946762 ] 
dist 68=[-2.5347192464574722245 ,.11093214930738930565] 
dist 69=[-3.1374169759109872756 ,-.34691583963532771234] 
dist 70=[-3.6137558118311059254 ,-.44988475417171491474] 
dist 71=[-4.0423237427940542114 ,-.45909081339025746307] 
dist 72=[-4.4075593231904029569 ,-.44593697808098429532] 
dist 73=[-4.6311431069197125790 ,-.39905924320685039939] 
dist 74=[-4.7939554856413710855 ,-.33445666800997071948] 
dist 75=[-4.9166771034459791243 ,-.25061402256938578973] 
dist 76=[-5.0124978188326260201 ,-.13700732062358589067] 
dist 77=[-5.0679349456959283947 ,.04628235437655689178] 
dist 78=[-5.1045807097854580888 ,.23198160858910881412] 
dist 79=[-5.1253401564791190891 ,.35520083858581648984] 
dist 80=[-5.1429692213982984111 ,.45575602551861793913] 
dist 81=[-5.1500056549110966415 ,.55109196475302211851] 
dist 82=[-5.1376755562905132826 ,.63529365994978534375] 
dist 83=[-5.1240423934380289864 ,.69145050456113537667] 
dist 84=[-2.4720570791495913956 ,.73756026478246986181] 
dist 85=[-2.2472693160785731041 ,.83363922856775781179] 
dist 86=[-1.7022949819639007436 ,.99208736012639778822] 
dist 87=[-1.6227809913711935838 ,1.0968314119043943471 ] 
dist 88=[-1.4973912128866013501 ,1.1820420358100406958 ] 
dist 89=[-1.0694321315608417187 ,1.2625618858207518707 ] 
dist 90=[-1.0103222510716846526 ,1.3954753451271273664 ] 
dist 91=[-.87531660594264406202,1.8130611238730168042 ] 
dist 92=[-.84793137267175618258,2.2071849169354051891 ] 
dist 93=[-.67703558227673120757,2.4562417372322150354 ] 
dist 94=[-.64632171181351365966,2.6466570260608326116 ] 
dist 95=[-.58678092777839854053,2.8067353340319787717 ] 
dist 96=[-.57227418728607257249,2.9355137986092676233 ] 
dist 97=[1.4161878523185510201 ,3.0010117707429828963 ] 
dist 98=[1.5002632407509816017 ,3.0359151861612215079 ] 
dist 99=[1.5155000475520276650 ,3.0425919514371669031 ] 
dist 100=[2.1440270444278747442 ,2.5649386416979840045 ] 
dist 101=[2.1859184633150143581 ,2.6520268094066072101 ] 
dist 102=[2.2555581142891528428 ,2.6937946527170831748 ] 
dist 103=[2.2634976132020429641 ,2.7132746998138394956 ] 
dist 104=[2.2503582342891988474 ,2.7139781465675110099 ] 
dist 105=[2.2062814500228168104 ,2.6878402016053599685 ] 
dist 106=[2.1311933327020586827 ,2.6918054055949056547 ] 
dist 107=[1.9942682559523927682 ,2.6850697875273102084 ] 
dist 108=[1.8427380631170592866 ,2.6788843744010449171 ] 
dist 109=[1.6406243888195941746 ,2.6314846118939804066 ] 
dist 110=[1.3895782355066154726 ,2.6169187910770246304 ] 
dist 111=[1.0747970019379288305 ,2.5620421898761736115 ] 
dist 112=[.59071178615268107102,2.5501733581032899012 ] 
dist 113=[.1043470062027267786 ,1.7272959962350075990 ] 
dist 114=[-.21954147563447822889,1.6828258550078924168 ] 
dist 115=[-.48647853938622218467,1.6690497908356446470 ] 
dist 116=[-.75446147584210503396,1.0119750791322918849 ] 
dist 117=[-1.0002016568277695861 ,.6466826403773989632 ] 
dist 118=[-1.1821112354882785737 ,.57921729518747641105] 
dist 119=[-1.3521653744290278056 ,.48187325509400601955] 
dist 120=[-1.5506006542415908000 ,.45427636591943522642] 
dist 121=[-1.7342039979560962274 ,-.04988782133880315433] 
dist 122=[-1.8450593818059015913 ,-.11268360703953397411] 
dist 123=[-1.9239182435548437700 ,-.25766300660909819105] 
dist 124=[-1.9798001180803451232 ,-.27937903560282905072] 
dist 125=[-2.0205288966084849040 ,-.46135440461835334941] 
dist 126=[-2.0389038283790034238 ,-.49199294218326384109] 
dist 127=[-2.0444572010763889578 ,-.53658939733405289148] 
dist 128=[-2.0427941899959598899 ,-.54634064446795153012] 
dist 129=[-2.0338908054400151114 ,-.46141195531426917512] 
dist 130=[-2.0366324561769457429 ,-.3350649532449940683 ] 
dist 131=[-2.0344214111421755628 ,-.12852873914008819367] 
dist 132=[-1.0481729023112029879 ,.08267788910368702053] 
dist 133=[-.84554473204200346054,.22766926827157816878] 
dist 134=[-.80666543003989005032,.35187108356489000208] 
dist 135=[-.74174594574078610085,.48011821881976801308] 
dist 136=[-.72540493144953482016,.60111728556379479818] 
dist 137=[-.42469520849735700029,.69639990295474604098] 
dist 138=[-.38525186681997069388,.79109254350684516478] 
dist 139=[-.29126261288768885152,.90974859622168415788] 
dist 140=[-.2768468329421397705 ,1.0231065880648927048 ] 
dist 141=[-.14671165062705219573,1.0966600064471949285 ] 
dist 142=[-.123295887401589061  ,1.1551738092361524899 ] 
dist 143=[-.09211615648843137754,1.2085129322392909521 ] 
dist 144=[-.08438315877095594370,1.2545160311228280632 ] 
dist 145=[.08286228321336829277,1.2837589621815358286 ] 
dist 146=[.01705906534898496370,1.3063988483783698426 ] 
dist 147=[-.20264115298661942662,1.3260662961055139860 ] 
dist 148=[-.42440508680144534729,1.3985343377094021504 ] 
dist 149=[-.57324415269314954737,1.4766650778025076760 ] 
dist 150=[-.69710878523095189115,1.5260436478645634446 ] 
dist 151=[-.81920288960647739631,1.5638703671573251593 ] 
dist 152=[-.93074754196295430234,1.5958966411756605914 ] 
dist 153=[-1.0125096821691162882 ,1.6197869184263783285 ] 
dist 154=[-1.0880736209645947916 ,1.6251374843644528441 ] 
dist 155=[-1.1748792314576499220 ,1.6237679436145568564 ] 
dist 156=[-1.2538355361143811297 ,1.6208215636701418307 ] 
dist 157=[-1.2980729800309327495 ,1.5630821439381139385 ] 
dist 158=[-1.3253137159219240693 ,1.5462785993896239677 ] 
dist 159=[-1.3364384444568792128 ,1.5314364533408706025 ] 
dist 160=[-1.3409269116039957113 ,1.5211261374110711933 ] 
dist 161=[-1.3416850722187550650 ,.80619309276438249011] 
dist 162=[-1.3398429271387969453 ,.76872732445608384016] 
dist 163=[-1.3351321223417180420 ,.75676867635885407611] 
dist 164=[-1.3424049115621031746 ,.07233179312464143959] 
dist 165=[-1.3926685831580036816 ,.01065145814470440658] 
dist 166=[-1.4192184476722980803 ,-.11904194486081230664] 
dist 167=[-1.4838237323864079025 ,-.14958960429773174545] 
dist 168=[-1.5566122453926988051 ,-.27329078603802898382] 
dist 169=[-1.6197933357787822075 ,-.29613189742990487794] 
dist 170=[-1.6577164005429660331 ,-.33307616088735656703] 
dist 171=[-1.6950482702659017522 ,-.34108837950620214574] 
dist 172=[-1.7204650718005110878 ,-.34546019173855142193] 
dist 173=[-1.7362829668042610451 ,-.33149549361710849353] 
dist 174=[-1.7384724957499317197 ,-.30351995112953599762] 
dist 175=[-1.7292498778608384683 ,-.24913821947925859501] 
dist 176=[-1.7248016997109744173 ,-.07759762819708916446] 
dist 177=[-1.4429643807830626351 ,.22329365476069976606] 
dist 178=[-1.4418422068868707858 ,.42260769272811092784] 
dist 179=[-1.4378316879726761554 ,.58566398520219287367] 
dist 180=[-1.3016004147335493558 ,.74184460825868293345] 
dist 181=[-1.3272540329981527343 ,.88162520412716879677] 
dist 182=[-1.3405949993038118066 ,.9792255444922753793 ] 
dist 183=[-1.3438245794418994072 ,1.0646030702895561504 ] 
dist 184=[-1.3219665334333197443 ,1.1555982581747346708 ] 
dist 185=[-1.3162956014343169889 ,1.2381368659781040881 ] 
dist 186=[-1.3128906989351721429 ,1.2897637311023431718 ] 
dist 187=[-1.3116882483620278378 ,1.3286212947510673501 ] 
dist 188=[-1.0722420758300966422 ,1.3602004609609109434 ] 
dist 189=[-1.0389679587160281451 ,1.3846812431326219955 ] 
dist 190=[-.97857624024782145226,1.3952114200503335497 ] 
dist 191=[-.9630944757205915085 ,1.3975458808233886157 ] 
dist 192=[-.91202157725056766392,1.3960272441017726535 ] 
dist 193=[-.89698896734711881511,1.2576174831861349450 ] 
dist 194=[-.88555498094764402429,1.2614134795369048307 ] 
dist 195=[-.88180829990894507612,1.2610837178063504056 ] 
dist 196=[.04313773601521900405,1.2089937392400142480 ] 
dist 197=[-.04856936554301165343,1.1985371944308907002 ] 
dist 198=[-.12947175935080791427,1.1646974174729696514 ] 
dist 199=[-.21795802794815737681,1.1577003836574398636 ] 
dist 200=[-.33993711188934953873,1.0736875480698712298 ] 
dist 201=[-.4618620993719434905 ,1.0543406552984699590 ] 
dist 202=[-.55013405489649683808,1.0335850532446586671 ] 
dist 203=[-.63067017742738895981,1.0235670888606381443 ] 
dist 204=[-.72172140522883771805,1.0456989805249123048 ] 
dist 205=[-.81258486164504774531,1.1007781508391648511 ] 
dist 206=[-.89237368483518982079,1.1497880082496450844 ] 
dist 207=[-.97935390533668265195,1.1935077174806608530 ] 
dist 208=[-1.0989244752997855145 ,1.2283310244384431952 ] 
dist 209=[-1.2137814885192797555 ,1.2451403457199304488 ] 
dist 210=[-1.2819479776770225041 ,1.2571848884727423235 ] 
dist 211=[-1.3289845299320542794 ,1.2708899567549163048 ] 
dist 212=[-1.3595000235399404333 ,1.2800207327237822577 ] 
dist 213=[-1.3809892067127683076 ,1.2807531984619908227 ] 
dist 214=[-1.3919975669070360781 ,1.2731860743294919753 ] 
dist 215=[-1.3974415258874953060 ,1.2691275906594640577 ] 
dist 216=[-1.3967227547505333561 ,1.2182101165078676772 ] 
dist 217=[-1.2452073637756319278 ,1.2041280422323489612 ] 
dist 218=[-1.2213256729019483932 ,1.1886825361121225206 ] 
dist 219=[-1.2052452378371861638 ,1.1803817482185791287 ] 
dist 220=[-1.2806420166555219595 ,.95418124725281796595] 
dist 221=[-1.3225201122192183335 ,.92189243417999872643] 
dist 222=[-1.3478795027275626455 ,.85648564107865826683] 
dist 223=[-1.3573410565789808353 ,.8381924050505828776 ] 
dist 224=[-1.3604710686227618870 ,.76597598476868965375] 
dist 225=[-1.3605574325571002922 ,.74988853983601302372] 
dist 226=[-1.3584331343555960987 ,.71432096748237746019] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 0, 2, 0, 0, 2] 
dist 0=[56.223412104286410391  ,56.223412104286410391  ] 
dist 1=[55.995350602593360271  ,56.313868936790236538  ] 
dist 2=[55.428945843370432618  ,56.447044537885338372  ] 
dist 3=[54.251554937495344532  ,56.510299885410245240  ] 
dist 4=[52.894345719353544320  ,56.495305336762919314  ] 
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dist 100=[-2.4881642195558672110 ,2.9543067274700005092 ] 
dist 101=[-2.4589928460288322296 ,3.0934009383307517801 ] 
dist 102=[1.2305750298039107290 ,3.2180596545272346090 ] 
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dist 109=[.30121728613056591818,3.7081594388760384036 ] 
dist 110=[.12242427911882162589,3.9019347383834797292 ] 
dist 111=[-.05836066752015348820,4.0119691690190175095 ] 
dist 112=[-.22640937439279184987,4.0817697881158383256 ] 
dist 113=[-.35437755898458244672,4.1149515424936872307 ] 
dist 114=[-.47738404371774412048,4.1280122385025980450 ] 
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dist 116=[-.76533755861399095451,4.0968464637057986702 ] 
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dist 119=[-1.1000333428876388226 ,3.1555605862716919850 ] 
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dist 121=[-1.6130766677369106670 ,2.9556523145322292731 ] 
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dist 128=[-3.2166337744562195175 ,1.2762077401086469346 ] 
dist 129=[-3.2856651666698071767 ,1.2190671591962306248 ] 
dist 130=[-3.3375626614693169978 ,1.0143994199957224476 ] 
dist 131=[-3.3600183409161773358 ,.96859826444360403392] 
dist 132=[-3.3638226764194267738 ,.90126083526916346113] 
dist 133=[-3.3579578539063720416 ,.88122114638149158045] 
dist 134=[-.75591601686186028966,-.04195938722703207114] 
dist 135=[-.75186738263967946298,.09190333587882451126] 
dist 136=[-.72360842080146672897,.20271268425508793676] 
dist 137=[-.71572918325387837431,.31100098369267692406] 
dist 138=[-.70260117225901236872,.40935864707405164986] 
dist 139=[-.69808859970111390558,.48053666041504851486] 
dist 140=[-.58218545033572449006,.54543135423523625794] 
dist 141=[-.56504270035220532252,.61871539477536339872] 
dist 142=[-.52818484845780007947,.70669259792418952903] 
dist 143=[-.51726988555732163861,.79364233682614081701] 
dist 144=[-.47035899021065175147,.8680813727023700777 ] 
dist 145=[-.46085700320932622934,.91421934384119909236] 
dist 146=[-.43439236319061034423,.94846907273767880468] 
dist 147=[-.4303008380691911248 ,.97546057634424793395] 
dist 148=[-.3748610278584752146 ,.99718625619836661572] 
dist 149=[-.3645125071592784989 ,1.0104189971815363268 ] 
dist 150=[-.3442236633786832441 ,1.0199736412200006554 ] 
dist 151=[-.33851920046302918964,1.0270184043053168621 ] 
dist 152=[-.31614712944571985906,1.0319220089875843348 ] 
dist 153=[-.3107643347246007054 ,1.0329308166798983266 ] 
dist 154=[-.29922421851665067539,1.0312880732304629022 ] 
dist 155=[-.29547030655753611352,1.0279985034956413627 ] 
dist 156=[-.27900597661982781516,.35608125962169816959] 
dist 157=[-.27450526622718093541,.34040016164581833055] 
dist 158=[-.27242006413729670365,.23417487274738847729] 
dist 159=[-.27306803516807351348,.21874656909964611772] 
dist 160=[-.27541253583902384344,.18456098672007862241] 
dist 161=[-.28365023327728361696,.17629806154238598833] 
dist 162=[-.34876430098174768928,.1352546184891053206 ] 
dist 163=[-.40605424249133754246,.12770600033506973985] 
dist 164=[-.4686052643678224197 ,.11054452866323918435] 
dist 165=[-.55472498226203337053,.10679147041721249835] 
dist 166=[-.6383020318946110443 ,.14989021645784542694] 
dist 167=[-.69690522772548391574,.22263810556019459458] 
dist 168=[-.75346183693382637966,.29963015676564285296] 
dist 169=[-.80491518007578302011,.37402121472790874966] 
dist 170=[-.84915155100151333112,.46073637761621661539] 
dist 171=[-.87690216936451287107,.5869110068855664937 ] 
dist 172=[-.89788965786368874002,.71075556997256297938] 
dist 173=[-.91513089994372261732,.78817051769572916101] 
dist 174=[-.92778690313177678407,.84637123704477715443] 
dist 175=[-.93047377826508337059,.89353201484706391777] 
dist 176=[-.92933014860939755626,.93120061648179556781] 
dist 177=[-.92669803896503816089,.95151935078361491853] 
dist 178=[-.89576402447686431963,.9630085937553744699 ] 
dist 179=[-.88650633523423554116,.96544232129845347371] 
dist 180=[-.87562242455768126982,.91756141862287356082] 
dist 181=[-.86995221093539933853,.9076370587425338222 ] 
dist 182=[-.6143324766202072858 ,.89802804737428088816] 
dist 183=[-.61324644910308802629,.89191538987135391092] 
dist 184=[-.60844751010480624443,.88387049691798451399] 
dist 185=[-.60606543166076046748,.87997344656543856978] 
dist 186=[-.59579674043316439812,.87722848913676952153] 
dist 187=[-.59313427869951909749,.87533903687415821718] 
dist 188=[-.55828801635776797884,.76877285520923344514] 
dist 189=[-.55110675960858326007,.81679327654400616734] 
dist 190=[-.53206573894645601374,.85943321344635089492] 
dist 191=[-.52649016173818200577,.88642715423954286401] 
dist 192=[-.4889906630473773219 ,.91638031713776078528] 
dist 193=[-.48037449246315813037,.93667477839985185445] 
dist 194=[-.46517220394224646627,.94773379769037468827] 
dist 195=[-.4608843079450300795 ,.94961355738638109688] 
dist 196=[-.3644639810598225392 ,.94628644764859982902] 
dist 197=[-.3507179138702318609 ,.93084249185397811703] 
dist 198=[-.31893469351884752474,.2978802766455752498 ] 
dist 199=[-.31101974149082371656,.2648042310587629567 ] 
dist 200=[-.2667741181373156558 ,.1898760750941412276 ] 
dist 201=[-.25794911403129688836,.1750058979827169921 ] 
dist 202=[-.24000399535867372162,.1279896893642808698 ] 
dist 203=[-.23494418673065585772,.23860850885347434282] 
dist 204=[-.0708216395114009723 ,.34829904083738113817] 
dist 205=[-.1453165805393808861 ,.42084574766055115171] 
dist 206=[-.2184861314981875522 ,.4800781179870207051 ] 
dist 207=[-.2693489406962444062 ,.53662737117761468406] 
dist 208=[-.3136195442193863486 ,.58712257775485538061] 
dist 209=[-.3604798754046163509 ,.62219136581598859103] 
dist 210=[-.40543486619328080382,.65267491485285690371] 
dist 211=[-.4421028197844589988 ,.68486863155704374456] 
dist 212=[-.47974033384113840638,.71291963475538697342] 
dist 213=[-.52856918883465222222,.72686843129465922946] 
dist 214=[-.57502074825252506598,.73400617911908527979] 
dist 215=[-.60317017216792426369,.73487344742283989715] 
dist 216=[-.62332342268798483416,.72562200731244801832] 
dist 217=[-.6378570092755345266 ,.72206036482114164431] 
dist 218=[-.64798559073338297484,.71886817375565488101] 
dist 219=[-.65055478656192923299,.71534325640718233972] 
dist 220=[-.65028949129832212301,.14359367531985297687] 
dist 221=[-.64910253178807807464,.18698802515434038744] 
dist 222=[-.61480534704680989601,.2311072104938761043 ] 
dist 223=[-.60781722903146009336,.26423740847979906438] 
dist 224=[-.59099850473711606877,.29566090886298825356] 
dist 225=[-.58485833499058488935,.3329704280629889124 ] 
dist 226=[-.5695054185101341919 ,.37121172569318074802] 
dist 227=[-.59378563469517562584,.40635577185590707649] 
dist 228=[-.61476620613346583587,.44596905365690333554] 
dist 229=[-.62456229403740483646,.50205067776999308026] 
dist 230=[-.62925055408528870547,.55649584459181514707] 
dist 231=[-.62984631311103974942,.58957808537414105676] 
dist 232=[-.61769342855115708881,.61335552570088452039] 
dist 233=[-.61385949161245008295,.63066180404056439806] 
dist 234=[-.61093976550865833352,.64326638675686525416] 
dist 235=[-.6085051398264869611 ,.64827697338951153336] 
dist 236=[-.49827984701473472931,.6494802938814951115 ] 
dist 237=[-.48367744739863152307,.64840808534673415831] 
dist 238=[-.44741890423735997996,.60614210351039183366] 
dist 239=[-.43982423077724836269,.59812588126090105583] 
dist 240=[-.38117582861171856346,.58204004420894089666] 
dist 241=[-.36921377857268443155,.57677881830793228464] 
dist 242=[-.35036031995736264501,.55255378911736033702] 
dist 243=[-.34494806613679650722,.5467341588544644963 ] 
dist 244=[-.2335614219533362603 ,.52941161875914311406] 
dist 245=[-.21857430243718217494,.52540857232789953355] 
dist 246=[-.18402365805332867472,.1972099844121682263 ] 
dist 247=[-.17673450510922576237,.1667410074074390431 ] 
dist 248=[-.13082518768573959015,.0993719205920603663 ] 
dist 249=[-.1222179861346378445 ,.0851381159901315221 ] 
dist 250=[-.10589781635326413678,.0072292691863844546 ] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 2, 0, 0, 0, 1] 
dist 0=[44.672222696922157853  ,44.672222696922157853  ] 
dist 1=[43.768540283142030103  ,45.266569140120541501  ] 
dist 2=[42.203812249809421662  ,45.595966189003489170  ] 
dist 3=[40.565590515991082913  ,45.816258504148714959  ] 
dist 4=[39.368341084397441790  ,45.974837149036407773  ] 
dist 5=[38.261982745161923027  ,46.219337349986905154  ] 
dist 6=[36.986522367218950546  ,46.365998551290658628  ] 
dist 7=[35.695510526308811274  ,46.398877920943409903  ] 
dist 8=[34.526830887598973011  ,46.286995521496255580  ] 
dist 9=[33.220029702044406835  ,44.890777578070173682  ] 
dist 10=[31.376994197652654027  ,44.620892315047576292  ] 
dist 11=[29.505216221254637384  ,44.134121027017603351  ] 
dist 12=[28.083414992791602537  ,43.986759429065573808  ] 
dist 13=[26.713357728404840986  ,43.379344490242570748  ] 
dist 14=[25.048005652906332008  ,43.204819756792746640  ] 
dist 15=[23.311241930382811878  ,42.806203542038498952  ] 
dist 16=[21.655578097089161575  ,42.590235560649836506  ] 
dist 17=[19.734135976504048963  ,30.508382927723700944  ] 
dist 18=[16.934931721746417208  ,29.421812069974940960  ] 
dist 19=[14.150076400548351920  ,26.824290626640159607  ] 
dist 20=[12.285887759728722030  ,26.412109147527302598  ] 
dist 21=[10.729814043615378382  ,22.708017386165336657  ] 
dist 22=[8.9786107314686807331 ,22.018930591893920968  ] 
dist 23=[6.4297998897842946209 ,21.117548509776277157  ] 
dist 24=[4.6310412950371314761 ,20.852101302727492231  ] 
dist 25=[3.0303015625262752970 ,15.272651591032091060  ] 
dist 26=[1.2720191586161918111 ,14.563991314313149232  ] 
dist 27=[-.46324257631460818188,13.055426706326773892  ] 
dist 28=[-1.9725668161052252106 ,12.687705204557422574  ] 
dist 29=[-3.6141782578126637867 ,11.099396875598555472  ] 
dist 30=[-5.8790155332385197247 ,10.810750951595985688  ] 
dist 31=[-8.0727299982004057548 ,10.169545785597065081  ] 
dist 32=[-9.4303597866087696556 ,10.040462929118534800  ] 
dist 33=[-10.444878332727636916  ,3.1128881378744015790 ] 
dist 34=[-11.267232127576049003  ,2.4762153091669079064 ] 
dist 35=[-11.923158055865597388  ,1.1231244829254751535 ] 
dist 36=[-12.272280191519049169  ,.83325350601495442686] 
dist 37=[-12.466804402071660690  ,-.54095854130247436268] 
dist 38=[-12.504876546603514984  ,-.77658046749342805548] 
dist 39=[-12.079942281675892181  ,-1.2600811827349294348 ] 
dist 40=[-11.975479506930929864  ,-1.3611211385707688739 ] 
dist 41=[-11.876636888891811196  ,-1.7586358079726127214 ] 
dist 42=[-11.955774891984008403  ,-1.7875713187092350046 ] 
dist 43=[-12.235219892995101262  ,-1.7054506086056593495 ] 
dist 44=[-12.403348439004539560  ,-1.4533784721239661213 ] 
dist 45=[-12.505198753619432639  ,-1.1139245015468164088 ] 
dist 46=[-12.519790799062112831  ,-.68286144613567686768] 
dist 47=[-12.491828882497918256  ,-.10362991583170055032] 
dist 48=[-12.454447209799711417  ,.82723757440139212709] 
dist 49=[-4.3989825348458211527 ,1.7758437399574315962 ] 
dist 50=[-4.3861463613875880087 ,2.4259882232756757805 ] 
dist 51=[-2.6800164665774592407 ,2.9809715196829601350 ] 
dist 52=[-2.5038005166382061462 ,3.5500680910046351910 ] 
dist 53=[-.87094076428545386013,4.0839552624980254064 ] 
dist 54=[-.58378119557511043505,4.4985608303806611963 ] 
dist 55=[-.2127976614055514043 ,4.9049946335847747010 ] 
dist 56=[-.14291512779944069563,5.4392732259968680496 ] 
dist 57=[1.1817102280344947152 ,5.9030317967860118257 ] 
dist 58=[1.2206235740284043179 ,6.3020034159155380502 ] 
dist 59=[1.4859138625291509460 ,6.6410734086089185268 ] 
dist 60=[1.3985152111163546354 ,6.8256568021816498987 ] 
dist 61=[1.2744608121620266008 ,6.9291381106429715532 ] 
dist 62=[1.0682474310645626518 ,6.9481373017631487060 ] 
dist 63=[.82522274127465977963,3.5715503161040946964 ] 
dist 64=[.55421689616220837366,3.6224384395688224348 ] 
dist 65=[.21089971160523537659,3.6522156823947568358 ] 
dist 66=[-.32075886213720190727,3.6629299899176091870 ] 
dist 67=[-.8561122655761377882 ,3.6627980397416542919 ] 
dist 68=[-1.2141884950470992842 ,3.6524633490429141491 ] 
dist 69=[-1.5109365528262582054 ,3.6288385230377284238 ] 
dist 70=[-1.8015281619973620407 ,3.6126076703965017536 ] 
dist 71=[-2.0658875471942286270 ,3.5728938127539362991 ] 
dist 72=[-2.2579408818155146814 ,3.5545736421879778413 ] 
dist 73=[-2.4337946242082252821 ,3.4536664795726043738 ] 
dist 74=[-2.6334975027661106059 ,3.4237734295409333084 ] 
dist 75=[-2.8147670072673960622 ,3.3718458669000991412 ] 
dist 76=[-2.9170443867141228377 ,3.3545489403151827744 ] 
dist 77=[-2.9810056556491653532 ,3.2836012868867544105 ] 
dist 78=[-3.0093340299315065881 ,3.2614173545261956785 ] 
dist 79=[-3.0228995518973783944 ,3.2124839143081339345 ] 
dist 80=[-3.0279427456028212238 ,3.1941464913763299155 ] 
dist 81=[-3.2296903734876202294 ,1.6278697595498034054 ] 
dist 82=[-3.8222147250305617744 ,1.6095161010410531892 ] 
dist 83=[-4.2874867616734126982 ,.92238321616956846827] 
dist 84=[-4.7013560038986655318 ,.84757172176478638158] 
dist 85=[-5.0510241657651538261 ,.72668268504910970448] 
dist 86=[-5.2600178022312030664 ,.69642893982684422132] 
dist 87=[-5.4062859227444540020 ,.64417396978293773252] 
dist 88=[-5.5055839463306257501 ,.65025575086208021953] 
dist 89=[-5.5784863201259299967 ,.68412215569608118537] 
dist 90=[-5.6193753136183311885 ,.76455078981307419846] 
dist 91=[-5.6448187158125994797 ,.85966301960589135379] 
dist 92=[-5.6560096334537440420 ,.95216011343979532527] 
dist 93=[-5.6572560388084546848 ,1.0604055873839725210 ] 
dist 94=[-5.6429682543917514249 ,1.2184189397306571487 ] 
dist 95=[-5.6145267524331276224 ,1.3963917403694172981 ] 
dist 96=[-5.5964098274629781811 ,1.5843333558870062846 ] 
dist 97=[-3.1649505452927395895 ,1.8156976244693355929 ] 
dist 98=[-2.7493731037664033386 ,2.1670332059463760901 ] 
dist 99=[-1.7546258689072707683 ,2.5190065614484934268 ] 
dist 100=[-1.6670572406309341350 ,2.7529264504164602239 ] 
dist 101=[-.79523579529616808011,2.9453595109921939167 ] 
dist 102=[-.63772067543769778411,3.1317263646569251304 ] 
dist 103=[-.44913326834575428998,3.3001566503565378608 ] 
dist 104=[-.41735068194720984896,3.4209957406632985466 ] 
dist 105=[.80946803024970700174,3.5302722001758441354 ] 
dist 106=[.95251822931096430768,3.6525617497547427282 ] 
dist 107=[.95012644952251035456,3.7625569265096804422 ] 
dist 108=[.6975772804741130209 ,3.8227595216979267188 ] 
dist 109=[.38410774481329545223,3.8581589089584883633 ] 
dist 110=[-.09444742919618626436,3.8691380792497867987 ] 
dist 111=[-.57371286682955008052,3.8637357893083518919 ] 
dist 112=[-.890020054933970786  ,3.8337467445325500665 ] 
dist 113=[-1.1475206511920332934 ,2.2876053164705670936 ] 
dist 114=[-1.3920788724901173027 ,2.3593113808822041413 ] 
dist 115=[-1.6095886990670096567 ,2.4061554283002663674 ] 
dist 116=[-1.7591342078204835056 ,2.4315216351747634997 ] 
dist 117=[-1.8875315044792582178 ,2.4442112212364480586 ] 
dist 118=[-2.0206344401972551869 ,2.4430773831338392246 ] 
dist 119=[-2.1401612998719837954 ,2.4301126761580275762 ] 
dist 120=[-2.2143720545635425518 ,2.4191650454189559179 ] 
dist 121=[-2.2695906024680503393 ,2.2321544988138635069 ] 
dist 122=[-2.3133109635265767674 ,2.1988876504076863987 ] 
dist 123=[-2.3462655762228943068 ,2.1205179552475312509 ] 
dist 124=[-2.3585111309206159246 ,2.0938107850155009460 ] 
dist 125=[-2.3584070849823103046 ,1.9649981223117943493 ] 
dist 126=[-2.3546094728212727296 ,1.9357160365516069126 ] 
dist 127=[-1.5843794619437826951 ,1.8686285325475929372 ] 
dist 128=[-1.7217662925985533764 ,1.8460887694723108330 ] 
dist 129=[-1.8252778374058197159 ,.89932430933219687261] 
dist 130=[-1.9097475930937126208 ,.8027400961678342891 ] 
dist 131=[-1.9758981433352244738 ,.59282770101295772089] 
dist 132=[-2.0062797655484340076 ,.54306676746870081448] 
dist 133=[-2.0207330860895780193 ,.30772054709673493485] 
dist 134=[-2.0232965953946510654 ,.26603165045747361487] 
dist 135=[-2.1582914819851285833 ,.23477954848870082219] 
dist 136=[-2.3068333621810231380 ,.24544587760248128834] 
dist 137=[-2.4397526383306042160 ,.25876141927309357493] 
dist 138=[-2.5171956674136901207 ,.2791471702789587757 ] 
dist 139=[-2.5688801695339465006 ,.30251034483921370492] 
dist 140=[-2.5989813348044987353 ,.32771708611317764492] 
dist 141=[-2.6148858954505260497 ,.35911450395615270255] 
dist 142=[-2.6151338324771687527 ,.40719670034464854985] 
dist 143=[-2.5983949933901976754 ,.45553787623159494753] 
dist 144=[-2.5882659887599442894 ,.4879721020872744163 ] 
dist 145=[-.98465073131640178223,.53606282411412841331] 
dist 146=[-1.0304722450990984645 ,.74305463820636364057] 
dist 147=[-1.0666589782978858707 ,.93128019192083591794] 
dist 148=[-1.0861776112180524935 ,1.0679923090657780089 ] 
dist 149=[-1.0972121804591514598 ,1.1931804318632381101 ] 
dist 150=[-1.0995377182077067068 ,1.3354073985144245116 ] 
dist 151=[-1.0343125030592118749 ,1.4664539140747015374 ] 
dist 152=[-1.0220397681289229437 ,1.5470167859332732458 ] 
dist 153=[-1.0080207986406871196 ,1.6060442375027503780 ] 
dist 154=[-1.0009107592999635508 ,1.6511372064831009002 ] 
dist 155=[-.98922671961516112719,1.6838728829807441852 ] 
dist 156=[-.98412729819127456925,1.6935754827217299920 ] 
dist 157=[-.98058703554765184183,1.6951492530056404669 ] 
dist 158=[-.97821697179987630536,1.6954409567428597145 ] 
dist 159=[-.58979502766674880614,1.4790401610770299299 ] 
dist 160=[-.90435478305512122238,1.5478185490774914498 ] 
dist 161=[-1.2174480459372015593 ,1.6125988966027267951 ] 
dist 162=[-1.4205706746474264174 ,1.6491788110471766250 ] 
dist 163=[-1.5819908218138768872 ,1.6721885806521824090 ] 
dist 164=[-1.7286464398160904715 ,1.6827902219785212239 ] 
dist 165=[-1.8545324970687519888 ,1.6853207533846029051 ] 
dist 166=[-1.9330584692888420403 ,1.6833363820767534295 ] 
dist 167=[-1.9918969547513043626 ,1.6649601501845268717 ] 
dist 168=[-2.0392048705952272418 ,1.6597687744486705524 ] 
dist 169=[-2.0761058361662892756 ,1.5502511147263276992 ] 
dist 170=[-2.0934089983875187071 ,1.5299800346563347730 ] 
dist 171=[-2.0996403680485165531 ,1.4734027113434998349 ] 
dist 172=[-2.0970913027230462451 ,1.4603811840244953931 ] 
dist 173=[-2.0774159387999086570 ,1.3440942652284396261 ] 
dist 174=[-2.0690432143581264115 ,1.3181674895430343585 ] 
dist 175=[-2.0306336694889482499 ,1.2824808802310892082 ] 
dist 176=[-2.0231012562541447418 ,1.2695582672315508630 ] 
dist 177=[-1.3921705140989598565 ,1.0934651373881112514 ] 
dist 178=[-1.4482652807626619753 ,1.1618655881352627939 ] 
dist 179=[-1.4960227527807898768 ,1.2205730365894644407 ] 
dist 180=[-1.6671730650221999508 ,1.2571632060463344182 ] 
dist 181=[-1.8182173435914665989 ,1.2845318918322289173 ] 
dist 182=[-1.9200939296070507174 ,1.3064309621059004032 ] 
dist 183=[-2.0054974775022286530 ,1.3220124782841827965 ] 
dist 184=[-2.0907942745447214656 ,1.3247731320600568970 ] 
dist 185=[-2.1638692899250164627 ,1.3215031029188240522 ] 
dist 186=[-2.2004904067282361253 ,1.3178588367605989947 ] 
dist 187=[-2.2178717378222563844 ,1.2704536029483824408 ] 
dist 188=[-2.2201770787907039087 ,1.2566952897755938544 ] 
dist 189=[-2.1986320088836331518 ,1.2416747582247958992 ] 
dist 190=[-2.1869686449286333234 ,1.2333427863389670691 ] 
dist 191=[-2.1657664989693592258 ,.49723808338117232686] 
dist 192=[-2.1563487528737862350 ,.48340356428086412702] 
dist 193=[-1.5859560574567886858 ,.4743034656895093843 ] 
dist 194=[-1.7100744079966751856 ,.49775888401862608973] 
dist 195=[-1.8023218982102932013 ,.55616505117860692535] 
dist 196=[-1.8752158764812252879 ,.77966628159488898191] 
dist 197=[-1.9315248403189736722 ,.9843391073510166464 ] 
dist 198=[-1.9575739689563557881 ,1.1354037023444065017 ] 
dist 199=[-1.9688966125129257423 ,1.2761496793760940494 ] 
dist 200=[-1.9682195217349404892 ,1.4396406861107364640 ] 
dist 201=[-1.8819803696361280629 ,1.5906545083639949653 ] 
dist 202=[-1.8628396391029927024 ,1.6815996635161348329 ] 
dist 203=[-1.8278218804704716646 ,1.7459705314689051668 ] 
dist 204=[-1.8160358527478690835 ,1.7909136485391262468 ] 
dist 205=[-1.7620985606315402019 ,1.8231379779687763287 ] 
dist 206=[-1.7469681571251633434 ,1.8367448247888834888 ] 
dist 207=[-1.7053870201673619880 ,1.8394339545600806884 ] 
dist 208=[-1.6898360311526982985 ,1.8375886456401437691 ] 
dist 209=[-1.7879094346906820184 ,1.5147807397410500765 ] 
dist 210=[-1.8832603932180187581 ,1.4776992035276399850 ] 
dist 211=[-1.9591615635340893198 ,1.4401242442500790324 ] 
dist 212=[-1.9976651284457407900 ,1.4639843023875279699 ] 
dist 213=[-2.0172558267854766991 ,1.4807833132884634319 ] 
dist 214=[-2.0201537320246191851 ,1.4846573693290184012 ] 
dist 215=[-1.9555755962888377223 ,1.4824214385842332520 ] 
dist 216=[-1.9389282604607951077 ,1.4748263755184409807 ] 
dist 217=[-1.9175555982240411243 ,1.4996486543630268924 ] 
dist 218=[-1.9067668015888493629 ,1.5852480330562740221 ] 
dist 219=[-1.8751174341311663479 ,1.6458979000381564034 ] 
dist 220=[-1.8618922049933482105 ,1.6883606666810887824 ] 
dist 221=[-1.8361390889897075884 ,1.7190206724291556250 ] 
dist 222=[-1.8259531500145726121 ,1.7325602753208132515 ] 
dist 223=[-.64085017505482983554,1.7361441445173353260 ] 
dist 224=[-.80749632667559330758,1.7345720769883344206 ] 
dist 225=[-1.1094897119172252293 ,1.7349413322350443831 ] 
dist 226=[-1.3070591089569346837 ,1.7772247363560791718 ] 
dist 227=[-1.4660145784069864205 ,1.8022998796808088916 ] 
dist 228=[-1.6138834712610792908 ,1.8104163207704063683 ] 
dist 229=[-1.7433503546692477406 ,1.8104165400827626495 ] 
dist 230=[-1.8288562810796242092 ,1.8055127467016756872 ] 
dist 231=[-1.8985612164700500240 ,1.7918532483802681138 ] 
dist 232=[-1.9649615938292451502 ,1.7836155108368315184 ] 
dist 233=[-2.0204722894949328675 ,1.6014182222507494162 ] 
dist 234=[-2.0467116907132834807 ,1.5712233020039541253 ] 
dist 235=[-2.0575888396592477661 ,1.5036233336384252321 ] 
dist 236=[-2.0575627551826574110 ,1.4817708152434864523 ] 
dist 237=[-2.0299202899553028813 ,1.3804853610643987643 ] 
dist 238=[-2.0179331473264350075 ,1.3582836679930812252 ] 
dist 239=[-1.9941504681994668123 ,1.3012541127400202854 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 1, 1, 0, 2] 
dist 0=[44.297125083050866043  ,44.297125083050866043  ] 
dist 1=[44.050311809545023304  ,44.494555234394049123  ] 
dist 2=[43.232213284875238599  ,45.115281425230754054  ] 
dist 3=[41.945283870805296622  ,45.765091035738945023  ] 
dist 4=[39.826096605977211219  ,46.078706939397629987  ] 
dist 5=[37.640445729241856439  ,46.234191564305713565  ] 
dist 6=[36.088007389253687648  ,46.252444355444725851  ] 
dist 7=[34.698369868952200799  ,45.738186856948392679  ] 
dist 8=[33.162669322366284558  ,45.590314194698992110  ] 
dist 9=[31.645312204385277572  ,45.371993881354136216  ] 
dist 10=[30.328714128219146360  ,45.274465408064802246  ] 
dist 11=[28.902676713445458674  ,44.896810426933175820  ] 
dist 12=[26.947825094981770187  ,44.766587103893832330  ] 
dist 13=[24.986923325909469855  ,44.435946387101387907  ] 
dist 14=[23.536504503563572271  ,44.298069051610294189  ] 
dist 15=[22.176472103788374572  ,33.159574703526518957  ] 
dist 16=[20.576318552181229419  ,32.152156085798738688  ] 
dist 17=[18.935197727646591187  ,29.724716537768413688  ] 
dist 18=[17.411126803316339331  ,29.336469465682634670  ] 
dist 19=[15.672922342144338668  ,25.793335494157042342  ] 
dist 20=[13.175565874665978645  ,25.124921088149031985  ] 
dist 21=[10.702813635819719232  ,24.265588034085313867  ] 
dist 22=[9.0628236507407389191 ,24.004946502478035227  ] 
dist 23=[7.7097691494087872998 ,18.334665509654624004  ] 
dist 24=[6.3838602814327712696 ,17.605736558123280328  ] 
dist 25=[5.1677139038673401241 ,16.074694841089910474  ] 
dist 26=[3.9452585102573496385 ,15.665686514750819490  ] 
dist 27=[2.0953967148284924254 ,14.102732680446684325  ] 
dist 28=[.45478791136341463799,13.801090449312346483  ] 
dist 29=[-1.3556817004416034723 ,13.154810313955304972  ] 
dist 30=[-3.8850882498839075278 ,12.985616213703072638  ] 
dist 31=[-6.3497059349229792122 ,4.5139835929188258228 ] 
dist 32=[-7.9014706757177017276 ,3.7493495259502664181 ] 
dist 33=[-9.0912578921029722186 ,2.0511852394754554553 ] 
dist 34=[-10.109200460435261996  ,1.7397526951790313688 ] 
dist 35=[-10.947768999052486920  ,.1021066288563903948 ] 
dist 36=[-11.420848747261063968  ,.06863440282305298304] 
dist 37=[-11.721722628333879055  ,-.19677125956860236113] 
dist 38=[-11.872575920212811947  ,-.23363570779637461004] 
dist 39=[-11.959872753573774852  ,-.30227757299440842937] 
dist 40=[-12.006677691551506973  ,-.31944550118108783102] 
dist 41=[-12.035802978080722609  ,-.38319786036629149222] 
dist 42=[-12.267741674590104689  ,-.39698712370158511302] 
dist 43=[-12.437959183791834971  ,-.43138028100903887026] 
dist 44=[-12.489357618333953599  ,-.44187375132177668483] 
dist 45=[-12.486718509831068585  ,-.57116692296216288839] 
dist 46=[-12.454574714461336451  ,-.59514320279291467159] 
dist 47=[-5.2651519527392546782 ,-.64998024249960278624] 
dist 48=[-4.8005182525113501624 ,-.6691117754456001495 ] 
dist 49=[-3.6860242557656871862 ,-.76362555731562125002] 
dist 50=[-3.5237075839649577145 ,-.78637793587398904271] 
dist 51=[-2.0322735928106336317 ,-.63782663755006867048] 
dist 52=[-2.0207499020764630178 ,.09229412525991727632] 
dist 53=[-1.3394916279355653176 ,.80472813258194892862] 
dist 54=[-1.2742511877832818660 ,1.6796589614011359719 ] 
dist 55=[.03630347738561265359,2.5075157531751116028 ] 
dist 56=[.08980434166400071061,3.0320857902385386131 ] 
dist 57=[.39826499119614875054,3.4352781928655946112 ] 
dist 58=[.44939148364010848021,3.7786972744961338423 ] 
dist 59=[.55498665653064774932,4.0588694684905671347 ] 
dist 60=[.57588672876302503339,4.2095758413751121018 ] 
dist 61=[.71521667895799654387,4.2945665964083556389 ] 
dist 62=[.73314910555520509482,4.3150124610488891370 ] 
dist 63=[.72449112179248504033,4.3014076049499562116 ] 
dist 64=[.67749792351499745641,4.2983617349204737888 ] 
dist 65=[.60964729043614575124,4.2723781377608457636 ] 
dist 66=[.51773300798132505686,4.2530620129156085835 ] 
dist 67=[.39070269344118860034,4.1239759549861413359 ] 
dist 68=[.1826980558146487955 ,4.0879227358282405528 ] 
dist 69=[-.03075950723797017501,4.0186154853362647003 ] 
dist 70=[-.17956096637914929459,3.9950982643663083109 ] 
dist 71=[-.30940267485562134352,3.9310396052906606738 ] 
dist 72=[-.44721113851966872602,3.9460079605270117314 ] 
dist 73=[-.5795157107918657744 ,3.9517764379850227133 ] 
dist 74=[-.68740081438585147639,3.9469973412094805258 ] 
dist 75=[-.79802826726709606643,3.9361618317029380474 ] 
dist 76=[-.9412865663189614294 ,3.9229604854772594068 ] 
dist 77=[-1.3559580724191102305 ,3.8936000696514733992 ] 
dist 78=[-2.2790973529378799207 ,3.8787251256221393111 ] 
dist 79=[-3.1926445386377349121 ,1.5849258424332279603 ] 
dist 80=[-3.7796678945435529975 ,1.4583518479739193599 ] 
dist 81=[-4.2403160121910962246 ,1.1799673176392301688 ] 
dist 82=[-4.6494095223161725593 ,1.1573225259456420094 ] 
dist 83=[-4.9944677133261649108 ,1.0999471363030972581 ] 
dist 84=[-5.1995143735697351596 ,1.0857451271869024927 ] 
dist 85=[-5.3415249733803143044 ,.55200839589982223658] 
dist 86=[-5.4349889551065932040 ,.52058954786093311398] 
dist 87=[-5.5061402316859473637 ,.11279505196153157551] 
dist 88=[-5.5545020213212788992 ,.05471407406353614953] 
dist 89=[-5.5881269246673295012 ,-.06804337027830502328] 
dist 90=[-5.6106120089037055408 ,-.09999583387615723561] 
dist 91=[-5.6243162450671595561 ,-.2273338294778868326 ] 
dist 92=[-5.6228627211737589664 ,-.25142559763795255803] 
dist 93=[-5.6100282368829480980 ,-.30405576474553183698] 
dist 94=[-5.5910639016724568102 ,-.31649197771152186015] 
dist 95=[-2.5106454171441744109 ,-1.0189988545057036534 ] 
dist 96=[-2.2558413297619505202 ,-.73867176197704125728] 
dist 97=[-2.2932806038426527233 ,-.21594689108743851121] 
dist 98=[-2.3031382562742492462 ,.31321333084429464747] 
dist 99=[-2.3027468747350245007 ,.80613250467116769906] 
dist 100=[-2.2992707457916985673 ,1.1842085249321652092 ] 
dist 101=[-2.2145796978790988654 ,1.5506582272677737098 ] 
dist 102=[-2.1958902001348643431 ,1.9971775253981529538 ] 
dist 103=[-2.1346145299547678095 ,2.4179939337128289302 ] 
dist 104=[-2.1220101607757132085 ,2.6818501320749765077 ] 
dist 105=[-1.9676301428705901832 ,2.8813124421107860408 ] 
dist 106=[-1.9319883969188590275 ,3.0450930155127995279 ] 
dist 107=[-1.8943081418045380724 ,3.1764169736437983668 ] 
dist 108=[-1.8762467186698908045 ,3.2463320041924223998 ] 
dist 109=[-1.4093759467132174932 ,3.2846646286723735083 ] 
dist 110=[-1.3456329884518563308 ,3.2915442569764921512 ] 
dist 111=[-1.2162506954419751608 ,2.3958826801111748392 ] 
dist 112=[-1.1811401438234818465 ,2.4294889618557425213 ] 
dist 113=[-1.0474598893527965601 ,2.4447007211340949640 ] 
dist 114=[-1.0182581270738817803 ,2.4463541893148832281 ] 
dist 115=[-.96010048220301044825,2.3926077104690944923 ] 
dist 116=[-.94369953492759952748,2.3215642259150415843 ] 
dist 117=[-.14572696557625438237,2.1840310037209794094 ] 
dist 118=[-.30689805933582861778,2.1828585296399063625 ] 
dist 119=[-.47222521467581014347,2.0809027994452420744 ] 
dist 120=[-.59858093690130611925,2.0598296676857804579 ] 
dist 121=[-.72056015456125707462,2.0012976846108073307 ] 
dist 122=[-.86844394885672440125,1.9838614074118757950 ] 
dist 123=[-1.0216920045647216374 ,1.8595921052017996412 ] 
dist 124=[-1.1650989083415013653 ,1.8305620008201865707 ] 
dist 125=[-1.3288284138048611410 ,1.7818536848363599773 ] 
dist 126=[-1.5817080355697389596 ,1.7671279195143179225 ] 
dist 127=[-1.8550913174737192039 ,.05282398528641518728] 
dist 128=[-2.0239466282442427881 ,-.04485614743145933232] 
dist 129=[-2.1486476463640932906 ,-.25493113352047155195] 
dist 130=[-2.2457879858098033912 ,-.29936714638211431284] 
dist 131=[-2.3216890120847649097 ,-.51655998779820150787] 
dist 132=[-2.3616091784652676086 ,-.5536121503625471833 ] 
dist 133=[-2.4317007741934942044 ,-.62683014122203124117] 
dist 134=[-2.5379481848379388322 ,-.6433602975625481223 ] 
dist 135=[-2.6293168447458244529 ,-.68680045203284547695] 
dist 136=[-2.6783282347830569936 ,-.67961585008096055354] 
dist 137=[-2.7057143159451298978 ,-.65058228732999787731] 
dist 138=[-2.7107670819450710926 ,-.58421112540646891185] 
dist 139=[-2.7043670261443134080 ,-.49897890074654529075] 
dist 140=[-2.6961333795642578104 ,-.39466348373898125617] 
dist 141=[-2.6649151760776623381 ,-.25642443726561910966] 
dist 142=[-2.6477094217928676688 ,-.03579572866938124652] 
dist 143=[-1.7897329911153346019 ,.26462723237545092288] 
dist 144=[-1.7087711815546889444 ,.56011613291660667463] 
dist 145=[-1.5076636015389488499 ,.80416419963490246959] 
dist 146=[-1.4742581325015029031 ,1.0418429593892982095 ] 
dist 147=[-1.1603470435360397804 ,1.2572491406024758225 ] 
dist 148=[-1.0996415012766433474 ,1.4123977335238270251 ] 
dist 149=[-1.0213092011923152576 ,1.5531220043018583217 ] 
dist 150=[-.994973232067378331  ,1.7109514537893143794 ] 
dist 151=[-.45465568429296841813,1.8554223813419035195 ] 
dist 152=[-.38557291802664395695,1.9428297774294982125 ] 
dist 153=[-.23537311454630376133,2.0051709742499166022 ] 
dist 154=[-.20076117672468237577,2.0496030916059308758 ] 
dist 155=[-.03390520906403859639,2.0801359612681973921 ] 
dist 156=[-.00477797766984661063,2.0869995342655830098 ] 
dist 157=[.06334601625280043158,2.0851574229799192962 ] 
dist 158=[0                     ,2.0809484705059933537 ] 
dist 159=[-.16753808274080440994,1.2181843980739062328 ] 
dist 160=[-.31090707909349147494,1.2099459270487273052 ] 
dist 161=[-.43175740592821195935,1.1809590488491168152 ] 
dist 162=[-.55342693896347390031,1.1746311737236178580 ] 
dist 163=[-.6662674150487719966 ,1.0958803906067189839 ] 
dist 164=[-.75188025121175761855,1.0773650509598766875 ] 
dist 165=[-.8339175735487275949 ,1.0577451368487233798 ] 
dist 166=[-.93248609731652130725,1.0479137052119200913 ] 
dist 167=[-1.0244846542957353201 ,.79990077341439718323] 
dist 168=[-1.0803004912811596092 ,.76588654625279809972] 
dist 169=[-1.1202733350457937748 ,.69665808807392357303] 
dist 170=[-1.1490423876148156927 ,.67779257031638522739] 
dist 171=[-1.1695722517982613170 ,.60554728895998714315] 
dist 172=[-1.1766639790554345822 ,.58981655701633621366] 
dist 173=[-1.1775435466669915572 ,.55798839650289218424] 
dist 174=[-1.1745818849538521288 ,.54889978539888936703] 
dist 175=[-1.1036340200975018856 ,.19564011229062436586] 
dist 176=[-1.1621181499888533916 ,.25203418361596407329] 
dist 177=[-1.2032416724255991121 ,.30334226615681956538] 
dist 178=[-1.2314684252062500158 ,.36112363740492282843] 
dist 179=[-1.2513558204691634568 ,.41863897558615462343] 
dist 180=[-1.2591902069438207464 ,.46888339816962680196] 
dist 181=[-1.2601518126326400988 ,.52341808093985062906] 
dist 182=[-1.2583878014965623956 ,.59805361813150375406] 
dist 183=[-1.1593472888588420497 ,.67237543849971762125] 
dist 184=[-1.1636665825033235986 ,.72565664376243616574] 
dist 185=[-1.1888908729132617681 ,.77371338497183982659] 
dist 186=[-1.2005521445803427567 ,.82718234853511991428] 
dist 187=[-1.2061516772977407199 ,.88001086903210533198] 
dist 188=[-1.2071791108639959249 ,.92550947536176866778] 
dist 189=[-1.2050578324223294570 ,.97432938622835895388] 
dist 190=[-1.2014218117922066477 ,1.0404089514419788648 ] 
dist 191=[-1.1820700516912428113 ,1.1028398030455266720 ] 
dist 192=[-1.1945261695824632112 ,1.1370970383411354669 ] 
dist 193=[-1.1992015899277359136 ,1.1572474395739151646 ] 
dist 194=[-1.1977278539725119228 ,1.1633802522359946257 ] 
dist 195=[-1.1719386377528226300 ,1.1642392690023364220 ] 
dist 196=[-1.1625648176849840408 ,1.1633436032995857380 ] 
dist 197=[-1.1528433302395544599 ,1.1609785152177074124 ] 
dist 198=[-1.1465393591234783455 ,1.1564459103195757037 ] 
dist 199=[-.95995240849104271658,1.0389767262436914669 ] 
dist 200=[-.93261763756763468224,1.0948933700429810241 ] 
dist 201=[-.87774583857981961621,1.1336540598998309104 ] 
dist 202=[-.86222139442431865381,1.1591764991705659462 ] 
dist 203=[-.80039080411488262182,1.1769511559765286182 ] 
dist 204=[-.78622502267204381711,1.1847829627107510301 ] 
dist 205=[-.75451734504710970954,1.1868381128394639906 ] 
dist 206=[-.74422785142987392397,1.1850665381019084404 ] 
dist 207=[-.08838851964466842460,1.0712552020223502834 ] 
dist 208=[-.02981615595482344713,1.0545537994108221446 ] 
dist 209=[-.07626337342226695057,1.0079937383197293947 ] 
dist 210=[-.18536274410281325579,.99891969702123037933] 
dist 211=[-.29011549313185338344,.92084906597703786783] 
dist 212=[-.37565454918614318725,.90408656781606049781] 
dist 213=[-.46351243600410764408,.88686589023506953463] 
dist 214=[-.57752196003963888597,.87901784864551938545] 
dist 215=[-.68833816783149369043,.89901301087377514112] 
dist 216=[-.76345128127189382682,.9480839762706132534 ] 
dist 217=[-.82680781971589933874,.98722803324117826339] 
dist 218=[-.89070048517308938778,1.0230657133704941952 ] 
dist 219=[-.95006453132019221103,1.0540339491297566074 ] 
dist 220=[-.99534688811025567833,1.0737399648436146859 ] 
dist 221=[-1.0390010823267349930 ,1.0889629140203867794 ] 
dist 222=[-1.0918688225926637136 ,1.1020337165865041318 ] 
dist 223=[-1.1398565154875569718 ,1.1110692486084526797 ] 
dist 224=[-1.1640322699988903439 ,1.1121245192114370841 ] 
dist 225=[-1.1768274845236190048 ,1.1062460180334438426 ] 
dist 226=[-1.1793878922298849189 ,1.1030921853074739579 ] 
dist 227=[-1.1652045223809871220 ,1.0590121981154403356 ] 
dist 228=[-1.1607665153671340754 ,1.0468020311584072392 ] 
dist 229=[-1.1574155152441998535 ,1.0342733646403221252 ] 
dist 230=[-1.1546744047114070184 ,1.0270399577747895141 ] 
dist 231=[-.98872825480001258493,.82841655948092739036] 
dist 232=[-1.0297876880273319087 ,.80015558582497713632] 
dist 233=[-1.0585212988631105880 ,.74345372766572314343] 
dist 234=[-1.0779625573071342065 ,.72773916829586662579] 
dist 235=[-1.0906900216940714271 ,.66664080538949166697] 
dist 236=[-1.0928911297204211958 ,.65276170914036593063] 
dist 237=[-1.0905512703319607326 ,.62354457320404402142] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 2, 0, 0, 2] 
dist 0=[57.797942029908360456  ,57.797942029908360456  ] 
dist 1=[57.011990131080153833  ,58.245169901931867500  ] 
dist 2=[55.494522161777582586  ,58.410336775339129692  ] 
dist 3=[53.781581233678163289  ,58.477544755449769831  ] 
dist 4=[52.214919499845834051  ,58.533738838332497038  ] 
dist 5=[50.452637069931118337  ,58.565183212389999637  ] 
dist 6=[47.958283624814424551  ,58.533331740394136598  ] 
dist 7=[45.177989226856313987  ,58.448398181224746202  ] 
dist 8=[42.273684435401896868  ,58.005196140331315739  ] 
dist 9=[38.715872703562127562  ,54.464560566658808236  ] 
dist 10=[33.325644578252722433  ,53.855560997941581648  ] 
dist 11=[27.909851566245041083  ,52.804485664642304064  ] 
dist 12=[24.249814995918115268  ,52.519750775378677760  ] 
dist 13=[21.166764263797984958  ,51.601236220136181994  ] 
dist 14=[18.054924776717163420  ,50.652218296931674015  ] 
dist 15=[15.153199776024516981  ,46.264954592875753863  ] 
dist 16=[12.908970057431217192  ,43.219236729335247688  ] 
dist 17=[10.709925362001839647  ,32.393321654161822715  ] 
dist 18=[7.9880797084919070472 ,31.860411119087278908  ] 
dist 19=[5.3893627280246357323 ,30.026049081275187003  ] 
dist 20=[3.6817564694664725809 ,29.589485518733972983  ] 
dist 21=[2.2929781051864667249 ,29.095808739859674464  ] 
dist 22=[.9672454943872314044 ,28.939798805085065927  ] 
dist 23=[-.2258773321163474457 ,15.307277011657596763  ] 
dist 24=[-1.0856058504804512013 ,15.008571401592952235  ] 
dist 25=[-1.8732684176132000133 ,8.2249182776428893313 ] 
dist 26=[-2.7799134436397271293 ,7.4259690738066734442 ] 
dist 27=[-3.6117437042507808370 ,5.6528505119553858100 ] 
dist 28=[-5.3295005192903928635 ,5.3931024675593308775 ] 
dist 29=[-7.1500772501144387103 ,3.4494347859833209680 ] 
dist 30=[-9.3348941469001292784 ,3.0798921062930465125 ] 
dist 31=[-11.384423967708126020  ,2.6172863579551399745 ] 
dist 32=[-12.664610475980652735  ,2.4156590866543995763 ] 
dist 33=[-13.629885389045285405  ,-4.4667930124136196132 ] 
dist 34=[-14.421578246469608866  ,-4.1288449328394039873 ] 
dist 35=[-15.045926438236947400  ,-3.7430161392306786371 ] 
dist 36=[-15.342871578892248272  ,-3.3963696880939263851 ] 
dist 37=[-15.490592880161576166  ,-3.0144634054421765200 ] 
dist 38=[-15.518830426012025651  ,-2.4872899162742985900 ] 
dist 39=[-7.8463047300385509250 ,-1.9090215632997122550 ] 
dist 40=[-7.8901786419916412286 ,-1.3229028090860485270 ] 
dist 41=[-7.8939788144448103079 ,-.61959399417449462103] 
dist 42=[-7.8749633563360892951 ,.4266293803609916991 ] 
dist 43=[-7.8379556690870073306 ,1.4721822209616959187 ] 
dist 44=[-7.8124553281838875175 ,2.1728966836679154729 ] 
dist 45=[-7.6874520883077780826 ,2.7548477488408728201 ] 
dist 46=[-7.6458513710377466559 ,3.3264123116688428068 ] 
dist 47=[-7.5159606925120662232 ,3.8470454564903913486 ] 
dist 48=[-7.4691968150245408971 ,4.2256849870231843773 ] 
dist 49=[-3.9967232701687570790 ,4.5723622708020574761 ] 
dist 50=[-3.6808054215880057878 ,4.9653131502669960371 ] 
dist 51=[-2.9380648269768269856 ,5.3207955590910689804 ] 
dist 52=[-2.8142664857056525639 ,5.5179697142047967530 ] 
dist 53=[-1.8106871309701870396 ,5.6365516076034197118 ] 
dist 54=[-1.6296325056026381957 ,5.6785962006082952969 ] 
dist 55=[-1.3581702183372416235 ,5.6908783671238625896 ] 
dist 56=[-1.2866402738013589934 ,5.6906410475908944224 ] 
dist 57=[-.0574649833001785764 ,5.6808599898226513263 ] 
dist 58=[.0961665804116651329 ,5.6574709851642210324 ] 
dist 59=[.1996448801461185058 ,3.8757016487779211192 ] 
dist 60=[-.41358631752678272561,3.9786315492668578279 ] 
dist 61=[-.92258898328279386086,4.0606721624601116732 ] 
dist 62=[-1.4220643504327800367 ,4.1369983967101215437 ] 
dist 63=[-1.8769908973188017003 ,4.1990081474838244935 ] 
dist 64=[-2.2082561051880661468 ,4.2238492014189290335 ] 
dist 65=[-2.5123881573538842542 ,4.2274291607693850784 ] 
dist 66=[-2.8590997052233825814 ,4.2230188677271121030 ] 
dist 67=[-3.1774411883608780563 ,4.1659300203971474385 ] 
dist 68=[-3.3683584193058737353 ,4.1460841603313889283 ] 
dist 69=[-3.5026234894523080567 ,4.0846411580526919841 ] 
dist 70=[-3.5948234829795335415 ,4.0592663640385661843 ] 
dist 71=[-3.6589051122669787394 ,1.6140367558629138058 ] 
dist 72=[-3.6809486318083177910 ,1.6434860701845399673 ] 
dist 73=[-3.6814646526587902301 ,1.6696343767878936226 ] 
dist 74=[-3.6722648121156395958 ,1.6831149149672029515 ] 
dist 75=[-3.8856605252753886910 ,1.6897588028592196046 ] 
dist 76=[-4.1243637133736634237 ,1.6897184463740033894 ] 
dist 77=[-4.3082405563576528805 ,1.6833343489535978156 ] 
dist 78=[-4.4655350494937979942 ,1.6789772302310376552 ] 
dist 79=[-4.5967510572058626666 ,1.6643148937127819270 ] 
dist 80=[-4.6765411630603967206 ,1.6567721851560916333 ] 
dist 81=[-4.7340562755954521511 ,1.5467446177728194916 ] 
dist 82=[-4.7763730981477216592 ,1.5262994898311282972 ] 
dist 83=[-4.8058764793948057926 ,1.4785821981520568397 ] 
dist 84=[-4.8122634925322014844 ,1.6767002858866011339 ] 
dist 85=[-4.8031123193178814775 ,1.8437271307834826384 ] 
dist 86=[-4.7891196540791525175 ,2.0028796899774729481 ] 
dist 87=[-2.8978910754164155112 ,2.1448595930731229348 ] 
dist 88=[-2.9035252912274562650 ,2.2433890920215223808 ] 
dist 89=[-2.7667784447080706043 ,2.3291086551584982159 ] 
dist 90=[-2.7387805773037258292 ,2.4200289871872106167 ] 
dist 91=[-2.7072789736166352581 ,2.4983889475366100860 ] 
dist 92=[-2.6903397216488614218 ,2.5339849808563537126 ] 
dist 93=[-2.6606694090171811781 ,2.5498038023333926514 ] 
dist 94=[-2.6470477965199911890 ,2.6128072529730611153 ] 
dist 95=[-2.6368718278199313850 ,2.8940060334029827266 ] 
dist 96=[-2.6289563352109227480 ,3.0682644088444297448 ] 
dist 97=[-1.6710527717239779688 ,3.1975840763806960214 ] 
dist 98=[-1.7271284322648294784 ,3.2993816951329417768 ] 
dist 99=[-1.7674208127130456458 ,3.3756099256439949076 ] 
dist 100=[-1.7967650918411714891 ,3.4028440999558266428 ] 
dist 101=[-1.8168493196484223022 ,3.4110312412132740838 ] 
dist 102=[-1.8202960950541995036 ,3.4112934157957510731 ] 
dist 103=[-1.8171029509250302884 ,2.7351159682061387313 ] 
dist 104=[-1.8116927374795406360 ,2.7262445249316320352 ] 
dist 105=[-1.7529856274268472684 ,2.7072217190034871100 ] 
dist 106=[-1.7393010792449372863 ,2.6964523374903894241 ] 
dist 107=[-1.6945544890612379720 ,2.3952946988610247621 ] 
dist 108=[-1.6850760524310549006 ,2.3496044917687479980 ] 
dist 109=[-1.5720126510640055836 ,2.2287192063097685253 ] 
dist 110=[-1.6820953259393729978 ,2.2032182007293150414 ] 
dist 111=[-1.9331563659389990869 ,1.9789573031998817163 ] 
dist 112=[-2.1095867112679972001 ,1.9308564602021851196 ] 
dist 113=[-2.2652033033240548513 ,1.8643244826205391557 ] 
dist 114=[-2.4332011793495344464 ,1.8411597556908981999 ] 
dist 115=[-2.5839466154806766834 ,1.3192826258083529444 ] 
dist 116=[-2.6707025348167640802 ,1.4979425789073452932 ] 
dist 117=[-2.7272590477297594778 ,1.6694595436246309491 ] 
dist 118=[-2.7574559088846142420 ,1.7819207377693896933 ] 
dist 119=[-2.7726768120013219640 ,1.8727359380654230469 ] 
dist 120=[-2.7708420341825794696 ,1.9578566007591993968 ] 
dist 121=[-2.7577160014962794620 ,2.0315096749707125750 ] 
dist 122=[-2.7460197229360913477 ,2.0765490800429706525 ] 
dist 123=[-1.9907965559305010607 ,2.1093037249493536383 ] 
dist 124=[-1.9105938015214932415 ,2.1339098572985070607 ] 
dist 125=[-1.7212714711871301408 ,2.1514243151062030865 ] 
dist 126=[-1.6795702833800399371 ,2.1558653790533478814 ] 
dist 127=[-1.4082584122540889333 ,2.1515813714493933981 ] 
dist 128=[-1.3551215861004753892 ,2.1468387843816957083 ] 
dist 129=[-1.2571265971066651813 ,1.4013241512733995103 ] 
dist 130=[-1.2322908991618037943 ,1.5890790841035460080 ] 
dist 131=[-.82767777847958227001,1.7644079187774886647 ] 
dist 132=[-.77188757175886030952,1.8711116178521675601 ] 
dist 133=[-.63986955780959386082,1.9479820469306555129 ] 
dist 134=[-.61630162364885893638,2.0042484869610145473 ] 
dist 135=[-.50591831551555253638,2.0450680572862389580 ] 
dist 136=[-.58782149909280463675,2.0602850933659978843 ] 
dist 137=[-.67355914980416590435,2.0635353595151359881 ] 
dist 138=[-.74207990921848549864,2.0589229964903802521 ] 
dist 139=[-.8111504500176868371 ,1.9282635980016585643 ] 
dist 140=[-.8990794273952921865 ,2.1108640926751404200 ] 
dist 141=[-.99245288828358993508,2.2928137875301301931 ] 
dist 142=[-1.0832540124537824563 ,2.4577554690989033667 ] 
dist 143=[-1.1896024717395602144 ,2.5991996659170630736 ] 
dist 144=[-1.3450331128281108565 ,2.6873636588233382018 ] 
dist 145=[-1.4981398568033079825 ,2.7534241158003540863 ] 
dist 146=[-1.5952114326825932546 ,2.8066497284250255080 ] 
dist 147=[-1.6698573585308028299 ,2.8457714030403368730 ] 
dist 148=[-1.7334490349094237991 ,2.8555368710511057935 ] 
dist 149=[-1.7850877100505688784 ,2.8528673521128417800 ] 
dist 150=[-1.8120214116698631045 ,2.8430527068013298250 ] 
dist 151=[-1.8260198265549470270 ,2.7614777664193825853 ] 
dist 152=[-1.8266182744452411550 ,2.7358370686705849100 ] 
dist 153=[-1.8184036384431341568 ,2.6963876874366127961 ] 
dist 154=[-1.8172509829158762490 ,2.6805513154558368505 ] 
dist 155=[-1.8399027261000988168 ,2.0767165124745571928 ] 
dist 156=[-1.9377828924158879622 ,2.0677517821089034678 ] 
dist 157=[-2.0831767659013552512 ,2.0170460726625270285 ] 
dist 158=[-2.2125584167884754132 ,2.0031119007370334150 ] 
dist 159=[-2.3217703228284664105 ,1.9529452141431810834 ] 
dist 160=[-2.3866614088445296076 ,1.9434242840802190131 ] 
dist 161=[-2.4315320297662579264 ,.9960846154566867705 ] 
dist 162=[-2.4608386377088203711 ,1.2229384269424876358 ] 
dist 163=[-2.6067557143545963657 ,1.4075372823815824074 ] 
dist 164=[-2.7066662212551371344 ,1.5827823279216953214 ] 
dist 165=[-2.7784907275502070930 ,1.7386427459682694466 ] 
dist 166=[-2.8307644824920066499 ,1.8458708942802423046 ] 
dist 167=[-2.8664697613825686574 ,1.9380376784027129974 ] 
dist 168=[-2.8730315673462950476 ,2.0337845881572404343 ] 
dist 169=[-2.8669673149239027599 ,2.1171594241487045259 ] 
dist 170=[-2.8591810382299131708 ,2.1599442300115810542 ] 
dist 171=[-2.2491966354578996534 ,2.1817792153406382970 ] 
dist 172=[-2.2349087674234367820 ,2.1855291334571072251 ] 
dist 173=[-2.1866464907521389308 ,2.1680320294956158074 ] 
dist 174=[-2.1727963405378900944 ,2.1569861528642301641 ] 
dist 175=[-2.0417983314512099230 ,2.1435273297423176640 ] 
dist 176=[-2.0099644116959275429 ,2.1342793098132201486 ] 
dist 177=[-1.9680261588801869470 ,2.0816953971722228520 ] 
dist 178=[-1.9509910495177756932 ,2.2239467840581214537 ] 
dist 179=[-1.5261769715245204539 ,2.3511039162635462553 ] 
dist 180=[-1.4664701610056660990 ,2.4212970327805175351 ] 
dist 181=[-1.3401530683449514832 ,2.4632007364974029338 ] 
dist 182=[-1.3041447562302914088 ,2.4774497720155006581 ] 
dist 183=[-1.2692890904540268887 ,2.5117191732672793620 ] 
dist 184=[-1.4345889248247999124 ,2.5298760855759456696 ] 
dist 185=[-1.5873628838248797248 ,2.5365366783991717911 ] 
dist 186=[-1.6783613001672653623 ,2.5322567131605481415 ] 
dist 187=[-1.7415442006053769182 ,2.0717606891479084422 ] 
dist 188=[-1.7832940381301217426 ,2.0618489499810867860 ] 
dist 189=[-1.8128627499902579057 ,1.9985645969266546204 ] 
dist 190=[-1.8274274345127648702 ,1.9809470634442244052 ] 
dist 191=[-1.8337947651981748946 ,1.9372353690562413625 ] 
dist 192=[-1.8309109779623141055 ,1.9200695514843569275 ] 
dist 193=[-1.5745296380141131621 ,.19418187002327297592] 
dist 194=[-1.5984286640910203990 ,.30854427981803761941] 
dist 195=[-1.6845289611721813908 ,.42841453965216262668] 
dist 196=[-1.7578864963042842253 ,.52430221983548616967] 
dist 197=[-1.8174444782783823725 ,.62099827957786580539] 
dist 198=[-1.8484638855257214287 ,.74409217579278265246] 
dist 199=[-1.8645152275520705175 ,.87474486085178672906] 
dist 200=[-1.8662217759094152853 ,1.0016081797263768851 ] 
dist 201=[-1.8563496478292051383 ,1.1500006147835926400 ] 
dist 202=[-1.9208984647004921150 ,1.3665790043562411355 ] 
dist 203=[-1.9785702669935877736 ,1.5795609249732306072 ] 
dist 204=[-2.0215513916701793333 ,1.7135981260722197361 ] 
dist 205=[-2.0517959474690337732 ,1.8154697524586697446 ] 
dist 206=[-2.0586309000986257811 ,1.9000707573337315273 ] 
dist 207=[-2.0570192847049675977 ,1.9670818057701198644 ] 
dist 208=[-2.0535525556762980932 ,1.9987469701171930383 ] 
dist 209=[-1.8003144682750434927 ,2.0139125306791178928 ] 
dist 210=[-1.8343038717844403201 ,2.0150723062734666685 ] 
dist 211=[-1.8518094895523642813 ,1.9783260641857878227 ] 
dist 212=[-1.8544837686032043758 ,1.9655919886465431689 ] 
dist 213=[-1.8437509303113802329 ,1.9381759153149705071 ] 
dist 214=[-1.8356401867196367367 ,1.9266793255992307106 ] 
dist 215=[-1.8183975553445128080 ,1.9060933694887782339 ] 
dist 216=[-1.8099114517162529413 ,1.9817497759642012036 ] 
dist 217=[-1.5963556757474360885 ,2.0460511122960432045 ] 
dist 218=[-1.5623411972391249683 ,2.0776122203534917360 ] 
dist 219=[-1.4875410540868749515 ,2.0919922606384606671 ] 
dist 220=[-1.4640447777018374484 ,2.0932710859712192830 ] 
dist 221=[-1.3576644233273057304 ,2.0695476268417503376 ] 
dist 222=[-1.3348944328932452909 ,2.0579586691979875885 ] 
dist 223=[-1.2739413885902548060 ,2.0365104041187083810 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 0, 1, 0, 0, 2] 
dist 0=[50.960063489203983917  ,50.960063489203983917  ] 
dist 1=[50.056608087769592336  ,51.380498800987809079  ] 
dist 2=[48.921024518924791824  ,51.599684504343252362  ] 
dist 3=[47.573521752766765186  ,51.699289507550199371  ] 
dist 4=[45.809114010054926974  ,51.722910829752164340  ] 
dist 5=[43.008319597727675290  ,51.511266191939481161  ] 
dist 6=[40.140014530890009335  ,51.393114910378355472  ] 
dist 7=[38.105894490896208256  ,51.179707737046021575  ] 
dist 8=[36.287796847545394002  ,51.082386118049175604  ] 
dist 9=[34.282152182538682989  ,50.534429552485715280  ] 
dist 10=[32.302309289603336337  ,50.381578255406658489  ] 
dist 11=[30.587118606411590319  ,49.836371859835117161  ] 
dist 12=[28.731812085574675157  ,49.726119638112967069  ] 
dist 13=[26.192044048975501070  ,48.239229845229328322  ] 
dist 14=[23.647232853033605029  ,47.877327141388994180  ] 
dist 15=[21.771622244360506996  ,45.929007616296406477  ] 
dist 16=[20.020341677169376980  ,33.707400610926729555  ] 
dist 17=[17.971922754616892983  ,29.612146381289986107  ] 
dist 18=[15.879314294273389985  ,28.835659211984374895  ] 
dist 19=[13.951204552216241124  ,27.926756011337717600  ] 
dist 20=[11.765841827186876971  ,27.709731461613891285  ] 
dist 21=[8.6449402039937430422 ,20.723849608231290382  ] 
dist 22=[5.5651743448246144350 ,19.843499703914927527  ] 
dist 23=[3.5440518282981523750 ,18.047275579602068347  ] 
dist 24=[1.9020774644441740261 ,17.581438708385774916  ] 
dist 25=[.33728746704431375971,15.895088623977997617  ] 
dist 26=[-1.0674135731074025147 ,15.548316653633061338  ] 
dist 27=[-2.0698171882320343629 ,14.961407435403382554  ] 
dist 28=[-2.9750223026779582382 ,14.823507996671349991  ] 
dist 29=[-3.9916419554813756965 ,7.0364612398275125665 ] 
dist 30=[-5.2384041912936341540 ,2.7724641441728081962 ] 
dist 31=[-7.4394957573441650290 ,1.4273435842173060343 ] 
dist 32=[-9.5615433476109700238 ,.2031707186475662387 ] 
dist 33=[-10.876152546389180944  ,-2.1546157118351593659 ] 
dist 34=[-11.860487995234236095  ,-2.5476612148600374880 ] 
dist 35=[-12.662441724646615326  ,-3.3017564111979554202 ] 
dist 36=[-13.296233189941457891  ,-3.4694165582114930912 ] 
dist 37=[-13.608212743004125762  ,-4.6545867471563088040 ] 
dist 38=[-13.770577392682841688  ,-4.0256153152932222115 ] 
dist 39=[-13.806055297706693968  ,-3.5459266250327209635 ] 
dist 40=[-13.537862220961403000  ,-3.0851634247275975885 ] 
dist 41=[-13.449502291345027696  ,-2.5313789517096680244 ] 
dist 42=[-13.292321129047526741  ,-1.9613933226758290841 ] 
dist 43=[-13.230786054083607941  ,-1.4358257289398495894 ] 
dist 44=[-12.931344075085003918  ,-.8427298099878580347 ] 
dist 45=[-12.841688147629204414  ,-.0031439807553940310 ] 
dist 46=[-12.587055656193407240  ,.8447779048558700643 ] 
dist 47=[-12.489652815516000714  ,1.4711894708077112448 ] 
dist 48=[-5.9224653664090428333 ,2.0549386313437148884 ] 
dist 49=[-5.3269524458440029015 ,2.7326414677639508768 ] 
dist 50=[-3.9815189420119134707 ,3.4184560632363488233 ] 
dist 51=[-3.7212341398247270531 ,4.0345825715541974122 ] 
dist 52=[-2.0769818791351654613 ,4.7173595112980820259 ] 
dist 53=[-1.7884799955123605710 ,5.6691421351701567442 ] 
dist 54=[-1.2367249783334582761 ,6.6031977316973827994 ] 
dist 55=[-1.1077130973193784149 ,7.2152161156376881646 ] 
dist 56=[.2602688289330012805 ,7.8605596774055364240 ] 
dist 57=[.4619914307346316467 ,8.3946187079294955973 ] 
dist 58=[.5115182735007777041 ,8.7890909521040987637 ] 
dist 59=[.1131906473670023542 ,9.0964730611572967370 ] 
dist 60=[-.5301504444419154297 ,9.3247070673227020132 ] 
dist 61=[-1.1829006231808610545 ,9.4033187950944272636 ] 
dist 62=[-1.6187744617209154243 ,9.4261538711011829714 ] 
dist 63=[-1.9779992816664192520 ,9.4316020984639147172 ] 
dist 64=[-2.3250415910548992968 ,4.3451735237713669028 ] 
dist 65=[-2.6363867029367151969 ,4.3380450667396814424 ] 
dist 66=[-2.8532155371219612050 ,4.2566704496194145949 ] 
dist 67=[-3.0415618133765776201 ,4.2286917298244498258 ] 
dist 68=[-3.2392469115277399114 ,4.1635913545127301560 ] 
dist 69=[-3.4151771776191873958 ,4.1366127488546509177 ] 
dist 70=[-3.5167472211557805003 ,2.8272287665785834776 ] 
dist 71=[-3.5827483557972573937 ,2.6503032442353088087 ] 
dist 72=[-3.6168498359135103868 ,2.6216971350810161144 ] 
dist 73=[-3.6297859863620493361 ,2.3334855085635083652 ] 
dist 74=[-3.6263130917706593605 ,2.2773336376664860029 ] 
dist 75=[-3.5858651233290730867 ,2.1843487783719225801 ] 
dist 76=[-3.5705118909079502321 ,2.1609688858036843617 ] 
dist 77=[-2.7956138526363237438 ,1.4496589237556422904 ] 
dist 78=[-3.0402062387624094686 ,1.0794172006803948982 ] 
dist 79=[-3.1931519285976608685 ,.8398535603158425331 ] 
dist 80=[-3.3083797622432153206 ,.7960907629879402674 ] 
dist 81=[-3.5127234697602289131 ,.59772817387665864468] 
dist 82=[-3.7069202594020465638 ,.4386808937280552036 ] 
dist 83=[-3.8607892116246633572 ,.37089356260824596756] 
dist 84=[-4.0001691999212280882 ,.3224168982406881104 ] 
dist 85=[-4.1162571148433280824 ,.27768427171667145216] 
dist 86=[-4.1771503062423444508 ,.1386041041903903608 ] 
dist 87=[-4.2094562311183939250 ,.1158539776925688050 ] 
dist 88=[-4.2113999490294939808 ,.0672501718596847869 ] 
dist 89=[-4.1957099675409343089 ,.0536037348013396767 ] 
dist 90=[-4.1830372703634093714 ,-.0034118529134727110 ] 
dist 91=[-4.1192834719994379618 ,-.0147787172218612405 ] 
dist 92=[-4.1026033952741924627 ,-.0423851573411621993 ] 
dist 93=[-2.4728739899139504246 ,-.0487155092578580883 ] 
dist 94=[-2.3153874158677369204 ,.0451635144139042593 ] 
dist 95=[-1.9349611831621369561 ,.4527548487317268449 ] 
dist 96=[-1.8719924515299725169 ,.8564575470810607486 ] 
dist 97=[-1.5929277165451296836 ,1.2266988166782234555 ] 
dist 98=[-1.6063690421542401300 ,1.5007596620514440464 ] 
dist 99=[-1.6105591760366024964 ,1.7568610229815807946 ] 
dist 100=[-1.6093748455519136165 ,2.0554489145038751758 ] 
dist 101=[-1.5631717658159272036 ,2.3331516568551553822 ] 
dist 102=[-1.5517974354793061873 ,2.5058968483241008746 ] 
dist 103=[-1.5189048489411938444 ,2.6348666105487770980 ] 
dist 104=[-1.5074498078538037880 ,2.7378283601522935365 ] 
dist 105=[-1.4314836827959749016 ,2.8162613833280192291 ] 
dist 106=[-1.4129387005851201931 ,2.8473381109758670759 ] 
dist 107=[-1.3802217305201090783 ,2.8594239527673398516 ] 
dist 108=[-1.3157805841113543207 ,2.8620414123324477194 ] 
dist 109=[.44660247761928665497,2.2563784943532782234 ] 
dist 110=[.34397174619432163339,2.1955487648653400608 ] 
dist 111=[.2499640659140298025 ,2.0515880633023384879 ] 
dist 112=[.1443719513327494704 ,2.0645345825212015054 ] 
dist 113=[-.0045295457607306018 ,2.0661187272645268897 ] 
dist 114=[-.1698209804278540198 ,2.0318782791211816062 ] 
dist 115=[-.3408497588036999877 ,2.0210309112146543009 ] 
dist 116=[-.54884937549772756624,2.0127578478766566987 ] 
dist 117=[-.86172633125667472609,2.0058756641893596466 ] 
dist 118=[-1.1739403634435090872 ,1.8440003479372012736 ] 
dist 119=[-1.3793008696536265533 ,1.9126605944924368131 ] 
dist 120=[-1.5457645171550005486 ,1.9868126745639479165 ] 
dist 121=[-1.7027258565727514971 ,2.0587344210926357978 ] 
dist 122=[-1.8416180414454272269 ,2.1184724650694938049 ] 
dist 123=[-1.9359617497289524718 ,2.1806198570189550985 ] 
dist 124=[-2.0157768976862077614 ,2.2621213184508728263 ] 
dist 125=[-2.0966833965759631570 ,2.3378084005562664138 ] 
dist 126=[-2.1653829492324018952 ,2.3767450761213067576 ] 
dist 127=[-2.1964753722388445834 ,2.3960628942026928365 ] 
dist 128=[-2.3404615927591472830 ,2.3982799198287964468 ] 
dist 129=[-2.5249441552888581856 ,2.3817554303075527757 ] 
dist 130=[-2.6434737100537858819 ,2.3710638603976775572 ] 
dist 131=[-2.7364774180930577690 ,2.3446527317550751341 ] 
dist 132=[-2.8190800682164417554 ,2.3316327912159640295 ] 
dist 133=[-2.8863828212639969938 ,2.0680857860833506115 ] 
dist 134=[-2.9183158978940274378 ,2.0250863870677406608 ] 
dist 135=[-2.9305188338922141096 ,1.9269648118459791701 ] 
dist 136=[-2.9297300937124019056 ,1.8951878443347903587 ] 
dist 137=[-2.8974367644599010640 ,1.7476662021512294385 ] 
dist 138=[-2.8832998672479854645 ,1.7152558902206222664 ] 
dist 139=[-2.8404682432884057921 ,1.6379075877403943299 ] 
dist 140=[-2.8200960122625753849 ,1.6245079855534217474 ] 
dist 141=[-1.7976344351158949639 ,1.7635810994174094774 ] 
dist 142=[-1.6926450944073913902 ,1.8896541129383734492 ] 
dist 143=[-1.4513255580158311827 ,1.9659335647195955138 ] 
dist 144=[-1.3992003122335981593 ,2.0203566990147101615 ] 
dist 145=[-1.0799127778233582733 ,2.0591892061764607564 ] 
dist 146=[-1.0198512834501197945 ,2.0850218147212761222 ] 
dist 147=[-.90376909416799473811,2.0903023501820779956 ] 
dist 148=[-.87413513229797880967,2.2211121928831521978 ] 
dist 149=[-.49462615342400078141,2.4067356254246688117 ] 
dist 150=[-.4397383013278151480 ,2.5142670166736326263 ] 
dist 151=[-.3265826449746565151 ,2.5852135459292144951 ] 
dist 152=[-.2970413429291029698 ,2.6248203111110386413 ] 
dist 153=[-.1892198232059933512 ,2.6490043657061236932 ] 
dist 154=[-.1672873296931825137 ,2.6583902325847167610 ] 
dist 155=[-.1297878870106708451 ,2.6587426365333323621 ] 
dist 156=[-.1211926891364617457 ,2.6519232027983225488 ] 
dist 157=[-.1048627700787796018 ,2.3349738961030295810 ] 
dist 158=[-.26047244666460992883,2.4865928139778066153 ] 
dist 159=[-.50904067261655124304,2.6489305166166587905 ] 
dist 160=[-.76321190768756906934,2.7896183890635069797 ] 
dist 161=[-1.0014899971222663161 ,2.9056680481282814281 ] 
dist 162=[-1.1866301949268275876 ,2.9696662836975027613 ] 
dist 163=[-1.3682889835789729144 ,3.0078207503794762264 ] 
dist 164=[-1.5926767303320628284 ,3.0207216673775451940 ] 
dist 165=[-1.8053591516923441113 ,3.0203254514492741685 ] 
dist 166=[-1.9403029033337657624 ,3.0129804317730636969 ] 
dist 167=[-2.0441424474459251122 ,2.9853192030026407298 ] 
dist 168=[-2.1326867306277201558 ,2.9687670044744007778 ] 
dist 169=[-2.2046359851685598078 ,2.8640108957166380772 ] 
dist 170=[-2.2422458319934498618 ,2.8350142800541185634 ] 
dist 171=[-2.2619255253980499878 ,2.7754377305590345793 ] 
dist 172=[-2.2636114730728137656 ,2.7542764076633940874 ] 
dist 173=[-2.2524748339230357592 ,2.0850992105592520900 ] 
dist 174=[-2.3274592357589764550 ,1.8809213387017266301 ] 
dist 175=[-2.4644176481915960430 ,1.8469101489738565836 ] 
dist 176=[-2.5811222434982822755 ,1.7797018860420638071 ] 
dist 177=[-2.6759093705516130176 ,1.7592913153843252769 ] 
dist 178=[-2.7253861911488508021 ,1.6720438259885881359 ] 
dist 179=[-2.7511640923890172747 ,1.6509065927553362797 ] 
dist 180=[-2.7546098371785243496 ,1.5961309469333990414 ] 
dist 181=[-2.8839233688393248640 ,1.5782826886169254108 ] 
dist 182=[-2.9951697182976420157 ,.8230941433792554624 ] 
dist 183=[-3.0736543054324428720 ,1.0557479370605864555 ] 
dist 184=[-3.1279527006435146872 ,1.2462215825539067508 ] 
dist 185=[-3.1627673766392206507 ,1.4289401179101789793 ] 
dist 186=[-3.1696661240609439752 ,1.5926979705352248549 ] 
dist 187=[-3.1547253019328978254 ,1.7074960730773442277 ] 
dist 188=[-3.1517071635769046177 ,1.8084267424253146568 ] 
dist 189=[-2.5956415351475089245 ,1.9168386512792242327 ] 
dist 190=[-2.5870931780555695879 ,2.0127738181908611659 ] 
dist 191=[-2.5500511092148733346 ,2.0639065604531034164 ] 
dist 192=[-2.5368235821353656310 ,2.0920207612531268784 ] 
dist 193=[-2.4101229147487436210 ,2.1000584703134616973 ] 
dist 194=[-2.3775864386422224577 ,2.2643177492541493672 ] 
dist 195=[-2.3349865978175695481 ,2.4104675998108202981 ] 
dist 196=[-2.3168928621832299969 ,2.5701412706373776517 ] 
dist 197=[-1.8510596644034661622 ,2.7126057777844631460 ] 
dist 198=[-1.7847956465298079638 ,2.7900687733394805200 ] 
dist 199=[-1.6455824424428683550 ,2.8347614028835648909 ] 
dist 200=[-1.6057607132845211970 ,2.8464279985493093744 ] 
dist 201=[-1.4420422741817604568 ,2.8524730121270038882 ] 
dist 202=[-1.4081707972878547975 ,2.8641794148199942284 ] 
dist 203=[-1.3226683023889620906 ,2.8621835901003154122 ] 
dist 204=[-1.3034722282699406084 ,2.8552955511160568416 ] 
dist 205=[-1.3274049189401106096 ,2.2887310114927574015 ] 
dist 206=[-1.4790283917102950147 ,2.3194504654546425948 ] 
dist 207=[-1.5696608556217114676 ,2.3276142315273552587 ] 
dist 208=[-1.6329753430610911528 ,2.3254048382308256348 ] 
dist 209=[-1.6755679453451075595 ,2.3182363981514962659 ] 
dist 210=[-1.7062320250300464180 ,2.2575495675607288894 ] 
dist 211=[-1.7219355999282123016 ,2.2383266046573489896 ] 
dist 212=[-1.7296865812883702165 ,2.2021935446222863468 ] 
dist 213=[-1.7286043352373377274 ,2.1890150831145086434 ] 
dist 214=[-1.5460073489249270447 ,.35984479893722723504] 
dist 215=[-1.5859813483357158581 ,.4620346825121548203 ] 
dist 216=[-1.6993068695480872107 ,.59697507212452515547] 
dist 217=[-1.8010363965129614417 ,.74264188591997233128] 
dist 218=[-1.8875408327426579331 ,.88764255075486178596] 
dist 219=[-1.9400964947112897612 ,1.0599293858042193319 ] 
dist 220=[-1.9778540179841182362 ,1.3144999962604509927 ] 
dist 221=[-2.0052924181693612696 ,1.5661088856895140746 ] 
dist 222=[-2.0231745922429498256 ,1.7265746683941955246 ] 
dist 223=[-2.0884836857391279190 ,1.8509980511530378056 ] 
dist 224=[-2.1494943366510034334 ,1.9587545949082146717 ] 
dist 225=[-2.1974980995596255182 ,2.0475386010825498649 ] 
dist 226=[-2.2334641239969429379 ,2.0962386664539827708 ] 
dist 227=[-2.2464287526648728465 ,2.1248962165033830131 ] 
dist 228=[-2.2475617118533304357 ,2.1336860829664422198 ] 
dist 229=[-2.2429953364077094298 ,2.1330853431501803671 ] 
dist 230=[-1.8437709085701912865 ,2.1269337084713216418 ] 
dist 231=[-1.8671016169775945006 ,2.1107453716988106050 ] 
dist 232=[-1.8765483698127460485 ,2.1011388442666177758 ] 
dist 233=[-1.8762994277592176390 ,2.0404918059997040149 ] 
dist 234=[-1.8500414095400874241 ,2.0237198023486180101 ] 
dist 235=[-1.8388576311632123431 ,1.9767379419169938744 ] 
dist 236=[-1.8164022925424857965 ,1.9672321768167255316 ] 
dist 237=[-1.8068309302333438704 ,2.0466379035138931543 ] 
dist 238=[-1.5733726467509805157 ,2.1142250716218582250 ] 
dist 239=[-1.5369319452610746539 ,2.1483314711396538459 ] 
dist 240=[-1.4558565911390622041 ,2.1644508581797800118 ] 
dist 241=[-1.4305043119261608248 ,2.1663485431336630366 ] 
dist 242=[-1.3161636504871998773 ,2.1480091402727764718 ] 
dist 243=[-1.2917941206687214230 ,2.1376527587556521744 ] 
dist 244=[-1.2297436570017986629 ,2.1136415696782383748 ] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 1, 0, 2, 0, 0, 1] 
dist 0=[49.869992361880251534  ,49.869992361880251534  ] 
dist 1=[49.134747231163222819  ,50.333244625586421304  ] 
dist 2=[48.201877919796621492  ,50.686837984381682091  ] 
dist 3=[46.949324641603231486  ,50.983912415929787153  ] 
dist 4=[45.219528206077981759  ,51.219643370643295027  ] 
dist 5=[42.380768222280270989  ,51.328105825384171468  ] 
dist 6=[39.460151994141151699  ,51.363410171136497421  ] 
dist 7=[37.403397591945064861  ,51.307708755238316384  ] 
dist 8=[35.580649499488010026  ,51.210740125554739571  ] 
dist 9=[33.594361768164956923  ,51.101061587239384090  ] 
dist 10=[31.648397245379224628  ,50.923643355089965910  ] 
dist 11=[29.986469382957468121  ,50.831366925502357347  ] 
dist 12=[28.209145362213803076  ,50.339871761046784682  ] 
dist 13=[25.801892842461307164  ,50.192503840679413261  ] 
dist 14=[23.401191779033303457  ,49.685285938790010476  ] 
dist 15=[21.649809576186820189  ,49.302905651403415824  ] 
dist 16=[19.088808823023279000  ,37.458873110007982928  ] 
dist 17=[16.436433489917997289  ,36.328400304262082609  ] 
dist 18=[14.301088814675384256  ,33.559293308605288954  ] 
dist 19=[12.129419059683622901  ,33.141068002683379775  ] 
dist 20=[9.3313998847014451661 ,28.966032395082541929  ] 
dist 21=[6.6062758230043115802 ,28.174395843942946623  ] 
dist 22=[4.7254121189609533118 ,27.246844442009672190  ] 
dist 23=[3.0956928881786467885 ,27.024487473382100665  ] 
dist 24=[1.3731973133390178914 ,19.907181461783753748  ] 
dist 25=[-.2874380070608225111 ,19.010975808390347285  ] 
dist 26=[-1.6706843869360386642 ,17.178902008087525530  ] 
dist 27=[-3.1243273148742540120 ,16.703382176698677444  ] 
dist 28=[-5.0674640022902555801 ,14.978598644801393026  ] 
dist 29=[-6.9327313311411595052 ,14.625604199703293995  ] 
dist 30=[-8.0754602909620986145 ,14.019693892037863587  ] 
dist 31=[-8.9169979595929185453 ,13.880116185913543945  ] 
dist 32=[-9.5782553853833621310 ,2.6810143594405319467 ] 
dist 33=[-10.097441750328395686  ,1.7293882975548799493 ] 
dist 34=[-10.370817715244580284  ,-.3347566726051263901 ] 
dist 35=[-10.519785194068345276  ,-.7327259523973232473 ] 
dist 36=[-10.542342003811628551  ,-2.4323755266936237359 ] 
dist 37=[-9.9430378810072564162 ,-2.0394321401807985423 ] 
dist 38=[-10.133983727200168811  ,-1.6171810199643334184 ] 
dist 39=[-11.374748144328903793  ,-1.3076018145586888730 ] 
dist 40=[-12.517517703610107873  ,-1.0236504986543040470 ] 
dist 41=[-13.197623854338493981  ,-.7031052591005737400 ] 
dist 42=[-13.671623942965507780  ,-.3855391867216985659 ] 
dist 43=[-13.991015835657921215  ,-.1132127142284719253 ] 
dist 44=[-14.218839905273924649  ,.1772604179757198011 ] 
dist 45=[-14.327054181430464113  ,.5674686786018721899 ] 
dist 46=[-14.369095223328984143  ,.9519746123722258293 ] 
dist 47=[-14.352158478873029950  ,1.2198292968892696068 ] 
dist 48=[-4.3082457826487541169 ,1.4533827287601958867 ] 
dist 49=[-3.7610495925945979772 ,2.2401166039664775677 ] 
dist 50=[-3.3800565195239348360 ,2.9808395539446629724 ] 
dist 51=[-3.3234534248041394911 ,3.7063420850148099372 ] 
dist 52=[-3.1757460384276328514 ,4.6007159419131775575 ] 
dist 53=[-3.1510175825995498940 ,5.4481111167650515272 ] 
dist 54=[.1027589186973553523 ,5.9862207403395940802 ] 
dist 55=[.2008621115919136264 ,6.4012192970278960195 ] 
dist 56=[1.8145848130692880052 ,6.7573648500046495798 ] 
dist 57=[1.9103730311863817582 ,7.0493761712010542611 ] 
dist 58=[2.6333560272512677949 ,7.2162186890405046248 ] 
dist 59=[2.7401706323986407361 ,7.3128592244284198123 ] 
dist 60=[2.3462895547027278060 ,7.3311149318155228120 ] 
dist 61=[1.6441439924734948897 ,4.0016245423812119095 ] 
dist 62=[1.1620200248793228431 ,4.0798922957069471157 ] 
dist 63=[.7492745591180203376 ,4.1003252649361275481 ] 
dist 64=[.3238805741793986623 ,4.0957287864206795154 ] 
dist 65=[-.0767081416878457048 ,4.0824618449460754224 ] 
dist 66=[-.3905311305761978917 ,4.0444901812572807051 ] 
dist 67=[-.7008067371407532868 ,4.0342074242935953177 ] 
dist 68=[-1.0873239490450334359 ,4.0296749465224448667 ] 
dist 69=[-1.4554863720938132331 ,4.0174693534970759783 ] 
dist 70=[-2.0941041560573257200 ,3.7739027092089922302 ] 
dist 71=[-2.6286913613904919346 ,3.7430405972755004396 ] 
dist 72=[-3.0536984456414443778 ,3.3748006109416414090 ] 
dist 73=[-3.4406017077621831479 ,3.3138783399683453509 ] 
dist 74=[-3.7737011764161738146 ,3.1568422315169151703 ] 
dist 75=[-3.9839572236297700249 ,3.1249867527701477756 ] 
dist 76=[-4.1446988178080542327 ,2.8549287750210000340 ] 
dist 77=[-4.2801825445153528023 ,2.7994060505641823944 ] 
dist 78=[-4.3925897689994538740 ,2.7179915930636511030 ] 
dist 79=[-4.4612094654902983015 ,2.6924572640218061798 ] 
dist 80=[-4.5110332735413011864 ,1.9797803865844467532 ] 
dist 81=[-4.5483602635056983280 ,1.9630333804545649694 ] 
dist 82=[-4.5748226951587130799 ,1.9075041651101215858 ] 
dist 83=[-4.5812419946330268616 ,1.8890691082144991022 ] 
dist 84=[-4.5741320837175597909 ,1.8600522647634630460 ] 
dist 85=[-4.5616124579707035990 ,1.8490799287075696467 ] 
dist 86=[-4.4584152489096543749 ,1.8077970955590783205 ] 
dist 87=[-4.5018617697359959455 ,1.7909305550278475176 ] 
dist 88=[-4.5892743297007584164 ,1.7757768084832928603 ] 
dist 89=[-4.6418482513655791577 ,1.7645198982312713122 ] 
dist 90=[-4.6791247632724287710 ,1.7440297611380820273 ] 
dist 91=[-4.7054766766370522603 ,1.7313198341686991621 ] 
dist 92=[-4.7230136406932379044 ,1.8674405209231111676 ] 
dist 93=[-4.7251154938140711278 ,2.0505684523856899005 ] 
dist 94=[-4.7164947630702645276 ,2.1582332411031280193 ] 
dist 95=[-4.7016466947773068530 ,2.2314065699270393374 ] 
dist 96=[-3.2865163343897108061 ,2.2768475943082732010 ] 
dist 97=[-3.2625309367720006340 ,2.3073155297035868704 ] 
dist 98=[-3.1404595321573700850 ,2.3207063738521566369 ] 
dist 99=[-3.1113956468763787765 ,2.3242180595004336697 ] 
dist 100=[-3.0187670278970130810 ,2.3747678212402571031 ] 
dist 101=[-3.0010086432591583591 ,2.5078051406823035064 ] 
dist 102=[-1.4361800937555977441 ,2.5799987630684966183 ] 
dist 103=[-1.2860708212352380640 ,2.7714666294851547310 ] 
dist 104=[-.94543500139222516807,3.0585002284299464865 ] 
dist 105=[-.87772887225999667576,3.2395911607288487589 ] 
dist 106=[-.45179208843321575391,3.3778653592022384197 ] 
dist 107=[-.37548579537815794365,3.4939468135750488799 ] 
dist 108=[-.2297341245966499386 ,3.5868581859145620327 ] 
dist 109=[-.1948460875099677327 ,3.6326123982772768379 ] 
dist 110=[-.4180364786913804547 ,3.6524738217191761606 ] 
dist 111=[-.6588538116597817863 ,3.6535508704318578621 ] 
dist 112=[-.89974327571557597712,3.0111937726954301018 ] 
dist 113=[-1.1222672426408514122 ,3.0793961819699103514 ] 
dist 114=[-1.2897784527460433050 ,3.1265616403120190634 ] 
dist 115=[-1.4490823123930689858 ,3.1377256178022353737 ] 
dist 116=[-1.6388421155257971944 ,3.1323277381515882240 ] 
dist 117=[-1.8152276297705079697 ,3.1312703936398113821 ] 
dist 118=[-1.9211468673426093453 ,1.3070320216027151696 ] 
dist 119=[-1.9957123292143755569 ,1.1800508985937652688 ] 
dist 120=[-2.0469504760940860068 ,.88677536373731143593] 
dist 121=[-2.0836738213255367812 ,.83251115071582118998] 
dist 122=[-2.1003126541829969282 ,.45113681223280487057] 
dist 123=[-2.1054225563626613791 ,.38259984874856443349] 
dist 124=[-2.1029529515396490325 ,.2613849497714310322 ] 
dist 125=[-1.8945540089605335386 ,.3039706134426727383 ] 
dist 126=[-1.8725166589533733264 ,.41617185918559933204] 
dist 127=[-1.8109847780535847621 ,.5148401212273412502 ] 
dist 128=[-1.7945093256159469924 ,.62247384256325980132] 
dist 129=[-1.6652858430265340823 ,.77045270704732806314] 
dist 130=[-1.6357215816553225626 ,.93299612600183008218] 
dist 131=[-1.5899007329540619879 ,1.0987538968258162708 ] 
dist 132=[-1.7436495028006717096 ,1.2985702499452646365 ] 
dist 133=[-2.0073074540739992142 ,1.5970358011002999089 ] 
dist 134=[-2.2651429470254431594 ,1.8930827884169236877 ] 
dist 135=[-2.4257537511558278175 ,2.0832453215369432708 ] 
dist 136=[-2.5459996901421637950 ,2.2321955824738959454 ] 
dist 137=[-2.6427091213947881810 ,2.3637661099058365452 ] 
dist 138=[-2.7169720710814404661 ,2.4740220360994980560 ] 
dist 139=[-2.7476193206206399183 ,2.5379050334469289849 ] 
dist 140=[-2.7600718411371742783 ,2.5800104981269841272 ] 
dist 141=[-2.7616971757700864008 ,2.6033485643284388805 ] 
dist 142=[-2.6826594239923539372 ,2.6147010071352180328 ] 
dist 143=[-2.6617101803065498639 ,2.6123101204546912521 ] 
dist 144=[-2.6128637084367247232 ,2.5962991646131075326 ] 
dist 145=[-2.5934466433859946734 ,2.5837838422909463405 ] 
dist 146=[-2.4901060936851585757 ,2.4987038022767468409 ] 
dist 147=[-2.4646084696506534529 ,2.4741935795934799044 ] 
dist 148=[-2.3953921664277851451 ,2.4254850132950050180 ] 
dist 149=[-2.3728518053394460528 ,2.4081060637035796363 ] 
dist 150=[-1.2187925196335289078 ,2.1641739893616296908 ] 
dist 151=[-1.1037094760580859000 ,2.1906783912452115135 ] 
dist 152=[-.9051018894351326363 ,2.1967199867625544302 ] 
dist 153=[-.9331559949599447021 ,2.1709863005412380648 ] 
dist 154=[-.9455989064299903492 ,2.1636818839791034674 ] 
dist 155=[-.9508490940607473512 ,2.2019329398356094863 ] 
dist 156=[-.9502005988630680925 ,2.3692211398793771322 ] 
dist 157=[-.9284657596225259783 ,2.5597739963605021438 ] 
dist 158=[-1.0099632606442115079 ,2.7325307310592111469 ] 
dist 159=[-1.1457394682079234159 ,2.8287895067140969504 ] 
dist 160=[-1.2764641987334815882 ,2.8874822308462169240 ] 
dist 161=[-1.3939476480403837723 ,2.9102987896678773782 ] 
dist 162=[-1.4768763668794939411 ,2.9190558127610691996 ] 
dist 163=[-1.5503883082203035792 ,2.9216272388385455264 ] 
dist 164=[-1.6302903191814074750 ,2.9201693640697875702 ] 
dist 165=[-1.7006679337085915785 ,2.9128308487766597001 ] 
dist 166=[-1.7682063595319667024 ,2.4924129794349493089 ] 
dist 167=[-1.8205058278978884111 ,2.5992549609361959643 ] 
dist 168=[-1.8638001077235310945 ,2.7132379132618940049 ] 
dist 169=[-1.8979836495676192514 ,2.8020875241005652723 ] 
dist 170=[-1.9139181716533994326 ,2.8685600905976673161 ] 
dist 171=[-1.9195260942267622441 ,2.8932275744141102837 ] 
dist 172=[-1.9171566805507614895 ,2.9012062252146535230 ] 
dist 173=[-1.8915069826424351493 ,2.9010680471762508821 ] 
dist 174=[-2.1176116273204200078 ,2.7865881065232484064 ] 
dist 175=[-2.2577393327641684071 ,2.7602513782287508937 ] 
dist 176=[-2.3617441603666262464 ,2.7003307305739342531 ] 
dist 177=[-2.4436738648497761432 ,2.6778461540684196503 ] 
dist 178=[-2.5054005383362855356 ,2.5621552145571527112 ] 
dist 179=[-2.5287652463000158075 ,2.5343202578310441156 ] 
dist 180=[-2.5369687259651573027 ,2.4576148850473713580 ] 
dist 181=[-2.5381835211533235113 ,2.4348673025306642124 ] 
dist 182=[-2.4440028549909135134 ,1.7092346372595197967 ] 
dist 183=[-2.4914726170178466189 ,1.7483639781693048851 ] 
dist 184=[-2.5874957049403946415 ,1.7741093027489091296 ] 
dist 185=[-2.6599256886097060427 ,1.7892694011954577408 ] 
dist 186=[-2.7126550829958689232 ,1.7916369526601597417 ] 
dist 187=[-2.7300437796859700101 ,1.7787222634846190201 ] 
dist 188=[-2.7335112038315749229 ,1.7766951010850096197 ] 
dist 189=[-2.7306729039652573893 ,.0366039092191327725 ] 
dist 190=[-2.7607401928274598668 ,.1333170437459433722 ] 
dist 191=[-2.8735167772450830871 ,.2270565461033344755 ] 
dist 192=[-2.9504835337454675030 ,.3412808500788031503 ] 
dist 193=[-2.9987127627429070740 ,.4599643868443458455 ] 
dist 194=[-3.0291503621203323844 ,.5715007684437859769 ] 
dist 195=[-3.0351036921090212051 ,.69918858222320602405] 
dist 196=[-3.0289428798201457633 ,.88233688754796110754] 
dist 197=[-3.0194330126077876096 ,1.0685933657653639022 ] 
dist 198=[-2.6766142832309319734 ,1.2086858925443374163 ] 
dist 199=[-2.6776163616005251240 ,1.3843687059958060724 ] 
dist 200=[-2.6617977886822214407 ,1.6470345755649242169 ] 
dist 201=[-2.6520199671806958612 ,1.9013666662364707285 ] 
dist 202=[-2.5488605560320341168 ,2.1309365417215616082 ] 
dist 203=[-2.5199958561286556360 ,2.2947675590249682903 ] 
dist 204=[-2.4843682200936884187 ,2.4418602098208559189 ] 
dist 205=[-2.4673761673494660653 ,2.6046232189919612536 ] 
dist 206=[-2.0088312220625780378 ,2.7499813107176236930 ] 
dist 207=[-1.9428724982072177190 ,2.8276037384808524447 ] 
dist 208=[-1.8066024141743144666 ,2.8711980915331149089 ] 
dist 209=[-1.7677659795530208233 ,2.8811389741993991517 ] 
dist 210=[-1.6098033197146358451 ,2.8722092638850056357 ] 
dist 211=[-1.5758976448929667844 ,2.8682019542165829558 ] 
dist 212=[-1.4937231959620115152 ,2.8641752475042064290 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 2, 0, 0, 0, 2] 
dist 0=[55.635227105460123555  ,55.635227105460123555  ] 
dist 1=[54.536619987700968444  ,56.120526218192194790  ] 
dist 2=[53.245316598907705531  ,56.378285385974680709  ] 
dist 3=[51.990379460053037880  ,56.651152312511144396  ] 
dist 4=[50.519447201221746770  ,56.759807183805471432  ] 
dist 5=[48.365364395931689800  ,56.746809051501706374  ] 
dist 6=[45.931286888590470129  ,56.669285707821139543  ] 
dist 7=[43.342062209238541485  ,56.446062494031078604  ] 
dist 8=[40.137268956515791241  ,56.314115649289866200  ] 
dist 9=[35.244717709960625175  ,53.610485889916715370  ] 
dist 10=[30.312761475545688914  ,53.120253290091385931  ] 
dist 11=[26.950488648596895144  ,52.349289423005735650  ] 
dist 12=[24.086270481737226235  ,52.107900181303117725  ] 
dist 13=[21.143149292599558523  ,51.336852774937379012  ] 
dist 14=[18.365292263068351360  ,46.490138959538864384  ] 
dist 15=[16.160844775539109784  ,45.624714284481695350  ] 
dist 16=[13.947714487718027513  ,40.593615904216644356  ] 
dist 17=[11.134697792251542617  ,30.911504590133117203  ] 
dist 18=[8.4130716649187094128 ,29.261538669737245985  ] 
dist 19=[6.5646781225491153883 ,28.062811716545559839  ] 
dist 20=[4.9950175523951490386 ,26.249659927030965215  ] 
dist 21=[3.3863056684416039645 ,25.843470195856325429  ] 
dist 22=[1.8660458037308175779 ,25.256313472830835037  ] 
dist 23=[.64915395416054718055,25.078392476639344871  ] 
dist 24=[-.58630354246742785351,17.125033126961619743  ] 
dist 25=[-2.1818862307559040573 ,11.211218640051313445  ] 
dist 26=[-3.7057188539633900902 ,10.478520996892845980  ] 
dist 27=[-4.6546973835731627172 ,8.9032819914779106979 ] 
dist 28=[-5.3724627256285112168 ,8.6134267737469903151 ] 
dist 29=[-5.9719272124712412706 ,7.0205294044801811844 ] 
dist 30=[-7.3669097195811946421 ,6.0847134449207444771 ] 
dist 31=[-9.1854317829132915939 ,5.6658254083915301123 ] 
dist 32=[-10.876998688368015362  ,4.8966731084107269916 ] 
dist 33=[-11.911014103859324327  ,-5.3605835106309257836 ] 
dist 34=[-12.664773223889721880  ,-5.8592792253901163037 ] 
dist 35=[-13.236848874552405768  ,-5.5453795593002175987 ] 
dist 36=[-13.677787172408063549  ,-5.1451633062458040279 ] 
dist 37=[-13.907732508559086099  ,-4.5254919690909020570 ] 
dist 38=[-14.028195623919562306  ,-3.8143887187403118424 ] 
dist 39=[-14.033145639484627459  ,-3.0489675910038374595 ] 
dist 40=[-11.280273141934428821  ,-2.0981779044030559858 ] 
dist 41=[-11.386577816850013011  ,-.6470307076127215576 ] 
dist 42=[-11.426098678355238463  ,.80996108227092299208] 
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dist 127=[-1.2935213658863912949 ,.69890522940080843758] 
dist 128=[-1.3619124375569740400 ,.75436001171678663353] 
dist 129=[-1.4300291123783938979 ,.81392802033603518062] 
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dist 133=[-1.5455447205108409721 ,.93658800915400244485] 
dist 134=[-1.5480260963932864079 ,.94555529942390843753] 
dist 135=[-1.5457828873842649236 ,.94700906142579071654] 
dist 136=[-.52648804655020867657,.94136190732136204118] 
dist 137=[-.46459130532792939389,.93980540411983867987] 
dist 138=[-.32493656478300144456,.6341681165223756548 ] 
dist 139=[-.29769294665326858029,.60448536886708498157] 
dist 140=[-.12751388946926993439,.5345768140303220204 ] 
dist 141=[-.09767378783004013349,.55060326338749829541] 
dist 142=[-.07029854900329089071,.56105747526654897342] 
dist 143=[-.13790195364382769141,.56661546592947093696] 
dist 144=[-.20724696095312624923,.58863523164347875144] 
dist 145=[-.29708938635585827563,.62610782657207235466] 
dist 146=[-.38431040334315628659,.65474711546054870877] 
dist 147=[-.44319367928098423123,.67886883664635216717] 
dist 148=[-.4925904189799083825 ,.70703164595476131282] 
dist 149=[-.54195047658007185108,.76528518474443025458] 
dist 150=[-.58750662190066731038,.82394947003606482014] 
dist 151=[-.62172230464591716389,.89864292210798586345] 
dist 152=[-.65418543076097725099,.9690068790478992452 ] 
dist 153=[-.69274835913452710919,1.0103917045023483157 ] 
dist 154=[-.72835579256307324329,1.0385695625217620299 ] 
dist 155=[-.74902292773758231387,1.0562062077751052740 ] 
dist 156=[-.76270585045805176721,1.0674704989004297669 ] 
dist 157=[-.77043625078716622119,1.0702015918778901844 ] 
dist 158=[-.77407290590945964452,1.0684568213843245107 ] 
dist 159=[-.77394335098496487831,1.0655591114283416831 ] 
dist 160=[-.80554807899251041989,.97976359509663085391] 
dist 161=[-.83059640578472887022,.96491558950858778817] 
dist 162=[-.84583391473280254184,.93315203322494245721] 
dist 163=[-.85161024850248533669,.92289801152942983457] 
dist 164=[-.85341600721114489101,.87544534715202630866] 
dist 165=[-.85280958883734949839,.86507165054040415722] 
dist 166=[-.8502937644574235475 ,.83359540721680472272] 
dist 167=[-.84741655414344144509,.82843324962532783946] 
dist 168=[-.73978998921281709186,.03866495909072717363] 
dist 169=[-.7356281499143087454 ,.21591785840775775766] 
dist 170=[-.77460022173682290861,.39232412191673569332] 
dist 171=[-.82992153584687690719,.50835986987944142807] 
dist 172=[-.87799202632768356394,.60239626889625326509] 
dist 173=[-.90911701811688218114,.69099892972576522435] 
dist 174=[-.93380988999808498116,.7693312938711114223 ] 
dist 175=[-.95620724502192217749,.82237740721370777309] 
dist 176=[-.97365436224628026138,.86706568152865416825] 
dist 177=[-.97858819010893029122,.91204159056379584822] 
dist 178=[-.97899525909600473561,.95136877260392215261] 
dist 179=[-.97836961634882040339,.97351127191437075023] 
dist 180=[-.94301191043402913608,.98731066786949712514] 
dist 181=[-.93312139568906331023,.99333580672330520683] 
dist 182=[-.92653234839606105829,.99456635387945945273] 
dist 183=[-.922728017464132464  ,.99307776581582586758] 
dist 184=[-.7024422343511821554 ,.98254031659160847145] 
dist 185=[-.67521757078555193542,.97837193133383964229] 
dist 186=[-.61136568754281939312,.53514263101266682822] 
dist 187=[-.59669120701369883259,.63905825951296682638] 
dist 188=[-.50579810231713000058,.73086299417941344867] 
dist 189=[-.48784718159046936327,.79292619156774856858] 
dist 190=[-.45374657494781376577,.84509984767496728987] 
dist 191=[-.44476848883741750388,.89743524276674859675] 
dist 192=[-.3514846093838129375 ,.94390081652825615885] 
dist 193=[-.43060274312525571903,.97264602581983008546] 
dist 194=[-.50506141903189279965,.9939250657259853503 ] 
dist 195=[-.55140160016447902841,1.0105874596820897895 ] 
dist 196=[-.58601903283566787063,1.0230091078414618044 ] 
dist 197=[-.61368906962958556888,1.0273597669283584228 ] 
dist 198=[-.63547608320131846162,1.0266270890766418398 ] 
dist 199=[-.64661252281925729934,1.0248252724658790007 ] 
dist 200=[-.65207769688784975106,.57092280561133474357] 
dist 201=[-.65289328620489848689,.53184192767946024802] 
dist 202=[-.7118180732411568755 ,.43610260658126687686] 
dist 203=[-.77101249943581755047,.42173930401490294039] 
dist 204=[-.81660599725414343217,.27963369020845006138] 
dist 205=[-.85558050019330116855,.25326053858684528489] 
dist 206=[-.88733445412348151992,.22116671495040079488] 
dist 207=[-.9041075361390288878 ,.23840322506925298434] 
dist 208=[-.9131282731369702411 ,.30522779447029004303] 
dist 209=[-.91428452190343682107,.35625818573691406199] 
dist 210=[-.91087890801767330511,.40549047568668622759] 
dist 211=[-.90770267157580097822,.46513590915482330559] 
dist 212=[-.89712097944452236629,.52690008239511374627] 
dist 213=[-.89151626531133177355,.58458644823167645972] 
dist 214=[-.85749267051204703684,.65032292089466099241] 
dist 215=[-.84830354589070383465,.7442126115836654425 ] 
dist 216=[-.82975819845315242142,.83562190878690702503] 
dist 217=[-.82333947177188247978,.89145809439644218708] 
dist 218=[-.69357958192948761648,.9319092444518952924 ] 
dist 219=[-.74060488572805056026,.96191625794167543427] 
dist 220=[-.78166375024147959563,.984339684830003079  ] 
dist 221=[-.80859165042552877094,.99452511250544180045] 
dist 222=[-.8303378812354304815 ,.99794776302483059108] 
dist 223=[-.85071414277390736008,.99745877363017412891] 
dist 224=[-.86683606179713066503,.92890295267623547063] 
dist 225=[-.87160076327258213517,.90960545513308809541] 
dist 226=[-.87222080413143808015,.88209482648013170513] 
dist 227=[-.87179802703873217999,.91465466092077920022] 
dist 228=[-.84060839378037222657,.93776494199789715164] 
dist 229=[-.8319724985267759573 ,.95402658952942473527] 
dist 230=[-.82629414108879644782,.96464371969161603112] 
dist 231=[-.82317112804376502104,.96661984140274761102] 
dist 232=[-.65270624506090477209,.96273924410660549905] 
dist 233=[-.63049160813279954597,.96111642413235842789] 
dist 234=[-.57771140433094680513,.64423811372109484625] 
dist 235=[-.56549889515881721226,.61388062066182313621] 
dist 236=[-.48754202572507711941,.54090661091069901515] 
dist 237=[-.47813296701954842862,.52695635272660189108] 
dist 238=[-.56309503972779746874,.41979788360852214844] 
dist 239=[-.62278803669627337225,.39915885685065872886] 
dist 240=[-.67540901320673366592,.36628309128096942229] 
dist 241=[-.73214358492197952018,.35751607105551566314] 
dist 242=[-.7836176342161696053 ,.19174960718663345826] 
dist 243=[-.81524205707960783905,.17018055685271680907] 
dist 244=[-.83838421946931852198,.11896550094693674864] 
dist 245=[-.85600328827198255097,.11089823478625825521] 
dist 246=[-.86872478642238560177,.04045271962696492085] 
dist 247=[-.87231951514355579566,.02778932025504044146] 
dist 248=[-.8719299293098348715 ,.01019324680625465892] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 0, 2, 1, 2] 
dist 0=[56.406240527055700263  ,56.406240527055700263  ] 
dist 1=[56.153852884447975889  ,56.534059688141075743  ] 
dist 2=[55.746433285178062035  ,56.595834617139605175  ] 
dist 3=[54.999266088884582970  ,56.584248862246888364  ] 
dist 4=[53.856941004100789108  ,56.535710773904163778  ] 
dist 5=[51.870999693673247132  ,56.449764242411922569  ] 
dist 6=[49.779112854887059721  ,56.319443510989137002  ] 
dist 7=[48.213618366524381866  ,55.929757695193189951  ] 
dist 8=[46.728504886628466250  ,52.660926384707010428  ] 
dist 9=[44.957851172458856708  ,52.089098242996105861  ] 
dist 10=[42.961260376525668574  ,51.180990978047826134  ] 
dist 11=[39.793799582889699540  ,50.910950367659160927  ] 
dist 12=[34.967310578478321113  ,50.227798078870277723  ] 
dist 13=[30.100411903518526161  ,50.022847362998799598  ] 
dist 14=[26.771473559813143921  ,49.775170883978275279  ] 
dist 15=[23.922645798639569736  ,48.214924726087622039  ] 
dist 16=[20.973165878939832512  ,31.319516760125146054  ] 
dist 17=[18.174370252438497771  ,30.828942477844051398  ] 
dist 18=[15.927201569461216832  ,29.139144108806938271  ] 
dist 19=[13.646591909988504636  ,28.739725990856923111  ] 
dist 20=[10.713857617288637028  ,28.284087554190799067  ] 
dist 21=[7.8595774426334142384 ,28.141576432704782469  ] 
dist 22=[5.8921252989932879952 ,14.965596649166508806  ] 
dist 23=[4.1901862707735445866 ,14.617408792626846351  ] 
dist 24=[2.3961792503168848501 ,8.9422711025621440453 ] 
dist 25=[.67051306532721404366,8.2331699625912624094 ] 
dist 26=[-.94229133555294787857,6.7632111520328185776 ] 
dist 27=[-2.6410809322431688177 ,6.4544051020185270768 ] 
dist 28=[-4.2582967504580243102 ,5.1900532796824280795 ] 
dist 29=[-6.1943220027663072546 ,4.9622984719221424991 ] 
dist 30=[-8.0095002956727252859 ,4.7134039669062049984 ] 
dist 31=[-9.1439804973415116485 ,4.2868414893714755640 ] 
dist 32=[-10.000750724569932368  ,-6.4131390853995931498 ] 
dist 33=[-10.706591736022288640  ,-6.6049363254066448909 ] 
dist 34=[-11.267905930727527283  ,-7.0513668452967289890 ] 
dist 35=[-11.547389013033858854  ,-7.0203726902996828879 ] 
dist 36=[-11.691987766769947798  ,-6.7983212688418532567 ] 
dist 37=[-11.714420845331711334  ,-6.2619574495232120229 ] 
dist 38=[-11.794909779988817941  ,-5.6690979065957906170 ] 
dist 39=[-11.834746852466122111  ,-5.2213634027570985519 ] 
dist 40=[-11.389162011172010091  ,-4.7966964045623679871 ] 
dist 41=[-11.291316071741382983  ,-4.2952521489282626756 ] 
dist 42=[-11.198671678423994800  ,-3.7847817310242535531 ] 
dist 43=[-11.135527741786392642  ,-3.3237774350234097094 ] 
dist 44=[-11.051248105160171784  ,-2.8114664380294422436 ] 
dist 45=[-11.011699203531603156  ,-2.0959386576292711243 ] 
dist 46=[-10.985797038641237945  ,-1.3771168194267358450 ] 
dist 47=[-10.972024694509530529  ,-.85148980202847310574] 
dist 48=[-3.8871160881287192836 ,-.36658998945978243304] 
dist 49=[-3.3148172296178566864 ,.3260498205229745692 ] 
dist 50=[-2.3201665915336088412 ,.9925365715872952832 ] 
dist 51=[-2.2728471815958401697 ,1.6472019478669600297 ] 
dist 52=[-2.1859184080382833584 ,2.4577262883504886678 ] 
dist 53=[-2.1638847743416032058 ,3.2283066131282416193 ] 
dist 54=[-2.0883846513520970253 ,3.7235156321137931241 ] 
dist 55=[-2.0667584813188018523 ,4.1123105426367477066 ] 
dist 56=[-2.0420810253417506472 ,4.4580483282559822958 ] 
dist 57=[-2.0301117724370012221 ,4.7499943661230616279 ] 
dist 58=[-2.0039058368250515426 ,4.9240234460745089763 ] 
dist 59=[-1.9911421986161676213 ,5.0450947784356259834 ] 
dist 60=[-1.9653280570074307728 ,5.1924060071783408296 ] 
dist 61=[-1.9537166498343185096 ,5.3389684460549118068 ] 
dist 62=[-1.8873880629334930872 ,5.4208177182880861473 ] 
dist 63=[-1.8683251493193620987 ,5.4398935533736183244 ] 
dist 64=[-1.8152948822775515661 ,4.7412067550808491434 ] 
dist 65=[-1.7936308221539417234 ,4.7236564455490251163 ] 
dist 66=[-1.6679018168769416718 ,4.6975702570307968560 ] 
dist 67=[-1.6357012469270301725 ,4.6861439179550894377 ] 
dist 68=[-1.5759367823577625755 ,4.6789382770432318194 ] 
dist 69=[-1.5569484490987175163 ,4.6756379934368368852 ] 
dist 70=[.2797522760529847384 ,2.4847819098784458480 ] 
dist 71=[-.29025802584448106613,2.4606255743726389574 ] 
dist 72=[-.76918995771965523903,1.6605897540314281839 ] 
dist 73=[-1.2491281366726967183 ,1.5582179554172402670 ] 
dist 74=[-1.6931138617810066309 ,1.3470380143516718042 ] 
dist 75=[-2.0285709524027654608 ,1.2913456876800905505 ] 
dist 76=[-2.3489209703559453519 ,1.0856320701846174022 ] 
dist 77=[-2.7326472801027752439 ,1.0433603159864975176 ] 
dist 78=[-3.0909062633582791003 ,.9676494122369591348 ] 
dist 79=[-3.3096212305215507114 ,.9502326889071858272 ] 
dist 80=[-3.4682105114144532866 ,-.39611700750994409422] 
dist 81=[-3.5864903804578535326 ,-.51166623903429512347] 
dist 82=[-3.6745881507148544174 ,-.74818115645485858629] 
dist 83=[-3.7126801704339760511 ,-.80451126667786784728] 
dist 84=[-3.7253149699122080143 ,-1.0021384724178894308 ] 
dist 85=[-3.7213173719880633366 ,-.86365254201195063816] 
dist 86=[-3.4814922024465047320 ,-.50391751021195298044] 
dist 87=[-3.4409309188048075982 ,-.15559266142673630427] 
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dist 97=[-2.8462735269109220156 ,2.5354645397886595834 ] 
dist 98=[-2.6330676824329079887 ,2.7035809389319088108 ] 
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dist 100=[-2.4905479827333433184 ,2.9488742942433186992 ] 
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dist 141=[-.57526864458136446496,.61338875329908005419] 
dist 142=[-.5567517230459215527 ,.68100155034532915612] 
dist 143=[-.51688951268117540824,.72338978238643415434] 
dist 144=[-.50519105616558551932,.79331417142517488498] 
dist 145=[-.45534030522494792667,.86946389639845989594] 
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dist 150=[-.3471773978075246802 ,1.0200213047029847354 ] 
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dist 152=[-.32192102327749537177,1.0375797047790829361 ] 
dist 153=[-.30199597213758221575,1.0424777071603606102 ] 
dist 154=[-.29682981356956783522,1.0430437527456358422 ] 
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dist 156=[-.28502166064851517886,1.0373641338088715244 ] 
dist 157=[-.2753909383454840756 ,.35138942495573989258] 
dist 158=[-.27321543524831922395,.29833856686481873165] 
dist 159=[-.27309442419765807048,.21461948869229118872] 
dist 160=[-.27572743471558943411,.18173124785620153368] 
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dist 163=[-.39502480179762579158,.12853096363662308178] 
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dist 167=[-.70739176457644022919,.14058815124801457931] 
dist 168=[-.76368955989325915905,.21330439420742084696] 
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dist 170=[-.8583794755294909484 ,.36522934318684534304] 
dist 171=[-.88550651565634329209,.4526052104727399105 ] 
dist 172=[-.90569350528392099205,.57997086062348723957] 
dist 173=[-.92168302115929031433,.70504060989990593137] 
dist 174=[-.93310844938048237775,.78325261831753772984] 
dist 175=[-.93507927048091932014,.84208891734346642695] 
dist 176=[-.93341362513778530301,.88983044531800235167] 
dist 177=[-.93032547674232232554,.92802410738359894643] 
dist 178=[-.89935247770420844864,.94875621827119542238] 
dist 179=[-.89009526415281569611,.96065602360997630327] 
dist 180=[-.87810655377165072271,.96360370740815113748] 
dist 181=[-.87247822897598512242,.91531472651297559525] 
dist 182=[-.61743482881503872672,.90541851255959809652] 
dist 183=[-.61745049177533791043,.89637565535687607897] 
dist 184=[-.61623012170971858884,.89025419449463485071] 
dist 185=[-.60826944211895592691,.88340388582342617281] 
dist 186=[-.60551874851814026827,.88021075630500627966] 
dist 187=[-.59304154416773584857,.878352631669671869  ] 
dist 188=[-.59122457350183820512,.87783172618151822298] 
dist 189=[-.54906392242370355301,.8155647006612614415 ] 
dist 190=[-.54097129718726604402,.85813056600271431363] 
dist 191=[-.52002001445059657847,.88520193296909394365] 
dist 192=[-.51407450259480338878,.90610803271437518944] 
dist 193=[-.47484971535451158412,.92406845710054307353] 
dist 194=[-.46599505499499238219,.93876582925649548597] 
dist 195=[-.45016280795331545911,.94914237985541855163] 
dist 196=[-.44571329780355556998,.95189186639299600037] 
dist 197=[-.35040518680333927805,.94850321741774248592] 
dist 198=[-.33684843880717509757,.3121255512455603512 ] 
dist 199=[-.30511528084150334151,.2795212042899883207 ] 
dist 200=[-.29766335264050371597,.2055008910477917924 ] 
dist 201=[-.25252521723277373271,.1908000336100292354 ] 
dist 202=[-.24357023785924322638,.0983965864305623962 ] 
dist 203=[-.22631205560800527011,.1436019967731690770 ] 
dist 204=[-.22168831547892953684,.25269054989797755452] 
dist 205=[-.1292579777123918091 ,.36078934603033892075] 
dist 206=[-.2029593310973166014 ,.43216905971267684441] 
dist 207=[-.2543814625337801620 ,.49032203920241019427] 
dist 208=[-.2993389168244878857 ,.54562918384137406348] 
dist 209=[-.3472400624375482752 ,.59487265197765801136] 
dist 210=[-.39338418807918035104,.6288236017146100607 ] 
dist 211=[-.43133100300469918388,.65807318026697953652] 
dist 212=[-.47055846635170340253,.68855162533125137077] 
dist 213=[-.52181815103575753129,.71494024586698246381] 
dist 214=[-.57073079125479444275,.72786616043681297864] 
dist 215=[-.60059090267086007569,.73429839771309675224] 
dist 216=[-.62223317724546312763,.73478516331863790273] 
dist 217=[-.63834306081285803614,.72478814626507789635] 
dist 218=[-.6498409105311640793 ,.72074995502894673779] 
dist 219=[-.65307277869861220913,.71701163151219472008] 
dist 220=[-.6532913860109965992 ,.71337549134696366756] 
dist 221=[-.65276013622493927036,.17706985465719130699] 
dist 222=[-.62249059807739360434,.22060203273524039069] 
dist 223=[-.61603740204340886544,.25352806705893452094] 
dist 224=[-.60019020654617908305,.28498881131711069807] 
dist 225=[-.59424706650489963849,.32267486798312839323] 
dist 226=[-.56368409926440741893,.36148219306943187805] 
dist 227=[-.57660296084966003475,.39741980963844076764] 
dist 228=[-.59935292689460852692,.43814557119915895485] 
dist 229=[-.61876871904506652852,.49606611552416107657] 
dist 230=[-.62737436380157132767,.55240790010253142828] 
dist 231=[-.63128334518507201444,.58683290955526809504] 
dist 232=[-.6319554174592750022 ,.61180479984286368932] 
dist 233=[-.61678639886214898671,.63041568366379913881] 
dist 234=[-.61255488689822758075,.64415474768015998403] 
dist 235=[-.60974474304966357486,.64968074658329617592] 
dist 236=[-.6081405689530739788 ,.65127205487360175228] 
dist 237=[-.4900228241470064072 ,.65017562424405735691] 
dist 238=[-.47471051515231734397,.61236953801175505854] 
dist 239=[-.43701489633852213686,.60486662681414665989] 
dist 240=[-.42910476429980809782,.58964274911721114712] 
dist 241=[-.36933568281772958104,.58453808278665826361] 
dist 242=[-.3572336415090998214 ,.56044946809513503916] 
dist 243=[-.33773136383318753769,.55473217107259584893] 
dist 244=[-.33231111263049248716,.53692148630197794789] 
dist 245=[-.22257621530379959315,.53340382529204007912] 
dist 246=[-.20783061711918329419,.2112118578621137307 ] 
dist 247=[-.17343586980677185507,.1810757508818375292 ] 
dist 248=[-.1666118286248872727 ,.1142784888931380370 ] 
dist 249=[-.11986540270530072859,.1001791711653317073 ] 
dist 250=[-.11112500224633747682,.0222573052435153908 ] 
dist 251=[-.09547961394731430171,.0086622868708178093 ] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 1, 1, 0, 0, 2] 
dist 0=[48.462588313850759276  ,48.462588313850759276  ] 
dist 1=[48.172430481989815129  ,48.896371470576601997  ] 
dist 2=[47.447370338208661946  ,49.345582241988567033  ] 
dist 3=[46.271493229719664389  ,49.553880961289129082  ] 
dist 4=[44.327363827174600837  ,49.626174658418496596  ] 
dist 5=[42.306391223320802804  ,49.615080227322035524  ] 
dist 6=[40.823540897235157460  ,49.377248716660086764  ] 
dist 7=[39.446737348541856503  ,48.959922390196812081  ] 
dist 8=[37.849236178268048541  ,47.185158184648193974  ] 
dist 9=[36.226286878266780315  ,47.030335015688064443  ] 
dist 10=[34.747739839256262630  ,46.432860487796134994  ] 
dist 11=[33.087046128243328364  ,46.246623583432852568  ] 
dist 12=[30.736369668616487914  ,45.868564324848844385  ] 
dist 13=[28.346732177374008861  ,45.732688953793387568  ] 
dist 14=[26.530300402329648756  ,45.123038379846045163  ] 
dist 15=[24.779661700598130334  ,44.318907337976094335  ] 
dist 16=[22.652651089714297642  ,27.871737922855194874  ] 
dist 17=[20.436832676357028238  ,27.438991207648422894  ] 
dist 18=[18.331211768379462047  ,26.096305804158128335  ] 
dist 19=[15.894617800704142754  ,25.432979086944763255  ] 
dist 20=[12.356191600441860290  ,25.292813979145201574  ] 
dist 21=[8.8460396605964297706 ,21.359676078879487240  ] 
dist 22=[6.5223160627306664378 ,16.588583970568143494  ] 
dist 23=[4.6132565761747790432 ,16.354070212216365908  ] 
dist 24=[2.7598047506065111232 ,14.898000727225401111  ] 
dist 25=[1.0743654843581273846 ,14.211681385777473507  ] 
dist 26=[-.16353239471124807245,13.979985584190503318  ] 
dist 27=[-1.3164936612726080908 ,12.851834162524808553  ] 
dist 28=[-2.6628651089804153428 ,10.732885214097774558  ] 
dist 29=[-3.9140006774682934483 ,9.5238771001541455280 ] 
dist 30=[-5.7219775911107393363 ,3.6140844160174723031 ] 
dist 31=[-8.4413204024739582638 ,1.2195914803247824404 ] 
dist 32=[-11.080754028868899598  ,-1.9684393289618760912 ] 
dist 33=[-12.724279571353716759  ,-2.2616135253684239911 ] 
dist 34=[-13.962571994826864464  ,-3.9726010576087850051 ] 
dist 35=[-14.982668321453909627  ,-4.2476226167047458992 ] 
dist 36=[-15.798155252434427938  ,-3.7809324154036009073 ] 
dist 37=[-16.218617995320039033  ,-3.2143420150273053267 ] 
dist 38=[-16.444858537071769254  ,-2.7752175257828511077 ] 
dist 39=[-16.486500739187140431  ,-2.3477757058948713825 ] 
dist 40=[-16.188467598424768322  ,-1.8272919962511794653 ] 
dist 41=[-16.082932537024457853  ,-1.2890337393902067506 ] 
dist 42=[-15.968161507353089810  ,-.7904430863560059574 ] 
dist 43=[-15.890895902604478053  ,-.2265932059685451584 ] 
dist 44=[-15.686101387678875794  ,.5722283807718803494 ] 
dist 45=[-15.589369887804607537  ,1.3780637427285397322 ] 
dist 46=[-15.412002600968205539  ,1.9699894350534793715 ] 
dist 47=[-15.341666284552537316  ,2.5178007575876329896 ] 
dist 48=[-6.1702835156125574570 ,3.1477142340728354417 ] 
dist 49=[-5.3855488594531784297 ,3.7814115442164800524 ] 
dist 50=[-3.5653406343928606768 ,4.3443690499552447538 ] 
dist 51=[-3.2598701785114644353 ,4.9628468595299159529 ] 
dist 52=[-2.7675930936667695080 ,5.8181232838762637800 ] 
dist 53=[-.48396234568781800181,6.6581523037457302516 ] 
dist 54=[.17747481953791880278,7.2158000723328068100 ] 
dist 55=[.33498868634762237888,7.6729819975278007458 ] 
dist 56=[2.4014221956923526405 ,8.1121224306906026949 ] 
dist 57=[2.3371156509119261663 ,8.5056900038158281946 ] 
dist 58=[2.2141610930706440832 ,8.7810183599267778411 ] 
dist 59=[2.0163828311951196698 ,9.1195803598702196368 ] 
dist 60=[1.7268410312187773921 ,9.4266831365003941540 ] 
dist 61=[1.2378235523842252336 ,9.5782601512494231260 ] 
dist 62=[.73424231205566063757,9.6450557858556659197 ] 
dist 63=[.3865686908069179171 ,9.6514928688852474419 ] 
dist 64=[.0875825527003225493 ,4.9353798110439307528 ] 
dist 65=[-.2218747757565091253 ,4.9360632531855016334 ] 
dist 66=[-.51332151217261098973,4.9217365200411120516 ] 
dist 67=[-.7405030645716461126 ,4.8881852506106449608 ] 
dist 68=[-.96352661557559845035,4.8678899087134141004 ] 
dist 69=[-1.2384155944395092214 ,2.3296480863263646381 ] 
dist 70=[-1.4975922597673244807 ,2.2200156800311311257 ] 
dist 71=[-1.6579533876680421974 ,2.1953114048667156100 ] 
dist 72=[-1.7762677993240433885 ,1.4038840517022439334 ] 
dist 73=[-1.8677342014224934235 ,1.1483009949217601716 ] 
dist 74=[-1.9379899345392235858 ,.9084476483986720012 ] 
dist 75=[-1.9716931154739539843 ,.8461737948018859915 ] 
dist 76=[-1.9855596515470049204 ,.6199092967504188962 ] 
dist 77=[-1.9859697357872048184 ,.5752383472735275302 ] 
dist 78=[-2.1836197709195487923 ,.5026658414973138591 ] 
dist 79=[-2.3492002201824760740 ,.4859144594082246835 ] 
dist 80=[-2.4895784896783447673 ,-.70324393727678201021] 
dist 81=[-2.6030569432311642402 ,-.80345859044276213968] 
dist 82=[-2.6613006466507320674 ,-1.0027351407405589792 ] 
dist 83=[-2.6907936393089622999 ,-1.0496679812542570642 ] 
dist 84=[-2.6959779489066500677 ,-1.1936419289591028608 ] 
dist 85=[-2.0723985635061989307 ,-1.2199174439335899793 ] 
dist 86=[-2.0215469004098666317 ,-1.1713632930269777053 ] 
dist 87=[-1.9687805721331315015 ,-1.0319264592252673063 ] 
dist 88=[-2.0898931747499942040 ,-.87605061343880592196] 
dist 89=[-2.1644625253075424596 ,-.6572726923715056673 ] 
dist 90=[-2.2195425798042763286 ,-.41511291146011455186] 
dist 91=[-2.2628171387846819086 ,-.1659256401826755314 ] 
dist 92=[-2.2955365494356892123 ,.1358900429603604493 ] 
dist 93=[-2.3084700426515857123 ,.5880606992594835736 ] 
dist 94=[-2.3095970595222854167 ,1.0388771478854624102 ] 
dist 95=[-2.3067250337848745019 ,1.3352917311050964435 ] 
dist 96=[-1.5912669250097041870 ,1.5750937622053064264 ] 
dist 97=[-1.6079827956957495453 ,1.8000091130225167303 ] 
dist 98=[-1.6232699797330959589 ,1.9978681346632312456 ] 
dist 99=[-1.6402854722162818665 ,2.1297038287344759120 ] 
dist 100=[-1.6638459050468202197 ,2.2382756005420956563 ] 
dist 101=[-1.6855105634991982319 ,2.3432948564587284048 ] 
dist 102=[-1.6949531136262731912 ,2.4334208716962848165 ] 
dist 103=[-1.6970307685073986751 ,2.4825635160648312891 ] 
dist 104=[-1.6940673567183892436 ,2.5110082061962914495 ] 
dist 105=[-1.6758017024726038827 ,2.5185513446237719652 ] 
dist 106=[-1.6687607805524429323 ,2.5137770903426326287 ] 
dist 107=[-1.6355089758108807292 ,2.5707636187553501661 ] 
dist 108=[-1.6303585429838385255 ,2.6030159414150408963 ] 
dist 109=[-1.5097075220766112172 ,2.6228529944536371766 ] 
dist 110=[-1.4877233262462689270 ,2.6313110205591799658 ] 
dist 111=[-1.4204990306257904199 ,2.6331486667736254194 ] 
dist 112=[-1.4106193501321846463 ,2.6265404039296026015 ] 
dist 113=[-1.2595101934345886822 ,2.6150900252962875140 ] 
dist 114=[-1.2265528004851271697 ,2.6040177116162799413 ] 
dist 115=[-1.2070769587117128703 ,2.5767156415095958849 ] 
dist 116=[-1.2129214441334163521 ,2.5631625526105289046 ] 
dist 117=[-1.2123460068685568893 ,1.1620024245953156992 ] 
dist 118=[-1.1906692744559194023 ,1.0378834620541250893 ] 
dist 119=[-1.1831640955112974038 ,.75798614933454052767] 
dist 120=[-1.1581820387842233133 ,.70106572118937146799] 
dist 121=[-1.1487731824951677025 ,.67477500709939571816] 
dist 122=[-1.2906159994525310503 ,.70698184708534812145] 
dist 123=[-1.4772298824655989813 ,.73379987505355386308] 
dist 124=[-1.7048841532282784843 ,.76173552940898703517] 
dist 125=[-1.9193446473454581274 ,.79837900231077538139] 
dist 126=[-2.0533029764709733974 ,.83226856490576887494] 
dist 127=[-2.1539844650576388951 ,.84920998435121893429] 
dist 128=[-2.2356317280343500816 ,.85809214770801160523] 
dist 129=[-2.2988602134497968212 ,.85985103002195407419] 
dist 130=[-2.3260330775971833763 ,.84784289164448290789] 
dist 131=[-2.3368559114353199557 ,.84423005855769535442] 
dist 132=[-2.3348027166682887149 ,.8415858986751880622 ] 
dist 133=[-2.2792710227728207938 ,.83953975417601409534] 
dist 134=[-2.3745308536589754915 ,.68707570178983912491] 
dist 135=[-2.4602922310595259634 ,.66529109031106029595] 
dist 136=[-2.5234367785151020325 ,.62567635594663265567] 
dist 137=[-2.5684724063383685813 ,.77356960770943310201] 
dist 138=[-2.5819472931749974120 ,.93204676918269636641] 
dist 139=[-2.5830938727406129103 ,1.0926801482941703471 ] 
dist 140=[-2.5789165599276887121 ,1.2982334504087292411 ] 
dist 141=[-2.4480554814502886231 ,1.4965943073022544617 ] 
dist 142=[-2.4209263502230713336 ,1.6285256359120785587 ] 
dist 143=[-2.3572390988180086596 ,1.7370614288296504809 ] 
dist 144=[-2.3340620054256022838 ,1.8420529011862619808 ] 
dist 145=[-2.2171155273963042754 ,1.9367516701526571261 ] 
dist 146=[-2.1894447831200015940 ,2.0042131618428959165 ] 
dist 147=[-2.1205356164811521363 ,2.0646737405083188448 ] 
dist 148=[-2.0957082676891836890 ,2.1314411434152284252 ] 
dist 149=[-.55966222146558192138,2.1886156267978949610 ] 
dist 150=[-.4063081871138033177 ,2.2567643077949777942 ] 
dist 151=[-.38555518042553915013,2.3449298879908246292 ] 
dist 152=[-.34061719655779042296,2.4101333705214792810 ] 
dist 153=[-.32805677973523069172,2.4574592204873173072 ] 
dist 154=[-.27592646289743568515,2.4742647529989185688 ] 
dist 155=[-.26599190232446981709,2.4777144932312679870 ] 
dist 156=[-.24051890363452950896,2.4717283067808793790 ] 
dist 157=[-.23672464458463345332,2.6309366473057670761 ] 
dist 158=[.04612550846688903627,2.7292508164344476078 ] 
dist 159=[.03519855641386208387,2.7938136235771507421 ] 
dist 160=[-.04388972035008318332,2.8292052151719051006 ] 
dist 161=[-.12252249611406271594,2.8491035969951315944 ] 
dist 162=[-.19481134390667942774,2.8518265231029295390 ] 
dist 163=[-.24858111323474880043,2.8434469724071488483 ] 
dist 164=[-.29906379259310185387,2.8359144662059440740 ] 
dist 165=[-.51390951541075241175,2.3953860771848838782 ] 
dist 166=[-.84896809980401028252,2.3669146905364494137 ] 
dist 167=[-1.1249110452551078309 ,2.2803252138097565034 ] 
dist 168=[-1.3923644906290872680 ,2.2646122896205249323 ] 
dist 169=[-1.6339212278020044253 ,2.0680602669207393298 ] 
dist 170=[-1.8065014018635475466 ,2.0242877228446882386 ] 
dist 171=[-1.9616254630878057355 ,1.9796654229655495408 ] 
dist 172=[-2.1335085576195505439 ,1.9617943498097944686 ] 
dist 173=[-2.2896885490500865860 ,1.4098433712344541052 ] 
dist 174=[-2.3821365146663499681 ,1.3358644233021980366 ] 
dist 175=[-2.4456116872360788668 ,1.1869825644815804695 ] 
dist 176=[-2.4861527555409133643 ,1.1472100579577942927 ] 
dist 177=[-2.5116678607007491199 ,.9994333522956437392 ] 
dist 178=[-2.5151687550079069079 ,.9666815041994226912 ] 
dist 179=[-2.5092696442376038779 ,.9070115726238385769 ] 
dist 180=[-2.4996243921581882410 ,.8916532771022027482 ] 
dist 181=[-.67053381826735612622,.2099341690403697461 ] 
dist 182=[-.70333621086320960657,.30050934221475195345] 
dist 183=[-.72074306449547549012,.37349741443321705479] 
dist 184=[-.73701012684412442898,.44155265401246323407] 
dist 185=[-.74987099379883623541,.50121785186771483037] 
dist 186=[-.75816674021660604671,.54072136131091470218] 
dist 187=[-.76013403523420101043,.57301918683646607811] 
dist 188=[-.75888812544722329053,.60392720175493206371] 
dist 189=[-.75668362141254346197,.63102315062411628588] 
dist 190=[-.61802459468968151261,.64810650663719094368] 
dist 191=[-.60366712760545146656,.66112802353350483475] 
dist 192=[-.56661049586249983464,.67201095832785710652] 
dist 193=[-.55915187732235927066,.68068368070869382035] 
dist 194=[-.49438857311830188301,.68488274854418257108] 
dist 195=[-.48367577228627044841,.68660487144079863608] 
dist 196=[-.48494415601545509555,.68538992573398399431] 
dist 197=[-.48443220630065710708,.68473393251578277351] 
dist 198=[-.47899478952210138651,.6768713859888235962 ] 
dist 199=[-.47684450425131035204,.68761316854540622033] 
dist 200=[-.4680956161905518005 ,.70576655149377909407] 
dist 201=[-.46584611311146407206,.71611866369385061123] 
dist 202=[-.43828798739750294859,.722373466786372915  ] 
dist 203=[-.43150915994778699182,.72417307054329978032] 
dist 204=[-.42423102575803981725,.72305349226320597981] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 1, 0, 1] 
dist 0=[59.793090680125039743  ,59.793090680125039743  ] 
dist 1=[58.810424823556716254  ,60.367701909461968516  ] 
dist 2=[57.011521743908219573  ,60.537053744459495237  ] 
dist 3=[55.084706193649526088  ,60.561851697147046774  ] 
dist 4=[53.591190486963335304  ,60.559229202863178787  ] 
dist 5=[52.125986711111593480  ,60.535901140402939036  ] 
dist 6=[50.312124524542899496  ,60.478117148836677312  ] 
dist 7=[48.408024461426311914  ,60.420355735193610538  ] 
dist 8=[46.582358443397240463  ,59.652011652801818793  ] 
dist 9=[44.460110539097181293  ,54.784659723726623492  ] 
dist 10=[41.371431867977651878  ,53.986028001886228699  ] 
dist 11=[38.199366528619734438  ,52.660499037579941857  ] 
dist 12=[35.744001128630541715  ,52.297680234554198497  ] 
dist 13=[33.337201140112526230  ,51.317167834864960587  ] 
dist 14=[30.358924272823570602  ,51.081005296673814370  ] 
dist 15=[27.082523629426931784  ,50.944529995207094743  ] 
dist 16=[23.091814760681225654  ,49.963347613828142204  ] 
dist 17=[19.725459923578970485  ,32.374479000805936784  ] 
dist 18=[15.636987336303683546  ,32.175072892261779706  ] 
dist 19=[10.568352512923823947  ,17.592455872827390779  ] 
dist 20=[7.1799034137692902287 ,16.874400847265726504  ] 
dist 21=[4.3638629224773558462 ,10.863928657995160243  ] 
dist 22=[1.5816694362029042186 ,10.621499261549859662  ] 
dist 23=[-.97499142805461349926,7.8015784579991161851 ] 
dist 24=[-2.8901389896329784836 ,7.5085867919228264182 ] 
dist 25=[-4.7072776725240499886 ,1.4576210431212707542 ] 
dist 26=[-6.8723855879346613503 ,1.1919304287262292683 ] 
dist 27=[-8.8945386816506266674 ,-1.6718668450669671850 ] 
dist 28=[-10.140673506667518441  ,-2.0776786020957078860 ] 
dist 29=[-11.060024970189282750  ,-2.5431337549232251557 ] 
dist 30=[-11.776983771545734955  ,-2.5381943995272817424 ] 
dist 31=[-12.331253483980693183  ,-2.3500274628764313653 ] 
dist 32=[-12.600969793915974380  ,-1.9134863958101911064 ] 
dist 33=[-12.720244466123045792  ,-1.2185098944676726150 ] 
dist 34=[-12.729536739374400411  ,0                     ] 
dist 35=[-9.1674486216024055137 ,-3.1427664882320311679 ] 
dist 36=[-9.1868375175117498920 ,-2.1689882010200460576 ] 
dist 37=[-9.0706039649100132049 ,-1.3088900058065186009 ] 
dist 38=[-9.0625857983012824635 ,-.3836611564823514736 ] 
dist 39=[-8.9513281605336613531 ,.5092297767981827787 ] 
dist 40=[-8.9101172527637200874 ,1.2407212383167219411 ] 
dist 41=[-7.9622257072465055769 ,1.9925961825273474820 ] 
dist 42=[-7.8855849249351929821 ,2.9672196343427777459 ] 
dist 43=[-7.5540260194532219349 ,3.9122574259011054996 ] 
dist 44=[-7.4748450171334796622 ,4.5462937130173204421 ] 
dist 45=[-7.2702622017825335782 ,5.0737044083647464084 ] 
dist 46=[-7.2053794880558613558 ,5.5935280016148618365 ] 
dist 47=[-5.7729860860345129135 ,6.0693811349327119641 ] 
dist 48=[-5.7201776392143173865 ,6.4215521469717753364 ] 
dist 49=[-1.7939361268884969695 ,6.7516416266546716397 ] 
dist 50=[-1.6296908982284012049 ,7.1397743576328456203 ] 
dist 51=[-.6024233980521574003 ,7.4901248344365301182 ] 
dist 52=[-.42334719161895164545,7.6694708553597473940 ] 
dist 53=[-.0793777082772212487 ,7.7627769337800124485 ] 
dist 54=[.0010024439084199779 ,7.7793922407924015175 ] 
dist 55=[.81780193564862889632,7.7147428183957843883 ] 
dist 56=[.93929078762653502422,7.6776933718827752205 ] 
dist 57=[1.1016883170891068180 ,7.6349660417466561599 ] 
dist 58=[1.1310757672219388915 ,7.5995712155696303321 ] 
dist 59=[1.1110256092240742001 ,6.4522857031086274557 ] 
dist 60=[1.0179029741083660177 ,6.2880290850294118091 ] 
dist 61=[.85405075147690540449,6.2909424637502073269 ] 
dist 62=[.5517543068070164994 ,6.2779884655914082326 ] 
dist 63=[.2347789435092091702 ,4.5753685942011817390 ] 
dist 64=[.0123060970100285744 ,3.8690695881687875687 ] 
dist 65=[-.1829990961642625895 ,1.3276150302046608456 ] 
dist 66=[-.3916929141516094584 ,1.2373763593096244837 ] 
dist 67=[-.5926225485486479229 ,.4114416795752801000 ] 
dist 68=[-.87136852247326450949,.2654624233299785280 ] 
dist 69=[-1.4117272913562728266 ,.0720976889666429346 ] 
dist 70=[-1.8118046969322003936 ,.0305272893733044333 ] 
dist 71=[-2.1859414208848915252 ,-.1740235448406714620 ] 
dist 72=[-2.6228682035152494007 ,-.0827300989901973180 ] 
dist 73=[-3.0279700949574321041 ,.0353981349911755866 ] 
dist 74=[-3.2750943343463020811 ,.2208724495815737676 ] 
dist 75=[-3.4541176104348186820 ,.4351416747421537654 ] 
dist 76=[-3.5873343053213106699 ,.6681388563422120315 ] 
dist 77=[-3.6870111765764734803 ,.9591355923644732381 ] 
dist 78=[-3.7321622991142291351 ,1.4047855503859585199 ] 
dist 79=[-3.7478104161971906096 ,1.8495528370064825475 ] 
dist 80=[-3.7457250409919231154 ,2.1370157082661706379 ] 
dist 81=[-3.0937912809913228384 ,2.3638151849429386221 ] 
dist 82=[-3.0206415939107121833 ,2.5665371891773428195 ] 
dist 83=[-2.8311331259728914737 ,2.7377388788969368685 ] 
dist 84=[-2.7939621037075392406 ,2.8387599830817140389 ] 
dist 85=[-2.4665003459939404467 ,2.9073950769921281845 ] 
dist 86=[-2.4268827925644619129 ,2.9493386675176318694 ] 
dist 87=[-2.3646511785990600959 ,2.9773442035974952270 ] 
dist 88=[-2.3479549595357378071 ,2.9903682985083804923 ] 
dist 89=[-2.2977229665232535729 ,2.9946689455193271981 ] 
dist 90=[-2.2818920928097098526 ,2.9879114737628823954 ] 
dist 91=[-2.1616168413715134176 ,2.9743490908703016060 ] 
dist 92=[-2.1326354393403554794 ,2.9614277802274585898 ] 
dist 93=[-2.0868077696812056258 ,2.9251313605278215362 ] 
dist 94=[-2.0716569712837258523 ,2.9065902358587375807 ] 
dist 95=[-1.7075175017249285146 ,2.2897801358589825945 ] 
dist 96=[-1.6557436013808466394 ,2.5407648097428845146 ] 
dist 97=[-1.5381138479723473391 ,2.7790960364270371718 ] 
dist 98=[-1.5057510883874670730 ,2.9194682567780118559 ] 
dist 99=[-1.3452609836558241738 ,3.0153304197815659997 ] 
dist 100=[-1.3124955237452849806 ,3.0759415279644951457 ] 
dist 101=[-1.2408480974341895588 ,3.1172878145224759044 ] 
dist 102=[-1.2190708587992097990 ,3.1362110457617664961 ] 
dist 103=[-.9856618271492040890 ,3.1824787186899860381 ] 
dist 104=[-.9493094189310561395 ,3.2091866371681486868 ] 
dist 105=[-.8644789432170866518 ,3.2195972825874621602 ] 
dist 106=[-.8446270001053544976 ,3.2152517877750580790 ] 
dist 107=[-.7246406281037009197 ,3.1898258316222419084 ] 
dist 108=[-.7008575546795446661 ,3.1779275131446078030 ] 
dist 109=[-.6550587937195539682 ,3.1196200508742305187 ] 
dist 110=[-.6427732345866939317 ,3.1095288798291852205 ] 
dist 111=[-.4661593069503714607 ,2.7340502838282913333 ] 
dist 112=[-.4377115420666932656 ,2.7236665882260468660 ] 
dist 113=[-.4098138949593308023 ,1.5286378282777828824 ] 
dist 114=[-.7226213099215149296 ,1.4225557169360633624 ] 
dist 115=[-1.0079780546105411879 ,1.1702720064217378806 ] 
dist 116=[-1.2166505506629428443 ,1.1271728466807670852 ] 
dist 117=[-1.4091233423635838177 ,.77283845178601151633] 
dist 118=[-1.6298379148827580562 ,.70726037486110054877] 
dist 119=[-1.8348069001581129058 ,.61044769097235675789] 
dist 120=[-1.9644357105221682696 ,.58362776785470952129] 
dist 121=[-2.0637180949425939943 ,-.17478578184374979854] 
dist 122=[-2.1475538107699540238 ,-.26101685862475832167] 
dist 123=[-2.2270149977178941182 ,-.42550370850120532617] 
dist 124=[-2.2970386247409675050 ,-.47866004943722431815] 
dist 125=[-2.3499316916813153854 ,-.5974114082939445885 ] 
dist 126=[-2.3768067048898795624 ,-.6085964896877634370 ] 
dist 127=[-2.3897668865767005994 ,-.6289359196415156349 ] 
dist 128=[-2.3890275293257639709 ,-.4433610712936740260 ] 
dist 129=[-1.4202899082418831409 ,-.2512114879525383195 ] 
dist 130=[-1.3898107095541336507 ,-.1173379442386431828 ] 
dist 131=[-1.1857838976227811652 ,-.0005831856945831016 ] 
dist 132=[-1.1454213478195975339 ,.1232586265094423529 ] 
dist 133=[-1.0723723211469845069 ,.24212295537994199677] 
dist 134=[-1.1102066245254547461 ,.33902041871844648219] 
dist 135=[-1.1907799453054405823 ,.43836686813717527195] 
dist 136=[-1.2515897338644115578 ,.56701499288432437451] 
dist 137=[-1.3095628192741444752 ,.69190058206461058077] 
dist 138=[-1.3788007781371625329 ,.77623602448459936582] 
dist 139=[-1.4499313697376692858 ,.84703015456972495974] 
dist 140=[-1.5154467098727145602 ,.917878073070781237  ] 
dist 141=[-1.5893356215832607201 ,.98338241193573403308] 
dist 142=[-1.6938659728480040779 ,1.2273005232791839723 ] 
dist 143=[-1.7949080379500567699 ,1.5732364404202919676 ] 
dist 144=[-1.8548720593484825445 ,1.7956143698575956027 ] 
dist 145=[-1.8961386945083667729 ,1.9701543404180948666 ] 
dist 146=[-1.9225693668041578877 ,2.1251438183463621873 ] 
dist 147=[-1.9378960127196211673 ,2.2557884951889166582 ] 
dist 148=[-1.9398079634557269197 ,2.3331573704911793865 ] 
dist 149=[-1.9269537910530329006 ,2.3863685756175451748 ] 
dist 150=[-1.9228983163023643518 ,2.4205926616314460616 ] 
dist 151=[-1.8088451443325743035 ,2.4432092870151557035 ] 
dist 152=[-1.7864418507848417827 ,2.4500889750715718144 ] 
dist 153=[-1.7268385628888773494 ,2.4467947490651236548 ] 
dist 154=[-1.7085902105449769916 ,2.4414341927758869381 ] 
dist 155=[-1.5893930426452670146 ,2.4032341170306698130 ] 
dist 156=[-1.5616894629296957178 ,2.3909213462435110171 ] 
dist 157=[-1.5120486660182531966 ,2.3403668624814704487 ] 
dist 158=[-1.4977449631314152263 ,2.3312108021426961025 ] 
dist 159=[-1.0098608615157773103 ,1.2722703147933493839 ] 
dist 160=[-1.0163281220336516333 ,1.1700533490825185417 ] 
dist 161=[-1.0189907878511060241 ,.93878780977877873234] 
dist 162=[-1.1251801667769687422 ,.88943496810390569766] 
dist 163=[-1.3495980572286255449 ,.59909508790040642001] 
dist 164=[-1.5183251779206884010 ,.5460915849992693051 ] 
dist 165=[-1.6785916136525191845 ,.44001674798784349164] 
dist 166=[-1.8692453986618536680 ,.41280158282500473096] 
dist 167=[-2.0464016682317814033 ,.13112834268991008777] 
dist 168=[-2.1527978637319809821 ,.0882687722002491157 ] 
dist 169=[-2.2277602439192105972 ,.0138971845501171212 ] 
dist 170=[-2.2794567838759527676 ,-.0023814231760615280 ] 
dist 171=[-2.3154579780497602131 ,-.0352241855633987482 ] 
dist 172=[-2.3277721578877689390 ,-.0307036757667265643 ] 
dist 173=[-2.3281071540541291016 ,-.0088420360196169927 ] 
dist 174=[-2.3227981417959800399 ,.0423712251327455618 ] 
dist 175=[-2.1484436189931421475 ,.1005681079197622145 ] 
dist 176=[-2.2543706115985721493 ,.26862570689211554064] 
dist 177=[-2.3664899411806568275 ,.48109400784856121654] 
dist 178=[-2.4578157164248499098 ,.69962565220987696102] 
dist 179=[-2.5288115491755341117 ,.90531207389909934417] 
dist 180=[-2.5597869592379270702 ,1.0665153420052268087 ] 
dist 181=[-2.5726886094453628053 ,1.2260054450946518910 ] 
dist 182=[-2.5715402105827473994 ,1.4248577815103113321 ] 
dist 183=[-2.5129640509923181507 ,1.6142730435676763385 ] 
dist 184=[-2.4955134927729312568 ,1.7360998501916026310 ] 
dist 185=[-2.4512383627262224757 ,1.8317528387092335360 ] 
dist 186=[-2.4326233067757619929 ,1.9167054388924510117 ] 
dist 187=[-2.3304949791445173874 ,1.9882941849458038168 ] 
dist 188=[-2.3046994388599295876 ,2.0306119854437708073 ] 
dist 189=[-2.2432956728835962092 ,2.0596121035513591349 ] 
dist 190=[-2.2207789124558950080 ,2.0780528016610729579 ] 
dist 191=[-.6025609327178420541 ,2.0872101126243807037 ] 
dist 192=[-.5945211924291503078 ,2.1577733261650980303 ] 
dist 193=[-.4505737064403782951 ,2.2572122287558028833 ] 
dist 194=[-.5476953301496864626 ,2.3358309337105370472 ] 
dist 195=[-.6261400568895521936 ,2.3951196204842475549 ] 
dist 196=[-.6995796536351188583 ,2.4174041443563150768 ] 
dist 197=[-.7641579678842475585 ,2.4252816721835366078 ] 
dist 198=[-.8072369682241770491 ,2.4270649393442935672 ] 
dist 199=[-.8428053236895418212 ,2.5336200355951002437 ] 
dist 200=[-.8774079247195238060 ,2.6316313753213891964 ] 
dist 201=[-.9068757586561276789 ,2.6982418575742558934 ] 
dist 202=[-.9219512186985123472 ,2.7394200557663517048 ] 
dist 203=[-.9293634720128070912 ,2.7645667423561077249 ] 
dist 204=[-.9301061944255135539 ,2.7671898294178278655 ] 
dist 205=[-.9234938311434131047 ,2.7597955884160250366 ] 
dist 206=[-.9193546119776561805 ,2.7493576882876047456 ] 
dist 207=[-.9083059823816744619 ,2.3354184477878439675 ] 
dist 208=[-1.0255870320091967661 ,2.3224662383952476801 ] 
dist 209=[-1.2656975969870607070 ,2.2748189252989482028 ] 
dist 210=[-1.5004603087309795616 ,2.2627437997573170270 ] 
dist 211=[-1.7138487316899283116 ,2.1246635840773168675 ] 
dist 212=[-1.8686481416806228112 ,2.0912007676420645301 ] 
dist 213=[-2.0101992976951810428 ,2.0533907585502426642 ] 
dist 214=[-2.1707110785551298653 ,2.0353049843273104389 ] 
dist 215=[-2.3158042584641684460 ,1.5740966411968981361 ] 
dist 216=[-2.3958151011084125326 ,1.5098848899427741410 ] 
dist 217=[-2.4434876819051791545 ,1.3784252198776391909 ] 
dist 218=[-2.4595078963465773816 ,1.3420383201170618032 ] 
dist 219=[-2.4781330750404668849 ,1.1995359102958851785 ] 
dist 220=[-2.4833125818655250408 ,1.1687599972891078697 ] 
dist 221=[-2.4719627776128380496 ,1.1017464095795197065 ] 
dist 222=[-2.4688377383705969186 ,1.0813367657025316025 ] 
dist 223=[-1.3752434233377689103 ,.7387548160293179790 ] 
dist 224=[-1.3731334278495061626 ,.7371386153366982483 ] 
dist 225=[.16644619085608375557,.57548164053116133365] 
dist 226=[.24787717720125348293,.61780071281366970806] 
dist 227=[.27324520133001610636,.70535564306600641071] 
dist 228=[.27324577336128520483,.79060932066449540907] 
dist 229=[.2648394481525514311 ,.86786109534693516601] 
dist 230=[.22897644639742779232,.92347867471011052567] 
dist 231=[.18587958496372039683,.97390350460273086115] 
dist 232=[.14287126198332082484,1.0304301640567292150 ] 
dist 233=[.09169680489393040566,1.0811654633354676250 ] 
dist 234=[.01600671654727070140,1.1117044466609003053 ] 
dist 235=[-.06964174406029209198,1.1464866568182346456 ] 
dist 236=[-.16056195960506061288,1.1731097028587006938 ] 
dist 237=[-.27275327720064546846,1.1924444150176128722 ] 
dist 238=[-.44329811856770145945,1.1981367896132852405 ] 
dist 239=[-.61376907682224727019,1.1980851105374908496 ] 
dist 240=[-.7256659218182308343 ,1.1944959112837824412 ] 
dist 241=[-.8160753015620931267 ,.81717910087349699398] 
dist 242=[-.9007875403737092003 ,.8415902710824748799 ] 
dist 243=[-.9753458618703144586 ,.8577731559468287514 ] 
dist 244=[-1.0252301590876650006 ,.8669622361925903326 ] 
dist 245=[-1.0665922953225335222 ,.8714167345249855222 ] 
dist 246=[-1.1071385589419524815 ,.8713052318966814854 ] 
dist 247=[-1.1413091731308834950 ,.8641561117635226814 ] 
dist 248=[-1.1572250401216203428 ,.8612974137511517048 ] 
dist 249=[-1.1641149550378867756 ,.8031909732688003370 ] 
dist 250=[-1.1638259903887626253 ,.7922744114578612338 ] 
dist 251=[-1.1450629518170618146 ,.7633897219437533425 ] 
dist 252=[-1.1359429637685253029 ,.7551573713772601973 ] 
dist 253=[-1.1027342226296707478 ,.6989353122272484651 ] 
dist 254=[-1.0569422114481371087 ,.6861355901032336073 ] 
dist 255=[-1.0333685002858224027 ,.6637634716146559565 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 0, 1, 2, 0, 0, 1] 
dist 0=[50.805547877517388416  ,50.805547877517388416  ] 
dist 1=[50.421581237194245105  ,51.033531659362702756  ] 
dist 2=[49.849027741840635431  ,51.189669726518592587  ] 
dist 3=[48.867722429276640767  ,51.286579272845862178  ] 
dist 4=[47.654235947024503221  ,51.358165164288700635  ] 
dist 5=[46.154345006310054057  ,51.412949085239670787  ] 
dist 6=[44.153424546444038406  ,51.445418344090941491  ] 
dist 7=[40.938910699132566129  ,51.427929352702337630  ] 
dist 8=[37.645794250731794102  ,51.369737647989688437  ] 
dist 9=[35.330890166807940476  ,51.288083373449422674  ] 
dist 10=[33.283338954307795772  ,51.073768935581819294  ] 
dist 11=[31.057809909949866693  ,50.957804521151345861  ] 
dist 12=[28.880609957924973917  ,50.655271451374129790  ] 
dist 13=[27.025891657065396840  ,50.514697888950311242  ] 
dist 14=[25.046393798335924318  ,37.675062494887144483  ] 
dist 15=[22.370465926694993076  ,36.525238931141105739  ] 
dist 16=[19.704436530611221618  ,33.703930482397559691  ] 
dist 17=[17.764276676432149331  ,33.289859948075405320  ] 
dist 18=[15.977314236378526132  ,29.033407708965859916  ] 
dist 19=[13.922926068910419610  ,28.229270973753925096  ] 
dist 20=[11.843564204527339022  ,27.318721439716915722  ] 
dist 21=[9.9564703057917987869 ,27.131391629016686216  ] 
dist 22=[7.8400766569769824253 ,19.846335928943064027  ] 
dist 23=[4.8439647419349556145 ,18.937447502444360385  ] 
dist 24=[1.8975974439064333703 ,17.102577069573907591  ] 
dist 25=[-.02017930988931039633,16.632999324912622611  ] 
dist 26=[-1.5612278218034093411 ,14.973838469282900827  ] 
dist 27=[-3.0022033089519696775 ,14.624746046084576393  ] 
dist 28=[-4.2890826034115901100 ,14.130675776688447530  ] 
dist 29=[-7.0192097651247572158 ,13.988672163403288025  ] 
dist 30=[-8.7451179156027335382 ,2.2565600807043897443 ] 
dist 31=[-10.075502073944465939  ,1.2847345212930270011 ] 
dist 32=[-11.225071611802791382  ,-.85453613162804862086] 
dist 33=[-12.179500489206146174  ,-1.2370294735475535834 ] 
dist 34=[-12.730257606429900361  ,-3.6329600345338883487 ] 
dist 35=[-13.095788960069933512  ,-4.0286727304058334686 ] 
dist 36=[-13.310554390482582152  ,-4.7839971639497930790 ] 
dist 37=[-13.451424066683564695  ,-4.9487261232953906802 ] 
dist 38=[-13.521613727869674990  ,-4.7885558510126929210 ] 
dist 39=[-13.556547295019808116  ,-3.5753593817866591757 ] 
dist 40=[-13.555870883541779240  ,-2.3291000791007065575 ] 
dist 41=[-13.534644544932228956  ,-1.4626029338264988447 ] 
dist 42=[-13.487136573042454173  ,-.70962488627954895515] 
dist 43=[-13.412028071168759391  ,.0838754078232818972 ] 
dist 44=[-13.365264891954303468  ,.8416458644140551278 ] 
dist 45=[-12.835674955991519533  ,1.4521504309999736327 ] 
dist 46=[-5.4416805471576246139 ,2.0712107063746179742 ] 
dist 47=[-3.9727606038747716841 ,2.8632081352223764329 ] 
dist 48=[-3.7462046850443679554 ,3.6267651625307291547 ] 
dist 49=[-1.7387877008276202234 ,4.1323542737136738869 ] 
dist 50=[-1.3804748680208823762 ,4.5455166405867724584 ] 
dist 51=[-1.0053276987399266044 ,4.9402236891954190679 ] 
dist 52=[-.76637921436400087503,5.2925393318498588068 ] 
dist 53=[-.48782299230837105501,5.5365109147376282575 ] 
dist 54=[-.34755463904470775998,5.7476066554482119477 ] 
dist 55=[-.31830814169988228278,5.9686736281565197302 ] 
dist 56=[1.2415287009525947765 ,6.1683227104892934392 ] 
dist 57=[1.1152904930128615361 ,6.2939546803115893408 ] 
dist 58=[.92296068599541824234,6.4569805830064475075 ] 
dist 59=[.65261845287055382082,6.5443080463697500141 ] 
dist 60=[.27435962507701767274,6.5611504596672940805 ] 
dist 61=[-.34847769766693299392,4.7078128135291281254 ] 
dist 62=[-.98496376027024749064,4.8488250489562841132 ] 
dist 63=[-1.4176986032019131257 ,4.9083541838899412179 ] 
dist 64=[-1.7828692117310470283 ,4.9322398637901250645 ] 
dist 65=[-2.1499046713916075585 ,4.9305593021626221999 ] 
dist 66=[-2.4888469465941039400 ,4.8131827357253822813 ] 
dist 67=[-2.7419737446612037373 ,4.7729584983999434078 ] 
dist 68=[-2.9800264240547233829 ,4.7402371917007519442 ] 
dist 69=[-3.2588355210459264913 ,4.7130768306890492815 ] 
dist 70=[-3.5142351007008565081 ,3.9081030620861457729 ] 
dist 71=[-3.6589051122669787490 ,3.7933185180503041000 ] 
dist 72=[-3.7496951656121671501 ,3.5648872701322637258 ] 
dist 73=[-3.7901651809808412587 ,3.5019488993270110424 ] 
dist 74=[-3.8085782689610316601 ,3.2610009386916719788 ] 
dist 75=[-3.8113936916053918164 ,3.2047264419796089946 ] 
dist 76=[-3.8031811770025402480 ,3.0945707560864851610 ] 
dist 77=[-3.7889332077652128983 ,3.0625013109166583133 ] 
dist 78=[-1.1742254484620523836 ,.5276719188384640883 ] 
dist 79=[-1.7120708730169520973 ,.5017406695055468746 ] 
dist 80=[-2.1534987295896652250 ,.0490184696156928435 ] 
dist 81=[-2.5791260595998270490 ,-.0075278141206159948 ] 
dist 82=[-2.9623705604181184799 ,-.1345639686293321885 ] 
dist 83=[-3.2346315087227748093 ,-.15527446868833371904] 
dist 84=[-3.4779805584500827305 ,-.30407860498299468058] 
dist 85=[-3.7458444493146275273 ,-.32872745021291666004] 
dist 86=[-3.9864401899853031259 ,-.37072378723126111212] 
dist 87=[-4.1209423451035543072 ,-.37914618110883413819] 
dist 88=[-4.2036786542249704772 ,-.48300199023639716926] 
dist 89=[-4.2376120355362616395 ,-.49569074422487688708] 
dist 90=[-4.2505529582908429515 ,-.52161208404263048743] 
dist 91=[-4.2494846272180829575 ,-.35588864130488005274] 
dist 92=[-4.2380294766368604801 ,-.07954499470259608625] 
dist 93=[-4.2240334449904960144 ,.20190436391256209706] 
dist 94=[-3.3293602672547100173 ,.392153289263744014  ] 
dist 95=[-3.2777893031018002708 ,.55193872526971611153] 
dist 96=[-3.2644002159066922119 ,.71183845636342727653] 
dist 97=[-3.2525802373711607778 ,.9055459053776371684 ] 
dist 98=[-3.1404595321573700989 ,1.2834340621933319452 ] 
dist 99=[-3.1082323934856254382 ,1.5750695656042443979 ] 
dist 100=[-3.0647796491954478418 ,1.8593905704364654727 ] 
dist 101=[-3.0456468852794278837 ,2.2081080333710991995 ] 
dist 102=[-2.5310282447151002651 ,2.5375499860796786248 ] 
dist 103=[-2.4566039324445372528 ,2.7449495159723266013 ] 
dist 104=[-2.2997689325292469094 ,2.9027381945967113545 ] 
dist 105=[-2.2543180524280104003 ,3.0341829094314317350 ] 
dist 106=[-2.0645736594409957326 ,3.1387722434490149986 ] 
dist 107=[-2.0252529696504931933 ,3.1893894077750399268 ] 
dist 108=[-1.9220252943976921208 ,3.2130285719461032226 ] 
dist 109=[-1.9010662945154794104 ,3.2144055497075180675 ] 
dist 110=[-.65656725728826979214,3.1670725105260845092 ] 
dist 111=[-.8214273780761571338 ,3.1520395398785695668 ] 
dist 112=[-.9839909124008298375 ,3.1776626842410431013 ] 
dist 113=[-1.1325137439470579082 ,3.2050996162630775819 ] 
dist 114=[-1.2413335940408085911 ,3.2168426492308624450 ] 
dist 115=[-1.3418219740963851511 ,3.2127544155127541021 ] 
dist 116=[-1.4570817550171504477 ,3.1989953423942626027 ] 
dist 117=[-1.5621650920277610067 ,3.1881955394307407889 ] 
dist 118=[-1.6220392858807408039 ,3.2025695618668586278 ] 
dist 119=[-1.6601727564535237129 ,3.3102550281907698273 ] 
dist 120=[-1.6785011022279108848 ,3.3788293898322351382 ] 
dist 121=[-1.6882076163155493073 ,3.4119897671306193868 ] 
dist 122=[-1.6919365904191943371 ,3.4283974259605960702 ] 
dist 123=[-1.6919541747406042555 ,3.4300970718341066450 ] 
dist 124=[-1.6868518786102763029 ,3.4213293520711406977 ] 
dist 125=[-.48254493659739664509,3.4121472466085964136 ] 
dist 126=[-.90132744339840794021,3.0216703823147054470 ] 
dist 127=[-1.2805512427135273791 ,3.0016985848161977922 ] 
dist 128=[-1.5951459874267740410 ,2.9324462385084723996 ] 
dist 129=[-1.9039965554677053249 ,2.9165471134228104686 ] 
dist 130=[-2.1856968146911718817 ,2.7280169302420985454 ] 
dist 131=[-2.3919193839333037202 ,2.6831399176588475549 ] 
dist 132=[-2.5824634595527310068 ,2.6345174264513123417 ] 
dist 133=[-2.8015865288346422854 ,2.6105053346452212360 ] 
dist 134=[-3.0014845927117060230 ,2.0001439631936226031 ] 
dist 135=[-3.1152903796853933779 ,1.9154804201195144312 ] 
dist 136=[-3.1879069555850342747 ,1.7441644688446241642 ] 
dist 137=[-3.2233898340642734765 ,1.6972673248156828425 ] 
dist 138=[-3.2421770906783939270 ,1.5168871376498654297 ] 
dist 139=[-3.2481453551814881376 ,1.4770594978700793909 ] 
dist 140=[-3.2458857810613421839 ,1.3952262462069136242 ] 
dist 141=[-3.2363967442585844222 ,1.3712192136232446590 ] 
dist 142=[-.93450165563520596016,.91120215021017441318] 
dist 143=[-.93019753989622885225,.95376275831443272508] 
dist 144=[-.80489621176907658739,.99053467721261615946] 
dist 145=[-.78567112121233170605,1.0092712158630717042 ] 
dist 146=[-.74415569970988648716,1.0184793709341766085 ] 
dist 147=[-.73150527049522480664,1.0199729539761813670 ] 
dist 148=[-.675720365635970123  ,1.0112130666391713780 ] 
dist 149=[-.66412273227467007353,1.0059018866013027605 ] 
dist 150=[-.63145516377127264549,1.0212569591148554750 ] 
dist 151=[-.62592275276842350913,1.0489906222290181446 ] 
dist 152=[-.17610122734687079342,1.0683851703273507789 ] 
dist 153=[-.13297940457355142056,1.0814877333786921210 ] 
dist 154=[-.04186599259719509823,1.0895553501024648000 ] 
dist 155=[-.01942984320976410274,1.0897757642136893225 ] 
dist 156=[.07107483113889387622,1.0846917183394991241 ] 
dist 157=[.08797593511571858477,1.0796116995656101051 ] 
dist 158=[.11988280821135547192,.62109838409095963424] 
dist 159=[.12709662982492516788,.57963200554959556654] 
dist 160=[.07669716853121576703,.51429166382841097566] 
dist 161=[-.00284326270432153713,.58425830480304531257] 
dist 162=[-.07693488135678147035,.64577074286939363478] 
dist 163=[-.16296862247650652267,.71182830150666390468] 
dist 164=[-.25010751593080081379,.77574527669180070116] 
dist 165=[-.3286124454479291845 ,.82871151528532577766] 
dist 166=[-.41584519417392734115,.88379076090804733389] 
dist 167=[-.5378231644935765621 ,.95613679536803000759] 
dist 168=[-.65745884633655071439,1.0244544201572460087 ] 
dist 169=[-.73534315258125438928,1.0634547974746347704 ] 
dist 170=[-.79757614826065590984,1.0884304910261982835 ] 
dist 171=[-.85474000843760953261,1.1007751652408081052 ] 
dist 172=[-.90428416102805946875,1.1072719410214858901 ] 
dist 173=[-.93610323111389057591,1.1089091437391094138 ] 
dist 174=[-.96103846159197102696,1.1072923663684142468 ] 
dist 175=[-.98310579820327136565,1.1040585577558544902 ] 
dist 176=[-1.0001426167046000210 ,.9703329570548910578 ] 
dist 177=[-1.0049992933465677273 ,.94938167878506528471] 
dist 178=[-1.0051863557652281441 ,.90962353809889828779] 
dist 179=[-1.0035839783268880165 ,.89828882158280181398] 
dist 180=[-.97028473878292532934,.85387463048196918975] 
dist 181=[-.96028523349704545792,.84226585513356542857] 
dist 182=[-.95153699349482301611,.81823309631409973942] 
dist 183=[-.94529900149848729359,.81025363011244897466] 
dist 184=[-.93138702670558906129,.69855771475213172891] 
dist 185=[-.93737708398036240087,.77763635277679222471] 
dist 186=[-.93849415744883639995,.83782233349557115783] 
dist 187=[-.93694330145563550383,.88794852298843259702] 
dist 188=[-.9091532954547842059 ,.92816979986781799973] 
dist 189=[-.90039856767972082486,.94882391279965182077] 
dist 190=[-.89199075737588586257,.9597008706963341824 ] 
dist 191=[-.88642716120967761922,.96151382725973745488] 
dist 192=[-.72633183881408242738,.93759326133487926378] 
dist 193=[-.70328199865943542166,.93039529011142125135] 
dist 194=[-.65730982089523513356,.92268182528412504999] 
dist 195=[-.6445174460941329404 ,.91770054035853797084] 
dist 196=[-.59470330987085116451,.90526055282966904853] 
dist 197=[-.5831853858692233619 ,.89921587176060324714] 
dist 198=[-.55900050546622184614,.88819269072203108354] 
dist 199=[-.55150468936517498587,.88151716534757543499] 
dist 200=[-.38875927035471756885,.89186785253457901222] 
dist 201=[-.3829754891291622395 ,.89545394096548142894] 
dist 202=[-.32533008410535647654,.89494486788454375416] 
dist 203=[-.31363451788886173265,.89312065994441005352] 
dist 204=[-.29929952881538604632,.88216887691274064622] 
dist 205=[-.29395367333259592333,.87852215006527842283] 
dist 206=[.13385855076059144599,.77444128501734150014] 
dist 207=[.0319114224814944719 ,.84788303096852354644] 
dist 208=[-.0560702232649783704 ,.91568949583144128595] 
dist 209=[-.1479897890901279465 ,.95562538740277537953] 
dist 210=[-.2354020862916496253 ,.98279500147908748925] 
dist 211=[-.30539543754237508224,.99964717651955239016] 
dist 212=[-.37603599661648375784,1.0104358255218192179 ] 
dist 213=[-.46603303576111876362,1.0134040647427181454 ] 
dist 214=[-.55270819535642771573,1.0118268066757934645 ] 
dist 215=[-.61009121824311820437,1.0094218941694353238 ] 
dist 216=[-.6570110341907991357 ,-.06044093215595177913] 
dist 217=[-.70192605126373549672,-.11686544353270094633] 
dist 218=[-.74212415741495286363,-.24139977600737280886] 
dist 219=[-.77021880572962180604,-.21422329260825266575] 
dist 220=[-.79483792608590066712,-.15884830242590672979] 
dist 221=[-.82116675476419082217,-.06803998063124154074] 
dist 222=[-.84385789142887314963,.02532380044937484486] 
dist 223=[-.85395825818530570788,.09089819384498925104] 
dist 224=[-.85798006287868926533,.14866485930872032393] 
dist 225=[-.8572708339592960939 ,.21086828602727899237] 
dist 226=[-.84155432442110951355,.27115405882209007289] 
dist 227=[-.83588723641860101052,.32126790033749979224] 
dist 228=[-.84842001006918234585,.3735253013852450368 ] 
dist 229=[-.8512902231589031013 ,.44236730491386877622] 
dist 230=[-.84983721716693202351,.50974506902823445937] 
dist 231=[-.84917433036942279431,.5561590490620265896 ] 
dist 232=[-.81200186130189620039,.59610430918730640897] 
dist 233=[-.80434844468213487954,.63766518541003755291] 
dist 234=[-.77976737620920126463,.67708566453239759661] 
dist 235=[-.77495533787501055953,.70848905546041959086] 
dist 236=[-.71473047931536773722,.74003838905124060007] 
dist 237=[-.70096952818652372915,.78004289654697700102] 
dist 238=[-.68677070915436607446,.8168939033439084919 ] 
dist 239=[-.68039443712474315165,.8358570922310850311 ] 
dist 240=[-.50129226776536474406,.84600881573675584562] 
dist 241=[-.47700441521132529869,.84772328126134564094] 
dist 242=[-.42796529554204639252,.84034770491557761124] 
dist 243=[-.41475031896317411194,.83734156594550515749] 
dist 244=[-.36502005551631271339,.8345397610765164445 ] 
dist 245=[-.3540403366838639421 ,.81722769768070020697] 
dist 246=[-.33311380312346164089,.69544361465740946998] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 2, 1, 0, 1] 
dist 0=[51.534659203108260032  ,51.534659203108260032  ] 
dist 1=[51.299708451068217659  ,51.748418258226601890  ] 
dist 2=[50.930907352169080445  ,52.032289914905541580  ] 
dist 3=[50.303385723225062552  ,52.289335657996929619  ] 
dist 4=[49.035092409724081302  ,52.395987186090837973  ] 
dist 5=[47.486325033079391045  ,52.412520126167203404  ] 
dist 6=[45.738640528042223450  ,52.362042367799824039  ] 
dist 7=[43.506021476232802454  ,52.138177458965678237  ] 
dist 8=[40.020351724277731919  ,52.038275932566511471  ] 
dist 9=[36.473523279574171880  ,51.634140225221797100  ] 
dist 10=[33.996549272732574769  ,51.522041346161780114  ] 
dist 11=[31.822431030800503635  ,50.250844348415413034  ] 
dist 12=[29.485020377465366058  ,49.928397544872824153  ] 
dist 13=[27.213420080482182263  ,48.673472084756547096  ] 
dist 14=[25.301966633511636709  ,46.422838433111813700  ] 
dist 15=[23.282209224237962996  ,32.197215864468744542  ] 
dist 16=[20.577687858567691849  ,31.428622366379613476  ] 
dist 17=[17.894705947369336565  ,30.556277753579897136  ] 
dist 18=[15.960788184563164565  ,30.355369183809592374  ] 
dist 19=[14.198204185270116791  ,23.187527646878824812  ] 
dist 20=[12.199319492542343757  ,22.281399381970929874  ] 
dist 21=[10.191357215615480876  ,20.453301711548650189  ] 
dist 22=[8.3921419109723543541 ,19.981637027134690351  ] 
dist 23=[6.3927578676344801956 ,18.296392590685512150  ] 
dist 24=[3.5844086488094888670 ,17.939030620619728393  ] 
dist 25=[.82841966794634227197,17.388626200225597168  ] 
dist 26=[-.96189422708370457975,17.241406013550910823  ] 
dist 27=[-2.3968101551913682818 ,12.881901470255909822  ] 
dist 28=[-3.7325950492124406218 ,12.396516752509343421  ] 
dist 29=[-4.9114159477898272241 ,10.477487245772856040  ] 
dist 30=[-5.7667481251447467926 ,9.4706402388253361658 ] 
dist 31=[-8.4357133357105026170 ,-1.7866383443499855164 ] 
dist 32=[-10.114629903162685536  ,-2.2432380472210471907 ] 
dist 33=[-11.399035149411217550  ,-3.0699203798828529475 ] 
dist 34=[-12.491528183684887823  ,-3.2413573997476873343 ] 
dist 35=[-13.385672823743020824  ,-5.1427974456144481825 ] 
dist 36=[-13.877653768953566034  ,-5.4096688863041570316 ] 
dist 37=[-14.173941136386254808  ,-5.7054952308265818095 ] 
dist 38=[-14.286615749209787847  ,-5.1940162440109098518 ] 
dist 39=[-14.328602350797657248  ,-4.3758294392479007501 ] 
dist 40=[-14.342364870227627473  ,-3.0483408531311863142 ] 
dist 41=[-14.340891761314882289  ,-1.6918319313027775911 ] 
dist 42=[-14.321307378147969544  ,-.75768140204298383028] 
dist 43=[-14.293652637935779313  ,.04497088729511266953] 
dist 44=[-14.259581704704280575  ,.87691082501125535286] 
dist 45=[-14.214956151643248267  ,1.6632189695824146573 ] 
dist 46=[-14.160458394564767280  ,2.2838570646622101957 ] 
dist 47=[-5.9047396104199130874 ,2.9016591505397895814 ] 
dist 48=[-5.2218408421954649383 ,3.6767194372859565608 ] 
dist 49=[-3.6013122340080549647 ,4.4168830084218179984 ] 
dist 50=[-3.3589544593986569790 ,4.8954344103193662005 ] 
dist 51=[-1.3846514453371765843 ,5.2738101465024046875 ] 
dist 52=[-1.2889313815368104024 ,5.6141713260132822300 ] 
dist 53=[-.79645633809770297803,5.9038061694193505726 ] 
dist 54=[-.71282033551601994188,6.0797121110423111359 ] 
dist 55=[-.52377149410751569336,6.2057893757714260194 ] 
dist 56=[-.49558022542467926856,6.2965004933834787964 ] 
dist 57=[-.58669190646688038565,6.3663164307611684758 ] 
dist 58=[-1.0674594921822478582 ,6.4089924114517823700 ] 
dist 59=[-1.5583799444248953103 ,6.4397074887222686884 ] 
dist 60=[-1.8896455645177055950 ,6.4618210286678884106 ] 
dist 61=[-2.1662091213832650375 ,6.4764246418820134828 ] 
dist 62=[-2.4389945805117894932 ,6.4771724057647197726 ] 
dist 63=[-2.6872013058152421846 ,5.6097500965877822125 ] 
dist 64=[-2.8657313907104662057 ,5.6448886306146563999 ] 
dist 65=[-3.0266317208700944239 ,5.6504777755821665060 ] 
dist 66=[-3.2044759183129535722 ,5.6355130380587896910 ] 
dist 67=[-3.3618301192972430049 ,5.3233314945857722184 ] 
dist 68=[-3.4410014116073454006 ,5.2618741998285165021 ] 
dist 69=[-3.4825756519686795545 ,5.1216168728877387578 ] 
dist 70=[-3.4900838772149491969 ,5.0725681615535048780 ] 
dist 71=[-3.4383778454001641596 ,4.8318274534371778198 ] 
dist 72=[-3.4215930414700372023 ,4.7763516633658266364 ] 
dist 73=[-3.4083108590592978267 ,4.6294373068967108678 ] 
dist 74=[-3.3960943290998902389 ,4.5864196539854470299 ] 
dist 75=[-1.1372554841142477526 ,2.9021772696918648245 ] 
dist 76=[-1.4026616189836983344 ,2.8471864211948592186 ] 
dist 77=[-1.6445403728496774642 ,2.7491095492708382654 ] 
dist 78=[-1.8213464658516582046 ,2.7232276308032506135 ] 
dist 79=[-1.9845094874661129554 ,2.2123159442269052310 ] 
dist 80=[-2.1719627405437137720 ,2.1948208346973291019 ] 
dist 81=[-2.3431261936272423784 ,1.7896814594309167700 ] 
dist 82=[-2.4412777101354949490 ,1.7319870799982001205 ] 
dist 83=[-2.5049401148193653044 ,1.6050676826042155333 ] 
dist 84=[-2.5384371427410482156 ,1.5676339003514030184 ] 
dist 85=[-2.7690104381483451546 ,1.4073193912929690206 ] 
dist 86=[-3.0814040312153766017 ,1.3749939912431985827 ] 
dist 87=[-3.3714186159665812237 ,1.2949989916020401151 ] 
dist 88=[-3.5460640374474927991 ,1.2771571833518638356 ] 
dist 89=[-3.6698779053819198649 ,.29055683360514369236] 
dist 90=[-3.7569528834764436859 ,.19639371205208117877] 
dist 91=[-3.8186129463646527091 ,-.02626585939829076702] 
dist 92=[-3.8409592007612626509 ,-.05914596075796221358] 
dist 93=[-3.8436400778630169560 ,-.3616366545591406385 ] 
dist 94=[-3.8360078341774592178 ,-.23829387675801244445] 
dist 95=[-1.8051856536957151223 ,.19195399711759631435] 
dist 96=[-1.7843121805050895013 ,.48503558673647092135] 
dist 97=[-1.4731638144456549875 ,.73375125016592274608] 
dist 98=[-1.4284770874462398672 ,.98694577284457728009] 
dist 99=[-1.3130340611174369247 ,1.2236771833579080881 ] 
dist 100=[-1.2963098147665433011 ,1.4067002134694758088 ] 
dist 101=[-1.2747687284480295299 ,1.5854974369477284142 ] 
dist 102=[-1.2677959978036691948 ,1.8053873611740257956 ] 
dist 103=[-1.2465823634400775145 ,2.0135811845073110722 ] 
dist 104=[-1.2383089861094865508 ,2.1457063842795908692 ] 
dist 105=[-1.2267774495388903687 ,2.2475299570809339658 ] 
dist 106=[-1.2098699762503947130 ,2.3347875296897539254 ] 
dist 107=[-.4715561138002866294 ,2.4061985915434734413 ] 
dist 108=[-.44772076705763443654,2.4447879609678751686 ] 
dist 109=[-.37061476856805671736,2.4668972303910976433 ] 
dist 110=[-.35173742299597152471,2.4725662017210887397 ] 
dist 111=[-.63928567985193096193,2.4680832325134248796 ] 
dist 112=[-.92230861423454820409,2.4972890738956439955 ] 
dist 113=[-1.1585268672778180538 ,2.5554939585194550858 ] 
dist 114=[-1.3924790156184003891 ,2.5875257186784562250 ] 
dist 115=[-1.6069367725734321736 ,2.6066188279356593136 ] 
dist 116=[-1.7653568591950215849 ,2.6131483097071783747 ] 
dist 117=[-1.9129938221862725213 ,2.6111514528902609262 ] 
dist 118=[-2.0844162437717615788 ,2.5863689450513055623 ] 
dist 119=[-2.2413369763855816742 ,2.3980269267099090656 ] 
dist 120=[-2.3310994276471749622 ,2.2470524047714599734 ] 
dist 121=[-2.3887999685694070582 ,1.5795437807805961806 ] 
dist 122=[-2.4177667044424379105 ,1.5435025525179243080 ] 
dist 123=[-2.4335169868703494765 ,1.4002860125080154350 ] 
dist 124=[-2.4384732785958306880 ,1.3696174031618567736 ] 
dist 125=[-2.4364488528649072943 ,1.3000432904837967559 ] 
dist 126=[-2.4291957406308731169 ,1.2782267658985570828 ] 
dist 127=[-1.2814691770296662121 ,.07013733170322135050] 
dist 128=[-1.2834158547868248751 ,-.03822985786762861143] 
dist 129=[-1.2991901472756307668 ,-.27142022960436403545] 
dist 130=[-1.5148018036286942550 ,-.32089032952592579959] 
dist 131=[-1.7098799430447685656 ,-.56286672137235478992] 
dist 132=[-1.8499882935118334783 ,-.60416796687769371375] 
dist 133=[-1.9767408909582707896 ,-.66057731588986492508] 
dist 134=[-2.1185140083586016763 ,-.52470387410306914982] 
dist 135=[-2.2457368489019440567 ,-.35711525385715591787] 
dist 136=[-2.3144121852049883670 ,-.10239589086818439888] 
dist 137=[-2.3536414720244623978 ,.1527663427897156911 ] 
dist 138=[-2.3633139813324282331 ,.32212394535026676276] 
dist 139=[-2.3609631679740479210 ,.46108248886932132648] 
dist 140=[-2.3601410176974593952 ,.59491159513081671636] 
dist 141=[-2.3594614353877883012 ,.71522148912572005322] 
dist 142=[-2.3588034416527137012 ,.80022036129205913164] 
dist 143=[-1.9847123302764353808 ,.87564553264379588194] 
dist 144=[-2.0014438917465555620 ,.95774399832523401119] 
dist 145=[-2.0067369218220527528 ,1.0325450440662390347 ] 
dist 146=[-2.0053226648434817792 ,1.0788441584619144085 ] 
dist 147=[-1.9502069643465363394 ,1.1131422764735300387 ] 
dist 148=[-1.9326449849891515192 ,1.1672323507456576411 ] 
dist 149=[-1.9191390786500804364 ,1.3271703469171899498 ] 
dist 150=[-1.9076295394207102302 ,1.5205874774853219267 ] 
dist 151=[-1.5664076532084577378 ,1.7019716687489794229 ] 
dist 152=[-1.5175803788384283510 ,1.8138844805783357146 ] 
dist 153=[-1.4226679273292631931 ,1.8963795134152039453 ] 
dist 154=[-1.3968592301745192314 ,1.9603483031866931664 ] 
dist 155=[-1.3003858523936012702 ,2.0084251811206957006 ] 
dist 156=[-1.2767829960897349434 ,2.0274837413637604963 ] 
dist 157=[-1.2334622519618498108 ,2.0341092263986562782 ] 
dist 158=[-1.2211106957246496609 ,2.0325617745640863530 ] 
dist 159=[-.11321447032407577042,1.9437493263467965952 ] 
dist 160=[-.17216165407030179072,1.9264556747849077355 ] 
dist 161=[-.23333168406539415335,1.8892715225965396295 ] 
dist 162=[-.28130915161455925805,1.8866315877714693560 ] 
dist 163=[-.32882549138761378519,1.8494856470583707690 ] 
dist 164=[-.38815879126494963131,1.8360100540348848297 ] 
dist 165=[-.45058104013151162611,1.8147703082393037942 ] 
dist 166=[-.51043019236429085509,1.8057602357143737492 ] 
dist 167=[-.57989256911538929617,1.7676041120728485098 ] 
dist 168=[-.68069181969355271931,1.8518398766020758404 ] 
dist 169=[-.77976787190122431832,1.9100253129482636386 ] 
dist 170=[-.84235280803121186405,1.9478715800110602861 ] 
dist 171=[-.89023155298998154051,1.9736519237616652054 ] 
dist 172=[-.93060411742179580649,1.9836785771977660128 ] 
dist 173=[-.96309789582571294009,1.9840814280220765258 ] 
dist 174=[-.97952717830492314671,1.9811028407138215398 ] 
dist 175=[-.98735442928332198963,1.9414401660099579705 ] 
dist 176=[-.98855183229706163941,1.9411854983409889569 ] 
dist 177=[-1.0603389080869525080 ,1.9258751127076102370 ] 
dist 178=[-1.2442509333073953661 ,1.9198602561143042745 ] 
dist 179=[-1.4121487257245023512 ,1.8359154004594344946 ] 
dist 180=[-1.5352964700203620654 ,1.8133919028942133297 ] 
dist 181=[-1.6493062233326292241 ,1.7906426009894075239 ] 
dist 182=[-1.7807309872620778037 ,1.7775338964678209790 ] 
dist 183=[-1.9007645760868425229 ,1.4213251375475374090 ] 
dist 184=[-1.9693057240920341039 ,1.3708873968655369247 ] 
dist 185=[-2.0132910040563820062 ,1.2700513435895479012 ] 
dist 186=[-2.0353064310688757312 ,1.2422748893464228048 ] 
dist 187=[-2.0467945819240001896 ,1.1352398977789533532 ] 
dist 188=[-2.0487570148993908342 ,1.1107819290103875629 ] 
dist 189=[-2.0441240718330166774 ,1.0607053692589931560 ] 
dist 190=[-2.0386254724386798750 ,1.0456640839856694083 ] 
dist 191=[-.21120467722719237185,.89429776413935221965] 
dist 192=[-.20109362661173412518,.95370466170710472159] 
dist 193=[-.08590476377348175274,1.0067404182576343140 ] 
dist 194=[-.06880953596823906149,1.0366184035033132155 ] 
dist 195=[-.03662779183180651272,1.0552649886410496089 ] 
dist 196=[-.02907574729486539783,1.0634687908778713737 ] 
dist 197=[-.00721236132511679352,1.0664558755095660934 ] 
dist 198=[-.00362074526153245334,1.0644950193365996939 ] 
dist 199=[-.00543304179890640427,1.0590378618799899413 ] 
dist 200=[-.01508989069078194757,1.0646893133243434350 ] 
dist 201=[-.02745973466399403147,1.0800498008964392212 ] 
dist 202=[-.04010092439612271863,1.0845373835013665747 ] 
dist 203=[-.07397620857060650683,1.0842066864825957320 ] 
dist 204=[-.17682795702382945438,1.0808513057129495575 ] 
dist 205=[-.27378785280322500835,1.0737802869820952946 ] 
dist 206=[-.35006244752148704401,1.0696076648571788110 ] 
dist 207=[-.42580198579105035493,.99532496451959714111] 
dist 208=[-.52062622572178930501,.996145474347690756  ] 
dist 209=[-.61115666238752529419,.98497680384756403422] 
dist 210=[-.66975812287789313817,.98014150209245610788] 
dist 211=[-.71619858597912691595,.96681693676376221844] 
dist 212=[-.75819026950898891855,.96053821828321035818] 
dist 213=[-.79411119209601067995,.9241708300352962571 ] 
dist 214=[-.81632107048746848815,.91463105631354597729] 
dist 215=[-.83274150647651506355,.89275453738998152426] 
dist 216=[-.84555454275337972075,.88472757675576518459] 
dist 217=[-.85476742850078838001,.1383505638528540303 ] 
dist 218=[-.8568180571966025115 ,.12197153705529953764] 
dist 219=[-.87888263310396930515,.06216353005415962415] 
dist 220=[-.91523401500828491138,.05018771865804768483] 
dist 221=[-.94393455147668569392,.02982229235337997288] 
dist 222=[-.95733519781593270394,.02523068441989335127] 
dist 223=[-.9633606116078294897 ,-.30938676881754424194] 
dist 224=[-.96315596460603699128,-.33790750791804591019] 
dist 225=[-.946783059362124755  ,-.39009447211026583128] 
dist 226=[-.9556417835523588388 ,-.36473638782317848195] 
dist 227=[-.98158508116009966989,-.31258092823419931415] 
dist 228=[-1.0010280957229895641 ,-.23575065845183146584] 
dist 229=[-1.0148058083896129693 ,-.14892043131421669212] 
dist 230=[-1.0181354231276260586 ,-.05684986550016954202] 
dist 231=[-1.0172066139805925603 ,.05671611654303830654] 
dist 232=[-1.0139882458735373175 ,.22934494457340459836] 
dist 233=[-.81090047617778344831,.40204983115058571625] 
dist 234=[-.80550950630455892762,.51591993802041033172] 
dist 235=[-.79012079399738142256,.60852225362257814309] 
dist 236=[-.78350322186756550818,.69633869176810520517] 
dist 237=[-.70726921371969350262,.77438049866639880227] 
dist 238=[-.65531516068772420935,.82796858975970536344] 
dist 239=[-.3841286476838243752 ,.87392135461895288461] 
dist 240=[-.37543676007780790787,.92148841682774331377] 
dist 241=[-.21784887740183249105,.96334436007687627264] 
dist 242=[-.19682064465936036673,.98650125037536768138] 
dist 243=[-.14695950357993477907,1.0004027035846222768 ] 
dist 244=[-.13882060483335679527,1.0053140813954546525 ] 
dist 245=[-.07005196461039569133,1.0056735015165250309 ] 
dist 246=[-.05757712181145857050,1.0032863693734140064 ] 
dist 247=[-.03963631817528360407,.99515273688381606345] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 2, 1, 0, 1, 2] 
dist 0=[56.152159282846121548  ,56.152159282846121548  ] 
dist 1=[55.848526301125979168  ,56.234843299149978945  ] 
dist 2=[55.266087343209771163  ,56.261370046651100423  ] 
dist 3=[54.189225827283875851  ,56.227482315181325481  ] 
dist 4=[52.957629149640833099  ,56.141518258412562961  ] 
dist 5=[51.757193920956917961  ,55.929261448430356673  ] 
dist 6=[50.346894323038781350  ,55.809250204600031217  ] 
dist 7=[48.276974160415257647  ,54.944910844090627083  ] 
dist 8=[45.934927195962803903  ,52.539520225060707619  ] 
dist 9=[43.437682458375833113  ,51.778857769722442965  ] 
dist 10=[40.341721949602110675  ,51.538144197241714312  ] 
dist 11=[35.608313813681827586  ,50.934665361158830072  ] 
dist 12=[30.829398390586991175  ,50.732454974638864383  ] 
dist 13=[27.551597409845696193  ,50.490771326101593021  ] 
dist 14=[24.736932589700274611  ,49.070208207888168746  ] 
dist 15=[21.807620270055643893  ,39.653911128201611001  ] 
dist 16=[19.018595904875308081  ,32.211099824664648739  ] 
dist 17=[16.764058779253219082  ,31.248689518483518542  ] 
dist 18=[14.462135607019016037  ,29.343451965904005619  ] 
dist 19=[11.483470514386984504  ,28.850707639327819506  ] 
dist 20=[8.5758000517487898067 ,27.103357268184684021  ] 
dist 21=[6.5572355172879186920 ,26.709801110245674600  ] 
dist 22=[4.7959458327745826646 ,26.141390598289781196  ] 
dist 23=[2.9156332564935415439 ,25.967995380412309618  ] 
dist 24=[1.0926489953055151040 ,10.798241282472788815  ] 
dist 25=[-.44005573043594380299,9.3250935385096388260 ] 
dist 26=[-2.0616864980507913925 ,9.0215679873268995935 ] 
dist 27=[-4.2407915016862007903 ,7.6490067110547044789 ] 
dist 28=[-6.3456100850013158200 ,7.4118924021825944280 ] 
dist 29=[-7.6705893070542226614 ,7.0605034253966287772 ] 
dist 30=[-8.6862506306047182366 ,6.7266548504022274043 ] 
dist 31=[-9.5548471029442692396 ,-.74607647111288273196] 
dist 32=[-10.270168015831708407  ,-4.1950320407389564524 ] 
dist 33=[-10.673400013542585489  ,-4.6341776336108104162 ] 
dist 34=[-11.079322222478865628  ,-5.4400926574345614005 ] 
dist 35=[-11.803825502251971778  ,-5.6074062713749714797 ] 
dist 36=[-12.191208865877230344  ,-5.9678310969890631737 ] 
dist 37=[-12.410816668821337990  ,-5.9165600506720748694 ] 
dist 38=[-12.464668478042100828  ,-5.6869036900083530965 ] 
dist 39=[-12.443306117094524006  ,-5.1578435371447206990 ] 
dist 40=[-12.427793509754130029  ,-4.5790103319633894425 ] 
dist 41=[-12.408146517893796495  ,-4.1505079165560105099 ] 
dist 42=[-12.380327557508142552  ,-3.7523011911924166011 ] 
dist 43=[-12.351094276261455508  ,-3.2937897197912301364 ] 
dist 44=[-12.325451977798240990  ,-2.5249189072866025618 ] 
dist 45=[-12.298013986284530392  ,-1.2904479277919057809 ] 
dist 46=[-12.261239199276756499  ,-.2508772357851954257 ] 
dist 47=[-4.9998082088543253959 ,.79518294599553222293] 
dist 48=[-4.4058697834409666663 ,1.7660851249412816345 ] 
dist 49=[-2.9966516859641941634 ,2.5056926924066141112 ] 
dist 50=[-2.7886420404588400521 ,3.2180663695542253098 ] 
dist 51=[-2.0367731944008907062 ,4.0803112559234062692 ] 
dist 52=[-1.9926300405424811043 ,4.8908014960093087202 ] 
dist 53=[-2.0105677284939272915 ,5.3965741490994385172 ] 
dist 54=[-2.0627230484918139583 ,5.7764018645358145420 ] 
dist 55=[-2.1733496837088012040 ,6.0840733124811444173 ] 
dist 56=[-2.2897929743176376149 ,6.3294048315158851260 ] 
dist 57=[-2.3651300187885643280 ,6.4603701113701272439 ] 
dist 58=[-2.4232756091129771569 ,6.5327435919270558750 ] 
dist 59=[-2.4713396062355028392 ,6.5442220650122325908 ] 
dist 60=[-2.5076133604935427536 ,6.1662919528299965780 ] 
dist 61=[-2.5187816015989457627 ,6.0996110338859362749 ] 
dist 62=[-2.5180834482700170542 ,5.9970340022081730930 ] 
dist 63=[-2.5104225638258868083 ,5.4759877060778301682 ] 
dist 64=[-2.4380994248362149147 ,5.5255895999481095202 ] 
dist 65=[-2.4175669746044260312 ,5.5307433337875460456 ] 
dist 66=[-2.3562716070846859722 ,5.5118918620901212640 ] 
dist 67=[-2.3333827454182517789 ,5.4886102241864641086 ] 
dist 68=[-2.1775311691485116732 ,5.3176201232970653905 ] 
dist 69=[-2.1380841379714761815 ,5.2668459892631064000 ] 
dist 70=[-2.0715843667319009982 ,5.1851521825499210183 ] 
dist 71=[-2.0503629217227669898 ,5.1549366388718249699 ] 
dist 72=[-.14209671456374464194,2.9254276104410458011 ] 
dist 73=[-.47791847591749764364,2.7069740209109741521 ] 
dist 74=[-.87167305278568991714,2.6509252607140042499 ] 
dist 75=[-1.4479254772475071360 ,2.4604733727529612206 ] 
dist 76=[-2.0171140256358787616 ,2.4114982892171026352 ] 
dist 77=[-2.3826911127214642743 ,2.3654487018155141203 ] 
dist 78=[-2.6695330647745108419 ,2.3531258679590384479 ] 
dist 79=[-2.9244116471400530551 ,2.1664726083626378284 ] 
dist 80=[-3.1396772132307611677 ,2.1425252213271496774 ] 
dist 81=[-3.2683943967933023280 ,2.1320647884247950150 ] 
dist 82=[-3.3586415536806529762 ,2.1015785035978092234 ] 
dist 83=[-3.4203653691790593757 ,2.0873033239164893943 ] 
dist 84=[-3.4652135370672015112 ,2.0029228282195977994 ] 
dist 85=[-3.4880851578474704302 ,1.9824125662951748064 ] 
dist 86=[-3.4994342275848377041 ,1.9274396848862351257 ] 
dist 87=[-3.4982304716236640797 ,1.9087079506691478586 ] 
dist 88=[-3.4891620128455744394 ,1.7929098195627722152 ] 
dist 89=[-3.4773014758842574043 ,1.7648339538286706115 ] 
dist 90=[-3.4440720674790868639 ,1.7139641432647993017 ] 
dist 91=[-3.4263148724103582749 ,1.6986853738462823692 ] 
dist 92=[-3.2700391794327399479 ,1.3592615148346276556 ] 
dist 93=[-3.2950551826517830750 ,1.3100300657638424827 ] 
dist 94=[-3.2966071426853236956 ,1.1919488142466824768 ] 
dist 95=[-2.9086975363009991095 ,1.1639436288296001825 ] 
dist 96=[-2.7408255731001270218 ,.98294029732356282199] 
dist 97=[-2.7083402453078929176 ,.94576727598375905015] 
dist 98=[-2.6371257863422462823 ,.87773604986860834067] 
dist 99=[-2.6127450326044444825 ,1.0587157851804060938 ] 
dist 100=[-2.4948224488652473648 ,1.2387613922624286856 ] 
dist 101=[-2.4679649164702790556 ,1.4126097930261053930 ] 
dist 102=[-2.3896560578154030032 ,1.6235516705574876436 ] 
dist 103=[-2.3725586750569909403 ,1.8218287318091836585 ] 
dist 104=[.30864682720892754348,1.9451378273315945213 ] 
dist 105=[.31259673339453186604,2.0372483854176436243 ] 
dist 106=[.29340198302706174139,2.1110092962394030621 ] 
dist 107=[.23789967273010646371,2.1683376273199641759 ] 
dist 108=[.17300298198520534437,2.3540855577301660776 ] 
dist 109=[.11631043797512263899,2.4955002300747525628 ] 
dist 110=[.05497738452863755088,2.6001346810825743622 ] 
dist 111=[-.1577594662238245917 ,2.6822149484721553756 ] 
dist 112=[-.39094017189750756514,2.7437571037294638221 ] 
dist 113=[-.58981794469094616958,2.7664032472627409055 ] 
dist 114=[-.79374460606587363603,2.7736471709272650061 ] 
dist 115=[-.98519258412491760717,2.7736544597944175662 ] 
dist 116=[-1.1342727383819175734 ,2.6866609741871321635 ] 
dist 117=[-1.2808042723893381380 ,2.6653974108402948992 ] 
dist 118=[-1.4620826685060157008 ,2.5804242650102450549 ] 
dist 119=[-1.6339254934539385468 ,2.4300529944570191378 ] 
dist 120=[-1.7428021545328083623 ,1.3660005566564031395 ] 
dist 121=[-1.8263569875199663332 ,1.2634393366507308165 ] 
dist 122=[-1.8971458754998473081 ,1.1422463995558889749 ] 
dist 123=[-1.9542682903905180643 ,1.0306568228823440374 ] 
dist 124=[-2.0638838137021933052 ,1.0033864832277966104 ] 
dist 125=[-2.2145486114085560275 ,.9731179124924527526 ] 
dist 126=[-2.3224879832792474154 ,.96298664986950405742] 
dist 127=[-2.4005014165256481323 ,-.32693802928154835122] 
dist 128=[-2.4593738617610076713 ,-.43036514753470055504] 
dist 129=[-2.4908997588528670270 ,-.65181549438030670063] 
dist 130=[-2.5084793383229948036 ,-.69641609581144811384] 
dist 131=[-2.5116648065032847450 ,-.91734720596971009176] 
dist 132=[-2.2853154512954639257 ,-.95448040127454172438] 
dist 133=[-2.2483482769004831571 ,-1.0200511477172642432 ] 
dist 134=[-2.1940483065015181277 ,-1.0319035574863243811 ] 
dist 135=[-2.1749363946540415420 ,-1.0427790560639535701 ] 
dist 136=[-2.1289133577802242348 ,-1.0196083824511475696 ] 
dist 137=[-2.1117213618464199656 ,-.97254701223289267551] 
dist 138=[-2.1004079396060253846 ,-.88061034651633030819] 
dist 139=[-2.0941679438345331568 ,-.76623212894360440833] 
dist 140=[-1.8086125418966012668 ,-.35345247962556524848] 
dist 141=[-1.8069294673328453950 ,-.07231342277156105514] 
dist 142=[-1.8028754909083976616 ,.16629586206722964976] 
dist 143=[-1.6655096712834397455 ,.40932051184392602522] 
dist 144=[-1.6484861466492627437 ,.63664589404626799967] 
dist 145=[-1.5928335759909028992 ,.8125925915740484702 ] 
dist 146=[-1.5846541849666015192 ,.98464252894491299349] 
dist 147=[-1.4492768714654961400 ,1.1964145187282839553 ] 
dist 148=[-1.4191757479506756173 ,1.3968664486215750062 ] 
dist 149=[-1.3948671837217302977 ,1.5237327929489861283 ] 
dist 150=[-1.3892540025881782168 ,1.6210181304686989405 ] 
dist 151=[-.98755027679311986134,1.7033982319924051359 ] 
dist 152=[-.93523839330444285198,1.7699090570510531640 ] 
dist 153=[-.83397901751541805977,1.8038524551128195500 ] 
dist 154=[-.80803240141346627438,1.8207504173663899015 ] 
dist 155=[-.71899138261103095813,1.8235235439898217912 ] 
dist 156=[-.69730285142414350566,1.5973222798327479032 ] 
dist 157=[-.67472756560831278645,1.6173378885705793962 ] 
dist 158=[-.66854770815100032526,1.6280443197856052760 ] 
dist 159=[.12311405582942398225,1.6314381442921625879 ] 
dist 160=[-.00245192859642648250,1.6302576139047542802 ] 
dist 161=[-.11181324534492125161,1.6115557341954627868 ] 
dist 162=[-.23025396542992634606,1.6088026563329136954 ] 
dist 163=[-.39206779861171062089,1.5211642005481013058 ] 
dist 164=[-.5531863605383059349 ,1.4992229908375264342 ] 
dist 165=[-.66885748859790003997,1.4861335239608288058 ] 
dist 166=[-.77342072027129329182,1.4827243164783008605 ] 
dist 167=[-.89021122053254566375,1.4107185224062026596 ] 
dist 168=[-1.0068261711121310805 ,1.4755045930238225240 ] 
dist 169=[-1.1093479469763296103 ,1.5229824811533654491 ] 
dist 170=[-1.2199281621136527876 ,1.5592618636303819411 ] 
dist 171=[-1.3705219844467211506 ,1.5855541364986035760 ] 
dist 172=[-1.5148838020569180160 ,1.5931632553522178474 ] 
dist 173=[-1.6005909935011614282 ,1.5936321165692109721 ] 
dist 174=[-1.6598182242985553654 ,1.5914339557723530452 ] 
dist 175=[-1.6984784560235037635 ,1.5369207888710289699 ] 
dist 176=[-1.7256868010712380176 ,1.5250473947826575122 ] 
dist 177=[-1.7391974979958443118 ,1.4827678776937691536 ] 
dist 178=[-1.7452868419805911714 ,1.4763776852878449107 ] 
dist 179=[-1.7428609740150634544 ,1.3657623313103692600 ] 
dist 180=[-1.5614157685818289072 ,1.3406091302017541656 ] 
dist 181=[-1.5323880642359071594 ,1.3194459902461261192 ] 
dist 182=[-1.4828544279152765966 ,1.3122999039767419628 ] 
dist 183=[-1.4686387033478391944 ,1.2436460934284672594 ] 
dist 184=[-1.4533727952547330940 ,1.2636829682603806226 ] 
dist 185=[-1.5031675309822200140 ,1.2725605530981517396 ] 
dist 186=[-1.5401951050450646322 ,1.2749529547009735909 ] 
dist 187=[-1.5665525931300721106 ,1.2730626650267476709 ] 
dist 188=[-1.5741327215912178553 ,.69864045787264783225] 
dist 189=[-1.5810158913763859113 ,.67185858572377339177] 
dist 190=[-1.5806743172084798462 ,.66236457885149417521] 
dist 191=[.22554167275241467235,.49887512931913930466] 
dist 192=[.39503309780265694883,.66893096490073640446] 
dist 193=[.49986526708039884276,.80198814766054989592] 
dist 194=[.584683964465592127  ,.93346076582415347107] 
dist 195=[.59746803432916559203,1.0971943524481561677 ] 
dist 196=[.68535073892059020838,1.2531392803102033541 ] 
dist 197=[.69149499832520888076,1.3535249482615187139 ] 
dist 198=[.67535529590327975334,1.4324670424387526412 ] 
dist 199=[.62459815763924248402,1.5028217940346038537 ] 
dist 200=[.55547831817253261837,1.5623056215888340491 ] 
dist 201=[.46604669019843686358,1.5978584273752851927 ] 
dist 202=[.34460394499190759075,1.6227132564081122708 ] 
dist 203=[.14771804890395906034,1.6395002020907008286 ] 
dist 204=[-.05398764119062240832,1.6624958749014783061 ] 
dist 205=[-.19466867048683396163,1.6712658181581824504 ] 
dist 206=[-.31759385104579642123,1.6719951142293555950 ] 
dist 207=[-.53753367975425263832,1.6682503719981695146 ] 
dist 208=[-.72465640277812691337,1.6424197079744618575 ] 
dist 209=[-.88036531812190358222,1.6330301929924266032 ] 
dist 210=[-1.0339461825661316354 ,1.6282570009193551827 ] 
dist 211=[-1.1744288984262193451 ,1.5777140165295824081 ] 
dist 212=[-1.2778573165501541026 ,1.5440116586056660204 ] 
dist 213=[-1.3739646242468778208 ,1.5251914580395551369 ] 
dist 214=[-1.4852247306994177762 ,1.5144773153627582820 ] 
dist 215=[-1.5870122665315473342 ,1.2215936290454895596 ] 
dist 216=[-1.6453103063603392911 ,1.1800101753872291302 ] 
dist 217=[-1.6829161259993108598 ,1.0962907488354273491 ] 
dist 218=[-1.7021125393888577341 ,1.0730694589730453733 ] 
dist 219=[-1.7123504037272539192 ,.99020353294454934773] 
dist 220=[-1.7142000306256993288 ,.96218341469508666917] 
dist 221=[-1.7102555703553542227 ,.91893031063538820212] 
dist 222=[-1.7057079530268350954 ,.90565003048579505139] 
dist 223=[-1.6812172909214283670 ,.01482578421782837074] 
dist 224=[-1.6616656463892251473 ,-.06430420356026406252] 
dist 225=[-1.6536583321175846978 ,-.22904397602365164496] 
dist 226=[-1.6461641792416323862 ,-.26913135333925767027] 
dist 227=[-1.6381411772001891981 ,-.41963940881077749361] 
dist 228=[-1.6782319134019443041 ,-.4483484755831576619 ] 
dist 229=[-1.7433047337642628635 ,-.48694325709536293596] 
dist 230=[-1.7860590239918730643 ,-.49241300183048920259] 
dist 231=[-1.8095444418226843443 ,-.485388610627128705  ] 
dist 232=[-1.8231403459115272705 ,-.45990200071493774459] 
dist 233=[-1.8264210725423257109 ,-.41600313671608492558] 
dist 234=[-1.8227735239630631561 ,-.33548673135738759129] 
dist 235=[-1.8184442197403263522 ,-.05140430649755198328] 
dist 236=[-1.6260758653092822421 ,.25196307621855303897] 
dist 237=[-1.5982718627752953554 ,.45675928840790941874] 
dist 238=[-1.5167846986503169317 ,.62861922177671395129] 
dist 239=[-1.5043040804615046109 ,.80052122982375209251] 
dist 240=[-1.3435069411424037548 ,.95934029144662431448] 
dist 241=[-1.3092101635095619488 ,1.0789792395815125368 ] 
dist 242=[-1.2758259644940436141 ,1.1928586927784682888 ] 
dist 243=[-1.2659878514612423114 ,1.3286877593335456927 ] 
dist 244=[-.85492085717219228321,1.4550894523055874594 ] 
dist 245=[-.80131950463890640555,1.5313392077724760445 ] 
dist 246=[-.6944604918101232786 ,1.5854646461461593286 ] 
dist 247=[-.66654172972156145511,1.6235571100941612280 ] 
dist 248=[-.56635314803504902081,1.6505147828900184884 ] 
dist 249=[-.54381621760360241502,1.6662365068811513528 ] 
dist 250=[-.51023182830948393955,1.6756165437279892024 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 1, 1, 0, 1, 2] 
dist 0=[55.151874934792525060  ,55.151874934792525060  ] 
dist 1=[54.777056103702797901  ,55.247961281351770474  ] 
dist 2=[54.103060478647754939  ,55.231289931792929817  ] 
dist 3=[52.811743201902964538  ,55.155722515328545538  ] 
dist 4=[51.409368141732942913  ,55.072441727708559694  ] 
dist 5=[50.291786185364970583  ,55.025007500751398978  ] 
dist 6=[49.164931275551576796  ,54.994881359129841892  ] 
dist 7=[47.725646651115257468  ,54.870049120431315658  ] 
dist 8=[46.189942526937714530  ,50.494777924462387865  ] 
dist 9=[44.678004426279138679  ,49.854260442973580634  ] 
dist 10=[42.889051203158596737  ,48.736300788899050389  ] 
dist 11=[40.246870699761064560  ,48.447197928858483353  ] 
dist 12=[37.514307095089882642  ,47.532396140744379348  ] 
dist 13=[35.364332914119504107  ,47.236485784586444469  ] 
dist 14=[31.219690425483159799  ,47.052494569024525332  ] 
dist 15=[26.234922128658032108  ,46.881728983204337985  ] 
dist 16=[22.845367339392096278  ,33.711398817969764694  ] 
dist 17=[19.965713115853420479  ,33.327890135344788590  ] 
dist 18=[17.017413739493107756  ,32.797523735630786656  ] 
dist 19=[14.239900602574974550  ,32.618823672521719346  ] 
dist 20=[11.976682732081077589  ,15.281280868457882354  ] 
dist 21=[8.7778113679770969187 ,14.378998408813277158  ] 
dist 22=[6.1287501832205511427 ,13.091621510569906641  ] 
dist 23=[3.5258805678958112497 ,12.742691857788089137  ] 
dist 24=[1.1422086739988668833 ,6.8789498036413010856 ] 
dist 25=[-.63127326909698002188,6.1625768326090551146 ] 
dist 26=[-2.3030228956215866931 ,4.6201694008480765105 ] 
dist 27=[-4.2803655330606951326 ,4.3495356040613013785 ] 
dist 28=[-6.1286239544770951247 ,2.8016116095277003811 ] 
dist 29=[-7.2848045172532834569 ,2.5586795218347690571 ] 
dist 30=[-8.1592988842818820551 ,2.1354895080835056216 ] 
dist 31=[-8.8824916161497600034 ,2.0649579636179241294 ] 
dist 32=[-9.4588730303691944452 ,-5.0479001170469982118 ] 
dist 33=[-9.7468761706075803002 ,-5.2319558619945243246 ] 
dist 34=[-9.8980511191663408090 ,-5.5193994894005256821 ] 
dist 35=[-10.132055819574506666  ,-5.5631169799572165928 ] 
dist 36=[-10.451379374202042632  ,-5.5478113401215441037 ] 
dist 37=[-10.693980419329577808  ,-5.4827465627741914316 ] 
dist 38=[-10.831065607253823085  ,-5.3723141966453301311 ] 
dist 39=[-10.862111386993953481  ,-5.1750925921913302703 ] 
dist 40=[-10.390980916462095695  ,-4.9401613985868677945 ] 
dist 41=[-10.294061943812254754  ,-4.6788379800438854712 ] 
dist 42=[-10.190605877322326834  ,-4.3494911603557820764 ] 
dist 43=[-10.130743915088652480  ,-3.8427601536664630086 ] 
dist 44=[-10.037533351288742603  ,-3.3145224002507729106 ] 
dist 45=[-9.9967102561457919576 ,-2.8991311058444443861 ] 
dist 46=[-9.9703630809146709322 ,-2.4871562703065962725 ] 
dist 47=[-9.9575894878073432534 ,-1.9343068085440465842 ] 
dist 48=[-3.9912459641930688084 ,-1.2873410361290922987 ] 
dist 49=[-3.9198309918458724446 ,-.53876742456204013235] 
dist 50=[-3.8379564437180385429 ,.36922676522160390688] 
dist 51=[-3.8089722963073860445 ,1.2103121570425239767 ] 
dist 52=[-3.0214695596135169159 ,1.8533671742243930461 ] 
dist 53=[-2.9193464394117289802 ,2.4686452327700817047 ] 
dist 54=[-2.6743135430213195539 ,3.2045697689547013799 ] 
dist 55=[-2.6255113825235292780 ,3.9028652832535221991 ] 
dist 56=[-2.2543568608764198009 ,4.3442047995053073660 ] 
dist 57=[-2.1796930573496644678 ,4.6824451671319346696 ] 
dist 58=[-2.0651218307374993388 ,4.9690590081525869379 ] 
dist 59=[-2.0317116107771348589 ,5.2009069867716415764 ] 
dist 60=[-1.3401880523407556502 ,5.3204482677458243334 ] 
dist 61=[-1.2450145016760895203 ,5.3859469205717088181 ] 
dist 62=[-1.0365859305606075613 ,5.4020800500305021306 ] 
dist 63=[-.97952110754807935777,5.2292480346670464460 ] 
dist 64=[-.72470089914166139034,5.2215938903278756823 ] 
dist 65=[-.67485690140680458093,5.2093190784069994052 ] 
dist 66=[-.5560029454793035418 ,5.1906652073455520938 ] 
dist 67=[-.52871808959761107201,5.1704625302311296734 ] 
dist 68=[1.5746829024039335360 ,2.9002237601037664085 ] 
dist 69=[1.3279258952423967236 ,2.8369306937514637299 ] 
dist 70=[.96247895934443357821,2.7708884098275426716 ] 
dist 71=[.58616742856643212401,2.7484410238123299651 ] 
dist 72=[.29599761106388161788,2.0067419182538235505 ] 
dist 73=[.01331975370800514522,1.9095288098595046997 ] 
dist 74=[-.33316311469621904783,1.8667786011097088305 ] 
dist 75=[-.69442442913067997643,1.8738952378579073295 ] 
dist 76=[-1.0361482935449907627 ,1.8927783755340283100 ] 
dist 77=[-1.4293607249552623283 ,1.9236268922470159100 ] 
dist 78=[-1.9962345695277906809 ,1.9783997130476788405 ] 
dist 79=[-2.5529260264124178996 ,2.0345106979614354494 ] 
dist 80=[-2.9055091389566615768 ,2.0706854313933823678 ] 
dist 81=[-3.1765567668555004072 ,2.0987773831336210540 ] 
dist 82=[-3.4077441564436805189 ,2.1226847697110102443 ] 
dist 83=[-3.5960843921102978850 ,2.1416114770645775143 ] 
dist 84=[-3.6960892615638377171 ,2.1498408156171667525 ] 
dist 85=[-3.7520017883989827591 ,2.1515107036069891188 ] 
dist 86=[-3.7644647930270246382 ,2.1461585624560480651 ] 
dist 87=[-3.7499669253487143199 ,2.1320766074793294139 ] 
dist 88=[-3.7405505851058558924 ,2.1223453937871915257 ] 
dist 89=[-3.7288183164997276185 ,2.0945449982281955188 ] 
dist 90=[-3.7133499705980922612 ,2.0806447758681872305 ] 
dist 91=[-3.6909548877812074816 ,1.9979314701499043243 ] 
dist 92=[-3.6721227220088579992 ,1.9756268857055421808 ] 
dist 93=[-3.6437580037279705613 ,1.9262926037765070373 ] 
dist 94=[-3.6288894725035429856 ,1.9082327967582006486 ] 
dist 95=[-3.4186192910671241008 ,1.6157309561377458576 ] 
dist 96=[-3.3305933248499430939 ,1.5688667775315346135 ] 
dist 97=[-3.3061425014094024190 ,1.4646806965403942686 ] 
dist 98=[-3.2307623860691903568 ,1.3760603320413215907 ] 
dist 99=[-3.2090292950217695574 ,1.1123254494079335838 ] 
dist 100=[-.14777368255361205797,1.2903062838282625137 ] 
dist 101=[.01991496334099334170,1.4204110929644607503 ] 
dist 102=[.05557002418067203088,1.5404284202822946237 ] 
dist 103=[.57512914507191272887,1.6781633300716125741 ] 
dist 104=[.64566593865532183621,1.8037160157006762384 ] 
dist 105=[.76872454062377471547,1.8751160011967075602 ] 
dist 106=[.79359118232112368237,1.9341657642813733532 ] 
dist 107=[.83360071407016287467,2.2000133129421739784 ] 
dist 108=[.81405043181820199877,2.4462305643239026501 ] 
dist 109=[.71654995116411484601,2.5967766983281526434 ] 
dist 110=[.49649196508017983806,2.7061104630437301748 ] 
dist 111=[.15128957010749921606,2.7878437214483312549 ] 
dist 112=[-.19777834512440957636,2.8482194306736693320 ] 
dist 113=[-.43326550404095342406,2.8722983054033585946 ] 
dist 114=[-.63058073973457015398,2.8792834561349232533 ] 
dist 115=[-.82730917494439578694,2.8742167765594971148 ] 
dist 116=[-1.0085341315417030911 ,1.3907773140106472611 ] 
dist 117=[-1.1439768289649985357 ,1.3550831922543114353 ] 
dist 118=[-1.2717866240491411811 ,1.3099728588983007286 ] 
dist 119=[-1.4225495450756497981 ,1.2929827793920225932 ] 
dist 120=[-1.5618673264614272147 ,.91153046439516283334] 
dist 121=[-1.6440000164418297728 ,.86060324737328462109] 
dist 122=[-1.6999465355990847816 ,.75210561864778274569] 
dist 123=[-1.7347558206851478461 ,.72212683509196914315] 
dist 124=[-1.7583596022720495178 ,.60296958434087245818] 
dist 125=[-1.8112169077702961782 ,.57974128920406826305] 
dist 126=[-2.1270373976403445025 ,.52525395475177098715] 
dist 127=[-2.4348561915622609904 ,.51351372305098492178] 
dist 128=[-2.6235864500180215396 ,-.17291523934659759361] 
dist 129=[-2.7613834902235970633 ,-.23506998477021427457] 
dist 130=[-2.8658843291515886315 ,-.36830475074015029766] 
dist 131=[-2.9459647413607488740 ,-.39521852198121994047] 
dist 132=[-2.9862742914379416569 ,-.52927921762787717154] 
dist 133=[-3.0052253357923305896 ,-.55178968686722548476] 
dist 134=[-3.0058032922260657456 ,-.59272323495781123957] 
dist 135=[-2.8044161849800722489 ,-.6005897649510885747 ] 
dist 136=[-2.7674544444244420304 ,-.61188223795633554655] 
dist 137=[-2.7092017099997702410 ,-.60009599294818149789] 
dist 138=[-2.6891577060597802146 ,-.57409578705751006996] 
dist 139=[-2.6248629575619784086 ,-.52191730730230539086] 
dist 140=[-2.6017616610234954206 ,-.4569027047382094116 ] 
dist 141=[-2.5649639160803653634 ,-.37966365077307879935] 
dist 142=[-2.5506524558178836795 ,-.2786575457898702816 ] 
dist 143=[-1.4391693877401998157 ,-.11877320133162981244] 
dist 144=[-1.0589040703497499215 ,.10481247643519231895] 
dist 145=[-1.0274727350157137328 ,.4004262272510058856 ] 
dist 146=[-1.0012582822547695764 ,.69726157780172833038] 
dist 147=[-.99687808244384313288,.97223257994672192486] 
dist 148=[-.92585550521526914787,1.1805775676969987275 ] 
dist 149=[-.90948010255988310561,1.3800670327320920674 ] 
dist 150=[-.89569885431970222853,1.6196937010396029109 ] 
dist 151=[-.89107748969577187173,1.8435707537077209657 ] 
dist 152=[-.66397152424392477513,1.9801972624351609736 ] 
dist 153=[-.63374874617789594607,2.0791068178986229900 ] 
dist 154=[-.57489916577230628256,2.1524390275768313113 ] 
dist 155=[-.55955227670565569417,2.2079862042077392817 ] 
dist 156=[-.50529963734550853386,2.2359082286583050016 ] 
dist 157=[-.49225646600191977606,2.2489538129122365200 ] 
dist 158=[-.4747213004692085535 ,2.2484508163353970707 ] 
dist 159=[-.46859780439055661275,1.2342756652971793083 ] 
dist 160=[.22087177126821094078,1.0404136133142168726 ] 
dist 161=[.25112598364303045756,1.0375241924396602835 ] 
dist 162=[.13775456297141590655,1.0370831776062409492 ] 
dist 163=[.00549958102041462910,1.0356196969967409409 ] 
dist 164=[-.11343922228679852288,1.0004033521156052381 ] 
dist 165=[-.24540953762928311923,.99014124343585063857] 
dist 166=[-.42968758656151684673,.98188447821302109618] 
dist 167=[-.61495958322271461696,.97592043798590499595] 
dist 168=[-.75090310761932601624,.85257662904423498594] 
dist 169=[-.87678402712701440488,.88986556053830432348] 
dist 170=[-1.0219007067708775305 ,.9154671295185956394 ] 
dist 171=[-1.1683538513225289270 ,.93182069005311043322] 
dist 172=[-1.2995772593747344072 ,.94272781577701469705] 
dist 173=[-1.4448557739360111843 ,.94658950430484126906] 
dist 174=[-1.6474239412360049271 ,.94603519650164167692] 
dist 175=[-1.8431543698942722808 ,.97325913054701614029] 
dist 176=[-1.9611420003848062098 ,1.0929365721093400868 ] 
dist 177=[-2.0448611355947937742 ,1.1916486649856360537 ] 
dist 178=[-2.1038005758449179001 ,1.2874813707962796023 ] 
dist 179=[-2.1471018654576522880 ,1.3740610706107373114 ] 
dist 180=[-2.1683950670948138789 ,1.4358463708381222847 ] 
dist 181=[-2.1776746354675401290 ,1.4912633777730715984 ] 
dist 182=[-2.1757407600513376156 ,1.5524270666961853255 ] 
dist 183=[-1.9851135260288699147 ,1.6067155039884528655 ] 
dist 184=[-1.9529563720889537049 ,1.6346946366151892886 ] 
dist 185=[-1.8984645104134053128 ,1.6487313922892322729 ] 
dist 186=[-1.8821321877834080812 ,1.6503940124060719093 ] 
dist 187=[-1.8257258903630377674 ,1.6395644010069218317 ] 
dist 188=[-1.8071716529147950051 ,1.6322957974617425676 ] 
dist 189=[-1.7785087246270540578 ,1.6140010525084313450 ] 
dist 190=[-1.7675341707287808250 ,1.6049288075692218558 ] 
dist 191=[-1.0807639417851616438 ,.66517834858105735454] 
dist 192=[-.30895164193974731517,.39574066729498519031] 
dist 193=[-.05662826402864858771,.61423160938578778013] 
dist 194=[-.00525280773943386674,.83593358728363663516] 
dist 195=[.28081084094881550706,1.0427830703322243112 ] 
dist 196=[.32934445022353658933,1.2019937424834346662 ] 
dist 197=[.43233280299465990767,1.3568396560523156241 ] 
dist 198=[.45290959594109531119,1.5462712465636690820 ] 
dist 199=[.54714994760739812601,1.7250168053398686433 ] 
dist 200=[.48625617357467055353,1.8372118240899277272 ] 
dist 201=[.41888911653254917395,1.9221788553726659995 ] 
dist 202=[.33385863071075861165,1.9922469686329161970 ] 
dist 203=[.20246315363081094613,2.0474160113842710871 ] 
dist 204=[.05127957494253067702,2.0729166719752000358 ] 
dist 205=[-.11273327945838427244,2.0832607409537750418 ] 
dist 206=[-.31759827886543510929,2.0825993868079187640 ] 
dist 207=[-.63183961476564604364,2.0486381074372199410 ] 
dist 208=[-.94731786083492059419,2.0692089716726966429 ] 
dist 209=[-1.1571195546326009597 ,2.0927645146917649137 ] 
dist 210=[-1.3297251988965720639 ,2.0970725953318414809 ] 
dist 211=[-1.4967377119087363804 ,2.0887407417337583372 ] 
dist 212=[-1.6474020800391845645 ,2.0799811709617804830 ] 
dist 213=[-1.7547547283368718016 ,2.0648500114825150151 ] 
dist 214=[-1.8509557193744152388 ,2.0570922409101898913 ] 
dist 215=[-1.9571078044388181335 ,2.0417423378116079974 ] 
dist 216=[-2.0514644122962883878 ,1.7639971139134069072 ] 
dist 217=[-2.1005841520397457902 ,1.7178956378710727284 ] 
dist 218=[-2.1272316911996001377 ,1.6554737616949425853 ] 
dist 219=[-2.1322446419657110221 ,1.6067339952046615231 ] 
dist 220=[-2.1172760264748728220 ,1.5215690996658775070 ] 
dist 221=[-2.1109063383790866173 ,1.4800779118863141136 ] 
dist 222=[-2.1047464274196609591 ,1.4421891770354005921 ] 
dist 223=[-2.0972618977629257775 ,1.4037820377186013317 ] 
dist 224=[-2.0196363473473812197 ,.28497063470216859188] 
dist 225=[-2.0214310938308589564 ,.18312573822424190892] 
dist 226=[-2.0213878561619003865 ,-.03351370396579407426] 
dist 227=[-1.9468403235189695220 ,-.08413884188565694020] 
dist 228=[-1.9273791452096880649 ,-.30250463060714083041] 
dist 229=[-1.9155824278987887972 ,-.34198708387610949677] 
dist 230=[-1.9980566365209401929 ,-.41742032597667788004] 
dist 231=[-2.1430530359025271188 ,-.43433239651396940317] 
dist 232=[-2.2244882685260408538 ,-.47653572928403177573] 
dist 233=[-2.2749697641883908647 ,-.46779063112233816202] 
dist 234=[-2.2964151440998995665 ,-.43582015219092309399] 
dist 235=[-2.3065538667267660976 ,-.36378095529169781588] 
dist 236=[-2.3119058467598261370 ,-.27147118178405151012] 
dist 237=[-2.3147763259036536176 ,-.15859216160007652556] 
dist 238=[-2.3150122965625637740 ,-.00899413026604473023] 
dist 239=[-2.0742196982064258007 ,.32068183925082561085] 
dist 240=[-2.0524882837588468932 ,.57435169723645571422] 
dist 241=[-1.9826250685442485939 ,.78787177935028715036] 
dist 242=[-1.9714078489603146775 ,1.0024916997832579377 ] 
dist 243=[-1.8031653125590308250 ,1.2014510704411409577 ] 
dist 244=[-1.7655342529244655712 ,1.3524632232881587647 ] 
dist 245=[-1.7326022061736137918 ,1.4973137016610106569 ] 
dist 246=[-1.7225692123279983676 ,1.6716800361386675818 ] 
dist 247=[-1.2253308383790750886 ,1.8347830993183901169 ] 
dist 248=[-1.1597631221956948826 ,1.9346769949267716809 ] 
dist 249=[-1.0314175317092117832 ,2.0074244371286463577 ] 
dist 250=[-.9980341982031078877 ,2.0621734086983924445 ] 
dist 251=[-.88017776648909281894,2.1018096166629537828 ] 
dist 252=[-.85226889365425528535,2.1142343233008869532 ] 
dist 253=[-.81546577422459501107,2.1162676072227807154 ] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 1, 0, 1, 0, 1] 
dist 0=[53.300375321113985322  ,53.300375321113985322  ] 
dist 1=[52.619678873777514258  ,53.732375597905870546  ] 
dist 2=[51.420053965167336201  ,53.938599493069719264  ] 
dist 3=[49.975324430458819905  ,54.031512988181199157  ] 
dist 4=[48.315647040920735444  ,54.011023150960990015  ] 
dist 5=[46.176530000425336785  ,53.903541990807172932  ] 
dist 6=[42.816922178876658228  ,53.830620295600042871  ] 
dist 7=[39.391801967246989410  ,53.320994428834577001  ] 
dist 8=[36.990959813221754289  ,53.171883279707867087  ] 
dist 9=[34.874640146629104000  ,52.602849976435193836  ] 
dist 10=[32.585691788903801372  ,52.495859686084916835  ] 
dist 11=[30.353355409607211216  ,50.606784528083520103  ] 
dist 12=[28.462964263542487387  ,50.183427570417597245  ] 
dist 13=[26.455293093836057816  ,49.834509166717144187  ] 
dist 14=[23.754213986249248325  ,49.005304665435553599  ] 
dist 15=[21.069505121356083649  ,44.041228168006355953  ] 
dist 16=[19.127027726406340740  ,40.904639113857723244  ] 
dist 17=[17.349507187897208380  ,30.452275413984975404  ] 
dist 18=[15.323397204997922440  ,30.222672935133455968  ] 
dist 19=[13.282668480856148220  ,22.805050840611343290  ] 
dist 20=[11.446382499273081133  ,21.867663372076145818  ] 
dist 21=[9.3998334726163521144 ,19.955794921717160198  ] 
dist 22=[6.5184217895540819190 ,19.459149154025481092  ] 
dist 23=[3.6846384166113066355 ,17.658330266718019143  ] 
dist 24=[1.8282620594755892629 ,17.286694130456949241  ] 
dist 25=[.3233331583968327939 ,16.652629210633992127  ] 
dist 26=[-1.1060396637367351514 ,16.504108269100297405  ] 
dist 27=[-2.3863531880074852132 ,9.2065159705966938061 ] 
dist 28=[-3.2957182326675716216 ,8.6770334987859241953 ] 
dist 29=[-4.1127153364510869461 ,6.1987431463022069580 ] 
dist 30=[-5.2751514786482750165 ,5.0307899376326897444 ] 
dist 31=[-6.9819521713918600345 ,1.1047508644789709776 ] 
dist 32=[-8.2306000472571875202 ,-.13111684094263311524] 
dist 33=[-10.158575085225213333  ,-3.0411224851565140578 ] 
dist 34=[-11.334567243905254628  ,-3.2221815569808663390 ] 
dist 35=[-12.189496168893311878  ,-4.4286433604113668714 ] 
dist 36=[-12.840271489158367818  ,-4.6270666201310397497 ] 
dist 37=[-13.341984595222733848  ,-4.1829250331456259129 ] 
dist 38=[-13.600841015292601500  ,-3.3160947077419877616 ] 
dist 39=[-13.810741109050700307  ,-2.4182262021280426308 ] 
dist 40=[-13.937373230065731756  ,-1.7886563955115455920 ] 
dist 41=[-13.997730382537643612  ,-1.2368469905459935814 ] 
dist 42=[-13.984342798370026849  ,-.64887760975341983016] 
dist 43=[-12.396241095067214078  ,-.08408788614269115076] 
dist 44=[-12.305399327579098638  ,.74742950424089307438] 
dist 45=[-12.017734150701435294  ,1.5371353698785319315 ] 
dist 46=[-11.913500196851376729  ,2.3735547783503955219 ] 
dist 47=[-11.772827540981863330  ,3.1748091484214857600 ] 
dist 48=[-11.708286904438842398  ,3.8243914604450611979 ] 
dist 49=[-3.7024869565070380644 ,4.4869179962639065557 ] 
dist 50=[-3.0292391675182932895 ,5.3400597081497254781 ] 
dist 51=[-1.5542691608163227636 ,6.1661581976934194761 ] 
dist 52=[-1.4492509388482407318 ,6.7208742607551784069 ] 
dist 53=[-1.2773282869728143162 ,7.1833251496342234189 ] 
dist 54=[-1.2471667089292000745 ,7.6413229419599688861 ] 
dist 55=[1.8469212967788091310 ,8.0623158121995456317 ] 
dist 56=[2.4482430918845023170 ,8.3772143518996782422 ] 
dist 57=[2.9440467207679691742 ,8.6756955661484018394 ] 
dist 58=[3.0465526449750837638 ,9.0314390444650976707 ] 
dist 59=[3.1304533411682994826 ,9.3539976744116197037 ] 
dist 60=[3.0407923898084895535 ,9.5200557824815403306 ] 
dist 61=[2.9229092076625844860 ,9.6045554931400174217 ] 
dist 62=[2.7371921326787941802 ,9.6104253652834284192 ] 
dist 63=[2.5232890463860208141 ,9.5562379490258790184 ] 
dist 64=[2.2927903685990486963 ,9.4095505564277768140 ] 
dist 65=[2.0065985147213084567 ,4.7806810168817250898 ] 
dist 66=[1.5703256926318401367 ,4.7923318948174156280 ] 
dist 67=[1.1167114054204740545 ,4.7346258747207324892 ] 
dist 68=[.76122879595729151673,4.7182752990460855463 ] 
dist 69=[.40979045557921848774,4.7072501693241881226 ] 
dist 70=[-.02782459330836215522,4.7007038954290515778 ] 
dist 71=[-.48740152220117657213,3.8926260878093503814 ] 
dist 72=[-.9282127433422236985 ,3.7895351074676455175 ] 
dist 73=[-1.4352329048978531914 ,3.5161780779262708140 ] 
dist 74=[-2.1721498018056251229 ,3.4729892164514700162 ] 
dist 75=[-2.8969943058552338998 ,2.9830565998815500136 ] 
dist 76=[-3.3574734656221244175 ,2.8831659967694971706 ] 
dist 77=[-3.7129202860049217238 ,2.7760897793982305270 ] 
dist 78=[-4.0184764227351252617 ,2.7452344611027436367 ] 
dist 79=[-4.2690030835446391239 ,1.6690817846341586302 ] 
dist 80=[-4.4047798022173349068 ,1.5302645966776533034 ] 
dist 81=[-4.4827359631127684573 ,1.2482663099505414803 ] 
dist 82=[-4.5024654381386090772 ,1.1742377409810328171 ] 
dist 83=[-4.5022232853010119010 ,.9040346250843934629 ] 
dist 84=[-4.5004523007324988212 ,.8464237726697508020 ] 
dist 85=[-4.4973826049037544972 ,.74919875811906774968] 
dist 86=[-4.4919325916883503878 ,.72523719797957287306] 
dist 87=[-4.4855449485968428663 ,-.05319330618963631753] 
dist 88=[-4.4787249136941766680 ,.28443389648313506307] 
dist 89=[-4.4703916586635759680 ,.63358261735539678127] 
dist 90=[-4.4579649715435881252 ,.90463595608114097597] 
dist 91=[-4.1114731302221853130 ,1.1702780415699126492 ] 
dist 92=[-4.0841144604435556096 ,1.4978983480124600408 ] 
dist 93=[-3.8240999096850801543 ,1.8403164984568924336 ] 
dist 94=[-3.7635606732554351551 ,2.1650674863993917486 ] 
dist 95=[-3.6841472539406214178 ,2.5392111937767087937 ] 
dist 96=[-3.6527613089026787911 ,3.0788377131289518917 ] 
dist 97=[-2.1161143996942191877 ,3.6076704506211896588 ] 
dist 98=[-2.0847653322348336164 ,3.9387457643780840891 ] 
dist 99=[-1.7355925583079448133 ,4.1885796648253698027 ] 
dist 100=[-1.6662582248150476968 ,4.3931243816793065973 ] 
dist 101=[-1.5906971886890169802 ,4.5538063633210909661 ] 
dist 102=[-1.5715122345160272254 ,4.6285465777435605225 ] 
dist 103=[-.7913716672842504094 ,4.6646694948782311664 ] 
dist 104=[-.69325681213789731237,4.7359286049498676396 ] 
dist 105=[-.5173469144745905892 ,4.9647258553847952134 ] 
dist 106=[-.47772887272990825428,5.0979832793789292604 ] 
dist 107=[-.37720921720796575368,5.1868536638693698832 ] 
dist 108=[-.37001233682517899646,5.2384681037880404117 ] 
dist 109=[-.39701055304967606883,5.2625696039094416465 ] 
dist 110=[-.47771851002148688169,5.2628587422534417565 ] 
dist 111=[-.57767152065580584123,5.2124794721241262320 ] 
dist 112=[-.68148383052875428414,5.2039081085041206563 ] 
dist 113=[-.80800702671762990628,3.3764408443939067770 ] 
dist 114=[-.99860902470484864286,3.2008855184275414004 ] 
dist 115=[-1.2724341134752813488 ,2.7703233133812423495 ] 
dist 116=[-1.7585555358327467987 ,2.6990580288726989900 ] 
dist 117=[-2.2014129699188538131 ,1.9626911427035560353 ] 
dist 118=[-2.5243534080096145792 ,1.5983408525003613110 ] 
dist 119=[-2.8213319106274692456 ,.6543588455088253443 ] 
dist 120=[-3.1605653213263955979 ,.6326743401540788677 ] 
dist 121=[-3.4731986337596368039 ,.5889767394732867379 ] 
dist 122=[-3.6640081219598283570 ,.5771353985394264555 ] 
dist 123=[-3.8021341556570124297 ,-.16040174462467753209] 
dist 124=[-3.9044941423571019314 ,-.22559970381476590593] 
dist 125=[-3.9782049590190521696 ,-.35841303270343267429] 
dist 126=[-4.0019809704519346369 ,-.39116948480506029881] 
dist 127=[-4.0054833147864396640 ,-.50071895152391850423] 
dist 128=[-3.9982775679520138716 ,-.51345667512341648973] 
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dist 155=[-.11167740491863000116,.93183802862900901827] 
dist 156=[-.25926236022924782871,.90248827322256863428] 
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dist 158=[-.50050450847280343089,.8151375991920408172 ] 
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dist 163=[-.90888239995745821365,.41842374535716565355] 
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dist 175=[-.8691513000087927819 ,-.31002547509620579296] 
dist 176=[-.86438749071677934731,-.12878995406507488636] 
dist 177=[-.66271585162675806249,.05318998856371070250] 
dist 178=[-.66067269226485093658,.17448463539327887878] 
dist 179=[-.64220400615907775027,.27453753921618540636] 
dist 180=[-.63762872362435926952,.37174157260821016582] 
dist 181=[-.62096545964880790833,.45966102501683723337] 
dist 182=[-.61823782283575113436,.52265964299133412608] 
dist 183=[-.57249675584103520321,.57946569315827727849] 
dist 184=[-.56195095938534942033,.64267214117068181909] 
dist 185=[-.55325596799756661034,.70062811597101144463] 
dist 186=[-.55047050189458134733,.73647880149048169442] 
dist 187=[-.38899036941819290668,.76300286552952366455] 
dist 188=[-.36875399633356456822,.78373262250498690836] 
dist 189=[-.32542789379255666936,.79914646221816520203] 
dist 190=[-.31325979124704211697,.80445224524742005758] 
dist 191=[-.26381970357103554378,.8053944829834053034 ] 
dist 192=[-.25420027148754431963,.80339529639706609905] 
dist 193=[-.22999708761568673668,.77175263109014984481] 
dist 194=[-.22577549569048375721,.80332350391834489585] 
dist 195=[-.18659763516782259461,.83017140979345419174] 
dist 196=[-.17869674423943469243,.84563453277592860101] 
dist 197=[-.1697264934496576548 ,.85572755258573333503] 
dist 198=[-.16709537167026995684,.86114066388608849078] 
dist 199=[-.16709026909282115155,.86313917008356879386] 
dist 200=[-.1711471843407095328 ,.86191103767504285311] 
dist 201=[-.17894782258227994758,.85437679848266357436] 
dist 202=[-.19388446043819571169,.84962727028087068609] 
dist 203=[-.20991062146908698418,.20855393660427274851] 
dist 204=[-.22206057400653563682,.16283005076139409773] 
dist 205=[-.2449673620085986502 ,.05792742890707874504] 
dist 206=[-.27210588236480812048,.05047877931988107547] 
dist 207=[-.29857843584808691006,.03894974292065374278] 
dist 208=[-.33214802158602964759,.03600336341692653775] 
dist 209=[-.40277504676982687107,-.01343022103286809652] 
dist 210=[-.44851816715550544541,-.02053617457989479952] 
dist 211=[-.48480959610806060395,-.02706103800155464951] 
dist 212=[-.51771023718828793542,.00711856798365574960] 
dist 213=[-.54593010255680682053,.05182562179976910040] 
dist 214=[-.56353860406861648025,.11075893850105360674] 
dist 215=[-.57675700318074844227,.17430754095658233813] 
dist 216=[-.58745488783024759553,.23743335019235606071] 
dist 217=[-.5952330856748528603 ,.31232291979396099658] 
dist 218=[-.59679751459447569284,.42281895636951809252] 
dist 219=[-.59598339374773071633,.53187064084283366479] 
dist 220=[-.59426526496419607682,.60099561221862927455] 
dist 221=[-.57470989229530904629,.65408770405589365498] 
dist 222=[-.56887041104157850483,.69915334037112133876] 
dist 223=[-.56187583631741018538,.73568801843558544296] 
dist 224=[-.55830781709880528278,.75473377317905484742] 
dist 225=[-.54119161089220555337,.7651869423583999304 ] 
dist 226=[-.54031613110833362196,.76742989930496774173] 
dist 227=[-.53114403890829406267,.75744183641705645189] 
dist 228=[-.52812427696387305018,.7537556610879089382 ] 
dist 229=[-.51779209326176891847,.75002160549821690829] 
dist 230=[-.51453783838772658947,.74632992625819666001] 
dist 231=[-.4857471271124450036 ,.74014254734225704922] 
dist 232=[-.47863646758530989954,.73515346269808985333] 
dist 233=[-.4687580375577027918 ,.71251556627779032076] 
dist 234=[-.46492649134875038473,.68821253591535003318] 
dist 235=[-.36898519482591515821,.59500293253925652917] 
dist 236=[-.35566923198385243812,.60566587159719177294] 
dist 237=[-.32486749242113506854,.61325268422006814432] 
dist 238=[-.31706865572874835171,.61515895985140757889] 
dist 239=[-.27392181605749371704,.61436430054157787474] 
dist 240=[-.26525364351816578746,.61247291568288471022] 
dist 241=[-.24754001911615401601,.37247037992846989557] 
dist 242=[-.24249352710817728494,.3507028310178466402 ] 
dist 243=[-.23004774080621154658,.29891899658075093594] 
dist 244=[-.2886292218075630027 ,.28922971307418839524] 
dist 245=[-.34091514182007800606,.2155971512193394663 ] 
dist 246=[-.37718615097670718209,.20169327403168237641] 
dist 247=[-.40867088820504381124,.17923288335864732241] 
dist 248=[-.44185271103740026372,.17347275292269860671] 
dist 249=[-.47189408976199547777,.06897053011916883638] 
dist 250=[-.4908446784785567372 ,.05543190690550352792] 
dist 251=[-.50529810346852645942,.02975948858161803342] 
dist 252=[-.5173915080064665212 ,.02457730268516606284] 
dist 253=[-.52704257268106002397,.00693037568487329093] 
dist 254=[-.5317489508420573494 ,.00313374543824719471] 
dist 255=[-.53373683228351965541,-.00034985999657758322] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 1, 0, 2] 
dist 0=[17.629545699043549069  ,17.629545699043549069  ] 
dist 1=[17.458080100037697063  ,17.755621710941913997  ] 
dist 2=[16.773092305368645938  ,18.259361480824911528  ] 
dist 3=[15.578074763906994700  ,19.138511521824125115  ] 
dist 4=[13.369084243771567806  ,20.764553878300547433  ] 
dist 5=[10.793459722743435113  ,22.434264713342199125  ] 
dist 6=[8.1338181282869325081 ,23.487889951961257731  ] 
dist 7=[4.8938508925856085300 ,24.296118058184970765  ] 
dist 8=[0                     ,24.985325375285578424  ] 
dist 9=[24.719947872410599518  ,25.548456680487821157  ] 
dist 10=[24.657250290025743122  ,25.852945016828536660  ] 
dist 11=[24.360056475394981761  ,26.027420214448381680  ] 
dist 12=[23.667768335691830832  ,26.071088693013611057  ] 
dist 13=[22.885969599005571010  ,22.920367493097394785  ] 
dist 14=[22.231251404802105897  ,22.632437584367934061  ] 
dist 15=[21.545084027680565257  ,22.016573946186441203  ] 
dist 16=[20.637196469966610409  ,21.833767596920015909  ] 
dist 17=[19.655866717693325106  ,21.050334343958921390  ] 
dist 18=[18.676177694480480590  ,20.889303178796341412  ] 
dist 19=[17.508845683561850955  ,20.445632041227069634  ] 
dist 20=[15.777971235873849385  ,20.370268994736817971  ] 
dist 21=[13.988963799566254745  ,19.508479408746362483  ] 
dist 22=[12.589307647646171699  ,19.338326125991369623  ] 
dist 23=[11.203933507162357493  ,19.039372043959570539  ] 
dist 24=[9.4716449196293580501 ,18.962049916661961285  ] 
dist 25=[7.6435626336488620470 ,18.715626150432999251  ] 
dist 26=[5.8753632717969941925 ,18.636207063021961951  ] 
dist 27=[3.8072468526800797076 ,18.590545403764747475  ] 
dist 28=[.7809452006254721520 ,18.579101179438691730  ] 
dist 29=[-2.2154896647308623242 ,-2.2080306813508292140 ] 
dist 30=[-4.1644307698556730631 ,-3.1981899014610753697 ] 
dist 31=[-5.7253112121581569325 ,-5.3838195239627873920 ] 
dist 32=[-7.1718157596326266154 ,-5.7263065762281231239 ] 
dist 33=[-8.4401499779666443792 ,-8.1199006444233133666 ] 
dist 34=[-9.2895145169615252801 ,-8.4932900978499284584 ] 
dist 35=[-9.9982472358797482885 ,-9.1556543850346174949 ] 
dist 36=[-10.705195337478348342  ,-9.2725080161443730206 ] 
dist 37=[-11.325902445157922010  ,-10.117378746874949948  ] 
dist 38=[-11.690168495130982597  ,-10.136338124572481400  ] 
dist 39=[-11.938826503388551556  ,-9.9543398228949856913 ] 
dist 40=[-12.097435157446161220  ,-9.4533854113642664461 ] 
dist 41=[-12.187821666952063358  ,-8.7880969628466451395 ] 
dist 42=[-12.195179589423876266  ,-7.9500221473817738206 ] 
dist 43=[-12.108284669270952370  ,-6.8261914190793019063 ] 
dist 44=[-12.072489050184559243  ,-5.0203354913500863795 ] 
dist 45=[-7.4040870231648397419 ,-3.1800816695290470790 ] 
dist 46=[-6.9723591159499604520 ,-1.9188634185309309103 ] 
dist 47=[-5.9086091005731322809 ,-.84122623208112815342] 
dist 48=[-5.7486008426190723111 ,.26655450374545666043] 
dist 49=[-4.1528569380733629490 ,1.3081364664604092176 ] 
dist 50=[-3.8557424587662652778 ,2.1216615701782204544 ] 
dist 51=[-3.4948675927999991378 ,2.9235808515947062993 ] 
dist 52=[-3.4123816063435248853 ,3.9189093454421490229 ] 
dist 53=[-.9263453534275711933 ,4.8642750919192259140 ] 
dist 54=[-.6252369634442731000 ,5.4668203780019658902 ] 
dist 55=[.0218024198839224069 ,5.9334643547127013706 ] 
dist 56=[.1583943739655195682 ,6.3364667543289883673 ] 
dist 57=[.8214158650237104549 ,6.6675890296423863884 ] 
dist 58=[.9347735730750843309 ,6.8473648728161619188 ] 
dist 59=[1.1510007486900680570 ,6.9506582497353242205 ] 
dist 60=[1.1969130461852877593 ,6.9765397954875746671 ] 
dist 61=[3.0682509272693922658 ,3.0719751574978645363 ] 
dist 62=[3.2265359369403480044 ,3.3766502418882092200 ] 
dist 63=[3.5421958132377326805 ,3.6078402084394124353 ] 
dist 64=[3.6022238263631921012 ,3.8002212098704946383 ] 
dist 65=[3.8035414440009958773 ,3.9538033118542107920 ] 
dist 66=[3.8124301221811237779 ,4.0300746468502945833 ] 
dist 67=[3.7600520800772251008 ,4.0686801465915854497 ] 
dist 68=[3.6109747533769336786 ,4.0731525659885027382 ] 
dist 69=[3.4286987615395316844 ,4.0237988420709405442 ] 
dist 70=[3.2437737008645655055 ,4.0025281543855400693 ] 
dist 71=[3.0217558027865111813 ,3.9570016850409525611 ] 
dist 72=[2.6913414390628644560 ,3.9370392182272304499 ] 
dist 73=[2.3166650740124868151 ,3.8253815522147965086 ] 
dist 74=[1.9179336942456917326 ,3.7969936287813593283 ] 
dist 75=[1.4251793237913134134 ,3.7014711617462740610 ] 
dist 76=[.67516939587513489773,3.6826847918456389053 ] 
dist 77=[-.07666917751138343979,1.9655962579795347012 ] 
dist 78=[-.5767385139861605037 ,1.8008876673706890245 ] 
dist 79=[-.9882725978396792365 ,1.4230686191715363783 ] 
dist 80=[-1.3867291195035290672 ,1.3503052039766939000 ] 
dist 81=[-1.7464156251144196110 ,.86452571855800820225] 
dist 82=[-2.0032023944173496235 ,.77675882035424785979] 
dist 83=[-2.2338753581275624620 ,.61642119824058656452] 
dist 84=[-2.4893321620759524158 ,.5796612870672286852 ] 
dist 85=[-2.7235461962229278902 ,.06833263887914377269] 
dist 86=[-2.8694347290745422613 ,-.00271008852401071962] 
dist 87=[-2.9786404237386479362 ,-.14011104863816383191] 
dist 88=[-3.0664496618839905481 ,-.17259050719860334116] 
dist 89=[-3.1339196616299972153 ,-.27065067282078916403] 
dist 90=[-3.1619565833947834967 ,-.28930667108776701294] 
dist 91=[-3.1698067193599580056 ,-.28692052398101732338] 
dist 92=[-3.1655356168052845560 ,-.25564830171296042928] 
dist 93=[-1.7035060803210408449 ,-.2169170960648704254 ] 
dist 94=[-1.5952174167434518744 ,-.1847512267738477038 ] 
dist 95=[-1.3292574487650722337 ,-.1515312140053967061 ] 
dist 96=[-1.2905727017218171547 ,-.1085183809378718906 ] 
dist 97=[-.8959878386354380987 ,-.0627383190551396842 ] 
dist 98=[-.8232308271475278573 ,-.0184349799097361835 ] 
dist 99=[-.7373980431298255477 ,.0331875281353927191 ] 
dist 100=[-.7211867631816762943 ,.1082203031961057876 ] 
dist 101=[-.4010631403694701252 ,.1849178670338244576 ] 
dist 102=[-.4596495758054479277 ,.2432116147904220360 ] 
dist 103=[-.5228154948075587495 ,.2992406679049001293 ] 
dist 104=[-.6086930900405956128 ,.3669380982610388654 ] 
dist 105=[-.7024648941623702047 ,.4371553715395519611 ] 
dist 106=[-.7971055714975110018 ,.5310329708386835904 ] 
dist 107=[-.9103401554409684477 ,.6262183009996136607 ] 
dist 108=[-1.0782654840129577952 ,.7455742156896696570 ] 
dist 109=[-1.2434269507604865010 ,.86011543504836767583] 
dist 110=[-1.3456222487610346728 ,.93608991039924636961] 
dist 111=[-1.4210127798579896872 ,.99862069777172034717] 
dist 112=[-1.4792253573415943359 ,1.0594668759258018730 ] 
dist 113=[-1.5247540382226761872 ,1.1148571059898723131 ] 
dist 114=[-1.5495495752535377924 ,1.1555997006502587824 ] 
dist 115=[-1.5637996743207046593 ,1.1935959388585170336 ] 
dist 116=[-1.5672908329752333035 ,1.2380268400986704488 ] 
dist 117=[-1.4487385065129761600 ,1.2792928703679896290 ] 
dist 118=[-1.4278097085708824218 ,1.3046486330753751645 ] 
dist 119=[-1.4029011850325598023 ,1.3233510930745946934 ] 
dist 120=[-1.3912561105543561188 ,1.3380343999811753898 ] 
dist 121=[-1.3722060433959077379 ,1.3491516079048225604 ] 
dist 122=[-1.3647078942693951161 ,1.3536088967437291736 ] 
dist 123=[-1.3603548502955472914 ,1.3541172519429186319 ] 
dist 124=[-1.3591291439406021080 ,1.3511101460160095143 ] 
dist 125=[-.90300606064046830357,-.9004790302370735254 ] 
dist 126=[-1.1066806875280533737 ,-1.0034051384805591959 ] 
dist 127=[-1.2714636806229973927 ,-1.2209357741003827600 ] 
dist 128=[-1.4263105563361077647 ,-1.2621731242971764745 ] 
dist 129=[-1.5629737892379307975 ,-1.4610863793437122833 ] 
dist 130=[-1.6551815234585117192 ,-1.4942345327552621155 ] 
dist 131=[-1.7325251419544748724 ,-1.5260716495139318127 ] 
dist 132=[-1.8098659800189711342 ,-1.5108804309421412894 ] 
dist 133=[-1.8762820924989579334 ,-1.4777904888395709731 ] 
dist 134=[-1.9100208061055920440 ,-1.4247536419349781333 ] 
dist 135=[-1.9263186427026182709 ,-1.3469852609777335220 ] 
dist 136=[-1.9288710680135944734 ,-1.2151814558588478112 ] 
dist 137=[-1.9126617196200680213 ,-1.0587738907358111254 ] 
dist 138=[-1.9030182066488288105 ,-.88280576506345937724] 
dist 139=[-1.8843124814027550420 ,-.65883249716350452177] 
dist 140=[-1.8756753478152889445 ,-.3108286281624858908 ] 
dist 141=[-1.3256352387404477095 ,.0399362655373091126 ] 
dist 142=[-1.2663375220487357116 ,.2749317495967036997 ] 
dist 143=[-1.1206303023993372477 ,.4700959216023259624 ] 
dist 144=[-1.0950992703782836200 ,.6618950292182884893 ] 
dist 145=[-.87226788894057001243,.8368314499856885311 ] 
dist 146=[-.8292539382108462759 ,.9646987152801587680 ] 
dist 147=[-.76917215914052951127,1.0825770389348262421 ] 
dist 148=[-.7505658754707081506 ,1.2176527828527981791 ] 
dist 149=[-.38144551890341295924,1.3421587972723109290 ] 
dist 150=[-.3339777886711066663 ,1.4178512127902262368 ] 
dist 151=[-.22763333489271241851,1.4722876156236376729 ] 
dist 152=[-.20586319609802036898,1.5119494507077160280 ] 
dist 153=[-.07792994685307521936,1.5404181747510623977 ] 
dist 154=[-.05540024419329177667,1.5501824720010334053 ] 
dist 155=[-.00987345976124597502,1.5516369446063012786 ] 
dist 156=[.00150586392010567487,1.5474742456564574969 ] 
dist 157=[.3565884461105355827 ,1.2013940565343559557 ] 
dist 158=[.3929326361262846637 ,1.1651351170154099781 ] 
dist 159=[.4522293429985832987 ,1.0729418470843987290 ] 
dist 160=[.4652746189337662453 ,1.0562119927816192587 ] 
dist 161=[.4770427551752025477 ,.90294492462313011264] 
dist 162=[.4615820152204119311 ,.87215437222751926935] 
dist 163=[.4276189604373919300 ,.83100853496251899447] 
dist 164=[.3595440915505450617 ,.8692217101571325365 ] 
dist 165=[.2820860012586713288 ,.95794134433778725876] 
dist 166=[.2106680689148000379 ,1.0207059372058594546 ] 
dist 167=[.1299921822230070688 ,1.0764751281970508412 ] 
dist 168=[.0155765091982811459 ,1.1372674242600136567 ] 
dist 169=[-.11180016278489122518,1.1966094355167795633 ] 
dist 170=[-.2442122325900329401 ,1.2465840409957764922 ] 
dist 171=[-.4057111737574786748 ,1.2992359600665137157 ] 
dist 172=[-.6491905825188507099 ,1.3692526048295274105 ] 
dist 173=[-.8920271697731874802 ,1.4350935906395817649 ] 
dist 174=[-1.0509616895260923598 ,1.4710782518910170117 ] 
dist 175=[-1.1789151259959453361 ,1.4920352132561861290 ] 
dist 176=[-1.2980923709932802831 ,1.4979046599004657824 ] 
dist 177=[-1.4025496608310023850 ,1.4971337124220829978 ] 
dist 178=[-1.4717499425126034648 ,1.4923107376830551183 ] 
dist 179=[-1.5284036847457073644 ,1.4823241872232290691 ] 
dist 180=[-1.5827844002365589758 ,1.4764872354535792011 ] 
dist 181=[-1.6282813936599944133 ,1.3062624781300531927 ] 
dist 182=[-1.6494764403641653242 ,1.2789289657581722237 ] 
dist 183=[-1.6583067542975490694 ,1.2206240295684376832 ] 
dist 184=[-1.6579420155704116083 ,1.2025227295389054494 ] 
dist 185=[-1.6331256282834401357 ,1.1213733260141016227 ] 
dist 186=[-1.6227149940168414525 ,1.1041758563852608496 ] 
dist 187=[-1.6043234786943270328 ,1.0529715326960556471 ] 
dist 188=[-1.5968895348956544147 ,1.0451906179668726050 ] 
dist 189=[-1.1254520850259633619 ,.4354485168664518420 ] 
dist 190=[-1.0732958350206610545 ,.6212996271867605659 ] 
dist 191=[-.95252747696385548494,.7753169077019475765 ] 
dist 192=[-.92514568645800604755,.9261578951314644924 ] 
dist 193=[-.76000977986433731163,1.0634140463488198355 ] 
dist 194=[-.72808432976209877968,1.1632125858286925613 ] 
dist 195=[-.66604103547428095398,1.2546923961538413820 ] 
dist 196=[-.64968518262039014033,1.3587489863526116319 ] 
dist 197=[-.42921090190728350049,1.4529769714926485677 ] 
dist 198=[-.39747429261401776332,1.5052295460624584027 ] 
dist 199=[-.32712248639930442687,1.5367501845696722556 ] 
dist 200=[-.31046827847031159409,1.5482327679367493584 ] 
dist 201=[-.22587368147651663514,1.5522581686638297337 ] 
dist 202=[-.21032335580099676107,1.5540135020572187576 ] 
dist 203=[-.17572103923674779067,1.5544458130660678618 ] 
dist 204=[-.16751603281181528106,1.5531843738714333998 ] 
dist 205=[-.09656289319792375358,1.3099003101569477703 ] 
dist 206=[-.18515831134839701694,1.4095887545588547062 ] 
dist 207=[-.33613552678620345775,1.5179760674378163693 ] 
dist 208=[-.48898688815725662017,1.6143980405740182818 ] 
dist 209=[-.63133072930881449142,1.6957625168316451893 ] 
dist 210=[-.74037184660940847449,1.7440510558643830900 ] 
dist 211=[-.84589798983203092673,1.7773675610651265176 ] 
dist 212=[-.9742145674851484609 ,1.7989751525062576374 ] 
dist 213=[-1.0948377665677549146 ,1.8121006956058911608 ] 
dist 214=[-1.1696591557722629293 ,1.8123127123513684014 ] 
dist 215=[-1.2252585703321478810 ,1.8051706488322086766 ] 
dist 216=[-1.2691644526465987318 ,1.7975833985689566754 ] 
dist 217=[-1.3023495516545088440 ,1.7429647842707047101 ] 
dist 218=[-1.3151590473562372654 ,1.7268020959647086892 ] 
dist 219=[-1.3198043559341103495 ,1.6951768118607958358 ] 
dist 220=[-1.3204053123915029097 ,1.6838237908343377949 ] 
dist 221=[-1.2708898222355903231 ,-.36066939234270608064] 
dist 222=[-1.3143431972762438591 ,-.48622542046992548393] 
dist 223=[-1.3998391888375889662 ,-.61275668059807744622] 
dist 224=[-1.4746060991191744689 ,-.63842062479187069172] 
dist 225=[-1.5367665572222402898 ,-.70884445989437910215] 
dist 226=[-1.5719453965282285308 ,-.71462106645397192884] 
dist 227=[-1.5941022738802077728 ,-.69879530172974211636] 
dist 228=[-1.6042873226898512988 ,-.64935663439973010425] 
dist 229=[-1.6510571822801533664 ,-.58768904885282032143] 
dist 230=[-1.7166858298789367218 ,-.52305361048433627667] 
dist 231=[-1.7640145944891367532 ,-.44386286721129586694] 
dist 232=[-1.7987442296455999587 ,-.32409943679663897043] 
dist 233=[-1.8227150550453444393 ,-.18740977650770476959] 
dist 234=[-1.8274285312071240929 ,-.0406608226109820258 ] 
dist 235=[-1.8244076322362493190 ,.1415792416766135511 ] 
dist 236=[-1.8201106002618081631 ,.4199249308767589404 ] 
dist 237=[-1.4968355471295239424 ,.6987952798966420735 ] 
dist 238=[-1.4979303383456008881 ,.88312987832870042621] 
dist 239=[-1.4916532131545673494 ,1.0335268515763263017 ] 
dist 240=[-1.4852450217646587184 ,1.1769429539720575730 ] 
dist 241=[-1.4344576192443038154 ,1.3049051178464497638 ] 
dist 242=[-1.4195314730745645192 ,1.3936215089797031111 ] 
dist 243=[-1.3970186601954902188 ,1.4705883880180150431 ] 
dist 244=[-1.3881321522243752718 ,1.5516558677823831231 ] 
dist 245=[-1.1506373562235539669 ,1.6229387656779682428 ] 
dist 246=[-1.1158222343446063500 ,1.6608526015720860638 ] 
dist 247=[-1.0412353638389862030 ,1.6815878828890367934 ] 
dist 248=[-1.0192098537681502853 ,1.6855892963298729100 ] 
dist 249=[-.92487439783250393358,1.6800778847513776625 ] 
dist 250=[-.90580000743430073736,1.6780592786426111215 ] 
dist 251=[-.8522020927226035393 ,1.6801059959974074025 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 0, 0, 0, 0, 2] 
dist 0=[53.876515068016491994  ,53.876515068016491994  ] 
dist 1=[53.277231930924848313  ,54.081832973137705726  ] 
dist 2=[52.564918968850428450  ,54.145950666570674332  ] 
dist 3=[51.908142369395103027  ,54.181740358951283672  ] 
dist 4=[51.164170048562160985  ,54.114507524676993194  ] 
dist 5=[50.103605208188330413  ,53.389271228458708100  ] 
dist 6=[48.916695456859177914  ,53.164556206964686441  ] 
dist 7=[47.668071227915237358  ,53.011807419104330415  ] 
dist 8=[46.131242334002149022  ,52.849595116570228047  ] 
dist 9=[43.793144488612372656  ,48.188648159187368787  ] 
dist 10=[41.347066294348508971  ,47.283928098812107452  ] 
dist 11=[39.378911361159247122  ,45.994484602140719501  ] 
dist 12=[37.377993334623508014  ,45.656643901400103502  ] 
dist 13=[34.801000826704519703  ,44.485403010694764059  ] 
dist 14=[31.835789088353162747  ,44.161031210213231762  ] 
dist 15=[26.708313965005812782  ,43.763714351316781510  ] 
dist 16=[21.569064404306155228  ,43.592670369947889162  ] 
dist 17=[18.103319584402709882  ,36.558641384831176838  ] 
dist 18=[15.190122441884277049  ,22.733487772383349869  ] 
dist 19=[12.257646992765167944  ,18.960581493583624406  ] 
dist 20=[9.5265827487157056268 ,18.400481878687922284  ] 
dist 21=[7.4176532279793421982 ,13.332278273855980390  ] 
dist 22=[5.3535330329839880048 ,12.434454573136533116  ] 
dist 23=[2.8010379308375129775 ,11.263636248066612507  ] 
dist 24=[.3641588043069787558 ,11.013275124357895040  ] 
dist 25=[-1.2383777547907794583 ,4.7273778396511196465 ] 
dist 26=[-2.5432708614952051183 ,3.9893129999608337470 ] 
dist 27=[-3.7915179404696485697 ,2.3633611529003975575 ] 
dist 28=[-4.9161498776439834194 ,2.1109512946737495879 ] 
dist 29=[-5.7276927312044386379 ,.34994744892327153798] 
dist 30=[-6.4715770996430398113 ,.07853941687028273317] 
dist 31=[-7.3269239229112186715 ,-.40449925860178094742] 
dist 32=[-8.1075830667976770774 ,-.48786881908711951342] 
dist 33=[-8.5531938890403635141 ,-5.5515276444002051833 ] 
dist 34=[-8.8447828678453729459 ,-6.6402374416753219163 ] 
dist 35=[-9.0094216116046623253 ,-6.7323071500707366276 ] 
dist 36=[-9.1129921034145693695 ,-6.8397926929635639194 ] 
dist 37=[-9.1600675044346236599 ,-6.7992979171856143938 ] 
dist 38=[-9.1767603562782858683 ,-6.7032859053644431083 ] 
dist 39=[-9.1580280039415209058 ,-6.5380537384480226984 ] 
dist 40=[-8.9806261685501658806 ,-6.2923646744508521927 ] 
dist 41=[-8.8445116226339856880 ,-5.8748963727892970569 ] 
dist 42=[-8.7951602639986529567 ,-5.4252954299174411446 ] 
dist 43=[-8.7135739944314068363 ,-5.0511128359219938876 ] 
dist 44=[-8.6780779823343830108 ,-4.6611748678787405971 ] 
dist 45=[-8.5158129875539687388 ,-4.1482946184230185181 ] 
dist 46=[-8.4645433213532011554 ,-3.5685877927950559411 ] 
dist 47=[-8.3229175104724504206 ,-2.1352702454247278364 ] 
dist 48=[-8.2638243134907236180 ,-.69969228560098667263] 
dist 49=[-4.9488788742254237203 ,.26422380711527498386] 
dist 50=[-3.8704266465492770959 ,1.0684129458850774830 ] 
dist 51=[-2.9946427187227196485 ,1.8662710849001891844 ] 
dist 52=[-2.8650788625384678040 ,2.6001569565285744567 ] 
dist 53=[-1.6112076750554640338 ,3.1489158939170146875 ] 
dist 54=[-1.3820234693633278256 ,3.6677770119276783102 ] 
dist 55=[-1.1012233119313726433 ,4.2822486641509243703 ] 
dist 56=[-1.0419781703465406895 ,4.8546471873769712745 ] 
dist 57=[.12923896366451816204,5.2055458470952379651 ] 
dist 58=[1.0009278501877009014 ,5.4617710511905070978 ] 
dist 59=[1.2364471872178648683 ,5.6562779987010668739 ] 
dist 60=[1.1989198579526601077 ,5.8049446451833199420 ] 
dist 61=[.94471092562716547416,5.8781173516201810460 ] 
dist 62=[.58810130497222934618,5.9099845389372267183 ] 
dist 63=[0                     ,5.9113792849843203080 ] 
dist 64=[1.9900887111357607269 ,4.3443673812252468916 ] 
dist 65=[1.8752519278074958895 ,4.1009134232334161770 ] 
dist 66=[1.4169824458183474324 ,3.5891954742427505041 ] 
dist 67=[1.0995718722507148652 ,3.4200278261479843303 ] 
dist 68=[.8247859629768467608 ,3.3659725290287236541 ] 
dist 69=[.5365655661741556160 ,3.1161250781984868756 ] 
dist 70=[.2618995668314237098 ,3.0623167770464257616 ] 
dist 71=[.0411700551180452184 ,2.9389886289087265856 ] 
dist 72=[-.18232526574035512481,2.8992411384444729514 ] 
dist 73=[-.46808040006903893686,2.4836162997224951839 ] 
dist 74=[-.74396025030404973292,2.4175418387914094286 ] 
dist 75=[-.92806662558926750859,2.2606853665026750871 ] 
dist 76=[-1.0803411843349385247 ,2.2242851662071216587 ] 
dist 77=[-1.2291989066929945336 ,1.9928887692932475518 ] 
dist 78=[-1.3826708880477082421 ,1.9462254553299971088 ] 
dist 79=[-1.6784642823222825083 ,1.8598330364412240805 ] 
dist 80=[-2.0105753659571607064 ,1.8372031701535437225 ] 
dist 81=[-2.6197855391003510529 ,1.5548775059315472738 ] 
dist 82=[-3.0684287089771468559 ,1.7125073851503176749 ] 
dist 83=[-3.4208697539220347172 ,1.8162308936621443791 ] 
dist 84=[-3.7347194871754837672 ,1.8998438347032781002 ] 
dist 85=[-4.0002091883086516034 ,1.9772990834920630571 ] 
dist 86=[-4.1596021166132462672 ,2.0443867801113017875 ] 
dist 87=[-4.2720740227429292561 ,2.0866589759362904655 ] 
dist 88=[-4.3502769242864201492 ,2.1185849514713720894 ] 
dist 89=[-4.4071175406095061527 ,2.1444012899365107167 ] 
dist 90=[-4.4343081008305119267 ,2.1616622991489933297 ] 
dist 91=[-4.4451705150350478905 ,2.1623204608680305760 ] 
dist 92=[-4.4367982159565935105 ,2.1501211833877818262 ] 
dist 93=[-4.4168554440369514701 ,2.1388838171720004141 ] 
dist 94=[-4.4005794825650187567 ,2.0548332082105503827 ] 
dist 95=[-4.3439539707097157246 ,2.0302699967808898533 ] 
dist 96=[-4.3151120561305528348 ,1.9916626577824552203 ] 
dist 97=[-3.3974700193061048824 ,1.9771350776726077240 ] 
dist 98=[-1.0302200121303673020 ,1.4857419441434680264 ] 
dist 99=[-.83164468793854866858,1.5916084003804571668 ] 
dist 100=[-.37537421274624233596,1.6694200240243363131 ] 
dist 101=[-.29689032453326416215,1.7294360311205064091 ] 
dist 102=[.2805257885339202708 ,1.7747229506478472615 ] 
dist 103=[.3812385996242647344 ,1.7937319461509493994 ] 
dist 104=[.5508370242568731339 ,1.8007426986156256891 ] 
dist 105=[.5881948422684473712 ,2.1187816579442801266 ] 
dist 106=[1.1338769228889035698 ,2.3177552632149857322 ] 
dist 107=[1.2060129347448349679 ,2.4639119904543536025 ] 
dist 108=[1.2431599434126314415 ,2.5763339863180077988 ] 
dist 109=[1.0793004938151709915 ,2.6639413289810015104 ] 
dist 110=[.8959083444841844784 ,2.7110424094099727375 ] 
dist 111=[.7039747552720663530 ,2.7375296086964271690 ] 
dist 112=[.4689983174287961292 ,2.7428221380305094344 ] 
dist 113=[.1137996274376098950 ,2.5367886365343643671 ] 
dist 114=[-.2420151919177981547 ,1.4404876667650198064 ] 
dist 115=[-.47945238527687711092,1.3806619705382566245 ] 
dist 116=[-.67567632270855578833,1.2313024727835282966 ] 
dist 117=[-.86699175803154983849,1.2060715952358611056 ] 
dist 118=[-1.0405292632152986668 ,.9695766354462694281 ] 
dist 119=[-1.1657927168368915706 ,.9234398288874706630 ] 
dist 120=[-1.2796905499755392563 ,.8636498961348060033 ] 
dist 121=[-1.4078593056625496882 ,.8432976503318690860 ] 
dist 122=[-1.5251240490217136423 ,.4246700438215895519 ] 
dist 123=[-1.5955012515595413160 ,.3708274811540343398 ] 
dist 124=[-1.6450083063792879914 ,.2536875696950883447 ] 
dist 125=[-1.6789808657511036102 ,.2262142891855096842 ] 
dist 126=[-1.7019513062545192048 ,.0951280761670833185 ] 
dist 127=[-1.8681235115655452572 ,.0720647572260625121 ] 
dist 128=[-2.2549059669234913295 ,.0174341366576677195 ] 
dist 129=[-2.6323018329207285274 ,.0596840775713548908 ] 
dist 130=[-2.8686969798096968088 ,.1624264118945986796 ] 
dist 131=[-3.0472415127636654355 ,.2305205941350184221 ] 
dist 132=[-3.1937100699844337161 ,.2862031539565652733 ] 
dist 133=[-3.3088580310375077019 ,.3394214610569843715 ] 
dist 134=[-3.3623743286751397429 ,.3869118097330001248 ] 
dist 135=[-3.3883452428286701264 ,.4197386491430919160 ] 
dist 136=[-3.3935309970723592534 ,.4480732567805962462 ] 
dist 137=[-3.3073489593364728055 ,.4776378342707000882 ] 
dist 138=[-3.2825457331877890545 ,.5038511816428425098 ] 
dist 139=[-3.2364215816082788350 ,.5188139610070952289 ] 
dist 140=[-3.2189883812357294666 ,.5283804212155949905 ] 
dist 141=[-3.1312523092443856498 ,.5330630078949524074 ] 
dist 142=[-3.1072335362807867518 ,.5347623337082163621 ] 
dist 143=[-3.0313533391318695883 ,.5341100621276789090 ] 
dist 144=[-3.0111996712784570575 ,.5289521118682096984 ] 
dist 145=[-1.3377171911293974060 ,.5261200591019975853 ] 
dist 146=[-1.1832265409951395170 ,.4879243444756526084 ] 
dist 147=[-.82933066303785730461,.8409037904940895589 ] 
dist 148=[-.76308331319662873573,1.1868881459713363580 ] 
dist 149=[-.31283629442345044982,1.5019575953859932746 ] 
dist 150=[-.23259953683456199983,1.7315456815314138109 ] 
dist 151=[-.1886741289990829627 ,1.9425302591804547254 ] 
dist 152=[-.2223717128058420558 ,2.1833489505039554930 ] 
dist 153=[-.2622051515792885054 ,2.4053610386962035787 ] 
dist 154=[-.2993260984438108532 ,2.5412828596907021346 ] 
dist 155=[-.3222001949555635198 ,2.6402052422090366141 ] 
dist 156=[-.3389959313668244663 ,2.7145401957683357552 ] 
dist 157=[-.3518647755355815902 ,2.7684276795644171476 ] 
dist 158=[-.3615685140686521310 ,2.7857343113040897390 ] 
dist 159=[-.3657339681812853015 ,2.7887879591621708211 ] 
dist 160=[-.3672286774005352241 ,2.7857851430821492391 ] 
dist 161=[-.3667414425712210763 ,1.4480045845130079020 ] 
dist 162=[-.29464090958054438968,1.1646445274449355914 ] 
dist 163=[-.35801406040341738176,.92689785768084010799] 
dist 164=[-.46315899374579370772,.87914557902342542625] 
dist 165=[-.58071922411316459343,.57434880376335297936] 
dist 166=[-.69950765379668216952,.51898267526878993245] 
dist 167=[-.78547578033383353534,.41427679179262696978] 
dist 168=[-.86385882615275023795,.45047513079427813874] 
dist 169=[-.95237808171927374989,.53077667375243298473] 
dist 170=[-1.0332758353881096533 ,.60332025846179711915] 
dist 171=[-1.0812406487546628512 ,.6840609852032977724 ] 
dist 172=[-1.1142643122045954734 ,.79707136671656067742] 
dist 173=[-1.1971710215321842351 ,.92213178197075889855] 
dist 174=[-1.3648287981668726478 ,1.0509590978557482197 ] 
dist 175=[-1.5570092751343125894 ,1.2071727012047203580 ] 
dist 176=[-1.8330406707294140274 ,1.4415226355593621763 ] 
dist 177=[-2.1031154337896792552 ,1.6742931934887117088 ] 
dist 178=[-2.2715219044781567124 ,1.8242019190125122152 ] 
dist 179=[-2.3977979357629753801 ,1.9420492654579906494 ] 
dist 180=[-2.4997014951699908708 ,2.0468673136936429816 ] 
dist 181=[-2.5787023556641489018 ,2.1352098525356893584 ] 
dist 182=[-2.6135569828862575079 ,2.1873040726762238367 ] 
dist 183=[-2.6291515261539314336 ,2.2227763580361478629 ] 
dist 184=[-2.6312679588992553245 ,2.2447781868738982220 ] 
dist 185=[-2.5486342827244867753 ,2.2563340654434985170 ] 
dist 186=[-2.5273469531009118548 ,2.2558068665707234630 ] 
dist 187=[-2.4845493921278925651 ,2.2387900828960745037 ] 
dist 188=[-2.4685718280984222571 ,2.2299680915808621852 ] 
dist 189=[-2.3871044596839710315 ,2.1362547776023888986 ] 
dist 190=[-2.3670206269861294020 ,2.1105421171278935234 ] 
dist 191=[-2.2987578692517662304 ,2.0790435568752313361 ] 
dist 192=[-2.2871421805708699606 ,2.0640694340798287779 ] 
dist 193=[-1.0346523019199731071 ,1.0747040929472512630 ] 
dist 194=[-.91620639187946513907,.88861668490883993574] 
dist 195=[-.6520729280679084325 ,1.1563513281994934942 ] 
dist 196=[-.59591856920997549147,1.4221124289895199061 ] 
dist 197=[-.2802435698419117088 ,1.6663146420314359476 ] 
dist 198=[-.22421370529786719984,1.8480024746754163018 ] 
dist 199=[-.10753987587986897238,2.0187332713521160198 ] 
dist 200=[-.07725339392110486525,2.2192066078560856835 ] 
dist 201=[.1493448079545762126 ,2.4041685358863072406 ] 
dist 202=[.0477665704968521221 ,2.5129894005718875538 ] 
dist 203=[-.0473169175954406032 ,2.5869104002215944982 ] 
dist 204=[-.15587797048962921968,2.6325747913142127033 ] 
dist 205=[-.31125124143158918864,2.6621043309137332362 ] 
dist 206=[-.48487360623211397401,2.6716211894131052007 ] 
dist 207=[-.66627496842008418432,2.6684001423453433935 ] 
dist 208=[-.88816704866916117481,2.6633917622383827599 ] 
dist 209=[-1.2234059616189217113 ,2.4083591793078796992 ] 
dist 210=[-1.5579878952816393352 ,2.4884089694783024420 ] 
dist 211=[-1.7772575069884823946 ,2.5781759151274673659 ] 
dist 212=[-1.9540926605684001511 ,2.6436966662905957315 ] 
dist 213=[-2.1192992058405278323 ,2.6904669552028971099 ] 
dist 214=[-2.2644205812669106357 ,2.7053925414321117070 ] 
dist 215=[-2.3610863478113717880 ,2.7069783812911811315 ] 
dist 216=[-2.4407860662966504609 ,2.7005043359943940399 ] 
dist 217=[-2.5181874028754515531 ,2.6534012691063670775 ] 
dist 218=[-2.5820039920089016414 ,2.5223159473416044304 ] 
dist 219=[-2.6074814384349005783 ,2.4549362062955198198 ] 
dist 220=[-2.6167434594578483537 ,2.4311487877871337518 ] 
dist 221=[-2.6158374994198031682 ,2.3135079386940744979 ] 
dist 222=[-2.5460889682296962062 ,2.2861304862398907620 ] 
dist 223=[-2.5241935966461554754 ,2.2105662138929937647 ] 
dist 224=[-2.5075961053127119060 ,2.1900917393666029607 ] 
dist 225=[-2.4938789530369567050 ,2.0790597116745362582 ] 
dist 226=[-2.3507744577584439382 ,.74913935588800041159] 
dist 227=[-2.3141296705477869980 ,.62448243419679849976] 
dist 228=[-2.3059189775151152261 ,.35317552746011862246] 
dist 229=[-2.1743092114002096476 ,.29208842475162031377] 
dist 230=[-2.1417741628764807918 ,-.00861556961238090840] 
dist 231=[-2.2821819001580677102 ,-.06055816171592117620] 
dist 232=[-2.4806482062831822983 ,-.18089165598975440936] 
dist 233=[-2.6610485546972655825 ,-.19835216751451204538] 
dist 234=[-2.7660401529286971539 ,-.34612238980049420562] 
dist 235=[-2.8359102023918637372 ,-.36898519482591514326] 
dist 236=[-2.8761265231910966598 ,-.36410557067843213402] 
dist 237=[-2.9001310916059042767 ,-.32007513747604036332] 
dist 238=[-2.9052935046296590081 ,-.25422120344211184843] 
dist 239=[-2.8984532317654785338 ,-.1122614613263026945 ] 
dist 240=[-2.8914788722630262455 ,.3459803576696077851 ] 
dist 241=[-2.5494939811826104093 ,.80709841079153399788] 
dist 242=[-2.5401504657761189807 ,1.1155254757784265955 ] 
dist 243=[-2.4990370768290377440 ,1.3712243938901465692 ] 
dist 244=[-2.4877941305828099454 ,1.6218838385531128226 ] 
dist 245=[-2.3503726895745797484 ,1.8501762820980829785 ] 
dist 246=[-2.3161156090396502408 ,2.0166004535419554306 ] 
dist 247=[-2.2790466168420381768 ,2.1696163886311042394 ] 
dist 248=[-2.2601066628194865301 ,2.3443933510496595570 ] 
dist 249=[-1.7667891269410197813 ,2.5030917247645497767 ] 
dist 250=[-1.6977936321270556485 ,2.5919321612317492448 ] 
dist 251=[-1.5578667442335168329 ,2.6466381503487366484 ] 
dist 252=[-1.5192716629792343721 ,2.6690918565016948367 ] 
dist 253=[-1.3693813460887752341 ,2.6785134696438385580 ] 
dist 254=[-1.3362986198096446108 ,2.6812009974315649823 ] 
dist 255=[-1.2664353243245094018 ,2.6794753222052277731 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 0, 0, 0, 2] 
dist 0=[44.621451165297067809  ,44.621451165297067809  ] 
dist 1=[43.166631409510245801  ,45.682302582560062162  ] 
dist 2=[40.790826560463298743  ,46.484964430641585091  ] 
dist 3=[38.346979447835919496  ,47.113518218338620030  ] 
dist 4=[36.620360785865080035  ,47.479127430753584572  ] 
dist 5=[35.085431943025587630  ,47.722322122407243239  ] 
dist 6=[33.406711869393581190  ,47.862013343562668292  ] 
dist 7=[31.759458072681930375  ,47.927241071402045124  ] 
dist 8=[30.349899253050743822  ,47.872920856951467710  ] 
dist 9=[28.840578171325724715  ,47.032960899799336636  ] 
dist 10=[26.794443021709131977  ,46.828907547395299627  ] 
dist 11=[24.753610706008357653  ,46.573708145539697476  ] 
dist 12=[23.265197083385514221  ,46.447851501622990105  ] 
dist 13=[21.890937579624169393  ,46.122600166316838097  ] 
dist 14=[20.305656081969027776  ,45.975885837670090572  ] 
dist 15=[18.697301816294690918  ,45.741680715026973236  ] 
dist 16=[17.230402501251831277  ,45.437862848836089960  ] 
dist 17=[15.578390602568423764  ,31.701193121288980692  ] 
dist 18=[13.229623090366520076  ,30.498557892323817157  ] 
dist 19=[10.907253498444434540  ,27.598236516918617832  ] 
dist 20=[9.3605971038051865014 ,27.159990567731138264  ] 
dist 21=[8.0770679850399476838 ,22.959815108267753831  ] 
dist 22=[6.8064709475462282184 ,22.179184486629738499  ] 
dist 23=[5.6322903786667802971 ,21.227166172317301082  ] 
dist 24=[4.7341123529291630730 ,21.000562891781331764  ] 
dist 25=[3.8604841266816952886 ,14.448226832599060662  ] 
dist 26=[2.7843028337077299907 ,13.632030198758815480  ] 
dist 27=[1.7538773063240402183 ,11.937834161653554117  ] 
dist 28=[.1755470373015997756 ,11.496984643033587180  ] 
dist 29=[-1.6726681515386246161 ,9.8798154306588353167 ] 
dist 30=[-4.2424047970351181384 ,9.5634693481726885331 ] 
dist 31=[-6.7437512262513830047 ,8.9869521142013507902 ] 
dist 32=[-8.3188963692694277922 ,8.8581562811259132034 ] 
dist 33=[-9.5269782570690975450 ,2.7990771536348086949 ] 
dist 34=[-10.561314673214827074  ,2.9775565448511115687 ] 
dist 35=[-11.414023346966657605  ,3.1668294635667268222 ] 
dist 36=[-11.896389025205422558  ,3.2854183666819037970 ] 
dist 37=[-12.204904032409464996  ,3.3704310957677840550 ] 
dist 38=[-12.363328826928453752  ,3.4266561575028663620 ] 
dist 39=[-12.455821248718231880  ,3.4623837086480220368 ] 
dist 40=[-12.500774511470407727  ,3.4661302959530461328 ] 
dist 41=[-12.522619440738957807  ,3.4539605760792155093 ] 
dist 42=[-12.522059872623871412  ,3.4377623344358332882 ] 
dist 43=[-12.509506058845928258  ,3.0633532334779293677 ] 
dist 44=[-12.612629802768234860  ,2.9933192644064156501 ] 
dist 45=[-12.769961774525076193  ,2.8528060836974596466 ] 
dist 46=[-12.799573531257931876  ,2.8068643957771761545 ] 
dist 47=[-12.777609089535264566  ,2.5923140258792645456 ] 
dist 48=[-12.745505562536539977  ,2.5423507637437418042 ] 
dist 49=[-3.6716137700762743632 ,2.3816589748640169886 ] 
dist 50=[-3.6498116046312294836 ,2.3543910612512652082 ] 
dist 51=[-3.0663322534145978344 ,-.0900364864770170082 ] 
dist 52=[-2.9842894585283365880 ,.66320422964279627146] 
dist 53=[-2.8005456390716564844 ,1.3898931269801037680 ] 
dist 54=[-2.7466217784897737558 ,2.2707150935120234273 ] 
dist 55=[-2.5041151466355635103 ,3.1015408334755578942 ] 
dist 56=[-2.4544843653227372062 ,3.6287041366033434083 ] 
dist 57=[-2.3377916367536242332 ,4.0347237304278892381 ] 
dist 58=[-2.3053286291670900479 ,4.3820539995731590542 ] 
dist 59=[-1.9793250605202550480 ,4.6656436338215224017 ] 
dist 60=[-1.9255101303756703776 ,4.8172948242718973195 ] 
dist 61=[-1.8065535413728073200 ,4.9018338801037430692 ] 
dist 62=[-1.7711999792893048640 ,4.9204539585158138199 ] 
dist 63=[-1.6186123481648052038 ,4.6100800671503353264 ] 
dist 64=[-1.5873249621254731804 ,4.5806636222297989619 ] 
dist 65=[-1.5121635460420613274 ,4.4803455302895202962 ] 
dist 66=[-1.4925801289078287686 ,4.4570271610345844872 ] 
dist 67=[-1.2909768178769383898 ,4.1971688272634915292 ] 
dist 68=[-1.2538074285126644245 ,4.1369536326002028513 ] 
dist 69=[-1.2008372938656473418 ,4.0654005025429778083 ] 
dist 70=[-1.1839462101602344882 ,4.0340441495910662776 ] 
dist 71=[-1.1593963495282972660 ,3.6544640156043672559 ] 
dist 72=[-1.1588935369276822354 ,3.7825828615364750545 ] 
dist 73=[-1.1695401094220256536 ,3.8679871976478227124 ] 
dist 74=[-1.1978980343231649278 ,3.9176842812714662105 ] 
dist 75=[-1.2318687041199549492 ,3.9493167755816558370 ] 
dist 76=[-1.2649273929069529803 ,3.9626045845672244067 ] 
dist 77=[-1.3034809170560116965 ,3.9651211382545033351 ] 
dist 78=[-1.3594129214088230692 ,3.9547241227037799220 ] 
dist 79=[-1.4220647536607756104 ,3.9343788503928921161 ] 
dist 80=[-1.4874501367892007418 ,3.9182368979378319170 ] 
dist 81=[-1.5672632829419521500 ,3.8726142918099666151 ] 
dist 82=[-1.6875037016688729837 ,3.8500085797410425638 ] 
dist 83=[-1.9019497200557770659 ,.8281788667579180214 ] 
dist 84=[-2.1173372127616320981 ,.62097947678131278286] 
dist 85=[-2.3131671039502687900 ,.51765813227217569227] 
dist 86=[-2.5342645913566171372 ,.48866258848933723152] 
dist 87=[-2.7351939831568819003 ,-.04581830191046098766] 
dist 88=[-2.8504942621510437507 ,-.11406941299153123236] 
dist 89=[-2.9255607864996411999 ,-.26782276918488430473] 
dist 90=[-2.9657923691336526504 ,-.29684087899992940481] 
dist 91=[-2.9901306766863529246 ,-.4846701524110349369 ] 
dist 92=[-3.0017200116530831549 ,-.5176402061378660739 ] 
dist 93=[-3.0063423701872541499 ,-.5791248266897260477 ] 
dist 94=[-3.0028609938622818863 ,-.4191677341862699032 ] 
dist 95=[-2.3501605504115127484 ,-.1045015418701562972 ] 
dist 96=[-2.3941068604205604657 ,.2125285126025012335 ] 
dist 97=[-2.4175742503280171018 ,.5920100353413964402 ] 
dist 98=[-2.4201535677978108872 ,1.1559224759703607587 ] 
dist 99=[-2.2767212277886485338 ,1.7163567533043664719 ] 
dist 100=[-2.2517031316258278904 ,2.0819484201202826346 ] 
dist 101=[-2.1949686086042710405 ,2.3747679781451821331 ] 
dist 102=[-2.1745252942812792570 ,2.6447411529007576065 ] 
dist 103=[-2.0721141214407005485 ,2.8792354225245462736 ] 
dist 104=[-2.0481411211711310202 ,3.0304364501284889609 ] 
dist 105=[-1.9822033506548189398 ,3.1494558448483645183 ] 
dist 106=[-1.9639239285805080181 ,3.2554751572430037810 ] 
dist 107=[-1.7408486418188748138 ,3.3443931880325773281 ] 
dist 108=[-1.7033029800612983922 ,3.3951617234168734469 ] 
dist 109=[-1.6074525444286969424 ,3.4275780103402706076 ] 
dist 110=[-1.5867968051897646879 ,3.4432914265221579767 ] 
dist 111=[-1.4217946161934561488 ,3.4469955419861806350 ] 
dist 112=[-1.3873026715233467341 ,3.4405898006477786674 ] 
dist 113=[-1.3344832346112258675 ,3.4099407247556006978 ] 
dist 114=[-1.3184389486471540961 ,3.3905625913929962517 ] 
dist 115=[-.2609695851888924963 ,2.4178128645244844785 ] 
dist 116=[-.3655979889559146001 ,2.6452968440476115238 ] 
dist 117=[-.4766015730756855222 ,2.8186237264799808659 ] 
dist 118=[-.6252290372537365263 ,2.9635159207055542939 ] 
dist 119=[-.7717062728033287667 ,3.0791646542305769831 ] 
dist 120=[-.8741411637180596845 ,3.1357620600206329474 ] 
dist 121=[-.9639108996035191313 ,3.1642463045032155855 ] 
dist 122=[-1.0598619923006165961 ,3.1676609386463837454 ] 
dist 123=[-1.1524817719017304800 ,3.1204392599545104217 ] 
dist 124=[-1.2289731235367954779 ,3.1018699500468447494 ] 
dist 125=[-1.3083694724046138698 ,3.0655454860395168708 ] 
dist 126=[-1.4126125782634613396 ,3.0502230852505405157 ] 
dist 127=[-1.5110497743899339482 ,2.9664594321425353734 ] 
dist 128=[-1.5672773433683298358 ,2.9447835545677720362 ] 
dist 129=[-1.6034559736730687406 ,2.8670194856065629858 ] 
dist 130=[-1.6218561222749804718 ,2.8542029006156536397 ] 
dist 131=[-1.6315147730761345618 ,1.3737085374829583895 ] 
dist 132=[-1.6327905868712590002 ,1.2342370780022213985 ] 
dist 133=[-1.6282062965813514487 ,.91352658209449345193] 
dist 134=[-1.6448299700325944148 ,.85310135648895676125] 
dist 135=[-1.7475598750299850026 ,.43959089531342037579] 
dist 136=[-1.8041136688347656340 ,.36522934936216764655] 
dist 137=[-1.8870570390896632593 ,.23145763408779281068] 
dist 138=[-2.1046567550940404677 ,.20156700099582861939] 
dist 139=[-2.3047356987877161661 ,-.2304910069830287848 ] 
dist 140=[-2.4281460437378939985 ,-.2898887068507005001 ] 
dist 141=[-2.5190587429033603468 ,-.3384563853402075289 ] 
dist 142=[-2.5894284571193038630 ,-.0251836555094811963 ] 
dist 143=[-2.6412406292285898069 ,.2881871891077186415 ] 
dist 144=[-2.6580852693742710277 ,.49807156484973684564] 
dist 145=[-2.6612252600116428463 ,.67239177399186193879] 
dist 146=[-2.6583281309604647874 ,.8438074698026030604 ] 
dist 147=[-1.2915099879470559863 ,1.0002764282568417386 ] 
dist 148=[-1.1933771945026265704 ,1.1149354409254178440 ] 
dist 149=[-1.0666078111386326509 ,1.2209461253341787411 ] 
dist 150=[-1.0535687929406988005 ,1.3428922828899959129 ] 
dist 151=[-.6323514171505783524 ,1.4544325425585425272 ] 
dist 152=[-.5780847126025160377 ,1.5189097336240113924 ] 
dist 153=[-.47264564539461548662,1.5612672763469622579 ] 
dist 154=[-.51561633889502468675,1.5845248618732978470 ] 
dist 155=[-.60628278941838848512,1.5987672788683458536 ] 
dist 156=[-.68445275653502134077,1.6051395005880243037 ] 
dist 157=[-.76842810484819001622,1.6069620101256715730 ] 
dist 158=[-.88225852834496473884,1.6030326208631855655 ] 
dist 159=[-1.0065305132241499130 ,1.4459038877316195096 ] 
dist 160=[-1.1321738289521788691 ,1.4399738011247073438 ] 
dist 161=[-1.2828459715429414647 ,1.4448335255720669505 ] 
dist 162=[-1.5070005453471505494 ,1.7242334452903090474 ] 
dist 163=[-1.7289230349765621324 ,1.9984184312352118804 ] 
dist 164=[-1.8706853785540257554 ,2.1706763267202487162 ] 
dist 165=[-1.9808151764000605578 ,2.3013406421922855062 ] 
dist 166=[-2.0764950421185799134 ,2.4094993148335109476 ] 
dist 167=[-2.1554959058541335708 ,2.4949866809537480847 ] 
dist 168=[-2.1990597564878774503 ,2.5351569910474619808 ] 
dist 169=[-2.2249681038667807700 ,2.5544496498644607230 ] 
dist 170=[-2.2335028566028985605 ,2.5565930399030373083 ] 
dist 171=[-2.2321750202829322726 ,2.5075601942880130816 ] 
dist 172=[-2.2269272352952118765 ,2.4911576437785080557 ] 
dist 173=[-2.2024299361496927191 ,2.4564442339046656966 ] 
dist 174=[-2.1897860703085768822 ,2.4420976080428273035 ] 
dist 175=[-2.0969252359427151343 ,2.3641048486153226912 ] 
dist 176=[-2.0717549708267284301 ,2.3445576739383358866 ] 
dist 177=[-2.0314192480030514267 ,2.2796425975056226812 ] 
dist 178=[-2.0171912499660153530 ,2.2668501399768486143 ] 
dist 179=[-1.1116869685832932856 ,1.1131818487101694831 ] 
dist 180=[-1.2051362457761844008 ,1.0017823894384428972 ] 
dist 181=[-1.2911207809418341989 ,.75271988372984569514] 
dist 182=[-1.4329324540621284861 ,.69912122974701781406] 
dist 183=[-1.6697108849769974723 ,.5033985446162662631 ] 
dist 184=[-1.8451824278597964672 ,.5388140344079478035 ] 
dist 185=[-2.0093868918675571092 ,.5638634008271136130 ] 
dist 186=[-2.2011986403335273007 ,.5812957913130245849 ] 
dist 187=[-2.3776430599296538913 ,.5941428336433434884 ] 
dist 188=[-2.4805126683081766106 ,.6008931905658102531 ] 
dist 189=[-2.5492184933770390939 ,.6044651501700841060 ] 
dist 190=[-2.5893036623554687823 ,.6046267765565526088 ] 
dist 191=[-2.6141716145575471696 ,.52947500353871315699] 
dist 192=[-2.6221364323551587683 ,.58898877732354838689] 
dist 193=[-2.6192516097844674354 ,.69590393656569729979] 
dist 194=[-2.6135024972480765285 ,.801415497925994469  ] 
dist 195=[-2.3386405732401456054 ,.89795967925715336172] 
dist 196=[-2.4297548225348118000 ,.9690848201211347084 ] 
dist 197=[-2.5299101374652146142 ,1.0352226158133821704 ] 
dist 198=[-2.6066597178845008371 ,1.1180173486085440276 ] 
dist 199=[-2.6633246601158853027 ,1.2034375190798975576 ] 
dist 200=[-2.6833140524518289894 ,1.2732689328432156135 ] 
dist 201=[-2.6886706037865745928 ,1.4519811634875618053 ] 
dist 202=[-2.6869305112288894952 ,1.6717790000299932092 ] 
dist 203=[-2.5695763177507180033 ,1.8796950830011189513 ] 
dist 204=[-2.5436826113577082695 ,2.0109858660621513297 ] 
dist 205=[-2.4844455418977016113 ,2.1113070110109176891 ] 
dist 206=[-2.4625414119930132729 ,2.1956166465247296793 ] 
dist 207=[-2.3508681224475439618 ,2.2632073889948598416 ] 
dist 208=[-2.3242031771178015871 ,2.2968014042860681217 ] 
dist 209=[-2.2523787329105324678 ,2.3119492750297287019 ] 
dist 210=[-2.2302838035720491461 ,2.3134186861799890883 ] 
dist 211=[-.9889573114309994081 ,2.2896048217747095682 ] 
dist 212=[-1.0283047867279918034 ,2.3437044675713306385 ] 
dist 213=[-1.0560277710688051504 ,2.4327086501199976573 ] 
dist 214=[-1.1011189104218459585 ,2.4987486712417731019 ] 
dist 215=[-1.1747697619397269083 ,2.5465444623614532713 ] 
dist 216=[-1.2170953884610665331 ,2.5627274921327526691 ] 
dist 217=[-1.2445775408485930053 ,2.5656626377306603780 ] 
dist 218=[-1.2589835092417371211 ,2.5605789270645651625 ] 
dist 219=[-1.2664802700523699412 ,2.6185960682593756817 ] 
dist 220=[-1.2663877198113185748 ,2.7228855984950810317 ] 
dist 221=[-1.2616770754402405672 ,2.7930880875824789160 ] 
dist 222=[-1.2575864248104224372 ,2.8351340471063775091 ] 
dist 223=[-.0813552564088553582 ,2.8608247563958269067 ] 
dist 224=[-.1808333945737162642 ,2.8657471451965703885 ] 
dist 225=[-.2754548971903602159 ,2.8591656546458828961 ] 
dist 226=[-.3998762165250221195 ,2.8510236666980648100 ] 
dist 227=[-.8530936041106438450 ,2.5035762933630293406 ] 
dist 228=[-1.1556960720579976976 ,2.4968072144920604898 ] 
dist 229=[-1.4059701174613644241 ,2.4626701173346351694 ] 
dist 230=[-1.6503251556490048376 ,2.4519401011428321390 ] 
dist 231=[-1.8722243266050251122 ,2.3267383092215640573 ] 
dist 232=[-2.0328692525425505138 ,2.2947817806746134432 ] 
dist 233=[-2.1794450653584631792 ,2.2587349725883946876 ] 
dist 234=[-2.3451910996005628301 ,2.2408368097848501282 ] 
dist 235=[-2.4947882844103638161 ,1.7716127825832403904 ] 
dist 236=[-2.5769084050507249288 ,1.7055202013144950493 ] 
dist 237=[-2.6253484101962862235 ,1.5705865354690006468 ] 
dist 238=[-2.6405149039193551570 ,1.5329983728020031088 ] 
dist 239=[-2.6437351755719130646 ,1.3848347519779178924 ] 
dist 240=[-2.6444910744198671528 ,1.3525063787543407917 ] 
dist 241=[-2.6435914840320411406 ,1.2809630163840016910 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 0, 1, 0, 1, 2] 
dist 0=[57.547461976923269377  ,57.547461976923269377  ] 
dist 1=[57.123099291293995078  ,57.693087263942029514  ] 
dist 2=[56.372652644282457208  ,57.736864752449247080  ] 
dist 3=[54.925099124372412049  ,57.754635344527112431  ] 
dist 4=[53.290910721666115549  ,57.752083985081952233  ] 
dist 5=[51.795028667718355398  ,57.714506747449206636  ] 
dist 6=[50.111051452104519610  ,57.643528396652279669  ] 
dist 7=[47.725497468530365413  ,57.532173432385780353  ] 
dist 8=[45.065013625062074117  ,53.514492328525702237  ] 
dist 9=[42.282953573570501354  ,52.894305121460701873  ] 
dist 10=[38.872371088232444428  ,51.847841602216878793  ] 
dist 11=[33.701637161229734499  ,51.559826911635065074  ] 
dist 12=[28.502606516762982291  ,50.702485839422039357  ] 
dist 13=[24.978897999153160921  ,50.416792237883263505  ] 
dist 14=[21.999125758935247716  ,49.177371180890424198  ] 
dist 15=[18.972182126027940106  ,46.852453928044849273  ] 
dist 16=[16.136793390815935492  ,35.202527383114134180  ] 
dist 17=[13.921781881121903077  ,33.215072844959408203  ] 
dist 18=[11.730214969295568333  ,32.695997492811295406  ] 
dist 19=[8.9879384847731737361 ,30.832084742997299666  ] 
dist 20=[6.3548641996762940807 ,30.407919444904119006  ] 
dist 21=[4.5991612492314206416 ,29.742701694317501682  ] 
dist 22=[3.1429031342686611368 ,29.553241066486315462  ] 
dist 23=[1.7054748552097114137 ,14.099474812060669430  ] 
dist 24=[.38068735846698063282,10.022581721806100593  ] 
dist 25=[-.62620938802556698422,6.9913323445856691777 ] 
dist 26=[-1.6006281265375121639 ,6.0089095444888766021 ] 
dist 27=[-4.0554404753511281802 ,5.0661869215193818469 ] 
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dist 30=[-9.7030395576753662529 ,2.6615344277115417474 ] 
dist 31=[-11.605636628232765022  ,2.4141054337988003965 ] 
dist 32=[-12.770669837931147469  ,-4.5565689680847893566 ] 
dist 33=[-13.622203432171711079  ,-5.4017276208534091335 ] 
dist 34=[-14.272756282445740087  ,-5.5664630257118417120 ] 
dist 35=[-14.774586317204491392  ,-5.3677575370121741792 ] 
dist 36=[-15.032013487387316925  ,-5.0670961956330909494 ] 
dist 37=[-15.160691278896905968  ,-4.7631349048550516603 ] 
dist 38=[-15.168932990519491285  ,-4.4008347743512440623 ] 
dist 39=[-8.9661141530750828014 ,-3.7853952080794714320 ] 
dist 40=[-8.6775954994115138520 ,-3.2068894786533037333 ] 
dist 41=[-8.6075897063171203030 ,-2.6311731144049848085 ] 
dist 42=[-8.5177167904656720695 ,-1.8538211288503446649 ] 
dist 43=[-8.4722918173083203314 ,-.67748586507410663865] 
dist 44=[-8.3529149800079243869 ,.50116556793021965226] 
dist 45=[-8.2989102535570458937 ,1.2878446230423653227 ] 
dist 46=[-8.2262383354500395428 ,1.9379547058450452342 ] 
dist 47=[-8.1896316761143594478 ,2.5715049302768956915 ] 
dist 48=[-3.3116782482622786000 ,3.1456709545388057405 ] 
dist 49=[-2.9013238078171507592 ,3.5587146572300454160 ] 
dist 50=[-1.9478449616738895937 ,3.9325243654122812839 ] 
dist 51=[-1.7926333489246104439 ,4.3499786575990365274 ] 
dist 52=[-.55417882623313214986,4.7315024397531837205 ] 
dist 53=[-.33693042918377125464,4.9619381722507834491 ] 
dist 54=[-.0045672918984721275 ,5.1255540662596074028 ] 
dist 55=[.0778261448349001475 ,5.2406053350423668332 ] 
dist 56=[1.3820041974983943846 ,5.3173333799957408715 ] 
dist 57=[1.5458727521254160260 ,5.3333767147033848810 ] 
dist 58=[1.8676791159351565885 ,5.3173193188605476942 ] 
dist 59=[1.9412142537249478692 ,5.3094165987597387200 ] 
dist 60=[2.1138143012726124576 ,5.4031825582605596925 ] 
dist 61=[1.6929052355236246485 ,5.5712936813493378293 ] 
dist 62=[1.3340500357819295025 ,5.7414223234971557094 ] 
dist 63=[.9665008371065515464 ,5.8860521492766382928 ] 
dist 64=[.6217302168609390869 ,5.9523278199679823228 ] 
dist 65=[.3537078999150530324 ,5.9789696900806532486 ] 
dist 66=[.0905631945338880248 ,5.9771306637256100252 ] 
dist 67=[-.23483768548433526858,5.8952765176713233986 ] 
dist 68=[-.63306917527280518195,5.8620083414922026492 ] 
dist 69=[-1.2436723625914855222 ,5.8001825322434812568 ] 
dist 70=[-2.1599103384843690844 ,5.7750950445721271134 ] 
dist 71=[-3.0718016565942631903 ,1.6373311564679740512 ] 
dist 72=[-3.6650921581231485040 ,1.3301525357742509865 ] 
dist 73=[-4.1389530250560053177 ,1.3038321012387670948 ] 
dist 74=[-4.5741429959060080591 ,1.2590628110275232118 ] 
dist 75=[-4.9515842534911658424 ,1.2476194931408160548 ] 
dist 76=[-5.1949545306402104257 ,1.2164073590147386114 ] 
dist 77=[-5.3870253965922558852 ,1.2079978026441368939 ] 
dist 78=[-5.5597435302488128442 ,1.2050199841542323535 ] 
dist 79=[-5.7011633423767618300 ,1.2079951986075619534 ] 
dist 80=[-5.7997700777679264593 ,1.2114823294086691360 ] 
dist 81=[-5.9091553362183089101 ,1.2105347576524253268 ] 
dist 82=[-5.9950099470621315422 ,1.2061281019066185099 ] 
dist 83=[-6.0592857913689788591 ,1.2027131246080949672 ] 
dist 84=[-6.0825019325141562693 ,1.1780826855080900665 ] 
dist 85=[-6.0800746588514048464 ,1.1702713473153977354 ] 
dist 86=[-6.0673403626896257768 ,1.1467850383141704729 ] 
dist 87=[-3.6199752822759791580 ,1.1373485081756873344 ] 
dist 88=[-3.4191512843459332919 ,1.0159517358735410449 ] 
dist 89=[-2.9420226264567616307 ,1.4015683595212257699 ] 
dist 90=[-2.8530952071844881065 ,1.9907306261940572937 ] 
dist 91=[-2.1789052672984176417 ,2.5279612266613206892 ] 
dist 92=[-2.0521970614691831462 ,2.9205171755834917080 ] 
dist 93=[-1.9843449613167640182 ,3.2823035456972083066 ] 
dist 94=[-1.9548330605174066525 ,3.6967319250859906581 ] 
dist 95=[-1.9424684593537706564 ,4.0796381614860432420 ] 
dist 96=[-1.0150950231842825113 ,4.3156071746778605808 ] 
dist 97=[-.93049155326375928476,4.4891331253713084399 ] 
dist 98=[-.73336375775804325346,4.6227932440363436314 ] 
dist 99=[-.69815547211627269343,4.7211062096512004898 ] 
dist 100=[-.43626115885339015106,4.7535558910356892328 ] 
dist 101=[-.38892945756083874281,4.7613180768614177919 ] 
dist 102=[-.31043790271880638393,4.7610885163734368819 ] 
dist 103=[-.29195151746291398492,3.0561643919999638136 ] 
dist 104=[.0096040609445532722 ,3.2522039620346870306 ] 
dist 105=[.0490574774009198112 ,3.3930093767185789123 ] 
dist 106=[.13033851547233034936,3.4955262277932640839 ] 
dist 107=[.03614421158190533541,3.5713234581248439042 ] 
dist 108=[-.29736523502242790433,3.6054551387705254227 ] 
dist 109=[-.52204414684197983259,3.6161044760130394857 ] 
dist 110=[-.7101974470039367445 ,3.6142154315872798334 ] 
dist 111=[-.8979018418364596029 ,3.3590674864677547741 ] 
dist 112=[-1.0711394391922103225 ,3.3128440629882182892 ] 
dist 113=[-1.2015453608720460702 ,3.2272430494068213032 ] 
dist 114=[-1.3256745946825427225 ,3.2009833094298128304 ] 
dist 115=[-1.4738626663408704255 ,3.0907082717861464540 ] 
dist 116=[-1.6120524081240380761 ,3.0602046468802010881 ] 
dist 117=[-1.6962699446586674232 ,2.9880668105172637712 ] 
dist 118=[-1.7571766446750940561 ,2.9612003514678303972 ] 
dist 119=[-1.8023074567595351714 ,1.4305053303200885209 ] 
dist 120=[-1.8352154981974037313 ,1.4147688257679238380 ] 
dist 121=[-1.8473195386321623163 ,1.4086745484309233821 ] 
dist 122=[-1.8501571538725818488 ,1.3858260541107163156 ] 
dist 123=[-1.8462564089623110559 ,1.3784479107778812130 ] 
dist 124=[-1.8544330616224763068 ,1.3093572005441629633 ] 
dist 125=[-2.0866745289222660726 ,1.2920793865534063728 ] 
dist 126=[-2.3580309741165010238 ,1.2690545245853952768 ] 
dist 127=[-2.6085951140031371508 ,1.2596297825947605408 ] 
dist 128=[-2.7578473260882047306 ,-.48316026562038184468] 
dist 129=[-2.8615146521158268116 ,-.58627713563739369711] 
dist 130=[-2.9301332105864973256 ,-.82004931743423902557] 
dist 131=[-2.9785782326236416170 ,-.80948876061059542323] 
dist 132=[-3.0017207951346780481 ,-.73822932870839883253] 
dist 133=[-3.0107731352280104740 ,-.62634709275442066553] 
dist 134=[-3.0061579688752399571 ,-.42988579973676508203] 
dist 135=[-1.4771601843394093105 ,-.22426392152632528607] 
dist 136=[-1.4807478872819083211 ,-.07581508279972927998] 
dist 137=[-1.4955386726672243740 ,.05911463806177311833] 
dist 138=[-1.5271747845102308556 ,.21080000805490355465] 
dist 139=[-1.5529523101950031963 ,.36160529670881289288] 
dist 140=[-1.5730058425963279720 ,.4930347586180913796 ] 
dist 141=[-1.5817935846290404012 ,.63544315202094672079] 
dist 142=[-1.5840168708593119759 ,.83008303389856049105] 
dist 143=[-1.5811477014111934639 ,1.0239264776184776647 ] 
dist 144=[-1.0309916767887515602 ,1.1631646540073397080 ] 
dist 145=[-1.0028476995074755023 ,1.2891120583875732518 ] 
dist 146=[-.93402667075873002913,1.4299191353562148456 ] 
dist 147=[-.91833145002407487187,1.5695992689277750608 ] 
dist 148=[-.80915443032788930288,1.6910604061327646178 ] 
dist 149=[-.78666273211770308173,1.8225387362952097579 ] 
dist 150=[-.9630491874896067844 ,2.0022240382008141366 ] 
dist 151=[-1.2469379388832957222 ,2.1744535526460612089 ] 
dist 152=[-1.4342398365379860339 ,2.2761747023151468010 ] 
dist 153=[-1.5865763973262759913 ,2.3458405634539239680 ] 
dist 154=[-1.7309233847737625404 ,2.3901075407223128965 ] 
dist 155=[-1.8589947375942812530 ,2.4193942102195608014 ] 
dist 156=[-1.9463758973222699806 ,2.4292560397722277511 ] 
dist 157=[-2.0206298518907430316 ,2.4273257809817157323 ] 
dist 158=[-2.0963075978715696905 ,2.4228633692314734334 ] 
dist 159=[-2.1601175615337244258 ,2.2072089258089499016 ] 
dist 160=[-2.1870073035895725993 ,2.1706910514884524572 ] 
dist 161=[-2.1984942708397799538 ,2.0980511134660100052 ] 
dist 162=[-2.2008442826527304833 ,2.0757145299851646786 ] 
dist 163=[-2.1391227070312491024 ,1.9789236300037449074 ] 
dist 164=[-2.1228696011899445958 ,1.9556376184312222111 ] 
dist 165=[-2.1128798726381378837 ,1.8936905898253544228 ] 
dist 166=[-2.1088140859893898841 ,1.8749097199501196391 ] 
dist 167=[-.88239100196064257257,.61507242544595357308] 
dist 168=[-1.0878377987149716247 ,.49940491236909369943] 
dist 169=[-1.2363432961357746640 ,.24856168860030998234] 
dist 170=[-1.4099848956641020006 ,.19228125850655407108] 
dist 171=[-1.6434923684955144647 ,.16443230813947655206] 
dist 172=[-1.8169148117105973294 ,.29530086736963584058] 
dist 173=[-1.9795820595957562845 ,.43911040529178316902] 
dist 174=[-2.1701653307806332682 ,.61998004535125464262] 
dist 175=[-2.3457946554158984315 ,.89876840378833935144] 
dist 176=[-2.4487761080640162975 ,1.1791667626935844065 ] 
dist 177=[-2.5182997442937052531 ,1.3664612389516471209 ] 
dist 178=[-2.5603855716766123760 ,1.5214499269552406614 ] 
dist 179=[-2.5871184993096737703 ,1.6729009481145514388 ] 
dist 180=[-2.6077020943436846352 ,1.8105027957393969236 ] 
dist 181=[-2.6206678091467253751 ,1.9102119521328378575 ] 
dist 182=[-2.6235531831734113198 ,2.0012641980077843643 ] 
dist 183=[-2.6180702982054405167 ,2.1043091302043889809 ] 
dist 184=[-2.4824926571625219693 ,2.1973013649839546274 ] 
dist 185=[-2.5409449153817849933 ,2.2482278395638196137 ] 
dist 186=[-2.5713920971260575366 ,2.2780775056707884993 ] 
dist 187=[-2.5880884920835007485 ,2.2869432480739605987 ] 
dist 188=[-2.5916523198409143958 ,2.2857850738616532940 ] 
dist 189=[-2.5862843982090680116 ,2.2793386255174885194 ] 
dist 190=[-2.5795637160398665247 ,2.2609196020414297074 ] 
dist 191=[-2.2964491962105884127 ,2.2501080001614181225 ] 
dist 192=[-2.2512199587186714494 ,2.0223776328887610583 ] 
dist 193=[-2.1627803514102401083 ,2.1054510445454492439 ] 
dist 194=[-2.1367482216303415022 ,2.1891546590048234196 ] 
dist 195=[-2.0295572746057641968 ,2.2564188522417252268 ] 
dist 196=[-2.0031861454612803932 ,2.2901679552845126684 ] 
dist 197=[-1.9405093418239924864 ,2.3058566498944808110 ] 
dist 198=[-1.9183473761573068538 ,2.3072227539097346572 ] 
dist 199=[.38968604239588377712,2.2859726863545338366 ] 
dist 200=[.55544634637010478608,2.2771843466649221318 ] 
dist 201=[.76881215542437997451,2.2371170214769397639 ] 
dist 202=[.75427985759127173665,2.2285508543185262900 ] 
dist 203=[.69368343155168364321,2.0952581084951673090 ] 
dist 204=[.60809700788883686752,2.1139853623357502115 ] 
dist 205=[.49382046102245585412,2.2116384845581627003 ] 
dist 206=[.33661710548592292496,2.3037945302023447049 ] 
dist 207=[.07969427949476632566,2.4126072809218153951 ] 
dist 208=[-.1843682291771743558 ,2.5110113783639390022 ] 
dist 209=[-.37006869605965138424,2.5616218938002907513 ] 
dist 210=[-.53395383655897830187,2.5875566773088362622 ] 
dist 211=[-.71094366499949104112,2.5921234927306963382 ] 
dist 212=[-.88283794766091404522,2.5723991917070831776 ] 
dist 213=[-1.0263849298521624156 ,2.5592753432743606578 ] 
dist 214=[-1.1766803457997403414 ,2.4745540823948309261 ] 
dist 215=[-1.3755099192139147518 ,2.4658291375929201743 ] 
dist 216=[-1.5705562091702618650 ,2.4585542851085014519 ] 
dist 217=[-1.7057511132154925176 ,2.4227453732345237214 ] 
dist 218=[-1.8230105622516424582 ,2.4126328754632339057 ] 
dist 219=[-1.9464699420158358040 ,2.2844406085429191447 ] 
dist 220=[-2.0644821737178722930 ,2.2521198590750947435 ] 
dist 221=[-2.1599999303299810545 ,2.2179413610694440873 ] 
dist 222=[-2.2582015773186406724 ,2.1999077695964994951 ] 
dist 223=[-2.4136571707601726399 ,1.7261523209559184492 ] 
dist 224=[-2.5016258742762349062 ,1.6598051486529304347 ] 
dist 225=[-2.5576984472469781060 ,1.5258251072360964002 ] 
dist 226=[-2.5899813993935952905 ,1.4889494376505555300 ] 
dist 227=[-2.5980194987810631139 ,1.3463837542535918603 ] 
dist 228=[-2.5696031792821070288 ,1.3146104673841734025 ] 
dist 229=[-2.5535104673747093919 ,1.2485734843078182622 ] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 2, 2, 2, 1, 1, 2] 
dist 0=[58.951197119223669419  ,58.951197119223669419  ] 
dist 1=[58.728623926369679135  ,59.025063514628395593  ] 
dist 2=[58.168200878146446855  ,59.097696025972783570  ] 
dist 3=[56.996815747143844485  ,59.052780192936904133  ] 
dist 4=[55.695498483432346464  ,58.981450976860271678  ] 
dist 5=[54.506292501672732199  ,58.594896817808381416  ] 
dist 6=[52.364965645513781398  ,58.455350434963368576  ] 
dist 7=[50.506771921559587695  ,58.229353243841986520  ] 
dist 8=[48.496175190273817499  ,56.650724980717499733  ] 
dist 9=[45.746063926817018157  ,52.898510938433538767  ] 
dist 10=[42.723340675292969536  ,52.131802949112940055  ] 
dist 11=[39.623930639909533422  ,50.753195500457864947  ] 
dist 12=[35.867249871978065926  ,50.397803465674518205  ] 
dist 13=[30.219465007931912197  ,49.217120172149956224  ] 
dist 14=[24.559432630015045397  ,48.863735324311500019  ] 
dist 15=[20.753722765139892953  ,48.443049449089097091  ] 
dist 16=[17.568346430280579353  ,46.881935652845396140  ] 
dist 17=[14.385512457585051656  ,35.770350673023058315  ] 
dist 18=[11.437588239284127047  ,35.257526836281058852  ] 
dist 19=[9.1901126681253101069 ,35.052206518123280331  ] 
dist 20=[7.0183540998023062069 ,18.986855154948681598  ] 
dist 21=[4.3722814502812858397 ,13.139321973001029598  ] 
dist 22=[1.8660458037308175724 ,12.110579540022487101  ] 
dist 23=[.25249180701885895299,10.811632691066046173  ] 
dist 24=[-1.0229769004214156601 ,10.584995633406745311  ] 
dist 25=[-2.8333280815796855336 ,3.3971765659362637448 ] 
dist 26=[-4.8290509308891294084 ,2.5728605499692730914 ] 
dist 27=[-7.2180403968863131898 ,.77256832806599665469] 
dist 28=[-9.4553544945780099226 ,.50160145117572549626] 
dist 29=[-10.845267578507539508  ,-1.3672353391326981648 ] 
dist 30=[-11.884192682728601770  ,-1.6422558317352591099 ] 
dist 31=[-12.719652809982237990  ,-2.1396961118837974223 ] 
dist 32=[-13.380594880921671599  ,-2.2193257629330806833 ] 
dist 33=[-13.722565353956629294  ,-5.5393022976340552489 ] 
dist 34=[-13.897549874693741771  ,-5.4192976090863384501 ] 
dist 35=[-13.927028751447409091  ,-5.2068284426574932522 ] 
dist 36=[-7.5500705529864169878 ,-4.8292812089149083292 ] 
dist 37=[-7.2245491726812718817 ,-4.2344737293912348934 ] 
dist 38=[-6.8986270377877857555 ,-3.6824378424385028998 ] 
dist 39=[-6.9298989503968400631 ,-3.0486292749527377394 ] 
dist 40=[-6.9203680068995498610 ,-2.4138785847325157928 ] 
dist 41=[-6.2063839849849441036 ,-1.8576744704178947090 ] 
dist 42=[-6.0951548201377029038 ,-1.2538780897069991440 ] 
dist 43=[-5.8877318198171757697 ,-.42884972873088176166] 
dist 44=[-5.8298858231431434642 ,.39086049006769401825] 
dist 45=[-5.6152791339786634311 ,1.1075629535351309744 ] 
dist 46=[-5.5546038567112161701 ,2.2454657771631554252 ] 
dist 47=[-5.4603557712493476204 ,2.9935082437069566889 ] 
dist 48=[-5.4277272514463272328 ,3.5995816326477068743 ] 
dist 49=[-1.7738218639512255034 ,4.1707433197030858197 ] 
dist 50=[-1.4214788581082318641 ,4.6759424876679416441 ] 
dist 51=[-.7197705326025722688 ,5.0186615441706729770 ] 
dist 52=[-.59299100851938381262,5.3079382822686630099 ] 
dist 53=[.24416075194927353867,5.5997074536134864425 ] 
dist 54=[.38699059847358055219,5.8548547574599751146 ] 
dist 55=[.65127752124412795818,5.9979765688430699918 ] 
dist 56=[.70856294276617163767,6.0863353624461945699 ] 
dist 57=[1.3248773363126115079 ,6.1230767148954249108 ] 
dist 58=[1.4134749103713604053 ,6.1281915446369874243 ] 
dist 59=[1.5099233160664705618 ,6.0703038571554410235 ] 
dist 60=[1.5027306754059788237 ,5.5611898393590813938 ] 
dist 61=[1.4528998895367246411 ,5.3021750446788104218 ] 
dist 62=[1.1395283310718566336 ,5.0090400923361719615 ] 
dist 63=[.50964876389615571225,5.0600509367548418949 ] 
dist 64=[-.0146210301004813616 ,5.0875977031386695647 ] 
dist 65=[-.53145673131427180423,5.0888285289792619876 ] 
dist 66=[-1.0037757018945246148 ,5.0543748058028200380 ] 
dist 67=[-1.6204354766246099654 ,5.0416623250314418515 ] 
dist 68=[-2.5365863415981025219 ,.1690937989259612851 ] 
dist 69=[-3.1282194291876910370 ,-.10653063090445539604] 
dist 70=[-3.5955117884420103360 ,-.152232690114570219  ] 
dist 71=[-4.0154109067495592099 ,-.2411439154779434029 ] 
dist 72=[-4.3728757260946071536 ,-.26083958172549745471] 
dist 73=[-4.5909986169113064267 ,-.40244847418033196588] 
dist 74=[-4.7489930270121287226 ,-.42158631091179085726] 
dist 75=[-4.8665112343308918873 ,-.41661673060821613763] 
dist 76=[-4.9575041638166862012 ,-.37770262937648071821] 
dist 77=[-5.0096228731356257784 ,-.32034280940297683327] 
dist 78=[-5.0434194554961542276 ,-.24180966890313016485] 
dist 79=[-5.0612236775381564591 ,-.1331410913664841849 ] 
dist 80=[-5.0853789127701074173 ,.04438218200660672992] 
dist 81=[-5.0957924342317015320 ,.2244747167084671745 ] 
dist 82=[-5.0872199819033190654 ,.34339318809881371698] 
dist 83=[-5.0739313206471533691 ,.43974847818710229058] 
dist 84=[-2.4452717793014650504 ,.52988627172819681729] 
dist 85=[-2.2231949104591717096 ,.60861419972318984836] 
dist 86=[-1.6858591461060802040 ,.65947356672149998858] 
dist 87=[-1.6065055656345580084 ,.69938258981483039385] 
dist 88=[-1.0420689001992547391 ,.76421725755036304892] 
dist 89=[-.73955037732759262915,1.1129549057317338051 ] 
dist 90=[-.64558572305703238812,1.4497846750991382959 ] 
dist 91=[-.55005197695949610894,1.8583271978442963702 ] 
dist 92=[-.52439766367390971121,2.2436012777007672042 ] 
dist 93=[-.46288243303279120318,2.4875628010425075332 ] 
dist 94=[-.40746506242878467051,2.6746527229240384591 ] 
dist 95=[-.36926395157324580112,2.8329466884937366487 ] 
dist 96=[-.3596666417828524747 ,2.9605135766686219466 ] 
dist 97=[1.3782446303679082774 ,3.0249646142113130417 ] 
dist 98=[1.4204042658439534665 ,3.0591118409026036554 ] 
dist 99=[1.4797460779145338845 ,3.0657542802851301412 ] 
dist 100=[2.1791224944956506071 ,2.6171151819524849543 ] 
dist 101=[2.2232684298068219265 ,2.6168349160664726171 ] 
dist 102=[2.1797091097793578896 ,2.5902012004550102998 ] 
dist 103=[2.0811799608979513648 ,2.5928208597334773493 ] 
dist 104=[1.9551364914145329969 ,2.5854513676710501636 ] 
dist 105=[1.7586957254080238715 ,2.5788503676428191576 ] 
dist 106=[1.5320923371346444025 ,2.5282140936299558087 ] 
dist 107=[1.2856444799915246806 ,2.5128751525144746090 ] 
dist 108=[.97745163653596520652,2.4611537762160332228 ] 
dist 109=[.50438788970670350704,2.4463990471675932318 ] 
dist 110=[.02942515364087002877,1.9092508861469354647 ] 
dist 111=[-.28635565478921420674,1.8856897844621604909 ] 
dist 112=[-.54604847299094849665,1.7966470615276220262 ] 
dist 113=[-.8049902608635636434 ,1.7728270817504736284 ] 
dist 114=[-1.0426071233094100024 ,1.7286757444441140767 ] 
dist 115=[-1.2175324869315328442 ,1.7150985670538111714 ] 
dist 116=[-1.3800992174897211589 ,.5087515872669583451 ] 
dist 117=[-1.5684021607248298168 ,.48266041883051235448] 
dist 118=[-1.7422200711874456346 ,.00719175997212822594] 
dist 119=[-1.8469724465014586010 ,-.05235019231272226016] 
dist 120=[-1.9212561644892354720 ,-.19101376407051968474] 
dist 121=[-1.9734508125629488653 ,-.21124613810347531354] 
dist 122=[-2.0109793068811040514 ,-.38942017389638411981] 
dist 123=[-2.0267225265664542472 ,-.41973365059099418496] 
dist 124=[-2.0300090411390319203 ,-.46132775570966050874] 
dist 125=[-2.0277686477280284237 ,-.46906051217734518265] 
dist 126=[-1.9579225618128944039 ,-.69656139586641329435] 
dist 127=[-2.0086610226459135001 ,-.55564295863727571365] 
dist 128=[-2.0450248616585036855 ,-.41019732913479649396] 
dist 129=[-2.0603565660951510316 ,-.25603867180647514247] 
dist 130=[-2.0633812505292713481 ,-.1081566424589982791 ] 
dist 131=[-2.0612792731542888763 ,.01224671493912953517] 
dist 132=[-.68934643034766045567,.13554684995798068937] 
dist 133=[-.67302010737489361986,.29499848558716014392] 
dist 134=[-.37899243020495431118,.44964331004162412679] 
dist 135=[-.34012964109864485945,.55376462639626658204] 
dist 136=[-.24961455862561256508,.64081038273466101233] 
dist 137=[-.23425125165616402506,.7273133588510279446 ] 
dist 138=[-.11512097682653648474,.80686885535663395786] 
dist 139=[-.09389390939576516946,.90563261101314515848] 
dist 140=[-.06035833560493608311,1.0228929023841391058 ] 
dist 141=[-.05216846787227940959,1.0993992279411566818 ] 
dist 142=[.07890355721634692305,1.1607365257643063939 ] 
dist 143=[.09775635713566952340,1.2386563990840259527 ] 
dist 144=[.11359710744534046351,1.3345484130609928890 ] 
dist 145=[.10951450408882996222,1.4210589526313689321 ] 
dist 146=[.00616476762563216533,1.4949959190121624738 ] 
dist 147=[-.21387965376617944108,1.5407011136336156183 ] 
dist 148=[-.43603899143987203189,1.5745304803031578590 ] 
dist 149=[-.58521561640708003854,1.6010697040264973038 ] 
dist 150=[-.70943908424787543952,1.6196781033873580731 ] 
dist 151=[-.83201370794772270651,1.6229453392601935811 ] 
dist 152=[-.94407937126291360793,1.6183054403395382359 ] 
dist 153=[-1.0263620454689121004 ,1.6140815973036710016 ] 
dist 154=[-1.1025453793321760192 ,1.5546223654224409725 ] 
dist 155=[-1.1902666389499621995 ,1.5376107615214220662 ] 
dist 156=[-1.2701646997823594673 ,1.5198425094236036027 ] 
dist 157=[-1.3151258001637994640 ,1.5095924628896762339 ] 
dist 158=[-1.3430688194998727073 ,.95612332854871303054] 
dist 159=[-1.3550501224561648238 ,.93679439268540874377] 
dist 160=[-1.3601951697314974204 ,.85753099035639057151] 
dist 161=[-1.3674082436891757765 ,.84081762072169526898] 
dist 162=[-1.4150332414898982093 ,.80380844503422326368] 
dist 163=[-1.4402046440259042022 ,.79212831357904103481] 
dist 164=[-1.4931419041201717845 ,.07441238901652854646] 
dist 165=[-1.5685662865144225931 ,.01020793317049817908] 
dist 166=[-1.6342415322338577356 ,-.12513377105256581844] 
dist 167=[-1.6746694052409473158 ,-.1566941680244162792 ] 
dist 168=[-1.7123129534130290525 ,-.28704585688425020918] 
dist 169=[-1.7373842821541992989 ,-.3109118029866168279 ] 
dist 170=[-1.7524605059978079040 ,-.35086741436183793871] 
dist 171=[-1.7546567403206347799 ,-.3591767967902807384 ] 
dist 172=[-1.7434106187024017771 ,-.36657191602210211598] 
dist 173=[-1.7403079358176994661 ,-.07722463981084042962] 
dist 174=[-1.4514000517575218287 ,.22646771119864958494] 
dist 175=[-1.4643679077537782714 ,.4277962855706886844 ] 
dist 176=[-1.4700862875951189938 ,.59267987299424612059] 
dist 177=[-1.4715608803040240805 ,.75091370792597999159] 
dist 178=[-1.4702153794118992509 ,.89273879772389846628] 
dist 179=[-1.4652944931941460017 ,.99213142910248968778] 
dist 180=[-1.3365061922893027242 ,1.0794616755863383908 ] 
dist 181=[-1.3616305393483974244 ,1.1731415840487763859 ] 
dist 182=[-1.3745056462628096418 ,1.2581897305078408709 ] 
dist 183=[-1.3774633910762612793 ,1.3110699565636672335 ] 
dist 184=[-1.3538197137631353250 ,1.3505017347861392753 ] 
dist 185=[-1.3474913398988156369 ,1.3818793972573769434 ] 
dist 186=[-1.3435157432741703594 ,1.4056757296690610538 ] 
dist 187=[-1.3417117561881861831 ,1.4148523110328396982 ] 
dist 188=[-1.0971257839583407588 ,1.4160472701762848850 ] 
dist 189=[-1.0630521677889360107 ,1.4137074653728644533 ] 
dist 190=[-1.0008381931410429476 ,1.1998354923278449219 ] 
dist 191=[-.98480153539590617865,1.2413592126212327518 ] 
dist 192=[-.93122819990729496023,1.2726909885163330032 ] 
dist 193=[-.91574149190114294684,1.2844839150115928315 ] 
dist 194=[-.90241155121437649679,1.2886439067210874657 ] 
dist 195=[-.89708809968728747446,1.2895018273460172417 ] 
dist 196=[-.25219326643106734374,1.2451478516115521683 ] 
dist 197=[-.37630599417936167606,1.2355578654214638805 ] 
dist 198=[-.50017227806438554257,1.2032230182727563411 ] 
dist 199=[-.5895389419167559937 ,1.1965666716607843753 ] 
dist 200=[-.67075977423548111778,1.1125949735921344871 ] 
dist 201=[-.7621157825383415353 ,1.0930795424630967084 ] 
dist 202=[-.85301687316956084371,1.0729014213734460490 ] 
dist 203=[-.93242410776581436525,1.0632911032576439398 ] 
dist 204=[-1.0186427136850541933 ,1.0857520371710281307 ] 
dist 205=[-1.1367340986649141461 ,1.1422552907524479433 ] 
dist 206=[-1.2499486296109986696 ,1.1930357977303981333 ] 
dist 207=[-1.3167017076304670399 ,1.2366997688276777714 ] 
dist 208=[-1.3622219340365800328 ,1.2711111864289056052 ] 
dist 209=[-1.3906841204291935320 ,1.2870043946790840383 ] 
dist 210=[-1.4102736218047627106 ,1.2971929426337239509 ] 
dist 211=[-1.4203787943291626515 ,1.3082483104472903641 ] 
dist 212=[-1.4254765511488877032 ,1.3145454178197062799 ] 
dist 213=[-1.4250811758138553209 ,1.3142986542658120344 ] 
dist 214=[-1.2611320497433969073 ,1.3039986017976602143 ] 
dist 215=[-1.2357604344830601869 ,1.2996445782768465939 ] 
dist 216=[-1.1938012601920807598 ,1.2435451503889550451 ] 
dist 217=[-1.1815020043333294672 ,1.2284251353123296472 ] 
dist 218=[-1.1445632303037560314 ,1.2122617343202904219 ] 
dist 219=[-1.2242370454163159756 ,1.2034686625494353733 ] 
dist 220=[-1.3036321253147524930 ,.96564580448374116887] 
dist 221=[-1.3481983999615332790 ,.93188323830462111317] 
dist 222=[-1.3758016624616679825 ,.86372416984348931236] 
dist 223=[-1.3874880790459730932 ,.84478140073813799416] 
dist 224=[-1.3924292528389983270 ,.7706761757256680682 ] 
dist 225=[-1.3931082206853604041 ,.75407762570409664929] 
dist 226=[-1.3907973796370879123 ,.71837455956837741001] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 0, 1, 2] 
dist 0=[49.117923027137617981  ,49.117923027137617981  ] 
dist 1=[48.832716014418816511  ,49.342908776797677253  ] 
dist 2=[48.326492899751759422  ,49.608501920017297069  ] 
dist 3=[47.560549401987365081  ,49.954425304721971462  ] 
dist 4=[46.238143398029659969  ,50.499805953795513535  ] 
dist 5=[44.643494665245880314  ,51.031693304855686737  ] 
dist 6=[42.790332028935985867  ,51.323739806875179516  ] 
dist 7=[40.388908195219677072  ,51.495457300285144921  ] 
dist 8=[36.604726161911675689  ,51.547241512762567696  ] 
dist 9=[32.759935209183836758  ,51.517546851285255864  ] 
dist 10=[30.116357964801723538  ,51.460942511928908215  ] 
dist 11=[27.840624870608663922  ,51.188455335277007148  ] 
dist 12=[25.464537720686826306  ,51.069536022528711712  ] 
dist 13=[23.198431929725947810  ,40.364551711091633384  ] 
dist 14=[21.361633152695789412  ,39.367986987383652027  ] 
dist 15=[19.481986153196833491  ,36.886628327177270252  ] 
dist 16=[17.044224080943394453  ,36.515164059307941059  ] 
dist 17=[14.661635416841581719  ,32.621195272447051183  ] 
dist 18=[13.002051949993278151  ,31.868988585861672470  ] 
dist 19=[11.547691377281801043  ,31.030998641291355063  ] 
dist 20=[9.9843920794367385064 ,30.837063921659906166  ] 
dist 21=[8.4610271902102225621 ,23.620284615448689768  ] 
dist 22=[7.1656276442505430309 ,22.703569278590635190  ] 
dist 23=[5.7809318762388084852 ,20.865579638532708903  ] 
dist 24=[3.8996868610222346928 ,20.391785140708669557  ] 
dist 25=[2.0743379537953866420 ,18.706909925841094098  ] 
dist 26=[.9127896927434916707 ,18.342869584576982257  ] 
dist 27=[.00604464249126626318,17.802523826978229779  ] 
dist 28=[-.81176819336720015117,17.649336167512062692  ] 
dist 29=[-3.3948325559770588173 ,4.2654899711028565424 ] 
dist 30=[-5.0508729447576890663 ,3.1482260462973969797 ] 
dist 31=[-6.3543897774177994415 ,.65743628486784314506] 
dist 32=[-7.5285559560723107181 ,.2237059200649438986 ] 
dist 33=[-8.5386292101510561057 ,-2.5498730706602094551 ] 
dist 34=[-9.1864532813367581884 ,-2.5857755005397024800 ] 
dist 35=[-9.6979131181255205340 ,-2.5283156391704875562 ] 
dist 36=[-10.285685560622662277  ,-2.3327831400981653773 ] 
dist 37=[-11.646895350759571279  ,-2.0671880950561693110 ] 
dist 38=[-12.477878651609803722  ,-1.7298700807742434115 ] 
dist 39=[-13.082609308315226706  ,-1.2776844878667884390 ] 
dist 40=[-13.539997305036282721  ,-.55363776799818601753] 
dist 41=[-13.887708455263391740  ,.1842163470545047998 ] 
dist 42=[-14.054304349353116520  ,.69161795056122163156] 
dist 43=[-14.121424202645635552  ,1.1255063617097342971 ] 
dist 44=[-14.124440969275878342  ,1.5702858927593798354 ] 
dist 45=[-6.4702523051090317358 ,1.9860873436197932005 ] 
dist 46=[-6.0679344521871854398 ,2.3044160145719868724 ] 
dist 47=[-5.0948826600949153440 ,2.6110842869108049902 ] 
dist 48=[-4.9430988107167250209 ,2.9803124469715881352 ] 
dist 49=[-3.5391445700282093856 ,3.3228203957787486074 ] 
dist 50=[-3.2806900550448491436 ,3.5228603786305653491 ] 
dist 51=[-2.9427611764015585356 ,3.6556613654073022202 ] 
dist 52=[-2.8511408330548702202 ,3.7298950089206830514 ] 
dist 53=[-.83657110812392069178,3.7768231466042504501 ] 
dist 54=[-.59085908581787853088,3.8008505612620208151 ] 
dist 55=[-.04673635461735292581,3.8124382645698937581 ] 
dist 56=[.05039604016036890974,3.9413547036654026719 ] 
dist 57=[.12310875322053273367,4.3560474980541968487 ] 
dist 58=[-.27907315386960747023,4.6606628822626169912 ] 
dist 59=[-.62275783322705153013,4.9440307885874825658 ] 
dist 60=[-.97614303335717099782,5.2740962999592461925 ] 
dist 61=[-1.3084819327110852492 ,5.5737565852118555808 ] 
dist 62=[-1.5682020553733702710 ,5.7357470789454392328 ] 
dist 63=[-1.8243814729822036428 ,5.8289851256527977585 ] 
dist 64=[-2.1426226552699637016 ,5.8539949518842611981 ] 
dist 65=[-2.4451332543641699577 ,5.8552254598755381239 ] 
dist 66=[-2.6385490757557150439 ,5.8534141366421169422 ] 
dist 67=[-2.7891059848841891475 ,5.8493570708221810174 ] 
dist 68=[-2.9205843023177102859 ,5.8414502338613910369 ] 
dist 69=[-3.0298392038530885581 ,5.4611476668178390746 ] 
dist 70=[-3.0917196526522962377 ,5.4433012731512228792 ] 
dist 71=[-3.1308727267193572538 ,5.4102244020500549688 ] 
dist 72=[-3.1494561115815488527 ,5.3926868056392789301 ] 
dist 73=[-3.1535124886482419130 ,5.2867506557946914740 ] 
dist 74=[-3.1497018422875410917 ,5.2576303859829597477 ] 
dist 75=[-3.1126982018365983467 ,5.1470693306997851219 ] 
dist 76=[-3.1040597820199684648 ,5.1292421218791731207 ] 
dist 77=[-2.9408552613768799503 ,2.9042783656120661720 ] 
dist 78=[-3.2478344407131893255 ,2.6953817500621237037 ] 
dist 79=[-3.6168561367462780564 ,2.1834692209405344187 ] 
dist 80=[-3.9437526982184012655 ,2.1097031640337824141 ] 
dist 81=[-4.2190077466209149366 ,2.2402266610081776274 ] 
dist 82=[-4.3818973145242083364 ,2.4071498196461055865 ] 
dist 83=[-4.4939639836866592673 ,2.5419706517691402629 ] 
dist 84=[-4.5663769835780603030 ,2.6682220463210265934 ] 
dist 85=[-4.6162960248873498702 ,2.7793157826138995622 ] 
dist 86=[-4.6385622215130635512 ,2.8536483807837300402 ] 
dist 87=[-4.6450449456615111700 ,2.9153209619375635546 ] 
dist 88=[-4.6537615719426657388 ,2.9759005262779365920 ] 
dist 89=[-4.6786828535973855442 ,3.0237083074916950685 ] 
dist 90=[-4.6837002545530948893 ,3.0350740143775889096 ] 
dist 91=[-4.6751047300589352322 ,3.0326946527647111494 ] 
dist 92=[-4.6618133548991667263 ,3.0309512724264443570 ] 
dist 93=[-3.3801987985367037258 ,2.9108883617390320977 ] 
dist 94=[-3.3469478662251435189 ,2.8788486292885673438 ] 
dist 95=[-3.2410645036918741919 ,2.8588022577036386658 ] 
dist 96=[-3.2230045255756484834 ,2.8498910631301165232 ] 
dist 97=[-2.9702175177465706620 ,2.8260216028136762748 ] 
dist 98=[-2.9135665803062533684 ,2.9663055387477294963 ] 
dist 99=[-2.8607874942279580819 ,3.0690083519576231665 ] 
dist 100=[-2.8422194838613726450 ,3.1473518684657430571 ] 
dist 101=[-2.1032881952897621194 ,3.2040840600770734859 ] 
dist 102=[-2.0049764386889043208 ,3.2205188196412202980 ] 
dist 103=[-1.8108334816759790066 ,3.2225490240956462126 ] 
dist 104=[-1.7597783691391044015 ,3.2217798910854723147 ] 
dist 105=[-1.5757484315672865644 ,3.1005880125222214457 ] 
dist 106=[-1.5331204563643935711 ,3.1220911573536458493 ] 
dist 107=[-1.4675153027133715770 ,3.1444910831187568862 ] 
dist 108=[-1.4481419366946413384 ,3.1499322868768932584 ] 
dist 109=[-1.6672603544941857403 ,2.7507710671956332271 ] 
dist 110=[-1.8800796757953308856 ,2.6995106465323862964 ] 
dist 111=[-2.0868123888577657945 ,2.6574953515576099457 ] 
dist 112=[-2.3393675864810154188 ,2.6451543133469476606 ] 
dist 113=[-2.5774862318741209370 ,2.2017473819257752879 ] 
dist 114=[-2.7265949195435740378 ,2.2056310771549863482 ] 
dist 115=[-2.8390904595089590205 ,2.2023826243506789192 ] 
dist 116=[-2.9310666359503864472 ,2.1968189480052178981 ] 
dist 117=[-3.0028293444326726143 ,1.9596983199149128474 ] 
dist 118=[-3.0346418079632220948 ,1.9222338085622624017 ] 
dist 119=[-3.0462453439289545272 ,1.8495272104156663355 ] 
dist 120=[-3.0438214628926698780 ,1.8283842106386018248 ] 
dist 121=[-.70499983157093010238,1.7428750740367145231 ] 
dist 122=[-.81451902633356845326,1.7214837101453441699 ] 
dist 123=[-.93889905564980082447,1.6731777558713803487 ] 
dist 124=[-1.1161591599377807629 ,1.6565270106221845771 ] 
dist 125=[-1.2889632988829444571 ,.60707979012117994218] 
dist 126=[-1.3955621503475181769 ,.58438418943033631892] 
dist 127=[-1.4741452902387998565 ,.54020733498792783263] 
dist 128=[-1.5351222729151005097 ,.52858320402491503493] 
dist 129=[-1.5822533019654547187 ,.48682192660245934307] 
dist 130=[-1.6055648349330742066 ,.47681485877816942605] 
dist 131=[-1.6159143658799814140 ,.46111298273113759244] 
dist 132=[-1.6169226856020279460 ,.45640641743844893283] 
dist 133=[-1.6765076793362238921 ,.44538846991482329349] 
dist 134=[-1.7637292903967689111 ,.44440099694518993933] 
dist 135=[-1.8233035629741354564 ,.44724944618787231352] 
dist 136=[-1.8607775152765153067 ,.45596254206497298648] 
dist 137=[-1.8864694662056836457 ,.46765608162202312832] 
dist 138=[-1.8990098400162448866 ,.48239699733358769078] 
dist 139=[-1.9043213419183120074 ,.50209705050787988895] 
dist 140=[-1.9011394261624158811 ,.53356981865135952383] 
dist 141=[-1.0422473096011732257 ,.56439687752591450548] 
dist 142=[-.98449489997273905413,.58152316734856054911] 
dist 143=[-.84250011789635823579,.59179845079670597502] 
dist 144=[-.81983033717546358345,.5953054792004145295 ] 
dist 145=[-.6049830080799090692 ,.61834029371399523258] 
dist 146=[-.56429960615716573914,.73276237411655677358] 
dist 147=[-.51237540019470129875,.84128422007434906255] 
dist 148=[-.49698726807102130496,.97013654148049548263] 
dist 149=[-.15075746986763515661,1.0899987449719445919 ] 
dist 150=[-.10750079749341633957,1.1626377516454516464 ] 
dist 151=[-.01322657329239901739,1.2145941363434556962 ] 
dist 152=[.00690128533004747440,1.2519100013188726600 ] 
dist 153=[.11049238907457954691,1.2797293385953488026 ] 
dist 154=[.04263952297997853649,1.2937801842237445321 ] 
dist 155=[-.06308041627215730338,1.3004262518322930424 ] 
dist 156=[-.25257887279212816421,1.2995543605725556266 ] 
dist 157=[-.44354731221367441523,1.3276621196499882816 ] 
dist 158=[-.57132623985499050944,1.3761797540212910472 ] 
dist 159=[-.6772485093730437986 ,1.4077703510866995376 ] 
dist 160=[-.78098393240654225094,1.4246315678201077243 ] 
dist 161=[-.87531682983047468336,1.4338278433155330616 ] 
dist 162=[-.94370989708731864984,1.4348128219778128580 ] 
dist 163=[-1.0061558535525772449 ,1.4304120849141878472 ] 
dist 164=[-1.0767459332832830197 ,1.4266501042298692948 ] 
dist 165=[-1.1402936278564258022 ,1.2864715443031303344 ] 
dist 166=[-1.1746304796139804534 ,1.2635357382561872616 ] 
dist 167=[-1.1942319453530122072 ,1.2160256833054140001 ] 
dist 168=[-1.1989867762175395266 ,1.2013635331021028410 ] 
dist 169=[-1.1974008310385566532 ,1.1366435537438435701 ] 
dist 170=[-1.1968209755599313707 ,1.1222345924489818803 ] 
dist 171=[-1.1963127877575296604 ,1.0810090358544450075 ] 
dist 172=[-1.1957654379672022486 ,1.0725193498173378488 ] 
dist 173=[-.83059169994020995935,.01608520001979608815] 
dist 174=[-.87080281028311831842,.06061645953460503797] 
dist 175=[-.89755707498013090086,.10014203858033716499] 
dist 176=[-.91297061174526909796,.14316135891113731122] 
dist 177=[-.92285023510103992684,.1851213157057190534 ] 
dist 178=[-.92751475746030718774,.22041725840591958558] 
dist 179=[-.92926356421540270634,.25757982144264539412] 
dist 180=[-.92750362465061297536,.30698674488991264734] 
dist 181=[-.87594212738214364323,.35551606011241698945] 
dist 182=[-.93090631935613561791,.38917482698817388046] 
dist 183=[-.97288322258382855712,.4183672817389116217 ] 
dist 184=[-1.0081383291830844516 ,.44907051974096247719] 
dist 185=[-1.0363971059627406438 ,.478364694865856205  ] 
dist 186=[-1.0504486173281948558 ,.50193173222778632936] 
dist 187=[-1.0567975537732604464 ,.52579197957198983485] 
dist 188=[-1.0570493321251471482 ,.55625190581456647631] 
dist 189=[-.08943692065119098093,.58455927583104837058] 
dist 190=[-.03812104460945079087,.59982900986833135438] 
dist 191=[.07546179562803891151,.60844624345012695056] 
dist 192=[.09746257038557164521,.61020893796935457769] 
dist 193=[.22676966646395391849,.60923350362695126962] 
dist 194=[.24844986264525974132,.6069253696445232748 ] 
dist 195=[.29269134949500902602,.61729076573771428226] 
dist 196=[.30244712874234164677,.67798677836082106437] 
dist 197=[.36836996424123348309,.74695701863421373852] 
dist 198=[.37791380086920055527,.78899488878815957609] 
dist 199=[.34211301593304327445,.81936524577020013812] 
dist 200=[.27623782292113666745,.84176837300234706638] 
dist 201=[.20445556873802428839,.85994621313563965361] 
dist 202=[.13205420219167735001,.87365844784005805751] 
dist 203=[.04534464321691943926,.88145570600874444745] 
dist 204=[-.08353933419932629903,.88324855652673069761] 
dist 205=[-.21235115305952843622,.88116520767202975784] 
dist 206=[-.2987718402131420784 ,.87917175176087197594] 
dist 207=[-.37066668038108053025,.86582485265899479606] 
dist 208=[-.4415054903311894101 ,.86376775893876822207] 
dist 209=[-.506215095035090606  ,.81178780191550180333] 
dist 210=[-.5536475039721298249 ,.79907085737684819773] 
dist 211=[-.5974896121383337614 ,.79069045349731821898] 
dist 212=[-.65016081533354799242,.78834088301422017786] 
dist 213=[-.71364880719616314821,.59092686689023646294] 
dist 214=[-.75304079953686684768,.56466086394836723525] 
dist 215=[-.7823276490097612796 ,.51476557368721478866] 
dist 216=[-.80548498588933262399,.50196115837321658081] 
dist 217=[-.82293613676764901206,.45843900101219314367] 
dist 218=[-.82944955027999241121,.44721255254465908042] 
dist 219=[-.8311954375919091923 ,.4365004808764793587 ] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 1] 
dist 0=[53.417165312101063590  ,53.417165312101063590  ] 
dist 1=[52.921551217394635639  ,53.791141316836368436  ] 
dist 2=[52.273572069567945912  ,53.953307356930414519  ] 
dist 3=[51.388238713898112160  ,53.991605045583700748  ] 
dist 4=[49.944520716411396889  ,53.955961230519827858  ] 
dist 5=[48.247427688752639252  ,53.666382707880435994  ] 
dist 6=[46.350036601875318832  ,53.556699744876034643  ] 
dist 7=[43.937077232037786782  ,53.097540036429349156  ] 
dist 8=[40.180678637788167683  ,52.995252645213810433  ] 
dist 9=[36.360281586543295156  ,51.193574370137248673  ] 
dist 10=[33.691653286264876443  ,50.796532525962978319  ] 
dist 11=[31.348220153116794711  ,50.385770385482638224  ] 
dist 12=[28.826599751900227011  ,50.186241371668367539  ] 
dist 13=[26.374414640502748649  ,45.059833186880790164  ] 
dist 14=[24.308199660652580121  ,44.581933871154213795  ] 
dist 15=[22.122483420882408952  ,40.623736200086902032  ] 
dist 16=[19.192743592073052657  ,34.380661848050794555  ] 
dist 17=[16.285502416241587728  ,29.658405646705854775  ] 
dist 18=[14.189508710126449860  ,28.048329464360384150  ] 
dist 19=[12.279153498606460054  ,24.401155467837300686  ] 
dist 20=[10.113208070498314359  ,23.733540056698823540  ] 
dist 21=[7.9385712784538182443 ,20.431451859869992098  ] 
dist 22=[5.9931987961988007858 ,20.069705913666833737  ] 
dist 23=[3.8348563687254932036 ,19.643031865996172766  ] 
dist 24=[.8088511534686462807 ,19.540575814723691264  ] 
dist 25=[-2.1552859902624143445 ,12.574530484576670983  ] 
dist 26=[-4.0665800765868852474 ,12.002572863326268745  ] 
dist 27=[-5.5814168769550270920 ,11.014687742470387194  ] 
dist 28=[-6.9614938342476638877 ,10.810848445413119074  ] 
dist 29=[-8.1577885040233311941 ,8.1583575169867027760 ] 
dist 30=[-8.9384454852504525992 ,7.8472643360631869211 ] 
dist 31=[-9.5689531918613537042 ,6.4413281334995265518 ] 
dist 32=[-10.165698081765782727  ,4.5240150434714640909 ] 
dist 33=[-10.682531922457933337  ,-5.2534498092987310230 ] 
dist 34=[-11.844144258130371570  ,-5.5616552725392860650 ] 
dist 35=[-13.026461160697988390  ,-6.0079308566532708274 ] 
dist 36=[-14.013888319073974527  ,-6.0872001325866283712 ] 
dist 37=[-14.808686337571454027  ,-6.0374753798106922650 ] 
dist 38=[-15.221432248320892268  ,-5.7990293758895541819 ] 
dist 39=[-15.448410282721353904  ,-5.3789853981013076422 ] 
dist 40=[-15.499953309797248147  ,-4.6043941055809903136 ] 
dist 41=[-15.388814007423789548  ,-3.7940760996215329212 ] 
dist 42=[-15.324787087911112191  ,-3.1817689418734414558 ] 
dist 43=[-15.247850837038360868  ,-2.2074112351233517902 ] 
dist 44=[-15.184757026116564308  ,-1.1753702330100101293 ] 
dist 45=[-15.012237339025308230  ,-.1852990477792898111 ] 
dist 46=[-14.928958198484175881  ,.6216129738383981914 ] 
dist 47=[-14.753502194404332726  ,1.4489849321077711852 ] 
dist 48=[-14.679205631010608094  ,2.5207741279314364322 ] 
dist 49=[-6.5330068450349148650 ,3.5618166075974468503 ] 
dist 50=[-5.8280292423069697484 ,4.2664751800730130116 ] 
dist 51=[-4.1781283394988935752 ,4.8597993348441664891 ] 
dist 52=[-3.9080935464049303677 ,5.4564376923050729916 ] 
dist 53=[-1.7176710159886517248 ,6.0095909852030643429 ] 
dist 54=[-1.3284675928095228499 ,6.4293188634373868807 ] 
dist 55=[-.74285176129383244854,6.8316437694816893521 ] 
dist 56=[-.59225409712350791202,7.3152730580169663669 ] 
dist 57=[.12944456591054478048,7.7714684061342144760 ] 
dist 58=[.08433734609958062228,8.0642791413219428862 ] 
dist 59=[.03834518386626706575,8.2932974663124307161 ] 
dist 60=[-.01913170473844793450,8.4948924956075947425 ] 
dist 61=[-.07806198486486511573,8.6631651819288066121 ] 
dist 62=[-.12994395509740498583,8.7591773439930143588 ] 
dist 63=[-.18568094321557062812,8.8395119301557831923 ] 
dist 64=[-.26001708120598110476,8.8544115040145046887 ] 
dist 65=[-.33133782816806797003,4.5701229026301555347 ] 
dist 66=[-.37509753219762954326,4.5093185797439206781 ] 
dist 67=[-.40637627989418880083,4.3957901963357862892 ] 
dist 68=[-.42803443974166636969,4.3607950470875252902 ] 
dist 69=[-.4426245865265271944 ,4.2129485301376731096 ] 
dist 70=[-.4457857413722278025 ,4.1724967900015460442 ] 
dist 71=[-.44387350667139970436,4.0759309754382180146 ] 
dist 72=[-.43950303046974821853,4.0399825144992665154 ] 
dist 73=[-.02323826933005145357,2.2491385755639095510 ] 
dist 74=[-.5764144250799808451 ,2.1639678752722914733 ] 
dist 75=[-1.0609456155139397673 ,1.9810143095250613826 ] 
dist 76=[-1.5395613016161873873 ,1.9298142439452915433 ] 
dist 77=[-1.9779512456735424025 ,1.7227597869335147204 ] 
dist 78=[-2.3019246723538579461 ,1.6827147340443801682 ] 
dist 79=[-2.6042717209539699410 ,1.5837138625577793532 ] 
dist 80=[-2.9563472735988978209 ,1.5660320376847073384 ] 
dist 81=[-3.2815131736576586875 ,.3728369109734697069 ] 
dist 82=[-3.4764526024891449765 ,.2615193308588624159 ] 
dist 83=[-3.6134424840530375070 ,.03083052364452367826] 
dist 84=[-3.7073024591566910384 ,-.02568716580263493296] 
dist 85=[-3.7744659463534075788 ,.0616725374507886142 ] 
dist 86=[-3.8048871148053272951 ,.1832655254820214461 ] 
dist 87=[-3.8142528467400912159 ,.3365903839262614731 ] 
dist 88=[-3.8097977026635029934 ,.57274212817371419966] 
dist 89=[-2.4859969874254833626 ,.8082578877591452665 ] 
dist 90=[-2.5668123511672213761 ,.95904978054219386313] 
dist 91=[-2.6183859126680308320 ,1.0762565645118003805 ] 
dist 92=[-2.6437790792259075355 ,1.1778106139363579160 ] 
dist 93=[-2.6565316266540250810 ,1.2613026770698646446 ] 
dist 94=[-2.6576169843071195820 ,1.3064669198025463116 ] 
dist 95=[-2.6503933180654806083 ,1.3321783559043353166 ] 
dist 96=[-2.6438957372156260988 ,1.3383966693369495801 ] 
dist 97=[-1.2824421525917601569 ,1.3304048798437219062 ] 
dist 98=[-1.2703152269087540785 ,1.3282288658916023932 ] 
dist 99=[-1.2337637127563055569 ,1.3278630932948495522 ] 
dist 100=[-1.2257695541847157206 ,1.4920566517172303359 ] 
dist 101=[-1.1418853284740628042 ,1.6555475260392604930 ] 
dist 102=[-1.1226506516677813104 ,1.7987492016936511940 ] 
dist 103=[-1.1001072797046615955 ,1.9546821390692414341 ] 
dist 104=[-1.1856270410630325033 ,2.1690290648924823514 ] 
dist 105=[-1.4947954630140590545 ,2.3753022983761484921 ] 
dist 106=[-1.6974598779077486505 ,2.4990130418720723541 ] 
dist 107=[-1.8607443169533018641 ,2.5861336845432049975 ] 
dist 108=[-2.0127665357234834798 ,2.6463300446889650066 ] 
dist 109=[-2.1457251839115700860 ,2.6883545139828936042 ] 
dist 110=[-2.2329326847534763301 ,2.7029230016323836838 ] 
dist 111=[-2.3032145315675720269 ,2.7036901134260492390 ] 
dist 112=[-2.3686207170304773972 ,2.6977696086854963587 ] 
dist 113=[-2.4213521423180940603 ,2.5056849609486241711 ] 
dist 114=[-2.4410529250529403096 ,2.4706696306408770328 ] 
dist 115=[-2.4463959931042283830 ,2.3977817073336088769 ] 
dist 116=[-2.4418539790489721951 ,2.3739878327034786128 ] 
dist 117=[-2.3761091856716012296 ,2.2634433640293376349 ] 
dist 118=[-2.3540767378503725596 ,2.2384534582782416181 ] 
dist 119=[-2.3303668575398152893 ,2.1609442224203052321 ] 
dist 120=[-2.3160596629467220485 ,2.1476977530674532823 ] 
dist 121=[-.77915203129674846719,1.2430785191126578002 ] 
dist 122=[-1.1189744838993195302 ,1.2247480743024431538 ] 
dist 123=[-1.4006552124117449141 ,1.1724589645824398153 ] 
dist 124=[-1.6767113351815831267 ,1.1626324874231739385 ] 
dist 125=[-1.9280961852356854027 ,1.0535777581856823928 ] 
dist 126=[-2.1113076372150100947 ,1.0296861121026524036 ] 
dist 127=[-2.2797241903517468047 ,1.0030044826451780552 ] 
dist 128=[-2.4720635807500540933 ,.99144138118424748375] 
dist 129=[-2.6467403954263241564 ,.70542030654653212345] 
dist 130=[-2.7446609231046452577 ,.66675779102984644337] 
dist 131=[-2.8051586696059879731 ,.58766280161584072763] 
dist 132=[-2.8304663677155136440 ,.56622783490331983867] 
dist 133=[-2.8416538845883195174 ,.48437706355437305087] 
dist 134=[-2.8457861669255024631 ,.46692122509840947477] 
dist 135=[-2.8455560542819052188 ,.43150349957962522246] 
dist 136=[-2.8393130912162653795 ,.42152580387029853854] 
dist 137=[-2.4544657999063495471 ,.42677274256005221168] 
dist 138=[-2.5654950545035151726 ,.52091025894346411234] 
dist 139=[-2.6417256236081477612 ,.61099800931243513215] 
dist 140=[-2.6904521292533039657 ,.88904784824703626134] 
dist 141=[-2.7225502740688397166 ,1.1483275835377767597 ] 
dist 142=[-2.7324053897461969260 ,1.3475605985545887533 ] 
dist 143=[-2.7296024560978193725 ,1.5409784973099072982 ] 
dist 144=[-2.7236083234825384664 ,1.7770546321263644800 ] 
dist 145=[-2.4920224250276042211 ,1.9994752317242350744 ] 
dist 146=[-2.4521325896671776128 ,2.1383933466479634235 ] 
dist 147=[-2.3710512645423948731 ,2.2427706655446177479 ] 
dist 148=[-2.3455870693653958939 ,2.3273328380571220698 ] 
dist 149=[-2.2319985196327076485 ,2.3927247761361509906 ] 
dist 150=[-2.2056582555848025183 ,2.4205926616314460708 ] 
dist 151=[-2.1301281214776383946 ,2.4318377745197417870 ] 
dist 152=[-2.1126410178930057980 ,2.4308670157668436965 ] 
dist 153=[.07240889683178889805,2.3697359086002102066 ] 
dist 154=[.0990357431741749646 ,2.3543408582947101343 ] 
dist 155=[.0197212567988647332 ,2.3813144596653170351 ] 
dist 156=[-.0600327297344584461 ,2.4117966133905653810 ] 
dist 157=[-.1339316143773285314 ,2.4289301629139595958 ] 
dist 158=[-.1898790951524339513 ,2.4296039530278718350 ] 
dist 159=[-.2433731130492201041 ,2.4180672290312571533 ] 
dist 160=[-.3074803770130689870 ,2.4069255616944976051 ] 
dist 161=[-.3677901366276360200 ,2.4806663708770900646 ] 
dist 162=[-.4061288181646097932 ,2.5922274968942632263 ] 
dist 163=[-.4357015378559276602 ,2.6664989532176787077 ] 
dist 164=[-.46102768094241622654,2.7093110925209954710 ] 
dist 165=[-.48167396180076211344,2.7364858167510459520 ] 
dist 166=[-.49257003861105435122,2.7483404982076755288 ] 
dist 167=[-.49840612906596972131,2.7512359032226968386 ] 
dist 168=[-.49947168082244910529,2.7447240449435757018 ] 
dist 169=[-.94319168467108254902,2.5552037157992410153 ] 
dist 170=[-1.2514518318730035715 ,2.5515792491162995487 ] 
dist 171=[-1.5058499298621675520 ,2.5251930215443071383 ] 
dist 172=[-1.7533372000833051184 ,2.5148450161131400234 ] 
dist 173=[-1.9868522166483166803 ,2.4002009383371114225 ] 
dist 174=[-2.1521287520710307577 ,2.3698797937572721904 ] 
dist 175=[-2.2961339339190019586 ,2.3341147426743694682 ] 
dist 176=[-2.4491011938807808271 ,2.3167970016005376110 ] 
dist 177=[-2.5963669876898284636 ,1.8577022062097844725 ] 
dist 178=[-2.6758951825345687485 ,1.7924075674811479587 ] 
dist 179=[-2.7213262280988507414 ,1.6583280269197305800 ] 
dist 180=[-2.7470678035412934222 ,1.6205672279031481300 ] 
dist 181=[-2.7623092817314945838 ,1.4694096348668549049 ] 
dist 182=[-2.7620045337513910887 ,1.4367114622763474099 ] 
dist 183=[-2.7435454406419881303 ,1.3609196488531936157 ] 
dist 184=[-2.7323559987749010438 ,1.3369574263255916167 ] 
dist 185=[-.99857179050152900083,.64549408557133973493] 
dist 186=[-.99307325733623532038,.7244914794793368732 ] 
dist 187=[-.97108228886522317361,.78446721773953792195] 
dist 188=[-.9671996448233028384 ,.834141615837109331  ] 
dist 189=[-.90139631787086379795,.87419977004457271113] 
dist 190=[-.88586190582302868887,.8957972835859553574 ] 
dist 191=[-.87297171665070481042,.90800069697064004248] 
dist 192=[-.86821108884674810536,.91056841352528989403] 
dist 193=[-.6458904594454091485 ,.87183283590577692405] 
dist 194=[-.61610849400750543752,.90774645251235647891] 
dist 195=[-.55807582634206006543,.93889341436378081332] 
dist 196=[-.55211739560199367964,.96119977285332890854] 
dist 197=[-.53536387602052439872,.97682361695312379329] 
dist 198=[-.53077576703592037028,.98129827504082493544] 
dist 199=[-.51836416676010097945,.98119158840298108487] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 0, 1, 2, 1, 2] 
dist 0=[50.757268089494044331  ,50.757268089494044331  ] 
dist 1=[50.526134383206433305  ,50.997338265965789520  ] 
dist 2=[50.230846181410664693  ,51.289780080561567429  ] 
dist 3=[49.544052114532455778  ,51.729749588923957522  ] 
dist 4=[48.110076010189617188  ,52.150930455233216563  ] 
dist 5=[46.374598166794701688  ,52.368348720336317429  ] 
dist 6=[44.446821536089015091  ,52.477683848825844629  ] 
dist 7=[42.004839243632006584  ,52.467572648252162485  ] 
dist 8=[38.215729019257031935  ,52.381006123663423055  ] 
dist 9=[34.373352839259728595  ,52.303977688959237600  ] 
dist 10=[31.718529825053547670  ,51.978977157492353407  ] 
dist 11=[29.419228664495850452  ,51.850409571877517228  ] 
dist 12=[26.996411721772778913  ,50.749936638257738039  ] 
dist 13=[24.672122111718316103  ,49.834509166717144230  ] 
dist 14=[22.766057012863743712  ,36.806322087058554638  ] 
dist 15=[20.795692055837304863  ,36.408893261877772688  ] 
dist 16=[18.214143050614808119  ,32.387413451559301228  ] 
dist 17=[15.679463150289819219  ,31.616059684850735469  ] 
dist 18=[13.896029009898243588  ,30.723267294015939874  ] 
dist 19=[12.314778187687282505  ,30.500718529229045353  ] 
dist 20=[10.587275484495390304  ,23.337381273726125079  ] 
dist 21=[8.8883371957716513493 ,22.426996563789696069  ] 
dist 22=[7.4206836059867125132 ,20.578381451486304169  ] 
dist 23=[5.8332432167779849203 ,20.097836088778176114  ] 
dist 24=[3.6547595032449764709 ,18.357196224593320403  ] 
dist 25=[1.5344400607742052265 ,17.993268098421453188  ] 
dist 26=[.1792026328247115075 ,17.377063092590411147  ] 
dist 27=[-.8840223605604859403 ,17.229215834281639300  ] 
dist 28=[-1.8372390481461772748 ,12.066698466521830979  ] 
dist 29=[-3.2870476633563119561 ,10.951185705938793710  ] 
dist 30=[-5.8859477922631112076 ,1.4033773024281887390 ] 
dist 31=[-7.5420751476644582288 ,.989169434682995931  ] 
dist 32=[-8.8339862579198860155 ,-1.7263575780296610658 ] 
dist 33=[-9.9773429235140358356 ,-2.1839845588298386508 ] 
dist 34=[-10.946419666842528083  ,-3.0249283891010917923 ] 
dist 35=[-11.541984532213182871  ,-3.2037351107421678761 ] 
dist 36=[-11.982788524854631694  ,-3.7355516814323639054 ] 
dist 37=[-12.333797763556072000  ,-3.4096394453090079159 ] 
dist 38=[-12.824239270720718685  ,-2.9897746061022908367 ] 
dist 39=[-13.190664885253220526  ,-2.4228997468945402219 ] 
dist 40=[-13.460203447563759038  ,-1.5102459057309153577 ] 
dist 41=[-13.601341827682511424  ,-.57962313537005400344] 
dist 42=[-13.676333876771182112  ,.05907496714576540387] 
dist 43=[-13.681501580369460059  ,.60440787672093403126] 
dist 44=[-12.652134800718074025  ,1.1627129601651992203 ] 
dist 45=[-12.583249622302022662  ,1.6847120074787397317 ] 
dist 46=[-7.1421678840005113913 ,2.0852330241018957764 ] 
dist 47=[-6.6489863731451891867 ,2.4722596271785065852 ] 
dist 48=[-5.4561451203366285133 ,2.9403609281791954947 ] 
dist 49=[-5.2749056922223039746 ,3.3775258051518166246 ] 
dist 50=[-3.5581056624249709596 ,3.6411781288157835663 ] 
dist 51=[-3.2433970522377650295 ,3.8273695687371227265 ] 
dist 52=[-2.8443545349392354150 ,3.9557097339210727703 ] 
dist 53=[-2.7487247868868473424 ,4.0491175544553117188 ] 
dist 54=[-.27528071809823398744,4.6504165137363460174 ] 
dist 55=[.02411812942901690945,5.1853038681349862348 ] 
dist 56=[.67446000675677329485,5.5836298906360001014 ] 
dist 57=[.80135688459380725366,5.9008010046822328310 ] 
dist 58=[.8821284446116656346 ,6.1520274089441227376 ] 
dist 59=[.57486833830531753871,6.2870089441121917751 ] 
dist 60=[.23550510084413127266,6.3628871024046115151 ] 
dist 61=[-.09829017594317879600,6.3778132184884397310 ] 
dist 62=[-.38336335906947090218,6.0172647455041306372 ] 
dist 63=[-.68726090710326107832,5.9619681856564686463 ] 
dist 64=[-1.0962224778579587259 ,5.7856647988353366367 ] 
dist 65=[-1.5004778289511812945 ,5.7511226410235813673 ] 
dist 66=[-1.7856124362196897448 ,5.3293729625502629732 ] 
dist 67=[-2.0381130114307523735 ,5.2343013444920052159 ] 
dist 68=[-2.3121457317066317757 ,5.1323793380699752243 ] 
dist 69=[-2.5791553330942726705 ,5.0871452720467643606 ] 
dist 70=[-2.8036470657428297956 ,4.7654050421936273119 ] 
dist 71=[-3.0401207597787469360 ,4.8057679125219750918 ] 
dist 72=[-3.3549912210599650436 ,4.8194365535421093377 ] 
dist 73=[-3.6545865362463450680 ,4.8158709147527943359 ] 
dist 74=[-3.8300971045070090816 ,4.7475104920769097970 ] 
dist 75=[-3.9484863730280269765 ,4.7209838636168720829 ] 
dist 76=[-4.0200698950801687134 ,4.6681962350313662993 ] 
dist 77=[-4.0669857639525771411 ,4.6465169688429622334 ] 
dist 78=[-4.0868976238640591863 ,4.1152084766574969097 ] 
dist 79=[-4.0908924382748238945 ,4.0357563890950668092 ] 
dist 80=[-4.0823392826326075847 ,3.8245248680535488579 ] 
dist 81=[-4.2299594786672428667 ,3.7834425795705113978 ] 
dist 82=[-4.3478554973407222519 ,3.3889692703298556705 ] 
dist 83=[-4.4322325942662251125 ,3.3045973314756287880 ] 
dist 84=[-4.4942696401566003544 ,3.1989191615286812373 ] 
dist 85=[-4.5311123491667056505 ,3.1580135466537416287 ] 
dist 86=[-4.5567667648090374561 ,2.9645460085097436362 ] 
dist 87=[-4.7096226158036724404 ,3.0349883462269709485 ] 
dist 88=[-4.8460815005659208139 ,3.1173838092918935556 ] 
dist 89=[-4.9376577390340529004 ,3.1905178176848714752 ] 
dist 90=[-4.9977177964030648642 ,3.2239969815420223849 ] 
dist 91=[-5.0083219818247598478 ,3.2354698277182910787 ] 
dist 92=[-4.9997623957218889407 ,3.2342497257957538564 ] 
dist 93=[-4.9833040291423937125 ,3.1904125441725986162 ] 
dist 94=[-3.7610171634481311241 ,3.1726204489201064544 ] 
dist 95=[-3.6430902104568702020 ,3.1272957900853702062 ] 
dist 96=[-3.3382634222376195488 ,3.1068971700128312464 ] 
dist 97=[-3.2902192003813617428 ,3.2415106153304123453 ] 
dist 98=[-2.7742260235760345761 ,3.4407568013528280978 ] 
dist 99=[-2.6717464904519488652 ,3.5861258566668074747 ] 
dist 100=[-2.5556049940382903654 ,3.6960338307433065228 ] 
dist 101=[-2.5226390729598871586 ,3.7780390367940063520 ] 
dist 102=[-1.4963238914232245623 ,3.8120301285469780423 ] 
dist 103=[-1.3656004337728839536 ,3.8230950313530967700 ] 
dist 104=[-1.0946012265808287092 ,3.8176667505837334569 ] 
dist 105=[-1.5953106735015419675 ,3.6139290606021284778 ] 
dist 106=[-2.0554987399415020475 ,3.5764552857997936101 ] 
dist 107=[-2.4301200873551399046 ,3.4717251188240802487 ] 
dist 108=[-2.7860028745657367202 ,3.4417802979159537995 ] 
dist 109=[-3.1026786626064387153 ,3.2175791432003924100 ] 
dist 110=[-3.3208118398336277613 ,3.1652987200709474336 ] 
dist 111=[-3.5085869501887996177 ,3.0817686183654077232 ] 
dist 112=[-3.7040961006202074164 ,3.0551429475708263690 ] 
dist 113=[-3.8763752458344734867 ,2.4327501620106846693 ] 
dist 114=[-3.9714287963114769162 ,2.3443127187233879515 ] 
dist 115=[-4.0281410196814946937 ,2.1479909700341213377 ] 
dist 116=[-4.0473762073248128041 ,2.0898517241025131686 ] 
dist 117=[-4.0482891790631810313 ,1.8367712267272259707 ] 
dist 118=[-4.0379327262415645072 ,1.3432736294727299358 ] 
dist 119=[-4.0068575800613077950 ,1.2805040364237202351 ] 
dist 120=[-3.9879126237703912532 ,1.0957610059821325884 ] 
dist 121=[.39607360115608015333,1.1384516564401619408 ] 
dist 122=[.18927059531344527552,1.3189691333630277287 ] 
dist 123=[-.11507273040538777233,1.4595396550679865756 ] 
dist 124=[-.4184531748935305308 ,1.5823929167185360200 ] 
dist 125=[-.62141632720132865938,1.6844897868332262226 ] 
dist 126=[-.78979220147161220558,1.7422132895609183962 ] 
dist 127=[-.95510728236614020391,1.7785057736089694812 ] 
dist 128=[-1.1058983265577662584 ,1.7950641424227536862 ] 
dist 129=[-1.2162965208409496624 ,1.8034388315065818126 ] 
dist 130=[-1.3183012664163164883 ,1.8070668538399381055 ] 
dist 131=[-1.4355854214007242413 ,1.8079255385406542408 ] 
dist 132=[-1.5425214919061162094 ,1.8052450647264561215 ] 
dist 133=[-1.6032178447064262449 ,1.8005083306514087698 ] 
dist 134=[-1.6416824480686688012 ,1.7931592748667043269 ] 
dist 135=[-1.6598731038211859467 ,1.7824971324501120237 ] 
dist 136=[-1.6694059275627661998 ,1.7755774015565344627 ] 
dist 137=[-1.6733156396252910466 ,.71033788057030211047] 
dist 138=[-1.6738651242329120601 ,.62018722361778956505] 
dist 139=[-1.6700014481998086156 ,.40609156562339129193] 
dist 140=[-.15918173833169023263,.4693160265118927172 ] 
dist 141=[-.2616796481607821305 ,.5964714059839806998 ] 
dist 142=[-.3834937545663948674 ,.69886570564645807939] 
dist 143=[-.5004958618870643335 ,.79414006865809715991] 
dist 144=[-.64153533600811772192,.87747472359917267276] 
dist 145=[-.7742622884596193198 ,.93222711618677171616] 
dist 146=[-.85808760312274132688,.97650497169322772718] 
dist 147=[-.92215317640424143049,1.0180465684475661595 ] 
dist 148=[-.97601399490169405016,1.0532179612610941091 ] 
dist 149=[-1.0192037163261508348 ,1.0720740363502797812 ] 
dist 150=[-1.0406788273837263944 ,1.0825886736745376176 ] 
dist 151=[-1.0518782851956586955 ,1.0844636374359844843 ] 
dist 152=[-1.0540518082719056298 ,1.0812825831262480493 ] 
dist 153=[-.82112116362440776179,1.0780542313969077344 ] 
dist 154=[-.80213539534627528898,1.0615094859995799900 ] 
dist 155=[-.76246250993430566836,1.0565156921829450165 ] 
dist 156=[-.75060007768163546874,.83213037941866255096] 
dist 157=[-.72025536825902742785,.8089708410784879185 ] 
dist 158=[-.72640767785682251261,.75132661200246464932] 
dist 159=[-.73462749671611767661,.73886227633593448924] 
dist 160=[-.74781440685537080771,.6456019348861958185 ] 
dist 161=[-.76180043858952630502,.6369415479523482390 ] 
dist 162=[-.77320741043417908273,.6303038033112901927 ] 
dist 163=[-.78489767248930805339,.6272947652427250893 ] 
dist 164=[-.80001167459262386456,.4916159580914847451 ] 
dist 165=[-.81614264841586955905,.4733105926995154369 ] 
dist 166=[-.8318886608768452271 ,.45168231411442016545] 
dist 167=[-.85715455203175938624,.6177982362625242824 ] 
dist 168=[-.8798471682358973212 ,.86111050306293194393] 
dist 169=[-.90359926446105221601,1.1009112403128115819 ] 
dist 170=[-.91965776455273560791,1.2530117928543521007 ] 
dist 171=[-.93123522498584002042,1.3700301858383367919 ] 
dist 172=[-.93968572493219678482,1.4698029114117127330 ] 
dist 173=[-.94544763013572255472,1.5510950466324234148 ] 
dist 174=[-.94629728236125453424,1.5943494022475794880 ] 
dist 175=[-.94369478483164499745,1.6185549592671150832 ] 
dist 176=[-.94114789035290486498,1.6239371593830058145 ] 
dist 177=[-1.0014644765884167103 ,1.6095501869426410645 ] 
dist 178=[-1.0648539893780493277 ,1.6046516372785990591 ] 
dist 179=[-1.1441767652453499342 ,1.5998874756349844803 ] 
dist 180=[-1.2199228931497706970 ,1.5940718700385195340 ] 
dist 181=[-1.2690352817104097199 ,1.5880371781975722108 ] 
dist 182=[-1.3080590058143500572 ,1.5823989799840575713 ] 
dist 183=[-1.3435343214609109562 ,1.5759806527528844803 ] 
dist 184=[-1.3740233278560314159 ,1.5689739525064865913 ] 
dist 185=[-1.3931429199925118253 ,.53334088513746680801] 
dist 186=[-1.4075974391291289975 ,.44672076205436292739] 
dist 187=[-1.4194639512953220912 ,.53604019304247980982] 
dist 188=[-1.4273216336570945349 ,.82869168536723745681] 
dist 189=[-1.4265313364025875040 ,1.0205585851856605764 ] 
dist 190=[-1.4199677561931294174 ,1.1753669658628485192 ] 
dist 191=[-1.4140393242446472165 ,1.3201056347265135671 ] 
dist 192=[-1.3725252379733544601 ,1.4473180413538942170 ] 
dist 193=[-1.3603902346088130752 ,1.5321738007251564911 ] 
dist 194=[-1.3342655944222479793 ,1.6022701081311653599 ] 
dist 195=[-1.3244493923886489419 ,1.6705741351907139148 ] 
dist 196=[-1.2359083427506251884 ,1.7291560746955231392 ] 
dist 197=[-1.3012591442852501373 ,1.7604477425663771676 ] 
dist 198=[-1.3458305022865391419 ,1.7777504337873378600 ] 
dist 199=[-1.3837419713912606806 ,1.7804945797709907938 ] 
dist 200=[-1.4225152338897507645 ,1.7757938026090191582 ] 
dist 201=[-1.4550508969766043546 ,1.7702410334614725945 ] 
dist 202=[-1.4680660474666174174 ,1.7492696368637036743 ] 
dist 203=[-1.4721685703285735074 ,1.7378152532927127414 ] 
dist 204=[-1.4695089289977221229 ,1.1421065876304027744 ] 
dist 205=[-1.4444868559009429346 ,1.0818956315627217233 ] 
dist 206=[-1.4444622175231590969 ,.93494737556375415205] 
dist 207=[-1.4329737325082470010 ,.91011678589849288636] 
dist 208=[-1.4286871742295182838 ,.76446226985112753358] 
dist 209=[-1.3369651332139175214 ,.88302227441309519109] 
dist 210=[-1.3195896026174736618 ,.96465984908103489853] 
dist 211=[-1.2735079958614052294 ,1.0348946870517645556 ] 
dist 212=[-1.2602493342473054969 ,1.1079451380886493818 ] 
dist 213=[-1.1698917824568746740 ,1.1772328332201669846 ] 
dist 214=[-1.1492346748049858106 ,1.2324514854387343213 ] 
dist 215=[-1.1131267740425550210 ,1.2879584744327624615 ] 
dist 216=[-1.1028782098515871162 ,1.3584010322086449576 ] 
dist 217=[-.22277142700222509482,1.4234534472224520124 ] 
dist 218=[-.31839286077342966009,1.4574469704779279304 ] 
dist 219=[-.46889946006627842516,1.4875808359009241656 ] 
dist 220=[-.62156126704768083137,1.6363247436995592901 ] 
dist 221=[-.72578498011422132749,1.7242129580430449677 ] 
dist 222=[-.81451858835849747609,1.7843449499228731219 ] 
dist 223=[-.90534993890576932029,1.8223063005961671660 ] 
dist 224=[-.99060903709479378041,1.8484900715883010260 ] 
dist 225=[-1.0570999901409284379 ,1.8616156280896716194 ] 
dist 226=[-1.1225956782221953117 ,1.8676831695189857762 ] 
dist 227=[-1.2038809001324873666 ,1.8656996294685327878 ] 
dist 228=[-1.2811525842554817247 ,1.6565259583720821814 ] 
dist 229=[-1.3306275051924197628 ,1.6389739247154512237 ] 
dist 230=[-1.3692237212678365757 ,1.6425958005737874809 ] 
dist 231=[-1.4030721742141611511 ,1.6406776460190862597 ] 
dist 232=[-1.4312785943914756789 ,1.6364731945137275527 ] 
dist 233=[-1.4473536331514265464 ,1.4503764475242578757 ] 
dist 234=[-1.4576156581191921828 ,1.4240065708853378593 ] 
dist 235=[-1.4626173536037590778 ,1.3489570968389024691 ] 
dist 236=[-1.4628428086731661973 ,1.3374887455173948892 ] 
dist 237=[-1.4601958378038470738 ,1.1858385907983872374 ] 
dist 238=[-1.4436585015901146587 ,1.1537676610399322992 ] 
dist 239=[-1.4375793965824117644 ,1.1233898668285223769 ] 
dist 240=[-1.3698847462225825339 ,1.1155455622789465284 ] 
dist 241=[-1.3521833844164751197 ,.73334460551205317824] 
dist 242=[-1.3451272596012390656 ,.68395946195530395034] 
dist 243=[-1.3935788078334230029 ,.58595024558697924877] 
dist 244=[-1.4277917444079266772 ,.56056098197540426046] 
dist 245=[-1.4520895544262346803 ,.47077701031189723518] 
dist 246=[-1.4609671717829715404 ,.45038700527214119041] 
dist 247=[-1.4620791389830292362 ,.42321027843258996111] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 0, 1, 0, 0, 2] 
dist 0=[56.498150278728855639  ,56.498150278728855639  ] 
dist 1=[55.198878412199784103  ,57.124503060531296564  ] 
dist 2=[53.586926516515796708  ,57.468549292330207652  ] 
dist 3=[51.712028889565391553  ,57.651982761887740993  ] 
dist 4=[49.281995337300741625  ,57.756557413405332926  ] 
dist 5=[45.453123575266002690  ,57.736067646342352690  ] 
dist 6=[41.551105151154487974  ,57.649713256406768122  ] 
dist 7=[38.828851952956820753  ,57.497539212515934444  ] 
dist 8=[36.444127283784678587  ,57.391636395986878396  ] 
dist 9=[33.889688055729176182  ,56.868636724811142763  ] 
dist 10=[31.414626838371666932  ,56.696950829982878802  ] 
dist 11=[29.346623847406808530  ,56.104809046418298673  ] 
dist 12=[27.175280771424190334  ,55.933944479934685224  ] 
dist 13=[24.287054166484393014  ,54.313471914124307460  ] 
dist 14=[21.432686727980172065  ,53.892525696665525108  ] 
dist 15=[19.396295739596488531  ,51.562214491000962972  ] 
dist 16=[17.562403487009209805  ,35.408908362927271147  ] 
dist 17=[15.516402483983868108  ,30.336486490591631017  ] 
dist 18=[13.480607464577138145  ,29.381466170031565835  ] 
dist 19=[11.686975881867485668  ,28.205371761881023960  ] 
dist 20=[9.7186522970988137503 ,27.893078410906040576  ] 
dist 21=[6.9840534716439209378 ,19.666836757323902105  ] 
dist 22=[4.3049852460216621520 ,18.630689116431895861  ] 
dist 23=[2.5583582610427102151 ,16.464132510455515989  ] 
dist 24=[1.1508892138681408745 ,15.894005824705846232  ] 
dist 25=[-.17277321481983239962,13.764244633469367783  ] 
dist 26=[-1.3506010297344261522 ,13.351192602059984609  ] 
dist 27=[-3.2811566076764000124 ,12.546154016802178821  ] 
dist 28=[-5.1502308085219214190 ,12.349517677995796303  ] 
dist 29=[-6.6554664390433585108 ,3.1117305845747764801 ] 
dist 30=[-8.1911176746175207697 ,.25961474361687475089] 
dist 31=[-10.183042840236591321  ,-1.7862046710485044448 ] 
dist 32=[-12.078149869998061633  ,-2.2397560264826790275 ] 
dist 33=[-13.227228588101241922  ,-4.1528834643460549253 ] 
dist 34=[-14.058932436090062034  ,-4.2619982864954176515 ] 
dist 35=[-14.685426618067478015  ,-4.0230323850153197392 ] 
dist 36=[-15.433824306340756939  ,-3.6431172134296545427 ] 
dist 37=[-16.596374253823483879  ,-2.9751911388626677759 ] 
dist 38=[-17.268565994359824299  ,-2.2804964536803284906 ] 
dist 39=[-17.713146702333009304  ,-1.7935821294702286996 ] 
dist 40=[-17.966625758166144304  ,-1.3676875009617942619 ] 
dist 41=[-18.113363642723581186  ,-.91601943245972026921] 
dist 42=[-18.131510030983097233  ,-.48402569947912039905] 
dist 43=[-18.078815138081957754  ,-.13641863010919034927] 
dist 44=[-18.021773503715284437  ,1.5570009572223188933 ] 
dist 45=[-13.253350604821399285  ,3.7112948844775764062 ] 
dist 46=[-12.894526562327277409  ,5.1514967438940708023 ] 
dist 47=[-12.778189201580740366  ,6.3434549361462706108 ] 
dist 48=[-4.8926742937411096491 ,7.5072887229668372410 ] 
dist 49=[-4.1736433552652482773 ,8.5634547091609966726 ] 
dist 50=[-2.5557755154762309581 ,9.3258652811170288153 ] 
dist 51=[-2.2408131981744891431 ,10.019124350679603830  ] 
dist 52=[-.2840430369834436929 ,10.799492230875558517  ] 
dist 53=[-.22562204447715522669,11.502447297445216256  ] 
dist 54=[.7201260626092758346 ,11.886827533123751241  ] 
dist 55=[.8765312401814926247 ,12.111976268376287513  ] 
dist 56=[1.7041654247702864318 ,12.179481420888333186  ] 
dist 57=[1.7528093479060955716 ,12.183331416751517743  ] 
dist 58=[1.9403993845618485135 ,12.154300645596739589  ] 
dist 59=[1.9740953083550485747 ,12.095739356401730321  ] 
dist 60=[1.9739488091054267546 ,12.045931509054618190  ] 
dist 61=[1.9242814301968894137 ,10.268905332428302611  ] 
dist 62=[1.8539535790710295444 ,10.012142968549183572  ] 
dist 63=[1.5980923310258517141 ,9.2836111742743673939 ] 
dist 64=[.88512566854682810555,2.4687997817518669433 ] 
dist 65=[.40213742117615759011,2.4697640985464491770 ] 
dist 66=[-.00455446491867319549,2.4256919172300207635 ] 
dist 67=[-.41312411455324176558,2.4109299099776402451 ] 
dist 68=[-.7914731760009362044 ,2.3990485222094020269 ] 
dist 69=[-1.0776151599704959301 ,2.3879642491692054124 ] 
dist 70=[-1.3510508081983105006 ,1.8970217059748179082 ] 
dist 71=[-1.6787675448744872977 ,1.8383915359094862522 ] 
dist 72=[-1.9848566356136343920 ,1.6851137015200502659 ] 
dist 73=[-2.1720092106975582499 ,1.6624738708968489105 ] 
dist 74=[-2.3081206106760452450 ,1.3969051071436495588 ] 
dist 75=[-2.4105239020269402622 ,1.3437977499156652887 ] 
dist 76=[-2.4884564525977049291 ,1.2895081032473564138 ] 
dist 77=[-2.5268567497198693444 ,1.2776504254045280921 ] 
dist 78=[-2.5437443662927495356 ,.71561231278094943592] 
dist 79=[-2.5442266269306546413 ,.6443782184484259587 ] 
dist 80=[-2.3472533890110989919 ,.50196324889975013882] 
dist 81=[-2.3168219892960551073 ,.46536384225046738968] 
dist 82=[-2.2269696368968063699 ,.33664893379428924489] 
dist 83=[-2.2093366129825455181 ,.3083084574848022827 ] 
dist 84=[-2.0237865708285534700 ,.28000162461135846365] 
dist 85=[-2.0247468054690274968 ,.44824986438434463564] 
dist 86=[-1.9235178139230681425 ,.62198488899042136543] 
dist 87=[-1.9024908787286210509 ,.8483762377195221027 ] 
dist 88=[-1.8100426863580528510 ,1.0685172488368953000 ] 
dist 89=[-1.7951258395576307788 ,1.2173372986886116356 ] 
dist 90=[-1.6639253173135709412 ,1.3423503893532701422 ] 
dist 91=[-1.6341797530921579874 ,1.4675281280115564666 ] 
dist 92=[-1.5926300081747640210 ,1.5833014337449569949 ] 
dist 93=[-1.5776171557846252964 ,1.6708200065790059464 ] 
dist 94=[-1.2243469193539715464 ,1.7545468750966121608 ] 
dist 95=[-1.1753364481420002832 ,1.8552512856266605811 ] 
dist 96=[-1.0695017463212452421 ,1.9470775735638577010 ] 
dist 97=[-1.0391681135377911648 ,1.9953780397914899679 ] 
dist 98=[-.91286432399265745213,2.0214031839883311576 ] 
dist 99=[-.88823257533889545709,2.0270405758712032633 ] 
dist 100=[-.82305841168988560369,2.0177879772763064606 ] 
dist 101=[-.81323561552009689305,2.0111643545700416377 ] 
dist 102=[-.04106412293975106324,2.0027533318275936297 ] 
dist 103=[-.0046391157646200986 ,1.9944077769144115264 ] 
dist 104=[-.1197818914491807059 ,2.0128536106455686230 ] 
dist 105=[-.2381532336303632160 ,2.0709135892742231738 ] 
dist 106=[-.3494573371364519179 ,2.1046884660981972284 ] 
dist 107=[-.4364011252060740793 ,2.1142317061148139288 ] 
dist 108=[-.5221113382767329267 ,2.1150414178797008705 ] 
dist 109=[-.62849804029143391009,2.1139448576833552567 ] 
dist 110=[-.72953590780467073361,2.1112457881549542290 ] 
dist 111=[-.79390334898225626406,2.1056425847026733706 ] 
dist 112=[-.84372017596903935368,1.7384979008021963738 ] 
dist 113=[-.8866938103268599242 ,1.6934286251680124452 ] 
dist 114=[-.92198689535182839613,1.5750734008334888420 ] 
dist 115=[-.94115650015882578634,1.5554616319802903069 ] 
dist 116=[-1.1206496886529151935 ,1.3224547823038611454 ] 
dist 117=[-1.2583645109301235176 ,1.1931252932666956937 ] 
dist 118=[-1.3874736376217398554 ,-.40529071161111257463] 
dist 119=[-1.5386803765396811637 ,-.44520270152244171188] 
dist 120=[-1.6780274342497633054 ,-.51961171124641937445] 
dist 121=[-1.7597946156749152674 ,-.52307171515530754344] 
dist 122=[-1.8150715832688148443 ,-.50484454760419084153] 
dist 123=[-1.8486741571684878713 ,-.45232857329377859659] 
dist 124=[-1.8710528871217416010 ,-.38185485440782544191] 
dist 125=[-1.8815299452559054326 ,-.29195146021098613667] 
dist 126=[-1.8853022251131740989 ,-.17063445263978004289] 
dist 127=[-1.8813183672975933215 ,.02521733970893553677] 
dist 128=[-1.0389427582086754388 ,.22408708078308138577] 
dist 129=[-1.0633209100196248632 ,.35745231749947523437] 
dist 130=[-1.0823473728166519995 ,.46834013123180057217] 
dist 131=[-1.0907758403144344596 ,.57750672696023449557] 
dist 132=[-1.0930431429172110696 ,.67718545870380631557] 
dist 133=[-1.0918811508643252751 ,.75021016112925086437] 
dist 134=[-1.0782595793058804375 ,.81768959859787400026] 
dist 135=[-1.0729258248011121387 ,.89524166960930403665] 
dist 136=[-1.0543104269764761694 ,.96589011145973179168] 
dist 137=[-1.0475366958154021067 ,1.0058190315694329910 ] 
dist 138=[-.99332608690789664649,1.0309017350423326066 ] 
dist 139=[-.97959165481034898142,1.0422999618307999744 ] 
dist 140=[-.95893088122335286832,1.0659933204361429696 ] 
dist 141=[-.95145282968786123789,1.1273366357520188053 ] 
dist 142=[-.76474891741627176281,1.1814215013084682381 ] 
dist 143=[-.73796644083637732581,1.2110120531723761052 ] 
dist 144=[-.67989244821204869862,1.2283358639305556825 ] 
dist 145=[-.6628452738854727204 ,1.2334587607044869491 ] 
dist 146=[-.59020062645101612175,1.2330085235365193924 ] 
dist 147=[-.57565794437636330513,1.2292757749533902757 ] 
dist 148=[-.53686327555630327928,1.2203021956555826411 ] 
dist 149=[-.5302851713521933655 ,1.2150130866660415746 ] 
dist 150=[-.5594801095328649231 ,.87194758850515409448] 
dist 151=[-.64452306086324598321,.83475560081915797296] 
dist 152=[-.724324038103636619  ,.74765289911369949596] 
dist 153=[-.77353628743544732416,.72815846915719559661] 
dist 154=[-.80975989650565430541,.60552802264367289559] 
dist 155=[-.83772550813903617681,.58159684673393361439] 
dist 156=[-.85870376518719598457,.53645621524652849603] 
dist 157=[-.86703895066997439297,.52479233173616707608] 
dist 158=[-.89564852776676135374,.34874820621439386421] 
dist 159=[-.94217724350744401731,.32405366179299462633] 
dist 160=[-.97482317428487083023,.26697602277878307046] 
dist 161=[-.99706170807970777969,.25557392864997410951] 
dist 162=[-1.0124556840016264292 ,.17998249259676151028] 
dist 163=[-1.0177829169978767191 ,.16601058769663306191] 
dist 164=[-1.0178109522101726655 ,.14039600987910515497] 
dist 165=[-1.0156084000882531218 ,.13433924575926129372] 
dist 166=[-.93472586296318733078,.04732169727690343523] 
dist 167=[-1.0088533454613785003 ,.1209324648656956548 ] 
dist 168=[-1.0915084489418242105 ,.2142671071234626793 ] 
dist 169=[-1.1660115210173368575 ,.31014963084373248348] 
dist 170=[-1.2295814816831864085 ,.40031666521963233608] 
dist 171=[-1.2685996464039889517 ,.47084067752298031411] 
dist 172=[-1.2971121857553514945 ,.54047592482473676746] 
dist 173=[-1.3187520063219164520 ,.62709646449637710542] 
dist 174=[-1.3339097823344148971 ,.70949221715702941706] 
dist 175=[-1.3365504438036934225 ,.76226624980764720322] 
dist 176=[-1.3339577690763273900 ,.80344401201827867437] 
dist 177=[-1.3288635659384598466 ,.83955821400970217839] 
dist 178=[-1.2890514171090967946 ,.86965166870252967151] 
dist 179=[-1.2768371029744875811 ,.88680047221316733005] 
dist 180=[-1.2564849973810073194 ,.89775297086038807749] 
dist 181=[-1.2490554584549142707 ,.90311734147076111549] 
dist 182=[-.9268103797561945714 ,.95175285933015336866] 
dist 183=[-.92072071869047592885,1.0056317481783683156 ] 
dist 184=[-.75626260093890637548,1.0530836839616258293 ] 
dist 185=[-.73235344854050685445,1.0855652975766442655 ] 
dist 186=[-.68207920567991767445,1.1346249685588601168 ] 
dist 187=[-.66748329920194095239,1.1623854003483271950 ] 
dist 188=[-.60649085424998833032,1.1798618214420667313 ] 
dist 189=[-.59377651442718471251,1.1878755233095577524 ] 
dist 190=[-.5604760683404262181 ,1.2397621075297617046 ] 
dist 191=[-.55351513262684396836,1.2870124349987373697 ] 
dist 192=[-.2136513216616235635 ,1.3207952355364900925 ] 
dist 193=[-.3268583887036720682 ,1.3450309104433575738 ] 
dist 194=[-.4212387706749386553 ,1.3612729394894558575 ] 
dist 195=[-.5145924698228726043 ,1.3643042304745231333 ] 
dist 196=[-.6001336401688057076 ,1.3602141848637389808 ] 
dist 197=[-.6633335915464089903 ,1.3572371504217359198 ] 
dist 198=[-.7222704426994099699 ,1.0849669384892537677 ] 
dist 199=[-.79079786106583880809,1.0808709370956055353 ] 
dist 200=[-.85363908020181072883,1.0641003446633431687 ] 
dist 201=[-.88988182156431780833,1.0583854319676029888 ] 
dist 202=[-.91358204904744092657,1.0035540980824228965 ] 
dist 203=[-.94266904435595251962,.98962184052729835259] 
dist 204=[-1.0038369854438216257 ,.97139340188607554446] 
dist 205=[-1.0705670549548535014 ,.96369926670272800561] 
dist 206=[-1.1301120146299502673 ,.76673521903482552198] 
dist 207=[-1.1626025878175258919 ,.738796974392686617  ] 
dist 208=[-1.1814969072171717293 ,.68000140412092115469] 
dist 209=[-1.1867759134912797242 ,.66319667090451701975] 
dist 210=[-1.1880708605710605237 ,.59413310891170087222] 
dist 211=[-1.1953405442111801724 ,.57990392323980205071] 
dist 212=[-1.1959785381873579553 ,.5439801730431151595 ] 
dist 213=[-1.1944051143811953998 ,.53604131780913528896] 
dist 214=[-1.1694789214526149485 ,.51144846504363827734] 
dist 215=[-1.1939027457401287659 ,.58962629681291333949] 
dist 216=[-1.2122709128595845745 ,.66344750467498659084] 
dist 217=[-1.2175395154682453918 ,.70980262680827420452] 
dist 218=[-1.2171268778328327842 ,.74491285433978191018] 
dist 219=[-1.2132770178566983880 ,.77385433039288409605] 
dist 220=[-1.1797616243855216838 ,.79661429247543700514] 
dist 221=[-1.1690396392289828271 ,.80705353756735283965] 
dist 222=[-1.1525616327914101242 ,.81142900624517192985] 
dist 223=[-1.1458676244969323211 ,.81105560920322290282] 
dist 224=[-.31962919885503033176,.79632190349147867374] 
dist 225=[-.38396472102790451957,.84466444254667686347] 
dist 226=[-.45279743621421797246,.90772769953717337987] 
dist 227=[-.5204269709279694774 ,.96366557973077163877] 
dist 228=[-.6001295292743007941 ,1.0107432470813350968 ] 
dist 229=[-.71714799616896932325,1.0384430106217277651 ] 
dist 230=[-.83250399827765876917,1.0572535318292244591 ] 
dist 231=[-.9055712900063629868 ,1.0688518873068124070 ] 
dist 232=[-.96165099829817488385,1.0984262090231654940 ] 
dist 233=[-1.0092061477951019977 ,1.1406589620602209468 ] 
dist 234=[-1.0476376919741971061 ,1.1713611851782690882 ] 
dist 235=[-1.0673032375092492786 ,1.1943541068056929625 ] 
dist 236=[-1.0769861370839892915 ,1.2106298393620050674 ] 
dist 237=[-1.0786336958714326683 ,1.2145221424491196728 ] 
dist 238=[-1.0696265977501347059 ,1.2131927822574068538 ] 
dist 239=[-1.0647286666700489326 ,1.2089061093372277047 ] 
dist 240=[-1.0517836724306325490 ,.96274932310610749916] 
dist 241=[-1.0454745041120711309 ,.96204807774547302282] 
dist 242=[-1.0084031685097142211 ,.95455917230763000247] 
dist 243=[-.99859237212999512386,.95005850775706689664] 
dist 244=[-.9739779185361272723 ,.91244934092664558939] 
dist 245=[-.96448698012139821495,.90199271381283033447] 
dist 246=[-.93335258092964260844,.8867647044132032202 ] 
dist 247=[-.98706606339069623271,.8807108128841387656 ] 
dist 248=[-1.0344635500634492105 ,.72167237578116106791] 
dist 249=[-1.0599137735396079816 ,.69859694853993740878] 
dist 250=[-1.0741609537859814841 ,.649275785669660776  ] 
dist 251=[-1.0769197810257363120 ,.63482565018233964135] 
dist 252=[-1.0749481807967164550 ,.57349083713319612316] 
dist 253=[-1.0709181722230500856 ,.56108934199832233197] 
dist 254=[-1.0645534094183740195 ,.52696120206890251737] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 1, 0, 0, 0, 1] 
dist 0=[51.482351495055751115  ,51.482351495055751115  ] 
dist 1=[50.468955073471068680  ,52.476742329609118893  ] 
dist 2=[49.246374024317106053  ,53.333057584482835058  ] 
dist 3=[47.416328343171295880  ,53.795079595362197674  ] 
dist 4=[45.331708153997164842  ,54.056692694735693006  ] 
dist 5=[43.092339980108436719  ,54.113040707489572464  ] 
dist 6=[40.305977117343243298  ,54.061507128778025969  ] 
dist 7=[36.036775659186772771  ,53.988582705544563743  ] 
dist 8=[31.728815082059449342  ,53.696735280269952604  ] 
dist 9=[28.787530376549858779  ,53.540393162746394683  ] 
dist 10=[26.277535584417522454  ,51.448935862882305190  ] 
dist 11=[23.691678156567347447  ,51.030663078896904439  ] 
dist 12=[21.246966222652964747  ,50.423408784429584268  ] 
dist 13=[19.300371919397292630  ,50.211531718623181790  ] 
dist 14=[17.340025432653712793  ,45.403662304560750718  ] 
dist 15=[14.839860158113999311  ,44.505166334036154159  ] 
dist 16=[12.416306844039799027  ,39.730489295605220638  ] 
dist 17=[10.761644848527689560  ,35.759845307277996079  ] 
dist 18=[9.3467599878891724329 ,29.305631436667053323  ] 
dist 19=[7.8804988414292634017 ,27.185282352676127569  ] 
dist 20=[6.4840185875092694536 ,25.256241586516853818  ] 
dist 21=[5.3472930424367095794 ,24.760057009343940353  ] 
dist 22=[4.1753195039790451936 ,23.013953345887065778  ] 
dist 23=[2.6368095116293151169 ,22.622039812062544371  ] 
dist 24=[1.1580716678382851475 ,22.087588134133203148  ] 
dist 25=[.22473295078652374292,21.915872760843044186  ] 
dist 26=[-.49630681423340671216,12.438285964122658099  ] 
dist 27=[-1.1261555430995028747 ,11.090534957649478378  ] 
dist 28=[-1.6577119777155213072 ,10.801002975426987677  ] 
dist 29=[-3.3146921838554343106 ,8.7230945234662985837 ] 
dist 30=[-5.3966483172618366783 ,8.3796013330770355903 ] 
dist 31=[-6.9487633960012461905 ,7.2007806551528119242 ] 
dist 32=[-8.4150585277623300820 ,5.5085618343394863813 ] 
dist 33=[-10.154202563557100423  ,-1.9617767579050573853 ] 
dist 34=[-11.776469961695699845  ,-1.8223621777532160373 ] 
dist 35=[-12.775900548841325099  ,-1.5536775472855685529 ] 
dist 36=[-13.513727204213929655  ,-1.2259730409222136868 ] 
dist 37=[-14.091017249595220550  ,-.85079037815950480498] 
dist 38=[-14.537537898366625571  ,-.37112308088684488173] 
dist 39=[-14.753022625192416196  ,.37358923502457541693] 
dist 40=[-14.849501959012821252  ,1.1262257030679670571 ] 
dist 41=[-14.854988294975375758  ,1.6376213214046064343 ] 
dist 42=[-9.9648719333203561850 ,2.0684630215209793805 ] 
dist 43=[-10.011831968784531945  ,2.4999081707124326166 ] 
dist 44=[-10.032010986422206550  ,2.8968896488227300400 ] 
dist 45=[-10.035544344615892346  ,3.1902757093176654188 ] 
dist 46=[-10.015710025676728213  ,3.4628170870332188650 ] 
dist 47=[-9.9757257364832461492 ,3.7765785776555045485 ] 
dist 48=[-9.9446532155511085738 ,4.0604382110835528522 ] 
dist 49=[-4.8988582476257013845 ,4.2137343005213311576 ] 
dist 50=[-4.4739086967978172837 ,4.3010117150180068252 ] 
dist 51=[-3.4502556526397669913 ,4.3216475248546528430 ] 
dist 52=[-3.3033788951549536459 ,4.3103569745024823813 ] 
dist 53=[-1.8566088607884715280 ,4.3058851464667071860 ] 
dist 54=[-1.5962346799321096494 ,4.3014430302385339528 ] 
dist 55=[-1.2819266700835396465 ,4.2951776947035271120 ] 
dist 56=[-1.2289657210333525566 ,3.3178273495889440053 ] 
dist 57=[.75965830408846708672,3.8001366504309153642 ] 
dist 58=[.99003874108793533254,4.2582260132418126738 ] 
dist 59=[1.4162221108014470334 ,4.5443956274114359018 ] 
dist 60=[1.3845519396513551072 ,4.7608370252368603816 ] 
dist 61=[1.2903976514539731395 ,4.9403802298894978653 ] 
dist 62=[1.1645622499805426397 ,5.0838997883602064300 ] 
dist 63=[1.0063357327784874917 ,5.1564681204185421060 ] 
dist 64=[.79476210778874840673,5.1918001852437798424 ] 
dist 65=[.45593858517403395829,5.1939989388009307005 ] 
dist 66=[.09754572178884007718,5.1606561118920005361 ] 
dist 67=[-.19220504305202581449,5.1443621127548672994 ] 
dist 68=[-.48681589138146086658,5.0669270745998468851 ] 
dist 69=[-.86475015563295955889,5.0502693320594719670 ] 
dist 70=[-1.2672143116962996496 ,4.7891913844033830250 ] 
dist 71=[-1.6598193223568172391 ,4.7256931153141448768 ] 
dist 72=[-2.1205272753151853622 ,4.6679546409817857336 ] 
dist 73=[-2.7949277947743843765 ,4.6406058824195968209 ] 
dist 74=[-3.4597676236509859002 ,3.4661590876698389946 ] 
dist 75=[-3.8823476393067613049 ,3.3861152814971532752 ] 
dist 76=[-4.2087155680538005521 ,3.3600708497880339360 ] 
dist 77=[-4.4895209513762276458 ,3.2398707264897527238 ] 
dist 78=[-4.7199491687948453705 ,3.2122120113960278784 ] 
dist 79=[-4.8452486992516808781 ,3.1283591064776755466 ] 
dist 80=[-4.9178264539353023234 ,3.1120346172633332460 ] 
dist 81=[-4.9378560341590052299 ,1.6084489061030479650 ] 
dist 82=[-4.9353478855091445379 ,1.4685471324188425704 ] 
dist 83=[-4.9722216609895484614 ,1.1298612476501068089 ] 
dist 84=[-5.0752138773018194118 ,1.0803555049961071079 ] 
dist 85=[-5.1567287903523309315 ,.58901115716653919874] 
dist 86=[-5.2183864084598281308 ,.49845941254590681896] 
dist 87=[-5.2421096363299417947 ,.3912882047946936147 ] 
dist 88=[-5.2426933982497001694 ,.37009050310286175052] 
dist 89=[-5.2326275540753734453 ,-.38188845660351529675] 
dist 90=[-2.8241965249844300224 ,.2564939501988137966 ] 
dist 91=[-2.6169048131251985610 ,.90998630677057492217] 
dist 92=[-2.4748621822039798384 ,1.4496919120924948898 ] 
dist 93=[-2.5221503140736959181 ,1.9752546910389797729 ] 
dist 94=[-2.5402116705728235897 ,2.4514819711057890522 ] 
dist 95=[-2.5454352107216823332 ,2.7942565877814663780 ] 
dist 96=[-2.5414672131889332804 ,3.1048631294257209662 ] 
dist 97=[-1.7808381901846370300 ,3.4526645781563514092 ] 
dist 98=[-1.7402959031251152839 ,3.7730728627022204304 ] 
dist 99=[-1.6356928891677922936 ,3.9743487375412453073 ] 
dist 100=[-1.6157431311569751224 ,4.1268210534535465388 ] 
dist 101=[-1.4351956115566836295 ,4.2524841656028911462 ] 
dist 102=[-1.3981185618003125309 ,4.3512904767198367229 ] 
dist 103=[-1.3479081224681183531 ,4.3965988030397746541 ] 
dist 104=[-1.3307354858559139720 ,4.4121674435164498549 ] 
dist 105=[-.95906307868430074754,4.4105843719067772367 ] 
dist 106=[-.90948247327543330516,3.1145345170130466779 ] 
dist 107=[-.801865690026239097  ,3.2622283267206637313 ] 
dist 108=[-.77329646097355833798,3.3617196512462811061 ] 
dist 109=[-.64926011172400084263,3.4217247736736668218 ] 
dist 110=[-.62610481927840509829,3.4610638158119675449 ] 
dist 111=[-.56833758364914475722,3.4780409049137929621 ] 
dist 112=[-.55941063075883979599,3.4819716141567522360 ] 
dist 113=[.05691243850703759977,3.4747868374009232187 ] 
dist 114=[.11564065582749498494,3.1075650780325564947 ] 
dist 115=[.23297386064976332978,3.0490689475797776327 ] 
dist 116=[.26155430439389407642,2.9421927331288396174 ] 
dist 117=[.35423273075255770691,2.9121800875865281345 ] 
dist 118=[.37389587192976609385,2.7990663132448109530 ] 
dist 119=[.38110381641634543012,2.7667037919976972576 ] 
dist 120=[.36573079530629190823,2.7077808271772872148 ] 
dist 121=[.34044530183728195812,2.6891084794344689924 ] 
dist 122=[-.03855686174539097631,1.6694286222336673078 ] 
dist 123=[-.44899057734718794743,1.6913411141846962400 ] 
dist 124=[-.79319626481710103842,1.6959148292989862895 ] 
dist 125=[-1.1371710934639822082 ,1.6875798826531957162 ] 
dist 126=[-1.4548104065841356978 ,1.6837511682097985440 ] 
dist 127=[-1.6938980342585256776 ,1.6798477908016808890 ] 
dist 128=[-1.9213252640982555977 ,1.6748316624588559850 ] 
dist 129=[-2.1924245140825873840 ,-.11823188021107231035] 
dist 130=[-2.4447174071408420626 ,-.21860953585596057557] 
dist 131=[-2.5970785779772008286 ,-.44362856462632360589] 
dist 132=[-2.7054765782129540449 ,-.48145340292197670968] 
dist 133=[-2.7822866721795165740 ,-.74204827049357080869] 
dist 134=[-2.8384841793405201553 ,-.78464300193637391593] 
dist 135=[-2.8646051932692602972 ,-.86186291517477436243] 
dist 136=[-2.8737169789904858128 ,-.73353225462551023852] 
dist 137=[-2.8714085170861665192 ,-.4852786643737119798 ] 
dist 138=[-1.3310126401356860753 ,-.2283109422881615536 ] 
dist 139=[-1.3593587639952698560 ,-.04654111477283783523] 
dist 140=[-1.3758403476157770066 ,.11491547301007711239] 
dist 141=[-1.3952761827914748294 ,.29082510104224147804] 
dist 142=[-1.4036401428057377417 ,.46254977577504376311] 
dist 143=[-1.4055112026341188577 ,.60731382908982464956] 
dist 144=[-1.4031459983301681168 ,.76007216101860225874] 
dist 145=[-1.2701031954605245240 ,.96371845210671457786] 
dist 146=[-1.2522674222458102012 ,1.1642621146368659548 ] 
dist 147=[-1.2049205958582497292 ,1.3046444030715762917 ] 
dist 148=[-1.1925324137945564792 ,1.4278965237157091111 ] 
dist 149=[-1.1014647404988122745 ,1.5600766429696178589 ] 
dist 150=[-1.0811112539170154552 ,1.6879849178119454645 ] 
dist 151=[-1.0477093765253115148 ,1.7941969700665449209 ] 
dist 152=[-1.0377282647669187236 ,1.9049597136945264956 ] 
dist 153=[-.8142752950568042236 ,2.0510531114174778025 ] 
dist 154=[-.96010073421287952276,2.1888592316791638689 ] 
dist 155=[-1.1489877394991453070 ,2.2665450689266311277 ] 
dist 156=[-1.3053855426580638976 ,2.3151787745432446644 ] 
dist 157=[-1.4582478235067355765 ,2.3370075006867136921 ] 
dist 158=[-1.5970599069590489451 ,2.3470967811866277586 ] 
dist 159=[-1.6973847466801733980 ,2.3488618949563543198 ] 
dist 160=[-1.7886861710054743576 ,2.3449060889847740015 ] 
dist 161=[-1.8914850082028982158 ,2.3376374999849724353 ] 
dist 162=[-1.9838935276452080687 ,2.0495044224069352310 ] 
dist 163=[-2.0337278935700154817 ,2.0050095677403267960 ] 
dist 164=[-2.0618849355952551705 ,1.9203593331155512518 ] 
dist 165=[-2.0677821439272205026 ,1.8964305972005036277 ] 
dist 166=[-2.0647568052460122313 ,1.8036168804043383716 ] 
dist 167=[-2.0573050508792354637 ,1.7794632153797954159 ] 
dist 168=[-2.0451692030059843173 ,1.7309395755523133438 ] 
dist 169=[-2.0375118345765445449 ,1.7152601548612710201 ] 
dist 170=[-.42379923721600327953,1.2872037185749339542 ] 
dist 171=[-.70466622913086672655,1.2954415477103318989 ] 
dist 172=[-.94008338146922024369,1.2960200675616874706 ] 
dist 173=[-1.1751042453230578196 ,1.2809492801111860726 ] 
dist 174=[-1.3919560959863327394 ,1.2738249499959132484 ] 
dist 175=[-1.5548546801632971239 ,1.2604296777706302936 ] 
dist 176=[-1.7094821268564117894 ,1.2546562405607146770 ] 
dist 177=[-1.8933244661766814986 ,.89294547651910983876] 
dist 178=[-2.0641623429123142355 ,.89393223493531367629] 
dist 179=[-2.1668845604737441372 ,.90446061159358461142] 
dist 180=[-2.2394266615777554936 ,.90668197756413716935] 
dist 181=[-2.2898020447708391286 ,.90271367611670535843] 
dist 182=[-2.3247495712071512704 ,.89945818226838341601] 
dist 183=[-2.3357081148262460896 ,.89509224666617145493] 
dist 184=[-2.3354304386230014570 ,.89155051062212098424] 
dist 185=[-2.3291605335886101739 ,.77253803401130272957] 
dist 186=[-2.1694332389829420427 ,.75443669679618251078] 
dist 187=[-2.1920302958522250141 ,.71863295854362699554] 
dist 188=[-2.2122898575830209832 ,.70834238910504938769] 
dist 189=[-2.2153873542006905225 ,.75551874735160022388] 
dist 190=[-2.1955902459519604476 ,.96288298233485278105] 
dist 191=[-2.1838979627573308122 ,1.1248904306679138669 ] 
dist 192=[-2.1692072651417839691 ,1.2847246661978566990 ] 
dist 193=[-2.1598946959365742366 ,1.4834194025779895779 ] 
dist 194=[-1.8635936228480033647 ,1.6724546247101620801 ] 
dist 195=[-1.8186187723392132448 ,1.7937367067347094500 ] 
dist 196=[-1.7266851508789442890 ,1.8886422148558383670 ] 
dist 197=[-1.6997377394926980292 ,1.9724016989756605801 ] 
dist 198=[-1.5872272470696660845 ,2.0426250618712582697 ] 
dist 199=[-1.5621256464199778205 ,2.0835063321013797978 ] 
dist 200=[-1.4982100401411189364 ,2.1107559828371490978 ] 
dist 201=[-1.4804090408242649644 ,2.1265777367964299663 ] 
dist 202=[-.83723190884739472959,2.1329388601027462695 ] 
dist 203=[-.86079291933619396938,2.1492065952104550155 ] 
dist 204=[-.87474575275401294454,2.1807057329929062561 ] 
dist 205=[-.88372851630029432694,2.1886965784179266223 ] 
dist 206=[-.88745083721584612359,2.1873457099402600509 ] 
dist 207=[-.88803163283377278066,2.1815545890869147184 ] 
dist 208=[-.88614964767671904006,2.1714084618789354923 ] 
dist 209=[-.8799374259118286244 ,2.1635899419080946113 ] 
dist 210=[-.90016878493659605604,2.1622585723667795583 ] 
dist 211=[-.9117188575949413126 ,2.2504643094628655307 ] 
dist 212=[-.91441446028898202046,2.3070859951949907110 ] 
dist 213=[-.91331707747467214872,2.3354142716630233472 ] 
dist 214=[-.91024372830619373363,2.3514379533441219155 ] 
dist 215=[-.90405934466620975237,2.3589473397121822566 ] 
dist 216=[-.90060063391061944263,2.3616564776643174293 ] 
dist 217=[-.79901422814132281695,2.3585256722311974340 ] 
dist 218=[-.78274466129987135791,2.1826517927656041359 ] 
dist 219=[-.75464383649617442332,2.1690169139933635282 ] 
dist 220=[-.97319490770961178675,2.1184702178086189145 ] 
dist 221=[-1.1910167657087787602 ,2.1087470883470520569 ] 
dist 222=[-1.3917727671526006949 ,1.9652961774985876412 ] 
dist 223=[-1.5453408559234710494 ,1.9314943542037732678 ] 
dist 224=[-1.6883520484979188097 ,1.9005900622543208570 ] 
dist 225=[-1.8535957746671482048 ,1.8873308131177790187 ] 
dist 226=[-2.0100340699104535469 ,1.4147020537733162728 ] 
dist 227=[-2.1036652471934110468 ,1.3506739846563581294 ] 
dist 228=[-2.1691431631235451941 ,1.2244004159568509991 ] 
dist 229=[-2.2133551246759340530 ,1.1908578801958303744 ] 
dist 230=[-2.2433325627404244277 ,1.0684019780433943684 ] 
dist 231=[-2.2519919480203499980 ,1.0397972741589674722 ] 
dist 232=[-2.2504225936072730831 ,.99230418422358356933] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 1, 0, 2, 1, 1, 2] 
dist 0=[51.866793972459642693  ,51.866793972459642693  ] 
dist 1=[51.590059687686363243  ,52.110975167617927990  ] 
dist 2=[51.236260117807621588  ,52.315412705144704529  ] 
dist 3=[50.684271719184413189  ,52.433355463647332278  ] 
dist 4=[49.911811664692775395  ,52.510046445681377682  ] 
dist 5=[48.725886287078976682  ,52.549564218458213829  ] 
dist 6=[47.223489286479363490  ,52.558438475298141318  ] 
dist 7=[45.197739426282033445  ,52.512811439559646612  ] 
dist 8=[41.921746448307998390  ,52.417784051700020952  ] 
dist 9=[38.562784532893503622  ,52.331220377387967241  ] 
dist 10=[36.205631229394655850  ,51.995833324327021172  ] 
dist 11=[34.125282307455092862  ,51.863339058546678959  ] 
dist 12=[30.058818585672039463  ,51.454061299686744414  ] 
dist 13=[26.927976558576015092  ,51.275425066978104691  ] 
dist 14=[24.225268514525125855  ,38.320996944679684418  ] 
dist 15=[21.391634477498317394  ,37.133019286762824592  ] 
dist 16=[18.682247192939205251  ,34.244327607203702891  ] 
dist 17=[16.475454587333581974  ,33.795990467623934911  ] 
dist 18=[14.207918263041500763  ,29.508976497521465570  ] 
dist 19=[11.255430082501557841  ,28.699435475410413959  ] 
dist 20=[8.3657011355236877097 ,27.704558584243914716  ] 
dist 21=[6.3485256127674613517 ,27.436022393682947570  ] 
dist 22=[4.5769960308234091956 ,20.397233946065104689  ] 
dist 23=[2.6679743573013445666 ,19.505538182309782241  ] 
dist 24=[.8062354855244650396 ,17.651358402903083184  ] 
dist 25=[-.7769912253103066699 ,17.163172783283227129  ] 
dist 26=[-2.4681503993427862159 ,15.342644540726154809  ] 
dist 27=[-4.7621939333212148519 ,14.984518586111655360  ] 
dist 28=[-6.9772488198666132119 ,14.287390153118481894  ] 
dist 29=[-8.3530216633731125505 ,14.114159631430981837  ] 
dist 30=[-9.3867333808465079842 ,3.8335971449311925246 ] 
dist 31=[-10.234653677431254379  ,2.9318393501304519848 ] 
dist 32=[-10.913943949068806455  ,.9812138097980044551 ] 
dist 33=[-11.273490677896159580  ,.5957528364457257297 ] 
dist 34=[-11.470982734977011864  ,-1.4954008851795702813 ] 
dist 35=[-11.514594297321927064  ,-1.8408613187654715945 ] 
dist 36=[-11.232335765639208028  ,-2.5790323425042696593 ] 
dist 37=[-11.888635776131262344  ,-2.7022288864055474430 ] 
dist 38=[-12.939405960307841733  ,-3.5761314164132939060 ] 
dist 39=[-13.553741226146980068  ,-3.7015340242086447028 ] 
dist 40=[-13.968846578563183730  ,-3.6656456725349746810 ] 
dist 41=[-14.223760686507118460  ,-3.0968085588148589347 ] 
dist 42=[-14.393856151109466099  ,-2.4837499045789811677 ] 
dist 43=[-14.470027750628272163  ,-1.9462209295751355871 ] 
dist 44=[-14.492675897201291769  ,-1.3732219418120240692 ] 
dist 45=[-14.466295549249720755  ,-.6020944741611178946 ] 
dist 46=[-4.7989362514279502951 ,.6017421842972399543 ] 
dist 47=[-4.2294240719319792697 ,1.4262960555035175600 ] 
dist 48=[-2.8948535997219723473 ,2.1295309450627844663 ] 
dist 49=[-2.6890061556775414711 ,2.8495593775398637387 ] 
dist 50=[-1.2887726355867472973 ,3.5243054785654285312 ] 
dist 51=[-.91620566914832544948,4.1719379720900120922 ] 
dist 52=[-.84542361910458609027,5.0820279990732799807 ] 
dist 53=[-.42355987627021393535,5.6593579699740330420 ] 
dist 54=[-.35359930640504628116,6.1039261103055580054 ] 
dist 55=[-.21181273356878202769,6.4842548575260040278 ] 
dist 56=[-.18137814697179628869,6.7952090483481502434 ] 
dist 57=[2.3132755177274310783 ,6.9630171143895200937 ] 
dist 58=[2.4784223763501362503 ,7.0591475057425921785 ] 
dist 59=[2.8130322944088878477 ,7.0842865017501908682 ] 
dist 60=[2.8810105341912728578 ,4.3358329106805905667 ] 
dist 61=[2.7151391112941693824 ,4.4296621300337038502 ] 
dist 62=[2.3989338007371684835 ,4.4966377889476788976 ] 
dist 63=[2.0389657249909043936 ,4.5207303272780929234 ] 
dist 64=[1.6789984629288083601 ,4.5200442131230335971 ] 
dist 65=[1.3623950082722723765 ,4.5127696071399256820 ] 
dist 66=[1.0170006938883128405 ,4.4366497599496311560 ] 
dist 67=[.5420278882663940962 ,4.4121277951944470604 ] 
dist 68=[.0676287326584744268 ,4.3294166671248020900 ] 
dist 69=[-.2755283151593002299 ,4.3038282172325330841 ] 
dist 70=[-.5884594249119356264 ,3.9464150930749829474 ] 
dist 71=[-.9422807528659155025 ,3.8858758921360369222 ] 
dist 72=[-1.2957914844132955840 ,3.7199570754954652061 ] 
dist 73=[-1.6075460007683601448 ,3.6903014188689244836 ] 
dist 74=[-1.9489226903680074129 ,3.3745904278267488583 ] 
dist 75=[-2.4207888924896856512 ,3.3085146816839686156 ] 
dist 76=[-2.8786908504998117421 ,3.2304083751922356859 ] 
dist 77=[-3.1643432301800084323 ,3.1995801823019889043 ] 
dist 78=[-3.5338561471805629753 ,1.5789575484924633287 ] 
dist 79=[-3.9354219209448579422 ,1.4747137214057074708 ] 
dist 80=[-4.2444520111296016212 ,1.4432024005451016831 ] 
dist 81=[-4.5087252695496763840 ,1.0042457569578409760 ] 
dist 82=[-4.7246623668279307832 ,1.0540079930390392603 ] 
dist 83=[-4.8407439128047054560 ,1.1257533041873237850 ] 
dist 84=[-4.9063300444750500060 ,1.1983315252831539789 ] 
dist 85=[-4.9642463832517809924 ,1.2514592714364597057 ] 
dist 86=[-5.0901791637726959605 ,1.3003794491350236064 ] 
dist 87=[-5.1657485250946227457 ,1.3562435565966633468 ] 
dist 88=[-5.2190616584008263204 ,1.4123284913776072394 ] 
dist 89=[-5.2561519952084067232 ,1.4621852342326607710 ] 
dist 90=[-5.2801912220714984900 ,1.5171773532120866581 ] 
dist 91=[-5.2814165858667734809 ,1.5938426436556986201 ] 
dist 92=[-5.2663271382049387578 ,1.6699267186851545563 ] 
dist 93=[-5.2515652331808473852 ,1.7226162969489795700 ] 
dist 94=[-2.5341050817063656636 ,1.7685381268130380508 ] 
dist 95=[-2.3013726208086164691 ,1.8175776699949539843 ] 
dist 96=[-1.7970886583375620757 ,1.8652008788000111419 ] 
dist 97=[-1.7058887012401584240 ,1.9054629227864868992 ] 
dist 98=[-1.1250549884307973895 ,2.1844598868891483441 ] 
dist 99=[-1.0205498948335439155 ,2.5090819358295139703 ] 
dist 100=[-.8225454778924576523 ,2.8025552429236895967 ] 
dist 101=[-.7753932813595196590 ,3.1304888817046031103 ] 
dist 102=[-.58063318010783378698,3.4330631910481056252 ] 
dist 103=[-.51000994527517167621,3.6253038026042215053 ] 
dist 104=[-.6114039430694212806 ,3.7736366799470826850 ] 
dist 105=[-.97132710992235881418,3.9009088457236701823 ] 
dist 106=[-1.3973541029541076855 ,4.0048804233923718149 ] 
dist 107=[-2.0250766733676543158 ,4.0601753614412338751 ] 
dist 108=[-2.6452197321022541124 ,4.0902972896906026706 ] 
dist 109=[-3.0410023116314067977 ,4.0937360528665955043 ] 
dist 110=[-3.3483099848834621935 ,2.5631526939742051179 ] 
dist 111=[-3.6153221968204505293 ,2.5955088913754540220 ] 
dist 112=[-3.8360913761088264986 ,2.6229744011605803776 ] 
dist 113=[-3.9588321491870601246 ,2.6395675931339614647 ] 
dist 114=[-4.0333413645390750518 ,2.6513209283633355017 ] 
dist 115=[-4.0616136653012429823 ,2.6597996805922511131 ] 
dist 116=[-4.0719087159706202783 ,2.6636309877354715651 ] 
dist 117=[-4.0746573724861370990 ,2.6264130944923074203 ] 
dist 118=[-4.0724468400900674088 ,2.5504052926609576934 ] 
dist 119=[-4.0629150967401146004 ,2.5393263418570651256 ] 
dist 120=[-4.0493696487246947922 ,2.5331905011422413256 ] 
dist 121=[-4.0312543848844212785 ,1.1868346876913247037 ] 
dist 122=[-4.0058291215998211753 ,1.1184205503642829807 ] 
dist 123=[-3.9901114121271667912 ,1.0987386663980024599 ] 
dist 124=[-2.4967579863297677382 ,-.95786118867860862779] 
dist 125=[-2.7407278592020054143 ,-1.0789781602301714229 ] 
dist 126=[-2.9281041382700146884 ,-1.0979910316310426914 ] 
dist 127=[-3.0874146834906455160 ,-1.0882294635677063498 ] 
dist 128=[-3.2166337744562195198 ,-1.0366669939270627550 ] 
dist 129=[-3.2838949873148952883 ,-.96825870478977818005] 
dist 130=[-3.3187271100911708883 ,-.8876324639692751864 ] 
dist 131=[-3.3254598020723471294 ,-.78352771805606451881] 
dist 132=[-3.3044144625568949082 ,-.64094507701210195092] 
dist 133=[-3.2900484532579805757 ,-.4654279446972048041 ] 
dist 134=[-3.2583283259240655692 ,-.2747584916399217523 ] 
dist 135=[-3.2427830294912819635 ,-.0364886957030636889 ] 
dist 136=[-3.1512631082171814947 ,.3290071155426428059 ] 
dist 137=[-3.1270465808836342553 ,.6956054913067392914 ] 
dist 138=[-3.0491944336739513621 ,.9382763048701447212 ] 
dist 139=[-3.0297986360159010884 ,1.1366083414235883306 ] 
dist 140=[-1.6909199964654672786 ,1.3262469525640374066 ] 
dist 141=[-1.5735990534214900736 ,1.4957496517487475274 ] 
dist 142=[-1.5461500930477022898 ,1.6137174439731007108 ] 
dist 143=[-1.5066456067152686151 ,1.7165117024619180694 ] 
dist 144=[-1.4924805934701504433 ,1.8254551861079073075 ] 
dist 145=[-1.1535045486845558703 ,1.9469925020093138247 ] 
dist 146=[-1.1060023989690952118 ,2.1008418661395874276 ] 
dist 147=[-1.0028293497951815810 ,2.3182514275078518972 ] 
dist 148=[-.9729631658598961218 ,2.5172221654309463169 ] 
dist 149=[-.8474084910809045124 ,2.6408042999284749522 ] 
dist 150=[-.8226905031829728619 ,2.7328614195245857198 ] 
dist 151=[-.7581325062728538354 ,2.8060048675689965715 ] 
dist 152=[-.7473608621523117958 ,2.8614289490544163908 ] 
dist 153=[.1483608178114358517 ,2.8827634410983247612 ] 
dist 154=[.1833005963169732152 ,2.8874842778633899780 ] 
dist 155=[.2175739421907978717 ,2.8820000814943998825 ] 
dist 156=[.2149979914735793225 ,1.4509172587036061278 ] 
dist 157=[.1961812811768932853 ,1.3437469375967166906 ] 
dist 158=[.1543706866209377782 ,1.0935551324795933997 ] 
dist 159=[.0877040568851533777 ,1.0465692462316044563 ] 
dist 160=[-.0303256175128432517 ,.87733898617190755468] 
dist 161=[-.1599206118701523912 ,1.0439929099141881153 ] 
dist 162=[-.2727509166919178171 ,1.1706784573464476175 ] 
dist 163=[-.3949339435861692292 ,1.2923644885573528652 ] 
dist 164=[-.56186228736276307507,1.4390602559509076724 ] 
dist 165=[-.74483027775072959192,1.5906185601165833193 ] 
dist 166=[-.93103642173389322901,1.7317098505465251336 ] 
dist 167=[-1.1553325773532017783 ,1.8921642426869557110 ] 
dist 168=[-1.4903374387959039502 ,2.1210024503259772381 ] 
dist 169=[-1.8231883412251615985 ,2.3438409206245706565 ] 
dist 170=[-2.0388875083054843248 ,2.4803477018898868682 ] 
dist 171=[-2.2101288596403301634 ,2.5797484226487517073 ] 
dist 172=[-2.3655273953418440962 ,2.6544869774698883909 ] 
dist 173=[-2.4988906703076193688 ,2.7092551902932462587 ] 
dist 174=[-2.5821789174441881515 ,2.7289494872744326033 ] 
dist 175=[-2.6447572927518066060 ,2.7337000554534387231 ] 
dist 176=[-2.6954580185022858739 ,2.7288255719996557420 ] 
dist 177=[-2.7328613236794977296 ,2.5912283985211225516 ] 
dist 178=[-2.7423639597808430178 ,2.5622806375666686641 ] 
dist 179=[-2.7400056363958220624 ,2.4989681901936836471 ] 
dist 180=[-2.7307886997771463427 ,2.4764913337735832059 ] 
dist 181=[-2.6918411924272622553 ,2.4548018372930130423 ] 
dist 182=[-2.6622212370615474221 ,2.4193106468179791242 ] 
dist 183=[-2.6477375922721301565 ,2.4022828541515829051 ] 
dist 184=[-2.5772218831005366389 ,2.3028705626971715149 ] 
dist 185=[-2.5399941473033372854 ,2.2766432222537850789 ] 
dist 186=[-2.4779404613040123913 ,2.2217091343801312822 ] 
dist 187=[-2.4554268268357017354 ,2.2025260191374497581 ] 
dist 188=[-1.4341954457043237520 ,.7746690101732760738 ] 
dist 189=[-1.2345677673210853788 ,1.1038529315850456906 ] 
dist 190=[-1.0893986896215543498 ,1.3770075453371901517 ] 
dist 191=[-.98754927818456507246,1.6451634091386391189 ] 
dist 192=[-.96240361562595672006,1.8896282070660440913 ] 
dist 193=[-1.0076797660492422570 ,2.0682262804964224905 ] 
dist 194=[-1.2200512539187740665 ,2.2328172613538581085 ] 
dist 195=[-1.4092083508980596959 ,2.4213798817149409577 ] 
dist 196=[-1.6161802976170006353 ,2.5929035037062713129 ] 
dist 197=[-1.8188040488677293158 ,2.6894878010724120509 ] 
dist 198=[-1.9906066320024319104 ,2.7497074394047069538 ] 
dist 199=[-2.1727700216357999526 ,2.7760876417323030895 ] 
dist 200=[-2.4167490449413884249 ,2.7884020298336429924 ] 
dist 201=[-2.6504238910646144587 ,2.7924756620296848130 ] 
dist 202=[-2.7914591339416349978 ,2.7913017893855942716 ] 
dist 203=[-2.8916630878191616433 ,2.7826578268555686303 ] 
dist 204=[-2.9623626202408083862 ,2.4991138941482906571 ] 
dist 205=[-3.0125305190133577702 ,2.6241802859771715408 ] 
dist 206=[-3.0307846064963487326 ,2.7002347198119184366 ] 
dist 207=[-3.0330089055216466275 ,2.7549576619188134355 ] 
dist 208=[-3.0268351219414504099 ,2.7948826437594979654 ] 
dist 209=[-2.8174628287129241825 ,2.8214917996484110562 ] 
dist 210=[-2.7786146201153551496 ,2.8246654588573742227 ] 
dist 211=[-2.6993180224512267201 ,2.8065983575038567884 ] 
dist 212=[-2.6734376552822626048 ,2.1883571860211652422 ] 
dist 213=[-2.5537705221566134741 ,2.1170744965327640562 ] 
dist 214=[-2.5258998516626517603 ,2.1170062135611455292 ] 
dist 215=[-2.4410223458909015804 ,2.2450114904393322842 ] 
dist 216=[-2.4241126940418804081 ,2.4211478837622260856 ] 
dist 217=[-2.4088094875989305778 ,2.5886093514742238523 ] 
dist 218=[-2.4186796627906390183 ,2.6819892704441203499 ] 
dist 219=[-2.4185556934365211133 ,2.7389689525930800110 ] 
dist 220=[-2.3494970408489925571 ,2.7611468385675267367 ] 
dist 221=[-2.3330653683363301706 ,2.7700409612452306351 ] 
dist 222=[-2.2767468033657421787 ,2.7740037310585667147 ] 
dist 223=[-2.2639441216397661303 ,2.7751051014183885611 ] 
dist 224=[-2.1135280199419938943 ,2.7725854394269666861 ] 
dist 225=[-2.0780303225946099470 ,2.3588280140523898186 ] 
dist 226=[-2.0389464898292061535 ,2.2984266529262577164 ] 
dist 227=[-2.0200950665802736118 ,2.1916310229795787661 ] 
dist 228=[-2.1464364918990672211 ,2.1638549001568334893 ] 
dist 229=[-2.2550740073527562508 ,2.0716555062048250716 ] 
dist 230=[-2.3407722403706101371 ,2.0425937214388123751 ] 
dist 231=[-2.4175779682108507256 ,2.0179242282702522764 ] 
dist 232=[-2.4827806091376067705 ,2.0048943904142281177 ] 
dist 233=[-2.5221625646177487184 ,.0759203379155238346 ] 
dist 234=[-2.5501540997310307868 ,-.0051840662436659616 ] 
dist 235=[-2.5698859867614136366 ,.3951525379853925021 ] 
dist 236=[-2.5804773466623325412 ,.7938098746238252230 ] 
dist 237=[-2.5790983996075760346 ,1.0619377505169553103 ] 
dist 238=[-2.5582869010092705212 ,1.2858344144667875227 ] 
dist 239=[-2.5481131688654431666 ,1.5079510149841484927 ] 
dist 240=[-2.4412196721489531714 ,1.7119650379834351409 ] 
dist 241=[-2.4121140244791416816 ,1.8636096513672701134 ] 
dist 242=[-2.3762443716710047190 ,2.0059676589872175247 ] 
dist 243=[-2.3593778289218892716 ,2.1729190244479655029 ] 
dist 244=[-1.9091922871348732034 ,2.3268426185008876173 ] 
dist 245=[-1.8447135935274498335 ,2.4172033687731083099 ] 
dist 246=[-1.7113660965281519428 ,2.4783355580330229258 ] 
dist 247=[-1.5888957746763608673 ,2.5155976661918541752 ] 
dist 248=[-1.2078031445581795551 ,2.5381519864477578738 ] 
dist 249=[-.0588097855640345998 ,2.5405768869866796622 ] 
dist 250=[.0618214188708500849 ,2.5336794923537091186 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 0, 0, 1, 0, 1] 
dist 0=[46.172100059446085578  ,46.172100059446085578  ] 
dist 1=[45.362269726544953009  ,46.704580920117837914  ] 
dist 2=[44.192079526280153106  ,47.098597289725384990  ] 
dist 3=[42.220465781209703427  ,47.355387296170121687  ] 
dist 4=[40.172535866764847289  ,47.561226417440246633  ] 
dist 5=[38.697507119117181005  ,47.751558271547007840  ] 
dist 6=[37.356017549093016903  ,47.880078941124754059  ] 
dist 7=[35.841202009509204549  ,47.887545404930060076  ] 
dist 8=[34.325609704660361036  ,47.664443059357016601  ] 
dist 9=[32.980815478112654035  ,46.820166318941240180  ] 
dist 10=[31.499165430709856721  ,46.597600961043010853  ] 
dist 11=[29.436607529522766561  ,46.209543777498132008  ] 
dist 12=[27.353944582067212459  ,46.083156253341395361  ] 
dist 13=[25.791795281023367239  ,45.539494944750046627  ] 
dist 14=[24.305792194685472894  ,45.375580079751296134  ] 
dist 15=[22.527023584125080711  ,44.971586496136791266  ] 
dist 16=[20.686766084598300920  ,44.411561093448314118  ] 
dist 17=[18.782298411058978361  ,32.551788390616926476  ] 
dist 18=[16.372613293380345131  ,31.445338323584980080  ] 
dist 19=[14.079688117030242157  ,28.793444579876535723  ] 
dist 20=[11.220023754161247334  ,28.369611055994551419  ] 
dist 21=[9.3181912160774550222 ,24.558503868387255165  ] 
dist 22=[7.0533141629720750855 ,23.845993326918479015  ] 
dist 23=[5.2034476818684445264 ,22.913479067005504314  ] 
dist 24=[3.5614058681922845248 ,22.631605077084562531  ] 
dist 25=[1.7642198387653924945 ,16.789590329274041790  ] 
dist 26=[-.0055968605944415525 ,16.043975276625453085  ] 
dist 27=[-1.5388609692111938804 ,14.457652274814486120  ] 
dist 28=[-3.2013339782584354167 ,14.064701274710023304  ] 
dist 29=[-5.4884441339537705329 ,12.391333777456299491  ] 
dist 30=[-7.7036928222931827825 ,12.084819938705089558  ] 
dist 31=[-9.0792317748320192440 ,11.399388987096418733  ] 
dist 32=[-10.112532941525980808  ,11.260715344105885767  ] 
dist 33=[-10.959890355849769671  ,3.6977797979920963966 ] 
dist 34=[-11.638150192098443963  ,3.0025769976359807784 ] 
dist 35=[-11.995389902057663143  ,1.5184694466478517537 ] 
dist 36=[-12.189218062175998180  ,1.2037314103047237784 ] 
dist 37=[-12.232821484059638215  ,-.32991030664520837545] 
dist 38=[-11.957509875622017854  ,-.59042531263637441578] 
dist 39=[-11.874396313233804140  ,-1.1432289415485418715 ] 
dist 40=[-11.796624875803250148  ,-1.2441703140901871518 ] 
dist 41=[-12.338614956369375103  ,-1.6008891959906014496 ] 
dist 42=[-12.799831935473393368  ,-1.4275548689844728135 ] 
dist 43=[-13.112225271665476575  ,-1.1506153274824308225 ] 
dist 44=[-13.305804917631382788  ,-.85902876944058819757] 
dist 45=[-13.425956963004550779  ,-.62707457027753487087] 
dist 46=[-13.444942037017568481  ,-.39496926812451070117] 
dist 47=[-13.417292172443614120  ,-.10250943154892707646] 
dist 48=[-13.375137658383497939  ,.79965223377610749184] 
dist 49=[-4.8681557481871723715 ,1.7769774965087421032 ] 
dist 50=[-4.3262986987840545514 ,2.4437613557149761648 ] 
dist 51=[-3.5547973454483605157 ,3.0095937239264799793 ] 
dist 52=[-2.8528460669431141145 ,3.5843319606640634386 ] 
dist 53=[-1.1113706710608330852 ,4.1199813852146592713 ] 
dist 54=[-.80443971411563508485,4.8643166089546011234 ] 
dist 55=[-.40567081708751446714,5.4294377482180080172 ] 
dist 56=[-.32728687463445879604,5.8580108604046076063 ] 
dist 57=[1.7800273572337465716 ,6.2130146107466556318 ] 
dist 58=[2.0242595366705150100 ,6.4944837858580130246 ] 
dist 59=[2.5515716661749987776 ,6.6296449587343590288 ] 
dist 60=[2.5586919524200386033 ,6.6935263872581577784 ] 
dist 61=[2.4367337579187230394 ,6.6964968787819224851 ] 
dist 62=[2.2774661126155548493 ,3.6850483865752654081 ] 
dist 63=[2.0259450564044994973 ,3.8114728174871452233 ] 
dist 64=[1.7345856842831638406 ,3.9027394579257112534 ] 
dist 65=[1.4162813493408219160 ,3.9711721627866521425 ] 
dist 66=[1.0173520717512743687 ,4.0064536193723426564 ] 
dist 67=[.40417142864772769963,4.0253705325111297318 ] 
dist 68=[-.21157450343985536585,4.0282867047587651026 ] 
dist 69=[-.62075663422320153739,4.0218921921334512374 ] 
dist 70=[-.95696811469090009312,4.0091101865974648762 ] 
dist 71=[-1.2814847335040375175 ,3.9780234549572025906 ] 
dist 72=[-1.5736495190489936657 ,3.9614669599222040773 ] 
dist 73=[-1.7807438439442260655 ,3.8652377420861228743 ] 
dist 74=[-1.9652017368130548359 ,3.8353250144588414196 ] 
dist 75=[-2.1670257084619399654 ,3.7791959447133473488 ] 
dist 76=[-2.3518388597088098161 ,3.7598059919341681050 ] 
dist 77=[-2.4684005536682425785 ,3.6694924023252948432 ] 
dist 78=[-2.5573004433287076927 ,3.6445098881942079510 ] 
dist 79=[-2.6316967771961905116 ,3.5758569158145888210 ] 
dist 80=[-2.6910539820792967051 ,3.5507634729239234540 ] 
dist 81=[-3.4893291351220970223 ,.07847423195641111039] 
dist 82=[-4.0594820298635932768 ,.04817413002236566344] 
dist 83=[-4.5085102462565886024 ,.04020882120519244515] 
dist 84=[-4.9558628151509860187 ,.03765109722971192093] 
dist 85=[-5.3393477210187382925 ,.03948070705430989609] 
dist 86=[-5.5697073127555232776 ,.04469254238679355035] 
dist 87=[-5.7323325866939084250 ,.05567014238943860929] 
dist 88=[-5.8454579321894067444 ,.06934052913948801190] 
dist 89=[-5.9300871864244343225 ,.08531582502698001639] 
dist 90=[-5.9789493256794100337 ,.10594874465393064732] 
dist 91=[-6.0111619962841276878 ,.13821975279548056067] 
dist 92=[-6.0292710461474822135 ,.17202571122649633263] 
dist 93=[-6.0370195425817513981 ,.3668828438775166139 ] 
dist 94=[-6.0278387767179454259 ,.57036954717890065582] 
dist 95=[-6.0044696197271119426 ,.7097470706310609524 ] 
dist 96=[-5.9850929230732225659 ,.82903596844190879366] 
dist 97=[-3.1736275061691571588 ,.95233314415282123024] 
dist 98=[-2.9423586058566189498 ,1.0690158830916210644 ] 
dist 99=[-2.3881524154963807739 ,1.1619086875681036317 ] 
dist 100=[-2.2982303905965299789 ,1.2553545579764026370 ] 
dist 101=[-1.5123060600280372508 ,1.5760927966971486680 ] 
dist 102=[-1.3678000282584588989 ,1.9749821020636783534 ] 
dist 103=[-1.1673343504774589118 ,2.3560742898663384040 ] 
dist 104=[-1.1082760277083760584 ,2.8127935887671695325 ] 
dist 105=[-.87610638121019106515,3.2399928673523145667 ] 
dist 106=[-.88380577792875115853,3.5032480726571929220 ] 
dist 107=[-.88458847784559437441,3.6969538696729297004 ] 
dist 108=[-.85899775632368041391,3.8465117020969200357 ] 
dist 109=[-.85196959350607600739,3.9626654170897653323 ] 
dist 110=[-1.1797603503225032620 ,4.0230355843392740216 ] 
dist 111=[-1.4291889017744097503 ,4.0541446928607882577 ] 
dist 112=[-1.6321685732960266001 ,4.0561106975684657438 ] 
dist 113=[-1.8249221127545156073 ,2.5306979863542086529 ] 
dist 114=[-1.9964247581858455985 ,2.6061230406522649890 ] 
dist 115=[-2.1145801231796363775 ,2.6542393231277901345 ] 
dist 116=[-2.2163265498264343231 ,2.6778901313638141683 ] 
dist 117=[-2.3223314933583542435 ,2.6881774115856708634 ] 
dist 118=[-2.4150228091184829605 ,2.6851785044584961156 ] 
dist 119=[-2.4636226314871397551 ,2.6705918091737574940 ] 
dist 120=[-2.4892291917012213911 ,2.6592726706928940508 ] 
dist 121=[-2.4941163971866518629 ,2.4309050133903064001 ] 
dist 122=[-2.4818555312052949634 ,2.3917256323838131540 ] 
dist 123=[-2.4711510155767469695 ,2.3022476969619343173 ] 
dist 124=[-2.4557207750001212785 ,2.2726026081376570518 ] 
dist 125=[-2.4464876967419424962 ,2.1325827668248348310 ] 
dist 126=[-.75508562322514269672,2.1013666770225192532 ] 
dist 127=[-.83436627632436314166,2.0243440809218789818 ] 
dist 128=[-.91290778501136235068,1.9999171163937304952 ] 
dist 129=[-.99655199239267206384,.90695415070474193934] 
dist 130=[-1.1473365304787036590 ,.79758642786940678634] 
dist 131=[-1.4406953373042124894 ,.59057894174600627328] 
dist 132=[-1.7220189646340383096 ,.72874684246812177193] 
dist 133=[-1.9742002326356947940 ,.84009502589567834763] 
dist 134=[-2.1512374918265998828 ,.93089177290693767084] 
dist 135=[-2.3072132470300774074 ,1.0173378255183392127 ] 
dist 136=[-2.4753306841088782938 ,1.0943265582123776090 ] 
dist 137=[-2.6263405580328661464 ,1.1473768275840358426 ] 
dist 138=[-2.7140314294279879086 ,1.1930198609047981664 ] 
dist 139=[-2.7721867328901523440 ,1.2404412073187136426 ] 
dist 140=[-2.8053021342235802735 ,1.2808712775034891274 ] 
dist 141=[-2.8230998393369428620 ,1.2986102629531118708 ] 
dist 142=[-2.8227993321911162651 ,1.3066892417302070899 ] 
dist 143=[-2.8089003053163316363 ,1.3085767172777638285 ] 
dist 144=[-2.7960769967386775710 ,1.2747919651841942775 ] 
dist 145=[-1.2775869947665643344 ,1.2661081478452447769 ] 
dist 146=[-1.2335149278765244913 ,1.2609605802582978598 ] 
dist 147=[-1.2252415129724270478 ,1.2592904834557496085 ] 
dist 148=[-.16983830296955763671,.74345289481213093885] 
dist 149=[.23549247240036623834,.84608903089525420099] 
dist 150=[.30573358774599947782,.93109079352722208558] 
dist 151=[.34591359438269151422,1.0194686808341743440 ] 
dist 152=[.26373958197347278302,1.1355913984274040750 ] 
dist 153=[.17863350229238774236,1.2491884603486010062 ] 
dist 154=[.07507594044331327591,1.3274916606218275700 ] 
dist 155=[-.08074431666357396349,1.3949811596240565588 ] 
dist 156=[-.24228572295560230888,1.4654237041828296489 ] 
dist 157=[-.36867896363830823993,1.5324579033876924223 ] 
dist 158=[-.49353999684330333487,1.5863518122896854184 ] 
dist 159=[-.64896758328880342072,1.6410229527840785572 ] 
dist 160=[-.91291054761935935917,1.7111772174551972780 ] 
dist 161=[-1.2519503843257552092 ,1.7766339398316063052 ] 
dist 162=[-1.4726690128947575118 ,1.8125557879157118503 ] 
dist 163=[-1.6489346726628066731 ,1.8338118085404276532 ] 
dist 164=[-1.8105595256569663505 ,1.8407149511823413362 ] 
dist 165=[-1.9503448561220259401 ,1.8394310197465400622 ] 
dist 166=[-2.0394460157190489825 ,1.8353935526001453528 ] 
dist 167=[-2.1084478157502070076 ,1.8146624653634134538 ] 
dist 168=[-2.1680110488254104147 ,1.8057644218242043113 ] 
dist 169=[-2.2161477528077355790 ,1.6672667445166648024 ] 
dist 170=[-2.2395449053575064350 ,1.6425301378049834950 ] 
dist 171=[-2.2492682780147868034 ,1.5772470622129205061 ] 
dist 172=[-2.2478236628622621364 ,1.5964933408611616363 ] 
dist 173=[-2.2280948984345014139 ,1.6070839861248888753 ] 
dist 174=[-2.2188260993787278107 ,1.6088290596891629809 ] 
dist 175=[-2.1819942602010176259 ,1.6065080860932769598 ] 
dist 176=[-2.1702343896356445741 ,1.5785067319706061272 ] 
dist 177=[-1.9814907145967096961 ,1.5686150835542504799 ] 
dist 178=[-1.9548904297466785935 ,1.5438400195454791974 ] 
dist 179=[-1.9448225273174727205 ,1.5331650393590555796 ] 
dist 180=[-1.7540836387995553401 ,1.3604278421252240040 ] 
dist 181=[-1.9198394861425934196 ,1.3321244128076274039 ] 
dist 182=[-2.0327441855265670670 ,1.2656328931118150486 ] 
dist 183=[-2.1285938248300769125 ,1.2449161540117172953 ] 
dist 184=[-2.2262792013140566536 ,1.1422687750100591118 ] 
dist 185=[-2.3106832552658458616 ,1.1197643127762265980 ] 
dist 186=[-2.3535212813757918430 ,1.0713612122625314290 ] 
dist 187=[-2.3746751855804634708 ,1.0561347667085642672 ] 
dist 188=[-2.3779437939181535333 ,.95724862938666721053] 
dist 189=[-2.3568995762038188018 ,1.0984103381807186548 ] 
dist 190=[-2.3444918046363890996 ,1.2167488618832480910 ] 
dist 191=[-2.3257455704576391734 ,1.3349317966705697670 ] 
dist 192=[-2.3158673183047858068 ,1.4440256528859303003 ] 
dist 193=[-1.7443962481299267935 ,1.5260897211833711596 ] 
dist 194=[-1.8691255822584563562 ,1.6041182976990595016 ] 
dist 195=[-1.9606297655701971657 ,1.6971128661562373569 ] 
dist 196=[-2.0307398134962662092 ,1.7827262866108475011 ] 
dist 197=[-2.0840454528113568890 ,1.8312934833748036118 ] 
dist 198=[-2.1084752624135221012 ,1.8620682483316254928 ] 
dist 199=[-2.1179950895259328412 ,1.8766561992191586947 ] 
dist 200=[-2.1170957100709903606 ,1.8820964282568910680 ] 
dist 201=[-1.9985530460760648742 ,1.8796918653497538631 ] 
dist 202=[-1.9749435319811784447 ,1.8664321675083369114 ] 
dist 203=[-1.9307245645091065828 ,1.8795440600186988399 ] 
dist 204=[-1.6932645418605812928 ,1.9263292776502305110 ] 
dist 205=[-1.6730001162969696956 ,1.9596868315910937861 ] 
dist 206=[-1.6501992240214471751 ,1.9749090689383715684 ] 
dist 207=[-1.5054005469510454219 ,1.9797674071301632804 ] 
dist 208=[-1.2654350067254508043 ,1.9772819844982987090 ] 
dist 209=[-1.3878674888262043716 ,1.6657456889829306246 ] 
dist 210=[-1.5244154964802042096 ,1.6283169011399429780 ] 
dist 211=[-1.7159431293144585210 ,1.5330954192764528153 ] 
dist 212=[-1.9012460175927220982 ,1.5122460701139773252 ] 
dist 213=[-2.0129484259027322484 ,1.3487153930276125893 ] 
dist 214=[-2.0921275119935232032 ,1.3144020349212398308 ] 
dist 215=[-2.1476182823681756915 ,1.2611651260321222745 ] 
dist 216=[-2.1877707143145226220 ,1.2451704546579587723 ] 
dist 217=[-2.2057307520092458227 ,1.3078720136757559913 ] 
dist 218=[-2.2108694484291222849 ,1.3898625736674554919 ] 
dist 219=[-2.2088295021994998321 ,1.4615273004839008022 ] 
dist 220=[-2.0266068328176819356 ,1.5378447225403717936 ] 
dist 221=[-1.9949681519091361728 ,1.6113087586921261774 ] 
dist 222=[-1.9372686650762148247 ,1.6715806303500156784 ] 
dist 223=[-1.9201431514561220158 ,1.7337214751167644010 ] 
dist 224=[-1.8511046851156411559 ,1.8146382291801863908 ] 
dist 225=[-1.8314471585994332787 ,1.8900999492040288139 ] 
dist 226=[-1.7889596424908661422 ,1.9304667790214223533 ] 
dist 227=[-1.7737524726214859978 ,1.9528297500407769709 ] 
dist 228=[-1.5171653049724156109 ,1.9564356282358681792 ] 
dist 229=[-1.6501632873207111395 ,1.9519576614501744543 ] 
dist 230=[-1.7428038060475454642 ,1.9447923473316511604 ] 
dist 231=[-1.8236509488431627994 ,1.9284059879601754174 ] 
dist 232=[-1.9095796170407205419 ,1.9196464174847472382 ] 
dist 233=[-1.9841866076567362244 ,1.7050268123120498836 ] 
dist 234=[-2.0198452453716824148 ,1.6703709196791994385 ] 
dist 235=[-2.0377725693320813606 ,1.5940057713334871305 ] 
dist 236=[-2.0416004208087430610 ,1.5698222755799131234 ] 
dist 237=[-2.0038465937490864612 ,1.4595849419371261811 ] 
dist 238=[-1.9934322272438949297 ,1.4358201157181943557 ] 
dist 239=[-1.9866163446410558972 ,1.3600333969454285017 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 1, 2, 2, 1, 2] 
dist 0=[54.506836897245436089  ,54.506836897245436089  ] 
dist 1=[53.684504364459967720  ,54.808451322135457403  ] 
dist 2=[52.679881540707457352  ,55.001755001898771530  ] 
dist 3=[51.650154402914309170  ,55.249419091400152835  ] 
dist 4=[50.402656567559732213  ,55.277654685311417858  ] 
dist 5=[48.528142579081033796  ,55.199884260796049994  ] 
dist 6=[46.388434450662451249  ,55.111720094629927955  ] 
dist 7=[44.081703231926340446  ,54.820031858873498735  ] 
dist 8=[41.204865940115919610  ,54.663012206597930222  ] 
dist 9=[36.788120331402071430  ,52.313229600653052240  ] 
dist 10=[32.323054710476378344  ,51.860017334453968816  ] 
dist 11=[29.253139464430715249  ,51.218503082682575856  ] 
dist 12=[26.609379508922742533  ,50.991076461539902257  ] 
dist 13=[23.846148435612304712  ,50.402900403313186530  ] 
dist 14=[21.208167346384496845  ,45.592906361830818861  ] 
dist 15=[19.064440213177548541  ,44.731963184347966445  ] 
dist 16=[16.865478956496933283  ,39.801497811124003679  ] 
dist 17=[14.006480522522954702  ,30.369235005467351661  ] 
dist 18=[11.209142468716909770  ,28.758483796659900883  ] 
dist 19=[9.2562346413620565139 ,26.302150896481656767  ] 
dist 20=[7.5406059532457825945 ,24.595797865811689975  ] 
dist 21=[5.6907226616722976379 ,24.212277910396127867  ] 
dist 22=[3.8859978879329206415 ,23.704413910020032729  ] 
dist 23=[2.3503134685624227332 ,23.536272186207499016  ] 
dist 24=[.7093818812931870687 ,17.095421990060044036  ] 
dist 25=[-1.5167120636666161486 ,11.947229448327875131  ] 
dist 26=[-3.6777006680616752125 ,11.283983950414820232  ] 
dist 27=[-5.0586542501431385916 ,9.9442772106219004326 ] 
dist 28=[-6.1412583982094936792 ,9.6215204885484444664 ] 
dist 29=[-7.1097837106666924648 ,8.5308986414990349257 ] 
dist 30=[-7.9391447667945972042 ,6.9517802182862026780 ] 
dist 31=[-8.4656570549027060526 ,6.6432399910983475667 ] 
dist 32=[-8.9310539521285976138 ,5.5085618343394863882 ] 
dist 33=[-9.8965535478597011128 ,-5.2286067975914012864 ] 
dist 34=[-10.612896127984905915  ,-5.8933986415694613006 ] 
dist 35=[-11.180296347035555274  ,-6.0242075346785127348 ] 
dist 36=[-11.740622965375674946  ,-6.1794263812340390395 ] 
dist 37=[-12.487437042449938177  ,-6.0328781286519734272 ] 
dist 38=[-12.888424174420163427  ,-5.7001515815701611072 ] 
dist 39=[-13.115719285523007387  ,-5.0300959396963363675 ] 
dist 40=[-13.170481820164279319  ,-4.3157238500866509698 ] 
dist 41=[-13.088933166445645751  ,-2.7564170147993835162 ] 
dist 42=[-13.062181925458802271  ,-1.0913365926968591343 ] 
dist 43=[-13.035424338838761673  ,.03505113439041340137] 
dist 44=[-13.004347771787746535  ,.9826409901078879707 ] 
dist 45=[-12.974605000071825933  ,1.9341768887400233929 ] 
dist 46=[-12.952797741531338074  ,2.8157745658416522628 ] 
dist 47=[-12.933077485530883853  ,3.4842701048402958014 ] 
dist 48=[-12.911258190616311646  ,4.1250369911043125278 ] 
dist 49=[-5.1436731232245725377 ,4.8960253033524550058 ] 
dist 50=[-4.5135326456356548669 ,5.6176716929836750165 ] 
dist 51=[-3.0231992734857561674 ,6.0614991225814898128 ] 
dist 52=[-2.8014493213716064240 ,6.3871675651250030591 ] 
dist 53=[-1.2491969277824919590 ,6.6371422782650848363 ] 
dist 54=[-.9826994087530853077 ,6.8300465134697610854 ] 
dist 55=[-1.0652083574248415721 ,6.9278648567673801290 ] 
dist 56=[-1.1565207364240791034 ,6.9747873989827967712 ] 
dist 57=[-1.2196571383873832133 ,6.9776191219638765148 ] 
dist 58=[-1.2726624142866573501 ,6.5426509736219385618 ] 
dist 59=[-1.3238002885722969241 ,6.4619322534235385816 ] 
dist 60=[-1.3681537812774559461 ,6.3284844796685762310 ] 
dist 61=[-1.3941762952139711671 ,6.2842735439638503723 ] 
dist 62=[-1.4107483898644502238 ,6.1228984596994139660 ] 
dist 63=[-1.4174034105438532522 ,6.0696542201697967060 ] 
dist 64=[-1.4173511941774008268 ,5.9562758769943958047 ] 
dist 65=[-1.4128642432235902981 ,4.2536224958227677714 ] 
dist 66=[-1.3938382596557751847 ,4.2292792728173832674 ] 
dist 67=[-1.3818526949468192162 ,4.1629764052597980856 ] 
dist 68=[-1.3043754926612019801 ,4.1338882358130749561 ] 
dist 69=[-1.2822357373366436916 ,3.9714666713078502494 ] 
dist 70=[-1.2429080733835898292 ,3.9306555076617947273 ] 
dist 71=[-1.2297796391375379441 ,3.8354320860507369030 ] 
dist 72=[-.47029228947597506078,3.8012010926685086820 ] 
dist 73=[-.90387219422753756557,3.3410326106266955264 ] 
dist 74=[-1.2608304807235858210 ,3.2702083152227694865 ] 
dist 75=[-1.6067135306453006228 ,3.0828462545507654544 ] 
dist 76=[-1.9191966198649791446 ,3.0518414138920461569 ] 
dist 77=[-2.1428593733414199309 ,2.7181550226314499254 ] 
dist 78=[-2.3444627921379797154 ,2.6501906643490095977 ] 
dist 79=[-2.5689308390983888937 ,2.5725018823769970019 ] 
dist 80=[-2.7722843695484648137 ,2.5466509223469876782 ] 
dist 81=[-2.8896105137751710319 ,1.6606154265316066951 ] 
dist 82=[-2.9665549156062229157 ,1.5523156198580487550 ] 
dist 83=[-3.1333603755750547992 ,1.3352375563958656717 ] 
dist 84=[-3.5242494368535848542 ,1.2790659046523760899 ] 
dist 85=[-3.8635781871600865415 ,1.0786247379697510384 ] 
dist 86=[-4.0830619988448738502 ,1.0349447952459951587 ] 
dist 87=[-4.2570615326750918155 ,1.0895303602239442955 ] 
dist 88=[-4.4148294481744165219 ,1.3484143091472345754 ] 
dist 89=[-4.5476996742762709072 ,1.5179787952768328182 ] 
dist 90=[-4.6223093049929170525 ,1.6541219643524024829 ] 
dist 91=[-4.6687128435593456433 ,1.7797153013237256364 ] 
dist 92=[-4.6889771291410253678 ,1.8884965221927775159 ] 
dist 93=[-4.6910829158208281652 ,1.9575869346643137927 ] 
dist 94=[-4.6829754408715105664 ,2.0106387961447224157 ] 
dist 95=[-4.6333268376789654856 ,2.0554480065480882119 ] 
dist 96=[-4.6130478115763256655 ,2.0883165676177028798 ] 
dist 97=[-2.9688093327717145313 ,2.0950961198751967237 ] 
dist 98=[-2.8807379367394671003 ,2.0898094367090200318 ] 
dist 99=[-2.8556275481657203206 ,2.0854821343189562833 ] 
dist 100=[-2.7608927193926400992 ,2.0063736973361310650 ] 
dist 101=[-2.7317813221515123900 ,2.0476129496807084276 ] 
dist 102=[-2.6798895196000992431 ,2.0695377332416424510 ] 
dist 103=[-2.6631031355474589920 ,2.0727412515339158080 ] 
dist 104=[-.65105462694934442547,2.0618982720703693611 ] 
dist 105=[-.47913412401361629725,2.0556929511738718367 ] 
dist 106=[-.0846266497763827425 ,2.0212168198639810079 ] 
dist 107=[-.0172233089291413970 ,2.1025904237253851037 ] 
dist 108=[.4798952765499693187 ,2.2284913652516246593 ] 
dist 109=[.5663126186186770171 ,2.3286763785789220004 ] 
dist 110=[.7112881013389224048 ,2.3802780963139035424 ] 
dist 111=[.7432059307906653971 ,2.4067044532526415264 ] 
dist 112=[1.2057740034632929116 ,2.4114536589866547161 ] 
dist 113=[1.1233914342010691399 ,2.3227321615648382846 ] 
dist 114=[1.0152199396673434024 ,2.3038938859185687804 ] 
dist 115=[.8480989791756909446 ,2.2591220839018007144 ] 
dist 116=[.6558546554714331210 ,2.2415620142291157468 ] 
dist 117=[.4473948893830507285 ,2.1550044808854835796 ] 
dist 118=[.1870771818164988295 ,2.1432481841639584468 ] 
dist 119=[-.2121670391300729283 ,2.1409436445981230394 ] 
dist 120=[-.61307980429570256367,2.0375933563440024648 ] 
dist 121=[-.88006201551199411085,2.0168384665059855986 ] 
dist 122=[-1.1001435949375666080 ,1.9527959281807401277 ] 
dist 123=[-1.3138568976941156797 ,1.9395383616073155232 ] 
dist 124=[-1.5072119336053063599 ,1.7884836990152310559 ] 
dist 125=[-1.6460376847911809906 ,1.7539521107148001061 ] 
dist 126=[-1.7715739366925662795 ,1.7157855503178621958 ] 
dist 127=[-1.9118920099008998053 ,1.6978957118102149370 ] 
dist 128=[-2.0394469001370980449 ,1.2558739763747414798 ] 
dist 129=[-2.4053526021567813360 ,1.1952077407615019455 ] 
dist 130=[-2.6372748650667758543 ,1.0717033603179883030 ] 
dist 131=[-2.8156154206482313067 ,1.0380122037059237056 ] 
dist 132=[-2.9676352703467177349 ,.9086506926891917582 ] 
dist 133=[-3.0912420063912167164 ,.8805744706623802083 ] 
dist 134=[-3.1561666742983316611 ,.8230278225245259118 ] 
dist 135=[-3.1906145877031137902 ,.8064315476211662904 ] 
dist 136=[-3.1967901082739983308 ,.4071433898628802312 ] 
dist 137=[-3.1810881183113484125 ,.6203174527897789118 ] 
dist 138=[-3.1682870199219009175 ,.7969132806290174409 ] 
dist 139=[-3.1377983927307229928 ,.9697125751334373313 ] 
dist 140=[-3.1223426372447091049 ,1.1268092992719067406 ] 
dist 141=[-3.0301002740866691274 ,1.2407383212055873349 ] 
dist 142=[-3.0054795014466733553 ,1.3448539397015744135 ] 
dist 143=[-2.9328697171227014419 ,1.4627891298972110818 ] 
dist 144=[-2.9099608345917090150 ,1.5696322722171748310 ] 
dist 145=[-1.5845787986232739572 ,1.6294792839022607949 ] 
dist 146=[-1.4536987804643518789 ,1.6663605886128809080 ] 
dist 147=[-1.1523035834625029910 ,1.6815431340034877970 ] 
dist 148=[-1.0933952354724738157 ,1.6880801799625594930 ] 
dist 149=[-.70016571312196113804,1.7066888906929785660 ] 
dist 150=[-.62838478218987672776,1.9175001872710183350 ] 
dist 151=[-.49724967089542155041,2.1049075754908643162 ] 
dist 152=[-.4668119179411471544 ,2.3094238701787817650 ] 
dist 153=[-.12527651912089975797,2.4960545479753455669 ] 
dist 154=[-.28660964398367602511,2.6120753584452130091 ] 
dist 155=[-.45052984172714651491,2.6986213235348737803 ] 
dist 156=[-.6035120206823202712 ,2.7676081937924585687 ] 
dist 157=[-.7211935053678059638 ,2.8200634691484204306 ] 
dist 158=[-.8355271404325798283 ,2.8406279457392635798 ] 
dist 159=[-.9751501263852485802 ,2.8447784924145119034 ] 
dist 160=[-1.1066554816121443263 ,2.8400087450808088476 ] 
dist 161=[-1.1885929856943606442 ,2.3160517846252478521 ] 
dist 162=[-1.2498967251321279080 ,2.3258095690136337211 ] 
dist 163=[-1.2990545898486655901 ,2.3238831218357302384 ] 
dist 164=[-1.3366369908046324973 ,2.2703840808781446084 ] 
dist 165=[-1.3517447603162785691 ,2.2513211395477716076 ] 
dist 166=[-1.3577717008141856944 ,2.2345122882357599785 ] 
dist 167=[-1.3591076792266338470 ,2.2216897183628557969 ] 
dist 168=[-1.3140449476634910056 ,.54957548223666101459] 
dist 169=[-1.3810587068806810015 ,.668324045458342289  ] 
dist 170=[-1.5123291584647738557 ,.76644127448353949312] 
dist 171=[-1.6343316865532039817 ,.86822518049738658607] 
dist 172=[-1.7410651804073303631 ,1.0016007756704245266 ] 
dist 173=[-1.8113920129836494706 ,1.1450357800267239422 ] 
dist 174=[-1.8685360266442511749 ,1.2869616596301903130 ] 
dist 175=[-1.9226537702488830093 ,1.4549216717596327070 ] 
dist 176=[-1.9663935223554446228 ,1.7022503728791850986 ] 
dist 177=[-2.0409472495599180306 ,1.9460942296919310592 ] 
dist 178=[-2.1609717837800506330 ,2.1001442162269535919 ] 
dist 179=[-2.2970082295457571396 ,2.2178520472277377781 ] 
dist 180=[-2.4128969048390659761 ,2.3166569309933208040 ] 
dist 181=[-2.5070437761579688848 ,2.3956742370020029458 ] 
dist 182=[-2.5562958590757342636 ,2.4344093318425678357 ] 
dist 183=[-2.5821345220701340755 ,2.4524935748355522764 ] 
dist 184=[-2.5862295331853879245 ,2.4539552350903879883 ] 
dist 185=[-2.5726392403710549313 ,2.4223305685155047050 ] 
dist 186=[-2.5625079826711139340 ,2.4094085707363488018 ] 
dist 187=[-2.5344373780979426027 ,2.3747203407099133024 ] 
dist 188=[-2.5200972807925776405 ,2.3586459670266720355 ] 
dist 189=[-2.4342443655526348803 ,2.2662098773215512368 ] 
dist 190=[-2.4112746353055837129 ,2.2420630975781378643 ] 
dist 191=[-2.3550279508396940336 ,2.1854482548943794809 ] 
dist 192=[-2.3334754229086585311 ,2.1644734861342355427 ] 
dist 193=[-1.3378240840756556299 ,1.9347907499472574097 ] 
dist 194=[-1.2356497310964347756 ,1.9686815819031055282 ] 
dist 195=[-1.1489819741745415492 ,2.0035140222288693798 ] 
dist 196=[-1.0384709277012955904 ,2.0290586209515582404 ] 
dist 197=[-1.0153992515054823358 ,2.0371178808715516594 ] 
dist 198=[-.9589560659143033328 ,2.0756236750960296587 ] 
dist 199=[-.9440615556966999399 ,2.2302186014237889832 ] 
dist 200=[-.47851184913193275202,2.4053003103806822815 ] 
dist 201=[-.2042486286930326752 ,2.5634753335776102838 ] 
dist 202=[-.1613416486841158685 ,2.6505915683524759998 ] 
dist 203=[-.0880465466689880156 ,2.7023688304941019513 ] 
dist 204=[-.0714930976879336368 ,2.7194943525419560508 ] 
dist 205=[-.0394185963812373231 ,2.7240229955343526541 ] 
dist 206=[-.0859824721621445973 ,2.7255177254968693393 ] 
dist 207=[-.1925970518398190387 ,2.7250848382996954222 ] 
dist 208=[-.3092714652883763984 ,2.7219072184371418199 ] 
dist 209=[-.41029707852481751973,2.2973149578756861615 ] 
dist 210=[-.51923349018775947587,2.4095216073040436213 ] 
dist 211=[-.66748433794364370149,2.5359960746740040023 ] 
dist 212=[-.90233458303642716847,2.6399298167748426199 ] 
dist 213=[-1.1532252657286727406 ,2.7214314359692023235 ] 
dist 214=[-1.3448018118155270471 ,2.7583717478757599620 ] 
dist 215=[-1.5296322012275045012 ,2.7746655178220205047 ] 
dist 216=[-1.7817716785660834986 ,2.7737578142432775467 ] 
dist 217=[-1.9717942317362374890 ,2.7179414123863204744 ] 
dist 218=[-2.1223853417208257614 ,2.7000398585093633164 ] 
dist 219=[-2.2585841494302979423 ,2.6558789275611555444 ] 
dist 220=[-2.3751404724435686797 ,2.6681156931907445915 ] 
dist 221=[-2.4473288643929315546 ,2.6946306413479600831 ] 
dist 222=[-2.5008559281810560661 ,2.7041279892501949016 ] 
dist 223=[-2.5429256497251294481 ,2.7015522619204124316 ] 
dist 224=[-2.5726758817657310246 ,2.5828196523158345329 ] 
dist 225=[-2.5777298878140942781 ,2.5563768912701909428 ] 
dist 226=[-2.5719459989389820727 ,2.5010369549522202110 ] 
dist 227=[-2.5640172607586994375 ,2.4812727787652783009 ] 
dist 228=[-2.4769040116704137281 ,2.3827575302334579069 ] 
dist 229=[-2.4512695688049797695 ,2.3596709082984770200 ] 
dist 230=[-2.4149736900564981196 ,2.2834082612400272334 ] 
dist 231=[-2.2915330050450992481 ,2.2711848697377151229 ] 
dist 232=[-2.4470385716134539432 ,.9924308876876471309 ] 
dist 233=[-2.6254956604378196550 ,.87025268116842436565] 
dist 234=[-2.7318277430703480062 ,.6002728488936629644 ] 
dist 235=[-2.8056975068866972985 ,.54104537970014041623] 
dist 236=[-2.8545856169544784625 ,.22648050076654518533] 
dist 237=[-2.8860165451705072513 ,.17100409305618184124] 
dist 238=[-2.8908072363848420943 ,.05011433522040214105] 
dist 239=[-2.8839318282726672223 ,.1644448042205486382 ] 
dist 240=[-2.8735817311885437659 ,.6154939567437225549 ] 
dist 241=[-2.5034221751204367422 ,1.0679684267367948181 ] 
dist 242=[-2.5060314824425763225 ,1.3682300161012826613 ] 
dist 243=[-2.4959693156447144019 ,1.6145410364015024383 ] 
dist 244=[-2.4867110365385615509 ,1.8516793473554515410 ] 
dist 245=[-2.3986009418191022996 ,2.0648191068837354844 ] 
dist 246=[-2.3730603601359257772 ,2.2153440394718841305 ] 
dist 247=[-2.3391214283455937901 ,2.3488626727536241125 ] 
dist 248=[-2.3238717688844423636 ,2.4941264672089566558 ] 
dist 249=[-1.9107720663323466545 ,2.6231209854617791494 ] 
dist 250=[-1.8508025894671507364 ,2.6917026907513354186 ] 
dist 251=[-1.7254519889304258869 ,2.7294226192513038240 ] 
dist 252=[-1.6892312517610969568 ,2.7379028565467166361 ] 
dist 253=[-1.5389613550645658676 ,2.7278088972813700071 ] 
dist 254=[-1.5073138819679060454 ,2.7210698962820752193 ] 
dist 255=[-1.4261393782265371534 ,2.7126706965290150909 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 1, 1, 2] 
dist 0=[49.585716379838231786  ,49.585716379838231786  ] 
dist 1=[48.879578660351707962  ,50.121020931954305917  ] 
dist 2=[47.861403309346674341  ,50.456882325256615645  ] 
dist 3=[46.416934567988705069  ,50.711624382740624624  ] 
dist 4=[44.008356468692259632  ,50.922740677988670903  ] 
dist 5=[41.513174996408368420  ,51.061596094738427895  ] 
dist 6=[39.722801725155772374  ,51.060430170230356729  ] 
dist 7=[38.101453017161159644  ,50.932020514773055439  ] 
dist 8=[36.281145936187736941  ,50.463128968489116115  ] 
dist 9=[34.466195736150361360  ,50.029044878051704711  ] 
dist 10=[32.866070596465922014  ,49.798598263371796703  ] 
dist 11=[31.111973166436681179  ,49.415957465416115616  ] 
dist 12=[28.681752828912219142  ,49.280125456149776547  ] 
dist 13=[26.234227341275749439  ,48.726075019092482861  ] 
dist 14=[24.410833050971183901  ,48.550171583700627992  ] 
dist 15=[21.828799603832745154  ,47.822232805292555307  ] 
dist 16=[19.040515928213326955  ,46.485303110273920149  ] 
dist 17=[16.370560530229555606  ,34.223726390057092463  ] 
dist 18=[14.189724852756074517  ,32.995447508525624208  ] 
dist 19=[11.943400589160091786  ,30.028694292165279285  ] 
dist 20=[9.0113912747269801570 ,29.579395666341669983  ] 
dist 21=[6.1385018005642618482 ,25.267195059390119432  ] 
dist 22=[4.1279971979949919608 ,24.464440808984322292  ] 
dist 23=[2.3570472847963175709 ,23.484932335949090855  ] 
dist 24=[.44052241638552219459,23.248603656627251016  ] 
dist 25=[-1.4333115994285797819 ,16.487731363714923615  ] 
dist 26=[-3.0343058927554089618 ,15.645056496000017306  ] 
dist 27=[-4.7508146521655610608 ,13.893003607824537096  ] 
dist 28=[-7.0872427109193500151 ,13.436340058533003304  ] 
dist 29=[-9.3403002251235013072 ,11.755651009979477104  ] 
dist 30=[-10.723955372712236681  ,11.428101840937945491  ] 
dist 31=[-11.745122600077597443  ,10.820661302221768576  ] 
dist 32=[-12.549554726676080526  ,10.681381817062802540  ] 
dist 33=[-13.183696539299952268  ,1.8496742197691857470 ] 
dist 34=[-13.524020385014909711  ,1.0846895167196761518 ] 
dist 35=[-13.717549885632295851  ,-.54373504371579728678] 
dist 36=[-13.764138176621122801  ,-.87670558566033711501] 
dist 37=[-12.967879808246942361  ,-2.5176684806736224320 ] 
dist 38=[-12.816918493771930871  ,-2.1361203921599933060 ] 
dist 39=[-12.634016491896146709  ,-1.7783999712935950681 ] 
dist 40=[-12.544961657760972296  ,-1.3660959291346524353 ] 
dist 41=[-12.381709852127011350  ,-.9525743296013851506 ] 
dist 42=[-12.315199856449145815  ,-.58971411836425542593] 
dist 43=[-12.346507967631325389  ,-.1955586720421054804 ] 
dist 44=[-12.536723229578139233  ,.3430779691768579619 ] 
dist 45=[-12.658076015875840047  ,.87787369316410632396] 
dist 46=[-12.717620661249017113  ,1.2568461304130363619 ] 
dist 47=[-12.743960971169837139  ,1.5939020226669406522 ] 
dist 48=[-12.732614325219425163  ,1.9616301737361476578 ] 
dist 49=[-3.1270956006079786910 ,2.6434995594914510503 ] 
dist 50=[-2.8251246664806779794 ,3.6087995260097986672 ] 
dist 51=[-2.6804662787254697526 ,4.5527238012055642447 ] 
dist 52=[-2.6440412820651051989 ,5.7140762887208804355 ] 
dist 53=[.4829982854435085165 ,6.8121977444722540483 ] 
dist 54=[.76512594825324471299,7.5037069233141404501 ] 
dist 55=[1.1390873367259201968 ,8.0294404270152628763 ] 
dist 56=[1.2038677594730988496 ,8.4658307931922382210 ] 
dist 57=[2.9480794035332697838 ,8.8105698781432840432 ] 
dist 58=[3.1488257514725664379 ,8.9703954555788599394 ] 
dist 59=[3.5340849513535080295 ,9.0475776446724376955 ] 
dist 60=[3.6154522608078693395 ,9.0628195680525834310 ] 
dist 61=[3.1633104363399346360 ,4.9449346673141220595 ] 
dist 62=[2.5928542598490649340 ,5.0597292523277434875 ] 
dist 63=[2.0918367941198013894 ,5.1237675570153286795 ] 
dist 64=[1.5551802268221845442 ,5.1355771263595064735 ] 
dist 65=[1.0370741503062164141 ,5.1261044877790014992 ] 
dist 66=[.61001654431676003134,5.1070307849925940828 ] 
dist 67=[.16796373659124092606,5.0723833305445443954 ] 
dist 68=[-.41007481968836415226,5.0539128969755338522 ] 
dist 69=[-.97398878725531410038,3.7352889594669712215 ] 
dist 70=[-1.3597137756323794927 ,3.5922854161330624970 ] 
dist 71=[-1.6889207407871955993 ,3.2230556589388510752 ] 
dist 72=[-2.0273139000994285066 ,3.1695538098485807266 ] 
dist 73=[-2.3460953381360502251 ,2.5507647042536594986 ] 
dist 74=[-2.5970820558437577882 ,2.4295260317054916196 ] 
dist 75=[-2.8468825535453152630 ,2.3032435384977655504 ] 
dist 76=[-3.1610364217057028964 ,2.2787146380676443640 ] 
dist 77=[-3.4584019123635556865 ,1.6827637227001867324 ] 
dist 78=[-3.6412047271966863917 ,1.6522963136886211424 ] 
dist 79=[-3.7756064075525891037 ,1.5960296305127985504 ] 
dist 80=[-3.8797107543788783514 ,1.5817237728521045479 ] 
dist 81=[-3.9569167501169837930 ,.24133435927887766774] 
dist 82=[-3.9839322635350183798 ,.1828474941324177386 ] 
dist 83=[-3.9895382068091010382 ,.10730936150882374282] 
dist 84=[-3.9811583155844425380 ,.31379650228650288521] 
dist 85=[-4.1487148646456313313 ,.60453704692883341751] 
dist 86=[-4.2705646135498740508 ,.83143210204989811842] 
dist 87=[-4.3415548093895165003 ,1.0548851235630259078 ] 
dist 88=[-4.3619904946889353591 ,1.3319483634510196095 ] 
dist 89=[-4.3633130556724192298 ,1.6222547963620676416 ] 
dist 90=[-4.3580006082322417539 ,1.8986039503193524863 ] 
dist 91=[-4.3469564810406999045 ,2.2177418253623655207 ] 
dist 92=[-4.3305418580778524705 ,2.6788839273980559762 ] 
dist 93=[-4.2988445941847131456 ,3.1308087272861845173 ] 
dist 94=[-4.2771889995716581322 ,3.4131696588928751544 ] 
dist 95=[-4.2320381792505459395 ,3.6255503975057463405 ] 
dist 96=[-4.2115666587933651074 ,3.7981459881504683275 ] 
dist 97=[-1.8834110318121510028 ,3.9331901464889226555 ] 
dist 98=[-1.8228997743852655420 ,3.9956756813431013862 ] 
dist 99=[-1.7266634255250863292 ,4.0268239897660541321 ] 
dist 100=[-1.6996274834556676980 ,4.2822523024420590382 ] 
dist 101=[-.6908031483902215554 ,4.5094910964535687850 ] 
dist 102=[-.57683843173871913663,4.6394997250358609413 ] 
dist 103=[-.35898406220781394699,4.7232341147667685893 ] 
dist 104=[-.30676501037561574575,4.7657643196353345805 ] 
dist 105=[-.14761223099645804932,4.7838824052702973937 ] 
dist 106=[-.11517321667297844164,4.7794593987677026565 ] 
dist 107=[-.11629324544570263146,4.7454010880149106274 ] 
dist 108=[-.16346688966302615936,4.7203501633947549320 ] 
dist 109=[-.23080952437815419483,3.2868187909081768501 ] 
dist 110=[-.7412408988949542795 ,3.1409842334180546462 ] 
dist 111=[-1.1735825056533145547 ,2.7759208222772614577 ] 
dist 112=[-1.5983170201987744447 ,2.7175100920605838467 ] 
dist 113=[-1.9856410030524827577 ,2.0859333274127661118 ] 
dist 114=[-2.2686703138053697235 ,1.9640485776179438272 ] 
dist 115=[-2.5295060519834087921 ,1.5815215581087185212 ] 
dist 116=[-2.8282514051356830340 ,1.4901564805941679166 ] 
dist 117=[-3.1031975594398066091 ,1.2357708943510448106 ] 
dist 118=[-3.2690462026479431268 ,1.1857100109237677300 ] 
dist 119=[-3.3867374982948968759 ,1.1262916982133753578 ] 
dist 120=[-3.4694785901906029901 ,1.1083980070699790500 ] 
dist 121=[-3.5277315866233966947 ,.62673380552204845082] 
dist 122=[-3.5476844409760161507 ,.56552386792705434794] 
dist 123=[-3.5490902703998692967 ,.4361472133321755156 ] 
dist 124=[-3.5405196032196621632 ,.40215990528570261317] 
dist 125=[-.2652188308611946746 ,.271019232436075376  ] 
dist 126=[-.39437193619651198967,.24580383819354841071] 
dist 127=[-.53633732709703175713,.19525970090139001312] 
dist 128=[-.73302774235960244042,.18258449183174008386] 
dist 129=[-.92575673805245319502,.20815050496806416151] 
dist 130=[-1.0519161042464159310 ,.27888613572400522271] 
dist 131=[-1.1535768078927046297 ,.34653524464026425069] 
dist 132=[-1.2485133828477604438 ,.42763490004033076579] 
dist 133=[-1.3319843146262028539 ,.50356381518697954608] 
dist 134=[-1.3878802564341353013 ,.55057819498284055121] 
dist 135=[-1.4559406242459135075 ,.58540758863013167885] 
dist 136=[-1.5419791967104938354 ,.61270662125109263989] 
dist 137=[-1.6210370076664851831 ,.63390346357879886582] 
dist 138=[-1.6671678626671713156 ,.6443799709276685473 ] 
dist 139=[-1.6980745008971608393 ,.64906026480818614363] 
dist 140=[-1.7163601801554841712 ,.64956314675822131762] 
dist 141=[-1.7252885395533493052 ,.5657045856169795282 ] 
dist 142=[-1.7256946297639930487 ,.55518516923563583877] 
dist 143=[-1.7094867290054969140 ,.53105418873511017465] 
dist 144=[-1.7068216505653781610 ,.62063103063865947012] 
dist 145=[.1684488217008135558 ,.87811466974376806497] 
dist 146=[.1215859428806643350 ,1.0710156959025564816 ] 
dist 147=[.0684093609282065791 ,1.2428743659276092118 ] 
dist 148=[-.0072547876501181161 ,1.4199572394424520409 ] 
dist 149=[-.0838774415975022657 ,1.5738584070429510986 ] 
dist 150=[-.1408825440696480478 ,1.6733271525757805535 ] 
dist 151=[-.1944219732873643441 ,1.7519518641617679801 ] 
dist 152=[-.2572184151124359802 ,1.8226647393840834166 ] 
dist 153=[-.32115820531527861163,1.8826127354113696705 ] 
dist 154=[-.37926500923383631264,1.9182752394703210569 ] 
dist 155=[-.44423744972205390062,1.9429728137608028016 ] 
dist 156=[-.53558531032984730986,1.9591608208474546451 ] 
dist 157=[-.6245770798794143758 ,1.9686425332662210804 ] 
dist 158=[-.68014717824198313502,1.9665764007014150093 ] 
dist 159=[-.72189327221269269636,1.9579030517487388564 ] 
dist 160=[-.76391627304482719828,1.9505409886401688288 ] 
dist 161=[-.81877119232142907257,1.0837422969686808942 ] 
dist 162=[-.85477810672114447106,1.0251154786692328495 ] 
dist 163=[-.88387133439710155681,.87986836977247402601] 
dist 164=[-.91113164992935203152,.85675202613213577456] 
dist 165=[-.93339258901899333805,.6331831446804324523 ] 
dist 166=[-.94253262290130581653,.59057072886798198152] 
dist 167=[-.94560523205928373284,.53714331420743525994] 
dist 168=[-.97163741420292567546,.52151861760482031384] 
dist 169=[-1.0491085240315463050 ,.14985357896808964321] 
dist 170=[-1.0974960122861724038 ,.1034418430450724193 ] 
dist 171=[-1.1338174277333478938 ,.0547649774840031879 ] 
dist 172=[-1.1631421680197321266 ,.04289682873186894406] 
dist 173=[-1.1857173308503334051 ,.16458623072863383269] 
dist 174=[-1.1951076173279786171 ,.28993025757172598009] 
dist 175=[-1.1970232684535792289 ,.39234426692277464669] 
dist 176=[-1.1955796001266747158 ,.49022597501333014969] 
dist 177=[-.51613303111087577438,.57768861073429599409] 
dist 178=[-.52759874011699645085,.63851886454695482459] 
dist 179=[-.53642615129399950654,.69148376853923461939] 
dist 180=[-.54399799239225326488,.74755476556482308849] 
dist 181=[-.55021260587313780567,.79822273908772880482] 
dist 182=[-.55361992349094915776,.82962383034227223681] 
dist 183=[-.55563789232059692291,.85292217721864124054] 
dist 184=[-.55630478735115276297,.87125211000132486986] 
dist 185=[-.55605245488699243461,.88498621294253950713] 
dist 186=[-.55439938166953247757,.88994291311856528751] 
dist 187=[-.55140728346083625491,.89012132159140192162] 
dist 188=[-.54950802963626478552,.88838899341579902632] 
dist 189=[-.53895127905752706464,.53453371598889398559] 
dist 190=[-.535742713942724334  ,.50335165828093079304] 
dist 191=[-.52400962401293777086,.42594680924003924188] 
dist 192=[-.52140521299360927487,.41426729528484489663] 
dist 193=[-.48749274403167941245,.5422922085655329167 ] 
dist 194=[-.4800153212149142765 ,.64039757151201623144] 
dist 195=[-.46612019351660315448,.71709934632598033567] 
dist 196=[-.46191583142660174175,.78465443588013047972] 
dist 197=[-.44441536712843498124,.8411682746221833278 ] 
dist 198=[-.4396458939499420723 ,.87380224594354182597] 
dist 199=[-.4283555423551923899 ,.89520119799589568059] 
dist 200=[-.4241632984875351894 ,.90687478468628798415] 
dist 201=[-.4031303190919839166 ,.91419506348493796797] 
dist 202=[-.39991376125262217288,.91821878344874628322] 
dist 203=[-.43054149298032774841,.92060726634547818145] 
dist 204=[-.4697181928217128966 ,.92139912287416275264] 
dist 205=[-.50677551915794499953,.92111242040951307838] 
dist 206=[-.52894468249131368045,.9191953000117702488 ] 
dist 207=[-.5444690584744305919 ,.91572083725427520918] 
dist 208=[-.55500298036477938525,.91219198839250740381] 
dist 209=[-.5619646994058188067 ,.2549529563106967162 ] 
dist 210=[-.56322954213719837421,.20380141776354399208] 
dist 211=[-.57706787313200302936,.13533860306467136766] 
dist 212=[-.60305495178257617014,.17430232333397511884] 
dist 213=[-.62714347685119732802,.21373423488988811271] 
dist 214=[-.64146219757518070427,.24304693619367119533] 
dist 215=[-.6513575762452065034 ,.27055783590187617268] 
dist 216=[-.6577922264318899452 ,.30280024528872752789] 
dist 217=[-.66149785924608960928,.3356175610071996888 ] 
dist 218=[-.66116902902379965833,.36542436320088689963] 
dist 219=[-.65757406962446587297,.39873909167116380415] 
dist 220=[-.65447286428347723376,.44555933916326893747] 
dist 221=[-.37486981884621649538,.49085430070415629328] 
dist 222=[-.38495486362451427877,.57228739587319051118] 
dist 223=[-.3973729633289188632 ,.65295022305647841756] 
dist 224=[-.41624494097619637621,.7255798935307762236 ] 
dist 225=[-.43518730709239409015,.78747923638659616813] 
dist 226=[-.44788619375520435112,.82531665455277068186] 
dist 227=[-.45845936486177844905,.852773659718429461  ] 
dist 228=[-.46891400447418530296,.87324469176019930675] 
dist 229=[-.4785061140355029657 ,.88917820744942563302] 
dist 230=[-.48563500963027397406,.89852505174786940946] 
dist 231=[-.49233121813228697326,.90821748495546954734] 
dist 232=[-.50019479806705186423,.91059639578866340286] 
dist 233=[-.50745332173423333713,.88816228977009055368] 
dist 234=[-.51173339858356039729,.88176725307466067132] 
dist 235=[-.51465143566587433594,.84765445833994028516] 
dist 236=[-.51647173617316665536,.7777229835843698206 ] 
dist 237=[-.51744098027189500069,.51286160679360347423] 
dist 238=[-.51696060242595035   ,.49720067690151778747] 
dist 239=[-.51531811231547037291,.45640201105800677032] 
dist 240=[-.51355291788331363758,.44981140411230683768] 
dist 241=[-.50691117405056702952,.3793039175130733429 ] 
dist 242=[-.50419407518715716695,.36513180849761587987] 
dist 243=[-.4954195055269351669 ,.34896731272624654396] 
dist 244=[-.49180705101292303282,.3439798003773108193 ] 
dist 245=[-.48686772831311442755,.19907835619494633719] 
dist 246=[-.51023036784404985752,.18046757233223935323] 
dist 247=[-.52593774365689377245,.14174444583501153781] 
dist 248=[-.5353031971266253989 ,.1314553141026451732 ] 
dist 249=[-.54140388394891836322,.09287537342507084559] 
dist 250=[-.54408053227600320275,.08511335613679146319] 
dist 251=[-.54475959430730268314,.07023696362783968596] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 0, 2, 0, 0, 0, 2] 
dist 0=[51.624233838560982526  ,51.624233838560982526  ] 
dist 1=[50.595662768214167618  ,52.637760209944895530  ] 
dist 2=[49.357940311922831402  ,53.511377150555643847  ] 
dist 3=[47.508900851916015358  ,53.981259554068483340  ] 
dist 4=[45.404351028282397286  ,54.245303755527209137  ] 
dist 5=[43.146116501633182692  ,54.297289763336087852  ] 
dist 6=[40.338138601174923351  ,54.240977216449243047  ] 
dist 7=[36.038058109076795983  ,54.163622789352183288  ] 
dist 8=[31.700498719967007918  ,53.875451508776792677  ] 
dist 9=[28.742707900314877668  ,53.714907200267689594  ] 
dist 10=[26.222736640349824757  ,51.522049667504618773  ] 
dist 11=[23.633318336143383265  ,51.090516585598074326  ] 
dist 12=[21.189526436524256710  ,50.461960944053499186  ] 
dist 13=[19.250827826978891460  ,50.244659992899247263  ] 
dist 14=[17.305033296756951254  ,45.344098073145584808  ] 
dist 15=[14.832342220150702058  ,44.429709595746141812  ] 
dist 16=[12.439556533884289371  ,39.579347333554407325  ] 
dist 17=[10.812582622526506897  ,35.962588503091197893  ] 
dist 18=[9.4284223388041998803 ,29.002436318147369225  ] 
dist 19=[8.0050350248555021124 ,27.244454892079657174  ] 
dist 20=[6.6559008968141674428 ,25.295423727285143593  ] 
dist 21=[5.5677382982224427958 ,24.796234160760909612  ] 
dist 22=[4.4544546508219670874 ,23.054430443659349913  ] 
dist 23=[3.0036887946169891819 ,22.659594848687377061  ] 
dist 24=[1.6129281879269324595 ,22.157260041953780640  ] 
dist 25=[.7392056697791311218 ,21.983756471792920939  ] 
dist 26=[.0683240745320150596 ,11.916097935907212117  ] 
dist 27=[-.51128759250009346053,10.559705929679021394  ] 
dist 28=[-.99652959303593448817,10.270352374224453728  ] 
dist 29=[-3.0999088196857617032 ,8.2132494859307057337 ] 
dist 30=[-5.1955660965201273611 ,7.8761077026257412245 ] 
dist 31=[-6.7641632473802145062 ,6.7415819509823271669 ] 
dist 32=[-8.2521153367957169097 ,5.1459767334442549048 ] 
dist 33=[-10.025609845897388139  ,-1.6397297370747653510 ] 
dist 34=[-11.684141693442571059  ,-1.5685211484991976018 ] 
dist 35=[-12.712867060082550825  ,-1.3956063170508026229 ] 
dist 36=[-13.480465298719057805  ,-1.1738543835606918898 ] 
dist 37=[-14.095923840448193265  ,-.90749925679530374491] 
dist 38=[-14.575088685533085775  ,-.5594156879605683442 ] 
dist 39=[-14.798303731916696101  ,-.0114361941101829859 ] 
dist 40=[-14.902262381943981526  ,.5458165706215647576 ] 
dist 41=[-14.904989171666983499  ,.9310086530995492738 ] 
dist 42=[-9.5470936122105350050 ,1.2623691303300078376 ] 
dist 43=[-9.5894614628104590308 ,1.6050273404549308483 ] 
dist 44=[-9.5888552797836581191 ,1.9270502234858476411 ] 
dist 45=[-9.5628030222422873593 ,2.1761143975185630949 ] 
dist 46=[-9.5341063682271076165 ,2.4183280916400534918 ] 
dist 47=[-9.4353237057372408335 ,2.7129465579649834858 ] 
dist 48=[-9.3829148510081427328 ,2.9873411363450835199 ] 
dist 49=[-5.2700994773359479321 ,3.1488356053361508632 ] 
dist 50=[-4.9020468728829295900 ,3.2573897711922778307 ] 
dist 51=[-4.0131906454081014924 ,3.3205508531111101019 ] 
dist 52=[-3.8800216932459192449 ,3.3591471182259391117 ] 
dist 53=[-2.6072219690352596749 ,3.3698700049788542222 ] 
dist 54=[-2.3748171895905333148 ,3.3619742353140589396 ] 
dist 55=[-2.0840581898387821144 ,3.3511519162091274003 ] 
dist 56=[-2.0192814039013281850 ,2.3917752612629683045 ] 
dist 57=[-1.0488871800445302049 ,2.8070651718271652733 ] 
dist 58=[-1.3755417930153327551 ,3.1788902891921285405 ] 
dist 59=[-1.6934967106557142283 ,3.4579459055534576534 ] 
dist 60=[-1.9812770552283883599 ,3.6839528662365677184 ] 
dist 61=[-2.1875427535026791961 ,3.8635205810159492658 ] 
dist 62=[-2.3735218407631519412 ,3.9572072065417234679 ] 
dist 63=[-2.5803792356894624538 ,4.0062829333729123168 ] 
dist 64=[-2.7670043013514331268 ,4.0145745891817124195 ] 
dist 65=[-2.8722462302482816533 ,3.7140625186354339171 ] 
dist 66=[-2.9380368399258550736 ,3.6729753521705997050 ] 
dist 67=[-2.9672009449601359122 ,3.5695847572510934850 ] 
dist 68=[-2.9800264240547233828 ,3.5322342277564677560 ] 
dist 69=[-2.9806156877831252367 ,3.5144683165162473757 ] 
dist 70=[-2.9724048735691552678 ,3.4865624803070210757 ] 
dist 71=[-2.9622684459495235315 ,3.4735601296007738754 ] 
dist 72=[-2.2880581083713983845 ,3.4314622692684017953 ] 
dist 73=[-2.2110334633536055984 ,3.4126094027086778601 ] 
dist 74=[-2.1470357871673442566 ,3.3067683506789867198 ] 
dist 75=[-2.6675518576171954411 ,3.2915362776278420968 ] 
dist 76=[-3.0771985882377906218 ,3.2816756151963229192 ] 
dist 77=[-3.4430810067597296991 ,3.2178277290177332812 ] 
dist 78=[-3.7532622791030211987 ,3.2000180404312564763 ] 
dist 79=[-3.9405930322715686154 ,3.1447788126083108818 ] 
dist 80=[-4.0741285948920858052 ,3.1280266280813610547 ] 
dist 81=[-4.1696316325404418079 ,2.0544795907689616059 ] 
dist 82=[-4.2431958850357892570 ,2.1423712427563364834 ] 
dist 83=[-4.2891447638632009364 ,2.2012079779800713686 ] 
dist 84=[-4.3239135377574009941 ,2.2436626337311528132 ] 
dist 85=[-4.3527541013685520716 ,2.2661858260147033012 ] 
dist 86=[-4.3756542373432141916 ,2.2784210867933232730 ] 
dist 87=[-4.3866477145948499304 ,2.2798580348970512216 ] 
dist 88=[-4.3909327493175660959 ,1.9953864076963410825 ] 
dist 89=[-4.3869649457947237489 ,1.9582927634109269839 ] 
dist 90=[-3.4010192136124558686 ,1.8558813083688836074 ] 
dist 91=[-3.4361764772842060236 ,1.8375772496986681641 ] 
dist 92=[-3.4649591792314138042 ,1.6384627564394895206 ] 
dist 93=[-3.4877393352540728778 ,1.5962963336018257650 ] 
dist 94=[-3.4989268981085290217 ,1.5479362256466518389 ] 
dist 95=[-3.5039555053623322902 ,1.8163388678242829829 ] 
dist 96=[-3.5021572385787885559 ,2.0794445214984560130 ] 
dist 97=[-2.3042840389777504983 ,2.3893532571046035563 ] 
dist 98=[-2.3440596301144377272 ,2.6772542350942794598 ] 
dist 99=[-2.3672931803520929618 ,2.8525105736103247261 ] 
dist 100=[-2.3741346900170996197 ,2.9788758767142069024 ] 
dist 101=[-2.3712606257045007558 ,3.0715878922831289682 ] 
dist 102=[-2.3662796348176866090 ,3.1409413171933118627 ] 
dist 103=[-2.3385876579660156889 ,3.1740797328016428015 ] 
dist 104=[-2.3294867616426727934 ,3.1870689924611236416 ] 
dist 105=[-2.1698126495588104217 ,3.1858362657660798983 ] 
dist 106=[-2.1408723371449204943 ,2.2955366801873251278 ] 
dist 107=[-2.0619915787187570214 ,2.2918199431008400860 ] 
dist 108=[-2.0433307731561662114 ,2.2420635948476955887 ] 
dist 109=[-2.0864378154252103350 ,2.2240710601451173548 ] 
dist 110=[-2.1926107651609783183 ,2.2004110951236200479 ] 
dist 111=[-2.3032145315675720487 ,2.1883957709425377125 ] 
dist 112=[-2.3995311188539592474 ,1.8386892660672181821 ] 
dist 113=[-2.4486783453133949012 ,1.7867171143610780743 ] 
dist 114=[-2.4738347197088966531 ,1.6793798475265959300 ] 
dist 115=[-2.4778712339724796148 ,1.7065154906258038842 ] 
dist 116=[-2.4558294133940083781 ,1.9588288502362433853 ] 
dist 117=[-2.4434539292242392514 ,2.1802850660701623052 ] 
dist 118=[-2.4291890262238308246 ,2.3276630893000747864 ] 
dist 119=[-2.4182449549104149552 ,2.4491081474741329423 ] 
dist 120=[-1.8257933443367884310 ,2.5670565652060813164 ] 
dist 121=[-1.7566031982044063090 ,2.6696902552833818016 ] 
dist 122=[-1.5959384268770565331 ,2.7300024852550077680 ] 
dist 123=[-1.5571229635025330560 ,2.7709328709393893131 ] 
dist 124=[-1.3326127549200528135 ,2.7961881852982853205 ] 
dist 125=[-1.2881395091898202236 ,2.8094774530362401082 ] 
dist 126=[-1.1995830873558084125 ,2.8083298428791551247 ] 
dist 127=[-1.1751951086913881010 ,2.7893490510525954943 ] 
dist 128=[-.8527465786845768577 ,2.7769031723932603586 ] 
dist 129=[-.8057722726100367337 ,2.2283616262413425430 ] 
dist 130=[-.6977571597906105859 ,2.2726896904072058135 ] 
dist 131=[-.6741671085442431463 ,2.2871222659420466311 ] 
dist 132=[-.70609504087187857422,2.2907895021397377457 ] 
dist 133=[-.77667738327143313566,2.2921517586594480303 ] 
dist 134=[-.84188119080892714027,2.2920934643659854017 ] 
dist 135=[-.91567803292874529788,2.2900948345327571448 ] 
dist 136=[-1.0205631623521427079 ,1.8935583872854638202 ] 
dist 137=[-1.1269050969619501818 ,2.1047089791705917058 ] 
dist 138=[-1.2065174221942430677 ,2.2858216096206970131 ] 
dist 139=[-1.2818485427818988962 ,2.4483113955777261953 ] 
dist 140=[-1.3711003089888402893 ,2.5864342025847207815 ] 
dist 141=[-1.4625418367529526229 ,2.6702911447832941121 ] 
dist 142=[-1.5466143342581833034 ,2.7304844106606074487 ] 
dist 143=[-1.6414491273102595308 ,2.7741610130521871062 ] 
dist 144=[-1.7758529416897691678 ,2.8043258737839115862 ] 
dist 145=[-1.9066357749017942656 ,2.8105882326097404782 ] 
dist 146=[-1.9870163396821066476 ,2.8053083839984163169 ] 
dist 147=[-2.0459199062590127020 ,2.7963118631445512074 ] 
dist 148=[-2.0909695276440245114 ,2.7243397215893605315 ] 
dist 149=[-2.1237016390087475030 ,2.7020467001989916367 ] 
dist 150=[-2.1334359535793357396 ,2.6543846529771045696 ] 
dist 151=[-2.1332883718064887497 ,2.6360356690724128911 ] 
dist 152=[-2.1268224477332491759 ,2.5882821167010922108 ] 
dist 153=[-2.0664500435331022098 ,2.6031853002101105050 ] 
dist 154=[-2.0511925260400622568 ,2.6052226596264959978 ] 
dist 155=[-2.0872686533727875789 ,2.5982181279391870767 ] 
dist 156=[-2.1810477177767918285 ,2.5911900864998580998 ] 
dist 157=[-2.2376839792086153276 ,2.5483270968688962169 ] 
dist 158=[-2.2779761006686077870 ,2.5348029551487242069 ] 
dist 159=[-2.3065208430148154869 ,2.4791525057258960977 ] 
dist 160=[-2.3892975532367915923 ,2.4697462029232129946 ] 
dist 161=[-2.4934283289647417835 ,1.2985509975062905864 ] 
dist 162=[-2.5693512873972235000 ,1.5715674428798323554 ] 
dist 163=[-2.6266292261774528462 ,1.7929443823395947010 ] 
dist 164=[-2.6675373011677887484 ,2.0017964552083875110 ] 
dist 165=[-2.6781248815686052813 ,2.1866703335821657484 ] 
dist 166=[-2.6768628558279714089 ,2.3123413781460527631 ] 
dist 167=[-2.6704739806031641722 ,2.4187499771619415284 ] 
dist 168=[-2.2299438476966936517 ,2.5267423339468837375 ] 
dist 169=[-2.2366396829124368548 ,2.6198134066312316340 ] 
dist 170=[-2.2337889706719075347 ,2.6666646359175333405 ] 
dist 171=[-2.2260660024190854961 ,2.6895281077194772021 ] 
dist 172=[-2.1628667704164563516 ,2.6926951702311462000 ] 
dist 173=[-2.1431003285625608174 ,2.6667084791306845857 ] 
dist 174=[-2.1091921853643406184 ,2.6522513297632536125 ] 
dist 175=[-2.0970208058924110058 ,2.6305634007963087318 ] 
dist 176=[-1.7682419824292776815 ,2.6192297009195083152 ] 
dist 177=[-1.7191222164868461161 ,2.5422940903164254389 ] 
dist 178=[-1.6116592105876173943 ,2.5693423408290437542 ] 
dist 179=[-1.5791609732153249266 ,2.5736326832846003936 ] 
dist 180=[-1.4368088193259621565 ,2.5655488725142542392 ] 
dist 181=[-1.4074082926707344107 ,2.5823999816707462494 ] 
dist 182=[-1.4007485915363984426 ,2.5905891898885926106 ] 
dist 183=[-1.5726704956414211441 ,2.5891073490248345890 ] 
dist 184=[-1.7729403778293350485 ,2.4675234175016003235 ] 
dist 185=[-1.9578994633818659729 ,2.4405179440255238578 ] 
dist 186=[-2.0687103173148651074 ,2.4278506276905395684 ] 
dist 187=[-2.1464415221776378024 ,2.3997624558690351345 ] 
dist 188=[-2.1993639454098482094 ,2.3869154253470443998 ] 
dist 189=[-2.2370236783203359983 ,2.3134805086002873386 ] 
dist 190=[-2.2538370104976225828 ,2.2943805602646737334 ] 
dist 191=[-2.2586052083482527177 ,2.2346585889593816436 ] 
dist 192=[-2.2558377318493355116 ,2.2192300277768767390 ] 
dist 193=[-1.8894566970467329212 ,.55591317493013542987] 
dist 194=[-1.8648932651638621398 ,.68070535025980725327] 
dist 195=[-1.9449206567666409537 ,.8383887291243065625 ] 
dist 196=[-2.0112449121229739146 ,1.0051640836923843462 ] 
dist 197=[-2.0637012980177935293 ,1.1662434982698529194 ] 
dist 198=[-2.0883737580900274166 ,1.3540157108278015344 ] 
dist 199=[-2.0980353471003873973 ,1.6273275954682236910 ] 
dist 200=[-2.0978612246459803576 ,1.8958304326386064587 ] 
dist 201=[-2.0745324599147260936 ,2.0644077371816088408 ] 
dist 202=[-2.1735929308078063046 ,2.1920711564135815535 ] 
dist 203=[-2.2448531366763322560 ,2.2972751915920034486 ] 
dist 204=[-2.2968104213570702778 ,2.3800662224102319463 ] 
dist 205=[-2.3331308027469909294 ,2.4182730112341991073 ] 
dist 206=[-2.3419782067586046427 ,2.4368214925895260329 ] 
dist 207=[-2.3409574269354181658 ,2.4411519406926370087 ] 
dist 208=[-2.3378912983921535917 ,2.3818533313092640235 ] 
dist 209=[-2.1567312876342598944 ,2.3642355092646090640 ] 
dist 210=[-2.2053908166539837482 ,2.3312817262172986423 ] 
dist 211=[-2.2331300160383205226 ,2.3186304769857955931 ] 
dist 212=[-2.2395374683377714533 ,2.2540419462922937708 ] 
dist 213=[-2.2363753040062335583 ,2.2365576636326031733 ] 
dist 214=[-2.2289781810706387680 ,2.2319699377015390728 ] 
dist 215=[-2.2109427025065369221 ,2.3205869860829478427 ] 
dist 216=[-2.2008601580930868070 ,2.4063047188016581752 ] 
dist 217=[-1.9625026446405378912 ,2.4784955912372081305 ] 
dist 218=[-1.9236645416909904968 ,2.5131211699061112347 ] 
dist 219=[-1.8375938389139830173 ,2.5281270735527265294 ] 
dist 220=[-1.8101353389703448486 ,2.5286562101456478212 ] 
dist 221=[-1.6842133806007586471 ,2.4962761667923989827 ] 
dist 222=[-1.6569044022256420450 ,2.4816742600060928517 ] 
dist 223=[-1.5849451857840966444 ,2.4540307366095921636 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 2, 2, 1, 2] 
dist 0=[48.677935920748824768  ,48.677935920748824768  ] 
dist 1=[47.569783210970180510  ,49.425467629381211518  ] 
dist 2=[45.672203403834313295  ,49.882122157450769693  ] 
dist 3=[43.665184712206557270  ,50.192397934736011399  ] 
dist 4=[42.119812093045425746  ,50.355002161455994777  ] 
dist 5=[40.609418445942559561  ,50.442025619084210029  ] 
dist 6=[38.742346236002000261  ,50.450166555958705612  ] 
dist 7=[36.778586715175213881  ,50.411666565584506540  ] 
dist 8=[34.881930088488494349  ,50.046935937744783075  ] 
dist 9=[32.662660410290083446  ,47.546344274939332205  ] 
dist 10=[29.409859576648214534  ,47.115614695677379348  ] 
dist 11=[26.049177487826880138  ,46.433125203355250107  ] 
dist 12=[23.398824079416093873  ,46.226588911920842825  ] 
dist 13=[20.749643577650352555  ,45.694550239520423856  ] 
dist 14=[17.393551956120718634  ,45.524335281635229848  ] 
dist 15=[13.821451403782641947  ,45.437790126173007825  ] 
dist 16=[10.309002639357294855  ,44.871731817981325320  ] 
dist 17=[6.1511869871725104526 ,29.006467926167017983  ] 
dist 18=[0                     ,27.660545571991413991  ] 
dist 19=[18.471643979396007620  ,24.747711963157381335  ] 
dist 20=[16.525843601749595989  ,24.100315751147862963  ] 
dist 21=[14.531011489269115043  ,20.918640771740486795  ] 
dist 22=[11.937693452936626954  ,20.371701911443955213  ] 
dist 23=[9.3989664282560297944 ,19.109324571805558393  ] 
dist 24=[7.6220928621299848229 ,18.927447853002875320  ] 
dist 25=[6.0559998788260727747 ,17.367901138764947868  ] 
dist 26=[4.3591388632915257962 ,16.546831004195700157  ] 
dist 27=[2.6989342068046489809 ,6.6300650707635989020 ] 
dist 28=[1.2790315947400228316 ,6.3433088846335904768 ] 
dist 29=[-.48546438187119189833,5.7414013539622606259 ] 
dist 30=[-2.4785407087335006223 ,5.6290541274607382795 ] 
dist 31=[-4.6870118006021592054 ,1.3228088027322454542 ] 
dist 32=[-7.7811889980794198931 ,.90675058952972344953] 
dist 33=[-10.793184358617463850  ,.08934216460126483942] 
dist 34=[-12.673534271396014224  ,-.10377276750991993486] 
dist 35=[-14.094970383225016121  ,-.70376718323452754212] 
dist 36=[-15.273331480294710140  ,-.8302435679012011121 ] 
dist 37=[-16.222315787481469977  ,-.85079037815950480616] 
dist 38=[-16.727039721392492562  ,-.727101579509580036  ] 
dist 39=[-17.006518040099441552  ,-.54456077885347314691] 
dist 40=[-17.070210112215646595  ,-.32753329953106713234] 
dist 41=[-16.758228412896580537  ,-.04632074652159428520] 
dist 42=[-16.667525384257047880  ,.39289578578639450106] 
dist 43=[-16.584165119659360807  ,.89744362777969656326] 
dist 44=[-16.499229957168938947  ,1.4395847975323763565 ] 
dist 45=[-16.405648855853832725  ,2.1115543375263234205 ] 
dist 46=[-16.339676730684166487  ,3.1343034633971558299 ] 
dist 47=[-16.277622618730011723  ,4.1649018237041952558 ] 
dist 48=[-16.205884851322441394  ,4.8683101345732579604 ] 
dist 49=[-5.4591013121783915202 ,5.4656462851211016142 ] 
dist 50=[-4.5737514743160112553 ,6.0731904116800490667 ] 
dist 51=[-2.5155455276726166150 ,6.6399770514507398856 ] 
dist 52=[-2.1825196985904404894 ,7.0747890874597550884 ] 
dist 53=[.48668425510442263956,7.4959255393948319273 ] 
dist 54=[.95283698573993137444,8.0082707336397258610 ] 
dist 55=[1.6658473737074304028 ,8.4900396411385276981 ] 
dist 56=[1.8415355692330768183 ,8.7892203545594742422 ] 
dist 57=[3.6887456500905027933 ,9.0120917536806484163 ] 
dist 58=[3.7514224994877375184 ,9.1893953612571391752 ] 
dist 59=[3.8557854642984617907 ,9.3243706430339567290 ] 
dist 60=[3.7995639741985903914 ,9.3783948696801280503 ] 
dist 61=[3.6574090801960888069 ,9.3840699132817904396 ] 
dist 62=[3.3623123648941486598 ,9.3620816921185096197 ] 
dist 63=[3.0406790338129383053 ,9.2456406765916154440 ] 
dist 64=[2.7925835551702472874 ,9.1603526145907931281 ] 
dist 65=[2.5518395876644710110 ,4.8440199227670930222 ] 
dist 66=[2.2593178519475312607 ,4.6742155935487402186 ] 
dist 67=[1.9567548931372301998 ,4.2602925501462387473 ] 
dist 68=[1.6758232493720575351 ,4.1795871721877116975 ] 
dist 69=[1.3573035257925261935 ,3.5535071986315853337 ] 
dist 70=[.90461943213315965898,3.4315856599352405459 ] 
dist 71=[.44654255034171511283,3.2373532387409193090 ] 
dist 72=[.10642775267998527321,3.1849145060389099798 ] 
dist 73=[-.21239621536058721058,2.1784812175275604429 ] 
dist 74=[-.58560912703475304256,2.0467935530571105887 ] 
dist 75=[-.9655356511863230688 ,1.7353990895081052393 ] 
dist 76=[-1.3112452744394097770 ,1.6837560841372590283 ] 
dist 77=[-1.6985416715210943125 ,1.2593648222584612218 ] 
dist 78=[-2.2588869548065037499 ,1.2448757008446420087 ] 
dist 79=[-2.8509667247742634120 ,1.0658885557274566584 ] 
dist 80=[-3.2246036312006161815 ,1.0352449386944957702 ] 
dist 81=[-3.5103070561807454737 ,.20249560835514847412] 
dist 82=[-3.7513112247491033480 ,.10554991307956811537] 
dist 83=[-3.9471553408060192891 ,-.06788168188093474994] 
dist 84=[-4.0525520882084025198 ,-.10546939095844197709] 
dist 85=[-4.1120675007193837210 ,-.19342077374779913865] 
dist 86=[-4.2310112137073384424 ,-.19271671053445231569] 
dist 87=[-4.3685842796248247826 ,-.15678585202430116601] 
dist 88=[-4.4928056227703943180 ,-.06392805078969171212] 
dist 89=[-4.5932171346079864410 ,.04732752474356176453] 
dist 90=[-4.6357256737612847539 ,.15672220874435773501] 
dist 91=[-4.6498839149922747714 ,.28544784415990783022] 
dist 92=[-4.6445173234663071615 ,.47393696034508396514] 
dist 93=[-4.5613725053299096411 ,.6862596880700330341 ] 
dist 94=[-4.5307647859509633628 ,.91015589886489818388] 
dist 95=[-4.4764203744980632039 ,1.1854036483751120129 ] 
dist 96=[-4.4556855083367036555 ,1.6027362252628007496 ] 
dist 97=[-1.0901284557033986890 ,2.0191417857607030615 ] 
dist 98=[-1.0227836061827238587 ,2.2907101374866769116 ] 
dist 99=[-.46034189146681169286,2.5082888240352189610 ] 
dist 100=[-.35982494696994027478,2.7092159567816119177 ] 
dist 101=[-.21355719250502274849,2.8842326858367493067 ] 
dist 102=[-.17418721956038415115,2.9984093701944273613 ] 
dist 103=[.49477538706888628688,3.0900404314492390084 ] 
dist 104=[.57745432250677865038,3.1751025910054741361 ] 
dist 105=[.75468282038699434046,3.2424001616607256151 ] 
dist 106=[.78753080175486475212,3.2701949273895823442 ] 
dist 107=[.96303881073666997157,3.3893191479949302171 ] 
dist 108=[.99136480697833580216,3.4896421878021260468 ] 
dist 109=[1.0398320206237206096 ,3.5703016075333060187 ] 
dist 110=[.72914608642287942587,3.6109405903098080306 ] 
dist 111=[.24684155915372162287,3.6301127854331581951 ] 
dist 112=[-.4862611938181864953 ,3.6274490726223285051 ] 
dist 113=[-1.2190821691519949910 ,2.3923675256414105249 ] 
dist 114=[-1.7002635771749826561 ,2.3038597851620165864 ] 
dist 115=[-2.0892204453292158200 ,2.1073259012957309092 ] 
dist 116=[-2.4539587666013758158 ,2.0520367058060064420 ] 
dist 117=[-2.7751609145053401216 ,1.8044286964911090921 ] 
dist 118=[-2.9903565156578933085 ,1.7555864778401482752 ] 
dist 119=[-3.1690819274707953291 ,1.6383849557457930066 ] 
dist 120=[-3.3447214134903186264 ,1.6113262045290856946 ] 
dist 121=[-3.4998648636828145892 ,.96952881876498731387] 
dist 122=[-3.5967832927751876753 ,.94537047471947409872] 
dist 123=[-3.6695680969811693458 ,.8359203177650066492 ] 
dist 124=[-3.7283828981684075526 ,.81427169472038887874] 
dist 125=[-3.7736296160021455199 ,.76295582444670260539] 
dist 126=[-3.7922527789495567319 ,.75044437494163310431] 
dist 127=[-3.7948579034299783167 ,.21009126549414103501] 
dist 128=[-3.7874488451517039490 ,.19939010060038781251] 
dist 129=[-2.5264325563698407628 ,-.0130663449113167813 ] 
dist 130=[-2.7447132988023984140 ,-.0429093095254842049 ] 
dist 131=[-2.9071465992475756972 ,-.1463689279176187330 ] 
dist 132=[-3.0360305377550914948 ,-.1674040851505731289 ] 
dist 133=[-3.1365610878037489395 ,-.1912420998083999333 ] 
dist 134=[-3.1858085361773103738 ,-.1923978934171097671 ] 
dist 135=[-3.2085698984643149357 ,-.1846645543222134807 ] 
dist 136=[-3.2104941412619503750 ,-.1647896154861702157 ] 
dist 137=[-3.0636419201484984644 ,-.1322651184990825452 ] 
dist 138=[-3.0320193440929619882 ,-.0740307297820246621 ] 
dist 139=[-2.9807485233937561425 ,-.0037633864195909689 ] 
dist 140=[-2.9622213353440265352 ,.07679467438002393595] 
dist 141=[-2.8917377647898691503 ,.18031155496161060009] 
dist 142=[-2.8683747469206647404 ,.34222052913453521772] 
dist 143=[-2.8168143879133321853 ,.50555857681062709778] 
dist 144=[-2.7968878684848903534 ,.61478311628633961151] 
dist 145=[-.99514657911151883441,.7052929227993902313 ] 
dist 146=[-.83734409705659544419,.7939399910147561841 ] 
dist 147=[-.47712955740755770254,.87462670336019689465] 
dist 148=[-.41181713290506718434,.93336848082065969681] 
dist 149=[.03843596207363207327,1.1567342704992159279 ] 
dist 150=[.11724815223232914885,1.3776118397214615114 ] 
dist 151=[.25878445587527045573,1.5859797235535975950 ] 
dist 152=[.28921533522551509393,1.8318103596334017180 ] 
dist 153=[.55706813132662240204,2.0600914979742794744 ] 
dist 154=[.45385765178502197349,2.1984143321574986685 ] 
dist 155=[.33541302777784537255,2.2973617402058647208 ] 
dist 156=[.20741594237319632517,2.3684835204029972211 ] 
dist 157=[.04791905300276965672,2.4212059969478936843 ] 
dist 158=[-.19624485504036409263,2.4467125249540258881 ] 
dist 159=[-.44094788978428855654,2.4571769202498202645 ] 
dist 160=[-.60259676221991545045,2.4555711425982094125 ] 
dist 161=[-.7343406277082999763 ,1.0074076550557678561 ] 
dist 162=[-.85969017304782727268,.96766372025030407975] 
dist 163=[-.97131092617029323407,.89200514791388945215] 
dist 164=[-1.0482617205613704533 ,.87530088401261659404] 
dist 165=[-1.1145405533356590940 ,.84290027684821813026] 
dist 166=[-1.1835678206004660626 ,.83337875403372304548] 
dist 167=[-1.2449374663381335166 ,.67107793266579832907] 
dist 168=[-1.2806531287234426099 ,.64777896679319411284] 
dist 169=[-1.3044038789861374385 ,.58983878554216586603] 
dist 170=[-1.3180185290989515523 ,.57934328982673134784] 
dist 171=[-1.3245647668757564333 ,.48762177793466530584] 
dist 172=[-1.3244733657548082469 ,.52390928300669668456] 
dist 173=[-1.3130868448605274706 ,.61767089854224814811] 
dist 174=[-1.3094162182978441999 ,.71924753663997760767] 
dist 175=[-1.4668141949220201290 ,.84595441297868975235] 
dist 176=[-1.6999528434092392705 ,1.0400005458160627445 ] 
dist 177=[-1.9265920475621449587 ,1.2342598928790218195 ] 
dist 178=[-2.0655300749032079706 ,1.3618164211798942119 ] 
dist 179=[-2.1669254423743088964 ,1.4648663672237851897 ] 
dist 180=[-2.2437045860643398339 ,1.5613263957379445016 ] 
dist 181=[-2.3019199599208493487 ,1.6460888447768920883 ] 
dist 182=[-2.3292115873784565939 ,1.7024555401456318092 ] 
dist 183=[-2.3397216067089368813 ,1.7487704395883088769 ] 
dist 184=[-2.3394554952500058823 ,1.7934150255466861362 ] 
dist 185=[-2.1948937783074856280 ,1.8294146329145926787 ] 
dist 186=[-2.1672899336608543525 ,1.8412285780930727976 ] 
dist 187=[-2.1178519462328843257 ,1.8434232096990717306 ] 
dist 188=[-2.1025250654137829529 ,1.8410417796327243218 ] 
dist 189=[-2.0383407727188827797 ,1.7821484475864896294 ] 
dist 190=[-2.0194471941587664959 ,1.7639577206048907384 ] 
dist 191=[-1.9759265406063862975 ,1.7489670119266844466 ] 
dist 192=[-1.9595221605849725410 ,1.7374298624990213401 ] 
dist 193=[-.65625841679427028081,.28854370716390890809] 
dist 194=[-.65188412273883006448,.57105326898891674555] 
dist 195=[-.66072087877035073803,.80893571053288677887] 
dist 196=[-.66356840773239505017,1.0481611665951998517 ] 
dist 197=[-.66334517734942753077,1.2699897601652097301 ] 
dist 198=[-.6618410367842516719 ,1.4384370560202592809 ] 
dist 199=[-.6139375559125244237 ,1.6000810758771429410 ] 
dist 200=[-.60528526900351406968,1.7947593721359253624 ] 
dist 201=[-.58746020252577683415,1.9769164875851430724 ] 
dist 202=[-.58168781992625246263,2.0885853018862234597 ] 
dist 203=[-.55507060423352460094,2.1700404824509587811 ] 
dist 204=[-.54899779834454033968,2.2316040390515168360 ] 
dist 205=[-.53033465175395063473,2.2763899889801261284 ] 
dist 206=[-.52694295490050996747,2.2908758068534560423 ] 
dist 207=[.10667036172226458362,2.2936816448663781364 ] 
dist 208=[.06956157185605070874,2.2918473877188557301 ] 
dist 209=[-.10356336364429638328,2.1854881513269300942 ] 
dist 210=[-.29587194205072333286,2.2362315442107425710 ] 
dist 211=[-.50172899625956007245,2.2853823902657963172 ] 
dist 212=[-.71425953770770519731,2.3117505258597727268 ] 
dist 213=[-.91482123267521299781,2.3257754386560317513 ] 
dist 214=[-1.0729101121960922040 ,2.3256574671321819476 ] 
dist 215=[-1.2301778968955464846 ,2.3174789250341684477 ] 
dist 216=[-1.4274662615797957190 ,2.3098838030398175601 ] 
dist 217=[-1.6160191637953577329 ,2.0929545815559626354 ] 
dist 218=[-1.7384232264612130403 ,2.0564840176570260722 ] 
dist 219=[-1.8358319386404570535 ,1.9787362058357930632 ] 
dist 220=[-1.9246232940968218170 ,1.9540259516054580248 ] 
dist 221=[-2.0011094534182936365 ,1.8410623790367919074 ] 
dist 222=[-2.0494073112490882739 ,1.8166424830064465077 ] 
dist 223=[-2.0863336022750117615 ,1.7427468901286532269 ] 
dist 224=[-2.1174385392641492036 ,1.7311185661236252042 ] 
dist 225=[-2.1391490390875148757 ,.66468532816021142635] 
dist 226=[-2.1846665485699105998 ,.68600456204220237189] 
dist 227=[-2.2393637107832257832 ,.70233511161972771224] 
dist 228=[-2.2706374903663042466 ,.7089184634410327066 ] 
dist 229=[-2.2891463547591402416 ,.71119591294757021277] 
dist 230=[-2.2928914150559380920 ,.71034891607989151661] 
dist 231=[-2.2872722961288824396 ,.69252731041180519438] 
dist 232=[-2.2816373724094125396 ,.68752895108054936383] 
dist 233=[-2.3306978203580198934 ,.67399423335695180859] 
dist 234=[-2.4220300746943991265 ,.66828808275219221198] 
dist 235=[-2.4803898302894604872 ,.63692457898912826531] 
dist 236=[-2.5090197488952179686 ,.62898025925324963958] 
dist 237=[-2.5245270278144427473 ,.61251695406258236615] 
dist 238=[-2.5305085075304667851 ,.60694849383873152629] 
dist 239=[-2.5306550212330147732 ,.15854292475667217229] 
dist 240=[-2.5230335315283904402 ,.29231872705800124643] 
dist 241=[-2.2595845678837166082 ,.50680747274173384537] 
dist 242=[-2.2420867408060740264 ,.78267605931407037729] 
dist 243=[-2.1820361484661638986 ,1.0133448196830248713 ] 
dist 244=[-2.1706056275817372963 ,1.2427031966599456317 ] 
dist 245=[-2.0125595894770717414 ,1.4600292550929337667 ] 
dist 246=[-1.9759323142566016728 ,1.6217611195312484770 ] 
dist 247=[-1.9409657680593086212 ,1.7702993386922140916 ] 
dist 248=[-1.9260536442206189777 ,1.9397094734034710752 ] 
dist 249=[-1.4298098013907742259 ,2.0963703412819689807 ] 
dist 250=[-1.3627065226769063427 ,2.1921514322419984573 ] 
dist 251=[-1.2293656877529618319 ,2.2579554808304111974 ] 
dist 252=[-1.1938256897844079380 ,2.3000815482456961178 ] 
dist 253=[-1.0629955484263947726 ,2.3279042073796772230 ] 
dist 254=[-1.0330110432372905833 ,2.3366159457249523577 ] 
dist 255=[-.9806069040634538899 ,2.3343501071351626350 ] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 1, 2, 0, 2] 
dist 0=[54.302022397648474318  ,54.302022397648474318  ] 
dist 1=[54.205442232046422191  ,54.295801722709529408  ] 
dist 2=[53.943486158912776471  ,54.302022397648474318  ] 
dist 3=[53.583489741376584717  ,53.951276517022205258  ] 
dist 4=[52.667329178814438128  ,53.806411572241588089  ] 
dist 5=[51.506729820256089159  ,53.531329953295450292  ] 
dist 6=[50.108978961147632719  ,53.414561121830177236  ] 
dist 7=[48.264198899536117752  ,52.777088064034869211  ] 
dist 8=[45.317612308824670610  ,52.607302642618443172  ] 
dist 9=[42.284138196376627387  ,52.007163965596621812  ] 
dist 10=[40.092169335127732985  ,51.895117882404487439  ] 
dist 11=[38.088371379603767863  ,50.285570990272327517  ] 
dist 12=[35.806524348923953786  ,49.898098408607454749  ] 
dist 13=[33.509139475849165773  ,48.425706898370535562  ] 
dist 14=[31.443075802330866919  ,45.823024799783606369  ] 
dist 15=[28.025512708524146063  ,32.873127927323062391  ] 
dist 16=[24.636258244101605856  ,32.570851841116934825  ] 
dist 17=[21.721040595205505766  ,29.092883693781151125  ] 
dist 18=[18.680966274179133072  ,28.840445535453545785  ] 
dist 19=[15.783895582611381231  ,24.171558212236303556  ] 
dist 20=[13.439482176369321214  ,23.809583609153051023  ] 
dist 21=[11.044000521970491188  ,21.637494497338755857  ] 
dist 22=[7.9424111810404362735 ,21.238021845541307684  ] 
dist 23=[4.9142788278948726423 ,20.464618270266265730  ] 
dist 24=[0                     ,20.271000816260535405  ] 
dist 25=[.97710925113308834612,15.733212949358997856  ] 
dist 26=[-.98240543194283434805,15.573069793089005584  ] 
dist 27=[-2.8833293068432156657 ,12.041378377539717217  ] 
dist 28=[-4.4846404648586100732 ,11.543455724600374876  ] 
dist 29=[-6.1824092332700063830 ,8.5250248119096075098 ] 
dist 30=[-8.4698759591110232754 ,7.1091869025144162437 ] 
dist 31=[-10.669138784978046734  ,-.76539008472328149804] 
dist 32=[-12.014738061244339751  ,-1.1325705883853469517 ] 
dist 33=[-13.002493887239868781  ,-1.8895946844280738910 ] 
dist 34=[-13.771585466404651247  ,-2.0410912463731470735 ] 
dist 35=[-14.372078615386334704  ,-3.0846882682456019838 ] 
dist 36=[-14.685689848305880410  ,-3.2562461442608347028 ] 
dist 37=[-14.852595461846014003  ,-3.2612858106403426692 ] 
dist 38=[-14.874771620290032473  ,-3.0446722148832881853 ] 
dist 39=[-14.041571906262983377  ,-2.7058571699956784607 ] 
dist 40=[-13.881238929808489002  ,-2.2229608902726371881 ] 
dist 41=[-13.647470559350290451  ,-1.5443214571351517249 ] 
dist 42=[-13.555681858485012236  ,-.42427928504721948634] 
dist 43=[-13.302898016367652195  ,.72733423406502919044] 
dist 44=[-13.198859119386710278  ,1.5321309838578855560 ] 
dist 45=[-13.083938382250790755  ,2.2352588251502272568 ] 
dist 46=[-13.016088845138266396  ,2.9815607850789531252 ] 
dist 47=[-4.3395279062402815739 ,3.6971903567726546784 ] 
dist 48=[-3.6153977218009185964 ,4.2781282306288253332 ] 
dist 49=[-2.0064831391797461728 ,4.8712111273978962361 ] 
dist 50=[-1.6962298751968499507 ,5.6355322692289544992 ] 
dist 51=[.15342010524383263363,6.3757138334010756953 ] 
dist 52=[.46473049073926827228,6.8725767753437120139 ] 
dist 53=[1.0933785919888406026 ,7.2865645820571931543 ] 
dist 54=[1.4641957107313596767 ,7.6961334289163917506 ] 
dist 55=[2.3472203768162476197 ,8.0723203403857483085 ] 
dist 56=[2.4163918747077833047 ,8.3532177233998313658 ] 
dist 57=[2.4882068408914374077 ,8.6190268563361508112 ] 
dist 58=[2.4628332912283424946 ,8.9479835852088853400 ] 
dist 59=[2.4085303274957178875 ,9.2267204829205750904 ] 
dist 60=[2.3344465709228800968 ,9.3717996220318820303 ] 
dist 61=[2.2329785867871537073 ,9.4467732584055096702 ] 
dist 62=[2.0691086990578229678 ,9.4461027931561273996 ] 
dist 63=[1.8788598236004232280 ,4.2302421808338653477 ] 
dist 64=[1.6719847386691807394 ,3.9486334038158009078 ] 
dist 65=[1.4139012384989762670 ,3.9097202313876109976 ] 
dist 66=[1.0191756087182782794 ,3.8925831534036048165 ] 
dist 67=[.60826058969059631213,3.7373958651393065153 ] 
dist 68=[.2854816936868907839 ,3.7024721134222959990 ] 
dist 69=[-.03434605704079080901,3.6089171982962883298 ] 
dist 70=[-.43362646268671105701,3.5794712976274331700 ] 
dist 71=[-.85353930507100550282,3.3932767759746752380 ] 
dist 72=[-1.2558170061157275080 ,3.3503232229458423844 ] 
dist 73=[-1.7225440859745061716 ,3.2707585214982200944 ] 
dist 74=[-2.3998446242870491473 ,3.2474365653394077930 ] 
dist 75=[-3.0672190133206026492 ,-.40176882237150552302] 
dist 76=[-3.4943544473800641652 ,-.46578477219972493567] 
dist 77=[-3.8278256735158444882 ,-.58015064233867280527] 
dist 78=[-4.1212862252446932245 ,-.60231808810349779141] 
dist 79=[-4.3671256434624068042 ,-.83545592410873853899] 
dist 80=[-4.5105028505848091580 ,-.86875300229647925594] 
dist 81=[-4.6066303772674635583 ,-.86925608553563374324] 
dist 82=[-4.6638843326646146768 ,-.82607136970697891772] 
dist 83=[-4.7155522245930483479 ,-.75887534150383969323] 
dist 84=[-4.7764383945389519008 ,-.66347579692637369337] 
dist 85=[-4.8231426991204025716 ,-.52954880858839883409] 
dist 86=[-4.8628893639025135020 ,-.30853544774432327932] 
dist 87=[-4.8952947100661080963 ,-.07216343385628245956] 
dist 88=[-4.9126932334454899204 ,.1231102165100950815 ] 
dist 89=[-4.9225466460923209486 ,.32549298081990966829] 
dist 90=[-4.9248429665559814861 ,.59033178917822201389] 
dist 91=[-3.7728835829165235294 ,.87504697177557907879] 
dist 92=[-3.7261474157284827818 ,1.1568227425164708037 ] 
dist 93=[-3.6844636586860668936 ,1.4905565114300832088 ] 
dist 94=[-3.6619835864487692002 ,1.9827380868705355835 ] 
dist 95=[-1.1946108124727250708 ,2.4701323646610162907 ] 
dist 96=[-1.0865698125548904891 ,2.7847789470811578459 ] 
dist 97=[-.90643522903856251905,3.0334149642716115389 ] 
dist 98=[-.86372932885552111976,3.2573151271372915610 ] 
dist 99=[-.15261489129270181493,3.4485063564602332216 ] 
dist 100=[-.05937761541910956880,3.5665879863639735680 ] 
dist 101=[.13879594177579901732,3.6539577629399146127 ] 
dist 102=[.18247719711245670129,3.7225857309931264889 ] 
dist 103=[.37960820724862451142,3.7723500303186144256 ] 
dist 104=[.41424226327191135655,3.8835507645503650171 ] 
dist 105=[.47886780097448706379,3.9682115421039686200 ] 
dist 106=[.49267678279770150077,4.0386377269504225938 ] 
dist 107=[.52303156230791087781,4.0946378768257292570 ] 
dist 108=[.5116907863727697397 ,4.1217212582710852309 ] 
dist 109=[.47965432827783209142,4.1328933248546762872 ] 
dist 110=[.03684601043620633242,4.1253964419297915860 ] 
dist 111=[-.74371168495167696001,2.5327591108674959028 ] 
dist 112=[-1.2600645296659051829 ,2.5308525383350314834 ] 
dist 113=[-1.6818428955562804360 ,2.5278541758931234142 ] 
dist 114=[-2.0849230328284339307 ,2.5226437812110103020 ] 
dist 115=[-2.4452176280720980443 ,2.1464797969667743576 ] 
dist 116=[-2.6962264184311317167 ,2.0919072106686847060 ] 
dist 117=[-2.9153128198879034975 ,1.9923178343104296561 ] 
dist 118=[-3.1481992845024614679 ,1.9660031202983873854 ] 
dist 119=[-3.3591282892208896421 ,1.8748492683195375809 ] 
dist 120=[-3.4905689853571687873 ,1.8484969389980482559 ] 
dist 121=[-3.5889788442937264964 ,1.8179752843881361968 ] 
dist 122=[-3.6680479016297426169 ,1.8036728244185181917 ] 
dist 123=[-3.7285880685270572620 ,.19323855409663232818] 
dist 124=[-3.7530245997913929818 ,.05939061796473857355] 
dist 125=[-3.7566149646447401281 ,-.23513484546292778317] 
dist 126=[-3.7517995588790978944 ,-.29252508543878324619] 
dist 127=[-2.4861801937541653369 ,-.62153132058503335469] 
dist 128=[-2.6356678057195618253 ,-.67616735547512709368] 
dist 129=[-2.7398953382083603820 ,-.78992481387415090791] 
dist 130=[-2.8098109091066497335 ,-.81188913720452730583] 
dist 131=[-2.8600918098358314879 ,-.9588301259438067409 ] 
dist 132=[-2.8859306685911767948 ,-.97617758912715553008] 
dist 133=[-2.8988745089946512864 ,-.96391913262971926336] 
dist 134=[-2.8976587088362023205 ,-.90813757771449171114] 
dist 135=[-2.6038004476754001922 ,-.82871714211685884336] 
dist 136=[-2.5569329542157914638 ,-.72210536119265383018] 
dist 137=[-2.4800783732927635627 ,-.57519213615788007725] 
dist 138=[-2.4568741439496274005 ,-.33491749651204216989] 
dist 139=[-2.3865362923546825716 ,-.08881285972560940301] 
dist 140=[-2.3615981062910929714 ,.08137388034272399988] 
dist 141=[-2.3381754890116538118 ,.22851716557444152309] 
dist 142=[-2.3229857351046519236 ,.38266195946544493121] 
dist 143=[-.45663185061749713574,.52950696240601235351] 
dist 144=[-.30206109997010436286,.64752291403939629645] 
dist 145=[.04532863411341748123,.76704141160970295925] 
dist 146=[.10862921244014010368,.91989468354768933113] 
dist 147=[.48525854461889836085,1.0674550322013123780 ] 
dist 148=[.46771107733688271576,1.1658535780528149714 ] 
dist 149=[.43085780551687252297,1.3183997762239152961 ] 
dist 150=[.35804980016888748458,1.5576008625159566497 ] 
dist 151=[.26773908263043816181,1.7829312446205188556 ] 
dist 152=[.1610335814993504463 ,1.9237137007741456515 ] 
dist 153=[.02191742214137627470,2.0295627178670874777 ] 
dist 154=[-.19774071004568894356,2.1154558214251723978 ] 
dist 155=[-.42035646264803268199,2.1819755107114037188 ] 
dist 156=[-.57127662239775893795,2.2104955356240641292 ] 
dist 157=[-.69852681301672413096,2.2230888742131031837 ] 
dist 158=[-.82667963248512149051,2.2260366080427737798 ] 
dist 159=[-.94554757473309097216,1.5908662103427189616 ] 
dist 160=[-1.0357432258001032757 ,1.5792960190263996821 ] 
dist 161=[-1.1221782894778779580 ,1.5712031169825892806 ] 
dist 162=[-1.2260379961802052920 ,1.5657686839565266005 ] 
dist 163=[-1.3229826883563550297 ,1.2758721899643425010 ] 
dist 164=[-1.3818206745569426804 ,1.2352243359849576354 ] 
dist 165=[-1.4239885385733582971 ,1.1585644481698490660 ] 
dist 166=[-1.4544047293238003001 ,1.1383244584217402644 ] 
dist 167=[-1.4750149624313206587 ,1.0669119813078125328 ] 
dist 168=[-1.4796560241742680471 ,1.0480324446210060843 ] 
dist 169=[-1.4756751435572449091 ,1.0233335072522509441 ] 
dist 170=[-1.4747205093488109694 ,1.0137141260896276460 ] 
dist 171=[-1.2918280204021813156 ,.08120849701645626273] 
dist 172=[-1.3932240453522952153 ,.17232931833904643628] 
dist 173=[-1.5005461389710405647 ,.29134053156574847466] 
dist 174=[-1.6441431386211110670 ,.47945877308428223475] 
dist 175=[-1.7804245874905830863 ,.67011820119083004689] 
dist 176=[-1.8585485562316749570 ,.79927092887961525748] 
dist 177=[-1.9091196366183847688 ,.90804087488700215719] 
dist 178=[-1.9354127209063585903 ,1.0173583504649093879 ] 
dist 179=[-1.9509917573782407821 ,1.1185956577699388969 ] 
dist 180=[-1.9587896738290085685 ,1.1951196825798612761 ] 
dist 181=[-1.9624128359079874692 ,1.2681590573026307099 ] 
dist 182=[-1.9613155732532347195 ,1.3554894198997149386 ] 
dist 183=[-1.7001930075000815016 ,1.4367624218144104190 ] 
dist 184=[-1.6613583811550349001 ,1.4856281418400195028 ] 
dist 185=[-1.5939404405553535920 ,1.5200848600404605788 ] 
dist 186=[-1.5758085902408995419 ,1.5438550176040202019 ] 
dist 187=[-1.5171648306790694853 ,1.5589127076341988606 ] 
dist 188=[-1.4980406291241082893 ,1.5611639715855479578 ] 
dist 189=[-1.4820999392162164100 ,1.5535353560806058264 ] 
dist 190=[-1.4730287925123273807 ,1.5496333262081975623 ] 
dist 191=[-1.3518581395518124061 ,.63106352673799765402] 
dist 192=[-1.3351575890496134466 ,.73720564374932649811] 
dist 193=[-1.3187469882786038840 ,.84219979031648750761] 
dist 194=[-1.3090717525979324411 ,.97310936479354891961] 
dist 195=[-1.0468808441167819426 ,1.0978573093258297111 ] 
dist 196=[-1.0099703617952006975 ,1.1782597541533221989 ] 
dist 197=[-.93618262653859212872,1.2415988842890694238 ] 
dist 198=[-.91594598080300621764,1.3674295676697747040 ] 
dist 199=[-.83842373900126727981,1.5313719388526646771 ] 
dist 200=[-.82071959629022506667,1.6350078389359628421 ] 
dist 201=[-.78514082517858930549,1.7143514933884088618 ] 
dist 202=[-.77463991561622647524,1.7813329926727346730 ] 
dist 203=[.37383886406231805939,1.8352819709599384457 ] 
dist 204=[.45386434395767626392,1.8626085986097172652 ] 
dist 205=[.36892535317376651376,1.8756942170472821567 ] 
dist 206=[.15308733778015445619,1.8766325539165258958 ] 
dist 207=[-.06808762231423614311,1.8617828591565720057 ] 
dist 208=[-.24556006924346700186,1.8671799066424733874 ] 
dist 209=[-.40515443227532039812,1.8702043624797501718 ] 
dist 210=[-.57167022215471893556,1.8664942348421772038 ] 
dist 211=[-.72990647012990402873,1.8177498814032758214 ] 
dist 212=[-.85645697507250192119,1.8016780004515315297 ] 
dist 213=[-.98405200674186242033,1.7834293954170614210 ] 
dist 214=[-1.1464607810617104747 ,1.7730989391305310518 ] 
dist 215=[-1.3028375866867017465 ,1.4796048730273811806 ] 
dist 216=[-1.4063587659942552289 ,1.4842866607388443691 ] 
dist 217=[-1.4910091425837450752 ,1.4823036087465934987 ] 
dist 218=[-1.5720679794616551790 ,1.4793663615519713153 ] 
dist 219=[-1.6446465955576568865 ,1.3898590127544875866 ] 
dist 220=[-1.6954519250174345024 ,1.3791597700916773496 ] 
dist 221=[-1.7400658991291002469 ,1.3413384949514307198 ] 
dist 222=[-1.7879379871496518909 ,1.3352486755611611271 ] 
dist 223=[-1.8281900994435068686 ,1.2341156362651505214 ] 
dist 224=[-1.8579624699858325804 ,1.2108962896569729146 ] 
dist 225=[-1.8771736660004463533 ,1.1918837338703013263 ] 
dist 226=[-1.8799041724814022538 ,1.1860322025723557411 ] 
dist 227=[-1.8609878807531734258 ,.86365456603479546502] 
dist 228=[-1.8525745986732832755 ,.82090889162487404606] 
dist 229=[-1.8441648363796636429 ,.73810501636743190873] 
dist 230=[-1.8354988009478038833 ,.71663449870666567256] 
dist 231=[-1.8484230023825906321 ,.64159621624470768881] 
dist 232=[-1.9245121511080846531 ,.6233106130432990145 ] 
dist 233=[-1.9748646889071285157 ,.6009313696843037548 ] 
dist 234=[-2.0032666113277359995 ,.59225891957343653711] 
dist 235=[-2.0204665186018743051 ,.22077230375668431837] 
dist 236=[-2.0261073904823428573 ,.37327358934754117057] 
dist 237=[-2.0243599722544284886 ,.50573896169954080557] 
dist 238=[-2.0196252698030317127 ,.64552072250372771165] 
dist 239=[-1.8463675847430326784 ,.77933339447438818255] 
dist 240=[-1.8248060109369456282 ,.88797480200934460982] 
dist 241=[-1.7566121803868009915 ,.99900635033181933459] 
dist 242=[-1.7465576828393283134 ,1.1423604727871501045 ] 
dist 243=[-1.5867793845490422522 ,1.2813718315723199764 ] 
dist 244=[-1.5515454740000584294 ,1.3750703813594135557 ] 
dist 245=[-1.5224749009018093345 ,1.4535404474918403025 ] 
dist 246=[-1.5157441268989492022 ,1.5317694927430103125 ] 
dist 247=[-1.0527676290406955163 ,1.6371710179910049734 ] 
dist 248=[-.99250078927123705588,1.7209469077454959737 ] 
dist 249=[-.8757305889505700171 ,1.7797819849987368335 ] 
dist 250=[-.84580417025536777451,1.8199752658549189172 ] 
dist 251=[-.7430189142722515636 ,1.8538196696781536046 ] 
dist 252=[-.71805973483785018124,1.8728918360682297846 ] 
dist 253=[-.69200367768875010707,1.8798273586409476169 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 0, 0, 0, 1, 2] 
dist 0=[45.343484206476135256  ,45.343484206476135256  ] 
dist 1=[45.104911295725230880  ,45.519438192800257297  ] 
dist 2=[44.327766279112654837  ,45.737069342757272317  ] 
dist 3=[43.469958581321546023  ,45.778615213840624530  ] 
dist 4=[42.769715024523144786  ,45.655689522577855428  ] 
dist 5=[42.048243448077899674  ,45.591965518022741283  ] 
dist 6=[41.105615132230679806  ,45.521563561299369251  ] 
dist 7=[40.088695970556280368  ,45.440998110751132350  ] 
dist 8=[39.070411262830404075  ,42.716001604533689198  ] 
dist 9=[37.852230810118231447  ,42.304291043876255341  ] 
dist 10=[36.036675546883169468  ,41.541195084632412292  ] 
dist 11=[34.150155419656407903  ,41.332438149965070564  ] 
dist 12=[32.648423263539339887  ,40.561690290897598342  ] 
dist 13=[31.135228975924893348  ,40.351043337704500121  ] 
dist 14=[29.202826480702889427  ,39.982228601494221030  ] 
dist 15=[27.139452786558198559  ,39.871156501395818563  ] 
dist 16=[23.875501485044743004  ,31.605957152770758006  ] 
dist 17=[21.355152401291864900  ,31.180548200008645133  ] 
dist 18=[19.110333106874130477  ,31.064743738283201691  ] 
dist 19=[15.532444019296594117  ,22.766206225062648174  ] 
dist 20=[13.114124782804559843  ,19.068990176946183342  ] 
dist 21=[11.072401500927724582  ,18.282152954515991375  ] 
dist 22=[8.9992710635046988964 ,17.463635544442606578  ] 
dist 23=[7.0545920087589522089 ,17.311448696481904658  ] 
dist 24=[5.3258766622978175107 ,14.884140922691789119  ] 
dist 25=[3.4412079486707995657 ,14.612899219209005305  ] 
dist 26=[1.7349538152450047024 ,13.629759624603462426  ] 
dist 27=[-.18342071988392955618,9.1468467642845491480 ] 
dist 28=[-2.1018654998210481176 ,7.8710162639905673925 ] 
dist 29=[-3.8088724047062675078 ,7.6170283447895171418 ] 
dist 30=[-5.6968596246535656601 ,7.2519962163433372059 ] 
dist 31=[-8.3392528565154980278 ,7.1559754804289967537 ] 
dist 32=[-10.910200180305650115  ,.15084125503533161361] 
dist 33=[-12.512911739327631764  ,-.42704326059507200169] 
dist 34=[-13.722841611750402257  ,-.76716327202054264334] 
dist 35=[-14.724141415312468582  ,-.81383372677669577057] 
dist 36=[-15.523989564096486814  ,-.7658113192745844975 ] 
dist 37=[-15.928692957751007327  ,-.66098064436630310546] 
dist 38=[-16.146704299368504586  ,-.45508717807402738466] 
dist 39=[-16.200222959225939402  ,-.20307551796619671313] 
dist 40=[-15.988442441091018455  ,.08611357765879201405] 
dist 41=[-15.896159886662823357  ,.45627775095145248468] 
dist 42=[-15.779277127520173621  ,1.0316334583743450472 ] 
dist 43=[-15.708503139542596567  ,1.6327058051981348854 ] 
dist 44=[-15.461014300786648743  ,2.1056442406319313078 ] 
dist 45=[-15.364711920634114901  ,2.5742966028114783347 ] 
dist 46=[-15.137492334445337690  ,3.1585068470638457080 ] 
dist 47=[-15.042678165078149898  ,3.7714582934864929837 ] 
dist 48=[-8.7344972951677835439 ,4.3549268967628539243 ] 
dist 49=[-8.5351232658757396159 ,5.0281633935919737037 ] 
dist 50=[-8.4680104536797529185 ,5.9994637716952611189 ] 
dist 51=[-3.7893149638491668270 ,6.9602485601864889240 ] 
dist 52=[-1.5353512649919220289 ,7.5915591785839312367 ] 
dist 53=[-1.1358142246614897114 ,8.1022364295776293310 ] 
dist 54=[-.4913887813198729784 ,8.5816143136613197831 ] 
dist 55=[-.3387771632415210533 ,9.0040831553206939084 ] 
dist 56=[1.8758429532821158881 ,9.2876548596965455632 ] 
dist 57=[1.9690671357969774534 ,9.5237817537560226557 ] 
dist 58=[2.0288368032761737427 ,9.7569158597525228515 ] 
dist 59=[1.9462682750878357488 ,9.9490026069912620250 ] 
dist 60=[1.8142902901184375491 ,10.021309864872598800  ] 
dist 61=[1.6225163769550294387 ,10.033027512426654966  ] 
dist 62=[1.3509024666796305513 ,10.012142968549183574  ] 
dist 63=[.90039717862003936186,9.7573556335146833152 ] 
dist 64=[.4385056874588254215 ,3.0171088599473019330 ] 
dist 65=[.12144299249064337054,2.9260241762980917606 ] 
dist 66=[-.1494588711395550898 ,2.6970268408877462309 ] 
dist 67=[-.42725510914057694715,2.6547876324685352907 ] 
dist 68=[-.68742060586019546593,2.2869308141994634974 ] 
dist 69=[-.88800849466548418581,2.2143903958926237588 ] 
dist 70=[-1.0829077927433203526 ,2.1108761149357476841 ] 
dist 71=[-1.3203870958685399222 ,2.0788287181062239477 ] 
dist 72=[-1.5429708935256947538 ,1.4306360936763005488 ] 
dist 73=[-1.6784500782577586138 ,1.3464683572109538721 ] 
dist 74=[-1.7757393095041816871 ,1.1562323596867010994 ] 
dist 75=[-1.8459730109931461308 ,1.1172717796876802145 ] 
dist 76=[-1.8986377682914076156 ,.88208443716637774157] 
dist 77=[-1.9258486886513144356 ,.84001520964048067465] 
dist 78=[-1.9395281395169117380 ,.75693720640256940696] 
dist 79=[-1.9382401165232999394 ,.73630609658529290604] 
dist 80=[-1.2706324068451812193 ,.05821826545895429166] 
dist 81=[-1.5210145843133757530 ,-.01172104536737570863] 
dist 82=[-1.7225045323434308554 ,-.14175361890917883039] 
dist 83=[-1.9105443324425399887 ,-.17075197560590705602] 
dist 84=[-2.0760507362667830545 ,-.2462118251082826835 ] 
dist 85=[-2.1875682164031843145 ,-.25137403991823926536] 
dist 86=[-2.2811822804970677176 ,-.23210710924081763442] 
dist 87=[-2.3752130953148203009 ,-.17486358568232053614] 
dist 88=[-2.4555767661465109619 ,-.10466667728654961218] 
dist 89=[-2.4946215803851941371 ,-.03368785266714327315] 
dist 90=[-2.5134060737781389134 ,.05121449738612254930] 
dist 91=[-2.5147065593206548873 ,.17702441680719086495] 
dist 92=[-2.4835435096630791469 ,.31924843346709805386] 
dist 93=[-2.4690443109295986577 ,.46967755755804201203] 
dist 94=[-2.4541007757371067193 ,.65477834033274549372] 
dist 95=[-2.4431467614200094888 ,.93538606557563726933] 
dist 96=[-1.5666304346920488331 ,1.2134799213879850191 ] 
dist 97=[-1.5668399490954495888 ,1.3885594828915693956 ] 
dist 98=[-1.5614169560189835458 ,1.5215966717391215475 ] 
dist 99=[-1.5562699255300601136 ,1.6319247966152510019 ] 
dist 100=[-1.5187528263425067304 ,1.7210271305783252914 ] 
dist 101=[-1.5076524566640723277 ,1.7693603534835477540 ] 
dist 102=[-1.4766819802382678891 ,1.7970527826201963758 ] 
dist 103=[-1.4636792092059398765 ,1.8037768791125419434 ] 
dist 104=[-1.3087903598149389183 ,1.7276522979670034104 ] 
dist 105=[-1.2830615960155886034 ,1.7109937715333263075 ] 
dist 106=[-1.2148442472746682605 ,1.6981863037410479721 ] 
dist 107=[-1.2010601852662025905 ,1.6872938595864161427 ] 
dist 108=[-1.0753485930085195712 ,1.6872401191296701541 ] 
dist 109=[-1.0487370350125336746 ,1.7022310122005712567 ] 
dist 110=[-1.0127581140585791859 ,1.7061235228634096528 ] 
dist 111=[-1.0000661334797488928 ,1.7034861786026726465 ] 
dist 112=[-.55004506153078772538,1.1014125983316889628 ] 
dist 113=[-.49825284173585566349,1.0474430768921934324 ] 
dist 114=[-.38471600347937112886,.91735866799707708204] 
dist 115=[-.35699063693975228234,.89501480384562617124] 
dist 116=[-.22388686874441919494,.77224607371354177532] 
dist 117=[-.19940963778707906639,.74756611705307341601] 
dist 118=[-.14279093697266993147,.71588713495507574157] 
dist 119=[-.13558679144277762646,.70600694290958605061] 
dist 120=[-.30017612597261067419,.74929036094703836554] 
dist 121=[-.41599515860567189418,.77943908337402504853] 
dist 122=[-.51826572943977109044,.80573319469966113682] 
dist 123=[-.62879798810076688799,.83361790778991369998] 
dist 124=[-.7362297398777903481 ,.86033688971608807274] 
dist 125=[-.82613993895626061128,.88196608726623342995] 
dist 126=[-.92050488649974099022,.90394287732932642347] 
dist 127=[-1.0457414750729919588 ,.93202712311238370309] 
dist 128=[-1.1659788962809791555 ,.95759033920201194368] 
dist 129=[-1.2403930546872368390 ,.96950266041015720794] 
dist 130=[-1.2955839529090702781 ,.9743807966263385274 ] 
dist 131=[-1.3390780788032506038 ,.97408644297654661046] 
dist 132=[-1.3718099162919842058 ,.95934113425043352823] 
dist 133=[-1.3840374727796967032 ,.95313608437402633158] 
dist 134=[-1.3882453233095894901 ,.94210007375084801078] 
dist 135=[-1.3889500825113915073 ,.9375941609219316519 ] 
dist 136=[-1.3432744038781834705 ,.80617803856858021233] 
dist 137=[-1.3321062454775600017 ,.78587858022584065358] 
dist 138=[-1.3050872457368024312 ,.74255245627845288296] 
dist 139=[-1.2945018480582170015 ,.72937870647567207133] 
dist 140=[-1.2386354709606456090 ,.67136839536307339369] 
dist 141=[-1.2249450732165762597 ,.65929311899851831493] 
dist 142=[-1.1909877929944060436 ,.6240392639020869345 ] 
dist 143=[-1.1784595862130162048 ,.61876843618874124812] 
dist 144=[-.77336064933601575476,.28329971455991943155] 
dist 145=[-.73682504411519138741,.46931119246529755308] 
dist 146=[-.65166782660886396272,.62141875190025122294] 
dist 147=[-.6331957785874807047 ,.76707736606734997662] 
dist 148=[-.51565226997689296916,.89748675675450647874] 
dist 149=[-.49306613580388052913,.98872890508119466338] 
dist 150=[-.45071290897873711021,1.0687835873516483624 ] 
dist 151=[-.43999934007620075504,1.1545410191121365385 ] 
dist 152=[-.28058864464513182611,1.2320036308524899646 ] 
dist 153=[-.25826056828854591116,1.2789503917153502188 ] 
dist 154=[-.20792720719525715573,1.3125563426608045385 ] 
dist 155=[-.19714330499033484362,1.3367688442289792002 ] 
dist 156=[-.13452544271918601339,1.3531118493248183419 ] 
dist 157=[-.12311050406670310764,1.3561402312577031655 ] 
dist 158=[-.10010144005666012297,1.3525974082467822602 ] 
dist 159=[-.09416376088303457746,1.3493558118490224189 ] 
dist 160=[-.04690702444570910725,.83630256036105098324] 
dist 161=[-.07555733189595390959,.90258912840531686143] 
dist 162=[-.17226690584605597003,.97248846269021732457] 
dist 163=[-.27253283609725035866,1.0348538735026522283 ] 
dist 164=[-.36605078346762056291,1.0876307561806859590 ] 
dist 165=[-.43790672508933093188,1.1192588664614209990 ] 
dist 166=[-.5076460018799215392 ,1.1414702079350111730 ] 
dist 167=[-.59271833705990861315,1.1566629328953198581 ] 
dist 168=[-.67281466107822875245,1.1663606067551975369 ] 
dist 169=[-.7226955301132738041 ,1.1670346190444163376 ] 
dist 170=[-.7599927977019128826 ,1.1630203377270212345 ] 
dist 171=[-.78986849703284012685,1.1581810864143325026 ] 
dist 172=[-.81270202049767590432,1.1227038831835561951 ] 
dist 173=[-.82189188300104313505,1.1121187108008783616 ] 
dist 174=[-.8255841819628776786 ,1.0928106586234409668 ] 
dist 175=[-.82647730002893055308,1.0861382406112264199 ] 
dist 176=[-.88200244461916765827,.80289107193659073122] 
dist 177=[-.93604441329564400017,.89104451151991922176] 
dist 178=[-.97659979837888189661,.9596452922110080297 ] 
dist 179=[-1.0094040207086263786 ,1.0194608718234645714 ] 
dist 180=[-1.0347546482189728349 ,1.0690169059051119903 ] 
dist 181=[-1.0455568301982736511 ,1.0966712986152502774 ] 
dist 182=[-1.0495130198329257095 ,1.1135578653205523270 ] 
dist 183=[-1.0481852368011905211 ,1.1201374150706143267 ] 
dist 184=[-1.0605724710343756238 ,1.1217153458175153369 ] 
dist 185=[-1.1016404013653333120 ,1.1189594661315839873 ] 
dist 186=[-1.1316648196546662726 ,1.1124785546930725165 ] 
dist 187=[-1.1544694089215447773 ,1.1081667724639348371 ] 
dist 188=[-1.1708882743311063152 ,1.0800018526537803818 ] 
dist 189=[-1.1754258513615927358 ,1.0720527673052822699 ] 
dist 190=[-1.1746517472545603977 ,1.0469095654885539129 ] 
dist 191=[-1.1710163567679507006 ,1.0394601769337219728 ] 
dist 192=[-.93965336853499898653,.49400665829184025646] 
dist 193=[-.93919473910571864667,.62533481571604520912] 
dist 194=[-.93293099722080588951,.73265401682039641135] 
dist 195=[-.92827256342798351688,.83529266276624708277] 
dist 196=[-.89436460578513779423,.92709053660709230629] 
dist 197=[-.88466856659928236067,.99114120679576622756] 
dist 198=[-.86911048736807827259,1.0471504815305318925 ] 
dist 199=[-.86345561451245017068,1.1068542982695428034 ] 
dist 200=[-.71547086833741996532,1.1594852353791946335 ] 
dist 201=[-.69373407394892869246,1.1872638954039002851 ] 
dist 202=[-.64645837766906423006,1.2021693074316956020 ] 
dist 203=[-.63235222878580518917,1.2053753732956372824 ] 
dist 204=[-.57131217832805448329,1.1998413467182614986 ] 
dist 205=[-.55887451970234774017,1.1955038922157065036 ] 
dist 206=[-.52561171981868255817,1.1897819582903472738 ] 
dist 207=[-.5194987051641412098 ,1.1848116807236632541 ] 
dist 208=[-.09551020947935646559,.90870249945652032468] 
dist 209=[-.16124532932707431737,.95727729783100432643] 
dist 210=[-.28199242720177136159,1.0117277497297215670 ] 
dist 211=[-.40247484500058431518,1.0571029419115978465 ] 
dist 212=[-.51357088633809210363,1.0931762461002390491 ] 
dist 213=[-.5968556198792832531 ,1.1104997472205758050 ] 
dist 214=[-.67572579192038705189,1.1186617713178002461 ] 
dist 215=[-.76920392513212139639,1.1189438890914188605 ] 
dist 216=[-.85587869528380189353,1.1019730753818100909 ] 
dist 217=[-.90759562471138222144,1.0955888561182605010 ] 
dist 218=[-.94361754270601512091,1.0800754036083290597 ] 
dist 219=[-.96764990338956280778,1.0732169230285861292 ] 
dist 220=[-.98489653352680467986,1.0346333868875415600 ] 
dist 221=[-.99383297311437350927,1.0247087253514665974 ] 
dist 222=[-.99839396610253752832,.99819217929125084586] 
dist 223=[-.99817108258359766085,.98844488700205545779] 
dist 224=[-.89068856368861904228,.87730786523562479538] 
dist 225=[-.88926882500364782595,.94835754798628211289] 
dist 226=[-.93059662626595112837,1.0019106080894787864 ] 
dist 227=[-.96473585618295721084,1.0455842651215220020 ] 
dist 228=[-.99165365224089047564,1.0795782924143358768 ] 
dist 229=[-1.0041562554532525653 ,1.0944974016017238004 ] 
dist 230=[-1.0093252630884666633 ,1.1013088768652971467 ] 
dist 231=[-1.0090603053845177724 ,1.1029439512857236002 ] 
dist 232=[-1.0117487184307140882 ,1.0726582654774328307 ] 
dist 233=[-1.0548022522435356047 ,1.0642891287399258208 ] 
dist 234=[-1.0854516774335037395 ,1.0472326397651463589 ] 
dist 235=[-1.1071892650299330379 ,1.0406532445809218947 ] 
dist 236=[-1.1217971578383123671 ,1.0062285783564943902 ] 
dist 237=[-1.1248992773349532177 ,.99783154726556215823] 
dist 238=[-1.1221589634723547596 ,.96825030678043653397] 
dist 239=[-1.1207136207347611119 ,.96391809366508968725] 
dist 240=[-.99381636391312209847,.53429062731694108287] 
dist 241=[-1.0060826374094727165 ,.65067980021608364318] 
dist 242=[-1.0110520108553422434 ,.74518526102230578119] 
dist 243=[-1.0106816582791727597 ,.83456133854302064705] 
dist 244=[-.99512394784815278378,.91382264795732538466] 
dist 245=[-.98871309638523701052,.967956579262871352  ] 
dist 246=[-.97725632761009873412,1.0140668756230194253 ] 
dist 247=[-.97263016623284405996,1.0613040195437474232 ] 
dist 248=[-.8392872545802855731 ,1.1021948346130442106 ] 
dist 249=[-.81882196917837059894,1.1229742565457345205 ] 
dist 250=[-.77467685533261572456,1.1333165801493550834 ] 
dist 251=[-.76122710340896997912,1.1349274454593265933 ] 
dist 252=[-.70191429537865475458,1.1249013842142169072 ] 
dist 253=[-.6895669767336545946 ,1.1189350948968006430 ] 
dist 254=[-.654769606542075028  ,1.1106123971754146600 ] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 0, 2, 0, 2] 
dist 0=[49.508653890517967682  ,49.508653890517967682  ] 
dist 1=[48.680997155909026822  ,50.147202660277362982  ] 
dist 2=[47.621896699765003045  ,50.451028915868257064  ] 
dist 3=[46.187454259788435717  ,50.583806129975421119  ] 
dist 4=[43.860576367226993312  ,50.586308773397124499  ] 
dist 5=[41.458062394832814174  ,50.269669649533032260  ] 
dist 6=[39.721468855038003623  ,50.154980373178320104  ] 
dist 7=[38.135272438092098823  ,49.604891381689624759  ] 
dist 8=[36.333366263573006308  ,48.741084629801524010  ] 
dist 9=[34.524195421990646214  ,48.204337470319409188  ] 
dist 10=[32.908878377709823979  ,48.032638855741966021  ] 
dist 11=[31.121060484901553345  ,47.633404263806345827  ] 
dist 12=[28.622681423836726528  ,47.477044947292258959  ] 
dist 13=[26.096930446030185582  ,46.707993775515939454  ] 
dist 14=[24.199658451612549372  ,46.520177307953375603  ] 
dist 15=[22.392939041717887041  ,45.341596158852385382  ] 
dist 16=[20.228702225585461578  ,43.193580281264500492  ] 
dist 17=[17.990443292879139225  ,27.864110356108139288  ] 
dist 18=[15.887789706246617393  ,26.400789137480921701  ] 
dist 19=[13.473287663144739198  ,23.638606654246440766  ] 
dist 20=[9.9887891093704307472 ,23.483967859006621151  ] 
dist 21=[6.5399230438712784825 ,18.841057199871154147  ] 
dist 22=[4.2676795206374907360 ,18.207615327889714426  ] 
dist 23=[2.4128266677199191837 ,16.881286071406924863  ] 
dist 24=[.63156434126883010905,16.580542972813937083  ] 
dist 25=[-.9755069152759481546 ,14.318916383583066216  ] 
dist 26=[-2.1345166061334623750 ,13.934310602435156683  ] 
dist 27=[-3.1929429676333611765 ,12.855262425440835902  ] 
dist 28=[-4.3984534765409808616 ,11.458338430100953401  ] 
dist 29=[-5.5104424412388393867 ,4.1806180959116721931 ] 
dist 30=[-6.1952026730022173377 ,3.4943171592643926626 ] 
dist 31=[-6.7020791825650287965 ,1.6698429785913098428 ] 
dist 32=[-8.4114781591606352830 ,-.4939647828188381812 ] 
dist 33=[-11.061123942949066544  ,-3.8123871402504475410 ] 
dist 34=[-12.712974692841236406  ,-4.1271192723797303925 ] 
dist 35=[-13.959728239688342184  ,-4.7435952052172922702 ] 
dist 36=[-14.990594008010469886  ,-4.3383790168673963153 ] 
dist 37=[-15.815852089169059190  ,-3.5297812748602960275 ] 
dist 38=[-16.240799201627855953  ,-2.9313596410833723452 ] 
dist 39=[-16.470792714022039337  ,-2.3742740983605411061 ] 
dist 40=[-16.516758455711964533  ,-1.7302117406625320529 ] 
dist 41=[-16.266087621312181136  ,-1.0812955753069420757 ] 
dist 42=[-16.166894449839867005  ,-.5046584999317983895 ] 
dist 43=[-16.063068871371340243  ,.1285567195851671271 ] 
dist 44=[-15.988149574046788176  ,1.0033809911661384098 ] 
dist 45=[-15.787799864534560235  ,1.8769834946820133143 ] 
dist 46=[-15.692790928864596225  ,2.5053890121571817913 ] 
dist 47=[-15.512069497962735084  ,3.0739375215448048211 ] 
dist 48=[-15.439088371026913458  ,3.7087465203662654394 ] 
dist 49=[-6.3664913260347840616 ,4.3369583462589050872 ] 
dist 50=[-5.5878900769303402251 ,4.8792037278381911432 ] 
dist 51=[-3.7785449680726517790 ,5.4619420879156945805 ] 
dist 52=[-3.4762483257000532142 ,6.2517463395937003532 ] 
dist 53=[-1.1180906838583952546 ,7.0232578907113843417 ] 
dist 54=[-.70204628012069877819,7.5330023357914400628 ] 
dist 55=[-.04707770057449991571,7.9482588283186306081 ] 
dist 56=[.11135184362032141222,8.3427221853367029703 ] 
dist 57=[1.9140766280952128206 ,8.6932876282214483532 ] 
dist 58=[1.7601858640762127136 ,8.9333651207047694721 ] 
dist 59=[1.5228911171160391533 ,9.1382967368910961632 ] 
dist 60=[1.1113164609694916901 ,9.3485962098923923964 ] 
dist 61=[.6848398828131754145 ,9.5263501696950301202 ] 
dist 62=[.3880662455912319853 ,9.6013964347457182253 ] 
dist 63=[.1306338690400472090 ,9.6154331238283883768 ] 
dist 64=[-.1390383269086529188 ,9.5497092636008398571 ] 
dist 65=[-.39477505057212173128,4.8842509987996675110 ] 
dist 66=[-.59667382800200562969,4.8639603842338148168 ] 
dist 67=[-.79714646952724941203,4.8171376077286822103 ] 
dist 68=[-1.0472307336586967667 ,4.7935671198028087182 ] 
dist 69=[-1.2842784302529896026 ,2.5781875876027941933 ] 
dist 70=[-1.4327727299626727925 ,2.4858185979534579574 ] 
dist 71=[-1.5444212951107021510 ,2.3907423630933089355 ] 
dist 72=[-1.6345287238126352381 ,2.3734727884792613417 ] 
dist 73=[-1.7041863305689228100 ,1.4383597180072532201 ] 
dist 74=[-1.7342663555630403881 ,1.3232141294211828006 ] 
dist 75=[-1.7471479378284416163 ,1.0883988237070131426 ] 
dist 76=[-1.9330158926255283376 ,1.0283717343536309625 ] 
dist 77=[-2.2783539888746470560 ,.8172542906497225162 ] 
dist 78=[-2.4946876387207851283 ,.7733599419110853059 ] 
dist 79=[-2.6579443369641422431 ,.7184250567753727412 ] 
dist 80=[-2.7914658883286570818 ,.7079929661594730743 ] 
dist 81=[-2.8957341567563313728 ,-.6370100287843671793 ] 
dist 82=[-2.9422321852715950950 ,-.7459425426557396537 ] 
dist 83=[-2.9639571533338902609 ,-.95990113806084376134] 
dist 84=[-2.9693588287888623721 ,-1.0092400565137092416 ] 
dist 85=[-1.9522062870733467121 ,-1.0224283173310938876 ] 
dist 86=[-1.8796100347626686760 ,-.9010049582509920393 ] 
dist 87=[-1.7955103073236699148 ,-.76270438604774122476] 
dist 88=[-1.9231835370125577445 ,-.56552199405032336443] 
dist 89=[-2.0655797711985573557 ,-.3459178904007261149 ] 
dist 90=[-2.1543040265348929049 ,-.1181401566112183545 ] 
dist 91=[-2.2208865405097037098 ,.1589789447390045296 ] 
dist 92=[-2.2748348128379596338 ,.57546945742370849996] 
dist 93=[-2.3165861436747920511 ,.99075796231155163112] 
dist 94=[-2.3344389767218028398 ,1.2630834348168236195 ] 
dist 95=[-2.3393058234892856543 ,1.4825333666214856923 ] 
dist 96=[-2.3370910714945151455 ,1.6868411712646439004 ] 
dist 97=[-1.4002226518527168322 ,1.8654764718731132364 ] 
dist 98=[-1.4455207214486750245 ,1.9824852918369590187 ] 
dist 99=[-1.5007206254202545618 ,2.0765943469993224860 ] 
dist 100=[-1.5836086166789322374 ,2.1638442849858882614 ] 
dist 101=[-1.6651200307564448044 ,2.2376039803243996426 ] 
dist 102=[-1.7148197760915189243 ,2.2778852020177020325 ] 
dist 103=[-1.7505186958926159146 ,2.3012598957058700483 ] 
dist 104=[-1.7761835245208662775 ,2.3942294443164962208 ] 
dist 105=[-1.7932007316123100469 ,2.5250667474643975814 ] 
dist 106=[-1.7950436525626094008 ,2.5958744993160959740 ] 
dist 107=[-1.7892953979378463030 ,2.6363916618937042156 ] 
dist 108=[-1.7814553537594898792 ,2.6463300446889650065 ] 
dist 109=[-1.7197918364093028670 ,2.6446030027127591593 ] 
dist 110=[-1.7051568663208915162 ,2.6385529566761477460 ] 
dist 111=[-1.6539306894404853432 ,2.6282689241169433026 ] 
dist 112=[-1.6454852134313268576 ,2.6182897684763068964 ] 
dist 113=[-1.5092256998989332204 ,2.5871054193866650544 ] 
dist 114=[-1.4779055728744559767 ,2.5728693287350189834 ] 
dist 115=[-1.4516919413800420604 ,2.5353588542976316961 ] 
dist 116=[-1.4431317965787317047 ,2.5184275903666901426 ] 
dist 117=[-.99643129290761193208,1.1085331502555108232 ] 
dist 118=[-.98289902852063897886,.98214747572280227766] 
dist 119=[-.9481453453754190515 ,.8025817232232217756 ] 
dist 120=[-1.0261491753335572772 ,.81526609986407304931] 
dist 121=[-1.2815515127282014472 ,.84393093200235712267] 
dist 122=[-1.4757847537235744197 ,.86527005556387848971] 
dist 123=[-1.6624392019389041498 ,.88525689656718399638] 
dist 124=[-1.8876011426522055769 ,.90849935305287735717] 
dist 125=[-2.0984525627218558222 ,.92845667410369328618] 
dist 126=[-2.2279934074063258676 ,.93532877029392635191] 
dist 127=[-2.3228227329152197030 ,.93724975516449047273] 
dist 128=[-2.3951330228891890837 ,.93748276481794019582] 
dist 129=[-2.4484520308147359387 ,.90518536522507496515] 
dist 130=[-2.4674753342828361469 ,.8967498581412900156 ] 
dist 131=[-2.4725694696449026624 ,.89160750695989306016] 
dist 132=[-2.4702920770746518273 ,.88958203613173384185] 
dist 133=[-2.3542379807329916692 ,.6978463020568591913 ] 
dist 134=[-2.4572012030496034389 ,.67140234406385311728] 
dist 135=[-2.5410496907724010662 ,.62271648043691511024] 
dist 136=[-2.6008400997935761673 ,.64918897451565503691] 
dist 137=[-2.6427091213947881816 ,.86210957697264579378] 
dist 138=[-2.6550197801112350221 ,1.0316180055594623389 ] 
dist 139=[-2.6549090981462558886 ,1.2017772728857241674 ] 
dist 140=[-2.6471942919784752128 ,1.4173017816861740798 ] 
dist 141=[-2.4926087591751479210 ,1.6242390056866527144 ] 
dist 142=[-2.4619555721053840382 ,1.7601287695997056399 ] 
dist 143=[-2.3927422118472640119 ,1.8700032842423283733 ] 
dist 144=[-2.3685058687798067268 ,1.9731141985582445462 ] 
dist 145=[-2.2493284531532270937 ,2.0640113715159233712 ] 
dist 146=[-2.2217434690891021851 ,2.1251438183463621878 ] 
dist 147=[-2.1476046568795974222 ,2.1762137396195599315 ] 
dist 148=[-2.1264290961009739214 ,2.2269596310356623577 ] 
dist 149=[-.48345190551864343534,2.2676693655454375806 ] 
dist 150=[-.46000039551251514982,2.3153124676193552666 ] 
dist 151=[-.4100284761200263651 ,2.3968322682414983492 ] 
dist 152=[-.39604253442520386718,2.4552843685683289234 ] 
dist 153=[-.33958164143929021846,2.4965689104133382184 ] 
dist 154=[-.32848186444362105914,2.5095621298630373600 ] 
dist 155=[-.30124030139485226196,2.5103006788543706847 ] 
dist 156=[-.29586544691350715842,2.5029505964095263591 ] 
dist 157=[.05183386492388302037,2.6470032429361196819 ] 
dist 158=[.08035588824969569110,2.7496042621207969693 ] 
dist 159=[.00048614673855352618,2.8170826520535377592 ] 
dist 160=[-.07942963149186812897,2.8542814780803461946 ] 
dist 161=[-.15322500619306038429,2.8757360625380330048 ] 
dist 162=[-.20866839602414096734,2.8803723003104238799 ] 
dist 163=[-.26126723373966675579,2.8735713613013775584 ] 
dist 164=[-.3237093353410774784 ,2.8668083759695650283 ] 
dist 165=[-.59013803770913915613,2.4706108767840952878 ] 
dist 166=[-.9320145496418868355 ,2.4463441837359798536 ] 
dist 167=[-1.2131571837721820076 ,2.3695739655824278544 ] 
dist 168=[-1.4849717821699018008 ,2.3546248560108260166 ] 
dist 169=[-1.7300255309893767029 ,2.1698561300248075574 ] 
dist 170=[-1.9043557265764435620 ,2.1278018725676510904 ] 
dist 171=[-2.0602900609745225680 ,2.0841264621959162463 ] 
dist 172=[-2.2319190366548608777 ,2.0645992898486017993 ] 
dist 173=[-2.3874536753015475100 ,1.5209215414221928017 ] 
dist 174=[-2.4791499837493242741 ,1.4471578705408040000 ] 
dist 175=[-2.5416545498100943284 ,1.2982810580195826461 ] 
dist 176=[-2.5806755072334556416 ,1.2581622809658290431 ] 
dist 177=[-2.6045039072597692840 ,1.1071801697131163534 ] 
dist 178=[-2.6067686686822402076 ,1.0738316690384262370 ] 
dist 179=[-2.5991066265871792908 ,1.0102133231506779170 ] 
dist 180=[-2.5885197735429275022 ,.9929643221729765699 ] 
dist 181=[-.76821098190210267124,.27639276406024749203] 
dist 182=[-.78987062972724999563,.3712186455290947717 ] 
dist 183=[-.80982366032866572101,.44717881746755398348] 
dist 184=[-.82360033805622224935,.51724006703473987273] 
dist 185=[-.83242151690231514254,.57813800972482828511] 
dist 186=[-.83498581993327471424,.61752717955511560376] 
dist 187=[-.8337597899338181262 ,.64870252848187065346] 
dist 188=[-.83194737558546441716,.67681944745609778648] 
dist 189=[-.6978438374126698910 ,.70092292848288915838] 
dist 190=[-.6833351901845098583 ,.71608006687503372082] 
dist 191=[-.6451331984547280549 ,.72758810524225191534] 
dist 192=[-.6375005093418570349 ,.73712598597746336132] 
dist 193=[-.5680948701881752615 ,.74466601774799965565] 
dist 194=[-.55346143725476523335,.74819930683835465594] 
dist 195=[-.53376216511912320502,.74947124672025065962] 
dist 196=[-.52680692354220941255,.7479843464174553147 ] 
dist 197=[-.47555423734411351613,.724669105992574234  ] 
dist 198=[-.47331453097937219532,.75503303842401591946] 
dist 199=[-.46600541704729626772,.77494150323573571021] 
dist 200=[-.46259568160916144947,.78575155479136599836] 
dist 201=[-.44165777278508159366,.79215449565655991705] 
dist 202=[-.4361492461941353502 ,.79447277265841718982] 
dist 203=[-.42611723943789857736,.79424280627221989058] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 0, 1, 2] 
dist 0=[50.335441173147194029  ,50.335441173147194029  ] 
dist 1=[50.076223329357202838  ,50.526134383206433269  ] 
dist 2=[49.603136111710887231  ,50.725451844855652075  ] 
dist 3=[48.881911164772981069  ,50.968974620227644962  ] 
dist 4=[47.631727918859511808  ,51.335877881777596136  ] 
dist 5=[46.113688760986705557  ,51.687523739794328852  ] 
dist 6=[44.322754297295663253  ,51.870127159151708451  ] 
dist 7=[41.984948527322476157  ,51.963303816134844698  ] 
dist 8=[38.282921333256102860  ,51.958181960881398408  ] 
dist 9=[34.512930860834064859  ,51.889837473289768072  ] 
dist 10=[31.903618019382297092  ,51.810726438987613321  ] 
dist 11=[29.639014683054015794  ,51.545714481284614355  ] 
dist 12=[27.245392303965699714  ,51.403096761587326336  ] 
dist 13=[24.944661620337126848  ,39.438032358265424196  ] 
dist 14=[23.050783850569207389  ,38.348979529424708485  ] 
dist 15=[21.086671717354425790  ,35.671673464448875623  ] 
dist 16=[18.504980476652265087  ,35.264155747293638602  ] 
dist 17=[15.966334502326052879  ,31.186780422571331612  ] 
dist 18=[14.173879778637798330  ,30.408878710263188749  ] 
dist 19=[12.578180952085933835  ,29.498700517755557946  ] 
dist 20=[10.825030745252458316  ,29.272191050433958988  ] 
dist 21=[9.0951533898251654497 ,22.170598130528080420  ] 
dist 22=[7.5919157200435865927 ,21.270424850952651877  ] 
dist 23=[5.9585946645816669712 ,19.435413189982670870  ] 
dist 24=[3.7080468105926015560 ,18.958025673712168688  ] 
dist 25=[1.5157172585218070349 ,17.223286522605047699  ] 
dist 26=[.1148119111277895405 ,16.864705204134261809  ] 
dist 27=[-.9836391712478985822 ,16.243016090423987388  ] 
dist 28=[-2.5229833447447466125 ,16.099307177819970409  ] 
dist 29=[-5.2130729272178304430 ,4.2421507424199220462 ] 
dist 30=[-6.9322132077458156749 ,3.2334739065233656361 ] 
dist 31=[-8.2786899759467029577 ,.99904329520284756337] 
dist 32=[-9.4795078930697442189 ,.59888465925022138296] 
dist 33=[-10.503664235725128920  ,-1.9638798460701947419 ] 
dist 34=[-11.144288456426828456  ,-2.3944353355630656638 ] 
dist 35=[-11.631555471429213759  ,-3.1998320870104158221 ] 
dist 36=[-12.043258158389413431  ,-3.3746861440080290693 ] 
dist 37=[-12.378749771290832908  ,-3.7111320991501811036 ] 
dist 38=[-12.561448048458705596  ,-3.2881578745202425481 ] 
dist 39=[-12.865276424764182443  ,-2.7143139983609143203 ] 
dist 40=[-13.201711034553467980  ,-1.7876812702612219772 ] 
dist 41=[-13.446047814960035513  ,-.84161089634921205701] 
dist 42=[-13.573853353855175256  ,-.19007925993898290683] 
dist 43=[-13.641627770342198500  ,.36858202885464886058] 
dist 44=[-13.646003955692057171  ,.94432212044027581694] 
dist 45=[-7.2246646337306319981 ,1.4850239612430246699 ] 
dist 46=[-6.7465618541009981770 ,1.9039393771798586755 ] 
dist 47=[-5.5845875606632365901 ,2.3126432970182057254 ] 
dist 48=[-5.4100152947975954940 ,2.8125557402267172777 ] 
dist 49=[-3.7196976757779102191 ,3.2812331888929557758 ] 
dist 50=[-3.4087792326478333671 ,3.5652902301686671028 ] 
dist 51=[-3.0234221095970726696 ,3.7673173803705506017 ] 
dist 52=[-2.9360582645461666784 ,3.9086884810156022333 ] 
dist 53=[-.4375366061596095743 ,4.4861322102705960796 ] 
dist 54=[-.13562055720513382061,5.0272028337766222175 ] 
dist 55=[.51389644063813267509,5.4346162488973490961 ] 
dist 56=[.64758518754736637235,5.7671668289623686507 ] 
dist 57=[1.1934912057854286510 ,6.0319323088007110918 ] 
dist 58=[.86370745789219962363,6.1686610730850591208 ] 
dist 59=[.56678997849234563604,6.2391796138267544361 ] 
dist 60=[.23743158653855130339,6.2521530097241894974 ] 
dist 61=[-.08732729591641971206,6.0289613475579699779 ] 
dist 62=[-.36592260997982270612,5.9872482635039237625 ] 
dist 63=[-.6639640371092064014 ,5.8406379709154836231 ] 
dist 64=[-1.0663689872368903876 ,5.8115010293666533064 ] 
dist 65=[-1.4647123296746056186 ,5.4216240090302870958 ] 
dist 66=[-1.7465633154616243287 ,5.3315997012803873525 ] 
dist 67=[-1.9970626649254418575 ,5.2408844565655342164 ] 
dist 68=[-2.2703025840835592948 ,5.2005493265946064503 ] 
dist 69=[-2.5373375622582745639 ,4.9144388589441785195 ] 
dist 70=[-2.7630932274042454413 ,4.9553594504809156884 ] 
dist 71=[-3.0019652897393958516 ,4.9692145601943344303 ] 
dist 72=[-3.3213869092341414191 ,4.9635539535290804196 ] 
dist 73=[-3.6257222004970240651 ,4.8793901743561609229 ] 
dist 74=[-3.8043851192005048267 ,4.8481009513432845377 ] 
dist 75=[-3.9253523165499624143 ,4.8002152249966975004 ] 
dist 76=[-3.9993862577503072196 ,4.7790286310306520290 ] 
dist 77=[-4.0484910189027829640 ,4.1539699007721185304 ] 
dist 78=[-4.0699390916348316802 ,4.0646926047149803401 ] 
dist 79=[-4.0752818644290441329 ,3.8291668247665640083 ] 
dist 80=[-4.0669705588045770149 ,3.7854301402851674910 ] 
dist 81=[-4.1184783710267097687 ,3.3554115244643286342 ] 
dist 82=[-4.2784682248686692036 ,3.2647779768647689893 ] 
dist 83=[-4.3855728234608045101 ,3.1538323254774028738 ] 
dist 84=[-4.4489261688390317878 ,3.1103904231793274703 ] 
dist 85=[-4.5016297961256358361 ,2.8919009853310630803 ] 
dist 86=[-4.6634304617513390651 ,2.9603228978979170164 ] 
dist 87=[-4.7903173148651148350 ,3.0228027388828162777 ] 
dist 88=[-4.8959951672883220308 ,3.0935812937244251321 ] 
dist 89=[-4.9683347475541792846 ,3.1552199477416565716 ] 
dist 90=[-4.9842659203220732444 ,3.1812216992911396622 ] 
dist 91=[-4.9785324427266353924 ,3.1878131495693315502 ] 
dist 92=[-4.9715743117020058745 ,3.1842947897649032091 ] 
dist 93=[-3.8030837490518842690 ,3.1315565063735180940 ] 
dist 94=[-3.6888787832431747564 ,3.1121848088717241826 ] 
dist 95=[-3.3913792236871294627 ,3.0645111757261516268 ] 
dist 96=[-3.3450774490877225010 ,3.0438497478320354167 ] 
dist 97=[-2.8341048204477632303 ,3.2200392636945332577 ] 
dist 98=[-2.7321940610057226938 ,3.4237446406970289699 ] 
dist 99=[-2.6196436070300718086 ,3.5739548239690424095 ] 
dist 100=[-2.5891113045333991518 ,3.6904891449224372531 ] 
dist 101=[-1.5492325696842469734 ,3.7781748428495826953 ] 
dist 102=[-1.4169810506182939716 ,3.8132321060289788450 ] 
dist 103=[-1.1448117297006511655 ,3.8255039991630316582 ] 
dist 104=[-1.0734021529985898487 ,3.8222425797384935476 ] 
dist 105=[-1.6215515299409687995 ,3.6584951565412007244 ] 
dist 106=[-2.0752167928067348390 ,3.6254232691906865332 ] 
dist 107=[-2.4444529578677580176 ,3.5298297076403257418 ] 
dist 108=[-2.7950816831377962804 ,3.5016886155170289561 ] 
dist 109=[-3.1069791805542079369 ,3.2854147504494223060 ] 
dist 110=[-3.3216272343166200834 ,3.2341977169657680922 ] 
dist 111=[-3.5061917981834068800 ,3.1543019285381530290 ] 
dist 112=[-3.6980195276702798656 ,3.1278361518383702370 ] 
dist 113=[-3.8667496481118130937 ,2.4987444589650275004 ] 
dist 114=[-3.9591215638134239020 ,2.4092301560422296122 ] 
dist 115=[-4.0132714005797237457 ,2.2123932446499853645 ] 
dist 116=[-4.0294339829838465025 ,2.0431158328592814792 ] 
dist 117=[-4.0277272974004036101 ,1.4242153520279741230 ] 
dist 118=[-4.0161466824211888463 ,1.3804037601944339235 ] 
dist 119=[-3.9848892644903772810 ,1.1768364730335031211 ] 
dist 120=[-3.9664915151811170804 ,1.1518661524126731007 ] 
dist 121=[.50507906897747514443,1.1761921456346286284 ] 
dist 122=[.38619744781696594142,1.3605158078585642367 ] 
dist 123=[.18313310662446214516,1.5041489257320355774 ] 
dist 124=[-.11860194331688384549,1.6298532269093640652 ] 
dist 125=[-.41934455199604435787,1.7344489196198215732 ] 
dist 126=[-.62103442505132482112,1.7938290413413239840 ] 
dist 127=[-.78889621756125211371,1.8314795118696976312 ] 
dist 128=[-.95460301965143347121,1.8493446431232733235 ] 
dist 129=[-1.1063417554304887335 ,1.8587463838173137005 ] 
dist 130=[-1.2184446588098919626 ,1.8626159060447488539 ] 
dist 131=[-1.3230374198002096487 ,1.8631873544623269898 ] 
dist 132=[-1.4447946830058430172 ,1.8594234887037460705 ] 
dist 133=[-1.5566076356961165928 ,1.8531747712339379655 ] 
dist 134=[-1.6215034170772318881 ,1.8451480434713014308 ] 
dist 135=[-1.6644770844142782668 ,1.8306246081246809682 ] 
dist 136=[-1.6887800905332012892 ,1.8234473970148567385 ] 
dist 137=[-1.7034612972955525081 ,.75376613307576886922] 
dist 138=[-1.7080323962972423120 ,.66232356075371686381] 
dist 139=[-1.7060826223245820647 ,.44520719127924829681] 
dist 140=[-1.7020646955647394242 ,.41154359183872492042] 
dist 141=[-.3096444292116959899 ,.49792772091106804575] 
dist 142=[-.4346138629875293979 ,.63988139888813621133] 
dist 143=[-.5540296372012923800 ,.75409808419488504479] 
dist 144=[-.69710252285682513925,.86022814345162170922] 
dist 145=[-.83154837622950136236,.95296880315333445822] 
dist 146=[-.91653204674665079939,1.0137571798060925186 ] 
dist 147=[-.98156773794291767444,1.0627595745040942270 ] 
dist 148=[-1.0363960824184872085 ,1.1084725745302625708 ] 
dist 149=[-1.0804782152033612014 ,1.1472851108271863031 ] 
dist 150=[-1.1026236232457635863 ,1.1687491951307768869 ] 
dist 151=[-1.1139858571187989476 ,1.1816150148173730689 ] 
dist 152=[-1.1154350003152453866 ,1.1861059732851417747 ] 
dist 153=[-.85546968811485008175,1.1848562652211660236 ] 
dist 154=[-.83393468077219252518,1.1824975125329032512 ] 
dist 155=[-.78798395771291902744,1.1643212000986332539 ] 
dist 156=[-.77421771093431677442,1.1613437640625092523 ] 
dist 157=[-.72306240167788023137,.88084515881718068124] 
dist 158=[-.73185154632058261864,.85379011311250150949] 
dist 159=[-.74314540988352587819,.78579904772768225851] 
dist 160=[-.76080702247748412758,.77254554966228654711] 
dist 161=[-.77937041553969163825,.66156844033311647521] 
dist 162=[-.79426109577313778481,.6392432175664454179 ] 
dist 163=[-.80930098321208013411,.60641079579714663071] 
dist 164=[-.82845709106738975356,.59637146950370126643] 
dist 165=[-.84876543003790130531,.4150428352844847265 ] 
dist 166=[-.86840081925967061732,.47155442363711589744] 
dist 167=[-.89127672716508922804,.64137437927267234839] 
dist 168=[-.92451171501254203192,.89028464675976904504] 
dist 169=[-.95697725757816479554,1.1356761174919396734 ] 
dist 170=[-.97678203590175251793,1.2914516980811779392 ] 
dist 171=[-.99107115973761408566,1.4114469887485751634 ] 
dist 172=[-1.0015291769179174391 ,1.5140237666012049427 ] 
dist 173=[-1.0086911902056654474 ,1.5975801408962494683 ] 
dist 174=[-1.0098282486400561448 ,1.6416571399019246566 ] 
dist 175=[-1.0068480337680527336 ,1.6663460930119556224 ] 
dist 176=[-1.0042995886441017982 ,1.6725143192490372793 ] 
dist 177=[-.98502896479837805697,1.6619481116236481201 ] 
dist 178=[-.99366248980237636484,1.6573785115989053115 ] 
dist 179=[-1.0584316620800475560 ,1.6523968001470719943 ] 
dist 180=[-1.1403076702385943389 ,1.6455612429717102450 ] 
dist 181=[-1.2188947053633580422 ,1.6380690099891162744 ] 
dist 182=[-1.2705348862376273395 ,1.6304667102820437142 ] 
dist 183=[-1.3123411030757524958 ,1.6213370120190205774 ] 
dist 184=[-1.3516738382378530066 ,1.6142842720003067436 ] 
dist 185=[-1.3864157875344894045 ,.57606203290654291561] 
dist 186=[-1.4098964382893838864 ,.48830769861904302614] 
dist 187=[-1.4296262788864568239 ,.28840658042394613267] 
dist 188=[-1.4493946484666530795 ,.58055299359520309417] 
dist 189=[-1.4651041447719744676 ,.87678746979927950986] 
dist 190=[-1.4686326087296509626 ,1.0708188038469557090 ] 
dist 191=[-1.4660721339122844026 ,1.2271681536034471501 ] 
dist 192=[-1.4616715582532306100 ,1.3730011402108185629 ] 
dist 193=[-1.4259559999013294076 ,1.5009379191820369811 ] 
dist 194=[-1.4148139405484922662 ,1.5858579729291174480 ] 
dist 195=[-1.3898455972168403482 ,1.6555477121316891327 ] 
dist 196=[-1.3799874517637112894 ,1.7226966576112159607 ] 
dist 197=[-1.3592728921897818181 ,1.7799497937824055828 ] 
dist 198=[-1.4011928384335597764 ,1.8101414818302470926 ] 
dist 199=[-1.4354480178621991360 ,1.8263012550010480093 ] 
dist 200=[-1.4682379799866923677 ,1.8275885657378616282 ] 
dist 201=[-1.4945856870126454315 ,1.8213501597011206931 ] 
dist 202=[-1.5031277016614638420 ,1.8151531179956195666 ] 
dist 203=[-1.5041511576366534121 ,1.7927911125575207606 ] 
dist 204=[-1.5004803628740201735 ,1.7808731737784152054 ] 
dist 205=[-1.4995370008748691202 ,1.1645405102872272414 ] 
dist 206=[-1.5006989749121111200 ,1.1021831326433415330 ] 
dist 207=[-1.4904677372439131751 ,.95057055658505296524] 
dist 208=[-1.4871682001835969464 ,.92459974758488958258] 
dist 209=[-1.3994388354839798726 ,.92611467980067114818] 
dist 210=[-1.3823843167530311446 ,1.0100335265102934559 ] 
dist 211=[-1.3367054671956775376 ,1.0816941440509342529 ] 
dist 212=[-1.3232554922182505536 ,1.1553759185219384657 ] 
dist 213=[-1.2317002020320132841 ,1.2247361898852665465 ] 
dist 214=[-1.2105788294774049005 ,1.2791505622882855411 ] 
dist 215=[-1.1736787386109889436 ,1.3330571259975146627 ] 
dist 216=[-1.1631211193857176875 ,1.4003947353866024890 ] 
dist 217=[-.14843844274727861544,1.4620866370688757479 ] 
dist 218=[-.22153475732896824349,1.4934597087201037130 ] 
dist 219=[-.31674682178770518874,1.5099602541568089388 ] 
dist 220=[-.46708202523928685915,1.5263534568402334795 ] 
dist 221=[-.61975106043461663517,1.6808926436398276429 ] 
dist 222=[-.72427832488134318996,1.7724750627492786365 ] 
dist 223=[-.81359087368122182843,1.8354703075492829771 ] 
dist 224=[-.90552855391568246918,1.8759102348139069566 ] 
dist 225=[-.99214850516042459395,1.9040397176359699626 ] 
dist 226=[-1.0602342368200163536 ,1.9179016507817144761 ] 
dist 227=[-1.1278016273205965249 ,1.9239608009200901602 ] 
dist 228=[-1.2123511860982906107 ,1.9209503479019051058 ] 
dist 229=[-1.2930666772514712444 ,1.7141141703012365998 ] 
dist 230=[-1.3453295914357597496 ,1.6810880325328516423 ] 
dist 231=[-1.3867673523881721074 ,1.6769985941584019763 ] 
dist 232=[-1.4242733310147461816 ,1.6731457943881025830 ] 
dist 233=[-1.4563818390532020030 ,1.4972221011286085625 ] 
dist 234=[-1.4762745052119306884 ,1.4716961771633160123 ] 
dist 235=[-1.4910234806413911966 ,1.3977874910087649414 ] 
dist 236=[-1.5025986411268010875 ,1.3867783570074730312 ] 
dist 237=[-1.5092450029873506915 ,1.2336785847205592700 ] 
dist 238=[-1.5086996406820408162 ,1.2011197331560304875 ] 
dist 239=[-1.4963981944400549547 ,1.1715829124335878436 ] 
dist 240=[-1.4910780980972086670 ,1.1646452951026462904 ] 
dist 241=[-1.4263668075094944455 ,.76846869062790466233] 
dist 242=[-1.4089392727731946337 ,.71739023472579285399] 
dist 243=[-1.4187322291954691399 ,.61683982096094285471] 
dist 244=[-1.4560030068537102236 ,.59096356819858507608] 
dist 245=[-1.4828255917321664755 ,.50073805210027784137] 
dist 246=[-1.4921705608542467865 ,.47980702485127001813] 
dist 247=[-1.4937028196609454109 ,.45497094936600899541] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 2, 2, 2, 1, 2] 
dist 0=[56.113020747802045596  ,56.113020747802045596  ] 
dist 1=[55.527031995905541316  ,56.297649533798544424  ] 
dist 2=[54.819352520380926584  ,56.340432522759706766  ] 
dist 3=[54.148696412861626970  ,56.359750139406090155  ] 
dist 4=[53.374546458614723597  ,56.261988494350520776  ] 
dist 5=[52.253567722084159950  ,55.371627297202339222  ] 
dist 6=[50.991315177162991570  ,55.111529161906989302  ] 
dist 7=[49.652925111394849476  ,54.951603840822817628  ] 
dist 8=[47.998477679051670306  ,54.764748729968120166  ] 
dist 9=[45.473857951194672418  ,50.222492770539982783  ] 
dist 10=[42.830292978666978909  ,48.416383989191533023  ] 
dist 11=[40.700754837650847999  ,46.976595264760936590  ] 
dist 12=[38.533885380631352804  ,46.606592698993001383  ] 
dist 13=[35.741182205245071555  ,45.370288999602377072  ] 
dist 14=[32.686858277648936312  ,45.016285725223565646  ] 
dist 15=[27.322815200177953863  ,44.696663149110723753  ] 
dist 16=[21.951980032858544297  ,44.506618765916119215  ] 
dist 17=[18.343082959552153326  ,37.651221198050134502  ] 
dist 18=[15.324226878276064311  ,21.315486438781908641  ] 
dist 19=[12.309790930765990919  ,17.185581598102609874  ] 
dist 20=[9.5167566459488155820 ,16.586851850297655342  ] 
dist 21=[6.6387402598024002016 ,11.066512555601467969  ] 
dist 22=[3.9843594581313718707 ,10.096247788103685005  ] 
dist 23=[1.9793702405770719268 ,8.8576419367365212094 ] 
dist 24=[.06053970836128951844,8.6314083987788795312 ] 
dist 25=[-2.2496481015562516002 ,3.3062270006741833285 ] 
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dist 30=[-8.3591924395128213643 ,-2.8399280983596148977 ] 
dist 31=[-8.7285036357870054647 ,-3.3029568807107187846 ] 
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dist 33=[-8.9771176008686686316 ,-5.4247533334249354473 ] 
dist 34=[-7.3822593465391996202 ,-5.2072640670529820439 ] 
dist 35=[-7.6836184436566227769 ,-4.9850762532521966634 ] 
dist 36=[-7.8794470245429586106 ,-4.7215079082130274735 ] 
dist 37=[-8.0144935040889213313 ,-4.3377944083435167491 ] 
dist 38=[-8.0725230917857507617 ,-3.9102045303811907499 ] 
dist 39=[-8.0871618023570039966 ,-3.4710420813599122776 ] 
dist 40=[-8.0768119614239676349 ,-2.9411899632589702506 ] 
dist 41=[-7.3665046518403013516 ,-2.1512871837524850489 ] 
dist 42=[-7.2513044669638429104 ,-1.3379828210631459290 ] 
dist 43=[-7.0250547615257404519 ,-.71448008392623633878] 
dist 44=[-6.9579295786363421073 ,-.11124195088652667301] 
dist 45=[-6.6817231802898074123 ,.62157706047429429182] 
dist 46=[-6.6126271440393372106 ,1.3817982362959988343 ] 
dist 47=[-6.4550165511214837863 ,2.0946617456828788538 ] 
dist 48=[-6.4005797104966602561 ,3.3672585033042835724 ] 
dist 49=[-4.5363370162849848179 ,4.3235850552716544241 ] 
dist 50=[-2.2548579597716352593 ,5.2277533660622531942 ] 
dist 51=[-1.4866316069567322285 ,5.9548788613944006533 ] 
dist 52=[-1.3484029927386062044 ,6.5143461279148178629 ] 
dist 53=[-.39674756190246591967,6.9927867498235252598 ] 
dist 54=[-.23053059408345774193,7.3839088507477943455 ] 
dist 55=[.06651479031784804821,7.5948181970264970722 ] 
dist 56=[.12994677264524582005,7.7150059571757099365 ] 
dist 57=[.99078814108542861515,7.7440593713705925021 ] 
dist 58=[1.1087824991781087586 ,7.7378841596866916183 ] 
dist 59=[1.3085371804326373569 ,7.7173837112183700747 ] 
dist 60=[1.3502533069975541857 ,7.6830493818816768392 ] 
dist 61=[1.1949016473274471975 ,7.5751341911759527150 ] 
dist 62=[.96503799813388235012,6.7055515866475098012 ] 
dist 63=[.69372214635594421202,6.1011791532266896876 ] 
dist 64=[.34030230674844006532,5.0270837045913755732 ] 
dist 65=[-.21730752662657475708,4.8281292028255761821 ] 
dist 66=[-.78028235968529283838,2.2798093595696598261 ] 
dist 67=[-1.1551484655930076668 ,2.1106786741614031567 ] 
dist 68=[-1.4639367339004380292 ,1.8104660282644231645 ] 
dist 69=[-1.7632278564796429140 ,1.2849740211358066376 ] 
dist 70=[-2.0335326146806937494 ,1.1890252829289511886 ] 
dist 71=[-2.2266606326374604800 ,1.0199579133344426578 ] 
dist 72=[-2.4003308539752038335 ,.98231669563645654826] 
dist 73=[-2.5930195441373954005 ,.6227778560464364309 ] 
dist 74=[-2.7654835968784178688 ,.6838303298519330774 ] 
dist 75=[-2.8584343801067154330 ,.76227321404333051481] 
dist 76=[-2.9112610288966015178 ,.88485830490458895486] 
dist 77=[-2.9909748161468354396 ,1.0262497735969615666 ] 
dist 78=[-3.0483220205221048773 ,1.1797171121815379818 ] 
dist 79=[-3.0644039822759427303 ,1.3712098188154132853 ] 
dist 80=[-3.1448743600314833858 ,1.6643015671056289770 ] 
dist 81=[-3.2346503853210006750 ,1.9568424729273739488 ] 
dist 82=[-3.2984950829468874778 ,2.1461287326053719199 ] 
dist 83=[-3.3445426890119366297 ,2.2957217572732754022 ] 
dist 84=[-3.3763960029423770346 ,2.4298819134591117581 ] 
dist 85=[-3.3835353754037858583 ,2.5435076107777359296 ] 
dist 86=[-3.3774987328095431148 ,2.6111557653710008966 ] 
dist 87=[-3.3689738403434461593 ,2.6578568077618416428 ] 
dist 88=[-3.2997186584016739583 ,2.6878717903348360598 ] 
dist 89=[-3.2793735019328428926 ,2.7057023833182214299 ] 
dist 90=[-3.2200544971564218859 ,2.7053234665196633371 ] 
dist 91=[-3.1973743703421784955 ,2.6933668237534774867 ] 
dist 92=[-3.0821201570793580108 ,2.6815558747801914074 ] 
dist 93=[-3.0217843439732397649 ,2.6450376347055303709 ] 
dist 94=[-2.9576245689656017664 ,2.6805561199608279139 ] 
dist 95=[-2.9379191246636036773 ,2.6904166655038282197 ] 
dist 96=[-2.8427680262155176190 ,3.0636551842502775765 ] 
dist 97=[-1.7488933707895612955 ,3.4714389684121152837 ] 
dist 98=[-1.6443566136469539053 ,3.7881868474355791607 ] 
dist 99=[-1.4248250444579538343 ,4.0638842249846062898 ] 
dist 100=[-1.3648661655565904656 ,4.2924066211951312678 ] 
dist 101=[-1.1306749955427527570 ,4.4208456787048750831 ] 
dist 102=[-1.0839745190949248312 ,4.5007480529043840861 ] 
dist 103=[-.97967191725268089774,4.5355378716401392111 ] 
dist 104=[-.95181364097733438936,4.5502698446917112560 ] 
dist 105=[-.82313308634523179465,4.5500991371789061160 ] 
dist 106=[-.79334706220703311575,4.5390818709095272517 ] 
dist 107=[-.78454273639895987982,4.5249604325684042453 ] 
dist 108=[-.80198833205271977303,4.4728055134990475758 ] 
dist 109=[-.83492514047662543169,4.4518174515730034528 ] 
dist 110=[-.88796291500794557202,4.4280126324295141959 ] 
dist 111=[-.96587981135984581435,4.4095466052467473783 ] 
dist 112=[-1.0981304315138732588 ,2.4609992398559687142 ] 
dist 113=[-1.2359104348465294171 ,2.1973661056212640284 ] 
dist 114=[-1.3359032710811352403 ,1.4463406992211353932 ] 
dist 115=[-1.4273974711276291801 ,1.3674756948014046927 ] 
dist 116=[-1.5312623259711907671 ,1.3364028608570835443 ] 
dist 117=[-1.6351932837521438549 ,1.3382747761846895287 ] 
dist 118=[-1.9187767248126241197 ,1.3130806877179995404 ] 
dist 119=[-2.2672467852725186365 ,1.3058752155465754010 ] 
dist 120=[-2.5931194378797702575 ,1.3009438962600632920 ] 
dist 121=[-2.7974191295057042711 ,1.2978351227014413472 ] 
dist 122=[-2.9518509372525023842 ,1.0691168365527101934 ] 
dist 123=[-3.0786684103563356373 ,1.0368587401388715304 ] 
dist 124=[-3.1780584481146528682 ,.97754374957257502563] 
dist 125=[-3.2230081230629712234 ,.96207677903418744159] 
dist 126=[-3.2440695345069440085 ,.90920973732225876603] 
dist 127=[-3.2481107674303326212 ,.8942769701863865326 ] 
dist 128=[-1.8377820351775844742 ,.87865211651645119614] 
dist 129=[-1.8377313113526523584 ,.87079991986784480973] 
dist 130=[-1.2580494739318791450 ,-.01144249087528501730] 
dist 131=[-1.2065396963188519075 ,-.08393147496726123643] 
dist 132=[-1.1092962144806682076 ,-.24749260133104931509] 
dist 133=[-1.1037061320181805746 ,-.27553235363070847354] 
dist 134=[-1.0821509498319094698 ,-.26946539607395522175] 
dist 135=[-1.0771905185259881577 ,-.23132195646867229363] 
dist 136=[-1.0065371436074304502 ,-.17866406528195596009] 
dist 137=[-.9972833705629649401 ,-.09245245389602635491] 
dist 138=[-.93509097754221926378,-.00024709846750925770] 
dist 139=[-.94863076421526741858,.07634131548070831159] 
dist 140=[-.99219408400525716423,.15617456469412332164] 
dist 141=[-1.0259904708287526222 ,.26134287054020861212] 
dist 142=[-1.0518665577087852584 ,.37481127368133806794] 
dist 143=[-1.0638184886801821090 ,.50284464755959248954] 
dist 144=[-1.0686699512572472570 ,.74167378710208482564] 
dist 145=[-1.1320961305394798659 ,.90938463570592174794] 
dist 146=[-1.2365994961983878617 ,1.0721420502435196526 ] 
dist 147=[-1.3007945122777907179 ,1.2066456953151075182 ] 
dist 148=[-1.3477025256870326788 ,1.3136472911325300788 ] 
dist 149=[-1.3832142603480622362 ,1.4111775794795231080 ] 
dist 150=[-1.4088589948040776253 ,1.4952322358189212967 ] 
dist 151=[-1.4163914456565813951 ,1.5484467505718374995 ] 
dist 152=[-1.4173225674296125926 ,1.5893126687665783016 ] 
dist 153=[-1.4166262265613265574 ,1.6240828087451989054 ] 
dist 154=[-1.3544235933633856016 ,1.6505990332762043789 ] 
dist 155=[-1.3407385667353038840 ,1.6585174789973765426 ] 
dist 156=[-1.3078610710781066161 ,1.6586558533148714698 ] 
dist 157=[-1.2954617920537732691 ,1.6541062728068745803 ] 
dist 158=[-1.2314426005793347420 ,1.6075635585794664673 ] 
dist 159=[-1.2159767583464577074 ,1.5927872929301107060 ] 
dist 160=[-1.1788316544873822747 ,1.5737445572642485130 ] 
dist 161=[-1.1654621447139412123 ,1.5644866740889148337 ] 
dist 162=[-.59457069650127258623,.04535660794756232514] 
dist 163=[-.62501564867646334729,.01680290796905202206] 
dist 164=[-.65296687165978289687,-.23484617761763840068] 
dist 165=[-.67370631396158899008,-.27834651547756872056] 
dist 166=[-.69313974354265207112,-.33809076597395292103] 
dist 167=[-.71588422590466967197,-.35068032046485633373] 
dist 168=[-.73685412305377276507,-.31339179115048271961] 
dist 169=[-.74920773844789635298,-.24141396772879651765] 
dist 170=[-.77394175374903564072,-.16392459604142372859] 
dist 171=[-.81502172682361161946,-.05865717713468145731] 
dist 172=[-.84748801432788646421,.05640209492729622584] 
dist 173=[-.8628403790600241644 ,.17297050811838024912] 
dist 174=[-.87045977369240649448,.31296186755617391077] 
dist 175=[-.8720592654382036769 ,.52150276871042379107] 
dist 176=[-.74965472461211074931,.72824133700872153307] 
dist 177=[-.73560357453472577375,.86103846801112360558] 
dist 178=[-.72510374075889389206,.96508104161518522438] 
dist 179=[-.72115508184966028325,1.0570562086366371198 ] 
dist 180=[-.70507929642589659971,1.1342062837202652884 ] 
dist 181=[-.69979799930327785901,1.1790790139956824666 ] 
dist 182=[-.68673794666766500165,1.2088825016296526490 ] 
dist 183=[-.68144527568783098528,1.2258866294410355947 ] 
dist 184=[-.65340404520787114483,1.2371327816074675347 ] 
dist 185=[-.64592427088983690365,1.2439554116477101943 ] 
dist 186=[-.63155010825637360485,1.2488281319870093385 ] 
dist 187=[-.62683086799157719034,1.2522945092773848072 ] 
dist 188=[-.60533989806482415756,1.2545747055768445111 ] 
dist 189=[-.59978060830119568876,1.2547141722742090104 ] 
dist 190=[-.58404842264161176799,1.2533022504177567101 ] 
dist 191=[-.57921837818161026841,1.2493909060503558716 ] 
dist 192=[-.54414384164530390998,1.0851711544712411588 ] 
dist 193=[-.53608790106778314404,1.0817033379498281390 ] 
dist 194=[-.52044370007160653247,1.0909455664241461404 ] 
dist 195=[-.51557584455076330312,1.1603458469912699211 ] 
dist 196=[-.49434428239275538935,1.2174083078159590897 ] 
dist 197=[-.48902554586233906673,1.2485305879282789182 ] 
dist 198=[-.4747561693138287558 ,1.2666252267653144666 ] 
dist 199=[-.47013104403544447662,1.2716908324635786052 ] 
dist 200=[-.44056370131014047528,1.2711824143176053987 ] 
dist 201=[-.43376586905308857415,1.2670285790736024720 ] 
dist 202=[-.4199378300141997373 ,1.2595066830991939266 ] 
dist 203=[-.41551776375533191518,1.2551146964424636230 ] 
dist 204=[-.39542006796499718146,1.2275957295368913633 ] 
dist 205=[-.40471442235870464361,1.2199315454648329970 ] 
dist 206=[-.45364921941822216302,1.1900291813031424363 ] 
dist 207=[-.49039024327288549212,1.1854826067220960558 ] 
dist 208=[-.52526443562415899576,.63069908707227261174] 
dist 209=[-.56675395812447352132,.72347838400862985408] 
dist 210=[-.6057223060791349178 ,.79601706469429643418] 
dist 211=[-.63053348881294062487,.85991126091085933156] 
dist 212=[-.64975623571693218373,.91336908843231721234] 
dist 213=[-.66641292358718889806,.94425351686129781842] 
dist 214=[-.73386188435361521812,.96452477027906711707] 
dist 215=[-.82174099159425902388,.97562345966206989244] 
dist 216=[-.90272622698859407839,.98228040433077418945] 
dist 217=[-.95334525576029212075,.98454102511013547538] 
dist 218=[-.9914162131808535672 ,.91175233401333345238] 
dist 219=[-1.0223198647386608876 ,.90026763077810623817] 
dist 220=[-1.0462553709119227857 ,.89246496074971230575] 
dist 221=[-1.0565155977003832419 ,.86595547226967544993] 
dist 222=[-1.0598980743254045050 ,.70056222740928044353] 
dist 223=[-1.0587010885858726621 ,.5933633703861132022 ] 
dist 224=[-.6384056347539769215 ,.4522215174024416056 ] 
dist 225=[-.63390834672893802864,.59936431731130019361] 
dist 226=[-.46742104058815608144,.74479729652756166341] 
dist 227=[-.44912854869896210214,.83838617800199025791] 
dist 228=[-.3426296375779054673 ,.91192224758796228339] 
dist 229=[-.32270874382814462613,.97731818257110037102] 
dist 230=[-.28273851732198884816,1.0324719702858738379 ] 
dist 231=[-.27221354805227509205,1.0651280142423607758 ] 
dist 232=[-.29865923985242552641,1.0875524802640841500 ] 
dist 233=[-.33173688858867837768,1.1018676236683604706 ] 
dist 234=[-.36655656703366689278,1.1109926278097702763 ] 
dist 235=[-.41286026525161457483,1.1127020726105110900 ] 
dist 236=[-.46300230376778267734,1.1098786080400078963 ] 
dist 237=[-.51314020526616777435,1.1069384534205364462 ] 
dist 238=[-.57287572744230619671,1.0837558921958225129 ] 
dist 239=[-.66132170843398349237,1.0766139258356031098 ] 
dist 240=[-.74878765483274133339,1.0546198452195945983 ] 
dist 241=[-.80461107051376852504,1.0466569470740074274 ] 
dist 242=[-.84793685539863884822,.93362924628840194896] 
dist 243=[-.88552258640283339869,.97978378046309323834] 
dist 244=[-.91652870393798904228,1.0172180996361441192 ] 
dist 245=[-.9335936417275960705 ,1.0366592582558443094 ] 
dist 246=[-.94370489975394194227,1.0466518726916773308 ] 
dist 247=[-.94695629491220640389,1.0481981350414789495 ] 
dist 248=[-.94606063290827741793,1.0416644232777195080 ] 
dist 249=[-.94396789655086926682,1.0373906018057610599 ] 
dist 250=[-.93236353759712496993,1.0252152088081994062 ] 
dist 251=[-.92821156020438323124,1.0190647612959196429 ] 
dist 252=[-.88305587403207725657,.98240040215703306373] 
dist 253=[-.86855466630601669719,.97260998923422447452] 
dist 254=[-.84195430250129006046,.9497326075215683721 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 0, 0, 1, 1, 2] 
dist 0=[46.609362567004139110  ,46.609362567004139110  ] 
dist 1=[46.308323848328363992  ,47.022393854313118430  ] 
dist 2=[45.519002128747004984  ,47.490283727856364840  ] 
dist 3=[44.265364241157789163  ,47.776737696044478561  ] 
dist 4=[42.177294152339816051  ,47.985682996260610821  ] 
dist 5=[40.012029891907349689  ,48.143829196773906678  ] 
dist 6=[38.450042299664143887  ,48.234568842718037350  ] 
dist 7=[37.026722964423052294  ,48.174166357810010098  ] 
dist 8=[35.415121712019880105  ,47.156386312755470412  ] 
dist 9=[33.800043151481280380  ,46.933315703401683497  ] 
dist 10=[32.362668171127057115  ,46.583518117179966024  ] 
dist 11=[30.775461978003959576  ,46.455459489392859305  ] 
dist 12=[28.561634500447034310  ,46.000840353132208536  ] 
dist 13=[26.324616538668286081  ,45.843978761377326993  ] 
dist 14=[24.644614516628069545  ,45.519050265677557717  ] 
dist 15=[23.044703179991829143  ,45.273578235202954785  ] 
dist 16=[21.127372274930385821  ,32.551833931312491983  ] 
dist 17=[19.143111468087413987  ,31.423091063703052811  ] 
dist 18=[17.275534837113142704  ,28.684970916626592365  ] 
dist 19=[15.127349454404639876  ,28.281540971132570749  ] 
dist 20=[12.021492639140638206  ,24.264800482899527937  ] 
dist 21=[8.9421451902767244570 ,23.515700983095448134  ] 
dist 22=[6.8997844176071744110 ,22.641249771749397003  ] 
dist 23=[5.2164977305602160170 ,22.458453117960750312  ] 
dist 24=[3.5719766107265765871 ,15.971168759874107560  ] 
dist 25=[2.0686373704155136794 ,15.166714324343478775  ] 
dist 26=[.6496852460606055145 ,13.526360128473127730  ] 
dist 27=[-1.1061854649553974920 ,13.105503670477869836  ] 
dist 28=[-3.0402854920594274800 ,11.604301444099091541  ] 
dist 29=[-5.7372227559258472550 ,11.298039822944082812  ] 
dist 30=[-8.3625445862185609903 ,10.828429377950779338  ] 
dist 31=[-10.010687549281482061  ,10.708379229913821846  ] 
dist 32=[-11.268274785025668905  ,1.2975763046548668923 ] 
dist 33=[-12.332835709645062904  ,.51146533505351631012] 
dist 34=[-13.200897290034943670  ,-1.2027159715701258418 ] 
dist 35=[-13.673412961529710211  ,-1.5185877068626229134 ] 
dist 36=[-13.951609773854763086  ,-1.5932919353122708622 ] 
dist 37=[-14.043683303853262882  ,-1.0758089880719014292 ] 
dist 38=[-14.064928185666475362  ,-.6885287151235207338 ] 
dist 39=[-14.060027321964305266  ,-.3249178794106814436 ] 
dist 40=[-14.038042897394615261  ,.0986201642115895216 ] 
dist 41=[-13.990311610785203737  ,.5259937623440480417 ] 
dist 42=[-13.931984934607410004  ,.9051187053482412980 ] 
dist 43=[-13.867317605989942612  ,1.3202778651458366389 ] 
dist 44=[-13.786443540607831973  ,1.8915645098528371573 ] 
dist 45=[-13.732435792754818444  ,2.4598365893657126265 ] 
dist 46=[-11.258642916264219698  ,2.8630452073742656992 ] 
dist 47=[-11.240190461465667088  ,3.2217137498974766518 ] 
dist 48=[-3.9043388056206115481 ,3.6123687191187698867 ] 
dist 49=[-3.6391224290973420148 ,3.9928147147333531097 ] 
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dist 52=[-3.4308921667779267122 ,5.0819136079533094406 ] 
dist 53=[-.10776444147356671582,5.5079030352980028528 ] 
dist 54=[.34953582716108878107,5.7901620950149020200 ] 
dist 55=[.93181947867151696053,6.0207230576964926417 ] 
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dist 60=[1.1410255109615371053 ,6.9410818520917123549 ] 
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dist 68=[-2.4357674274110997838 ,4.1907635912809389215 ] 
dist 69=[-2.6906551586441838412 ,4.1425949659919943719 ] 
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dist 74=[-3.6694888408520455956 ,2.9823115279934393619 ] 
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dist 80=[-1.4236308375706706054 ,.4122494541035225261 ] 
dist 81=[-1.8779826372983557359 ,.22825925657323909735] 
dist 82=[-2.2593059196166234495 ,.1542024169784292973 ] 
dist 83=[-2.6222412212674196058 ,.1089999127337878248 ] 
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dist 85=[-3.1704783952372683571 ,-.69504863945788688009] 
dist 86=[-3.3656942053969754922 ,-.77232989215875436391] 
dist 87=[-3.5721949933661447203 ,-.76930525156970085118] 
dist 88=[-3.7548110811529744683 ,-.73586967420098217067] 
dist 89=[-3.8546844657786592161 ,-.65248158053241692698] 
dist 90=[-3.9132412903191888959 ,-.5435832152207019017 ] 
dist 91=[-3.9309067325199033674 ,-.40830219630228144279] 
dist 92=[-3.9308287655378341799 ,-.22787810569550958134] 
dist 93=[-3.9185688703292020008 ,.06122105854601156070] 
dist 94=[-3.8956972422502977974 ,.35477520536973260802] 
dist 95=[-3.8819905874054075005 ,.55299693257471273711] 
dist 96=[-2.8829270591317502555 ,.71932912204412910557] 
dist 97=[-2.8670088503659605927 ,.88562999937737727296] 
dist 98=[-2.8703712981862770572 ,1.0392298605551545123 ] 
dist 99=[-2.8637875012413550357 ,1.1548881363314522104 ] 
dist 100=[-2.7909675363960559055 ,1.2738671396469026425 ] 
dist 101=[-2.7670398009041917913 ,1.5415719477716157586 ] 
dist 102=[-2.7371245681802799887 ,1.7988610542692942114 ] 
dist 103=[-2.7218615978136547672 ,2.1092613765793365763 ] 
dist 104=[-2.2890789817677678875 ,2.3999534307605144252 ] 
dist 105=[-2.2258262710949329320 ,2.5785908807272635061 ] 
dist 106=[-2.0949575256887850252 ,2.7094246737119302963 ] 
dist 107=[-2.0572219453818010048 ,2.8093277863026176405 ] 
dist 108=[-1.9016563080964273893 ,2.8852803121604032632 ] 
dist 109=[-1.8681463251053132730 ,2.9205057805619875001 ] 
dist 110=[-1.7840866688457395180 ,2.9343383153624368664 ] 
dist 111=[-1.7621585276245498994 ,2.9335288745118640479 ] 
dist 112=[-1.0255484414095881813 ,2.7583698140396730025 ] 
dist 113=[-1.2120383350406690762 ,2.7289062682224633795 ] 
dist 114=[-1.3817752970802522328 ,2.7225275428652245715 ] 
dist 115=[-1.5051410042767361961 ,2.7439077084363266264 ] 
dist 116=[-1.6181077493470236018 ,2.7520993252900300531 ] 
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dist 118=[-1.8627263848482044481 ,2.7322127559771755800 ] 
dist 119=[-1.9284905873544182303 ,2.7205639131066240472 ] 
dist 120=[-1.9696889468697234584 ,2.7076555372733851606 ] 
dist 121=[-1.9880450559787400112 ,2.8069734785369368491 ] 
dist 122=[-1.9967244113262555122 ,2.8720159998806198582 ] 
dist 123=[-1.9993061343847431615 ,2.9073143349571601311 ] 
dist 124=[-1.9978745136515548952 ,2.9274695483342362535 ] 
dist 125=[-1.9914847842391765153 ,2.9320630103976937019 ] 
dist 126=[-.12728209553048323073,2.9261186585556583507 ] 
dist 127=[-.55923530307112628323,2.9193275382978136826 ] 
dist 128=[-1.0489485554681775534 ,2.6610969199681638924 ] 
dist 129=[-1.3746637479623574192 ,2.6577315265144659147 ] 
dist 130=[-1.6427767276423539330 ,2.6322623994920146983 ] 
dist 131=[-1.9025624447132376022 ,2.6212724347391455646 ] 
dist 132=[-2.1372741919907374416 ,2.5074855655561962720 ] 
dist 133=[-2.3053027741117056654 ,2.4769691294156645771 ] 
dist 134=[-2.4567672934300798296 ,2.4393731799058374150 ] 
dist 135=[-2.6253670616904436785 ,2.4218491307209753111 ] 
dist 136=[-2.7762699579968113198 ,1.9564893931711351493 ] 
dist 137=[-2.8570946626158905238 ,1.8897998471920698104 ] 
dist 138=[-2.9029598513117760653 ,1.7524010034891056214 ] 
dist 139=[-2.9143039329575033014 ,1.7134072818925080472 ] 
dist 140=[-2.9063705219130778945 ,1.5556294575519569163 ] 
dist 141=[-2.9052064578439554044 ,1.5216745325275074602 ] 
dist 142=[-2.9027101170103628392 ,1.4403879039920609188 ] 
dist 143=[-2.9019416679395259545 ,1.4167930792963316244 ] 
dist 144=[-1.2021744451595017232 ,.78721789139751195057] 
dist 145=[-1.1885829182065371301 ,.77376569614212462887] 
dist 146=[-1.1816664584549387449 ,.76923387231473306108] 
dist 147=[-1.1757442455330838351 ,.75394090732715167062] 
dist 148=[-1.1696429989584939537 ,.76804712428151820122] 
dist 149=[-.32914960696877271992,.82279992445293356047] 
dist 150=[-.25952671049654175682,.87166220911480847587] 
dist 151=[-.10134621290551774861,.9252877229194965773 ] 
dist 152=[-.07285080909369275391,.972838542767900545  ] 
dist 153=[.1214973375440668209 ,.99745710064933936107] 
dist 154=[.15509219928664687907,1.0108668568755962072 ] 
dist 155=[.21602906497945945578,1.0136712941953178572 ] 
dist 156=[.22908236653025583621,1.0049752844426828942 ] 
dist 157=[.14243446788407068322,1.0020245729815816321 ] 
dist 158=[.05296992572400294961,.99962508852918385901] 
dist 159=[-.03552530750210696315,.9973480379675787802 ] 
dist 160=[-.16804571239189992281,.8242206019113333191 ] 
dist 161=[-.29812689668467652149,.87346122032525074911] 
dist 162=[-.40557079128728796816,.91026571705772044967] 
dist 163=[-.51018374365734411353,.94185086640329367431] 
dist 164=[-.68646918487811535833,.97457573614084766971] 
dist 165=[-.86932479580415396338,1.0030440991337519473 ] 
dist 166=[-.98633196972752388251,1.0176403486833201363 ] 
dist 167=[-1.0775113484513097832 ,1.0248717383610692600 ] 
dist 168=[-1.1572804511429726929 ,1.0250907485624580422 ] 
dist 169=[-1.2236023730752535915 ,1.0189995980051703077 ] 
dist 170=[-1.2611094282116363738 ,1.0150919651278950162 ] 
dist 171=[-1.2846837287682161849 ,1.0009574838658326296 ] 
dist 172=[-1.2953941430580489523 ,.99433945206288218492] 
dist 173=[-1.3002517924266140659 ,.90513248615022038404] 
dist 174=[-1.3004665799967615810 ,.88964976168938076952] 
dist 175=[-1.2973131086221990585 ,.84945228916016244817] 
dist 176=[-1.2931903579804551102 ,.83940711544798623295] 
dist 177=[-1.2773121053467810878 ,.76571612185503153181] 
dist 178=[-1.2706694562443029606 ,.74956796621135996762] 
dist 179=[-1.2489990051838373273 ,.72301260556017082478] 
dist 180=[-1.2400829774909508793 ,.72276537694864094938] 
dist 181=[-1.0424701514419463121 ,.77533604510529699588] 
dist 182=[-1.1101690098848424857 ,.80607532228703609275] 
dist 183=[-1.1584696600744580143 ,.82668578166980940554] 
dist 184=[-1.1929432140354347747 ,.83883295901099737674] 
dist 185=[-1.2183765472150366817 ,.84612997689646741412] 
dist 186=[-1.2305935088573501204 ,.84738529387889230677] 
dist 187=[-1.2354733302729762977 ,.84522463819286717442] 
dist 188=[-1.2345618095618899748 ,.8427447036571143346 ] 
dist 189=[-1.1314037609328947450 ,.76508282281140525353] 
dist 190=[-1.1136245128883988580 ,.75182044547362656911] 
dist 191=[-1.0827593082115345835 ,.72418721741806501224] 
dist 192=[-1.0736470261871771932 ,.71543652503055926789] 
dist 193=[-1.0397812551128588526 ,.67575477110787022351] 
dist 194=[-1.0291247854509473926 ,.66694901597177681686] 
dist 195=[-1.0096170929148883812 ,.64038583893728603988] 
dist 196=[-1.0030408124942191654 ,.63575149353782601922] 
dist 197=[-.91636315757441543526,.60947551591403757751] 
dist 198=[-.91459588921679461144,.64379392521907452443] 
dist 199=[-.91174765442404964349,.68450905927886363767] 
dist 200=[-.79836171389080753389,.72231138238637717083] 
dist 201=[-.78068982092903599093,.74500447403367193181] 
dist 202=[-.74706558515647904987,.76099198054748000739] 
dist 203=[-.73749693211415773173,.77202980108615231899] 
dist 204=[-.70003628808151384351,.7994984173614926372 ] 
dist 205=[-.69030830641044105795,.89396991749064226944] 
dist 206=[-.67020188931590542676,.9510877799282493931 ] 
dist 207=[-.64064141004064536872,.9917827586473504774 ] 
dist 208=[-.39351939956597873963,1.0207055344031163980 ] 
dist 209=[-.50504639646776966025,1.0419611775061441043 ] 
dist 210=[-.59674232303027118917,1.0520547742122574846 ] 
dist 211=[-.68534206793416919516,1.0559050130562399609 ] 
dist 212=[-.76516330748281040703,1.0550627315460467700 ] 
dist 213=[-.82182237623818234139,.25002753012608793788] 
dist 214=[-.8723621390400015762 ,.20532329390168565943] 
dist 215=[-.92775963950516148043,.10814979762705132326] 
dist 216=[-.97703194508409976176,.08635692073436983446] 
dist 217=[-1.0031249431213422641 ,-.02053951887112887073] 
dist 218=[-1.0175397686253772085 ,-.03900846334151161516] 
dist 219=[-1.0206529781395108971 ,-.08109079673819531215] 
dist 220=[-1.0159759422287772267 ,-.08758044264421835312] 
dist 221=[-1.0136431743002158010 ,-.08304605242623947767] 
dist 222=[-1.0111218742451464156 ,-.06429896505298650982] 
dist 223=[-1.0076818801708143966 ,-.03786383109509110701] 
dist 224=[-.80563884321613721624,.04668446968943468301] 
dist 225=[-.78108975585181275036,.1696497233499093321 ] 
dist 226=[-.74564298797989261149,.2726612131846422055 ] 
dist 227=[-.79558981123587408481,.37537177067829858084] 
dist 228=[-.86012512278977360073,.47002444502059426211] 
dist 229=[-.920899597262075832  ,.54087500457721447   ] 
dist 230=[-.95583612298399659081,.60785807112601740549] 
dist 231=[-.97854185280030703877,.68707440007516275936] 
dist 232=[-.9904994192422847968 ,.76041352248861853017] 
dist 233=[-.99703903478908714264,.80393924919150918976] 
dist 234=[-.9981195793054342452 ,.83395782947796168946] 
dist 235=[-.99540975689308570331,.85338694592888777633] 
dist 236=[-.99285925847568199039,.86702394030964365933] 
dist 237=[-.88571947192814898539,.87392536069676536341] 
dist 238=[-.86840211157575798337,.87721374936208048449] 
dist 239=[-.83381893073946317441,.87643175712730075717] 
dist 240=[-.82343709722455819271,.77784323368537514366] 
dist 241=[-.77942589755040476169,.76393499786852162789] 
dist 242=[-.76900704619024153177,.72755944445391645988] 
dist 243=[-.74226557070178724343,.70547345819188029404] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 1, 0, 0, 1, 0, 2] 
dist 0=[47.925769114742081681  ,47.925769114742081681  ] 
dist 1=[47.286784455956121747  ,48.172430481989815129  ] 
dist 2=[46.240679686484614565  ,48.518560053126745441  ] 
dist 3=[44.489567950291974658  ,48.874433173418231732  ] 
dist 4=[42.661344570112110307  ,49.035025939988874254  ] 
dist 5=[41.307193960113781067  ,49.083791760879939354  ] 
dist 6=[40.037151829373104115  ,49.058925786706092643  ] 
dist 7=[38.544779139399640255  ,48.795576782948853571  ] 
dist 8=[37.018197517263258449  ,46.861292323735061685  ] 
dist 9=[35.611422700940777217  ,46.294422844183691109  ] 
dist 10=[34.018426825081534850  ,46.130698645144656513  ] 
dist 11=[31.747848336053281848  ,45.501119615618606803  ] 
dist 12=[29.432771164148975503  ,45.308170503905439199  ] 
dist 13=[27.661921718369697956  ,44.936708016626058223  ] 
dist 14=[25.944502044619503268  ,44.808871033423361405  ] 
dist 15=[23.842674850077575666  ,44.128946576332719154  ] 
dist 16=[21.645058272080974248  ,29.744181753586197593  ] 
dist 17=[19.544775627817937304  ,27.103452563513339079  ] 
dist 18=[17.105165977537591548  ,26.477664700924257221  ] 
dist 19=[13.551584691508183562  ,26.311980216836243001  ] 
dist 20=[10.022482893691245526  ,21.429518160387859948  ] 
dist 21=[7.6805879867923487932 ,20.535337277577749579  ] 
dist 22=[5.7504439811800640548 ,20.376772086802557936  ] 
dist 23=[3.8664002231893903782 ,16.159853677453644108  ] 
dist 24=[2.1465483083941753356 ,14.552002734628905468  ] 
dist 25=[.87230411153933790765,14.302721803821067323  ] 
dist 26=[-.32544720939415064605,13.318341506853540385  ] 
dist 27=[-1.7399544549429451354 ,11.971911284881001901  ] 
dist 28=[-3.0607968555225421920 ,9.2357689807903204599 ] 
dist 29=[-3.8844630473440294386 ,8.8515299547237688575 ] 
dist 30=[-5.7698835918745384997 ,8.7727699762023150627 ] 
dist 31=[-8.4724956164451061134 ,.12539875769599182693] 
dist 32=[-11.095902914964204839  ,-.57761205626186780153] 
dist 33=[-12.728074371898079273  ,-2.0953477985518743536 ] 
dist 34=[-13.956279807888944636  ,-2.3758748875118871885 ] 
dist 35=[-14.965402842402951267  ,-3.4713970032965941333 ] 
dist 36=[-15.771276293588791680  ,-3.0337033378241589633 ] 
dist 37=[-16.187077864870100312  ,-2.6796482615776491930 ] 
dist 38=[-16.409842982373019092  ,-2.3216749243836615940 ] 
dist 39=[-16.451369539985421191  ,-1.8677841635851722706 ] 
dist 40=[-16.118020184057668280  ,-1.3893914547604691964 ] 
dist 41=[-16.008379106249778193  ,-.9334052178744312384 ] 
dist 42=[-15.885967325936199615  ,-.4078058552276768432 ] 
dist 43=[-15.807281207049559344  ,.3485306487184245464 ] 
dist 44=[-15.599288681031687101  ,1.1161911514746596784 ] 
dist 45=[-15.501562551918459548  ,1.6870770098027375197 ] 
dist 46=[-15.326371757120949174  ,2.2222744265765499890 ] 
dist 47=[-15.257766299042869068  ,2.8476622969405820751 ] 
dist 48=[-6.0450036958132274913 ,3.4822882611369066465 ] 
dist 49=[-5.2581595930067259030 ,4.0544089882948338085 ] 
dist 50=[-3.4349437987232978482 ,4.6897875850179368810 ] 
dist 51=[-3.2459813294001081997 ,5.5768790487822419828 ] 
dist 52=[-.77074288225172902728,6.4503945606395851795 ] 
dist 53=[-.35621960645416194891,7.0316190213584967885 ] 
dist 54=[.30744740501903370678,7.5096049628301844280 ] 
dist 55=[.46416630850637216228,7.9711756391031215097 ] 
dist 56=[2.5078207461193706173 ,8.3864876763532194876 ] 
dist 57=[2.5447310735495755135 ,8.6798885861252225825 ] 
dist 58=[2.4623878306320439872 ,8.9399959967737654674 ] 
dist 59=[2.3204661015132869491 ,9.2224547825056044265 ] 
dist 60=[2.1044738744126730208 ,9.4706904929167535387 ] 
dist 61=[1.7937427229637815263 ,9.5942264020512557789 ] 
dist 62=[1.2738712682122975967 ,9.6499879268768392134 ] 
dist 63=[.73975311762476195307,9.6277544938782164374 ] 
dist 64=[.3721546455712777459 ,4.9430937069537144351 ] 
dist 65=[.0571514628957088548 ,4.9318936651061827012 ] 
dist 66=[-.2672374132180418751 ,4.9049408797950299242 ] 
dist 67=[-.57182709395283151582,4.8862288820139547315 ] 
dist 68=[-.80788375979492257845,2.3450095260734763696 ] 
dist 69=[-1.0383867534506161801 ,2.2440777413783495103 ] 
dist 70=[-1.3208471875575156172 ,2.1267415868895632274 ] 
dist 71=[-1.5864356027356541180 ,2.0982169891426124533 ] 
dist 72=[-1.7496452692475157051 ,1.1694252323714697124 ] 
dist 73=[-1.8687643119795105298 ,1.0545242881364933316 ] 
dist 74=[-1.9584791436094075153 ,.8123271206261512056 ] 
dist 75=[-2.0270250881838633178 ,.7519901860249734112 ] 
dist 76=[-2.0616968703609131799 ,.5146034334330236292 ] 
dist 77=[-2.0780918800460255824 ,.4697653327340374926 ] 
dist 78=[-2.1885549563723328268 ,.3883439987975314872 ] 
dist 79=[-2.3322368116796471759 ,.3709706937272097360 ] 
dist 80=[-2.4502144570080163274 ,-.69985762082860444436] 
dist 81=[-2.5140694185646600346 ,-.79231835842526957478] 
dist 82=[-2.5504048298960641276 ,-.97258541920413011393] 
dist 83=[-2.5585005520664498478 ,-1.0140007840556975872 ] 
dist 84=[-2.1277736196246273651 ,-1.1336416416690899626 ] 
dist 85=[-2.0880171898955349044 ,-1.1499354181289996540 ] 
dist 86=[-1.9911164188221495014 ,-1.1357651913331515517 ] 
dist 87=[-2.0470399594625673899 ,-1.0768100282683871889 ] 
dist 88=[-2.1557384797707759330 ,-1.0011089862797100844 ] 
dist 89=[-2.2207751206959001695 ,-.9200722743977892756 ] 
dist 90=[-2.2666065316254654275 ,-.69448328582145799744] 
dist 91=[-2.2986001659135363781 ,-.4416981743379590427 ] 
dist 92=[-2.3195922849324603320 ,-.1824814577399272805 ] 
dist 93=[-2.3218909469193757622 ,.1308612689219201828 ] 
dist 94=[-2.3156592206142569987 ,.5996368562370123585 ] 
dist 95=[-2.3068129589098891924 ,1.0669683975284800318 ] 
dist 96=[-1.7106364080917621103 ,1.3745513664455395080 ] 
dist 97=[-1.7109988716157455736 ,1.6237581434340931886 ] 
dist 98=[-1.7089572758024839991 ,1.8581468844819599753 ] 
dist 99=[-1.7033975185940480356 ,2.0648122678727163489 ] 
dist 100=[-1.6945393152819956930 ,2.2033893511816509512 ] 
dist 101=[-1.6867928899917771426 ,2.3184888205620286511 ] 
dist 102=[-1.6705815623522333065 ,2.4314609248380598312 ] 
dist 103=[-1.6627218749884465740 ,2.5288896129863260706 ] 
dist 104=[-1.6164850479736581101 ,2.5819641495047067017 ] 
dist 105=[-1.6040311538225889150 ,2.6126283425891292072 ] 
dist 106=[-1.5634479014531518890 ,2.6206378513814819555 ] 
dist 107=[-1.5532504258165389153 ,2.6159549039410556697 ] 
dist 108=[-1.4021673658050445126 ,2.6045035375499600241 ] 
dist 109=[-1.3763880183062787207 ,2.6204232360994040899 ] 
dist 110=[-1.3011569127502827741 ,2.6284502056008646844 ] 
dist 111=[-1.2903520885978547595 ,2.6279147355922443889 ] 
dist 112=[-1.1325935138836753324 ,2.6219984694565382794 ] 
dist 113=[-1.1611453411059157538 ,2.6125703777438992071 ] 
dist 114=[-1.2140472380316058537 ,2.5902196455519043135 ] 
dist 115=[-1.2574187861192082714 ,2.5782631727764407841 ] 
dist 116=[-1.2804945758025182774 ,1.1892776326616798372 ] 
dist 117=[-1.2929929526034789086 ,1.0668650258915471834 ] 
dist 118=[-1.2941479826400096901 ,.79000678029969926077] 
dist 119=[-1.2891095075774948070 ,.73406676039653857479] 
dist 120=[-1.2844477147261893739 ,.54157732415194741389] 
dist 121=[-1.2639965277432481185 ,.57192935850932756659] 
dist 122=[-1.3827438443855680342 ,.60598426146445382786] 
dist 123=[-1.6107128839134299095 ,.63975666421013802735] 
dist 124=[-1.8260708389464023632 ,.66896819569455427508] 
dist 125=[-1.9616195469842906672 ,.70036376073230758754] 
dist 126=[-2.0647015690456241562 ,.74282976762819211563] 
dist 127=[-2.1504806994327511767 ,.78277353342097371639] 
dist 128=[-2.2186373734928235590 ,.80409965365309584767] 
dist 129=[-2.2513896410061311554 ,.81604287451776649625] 
dist 130=[-2.2657967321680696186 ,.81867559256466722845] 
dist 131=[-2.2664069594330734642 ,.81535779285557080499] 
dist 132=[-2.2341849311363948328 ,.81396580772252700102] 
dist 133=[-2.3259422461405345041 ,.8126013457246593224 ] 
dist 134=[-2.4129191712626378449 ,.81088555660366785754] 
dist 135=[-2.4780757329610937252 ,.67524750697554714671] 
dist 136=[-2.5250118228215772105 ,.72800352547093240131] 
dist 137=[-2.5392569757204049772 ,.88057661769624978021] 
dist 138=[-2.5411888094049095275 ,1.0360159736094720735 ] 
dist 139=[-2.5389715938598806894 ,1.2359817063496333325 ] 
dist 140=[-2.4214436572730927245 ,1.4294492937565030867 ] 
dist 141=[-2.3962953778593623362 ,1.5589578537192606638 ] 
dist 142=[-2.3358332774611473742 ,1.6664140570739012287 ] 
dist 143=[-2.3133138031226042606 ,1.7718736927957368095 ] 
dist 144=[-2.1979971244445505863 ,1.8679973214608098475 ] 
dist 145=[-2.1703791667866198055 ,1.9381978237554676419 ] 
dist 146=[-2.1043623864679764511 ,2.0028834665716712046 ] 
dist 147=[-2.0808220129311783858 ,2.0770070180752134837 ] 
dist 148=[-.54392158144120991307,2.1418491079037372385 ] 
dist 149=[-.52523457145021252039,2.2197918592607151098 ] 
dist 150=[-.51877775579516887363,2.3112346371933930358 ] 
dist 151=[-.37535859894516984233,2.3798764753851448348 ] 
dist 152=[-.35596550803338311614,2.4303060869316802957 ] 
dist 153=[-.31383688963855873411,2.4490537012004108133 ] 
dist 154=[-.3022330066763278662 ,2.4539194216590225398 ] 
dist 155=[-.25300372917508090813,2.4490824826094261223 ] 
dist 156=[-.24363725632054009023,2.6151208880690427160 ] 
dist 157=[-.22000943052721719643,2.7110751025599255450 ] 
dist 158=[-.21621247552685785617,2.7740753468090678355 ] 
dist 159=[.04335583849304924298,2.8085836101442867822 ] 
dist 160=[.01419962848712344489,2.8277505019439140788 ] 
dist 161=[-.06391124487691816331,2.8295170739807259858 ] 
dist 162=[-.14143605989065473923,2.8206651236236503673 ] 
dist 163=[-.21261834674950557787,2.8124468481246940481 ] 
dist 164=[-.47608810168378121908,2.3509477667408411757 ] 
dist 165=[-.80690369039221061805,2.3206052074515695800 ] 
dist 166=[-1.0795285762145306517 ,2.2297365379662797286 ] 
dist 167=[-1.3440532519305156700 ,2.2137105674883164785 ] 
dist 168=[-1.5831510768842932288 ,2.0124142623597458630 ] 
dist 169=[-1.7542888597408318247 ,1.9680087578686465122 ] 
dist 170=[-1.9084363893474688052 ,1.9230749324386869483 ] 
dist 171=[-2.0797201284871688772 ,1.9060040436214451049 ] 
dist 172=[-2.2355439779399447074 ,1.3524909774085003774 ] 
dist 173=[-2.3279863556114393841 ,1.2787114230536358290 ] 
dist 174=[-2.3917101858586052265 ,1.1304019019326909763 ] 
dist 175=[-2.4329103205696322631 ,1.0909374164561110706 ] 
dist 176=[-2.4592003750596956499 ,.9451520493229962945 ] 
dist 177=[-2.4634126830930200052 ,.9128026539578042808 ] 
dist 178=[-2.4581620221024142717 ,.8551265670090062567 ] 
dist 179=[-2.4489041319642372105 ,.8406721970743913976 ] 
dist 180=[-.56742665546505097075,.1765028602601030843 ] 
dist 181=[-.59815183567942806051,.2641052374790712858 ] 
dist 182=[-.63222200070492593577,.33485304898190166277] 
dist 183=[-.66261352413549408504,.40108106624670537287] 
dist 184=[-.67865561150402472921,.45932368052047314597] 
dist 185=[-.69335572824423708772,.49820200586197267068] 
dist 186=[-.70548466001508250574,.53033866645129959341] 
dist 187=[-.71331734744783532328,.56167615313590686471] 
dist 188=[-.71517218208171472957,.58936530036570856198] 
dist 189=[-.71400888534030757915,.60694098071310832658] 
dist 190=[-.71192425583845884035,.62047490923213828125] 
dist 191=[-.57965302956223186739,.63203122246428740592] 
dist 192=[-.56601041888470169199,.64142880182014581295] 
dist 193=[-.53088064217816761964,.64634572447230867248] 
dist 194=[-.52380094558609610317,.64891769996995160308] 
dist 195=[-.47167635279401579031,.64895437972846624731] 
dist 196=[-.47688767698212288431,.64586057222716034718] 
dist 197=[-.47925409650452682185,.65337145626594359587] 
dist 198=[-.47894433418326357918,.65513897655017392831] 
dist 199=[-.47555787314970069085,.6447724604484372397 ] 
dist 200=[-.47384030929756155167,.64809285612873325914] 
dist 201=[-.46558835673745631035,.66517148732393761233] 
dist 202=[-.46386854591887437863,.67496074337751576561] 
dist 203=[-.43551158984575544737,.68088292805311980338] 
dist 204=[-.42856587409654525292,.68252669183236183958] 
dist 205=[-.42257622468115057177,.68135090207778588345] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 1, 1, 2] 
dist 0=[49.514567129146998007  ,49.514567129146998007  ] 
dist 1=[48.447307505962773934  ,50.370669033633496849  ] 
dist 2=[47.175441139754047808  ,50.799125777553401693  ] 
dist 3=[45.507330279290072278  ,51.016419234197132344  ] 
dist 4=[42.857488885972804535  ,51.042589624323566429  ] 
dist 5=[40.145967776753397386  ,50.769999953316085212  ] 
dist 6=[38.231419742668192985  ,50.642404282784874516  ] 
dist 7=[36.529483668794871777  ,50.398817962609270118  ] 
dist 8=[34.666850095755046388  ,50.291112615632485193  ] 
dist 9=[32.837322391336217922  ,49.687051229469779702  ] 
dist 10=[31.267388110291781679  ,49.527890738192818076  ] 
dist 11=[29.582054281181035296  ,48.942835695226465556  ] 
dist 12=[27.291239693799700443  ,48.848714385431252327  ] 
dist 13=[25.002961128281598913  ,47.234949960992031263  ] 
dist 14=[23.327538699947546085  ,46.855706263418851537  ] 
dist 15=[21.773962430329519228  ,45.428264732908889949  ] 
dist 16=[19.972069007750014454  ,42.926466125559412068  ] 
dist 17=[18.138919820578362166  ,28.900623126538612615  ] 
dist 18=[16.460093132343570026  ,28.125281659636240360  ] 
dist 19=[14.564518544428593780  ,27.215277247932174200  ] 
dist 20=[11.864706921497312743  ,26.994617613985841590  ] 
dist 21=[9.1953470776172968412 ,20.015813106533922248  ] 
dist 22=[7.4213463563183728021 ,19.136199311045627041  ] 
dist 23=[5.9542842578563282206 ,17.336690695726656700  ] 
dist 24=[4.5116581518094076601 ,16.869110230034922205  ] 
dist 25=[3.1858608110444471870 ,15.169986098494567693  ] 
dist 26=[2.1856818889389530116 ,14.822700028789359967  ] 
dist 27=[.8315225262837924348 ,14.219244326449602634  ] 
dist 28=[-.88483411846402663845,14.082092108162952214  ] 
dist 29=[-2.5320343958720398891 ,3.0881551840097658384 ] 
dist 30=[-3.8920801945538839877 ,2.1522265141674907680 ] 
dist 31=[-5.3108774517089552958 ,.1241181684666259094 ] 
dist 32=[-7.1940700056240633944 ,-.2689777267180113814 ] 
dist 33=[-8.9950293002592184990 ,-1.3043455687740403145 ] 
dist 34=[-10.085482884163782573  ,-1.3606122524041532648 ] 
dist 35=[-10.873427889434104030  ,-1.3322684544339190179 ] 
dist 36=[-11.465113740023492715  ,-1.1856742141473515649 ] 
dist 37=[-12.066198382299389792  ,-1.0101536897337233928 ] 
dist 38=[-12.734018208569886099  ,-.8662031937820984472 ] 
dist 39=[-13.197085966330674221  ,-.7205761067924782044 ] 
dist 40=[-13.504429217546283721  ,-.5377233667478368617 ] 
dist 41=[-13.722467545302507674  ,-.3473229367792128279 ] 
dist 42=[-13.828797110919812084  ,-.1712867960504765196 ] 
dist 43=[-13.874368214481855997  ,.0268049304971908646 ] 
dist 44=[-13.855416258690223223  ,.3054449398322028722 ] 
dist 45=[-10.594046749810723103  ,.5848763036530418647 ] 
dist 46=[-10.506051154966743146  ,1.3124002982756203271 ] 
dist 47=[-10.446238621935452084  ,2.1185004973612777627 ] 
dist 48=[-10.410565302660748520  ,2.9480434856287870228 ] 
dist 49=[-4.0000202159388263206 ,3.7281855307174638519 ] 
dist 50=[-3.9545179150476109502 ,4.3373127459702445009 ] 
dist 51=[-3.8263682553354018215 ,4.9375447655193486567 ] 
dist 52=[-3.8040155938970124213 ,5.6823818956771346495 ] 
dist 53=[.2656327967474754514 ,6.3903380717392526019 ] 
dist 54=[.5417604179270349485 ,6.8434796766272695123 ] 
dist 55=[1.1698020528871090512 ,7.1970366624726437766 ] 
dist 56=[1.2655266497525481611 ,7.5076589280083858348 ] 
dist 57=[2.0213597675029053614 ,7.7677558221727634324 ] 
dist 58=[2.1461017230953487195 ,7.9197827203183068623 ] 
dist 59=[2.1723547090402568571 ,8.0226698116763548214 ] 
dist 60=[1.8979883616026391252 ,8.0868906487725538090 ] 
dist 61=[1.5965183974635497699 ,8.1198014574527446055 ] 
dist 62=[1.3350755929221470836 ,8.1072591832352026605 ] 
dist 63=[1.0531243429865367601 ,8.0509243563421844299 ] 
dist 64=[.6697161891226279717 ,7.8923140869419291153 ] 
dist 65=[.2505520035603431352 ,3.9582121827464449820 ] 
dist 66=[-.1741585834871462553 ,3.9250932399946648353 ] 
dist 67=[-.68430665183937070535,3.8371896914832049137 ] 
dist 68=[-1.4445308738435027202 ,3.8025602595726762448 ] 
dist 69=[-2.1992081509116577982 ,3.4077975383198399920 ] 
dist 70=[-2.6872347424975015412 ,3.3442816976770205227 ] 
dist 71=[-3.0735138064517664074 ,3.1742802989332210939 ] 
dist 72=[-3.4220861457053299426 ,3.1459454167505940262 ] 
dist 73=[-3.7198974709771325504 ,2.8386075516402936540 ] 
dist 74=[-3.9035782278482502845 ,2.7759548608229189849 ] 
dist 75=[-4.0389484293164734376 ,2.7037660734882002373 ] 
dist 76=[-4.1439507113919506726 ,2.6794520168329175425 ] 
dist 77=[-4.2275473033227004174 ,2.2863147413943983127 ] 
dist 78=[-4.2774706884393185031 ,2.2597581455608193789 ] 
dist 79=[-4.3123659114454368549 ,2.2135583811021951296 ] 
dist 80=[-4.3359376782002081344 ,2.1992458474842379805 ] 
dist 81=[-4.3504110484207920000 ,2.1404459045740270859 ] 
dist 82=[-4.3993834200825403486 ,2.1226847697110102586 ] 
dist 83=[-4.4487790253932362182 ,2.0805260855371465797 ] 
dist 84=[-4.4577942455309383580 ,2.0639070652025230240 ] 
dist 85=[-4.5401117025816133544 ,1.9772990834920630727 ] 
dist 86=[-4.6019997871766128506 ,1.9529081838692438455 ] 
dist 87=[-4.6451198866723465752 ,1.9126816369179332950 ] 
dist 88=[-4.6741037404272748186 ,1.8988934871443694291 ] 
dist 89=[-4.6919949411109532721 ,1.8443435918550620228 ] 
dist 90=[-4.6908461263252417332 ,1.8269835404877153668 ] 
dist 91=[-4.6756948748705308034 ,1.7857841134229154846 ] 
dist 92=[-4.6622346071840987438 ,1.7694293281735830783 ] 
dist 93=[-3.3348758217327166370 ,1.6840074222346532768 ] 
dist 94=[-3.3095469294987850891 ,1.6608287782427297220 ] 
dist 95=[-3.2587919177140278900 ,1.6169154991436437418 ] 
dist 96=[-3.2393592305983530579 ,1.8197339979971944934 ] 
dist 97=[-3.1387080094423442835 ,2.0888460504757994028 ] 
dist 98=[-3.1136592382824631071 ,2.2536381068219791440 ] 
dist 99=[-3.0273489646714403649 ,2.4876489233633821564 ] 
dist 100=[-3.0128834297947073916 ,2.7853850830788981464 ] 
dist 101=[-1.4171958579405929655 ,3.0602865253765414618 ] 
dist 102=[-1.2670173650555951253 ,3.2350531801970425328 ] 
dist 103=[-.92329617923169267226,3.3699358398132062969 ] 
dist 104=[-.85779954115955797982,3.4856824787842339900 ] 
dist 105=[-.41991951327174893861,3.5803596227437710956 ] 
dist 106=[-.34146711462083334563,3.6311748686067745112 ] 
dist 107=[-.1979874764269186056 ,3.6597164216572850342 ] 
dist 108=[-.1653904421567135696 ,3.6655391626475562037 ] 
dist 109=[.2736216903982884772 ,2.8818511919745094888 ] 
dist 110=[.3349482781620015616 ,2.8750550826087546875 ] 
dist 111=[.4461989399942642978 ,2.8505189331401697645 ] 
dist 112=[.4700396652725957112 ,2.8355156789160291640 ] 
dist 113=[.0329341396040701159 ,2.8718319133835233556 ] 
dist 114=[-.2841616760437362300 ,2.8860612297408110937 ] 
dist 115=[-.5499940548620951177 ,2.8870539090379143697 ] 
dist 116=[-.81540390147961831209,2.8862915020270095630 ] 
dist 117=[-1.0602491646286627817 ,1.3252749043854931572 ] 
dist 118=[-1.2439980050851479913 ,1.2155870618172969115 ] 
dist 119=[-1.4181890545378800094 ,1.1023914906918155080 ] 
dist 120=[-1.6248792715466781343 ,1.0848480281959076852 ] 
dist 121=[-1.8166571375430139677 ,.58373453440611968788] 
dist 122=[-1.9313297333237837470 ,.52376696985122081272] 
dist 123=[-2.0114766880569587914 ,.4149712293347956607 ] 
dist 124=[-2.0654630781956175455 ,.46307338176347205233] 
dist 125=[-2.1046235710995716487 ,.55807649328571624974] 
dist 126=[-2.1255929104512725870 ,.6412820087248597756 ] 
dist 127=[-2.1372390251982324512 ,.73176274377205057134] 
dist 128=[-2.1391682517046791840 ,.85579594374220970294] 
dist 129=[-1.8612761280603316205 ,.99185543773820440245] 
dist 130=[-1.8456375333463411292 ,1.1303283483196588881 ] 
dist 131=[-1.7968828039440945779 ,1.2970409641163566630 ] 
dist 132=[-1.8447538690268914223 ,1.5457962856638461933 ] 
dist 133=[-2.1188496201357060272 ,1.7923491074706642505 ] 
dist 134=[-2.2905093418345849455 ,1.9502700567467111631 ] 
dist 135=[-2.4201016806123076685 ,2.0734353089945054888 ] 
dist 136=[-2.5262770595817423210 ,2.1812825606447262537 ] 
dist 137=[-2.6093590849531553249 ,2.2709496993181562648 ] 
dist 138=[-2.6467714995721845552 ,2.3215586672100799974 ] 
dist 139=[-2.6639802842540231189 ,2.3532023537842568191 ] 
dist 140=[-2.6664062074573755103 ,2.3671762792613352011 ] 
dist 141=[-2.6043883449592315970 ,2.3705001150100930245 ] 
dist 142=[-2.5858929465840881865 ,2.3663816994471260866 ] 
dist 143=[-2.5457599408492287040 ,2.3445475854372954955 ] 
dist 144=[-2.5295843935835910339 ,2.3309983549249953243 ] 
dist 145=[-2.4428341721806730411 ,2.2399266654714845697 ] 
dist 146=[-2.4213112935804387294 ,2.2145114574551237799 ] 
dist 147=[-2.3533711953918643453 ,2.1710972979187921822 ] 
dist 148=[-2.3381909010200414753 ,2.1565703538930196344 ] 
dist 149=[-1.1537051454690977415 ,1.4668184736448528417 ] 
dist 150=[-1.0386937733733329712 ,1.5813750980545380343 ] 
dist 151=[-.78097405322568218744,1.6860566802724198940 ] 
dist 152=[-.72602365752356957909,1.8046834804508258969 ] 
dist 153=[-.5262604127742625388 ,1.9119285576125818486 ] 
dist 154=[-.5737005029890045363 ,1.9711830990025657049 ] 
dist 155=[-.6117065734644530423 ,2.1301731385771130021 ] 
dist 156=[-.6467334594032969284 ,2.3232042683247490241 ] 
dist 157=[-.6771321643270634044 ,2.4999718704555606227 ] 
dist 158=[-.6966700064009483902 ,2.6016314622819937566 ] 
dist 159=[-.7119793714277983018 ,2.6677768645158557708 ] 
dist 160=[-.72550477929050909198,2.7027946951183611126 ] 
dist 161=[-.73574843645625566444,2.7228625278715323810 ] 
dist 162=[-.84075422775345933536,2.7293327324252207178 ] 
dist 163=[-.97799248950458756591,2.7270900618360048181 ] 
dist 164=[-1.1109760698361491660 ,2.7197766715256913935 ] 
dist 165=[-1.2310528962862130788 ,2.3978546426767977865 ] 
dist 166=[-1.3167798273570743362 ,2.4801456659889785644 ] 
dist 167=[-1.3937747490147561173 ,2.5827063781918154386 ] 
dist 168=[-1.4834919413843866132 ,2.6617583706387667631 ] 
dist 169=[-1.5817005705324827613 ,2.7202176545312148164 ] 
dist 170=[-1.6427263807592980347 ,2.7405845755724239865 ] 
dist 171=[-1.6882008968250965152 ,2.7461284574752952980 ] 
dist 172=[-1.7393044768550000409 ,2.7454235892907356861 ] 
dist 173=[-1.9543572468909411593 ,2.6317460878238543534 ] 
dist 174=[-2.0894775040581556924 ,2.6061800564300795040 ] 
dist 175=[-2.1919411530313886557 ,2.5466043019266734518 ] 
dist 176=[-2.2766544109426334303 ,2.5242387568509938454 ] 
dist 177=[-2.3435036292644792858 ,2.4091283992020301562 ] 
dist 178=[-2.3746698089253531033 ,2.3814288058241670415 ] 
dist 179=[-2.3878865004371199886 ,2.3093836866212051453 ] 
dist 180=[-2.3873780548397637552 ,2.2849021223922553224 ] 
dist 181=[-2.3479884351099362259 ,1.1155938632059862604 ] 
dist 182=[-2.4180976145870213326 ,1.1817784648496735060 ] 
dist 183=[-2.5141287714425338529 ,1.2354241332758058882 ] 
dist 184=[-2.5861866350570976060 ,1.3309887980056539887 ] 
dist 185=[-2.6389078612624204974 ,1.4256267029844888948 ] 
dist 186=[-2.6577578000991328883 ,1.4815550543915028203 ] 
dist 187=[-2.6622032391999875682 ,1.5198302119343558362 ] 
dist 188=[-2.6574286244916889568 ,1.5440098877944550026 ] 
dist 189=[-2.6944247539328753951 ,1.5587661655039622519 ] 
dist 190=[-2.7994639688202766881 ,1.5603537807420863378 ] 
dist 191=[-2.8704673109633852905 ,1.5546965278382045214 ] 
dist 192=[-2.9135948223434470391 ,1.5478853261538314476 ] 
dist 193=[-2.9398937085301999173 ,.1319871582815291680 ] 
dist 194=[-2.9437274304148749726 ,.2318776476369929584 ] 
dist 195=[-2.9363928959457486588 ,.3268088578038593043 ] 
dist 196=[-2.9267031995100774963 ,.4413094850512670006 ] 
dist 197=[-2.5537416814312458265 ,.9024607548074329200 ] 
dist 198=[-2.5486340419113921951 ,1.2101111395227375513 ] 
dist 199=[-2.5183192104830200737 ,1.4642909784659111000 ] 
dist 200=[-2.5077644183052572354 ,1.7120206698674947709 ] 
dist 201=[-2.3867393610024610220 ,1.9367005221996713734 ] 
dist 202=[-2.3552994569359066082 ,2.0988803343924393244 ] 
dist 203=[-2.3192295705996439488 ,2.2463760997488475397 ] 
dist 204=[-2.3014397433183726180 ,2.4124485482905080367 ] 
dist 205=[-1.8321007794578137691 ,2.5619620030506054061 ] 
dist 206=[-1.7656942239723753766 ,2.6433649265082904524 ] 
dist 207=[-1.6298294304940680938 ,2.6904893448356064468 ] 
dist 208=[-1.5918031469988073931 ,2.7031832220866925183 ] 
dist 209=[-1.4409324069124029686 ,2.7040373928185095922 ] 
dist 210=[-1.4081067667906481260 ,2.7039023369173349974 ] 
dist 211=[-1.3340361840557258837 ,2.7030225943670009055 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 0, 0, 0, 0, 1] 
dist 0=[43.042643152681033158  ,43.042643152681033158  ] 
dist 1=[42.189267717081971891  ,43.506691537840646338  ] 
dist 2=[41.270577836839049592  ,43.775489569172452709  ] 
dist 3=[40.545571775007947181  ,43.848878326769007990  ] 
dist 4=[39.821371316266477356  ,43.849929129789241206  ] 
dist 5=[38.905779799085712984  ,43.829852053912712319  ] 
dist 6=[37.933392334022445692  ,43.790392098520325002  ] 
dist 7=[36.982213799986966826  ,43.725581324504740662  ] 
dist 8=[35.860868993759453559  ,43.556316249994310558  ] 
dist 9=[34.208550616577007567  ,40.999359818886349692  ] 
dist 10=[32.499297217196542966  ,40.341721949602110665  ] 
dist 11=[31.150408964474338647  ,40.162639494002524508  ] 
dist 12=[29.801863893052348984  ,39.512896879071493205  ] 
dist 13=[28.093832799968703935  ,39.325544356137074432  ] 
dist 14=[26.276671669748991659  ,39.026427744649030816  ] 
dist 15=[24.491960058303605850  ,38.924080412124077655  ] 
dist 16=[22.381281138033556047  ,38.504697995370589382  ] 
dist 17=[19.261451738897535813  ,29.665919383004159536  ] 
dist 18=[16.142694456591893370  ,23.291165553400419373  ] 
dist 19=[14.036256398867520942  ,22.722455589670415300  ] 
dist 20=[12.258764372046067970  ,20.334587060710288687  ] 
dist 21=[10.454449406992954358  ,18.489871555596987873  ] 
dist 22=[8.7613025443749253420 ,17.692806971604943464  ] 
dist 23=[7.4279963019053568807 ,17.520088992927002345  ] 
dist 24=[6.0968183801711292038 ,16.366143747416265552  ] 
dist 25=[4.4120825631620688838 ,15.614543248988671736  ] 
dist 26=[2.7818494196335181645 ,10.107702570018406461  ] 
dist 27=[1.6683898931011752552 ,9.7544893494942592362 ] 
dist 28=[.7148506394686451042 ,8.4762612834838251021 ] 
dist 29=[-.27646575335005121602,8.2255663742313394803 ] 
dist 30=[-1.6909233194528913970 ,7.7928282821664550335 ] 
dist 31=[-3.5465501058947948215 ,7.6993737712298649508 ] 
dist 32=[-6.1590522138973287392 ,1.3432766983812979715 ] 
dist 33=[-8.7053384023579119259 ,1.2883947242130099683 ] 
dist 34=[-10.296570672613129744  ,.67127385471754456857] 
dist 35=[-11.502429386446935972  ,.5845887575562506568 ] 
dist 36=[-12.508649937679703958  ,.50982618431815166897] 
dist 37=[-13.321206858621911008  ,.53136149133936142917] 
dist 38=[-13.752936072810241936  ,.59280700951598667465] 
dist 39=[-13.993966683572129626  ,.70366734598327183785] 
dist 40=[-14.049844566861792048  ,.86992307028271805095] 
dist 41=[-13.921539384915742055  ,1.1525735173783714436 ] 
dist 42=[-13.874810038086907631  ,1.4549495627413448419 ] 
dist 43=[-13.826928453625279038  ,1.7000620094617797925 ] 
dist 44=[-13.768209328625714253  ,1.9487277245823599538 ] 
dist 45=[-13.709328367015362617  ,2.2655575257563095242 ] 
dist 46=[-13.660434690054422176  ,2.6005185684030775106 ] 
dist 47=[-13.610386943979380518  ,2.9216416625193931158 ] 
dist 48=[-13.551890133438821378  ,3.2932677281217322076 ] 
dist 49=[-6.6505540639218392685 ,3.8297994599974661610 ] 
dist 50=[-4.3769667726574598302 ,4.3640473611979311979 ] 
dist 51=[-2.7361915421672652123 ,4.7266153171808073944 ] 
dist 52=[-2.4799527477818550024 ,5.0322141884700697673 ] 
dist 53=[-.50398491981260639729,5.3392551591432553597 ] 
dist 54=[.07711230797693807965,5.6232231779885565802 ] 
dist 55=[.24907989276339733023,5.8368124600679287344 ] 
dist 56=[.77097253657169203512,6.0395606819058625844 ] 
dist 57=[1.0061382844324287658 ,6.2803298243423891504 ] 
dist 58=[1.1488122454032143848 ,6.5036494669667161054 ] 
dist 59=[.97087204071088338388,6.6367951744955777819 ] 
dist 60=[.74179453524642146538,6.7294092181460801221 ] 
dist 61=[.46149129356799955218,6.7910150613213495736 ] 
dist 62=[.09049350319847288128,6.8281831259443583134 ] 
dist 63=[-.50047398433870988654,6.8233094379471871079 ] 
dist 64=[-1.0995517202460097073 ,6.7869687377297951922 ] 
dist 65=[-1.5029223151702106421 ,4.3509322491265044480 ] 
dist 66=[-1.8395886301770540123 ,4.4075620467157042360 ] 
dist 67=[-2.1725352304077388543 ,4.4187942843818829314 ] 
dist 68=[-2.4769845667948081421 ,4.4097358690622348497 ] 
dist 69=[-2.6999459410745436280 ,4.3940856477598206938 ] 
dist 70=[-2.9055377449456975654 ,4.3700315699916153120 ] 
dist 71=[-3.1406620215463771590 ,4.3545302293024410338 ] 
dist 72=[-3.3535936866747542627 ,3.8360202232571095370 ] 
dist 73=[-3.4706312098645285633 ,3.7566279094938761349 ] 
dist 74=[-3.5395393459965533154 ,3.5907621290807075218 ] 
dist 75=[-3.5604390073942588124 ,3.5412427209657423218 ] 
dist 76=[-3.5644779826776942787 ,3.3290888364872172865 ] 
dist 77=[-3.5661233334153641046 ,3.2833140597159557575 ] 
dist 78=[-3.5662141129442203803 ,3.1583859455700616719 ] 
dist 79=[-3.5640806743335099746 ,3.1320126004603651640 ] 
dist 80=[-1.9765781726777871524 ,1.7590087499609626804 ] 
dist 81=[-2.4296242783497731831 ,1.7487563794255134281 ] 
dist 82=[-2.8726213097746954349 ,.60979748999572817389] 
dist 83=[-3.1518297427012847106 ,.54354372201058580414] 
dist 84=[-3.3649134798283287230 ,.24603347593162605718] 
dist 85=[-3.5439137309197921185 ,.19279860856966866222] 
dist 86=[-3.6876604980154207298 ,.07539244748340685356] 
dist 87=[-3.7600038952813067076 ,.05245487135491106996] 
dist 88=[-3.7977984528467213194 ,-.07555564975986254414] 
dist 89=[-3.8035718862242125769 ,-.09446065496114437180] 
dist 90=[-3.7615003011796824748 ,-.08641270616616707545] 
dist 91=[-3.7419183183231617129 ,-.03963882316337408583] 
dist 92=[-3.7088365864217089195 ,.02833856276440930953] 
dist 93=[-3.6939568452963680183 ,.12103372487163165214] 
dist 94=[-3.6177125793448790318 ,.24955370622402671146] 
dist 95=[-3.5949527781142017418 ,.46053546590548283336] 
dist 96=[-3.5213717201847435921 ,.67766712652273593826] 
dist 97=[-3.4999358410364271527 ,.83074387022316293589] 
dist 98=[-1.7405418028272513962 ,1.0509954598151632012 ] 
dist 99=[-1.5789730785019593498 ,1.2612416513954810235 ] 
dist 100=[-1.2002893532184175361 ,1.4681121067990512586 ] 
dist 101=[-1.1356140985205597043 ,1.6570757495257955473 ] 
dist 102=[-.62647509815936649372,1.7958603251225296035 ] 
dist 103=[-.53455877109673225242,1.9245589104111442338 ] 
dist 104=[-.39172026346795811169,2.0732858839021109107 ] 
dist 105=[-.35554365617010007692,2.2094603919291897770 ] 
dist 106=[.25397379358805207662,2.3833348257875646681 ] 
dist 107=[.33146762465054788292,2.5507878703198794394 ] 
dist 108=[.49653338948481194809,2.6758700864211778745 ] 
dist 109=[.53018879361219820873,2.7759406625170349179 ] 
dist 110=[.53298520536818472245,2.8533202219530084068 ] 
dist 111=[.22768585628468801485,2.8878170199331606881 ] 
dist 112=[-.24341284570962859631,2.9029639196128713971 ] 
dist 113=[-.7168905085570666409 ,2.9031055707131712629 ] 
dist 114=[-1.0316861742618370381 ,2.1231475758338420740 ] 
dist 115=[-1.2904538492825190428 ,2.0350909588284471200 ] 
dist 116=[-1.5403249941690903136 ,2.0115059792785082413 ] 
dist 117=[-1.7652742253937355571 ,1.8513242566814438266 ] 
dist 118=[-1.9245780848503201586 ,1.8159832712491576082 ] 
dist 119=[-2.0662614046493930152 ,1.7533489690270568166 ] 
dist 120=[-2.2208846431872624053 ,1.7362561111654499962 ] 
dist 121=[-2.3601401131333594284 ,1.3697347615932360196 ] 
dist 122=[-2.4404886252307230005 ,1.3181779847727177851 ] 
dist 123=[-2.4930345160693931117 ,1.1969224044366825851 ] 
dist 124=[-2.5213262028760427688 ,1.1699033894866665412 ] 
dist 125=[-2.5359623906239341957 ,.99731937895050123153] 
dist 126=[-2.5343511890306650713 ,.96351676037101007234] 
dist 127=[-2.5238594130289603543 ,.90043710921971030847] 
dist 128=[-2.5138621396758150695 ,.88423274674105931755] 
dist 129=[-1.2794058190864838473 ,.66735076650040501889] 
dist 130=[-1.5018443373548665474 ,.61424139687464849053] 
dist 131=[-1.6800678178037522956 ,.60331872892647558643] 
dist 132=[-1.8446815916905266471 ,.58382498971093620802] 
dist 133=[-1.9880630320781784814 ,.57833357307670440901] 
dist 134=[-2.0815364503849717066 ,.5576666563698441128 ] 
dist 135=[-2.1564227634229561046 ,.55150709357724885692] 
dist 136=[-2.2256168768622364691 ,.54011088584636013809] 
dist 137=[-2.2827153848380808418 ,.53633239749490433827] 
dist 138=[-2.3093196805216341964 ,.52006838384385826248] 
dist 139=[-2.3195287416171289002 ,.51440084774102526758] 
dist 140=[-2.3190947200478699576 ,.50991032024983363296] 
dist 141=[-2.2881406263497687507 ,.50653908193555648511] 
dist 142=[-2.2751374298465750301 ,.50400422592669052361] 
dist 143=[-2.2459635746345376778 ,.50303352736862244022] 
dist 144=[-2.2331633177909525147 ,.50300822188121677438] 
dist 145=[-1.5443313534108684106 ,.50424753497692375363] 
dist 146=[-1.6022983547130001123 ,.5058274236416230345 ] 
dist 147=[-1.6392348285213826561 ,.57857583203012953833] 
dist 148=[-1.6571308662013387752 ,.81202415285334601784] 
dist 149=[-1.6665838991228560858 ,1.0250785790935060134 ] 
dist 150=[-1.6698199767788321568 ,1.1811413445156568407 ] 
dist 151=[-1.6691150629988647257 ,1.3253860523348434069 ] 
dist 152=[-1.6641759818819832772 ,1.4912754884698365379 ] 
dist 153=[-1.4590561263611909621 ,1.6443840416818411096 ] 
dist 154=[-1.4274541134059708332 ,1.7376141290209564176 ] 
dist 155=[-1.3693432575774800118 ,1.8048632574477585181 ] 
dist 156=[-1.3533244985792275433 ,1.8542628571135375652 ] 
dist 157=[-1.2940713916475572526 ,1.8900887826486319446 ] 
dist 158=[-1.2774114083962641205 ,1.9031606020216252047 ] 
dist 159=[-1.2485106322911848803 ,1.9058505707077110018 ] 
dist 160=[-1.2395478909291050743 ,1.9014924597662217044 ] 
dist 161=[-.61937075267704090836,1.5066143826494235837 ] 
dist 162=[-.79305184600899116893,1.4644764179144251164 ] 
dist 163=[-.90350788115802751787,1.4014739556279212818 ] 
dist 164=[-.98879089318533686433,1.4007754104379194176 ] 
dist 165=[-1.0620010590142403882 ,1.3874767554740887946 ] 
dist 166=[-1.1218278313607324189 ,1.3815586314154166466 ] 
dist 167=[-1.1536940503177798056 ,1.3605380972435433261 ] 
dist 168=[-1.1716352940516393065 ,1.3523074221333461747 ] 
dist 169=[-1.1758892532022402381 ,1.2916091668145540253 ] 
dist 170=[-1.1709220408024525018 ,1.3643712005649410874 ] 
dist 171=[-1.1684721354203523194 ,1.4150165252490286314 ] 
dist 172=[-1.1656633212433136214 ,1.4487131899023489547 ] 
dist 173=[-1.1616169951370219799 ,1.4728683181121593547 ] 
dist 174=[-1.1570770814357200987 ,1.4854312641074804668 ] 
dist 175=[-1.1523005498904853440 ,1.4919044094355738494 ] 
dist 176=[-1.1464352526501313059 ,1.4917647398865975192 ] 
dist 177=[-1.1414438523181245997 ,1.5740455556187232503 ] 
dist 178=[-1.1784581821859613705 ,1.6211011216782236862 ] 
dist 179=[-1.3166858792252400811 ,1.6510082340663212052 ] 
dist 180=[-1.4457393008604911574 ,1.6652782210925029289 ] 
dist 181=[-1.5590944555417697618 ,1.6713142981614413123 ] 
dist 182=[-1.6346620749991335152 ,1.6689681664361149540 ] 
dist 183=[-1.6970684738061125115 ,1.6606302145441123485 ] 
dist 184=[-1.7578928118227930697 ,1.6540800260464038511 ] 
dist 185=[-1.8089614608710105500 ,1.4973450696290391033 ] 
dist 186=[-1.8324266499313559641 ,1.4708600374096453200 ] 
dist 187=[-1.8424365269613904554 ,1.4129401994500773307 ] 
dist 188=[-1.8416671214516517033 ,1.3942497372068534893 ] 
dist 189=[-1.8115383146277854901 ,1.3077302090398114498 ] 
dist 190=[-1.7992184023949611634 ,1.2887772599653524697 ] 
dist 191=[-1.7830627778087109951 ,1.2360183203761107037 ] 
dist 192=[-1.7743641850254497842 ,1.2244712028233667104 ] 
dist 193=[-1.0716522816906078753 ,.48419738473132463044] 
dist 194=[-.51299391610212547004,.53714946081776775945] 
dist 195=[-.61754198266599769347,.58081212285245747197] 
dist 196=[-.70105787963938336371,.62323226011263915768] 
dist 197=[-.77771455923646513738,.66162639284945653963] 
dist 198=[-.84410211034633728264,.68922057773020480693] 
dist 199=[-.88663160464114461466,.71420355581745630725] 
dist 200=[-.91983564848411917643,.74217751478465658333] 
dist 201=[-.94900391673654739738,.77094739479424817403] 
dist 202=[-.97304492576841800604,.84977687038089794117] 
dist 203=[-.98578404730611513395,.89831377786973008928] 
dist 204=[-.99268703473819700066,.93395805352068666498] 
dist 205=[-.9934314364974909314 ,.96132994147748373646] 
dist 206=[-.99015469277787558997,.98134084324627786749] 
dist 207=[-.98755719825255230339,.98760507882977491083] 
dist 208=[-.97201168132213183526,.98889033857678801643] 
dist 209=[-.96935499253525603764,.98902898093376501598] 
dist 210=[-.59544764382849723273,.70553746079058201742] 
dist 211=[-.69199083703712403895,.68072588400145779326] 
dist 212=[-.78074862004985256023,.6723905038191899158 ] 
dist 213=[-.85771036786025529783,.63260897431239726741] 
dist 214=[-.90717331203612531804,.62365375239572732865] 
dist 215=[-.9459688017588671242 ,.60083952257600014283] 
dist 216=[-.9803552049467744545 ,.5939534042295260546 ] 
dist 217=[-1.0092806269651607473 ,.51640535137928099015] 
dist 218=[-1.0262794839841891409 ,.54227118365673843193] 
dist 219=[-1.0377989027940891760 ,.58724191310049702606] 
dist 220=[-1.0448519331144389979 ,.62079854482678368801] 
dist 221=[-1.0484881190221041972 ,.64755106191730239683] 
dist 222=[-1.0469536899686624307 ,.66843558110473182191] 
dist 223=[-1.0412949523645012675 ,.67857096999681408971] 
dist 224=[-1.0369672851514600256 ,.68324539826919663633] 
dist 225=[-.74405686441267628238,.68352388576185838351] 
dist 226=[-.85511688397476199898,.65766322562028713042] 
dist 227=[-.92407748976101657626,.71587897988044403204] 
dist 228=[-.97541463523610756165,.76193081668598020255] 
dist 229=[-1.0161335005234261078 ,.80341622543796719944] 
dist 230=[-1.0476433723812636834 ,.8387837342221508879 ] 
dist 231=[-1.0622240361406352717 ,.8604175989402379593 ] 
dist 232=[-1.0686322356080752180 ,.87612935030779404971] 
dist 233=[-1.0682593454132996638 ,.88785985482170642273] 
dist 234=[-1.0225306969768278838 ,.89534361119639849281] 
dist 235=[-1.0121897094298037269 ,.896414506870845474  ] 
dist 236=[-.99325539236883145282,.89060304411051850857] 
dist 237=[-.98683310816244243469,.88904854654599952745] 
dist 238=[-.95725028223694927405,.84738370496364813495] 
dist 239=[-.94895932422472959443,.83630690182574789205] 
dist 240=[-.92598627697364038218,.82857865952341925468] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 1, 2, 2, 0, 1] 
dist 0=[54.707794148948325079  ,54.707794148948325079  ] 
dist 1=[54.498543140880100007  ,54.889512645739240046  ] 
dist 2=[53.844572848423651156  ,55.054896491586823412  ] 
dist 3=[53.012166044106813167  ,55.061071645179178769  ] 
dist 4=[52.112623731503699368  ,54.873731569567152772  ] 
dist 5=[50.989200230276990030  ,54.767593152928537797  ] 
dist 6=[49.262512909697811613  ,54.428792480923515938  ] 
dist 7=[47.274185605443692419  ,54.258617557247002439  ] 
dist 8=[45.105691869740997805  ,51.942123751744974098  ] 
dist 9=[42.383598293498641683  ,51.486916758632336340  ] 
dist 10=[38.184048658000961476  ,50.898853854091014487  ] 
dist 11=[33.927318181900601605  ,50.669220160297148248  ] 
dist 12=[30.976785076653102029  ,50.350290950743477422  ] 
dist 13=[28.409726520097505771  ,50.139661149778710660  ] 
dist 14=[25.684559037331759484  ,48.511447139765036944  ] 
dist 15=[23.056526885464414213  ,44.674105110810890540  ] 
dist 16=[20.877323462772633887  ,29.631831723289521693  ] 
dist 17=[18.602624665180588652  ,27.990710315996201856  ] 
dist 18=[15.592908270922374059  ,26.038917078291421598  ] 
dist 19=[12.624086291473574864  ,25.564167677321093493  ] 
dist 20=[10.512583131911707772  ,23.926806663705455911  ] 
dist 21=[8.6173508746567417770 ,23.554749564544115113  ] 
dist 22=[6.5121811149703779466 ,23.126731123873590309  ] 
dist 23=[4.4230802720610434166 ,23.016329887077500068  ] 
dist 24=[2.5917231228263531217 ,11.551144822676320091  ] 
dist 25=[.59030172295646351354,10.923640646956264419  ] 
dist 26=[-2.1788129418869500952 ,10.466223055517167016  ] 
dist 27=[-4.8785146535544525906 ,9.4658165973257726479 ] 
dist 28=[-6.6027485938949047263 ,8.7566247206784510194 ] 
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dist 31=[-10.165114553264525291  ,6.4669089688656954062 ] 
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dist 38=[-14.663843228592659237  ,-5.8534333468734432436 ] 
dist 39=[-14.710961484637478080  ,-5.2865848506721125466 ] 
dist 40=[-14.622031311618811089  ,-4.6776302945597066400 ] 
dist 41=[-14.565334208904812588  ,-4.2410758152016193882 ] 
dist 42=[-14.495344177938113904  ,-3.8492915656904342410 ] 
dist 43=[-14.436807388023593553  ,-3.4184602498244504826 ] 
dist 44=[-14.275826496181972051  ,-2.9970636007901584312 ] 
dist 45=[-14.198064262510961969  ,-2.0453981007765894220 ] 
dist 46=[-14.031578013710134772  ,-.92655264663754818483] 
dist 47=[-13.960620384805028320  ,.1366318878890867785 ] 
dist 48=[-6.3307661492784037340 ,.9875002813257523100 ] 
dist 49=[-5.6696634821692901910 ,1.8462140126663966742 ] 
dist 50=[-4.1187745460151726469 ,2.9407548370339209114 ] 
dist 51=[-3.8672160122005704102 ,3.9960833200831562243 ] 
dist 52=[-1.7961624597523920782 ,4.6982738388464453218 ] 
dist 53=[-1.4274806505748171380 ,5.2766106927760357703 ] 
dist 54=[-.91615529315388186955,5.8375177162602576269 ] 
dist 55=[-.89139547049319010909,6.3445405808795169538 ] 
dist 56=[-.31711845630383280548,6.7077539819111644803 ] 
dist 57=[-.26899959117354119523,7.0352319187175713324 ] 
dist 58=[-.17005903666078921807,7.4066996173265537733 ] 
dist 59=[-.147384967473737533  ,7.8093123751334056026 ] 
dist 60=[-.05132313863491774764,8.1348214377471004965 ] 
dist 61=[-.03435835704375186748,8.3021056424558431522 ] 
dist 62=[.00555760501611566563,8.3879258530596176255 ] 
dist 63=[.01155885405249797231,8.4027643819699653157 ] 
dist 64=[.07399352929026089124,4.7665356639127469629 ] 
dist 65=[.08513502257002630116,4.7583388062039706466 ] 
dist 66=[.11270757244623954554,4.7473540164253788916 ] 
dist 67=[.11950979325388791668,4.2652867466434172307 ] 
dist 68=[.16999582463117529328,4.1880534751992255525 ] 
dist 69=[.18164423816125171078,4.0348943827804581395 ] 
dist 70=[.19858555241540648248,3.9893821698039445182 ] 
dist 71=[.20452421223764498064,3.7994114324356538484 ] 
dist 72=[.35022970796982183919,3.7537044860359060018 ] 
dist 73=[.05558817959113230925,3.6416768830315620589 ] 
dist 74=[-.19242949704906560369,3.6018004679511260418 ] 
dist 75=[-.44179502794103330031,2.1664555759369984251 ] 
dist 76=[-.94326228342603670125,1.9633768647830601037 ] 
dist 77=[-1.4130704995640898266 ,1.9233795808209778747 ] 
dist 78=[-1.8745701050912826567 ,1.8275778966060968900 ] 
dist 79=[-2.2957193824923662709 ,1.8054114456942400454 ] 
dist 80=[-2.6044653513737942141 ,.70654510834736285915] 
dist 81=[-2.8902028049799220645 ,.59906338003502633225] 
dist 82=[-3.2195184205004895746 ,.37275447596081558597] 
dist 83=[-3.5218522602627912428 ,.31771417135501703904] 
dist 84=[-3.6998887290512037175 ,.2558663268120643280 ] 
dist 85=[-3.8211171358125269092 ,.3335040885176595363 ] 
dist 86=[-3.8966874921315792055 ,.4351461517506065260 ] 
dist 87=[-3.9475139139613048216 ,.59551400592419150302] 
dist 88=[-3.9699624678807228912 ,.75620528481259714145] 
dist 89=[-3.9759652002308312836 ,.85914272775554371969] 
dist 90=[-3.9683088831255855924 ,.93905448159297258105] 
dist 91=[-2.7506260552958951930 ,1.0079346073616439184 ] 
dist 92=[-2.7693544397951500609 ,1.0640487997989113479 ] 
dist 93=[-2.7709362020522924306 ,1.0930496330812379332 ] 
dist 94=[-2.7563436634937224296 ,1.1084920324396581113 ] 
dist 95=[-2.7481435469497571668 ,1.1110567060178961318 ] 
dist 96=[-1.4934813625883726844 ,1.0984739904386715835 ] 
dist 97=[-1.4821942093858833048 ,1.0910925312801370664 ] 
dist 98=[-1.4505369512178498335 ,1.2253221477189989461 ] 
dist 99=[-1.4390026490442128977 ,1.4369283208686840585 ] 
dist 100=[-1.3683297543617787461 ,1.5841891787568800756 ] 
dist 101=[-1.3511841447387959739 ,1.7125985583414716672 ] 
dist 102=[-1.3191659319207827963 ,1.8489784505791941430 ] 
dist 103=[-1.3093302258757645603 ,1.9802129329459160929 ] 
dist 104=[-.81811268547972836582,2.0881037440644947404 ] 
dist 105=[-.76585503127420405669,2.1997244839133171645 ] 
dist 106=[-1.0226409108776299885 ,2.3458848933526408452 ] 
dist 107=[-1.4034803494793701412 ,2.4836273075364589982 ] 
dist 108=[-1.6542055458633988360 ,2.5616502040471525723 ] 
dist 109=[-1.8574829742494799987 ,2.6110592338834042613 ] 
dist 110=[-2.0489723318194815132 ,2.6345591847277798180 ] 
dist 111=[-2.2180644047272467840 ,2.6447096820852197942 ] 
dist 112=[-2.3319580122782554364 ,2.6410292977345694086 ] 
dist 113=[-2.4271322549976062800 ,2.6290281975743546499 ] 
dist 114=[-2.5215125083201880266 ,2.6193060826945642041 ] 
dist 115=[-2.6014902269360012910 ,2.3676803741400982298 ] 
dist 116=[-2.6391861336396352289 ,2.3258667779560956503 ] 
dist 117=[-2.6558184070493255658 ,2.2343959455487168709 ] 
dist 118=[-2.6555721464827887740 ,2.2051337542650746880 ] 
dist 119=[-2.6142138956534803461 ,2.0706896385586261661 ] 
dist 120=[-2.5964167032311196596 ,2.0415369969380876937 ] 
dist 121=[-2.5717967821201089419 ,1.9601511261378856962 ] 
dist 122=[-2.5589679928472386834 ,1.9431608529730907663 ] 
dist 123=[-.99766026286726707434,1.3330782739104167183 ] 
dist 124=[-1.3308633171633052111 ,1.2639674680291554112 ] 
dist 125=[-1.6052536642373601108 ,1.2482214453238154668 ] 
dist 126=[-1.8712172712211240693 ,1.1962364967061694160 ] 
dist 127=[-2.1114957401024664491 ,1.1177045135740895417 ] 
dist 128=[-2.2833683975087480027 ,.68629576488398922625] 
dist 129=[-2.4381107389803856080 ,.64547222698956065324] 
dist 130=[-2.6100209445715159547 ,.55791274506943338928] 
dist 131=[-2.7639939611749042109 ,.53342753079935093806] 
dist 132=[-2.8471408981950735229 ,.43435501227175241651] 
dist 133=[-2.8943720356801952901 ,.41523336414604522089] 
dist 134=[-2.9058788726624539799 ,.36753332700333295767] 
dist 135=[-2.9031583578787334708 ,.35933292995588267655] 
dist 136=[-2.9007565937222100291 ,.42989720325675997348] 
dist 137=[-2.8974897893656423985 ,.5146450893348164492 ] 
dist 138=[-2.8922146045552089014 ,.58212801828419279258] 
dist 139=[-2.4028895547255738246 ,.64364434750976250861] 
dist 140=[-2.5113311131159123595 ,.69657868716820816744] 
dist 141=[-2.5852683900898518554 ,.72981348474664848336] 
dist 142=[-2.6314936357046062297 ,.94941898948158985996] 
dist 143=[-2.6617101803065498553 ,1.2172113988519750919 ] 
dist 144=[-2.6717461150813162262 ,1.4206191189257641168 ] 
dist 145=[-2.6690672177669779854 ,1.6158424848749384791 ] 
dist 146=[-2.6642747641796479987 ,1.8509746931413763741 ] 
dist 147=[-2.4205915235342916618 ,2.0709450933211221148 ] 
dist 148=[-2.3796480587825069557 ,2.2056560441681643291 ] 
dist 149=[-2.2988809155123775697 ,2.3037388173190848402 ] 
dist 150=[-2.2742564701965577154 ,2.3775177846591474942 ] 
dist 151=[-2.1686774309126395554 ,2.4325102730702450741 ] 
dist 152=[-2.1429673418183096502 ,2.4556053277634939573 ] 
dist 153=[-2.0760645795105894927 ,2.4631074937982911054 ] 
dist 154=[-2.0542254719293305012 ,2.4598091915853875461 ] 
dist 155=[-.2118771049012453317 ,2.3165487114958461567 ] 
dist 156=[-.2853348261009275834 ,2.2914489469387791792 ] 
dist 157=[-.3388634967819792956 ,2.2850550276668917763 ] 
dist 158=[-.3880248095453061433 ,2.3059037888789927710 ] 
dist 159=[-.44405105692406454273,2.3150646675810174149 ] 
dist 160=[-.49604194018096015813,2.3134081646318421085 ] 
dist 161=[-.52909858240241626053,2.2966484226131319209 ] 
dist 162=[-.55460008540785528185,2.2856678507367229363 ] 
dist 163=[-.57644114233756461563,2.3312038889924353763 ] 
dist 164=[-.59424593740962024138,2.4424737633797456458 ] 
dist 165=[-.6036403304330081469 ,2.5170846444727817381 ] 
dist 166=[-.60867041356476428301,2.5611855735114172290 ] 
dist 167=[-.60905930018655445701,2.5901264454586531276 ] 
dist 168=[-.4120087556370120142 ,2.6042256247876131966 ] 
dist 169=[-.39441664019947908798,2.6101451702223932995 ] 
dist 170=[-.6157927123332469652 ,2.6064316150799490813 ] 
dist 171=[-1.0604195213205448703 ,2.4957604627470463762 ] 
dist 172=[-1.3557830309743047945 ,2.5006892725822836058 ] 
dist 173=[-1.5984471610974764625 ,2.4959103235960077285 ] 
dist 174=[-1.8327263316265290518 ,2.4877451012238200740 ] 
dist 175=[-2.0437606280541506593 ,2.4062618891530159181 ] 
dist 176=[-2.1936445218106080762 ,2.3819021512456201894 ] 
dist 177=[-2.3274877673348099720 ,2.3504808513918556366 ] 
dist 178=[-2.4744988576001373745 ,2.3356645273650828735 ] 
dist 179=[-2.6053087636003149528 ,1.9281559278809838683 ] 
dist 180=[-2.6744854451399843989 ,1.8688412466462629452 ] 
dist 181=[-2.7128909967476979109 ,1.7458028666335381736 ] 
dist 182=[-2.7210817597167956869 ,1.7103636465916834972 ] 
dist 183=[-2.7291450700703179442 ,1.5642622456167627274 ] 
dist 184=[-2.7281485609021299903 ,1.5330206848661516642 ] 
dist 185=[-2.7052670246926162292 ,1.4545345393502319604 ] 
dist 186=[-2.6961986740614404656 ,1.4345856795586080215 ] 
dist 187=[-1.0872839055469827316 ,.87616668022831989856] 
dist 188=[-1.0358617039828599637 ,.91524530996190038737] 
dist 189=[-1.0223971457554324618 ,.93492934891105378573] 
dist 190=[-1.0141989501823346083 ,.94524497038278369479] 
dist 191=[-1.0110468378695553892 ,.94693502752191060098] 
dist 192=[-.78086007119549613062,.92612576835203860642] 
dist 193=[-.7497366639670510604 ,.9193128843184327618 ] 
dist 194=[-.69543693040336142117,.94671706150655686192] 
dist 195=[-.69302490534249040179,.9776652723943128195 ] 
dist 196=[-.65067052404101904047,1.0022916188162164404 ] 
dist 197=[-.64035972918826578397,1.0141664816283108764 ] 
dist 198=[-.63180209910354070788,1.0189804875310836443 ] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 0, 0, 0, 0, 1] 
dist 0=[58.365219452347897843  ,58.365219452347897843  ] 
dist 1=[57.821272408185418457  ,58.505197785467334491  ] 
dist 2=[57.146277983412298989  ,58.517620852552289149  ] 
dist 3=[56.482933305084602139  ,58.529130518802960310  ] 
dist 4=[55.699022588915473028  ,58.407402115962694104  ] 
dist 5=[54.542591934110809874  ,57.365132186852907656  ] 
dist 6=[53.231270434421460826  ,57.061432258049280102  ] 
dist 7=[51.828781728069089417  ,56.875611968784323047  ] 
dist 8=[50.045900259203406714  ,56.668073530266367624  ] 
dist 9=[47.421135887341408760  ,52.405093111304384243  ] 
dist 10=[44.627397585384700100  ,49.713908212104454243  ] 
dist 11=[42.375429165611462302  ,48.135110240106797054  ] 
dist 12=[39.804642000718203297  ,47.729256408322387087  ] 
dist 13=[36.617875411449791347  ,46.368932297051859580  ] 
dist 14=[32.784302451413698461  ,45.984397538959030589  ] 
dist 15=[27.053153900092529591  ,45.630419616078477197  ] 
dist 16=[21.317620607472965195  ,45.425788201007143976  ] 
dist 17=[17.466521498731727563  ,38.970888258548717190  ] 
dist 18=[14.249138590172803297  ,20.691967035427038889  ] 
dist 19=[11.044573356506983628  ,16.309649872193677678  ] 
dist 20=[8.0843085048126368205 ,15.665351477767318245  ] 
dist 21=[5.8426171649259933227 ,9.8726605171106380340 ] 
dist 22=[3.4291973939871926985 ,8.8580398908687765634 ] 
dist 23=[1.0983071088568061909 ,7.5279413022812938183 ] 
dist 24=[-1.3412719222746982656 ,7.2648830113859539389 ] 
dist 25=[-3.3624987367046270235 ,1.5344400607742052418 ] 
dist 26=[-5.7524499936119625107 ,-.3577297694607059087 ] 
dist 27=[-7.2647971564536222273 ,-2.1010254868530135451 ] 
dist 28=[-8.4274749333955595368 ,-2.3582939789173659753 ] 
dist 29=[-9.4208442020694212484 ,-4.2183527470504889503 ] 
dist 30=[-10.231942780519800723  ,-4.4960499339542162152 ] 
dist 31=[-10.666617473254205915  ,-4.9807131777629760955 ] 
dist 32=[-10.909541023286502754  ,-5.0580796905837085832 ] 
dist 33=[-10.962407060434469315  ,-5.7561007499979190567 ] 
dist 34=[-6.6433955854238584586 ,-5.2978088154069907107 ] 
dist 35=[-6.4806086485683826140 ,-4.8193364301163891540 ] 
dist 36=[-6.2751362350440099047 ,-4.3542345724321619907 ] 
dist 37=[-6.1719912680278040780 ,-3.7909972701580576522 ] 
dist 38=[-6.1316701030079552484 ,-3.2117621020502068539 ] 
dist 39=[-6.0963745062213649666 ,-2.6823377953576644835 ] 
dist 40=[-6.0629688310692490817 ,-2.0898984322784309812 ] 
dist 41=[-5.0385866210148223315 ,-1.2588081939512724877 ] 
dist 42=[-4.8947761757547103639 ,-.4243598562773880636 ] 
dist 43=[-4.6015391617147744475 ,.1817304060029662035 ] 
dist 44=[-4.5204000565014747715 ,.73596979045271230185] 
dist 45=[-4.2065115214539113722 ,1.3638621597309401712 ] 
dist 46=[-4.1364115417201941700 ,1.9912148990205562629 ] 
dist 47=[-3.9962454107862720808 ,2.5435553151771091806 ] 
dist 48=[-3.9561606445209388175 ,3.2912088040371770269 ] 
dist 49=[-2.1511976219935487942 ,3.9846109320919293362 ] 
dist 50=[-.75665138139255382271,4.7876474615925917988 ] 
dist 51=[-.19815367127017115951,5.2857009884011249381 ] 
dist 52=[-.08396256840147231532,5.6540261296923688921 ] 
dist 53=[.52015581045749320454,5.9428582733938242536 ] 
dist 54=[.62042534034301254184,6.1687381985710704747 ] 
dist 55=[.8414473292019360049 ,6.2856939839162520206 ] 
dist 56=[.87384528865748258559,6.3457168539317331831 ] 
dist 57=[1.1112905493444211295 ,6.3525318714595038102 ] 
dist 58=[1.1387099817271697750 ,5.7648079019664186264 ] 
dist 59=[1.1150029179652105370 ,5.6738430209901273567 ] 
dist 60=[1.0161155888311687883 ,5.5641134468887276320 ] 
dist 61=[.8002881239284014560 ,5.4064158823972919018 ] 
dist 62=[.5343195990297281322 ,4.3462665698538890540 ] 
dist 63=[.2423093141966726683 ,4.3080076134940528463 ] 
dist 64=[-.1245432095648977412 ,4.2859935641764312863 ] 
dist 65=[-.68929511687452068824,4.2699191836381687283 ] 
dist 66=[-1.2550878290150611515 ,-.11142953815181453868] 
dist 67=[-1.6261302389133493233 ,-.39804095103878664679] 
dist 68=[-1.9255855929833955985 ,-.68003964215454848421] 
dist 69=[-2.2591516311902452588 ,-1.1867463014822395774 ] 
dist 70=[-2.6177542781638996495 ,-1.2361543986937721211 ] 
dist 71=[-2.8617427430051472110 ,-1.3308262524119960021 ] 
dist 72=[-3.0685003154571370537 ,-1.3468449180347134849 ] 
dist 73=[-3.2785317431091067388 ,-1.3795674079941101135 ] 
dist 74=[-3.4648956744153462501 ,-1.3535624606029320422 ] 
dist 75=[-3.5772004936180723752 ,-1.2951723887880872607 ] 
dist 76=[-3.6568179884454363570 ,-1.1775689576668973867 ] 
dist 77=[-3.7127225420992562861 ,-1.0312619724700124202 ] 
dist 78=[-3.7491993051387861498 ,-.8583550346618181127 ] 
dist 79=[-3.7524027212186316262 ,-.63320645613368981694] 
dist 80=[-3.7392424489944674973 ,-.27848544651210204583] 
dist 81=[-3.7222466116739451696 ,.0801293218239381147 ] 
dist 82=[-2.2541420963776477707 ,.3208149681061016271 ] 
dist 83=[-2.2049679636958358136 ,.52075073248519716873] 
dist 84=[-1.8233481124935984807 ,.81174852114187019243] 
dist 85=[-1.7490925900529095856 ,1.1229655875201711700 ] 
dist 86=[-1.6299235035732746293 ,1.4039299280360549967 ] 
dist 87=[-1.5980439151128962759 ,1.6040726503729214376 ] 
dist 88=[-1.2835072092697213972 ,1.7832332393745404096 ] 
dist 89=[-1.0504047931228120696 ,1.9804737911231631858 ] 
dist 90=[-.7252281818586135768 ,2.1613719048259361080 ] 
dist 91=[-.69723460252430894629,2.2753129754829591550 ] 
dist 92=[-.43931695873469591863,2.3619586899400002174 ] 
dist 93=[-.39367739593609011145,2.4339146244203954898 ] 
dist 94=[-.333283908238528361  ,2.4908115946822737472 ] 
dist 95=[-.32020827215352248232,2.5173479288735187771 ] 
dist 96=[-.12970053604589683812,2.5266341036164364523 ] 
dist 97=[-.08271996596219422728,2.5665433224848391870 ] 
dist 98=[.03379568770399488169,2.6763288890427507328 ] 
dist 99=[.02123312139899061482,2.7561589905094166970 ] 
dist 100=[.00282695099231631189,2.8148154135878242222 ] 
dist 101=[-.01785456749192427974,2.8400584595546941803 ] 
dist 102=[-.03949941139495839142,2.8561129689275930793 ] 
dist 103=[-.06594557830979709808,2.9119325138777287385 ] 
dist 104=[-.10578673594443742983,2.9533365597618217113 ] 
dist 105=[-.14698537602374294117,2.9656671878333653511 ] 
dist 106=[-.17885059285683455003,2.9643706555861287716 ] 
dist 107=[-.20993260123798920775,2.9562711183380752321 ] 
dist 108=[-.24801175327523528622,2.8845648261362537426 ] 
dist 109=[-.28761800199904444332,2.8615647201825649924 ] 
dist 110=[-.32479652974763026303,2.8174568981194069633 ] 
dist 111=[-.36728028579816009665,2.8010778958207605026 ] 
dist 112=[-.42805883316005231295,1.8799406647615369882 ] 
dist 113=[-.68944242483317376484,1.7811787301578860701 ] 
dist 114=[-.99793135635554605275,1.5435904324937042514 ] 
dist 115=[-1.2934897656772776622 ,1.5001598443438741513 ] 
dist 116=[-1.5581928173530646877 ,1.1525015128332466644 ] 
dist 117=[-1.7435359851681460797 ,1.0860950695138148019 ] 
dist 118=[-1.9063135206087585437 ,.98508041774167848124] 
dist 119=[-2.0809645032526010479 ,.95697915095903665216] 
dist 120=[-2.2395313724364404329 ,.5002766564556103496 ] 
dist 121=[-2.3381117128896910143 ,.5114700909871282510 ] 
dist 122=[-2.4117004518088132829 ,.5160251209493384876 ] 
dist 123=[-2.4705023019585118476 ,.5174658462318059100 ] 
dist 124=[-2.5153531065483251026 ,.5166179278639510611 ] 
dist 125=[-2.5332503763764967474 ,.50565637681646354708] 
dist 126=[-2.5363209829974941650 ,.50171129330990164516] 
dist 127=[-2.5325911379848441019 ,.49615720827040479194] 
dist 128=[-1.5764305355569446008 ,.49352857084048722669] 
dist 129=[-1.4912462226503204589 ,.41671923090762785131] 
dist 130=[-1.2898194747471410775 ,.40584582592539435617] 
dist 131=[-1.2504439676639482452 ,.37812673314574271764] 
dist 132=[-.96722212210639873719,.37247842677273425832] 
dist 133=[-.91363680771432119318,.3533326938480722265 ] 
dist 134=[-.82171066945966667525,.5110674452256312128 ] 
dist 135=[-.79964264260585044452,.7139766125898132965 ] 
dist 136=[-.40913593795370719459,.91028321041833634425] 
dist 137=[-.35730725860852868453,1.0416731295323792994 ] 
dist 138=[-.23903960366487703923,1.1506731347020812921 ] 
dist 139=[-.21732863277299497015,1.2576285231958766118 ] 
dist 140=[-.06935269024551818443,1.3551204302495533390 ] 
dist 141=[-.0493669421310440723 ,1.4263595017751949840 ] 
dist 142=[-.09593783673837118245,1.4920621011493709861 ] 
dist 143=[-.14890880432323268703,1.5674741463481789252 ] 
dist 144=[-.22442726457154173417,1.6355362470444541749 ] 
dist 145=[-.29917214993469635435,1.7254843077009394726 ] 
dist 146=[-.34905512740496765737,1.8488172888922995534 ] 
dist 147=[-.39024880279179895296,1.9594896468092630593 ] 
dist 148=[-.43031835975133185277,2.0536202088311006538 ] 
dist 149=[-.47090000714196279277,2.1109288984124168610 ] 
dist 150=[-.51631041744682106409,2.1522850221777356126 ] 
dist 151=[-.65013202226427208112,2.1827468426703268891 ] 
dist 152=[-.78324686953927412049,2.2026033309398840392 ] 
dist 153=[-.87838370562086973923,2.2052848500105827922 ] 
dist 154=[-.96389147242186815335,2.1941856900736538047 ] 
dist 155=[-1.0585850645089982326 ,2.1882159664743989524 ] 
dist 156=[-1.1519226169848318613 ,2.0989873558647500471 ] 
dist 157=[-1.2320245942810175036 ,2.0743081245657862646 ] 
dist 158=[-1.3177791422198897069 ,2.0498132790059899556 ] 
dist 159=[-1.4336859421909270030 ,2.0351775613468143170 ] 
dist 160=[-1.5438224708106106539 ,.5138162616904584432 ] 
dist 161=[-1.7030523679670441172 ,.3305838018474674896 ] 
dist 162=[-1.8311707598479591567 ,.3883222015216413538 ] 
dist 163=[-1.9411755598316069811 ,.4346376809055055836 ] 
dist 164=[-2.0311324765177781344 ,.4774753270429110478 ] 
dist 165=[-2.0792361054431603680 ,.5147992173157915756 ] 
dist 166=[-2.1059073675433394455 ,.5391077549959573480 ] 
dist 167=[-2.2012549972932296937 ,.5585379333079783406 ] 
dist 168=[-2.3260099942900300698 ,.5763909074337546097 ] 
dist 169=[-2.3994910004707592526 ,.5911096536298272481 ] 
dist 170=[-2.4494844676457687523 ,.5980302688310977100 ] 
dist 171=[-2.4804959548812141448 ,.6006370312684414238 ] 
dist 172=[-2.4973721432060818098 ,.6005846993498007220 ] 
dist 173=[-2.4990263138118276820 ,.5929578100707621443 ] 
dist 174=[-2.4791431262409889197 ,.5896930978535839261 ] 
dist 175=[-2.4745411393600869210 ,.5816451292059687456 ] 
dist 176=[-1.8315265896876296067 ,.5780015379112509227 ] 
dist 177=[-1.7932451896424614469 ,.46493547529873785711] 
dist 178=[-1.6871364783928366431 ,.69693745106667678012] 
dist 179=[-1.6703806501793890421 ,.92233140097560953289] 
dist 180=[-1.4647355635254771174 ,1.1261992155767394630 ] 
dist 181=[-1.4217352690058189280 ,1.2722870772103312629 ] 
dist 182=[-1.3782032739410985086 ,1.4040146605569930970 ] 
dist 183=[-1.3656860357105135588 ,1.5505678828907840019 ] 
dist 184=[-.87288114153474107604,1.6847865901186531176 ] 
dist 185=[-.80914021302785602012,1.7672856775383228231 ] 
dist 186=[-.68064277228854226818,1.8276883501235571644 ] 
dist 187=[-.64700650308775489562,1.8737187277527293592 ] 
dist 188=[-.5253468933481039412 ,1.9069817847488767084 ] 
dist 189=[-.4987881817237389418 ,1.9164294402070599053 ] 
dist 190=[-.4954459118053893823 ,1.9167786757619999985 ] 
dist 191=[-.4960273870405576791 ,1.9137267457184363322 ] 
dist 192=[-.4955902803648056454 ,.77895349084220647381] 
dist 193=[-.37700853706673635422,.11247052669168736443] 
dist 194=[-.44630939806445193792,.08194276545502111079] 
dist 195=[-.50832132167469230893,.07476437608371788076] 
dist 196=[-.56653686741184479908,.05411154246836404358] 
dist 197=[-.61784343960729439177,.05071866981138345751] 
dist 198=[-.65227990790940323527,.05250770342292835707] 
dist 199=[-.68094459716771456706,.06184717728407749126] 
dist 200=[-.70921359472050062159,.07424440749717151118] 
dist 201=[-.73336601771777990489,.08823613011131721584] 
dist 202=[-.74560116083151012924,.10607779599801327124] 
dist 203=[-.7514417916683144351 ,.13383843672279680853] 
dist 204=[-.75349306787769297617,.16584627689023522663] 
dist 205=[-.76140377761530436818,.20063742937962587735] 
dist 206=[-.76254421412399509639,.24412404480366243194] 
dist 207=[-.75997325085769566273,.31083398101771814775] 
dist 208=[-.75734704353002067272,.37771105063238979874] 
dist 209=[-.47521515437500385395,.42186423699409982234] 
dist 210=[-.49071550875830523901,.4578135685483683768 ] 
dist 211=[-.5021877521646120144 ,.4919491926593733249 ] 
dist 212=[-.5094084371563310040 ,.5222905862108409645 ] 
dist 213=[-.5136509400967268579 ,.5506268759137311493 ] 
dist 214=[-.5141079766429783318 ,.5703005884639725447 ] 
dist 215=[-.5113506617417082920 ,.5841837563875261710 ] 
dist 216=[-.5097180653894437205 ,.5947685983877255462 ] 
dist 217=[-.4767213496444638698 ,.6014482677579326466 ] 
dist 218=[-.4704150708333781733 ,.6039945887940765901 ] 
dist 219=[-.4544920404048867484 ,.6032252724571446405 ] 
dist 220=[-.4491035025868094345 ,.6009937489514009926 ] 
dist 221=[-.4196382556021931125 ,.5910973152749767069 ] 
dist 222=[-.4127702869977924758 ,.5878320780313264630 ] 
dist 223=[-.3990778664544343905 ,.5758474967359679039 ] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 1, 0, 0, 2, 1, 2] 
dist 0=[47.710462299122063326  ,47.710462299122063326  ] 
dist 1=[47.420859759072649917  ,48.070065509349792634  ] 
dist 2=[46.623867762382145635  ,48.492979439896133846  ] 
dist 3=[45.356122779597331178  ,48.776551608277650865  ] 
dist 4=[43.217320403373850876  ,49.054248591474475780  ] 
dist 5=[40.997500440581180539  ,49.321343186842173017  ] 
dist 6=[39.406150821104264285  ,49.433309131969678384  ] 
dist 7=[37.966655854180626267  ,49.407047269103060502  ] 
dist 8=[36.353075225701611083  ,48.463490401920746886  ] 
dist 9=[34.745684021886068040  ,48.246185607545054860  ] 
dist 10=[33.330698270546004602  ,47.852128617657422647  ] 
dist 11=[31.781185746229434735  ,47.718432066829863746  ] 
dist 12=[29.636131367215878455  ,47.101651674096386194  ] 
dist 13=[27.475839871711990381  ,46.927864445168756598  ] 
dist 14=[25.854433145980528894  ,46.442334931948503842  ] 
dist 15=[22.865203544582829593  ,46.264954592875753878  ] 
dist 16=[20.291499155421862250  ,33.809131624998628567  ] 
dist 17=[17.603984347889330090  ,32.668442676038165630  ] 
dist 18=[15.041033066961565117  ,29.902936554268727098  ] 
dist 19=[12.964469814702613117  ,29.483271338974771538  ] 
dist 20=[10.840515466758080941  ,25.419217643931946919  ] 
dist 21=[8.0877374978052184800 ,24.657723116404445010  ] 
dist 22=[5.3989032238264029518 ,23.737893238321457100  ] 
dist 23=[3.5300129680068637047 ,23.513171142642477713  ] 
dist 24=[1.8967970384884673214 ,16.958255407560056834  ] 
dist 25=[.1488181925432346035 ,16.136994132108002982  ] 
dist 26=[-1.5494931714399138274 ,14.438534860693361837  ] 
dist 27=[-2.9849199066457139049 ,13.995870284129719378  ] 
dist 28=[-4.5114148583925845924 ,12.371134809788365104  ] 
dist 29=[-6.5747628101779655907 ,12.049329285623589791  ] 
dist 30=[-8.5601238163197318645 ,11.460507797773648342  ] 
dist 31=[-9.7752352597616631691 ,11.325452263354164468  ] 
dist 32=[-10.668135020265639518  ,2.1029280725340437923 ] 
dist 33=[-11.365558420523055981  ,1.3077202252797843988 ] 
dist 34=[-11.911509540123909819  ,-.3944867027806892723 ] 
dist 35=[-12.198711505747278801  ,-.73809639092308303314] 
dist 36=[-12.354665133990592883  ,-1.0351864128440539784 ] 
dist 37=[-12.376001927325969442  ,-1.0210961959918422489 ] 
dist 38=[-11.655745109234885669  ,-.9801697696351816836 ] 
dist 39=[-11.515732543941398238  ,-.9149284436567198749 ] 
dist 40=[-11.594842730640327375  ,-.8030755455445796571 ] 
dist 41=[-12.138384484639981904  ,-.6726246815568101905 ] 
dist 42=[-12.502800701234006302  ,-.5328413467087075107 ] 
dist 43=[-12.720447306691456638  ,-.3608302192886931529 ] 
dist 44=[-12.865029189057464976  ,-.1015304747584627510 ] 
dist 45=[-12.937548243071949474  ,.1654740809387960255 ] 
dist 46=[-12.971804919509371114  ,.3684038151530902863 ] 
dist 47=[-12.963540998286936884  ,.5627156979221500041 ] 
dist 48=[-4.8949241754477379231 ,1.0121126328205603259 ] 
dist 49=[-4.6875117167573474203 ,1.9081484208686963002 ] 
dist 50=[-4.6399384914863796364 ,2.6708337673733341394 ] 
dist 51=[-4.5242670666174743873 ,3.4497093042939105872 ] 
dist 52=[-4.4838549211190393153 ,4.1785931389944934872 ] 
dist 53=[.1744435711122027697 ,4.9660232850703985717 ] 
dist 54=[.5178877883415572966 ,5.9148179712197029340 ] 
dist 55=[.6662625722833019426 ,6.5148145015306966716 ] 
dist 56=[1.3226459747891197280 ,6.9746890040268621043 ] 
dist 57=[2.1714939449663181626 ,7.3642939080989631026 ] 
dist 58=[2.3117344691597833297 ,7.6798515132696747162 ] 
dist 59=[2.4081072045076041006 ,7.8442761385082000746 ] 
dist 60=[2.1613089929206523715 ,7.9303711917046465584 ] 
dist 61=[1.8834438433466353823 ,7.9387714882336993846 ] 
dist 62=[1.6327347043171707154 ,4.1799638195470712896 ] 
dist 63=[1.3541780918888356007 ,4.1912559865730519042 ] 
dist 64=[.9650866085081494410 ,4.0667742306715606653 ] 
dist 65=[.5349019963513668268 ,4.0381274999167668660 ] 
dist 66=[.0922901290561644156 ,3.9600236110588559271 ] 
dist 67=[-.4441695990962196884 ,3.9273484083774885085 ] 
dist 68=[-1.2489686636768560622 ,3.8991186928262559449 ] 
dist 69=[-2.0497130188628129420 ,3.7058370913995902939 ] 
dist 70=[-2.5700067678807316304 ,3.6077099961235410280 ] 
dist 71=[-2.9845522043416421071 ,3.5737821541939935099 ] 
dist 72=[-3.3632358030810433014 ,3.1058285728909031065 ] 
dist 73=[-3.6899651950884560406 ,3.0355127730046382424 ] 
dist 74=[-3.8971544300624782576 ,2.8501442311682350880 ] 
dist 75=[-4.0565285397796998604 ,2.8219294974745508511 ] 
dist 76=[-4.1924271218055748052 ,2.4995780375810844629 ] 
dist 77=[-4.3054945808209162238 ,2.4355145649979584778 ] 
dist 78=[-4.3737357091621777358 ,2.3660909318135543617 ] 
dist 79=[-4.4222546246809521534 ,2.3487692193213342074 ] 
dist 80=[-4.4565704729380157510 ,2.1294363557203664193 ] 
dist 81=[-4.4790893688244529875 ,2.0435688437533309440 ] 
dist 82=[-4.4804966652564396752 ,2.0219650766585924328 ] 
dist 83=[-4.4666159313220808635 ,1.9672046136051972440 ] 
dist 84=[-4.4543649738659348479 ,1.9470731506146133154 ] 
dist 85=[-4.2474493134714453523 ,1.8402744183699738854 ] 
dist 86=[-4.2878811231384386026 ,1.8131748801719562882 ] 
dist 87=[-4.2940873302853395874 ,1.7654754581647723838 ] 
dist 88=[-4.2863376212492759059 ,1.7509915609894664238 ] 
dist 89=[-4.3401921361733587553 ,1.6911740355226511093 ] 
dist 90=[-4.3778305809954484001 ,1.6734644769019087600 ] 
dist 91=[-4.4033794793508350228 ,1.6320262640191042131 ] 
dist 92=[-4.4194091450346114611 ,1.6161262930081182945 ] 
dist 93=[-4.4190575253106099628 ,1.6118742419497976084 ] 
dist 94=[-4.4067977875101854711 ,1.8800933009762306341 ] 
dist 95=[-4.3938106330686864916 ,2.0463236739259765794 ] 
dist 96=[-3.3494809144518165455 ,2.1698444267695908210 ] 
dist 97=[-3.2511510747460987535 ,2.2675788078978747705 ] 
dist 98=[-3.2254322755479815784 ,2.3434673457212832928 ] 
dist 99=[-3.1422284982512924983 ,2.3797754621460629610 ] 
dist 100=[-3.1232427644076410579 ,2.3962173291227625522 ] 
dist 101=[-1.4145401469120807725 ,2.4426215246239893393 ] 
dist 102=[-1.2557899109599406058 ,2.5625225119765572114 ] 
dist 103=[-.89236124679569447487,2.6746134100648268976 ] 
dist 104=[-.82393762866652138051,2.9400651362266574067 ] 
dist 105=[-.36175862138463016613,3.1085395854224408105 ] 
dist 106=[-.27927519712147176075,3.2382501618083931242 ] 
dist 107=[-.1294285638823448538 ,3.3490132076759983568 ] 
dist 108=[-.0958431414144293229 ,3.4392145159682293839 ] 
dist 109=[.16842450044802591575,3.4868814111666564538 ] 
dist 110=[-.0350163038010991094 ,3.5126413646698866151 ] 
dist 111=[-.3376206239042939733 ,3.5154481840239293641 ] 
dist 112=[-.59011623738874309918,2.8502560070353122969 ] 
dist 113=[-.84025738189327455901,2.9051486469986623388 ] 
dist 114=[-1.0697425743181393055 ,2.9214718824345470156 ] 
dist 115=[-1.2397912079491723961 ,2.9236313746153881839 ] 
dist 116=[-1.3988633491803741495 ,2.9219877066187450411 ] 
dist 117=[-1.5845317710068232023 ,1.3343084169694672915 ] 
dist 118=[-1.7562855547301220774 ,1.2246541073622260261 ] 
dist 119=[-1.8598219962358740491 ,.97258418192640983901] 
dist 120=[-1.9332042124754550400 ,.92317651284425148864] 
dist 121=[-1.9846151293295048315 ,.59667354384546270292] 
dist 122=[-2.0216722526277786984 ,.53737443381018551069] 
dist 123=[-2.0377622989170478976 ,.42796070530142644766] 
dist 124=[-2.0415591839412828042 ,.46894320991371880314] 
dist 125=[-2.0396849831666762914 ,.55607688080144388209] 
dist 126=[-1.7416475638486869375 ,.63392900190571980705] 
dist 127=[-1.7371414193230649644 ,.71987369049011891748] 
dist 128=[-1.7137713648677332397 ,.83929848754737148857] 
dist 129=[-1.7062252294971759841 ,.97105143262848227889] 
dist 130=[-1.6198432925611563773 ,1.1061920464406607395 ] 
dist 131=[-1.5978329345299535661 ,1.2696422888462687371 ] 
dist 132=[-1.8706325923613759711 ,1.5143683131823824152 ] 
dist 133=[-2.1475265179407904386 ,1.7572252820303749222 ] 
dist 134=[-2.3205310360035875030 ,1.9132144984672301664 ] 
dist 135=[-2.4506676883799998237 ,2.0353627741066274800 ] 
dist 136=[-2.5564452961886301628 ,2.1431663756025911162 ] 
dist 137=[-2.6385736010880191212 ,2.2334108030399442215 ] 
dist 138=[-2.6743079367989297503 ,2.2854815275001901787 ] 
dist 139=[-2.6904724351553305153 ,2.3195099587590724022 ] 
dist 140=[-2.6944787455243800370 ,2.3377450801432821854 ] 
dist 141=[-2.6203939720411366188 ,2.3452794306579346476 ] 
dist 142=[-2.6000950235639519434 ,2.3429125771403957488 ] 
dist 143=[-2.5578327791376919806 ,2.3231830290381544131 ] 
dist 144=[-2.5414767551732490353 ,2.3118121701163847409 ] 
dist 145=[-2.4557643046598974808 ,2.2180117802371321920 ] 
dist 146=[-2.4348755766016806125 ,2.1920534085689771989 ] 
dist 147=[-2.3639129243684369825 ,2.1539896942223204745 ] 
dist 148=[-2.3520612316128121100 ,2.1390109186739456677 ] 
dist 149=[-1.1118106305500645139 ,1.5766781434020083909 ] 
dist 150=[-.99308391889992408414,1.6882052337818974443 ] 
dist 151=[-.72749260840942782234,1.7525232310261065170 ] 
dist 152=[-.67115535564065846105,1.7946089654573023233 ] 
dist 153=[-.4971119553252261871 ,1.8173990817852474470 ] 
dist 154=[-.5178424735925643133 ,1.9338782309832491616 ] 
dist 155=[-.5297823449166030989 ,2.1047432101752976355 ] 
dist 156=[-.5375527784068613364 ,2.3039250106655532714 ] 
dist 157=[-.5416446504854423900 ,2.4869458374997695016 ] 
dist 158=[-.54327573838256519816,2.5933082572563536602 ] 
dist 159=[-.6377727897132051001 ,2.6639229518857403470 ] 
dist 160=[-.7654278253892720375 ,2.7042619324294370963 ] 
dist 161=[-.8909941886471452006 ,2.7289194883963034564 ] 
dist 162=[-1.0056108527514529891 ,2.7369394578519273602 ] 
dist 163=[-1.0895658289143581245 ,2.7343166526652946890 ] 
dist 164=[-1.1813742841619375288 ,2.7279843315487231777 ] 
dist 165=[-1.2835433607966661255 ,2.4315548781004711405 ] 
dist 166=[-1.3761321287689007000 ,2.5115234148582354166 ] 
dist 167=[-1.4326862062685109888 ,2.6084780880935351578 ] 
dist 168=[-1.4736726534563395135 ,2.6813964628958359035 ] 
dist 169=[-1.5041252198795640188 ,2.7344488331332927344 ] 
dist 170=[-1.5254651454328468571 ,2.7521097824999918155 ] 
dist 171=[-1.5300790167930208591 ,2.7556183393848784817 ] 
dist 172=[-1.7343975920899643627 ,2.7521829457396544310 ] 
dist 173=[-1.9514656450886090448 ,2.6209068990058017033 ] 
dist 174=[-2.0885356809074202673 ,2.5929383820861034414 ] 
dist 175=[-2.1932747679337332698 ,2.5288243787569210130 ] 
dist 176=[-2.2813033078399505298 ,2.5054451185241916642 ] 
dist 177=[-2.3518835378612221270 ,2.3873083372742601360 ] 
dist 178=[-2.3869846162028808199 ,2.3593066223289801251 ] 
dist 179=[-2.4028464896613191144 ,2.2850379265827415919 ] 
dist 180=[-2.4044249141403098807 ,2.2617546771406084641 ] 
dist 181=[-2.3797201010660217049 ,1.1692192806187517261 ] 
dist 182=[-2.4486833735497640738 ,1.2551799668726744305 ] 
dist 183=[-2.5411814734637809664 ,1.3049689593983721030 ] 
dist 184=[-2.6091229632726984321 ,1.3377873480580052228 ] 
dist 185=[-2.6581812616784587822 ,1.3560144123594434547 ] 
dist 186=[-2.6753077310843811381 ,1.3664222586963948743 ] 
dist 187=[-2.6783817791009174764 ,1.3680350974676383285 ] 
dist 188=[-2.6715338356786200416 ,1.3640027076991202668 ] 
dist 189=[-2.7142172310314067907 ,1.3602801487675553269 ] 
dist 190=[-2.8199324518492407601 ,.1390943396586557687 ] 
dist 191=[-2.8908698890589133730 ,.2469380128657146024 ] 
dist 192=[-2.9329022702797858767 ,.3483784480030081448 ] 
dist 193=[-2.9582132635112839331 ,.4676358446280928109 ] 
dist 194=[-2.9624089674865496906 ,.5892513537791590715 ] 
dist 195=[-2.9550399577167438511 ,.70010268148953859708] 
dist 196=[-2.9462831731863637452 ,.82432399582238282689] 
dist 197=[-2.5773356052456968240 ,.99930295509730053814] 
dist 198=[-2.5698793295877534886 ,1.1758887945977338825 ] 
dist 199=[-2.5334479202087535818 ,1.4321256918219462037 ] 
dist 200=[-2.5223831733489436664 ,1.6840359834622459104 ] 
dist 201=[-2.3914286586904447020 ,1.9129855838707646576 ] 
dist 202=[-2.3581773958205822847 ,2.0790678476908285865 ] 
dist 203=[-2.3211263262241521547 ,2.2309454851583031462 ] 
dist 204=[-2.3025511492047803348 ,2.4032011063538078957 ] 
dist 205=[-1.8160286423358193414 ,2.5589593135046317057 ] 
dist 206=[-1.7476071615529507966 ,2.6449898052813266529 ] 
dist 207=[-1.6082234468962731020 ,2.6964440032358132999 ] 
dist 208=[-1.5694993760150821647 ,2.7141938985821574619 ] 
dist 209=[-1.4174850797551882903 ,2.7193807253611193024 ] 
dist 210=[-1.3841856011567137492 ,2.7206882797851598103 ] 
dist 211=[-1.3114393573619159690 ,2.7194101901955659581 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 1, 1, 1, 1, 2] 
dist 0=[40.339259592604330486  ,40.339259592604330486  ] 
dist 1=[39.662431884735077054  ,40.684032820639941422  ] 
dist 2=[38.925030223264079940  ,40.876730567241901894  ] 
dist 3=[38.338273075192484591  ,40.946043307558801502  ] 
dist 4=[37.747529189985118885  ,40.966564383830619805  ] 
dist 5=[36.994074908432033518  ,40.950011043883937821  ] 
dist 6=[36.190182535103426192  ,40.923135310134265235  ] 
dist 7=[35.397836037855163755  ,40.881737410913421466  ] 
dist 8=[34.458909810935267503  ,40.825391594030418328  ] 
dist 9=[33.069248630436541054  ,38.815038394954253259  ] 
dist 10=[31.628075153347930106  ,38.505947266315937028  ] 
dist 11=[30.483247645072238204  ,37.942911908493858474  ] 
dist 12=[29.331201654703833359  ,37.788810176612015138  ] 
dist 13=[27.861043624692752003  ,37.223926566508197185  ] 
dist 14=[26.290459081521661812  ,37.063315619073994373  ] 
dist 15=[24.736980033114165993  ,36.792115974004003355  ] 
dist 16=[22.890803499694043403  ,36.705074190558971082  ] 
dist 17=[20.150351632446743126  ,29.209157771302660997  ] 
dist 18=[17.408863509022723408  ,25.360826363335530030  ] 
dist 19=[15.558517288303252887  ,23.215200606001667795  ] 
dist 20=[13.997636650475266364  ,22.872917584072246457  ] 
dist 21=[12.413015150615276925  ,19.864922432908289060  ] 
dist 22=[10.925100200650149808  ,19.308092415332446921  ] 
dist 23=[9.7507032311572360828 ,18.567150470192394031  ] 
dist 24=[8.5752495834858876138 ,18.344214762283840283  ] 
dist 25=[7.0830855773874782213 ,16.377469658762651707  ] 
dist 26=[5.6363795807196538118 ,13.364361945415615914  ] 
dist 27=[4.1965510195540391794 ,12.164716935728910484  ] 
dist 28=[2.4599926873076295251 ,11.867017793556242302  ] 
dist 29=[.8759283019429144019 ,10.600727645857765114  ] 
dist 30=[-.90873645667724698294,10.368779743157709459  ] 
dist 31=[-3.4476004395974612901 ,9.8451944244898772678 ] 
dist 32=[-5.9320663596078637617 ,9.7420937530413682878 ] 
dist 33=[-7.4995155696287724821 ,3.8694743770849888174 ] 
dist 34=[-8.7050512221797068743 ,3.3298538145575325615 ] 
dist 35=[-9.7430763274071193633 ,2.1072729133699664092 ] 
dist 36=[-10.603084412649674592  ,1.8997884284827884898 ] 
dist 37=[-11.097320048593146029  ,.3845598988478334264 ] 
dist 38=[-11.423254174936724462  ,.1185579566884879595 ] 
dist 39=[-11.611125405204596875  ,-.3145029039522715779 ] 
dist 40=[-11.735134940196984775  ,-.4146058731014444515 ] 
dist 41=[-11.805778681518799450  ,-1.9822854211164708627 ] 
dist 42=[-11.853920248864261069  ,-2.1837796814705842938 ] 
dist 43=[-11.887318204949491529  ,-2.6164610027470812230 ] 
dist 44=[-11.911040682019301439  ,-2.7024240562502950147 ] 
dist 45=[-11.920167092346668208  ,-2.3551607151651454774 ] 
dist 46=[-11.921205697014727172  ,-1.9396586958200276190 ] 
dist 47=[-11.912253403511023388  ,-1.4793065220532663630 ] 
dist 48=[-8.8042414741330502323 ,-.89808493770422796996] 
dist 49=[-4.9265117478094323083 ,0                     ] 
dist 50=[-4.2941586795964567705 ,-2.9235215305239843548 ] 
dist 51=[-3.5854831113867473874 ,-1.9546801174719936719 ] 
dist 52=[-3.4576242034760765180 ,-1.0477986234345308265 ] 
dist 53=[-2.5109782784934314387 ,-.34433157902299250283] 
dist 54=[-2.3390916749990508901 ,.34547290683243344749] 
dist 55=[-2.0525559604501016635 ,1.1980082259457049513 ] 
dist 56=[-1.9850578305975080460 ,2.0084339863952458896 ] 
dist 57=[-.87320884636028639444,2.5302254753826657996 ] 
dist 58=[-.72757090280407111681,2.9414736972404516245 ] 
dist 59=[-.41997970641794534326,3.3106813752130070153 ] 
dist 60=[-.35125676512637115498,3.6260513330843078507 ] 
dist 61=[-.05157843729445999351,3.8234725786101771745 ] 
dist 62=[.00166823380006817851,4.0048860546887843814 ] 
dist 63=[.09870937447865007978,4.1774114459790126131 ] 
dist 64=[.11907545001897229497,4.3226285446568146037 ] 
dist 65=[.16379276169985033751,4.3950146681448451996 ] 
dist 66=[.1555954562179086935 ,4.4309436345446492556 ] 
dist 67=[.12412313606358412105,4.4360811335759416411 ] 
dist 68=[.05364422016810989323,4.5414298317252288542 ] 
dist 69=[-.03570425149322469158,4.7052713303709342568 ] 
dist 70=[-.14255854333431375722,4.7883732433457287147 ] 
dist 71=[-.28226556325230331473,4.8291889587914400102 ] 
dist 72=[-.50277766868814164702,4.8359059905923598847 ] 
dist 73=[-.73480176965812433913,4.7962658555203713329 ] 
dist 74=[-.92049937157399914888,4.7763025766280849536 ] 
dist 75=[-1.1075934255027608945 ,4.7204949144188439755 ] 
dist 76=[-1.3452793833915384034 ,4.6935998738117406331 ] 
dist 77=[-1.5972025925294235832 ,4.5364976457041105884 ] 
dist 78=[-1.8411745522590683648 ,4.4952418088236682734 ] 
dist 79=[-2.1261065639241093337 ,4.3985408304004513299 ] 
dist 80=[-2.5415818650989264829 ,4.3626870915526688087 ] 
dist 81=[-2.9501800700251757103 ,1.1248096526384783716 ] 
dist 82=[-3.2076852593244156161 ,.71963097682635714505] 
dist 83=[-3.4040060853918017228 ,.65431504546649571092] 
dist 84=[-3.5683954703013527402 ,.11305572376371912225] 
dist 85=[-3.6999303879271737614 ,.01605942899702584421] 
dist 86=[-3.7651284725056741264 ,-.12405238289945130755] 
dist 87=[-3.7960048178062854363 ,-.1622176144587656902 ] 
dist 88=[-3.7994965532576977788 ,-.8217907545883502863 ] 
dist 89=[-3.7545138215743043503 ,-.90297246837408434845] 
dist 90=[-3.8314755076637318151 ,-1.0857946483429380004 ] 
dist 91=[-3.9546796050099537394 ,-1.1138338885812726354 ] 
dist 92=[-4.0494531145593317177 ,-1.3277393291440548977 ] 
dist 93=[-4.1188336168469339206 ,-1.3624409472939290088 ] 
dist 94=[-4.1406769689618952832 ,-1.1398600050285329288 ] 
dist 95=[-4.1420903413234303765 ,-.58527871240757688461] 
dist 96=[-4.1298967181987498943 ,.25380296306074853756] 
dist 97=[-2.7829944626161318806 ,1.0930159853817337985 ] 
dist 98=[-2.6561833770862447071 ,1.6481180156169211493 ] 
dist 99=[-2.3574254899737681790 ,2.1014341634023351675 ] 
dist 100=[-2.2939193979562499608 ,2.5343696323943778969 ] 
dist 101=[-1.8706255619413478900 ,2.9210196830518663018 ] 
dist 102=[-1.7887373582981904402 ,3.1895785368869602741 ] 
dist 103=[-1.6399497375552267269 ,3.4229857625865371215 ] 
dist 104=[-1.6032748789892453451 ,3.6693007253588093470 ] 
dist 105=[-.9935410709794169936 ,3.8913504136859408513 ] 
dist 106=[-.91011390769755089935,4.0279114117024033913 ] 
dist 107=[-.71689433932565701344,4.1279006967981256934 ] 
dist 108=[-.68051815987558521598,4.2040273940086793864 ] 
dist 109=[-.42657670382511424423,4.2589595519902143295 ] 
dist 110=[-.38058229295797980136,4.2743846836636488839 ] 
dist 111=[-.29873227550696536505,4.2706307257653455364 ] 
dist 112=[-.28052550516586186657,4.2587810907800111431 ] 
dist 113=[.1587128071853435636 ,3.0204608722925958676 ] 
dist 114=[.1526529525915807474 ,3.2183487617032444406 ] 
dist 115=[.1314290563692446465 ,3.3614745548165116246 ] 
dist 116=[.1022746828320218365 ,3.4675231582319837161 ] 
dist 117=[.0645437406140673744 ,3.5466404292461096048 ] 
dist 118=[.0134014450364202953 ,3.5822511456629993226 ] 
dist 119=[-.0692943800198890752 ,3.5942698983324616974 ] 
dist 120=[-.1572046856020147066 ,3.5922644738412911201 ] 
dist 121=[-.2291719374732600072 ,3.3595147944836823580 ] 
dist 122=[-.3032066285904578634 ,3.3160466795016188668 ] 
dist 123=[-.3993926553196475990 ,3.2353497265840914181 ] 
dist 124=[-.50247289626451390656,3.2101471706069485647 ] 
dist 125=[-.60404084905853001306,3.1021961650989041782 ] 
dist 126=[-.72400626831966316913,3.0725138866489126806 ] 
dist 127=[-.9005408194379853537 ,2.9993501481265355878 ] 
dist 128=[-1.0751077629453342930 ,2.9715475847843977183 ] 
dist 129=[-1.1872247630613533324 ,1.0519836584118298328 ] 
dist 130=[-1.2751513033968382638 ,.88016602373450389636] 
dist 131=[-1.3531568647094550338 ,.49236531231281407518] 
dist 132=[-1.4189088842707482872 ,.41843798526248323722] 
dist 133=[-1.5878723005949740829 ,-.05343431878288078780] 
dist 134=[-1.8327855400384158834 ,-.13572583602531257406] 
dist 135=[-2.0612831326003812611 ,-.29205581300268830236] 
dist 136=[-2.3272195976604746798 ,-.32806242469707818713] 
dist 137=[-2.5727544992771706760 ,-.70843135886021745917] 
dist 138=[-2.7198212683684303744 ,-.76448806296844743275] 
dist 139=[-2.8229746455497646827 ,-.80585694148971788171] 
dist 140=[-2.8932313779317394543 ,-.6436213002006956092 ] 
dist 141=[-2.9432445195109741869 ,-.4720065337701499277 ] 
dist 142=[-2.9655933730115149387 ,-.2606263942846229453 ] 
dist 143=[-2.9719726257577750319 ,.0603316852943749704 ] 
dist 144=[-2.9683669506726828983 ,.38123774158777386786] 
dist 145=[-1.0227213173778558025 ,.59241219626410041546] 
dist 146=[-.9030179797027697455 ,.76367720952550641145] 
dist 147=[-.76070411756070693099,.92529157876919472497] 
dist 148=[-.61248022676731677978,1.0683650053934645901 ] 
dist 149=[-.58441968460125076819,1.1656276319753506055 ] 
dist 150=[-.52715457819113691547,1.2479823957603149426 ] 
dist 151=[-.51166724925629476106,1.3315554792465034834 ] 
dist 152=[-.34291020591041331932,1.4063646460173312365 ] 
dist 153=[-.31728294329345352145,1.4537380976092405262 ] 
dist 154=[-.2659748614113817944 ,1.4900988112339733392 ] 
dist 155=[-.29763471955550865476,1.5209458674717938477 ] 
dist 156=[-.41602115645735713828,1.5458823158506021479 ] 
dist 157=[-.55136061676012559177,1.5586468342196295871 ] 
dist 158=[-.69686381721728186486,1.6778016047065548590 ] 
dist 159=[-.87763377391508693664,1.8399910303538293115 ] 
dist 160=[-1.1537160868660625822 ,2.0664603607261388683 ] 
dist 161=[-1.4299534373139270662 ,2.2854652081829223902 ] 
dist 162=[-1.6113411813189069405 ,2.4178619040545676814 ] 
dist 163=[-1.7579154952769094076 ,2.5122741499925697784 ] 
dist 164=[-1.8952163450613135197 ,2.5796524080258806808 ] 
dist 165=[-2.0159710273423745312 ,2.6283756777897354366 ] 
dist 166=[-2.0965102296943515306 ,2.6483187040801818998 ] 
dist 167=[-2.1629708055076462061 ,2.6527884003262708307 ] 
dist 168=[-2.2275357188320940492 ,2.6493130473264913803 ] 
dist 169=[-2.2800801933592500704 ,2.4610136075301257846 ] 
dist 170=[-2.2985665091081995742 ,2.4266999716014279272 ] 
dist 171=[-2.3041240297292243586 ,2.3597913468736241466 ] 
dist 172=[-2.3050795045310533930 ,2.3386261764227607885 ] 
dist 173=[-2.2250542786999422940 ,2.2450568033002676312 ] 
dist 174=[-2.2043068705946587178 ,2.2215529626933516895 ] 
dist 175=[-2.1918517363560768945 ,2.1577994773287117808 ] 
dist 176=[-2.1874527354186655907 ,2.1375244740717874607 ] 
dist 177=[-.54350842226128546588,.76058185861771732656] 
dist 178=[-.86494152132177088349,.63451841193954477932] 
dist 179=[-1.1338135533539611320 ,.35605719812004956632] 
dist 180=[-1.4013225036240004115 ,.35814917706214750447] 
dist 181=[-1.6475465473707774101 ,.37253501559332015531] 
dist 182=[-1.8314643154913597149 ,.38352644449956171547] 
dist 183=[-2.0050136314050472928 ,.39272957790645921488] 
dist 184=[-2.2098575972139500134 ,.40007318454936658479] 
dist 185=[-2.3994204715166886686 ,.40364306999532868076] 
dist 186=[-2.5119784084123256146 ,.40511145349936535809] 
dist 187=[-2.5897253031907924674 ,.40473207436973372935] 
dist 188=[-2.6403434749699037443 ,.40160128067290008972] 
dist 189=[-2.6741556121285606837 ,.40013580496351287698] 
dist 190=[-2.6848186499431238127 ,.39337618853106672366] 
dist 191=[-2.6826970322340193320 ,.3919207827611996984 ] 
dist 192=[-2.6766988303065935249 ,.04084775643721720175] 
dist 193=[-2.4508488494332129468 ,.14506150659178981472] 
dist 194=[-2.5096353359638568047 ,.36672509867876296331] 
dist 195=[-2.5712154151345836729 ,.61696696961519436256] 
dist 196=[-2.6072179087999009240 ,.87286822185488286768] 
dist 197=[-2.6285171312411418308 ,1.1128392756291418722 ] 
dist 198=[-2.6314089590698726821 ,1.2995020707332711244 ] 
dist 199=[-2.6243184345526102179 ,1.4828862978319220645 ] 
dist 200=[-2.6162339976923981530 ,1.7097760628859326002 ] 
dist 201=[-2.3856161355586664890 ,1.9250878236591141940 ] 
dist 202=[-2.3461121200204595910 ,2.0622629050342313259 ] 
dist 203=[-2.2621868757863097623 ,2.1684959867023284007 ] 
dist 204=[-2.2353097674079644494 ,2.2603108282643885880 ] 
dist 205=[-2.1116745616752393641 ,2.3358663649439990602 ] 
dist 206=[-2.0847767705771267947 ,2.3772065677348980823 ] 
dist 207=[-2.0021808225733925489 ,2.4014312803797608018 ] 
dist 208=[-1.9895074243756569944 ,2.4086804177706090487 ] 
dist 209=[-.4551054754991532394 ,2.4052048177179701533 ] 
dist 210=[-.4582860640847202552 ,2.4433702341266425410 ] 
dist 211=[-.47026150853598154511,2.5065232335267183415 ] 
dist 212=[-.52612411606089148618,2.5442303365074815405 ] 
dist 213=[-.56775548435565030566,2.5672948925850983232 ] 
dist 214=[-.60691457467569019938,2.5720009625617103798 ] 
dist 215=[-.65290572005954868991,2.5662765430614986170 ] 
dist 216=[-.69526026199728017239,2.5592980884524782742 ] 
dist 217=[-.71990372585057248529,2.5883830978298680395 ] 
dist 218=[-.7362633345767075632 ,2.6918407628885976809 ] 
dist 219=[-.74555587361258628407,2.7589460606996737004 ] 
dist 220=[-.75074642299968839142,2.7939970102593525703 ] 
dist 221=[-.7507386947238024193 ,2.8140157445787095713 ] 
dist 222=[-.74814474856448545263,2.8211207209358977335 ] 
dist 223=[-.74536547269993563619,2.8201230177128467903 ] 
dist 224=[-.25736189726894664161,2.8124229818687035410 ] 
dist 225=[-.71290371339994464313,2.5421611536778289146 ] 
dist 226=[-1.0185296337697041852 ,2.5304990366153800600 ] 
dist 227=[-1.2729351147786781972 ,2.4829821492932178480 ] 
dist 228=[-1.5240340407868608136 ,2.4718389354109632358 ] 
dist 229=[-1.7538582138983229209 ,2.3235354971348340638 ] 
dist 230=[-1.9233476347724926617 ,2.2874181129875034647 ] 
dist 231=[-2.0811464213217387138 ,2.2510843726046382963 ] 
dist 232=[-2.2643101963935981125 ,2.2316367255570517221 ] 
dist 233=[-2.4322005459309227201 ,1.7187959964063546022 ] 
dist 234=[-2.5290369051406062351 ,1.6477432641943728390 ] 
dist 235=[-2.5923988684485963180 ,1.5053863049055071189 ] 
dist 236=[-2.6266776911160565200 ,1.4667289933181596490 ] 
dist 237=[-2.6464997277570247948 ,1.3203136968711080057 ] 
dist 238=[-2.6521562499271972582 ,1.2872221501971325172 ] 
dist 239=[-2.6485243023201918902 ,1.2229849576039896518 ]