8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 0, 2, 2, 1, 2] 
dist 0=[64.684467255592428214  ,64.684467255592428214  ] 
dist 1=[64.398978388289227260  ,65.074418514392034503  ] 
dist 2=[63.649361129775956479  ,65.439555808318957069  ] 
dist 3=[62.348431595371816718  ,65.613094410803848857  ] 
dist 4=[60.134649481161936822  ,65.679212041668746595  ] 
dist 5=[57.500630153154762786  ,65.615504732571750539  ] 
dist 6=[54.521904803578989067  ,65.472420170590474072  ] 
dist 7=[50.716758535374055361  ,65.321685086994647574  ] 
dist 8=[44.783272954110755043  ,64.920349855761285412  ] 
dist 9=[38.774053480430005547  ,64.713711004481321574  ] 
dist 10=[34.666398980984950071  ,63.533044316404408116  ] 
dist 11=[31.160097229783051568  ,63.141240434378375800  ] 
dist 12=[27.551337442320093011  ,62.867659735569657686  ] 
dist 13=[24.146201349742200806  ,61.905945156250404522  ] 
dist 14=[21.452444488018307008  ,55.712369928630012150  ] 
dist 15=[18.758474450238879165  ,51.626567757473412226  ] 
dist 16=[15.351676807657803478  ,33.868068021963713582  ] 
dist 17=[12.068355560422036030  ,31.580235587440654882  ] 
dist 18=[9.8669550776420432073 ,26.247076870463183251  ] 
dist 19=[8.0295295254689281040 ,25.388313942108953768  ] 
dist 20=[6.1989721460482525499 ,18.379081345248469987  ] 
dist 21=[4.5021993785065499553 ,17.141912525692579865  ] 
dist 22=[3.1981679066796471197 ,15.301211313880796428  ] 
dist 23=[1.9228106203409967928 ,14.826116769594720448  ] 
dist 24=[.33872276150971364383,11.440588088859435233  ] 
dist 25=[-2.7110917077217757916 ,11.225862920236506884  ] 
dist 26=[-6.1010643610085338196 ,4.1914487665042647704 ] 
dist 27=[-8.2973239564421903724 ,3.7437549791557608277 ] 
dist 28=[-10.048510759757227394  ,2.3153436027232696637 ] 
dist 29=[-11.660636130556118263  ,.97102814187816372219] 
dist 30=[-13.069189303362742369  ,-.12132812379373616015] 
dist 31=[-14.007386219229315715  ,-.79466434400026001374] 
dist 32=[-14.786423265232688527  ,-1.3073318149798568049 ] 
dist 33=[-15.559736929284655865  ,-1.4255947617012262484 ] 
dist 34=[-16.214017324016731453  ,-1.7603432476630847649 ] 
dist 35=[-16.517609690921257582  ,-1.7654910305181847892 ] 
dist 36=[-16.664229051107421403  ,-1.6533913141456266962 ] 
dist 37=[-16.690429360887934373  ,-1.3559273264577004279 ] 
dist 38=[-16.326522090698535881  ,-.96470027163108301883] 
dist 39=[-16.230152946012494562  ,-.4778623824235278772 ] 
dist 40=[-16.145164132733391510  ,.17144502796804515513] 
dist 41=[-16.097487700331528981  ,1.2116317409733809359 ] 
dist 42=[-15.235953621318220632  ,3.8445298285568049474 ] 
dist 43=[-15.092701188101664016  ,6.0935240588730953179 ] 
dist 44=[-14.321762289451507614  ,7.9424418755583754131 ] 
dist 45=[-14.132030781806731328  ,9.7253514126776976560 ] 
dist 46=[-13.729665031056523263  ,11.326920968682089325  ] 
dist 47=[-13.594729538444754650  ,12.452459558466280914  ] 
dist 48=[-7.3733461569541203590 ,13.443938936131934173  ] 
dist 49=[-6.7229662273160897151 ,14.510826306031822167  ] 
dist 50=[-5.2768005339372801608 ,15.460397900809322184  ] 
dist 51=[-4.9472700951498073952 ,15.983759184554774006  ] 
dist 52=[-3.2058218402673484269 ,16.294947319534110089  ] 
dist 53=[-2.8888975401031176394 ,16.397656423765500146  ] 
dist 54=[-2.2027566992578891580 ,16.409534709645590686  ] 
dist 55=[-2.0297725247755436514 ,16.358332320246628773  ] 
dist 56=[-.56952314790130493584,16.251465556495209888  ] 
dist 57=[-.32563957465780573699,16.185497682935558316  ] 
dist 58=[-.35952121951871644466,11.370929660330048172  ] 
dist 59=[-.55723395035896149028,10.840036912011084541  ] 
dist 60=[-.75076281835288745839,9.5577182471326051600 ] 
dist 61=[-.9534203774715688692 ,9.3036661881112452475 ] 
dist 62=[-1.4657269629030479983 ,7.4025332013813344497 ] 
dist 63=[-1.8665870206778200017 ,6.5017072251920473267 ] 
dist 64=[-2.2619227571210937949 ,-.95804076310812740847] 
dist 65=[-2.7522278953784368817 ,-1.0048157114508573142 ] 
dist 66=[-3.2167673882733042807 ,-.9885993491950905454 ] 
dist 67=[-3.5093228843389370854 ,-.94100177670202880312] 
dist 68=[-3.7315146275602962471 ,-.84237295116440403762] 
dist 69=[-3.9153361026908635476 ,-.71897047901060160994] 
dist 70=[-4.0601476695521069731 ,-.57257190184452037732] 
dist 71=[-4.1267080784970890561 ,-.38180396373718641838] 
dist 72=[-4.1540255003784059672 ,-.08145705198608633477] 
dist 73=[-4.1517554239561812915 ,.22227203281459862407] 
dist 74=[-2.5316779003055020632 ,.71381220537754481832] 
dist 75=[-2.5254162293899349653 ,1.1420693386169907379 ] 
dist 76=[-2.4933992072071800405 ,1.4985220893806644609 ] 
dist 77=[-2.4800246763894838267 ,1.8488594341922201775 ] 
dist 78=[-2.4251642074794383261 ,2.1673590601959473150 ] 
dist 79=[-2.4114171844211081397 ,2.3968373504002761250 ] 
dist 80=[-1.0200877265359299589 ,2.6044845800010901701 ] 
dist 81=[-.89009500905884984666,2.8359227707815661795 ] 
dist 82=[-.60028996028598372856,3.0424602726132840514 ] 
dist 83=[-.53802495556018902374,3.1507957869028852868 ] 
dist 84=[-.19435607057951044388,3.2106668531057423738 ] 
dist 85=[-.13386950547380122743,3.2238929099335417402 ] 
dist 86=[-.00500916855301978403,3.1938427559390924104 ] 
dist 87=[.02509673167181951397,3.1838334404059611278 ] 
dist 88=[.02621074069293410498,3.1758480224183491299 ] 
dist 89=[-.36197004593967360329,3.1685812961290989470 ] 
dist 90=[-1.0494630977398052685 ,2.3690319367338378382 ] 
dist 91=[-1.5059078216979185292 ,2.3751095810397311089 ] 
dist 92=[-1.8792309184173461780 ,2.3978961010525349235 ] 
dist 93=[-2.2352259771062015266 ,2.4056504120822926465 ] 
dist 94=[-2.5516257368675653962 ,2.4039060738660649398 ] 
dist 95=[-2.7670396251803971635 ,2.3953159967318455458 ] 
dist 96=[-2.9491435696342470598 ,1.4053195044973698359 ] 
dist 97=[-3.1327030121803102120 ,1.3695680740579241494 ] 
dist 98=[-3.2914942418346135370 ,.81241833495470600867] 
dist 99=[-3.3748183111374619286 ,.73406320324093039009] 
dist 100=[-3.4186091241298752096 ,.55463358657624271993] 
dist 101=[-3.4241561338447664237 ,.51714548174966666583] 
dist 102=[-3.4022164686095800856 ,.28695590196402194484] 
dist 103=[-3.3837307143064835826 ,.24511036328257123   ] 
dist 104=[-3.3349500169732893314 ,.1629255284837746907 ] 
dist 105=[-3.3100397814040323086 ,.14246641563675347852] 
dist 106=[-2.6662301231998783175 ,.73498247101611053391] 
dist 107=[-2.7287844763655010388 ,1.2191698431472439341 ] 
dist 108=[-2.7685136175054223324 ,1.6115176587506764722 ] 
dist 109=[-2.7759726805815744088 ,1.9795042077425170244 ] 
dist 110=[-2.7575505035607395273 ,2.3023853409876104752 ] 
dist 111=[-2.7528195619890286011 ,2.5148486650650582359 ] 
dist 112=[-2.5557118511400386687 ,2.6865147657717457109 ] 
dist 113=[-2.5162753733101941215 ,2.8466936278807106783 ] 
dist 114=[-2.4079007032744774594 ,2.9847916013331697588 ] 
dist 115=[-2.3765461019715732198 ,3.0683956412359793089 ] 
dist 116=[-2.1523370428505800374 ,3.1278586228191295175 ] 
dist 117=[-2.1008413600636109596 ,3.1696748341516253820 ] 
dist 118=[-2.0134035945141719424 ,3.1967989574171977315 ] 
dist 119=[-1.9876717476322794021 ,3.1976648576522813788 ] 
dist 120=[-1.4072430954624270877 ,3.1826731028484928073 ] 
dist 121=[-1.3263468130450079216 ,3.1465596863495530566 ] 
dist 122=[-1.1365604193574736979 ,1.2085304058692400419 ] 
dist 123=[-1.0943270569440915035 ,1.2058834714770503882 ] 
dist 124=[-.82903589598009656205,1.1837527000665624239 ] 
dist 125=[-.77797493114064859762,1.1759089379367695593 ] 
dist 126=[-.74956941935887740626,1.1445844489643457921 ] 
dist 127=[-.8300132439715799049 ,1.1373349160526015061 ] 
dist 128=[-.92707481362313938793,-.27441042047643012424] 
dist 129=[-1.0174549398650978886 ,-.26738204756323093836] 
dist 130=[-1.1946646937062163054 ,-.25380140801762849436] 
dist 131=[-1.3288672685227696544 ,-.23285998967025855753] 
dist 132=[-1.4331799164701687313 ,-.19647657226167538082] 
dist 133=[-1.5235418170893763424 ,-.15308506872688115747] 
dist 134=[-1.5977054087443479897 ,-.02694042782502684762] 
dist 135=[-1.6374174394487784054 ,.13303634319486109349] 
dist 136=[-1.6593852761474863207 ,.37773500655881006797] 
dist 137=[-1.6627830681349753377 ,.62231642170974557234] 
dist 138=[-1.0160193784859661286 ,.78182552340747544287] 
dist 139=[-.96566387589162801793,.90910153242701990729] 
dist 140=[-.95177091678241401201,1.0251347714276580669 ] 
dist 141=[-.85347817410776607354,1.1246497856692213306 ] 
dist 142=[-.83139728981630396046,1.1860497589309365676 ] 
dist 143=[-.7933775797527446621 ,1.2311101203428800486 ] 
dist 144=[-.78256387143638307632,1.2654613772220552178 ] 
dist 145=[-.54431663732409964199,1.2912585944862171586 ] 
dist 146=[-.5113041703781952496 ,1.3022047802793002797 ] 
dist 147=[-.43292211335976661028,1.3043371571457683742 ] 
dist 148=[-.416716325595930559  ,1.3015829169623911373 ] 
dist 149=[-.30515633935029574429,1.2795814291840056516 ] 
dist 150=[-.28386489329524878468,1.2715032531249938238 ] 
dist 151=[-.24549610321501815775,1.2376549008591761238 ] 
dist 152=[-.23633148158170949207,1.2304875224591230436 ] 
dist 153=[-.2513004365429459892 ,1.1058378720347907066 ] 
dist 154=[-.41740579699228661144,.74503672418040591939] 
dist 155=[-.55224914961239913047,.70397643512100015841] 
dist 156=[-.67912469913063463535,.60765887326161357476] 
dist 157=[-.79071875546638181362,.58585668289048678174] 
dist 158=[-.86461823221656390513,.45084084285874378434] 
dist 159=[-.92484355151852390689,.42472760123769416435] 
dist 160=[-.98190391305514720333,.3743235856545839484 ] 
dist 161=[-1.0312678296060884284 ,.36120299655734184275] 
dist 162=[-1.0740837076542566931 ,.18132741212138464757] 
dist 163=[-1.1106607038131468515 ,.15543534227099070464] 
dist 164=[-1.1315070118977611777 ,.10149669139658543203] 
dist 165=[-1.1362430033104285454 ,.08732599294157549428] 
dist 166=[-1.1342929594718517649 ,.03525762957404643268] 
dist 167=[-1.1286912524520195289 ,.02476617534206673193] 
dist 168=[-1.1187436520756281417 ,.00716073772945319885] 
dist 169=[-1.1132561075610138672 ,.00310815048642002558] 
dist 170=[-.36171029518694162314,.23645195864615357611] 
dist 171=[-.22840129882088922104,.39283514128403135466] 
dist 172=[-.200595992730888256  ,.52009608656241250426] 
dist 173=[-.03984117573187553449,.64035904138338951442] 
dist 174=[-.01165067866569248296,.74649363926082492652] 
dist 175=[.04671193519652445323,.81740949951957490335] 
dist 176=[.06148989722226892067,.87590223424747313391] 
dist 177=[.17322248336123968444,.93249235794063767827] 
dist 178=[.19185127961554106996,.98168185366610168723] 
dist 179=[.20305105054748660466,1.0106602545191287632 ] 
dist 180=[.19307256381392847502,1.0302997363714766125 ] 
dist 181=[.17252818667940774432,1.0422448216194626717 ] 
dist 182=[.13810026032756680687,1.0482894365845552359 ] 
dist 183=[.08701179288312270412,1.0472283806195379902 ] 
dist 184=[2.37783517932798270000e-05,1.0371341663396141821 ] 
dist 185=[-.16372279329986505658,1.0297346509055858525 ] 
dist 186=[-.27563367857482446001,.43599566371165821914] 
dist 187=[-.37067842561527274027,.38180716970734048308] 
dist 188=[-.46716456952971796768,.25952307786152806503] 
dist 189=[-.55684907066400911764,.23382334463628932663] 
dist 190=[-.62476829085864898453,.08423434222137985356] 
dist 191=[-.68955297663390185286,.05772672344898573067] 
dist 192=[-.76673668938769663355,.00326003976459184314] 
dist 193=[-.83811133060309019919,-.01057221098250693777] 
dist 194=[-.87972894782465380001,-.12425659775049120212] 
dist 195=[-.90739914808392794261,-.14274856596608120965] 
dist 196=[-.92315031095027297066,-.15871651262167927272] 
dist 197=[-.93191563727622351158,-.15415142954633349119] 
dist 198=[-.93172572868025785654,-.14017426769504079573] 
dist 199=[-.92724379903199409935,-.11329074316936764873] 
dist 200=[-.90125578607488643105,-.05522153657086491944] 
dist 201=[-.84939684838901381366,.02653038536915328445] 
dist 202=[-.19736603703428370011,.14336508408554776811] 
dist 203=[-.15516114850357696141,.24131468929080437691] 
dist 204=[-.14603786314634407342,.32447309761833390432] 
dist 205=[-.09160987697761864350,.40884577747922873653] 
dist 206=[-.08160905708948816230,.48724110069417118401] 
dist 207=[-.06159006995573408768,.54656130395328855155] 
dist 208=[-.05645429681174616882,.60309589310959502728] 
dist 209=[-.00251422688385685828,.6703819514910237162 ] 
dist 210=[.00571144267521098877,.73256870983779706686] 
dist 211=[.01869723758210548312,.76876685779659552607] 
dist 212=[.02183668214952067119,.79275579051087571552] 
dist 213=[.02470523782774435242,.80625116200639152372] 
dist 214=[.02158802009106001877,.81368185895710201247] 
dist 215=[.01445506768508337770,.81348435477407933663] 
dist 216=[-.05762534171499833090,.80952683940293137358] 
dist 217=[-.23137389730359107443,.80535257046654141669] 
dist 218=[-.40525399236374199805,.70837340460036549288] 
dist 219=[-.51909276830427773197,.69246390846313328203] 
dist 220=[-.61042121976125229313,.6514353663835222385 ] 
dist 221=[-.6945282319746957493 ,.64063160269542800612] 
dist 222=[-.76725903688269636093,.56636389809223910739] 
dist 223=[-.81321820900547683312,.55014031720079369552] 
dist 224=[-.84823521802793975558,.52136371044348390955] 
dist 225=[-.87732774882700303295,.51360916209313342795] 
dist 226=[-.90029954132255341341,.34952824416436434305] 
dist 227=[-.91090652686552714179,.32691486069939063253] 
dist 228=[-.91445724030102607023,.27213349632864688854] 
dist 229=[-.91320700162195822504,.26208755131450888443] 
dist 230=[-.89972342727678440369,.18154857141236222111] 
dist 231=[-.89421022281059767728,.16630767698289952567] 
dist 232=[-.87259460410736113352,.1425764891223534659 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 0, 1, 1, 1, 2] 
dist 0=[75.950268817011275739  ,75.950268817011275739  ] 
dist 1=[75.434964799533507987  ,76.194963375972928506  ] 
dist 2=[74.673550308579518969  ,76.289582190166751845  ] 
dist 3=[73.446376842869182396  ,76.205240668684093940  ] 
dist 4=[71.640745584903374800  ,76.012300467349642973  ] 
dist 5=[68.570646343265946512  ,75.810903403555594389  ] 
dist 6=[64.919379055712938261  ,75.267789644536016015  ] 
dist 7=[60.794044808645346990  ,74.987983927397337104  ] 
dist 8=[55.096361585977449479  ,73.386328634790715021  ] 
dist 9=[47.325725926733587100  ,72.857162375015074269  ] 
dist 10=[39.014688839750477909  ,72.488581445667320264  ] 
dist 11=[33.316915067935150219  ,72.240811368462728981  ] 
dist 12=[28.439530948588445700  ,72.088325074060970993  ] 
dist 13=[23.403509688195708161  ,70.704940300758113465  ] 
dist 14=[18.648712100736805425  ,62.686256513323317079  ] 
dist 15=[14.894029159319030521  ,57.282777142292298829  ] 
dist 16=[11.151679285773088361  ,33.592271712076408972  ] 
dist 17=[6.4462723816946038317 ,30.553119442709156384  ] 
dist 18=[1.9433115151038257156 ,23.404353767083530036  ] 
dist 19=[-.99094095845977836125,22.343891275041519200  ] 
dist 20=[-3.3386065578723335438 ,12.839519448695148262  ] 
dist 21=[-5.5002608462524175660 ,11.177814984535897026  ] 
dist 22=[-7.3775035967251508416 ,8.9562532169274042190 ] 
dist 23=[-8.5900048879099861003 ,8.4965641879376278578 ] 
dist 24=[-9.5482439817001889650 ,7.2508934584966153080 ] 
dist 25=[-10.410724419145324224  ,-.61185038074220382531] 
dist 26=[-11.141708682282936682  ,-1.2509670435498465057 ] 
dist 27=[-11.575308534820837753  ,-2.5524940191247852061 ] 
dist 28=[-11.875395776417089944  ,-2.8029535825238031791 ] 
dist 29=[-12.074011801253816681  ,-3.4836329686013916126 ] 
dist 30=[-12.195781685912148893  ,-3.1875443003021293672 ] 
dist 31=[-12.189703961734943302  ,-2.8446081993132656312 ] 
dist 32=[-9.2419784393286339719 ,-2.4075995861148376646 ] 
dist 33=[-9.0977493129010268867 ,-1.7356367293125145267 ] 
dist 34=[-8.6424576700447692112 ,-1.0440089650107968602 ] 
dist 35=[-8.5608901328571395324 ,-.5280338489222437555 ] 
dist 36=[-7.5545734342682060845 ,-.04560773665340098674] 
dist 37=[-7.4475679578539123630 ,.5131326724609551101 ] 
dist 38=[-7.4913795378373662950 ,1.0754729846019375206 ] 
dist 39=[-7.5020068567290742835 ,1.5727862058397125141 ] 
dist 40=[-7.4946889778059156727 ,2.1168773317693169412 ] 
dist 41=[-4.4211973489105070140 ,2.8664417398467372702 ] 
dist 42=[-3.7823127501364757428 ,3.5911899609599714445 ] 
dist 43=[-3.6386351992093972755 ,4.0364601695750562812 ] 
dist 44=[-3.0760020644123882141 ,4.3627178519957371295 ] 
dist 45=[-3.0806856434453326188 ,4.6126089740624089080 ] 
dist 46=[-3.0729650907866065708 ,4.8032007262403129476 ] 
dist 47=[-3.0631763574969682552 ,4.9014881651293756295 ] 
dist 48=[-3.0231226599869119551 ,5.2440951663297766849 ] 
dist 49=[-3.0026267751078970803 ,5.5414803530779985974 ] 
dist 50=[-2.7087796852810868135 ,5.6921924858363197124 ] 
dist 51=[-2.6537686584809177772 ,5.7691913992508403497 ] 
dist 52=[-2.5264373801471340345 ,5.7809078772008793327 ] 
dist 53=[-2.4822587995806350376 ,5.7092973913073911864 ] 
dist 54=[-2.2659302588255450303 ,5.6713407577740819245 ] 
dist 55=[-2.2156858143470418956 ,5.6291966020828935837 ] 
dist 56=[-2.0968135752407789335 ,5.5958095939835210735 ] 
dist 57=[-2.0553313051756549165 ,4.8018175370120122179 ] 
dist 58=[-2.3112544659280706027 ,4.8531730465173022590 ] 
dist 59=[-2.9713696928362794985 ,4.8624047716643487167 ] 
dist 60=[-3.6043271485341772076 ,4.8239161799137921417 ] 
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dist 64=[-5.2425563958800474370 ,1.9641295184071619139 ] 
dist 65=[-5.5466864565666296156 ,1.0627224485480023254 ] 
dist 66=[-5.7082847046998532821 ,.93378183711269191043] 
dist 67=[-5.7962325119985044769 ,.6552601913808258965 ] 
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dist 91=[-1.4285185541282233003 ,3.7727984136252673109 ] 
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dist 120=[-2.0467251427551791246 ,5.7657279110114325986 ] 
dist 121=[-3.2133968610379200911 ,5.7351845913880136894 ] 
dist 122=[-3.9713445399999510328 ,5.0329349835410678607 ] 
dist 123=[-4.5728507052406795234 ,4.8267349707013458010 ] 
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dist 128=[-6.1831705797101189459 ,4.0042008720272439837 ] 
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dist 130=[-6.3093017436311480902 ,2.6742242633026872409 ] 
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dist 134=[-6.1288883593273265470 ,1.5839774948276023223 ] 
dist 135=[-5.9514945767555019602 ,1.3860333211054858245 ] 
dist 136=[-5.9248467619423968159 ,1.3338912710099162866 ] 
dist 137=[-3.1514912118947467204 ,.74067415930304232537] 
dist 138=[-3.2117585682536311158 ,1.2280259414760313370 ] 
dist 139=[-3.2596563174514919013 ,1.6215980358225671944 ] 
dist 140=[-3.2957735095327809544 ,1.9884551663683741939 ] 
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dist 143=[-3.2961007678139996681 ,2.6815453920799061171 ] 
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dist 145=[-.79331371590947485073,2.9568549662237568056 ] 
dist 146=[-.36184757168347374573,3.0356562659249662484 ] 
dist 147=[-.27330215925202990582,3.0941115077504917968 ] 
dist 148=[.23079742547273532893,3.1398371903739467666 ] 
dist 149=[.31711565685636131285,3.1737216946313305433 ] 
dist 150=[.49898150491017985782,3.1849533012684540844 ] 
dist 151=[.53810567122789680876,3.1817111415572420964 ] 
dist 152=[.82145906153355216859,3.1703390609234166530 ] 
dist 153=[.60179543670409539207,2.3716618593840384123 ] 
dist 154=[.19592372661981549626,2.5357706116508296939 ] 
dist 155=[-.15574417096390024766,2.6712762235279467742 ] 
dist 156=[-.52394271072719628653,2.7775525216426694096 ] 
dist 157=[-.87327282751133736245,2.8250920350336572674 ] 
dist 158=[-1.1496918645918156817 ,2.8447932226166325619 ] 
dist 159=[-1.4248309231798758697 ,2.8415740134677799648 ] 
dist 160=[-1.7690563879785875639 ,-.34591108275907282856] 
dist 161=[-2.0958034497476308905 ,-.46169930469774720301] 
dist 162=[-2.3012371578030644906 ,-.71797340291523684952] 
dist 163=[-2.4565544616964476115 ,-.76124256432412112935] 
dist 164=[-2.5834330516796405579 ,-.746745147510444157  ] 
dist 165=[-2.6818772456503870815 ,-.6514058132993770513 ] 
dist 166=[-2.7237957649361305056 ,-.51425639877077117587] 
dist 167=[-2.7404013961625459649 ,-.32062281260049944685] 
dist 168=[-2.7378956429113938739 ,-1.98139058328583490000e-05] 
dist 169=[-2.1227639953288277348 ,.41735134119892288359] 
dist 170=[-2.1678058697506317099 ,.69975960431700527404] 
dist 171=[-2.1783723273075825160 ,.93656640088398280272] 
dist 172=[-2.1656855126380713020 ,1.1720780767342603780 ] 
dist 173=[-2.1615038869454527258 ,1.3878950517066675251 ] 
dist 174=[-2.1581949207541356702 ,1.5461577139433740446 ] 
dist 175=[-2.1552256463353053262 ,1.6921082898207963310 ] 
dist 176=[-1.6588232546735643984 ,1.8588236236021062003 ] 
dist 177=[-1.5940202610974589856 ,2.0093135679869317381 ] 
dist 178=[-1.4377389804106423988 ,2.0905559161037343587 ] 
dist 179=[-1.4006184558910609156 ,2.1364069293016021347 ] 
dist 180=[-1.1622618999999016020 ,2.1474643601146354958 ] 
dist 181=[-1.1140215714108765973 ,2.1426087998071473562 ] 
dist 182=[-1.0238297909700677746 ,2.1389380753364261586 ] 
dist 183=[-1.0000488257016132870 ,2.1493817899528775569 ] 
dist 184=[-.60689757822810599637,2.2522280088608336917 ] 
dist 185=[-.78505369995487653533,2.3058586224283196511 ] 
dist 186=[-1.0897674794383367257 ,2.3335551403816661756 ] 
dist 187=[-1.3380423970214679637 ,2.3365099666504147599 ] 
dist 188=[-1.5731781639144596982 ,2.3197632513118815103 ] 
dist 189=[-1.7810393078600731465 ,2.3070768876565100373 ] 
dist 190=[-1.9205407153615300982 ,2.2709421088944319368 ] 
dist 191=[-2.0362781522590377696 ,2.2525447524475226093 ] 
dist 192=[-2.1493665649520774067 ,1.0349886840996515597 ] 
dist 193=[-2.2459500813345070529 ,.64038947631092304254] 
dist 194=[-2.2958645899384943445 ,.58575878163838830751] 
dist 195=[-2.3210093218010793539 ,.4551666858133274803 ] 
dist 196=[-2.3231542770904942548 ,.43207855841149710963] 
dist 197=[-2.3042282044801359387 ,.24796965324155674779] 
dist 198=[-2.2914343639916323514 ,.21407864555542673585] 
dist 199=[-2.2530334352700492187 ,.16090494353031810934] 
dist 200=[-2.2336180424364596884 ,.14724498241409633672] 
dist 201=[-1.1226957580320172251 ,.23685837320918052874] 
dist 202=[-1.1444194272244278292 ,.39369753309153417822] 
dist 203=[-1.1593618760812251720 ,.52150020678435520114] 
dist 204=[-1.1687505103464206714 ,.64256136000179413308] 
dist 205=[-1.1683250912795629471 ,.74959493614252225475] 
dist 206=[-1.1624047394086539099 ,.8214544432049328936 ] 
dist 207=[-1.1569333509489393792 ,.88110142207709956997] 
dist 208=[-.42770283200651134059,.93943040043016418011] 
dist 209=[-.36377867659559327003,.99025373097767068676] 
dist 210=[-.22028961817001768529,1.0199675499781748170 ] 
dist 211=[-.19045908907849914081,1.0398230449124966004 ] 
dist 212=[-.01852343391852816244,1.0513305430073974460 ] 
dist 213=[.01148688549063499503,1.0565526175645890908 ] 
dist 214=[.07383076333223130157,1.0554758659379468398 ] 
dist 215=[.08924397139065573034,1.0433041823937742033 ] 
dist 216=[.20411788552939470802,1.0372566451967804181 ] 
dist 217=[.04530859512087508480,.89707548250456194645] 
dist 218=[-.09441117661564252298,.94688757876122245931] 
dist 219=[-.21341126158296063933,.98383429331527655886] 
dist 220=[-.33475870035239771142,1.0107957523647921000 ] 
dist 221=[-.44789543053982441248,1.0207858003568990467 ] 
dist 222=[-.53415051335887166963,1.0229918845691457167 ] 
dist 223=[-.61698115241139801153,1.0198532240671772892 ] 
dist 224=[-.71646091033484623156,.01502160670578965122] 
dist 225=[-.80886213178069790826,-.10359941959373909333] 
dist 226=[-.86346296705166692395,-.12266177483729914129] 
dist 227=[-.90067334234879889169,-.14161625850101690188] 
dist 228=[-.92371993469927824474,-.13965551015005801054] 
dist 229=[-.93895047159747303901,-.12854543368574686843] 
dist 230=[-.94498975491234289008,-.1045805278025321692 ] 
dist 231=[-.94543587131973977049,-.06668147755258171444] 
dist 232=[-.94289962897716583984,-8.51874401828128400000e-07] 
dist 233=[-.4262100581723342642 ,.06900223801376226150] 
dist 234=[-.43449327839019270827,.11616347247298356515] 
dist 235=[-.43953892525385999996,.15621992176679002718] 
dist 236=[-.44210025033413918879,.19688852604913672844] 
dist 237=[-.44165320752231311895,.23469323158193946762] 
dist 238=[-.4374221328606249446 ,.26332820987408331204] 
dist 239=[-.43428374501839765508,.29064649046996591385] 
dist 240=[-.18363512609844333146,.32320009401806416926] 
dist 241=[-.16076758804166916427,.35330718295402549147] 
dist 242=[-.10916670605895859668,.37086855585179629062] 
dist 243=[-.09832347156228739249,.38255248902388932704] 
dist 244=[-.03521487598767064790,.38921984995817771849] 
dist 245=[-.02403370597727443380,.39293813275528118378] 
dist 246=[-.00105658517731499645,.39286089211197506636] 
dist 247=[.00477830771664619870,.39097539082050710354] 
dist 248=[.05267456288233716356,.38891081904760495694] 
dist 249=[.06046815797608833773,.34320520635383549777] 
dist 250=[.06716732895573160230,.33563350661542593793] 
dist 251=[.06520951025769255865,.31605339677733151568] 
dist 252=[.05927805409295412035,.31087754879451118526] 
dist 253=[.04790152333962966116,.27521412705964619829] 
dist 254=[.03039166939988222037,.26740459562531155265] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 0, 0, 0, 2] 
dist 0=[66.535838863359125082  ,66.535838863359125082  ] 
dist 1=[65.798962645298977598  ,67.032451771166401456  ] 
dist 2=[64.551044785737199530  ,67.321033521052901648  ] 
dist 3=[62.687875992180317102  ,67.512647278611729693  ] 
dist 4=[59.494451341024652407  ,67.622011180193635996  ] 
dist 5=[56.153289998921180270  ,67.649204581582263373  ] 
dist 6=[53.700194002241003566  ,67.547908714825122674  ] 
dist 7=[51.424228828603348989  ,66.725262118348442098  ] 
dist 8=[48.790155015233278422  ,64.700106048610052559  ] 
dist 9=[46.122194406375576830  ,63.065850167383227135  ] 
dist 10=[43.710750762102889325  ,62.348810666778643941  ] 
dist 11=[41.020860730385639730  ,61.178206995078657694  ] 
dist 12=[35.277379650856117404  ,60.827232889349482114  ] 
dist 13=[28.052641343932545293  ,59.782326578859785634  ] 
dist 14=[23.178838427659498087  ,59.409459536185090547  ] 
dist 15=[19.086729260921564903  ,57.819055281085391315  ] 
dist 16=[14.983143669626651267  ,54.781331562045944795  ] 
dist 17=[11.179041350956350531  ,30.463518531508242774  ] 
dist 18=[8.2826766428362496959 ,28.121166582040408496  ] 
dist 19=[5.4921429145040671730 ,26.552440760982542824  ] 
dist 20=[2.1105110945963505695 ,26.342863423419694948  ] 
dist 21=[-1.0715789548100213077 ,14.270489212842476339  ] 
dist 22=[-3.0655302541244352342 ,12.942906304276185061  ] 
dist 23=[-4.5745972936139387521 ,11.253792519727380833  ] 
dist 24=[-5.8209849927241132856 ,10.937282612094603282  ] 
dist 25=[-6.8255246686599104918 ,1.5309400220329855277 ] 
dist 26=[-8.2040627364824192176 ,.43714581836141597748] 
dist 27=[-9.9130936807121100473 ,-1.9438260376007383227 ] 
dist 28=[-11.926823113039738282  ,-2.3323816105593759398 ] 
dist 29=[-13.798662258857864935  ,-4.7070959465900791884 ] 
dist 30=[-14.940986474092971189  ,-4.9842858768452628391 ] 
dist 31=[-15.771647130983967832  ,-4.9774043546175622135 ] 
dist 32=[-16.398613929401498135  ,-4.5873420559436064061 ] 
dist 33=[-16.861794330997346373  ,-3.9866973340915199428 ] 
dist 34=[-17.038269896768878464  ,-3.1392410238208455354 ] 
dist 35=[-17.091002726313339831  ,-1.9528722517956470991 ] 
dist 36=[-17.059722803748756916  ,0                     ] 
dist 37=[-9.4004255872691092612 ,.83460454274533540996] 
dist 38=[-9.4172546974385342428 ,2.5514715665409756398 ] 
dist 39=[-9.3645569953853863378 ,3.9633122296293573927 ] 
dist 40=[-9.3409324193840584246 ,5.3235646089800008602 ] 
dist 41=[-8.8823773315587205776 ,6.5433970625211212493 ] 
dist 42=[-8.7897432713569645273 ,7.3952983094069243610 ] 
dist 43=[-8.4831694495950891182 ,8.1396502608191576868 ] 
dist 44=[-8.4384994575425803161 ,8.9307112771402836537 ] 
dist 45=[-7.6943688456218891762 ,9.6416470013141019133 ] 
dist 46=[-7.5310945243642111939 ,10.066338273478876774  ] 
dist 47=[-7.3947028117400108396 ,10.362398297835611372  ] 
dist 48=[-7.3629582711178135246 ,10.559869245853122229  ] 
dist 49=[-5.0899219951855799059 ,10.678183664486514684  ] 
dist 50=[-4.8045376814218045900 ,10.697244290548966801  ] 
dist 51=[-4.1685600929238701509 ,10.604574430720601275  ] 
dist 52=[-4.0046401415880265540 ,10.588819355874991020  ] 
dist 53=[-3.2009056147733461745 ,6.1641838542267863532 ] 
dist 54=[-3.0447313815877370155 ,5.7444862170931663304 ] 
dist 55=[-2.6957648416021284037 ,4.7503766957143244069 ] 
dist 56=[-2.5971144477365849359 ,4.5644961674205393305 ] 
dist 57=[-1.6834843819901206343 ,3.1861632422429894096 ] 
dist 58=[-1.5337361599777619043 ,2.9316393889709564289 ] 
dist 59=[-1.2349023746923559066 ,2.5008809171374743770 ] 
dist 60=[-1.1557666297985512568 ,2.4610824699975667706 ] 
dist 61=[-.86721001220237047089,.6881880420713273295 ] 
dist 62=[-1.1401685265621443105 ,.4615056406716164331 ] 
dist 63=[-1.3961030933384906144 ,-.0050557177310396697 ] 
dist 64=[-1.6432417275008420114 ,-.30754906374041827591] 
dist 65=[-1.8654979292657156867 ,-.60603889673190931388] 
dist 66=[-2.0221712643690290269 ,-.56554251750554032593] 
dist 67=[-2.1606917674941562190 ,-.51976768868390360843] 
dist 68=[-2.3105430203299815382 ,-.45594734351907737445] 
dist 69=[-2.4420077646349403588 ,-.38646801910717581392] 
dist 70=[-2.5071722818526911280 ,-.31806902984623290179] 
dist 71=[-2.5409998008088270164 ,-.2380312116042159030 ] 
dist 72=[-2.5474046196515213512 ,-.1221029458036745600 ] 
dist 73=[-2.5004820170722550032 ,-.0052006667212885630 ] 
dist 74=[-2.4858114816095515820 ,.0787686594571779041 ] 
dist 75=[-2.4748130328665545563 ,.15419732929373117485] 
dist 76=[-2.4660739470316964720 ,.46315827563927468896] 
dist 77=[-1.9018788951726774002 ,1.0172784015877572717 ] 
dist 78=[-1.8273113357752999225 ,1.3827901748517265268 ] 
dist 79=[-1.6499519864057659012 ,1.6792323410692491361 ] 
dist 80=[-1.6066349135123938272 ,1.9578831760266620610 ] 
dist 81=[-1.3430705176525962089 ,2.2029756416472009458 ] 
dist 82=[-1.2897484564246971610 ,2.3655812086569854136 ] 
dist 83=[-1.1868826555278857302 ,2.4985610443132136659 ] 
dist 84=[-1.1589393829961569204 ,2.6255090289482822802 ] 
dist 85=[-.73660531163792243976,2.7325745519379154908 ] 
dist 86=[-.67666210511991256852,2.7862536273802557760 ] 
dist 87=[-.53583371995898495316,2.8110539004260582434 ] 
dist 88=[-.50818028356179792978,2.8127051835675128902 ] 
dist 89=[-.40307293484313854831,2.7807690792833853132 ] 
dist 90=[-.39353829571531342198,2.7636654265936865692 ] 
dist 91=[-.37566990763144560569,2.7159596330685495525 ] 
dist 92=[-.37025775177471882227,2.6928730026017004740 ] 
dist 93=[-.64197532147950239459,.56742868382747731931] 
dist 94=[-1.0441225415229140769 ,.55778617390461013872] 
dist 95=[-1.3681341252475260012 ,.53796094973066269843] 
dist 96=[-1.6689309414696769584 ,.5316018578453705835 ] 
dist 97=[-1.9307677159305186647 ,.03958878348316908249] 
dist 98=[-2.0994019620391052782 ,.11135785206417305665] 
dist 99=[-2.2316003907736584055 ,.17942719161063066511] 
dist 100=[-2.3481283120708701471 ,.25989341328118493946] 
dist 101=[-2.4469729963907990434 ,.34180954547836495022] 
dist 102=[-2.5086474117375647738 ,.41566426831018465298] 
dist 103=[-2.5547501527090809265 ,.49749725904068637893] 
dist 104=[-2.5914882882137835920 ,.61123209829791232662] 
dist 105=[-2.6192868002771916379 ,.72464936626513864556] 
dist 106=[-2.6297345399699098973 ,.8052194961547690774 ] 
dist 107=[-2.6294513659450185536 ,.8768956101440238715 ] 
dist 108=[-2.6196977131196053382 ,.95485267632910469593] 
dist 109=[-1.3854961114795179857 ,1.0305880838639286038 ] 
dist 110=[-1.4314287096249744390 ,1.0934102902530237437 ] 
dist 111=[-1.4734705027727527748 ,1.1586246755900630043 ] 
dist 112=[-1.5210116464567280147 ,1.2439086456038925534 ] 
dist 113=[-1.5615499125181893976 ,1.3230284204113611158 ] 
dist 114=[-1.5756609617022452165 ,1.4203712055431289420 ] 
dist 115=[-1.5783909967818127447 ,1.5611032351139523612 ] 
dist 116=[-1.5735468015270711634 ,1.6781326636522238667 ] 
dist 117=[-1.5159643360107963807 ,1.7713348371367269578 ] 
dist 118=[-1.4971616604823149833 ,1.8834486086095116004 ] 
dist 119=[-1.4745371642304988774 ,2.0146293029706327021 ] 
dist 120=[-1.4625479737622182895 ,2.1234101763533263331 ] 
dist 121=[-1.1231185630812716668 ,2.2090959207047519146 ] 
dist 122=[-1.0742974703188377473 ,2.2481698119961502871 ] 
dist 123=[-.9715916716219483822 ,2.2646117637086649458 ] 
dist 124=[-.94202646606360923362,2.2628543676546635576 ] 
dist 125=[-.82021276979053218946,1.6635752266044207783 ] 
dist 126=[-.79468461287030992939,1.6465391842064335138 ] 
dist 127=[-.76162178115069070482,1.6030599696662392694 ] 
dist 128=[-.95119556319189243187,1.5852053768701906945 ] 
dist 129=[-1.1244064264655349738 ,-.42803082477058040504] 
dist 130=[-1.2505654796001394558 ,-.56876947934065736458] 
dist 131=[-1.3660538971066880810 ,-.88706064206722987633] 
dist 132=[-1.4967094545314020523 ,-.93468762964352803266] 
dist 133=[-1.6139789040870101422 ,-.97915104267821550293] 
dist 134=[-1.6760822124672543548 ,-.95961332249199564876] 
dist 135=[-1.7109653020244854472 ,-.87927267055941901882] 
dist 136=[-1.7196774380911766156 ,-.74046819354806540374] 
dist 137=[-1.7059078000665699609 ,-.5752176745367878121 ] 
dist 138=[-1.7417540650635925079 ,-.38940759256282943945] 
dist 139=[-1.7749466811375755161 ,-.1535022071588533109 ] 
dist 140=[-1.8004852776788442619 ,.2115331164491362521 ] 
dist 141=[-1.8190637854713991089 ,.57847613203642354719] 
dist 142=[-1.8244984874787263620 ,.82198970692605321942] 
dist 143=[-1.8213322366170886726 ,1.0210184282944287954 ] 
dist 144=[-1.8148806628389542570 ,1.2105520311492542386 ] 
dist 145=[-.89917040260176151835,1.3788061598568312318 ] 
dist 146=[-.86094764885282421906,1.4929705473069349646 ] 
dist 147=[-.78926941427131735367,1.5890461579205706031 ] 
dist 148=[-.77038605851760252207,1.6851607955885360550 ] 
dist 149=[-.46304309266484460281,1.7680646673219786153 ] 
dist 150=[-.42015949814947523094,1.8114545695557115002 ] 
dist 151=[-.32026253649428832155,1.8340858538381176182 ] 
dist 152=[-.30074561152319216679,1.8366986654515429031 ] 
dist 153=[-.16761392599094296041,1.8243306366551391332 ] 
dist 154=[-.14332037504709129215,1.8144160792148068970 ] 
dist 155=[-.09900401730939872734,1.7869257426261380335 ] 
dist 156=[-.08881936441905539135,1.7728849240265573262 ] 
dist 157=[-.39639778472284419026,1.5423144351185576609 ] 
dist 158=[-.65989377042828209329,1.5643614906800817077 ] 
dist 159=[-.8758966223252088866 ,1.5726632614924130575 ] 
dist 160=[-1.0826660626032202892 ,1.5722491256769249918 ] 
dist 161=[-1.2669426638754150459 ,-.18319828455152678968] 
dist 162=[-1.3932421625989855468 ,-.24426228591210835136] 
dist 163=[-1.5008930991990969508 ,-.38069902707882165523] 
dist 164=[-1.6107976637827299526 ,-.40259181712645342229] 
dist 165=[-1.7074563975882003111 ,-.55481068286125018968] 
dist 166=[-1.7622818256682362229 ,-.57839536805687258239] 
dist 167=[-1.7968055163748641982 ,-.62183727703364431815] 
dist 168=[-1.8124991544293475712 ,-.62978634176122774362] 
dist 169=[-1.8162084886285440203 ,-.66820205628989845694] 
dist 170=[-1.8129204636308824764 ,-.61242862037690436096] 
dist 171=[-1.7864129390756692140 ,-.50268367807416394391] 
dist 172=[-1.7771448950778350819 ,-.26905094470891917435] 
dist 173=[-1.2588433738928626878 ,.09164728458369787189] 
dist 174=[-1.2568922654307939063 ,.33667735621111354658] 
dist 175=[-1.2533413802360660040 ,.54319220269148508192] 
dist 176=[-1.2466922388383950466 ,.7502884465568443862 ] 
dist 177=[-.99437255886624152107,.94117168247043102056] 
dist 178=[-.95969453242633380038,1.0830276816243111517 ] 
dist 179=[-.87512290536245937498,1.2157235025937494774 ] 
dist 180=[-.85465921223882268588,1.3700751820825343390 ] 
dist 181=[-.72153530322915264292,1.5109354915050520705 ] 
dist 182=[-.69417015321281300814,1.5898265793975336994 ] 
dist 183=[-.64355607332515240921,1.6382055559944245600 ] 
dist 184=[-.63015082584938264124,1.6573809521948802223 ] 
dist 185=[-.3956550696028280307 ,1.6654946399127253638 ] 
dist 186=[-.36332177408828018943,1.6697585737895274424 ] 
dist 187=[-.2849551885234771761 ,1.6720068794773149369 ] 
dist 188=[-.27185902116917747112,1.6720820643705506638 ] 
dist 189=[-.32480686657837536451,1.3584541795798107208 ] 
dist 190=[-.54969299942029543868,1.3508135573892453424 ] 
dist 191=[-.74381336438852558357,1.3269565020189572545 ] 
dist 192=[-.94590457344480599135,1.3149586999798604730 ] 
dist 193=[-1.1369314049976608125 ,-.12500792967940067407] 
dist 194=[-1.2869260941862432166 ,-.14334048608959685046] 
dist 195=[-1.4351510190831285814 ,-.11737295561031413546] 
dist 196=[-1.6191198818499959870 ,-.06607091491144506589] 
dist 197=[-1.7930269938716674032 ,-.00818141425331630288] 
dist 198=[-1.9011248022768788378 ,.04405746644634789880] 
dist 199=[-1.9814051267412842970 ,.10200794332317540555] 
dist 200=[-2.0443737488934845594 ,.18267577884008811812] 
dist 201=[-2.0911759752600325018 ,.27147915923762064477] 
dist 202=[-2.1069833393145869483 ,.36187488206542748725] 
dist 203=[-2.1080915535770382572 ,.47048213041844515651] 
dist 204=[-2.1009224979750693944 ,.90105292016932262047] 
dist 205=[-2.0295056207626866354 ,1.3446924504526190310 ] 
dist 206=[-2.0096764499730694179 ,1.6314570349668485221 ] 
dist 207=[-1.9484116212712280682 ,1.8573947919065414474 ] 
dist 208=[-1.9285084541211837891 ,2.0584517756395055103 ] 
dist 209=[-1.7759848104515274240 ,2.2274193304350467555 ] 
dist 210=[-1.7390877074476129327 ,2.3253817238644169932 ] 
dist 211=[-1.6803310892483965042 ,2.3898098634464960597 ] 
dist 212=[-1.6609995265957948446 ,2.4250399710745126055 ] 
dist 213=[-1.2006582377556632505 ,2.4449831315738016668 ] 
dist 214=[-1.1361356238448580946 ,2.4484456291928748783 ] 
dist 215=[-.989061063435971162  ,2.4404901017311199358 ] 
dist 216=[-.95138825794611473492,2.4314064813508294744 ] 
dist 217=[-.75636900851047795546,2.3800217142456461938 ] 
dist 218=[-.71838361801702429725,2.3628882751277338390 ] 
dist 219=[-.63547623586385007493,2.2952600807041277799 ] 
dist 220=[-.61135914857509332695,2.2810788050258415696 ] 
dist 221=[-.04861727215927168147,1.3063479548469517055 ] 
dist 222=[-.08195273545465223018,1.3071457137110136411 ] 
dist 223=[-.11038278494685437519,1.3056140978706192325 ] 
dist 224=[-.13943464249678198866,1.3005078382942649237 ] 
dist 225=[-.25999195036266597964,-.02517694257860063447] 
dist 226=[-.4405066700002469361 ,-.03424024470677063606] 
dist 227=[-.59685095797247403676,-.04982428353316123058] 
dist 228=[-.76044542688989587593,-.05314166045208403378] 
dist 229=[-.91559572382538294812,-.05837780408710129600] 
dist 230=[-1.0382639378672110040 ,-.04318174932818743468] 
dist 231=[-1.1602719387803925520 ,-.01361754226067458094] 
dist 232=[-1.3127892499906501190 ,.03858429357602907320] 
dist 233=[-1.4575005457047530228 ,.09556901813678028778] 
dist 234=[-1.5483774946483279552 ,.14420779125588052369] 
dist 235=[-1.6169605520793040528 ,.19590518787790333853] 
dist 236=[-1.6727619170641294473 ,.26508796325113344007] 
dist 237=[-1.7158815429716062368 ,.33996449307827379076] 
dist 238=[-1.7338887490127621943 ,.41436906584692579785] 
dist 239=[-1.7377729730483049638 ,.50245787846473368095] 
dist 240=[-1.7350299409558787213 ,.78403956321183713416] 
dist 241=[-1.6953155657809428209 ,1.1474445260779990275 ] 
dist 242=[-1.6821429795943913542 ,1.3818013594381792835 ] 
dist 243=[-1.6383784489619496967 ,1.5658304107752813451 ] 
dist 244=[-1.6232078800347347230 ,1.7285239112724660180 ] 
dist 245=[-1.5037344940132853632 ,1.8644784539743852114 ] 
dist 246=[-1.4741751271160621266 ,1.9418702742907590914 ] 
dist 247=[-1.4282252152084533945 ,1.9909622078599775948 ] 
dist 248=[-1.4124450681702724165 ,2.0140544026327423320 ] 
dist 249=[-1.0291895223997989329 ,2.0246731057216846365 ] 
dist 250=[-.97532636643008247547,2.0240196966514635273 ] 
dist 251=[-.85377018990094044043,2.0149870488719619463 ] 
dist 252=[-.82112986691121049706,2.0066747343948327300 ] 
dist 253=[-.66292846063828369794,1.9623713945564482460 ] 
dist 254=[-.63194600032299130984,1.9475837951001934413 ] 
dist 255=[-.56116877479003615171,1.8924295175698338756 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 2, 2, 1, 0, 2] 
dist 0=[61.514937402131843459  ,61.514937402131843459  ] 
dist 1=[59.935877869508009849  ,62.143025282595866206  ] 
dist 2=[57.421852211842683743  ,63.070673127859213275  ] 
dist 3=[53.290614464289026833  ,64.079178800066663286  ] 
dist 4=[49.030351642731977546  ,64.630432084680758656  ] 
dist 5=[46.001303723411779853  ,64.952039226836454171  ] 
dist 6=[43.293854778459830013  ,65.044082597164879851  ] 
dist 7=[40.317173093819538263  ,64.961933439153246937  ] 
dist 8=[37.394941595258532396  ,61.446901419681602162  ] 
dist 9=[34.904773427020868034  ,60.849758293858489239  ] 
dist 10=[32.253762566772463958  ,60.019521907815368223  ] 
dist 11=[28.689442906616048501  ,59.705043478311624341  ] 
dist 12=[25.165917558425520274  ,59.024175148561672760  ] 
dist 13=[22.677631354937957928  ,58.769539242754590227  ] 
dist 14=[20.470312984641976598  ,58.610106294256124272  ] 
dist 15=[18.068044334392833443  ,58.391036649972069133  ] 
dist 16=[15.722547890440374046  ,29.714531188327986506  ] 
dist 17=[13.741607794680561830  ,27.389810329405903312  ] 
dist 18=[11.646472195414727870  ,21.905066801379705416  ] 
dist 19=[8.8447189419610024917 ,21.110083979864621454  ] 
dist 20=[6.1003058301375742769 ,13.767138313460109786  ] 
dist 21=[4.2338166493376068295 ,12.481516902019052421  ] 
dist 22=[2.5992745022293364652 ,10.826437351566654160  ] 
dist 23=[-1.0121850740928058259 ,10.529229156796688126  ] 
dist 24=[-3.3866464419544088095 ,4.2879123208681459896 ] 
dist 25=[-5.3162711675115510511 ,3.2410344580296854638 ] 
dist 26=[-7.1525062686207731938 ,1.9307801639629147930 ] 
dist 27=[-8.7991242407532190843 ,1.7379343248693520522 ] 
dist 28=[-9.9727263728201004226 ,.89856068543009130488] 
dist 29=[-11.034518534444793793  ,.76063472866479118751] 
dist 30=[-12.236988359942652350  ,.75984404561588126453] 
dist 31=[-13.317465813489955498  ,.93835318510052120298] 
dist 32=[-13.892312088909840282  ,1.2112684182879736900 ] 
dist 33=[-14.218100396114051827  ,1.5874295755340518440 ] 
dist 34=[-14.302280972585133637  ,2.1063161920931693050 ] 
dist 35=[-14.303887888042245583  ,2.9485253174129316586 ] 
dist 36=[-14.298725504042736859  ,3.7919297201502140200 ] 
dist 37=[-14.291630025885795136  ,4.3158249949326536259 ] 
dist 38=[-14.283652091206636383  ,4.7017150045672274608 ] 
dist 39=[-11.704494500121307225  ,4.9958151935051912908 ] 
dist 40=[-11.349533859702594673  ,5.2245148467360035056 ] 
dist 41=[-10.681851488057307408  ,5.3497597524883859795 ] 
dist 42=[-10.507719308316451855  ,5.4220346499131279492 ] 
dist 43=[-9.9128401530622463202 ,5.4397065250132708344 ] 
dist 44=[-9.7502799233524724001 ,4.7241938367456378043 ] 
dist 45=[-9.6066913580719948177 ,4.6060542247171385193 ] 
dist 46=[-9.5634648506675201523 ,4.4400854299143101904 ] 
dist 47=[-5.8298221518843755266 ,4.3777224565554670795 ] 
dist 48=[-5.4473648727251203835 ,4.2399603152711468672 ] 
dist 49=[-5.3348046842540922863 ,4.1878224765034441097 ] 
dist 50=[-5.2544117656426210982 ,4.5212267394527733068 ] 
dist 51=[-5.2359816681933756880 ,5.0737557353270819278 ] 
dist 52=[1.5534160108721632460 ,5.5979414841140719495 ] 
dist 53=[2.1054564082352118624 ,6.4871172401427635546 ] 
dist 54=[3.2410628381646905441 ,7.5796870623795625720 ] 
dist 55=[3.5175828678436158108 ,8.6141648626666376841 ] 
dist 56=[3.8597101672266907307 ,9.2714834149007579607 ] 
dist 57=[3.6159193074830563744 ,9.7790568919909430298 ] 
dist 58=[3.1353828009916060551 ,10.215771476037334975  ] 
dist 59=[2.4294833067423895627 ,10.580171882105122811  ] 
dist 60=[1.6354647019482912520 ,10.777562829375868158  ] 
dist 61=[.80329352627192973447,10.889655996311473748  ] 
dist 62=[-.83912040541798018215,10.914371149563185256  ] 
dist 63=[-2.5433544858698599023 ,6.5275871975053427927 ] 
dist 64=[-3.6577445518054171040 ,5.1469632049127885886 ] 
dist 65=[-4.5512917142732770864 ,4.9570407577088535797 ] 
dist 66=[-5.3746258302241605299 ,4.5096591048668091031 ] 
dist 67=[-6.0880319076336540617 ,4.3949758649379326962 ] 
dist 68=[-6.5431104271382567703 ,3.7370572868307021407 ] 
dist 69=[-6.9087386932239968540 ,3.6025120583284913066 ] 
dist 70=[-7.2424843564428226883 ,3.3342062506805909594 ] 
dist 71=[-7.5425001806571212465 ,3.2584460620718366540 ] 
dist 72=[-7.7877403704077785137 ,2.1949372061323079205 ] 
dist 73=[-7.9029936224851017953 ,2.0409432486276669269 ] 
dist 74=[-7.9452361644194338823 ,1.6741811890649332297 ] 
dist 75=[-7.9431094071761251501 ,1.6025193651957456155 ] 
dist 76=[-7.8170381767585416902 ,1.0783759793936744459 ] 
dist 77=[-7.7635043396482469280 ,.97892281789018254444] 
dist 78=[-7.6122305705528032017 ,.80987372727280503332] 
dist 79=[-7.5420302376400824687 ,.76872277373819654588] 
dist 80=[-2.4664143026353604189 ,1.9210940169087964461 ] 
dist 81=[-1.5254803662059851642 ,3.0781729448668838364 ] 
dist 82=[-1.3280790231000694433 ,4.0168003725622760242 ] 
dist 83=[-.20906234995873904013,4.8991022034332628872 ] 
dist 84=[-.01375631762655807325,5.6748114654975811066 ] 
dist 85=[.39627459731911821495,6.1883276718949289612 ] 
dist 86=[.49382838876574422552,6.6067981961006364600 ] 
dist 87=[1.2308614052218704315 ,7.0034548201868313560 ] 
dist 88=[1.3560603329663147997 ,7.3455378258306947363 ] 
dist 89=[1.4155676266140843385 ,7.5463526896571076697 ] 
dist 90=[1.3329030918471679655 ,7.6816790462749424128 ] 
dist 91=[1.1765505680216826324 ,7.7625574521312531305 ] 
dist 92=[.92510834437226082182,7.8020567223745494398 ] 
dist 93=[.55659805877202879141,7.7916503259746805393 ] 
dist 94=[-.06667421085076746262,7.7177025714724239866 ] 
dist 95=[-1.2651324503251467534 ,7.6633810557507473921 ] 
dist 96=[-2.0918872381632139245 ,3.1710096952307585703 ] 
dist 97=[-2.7935809175015960666 ,2.7636089831592451214 ] 
dist 98=[-3.5053065182421046604 ,1.8456723483360295156 ] 
dist 99=[-4.1666006057592063641 ,1.6533159777648411425 ] 
dist 100=[-4.6671657685647355140 ,.53652636767859085921] 
dist 101=[-5.1444781484569382248 ,.33932171584470375352] 
dist 102=[-5.7130396211560799205 ,-.06680586639421462781] 
dist 103=[-6.2389385645264691645 ,-.16984253194185742139] 
dist 104=[-6.5461034366799464918 ,-.99522952578377734414] 
dist 105=[-6.7510406733561721708 ,-1.1304388951395855633 ] 
dist 106=[-6.8692290633845851005 ,-1.1200678219552292160 ] 
dist 107=[-6.9355502679837440604 ,-1.0237416271349755134 ] 
dist 108=[-6.9351599393691253642 ,-.88279655912418680906] 
dist 109=[-6.9005304435552515588 ,-.69000640692430956352] 
dist 110=[-6.7179061722687874534 ,-.26618455408196422765] 
dist 111=[-6.0850885863789574144 ,.34069331650269728933] 
dist 112=[-1.5476490520641201294 ,.75059225990241866465] 
dist 113=[-1.2529108966466939010 ,1.0935405285001210796 ] 
dist 114=[-1.1884725102388669926 ,1.4334109785451309170 ] 
dist 115=[-.80215293476550862595,1.7441233212127475761 ] 
dist 116=[-.73033982438066376872,1.9707862397967311975 ] 
dist 117=[-.58751783605236940712,2.1786567867315042608 ] 
dist 118=[-.55068188283420273809,2.4144250423823716293 ] 
dist 119=[-.13936999020201142184,2.6277205126660947942 ] 
dist 120=[-.07752689953600572454,2.7459656908414244910 ] 
dist 121=[.03168438435492148375,2.8169106196826354373 ] 
dist 122=[.05512177611060428879,2.8415614056310188704 ] 
dist 123=[.10523769048117530956,2.8482031628634320110 ] 
dist 124=[.09948941040741014968,2.8088998713529368736 ] 
dist 125=[.06848226607428711320,2.7852393166227631327 ] 
dist 126=[-.00499636422287327291,2.5732472357801691498 ] 
dist 127=[-.17932540614661304291,2.4095374449800194669 ] 
dist 128=[-.69745789142370032517,1.7391218722561414681 ] 
dist 129=[-1.0427034217211124398 ,1.6573858070042330513 ] 
dist 130=[-1.3264277041385096051 ,1.4634885555004616041 ] 
dist 131=[-1.5992078690983171228 ,1.4186253635132858664 ] 
dist 132=[-1.8431167945297372662 ,1.1368922540569280003 ] 
dist 133=[-2.0117001327649295133 ,1.0812725271821450634 ] 
dist 134=[-2.1569069721716784108 ,.97532895824566553475] 
dist 135=[-2.3075888327598084360 ,.94755668230701878674] 
dist 136=[-2.4394871641829660990 ,.53277253526362275644] 
dist 137=[-2.5097833846734453963 ,.4740107032678906373 ] 
dist 138=[-2.5482203485353990575 ,.34390214994674868016] 
dist 139=[-2.5541870305194315766 ,.31353243206395879334] 
dist 140=[-2.5435098961024280127 ,.1606006643851941155 ] 
dist 141=[-2.5302143178692640170 ,.13328700763904787484] 
dist 142=[-2.4993104371485115212 ,.07086065137383866030] 
dist 143=[-2.4831389097627539315 ,.05915347138546627476] 
dist 144=[-.16519562886980473301,.54345965897820786   ] 
dist 145=[-.12698196827915740302,.90310497262934611863] 
dist 146=[-.1187654384989952339 ,1.1969130518290531246 ] 
dist 147=[-.07014280122967290773,1.4764747027113059008 ] 
dist 148=[-.06128124951090094311,1.7244941878607817285 ] 
dist 149=[-.04341265691736360262,1.8925093966155484290 ] 
dist 150=[-.03883172997578850301,2.0336098285291352310 ] 
dist 151=[.00670323838306920457,2.1742909406364859502 ] 
dist 152=[.01374305105808495698,2.2973827433192442628 ] 
dist 153=[.02389572644298610561,2.3683354449725596108 ] 
dist 154=[.02660043279586634337,2.4144800375884263810 ] 
dist 155=[.02673726504151658888,2.4386347478318836772 ] 
dist 156=[.02264992059218585093,2.4467268342283179769 ] 
dist 157=[.01473685868309913428,2.4441724908632063715 ] 
dist 158=[-.00043695592359482866,2.4069453322946328301 ] 
dist 159=[-.06466550774391647049,2.3992755603619210246 ] 
dist 160=[-.10909835039324316668,1.1486250221910458344 ] 
dist 161=[-.32254889020692055806,1.0300205550858005669 ] 
dist 162=[-.59939537986426660489,.7606619917237953346 ] 
dist 163=[-.87962053397643467424,.70332045996368123664] 
dist 164=[-1.1395736270791761782 ,.36577308092361129306] 
dist 165=[-1.3355734312284621966 ,.30493381253663129909] 
dist 166=[-1.5216907584011693594 ,.18144373063716620977] 
dist 167=[-1.7422317513974468737 ,.14993143575379970987] 
dist 168=[-1.9455616342520838224 ,.00116439123682208483] 
dist 169=[-2.0630395714987224746 ,.01229266024553893904] 
dist 170=[-2.1397894657738278532 ,.02796043626282830870] 
dist 171=[-2.1806923363311746160 ,.04528987551669652480] 
dist 172=[-2.2049525681535412715 ,.06304506234705737734] 
dist 173=[-2.2153301298690264279 ,.08661288935029112271] 
dist 174=[-2.2174965699305396011 ,.17411290559333954029] 
dist 175=[-2.2090100491733098705 ,.26133309703211643677] 
dist 176=[-.39250948373218973335,.41278124599411197398] 
dist 177=[-.3800294943107225256 ,.69740720032387120442] 
dist 178=[-.37603887908681682802,.94192341780217743376] 
dist 179=[-.34569944042217293242,1.1946274456342822530 ] 
dist 180=[-.33840476449448013988,1.4323529838782541435 ] 
dist 181=[-.32670547354114609679,1.6171337130330023503 ] 
dist 182=[-.32290373627685758879,1.7979789339742119874 ] 
dist 183=[-.23289236428856727542,2.0200093376448741052 ] 
dist 184=[-.22028475418995204079,2.2287021902495681453 ] 
dist 185=[-.19146090787912497783,2.3563561185476108944 ] 
dist 186=[-.18418111314834821746,2.4487255666729028876 ] 
dist 187=[-.14574764557996344119,2.5167008912636948802 ] 
dist 188=[-.13827237548232656539,2.5635582692902059681 ] 
dist 189=[-.1818481732549241627 ,2.5731537704853032283 ] 
dist 190=[-.45851586018931617771,2.5664338224266410624 ] 
dist 191=[-1.0049925784222825404 ,2.5597591988026746586 ] 
dist 192=[-1.5502249470680390960 ,2.4210005148636856709 ] 
dist 193=[-1.9038723754557719463 ,2.3897866429122438915 ] 
dist 194=[-2.1838819818450447307 ,2.3001822786512940706 ] 
dist 195=[-2.4354404695537618140 ,2.2731958705368659446 ] 
dist 196=[-2.6485708085979554271 ,2.0735651543669812641 ] 
dist 197=[-2.7753256999476272230 ,2.0267378214803370737 ] 
dist 198=[-2.8627179096666606911 ,1.9496665590657333917 ] 
dist 199=[-2.9188665403529259874 ,1.9257854743501712629 ] 
dist 200=[-2.9561189456814584466 ,1.3737892603201006410 ] 
dist 201=[-2.9681514031176732007 ,1.2967432342045026127 ] 
dist 202=[-2.9639809292224359879 ,1.1184007403930428626 ] 
dist 203=[-2.9547595273640539386 ,1.0760711388383121844 ] 
dist 204=[-2.8965364270744523506 ,.8329455761775461135 ] 
dist 205=[-2.8771572819768043322 ,.78596530216906582703] 
dist 206=[-2.7935005485331842187 ,.69045755743130834262] 
dist 207=[-2.7801337986366354913 ,.66440546399835706497] 
dist 208=[-.37463207151564498389,.25467752179156724129] 
dist 209=[-.33066582008412434308,.4219123136403916475 ] 
dist 210=[-.32050839528603664167,.55664363070123744095] 
dist 211=[-.28089871702998280329,.68168366843754666032] 
dist 212=[-.28991823613992132907,.79048218921245843758] 
dist 213=[-.29474809301596575518,.86044095907563769218] 
dist 214=[-.29563783772364830738,.91514395025352716848] 
dist 215=[-.2924757823258815917 ,.96310113226550109178] 
dist 216=[-.29045727404426205294,1.0038135496858403993 ] 
dist 217=[-.28762220472476209253,1.0296238048132380511 ] 
dist 218=[-.2859637592241930786 ,1.0493861278949580141 ] 
dist 219=[-.27855001355761280059,1.0659788776759915269 ] 
dist 220=[-.27606668987015460027,1.0792061748594684995 ] 
dist 221=[-.26859105610883777903,1.0855467866344557461 ] 
dist 222=[-.26566736564220687972,1.0880389903108952185 ] 
dist 223=[-.1236774927919715002 ,1.0859185086544673530 ] 
dist 224=[-.21041801264399182719,.29446599540551600076] 
dist 225=[-.28646279778020291914,.22940234527143382269] 
dist 226=[-.36748207797423067411,.21455667677776689957] 
dist 227=[-.44520860590870515253,.26269884584740539453] 
dist 228=[-.50812161583668016765,.30307794387804222076] 
dist 229=[-.57204780537312269889,.34538511815984491074] 
dist 230=[-.65381497986635490729,.40121661859895913176] 
dist 231=[-.73230460735152307402,.4556306767977142141 ] 
dist 232=[-.78315966119843417521,.4922849714813020101 ] 
dist 233=[-.82336369081616061723,.5228431087631457750 ] 
dist 234=[-.85937612928126185108,.5529451752497282222 ] 
dist 235=[-.88981108362061116276,.5803432760450684878 ] 
dist 236=[-.90777163284388757346,.6001177694477616606 ] 
dist 237=[-.91998224263937822509,.6180372337009162547 ] 
dist 238=[-.92951024719386900714,.6380373217020881624 ] 
dist 239=[-.93056920220240550614,.6549964529885540949 ] 
dist 240=[-.60359082237215714946,.6607883242591040471 ] 
dist 241=[-.6431089207403327822 ,.6618319082039658438 ] 
dist 242=[-.6919384839866714961 ,.6598544666078617917 ] 
dist 243=[-.7308872787492723515 ,.6535902813463667727 ] 
dist 244=[-.7500276531378126056 ,.65647778684461389879] 
dist 245=[-.7597577498014661867 ,.65771216347382385224] 
dist 246=[-.7611775592399580678 ,.65700728141312164252] 
dist 247=[-.7350053282648235756 ,.58942547603763155404] 
dist 248=[-.7272958461720234611 ,.57893399329838235938] 
dist 249=[-.7154274632977306299 ,.56166632482747703783] 
dist 250=[-.7102822728744081129 ,.5559428347603933539 ] 
dist 251=[-.6894817503021882606 ,.53572028615761993805] 
dist 252=[-.6824993358992000990 ,.52890895239338976095] 
dist 253=[-.6647604426758793807 ,.51639781480122422019] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 1, 0, 2, 0, 2] 
dist 0=[76.984053479001025881  ,76.984053479001025881  ] 
dist 1=[76.742464543054835530  ,77.001859411229345292  ] 
dist 2=[76.289582190166751845  ,76.984053479001025881  ] 
dist 3=[75.263667812718459907  ,76.709809997513307345  ] 
dist 4=[73.307921639322510451  ,76.138165345287483167  ] 
dist 5=[70.857534068841030806  ,75.824653485728148892  ] 
dist 6=[67.834217190573833021  ,73.943698046742489782  ] 
dist 7=[63.812931188224581975  ,73.366280016952319739  ] 
dist 8=[57.379168583922611430  ,72.833692179164671522  ] 
dist 9=[50.812821282554678481  ,72.490417403494061556  ] 
dist 10=[46.262074171893839855  ,72.307125156932360276  ] 
dist 11=[42.315924033856179651  ,72.142152087062436757  ] 
dist 12=[36.233693966379042448  ,72.027651715962792412  ] 
dist 13=[30.292314257841021632  ,70.709298350066425191  ] 
dist 14=[25.232943563672289509  ,34.137767853239579702  ] 
dist 15=[20.050620568042797072  ,31.394789400488707639  ] 
dist 16=[15.183002485137127015  ,31.100967790918514454  ] 
dist 17=[11.380032138440681588  ,22.948594559020605763  ] 
dist 18=[7.6270919001672211075 ,18.069248372227727634  ] 
dist 19=[2.9593737478384549612 ,15.161060685599836610  ] 
dist 20=[-1.4831841746440501943 ,14.511400241989939771  ] 
dist 21=[-4.3373227303689113952 ,11.780587855847627947  ] 
dist 22=[-6.5751902279681158638 ,11.288985738276128537  ] 
dist 23=[-8.5578779807809797449 ,10.564019260334511579  ] 
dist 24=[-10.225272654279112379  ,10.431542811308910997  ] 
dist 25=[-11.204654537499766857  ,.72697872613331242302] 
dist 26=[-11.867836659430513050  ,-.06055171488860139168] 
dist 27=[-12.273153102972938906  ,-1.7059286688848558343 ] 
dist 28=[-12.612446511018081106  ,-2.0121025599814505110 ] 
dist 29=[-12.690470378464012882  ,-3.5296455668212942695 ] 
dist 30=[-7.7454294180933678912 ,-3.7762551550985226822 ] 
dist 31=[-7.5776839989197864889 ,-4.1631350901711160145 ] 
dist 32=[-7.0912679885868683675 ,-4.2377648982591866264 ] 
dist 33=[-7.3287422265537634216 ,-3.9397561667952541438 ] 
dist 34=[-7.7225981548119658708 ,-3.3630421959369734366 ] 
dist 35=[-8.0130191067643326171 ,-2.5214879516942220703 ] 
dist 36=[-8.2445742657262605213 ,-1.6696582092752868198 ] 
dist 37=[-8.4251300812690792256 ,-1.0514314681975475417 ] 
dist 38=[-8.5112688359410542057 ,-.4891831960489008045 ] 
dist 39=[-8.5464279516726446316 ,.14023761032527816784] 
dist 40=[-8.5435351581770970969 ,.76265507195234846842] 
dist 41=[-2.6637281752685214413 ,1.2975059596985937859 ] 
dist 42=[-2.2246990910035112926 ,2.0097044152274373455 ] 
dist 43=[-2.1891668168470470568 ,2.7231976162917162727 ] 
dist 44=[-2.0319399352025841844 ,3.4054441945973863464 ] 
dist 45=[-1.9980006890979987536 ,4.0147814309678853880 ] 
dist 46=[-1.9431262355979636081 ,4.4374827259698693871 ] 
dist 47=[-1.9277695670944490841 ,4.8044083469532555092 ] 
dist 48=[-1.8761749632303401868 ,5.1913500279380911934 ] 
dist 49=[-1.8600758619052730914 ,5.5311570980682482325 ] 
dist 50=[-1.8224222930003499704 ,5.7100397983446984946 ] 
dist 51=[-1.8065344566004463649 ,5.8057679668290429370 ] 
dist 52=[-1.7149627401268841900 ,5.8258332107048511054 ] 
dist 53=[-1.6928929339941881043 ,5.7900929633410015418 ] 
dist 54=[-1.6202264810850829047 ,5.7597776984582714969 ] 
dist 55=[-1.6053460521462414769 ,5.7191221126653997959 ] 
dist 56=[-1.4137449113947848694 ,5.6879397078323409404 ] 
dist 57=[-1.3682873834645675584 ,4.2103664582052237387 ] 
dist 58=[-2.1361194343505034012 ,4.0594421048190128600 ] 
dist 59=[-2.7963412833360337352 ,4.0235749322021937381 ] 
dist 60=[-3.4323996512149307736 ,3.7980707271321803005 ] 
dist 61=[-4.0022322522171558414 ,3.7717455966541932412 ] 
dist 62=[-4.3983629348926221458 ,2.2713902729695873609 ] 
dist 63=[-4.7421794072684339317 ,2.0202543416265356733 ] 
dist 64=[-5.1034150329810025717 ,1.9560307471936332759 ] 
dist 65=[-5.4213460816297566099 ,1.0154728709508185521 ] 
dist 66=[-5.5924540415506099995 ,.88249698779905413824] 
dist 67=[-5.6885057543061061095 ,.59453806534116228325] 
dist 68=[-5.7070528692879061667 ,.52368092575644633941] 
dist 69=[-5.6925407108189682287 ,.2076652325932271302 ] 
dist 70=[-5.6643879967353987175 ,.15034036838484476435] 
dist 71=[-5.6043373307373291258 ,.02091798399478626700] 
dist 72=[-5.5719508042345549124 ,-.00369606306917600784] 
dist 73=[-4.8874474409919270881 ,1.1487980011486048645 ] 
dist 74=[-4.8013402003231439927 ,1.9405952227195468910 ] 
dist 75=[-4.7835417307869214981 ,2.5866962838691944911 ] 
dist 76=[-3.9567403716362305977 ,3.2002029628865548832 ] 
dist 77=[-3.9403140595568303207 ,3.7436403539082232101 ] 
dist 78=[-1.4413344525090590617 ,4.1103060807380300546 ] 
dist 79=[-1.3249356992963349653 ,4.4166591239164805167 ] 
dist 80=[-.65110611321871365466,4.7195729666052161696 ] 
dist 81=[-.53041977771219947049,4.9842430446460261696 ] 
dist 82=[-.28249525508740681962,5.1380774486340125563 ] 
dist 83=[-.2188168810203352036 ,5.2397699387639864447 ] 
dist 84=[.33229876066492246861,5.2964874933807989118 ] 
dist 85=[.42076225007715610165,5.3197921385632927873 ] 
dist 86=[.51970757482570024865,5.3146618716958669761 ] 
dist 87=[.52352632497531456656,5.2448372186281836232 ] 
dist 88=[.48772765806470907881,5.2209776561388373729 ] 
dist 89=[.13372920436251932984,4.5045756460776539815 ] 
dist 90=[-.57174720684870054853,4.5069558028643308883 ] 
dist 91=[-1.1712754864223173940 ,4.4894735151987184665 ] 
dist 92=[-1.7804855743604525802 ,3.5544025584965585894 ] 
dist 93=[-2.3471172098543234695 ,3.5556729484271326778 ] 
dist 94=[-2.7768412158086777322 ,.54078063145410472743] 
dist 95=[-3.1873195740361684273 ,.26995470868961830678] 
dist 96=[-3.6772001805663691519 ,.2010667173713653854 ] 
dist 97=[-4.1306523508116519310 ,-.41719621766558130339] 
dist 98=[-4.3958515920874613020 ,-.51528030790706561235] 
dist 99=[-4.5731791358951631051 ,-.62519769792687670715] 
dist 100=[-4.6761910139247726198 ,-.55471950326775391258] 
dist 101=[-4.8219875656961355872 ,-.451260798722782668  ] 
dist 102=[-5.0069623042641763857 ,-.32561636574985783135] 
dist 103=[-5.1414796301482660535 ,-.13735891717948253898] 
dist 104=[-5.2328180282202218999 ,.07603707100397814488] 
dist 105=[-5.2514400629497067800 ,.86588958447259702352] 
dist 106=[-5.2325250574997921395 ,1.4654826473077395418 ] 
dist 107=[-5.2208471362827655831 ,2.0348805404701915216 ] 
dist 108=[-4.9220464901128273966 ,3.1497245213862118883 ] 
dist 109=[-4.8564488825640334121 ,3.8730029123888361608 ] 
dist 110=[-4.6698207957070811496 ,4.4458836670466966903 ] 
dist 111=[-4.6139983001319659828 ,4.9609282215929424765 ] 
dist 112=[-4.2040881001055999455 ,5.3975789509749702001 ] 
dist 113=[-4.1082882983736478069 ,5.6578184239977812495 ] 
dist 114=[-3.9495938130577188025 ,5.8379330295013899848 ] 
dist 115=[-3.9009135247716275420 ,5.9550397418170980363 ] 
dist 116=[-2.7805355612815808899 ,6.0334948573503625950 ] 
dist 117=[-2.6241583786538302952 ,6.0594627904888117204 ] 
dist 118=[-2.2613267188081925248 ,6.0518939143965095520 ] 
dist 119=[-2.1761090669414577388 ,6.0334316137895738797 ] 
dist 120=[-1.9901664695816083559 ,5.9150713249833047709 ] 
dist 121=[-3.1227476791493809826 ,5.8757775591890598375 ] 
dist 122=[-3.8585144792954468390 ,5.7045333555880461372 ] 
dist 123=[-4.4423787531235956962 ,5.6781564407044910847 ] 
dist 124=[-4.9691601918269289565 ,4.6319649054931693283 ] 
dist 125=[-5.4170721065351459179 ,4.2056149237782908387 ] 
dist 126=[-5.6863982115878262547 ,4.1069048002941361738 ] 
dist 127=[-5.8757067042618829026 ,3.9422407726564134497 ] 
dist 128=[-6.0045017365150498791 ,3.8924945163392004635 ] 
dist 129=[-6.0939424036733290402 ,2.7581635304823464936 ] 
dist 130=[-6.1263024498190932170 ,2.6001606825604771113 ] 
dist 131=[-6.1229564929135480822 ,2.2318320473030794739 ] 
dist 132=[-6.1056363986947837597 ,2.1475792239083814876 ] 
dist 133=[-5.9896628767542178393 ,1.6392654685504973021 ] 
dist 134=[-5.9507400076203602768 ,1.5413953608417779970 ] 
dist 135=[-5.7782868934526710689 ,1.3489203032142200238 ] 
dist 136=[-5.7525411627738623589 ,1.2981371987824525458 ] 
dist 137=[-3.0466553005380797740 ,.70933142874329586227] 
dist 138=[-3.0800957004489151698 ,1.1762287045659776407 ] 
dist 139=[-3.0920219135163694074 ,1.5532202521659596137 ] 
dist 140=[-3.0904403887340254675 ,1.9045169012933849618 ] 
dist 141=[-3.0792585227694416051 ,2.2111675270471220007 ] 
dist 142=[-.92983952148964578658,2.4101069962083331252 ] 
dist 143=[-.74951996804616751224,2.5676678587891165474 ] 
dist 144=[-.34722487169174351473,2.7092971301798851039 ] 
dist 145=[-.26462904249999954535,2.8302905311442609317 ] 
dist 146=[.20581775315247906665,2.9055538177920674889 ] 
dist 147=[.28642984797524811164,2.9615146982410170927 ] 
dist 148=[.45618322659390020755,3.0055285028726585046 ] 
dist 149=[.49290175742552072906,3.0383408017956748197 ] 
dist 150=[.75914822430078740118,3.0496291460105110806 ] 
dist 151=[.80176271400977683681,3.0472812217167423038 ] 
dist 152=[.80048480814187784292,3.0363392810366547089 ] 
dist 153=[.58531910175231450452,2.4999260463438665926 ] 
dist 154=[.19703921424310055835,2.5980841660213431852 ] 
dist 155=[-.13950903423023598965,2.6413632886683480414 ] 
dist 156=[-.49207052666425317926,2.6590705187697882619 ] 
dist 157=[-.82668336693969971103,2.6553918023806384235 ] 
dist 158=[-1.0916508778483817364 ,-.26968047629511182135] 
dist 159=[-1.3555708781344850522 ,-.42838677940270578907] 
dist 160=[-1.6860061572159669263 ,-.47332295320679724052] 
dist 161=[-1.9997830699068028889 ,-.70635214500985379001] 
dist 162=[-2.1972681010872876850 ,-.78088946717398800753] 
dist 163=[-2.3468156607457256154 ,-.78059015230503184495] 
dist 164=[-2.4694138973194830966 ,-.72128053061776817991] 
dist 165=[-2.5648774220840793060 ,-.62880572218061704791] 
dist 166=[-2.6062094635389412589 ,-.49624084584471512008] 
dist 167=[-2.6228439384298733053 ,-.30931605654334712581] 
dist 168=[-2.6198114897010953922 ,-4.93268709020745090000e-05] 
dist 169=[-2.0503758510952944427 ,.39769889150642924884] 
dist 170=[-2.0411231988728693893 ,.66672249032514839183] 
dist 171=[-2.0373176392524688573 ,.892190268643661513  ] 
dist 172=[-2.0337517398510051537 ,1.1162366323443232101 ] 
dist 173=[-2.0295951200347926325 ,1.3214253810034732531 ] 
dist 174=[-1.5717460749625370604 ,1.4716873951303789300 ] 
dist 175=[-1.5114960376409072186 ,1.6100531871327337732 ] 
dist 176=[-1.3659341606385139213 ,1.7677987955201779331 ] 
dist 177=[-1.3312563060257252635 ,1.9100282518186585222 ] 
dist 178=[-1.1081036845880322564 ,1.9865143166268118872 ] 
dist 179=[-1.0628237095850460781 ,2.0296443315927261906 ] 
dist 180=[-.97831932885483003056,2.0397618969988574413 ] 
dist 181=[-.95602172445450171426,2.0330647657852903525 ] 
dist 182=[-.58382352248481325704,2.1279662461109244601 ] 
dist 183=[-.53211152026508258924,2.1775792856391106805 ] 
dist 184=[-.40995626705014627375,2.2030127187344831417 ] 
dist 185=[-.73278243858746408505,2.2055668143495725265 ] 
dist 186=[-1.0221291921391917254 ,2.1890807965974587561 ] 
dist 187=[-1.2580448303932016793 ,2.1770512596931070878 ] 
dist 188=[-1.4817459603968691181 ,2.1422088323333478413 ] 
dist 189=[-1.6796823717285984049 ,2.1245101214151516255 ] 
dist 190=[-1.8128461264505655140 ,1.0740714933820129155 ] 
dist 191=[-1.9236781383851387669 ,.99049933176110114244] 
dist 192=[-2.0325536639530767145 ,.96842905340668102074] 
dist 193=[-2.1257514895953490284 ,.59567389087289276306] 
dist 194=[-2.1740595036530611435 ,.54398498287589443416] 
dist 195=[-2.1985979440959753108 ,.42109019477758516073] 
dist 196=[-2.2008670745300085356 ,.39889281742096654928] 
dist 197=[-2.1836215299286380781 ,.22759969355465715775] 
dist 198=[-2.1715558865256849354 ,.1961233161147696735 ] 
dist 199=[-2.1359146725806261380 ,.1449752377140589651 ] 
dist 200=[-2.1178560556896544539 ,.13237709095142310777] 
dist 201=[-1.0643923699878619322 ,.23314845642007864454] 
dist 202=[-1.0720377815851109261 ,.38734406941968763657] 
dist 203=[-1.0709670389862149663 ,.51278377172264045518] 
dist 204=[-1.0639946388025766590 ,.63125668206552642783] 
dist 205=[-1.0578885342833951100 ,.73576456630947062646] 
dist 206=[-.41362505760303561248,.80551056065742210149] 
dist 207=[-.35627129956709098161,.86294738695489933914] 
dist 208=[-.22726668029701857264,.91836526536014047292] 
dist 209=[-.20033448150922683481,.96650672691105094937] 
dist 210=[-.04450836159250996634,.99492458597172409577] 
dist 211=[-.01714798419796049769,1.0142548303689210643 ] 
dist 212=[.03944626428202856872,1.0261541144856248839 ] 
dist 213=[.05378191745527352407,1.0323258099889618376 ] 
dist 214=[.16329055580959324181,1.0312840124337952317 ] 
dist 215=[.18149177473513835233,1.0218400654396930172 ] 
dist 216=[.19303723494834326397,1.0146185660649492442 ] 
dist 217=[.07163658539247586052,.91258070448902621067] 
dist 218=[-.06406709729468137630,.93460657389095895623] 
dist 219=[-.1799983893250377983 ,.94288489825553860989] 
dist 220=[-.29878033983271732117,.94409331235351761332] 
dist 221=[-.40988043839218400985,.94166050159562718598] 
dist 222=[-.49517585337259023822,.05067946177807617928] 
dist 223=[-.57765466627387337123,-.00308933052474784707] 
dist 224=[-.67752191667077891337,-.01673876915520787428] 
dist 225=[-.77069533973054416618,-.12770236705260202378] 
dist 226=[-.82647860159502263701,-.14580865663778219005] 
dist 227=[-.86539482474989439649,-.16083021935669011213] 
dist 228=[-.89130106739554568683,-.15568495719301738985] 
dist 229=[-.90917430478860553857,-.14118777410336635259] 
dist 230=[-.91605422194825106151,-.11394266258546583928] 
dist 231=[-.91621232055438099308,-.07222318019853805602] 
dist 232=[-.91442023487402961802,-9.78976700118993000000e-07] 
dist 233=[-.39631735090319191449,.07433755902243666488] 
dist 234=[-.39673271196001101864,.12449717188152443562] 
dist 235=[-.39563177086753421115,.16640564148045966211] 
dist 236=[-.39070588191515020206,.20783792060250077659] 
dist 237=[-.387642236415685816  ,.24564585131111408236] 
dist 238=[-.22085565501624220131,.27310011216489382438] 
dist 239=[-.20375547861680661673,.29814788102307347922] 
dist 240=[-.16443085385833814887,.32635851765129202456] 
dist 241=[-.15585335706124148615,.35165967162935665449] 
dist 242=[-.10429299368626897741,.3651041769135574626 ] 
dist 243=[-.09471684780622854905,.37263033037619529544] 
dist 244=[-.07569446322663433901,.37432859556164784838] 
dist 245=[-.07079955252688510510,.37191020678756178138] 
dist 246=[-.01609131427976841059,.37104600909139094912] 
dist 247=[-.00786909230902370831,.37031441269415109395] 
dist 248=[.00649295424922745097,.36957551169505949574] 
dist 249=[.00960856187033205752,.27735156423905427582] 
dist 250=[.01584700888878438062,.26566684769564371889] 
dist 251=[.01480785398957023372,.23767909969174788746] 
dist 252=[.01032878219613844096,.22890104584198591636] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 0, 1, 2, 2, 0, 1] 
dist 0=[65.574974051064244167  ,65.574974051064244167  ] 
dist 1=[65.243192543574873672  ,65.964820643529027497  ] 
dist 2=[64.309291793333341245  ,66.364796329896686669  ] 
dist 3=[63.056202737197525769  ,66.585457977302512288  ] 
dist 4=[61.630807938029234367  ,66.673465506892322107  ] 
dist 5=[59.806462504913420571  ,66.602353783279443426  ] 
dist 6=[56.820313561946228719  ,66.319750011117351790  ] 
dist 7=[51.913233833093527006  ,66.127454551427566155  ] 
dist 8=[46.872229154455641454  ,64.897621188343826865  ] 
dist 9=[43.320852491660727547  ,64.507872747220435057  ] 
dist 10=[38.705091228025276706  ,64.012400687398225727  ] 
dist 11=[31.744986515532732079  ,63.774471435925807750  ] 
dist 12=[27.016074491995624079  ,63.176381814317451046  ] 
dist 13=[23.012090089368032200  ,62.902686749234733991  ] 
dist 14=[18.945351590165173820  ,61.007592246803035268  ] 
dist 15=[15.143568064852516476  ,56.476299909348176695  ] 
dist 16=[12.196735580781868823  ,37.042324971088254325  ] 
dist 17=[9.3065263364136328763 ,34.903001355267550947  ] 
dist 18=[5.7297049709369246338 ,29.850756000003977451  ] 
dist 19=[2.3204158701793810636 ,29.066908717431638502  ] 
dist 20=[.0984750386949301953 ,22.199951547911648396  ] 
dist 21=[-1.6867769501829905022 ,20.969626444418145419  ] 
dist 22=[-3.3532694167044820850 ,19.290611836171985359  ] 
dist 23=[-4.8280825449861287418 ,18.847260552901515864  ] 
dist 24=[-5.8490738023101559673 ,10.190595386382456501  ] 
dist 25=[-6.7439738996125850040 ,9.1402863222489431213 ] 
dist 26=[-7.8674969689597686553 ,6.8017036741090548968 ] 
dist 27=[-9.5756969517591364726 ,6.4206442616852019187 ] 
dist 28=[-11.072698947350108276  ,3.7617799343907439146 ] 
dist 29=[-12.074497638275748989  ,3.3334104348807674363 ] 
dist 30=[-12.909841232254151752  ,2.5687225405844579632 ] 
dist 31=[-13.742292146939392349  ,2.4226780826823224231 ] 
dist 32=[-14.456304377491572518  ,-1.3211574391359642408 ] 
dist 33=[-14.818657769764923048  ,-1.7107058054113367790 ] 
dist 34=[-14.999501801860336932  ,-2.4779842202288049220 ] 
dist 35=[-15.029758074278175661  ,-2.6590250843002137818 ] 
dist 36=[-14.874822383569199020  ,-3.2312987683720519459 ] 
dist 37=[-14.779862080535968723  ,-3.3454886375123133544 ] 
dist 38=[-14.637682432963449785  ,-3.2624844552450628081 ] 
dist 39=[-14.561435836186210933  ,-.2179988520156041956 ] 
dist 40=[-12.376687849426766036  ,2.8419883386336950897 ] 
dist 41=[-12.382995009674560825  ,4.8750493437786722988 ] 
dist 42=[-12.290049378945306666  ,6.5411066288522840217 ] 
dist 43=[-12.258384713544887757  ,8.1372541657115138433 ] 
dist 44=[-11.721421139264508091  ,9.5627774235410654140 ] 
dist 45=[-11.584264664633558900  ,10.548287045691731685  ] 
dist 46=[-11.446504018533294683  ,11.398655555116921481  ] 
dist 47=[-11.369049438787692340  ,12.285191374199135408  ] 
dist 48=[-2.5586604328041172893 ,13.071313809519840072  ] 
dist 49=[-2.2272738744954645419 ,13.521087878562924160  ] 
dist 50=[-1.4969544294190409244 ,13.810048498880812269  ] 
dist 51=[-1.3331724732499558546 ,13.954468087025778627  ] 
dist 52=[-.4914099391289156906 ,14.009239388001041251  ] 
dist 53=[-.3436931610303259190 ,13.991667939211450920  ] 
dist 54=[-.0114367692707651867 ,13.837840277114993598  ] 
dist 55=[.0498754329502578182 ,13.756668728359108099  ] 
dist 56=[.57332336879111485995,6.6420544884778147640 ] 
dist 57=[.50571741684825035636,6.6825577886738574546 ] 
dist 58=[-.48493025098331707282,6.6827568374750561637 ] 
dist 59=[-1.5622964850539534136 ,1.0173040649346155946 ] 
dist 60=[-2.2801914072677082941 ,1.1438148172770198591 ] 
dist 61=[-2.8708500406239774025 ,1.2376800421865500189 ] 
dist 62=[-3.4406974317101040584 ,1.3253897651505691049 ] 
dist 63=[-3.9523133641433698913 ,1.4273241178819804034 ] 
dist 64=[-4.3107057989518233512 ,1.5202705367778800947 ] 
dist 65=[-4.6249313378216684781 ,1.5721211900395659102 ] 
dist 66=[-4.9603974048283531624 ,1.6036257925146304368 ] 
dist 67=[-5.2547771556855617634 ,1.6154150145515989553 ] 
dist 68=[-5.4051151552319615077 ,1.6174817768915164609 ] 
dist 69=[-5.4836688504618480741 ,1.6124716894647021650 ] 
dist 70=[-5.4959779521483504688 ,1.5979372750550549903 ] 
dist 71=[-5.4281959758037076586 ,1.5886803357325597789 ] 
dist 72=[-5.3963701637998005757 ,1.3779532337057936109 ] 
dist 73=[-5.3634479585065847079 ,1.3441977834481467645 ] 
dist 74=[-5.3301859314966140934 ,1.2596517747006989579 ] 
dist 75=[-3.7557549291704491684 ,1.6214302202308257078 ] 
dist 76=[-3.5674402713806254929 ,2.3992496149220359166 ] 
dist 77=[-3.1259810003141777776 ,3.0372630682221190636 ] 
dist 78=[-3.0232523833016398286 ,3.6489141456521711768 ] 
dist 79=[-2.4004273960754651165 ,4.1949015714430319015 ] 
dist 80=[-2.2785953498159206316 ,4.5710398659734173166 ] 
dist 81=[-2.0410925611261635407 ,4.8938812293878227313 ] 
dist 82=[-1.9779553379466551765 ,5.2273248685630293148 ] 
dist 83=[-1.9258768475293137467 ,5.5183296813222314004 ] 
dist 84=[-1.8916877217625411385 ,5.6719107680030877019 ] 
dist 85=[-1.8788695847778886611 ,5.7539417621321509439 ] 
dist 86=[-1.8339171196666934369 ,5.7670122894808769473 ] 
dist 87=[-1.8184475774784069535 ,5.7337423613838597166 ] 
dist 88=[-.30219308845467940328,5.7018583121534761221 ] 
dist 89=[-.18660262222679435177,5.6330362884723167820 ] 
dist 90=[-.28482684917487233814,5.5981911215154661988 ] 
dist 91=[-1.2618026163776593049 ,1.3529549100703625323 ] 
dist 92=[-2.0639954339641570208 ,1.6389780354295986597 ] 
dist 93=[-2.7104610355315965773 ,1.8736653553769430649 ] 
dist 94=[-3.3108075634868854840 ,2.1150296119643165762 ] 
dist 95=[-3.8335037210020644536 ,2.4276798383438069726 ] 
dist 96=[-4.1702913520922038836 ,2.7297187674769497226 ] 
dist 97=[-4.4344616908644197711 ,2.9287621140639397762 ] 
dist 98=[-4.6675545444982462693 ,3.0899145776063024092 ] 
dist 99=[-4.8654600211810182281 ,3.2408362260027036598 ] 
dist 100=[-4.9892977275579816623 ,3.3731025850628788463 ] 
dist 101=[-5.0822700550791903811 ,3.4598528479134214895 ] 
dist 102=[-5.1570742480058625895 ,3.5296203457039740926 ] 
dist 103=[-5.2142416206827122331 ,3.5941534762387285234 ] 
dist 104=[-5.2368725710208455989 ,3.6416776638648908379 ] 
dist 105=[-5.2384855812448959222 ,3.6478243648556792543 ] 
dist 106=[-5.2190189070612093709 ,3.6291870565193458889 ] 
dist 107=[-2.8352845984830145388 ,3.6114821436789252526 ] 
dist 108=[-2.8391618290871286285 ,3.4359712937454449507 ] 
dist 109=[-2.8379476169005773628 ,3.3854388699874683195 ] 
dist 110=[-2.8327804806543208125 ,3.3188981003888698415 ] 
dist 111=[-2.8208915938540052505 ,3.2888181961351761592 ] 
dist 112=[-2.2546575706130170569 ,2.6796334555689865747 ] 
dist 113=[-2.1719250346432383354 ,2.6185672651914498873 ] 
dist 114=[-2.0160734961769944726 ,2.8400139863986556260 ] 
dist 115=[-1.9739358474017828556 ,3.3859605549022536895 ] 
dist 116=[-1.8211952349559400088 ,3.7312464341503817053 ] 
dist 117=[-1.7801672291087023982 ,3.9946863818861852888 ] 
dist 118=[-1.7192606792646957988 ,4.2142208160444869628 ] 
dist 119=[-1.6980295163200075954 ,4.3879756840515294332 ] 
dist 120=[-.65772716183828741886,4.4688407850673632700 ] 
dist 121=[-1.0926795242078495006 ,4.5034674182936398964 ] 
dist 122=[-1.4443819173663211996 ,4.5017303089888490566 ] 
dist 123=[-1.7729627580106187785 ,-.56255259115774575281] 
dist 124=[-2.0603673951539314488 ,-.75022466045705656483] 
dist 125=[-2.2478557923226940421 ,-1.1637063862145914239 ] 
dist 126=[-2.3975137862552376056 ,-1.2351449245182625197 ] 
dist 127=[-2.5340476590033405301 ,-1.6783036838240588774 ] 
dist 128=[-2.6511268021180454897 ,-1.7469397286801562676 ] 
dist 129=[-2.7231978296818042905 ,-1.8799497988235866038 ] 
dist 130=[-2.9459368855816596932 ,-1.9015204581962792529 ] 
dist 131=[-3.1749781874296951653 ,-1.9513922238140333436 ] 
dist 132=[-3.2964768634512750347 ,-1.9099564794609102725 ] 
dist 133=[-3.3645656210177740871 ,-1.7537682211516660846 ] 
dist 134=[-3.3806024638811693526 ,-1.4826935453654214338 ] 
dist 135=[-3.3563532938868896676 ,-1.0114945044723762878 ] 
dist 136=[-3.3488340865535603399 ,-.4845739731905818701 ] 
dist 137=[-3.3432211223644088673 ,-.11928709377662695933] 
dist 138=[-3.3387661522760490598 ,.38307587195780163517] 
dist 139=[-2.5205510637217445208 ,1.1031102438236917929 ] 
dist 140=[-2.4161882104661471358 ,1.5813273249009335963 ] 
dist 141=[-2.1658559688840684845 ,1.9726054344568868630 ] 
dist 142=[-2.1069176846539230085 ,2.3459197572336175538 ] 
dist 143=[-1.7310328595389784317 ,2.6777945356899142954 ] 
dist 144=[-1.6555567012928273646 ,2.9038082494769140902 ] 
dist 145=[-1.5136396453807404065 ,3.0949053257901421981 ] 
dist 146=[-1.4762976170865703243 ,3.2875297140048475023 ] 
dist 147=[-.87751965598753276805,3.4541975986247874308 ] 
dist 148=[-.79376070717677454228,3.5417778633895514645 ] 
dist 149=[-.60037417138596948279,3.5879475863730832594 ] 
dist 150=[-.56134168079315550322,3.5936804631584518899 ] 
dist 151=[-.30886562056148488028,3.5712993648101795959 ] 
dist 152=[-.38453576455470769774,3.5520498420315658510 ] 
dist 153=[-.64555538593346126839,3.5001882497541681599 ] 
dist 154=[-.86513484629738262204,3.4735851724827443656 ] 
dist 155=[-1.0846651962971316877 ,-.45640556750254938039] 
dist 156=[-1.2869252205650529038 ,-.60816357779356377426] 
dist 157=[-1.7078496429092181379 ,-.88208278533426165001] 
dist 158=[-2.1103613447021950431 ,-.94675326846393046214] 
dist 159=[-2.4688050992939091666 ,-.95792234836851202644] 
dist 160=[-2.7139828063206580554 ,-1.0351765049740444219 ] 
dist 161=[-2.9224327510903385206 ,-1.0258773779860965470 ] 
dist 162=[-3.1344030903784036340 ,-.92518373936869891663] 
dist 163=[-3.3206707740785596056 ,-.75577883487630422763] 
dist 164=[-3.4266163319723080434 ,-.55579335687986276783] 
dist 165=[-3.4937092142516704820 ,-.33314182923006993876] 
dist 166=[-3.5250290692301564290 ,-.05190529761145388718] 
dist 167=[-3.5329043478674939558 ,.38172210177841968951] 
dist 168=[-3.5271407398541184223 ,.81684884794632609786] 
dist 169=[-3.4741647066585985194 ,1.1040648901813760580 ] 
dist 170=[-3.4584009545911118274 ,1.3371047994946079849 ] 
dist 171=[-1.7888027129145875018 ,1.5561725423838644538 ] 
dist 172=[-1.6255303847730543089 ,1.7487172100517406498 ] 
dist 173=[-1.2528866909056673382 ,1.8759808477705993693 ] 
dist 174=[-1.1727849408671299666 ,1.9794277736045994112 ] 
dist 175=[-1.0628360370619724886 ,2.0769893700754532299 ] 
dist 176=[-.67903237557053747942,2.1590249511786254569 ] 
dist 177=[-.62639823425921812801,2.3352865164821482411 ] 
dist 178=[-.49653956809738515182,2.6387599606148866624 ] 
dist 179=[-.4764371829486058732 ,2.9161632898607917923 ] 
dist 180=[-.28143658443250489962,3.0722005417232631269 ] 
dist 181=[-.24520433243757733949,3.1687685735540971302 ] 
dist 182=[-.19906467034554681988,3.2090035795532058919 ] 
dist 183=[-.18714431111461280249,3.2274193671250479249 ] 
dist 184=[-.48859326122806468825,3.2369704859393977294 ] 
dist 185=[-.8145451424531878235 ,3.2418298758861781269 ] 
dist 186=[-1.0828171649705890839 ,3.2415346246784787445 ] 
dist 187=[-1.3414038487285403955 ,-.14876384858331801878] 
dist 188=[-1.5730567897277743880 ,-.20266072598486232023] 
dist 189=[-1.7339147633514065045 ,-.29186788961355730709] 
dist 190=[-1.8732521542338120464 ,-.31175653628674877924] 
dist 191=[-2.1863031604933667031 ,-.33533393761192445126] 
dist 192=[-2.4736819531232501298 ,-.31656470150812831493] 
dist 193=[-2.7572243227065566575 ,-.27153215881869782605] 
dist 194=[-3.1085261898616292452 ,-.17904834822695894131] 
dist 195=[-3.4403111104012080299 ,-.07360105943770022520] 
dist 196=[-3.6460182400677296967 ,.02313093539441812563] 
dist 197=[-3.7981709148620615736 ,.13171959538569705966] 
dist 198=[-3.9163761209960292978 ,.2844522772334227039 ] 
dist 199=[-4.0033021046025924641 ,.4533157849603254155 ] 
dist 200=[-4.0307105831455965792 ,.6262355507542162214 ] 
dist 201=[-4.0311471525661676730 ,.84725845104772938391] 
dist 202=[-4.0156444833146137328 ,1.6996305765241745887 ] 
dist 203=[-3.8682270244805954157 ,2.5492728161357586524 ] 
dist 204=[-3.8285115299731153820 ,3.0987826357599445976 ] 
dist 205=[-3.7075420812306052068 ,3.5320834884218850356 ] 
dist 206=[-3.6687823947094863829 ,3.9182745133000685962 ] 
dist 207=[-3.3735775450163205130 ,4.2432657558443734133 ] 
dist 208=[-3.3025368018748835117 ,4.4324966872738190948 ] 
dist 209=[-3.1887730322745959388 ,4.5579745905134187348 ] 
dist 210=[-3.1517185479591236699 ,4.6287133516912597831 ] 
dist 211=[-2.2735818828336544111 ,4.6701474947272082330 ] 
dist 212=[-2.1505822381315405468 ,4.6787560951404743019 ] 
dist 213=[-1.8695219672109734634 ,4.6649455576120778163 ] 
dist 214=[-1.7983810700928666723 ,4.6480427300798418797 ] 
dist 215=[-1.4240099175118780471 ,4.5508858450417690707 ] 
dist 216=[-1.3511861991286557049 ,4.5184990581941094841 ] 
dist 217=[-1.1940272103197441319 ,4.3888423606702968530 ] 
dist 218=[-1.1487506835716488384 ,4.3627154019623127968 ] 
dist 219=[-1.2734234930055891499 ,.00418352135887982123] 
dist 220=[-1.5343457437786888531 ,.01954963892163973371] 
dist 221=[-1.7412301266680690113 ,.03939686295822974833] 
dist 222=[-1.9475462042748617858 ,.06626862881435646104] 
dist 223=[-2.2062020053280038422 ,.12922244099995282273] 
dist 224=[-2.4519854131265201295 ,.23200720525465009383] 
dist 225=[-2.6069652950651580503 ,.31813639407691001327] 
dist 226=[-2.7246613617486542383 ,.40830728247005279765] 
dist 227=[-2.8217537533146933729 ,.52721068682895005081] 
dist 228=[-2.8978315397601126142 ,.65505215994713626099] 
dist 229=[-2.9317195795956563081 ,.7808688241462566446 ] 
dist 230=[-2.9410966039996181095 ,.9289267678626412055 ] 
dist 231=[-2.9378676807744763495 ,1.3549627255434922726 ] 
dist 232=[-2.8838339452415453795 ,1.9682662091168958440 ] 
dist 233=[-2.8637262468965516840 ,2.3634037565001196489 ] 
dist 234=[-2.7943061772358705688 ,2.6732581963181907100 ] 
dist 235=[-2.7694868997294609483 ,2.9464454153445260869 ] 
dist 236=[-2.5716359766717722229 ,3.1741931082901989956 ] 
dist 237=[-2.5222094896399338585 ,3.3028308650241032365 ] 
dist 238=[-2.4461693609367541664 ,3.3831338061286973486 ] 
dist 239=[-2.4195760305367683776 ,3.4181181557012992151 ] 
dist 240=[-1.7685054239010572841 ,3.4320852072177090876 ] 
dist 241=[-1.6769045409020255192 ,3.4285693815577639897 ] 
dist 242=[-1.4710118402676757121 ,3.4115856207879549442 ] 
dist 243=[-1.4146946798143292168 ,3.3969546276287075977 ] 
dist 244=[-1.1487748814622101990 ,3.3206562971809830149 ] 
dist 245=[-1.0965790890142721738 ,3.2951793019898897373 ] 
dist 246=[-.9875596898703844643 ,3.2022657543764020525 ] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 1, 0, 0, 1] 
dist 0=[69.777468393512332797  ,69.777468393512332797  ] 
dist 1=[69.309953437707457299  ,69.979793965862431700  ] 
dist 2=[68.057038331907888126  ,70.174499106922477608  ] 
dist 3=[66.394734311409364907  ,70.259942724480061133  ] 
dist 4=[64.292630487554877098  ,70.026544406072299207  ] 
dist 5=[61.463926723214363881  ,69.652089834259890476  ] 
dist 6=[56.900573428942335199  ,69.436044784211742744  ] 
dist 7=[52.209335523888992987  ,68.719220053559287175  ] 
dist 8=[48.869925876048553752  ,68.435857273801014252  ] 
dist 9=[45.877619167214872208  ,64.743059685510798399  ] 
dist 10=[42.571910417675798354  ,64.430385113735316625  ] 
dist 11=[38.757358311976976730  ,63.143546045237597617  ] 
dist 12=[34.171711226066921087  ,62.757721496037044669  ] 
dist 13=[30.224829687923745474  ,62.532870242401960339  ] 
dist 14=[26.109925462950914001  ,61.124345142083711888  ] 
dist 15=[22.195712139523777159  ,53.467015945221160961  ] 
dist 16=[19.050455070413331073  ,48.501802858385480822  ] 
dist 17=[15.862815687482454285  ,27.169643934527077805  ] 
dist 18=[11.779867117487224255  ,24.458186164722799337  ] 
dist 19=[7.8324760917742372182 ,20.409411449401054424  ] 
dist 20=[5.1862379176455696835 ,19.915590662464370155  ] 
dist 21=[2.9849149006302698093 ,18.907177187663514240  ] 
dist 22=[.81392882298304867131,18.651577561344729584  ] 
dist 23=[-1.1716484399840863702 ,6.1245928011052166542 ] 
dist 24=[-3.3421539612938716700 ,5.3210947709549413412 ] 
dist 25=[-5.5551122879104499554 ,2.5805025224160866442 ] 
dist 26=[-7.6621802322226677792 ,2.1058604319546302689 ] 
dist 27=[-9.5502884846156324862 ,-.50263412363326584268] 
dist 28=[-10.888731297417416635  ,-.93532869705131634968] 
dist 29=[-12.087188648481397554  ,-1.8453699725283405722 ] 
dist 30=[-13.416505578068531770  ,-2.0131392141968407985 ] 
dist 31=[-14.614770264139947861  ,-3.2086956093664763799 ] 
dist 32=[-15.289822371501326454  ,-3.4113467091184352658 ] 
dist 33=[-15.715715893860371544  ,-3.4242931389741798837 ] 
dist 34=[-15.918577116348564361  ,-3.1873418912809273667 ] 
dist 35=[-16.021167842722079705  ,-2.8123269718711866983 ] 
dist 36=[-16.046224317840428591  ,-2.2737911644216171014 ] 
dist 37=[-16.020854774001696788  ,-1.5146287466774233766 ] 
dist 38=[-15.966660522453531885  ,-.25878455789418092539] 
dist 39=[-10.583365008079879470  ,2.4380616033810050359 ] 
dist 40=[-10.451065716896699869  ,4.3603438271674708206 ] 
dist 41=[-10.349555591126455684  ,5.9250684864274719336 ] 
dist 42=[-10.280408735437195977  ,7.4065907529971636921 ] 
dist 43=[-7.9239355846500044072 ,8.7181929298113563218 ] 
dist 44=[-7.6086268967397023671 ,9.6052444939191373535 ] 
dist 45=[-6.8680329712265743307 ,10.350109346086804733  ] 
dist 46=[-6.6864849274305309776 ,11.094727093655498437  ] 
dist 47=[-5.6122380654801984834 ,11.748107339501546687  ] 
dist 48=[-5.3953623827205095921 ,12.128975883010580474  ] 
dist 49=[-4.9719564933983452316 ,12.383078637320754924  ] 
dist 50=[-4.8555424862543084648 ,12.530452042258935106  ] 
dist 51=[-3.1604250031485336227 ,12.597621626580613784  ] 
dist 52=[-2.9180548166056001672 ,12.593036493982533237  ] 
dist 53=[-2.3420252704991315598 ,12.404956726056271529  ] 
dist 54=[-2.2317511012091706793 ,11.867353738536958903  ] 
dist 55=[-1.4163387369643096960 ,6.3910954372751614106 ] 
dist 56=[-1.2631455628153140776 ,5.8273531395428552750 ] 
dist 57=[-1.0045409485038843178 ,4.5293353901775111046 ] 
dist 58=[-.94184065420960921131,3.4225703942566494843 ] 
dist 59=[-1.0132805168559675918 ,3.2257632058818929526 ] 
dist 60=[-1.4297436700169097713 ,3.2736144931290046645 ] 
dist 61=[-1.8466152090157489691 ,3.3078328743845977513 ] 
dist 62=[-2.3716564703402809774 ,3.3184473205456830217 ] 
dist 63=[-2.8722988480316287022 ,3.3151912978474650450 ] 
dist 64=[-3.1918626578646894318 ,3.3093189941253755943 ] 
dist 65=[-3.4392573205398747855 ,1.4596167962173988966 ] 
dist 66=[-3.6520401307942055462 ,1.6310433958743968104 ] 
dist 67=[-3.8257180886812307204 ,1.7869687614062427312 ] 
dist 68=[-3.9171336594090206781 ,1.8756695400609191342 ] 
dist 69=[-3.9656008310137725251 ,1.9316761121346302049 ] 
dist 70=[-3.9703234900705416139 ,1.9572576094693731547 ] 
dist 71=[-2.9904448547096367469 ,1.9686658126563989975 ] 
dist 72=[-3.1620967915562379136 ,1.9681768969732136162 ] 
dist 73=[-3.3092070238399845344 ,1.9588479898756845511 ] 
dist 74=[-3.3781532149919766670 ,1.9503760464717527585 ] 
dist 75=[-3.4111027718903111671 ,1.7692318879282426253 ] 
dist 76=[-3.4145109556786272680 ,1.9652388102055558739 ] 
dist 77=[-3.3340917880518954002 ,2.1406955758165173176 ] 
dist 78=[-3.3071743570831774552 ,2.3332946354651686682 ] 
dist 79=[-3.2856040615769537749 ,2.5052958012354732196 ] 
dist 80=[-3.2657908046040631063 ,2.5986073074711035142 ] 
dist 81=[-2.3362249976812535015 ,2.6519039662346512451 ] 
dist 82=[-2.2223829498089382247 ,2.6643176425231563079 ] 
dist 83=[-1.9571870015336139720 ,2.6609506723520977429 ] 
dist 84=[-1.8939150048091106528 ,2.6513101349820116745 ] 
dist 85=[-1.9092016652547708117 ,2.7802151403185521179 ] 
dist 86=[-1.9225383314530550042 ,3.0086118180344077601 ] 
dist 87=[-1.9237205068323231046 ,3.2011284046441720602 ] 
dist 88=[-1.9164042946216007050 ,3.3945143087165005480 ] 
dist 89=[-1.9014586822349871954 ,3.5611289237090925639 ] 
dist 90=[-1.8925812463922177062 ,3.6468661789210723625 ] 
dist 91=[-1.8638825781193024452 ,3.6896953733499511236 ] 
dist 92=[-2.0517450018712507298 ,3.6956915982394198102 ] 
dist 93=[-2.2166360669954479432 ,3.6616671223909980456 ] 
dist 94=[-2.3926151642923223193 ,3.6393649869594113491 ] 
dist 95=[-2.5483816642817732027 ,3.5893889954491516112 ] 
dist 96=[-2.6326637685450108747 ,3.5652828900548275033 ] 
dist 97=[-2.6804837061431324516 ,1.8145020619482978434 ] 
dist 98=[-2.6908356900735455934 ,2.0736377667845121572 ] 
dist 99=[-2.6854094455059708230 ,2.3218545466778779040 ] 
dist 100=[-2.6721713762101334478 ,2.4817226219651753031 ] 
dist 101=[-2.6465157669541688411 ,2.6070167980618023225 ] 
dist 102=[-2.7090594717049750752 ,2.7173535020090262409 ] 
dist 103=[-2.8718806633633767141 ,2.8092383867996707212 ] 
dist 104=[-3.0101763150642774656 ,2.8609474242962982172 ] 
dist 105=[-3.1262106238424735752 ,2.8929829044218150258 ] 
dist 106=[-3.2002482876489154736 ,2.9064110396088819120 ] 
dist 107=[-3.2575298865264116684 ,2.9058886191395745421 ] 
dist 108=[-3.3067283218072135582 ,2.8977273772337927550 ] 
dist 109=[-3.3468244802553533120 ,2.8539212935401292930 ] 
dist 110=[-3.3677987967836197504 ,2.8343824106798444983 ] 
dist 111=[-3.3787303734299345695 ,2.6622236907558512638 ] 
dist 112=[-3.3787671762917384655 ,2.6167528261124409652 ] 
dist 113=[-1.9856459237708774506 ,2.5520329183833444525 ] 
dist 114=[-1.9857946555694122641 ,2.5264648833880155973 ] 
dist 115=[-1.6211091590939910245 ,2.5033521467219472536 ] 
dist 116=[-1.5676773815999625441 ,2.5008638411049494213 ] 
dist 117=[-1.4738629709201642504 ,2.4726133579523710379 ] 
dist 118=[-1.4491060333079026967 ,2.4579714877276537502 ] 
dist 119=[-1.3685706485177571359 ,1.4346015864699565507 ] 
dist 120=[-1.3425691139465759016 ,1.4090966382613003611 ] 
dist 121=[-1.3236409186175678688 ,1.6688681935904645109 ] 
dist 122=[-1.3151024678324286522 ,1.8485271400776834651 ] 
dist 123=[-1.0544528190510878340 ,1.9872479649894603833 ] 
dist 124=[-1.2589828288618288190 ,2.1058110407303196710 ] 
dist 125=[-1.4555123436283037466 ,2.2019430897385438363 ] 
dist 126=[-1.6917134057185381085 ,2.2512045349714156110 ] 
dist 127=[-1.9111914473169082270 ,2.2754315495427738804 ] 
dist 128=[-2.0410282204918614543 ,2.2779663558624784649 ] 
dist 129=[-2.1296907529389317012 ,-.30491103021274057377] 
dist 130=[-2.1849626025477719763 ,-.3343870305248398628 ] 
dist 131=[-2.2216426547606405368 ,-.30750644460951049987] 
dist 132=[-2.2361596197118007066 ,-.25012964210962588901] 
dist 133=[-2.2371809027457225663 ,-.15959767332892187668] 
dist 134=[-2.2313145092915450111 ,-.00048414179963242225] 
dist 135=[-1.2957268505359942300 ,.3999533814684715227 ] 
dist 136=[-1.4114750010309709255 ,.67516449529742107422] 
dist 137=[-1.5148720692168089092 ,.91055003534374100244] 
dist 138=[-1.5703837452705627011 ,1.1521598867232693081 ] 
dist 139=[-1.6012939040793652263 ,1.3784175062369121284 ] 
dist 140=[-1.6082052470040289534 ,1.5525770859977484311 ] 
dist 141=[-1.6027148278856709394 ,1.7214181989517991322 ] 
dist 142=[-1.5971511445442315649 ,1.9264653511185236327 ] 
dist 143=[-1.5892930890032997799 ,2.1180764705571387879 ] 
dist 144=[-1.5803232102285099243 ,2.2333335769159301115 ] 
dist 145=[-1.1157684770585665903 ,2.3143997651162474921 ] 
dist 146=[-1.0605066873237739417 ,2.3696546659016051651 ] 
dist 147=[-.92990660546312090846,2.4049014254622710412 ] 
dist 148=[-.89992122704978280226,2.4112209922912612116 ] 
dist 149=[-.71242329352151908196,2.3970982276416670639 ] 
dist 150=[-.85009812756630736158,2.3910791957127060694 ] 
dist 151=[-1.3626135502256558689 ,2.2083563314476570683 ] 
dist 152=[-1.6961624654929611452 ,2.1727033745745095968 ] 
dist 153=[-1.9615255973817799366 ,2.0752712413025270737 ] 
dist 154=[-2.2021103639659254113 ,2.0475753113277644214 ] 
dist 155=[-2.4075054194401493265 ,1.8486601641204758468 ] 
dist 156=[-2.5325290113959371427 ,1.8032700621223888682 ] 
dist 157=[-2.6222607795813175640 ,1.7263402356772331365 ] 
dist 158=[-2.6869090538304189924 ,1.7037752961334430361 ] 
dist 159=[-2.7336946589034154715 ,1.6253027547998680540 ] 
dist 160=[-2.7521885990242439709 ,1.6156120570237784507 ] 
dist 161=[-2.7534480622796071703 ,.96169692425118351459] 
dist 162=[-2.7465731767391804540 ,.92556130564245589651] 
dist 163=[-2.6970346517854596037 ,.69382997637610675439] 
dist 164=[-2.6797344129386428093 ,.64939358008713226025] 
dist 165=[-2.6050189492256234429 ,.56549324419072120818] 
dist 166=[-2.5917832017262168370 ,.54430837024240317338] 
dist 167=[-1.3060511658806653346 ,.41955069379250632301] 
dist 168=[-1.3945598118647743936 ,.69618749212293538568] 
dist 169=[-1.4718529036053290120 ,.9202741644473031175 ] 
dist 170=[-1.5167000269546555492 ,1.1303037661429482206 ] 
dist 171=[-1.5462396109294303288 ,1.3144796994230273495 ] 
dist 172=[-1.5624848545086951236 ,1.4354597533331430078 ] 
dist 173=[-1.5688874055488467970 ,1.5329655336299144695 ] 
dist 174=[-1.5672680760145263776 ,1.6235240752723070249 ] 
dist 175=[-1.5461391915407720978 ,1.7015007609499276940 ] 
dist 176=[-1.5393000326326917495 ,1.7488290343383077523 ] 
dist 177=[-.71032492175550270556,1.7826338118852997349 ] 
dist 178=[-.63269930886187085789,1.8066776519488105440 ] 
dist 179=[-.4567702767947508827 ,1.8225241394757548409 ] 
dist 180=[-.41947359805318472638,1.8236371806359788332 ] 
dist 181=[-.20070911691696243392,1.8153936150182570932 ] 
dist 182=[-.16149105073145806916,1.8082122680911963991 ] 
dist 183=[-.08157921886382805390,.94755922974652512336] 
dist 184=[-.06121858768126662775,1.0919558689208075946 ] 
dist 185=[-.18578060288655636479,1.2255647793778035980 ] 
dist 186=[-.39648833368065583688,1.3036127853936198261 ] 
dist 187=[-.59521033530361576342,1.3556834394535675961 ] 
dist 188=[-.75050694151544946222,1.3856924266044775109 ] 
dist 189=[-.90328060319351956068,1.4045877652011589427 ] 
dist 190=[-1.0919408858636729645 ,1.4123362204127560124 ] 
dist 191=[-1.2698127783359140554 ,1.4133814817611637413 ] 
dist 192=[-1.3795614246898423708 ,1.4087222445201444497 ] 
dist 193=[-1.4601090406880787451 ,-.09190500512808326071] 
dist 194=[-1.5215247490409380502 ,-.12375418885281386096] 
dist 195=[-1.5669253594977986915 ,-.18695667783851208564] 
dist 196=[-1.5836034075997505441 ,-.20189414748924272842] 
dist 197=[-1.5880561039750993421 ,-.16023516679173182994] 
dist 198=[-1.5847009780262924218 ,-1.17315038520592450000e-05] 
dist 199=[-.67005711612632825684,.16324060541032813298] 
dist 200=[-.73872554870332070977,.27067398341468248238] 
dist 201=[-.80120025722650555842,.3574817950375259315 ] 
dist 202=[-.83581438782953848403,.43847762493002590691] 
dist 203=[-.85654956074943535318,.50925202629557412534] 
dist 204=[-.86367379945407331523,.55529591448816157723] 
dist 205=[-.86532809866215940219,.59190858570253878514] 
dist 206=[-.86424868489201972219,.6250704941414935627 ] 
dist 207=[-.86096349034933142215,.65345306202795220476] 
dist 208=[-.85671773277162468301,.67100531728578966432] 
dist 209=[-.69933321252142128382,.68393482061724722249] 
dist 210=[-.67706077919383343859,.69388146008503523506] 
dist 211=[-.62220564047304636062,.70111488807621966497] 
dist 212=[-.60872231647904263923,.70322387229554903523] 
dist 213=[-.52004036555238360297,.75004085624653433281] 
dist 214=[-.50158048860541608922,.80400864231570351671] 
dist 215=[-.47978021491947842791,.84773057952537107172] 
dist 216=[-.47421376784828479515,.88871981659873482279] 
dist 217=[-.34219987033468656991,.92309291003763954676] 
dist 218=[-.32370679174247528861,.94042910433957440418] 
dist 219=[-.28146500756959184926,.9485559354760113505 ] 
dist 220=[-.27075326543070080879,.94872418894020817661] 
dist 221=[-.21452550062537295244,.93895029710698982429] 
dist 222=[-.20358564611332181814,.9335615244734971001 ] 
dist 223=[-.17993583922050267282,.91567532895467279966] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 2, 1, 0, 1, 2] 
dist 0=[66.642023679200057455  ,66.642023679200057455  ] 
dist 1=[66.294557492508581896  ,66.803886589847731016  ] 
dist 2=[65.548540515976192918  ,67.102233593627041779  ] 
dist 3=[64.277797146267439224  ,67.253924669702609704  ] 
dist 4=[62.793595244481641353  ,67.208841316892566612  ] 
dist 5=[60.766275607041496107  ,66.944050677863305004  ] 
dist 6=[57.881663158080963820  ,66.746438096943325272  ] 
dist 7=[53.149848137270686808  ,65.436777507319332428  ] 
dist 8=[48.278858993237222635  ,65.037759029051842971  ] 
dist 9=[44.838630492668307818  ,64.456246021948316772  ] 
dist 10=[41.782736711428440284  ,64.216921838100648063  ] 
dist 11=[37.039198494915867311  ,63.447789865571196151  ] 
dist 12=[29.794555480554955374  ,63.157377206635810868  ] 
dist 13=[24.885106454167267995  ,62.600479396630839221  ] 
dist 14=[20.741907538686463877  ,61.234251088024134842  ] 
dist 15=[16.555592422516208763  ,37.824537854370093022  ] 
dist 16=[12.655667599134167607  ,35.711730774990875128  ] 
dist 17=[9.6551805617857413858 ,30.677028616221514348  ] 
dist 18=[6.7333952275174316868 ,29.925031556249659424  ] 
dist 19=[3.1465386151406812776 ,22.943254311529709258  ] 
dist 20=[-.25846658085468674632,21.686843517952628843  ] 
dist 21=[-2.4548265038659324386 ,20.079792530454507023  ] 
dist 22=[-4.1942156427466178358 ,19.726337837080706934  ] 
dist 23=[-5.7754425119044664010 ,14.251321079163508884  ] 
dist 24=[-7.1464284495377081810 ,9.2625471021194918146 ] 
dist 25=[-8.0474634340433835531 ,6.8427734209623124101 ] 
dist 26=[-8.7877679603261250146 ,6.3873060420318797548 ] 
dist 27=[-9.5194247035360880953 ,3.8541997467815360336 ] 
dist 28=[-10.138136180815790207  ,3.4472121866738931617 ] 
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dist 30=[-11.886883532828438770  ,2.4890344325041780120 ] 
dist 31=[-12.841151921751574563  ,-2.7778740155194774654 ] 
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dist 34=[-14.355395881916261145  ,-4.3610526564145651219 ] 
dist 35=[-14.404915898175175982  ,-4.8456953532562352806 ] 
dist 36=[-14.345066918854595930  ,-4.8590542246562621800 ] 
dist 37=[-14.277684114004204887  ,-4.7069553057752448213 ] 
dist 38=[-14.181290702222996962  ,-3.2341708558219907066 ] 
dist 39=[-14.110579454309038518  ,-.35121141431366180404] 
dist 40=[-12.054048200896931017  ,2.5496218286768410661 ] 
dist 41=[-12.121911566883827015  ,4.4765649772133766352 ] 
dist 42=[-12.124959971658410335  ,6.0548886399915424760 ] 
dist 43=[-12.011150682735967622  ,7.5652774775998215604 ] 
dist 44=[-11.958423879761297391  ,8.9127105528759870372 ] 
dist 45=[-11.803328850566306253  ,9.8410967910919908292 ] 
dist 46=[-11.729965306028964903  ,10.638644771161022405  ] 
dist 47=[-5.2853439888812961252 ,11.464255424732685407  ] 
dist 48=[-2.8300474399307475215 ,12.196477568213499595  ] 
dist 49=[-2.4980000939255665693 ,12.621463701016726002  ] 
dist 50=[-1.7365175970262515034 ,12.902074412973387286  ] 
dist 51=[-1.5917208966988892463 ,13.058195353552805040  ] 
dist 52=[-.62382709227251852026,13.126964015829446011  ] 
dist 53=[-.45188096031954767811,13.121835207025799843  ] 
dist 54=[-.13453903135222012137,12.962994545537671140  ] 
dist 55=[-.06272136415925276794,12.918832629075307185  ] 
dist 56=[.85185824380970732487,7.6927041509369684938 ] 
dist 57=[.97206365094965803046,7.6914576468096493650 ] 
dist 58=[.40335099840177581324,7.6676364102797274748 ] 
dist 59=[-.64992599521997283467,7.6320869326688657733 ] 
dist 60=[-1.9004411557905014790 ,7.5900452899720709683 ] 
dist 61=[-2.7360771849013097219 ,7.5177603232799560337 ] 
dist 62=[-3.4262678403117656466 ,7.4820360320389187399 ] 
dist 63=[-4.0966137210221781833 ,2.1779688931268511438 ] 
dist 64=[-4.7014718189106920312 ,1.7654859798174145299 ] 
dist 65=[-5.1304438129689360754 ,1.7779360868612461058 ] 
dist 66=[-5.5120525136825351909 ,1.7857421831877187876 ] 
dist 67=[-5.9280043664013476600 ,1.7892771769363147505 ] 
dist 68=[-6.2944344341731354596 ,1.7898247386889574301 ] 
dist 69=[-6.4785060818731315594 ,1.7857093945117259641 ] 
dist 70=[-6.5764283638849257523 ,1.7774167982132843449 ] 
dist 71=[-6.5991248012636464864 ,1.7692023928418048977 ] 
dist 72=[-6.4819368387839952044 ,.46976327028166365126] 
dist 73=[-6.5633432176311018619 ,.36035855406019041371] 
dist 74=[-6.8193109169088724124 ,.11920451804373198784] 
dist 75=[-7.0073119160559547232 ,.91601577689783888675] 
dist 76=[-7.0697290196096700893 ,2.3371806783995700119 ] 
dist 77=[-7.0841831876830167970 ,3.2782604789908694690 ] 
dist 78=[-7.0808225962978222115 ,4.0454360011347182566 ] 
dist 79=[-3.9989380005573942838 ,4.7730298138386027842 ] 
dist 80=[-3.2859526310174454653 ,5.4172573183089179821 ] 
dist 81=[-3.1433900925804699762 ,5.8519548209649067106 ] 
dist 82=[-2.8691257893623453059 ,6.2153821745124925327 ] 
dist 83=[-2.7956229121226097731 ,6.5753869811284424134 ] 
dist 84=[-1.7012562536432244679 ,6.8842318674274713094 ] 
dist 85=[-1.6669198029893383171 ,7.0436143688954938544 ] 
dist 86=[-1.6751495454899013422 ,7.1237545917794435304 ] 
dist 87=[-1.6728980268551011845 ,7.1328226556889646562 ] 
dist 88=[-.65667168099675799364,7.0720182392448040387 ] 
dist 89=[-.57285450012800540145,7.0311786017144701380 ] 
dist 90=[-.40624506191016340608,6.9240989081355064337 ] 
dist 91=[-.36387149709594731351,6.8709596930514429859 ] 
dist 92=[-1.5787556345694760637 ,6.2905601173959094958 ] 
dist 93=[-2.5994837864576312563 ,6.2614817998527980732 ] 
dist 94=[-3.4331797534211303953 ,6.2311888147751037275 ] 
dist 95=[-4.2262642495508114615 ,5.1239271244849286245 ] 
dist 96=[-4.9298446200715391230 ,4.9655945012425960882 ] 
dist 97=[-5.4065872595046962030 ,4.5753668619884670403 ] 
dist 98=[-5.8071530001677643452 ,4.4785743436723634415 ] 
dist 99=[-6.2069340067978125116 ,3.8450233880853524958 ] 
dist 100=[-6.5566597248680855864 ,3.7126150135413000343 ] 
dist 101=[-6.7575938767720597564 ,3.4694675659364009315 ] 
dist 102=[-6.8874799935173627323 ,3.4044842161821653991 ] 
dist 103=[-6.9538396378914009009 ,2.2151892913038026852 ] 
dist 104=[-6.9740706081480589511 ,2.0522988079276471955 ] 
dist 105=[-6.9665695733903822707 ,1.6451021716763304651 ] 
dist 106=[-6.7927707540352612023 ,1.5853400154059851740 ] 
dist 107=[-6.2245867211674176741 ,.95776586185673524091] 
dist 108=[-3.3365273741198288615 ,.84051454389220618505] 
dist 109=[-3.0945392798680665151 ,.72472069550084817669] 
dist 110=[-3.0965930292023486278 ,.67592270321425411622] 
dist 111=[-1.3922363672275893273 ,.65325470929941426588] 
dist 112=[-1.4541838846101022638 ,.82024817109987142583] 
dist 113=[-1.4860482087380853604 ,1.0776988220390835678 ] 
dist 114=[-1.5018971232796985416 ,1.3171568620213337630 ] 
dist 115=[-1.5032645839572945783 ,1.5258992956815392984 ] 
dist 116=[-1.4901356080184625206 ,1.6608528750509106892 ] 
dist 117=[-1.4816663745327529110 ,1.7672238215431866843 ] 
dist 118=[-1.4569739746559813405 ,1.8619765128847302205 ] 
dist 119=[-1.4446068271111172749 ,1.9426276141850018054 ] 
dist 120=[.16713797967352142426,1.9927593550431440652 ] 
dist 121=[.22146536069769801436,2.0300027573539995353 ] 
dist 122=[.34300827823502622059,2.0592513322775187101 ] 
dist 123=[.36230486702422869346,2.0810306196018925578 ] 
dist 124=[.49832211481708193368,2.0884843253836622124 ] 
dist 125=[.51939556002230591107,2.0868547621236327465 ] 
dist 126=[.55778451492059299902,2.0792629337667711130 ] 
dist 127=[.40038312702120875149,1.3388333603019606004 ] 
dist 128=[.13416656312048248637,1.4201037529446454755 ] 
dist 129=[-.09654126734590983310,1.4659115138335697527 ] 
dist 130=[-.33817219036491076455,1.4943855578138354257 ] 
dist 131=[-.56747788107253081722,1.5065270237748534523 ] 
dist 132=[-.7490317289241087072 ,1.5088584118973662508 ] 
dist 133=[-.92985159529810377053,1.5055364154599149917 ] 
dist 134=[-1.1562306674808369401 ,1.4845663528701079758 ] 
dist 135=[-1.3712079539406841025 ,1.4749631285597058798 ] 
dist 136=[-1.5065562602322289366 ,.79818404681237385294] 
dist 137=[-1.6091094950521959719 ,.73056743994183556641] 
dist 138=[-1.6932959066080763701 ,.57575705389334208724] 
dist 139=[-1.7589436592333355931 ,.54225762256441417327] 
dist 140=[-1.7875623843397532750 ,.34239923264809808396] 
dist 141=[-1.7991399992335885407 ,.30564444023354039506] 
dist 142=[-1.7968254002811351536 ,.23209108919921841704] 
dist 143=[-1.1613476057299383061 ,.27392708579942399612] 
dist 144=[-1.2755951749577369386 ,.45825512533230479746] 
dist 145=[-1.3393984791415528827 ,.61267927280946337981] 
dist 146=[-1.3782871273043993504 ,.76603332000157326263] 
dist 147=[-1.3931725545181801674 ,.90641946226233631078] 
dist 148=[-1.3988957017651823780 ,1.0091264744587381327 ] 
dist 149=[-1.4012442401866432411 ,1.1036042463976461138 ] 
dist 150=[-1.4015643492230443348 ,1.2111715311255474046 ] 
dist 151=[-1.3991978619649492329 ,1.3080847074065045198 ] 
dist 152=[.05328644850552288052,1.3600728994804841693 ] 
dist 153=[.07304521397607680486,1.3893636120694353787 ] 
dist 154=[.09979506580547576755,1.3961145763420084658 ] 
dist 155=[.10539337382569462411,1.3906479114881780643 ] 
dist 156=[.10300867702187348181,1.3880837614144537839 ] 
dist 157=[.08849757308659889173,1.3854286332380679052 ] 
dist 158=[-.19855951591995771967,1.3819660909579775382 ] 
dist 159=[-.4974370625921981156 ,1.3806686613780237667 ] 
dist 160=[-.69547046969803373542,1.5306266802079528234 ] 
dist 161=[-.85698484171223939538,1.6242673266219512772 ] 
dist 162=[-1.0102213554945540149 ,1.6943168218340041617 ] 
dist 163=[-1.1458669419590794254 ,1.7501912470523160159 ] 
dist 164=[-1.2372272111954168686 ,1.7924829488113586121 ] 
dist 165=[-1.3133792685019056856 ,1.8083633394678395239 ] 
dist 166=[-1.3883732613346204128 ,1.8106897843869031234 ] 
dist 167=[-1.4526349642206476372 ,1.8060019916708290030 ] 
dist 168=[-1.4859857106014162215 ,1.7535610800981804169 ] 
dist 169=[-1.5029855206349885561 ,1.7380037811427994470 ] 
dist 170=[-1.6116836313582591591 ,1.6885156295127802887 ] 
dist 171=[-1.7829658473100163304 ,1.6719940862888349911 ] 
dist 172=[-1.9265498129700503033 ,1.5439075367129830565 ] 
dist 173=[-2.0091273548398481096 ,1.5126160934274178245 ] 
dist 174=[-2.0625931514722722282 ,1.4633024811364400588 ] 
dist 175=[-2.0900770154383193059 ,1.4467717309283217858 ] 
dist 176=[-2.1044894250377483454 ,1.0496520763744298884 ] 
dist 177=[-2.1058251428559438488 ,.99392219696332437587] 
dist 178=[-2.0978350806161572294 ,.89339611119019044955] 
dist 179=[-2.0896478832353185045 ,1.0461277121444401672 ] 
dist 180=[-2.0445977329725264476 ,1.1512259515504157882 ] 
dist 181=[-2.0295705406173082203 ,1.2412538172712218686 ] 
dist 182=[-1.9717544366973726007 ,1.3338834954771820156 ] 
dist 183=[-1.9587590201873385727 ,1.4154830342838577956 ] 
dist 184=[.00026769268350872661,1.4615217621785079759 ] 
dist 185=[-.00115290571510947067,1.4901959786646377092 ] 
dist 186=[-.00404849641533280879,1.5025443490573364372 ] 
dist 187=[-.00970332892312511909,1.5050715672823186242 ] 
dist 188=[-.01667807289051839268,1.5018170615726164792 ] 
dist 189=[-.02483758379296594253,1.4810471001391483356 ] 
dist 190=[-.03540339593245866258,1.4714597285795706300 ] 
dist 191=[-.10330779577608930427,.79720372201008995314] 
dist 192=[-.30710294019099570462,.72981927998305085757] 
dist 193=[-.47851979176430106964,.57550409112124279939] 
dist 194=[-.64986094416328838921,.54211419670808905118] 
dist 195=[-.80743051542975622257,.34276190479619711772] 
dist 196=[-.92392513534191274909,.30609009032700057878] 
dist 197=[-1.0323018138172635576 ,.23274174194349399582] 
dist 198=[-1.1574963521534349557 ,.21391813399867083243] 
dist 199=[-1.2714809230393583446 ,.19890289370243597034] 
dist 200=[-1.3351512978935166501 ,.22491490033817511765] 
dist 201=[-1.3739759513259790776 ,.24001700640518564459] 
dist 202=[-1.3888736641744744374 ,.24997605326168808779] 
dist 203=[-1.3946265883464841927 ,.25547710275396404905] 
dist 204=[-1.3969810429558116365 ,.25894966594275758441] 
dist 205=[-1.3972903342646688857 ,.26081893894893164889] 
dist 206=[-1.3948869701648808607 ,.26186638103562183848] 
dist 207=[-.26355559960686372017,.27447749013288155711] 
dist 208=[-.21652631182733915692,.46475788648682311575] 
dist 209=[-.20961482237829577543,.6292574962099943778 ] 
dist 210=[-.19777206870876036332,.80090822134508143405] 
dist 211=[-.19453614210301754381,.96340589436920555517] 
dist 212=[-.18459331576308711671,1.0914023560659731603 ] 
dist 213=[-.18128475807113383037,1.2182644506743342796 ] 
dist 214=[-.17930361885326684409,1.3762381722398167604 ] 
dist 215=[-.17862479169469661231,1.5258276117609850102 ] 
dist 216=[-.08924869566648919700,1.6192524778894192302 ] 
dist 217=[-.1407554929836213643 ,1.6891571731508060564 ] 
dist 218=[-.21112590368030056148,1.7449461740374176658 ] 
dist 219=[-.28798049011297330819,1.7871973057158180756 ] 
dist 220=[-.36534673179823458894,1.8031118288750968376 ] 
dist 221=[-.45767609986810677923,1.8054794177173255357 ] 
dist 222=[-.79141470437097841388,1.8008515018799283787 ] 
dist 223=[-1.1702713141590334110 ,1.7488335648602838828 ] 
dist 224=[-1.4149006456818658457 ,1.7333660269315803560 ] 
dist 225=[-1.6073458434659935312 ,1.6841130237236998956 ] 
dist 226=[-1.7780877027084663936 ,1.6676572290817657450 ] 
dist 227=[-1.9212096897045976670 ,1.5400157348882387048 ] 
dist 228=[-2.0035044949871809508 ,1.5088239554100349936 ] 
dist 229=[-2.0567653784361239426 ,1.4596883726813109635 ] 
dist 230=[-2.0840976236002931938 ,1.4432060796616513897 ] 
dist 231=[-2.0983984815459000630 ,1.0471408281146784195 ] 
dist 232=[-2.0996890874566133062 ,.99155803522447890575] 
dist 233=[-2.0916939601422627055 ,.86544411416319796081] 
dist 234=[-2.0835206495201896836 ,.8324221958633433253 ] 
dist 235=[-2.0385833021755050794 ,.66661977563129807968] 
dist 236=[-2.0235923241787921598 ,.63424477942981901265] 
dist 237=[-1.9659556326606462026 ,.56207648086069889985] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 0, 0, 0, 0, 1] 
dist 0=[61.557843504620468710  ,61.557843504620468710  ] 
dist 1=[60.253875622854726526  ,62.179707354614227507  ] 
dist 2=[58.778898565005358698  ,62.463900523293262065  ] 
dist 3=[57.474685579310307307  ,62.470210999372572516  ] 
dist 4=[56.045260387644853317  ,62.134199260103478492  ] 
dist 5=[54.071358593070720565  ,61.598804149230790522  ] 
dist 6=[51.900220832397576710  ,61.261422944503410509  ] 
dist 7=[49.684206092658291408  ,61.066134220163911791  ] 
dist 8=[47.013438332533711652  ,60.204374592444628393  ] 
dist 9=[43.028283151233022052  ,54.212350006304906253  ] 
dist 10=[38.920579017794157863  ,52.377381186912315541  ] 
dist 11=[35.761012965526592770  ,51.842918520798346838  ] 
dist 12=[32.695523411287880186  ,49.628906313232876752  ] 
dist 13=[28.963237126926342358  ,49.138834183933254310  ] 
dist 14=[25.094962506286196495  ,47.930078492033479202  ] 
dist 15=[21.486932873275043008  ,47.575694859594253279  ] 
dist 16=[17.383910371679066674  ,45.367457276330617733  ] 
dist 17=[11.540703968836813581  ,33.538897819497197117  ] 
dist 18=[5.7985166565610314937 ,18.872987979457049887  ] 
dist 19=[2.0980662967941407696 ,18.185805061523756619  ] 
dist 20=[-.8118373425956845687 ,11.968461820859011102  ] 
dist 21=[-3.4013019178027431045 ,10.878507933956480931  ] 
dist 22=[-5.5887979490957307528 ,9.4422209630446537775 ] 
dist 23=[-6.8963173317492891323 ,9.1525763058795715210 ] 
dist 24=[-7.8158616476823163069 ,1.8560382942853233518 ] 
dist 25=[-8.4581350419783115482 ,1.0076231796934403550 ] 
dist 26=[-8.9151037749459148064 ,-.8198186396177649562 ] 
dist 27=[-9.0948622414786628761 ,-1.1104755673801964505 ] 
dist 28=[-9.1138302764962215229 ,-2.9268000998037075338 ] 
dist 29=[-9.0655300749236213185 ,-3.1988052901604381685 ] 
dist 30=[-9.2825455195267316168 ,-3.6772176598527776339 ] 
dist 31=[-9.5693115956838320121 ,-2.8069238137982682674 ] 
dist 32=[-9.7266742717894648882 ,0                     ] 
dist 33=[-9.7487632698183742894 ,-2.6357585716867255565 ] 
dist 34=[-8.6182670828437266458 ,-1.2978026304751655474 ] 
dist 35=[-8.4583807785599387006 ,-.3734750887971371671 ] 
dist 36=[-7.9672065805662423885 ,.4179046704568423662 ] 
dist 37=[-7.8917963756598935365 ,1.2265188037130295266 ] 
dist 38=[-6.8214169073944056557 ,1.9773397888107334929 ] 
dist 39=[-6.5955145063607928925 ,2.5385574480914008697 ] 
dist 40=[-6.3769868296290046488 ,3.0643850035484094295 ] 
dist 41=[-6.3225092463731101893 ,3.6741733165112824808 ] 
dist 42=[-5.4096410507268534980 ,4.2411155002688786012 ] 
dist 43=[-5.3549105225137240307 ,4.5962407845282407236 ] 
dist 44=[-4.8259360235982156468 ,4.8616213973349328697 ] 
dist 45=[-4.7212488607220245764 ,5.0710658915314698560 ] 
dist 46=[-4.5811090408424548898 ,5.2265936269269433396 ] 
dist 47=[-4.5343638624678843273 ,5.2771554883780121210 ] 
dist 48=[-1.5102610496749628918 ,5.2833439916341474405 ] 
dist 49=[-1.4577941893907355420 ,5.2620763602711196094 ] 
dist 50=[2.4616228609392342567 ,4.7391018019348925436 ] 
dist 51=[2.7763197558690030486 ,5.3009044392079559251 ] 
dist 52=[3.4458815308203995907 ,5.7697335965913132641 ] 
dist 53=[3.5600671018532390106 ,6.0390961652441681965 ] 
dist 54=[4.1764040341803048837 ,6.2145265242909994098 ] 
dist 55=[4.2736708627121197080 ,6.3086283601647987556 ] 
dist 56=[4.3596257066032755560 ,6.3638193464720214331 ] 
dist 57=[4.2991429320762941110 ,6.3839595463419025345 ] 
dist 58=[4.1848631156890762275 ,6.3830627954900373888 ] 
dist 59=[4.0174810181189805257 ,6.3600169403824116562 ] 
dist 60=[3.7800868597580158876 ,6.3102254548467846430 ] 
dist 61=[3.3863839343036895692 ,6.2751307298136110244 ] 
dist 62=[2.7386694908629030504 ,6.1821182551575365343 ] 
dist 63=[1.4818673367662595715 ,6.1374267795258454839 ] 
dist 64=[.2116828333868986397 ,4.7296749069223390376 ] 
dist 65=[-.6552398877983762338 ,4.7014968037092301849 ] 
dist 66=[-1.3910632260166971070 ,1.9648887452594027532 ] 
dist 67=[-2.1383263591820485600 ,1.7097686532747913017 ] 
dist 68=[-2.8340534349910423198 ,1.1415367822513698102 ] 
dist 69=[-3.3643242321199523360 ,1.0191920691304894624 ] 
dist 70=[-3.8740381797613513839 ,.34716618714420933376] 
dist 71=[-4.4878043193844178164 ,.22901080320817141583] 
dist 72=[-5.0601679344727226491 ,-.02371453951577126877] 
dist 73=[-5.4047307474036692108 ,-.08161397139082682277] 
dist 74=[-5.6479327497255814526 ,-.5361950527374651834 ] 
dist 75=[-5.8159390836358316355 ,-.6141336291956245611 ] 
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dist 77=[-5.9714058285791794047 ,-.6277286726588076932 ] 
dist 78=[-5.9714105547823280956 ,-.41561265922477966135] 
dist 79=[-5.9528313257369071535 ,.15914647324589253357] 
dist 80=[-4.7149345524152937876 ,1.2038685228526637283 ] 
dist 81=[-4.6987706124433701288 ,1.9159443981238412764 ] 
dist 82=[.47171413843314289768,2.5182386615749394745 ] 
dist 83=[.59006976334802497056,3.1259477415399901799 ] 
dist 84=[.82974874986162060683,3.6886892899043303980 ] 
dist 85=[.88717781798852616174,4.1116400066812499073 ] 
dist 86=[1.0681396410094526191 ,4.5120965748351013515 ] 
dist 87=[1.1022332146773610194 ,4.9851279794392760678 ] 
dist 88=[1.0983709328304912751 ,5.4207631874526494562 ] 
dist 89=[1.0418295670422648263 ,5.6720691943722381033 ] 
dist 90=[.9631029610583005340 ,5.8358469204631300659 ] 
dist 91=[.8707554418053023409 ,5.9223804589906946662 ] 
dist 92=[.7510837796193844080 ,5.9662789669043067227 ] 
dist 93=[.40958744733067449561,5.9600134879422710172 ] 
dist 94=[-.42864444668335851467,5.9277046051312913061 ] 
dist 95=[-1.7113245876232738692 ,5.8973487321789962421 ] 
dist 96=[-2.9943876905013592959 ,5.3728776427277097944 ] 
dist 97=[-3.8341540239899140645 ,5.3610281211078864831 ] 
dist 98=[-4.5076490345660016080 ,4.9616204296154587951 ] 
dist 99=[-5.1276025003192939284 ,4.8828786965814008587 ] 
dist 100=[-5.6635831228622052412 ,4.6678521261624871136 ] 
dist 101=[-6.0021863298207908362 ,4.6059274903331707901 ] 
dist 102=[-6.2601283001215552200 ,4.1660691859913640087 ] 
dist 103=[-6.4744277895749547085 ,4.0653707473432856977 ] 
dist 104=[-6.6435189273537765837 ,3.8933000611410008949 ] 
dist 105=[-6.7211628409183631563 ,3.8431527954120001130 ] 
dist 106=[-6.7465133701521660266 ,2.7169949376904051481 ] 
dist 107=[-6.7374329029231513118 ,2.5600686086823562480 ] 
dist 108=[-6.6354571044331660594 ,2.1908385826096940721 ] 
dist 109=[-6.5941663192099411806 ,2.1098024751729373020 ] 
dist 110=[-6.4359273885406957575 ,1.5909343863877737153 ] 
dist 111=[-6.3879408550047520908 ,1.4911491398375313000 ] 
dist 112=[-5.8838197031603712819 ,1.5316646542966841862 ] 
dist 113=[-5.8541177133853763548 ,2.5292963752561134790 ] 
dist 114=[1.4381261172432499059 ,3.3344183180984250652 ] 
dist 115=[1.9126572318177713576 ,4.0840023084939533878 ] 
dist 116=[2.9872227760197264316 ,4.7378878739807722857 ] 
dist 117=[3.1469261729956357565 ,5.1613557690113984389 ] 
dist 118=[4.3885271471097700155 ,5.4959228631034934527 ] 
dist 119=[4.5826677123876186515 ,5.7952646431548984545 ] 
dist 120=[4.9010647955423015326 ,6.0505882552982882101 ] 
dist 121=[4.9613244102429345397 ,6.2096063696453593307 ] 
dist 122=[5.4544679095232574405 ,6.3280830166097670724 ] 
dist 123=[5.3455164261697603833 ,6.4217213702692144317 ] 
dist 124=[4.9082242423030620098 ,6.4919099591039755250 ] 
dist 125=[4.3613722534670891822 ,6.5168655770383664056 ] 
dist 126=[3.6311588160096749952 ,6.5134002310741454225 ] 
dist 127=[2.4626029708564737053 ,6.4898087242422328075 ] 
dist 128=[1.2691944643909008796 ,6.1324330405626562763 ] 
dist 129=[.4398656961229039525 ,6.1103525172323090306 ] 
dist 130=[-.2791865394247283378 ,1.8640171907037064638 ] 
dist 131=[-1.0328025841773876157 ,1.5070992340252116624 ] 
dist 132=[-1.7482764907061902712 ,.71061913456013276487] 
dist 133=[-2.3152147110538037665 ,.54699549302494760382] 
dist 134=[-2.8802703219920317753 ,-.38535380890277375942] 
dist 135=[-3.5882367196353667451 ,-.54524371770804072516] 
dist 136=[-4.2607723932144569145 ,-.88176133694844519697] 
dist 137=[-4.6845270207906454087 ,-.954988980824619466  ] 
dist 138=[-5.0059766280281335289 ,-1.4867459772442966644 ] 
dist 139=[-5.2705099797741095560 ,-1.5574514157278996698 ] 
dist 140=[-5.4772910557051176763 ,-1.3564337935592119574 ] 
dist 141=[-5.5684189950050291835 ,-1.0696480990078451800 ] 
dist 142=[-5.6056819378622546467 ,-.66596640839304458035] 
dist 143=[-5.5978830436681478416 ,.00124321958880904481] 
dist 144=[-5.2813540292043689503 ,.84753908516221219127] 
dist 145=[-5.2752543176588730498 ,1.4196607422537513435 ] 
dist 146=[.6322705196112457216 ,1.8988512356884667965 ] 
dist 147=[.84361169907129280393,2.3745296071621278243 ] 
dist 148=[1.3129496043787855013 ,2.8098553349934411376 ] 
dist 149=[1.3907900127990482810 ,3.1281160313866933314 ] 
dist 150=[1.9058405557549361185 ,3.4206481205300032592 ] 
dist 151=[1.9852822603975269404 ,3.7533660227705359625 ] 
dist 152=[2.1376069763129468356 ,4.0529382813206969468 ] 
dist 153=[2.1641786397907926491 ,4.2132826468272949682 ] 
dist 154=[2.1590492750444564974 ,4.3035966928530415606 ] 
dist 155=[1.8069412418767607752 ,4.3240608594344990698 ] 
dist 156=[1.3885062801441235456 ,4.3045996614437500428 ] 
dist 157=[.91900169355052771773,4.2965662268666563634 ] 
dist 158=[.3235611714405374130 ,4.2890154575740048092 ] 
dist 159=[-.5971172176159825590 ,4.2801800768760198501 ] 
dist 160=[-1.5222475790304078738 ,4.0805040725271619067 ] 
dist 161=[-2.1354430175956053534 ,4.0688489690859326210 ] 
dist 162=[-2.6357942026284218392 ,3.1744161469206809779 ] 
dist 163=[-3.1108920872088043325 ,3.0555188853344648920 ] 
dist 164=[-3.5317134549591966296 ,2.7676271581598047804 ] 
dist 165=[-3.8156052935651928993 ,2.6987849243473653226 ] 
dist 166=[-4.0527377338613950250 ,2.2546218986029641835 ] 
dist 167=[-4.2870786964817105117 ,2.1642104890613179534 ] 
dist 168=[-4.4881815526051960870 ,1.9958478853626794990 ] 
dist 169=[-4.5927575789432354718 ,1.9513822956956964400 ] 
dist 170=[-4.6463540262397924356 ,1.2004638991171285348 ] 
dist 171=[-4.6517272947265508041 ,1.0963333737240503996 ] 
dist 172=[-4.6169092972091908357 ,.84874248669441390474] 
dist 173=[-4.5915330017222174478 ,.80402698947754555233] 
dist 174=[-4.5180077346748255352 ,.45888794895283449596] 
dist 175=[-4.4806630185966254709 ,.39546306882360077392] 
dist 176=[-4.3036478530828039265 ,1.0081938008560913281 ] 
dist 177=[-4.2672525799051376471 ,1.6791519309430959728 ] 
dist 178=[.46828818960569592789,2.2297122948108794206 ] 
dist 179=[.62472075353256375009,2.7576321683136996705 ] 
dist 180=[.97432646067143932453,3.2287231781881223795 ] 
dist 181=[1.0303700745081452840 ,3.5526452125289729332 ] 
dist 182=[1.4206875267058226638 ,3.8298559791311208994 ] 
dist 183=[1.4811800237365867782 ,4.1146584969514637807 ] 
dist 184=[1.5924564950175165841 ,4.3654720314351381275 ] 
dist 185=[1.6127793616121377463 ,4.5071318441170901279 ] 
dist 186=[1.7124040313922827157 ,4.5955560463808444593 ] 
dist 187=[1.6975752989953129517 ,4.6340614296654559135 ] 
dist 188=[1.5376291244754180883 ,4.6422049392175885466 ] 
dist 189=[1.3370796854571163429 ,4.6324937050238097906 ] 
dist 190=[1.0721435117963060295 ,4.5677156517593679565 ] 
dist 191=[.62384584999688867473,4.5393035335286308107 ] 
dist 192=[-.3019501203458571423 ,4.3738146562691131432 ] 
dist 193=[-.9300731668798010832 ,4.3445511270682813069 ] 
dist 194=[-1.4586122021054715366 ,2.3658281227763671204 ] 
dist 195=[-1.9872586898658946470 ,2.1675688429448315721 ] 
dist 196=[-2.4736340471005638037 ,1.7133603423158171054 ] 
dist 197=[-2.8335922308146634728 ,1.6150064044570049459 ] 
dist 198=[-3.1688333858575271523 ,1.0274028257046498123 ] 
dist 199=[-3.5566351422411473931 ,.9192102452478154714 ] 
dist 200=[-3.9098797074277936291 ,.7029559137210326871 ] 
dist 201=[-4.1073038509465715708 ,.6474438427640696908 ] 
dist 202=[-4.2278273097982106614 ,.05721025524703721771] 
dist 203=[-4.2743854103969162274 ,-.03253517476736327715] 
dist 204=[-4.2927236468957688672 ,-.17724113538292487569] 
dist 205=[-4.3007038890585953591 ,-.21144463683904212664] 
dist 206=[-4.3026024158926322096 ,-.16328205114518677256] 
dist 207=[-4.2966862526137066817 ,1.05792130653330100000e-05] 
dist 208=[-4.1319549538018300868 ,.84332309789189964146] 
dist 209=[-4.1236251491763282143 ,1.4278287043064797370 ] 
dist 210=[.14800375265090525207,1.9329921428785751482 ] 
dist 211=[.19825896941918089539,2.4598815475186648430 ] 
dist 212=[.28248063520651760046,2.9585308498260722523 ] 
dist 213=[.2874872589025292339 ,3.3510703655549686249 ] 
dist 214=[.20967811281902634071,3.7399101652647385450 ] 
dist 215=[.06329894861942002921,4.2238046869686142100 ] 
dist 216=[-.0996044292070612388 ,4.6818676230937311289 ] 
dist 217=[-.2433135411173527812 ,4.9676888684000123629 ] 
dist 218=[-.4000623462176477057 ,5.1812503452063370306 ] 
dist 219=[-.6149691287724074832 ,5.3511351945873913966 ] 
dist 220=[-.8500313777355918202 ,5.4793505035846138210 ] 
dist 221=[-1.0871618935812726890 ,5.5267303182926766751 ] 
dist 222=[-1.3705212024819336654 ,5.5331548978167779693 ] 
dist 223=[-2.4138407434235909389 ,5.5180855410311993127 ] 
dist 224=[-3.5755449539825479446 ,5.3606913870539141883 ] 
dist 225=[-4.3258154587597561369 ,5.3476833155341274459 ] 
dist 226=[-4.9162125486315765326 ,5.1976681410273147295 ] 
dist 227=[-5.4403280237438965990 ,5.1524773287502156921 ] 
dist 228=[-5.8798788076630280617 ,5.0077979618194029249 ] 
dist 229=[-6.1330247383775551388 ,4.9592247514602511012 ] 
dist 230=[-6.2973760326681548532 ,4.5816883982290188460 ] 
dist 231=[-6.3828062774796466151 ,4.4892740987592850906 ] 
dist 232=[-6.4282641257056016109 ,4.3439595118627477275 ] 
dist 233=[-6.4332021126310321928 ,4.2950574523719575278 ] 
dist 234=[-6.4093932661536136234 ,3.1182140368871372284 ] 
dist 235=[-6.3845759255766629106 ,2.9530254721894466911 ] 
dist 236=[-6.2474042443389956016 ,2.5785037363082436301 ] 
dist 237=[-6.2016482642304914931 ,2.4800906990010504008 ] 
dist 238=[-6.0528994348761580744 ,1.9883948104713768097 ] 
dist 239=[-6.0082359048458035299 ,1.8923458444562865577 ] 
dist 240=[-5.8372431081472759290 ,1.6775060308861449561 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 1, 0, 2, 0, 2] 
dist 0=[63.825992140589246397  ,63.825992140589246397  ] 
dist 1=[63.668402806667578901  ,63.905310979304079234  ] 
dist 2=[63.200429850668054199  ,63.942486845941099797  ] 
dist 3=[62.255945014259523354  ,63.931657880380067116  ] 
dist 4=[60.435328615368397888  ,63.895516064397400158  ] 
dist 5=[58.198976042176860766  ,63.831592596542400215  ] 
dist 6=[55.594678767154612492  ,63.734633525549399794  ] 
dist 7=[52.218933016786487986  ,63.586302500170319251  ] 
dist 8=[46.902565250222019513  ,63.365200156302998539  ] 
dist 9=[41.497406712205507013  ,63.180221076257034427  ] 
dist 10=[37.767046371426717543  ,62.843992617593385836  ] 
dist 11=[34.544500166201726129  ,62.691442171171088649  ] 
dist 12=[31.166442477561612955  ,61.921213689689366792  ] 
dist 13=[27.940668107766265198  ,60.748172419322030241  ] 
dist 14=[25.325763584620044253  ,34.541354423921177554  ] 
dist 15=[22.652450325578876792  ,33.810613368386517265  ] 
dist 16=[19.192788848465743796  ,27.686264753635895906  ] 
dist 17=[15.821423260218222576  ,26.568733522582016632  ] 
dist 18=[13.500272505455958940  ,24.968573078774185577  ] 
dist 19=[11.497322505968817837  ,24.517910029474590292  ] 
dist 20=[9.3959969006722657288 ,16.394547975448820236  ] 
dist 21=[7.3820367070662542362 ,15.468067217639944608  ] 
dist 22=[3.5608177509991675524 ,13.083110974322993390  ] 
dist 23=[.9628298078349055183 ,12.681500889769752541  ] 
dist 24=[-1.2385156652936443830 ,9.9315941055249986641 ] 
dist 25=[-3.4830507582778802886 ,9.4634751684860518981 ] 
dist 26=[-5.5933945920812406893 ,8.6214208441727540474 ] 
dist 27=[-7.2595736988414142471 ,8.4441985642076612000 ] 
dist 28=[-8.9278009743974194100 ,3.7296399995892440313 ] 
dist 29=[-11.047813379007561767  ,2.2883359270740285805 ] 
dist 30=[-13.060307887906607331  ,1.0542162387837027551 ] 
dist 31=[-14.299283290086330668  ,.7764714021798949184 ] 
dist 32=[-15.217749049556063559  ,-.4781164393190042235 ] 
dist 33=[-15.949156600738351862  ,-.6977128833218232587 ] 
dist 34=[-16.512504946092827791  ,-1.1795452277797918249 ] 
dist 35=[-16.759437511455268166  ,-1.2682250269277364257 ] 
dist 36=[-16.863589210341605498  ,-1.8053286803206955880 ] 
dist 37=[-16.855346503661837100  ,-1.8985820813287661268 ] 
dist 38=[-16.437407480884702716  ,-1.8928990450452890233 ] 
dist 39=[-16.316358327337330589  ,-1.7511896839787607334 ] 
dist 40=[-15.979420390549708879  ,-1.5314627893848114039 ] 
dist 41=[-15.836852159385372998  ,-1.2136790091999588214 ] 
dist 42=[-15.449636725481987244  ,-.72903236055246540416] 
dist 43=[-15.350457205137426093  ,.92987533534784359139] 
dist 44=[-14.451251821043208768  ,4.3782234612841912162 ] 
dist 45=[-14.314999655285739345  ,6.6706681366118206905 ] 
dist 46=[-7.9246461405508100621 ,8.5524326310078401660 ] 
dist 47=[-7.2535148088445082599 ,10.362398297835611372  ] 
dist 48=[-5.7563169587936252765 ,11.985254731555681953  ] 
dist 49=[-5.4167512276236988392 ,13.120591631773101386  ] 
dist 50=[-3.5958585828145480264 ,14.115308112291266644  ] 
dist 51=[-3.2631974126480780448 ,15.177274845353235275  ] 
dist 52=[-2.5514467639594817881 ,16.119331050132718410  ] 
dist 53=[-2.3618171213399617115 ,16.635568299646737533  ] 
dist 54=[-.7744673674774699640 ,16.938498415362889856  ] 
dist 55=[-.5129264407400764589 ,17.029170951733816412  ] 
dist 56=[-.1200434221999708959 ,17.027816633549127493  ] 
dist 57=[-.23940234755330369939,16.963591612958766401  ] 
dist 58=[-.64979064826440407923,16.392117608233350471  ] 
dist 59=[-.99791518399822576059,15.655047376533274890  ] 
dist 60=[-1.3504428438744828609 ,11.639608377610487869  ] 
dist 61=[-1.6774444656652121447 ,10.517667122077854977  ] 
dist 62=[-1.9238018552656006497 ,-.89409765117251032292] 
dist 63=[-2.1575258113126020038 ,-.99046324984451109915] 
dist 64=[-2.4341769309847846323 ,-1.0082142737215011729 ] 
dist 65=[-2.6891778807340428820 ,-1.1707733644632338781 ] 
dist 66=[-2.8365722198376607394 ,-1.1817472886363871263 ] 
dist 67=[-2.9330016227231450027 ,-1.1605613136188464626 ] 
dist 68=[-2.9847569490070741168 ,-1.0108478291140907965 ] 
dist 69=[-3.0135004060899592920 ,-.72922350885480560753] 
dist 70=[-3.0181477030641688425 ,-.41130651316847866075] 
dist 71=[-3.0060483126605936934 ,-.00696502007232985040] 
dist 72=[-2.9956330031397308363 ,.61930873103176082816] 
dist 73=[-2.5530832631386120664 ,1.2479670459724205572 ] 
dist 74=[-2.4863965040341445657 ,1.6618198665850074366 ] 
dist 75=[-2.3159067494740592591 ,1.9962674494278596067 ] 
dist 76=[-2.2741629102028384595 ,2.3082736246485797223 ] 
dist 77=[-2.2049449763473310234 ,2.5807655420763426932 ] 
dist 78=[-1.9122354771078590866 ,2.7576368303464786970 ] 
dist 79=[-1.8026002993471986715 ,2.8977684127138999480 ] 
dist 80=[-1.7729067848117092738 ,3.0237457089736333366 ] 
dist 81=[-1.1532166141917454093 ,3.1276001616578311992 ] 
dist 82=[-1.0690366182740278234 ,3.1795095092392858407 ] 
dist 83=[-.86519785412573432527,3.2031324817068631375 ] 
dist 84=[-.82969231075922328421,3.2015831399777738555 ] 
dist 85=[-.5330707192206856502 ,3.1684995588520335693 ] 
dist 86=[-.47776532875099049551,3.1512209266164712631 ] 
dist 87=[-.39513775521240253619,3.0826935796477459236 ] 
dist 88=[-.37234691584541192072,3.0590018887755237144 ] 
dist 89=[-.67305511234278307059,2.1666946588852040031 ] 
dist 90=[-1.1411329711101507502 ,2.1890166086636241408 ] 
dist 91=[-1.5194529475994581384 ,2.1965202436080428130 ] 
dist 92=[-1.8725770334202156086 ,2.1946336225215012980 ] 
dist 93=[-2.1811918892745772484 ,2.1871858256052958353 ] 
dist 94=[-2.3820085213570765180 ,-.13910242822876305431] 
dist 95=[-2.5417168144645134296 ,-.11759568066080656137] 
dist 96=[-2.6863904379364306134 ,-.07222660696325311561] 
dist 97=[-2.8104257384164289477 ,-.02009623959077380622] 
dist 98=[-2.8878284061262230666 ,.02837237160224524212] 
dist 99=[-2.9456598036447790975 ,.08331099434467244295] 
dist 100=[-2.9916460699527250906 ,.16123846358664516973] 
dist 101=[-3.0263294258981878844 ,.24769716887605160397] 
dist 102=[-3.0390853440882560373 ,.33665522280629869743] 
dist 103=[-3.0381829789442817968 ,.44421071542409610808] 
dist 104=[-3.0273688720286700084 ,.60483210021565962462] 
dist 105=[-2.4679933969610169031 ,.76341423868283700387] 
dist 106=[-2.5025409133490436790 ,.86283494487243041678] 
dist 107=[-2.5085615605367784006 ,.93765123221486148007] 
dist 108=[-2.4920692294021925471 ,.99810819193384558027] 
dist 109=[-2.4862329051201015152 ,1.0456607790575932081 ] 
dist 110=[-2.2989864194945380900 ,1.4462625548824817141 ] 
dist 111=[-2.2622313961101516594 ,1.7946817681979589321 ] 
dist 112=[-2.1619079115816414877 ,2.0715103368980916958 ] 
dist 113=[-2.1331624073009763024 ,2.3218934782950974050 ] 
dist 114=[-1.9282921305387951614 ,2.5352615300756312103 ] 
dist 115=[-1.8814491196644020417 ,2.6644706604105126342 ] 
dist 116=[-1.8016260065102335565 ,2.7564245213739476028 ] 
dist 117=[-1.7783149042111713469 ,2.8212167430583375037 ] 
dist 118=[-1.2549851941104434178 ,2.8673418380678640208 ] 
dist 119=[-1.1821139071863597915 ,2.8848483952347209218 ] 
dist 120=[-1.0107432091229637479 ,2.8847122439921617434 ] 
dist 121=[-.97312851641473587781,2.8771777846499299810 ] 
dist 122=[-.73265079372198703729,2.8233146454924625836 ] 
dist 123=[-.87526896478528557545,2.8048924070526614291 ] 
dist 124=[-1.0956719554755709253 ,2.7258713184288683157 ] 
dist 125=[-1.2974149706393890121 ,2.7120803201311859834 ] 
dist 126=[-1.4449620177425890371 ,-.66550730232584327808] 
dist 127=[-1.5806336127215456661 ,-.88527900324765609399] 
dist 128=[-1.7350164082092154683 ,-1.0679643892719749764 ] 
dist 129=[-1.8740526511698826864 ,-1.1127339335507610417 ] 
dist 130=[-2.0645331849968088408 ,-1.0936718990928785705 ] 
dist 131=[-2.2495270470722721372 ,-.99917405320920126589] 
dist 132=[-2.3958904365746485436 ,-.8366135139240112765 ] 
dist 133=[-2.5271983887754813202 ,-.64334052668038359282] 
dist 134=[-2.6392827693850140465 ,-.42635920329423495273] 
dist 135=[-2.7089806599447289742 ,-.15109911670951834365] 
dist 136=[-2.7607795247442953112 ,.27459401057129080444] 
dist 137=[-2.8014802299787264163 ,.70236815801397189882] 
dist 138=[-2.8317934648274644513 ,.98592740420258489238] 
dist 139=[-2.8421657410547770420 ,1.2173266411800331039 ] 
dist 140=[-2.8398896363599671794 ,1.4370823914220702817 ] 
dist 141=[-2.8296652486950331885 ,1.6317546539264792059 ] 
dist 142=[-1.0370680021285190063 ,1.7631188521450891958 ] 
dist 143=[-.95462283013530851766,1.8728835948114236120 ] 
dist 144=[-.93287841324440788523,1.9814153619597067124 ] 
dist 145=[-.56937262290305704352,2.0745779947464023648 ] 
dist 146=[-.51888412895790486453,2.1230493966660398208 ] 
dist 147=[-.39960308138217433161,2.1479266505016163112 ] 
dist 148=[-.3775293943674774565 ,2.1504327204874433842 ] 
dist 149=[-.21354886788625215982,2.1344771124654495000 ] 
dist 150=[-.18348633366212108426,2.1227682744302340558 ] 
dist 151=[-.13260149751390951339,2.0888267328722219888 ] 
dist 152=[-.12067460480371166133,2.1884339949085959410 ] 
dist 153=[-.46560474024690066227,2.3026510561900894950 ] 
dist 154=[-.77574039880086641252,2.3915836030644843992 ] 
dist 155=[-1.0302320312714415108 ,2.4300806951145842440 ] 
dist 156=[-1.2742696975009291953 ,2.4455667999568361033 ] 
dist 157=[-1.4920445942554000988 ,2.4427292788798897766 ] 
dist 158=[-1.6417980935505842037 ,-.29276968357437064772] 
dist 159=[-1.7699683049265095692 ,-.3906478487055514237 ] 
dist 160=[-1.9016672225589769165 ,-.60800500499764694363] 
dist 161=[-2.0176550415105653266 ,-.64406070032164867262] 
dist 162=[-2.0831680770309831805 ,-.87033947078602679902] 
dist 163=[-2.1240649676873932125 ,-.84488086946167811382] 
dist 164=[-2.1418815624180284688 ,-.7858421690186441411 ] 
dist 165=[-2.1456618803645044118 ,-.70995596704557414682] 
dist 166=[-2.1411759195662663564 ,-.61730814323474918304] 
dist 167=[-2.1112562346874750123 ,-.49491373044449138633] 
dist 168=[-2.0981120660647078672 ,-.28824874366582414257] 
dist 169=[-1.9025794144459438568 ,.13965497693083170532] 
dist 170=[-1.8962645565267520818 ,.42997355464391234986] 
dist 171=[-1.8928747727368060182 ,.67426373395032712362] 
dist 172=[-1.8890642330392749370 ,.91860230855639382483] 
dist 173=[-1.8836983242046518937 ,1.1434022785285351378 ] 
dist 174=[-1.4694084740313175130 ,1.3097708461532686035 ] 
dist 175=[-1.4143477087650087434 ,1.4647132585807200000 ] 
dist 176=[-1.2810317972958160082 ,1.6439447438817488853 ] 
dist 177=[-1.2491550508735058631 ,1.8072040539174578416 ] 
dist 178=[-1.0434977730669018210 ,1.8984480845846961289 ] 
dist 179=[-1.0016378380945359315 ,1.9541510733233350339 ] 
dist 180=[-.92368418227203820353,1.9756697252777966539 ] 
dist 181=[-.90309663197033279455,1.9841445030903726495 ] 
dist 182=[-.55549266701974180742,1.9878274287081856507 ] 
dist 183=[-.50728854653674335785,2.0278988987466602230 ] 
dist 184=[-.39268772869726735867,2.0507831786060064671 ] 
dist 185=[-.38976777854814627319,2.0528999791648455983 ] 
dist 186=[-.65994261331576063864,2.0368019347982366008 ] 
dist 187=[-.89344581966573361139,2.0255446164875754449 ] 
dist 188=[-1.1369954432763789651 ,1.9923029426523828690 ] 
dist 189=[-1.3674937343186275626 ,1.9754617854026551143 ] 
dist 190=[-1.5489471208826060483 ,-.13257077778660073002] 
dist 191=[-1.7286938376295324322 ,-.09657326229169934509] 
dist 192=[-1.9523857842642495669 ,-.02887289522812734281] 
dist 193=[-2.1641387542373624128 ,.04646340308093243719] 
dist 194=[-2.2962718217995698601 ,.11291365778110979315] 
dist 195=[-2.3950042214345882807 ,.18538555757340259486] 
dist 196=[-2.4735525020816117417 ,.28473668068781880656] 
dist 197=[-2.5328409715548769746 ,.39340107974943331783] 
dist 198=[-2.5547636152258734983 ,.50301510968836134437] 
dist 199=[-2.5577459457500447458 ,.63399377651450777225] 
dist 200=[-2.5507929105663762340 ,1.1159696013026558400 ] 
dist 201=[-2.4746993197596554801 ,1.6529653476555124431 ] 
dist 202=[-2.4523892225454343981 ,1.9997745611859452264 ] 
dist 203=[-2.3817693307532121241 ,2.2726806916349725106 ] 
dist 204=[-2.3583021652510414977 ,2.5149446771106334802 ] 
dist 205=[-2.1766917042032200777 ,2.7181170570744072322 ] 
dist 206=[-2.1323959447169255679 ,2.8351225501291942276 ] 
dist 207=[-2.0624761186231487430 ,2.9110796830711825167 ] 
dist 208=[-2.0391066779218611870 ,2.9505477215984717802 ] 
dist 209=[-1.4784872904259760689 ,2.9715387703954077661 ] 
dist 210=[-1.3998296481907513097 ,2.9738081023498573508 ] 
dist 211=[-1.2212082795812938100 ,2.9627929916525422207 ] 
dist 212=[-1.1746261054771051971 ,2.9513178514866524686 ] 
dist 213=[-.93941950463907398316,2.8879023272676718826 ] 
dist 214=[-.89351384047314887473,2.8667488102150356834 ] 
dist 215=[-.79158099543689402604,2.7850234417183594874 ] 
dist 216=[-.76183300090844807319,2.7668539358358419614 ] 
dist 217=[-.01064473169886531584,1.9018307929237291492 ] 
dist 218=[-.01977333402891117271,1.9094807043670418092 ] 
dist 219=[-.02951074629158552707,1.9124382203110001988 ] 
dist 220=[-.04258624994532110676,1.9125165673025979635 ] 
dist 221=[-.05675930407279420305,1.9086841076731927231 ] 
dist 222=[-.37634224146919342087,.00347279407612443626] 
dist 223=[-.63729959025418031423,.01598921274626076228] 
dist 224=[-.86295498539702636788,.03696472143992079678] 
dist 225=[-1.0985064890878190022 ,.05947266121754454506] 
dist 226=[-1.3215507177122900092 ,.07810054475460695235] 
dist 227=[-1.4973260392969428748 ,.09739908272129490046] 
dist 228=[-1.6716248471778464863 ,.1225816484591135767 ] 
dist 229=[-1.8887806141606802371 ,.14952791212957694364] 
dist 230=[-2.0944660086447288166 ,.17586022651564077988] 
dist 231=[-2.2230199981208225708 ,.20670815412527514317] 
dist 232=[-2.3193211132912705977 ,.25166306558721914662] 
dist 233=[-2.3963793092302803082 ,.30186401302361203258] 
dist 234=[-2.4549017923593192268 ,.4076382274066814818 ] 
dist 235=[-2.4772809125286489681 ,.51393236690064511454] 
dist 236=[-2.4808395099333981971 ,.64065040813818651509] 
dist 237=[-2.4748058665332999146 ,1.0916884452892638635 ] 
dist 238=[-2.4052982926951991887 ,1.6120234514677094840 ] 
dist 239=[-2.3843709774102534045 ,1.9479499038933034475 ] 
dist 240=[-2.3173865467691030931 ,2.2121531717813633988 ] 
dist 241=[-2.2949023093650054135 ,2.4464500361298891539 ] 
dist 242=[-2.1201575807470466168 ,2.6427661453413520508 ] 
dist 243=[-2.0773860539659575224 ,2.7554989411536039711 ] 
dist 244=[-2.0101260915831130407 ,2.8282700062467817060 ] 
dist 245=[-1.9874943496682189310 ,2.8652153448901326596 ] 
dist 246=[-1.4428869760743835396 ,2.8842679330161553029 ] 
dist 247=[-1.3664433546471127661 ,2.8856811917166634240 ] 
dist 248=[-1.1931222430393952773 ,2.8744413676995864560 ] 
dist 249=[-1.1475851818543626391 ,2.8631261032554229349 ] 
dist 250=[-.92002534298415052966,2.8011798992924611437 ] 
dist 251=[-.87557403596677274012,2.7805132350751517947 ] 
dist 252=[-.77616026091714516999,2.7013780222687675077 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 2, 0, 2, 0, 1] 
dist 0=[67.822354316251318550  ,67.822354316251318550  ] 
dist 1=[67.179247056054792886  ,68.120489371174596897  ] 
dist 2=[65.835535869923854688  ,68.129680601521412335  ] 
dist 3=[64.111786663799085421  ,67.918189716204006856  ] 
dist 4=[61.951324707008009537  ,67.252624960674595521  ] 
dist 5=[59.053408137636874014  ,66.508434667976490339  ] 
dist 6=[54.385332558032524559  ,66.242840502129803931  ] 
dist 7=[49.593817727313813721  ,65.356166790671358779  ] 
dist 8=[46.203222195531014200  ,65.121680875738861323  ] 
dist 9=[43.185143132022479744  ,64.106371031523586677  ] 
dist 10=[39.881383327125130022  ,63.795213596094647710  ] 
dist 11=[36.642967845041394906  ,63.010695907115254826  ] 
dist 12=[33.886126064957088221  ,62.696762854952052587  ] 
dist 13=[30.952098759773966802  ,61.107860985553741041  ] 
dist 14=[27.006822116762683688  ,59.451842028331672405  ] 
dist 15=[23.105334339883211600  ,32.589406750627073845  ] 
dist 16=[20.309458619153727381  ,31.849302647828481125  ] 
dist 17=[16.904465691330969041  ,25.016304281883828939  ] 
dist 18=[12.513786774590902161  ,23.781813751822689970  ] 
dist 19=[8.4535280824932352976 ,22.191675878436889016  ] 
dist 20=[5.3799282621432815395 ,21.823422625412513107  ] 
dist 21=[2.4347499348295397982 ,14.833005201346187063  ] 
dist 22=[-1.1140300274655243472 ,14.720516273645001288  ] 
dist 23=[-4.4502615586783610500 ,9.0380416062394554378 ] 
dist 24=[-6.5475070681534178183 ,8.5693501393329430840 ] 
dist 25=[-8.1468109624382395416 ,6.0257810166957262660 ] 
dist 26=[-9.4957399988968037229 ,5.6118567267992892052 ] 
dist 27=[-10.593298464051304292  ,4.7634684078998940802 ] 
dist 28=[-11.190108112277520606  ,4.6180945818434427934 ] 
dist 29=[-11.545657692120694887  ,-1.3858318784886738129 ] 
dist 30=[-11.682525515237209116  ,-1.9373611354494791817 ] 
dist 31=[-12.329003898137960925  ,-3.0585410516421618473 ] 
dist 32=[-12.843433443134763797  ,-3.3010281526571974262 ] 
dist 33=[-13.141335955793941013  ,-4.2343629911551273150 ] 
dist 34=[-13.225203073245819366  ,-4.4034923765056405147 ] 
dist 35=[-13.229327563793719027  ,-4.5688059748469493312 ] 
dist 36=[-13.208625195739869605  ,-4.4110475887133934897 ] 
dist 37=[-13.167046919474661948  ,-2.7304330713452347573 ] 
dist 38=[-13.099903337567707151  ,-.1057945273733576640 ] 
dist 39=[-11.457017992273451397  ,2.5370396241029543369 ] 
dist 40=[-11.465209695622721401  ,4.2904238266814562672 ] 
dist 41=[-11.373372741690733313  ,5.7235323986085750022 ] 
dist 42=[-11.326053234732314968  ,7.0891027939366230749 ] 
dist 43=[-11.193642128866524867  ,8.3028000118004799211 ] 
dist 44=[-11.130607138555906829  ,9.1302306370442111465 ] 
dist 45=[-5.8221189123244300084 ,9.8313727928458186971 ] 
dist 46=[-5.6933621069833373662 ,10.541429920013204028  ] 
dist 47=[-3.2416962142583799350 ,11.166182553949016404  ] 
dist 48=[-2.9169582015666538716 ,11.527047560953362891  ] 
dist 49=[-2.1334394111588906780 ,11.762982746311175123  ] 
dist 50=[-2.0143052955869996816 ,11.889280204026267743  ] 
dist 51=[-.90198643181168730112,11.935991708185257206  ] 
dist 52=[-.70101663030016094599,11.927825919318343075  ] 
dist 53=[-.4379764742506971621 ,11.753789722810099303  ] 
dist 54=[-.3754490555480237815 ,11.723929377203133657  ] 
dist 55=[1.0972517195499367376 ,5.8202994970038437119 ] 
dist 56=[1.2738043209243782678 ,6.1632453838606863390 ] 
dist 57=[1.6425513395486770955 ,6.4253558980189287931 ] 
dist 58=[1.7171766383062570292 ,6.6470383080427070238 ] 
dist 59=[1.6002444448477791619 ,6.8267653524786999538 ] 
dist 60=[1.0145666304024107190 ,6.9212694273066872285 ] 
dist 61=[.27509342609299825544,6.9718183118482366050 ] 
dist 62=[-.8660495283520082389 ,6.9759425723320553106 ] 
dist 63=[-2.0320760814447386232 ,2.8228628311824564760 ] 
dist 64=[-2.8042685815883261960 ,2.8827016749769642111 ] 
dist 65=[-3.4346750014341698495 ,2.9109289561682035291 ] 
dist 66=[-4.0350872383685916528 ,2.9131604885393048088 ] 
dist 67=[-4.5692975021502317431 ,2.8667244383304190303 ] 
dist 68=[-4.9356200149106913011 ,2.8444422112788570214 ] 
dist 69=[-5.2487352667387913924 ,2.8135343857610504704 ] 
dist 70=[-5.5707217603363558798 ,2.7968378210560389296 ] 
dist 71=[-5.8488449683015122731 ,1.8255635913855680909 ] 
dist 72=[-5.9869803698664798916 ,1.7159654418215073123 ] 
dist 73=[-6.0547770682516700399 ,1.4627567321596509064 ] 
dist 74=[-6.0621545070110452748 ,1.4045456498702350919 ] 
dist 75=[-5.9714844039622035632 ,1.0624865897426687916 ] 
dist 76=[-5.9251611926371598613 ,.99698790041095239205] 
dist 77=[-5.8735269629394424407 ,.86607764549180003692] 
dist 78=[-5.8381172719188134915 ,.83114214973055806664] 
dist 79=[-3.9210411362821701238 ,1.6758937373670230730 ] 
dist 80=[-3.7007693220847920696 ,2.5351378933359339308 ] 
dist 81=[-3.1904607757881812953 ,3.2414501209705092385 ] 
dist 82=[-3.0721344832896558277 ,3.9212351940105678620 ] 
dist 83=[-3.0438025201384066778 ,4.5299544408370192243 ] 
dist 84=[-3.0265357567445326109 ,4.9528408975730305324 ] 
dist 85=[-3.0003486561377608550 ,5.3196397427210562773 ] 
dist 86=[-2.9848603967183887728 ,5.7046860134041279408 ] 
dist 87=[-1.0227258373037436270 ,6.0426457881033213965 ] 
dist 88=[-.89249578741095796281,6.2216419153479680073 ] 
dist 89=[-.62565103040220789412,6.3181763383248566160 ] 
dist 90=[-.55599883533860685032,6.3354825892375519703 ] 
dist 91=[-.30391880777833605419,6.3017252741144590299 ] 
dist 92=[-.25108478423922254844,6.2660808821164653551 ] 
dist 93=[-.36249669427602762686,6.2011870605792887695 ] 
dist 94=[-.55713564964891808604,6.1686328071999374358 ] 
dist 95=[-1.4067003330130270365 ,3.7748127332790079140 ] 
dist 96=[-2.2800419868810525161 ,4.0214212190688016838 ] 
dist 97=[-2.9832964459661897110 ,4.2128235904641865309 ] 
dist 98=[-3.6354964431533205742 ,4.3781566914921467720 ] 
dist 99=[-4.2027676783594139160 ,4.5135116326889836057 ] 
dist 100=[-4.5673149749534949810 ,4.5853524603260508039 ] 
dist 101=[-4.8521906953398055848 ,4.6242163091533724996 ] 
dist 102=[-5.1017246115929638880 ,4.6280481190501437705 ] 
dist 103=[-5.3129894940443952892 ,4.6100255964120318002 ] 
dist 104=[-5.4452408066716799589 ,4.5912085084814331721 ] 
dist 105=[-5.5446099301629259949 ,4.5094913271324592501 ] 
dist 106=[-5.6247258084051166494 ,4.4757484150280762958 ] 
dist 107=[-5.6860981149610703063 ,4.1914506325749603231 ] 
dist 108=[-5.7107095648229154401 ,4.1176293494331468629 ] 
dist 109=[-5.7130530856698264000 ,4.0090956941279224422 ] 
dist 110=[-5.6915995928769140587 ,3.9681546964734252210 ] 
dist 111=[-2.5027189193342265312 ,2.9348461267773575889 ] 
dist 112=[-2.4243248301253256095 ,2.7888719418796787998 ] 
dist 113=[-2.2897243761942603102 ,2.4660438686065587075 ] 
dist 114=[-2.2529110352687393512 ,2.3712407409894111018 ] 
dist 115=[-2.1385596532596417073 ,2.0555216705536900222 ] 
dist 116=[-2.1001041982684935040 ,2.0166424876603180290 ] 
dist 117=[-2.0758215508905991384 ,2.4676214001354468423 ] 
dist 118=[-2.0656246965397527170 ,3.0945412746493413877 ] 
dist 119=[-.60757544160462888405,3.6909978141591620107 ] 
dist 120=[-1.0107395385295940236 ,4.0684852316502210511 ] 
dist 121=[-1.3369499252473655879 ,4.3567998620278337203 ] 
dist 122=[-1.6420699236011824954 ,4.5976216474672348343 ] 
dist 123=[-1.9091955487549519292 ,4.7886630251952692494 ] 
dist 124=[-2.0838814232245489216 ,4.8784457213699562683 ] 
dist 125=[-2.2237973881214314050 ,4.9171700494334191623 ] 
dist 126=[-2.3522577536369314598 ,4.9162410555132832450 ] 
dist 127=[-2.4625950600836557143 ,-.62115755666018275394] 
dist 128=[-2.5302349589882152380 ,-.8275098366054691657 ] 
dist 129=[-2.5793538619166740997 ,-1.2815407227318891492 ] 
dist 130=[-2.6158284486756446648 ,-1.3604767518314983330 ] 
dist 131=[-2.6412554034666437251 ,-1.8448986653784783299 ] 
dist 132=[-2.6837173587400417299 ,-1.6987254321898326240 ] 
dist 133=[-2.9289961395392613120 ,-1.3974222446851725062 ] 
dist 134=[-3.2051285276000186736 ,-.9163142610414440206 ] 
dist 135=[-3.4527145971140382035 ,-.42551805287542982314] 
dist 136=[-3.5841478747230608705 ,-.08557759580542669924] 
dist 137=[-3.6576761581901203319 ,.2079698561700309747 ] 
dist 138=[-3.6743301809013713024 ,.51374696809988892809] 
dist 139=[-3.6496145332133760376 ,.80288933941279493526] 
dist 140=[-3.6409783827860450101 ,1.0300960511422531004 ] 
dist 141=[-3.6337964455530092130 ,1.2547802947578509926 ] 
dist 142=[-3.6267515951075308716 ,1.5338627519702162152 ] 
dist 143=[-2.7228666152383611829 ,1.7977840465988834947 ] 
dist 144=[-2.6082786953960464128 ,1.9620043643128499989 ] 
dist 145=[-2.3338343718995323579 ,2.1246508485339725698 ] 
dist 146=[-2.2693661337739759640 ,2.5308263962111824507 ] 
dist 147=[-1.8590746920624066851 ,2.8921798776419641410 ] 
dist 148=[-1.7768703914231689112 ,3.1387358167916262198 ] 
dist 149=[-1.6220372906155628361 ,3.3477044192115659088 ] 
dist 150=[-1.5813148233961610645 ,3.5591566021051671896 ] 
dist 151=[-.93421061866557067727,3.7424015070436950599 ] 
dist 152=[-.84354850383681332699,3.8388769530281369520 ] 
dist 153=[-.81499291638678645405,3.8899936786835941842 ] 
dist 154=[-1.0226801481491345116 ,3.8965666334934631646 ] 
dist 155=[-1.2140260046769149164 ,3.8732746524081475179 ] 
dist 156=[-1.3560861055746902230 ,3.8524729796363316875 ] 
dist 157=[-1.4888347072777220408 ,3.7973667647246533211 ] 
dist 158=[-1.6430455130008679170 ,3.7690406466302362263 ] 
dist 159=[-1.7836255072930070550 ,-.50918886239206824318] 
dist 160=[-1.8620133040820848753 ,-.67831229231782684228] 
dist 161=[-1.9096304337938132364 ,-.85241426913085231407] 
dist 162=[-2.2838548119791473280 ,-.68991331436285455192] 
dist 163=[-2.6712277942914793173 ,-.49849074045391960854] 
dist 164=[-2.9358812591399696526 ,-.28591661344424117564] 
dist 165=[-3.1605556402656377285 ,-.01776697171084227186] 
dist 166=[-3.3884886659720250461 ,.39529539961295500505] 
dist 167=[-3.5886815944772284996 ,.80959722425394491243] 
dist 168=[-3.7027260828387279794 ,1.0826898917162334800 ] 
dist 169=[-3.7751779062850436319 ,1.3038516432366278183 ] 
dist 170=[-3.8094956456785326817 ,1.5110485835098381154 ] 
dist 171=[-3.8183957397597323187 ,1.6926778509230296980 ] 
dist 172=[-3.8125505277940183238 ,1.8118735562003733580 ] 
dist 173=[-3.7544099083570413626 ,1.9078167548659241389 ] 
dist 174=[-3.7387677541835955338 ,1.9967130454825171692 ] 
dist 175=[-1.9162145754603221587 ,2.0708602034160876310 ] 
dist 176=[-1.7386891696182998288 ,2.1079826186215963124 ] 
dist 177=[-1.3337703273385362172 ,2.1249867845243971615 ] 
dist 178=[-1.2468371682966706422 ,2.1249661970263177096 ] 
dist 179=[-.73127013191523161031,2.1019359751771135828 ] 
dist 180=[-.63733555769378521271,2.2236987584331592288 ] 
dist 181=[-.44815325980718290635,2.5058770824017139712 ] 
dist 182=[-.3997331796045216486 ,2.8358583753038908462 ] 
dist 183=[-.46976373446102399997,3.1378226914292231497 ] 
dist 184=[-.78338839808152327973,3.3082669256913665539 ] 
dist 185=[-1.0417614529431829562 ,3.4145215749639168635 ] 
dist 186=[-1.2912160146121312629 ,3.4604923262797243473 ] 
dist 187=[-1.5149609360445435678 ,3.4825882247300144651 ] 
dist 188=[-1.6708017670218110216 ,3.4936279002582709437 ] 
dist 189=[-1.8062933212533390554 ,3.4986514023488181482 ] 
dist 190=[-1.9488836009109861194 ,3.4967542433146503504 ] 
dist 191=[-2.0750828733143673961 ,-.16611031739808146456] 
dist 192=[-2.1452057027631641988 ,-.2259881063374813522 ] 
dist 193=[-2.1874789812361801549 ,-.32803125574800087299] 
dist 194=[-2.2026118893083361610 ,-.33650114099056995938] 
dist 195=[-2.3474860230304211720 ,-.27028691696994435891] 
dist 196=[-2.6553845222685030438 ,-.19515933932520227279] 
dist 197=[-2.9588927285238047645 ,-.09933711023970752303] 
dist 198=[-3.3345444249136311264 ,.04940913144828475518] 
dist 199=[-3.6891353491880503736 ,.27394917977946824616] 
dist 200=[-3.9086514066952573608 ,.57568932880083748906] 
dist 201=[-4.0706271494877867222 ,.82795029907759637887] 
dist 202=[-4.1957424060563296235 ,1.0776004742447420550 ] 
dist 203=[-4.2871533386486869757 ,1.3055782060740321891 ] 
dist 204=[-4.3147133710580179159 ,1.4714076343738967559 ] 
dist 205=[-4.3141225593990719720 ,1.6229869913996390055 ] 
dist 206=[-4.2964040750741166857 ,1.8042538777244950535 ] 
dist 207=[-4.1318174633693709904 ,2.7143597361165537516 ] 
dist 208=[-4.0881842084971405481 ,3.3031682535096494711 ] 
dist 209=[-3.9563240736225740842 ,3.7676762578921103506 ] 
dist 210=[-3.9144033472610820210 ,4.1820611290280365271 ] 
dist 211=[-3.5962487712018242003 ,4.5310520250940873654 ] 
dist 212=[-3.5199164590889104936 ,4.7347633119476947014 ] 
dist 213=[-3.3972818959414699885 ,4.8704798162339605492 ] 
dist 214=[-3.3575709868231409396 ,4.9483017555103634681 ] 
dist 215=[-2.4191394456369162689 ,4.9947163399179099653 ] 
dist 216=[-2.2877460796580644343 ,5.0051776482762048503 ] 
dist 217=[-1.9870696029990862142 ,4.9912783334142936055 ] 
dist 218=[-1.9114993525216638656 ,4.9734823739450946436 ] 
dist 219=[-1.5099371481880361443 ,4.8701972901188272394 ] 
dist 220=[-1.7099525838988416153 ,4.8357732900410293834 ] 
dist 221=[-1.9137816437422054960 ,4.6968033182444901887 ] 
dist 222=[-2.1698515215150876716 ,4.6694648613204187703 ] 
dist 223=[-2.4134370978377310807 ,.28720278214357070336] 
dist 224=[-2.5674777051178661790 ,.36711635835270299492] 
dist 225=[-2.6849791887319123899 ,.45815638719470454752] 
dist 226=[-2.7828436423185296530 ,.57698866585717366909] 
dist 227=[-2.8602527444063466503 ,.70416056941390029145] 
dist 228=[-2.8961765522211899162 ,.8284597290035957005 ] 
dist 229=[-2.9084891760807290817 ,.9740929706550736726 ] 
dist 230=[-2.9052497800007374356 ,1.3593593410251224093 ] 
dist 231=[-2.8611983125135591525 ,1.9644068557723652739 ] 
dist 232=[-2.8428738856721847692 ,2.3539568271789799392 ] 
dist 233=[-2.7775512312518005734 ,2.6591244935763723932 ] 
dist 234=[-2.7536242260349971821 ,2.9276482207809479617 ] 
dist 235=[-2.5611294679039650770 ,3.1511208875100323796 ] 
dist 236=[-2.5126958501362675196 ,3.2766211045931697251 ] 
dist 237=[-2.4387534502818254871 ,3.3540280122040349759 ] 
dist 238=[-2.4125453306489362016 ,3.3857004825546752919 ] 
dist 239=[-1.7672006029971094893 ,3.3966625876227507665 ] 
dist 240=[-1.6763354343351269141 ,3.3914748024298521852 ] 
dist 241=[-1.4726821045306947852 ,3.3734801321970691950 ] 
dist 242=[-1.4162457890238849446 ,3.3586167289029716373 ] 
dist 243=[-1.1546682647787858874 ,3.2822557698583103122 ] 
dist 244=[-1.1032406898457332349 ,3.2567508369769321968 ] 
dist 245=[-1.0311352940540146230 ,3.1652077511762840069 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 1, 2, 2, 0, 2] 
dist 0=[73.368242977168807195  ,73.368242977168807195  ] 
dist 1=[72.761127255423897920  ,73.659788196825459671  ] 
dist 2=[71.920307264516777401  ,73.777161216536371944  ] 
dist 3=[70.695760123935723638  ,73.688532657479209591  ] 
dist 4=[68.953332863729208789  ,73.474274207261463010  ] 
dist 5=[66.045417026842094440  ,73.293258569613564826  ] 
dist 6=[62.606939822856159843  ,72.675812015613071136  ] 
dist 7=[58.746633303617088812  ,72.356692271735891710  ] 
dist 8=[53.834313320375865274  ,70.480301365762641302  ] 
dist 9=[46.196254009686018935  ,69.916661382750368903  ] 
dist 10=[38.461569724957692104  ,69.446773596674339540  ] 
dist 11=[33.163621450440678400  ,69.154997785535060585  ] 
dist 12=[28.632161008697700973  ,68.970712512815179033  ] 
dist 13=[23.957527543750090017  ,67.634187964212892349  ] 
dist 14=[19.545109548389488653  ,60.032421221540578404  ] 
dist 15=[16.060543969188802043  ,54.930522962183925699  ] 
dist 16=[12.586318458521343636  ,32.600072460060392143  ] 
dist 17=[8.2153429084029300179 ,29.740370513798371310  ] 
dist 18=[4.0293348999660188979 ,22.992572623752585407  ] 
dist 19=[1.2935010692478922808 ,22.014680504072262903  ] 
dist 20=[-.9051495409596644157 ,14.202511098230689388  ] 
dist 21=[-2.9468769334189567227 ,11.615539341778636326  ] 
dist 22=[-4.7324876425133350082 ,11.137467342174219390  ] 
dist 23=[-5.9088162255787471298 ,10.458293678811642412  ] 
dist 24=[-6.8646818527242402364 ,10.342555758254374194  ] 
dist 25=[-7.7703244924526102930 ,.0765558352708423068 ] 
dist 26=[-8.5597468251382613879 ,-.75343473060483892692] 
dist 27=[-9.0518946666703809191 ,-2.4782089372403505816 ] 
dist 28=[-9.4216503591188632068 ,-2.8144374344966558780 ] 
dist 29=[-9.7230538002737479786 ,-4.3635788988326150722 ] 
dist 30=[-10.047123852190040563  ,-4.3636994298087144018 ] 
dist 31=[-10.128210899258884398  ,-4.0853821137837211594 ] 
dist 32=[-9.5524556169988969610 ,-3.6741655128072908199 ] 
dist 33=[-9.5107309619788696011 ,-2.9816238168462699500 ] 
dist 34=[-9.2930722321908165758 ,-2.2446414182398641360 ] 
dist 35=[-9.4015284121360223543 ,-1.6556503466148438967 ] 
dist 36=[-9.6946597387999471378 ,-1.0661802126982836785 ] 
dist 37=[-9.9291282153611337169 ,-.32637836853929662447] 
dist 38=[-10.050086659661182110  ,.45007959395737860713] 
dist 39=[-10.112531513673041513  ,1.1862678159059171877 ] 
dist 40=[-10.112776858452110439  ,2.0324098048129788391 ] 
dist 41=[-5.7153284174223577281 ,3.2480425403040912704 ] 
dist 42=[-5.1164353998947255432 ,4.4406411937321197108 ] 
dist 43=[-4.9587369975974923805 ,5.1950694493567874186 ] 
dist 44=[-4.6013414221524475054 ,5.7725497064360757434 ] 
dist 45=[-4.5609065068793558744 ,6.2592396990580146422 ] 
dist 46=[-4.3401660631104215905 ,6.6505879420098807122 ] 
dist 47=[-4.2832394901242431140 ,6.8477530043622658403 ] 
dist 48=[-4.1562239073548420145 ,6.9504363252085634691 ] 
dist 49=[-4.1105009743096241642 ,7.0478081671822850616 ] 
dist 50=[-3.4096941390777158557 ,7.2487090971128156703 ] 
dist 51=[-3.2991337668342284752 ,7.3520598599889351590 ] 
dist 52=[-3.0300723356009292804 ,7.3722671420723950215 ] 
dist 53=[-2.9611854787525110924 ,7.3097158999333638616 ] 
dist 54=[-2.5270548959174026860 ,7.2631163470128084944 ] 
dist 55=[-2.4351044729481416713 ,7.1991287143553217827 ] 
dist 56=[-2.2642428713984293155 ,7.1600746416337333425 ] 
dist 57=[-2.2172440187364037708 ,6.1241999747291702364 ] 
dist 58=[-2.7058737305469927523 ,5.9849682646001421428 ] 
dist 59=[-3.5496867423296723467 ,6.0180785157031660372 ] 
dist 60=[-4.3649097151688235374 ,6.0201679292767080774 ] 
dist 61=[-5.0968650468517904331 ,6.0012992875038761166 ] 
dist 62=[-5.6086128922764101461 ,5.9641283691209611248 ] 
dist 63=[-6.0558740281558938405 ,5.9421952103802982955 ] 
dist 64=[-6.5306833503809933518 ,2.2615334977235222532 ] 
dist 65=[-6.9499469879998461140 ,1.1382537762404566300 ] 
dist 66=[-7.1756712734604647183 ,.9760541785230958284 ] 
dist 67=[-7.3024674720255781415 ,.6385638089134407809 ] 
dist 68=[-7.3271197596893940198 ,.5498035789744202718 ] 
dist 69=[-7.3096563780895906488 ,.2227399415043100059 ] 
dist 70=[-7.2725667640502895328 ,.1568644501772535918 ] 
dist 71=[-7.2038577062260340583 ,.04220906530709819557] 
dist 72=[-7.1670165081729237960 ,.01673091101960256359] 
dist 73=[-6.8218363984986581440 ,1.4080877257422119143 ] 
dist 74=[-5.1983504345190316532 ,2.3441882424326960334 ] 
dist 75=[-5.2391018839951125352 ,3.1065949799861539401 ] 
dist 76=[-5.2688151950455380739 ,3.8281800832105676062 ] 
dist 77=[-5.2780786331942201353 ,4.4658025240060071442 ] 
dist 78=[-5.2742236804003489867 ,4.8933628362767377519 ] 
dist 79=[-5.2515662681758671049 ,5.2477381136420119777 ] 
dist 80=[-1.3646956856743551961 ,5.5934992622673164492 ] 
dist 81=[-1.0426749197422193554 ,5.8944800199018656421 ] 
dist 82=[-.33001071487512723768,6.0702656347377338691 ] 
dist 83=[-.18355398812564099683,6.1875483562872033499 ] 
dist 84=[.62782215705898352684,6.2552031583860909161 ] 
dist 85=[.76482610563660047691,6.2855898403118393146 ] 
dist 86=[1.0600348927855894411 ,6.2789718884899283021 ] 
dist 87=[.91703336442599039467,6.2062293238606536199 ] 
dist 88=[.57141437880938971712,6.1701882389068865977 ] 
dist 89=[-.01224373643018398205,6.0392355581106149804 ] 
dist 90=[-1.0187301881567387059 ,4.1497411863456937827 ] 
dist 91=[-1.7049689969320495511 ,4.3740590758661788696 ] 
dist 92=[-2.2860660476012591094 ,4.5530533092605688916 ] 
dist 93=[-2.8732381137018555834 ,4.6394365119737279780 ] 
dist 94=[-3.4173133039513173672 ,4.6769908040142337181 ] 
dist 95=[-3.8265369038630254645 ,4.6787057049040614497 ] 
dist 96=[-4.2585303894054484126 ,.09234139887292419515] 
dist 97=[-4.8065251947403264373 ,-.6134600640003112794 ] 
dist 98=[-5.1301472963710365955 ,-.72674347429279781351] 
dist 99=[-5.3504691530385438195 ,-.83994239449679236264] 
dist 100=[-5.4934297329165271548 ,-.82883973642355917418] 
dist 101=[-5.5762534623753129899 ,-.76347599538981353034] 
dist 102=[-5.6151967417604378193 ,-.62182537580722763032] 
dist 103=[-5.6075287719807773085 ,-.39759445709184222926] 
dist 104=[-5.3948326389017149779 ,-.00289188539235965151] 
dist 105=[-3.4249075196475322608 ,.4056312548880508257 ] 
dist 106=[-3.4911163535270878638 ,.68498056275203422784] 
dist 107=[-3.5051213295397686368 ,.92239378379836415729] 
dist 108=[-3.4813366294520329276 ,1.1636729267882610876 ] 
dist 109=[-3.4703519347041273190 ,1.3881133108854827111 ] 
dist 110=[-3.4591039277263764908 ,1.5583725745788386030 ] 
dist 111=[-3.4446043704684673844 ,1.7210546379978867220 ] 
dist 112=[-2.5311394882833875107 ,1.9152771268009570444 ] 
dist 113=[-2.4177700132618168485 ,2.0950970649664917609 ] 
dist 114=[-2.1480302606759873268 ,2.2003405839738682647 ] 
dist 115=[-2.0850671604764449094 ,2.3604044000044456073 ] 
dist 116=[-1.6891555692050284398 ,2.7069572827383192630 ] 
dist 117=[-1.6104976927557403461 ,2.9447557504485184798 ] 
dist 118=[-1.4610062705990866091 ,3.1477601021324178806 ] 
dist 119=[-1.4216614342519680436 ,3.3555523507060232812 ] 
dist 120=[-.82245423039587512932,3.5364266568206443440 ] 
dist 121=[-.73783742450660504138,3.6320787787622981483 ] 
dist 122=[-.54737468275942655876,3.6833651059741709086 ] 
dist 123=[-.50518525281823270424,3.6906745216113413452 ] 
dist 124=[-.41944102411048365514,3.6708152095595135823 ] 
dist 125=[-.51670842654729605982,3.6511574423219665600 ] 
dist 126=[-.60276187464414694181,3.6025911824123332515 ] 
dist 127=[-.66063842749442328249,3.5775495015395412380 ] 
dist 128=[-.79318528271251394027,-.53928387746597905427] 
dist 129=[-1.3163996882937908986 ,-.65096518350864527853] 
dist 130=[-1.7442503945875206544 ,-.68302379622866721398] 
dist 131=[-2.1520564733002328278 ,-.67506390599302813111] 
dist 132=[-2.5143292613195551697 ,-.65133565399837210461] 
dist 133=[-2.7605891599502236996 ,-.59997089923727528497] 
dist 134=[-2.9683182040614620975 ,-.53496368132668853607] 
dist 135=[-3.1769267772969271513 ,-.45682794255517820284] 
dist 136=[-3.3597154573377109898 ,-.35434307460950338448] 
dist 137=[-3.4644722982120001926 ,-.19222922573322202995] 
dist 138=[-3.5318335051101507244 ,-.02755775421186780203] 
dist 139=[-3.5654843149342521926 ,.08512721311684302150] 
dist 140=[-3.5750774447178920403 ,.18098432363021955228] 
dist 141=[-3.5709764299750730873 ,.27854487781706232286] 
dist 142=[-3.5131323621035706134 ,.36938682658695990078] 
dist 143=[-3.5036693122217396611 ,.43844959055609839508] 
dist 144=[-1.7296568067963688983 ,.50458381630175788287] 
dist 145=[-1.5594630800435375844 ,.58374656696760819923] 
dist 146=[-1.1722386133528357136 ,.93958721821052000723] 
dist 147=[-1.0894962953075729014 ,1.3485558052357043322 ] 
dist 148=[-.60093778319292118059,1.7271395956052129493 ] 
dist 149=[-.5124654123244331521 ,2.0112468095559443530 ] 
dist 150=[-.3334775401634182366 ,2.2797307461257625219 ] 
dist 151=[-.28773853541046962756,2.5960077753104915264 ] 
dist 152=[.05137088041711260567,2.8866437951841984455 ] 
dist 153=[-8.00856949758269300000e-05,3.0528691235531884293 ] 
dist 154=[-.13826598907353292295,3.1593182091956265284 ] 
dist 155=[-.23333408624358029384,3.2115610533038874026 ] 
dist 156=[-.31474778256791328636,3.2403664861623823701 ] 
dist 157=[-.39847879979589210216,3.2533449040749567307 ] 
dist 158=[-.47699272673645703219,3.2571788987131990675 ] 
dist 159=[-.53760022569759734882,3.2495152215943597192 ] 
dist 160=[-.6154663594931978797 ,-.14904603324942391749] 
dist 161=[-1.0402168102838861393 ,-.14094249783623003983] 
dist 162=[-1.4056937264674888300 ,-.12943161675961441242] 
dist 163=[-1.7843353522818518870 ,-.11561340270752293683] 
dist 164=[-2.1411101912018978791 ,-.09749972018462193702] 
dist 165=[-2.4193804981957712935 ,-.06885812206191778742] 
dist 166=[-2.6926235669667794725 ,-.03574613199137977345] 
dist 167=[-3.0293493725542243152 ,.01001085046212831534] 
dist 168=[-3.3464733258383699335 ,.12717499108454162995] 
dist 169=[-3.5415425149959023432 ,.30599535368003814959] 
dist 170=[-3.6839982515591098861 ,.48454498351417234469] 
dist 171=[-3.7912951873106077831 ,.60062942560146753145] 
dist 172=[-3.8674084668064543600 ,.69285171083560373955] 
dist 173=[-3.8855010711856620219 ,.77623703586045264061] 
dist 174=[-3.8809698165785472655 ,.84726599909393812314] 
dist 175=[-3.8668572125998028039 ,1.5677662219933081756 ] 
dist 176=[-3.6869549078540084898 ,2.3896131997159962317 ] 
dist 177=[-3.6434364869251798480 ,2.9220497846847905252 ] 
dist 178=[-3.5157597047695597145 ,3.3429113452198332204 ] 
dist 179=[-3.4763853795862309682 ,3.7197876534022308312 ] 
dist 180=[-3.1817751626341074582 ,4.0382180660957575961 ] 
dist 181=[-3.1119584459830770948 ,4.2259924401008479644 ] 
dist 182=[-2.9982953521356014190 ,4.3534778315302173605 ] 
dist 183=[-2.9623638332090431668 ,4.4314706825174293645 ] 
dist 184=[-2.1232717020970926164 ,4.4810367961033309249 ] 
dist 185=[-2.0059818467310101724 ,4.4951539362164367966 ] 
dist 186=[-1.7359287740212017350 ,4.4859693027405938102 ] 
dist 187=[-1.6700787687859663491 ,4.4710661718511062858 ] 
dist 188=[-1.3053974893835055596 ,4.3807550943835945347 ] 
dist 189=[-1.2347370262909971626 ,4.3506774176310424411 ] 
dist 190=[-1.0874862834560972800 ,4.2248578074075872291 ] 
dist 191=[-1.0463678378781734876 ,4.2026126902836315389 ] 
dist 192=[-.87506226751853588693,.17374525666014252256] 
dist 193=[-.95241285664206843646,.206847676059735413  ] 
dist 194=[-1.0214617965580425349 ,.23967280754249725895] 
dist 195=[-1.0587415266025607171 ,.26272958952610978985] 
dist 196=[-1.0797821075657956670 ,.28297937855394929353] 
dist 197=[-1.0842652752015951590 ,.30460998620256604829] 
dist 198=[-1.0820622904284141199 ,.32539536006376780913] 
dist 199=[-1.1019630692003006706 ,.34227428637824329784] 
dist 200=[-1.1561964245472112042 ,.3594747464232252562 ] 
dist 201=[-1.1888512104413600074 ,.38154242573487688059] 
dist 202=[-1.2118587144031619330 ,.40179160385375903212] 
dist 203=[-1.2276178829249388858 ,.41637418041819413036] 
dist 204=[-1.2374576930646779097 ,.54156831959946532415] 
dist 205=[-1.2368582890191488452 ,.66282695066879542335] 
dist 206=[-1.2305070244193914351 ,.7718451181246446137 ] 
dist 207=[-1.2246005128980888323 ,.84822325067820125917] 
dist 208=[-.46662621257878870962,.91509690577590343426] 
dist 209=[-.46710108945401222565,.98621041170082229778] 
dist 210=[-.43336683061740122969,1.0490566506168255839 ] 
dist 211=[-.42655830012206746574,1.0829597436764583577 ] 
dist 212=[-.41549082931906372743,1.1020568694382919973 ] 
dist 213=[-.41161826481080952938,1.1058556542739892176 ] 
dist 214=[-.39749462182059742114,1.1032330974712317666 ] 
dist 215=[-.39274132020309791684,1.0976894585826380250 ] 
dist 216=[-.38318308937080552458,1.0867620510740666980 ] 
dist 217=[-.37966318732577141522,1.0808544162825162982 ] 
dist 218=[-.23434320858542683076,1.0039317501479271082 ] 
dist 219=[-.39842273149162926423,1.0427308430475764356 ] 
dist 220=[-.54197873540287605323,1.0709950482470945148 ] 
dist 221=[-.694471795492553115  ,1.0814800282994271869 ] 
dist 222=[-.84049366378062873496,1.0837307407211466550 ] 
dist 223=[-.95824200607618238068,1.0804541331384245265 ] 
dist 224=[-1.0774849011863735378 ,.20967626444115334619] 
dist 225=[-1.2294671729043106686 ,.28749866113514472424] 
dist 226=[-1.3750994121287609824 ,.36827752089462568026] 
dist 227=[-1.4690178391574778805 ,.43097055241681676644] 
dist 228=[-1.5427690238275759335 ,.49223853999342019327] 
dist 229=[-1.6079725902360700416 ,.56733420383591663959] 
dist 230=[-1.6624618597913741695 ,.64529989801598909195] 
dist 231=[-1.6934835199651251046 ,.71801381005473065291] 
dist 232=[-1.7131663253929496130 ,.80059228007137870138] 
dist 233=[-1.7224352805845511447 ,.91789866808039499205] 
dist 234=[-1.7234949721961821761 ,1.2305428407274479171 ] 
dist 235=[-1.7190825994214878512 ,1.4550618037679165062 ] 
dist 236=[-1.6942152822845089452 ,1.6296946936198481839 ] 
dist 237=[-1.6826454188269537653 ,1.7811760818392749685 ] 
dist 238=[-1.5821956879533285531 ,1.9056497213874450511 ] 
dist 239=[-1.5554866367404115457 ,1.9725734194047295372 ] 
dist 240=[-1.5170640007455654489 ,2.0099651245018433915 ] 
dist 241=[-1.5019964468619030813 ,2.0177570877819900388 ] 
dist 242=[-1.1157710773841258286 ,2.0114636219740883714 ] 
dist 243=[-1.0611050437533548045 ,2.0014106863347515109 ] 
dist 244=[-.94097157552353653832,1.9859070131674768930 ] 
dist 245=[-.90688321185913835672,1.9755382497128589000 ] 
dist 246=[-.86219304769003315642,1.9268441519351034370 ] 
dist 247=[-.84708555493611181056,1.9105517224287461169 ] 
dist 248=[-.83663656308022001395,1.8580225431860131711 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 0, 1, 0, 1, 2] 
dist 0=[87.886504136951037045  ,87.886504136951037045  ] 
dist 1=[87.110604980286008394  ,88.416278133713414152  ] 
dist 2=[84.546384428924820585  ,88.986531376924015927  ] 
dist 3=[81.250270233478057478  ,88.988766161865874815  ] 
dist 4=[77.317922177930546228  ,87.623262541981124531  ] 
dist 5=[72.177918599860319700  ,87.128578815646560371  ] 
dist 6=[64.065222148339543053  ,85.854907689422676815  ] 
dist 7=[55.777562670853165314  ,85.287882127699233246  ] 
dist 8=[49.939571236509894398  ,82.086300828844831967  ] 
dist 9=[44.793647545340542234  ,81.258674700503125875  ] 
dist 10=[39.265712469261928432  ,79.258337358062386555  ] 
dist 11=[33.932153373788958762  ,78.511954581244701572  ] 
dist 12=[29.561128475871657391  ,68.932287603053472146  ] 
dist 13=[25.068168266791420660  ,67.075388314915377491  ] 
dist 14=[18.588011454415038120  ,60.588274335783546404  ] 
dist 15=[0                     ,49.936540561453808745  ] 
dist 16=[9.8816839025526272505 ,21.760860861294193372  ] 
dist 17=[6.8259409742829026820 ,19.787481887898119139  ] 
dist 18=[3.9069307781866381047 ,17.262968233570226666  ] 
dist 19=[1.3044900395999125769 ,16.772176132574529973  ] 
dist 20=[-.4888549660241436708 ,5.2563114115933315783 ] 
dist 21=[-2.0316905131854847143 ,4.0486870728259037871 ] 
dist 22=[-4.5783141260277034400 ,3.8224519362695868777 ] 
dist 23=[-6.9722436717460940810 ,-1.1702441239883418970 ] 
dist 24=[-9.0143944311018824607 ,-1.6663271035708748810 ] 
dist 25=[-10.283614640587635413  ,-2.5946922846814343995 ] 
dist 26=[-11.241357395760831350  ,-2.7872969917729003366 ] 
dist 27=[-12.044058116359628719  ,-3.2367161887280918513 ] 
dist 28=[-12.675301419775205802  ,-3.2238875316175232843 ] 
dist 29=[-12.948990262695019866  ,-3.0435523829109873472 ] 
dist 30=[-13.065905075670489292  ,-2.5999696388217183927 ] 
dist 31=[-13.065828592109727087  ,-2.0887672894589367235 ] 
dist 32=[-12.681502297874703911  ,-1.6379552372235827343 ] 
dist 33=[-12.548347310081499418  ,-1.1518037697743422506 ] 
dist 34=[-12.421102735617330392  ,-.4980606519231198474 ] 
dist 35=[-12.332877558752516924  ,.2073723449283387874 ] 
dist 36=[-9.8131349178372987974 ,.9005040764296567318 ] 
dist 37=[-9.4678282378761424347 ,1.7144605061699129458 ] 
dist 38=[-8.7227654454839269445 ,2.9026252755081223968 ] 
dist 39=[-8.5122026636224982633 ,4.0711053996834936046 ] 
dist 40=[-7.6610811682150424601 ,4.8068533989855957362 ] 
dist 41=[-7.4915875248450147087 ,5.3653659897378521349 ] 
dist 42=[-7.0994092908921971992 ,5.8270244160899722834 ] 
dist 43=[-7.0044613576672627498 ,6.1946797813150025207 ] 
dist 44=[-5.2715644573323086918 ,6.3782034313998281081 ] 
dist 45=[-5.1637683297575333032 ,6.4720214774521757546 ] 
dist 46=[-5.1276901639509130751 ,6.4827823918450953578 ] 
dist 47=[-4.2027606596863709105 ,6.2320636869806666098 ] 
dist 48=[-4.0621329194808904309 ,6.1860112753033541723 ] 
dist 49=[-3.7592514787618732154 ,6.8199212993515780055 ] 
dist 50=[-3.6675549007111631473 ,7.3903735157460449432 ] 
dist 51=[-3.2651784186982803900 ,8.0257753525940160432 ] 
dist 52=[-3.1818045559055974880 ,8.5981422306332544075 ] 
dist 53=[-2.9496657206794770549 ,8.9170039361744655501 ] 
dist 54=[-2.9094430988456628067 ,9.1129615861705628276 ] 
dist 55=[-1.2989540933757278313 ,9.1945488640776556545 ] 
dist 56=[-2.2631161755450721259 ,9.2237212975364449859 ] 
dist 57=[-3.0483965384019944930 ,9.2102619094132791912 ] 
dist 58=[-3.7917162553404638846 ,9.1636753855786918777 ] 
dist 59=[-4.4487235743567976821 ,9.1327035730221561385 ] 
dist 60=[-4.8898076773622423928 ,-2.6126963493883665301 ] 
dist 61=[-5.2560905659361473818 ,-3.2081398863897035372 ] 
dist 62=[-5.6148200298870290479 ,-4.5279401531301762390 ] 
dist 63=[-5.9274709157540395599 ,-4.7344469335399406139 ] 
dist 64=[-6.3412307111646066072 ,-5.0524074513230794042 ] 
dist 65=[-6.8148749189839095207 ,-4.8821455672946602934 ] 
dist 66=[-7.1784746885609159724 ,-4.5060310946016682865 ] 
dist 67=[-7.4864117955622752837 ,-4.0279657415536597646 ] 
dist 68=[-7.7400012789236942009 ,-3.4510956129254407696 ] 
dist 69=[-7.8868088587892257448 ,-2.6931734808181143062 ] 
dist 70=[-7.9836032693294235037 ,-1.4930394326607632500 ] 
dist 71=[-8.0376143643638592434 ,-.2736558828423892843 ] 
dist 72=[-8.0602361465872642099 ,.56104704849177926308] 
dist 73=[-8.0392101368092514878 ,1.2713627293127032135 ] 
dist 74=[-7.9755444411935647469 ,1.9946963768718831162 ] 
dist 75=[-7.9317345755819307939 ,2.6684657948300013018 ] 
dist 76=[-2.8438404577405365973 ,3.1811246773217792397 ] 
dist 77=[-2.3967400462955655457 ,3.6724714689410006640 ] 
dist 78=[-1.3983167194390421242 ,4.2612576054320780209 ] 
dist 79=[-1.1898809881686340416 ,4.8075714241861396738 ] 
dist 80=[-.01151124499869168471,5.1295363995106899275 ] 
dist 81=[.19291366117755745406,5.3479277761939400114 ] 
dist 82=[.62364798207725624974,5.4811745044299362754 ] 
dist 83=[.72210124400202112488,5.5684746717288567262 ] 
dist 84=[.6173437959817830176 ,5.9434102275475153764 ] 
dist 85=[.40066220599962680077,6.4041660266388489443 ] 
dist 86=[.01709364066431027918,6.7358087740403556408 ] 
dist 87=[-.99092523532832882906,6.9768533970670295286 ] 
dist 88=[-1.6845531746478393042 ,7.1503527016984464535 ] 
dist 89=[-2.2783755846787427696 ,7.2125809863449642152 ] 
dist 90=[-2.8887958470047169104 ,7.2228223647225318286 ] 
dist 91=[-3.4609832002134591886 ,7.2003735020981282057 ] 
dist 92=[-3.9023319243146256167 ,-.77195020988894351577] 
dist 93=[-4.3310717162605942256 ,-1.0077940063671750758 ] 
dist 94=[-4.8529761197984495565 ,-1.0566361664347941135 ] 
dist 95=[-5.3413101818014976350 ,-.9783286020437853669 ] 
dist 96=[-5.6361694922002729177 ,-.8812316095395791059 ] 
dist 97=[-5.8449263549102652761 ,-.7520677362250195960 ] 
dist 98=[-5.9898766666503322705 ,-.5458750162769277542 ] 
dist 99=[-6.0834977910943346487 ,-.3067107151953626240 ] 
dist 100=[-6.2141586233697520824 ,.0492019525577221807 ] 
dist 101=[-6.5076227263793288397 ,.89882670207961893943] 
dist 102=[-6.6980612484918074379 ,2.1960189746565566233 ] 
dist 103=[-6.7969139550141192631 ,3.4914181257064055098 ] 
dist 104=[-6.8467899225032607454 ,4.3338919837815594908 ] 
dist 105=[-6.8418994372002719028 ,5.0034830952292273464 ] 
dist 106=[-6.8055769077415390012 ,5.6094125446460489416 ] 
dist 107=[-6.7735724544234172798 ,6.1259032062014139068 ] 
dist 108=[-5.8751974275113215476 ,6.4388054955388741052 ] 
dist 109=[-5.7331606853688453282 ,6.6615930979016500291 ] 
dist 110=[-5.3713038459757422024 ,6.8186992828731933377 ] 
dist 111=[-5.2772524452509257298 ,6.9307187732528769707 ] 
dist 112=[-4.6397325006524161802 ,6.9736971013303984801 ] 
dist 113=[-4.5018393686504972195 ,6.9742111465206459452 ] 
dist 114=[-4.2549886428365598388 ,7.0846101120884459793 ] 
dist 115=[-4.1885012916542365950 ,7.3425305002930922867 ] 
dist 116=[-2.8294935668704384654 ,7.5486737324581944871 ] 
dist 117=[-2.6424337431885569614 ,7.6455265007477016677 ] 
dist 118=[-2.1853295031226222485 ,7.6806158469097795318 ] 
dist 119=[-2.1057545521141112686 ,7.6720335087555756337 ] 
dist 120=[-2.6500957952535878698 ,7.5630467063912980052 ] 
dist 121=[-3.4997144868630426571 ,7.5168955353424887682 ] 
dist 122=[-4.2914706152935461662 ,7.3416248040139111471 ] 
dist 123=[-4.9826340198034565754 ,7.2849100950073318351 ] 
dist 124=[-5.4310805933536912237 ,-1.7261549079071188205 ] 
dist 125=[-5.7863135880174868630 ,-2.2983147612240013638 ] 
dist 126=[-6.1057335053029940444 ,-3.5946432508942184780 ] 
dist 127=[-6.3786377474123245210 ,-3.7868511326201009707 ] 
dist 128=[-6.5483623707276103626 ,-5.2868305268246077885 ] 
dist 129=[-6.6745185882431943298 ,-5.5214975839532997712 ] 
dist 130=[-6.7736684159224370882 ,-5.6192243103294009995 ] 
dist 131=[-6.8475247839477387650 ,-5.1576202612130346702 ] 
dist 132=[-6.8728085768964663587 ,-4.5803615173331125044 ] 
dist 133=[-7.0414797461678560926 ,-3.8095448867286723074 ] 
dist 134=[-7.1765458299529070512 ,-2.5760157495994231195 ] 
dist 135=[-7.2834434822980516388 ,-1.3163274670217701321 ] 
dist 136=[-7.3636848979270864551 ,-.4411859692531469822 ] 
dist 137=[-7.3924430124191653043 ,.31732021890691001043] 
dist 138=[-7.3889174716524253163 ,1.1118571034007970024 ] 
dist 139=[-7.3621904016334660782 ,1.8659078909313053186 ] 
dist 140=[-2.2218502461114086055 ,2.4629521337767406852 ] 
dist 141=[-1.7906843317671975160 ,3.0575798587050293775 ] 
dist 142=[-.82874150318503620123,3.8019933837046608669 ] 
dist 143=[-.63125536175938946352,4.5088406780935030881 ] 
dist 144=[.49364752821330887926,4.9536511198102802394 ] 
dist 145=[.68639681113612806236,5.2904122496410878314 ] 
dist 146=[1.0922779387359594319 ,5.5663497979594864645 ] 
dist 147=[1.1800700987989063193 ,5.7811063431843057726 ] 
dist 148=[1.1171266667612457698 ,5.8738724818408162759 ] 
dist 149=[.69637632732353726599,5.9111266365489434809 ] 
dist 150=[.00016834608785471400,5.9044967253377182966 ] 
dist 151=[-.89678437184496210778,5.9749404253041063133 ] 
dist 152=[-1.5034847214970444324 ,6.2099503800006434418 ] 
dist 153=[-2.0119963459368741865 ,6.3137415138699765521 ] 
dist 154=[-2.5173641331599617819 ,6.3562737611008638524 ] 
dist 155=[-2.9802359398130829795 ,6.3476590478950825396 ] 
dist 156=[-3.3192700041524275622 ,-.76744007784997144319] 
dist 157=[-3.6315306292058715795 ,-1.0243727624866390123 ] 
dist 158=[-3.9876276987566199678 ,-1.5938150812980350678 ] 
dist 159=[-4.3087522366022777994 ,-1.6892821556429640530 ] 
dist 160=[-4.4815394507178818906 ,-2.3107530799919417766 ] 
dist 161=[-4.5789854363610066215 ,-2.2679028089126944359 ] 
dist 162=[-4.6019382161613124183 ,-1.8915146683690160457 ] 
dist 163=[-4.5875103129413037576 ,-1.4446748177029338754 ] 
dist 164=[-4.5901009586435732125 ,-.94388578496941855267] 
dist 165=[-4.7715541659413760183 ,-.3091527378997671965 ] 
dist 166=[-4.8737539923973782249 ,.6718671784624530676 ] 
dist 167=[-4.8968381430233890785 ,1.6574237649916224178 ] 
dist 168=[-4.8742523968697612079 ,2.3102494330408166535 ] 
dist 169=[-4.8651412227913131083 ,2.8424714429834609116 ] 
dist 170=[-4.8567454426485877037 ,3.3470504228448983811 ] 
dist 171=[-4.8471650728119447350 ,3.7934554593179753303 ] 
dist 172=[-3.7512969329779919973 ,4.0936748531486051275 ] 
dist 173=[-3.6072113822773824718 ,4.3434336029443003106 ] 
dist 174=[-3.2591694093246274330 ,4.5885973123370742364 ] 
dist 175=[-3.1762812859782055719 ,4.7983902452760307286 ] 
dist 176=[-2.6430001835671877780 ,4.9070873425749365127 ] 
dist 177=[-2.5348212970940904595 ,4.9622349993843981972 ] 
dist 178=[-2.3328960711028564570 ,4.9672794364165815637 ] 
dist 179=[-2.2796203907273781192 ,4.9281277216438887704 ] 
dist 180=[-1.3911813006052866254 ,5.0801713054763306964 ] 
dist 181=[-1.2677250611179170190 ,5.1988919843979334230 ] 
dist 182=[-.9762598743228958501 ,5.2598040921114038632 ] 
dist 183=[-1.0790536070525472565 ,5.2659631921659847387 ] 
dist 184=[-1.7975300637626110757 ,5.2267853408828673426 ] 
dist 185=[-2.3873744693560836656 ,5.1980797251863339094 ] 
dist 186=[-2.9534493535698610454 ,5.1150788456686177329 ] 
dist 187=[-3.4589138417952321990 ,5.0729059339430476403 ] 
dist 188=[-3.8070388498442845962 ,-.58355716234891611864] 
dist 189=[-4.1055670480674013998 ,-.77829259013977132395] 
dist 190=[-4.4132352536658340965 ,-1.2150698715549833630 ] 
dist 191=[-4.6843647023622951351 ,-1.2837093478145815936 ] 
dist 192=[-4.8371732405994395705 ,-1.7760516343335553694 ] 
dist 193=[-4.9321339685569145913 ,-1.8278811288504081273 ] 
dist 194=[-4.9725614465877977457 ,-1.6923237147707552891 ] 
dist 195=[-4.9805623977477085158 ,-1.5194219370510125236 ] 
dist 196=[-4.9694280286636305712 ,-1.3099511754457902736 ] 
dist 197=[-5.0997093078823980596 ,-1.0341978608409899754 ] 
dist 198=[-5.1997601997578435944 ,-.59695564377852675534] 
dist 199=[-5.2434244600672173831 ,.3609360208064212588 ] 
dist 200=[-5.2527180503709999749 ,1.0358421992028745886 ] 
dist 201=[-5.2418030133659876422 ,1.6032829570623224909 ] 
dist 202=[-5.1683468766340812728 ,2.1700856268168101531 ] 
dist 203=[-5.1364568996548957617 ,2.6910820625823009572 ] 
dist 204=[-2.7631276011172711428 ,3.0758436752521557075 ] 
dist 205=[-2.5267729837812546238 ,3.4333744571114232526 ] 
dist 206=[-1.9857944648197524486 ,3.8457720302883011973 ] 
dist 207=[-1.8688636185352612117 ,4.2210534148970321673 ] 
dist 208=[-1.1713470197111747938 ,4.4305616898087019707 ] 
dist 209=[-1.0431983020641431436 ,4.5581581969779542691 ] 
dist 210=[-.7866528303868458241 ,4.6067685073576319896 ] 
dist 211=[-.7208388165054243847 ,4.6251316419905811851 ] 
dist 212=[-.0301454553093273823 ,4.6320998479893154695 ] 
dist 213=[.0752028051527583674 ,4.6450528356088232218 ] 
dist 214=[1.52015525500470000000e-06,4.7815997492878922731 ] 
dist 215=[-.91196537911857832933,4.8344169429098736487 ] 
dist 216=[-1.5443712565662639236 ,4.8552998336281218238 ] 
dist 217=[-2.0912663333925241987 ,4.8644900369175380335 ] 
dist 218=[-2.6622089330682457196 ,4.8668491011413567660 ] 
dist 219=[-3.2028747622290284912 ,4.8604888285344943951 ] 
dist 220=[-3.6290235109800766349 ,-.18911192349974770769] 
dist 221=[-4.0516522202712071216 ,-.17568107913622020661] 
dist 222=[-4.5782798335927430201 ,-.0103081293566477054 ] 
dist 223=[-5.0771307177211380640 ,.1726226453552395067 ] 
dist 224=[-5.3889834757444440940 ,.3323669966120877465 ] 
dist 225=[-5.6226769696484286225 ,.5052507207118002535 ] 
dist 226=[-5.8098220811836952971 ,.7405824281999187447 ] 
dist 227=[-5.9520700768869543014 ,.9971901595992726680 ] 
dist 228=[-6.0067100659504025479 ,1.2549244709939063642 ] 
dist 229=[-6.0155627717912770887 ,1.5620829601361106407 ] 
dist 230=[-6.0011707662453841114 ,2.6502394372259383348 ] 
dist 231=[-6.0479705183748542230 ,3.9117786858765159241 ] 
dist 232=[-6.1925787118648951053 ,4.7261828898653946023 ] 
dist 233=[-6.2458090173689520203 ,5.3666581602551184810 ] 
dist 234=[-6.2528827649526785047 ,5.9345540733363954016 ] 
dist 235=[-6.2356543292421571798 ,6.4103324004100832350 ] 
dist 236=[-6.0482371354571933170 ,6.6834349266351875750 ] 
dist 237=[-5.9934653595539207666 ,6.8595885496383554147 ] 
dist 238=[-5.8203328737980015252 ,6.9487264297877138813 ] 
dist 239=[-5.7628730621259516744 ,6.9944874583932087742 ] 
dist 240=[-5.3184405840409311973 ,6.9976505193040482528 ] 
dist 241=[-5.2100897252507762409 ,6.9702099909173421633 ] 
dist 242=[-5.0389769982843565757 ,7.1151892936376111202 ] 
dist 243=[-4.9818350584998880175 ,7.2121060153144606297 ] 
dist 244=[-3.6115794689517019006 ,7.2638428782860299270 ] 
dist 245=[-3.4193361644993286760 ,7.2696437774219275087 ] 
dist 246=[-2.9826877778404171324 ,7.2428936387103362325 ] 
dist 247=[-2.8689246188298870767 ,7.2149000156654934172 ] 
dist 248=[-2.2937330566341835226 ,7.0600081194360901384 ] 
dist 249=[-2.1814841118638784528 ,7.0083421776437055095 ] 
dist 250=[-1.9324677416552017118 ,6.8085052769223058481 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 0, 1, 0, 2] 
dist 0=[70.347525851560668050  ,70.347525851560668050  ] 
dist 1=[69.777075170238540200  ,70.588606982079615892  ] 
dist 2=[68.585045580756589593  ,70.595860914516038107  ] 
dist 3=[67.035427486094958311  ,70.246365200646345844  ] 
dist 4=[65.037461757761380638  ,69.809040011047579328  ] 
dist 5=[62.326740519740784391  ,69.146720802168836922  ] 
dist 6=[57.931329823095971122  ,68.836805271424242458  ] 
dist 7=[53.405319217757113213  ,66.907036815832757628  ] 
dist 8=[50.173040659444973004  ,66.631850234484047177  ] 
dist 9=[47.265923532058821043  ,65.573726930102953898  ] 
dist 10=[44.037826574993678300  ,65.230903483348157838  ] 
dist 11=[40.845315814339086556  ,64.481430881913719882  ] 
dist 12=[38.079996442633446898  ,64.195905115769236699  ] 
dist 13=[35.093546521734644097  ,62.835408710459253325  ] 
dist 14=[31.017641671770270825  ,61.196246300523949713  ] 
dist 15=[26.949614034722750750  ,30.129534493548731397  ] 
dist 16=[21.556271977127801202  ,29.318200250013571708  ] 
dist 17=[17.026753649934617545  ,24.964569538148341586  ] 
dist 18=[12.554633955715763750  ,24.276400239371668061  ] 
dist 19=[8.4557771853387904785 ,21.709599478045487408  ] 
dist 20=[5.4163403269918535684 ,21.209026949646887149  ] 
dist 21=[2.5670857956552642138 ,20.246936662518513838  ] 
dist 22=[-.77274722864485319515,20.015600731637746951  ] 
dist 23=[-3.8940620613569890443 ,6.2279725238894949774 ] 
dist 24=[-5.8710831305299102892 ,5.0220155803661732767 ] 
dist 25=[-7.3919122143089316225 ,2.4059572214217242561 ] 
dist 26=[-8.6921903147753602524 ,1.9013645474280223554 ] 
dist 27=[-9.7651408734946291190 ,-.92530479156086615012] 
dist 28=[-10.348783710608348080  ,-1.2124893732126713479 ] 
dist 29=[-11.542090239491833908  ,-2.3626494284054750316 ] 
dist 30=[-13.012254921084946036  ,-2.5478818068573196993 ] 
dist 31=[-14.351275453503706054  ,-3.8299176721638864110 ] 
dist 32=[-15.127824062933356822  ,-4.0387509347003417983 ] 
dist 33=[-15.645772919208664237  ,-4.0395157757878355398 ] 
dist 34=[-15.951687543829395266  ,-3.7624836990643929883 ] 
dist 35=[-16.143049569074844448  ,-3.3329521615528399072 ] 
dist 36=[-16.203181364283196339  ,-2.7246525470236523597 ] 
dist 37=[-16.180222397341267860  ,-1.8715856475342221405 ] 
dist 38=[-16.142670661098336266  ,-.46495627567147772507] 
dist 39=[-11.160795041823447193  ,2.0342253687764959246 ] 
dist 40=[-11.115846609072971583  ,3.8994795950791073505 ] 
dist 41=[-10.562218440488214942  ,5.4295905212652434875 ] 
dist 42=[-10.416406725177964613  ,6.8981750356676054993 ] 
dist 43=[-10.248880691767150229  ,8.2118179683723873021 ] 
dist 44=[-10.165656751283459709  ,9.1240020501464749028 ] 
dist 45=[-6.7579146714008643170 ,9.9156838090052310787 ] 
dist 46=[-6.3590036785667926382 ,10.748835542224378741  ] 
dist 47=[-5.4508195272723175748 ,11.489667961083167483  ] 
dist 48=[-5.2367124781949793986 ,11.913035192743606627  ] 
dist 49=[-4.0460337058041843904 ,12.184751934299169782  ] 
dist 50=[-3.8180524581972432951 ,12.320309960696836069  ] 
dist 51=[-3.3480222281396788757 ,12.375210073622805176  ] 
dist 52=[-3.2186175322956362035 ,12.358621534859957399  ] 
dist 53=[-1.8109914708079611140 ,12.239494758932227510  ] 
dist 54=[-1.5959386301835159538 ,12.154396207228166817  ] 
dist 55=[-1.1619237058364787809 ,7.4538936399600688383 ] 
dist 56=[-1.0490316575645622786 ,6.9763227853275054084 ] 
dist 57=[-.64509736773730892616,5.8532840518986269372 ] 
dist 58=[-.55709862403341164083,5.6276055596552330505 ] 
dist 59=[-1.0486018652849904212 ,4.0797400918148400879 ] 
dist 60=[-1.5128762126036193889 ,3.4007106010572668654 ] 
dist 61=[-1.9789550190771801042 ,2.3254156240297526499 ] 
dist 62=[-2.5677145149607905070 ,2.3201141101548744403 ] 
dist 63=[-3.1297953322262490298 ,-.29423827712562778552] 
dist 64=[-3.4894774198606950497 ,-.24040194683506501921] 
dist 65=[-3.7689054613057294408 ,-.18049018252169204214] 
dist 66=[-4.0108918245631598066 ,-.11944555890355834243] 
dist 67=[-4.2095885536157596952 ,-.04639265896779790513] 
dist 68=[-4.3163526749650271327 ,.06142657100791824694] 
dist 69=[-4.3759697578363091354 ,.17116309426573068828] 
dist 70=[-4.3866141758711037421 ,.25189362939502303636] 
dist 71=[-2.5023130167732323282 ,.53841961947370506193] 
dist 72=[-2.5450442414425152405 ,.94265653639769034307] 
dist 73=[-2.5636975653519016785 ,1.2780938782354883583 ] 
dist 74=[-2.5634529013128577961 ,1.6059174517476609253 ] 
dist 75=[-2.4960766970049667083 ,1.9025766101938196805 ] 
dist 76=[-2.4723728411663490606 ,2.1137354276990697007 ] 
dist 77=[-2.4525727704076937130 ,2.3020916767733098932 ] 
dist 78=[-2.4353427909779836918 ,2.5078206965163500220 ] 
dist 79=[-1.7042242749586338348 ,2.6914725831095358992 ] 
dist 80=[-1.6162876601115170198 ,2.7917850872731058561 ] 
dist 81=[-1.4128837819568780541 ,2.8499895636605502336 ] 
dist 82=[-1.3644332980370370318 ,2.8657079274099608909 ] 
dist 83=[-1.0859458242617100580 ,2.8640642301322474505 ] 
dist 84=[-1.0317085728198418805 ,2.8530259832296676654 ] 
dist 85=[-.92229123176052534005,2.8330348228260506858 ] 
dist 86=[-.89237387796726062541,2.8190123819227430130 ] 
dist 87=[-.64673862190664725198,2.6694262629966831610 ] 
dist 88=[-1.0013520815083063216 ,2.7346178904387212272 ] 
dist 89=[-1.3305303465760345018 ,2.7671401375245443287 ] 
dist 90=[-1.6510353038287674609 ,2.7720068668993974373 ] 
dist 91=[-1.9402827098457459319 ,2.7459676631971594558 ] 
dist 92=[-2.1448054011223085512 ,2.7289787724269791518 ] 
dist 93=[-2.3258322274318229828 ,2.6931128878152373360 ] 
dist 94=[-2.5213779636699033040 ,2.6760142476044542995 ] 
dist 95=[-2.6952712511344181949 ,.44153937971737070181] 
dist 96=[-2.7899470608823606851 ,.53682755060386443279] 
dist 97=[-2.8444521972080637659 ,.67479362922444168387] 
dist 98=[-2.8581419493616839760 ,.79552734862624950426] 
dist 99=[-2.8547713739832723679 ,.92637535450447014962] 
dist 100=[-2.8412388041634607869 ,1.1046779122033169306 ] 
dist 101=[-2.8177115324296153622 ,1.2809950276811856364 ] 
dist 102=[-2.8040545540860441261 ,1.4039271919958502778 ] 
dist 103=[-2.5054076797680063127 ,1.5109180260672315537 ] 
dist 104=[-2.5764835908682787627 ,1.6236665058317210439 ] 
dist 105=[-2.6231614671660212352 ,1.7310723004605452165 ] 
dist 106=[-2.6485856247066169632 ,1.8167602474862726001 ] 
dist 107=[-2.6583473258260953852 ,1.9026998534522412593 ] 
dist 108=[-2.6548081054328140339 ,2.0288767885954813204 ] 
dist 109=[-2.6207681278767281014 ,2.1715748099045387360 ] 
dist 110=[-2.6065977860325602929 ,2.3073049897007856221 ] 
dist 111=[-2.2675156250449810923 ,2.4248964362343217274 ] 
dist 112=[-2.2640866518055692550 ,2.4952563130540035255 ] 
dist 113=[-2.3581339659129504815 ,2.5442827524319721303 ] 
dist 114=[-2.4100717612085706914 ,2.5767982048273769058 ] 
dist 115=[-2.4341333351188491756 ,2.5961010312826854914 ] 
dist 116=[-2.4366140054947777235 ,2.5924368388741595378 ] 
dist 117=[-2.2763432837788422621 ,2.4650343047709090124 ] 
dist 118=[-2.2425967238521528852 ,2.3893251753977601994 ] 
dist 119=[-2.1882876315790666834 ,2.0626852826336376267 ] 
dist 120=[-2.1686724435003040911 ,2.1975661340992481253 ] 
dist 121=[-2.0964194959412620677 ,2.2886587391221818173 ] 
dist 122=[-2.0720155446116603112 ,2.3434383910341721818 ] 
dist 123=[-2.0211484882166225174 ,2.3789122341546290046 ] 
dist 124=[-2.0020091197196274818 ,2.3930090810343443906 ] 
dist 125=[-.99188907154932963428,2.3941114692420707597 ] 
dist 126=[-1.2577299740319563274 ,2.3871050310421112992 ] 
dist 127=[-1.5111330088401524835 ,-.17137663006820941367] 
dist 128=[-1.6722756681191768528 ,-.22889381392777509699] 
dist 129=[-1.7962283397391906792 ,-.34572966216509446649] 
dist 130=[-1.9013148480427984018 ,-.37401627073025253494] 
dist 131=[-1.9858619143911329965 ,-.46472639247493547982] 
dist 132=[-2.0279017066180610006 ,-.42009890021369841832] 
dist 133=[-2.0468680060793614492 ,-.26140027684728759885] 
dist 134=[-2.0964361665958146132 ,-.00063680013881526352] 
dist 135=[-2.3059550738775305680 ,.29585235451243109296] 
dist 136=[-2.4324236975268433037 ,.49552552178306315088] 
dist 137=[-2.5219142772509824715 ,.6619377829902105776 ] 
dist 138=[-2.5839606242165597378 ,.82577997814483756554] 
dist 139=[-2.6239429885176714952 ,.97484771301039473405] 
dist 140=[-2.6317216415897918991 ,1.0823382219410011814 ] 
dist 141=[-2.6158027469279886067 ,1.1796446013985680874 ] 
dist 142=[-2.6113791097687333777 ,1.2880971922750090963 ] 
dist 143=[-2.4243832682317493918 ,1.5104308583098988499 ] 
dist 144=[-2.3869811903267883874 ,1.8741133052597881859 ] 
dist 145=[-2.2838519240026583564 ,2.1631274986221193325 ] 
dist 146=[-2.2541851774191193530 ,2.4246042596829730289 ] 
dist 147=[-2.0400297787063067144 ,2.6474479688635397276 ] 
dist 148=[-1.9908775685989555172 ,2.7823902678205561141 ] 
dist 149=[-1.9080191732081880218 ,2.8783977461377062826 ] 
dist 150=[-1.8834518330268445500 ,2.9459661938827434816 ] 
dist 151=[-1.3287276292393973315 ,2.9940685862819150045 ] 
dist 152=[-1.2515501014274795023 ,3.0124436710729669081 ] 
dist 153=[-1.0706796366220391272 ,3.0125117898232108605 ] 
dist 154=[-1.0304277876666985078 ,3.0045668543480142016 ] 
dist 155=[-1.1091924563648501704 ,2.9491046566524203882 ] 
dist 156=[-1.2102301581864017862 ,2.9300728997415169641 ] 
dist 157=[-1.2971732805581534396 ,2.8470406552264231328 ] 
dist 158=[-1.3872558892881086893 ,2.8333025198827754885 ] 
dist 159=[-1.4660686595291703133 ,.32577451842434538234] 
dist 160=[-1.5080667226530611439 ,.29026705747507021422] 
dist 161=[-1.5310197229488888187 ,.21126244253664335503] 
dist 162=[-1.5345322530390955576 ,.19314399394789421574] 
dist 163=[-1.5280883348350625520 ,.09911233748971873096] 
dist 164=[-1.5201235452038732949 ,.08229346818398532336] 
dist 165=[-1.5187346633815446232 ,.04473458684899672438] 
dist 166=[-1.6064677887789966039 ,.03690814335903851878] 
dist 167=[-1.6818218515571145616 ,.32595000739693738429] 
dist 168=[-1.7278998940145019021 ,.54229225060333567778] 
dist 169=[-1.7612242329365505613 ,.71909968937027048766] 
dist 170=[-1.7857153692973337811 ,.88744815451545477077] 
dist 171=[-1.8025697325154628027 ,1.0368781438758991803 ] 
dist 172=[-1.8054379297339808936 ,1.1382371009862141609 ] 
dist 173=[-1.7986031825345177980 ,1.2234998565668376347 ] 
dist 174=[-1.7925179997497223800 ,1.3087368310849197293 ] 
dist 175=[-.60683569605489644846,1.3833664338228419723 ] 
dist 176=[-.50507176998559742534,1.4263260936716408987 ] 
dist 177=[-.27730041773277675033,1.4541902906350335659 ] 
dist 178=[-.23022731398325112283,1.4686179125729902143 ] 
dist 179=[.03960580171692683601,1.4732566783517899282 ] 
dist 180=[.08630217604657007377,1.4717310173805567880 ] 
dist 181=[.1839180178789058053 ,1.4487011974477616252 ] 
dist 182=[.20665152749785839812,1.4445410520117721784 ] 
dist 183=[-.00453209651450828698,1.2339098627865425743 ] 
dist 184=[-.2013660002303967406 ,1.3451962561811975619 ] 
dist 185=[-.36814020476667993638,1.4277425732486585170 ] 
dist 186=[-.53680900031426843676,1.4923011012867581228 ] 
dist 187=[-.69318610362213190824,1.5405734408644797434 ] 
dist 188=[-.81093999628214911353,1.5581690338270519714 ] 
dist 189=[-.92260905176651641667,1.5635871122873853397 ] 
dist 190=[-1.0547193058345095197 ,1.5632944690499026131 ] 
dist 191=[-1.1764089045440063207 ,-.07891737797617328449] 
dist 192=[-1.2465195027929954788 ,-.10678304435500042889] 
dist 193=[-1.2920723136980431034 ,-.14187472152770623576] 
dist 194=[-1.3158233766067919110 ,-.1471361042456457401 ] 
dist 195=[-1.3296563775057663787 ,-.14066044907781655261] 
dist 196=[-1.3356551175594632255 ,-.1167248362304972776 ] 
dist 197=[-1.3370469367410133530 ,-.07548767010403407832] 
dist 198=[-1.3325071482904458885 ,-5.84691033565348100000e-06] 
dist 199=[-.67175400682236735464,.12614418701962843316] 
dist 200=[-.68932472989686503183,.2112155291031993891 ] 
dist 201=[-.70257294075303314017,.2822408722933568622 ] 
dist 202=[-.71333030689020653333,.35237427236791124798] 
dist 203=[-.72162570153750150176,.41631746238329921587] 
dist 204=[-.72505535665117914277,.46265572320929011074] 
dist 205=[-.72556791121628951432,.50483726326771760469] 
dist 206=[-.72288752956433871035,.5522030983539918475 ] 
dist 207=[-.20896922587777773255,.59465999253971726055] 
dist 208=[-.16618886971772446699,.61726426035926265191] 
dist 209=[-.07084355810981281185,.62988680398462476993] 
dist 210=[-.05131356232144991098,.63265177751142167435] 
dist 211=[.11170809159217874609,.62903654831272368684] 
dist 212=[.14043944141236481614,.6274614915202964938 ] 
dist 213=[.07149553547286165719,.6259150583080412871 ] 
dist 214=[-.06204449624337676184,.62400957893600111009] 
dist 215=[-.19637787017261666233,.62208418479363216556] 
dist 216=[-.28570956421067626107,.62213755567640893472] 
dist 217=[-.3589252927901476702 ,.61675912989590135216] 
dist 218=[-.42898683016277212636,.61328952644077500797] 
dist 219=[-.49141037541570513319,.58088358133965879502] 
dist 220=[-.53416514382614498768,.57185561236971718639] 
dist 221=[-.57057585850028558379,.53516191376284146908] 
dist 222=[-.60769877945777171246,.46824532751097167231] 
dist 223=[-.63996925702913970932,.15463481082426240518] 
dist 224=[-.65702801616022022946,.13911787370872773616] 
dist 225=[-.66616189996023250706,.1037984002685529789 ] 
dist 226=[-.66740967641711806121,.09630063377662289233] 
dist 227=[-.66379400758506331126,.05174259298739778919] 
dist 228=[-.66026407314536417027,.04368806410097654577] 
dist 229=[-.65119932376989151264,.02746202278932087667] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 1, 1, 0, 1] 
dist 0=[63.835872045040365290  ,63.835872045040365290  ] 
dist 1=[62.793116071432979406  ,64.429772721651025539  ] 
dist 2=[60.832637575665009817  ,64.598151313787143047  ] 
dist 3=[58.721425222271608882  ,64.617058947385965642  ] 
dist 4=[57.076765817251610990  ,64.614046671769401164  ] 
dist 5=[55.456602532750475873  ,64.599956930191244949  ] 
dist 6=[53.443015437842724116  ,64.574629654103984793  ] 
dist 7=[51.326596669684693807  ,64.535909002752125792  ] 
dist 8=[49.295676907763447390  ,63.790599241072460699  ] 
dist 9=[46.934614190435318503  ,58.646880536804139056  ] 
dist 10=[43.499679016902817597  ,57.794002891239524516  ] 
dist 11=[39.975273615686915122  ,56.279690690311228288  ] 
dist 12=[37.256780172981746701  ,55.884092197784251261  ] 
dist 13=[34.602267819416411762  ,54.553181844274387320  ] 
dist 14=[30.730761870178803515  ,54.142088853056791648  ] 
dist 15=[23.741940772975410931  ,53.738607263154989385  ] 
dist 16=[19.033454661471603589  ,52.917574789891312296  ] 
dist 17=[15.085830533345501973  ,33.543529202867458734  ] 
dist 18=[11.135192273825916182  ,33.323339060145436806  ] 
dist 19=[7.4770918372791700518 ,18.652355266956363906  ] 
dist 20=[4.6975735634470439162 ,17.850310422749006978  ] 
dist 21=[2.0245958838475207629 ,10.924358463981245738  ] 
dist 22=[-1.2081320507506948815 ,9.7101180457824919472 ] 
dist 23=[-4.2475596381531420193 ,8.0320349181924767609 ] 
dist 24=[-6.1487395753354683209 ,7.6277950669329305251 ] 
dist 25=[-7.5835658189451702188 ,-.22977298605284258287] 
dist 26=[-9.0708784193774874239 ,-.87024703683767322455] 
dist 27=[-11.273812387166002746  ,-3.1745819906971431433 ] 
dist 28=[-12.637619695419158662  ,-3.5178683928770657858 ] 
dist 29=[-13.651838913763979928  ,-5.3382403887007122340 ] 
dist 30=[-14.458573654455052958  ,-5.3827513976062944669 ] 
dist 31=[-15.078674817702020147  ,-5.2193834937990793116 ] 
dist 32=[-15.347539574030076958  ,-4.7629069540572376266 ] 
dist 33=[-15.463601129413040414  ,-4.0090609216084941209 ] 
dist 34=[-15.473260570644775120  ,-2.6591838718973001365 ] 
dist 35=[-6.3458251902389836236 ,-1.0043405156469294860 ] 
dist 36=[-6.3104276872244681708 ,.3401640821027681403 ] 
dist 37=[-6.0887171206317568304 ,1.4518434246900573965 ] 
dist 38=[-6.0323820808319451312 ,2.5311345827975250752 ] 
dist 39=[-5.8457087748027541286 ,3.5032299449205623371 ] 
dist 40=[-5.8082256603291331480 ,4.1876640464574591151 ] 
dist 41=[-5.2375547344129107101 ,4.7910093659061400471 ] 
dist 42=[-5.1346343154802197657 ,5.4400197098840286774 ] 
dist 43=[-4.8902737156916788367 ,6.0317907184577492367 ] 
dist 44=[-4.8168616169525826941 ,6.4068339240453672848 ] 
dist 45=[-4.4369533701956448001 ,6.6945186497322846002 ] 
dist 46=[-4.3538150299679844561 ,6.9375243810585417948 ] 
dist 47=[-4.1811889583126131777 ,7.1322271797747594790 ] 
dist 48=[-4.1286763580266036599 ,7.2269943103612126148 ] 
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dist 120=[-.19622629529332625845,.39190156506616941585] 
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dist 133=[-.27125480114636447054,.17254332266223994815] 
dist 134=[-.29418784617819782592,.2150979386158462777 ] 
dist 135=[-.31458948457674849279,.25359702136171069345] 
dist 136=[-.32561901408499583748,.280981436231070001  ] 
dist 137=[-.3318662340384314951 ,.30538723651905077425] 
dist 138=[-.33319506175217138428,.33200734345461701963] 
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dist 145=[-.17767883441726075502,.37331716234585444621] 
dist 146=[-.17118416550580884636,.37144727219078799395] 
dist 147=[-.13115154094994724791,.2479879719162465823 ] 
dist 148=[-.13397238785402132558,.25386916034711324638] 
dist 149=[-.17751518329444674639,.27487317171705594334] 
dist 150=[-.21991029257028582679,.29748908353621788597] 
dist 151=[-.25817156376536614354,.31756768710813917336] 
dist 152=[-.28522826772883144547,.32845263496751711728] 
dist 153=[-.30917964862337802536,.3346573563652845266 ] 
dist 154=[-.33505659009324569905,.33607054982715961883] 
dist 155=[-.35806347457377518252,.33550792511219890168] 
dist 156=[-.3705688616043129146 ,.33384394334528398681] 
dist 157=[-.3777401625824011719 ,.33102723438436696786] 
dist 158=[-.37947440436421228679,.32940143362603834115] 
dist 159=[-.3789573313178276086 ,.00994159696093113311] 
dist 160=[-.37715026480043694365,.00648676012852672198] 
dist 161=[-.37405747730815163772,.00135095544478647211] 
dist 162=[-.37222727894106153063,-8.11509854431467000000e-06] 
dist 163=[-.22056387456514058955,.07853414969416067992] 
dist 164=[-.241417175551338278  ,.13057745177511062854] 
dist 165=[-.25857412418651325745,.17290926757417323656] 
dist 166=[-.27510179008197905878,.21287979927665833094] 
dist 167=[-.28945215376512879011,.24813160081142471127] 
dist 168=[-.29792582190099121303,.27164472679786907878] 
dist 169=[-.30369326887054754258,.29099363269616469088] 
dist 170=[-.3072509412232872122 ,.30963816878465679405] 
dist 171=[-.30910404171016032585,.32583107931569837913] 
dist 172=[-.30878752037072364563,.33540270347475283692] 
dist 173=[-.30599654018273743872,.34192942515605352998] 
dist 174=[-.30385510048741339784,.34597903476368988411] 
dist 175=[-.1266463402095028284 ,.34811260123074761102] 
dist 176=[-.11055316640124703856,.347764486081699579  ] 
dist 177=[-.07426297356270364153,.34468532780177376972] 
dist 178=[-.06664638314112309916,.34230034279867342078] 
dist 179=[-.02237477133664232324,.14224800433070518891] 
dist 180=[-.02040451054337088382,.14785226564682243247] 
dist 181=[-.05948139666285348367,.17257456472487536646] 
dist 182=[-.09954356711062927441,.20252166799128515329] 
dist 183=[-.13703005603585055325,.23046826606156547087] 
dist 184=[-.16583490487561890246,.24721237609849950625] 
dist 185=[-.19371250611329947632,.25890887490701457252] 
dist 186=[-.22750104695359842065,.26672514586020780937] 
dist 187=[-.25904167080826381567,.27212914378495363101] 
dist 188=[-.27795439137602714083,.27420527702323308817] 
dist 189=[-.29118422571736131044,.27426798059470577509] 
dist 190=[-.30006103179212585868,.27372165911444599881] 
dist 191=[-.30621258056699601049,-.02217820397251506507] 
dist 192=[-.30857386676292586632,-.02969611497946673457] 
dist 193=[-.30866493485321530097,-.02465209218295987942] 
dist 194=[-.30804070356811634802,-1.48150221521177295000e-05] 
dist 195=[-.16411844281350016012,.0538057285265154639 ] 
dist 196=[-.18454114273480254639,.09070163272860753361] 
dist 197=[-.20420737160038542013,.12215859340247105154] 
dist 198=[-.22790384252588083335,.15428817050569184934] 
dist 199=[-.24995357812412121933,.18427658008244138961] 
dist 200=[-.26305248526153303584,.20719438344671969094] 
dist 201=[-.27206552164064593898,.22925488774138143332] 
dist 202=[-.27782045229171062046,.25582431538390703567] 
dist 203=[-.28133094808723134649,.28054117613781458237] 
dist 204=[-.2817372835201198717 ,.29521348760070295653] 
dist 205=[-.28021000451806081326,.30529550803509800794] 
dist 206=[-.27875525785937079135,.31170590240479802398] 
dist 207=[-.25306703933443353041,.31560457872869683285] 
dist 208=[-.24837400791218330326,.31603841638622809128] 
dist 209=[-.23588184953344070687,.31433512284009518472] 
dist 210=[-.23244722389418690834,.31265203562411943513] 
dist 211=[-.20823374581814949536,.2835401546743655649 ] 
dist 212=[-.2137489824967908171 ,.29036235014374436911] 
dist 213=[-.24882357750909613262,.30149087200451891428] 
dist 214=[-.28083407921096068033,.31003221080004951367] 
dist 215=[-.30831204844171729886,.31647337727774561312] 
dist 216=[-.32531051962434077089,.31922623342259066501] 
dist 217=[-.33783876221263299554,.31979675564666800234] 
dist 218=[-.34748908035177823535,.31913832611448265655] 
dist 219=[-.35478273357488673823,.31378627305679260859] 
dist 220=[-.35791239704656063768,.31180825930304106552] 
dist 221=[-.35858236250834191173,.30356440204582710023] 
dist 222=[-.3578539258196796747 ,.30177358429255783534] 
dist 223=[-.35188194707447015353,.08245941855982969641] 
dist 224=[-.34966644609804341229,.07659446395074550244] 
dist 225=[-.34045301428949304727,.06614677401969114186] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 2, 1, 0, 0, 2] 
dist 0=[69.741711696348288913  ,69.741711696348288913  ] 
dist 1=[69.339985950565387025  ,70.032834461364703512  ] 
dist 2=[68.780531571441862154  ,70.170271785599886746  ] 
dist 3=[67.859094445005051757  ,70.150903793090718689  ] 
dist 4=[66.420243559887345904  ,69.690451125448384527  ] 
dist 5=[64.520450050891375766  ,69.606695920124613571  ] 
dist 6=[62.266383899521991004  ,67.271814497709080650  ] 
dist 7=[57.990152438429996366  ,66.725624131672161273  ] 
dist 8=[53.560509535847355719  ,65.850960978676577460  ] 
dist 9=[50.386347146104956086  ,65.552569695042670447  ] 
dist 10=[47.520376915473978970  ,64.535012638708176162  ] 
dist 11=[44.090662157558524660  ,64.182808359989574289  ] 
dist 12=[36.443794241677305018  ,63.542054312417397460  ] 
dist 13=[28.756117144233437304  ,63.317527290418702276  ] 
dist 14=[23.573441598467995058  ,39.435766706917092193  ] 
dist 15=[19.229698082657212247  ,39.071198150439260952  ] 
dist 16=[14.890834305576206934  ,29.096672298581480098  ] 
dist 17=[10.883034570054839725  ,27.835680861829910442  ] 
dist 18=[7.8606598219866189103 ,25.202654375063866478  ] 
dist 19=[4.9781389248826820496 ,24.508527234851194123  ] 
dist 20=[1.5281606001091830800 ,21.918321368220492464  ] 
dist 21=[-1.6954797178224589749 ,21.410850008867446499  ] 
dist 22=[-3.6747119449247844053 ,20.435643040242235560  ] 
dist 23=[-5.1250783992987016621 ,20.199956632914118636  ] 
dist 24=[-6.2377400055924338938 ,5.9735503398799825746 ] 
dist 25=[-7.0998896941569507289 ,4.7296053736127057527 ] 
dist 26=[-7.5501128676188026453 ,2.0388380114063684587 ] 
dist 27=[-7.7871752425148102294 ,1.5124806668653747726 ] 
dist 28=[-9.5706321231846270239 ,0                     ] 
dist 29=[-11.059492818287567068  ,-1.8425165967357941771 ] 
dist 30=[-12.415412888168497975  ,-2.8485554113764062474 ] 
dist 31=[-13.952778974932512493  ,-3.0199632343632585276 ] 
dist 32=[-15.354569548566980874  ,-4.2184222443213417761 ] 
dist 33=[-16.169018550641462775  ,-4.3926963613950940489 ] 
dist 34=[-16.713830605020653784  ,-4.3493921653801352359 ] 
dist 35=[-17.038480442809486307  ,-4.0038276554987127199 ] 
dist 36=[-17.242082856544910630  ,-3.4953543304695227192 ] 
dist 37=[-17.303166206999793756  ,-2.8014523256419165578 ] 
dist 38=[-17.273068123277366500  ,-1.8415841680651776952 ] 
dist 39=[-17.234697836687746734  ,-.27142441526331647302] 
dist 40=[-11.436353863721314498  ,2.2533264119537083200 ] 
dist 41=[-11.383731150122079706  ,4.2449282760701774866 ] 
dist 42=[-10.689395938016390283  ,5.8764638282858454177 ] 
dist 43=[-10.519766525049647054  ,7.4390543988266004084 ] 
dist 44=[-10.340431294400490810  ,8.8348278522635619181 ] 
dist 45=[-10.247790487124940926  ,9.8010438813593405946 ] 
dist 46=[-6.8758761161265548721 ,10.636600289489495491  ] 
dist 47=[-6.4727441401055701757 ,11.511357081312580978  ] 
dist 48=[-5.5610772146640577853 ,12.289003025272064976  ] 
dist 49=[-5.3406421498948995542 ,12.737110991401398952  ] 
dist 50=[-4.1598843999384315594 ,13.029512005282766202  ] 
dist 51=[-3.9331310020480664043 ,13.185649359857892682  ] 
dist 52=[-3.4541646335609311413 ,13.254993250651500500  ] 
dist 53=[-3.3191472461542989833 ,13.244971932652100638  ] 
dist 54=[-1.9500765653034252012 ,13.111990505184836113  ] 
dist 55=[-1.7360582246635665745 ,13.040372842891907787  ] 
dist 56=[-1.3081845175140168713 ,7.8815316462110578859 ] 
dist 57=[-1.1970668488541377510 ,7.3680615863957412232 ] 
dist 58=[-.8024014351582930721 ,6.1581332845854921302 ] 
dist 59=[-.74451863338197512844,5.9209814099184992283 ] 
dist 60=[-1.4137947266438471066 ,4.2509371958597424094 ] 
dist 61=[-1.9447920336328756095 ,3.5205682197050779646 ] 
dist 62=[-2.4748298334325054334 ,-.53491347205457753518] 
dist 63=[-3.1403164446417501962 ,-.50551505186828483056] 
dist 64=[-3.7737410691213384996 ,-.46840283027585970903] 
dist 65=[-4.1759099175802314983 ,-.41203535912305257256] 
dist 66=[-4.4847430784402717500 ,-.34853364366291104495] 
dist 67=[-4.7458923732891019056 ,-.2829201650582285888 ] 
dist 68=[-4.9556715716295840691 ,-.2037968479502745178 ] 
dist 69=[-5.0596097337834066998 ,-.0863878380787754401 ] 
dist 70=[-5.1064986226369179937 ,.0333121763006238759 ] 
dist 71=[-5.1115293928407226450 ,.1216135112518242689 ] 
dist 72=[-.4278027601336722193 ,.68653870887836600375] 
dist 73=[-.4418752564526157989 ,1.1824250132407600191 ] 
dist 74=[-.46088059476917992299,1.5957596692979619654 ] 
dist 75=[-.48523229339258935811,2.0027804540157096733 ] 
dist 76=[-.51800573703985007129,2.3731484608090095489 ] 
dist 77=[-.57051655241102979469,2.6403155742030752999 ] 
dist 78=[-.62238740888697784135,2.8822885219156439276 ] 
dist 79=[-.65259108264891525429,3.1521881593907022300 ] 
dist 80=[-.672403779659406399  ,3.3939341403189404800 ] 
dist 81=[-.68286400647472247625,3.5236289043163668896 ] 
dist 82=[-.68879021734931796572,3.5958198931673436422 ] 
dist 83=[-.69054390083018077264,3.6126941643070854908 ] 
dist 84=[-.68947043634332908965,3.5993256372969373118 ] 
dist 85=[-.68698610260103045075,3.5894529414454722512 ] 
dist 86=[-.58059817645151847493,3.5767113043228104290 ] 
dist 87=[-.56371686142795927023,3.5567847681970688851 ] 
dist 88=[-1.0240918307698874813 ,2.5841703235155901151 ] 
dist 89=[-1.5315128174501648077 ,2.4649909045151594653 ] 
dist 90=[-1.9484293764741355414 ,2.1814043345097319807 ] 
dist 91=[-2.3490983812871429120 ,2.1159658950361131370 ] 
dist 92=[-2.7072292008652604622 ,1.7008892071327592118 ] 
dist 93=[-2.9545020951690590486 ,1.6187650535847131073 ] 
dist 94=[-3.1672041457236706742 ,1.4633901610531462191 ] 
dist 95=[-3.3874657293838732322 ,1.4228414057221410781 ] 
dist 96=[-3.5801643681410190932 ,.80206508392644173466] 
dist 97=[-3.6829437022355857278 ,.71459583720555220023] 
dist 98=[-3.7392464414879453549 ,.52848991236804696157] 
dist 99=[-3.7478023154586695734 ,.63163417255973178538] 
dist 100=[-3.7327332891870644493 ,.74493128686520853555] 
dist 101=[-3.7134519883190779649 ,.90120335468586788559] 
dist 102=[-3.6671818332168409933 ,1.0565528935258379290 ] 
dist 103=[-3.6428587866034491063 ,1.1661741356673972445 ] 
dist 104=[-1.6377614817318796275 ,1.2629459251932828101 ] 
dist 105=[-1.7335951253116337612 ,1.3670598718805569360 ] 
dist 106=[-1.8218810674760776224 ,1.7331384281901552867 ] 
dist 107=[-1.8874306159253732955 ,2.1255002359733144873 ] 
dist 108=[-1.9486846097256130236 ,2.4676626373556277276 ] 
dist 109=[-2.0198319816423462309 ,2.6890387867374078392 ] 
dist 110=[-2.0815554453079785687 ,2.8636889405052120472 ] 
dist 111=[-2.1052239562404507716 ,3.0195046870743972584 ] 
dist 112=[-2.1120968450433152063 ,3.1523925263215781818 ] 
dist 113=[-2.1068432643522051562 ,3.2356044860624036778 ] 
dist 114=[-2.0572196495207634969 ,3.2981226356010612889 ] 
dist 115=[-2.0994766843221969810 ,3.3484819502346938087 ] 
dist 116=[-2.1185255671131563750 ,3.3869954140218703963 ] 
dist 117=[-2.1204448498019597367 ,3.4022713584360388758 ] 
dist 118=[-1.9550946533178610450 ,3.4034078723287474108 ] 
dist 119=[-1.9227568638585407419 ,3.3909497021683932757 ] 
dist 120=[-1.8703980275738355188 ,1.2755316268546547572 ] 
dist 121=[-1.8522913245252174598 ,1.2432098167276241944 ] 
dist 122=[-1.7881221793963148467 ,1.1185360020002745722 ] 
dist 123=[-1.7662620028093955184 ,1.0890123252180494913 ] 
dist 124=[-1.7244058051413653011 ,1.0306100327054452025 ] 
dist 125=[-1.7093525144383205127 ,1.0132775535446211883 ] 
dist 126=[-1.4684809769161392600 ,.47006734967172616943] 
dist 127=[-1.8411812809456958881 ,.78231414092908955016] 
dist 128=[-2.1956809655992832188 ,1.0347568062598214963 ] 
dist 129=[-2.4198069671322933844 ,1.2705321535464292172 ] 
dist 130=[-2.5907044025335463322 ,1.4767084852119725020 ] 
dist 131=[-2.7329242481567282673 ,1.6111079471092834974 ] 
dist 132=[-2.8453269050520399206 ,1.7182745743394975506 ] 
dist 133=[-2.8973109626688942797 ,1.8158440116002699722 ] 
dist 134=[-2.9194830398146982892 ,1.8994867011553480097 ] 
dist 135=[-2.9179885955140056350 ,1.9511125090601228304 ] 
dist 136=[.35990333653048598685,1.9890197814140376708 ] 
dist 137=[.48084881548837574249,2.0179524997890383401 ] 
dist 138=[.74761427574659091289,2.0387989775181639476 ] 
dist 139=[.79349083029059027145,2.0444580371851154377 ] 
dist 140=[1.0804973838858153037 ,2.0400594999959065240 ] 
dist 141=[.73551549990580609668,2.0329546706688060156 ] 
dist 142=[.35852082915456435638,1.7450704029257079187 ] 
dist 143=[.09702377287196852917,1.9117125029372200389 ] 
dist 144=[-.1291861727949552775 ,2.0612585927121496455 ] 
dist 145=[-.36545294335080955902,2.1405754601991212895 ] 
dist 146=[-.58925597219793338331,2.1850924271935290896 ] 
dist 147=[-.76575944076350368334,2.1958536395137549539 ] 
dist 148=[-.9408994741914220363 ,2.1796109710412081419 ] 
dist 149=[-1.1592648640346478934 ,2.1749664706831853102 ] 
dist 150=[-1.3661708349170185516 ,2.1717957047882574690 ] 
dist 151=[-1.4956098075379999449 ,2.1698207704319216037 ] 
dist 152=[-1.5927154042962504068 ,1.6444331571754305694 ] 
dist 153=[-1.6706734882316903620 ,1.5771276179510652326 ] 
dist 154=[-1.7300837480904479964 ,1.4154970183076996693 ] 
dist 155=[-1.7532192523658688350 ,1.3773857235321413235 ] 
dist 156=[-1.7615616705774874260 ,1.1338966383679413767 ] 
dist 157=[-1.8928660445097940160 ,1.0849283702099586063 ] 
dist 158=[-2.0164977778754300239 ,.99298049872608015672] 
dist 159=[-2.1408002481352361151 ,.96878267571592099944] 
dist 160=[-2.2482423183260780190 ,.61470936006624996937] 
dist 161=[-2.3046333568525290373 ,.77039263181261403578] 
dist 162=[-2.3342662352649841096 ,.91345056838664637367] 
dist 163=[-2.3378549045475727628 ,1.0190254642448334664 ] 
dist 164=[-2.3229416175696682582 ,1.1170537600107650534 ] 
dist 165=[-2.3103981515300022304 ,1.2300152036907826008 ] 
dist 166=[-2.2762066949958201838 ,1.3325098059323840061 ] 
dist 167=[-2.2586865309208972943 ,1.3887954758305159717 ] 
dist 168=[.29070063604104354849,1.4218494341076675936 ] 
dist 169=[.38748600171932206098,1.4316940856376439797 ] 
dist 170=[.40574048172429241486,1.4327460743449449778 ] 
dist 171=[.24869766264470039892,1.4307341814754967234 ] 
dist 172=[.05017600379508100073,1.6082495446799345505 ] 
dist 173=[-.25608638033816664683,1.7682515875549925223 ] 
dist 174=[-.56348935750371380778,1.9044300145652002420 ] 
dist 175=[-.76655977670099668109,2.0431404213741714009 ] 
dist 176=[-.93150523890978960655,2.1650765789457218507 ] 
dist 177=[-1.0868626623921596912 ,2.2343578803806998644 ] 
dist 178=[-1.2236165042753626258 ,2.2781370252854444327 ] 
dist 179=[-1.3143693042098562886 ,2.2983684262760559413 ] 
dist 180=[-1.3885419957731313314 ,2.3033465076013332394 ] 
dist 181=[-1.4591729478681903090 ,2.2994288813196450241 ] 
dist 182=[-1.5188208896266584115 ,2.2652686712167767847 ] 
dist 183=[-1.5491924125617414959 ,2.2544018142849123129 ] 
dist 184=[-1.5638478169101973091 ,1.1735178343107312507 ] 
dist 185=[-1.5645384548123805618 ,1.0675185413108594860 ] 
dist 186=[-1.5496207870340628708 ,.82548260117081695962] 
dist 187=[-1.5408313503263687906 ,.77341078599410209201] 
dist 188=[-1.5126199651165693017 ,.46402440828299371996] 
dist 189=[-1.4984782276745587298 ,.40750773896807894072] 
dist 190=[-1.5301553784696788450 ,.34321392008190706013] 
dist 191=[-1.7271750671312304775 ,.57209632040314924608] 
dist 192=[-1.9071304481531286843 ,.76037192717956163432] 
dist 193=[-2.0081044082369158477 ,.94167743889734398997] 
dist 194=[-2.0702699086454526338 ,1.1039833792304958303 ] 
dist 195=[-2.0954538651756388873 ,1.2164870850322949929 ] 
dist 196=[-2.1065357397120338140 ,1.3137280956029920813 ] 
dist 197=[-2.1124609434713352182 ,1.4151651118378505162 ] 
dist 198=[-2.1157265153936876540 ,1.5047799073547391548 ] 
dist 199=[-2.1162015554050004991 ,1.5548729010803768038 ] 
dist 200=[.09472085012362934083,1.5854645795305248884 ] 
dist 201=[.1291711198121547832 ,1.5973064827662111926 ] 
dist 202=[.18494863981689857312,1.5989288374091104755 ] 
dist 203=[.19771912225834950024,1.5944402332535196467 ] 
dist 204=[.18408875456784636415,1.5747072323621791078 ] 
dist 205=[.06218734784140145655,1.6204184664166064557 ] 
dist 206=[-.16303264231266306485,1.8065234372496811184 ] 
dist 207=[-.38097966081901067933,2.0372670089825441743 ] 
dist 208=[-.56363138781803368527,2.2552723274407698796 ] 
dist 209=[-.74511708938549230565,2.3905760643996429532 ] 
dist 210=[-.91131805866061447172,2.4908199071376116848 ] 
dist 211=[-1.0330129767877564507 ,2.5690033954434195085 ] 
dist 212=[-1.1450574210380339185 ,2.6267507786442900855 ] 
dist 213=[-1.2727714805991045929 ,2.6454937019169605398 ] 
dist 214=[-1.3885185043483016791 ,2.6462284380997663326 ] 
dist 215=[-1.4528373958347955943 ,2.6365292247055817472 ] 
dist 216=[-1.6793229972784013226 ,2.5426455245694405791 ] 
dist 217=[-2.0397390146398402193 ,2.5170528165149067120 ] 
dist 218=[-2.3238424034127977080 ,2.4386585380435232550 ] 
dist 219=[-2.5768965759208918347 ,2.4134013092459291996 ] 
dist 220=[-2.7897334005090870154 ,2.2205579148935258853 ] 
dist 221=[-2.9134465955759727841 ,2.1740524532446842979 ] 
dist 222=[-2.9952106555960078680 ,2.0997473866997059141 ] 
dist 223=[-3.0407507724602443320 ,2.0754465033873642373 ] 
dist 224=[-3.0670733450288300398 ,1.4984257464226928257 ] 
dist 225=[-3.0721962089581804029 ,1.4175812229879479458 ] 
dist 226=[-3.0627577521482100654 ,1.2330321699175446590 ] 
dist 227=[-3.0515378259891027037 ,1.2080299047781684242 ] 
dist 228=[-2.9874670506944792541 ,1.3506518473722735716 ] 
dist 229=[-2.9661069538822534341 ,1.5292298469322192271 ] 
dist 230=[-2.8810841714375648521 ,1.6988107945060268088 ] 
dist 231=[-2.8636697738842488162 ,1.8055517310772786161 ] 
dist 232=[-.25905740184152844231,1.8863941066059477560 ] 
dist 233=[-.34067565715442720237,1.9526893974333888737 ] 
dist 234=[-.428680443416844545  ,2.0043281658424620398 ] 
dist 235=[-.51565502485631020549,2.0267190876416923061 ] 
dist 236=[-.61827520181261137515,2.0320575502643976007 ] 
dist 237=[-.9278755798796821322 ,2.0296989484717723239 ] 
dist 238=[-1.3522041184323515246 ,1.9883948104713768104 ] 
dist 239=[-1.6257030896827663014 ,1.9738422090566290287 ] 
dist 240=[-1.8403016413805366816 ,1.9244727062882574817 ] 
dist 241=[-2.0297303123136674875 ,1.9070645041469217168 ] 
dist 242=[-2.1878151148090002848 ,1.7690360934702885743 ] 
dist 243=[-2.2774116613344822203 ,1.7347004729761055427 ] 
dist 244=[-2.3337399150394395981 ,1.6816353853637358530 ] 
dist 245=[-2.3591479446489980203 ,1.6632246156762407765 ] 
dist 246=[-2.3700044894631208010 ,1.2140525038401748717 ] 
dist 247=[-2.3683001879854572516 ,1.1508868658667235490 ] 
dist 248=[-2.3570745790300267329 ,1.0086604503800091622 ] 
dist 249=[-2.3471336337641533932 ,.9700676079033767796 ] 
dist 250=[-2.2948063888597240244 ,.78576163343677506106] 
dist 251=[-2.2773366164558234354 ,.74962094912838000803] 
dist 252=[-2.2130014805225024254 ,.66620541311202859368] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 2, 2, 0, 1, 1, 2] 
dist 0=[75.253026147816764855  ,75.253026147816764855  ] 
dist 1=[74.746838628943988956  ,75.326767983416383858  ] 
dist 2=[73.827171016682208113  ,75.253026147816764855  ] 
dist 3=[72.103397867319498136  ,75.028136800754066507  ] 
dist 4=[69.926173086883568095  ,74.419797640604338830  ] 
dist 5=[67.196623917753713013  ,74.118900158196398251  ] 
dist 6=[63.539785492824990363  ,72.062731019732221066  ] 
dist 7=[57.661093477620348877  ,71.453672345916815581  ] 
dist 8=[51.648705531791335165  ,71.130948559605297040  ] 
dist 9=[47.457969157742382832  ,70.574749159558316332  ] 
dist 10=[43.797856592171803405  ,70.307521962890834910  ] 
dist 11=[39.902898851689616864  ,70.092372645674582648  ] 
dist 12=[36.151894844256797711  ,69.891630424744626697  ] 
dist 13=[33.065816511072915336  ,69.485431746949697577  ] 
dist 14=[29.872093706806067364  ,33.585327873050512836  ] 
dist 15=[25.175096098301460886  ,33.293319360899303054  ] 
dist 16=[20.228219097474306383  ,25.293042809288458424  ] 
dist 17=[15.583158805624172542  ,22.408152263734207366  ] 
dist 18=[11.954782606375762251  ,17.758950480443388411  ] 
dist 19=[8.3741785816724073416 ,17.080482468816101617  ] 
dist 20=[3.9200270430701119842 ,14.435359447821937331  ] 
dist 21=[-.32085407390983069024,13.940232510196111246  ] 
dist 22=[-3.0500641061538561946 ,13.197098926293597475  ] 
dist 23=[-5.3795968067050055253 ,13.021495213364215324  ] 
dist 24=[-7.3128432111751004283 ,1.8196490027937642876 ] 
dist 25=[-8.9174558645646657022 ,.89754850014943634968] 
dist 26=[-10.210566214317058416  ,-1.0535230344124111667 ] 
dist 27=[-10.900563374956868884  ,-1.4203020444790320794 ] 
dist 28=[-11.281928299112565394  ,-3.3217821515525440470 ] 
dist 29=[-11.357991382483591201  ,-3.6294183172713755140 ] 
dist 30=[-7.7661922050667862796 ,-4.1989135177660868304 ] 
dist 31=[-8.0035219493181179850 ,-4.3129964914001253589 ] 
dist 32=[-8.8787595291321741702 ,-4.5409054726445604244 ] 
dist 33=[-9.4126504354820749594 ,-4.4659834616199264454 ] 
dist 34=[-9.8040865882091688214 ,-4.2496035020363727455 ] 
dist 35=[-10.109452648844086707  ,-3.7901724116538607838 ] 
dist 36=[-10.340474206207802973  ,-3.2148685153410798396 ] 
dist 37=[-10.434518218053596229  ,-2.4602778849472638929 ] 
dist 38=[-10.463043826937099470  ,-1.6524128301757921978 ] 
dist 39=[-10.447318407026272162  ,-.26376899948571858938] 
dist 40=[-4.4977645161815381228 ,1.3655402292495766026 ] 
dist 41=[-4.1732213505963278633 ,2.4533064255182178048 ] 
dist 42=[-4.1081723713090200183 ,3.3507059133854808954 ] 
dist 43=[-3.9311490193305538826 ,4.2209281521312925882 ] 
dist 44=[-3.9035913536022115697 ,5.0057360547825520897 ] 
dist 45=[-3.5556800456295389007 ,5.5624806931038053173 ] 
dist 46=[-3.4887186838146484244 ,6.0583528594636715756 ] 
dist 47=[-3.3477929628699311132 ,6.6004451352667129926 ] 
dist 48=[-3.3032401722800134556 ,7.0814905358496522969 ] 
dist 49=[-3.0990500998900279104 ,7.3338397681087770061 ] 
dist 50=[-3.0528880806745436683 ,7.4724966953031720685 ] 
dist 51=[-2.9251877999768583462 ,7.5004665219686167904 ] 
dist 52=[-2.8930856404693378769 ,7.4403283077836595423 ] 
dist 53=[-2.4791556372939940351 ,7.4149969912191692088 ] 
dist 54=[-2.4098396824482539218 ,7.3910333127548256100 ] 
dist 55=[-2.2116925495741895328 ,7.3630005295630318271 ] 
dist 56=[-2.2179368852613356568 ,6.4978530607211797442 ] 
dist 57=[-3.2633223899715372205 ,6.2497911668348924365 ] 
dist 58=[-4.1180936958693330521 ,6.1859027343110079725 ] 
dist 59=[-4.9328064130489965967 ,5.9859776060750730390 ] 
dist 60=[-5.6567402898368446067 ,5.9358672142145971423 ] 
dist 61=[-6.1495023667743857938 ,3.9569418196583866574 ] 
dist 62=[-6.5660596754904145350 ,3.1914920207643350244 ] 
dist 63=[-6.9861194083828965477 ,3.1111464117099136056 ] 
dist 64=[-7.3498756611804401625 ,1.8032303291872071669 ] 
dist 65=[-7.5418850547370748779 ,1.6215537123737943250 ] 
dist 66=[-7.6445112213722815509 ,1.2019669564021173466 ] 
dist 67=[-7.6576382801168740392 ,1.1188412086538308268 ] 
dist 68=[-7.6164826076055063362 ,.57124068571162931771] 
dist 69=[-7.5767871842294063561 ,.47193802938508125704] 
dist 70=[-7.4684030465737694480 ,.28653944216863284445] 
dist 71=[-7.4121792562371452130 ,.24301375230368031964] 
dist 72=[-6.8100116026210710982 ,1.5807421407323655531 ] 
dist 73=[-6.8315539222867719281 ,2.6620944925328336080 ] 
dist 74=[-6.8179593776815665651 ,3.5407865745207207042 ] 
dist 75=[-6.7466624654568003725 ,4.3689843005957485217 ] 
dist 76=[-6.6984886783581151348 ,5.0984119725130941872 ] 
dist 77=[-3.7979435972036160589 ,5.5832081459916170395 ] 
dist 78=[-2.3418456600131231851 ,5.9802618095426415962 ] 
dist 79=[-1.5301968483799974565 ,6.3597738918520337463 ] 
dist 80=[-1.3597204621089323419 ,6.6889239554485045593 ] 
dist 81=[-.38127510588874984764,6.8851300146674718472 ] 
dist 82=[-.20919055749800733524,7.0209877713418401481 ] 
dist 83=[.14832510280159763362,7.1094561246726757524 ] 
dist 84=[.2394962062484965448 ,7.1604078012436336344 ] 
dist 85=[.93040785946889072992,7.1538003211014162945 ] 
dist 86=[1.0456514571484242701 ,7.1042559629539674883 ] 
dist 87=[1.1249204528800546263 ,7.0617126182786210284 ] 
dist 88=[.67336385843219585477,5.9646172172033519482 ] 
dist 89=[-.26176868224157935849,6.0831493323508314350 ] 
dist 90=[-1.0626874715013633652 ,6.1274048106144706012 ] 
dist 91=[-1.8865532220332030307 ,6.1279207671243070196 ] 
dist 92=[-2.6591779735762996177 ,6.1145291732573299419 ] 
dist 93=[-3.2557443019832056458 ,3.3744549080149060766 ] 
dist 94=[-3.8358517686028184961 ,-.19386002809016969598] 
dist 95=[-4.5428378975466910947 ,-.2889042033154814389 ] 
dist 96=[-5.2047548493342419405 ,-1.0185263890006047813 ] 
dist 97=[-5.6051222297871729007 ,-1.0841394477341997099 ] 
dist 98=[-5.8894176813938196846 ,-1.2085193997838658868 ] 
dist 99=[-6.0884281785762414644 ,-1.1049074300473833354 ] 
dist 100=[-6.2296919339536718766 ,-.95451523110059208406] 
dist 101=[-6.2836874020092751208 ,-.75007279665858522789] 
dist 102=[-6.2905127850110187322 ,-.46749737923826075737] 
dist 103=[-6.2759168058859805756 ,-.00550496456272389311] 
dist 104=[-2.5475284290700587376 ,.54159530340346648518] 
dist 105=[-2.5375540963994996232 ,.91075761419060628224] 
dist 106=[-2.5274972456869285346 ,1.2157301364619877509 ] 
dist 107=[-2.5133125819382635816 ,1.5115726023167238883 ] 
dist 108=[-2.4992882245733940539 ,1.7778515038559750190 ] 
dist 109=[-2.2730838553647309333 ,1.9649229448341200495 ] 
dist 110=[-1.6518628420241258812 ,2.1292551377161994336 ] 
dist 111=[-1.4418506485338886640 ,2.3048490735573200805 ] 
dist 112=[-1.3938493473349282711 ,2.4608141873817657179 ] 
dist 113=[-1.1694969829549040784 ,2.5468645258913035963 ] 
dist 114=[-1.0363126091737253053 ,2.5979320443357111526 ] 
dist 115=[-.92428287150015209329,2.6143803321585616863 ] 
dist 116=[-.89502653280452620317,2.6146598499651805490 ] 
dist 117=[-.70447677862368674809,2.6046258381717207623 ] 
dist 118=[-.41750896917866135134,2.5794550091976177722 ] 
dist 119=[-.29205897719232973314,2.5642628504109314913 ] 
dist 120=[-.47517647866841793508,2.3253987013999160953 ] 
dist 121=[-.7913102626781764835 ,2.3354434105399714487 ] 
dist 122=[-1.0532045006088484706 ,2.3317598928339290108 ] 
dist 123=[-1.3084663376679410005 ,2.3206315588405034530 ] 
dist 124=[-1.5390204424164373696 ,2.3019560614663156696 ] 
dist 125=[-1.7023783075543360763 ,2.2905846327834460422 ] 
dist 126=[-1.8473217913599795749 ,.71816915115875564236] 
dist 127=[-2.0044378821603227653 ,.6914903095590833197 ] 
dist 128=[-2.1442956948398148433 ,.33338857552843247896] 
dist 129=[-2.2204117987523075265 ,.28163414324987448445] 
dist 130=[-2.2641936601249799515 ,.17561202075164966869] 
dist 131=[-2.2750999559571895395 ,.14826000745600475252] 
dist 132=[-2.2724607890366060933 ,.05108270727078035174] 
dist 133=[-2.2622222744847693878 ,.03077384036659826302] 
dist 134=[-2.2444870655405628524 ,.00463683589543888655] 
dist 135=[-2.2334730074523024923 ,-.00056815917299680573] 
dist 136=[-2.0994980428153074079 ,.4701462215887312523 ] 
dist 137=[-2.1244888109693590498 ,.78129006952310356019] 
dist 138=[-2.1380389047179845868 ,1.0342289220335340917 ] 
dist 139=[-2.1358202551654930491 ,1.2728172837309790729 ] 
dist 140=[-2.1183890351365364960 ,1.4830755769997701539 ] 
dist 141=[-2.1045193925679228899 ,1.6230317648323278770 ] 
dist 142=[-.85688136949618726028,1.7378867643621904103 ] 
dist 143=[-.74441854331380956901,1.8480394266973017711 ] 
dist 144=[-.4910738599301687532 ,1.9436013313322729907 ] 
dist 145=[-.43800427005419038697,2.0002671799001585807 ] 
dist 146=[-.13014372337835527189,2.0391292706468114480 ] 
dist 147=[-.07584589059802984956,2.0636883248485069160 ] 
dist 148=[.03612299668584273123,2.0770902505073355323 ] 
dist 149=[.06452656584717010783,2.0750109779013056270 ] 
dist 150=[.28938948560203913036,2.0582227225372627826 ] 
dist 151=[.32636788038972908213,2.0447757362599426887 ] 
dist 152=[.16883823181765007993,1.7797220438717142831 ] 
dist 153=[-.10346163752068883708,1.8364460972301181717 ] 
dist 154=[-.33640627509517479186,1.8761732194618134794 ] 
dist 155=[-.57558933148041445772,1.8912945331639504669 ] 
dist 156=[-.79962385367950722471,1.8924328963872617908 ] 
dist 157=[-.97215486128846719836,1.8882584330503543298 ] 
dist 158=[-1.1394958810117439476 ,-.03419886073700325566] 
dist 159=[-1.3428322895348112104 ,-.06178561307729061688] 
dist 160=[-1.5329007616163841069 ,-.28066046061585083047] 
dist 161=[-1.6473281352723008025 ,-.3166294494079959339 ] 
dist 162=[-1.7279303020418918577 ,-.34373167175594718471] 
dist 163=[-1.7831010105537527630 ,-.3304942414228229125 ] 
dist 164=[-1.8217531569637175717 ,-.29807076198224123497] 
dist 165=[-1.8364779151968977745 ,-.23982835408883774355] 
dist 166=[-1.8376079136181376155 ,-.15169307443809034508] 
dist 167=[-1.8335601738698138845 ,-5.28977707235597520000e-05] 
dist 168=[-1.8446582583590861598 ,.31756171671446319179] 
dist 169=[-1.8815842971046066667 ,.53512045680800252588] 
dist 170=[-1.9035968179139982738 ,.72041613337572862236] 
dist 171=[-1.9054002375736679455 ,.90936637371212909254] 
dist 172=[-1.8954213495754516352 ,1.0855313276122821907 ] 
dist 173=[-1.8839064815927996009 ,1.2198382014565376370 ] 
dist 174=[-1.6973728996691757031 ,1.3488121793505702987 ] 
dist 175=[-1.6641340941479018302 ,1.5037090940941924949 ] 
dist 176=[-1.5764976689550454634 ,1.6475836222177245810 ] 
dist 177=[-1.5527048686561761662 ,1.7325993909642682804 ] 
dist 178=[-1.3861841326653642592 ,1.8441926223349663260 ] 
dist 179=[-1.3491294572565355143 ,1.9479227622382940404 ] 
dist 180=[-1.2846097548047800473 ,2.0250161673067562310 ] 
dist 181=[-1.2666347974388018131 ,2.0855897036166089315 ] 
dist 182=[-.87535278511365493605,2.1319228793179389782 ] 
dist 183=[-.82122128965093744139,2.1522245090513913229 ] 
dist 184=[-.97652106998673192536,2.1572881058771618303 ] 
dist 185=[-1.2340519712368885112 ,2.1532471084017925012 ] 
dist 186=[-1.4398985146639280391 ,2.1182959986506469047 ] 
dist 187=[-1.6281742016799217775 ,2.1050433088529031565 ] 
dist 188=[-1.7900808866209397338 ,2.0506728574434449272 ] 
dist 189=[-1.8907656130754927342 ,2.0378693035530316135 ] 
dist 190=[-1.9655949041254300832 ,1.2471360661265026684 ] 
dist 191=[-2.0243879182486270685 ,1.2296864902606091375 ] 
dist 192=[-2.0693587707715134365 ,.84980908530389815172] 
dist 193=[-2.0890641082438033213 ,.79725604019773589292] 
dist 194=[-2.0939798981144013460 ,.67165012818965050466] 
dist 195=[-2.0900566006542414724 ,.64664057238608221931] 
dist 196=[-2.0561365811419379480 ,.46589307939446436076] 
dist 197=[-2.0432743737670306709 ,.43148977281966864619] 
dist 198=[-1.9904946151610095902 ,.37190127521844974263] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 1, 2, 0, 1, 1, 2] 
dist 0=[67.955446413430292244  ,67.955446413430292244  ] 
dist 1=[67.462470617719507068  ,68.267194997610566897  ] 
dist 2=[66.741546042388203181  ,68.427387830709066506  ] 
dist 3=[65.519277700434986228  ,68.383968075018269129  ] 
dist 4=[63.943087702605222409  ,68.099757080441372618  ] 
dist 5=[61.809045638516290145  ,67.888392997989771011  ] 
dist 6=[58.854012619571447026  ,66.483599962043138195  ] 
dist 7=[54.000188813935146578  ,66.062913915037279398  ] 
dist 8=[49.003469361683508080  ,65.436646684187762066  ] 
dist 9=[45.477974972106100331  ,65.186619327629522936  ] 
dist 10=[42.350380429640522004  ,64.361769314612023699  ] 
dist 11=[38.942242866144469367  ,64.057465809901813640  ] 
dist 12=[35.608812564390753402  ,63.465129705070955932  ] 
dist 13=[29.306639958906866121  ,63.242038333633481869  ] 
dist 14=[24.216072435231203817  ,37.924621604942245337  ] 
dist 15=[19.930463657884370269  ,35.743097916190405045  ] 
dist 16=[15.617674850255151719  ,30.578320665601937839  ] 
dist 17=[11.611450880413166928  ,29.783048391427146405  ] 
dist 18=[8.5490343836030529842 ,22.724742650902642591  ] 
dist 19=[5.5860481463633275856 ,21.458817158932354598  ] 
dist 20=[1.9755785796489862894 ,19.753508986558881478  ] 
dist 21=[-1.4383063743724840637 ,19.317776089937790639  ] 
dist 22=[-3.6170950424815017672 ,14.060360127375585243  ] 
dist 23=[-5.3162432188317253284 ,13.889348270764655673  ] 
dist 24=[-6.8159158243606916627 ,6.8060304643137543918 ] 
dist 25=[-8.0852839852053785316 ,6.4100265370383625343 ] 
dist 26=[-8.8660433797477349704 ,3.6941713909472375435 ] 
dist 27=[-9.4496461319619695309 ,3.2595521215237082605 ] 
dist 28=[-9.9343814657837934851 ,2.4723804680645618714 ] 
dist 29=[-10.688446769196309994  ,2.3203731424957025643 ] 
dist 30=[-11.672823742346285963  ,-1.4067982078886742852 ] 
dist 31=[-12.730298770550856472  ,-1.7916422699385080749 ] 
dist 32=[-13.663181212371729912  ,-2.4945468525862350030 ] 
dist 33=[-14.150024463497042969  ,-2.6427687788695993584 ] 
dist 34=[-14.419469000583788280  ,-2.9906442974229406623 ] 
dist 35=[-14.483557106092461612  ,-2.9908034182488970414 ] 
dist 36=[-14.358034110650823327  ,-2.8637973139194046787 ] 
dist 37=[-14.320733677469859127  ,-2.5373131339598525364 ] 
dist 38=[-14.294811783657946748  ,-2.0936634392298699935 ] 
dist 39=[-14.278764976912221361  ,.86435589803676620068] 
dist 40=[-12.695561986735693225  ,3.8342396451987790810 ] 
dist 41=[-12.663802303453773334  ,5.7931905620128231230 ] 
dist 42=[-12.136273677093231231  ,7.3823178449969848099 ] 
dist 43=[-11.995917371628980536  ,8.8772127330873715737 ] 
dist 44=[-11.854102452375047936  ,10.193386617432275327  ] 
dist 45=[-11.772822212803235890  ,11.069711277391230290  ] 
dist 46=[-7.0019287690244854271 ,11.790082538600643942  ] 
dist 47=[-6.8631867184263891782 ,12.484276628929524619  ] 
dist 48=[-4.1527792305433122355 ,13.083793746370671203  ] 
dist 49=[-3.7919891944959113392 ,13.426470156397206242  ] 
dist 50=[-2.9130971573081916294 ,13.646124844061986101  ] 
dist 51=[-2.7792827339749279359 ,13.754713457617149778  ] 
dist 52=[-1.4983619944246656425 ,13.783036904797462337  ] 
dist 53=[-1.2635611815414958508 ,13.762486215601448457  ] 
dist 54=[-.96409809697226989766,13.561252472888122824  ] 
dist 55=[-.89212868754227977004,13.508332200907139213  ] 
dist 56=[1.2274928063375328950 ,6.5961347661066280819 ] 
dist 57=[1.4232940086671935997 ,6.7382411092624215545 ] 
dist 58=[.92861786609048739528,6.7906325216644204821 ] 
dist 59=[.29546261534217873514,6.8016917376191243433 ] 
dist 60=[-.69050461557183597516,6.7853745965175741425 ] 
dist 61=[-1.8665290931622460204 ,5.4028706813555843310 ] 
dist 62=[-2.6542519314011226055 ,3.0977324826958050874 ] 
dist 63=[-3.3041770342003149606 ,3.2356677084497329869 ] 
dist 64=[-3.9343864990495959234 ,3.3506454436910937954 ] 
dist 65=[-4.5024531579237933463 ,3.4146456087316693070 ] 
dist 66=[-4.9044967145963691898 ,3.4534391241244567384 ] 
dist 67=[-5.2613508579161750055 ,3.4678728926774643822 ] 
dist 68=[-5.6491795476769917784 ,3.4655440782352541241 ] 
dist 69=[-5.9901710558358151682 ,3.4556650730722827343 ] 
dist 70=[-6.1601916600872446347 ,3.4043711456074107001 ] 
dist 71=[-6.2501161320820912102 ,3.3819210752513178088 ] 
dist 72=[-6.2715081326357992292 ,1.4214393735779308081 ] 
dist 73=[-6.1520833285716245665 ,1.2407374918394530728 ] 
dist 74=[-6.1202333048027926689 ,.83542037181475989174] 
dist 75=[-6.1004069336179408946 ,.74903501345625914779] 
dist 76=[-6.0919163804828658996 ,.9016955463217469476 ] 
dist 77=[-5.1744448703775814706 ,2.2553154799449275091 ] 
dist 78=[-4.3813764946783972446 ,3.1511014419976014176 ] 
dist 79=[-3.9224054078822516846 ,3.8807694302268603372 ] 
dist 80=[-3.8125913482472629223 ,4.5718651203558169597 ] 
dist 81=[-3.1397207490761839213 ,5.1831949398989260023 ] 
dist 82=[-3.0932229559389286026 ,5.5947409305117267897 ] 
dist 83=[-3.1673530568233541412 ,5.9378037381329738624 ] 
dist 84=[-3.2155967387808332722 ,6.2760229101233770853 ] 
dist 85=[-3.2334882129143039883 ,6.5657228020345487770 ] 
dist 86=[-3.2325421123413227551 ,6.7152688418499862692 ] 
dist 87=[-3.2239083633228848559 ,6.7905356362926799993 ] 
dist 88=[-1.0844728501548173066 ,6.7985448738649121986 ] 
dist 89=[-.64706579834372825876,6.7418905498712530847 ] 
dist 90=[-.56670894405767406089,6.7036767717633183813 ] 
dist 91=[-.40886186917619476531,6.5998079541771014824 ] 
dist 92=[-.36909654284878146814,6.5479804315463345795 ] 
dist 93=[-.96885212447191422435,3.9258261452288583797 ] 
dist 94=[-1.5713873144174281817 ,2.8454873560612863578 ] 
dist 95=[-2.0593606605734633794 ,2.8386179805601062846 ] 
dist 96=[-2.5166484808967586337 ,3.1115685282901065484 ] 
dist 97=[-2.9176904459822406677 ,3.2746974506789874292 ] 
dist 98=[-3.1813473505700309534 ,3.3881734343228455548 ] 
dist 99=[-3.3941555634047838810 ,3.4630954750144947783 ] 
dist 100=[-3.6014338368363403910 ,3.5097042847525134921 ] 
dist 101=[-3.8412355927801020568 ,3.5167114997537962290 ] 
dist 102=[-4.0501122774275261586 ,3.4959359910008945981 ] 
dist 103=[-4.1604324029449224260 ,3.4831935863730475536 ] 
dist 104=[-4.2194208262557180849 ,3.1949766837773488391 ] 
dist 105=[-4.2281630089814066819 ,3.1404360290234202844 ] 
dist 106=[-4.2044783837435883329 ,2.9931561047559112514 ] 
dist 107=[-4.1815999909745966915 ,2.9519673123336310364 ] 
dist 108=[-4.1276547919378088388 ,2.6580874279857297038 ] 
dist 109=[-4.1000417827243534762 ,2.5915380881241360639 ] 
dist 110=[-1.3515272779682630800 ,2.4780340914292874501 ] 
dist 111=[-1.4141454846956249018 ,2.4451841128009753106 ] 
dist 112=[-1.4663234062812617855 ,2.0020926842854504693 ] 
dist 113=[-1.4923307358488315022 ,2.4663823787865374881 ] 
dist 114=[-1.5040850692818260534 ,2.8782013435525346950 ] 
dist 115=[-1.5040830523632582716 ,3.1570586244188134759 ] 
dist 116=[-1.4871380827881965441 ,3.3911282606060078594 ] 
dist 117=[-1.4783865199228110453 ,3.6243305487900087592 ] 
dist 118=[-1.4494128811109014308 ,3.8282472941663732158 ] 
dist 119=[-1.4350867871942742589 ,3.9455228342859109134 ] 
dist 120=[-.06948183235064244074,4.0214656368940944450 ] 
dist 121=[-.11901515030895273483,4.0605411565365190323 ] 
dist 122=[-.16026099093421342647,4.0728092571979840679 ] 
dist 123=[-.20080469690658594666,4.0683291619259486205 ] 
dist 124=[-.23764478782270104726,4.0047807923669416205 ] 
dist 125=[-.26412055040935423724,3.9927576991174414296 ] 
dist 126=[-.28799432210370977543,1.9207848529430812253 ] 
dist 127=[-.55388914131854592057,1.7238882645062751946 ] 
dist 128=[-1.0150875828396270567 ,1.2766659686209038209 ] 
dist 129=[-1.4815492528605171482 ,1.1813870899427233023 ] 
dist 130=[-1.9140420314416128825 ,.6205791026783469786 ] 
dist 131=[-2.2397697482992113319 ,.51943577634020577072] 
dist 132=[-2.5487262577417649408 ,.3141649165499973822 ] 
dist 133=[-2.9143346087925887814 ,.26175580217077112396] 
dist 134=[-3.2511712579840165854 ,-.05836416139457942740] 
dist 135=[-3.4453835089444887222 ,.01650350867207899763] 
dist 136=[-3.5717605306736966433 ,.09193964739385348527] 
dist 137=[-3.6380631769009291834 ,.14232774788181548598] 
dist 138=[-3.6768680043954673840 ,.18386957823127910488] 
dist 139=[-3.6935805399437593269 ,.22402617514287752528] 
dist 140=[-3.6972649148003886207 ,.26007438077154855866] 
dist 141=[-3.6841112103527365422 ,.28523161463409640562] 
dist 142=[-.13431492727905167338,.69150177173743251424] 
dist 143=[-.13019509233181637247,1.1676464081269751743 ] 
dist 144=[-.07016360839145540141,1.5767948305201470511 ] 
dist 145=[-.06162380606073583057,1.9998085745702561724 ] 
dist 146=[-.04312546545012062158,2.3978532397017236361 ] 
dist 147=[-.03850856779272407404,2.7074228297544515384 ] 
dist 148=[-.01821974752920275364,3.0105652700696097129 ] 
dist 149=[-.01450884650199486077,3.3829779719318317969 ] 
dist 150=[-.00619762546126262918,3.7331385212283461729 ] 
dist 151=[-.00453531174965460637,3.9475373980960509566 ] 
dist 152=[-.07815855896940141235,4.1029290449567158712 ] 
dist 153=[-.13318982945075281509,4.2177634359344569947 ] 
dist 154=[-.18138546674236018025,4.2973423100016530197 ] 
dist 155=[-.33194453085600640253,4.3135978952629034632 ] 
dist 156=[-.77933327823824619381,4.3039574369555420762 ] 
dist 157=[-1.6953893584537925100 ,4.2919547455813754003 ] 
dist 158=[-2.6092908010198736153 ,4.0652249777360828992 ] 
dist 159=[-3.2019323433501333223 ,4.0136135186248926057 ] 
dist 160=[-3.6710241174654370941 ,3.8649139421626283961 ] 
dist 161=[-4.0921985745953301697 ,3.8199419706730251371 ] 
dist 162=[-4.4488533102346257662 ,3.4866435652934805458 ] 
dist 163=[-4.6606349656554602589 ,3.4083192928352585468 ] 
dist 164=[-4.8062419012279691330 ,3.2796437076287176651 ] 
dist 165=[-4.8989862813370002314 ,3.2396347687034307650 ] 
dist 166=[-4.9600691711037201492 ,2.3131570146622235270 ] 
dist 167=[-4.9794073622974999069 ,2.1838044033189707345 ] 
dist 168=[-4.9718173934073977901 ,1.8846698086884467989 ] 
dist 169=[-4.9561554332500422051 ,1.8133194420719534891 ] 
dist 170=[-4.8580307091206032001 ,1.4061981005510065120 ] 
dist 171=[-4.8253703021341973225 ,1.3274877518248402217 ] 
dist 172=[-4.6852016644023539600 ,1.1667612549570798424 ] 
dist 173=[-4.6623724835509654822 ,1.1227292371200655305 ] 
dist 174=[-.51529254356758017039,.67979538923744024841] 
dist 175=[-.5102176079837082051 ,.68241327891496847081] 
dist 176=[-.37954053263981183947,.89055058509741602106] 
dist 177=[-.36103515164032329511,1.0910974308584009692 ] 
dist 178=[-.32117928069449321354,1.2658228754178744612 ] 
dist 179=[-.31630107911921623804,1.3785810692356851052 ] 
dist 180=[-.30101878385297172367,1.4672147033004304338 ] 
dist 181=[-.29585587731370045024,1.5457293637537356704 ] 
dist 182=[-.29192660061264181034,1.6125576229607357769 ] 
dist 183=[-.28972215253101966071,1.6545848912335726728 ] 
dist 184=[-.16073432662896362561,1.6863720525682111954 ] 
dist 185=[-.26936753482084922151,1.7123618718650608601 ] 
dist 186=[-.36029711773411043196,1.7325452982880574156 ] 
dist 187=[-.45046519449532795015,1.7411760580467635706 ] 
dist 188=[-.53292221464347951204,1.7429727718349248260 ] 
dist 189=[-.59309945129268057908,1.7364945047409615581 ] 
dist 190=[-.6483054495183349611 ,.4957689254564326548 ] 
dist 191=[-.71093674886918424662,.42639784570569620054] 
dist 192=[-.76724287492589663343,.46919611235038167239] 
dist 193=[-.79722354814772781001,.49504933263885039698] 
dist 194=[-.81409232676876611871,.51336646766482531261] 
dist 195=[-.81810711394223550072,.52611017946515553988] 
dist 196=[-.81298926866235882236,.53434517801697222899] 
dist 197=[-.93011192841205101426,.53597048831122463432] 
dist 198=[-1.1130670822547165545 ,.53274330114114590331] 
dist 199=[-1.2290730027577987339 ,.53190986970612168861] 
dist 200=[-1.3179177295017072757 ,.49420756222226569989] 
dist 201=[-1.3925517274701083951 ,.48663657568737788087] 
dist 202=[-1.4520775033361343720 ,.49146480687100214257] 
dist 203=[-1.4806693522824837372 ,.5815076996042844006 ] 
dist 204=[-1.4932355802921938753 ,.66136332094663386724] 
dist 205=[-1.4936356368838282462 ,.71540957525149711708] 
dist 206=[-.58626422562084491554,.76074336384789542259] 
dist 207=[-.59996641739575284943,.80585293145664032162] 
dist 208=[-.60970649423370007334,.84467655102522624033] 
dist 209=[-.61341625163305695637,.86494144591333771987] 
dist 210=[-.61340875701523902881,.87543456221953973624] 
dist 211=[-.61178248578433835574,.87657623704282640489] 
dist 212=[-.60047243420718713495,.87725699434328403071] 
dist 213=[-.59659664380071898679,.9594458198865070582 ] 
dist 214=[-.579659190965971359  ,1.0331095273624465565 ] 
dist 215=[-.57688076521617318553,1.0723406381142389272 ] 
dist 216=[-.05518484323928297292,1.0942386592119571950 ] 
dist 217=[-.09777283560593251646,1.0990496236944382949 ] 
dist 218=[-.13916250943164746266,1.0928637169810135649 ] 
dist 219=[-.18957177748036817406,1.0900941405436558240 ] 
dist 220=[-.24173895409009714618,1.0873185796513618076 ] 
dist 221=[-.29013931641289202306,1.0838202882025353042 ] 
dist 222=[-.34490724379537485749,.80432014017241012601] 
dist 223=[-.49457025374658281293,.79523504847996762027] 
dist 224=[-.62175478328410805565,.8989395914606414525 ] 
dist 225=[-.74349527542547161149,.9679755817049061536 ] 
dist 226=[-.85198744916402312908,1.0246368929196884213 ] 
dist 227=[-.92633656148055267403,1.0789901658541045945 ] 
dist 228=[-.98969773750618006341,1.1275072256211844784 ] 
dist 229=[-1.0543690897888015959 ,1.1608932233666340923 ] 
dist 230=[-1.1106118807069063306 ,1.1894921280750785026 ] 
dist 231=[-1.1403592391254802847 ,1.2189178542721372924 ] 
dist 232=[-1.1563097923821594879 ,1.2425341347192108422 ] 
dist 233=[-1.1585074148501514191 ,1.2479644769544064291 ] 
dist 234=[-1.2077099376866225605 ,1.2462189933394423465 ] 
dist 235=[-1.3048561240362189519 ,1.2412174721652549274 ] 
dist 236=[-1.3827139879887393452 ,1.1870105411328985291 ] 
dist 237=[-1.4208942452400706987 ,1.1706515204205711337 ] 
dist 238=[-1.4407732802736443849 ,1.1501377929628712239 ] 
dist 239=[-1.4456443179804805871 ,1.1401200617996814325 ] 
dist 240=[-1.4095233487027968790 ,1.0106232345471985097 ] 
dist 241=[-1.3967050963844108418 ,.9901826574975596317 ] 
dist 242=[-1.3774813843178185233 ,.9561658718428223235 ] 
dist 243=[-1.3683433510308544887 ,.94544344237803670009] 
dist 244=[-1.3300701520995537255 ,.90875507284395334143] 
dist 245=[-1.3172329493774467237 ,.89638684093279146039] 
dist 246=[-1.2824326425211943406 ,.8767135956666642182 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 0, 1, 2] 
dist 0=[67.961426066689934632  ,67.961426066689934632  ] 
dist 1=[67.583429902439431045  ,68.180452687909194701  ] 
dist 2=[67.003855118510995953  ,68.151530017405102397  ] 
dist 3=[66.166150474346419708  ,67.946869865870545281  ] 
dist 4=[64.758164529912434337  ,67.768762749107790789  ] 
dist 5=[63.128673271302437126  ,66.553365742290056866  ] 
dist 6=[61.406772679464265609  ,66.171408944635059294  ] 
dist 7=[58.608451658182028918  ,65.571791184682949795  ] 
dist 8=[53.793070762164408426  ,65.338623971687785120  ] 
dist 9=[48.833846393816663495  ,64.457063065432255698  ] 
dist 10=[45.334759754919551851  ,64.158092455572062852  ] 
dist 11=[42.230099601507983232  ,63.477266918328292374  ] 
dist 12=[35.980143066800315170  ,63.208150991651356132  ] 
dist 13=[28.395399249716269962  ,39.269240096607826444  ] 
dist 14=[23.270604297588533122  ,37.172546234220054431  ] 
dist 15=[18.962089336574429432  ,33.382595460118956133  ] 
dist 16=[14.635360323975044267  ,33.105948243770934924  ] 
dist 17=[10.621614527319663864  ,24.428685548217019211  ] 
dist 18=[7.5619432644413990436 ,23.167104343321808975  ] 
dist 19=[4.6095256128650131480 ,21.563629649722953949  ] 
dist 20=[1.0227805420761874731 ,21.211079350358195804  ] 
dist 21=[-2.3637120631109398563 ,15.260050434106016066  ] 
dist 22=[-4.5172682933460159869 ,14.776498224346920160  ] 
dist 23=[-6.1880417529760210223 ,13.976873160663187751  ] 
dist 24=[-7.6477291403998454413 ,13.803006128453928740  ] 
dist 25=[-8.8727197880044944519 ,5.0705047802945490260 ] 
dist 26=[-9.6075390516855382808 ,4.6535241967112175186 ] 
dist 27=[-10.135186152710115473  ,3.8283304040843640349 ] 
dist 28=[-10.535518211134780444  ,3.6678447809213918000 ] 
dist 29=[-10.820774846417587805  ,-2.2330714711993932165 ] 
dist 30=[-10.889036867964665051  ,-2.7685259402494557838 ] 
dist 31=[-11.505127999651763601  ,-3.7961435929262741221 ] 
dist 32=[-12.458529636611414293  ,-4.0258042190949638853 ] 
dist 33=[-13.292696108464657610  ,-4.6603538602000765566 ] 
dist 34=[-13.735880424489921190  ,-4.7346455816317793268 ] 
dist 35=[-13.980672696552337646  ,-4.6410951846511503026 ] 
dist 36=[-14.031075868822191800  ,-4.3015364342068114707 ] 
dist 37=[-13.987257692141607824  ,-3.8794935855368049051 ] 
dist 38=[-13.925328121620668590  ,-3.4563055468689412648 ] 
dist 39=[-13.833182217315374273  ,-2.9550012660750698136 ] 
dist 40=[-13.764853229209293769  ,-.3176618474193868396 ] 
dist 41=[-12.167962511940123132  ,2.5208210288136190965 ] 
dist 42=[-12.123214154739752927  ,4.4079860554004417447 ] 
dist 43=[-11.981192551942669637  ,5.9553583465009248937 ] 
dist 44=[-11.909554727028455522  ,7.4386199753661137246 ] 
dist 45=[-6.2213192767622573316 ,8.7633018343243180578 ] 
dist 46=[-5.9133981661143054930 ,9.6781916924873066841 ] 
dist 47=[-5.3478207524012332404 ,10.466300157887599439  ] 
dist 48=[-5.2074331893854600812 ,11.285326603339157928  ] 
dist 49=[-2.9490555984973532819 ,12.012144534765591504  ] 
dist 50=[-2.6372225855201381925 ,12.432409197353157153  ] 
dist 51=[-1.9372320000075619739 ,12.707771778820515112  ] 
dist 52=[-1.7887178296596598489 ,12.856436081759167149  ] 
dist 53=[-.9385181427045244475 ,12.919372918388499385  ] 
dist 54=[-.7868252963194469237 ,12.910816749452264035  ] 
dist 55=[-.474534127484369739  ,12.757020604997903306  ] 
dist 56=[-.39429136537408800155,12.312793043135743249  ] 
dist 57=[1.3063423744356268257 ,7.5803196542508241750 ] 
dist 58=[.82581485755259558569,7.5409713656182896322 ] 
dist 59=[.20945822350206319088,7.4412180462969732383 ] 
dist 60=[-.7518369372345622328 ,7.3918820489471976941 ] 
dist 61=[-2.0445462226822508041 ,2.5028209243431031859 ] 
dist 62=[-2.9120336163062603211 ,2.0721227148409413507 ] 
dist 63=[-3.6318935751366356755 ,1.1180721055422593968 ] 
dist 64=[-4.3366838130715234133 ,.91747034302079216613] 
dist 65=[-4.9763931721562489654 ,-.18181854762352530381] 
dist 66=[-5.4366493818664102989 ,-.37067812519626988064] 
dist 67=[-5.8528818036160675580 ,-.77800014021633296657] 
dist 68=[-6.3169980831176544648 ,-.8589993841658123428 ] 
dist 69=[-6.7311166779353780674 ,-1.4722058171456257649 ] 
dist 70=[-6.9478987433657311805 ,-1.5755762014151611270 ] 
dist 71=[-7.0649543672736289710 ,-1.5801799338038061039 ] 
dist 72=[-7.0881168582392337080 ,-1.4515270001543001544 ] 
dist 73=[-7.0295137310699690052 ,-1.2477716219895233570 ] 
dist 74=[-7.0541980398317707640 ,-.95278117881382845286] 
dist 75=[-7.0575110534535028960 ,-.1033263335763465524 ] 
dist 76=[-7.0348161031033151987 ,1.4386003159172480497 ] 
dist 77=[-5.5194004187515893663 ,2.9827830186532386201 ] 
dist 78=[-5.3255596800555272643 ,4.0001390042106352491 ] 
dist 79=[-4.8581332192385835131 ,4.8237742439689639742 ] 
dist 80=[-4.7425231108922776101 ,5.5953510567004131088 ] 
dist 81=[-4.0216540500995450362 ,6.2720621539982655240 ] 
dist 82=[-3.8735139665181797415 ,6.7173569197119122070 ] 
dist 83=[-3.5927518598575060493 ,7.0773740767107494559 ] 
dist 84=[-3.5166563799701700413 ,7.4139992276802427721 ] 
dist 85=[-2.2736020147500791649 ,7.6954553013324138234 ] 
dist 86=[-2.0997172642655548729 ,7.8354370421889634928 ] 
dist 87=[-1.6787614685063334738 ,7.8983862883162204573 ] 
dist 88=[-1.6059331293036430174 ,7.9000091263355381030 ] 
dist 89=[-.99260185993078149908,7.8074511776347891245 ] 
dist 90=[-.87808816463350146838,7.7600469381641455741 ] 
dist 91=[-.70913441628062636616,7.6153585307406645607 ] 
dist 92=[-1.8817796586163590125 ,7.5447967867330320613 ] 
dist 93=[-3.3609758078021037037 ,5.9032014583478423625 ] 
dist 94=[-4.3299139746115543688 ,5.7607945941497769868 ] 
dist 95=[-5.1079175550134403662 ,5.3983184596004366952 ] 
dist 96=[-5.8256403683093887777 ,5.3040791449327567875 ] 
dist 97=[-6.4472530674317211664 ,4.6663468931304051521 ] 
dist 98=[-6.8419578938614199387 ,4.5284038703457350125 ] 
dist 99=[-7.1449619637790149306 ,4.2813315776343084453 ] 
dist 100=[-7.4008643242928665399 ,4.2147348692721447156 ] 
dist 101=[-7.6048738829175630377 ,2.8553370376165424564 ] 
dist 102=[-7.7009181678995735141 ,2.6680715034518882449 ] 
dist 103=[-7.7360347615442457190 ,2.2107686283624100033 ] 
dist 104=[-7.7269005356705627859 ,2.1306859479966406134 ] 
dist 105=[-6.8726976704920305678 ,1.4489529270423636388 ] 
dist 106=[-6.7803945378608319475 ,1.3200891155452390398 ] 
dist 107=[-5.9138148323510401635 ,1.1317669758629609208 ] 
dist 108=[-4.4448796472319759085 ,1.0776382870914305890 ] 
dist 109=[-.87288834252603620978,.23152257491954633973] 
dist 110=[-.67555600112329386273,.37496286986299673326] 
dist 111=[-.23688177261736493075,.49065333590970046137] 
dist 112=[-.1472626858677795773 ,.59826209776812932722] 
dist 113=[.35871887736106958506,.77702163047471581622] 
dist 114=[.44456980160407819685,1.0656489993127172193 ] 
dist 115=[.62697856855350269136,1.3552845243303050571 ] 
dist 116=[.66318983265748920058,1.7209010161248701942 ] 
dist 117=[.83457268860806819533,2.0696088809915497272 ] 
dist 118=[.83265412350734400232,2.2918102130647973013 ] 
dist 119=[.81265727049357016926,2.4632767184551698076 ] 
dist 120=[.76283989914556872806,2.6096444306857326588 ] 
dist 121=[.69785772719850764558,2.7281826530271786335 ] 
dist 122=[.58550501386167396707,2.7886597669740921280 ] 
dist 123=[.36144620267380135202,2.8180222186328429944 ] 
dist 124=[-.00556908717220469702,2.8211558755734465157 ] 
dist 125=[-.41051630699840115747,.29502580344033195223] 
dist 126=[-.68283671167550149935,.24067286872274894967] 
dist 127=[-.90937350318092770177,.11934104915390581922] 
dist 128=[-1.1317311439691561876 ,.09435585070972607082] 
dist 129=[-1.3336030633695877864 ,-.04795582447394717788] 
dist 130=[-1.4784408856346077061 ,-.07241401281249834558] 
dist 131=[-1.6088218370779951767 ,-.12386515510636067528] 
dist 132=[-1.7530386783238986705 ,-.13519907685007576948] 
dist 133=[-1.8818984030055688137 ,-.21793952934364502789] 
dist 134=[-1.9510335588999773734 ,-.23168898939873581543] 
dist 135=[-1.9894654193176295873 ,-.23225756507908013238] 
dist 136=[-1.9981298287145277902 ,-.21498027542132432436] 
dist 137=[-1.9909527965591828995 ,-.18762274908657152473] 
dist 138=[-1.9841779717212778556 ,-.14798983981693914032] 
dist 139=[-1.9747710562272228763 ,-.09189300299108646404] 
dist 140=[-1.9635402444185960695 ,.1147059752684650137 ] 
dist 141=[-1.3920547233072027072 ,.53512203904736187695] 
dist 142=[-1.3237774125183245704 ,.8156315556394894081 ] 
dist 143=[-1.1622968603925730385 ,1.0465652105068887582 ] 
dist 144=[-1.1251738668085374955 ,1.2692684084220035585 ] 
dist 145=[-.89280245349426671039,1.4688497996248867884 ] 
dist 146=[-.84718269683027343519,1.6075717423192268183 ] 
dist 147=[-.76000524272279309331,1.7278784173748668779 ] 
dist 148=[-.73720400986378751454,1.8540183270852239397 ] 
dist 149=[-.40387867406332572674,1.9648861009540159490 ] 
dist 150=[-.35647581614524466039,2.0242860831963823702 ] 
dist 151=[-.25311635737402106834,2.0571920140059551178 ] 
dist 152=[-.22778828130967995917,2.0626104575328224366 ] 
dist 153=[-.11171590167047692961,2.0558362958817669164 ] 
dist 154=[-.09083097558038877413,2.0452639165172043916 ] 
dist 155=[-.04212763512665713143,2.0221454263966314022 ] 
dist 156=[-.11303887804783452512,2.0099016558583199398 ] 
dist 157=[-.43608286732114101308,.52113694601896719314] 
dist 158=[-.72482742197305311485,.50319818565615126516] 
dist 159=[-.9604850601564265124 ,.45939682430420547486] 
dist 160=[-1.1843325285654322563 ,.44877165401522037907] 
dist 161=[-1.3826641717139945441 ,.37958387495311665787] 
dist 162=[-1.5165625220803519087 ,.36533592719297660875] 
dist 163=[-1.6285167572634548535 ,.33900768741244708678] 
dist 164=[-1.7393334263205199866 ,.33202883908433526483] 
dist 165=[-1.8361455861557424877 ,.20928154580923398372] 
dist 166=[-1.8922486230176568658 ,.19237067420618592879] 
dist 167=[-1.9291144529063527586 ,.15124396326493740675] 
dist 168=[-1.9492069009637568294 ,.14446574616776559436] 
dist 169=[-1.9569132275062557693 ,.08440461452463604100] 
dist 170=[-1.9548911883541646390 ,.07328791271500734325] 
dist 171=[-1.9278935019896237375 ,.05770222279137523345] 
dist 172=[-1.9198170430094183737 ,.05312721213472489097] 
dist 173=[-.89221337627137494579,.15708006905142938559] 
dist 174=[-.79576196619554234787,.26171508128706516152] 
dist 175=[-.57708141872507525003,.44710290704645911514] 
dist 176=[-.53068556762422131942,.67146969500163527962] 
dist 177=[-.25836251407111270985,.88000918084006858702] 
dist 178=[-.20949321822107037487,1.0379211164028381959 ] 
dist 179=[-.109989166903275326  ,1.1885284358350832448 ] 
dist 180=[-.08462948928926093250,1.3679365160665906576 ] 
dist 181=[.14397026179556106915,1.5338303247055259233 ] 
dist 182=[.18021165846304723394,1.6305415740606456482 ] 
dist 183=[.20753860669980166851,1.6948177878852398333 ] 
dist 184=[.18836423684832457179,1.7313578754741901377 ] 
dist 185=[.16451346554954355927,1.7541398307532532229 ] 
dist 186=[.13635761254730850364,1.7635474152182789937 ] 
dist 187=[.09973945093024707507,1.7649331854033079503 ] 
dist 188=[-4.64566302972866860000e-05,1.7589325830267815873 ] 
dist 189=[-.32397453359699341225,.40295749098321693832] 
dist 190=[-.54711481257744946818,.37130633292234016792] 
dist 191=[-.73851053140737354917,.29857139742881040221] 
dist 192=[-.93583931760365361598,.28272778498532532623] 
dist 193=[-1.1211758834783415098 ,.18760060276092140733] 
dist 194=[-1.2647456102224580345 ,.16996115882966676406] 
dist 195=[-1.4047959796219075444 ,.13488098192461311921] 
dist 196=[-1.5760970524660812268 ,.12585794205374524769] 
dist 197=[-1.7367871895669935827 ,.02592176720180464913] 
dist 198=[-1.8345202443301402621 ,.01087082895630351938] 
dist 199=[-1.9045704845399788117 ,-.01505822306888905058] 
dist 200=[-1.9548591982772953547 ,-.01792964448352042651] 
dist 201=[-1.9884230222248690277 ,-.01367708797565544892] 
dist 202=[-1.9953840388886596450 ,.07173927277299392913] 
dist 203=[-1.9859276379385473960 ,.32904997175270821676] 
dist 204=[-1.9828198518371956116 ,.75312568171665504714] 
dist 205=[-1.8601245264470408048 ,1.1763959617713994582 ] 
dist 206=[-1.8340852343287739370 ,1.4512576358991988181 ] 
dist 207=[-1.7607440436638273348 ,1.6692490512701133168 ] 
dist 208=[-1.7391271295830155510 ,1.8657159160660926252 ] 
dist 209=[-1.5809311487377538893 ,2.0326174434346752271 ] 
dist 210=[-1.5441866071079516966 ,2.1326997863184952570 ] 
dist 211=[-1.4830714266812180198 ,2.2027135643337726386 ] 
dist 212=[-1.4644994291789051346 ,2.2496991068618800099 ] 
dist 213=[-1.0396016593337376240 ,2.2819865742014549816 ] 
dist 214=[-.98038335425115195654,2.2933831807537555026 ] 
dist 215=[-.84256806930957530229,2.2916276863906667460 ] 
dist 216=[-.81075496487619589036,2.2849822903877401877 ] 
dist 217=[-.62110066553989749295,2.2410927854537875106 ] 
dist 218=[-.58455070475767211433,2.2264853595754138944 ] 
dist 219=[-.51209207123465506346,2.1614445102347881903 ] 
dist 220=[-.49281469276349860706,2.1520950174118756828 ] 
dist 221=[-.60685377047732431902,.89516426407208555711] 
dist 222=[-.73039053412432186443,.88834558942742407282] 
dist 223=[-.82737246795494372846,.86553585380064765511] 
dist 224=[-.91306640650856833132,.85758414040107245459] 
dist 225=[-.98464419324551511728,.79481971171043159367] 
dist 226=[-1.0253297165592647861 ,.77926264996936622824] 
dist 227=[-1.0510605938924449652 ,.75512638684940567493] 
dist 228=[-1.0629979845462414373 ,.74680899204778768798] 
dist 229=[-1.0683610405950385523 ,.54449397735850429124] 
dist 230=[-1.0678729135630810294 ,.51605451407181628722] 
dist 231=[-1.0630071656150389944 ,.45192277666828205049] 
dist 232=[-1.0585888190511239692 ,.43464075179670021124] 
dist 233=[-.8954544526486526822 ,.35129686010443389196] 
dist 234=[-.87704780867113665562,.33496762770126916453] 
dist 235=[-.73163968561009751706,.29753433863371275736] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 0, 0, 0, 1, 2] 
dist 0=[56.935146559905188763  ,56.935146559905188763  ] 
dist 1=[56.017611219210858483  ,57.714908621401152388  ] 
dist 2=[53.135571313996925549  ,58.866651933635303226  ] 
dist 3=[50.125703303506726512  ,59.574950318890578203  ] 
dist 4=[47.921929238071956428  ,60.060134746038138713  ] 
dist 5=[45.886906538759343527  ,60.321448294626149487  ] 
dist 6=[43.550425052204775285  ,60.468324660512208532  ] 
dist 7=[41.199039684720028092  ,60.497068495548812116  ] 
dist 8=[39.104415094593392297  ,56.018903996364341050  ] 
dist 9=[36.796396752699795556  ,55.337625210238650784  ] 
dist 10=[33.593101658266999623  ,54.254751424533399186  ] 
dist 11=[30.380646078009243435  ,53.924391508829166079  ] 
dist 12=[28.035925183545978417  ,53.038372071631398620  ] 
dist 13=[25.876815372987736197  ,52.734304106111532205  ] 
dist 14=[23.404966170900334344  ,52.552005511841194679  ] 
dist 15=[20.919078946472009391  ,52.488466512834361469  ] 
dist 16=[18.703666608911712762  ,26.019789426629988435  ] 
dist 17=[16.259780626054432398  ,25.145213426244037263  ] 
dist 18=[12.861403878051674683  ,24.955242506736139659  ] 
dist 19=[9.5022354155058313721 ,18.232028224994118903  ] 
dist 20=[7.2146219241863288521 ,12.578577872005493840  ] 
dist 21=[5.2703099230221974912 ,11.623529952228838999  ] 
dist 22=[3.2812915437452186869 ,9.8243297424253962336 ] 
dist 23=[1.4101062992589934114 ,9.4299462612648713526 ] 
dist 24=[-1.7426776513945520275 ,5.7497539337188208087 ] 
dist 25=[-3.9512972962745210713 ,5.1984227543649978699 ] 
dist 26=[-5.7624635089670009089 ,4.6828725646318940361 ] 
dist 27=[-7.5139017604819944286 ,2.7431295681624272076 ] 
dist 28=[-9.1037854106175557832 ,2.4608575846202957426 ] 
dist 29=[-10.270915903721875434  ,2.0410153613356471029 ] 
dist 30=[-11.361727206130164067  ,1.9385751653626891492 ] 
dist 31=[-12.649080673569158672  ,1.9011299668124036055 ] 
dist 32=[-13.824327610113549930  ,2.0226333228757663826 ] 
dist 33=[-14.467637797135711438  ,2.2666356294585481946 ] 
dist 34=[-14.855564885721419194  ,2.7339092508381772852 ] 
dist 35=[-15.009269252807857244  ,3.2175640859199973663 ] 
dist 36=[-15.068923487790902967  ,3.5271810284530699829 ] 
dist 37=[-15.080116159018973749  ,3.7638893750294996990 ] 
dist 38=[-15.061881009111540632  ,3.9577176950260991493 ] 
dist 39=[-15.003010683697413696  ,4.1058152597733753353 ] 
dist 40=[-12.762036196386822216  ,4.1606006457891946150 ] 
dist 41=[-12.434638227040004469  ,4.1788180353319354059 ] 
dist 42=[-11.795611112817191643  ,4.1815926562429728552 ] 
dist 43=[-11.619360467758402080  ,3.9371394511520675194 ] 
dist 44=[-10.955181248748307434  ,3.8784793239140430523 ] 
dist 45=[-10.789518168523229548  ,3.7453603480842543953 ] 
dist 46=[-10.493854747168703587  ,3.6944843252466962769 ] 
dist 47=[-10.411677344382574057  ,3.4295438593104934357 ] 
dist 48=[-7.1477849638609318980 ,3.3648863931615257413 ] 
dist 49=[-6.9097779972893112169 ,3.1988743230992610444 ] 
dist 50=[-6.8283558030676158827 ,3.5997396422983254797 ] 
dist 51=[.32459551408990520424,4.8292634449932843900 ] 
dist 52=[-.21623215496118626622,6.0891974577707907897 ] 
dist 53=[-.67391415019315242173,7.0355197837367058678 ] 
dist 54=[-1.1345236228659685003 ,7.9341173354296971495 ] 
dist 55=[-1.5590037177864618904 ,9.0037107546126428726 ] 
dist 56=[-1.8727071667120095321 ,9.9997814950632845578 ] 
dist 57=[-2.1638552121318690107 ,10.604939138427062593  ] 
dist 58=[-2.4984631717191101992 ,11.040502551629019650  ] 
dist 59=[-2.8056632033614483723 ,11.359565320950631563  ] 
dist 60=[-2.9875591345993200355 ,11.586667732519293777  ] 
dist 61=[-3.1116796574283149519 ,11.655086375682123471  ] 
dist 62=[-3.1885423499390549787 ,11.661039530959691156  ] 
dist 63=[-3.2365914661672072173 ,11.638713874852886775  ] 
dist 64=[-3.2458583493389095098 ,3.0813943513685097109 ] 
dist 65=[-3.2349386109594437394 ,2.9122129111063242636 ] 
dist 66=[-3.2197690909044424805 ,2.5271972366989658166 ] 
dist 67=[-3.6503322188274703244 ,2.4332982035256982517 ] 
dist 68=[-4.1290206996796050471 ,1.9267292888989822485 ] 
dist 69=[-4.4519139102859555387 ,1.8288945960535100124 ] 
dist 70=[-4.7221435761687057047 ,1.6228075064131113886 ] 
dist 71=[-4.9908128082512626095 ,1.6518729570481999478 ] 
dist 72=[-5.2206286352567501424 ,1.8907433129379179517 ] 
dist 73=[-5.3358697344203415231 ,2.1114473760579152464 ] 
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dist 75=[-5.3972656988690868417 ,2.5934280799427075137 ] 
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dist 77=[-5.2942472809500498221 ,2.8063093268869660464 ] 
dist 78=[-5.2228253864985028949 ,2.8437618057980400427 ] 
dist 79=[-5.1906077553340904690 ,2.8607168894850285876 ] 
dist 80=[.07576031664522296646,2.8613306011403454370 ] 
dist 81=[.10073189158044563779,2.8500259936979729567 ] 
dist 82=[.09474722846617905022,2.8375689287114355894 ] 
dist 83=[-.46266975030480329621,3.2402967731861410230 ] 
dist 84=[-.86048233277212719869,3.7274077393251050910 ] 
dist 85=[-1.2082226388434014898 ,4.0381598828476803383 ] 
dist 86=[-1.5770134449370517859 ,4.2784781581689633752 ] 
dist 87=[-1.9296960753438088575 ,4.4846902827347161359 ] 
dist 88=[-2.2132019248916432624 ,4.6577104102603809793 ] 
dist 89=[-2.4994442701341899904 ,4.7656471140679400192 ] 
dist 90=[-2.8630439771997704622 ,4.8463693394279585224 ] 
dist 91=[-3.2107593156834881108 ,4.9108320283266727282 ] 
dist 92=[-3.4336590828847850950 ,4.9597694414886952261 ] 
dist 93=[-3.6071413155282992947 ,4.9785623980179067731 ] 
dist 94=[-3.7577880680559014015 ,4.9788513329055796540 ] 
dist 95=[-3.8816901612415918290 ,4.9597285593782921459 ] 
dist 96=[-3.9485207328902415310 ,1.5057666726670319431 ] 
dist 97=[-3.9861657239099518170 ,1.7004281346555237700 ] 
dist 98=[-3.9936848257253255058 ,1.9807899728162689223 ] 
dist 99=[-3.9817710480360273106 ,2.2521582333895901143 ] 
dist 100=[-3.9668800897740200044 ,2.4109481690022421194 ] 
dist 101=[-3.8980722640966289582 ,2.5171925019732678967 ] 
dist 102=[-3.8702209316047620493 ,2.5790051125164675175 ] 
dist 103=[-3.6230394215341284333 ,2.6196531813426389536 ] 
dist 104=[-3.5589152911991781045 ,2.6414950730573585330 ] 
dist 105=[-3.5717339288445349607 ,2.6536644604840349863 ] 
dist 106=[-3.8222120940949134272 ,2.6557474173008825254 ] 
dist 107=[-4.0311481762514643342 ,2.1869809121769488069 ] 
dist 108=[-4.1967030851656333584 ,2.1178182780312289705 ] 
dist 109=[-4.2741666247700707801 ,1.9997002490988801329 ] 
dist 110=[-4.3073828747899456104 ,1.9672296110943479193 ] 
dist 111=[-4.3062029284627167954 ,1.8677752305096160785 ] 
dist 112=[-1.8258453652942627726 ,1.8344074881854188107 ] 
dist 113=[-1.8057379665727553196 ,1.8141346091226544012 ] 
dist 114=[-1.7998564563671562599 ,1.8065213171286461390 ] 
dist 115=[.56380562182127118806,1.8049892924570032974 ] 
dist 116=[.74828448114107614575,2.1305555440549292888 ] 
dist 117=[1.1646014840011159174 ,2.3668153069610451692 ] 
dist 118=[1.2276225323294284616 ,2.5822270870517886788 ] 
dist 119=[1.7043423304468403575 ,2.8246500317838411010 ] 
dist 120=[1.7786819760710327979 ,3.0419429887646496020 ] 
dist 121=[1.8379951135170168968 ,3.1571334916873210788 ] 
dist 122=[1.6883543871060870163 ,3.2215316102547383255 ] 
dist 123=[1.4287916937799988678 ,3.2362562101719356484 ] 
dist 124=[1.1193953502167244298 ,3.2131780225594169184 ] 
dist 125=[.77101196211750767025,3.2054359102179917362 ] 
dist 126=[.32838047663265696278,3.1992140692501256194 ] 
dist 127=[-.35688770662520814244,3.1934671908169906941 ] 
dist 128=[-1.0459449849290459883 ,2.4013317226306832909 ] 
dist 129=[-1.5036884204322590951 ,2.3933864464776347159 ] 
dist 130=[-1.8783294094411945168 ,2.3851528435938679161 ] 
dist 131=[-2.2359667380833799877 ,2.0018053472915476647 ] 
dist 132=[-2.5540423855749213780 ,1.6411112821164734185 ] 
dist 133=[-2.7709080357069173549 ,1.5688131419799554171 ] 
dist 134=[-2.9545424020671332943 ,1.4326081143042002723 ] 
dist 135=[-3.1400892249867420861 ,1.3967620094516288851 ] 
dist 136=[-3.3007831149527438061 ,.82705161995087733718] 
dist 137=[-3.3853015914092800766 ,.74722948222444992953] 
dist 138=[-3.4299682430913625968 ,.56367751239228319598] 
dist 139=[-3.4356511944244998992 ,.52605387338024337947] 
dist 140=[-3.4146460333818383978 ,.28863207153166032591] 
dist 141=[-3.3962471109826121624 ,.24550904660597861652] 
dist 142=[-3.3473479352225256726 ,.16238246849336497006] 
dist 143=[-3.3222533876786079899 ,.14212545080637600906] 
dist 144=[-2.0695539497539645172 ,.73927659953443133318] 
dist 145=[-2.0772403193792251159 ,1.2298164347830063170 ] 
dist 146=[-2.0783940614201283613 ,1.6315743908360287388 ] 
dist 147=[.23035798651785149588,2.0155504734147970503 ] 
dist 148=[.30676260677373034069,2.3573498805343371770 ] 
dist 149=[.47939108003171676634,2.5909036411965942560 ] 
dist 150=[.50540197850995953982,2.7892158004905042113 ] 
dist 151=[.7037327620693588868 ,2.9904687469881294119 ] 
dist 152=[.73470297225119715609,3.1672355828714468323 ] 
dist 153=[.78673366989501780899,3.2678949897354465891 ] 
dist 154=[.79627936094399162452,3.3317926421140036250 ] 
dist 155=[.87043792585358385084,3.3619502559161115675 ] 
dist 156=[.86466402324689187844,3.3696975911406838889 ] 
dist 157=[.77681231394969954081,3.3644602961622084066 ] 
dist 158=[.6298570331163494026 ,3.3132792702666795547 ] 
dist 159=[.45669667452553427339,3.2992310308408633456 ] 
dist 160=[-.12502830498224625332,1.7471582048670688938 ] 
dist 161=[-.5784370801333432579 ,1.7400217003955868348 ] 
dist 162=[-.96114222199218588839,1.7317313119991133032 ] 
dist 163=[-1.3458417198583846943 ,1.4225403870224152294 ] 
dist 164=[-1.7010121053465932495 ,1.3784007697186103383 ] 
dist 165=[-1.9659526542722040403 ,1.2693710485122942465 ] 
dist 166=[-2.2147645896799548000 ,1.2424427065955870288 ] 
dist 167=[-2.5056127476097727293 ,1.0648034570692768460 ] 
dist 168=[-2.7717075740501946243 ,1.0276923467420070966 ] 
dist 169=[-2.9218011030581354224 ,.95981356527572291064] 
dist 170=[-3.0152343353315850321 ,.94175194002004889737] 
dist 171=[-3.0553629809848977168 ,.60782636007695892177] 
dist 172=[-3.0744739209325471203 ,.56217779343319553089] 
dist 173=[-3.0840866892669030288 ,.44833962877309042583] 
dist 174=[-3.0885554499598808727 ,.43154556352404207901] 
dist 175=[-3.0871515569593030133 ,.25712101857699552132] 
dist 176=[-1.8902572068706512476 ,.59395732365913322836] 
dist 177=[-1.8532454790600526790 ,1.0047517543622594174 ] 
dist 178=[-1.8351702033740281026 ,1.3589315045495989696 ] 
dist 179=[.13261240096662139197,1.7269971948336528273 ] 
dist 180=[.17747365233748641485,2.0745060285037487010 ] 
dist 181=[.27372588220896158494,2.3467032896533361423 ] 
dist 182=[.27810195240606799141,2.6150664301465661488 ] 
dist 183=[.19308748220928543273,2.9472844707832026296 ] 
dist 184=[.09564110923418872622,3.2609092542475738297 ] 
dist 185=[.00550955887078624916,3.4551209010955871008 ] 
dist 186=[-.09625974419707860700,3.5984919328256943003 ] 
dist 187=[-.24011848784598808799,3.7093600054211928499 ] 
dist 188=[-.39949863589987787309,3.7904646690010151995 ] 
dist 189=[-.5631686321744217002 ,3.8151366851219148076 ] 
dist 190=[-.79081774920694046153,3.8147944109484009668 ] 
dist 191=[-1.5979656683826872608 ,3.7993195448996537722 ] 
dist 192=[-2.4025968797475763243 ,3.6549506692320277371 ] 
dist 193=[-2.9231332922907115560 ,3.6165611477795934639 ] 
dist 194=[-3.3337439068900132259 ,3.5003742079065756908 ] 
dist 195=[-3.6999817123058869583 ,3.4633808035203250428 ] 
dist 196=[-4.0083764658686179425 ,3.1824339027340073076 ] 
dist 197=[-4.1883040851308764608 ,3.1149891387133680982 ] 
dist 198=[-4.3080661950545642012 ,3.0067001162226891368 ] 
dist 199=[-4.3765157990088523104 ,2.9715951644484740247 ] 
dist 200=[-4.4172009286438200343 ,2.1415555537836315299 ] 
dist 201=[-4.4262359576860191902 ,2.0253294803055997138 ] 
dist 202=[-4.4137932134059439815 ,1.7594360052695053806 ] 
dist 203=[-4.3980063704958418165 ,1.6925160227109152146 ] 
dist 204=[-4.3065553435130892046 ,1.3375884801604410381 ] 
dist 205=[-4.2760747711782825639 ,1.2685893937177159421 ] 
dist 206=[-4.1532251067909284989 ,1.1204834043767947078 ] 
dist 207=[-4.1289437904558519039 ,1.0780137849524415334 ] 
dist 208=[-1.8974025674634747642 ,.15727539088216348595] 
dist 209=[-1.8918549214504511354 ,.2624920735607709341 ] 
dist 210=[-1.8823021405429197412 ,.34942748984935383961] 
dist 211=[-.00913984054823725495,.43378451400648329668] 
dist 212=[-.01955967966016470386,.64972777288431792634] 
dist 213=[-.03287575262749050977,.88109518345418037213] 
dist 214=[-.05357429281199919892,1.1240064305966192166 ] 
dist 215=[-.07735843303482186819,1.3548796537341232843 ] 
dist 216=[-.10298014075713275187,1.5382384036909156856 ] 
dist 217=[-.13477902581052286668,1.7213707343487587653 ] 
dist 218=[-.18319827282257529663,1.9513409784841453842 ] 
dist 219=[-.2416636525300793667 ,2.1700515212563636378 ] 
dist 220=[-.32008575039834575985,2.3082792076102112829 ] 
dist 221=[-.40152145480014801473,2.4136234163698722907 ] 
dist 222=[-.50803713798781274598,2.5011918603293917547 ] 
dist 223=[-.62213620707969582729,2.5703254867517047510 ] 
dist 224=[-.7338150985952001438 ,2.6021500788636186310 ] 
dist 225=[-.86477983536805193746,2.6126493462698061937 ] 
dist 226=[-1.2175120793487729781 ,2.6097479380416053380 ] 
dist 227=[-1.7612859478620395674 ,2.5684459714147262623 ] 
dist 228=[-2.1114354749486622764 ,2.5516975461838988863 ] 
dist 229=[-2.3857938401352313423 ,2.4924053494911809773 ] 
dist 230=[-2.6273061280498038991 ,2.4707982310287189037 ] 
dist 231=[-2.8283709637848397298 ,2.2973001043790789929 ] 
dist 232=[-2.9414214599256140163 ,2.2537109501191576146 ] 
dist 233=[-3.0113247173800310591 ,2.1870581697478200491 ] 
dist 234=[-3.0403147067593394585 ,2.1634991985181390008 ] 
dist 235=[-3.0506872508679849884 ,1.5840726919401901967 ] 
dist 236=[-3.0463425577008188123 ,1.5025017020884074907 ] 
dist 237=[-3.0303992765623467434 ,1.3195713752570063724 ] 
dist 238=[-3.0171204662406362660 ,1.2690127600659111338 ] 
dist 239=[-2.9486939563977388564 ,1.0337847481845485257 ] 
dist 240=[-2.9258404821093600850 ,.98755320916439133761] 
dist 241=[-2.8435458809330019435 ,.91619107729732095201] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 0, 2, 2, 0, 1] 
dist 0=[75.883428975226612784  ,75.883428975226612784  ] 
dist 1=[75.399008191682731476  ,76.175891086127597130  ] 
dist 2=[74.479894041431864137  ,76.337588504120868250  ] 
dist 3=[72.453005727840360814  ,76.300404741112808135  ] 
dist 4=[69.870731315897647748  ,76.138165345287483169  ] 
dist 5=[66.734746104978724969  ,75.954742394140360701  ] 
dist 6=[62.593074680725895756  ,75.399813495068697707  ] 
dist 7=[55.996613952348744372  ,75.105114747781503985  ] 
dist 8=[49.273724039760272029  ,73.377657045218194390  ] 
dist 9=[44.627170563967456117  ,72.824125812635136648  ] 
dist 10=[40.611183025565527412  ,72.384316367077141533  ] 
dist 11=[36.404471681022708767  ,72.077141990018093154  ] 
dist 12=[31.947748519743032319  ,71.862104103875346736  ] 
dist 13=[27.019583883681665721  ,71.542067542487487594  ] 
dist 14=[21.949153445937538588  ,68.685214044819707076  ] 
dist 15=[17.172822289038861915  ,61.647749863901583260  ] 
dist 16=[13.418757418844550215  ,33.725518336292726039  ] 
dist 17=[9.6931852358901844592 ,30.705310307954645460  ] 
dist 18=[5.0307339661839214511 ,23.605220599650622112  ] 
dist 19=[.57907825672725888036,22.544371038686422659  ] 
dist 20=[-2.3050650983194780270 ,13.108755324790761176  ] 
dist 21=[-4.5940653443911128577 ,11.457102124793844585  ] 
dist 22=[-6.6702372503465891501 ,9.2298072467120015544 ] 
dist 23=[-8.4514732493679605561 ,8.7932533240290641170 ] 
dist 24=[-9.5632929948699980208 ,.06374454039359354806] 
dist 25=[-10.398239383245448261  ,-.64555664150294463169] 
dist 26=[-11.074461042769410392  ,-2.1104421148523993992 ] 
dist 27=[-11.618676518053113953  ,-2.3873362381362767689 ] 
dist 28=[-11.926936386133224057  ,-3.6701157123856415998 ] 
dist 29=[-12.122728735565996249  ,-3.8824600964415635108 ] 
dist 30=[-12.218542803576700939  ,-3.6128340472333155160 ] 
dist 31=[-12.246328831895082333  ,-3.2535026154299742255 ] 
dist 32=[-8.9971338246150349713 ,-2.8786346104596050475 ] 
dist 33=[-8.8617135891594138214 ,-2.4263523580021028244 ] 
dist 34=[-8.4478537559154008243 ,-1.7575745040122520921 ] 
dist 35=[-8.3572545997207152400 ,-1.0792946291298453241 ] 
dist 36=[-7.9012306535716699279 ,-.58858421830159321468] 
dist 37=[-7.9647343173521077030 ,-.14468845605982480088] 
dist 38=[-7.9861434268339150722 ,.34776951577252186293] 
dist 39=[-7.9810076413408148274 ,.83156748759022671714] 
dist 40=[-4.9401988406824598034 ,1.3300200364865134442 ] 
dist 41=[-4.6840778632665238978 ,2.1748275665709952496 ] 
dist 42=[-4.0885370493461365640 ,2.8644782544185246274 ] 
dist 43=[-3.9790018124102388526 ,3.5217788221310795554 ] 
dist 44=[-3.2088826585650660242 ,4.1075664644336552682 ] 
dist 45=[-3.0735309808133175230 ,4.5119768596824414105 ] 
dist 46=[-2.8284809774640526927 ,4.8610560464681084378 ] 
dist 47=[-2.7750198719461978727 ,5.2262052639797724361 ] 
dist 48=[-1.8625551040557392393 ,5.5451509917788543156 ] 
dist 49=[-1.8550121570624698864 ,5.7098944364098114575 ] 
dist 50=[-1.8475134634079798754 ,5.7959204343164454396 ] 
dist 51=[-1.7902968122280205981 ,5.8118871235427696930 ] 
dist 52=[-1.7738195561427409159 ,5.7564252223636324929 ] 
dist 53=[-1.7207384816436279527 ,5.7223532805554762739 ] 
dist 54=[-1.7036397682951632390 ,5.6816503923074228833 ] 
dist 55=[-1.5572432982271715451 ,5.6490544405310821794 ] 
dist 56=[-1.5204277411971359937 ,5.5088942196964078008 ] 
dist 57=[-2.2497771085311400660 ,5.5531915623690787970 ] 
dist 58=[-2.9113214058315731290 ,5.5631347047686257294 ] 
dist 59=[-3.5467943548802839665 ,5.5585847651691813622 ] 
dist 60=[-4.1149403066860940365 ,5.3554373684146739591 ] 
dist 61=[-4.5079964450748140795 ,5.2945847480928292094 ] 
dist 62=[-4.8471869686389468858 ,5.2505075132482017447 ] 
dist 63=[-5.2005465442871750832 ,5.2193490742679769747 ] 
dist 64=[-5.5103564395146807528 ,1.0570514268975918294 ] 
dist 65=[-5.6758572074339579918 ,.9257261525007454623 ] 
dist 66=[-5.7671137210421168077 ,.64101432880611815567] 
dist 67=[-5.7822270341022216921 ,.57050781840158206316] 
dist 68=[-5.7616942215386904519 ,.25555861056390008372] 
dist 69=[-5.7319445790418551776 ,.19838673840718333335] 
dist 70=[-5.6675211364853695970 ,.06704363787710483824] 
dist 71=[-5.6336561398397364141 ,.04332600527974595347] 
dist 72=[-5.3678215072047222662 ,1.1924438319232037857 ] 
dist 73=[-5.4715852395289658254 ,1.9982771602283474166 ] 
dist 74=[-5.5337926349173847285 ,2.6556524211216304896 ] 
dist 75=[-5.5556930043679331777 ,3.2795939493211136302 ] 
dist 76=[-5.5502439359245329762 ,3.8321163175072116851 ] 
dist 77=[-5.5342735841863836489 ,4.2046710987639989876 ] 
dist 78=[-5.4492835512209967319 ,4.5156970591999836410 ] 
dist 79=[-5.4153126738648427957 ,4.8228447836683831254 ] 
dist 80=[-2.3150534015851299673 ,5.0910083749396328752 ] 
dist 81=[-2.0285635556573149256 ,5.2465619458737832333 ] 
dist 82=[-1.3850754231194910869 ,5.3490071773892306915 ] 
dist 83=[-1.2485504131445103948 ,5.4053618795419150539 ] 
dist 84=[-.47026065048122215563,5.4276232478095918568 ] 
dist 85=[-.33258845556948160056,5.4220575350091006245 ] 
dist 86=[-.04583199655063679488,5.3490594995617293636 ] 
dist 87=[.02794163120533929735,5.3254121090340215017 ] 
dist 88=[.11843750161748283266,4.4305596912963979492 ] 
dist 89=[-.60225528042542899356,4.7091549257807760783 ] 
dist 90=[-1.2144710324435708416 ,4.8968165011679406341 ] 
dist 91=[-1.8361930611308524548 ,5.0088652091687690632 ] 
dist 92=[-2.4142322991867077266 ,5.0806270413947348515 ] 
dist 93=[-2.8522393578067832101 ,5.1075923557829339336 ] 
dist 94=[-3.2702811684709991117 ,5.1068820001213711863 ] 
dist 95=[-3.7686998122504693797 ,5.0921800295318056412 ] 
dist 96=[-4.2298209120833724180 ,-.41586387868123086238] 
dist 97=[-4.4991171583229228862 ,-.51599325932810068661] 
dist 98=[-4.6787037873541103622 ,-.6289521660377945346 ] 
dist 99=[-4.7820534669234814800 ,-.63334525483355375118] 
dist 100=[-4.8470741191522326401 ,-.59263955975015507541] 
dist 101=[-4.8738000578227436581 ,-.48683070776589421087] 
dist 102=[-4.8775202443806965870 ,-.31339139461441242185] 
dist 103=[-4.8613852906354826770 ,-.00291717841441403227] 
dist 104=[-4.9517814412855416842 ,.88936426015421234458] 
dist 105=[-5.2156793185809588464 ,1.5038686146642336096 ] 
dist 106=[-5.4006814167616255140 ,2.0307911370527323974 ] 
dist 107=[-5.5256317261950008440 ,2.5737896429304938825 ] 
dist 108=[-5.6045295786508439888 ,3.0836268349648812300 ] 
dist 109=[-5.6180943214680812596 ,3.4782996928262382821 ] 
dist 110=[-5.5836629300381668635 ,3.8630436757068861531 ] 
dist 111=[-5.5686761320628088807 ,4.3332842018201286463 ] 
dist 112=[-5.1379053171381644705 ,4.7742220685552591498 ] 
dist 113=[-5.0542218832296168116 ,5.0421047015321063647 ] 
dist 114=[-4.8263147277214646981 ,5.2337505078468415994 ] 
dist 115=[-4.7614786324547494396 ,5.3706493385196706849 ] 
dist 116=[-4.2986332733317735821 ,5.6283606183191964904 ] 
dist 117=[-4.1930989206529262661 ,5.9198031993098744605 ] 
dist 118=[-4.0133422213851244566 ,6.1287149712570827417 ] 
dist 119=[-3.9609415200281463835 ,6.2787593116429361469 ] 
dist 120=[-3.2161278678762529419 ,6.3870918560903760732 ] 
dist 121=[-3.9712882287528970196 ,6.4296520081032772346 ] 
dist 122=[-4.5703991306780825623 ,6.4320795239873554477 ] 
dist 123=[-5.1106915802426229731 ,6.4159486474567531615 ] 
dist 124=[-5.5699182422121644636 ,6.2994973991740952959 ] 
dist 125=[-5.8457320673877703168 ,6.2589708104778048847 ] 
dist 126=[-6.0392168431763199002 ,6.0844774927125009522 ] 
dist 127=[-6.1701084357890321388 ,6.0534392326256857766 ] 
dist 128=[-6.2606128370759622211 ,2.8412194363335567868 ] 
dist 129=[-6.2930301182417442404 ,2.6788406648851197361 ] 
dist 130=[-6.2890154936839478076 ,2.3005770194894454262 ] 
dist 131=[-6.2710387538529236667 ,2.2137210546755932723 ] 
dist 132=[-6.1513631625516598280 ,1.6923133705882985940 ] 
dist 133=[-6.1113389305556878667 ,1.5918827612556177817 ] 
dist 134=[-5.9336398087230958515 ,1.3937110131437612334 ] 
dist 135=[-5.9075241069110458761 ,1.3412419890221116844 ] 
dist 136=[-2.9390329710642588564 ,.71009805967055069886] 
dist 137=[-2.9360978099463305917 ,1.1772529050924207741 ] 
dist 138=[-2.9255894899614716348 ,1.5543151132227330580 ] 
dist 139=[-.90008363926775180279,1.9054457002152742159 ] 
dist 140=[-.72958900939765537909,2.2117917283143553080 ] 
dist 141=[-.34901592208951387037,2.4102493580955100135 ] 
dist 142=[-.27080532457490648022,2.5671078752809405239 ] 
dist 143=[.17515678457618766752,2.7075531530093041788 ] 
dist 144=[.25169181841450225305,2.8274172102393797975 ] 
dist 145=[.41266299744237817671,2.9021960901683416999 ] 
dist 146=[.44790890837313280658,2.9580537225853969128 ] 
dist 147=[.70412084764392264489,3.0024582473042541110 ] 
dist 148=[.74590786909501588984,3.0359474667330445548 ] 
dist 149=[.74619080603330185784,3.0482739380111998032 ] 
dist 150=[.68988083153362437932,3.0474244915711527884 ] 
dist 151=[.6017190255464418658 ,3.0363771151137381665 ] 
dist 152=[.47497407728417362532,2.5135584577888345042 ] 
dist 153=[.21560544198974696806,2.5289577248857109198 ] 
dist 154=[-.12045411952437062754,2.5265719014967524356 ] 
dist 155=[-.47288419714538759181,.25392129063192139921] 
dist 156=[-.80760580733709916081,-.21038684140694001249] 
dist 157=[-1.0730425089323007663 ,-.28990848020093232985] 
dist 158=[-1.3377842300293169173 ,-.45740229392278792405] 
dist 159=[-1.6697342050264522685 ,-.49351621441489317213] 
dist 160=[-1.9851868604454516260 ,-.75510510856912293182] 
dist 161=[-2.1841358776232345604 ,-.79671114741531652204] 
dist 162=[-2.3352684462380464261 ,-.79495178270941982412] 
dist 163=[-2.4600250602297526335 ,-.73353187690476437081] 
dist 164=[-2.5578425527108817041 ,-.6386980390021357014 ] 
dist 165=[-2.6015396252911516424 ,-.50368108691197414646] 
dist 166=[-2.6196315115169855860 ,-.31377370314878802499] 
dist 167=[-2.6166022433212479290 ,-3.21795700206027790000e-05] 
dist 168=[-1.9720965346460524483 ,.39381249561565489556] 
dist 169=[-1.9677391393983557384 ,.65997908722274046663] 
dist 170=[-1.9609585087248829234 ,.88281897349475882652] 
dist 171=[-1.5381502133183836113 ,1.1038737362259515134 ] 
dist 172=[-1.4815150225599708586 ,1.3060768163595575858 ] 
dist 173=[-1.3441485723708973408 ,1.4537345969516769329 ] 
dist 174=[-1.3112109436152767296 ,1.5892844821291466337 ] 
dist 175=[-1.0982651388637735756 ,1.7432002511062099758 ] 
dist 176=[-1.0548174440333526580 ,1.8816444280976508286 ] 
dist 177=[-.97404527089693236738,1.9554922945345700209 ] 
dist 178=[-.95269959209914697296,1.9970593743980250997 ] 
dist 179=[-.58908285293592365806,2.0702248641736961764 ] 
dist 180=[-.5387314926766295306 ,2.1163504567670799158 ] 
dist 181=[-.41844543924065097415,2.1396076146014778054 ] 
dist 182=[-.39712479797032609189,2.1416113381505947512 ] 
dist 183=[-.26585652692797440124,2.1242335121700703801 ] 
dist 184=[-.69476570287143341593,2.1124438578864624217 ] 
dist 185=[-.97918671758979842582,2.0771268189837556556 ] 
dist 186=[-1.2114114285631228286 ,2.0592672385909320811 ] 
dist 187=[-1.4321573203310497049 ,1.2918026621066301302 ] 
dist 188=[-1.6278478819273368992 ,1.0723388493318122791 ] 
dist 189=[-1.7601498119291940272 ,1.0279087914068408626 ] 
dist 190=[-1.8709711965681788030 ,.94486259513898342922] 
dist 191=[-1.9809955215958561617 ,.92296496784430780204] 
dist 192=[-2.0755985555383998837 ,.56048728038179914254] 
dist 193=[-2.1249185235337775103 ,.5100560608702721481 ] 
dist 194=[-2.1503717127376373626 ,.39149792887744972695] 
dist 195=[-2.1530703976458659102 ,.36912677125915284631] 
dist 196=[-2.1375786843663518276 ,.20787514265580867241] 
dist 197=[-2.1258849937935708133 ,.17835803592636760556] 
dist 198=[-2.0853506889995456136 ,.12675785875062038565] 
dist 199=[-1.9586321299700803637 ,.11512651402934477953] 
dist 200=[-.97661113770381904205,.24580141486267701769] 
dist 201=[-.96563100142774289165,.40799614247027646348] 
dist 202=[-.95983607420026328286,.53953617557324663608] 
dist 203=[-.4217054819518691888 ,.66308749205282407895] 
dist 204=[-.37207864041022834703,.7716104378073630179 ] 
dist 205=[-.25989031515559703841,.84321605437395979441] 
dist 206=[-.23622830170463327899,.90128445147131403873] 
dist 207=[-.09805868810872496503,.95581981824116621753] 
dist 208=[-.07345630983132193354,1.0029014358092490758 ] 
dist 209=[-.02308096031733256310,1.0312436491892981599 ] 
dist 210=[-.01027061025933327000,1.0512048416537493725 ] 
dist 211=[.09891569171010481678,1.0648622374035452672 ] 
dist 212=[.11649365758601627737,1.0733754626057113022 ] 
dist 213=[.13362752166415025935,1.0728212668458500437 ] 
dist 214=[.13144013458315675772,1.0672931595492241110 ] 
dist 215=[.12073946040730516148,1.0621430166896273309 ] 
dist 216=[.09812284155055934757,.87354411919775223701] 
dist 217=[-.01137022983424561059,.87392088179273740056] 
dist 218=[-.13124475629789810915,.87165707769013034642] 
dist 219=[-.25517552216908659208,.1778845670264538992 ] 
dist 220=[-.37178667013744290056,.02019652354993129447] 
dist 221=[-.46246993974135603447,-.00734573514732569246] 
dist 222=[-.5512623238208356608 ,-.06453384027171497410] 
dist 223=[-.66033245991250356255,-.07873800031954284068] 
dist 224=[-.76287860626244766919,-.18469372067186617215] 
dist 225=[-.8256527660771187618 ,-.18859475338232797133] 
dist 226=[-.87113358947626653838,-.18222532262004647732] 
dist 227=[-.90471244395940160683,-.17187957335974733894] 
dist 228=[-.92916215437436531202,-.1579646493733157253 ] 
dist 229=[-.93823517719704646579,-.138811722842867004  ] 
dist 230=[-.94016740220392279099,-.08895707782515726179] 
dist 231=[-.93733645087848520498,-4.42067511749567000000e-07] 
dist 232=[-.36182950085390125431,.09085695785630424808] 
dist 233=[-.35997159644505796234,.15100998003792932852] 
dist 234=[-.35830026870388584384,.20001680544292925836] 
dist 235=[-.31086804651881239479,.24642222753382609528] 
dist 236=[-.30336713415250133569,.28743949885874228541] 
dist 237=[-.28422737779165721308,.3149579221474733066 ] 
dist 238=[-.2792634480499413974 ,.33777832968507208815] 
dist 239=[-.24545665236417934573,.36005951584918486107] 
dist 240=[-.23814378309127016502,.37946682355134529898] 
dist 241=[-.22508550231608921937,.39082596007918152271] 
dist 242=[-.22157652139445516449,.39843228315242481264] 
dist 243=[-.14937319814001104638,.40287305251763352781] 
dist 244=[-.13944400096289148426,.40492421646830343035] 
dist 245=[-.11520423675622208141,.40451201833289115957] 
dist 246=[-.11097479764170868616,.39258623611941512136] 
dist 247=[-.07491031000037283743,.35474418531546630354] 
dist 248=[-.06810738762610947043,.17469936986072471284] 
dist 249=[-.05817196420385278617,.15414570472523293735] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 2, 0, 2, 1, 2] 
dist 0=[75.478095693579497487  ,75.478095693579497487  ] 
dist 1=[75.233015326188176065  ,75.541590492202842834  ] 
dist 2=[74.586027496481996557  ,75.478095693579497487  ] 
dist 3=[73.407805620569148298  ,75.299536615065222187  ] 
dist 4=[71.042132057132387938  ,75.087324217750197919  ] 
dist 5=[68.093001698792686068  ,74.642363423969362382  ] 
dist 6=[64.586062619601551166  ,74.414931877271264387  ] 
dist 7=[59.997819331645853848  ,73.397310443281755805  ] 
dist 8=[52.732828154613031025  ,73.161654782897475958  ] 
dist 9=[45.334325042765719184  ,72.910722929895955458  ] 
dist 10=[40.213251086966732641  ,72.682421690955453846  ] 
dist 11=[35.779018577043876099  ,72.264379686720665540  ] 
dist 12=[31.122114998604081100  ,72.137254601150565178  ] 
dist 13=[26.678191025203176925  ,70.016876991388693421  ] 
dist 14=[23.094114159927862595  ,65.829026557378195233  ] 
dist 15=[19.453337159586121129  ,34.294779340454399624  ] 
dist 16=[14.783172272430410314  ,31.305703585197081759  ] 
dist 17=[10.270684173361070976  ,24.259280784701859304  ] 
dist 18=[7.2592070689483297738 ,23.226550032138071501  ] 
dist 19=[4.7704379507274801779 ,13.833331782976019427  ] 
dist 20=[2.3440691031332327382 ,12.196801293753194322  ] 
dist 21=[.14298125157198136811,10.029664053748136314  ] 
dist 22=[-1.4467829056193327515 ,9.6074995535725925049 ] 
dist 23=[-2.8939857542197229321 ,3.6570445946749180536 ] 
dist 24=[-4.7541935135496034288 ,3.4866709430585285174 ] 
dist 25=[-6.7207321918672490933 ,.15291293767952365354] 
dist 26=[-8.4027239205588930331 ,-.20612249711985447008] 
dist 27=[-9.7846554141294981439 ,-.87005063085497455491] 
dist 28=[-10.554466196479582083  ,-1.0079428455606522965 ] 
dist 29=[-11.033896939475041140  ,-1.3276808697335837016 ] 
dist 30=[-11.259153150860888663  ,-1.3214741178431706999 ] 
dist 31=[-11.348620610782872799  ,-1.1972154182109771699 ] 
dist 32=[-11.350802853210870292  ,-.88834798951269289504] 
dist 33=[-11.194520625011549551  ,-.53179209742778722772] 
dist 34=[-11.164041321377637189  ,-.21675954064767785009] 
dist 35=[-10.389395754361966532  ,.12338371714159259304] 
dist 36=[-10.203121031325788840  ,.58119887646393521129] 
dist 37=[-10.049534633439676416  ,1.0752577714310866863 ] 
dist 38=[-9.9960746174201004134 ,1.5605043559287007845 ] 
dist 39=[-7.3193324167686427285 ,2.1300086769579618669 ] 
dist 40=[-6.9747049613674311762 ,2.9606438313264370382 ] 
dist 41=[-6.2656537121078862463 ,3.7738815426614823488 ] 
dist 42=[-6.0781082799184168284 ,4.2741973447426241846 ] 
dist 43=[-5.3908851147617548392 ,4.6400643229776749039 ] 
dist 44=[-5.3296781401051814784 ,4.9171401224993153350 ] 
dist 45=[-5.3084384310767741718 ,5.1304108971277042017 ] 
dist 46=[-5.2886964857774886628 ,5.2417866168864995897 ] 
dist 47=[-5.2611272661720504409 ,5.2998353024236096019 ] 
dist 48=[-5.2361288255300701116 ,5.3005720337636731218 ] 
dist 49=[-4.3772281143135349557 ,5.2288568256800374455 ] 
dist 50=[-4.2455288336836935884 ,5.4350043524106063303 ] 
dist 51=[-3.9920626907419166743 ,5.6016824168105172531 ] 
dist 52=[-3.9202091319620692627 ,5.6652506794902335959 ] 
dist 53=[-3.6385504587658456206 ,5.6862744473936445980 ] 
dist 54=[-3.5675065628790524324 ,5.6828379384799431564 ] 
dist 55=[-3.4197381775165029370 ,6.0560476357316913928 ] 
dist 56=[-3.3719167117917825086 ,6.3725275304130572412 ] 
dist 57=[-.88941238844626347833,6.6041903261643921270 ] 
dist 58=[-1.6481757014218775999 ,6.7821423015159507118 ] 
dist 59=[-2.2709673700355670960 ,6.9131401827909317318 ] 
dist 60=[-2.8792392736557568274 ,6.9572783895677023390 ] 
dist 61=[-3.5424380112463630578 ,6.9629304708666488164 ] 
dist 62=[-4.1688184289243644052 ,6.9433680061903647540 ] 
dist 63=[-4.7222401249550732928 ,2.4288481143087034882 ] 
dist 64=[-5.0944565965059055701 ,2.3118389003174031365 ] 
dist 65=[-5.4047175561421337324 ,2.0743317744349287650 ] 
dist 66=[-5.7110761355340305072 ,2.0089299726761869879 ] 
dist 67=[-5.9727909408857265302 ,1.2239001389466444973 ] 
dist 68=[-6.1049728389399503450 ,1.1067670882649786920 ] 
dist 69=[-6.1676538718083725411 ,.85557245809200207352] 
dist 70=[-6.1758954228070164572 ,.78658905491235831174] 
dist 71=[-6.1062432917905977358 ,.51056968889803933231] 
dist 72=[-6.0669305828141327727 ,.45763903942545221455] 
dist 73=[-5.9801911657917629421 ,.33360047404367911288] 
dist 74=[-5.9396607988812820563 ,.85229373974226329985] 
dist 75=[-5.4648408533936847627 ,1.4461615797479285283 ] 
dist 76=[-5.4659988562161150409 ,2.3230718012360902868 ] 
dist 77=[-5.4515783763344816702 ,3.0365313442993547711 ] 
dist 78=[-5.4281615123500602007 ,3.7107200697117011549 ] 
dist 79=[-1.4976242067226547273 ,4.3058842502761500154 ] 
dist 80=[-1.1685405460012747710 ,4.7041811871951337920 ] 
dist 81=[-.43974468958809339645,5.0335220718206129264 ] 
dist 82=[-.28939806510449734768,5.3536848053561225919 ] 
dist 83=[.2889975699042262209 ,5.6313802444251280060 ] 
dist 84=[.32722511438025856664,5.7913502843388650474 ] 
dist 85=[.35274763485185320442,5.8953603814026391162 ] 
dist 86=[.30864034260299908777,5.9498594647974448072 ] 
dist 87=[.21381700125343211063,5.9682668721397266691 ] 
dist 88=[.02537210774302706350,5.9600521394822015573 ] 
dist 89=[-.85182532839143952748,5.8768922302420982714 ] 
dist 90=[-1.4596331345625807259 ,5.8494382665681819929 ] 
dist 91=[-1.9845492602266109405 ,4.7715051773520176854 ] 
dist 92=[-2.5314026536357817916 ,4.8460421892060787619 ] 
dist 93=[-3.0485311254291379438 ,4.8757130947111546691 ] 
dist 94=[-3.4549042396946512408 ,4.8687932494434050359 ] 
dist 95=[-3.8567733595492703792 ,.72602920225072886393] 
dist 96=[-4.3559415907638243000 ,.57714743643782397806] 
dist 97=[-4.8279880864232973678 ,.27275297800693427808] 
dist 98=[-5.1216949070005325005 ,.19508627714141786186] 
dist 99=[-5.3401598468153488676 ,.30816429116692002537] 
dist 100=[-5.5121376413655161696 ,.52561070960315504302] 
dist 101=[-5.6404751901100877698 ,.76492763916967718397] 
dist 102=[-5.6849007031261694759 ,1.0084466855282961611 ] 
dist 103=[-5.6889584511013487852 ,1.3009569144956716028 ] 
dist 104=[-5.6705159375779352027 ,2.4338513637438647935 ] 
dist 105=[-5.4828342960325836934 ,3.6291773757022323488 ] 
dist 106=[-5.4301632590240387196 ,4.4017610460101169830 ] 
dist 107=[-5.2664721895404362294 ,5.0103858494329333332 ] 
dist 108=[-5.2131463982182246630 ,5.5518316666631608321 ] 
dist 109=[-4.8026006219299785063 ,6.0067376318791757935 ] 
dist 110=[-4.7031403222704783890 ,6.2702348569764959188 ] 
dist 111=[-4.5453548651061433686 ,6.4432182346566993032 ] 
dist 112=[-4.4931678284410224383 ,6.5371476388224664464 ] 
dist 113=[-3.2482285224981606687 ,6.5898977368194176567 ] 
dist 114=[-3.0737535205309787454 ,6.5986551115417522795 ] 
dist 115=[-2.6765212843320529202 ,6.5768386634990372253 ] 
dist 116=[-2.5743056251889275383 ,6.5521940019524279481 ] 
dist 117=[-2.0489086251768899491 ,6.4135868541996022529 ] 
dist 118=[-1.9465590102304354613 ,6.3672944654474616045 ] 
dist 119=[-1.7220384984886794653 ,6.1852971378652033444 ] 
dist 120=[-1.6564718174925349828 ,6.1466169706466753464 ] 
dist 121=[-.96426937566294729301,6.0161042664451797797 ] 
dist 122=[-2.2512693277160783757 ,6.0094689964675787748 ] 
dist 123=[-3.5359896040468328310 ,5.6165804326257130380 ] 
dist 124=[-4.3706438634316471023 ,5.5350888764610620816 ] 
dist 125=[-5.0330451829494800273 ,5.3074416714195931109 ] 
dist 126=[-5.6308059032852729574 ,5.2409285726813609674 ] 
dist 127=[-6.1391638952878054508 ,4.7568635924704892359 ] 
dist 128=[-6.4450195781314204342 ,4.6449129018723429061 ] 
dist 129=[-6.6602337069263074289 ,4.4577257204307935305 ] 
dist 130=[-6.8071057993773177803 ,4.4013709243923156059 ] 
dist 131=[-6.9093317916063047183 ,3.1181932983184052803 ] 
dist 132=[-6.9464932173386155416 ,2.9394489909044610710 ] 
dist 133=[-6.9430100561231023215 ,2.5224119381616088476 ] 
dist 134=[-6.9234991118291337456 ,2.4273737012559795904 ] 
dist 135=[-6.7922231542536959797 ,1.8508579213148360808 ] 
dist 136=[-6.7480899878277722015 ,1.7398665178392334212 ] 
dist 137=[-6.5530089663758909455 ,1.5224046118264967165 ] 
dist 138=[-6.5235146781325484798 ,1.4652354404693329187 ] 
dist 139=[-3.8171480517084441193 ,.8314292476496202213 ] 
dist 140=[-3.8333247462680070727 ,1.3778763657720143041 ] 
dist 141=[-3.8333716598401989529 ,1.8192609991683289726 ] 
dist 142=[-3.8193582679914398028 ,2.2308368470065058428 ] 
dist 143=[-1.1310607272957327761 ,2.5902975022229155935 ] 
dist 144=[-.90631240973985023092,2.8238423164673173460 ] 
dist 145=[-.40514601699347673411,3.0092013960288349732 ] 
dist 146=[-.30235517221741068686,3.1764933013409972475 ] 
dist 147=[.28253173654848018211,3.3195425131280708177 ] 
dist 148=[.38259731466509508829,3.4082196271593697367 ] 
dist 149=[.59356058984748580671,3.4737949980184185423 ] 
dist 150=[.6386427109511485346 ,3.5247123143136688451 ] 
dist 151=[.9646526789846418301 ,3.5621341621727103467 ] 
dist 152=[1.0158028289992271125 ,3.5738883545316501765 ] 
dist 153=[1.0122409531758608762 ,3.5690594484036711930 ] 
dist 154=[.9330644134300944604 ,3.5563789061532015035 ] 
dist 155=[.66096097747917596275,3.2131657375789545980 ] 
dist 156=[.20496931257344399059,3.2700267197204906536 ] 
dist 157=[-.18993066154458395506,3.2939491339261812450 ] 
dist 158=[-.60308770094730292687,3.2912693879951180196 ] 
dist 159=[-.99488536442690282083,-.19561554918734301443] 
dist 160=[-1.3046023499617966358 ,-.28860428647367738627] 
dist 161=[-1.6126024412602628301 ,-.48402525805258874959] 
dist 162=[-1.9975530295367728545 ,-.52716673843122609167] 
dist 163=[-2.3627692287377380073 ,-.84133021759369659799] 
dist 164=[-2.5920668878554289026 ,-.89321631912518339845] 
dist 165=[-2.7650510933811356947 ,-.89481886813682999361] 
dist 166=[-2.9056843761613313066 ,-.8281812252851867074 ] 
dist 167=[-3.0142682677073732432 ,-.72303512036647117687] 
dist 168=[-3.0594367324485420520 ,-.57106261058819775302] 
dist 169=[-3.0769209125179028037 ,-.35613674893339747802] 
dist 170=[-3.0750974652289543320 ,7.27208273090286958220e-05] 
dist 171=[-2.4812063283773314052 ,.47139412569678519246] 
dist 172=[-2.4762061582647389670 ,.79047326743157586697] 
dist 173=[-2.4731152116952917411 ,1.0582094994280589362 ] 
dist 174=[-2.4718353428278439688 ,1.3247745708589672664 ] 
dist 175=[-1.8874915160582338729 ,1.5692376042158317484 ] 
dist 176=[-1.8119579273636867428 ,1.7488290343383077634 ] 
dist 177=[-1.6302047512907749667 ,1.9147708742326772226 ] 
dist 178=[-1.5871958880598930085 ,2.1047981902098995404 ] 
dist 179=[-1.3117763623839413064 ,2.2765865077769529468 ] 
dist 180=[-1.2562172229529219935 ,2.3697896701144440166 ] 
dist 181=[-1.1521044769694855147 ,2.4230094186235062086 ] 
dist 182=[-1.1246785337495328317 ,2.4518564752345526191 ] 
dist 183=[-.67683190715161950395,2.5720816234174652167 ] 
dist 184=[-.61438042769529537201,2.6349846382312271301 ] 
dist 185=[-.46869413648752735928,2.6677645450273406551 ] 
dist 186=[-.44038997650471412191,2.6715106608313749682 ] 
dist 187=[-.91054566630299303193,2.6534247022683462508 ] 
dist 188=[-1.2562757271417245017 ,2.6390045422962171415 ] 
dist 189=[-1.5377175039040374945 ,2.5988340527842606286 ] 
dist 190=[-1.8038419597023881160 ,2.5783181247300119563 ] 
dist 191=[-2.0388103856072602251 ,1.3746490538922393656 ] 
dist 192=[-2.1959992721970022585 ,1.3214521479585671326 ] 
dist 193=[-2.3258600769451562771 ,1.2228218279904293113 ] 
dist 194=[-2.4518417961847542372 ,1.1967283153632092470 ] 
dist 195=[-2.5591049771252932770 ,.74598503311541207686] 
dist 196=[-2.6143146592354723152 ,.68370992635580076708] 
dist 197=[-2.6418093037247724117 ,.53380577413355769637] 
dist 198=[-2.6438799246440809428 ,.50803716841273764243] 
dist 199=[-2.6212700083282408266 ,.29363514634215301331] 
dist 200=[-2.6066239356689892536 ,.25408102037470204632] 
dist 201=[-2.5617680805915690340 ,.19477420489081383257] 
dist 202=[-2.4800851245171260293 ,.17869334551226565654] 
dist 203=[-1.3850480931459471155 ,.25589028465532006361] 
dist 204=[-1.3867735544419119936 ,.42562039436415557767] 
dist 205=[-1.3809979133152056231 ,.56425339881641656562] 
dist 206=[-1.3762116826414142896 ,.69611974116329293284] 
dist 207=[-.47358390752533961594,.81307695887474476125] 
dist 208=[-.39583014409055189006,.8922511100548794821 ] 
dist 209=[-.22171013304369338636,.95868110225505910583] 
dist 210=[-.18568786829230933017,1.0248135338007085204 ] 
dist 211=[.02100567061923604905,1.0826630447633997480 ] 
dist 212=[.05683006817196998787,1.1160600468664604243 ] 
dist 213=[.13163398062038479954,1.1378447314462433714 ] 
dist 214=[.14924719566578071007,1.1493833336375103047 ] 
dist 215=[.27926113547954113225,1.1534144666904076871 ] 
dist 216=[.30143808272668221387,1.1522228947030668190 ] 
dist 217=[.30733149781333209275,1.1351125079553503639 ] 
dist 218=[.23201825963741632078,1.1500507925856061794 ] 
dist 219=[.00673742032111326819,1.1862242200663183445 ] 
dist 220=[-.14705972156641726503,1.1994448632450897925 ] 
dist 221=[-.27750045292557613153,1.2033317790477814138 ] 
dist 222=[-.40963394626230832199,1.2022815074654095294 ] 
dist 223=[-.53227227293158869373,.16735969102818967525] 
dist 224=[-.62484547445081840376,.13864579263778345796] 
dist 225=[-.71285392259802863555,.08032041173415289124] 
dist 226=[-.81728762596004523288,.06544234758857138485] 
dist 227=[-.91364665153307030422,-.07176106668132042775] 
dist 228=[-.96945259970865592493,-.09338113256421895995] 
dist 229=[-1.0060791774406819340 ,-.11953442982728247591] 
dist 230=[-1.0259492464192336722 ,-.1224354321394281097 ] 
dist 231=[-1.0379051881126281890 ,-.11599211142464116037] 
dist 232=[-1.0429695545340431800 ,-.09580875742722282493] 
dist 233=[-1.0439412751285863817 ,-.06175596853036266264] 
dist 234=[-1.0400504812045452409 ,-1.64873845215468762000e-07] 
dist 235=[-.53934986307713815219,.06452966965918249409] 
dist 236=[-.54312943421778619714,.10964552909355696929] 
dist 237=[-.54524542676601219368,.14904917524452964532] 
dist 238=[-.54563486366075374835,.19079821884764364211] 
dist 239=[-.13805030254826908242,.23071047584560820355] 
dist 240=[-.10498611647907778307,.26278886130821706513] 
dist 241=[-.03150230332926707826,.29517826812615901385] 
dist 242=[-.01653973296716824305,.33633090477670126237] 
dist 243=[.06804342297915309066,.37570196380735901654] 
dist 244=[.08235635589507534522,.4009862879823493643 ] 
dist 245=[.11277087923446600297,.4207207441918563584 ] 
dist 246=[.12130449479366288401,.4379584589856914299 ] 
dist 247=[.16297011654075196928,.45221136553831531017] 
dist 248=[.16834598553439474934,.46004215327833042741] 
dist 249=[.16564096961600088575,.46464578298097166941] 
dist 250=[.15120657272478261152,.46602850951419987573] 
dist 251=[.13039187544356393768,.46519010875543108126] 
dist 252=[.10224168031530827911,.46361620715034822501] 
dist 253=[.06341067486287250007,.45606726669213973725] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 1, 2, 2, 1, 2] 
dist 0=[75.514151212972864803  ,75.514151212972864803  ] 
dist 1=[75.114869803787972507  ,75.680972069670874455  ] 
dist 2=[74.147403956392914903  ,75.948333127721460604  ] 
dist 3=[72.028375657821302537  ,76.065489947266057103  ] 
dist 4=[69.352862449305388316  ,76.001024017772572602  ] 
dist 5=[66.132796740977092764  ,75.824653485728148891  ] 
dist 6=[61.897541397114572025  ,75.630411308796095608  ] 
dist 7=[55.169902616480128283  ,75.096975441684613117  ] 
dist 8=[48.319306196841489671  ,74.818799717348675956  ] 
dist 9=[43.593029166129981042  ,73.215917014928531793  ] 
dist 10=[38.531662914865477950  ,72.682421690955453828  ] 
dist 11=[32.835862341041270782  ,72.305621642212263890  ] 
dist 12=[27.964652371832965491  ,72.042147168233892184  ] 
dist 13=[22.942123747117215191  ,71.597545430720081690  ] 
dist 14=[18.204432537890117455  ,62.575097223361375964  ] 
dist 15=[14.470334998445280091  ,60.916470857314843067  ] 
dist 16=[10.754992746084696795  ,51.550830664500956209  ] 
dist 17=[6.0923026846879495163 ,33.715973021400897962  ] 
dist 18=[1.6342275766272760744 ,30.698997584617073254  ] 
dist 19=[-1.2643683675921734968 ,23.598159363709072659  ] 
dist 20=[-3.5764263542897491781 ,22.545090779730326376  ] 
dist 21=[-5.6933907519710673037 ,13.086894813996386110  ] 
dist 22=[-7.5237095919059482563 ,11.431349710347268468  ] 
dist 23=[-8.6916955795933886947 ,9.2236692412461646084 ] 
dist 24=[-9.5988099788093545269 ,8.7673390370406868318 ] 
dist 25=[-10.388012121264708908  ,-1.0728244680351364652 ] 
dist 26=[-11.047062041949246975  ,-2.4149254459830401521 ] 
dist 27=[-11.434895890829665603  ,-2.6720087327641912177 ] 
dist 28=[-11.699772988699506735  ,-3.5113996941530460609 ] 
dist 29=[-11.868544607756941243  ,-3.2632273685031082152 ] 
dist 30=[-11.966314180425003932  ,-2.9624136549490526919 ] 
dist 31=[-11.948328052253403467  ,-2.6312345520636118985 ] 
dist 32=[-11.846004701622132644  ,-2.2202470627350119559 ] 
dist 33=[-9.3404108846122929430 ,-1.6004499434167290101 ] 
dist 34=[-9.2198411138586449209 ,-.96788638114854247629] 
dist 35=[-8.8347271882611201766 ,-.50544736534622093759] 
dist 36=[-8.7494130364875562785 ,-.08259512979061952429] 
dist 37=[-7.8730873124516984791 ,.39299632009936215413] 
dist 38=[-7.6835991318730800800 ,.86369554301779047937] 
dist 39=[-7.6146379822521932968 ,1.2675637431373689809 ] 
dist 40=[-7.3324768003311809069 ,1.6992569811571152100 ] 
dist 41=[-5.2916720335468760130 ,2.2899100960032845570 ] 
dist 42=[-5.0260999996859841763 ,2.9643557737633720895 ] 
dist 43=[-4.4164922439718125590 ,3.6054889090387571609 ] 
dist 44=[-4.2950260102697847975 ,4.1758720612539587336 ] 
dist 45=[-3.5257849849526971704 ,4.5681074311568857450 ] 
dist 46=[-3.3899434357083951486 ,4.9051174235960279382 ] 
dist 47=[-3.1252382884307279281 ,5.2552733731047523550 ] 
dist 48=[-3.0616255863639278649 ,5.5598208341478945946 ] 
dist 49=[-2.1412352010078040588 ,5.7148632162749877558 ] 
dist 50=[-2.0297852194848557629 ,5.7946396497885732596 ] 
dist 51=[-2.0035781514911558223 ,5.8073938079718750189 ] 
dist 52=[-1.9356145301321562556 ,5.7387704144658421728 ] 
dist 53=[-1.9083270873331603050 ,5.7019588469710443481 ] 
dist 54=[-1.7617032118657165407 ,5.6608213767562064258 ] 
dist 55=[-1.7247535626731161196 ,5.6273249767577455792 ] 
dist 56=[-1.6511899921080614877 ,5.5288189109770721701 ] 
dist 57=[-2.3208272142619518674 ,5.7028812354994583860 ] 
dist 58=[-2.9836904230311374162 ,5.7704887662235271369 ] 
dist 59=[-3.6192894067074012382 ,5.7957349477984846169 ] 
dist 60=[-4.1868392704417687423 ,5.8002196391242983296 ] 
dist 61=[-4.5783309858646901149 ,5.5999460455032192813 ] 
dist 62=[-4.9149846351084063275 ,5.5465362303986210034 ] 
dist 63=[-5.2638685266239403931 ,5.5135482512695866335 ] 
dist 64=[-5.5690149307054563700 ,5.5004475492298911985 ] 
dist 65=[-5.7312272384326358585 ,.94928140072245336957] 
dist 66=[-5.8196025647412087526 ,.66707498258009465265] 
dist 67=[-5.8339891956739400923 ,.59666516091489997718] 
dist 68=[-5.8082874587216434865 ,.28390883876134671323] 
dist 69=[-5.7774992370136681686 ,.22695717199488440224] 
dist 70=[-5.7104826082945440021 ,.09535538488774124472] 
dist 71=[-5.6757776994491407295 ,.07177888930769584981] 
dist 72=[-5.3261469897484447974 ,1.2207930681604486689 ] 
dist 73=[-5.5176095014919602986 ,2.0356781430127291671 ] 
dist 74=[-5.6236254030584832767 ,2.7002773938408431294 ] 
dist 75=[-5.6874256676637341682 ,3.3308266812819238567 ] 
dist 76=[-5.7104383865934076526 ,3.8890486207494926801 ] 
dist 77=[-5.7057107532471673283 ,4.2652043329036177210 ] 
dist 78=[-5.6892813743300306752 ,4.5789827849596510748 ] 
dist 79=[-5.6040154481962861188 ,4.8884457877651033396 ] 
dist 80=[-5.5675721825851591847 ,5.1584674757050658606 ] 
dist 81=[-2.3588479068563579036 ,5.3149495253935207559 ] 
dist 82=[-2.0630613511627439524 ,5.4178236534991615596 ] 
dist 83=[-1.3989650437831752302 ,5.4740425739657527397 ] 
dist 84=[-1.2581786573959004956 ,5.4958212886136002045 ] 
dist 85=[-.45624881513194368782,5.4899737475922716963 ] 
dist 86=[-.31455820788965706112,5.4154189504743373150 ] 
dist 87=[-.01916715144838986345,5.3915747084469119675 ] 
dist 88=[.05664092066904393317,4.0479009325094293674 ] 
dist 89=[-.61629753604681613318,4.5385347081789870467 ] 
dist 90=[-1.2364768905934831100 ,4.8271008781112358658 ] 
dist 91=[-1.8661533339304341178 ,5.0222858597340912712 ] 
dist 92=[-2.4515109866825273423 ,5.1404594565940711172 ] 
dist 93=[-2.8949450896986323263 ,5.2168634882063060906 ] 
dist 94=[-3.3180566739920878771 ,5.2454383181420715674 ] 
dist 95=[-3.8223690942218886018 ,5.2444210856935063436 ] 
dist 96=[-4.2888761515556903220 ,5.2299364736881600081 ] 
dist 97=[-4.5612167017941046252 ,-.45030046501265790945] 
dist 98=[-4.7427104144869041418 ,-.58496479236892483789] 
dist 99=[-4.8469098191422188916 ,-.63998894535097968281] 
dist 100=[-4.9123419573922676119 ,-.59871560022960322189] 
dist 101=[-4.9392266927846740382 ,-.49156551439547013849] 
dist 102=[-4.9429514785305402528 ,-.31596520504900809666] 
dist 103=[-4.9265253988527661202 ,-.00167082307016824181] 
dist 104=[-4.6093120678397193159 ,.90321643283704345712] 
dist 105=[-5.0564631939266742030 ,1.5264030898591323234 ] 
dist 106=[-5.3243929242529819902 ,2.0607728506958857584 ] 
dist 107=[-5.5116142293572970010 ,2.6114514461357496286 ] 
dist 108=[-5.6368812558537055295 ,3.1285049376650580992 ] 
dist 109=[-5.7154772907157473749 ,3.5287753316721519695 ] 
dist 110=[-5.7283031056901069306 ,3.9189877708340479873 ] 
dist 111=[-5.6935506935217040237 ,4.3959298053448964942 ] 
dist 112=[-5.6760102931841844967 ,4.8431627063583640678 ] 
dist 113=[-5.2237478587252953351 ,5.1148926564172620832 ] 
dist 114=[-5.1368378851812622447 ,5.3093191685828839136 ] 
dist 115=[-4.9011321609512796244 ,5.4482590570773610279 ] 
dist 116=[-4.8344269251976157497 ,5.5404217717062457212 ] 
dist 117=[-4.3595930495529937451 ,5.7207911328421419058 ] 
dist 118=[-4.2516195704274014900 ,6.0194911964979569260 ] 
dist 119=[-4.0671694347787972140 ,6.2344291543375275688 ] 
dist 120=[-4.0136970660090383964 ,6.3903709402923708180 ] 
dist 121=[-4.0306198414538913086 ,6.5037428523937100254 ] 
dist 122=[-4.6383788673877970271 ,6.5489070546233101404 ] 
dist 123=[-5.1864283033446497208 ,6.5526464433099052946 ] 
dist 124=[-5.6522187746815038526 ,6.5366321773258666819 ] 
dist 125=[-5.9319222191788627160 ,6.4191950605582245131 ] 
dist 126=[-6.1280718390700461594 ,6.3780017498382555103 ] 
dist 127=[-6.2606427478792996432 ,6.2015385139935155609 ] 
dist 128=[-6.3522425590045310184 ,6.1691578632075983102 ] 
dist 129=[-6.3849959841406497158 ,2.7190594597378277466 ] 
dist 130=[-6.3808251042801711886 ,2.3353210173962428762 ] 
dist 131=[-6.3625560045651538941 ,2.2471624704087197909 ] 
dist 132=[-6.2410351999889963740 ,1.7182745743394975506 ] 
dist 133=[-6.2004176675652651787 ,1.6163958587756833181 ] 
dist 134=[-6.0200378041893858874 ,1.4152818537300253443 ] 
dist 135=[-5.9935890889815153626 ,1.3620092796459381414 ] 
dist 136=[-2.9504324222857628350 ,.7183451489063490459 ] 
dist 137=[-2.9398884882853320811 ,1.1908276947774230936 ] 
dist 138=[-.90667599740086156213,1.5721716040242604016 ] 
dist 139=[-.73545768854788718841,1.9272582630949917822 ] 
dist 140=[-.3532423710326358512 ,2.2370344613829677406 ] 
dist 141=[-.2746846356603652201 ,2.4376764457022149566 ] 
dist 142=[.17332550898274541873,2.5962188415083991785 ] 
dist 143=[.25022778090218883299,2.7380983497827034817 ] 
dist 144=[.4119445272780982434 ,2.8591700533372727074 ] 
dist 145=[.44741106956580985658,2.9347291684338061421 ] 
dist 146=[.70530977216022428085,2.9912011944658165102 ] 
dist 147=[.74747371892174982721,3.0361519561055318576 ] 
dist 148=[.74795651183686479302,3.0700999422178222840 ] 
dist 149=[.69165597468246459514,3.0826919575787883001 ] 
dist 150=[.60338043616860381431,3.0820166310506629762 ] 
dist 151=[.47634415270225201153,3.0708303686782968270 ] 
dist 152=[.29696412683576974166,2.5416221934287508846 ] 
dist 153=[-6.29427439612671480000e-05,2.5393874666803811674 ] 
dist 154=[-.38743114883939845192,.33689142382234853196] 
dist 155=[-.6495502702078213989 ,.2544093010748058538 ] 
dist 156=[-.8693591581660017661 ,-.21529327151611450397] 
dist 157=[-1.0879905661990362910 ,-.29572433673782131084] 
dist 158=[-1.3507900224594421563 ,-.46515660449792410738] 
dist 159=[-1.6866927751271082341 ,-.50163721703454727044] 
dist 160=[-2.0059308365449873303 ,-.7658007791167419087 ] 
dist 161=[-2.2073174754399255155 ,-.80772048372773487553] 
dist 162=[-2.3603601959142228104 ,-.80575789413513847027] 
dist 163=[-2.4867986115210091190 ,-.74337675421893232598] 
dist 164=[-2.5860165241224446559 ,-.64717165021593468712] 
dist 165=[-2.6305015697227054340 ,-.51031622547844280446] 
dist 166=[-2.6489787316520237474 ,-.31788150668028012794] 
dist 167=[-2.6460882071489935973 ,-2.14683763493196150000e-05] 
dist 168=[-1.9819335992224283350 ,.39781439613917965814] 
dist 169=[-1.9747511998502191125 ,.66665101874614458241] 
dist 170=[-1.5514751422891615707 ,.8916969775446427061 ] 
dist 171=[-1.4946437506980361088 ,1.1148923258398558436 ] 
dist 172=[-1.3567304748219162590 ,1.3190224864805883426 ] 
dist 173=[-1.3236339338690837422 ,1.4680348630077003975 ] 
dist 174=[-1.1095309071138824021 ,1.6555495466730759840 ] 
dist 175=[-1.0658161187083533065 ,1.7849903129540478292 ] 
dist 176=[-.98458787548502888458,1.8995122812050263127 ] 
dist 177=[-.9631174458425348469 ,1.9971293774783955560 ] 
dist 178=[-.59642876615743816515,2.0866026980451414622 ] 
dist 179=[-.54567340678261602403,2.1328211324119632244 ] 
dist 180=[-.4242512013597187778 ,2.1560734988548028801 ] 
dist 181=[-.40285029439935497904,2.1580319218544036124 ] 
dist 182=[-.23139107943167701336,2.1403467120586603519 ] 
dist 183=[-.26514964080822035815,2.1284528625739390403 ] 
dist 184=[-.6979570767621710708 ,2.0926758396876837118 ] 
dist 185=[-.98500016868711988495,2.0745933912762430282 ] 
dist 186=[-1.2194066709734534162 ,1.3351357967357266974 ] 
dist 187=[-1.4422949253368527080 ,1.3005815061491396783 ] 
dist 188=[-1.6399309348370019959 ,1.0787515811114421821 ] 
dist 189=[-1.7736293438639990160 ,1.0338725828438434956 ] 
dist 190=[-1.8857084537774955832 ,.94994792227122776432] 
dist 191=[-1.9971248655050320225 ,.9278228411689124664 ] 
dist 192=[-2.0929764895948273232 ,.56249999169673685865] 
dist 193=[-2.1429819064506941972 ,.51165156684511972647] 
dist 194=[-2.1688373372173845319 ,.3922835115493103728 ] 
dist 195=[-2.1716198246592004721 ,.36963664753121934426] 
dist 196=[-2.1561687741972699013 ,.20779641908391822943] 
dist 197=[-2.1351744777773621343 ,.17818655699995798687] 
dist 198=[-2.0018952991870982073 ,.12594408028740728315] 
dist 199=[-1.8656381947483333291 ,.11430029235594198484] 
dist 200=[-.96442447064210527187,.25016265436832966662] 
dist 201=[-.95907560484368846785,.41519124410232356025] 
dist 202=[-.4274992505275212757 ,.54898160612367505642] 
dist 203=[-.3782652971609127418 ,.67456588691269299531] 
dist 204=[-.26688446254549449847,.78481931336822482261] 
dist 205=[-.24335850703420303502,.85746892854705442291] 
dist 206=[-.10580511919242976155,.91627538433431877374] 
dist 207=[-.08126467242153894930,.97132111748537414768] 
dist 208=[-.03108693965827986525,1.0188064325725867800 ] 
dist 209=[-.01831989102937671321,1.0474613001289794093 ] 
dist 210=[.09206756034418270840,1.0677274196370433247 ] 
dist 211=[.10976813579799019977,1.0817576962777870178 ] 
dist 212=[.12778885292196741874,1.0906576002891474139 ] 
dist 213=[.12643088041944136918,1.0904633587514088136 ] 
dist 214=[.11667043173797191979,1.0850514552371371696 ] 
dist 215=[.09504929878124111696,1.0800992960195947718 ] 
dist 216=[.06066411116299173518,.87534105408114187106] 
dist 217=[-.00497367567243025647,.8728943431479899261 ] 
dist 218=[-.15758439002705564965,.20202432084712185594] 
dist 219=[-.2659420535795586692 ,.17412653486034796522] 
dist 220=[-.37129460172657627504,.01341343368118487913] 
dist 221=[-.46367568763962012225,-.01461531686226677178] 
dist 222=[-.55425903595541120714,-.07287679747503382652] 
dist 223=[-.66570839352377229034,-.08720167267194357392] 
dist 224=[-.77058065044247633029,-.17916347671830578476] 
dist 225=[-.83493396368279139572,-.1712176138440696382 ] 
dist 226=[-.8817446164218683395 ,-.15932962049289434467] 
dist 227=[-.91665525579913574586,-.14436601796065183123] 
dist 228=[-.94219725535487694309,-.12432817319918573141] 
dist 229=[-.95164497809413024803,-.09220367139351756325] 
dist 230=[-.95381886624809520804,-.05488614410224279862] 
dist 231=[-.95035219676816165991,-2.85166430456987000000e-07] 
dist 232=[-.36373574822261406049,.09393542872203501416] 
dist 233=[-.36153464054693578808,.1560096864243362322 ] 
dist 234=[-.3255484033984458362 ,.20645254170573202136] 
dist 235=[-.31915103541710778282,.25400123649430048039] 
dist 236=[-.30229349005004393604,.29588211115400639565] 
dist 237=[-.29772065675224845696,.32372121917918144987] 
dist 238=[-.26572828205012452702,.35364648437827355355] 
dist 239=[-.25861259023545370918,.37357127363123230421] 
dist 240=[-.24621746727074216085,.38838981345881480837] 
dist 241=[-.24276728429800106158,.40005169947767711886] 
dist 242=[-.16770637820790296914,.40898051197852685166] 
dist 243=[-.1573232976901152256 ,.41289932286120753258] 
dist 244=[-.1324978528440264956 ,.41388760023098324646] 
dist 245=[-.12756538356687029048,.4090591330320009504 ] 
dist 246=[-.09182021163332831432,.3632976665948000987 ] 
dist 247=[-.08501757009670659686,.32797404910704741814] 
dist 248=[-.07326779403094770163,.16397215640898297884] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 0, 0, 0, 1, 2] 
dist 0=[62.311145538079052189  ,62.311145538079052189  ] 
dist 1=[61.761422873462048283  ,62.727132997449594728  ] 
dist 2=[59.982506347085318826  ,63.238883023958409192  ] 
dist 3=[58.026988007423964927  ,63.348560031998796107  ] 
dist 4=[56.448847936330586801  ,63.156399614798956628  ] 
dist 5=[54.843452899163030889  ,63.027946946211459029  ] 
dist 6=[52.779609485077392473  ,62.868225830536846055  ] 
dist 7=[50.578131510021080945  ,62.698831755240760604  ] 
dist 8=[48.423657953660026265  ,56.938936427377841036  ] 
dist 9=[45.890818460221447292  ,56.075682523715724989  ] 
dist 10=[42.179482077278740971  ,54.414766215088256332  ] 
dist 11=[38.373755827340252544  ,53.951381330551966979  ] 
dist 12=[35.464302703488677018  ,52.172942644419299376  ] 
dist 13=[32.654765123609809709  ,51.723415340838642939  ] 
dist 14=[29.247883430351052244  ,50.842968811251193060  ] 
dist 15=[24.943073356626699874  ,50.570629955312946344  ] 
dist 16=[17.748566827195918052  ,32.746021140493889587  ] 
dist 17=[12.928008585640241122  ,31.893317520997204570  ] 
dist 18=[8.9216030109882164961 ,31.665877088122426047  ] 
dist 19=[4.9760056808222421952 ,18.439936762992489287  ] 
dist 20=[1.3671968622742011101 ,11.863698676680222652  ] 
dist 21=[-1.2956669129207322421 ,10.714213378239915088  ] 
dist 22=[-3.7803417221154305447 ,9.2413957449973060616 ] 
dist 23=[-6.6793436780971872273 ,8.9860895685595309534 ] 
dist 24=[-9.3588934694834859382 ,1.2035250115876608563 ] 
dist 25=[-10.968292840989502830  ,.31432004381370159667] 
dist 26=[-12.110164140609488399  ,-1.6225861478604658251 ] 
dist 27=[-12.924119350640863363  ,-1.9060986690904557110 ] 
dist 28=[-13.511444827581053609  ,-3.9024099968708454216 ] 
dist 29=[-13.747189895119895585  ,-4.1968640432585209181 ] 
dist 30=[-13.810010101463699701  ,-4.7058388382594076532 ] 
dist 31=[-13.763988215118971387  ,-4.7856878907554567580 ] 
dist 32=[-12.074542056926431403  ,-5.1055008137626862783 ] 
dist 33=[-11.806477287045415454  ,-4.6376909761457208254 ] 
dist 34=[-11.153182324425596044  ,-2.9694839013744623563 ] 
dist 35=[-10.891394531354177600  ,-1.2497697987022724422 ] 
dist 36=[-9.2722047679333755295 ,-.08000618603107654864] 
dist 37=[-8.9441161266755184416 ,.90426989839665967887] 
dist 38=[-8.6103757195414324140 ,1.8849577858082627057 ] 
dist 39=[-8.5415527069498241002 ,2.7818264717684371320 ] 
dist 40=[-5.8619598013314645466 ,3.4320954128868585454 ] 
dist 41=[-5.5214374283870114766 ,4.0227291761563931725 ] 
dist 42=[-5.4010455649977950291 ,4.6818753023335164805 ] 
dist 43=[-3.9723771964959438190 ,5.2905135887560298911 ] 
dist 44=[-3.7310467199212809170 ,5.6798384018151542173 ] 
dist 45=[-3.6765357874942983759 ,5.9808792868292511453 ] 
dist 46=[-3.5959725308578524866 ,6.2376928603772474838 ] 
dist 47=[-3.5719455480123961736 ,6.4446341938611690303 ] 
dist 48=[-.69908267789728633023,6.5468952431834879607 ] 
dist 49=[-.3926079949454640796 ,6.5913615676910431630 ] 
dist 50=[-.33170640967041186759,6.5829968483832899920 ] 
dist 51=[1.9823653209886178894 ,4.1263473698922971901 ] 
dist 52=[2.1973721280556679748 ,4.3966049162277639861 ] 
dist 53=[2.6402803655766844295 ,4.5390935429397520747 ] 
dist 54=[2.6951516350435295583 ,4.6157980158462453133 ] 
dist 55=[2.5241272115916188505 ,4.6324108046128425646 ] 
dist 56=[2.3069391192994965176 ,4.6556126099338811126 ] 
dist 57=[2.0831759552494248105 ,4.8126942275310334591 ] 
dist 58=[1.8137974241080601193 ,4.9266093393281197147 ] 
dist 59=[1.4141394359975876319 ,5.0135727179288825082 ] 
dist 60=[.96326808493796263327,5.0781726451367906911 ] 
dist 61=[.48929833494324803577,5.1025923909829074856 ] 
dist 62=[-.09138400109438464093,5.1028841813117830726 ] 
dist 63=[-.96830576263000231376,5.0959765524152249316 ] 
dist 64=[-1.9216036293371991300 ,3.5671144645897844564 ] 
dist 65=[-2.5517450599377946125 ,3.4872148775445322871 ] 
dist 66=[-3.0651894944543671580 ,3.4529540204127101246 ] 
dist 67=[-3.5529131412648885920 ,1.8241894863911336517 ] 
dist 68=[-3.9863200233814393481 ,1.6581303337484752918 ] 
dist 69=[-4.2830722971993978743 ,1.2849670118280064124 ] 
dist 70=[-4.5364403112844617673 ,1.2017614075248762483 ] 
dist 71=[-4.7967943090318375008 ,.74197596384024514664] 
dist 72=[-5.0199912463836560953 ,.65830471248949543881] 
dist 73=[-5.1251193690724244726 ,.48197586508758080228] 
dist 74=[-5.1753483564239095382 ,.43476230294625963883] 
dist 75=[-5.1793945180120804461 ,.03648990717398973120] 
dist 76=[-5.0625644498210728108 ,-.02847186388172811431] 
dist 77=[-5.0214599357335202705 ,-.11794295803747976915] 
dist 78=[-4.9871158060227226185 ,-.14148615270782251744] 
dist 79=[-4.9531703806317271381 ,.62960933257106089636] 
dist 80=[-3.7007693220847920977 ,1.7486608395690011316 ] 
dist 81=[-3.6917742924259781436 ,2.4905223719418428981 ] 
dist 82=[-3.6779481994179869178 ,3.0963893594827471520 ] 
dist 83=[-2.8385509117990624772 ,3.6730428764923549010 ] 
dist 84=[-2.2730079559881224302 ,4.1852103232295639884 ] 
dist 85=[-2.1622507225226375112 ,4.5338907591998412682 ] 
dist 86=[-1.9413325404349934759 ,4.8288874261461326429 ] 
dist 87=[-1.8812609336530260221 ,5.1269691416966963544 ] 
dist 88=[-1.1134479316712813628 ,5.3844291759675805369 ] 
dist 89=[-1.0005982344830051295 ,5.5174033768111787596 ] 
dist 90=[-.75764372019052781727,5.5845124131955338238 ] 
dist 91=[-.6928858086323944371 ,5.5943221124732845362 ] 
dist 92=[-.42573304568449019892,5.5451237857320861465 ] 
dist 93=[-.37527564814184773027,5.5115772212101100153 ] 
dist 94=[-.56463116439069301768,5.4382028002483076955 ] 
dist 95=[-.78396255096567650604,5.4027190675208426470 ] 
dist 96=[-1.2820952871623169871 ,5.0408045062120977378 ] 
dist 97=[-2.0736444882330301334 ,5.0453721794752605681 ] 
dist 98=[-2.7181696006630530068 ,5.0315138452872341380 ] 
dist 99=[-3.3280228962971735424 ,4.8828786965814008634 ] 
dist 100=[-3.9980343891022872466 ,4.8391264897459710614 ] 
dist 101=[-4.5384965876331373709 ,4.7011369783029878230 ] 
dist 102=[-5.0173794315568511445 ,4.6547400126848649880 ] 
dist 103=[-5.4183995715265367391 ,4.3003379751385674991 ] 
dist 104=[-5.6483372697376384050 ,4.2137089151487066726 ] 
dist 105=[-5.7963647164498945871 ,4.0756811440424846736 ] 
dist 106=[-5.8707207397260689793 ,4.0299491869246905172 ] 
dist 107=[-5.9084623652879287699 ,2.9331629449158359024 ] 
dist 108=[-5.9104656880412998792 ,2.7789487782513525119 ] 
dist 109=[-5.8866982896520705390 ,2.4283778770723964455 ] 
dist 110=[-5.8634699548278261129 ,2.3368707480696332147 ] 
dist 111=[-5.7353151384364004872 ,1.8733841662669844278 ] 
dist 112=[-5.6928964906160970274 ,1.7827150849888067223 ] 
dist 113=[-5.5303965921791219904 ,1.5820345969260832635 ] 
dist 114=[-5.4938808057147416079 ,1.7801353491313248112 ] 
dist 115=[-1.4104044518980380224 ,2.1781227861071918268 ] 
dist 116=[-.65893014609043828826,2.5249949613061983597 ] 
dist 117=[-.52445565083835104279,2.8508403173980273843 ] 
dist 118=[-.24964213235298464638,3.2665758240985738906 ] 
dist 119=[-.17953233964453195417,3.7622183097793800625 ] 
dist 120=[.436298295889931362  ,4.2208155889765299372 ] 
dist 121=[.53464905724063054849,4.4888101604838972933 ] 
dist 122=[.64143444942704639085,4.6677651694718472044 ] 
dist 123=[.64140927877801159766,4.7712582919574390554 ] 
dist 124=[.59626654274295193942,4.8365115150296462851 ] 
dist 125=[.48654670396913859418,4.8629583001124247929 ] 
dist 126=[.30883987659031045907,4.8659765165094726148 ] 
dist 127=[-.00745605656541491668,4.8501651355480539651 ] 
dist 128=[-.89740052279746168223,1.0197172501007979936 ] 
dist 129=[-1.5100791019367022299 ,.81645937693770269116] 
dist 130=[-2.0351345513886136575 ,.36328624255532390887] 
dist 131=[-2.5757423740280328614 ,.27033635104089659585] 
dist 132=[-3.0830558531348343966 ,-.25826871825817048821] 
dist 133=[-3.4753303874896127881 ,-.34868103740794921632] 
dist 134=[-3.8573225988897355778 ,-.53937542674175500842] 
dist 135=[-4.3236294759808094159 ,-.58000287092559617834] 
dist 136=[-4.7606068467783577206 ,-.74749554975542099748] 
dist 137=[-5.0256299833197215500 ,-.65200710318211250699] 
dist 138=[-5.2146875281689325070 ,-.53025643117897079945] 
dist 139=[-5.3487060058427686423 ,-.34131043615023461968] 
dist 140=[-5.4366301373459833660 ,-.12432603934335977854] 
dist 141=[-5.4549444250131687857 ,.10924517939239933479] 
dist 142=[-5.4235512458810403138 ,.86843363430533695994] 
dist 143=[-5.4176133831123761681 ,2.0285934838520297838 ] 
dist 144=[-5.0631758434678552584 ,3.1867112734718107381 ] 
dist 145=[-4.9896794447879209959 ,3.9391310864756227475 ] 
dist 146=[-4.7843776844543663223 ,4.5362870237391745355 ] 
dist 147=[-4.7244023774568170781 ,5.0751990758753104985 ] 
dist 148=[-4.2879054946656608345 ,5.5335300402986450269 ] 
dist 149=[-4.1869621001037447722 ,5.8093217422210422855 ] 
dist 150=[-4.0181790390489480333 ,6.0034231954587581512 ] 
dist 151=[-3.9673677030103658880 ,6.1359666882748700508 ] 
dist 152=[-2.8104791161827826920 ,6.2282618576695796593 ] 
dist 153=[-2.6493323516200002462 ,6.2618493855666720535 ] 
dist 154=[-2.2733362206428610695 ,6.2587733258484339425 ] 
dist 155=[-2.1876752871836896213 ,6.2412036547244725406 ] 
dist 156=[-1.6678667532554471310 ,6.1229316162515376729 ] 
dist 157=[-1.5677979144043578141 ,6.0831542110486339655 ] 
dist 158=[-1.3717781188769773992 ,5.9073486958235003764 ] 
dist 159=[-1.3202590407249768993 ,5.8807332089302643459 ] 
dist 160=[-.76186300164866665422,1.7054665321043237739 ] 
dist 161=[-1.2437438643987901528 ,1.6370952104897437624 ] 
dist 162=[-1.6421975851796559383 ,1.4726088042820592106 ] 
dist 163=[-2.0137576010882505138 ,1.4336938732521200422 ] 
dist 164=[-2.3382800009614511042 ,1.1845740722179342189 ] 
dist 165=[-2.5491437008425368159 ,1.1343325114081125082 ] 
dist 166=[-2.7165220818776451536 ,1.0401612167473058075 ] 
dist 167=[-2.8676213640286710316 ,1.0153539438734040279 ] 
dist 168=[-2.9968328713386300289 ,.61073126453052166303] 
dist 169=[-3.0769209125179028159 ,.55429586432565082751] 
dist 170=[-3.1361316393495549296 ,.42271345056724992417] 
dist 171=[-3.1820825160651443075 ,.39709665920245969361] 
dist 172=[-3.2158338551398866896 ,.22139775947586176211] 
dist 173=[-3.2263917168380661855 ,.18932966361884832452] 
dist 174=[-3.2219529774427745413 ,.13105140205928892811] 
dist 175=[-3.2105119282510774162 ,.11771669163355245454] 
dist 176=[-1.0014250189826488687 ,.52115514912226312208] 
dist 177=[-.81499700617682910954,.86772077349690741852] 
dist 178=[-.3987015749266251984 ,1.1518409816904296752 ] 
dist 179=[-.31308449972871458726,1.4238496544245022826 ] 
dist 180=[.17547484021246879431,1.6662909336562281916 ] 
dist 181=[.25941729300593247339,1.8324938668509357959 ] 
dist 182=[.43581679684569634114,1.9741973331352962320 ] 
dist 183=[.47478214838539040082,2.1189326657505377991 ] 
dist 184=[.75857025508451590205,2.2462379505472637165 ] 
dist 185=[.80548126514808534362,2.3406877248723969445 ] 
dist 186=[.80700955908093608782,2.4967649153369477716 ] 
dist 187=[.7469696606475257296 ,2.6236061110910043317 ] 
dist 188=[.65217971769513249194,2.7215038618050855307 ] 
dist 189=[.51512185253939651807,2.7621521017608955153 ] 
dist 190=[.32126173247368684103,2.7778573171011868923 ] 
dist 191=[-6.04644270023758280000e-05,2.7762801244299278902 ] 
dist 192=[-.42574950518242703111,1.2304278525594559439 ] 
dist 193=[-.71395115098104466966,1.1212828576724291257 ] 
dist 194=[-.95579092906123682474,.87186955719542049988] 
dist 195=[-1.1965932539443477350 ,.81812870085705068811] 
dist 196=[-1.4174428194292313439 ,.49840845573496527215] 
dist 197=[-1.5797093005652024025 ,.43989395667182059712] 
dist 198=[-1.7296652417652978350 ,.32242933247348077813] 
dist 199=[-1.9014193345493735039 ,.2923276120523806413 ] 
dist 200=[-2.0567058788349325753 ,-.01632266266194398396] 
dist 201=[-2.1409878355084838866 ,-.06366514560586010789] 
dist 202=[-2.1891563961853854319 ,-.13526765176990295411] 
dist 203=[-2.2005245758429345728 ,-.15338783084053275407] 
dist 204=[-2.1987113283833097080 ,-.1622461934270729615 ] 
dist 205=[-2.1951482409402254044 ,-.13959197030324977412] 
dist 206=[-2.0989370036517103371 ,-.09252255157913588321] 
dist 207=[-1.8928206972971140801 ,1.00590918237243310000e-05] 
dist 208=[-.62447632234220332157,.17446736465938800546] 
dist 209=[-.55034220549470408939,.2930667263002899315 ] 
dist 210=[-.38280031201467765026,.39311725017910351467] 
dist 211=[-.34748407946983670825,.49360051917930681125] 
dist 212=[-.14136905044823676815,.60825728337567572613] 
dist 213=[-.10469706043880998083,.72746035990668463851] 
dist 214=[-.02956572548549400829,.84211592161684155962] 
dist 215=[-.01046415462345337644,.98008055729441919555] 
dist 216=[.45187992125410577679,1.1083622259532359611 ] 
dist 217=[.45055626550035683429,1.1844012931201400039 ] 
dist 218=[.40263038954286791165,1.2365144670327875384 ] 
dist 219=[.32300552091421077811,1.2693776384452908335 ] 
dist 220=[.22939067408379689733,1.2913403113086924006 ] 
dist 221=[.12567157718551982902,1.2999813685118200124 ] 
dist 222=[-.00500571268024054417,1.3004946633242573036 ] 
dist 223=[-.20613212119301174377,1.2972331402821678070 ] 
dist 224=[-.40777963700285555188,.77702916110946491427] 
dist 225=[-.54053514754493823673,.75442343265735094114] 
dist 226=[-.64786481841472210657,.69815332331074613061] 
dist 227=[-.74811192912501809239,.68409082497962432826] 
dist 228=[-.83577938083967874933,.59056509360098204534] 
dist 229=[-.89294030482543181038,.57085093836427799865] 
dist 230=[-.9385357510329791521 ,.53501820467470369729] 
dist 231=[-.98007909683989844739,.52546034508873986313] 
dist 232=[-1.0144583250695231632 ,.34352474289668923299] 
dist 233=[-1.0314826623562009909 ,.31866662341063322513] 
dist 234=[-1.0390059145436061421 ,.25659942548536046993] 
dist 235=[-1.0387356249349784160 ,.24735934985285196306] 
dist 236=[-.93762655823088537737,.15186399978638456055] 
dist 237=[-.92681612098429773482,.13400910665347390868] 
dist 238=[-.81793492980896259232,.11273400245553603016] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 0, 2] 
dist 0=[70.915235327832327241  ,70.915235327832327241  ] 
dist 1=[70.722429453772905104  ,70.906090871466278622  ] 
dist 2=[69.955123594692337299  ,70.915235327832327241  ] 
dist 3=[68.619666851894209286  ,70.799444599778883842  ] 
dist 4=[66.159059490626227420  ,70.674179410774011146  ] 
dist 5=[63.162361212502035784  ,70.521737760418196115  ] 
dist 6=[59.687048110413461908  ,70.345413286041093085  ] 
dist 7=[55.194108339856329282  ,70.117932947766443246  ] 
dist 8=[48.135416954969400737  ,69.925841445160606406  ] 
dist 9=[40.972524731352833221  ,69.414510970780675598  ] 
dist 10=[36.063503520095716947  ,69.226079858413206054  ] 
dist 11=[31.863109970872971080  ,69.117687396993474323  ] 
dist 12=[27.528350319589574881  ,69.090283935178343273  ] 
dist 13=[23.434945637185022901  ,61.030838845227844810  ] 
dist 14=[20.197480519513745897  ,60.378543860140652883  ] 
dist 15=[16.963019952602273833  ,53.918327355376372749  ] 
dist 16=[12.879843898405372271  ,43.603395484182521138  ] 
dist 17=[8.9528711414553165562 ,35.752367446180909510  ] 
dist 18=[6.3443347247677543370 ,33.111908823354846418  ] 
dist 19=[4.1957609399352121174 ,26.849864871234071240  ] 
dist 20=[2.1042929764475776322 ,25.946574483238805591  ] 
dist 21=[.19884140698978430993,17.453192973651320425  ] 
dist 22=[-1.2081320507506948798 ,15.957469777433762447  ] 
dist 23=[-2.5293194299484968666 ,14.064736534293563081  ] 
dist 24=[-4.0945480993554249071 ,13.735599446026115049  ] 
dist 25=[-5.5520982693082038194 ,3.2832024137710764249 ] 
dist 26=[-6.4434881839233164198 ,2.0852603869539420378 ] 
dist 27=[-7.1022033257358802868 ,-.5345236244095729577 ] 
dist 28=[-7.6288425683079976784 ,-.9252529548986045929 ] 
dist 29=[-8.0411362022007858533 ,-3.6461655356682236085 ] 
dist 30=[-8.2425549942742026593 ,-4.0431291890925626753 ] 
dist 31=[-8.3384040939826886793 ,-4.7620666825201213577 ] 
dist 32=[-8.3508236420155759313 ,-4.8670561627396375402 ] 
dist 33=[-8.2305957908734980252 ,-5.9668815972912249683 ] 
dist 34=[-8.1856793837828326432 ,-5.3972104745004288508 ] 
dist 35=[-8.0227555387798381878 ,-4.7683545586619692722 ] 
dist 36=[-7.9682397795167870064 ,-3.8998010922163491972 ] 
dist 37=[-7.5108323611949472009 ,-2.9479974461433667590 ] 
dist 38=[-7.4003321850237809970 ,-1.9864422581445293632 ] 
dist 39=[-7.2290672900243202934 ,-.8358288900655700108 ] 
dist 40=[-7.1710597256550575716 ,.87080945179061651017] 
dist 41=[-6.4462744633742387740 ,2.5691291517467442083 ] 
dist 42=[-6.3304665420973202374 ,3.6867772466757381333 ] 
dist 43=[-6.0764180895183964413 ,4.5919536810385849225 ] 
dist 44=[-6.0020554787814540049 ,5.4426925585835182728 ] 
dist 45=[-5.6948825588274982108 ,6.1928373519193305477 ] 
dist 46=[-5.6309813331637641893 ,6.6967675124073799909 ] 
dist 47=[-5.4885717302269920666 ,7.1170268113233313611 ] 
dist 48=[-5.4466144128659893532 ,7.5335197068742909885 ] 
dist 49=[-1.1268771305129895687 ,7.8893015563310581391 ] 
dist 50=[-.9904946044964109876 ,8.0673336603502360484 ] 
dist 51=[-.7244422243276394511 ,8.1520397158871932863 ] 
dist 52=[-.6570001504527962829 ,8.1635333728392482010 ] 
dist 53=[-.42708197905158174172,8.0618918023318043834 ] 
dist 54=[-.37322144265323612371,8.0071127551744310589 ] 
dist 55=[-.31841690275425454567,7.9064994444231588404 ] 
dist 56=[-.30817625861334901186,7.8621405454306087469 ] 
dist 57=[-1.8925338491956937079 ,8.0110494169745496192 ] 
dist 58=[-3.0320757898569832209 ,8.1137272168106683293 ] 
dist 59=[-3.9574535120709892734 ,8.1527744876907569479 ] 
dist 60=[-4.8291285316792486310 ,8.1610301032917945776 ] 
dist 61=[-5.5969440924089415234 ,7.8522878703480328788 ] 
dist 62=[-6.1081126994676898592 ,7.7718797466858859941 ] 
dist 63=[-6.5279966392235516044 ,7.7234828865718471732 ] 
dist 64=[-6.9317689067789099664 ,7.7062996350975997102 ] 
dist 65=[-7.2806579842765688516 ,5.6815045002957586614 ] 
dist 66=[-7.4816460884726253993 ,5.4246223169397339280 ] 
dist 67=[-7.6124467441314165736 ,4.8284582952642828196 ] 
dist 68=[-7.6813656587079034588 ,4.6813825676901709964 ] 
dist 69=[-7.7052032908729282009 ,3.8485509257871145508 ] 
dist 70=[-7.7016429938022092924 ,3.6832492010104488557 ] 
dist 71=[-8.1335327933877869746 ,3.3483287553420316654 ] 
dist 72=[-8.5484868617466249061 ,3.2548567472561501635 ] 
dist 73=[-8.8985881859264292742 ,2.0783272487160494140 ] 
dist 74=[-9.0717898519689238944 ,1.9041753204090631071 ] 
dist 75=[-9.1486387278499610331 ,1.6907146675968914163 ] 
dist 76=[-9.1556539939587473824 ,2.5749026450676276514 ] 
dist 77=[-9.0364109139476141551 ,3.3971209351645736583 ] 
dist 78=[-8.9766002190450345401 ,4.0206200588131575566 ] 
dist 79=[-8.8319363643040925134 ,4.6162435940400873144 ] 
dist 80=[-8.7646669949584760029 ,5.3273011490545135501 ] 
dist 81=[.69012360532014395837,5.9858438943322748294 ] 
dist 82=[.82876612649424642365,6.3720295750068152906 ] 
dist 83=[.97186528437002591889,6.6316460466247055090 ] 
dist 84=[.96364791860423731521,6.7853981235624735649 ] 
dist 85=[.89022035599913553774,6.8839828354824371279 ] 
dist 86=[.72452028240791554917,6.9589458974769266792 ] 
dist 87=[.46000246991039601137,7.4081788771035063744 ] 
dist 88=[-.00753219865318348836,7.8188027778810113238 ] 
dist 89=[-1.2520846622401181740 ,8.1696588691027421060 ] 
dist 90=[-2.1174046938130104850 ,8.3805206750381426437 ] 
dist 91=[-2.8580067416500531943 ,8.5287420066243231496 ] 
dist 92=[-3.6190480906904988411 ,8.6297499125493437276 ] 
dist 93=[-4.3323247068091837015 ,8.6924411504183396595 ] 
dist 94=[-4.8824373392415045547 ,8.6878339807383317694 ] 
dist 95=[-5.4168145650650855440 ,8.6427103530912622338 ] 
dist 96=[-6.0673400730380186428 ,8.6042264343042832839 ] 
dist 97=[-6.6761232214273788408 ,3.0839788662030087082 ] 
dist 98=[-7.0440264610427390109 ,2.6028174005779185145 ] 
dist 99=[-7.3049094323197168493 ,1.5248754735949815252 ] 
dist 100=[-7.4868781301010693073 ,1.3010245088575235024 ] 
dist 101=[-7.6048281675073577914 ,.01789704036695832472] 
dist 102=[-7.6283568416825351925 ,.01472693387713135409] 
dist 103=[-7.5835370500487068618 ,.42332016375838789704] 
dist 104=[-7.5722007507465540653 ,1.0470372409060685273 ] 
dist 105=[-7.0416941361167320076 ,1.6698709674669832932 ] 
dist 106=[-6.9350749770395958775 ,2.0749421803812192984 ] 
dist 107=[-6.6393513975982983042 ,2.3969089229930725855 ] 
dist 108=[-6.5549451108386821464 ,2.6883139924629608620 ] 
dist 109=[-5.9358212900855700228 ,2.9367557925296330155 ] 
dist 110=[-5.7936414413245282511 ,3.0873810261571812852 ] 
dist 111=[-5.2968304615311970176 ,3.1947726798107664641 ] 
dist 112=[-5.2367702068184783223 ,3.2707952879445079351 ] 
dist 113=[-1.4695278765639246153 ,3.3252030276228076814 ] 
dist 114=[-1.3838396425315769304 ,3.3463916268116962953 ] 
dist 115=[-1.1829716939069725250 ,3.3472482651496529672 ] 
dist 116=[-1.1384145469661278486 ,3.3385372513826987628 ] 
dist 117=[-.85854866738782411152,3.2786901589798353487 ] 
dist 118=[-.80481168417441025925,3.2579515856676048685 ] 
dist 119=[-.70196048285739703096,3.1660281988207406610 ] 
dist 120=[-.67559499361747960042,3.3751432358866810397 ] 
dist 121=[.28847912423050116517,3.6303973046950747775 ] 
dist 122=[.38456103446808663984,3.7662116242814183069 ] 
dist 123=[.5996467973232432944 ,3.8417551874433706653 ] 
dist 124=[.6338057020952779178 ,3.8582956043791687054 ] 
dist 125=[.87499670743152136906,3.8360644308607179404 ] 
dist 126=[.91241957907865859929,3.8254313249192715313 ] 
dist 127=[.45723531262226756101,3.8142780934798007535 ] 
dist 128=[-.3562998080899870098 ,3.7995448569768776848 ] 
dist 129=[-1.1747315944900156785 ,2.8022699901265500894 ] 
dist 130=[-1.7192178438758357817 ,2.6781447737345430782 ] 
dist 131=[-2.1657347880019918887 ,2.3822280836368400780 ] 
dist 132=[-2.5934562671213771815 ,2.3132035246071866613 ] 
dist 133=[-2.9748536193899958199 ,1.8767643307653102356 ] 
dist 134=[-3.2366260351144548050 ,1.7899211419495031199 ] 
dist 135=[-3.4601486948731008923 ,1.6254702766950697655 ] 
dist 136=[-3.6890032464228937940 ,1.5822789661020969640 ] 
dist 137=[-3.8882668970199418209 ,.9154571242889765946 ] 
dist 138=[-3.9937781737537587983 ,.8215538113667819571 ] 
dist 139=[-4.0505234181310822098 ,.60937535839897194316] 
dist 140=[-4.0585552947193027196 ,.56312203996164615058] 
dist 141=[-4.0375281986499002445 ,.30018468827213235229] 
dist 142=[-4.0160938853113807233 ,.25277833600734541037] 
dist 143=[-3.9624416226582886912 ,.15408467766683866696] 
dist 144=[-3.9346651375280042842 ,.12825879184977260825] 
dist 145=[-.93668133125661313433,.86842879303603412223] 
dist 146=[-1.0071541667519232631 ,1.4441069565227394655 ] 
dist 147=[-1.0569186203221939685 ,1.9150398896275265012 ] 
dist 148=[-1.0912214033977639827 ,2.3642053358714127767 ] 
dist 149=[-1.1153434311767931563 ,2.7634126285196466443 ] 
dist 150=[-1.1245061544735353417 ,3.0351081662575463048 ] 
dist 151=[-1.1253283037980417179 ,3.2646434777726026868 ] 
dist 152=[-1.1227722779647806467 ,3.4957122615948676587 ] 
dist 153=[.09575693161392055495,3.6983168252650570326 ] 
dist 154=[.12807969951408880867,3.8143343293543824868 ] 
dist 155=[.19787649017078761035,3.8888107267690734440 ] 
dist 156=[.21120901741387974964,3.9257455435347360010 ] 
dist 157=[.2809905908472872172 ,3.9362163146844863832 ] 
dist 158=[.29246125735759966355,3.9314733519082684641 ] 
dist 159=[.31044822686448768421,3.8685868881202930396 ] 
dist 160=[.31313743188542501257,3.8571225459292693952 ] 
dist 161=[-.07507866340600665961,1.9180967944193980640 ] 
dist 162=[-.60279079978773213211,1.7315564430583235067 ] 
dist 163=[-1.0491089381795009413 ,1.3069228127611414668 ] 
dist 164=[-1.4992028879319741407 ,1.2161104623664099252 ] 
dist 165=[-1.9156749817776399707 ,1.1246225738121290903 ] 
dist 166=[-2.2279063234065378788 ,1.1255124208106585886 ] 
dist 167=[-2.5226644558870711414 ,1.1196898889420569791 ] 
dist 168=[-2.8694519757548815999 ,1.1130108202354563537 ] 
dist 169=[-3.1878918892196349207 ,.99997164387470668222] 
dist 170=[-3.3695973368921589085 ,.98005455434360688424] 
dist 171=[-3.4854178548460649596 ,.92769185700017750311] 
dist 172=[-3.5411029387701158678 ,.91353109806141537109] 
dist 173=[-3.5712001140022520977 ,.814639908111010541  ] 
dist 174=[-3.5849737917650579700 ,.79268415642479488438] 
dist 175=[-3.5893890161571731256 ,.75436403982179815052] 
dist 176=[-3.5821637660374725175 ,.74373753712478136323] 
dist 177=[-1.2576708005995119382 ,.68002503413224358875] 
dist 178=[-1.2699856112268405137 ,1.1497153608340914492 ] 
dist 179=[-1.2732078007044851288 ,1.5540138075572495364 ] 
dist 180=[-1.2708997011833477917 ,1.9731175177450429461 ] 
dist 181=[-1.2504936490435571443 ,2.3681673729658632847 ] 
dist 182=[-1.2426894403190023410 ,2.6765370046126195595 ] 
dist 183=[-1.2108377996260839496 ,2.9795665604074307657 ] 
dist 184=[-1.2031426861573194735 ,3.3533197473498277190 ] 
dist 185=[-.00082823128605586520,3.7054737605046410231 ] 
dist 186=[-.00415685126077531654,3.9223639705161862982 ] 
dist 187=[-.00993879348216091877,4.0810804156808884591 ] 
dist 188=[-.125566432587697211  ,4.2012324880931963002 ] 
dist 189=[-.30327587991495169829,4.2869830080090541008 ] 
dist 190=[-.4880913802497840287 ,4.3085031237641735348 ] 
dist 191=[-.83731946781383477961,4.3043455260164334002 ] 
dist 192=[-1.7506355489647863541 ,4.2876911414602366439 ] 
dist 193=[-2.6614476993375437946 ,4.0956479257293396182 ] 
dist 194=[-3.2513654371730657349 ,4.0483032267278062689 ] 
dist 195=[-3.7174869715320033348 ,3.9086515238447570759 ] 
dist 196=[-4.1345893621376650474 ,3.8653412232657139533 ] 
dist 197=[-4.4867895125639713686 ,3.5403966086938629874 ] 
dist 198=[-4.6940754101599243514 ,3.4632096739604447586 ] 
dist 199=[-4.8343081961537100707 ,3.3378688671455826552 ] 
dist 200=[-4.9190948561212742181 ,3.2980614437064391439 ] 
dist 201=[-4.9723914528263141641 ,2.3663020917701787971 ] 
dist 202=[-4.9870391925890435388 ,2.2360175946488018868 ] 
dist 203=[-4.9761414176748606931 ,1.9364051555087695543 ] 
dist 204=[-4.9593752577390384522 ,1.8629099940434331769 ] 
dist 205=[-4.8586578586446473164 ,1.4591850202085976898 ] 
dist 206=[-4.8251086199926786622 ,1.3809120877574099816 ] 
dist 207=[-4.6857396505276610849 ,1.2168895301248503094 ] 
dist 208=[-4.6605625992567967081 ,1.1708541050282463947 ] 
dist 209=[-1.3159910000076230597 ,.38035284339080263755] 
dist 210=[-1.3629262028244491798 ,.47962337181601997735] 
dist 211=[-1.3899417345108307992 ,.6347306908884013075 ] 
dist 212=[-1.3967156663085829427 ,.7809788469956901803 ] 
dist 213=[-1.3951685495120602536 ,.90982154573528047238] 
dist 214=[-1.3889990335771997884 ,.99551442478859310458] 
dist 215=[-1.3782805954189897263 ,1.0657615684743054506 ] 
dist 216=[-1.3715064708479526307 ,1.1330053655542989301 ] 
dist 217=[-.09820121883118737380,1.1913148802887787716 ] 
dist 218=[-.16958020194082803172,1.2259313477103022682 ] 
dist 219=[-.23477181170531128266,1.2497217006564362700 ] 
dist 220=[-.30829913162565222277,1.2648557501661439817 ] 
dist 221=[-.38129338972578171209,1.2732158370290641060 ] 
dist 222=[-.44435910384764208784,1.2719377516917251985 ] 
dist 223=[-.51204468836219377896,1.3345491547893301303 ] 
dist 224=[-.60346338152542979726,1.5200867447501555464 ] 
dist 225=[-.69353207461721984177,1.6975243426645949505 ] 
dist 226=[-.75583374436112483335,1.8113600094807961259 ] 
dist 227=[-.80954577941192598368,1.9000768656566897092 ] 
dist 228=[-.86535828075924375622,1.9773385166360256104 ] 
dist 229=[-.91805025454759421781,2.0410519302387712371 ] 
dist 230=[-.95931736096419371906,2.0757372668398861776 ] 
dist 231=[-.99999798438182471968,2.0957019281402495982 ] 
dist 232=[-1.0503544760083835457 ,2.1007080402811135867 ] 
dist 233=[-1.4810047541331779896 ,2.0957020094765012770 ] 
dist 234=[-1.7572898423720204548 ,2.0881929141811128817 ] 
dist 235=[-1.9726102541913779712 ,2.0532697358359245253 ] 
dist 236=[-2.1601282608603777867 ,2.0382813451423577837 ] 
dist 237=[-2.3147639768361673675 ,1.9111222569223780082 ] 
dist 238=[-2.3989470250809839118 ,1.8778472586580434052 ] 
dist 239=[-2.4474022052899423500 ,1.8291473125912013395 ] 
dist 240=[-2.4595521539704408730 ,1.8105929965225107171 ] 
dist 241=[-2.4570490713175800272 ,1.3401461429614086095 ] 
dist 242=[-2.4470667200354226319 ,1.2736523198628745018 ] 
dist 243=[-2.4297240316797004765 ,1.1267526463341356961 ] 
dist 244=[-2.4175740303936411580 ,1.0836142616231106867 ] 
dist 245=[-2.3592364502101350794 ,.96929354248683329798] 
dist 246=[-2.3397261050363630097 ,.95195087849189775514] 
dist 247=[-2.2750070594109512666 ,.94196855175245347379] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 2, 1, 2, 0, 1] 
dist 0=[68.988110876803235773  ,68.988110876803235773  ] 
dist 1=[68.683068798226520043  ,69.243237709987759347  ] 
dist 2=[67.720503896277787238  ,69.445152629860564275  ] 
dist 3=[66.365456501962583979  ,69.444469243644543911  ] 
dist 4=[64.559942330726910083  ,69.008227197158602947  ] 
dist 5=[62.076586450864286970  ,68.806879142182355444  ] 
dist 6=[58.015025696971904327  ,68.237304392777806514  ] 
dist 7=[53.822258222340946820  ,67.966961689099637019  ] 
dist 8=[50.814926861843613238  ,63.905049378214298131  ] 
dist 9=[48.096068004595683785  ,63.511576416263922154  ] 
dist 10=[45.054861046472207412  ,62.846203653493455699  ] 
dist 11=[42.033620286148218822  ,62.607275991027974431  ] 
dist 12=[36.327835656816498548  ,61.551888900772551622  ] 
dist 13=[31.735604052036842058  ,61.328557118402991773  ] 
dist 14=[27.805125996863605440  ,59.214629768007788791  ] 
dist 15=[23.741603921356445981  ,55.343763598907037039  ] 
dist 16=[19.896662463104561922  ,28.631347523956349529  ] 
dist 17=[16.839219003702468576  ,26.031293262611399744  ] 
dist 18=[13.769332071694460203  ,25.355199099334628454  ] 
dist 19=[9.8751135225996481948 ,22.899276080252147748  ] 
dist 20=[6.1269312170414014491 ,22.397926551595713206  ] 
dist 21=[3.6402774812864896907 ,21.551644443837645976  ] 
dist 22=[1.5996228470508929278 ,21.354271132528286225  ] 
dist 23=[-.36776628108978562863,6.2803002586106030995 ] 
dist 24=[-2.8280261545355324927 ,4.3369404274993088388 ] 
dist 25=[-4.8218167037928528639 ,1.4522107414331297845 ] 
dist 26=[-6.3508939796376010667 ,.9009198804251554118 ] 
dist 27=[-7.7557296777645856335 ,-1.4325206239408637490 ] 
dist 28=[-9.3138997758074930663 ,-2.7024799790129440642 ] 
dist 29=[-10.762417094747359481  ,-3.7584299972178091089 ] 
dist 30=[-12.448182215518451410  ,-3.9417468562479482207 ] 
dist 31=[-14.007089882203461549  ,-5.1448067205360023623 ] 
dist 32=[-14.948907510472995922  ,-5.2821912945964853674 ] 
dist 33=[-15.623451047628533788  ,-5.1714423362953918640 ] 
dist 34=[-16.114618523703869040  ,-4.6982094372046948455 ] 
dist 35=[-16.465441331832026987  ,-4.0324775859107266462 ] 
dist 36=[-16.579281545325590643  ,-3.1531657033241533609 ] 
dist 37=[-16.595824645620473800  ,-1.9516478261166398612 ] 
dist 38=[-16.557713345523782868  ,0                     ] 
dist 39=[-10.105786829014741145  ,1.9167478063276241736 ] 
dist 40=[-9.5138350052662405286 ,3.6954837641824382558 ] 
dist 41=[-9.3648649427396378132 ,5.1491594678419189700 ] 
dist 42=[-9.2704321707983448025 ,6.5352622411609016360 ] 
dist 43=[-9.2405634134782601514 ,7.7690192186850315383 ] 
dist 44=[-6.6765865165929500533 ,8.6151250433805675985 ] 
dist 45=[-6.3540461637926405232 ,9.3383022558338892572 ] 
dist 46=[-5.6120037181439077379 ,10.081891148563940033  ] 
dist 47=[-5.4317318902327044266 ,10.740182100200395448  ] 
dist 48=[-4.4180631465729012056 ,11.123053875685623920  ] 
dist 49=[-4.2185872245307046681 ,11.377384389166840159  ] 
dist 50=[-3.8136480508810500020 ,11.522584537621791514  ] 
dist 51=[-3.7009709625277975682 ,11.589167071200273030  ] 
dist 52=[-2.3179537489948630305 ,11.587611073147272096  ] 
dist 53=[-2.1123953573903228791 ,11.445761639322435111  ] 
dist 54=[-1.6581562621008337011 ,11.344072636723982472  ] 
dist 55=[-1.5433755064535321066 ,6.3799191437638356465 ] 
dist 56=[-.9967188462694509505 ,5.8955347433615183038 ] 
dist 57=[-.89501738043931666839,4.7680307626273882048 ] 
dist 58=[-.65640967291823657093,4.4382206854921978666 ] 
dist 59=[-.60832004281766453601,3.7388395820833926516 ] 
dist 60=[-.14988664445634186169,3.7963171525611526899 ] 
dist 61=[-.07732255614572432564,3.8173136589135121518 ] 
dist 62=[.01726696029110288631,3.8186926860909375020 ] 
dist 63=[-.60262988060046996231,3.8120690728658791189 ] 
dist 64=[-1.2987164221353114334 ,.41337822355533037272] 
dist 65=[-1.7604535002524675932 ,.52253676165686317256] 
dist 66=[-2.1382476210989910400 ,.63233753930836176857] 
dist 67=[-2.4996208025010731825 ,.77087063200380307855] 
dist 68=[-2.8223301154105189222 ,.90233630036864542709] 
dist 69=[-3.0458831401787750841 ,.98398076415507810984] 
dist 70=[-3.2394554003628895777 ,1.0443457838381351510 ] 
dist 71=[-3.4425784970592160329 ,1.0910167906411936202 ] 
dist 72=[-3.6183906522910767724 ,1.1251616623516618973 ] 
dist 73=[-3.7030092106590968829 ,1.1355921058220677652 ] 
dist 74=[-3.7451662871381220914 ,1.1375002842914584545 ] 
dist 75=[-3.7515016944041082510 ,1.1376914838449080600 ] 
dist 76=[-3.6706384050332420457 ,1.0670155814401708498 ] 
dist 77=[-3.6444403425816364951 ,1.0521632724165395312 ] 
dist 78=[-3.6240544300397700500 ,1.0086088242797322929 ] 
dist 79=[-3.6063655791598263014 ,.99654781015645559926] 
dist 80=[-2.6125440111438289719 ,1.2967195257276146592 ] 
dist 81=[-2.4896989335549151279 ,1.8333109814033858570 ] 
dist 82=[-2.2021220211666007514 ,2.2711272540550167728 ] 
dist 83=[-2.1335303287463386132 ,2.6871044362417004663 ] 
dist 84=[-1.7264700390007482334 ,3.0560312452135216969 ] 
dist 85=[-1.6461472486073207482 ,3.3062002933109706118 ] 
dist 86=[-1.4878109580808019747 ,3.5167583199906307604 ] 
dist 87=[-1.4449267997216048706 ,3.7277196177657023163 ] 
dist 88=[-1.1781627814303723267 ,3.9093623498101753731 ] 
dist 89=[-1.1722049806161781808 ,4.0029829728618992586 ] 
dist 90=[-1.1416530135485775735 ,4.0499394263016964162 ] 
dist 91=[-1.1369195773339762878 ,4.0562231456558059106 ] 
dist 92=[-.33450226255922780323,4.0200090834121716323 ] 
dist 93=[-.29472332275373953016,3.9959144760228154821 ] 
dist 94=[-.32293912934152552011,3.9396414328899639157 ] 
dist 95=[-.42646011332777440143,3.9122396890942795819 ] 
dist 96=[-.9208864659686103399 ,.99027516611120866008] 
dist 97=[-1.4913578974625996490 ,1.1450761714846619607 ] 
dist 98=[-1.9507793470443085922 ,1.3063558403518103652 ] 
dist 99=[-2.3769406691558443612 ,1.5179728167656136952 ] 
dist 100=[-2.7476766155123449125 ,1.7236078288711140092 ] 
dist 101=[-2.9860542287875058393 ,1.8610327464760110964 ] 
dist 102=[-3.1724862614610576618 ,1.9743977300608755561 ] 
dist 103=[-3.3360587069966145558 ,2.0840846851546541158 ] 
dist 104=[-3.4745865624321862646 ,2.1826170009443762965 ] 
dist 105=[-3.5611356980437482108 ,2.2514995194383154294 ] 
dist 106=[-3.6259704971138737988 ,2.3116568361471610798 ] 
dist 107=[-3.6778912974248741746 ,2.3753965704152558718 ] 
dist 108=[-3.7173867829602611946 ,2.4276839604203667021 ] 
dist 109=[-3.7326636615785491545 ,2.4421693432090665982 ] 
dist 110=[-3.7330939969269859742 ,2.4413968533717632045 ] 
dist 111=[-3.7191367876477090350 ,2.4328306401340476112 ] 
dist 112=[-2.0561867890175903700 ,2.3306397536332706846 ] 
dist 113=[-2.0483621925300866855 ,2.2992631988724536189 ] 
dist 114=[-2.0390096922256903294 ,2.2904066723185519984 ] 
dist 115=[-2.0268135924273085405 ,2.2903807349368772468 ] 
dist 116=[-1.6093855901929952233 ,2.0672239079660297609 ] 
dist 117=[-1.5482682669716483266 ,2.0272295537092204832 ] 
dist 118=[-1.4295005184296413323 ,1.9605942551777783254 ] 
dist 119=[-1.3967307697703934976 ,2.0341240950847826698 ] 
dist 120=[-1.2727208584423331572 ,2.4226461855445755991 ] 
dist 121=[-1.2418541349221293416 ,2.6682468490232200682 ] 
dist 122=[-1.1847547465789957268 ,2.8554972008129568859 ] 
dist 123=[-1.1682463741123582453 ,3.0113090682262293055 ] 
dist 124=[-.5073962836294854796 ,3.1344574517060132137 ] 
dist 125=[-.83949030828931080514,3.1914406730832985537 ] 
dist 126=[-1.1078902282436669446 ,3.2157063401490395293 ] 
dist 127=[-1.3584309571281044875 ,3.2141073085959063287 ] 
dist 128=[-1.5774349903384230845 ,-.40301497649733707081] 
dist 129=[-1.7200638001453191727 ,-.53677301984134478441] 
dist 130=[-1.8336505169369091206 ,-.83158146064268225644] 
dist 131=[-1.9368322934200803452 ,-.8823816331977884646 ] 
dist 132=[-2.0251847426370033536 ,-1.1987147430239133948 ] 
dist 133=[-2.0796306850730422976 ,-1.2476419459075463887 ] 
dist 134=[-2.1195113121903160727 ,-1.3427014380157803974 ] 
dist 135=[-2.1497755134704443892 ,-1.3578739094867720796 ] 
dist 136=[-2.2765171693903710938 ,-1.3944911904500406866 ] 
dist 137=[-2.3635925931397441386 ,-1.3651709646595353252 ] 
dist 138=[-2.4124064755258102449 ,-1.1721695274376041938 ] 
dist 139=[-2.4241124702881679116 ,-.77817307312623521039] 
dist 140=[-2.4058783584001680940 ,-.37610143463135416953] 
dist 141=[-2.4005518454657672788 ,-.09729958586380483071] 
dist 142=[-2.3968235468941103641 ,.14378857917459662487] 
dist 143=[-2.3943179019804960201 ,.39545480589374452747] 
dist 144=[-1.8121557036589874652 ,.79797482004603828124] 
dist 145=[-1.7376811086374779247 ,1.1410034137343239405 ] 
dist 146=[-1.5589363480737967309 ,1.4215824920845075180 ] 
dist 147=[-1.5167977277762774951 ,1.6891349566800439871 ] 
dist 148=[-1.2479194695678761982 ,1.9268912609039913778 ] 
dist 149=[-1.1938754654663701395 ,2.0886407352429618480 ] 
dist 150=[-1.0923094308113440103 ,2.2252222010237420578 ] 
dist 151=[-1.0655721885527820523 ,2.3626064841902741339 ] 
dist 152=[-.63540584159178197737,2.4813739610901102474 ] 
dist 153=[-.5752656999278430636 ,2.5437099300840213058 ] 
dist 154=[-.43609299637524090343,2.5764694902516377269 ] 
dist 155=[-.40822982126083068735,2.5804615967907684743 ] 
dist 156=[-.29286807532647932658,2.5639941422929721200 ] 
dist 157=[-.4912738718014859603 ,2.5501348379413309007 ] 
dist 158=[-.65808349536333153113,2.5125179532422110000 ] 
dist 159=[-.82469945575803301054,2.4932501080020319684 ] 
dist 160=[-.97784680111481198879,-.32375801775181115721] 
dist 161=[-1.0909424415972556616 ,-.43137533635762123231] 
dist 162=[-1.2276458778790759105 ,-.67477458049918558071] 
dist 163=[-1.5170567742002041532 ,-.71124725611317027202] 
dist 164=[-1.7748317308655743666 ,-.79299560734760304506] 
dist 165=[-1.9512382286388395767 ,-.78494019798614034746] 
dist 166=[-2.1013121192369965086 ,-.70905132396309597949] 
dist 167=[-2.2540704197189724382 ,-.58108135123257379132] 
dist 168=[-2.3883324925304614834 ,-.42989762198950056247] 
dist 169=[-2.4646418367071238012 ,-.26143028112607502057] 
dist 170=[-2.5128943011327219441 ,-.04853727497510755388] 
dist 171=[-2.5352630803898980243 ,.27981982353691952527] 
dist 172=[-2.5407968725984015520 ,.60936575350516478267] 
dist 173=[-2.5365327567186649494 ,.82699993589510092148] 
dist 174=[-2.4986880580217327372 ,1.0037043677254958725 ] 
dist 175=[-2.4869337430833102574 ,1.1700189780239824764 ] 
dist 176=[-1.2915371992744354351 ,1.3163376152264072257 ] 
dist 177=[-1.1744279772757496532 ,1.4132964126004148758 ] 
dist 178=[-.90707029763781249382,1.4923854919759932887 ] 
dist 179=[-.84956845278559380112,1.5674381876805688450 ] 
dist 180=[-.50802569383480143653,1.6307221942156312462 ] 
dist 181=[-.46525398377739487545,1.6628767379187986754 ] 
dist 182=[-.36772827859790441583,1.6849789774840549317 ] 
dist 183=[-.35228689275460976502,1.9026345952006923840 ] 
dist 184=[-.20726784039870224837,2.1014930488171499708 ] 
dist 185=[-.18035962951368867708,2.2131720298056262088 ] 
dist 186=[-.14489556959375145847,2.2820568051687386116 ] 
dist 187=[-.13488431021983878281,2.3102482995078489594 ] 
dist 188=[-.36874369981093871851,2.3228354142248289772 ] 
dist 189=[-.61464576165779540538,2.3294885760720871534 ] 
dist 190=[-.81695963329702530628,2.3330501149324089439 ] 
dist 191=[-1.0118470657038880192 ,2.3333075427274681751 ] 
dist 192=[-1.1863540057522623851 ,-.10543387604405103367] 
dist 193=[-1.3073887453694722139 ,-.14371386687226992218] 
dist 194=[-1.4120814917329924840 ,-.20619923539135935264] 
dist 195=[-1.5214151781166268269 ,-.22036558184552329737] 
dist 196=[-1.6180282725632567721 ,-.23520561633226806821] 
dist 197=[-1.7845283073500611389 ,-.22075617368465600802] 
dist 198=[-1.9893296121617166856 ,-.18736164976988537526] 
dist 199=[-2.2431879956661869096 ,-.11950376057156900219] 
dist 200=[-2.4829996447648641376 ,-.04234998333412759117] 
dist 201=[-2.6317813792096220681 ,.02811733276330886625] 
dist 202=[-2.7419447786633927344 ,.10697475151694443858] 
dist 203=[-2.8277432240966392151 ,.21758897841995098526] 
dist 204=[-2.8910149359079186512 ,.33974832148593061054] 
dist 205=[-2.9113398058692285523 ,.46464864799024959567] 
dist 206=[-2.9119690715728870231 ,.61661800682792272249] 
dist 207=[-2.9011052864115038780 ,1.2321294602681109727 ] 
dist 208=[-2.7966417726262053717 ,1.8456408618776045231 ] 
dist 209=[-2.7682882084160103887 ,2.2423744020601166865 ] 
dist 210=[-2.6816166040140626518 ,2.5551424634341157818 ] 
dist 211=[-2.6537485999662918781 ,2.8337924148765683438 ] 
dist 212=[-2.4411646115988113307 ,3.0682032017678329610 ] 
dist 213=[-2.3899377743928045890 ,3.2045417237683265557 ] 
dist 214=[-2.3080213603205152169 ,3.2947575443509685478 ] 
dist 215=[-2.2812709245510954165 ,3.3452270881885192323 ] 
dist 216=[-1.6465355453272006764 ,3.3745414483863349981 ] 
dist 217=[-1.5576134167603004160 ,3.3803886017445821106 ] 
dist 218=[-1.3545514304647345191 ,3.3701502388617261590 ] 
dist 219=[-1.3029939733611473446 ,3.3578528976010211706 ] 
dist 220=[-1.0328313770616198662 ,3.2874636976006619690 ] 
dist 221=[-.980260822516119385  ,3.2639982059090743023 ] 
dist 222=[-.86647698635887821872,3.1704010652573957918 ] 
dist 223=[-.95360356993644438621,3.1513427187728802926 ] 
dist 224=[-1.1487580407939114239 ,-.01035603498230378455] 
dist 225=[-1.3033704922901894028 ,.00113776896531960282] 
dist 226=[-1.4574428773017758421 ,.01790155241755148538] 
dist 227=[-1.6504435173613017202 ,.08300169895921278818] 
dist 228=[-1.8337622027905534744 ,.15840422339970410512] 
dist 229=[-1.9492221316108864947 ,.22190507080288094826] 
dist 230=[-2.0367517001116154761 ,.28866265394749376   ] 
dist 231=[-2.1086817396758421870 ,.3770533172012842036 ] 
dist 232=[-2.1648277448237490653 ,.47226432820063980773] 
dist 233=[-2.1894092453207432176 ,.56622203681525823813] 
dist 234=[-2.1955071103146804450 ,.67697869365220049074] 
dist 235=[-2.1931104573901873520 ,1.0057087808746045340 ] 
dist 236=[-2.1499902845610570891 ,1.4639677312948993153 ] 
dist 237=[-2.1345170184134716422 ,1.7592932360245076577 ] 
dist 238=[-2.0817079868630560346 ,1.9909687481061724496 ] 
dist 239=[-2.0629974526596386630 ,2.1953861305613552963 ] 
dist 240=[-1.9143648222965250310 ,2.3659174306051774549 ] 
dist 241=[-1.8773363197033606619 ,2.4624523726482834709 ] 
dist 242=[-1.8202005999380626467 ,2.5229930472613187794 ] 
dist 243=[-1.8003220680625497440 ,2.5499761567096863859 ] 
dist 244=[-1.3147458168103745852 ,2.5612480667659472469 ] 
dist 245=[-1.2464495055044872694 ,2.5591311459024625007 ] 
dist 246=[-1.0927650375554108110 ,2.5468086742023545584 ] 
dist 247=[-1.0509453393057460842 ,2.5360038244111868716 ] 
dist 248=[-.85202451519135440041,2.4793171750725575867 ] 
dist 249=[-.81300449588611795025,2.4603908684612221698 ] 
dist 250=[-.72269228964262838885,2.3909305521306398187 ] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 2, 0, 1] 
dist 0=[66.024155663004592523  ,66.024155663004592523  ] 
dist 1=[65.751920972682556015  ,66.148936775467061240  ] 
dist 2=[64.804777824259408174  ,66.507205059545183961  ] 
dist 3=[63.231431997198139056  ,66.876418640004534953  ] 
dist 4=[60.459153667549993505  ,67.044898209895291379  ] 
dist 5=[57.533050761182478022  ,67.098408195954566993  ] 
dist 6=[55.345478705238872415  ,67.008984682276406367  ] 
dist 7=[53.277408933659919033  ,62.164356731622416249  ] 
dist 8=[50.828185055115551779  ,61.406553273377870427  ] 
dist 9=[48.317153864524790789  ,60.089916901829554303  ] 
dist 10=[46.002088096337748842  ,59.727688575336709536  ] 
dist 11=[43.383264662168568275  ,58.490129116343533524  ] 
dist 12=[39.659034134322022454  ,58.094701015596091917  ] 
dist 13=[35.874615351060868761  ,57.599336757495439776  ] 
dist 14=[32.582670325172454048  ,57.370329511503562479  ] 
dist 15=[25.164490694303063282  ,33.879308167193945085  ] 
dist 16=[20.171054192384476183  ,33.242385869827549395  ] 
dist 17=[15.990372319642974487  ,30.914306472147302112  ] 
dist 18=[11.817348262533791991  ,30.416813799359198027  ] 
dist 19=[7.9613693646612214223 ,29.550971981892617728  ] 
dist 20=[5.0465399954721701227 ,29.343180139726949805  ] 
dist 21=[2.2584702649146867863 ,11.128937789126712510  ] 
dist 22=[-1.0914944273647357113 ,10.263765966366451134  ] 
dist 23=[-4.2333306778472440964 ,6.1212671279593231262 ] 
dist 24=[-6.1905457906409523005 ,5.5056265455476807238 ] 
dist 25=[-7.6584169565161373874 ,1.4747130509999157663 ] 
dist 26=[-8.8467606074682993212 ,.79245846822195569687] 
dist 27=[-9.7920859257984786865 ,-.4643063010032399077 ] 
dist 28=[-11.043194650622703136  ,-.7336119563861780239 ] 
dist 29=[-12.929132130058735915  ,-3.6038355652089152874 ] 
dist 30=[-14.064399907361084502  ,-4.0138508628812361875 ] 
dist 31=[-14.871565169549869928  ,-4.5041691665592119154 ] 
dist 32=[-15.447035901714968972  ,-4.5231181118339285331 ] 
dist 33=[-15.866247308691242084  ,-4.3589797390281056924 ] 
dist 34=[-16.049204049611157252  ,-3.9388876377010548669 ] 
dist 35=[-16.099748312143326464  ,-3.2547147556187940166 ] 
dist 36=[-16.083668401468787409  ,-2.0366953055921696975 ] 
dist 37=[-7.5788706691588346126 ,-.03193136694823031709] 
dist 38=[-7.5408166721413253472 ,1.5782207232016820643 ] 
dist 39=[-7.1904870126905217364 ,2.9037038182618933345 ] 
dist 40=[-7.1114425679528783623 ,4.1820501571716475103 ] 
dist 41=[-6.8888749638608650224 ,5.3285147338383592030 ] 
dist 42=[-6.8264598984909725240 ,6.1282000507770020872 ] 
dist 43=[-6.3523239364752972836 ,6.8255376266958879538 ] 
dist 44=[-6.2423505094732216484 ,7.5640405729084563488 ] 
dist 45=[-6.0691380945104126728 ,8.2307980520784430629 ] 
dist 46=[-6.0133012675028773948 ,8.6419457168939627456 ] 
dist 47=[-4.7010061903911987713 ,8.9441576554138159244 ] 
dist 48=[-4.5139204409933382472 ,9.1760845675540255865 ] 
dist 49=[-4.0936713470975973622 ,9.3442508031990970663 ] 
dist 50=[-3.9730909255864674462 ,9.3918970886801154214 ] 
dist 51=[-3.4080725934220173491 ,9.3819918703456115011 ] 
dist 52=[-3.2914838373684427090 ,9.3453317988240049299 ] 
dist 53=[-3.0279552243324924890 ,4.8033549205673476432 ] 
dist 54=[-2.9455744712083700615 ,4.4003409877036480132 ] 
dist 55=[-2.1252881095163058616 ,3.4545191199594666960 ] 
dist 56=[-1.9938546646478487826 ,3.2804326690947406070 ] 
dist 57=[-1.6932642233475241837 ,2.0093631861059585646 ] 
dist 58=[-1.6155550225368672772 ,1.7795589580639253602 ] 
dist 59=[-1.2085231710228688562 ,1.4052405818161979094 ] 
dist 60=[-1.5432993262426994618 ,1.3977782993702595586 ] 
dist 61=[-1.9588819538938348243 ,1.3869534880490610158 ] 
dist 62=[-2.2250753051457394757 ,1.3823923564575671175 ] 
dist 63=[-2.4318969687718686380 ,-.3949796580819266562 ] 
dist 64=[-2.6107419955920880999 ,-.23817881260533995282] 
dist 65=[-2.7571797611527712848 ,-.09960783439827073331] 
dist 66=[-2.8347782392114867503 ,.04884159370843466325] 
dist 67=[-2.8765512482658665866 ,.19095760296208364124] 
dist 68=[-2.8817626723973096843 ,.30432347719507453199] 
dist 69=[-1.5322264106827018278 ,.41755930499177736169] 
dist 70=[-1.5982781439095638498 ,.55918733394083585838] 
dist 71=[-1.6526499754788626863 ,.69277979643613339151] 
dist 72=[-1.6751242442444537407 ,.86554215841681805021] 
dist 73=[-1.6836756401450589428 ,1.0556002938652301670 ] 
dist 74=[-1.6824184135868857687 ,1.1934004439966737266 ] 
dist 75=[-1.6315315794309708538 ,1.3188183921720131505 ] 
dist 76=[-1.6141343567238697460 ,1.4595068742191682785 ] 
dist 77=[-1.5997280091173565410 ,1.5865390609923500048 ] 
dist 78=[-1.5881864753014522490 ,1.6575029712967502989 ] 
dist 79=[-1.1016766019577480916 ,1.7007337835285579410 ] 
dist 80=[-1.0434438268746399866 ,1.7171772273355992557 ] 
dist 81=[-.9094084447195507084 ,1.7221124232457792795 ] 
dist 82=[-.87733278324722107955,1.7194561847189640765 ] 
dist 83=[-.69610809345224005196,1.7107362068073127282 ] 
dist 84=[-.66093463595243604107,1.7026386741288623873 ] 
dist 85=[-.66507137957849071647,1.5859938357425139402 ] 
dist 86=[-.71984410508711970668,1.6816183020542806627 ] 
dist 87=[-.777364940758325292  ,1.7639374036061012984 ] 
dist 88=[-.96809887151579306708,1.8059443733522136648 ] 
dist 89=[-1.1403627023927647360 ,1.8264616589894156664 ] 
dist 90=[-1.2622979104279436619 ,1.8295669688283533070 ] 
dist 91=[-1.3703188327108290332 ,1.8105198812866931050 ] 
dist 92=[-1.4870918474340178467 ,1.7989193277592403218 ] 
dist 93=[-1.5910584224720238230 ,1.7752338018491876657 ] 
dist 94=[-1.6480094690819274399 ,1.7641681431748869026 ] 
dist 95=[-1.6812329932151738004 ,.1595515483500999513 ] 
dist 96=[-1.6905813013381861296 ,.24813492816050678246] 
dist 97=[-1.6895691409212062435 ,.35985168832638175842] 
dist 98=[-1.6819965366007675228 ,.48161785369068341354] 
dist 99=[-1.6673660629113740724 ,.60002285250812778226] 
dist 100=[-1.6588241146158591111 ,.69833785023837573104] 
dist 101=[-1.4456207952601715361 ,.80043651992851753426] 
dist 102=[-1.5196005674385964429 ,.93393185405536725732] 
dist 103=[-1.5821534553256949078 ,1.0633801664661037863 ] 
dist 104=[-1.6205936499846029208 ,1.1493423857902273592 ] 
dist 105=[-1.6486571382108360026 ,1.2196373718419152934 ] 
dist 106=[-1.6698156330853234274 ,1.2866126290411773279 ] 
dist 107=[-1.6848639207593377784 ,1.3460786316312266952 ] 
dist 108=[-1.6885523941624292537 ,1.3864319113815682718 ] 
dist 109=[-1.6846153572236609330 ,1.4581017905603711582 ] 
dist 110=[-1.6784678186695021942 ,1.5033310508501948100 ] 
dist 111=[-1.1401585097224519164 ,1.5336689957104375264 ] 
dist 112=[-1.1845838661692187950 ,1.5514766768036634965 ] 
dist 113=[-1.2098172709144694994 ,1.5598003430653937459 ] 
dist 114=[-1.2156300065406205875 ,1.5584576974302578635 ] 
dist 115=[-1.2137955077058157516 ,1.5405914045816483222 ] 
dist 116=[-1.2110122008783087941 ,1.5320036099079853286 ] 
dist 117=[-1.2067710587756430164 ,1.3665268478315921656 ] 
dist 118=[-1.2000091406430167927 ,1.3543739597362459392 ] 
dist 119=[-.9603259216074070649 ,1.2085404045781665723 ] 
dist 120=[-.92501501729985727862,1.1834524655307504414 ] 
dist 121=[-.85717031991293939468,1.1412911242540863782 ] 
dist 122=[-.83851897140009067629,1.1665473224758974623 ] 
dist 123=[-.90986991383609733058,1.2184698210521946566 ] 
dist 124=[-1.0564979640961892440 ,1.2445712566565681225 ] 
dist 125=[-1.1926625308034598113 ,1.2566866045271512104 ] 
dist 126=[-1.2730491027495934594 ,1.2580593086455743334 ] 
dist 127=[-1.3277353768095840757 ,-.1671746545913652127 ] 
dist 128=[-1.3614060788641649721 ,-.20267442266872465198] 
dist 129=[-1.3835879135735178171 ,-.18728656106344046844] 
dist 130=[-1.3924562894622013926 ,-.1529140146302346017 ] 
dist 131=[-1.3932445672283673097 ,-.09815536233457767018] 
dist 132=[-1.3894144727789933892 ,-.00144608132878898885] 
dist 133=[-.72521052263264240772,.24876732642357478141] 
dist 134=[-.79073664782706448615,.42082603904009925677] 
dist 135=[-.84931669628743611537,.56808403423970235996] 
dist 136=[-.880661217926052573  ,.71939028436893010598] 
dist 137=[-.89798300002529481327,.86117722275467491227] 
dist 138=[-.90197547950909024046,.97047146762930037148] 
dist 139=[-.89811689753090213236,1.0765746239651766025 ] 
dist 140=[-.89522139354740055124,1.2056352324138702268 ] 
dist 141=[-.89146151639898919576,1.3263396401642700867 ] 
dist 142=[-.88626434023997860012,1.3991176590479763922 ] 
dist 143=[-.63634555907474493036,1.4505153016890153273 ] 
dist 144=[-.60606482863634862083,1.4859532435199811822 ] 
dist 145=[-.53428663669757794785,1.5087329157438594243 ] 
dist 146=[-.51771494333218533751,1.5130483657940151867 ] 
dist 147=[-.41369060932723115584,1.5040952273947566537 ] 
dist 148=[-.54060153892913044181,1.5010773991901696844 ] 
dist 149=[-.86200868842083922389,1.3907900127990482808 ] 
dist 150=[-1.0710961924796541919 ,1.3689489624723510193 ] 
dist 151=[-1.2373428778996242865 ,1.3089183828185521062 ] 
dist 152=[-1.3878972689459074964 ,1.2917406779908832358 ] 
dist 153=[-1.5163100680279369891 ,1.1678641269032363065 ] 
dist 154=[-1.5942542210761032323 ,1.1394986487963863727 ] 
dist 155=[-1.6499304502601320617 ,1.0916173734344088908 ] 
dist 156=[-1.6895368615206192454 ,1.0774689314331625347 ] 
dist 157=[-1.7179490483237290756 ,.91690340438435157761] 
dist 158=[-1.7289817986985671186 ,.91108578801341417312] 
dist 159=[-1.7293653042428163009 ,.61045861280814926046] 
dist 160=[-1.7249109323012091062 ,.5874846857989251385 ] 
dist 161=[-1.6934158948955386252 ,.44238654921778461659] 
dist 162=[-1.6825213988475074470 ,.41453715102538265726] 
dist 163=[-1.6351667304371334523 ,.3614174835899720956 ] 
dist 164=[-1.6271054194596748670 ,.34785326240513625417] 
dist 165=[-.74361684926164153479,.24767302750874792259] 
dist 166=[-.79483755184605761386,.41097795367783138342] 
dist 167=[-.8396363550154923795 ,.54317735395613128635] 
dist 168=[-.86549963826061674455,.6669420613364706235 ] 
dist 169=[-.88237108190877043344,.77537456467787639459] 
dist 170=[-.8913096098071607251 ,.84642784094502989118] 
dist 171=[-.89443538681430519307,.9035013147554557405 ] 
dist 172=[-.89350631477122543982,.95618117928989569144] 
dist 173=[-.88026436333818301469,1.0014759330749854277 ] 
dist 174=[-.87720712987856532863,1.0290969657736689654 ] 
dist 175=[-.41645287323932021614,1.0489814294158000883 ] 
dist 176=[-.3728883338046049029 ,1.0634221106419672137 ] 
dist 177=[-.27399760701887057717,1.0732083748245283287 ] 
dist 178=[-.25296614322057341554,1.0745306399147773725 ] 
dist 179=[-.12926268618246927117,1.0700475124446266714 ] 
dist 180=[-.10699424098646037041,1.0663245348073799458 ] 
dist 181=[-.06175443748978043520,.55250916827663057264] 
dist 182=[-.05021436554671683233,.63352830805037237101] 
dist 183=[-.09738978156112289773,.70828873331150174473] 
dist 184=[-.2215569447099650641 ,.75159638567562307828] 
dist 185=[-.3388097530970425598 ,.78003341481577436892] 
dist 186=[-.43068532616897622016,.79548850615395070804] 
dist 187=[-.52129809146114570489,.80480087933159629671] 
dist 188=[-.63351470958633049518,.80874021004530601299] 
dist 189=[-.73947202310737623491,.80948700904528552543] 
dist 190=[-.8051221524525922754 ,.80648009707259670261] 
dist 191=[-.85362919941761848237,-.04889523613585757790] 
dist 192=[-.89121845708132862411,-.06597798421269642748] 
dist 193=[-.91921061905395196317,-.09893941730869087482] 
dist 194=[-.92944364103108646638,-.10648966062905801284] 
dist 195=[-.9324448955140180097 ,-.09733063100156831877] 
dist 196=[-.93159616319787752378,-1.74605495075020700000e-05] 
dist 197=[-.33579097558645128602,.09901532113666794659] 
dist 198=[-.36857413394006757764,.16398893490495138155] 
dist 199=[-.39811197434345979694,.2162681700461631863 ] 
dist 200=[-.41395895870932373395,.26467469316613793353] 
dist 201=[-.42289006149907948076,.30671592489477953009] 
dist 202=[-.42494928487082144828,.33360983724361748058] 
dist 203=[-.42329276271519995568,.3544805642460220838 ] 
dist 204=[-.42252171084331501222,.37250081941125092855] 
dist 205=[-.4217273928544352578 ,.38773911449016827697] 
dist 206=[-.4206968207340766678 ,.39751514996656842695] 
dist 207=[-.35986400061887128892,.40513383962742683202] 
dist 208=[-.35857497375355449486,.4117684627903126918 ] 
dist 209=[-.35257926049258642842,.41723941460282288221] 
dist 210=[-.35000557761651622765,.42021728821465820019] 
dist 211=[-.32817242423060117384,.42193067501805488454] 
dist 212=[-.32245895175446967263,.42235875160338722926] 
dist 213=[-.31409654108230572916,.39948741626310826042] 
dist 214=[-.31091063083354573499,.42234850964567469495] 
dist 215=[-.23013084363766901435,.44194329094881824977] 
dist 216=[-.21871314309975957967,.45211711175963840382] 
dist 217=[-.19348880864106635052,.45730915058903641453] 
dist 218=[-.18608138810301004902,.45781030759392861982] 
dist 219=[-.15454923752700529707,.45430592374493087744] 
dist 220=[-.1483048880465155181 ,.45180255448002363853] 
dist 221=[-.13260494071982395477,.44447969963418971754] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 2, 0, 0, 2] 
dist 0=[73.464485796284139224  ,73.464485796284139224  ] 
dist 1=[72.352892269200980066  ,74.071509907926190092  ] 
dist 2=[70.092931731484747021  ,74.317363654126058897  ] 
dist 3=[67.266772526159097752  ,74.392878525082539038  ] 
dist 4=[63.895335970063930498  ,74.319775542481052951  ] 
dist 5=[59.477880355082972092  ,74.155850339219993042  ] 
dist 6=[52.476698456770970668  ,73.952185481976858127  ] 
dist 7=[45.343919863157585699  ,73.493066845128926954  ] 
dist 8=[40.401263779142397894  ,73.257013223826552968  ] 
dist 9=[36.115756323972952566  ,71.940543462197489536  ] 
dist 10=[31.606018239196071597  ,71.491933684298713873  ] 
dist 11=[27.296990633888332179  ,71.177692339855828123  ] 
dist 12=[23.812638487328842541  ,70.964504682241668288  ] 
dist 13=[20.264852027385124939  ,70.832983519947417308  ] 
dist 14=[15.702660803053516381  ,69.513391431783410741  ] 
dist 15=[11.288766590252296704  ,61.806711080427939688  ] 
dist 16=[8.3328237973165000631 ,56.601251595947991647  ] 
dist 17=[5.8784978002142136548 ,33.757280479448341500  ] 
dist 18=[3.4665305764585385271 ,30.826415808846730098  ] 
dist 19=[1.2655333386203409647 ,23.931758381783381487  ] 
dist 20=[-.34692982914963421609,22.909470552766286737  ] 
dist 21=[-1.8381647438850669032 ,13.758898040586337674  ] 
dist 22=[-3.5556570246266722172 ,12.165487197950282751  ] 
dist 23=[-5.1624631507211700954 ,10.016196981457178586  ] 
dist 24=[-6.2121651576186964670 ,9.5661991891884770191 ] 
dist 25=[-7.0570828713204463505 ,.18658703140559644214] 
dist 26=[-7.8469158556796276530 ,.02591259117166018034] 
dist 27=[-8.5455753885392405035 ,-.42968692906247000759] 
dist 28=[-9.0271054200176501073 ,-.50026429340078177749] 
dist 29=[-9.9032658378051031737 ,-.4694399537450197849 ] 
dist 30=[-10.726950583675964080  ,-.3010891141284390624 ] 
dist 31=[-11.278927432199020193  ,-.09001380384427126250] 
dist 32=[-11.620838201225619432  ,.111777069069265736  ] 
dist 33=[-11.829098020562549162  ,.340679588914860026  ] 
dist 34=[-11.868266453309360724  ,.66099904603405262491] 
dist 35=[-11.807706782975514246  ,1.0113161231891930884 ] 
dist 36=[-11.778644056588916801  ,1.3603950509716331509 ] 
dist 37=[-11.146361005370773838  ,1.7732795067176985528 ] 
dist 38=[-10.982586973604085164  ,2.3785523810003584203 ] 
dist 39=[-10.824708546724948294  ,2.9706943734096818418 ] 
dist 40=[-10.736748052523486679  ,3.3314175334765709868 ] 
dist 41=[-8.2751536072340392667 ,3.5907490454674164611 ] 
dist 42=[-7.9453899401114941084 ,3.7786543414368170810 ] 
dist 43=[-7.2511415459615072786 ,3.9204191870157517947 ] 
dist 44=[-7.0608393843800588979 ,3.9957338096881462038 ] 
dist 45=[-6.3230032361797374869 ,4.0367403129860150864 ] 
dist 46=[-6.1718567115422378552 ,4.2638169601287362510 ] 
dist 47=[-5.8627164940363828919 ,4.6875646504233451816 ] 
dist 48=[-5.7790960679975902204 ,4.9650050526029463922 ] 
dist 49=[-3.6454000052551370424 ,5.1891946294545793068 ] 
dist 50=[-3.5911786921880267812 ,5.4004942023445761808 ] 
dist 51=[-3.3951106895640832387 ,5.5723348627920889055 ] 
dist 52=[-3.3376995509500290231 ,5.6390409189607584040 ] 
dist 53=[-3.2507916995220180517 ,5.6623182962102026601 ] 
dist 54=[-3.2191555143652773320 ,5.6605275968677410335 ] 
dist 55=[-.51280205850098024108,6.1443055357778154020 ] 
dist 56=[-1.0672869483726830361 ,6.7312232492060871092 ] 
dist 57=[-1.5195120349249749618 ,7.2681525160236330369 ] 
dist 58=[-1.9483746308722630053 ,7.5810791249443495952 ] 
dist 59=[-2.3278015027551900139 ,7.7911839179725371715 ] 
dist 60=[-2.8909551223996143130 ,7.9175269056744005048 ] 
dist 61=[-3.5513690980332500812 ,7.9917330411292067539 ] 
dist 62=[-4.1746706000251178902 ,7.9969796293826470006 ] 
dist 63=[-4.7250504538831206279 ,7.9658620152793222702 ] 
dist 64=[-5.0946305083119050417 ,7.9289036943740372243 ] 
dist 65=[-5.4020413333908380562 ,2.1071442702041143050 ] 
dist 66=[-5.7045053598659100395 ,2.0422463414713068514 ] 
dist 67=[-5.9625156626172672138 ,1.2511339829129528939 ] 
dist 68=[-6.0926062269878775278 ,1.1335166324587169820 ] 
dist 69=[-6.1539727939213255995 ,.8792748288923961883 ] 
dist 70=[-6.1617200335934893240 ,.81119620436604632983] 
dist 71=[-6.1796454479853316995 ,.52450243342201187989] 
dist 72=[-6.4503530492000251647 ,.47071074036336422299] 
dist 73=[-6.6742269374082613543 ,.39429813456930420842] 
dist 74=[-6.8000565562509593160 ,.78878775179422513021] 
dist 75=[-6.8782367118535399649 ,1.4419786389364033170 ] 
dist 76=[-6.9119765444028595300 ,2.3184752284190004881 ] 
dist 77=[-6.9148164390301734646 ,3.0319331917478258245 ] 
dist 78=[-6.8953111408556147800 ,3.7066772201552645614 ] 
dist 79=[-6.8098146714852781303 ,4.3027050093101771057 ] 
dist 80=[-6.7578302142054735233 ,4.7022300871396092105 ] 
dist 81=[-2.6956441582961911461 ,5.0332945055888333111 ] 
dist 82=[-2.3273452767699566066 ,5.3562965162370194895 ] 
dist 83=[-1.5023874183378096336 ,5.6367120471131602538 ] 
dist 84=[-1.3284460725592504334 ,5.7979304917349127947 ] 
dist 85=[-.34171052777867793409,5.9023440821898583999 ] 
dist 86=[-.16861975485301270358,5.9561942368188198285 ] 
dist 87=[-.4599661116917825702 ,5.9733264693622939778 ] 
dist 88=[-.79628358158014302656,5.9651449764666755185 ] 
dist 89=[-1.0822524104695809636 ,5.8786735662202138703 ] 
dist 90=[-1.3730650502381654834 ,5.8535706990165682825 ] 
dist 91=[-1.6436686231492309419 ,5.9823725586753198882 ] 
dist 92=[-1.8490448067448558178 ,6.1497702140744064648 ] 
dist 93=[-2.0453575955103296537 ,6.2637083252686156632 ] 
dist 94=[-2.2798177165258358113 ,6.3053746309268244638 ] 
dist 95=[-2.7234806461022716956 ,6.3033892564130931441 ] 
dist 96=[-3.2048074578447780237 ,6.2895583913593934642 ] 
dist 97=[-3.6631439412589905009 ,.3163160995645765162 ] 
dist 98=[-4.2081646210717680199 ,.23877778511034055788] 
dist 99=[-4.7117643818745099126 ,-.44881745595637504603] 
dist 100=[-5.0049085542267583035 ,-.17786988837258071616] 
dist 101=[-5.1992313151567690469 ,.20898389349976630774] 
dist 102=[-5.3087123263343023298 ,.80242397886913142393] 
dist 103=[-5.3764207308119375645 ,1.3963236480381095191 ] 
dist 104=[-5.4041441717725933140 ,1.7850096972218176334 ] 
dist 105=[-5.8415455217672718197 ,2.0966712207124357163 ] 
dist 106=[-6.1390060468331608612 ,2.3833922127624253366 ] 
dist 107=[-6.3420141095314461963 ,2.6311115275705388733 ] 
dist 108=[-6.4683735953704769453 ,2.7872316630853212904 ] 
dist 109=[-6.5436147826573751115 ,2.9056923414037817534 ] 
dist 110=[-6.5502983904815646742 ,3.0032226505192429259 ] 
dist 111=[-6.5134761371365180226 ,3.4524504222786464276 ] 
dist 112=[-6.4753848514588349676 ,3.8928834784786165413 ] 
dist 113=[-5.8541177133853763577 ,4.3223382404300241949 ] 
dist 114=[-5.7420848144026009196 ,4.8473814541275177287 ] 
dist 115=[-5.4459706303177383335 ,5.3398065117266217756 ] 
dist 116=[-5.3649315971943088304 ,5.8251843446099491621 ] 
dist 117=[-4.7986447861588130130 ,6.3967143311121884823 ] 
dist 118=[-4.6722134000028056617 ,6.7505890113855931591 ] 
dist 119=[-4.4519869466605355306 ,7.0117997045639034736 ] 
dist 120=[-4.3904821529427702586 ,7.2137790078907449143 ] 
dist 121=[-3.0473468924858098413 ,7.3667665063132473694 ] 
dist 122=[-2.8612484918679539838 ,7.4325919439222198552 ] 
dist 123=[-3.6153017476269789268 ,7.4470088745799100799 ] 
dist 124=[-4.4601697203439317264 ,7.4321671337876640755 ] 
dist 125=[-5.1302188549612498617 ,7.3083246687695946408 ] 
dist 126=[-5.7340928918608138754 ,7.2622593780046268259 ] 
dist 127=[-6.2470884754673554998 ,7.0721235400417296133 ] 
dist 128=[-6.5547066569244473032 ,7.0292411210188847994 ] 
dist 129=[-6.7699097149150141836 ,4.5533081125614076000 ] 
dist 130=[-6.9143462465725910189 ,4.4962753686832340164 ] 
dist 131=[-7.0136049232421530745 ,3.1920936082430287185 ] 
dist 132=[-7.0486346019199831488 ,3.0103118559162079100 ] 
dist 133=[-7.0432296371172404244 ,2.5871443760865811466 ] 
dist 134=[-7.0228193242633360869 ,2.4895598528691173834 ] 
dist 135=[-6.8878759831636692430 ,1.9068538499927049666 ] 
dist 136=[-6.8429672898748965032 ,1.7945479294201063907 ] 
dist 137=[-6.6431562387961988463 ,1.5721680761341894208 ] 
dist 138=[-6.6143537909356275408 ,1.5130644158448934325 ] 
dist 139=[.15622292614674298991,.85166436053704967771] 
dist 140=[.23511438336722158166,1.2856569114720392521 ] 
dist 141=[.40079716303316237116,1.6968129745687538300 ] 
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dist 151=[-.40119989119973918441,3.3075590505243679176 ] 
dist 152=[-.67309770555688785171,3.3221407171756312359 ] 
dist 153=[-.90135166449289966172,3.3228852678939483276 ] 
dist 154=[-1.1287809725170966525 ,3.3107162509083481384 ] 
dist 155=[-1.3374648354964423404 ,.97432917867376069736] 
dist 156=[-1.4909603853891903030 ,.77923931211774861602] 
dist 157=[-1.6329776494057235187 ,.34425289904148035828] 
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dist 165=[-2.5334867050812431116 ,-.10236904672117160773] 
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dist 167=[-2.7812349157100522081 ,.78905705278631955479] 
dist 168=[-2.8315379068643387597 ,1.0844509848108950243 ] 
dist 169=[-2.8529018430260970871 ,1.3247760311767960875 ] 
dist 170=[-2.8511739024757477707 ,1.5517855548273178143 ] 
dist 171=[-1.1866275027028485204 ,1.7520578321364404307 ] 
dist 172=[-1.1413091167698950899 ,1.8857524745925079520 ] 
dist 173=[-1.0574275374867620414 ,1.9958933749478020723 ] 
dist 174=[-1.0352216996322451333 ,2.1022313267646188011 ] 
dist 175=[-.64833619643656856156,2.1925805132972413067 ] 
dist 176=[-.59495731703681624682,2.2389568672658023952 ] 
dist 177=[-.46588253105618959116,2.2618709711134739714 ] 
dist 178=[-.44410616969133072783,2.2634367126131013880 ] 
dist 179=[-.25778223712599270795,2.2434860444703408307 ] 
dist 180=[-.22336095689639782365,2.2309002172473001431 ] 
dist 181=[-.17326625047437779896,2.1918527182836083205 ] 
dist 182=[-.15919632006418390726,2.1721952951848907725 ] 
dist 183=[-.49441791339883343197,2.1357715617968933840 ] 
dist 184=[-.82391365496518477874,2.1313016210490474405 ] 
dist 185=[-1.0947206701113971150 ,2.1284488341862417125 ] 
dist 186=[-1.3551175571259785212 ,2.1270695427451991177 ] 
dist 187=[-1.5879700350310137729 ,1.6157884171016707181 ] 
dist 188=[-1.7489276123185851549 ,1.5501102309452262219 ] 
dist 189=[-1.8875777710137112381 ,1.3922935984235951858 ] 
dist 190=[-2.0314663724955254069 ,1.3550397081057430497 ] 
dist 191=[-2.1584497363464303420 ,1.1168739443880797182 ] 
dist 192=[-2.2296803733752929236 ,1.0689313662890304606 ] 
dist 193=[-2.2735074603384355227 ,.97896182552698744696] 
dist 194=[-2.2912031408872614363 ,.95527666495785388713] 
dist 195=[-2.2941179363755569377 ,.57158100465479737324] 
dist 196=[-2.2882445858707990840 ,.51800336044228482582] 
dist 197=[-2.2586564849013013912 ,.39360320026914709864] 
dist 198=[-2.1866804434902535426 ,.36901157025862768217] 
dist 199=[-1.4736701540874412045 ,.20448183003967015117] 
dist 200=[-1.4781409290083254035 ,.17450103005860912265] 
dist 201=[-1.4803277477670231165 ,.25714078763083546692] 
dist 202=[-1.4799592372952063871 ,.36688289471234602206] 
dist 203=[-.16728223293226786368,.46841113721195152983] 
dist 204=[-.14356032614313908638,.54449982166752255428] 
dist 205=[-.09563210662728659213,.61853222286320027652] 
dist 206=[-.08338079812149793292,.75899023680965844642] 
dist 207=[.03532850074726203141,.88186111165196504112] 
dist 208=[.05379567657114344309,.96204379068518285711] 
dist 209=[.07877852555941459135,1.0260798179038948294 ] 
dist 210=[.08416637945205301797,1.0845564766164583785 ] 
dist 211=[.08215891550771413209,1.1347048067097944953 ] 
dist 212=[.06889184156998807578,1.1655267528767232923 ] 
dist 213=[.04487621980841235908,1.1880053497468748587 ] 
dist 214=[2.63731048422697800000e-06,1.2048796939921591197 ] 
dist 215=[-.16603919932210929545,1.2168016964484651117 ] 
dist 216=[-.2807594553189997923 ,1.2195299335716807090 ] 
dist 217=[-.37952180410213180377,1.2160388286005281469 ] 
dist 218=[-.4819226861789734592 ,1.2118481041852450689 ] 
dist 219=[-.57845993117422926645,.3979859218815321503 ] 
dist 220=[-.65383759818985710362,.32859131600359736576] 
dist 221=[-.72793076149152951567,.17340847471376526208] 
dist 222=[-.81934529681593772176,.14139747992968665942] 
dist 223=[-.90549121542562314748,-.04178482594905456098] 
dist 224=[-.9585726886513307777 ,-.03219226460044671138] 
dist 225=[-.99744595136059111045,-.00523398979150917101] 
dist 226=[-1.0269283219765941646 ,.03368959418925949320] 
dist 227=[-1.0480155480973166609 ,.07718368641846537250] 
dist 228=[-1.0534082629120076244 ,.12236953532110612284] 
dist 229=[-1.0524697566509163195 ,.17731483608599864604] 
dist 230=[-1.0483075359732847316 ,.2597304494430276965 ] 
dist 231=[-1.0020230114485230182 ,.34131183358015160273] 
dist 232=[-.99052939662306026352,.39293015730861961726] 
dist 233=[-.95655821592826878394,.43233592229901238955] 
dist 234=[-.907615409686729624  ,.4652125865852502229 ] 
dist 235=[-.42675118200522701331,.4914400166610208793 ] 
dist 236=[-.42132668986060855876,.50432807184664572293] 
dist 237=[-.41498392037210455843,.51088413587842548885] 
dist 238=[-.41154211773016920851,.51185904843698433248] 
dist 239=[-.31426710127177877081,.49438531739937579808] 
dist 240=[-.30033582000553890399,.48921793381467207734] 
dist 241=[-.27107907407874931154,.48126776781977798302] 
dist 242=[-.26269123796388959237,.47781372537723232143] 
dist 243=[-.22831960170707371066,.4638378180677408441 ] 
dist 244=[-.22110000240731196122,.45914638869001251491] 
dist 245=[-.20352910465819118358,.4391151145910172402 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 2, 2, 1, 0, 0, 2] 
dist 0=[69.410245161453925544  ,69.410245161453925544  ] 
dist 1=[69.052877628010836128  ,69.587995578064755823  ] 
dist 2=[68.495281386403951761  ,69.606581179761574939  ] 
dist 3=[67.517977211150656871  ,69.548838946436275787  ] 
dist 4=[66.225142548175018475  ,69.021067558756268750  ] 
dist 5=[64.407713034428628855  ,68.922183063252596625  ] 
dist 6=[61.855344207196669302  ,66.720120083433798431  ] 
dist 7=[57.628157675365585691  ,65.805355194039084032  ] 
dist 8=[53.256140623194731852  ,64.966782477156912487  ] 
dist 9=[50.125462092117578110  ,64.659778168523404840  ] 
dist 10=[47.300285263898186540  ,63.844785106182797204  ] 
dist 11=[44.147867151733467332  ,63.510435550711247386  ] 
dist 12=[38.314001376860039127  ,63.178670683900763533  ] 
dist 13=[30.876639217240595750  ,62.961071696399289462  ] 
dist 14=[25.859884290219140037  ,39.343780383406695331  ] 
dist 15=[21.649310429474258947  ,38.982129646358685432  ] 
dist 16=[17.430674557528087506  ,29.161453886227147285  ] 
dist 17=[13.523323094646325447  ,27.917533267845176144  ] 
dist 18=[10.555525421178180563  ,25.323995468707371467  ] 
dist 19=[7.7036127466616651072 ,24.640129053056920272  ] 
dist 20=[4.2588151410396490799 ,22.088386446321072666  ] 
dist 21=[1.0140676782584334311 ,21.586608765296395193  ] 
dist 22=[-1.0392801833304213545 ,20.621642879932977506  ] 
dist 23=[-2.6165274619530714021 ,20.387110045142846695  ] 
dist 24=[-3.9607241268088520179 ,6.0931618516341550284 ] 
dist 25=[-5.0565316151796365004 ,4.8431602239126367543 ] 
dist 26=[-5.6424231144915996853 ,2.1364520421527620197 ] 
dist 27=[-7.4441181827470884776 ,1.6069443550647341177 ] 
dist 28=[-9.5298649550435676231 ,-1.3010674018584580824 ] 
dist 29=[-11.034557410220632638  ,-1.7810680401686735172 ] 
dist 30=[-12.407798355456497336  ,-2.7959625099124789213 ] 
dist 31=[-13.968769661284073509  ,-2.9731743889255497502 ] 
dist 32=[-15.393565148175546635  ,-4.2142215926487003878 ] 
dist 33=[-16.222948428092977738  ,-4.3994973820016634313 ] 
dist 34=[-16.779477534907619453  ,-4.3645065125815854334 ] 
dist 35=[-17.114331246862134285  ,-4.0256339721000459404 ] 
dist 36=[-17.326128107225408235  ,-3.5222212822603772708 ] 
dist 37=[-17.390932404035322237  ,-2.8301424348447738035 ] 
dist 38=[-17.362729543822333116  ,-1.8700669173377395276 ] 
dist 39=[-17.324148410556376147  ,-.29688990575022132192] 
dist 40=[-11.391916470733780335  ,2.2538208020557955715 ] 
dist 41=[-11.346448645516981481  ,4.2472429102015448052 ] 
dist 42=[-10.587485394159093512  ,5.8768603126875316021 ] 
dist 43=[-10.407022344398320525  ,7.4319277250977872209 ] 
dist 44=[-10.247103667712132944  ,8.8172297639835828673 ] 
dist 45=[-10.178888514237374960  ,9.7697930144127708901 ] 
dist 46=[-7.0224149074669700181 ,10.586881180520412736  ] 
dist 47=[-6.6362684626079574335 ,11.431999773043268646  ] 
dist 48=[-5.7485286848271891206 ,12.181629851717268114  ] 
dist 49=[-5.5418072215859183120 ,12.617727993730517653  ] 
dist 50=[-4.3405942226948798216 ,12.907647599959232458  ] 
dist 51=[-4.1074352669113941419 ,13.073697632430732567  ] 
dist 52=[-3.6439204146981166907 ,13.152305273731987561  ] 
dist 53=[-3.5186331909020963511 ,13.150835214622661148  ] 
dist 54=[-1.9343760505172043690 ,13.004062677668345452  ] 
dist 55=[-1.7016100002328851762 ,12.961138660319032372  ] 
dist 56=[-1.2004663331881665614 ,7.5532914488626396200 ] 
dist 57=[-1.0673022489421246412 ,7.0291309883407544767 ] 
dist 58=[-.51870353781810795591,5.8113063180926835598 ] 
dist 59=[-1.0919172382309294860 ,5.5653883901203383424 ] 
dist 60=[-1.7657775722178853208 ,3.9440036384668097890 ] 
dist 61=[-2.2936662206098843925 ,3.2589246282341695435 ] 
dist 62=[-2.8143634939946360069 ,-.69195297435458435299] 
dist 63=[-3.4595800149049790231 ,-.77089709931833106083] 
dist 64=[-4.0695408546523754956 ,-1.3382251438687834321 ] 
dist 65=[-4.4496328289602420595 ,-1.4385711446703037926 ] 
dist 66=[-4.7332315841234009198 ,-1.4577668558485657106 ] 
dist 67=[-4.9583267932681864154 ,-1.3619770166754491832 ] 
dist 68=[-5.1279782420142765347 ,-1.2023975966698426598 ] 
dist 69=[-5.1904370957244319181 ,-.96367414172618471618] 
dist 70=[-5.2116062967206062849 ,-.62204780561089047464] 
dist 71=[-5.2165593433218759155 ,-.05206537774821847919] 
dist 72=[-3.9992542587609175229 ,.75884428681490120682] 
dist 73=[-4.0021953459211432646 ,1.3104512946761958896 ] 
dist 74=[-3.9885540292572240140 ,1.7746565759331583049 ] 
dist 75=[-3.9602588942604313737 ,2.2390236680342613696 ] 
dist 76=[-3.9427983622180042318 ,2.6663071909569091909 ] 
dist 77=[-3.3240967558542553271 ,2.9826270270190299145 ] 
dist 78=[-3.2316383352477900001 ,3.2773366491655053779 ] 
dist 79=[-3.0026886808081682585 ,3.6184451626002971253 ] 
dist 80=[-2.9437203125905747822 ,3.9288201950775220847 ] 
dist 81=[-2.5642694343398239635 ,4.1009636110692728559 ] 
dist 82=[-2.4836803985530418408 ,4.2043510380295744975 ] 
dist 83=[-2.3347656266686635440 ,4.2405177292720166959 ] 
dist 84=[-2.2941338021012969924 ,4.3434120031004413743 ] 
dist 85=[-1.5467023815895990035 ,4.4707785751777958613 ] 
dist 86=[-1.4434655123673986198 ,4.5304933845710001234 ] 
dist 87=[-1.1852298260526291676 ,4.5520268264922292163 ] 
dist 88=[-1.7070093406148545550 ,4.5480595427331865774 ] 
dist 89=[-2.3070153713857487283 ,4.4805624792439635725 ] 
dist 90=[-2.7935954566803876701 ,4.4520912457036764400 ] 
dist 91=[-3.2505782678515598845 ,4.3532780131074549397 ] 
dist 92=[-3.6519428066420342130 ,4.3144343390093008943 ] 
dist 93=[-3.9167133621933847057 ,2.4607115412196486462 ] 
dist 94=[-4.1313649371809406681 ,2.2948942718794501288 ] 
dist 95=[-4.3328512824565309180 ,2.2510621797876414936 ] 
dist 96=[-4.5020795217158174162 ,1.4400859040868705411 ] 
dist 97=[-4.5880819449817907508 ,1.3293437494421013541 ] 
dist 98=[-4.6293408593381825818 ,1.0543854116160510662 ] 
dist 99=[-4.6302638499840558204 ,1.0132734902122319760 ] 
dist 100=[-4.5867372768515786230 ,.59573132225624940215] 
dist 101=[-4.5614522192369412314 ,.51811353767652384163] 
dist 102=[-4.4741593513744266724 ,.42402259396162037842] 
dist 103=[-4.4300831967784436438 ,.40329482844148620312] 
dist 104=[-1.0214778094320281139 ,.32960406378484665164] 
dist 105=[-1.0330435989139098697 ,.54989602945096721869] 
dist 106=[-1.0389449422572689362 ,.72728947955237076397] 
dist 107=[-1.0418179559950814666 ,.89177585645089273597] 
dist 108=[-1.0413028794119496824 ,1.0347902014376223794 ] 
dist 109=[-.26521198209096458713,1.1265519997746437913 ] 
dist 110=[-.20194247327286726711,1.1980755315920230005 ] 
dist 111=[-.06146791583698708359,1.2603785110025743164 ] 
dist 112=[-.03281861103027851552,1.3132118458158901387 ] 
dist 113=[.12843888783507860143,1.3469698969413896303 ] 
dist 114=[.15570705214353635002,1.3731214191200754950 ] 
dist 115=[.21382134098029242616,1.3956194960178796126 ] 
dist 116=[.22500539579721899551,1.4139677693023071076 ] 
dist 117=[.3043559227850747526 ,1.4235696208271359618 ] 
dist 118=[.31472152766149593864,1.4285757211223833918 ] 
dist 119=[.30977940030926036724,1.4285958282566810230 ] 
dist 120=[.28267376321919271409,.82431438117698353486] 
dist 121=[.1683360952310649511 ,.86328492910175172164] 
dist 122=[.01272286389245027298,.8838702350248802818 ] 
dist 123=[-.15184926822639739446,.89487498342850299573] 
dist 124=[-.3089945146059817598 ,.89588264783630967043] 
dist 125=[-.434988833305932347  ,-.12312931082878677134] 
dist 126=[-.56192373794421617196,-.16384494718401233323] 
dist 127=[-.72282016995245727673,-.25207786993430297634] 
dist 128=[-.87656473118243394908,-.26860009046142149138] 
dist 129=[-.97497746525480845083,-.35790947862872970648] 
dist 130=[-1.0514195460181687991 ,-.37241196233352210848] 
dist 131=[-1.1175435130567839460 ,-.38679155394842169194] 
dist 132=[-1.1717411552523818199 ,-.3341930352945195668 ] 
dist 133=[-1.2006201623340905459 ,-.26243190144343132311] 
dist 134=[-1.2164002812402693670 ,-.16310433477497188715] 
dist 135=[-1.2183585719095354361 ,-.00056875509692372796] 
dist 136=[-.61752006303333139269,.16972327435979126558] 
dist 137=[-.61622837621462921782,.28404352612401050468] 
dist 138=[-.61376859105362143507,.37892428942410015128] 
dist 139=[-.60992074292672908426,.47169009378830263219] 
dist 140=[-.60667628638457701648,.55566659212967573894] 
dist 141=[-.4150317639467438412 ,.61549490327995717544] 
dist 142=[-.39292169361020613929,.66891739529243205939] 
dist 143=[-.34095050320356243146,.72734697283705976292] 
dist 144=[-.32912925457884298842,.77946097867957595486] 
dist 145=[-.25577247948428895421,.80769646364938636716] 
dist 146=[-.2415241995062132824 ,.8237665540836975413 ] 
dist 147=[-.21408473697458024175,.82736398904521118783] 
dist 148=[-.20692816925808813386,.82610409858966721002] 
dist 149=[-.10713493879076034092,.82280279873551027653] 
dist 150=[-.09281595500196080539,.81738378365777672948] 
dist 151=[-.06257120965414355532,.81314007742411055291] 
dist 152=[-.1897070567000750585 ,.62810925215009128463] 
dist 153=[-.30516309581656784968,.62671926637864678258] 
dist 154=[-.40060616052598794438,.62357547786368905029] 
dist 155=[-.49329649472888186532,.61758745488950904588] 
dist 156=[-.57679415909777441383,.61433855673438612229] 
dist 157=[-.63557608674036565247,.31681234717212692449] 
dist 158=[-.68733938519644309131,.27986328574225999878] 
dist 159=[-.74284616118314615547,.27024278355104865194] 
dist 160=[-.79205569299860086124,.13719822016493750428] 
dist 161=[-.81870505874610640264,.1180802697230063677 ] 
dist 162=[-.83385564670877034984,.07802429724302112047] 
dist 163=[-.83720710991028301874,.06743834906965162309] 
dist 164=[-.83564589275408909235,.02812594620675663953] 
dist 165=[-.83150546157425717328,.02029839517077680136] 
dist 166=[-.82394545514939696163,.00626894911927392185] 
dist 167=[-.81979482015468319618,.00318839740363955660] 
dist 168=[-.58160375876779734663,.17441947010300397765] 
dist 169=[-.58463866017863938343,.28986843610883306323] 
dist 170=[-.58404033615854776122,.38385315133229162993] 
dist 171=[-.57765894143380539335,.47272842007524603772] 
dist 172=[-.57405649064089120789,.55120251055460121841] 
dist 173=[-.25029943885995704728,.60370644870129827321] 
dist 174=[-.22050739837684209421,.64708930592596115843] 
dist 175=[-.15318475550082744344,.68918775398041658491] 
dist 176=[-.13899594788729364627,.72580623694188158385] 
dist 177=[-.05620431805150234398,.74733453162317288486] 
dist 178=[-.04147763269028181748,.76186972300309568008] 
dist 179=[-.01130014469531085757,.77059912381656076464] 
dist 180=[-.00362798235429804035,.77489900331596760901] 
dist 181=[.06125915921530460892,.77411458437429484911] 
dist 182=[.07172817800975560628,.76625932082078835242] 
dist 183=[.08169119914345151079,.76106971915742504238] 
dist 184=[.04520414486839826132,.50952244486925852733] 
dist 185=[-.05691308558236890465,.51838850516113253121] 
dist 186=[-.14404083777076382622,.52187289687570406281] 
dist 187=[-.2331340081991209297 ,.5220726456950533653 ] 
dist 188=[-.31635434154559677206,.52077488423403260006] 
dist 189=[-.38006072185634278126,.04765437125970249273] 
dist 190=[-.44148711763737851855,.00749873229081370144] 
dist 191=[-.51561467839013633289,-.00270330064103224083] 
dist 192=[-.58464795565398105113,-.08552341424105211686] 
dist 193=[-.62575791788804176323,-.1013035181716150311 ] 
dist 194=[-.65416779295308321204,-.11319492454754042219] 
dist 195=[-.67255204948313996111,-.11082999462113175908] 
dist 196=[-.68503063965494998223,-.10109138283579766388] 
dist 197=[-.68988821885408796276,-.08184253021180687346] 
dist 198=[-.69007989547780602508,-.05199848144395918419] 
dist 199=[-.68853397118239346004,-5.25087841878304300000e-06] 
dist 200=[-.54868286471607290303,.12200567856393010245] 
dist 201=[-.55661699232756939335,.20575880034066531078] 
dist 202=[-.55795903969312868815,.27728345676806419504] 
dist 203=[-.55473236132834321737,.3505262302155314382 ] 
dist 204=[-.55306998014486645184,.41900677860382119519] 
dist 205=[-.50923218742175223406,.47153927794192783037] 
dist 206=[-.50079298370792467246,.52229660707683537352] 
dist 207=[-.47785050631188578387,.58369762618779633524] 
dist 208=[-.4713702159372027818 ,.64095425702613433729] 
dist 209=[-.42499573030875448096,.67518341465596540285] 
dist 210=[-.41444874759343896292,.69900089719997495454] 
dist 211=[-.39650749723908781031,.7147348859356618813 ] 
dist 212=[-.391280909865070661  ,.72456465962739957284] 
dist 213=[-.27446417425213169066,.72603986757453103076] 
dist 214=[-.25823900544052547549,.72194486422218013471] 
dist 215=[-.24633077959478632018,.71916534829473165023] 
dist 216=[-.40083285876305894978,.65856284273063014933] 
dist 217=[-.50150176131844054718,.64714892211831927236] 
dist 218=[-.5817240195640139146 ,.61966058580407374421] 
dist 219=[-.65468314765872629588,.60779064325872846558] 
dist 220=[-.71713212975530866155,.59939366749347234288] 
dist 221=[-.75543903460154721415,.53282003416502653665] 
dist 222=[-.78328680657954493084,.5091560024216190276 ] 
dist 223=[-.80402387984842229571,.50234234175011282954] 
dist 224=[-.81936555023752626848,.35107717418246226141] 
dist 225=[-.82569599815845765131,.33008856825702642389] 
dist 226=[-.8266200416176962371 ,.2804540078869266619 ] 
dist 227=[-.82473633561526492533,.26994853920610392503] 
dist 228=[-.81038120444030046847,.19975760272319135989] 
dist 229=[-.80522781263258767269,.18633324363341669266] 
dist 230=[-.78335577351389589936,.16166462017273721182] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 0, 2, 2, 0, 2] 
dist 0=[69.500793037563213612  ,69.500793037563213612  ] 
dist 1=[69.058005246637751329  ,69.648231940869363517  ] 
dist 2=[68.313669493773665047  ,69.794782427106054399  ] 
dist 3=[67.241190495346353399  ,69.793558925127819284  ] 
dist 4=[65.372047794894224816  ,69.719935172218817268  ] 
dist 5=[63.079851897356002060  ,69.103114499304817380  ] 
dist 6=[60.036425811116141182  ,68.891419407115874764  ] 
dist 7=[55.167854770126342765  ,68.074480656335186182  ] 
dist 8=[50.178498749144161982  ,67.875417692000205330  ] 
dist 9=[46.652713991449291171  ,65.027438947739143190  ] 
dist 10=[40.532749312386966993  ,63.955391259117910619  ] 
dist 11=[36.103639707212576988  ,63.261685923747248998  ] 
dist 12=[32.280278108937454189  ,62.956827516761091613  ] 
dist 13=[28.276602640263720829  ,62.524433845379030540  ] 
dist 14=[24.457558769906024754  ,53.825157322054567614  ] 
dist 15=[21.371678794296234585  ,52.271942932767753238  ] 
dist 16=[18.228727409801221757  ,43.739809798250659528  ] 
dist 17=[14.182280014179143983  ,27.737582052747800958  ] 
dist 18=[10.260385062973033030  ,25.046705494096894786  ] 
dist 19=[7.6148818298658747406 ,20.375501106001422340  ] 
dist 20=[5.3963038381802729212 ,17.849955681610085838  ] 
dist 21=[3.1789659921431663533 ,17.250015595347903241  ] 
dist 22=[1.1317518967201356977 ,16.261225314997471993  ] 
dist 23=[-.40745617588799760755,16.014629882760404951  ] 
dist 24=[-1.8688360355207865667 ,6.0494283085236203522 ] 
dist 25=[-4.2832687293801550555 ,3.5519865848559837993 ] 
dist 26=[-6.3131206310925422144 ,1.3572599193717591416 ] 
dist 27=[-8.2384788161822953435 ,.91401898559387816238] 
dist 28=[-9.9595085197248375932 ,-1.3568638580670383273 ] 
dist 29=[-11.173245885568936944  ,-1.7330072691815112674 ] 
dist 30=[-12.254034349922838905  ,-2.5338608793932169885 ] 
dist 31=[-13.444351698559749863  ,-2.6641055091439473571 ] 
dist 32=[-14.513729238170237984  ,-3.4248294893808726731 ] 
dist 33=[-15.111477142221035358  ,-3.5081792509597780783 ] 
dist 34=[-15.482942638960604122  ,-3.4193556840904762805 ] 
dist 35=[-15.648237065584966884  ,-3.0776982646551782697 ] 
dist 36=[-15.721171163387887941  ,-2.6038363540667749355 ] 
dist 37=[-15.723383574757851597  ,-1.9869083159267605981 ] 
dist 38=[-15.675741102793381872  ,-1.1491055026078386678 ] 
dist 39=[-15.623117502899947231  ,.2066116348077097599 ] 
dist 40=[-11.007818926917762211  ,3.0098710641484266162 ] 
dist 41=[-10.932077044398160731  ,4.9310056868748838933 ] 
dist 42=[-8.6702411455282994803 ,6.4880811692283029593 ] 
dist 43=[-8.3604651139874420189 ,7.9514071625063568280 ] 
dist 44=[-7.6199288850537590113 ,9.2396959877385535906 ] 
dist 45=[-7.4409309244195868955 ,10.098654533074610802  ] 
dist 46=[-6.3206333326853669056 ,10.806698851396472752  ] 
dist 47=[-6.0918079077298799659 ,11.493162849656970973  ] 
dist 48=[-5.6616654207971046344 ,12.088283347283498050  ] 
dist 49=[-5.5461664450470668271 ,12.431900429087986826  ] 
dist 50=[-3.6314664428181151138 ,12.657126643171665181  ] 
dist 51=[-3.3653232070607020311 ,12.779649847013359184  ] 
dist 52=[-2.7083418479540148459 ,12.826596926576130793  ] 
dist 53=[-2.6043558780796676383 ,12.711125407433771486  ] 
dist 54=[-1.6080706756266568253 ,11.562625625568093488  ] 
dist 55=[-1.4208837950099331598 ,10.624453841314640961  ] 
dist 56=[-1.1804156144834808040 ,6.1659626609749109849 ] 
dist 57=[-1.1115974219454015718 ,5.0023017766661709976 ] 
dist 58=[-.12065082164528108756,4.3645403698942063508 ] 
dist 59=[-.75000373957109580775,4.4780392978493641423 ] 
dist 60=[-1.3467850013784647049 ,4.5571775931253176578 ] 
dist 61=[-1.8190894759114010080 ,4.6093400943006953741 ] 
dist 62=[-2.2895803278533012520 ,4.6182718002793287671 ] 
dist 63=[-2.8791636571539373145 ,4.6045967651035840740 ] 
dist 64=[-3.4400652759935849000 ,4.5922203105622354106 ] 
dist 65=[-3.7961610267153787122 ,2.1691655687150339383 ] 
dist 66=[-4.0696803934039388917 ,2.3093266297059892446 ] 
dist 67=[-4.3011972835650078912 ,2.3924046856014789956 ] 
dist 68=[-4.4874272153405798116 ,2.4492017553516630624 ] 
dist 69=[-4.5803019613499490632 ,2.4845841088765751793 ] 
dist 70=[-4.6224030636730911642 ,2.5032588812381760376 ] 
dist 71=[-4.6272381597522255963 ,2.5030867371077093107 ] 
dist 72=[-4.3016315681300219451 ,2.4760118740978590908 ] 
dist 73=[-4.5473908509478256803 ,2.4643457266939489102 ] 
dist 74=[-4.6692661524845878640 ,1.4919528953291376656 ] 
dist 75=[-4.7327270259369689294 ,1.8613175456239898844 ] 
dist 76=[-4.7453868440475594799 ,2.1968236810927369428 ] 
dist 77=[-4.6569331956775495602 ,2.4378945501208221097 ] 
dist 78=[-4.6301803079966113444 ,2.6552979260078645861 ] 
dist 79=[-4.6107863823231393003 ,2.8964224453566575735 ] 
dist 80=[-4.5965649206933936486 ,3.1119289076091632150 ] 
dist 81=[-3.5350018394042873805 ,3.2271641675495759926 ] 
dist 82=[-3.3953548127071917575 ,3.2908835256745840945 ] 
dist 83=[-3.0633262013508515814 ,3.3055154725362282142 ] 
dist 84=[-2.9824160955167238543 ,3.6305709972502931961 ] 
dist 85=[-2.4897801091767942686 ,4.0886898090916676070 ] 
dist 86=[-2.3902378937939037364 ,4.3932055277139775399 ] 
dist 87=[-2.2314373504996987690 ,4.6428707721091423711 ] 
dist 88=[-2.2335804382746909016 ,4.8822455791745637870 ] 
dist 89=[-2.2269679614063875886 ,5.0847522257026956207 ] 
dist 90=[-1.7715552207637500333 ,5.1873667062626875352 ] 
dist 91=[-2.1386032929297451059 ,5.2363318539825162183 ] 
dist 92=[-2.4668545911503617139 ,5.2397705723722318943 ] 
dist 93=[-2.6938240115604651795 ,5.1868508409043094986 ] 
dist 94=[-2.8894199292815907007 ,5.1565070019540651412 ] 
dist 95=[-3.0925534399382570705 ,5.0686134616023500154 ] 
dist 96=[-3.2704411164682556400 ,5.0253583895688112830 ] 
dist 97=[-3.3653543443372375625 ,1.9389568767764374566 ] 
dist 98=[-3.4174032378625388452 ,2.1362206982957076781 ] 
dist 99=[-3.4255148652542505336 ,2.2557045906762164753 ] 
dist 100=[-3.4119126000705478786 ,2.3407469746652046079 ] 
dist 101=[-3.3942063063548938893 ,2.4006564235702098823 ] 
dist 102=[-3.3530037448318079513 ,2.4398050431622962174 ] 
dist 103=[-3.3313684758444478057 ,2.4479168585467692073 ] 
dist 104=[-2.5079944208044537798 ,2.4337851404442265892 ] 
dist 105=[-2.6207676295827542804 ,2.4310150477396684120 ] 
dist 106=[-2.6885982552298635821 ,2.2655848370503978719 ] 
dist 107=[-2.7363432373300347301 ,2.2319441164116161578 ] 
dist 108=[-2.7690043527224336352 ,2.3079126463134716216 ] 
dist 109=[-2.7893947421656164724 ,2.5332236118066604167 ] 
dist 110=[-2.7881982655662342319 ,2.7225037964237747785 ] 
dist 111=[-2.7738640736522512521 ,2.9113227182389124053 ] 
dist 112=[-2.7616892827255127004 ,3.0765664638545836598 ] 
dist 113=[-1.0570374625762278172 ,3.1718268835671072754 ] 
dist 114=[-1.0722780125059781932 ,3.2337939091558074556 ] 
dist 115=[-1.0777731239260475907 ,3.2662603824197408990 ] 
dist 116=[-1.0771616630734779990 ,3.2771735764055309256 ] 
dist 117=[-1.0740278401134164985 ,3.2737892645664011267 ] 
dist 118=[-1.0541979257956286654 ,3.2239023252960651079 ] 
dist 119=[-1.0474046927787967287 ,3.2137094925721783040 ] 
dist 120=[-1.0174706831590155779 ,1.5398879806097536425 ] 
dist 121=[-1.0127594366386775226 ,1.3811166424992336171 ] 
dist 122=[-.80310431075087519164,1.0205018868190453819 ] 
dist 123=[-1.1783748836360675685 ,.94373672720133614056] 
dist 124=[-1.5264868892783370771 ,.49170142133744985838] 
dist 125=[-1.7889373521061700870 ,.41021590777296666567] 
dist 126=[-2.0381353560669240822 ,.24486124581270298372] 
dist 127=[-2.3333955930206636414 ,.20267133944622498363] 
dist 128=[-2.6055981140698319723 ,-.189814869961342955  ] 
dist 129=[-2.7628400145073914487 ,-.2515169258353366289 ] 
dist 130=[-2.8655317529056586612 ,-.32770415259728301663] 
dist 131=[-2.9201835099536687303 ,-.33327317094310800645] 
dist 132=[-2.9525638333178361645 ,-.31833205538865175628] 
dist 133=[-2.9664351384273947435 ,-.26605621328196107487] 
dist 134=[-2.9693656533197403998 ,-.17183570891134931642] 
dist 135=[-2.9581130813672909744 ,-.00018988639769769475] 
dist 136=[-.44592431959071912952,.55251538659657848673] 
dist 137=[-.44321365117775704327,.93374648372331442001] 
dist 138=[-.23768293869320813761,1.2612705166155355882 ] 
dist 139=[-.21724117780309623198,1.5997875201299843200 ] 
dist 140=[-.17047001574467472746,1.9182552288439053935 ] 
dist 141=[-.16036438487990470924,2.1658210054359032457 ] 
dist 142=[-.10012988513068771153,2.4081377290383070196 ] 
dist 143=[-.08907070409451613554,2.7056718043144737096 ] 
dist 144=[-.06691658892057488158,2.9853488735339867222 ] 
dist 145=[-.06123302744621983123,3.1564503535001328231 ] 
dist 146=[-.00185300883481547751,3.2802912358700672819 ] 
dist 147=[.00721381376807031198,3.3714890313236125718 ] 
dist 148=[-.09920154391951058180,3.4344088588437513136 ] 
dist 149=[-.24697370270668991308,3.4472909863911855757 ] 
dist 150=[-.61544795156557093103,3.4384973657949946119 ] 
dist 151=[-1.3475379527812663909 ,3.4294585988458230753 ] 
dist 152=[-2.0779546783250866188 ,3.2442808715498004068 ] 
dist 153=[-2.5517017587979575579 ,3.2025507776120403316 ] 
dist 154=[-2.9267872091884278735 ,3.0826883423079171601 ] 
dist 155=[-3.2637330079027838772 ,3.0465680999920910819 ] 
dist 156=[-3.5491866258060088860 ,2.7792720485845201698 ] 
dist 157=[-3.7189169034059406644 ,2.7165554836408755657 ] 
dist 158=[-3.8358927101425325632 ,2.6133682219459449804 ] 
dist 159=[-3.9109570356556736317 ,2.5813759188329291331 ] 
dist 160=[-3.9607084889593675008 ,1.8416800357886990333 ] 
dist 161=[-3.9767344182955487772 ,1.7384321376014565514 ] 
dist 162=[-3.9710806652772604537 ,1.4994765935459365145 ] 
dist 163=[-3.9587036208313611567 ,1.4427164270120951831 ] 
dist 164=[-3.8806492119358772749 ,1.1170537600107650520 ] 
dist 165=[-3.8546679008969597348 ,1.0541202648236451306 ] 
dist 166=[-3.7426067637944284648 ,.92608796644648161867] 
dist 167=[-3.7246490292542795584 ,.89113985819942623942] 
dist 168=[-.53845780683324703314,.33849708568215716623] 
dist 169=[-.53693401195289965223,.56081963535732843053] 
dist 170=[-.5205539289233416121 ,.73995856938942929497] 
dist 171=[-.51579746812491559421,.90625703783354236837] 
dist 172=[-.50080441081033251369,1.0509860737268778184 ] 
dist 173=[-.49584071876240985568,1.1441042844067991306 ] 
dist 174=[-.45749339055174835398,1.2169797849936356498 ] 
dist 175=[-.44815278066708507212,1.2809791790745697934 ] 
dist 176=[-.43338643976601104801,1.3353345001515935063 ] 
dist 177=[-.42846411726526274022,1.3697486208664040437 ] 
dist 178=[-.31052238661375582896,1.3960464241670760652 ] 
dist 179=[-.29397700227608326378,1.4180331837050853819 ] 
dist 180=[-.2563815372097423661 ,1.4354890469158659819 ] 
dist 181=[-.24660515757302975753,1.4437172516412420998 ] 
dist 182=[-.19704256357492467487,1.4467383752185682757 ] 
dist 183=[-.18737232554275471083,1.4434279573412934785 ] 
dist 184=[-.16595954714492686805,.58632400256563191824] 
dist 185=[-.15966027758943075661,.58253141330155605127] 
dist 186=[-.14636329819148153113,.11618154158272587196] 
dist 187=[-.24494517051597280737,.08139876613764343682] 
dist 188=[-.33970313062357420321,.11069215276292687942] 
dist 189=[-.46675920616690835513,.14176929149059078398] 
dist 190=[-.59429140208030424568,.17150349203915401247] 
dist 191=[-.75530654758284853577,.19544112719840972594] 
dist 192=[-.90885934175393612365,.21964691649169349726] 
dist 193=[-1.0066310481531473645 ,.25045053773565250528] 
dist 194=[-1.0819830997910772739 ,.27994403847840405482] 
dist 195=[-1.1461244102345984204 ,.29892495664487061763] 
dist 196=[-1.1979253869265832067 ,.31378522754403824506] 
dist 197=[-1.2240631414159292442 ,.32684523981055514246] 
dist 198=[-1.2363329867162217555 ,.33770254225274641668] 
dist 199=[-1.2377335625458164805 ,.34377822098454741375] 
dist 200=[-.72016518881727500681,.34749734038904609471] 
dist 201=[-.71638579486568514999,.34895648618977000636] 
dist 202=[-.52167719128602700513,.39756991038598121439] 
dist 203=[-.49774218725823440204,.49565674133513835666] 
dist 204=[-.44082236852236533593,.58481046624880837541] 
dist 205=[-.42762314821548766614,.64894776138622800313] 
dist 206=[-.3854459205198114623 ,.70685616637284982631] 
dist 207=[-.39917477234603519434,.77116854927696211306] 
dist 208=[-.40693995009793920221,.82869519381773516524] 
dist 209=[-.40856193634783986468,.85954149893091691397] 
dist 210=[-.40776418886951488677,.8766627836156674166 ] 
dist 211=[-.40587926351058217197,.88060145837943601659] 
dist 212=[-.40284262651050788275,.8772569943432840341 ] 
dist 213=[-.40077499610973706652,.87449373505380300281] 
dist 214=[-.3909800030821667542 ,.87079386935713585591] 
dist 215=[-.38770325363851609438,.86575626284017050543] 
dist 216=[-.37701778451434410775,.62050582862195211078] 
dist 217=[-.37346675201815182126,.59086085900936657718] 
dist 218=[-.4685021415824028675 ,.52058841062161491674] 
dist 219=[-.56652275243252097421,.50438425714013548495] 
dist 220=[-.65427104563989459327,.40257250801733922976] 
dist 221=[-.71509379523472493622,.38251506354534151651] 
dist 222=[-.76766436465463961896,.36358278852174632828] 
dist 223=[-.8225022636676794758 ,.41916742191194233373] 
dist 224=[-.8706066785668241072 ,.47729777571054617043] 
dist 225=[-.8963235423928024453 ,.55386938575467907664] 
dist 226=[-.91049233239290504217,.6284315844431397929 ] 
dist 227=[-.91275324191628943676,.6785482354077896741 ] 
dist 228=[-.90940865928692294055,.7202103595588189272 ] 
dist 229=[-.90470918067083862621,.7610551886010688945 ] 
dist 230=[-.8940392483941423318 ,.7981035521117018922 ] 
dist 231=[-.88841439495387641345,.8246250499184645907 ] 
dist 232=[-.65313551484801344605,.8484373178586958364 ] 
dist 233=[-.70250051329571468826,.8746810430823071700 ] 
dist 234=[-.74851734044633938463,.8967559633775424623 ] 
dist 235=[-.79814598493440305819,.9039426838238415374 ] 
dist 236=[-.8788414271511555763 ,.9048734183031512608 ] 
dist 237=[-.9462978271016764767 ,.9019989360195981620 ] 
dist 238=[-1.0001536595138040146 ,.86688581543527936902] 
dist 239=[-1.0266088851510730445 ,.86309978370227049232] 
dist 240=[-1.0401203389601122728 ,.8703856139431220133 ] 
dist 241=[-1.0423553117766465427 ,.87069384855522921299] 
dist 242=[-1.0083312627701050394 ,.79260642835216648722] 
dist 243=[-.9980177141787015641 ,.77817062340962813717] 
dist 244=[-.9822085678479079122 ,.75436110386825076674] 
dist 245=[-.9752474851623822632 ,.73302021816343446767] 
dist 246=[-.9469278958612439146 ,.56329357446497229994] 
dist 247=[-.9374228633066962423 ,.45647231085226339301] 
dist 248=[-.9129828203686861039 ,.41098082985264177598] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 2, 2, 2, 0, 1] 
dist 0=[53.534457150770011256  ,53.534457150770011256  ] 
dist 1=[53.093489146469954045  ,53.879018360796525553  ] 
dist 2=[51.676867172496358951  ,54.324379931288504392  ] 
dist 3=[50.139394668922763170  ,54.439296664557567806  ] 
dist 4=[48.928057798867153625  ,54.431808667199153780  ] 
dist 5=[47.720798501993909239  ,54.388381043310668855  ] 
dist 6=[46.199724511086229026  ,54.310680516608799092  ] 
dist 7=[44.589281509442872071  ,54.201338264358565462  ] 
dist 8=[43.025192433669513746  ,50.271248271097444535  ] 
dist 9=[41.192143102474215861  ,49.674386347491247667  ] 
dist 10=[38.507674879977586676  ,48.558747916244979954  ] 
dist 11=[35.745528956524893219  ,48.250750680934081905  ] 
dist 12=[33.602249055837236477  ,47.098363140103496330  ] 
dist 13=[31.497292603018690985  ,46.787846377543529030  ] 
dist 14=[28.888041046385184114  ,46.225031358927903721  ] 
dist 15=[26.146985513988118840  ,46.054868685165842924  ] 
dist 16=[22.437619891756362601  ,31.244662624677239558  ] 
dist 17=[18.819877232252795171  ,30.720977324183681707  ] 
dist 18=[15.726851731027640015  ,30.552392214118272220  ] 
dist 19=[11.566148036166704118  ,21.617864945241861120  ] 
dist 20=[8.6352522724855934602 ,16.866024423942445388  ] 
dist 21=[6.2315476048670740431 ,16.019511808634015122  ] 
dist 22=[3.9096174149930389436 ,14.656695057212072512  ] 
dist 23=[1.6378224726949703035 ,14.331042456752629507  ] 
dist 24=[-1.3279903196470968598 ,9.0475631016684162160 ] 
dist 25=[-3.3362648637351542990 ,8.3702670974530264826 ] 
dist 26=[-5.0348115202166933817 ,6.8948264285525722143 ] 
dist 27=[-6.7643635722570236664 ,6.6136245980223890758 ] 
dist 28=[-8.3923704268248645429 ,4.9873826563172946542 ] 
dist 29=[-9.6862062484832017119 ,4.7123916057676803284 ] 
dist 30=[-10.992470336363662401  ,4.1662542432870062594 ] 
dist 31=[-12.671880415724236546  ,4.0377926149507694642 ] 
dist 32=[-14.259107697038674532  ,2.9858987448890596256 ] 
dist 33=[-15.197341607569262422  ,2.8200914971903319849 ] 
dist 34=[-15.850098653279978726  ,2.5238005232637218273 ] 
dist 35=[-16.295805007251137057  ,2.4524142811943361557 ] 
dist 36=[-16.601723682295680745  ,2.2248686910412822047 ] 
dist 37=[-16.695320287874782224  ,2.1644710095582198928 ] 
dist 38=[-16.695967998132277477  ,2.0836903384155492801 ] 
dist 39=[-16.641619522280902876  ,2.0526516708301448457 ] 
dist 40=[-15.484230183576635246  ,1.9780588831899697188 ] 
dist 41=[-15.269246558883753866  ,1.9461656390706212490 ] 
dist 42=[-14.763891882253295164  ,1.9194690967699333078 ] 
dist 43=[-14.589560888182468886  ,1.8938977673223596195 ] 
dist 44=[-13.743291945323307327  ,1.8658889958556519904 ] 
dist 45=[-13.552169805303546247  ,1.8466596229449453933 ] 
dist 46=[-13.082095691866691702  ,1.8299453673422914296 ] 
dist 47=[-12.927209438530211778  ,1.8148033363732158735 ] 
dist 48=[-6.1463831152051816970 ,4.0014221741962731554 ] 
dist 49=[-5.4660069949505086460 ,6.0497695555701647054 ] 
dist 50=[-3.9705523793537854638 ,7.7384743221793981017 ] 
dist 51=[-3.6342711879392955628 ,9.3907591954096078709 ] 
dist 52=[-1.9092929888835133218 ,10.898701495874723559  ] 
dist 53=[-1.6035217528128704690 ,11.959737189531615807  ] 
dist 54=[-.92254255643074395342,12.896924580382242194  ] 
dist 55=[-.78452806187870876897,13.910843071926039590  ] 
dist 56=[.38715701044468157905,14.811691665436517558  ] 
dist 57=[.47191661745907699905,15.297639474357423387  ] 
dist 58=[.29223991958259408583,15.573417316382831883  ] 
dist 59=[.11228221597249623604,15.635293609380829132  ] 
dist 60=[-.01542067328524906576,15.298055191492669527  ] 
dist 61=[-.12864091674232978757,15.266668863823406784  ] 
dist 62=[-.25098515377259839675,14.433891968773792274  ] 
dist 63=[-.81665317848974593395,12.830226403719920276  ] 
dist 64=[-1.5593705961907366374 ,1.7486023921892849544 ] 
dist 65=[-2.0358332180139004489 ,1.7424083510341375759 ] 
dist 66=[-2.4081179885974617957 ,1.7361323926395878135 ] 
dist 67=[-2.7352081161906018426 ,1.7097686532747913047 ] 
dist 68=[-3.0081181609519435961 ,1.6987512126915434598 ] 
dist 69=[-3.1642618391376087835 ,1.6667653276958102017 ] 
dist 70=[-3.2649336614253780881 ,1.6518015721328623115 ] 
dist 71=[-3.3165816681466705533 ,1.5651828346507620458 ] 
dist 72=[-3.3474633836413282697 ,1.5422167272186618021 ] 
dist 73=[-3.3652723896986252565 ,1.4965124278426302789 ] 
dist 74=[-3.3772644019211260758 ,1.4809729529805826706 ] 
dist 75=[-3.3848512177037844645 ,1.1792341510590343784 ] 
dist 76=[-3.3893264996343494627 ,1.1337757753003632760 ] 
dist 77=[-3.3888575664706295782 ,1.0263714202068797501 ] 
dist 78=[-3.3847977763928450804 ,.99814148937642569235] 
dist 79=[-3.3748961136565843972 ,.83756010546391106652] 
dist 80=[-2.3516992703674936351 ,.80431585146773530375] 
dist 81=[-2.2821099588760276570 ,.73783520166258299783] 
dist 82=[-2.2637319227367696562 ,.71884479972774814292] 
dist 83=[.01177295132008445811,.65622077183450296451] 
dist 84=[-.01292104594166296624,.99721111971545447578] 
dist 85=[-.06145237810280854056,1.2984747122274386539 ] 
dist 86=[-.11421437558521923727,1.5982496997378340861 ] 
dist 87=[-.16534924529604019067,1.9735605643730377253 ] 
dist 88=[-.20739818998086926799,2.3305903767139096861 ] 
dist 89=[-.25065075343121732528,2.5574447972644691250 ] 
dist 90=[-.30658892468279926   ,2.7319606985670124178 ] 
dist 91=[-.36044194197216103324,2.8802063539704015138 ] 
dist 92=[-.39538534566532020389,2.9998907497357566703 ] 
dist 93=[-.42302646303097942105,3.0604722467049902026 ] 
dist 94=[-.44777345354257433609,3.0892584122624107993 ] 
dist 95=[-.46866400215744342329,3.0918338514567883012 ] 
dist 96=[-.56156567820344197121,.90724664369534872975] 
dist 97=[-.83396043103857715672,.88366913765632579231] 
dist 98=[-1.0890888347348680798 ,.82533082975865262175] 
dist 99=[-1.3383027874024444889 ,.80971438713789580252] 
dist 100=[-1.5638528838399376281 ,.71230048748373575273] 
dist 101=[-1.7246042604781648412 ,.69137503436207469539] 
dist 102=[-1.8682673050408222272 ,.65207561147469811288] 
dist 103=[-2.0256674470900465157 ,.6410931450695837005 ] 
dist 104=[-2.1656302070153163835 ,.44463092042960946679] 
dist 105=[-2.2397476814155745984 ,.41721295318437128605] 
dist 106=[-2.2800522223844300142 ,.34847644181621396543] 
dist 107=[-2.2887591355304290015 ,.33763991380825384358] 
dist 108=[-2.2743536229774910880 ,.22972608682112714665] 
dist 109=[-2.2649129947193311471 ,.20914429737784845631] 
dist 110=[-2.2532609581938950342 ,.18365932558359487664] 
dist 111=[-2.2400813149748259707 ,.1765310013469642528 ] 
dist 112=[-1.5854212774342032079 ,.63380170182383016991] 
dist 113=[-1.5071535473241758910 ,.95605349995252779111] 
dist 114=[-1.3225657636329685273 ,1.2210486897848888159 ] 
dist 115=[-1.2799446893521105951 ,1.4761279721100936987 ] 
dist 116=[-1.0159591745310962294 ,1.7044417804178264390 ] 
dist 117=[-.96418646934101353115,1.8626936781281688002 ] 
dist 118=[-.86459668456041158131,1.9994949976830204861 ] 
dist 119=[-.83840377638643862261,2.1422634033744637963 ] 
dist 120=[-.46380771402436274963,2.2674718400354905981 ] 
dist 121=[-.41026997335089901189,2.3342410895945555350 ] 
dist 122=[-.29390611726289220843,2.3708175921789797353 ] 
dist 123=[-.26491694872048669798,2.3767831304011141443 ] 
dist 124=[-.1352258563701953653 ,2.3670375868134991255 ] 
dist 125=[-.11164783463976187182,2.3545373913477611472 ] 
dist 126=[-.05713913048594960491,2.3273393849418409347 ] 
dist 127=[-.04744253946471757622,2.3131521466877423646 ] 
dist 128=[-.50892852349718107676,.36959254404405187446] 
dist 129=[-.84206311937182949118,.29921362240757389585] 
dist 130=[-1.1138233598592003595 ,.14219725392980711903] 
dist 131=[-1.3717617172491529314 ,.10991477473696880571] 
dist 132=[-1.6001697093706843419 ,-.07379576644817207479] 
dist 133=[-1.7541600977190133180 ,-.10530360363515280564] 
dist 134=[-1.8826876072504900443 ,-.17166977904505851189] 
dist 135=[-2.0095475598538947027 ,-.18607365598538803168] 
dist 136=[-2.1202660842689166006 ,-.29082195467211323131] 
dist 137=[-2.1844198697265950002 ,-.30779731263389339092] 
dist 138=[-2.2265699120690618453 ,-.30768532037111517817] 
dist 139=[-2.2495345775326027577 ,-.28421844951389180677] 
dist 140=[-2.2583368878787961883 ,-.24762722935650615214] 
dist 141=[-2.2559111008266332030 ,-.19517359423912450158] 
dist 142=[-2.2250406612634379408 ,-.12121118930023408364] 
dist 143=[-2.2153623428314610242 ,.00115963330901263835] 
dist 144=[-1.0241630385043353773 ,.16080021410987570015] 
dist 145=[-.912527044056337325  ,.26880960054844985934] 
dist 146=[-.65952254177365096879,.51222046317933433787] 
dist 147=[-.60586649733916326248,.77123523063133916813] 
dist 148=[-.291238566986728355  ,1.0120228167511984639 ] 
dist 149=[-.23482463813306539147,1.1944331234488317147 ] 
dist 150=[-.11986010411414166574,1.3684845548148317604 ] 
dist 151=[-.09055869777516807875,1.5759364573593406973 ] 
dist 152=[.17178838175255222394,1.7678272946716047123 ] 
dist 153=[.21345787677453814999,1.8798197696180425947 ] 
dist 154=[.26038206094299621275,1.9544122410338131504 ] 
dist 155=[.26215417303104271269,1.9971481576754148051 ] 
dist 156=[.24515109694525656989,2.0239387196254049149 ] 
dist 157=[.16342790780889852771,2.0349394278342011337 ] 
dist 158=[.04980909994274870210,2.0364500998784729940 ] 
dist 159=[-.12570697859293110496,2.0296521620240024081 ] 
dist 160=[-.37365937539098303711,.6397780145902142951 ] 
dist 161=[-.63062490023896307038,.61635330052183989717] 
dist 162=[-.85097229268946974634,.55951415503963395505] 
dist 163=[-1.0780530937232720531 ,.54586871956016206198] 
dist 164=[-1.2912737851541121524 ,.45764133771980041795] 
dist 165=[-1.4563458719464432338 ,.43962627486488673786] 
dist 166=[-1.6172794588908720790 ,.40614235901075908663] 
dist 167=[-1.8139954819083737591 ,.39728883607657486273] 
dist 168=[-1.9984634100380478605 ,.24618463639304594895] 
dist 169=[-2.1105505183950034205 ,.22526635209329369316] 
dist 170=[-2.1907596090989153679 ,.17521591431078895899] 
dist 171=[-2.2480951709353405647 ,.16639626911010756186] 
dist 172=[-2.2861421587507698624 ,.09569079167446128053] 
dist 173=[-2.2940478538900179123 ,.08266928216931132811] 
dist 174=[-2.2823710346354500898 ,.37351751497352373256] 
dist 175=[-2.2791803832269733870 ,.86115561803378537772] 
dist 176=[-2.1353062890357321383 ,1.3478945896396674971 ] 
dist 177=[-2.1050275651387025922 ,1.6640283918962796224 ] 
dist 178=[-2.0199937667073663135 ,1.9148171064848703079 ] 
dist 179=[-1.9950119911876993133 ,2.1409543124918394620 ] 
dist 180=[-1.8125229786224208193 ,2.3331409885718442744 ] 
dist 181=[-1.7702017881335495581 ,2.4485321108021742031 ] 
dist 182=[-1.6996870938449523769 ,2.5294345476874094494 ] 
dist 183=[-1.6783273143273250227 ,2.5840774368909536643 ] 
dist 184=[-1.1904703301658404156 ,2.6218132035919428246 ] 
dist 185=[-1.1224923070355712024 ,2.6352885874316609695 ] 
dist 186=[-.9641500547244997145 ,2.6335360740764409491 ] 
dist 187=[-.92776623134012289953,2.6259874452559825487 ] 
dist 188=[-.70952210591063531246,2.5757985729826045832 ] 
dist 189=[-.66747945303506173986,2.5590307272766372394 ] 
dist 190=[-.58447757941823163797,2.4845615000158640388 ] 
dist 191=[-.56248828760493829863,2.4736553916130153679 ] 
dist 192=[-.29657310602422946761,.48191326089481300785] 
dist 193=[-.49154766526592354956,.44224567606831984405] 
dist 194=[-.64891110691946787657,.35129277262026801991] 
dist 195=[-.79543636832008839303,.33156611289458395073] 
dist 196=[-.9232624795022687867 ,.21355312945013219953] 
dist 197=[-1.0060521233497589342 ,.19178195069491770763] 
dist 198=[-1.0714667947580337175 ,.14832573699670550329] 
dist 199=[-1.1300000446336618593 ,.13716444101775603372] 
dist 200=[-1.1799469190485246915 ,.01714014361609698773] 
dist 201=[-1.2111183940150606018 ,-.00106082586938670536] 
dist 202=[-1.2344160231193580950 ,-.03097082112537033355] 
dist 203=[-1.2529613217325142928 ,-.03789837299798003811] 
dist 204=[-1.2669678564931466691 ,-.04711633338878104641] 
dist 205=[-1.2721645041244347064 ,-.03912133235715910928] 
dist 206=[-1.2718884315702528126 ,-.02496759022346493900] 
dist 207=[-1.2672712637153877037 ,9.74598601030712500000e-06] 
dist 208=[-.37920950039375146302,.16507703120609123841] 
dist 209=[-.30483976635232472155,.27958948314973893939] 
dist 210=[-.13894940293241846868,.37866338533763125198] 
dist 211=[-.10490910808658721623,.48216514347047223422] 
dist 212=[.05186709040501955283,.58022227647288939502] 
dist 213=[.04183767653886377835,.65758255205320039214] 
dist 214=[.02483485599959965588,.73437109858341285751] 
dist 215=[-.00606621380375098934,.83014812887196178195] 
dist 216=[-.04010282393167020134,.92091893377024636484] 
dist 217=[-.06961044588690221942,.97774222804406213711] 
dist 218=[-.10136492786620046439,1.0204161110061732415 ] 
dist 219=[-.14436220848300937665,1.0547578599814277504 ] 
dist 220=[-.19113949528376028693,1.0809955536815368232 ] 
dist 221=[-.23796896388875032166,1.0913497747144174586 ] 
dist 222=[-.29366693707950329795,1.0932120181719856540 ] 
dist 223=[-.37581257414918024449,1.0796514933106516948 ] 
dist 224=[-.45642759453858044967,.52041611254933019263] 
dist 225=[-.5060213391595369081 ,.53916891119480544837] 
dist 226=[-.54224570258823998075,.54948450330712036792] 
dist 227=[-.56954249671527383921,.55175802227651042535] 
dist 228=[-.59037488708635856008,.5486109640466308501 ] 
dist 229=[-.60081865941964685852,.54668011219221461906] 
dist 230=[-.60562280357971647231,.54436143996598977848] 
dist 231=[-.60556155786423142338,.54110382787907064469] 
dist 232=[-.54526519642441514039,.42898969613113750331] 
dist 233=[-.53453835511623083449,.41260570551227194455] 
dist 234=[-.51672750620962963663,.38089459911169935194] 
dist 235=[-.51105418516873399799,.3721830341012649987 ] 
dist 236=[-.44084593678605281735,.33947047576079287743] 
dist 237=[-.43800686452972953535,.33125027968083271052] 
dist 238=[-.42565311367643496419,.31644735366006117396] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 2, 2, 0, 0, 0, 1] 
dist 0=[70.087625500061923186  ,70.087625500061923186  ] 
dist 1=[69.681704423546054351  ,70.199738147094055653  ] 
dist 2=[69.067347559384624975  ,70.119767747041446950  ] 
dist 3=[68.123006209830306022  ,70.030532450933254459  ] 
dist 4=[66.753001058909206590  ,69.271563011721776520  ] 
dist 5=[64.439315631757261542  ,69.030882305600745843  ] 
dist 6=[61.690021322188390266  ,68.172302368288390520  ] 
dist 7=[58.580816702689813548  ,67.943655875391776024  ] 
dist 8=[54.606602426806096448  ,65.976202745323826706  ] 
dist 9=[48.403515693858680283  ,65.647489012900311185  ] 
dist 10=[42.103058143631985973  ,63.583151977387980151  ] 
dist 11=[37.740240917291008652  ,63.040599227055542218  ] 
dist 12=[33.954713654805932387  ,62.781849186915860951  ] 
dist 13=[29.959766635878171142  ,61.361968280884922922  ] 
dist 14=[26.130059913439207421  ,53.373855346754802531  ] 
dist 15=[23.004680632597964283  ,48.273250758802148391  ] 
dist 16=[19.793669140839366928  ,34.153081311811460803  ] 
dist 17=[15.622657721839706779  ,24.083758634063749855  ] 
dist 18=[11.563290425106343662  ,22.835786634617513169  ] 
dist 19=[8.7982483981701109417 ,20.217305963457086894  ] 
dist 20=[6.4507386060500956698 ,19.562016675232570856  ] 
dist 21=[4.0584689177161897490 ,17.004962666653795183  ] 
dist 22=[1.7457361222992929906 ,16.521330516393857406  ] 
dist 23=[-1.6745919152566594519 ,15.620459925852296191  ] 
dist 24=[-4.8676295502767590472 ,15.418716185235442902  ] 
dist 25=[-6.8639025752383830961 ,3.4166176464410778682 ] 
dist 26=[-8.3713455517857871187 ,2.3747497255185992763 ] 
dist 27=[-9.6112798973506840075 ,.15711886214843623169] 
dist 28=[-10.593395945626888562  ,-.28818785200753997981] 
dist 29=[-11.071684485195929328  ,-2.5241277748244543793 ] 
dist 30=[-11.312741448208525900  ,-2.8957769889649102915 ] 
dist 31=[-11.346518024256313670  ,-3.6383350647862230750 ] 
dist 32=[-12.401812846529595012  ,-3.7881065089845891762 ] 
dist 33=[-13.515199978182022974  ,-4.3050088345293927917 ] 
dist 34=[-14.163158368463834998  ,-4.3025472306328009707 ] 
dist 35=[-14.598823151369127988  ,-4.1233959102674249688 ] 
dist 36=[-14.863920514250303242  ,-3.6619290039362656636 ] 
dist 37=[-15.027558757447872743  ,-3.0588475903266091123 ] 
dist 38=[-15.057685511928761982  ,-2.3140627324299506713 ] 
dist 39=[-15.021906728055573822  ,-1.3252430948791068571 ] 
dist 40=[-14.969946135062658034  ,.25206440785857019849] 
dist 41=[-11.511507591869052063  ,2.8087578270546725539 ] 
dist 42=[-7.3224782446851138279 ,4.5833196748219401600 ] 
dist 43=[-6.8604837147183745557 ,6.0368593693184941506 ] 
dist 44=[-5.7992551210736590460 ,7.4288158820295887932 ] 
dist 45=[-5.5626086813865764687 ,8.6721681970688483893 ] 
dist 46=[-4.1570709268050201213 ,9.5330027909350597589 ] 
dist 47=[-3.8913130295831418398 ,10.277588698291885358  ] 
dist 48=[-3.3651429298174046931 ,11.057361644251804236  ] 
dist 49=[-3.2272653697841938100 ,11.744767915092153160  ] 
dist 50=[-1.5759334818642736575 ,12.120843214181289486  ] 
dist 51=[-1.3317465624370380788 ,12.340839118173253952  ] 
dist 52=[-.84424142507762057808,12.405338197541756165  ] 
dist 53=[-.72087504952356774988,12.398329274234231200  ] 
dist 54=[-.29917379900204363924,11.778275263168726879  ] 
dist 55=[-.20572421737727152286,11.609651620322470174  ] 
dist 56=[-.12072405481029758524,10.392893997084462722  ] 
dist 57=[-.12621427537826657593,7.8096335993307827989 ] 
dist 58=[-.15081823528126704284,3.2127695670534727446 ] 
dist 59=[-.61320348338145792402,3.2474324603887908281 ] 
dist 60=[-1.3646221128124171384 ,3.2701791732794078469 ] 
dist 61=[-2.0718084191804354508 ,3.2735585531793018918 ] 
dist 62=[-2.6226360857948418989 ,3.2661184443701467044 ] 
dist 63=[-3.1631173541561954816 ,3.2582652123728429588 ] 
dist 64=[-3.8290763409797669467 ,-.09237413156012485748] 
dist 65=[-4.4570342383638113815 ,-.04723746547465411400] 
dist 66=[-4.8459532077932022691 ,.00051225369570600354] 
dist 67=[-5.1334207178403447090 ,.03836354924711158268] 
dist 68=[-5.3567163141830645089 ,.07597585990042565170] 
dist 69=[-5.5229222739290592028 ,.12281288471367980929] 
dist 70=[-5.5826708656747761914 ,.17175315502133361181] 
dist 71=[-5.6001913727200411934 ,.21777779247786184776] 
dist 72=[-5.5979477539737643125 ,.27034745993659019129] 
dist 73=[-3.4446910183618322184 ,.89260318772558017826] 
dist 74=[-3.4769082809900794056 ,1.5018262189725758863 ] 
dist 75=[-3.4809183908275930522 ,2.0149889297939613502 ] 
dist 76=[-3.3927648162857297977 ,2.5291542170111400228 ] 
dist 77=[-3.3649353736107729088 ,3.0028385241179326554 ] 
dist 78=[-3.3438099652964685337 ,3.3545631278932045458 ] 
dist 79=[-3.3264096059804615904 ,3.6833284075777850934 ] 
dist 80=[-2.3972516596003064212 ,4.0654552731417572698 ] 
dist 81=[-2.2826526353748053962 ,4.4140419487520124904 ] 
dist 82=[-2.0155733698577891636 ,4.6090446951219085465 ] 
dist 83=[-1.9515413442507370612 ,4.7283726597763263428 ] 
dist 84=[-1.5774683214908333542 ,4.7751517445640668873 ] 
dist 85=[-1.5038291971404179714 ,4.7906527539502197890 ] 
dist 86=[-1.3571652096858842165 ,4.7852354022162546432 ] 
dist 87=[-1.3171486853960125733 ,4.7634892851138536085 ] 
dist 88=[-1.0188350615037600428 ,4.7419542163053249165 ] 
dist 89=[-2.0455636792732210083 ,3.9323314078993909135 ] 
dist 90=[-2.7217484320701691634 ,3.8151551970358113544 ] 
dist 91=[-3.2686904480888919961 ,3.7878670356128633758 ] 
dist 92=[-3.7799904708156730973 ,3.7508747603751208542 ] 
dist 93=[-4.2274503446446436269 ,3.7277999173844364868 ] 
dist 94=[-4.5197940950035510111 ,3.6748333979106283522 ] 
dist 95=[-4.7536626848557664013 ,3.6493970686895382170 ] 
dist 96=[-4.9679211615219323577 ,2.6395610994879436040 ] 
dist 97=[-5.1456935641128537850 ,1.7183576249036655305 ] 
dist 98=[-5.2340522658853268902 ,1.5925929741943001491 ] 
dist 99=[-5.2735947901064439285 ,1.2778608975433955142 ] 
dist 100=[-5.2726787389720719052 ,1.2318663335146778627 ] 
dist 101=[-5.2129790717945671689 ,.83504238827301761767] 
dist 102=[-5.1826029241356110983 ,.89291987264560949273] 
dist 103=[-5.0774533650155040365 ,.93991540886981764941] 
dist 104=[-5.0299790533174897187 ,.98780139447425580892] 
dist 105=[-3.5695598007593555509 ,1.0492320448329773450 ] 
dist 106=[-3.6350330841346329243 ,1.1056188328942702098 ] 
dist 107=[-3.6685229947718058344 ,1.1333901480870778624 ] 
dist 108=[-3.6788155402265361959 ,1.2025089315634977656 ] 
dist 109=[-3.6740390461045389946 ,1.2883925887691549242 ] 
dist 110=[-3.6187418651119773417 ,1.3565193646127295192 ] 
dist 111=[-3.6051651393052541150 ,1.3900675073151190462 ] 
dist 112=[-1.6932149506433896670 ,1.4066470022277208708 ] 
dist 113=[-1.5128620828837084163 ,1.4080311944020430808 ] 
dist 114=[-1.1882496445369209989 ,1.3451167410920106055 ] 
dist 115=[-1.1695136823641425165 ,1.3290478991304547460 ] 
dist 116=[-1.1391333096170272633 ,1.7027194638639662042 ] 
dist 117=[-1.1284840388679949647 ,1.9982920898764250868 ] 
dist 118=[-1.0898544586056112630 ,2.2792528055062888105 ] 
dist 119=[-1.0768090479418340776 ,2.6126311249256139390 ] 
dist 120=[-1.0507265043124306152 ,2.9202827232132982664 ] 
dist 121=[-1.0411386862011074596 ,3.0986420360709467262 ] 
dist 122=[.28649221793548458231,3.2159568859428885899 ] 
dist 123=[.38217136850229674784,3.2801531432405857467 ] 
dist 124=[.37754183355046822611,3.3189919355683303987 ] 
dist 125=[.30988896536623606363,3.3351760388645767225 ] 
dist 126=[.19744324288788241756,3.3378242675662765845 ] 
dist 127=[-.00511796647108415667,3.3256528011966810467 ] 
dist 128=[-.62326980436559991781,1.0507740654474288392 ] 
dist 129=[-1.0493235197302800460 ,1.1130809677834304051 ] 
dist 130=[-1.4149669706627812631 ,1.1667550899728845511 ] 
dist 131=[-1.7922732676463273487 ,1.1993140120618046600 ] 
dist 132=[-2.1468618695138873691 ,1.2225461721121028734 ] 
dist 133=[-2.4219050636084927422 ,1.2390245437044959566 ] 
dist 134=[-2.6905548361157339613 ,1.2498430333751182294 ] 
dist 135=[-3.0196460669682306914 ,1.2505032009094204473 ] 
dist 136=[-3.3286112399675309239 ,1.2447935742479077941 ] 
dist 137=[-3.5169962288233008775 ,1.2397788052346590694 ] 
dist 138=[-3.6525908588023938654 ,.44119483545844091539] 
dist 139=[-3.7510224294545796412 ,.37186220701567139748] 
dist 140=[-3.8176946816172099158 ,.21643002006843370873] 
dist 141=[-3.8314103891652108372 ,.19945189996490309234] 
dist 142=[-3.8168830291995847385 ,.65686083461909559821] 
dist 143=[-3.8090508170417206099 ,1.4711782433849099928 ] 
dist 144=[-3.5868332588362085461 ,2.2837796552444004505 ] 
dist 145=[-3.5384596263316884907 ,2.8111532282381171194 ] 
dist 146=[-3.4010895227459075453 ,3.2290625543419060101 ] 
dist 147=[-3.3601869524194158510 ,3.6051111122510681001 ] 
dist 148=[-3.0596007224778283751 ,3.9241478060560717961 ] 
dist 149=[-2.9894641293960687650 ,4.1146889714461185882 ] 
dist 150=[-2.8733061309017634375 ,4.2470471767007724494 ] 
dist 151=[-2.8377110312223362220 ,4.3340454137369543555 ] 
dist 152=[-2.0195386838347499116 ,4.3928538822964790737 ] 
dist 153=[-1.9054164457896971145 ,4.4127887630596473702 ] 
dist 154=[-1.6404690640016969244 ,4.4080120478860885290 ] 
dist 155=[-1.5785095090627292453 ,4.3947770610736855678 ] 
dist 156=[-1.2153939519580963117 ,4.3092409021776377097 ] 
dist 157=[-1.1453187173902980926 ,4.2807962053678412132 ] 
dist 158=[-1.0047970701480985280 ,4.1559588407632037595 ] 
dist 159=[-.96697214238629642417,4.1371228097476359669 ] 
dist 160=[-.43500320007418766244,.73656248063825281406] 
dist 161=[-.72030345698384879979,.81554214876079696195] 
dist 162=[-.95010380036313775186,.88801510254103772877] 
dist 163=[-1.1632914495148599935 ,.92927785029750579249] 
dist 164=[-1.3487312455623509204 ,.95546186347944010605] 
dist 165=[-1.4678707855400276265 ,.96779956018016341603] 
dist 166=[-1.5609157858991723624 ,.97339807143212206127] 
dist 167=[-1.6422883612921566988 ,.97270564847528927748] 
dist 168=[-1.7113218348860252820 ,.9673232161414064643 ] 
dist 169=[-1.7551574252495810855 ,.96356852915732874342] 
dist 170=[-1.7888034848808028279 ,.81894831066962267091] 
dist 171=[-1.8172001553909170861 ,.79709336257538806978] 
dist 172=[-1.8399499831651165982 ,.74209344991419895249] 
dist 173=[-1.8510759035740777297 ,.72811778898065719028] 
dist 174=[-1.8557861850365799156 ,.63415479062418429676] 
dist 175=[-1.8529498414677957253 ,.61410995335472237335] 
dist 176=[-.98604755610824514696,.57797499664249594426] 
dist 177=[-1.0261530026472159594 ,.56830359228814869434] 
dist 178=[-1.0588800277608748973 ,.37729378868565042163] 
dist 179=[-1.0747644847572242566 ,.35111433894174150874] 
dist 180=[-1.0813081320078028317 ,.42512758342204162596] 
dist 181=[-1.0806027351638408013 ,.5883641771887549959 ] 
dist 182=[-1.0668829358654214143 ,.75240756231655224481] 
dist 183=[-1.0605382533189064740 ,.95978541994778425296] 
dist 184=[-1.0373710748585062035 ,1.1576814164709833450 ] 
dist 185=[-1.0285704600594990353 ,1.2839103272312161481 ] 
dist 186=[.04618445405974632191,1.3814503677438755819 ] 
dist 187=[.06217667674791776070,1.4649326722494484026 ] 
dist 188=[.09405262079874330467,1.5326965047333214665 ] 
dist 189=[.10162231360828423091,1.5675499203541525174 ] 
dist 190=[.12479998251304790287,1.5848708753624489385 ] 
dist 191=[-4.24804677727567140000e-05,1.5866885218907553214 ] 
dist 192=[-.22619546852545401593,.93448116217229888635] 
dist 193=[-.37827340897837433009,1.0104816579160378001 ] 
dist 194=[-.50477282540383562104,1.0779049551718443130 ] 
dist 195=[-.62891648690473794062,1.1150753816094728116 ] 
dist 196=[-.74160370290921813004,1.1370966474754901405 ] 
dist 197=[-.82241384263201870492,1.1441038055574283405 ] 
dist 198=[-.89511406984083835515,1.1440444106803362187 ] 
dist 199=[-.9754582691279603764 ,1.1396558502451873927 ] 
dist 200=[-1.0472572553545612933 ,1.1281839107894856941 ] 
dist 201=[-1.0858784461259477157 ,1.1213064120960845685 ] 
dist 202=[-1.1074817761429631166 ,.69027129722724954186] 
dist 203=[-1.1122798981500419752 ,.64426036773063788252] 
dist 204=[-1.1089718096485274087 ,.53760234192830397546] 
dist 205=[-1.1051687254367766233 ,.51398427462467363377] 
dist 206=[-1.0996503673580190887 ,.37023012116190836121] 
dist 207=[-1.0934970307285655367 ,.34306714693353272127] 
dist 208=[-.77004904431326148929,.28976917075906653851] 
dist 209=[-.73168666345094328564,.28275138478498291061] 
dist 210=[-.64104105952409271252,.39669853026446796059] 
dist 211=[-.62025663676113594453,.50900744517074600887] 
dist 212=[-.49022933909532893845,.61126876464344415765] 
dist 213=[-.46475296498260298785,.68514524787676815486] 
dist 214=[-.41602934625851474046,.75216218501129704277] 
dist 215=[-.39429407382782993741,.82706705458344497062] 
dist 216=[-.32568165754856833969,.89448746998827098132] 
dist 217=[-.32391352308433861959,.93165576834805616644] 
dist 218=[-.03465432945279980268,.95367507722392866146] 
dist 219=[-.06116410706182968109,.96068003377493564111] 
dist 220=[-.08670757810480544773,.9617114878473314045 ] 
dist 221=[-.11750784696598784808,.95990796032011110295] 
dist 222=[-.14921887259843133476,.95568793439133542684] 
dist 223=[-.17839451891084118871,.95090159410974149696] 
dist 224=[-.21121461232598058512,.39462852683576077786] 
dist 225=[-.32188649681689400395,.4565479976339257233 ] 
dist 226=[-.42526627007079756795,.51668533923777554065] 
dist 227=[-.52190480852248823264,.55684225307233189159] 
dist 228=[-.6064720128132149372 ,.58993699477401819351] 
dist 229=[-.66171028180833137096,.62190979506164786174] 
dist 230=[-.70588303565611061641,.65060096539471920428] 
dist 231=[-.74632002747908279311,.67060828856880801559] 
dist 232=[-.78101852312147522609,.68802793456522447312] 
dist 233=[-.80230566738064473531,.70639922889532293676] 
dist 234=[-.81778389921509095362,.72140376498934570378] 
dist 235=[-.8293159586509876039 ,.72539649363215883028] 
dist 236=[-.83738889803916645096,.72494614586495611302] 
dist 237=[-.83907186528791340412,.72223131638351451042] 
dist 238=[-.8363919717624427255 ,.69178967865379793793] 
dist 239=[-.8335288972664177107 ,.68245567225935523453] 
dist 240=[-.60069626221518247778,.67095233030093990929] 
dist 241=[-.59708540967011200695,.6690605232606223967 ] 
dist 242=[-.47316985849270715482,.6030114945513071787 ] 
dist 243=[-.45506604210361534166,.5912252063261488249 ] 
dist 244=[-.41998769891202916125,.5716657417128157313 ] 
dist 245=[-.41034521748607054432,.5654199716578282206 ] 
dist 246=[-.37408875343883404672,.54386591288834970633] 
dist 247=[-.36500183753504670133,.53660143850921599152] 
dist 248=[-.34856144565353435862,.52449215735170406763] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 0, 2, 1, 1, 2] 
dist 0=[67.940776202467873218  ,67.940776202467873218  ] 
dist 1=[67.423212241058745098  ,68.253812205674758430  ] 
dist 2=[66.657252636952359114  ,68.410902149812586343  ] 
dist 3=[65.353063800226874437  ,68.362905510797907414  ] 
dist 4=[63.828053516512411072  ,68.093953853389428793  ] 
dist 5=[62.180640652511267843  ,67.892569407376943718  ] 
dist 6=[60.128304782303983397  ,66.559469876692427862  ] 
dist 7=[56.986585744606792617  ,66.150211973258579902  ] 
dist 8=[53.383654829010729396  ,65.556537372353266438  ] 
dist 9=[48.640733025190857918  ,65.310143256765921635  ] 
dist 10=[44.635504244628221309  ,64.521113506080080325  ] 
dist 11=[37.196477392234406031  ,64.221918541509910785  ] 
dist 12=[29.703417040420947766  ,63.647946680063222544  ] 
dist 13=[24.632927545321128395  ,63.130316646346067350  ] 
dist 14=[20.362138626687803967  ,38.085592587255570108  ] 
dist 15=[16.060848295634062645  ,35.904257257050929238  ] 
dist 16=[12.063098418622658795  ,32.669003541936551697  ] 
dist 17=[9.0034355207023349739 ,29.943883302785942026  ] 
dist 18=[6.0395439474646547039 ,22.887641613143757636  ] 
dist 19=[2.4229515536610150399 ,21.621638164438054388  ] 
dist 20=[-.99917911219659088665,19.912050412748972005  ] 
dist 21=[-3.1873424587643312416 ,19.471036439076459145  ] 
dist 22=[-4.8984642848003270363 ,14.456756787346366952  ] 
dist 23=[-6.4167518871453178712 ,13.605065814574652295  ] 
dist 24=[-7.7075314122239663496 ,13.431965518773024793  ] 
dist 25=[-8.5114203991839465679 ,6.5627023965924539711 ] 
dist 26=[-9.1237955522951775088 ,3.8335980842566249613 ] 
dist 27=[-9.6524530607918980447 ,3.3960352629954280685 ] 
dist 28=[-10.066463166475690802  ,2.6068085127442736822 ] 
dist 29=[-10.221174855257940141  ,2.4549796194847542370 ] 
dist 30=[-10.950535352104182764  ,-1.2932787421934872028 ] 
dist 31=[-11.909223444197735531  ,-1.6818050880665388074 ] 
dist 32=[-12.932360056452684404  ,-2.3933778951303075299 ] 
dist 33=[-13.831937404186353624  ,-2.5443427206225277160 ] 
dist 34=[-14.297214489588245352  ,-2.9051781979925473282 ] 
dist 35=[-14.551972072139946645  ,-2.9116759162100591586 ] 
dist 36=[-14.610213853425457381  ,-2.7915886865377750154 ] 
dist 37=[-14.459013988060383093  ,-2.4746296073944658157 ] 
dist 38=[-14.412347471168095681  ,-2.1007338553282582272 ] 
dist 39=[-14.378334264637295629  ,-1.7529053811227532288 ] 
dist 40=[-14.353786943420989271  ,.90418574822821529466] 
dist 41=[-12.850071641400411516  ,3.9081673880011827561 ] 
dist 42=[-12.303311887199084531  ,5.8895692918792862013 ] 
dist 43=[-12.158550396832590119  ,7.4969850331009322813 ] 
dist 44=[-12.020328424797430286  ,9.0093529898300388051 ] 
dist 45=[-11.936472694231705772  ,10.341212548170497046  ] 
dist 46=[-7.4732230100735851023 ,11.228687944162558618  ] 
dist 47=[-6.9278580092144449531 ,11.959069485985259377  ] 
dist 48=[-6.7888000861634097841 ,12.664397296191319613  ] 
dist 49=[-4.0933579429582406150 ,13.273686510041665676  ] 
dist 50=[-3.7344242924858819282 ,13.620935977403337290  ] 
dist 51=[-2.8547356150545443706 ,13.842265597659735484  ] 
dist 52=[-2.7256148444258865694 ,13.949051439650904851  ] 
dist 53=[-1.4293719324757393916 ,13.973504526717578589  ] 
dist 54=[-1.1917094702338850282 ,13.952422438268433357  ] 
dist 55=[-.90411800360206571179,13.740717311034060471  ] 
dist 56=[-.84716180915412125893,13.558507598592607259  ] 
dist 57=[.9272422770482557218 ,6.7252450607622492753 ] 
dist 58=[.30522406383720851171,6.7359694311602190669 ] 
dist 59=[-.66442111474044146369,6.7191208285102979215 ] 
dist 60=[-1.8276614020750445916 ,5.3959371154059804407 ] 
dist 61=[-2.6070496410473511806 ,5.3685447737893282150 ] 
dist 62=[-3.2504167196317667279 ,2.8259952473266048888 ] 
dist 63=[-3.8747732666869501656 ,2.9778187372771081930 ] 
dist 64=[-4.4378814513030241007 ,3.1135839350410709209 ] 
dist 65=[-4.8369361745521308967 ,3.2271541585211729156 ] 
dist 66=[-5.1916653964025410108 ,3.2904458502330051635 ] 
dist 67=[-5.5779822578003428385 ,3.3288967106231442444 ] 
dist 68=[-5.9179107705222444656 ,3.3433849948037726431 ] 
dist 69=[-6.0875977211342802680 ,3.3413514385983580645 ] 
dist 70=[-6.1776112468661915575 ,3.3320682953723340191 ] 
dist 71=[-6.1996299216944839727 ,3.2817908979854452909 ] 
dist 72=[-6.0814326908458813784 ,3.2611307132375950445 ] 
dist 73=[-6.0507030669759840588 ,1.3853858762028247611 ] 
dist 74=[-6.0322725080591524689 ,1.2120489116998953591 ] 
dist 75=[-6.0259138043082713646 ,.9044089205875326936 ] 
dist 76=[-5.1436871275181067189 ,2.2427132928131649463 ] 
dist 77=[-5.1458383628625639682 ,3.1282204823762470902 ] 
dist 78=[-3.8979610876673247358 ,3.8493500531338262669 ] 
dist 79=[-3.7898133332653396196 ,4.5320722978320518407 ] 
dist 80=[-3.1258121094722988847 ,5.1357933619257593700 ] 
dist 81=[-2.9927595378542429071 ,5.5418510998647869330 ] 
dist 82=[-2.8712793153732950362 ,5.8799364865972889705 ] 
dist 83=[-2.9869038280486438875 ,6.2125842105313628207 ] 
dist 84=[-3.0567770370038001834 ,6.4972765570954151989 ] 
dist 85=[-3.1018823031236506281 ,6.6440946715545570194 ] 
dist 86=[-3.1187178370480616287 ,6.7177839040426747463 ] 
dist 87=[-3.1180399741610097099 ,6.7254231738651841757 ] 
dist 88=[-3.1093599955509222731 ,6.6687185489002861879 ] 
dist 89=[-.56848766347796621671,6.6308809652347946154 ] 
dist 90=[-.4123130598013012202 ,6.5271657699200576542 ] 
dist 91=[-.37350373455943525449,6.4754302956068402019 ] 
dist 92=[-.94214044447909472562,3.9260727393991186334 ] 
dist 93=[-1.5284102309140453718 ,3.9043411946616809568 ] 
dist 94=[-2.0031150353103416730 ,2.8287253808531827250 ] 
dist 95=[-2.4478061908898725898 ,2.6967516737267768569 ] 
dist 96=[-2.8376885584069354590 ,2.7512230815956026423 ] 
dist 97=[-3.0938082334352260914 ,3.0171219298601111758 ] 
dist 98=[-3.3003089726160688996 ,3.1763595260382664707 ] 
dist 99=[-3.4923069491897897763 ,3.2875234549021689658 ] 
dist 100=[-3.6573216866121040388 ,3.3616926376688477031 ] 
dist 101=[-3.8197629628533048010 ,3.4081739686215555311 ] 
dist 102=[-4.0276372094530439303 ,3.4156280264903868245 ] 
dist 103=[-4.1374356019685000147 ,3.3952523051731836616 ] 
dist 104=[-4.1961561080214484368 ,3.3843054348932409106 ] 
dist 105=[-4.2048724277670548173 ,3.1126049829930911016 ] 
dist 106=[-4.1813590287186415177 ,3.0606314911886700122 ] 
dist 107=[-4.1586065933807124809 ,2.9196777043974770738 ] 
dist 108=[-4.1050344688617597086 ,2.8800483955763815771 ] 
dist 109=[-4.0776116287634697436 ,2.5964225253546594689 ] 
dist 110=[-1.2717669231812797954 ,2.5320123021966030151 ] 
dist 111=[-1.3341896094791351919 ,2.4225010607528550063 ] 
dist 112=[-1.3900559536755073911 ,2.3906195178349799598 ] 
dist 113=[-1.4358661341910564723 ,2.4525753315784912228 ] 
dist 114=[-1.4581829874543707014 ,2.8620258566606808864 ] 
dist 115=[-1.4675110393836405847 ,3.1392514345683777147 ] 
dist 116=[-1.4667985089369621377 ,3.3719213287557357733 ] 
dist 117=[-1.4482571745037152594 ,3.6036802581814770392 ] 
dist 118=[-1.4395661634644049591 ,3.8063247122826455689 ] 
dist 119=[-1.4090889670808881118 ,3.9228827403874806971 ] 
dist 120=[-1.3963744382308530754 ,3.9983790970787597904 ] 
dist 121=[-.07769068640945298176,4.0372633543292623100 ] 
dist 122=[-.13243724504099836208,4.0495194932903945053 ] 
dist 123=[-.17786005809146381908,4.0450636603295006589 ] 
dist 124=[-.22224161327962233102,3.9820222961366170731 ] 
dist 125=[-.26239462261019083394,3.9699634411225746185 ] 
dist 126=[-.29095387788403288527,1.9083617444888367592 ] 
dist 127=[-.54905805392422218926,1.7125046306963205026 ] 
dist 128=[-1.0076004464415094360 ,1.2676640563469724494 ] 
dist 129=[-1.4714086159418813297 ,1.1729009518926044939 ] 
dist 130=[-1.9014620719934970166 ,.61517537148853228725] 
dist 131=[-2.2253879001526660237 ,.51459970412092808146] 
dist 132=[-2.5326696404019583482 ,.31046320386818981614] 
dist 133=[-2.8963456335076214067 ,.25834526029108364479] 
dist 134=[-3.2314276857082194034 ,-.13182502104922967218] 
dist 135=[-3.4246740927533690359 ,-.08015874421894523705] 
dist 136=[-3.5504808664819851026 ,.00043044155762195660] 
dist 137=[-3.6166065831635316791 ,.08173314111332941518] 
dist 138=[-3.6553680575854401454 ,.1362448099702684731 ] 
dist 139=[-3.6720430577879082640 ,.18141123814054322434] 
dist 140=[-3.6756870836324446733 ,.22544445343094801234] 
dist 141=[-3.6624788028041846925 ,.26522085572188891386] 
dist 142=[-.14277283566182407059,.6872377071432007913 ] 
dist 143=[-.12506106657513775633,1.1604240661087552764 ] 
dist 144=[-.12046237062972882504,1.5670142596105573949 ] 
dist 145=[-.05833005460805092702,1.9873573612735349873 ] 
dist 146=[-.04936269605249934313,2.3828730561593039991 ] 
dist 147=[-.03093986977736541928,2.6904494178226286592 ] 
dist 148=[-.02617372965750737330,2.9916151774360708504 ] 
dist 149=[-.00914882448730476950,3.3615649027777359060 ] 
dist 150=[-.00561395169882190058,3.7093924483110487805 ] 
dist 151=[-.00084912804258329623,3.9223329867014161468 ] 
dist 152=[.00035163316092071925,4.0766319401018007889 ] 
dist 153=[-.08176164220624816262,4.1905915500645171086 ] 
dist 154=[-.14231127336024117651,4.2695057206606566109 ] 
dist 155=[-.32609242707332243367,4.2856300638503310098 ] 
dist 156=[-.77286810282310386013,4.2758249433389901312 ] 
dist 157=[-1.6830018357430324574 ,4.2640104770700118802 ] 
dist 158=[-2.5910033458738603390 ,4.0379443864825510745 ] 
dist 159=[-3.1798360153926590006 ,3.9865695714829002252 ] 
dist 160=[-3.6459322614018738587 ,3.8386281860056300555 ] 
dist 161=[-4.0644504737202559751 ,3.7939109209072019959 ] 
dist 162=[-4.4188797060405244897 ,3.4625928554323041202 ] 
dist 163=[-4.6293836669706936663 ,3.3847534426543546385 ] 
dist 164=[-4.7741661872050273682 ,3.2568400558876674530 ] 
dist 165=[-4.8664927797753990773 ,3.2170877339666684250 ] 
dist 166=[-4.9273607538626816162 ,2.2967867775450236496 ] 
dist 167=[-4.9466835998363990312 ,2.1683011939730613889 ] 
dist 168=[-4.9392215643617222815 ,1.8711321583396731688 ] 
dist 169=[-4.9236880785989437001 ,1.8002985184433648626 ] 
dist 170=[-4.8262661647150586773 ,1.3957571795783159255 ] 
dist 171=[-4.7938402410751871379 ,1.3175508369920638647 ] 
dist 172=[-4.6545688439175374999 ,1.1579522050853656958 ] 
dist 173=[-4.6319443117577476237 ,1.1142551159885176744 ] 
dist 174=[-.5301582683125238042 ,.67637866923076699672] 
dist 175=[-.5165060422625807553 ,.6899269320899035989 ] 
dist 176=[-.51128155012229753692,.89074875181305597113] 
dist 177=[-.3786027910629943758 ,1.0912627649538197285 ] 
dist 178=[-.35984702377968314364,1.2659261061185638259 ] 
dist 179=[-.31844466569908131956,1.3785843822045774354 ] 
dist 180=[-.30629149644729928083,1.4670715616303426831 ] 
dist 181=[-.2767312192872721626 ,1.5453385255563432968 ] 
dist 182=[-.27177230783674012023,1.6119307017064613274 ] 
dist 183=[-.26885915081024457544,1.6538578308377228787 ] 
dist 184=[-.26798910869555327686,1.6856255400768734980 ] 
dist 185=[-.16344878435071161505,1.7117010630778443061 ] 
dist 186=[-.27384973338212950453,1.7320308940592233197 ] 
dist 187=[-.36618844400253075115,1.7408842818673407839 ] 
dist 188=[-.45763880738335757777,1.7430014314790196315 ] 
dist 189=[-.54119391844120210003,1.7365008722673641172 ] 
dist 190=[-.60204569463623399157,.49226095093356467456] 
dist 191=[-.65774320565352730202,.38902145951712551834] 
dist 192=[-.72074266976379236159,.40470525262199703281] 
dist 193=[-.77729023003958131752,.44623883738671238287] 
dist 194=[-.80725700297132392861,.47157237306247817241] 
dist 195=[-.82409135177690713588,.48981748716795246697] 
dist 196=[-.82826570070370297814,.50308183832212440546] 
dist 197=[-.92662714768782928124,.51208358946869474627] 
dist 198=[-1.1099400414497879520 ,.51393817291363138256] 
dist 199=[-1.2262585111415539751 ,.51204979015142220164] 
dist 200=[-1.3154416232810160222 ,.51098243419927828281] 
dist 201=[-1.3905363981232758926 ,.48132754969703664797] 
dist 202=[-1.4505646857383057762 ,.47485736353074008217] 
dist 203=[-1.4796613622865756671 ,.48940198496176185346] 
dist 204=[-1.4925387116511021197 ,.58073472399598586854] 
dist 205=[-1.4932376052288918322 ,.66184615679079349573] 
dist 206=[-.55182371628205310523,.71693871384169199426] 
dist 207=[-.56956686316334324929,.76336264915720319756] 
dist 208=[-.58122372845640632629,.8099028817862611647 ] 
dist 209=[-.58910064972085732569,.85008210207690838335] 
dist 210=[-.59176905852532642412,.871137780850671315  ] 
dist 211=[-.59112577117199105527,.88215710531692265181] 
dist 212=[-.58934887084626707339,.88345447399246856942] 
dist 213=[-.57788031213700412988,.95418233290819898311] 
dist 214=[-.57406445684745692162,1.0270888387842549412 ] 
dist 215=[-.55732765096182613298,1.0659605441229657604 ] 
dist 216=[-.55479444357707361793,1.0876265491090867121 ] 
dist 217=[-.05606408314115630438,1.0924372461111370004 ] 
dist 218=[-.09914097738716110048,1.0866263703176155192 ] 
dist 219=[-.14082597846666081821,1.0837592523740107321 ] 
dist 220=[-.19134231441815366441,1.0806907853412020333 ] 
dist 221=[-.24348702329445957062,1.0765574446892557824 ] 
dist 222=[-.33129585409192604271,.79445807589572827451] 
dist 223=[-.48539667932167129575,.7593361298684272679 ] 
dist 224=[-.61179180342782729814,.7729793719593032829 ] 
dist 225=[-.73289998977512011471,.8742709580555532229 ] 
dist 226=[-.84091144015366216291,.9418014664471149316 ] 
dist 227=[-.91507567064857132389,.9973380799887225542 ] 
dist 228=[-.97843378630973307353,1.0507969956794698672 ] 
dist 229=[-1.0433495346374791457 ,1.0986393274179601460 ] 
dist 230=[-1.0998915815973378644 ,1.1317765274509855566 ] 
dist 231=[-1.1298546659660360180 ,1.1603916845952164631 ] 
dist 232=[-1.1460004431346468958 ,1.1901997252653490349 ] 
dist 233=[-1.1482897208172979992 ,1.2143351922436423764 ] 
dist 234=[-1.1424796698221463200 ,1.2203276443006163098 ] 
dist 235=[-1.1818156599670297193 ,1.2190812131326166585 ] 
dist 236=[-1.2762001780173024956 ,1.2143474003128982981 ] 
dist 237=[-1.3518012546318362876 ,1.1622115284761065298 ] 
dist 238=[-1.3888842959470232553 ,1.1463575112694066171 ] 
dist 239=[-1.4081369307348634004 ,1.1266411629196735403 ] 
dist 240=[-1.4126288340096525201 ,1.1168897985217856056 ] 
dist 241=[-1.3756590681077837394 ,1.0009479624989696230 ] 
dist 242=[-1.3629088798635237228 ,.98103766305873591822] 
dist 243=[-1.3437155546501862459 ,.94794831154415426462] 
dist 244=[-1.3347081322836167307 ,.9374525700453985486 ] 
dist 245=[-1.2971572763091913707 ,.90139045043827234827] 
dist 246=[-1.2845610206975532359 ,.88923472877964678599] 
dist 247=[-1.2506922495317955482 ,.86882202627996487496] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 1, 0, 1, 0, 1] 
dist 0=[69.465865949660493981  ,69.465865949660493981  ] 
dist 1=[68.486324642543256752  ,69.762083990441049681  ] 
dist 2=[67.121170713880349373  ,69.964767954301772845  ] 
dist 3=[65.319770197236038698  ,70.124487476091266163  ] 
dist 4=[62.852887934631087679  ,70.085858418012729943  ] 
dist 5=[58.830700869269331321  ,69.328986604513714113  ] 
dist 6=[54.677119928369936432  ,69.047098735581952863  ] 
dist 7=[51.685503103167221413  ,68.469457242767027447  ] 
dist 8=[48.969385324415971983  ,67.045463099248621851  ] 
dist 9=[45.915400727370936309  ,64.009192122648464311  ] 
dist 10=[42.873697892357471314  ,63.032012928557347420  ] 
dist 11=[40.206328259048904003  ,62.650881644750745820  ] 
dist 12=[37.298417060362958139  ,60.737892587450186301  ] 
dist 13=[32.711912559748369521  ,60.276831668997520631  ] 
dist 14=[28.689041690011204898  ,59.777638970887682741  ] 
dist 15=[24.459204148227791271  ,56.748307025054636156  ] 
dist 16=[20.414844893393995010  ,49.649781442367961434  ] 
dist 17=[17.133203801050250939  ,26.073362615965112421  ] 
dist 18=[13.779949210803631012  ,23.567595548452718308  ] 
dist 19=[9.4507249203932363978 ,23.059773865254777957  ] 
dist 20=[5.2546316822118583801 ,22.175083956040439465  ] 
dist 21=[2.4332818783304030247 ,21.976850938641990874  ] 
dist 22=[.07984229151449877723,6.3796439704421350682 ] 
dist 23=[-2.2480538887996624460 ,5.0516921276984167107 ] 
dist 24=[-4.3775001355762013745 ,2.5413922315523671550 ] 
dist 25=[-7.2333906346072705488 ,1.6156612878904113728 ] 
dist 26=[-9.0686991014618988796 ,-1.3097679239381141816 ] 
dist 27=[-10.370979797283288458  ,-1.5044378724679979368 ] 
dist 28=[-11.291892101274035166  ,-3.0883912832689079081 ] 
dist 29=[-12.265718892691566034  ,-3.2965390305420949173 ] 
dist 30=[-13.804962262195461632  ,-3.3324179153949731897 ] 
dist 31=[-14.727625154117034100  ,-2.1123020708810964078 ] 
dist 32=[-15.379894524450707059  ,0                     ] 
dist 33=[-15.838934793142368300  ,-4.5377537112686910690 ] 
dist 34=[-16.162036528515453754  ,-4.0244264267362549536 ] 
dist 35=[-16.271167601289301259  ,-3.3111493503241168391 ] 
dist 36=[-16.282066435109872858  ,-2.3180929574749207879 ] 
dist 37=[-16.234127681006455465  ,-.68805326087016110068] 
dist 38=[-9.8959015205584607257 ,1.7174723112868502363 ] 
dist 39=[-9.8842103419898914292 ,3.4723410555173104745 ] 
dist 40=[-9.3564970455482907963 ,4.9084142512205667654 ] 
dist 41=[-9.2192977217774353801 ,6.2806606606305247368 ] 
dist 42=[-9.1367354705902597237 ,7.5038688363286419393 ] 
dist 43=[-9.1071328017186358836 ,8.3455884809756578936 ] 
dist 44=[-6.5890928295547296442 ,9.0679679240211342209 ] 
dist 45=[-6.2723585590138468087 ,9.8153385880854494177 ] 
dist 46=[-5.5416285878582851941 ,10.478028129428322124  ] 
dist 47=[-5.3639865439258867006 ,10.862581971582188059  ] 
dist 48=[-4.3588371939249670674 ,11.116919090099933440  ] 
dist 49=[-4.1606912609450982422 ,11.259875148675147934  ] 
dist 50=[-3.7597702581138925089 ,11.325243468144284898  ] 
dist 51=[-3.6484294038294068981 ,11.322081358512705637  ] 
dist 52=[-2.2635594205337766695 ,11.188488229705103999  ] 
dist 53=[-2.0582846550389013165 ,11.148457556713401139  ] 
dist 54=[-1.6056054184841303732 ,6.2895013359907471974 ] 
dist 55=[-1.4909369623049632717 ,5.8176599759346864184 ] 
dist 56=[-.9506112224633313612 ,4.7191250582639098384 ] 
dist 57=[-.8505164416197719304 ,4.4990227700337427747 ] 
dist 58=[-1.4796881748321242961 ,3.0301682984477140248 ] 
dist 59=[-2.0157488333590616640 ,2.4090464831753402154 ] 
dist 60=[-2.5494588543815570546 ,-.1305050058178936183 ] 
dist 61=[-3.2175169546436695262 ,.01209628445027365837] 
dist 62=[-3.8521657530538217998 ,.13754543645596758868] 
dist 63=[-4.2526403372379275310 ,.2713209936759020785 ] 
dist 64=[-4.5572419370929100724 ,.3992460480537070573 ] 
dist 65=[-4.8095159864579689942 ,.5013938357394881823 ] 
dist 66=[-5.0080820132538851046 ,.6036436369158703614 ] 
dist 67=[-5.0984751936955454085 ,.7319924734340754958 ] 
dist 68=[-5.1369197602922687144 ,.8535105180176196773 ] 
dist 69=[-5.1327044531224254520 ,.9285455037612409098 ] 
dist 70=[.3334370324366471301 ,.9835261274399986266 ] 
dist 71=[.2641385648430503631 ,1.1918020586777134764 ] 
dist 72=[.1777084185277429380 ,1.6209042129028836110 ] 
dist 73=[.0753405239503955597 ,2.0467855623202842544 ] 
dist 74=[-.0579573716010759627 ,2.4364501569895403070 ] 
dist 75=[-.26768637937516099114,2.7211258678802846956 ] 
dist 76=[-.47881692009020256344,2.9825750708997462340 ] 
dist 77=[-.61769089254127346815,3.2796194020381990232 ] 
dist 78=[-.72968970711519839819,3.5469179795289078995 ] 
dist 79=[-.8336531797733384587 ,3.6897422532458683903 ] 
dist 80=[-.92395368517660390971,3.7704837812108309897 ] 
dist 81=[-.98146636475020891806,3.7901873980634366046 ] 
dist 82=[-1.0256918961100275792 ,3.7694704995903663322 ] 
dist 83=[-1.0629971019294569956 ,3.7634960646060029520 ] 
dist 84=[-1.0929196418935066583 ,3.7593781201632054863 ] 
dist 85=[-1.1077098355634207262 ,3.7567356327607403316 ] 
dist 86=[-1.2672029384359239632 ,2.8797145224391960585 ] 
dist 87=[-1.8027322779915658288 ,2.7660019719201168260 ] 
dist 88=[-2.2404047827784486033 ,2.4915687939008712423 ] 
dist 89=[-2.6571201838880502325 ,2.4268692621414452984 ] 
dist 90=[-3.0269717481733196956 ,2.0083424931891907161 ] 
dist 91=[-3.2777497951735970724 ,1.9237967749025834264 ] 
dist 92=[-3.4885908916240504669 ,1.7663866462310422977 ] 
dist 93=[-3.6991723657639676611 ,1.7251238932187712855 ] 
dist 94=[-3.8807473884440271667 ,1.0368667732258818768 ] 
dist 95=[-3.9759095444110945614 ,.94132073338122227955] 
dist 96=[-4.0257194805793983542 ,.92557274046179093352] 
dist 97=[-4.0313043507045386526 ,1.0693710405169758837 ] 
dist 98=[-4.0050886047461836908 ,1.2190795297828776434 ] 
dist 99=[-3.9836089518217268698 ,1.4153655059801807164 ] 
dist 100=[-3.9224467542097203142 ,1.6060222700068919128 ] 
dist 101=[-3.8910506206838002704 ,1.7332828887428924689 ] 
dist 102=[-1.1498816901373575910 ,1.8380897132800128827 ] 
dist 103=[-1.2547200853573629154 ,1.9392043956854188691 ] 
dist 104=[-1.3585179057924451317 ,2.0298387873801885512 ] 
dist 105=[-1.4477678859501170850 ,2.3205786766334060858 ] 
dist 106=[-1.5431904952637410278 ,2.6947775617317188724 ] 
dist 107=[-1.6716008260834187932 ,2.9370944933856640334 ] 
dist 108=[-1.7921621120699948342 ,3.1285049376650580608 ] 
dist 109=[-1.9746996388280093198 ,3.2996850095343661534 ] 
dist 110=[-2.1808768513758871574 ,3.4457782436436584776 ] 
dist 111=[-2.3545650168581694845 ,3.5371406349615367384 ] 
dist 112=[-2.4936799326552765722 ,3.6056419197223001358 ] 
dist 113=[-2.5619773309424117653 ,3.6605636729316946745 ] 
dist 114=[-2.5974069420122862992 ,3.7023598579480661215 ] 
dist 115=[-2.6054437136996811943 ,3.7185155429248397818 ] 
dist 116=[-2.5358186325464888941 ,3.7189371270895518003 ] 
dist 117=[-2.5120838466441296236 ,3.7053933194571792561 ] 
dist 118=[-2.4765645143691036926 ,1.3505837162891350194 ] 
dist 119=[-2.4598551792444682730 ,1.3070149126040742153 ] 
dist 120=[-2.3909462193228549298 ,1.1272467078414798264 ] 
dist 121=[-2.3676847041774121222 ,1.0901482670060732278 ] 
dist 122=[-2.3056952378690672068 ,.99765463322431508274] 
dist 123=[-2.2796190550241596440 ,.97648191605958969054] 
dist 124=[-1.6142867205846029352 ,.60071608848298785069] 
dist 125=[-2.0207131447378643904 ,.99757228356784112763] 
dist 126=[-2.4071618430524891329 ,1.3182448214538273584 ] 
dist 127=[-2.6512595865918697185 ,1.6174551812679827267 ] 
dist 128=[-2.8371212975642256785 ,1.8789077344520130378 ] 
dist 129=[-2.9913201562038248390 ,2.0489990269938340140 ] 
dist 130=[-3.1128235678815203092 ,2.1842450985929201178 ] 
dist 131=[-3.1682932761937662230 ,2.3067319142275320174 ] 
dist 132=[-3.1916993499392068809 ,2.4115798574334197082 ] 
dist 133=[-3.1892725544881886637 ,2.4764807414316584789 ] 
dist 134=[.39056254229207530838,2.5243592311450168440 ] 
dist 135=[.52180259380985786988,2.5613208447152106034 ] 
dist 136=[.81169405971862075348,2.5883062441887171191 ] 
dist 137=[.86117722275467489656,2.5963989845658645370 ] 
dist 138=[1.1745555676379990958 ,2.5921795886418547349 ] 
dist 139=[.94935472628003276727,2.5830383361812505783 ] 
dist 140=[.47167410272210789444,1.9182552288439054388 ] 
dist 141=[.14013674473987195531,2.1025133572981281960 ] 
dist 142=[-.14687546424222403951,2.2679511277761648000 ] 
dist 143=[-.44698606008083155901,2.3556528305369423812 ] 
dist 144=[-.73147486688042718447,2.4049533525235783345 ] 
dist 145=[-.95618604114622103052,2.4172440791828257696 ] 
dist 146=[-1.1794853868873317366 ,2.3985279204927797755 ] 
dist 147=[-1.4583436140199155539 ,2.3936990865353743762 ] 
dist 148=[-1.7227903822260836605 ,2.3908312964388697581 ] 
dist 149=[-1.8886156488473835875 ,2.3899025326537862872 ] 
dist 150=[-2.0134751027622973324 ,1.8228655344725336207 ] 
dist 151=[-2.1145469429754832510 ,1.7496720407601792778 ] 
dist 152=[-2.1922389324924628997 ,1.5735952728486767558 ] 
dist 153=[-2.2238576768690247384 ,1.5319560603061633158 ] 
dist 154=[-2.2358259611768429552 ,1.2653531498977020145 ] 
dist 155=[-2.2351503969917948234 ,1.2115971471092671224 ] 
dist 156=[-2.2330065562219271891 ,1.1108433019695400725 ] 
dist 157=[-2.3681582603713004858 ,1.0843087910970775304 ] 
dist 158=[-2.4847439765931380393 ,.77277835266617760734] 
dist 159=[-2.5457784409105198440 ,.96783538375134267353] 
dist 160=[-2.5776341563267955047 ,1.1468464202703302228 ] 
dist 161=[-2.5813108286070105980 ,1.2785693468614215621 ] 
dist 162=[-2.5640227920840695100 ,1.4004948480785023999 ] 
dist 163=[-2.5501077231838012617 ,1.5404329133396958672 ] 
dist 164=[-2.5114649386428351132 ,1.6671075128570828304 ] 
dist 165=[-2.4917159342942870111 ,1.7361372019187807008 ] 
dist 166=[.31025736166588458191,1.7759622897170731557 ] 
dist 167=[.41363373629702535378,1.7861665113244542660 ] 
dist 168=[.52746577924522102248,1.7856922658276069013 ] 
dist 169=[.33203730966964109831,1.7829307409049524412 ] 
dist 170=[.08474282638079464190,1.7803496258852931221 ] 
dist 171=[-.29703068709096412901,1.9579228985042857992 ] 
dist 172=[-.68035769379474319477,2.1093059826226821386 ] 
dist 173=[-.93384762752763342125,2.2639043011714029726 ] 
dist 174=[-1.1400396357598234745 ,2.3998817121979915829 ] 
dist 175=[-1.3347385084335923316 ,2.4770030419119144406 ] 
dist 176=[-1.5064588995521545684 ,2.5255585722178694728 ] 
dist 177=[-1.6210107737009041493 ,2.5476131626948274837 ] 
dist 178=[-1.7152908270889941231 ,2.5528240153988187092 ] 
dist 179=[-1.8061654710619073206 ,2.5481859305337865163 ] 
dist 180=[-1.8833207317525563335 ,2.5109930282021196156 ] 
dist 181=[-1.9228867255981997631 ,2.4978844105803868002 ] 
dist 182=[-1.9423818103776450972 ,1.3136559131658727796 ] 
dist 183=[-1.9436664118481760401 ,1.1969812091802892151 ] 
dist 184=[-1.9263600054487292608 ,.93037536223619421648] 
dist 185=[-1.9155380844760288505 ,.87293604383566055126] 
dist 186=[-1.8818205635150227054 ,.53124255530145191952] 
dist 187=[-1.8648558740208554519 ,.46871465150075064073] 
dist 188=[-1.7097649465680380327 ,.42480480784025731034] 
dist 189=[-1.9266078082644997030 ,.70792304600988026331] 
dist 190=[-2.1244867611580715024 ,.94063764692414804092] 
dist 191=[-2.2353063363059054886 ,1.1644470923721241655 ] 
dist 192=[-2.3032574226314566324 ,1.3646094569437640634 ] 
dist 193=[-2.3301732132373733765 ,1.5030174944770451759 ] 
dist 194=[-2.3415411386964529425 ,1.6222933700179187375 ] 
dist 195=[-2.3474860230304211712 ,1.7461550493891186516 ] 
dist 196=[-2.3505798862868413164 ,1.8554788154748937948 ] 
dist 197=[-2.3505776993335752442 ,1.9167762610780663470 ] 
dist 198=[.10094587249765544193,1.9544561808258165942 ] 
dist 199=[.13789056536130634805,1.9695912548685495831 ] 
dist 200=[.1954248798510085534 ,1.9720332823834322201 ] 
dist 201=[.20922612300548130777,1.9669237608379935265 ] 
dist 202=[.21750584314459387571,1.9416248695515744029 ] 
dist 203=[.13712255091502288923,1.9260153697715354301 ] 
dist 204=[-.17906646201061986646,2.0183695927274606072 ] 
dist 205=[-.44727378958361923077,2.2771876599667101690 ] 
dist 206=[-.67232089116981423066,2.5218619340509197891 ] 
dist 207=[-.89637843711185450908,2.6739674894326233927 ] 
dist 208=[-1.1018549908665047900 ,2.7869543568066036659 ] 
dist 209=[-1.2527995197591317255 ,2.8756199873596575982 ] 
dist 210=[-1.3922656403811496690 ,2.9415573131883753726 ] 
dist 211=[-1.5519653277283280553 ,2.9639017749021550970 ] 
dist 212=[-1.6969295273185616332 ,2.9655250422525039439 ] 
dist 213=[-1.7776292736943280666 ,2.9555081893475854032 ] 
dist 214=[-1.8924457481485538421 ,2.8554547873609844122 ] 
dist 215=[-2.2958025410726933166 ,2.8276285068083612830 ] 
dist 216=[-2.6135885993719346606 ,2.7415895027658769729 ] 
dist 217=[-2.8963567106660435188 ,2.7136176066718388740 ] 
dist 218=[-3.1339776363577447642 ,2.4991904689246780226 ] 
dist 219=[-3.2717128902345870831 ,2.4473041747051514246 ] 
dist 220=[-3.3622606022228098248 ,2.3647025723070694986 ] 
dist 221=[-3.4116936094535267634 ,2.3375114079982163533 ] 
dist 222=[-3.4396247453287996179 ,1.6898490556519351707 ] 
dist 223=[-3.4444211712552315732 ,1.5990680364049244127 ] 
dist 224=[-3.4331774691328818276 ,1.3921656585917925201 ] 
dist 225=[-3.4203817431778551343 ,1.4698566038481071533 ] 
dist 226=[-3.3480562992076540888 ,1.6425179903256095449 ] 
dist 227=[-3.3239400845646035468 ,1.8583266234551499189 ] 
dist 228=[-3.2288182853485622294 ,2.0630759890039919661 ] 
dist 229=[-3.2088317200489229043 ,2.1916320787017249020 ] 
dist 230=[-.27429827502955903474,2.2886227993228893548 ] 
dist 231=[-.37212936810747749896,2.3674867968104062545 ] 
dist 232=[-.47804443164824790134,2.4283876283862395947 ] 
dist 233=[-.58333857292559389919,2.4537397204161559800 ] 
dist 234=[-.7080324632499118575 ,2.4591586033387556454 ] 
dist 235=[-1.1084256634400861125 ,2.4551938914792944580 ] 
dist 236=[-1.6227474618556936207 ,2.3984910176976933260 ] 
dist 237=[-1.9544437215058468721 ,2.3797670210792598490 ] 
dist 238=[-2.2149250718387588988 ,2.3176582085146812767 ] 
dist 239=[-2.4452357732011225505 ,2.2961576182223240159 ] 
dist 240=[-2.6377151917903507666 ,2.1269240486736221783 ] 
dist 241=[-2.7473221784792336379 ,2.0850714742676624469 ] 
dist 242=[-2.8168986924224295132 ,2.0199816491735600642 ] 
dist 243=[-2.8497331912246983223 ,1.9976467299727843803 ] 
dist 244=[-2.8649128476240115520 ,1.4553922391776495627 ] 
dist 245=[-2.8640803530538113005 ,1.3791869867362178703 ] 
dist 246=[-2.8513631030161210516 ,1.2071784854520121738 ] 
dist 247=[-2.8396218329982172651 ,1.1610300225229015093 ] 
dist 248=[-2.7769784774704840886 ,.9370887271331557975 ] 
dist 249=[-2.7560696958897261302 ,.8932361454396889898 ] 
dist 250=[-2.6780042398776640440 ,.79314159734465515137] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 1, 2] 
dist 0=[69.681064921633864737  ,69.681064921633864737  ] 
dist 1=[69.487838799693915492  ,69.681704423546054331  ] 
dist 2=[68.851120907895803221  ,69.681064921633864737  ] 
dist 3=[67.764919961965520043  ,69.301233562069541066  ] 
dist 4=[65.777296453024706738  ,69.153511096180129972  ] 
dist 5=[63.356919452312924735  ,68.219304271411875388  ] 
dist 6=[60.542951958752121021  ,67.961709370256598297  ] 
dist 7=[56.896416601676378446  ,66.947325097938730493  ] 
dist 8=[51.151838125469445978  ,66.802035221790049220  ] 
dist 9=[45.297178077619393301  ,63.846273569226919702  ] 
dist 10=[41.211309393918586951  ,63.161334054457960534  ] 
dist 11=[37.632718718002976632  ,62.669444264644266976  ] 
dist 12=[33.804030003221932072  ,62.556481795333725710  ] 
dist 13=[30.102376880126481322  ,53.032266620763082118  ] 
dist 14=[27.031414607089022518  ,52.259380053983528237  ] 
dist 15=[23.831711550659278605  ,45.207346800688079308  ] 
dist 16=[19.616695478975073699  ,34.237764523721093292  ] 
dist 17=[15.487757614012747401  ,25.960939368452023246  ] 
dist 18=[12.631960863704027423  ,23.187340603021250439  ] 
dist 19=[10.161107949074946839  ,16.780527336166521289  ] 
dist 20=[7.5691308728691293073 ,15.812213703991118325  ] 
dist 21=[5.0982210197334998559 ,13.236790983553835121  ] 
dist 22=[3.1109577007955352358 ,12.771756897922889568  ] 
dist 23=[.98012611799623727575,11.894987962337466672  ] 
dist 24=[-2.4629192812183537463 ,11.702164231584399665  ] 
dist 25=[-5.6709652023141317145 ,1.6478525816717909517 ] 
dist 26=[-7.6565736730011181519 ,.7690513569447032431 ] 
dist 27=[-9.1324467814493026497 ,-1.0671790021037132852 ] 
dist 28=[-10.303923376115253969  ,-1.4514293822096877604 ] 
dist 29=[-11.221422230821507194  ,-3.1692551951893740685 ] 
dist 30=[-11.683508846425165211  ,-3.4660297507082827280 ] 
dist 31=[-11.904001285556688947  ,-3.9629221092626082956 ] 
dist 32=[-12.143146354290475983  ,-4.0599183497391262862 ] 
dist 33=[-12.760805252980007358  ,-4.1488778538907015023 ] 
dist 34=[-13.261684283835282910  ,-4.0185839630071628251 ] 
dist 35=[-13.588517833700520957  ,-3.7443940632328854333 ] 
dist 36=[-13.768489405330735327  ,-3.2074071199053986281 ] 
dist 37=[-13.865053143473391038  ,-2.5466827509301688199 ] 
dist 38=[-13.862189546514357441  ,-1.7781829131581955840 ] 
dist 39=[-13.804966214729804395  ,-.78556396167421300509] 
dist 40=[-13.747311869467196098  ,.81951203697233516335] 
dist 41=[-7.9035482331765436767 ,3.3889150746445216314 ] 
dist 42=[-7.4149265142082163611 ,5.0918300380887733398 ] 
dist 43=[-6.2815185521386545275 ,6.4833398703201414476 ] 
dist 44=[-6.0364409914236474615 ,7.8105834127684297896 ] 
dist 45=[-4.5051375958781976075 ,8.9927490637189284546 ] 
dist 46=[-4.2155761025135564215 ,9.8055847422812272611 ] 
dist 47=[-3.6609976324557700974 ,10.502763092271705748  ] 
dist 48=[-3.5204807005831063239 ,11.223671550307222423  ] 
dist 49=[-1.6447687984538566517 ,11.853122477038738000  ] 
dist 50=[-1.3755089483909943573 ,12.185417240829722719  ] 
dist 51=[-.82465162872741004106,12.363720913294746143  ] 
dist 52=[-.68291009706840180246,12.394641508357312791  ] 
dist 53=[-.17968404416357310223,11.772832301630497877  ] 
dist 54=[-.07521299378618269210,11.707805962898104272  ] 
dist 55=[.06372544053516655999,10.785981476876674965  ] 
dist 56=[.09741787730223629333,9.1094910044001063327 ] 
dist 57=[.10922622602956345738,3.5004389305552485220 ] 
dist 58=[-.08037236105323307565,3.5962603801549942003 ] 
dist 59=[-.83464189874245086608,3.6635204337648580966 ] 
dist 60=[-1.6105119018210969108 ,3.7112622876232305716 ] 
dist 61=[-2.3387109036889012070 ,3.7441994072813750383 ] 
dist 62=[-2.9028693876809840035 ,3.7521662897068617759 ] 
dist 63=[-3.4536861166430936667 ,3.7460435403365558157 ] 
dist 64=[-4.1287105226553778685 ,3.7379512547020622059 ] 
dist 65=[-4.7636283304276877744 ,.27634628566222576127] 
dist 66=[-5.1544781688896140431 ,.29979767694090086006] 
dist 67=[-5.4406424703785102003 ,.32117530602501166808] 
dist 68=[-5.6579792171441155670 ,.34514244884273308655] 
dist 69=[-5.8177217309927295958 ,.36878301761327212799] 
dist 70=[-5.8741421867325580598 ,.38886363421638865139] 
dist 71=[-5.8879027411696100219 ,.41008440012412062252] 
dist 72=[-5.8774631920720226484 ,.43827536507131360021] 
dist 73=[-3.8140168062397511210 ,1.0048126362355236964 ] 
dist 74=[-3.8925987710092076730 ,1.6605831937920477132 ] 
dist 75=[-3.9300787088745877642 ,2.2133983870796318554 ] 
dist 76=[-3.9346673365593682298 ,2.7680706291639710058 ] 
dist 77=[-3.8379533380113526589 ,3.2796194020381990025 ] 
dist 78=[-3.8069600345133215050 ,3.6604546984506230214 ] 
dist 79=[-3.7830889428759502700 ,4.0174388014359626784 ] 
dist 80=[-3.7628068083064051458 ,4.4338715597170011269 ] 
dist 81=[-2.7083523431058887359 ,4.8145918275540322690 ] 
dist 82=[-2.5784793985865035886 ,5.0291471569059934252 ] 
dist 83=[-2.2757412875884411248 ,5.1625172505931035605 ] 
dist 84=[-2.2032452381356553597 ,5.2194469445136406606 ] 
dist 85=[-1.7791604875123512260 ,5.2414226840023256376 ] 
dist 86=[-1.6957065214656864712 ,5.2353856796944439702 ] 
dist 87=[-1.5296069232552592287 ,5.2077109243940545454 ] 
dist 88=[-1.4843316366191193696 ,5.1859441137421857433 ] 
dist 89=[-2.3386045764744741404 ,4.3588998981454585987 ] 
dist 90=[-3.0781261453922749602 ,4.2364651743744273651 ] 
dist 91=[-3.6749875764535576915 ,4.2699657166174887636 ] 
dist 92=[-4.2307625729737438234 ,4.2764150497142023428 ] 
dist 93=[-4.7156587331367434917 ,4.2355113791262215461 ] 
dist 94=[-5.0298502443804140075 ,4.2095697660196849440 ] 
dist 95=[-5.2782824387028258028 ,4.1502938402638675684 ] 
dist 96=[-5.5009274297014874525 ,4.1217670220870070055 ] 
dist 97=[-5.6837069792725967521 ,1.9673545225180625727 ] 
dist 98=[-5.7731510119278924343 ,1.8283792966222668057 ] 
dist 99=[-5.8111204512166438270 ,1.4829341735874489241 ] 
dist 100=[-5.8083368976670553435 ,1.4296027957926954739 ] 
dist 101=[-5.7370586348689251149 ,1.1474292553153463223 ] 
dist 102=[-5.7031114195186880118 ,1.1892064873479526290 ] 
dist 103=[-5.5819470242174493416 ,1.2280821494895868142 ] 
dist 104=[-5.5326432105328964619 ,1.2730004206255392415 ] 
dist 105=[-3.9110370167923709850 ,1.3118912498597195431 ] 
dist 106=[-4.0252450244380167628 ,1.3267288362951123864 ] 
dist 107=[-4.0991574028509887275 ,1.3309906115189659358 ] 
dist 108=[-4.1371337656825649376 ,1.3277054740666441729 ] 
dist 109=[-4.1490171499196423076 ,1.3005308399768082526 ] 
dist 110=[-4.1436531748155839753 ,1.3271131147704394228 ] 
dist 111=[-4.0818076931997271195 ,1.3391521440983069038 ] 
dist 112=[-4.0661639381883621174 ,1.3402950829729422400 ] 
dist 113=[-1.9052088293507418040 ,1.2341127438549551716 ] 
dist 114=[-1.7015375174029006441 ,1.2135099138879007610 ] 
dist 115=[-1.4266062476289346361 ,1.1801022252904382310 ] 
dist 116=[-1.4159070276155150233 ,1.4727794191114399120 ] 
dist 117=[-1.3731730334409362946 ,1.9146005777969481363 ] 
dist 118=[-1.3588852054701032040 ,2.2481624331097956009 ] 
dist 119=[-1.3237192825720307858 ,2.5653558712134975602 ] 
dist 120=[-1.3094350329016267616 ,2.9419003401300232479 ] 
dist 121=[.28436672711659717476,3.2894748003984866065 ] 
dist 122=[.36113416259183758559,3.4911322163580697090 ] 
dist 123=[.45021805966421366546,3.6239640101386909984 ] 
dist 124=[.45650684503285523541,3.6970507096789518794 ] 
dist 125=[.42885004867215197595,3.7414584698055318656 ] 
dist 126=[.3518210610301841053 ,3.7599128857483728884 ] 
dist 127=[.22410592419110226748,3.7628440330772014795 ] 
dist 128=[-.00570323045723908520,3.7492599733521635195 ] 
dist 129=[-.70175849693175253993,1.4205389735381193305 ] 
dist 130=[-1.1814577604076076615 ,1.4596638096711690839 ] 
dist 131=[-1.5930891369891261676 ,1.4877785630733902442 ] 
dist 132=[-2.0177686311727809823 ,1.5080996765455011637 ] 
dist 133=[-2.4168271342835113427 ,1.5217860496727153219 ] 
dist 134=[-2.7262796415208339872 ,1.5234408329460038781 ] 
dist 135=[-3.0284589069837620906 ,1.5169591838161105872 ] 
dist 136=[-3.3985112508027161106 ,1.5115346035174541652 ] 
dist 137=[-3.7458764100770149637 ,.52326596041177885842] 
dist 138=[-3.9575768617541454633 ,.43801135183379226643] 
dist 139=[-4.1098354154699085270 ,.24706459527441800205] 
dist 140=[-4.2201399460100566300 ,.20754302748360408573] 
dist 141=[-4.2946561620637233079 ,.02741603303275259772] 
dist 142=[-4.3100017605355182384 ,.21217118912681655929] 
dist 143=[-4.2929153217428827936 ,.73423499501690508322] 
dist 144=[-4.2844686414853367650 ,1.6503209718468772081 ] 
dist 145=[-4.0318405539460225538 ,2.5645050195825288866 ] 
dist 146=[-3.9771020442124934749 ,3.1578619226873202479 ] 
dist 147=[-3.8218944138810777960 ,3.6281228207619732535 ] 
dist 148=[-3.7757612748466667337 ,4.0513893870950133786 ] 
dist 149=[-3.4370302904439955134 ,4.4105642177089004677 ] 
dist 150=[-3.3580564444657573308 ,4.6252218236256042641 ] 
dist 151=[-3.2271513682797640238 ,4.7745093827787074064 ] 
dist 152=[-3.1871004327403085833 ,4.8729830570103016180 ] 
dist 153=[-2.2672771631319090998 ,4.9397378901187532593 ] 
dist 154=[-2.1389918365104994534 ,4.9625278684895882040 ] 
dist 155=[-1.8410325272859063377 ,4.9574157905429812894 ] 
dist 156=[-1.7715112830064360722 ,4.9426168361425329098 ] 
dist 157=[-1.3628393394154210343 ,4.8466181635330337229 ] 
dist 158=[-1.2839897596596263073 ,4.8146958040944781160 ] 
dist 159=[-1.1261970112126832814 ,4.6742272684628923086 ] 
dist 160=[-1.0838099909504912506 ,4.6532256196497013451 ] 
dist 161=[-.49846563044038875381,1.0585891318648321688 ] 
dist 162=[-.82546779406663086527,1.1066130977620524325 ] 
dist 163=[-1.0889363551247578608 ,1.1365437538937548490 ] 
dist 164=[-1.3334915751618296450 ,1.1494769249317978469 ] 
dist 165=[-1.5463085254419559118 ,1.1546468791693169774 ] 
dist 166=[-1.6832021613043370402 ,1.1536171614045951570 ] 
dist 167=[-1.7903008542517755640 ,1.1478524675582144941 ] 
dist 168=[-1.8842930630322447625 ,1.1430362370321966397 ] 
dist 169=[-1.9641040416017772175 ,.95878385179544097369] 
dist 170=[-2.0146467572522415497 ,.93160582891882427523] 
dist 171=[-2.0532834305266113441 ,.86373794294135815838] 
dist 172=[-2.0856120020773923584 ,.84669278197920957381] 
dist 173=[-2.1112986090323379728 ,.73296766583607737166] 
dist 174=[-2.1234465070558089987 ,.70890906779034620252] 
dist 175=[-2.1279690281473029050 ,.66528705974681868271] 
dist 176=[-2.1232449195659276379 ,.65363922720734685552] 
dist 177=[-1.2480668374178497280 ,.42942724212737844389] 
dist 178=[-1.2683230440732876959 ,.39876289422005996105] 
dist 179=[-1.2771003477239638801 ,.32245344621230773772] 
dist 180=[-1.2766134952134727276 ,.31080563512877356804] 
dist 181=[-1.2614017236325198892 ,.49869517257060197548] 
dist 182=[-1.2539854665404434451 ,.68560622963819130188] 
dist 183=[-1.2276962098307406321 ,.87323565684796689528] 
dist 184=[-1.2166748219555390664 ,1.1101510464541081791 ] 
dist 185=[.06755697235692388572,1.3360990629007401322 ] 
dist 186=[.09067945836596040021,1.4799896667092265130 ] 
dist 187=[.13852800988547414828,1.5909115703271140447 ] 
dist 188=[.14956161718401570193,1.6853775649800384796 ] 
dist 189=[.18985802596943093005,1.7617045254463730219 ] 
dist 190=[.19754100615032050043,1.8002863941085135535 ] 
dist 191=[.20150605862235862548,1.8184977950232611020 ] 
dist 192=[-4.70119400655962930000e-05,1.8205595173651102790 ] 
dist 193=[-.26167043386662324418,1.2621009214234463833 ] 
dist 194=[-.43773633397836852596,1.3052555178075398618 ] 
dist 195=[-.5843361688309064347 ,1.3310076690951483107 ] 
dist 196=[-.72844733780288333784,1.3396297844070089212 ] 
dist 197=[-.85941743989703750443,1.3399059447948281325 ] 
dist 198=[-.9536095850731096224 ,1.3351002419120410255 ] 
dist 199=[-1.0386256184154310124 ,1.3209112227718128439 ] 
dist 200=[-1.1330006108834166358 ,1.3123171532624981582 ] 
dist 201=[-1.2174102208780480356 ,.7937368305466587428 ] 
dist 202=[-1.2626834610740298985 ,.73893970647000100824] 
dist 203=[-1.2878289347060575557 ,.61216488618773716453] 
dist 204=[-1.2935956079907575560 ,.58419587092175259396] 
dist 205=[-1.2887741138915564818 ,.41447339949027357679] 
dist 206=[-1.2846807785587036352 ,.38253579998414815364] 
dist 207=[-1.2791563032201246870 ,.31968463490528492267] 
dist 208=[-1.2717778920396266365 ,.30345192012264604725] 
dist 209=[-.91007229615927010731,.15091861146815858251] 
dist 210=[-.86642778858888406538,.29845502765946197081] 
dist 211=[-.76300082994982194006,.42675033158562113242] 
dist 212=[-.73916380877156770919,.55360313697384741906] 
dist 213=[-.58945515497206403383,.66936926600489003215] 
dist 214=[-.55997648030336105382,.75344996494966737918] 
dist 215=[-.47318059014709586403,.83017779969403838324] 
dist 216=[-.40179933241240642158,.91662008469877972579] 
dist 217=[-.07696971606364312092,.99464377885269273799] 
dist 218=[-.05314603024798203883,1.0377975583825442232 ] 
dist 219=[-.07118578876615335440,1.0635487753338893435 ] 
dist 220=[-.09879544775259973638,1.0721695693530916428 ] 
dist 221=[-.12785861590396240189,1.0740379776930897295 ] 
dist 222=[-.15556118579676082035,1.0728601057446683926 ] 
dist 223=[-.18749087901632602005,1.0692289498441567626 ] 
dist 224=[-.23341217345617948282,1.0638437117310829048 ] 
dist 225=[-.27992068727114292227,.59021747539003514614] 
dist 226=[-.35650371142439557762,.63411237624506631957] 
dist 227=[-.47074976881569641145,.6697307018297578603 ] 
dist 228=[-.57725061485657039755,.7032187316645948847 ] 
dist 229=[-.67024516085416991172,.73265588567425832104] 
dist 230=[-.73062694829131345105,.75211897475429430341] 
dist 231=[-.77850792532410786212,.76794677050480273794] 
dist 232=[-.82164817956276759295,.78288606618382811458] 
dist 233=[-.8585231111321914267 ,.79409406798062901721] 
dist 234=[-.88141744986956615508,.79571205242831304102] 
dist 235=[-.89838900341762373591,.79223400281985684735] 
dist 236=[-.91164336464639862625,.78846984248060563804] 
dist 237=[-.92144778849916639174,.75073058560687995859] 
dist 238=[-.92466069881993333432,.73978322641937894383] 
dist 239=[-.92365162380499823968,.72545137218627555149] 
dist 240=[-.91661841166077070006,.71890545120501186107] 
dist 241=[-.49533861014388992577,.5970588583669510419 ] 
dist 242=[-.47708142756671673033,.5837509887782381120 ] 
dist 243=[-.44253047738479481464,.5614387161301797634 ] 
dist 244=[-.43315889204311420471,.5546473999222379851 ] 
dist 245=[-.3989530958195836587 ,.5319598302010116099 ] 
dist 246=[-.3898719180604759709 ,.5243064024973407020 ] 
dist 247=[-.37581314134375030941,.5137970990666102642 ] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 1, 0, 1, 2] 
dist 0=[61.976089103623736688  ,61.976089103623736688  ] 
dist 1=[61.223309740297233631  ,62.437276879742384814  ] 
dist 2=[59.874719322901648998  ,62.621699233681250423  ] 
dist 3=[58.189035813652378316  ,62.669622893416361331  ] 
dist 4=[56.090320246268162333  ,62.585742201650893429  ] 
dist 5=[53.284074701532488646  ,62.404360076299310844  ] 
dist 6=[48.773266197896161834  ,62.283907369268860957  ] 
dist 7=[44.156280183529327562  ,61.555834830663461325  ] 
dist 8=[40.925794077187725157  ,61.268627655545562153  ] 
dist 9=[38.086650735950010156  ,61.018263544765206405  ] 
dist 10=[35.031438880854872127  ,60.825916774818132395  ] 
dist 11=[32.061822374931204949  ,60.526804162132705468  ] 
dist 12=[29.563632908168844257  ,60.338060378910377744  ] 
dist 13=[26.923766147707870263  ,60.149323866557029115  ] 
dist 14=[23.386839779984791603  ,59.536520185831627172  ] 
dist 15=[19.871578722984288276  ,37.064908134524737499  ] 
dist 16=[17.317435222337187119  ,35.139377610625625118  ] 
dist 17=[14.965287003405819576  ,30.600855024985814984  ] 
dist 18=[12.255853527146564585  ,29.871561133346704155  ] 
dist 19=[9.5027287949889647001 ,23.690664564355801395  ] 
dist 20=[6.9747242207682241785 ,22.573205369788255720  ] 
dist 21=[4.1082093644577032866 ,20.994389089107222189  ] 
dist 22=[0                     ,20.548359371993766496  ] 
dist 23=[.37268776138318706112,12.616043576725114080  ] 
dist 24=[-1.9226517557484989123 ,11.633804011495476143  ] 
dist 25=[-4.1111838042982414536 ,9.4222389099428246786 ] 
dist 26=[-5.8895128372117656070 ,9.0576068285093557336 ] 
dist 27=[-7.7167195105862327019 ,6.4331198580789969071 ] 
dist 28=[-10.101974635108181453  ,5.9955290356565702970 ] 
dist 29=[-12.384349122163756138  ,5.2409396857628136284 ] 
dist 30=[-13.800825961178727602  ,5.0899939639099960628 ] 
dist 31=[-14.863740690569298563  ,.86785264383227776604] 
dist 32=[-15.733001749259190409  ,.41248092247597763743] 
dist 33=[-16.420062714678821619  ,-.4694398622100311144 ] 
dist 34=[-16.754969476369529683  ,-.67736262222062997093] 
dist 35=[-16.914609556457364782  ,-1.3209072456454756248 ] 
dist 36=[-16.929790868002126682  ,-1.4610369108321804501 ] 
dist 37=[-16.681879966046648172  ,-1.5027577331182449956 ] 
dist 38=[-16.585813008403108261  ,-1.3999895715929493513 ] 
dist 39=[-16.311391853241646681  ,-1.2389926936342811112 ] 
dist 40=[-16.186192193241285191  ,-1.0409703303271988052 ] 
dist 41=[-15.495922770629038740  ,-.78069266599859176141] 
dist 42=[-15.476962818856709519  ,-.37030044960567630493] 
dist 43=[-14.888597507421900544  ,.10361590012932938479] 
dist 44=[-14.746641559111244339  ,.6460209296582489370 ] 
dist 45=[-14.569707791921583581  ,4.1473703897063465309 ] 
dist 46=[-14.493572350606778921  ,6.4702674416842288721 ] 
dist 47=[-5.9106774518117664357 ,8.3727665477112132352 ] 
dist 48=[-5.5676849227375106966 ,10.196805261351320229  ] 
dist 49=[-3.6804649576239462146 ,11.829438837632231873  ] 
dist 50=[-3.3360843506368777289 ,12.968308980569864779  ] 
dist 51=[-2.6124762430145686971 ,13.963301134565691049  ] 
dist 52=[-2.4182093954526500529 ,15.022024372926110613  ] 
dist 53=[-.73478393997228252579,15.960312050360098493  ] 
dist 54=[-.46297783615283608689,16.474706165266740900  ] 
dist 55=[-.04043368103452830521,16.777382792968298661  ] 
dist 56=[.06609196609854130564,16.870582520245801977  ] 
dist 57=[.17648313229885527917,16.872360416527531146  ] 
dist 58=[.09283486124658251673,16.810207684635349525  ] 
dist 59=[-.11436922867540171372,16.243947969086526880  ] 
dist 60=[-.54406736455127471397,15.516636828622314367  ] 
dist 61=[-.99520463118665079539,4.7945612831632096913 ] 
dist 62=[-1.2880008088641421128 ,4.7798528513810783951 ] 
dist 63=[-1.5207374103573525646 ,.8914881217668628406 ] 
dist 64=[-1.7322442025016764713 ,.57399095266662844091] 
dist 65=[-1.9139296930984699492 ,-.11795988705801319213] 
dist 66=[-2.0276914188801174755 ,-.2613297219382765179 ] 
dist 67=[-2.1135977031798306360 ,-1.0079439792748311634 ] 
dist 68=[-2.1841707813197081725 ,-1.1329292486069610099 ] 
dist 69=[-2.4964468571448725890 ,-1.3981477849885580172 ] 
dist 70=[-3.0277639706841793778 ,-1.4437881213888761996 ] 
dist 71=[-3.5323613553537809586 ,-1.6150239583720116998 ] 
dist 72=[-3.8527611093098476342 ,-1.4304826450115251646 ] 
dist 73=[-4.0992577180019613795 ,-1.2138551930372877963 ] 
dist 74=[-4.3089830374166691164 ,-.97437783501404219114] 
dist 75=[-4.4787758647099456907 ,-.67293607838436974976] 
dist 76=[-4.5659414935953422271 ,-.20910387941254319503] 
dist 77=[-4.6092040888770142854 ,.2581090981942561489 ] 
dist 78=[-4.6120674483103969993 ,.57305580622699840031] 
dist 79=[-.73328027342731992701,.86519707430962190573] 
dist 80=[-.68095040230665244398,1.3304541580356329612 ] 
dist 81=[-.38541358608524182021,1.7149496725704560806 ] 
dist 82=[-.33210802693001616773,2.0884384827056596836 ] 
dist 83=[-.22112427842989858046,2.4251955410416532596 ] 
dist 84=[-.19200462255319843359,2.6631917439045909808 ] 
dist 85=[.05547760400471284535,2.8738878817931117531 ] 
dist 86=[.09556517258739017524,3.1017686234367141122 ] 
dist 87=[.14605738552917810602,3.3033955125055416396 ] 
dist 88=[.15479291618444379933,3.4093788404185470460 ] 
dist 89=[.14718592687914134443,3.4660961160955472809 ] 
dist 90=[.11516223399485852306,3.4778002130808084310 ] 
dist 91=[.05921111990758899412,3.4518452881888489369 ] 
dist 92=[-.04384801386317994194,3.4347290959859047323 ] 
dist 93=[-.47665267229168401904,3.4135558609714670517 ] 
dist 94=[-.77623769500097605007,3.3938167744921438668 ] 
dist 95=[-1.0340232668832778135 ,2.3588975374129339466 ] 
dist 96=[-1.4248615250797568386 ,2.2372449022358310502 ] 
dist 97=[-1.8277223819306036100 ,1.9516914704276467800 ] 
dist 98=[-2.2159605997975705496 ,1.8859469179726993057 ] 
dist 99=[-2.5638002305630540867 ,1.4829815841098538258 ] 
dist 100=[-2.8055470562474827224 ,1.4044206406527487059 ] 
dist 101=[-3.0152353294550161479 ,1.2521360210050230146 ] 
dist 102=[-3.2352257951790981242 ,1.2120096808131004241 ] 
dist 103=[-3.4285239220749460356 ,.65866633595052450396] 
dist 104=[-3.5317570236140980591 ,.57898895881429201084] 
dist 105=[-3.5885389106039303072 ,.40872954729536085302] 
dist 106=[-3.5981686060326611553 ,.41627365300814500911] 
dist 107=[-3.5843609262343106172 ,.59117028688199128955] 
dist 108=[-3.5654184825179411159 ,1.1869509264669753152 ] 
dist 109=[-3.5264217628690394054 ,1.7806604716162433132 ] 
dist 110=[-3.5060641241977373923 ,2.1645271332552565062 ] 
dist 111=[-2.5711095592054371614 ,2.4671046063527770340 ] 
dist 112=[-2.5439106246036962256 ,2.7366234758977515094 ] 
dist 113=[-2.3387037040045441319 ,2.9633432590864148028 ] 
dist 114=[-2.2894170236699580091 ,3.0952335396288550793 ] 
dist 115=[-2.2099217030864734083 ,3.1825554686289718877 ] 
dist 116=[-2.1842708832363053204 ,3.2315330704181131194 ] 
dist 117=[-1.5780198186020954150 ,3.2600923578059977173 ] 
dist 118=[-1.4930254898697974375 ,3.2659825274607116430 ] 
dist 119=[-1.2985397093697360085 ,3.2563907537016598111 ] 
dist 120=[-1.2494967511519855844 ,3.2445737004478801501 ] 
dist 121=[-.98947423805666289605,3.1775085975266247997 ] 
dist 122=[-.93884640384744113345,3.1108964955924025772 ] 
dist 123=[-.83022989697467482902,2.7395680096818925686 ] 
dist 124=[-.79905546935661706492,2.7446768370131787920 ] 
dist 125=[.20564569601096953646,2.7470093382410822600 ] 
dist 126=[.27550059175113880182,2.7367400184051210035 ] 
dist 127=[.43287290407399008045,.7812392481609379991 ] 
dist 128=[.23224606942384307601,.61871210260122976469] 
dist 129=[-.06985191435203352345,.65460514498599334637] 
dist 130=[-.3874078683106960312 ,.71546917398251163407] 
dist 131=[-.68947109354397886395,.76466755608704721517] 
dist 132=[-.92978284807284291239,.81059933364946074147] 
dist 133=[-1.1701862120958389118 ,.85022639917832479794] 
dist 134=[-1.4726153287467163976 ,.87428126993900949072] 
dist 135=[-1.7605161218760752863 ,.89146343340186351061] 
dist 136=[-1.9429790363951759366 ,.9036822468461799831 ] 
dist 137=[-2.0826275397857838296 ,.91173082339317203819] 
dist 138=[-2.1997795231690804025 ,.91228211677669976328] 
dist 139=[-2.2930990032177095838 ,.9081614093667706233 ] 
dist 140=[-2.3377007199421998427 ,.90449739133901360399] 
dist 141=[-2.3572151609701308690 ,.3229706977206923722 ] 
dist 142=[-2.3575947366732554798 ,.27246165250425764749] 
dist 143=[-.09402435708107312901,.34833330897390202534] 
dist 144=[-.19938431161444315436,.58237665487195454162] 
dist 145=[-.29874041057080405896,.77777433557361324772] 
dist 146=[-.37636372694243098485,.97071509748791612572] 
dist 147=[-.45270447448359703534,1.1466262585621740766 ] 
dist 148=[-.54694543602748032638,1.2741084174315298446 ] 
dist 149=[-.63577712194672377973,1.3901594301810169473 ] 
dist 150=[-.6905452878392759008 ,1.5204822602707078788 ] 
dist 151=[-.73069002974110758795,1.6372903204246986855 ] 
dist 152=[-.76120260255797036482,1.6994432133649944041 ] 
dist 153=[-.78372910621005397905,1.7341479488218458248 ] 
dist 154=[-.7920249424087226851 ,1.7417152357270395553 ] 
dist 155=[-.7942019957995248277 ,1.7315196225747876378 ] 
dist 156=[-.79232647607138573719,1.7271792939760407580 ] 
dist 157=[.08052325092976389367,1.7229948442223527630 ] 
dist 158=[-.17298190199108909048,1.7179460867608082937 ] 
dist 159=[-.54293266539950758087,1.2782351409707896500 ] 
dist 160=[-.78892244464434450559,1.2230288058222639910 ] 
dist 161=[-.99050447929470303987,1.0910897322711554188 ] 
dist 162=[-1.1833533683073705190 ,1.0602224096609306758 ] 
dist 163=[-1.3551461477958150320 ,.86424925872659409594] 
dist 164=[-1.4727546390558454967 ,.82512135109933078998] 
dist 165=[-1.5728540303782480129 ,.75126134745262428589] 
dist 166=[-1.6748190784113510218 ,.73185935419710165797] 
dist 167=[-1.7634225675769162671 ,.69683461870227981171] 
dist 168=[-1.8102349014922042765 ,.70592054710580535676] 
dist 169=[-1.8352656530026698040 ,.71007843883490876078] 
dist 170=[-1.8386631129299382557 ,.70959054058213797271] 
dist 171=[-1.8285612167360781298 ,.70568119927661477115] 
dist 172=[-1.8188216699747411983 ,.70292216833103883386] 
dist 173=[-1.7937310945600807604 ,.5979355178160716449 ] 
dist 174=[-1.7807732224254792984 ,.58204334077236817914] 
dist 175=[-.50468805233345397326,.54202556741896190529] 
dist 176=[-.57949633040630305148,.65532657158396945367] 
dist 177=[-.6446564806897466186 ,.86940531351113465442] 
dist 178=[-.68667791756444492632,1.0738004639286467851 ] 
dist 179=[-.71967539711005878444,1.2556035143459540704 ] 
dist 180=[-.74884722884341205202,1.3795830435732568227 ] 
dist 181=[-.77263816265002473222,1.4845889216244499278 ] 
dist 182=[-.78417617232227070568,1.5907234475316796339 ] 
dist 183=[-.78891529053274485787,1.6838686130230754699 ] 
dist 184=[-.78838821804779412788,1.7370718139210412416 ] 
dist 185=[-.7783484206969921656 ,1.7710525633854466204 ] 
dist 186=[-.77371785538424638395,1.7875369388827414890 ] 
dist 187=[-.75677514890250892916,1.7920292164798630364 ] 
dist 188=[-.75037970081896576963,1.7895843776268544931 ] 
dist 189=[.03312141947267468185,1.7616389350285227489 ] 
dist 190=[.04461175647203822458,1.7553604086017149235 ] 
dist 191=[-.04926644059783592197,.88634340844621466928] 
dist 192=[-.2899156228808199224 ,.80222682858997004783] 
dist 193=[-.49325706320713614576,.61055481596856792656] 
dist 194=[-.69801145309678527984,.62994405809878784147] 
dist 195=[-.88727462188194151472,.68207204883575921155] 
dist 196=[-1.0288357604771708038 ,.7375956633495267095 ] 
dist 197=[-1.1621516917847836406 ,.78685660735917193618] 
dist 198=[-1.3185322804547745657 ,.81400853878545867122] 
dist 199=[-1.4618861387712885394 ,.83008697831439842545] 
dist 200=[-1.5432503627697880107 ,.83518590395083473732] 
dist 201=[-1.5945538241563729006 ,.83512908354651775533] 
dist 202=[-1.6180228005235468060 ,.83191169797005709638] 
dist 203=[-1.6300641045760183181 ,.82357005421262378081] 
dist 204=[-1.6357930323544672996 ,.81857260173378815198] 
dist 205=[-1.6379788618823298758 ,.5045088211553873729 ] 
dist 206=[-1.6358899798528834848 ,.47096022636230039318] 
dist 207=[-.34110051584158905716,.39318056658376697263] 
dist 208=[-.43543606016313448599,.52846842162586957614] 
dist 209=[-.52123507832640673337,.71453855859181649744] 
dist 210=[-.58305303519608113317,.90765377190520614795] 
dist 211=[-.63896308266829001566,1.0898286708672441971 ] 
dist 212=[-.70120085567203396061,1.2322679064432766462 ] 
dist 213=[-.75713900637033569651,1.3724622716641282057 ] 
dist 214=[-.78792562665608922682,1.5456844379513525982 ] 
dist 215=[-.8060957052041350547 ,1.7090486406287342934 ] 
dist 216=[-.81171802130737568418,1.8099286103493721521 ] 
dist 217=[-.81232462286850417001,1.8840654547598027319 ] 
dist 218=[-.81049160810265110635,1.9407758032850623844 ] 
dist 219=[-.80652610357821945343,1.9817472294167565135 ] 
dist 220=[-.80249814456131813134,1.9931159150404958682 ] 
dist 221=[-.39974477674972887194,1.9920330460202102727 ] 
dist 222=[-.82184368566268680663,1.9833466158688052040 ] 
dist 223=[-1.2427092576871194952 ,1.9017647885564067349 ] 
dist 224=[-1.5151437864763888411 ,1.8807516433646946816 ] 
dist 225=[-1.7302339383959488666 ,1.8180274180453336403 ] 
dist 226=[-1.9224052727123683963 ,1.7983334311766147775 ] 
dist 227=[-2.0844594383224689778 ,1.6497190632626104015 ] 
dist 228=[-2.1794397676985115491 ,1.6142391656412790443 ] 
dist 229=[-2.2432029534352239567 ,1.5569351209885734530 ] 
dist 230=[-2.2807605035150979944 ,1.5385562359519315461 ] 
dist 231=[-2.3037808970752067129 ,1.1062677738191175153 ] 
dist 232=[-2.3095686696278521326 ,1.1034815547191235384 ] 
dist 233=[-2.3038261168748323233 ,1.1361546490179661190 ] 
dist 234=[-2.2958338693964818862 ,1.1524795049994174997 ] 
dist 235=[-2.2486734227617968296 ,1.1599086792075970301 ] 
dist 236=[-2.2329594711155051978 ,1.1585784620901572991 ] 
dist 237=[-2.1686286751231669894 ,1.1487865307655978197 ] 
dist 238=[-2.1564824131171420231 ,1.1427717800433417791 ] 
dist 239=[-1.0733098306563322618 ,1.1194787422674840965 ] 
dist 240=[-1.1790427019917409769 ,1.1104480201885859192 ] 
dist 241=[-1.2667136046673138978 ,1.0363017412423057653 ] 
dist 242=[-1.3153450406473610756 ,1.0173550334802593045 ] 
dist 243=[-1.3445528712411089804 ,.9889064766731154738 ] 
dist 244=[-1.3547607884934603482 ,.9785295412763187599 ] 
dist 245=[-1.3567706454734460989 ,.71992852947286705857] 
dist 246=[-1.3532839166200073260 ,.68345948455185944392] 
dist 247=[-1.3451138566487186388 ,.60220639556781503939] 
dist 248=[-1.3388592970320573675 ,.57908336525324999429] 
dist 249=[-1.3076535784902148463 ,.47592120883559314946] 
dist 250=[-1.2972249621415330856 ,.46532939607465094302] 
dist 251=[-1.2609995263834871028 ,.45640218041345658991] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 0, 0, 0, 0, 0, 1] 
dist 0=[62.718435134264675948  ,62.718435134264675948  ] 
dist 1=[61.163713292188706011  ,63.499128107178447095  ] 
dist 2=[59.462362807630232247  ,63.916009167185412583  ] 
dist 3=[58.096137253386169850  ,64.018594765901351946  ] 
dist 4=[56.712846286851870789  ,63.960476209779698681  ] 
dist 5=[54.942950860030945468  ,63.493117958418264587  ] 
dist 6=[53.057242689914862943  ,63.364044314697472666  ] 
dist 7=[51.211255916487681748  ,63.292561308467635629  ] 
dist 8=[49.037670266791340374  ,63.095536895203160993  ] 
dist 9=[45.843505926997086985  ,56.493217263750378584  ] 
dist 10=[42.552874537365807971  ,55.540141635182613288  ] 
dist 11=[39.993849824177740345  ,53.858990041604472400  ] 
dist 12=[37.475167234209929317  ,53.433374956469798200  ] 
dist 13=[34.345245988412885999  ,52.078357197376564053  ] 
dist 14=[31.052426177245833592  ,51.649881806194183127  ] 
dist 15=[27.882849285184447472  ,51.410469644136285391  ] 
dist 16=[22.743749173717253117  ,51.164613180937369774  ] 
dist 17=[18.090157399709188859  ,35.750698898874635383  ] 
dist 18=[13.426268342951929852  ,20.193351849242138690  ] 
dist 19=[9.8229464993676490990 ,14.843418289638087661  ] 
dist 20=[6.5329864026893723295 ,13.998232326197251776  ] 
dist 21=[3.7028683765757975059 ,7.2046948719523919071 ] 
dist 22=[.95012760920222429117,6.0311483529937706792 ] 
dist 23=[-2.4224734072080031535 ,4.2666314685391757199 ] 
dist 24=[-5.6138114219070564235 ,3.8302052465035859671 ] 
dist 25=[-7.6427583788144554663 ,-.42286560890624001331] 
dist 26=[-9.2115747606708156925 ,-3.7141538126810724384 ] 
dist 27=[-10.565697998187165527  ,-4.7994732403434165984 ] 
dist 28=[-11.680288294658035016  ,-5.5440644783220238539 ] 
dist 29=[-12.292700535194059954  ,-5.6845212352850399539 ] 
dist 30=[-12.655268764569027407  ,-5.6163291838727152733 ] 
dist 31=[-12.772289094898105277  ,-5.2437468350631465814 ] 
dist 32=[-12.857604358015122739  ,-4.5822759797327088265 ] 
dist 33=[-12.917425422863472599  ,-3.3615565430036419648 ] 
dist 34=[-4.3674117937041894762 ,-2.0880976347197416787 ] 
dist 35=[-3.6256566969069947325 ,-1.2159111429398392760 ] 
dist 36=[-3.5120955342065418257 ,-.47560518272871700477] 
dist 37=[-2.3780641935461207500 ,.27263553775747004545] 
dist 38=[-2.1701056325985618718 ,.96441390767993830814] 
dist 39=[-1.9548888401659436100 ,1.4798882612328228873 ] 
dist 40=[-1.8365505354952418491 ,1.9629343844660704086 ] 
dist 41=[-.38194812905441681264,2.5256959447036060007 ] 
dist 42=[-.06620355083507619095,3.0472496185896176488 ] 
dist 43=[.05207072570726858393,3.3660609341864246179 ] 
dist 44=[.31789469515724215481,3.5966546060578254663 ] 
dist 45=[.36508829579805583603,3.7664023452963583683 ] 
dist 46=[.35710032340908268965,3.8885873348305570226 ] 
dist 47=[.27381852353634075307,3.9295180706904880454 ] 
dist 48=[.17183345903318083156,3.9356549204994094528 ] 
dist 49=[.08931398003108057206,3.9190095654738126611 ] 
dist 50=[.00727116740585004405,2.4662104552265431893 ] 
dist 51=[-.09309587609861525686,2.3178849891306217822 ] 
dist 52=[-.43316524838320622824,2.1513716074059380543 ] 
dist 53=[-.82860259537016979429,2.1334979798265417683 ] 
dist 54=[-1.1974872438565096099 ,2.1136236843760414927 ] 
dist 55=[-1.4773456538368604073 ,2.0999894071732017664 ] 
dist 56=[-1.7441375503498892116 ,1.6854051316857446211 ] 
dist 57=[-2.0609719038547673042 ,1.6272293825453490005 ] 
dist 58=[-2.3532602061417758654 ,1.4974880782208482083 ] 
dist 59=[-2.5222243176935963412 ,1.4596458661152122818 ] 
dist 60=[-2.6323940646380341621 ,1.2980705183530875077 ] 
dist 61=[-2.6903343475068268810 ,1.2666557231798532103 ] 
dist 62=[-2.7245329617454341696 ,1.1867299627159997086 ] 
dist 63=[-2.7400659399899337059 ,1.1731112142644094182 ] 
dist 64=[-2.7448136680962612024 ,.70034227571618358712] 
dist 65=[-2.7360109166671550538 ,0                     ] 
dist 66=[-1.2641308481253813477 ,.18183735583720408277] 
dist 67=[-1.4438456735737430962 ,.49176299054401542469] 
dist 68=[-1.5960501864915870454 ,.74773880238719154942] 
dist 69=[-1.6872890446517287824 ,.99557601701221673062] 
dist 70=[-1.7513981206434832587 ,1.2180083863500025325 ] 
dist 71=[-1.7953892433318948916 ,1.3726917509896162786 ] 
dist 72=[-1.8274825015895186453 ,1.5067407630057723916 ] 
dist 73=[-1.8441188195413901235 ,1.6468969760453915073 ] 
dist 74=[-1.8527837717149314599 ,1.7724496524140910891 ] 
dist 75=[-1.8530366703802730529 ,1.8482725020042523787 ] 
dist 76=[-1.8480422708716007049 ,1.9018565860181993825 ] 
dist 77=[-1.8399023835497760368 ,1.9387447819324053488 ] 
dist 78=[-1.8193184001724361946 ,1.9618542414285152791 ] 
dist 79=[-1.8082542453986381646 ,1.9639847479815348154 ] 
dist 80=[-1.2112925722076860507 ,1.9506328316205835975 ] 
dist 81=[-.50454510042991138511,1.9398107975854075697 ] 
dist 82=[-.27125520885848052021,.88821184312997787016] 
dist 83=[-.22217559787060036189,.79136235617404586978] 
dist 84=[-.30496393592532522641,.7580019040531099919 ] 
dist 85=[-.52708594626842371826,.91428537571037518772] 
dist 86=[-.73508678512104455924,1.0656992350533956470 ] 
dist 87=[-.89499411635261038207,1.2496445704368852950 ] 
dist 88=[-1.0497455868027285453 ,1.4219007883249429712 ] 
dist 89=[-1.2371800980958012227 ,1.5266910023111117554 ] 
dist 90=[-1.4118842823313865440 ,1.6019461311100912902 ] 
dist 91=[-1.5158697483534738653 ,1.6563874311938667742 ] 
dist 92=[-1.5875947068709656888 ,1.6952128585255183478 ] 
dist 93=[-1.6336561496830041377 ,1.7081739595718689347 ] 
dist 94=[-1.6651371919671434517 ,1.7096068663138416261 ] 
dist 95=[-1.6787237020027894666 ,1.7035173443935318577 ] 
dist 96=[-1.6817429679060538310 ,1.1423387166576068839 ] 
dist 97=[-1.6776025784254516795 ,-.02890550939485843252] 
dist 98=[-.41793798413786553057,.08914789038555080963] 
dist 99=[-.50380933479534739352,.17047732269540234691] 
dist 100=[-.57875125328826857508,.24021726241841241206] 
dist 101=[-.62741301744527387717,.31205470780127693635] 
dist 102=[-.67277109548262186235,.37945585067899421568] 
dist 103=[-.72918494817519531372,.43150504833595657589] 
dist 104=[-.79163690739939773315,.48210648734805097511] 
dist 105=[-.84723034649494684364,.5437345748929845727 ] 
dist 106=[-.87628989466112956873,.60137759113992631616] 
dist 107=[-.89220924278670137771,.63608793670722459062] 
dist 108=[-.89538908284390767953,.6605361686610004848 ] 
dist 109=[-.88686852212248843147,.67725724880231851712] 
dist 110=[-.8836219227083489741 ,.68814559571495048855] 
dist 111=[-.88074325380900011035,.69009202239181615535] 
dist 112=[-.87762785097888108254,.68721167742300071138] 
dist 113=[-.64805152647673344814,.68490774289413094338] 
dist 114=[-.61937995444765843368,.62961613375655985634] 
dist 115=[-.55123078990311330951,.61912172988730743426] 
dist 116=[-.53522368216936277991,.61549532796568319057] 
dist 117=[-.43528072654135696912,.70375125326338210121] 
dist 118=[-.41539356078176987359,.76403637320400096533] 
dist 119=[-.37745237627554607648,.81521485774918192371] 
dist 120=[-.36741356162472253635,.86715345409890413904] 
dist 121=[-.21575437832959547864,.91219224907135908969] 
dist 122=[-.19429197514166731266,.93585302045791209899] 
dist 123=[-.14579620213870386894,.94832752789836275378] 
dist 124=[-.13513459260146175438,.95002145997055540375] 
dist 125=[-.07485291894428897553,.94400525025519329928] 
dist 126=[-.06393351348063849874,.93882108730708347214] 
dist 127=[-.04115295117985860824,.92583389057848121467] 
dist 128=[-.07132547416251303318,.9192234140342802532 ] 
dist 129=[-.20657544554497509275,-.09313665944768083518] 
dist 130=[-.34166945495696047452,-.14226943497340023627] 
dist 131=[-.45214159308483099282,-.15009336829919076898] 
dist 132=[-.55744264814607366008,-.20471373439142091148] 
dist 133=[-.65099207554970356025,-.21314288352627413989] 
dist 134=[-.71459760718374174171,-.22861254459221529207] 
dist 135=[-.76826798397665162328,-.2314060126854649438 ] 
dist 136=[-.82219522131455559492,-.24447786564460898436] 
dist 137=[-.86944059833116832231,-.24212746045176773572] 
dist 138=[-.89646297963617589574,-.2343280346590987488 ] 
dist 139=[-.91377122064805536668,-.21708464022879590233] 
dist 140=[-.92227523997372318264,-.19515624373661857402] 
dist 141=[-.92458877837114660859,-.16867190826259447952] 
dist 142=[-.92342741547329487948,-.13385643716240278497] 
dist 143=[-.90856859829504129125,-.07870180642105650499] 
dist 144=[-.90585838531776998203,-.02261661404757887044] 
dist 145=[-.45013787506561267044,.01842605489549340820] 
dist 146=[-.40629700852379578444,.142450501078477657  ] 
dist 147=[-.30651876923514153067,.24733075470591963398] 
dist 148=[-.28517797163567291122,.35307599922743301456] 
dist 149=[-.15912720384334941579,.45090950804354152166] 
dist 150=[-.13627853365720135625,.52423710745232611031] 
dist 151=[-.09007687676111316797,.59344401174713420746] 
dist 152=[-.07826457022884424975,.67484395239980737849] 
dist 153=[.03556643199996927585,.74958091703757020426] 
dist 154=[.04892736042162611695,.79221525395147541368] 
dist 155=[.04689451160505376992,.81937709713634298084] 
dist 156=[.04215100220980263657,.83240817487004190857] 
dist 157=[.03378105665326414516,.83943382435006915852] 
dist 158=[.02117679357202962009,.84264534051990282942] 
dist 159=[-.00045384514230782551,.84366914831872083446] 
dist 160=[-.04551836377588908036,.84196980765224941284] 
dist 161=[-.1601395522119590852 ,-.02989600825119708481] 
dist 162=[-.27058066349049468762,-.04591135046676139670] 
dist 163=[-.36564157563642162951,-.04900228498957464839] 
dist 164=[-.4641772701822089602 ,-.06484743175669249957] 
dist 165=[-.5570541046573592231 ,-.06747112334012802449] 
dist 166=[-.62954699702814600374,-.07140359849955216990] 
dist 167=[-.70077980771048151336,-.07183332655144092952] 
dist 168=[-.78863134027222836462,-.07101447554460791361] 
dist 169=[-.87140343443641958572,-.05621529456524937325] 
dist 170=[-.92237899550658597647,-.03396051240898679067] 
dist 171=[-.95967812243669556963,-.00812565082355740156] 
dist 172=[-.98790737308121878565,.02924807117545863359] 
dist 173=[-1.0080482379431678993 ,.07104230223564592296] 
dist 174=[-1.0130901563179929141 ,.11450656815031772719] 
dist 175=[-1.0121015742479344048 ,.19685549128569664805] 
dist 176=[-1.0081922832736072408 ,.41162900253123514547] 
dist 177=[-.96297393422771503401,.6258130078182276678 ] 
dist 178=[-.95183385869719903382,.76453641467836103191] 
dist 179=[-.91898232691189676769,.87414838215388270339] 
dist 180=[-.90879523119855306216,.97223349162747775927] 
dist 181=[-.83238213927441007343,1.0550566975842320210 ] 
dist 182=[-.81423237169832070316,1.1038028998625139751 ] 
dist 183=[-.78475407879236170974,1.1367819085776142264 ] 
dist 184=[-.77539445028362982944,1.1567242172439726274 ] 
dist 185=[-.55633688743018149896,1.1692614156680466933 ] 
dist 186=[-.52570649209572543324,1.1727082094747860190 ] 
dist 187=[-.45526268632698211237,1.1701469453431532898 ] 
dist 188=[-.43798618894591705942,1.1662052505131422717 ] 
dist 189=[-.3430525570239306327 ,1.1425208123902110807 ] 
dist 190=[-.32464703010323933734,1.1346322501259813133 ] 
dist 191=[-.28608667226648036057,1.1018576681155660056 ] 
dist 192=[-.27526609005401113951,1.0959402598080187469 ] 
dist 193=[-.11297760482585611583,.00159677533804071655] 
dist 194=[-.15054136678236803644,.00316959831567179834] 
dist 195=[-.18717217578167342138,.00586724349832568161] 
dist 196=[-.22026978194418399762,.00907148567828268662] 
dist 197=[-.2437428304468554562 ,.01266466137876611132] 
dist 198=[-.26459274795452308457,.01722019744627414433] 
dist 199=[-.28722908694019381353,.02426241272900945748] 
dist 200=[-.30738801805919521603,.03160302955273562184] 
dist 201=[-.31835782063658119088,.03734861927492343644] 
dist 202=[-.32466576164392191968,.04300933297152080078] 
dist 203=[-.32623278524260802042,.05001146735247388006] 
dist 204=[-.32585880500543918967,.05731465955656436313] 
dist 205=[-.32442585266574330998,.06417602389735403387] 
dist 206=[-.32194708497627008452,.07200757702348419852] 
dist 207=[-.32035814992439814332,.08317997292070949957] 
dist 208=[-.29604956026335908544,.09395572903087646499] 
dist 209=[-.19946257889836942615,.1135305225832430463 ] 
dist 210=[-.17098056154450766481,.15111417374616463288] 
dist 211=[-.16456746574097912278,.18774790812722178006] 
dist 212=[-.12501041363038767942,.22083726583351959161] 
dist 213=[-.11740088365230089172,.24428564278747218229] 
dist 214=[-.1099512807920461694 ,.2650941829424945842 ] 
dist 215=[-.11004279020964045477,.28765564960961480647] 
dist 216=[-.09058443793244693941,.30774002442363249439] 
dist 217=[-.08771722258602646239,.31866971122332175576] 
dist 218=[-.08280717607691735618,.32495517790307224202] 
dist 219=[-.08146234707787889008,.32651800421678079941] 
dist 220=[-.07732422300441099953,.32613783559060277176] 
dist 221=[-.07593839725495591023,.32467447159820125899] 
dist 222=[-.07509795828259775877,.32214181255906294535] 
dist 223=[-.07478577548612488589,.32055920633937983023] 
dist 224=[-.06833084471795045096,.26493631006734534943] 
dist 225=[-.11608865447590191867,.00314203536797623003] 
dist 226=[-.15778630835700890864,.00727969620441884387] 
dist 227=[-.20194489974146674197,.01481715430664881688] 
dist 228=[-.24414796143291734843,.02393536024827415124] 
dist 229=[-.27804679704027677083,.03437717755572989643] 
dist 230=[-.3122554243081348563 ,.04775737891764591700] 
dist 231=[-.35569396163018125607,.06859410943401009247] 
dist 232=[-.39723968724482424164,.09037448640507107276] 
dist 233=[-.423899620662113919  ,.10751803010142809207] 
dist 234=[-.44468382347415879709,.12449804564857578099] 
dist 235=[-.46279663622925632115,.1456262594312415616 ] 
dist 236=[-.47774233847736951095,.16772758057491539376] 
dist 237=[-.4858958354265608146 ,.18858843137945628644] 
dist 238=[-.49061196266379287016,.21247429961804790288] 
dist 239=[-.49184914224662140063,.24663964755896267533] 
dist 240=[-.49074214820602729969,.34696118773065566823] 
dist 241=[-.48900599700305692196,.41162390831208015438] 
dist 242=[-.48087677639336911349,.46201388694322746734] 
dist 243=[-.47737653554087430543,.50588982503717713112] 
dist 244=[-.44765232876097452528,.54206625310423624092] 
dist 245=[-.43986875331212350591,.56174993287890207944] 
dist 246=[-.42848539854493016234,.57306543766273174623] 
dist 247=[-.42414303567163041222,.57586887441051232613] 
dist 248=[-.31398916353742829416,.57524300402430719143] 
dist 249=[-.29841883919191874828,.57288214106024745194] 
dist 250=[-.26402853186505798266,.56880534876297446941] 
dist 251=[-.25393058178222707318,.56595546063269774256] 
dist 252=[-.22779472099735073978,.55228562414002163767] 
dist 253=[-.22371811391882673278,.54771382248532422423] 
dist 254=[-.22135746160781669223,.53256754727629004092] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 0, 2, 0, 1] 
dist 0=[67.824662600219493008  ,67.824662600219493008  ] 
dist 1=[67.170810376957111103  ,68.276067251318673370  ] 
dist 2=[66.068020567330137318  ,68.570102875105606198  ] 
dist 3=[64.624934889003622594  ,68.708265901975377048  ] 
dist 4=[62.612372506287322925  ,68.672181246828145841  ] 
dist 5=[59.793716947257732072  ,68.288510205337412646  ] 
dist 6=[55.132543976774180444  ,68.115423376267586296  ] 
dist 7=[50.323135247564140982  ,66.255756790036889027  ] 
dist 8=[46.912724280683585226  ,65.771897309635399671  ] 
dist 9=[43.869626305655076046  ,65.013657106493117855  ] 
dist 10=[40.526691903237930612  ,64.740644927973482945  ] 
dist 11=[37.241424395137464782  ,63.818788759289716366  ] 
dist 12=[34.428479593842786791  ,63.492579230114617531  ] 
dist 13=[28.505340627386162323  ,62.884478765562260581  ] 
dist 14=[23.370984470644221354  ,62.340015439599591875  ] 
dist 15=[19.057149899840339875  ,36.610125748566753346  ] 
dist 16=[14.730560994371107506  ,34.375792827566277867  ] 
dist 17=[10.721270512702030829  ,29.104917405593404660  ] 
dist 18=[7.6734005468109011254 ,28.289431570272736753  ] 
dist 19=[4.7407907867115384653 ,21.157299471530813125  ] 
dist 20=[1.1903621912687253001 ,19.884547222047397674  ] 
dist 21=[-2.1554670817611345717 ,18.140954049639244970  ] 
dist 22=[-4.2719384909016396652 ,17.686365987982820115  ] 
dist 23=[-5.9011439723785603032 ,8.8774429218200909293 ] 
dist 24=[-7.3023933507333414063 ,7.8170513525711423759 ] 
dist 25=[-8.4629332125319915763 ,5.4364571937038370259 ] 
dist 26=[-9.1322838942098071546 ,5.0810624029587317586 ] 
dist 27=[-9.5816574858288155227 ,2.3396675674936925658 ] 
dist 28=[-10.662785466679807951  ,1.9031152539118413189 ] 
dist 29=[-11.712255321512076640  ,1.2056730879926180656 ] 
dist 30=[-12.840796458160595974  ,1.0647257166611623690 ] 
dist 31=[-13.839733385833990787  ,-1.5179323227044857144 ] 
dist 32=[-14.371673532568925698  ,-1.8080952236201392239 ] 
dist 33=[-14.668434668091830188  ,-2.3008353927311760547 ] 
dist 34=[-14.737693717167360661  ,-2.3964210917813565474 ] 
dist 35=[-14.688880159701767788  ,-2.5346738245564178168 ] 
dist 36=[-14.657757045051099056  ,-2.4661247323408139859 ] 
dist 37=[-14.620837590389122049  ,-2.2884405083141548317 ] 
dist 38=[-14.567642360068838784  ,.40019382300524066994] 
dist 39=[-12.324368551167527612  ,3.3932030028917276544 ] 
dist 40=[-12.295183620892252743  ,5.3729185214985465379 ] 
dist 41=[-12.103960420267173203  ,6.9847859503155544488 ] 
dist 42=[-12.070313964287548557  ,8.5107231832683986825 ] 
dist 43=[-11.356810197469676030  ,9.8605747597239872174 ] 
dist 44=[-11.186703041457906229  ,10.770163895649401539  ] 
dist 45=[-11.050588346455807836  ,11.529644977241710700  ] 
dist 46=[-11.003045045952781870  ,12.280832928622317501  ] 
dist 47=[-3.9196429613744735883 ,12.936466109533868181  ] 
dist 48=[-3.5562454238878322130 ,13.314762817993377560  ] 
dist 49=[-2.6666045731558717132 ,13.561667078041224141  ] 
dist 50=[-2.5385798188758832421 ,13.693017415308371294  ] 
dist 51=[-1.2355984581615995515 ,13.739365676767581699  ] 
dist 52=[-.99829080280106664417,13.726207597786732579  ] 
dist 53=[-.7154593308825117604 ,13.532170449660313708  ] 
dist 54=[-.66623408386647251425,13.488645558132223262  ] 
dist 55=[1.2172193619269037294 ,5.6030589447849208010 ] 
dist 56=[1.4365118834312175725 ,5.7660118466770602527 ] 
dist 57=[1.2783653939872729103 ,5.8906748866633024928 ] 
dist 58=[.81408283811849181463,5.9425075593875808322 ] 
dist 59=[.22579469409927121787,5.9559987990578468877 ] 
dist 60=[-.68398291465160461786,5.9483356817413331722 ] 
dist 61=[-1.7165707845065965298 ,4.6139349756836278491 ] 
dist 62=[-2.4039498476202165193 ,4.6024623656995499547 ] 
dist 63=[-2.9687216369808533926 ,3.2893500354877585912 ] 
dist 64=[-3.5125796575855607811 ,3.3591267775011609493 ] 
dist 65=[-4.0004270251671955084 ,3.3942223301536162863 ] 
dist 66=[-4.3417734538879691595 ,3.3973325781962923928 ] 
dist 67=[-4.6407751913837518384 ,3.3707931882818107549 ] 
dist 68=[-4.9597296709092077967 ,3.3529522363248443677 ] 
dist 69=[-5.2382958648636726997 ,3.3000716902960413104 ] 
dist 70=[-5.3761843749020765523 ,3.2733755353148974393 ] 
dist 71=[-5.4472658975257531406 ,1.8557381204472092473 ] 
dist 72=[-5.4592323422888406794 ,1.7089341884592462844 ] 
dist 73=[-5.3595442245020839397 ,1.3740977904215622944 ] 
dist 74=[-5.3263963737384792126 ,1.2997675074823317645 ] 
dist 75=[-5.2999899808430568916 ,.86889111621675767794] 
dist 76=[-5.2760097656559161519 ,.78907148987212290513] 
dist 77=[-4.4856145296728061616 ,1.8443609496079594960 ] 
dist 78=[-4.4882343300917674627 ,2.6229202404694691947 ] 
dist 79=[-3.2474060608890155593 ,3.2586806251354812212 ] 
dist 80=[-3.2644441012142600607 ,3.8635054180729314759 ] 
dist 81=[-3.3392617633687649576 ,4.4003614772149453207 ] 
dist 82=[-3.3600362707405427642 ,4.7650504344415185711 ] 
dist 83=[-3.3608473277987695200 ,5.0726402575826919253 ] 
dist 84=[-3.3560372362819004852 ,5.3817890782310668089 ] 
dist 85=[-3.3462296996624541939 ,5.6484799105075522512 ] 
dist 86=[-3.3285191564967489381 ,5.7867290466121043447 ] 
dist 87=[-.87549195565230110346,5.8571541004518979487 ] 
dist 88=[-.80977879398743232711,5.8665746142636928147 ] 
dist 89=[-.47794046736068147586,5.8187172274916012709 ] 
dist 90=[-.417530292451668806  ,5.7847632843832236081 ] 
dist 91=[-.28088100114772205355,5.7035466371972578792 ] 
dist 92=[-.25168034537213190864,5.6634611530279123082 ] 
dist 93=[-1.3099741378106815297 ,3.3028451807241277704 ] 
dist 94=[-2.1345377875638502396 ,3.4972418998395502453 ] 
dist 95=[-2.7987391095382923190 ,3.8770302109965318875 ] 
dist 96=[-3.4150925384225413852 ,4.1157430034943969340 ] 
dist 97=[-3.9514335758799673726 ,4.2961662175450138034 ] 
dist 98=[-4.2965355424902686254 ,4.4434815275390099659 ] 
dist 99=[-4.5667024722047502291 ,4.5577377560910502539 ] 
dist 100=[-4.8041963908686858527 ,4.6063127239161285343 ] 
dist 101=[-5.0055957432720138349 ,4.6171122785477899904 ] 
dist 102=[-5.1318102474511594314 ,4.6108044105505407306 ] 
dist 103=[-5.2268002935305881188 ,4.5121426618160982927 ] 
dist 104=[-5.3036613926343450060 ,4.4783617258704749530 ] 
dist 105=[-5.3627479400514671808 ,4.3648391161644877921 ] 
dist 106=[-5.3868439805451277518 ,4.3251593993379784859 ] 
dist 107=[-5.3898595235426794091 ,4.0110601464731925613 ] 
dist 108=[-5.3697404418286543498 ,3.9330964311034210917 ] 
dist 109=[-3.4013426520662754161 ,3.8125088819174100970 ] 
dist 110=[-3.3828943656161766970 ,3.7707722442163409822 ] 
dist 111=[-2.3484006693666865334 ,2.7538366901654959619 ] 
dist 112=[-2.2962330164380873981 ,2.6108175035812063053 ] 
dist 113=[-2.2083495404874216699 ,2.2888482687733123451 ] 
dist 114=[-2.1817384516131466578 ,2.2014387310608705824 ] 
dist 115=[-2.0918993273663073431 ,2.3155357460164927198 ] 
dist 116=[-2.0618218059620851748 ,2.5344702631358254061 ] 
dist 117=[-2.0195631453660812220 ,2.7153803688689924486 ] 
dist 118=[-2.0016463745186612749 ,2.8909719633590680314 ] 
dist 119=[1.1294115663794020434 ,3.0435960173179855662 ] 
dist 120=[1.0326545059738280128 ,3.1329087201202101127 ] 
dist 121=[.89144857776423838054,3.1992164183859832193 ] 
dist 122=[.6986770317512084524 ,3.2734484349048963331 ] 
dist 123=[.43178824165028039267,3.3115966263657339722 ] 
dist 124=[-.00500701988909161680,3.3153525281964543797 ] 
dist 125=[-.47593420138245177329,3.2044310016361680802 ] 
dist 126=[-.79235774183197676046,3.1842565483773183429 ] 
dist 127=[-1.0552899185813421367 ,1.3846250037103785218 ] 
dist 128=[-1.3128885129770944603 ,1.2190880210063536225 ] 
dist 129=[-1.5464363590314678709 ,.84514393702348864792] 
dist 130=[-1.7134519641106531506 ,.76633059914205546512] 
dist 131=[-1.8632353878855123052 ,.30694959005542740967] 
dist 132=[-2.0280599827449026716 ,.22527783362338529946] 
dist 133=[-2.1751963423338571997 ,.05778184009517375761] 
dist 134=[-2.2544373017057865355 ,.01518316662797297434] 
dist 135=[-2.4701111487628299687 ,-.34313657936718565502] 
dist 136=[-2.6396539495678501624 ,-.40104213640240610413] 
dist 137=[-2.7559392933525786599 ,-.45553694299880273203] 
dist 138=[-2.8294557121125029472 ,-.44622347343790850165] 
dist 139=[-2.8786490869416658611 ,-.38383333842698694836] 
dist 140=[-2.8979311863805191561 ,.09653270239934959474] 
dist 141=[-2.8989428420130726212 ,.58048946393081523261] 
dist 142=[-2.8917619447792670278 ,.90381778836015423433] 
dist 143=[-1.3059778807834321829 ,1.1704667197125983750 ] 
dist 144=[-1.2623776501410552028 ,1.4283811478802993268 ] 
dist 145=[-.99063719132128063687,1.6600294880765212914 ] 
dist 146=[-.93759866396610188751,1.8219270493940292620 ] 
dist 147=[-.83584158770795989466,1.9632669200074353112 ] 
dist 148=[-.80927476342513878696,2.1129296028117425143 ] 
dist 149=[-.43038107242864268876,2.2449746934866920540 ] 
dist 150=[-.37624976371891268533,2.4814762085087812815 ] 
dist 151=[-.26020452139933233009,2.7265941866667347482 ] 
dist 152=[-.23023306511526845344,2.8736482385663426159 ] 
dist 153=[-.10739725444584406591,2.9766073416467930258 ] 
dist 154=[-.08426895044429211107,3.0458705909557169063 ] 
dist 155=[-.03546279102649916290,3.0896644833322589556 ] 
dist 156=[-.02300850179183370123,3.0969941452013639152 ] 
dist 157=[-.49678642478777240871,3.0790818462009953571 ] 
dist 158=[-1.0753370614207232581 ,3.0696240318223548436 ] 
dist 159=[-1.7340323741996332478 ,2.8249812878882229257 ] 
dist 160=[-2.1629171074576679670 ,2.7779788333200878079 ] 
dist 161=[-2.5043539129844726142 ,2.6503081982463512523 ] 
dist 162=[-2.8142994389245465048 ,2.6142771311451491073 ] 
dist 163=[-3.0791878810717543874 ,2.3566201796727998112 ] 
dist 164=[-3.2409332168067604465 ,2.2980500106872313326 ] 
dist 165=[-3.3576331590356509651 ,2.1983474962925377049 ] 
dist 166=[-3.4428767916401673256 ,2.1693372007977311700 ] 
dist 167=[-3.5051449608047372403 ,1.5213396132410681641 ] 
dist 168=[-3.5302167688520683577 ,1.4313405674258134720 ] 
dist 169=[-3.5327729173424417180 ,1.2192060984493378026 ] 
dist 170=[-3.5242657756125978763 ,1.1734705710679223227 ] 
dist 171=[-3.4615885764072099871 ,.87510993862204853234] 
dist 172=[-3.4394588363345835575 ,.81795642646143092266] 
dist 173=[-3.3445765243572780473 ,.71126486916965099544] 
dist 174=[-3.3270190418656138069 ,.68466991440387079996] 
dist 175=[-.61525256945986208572,.57412121058795464698] 
dist 176=[-.56197621440543898258,.95271737869217740572] 
dist 177=[-.25025866609406378515,1.2595864543263965782 ] 
dist 178=[-.19458535988306137255,1.5475282209349580735 ] 
dist 179=[-.08083820003563549852,1.8002472268959358129 ] 
dist 180=[-.05188731222102883032,1.9666449438439424225 ] 
dist 181=[.20040877061545441147,2.1011948903018991695 ] 
dist 182=[.24077653342282785601,2.2269022928707438038 ] 
dist 183=[.28284219304545698239,2.3352948673748088991 ] 
dist 184=[.2808115487603262309 ,2.4007918032959116796 ] 
dist 185=[.25983346765717122943,2.4472210761685351308 ] 
dist 186=[.21198127712286815611,2.4795701645833415450 ] 
dist 187=[.13542256672949594932,2.5002816263287043290 ] 
dist 188=[-4.14441425985868902000e-05,2.5002990399188103481 ] 
dist 189=[-.35974106220374136189,2.4881497451108322236 ] 
dist 190=[-.60717124621419630118,2.4771517880241438686 ] 
dist 191=[-.81901955533557379383,.9011193777381467371 ] 
dist 192=[-1.0368272639400454065 ,.76353553544756406478] 
dist 193=[-1.2410194916259988003 ,.45487584415729747777] 
dist 194=[-1.3985681083762316733 ,.39078096156223483561] 
dist 195=[-1.5516613807649492795 ,.02173996770032521877] 
dist 196=[-1.7380853213431757940 ,-.04256860646733389769] 
dist 197=[-1.9125465799247217581 ,-.17632276061129046551] 
dist 198=[-2.0179316587437967306 ,-.2090242581538609713 ] 
dist 199=[-2.0925950097665767131 ,-.2639012018597149497 ] 
dist 200=[-2.1445353990435019367 ,-.18976562690146489791] 
dist 201=[-2.1780981932995050867 ,-.10391900215474574964] 
dist 202=[-2.1847194727106074584 ,-.01054666865853826299] 
dist 203=[-2.1715713538242448423 ,.1059442461837966236 ] 
dist 204=[-2.1681617711053016232 ,.31761684049971004472] 
dist 205=[-2.0144101196336470373 ,.6137008572087117363 ] 
dist 206=[-1.9501144282038669327 ,.80845174006569541151] 
dist 207=[-1.0388751159586100904 ,.96570594922378569085] 
dist 208=[-1.0185951701551221730 ,1.1122500508306496003 ] 
dist 209=[-.88304771038530142512,1.2401757259737824544 ] 
dist 210=[-.85431741615310573826,1.3231780718323977675 ] 
dist 211=[-.80229473055329361114,1.3889283814753724521 ] 
dist 212=[-.78839640666682025107,1.4480514747213497558 ] 
dist 213=[-.51925524710614358484,1.4966711489358132039 ] 
dist 214=[-.48242776766376515135,1.5205329316881665315 ] 
dist 215=[-.39094281651069268146,1.5307607485846347731 ] 
dist 216=[-.37679672952370459869,1.5300803858839251417 ] 
dist 217=[-.23708263848903590912,1.5115706117889111643 ] 
dist 218=[-.21488032452571139811,1.5026599064551099382 ] 
dist 219=[-.18645527470808452232,1.4708488412360508172 ] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 1, 1, 2, 0, 1] 
dist 0=[74.278137789990491751  ,74.278137789990491751  ] 
dist 1=[73.415242163551594008  ,74.746838628943988951  ] 
dist 2=[71.789442409719334352  ,74.799584761178325015  ] 
dist 3=[69.726130851466724577  ,74.629838435800338593  ] 
dist 4=[67.116975961762119170  ,74.484892439676053591  ] 
dist 5=[63.608382304164043697  ,73.781229227490483538  ] 
dist 6=[57.954764835152180594  ,73.573338209376957099  ] 
dist 7=[52.167038614507592187  ,71.053589583918552006  ] 
dist 8=[48.122898550187802748  ,70.413134011724165474  ] 
dist 9=[44.580307454857857339  ,69.769952231862099593  ] 
dist 10=[40.793961085087451610  ,69.473439730275323349  ] 
dist 11=[37.137566020963977007  ,69.227739476419951006  ] 
dist 12=[34.113122721268056819  ,68.986677248395816149  ] 
dist 13=[30.968717650887857170  ,68.806295797571256317  ] 
dist 14=[26.832421088870651134  ,67.485321419892319698  ] 
dist 15=[22.774336883673001016  ,32.245419617353718226  ] 
dist 16=[19.941573287029461841  ,29.345432338191038355  ] 
dist 17=[15.478902656872498891  ,22.545605611891923705  ] 
dist 18=[11.882124224047937758  ,21.523367910316953238  ] 
dist 19=[8.3275036975835587267 ,15.674063529417277065  ] 
dist 20=[3.8982865150264760749 ,15.179047389119118891  ] 
dist 21=[-.32280572973654127627,14.450219523947951735  ] 
dist 22=[-3.0465655922761025831 ,14.278961712135167683  ] 
dist 23=[-5.1962896518885600927 ,2.4514013793287874343 ] 
dist 24=[-7.1259473228470799718 ,1.4798245353462745793 ] 
dist 25=[-8.7672781069291744713 ,-.58986275411016383998] 
dist 26=[-9.7660671504681196516 ,-.97399512725730520891] 
dist 27=[-10.626044151508368419  ,-3.0460814344617335415 ] 
dist 28=[-11.298652628860082280  ,-3.3775697086536202542 ] 
dist 29=[-11.681408991087206184  ,-4.0284157957829296912 ] 
dist 30=[-11.770484135109853980  ,-4.1466820602934384133 ] 
dist 31=[-8.8498047043378675468 ,-4.5452117704592650844 ] 
dist 32=[-9.4352040848916223187 ,-4.5178131333735094261 ] 
dist 33=[-9.8672207168998011662 ,-4.3384781484668825722 ] 
dist 34=[-10.208786645118661118  ,-3.9115665867408609446 ] 
dist 35=[-10.470360526794149721  ,-3.3635231870397398251 ] 
dist 36=[-10.582451425030736537  ,-2.7002202590638837134 ] 
dist 37=[-10.621399064854750807  ,-1.8282554169521989271 ] 
dist 38=[-10.609681330385292724  ,-.44710249528755666833] 
dist 39=[-4.2168317427341102899 ,1.1659070543455936325 ] 
dist 40=[-4.1522258608735556957 ,2.2439899298229827952 ] 
dist 41=[-3.8967479279368308505 ,3.1345456999660598065 ] 
dist 42=[-3.8401278573750719655 ,3.9998166697614768691 ] 
dist 43=[-3.7162479274006477472 ,4.7811127208633223350 ] 
dist 44=[-3.6768927970820530211 ,5.3367735058245678704 ] 
dist 45=[-3.4969831700817614234 ,5.8330513220720570674 ] 
dist 46=[-3.4530038284413475442 ,6.3775864975536285990 ] 
dist 47=[-3.3617844206712919113 ,6.8620900670161658756 ] 
dist 48=[-3.3304055617498711701 ,7.1189025433006670497 ] 
dist 49=[-3.1766166118751887877 ,7.2610819407496810210 ] 
dist 50=[-3.1392225547949366136 ,7.2921832358432987813 ] 
dist 51=[-3.0318067382632399522 ,7.2500723903797749996 ] 
dist 52=[-3.0018418574717662475 ,7.2286207737598897431 ] 
dist 53=[-2.6065258615652146320 ,7.2054657373541295611 ] 
dist 54=[-2.5388327074782280714 ,7.1742697058436562611 ] 
dist 55=[-2.3529537895723488651 ,6.1709306172010909223 ] 
dist 56=[-3.0803326164503308964 ,6.1257738340419134742 ] 
dist 57=[-3.9094295741215542186 ,5.8789398266422765259 ] 
dist 58=[-4.7012043471988041334 ,5.8178271416116974408 ] 
dist 59=[-5.4057221458565173794 ,5.6138146610615126114 ] 
dist 60=[-5.8868590429947445811 ,5.5759341297267195648 ] 
dist 61=[-6.2952605992124466679 ,3.9172015581160298975 ] 
dist 62=[-6.7097413816188804562 ,3.8975219836771875060 ] 
dist 63=[-7.0697238193630606036 ,1.7175479195150032187 ] 
dist 64=[-7.2607798510337499852 ,1.5399064005006786972 ] 
dist 65=[-7.3643080515584376724 ,1.1303172811540678799 ] 
dist 66=[-7.3780794075351964272 ,1.0491916745024361911 ] 
dist 67=[-7.3445080752796640471 ,.5175820145918884672 ] 
dist 68=[-7.3071688177753770510 ,.42149355189901424118] 
dist 69=[-7.2054639933920968440 ,.24128998655595835495] 
dist 70=[-7.1520955430743904868 ,.19892862624579384765] 
dist 71=[-6.4392608655187506362 ,1.5033798893792049958 ] 
dist 72=[-6.4918387373717698863 ,2.5428119005126435034 ] 
dist 73=[-6.5122032895360079388 ,3.3875095940653524795 ] 
dist 74=[-6.4994041106281761302 ,4.1837603585813007668 ] 
dist 75=[-6.4301742283036194294 ,4.8850951933592000257 ] 
dist 76=[-6.3835348924608009830 ,5.3512686255989647525 ] 
dist 77=[-3.6847421912066423035 ,5.7331122287774863474 ] 
dist 78=[-3.6855997752941385375 ,6.0981419870577452363 ] 
dist 79=[-1.4789172256883419587 ,6.4148369620761250548 ] 
dist 80=[-1.3167799281095369531 ,6.6039186171355926166 ] 
dist 81=[-.38538718302488013165,6.7352048300906626741 ] 
dist 82=[-.22144333111766094189,6.8214012017985354850 ] 
dist 83=[.11887878929323253439,6.8717341968814424888 ] 
dist 84=[.20566390014484983698,6.8656301279956468014 ] 
dist 85=[.86840912827517688561,6.8201512293258248458 ] 
dist 86=[.94206117188682912215,6.7802043465873208288 ] 
dist 87=[.66802854776863506457,5.5274575780986191405 ] 
dist 88=[-.22850805276002197289,5.6891852015390921727 ] 
dist 89=[-.99667539000192708113,5.8003246842714282394 ] 
dist 90=[-1.7873289239342003372 ,5.8419254045737345159 ] 
dist 91=[-2.5290970989159910605 ,5.8418752237007063693 ] 
dist 92=[-3.1023066557360089700 ,5.8294372743552098414 ] 
dist 93=[-3.6601407113369050158 ,3.2775507638122202182 ] 
dist 94=[-4.3405906397196012441 ,3.2875018050708187587 ] 
dist 95=[-4.9779561625376345060 ,-.50804358323064273448] 
dist 96=[-5.3639659126072951091 ,-.6632765540569712416 ] 
dist 97=[-5.6386584306914829793 ,-.99734065469518463464] 
dist 98=[-5.8320807888490743753 ,-1.0613038461036102709 ] 
dist 99=[-5.9698017355793226508 ,-.92156937747362066215] 
dist 100=[-6.0223518940859885451 ,-.72458374367898682466] 
dist 101=[-6.0295616258964437917 ,-.45216838316122332877] 
dist 102=[-6.0152288343730931466 ,-.00664337352364250370] 
dist 103=[-2.4122695217739704679 ,.522788644015229579  ] 
dist 104=[-2.4224450577151086932 ,.87947071911636545818] 
dist 105=[-2.4102681550504567665 ,1.1737553027221710744 ] 
dist 106=[-2.4016604147067905933 ,1.4586034941156739288 ] 
dist 107=[-2.3907181015554666745 ,1.7145700817603824889 ] 
dist 108=[-2.3767542353146245072 ,1.8936733395450542302 ] 
dist 109=[-2.2341742422957379290 ,2.0502505952069361162 ] 
dist 110=[-2.2227640114988951639 ,2.2163826285745237018 ] 
dist 111=[-1.4722890284320428174 ,2.3637424116982056939 ] 
dist 112=[-1.3879129845127326084 ,2.4454540036971589882 ] 
dist 113=[-1.1908393469473834608 ,2.4944888813430988532 ] 
dist 114=[-1.1462783971738700793 ,2.5115291346384977292 ] 
dist 115=[-.9354512523881455372 ,2.5128230500133680215 ] 
dist 116=[-.90792630037904580755,2.5041391185419325420 ] 
dist 117=[-.71865460471546335567,2.4778441794891971663 ] 
dist 118=[-.69198073276385506777,2.4617221670176960844 ] 
dist 119=[-.46120466607029684282,2.1600499104834834668 ] 
dist 120=[-.76665813839684896545,2.2345702233160485724 ] 
dist 121=[-1.0196792693575197380 ,2.2770351609886759838 ] 
dist 122=[-1.2662504416646206179 ,2.2866830926594006295 ] 
dist 123=[-1.4889265357550873838 ,2.2829132740946869717 ] 
dist 124=[-1.6466522294807221072 ,2.2718651787681524724 ] 
dist 125=[-1.7865460105462568619 ,2.2534072000283244409 ] 
dist 126=[-1.9381069980220089588 ,2.2422737949136312669 ] 
dist 127=[-2.0729941115609290631 ,.32457299944235866149] 
dist 128=[-2.1463911905855517911 ,.27451038307512867903] 
dist 129=[-2.1885901587227764079 ,.17179981402307047083] 
dist 130=[-2.1990568427160052973 ,.14525999239395236208] 
dist 131=[-2.1964374272982450325 ,.05068219698241207632] 
dist 132=[-2.1864480448513216804 ,.03098410077107927780] 
dist 133=[-2.1691768500980607248 ,.00495499660584326649] 
dist 134=[-2.1585383079917468787 ,-.00067123396749299048] 
dist 135=[-1.9622863481907806230 ,.4544843135189667111 ] 
dist 136=[-2.0191054675402876944 ,.75536564418834908152] 
dist 137=[-2.0579866072954471781 ,.99998588453893128734] 
dist 138=[-2.0823905279211430673 ,1.2307679123131944123 ] 
dist 139=[-2.0955409281628478518 ,1.4341740859014633645 ] 
dist 140=[-2.0933595582843172773 ,1.5696171524024363904 ] 
dist 141=[-2.0760064173397061169 ,1.6808210728436549088 ] 
dist 142=[-2.0622839431848887671 ,1.7875595106917337926 ] 
dist 143=[-.84226617484832842381,1.8801775720807343427 ] 
dist 144=[-.73218403053447646256,1.9350682675301558210 ] 
dist 145=[-.48417296740084490688,1.9726763782633790949 ] 
dist 146=[-.43220668676559419739,1.9963700906197516935 ] 
dist 147=[-.13068651465961093784,2.0092256190133432220 ] 
dist 148=[-.07748839248552774027,2.0072152189672612280 ] 
dist 149=[.03218699391041791250,1.9907163127158856437 ] 
dist 150=[.06001202673676419215,1.9775801571535700507 ] 
dist 151=[.16041304217741242724,1.5498674278600606148 ] 
dist 152=[-.10307428722790144467,1.6649855710335467058 ] 
dist 153=[-.32844255984567789652,1.7459714302795920619 ] 
dist 154=[-.55978644681822214585,1.8012074624943856500 ] 
dist 155=[-.77644073348045860127,1.8398264224352488261 ] 
dist 156=[-.94322564251931712988,1.8545417419101944517 ] 
dist 157=[-1.1049339099130887080 ,1.8555609082569483925 ] 
dist 158=[-1.3013421132235347017 ,1.8515206428260201782 ] 
dist 159=[-1.4848921510787855518 ,-.15550496611428305644] 
dist 160=[-1.5953209756445359732 ,-.20798592035390049212] 
dist 161=[-1.6730162146296561045 ,-.32077151837646570516] 
dist 162=[-1.7260219765502591145 ,-.3176259481320884146 ] 
dist 163=[-1.7630912961667734544 ,-.2866565844927270992 ] 
dist 164=[-1.7772306756015216614 ,-.23073168593477961162] 
dist 165=[-1.7782275146440845565 ,-.14598328451961351216] 
dist 166=[-1.7743652689759926002 ,-6.17870447418148390000e-05] 
dist 167=[-1.6680985890168537107 ,.30774900950682516127] 
dist 168=[-1.7543096515466243821 ,.51862255219870767633] 
dist 169=[-1.8131319825684685484 ,.69825639583595930994] 
dist 170=[-1.8497039928316297478 ,.88148438096378188324] 
dist 171=[-1.8715771700342488012 ,1.0523465490729935822 ] 
dist 172=[-1.8734763694361615170 ,1.1826644697654813044 ] 
dist 173=[-1.8636159343927991357 ,1.3078596083756002630 ] 
dist 174=[-1.8522071768125918794 ,1.4582916888761642308 ] 
dist 175=[-1.6708293732076839199 ,1.5980564983994572064 ] 
dist 176=[-1.6383487951594238864 ,1.6807096597627947743 ] 
dist 177=[-1.5526041773891681912 ,1.7371178090174723885 ] 
dist 178=[-1.5292857092679352078 ,1.7722152945660665865 ] 
dist 179=[-1.3659279003712852105 ,1.8156394360456191038 ] 
dist 180=[-1.3295416233578195718 ,1.9174350892630013113 ] 
dist 181=[-1.2662509835421472989 ,1.9929900495680184170 ] 
dist 182=[-1.2485831113560586563 ,2.0521698084140236661 ] 
dist 183=[-.95063612854713185694,2.0973526709745660973 ] 
dist 184=[-1.2005057404327805813 ,2.1170868116573671674 ] 
dist 185=[-1.4001882567763460789 ,2.1219027971675265057 ] 
dist 186=[-1.5827572366472115279 ,2.1178738870704265965 ] 
dist 187=[-1.7397081081544563950 ,2.0833399356070493511 ] 
dist 188=[-1.8372234351587276227 ,2.0702923607245562805 ] 
dist 189=[-1.9095941161607350614 ,2.0166461169944980449 ] 
dist 190=[-1.9662660048198440126 ,2.0041503310318332912 ] 
dist 191=[-2.0095282321481137203 ,.82766226233793880468] 
dist 192=[-2.0284200456844851228 ,.77659843592252787329] 
dist 193=[-2.0330245067571400791 ,.65463995390723859744] 
dist 194=[-2.0291598860242094619 ,.63025323532181695562] 
dist 195=[-1.9960681599563094641 ,.45495960500426256401] 
dist 196=[-1.9835679961517103054 ,.42158373972055699087] 
dist 197=[-1.9321526844173976124 ,.36345469818570166762] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 2, 1, 0, 1] 
dist 0=[75.253026147816764850  ,75.253026147816764850  ] 
dist 1=[74.746838628943988953  ,75.326767983416383852  ] 
dist 2=[73.827171016682208108  ,75.253026147816764850  ] 
dist 3=[72.103397867319498133  ,75.028136800754066504  ] 
dist 4=[69.926173086883568088  ,74.419797640604338830  ] 
dist 5=[67.196623917753713012  ,74.118900158196398242  ] 
dist 6=[63.539785492824990356  ,72.062731019732221066  ] 
dist 7=[57.661093477620348870  ,71.453672345916815584  ] 
dist 8=[51.648705531791335153  ,71.130948559605297040  ] 
dist 9=[47.457969157742382822  ,70.574749159558316336  ] 
dist 10=[43.797856592171803397  ,70.307521962890834911  ] 
dist 11=[39.902898851689616858  ,70.092372645674582644  ] 
dist 12=[36.151894844256797698  ,69.891630424744626697  ] 
dist 13=[33.065816511072915329  ,69.485431746949697577  ] 
dist 14=[29.872093706806067356  ,33.585327873050512824  ] 
dist 15=[25.175096098301460908  ,33.293319360899303044  ] 
dist 16=[20.228219097474306403  ,25.293042809288458442  ] 
dist 17=[15.583158805624172555  ,22.408152263734207353  ] 
dist 18=[11.954782606375762271  ,17.758950480443388404  ] 
dist 19=[8.3741785816724073600 ,17.080482468816101608  ] 
dist 20=[3.9200270430701119991 ,14.435359447821937320  ] 
dist 21=[-.32085407390983067634,13.940232510196111243  ] 
dist 22=[-3.0500641061538561783 ,13.197098926293597473  ] 
dist 23=[-5.3795968067050055332 ,13.021495213364215318  ] 
dist 24=[-7.3128432111751004355 ,1.8196490027937642824 ] 
dist 25=[-8.9174558645646657057 ,.89754850014943634912] 
dist 26=[-10.210566214317058418  ,-1.0535230344124111684 ] 
dist 27=[-10.900563374956868889  ,-1.4203020444790320804 ] 
dist 28=[-11.281928299112565396  ,-3.3217821515525440470 ] 
dist 29=[-11.357991382483591202  ,-3.6294183172713755148 ] 
dist 30=[-7.7661922050667862983 ,-4.1989135177660868292 ] 
dist 31=[-8.0035219493181179789 ,-4.3129964914001253570 ] 
dist 32=[-8.8787595291321741656 ,-4.5409054726445604226 ] 
dist 33=[-9.4126504354820749551 ,-4.4659834616199264434 ] 
dist 34=[-9.8040865882091688135 ,-4.2496035020363727417 ] 
dist 35=[-10.109452648844086702  ,-3.7901724116538607817 ] 
dist 36=[-10.340474206207802964  ,-3.2148685153410798372 ] 
dist 37=[-10.434518218053596224  ,-2.4602778849472638799 ] 
dist 38=[-10.463043826937099465  ,-1.6524128301757921943 ] 
dist 39=[-10.447318407026272156  ,-.26376899948571858644] 
dist 40=[-4.4977645161815380969 ,1.3655402292495766089 ] 
dist 41=[-4.1732213505963278389 ,2.4533064255182178096 ] 
dist 42=[-4.1081723713090199937 ,3.3507059133854809024 ] 
dist 43=[-3.9311490193305538570 ,4.2209281521312925941 ] 
dist 44=[-3.9035913536022115449 ,5.0057360547825520956 ] 
dist 45=[-3.5556800456295388746 ,5.5624806931038053241 ] 
dist 46=[-3.4887186838146483971 ,6.0583528594636715808 ] 
dist 47=[-3.3477929628699310861 ,6.6004451352667129979 ] 
dist 48=[-3.3032401722800134282 ,7.0814905358496523006 ] 
dist 49=[-3.0990500998900278838 ,7.3338397681087770106 ] 
dist 50=[-3.0528880806745436412 ,7.4724966953031720733 ] 
dist 51=[-2.9251877999768583201 ,7.5004665219686167940 ] 
dist 52=[-2.8930856404693378501 ,7.4403283077836595466 ] 
dist 53=[-2.4791556372939940079 ,7.4149969912191692128 ] 
dist 54=[-2.4098396824482538938 ,7.3910333127548256141 ] 
dist 55=[-2.2116925495741895060 ,7.3630005295630318309 ] 
dist 56=[-2.2179368852613356534 ,6.4978530607211797094 ] 
dist 57=[-3.2633223899715372171 ,6.2497911668348923996 ] 
dist 58=[-4.1180936958693330486 ,6.1859027343110079353 ] 
dist 59=[-4.9328064130489965941 ,5.9859776060750730017 ] 
dist 60=[-5.6567402898368446043 ,5.9358672142145971046 ] 
dist 61=[-6.1495023667743857922 ,3.9569418196583866620 ] 
dist 62=[-6.5660596754904145329 ,3.1914920207643350209 ] 
dist 63=[-6.9861194083828965461 ,3.1111464117099136028 ] 
dist 64=[-7.3498756611804401613 ,1.8032303291872071612 ] 
dist 65=[-7.5418850547370748778 ,1.6215537123737943198 ] 
dist 66=[-7.6445112213722815500 ,1.2019669564021173405 ] 
dist 67=[-7.6576382801168740388 ,1.1188412086538308208 ] 
dist 68=[-7.6164826076055063350 ,.5712406857116293109 ] 
dist 69=[-7.5767871842294063557 ,.4719380293850812495 ] 
dist 70=[-7.4684030465737694488 ,.28653944216863283815] 
dist 71=[-7.4121792562371452129 ,.24301375230368031392] 
dist 72=[-6.8100116026210711368 ,1.5807421407323655548 ] 
dist 73=[-6.8315539222867719666 ,2.6620944925328336101 ] 
dist 74=[-6.8179593776815666025 ,3.5407865745207207055 ] 
dist 75=[-6.7466624654568004086 ,4.3689843005957485227 ] 
dist 76=[-6.6984886783581151710 ,5.0984119725130941888 ] 
dist 77=[-3.7979435972036160651 ,5.5832081459916170405 ] 
dist 78=[-2.3418456600131231903 ,5.9802618095426415963 ] 
dist 79=[-1.5301968483799974571 ,6.3597738918520337456 ] 
dist 80=[-1.3597204621089323421 ,6.6889239554485045582 ] 
dist 81=[-.3812751058887498398 ,6.8851300146674718463 ] 
dist 82=[-.20919055749800732594,7.0209877713418401470 ] 
dist 83=[.14832510280159764447,7.1094561246726757506 ] 
dist 84=[.23949620624849655468,7.1604078012436336332 ] 
dist 85=[.93040785946889074852,7.1538003211014162930 ] 
dist 86=[1.0456514571484242904 ,7.1042559629539674878 ] 
dist 87=[1.1249204528800546486 ,7.0617126182786210284 ] 
dist 88=[.67336385843219587164,5.9646172172033519704 ] 
dist 89=[-.26176868224157934147,6.0831493323508314583 ] 
dist 90=[-1.0626874715013633475 ,6.1274048106144706252 ] 
dist 91=[-1.8865532220332030124 ,6.1279207671243070432 ] 
dist 92=[-2.6591779735762995990 ,6.1145291732573299667 ] 
dist 93=[-3.2557443019832056278 ,3.3744549080149060824 ] 
dist 94=[-3.8358517686028184784 ,-.19386002809016971721] 
dist 95=[-4.5428378975466910777 ,-.28890420331548145974] 
dist 96=[-5.2047548493342419252 ,-1.0185263890006047935 ] 
dist 97=[-5.6051222297871728860 ,-1.0841394477341997217 ] 
dist 98=[-5.8894176813938196717 ,-1.2085193997838658778 ] 
dist 99=[-6.0884281785762414532 ,-1.1049074300473833258 ] 
dist 100=[-6.2296919339536718666 ,-.95451523110059207509] 
dist 101=[-6.2836874020092751118 ,-.75007279665858521887] 
dist 102=[-6.2905127850110187237 ,-.46749737923826074866] 
dist 103=[-6.2759168058859805659 ,-.00550496456272388428] 
dist 104=[-2.5475284290700587171 ,.54159530340346645642] 
dist 105=[-2.5375540963994996035 ,.91075761419060625378] 
dist 106=[-2.5274972456869285160 ,1.2157301364619877226 ] 
dist 107=[-2.5133125819382635627 ,1.5115726023167238609 ] 
dist 108=[-2.4992882245733940351 ,1.7778515038559749926 ] 
dist 109=[-2.2730838553647309152 ,1.9649229448341200226 ] 
dist 110=[-1.6518628420241258704 ,2.1292551377161994078 ] 
dist 111=[-1.4418506485338886560 ,2.3048490735573200552 ] 
dist 112=[-1.3938493473349282628 ,2.4608141873817656939 ] 
dist 113=[-1.1694969829549040626 ,2.5468645258913035736 ] 
dist 114=[-1.0363126091737252996 ,2.5979320443357111301 ] 
dist 115=[-.92428287150015208756,2.6143803321585616651 ] 
dist 116=[-.89502653280452619821,2.6146598499651805283 ] 
dist 117=[-.70447677862368673415,2.6046258381717207420 ] 
dist 118=[-.4175089691786613493 ,2.5794550091976177518 ] 
dist 119=[-.29205897719232972107,2.5642628504109314712 ] 
dist 120=[-.47517647866841794139,2.3253987013999160707 ] 
dist 121=[-.79131026267817648842,2.3354434105399714239 ] 
dist 122=[-1.0532045006088484755 ,2.3317598928339289865 ] 
dist 123=[-1.3084663376679410041 ,2.3206315588405034275 ] 
dist 124=[-1.5390204424164373724 ,2.3019560614663156452 ] 
dist 125=[-1.7023783075543360788 ,2.2905846327834460172 ] 
dist 126=[-1.8473217913599795770 ,.71816915115875564892] 
dist 127=[-2.0044378821603227660 ,.69149030955908332577] 
dist 128=[-2.1442956948398148435 ,.33338857552843248898] 
dist 129=[-2.2204117987523075256 ,.28163414324987449402] 
dist 130=[-2.2641936601249799508 ,.17561202075164967929] 
dist 131=[-2.2750999559571895374 ,.1482600074560047626 ] 
dist 132=[-2.2724607890366060912 ,.05108270727078036371] 
dist 133=[-2.2622222744847693860 ,.03077384036659827530] 
dist 134=[-2.2444870655405628505 ,.00463683589543889909] 
dist 135=[-2.2334730074523024896 ,-.00056815917299682949] 
dist 136=[-2.0994980428153074322 ,.47014622158873125158] 
dist 137=[-2.1244888109693590729 ,.78129006952310355987] 
dist 138=[-2.1380389047179846093 ,1.0342289220335340919 ] 
dist 139=[-2.1358202551654930711 ,1.2728172837309790718 ] 
dist 140=[-2.1183890351365365174 ,1.4830755769997701536 ] 
dist 141=[-2.1045193925679229111 ,1.6230317648323278756 ] 
dist 142=[-.85688136949618726388,1.7378867643621904080 ] 
dist 143=[-.74441854331380957075,1.8480394266973017679 ] 
dist 144=[-.49107385993016875065,1.9436013313322729853 ] 
dist 145=[-.43800427005419038422,2.0002671799001585750 ] 
dist 146=[-.13014372337835526536,2.0391292706468114427 ] 
dist 147=[-.07584589059802984117,2.0636883248485069115 ] 
dist 148=[.03612299668584273957,2.0770902505073355282 ] 
dist 149=[.06452656584717011632,2.0750109779013056232 ] 
dist 150=[.28938948560203914474,2.0582227225372627801 ] 
dist 151=[.32636788038972909721,2.0447757362599426863 ] 
dist 152=[.16883823181765010074,1.7797220438717142977 ] 
dist 153=[-.10346163752068881382,1.8364460972301181872 ] 
dist 154=[-.33640627509517476773,1.8761732194618134954 ] 
dist 155=[-.57558933148041443285,1.8912945331639504831 ] 
dist 156=[-.79962385367950719941,1.8924328963872618072 ] 
dist 157=[-.97215486128846717285,1.8882584330503543463 ] 
dist 158=[-1.1394958810117439226 ,-.03419886073700328429] 
dist 159=[-1.3428322895348111861 ,-.06178561307729064452] 
dist 160=[-1.5329007616163840847 ,-.28066046061585086246] 
dist 161=[-1.6473281352723007809 ,-.31662944940799596695] 
dist 162=[-1.7279303020418918386 ,-.3437316717559472184 ] 
dist 163=[-1.7831010105537527466 ,-.33049424142282294657] 
dist 164=[-1.8217531569637175585 ,-.29807076198224126996] 
dist 165=[-1.8364779151968977607 ,-.23982835408883777832] 
dist 166=[-1.8376079136181376026 ,-.15169307443809037952] 
dist 167=[-1.8335601738698138708 ,-5.28977707235132240000e-05] 
dist 168=[-1.8446582583590861532 ,.31756171671446322716] 
dist 169=[-1.8815842971046066618 ,.5351204568080025616 ] 
dist 170=[-1.9035968179139982703 ,.72041613337572865695] 
dist 171=[-1.9054002375736679424 ,.90936637371212912622] 
dist 172=[-1.8954213495754516321 ,1.0855313276122822239 ] 
dist 173=[-1.8839064815927995971 ,1.2198382014565376689 ] 
dist 174=[-1.6973728996691757068 ,1.3488121793505703294 ] 
dist 175=[-1.6641340941479018341 ,1.5037090940941925224 ] 
dist 176=[-1.5764976689550454699 ,1.6475836222177246064 ] 
dist 177=[-1.5527048686561761717 ,1.7325993909642683034 ] 
dist 178=[-1.3861841326653642677 ,1.8441926223349663298 ] 
dist 179=[-1.3491294572565355238 ,1.9479227622382940432 ] 
dist 180=[-1.2846097548047800573 ,2.0250161673067562327 ] 
dist 181=[-1.2666347974388018227 ,2.0855897036166089325 ] 
dist 182=[-.87535278511365494825,2.1319228793179389782 ] 
dist 183=[-.82122128965093745439,2.1522245090513913220 ] 
dist 184=[-.97652106998673191153,2.1572881058771618290 ] 
dist 185=[-1.2340519712368885006 ,2.1532471084017924999 ] 
dist 186=[-1.4398985146639280301 ,2.1182959986506469028 ] 
dist 187=[-1.6281742016799217711 ,2.1050433088529031553 ] 
dist 188=[-1.7900808866209397298 ,2.0506728574434449259 ] 
dist 189=[-1.8907656130754927314 ,2.0378693035530316123 ] 
dist 190=[-1.9655949041254300820 ,1.2471360661265026468 ] 
dist 191=[-2.0243879182486270708 ,1.2296864902606091156 ] 
dist 192=[-2.0693587707715134408 ,.84980908530389812171] 
dist 193=[-2.0890641082438033267 ,.79725604019773586283] 
dist 194=[-2.0939798981144013523 ,.67165012818965047234] 
dist 195=[-2.0900566006542414795 ,.64664057238608218712] 
dist 196=[-2.0561365811419379562 ,.4658930793944643271 ] 
dist 197=[-2.0432743737670306790 ,.4314897728196686128 ] 
dist 198=[-1.9904946151610095988 ,.37190127521844970798] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 2, 0, 0, 2] 
dist 0=[62.749797026820359909  ,62.749797026820359909  ] 
dist 1=[61.758761365049321015  ,63.333312311916137103  ] 
dist 2=[59.951212937435345968  ,63.513729439623028430  ] 
dist 3=[57.754456388824074224  ,63.537389574674234355  ] 
dist 4=[55.209442483127483045  ,63.495049345697491439  ] 
dist 5=[51.918572001511410914  ,63.395811665801125244  ] 
dist 6=[46.743882923180064860  ,63.261629802021443338  ] 
dist 7=[41.484096331843400535  ,62.936970812195309255  ] 
dist 8=[37.853350477290483433  ,62.751899867125118565  ] 
dist 9=[34.715737970714918219  ,62.298428775492939414  ] 
dist 10=[31.424514648138073714  ,62.088814231981505397  ] 
dist 11=[28.279951706853411432  ,60.955746960781979384  ] 
dist 12=[25.727569469668474035  ,60.611038631568158257  ] 
dist 13=[23.114991159333088220  ,60.407373258516966178  ] 
dist 14=[19.729442218378202292  ,59.405808058604795364  ] 
dist 15=[16.427872516726134548  ,53.321786239056604104  ] 
dist 16=[14.150253583071525329  ,49.324410705211836753  ] 
dist 17=[12.179989332790810914  ,32.003573705244251456  ] 
dist 18=[10.105211223703781659  ,29.772196085878029960  ] 
dist 19=[8.1120339753204495817 ,24.628900539346888113  ] 
dist 20=[6.4669291266160259793 ,23.769173526473258672  ] 
dist 21=[4.7530639375439563018 ,17.200710556844059512  ] 
dist 22=[2.4838000678224275259 ,16.052405417879025587  ] 
dist 23=[.29462307381230052917,14.209382351412785297  ] 
dist 24=[-1.0995429071652973861 ,13.778885815979609361  ] 
dist 25=[-2.1879241305928831364 ,9.9136827112678818237 ] 
dist 26=[-3.6984788481284717565 ,9.6960645642286345312 ] 
dist 27=[-6.8852888000234365822 ,4.8531741670982083312 ] 
dist 28=[-8.9458269167401484328 ,4.3672993199923150229 ] 
dist 29=[-10.584148297830395951  ,1.3905959666725954748 ] 
dist 30=[-12.084425634745844420  ,.58934997619885785583] 
dist 31=[-13.389760959013725113  ,-.6887184393642585517 ] 
dist 32=[-14.249571718318703694  ,-.9261698899973286873 ] 
dist 33=[-14.953049777356551422  ,-1.3440218172892313430 ] 
dist 34=[-15.634439648519754882  ,-1.4311710101249227496 ] 
dist 35=[-16.201946284843268731  ,-1.6120160754263178779 ] 
dist 36=[-16.450558466566924938  ,-1.5691459830441825077 ] 
dist 37=[-16.561329735405788014  ,-1.4213228204455001691 ] 
dist 38=[-16.577212653718140622  ,-1.0951776723462042357 ] 
dist 39=[-16.496805493644848322  ,-.68163466669012430451] 
dist 40=[-16.488659383739509348  ,-.18449273065494091769] 
dist 41=[-15.968009798157872220  ,.46852464121757334277] 
dist 42=[-15.884105924478206525  ,1.5047172020748001109 ] 
dist 43=[-15.466736370119193515  ,4.1732651393026000724 ] 
dist 44=[-15.321989836343274161  ,6.4327535039512689316 ] 
dist 45=[-14.494836991406808501  ,8.2839692905386086379 ] 
dist 46=[-14.292278862131701579  ,10.058813875098904621  ] 
dist 47=[-13.897210140773822513  ,11.646543082467715720  ] 
dist 48=[-13.772224093012846573  ,12.751349094687675767  ] 
dist 49=[-7.7661911927645694230 ,13.713319798136149596  ] 
dist 50=[-7.1273161302139402870 ,14.731390491866428196  ] 
dist 51=[-5.6869732483790768891 ,15.633192079638650016  ] 
dist 52=[-5.3698885004856384225 ,16.131197861427348260  ] 
dist 53=[-3.5650912507671777673 ,16.428779602011987716  ] 
dist 54=[-3.2327439117208388215 ,16.530489176830536657  ] 
dist 55=[-2.5537855501420929284 ,16.541287270542167674  ] 
dist 56=[-2.3745323225764462598 ,16.487115463104118861  ] 
dist 57=[-.89476613016283207517,16.360468731582821039  ] 
dist 58=[-1.2387009904874327203 ,16.281930754694498814  ] 
dist 59=[-1.5607971614192727502 ,11.108532120341502248  ] 
dist 60=[-1.8085110353933713243 ,10.553033472245350455  ] 
dist 61=[-2.0483986445841166875 ,9.2362438481907940967 ] 
dist 62=[-2.3393169821144868662 ,8.9650045920716136278 ] 
dist 63=[-2.6109946795622073720 ,7.0956782497012773529 ] 
dist 64=[-2.7741651344600219999 ,6.2398051568974385705 ] 
dist 65=[-2.8886640444953466857 ,-.51762437381197304284] 
dist 66=[-2.9662499885395903041 ,-.43170834805214986016] 
dist 67=[-3.3231597503312565097 ,-.32509039427328870787] 
dist 68=[-3.6289903669838774972 ,-.16633209236986550519] 
dist 69=[-3.8627598233170946069 ,.23850612922147767917] 
dist 70=[-4.0588691153594079253 ,.86318754651699367613] 
dist 71=[-4.2154746977284709698 ,1.4889166757099040442 ] 
dist 72=[-4.2916382391265419443 ,1.8979329057933566034 ] 
dist 73=[-4.3242831683581220153 ,2.2252222974455264918 ] 
dist 74=[-4.3265202909825633548 ,2.5250413232516995780 ] 
dist 75=[-2.2494599240914717692 ,2.7830739508371613770 ] 
dist 76=[-2.1895331619018064920 ,2.9437254899732972776 ] 
dist 77=[-2.0926772685297489251 ,3.0632771968309199705 ] 
dist 78=[-2.0632275777215656556 ,3.1574056510324884287 ] 
dist 79=[-1.4062675154085275839 ,3.2298292852815520741 ] 
dist 80=[-1.3161566599842487441 ,3.2628261071265442745 ] 
dist 81=[-1.1059926138553431646 ,3.2731270799333485186 ] 
dist 82=[-1.0602245784527388641 ,3.2668138848584313354 ] 
dist 83=[-.7731356177387702378 ,3.2208401265661421315 ] 
dist 84=[-.71879307676147330713,3.2290101797103905060 ] 
dist 85=[-.61432207042871807626,3.2873621157256733050 ] 
dist 86=[-.5878129136628206437 ,3.2990039146097872354 ] 
dist 87=[-.69531900029815577023,3.2715913293212278402 ] 
dist 88=[-1.1930460037313217018 ,3.2588163119526310579 ] 
dist 89=[-1.6035509374264837278 ,3.2456618508175190045 ] 
dist 90=[-2.0006180698666163962 ,3.2286108078296245954 ] 
dist 91=[-2.3572214883400657438 ,2.3444660733473826128 ] 
dist 92=[-2.6063568700152149605 ,2.2357141773798830305 ] 
dist 93=[-2.8237438693272482678 ,1.9781794972294990924 ] 
dist 94=[-3.0537347066863444572 ,1.9180264128879973214 ] 
dist 95=[-3.2578655313973286775 ,1.5445943337878512486 ] 
dist 96=[-3.3721201413124090701 ,1.4707307751541388037 ] 
dist 97=[-3.4420777558753957080 ,1.3291052990025455109 ] 
dist 98=[-3.4695444485706496955 ,1.2916705422698861591 ] 
dist 99=[-3.4746960390888772278 ,.7412270198586984276 ] 
dist 100=[-3.4646955098115494898 ,.66292630048155772714] 
dist 101=[-3.4267527741685127948 ,.48893187158304085864] 
dist 102=[-3.3355151625080582417 ,.45603174543666853401] 
dist 103=[-2.6515339998036471671 ,.24129964683445294984] 
dist 104=[-2.6492724062537230734 ,.2040544865896227138 ] 
dist 105=[-2.6418313401220736087 ,.12016819932265010003] 
dist 106=[-2.6283000213378817029 ,.10288858350485777703] 
dist 107=[-.18909081814358158989,.53855728053437563773] 
dist 108=[-.22787924141832870795,.88630814153912131087] 
dist 109=[-.26539654044020397186,1.1665294022501116322 ] 
dist 110=[-.31085401672112230293,1.4267089523221058089 ] 
dist 111=[-.35330738456675129613,1.6531882834844558858 ] 
dist 112=[-.3788433681596963434 ,1.7990099592528578080 ] 
dist 113=[-.39681333435831767689,1.9132622597670615828 ] 
dist 114=[-.40909049069219133383,2.0138405707216147900 ] 
dist 115=[-.41764982578380795938,2.0992442689358042201 ] 
dist 116=[-.42079140872077372687,2.1529783918883983148 ] 
dist 117=[-.420938615890378066  ,2.1936572826569043343 ] 
dist 118=[-.41991062009217656536,2.2269937356587565375 ] 
dist 119=[.04057299050873194316,2.2529495697124091358 ] 
dist 120=[.05297960961604641151,2.2641928622913693974 ] 
dist 121=[.07982839338268276393,2.2667829034176797148 ] 
dist 122=[.08484238319683940319,2.2582803614205099989 ] 
dist 123=[.11184834768673412983,.63844367878506127939] 
dist 124=[.11623330677441566768,.50404638939189390378] 
dist 125=[-.04898130739298040550,.3131873463693190022 ] 
dist 126=[-.31090906001282704414,.34822479294174160086] 
dist 127=[-.56016364719819684505,.38070099431546924863] 
dist 128=[-.75863299802346978602,.39978056415938714595] 
dist 129=[-.95733389980057703348,.41264750022873045883] 
dist 130=[-1.2075123444407377750 ,.42034655186215397043] 
dist 131=[-1.4457728320725843006 ,.42479429627269367879] 
dist 132=[-1.5969437475818766488 ,.42498091158032267059] 
dist 133=[-1.7128367635033214440 ,.42271300914006792557] 
dist 134=[-1.8104051122598403890 ,.42023556284219494935] 
dist 135=[-1.8883884063623929600 ,.37594896761491303837] 
dist 136=[-1.9261740581505886532 ,.36826592378486251633] 
dist 137=[-1.9428841117940130113 ,.34817947653067793928] 
dist 138=[-1.9437772958069407511 ,.34276317560690370181] 
dist 139=[-.410033813360367338  ,.30523860232897347069] 
dist 140=[-.43341189458554540543,.47715307509776855719] 
dist 141=[-.4508882304076557757 ,.63720190899643139919] 
dist 142=[-.46480774797420373918,.79508063945027149879] 
dist 143=[-.47553756597951329663,.93892150969194828774] 
dist 144=[-.4802930338697715965 ,1.0429861587978514983 ] 
dist 145=[-.48157034943699471637,1.1375410858656276585 ] 
dist 146=[-.48072667363402065276,1.2434564228001400251 ] 
dist 147=[-.47302334634111500121,1.3383446551743999938 ] 
dist 148=[-.47006254459051090139,1.3889225107205870184 ] 
dist 149=[-.45812455975742734075,1.4171060344819266786 ] 
dist 150=[-.45512423027994010107,1.4233522444531273995 ] 
dist 151=[.00205981059989300259,1.4156963054955366272 ] 
dist 152=[.00214364624634321199,1.4119375312274852916 ] 
dist 153=[.00106545577150429800,1.4079274239387821121 ] 
dist 154=[-.13014639799031260398,1.4025418847353443122 ] 
dist 155=[-.4319260936651115863 ,1.0349879170446816080 ] 
dist 156=[-.63271742340597725507,.989226695849097209  ] 
dist 157=[-.79740389937185314999,.88007557009422379132] 
dist 158=[-.95519436805711952515,.85462780961102653881] 
dist 159=[-1.0959167464325810808 ,.69345842394281709267] 
dist 160=[-1.1925342388711438028 ,.66138019141451251006] 
dist 161=[-1.2750667793397029542 ,.60069729344779198746] 
dist 162=[-1.3596172068601001369 ,.58477168437557033331] 
dist 163=[-1.4332566979340432627 ,.52640985995020755668] 
dist 164=[-1.4722754817958548571 ,.52402381174371004389] 
dist 165=[-1.4932948057095758814 ,.51984323506007206624] 
dist 166=[-1.4962736228003324617 ,.51731873050205317294] 
dist 167=[-1.4886757700921120773 ,.33893306445795211976] 
dist 168=[-1.4808004937032939167 ,.31907951918053048782] 
dist 169=[-1.4610474596796974210 ,.27269601664359920938] 
dist 170=[-1.4508034216349094658 ,.26227378982256387672] 
dist 171=[-.35341395968189686815,.31962807835490421234] 
dist 172=[-.39142569505009130768,.53185023208043776693] 
dist 173=[-.42523727774393790707,.70547317854433461499] 
dist 174=[-.46201923958682350718,.87109489358440059949] 
dist 175=[-.49480283217676709831,1.0183108228436873371 ] 
dist 176=[-.51266857116446880241,1.1185299344301610348 ] 
dist 177=[-.52297695418845242235,1.2032248240912389211 ] 
dist 178=[-.52562113689415179691,1.2885288442809722136 ] 
dist 179=[-.52512415759229375785,1.3633365309360152719 ] 
dist 180=[-.52290530601575480714,1.4061711486436914518 ] 
dist 181=[-.51900694599168208901,1.4336648085436048804 ] 
dist 182=[-.51645164021874970492,1.4472914393646823335 ] 
dist 183=[-.03500659311690820162,1.4511605214291242361 ] 
dist 184=[-.06053424910025742639,1.4494030355996422735 ] 
dist 185=[-.08390817062419770431,1.4262748595731502686 ] 
dist 186=[-.11035907761594604399,1.4219879082753944276 ] 
dist 187=[-.13666846580541699888,.70799730193234217964] 
dist 188=[-.22300876406051894452,.63927820053820879012] 
dist 189=[-.38755387704231949938,.50091458880034662776] 
dist 190=[-.5534765960609320518 ,.57040431674409819769] 
dist 191=[-.70699545435428196926,.63684139187056441043] 
dist 192=[-.82207292027167170246,.67943201053421763908] 
dist 193=[-.93069409693418727259,.71258779019137713893] 
dist 194=[-1.0584647300897363567 ,.7413979202161587328 ] 
dist 195=[-1.1757779885597980278 ,.7651084358466693526 ] 
dist 196=[-1.2426942670347831141 ,.7779265164120954638 ] 
dist 197=[-1.2853162288665514806 ,.7851836613615526643 ] 
dist 198=[-1.3057416851655618025 ,.7867166883514602937 ] 
dist 199=[-1.3167460150657068685 ,.7845003140563350474 ] 
dist 200=[-1.3217957212516676455 ,.7815727569931351311 ] 
dist 201=[-1.3234362772501439792 ,.7682450552707497416 ] 
dist 202=[-1.3208446208688078323 ,.7625842375287992703 ] 
dist 203=[-.8663886762743890448 ,.71471198790660238662] 
dist 204=[-.8980540027192725676 ,.70221271878207509161] 
dist 205=[-.9163546337851820168 ,.68387473646522817415] 
dist 206=[-.9211196774475800561 ,.72786751136921475403] 
dist 207=[-.9203892971159586017 ,.87363514575864774859] 
dist 208=[-.9167737104239511243 ,.98743409686087337246] 
dist 209=[-.9103631580506315923 ,1.0992764564193783319 ] 
dist 210=[-.9058396886942601778 ,1.2372410383072700916 ] 
dist 211=[-.8840482487340606157 ,1.3672422077671496639 ] 
dist 212=[-.8767609313432158118 ,1.4473258028861111454 ] 
dist 213=[-.8524877518144904978 ,1.5059490480593052604 ] 
dist 214=[-.8447807055297554863 ,1.5503645205111408276 ] 
dist 215=[-.11394228373582554895,1.5820938853427469934 ] 
dist 216=[-.18215037846573711409,1.5901238565569791232 ] 
dist 217=[-.30977259247525311401,1.5886415441281102450 ] 
dist 218=[-.64681965253307076011,1.5824351148001674665 ] 
dist 219=[-.98293824262954465154,1.5120027463112288069 ] 
dist 220=[-1.2006274657696384437 ,1.4945838061428001041 ] 
dist 221=[-1.3726235197866512226 ,1.4431577607157671029 ] 
dist 222=[-1.5265138767596458067 ,1.4271943342273080100 ] 
dist 223=[-1.6564455870235365227 ,1.3073711864965889773 ] 
dist 224=[-1.7328925264375367753 ,1.2788976713689751345 ] 
dist 225=[-1.7845806545534439786 ,1.2326801616879603112 ] 
dist 226=[-1.8157721261810504885 ,1.2179906299305415713 ] 
dist 227=[-1.8353435813270886070 ,.87402860615954455219] 
dist 228=[-1.8406900982121425795 ,.82593125706956830087] 
dist 229=[-1.8366260007155943392 ,.71534433974730976894] 
dist 230=[-1.8304239509287077458 ,.68819122424549901938] 
dist 231=[-1.7932189228260926398 ,.53922885228942287731] 
dist 232=[-1.7808254121009406344 ,.5103457106367152686 ] 
dist 233=[-1.7293980813373096218 ,.44976613417120676439] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 0, 0, 0, 1, 2] 
dist 0=[58.316342405798443263  ,58.316342405798443263  ] 
dist 1=[57.260933306173005814  ,59.228306053341253525  ] 
dist 2=[53.961229856280840698  ,60.589715852034904026  ] 
dist 3=[50.525972901994389467  ,61.480979174351123171  ] 
dist 4=[48.027504175986341022  ,62.115906619988310510  ] 
dist 5=[45.737935805247224654  ,62.454369696045250511  ] 
dist 6=[43.136179836078347157  ,62.639747967138940448  ] 
dist 7=[40.533852422070362516  ,62.663987155077568088  ] 
dist 8=[38.241838245465313884  ,58.232308205995784440  ] 
dist 9=[35.738412458895757259  ,57.542721191549467628  ] 
dist 10=[32.292074975009947702  ,56.459191011794983925  ] 
dist 11=[28.849549142655118498  ,56.119191883196181477  ] 
dist 12=[26.361153752496156859  ,55.207664935914516229  ] 
dist 13=[24.094527588411790130  ,54.879070362765880825  ] 
dist 14=[21.536812159633755906  ,54.663635634521250325  ] 
dist 15=[18.985808670436886413  ,54.545734595349095458  ] 
dist 16=[16.745632860242412335  ,26.773406263138861141  ] 
dist 17=[14.301843257989563342  ,24.513084387531047569  ] 
dist 18=[10.937491983991467002  ,23.631692161194027841  ] 
dist 19=[7.6231911775318708943 ,18.501842186860289326  ] 
dist 20=[5.3789172639041577211 ,12.339110997419505156  ] 
dist 21=[3.4849853118367426047 ,11.293547257395955073  ] 
dist 22=[1.5689247115435181110 ,9.5776842722823120532 ] 
dist 23=[-.2206215741704588867 ,9.0040314100082014106 ] 
dist 24=[-2.2811403938788655767 ,6.6342176850941153118 ] 
dist 25=[-4.5323935246474400518 ,5.8498671168272432922 ] 
dist 26=[-6.3535281664213127991 ,5.6805213080491779186 ] 
dist 27=[-8.0728170816436701144 ,3.6171118390161543938 ] 
dist 28=[-9.6059662877581112997 ,3.3312763278760272477 ] 
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dist 39=[-14.293749239875617842  ,2.8429979550300056214 ] 
dist 40=[-11.843495746513019742  ,2.8459656773141134906 ] 
dist 41=[-11.498654071492991306  ,2.8252892939784146002 ] 
dist 42=[-10.818777030271104004  ,2.8070160307058813131 ] 
dist 43=[-10.634016083377519258  ,2.6320127366951859074 ] 
dist 44=[-9.9473435444389463188 ,2.5918616181756071425 ] 
dist 45=[-9.7810435813572331314 ,2.4583581822837620249 ] 
dist 46=[-9.5017708376178444200 ,2.4330319607362142907 ] 
dist 47=[-9.4226779957812745929 ,2.0912908064170762108 ] 
dist 48=[-7.3388731848985992898 ,2.4450959233480584458 ] 
dist 49=[-7.0816094582501481505 ,2.7885220503932873606 ] 
dist 50=[-7.0335239660575961088 ,3.4726122978549652779 ] 
dist 51=[.69901125325382627706,4.7513665336768254483 ] 
dist 52=[.41391373859319148628,5.9309089481513582023 ] 
dist 53=[.16750220237739393373,6.8172686516559314294 ] 
dist 54=[-.08815549349009585935,7.6593536519187770061 ] 
dist 55=[-.32816661061990175494,8.6622566435836258858 ] 
dist 56=[-.51228654301171703404,9.5962927587766914494 ] 
dist 57=[-.68962142116592422712,10.163490507759906221  ] 
dist 58=[-.90265399225836440173,10.571259710136359777  ] 
dist 59=[-1.1018649402835208984 ,10.868843567324670514  ] 
dist 60=[-1.2241309689177197263 ,11.079557136337793230  ] 
dist 61=[-1.3128023117673924266 ,11.140537114375672281  ] 
dist 62=[-1.3781103888466276679 ,11.143168597854281172  ] 
dist 63=[-1.4258404067675714735 ,11.120890265170244318  ] 
dist 64=[-2.2823741769125346124 ,2.5008975545396559540 ] 
dist 65=[-3.2052201879497193872 ,2.3832761429520953253 ] 
dist 66=[-3.9411865973712654484 ,2.1160523704990280311 ] 
dist 67=[-4.6127591562002644387 ,2.0475482178978471113 ] 
dist 68=[-5.1903075911447724612 ,1.6918702902006525790 ] 
dist 69=[-5.5512288420139623631 ,1.6216457672557421867 ] 
dist 70=[-5.8222028057326661178 ,1.4710360256064683119 ] 
dist 71=[-6.0409984283847299375 ,1.4271578045088089432 ] 
dist 72=[-6.2172778558850411712 ,.96777685420575301665] 
dist 73=[-6.3186454320540072753 ,.89618391417133783923] 
dist 74=[-6.3846989683560264841 ,.8456311463348816789 ] 
dist 75=[-6.4200375918140346678 ,.95448689002314698472] 
dist 76=[-6.4331708422676843029 ,1.0183500081432478889 ] 
dist 77=[-6.4137762931890353230 ,1.0610794768574706597 ] 
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dist 79=[-6.3333770320416378006 ,1.1007918787293338723 ] 
dist 80=[-2.1653302671698104026 ,1.1157332239152069974 ] 
dist 81=[-1.8020664042136875039 ,1.7479705397017137362 ] 
dist 82=[-.9929660100945672864 ,2.2619092598217767031 ] 
dist 83=[-.82409331010832019666,2.7468919336012041439 ] 
dist 84=[-.26366068982106286412,3.1746551147721792009 ] 
dist 85=[-.39330895841532832454,3.4603876477281702947 ] 
dist 86=[-.53248171090362281987,3.6961114381279482091 ] 
dist 87=[-.66650867529323759597,4.1293283536685554415 ] 
dist 88=[-.77564137151552501027,4.7413037355785301746 ] 
dist 89=[-.88704814489484562541,5.1161044508393871300 ] 
dist 90=[-1.0301468467545942435 ,5.3881136027293802677 ] 
dist 91=[-1.1676557367931059338 ,5.5900894294099286148 ] 
dist 92=[-1.2567761983342438055 ,5.7368610663315458236 ] 
dist 93=[-1.3272168491442659313 ,5.7886754875701712779 ] 
dist 94=[-1.3902450101838224013 ,5.7989408294865393206 ] 
dist 95=[-1.4434437810085355289 ,5.7799789150104240910 ] 
dist 96=[-1.4746941063699230827 ,1.9832396759365012464 ] 
dist 97=[-1.6985928239339840070 ,1.7689467301126414289 ] 
dist 98=[-2.2552825297446100315 ,1.2838404040796908169 ] 
dist 99=[-2.8155852341208757804 ,1.1806281766203411465 ] 
dist 100=[-3.3334373158161780704 ,1.2422189458093165676 ] 
dist 101=[-3.7208266624332504948 ,1.3917379546643775681 ] 
dist 102=[-4.0857737193731305335 ,1.5215619834772460240 ] 
dist 103=[-4.5141239779213494233 ,1.6282888638098738279 ] 
dist 104=[-4.9070689595283882051 ,1.6856953795466355692 ] 
dist 105=[-5.1308116586194180916 ,1.7177729342432759388 ] 
dist 106=[-5.2728596975861661340 ,1.7245081828706169704 ] 
dist 107=[-5.3399846664326694034 ,1.7190525175626627129 ] 
dist 108=[-5.3701320266291150757 ,1.7106771149785665965 ] 
dist 109=[-5.3647047845980581479 ,1.6978111282042173728 ] 
dist 110=[-5.3343334044885794396 ,1.6888356789287910844 ] 
dist 111=[-5.3122205355148605924 ,1.6488315433173121382 ] 
dist 112=[-4.5364590180630200198 ,2.5082254804180826103 ] 
dist 113=[-4.4180373966514474854 ,3.2648857313296234171 ] 
dist 114=[-4.1196122706038025310 ,3.8741781242904727044 ] 
dist 115=[-4.0432280390478086862 ,4.4391674072994222055 ] 
dist 116=[-3.5309506948535901649 ,4.9304798216761711351 ] 
dist 117=[-3.4213168665370915298 ,5.2459420798318082201 ] 
dist 118=[-3.2235424283537166995 ,5.4921178522688783660 ] 
dist 119=[-3.1704117511671605724 ,5.7071110803940609380 ] 
dist 120=[-2.1189878944917395306 ,5.8813500327867513456 ] 
dist 121=[-1.9745959395269166231 ,5.9649924173345951589 ] 
dist 122=[-1.6185758068197758616 ,5.9980713082718247102 ] 
dist 123=[-1.6296245571852239457 ,5.9932246068143845263 ] 
dist 124=[-1.6750061351296159010 ,5.9137559657993889639 ] 
dist 125=[-1.7079165093009265312 ,5.8782253259876010668 ] 
dist 126=[-1.7322661327585670587 ,5.7471643925764681940 ] 
dist 127=[-1.7491604295457077048 ,5.6997120151328262073 ] 
dist 128=[-2.7054700589941489036 ,4.2520895328493857623 ] 
dist 129=[-3.3320012877577545212 ,4.1940270382419735913 ] 
dist 130=[-3.8285732220646465312 ,4.0296636237142154804 ] 
dist 131=[-4.2755583018970820405 ,3.9808555727406169958 ] 
dist 132=[-4.6548906054430574359 ,3.6230687898036635061 ] 
dist 133=[-4.8816574720738150735 ,3.5397038659833980310 ] 
dist 134=[-5.0394458900250428324 ,3.4013265359995066991 ] 
dist 135=[-5.1436865714855289241 ,3.3590761125467673600 ] 
dist 136=[-5.2144345388751668643 ,2.3895221705846583484 ] 
dist 137=[-5.2386508159674908544 ,2.2542938479017093342 ] 
dist 138=[-5.2333562330447369354 ,1.9400610371430780798 ] 
dist 139=[-5.2177804071956225210 ,1.8668860409858146283 ] 
dist 140=[-5.1164666864394798484 ,1.4354757437436900823 ] 
dist 141=[-5.0828009957313769384 ,1.3820601766509109293 ] 
dist 142=[-4.9344427239814796993 ,1.4451086234761365221 ] 
dist 143=[-4.9124055615365050844 ,1.4923096375293252422 ] 
dist 144=[.25935429240545230136,1.5095310403831788145 ] 
dist 145=[.16253540994692191467,1.5149106899431383531 ] 
dist 146=[.00073861397870703247,1.5148861709152857034 ] 
dist 147=[-.23996078613205436028,1.4378699484943567482 ] 
dist 148=[-.40349776397220403016,1.6674848843600215728 ] 
dist 149=[-.54135419354354159354,1.8153537102131059392 ] 
dist 150=[-.67963823989649242543,1.9312330262590984555 ] 
dist 151=[-.80712054260483300044,2.0332711187421341640 ] 
dist 152=[-.90189872835535072101,2.1199825721153275134 ] 
dist 153=[-.99059435071491801746,2.1747378844888355342 ] 
dist 154=[-1.0938188601633302024 ,2.2164133794260951603 ] 
dist 155=[-1.1880176504974696473 ,2.2509611826407862885 ] 
dist 156=[-1.2407179902722061481 ,2.2781631598627978205 ] 
dist 157=[-1.2729604224381706555 ,2.2905427477718628674 ] 
dist 158=[-1.2855715038658344915 ,2.2944006209782020810 ] 
dist 159=[-1.2897589413338317591 ,2.2876171285960000377 ] 
dist 160=[-1.2884072287333251871 ,.63581630558422120408] 
dist 161=[-1.2827434494645746525 ,.49932359057112635698] 
dist 162=[-1.2769005697711323641 ,.27078512758172760188] 
dist 163=[-1.0569424342987575317 ,.54715428640677298956] 
dist 164=[-1.0251889781107076649 ,.7292433919448292331 ] 
dist 165=[-.94644777083120700783,.87661385987039897996] 
dist 166=[-.95372874820647275916,1.0145221655204151217 ] 
dist 167=[-1.2081605585021994014 ,1.1353051052290539373 ] 
dist 168=[-1.4506576936006011542 ,1.2143781606758958514 ] 
dist 169=[-1.6048201700178943354 ,1.2778115809969753865 ] 
dist 170=[-1.7233534779177073067 ,1.3362223090195142193 ] 
dist 171=[-1.8237583543416356976 ,1.3848020025845261760 ] 
dist 172=[-1.9044741526408388975 ,1.4090284388895676612 ] 
dist 173=[-1.9444856827726430874 ,1.4199857798042777038 ] 
dist 174=[-1.9624904865640018332 ,1.4198369133154174719 ] 
dist 175=[-1.9644254236219050157 ,1.4040692181402175255 ] 
dist 176=[-.17272361265960973807,1.3959155466828281616 ] 
dist 177=[-.1447045363844405456 ,1.3678952228996434789 ] 
dist 178=[-.13969858367991179265,1.3549409991982433996 ] 
dist 179=[-.31433613769974605923,.79394222253832839001] 
dist 180=[-.52428179457724026876,.93718300546838413151] 
dist 181=[-.6972974092288999367 ,1.0405053699900697359 ] 
dist 182=[-.86443417511375827674,1.1340731277580222183 ] 
dist 183=[-1.0144072836960639386 ,1.2384117160736610650 ] 
dist 184=[-1.1189727795775544687 ,1.3318126544442490166 ] 
dist 185=[-1.2099974611426925745 ,1.3817601325841651081 ] 
dist 186=[-1.3059686526900060276 ,1.4094907158153981763 ] 
dist 187=[-1.3909402463241228474 ,1.4158205782701291671 ] 
dist 188=[-1.4380975997193598250 ,1.4094329260835813371 ] 
dist 189=[-1.4664507294354325678 ,1.4053231631610098685 ] 
dist 190=[-1.4764294888274313839 ,1.4002856682404046492 ] 
dist 191=[-1.4771284064652265063 ,1.3926846382448334200 ] 
dist 192=[-1.4722078883345084676 ,1.0124305499068319245 ] 
dist 193=[-1.4557239792016144954 ,.96575972885166886341] 
dist 194=[-1.4456451155885097068 ,.8548151095778575441 ] 
dist 195=[-.85853104507670375694,.82910433655452650238] 
dist 196=[-.79710292541355523044,.66696495030287536838] 
dist 197=[-.77566896010179634631,.63487177838333249064] 
dist 198=[-.85827367689744977615,.57392975930805805522] 
dist 199=[-.95212023244718316025,.55796265147828346576] 
dist 200=[-1.0370756540591013744 ,.39354425990550496705] 
dist 201=[-1.0842217725410020250 ,.41938137920459371993] 
dist 202=[-1.1125652584118974649 ,.44540385462969208927] 
dist 203=[-1.1225341767899994728 ,.46791267967816569813] 
dist 204=[-1.1253329810964937752 ,.47973706488138711101] 
dist 205=[-1.1250814390676355484 ,.48596545642396766494] 
dist 206=[-1.1225483115723417753 ,.48673216474145884557] 
dist 207=[-1.1168588901718584953 ,.48368319351863156113] 
dist 208=[-.03590952607812699438,.48107607935398804852] 
dist 209=[-.02413047674595088225,.47401862529958881929] 
dist 210=[-.02133058201707775816,.48831957679878145465] 
dist 211=[-.10591403159187248822,.59823164185123641871] 
dist 212=[-.1803535775732896334 ,.69396272139130882018] 
dist 213=[-.24577142686887352197,.75568988569027347073] 
dist 214=[-.31571346845240595887,.8041510111489853769 ] 
dist 215=[-.38296060903315762441,.84697600393266349288] 
dist 216=[-.43763096477441193624,.88340504708316541124] 
dist 217=[-.49339848387021527171,.90635858238468808337] 
dist 218=[-.5650212048213758046 ,.92377044148048759154] 
dist 219=[-.6339121480169630149 ,.93809880702889548269] 
dist 220=[-.67878510615434920747,.94929838591833011705] 
dist 221=[-.7145279301413179067 ,.95423237669360938488] 
dist 222=[-.74700712535345920604,.95550763113254262684] 
dist 223=[-.77478805060216552825,.9521158569831671641 ] 
dist 224=[-.7917937763506077954 ,.39404313780971228898] 
dist 225=[-.80411406738741184581,.43200919293840617151] 
dist 226=[-.81320908272620240789,.48515684505411710036] 
dist 227=[-.81842824631635432062,.53599223597735792551] 
dist 228=[-.81793914910845195329,.56473679692197489828] 
dist 229=[-.80964088384157787685,.58272151944293778925] 
dist 230=[-.804836018529414625  ,.59064576218997068591] 
dist 231=[-.76089377760026105457,.59447539046466218102] 
dist 232=[-.74880827402631509463,.59613044349043268203] 
dist 233=[-.73204595438896832519,.59650485216521524178] 
dist 234=[-.72506525595344441249,.59522716298439306805] 
dist 235=[-.54226765905545301242,.48008992547055027385] 
dist 236=[-.52166327532895869868,.46326648855480828781] 
dist 237=[-.49773420539929582268,.43250246413430916134] 
dist 238=[-.4908346780808303822 ,.42432589872951272348] 
dist 239=[-.46869020475265356948,.39587614926849217681] 
dist 240=[-.46121138313456825817,.38761578600851836997] 
dist 241=[-.45374402975141460323,.37820519925536423164] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 2, 1, 0, 1, 0, 1] 
dist 0=[66.276067806529358687  ,66.276067806529358687  ] 
dist 1=[65.695163009955742551  ,66.530098767650131325  ] 
dist 2=[64.635031630126726570  ,66.964337233976567429  ] 
dist 3=[62.946955503097701124  ,67.378458665946869358  ] 
dist 4=[60.471289986358438545  ,67.777228361772067135  ] 
dist 5=[56.267338114174064998  ,68.035131380794113018  ] 
dist 6=[51.893466724514311432  ,68.056565117082745139  ] 
dist 7=[48.739920931138974639  ,67.658191737915325058  ] 
dist 8=[45.873174364649779356  ,67.347672017662007166  ] 
dist 9=[42.645253549742419764  ,65.214970148426930005  ] 
dist 10=[39.431130668031514365  ,64.679669379507816015  ] 
dist 11=[32.081169827389747595  ,63.687096021794262985  ] 
dist 12=[24.458018522891305988  ,63.375174081227380104  ] 
dist 13=[19.414818846470553830  ,62.036214148055470078  ] 
dist 14=[15.297116682630176008  ,61.665098851556807934  ] 
dist 15=[11.367324967857463237  ,59.759733669651809926  ] 
dist 16=[7.8597321970105264244 ,55.529022641840807702  ] 
dist 17=[5.4267140991490494409 ,36.004419350414333913  ] 
dist 18=[3.3142831595163668115 ,33.839198118632752657  ] 
dist 19=[1.0855657576465660250 ,28.685048546215773585  ] 
dist 20=[-.9324103303952447541 ,27.918903695021329914  ] 
dist 21=[-2.2121523580348367176 ,20.806831041736209040  ] 
dist 22=[-3.2091870735340602757 ,19.533097593050193732  ] 
dist 23=[-4.0626477383394419256 ,17.900024687142315849  ] 
dist 24=[-4.7603768858055093385 ,17.551492263207726208  ] 
dist 25=[-6.3852905609687780645 ,8.2351528645400165116 ] 
dist 26=[-8.2283948368772506289 ,7.1310435294378424042 ] 
dist 27=[-9.5201645113593677534 ,4.7256409757480478290 ] 
dist 28=[-10.659142773064973852  ,4.3037705013660442636 ] 
dist 29=[-11.892334086848882298  ,1.7592626251311721586 ] 
dist 30=[-12.994882558108549031  ,1.3638395825486558922 ] 
dist 31=[-13.612219648284191699  ,.5682187274683486702 ] 
dist 32=[-13.995061142438818814  ,.4527938964052848471 ] 
dist 33=[-14.161117872383569316  ,-3.5626273709929039846 ] 
dist 34=[-14.229813517091580484  ,-3.9367145213623973127 ] 
dist 35=[-14.223812767572086640  ,-4.5956329638647522910 ] 
dist 36=[-14.163228111622279430  ,-3.7368024863707367770 ] 
dist 37=[-14.104816017948379392  ,-.9975711309238053226 ] 
dist 38=[-10.074196701336202527  ,1.7690786873733431652 ] 
dist 39=[-10.318064675493966221  ,3.6145341733801320562 ] 
dist 40=[-10.518871158125348664  ,5.1336244716258655734 ] 
dist 41=[-10.671197191896115032  ,6.5987305722300318456 ] 
dist 42=[-10.721230381255654207  ,7.9124051824895537547 ] 
dist 43=[-10.718105044056104956  ,8.8275688385677039018 ] 
dist 44=[-10.697112217032133478  ,9.6237818643758406508 ] 
dist 45=[-10.497845166603265170  ,10.463045337521960458  ] 
dist 46=[-10.435585376609463866  ,11.214352672545700774  ] 
dist 47=[-10.263535406054838129  ,11.659718328320914753  ] 
dist 48=[-10.190872776674240124  ,11.965042690133102887  ] 
dist 49=[-1.6553751149998829639 ,12.157677994211323206  ] 
dist 50=[-.5840679580886239040 ,12.262024192753497100  ] 
dist 51=[-.3940291144937055767 ,12.273089196089734298  ] 
dist 52=[-.0935532490157421827 ,12.136581988082283678  ] 
dist 53=[-.0206871539801483818 ,12.115212509326628650  ] 
dist 54=[1.1362867022217153784 ,6.9605840913816117305 ] 
dist 55=[1.2814884718129657222 ,7.1232463499415831999 ] 
dist 56=[1.5795498569844715958 ,7.1739790431419826587 ] 
dist 57=[1.6410926821869686250 ,7.1824685690791475496 ] 
dist 58=[1.8753663142180980690 ,7.1765201326422391560 ] 
dist 59=[1.9167741962412555858 ,7.1599627987733104538 ] 
dist 60=[1.9113868032953785273 ,7.1259321442793870552 ] 
dist 61=[1.8411067920003615105 ,7.0841282597738967207 ] 
dist 62=[1.7438296888008135754 ,7.0414255539786817952 ] 
dist 63=[1.6307355549110833075 ,6.9770197419750988588 ] 
dist 64=[1.4848506044206538212 ,6.9423543283841765371 ] 
dist 65=[.6660496142700963936 ,2.5160946889989082828 ] 
dist 66=[-.29720158383651397302,2.4577417495670548471 ] 
dist 67=[-1.1198533568161095698 ,2.4355280958235546217 ] 
dist 68=[-1.9635753069483926478 ,2.4026525276150285236 ] 
dist 69=[-2.7544657741864685637 ,2.3874594360824726314 ] 
dist 70=[-3.3663942417167321610 ,1.5325037921209080813 ] 
dist 71=[-3.9634343301098015591 ,1.4365123671700985530 ] 
dist 72=[-4.6949767878487978799 ,1.2163106179707522266 ] 
dist 73=[-5.3836767661908090521 ,1.1654230183312955232 ] 
dist 74=[-5.8098145689177433265 ,.8733988147504893211 ] 
dist 75=[-6.1246466174945001759 ,.81779837505418506113] 
dist 76=[-6.3692967426530586333 ,.70485940065908661766] 
dist 77=[-6.5498344076819845315 ,.67440874170812982834] 
dist 78=[-6.6088873222022550749 ,.33333751632533237532] 
dist 79=[-6.6235812276361071913 ,.28170290401936163221] 
dist 80=[-6.6271277438459842203 ,.19030782125473015791] 
dist 81=[-2.6765172260717109326 ,1.2788618577726824857 ] 
dist 82=[-2.6582195882258086409 ,2.0151483277275765021 ] 
dist 83=[-2.6420948044300896911 ,2.6321767850159431518 ] 
dist 84=[-2.6193592989659219093 ,3.2455303024132947284 ] 
dist 85=[-2.6054371592011535975 ,3.8076763706608818819 ] 
dist 86=[.07594755273769756165,4.2204741845395616568 ] 
dist 87=[.06745970035960665994,4.6018965499648256302 ] 
dist 88=[.04262690229251386209,5.0389131474507047909 ] 
dist 89=[-.01083260577188397320,5.4344721706298152121 ] 
dist 90=[-.07832970253588961035,5.6505443071942349074 ] 
dist 91=[-.15914971116026978726,5.7760140506573029964 ] 
dist 92=[-.26492368663904233064,5.8102041419704372631 ] 
dist 93=[-.43194114665932671999,5.8096997049916219568 ] 
dist 94=[-.60733895323262801271,5.7967908856199305265 ] 
dist 95=[-.74653848849564706149,5.7723940730076417282 ] 
dist 96=[-1.1582290778702491660 ,5.7423406908110405852 ] 
dist 97=[-2.4136292586814943064 ,4.6606060937811554184 ] 
dist 98=[-3.2413477099370908300 ,4.5084707143212833658 ] 
dist 99=[-3.9119734929962944040 ,4.1361299877639932969 ] 
dist 100=[-4.5408683937623596456 ,4.0476263255042690953 ] 
dist 101=[-5.0926809956498395687 ,4.0462128013268627813 ] 
dist 102=[-5.4558950170807313647 ,4.0257792635394345208 ] 
dist 103=[-5.7495310875947603188 ,4.0076624408831320695 ] 
dist 104=[-6.0238644639870937088 ,3.9329769403207650236 ] 
dist 105=[-6.2534102932591106562 ,3.9024336125150336096 ] 
dist 106=[-6.3684257995793261835 ,3.6515276595440622743 ] 
dist 107=[-6.4212985039722007953 ,3.5866307668197524017 ] 
dist 108=[-6.4222361208190228992 ,3.4893557905139038244 ] 
dist 109=[-6.3520145113861832350 ,3.4535196826233839129 ] 
dist 110=[-6.3147163088703482819 ,2.5540588930446979993 ] 
dist 111=[-6.1939581986497670740 ,2.4268827780237387484 ] 
dist 112=[-6.1342016668618305788 ,2.1442428136682334139 ] 
dist 113=[-4.6966155723763001437 ,2.0625544946531799861 ] 
dist 114=[-4.5837365917083229868 ,2.3558165505402178372 ] 
dist 115=[-4.5463464414258357176 ,3.1042234400161049066 ] 
dist 116=[-4.4191445720594578041 ,3.8005887229560511797 ] 
dist 117=[-4.3810367273559223877 ,4.4077687548559882097 ] 
dist 118=[1.1229119419784594152 ,4.8004966030017844635 ] 
dist 119=[1.4944894628078557492 ,5.1102236895053048137 ] 
dist 120=[2.3354876932239310169 ,5.3863898713268554792 ] 
dist 121=[2.4609099862853908751 ,5.6217166424493871506 ] 
dist 122=[3.4314131213960745026 ,5.7685717490604124530 ] 
dist 123=[3.5831296215164206804 ,5.8783319321538657297 ] 
dist 124=[3.8334159491596734575 ,5.9657180318841540589 ] 
dist 125=[3.8804367080752860953 ,6.0317403785327200630 ] 
dist 126=[4.0729517005644193421 ,6.0562984284341184089 ] 
dist 127=[3.3956190103817308069 ,6.0551215553680124240 ] 
dist 128=[2.3114168568703430520 ,6.0330249430430003033 ] 
dist 129=[1.2040126052119577247 ,4.7442447600512063142 ] 
dist 130=[.43414699827714705232,4.7946165671542321185 ] 
dist 131=[-.23367015446401270258,4.8106574676367491946 ] 
dist 132=[-.93409618560255029378,4.8045792995841875783 ] 
dist 133=[-1.5993856884613900520 ,4.7874507371747344059 ] 
dist 134=[-2.1270754797869325092 ,1.4855587680003953859 ] 
dist 135=[-2.6534929092429501885 ,1.2071543313023170992 ] 
dist 136=[-3.3137087342087572808 ,.5855872559351362195 ] 
dist 137=[-3.9412095068077261771 ,.45778082187668091698] 
dist 138=[-4.3371562356104022458 ,-.27119019941085292376] 
dist 139=[-4.6381730783486884173 ,-.39638102107877747707] 
dist 140=[-4.8870839441352284066 ,-.65957930231447410197] 
dist 141=[-5.0825854047475918988 ,-.71748945088702794896] 
dist 142=[-5.1706001755687505489 ,-1.0048026760112920971 ] 
dist 143=[-5.2072732990818756934 ,-.62523520811315223259] 
dist 144=[-5.2019835944458115181 ,.00145184385476588227] 
dist 145=[-3.9096812548502039220 ,.78287181169736485617] 
dist 146=[-4.0566135075525129123 ,1.3108262734708100525 ] 
dist 147=[-4.1181888336146524772 ,1.7526892331749860439 ] 
dist 148=[-4.1421975829488812815 ,2.1907688380813780589 ] 
dist 149=[-4.1393108090379899113 ,2.5913332329506588851 ] 
dist 150=[.48849290222910492704,2.8835823188451417208 ] 
dist 151=[.65169244191320740932,3.1516067837704412139 ] 
dist 152=[1.0152507278198757791 ,3.4555613898274419459 ] 
dist 153=[1.0745517016906928744 ,3.7287588117098954287 ] 
dist 154=[1.4769336495152222434 ,3.8741209169247679338 ] 
dist 155=[1.5391453222629329068 ,3.9558855426821521239 ] 
dist 156=[1.6560132277488325624 ,3.9754503810820348578 ] 
dist 157=[1.3083781732543432386 ,3.9496876391345120088 ] 
dist 158=[.87806293833864240482,3.9419183426494668597 ] 
dist 159=[.3319280431322207237 ,3.9362843642365368171 ] 
dist 160=[-.5129391914544991268 ,3.9321157094870514846 ] 
dist 161=[-1.3620997758767433059 ,3.2691445018042373776 ] 
dist 162=[-1.9253570019387553980 ,3.2646773630054401372 ] 
dist 163=[-2.3854198815961378676 ,3.2592607545397706046 ] 
dist 164=[-2.8230326346073780617 ,3.2513207579154765727 ] 
dist 165=[-3.2111723491064087923 ,3.2378915263453199619 ] 
dist 166=[-3.4739325633122640116 ,2.5555034517124982869 ] 
dist 167=[-3.6944084274679890605 ,2.4632571666024370961 ] 
dist 168=[-3.9139146175170227483 ,2.2390766517622928071 ] 
dist 169=[-4.1028748093796707991 ,2.1851457779455381723 ] 
dist 170=[-4.2015306111226527426 ,1.8356902266461056394 ] 
dist 171=[-4.2526480843778273447 ,1.7641956537844006898 ] 
dist 172=[-4.2582469456302461225 ,1.6315301431244936617 ] 
dist 173=[-4.2283308086437281665 ,1.5964423947630820485 ] 
dist 174=[-4.2052567766662572530 ,.99287042171666597889] 
dist 175=[-4.1400710518190259821 ,.90942345414907501908] 
dist 176=[-4.1068476029577599466 ,.70900083842033597523] 
dist 177=[-3.5449805972446700297 ,.92038528373116448048] 
dist 178=[-3.5150996305074080376 ,1.5326307105124310004 ] 
dist 179=[-3.4954941445642065149 ,2.0347318002570480745 ] 
dist 180=[-3.4358391413117487666 ,2.5157158872840782292 ] 
dist 181=[-3.4057354799557911807 ,2.9446091869547489747 ] 
dist 182=[.3476025087246170706 ,3.2389677969925799947 ] 
dist 183=[.46394646580510698566,3.4902943352697871109 ] 
dist 184=[.72243930776166583686,3.7475720896269449551 ] 
dist 185=[.76521339512616650563,3.9739735401046267059 ] 
dist 186=[1.0492558388820354062 ,4.1021627530409936234 ] 
dist 187=[1.0930853805315311206 ,4.1825901936552611014 ] 
dist 188=[1.1768801571764465300 ,4.2185136192236903924 ] 
dist 189=[1.1917431765337453439 ,4.2266481409875584863 ] 
dist 190=[1.2464880548756784029 ,4.2185020444871571574 ] 
dist 191=[1.0887896935519053365 ,4.1579550695307763552 ] 
dist 192=[.60185313427456862182,4.1345880620213446940 ] 
dist 193=[-.2390171442301033019 ,3.5717725380980574521 ] 
dist 194=[-.8099385822401442143 ,3.5768167823201941183 ] 
dist 195=[-1.2907958829111563647 ,3.5681457251661168178 ] 
dist 196=[-1.7724827434547998636 ,3.5209111328690283959 ] 
dist 197=[-2.2161235358761782657 ,3.4947470074412649412 ] 
dist 198=[-2.5452498925273434232 ,1.9359788102674097508 ] 
dist 199=[-2.8525634229681361045 ,1.7783984851814922931 ] 
dist 200=[-3.2092128212778865069 ,1.4168937460232300349 ] 
dist 201=[-3.5344376768263385033 ,1.3384081204320365897 ] 
dist 202=[-3.7164274628873637681 ,.86846279507602124919] 
dist 203=[-3.8278241188996835697 ,.78166084823205753809] 
dist 204=[-3.8715175701640864607 ,.60855334268388406755] 
dist 205=[-3.8894884515919920150 ,.56407760711549244739] 
dist 206=[-3.8983013111658475193 ,.08237896980976148913] 
dist 207=[-3.9020683541472647674 ,.00945459775337822181] 
dist 208=[-3.8999160871785243416 ,1.22087781831718000000e-05] 
dist 209=[-3.3279762431185206602 ,.76085436067262857383] 
dist 210=[-3.3399294792948303674 ,1.2878932860028521141 ] 
dist 211=[-3.3434361595413563584 ,1.7430674145748616570 ] 
dist 212=[-3.3414175644647177530 ,2.2173068607850441522 ] 
dist 213=[-3.3313355327602575723 ,2.6658135134919803554 ] 
dist 214=[.09048449270059361998,3.0183630794524012763 ] 
dist 215=[.12190582242749403271,3.3671084653350262593 ] 
dist 216=[.11349689737137547175,3.8004437260482365426 ] 
dist 217=[-.0269127444386855887 ,4.2103204999039844215 ] 
dist 218=[-.1523619602226641702 ,4.4655114502009416996 ] 
dist 219=[-.2905087259647361285 ,4.6555253488013643624 ] 
dist 220=[-.4815572767268791710 ,4.8054705106540874512 ] 
dist 221=[-.6912949255865015367 ,4.9176612852067179086 ] 
dist 222=[-.9039754011847147709 ,4.9571074839127881778 ] 
dist 223=[-1.1589148617170105813 ,4.9610562532564222088 ] 
dist 224=[-2.1390925176151380400 ,4.9456138680618231002 ] 
dist 225=[-3.1820865493797353769 ,4.7861888563911354449 ] 
dist 226=[-3.8560228119786201344 ,4.7409557716915860792 ] 
dist 227=[-4.3867292831339883628 ,4.5998186617433918012 ] 
dist 228=[-4.8585107611099424157 ,4.5535375588621659764 ] 
dist 229=[-5.2546458587233394440 ,4.3857654972384849124 ] 
dist 230=[-5.4836681505681238138 ,4.2748487755759974415 ] 
dist 231=[-5.6334770637906719534 ,4.2398009721575231585 ] 
dist 232=[-5.7137024909325520726 ,4.1254412482428868004 ] 
dist 233=[-5.7580103606635170531 ,4.0864014684107700680 ] 
dist 234=[-5.7645770089359207083 ,3.7808541897821159752 ] 
dist 235=[-5.7447390877859430277 ,3.7056363896455447927 ] 
dist 236=[-5.7229904870930367660 ,3.5880788398650735107 ] 
dist 237=[-5.6011879546663687109 ,3.5480892155719261845 ] 
dist 238=[-5.5605678073204409617 ,2.5809909062745660744 ] 
dist 239=[-5.4016839541114610075 ,2.4451525273249539224 ] 
dist 240=[-5.3675217868963316713 ,2.1379379706874267670 ] 
dist 241=[-5.0731190818725661218 ,2.0562658501242153578 ] 
dist 242=[-4.9621511883627937225 ,1.6548086402781614059 ] 
dist 243=[-4.9251202457142514085 ,1.5762801995212680544 ] 
dist 244=[-4.7853224508761939938 ,1.3986329674959569679 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 2, 1, 0, 1, 2] 
dist 0=[75.150377393635222315  ,75.150377393635222315  ] 
dist 1=[74.691392496466994213  ,75.263871352791493573  ] 
dist 2=[73.761795640817193343  ,75.257789991535322785  ] 
dist 3=[72.011936647011188108  ,75.092869817693904820  ] 
dist 4=[69.804811949069308559  ,74.937710429029238499  ] 
dist 5=[67.050106971371543208  ,74.282170239286275738  ] 
dist 6=[63.366743478878473932  ,74.014955113157520946  ] 
dist 7=[57.452686255827109873  ,71.775933313749516172  ] 
dist 8=[51.406244971114162231  ,71.164358195547666163  ] 
dist 9=[47.194221034108338197  ,70.542780384655939304  ] 
dist 10=[43.518075996073412424  ,70.191933746432099044  ] 
dist 11=[39.610044022742556992  ,69.935378377711648529  ] 
dist 12=[35.848852371402224056  ,69.746141986859446980  ] 
dist 13=[30.491857032260624326  ,69.441662995971444110  ] 
dist 14=[25.685044683764226613  ,66.691936013305132541  ] 
dist 15=[20.757659183897057161  ,32.979872940066861459  ] 
dist 16=[16.126111680824285917  ,30.012202147849447748  ] 
dist 17=[12.500443667886074819  ,23.159078599583695213  ] 
dist 18=[8.9151813866988537827 ,22.132342977143524822  ] 
dist 19=[4.4451325951700345590 ,16.785802169335617228  ] 
dist 20=[.184182608508507233  ,14.138280043025567222  ] 
dist 21=[-2.5663422924329175131 ,13.644654411208545456  ] 
dist 22=[-4.7382511334654927265 ,12.901604954225204515  ] 
dist 23=[-6.6895134539140088250 ,12.727183716832989610  ] 
dist 24=[-8.3503275114042718498 ,1.6929088280140948085 ] 
dist 25=[-9.3628489363466003133 ,.78451391824456370272] 
dist 26=[-10.094647957066353184  ,-1.1347836905589184765 ] 
dist 27=[-10.634903672572827413  ,-1.4963822556989957417 ] 
dist 28=[-11.048144063121936585  ,-3.3558996285545077147 ] 
dist 29=[-11.350497871016739785  ,-3.6574098611377118253 ] 
dist 30=[-11.442461663183917524  ,-4.2081819109436933407 ] 
dist 31=[-8.1015834443639029363 ,-4.3161055152005841061 ] 
dist 32=[-8.8215320392008816308 ,-4.5138235758553202133 ] 
dist 33=[-9.3424781349652844630 ,-4.4298534199166176365 ] 
dist 34=[-9.7239798869776502590 ,-4.0502989381584967338 ] 
dist 35=[-10.020923245129861646  ,-3.1851879843895157256 ] 
dist 36=[-10.245138755192537237  ,-2.2904735917283443992 ] 
dist 37=[-10.335700497695104415  ,-1.6100313622805297818 ] 
dist 38=[-10.362403816133185649  ,-.95971724954903542609] 
dist 39=[-10.346384410422545751  ,-.18432276604558616276] 
dist 40=[-4.2065183856350693532 ,1.3971986052310216542 ] 
dist 41=[-4.1489981283616572953 ,2.4791898545458607889 ] 
dist 42=[-4.0100578898462967452 ,3.3715192011314224854 ] 
dist 43=[-3.9689884321009297391 ,4.2363581430964971971 ] 
dist 44=[-3.7325993689928388932 ,5.0160341625750766069 ] 
dist 45=[-3.6792549976586808122 ,5.5687081368952057143 ] 
dist 46=[-3.5655052508167887124 ,6.0605282684407880656 ] 
dist 47=[-3.5270534190657997687 ,6.5975602256561594246 ] 
dist 48=[-3.3412860068888970312 ,7.0738018550005386990 ] 
dist 49=[-3.2970923984464636677 ,7.3231209972355409737 ] 
dist 50=[-3.1772996266588235752 ,7.4598422796709604423 ] 
dist 51=[-3.1408459462465446690 ,7.4869711694584915090 ] 
dist 52=[-2.6931826530476333334 ,7.4239021252065972683 ] 
dist 53=[-2.6179840845930220992 ,7.3977881726794160823 ] 
dist 54=[-2.4131181391040797663 ,7.3734276606261278800 ] 
dist 55=[-2.3754919216879080308 ,7.3454187264796615318 ] 
dist 56=[-2.2253924276326467815 ,6.1901703900903753634 ] 
dist 57=[-3.2695480880265625184 ,6.1274298680377883177 ] 
dist 58=[-4.1232054118821032440 ,5.9180923887992191524 ] 
dist 59=[-4.9366912388314616829 ,5.8770854127093019665 ] 
dist 60=[-5.6594376217558854194 ,4.1708391887826468451 ] 
dist 61=[-6.1512419705155485704 ,4.1374530822637599401 ] 
dist 62=[-6.5668372468547057054 ,4.1169876425643597673 ] 
dist 63=[-6.9856919837423924734 ,3.1015622000579076770 ] 
dist 64=[-7.3482927012793688812 ,1.7998425764161289045 ] 
dist 65=[-7.5395366745334705429 ,1.6188639712513138219 ] 
dist 66=[-7.6415439740768038683 ,1.2011823126223298027 ] 
dist 67=[-7.6545702741141146455 ,1.1181048859690573034 ] 
dist 68=[-7.6124857792204324426 ,.57369105938573375022] 
dist 69=[-7.5726300504949665506 ,.47493794655655950735] 
dist 70=[-7.4641646399161662987 ,.28990260094025036938] 
dist 71=[-7.4080074942209782296 ,.24626296039105030638] 
dist 72=[-6.8061576089354658999 ,1.5843867954945468505 ] 
dist 73=[-6.7931172217076203704 ,2.6653346982958646091 ] 
dist 74=[-6.7216927803876052268 ,3.5435248159319536016 ] 
dist 75=[-6.6732109768417416558 ,4.3709626762032454665 ] 
dist 76=[-3.8472279414040159326 ,5.0995294930845921989 ] 
dist 77=[-3.8536351045229641642 ,5.5834206739533154196 ] 
dist 78=[-3.8546475442778610413 ,5.9793685294729766242 ] 
dist 79=[-1.3774601733234731785 ,6.3572187187682753601 ] 
dist 80=[-.61952158726186636262,6.6847819871199069614 ] 
dist 81=[-.23227515538396868358,6.8801816103526318227 ] 
dist 82=[.02419164154687164503,7.0156539584182358305 ] 
dist 83=[.21405016339306117927,7.1042144140683062406 ] 
dist 84=[.72480366787137601499,7.1555594121308211679 ] 
dist 85=[.94303681040917937744,7.1488964583911403704 ] 
dist 86=[.97887628853174618124,7.1006910131399959352 ] 
dist 87=[1.0588049922657714687 ,7.0588544085854054707 ] 
dist 88=[.68786955279640481972,6.0555795631030682135 ] 
dist 89=[-.24626048237214899001,6.0993173876998234154 ] 
dist 90=[-1.0465257293583876466 ,6.0994752964472864367 ] 
dist 91=[-1.8700466012951147173 ,6.0864942073737956484 ] 
dist 92=[-2.6425531539077341828 ,3.3749787384992331507 ] 
dist 93=[-3.2393700604438847776 ,3.4204297780010551370 ] 
dist 94=[-3.8200462189751735424 ,3.4308696104314059189 ] 
dist 95=[-4.5281830105165353622 ,-.30867840581137853843] 
dist 96=[-5.1914092498756709723 ,-.68918302021434976439] 
dist 97=[-5.5929779816485682396 ,-1.0375155994239444290 ] 
dist 98=[-5.8786233642479122013 ,-1.1041977322650064204 ] 
dist 99=[-6.0795356444642738409 ,-1.1097750217566397230 ] 
dist 100=[-6.2224849576695975306 ,-.95868160499856700755] 
dist 101=[-6.2769679387014151205 ,-.75327643713960307834] 
dist 102=[-6.2842826411909545942 ,-.46936513858928191062] 
dist 103=[-6.2693373645945054890 ,-.00518318618800161406] 
dist 104=[-2.5159089866561184003 ,.54659658842693739049] 
dist 105=[-2.5069075248669029785 ,.91816092835488814056] 
dist 106=[-2.4952993538632265024 ,1.2247336118908059248 ] 
dist 107=[-2.4807959502371467200 ,1.5214938073624690617 ] 
dist 108=[-2.3463923125952753322 ,1.7881787658076592418 ] 
dist 109=[-2.3280977735132917811 ,1.9748097263216039501 ] 
dist 110=[-2.3162251393344139381 ,2.1379984629061487303 ] 
dist 111=[-1.5340290945980399595 ,2.3111948748300152144 ] 
dist 112=[-1.4461013594630835887 ,2.4648151961704442667 ] 
dist 113=[-1.2407184862403852037 ,2.5499324139532942091 ] 
dist 114=[-1.1942879615695129430 ,2.6009250374348757849 ] 
dist 115=[-.94312931434791484379,2.6184513749711242335 ] 
dist 116=[-.85507420405843892199,2.6195975772588220497 ] 
dist 117=[-.74860018326297815077,2.6104199369558226852 ] 
dist 118=[-.7208097511750674506 ,2.5831301475375649086 ] 
dist 119=[-.35351946746360288891,2.5220539369085414019 ] 
dist 120=[-.48111354527319651022,2.3274100201147831057 ] 
dist 121=[-.79942867777367252522,2.3717099112694044881 ] 
dist 122=[-1.0630959290379276703 ,2.3818167548639578861 ] 
dist 123=[-1.3200298937147813553 ,2.3779391547794925521 ] 
dist 124=[-1.5520575441837447871 ,2.3664659896726308307 ] 
dist 125=[-1.7163964591762399573 ,2.3472704067634984666 ] 
dist 126=[-1.8621453747459156661 ,2.3356763182568076983 ] 
dist 127=[-2.0200346368049225297 ,.69910022977104700993] 
dist 128=[-2.1605474667662482989 ,.33818427194979259076] 
dist 129=[-2.2369977877268332152 ,.28604037147258247618] 
dist 130=[-2.2809420116925527615 ,.1790769292049437329 ] 
dist 131=[-2.2918179299953281714 ,.15144135918763524957] 
dist 132=[-2.2890610136469909648 ,.05298184380056128278] 
dist 133=[-2.2786364037945845806 ,.03246749548335545268] 
dist 134=[-2.2606299747340165026 ,.00541124960118851982] 
dist 135=[-2.2495400492089054847 ,-.00053776464415403350] 
dist 136=[-2.1026864590627062623 ,.47384207818567189644] 
dist 137=[-2.1431913824626063682 ,.78742791265102685347] 
dist 138=[-2.1686236177120101695 ,1.0423731330470234222 ] 
dist 139=[-2.1823373720074283308 ,1.2828896849998155407 ] 
dist 140=[-2.1800691523553989244 ,1.4948715488906194474 ] 
dist 141=[-2.1620220456623676563 ,1.6360180628147912072 ] 
dist 142=[-2.1477413748102442288 ,1.7518973028762728849 ] 
dist 143=[-.87701312848247355127,1.8631111727155053728 ] 
dist 144=[-.76236302954824430204,1.9596090744693783746 ] 
dist 145=[-.50406129030765599965,2.0167998123095450460 ] 
dist 146=[-.44993992529992281434,2.0559846804151606514 ] 
dist 147=[-.13591408216880248995,2.0806736873888765483 ] 
dist 148=[-.08051050505206516440,2.0940712816790404806 ] 
dist 149=[.03371205471371943328,2.0919733731397740150 ] 
dist 150=[.06269026695560033587,2.0747900021057258726 ] 
dist 151=[.29270145114403263814,2.0611067194521656322 ] 
dist 152=[.1673397440245384765 ,1.7337682345649213054 ] 
dist 153=[-.10727231899396038553,1.8181300392820126704 ] 
dist 154=[-.34215759684888610002,1.8756818758128905484 ] 
dist 155=[-.58327363509472248361,1.9159251716478310817 ] 
dist 156=[-.80908141975457779759,1.9312588023623894524 ] 
dist 157=[-.98291609322419625439,1.9323279659623618095 ] 
dist 158=[-1.1514626672298297327 ,1.9281170487255198216 ] 
dist 159=[-1.3561810618936314268 ,-.05900298625569293000] 
dist 160=[-1.5474996805304593049 ,-.216641690142409071  ] 
dist 161=[-1.6626068204902194753 ,-.31649901485189882731] 
dist 162=[-1.7435991795019612769 ,-.34418837322173667491] 
dist 163=[-1.7988651861390663962 ,-.33118043493375544157] 
dist 164=[-1.8375191684965318370 ,-.29887281944087520293] 
dist 165=[-1.8522613823021983533 ,-.24055499142144732625] 
dist 166=[-1.8533058797037923727 ,-.15218996826665666482] 
dist 167=[-1.8492767415888612266 ,-5.02075857741443112000e-05] 
dist 168=[-1.8265715391382822948 ,.32073008118191042103] 
dist 169=[-1.8878043931683952559 ,.5404863036816624909 ] 
dist 170=[-1.9258646088699034552 ,.72768457148816773136] 
dist 171=[-1.9486232241470102683 ,.91862460524395720687] 
dist 172=[-1.9505922301315006548 ,1.0966760200565542386 ] 
dist 173=[-1.9403297540090029523 ,1.2324733862672831217 ] 
dist 174=[-1.9284574274302570565 ,1.3629288912842666602 ] 
dist 175=[-1.7394750356784187874 ,1.5196765128899146993 ] 
dist 176=[-1.7056437471836315547 ,1.6653064018799236524 ] 
dist 177=[-1.6163406742195554334 ,1.7514234496412414163 ] 
dist 178=[-1.5920572268458181533 ,1.8101899482864980806 ] 
dist 179=[-1.4219492781893929762 ,1.8902065144074549762 ] 
dist 180=[-1.3840619078146646257 ,1.9962058386341154606 ] 
dist 181=[-1.3181560095993600241 ,2.0748879260764444030 ] 
dist 182=[-1.2997604281473134843 ,2.1365300582928120636 ] 
dist 183=[-.89886199378158189615,2.1835988460186668120 ] 
dist 184=[-.99041026801342176905,2.2041611895809085785 ] 
dist 185=[-1.2507893924355408239 ,2.2091868381977024099 ] 
dist 186=[-1.4588732091394465406 ,2.2049959766805980593 ] 
dist 187=[-1.6491280118671887680 ,2.1690525173777936000 ] 
dist 188=[-1.8126894319701117065 ,2.1554691169052212573 ] 
dist 189=[-1.9143177744763005169 ,2.0996277472608089558 ] 
dist 190=[-1.9897477686441946115 ,2.0866112109318158256 ] 
dist 191=[-2.0488279520441646247 ,1.2467881217924071922 ] 
dist 192=[-2.0939343651561725303 ,.86226141399763414264] 
dist 193=[-2.1136357772638168877 ,.80905511110034405067] 
dist 194=[-2.1184447384620397688 ,.68197357788869915292] 
dist 195=[-2.1144214394091516641 ,.65656949574859907099] 
dist 196=[-2.0799494868843320223 ,.47389812369707890484] 
dist 197=[-2.0669248342430636238 ,.43911823261160369496] 
dist 198=[-2.0133607731697801023 ,.3785658002701032208 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 2, 0, 0, 0, 1] 
dist 0=[69.012422251492114453  ,69.012422251492114453  ] 
dist 1=[68.831063604281567798  ,69.005935728749082269  ] 
dist 2=[68.458188828170518233  ,69.012422251492114453  ] 
dist 3=[67.549119148970406422  ,68.736310244349415578  ] 
dist 4=[65.764372654613796650  ,67.993964654007845381  ] 
dist 5=[63.549164235892559261  ,67.816319751570840906  ] 
dist 6=[60.921231659887152418  ,66.944437606910694027  ] 
dist 7=[57.483232081060942199  ,66.674155208795884228  ] 
dist 8=[52.033765322096087686  ,65.818799890628083549  ] 
dist 9=[46.471172703779391774  ,65.543039206581629925  ] 
dist 10=[42.581661059357242871  ,63.386563450621251799  ] 
dist 11=[39.167786004384056768  ,62.818604544946174012  ] 
dist 12=[35.504655815010026613  ,62.522034756680184239  ] 
dist 13=[31.957104421196263633  ,61.165460167552010685  ] 
dist 14=[28.975098375712139411  ,53.378901956025564919  ] 
dist 15=[25.921382730400007672  ,48.409734316388922882  ] 
dist 16=[21.849159391761176958  ,29.312424629164947039  ] 
dist 17=[17.855268458455028238  ,26.499141805497417232  ] 
dist 18=[15.042437529078027066  ,18.369080134014338446  ] 
dist 19=[12.317080150984328769  ,17.403777951102241924  ] 
dist 20=[8.6484188904158830867 ,13.503465072609189984  ] 
dist 21=[5.5158840041005207137 ,12.792193990831221090  ] 
dist 22=[2.5284184596486963715 ,10.427783623461398869  ] 
dist 23=[-1.0512598940881227266 ,9.6880222935923914912 ] 
dist 24=[-4.4064980316707342660 ,9.5074131703092753380 ] 
dist 25=[-6.4985259369031347103 ,8.5463435298521165206 ] 
dist 26=[-8.0738960021144690183 ,1.0662103821401092368 ] 
dist 27=[-9.3670568481231288332 ,.37251861592305198554] 
dist 28=[-10.395563271472857641  ,-1.0443985928364231648 ] 
dist 29=[-10.913158607696982036  ,-1.3652505346657772996 ] 
dist 30=[-11.187995374990126496  ,-2.5810952692057197145 ] 
dist 31=[-11.386716350377068251  ,-2.8056244349915459115 ] 
dist 32=[-12.046104183703435459  ,-3.0832582398044358934 ] 
dist 33=[-12.721501970514535178  ,-3.1018748542000820994 ] 
dist 34=[-13.305336101198438978  ,-3.0336479298019760653 ] 
dist 35=[-13.598943453954132725  ,-2.8609337208749464040 ] 
dist 36=[-13.746652352267817498  ,-2.5826453481444485360 ] 
dist 37=[-13.770224928822801030  ,-2.0920191083340558416 ] 
dist 38=[-13.640711637067262190  ,-1.5056338761276831196 ] 
dist 39=[-13.564742349862128550  ,-.84464508899600156859] 
dist 40=[-13.471042614560378478  ,1.7164830192304693519 ] 
dist 41=[-13.410775105350874233  ,4.4201546125126094521 ] 
dist 42=[-9.8161396834158400240 ,6.1954922840646915650 ] 
dist 43=[-8.9867619929031436042 ,7.6268564782323170769 ] 
dist 44=[-8.8004081327418882175 ,8.9586366840004623846 ] 
dist 45=[-7.4757092877964683756 ,10.121304095768610544  ] 
dist 46=[-7.2048585243293333357 ,10.878193845522134431  ] 
dist 47=[-6.7370029213345701455 ,11.481582153533851525  ] 
dist 48=[-6.6155589865715168583 ,12.032070697382626902  ] 
dist 49=[-4.1957182648729562643 ,12.494389823030135175  ] 
dist 50=[-3.8696638061149906129 ,12.746037442861860229  ] 
dist 51=[-3.0777076700423591012 ,12.891354562985007625  ] 
dist 52=[-2.9482886284100568311 ,12.929292773523953426  ] 
dist 53=[-1.7909469219020979419 ,12.893515508312816203  ] 
dist 54=[-1.5760172449766918638 ,11.567707342801556956  ] 
dist 55=[-1.2805992842472398267 ,11.282691110137418251  ] 
dist 56=[-1.1915826242557997296 ,9.4861633966758611837 ] 
dist 57=[1.0587212190371600280 ,5.6931912291820810029 ] 
dist 58=[1.0213000695725722077 ,5.7694716891506666743 ] 
dist 59=[.26811611373475284028,5.9064858811700513693 ] 
dist 60=[-.38065463452961173057,6.0060346247774066140 ] 
dist 61=[-1.0546679907939602391 ,6.0371882652495496259 ] 
dist 62=[-1.6917052182217643964 ,6.0377980939722797790 ] 
dist 63=[-2.1930069393985138734 ,6.0203073877396786465 ] 
dist 64=[-2.6899661674610734142 ,3.2001046421632029889 ] 
dist 65=[-3.3097170473463417027 ,3.3361541091414945155 ] 
dist 66=[-3.8983327628012779686 ,3.4142374759497254880 ] 
dist 67=[-4.2710961222964951872 ,3.4645921403764718243 ] 
dist 68=[-4.5565168676574917953 ,3.4900542223153537466 ] 
dist 69=[-4.7966951043553476483 ,3.4974810732684528185 ] 
dist 70=[-5.0059697297754856043 ,3.4902622314432893565 ] 
dist 71=[-5.3519473563887149791 ,3.4465186639339657649 ] 
dist 72=[-5.6544547879395633917 ,3.4227637699160479959 ] 
dist 73=[-5.8024490601082415969 ,1.4384949989606375633 ] 
dist 74=[-5.8792246332812853456 ,1.2564524147051615198 ] 
dist 75=[-5.8975248234602792538 ,1.3679034970954311531 ] 
dist 76=[-5.7695337425362832039 ,1.7958695492614210985 ] 
dist 77=[-5.7357874041439769714 ,2.2150459569626329548 ] 
dist 78=[-5.7151172265174959595 ,2.5951631517722768619 ] 
dist 79=[-5.7069949952108307294 ,2.8673544449044775058 ] 
dist 80=[-4.2792580995982325701 ,3.1119289076091632172 ] 
dist 81=[-4.0970941228095737949 ,3.3819105078664794187 ] 
dist 82=[-3.6663644260949216670 ,3.7006885933771086034 ] 
dist 83=[-3.5628037031609837352 ,4.3509401726751861974 ] 
dist 84=[-3.1328418836797548575 ,4.9255970308375945137 ] 
dist 85=[-3.1862989294350590742 ,5.3116108775596048146 ] 
dist 86=[-3.2065085581668037350 ,5.6325175736355791955 ] 
dist 87=[-3.2061864880310917249 ,5.9475264821845328365 ] 
dist 88=[-3.1985216520387442241 ,6.2167853510900307817 ] 
dist 89=[-1.4076540210158720047 ,6.3552165379106074953 ] 
dist 90=[-1.1268088641885596387 ,6.4241221138651138182 ] 
dist 91=[-1.6674405822304678218 ,6.4312008129586017318 ] 
dist 92=[-2.1111483835853674328 ,6.3747812975081617453 ] 
dist 93=[-2.5368059820325031134 ,6.3382504372546217093 ] 
dist 94=[-2.9168274410900251204 ,6.2391344309332638863 ] 
dist 95=[-3.1785348660558951008 ,6.1899658902508822506 ] 
dist 96=[-3.4029722204416255406 ,2.7580528117885074375 ] 
dist 97=[-3.6343604906061897456 ,3.0240670055033277211 ] 
dist 98=[-3.8363358646650928689 ,3.1827338879844036251 ] 
dist 99=[-3.9434700880203382267 ,3.2927115255258611395 ] 
dist 100=[-4.0013738536176582990 ,3.3645432192390901894 ] 
dist 101=[-4.0101087352762707221 ,3.4090009464415619956 ] 
dist 102=[-3.9903316874254150188 ,3.4151944061666177629 ] 
dist 103=[-3.9690531798161755237 ,3.3958887156027793380 ] 
dist 104=[-3.9188936719452313286 ,3.3816335419659643404 ] 
dist 105=[-3.8929455020022839985 ,3.0909558784414889169 ] 
dist 106=[-3.8117962227087365789 ,3.0367095934810265207 ] 
dist 107=[-3.8561733166752447820 ,2.8908417508578779615 ] 
dist 108=[-3.8819261485704639240 ,2.8504498520035514765 ] 
dist 109=[-3.8770125030810496447 ,2.5620947221877227859 ] 
dist 110=[-3.8530290924506768964 ,2.7187290342849074786 ] 
dist 111=[-3.8321689148150890330 ,2.9832262838206253927 ] 
dist 112=[-1.4594384844081355721 ,3.2054260566916490174 ] 
dist 113=[-1.4096558890632211769 ,3.4270933592395220702 ] 
dist 114=[-1.4387494088743471122 ,3.6210282782556918608 ] 
dist 115=[-1.4529670398583175728 ,3.7326285272587868290 ] 
dist 116=[-1.4538455481111946450 ,3.8049752314461672194 ] 
dist 117=[-1.4405135210591218550 ,3.8423620650609477541 ] 
dist 118=[-1.4323790062730743387 ,3.8542982031775974725 ] 
dist 119=[-1.4070311203285448521 ,3.8501750264938476569 ] 
dist 120=[-1.3943173804673007845 ,3.7901700660024107425 ] 
dist 121=[-.05795882903528794370,3.7788918485636086864 ] 
dist 122=[-.09875448211976389493,1.8198571552473993083 ] 
dist 123=[-.52317659384165524237,1.6336526099434158848 ] 
dist 124=[-.95952278130589765347,1.2106496203740816691 ] 
dist 125=[-1.4008755907889644274 ,1.1205332981004255191 ] 
dist 126=[-1.8101012144556333540 ,.5898486098376104677 ] 
dist 127=[-2.1183215778747048730 ,.49411783129465678444] 
dist 128=[-2.4106850513354739912 ,.29990394096982407138] 
dist 129=[-2.7566724279032741887 ,.25032671633444228668] 
dist 130=[-3.0754331692015383846 ,-.17177694312299350268] 
dist 131=[-3.2592143848593306637 ,-.15797193630730532561] 
dist 132=[-3.3787901401422214360 ,-.13384150952078854546] 
dist 133=[-3.4414933184679151247 ,-.10500910828754940526] 
dist 134=[-3.4781824914357688598 ,-.07245248446275412888] 
dist 135=[-3.4940117156034762212 ,-.03102950997577265630] 
dist 136=[-3.4975481577336654328 ,.03316229608532880461] 
dist 137=[-3.4852120490085529517 ,.09772355744417468450] 
dist 138=[-.21698099860073693148,.65349368621023882526] 
dist 139=[-.19444240856537663944,1.1039463258685144516 ] 
dist 140=[-.1891443543471624271 ,1.4910406976906075224 ] 
dist 141=[-.15528212169176308123,1.8912884779773322474 ] 
dist 142=[-.14848475602505093813,2.2679320687884977612 ] 
dist 143=[-.13571851476836384571,2.5608909331481365906 ] 
dist 144=[-.13236432650003352804,2.8477983981693505308 ] 
dist 145=[-.07843001727085663028,3.2003085414220390851 ] 
dist 146=[-.07089050103127669914,3.5317754221427237280 ] 
dist 147=[-.05349575091731281514,3.7347605301464795189 ] 
dist 148=[-.04998113241755041241,3.8819177293691896048 ] 
dist 149=[-.02732167924362046857,3.9907380096788018464 ] 
dist 150=[-.14263669156167260446,4.0662107925002048198 ] 
dist 151=[-.31766355226844852508,4.0816268323939383709 ] 
dist 152=[-.73859015750903281685,4.0727415552607349043 ] 
dist 153=[-1.6053279353698474374 ,4.0612814896340031019 ] 
dist 154=[-2.4700222882834027354 ,3.8475258711095034108 ] 
dist 155=[-3.0307409428077633079 ,3.7987849047004818224 ] 
dist 156=[-3.4745495137094361401 ,3.6582766536091003937 ] 
dist 157=[-3.8729965329674760891 ,3.6157599192073451890 ] 
dist 158=[-4.2103858333422018045 ,3.3005387004548094056 ] 
dist 159=[-4.4106910502059630462 ,3.2264441968213666819 ] 
dist 160=[-4.5483621328923730482 ,3.1047593814396531848 ] 
dist 161=[-4.6359612203624755491 ,3.0669023180507048396 ] 
dist 162=[-4.6936047694201112755 ,2.1900202203609051537 ] 
dist 163=[-4.7118106080743788668 ,2.0675894617563817519 ] 
dist 164=[-4.7045642614876973588 ,1.7845031424475269901 ] 
dist 165=[-4.6897217619399733922 ,1.7169340004098937322 ] 
dist 166=[-4.5968270483771731716 ,1.3317592598413992089 ] 
dist 167=[-4.5659048660623490355 ,1.2572881251868080473 ] 
dist 168=[-4.4332925624460182289 ,1.1051175662212996324 ] 
dist 169=[-4.4116396868659009217 ,1.0634038376814789427 ] 
dist 170=[-.53949615609395235719,.46146407377855374807] 
dist 171=[-.53397489139393305307,.633609624435338689  ] 
dist 172=[-.53079698545506126775,.83623809106829418389] 
dist 173=[-.50175636531472626276,1.0246529911159488910 ] 
dist 174=[-.49377549773241746061,1.1888449761463982396 ] 
dist 175=[-.48270026141397224869,1.2948704040590962810 ] 
dist 176=[-.47809276144059319745,1.3782853975974818220 ] 
dist 177=[-.3574916968802365725 ,1.4523050574328854096 ] 
dist 178=[-.34339398103599687369,1.5153351962745560820 ] 
dist 179=[-.32759461625684298812,1.5549230453457190277 ] 
dist 180=[-.32304364206418030745,1.5848059032455696370 ] 
dist 181=[-.30844105162845272638,1.6091317016954683904 ] 
dist 182=[-.30351053618216605781,1.6279387224376338045 ] 
dist 183=[-.29861211903687453722,1.6358122195174160951 ] 
dist 184=[-.29568163373456632449,1.6371623414313498695 ] 
dist 185=[-.14811971704252107243,1.6311011245309177624 ] 
dist 186=[-.24828785970451765254,.46940052508055828081] 
dist 187=[-.3322062675638689494 ,.37276956347255377416] 
dist 188=[-.41554320078098864855,.25428694256127774297] 
dist 189=[-.49183189015873621551,.30396248435381183655] 
dist 190=[-.54764130490510251849,.34207049988746059334] 
dist 191=[-.5989746334705750756 ,.37889187755732753353] 
dist 192=[-.69718593948643414258,.42343619854914960268] 
dist 193=[-.87732800758595779338,.46497476073986495895] 
dist 194=[-1.0488022815856837682 ,.489808915911218295  ] 
dist 195=[-1.1574380525277368236 ,.50709106938643057438] 
dist 196=[-1.2405336901642582826 ,.51851160390856850595] 
dist 197=[-1.3101517410231346542 ,.52564802751472734608] 
dist 198=[-1.3655343425477448271 ,.52672137772262928028] 
dist 199=[-1.3918577977292383899 ,.52374845486337882153] 
dist 200=[-1.4033328356848426662 ,.52173987346047061054] 
dist 201=[-1.4033929196033444616 ,.47782013343752566837] 
dist 202=[-.56042278085154621946,.46954520180098827551] 
dist 203=[-.50687736407012404922,.46381402194497947885] 
dist 204=[-.49410445117689107001,.54702660964266584802] 
dist 205=[-.52033583488296312734,.62070632991207313726] 
dist 206=[-.54812074209227422907,.68309487683743533497] 
dist 207=[-.56831625022730122077,.75927460217940933504] 
dist 208=[-.58334911613219401595,.82869519381773516218] 
dist 209=[-.59446786370230475753,.90675961129885765917] 
dist 210=[-.5990535355269352958 ,.97675228271798660983] 
dist 211=[-.5997188808849736244 ,1.0139820663298968164 ] 
dist 212=[-.59835063938328707692,1.0347962273534903933 ] 
dist 213=[-.58793084027672904007,1.0393220018114987717 ] 
dist 214=[-.58419155911964098493,1.0331095273624465602 ] 
dist 215=[-.56831842010679046361,1.0306113458758221262 ] 
dist 216=[-.56520160565388383403,1.0283139174841560057 ] 
dist 217=[-.10648603551662573988,1.0256991142763207249 ] 
dist 218=[-.32738949773921863369,.76591386986122802791] 
dist 219=[-.47423742418227074964,.73317575070895593892] 
dist 220=[-.59453488468820666918,.65485870352194434217] 
dist 221=[-.70955283729278731878,.63651086597220077744] 
dist 222=[-.81196660216712719178,.58835364071836770967] 
dist 223=[-.88199749322351063552,.66736345494523614467] 
dist 224=[-.94151540494054991717,.77047504806883392077] 
dist 225=[-1.0020025168489071478 ,.8704337552883506163 ] 
dist 226=[-1.0545147904997127333 ,.9368695930436932624 ] 
dist 227=[-1.0822283709465054066 ,.9912795919849935667 ] 
dist 228=[-1.0970043925578012553 ,1.0432782338276400529 ] 
dist 229=[-1.0989717644312747736 ,1.0895628638842408800 ] 
dist 230=[-1.0927660773943998248 ,1.1211848990196412784 ] 
dist 231=[-1.0869334024912791394 ,1.1480303430808173110 ] 
dist 232=[-1.0717354964886624341 ,1.1752655225341246515 ] 
dist 233=[-1.0638970057478525336 ,1.1968993002398283336 ] 
dist 234=[-1.0503499022948319463 ,1.2014058790374215742 ] 
dist 235=[-1.1617529742431732767 ,1.1992389357205219791 ] 
dist 236=[-1.2559198658873339709 ,1.1942581415640817158 ] 
dist 237=[-1.3314701503192772821 ,1.1411533754909919365 ] 
dist 238=[-1.3686286140856963477 ,1.1252538217424764114 ] 
dist 239=[-1.3880308708088153278 ,1.1051428172923198443 ] 
dist 240=[-1.3927678955914251380 ,1.0954517685749392650 ] 
dist 241=[-1.3597370845049410129 ,.95949207931878946908] 
dist 242=[-1.3476251413790999879 ,.93973205257349909797] 
dist 243=[-1.3295364694661354863 ,.90680026301529125258] 
dist 244=[-1.3208151974697297120 ,.89648923332460592383] 
dist 245=[-1.2841022770277483593 ,.85703503145682924872] 
dist 246=[-1.2717898122531123276 ,.64543501257519274879] 
dist 247=[-1.2381178270788007384 ,.60782802037040455172] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 0, 1, 1, 0, 1] 
dist 0=[68.794909074325418904  ,68.794909074325418904  ] 
dist 1=[68.366765616369252312  ,68.902788161176836326  ] 
dist 2=[67.474625486129068966  ,68.905472023415526588  ] 
dist 3=[65.713026435524119480  ,68.764355845130120817  ] 
dist 4=[63.523050452961925065  ,68.643899775801887599  ] 
dist 5=[60.920650778120512120  ,67.892569407376943718  ] 
dist 6=[57.513330005766832422  ,67.663189912612704774  ] 
dist 7=[52.109641394345090054  ,66.724898860950840868  ] 
dist 8=[46.592394644897383362  ,66.573458601675234042  ] 
dist 9=[42.731836169347781223  ,65.356708119554620721  ] 
dist 10=[39.340488896154458767  ,63.194733692240528002  ] 
dist 11=[35.697051212495417549  ,62.627677358500052552  ] 
dist 12=[32.165896489034276984  ,62.335693986589139500  ] 
dist 13=[29.223177236960316507  ,62.002615771217241854  ] 
dist 14=[26.145577720199380468  ,53.188268225481694202  ] 
dist 15=[22.076432017314930970  ,51.613215847874792134  ] 
dist 16=[18.083314033668125025  ,43.053161636847004909  ] 
dist 17=[15.309428123336343461  ,27.083398228428729031  ] 
dist 18=[12.896520895065054145  ,24.394297967313812966  ] 
dist 19=[10.344603811899089331  ,18.204317132115425123  ] 
dist 20=[7.8986035489715483673 ,17.238704666299501720  ] 
dist 21=[5.9087159684893416307 ,12.695080091824054938  ] 
dist 22=[3.7346551559895915341 ,10.020163591086621124  ] 
dist 23=[.65747907788769095153,9.7804211448138526787 ] 
dist 24=[-2.3377766577327306567 ,8.6268830664045105436 ] 
dist 25=[-4.5348495517076161083 ,8.4684850205480465080 ] 
dist 26=[-6.6203454458447731280 ,1.0126301270604669676 ] 
dist 27=[-8.1894543465263133378 ,.3222455278616700829 ] 
dist 28=[-9.4750907379475016004 ,-1.0874061569780378316 ] 
dist 29=[-10.496660513453890459  ,-1.4064236720813205431 ] 
dist 30=[-11.010339625156299138  ,-2.6133505625851576685 ] 
dist 31=[-11.355862065600110255  ,-2.8363051733137105898 ] 
dist 32=[-12.136444916114832945  ,-3.1083427133790793572 ] 
dist 33=[-12.603789468933916407  ,-3.1226465901607607869 ] 
dist 34=[-13.184673557187956667  ,-3.0503347354642814178 ] 
dist 35=[-13.477715590027819187  ,-2.8750029865013541048 ] 
dist 36=[-13.625385582071100862  ,-2.5946660200817276471 ] 
dist 37=[-13.649876966967678272  ,-2.1022288109098102341 ] 
dist 38=[-13.527611044131712396  ,-.98841436491632089743] 
dist 39=[-13.453851292344144366  ,1.6884355196177972451 ] 
dist 40=[-13.358752245844880713  ,4.3695078549335760305 ] 
dist 41=[-13.299822472171806415  ,6.1300606562406123038 ] 
dist 42=[-8.9837370940483022003 ,7.5495019502919072839 ] 
dist 43=[-8.7998741134538052929 ,8.8701100349103925904 ] 
dist 44=[-7.4844984816488772267 ,10.022908321877629821  ] 
dist 45=[-7.2151753861408946623 ,10.773076873283342913  ] 
dist 46=[-6.7527886188519645978 ,11.370739671223543950  ] 
dist 47=[-6.6317593900812749067 ,11.915332172870864983  ] 
dist 48=[-4.2106951722382435759 ,12.372598875596306619  ] 
dist 49=[-3.8845711955154172866 ,12.621889273579481884  ] 
dist 50=[-3.0948349285954234632 ,12.766353443058111603  ] 
dist 51=[-2.9636422469384103103 ,12.805247649536076541  ] 
dist 52=[-1.8159816121020973810 ,12.772988017782623089  ] 
dist 53=[-1.6028750425635329578 ,12.622800400895951999  ] 
dist 54=[-1.3029109662374603641 ,11.445925580428533272  ] 
dist 55=[-1.2149033144924990187 ,10.467725753809407975  ] 
dist 56=[1.0829698445998072099 ,5.7156832870212281870 ] 
dist 57=[1.3350265165014105066 ,5.6923648536607559949 ] 
dist 58=[1.0219636911105132208 ,5.6042287576299353660 ] 
dist 59=[.26903401862388184519,5.7854827656150069551 ] 
dist 60=[-.37953838518489421746,5.9230250456350564159 ] 
dist 61=[-1.0533750132477095742 ,6.0231375685068331366 ] 
dist 62=[-1.6902599393365865454 ,6.0548495035914038036 ] 
dist 63=[-2.1914608019889177123 ,6.0557472038071804422 ] 
dist 64=[-2.6883354060890874271 ,6.0385847856726183765 ] 
dist 65=[-3.3079986338259017329 ,3.4600997543315640631 ] 
dist 66=[-3.8965344609706314364 ,3.5104121037692019801 ] 
dist 67=[-4.2692442864397002494 ,3.5357316026927091664 ] 
dist 68=[-4.5546187249760275194 ,3.5429678981804902405 ] 
dist 69=[-4.7947463617022902653 ,3.5354911245351978853 ] 
dist 70=[-4.9869575592195823872 ,3.4913995588601449523 ] 
dist 71=[-5.0811774003905556312 ,3.4669065189566522998 ] 
dist 72=[-5.3686255970708527866 ,1.4503548658508278129 ] 
dist 73=[-5.6709872096739228914 ,1.2655352688080141942 ] 
dist 74=[-5.8188660933031159096 ,.85185916301841362712] 
dist 75=[-5.8954825553280112343 ,1.3668620004480148991 ] 
dist 76=[-5.9134615261471652411 ,1.7946584125485228469 ] 
dist 77=[-5.7855045430303811698 ,2.2136879748990797030 ] 
dist 78=[-5.7513902008934744093 ,2.5936839412334536845 ] 
dist 79=[-5.7301589839985846004 ,2.8658077834293634295 ] 
dist 80=[-5.7210675131804999812 ,3.1103409637572889456 ] 
dist 81=[-4.2831899636179376658 ,3.3803056972360613088 ] 
dist 82=[-4.1000329169926194213 ,3.6208305298360194360 ] 
dist 83=[-3.6671430741702445895 ,3.7479489644027879187 ] 
dist 84=[-3.5631188793607922265 ,4.3557480355525824677 ] 
dist 85=[-3.2486333265514158456 ,4.9322400323192487452 ] 
dist 86=[-3.2481892307316958066 ,5.3196740206389213509 ] 
dist 87=[-3.2405671796756787330 ,5.6419667160218671579 ] 
dist 88=[-2.4969894534127529185 ,5.9586745779886617459 ] 
dist 89=[-1.5401161630306579720 ,6.2295078268490320035 ] 
dist 90=[-1.4032943941338950519 ,6.3688280369521921575 ] 
dist 91=[-1.6673035780996379235 ,6.4382896340530020712 ] 
dist 92=[-2.1108262513708431193 ,6.4455259596862607896 ] 
dist 93=[-2.5362957478798066992 ,6.3893433699391282288 ] 
dist 94=[-2.9161419893215469540 ,6.3527548928687816417 ] 
dist 95=[-3.1777156710002531632 ,6.2538833342416198486 ] 
dist 96=[-3.4020242509874464593 ,6.2048245912315888602 ] 
dist 97=[-3.6332571082877840952 ,3.2175878418258978664 ] 
dist 98=[-3.8350892815220869679 ,3.3282798020994817161 ] 
dist 99=[-3.9421434437734819861 ,3.4002371647859823901 ] 
dist 100=[-3.9999981425672559267 ,3.4446199451776292485 ] 
dist 101=[-4.0087192207204783854 ,3.4505938811775974118 ] 
dist 102=[-3.9889260463272122109 ,3.4311630543475205561 ] 
dist 103=[-3.9676542133557908419 ,3.4161430357953967475 ] 
dist 104=[-3.9174762722485853601 ,3.1188954077942153220 ] 
dist 105=[-3.8915195973917303154 ,3.0636542862603893498 ] 
dist 106=[-3.7817628835471524004 ,2.9153714632192496476 ] 
dist 107=[-3.8503611327551553263 ,2.8743964403470132676 ] 
dist 108=[-3.8950560849715094984 ,2.5822810386647783664 ] 
dist 109=[-3.9208503452390249320 ,2.5164741236867150513 ] 
dist 110=[-3.9158896256491429895 ,2.7179493322495586418 ] 
dist 111=[-3.8911515706114572901 ,2.9823977615672648821 ] 
dist 112=[-3.8698274616679495098 ,3.2045696746144510267 ] 
dist 113=[-1.4792771517932429916 ,3.4262305014721533211 ] 
dist 114=[-1.4651220009457472180 ,3.6201641085135075806 ] 
dist 115=[-1.4663173747357133595 ,3.7317570933864308778 ] 
dist 116=[-1.4537407775537174901 ,3.8040907690108227736 ] 
dist 117=[-1.4456026293924401488 ,3.8414533095973286492 ] 
dist 118=[-1.4210057051001476289 ,3.8533598328874337311 ] 
dist 119=[-1.4086254004238137999 ,3.8492380535570996801 ] 
dist 120=[-.05409567409100472418,3.7891830240939372124 ] 
dist 121=[-.09242609191082428185,3.7779542575494930194 ] 
dist 122=[-.12456998090737947128,1.8200559641172335531 ] 
dist 123=[-.5237974297714394701 ,1.6339353041034038418 ] 
dist 124=[-.96004598574613938738,1.2111136954324862138 ] 
dist 125=[-1.4012852460804367120 ,1.1210322632273852500 ] 
dist 126=[-1.8103961627552925924 ,.59053256864563644383] 
dist 127=[-2.1185142767133238548 ,.49482993100623836284] 
dist 128=[-2.4107653261949501487 ,.30068095155946378251] 
dist 129=[-2.7565974172217571343 ,.2511195876850492918 ] 
dist 130=[-3.0752035618045841630 ,-.14334900202298118096] 
dist 131=[-3.2588751012921700654 ,-.11995969246381902666] 
dist 132=[-3.3783533840067166757 ,-.09212571794464121296] 
dist 133=[-3.4409506383884258306 ,-.06084349012290086523] 
dist 134=[-3.4775508259081261760 ,-.02113734852899663718] 
dist 135=[-3.4933501320457386747 ,.04029153645486074773] 
dist 136=[-3.4968942731356787582 ,.10202356878056187808] 
dist 137=[-3.4846192018436309125 ,.1429385925452389943 ] 
dist 138=[-.19393246277965919368,.65347515921412943765] 
dist 139=[-.18907934752819586758,1.1039240327435905258 ] 
dist 140=[-.15772086581203876606,1.4910223880353920044 ] 
dist 141=[-.1513446147753726093 ,1.8912857526010579040 ] 
dist 142=[-.13947773469245883543,2.2679511277761647857 ] 
dist 143=[-.13634880063526653674,2.5609387021093067801 ] 
dist 144=[-.08351885431439979525,2.8478853594572577961 ] 
dist 145=[-.07619391496007065057,3.2004590913990048840 ] 
dist 146=[-.05881671780369802590,3.5319934346685053480 ] 
dist 147=[-.05565557740271427482,3.7350331845149634550 ] 
dist 148=[-.03155849787122328105,3.8822459357330188451 ] 
dist 149=[-.02713622922263195295,3.9911373092239220668 ] 
dist 150=[-.14430336416279860594,4.0666854748386365984 ] 
dist 151=[-.31935381735109268223,4.0821148791892940357 ] 
dist 152=[-.73930956588120497484,4.0733299471249209770 ] 
dist 153=[-1.6061434598745230313 ,4.0618192002455634207 ] 
dist 154=[-2.4709299056508952383 ,3.8483981096056144618 ] 
dist 155=[-3.0317006434427682256 ,3.7996950718248923409 ] 
dist 156=[-3.4755418128855546690 ,3.6592619878947245528 ] 
dist 157=[-3.8740032183277650287 ,3.6167566348776474912 ] 
dist 158=[-4.2113940487931694365 ,3.3015784419700219209 ] 
dist 159=[-4.4116805929889605750 ,3.2274853447760903837 ] 
dist 160=[-4.5493146834527453873 ,3.1058181691257450258 ] 
dist 161=[-4.6368422409593872822 ,3.0679578287473749154 ] 
dist 162=[-4.6944117523519736219 ,2.1908951713136230038 ] 
dist 163=[-4.7125705979488905278 ,2.0684371277362828316 ] 
dist 164=[-4.7052882042537637544 ,1.7853053432907535925 ] 
dist 165=[-4.6904318976796833580 ,1.7177039625647225122 ] 
dist 166=[-4.5974962948712100725 ,1.3325098059323839726 ] 
dist 167=[-4.5665602585674196922 ,1.2580325903062649366 ] 
dist 168=[-4.4339372465791606394 ,1.1058055428953161112 ] 
dist 169=[-4.4122564839914674213 ,1.0640647515891547024 ] 
dist 170=[-.53010210727295050991,.51137859710524201807] 
dist 171=[-.52710372930762109426,.63165161784554632772] 
dist 172=[-.49915095423683866343,.83367245002387741822] 
dist 173=[-.49137448304675050235,1.0215441339174581320 ] 
dist 174=[-.48072511355509249137,1.1852777995962202986 ] 
dist 175=[-.47619850606354180618,1.2910341687069262124 ] 
dist 176=[-.36230605483735864483,1.3742679887830285894 ] 
dist 177=[-.35314132262076873616,1.4481798234413860295 ] 
dist 178=[-.33764015706851770152,1.5111294601910935602 ] 
dist 179=[-.33311543807711556102,1.5506451025952243994 ] 
dist 180=[-.31844824270989531731,1.5804482138967684376 ] 
dist 181=[-.31349743563259555686,1.6046634404253031063 ] 
dist 182=[-.30809980932974370159,1.6233489389681362926 ] 
dist 183=[-.30515303717657089503,1.6310990188434681269 ] 
dist 184=[-.14646055528735555975,1.6323010636233223679 ] 
dist 185=[-.24553720601032447714,1.6262678204374746513 ] 
dist 186=[-.32857349163593860044,.46958774057773919413] 
dist 187=[-.41108705714503607861,.37331999167709159053] 
dist 188=[-.48665607357796878543,.31071669349440347068] 
dist 189=[-.54199690961650744674,.34947956500401647117] 
dist 190=[-.5929572111449083433 ,.38684881716271823061] 
dist 191=[-.65105628441348666123,.43193599918695407386] 
dist 192=[-.70344122266683039949,.47392019531625170082] 
dist 193=[-.8762967039423148199 ,.49891447502450640238] 
dist 194=[-1.0471023110051703893 ,.51617783155759271017] 
dist 195=[-1.1552758280896717689 ,.52733044579029047883] 
dist 196=[-1.2379732310330934853 ,.53419079509632013714] 
dist 197=[-1.3071779288466116676 ,.53506805638369653512] 
dist 198=[-1.3621705694827214816 ,.53212856253205146415] 
dist 199=[-1.3881890798955915115 ,.52960450954662755242] 
dist 200=[-1.3994902435127824244 ,.48219641319543070414] 
dist 201=[-1.3994157814310862054 ,.4734510264327094399 ] 
dist 202=[-.50593082145149907816,.46336797242704073336] 
dist 203=[-.49334664912563614387,.54575416374993174649] 
dist 204=[-.52465431548546494631,.6186510224287549084 ] 
dist 205=[-.55321034631858618463,.66769219968018061199] 
dist 206=[-.57414094273456415205,.70850808386670748557] 
dist 207=[-.59004894470005962237,.75875443478839045343] 
dist 208=[-.60197250908856972967,.82823991853118974342] 
dist 209=[-.60701283007458571757,.90644091701204882506] 
dist 210=[-.60796208147375282502,.97656677308376232057] 
dist 211=[-.60666562053131778044,1.0138479038796624154 ] 
dist 212=[-.59636306629137828119,1.0347047475241991393 ] 
dist 213=[-.5925927944461786779 ,1.0393291516249418540 ] 
dist 214=[-.57678189340169930557,1.0328545359478524451 ] 
dist 215=[-.57345860202673998489,1.0304076112144903519 ] 
dist 216=[-.05036036873242350898,1.0282486881310826998 ] 
dist 217=[-.10906428150672599421,1.0259271702127166859 ] 
dist 218=[-.33007110317471703341,.76807998053768029518] 
dist 219=[-.4769577547829491417 ,.73549549390555614014] 
dist 220=[-.59725390247581179312,.65749509137763455328] 
dist 221=[-.7122155396692897352 ,.63920101317958093527] 
dist 222=[-.81454215915375892275,.67424786361359475285] 
dist 223=[-.88444878482339327716,.77820027370570693547] 
dist 224=[-.94379181152574789696,.8789479096720437349 ] 
dist 225=[-1.0039899026679910709 ,.9458639191970374151 ] 
dist 226=[-1.0562121058101029686 ,1.0006184895495343939 ] 
dist 227=[-1.0837466147818308323 ,1.0528652743928695274 ] 
dist 228=[-1.0983910977188490225 ,1.0993162159636898817 ] 
dist 229=[-1.1003114317078049490 ,1.1309564715918959295 ] 
dist 230=[-1.0939554945933583987 ,1.1577151055649358127 ] 
dist 231=[-1.0881042890115887367 ,1.1846977256548046762 ] 
dist 232=[-1.0727338671620038977 ,1.2060339897112825245 ] 
dist 233=[-1.0648159960076294425 ,1.2102744769120849471 ] 
dist 234=[-1.1699554854143259262 ,1.2078895584776228302 ] 
dist 235=[-1.2650852515496452436 ,1.2028031432788583824 ] 
dist 236=[-1.3414532468035076890 ,1.1489244211661895736 ] 
dist 237=[-1.3791015637182530551 ,1.1328448854127749653 ] 
dist 238=[-1.3987811287681327349 ,1.1124349082269121667 ] 
dist 239=[-1.4034882175888235808 ,1.1026527910354695538 ] 
dist 240=[-1.3709368772763511225 ,.96100091970871923718] 
dist 241=[-1.3588301993807381332 ,.94106097951543548425] 
dist 242=[-1.3407814337902449418 ,.90780970813637763541] 
dist 243=[-1.3320272622123980458 ,.89742728709207482489] 
dist 244=[-1.2950982744420085663 ,.8621267926705580834 ] 
dist 245=[-1.2827139341147740330 ,.82454288065934980128] 
dist 246=[-1.2487228151039443121 ,.6451532488446118776 ] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 2, 0, 2, 0, 0, 1] 
dist 0=[70.224038262586344093  ,70.224038262586344093  ] 
dist 1=[68.370983630358149409  ,71.201279401036726246  ] 
dist 2=[66.050249018753004040  ,71.724207839286167048  ] 
dist 3=[63.206242232364796310  ,71.815658079145815063  ] 
dist 4=[59.433243304528116791  ,71.580527263142197636  ] 
dist 5=[53.404455266651755022  ,71.410758557546544159  ] 
dist 6=[47.243896365332882112  ,70.812281748460901643  ] 
dist 7=[42.944976660762872046  ,70.497274418304961316  ] 
dist 8=[39.185538406255105210  ,68.750237970748267358  ] 
dist 9=[35.178420884102622512  ,68.239146617831384411  ] 
dist 10=[31.318079365483999573  ,67.952622705929876309  ] 
dist 11=[28.144546827554417487  ,67.677908035986802876  ] 
dist 12=[24.865880411290334070  ,67.456301444795724311  ] 
dist 13=[20.585948042697575022  ,67.062707840182410550  ] 
dist 14=[16.414270328514645611  ,66.739487027421496002  ] 
dist 15=[13.567651259874971669  ,64.043316812284565814  ] 
dist 16=[11.146083231099471647  ,31.872029930997194462  ] 
dist 17=[8.6707988459356667375 ,29.100544224684945588  ] 
dist 18=[6.3495061333673998942 ,22.646884562026349928  ] 
dist 19=[4.5424250353343527533 ,21.648680442682850504  ] 
dist 20=[2.7648842722655820828 ,15.590675818611115298  ] 
dist 21=[.56120006625619449355,11.841435828275003941  ] 
dist 22=[-1.5486624058320473211 ,9.7360153160226637176 ] 
dist 23=[-2.9519646537416730838 ,9.1948003623297826032 ] 
dist 24=[-4.1085732126394197238 ,1.1429379164803827570 ] 
dist 25=[-5.2341988481032274705 ,.56593982500019456284] 
dist 26=[-6.7940681124526912911 ,-.43102608670202981203] 
dist 27=[-8.5010598512016407599 ,-.61975643785637716075] 
dist 28=[-9.9451861129585949636 ,-.7440229829773881627 ] 
dist 29=[-10.827507662596167614  ,-.6403556975526951816 ] 
dist 30=[-11.477734259127273679  ,-.45679201144344712922] 
dist 31=[-11.997747699395525875  ,-.21630490115747251851] 
dist 32=[-12.387381303028505468  ,.1064558355815654671 ] 
dist 33=[-12.517178766299556529  ,.61930527244682411424] 
dist 34=[-12.549739512910286871  ,1.2093058521632988958 ] 
dist 35=[-12.546899645113781282  ,1.8402856212372614060 ] 
dist 36=[-12.009467027555327123  ,2.6185188770547862091 ] 
dist 37=[-11.857323487488528767  ,3.7961924454403609922 ] 
dist 38=[-11.752307090971995743  ,4.9606084339252739835 ] 
dist 39=[-11.695459704745919366  ,5.6861784847785918244 ] 
dist 40=[-9.0630445400105197767 ,6.2265531360697532539 ] 
dist 41=[-8.7132391854622149957 ,6.6526061527415252869 ] 
dist 42=[-8.0466829708409711127 ,6.9874573645264078118 ] 
dist 43=[-7.9977536457205504696 ,7.1642079365737559277 ] 
dist 44=[-7.9508529089320570400 ,7.2584531501803508049 ] 
dist 45=[-7.9030115882076523673 ,7.2665908648845232383 ] 
dist 46=[-6.7009467443975172879 ,6.6111214807229120537 ] 
dist 47=[-6.6329766283078349778 ,6.4880044910418180761 ] 
dist 48=[-5.6924003196001087779 ,6.3189990144842324896 ] 
dist 49=[-5.5718514132872543058 ,6.2497640679055033435 ] 
dist 50=[-5.1172590476055389735 ,6.0824565215533486178 ] 
dist 51=[-5.0033990612085156891 ,6.2621127139058414708 ] 
dist 52=[-4.7942518844764534330 ,6.5649415803950362215 ] 
dist 53=[-4.7341354434073656875 ,6.8194837664371632177 ] 
dist 54=[-1.1243226512355076294 ,6.9275753347724643787 ] 
dist 55=[-2.1915106941705478707 ,6.9741024965046334114 ] 
dist 56=[-3.0653048331567107261 ,7.4996835944215899010 ] 
dist 57=[-3.8996298777738853117 ,7.9103420249785338433 ] 
dist 58=[-4.6415176927514381951 ,8.2071390275583984830 ] 
dist 59=[-5.1467120009957470972 ,8.4273324705240912921 ] 
dist 60=[-5.5737199667532538668 ,8.5823588615212101637 ] 
dist 61=[-6.0038389206843703147 ,8.6198302331056083283 ] 
dist 62=[-6.3831232000857907725 ,8.6157168621883198314 ] 
dist 63=[-6.6074133732728943183 ,8.6116273689201136170 ] 
dist 64=[-6.7604830188375911925 ,4.1743623319565630368 ] 
dist 65=[-6.8557346084266627900 ,3.4681178387473606631 ] 
dist 66=[-6.9062216563947107683 ,3.3266731344433446522 ] 
dist 67=[-6.9759551922741589254 ,3.0449196212299602188 ] 
dist 68=[-7.3165010417967228438 ,2.9668221453605947712 ] 
dist 69=[-7.6019443226303905882 ,1.9119819446609566741 ] 
dist 70=[-7.7422055968529833365 ,1.7584431932979248639 ] 
dist 71=[-7.8030433612960502084 ,1.4064832028640275636 ] 
dist 72=[-7.8068927480003312589 ,1.3286768111544787176 ] 
dist 73=[-7.7030024764741189055 ,2.0870931390540810541 ] 
dist 74=[-7.6524213537152507529 ,2.8202362807638545790 ] 
dist 75=[-7.5212957840771675724 ,3.3796453336415714407 ] 
dist 76=[-7.4598123975341153277 ,3.9171958287614730423 ] 
dist 77=[-5.2037766287077456837 ,4.5631691532944041827 ] 
dist 78=[-5.2102553076115257767 ,5.1631855812649440472 ] 
dist 79=[-5.2082904202733009521 ,5.5174627082911387041 ] 
dist 80=[-1.1807028788166511627 ,5.7584921320050206531 ] 
dist 81=[-.85364390455281300543,5.9068827558025727979 ] 
dist 82=[-.13230448474542499797,6.0049774245135139434 ] 
dist 83=[.01546879651545308312,6.3272007978610851908 ] 
dist 84=[.45104941024500211046,6.6817189369035696746 ] 
dist 85=[.04587097496194893147,6.9849666042115319472 ] 
dist 86=[-1.0264865989740260940 ,7.1671470281162526544 ] 
dist 87=[-1.7712860275822470528 ,7.2951139281312629069 ] 
dist 88=[-2.4092489351855110388 ,7.3821303521101927319 ] 
dist 89=[-3.0655535357193840548 ,7.4359612493426307152 ] 
dist 90=[-3.6810532245431699922 ,7.4315690426931222402 ] 
dist 91=[-4.1562864890433925141 ,7.3926845917963192742 ] 
dist 92=[-4.6183856601648515225 ,7.3591588256384393253 ] 
dist 93=[-5.1815091317913717870 ,4.5844737705948199213 ] 
dist 94=[-5.7087018334689358848 ,4.6423589843908177309 ] 
dist 95=[-6.0275081747368511306 ,4.6510713483539975312 ] 
dist 96=[-6.2538023981102163899 ,1.1213061937070907542 ] 
dist 97=[-6.4120515275281757798 ,.02421952106880054010] 
dist 98=[-6.5150598903368766188 ,-.16661555667219072359] 
dist 99=[-6.5357667305340674719 ,.00103499786663923367] 
dist 100=[-6.4987285140271530301 ,.35015018862245161295] 
dist 101=[-6.4888614822313782914 ,.88404823857270738635] 
dist 102=[-6.0327376557628722585 ,1.4174527657255806070 ] 
dist 103=[-5.9411624703900802313 ,1.7645981555001068896 ] 
dist 104=[-5.6870371142241140059 ,2.0407680634585126046 ] 
dist 105=[-5.6146166328916956744 ,2.2911169151562637005 ] 
dist 106=[-5.0824449961557683820 ,2.5048068720641217337 ] 
dist 107=[-4.9602841746880369347 ,2.6347776606388999216 ] 
dist 108=[-4.3832101970589297401 ,2.7279243506155972101 ] 
dist 109=[-3.2276894724539263148 ,2.7947551278008413657 ] 
dist 110=[-3.2045956900422981772 ,2.8430769778218013774 ] 
dist 111=[-3.1877143738290670936 ,2.8624086112735544992 ] 
dist 112=[-2.1453860903885474655 ,2.8641381940716116849 ] 
dist 113=[-2.0266577555879674337 ,2.8568642486022392029 ] 
dist 114=[-1.7487080700061841132 ,2.8072249169503080401 ] 
dist 115=[-1.6855821430318432379 ,2.7897572301307715181 ] 
dist 116=[-1.2977102872308067545 ,2.7113925356469315022 ] 
dist 117=[-1.2227500771793819478 ,2.6990967079968218502 ] 
dist 118=[-1.0773418358570715424 ,2.7146870004188661129 ] 
dist 119=[-1.0393298172707275034 ,2.9324507969313158319 ] 
dist 120=[-.52701286235453839733,3.1253776930922021441 ] 
dist 121=[-.45296980163077735864,3.2296143717438690276 ] 
dist 122=[-.29913409786006574012,3.2885675805901373138 ] 
dist 123=[-.25876733122950364572,3.3008944171400022743 ] 
dist 124=[-.11083338851167449693,3.2940224691157016675 ] 
dist 125=[-.61259462952276335246,3.2773801039606746853 ] 
dist 126=[-.98590849997725566259,3.2477158174723692338 ] 
dist 127=[-1.2945039883847197389 ,3.2316208563885586844 ] 
dist 128=[-1.5941918944159249214 ,1.3984523486288290260 ] 
dist 129=[-1.8641606531678079279 ,1.0786452412150866030 ] 
dist 130=[-2.0542337080600610120 ,1.0167415101685166700 ] 
dist 131=[-2.2216342616829998141 ,.89722712868655127907] 
dist 132=[-2.4011835399551037789 ,.86608395386297345928] 
dist 133=[-2.5603664912805323682 ,.43859471459770297242] 
dist 134=[-2.6465441517808631082 ,.37706793104604455811] 
dist 135=[-2.7168364033811964160 ,.24854059036814003827] 
dist 136=[-2.8590408049518917397 ,.21466588471638557496] 
dist 137=[-2.9427915591367516911 ,.08948900655606647991] 
dist 138=[-2.9995262610079271892 ,.06440882771417458553] 
dist 139=[-3.0339872398147202146 ,.02060866104068672240] 
dist 140=[-3.0513809734888912593 ,.01097963901000228509] 
dist 141=[-3.0481887443587866887 ,.56487616392755536211] 
dist 142=[-3.0188963765323974083 ,.93789245407967222361] 
dist 143=[-2.9971203154052440687 ,1.2414875234561719408 ] 
dist 144=[-1.2652154690597002847 ,1.5284621171714082814 ] 
dist 145=[-1.1072505641462856689 ,1.7817750797701909016 ] 
dist 146=[-.75086201097856920382,1.9511246879642226720 ] 
dist 147=[-.67597356346705075317,2.0909111620142702471 ] 
dist 148=[-.24034263782234457562,2.2263238830912885798 ] 
dist 149=[-.16318191720312655141,2.3440547115358673043 ] 
dist 150=[-.00455326492466987869,2.4133242404501985094 ] 
dist 151=[.03573558784905428415,2.4601618442019488532 ] 
dist 152=[.36548641593590184871,2.4884320410885424861 ] 
dist 153=[.41918999568978577853,2.5025088729230044948 ] 
dist 154=[.46501982714574075751,2.5664382245089762511 ] 
dist 155=[.4511776989599630588 ,2.6413017791380070408 ] 
dist 156=[.40988777781213831569,2.6926194441797039300 ] 
dist 157=[.1522494495130075857 ,2.7124379991272666839 ] 
dist 158=[-.17736931241379646631,2.7129233312265140223 ] 
dist 159=[-.45868251170143581765,2.7073678574240640898 ] 
dist 160=[-.74646733342164984678,.56600654458269443106] 
dist 161=[-1.0153617677637796409 ,.20949818546803603407] 
dist 162=[-1.2213385139150075768 ,.14627370034611237828] 
dist 163=[-1.4200724601976003695 ,.01643375798472602116] 
dist 164=[-1.6600820439064703568 ,-.01654853387296102869] 
dist 165=[-1.8836916856315617837 ,-.2892467810220591447 ] 
dist 166=[-2.0364436140470162999 ,-.33352829343768786682] 
dist 167=[-2.2741185526965855563 ,-.37260090293154208255] 
dist 168=[-2.4954969259291854400 ,-.36259049737512482242] 
dist 169=[-2.6273975921178437180 ,-.3302278533061146031 ] 
dist 170=[-2.7186340817410844302 ,-.26711124575525182481] 
dist 171=[-2.7778401377320536610 ,-.16956811753569329457] 
dist 172=[-2.8143721334855852062 ,9.11515751906732649000e-05] 
dist 173=[-2.8192106130085097803 ,.3928829178124307265 ] 
dist 174=[-2.8036245429499641719 ,.66244745341982792569] 
dist 175=[-2.7908305982806433082 ,.93668290645361403982] 
dist 176=[-2.5439637846443094044 ,1.5370029713913847571 ] 
dist 177=[-2.4982403668741386983 ,1.9283945846876485810 ] 
dist 178=[-2.3758413363931866108 ,2.2405628021450771989 ] 
dist 179=[-2.3419380089690978572 ,2.5249332321962451425 ] 
dist 180=[-2.1019418972980658605 ,2.7686675857636774177 ] 
dist 181=[-2.0479293000534461922 ,2.9187756848145948275 ] 
dist 182=[-1.9550092365126365124 ,3.0286141187385741577 ] 
dist 183=[-1.9285135408246550869 ,3.1117496488702950746 ] 
dist 184=[-1.3436262702988643895 ,3.1738997099255261189 ] 
dist 185=[-1.2625382392974495466 ,3.2000462985376440950 ] 
dist 186=[-1.0701900360157415772 ,3.2047533211629312298 ] 
dist 187=[-1.0301742970704569893 ,3.1978221455565440462 ] 
dist 188=[-.78480822912756966989,3.1432316983240537882 ] 
dist 189=[-1.2811285049577942300 ,3.1233350569211735994 ] 
dist 190=[-1.6045925064547484374 ,3.0396924433173096418 ] 
dist 191=[-1.8624446598291180292 ,3.0223484376847770795 ] 
dist 192=[-2.0970993168464961747 ,1.9462600119021779717 ] 
dist 193=[-2.2980552458370083441 ,1.7490708100275517892 ] 
dist 194=[-2.4215140130214771626 ,1.7045630033951208018 ] 
dist 195=[-2.5114912896086595744 ,1.6282372486888356100 ] 
dist 196=[-2.5789201961539050725 ,1.6063420065954357134 ] 
dist 197=[-2.6290103404797114499 ,1.1213116356981445718 ] 
dist 198=[-2.6498391578366920215 ,1.0540334353779935948 ] 
dist 199=[-2.6531636659223556946 ,.89474631428814435853] 
dist 200=[-2.6472355961755522679 ,.86125200410502510223] 
dist 201=[-2.6015034142874841492 ,.635558434443570781  ] 
dist 202=[-2.5849904071459479572 ,.59241633792572303056] 
dist 203=[-2.4922196230243485919 ,.51357909561732322732] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 0, 0, 1, 1, 2] 
dist 0=[68.506555256786571350  ,68.506555256786571350  ] 
dist 1=[67.701757387504535710  ,69.018794451391338918  ] 
dist 2=[66.288181087225798114  ,69.264464428901436774  ] 
dist 3=[64.650706689037010894  ,69.318094061881635551  ] 
dist 4=[62.952041742643212348  ,69.269897470783390290  ] 
dist 5=[60.882852534990358404  ,68.769585626751406351  ] 
dist 6=[57.766052728222624609  ,68.665940303116214374  ] 
dist 7=[54.212276819146155129  ,66.382751737867169721  ] 
dist 8=[50.398538844312601790  ,65.840034176998169932  ] 
dist 9=[45.661143650752324870  ,65.047301251223249360  ] 
dist 10=[38.419877556052622843  ,64.749488126464779126  ] 
dist 11=[31.130531162958197305  ,63.926154172640359276  ] 
dist 12=[26.201091571663256098  ,63.593899172838027795  ] 
dist 13=[22.052450874837693401  ,62.088784659549475362  ] 
dist 14=[17.879984720506545958  ,59.117383873710884822  ] 
dist 15=[14.007131461701842140  ,37.973040050414674510  ] 
dist 16=[11.054382008774842718  ,37.589846520978778646  ] 
dist 17=[8.2068979193355996396 ,27.843966563076783332  ] 
dist 18=[4.7538764481589870337 ,26.610562991538841617  ] 
dist 19=[1.5045069023502146720 ,24.017091145026523042  ] 
dist 20=[-.5301952057857288170 ,23.340249378113007460  ] 
dist 21=[-2.0683156526128717008 ,20.741389110609214216  ] 
dist 22=[-3.3355070223808816405 ,20.242610697187102286  ] 
dist 23=[-4.3433719047936057502 ,19.243793576405294624  ] 
dist 24=[-4.8461950907282089185 ,18.993290517702807979  ] 
dist 25=[-5.1065097799791260482 ,5.7059013146859165418 ] 
dist 26=[-5.1459259341909269499 ,4.5273804390287446491 ] 
dist 27=[-6.0268293576087495703 ,1.9858505251334014751 ] 
dist 28=[-8.2407194105355638070 ,1.4807179370258158341 ] 
dist 29=[-10.231684725991015393  ,-1.2205696969211150141 ] 
dist 30=[-11.654035167221069795  ,-1.6659760247605726795 ] 
dist 31=[-12.938352025662733662  ,-2.6270407858354381118 ] 
dist 32=[-14.378302301332333510  ,-2.7780599501344977898 ] 
dist 33=[-15.683139882598294005  ,-3.8635291091985071409 ] 
dist 34=[-16.427849981432449105  ,-4.0171164874364580317 ] 
dist 35=[-16.909469425036145765  ,-3.9659255302990740799 ] 
dist 36=[-17.163325973107278629  ,-3.6275564484573331082 ] 
dist 37=[-17.305923941495276473  ,-3.1350675094606508144 ] 
dist 38=[-17.342881101747881549  ,-2.4683440808329930030 ] 
dist 39=[-17.311014127119274500  ,-1.5487697543009650429 ] 
dist 40=[-17.261092250290743515  ,-.04689300781018761510] 
dist 41=[-12.020503896963815773  ,2.4918814025858739003 ] 
dist 42=[-11.949662019792793815  ,4.5475541949050000695 ] 
dist 43=[-11.207514961776744513  ,6.2324910528558279486 ] 
dist 44=[-11.028849581974686590  ,7.8479781558267502876 ] 
dist 45=[-10.805419767703070410  ,9.2923392280971334586 ] 
dist 46=[-10.710039879991715348  ,10.294747475673087437  ] 
dist 47=[-6.9233713790619963629 ,11.164371621541072877  ] 
dist 48=[-6.4830954929291046794 ,12.079226464827855509  ] 
dist 49=[-5.4932458560326283768 ,12.893100802933273294  ] 
dist 50=[-5.2555686636585164296 ,13.359825163142575008  ] 
dist 51=[-3.9992683115406565971 ,13.661494299325521989  ] 
dist 52=[-3.7606486645017437295 ,13.816539420559138858  ] 
dist 53=[-3.2505199687776736535 ,13.882741188455490991  ] 
dist 54=[-3.1065638972702662466 ,13.867736099755037483  ] 
dist 55=[-1.7509245559301277531 ,13.738249825637526210  ] 
dist 56=[-1.5346233354231551900 ,13.648867338175364068  ] 
dist 57=[-1.1217674076811845307 ,8.4859145949766757980 ] 
dist 58=[-1.0196483250702510527 ,7.9644078284133376489 ] 
dist 59=[-.69217050188568839762,6.7297072255690226350 ] 
dist 60=[-.71210663166075003104,6.4889291641419022738 ] 
dist 61=[-1.3625494228579180989 ,4.7626697729953559526 ] 
dist 62=[-1.8791441182832744476 ,3.9971799855660144641 ] 
dist 63=[-2.3953578448013022591 ,-.68951213690045992294] 
dist 64=[-3.0443173584305236492 ,-.70928124615964326939] 
dist 65=[-3.6625294467987839480 ,-.72116839168973798628] 
dist 66=[-4.0561135055534092568 ,-.70377220678871587294] 
dist 67=[-4.3596324708396083377 ,-.67337830974335333213] 
dist 68=[-4.6186039620654928032 ,-.62773265711570394433] 
dist 69=[-4.8284230069820825724 ,-.56276071837288328951] 
dist 70=[-4.9358865917525436843 ,-.45525973621123083625] 
dist 71=[-4.9887240840991548606 ,-.3412315747176789184 ] 
dist 72=[-4.9943273713424235905 ,-.03094805131195989656] 
dist 73=[-.77039359921530169809,.68116872838330890306] 
dist 74=[-.76664318181513585259,1.1599161957297855025 ] 
dist 75=[-.74903765723364672379,1.5580106574084168085 ] 
dist 76=[-.74358620345733160204,1.9484851958092825349 ] 
dist 77=[-.72795351298783379266,2.3028150577268978018 ] 
dist 78=[-.72184494363534444576,2.5567668679578972698 ] 
dist 79=[-.68325517810291673149,2.7851127160715140097 ] 
dist 80=[-.67425178678734666353,3.0373311184980633444 ] 
dist 81=[-.65139906467857529892,3.2627148614376772845 ] 
dist 82=[-.64302060032834530982,3.3840418234149156082 ] 
dist 83=[-.59813033040738058549,3.4520657645551938453 ] 
dist 84=[-.58718222568935958131,3.4671765635499282576 ] 
dist 85=[-.56568136262669291704,3.4577030516159526390 ] 
dist 86=[-.55882267653507821015,3.4461119601567876097 ] 
dist 87=[-.43269419058143737969,3.4291037405076632628 ] 
dist 88=[-.41396194861645872481,3.4099668907394716438 ] 
dist 89=[-.89891199814517779285,2.4038422747224560956 ] 
dist 90=[-1.3843819646703971597 ,2.2844958203244680356 ] 
dist 91=[-1.7842793481560258750 ,2.0022591124673781959 ] 
dist 92=[-2.1702901627399894914 ,1.9377187908217998984 ] 
dist 93=[-2.5164623521693034020 ,1.5321958681539048982 ] 
dist 94=[-2.7574818916641358938 ,1.4527337182589114629 ] 
dist 95=[-2.9669357170604209481 ,1.3012083915587403393 ] 
dist 96=[-3.1872234908139826532 ,1.2617307681294710137 ] 
dist 97=[-3.3811016314043963862 ,.68312629673405229102] 
dist 98=[-3.4852318752892454616 ,.6009415694239371184 ] 
dist 99=[-3.5432699440773718137 ,.4221689311451793812 ] 
dist 100=[-3.5533271142047670987 ,.42516751110350553281] 
dist 101=[-3.5429602560431123147 ,.5199511260771185653 ] 
dist 102=[-3.5249829696919321474 ,.65526902827998489525] 
dist 103=[-3.4861280525977942668 ,.7917970692221819387 ] 
dist 104=[-3.4653853124770338546 ,.89141048824190572428] 
dist 105=[-1.8268250277914923644 ,.9827395826162637517 ] 
dist 106=[-1.9169977512517246316 ,1.2351112336073372179 ] 
dist 107=[-1.9968249732447299104 ,1.6315868929208882483 ] 
dist 108=[-2.0506176953230341052 ,2.0004958341841152234 ] 
dist 109=[-2.0954819025763744991 ,2.3221439787078284818 ] 
dist 110=[-2.1396929394486438736 ,2.5301400981904149446 ] 
dist 111=[-2.1739350340789537560 ,2.6941139965541489088 ] 
dist 112=[-2.1795753665595160359 ,2.8401983405959663830 ] 
dist 113=[-2.1730737849829756435 ,2.9647331152653983076 ] 
dist 114=[-2.1631703802635604505 ,3.0427656559567943586 ] 
dist 115=[-2.0642841350356438363 ,3.1014532470252094285 ] 
dist 116=[-2.0350839338611000469 ,3.1488386265473077048 ] 
dist 117=[-1.9967629532315422511 ,3.1851676027680886296 ] 
dist 118=[-1.9791395425933710833 ,3.1997612390662781454 ] 
dist 119=[-1.6606713653537412497 ,3.2011873435316832288 ] 
dist 120=[-1.6250356665284279445 ,3.1894360278176248026 ] 
dist 121=[-1.5660102454039962337 ,1.2193538377702565483 ] 
dist 122=[-1.5475924699866167751 ,1.1926567876773243856 ] 
dist 123=[-1.4866236996901200119 ,1.0949039210228772271 ] 
dist 124=[-1.4657696514332736392 ,1.0693062269774495512 ] 
dist 125=[-1.4363488915502831306 ,1.0290107057954540113 ] 
dist 126=[-1.4237830765135012384 ,1.0160057992200342990 ] 
dist 127=[-1.3770836232393615141 ,.40349131375235097656] 
dist 128=[-1.7280066560923409501 ,.67235326085676714742] 
dist 129=[-2.0618497803219232468 ,.88979553134130209769] 
dist 130=[-2.2730167903876893262 ,1.0930063031908178504 ] 
dist 131=[-2.4341501378375955132 ,1.2707904760750259889 ] 
dist 132=[-2.5684548414908967758 ,1.3868295212165302231 ] 
dist 133=[-2.6747647480936714546 ,1.4795206811239587187 ] 
dist 134=[-2.7242524987765248704 ,1.5641914661254861468 ] 
dist 135=[-2.7454717127158305552 ,1.6368429702544655008 ] 
dist 136=[-2.7444189357039700325 ,1.6816004806718277954 ] 
dist 137=[.33980581622876550129,1.7143636889821734899 ] 
dist 138=[.45398394479517243027,1.7391817005372422007 ] 
dist 139=[.70563443092236648039,1.7569040817524418081 ] 
dist 140=[.74907712654979653689,1.7613697654577279640 ] 
dist 141=[.94556245745343910271,1.7569668232360804021 ] 
dist 142=[.62681803865635332771,1.7508976865875385938 ] 
dist 143=[.30152832040020610069,1.6364791603348499098 ] 
dist 144=[.07598628972310421324,1.7922625927007664014 ] 
dist 145=[-.11902434082768299909,1.9320350376698963263 ] 
dist 146=[-.32255234928175487273,2.0062162187899131140 ] 
dist 147=[-.51524927354114907152,2.0478136679109122462 ] 
dist 148=[-.66706460228757115587,2.0576394606126053033 ] 
dist 149=[-.81756171594566265587,2.0430867901839542583 ] 
dist 150=[-1.0050013248871387566 ,2.0385978025841348993 ] 
dist 151=[-1.1825047646928700409 ,2.0352644309546046747 ] 
dist 152=[-1.2933756769004157448 ,2.0326507061843123593 ] 
dist 153=[-1.3763472588973550763 ,1.5352856818496640029 ] 
dist 154=[-1.4425862082062379428 ,1.4718162517566565978 ] 
dist 155=[-1.4927673795259719243 ,1.3195349681968780706 ] 
dist 156=[-1.5116994101994910157 ,1.2836822154117273031 ] 
dist 157=[-1.6298443199089214013 ,1.0548812174102181975 ] 
dist 158=[-1.7674016187632974733 ,1.0089290117383797091 ] 
dist 159=[-1.8837051760903014430 ,.92256183404158490713] 
dist 160=[-2.0009326073822446267 ,.89984111824859247007] 
dist 161=[-2.1023633656574145132 ,.53492978648280917261] 
dist 162=[-2.1556684586668300731 ,.66847315172832355818] 
dist 163=[-2.1837761700314885473 ,.7929186327252543717 ] 
dist 164=[-2.1872608243892844252 ,.88492928011997287989] 
dist 165=[-2.1736729046862283333 ,.97053302658750246961] 
dist 166=[-2.1619663046429940514 ,1.0694272303609805060 ] 
dist 167=[-2.1303739884954703168 ,1.1592904445496327189 ] 
dist 168=[-2.1141626159492731708 ,1.2088778675579189152 ] 
dist 169=[.276761975292145617  ,1.2383161140518149243 ] 
dist 170=[.36886929707544970214,1.2478228002007879927 ] 
dist 171=[.34413557480764002787,1.2495362624740451353 ] 
dist 172=[.20703916660293545405,1.2843730304277417478 ] 
dist 173=[.03384353961114780830,1.5025985499461158425 ] 
dist 174=[-.23322777001276685675,1.6518883502407802900 ] 
dist 175=[-.50123484789272010272,1.7788380108202550743 ] 
dist 176=[-.67816237385981189865,1.9079691610461843714 ] 
dist 177=[-.82174224916189535101,2.0214510981535644089 ] 
dist 178=[-.95675607727493302547,2.0859903718413875230 ] 
dist 179=[-1.0754523018992274376 ,2.1268522519945663625 ] 
dist 180=[-1.1539561893875335086 ,2.1459067395818106786 ] 
dist 181=[-1.2178247311510343511 ,2.1506913511783298850 ] 
dist 182=[-1.2781539428625176833 ,2.1471654158558614966 ] 
dist 183=[-1.3289182874881534942 ,2.1149713160358825429 ] 
dist 184=[-1.3546413372465490278 ,2.1052997210154841491 ] 
dist 185=[-1.3668736549265834210 ,1.0899263765294934718 ] 
dist 186=[-1.3672867381636852458 ,.99059278839285515866] 
dist 187=[-1.3537019942029361820 ,.76386371990225113041] 
dist 188=[-1.3459771242082576102 ,.71512140304543422671] 
dist 189=[-1.3207286804699888349 ,.42570308631164169622] 
dist 190=[-1.3081003099260416233 ,.37288295509764805615] 
dist 191=[-1.4225536041415094208 ,.3006491959952085898 ] 
dist 192=[-1.6071921645007966642 ,.50122318967527112455] 
dist 193=[-1.7759518500906840912 ,.6662906026250792666 ] 
dist 194=[-1.8708463899529960695 ,.82537642652159824408] 
dist 195=[-1.9295334375340668767 ,.96787742241121438895] 
dist 196=[-1.9538945758917377976 ,1.0668031358720189847 ] 
dist 197=[-1.9649886695031180183 ,1.1524666541148094588 ] 
dist 198=[-1.9707656189906951324 ,1.2420768894452524778 ] 
dist 199=[-1.9737374473953447621 ,1.3212888473555211484 ] 
dist 200=[-1.9736444819824979886 ,1.3654831556284885165 ] 
dist 201=[.09024388531525521298,1.3923628490782938390 ] 
dist 202=[.12296290488522259494,1.4025226624322751862 ] 
dist 203=[.17695557938139408089,1.4037500540479415139 ] 
dist 204=[.18903695691891811821,1.3996190272879138891 ] 
dist 205=[.13080737328696889888,1.3827236954947512013 ] 
dist 206=[.02763299323117033539,1.5068108506751229441 ] 
dist 207=[-.15295323990101155659,1.6795778012550043090 ] 
dist 208=[-.34456218490657502816,1.8936535064395002886 ] 
dist 209=[-.5050186685287310479 ,2.0958467124001799230 ] 
dist 210=[-.66425128717899179256,2.2212252487388798562 ] 
dist 211=[-.8099442966766728184 ,2.3139841208726931079 ] 
dist 212=[-.91640367043985485582,2.3860873406039826499 ] 
dist 213=[-1.0142013896509414363 ,2.4391439864706594648 ] 
dist 214=[-1.1253509845424281775 ,2.4559435073633717895 ] 
dist 215=[-1.2259836227830687862 ,2.4562685759693442378 ] 
dist 216=[-1.2818388279984605530 ,2.4468851424759804554 ] 
dist 217=[-1.5540902306270902682 ,2.3574391393311750441 ] 
dist 218=[-1.8888780042874950436 ,2.3333023299991246157 ] 
dist 219=[-2.1528536320130755471 ,2.2597259827169348687 ] 
dist 220=[-2.3881081044550693738 ,2.2361333036639323858 ] 
dist 221=[-2.5860666684057496340 ,2.0563813695991612890 ] 
dist 222=[-2.7013030505934764856 ,2.0131114309670142001 ] 
dist 223=[-2.7776805003987451417 ,1.9438417604852541823 ] 
dist 224=[-2.8206663469238652871 ,1.9212666298424827666 ] 
dist 225=[-2.8457987962756279611 ,1.3861215357348489053 ] 
dist 226=[-2.8509753843532331737 ,1.3111615353008616759 ] 
dist 227=[-2.8425118134351966024 ,1.1398984982323773792 ] 
dist 228=[-2.8321963648442108429 ,1.0965193303877635346 ] 
dist 229=[-2.7729586434568473692 ,1.1961793045006738935 ] 
dist 230=[-2.7532116584623060119 ,1.3549398331435705879 ] 
dist 231=[-2.6742208843225385383 ,1.5057849557457197760 ] 
dist 232=[-2.6582667143134589590 ,1.6008761682456682278 ] 
dist 233=[-.24760828151583802827,1.6730621896707706929 ] 
dist 234=[-.32052750192902229198,1.7325594688911917480 ] 
dist 235=[-.39896121884171884814,1.7791387150658326698 ] 
dist 236=[-.47620058043137106608,1.7998065258634662748 ] 
dist 237=[-.56712961100996372998,1.8053932023587165597 ] 
dist 238=[-.8306608713084651016 ,1.8034137169938346920 ] 
dist 239=[-1.2072184791547951928 ,1.7697219966444011290 ] 
dist 240=[-1.4498409974633281126 ,1.7572918923443602827 ] 
dist 241=[-1.6401149736161758133 ,1.7144928227802233368 ] 
dist 242=[-1.8079021564842822704 ,1.6992231004717611243 ] 
dist 243=[-1.9478027170905344743 ,1.5775958512456192337 ] 
dist 244=[-2.0268624789796151069 ,1.5472305662725266728 ] 
dist 245=[-2.0762683310352538458 ,1.5004833601302064707 ] 
dist 246=[-2.0979065845788484977 ,1.4841539878061885216 ] 
dist 247=[-2.1066392451152330586 ,1.0845770398744232288 ] 
dist 248=[-2.1045764980166741753 ,1.0283633821887017798 ] 
dist 249=[-2.0942179138658440785 ,.9019784399076628207 ] 
dist 250=[-2.0852586873327422246 ,.8674495735752191094 ] 
dist 251=[-2.0384736485586810817 ,.70413686110970092863] 
dist 252=[-2.0228519059441573049 ,.67208588799619446676] 
dist 253=[-1.9657979412750985359 ,.60317440694659337645] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 2, 0, 2, 0, 1] 
dist 0=[43.726600633929072612  ,43.726600633929072612  ] 
dist 1=[41.713084051218983937  ,46.028739864287868838  ] 
dist 2=[35.978987467430523047  ,49.483615488552613485  ] 
dist 3=[29.233684438785507866  ,53.001683790379260540  ] 
dist 4=[22.101242410739325700  ,56.151797529886750799  ] 
dist 5=[13.321038145689730714  ,58.138260914272917402  ] 
dist 6=[0                     ,59.654503040570594471  ] 
dist 7=[41.765847708109113256  ,60.927341635719987513  ] 
dist 8=[54.656898875304975424  ,61.947479505492132642  ] 
dist 9=[51.934693818756517875  ,62.454882453794468027  ] 
dist 10=[48.016004256490195958  ,62.684204104604055600  ] 
dist 11=[41.454004978048491901  ,62.594203278720532045  ] 
dist 12=[34.691448208375410425  ,62.338224135937362554  ] 
dist 13=[29.972483112774615809  ,62.084417898202447718  ] 
dist 14=[25.858081479257452172  ,60.588274335783546404  ] 
dist 15=[21.506762810213242822  ,57.303913298498944160  ] 
dist 16=[17.348583392105836264  ,32.033383763460337131  ] 
dist 17=[14.004447295030728155  ,29.616696722755960808  ] 
dist 18=[10.623733613485961987  ,23.801437674891278180  ] 
dist 19=[6.3195122269994983045 ,22.934774050731862625  ] 
dist 20=[2.1919150922235627386 ,14.771701667033822844  ] 
dist 21=[-.4843473084686757075 ,13.310816258113798103  ] 
dist 22=[-2.6043651516029116029 ,11.420673646414037682  ] 
dist 23=[-4.5132756197946312980 ,11.019868024231628478  ] 
dist 24=[-6.1359128505413171144 ,.5089092816766131101 ] 
dist 25=[-7.1141198992790363737 ,-.7199961417585137645 ] 
dist 26=[-7.8061257943245288341 ,-3.4003584219284373832 ] 
dist 27=[-8.2873298468290342860 ,-3.8215098341723237185 ] 
dist 28=[-8.6449332944474086044 ,-5.2459478126480542911 ] 
dist 29=[-8.8441146712596402711 ,-5.3463099665901614068 ] 
dist 30=[-8.9665663318933551870 ,-5.3487662746515636885 ] 
dist 31=[-9.0248390942653974143 ,-5.1737316153393377560 ] 
dist 32=[-8.1242219896100684697 ,-4.9176028184638808810 ] 
dist 33=[-8.1335638073315471783 ,-4.5814730768277497156 ] 
dist 34=[-8.0604301474378863566 ,-4.1284289201307199714 ] 
dist 35=[-8.0135358068548587406 ,-3.4053955098851713953 ] 
dist 36=[-7.5616221316992133689 ,-2.6507559667195210613 ] 
dist 37=[-7.4448206970593008608 ,-2.0711111604702012063 ] 
dist 38=[-7.2617948498551002074 ,-1.5126875402846181355 ] 
dist 39=[-7.1976028863922025008 ,-.8416800409735043631 ] 
dist 40=[-5.6436989829214108802 ,-.1527171534496495953 ] 
dist 41=[-5.4329543123893478822 ,.4779206097634702799 ] 
dist 42=[-4.9310403784961040734 ,1.1855993616129996526 ] 
dist 43=[-4.8319071030267998507 ,2.1826048553128552613 ] 
dist 44=[-4.1328849555833602835 ,3.1575868183974583891 ] 
dist 45=[-4.0037452123873886841 ,3.7776116172030569766 ] 
dist 46=[-3.7704158735111632521 ,4.2567197307143285754 ] 
dist 47=[-3.7164885887453345461 ,4.6694471232972338159 ] 
dist 48=[-2.2557863108768815315 ,5.0089749488714869165 ] 
dist 49=[-2.2094700530531810630 ,5.1960661125135531325 ] 
dist 50=[-2.0843198830569317721 ,5.3083751209036897375 ] 
dist 51=[-2.0615870950108773746 ,5.3496725103542097501 ] 
dist 52=[-1.7618169970424714272 ,5.3570960134647933331 ] 
dist 53=[-1.7093025494050128706 ,5.3405810899865753473 ] 
dist 54=[-1.5735157310053901888 ,5.5457962026668801777 ] 
dist 55=[-1.5434772178907589109 ,5.7667772437594799055 ] 
dist 56=[-1.2943362146845018535 ,5.9453973149342282862 ] 
dist 57=[-1.2400020204579300075 ,6.0173328921827743417 ] 
dist 58=[-1.1627705258417889995 ,6.0428730546361489366 ] 
dist 59=[-1.1362860942774109854 ,6.0358558845487786988 ] 
dist 60=[-1.4789511149642309965 ,5.8620918659702527745 ] 
dist 61=[-2.2723345975399146085 ,5.8032402857156521904 ] 
dist 62=[-2.9127557544088247533 ,5.7474808926626752941 ] 
dist 63=[-3.5097955377765889901 ,5.7088363728071292795 ] 
dist 64=[-4.0317062611266392847 ,-1.8348103899225019536 ] 
dist 65=[-4.3724891233872097015 ,-2.2633727701855050668 ] 
dist 66=[-4.6452270062870919066 ,-3.2115488743280665230 ] 
dist 67=[-4.8957707863451667848 ,-3.3620476500551891474 ] 
dist 68=[-5.1087404178625736928 ,-4.3837890697457421517 ] 
dist 69=[-5.2316080824367690965 ,-4.4270181059160633982 ] 
dist 70=[-5.3119255370169454455 ,-4.2649589445972692341 ] 
dist 71=[-5.3854620224211162281 ,-3.9297183152488424215 ] 
dist 72=[-5.5810287574819729874 ,-3.5102027823411838929 ] 
dist 73=[-5.6933230144777401665 ,-3.0119993942056526327 ] 
dist 74=[-5.7661572993130662808 ,-2.3622172090675800886 ] 
dist 75=[-5.8042700470493963445 ,-1.3381303724026767093 ] 
dist 76=[-5.8173161637673835223 ,-.2983952841181240612 ] 
dist 77=[-5.8027352523822393933 ,.41381306900268152624] 
dist 78=[-5.7459210854146641487 ,1.0205548477917153654 ] 
dist 79=[-5.7085940132395794580 ,1.6396752937165115307 ] 
dist 80=[-2.1768155945426596345 ,2.2173442848699951976 ] 
dist 81=[-1.8616352424931565568 ,2.6587761674566439825 ] 
dist 82=[-1.1561286383891623714 ,3.0837939963358201839 ] 
dist 83=[-1.0082962377489930417 ,3.5960135641078454770 ] 
dist 84=[-.16799401386424449011,4.0730201709500267999 ] 
dist 85=[-.02126871382786091175,4.3576002659877159742 ] 
dist 86=[.28614645991121504545,4.5550212741761271539 ] 
dist 87=[.35997230823664834005,4.6844030908473490962 ] 
dist 88=[.7314112962747449924 ,4.7726406980168871035 ] 
dist 89=[.58492360357254230445,4.8059583030485029723 ] 
dist 90=[.36305757447726757092,4.9198417658518710995 ] 
dist 91=[-.01884952696477645984,5.0773742097261469998 ] 
dist 92=[-.86630181402124370222,5.1881188709183222487 ] 
dist 93=[-1.4472994003128633598 ,5.2284443872387241501 ] 
dist 94=[-1.9425228633688662444 ,5.2315738037049823758 ] 
dist 95=[-2.4481678331106006595 ,5.2179259747028271822 ] 
dist 96=[-2.9200480658641472800 ,-.51452897627933788462] 
dist 97=[-3.2806146864048643828 ,-.67310164420360716047] 
dist 98=[-3.6276669748062860954 ,-1.0188352901382431437 ] 
dist 99=[-4.0456522129802208348 ,-1.0810398094420010465 ] 
dist 100=[-4.4345541370456386297 ,-1.1898748957715015896 ] 
dist 101=[-4.6656181404177040189 ,-1.1294502304208297106 ] 
dist 102=[-4.8246673180526757312 ,-1.0371961608949634877 ] 
dist 103=[-4.9263622042604800542 ,-.87775551242809756086] 
dist 104=[-4.9883254288589944064 ,-.67677440172000360816] 
dist 105=[-4.9956150183181370137 ,-.11821870496469818715] 
dist 106=[-5.0507111835695647474 ,.57890495254877745367] 
dist 107=[-5.1400756741955789108 ,1.6446942249055171674 ] 
dist 108=[-5.1903504226335287852 ,2.7098525231892214671 ] 
dist 109=[-5.1904372130523523873 ,3.4044612910582320435 ] 
dist 110=[-5.1635031082597676446 ,3.9586540727382737978 ] 
dist 111=[-5.1347217511057405199 ,4.4638213480001419700 ] 
dist 112=[-4.5591702819375491583 ,4.8970412770256361955 ] 
dist 113=[-4.4619106902413851520 ,5.1643021774130470323 ] 
dist 114=[-4.2093821064222199534 ,5.3604143252224109056 ] 
dist 115=[-4.1419756645437912293 ,5.5098878632471008638 ] 
dist 116=[-3.6773523092318590714 ,5.6221066856191232874 ] 
dist 117=[-3.5751238529497565200 ,5.6696434264059656595 ] 
dist 118=[-3.3943568862320534615 ,5.6787767774324939080 ] 
dist 119=[-3.3453501099757089898 ,5.6668085726143366669 ] 
dist 120=[-2.2950247689005585486 ,5.7863378281870915356 ] 
dist 121=[-2.1499321905116615762 ,5.8481380497028034295 ] 
dist 122=[-1.8000714111590109048 ,5.8664174973879774652 ] 
dist 123=[-1.7338110498685682957 ,5.8570317398691176628 ] 
dist 124=[-1.2938563468596222979 ,5.7657944413820267459 ] 
dist 125=[-2.1437983260487481910 ,5.7299392045646936738 ] 
dist 126=[-2.8299919040462660977 ,5.5872664248758090080 ] 
dist 127=[-3.4692786851619959571 ,5.5491377626654842341 ] 
dist 128=[-4.0272281832194199144 ,-1.3273271345482803344 ] 
dist 129=[-4.3890417887696716730 ,-1.7675743519504183409 ] 
dist 130=[-4.6754261982957789002 ,-2.7649099485488939433 ] 
dist 131=[-4.9325578019930817361 ,-2.9129052714870388231 ] 
dist 132=[-5.1521435987188102928 ,-4.0665733364048828203 ] 
dist 133=[-5.2887920528741554287 ,-4.2470507589949000816 ] 
dist 134=[-5.3904633176955194344 ,-4.5420781842322540411 ] 
dist 135=[-5.4705567132099703316 ,-4.5441920063685775040 ] 
dist 136=[-5.5303726065683582440 ,-4.1716368447885563638 ] 
dist 137=[-5.5511752400591098010 ,-3.7056595194369783608 ] 
dist 138=[-5.5473265717409903067 ,-3.0833912806259532239 ] 
dist 139=[-5.6061465915804587506 ,-2.0875343212911698074 ] 
dist 140=[-5.6676514322195743954 ,-1.0705229848588597770 ] 
dist 141=[-5.6893730495226538033 ,-.36388916003745466883] 
dist 142=[-5.6860531625394585242 ,.24866026956393651485] 
dist 143=[-5.6655325157296422259 ,.89045507261191226103] 
dist 144=[-1.7167507528380612291 ,1.4996392599003879707 ] 
dist 145=[-1.3852920720598436723 ,1.9821348281276492843 ] 
dist 146=[-.64571796418711902058,2.4628213217484008178 ] 
dist 147=[-.49385239491075337588,3.0647908689546964954 ] 
dist 148=[.3713883911486435435 ,3.6364825673521645593 ] 
dist 149=[.51969435399215581829,3.9964184047407051958 ] 
dist 150=[.83190904824971951915,4.2691291677396954267 ] 
dist 151=[.89961696974099808836,4.4929596905095884457 ] 
dist 152=[1.1478476422261557787 ,4.6674573414337579745 ] 
dist 153=[.90568364739511372641,4.7434243223965192787 ] 
dist 154=[.56438714029310188311,4.7741521169363286411 ] 
dist 155=[-.00012289240160974217,4.7682319215014076648 ] 
dist 156=[-.72310266075555650591,4.7815645712486030054 ] 
dist 157=[-1.2120282702500564478 ,4.8604634062138860464 ] 
dist 158=[-1.6217188423207813532 ,4.8925946105416883847 ] 
dist 159=[-2.0287025578790970768 ,4.8859647039737774492 ] 
dist 160=[-2.4013512405009182968 ,-.58866591620397993756] 
dist 161=[-2.6741107926452567842 ,-.78572597565663407479] 
dist 162=[-2.9251409678494345360 ,-1.2227822872467091319 ] 
dist 163=[-3.2111310663099157656 ,-1.2957812155557926795 ] 
dist 164=[-3.4688839750655280293 ,-1.7737083470232263591 ] 
dist 165=[-3.6073018343847549052 ,-1.8473542764457861797 ] 
dist 166=[-3.6853292320174532362 ,-1.8342223431794595858 ] 
dist 167=[-3.7034486523795231066 ,-1.5318384968320499556 ] 
dist 168=[-3.6899447358434826781 ,-1.1727144909963489372 ] 
dist 169=[-3.6844995802349634173 ,-.77004765679978060504] 
dist 170=[-3.7637913690610607492 ,-.2595608856551862443 ] 
dist 171=[-3.7819445727611243939 ,.5295582019745631930 ] 
dist 172=[-3.7662684201883481335 ,1.3223905722134163361 ] 
dist 173=[-3.7593448390264700216 ,1.8476862401423379808 ] 
dist 174=[-3.7524762114067965640 ,2.2760811775077350855 ] 
dist 175=[-3.7439143941952387005 ,2.6824652183501369940 ] 
dist 176=[-2.9056916208999023813 ,3.0421588481099876954 ] 
dist 177=[-2.7950637164369176621 ,3.2843484698453730965 ] 
dist 178=[-2.5276139334821299468 ,3.4861426035804704631 ] 
dist 179=[-2.4638301387861411566 ,3.6847356094808168897 ] 
dist 180=[-2.0530462578098077420 ,3.8548628866382262398 ] 
dist 181=[-1.9696163116088252951 ,3.9431332775015800123 ] 
dist 182=[-1.8140182081909677386 ,3.9880937894014968826 ] 
dist 183=[-1.7729515484138512499 ,3.9923593343159940914 ] 
dist 184=[-1.0850470103700537235 ,3.9614963031573640431 ] 
dist 185=[-.98952745354313415295,4.0208124484388223373 ] 
dist 186=[-.76345205386254739858,4.0673069162144081099 ] 
dist 187=[-.72188418123163243027,4.0718690606477571020 ] 
dist 188=[-.86649957603951817398,4.0409983304949730499 ] 
dist 189=[-1.4433528928035483550 ,4.0187559656960392651 ] 
dist 190=[-1.9168415817827535245 ,3.9539516885037814091 ] 
dist 191=[-2.3711033335936843887 ,3.9210584096864199512 ] 
dist 192=[-2.7766287518299647306 ,-.44372617130866286373] 
dist 193=[-3.0557528101650660273 ,-.59186060586511115   ] 
dist 194=[-3.2949290946290946318 ,-.92370832913603523691] 
dist 195=[-3.5411394044923390072 ,-.97621460319178984267] 
dist 196=[-3.7580563949589318054 ,-1.3490645032245922681 ] 
dist 197=[-3.8804084371188448556 ,-1.4069497544290388626 ] 
dist 198=[-3.9565693125607310890 ,-1.5072382458392372928 ] 
dist 199=[-3.9892720103861723208 ,-1.3980103084226258653 ] 
dist 200=[-3.9959139791434951902 ,-1.2582846985178066631 ] 
dist 201=[-3.9871966901517423617 ,-1.0885106061279282564 ] 
dist 202=[-4.0278140443310973004 ,-.86471507462633181973] 
dist 203=[-4.0613782800115117912 ,-.50954738198847695153] 
dist 204=[-4.0683642567153963499 ,.2784336099550018143 ] 
dist 205=[-4.0597053215492879550 ,.8196099713333345955 ] 
dist 206=[-4.0032733148963056536 ,1.2747545126856075021 ] 
dist 207=[-3.9778368984240699193 ,1.7296142443149360409 ] 
dist 208=[-2.1491315185771826904 ,2.1478604575719877674 ] 
dist 209=[-1.9666261943691664111 ,2.4569871833408621544 ] 
dist 210=[-1.5487629765822761184 ,2.7444812654387607055 ] 
dist 211=[-1.4583855783964463772 ,3.0764546622192141044 ] 
dist 212=[-.91897351530404403715,3.3786618220472257607 ] 
dist 213=[-.81979528408294434612,3.5474456268524722487 ] 
dist 214=[-.62135699285673435304,3.6503324910919632110 ] 
dist 215=[-.57043870030562925794,3.6897370625291701162 ] 
dist 216=[-.03359417762416896763,3.7048653329261982298 ] 
dist 217=[.04819760102728319198,3.7109362493711688027 ] 
dist 218=[.13574457489730117422,3.7115180385597894423 ] 
dist 219=[-9.54908804141390000000e-07,3.7503396534517647200 ] 
dist 220=[-.72950697862971953944,3.7661386734138235212 ] 
dist 221=[-1.2352905915035393040 ,3.7728010870941548121 ] 
dist 222=[-1.6725850517230635220 ,3.7740278631833396869 ] 
dist 223=[-2.1289505580634805477 ,3.7681490985583852273 ] 
dist 224=[-2.5610184897612567633 ,-.14368035981204151391] 
dist 225=[-2.9014121620089421904 ,-.19728092961998533931] 
dist 226=[-3.2388463663982562652 ,-.15579314732487660025] 
dist 227=[-3.6591116894466277608 ,-.02562233584796501488] 
dist 228=[-4.0571105200738631050 ,.1186865726509979602 ] 
dist 229=[-4.3057440645193936426 ,.2451742403254069976 ] 
dist 230=[-4.4918609870455405190 ,.3824599341035527674 ] 
dist 231=[-4.6405382280092059534 ,.5698322866261428933 ] 
dist 232=[-4.7532518495429874603 ,.7743793977371249336 ] 
dist 233=[-4.7959428080323259947 ,.9801594852955781451 ] 
dist 234=[-4.8024549771164454051 ,1.2256450579791834656 ] 
dist 235=[-4.7903733633285717893 ,2.1080735629426410381 ] 
dist 236=[-4.8172783343764199240 ,3.1156392125480219910 ] 
dist 237=[-4.8595940154108516982 ,3.7661894307968136373 ] 
dist 238=[-4.8656326019407092238 ,4.2779202885633413439 ] 
dist 239=[-4.8527958952399290253 ,4.7318625572720878341 ] 
dist 240=[-4.7104037317605853479 ,5.1123173768585398782 ] 
dist 241=[-4.6683541611256728626 ,5.3309740561200706126 ] 
dist 242=[-4.5348442182260705609 ,5.4723554052504140596 ] 
dist 243=[-4.4903546357857339404 ,5.5446296557082054833 ] 
dist 244=[-4.1456482235243997104 ,5.5822505594149377777 ] 
dist 245=[-4.0614898208155159710 ,5.5854314232154532072 ] 
dist 246=[-3.9287866945897561321 ,5.5639871654589363712 ] 
dist 247=[-3.8843501094560714266 ,5.6147447756599290983 ] 
dist 248=[-2.8174165983844354042 ,5.6539565132591090027 ] 
dist 249=[-2.6677025915541514224 ,5.6578395970131719011 ] 
dist 250=[-2.3278709439331205538 ,5.6365791247989117275 ] 
dist 251=[-2.2390619267798258251 ,5.6146478424048354111 ] 
dist 252=[-1.7919413902968445363 ,5.4937700638446702236 ] 
dist 253=[-1.7046551230106073818 ,5.4534472040427021778 ] 
dist 254=[-1.5104472778584020569 ,5.2980524621935435040 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 1, 2, 0, 0, 2] 
dist 0=[68.831926410671209156  ,68.831926410671209156  ] 
dist 1=[68.205695565349550243  ,69.211124160310364747  ] 
dist 2=[67.279446371883936951  ,69.401766522975769996  ] 
dist 3=[65.703220000315620872  ,69.376554394099197201  ] 
dist 4=[63.893881854183651067  ,69.051986805664513166  ] 
dist 5=[62.037164520308394896  ,68.852893119091833821  ] 
dist 6=[59.791006307380253517  ,67.165987983237235563  ] 
dist 7=[56.426703470192164140  ,66.704801499389917319  ] 
dist 8=[52.600535717787138489  ,65.952274254388451827  ] 
dist 9=[48.510491175734924458  ,65.687806739988839336  ] 
dist 10=[43.442129344876347098  ,64.697337930289745215  ] 
dist 11=[35.710463471301211161  ,64.368661132889048502  ] 
dist 12=[27.936098389097331377  ,63.673457421882080165  ] 
dist 13=[22.696981953928067152  ,63.181591431710036349  ] 
dist 14=[18.308297874272241936  ,38.000979410911766042  ] 
dist 15=[13.928025548258445950  ,35.794859441552376571  ] 
dist 16=[9.8826222114696258202 ,34.757840181857982188  ] 
dist 17=[6.8300050828212909628 ,29.763467432675120939  ] 
dist 18=[3.9145514985341604766 ,22.546834498567453272  ] 
dist 19=[.41538144696827021573,21.252941263862161725  ] 
dist 20=[-2.8675253549654447078 ,19.569171156503168615  ] 
dist 21=[-4.9203043603973903819 ,19.185959182491684507  ] 
dist 22=[-6.4733250786708975355 ,15.678472431941948827  ] 
dist 23=[-7.7617924441978049989 ,14.826116769594720447  ] 
dist 24=[-8.7950766133325508819 ,14.640792072592029896  ] 
dist 25=[-9.3304937593266076337 ,5.7635544829100204635 ] 
dist 26=[-9.6157332686086184778 ,3.1212068815974878780 ] 
dist 27=[-9.6768129466264324055 ,2.7053669747040881426 ] 
dist 28=[-9.5764423438392128735 ,1.8805637202576079483 ] 
dist 29=[-10.930626451376100675  ,1.7389012106627258308 ] 
dist 30=[-12.059163140500828778  ,-2.5580373024214904894 ] 
dist 31=[-12.999243358763040882  ,-2.9695130516218995829 ] 
dist 32=[-13.933591671391519416  ,-3.7200744543223722766 ] 
dist 33=[-14.742118298969541138  ,-3.8749888073872354082 ] 
dist 34=[-15.179764793514768189  ,-4.2152493715852323949 ] 
dist 35=[-15.432659718313246130  ,-4.1873552855533970798 ] 
dist 36=[-15.503114497498082882  ,-4.0120051141769306921 ] 
dist 37=[-15.484433341977062842  ,-3.5970598837853434762 ] 
dist 38=[-15.429127045212035945  ,-3.1160587308143114074 ] 
dist 39=[-15.245541114738425345  ,-2.6765989685497161966 ] 
dist 40=[-15.140689925376128524  ,-1.7690185261628406076 ] 
dist 41=[-11.626813122069309962  ,1.2857465587694053974 ] 
dist 42=[-11.351195594834585690  ,3.3328964878571013454 ] 
dist 43=[-11.265150695285489807  ,5.0294184398066866257 ] 
dist 44=[-11.098779721867299096  ,6.6857243029760494222 ] 
dist 45=[-11.038517789856567682  ,8.1852242703077778790 ] 
dist 46=[-4.6749496148240447098 ,9.2563334995751247479 ] 
dist 47=[-4.0073954674983467122 ,10.216689622577877294  ] 
dist 48=[-3.8465153230055238376 ,11.274468731413953823  ] 
dist 49=[-1.4941473059110000206 ,12.231515313352391421  ] 
dist 50=[-1.1654184132520613665 ,12.790019559507129911  ] 
dist 51=[-.49724164228806401717,13.162460351821132519  ] 
dist 52=[-.32876818802473166193,13.377145673671749446  ] 
dist 53=[.25008802894324257198,13.496577929238571295  ] 
dist 54=[.37084732882235624215,13.495538008646671968  ] 
dist 55=[.48741985143649470967,13.425579871205436199  ] 
dist 56=[.47539949283672543671,13.353580172090316129  ] 
dist 57=[.43510165397502492197,6.7163081412927008365 ] 
dist 58=[.11647842739339823884,6.6582325866956240590 ] 
dist 59=[-.66564369234524025568,6.6176330355170887953 ] 
dist 60=[-1.5320383340606718243 ,6.5326455738036355763 ] 
dist 61=[-2.1069021038960897400 ,6.4941400162077792387 ] 
dist 62=[-2.5775038611560748556 ,1.9935627585614583527 ] 
dist 63=[-3.0279700643347784407 ,1.6027911771588534853 ] 
dist 64=[-3.4303834742232685272 ,.74130968130682685629] 
dist 65=[-3.7092978562930878785 ,.56032556425979558214] 
dist 66=[-3.9509296884822117667 ,.30261775367574920291] 
dist 67=[-4.2046391465284683128 ,.30505317964235679002] 
dist 68=[-4.4246873382197867064 ,.31393265031703992494] 
dist 69=[-4.5870477003017130322 ,.3261689780102530771 ] 
dist 70=[-5.2091780807343509165 ,.34196586275237106297] 
dist 71=[-5.5888171352556494825 ,.36323981744620007938] 
dist 72=[-5.8630584114734185700 ,.39727726059261936101] 
dist 73=[-6.0647063304037385248 ,.43085240233732497684] 
dist 74=[-6.2094922446462338314 ,.45027810433989031583] 
dist 75=[-6.2568734133751196068 ,.53311867033593346445] 
dist 76=[-6.2633017405113836897 ,1.5210534099333384203 ] 
dist 77=[-6.2446836254126278339 ,2.1762845259886215405 ] 
dist 78=[-2.6590099798746144771 ,2.7116568710805674861 ] 
dist 79=[-2.5742919855683934935 ,3.2215588239100395625 ] 
dist 80=[-2.0697651350487034441 ,3.6745962628935946885 ] 
dist 81=[-1.9705744169282467794 ,3.9831822055985508582 ] 
dist 82=[-1.7753042433029407673 ,4.2443838268600165808 ] 
dist 83=[-1.7226585967899848407 ,4.5084576517951633878 ] 
dist 84=[-1.0161625002141031140 ,4.7367383038255010213 ] 
dist 85=[-.91354654672305524161,5.0034292761450328793 ] 
dist 86=[-.68928325904944682022,5.4190513424640779952 ] 
dist 87=[-.63284131235235673357,5.6530702753488434952 ] 
dist 88=[-.52851973498518067856,5.7983173948507516119 ] 
dist 89=[-.3282058833825783004 ,5.8598727445572478699 ] 
dist 90=[-.21393586525585799013,5.8826493743657014937 ] 
dist 91=[-.19713930724747886028,5.8732299017912025897 ] 
dist 92=[-1.1105684554321064075 ,5.8384823896950531507 ] 
dist 93=[-1.8081776621292915529 ,5.8145683927027723689 ] 
dist 94=[-2.7133320263328629183 ,4.9148141588021480274 ] 
dist 95=[-3.5460592371832220235 ,4.7801244403617975753 ] 
dist 96=[-4.2170543725589118663 ,4.4435152384287052721 ] 
dist 97=[-4.8400785442080303285 ,4.3578672863515285261 ] 
dist 98=[-5.3824791746868988984 ,3.7908531999472780259 ] 
dist 99=[-5.7319392959581150277 ,3.6703020009628446606 ] 
dist 100=[-6.0060452436558769325 ,3.4510260306171571547 ] 
dist 101=[-6.2479297153713283213 ,3.3920168976180168008 ] 
dist 102=[-6.4449499811834923214 ,2.2586809807572497095 ] 
dist 103=[-6.5401290432539023820 ,2.1030497847771834002 ] 
dist 104=[-6.5787131266416115524 ,1.7165459663200569655 ] 
dist 105=[-6.5743245582318733569 ,1.6558744008236592598 ] 
dist 106=[-6.4889318315670256212 ,1.5212183749717638302 ] 
dist 107=[-6.4500038815525870395 ,1.5237110300306935960 ] 
dist 108=[-6.3095720963320911217 ,1.5190100207574584121 ] 
dist 109=[-6.2554262529434114235 ,1.4628250845369961940 ] 
dist 110=[-1.7499355078674044882 ,1.4445539074737440516 ] 
dist 111=[-1.7723040134173922519 ,1.6784860437357874398 ] 
dist 112=[-1.7753953477261635769 ,2.1845870018157587927 ] 
dist 113=[-1.7128161113256230609 ,2.5668394634962807771 ] 
dist 114=[-1.6946698633415165381 ,2.9304839335087526255 ] 
dist 115=[-1.6662238709258584555 ,3.3623764963221706460 ] 
dist 116=[-1.6542002263216180411 ,3.7611305473098108601 ] 
dist 117=[-1.6047251020106049607 ,3.9926148026167917804 ] 
dist 118=[-1.5883631315513237392 ,4.1452560053211349541 ] 
dist 119=[-1.5464760851378740753 ,4.2295724686494672572 ] 
dist 120=[-1.5292386135395381649 ,4.2809747623558179735 ] 
dist 121=[.40475254095866068167,4.3023484565076234613 ] 
dist 122=[.25843337966287996257,4.3057639625416108547 ] 
dist 123=[-.00489936688333274235,4.2903130768852879423 ] 
dist 124=[-.80060668977732219916,1.1031952814705218695 ] 
dist 125=[-1.3489678107412329654 ,1.2815915490954381882 ] 
dist 126=[-1.8195181595307181680 ,1.3983746783977448381 ] 
dist 127=[-2.3049819131189874286 ,1.4920549973627147674 ] 
dist 128=[-2.7611537894528795059 ,1.5783152325412379623 ] 
dist 129=[-3.1148855096541058487 ,1.6524091311137263164 ] 
dist 130=[-3.4602926195376418806 ,1.6975688383137435490 ] 
dist 131=[-3.8832654007347906506 ,1.7300542988797515147 ] 
dist 132=[-4.2802949412179561129 ,1.7536016241772530537 ] 
dist 133=[-4.5222378631570071537 ,1.7695222233336842164 ] 
dist 134=[-4.6962158758952664816 ,1.7715913187292735732 ] 
dist 135=[-4.8221944421173463602 ,1.7641304837730058209 ] 
dist 136=[-4.9072448138140443529 ,1.7579826082417311213 ] 
dist 137=[-4.9247738678191127414 ,.60446715971528061949] 
dist 138=[-4.9050365752811459219 ,.83689066750553979469] 
dist 139=[-4.8955189304132684098 ,1.8835689040515512325 ] 
dist 140=[-4.6059529638749931389 ,2.9280920453490352822 ] 
dist 141=[-4.5432969657294513732 ,3.6060733749686525612 ] 
dist 142=[-4.3657083419430711691 ,4.1434325692921985596 ] 
dist 143=[-4.3129560658299103891 ,4.6271425711571371185 ] 
dist 144=[-3.9256540304100406723 ,5.0376435085072117512 ] 
dist 145=[-3.8353787428740609934 ,5.2830387402899815814 ] 
dist 146=[-3.6857235039139775098 ,5.4537799984139642472 ] 
dist 147=[-3.6399508524888013447 ,5.5665546847297256000 ] 
dist 148=[-2.5889630597459860719 ,5.6430858488411256500 ] 
dist 149=[-2.4423944445414203556 ,5.6692847344689576750 ] 
dist 150=[-2.1019323049628695382 ,5.6635604675019977853 ] 
dist 151=[-2.0225472874843111182 ,5.6466888836320381367 ] 
dist 152=[-1.5555040309988015046 ,5.5371150754789180284 ] 
dist 153=[-1.4654010505451619179 ,5.5006743012391747805 ] 
dist 154=[-1.2851867439271146017 ,5.3401743782054985496 ] 
dist 155=[-1.2368050548503659940 ,5.3162491591941217969 ] 
dist 156=[-.5718860293726990288 ,.69918945461975106262] 
dist 157=[-.94717705737819687306,.83056990276431726303] 
dist 158=[-1.2495763389123295366 ,.92851044715916973594] 
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