8 phat 4 dirichlet min maxes function [2, 0, 0, 0, 2, 2, 1, 2] 
dist 0=[47.900144412567235406  ,47.900144412567235406  ] 
dist 1=[47.113851259990379702  ,48.378506481026115109  ] 
dist 2=[45.698704033887827191  ,48.563865609325558275  ] 
dist 3=[44.193919244094240836  ,48.647739045191448405  ] 
dist 4=[43.049620316649303378  ,48.762446930083894931  ] 
dist 5=[41.947058327320697254  ,48.932673927297052182  ] 
dist 6=[40.608899247798552093  ,48.997150781043259703  ] 
dist 7=[39.216869401567509272  ,48.996768871377764211  ] 
dist 8=[37.899060949817503754  ,48.714971645479840963  ] 
dist 9=[36.379084289910754395  ,46.418594951463029661  ] 
dist 10=[34.179403525354191328  ,46.017550153354215480  ] 
dist 11=[31.922806670678903610  ,45.298019142186302304  ] 
dist 12=[30.175393921749917933  ,45.098482992718850771  ] 
dist 13=[28.460540761845165408  ,44.361772557802527005  ] 
dist 14=[26.333836648176898981  ,44.143888346733276227  ] 
dist 15=[24.095910786372865823  ,43.769377883683843856  ] 
dist 16=[21.936576643096934431  ,43.443050321573146069  ] 
dist 17=[19.413044958413823759  ,28.925979642280143646  ] 
dist 18=[15.719878827473588167  ,28.497700628235404435  ] 
dist 19=[12.047680325033560198  ,24.629623744869880206  ] 
dist 20=[9.6078427155906992155 ,24.194587865834614019  ] 
dist 21=[7.5942245499413181866 ,19.870274633698170971  ] 
dist 22=[5.6248306553685439174 ,19.080287512707101949  ] 
dist 23=[3.8251866663740791761 ,18.158493896102966302  ] 
dist 24=[2.4896628260606246258 ,17.999586267080420732  ] 
dist 25=[.9354547458467639954 ,12.803066349324014988  ] 
dist 26=[-1.0582338022211770974 ,11.461824039626543805  ] 
dist 27=[-3.0305645848389968707 ,9.1255538820441493280 ] 
dist 28=[-4.7518095894224299512 ,8.7193624924999562444 ] 
dist 29=[-6.6277503043051949042 ,7.2956486410912054042 ] 
dist 30=[-9.2191211351558599068 ,7.0129214915224209215 ] 
dist 31=[-11.728278894821720746  ,6.6379661365223786510 ] 
dist 32=[-13.275970267161799516  ,6.5701961406669522038 ] 
dist 33=[-14.425337077639918148  ,-1.0189863244344105462 ] 
dist 34=[-15.342726496403393389  ,-1.6339271362550659016 ] 
dist 35=[-16.066657776858973656  ,-2.9335897802660952134 ] 
dist 36=[-16.442702289708895243  ,-3.1882079913065723471 ] 
dist 37=[-16.639246080249207470  ,-3.8775127691549841479 ] 
dist 38=[-16.674369571171946152  ,-3.6385673401232839336 ] 
dist 39=[-15.969435174120501802  ,-3.2863520774737518747 ] 
dist 40=[-15.814387303662102861  ,-2.9045681189521213385 ] 
dist 41=[-15.608580427216516404  ,-2.4296133202313276619 ] 
dist 42=[-15.513053823463220268  ,-1.7054311398668674156 ] 
dist 43=[-15.262268034971384274  ,-.95383548994903994812] 
dist 44=[-15.151148208977915507  ,-.3693637094291523830 ] 
dist 45=[-15.007888300963509799  ,.2034943645357601502 ] 
dist 46=[-14.933153016392001825  ,.9089469656968054344 ] 
dist 47=[-9.4349609144426398098 ,1.6445098732017843013 ] 
dist 48=[-9.4356392708658858286 ,2.3376110160459705215 ] 
dist 49=[-3.0083045626617267439 ,3.1316678403717568864 ] 
dist 50=[-2.9933686880101660455 ,4.2701564012515958786 ] 
dist 51=[.41034476581205072715,5.4006187157884663945 ] 
dist 52=[.82484993611583566004,6.1626830773413952287 ] 
dist 53=[1.5350989641680646233 ,6.8002747319112568316 ] 
dist 54=[1.6872976991643721614 ,7.4340763680153767331 ] 
dist 55=[3.0402713273498485404 ,8.0696670398853083276 ] 
dist 56=[3.1016582647959993939 ,8.8083067128215621589 ] 
dist 57=[3.7519269844089902664 ,9.3511581000820984342 ] 
dist 58=[3.8307891231918591326 ,9.7691976189294651678 ] 
dist 59=[3.8177438548399430238 ,10.090779243645669152  ] 
dist 60=[3.6766198076419094046 ,10.248594922760958897  ] 
dist 61=[3.4648265795907009806 ,10.316798674346328546  ] 
dist 62=[3.1697701314098034900 ,10.322090533907756645  ] 
dist 63=[2.7579355689278280487 ,4.7574662776031850370 ] 
dist 64=[2.0801898552285652049 ,4.7385419187590203059 ] 
dist 65=[1.3857018452041817128 ,4.3637217033566552814 ] 
dist 66=[.90703871460144228017,4.3427206755583886402 ] 
dist 67=[.49562883696449332581,2.2637189826640624927 ] 
dist 68=[.06941043565080745152,2.2009798838884984768 ] 
dist 69=[-.33288191053929070008,1.5545297078806976797 ] 
dist 70=[-.7600093889540272540 ,1.4337168620041955461 ] 
dist 71=[-1.2109659117051146347 ,1.2906362558044648033 ] 
dist 72=[-1.5580405375418506820 ,1.2602987747121675472 ] 
dist 73=[-1.8952566376902752175 ,.2290034632809063226 ] 
dist 74=[-2.3068878387575416414 ,.1051780373307527268 ] 
dist 75=[-2.6942362102133776722 ,-.16083805840861753584] 
dist 76=[-2.9345564506752720646 ,-.21621295085305111201] 
dist 77=[-3.1130618497989711255 ,-.4854018968497280953 ] 
dist 78=[-3.2537376103802776220 ,-.53130759297998365888] 
dist 79=[-3.3615905317834475072 ,-.6143819172857254259 ] 
dist 80=[-3.4091163158804135310 ,-.63029613289962029307] 
dist 81=[-3.4286477041438482133 ,-1.0616752752882252332 ] 
dist 82=[-3.4247819819864715863 ,-.7683522186738512379 ] 
dist 83=[-2.2380508323336668648 ,-.4633076824324700922 ] 
dist 84=[-2.2664829518858979521 ,-.2491310201594055962 ] 
dist 85=[-2.2836113509344880162 ,-.0608421468854902657 ] 
dist 86=[-2.2902958212828248727 ,.1786302454319159492 ] 
dist 87=[-2.2902171058312611324 ,.4095587599797179623 ] 
dist 88=[-2.2848418813502086986 ,.5874209892119954483 ] 
dist 89=[-2.2664691526427307085 ,.7602636919904802106 ] 
dist 90=[-2.2556201558527337424 ,.9711819637643327964 ] 
dist 91=[-2.1874016057477932167 ,1.1694835975388951927 ] 
dist 92=[-2.1687562571902991716 ,1.2919950285879679599 ] 
dist 93=[-2.1258882522255186954 ,1.3823510685296528256 ] 
dist 94=[-2.1098467342455428444 ,1.5511638117685743575 ] 
dist 95=[-1.5157379020550983819 ,1.9925042336766791631 ] 
dist 96=[-1.5062719039696881089 ,2.2729383207471916522 ] 
dist 97=[-.35990851751812876653,2.4892180425118156140 ] 
dist 98=[-.36006764622460894358,2.6745092359511105140 ] 
dist 99=[-.60093490341623740959,2.8257241824406690490 ] 
dist 100=[-.76210975298167159068,2.9060023880920099228 ] 
dist 101=[-.89548377923845385605,2.9501652393862990579 ] 
dist 102=[-1.0254429790285540106 ,2.9612108956473595641 ] 
dist 103=[-1.1429636274238326129 ,3.0518244885447012956 ] 
dist 104=[-1.2267138209117823485 ,3.1001128137558137807 ] 
dist 105=[-1.3015996976877492034 ,3.1267213080892152975 ] 
dist 106=[-1.3837522261268253388 ,3.1307932431055877064 ] 
dist 107=[-1.4561925069883163787 ,3.1210297389820756324 ] 
dist 108=[-1.4923305853216705967 ,3.1124526627628098690 ] 
dist 109=[-1.5114398159492521278 ,3.0636055473310159036 ] 
dist 110=[-1.5159542888749162863 ,3.0530881462466112862 ] 
dist 111=[-1.4900275331092617622 ,1.7855158433619121742 ] 
dist 112=[-1.4831318322243906996 ,1.6640026669293799221 ] 
dist 113=[-1.4788264528281487321 ,1.3695065014199739906 ] 
dist 114=[-1.4769147843414648746 ,1.3217166967792256152 ] 
dist 115=[-1.1313360581709423774 ,.89212728291378389574] 
dist 116=[-1.3306841612953388331 ,.81213844907025081688] 
dist 117=[-1.4960011535848553173 ,.70394172668685736853] 
dist 118=[-1.7023270057913983275 ,.6706463147273918845 ] 
dist 119=[-1.9300218535818214930 ,.04065462476183731303] 
dist 120=[-2.0661063848290851164 ,-.03760614913029047174] 
dist 121=[-2.1611504288927073027 ,-.21347748315937921328] 
dist 122=[-2.2250710294374118152 ,-.24412146018312671039] 
dist 123=[-2.2713897404365903892 ,-.3420026851772318377 ] 
dist 124=[-2.2961759975588826871 ,-.3021110864553628071 ] 
dist 125=[-2.3099446900296462436 ,-.25162503178656592097] 
dist 126=[-2.3122485675756857160 ,-.19086881764037520063] 
dist 127=[-1.5108396910777037176 ,-.11106887981820131456] 
dist 128=[-1.4573895010249119488 ,.01539285423393215394] 
dist 129=[-1.3186011394127085266 ,.14317734050572508139] 
dist 130=[-1.2977693711263494351 ,.22825564568716220316] 
dist 131=[-1.0626987190717031850 ,.29819539260046945465] 
dist 132=[-1.0164186865766414795 ,.36558751726079282159] 
dist 133=[-.9662947558641976522 ,.4260408847284097936 ] 
dist 134=[-.9546744358226804469 ,.4682995736898234784 ] 
dist 135=[-.58522508717649146445,.5052496334789124437 ] 
dist 136=[-.57871443186582390471,.5445246833058928994 ] 
dist 137=[-.42038816586510466035,.5796487329763869630 ] 
dist 138=[-.39889814748350119081,.6000375306624617193 ] 
dist 139=[-.35418613579727746252,.6134952187675328479 ] 
dist 140=[-.3419070926323719655 ,.6209646963973221587 ] 
dist 141=[-.29406463681645776146,.6245443025238208716 ] 
dist 142=[-.28413777275590718794,.6242811690295711069 ] 
dist 143=[-.26292026414328038811,.68649074259398080393] 
dist 144=[-.25680275870125757505,.80907334414133318491] 
dist 145=[.02628243099801596720,.91233200902862592225] 
dist 146=[.03861378955669938359,1.0162646380775616043 ] 
dist 147=[.05202609994204203183,1.1127195244634406744 ] 
dist 148=[.05240345059592138945,1.1861309421260188374 ] 
dist 149=[.0473059480133782808 ,1.2567511510303634579 ] 
dist 150=[.0343480647835581228 ,1.3420657778419737285 ] 
dist 151=[.0131735291152229441 ,1.4220463071885405216 ] 
dist 152=[-.0247140741008749717 ,1.4713752105268919810 ] 
dist 153=[-.0663719324049949490 ,1.5077180766547669405 ] 
dist 154=[-.1025934030596858304 ,1.5358632624283808749 ] 
dist 155=[-.1417388636908557604 ,1.5565997851402180650 ] 
dist 156=[-.1950684521483610097 ,1.5633702441424050833 ] 
dist 157=[-.30271733508499555811,1.5623729558907562590 ] 
dist 158=[-.61639798058355709698,1.5589539914977411810 ] 
dist 159=[-.92844656947669686472,.59977382486412802199] 
dist 160=[-1.1293633107894258971 ,.67197581774881034443] 
dist 161=[-1.2872937950463081161 ,.74207972241109209138] 
dist 162=[-1.4277883353402409487 ,.78457349399221282489] 
dist 163=[-1.5462737426410287143 ,.81496600512829276117] 
dist 164=[-1.6163681198069683786 ,.8367737484347869047 ] 
dist 165=[-1.6674479620031178930 ,.85234684544500529456] 
dist 166=[-1.7168340213076510686 ,.85785802020633241879] 
dist 167=[-1.7566936344438654594 ,.85860765026464408504] 
dist 168=[-1.7804858811002520972 ,.85651533466453052612] 
dist 169=[-1.7970682868894051327 ,.7986311186824638484 ] 
dist 170=[-1.8081526018486694578 ,.7875361442531881173 ] 
dist 171=[-1.8148619148816772930 ,.76428501867874582483] 
dist 172=[-1.8139836571214659195 ,.75649986131123715148] 
dist 173=[-1.8073866024111859998 ,.71945540636929497671] 
dist 174=[-1.8016060783849399830 ,.71111389289377713014] 
dist 175=[-.78011129964462928961,.68413467592989453026] 
dist 176=[-.75408630645699686152,.68018059425838346409] 
dist 177=[-.48558289507762425294,.2452097918058364618 ] 
dist 178=[-.45492813700430149107,.2036690445749011353 ] 
dist 179=[-.27303007146252524307,.1504849639901629151 ] 
dist 180=[-.25239031091447746339,.27015292473554132714] 
dist 181=[-.1685644224916190962 ,.38603902074066765233] 
dist 182=[-.1634728911783272202 ,.52701523459655909495] 
dist 183=[-.2407270674968874607 ,.66016223701485723269] 
dist 184=[-.3448939346616907227 ,.74690278529857056392] 
dist 185=[-.4479011727250439476 ,.81386548247877908785] 
dist 186=[-.5205258149941975923 ,.86991904588329330305] 
dist 187=[-.58477283672847318048,.91518518566624208976] 
dist 188=[-.65434399296741145718,.93909560912717987347] 
dist 189=[-.72196848299715872925,.95198208452288317785] 
dist 190=[-.77844437102623023327,.95477127439904366416] 
dist 191=[-.83753541566945190611,.84608494883747400431] 
dist 192=[-.91559212139492433992,.8545895567415814788 ] 
dist 193=[-.98970876127012176721,.9535805263867172090 ] 
dist 194=[-1.0330750337098248204 ,1.0135188565625469478 ] 
dist 195=[-1.0621830890338321300 ,1.0563184989035921629 ] 
dist 196=[-1.0794001529665975252 ,1.0869103850307588557 ] 
dist 197=[-1.0899943624819636230 ,1.1090806338058589605 ] 
dist 198=[-1.0926744058145970759 ,1.1182694814222359287 ] 
dist 199=[-1.0903274677411871909 ,1.1203794303174226340 ] 
dist 200=[-1.0876944038221788650 ,1.1189139117264145718 ] 
dist 201=[-.9769048072228489112 ,1.0323876183612558675 ] 
dist 202=[-.95841113262742770828,1.0167144138202398643 ] 
dist 203=[-.92117051128163111694,.9863065767914698888 ] 
dist 204=[-.90973070870494367045,.9767434899000214754 ] 
dist 205=[-.85995097372911122942,.93479556491308193503] 
dist 206=[-.84827859622663143515,.92416095851392282791] 
dist 207=[-.81659351430182045045,.89587479135195780942] 
dist 208=[-.80795275739238711232,.88633316542595692345] 
dist 209=[-.77178223132529784842,.01518674695094724070] 
dist 210=[-.77708962607397056462,.00804217401676289523] 
dist 211=[-.8318289505190025947 ,-.00449727320521211098] 
dist 212=[-.8696817820298809769 ,-.00158224107672584631] 
dist 213=[-.9006109901937525319 ,.00909670038731377203] 
dist 214=[-.9301719399302243652 ,.03314602207800101928] 
dist 215=[-.9543798379903858808 ,.06128673871146675380] 
dist 216=[-.9639457604240691848 ,.08829419064050593179] 
dist 217=[-.9672111980959709062 ,.11962690620518979957] 
dist 218=[-.9662726540683847451 ,.16503055195811779244] 
dist 219=[-.9396233793841213009 ,.21597744687919553302] 
dist 220=[-.9306883107611467236 ,.26943298459864483088] 
dist 221=[-.9231550126903361309 ,.3349425861513982553 ] 
dist 222=[-.9172805179477813723 ,.43399559697638136707] 
dist 223=[-.47719390152227383722,.5324023215685675626 ] 
dist 224=[-.46935285943778247571,.5953332755364164924 ] 
dist 225=[-.15364348711222106803,.6443037287252696406 ] 
dist 226=[-.12092314838093630814,.6869977574223173847 ] 
dist 227=[-.05541601684735451958,.7223701690046884958 ] 
dist 228=[-.03904372345070015150,.7850092129427581454 ] 
dist 229=[.01602698871656535782,.8489084571919184884 ] 
dist 230=[.02799647046534181687,.9199106890717745331 ] 
dist 231=[.03682871531350190187,.9840260242796170145 ] 
dist 232=[.03325913269544212196,1.0204415340221200778 ] 
dist 233=[.02429993610706466801,1.0435231626438819818 ] 
dist 234=[.00901243912685919158,1.0544266579121054202 ] 
dist 235=[-.01383310471029342506,1.0595590389603464387 ] 
dist 236=[-.05295399232977099960,1.0596095384272347434 ] 
dist 237=[-.09952175017774076651,1.0364397409100998917 ] 
dist 238=[-.15208539598632316403,1.0011874069290914812 ] 
dist 239=[-.21908535622674280842,.80101164746650453522] 
dist 240=[-.3232639519593571641 ,.74100264197530193078] 
dist 241=[-.4278515240349850045 ,.26071108469063571678] 
dist 242=[-.4964834381123430139 ,.24493178591884894659] 
dist 243=[-.5518862471142102364 ,.15172117338072931868] 
dist 244=[-.6036801537758569432 ,.13482405610299891506] 
dist 245=[-.6491564673121954658 ,.10097845746917893633] 
dist 246=[-.6793473673429036872 ,.09235996176621312423] 
dist 247=[-.7041063704249932967 ,.00581241705606442276] 
dist 248=[-.7279050353624169667 ,-.00745040893248606462] 
dist 249=[-.7474931283220209986 ,-.02840410227027540231] 
dist 250=[-.7554490873422336699 ,-.03346066645207251107] 
dist 251=[-.7582834035449192057 ,-.03837538711107793728] 
dist 252=[-.7574331909408572485 ,-.03364895758379076884] 
dist 253=[-.7228384849412259399 ,-.02258614652660689570] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 0, 0, 2, 0, 2] 
dist 0=[58.883433873049078418  ,58.883433873049078418  ] 
dist 1=[58.196557315773578720  ,59.263721958402186526  ] 
dist 2=[56.798615970856265836  ,59.437643199149771347  ] 
dist 3=[55.197666195906906284  ,59.522913347315366478  ] 
dist 4=[53.699996708088737394  ,59.549328019670518504  ] 
dist 5=[51.988448268601337408  ,59.534248868028507640  ] 
dist 6=[49.533198311224122547  ,59.453616243554449587  ] 
dist 7=[46.781534035891904435  ,59.308872784605507120  ] 
dist 8=[43.886151385375520790  ,58.909585765705323814  ] 
dist 9=[40.324507379021857671  ,55.403532815053775686  ] 
dist 10=[34.911988042700781596  ,54.787386061386414316  ] 
dist 11=[29.467203917894873292  ,53.776042673991732236  ] 
dist 12=[25.776589758296678410  ,53.484389308666590892  ] 
dist 13=[22.655887170940460890  ,52.659733682196623557  ] 
dist 14=[19.486823869710245016  ,51.673955109538984820  ] 
dist 15=[16.519592919458668138  ,46.986646065680220696  ] 
dist 16=[14.204653225427689620  ,43.770656014199234201  ] 
dist 17=[11.917477925114644075  ,31.695542343720542812  ] 
dist 18=[9.0605877292681776081 ,31.145904247355860104  ] 
dist 19=[6.3207144839059411062 ,29.181865458608599843  ] 
dist 20=[4.5005827512100230583 ,28.739667333567080433  ] 
dist 21=[2.9986240386149214281 ,28.069753314151029566  ] 
dist 22=[1.5291256036320843194 ,27.874712457369378714  ] 
dist 23=[.18347125694507973049,14.584467733076409708  ] 
dist 24=[-.82442566211972874365,14.238749427270136173  ] 
dist 25=[-1.7855258198325580553 ,7.5070627793462696067 ] 
dist 26=[-2.9455680334129692284 ,6.7014420732749059245 ] 
dist 27=[-5.3740411738075594579 ,4.9633053614161609650 ] 
dist 28=[-7.2308907314187589199 ,4.6716985035713303751 ] 
dist 29=[-8.9771240985373077530 ,2.9374599902586528402 ] 
dist 30=[-11.036086779092029610  ,2.4325284910876674843 ] 
dist 31=[-12.949359515446287587  ,1.8288887665834382589 ] 
dist 32=[-14.113685495742327255  ,1.5161293431458577439 ] 
dist 33=[-14.955814249519162248  ,-5.7114200164281195376 ] 
dist 34=[-15.582179631984054099  ,-5.5059209881948708658 ] 
dist 35=[-16.059089753980212224  ,-5.2456910974517246925 ] 
dist 36=[-16.304292541864420290  ,-4.9788310970747703411 ] 
dist 37=[-16.427796210203352209  ,-4.6584116525183548997 ] 
dist 38=[-16.426687708571899980  ,-4.0300319926273452651 ] 
dist 39=[-9.1416541930686310373 ,-2.8327766550923361065 ] 
dist 40=[-9.1585327883939672647 ,-1.9993762644760337505 ] 
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dist 58=[1.2506336259607297705 ,4.9794564354798443699 ] 
dist 59=[.6301668533726043143 ,4.1412292933623250196 ] 
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dist 63=[-.78472693108628504368,4.4756989624777517372 ] 
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dist 65=[-1.2228540487323561033 ,4.1764097454287557682 ] 
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dist 72=[-4.3872920928379177608 ,1.0689864585390534376 ] 
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dist 74=[-5.2987396571776232401 ,.6222420620137552787 ] 
dist 75=[-5.6507637248230702568 ,.5441026979471109121 ] 
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dist 85=[-6.2708517080719724482 ,.77783531156276308425] 
dist 86=[-6.2358956232976587023 ,.87756409872025935714] 
dist 87=[-2.9077884954228470107 ,.96932719911044295469] 
dist 88=[-2.6141678956983194220 ,1.0379410367334718398 ] 
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dist 90=[-1.8018985058205377032 ,1.1800849353253401558 ] 
dist 91=[-1.2832157381751298124 ,1.2505676567441213876 ] 
dist 92=[-1.2772810982503289157 ,1.6158300550474628307 ] 
dist 93=[-1.2283224551728407214 ,2.0067917676537068780 ] 
dist 94=[-1.2166217265400653801 ,2.4680197587509575683 ] 
dist 95=[-1.1961544624461922219 ,2.8998505277583236594 ] 
dist 96=[-1.1890440894409925069 ,3.1734904383310984036 ] 
dist 97=[-.6726470226168996276 ,3.3836677262764949799 ] 
dist 98=[-.6243509487598007747 ,3.5622048789803480677 ] 
dist 99=[-.5135503288963461932 ,3.7067537339668182629 ] 
dist 100=[-.4923054216691469201 ,3.7812766755461442504 ] 
dist 101=[-.3495230228523292843 ,3.8187890109141406831 ] 
dist 102=[-.3236640366230933519 ,3.8248172857541051628 ] 
dist 103=[-.27678014951643678962,2.7638263470722432539 ] 
dist 104=[-.26607029107780204887,2.6773612017032028637 ] 
dist 105=[-.11205269294624337905,2.4604365671051045091 ] 
dist 106=[-.09082765292083062529,2.4184714187968756880 ] 
dist 107=[-.04844620714410537601,2.0656705993146734184 ] 
dist 108=[-.16961903123827846586,1.9947821603007685445 ] 
dist 109=[-.29451313186657586374,1.8912987860308015057 ] 
dist 110=[-.4188868906429509272 ,1.8594351026935945066 ] 
dist 111=[-.5335594748538019146 ,1.2018253391613557362 ] 
dist 112=[-.6197164239010590874 ,1.1150060804210404971 ] 
dist 113=[-.7015582486410714222 ,.9188684661502731402 ] 
dist 114=[-.7989919209474562746 ,.87618831456554214349] 
dist 115=[-.8896822897318956607 ,.6305621366609714416 ] 
dist 116=[-.96062465835102078342,.6153600394332820195 ] 
dist 117=[-1.2160496588192821140 ,.4941258548841346782 ] 
dist 118=[-1.5720084572906782536 ,.4701977725416194310 ] 
dist 119=[-1.9205189367190934860 ,.41769861119253678361] 
dist 120=[-2.1462224173895841812 ,.4120541974626314185 ] 
dist 121=[-2.3252463128727406339 ,.15866825764128849494] 
dist 122=[-2.5246756067611263314 ,.1277143941629002883 ] 
dist 123=[-2.7222370676121230113 ,.0636811800169760053 ] 
dist 124=[-2.8597970842766705699 ,.0472548486001454789 ] 
dist 125=[-2.9797893126182768592 ,.04695692476042791012] 
dist 126=[-3.1072406265127707791 ,.15689379994731009666] 
dist 127=[-3.2178749469197614577 ,.27763986049062445046] 
dist 128=[-3.2707480616125542084 ,.38245057502604346678] 
dist 129=[-3.2956087798402199799 ,.49558885539449695023] 
dist 130=[-3.2962225030615753214 ,.64958565369286647348] 
dist 131=[-3.2454081111925757542 ,.8179900165495723688 ] 
dist 132=[-3.2231174664011634296 ,.98863758792204447867] 
dist 133=[-3.2010740151673645837 ,1.1935764479754181973 ] 
dist 134=[-3.1845371977545477694 ,1.4988475663164436139 ] 
dist 135=[-.5693008727826372447 ,1.8820038419724247559 ] 
dist 136=[-.5972037572103183015 ,2.1789461403761271962 ] 
dist 137=[-.62255119374742638814,2.4120891628807328144 ] 
dist 138=[-.63676556396536331594,2.6190574678139897525 ] 
dist 139=[-.6455400301472935447 ,2.7933176358503839687 ] 
dist 140=[-.64916520469321991705,2.9225697977012180699 ] 
dist 141=[-.64992786605695626169,3.1054955514366355049 ] 
dist 142=[-.64878409671338789772,3.2915830322054378754 ] 
dist 143=[-.64348176947081650724,3.4559360085171595281 ] 
dist 144=[-.64009778040621674674,3.5521208811300302928 ] 
dist 145=[-.5876451878393509211 ,3.6167695326629118824 ] 
dist 146=[-.57879632823551126022,3.6552628804998404143 ] 
dist 147=[-.55349547831827725843,3.6739884079882674954 ] 
dist 148=[-.54877434652734275462,3.6741809351617106268 ] 
dist 149=[-.49570332752878588146,3.6388363747609139600 ] 
dist 150=[-.48404481859179397591,3.6309595797938485210 ] 
dist 151=[-.47123472842791490291,2.4081146072287726359 ] 
dist 152=[-.67188619907424458158,2.3183950442743222492 ] 
dist 153=[-.95078472519744236984,2.0875209701169464519 ] 
dist 154=[-1.2223531441514128437 ,2.0516254720418049991 ] 
dist 155=[-1.4683034093905657694 ,1.6652195483688379163 ] 
dist 156=[-1.6449613447214550124 ,1.5890309174299033644 ] 
dist 157=[-1.8046257416800145513 ,1.5028883036064052453 ] 
dist 158=[-1.9827534241748126056 ,1.4796846862398670039 ] 
dist 159=[-2.1452733220312851282 ,.72787563928309620012] 
dist 160=[-2.2426497882514230834 ,.65245260755200313816] 
dist 161=[-2.3109111687015510254 ,.49777591182271532035] 
dist 162=[-2.3572422415933051714 ,.48029795604028522936] 
dist 163=[-2.3878016351980543136 ,.43851414142994318966] 
dist 164=[-2.3931198106557898189 ,.42920884137079803638] 
dist 165=[-2.3935502094559057990 ,.36707439945423904777] 
dist 166=[-2.3920594190911037187 ,.35467849960703889935] 
dist 167=[-.54350288410701663349,.33227923579944906681] 
dist 168=[-.53069958769573356856,.32661312805145847549] 
dist 169=[-.4995660422336592376 ,.2251093965767468367 ] 
dist 170=[-.49143697858845115842,.2113419144253915697 ] 
dist 171=[-.44167128407430722539,.1771199456909704937 ] 
dist 172=[-.43115347578667431973,.1722041140835415918 ] 
dist 173=[-.4111733472664572175 ,.1197260142717788628 ] 
dist 174=[-.4055938146669037901 ,.1098700362328477074 ] 
dist 175=[-.32086168628572958064,.0988610227086982559 ] 
dist 176=[-.34437895410845187159,.0969298276217834048 ] 
dist 177=[-.43329982412380565449,.0095585928583926599 ] 
dist 178=[-.49129567489899277   ,.01154618540545806856] 
dist 179=[-.53774417336359990063,.08069439473715275686] 
dist 180=[-.58057838213746611607,.14550686663611567997] 
dist 181=[-.61781361908199349615,.21956039940696957253] 
dist 182=[-.64191652791994126673,.32559458475332512322] 
dist 183=[-.66102091091176838697,.43020125197807349877] 
dist 184=[-.67830793797370239561,.49855789756753956358] 
dist 185=[-.6919494084606170092 ,.55345673299099351422] 
dist 186=[-.69650343328732333617,.60434937678224929088] 
dist 187=[-.69735382338482282678,.64877662866189960839] 
dist 188=[-.69621136794712670617,.67787027706212243999] 
dist 189=[-.67493418743390046749,.70130697536358009981] 
dist 190=[-.66825051286943507331,.72315591743816594973] 
dist 191=[-.66195207460645506678,.74102459629361819638] 
dist 192=[-.65770639739763955122,.74857515027404581478] 
dist 193=[-.11213484513898547569,.75118511494222684891] 
dist 194=[-.14617934518081065591,.75016795281387823669] 
dist 195=[-.18434087184557698341,.73487025588810875977] 
dist 196=[-.22432698919592290116,.72924131688002668413] 
dist 197=[-.27329242731788186664,.72073460880333113198] 
dist 198=[-.34728965829460743887,.7169443668406013093 ] 
dist 199=[-.42079699811482786687,.5789795157237480402 ] 
dist 200=[-.46780787975960359363,.5906876552945579036 ] 
dist 201=[-.50439475709742681471,.59938347710929598288] 
dist 202=[-.53630242937217644618,.60154506054558373775] 
dist 203=[-.56274708608385540005,.60104618896613663667] 
dist 204=[-.57753260978164593364,.59912280433054805304] 
dist 205=[-.58660616479427587295,.58061496721852897451] 
dist 206=[-.59025638043047128181,.57489073977320156303] 
dist 207=[-.59114829925755626612,.56723587883288899807] 
dist 208=[-.58977057899210592852,.56370341264530276916] 
dist 209=[-.5857424461663645416 ,.38997727454692828481] 
dist 210=[-.58309382308232916701,.37030345831010255185] 
dist 211=[-.56585597513984800067,.3239114880047700167 ] 
dist 212=[-.5610079578357915906 ,.31428135721501523696] 
dist 213=[-.54796018383484560267,.2486066687418594165 ] 
dist 214=[-.54264402550725582235,.2359585363023587197 ] 
dist 215=[-.29974839657108312046,.2133391768648962057 ] 
dist 216=[-.27515942899710172241,.2078889969497262868 ] 
dist 217=[-.2196328522506955824 ,.1133785712367790685 ] 
dist 218=[-.2076764371710445946 ,.1005867415420687878 ] 
dist 219=[-.15294925334932099824,.0707624168239491447 ] 
dist 220=[-.1520235951916541355 ,.0654110274390971708 ] 
dist 221=[-.146700882854554132  ,.06077150972963803980] 
dist 222=[-.14531814368432923416,.06065180730953468574] 
dist 223=[-.14127730841318923277,.05963903803912117708] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 2, 0, 0, 1, 2] 
dist 0=[61.911137871786249984  ,61.911137871786249984  ] 
dist 1=[61.596786785611150347  ,62.151366654910530564  ] 
dist 2=[60.581814158432224656  ,62.392370143144305480  ] 
dist 3=[59.349102355492857315  ,62.420081231509106429  ] 
dist 4=[58.095065162827855079  ,62.077478173884878048  ] 
dist 5=[56.582761690732525495  ,61.900683553101590545  ] 
dist 6=[54.318566489462565095  ,61.565412536510543837  ] 
dist 7=[51.738358251936180139  ,61.415957219102141486  ] 
dist 8=[48.963997194258274986  ,57.338800170642903734  ] 
dist 9=[45.509821901555008837  ,56.644583861642968806  ] 
dist 10=[40.214687774861728507  ,55.796640742537560333  ] 
dist 11=[34.870062625497043323  ,55.351859025522852403  ] 
dist 12=[31.218151712037673765  ,54.850328342002196863  ] 
dist 13=[28.098722755465057924  ,54.551577274473529675  ] 
dist 14=[24.880372005851121484  ,52.308347944434735713  ] 
dist 15=[21.835226301554347698  ,47.111787965578429118  ] 
dist 16=[19.407269747587784826  ,31.892778357568936036  ] 
dist 17=[16.959717305214848135  ,30.715067679263949348  ] 
dist 18=[13.835847195964246744  ,28.395676646306846371  ] 
dist 19=[10.808611897637998904  ,27.805104330728200694  ] 
dist 20=[8.7467319144848846325 ,25.766796387628864745  ] 
dist 21=[6.9900248866321260811 ,25.302504615977414292  ] 
dist 22=[5.1812546407807068803 ,24.774880463969827576  ] 
dist 23=[3.4677103744214705886 ,24.644465910468250693  ] 
dist 24=[.62426981302788985461,5.7329552689339068634 ] 
dist 25=[-1.3693352320184420139 ,4.7078938425684297837 ] 
dist 26=[-2.9768187511022069266 ,4.6020758654457438009 ] 
dist 27=[-4.4870402780116496697 ,.72500235643131921621] 
dist 28=[-5.8290111439888201294 ,.08673059725699113142] 
dist 29=[-7.1507526375573834664 ,-.21608145316186456126] 
dist 30=[-8.8632353441509619639 ,-1.0316353567324781965 ] 
dist 31=[-10.927635883691496466  ,-2.2632052231130421888 ] 
dist 32=[-12.869816210015441318  ,-6.2690079450055307772 ] 
dist 33=[-14.094134208853285388  ,-6.5780196205617541497 ] 
dist 34=[-15.030838515796172923  ,-6.6240604592672620803 ] 
dist 35=[-15.824227957013740338  ,-6.8170454166060407830 ] 
dist 36=[-16.468024600000059411  ,-6.7485077668096266746 ] 
dist 37=[-16.807261264335069867  ,-6.4340756226389461156 ] 
dist 38=[-16.989844540562014242  ,-5.1786003523932588799 ] 
dist 39=[-17.010578586697673102  ,-3.1082741258204201858 ] 
dist 40=[-8.6558757931982777938 ,-.99195678426256146293] 
dist 41=[-8.4395548429262205921 ,.44726448304689156818] 
dist 42=[-7.9939967332225669030 ,1.6634010963708213457 ] 
dist 43=[-7.8642632774867366746 ,2.8900331899822829651 ] 
dist 44=[-7.3307947017339808986 ,4.0273729707731260014 ] 
dist 45=[-7.2111823082977812826 ,4.8874564056737495682 ] 
dist 46=[-6.9298674027076032598 ,5.7083174429739939509 ] 
dist 47=[-6.8371203106947526193 ,6.6894101892099839032 ] 
dist 48=[-1.4903674150124175318 ,7.6025733336520648011 ] 
dist 49=[-1.0063886251830860866 ,8.1524954719473075076 ] 
dist 50=[.03373083642529348299,8.5417414290188276309 ] 
dist 51=[.26402170111038840162,8.8138593106028582011 ] 
dist 52=[1.3510870800568688168 ,9.0071729034673967491 ] 
dist 53=[1.5401509542994087274 ,9.0818276328799717317 ] 
dist 54=[1.8598857371376164866 ,9.0934303619258344759 ] 
dist 55=[2.0145708850224594949 ,9.0744768210568714969 ] 
dist 56=[2.0541096310948209098 ,8.2421879326193505204 ] 
dist 57=[1.7518164761881574965 ,8.1094265660618541803 ] 
dist 58=[1.3654834242168370322 ,7.7256529095574544155 ] 
dist 59=[.93864670460459743374,7.6524746530482122771 ] 
dist 60=[.52000432331397158386,6.8497820567661072145 ] 
dist 61=[.16624315040267902977,6.6758586767370816396 ] 
dist 62=[-.20691135160151675622,6.0771045974765139422 ] 
dist 63=[-.70304240671143421591,5.1191918272134561996 ] 
dist 64=[-1.2966686812141465264 ,1.9409445745711211354 ] 
dist 65=[-1.9296656958235309334 ,1.8117703312002001516 ] 
dist 66=[-2.4471689450788263492 ,1.5152396778485889589 ] 
dist 67=[-2.9418774068088249146 ,1.4582594469375876713 ] 
dist 68=[-3.3838154622883090335 ,1.0812079551553532922 ] 
dist 69=[-3.6907905167016812420 ,1.0140835795265443551 ] 
dist 70=[-3.9577099732305334716 ,.89062104413323591579] 
dist 71=[-4.2398863129621126449 ,.8607501138528240597 ] 
dist 72=[-4.4888055094240497223 ,.7337753575274168489 ] 
dist 73=[-4.6230123112496896894 ,.69903443415933861993] 
dist 74=[-4.6990800956518420087 ,.68863351960016914728] 
dist 75=[-4.7159164375844601020 ,.48765043423301837562] 
dist 76=[-4.7088360597291276753 ,.46080989848395722933] 
dist 77=[-4.6894522342631937596 ,.40555369159240950393] 
dist 78=[-4.6575319088635931469 ,.39060651359094430737] 
dist 79=[-4.6375460679455621531 ,.33236822641502255523] 
dist 80=[-4.2963248377317031701 ,.51175348898152000405] 
dist 81=[-4.3645749373130055624 ,1.1232458916528242428 ] 
dist 82=[-4.3966049474315194592 ,1.6241015751473993864 ] 
dist 83=[-4.3984672314087829444 ,2.1039192333270806472 ] 
dist 84=[-4.3159545743755595119 ,2.5326240404608561180 ] 
dist 85=[-4.2869214054027604539 ,2.8295349762966443039 ] 
dist 86=[-4.2626373783512606061 ,3.0862724068668349587 ] 
dist 87=[-4.2387371803359382099 ,3.3546608542940958367 ] 
dist 88=[-3.4867190782146313440 ,3.5970997272823119285 ] 
dist 89=[-3.3849453048556116046 ,3.7503099960590239682 ] 
dist 90=[-3.1309310062817626230 ,3.8671979793789480277 ] 
dist 91=[-3.0776890928385964617 ,3.9647697477300914121 ] 
dist 92=[-2.6613982056029176867 ,4.0423018935803798807 ] 
dist 93=[-2.5759785628825436318 ,4.0792702578347884356 ] 
dist 94=[-2.4433437289519332167 ,4.0936337682964924206 ] 
dist 95=[-2.4043931291730136051 ,4.0866977674716808548 ] 
dist 96=[-1.5925809674446246075 ,3.9113520759529002393 ] 
dist 97=[-1.4829989268768024041 ,4.0165674244574340521 ] 
dist 98=[-1.2329955297867425041 ,4.0934463337951500100 ] 
dist 99=[-1.1771363358034335180 ,4.1518535148203243741 ] 
dist 100=[-.85137950509414779313,4.1939824723884701276 ] 
dist 101=[-.79011613945202873865,4.2058781250658769693 ] 
dist 102=[-.66735279544904740315,4.1979227403228991574 ] 
dist 103=[-.63490019227535201441,4.1880714718386772240 ] 
dist 104=[-.77611509668745658879,2.0569856510071522930 ] 
dist 105=[-1.0143877143464619607 ,1.8746224571564283582 ] 
dist 106=[-1.2146688363492692209 ,1.4381714147477445878 ] 
dist 107=[-1.4153880037193797652 ,1.6562731791255045958 ] 
dist 108=[-1.6010292436986665380 ,1.8860617788258897641 ] 
dist 109=[-1.7411642476187899486 ,2.1028674047686081310 ] 
dist 110=[-1.8748831306143324639 ,2.3515164269841252287 ] 
dist 111=[-2.0349655275605202116 ,2.7083381069184174435 ] 
dist 112=[-2.1853555303727140854 ,3.0555945648265303989 ] 
dist 113=[-2.3451714482872249656 ,3.2660607371465948234 ] 
dist 114=[-2.5109722511982358323 ,3.4163774171537602063 ] 
dist 115=[-2.6578016430073597908 ,3.5236074250960255500 ] 
dist 116=[-2.7812730873320715490 ,3.6029834928737270758 ] 
dist 117=[-2.8538585851906030209 ,3.6421622538524731451 ] 
dist 118=[-2.9031514456414829140 ,3.6593151140381126160 ] 
dist 119=[-2.9336789198973414852 ,3.6561600482996303596 ] 
dist 120=[-2.9494173285662751754 ,3.3187036366420205262 ] 
dist 121=[-2.9490332215807862577 ,3.2610354317919769681 ] 
dist 122=[-2.9235250867837824639 ,3.1654266927818953578 ] 
dist 123=[-2.9135824511046586643 ,3.1358252286885429607 ] 
dist 124=[-2.7747453434023772956 ,3.0368119450664688472 ] 
dist 125=[-2.7377348640026890185 ,3.0032902272069067313 ] 
dist 126=[-2.6998585712617751562 ,2.9528569114437808750 ] 
dist 127=[-2.6784205506567972553 ,2.9327301899613918419 ] 
dist 128=[-1.8577494832619445338 ,-.61481275917853788501] 
dist 129=[-1.7634229386462469890 ,-.64455444551185312623] 
dist 130=[-1.5257606729543633476 ,-.60074965283392702333] 
dist 131=[-1.4913095115007807147 ,-.53589426768709798943] 
dist 132=[-1.1160043119998449110 ,-.48088037463626720305] 
dist 133=[-1.0446708118968932055 ,-.42255216177617797162] 
dist 134=[-.97920419453067547958,-.34445938332854200549] 
dist 135=[-.97828042844730878797,-.25962972178588121869] 
dist 136=[-.97600511368913803646,-.17440660621073891546] 
dist 137=[-.97230262263533999018,-.07254991367945634491] 
dist 138=[-.96862316614450260248,.07867802882274237073] 
dist 139=[-.7612840726215987529 ,.22943794053337735566] 
dist 140=[-.74264345532910466427,.35855257644105512954] 
dist 141=[-.69310577911414816709,.49044558458621486808] 
dist 142=[-.68473667458310827147,.62931212889566567948] 
dist 143=[-.59485572264328325424,.81408501257442505424] 
dist 144=[-.57630082404941590517,.9947676260394636107 ] 
dist 145=[-.5552048317764165249 ,1.1173129437688296228 ] 
dist 146=[-.54780653556272855502,1.2208128024565725099 ] 
dist 147=[-.34787965531313322813,1.3254700832409147487 ] 
dist 148=[-.32166059743524544249,1.4229415045759248299 ] 
dist 149=[-.26752756515976541915,1.4977574711838092353 ] 
dist 150=[-.25303466983277177979,1.5703585622478116555 ] 
dist 151=[-.19832486565253934946,1.6589901948237978776 ] 
dist 152=[-.1870289177828628412 ,1.7425957301101853862 ] 
dist 153=[-.16489389482920974206,1.7951336528375729139 ] 
dist 154=[-.15908966825512262424,1.8350139313327332654 ] 
dist 155=[-.16691378731094891848,1.8680911812815760966 ] 
dist 156=[-.2095733646133702109 ,1.8942965850846660323 ] 
dist 157=[-.24972645693218839307,1.9067453738440197690 ] 
dist 158=[-.48535024234074282735,1.9115152963921269630 ] 
dist 159=[-.91150304799204572341,1.9077837210769062599 ] 
dist 160=[-1.3348668903669463353 ,-.17994945788875542953] 
dist 161=[-1.6076572879372741361 ,-.14554463592539066878] 
dist 162=[-1.8234717186189790084 ,-.08358576072017565801] 
dist 163=[-2.0224610334031992147 ,-.01526102673955413904] 
dist 164=[-2.1917609700124697412 ,.04454737824884544259] 
dist 165=[-2.2946771476418441618 ,.1095432577720879017 ] 
dist 166=[-2.3686578285386798521 ,.19856865655011943262] 
dist 167=[-2.4224775656103126670 ,.2961717317507393381 ] 
dist 168=[-2.4635345048323744858 ,.39539762520194804636] 
dist 169=[-2.4865795280806893168 ,.51476637035335760564] 
dist 170=[-2.5008482811342343937 ,.69275178225957641749] 
dist 171=[-2.5068797521644441590 ,.86903855302755356037] 
dist 172=[-2.5071693813338080780 ,.9816282319060486661 ] 
dist 173=[-2.4993896378522188109 ,1.0690564853828336365 ] 
dist 174=[-2.4831179642550700296 ,1.1449324123419508462 ] 
dist 175=[-2.4732574707670778462 ,1.2075179588202553886 ] 
dist 176=[-1.1420543974046048499 ,1.2419083736166288761 ] 
dist 177=[-1.1383336515085733269 ,1.2622063398361574888 ] 
dist 178=[-1.1340182876031153996 ,1.2685525508312639972 ] 
dist 179=[-1.0559696794521535311 ,1.2689829708474899083 ] 
dist 180=[-1.0410961113015558297 ,1.2656728501805807004 ] 
dist 181=[-1.0053323938602065210 ,1.2589826786954217217 ] 
dist 182=[-.9926733582754584531 ,1.2543524896323924616 ] 
dist 183=[-.92997250803537923246,1.2297721826619979027 ] 
dist 184=[-.91538997560479503035,1.2219837588059298122 ] 
dist 185=[-.88250966738035013396,1.2038796998531500361 ] 
dist 186=[-.87142231371549614102,1.2913513044582157643 ] 
dist 187=[-.39704052039536312492,1.3650512647836824028 ] 
dist 188=[-.34781861536383025615,1.4242345261864263631 ] 
dist 189=[-.2461750564349498206 ,1.4537707186353508814 ] 
dist 190=[-.21961383004141867483,1.4687835883491364012 ] 
dist 191=[-.1226110063040144189 ,1.4704912479942830158 ] 
dist 192=[-.10289594187048497036,1.0863364507372055856 ] 
dist 193=[-.18737515933010284874,1.0559590124041917646 ] 
dist 194=[-.34223130027683179777,.9813171977512168134 ] 
dist 195=[-.49539442934982547188,.96420819634534078222] 
dist 196=[-.60343170656485875944,.84495108848558892891] 
dist 197=[-.69906439980620504069,.82039820873986814065] 
dist 198=[-.80272382810043079166,.835021867370570676  ] 
dist 199=[-.90356558503049655313,.94385857368500714057] 
dist 200=[-.98795413379271625844,1.0389158257524609566 ] 
dist 201=[-1.0764267077328184229 ,1.1420462154215847958 ] 
dist 202=[-1.1935683075786856536 ,1.2830992885593848814 ] 
dist 203=[-1.3054454707828334492 ,1.4185446777904580240 ] 
dist 204=[-1.3729082406534474316 ,1.4992955935807012403 ] 
dist 205=[-1.4207329520870541000 ,1.5554061609785728810 ] 
dist 206=[-1.4542357916812183377 ,1.5925177906763912784 ] 
dist 207=[-1.4774362677697241311 ,1.6183853437881195755 ] 
dist 208=[-1.4841458457870823692 ,1.6296236035671415781 ] 
dist 209=[-1.4836141203444170439 ,1.6322890148708786247 ] 
dist 210=[-1.4788088737326045857 ,1.6297238083142575192 ] 
dist 211=[-1.3795776206707421492 ,1.4670679516051462375 ] 
dist 212=[-1.3604430608731733046 ,1.4400032028426619177 ] 
dist 213=[-1.3198394088858418342 ,1.3901231476713686547 ] 
dist 214=[-1.3632270710476741230 ,1.3756157033929646001 ] 
dist 215=[-1.4035253631036332794 ,1.3182621812413710997 ] 
dist 216=[-1.4359938076500323726 ,1.3022319953427652482 ] 
dist 217=[-1.4481326393995068060 ,1.2690199670817851388 ] 
dist 218=[-1.4515583082061340769 ,1.2575700572265764782 ] 
dist 219=[-1.4492494605567967572 ,.2700421785108849281 ] 
dist 220=[-1.4088701468899491854 ,.34782714877958574815] 
dist 221=[-1.3955248182561730736 ,.42884557962522730562] 
dist 222=[-1.3822277822416745612 ,.52772587155995096093] 
dist 223=[-1.3735776293842223556 ,.67679720578323197532] 
dist 224=[-1.0365784150767907122 ,.82482297778325004195] 
dist 225=[-1.0108785943492884910 ,.91953135023064749544] 
dist 226=[-1.0021481960549730052 ,.99329272037987999221] 
dist 227=[-.83732882118047471943,1.0577220449603920394 ] 
dist 228=[-.81259528685340134049,1.1112003827576491108 ] 
dist 229=[-.75338859434216567915,1.1529061757553370722 ] 
dist 230=[-.73871510526824543134,1.2466014458247041611 ] 
dist 231=[-.64843265688388260088,1.3499492023070106560 ] 
dist 232=[-.62983626587138277349,1.4433016111773296928 ] 
dist 233=[-.59453927949396066993,1.4971068785284356025 ] 
dist 234=[-.58489954961950524254,1.5322284583334137347 ] 
dist 235=[-.18945704402098741118,1.5510168794346738533 ] 
dist 236=[-.14703098063625265839,1.5609945978995603468 ] 
dist 237=[-.06468992933435708718,1.5609537210158199566 ] 
dist 238=[-.04476719963456148832,1.5551073504133285613 ] 
dist 239=[.01753214369194608775,1.5497508978942455889 ] 
dist 240=[-.20243758787659494609,1.1465684302435760502 ] 
dist 241=[-.36561849359555640174,1.1033363760481905288 ] 
dist 242=[-.49973832445728145779,.99298404753898363343] 
dist 243=[-.62919164961366267227,.97514571814784032958] 
dist 244=[-.74567503412590688233,.79283070671653670101] 
dist 245=[-.8280336782686848773 ,.75689679195876229952] 
dist 246=[-.90113537251003327683,.71404415328843408829] 
dist 247=[-.98067509750432344371,.68344845002795935703] 
dist 248=[-1.0528090643931197835 ,.27693091738221256075] 
dist 249=[-1.0963558021080394986 ,.22577663686121245754] 
dist 250=[-1.1272819700889249624 ,.06403377250210092974] 
dist 251=[-1.1490506273819934616 ,-.02726316341651311725] 
dist 252=[-1.1632551616886558099 ,-.04184993535441762454] 
dist 253=[-1.1661459350888099072 ,-.03870667049490705844] 
dist 254=[-1.1608832169014580382 ,-.02684395518303578029] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 0, 0, 2, 0, 2] 
dist 0=[58.813283420039845087  ,58.813283420039845087  ] 
dist 1=[58.360848857703205752  ,59.040442659434588490  ] 
dist 2=[57.295151923773877878  ,59.206691898026014465  ] 
dist 3=[56.030420786758034790  ,59.302558010762785598  ] 
dist 4=[54.783033616084696076  ,59.248779352522489164  ] 
dist 5=[53.306761121747550083  ,59.129612966849635046  ] 
dist 6=[51.127796505565638054  ,58.996277585187069959  ] 
dist 7=[48.657529564539832889  ,58.743174209246240193  ] 
dist 8=[46.017791983983121754  ,58.402197022901105360  ] 
dist 9=[42.741742068506932348  ,55.073207460098776623  ] 
dist 10=[37.730091945976491390  ,54.470129188852998544  ] 
dist 11=[32.672023339834497019  ,53.585353390866751213  ] 
dist 12=[29.210496740989033889  ,53.295206496281557662  ] 
dist 13=[26.247012077422046744  ,52.720743514861182939  ] 
dist 14=[23.177830794823486980  ,51.719564663589800010  ] 
dist 15=[20.265591620638842027  ,46.712496047415476260  ] 
dist 16=[17.928693075247291474  ,43.363077147031418153  ] 
dist 17=[15.558675686074642970  ,29.184345707831002545  ] 
dist 18=[12.513736266332599378  ,28.645760407344330352  ] 
dist 19=[9.5523115591923932622 ,26.805020547637121563  ] 
dist 20=[7.5156164076699786024 ,26.375380393843582334  ] 
dist 21=[5.7589065791650874401 ,25.924927967991337440  ] 
dist 22=[3.9154651827672309837 ,25.829805840441006734  ] 
dist 23=[2.1473722579074283726 ,13.629671566053774267  ] 
dist 24=[.69116273900009769791,13.254946508331844726  ] 
dist 25=[-.82344767946341894502,7.2810034609138217719 ] 
dist 26=[-2.8258325442641215830 ,6.5340903923802154083 ] 
dist 27=[-4.7539187390190196174 ,5.0478868833323944196 ] 
dist 28=[-5.9718214989523296043 ,4.7032134888379579591 ] 
dist 29=[-6.9108593218502608470 ,3.6808645367697327552 ] 
dist 30=[-8.4611980718878431177 ,3.1561843446344213225 ] 
dist 31=[-10.341682417475456692  ,1.8741805261540213160 ] 
dist 32=[-11.528939240306298333  ,1.2578403249093147082 ] 
dist 33=[-12.439385833433310103  ,-7.9215162213239406931 ] 
dist 34=[-13.214158108549237294  ,-7.8888299882479606753 ] 
dist 35=[-13.845325804033711486  ,-7.6668514406469043532 ] 
dist 36=[-14.182160670063830900  ,-7.1841664586495082188 ] 
dist 37=[-14.369019800441859972  ,-6.4210056995560104010 ] 
dist 38=[-14.401149597210139644  ,-5.0796221236014824220 ] 
dist 39=[-12.070740059217325934  ,-3.6892567930529915441 ] 
dist 40=[-12.078647240116095805  ,-2.7304106020317391567 ] 
dist 41=[-11.264357779006957469  ,-1.9063016423328955314 ] 
dist 42=[-11.118774964441837677  ,-1.0531058511856824534 ] 
dist 43=[-10.892813530228898969  ,-.2482604045852055020 ] 
dist 44=[-10.813959416814538774  ,.3831592489017189470 ] 
dist 45=[-10.583576225616354701  ,1.0078188022217596986 ] 
dist 46=[-10.495322500362494189  ,1.7859474484453635439 ] 
dist 47=[-10.403553188806028052  ,2.5265092514893779731 ] 
dist 48=[-10.347759190240832032  ,3.0013879869860495634 ] 
dist 49=[-3.2661287089321820070 ,3.3727544513641867156 ] 
dist 50=[-2.6773674225163056614 ,3.7565692858358305626 ] 
dist 51=[-1.3152613705593070826 ,4.1913151391527915427 ] 
dist 52=[-1.0939644650069385609 ,4.5175770050599681284 ] 
dist 53=[.12496036887013293429,4.8277398866030238416 ] 
dist 54=[-.34506956968957072148,5.1984930381931952503 ] 
dist 55=[-.83305625369386847589,5.5374467856461635686 ] 
dist 56=[-1.1718232389812505116 ,5.7207233700419901668 ] 
dist 57=[-1.4645478294073947652 ,5.8262546831483233264 ] 
dist 58=[-1.7690576440446552512 ,5.8547448887019360974 ] 
dist 59=[-2.0562044331102317642 ,5.9913501340191408515 ] 
dist 60=[-2.2797461544256011529 ,6.3020160074439214355 ] 
dist 61=[-2.4985838976233089589 ,6.5450277354600062681 ] 
dist 62=[-2.7670124893716591025 ,6.6581073876017298680 ] 
dist 63=[-3.0188015646272885397 ,6.7118928402043706291 ] 
dist 64=[-3.1713074030023194960 ,6.7181707883199235722 ] 
dist 65=[-3.2797268220340944101 ,4.5685677999832331951 ] 
dist 66=[-3.3557377465107382460 ,4.4979501741786905842 ] 
dist 67=[-3.4047678330358928212 ,4.2209480958797782299 ] 
dist 68=[-3.4146654711305009516 ,4.1544349231092804732 ] 
dist 69=[-3.3932794633061866062 ,4.0149910502123429265 ] 
dist 70=[-3.3897702617814998429 ,3.9706325238622561028 ] 
dist 71=[-1.3877377117759651222 ,.5625644008122043486 ] 
dist 72=[-1.8836588138077307686 ,.5156579765643719846 ] 
dist 73=[-2.2877562873371802088 ,.4577359246388542626 ] 
dist 74=[-2.6721620535276229767 ,.4472570068357962544 ] 
dist 75=[-3.0145354335290385938 ,-.8546081672143009470 ] 
dist 76=[-3.2509041562866482477 ,-.8997942811392998026 ] 
dist 77=[-3.4549996707659889850 ,-1.0255737437749246691 ] 
dist 78=[-3.6686127207787393434 ,-1.0360699313261268038 ] 
dist 79=[-3.8559000760961672594 ,-1.0090787394709424115 ] 
dist 80=[-3.9549286527827074917 ,-.9243233242390578177 ] 
dist 81=[-4.0084305219885897076 ,-.8240958003547287971 ] 
dist 82=[-4.0189204499957611448 ,-.7353709917467653071 ] 
dist 83=[-4.0014332749446567487 ,-.6384898731255998816 ] 
dist 84=[-3.9827361574968668663 ,-.5056573951193193762 ] 
dist 85=[-3.9560656766097115071 ,-.3603623740167913438 ] 
dist 86=[-3.9388811792276256669 ,-.2137288795145087331 ] 
dist 87=[-2.8505342623868011411 ,.31980765552426392022] 
dist 88=[-2.8112699832228320485 ,.82506583679382248881] 
dist 89=[-2.8273217157692515363 ,1.2395444688085309395 ] 
dist 90=[-2.8296546089421621463 ,1.6379645720549806353 ] 
dist 91=[-2.1137054932976482988 ,1.9951316788527806700 ] 
dist 92=[-2.0991649803993222260 ,2.2450029542512351705 ] 
dist 93=[-1.9239316930685849112 ,2.4639140819752806805 ] 
dist 94=[-1.8855280328209739689 ,2.6975443707818651024 ] 
dist 95=[-1.8446539150961259178 ,2.9097071089662023655 ] 
dist 96=[-1.8282632583955050105 ,3.0429540385294464725 ] 
dist 97=[-.6909530219373838330 ,3.1437865563567496249 ] 
dist 98=[-.6591291512819820349 ,3.2265962595435196492 ] 
dist 99=[-.3534634196499531584 ,3.2913487157316971895 ] 
dist 100=[-.2983583465640086611 ,3.3201179259156922204 ] 
dist 101=[-.2289495602788976995 ,3.3279567096009374605 ] 
dist 102=[-.2144506540053322217 ,3.3239230011501093111 ] 
dist 103=[.24828873173943914329,2.9060525014691237677 ] 
dist 104=[.30579606592844579154,2.9117859706034246267 ] 
dist 105=[.39256854993154515997,2.9562814536112302608 ] 
dist 106=[.414187737146210165  ,3.0259105504316663330 ] 
dist 107=[.4238786665422838736 ,3.0627111466685045888 ] 
dist 108=[.39636796904929825587,3.0684222567564155649 ] 
dist 109=[.3397489455432624354 ,3.0372110793995467639 ] 
dist 110=[.1389369825560232466 ,3.0243957942369782646 ] 
dist 111=[-.1123851317668218119 ,3.0124384309012147870 ] 
dist 112=[-.3074796858256580306 ,2.9986347044838488711 ] 
dist 113=[-.4986590897576503170 ,2.3369878105614605205 ] 
dist 114=[-.80919389525888876085,2.2564570285806018064 ] 
dist 115=[-1.1311920689990150868 ,2.0606036996378963329 ] 
dist 116=[-1.4413462266184758133 ,2.0197949264006438427 ] 
dist 117=[-1.7199704274086275792 ,1.6070419155155532033 ] 
dist 118=[-1.9161498661278329209 ,1.3860077160215198339 ] 
dist 119=[-2.0894372228522160890 ,-1.1920135639162179607 ] 
dist 120=[-2.2767177987491034356 ,-1.2167014593733841077 ] 
dist 121=[-2.4465907524415292333 ,-1.2550320102229728919 ] 
dist 122=[-2.5504058878993896493 ,-1.2175502860402757825 ] 
dist 123=[-2.6256801531136742353 ,-1.1704920413534074400 ] 
dist 124=[-2.6816326211471393882 ,-1.1273592437634916263 ] 
dist 125=[-2.7208062931748592260 ,-1.0789239738092513468 ] 
dist 126=[-2.7291038787371766124 ,-1.0106916340572752303 ] 
dist 127=[-2.7255845121905594434 ,-.9350512623548493203 ] 
dist 128=[-2.7176295329377352754 ,-.8570462357184956351 ] 
dist 129=[-1.7507936081134484940 ,-.7624309269020821334 ] 
dist 130=[-1.6618028124911185384 ,-.6204981781408069506 ] 
dist 131=[-1.4372972741809242705 ,-.4736894862368176268 ] 
dist 132=[-1.4050281366072084221 ,-.3596111544749427767 ] 
dist 133=[-1.0498374674422263624 ,-.2477186902827139578 ] 
dist 134=[-.9823489714038220598 ,-.1096253019924537047 ] 
dist 135=[-.9083685443704677788 ,.0346791157730483625 ] 
dist 136=[-.8951109674798732137 ,.1713640730518880696 ] 
dist 137=[-.48856712322282363954,.3286102818504705168 ] 
dist 138=[-.47951366120154823368,.5549787592368607520 ] 
dist 139=[-.11982070268482318291,.7789483357857287607 ] 
dist 140=[-.08061502829606025140,.9282727986615004713 ] 
dist 141=[-.00704390863611427974,1.0507768772826224570 ] 
dist 142=[.00998524451871478230,1.1668677941779898547 ] 
dist 143=[.05781443929933214387,1.2699266494905124826 ] 
dist 144=[.0637149879544461052 ,1.3404216457701659729 ] 
dist 145=[.0555673528220691883 ,1.4005582701695133166 ] 
dist 146=[.0275904365877816525 ,1.4622800427613597532 ] 
dist 147=[-.0077329604810026629 ,1.5149920302098572266 ] 
dist 148=[-.0452000587889597990 ,1.5391712148118686908 ] 
dist 149=[-.0913800004230897581 ,1.5504608489103557958 ] 
dist 150=[-.1614784625495173242 ,1.5517264519423353053 ] 
dist 151=[-.2415363618469192475 ,1.5180598709305319655 ] 
dist 152=[-.3274640903991042906 ,1.5391004892350054051 ] 
dist 153=[-.4341082843550117291 ,1.6186829495694803866 ] 
dist 154=[-.5968424912835906873 ,1.6691015224124777670 ] 
dist 155=[-.7590416058571085814 ,1.7078487773251552348 ] 
dist 156=[-.8635516355303028776 ,1.7408392160644002237 ] 
dist 157=[-.9457708786922795989 ,1.7676321905229238916 ] 
dist 158=[-1.0190146687293774469 ,1.7816390583923225241 ] 
dist 159=[-1.0808467886812725782 ,1.7889718172479622970 ] 
dist 160=[-1.1589151305040395691 ,1.7891215961591060712 ] 
dist 161=[-1.2548573087126345438 ,-1.0064224953405449448 ] 
dist 162=[-1.5069893585207169332 ,-.9677608042803482906 ] 
dist 163=[-1.7106558554154179619 ,-.9180057438508402650 ] 
dist 164=[-1.8927874937896905044 ,-.8639232574536639141 ] 
dist 165=[-2.0470961675195416201 ,-.7963414519249141322 ] 
dist 166=[-2.1397215966839503739 ,-.69271373964770019581] 
dist 167=[-2.2048889949632977601 ,-.57390895105717727621] 
dist 168=[-2.2496139509578495344 ,-.44575960545887491552] 
dist 169=[-2.2837238140657845185 ,-.28628087497191038688] 
dist 170=[-2.3036016645428178414 ,-.04244972468489207851] 
dist 171=[-2.3162121453151474209 ,.20209446671278370537] 
dist 172=[-2.3222136328068541746 ,.36441869007990034966] 
dist 173=[-2.3235222729615656812 ,.49751935599053203328] 
dist 174=[-2.3174039867642705656 ,.62544078972620394248] 
dist 175=[-2.3046872538531926593 ,.7401593331040820254 ] 
dist 176=[-2.2966056936968930981 ,.8205707188540185460 ] 
dist 177=[-.95929974102541171066,.8912072679902566215 ] 
dist 178=[-.84543413495763833455,.9669162002135029588 ] 
dist 179=[-.57382734950976375857,1.0353891175668917976 ] 
dist 180=[-.53216322720979143673,1.0771491830910568620 ] 
dist 181=[-.18655778010974393741,1.1073132903886924921 ] 
dist 182=[-.16246524188350210098,1.1295122251502277856 ] 
dist 183=[-.0657755249899234379 ,1.1448765737620766496 ] 
dist 184=[-.0473859158971202209 ,1.1477672185518418562 ] 
dist 185=[-.0115697116112188873 ,1.1458204397862603415 ] 
dist 186=[-.0029151053010001671 ,1.1418788843816357851 ] 
dist 187=[-.00438823283203493578,1.1763477114289042503 ] 
dist 188=[-.02557600956587336166,1.2450744977856222555 ] 
dist 189=[-.04916512354783999863,1.2998012582159550798 ] 
dist 190=[-.0821693037258200488 ,1.3263600094794113620 ] 
dist 191=[-.1186701636018676762 ,1.3399764901671194750 ] 
dist 192=[-.1562151470784907144 ,1.3430499826366265854 ] 
dist 193=[-.2016948562273294178 ,.99900397560148490743] 
dist 194=[-.2698625701720771115 ,.97293633621052872287] 
dist 195=[-.3403633968038879139 ,.90985317777862012216] 
dist 196=[-.3951550432112308895 ,.89392274352834629013] 
dist 197=[-.4489089136297438512 ,.7948555691377077171 ] 
dist 198=[-.5152700382604403494 ,.7741745139102145304 ] 
dist 199=[-.5846263406380237562 ,.7352325139424218841 ] 
dist 200=[-.6503346612371794262 ,.7245519909971070296 ] 
dist 201=[-.7259352155438639744 ,.59205081938641808998] 
dist 202=[-.8347714089669052974 ,.72193176648001986366] 
dist 203=[-.9410855269389320622 ,.85013858134209202425] 
dist 204=[-1.0066213893884923854 ,.93135293828898209819] 
dist 205=[-1.0548166207608007240 ,.99365856924695659172] 
dist 206=[-1.0919269863535053363 ,1.0464044713193024536 ] 
dist 207=[-1.1197233126602103204 ,1.0889316953098305412 ] 
dist 208=[-1.1307472232567574115 ,1.1104561993996456919 ] 
dist 209=[-1.1344145914417199422 ,1.1211472397641400646 ] 
dist 210=[-1.1328516893123940250 ,1.1227016223140344756 ] 
dist 211=[-1.0769713939230051722 ,1.1108341163243001318 ] 
dist 212=[-1.1452244215464896344 ,1.1049930716097615785 ] 
dist 213=[-1.2264009077686603571 ,1.0911823815388372966 ] 
dist 214=[-1.2796086429104084112 ,1.0847077516617420936 ] 
dist 215=[-1.3225146620931027991 ,1.0472930836099169792 ] 
dist 216=[-1.3625794191902859617 ,1.0375065109779530349 ] 
dist 217=[-1.3949881897555370818 ,1.0093445574691198086 ] 
dist 218=[-1.4073393783968862836 ,1.0002988097445553460 ] 
dist 219=[-1.4110262101386337398 ,.4992183850053196464 ] 
dist 220=[-1.4088525000243925825 ,.4491077195794440945 ] 
dist 221=[-1.3703569050596103463 ,.3396511537524459672 ] 
dist 222=[-1.3575006137232924244 ,.41612507770971170631] 
dist 223=[-1.3446966442424926926 ,.51092846866988900011] 
dist 224=[-1.3363254443192122856 ,.6537911285373425462 ] 
dist 225=[-.0023872867335240273 ,.7956073286273499192 ] 
dist 226=[.0077277427938308406 ,.8862352056412189847 ] 
dist 227=[.0368181139535638886 ,.9566934308241134963 ] 
dist 228=[.03544470589696268515,1.0180159678459540706 ] 
dist 229=[.02192878928170565339,1.0687509366176278112 ] 
dist 230=[-.01168495525898228427,1.1222236754558803211 ] 
dist 231=[-.05562796861703936490,1.2132110340211231506 ] 
dist 232=[-.11036550442682350372,1.3138283313197503362 ] 
dist 233=[-.18347193863689829993,1.4046976451113570011 ] 
dist 234=[-.30072064204267622904,1.4567825058652634944 ] 
dist 235=[-.4202000228925775652 ,1.4904118656692287788 ] 
dist 236=[-.50220860733162463566,1.5079628855755238742 ] 
dist 237=[-.5724377171278963584 ,1.5175258019566449699 ] 
dist 238=[-.6449083683940319683 ,1.5176687802272507417 ] 
dist 239=[-.7132334520126036637 ,1.5120364307726287902 ] 
dist 240=[-.7669187457598795151 ,1.5058995682722086736 ] 
dist 241=[-.8201387275640056043 ,1.1263551050683540657 ] 
dist 242=[-.8866069795972864120 ,1.0850993333517276105 ] 
dist 243=[-.9499252127425388653 ,.97903798690021410257] 
dist 244=[-.9905743082325599563 ,.96221954858943481713] 
dist 245=[-1.0223843350026510745 ,.78469180686874176501] 
dist 246=[-1.0504280963477725825 ,.74960351363354498174] 
dist 247=[-1.0738890189129711044 ,.70907614785842841347] 
dist 248=[-1.0874101237214369633 ,.69735452663909449329] 
dist 249=[-1.0962335542443445901 ,.35254653425720780019] 
dist 250=[-1.1009473174069992942 ,.30882948018900987884] 
dist 251=[-1.1022238938732076741 ,.21707517428723477215] 
dist 252=[-1.1034020022611090183 ,.19275707844226762647] 
dist 253=[-1.1167063270094680106 ,.10156761797739196836] 
dist 254=[-1.1192988467946734502 ,.08368226182022851374] 
dist 255=[-1.1142513575523928150 ,.04937167161386697952] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 0, 2, 0, 1, 2] 
dist 0=[62.058573222711918063  ,62.058573222711918063  ] 
dist 1=[61.749363712395886978  ,62.197586597634342914  ] 
dist 2=[61.153543619451919092  ,62.226570678161250390  ] 
dist 3=[59.870130883980098234  ,62.153232263854186571  ] 
dist 4=[58.378054639873580998  ,61.921264519170669808  ] 
dist 5=[56.948869348925626632  ,61.769377224337642141  ] 
dist 6=[55.289020341852840938  ,61.605014654996649192  ] 
dist 7=[52.875669982730571922  ,61.455844087548171800  ] 
dist 8=[50.155960809656566659  ,56.608860923089497083  ] 
dist 9=[47.272574314316712621  ,55.849870580165488689  ] 
dist 10=[43.710250700017550897  ,54.716200015689652763  ] 
dist 11=[38.279039546690708440  ,54.388863785739367308  ] 
dist 12=[32.806727697846817020  ,53.687128346587587332  ] 
dist 13=[29.080285018266043593  ,53.574100712460094059  ] 
dist 14=[25.910893695369999026  ,51.847971994870650269  ] 
dist 15=[22.663380648386011157  ,48.738069067091758577  ] 
dist 16=[19.605949644895759189  ,34.024615652178684340  ] 
dist 17=[17.191778090794884135  ,31.744528587968184847  ] 
dist 18=[14.774578749223722663  ,31.163884814735550755  ] 
dist 19=[11.715319482233147318  ,29.170256318073151118  ] 
dist 20=[8.7625125347092109569 ,28.702868640863211249  ] 
dist 21=[6.7702092251854871656 ,28.193996169419196458  ] 
dist 22=[5.0928282322452286469 ,28.064759838700933181  ] 
dist 23=[2.9853886262223926541 ,8.7240386526108055333 ] 
dist 24=[.07327526299551670553,6.1160517309305303596 ] 
dist 25=[-1.8083299148270611313 ,3.1176713457314293347 ] 
dist 26=[-3.3025853644316289242 ,2.5811707125897842462 ] 
dist 27=[-4.6681756706162615738 ,2.4793409040143838447 ] 
dist 28=[-6.0566934271928838828 ,-1.2377403486404022899 ] 
dist 29=[-7.9049844210539929394 ,-1.5460610036585675080 ] 
dist 30=[-10.136066984265226924  ,-2.2798516662864036633 ] 
dist 31=[-12.235982567313612067  ,-3.0006720270568221613 ] 
dist 32=[-13.560390173075782814  ,-6.3875280986877385219 ] 
dist 33=[-14.574214655120994789  ,-6.5309962161541121442 ] 
dist 34=[-15.433638085528049720  ,-6.7561350641193720510 ] 
dist 35=[-16.131350019861694726  ,-6.7694222652534422780 ] 
dist 36=[-16.499324434439229916  ,-6.7172020314499412092 ] 
dist 37=[-16.697719942248038988  ,-5.9480632411250871119 ] 
dist 38=[-16.725250483288086133  ,-4.0905389627295171618 ] 
dist 39=[-8.6773787067445168019 ,-2.1798716739725601804 ] 
dist 40=[-7.0585539678330762812 ,-.86975806210658812433] 
dist 41=[-6.8287933485828512738 ,.24830502607416433269] 
dist 42=[-6.7600675924002142769 ,1.3932129424262851604 ] 
dist 43=[-6.7323256324713523227 ,2.4652966289297546362 ] 
dist 44=[-5.7496532808454958335 ,3.2930582445840421268 ] 
dist 45=[-5.6366945285081004658 ,4.0993654560983429925 ] 
dist 46=[-5.4219625601610632939 ,5.0861278648494081806 ] 
dist 47=[-5.3624524295874857368 ,6.0160683289577267817 ] 
dist 48=[-.40235092753659936794,6.5957810466480812977 ] 
dist 49=[-.22209460112533872442,7.0299421695388390088 ] 
dist 50=[.04210793542936148917,7.3792268847029452498 ] 
dist 51=[.11082799140072372575,7.6480050370916974314 ] 
dist 52=[1.2205496537658466711 ,7.7610613491081693895 ] 
dist 53=[1.3574643324351551907 ,7.8069011921044505514 ] 
dist 54=[1.6306451021491855178 ,7.8069788970870237316 ] 
dist 55=[1.6929229548392974700 ,7.5476341278133420068 ] 
dist 56=[1.6778364018685984147 ,7.4868508949718883523 ] 
dist 57=[1.4262663827464112412 ,7.2647959627746208224 ] 
dist 58=[1.1261655085909121946 ,7.2257634044409301987 ] 
dist 59=[.8193470728118442875 ,6.6206324191213615936 ] 
dist 60=[.5408433557377210564 ,6.4820943609037508700 ] 
dist 61=[.2305614065224397568 ,6.3133161357252349315 ] 
dist 62=[-.20316443850417020689,5.7529412268129516998 ] 
dist 63=[-.6378620510408073237 ,4.4233196598358197144 ] 
dist 64=[-1.3459424066220230698 ,2.7136077371821990128 ] 
dist 65=[-2.0087562817084971428 ,2.4987340870012526289 ] 
dist 66=[-2.5379679387631275193 ,2.4608393237960125892 ] 
dist 67=[-3.0227216618243404416 ,2.1246507247758783374 ] 
dist 68=[-3.4415375375284072940 ,2.0593874628113801833 ] 
dist 69=[-3.7076706751603379266 ,1.9686953953751228354 ] 
dist 70=[-3.9129504682922199991 ,1.9402719641789663035 ] 
dist 71=[-4.0890020818496269267 ,1.0239110338103333057 ] 
dist 72=[-4.2367686801250231992 ,.93205367436752454983] 
dist 73=[-4.3291795403953192506 ,.91391210400824784573] 
dist 74=[-4.3989419657381134798 ,.87760884201742608518] 
dist 75=[-4.4562672377941406978 ,.86760804607546380478] 
dist 76=[-4.5013824615960396310 ,.73432146266220327677] 
dist 77=[-4.5223864077791193012 ,.71373263498077521683] 
dist 78=[-4.5298169324954903964 ,.66907203562530487514] 
dist 79=[-4.5207297917171035597 ,.65567491195242651777] 
dist 80=[-4.5223098480419566400 ,.59710224454716156024] 
dist 81=[-4.5610412455326085776 ,.58461028274185836894] 
dist 82=[-4.5649419686834716079 ,.55440210097686432311] 
dist 83=[-4.5101320866256717639 ,.54547065325233089253] 
dist 84=[-4.4825689816912792782 ,.44898728365891774373] 
dist 85=[-4.4507463381634221673 ,.6726119615135443351 ] 
dist 86=[-4.4297762915247912700 ,.9975632841877794863 ] 
dist 87=[-3.2668037953735704943 ,1.4022353220883972748 ] 
dist 88=[-3.1352782950604200128 ,1.7864560602324135944 ] 
dist 89=[-2.8060108392322931162 ,2.0298170142482574235 ] 
dist 90=[-2.7498164681925016307 ,2.2162479463299144227 ] 
dist 91=[-2.2243301171130440796 ,2.3733375724549206022 ] 
dist 92=[-2.1212751585667996696 ,2.4992647171099042301 ] 
dist 93=[-1.9874330206043204805 ,2.6848940267904956408 ] 
dist 94=[-1.9417241783718787131 ,2.9673348775976070591 ] 
dist 95=[-.99516418626111382387,3.2249712468893980328 ] 
dist 96=[-.8727831398187379724 ,3.3817804178223975140 ] 
dist 97=[-.60728273421499011653,3.4948225180486748669 ] 
dist 98=[-.54320547808070688261,3.5777564829796823094 ] 
dist 99=[-.24721179075340639519,3.6350263490343072917 ] 
dist 100=[-.1943918218136714018 ,3.6482139736927462384 ] 
dist 101=[-.06944428031770011325,3.6412197120463461960 ] 
dist 102=[-.05020186659889234114,3.6386011659018611749 ] 
dist 103=[-.1638989595329798170 ,2.4977977384888243506 ] 
dist 104=[-.4900521876197644203 ,2.3889007166397469222 ] 
dist 105=[-.7594201803618524814 ,2.1137539297206491666 ] 
dist 106=[-1.0212787856030409301 ,2.0712757094053585986 ] 
dist 107=[-1.2578875147279200388 ,1.6308340419680233600 ] 
dist 108=[-1.4265036992553407460 ,1.5459063447337183826 ] 
dist 109=[-1.5773915810845454448 ,1.4461938586471713223 ] 
dist 110=[-1.7432552059480026596 ,1.4202660061970947673 ] 
dist 111=[-1.8943957054387284797 ,.71470118912212519001] 
dist 112=[-1.9865407999488121634 ,.81469196789589279926] 
dist 113=[-2.0529918916153998835 ,.88279991264407783539] 
dist 114=[-2.1344045872173191637 ,.94039545376773648327] 
dist 115=[-2.2180810249713626322 ,.99845946745093067132] 
dist 116=[-2.2810248219106111848 ,1.0521615200459349749 ] 
dist 117=[-2.3083590067810064178 ,1.0923585285988518642 ] 
dist 118=[-2.3180785998209236846 ,1.1302280637328094565 ] 
dist 119=[-2.3153274473161768054 ,1.1746425512486937729 ] 
dist 120=[-2.1679772009004295986 ,1.2152974516965974087 ] 
dist 121=[-2.1386088291158434490 ,1.2381708807437561231 ] 
dist 122=[-2.0808997940159547012 ,1.2523037655604842192 ] 
dist 123=[-2.0618012845862621691 ,1.2580985552573092440 ] 
dist 124=[-2.1235841875307925264 ,1.2580186289541505882 ] 
dist 125=[-2.2247548590480967067 ,1.2551162524366795377 ] 
dist 126=[-2.3434912324913334806 ,1.2377879892103959731 ] 
dist 127=[-2.4531054906971739650 ,1.2312156617122170155 ] 
dist 128=[-2.5178644083082134118 ,-.5377041584824149692 ] 
dist 129=[-2.5622215186797650850 ,-.46786895077308078551] 
dist 130=[-2.5903962492663687819 ,-.2229985624170019923 ] 
dist 131=[-2.6060609197045602459 ,.04916347014106005871] 
dist 132=[-2.6062180118915567778 ,.3311926456435738616 ] 
dist 133=[-2.5884834963173313633 ,.6744026936325278695 ] 
dist 134=[-2.5785144213907302075 ,1.1907463793403601810 ] 
dist 135=[-1.0549801389696473201 ,1.7033727535155862023 ] 
dist 136=[-1.0576361233858989368 ,2.0317507503297920164 ] 
dist 137=[-1.0576319370223460821 ,2.2879815458347598454 ] 
dist 138=[-1.0556770016420565106 ,2.5126706950410459837 ] 
dist 139=[-1.0520950562476389044 ,2.6998351054215221134 ] 
dist 140=[-.5954248543875625860 ,2.8440552788067714775 ] 
dist 141=[-.5787617276742870995 ,2.9590260555191462937 ] 
dist 142=[-.5345461494459766845 ,3.0560917718113619506 ] 
dist 143=[-.5278648988194882113 ,3.1358825762401696863 ] 
dist 144=[-.44892715613058350702,3.1819102092131122462 ] 
dist 145=[-.4329444327682876955 ,3.2120230899967180347 ] 
dist 146=[-.41652705754183816344,3.2282981236308043634 ] 
dist 147=[-.41253617418092031257,3.2344473438013742465 ] 
dist 148=[-.23994812359058084925,3.2275050506284839637 ] 
dist 149=[-.21794116991423750013,3.2054084532525389194 ] 
dist 150=[-.17368340854055786903,3.1905728544440098084 ] 
dist 151=[-.16222085362648968629,1.5349385000367641935 ] 
dist 152=[-.12137543691583912763,1.3899152600943042859 ] 
dist 153=[-.11247732144292548695,1.0387335636150216486 ] 
dist 154=[-.16960300153003668427,.98651891563522950894] 
dist 155=[-.45001197365553493869,.6345703669856252244 ] 
dist 156=[-.66326912648019713903,.39273820677487979903] 
dist 157=[-.86811534333334073252,.38261847321404012259] 
dist 158=[-1.1149626306045874731 ,.37917343292522015019] 
dist 159=[-1.3472279823564834741 ,.38393243329526435996] 
dist 160=[-1.4938801974556846590 ,.39359050337834565665] 
dist 161=[-1.6058650208530324424 ,.4096960269351366006 ] 
dist 162=[-1.6997738652138462613 ,.4335959148725213826 ] 
dist 163=[-1.7748409519578939084 ,.47435816660146182715] 
dist 164=[-1.8116286584340593557 ,.51851615281393331702] 
dist 165=[-1.8305176771255591309 ,.55596735106705463716] 
dist 166=[-1.8341547517517112219 ,.59565354276139073657] 
dist 167=[-1.5786916136035599175 ,.64873135539204942906] 
dist 168=[-1.5518701938539414728 ,.70631535838168330615] 
dist 169=[-1.4783965003274981242 ,.7639843749724659157 ] 
dist 170=[-1.4630521590216963710 ,.8327276739809902922 ] 
dist 171=[-1.3189769847614324396 ,.9345050782133557487 ] 
dist 172=[-1.3062283404623365653 ,1.0350084766011901877 ] 
dist 173=[-1.4341419741439327440 ,1.0986679451923023025 ] 
dist 174=[-1.5294509818979157171 ,1.1474919615916495035 ] 
dist 175=[-1.6051349851027082362 ,1.1887932744285362233 ] 
dist 176=[-1.6646137902808422707 ,1.2220677033170102411 ] 
dist 177=[-1.6952503333075136235 ,1.2388598069069465321 ] 
dist 178=[-1.7106161883926890050 ,1.2467841149715670291 ] 
dist 179=[-1.7125837455199579882 ,1.2466047895608322456 ] 
dist 180=[-1.6174993300243035853 ,1.2369805569227231110 ] 
dist 181=[-1.5981910040733221708 ,1.2323622748373931360 ] 
dist 182=[-1.5717710088006951029 ,1.2092049691174138846 ] 
dist 183=[-1.5605025873754278015 ,1.2050695081156103293 ] 
dist 184=[-1.5303738917671417418 ,1.1247770626937088372 ] 
dist 185=[-1.5175118277008370886 ,1.1488077206276822392 ] 
dist 186=[-1.4999411683665754137 ,1.2831235008420125247 ] 
dist 187=[-1.4913932063941180881 ,1.4150782212350147560 ] 
dist 188=[-.3665791914555270628 ,1.5110247374965046129 ] 
dist 189=[-.2708026058942984625 ,1.5989537155181834288 ] 
dist 190=[-.07030516234382031795,1.6989134287894751903 ] 
dist 191=[-.12079844452667803328,1.7893633779986016388 ] 
dist 192=[-.16727744383761637971,1.8393402786612954807 ] 
dist 193=[-.2196897312644960632 ,1.8692395258162908596 ] 
dist 194=[-.29386541880756480778,1.8795606890136672969 ] 
dist 195=[-.37631514380384536666,1.8808023279658270704 ] 
dist 196=[-.46174981827583152476,1.8754995211862708513 ] 
dist 197=[-.56570515761195846646,1.8630888366396244516 ] 
dist 198=[-.7220702673827320404 ,1.8553059955123281121 ] 
dist 199=[-.8771633192460006252 ,.44670086779884205472] 
dist 200=[-.9760431347534169125 ,.46977717655555872393] 
dist 201=[-1.1194583149391955242 ,.50091235609967201804] 
dist 202=[-1.3138774832134569830 ,.54389867022419628328] 
dist 203=[-1.4853759190724444099 ,.61426819243323977366] 
dist 204=[-1.6006829921384539314 ,.68648526825320509864] 
dist 205=[-1.7020052281982621660 ,.73684435554203121897] 
dist 206=[-1.8057010541439982094 ,.78080792702382273538] 
dist 207=[-1.8883027768830507321 ,.82750276078944333398] 
dist 208=[-1.9525452252124095412 ,.87234644910761472958] 
dist 209=[-1.9829716083487908542 ,.9089226406007002362 ] 
dist 210=[-1.9967047967067502158 ,.94642676044485089476] 
dist 211=[-1.9967181072044995361 ,.99497314729404683039] 
dist 212=[-1.9058507801256739260 ,1.0420413490497024011 ] 
dist 213=[-1.8854613548520341710 ,1.0736464708846443497 ] 
dist 214=[-1.7680545977829039819 ,1.0999576930047440928 ] 
dist 215=[-1.2559713216584831308 ,1.1258998995211599546 ] 
dist 216=[-1.2110125605678433266 ,1.1495984299958563229 ] 
dist 217=[-1.0944836944999628446 ,1.1669558111828711295 ] 
dist 218=[-1.0765183702973035244 ,1.1829801859824621900 ] 
dist 219=[-.87873399895629915475,1.2013587080659682069 ] 
dist 220=[-.83956255762396181286,1.2166689893929287562 ] 
dist 221=[-.79617535820681453461,1.2204490027574177769 ] 
dist 222=[-.78485855478687975543,1.2186093914922763221 ] 
dist 223=[-.39161759907384728335,1.2147059980377570867 ] 
dist 224=[-.34207094551742720566,1.1823536151709793617 ] 
dist 225=[-.23929533199742007602,1.1768155809111859164 ] 
dist 226=[-.21235117498654431891,1.1993159726775121000 ] 
dist 227=[-.11332876391498101884,1.2138635623300803005 ] 
dist 228=[-.09340439123968557690,1.2163654246550008080 ] 
dist 229=[-.05836372295497847470,1.2124849235483888814 ] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 2, 0, 0, 0, 2] 
dist 0=[50.484091171027375556  ,50.484091171027375556  ] 
dist 1=[49.510485811367634140  ,51.414705307830713617  ] 
dist 2=[48.318272956605444574  ,52.220273118372578171  ] 
dist 3=[46.514410260345166258  ,52.694533073993020909  ] 
dist 4=[44.452148084439333713  ,53.016454995020558334  ] 
dist 5=[42.227938275261530097  ,53.213978715078498790  ] 
dist 6=[39.455131081255855586  ,53.315579237897599606  ] 
dist 7=[35.202044611582454607  ,53.298555652819509235  ] 
dist 8=[30.900419870397966070  ,53.137078080799077235  ] 
dist 9=[27.933622936481055253  ,53.013681125994724389  ] 
dist 10=[25.370624543690097124  ,52.181257563502071112  ] 
dist 11=[22.681114965057878504  ,51.937071325366259439  ] 
dist 12=[20.108450953452878608  ,51.565885847863459838  ] 
dist 13=[18.011705037795340937  ,51.422017053458442480  ] 
dist 14=[15.856057417813524308  ,47.732046058639720457  ] 
dist 15=[13.047521600196952450  ,47.011287631317527663  ] 
dist 16=[10.297218089608302442  ,43.050426859680052465  ] 
dist 17=[8.3737803297867784157 ,35.478764879925614861  ] 
dist 18=[6.6803504560239497655 ,34.186161828414352799  ] 
dist 19=[4.8482158281932982309 ,31.043330793486674396  ] 
dist 20=[3.0561308844928810371 ,30.590277672222153282  ] 
dist 21=[1.5220224971204955613 ,26.095997053022633148  ] 
dist 22=[-.1263229619085298494 ,25.112139101448396244  ] 
dist 23=[-2.3760852827813944952 ,24.134446869233219836  ] 
dist 24=[-4.5523188579201575688 ,23.956567283944385330  ] 
dist 25=[-5.9071024687373575881 ,22.645624360532159672  ] 
dist 26=[-6.9298244158505275918 ,15.583370490781714574  ] 
dist 27=[-7.7787215370450532989 ,13.727544927955241921  ] 
dist 28=[-8.4607899148613755708 ,13.256368462204257913  ] 
dist 29=[-8.8168792161189136287 ,11.605934776936224737  ] 
dist 30=[-9.0136770192345889028 ,11.266260951660818263  ] 
dist 31=[-9.0577685189685380087 ,10.818531325894529062  ] 
dist 32=[-8.9948209956418593141 ,10.714536826659173155  ] 
dist 33=[-8.9484954295199502235 ,.2894648744335396680 ] 
dist 34=[-8.8896201837781561109 ,-.5616710600983555278 ] 
dist 35=[-8.8426742938935330885 ,-2.3793722394035330193 ] 
dist 36=[-8.7066863741508004107 ,-2.7340820283055177951 ] 
dist 37=[-8.6434100546268580629 ,-4.5663251601097585533 ] 
dist 38=[-8.5146845132769398014 ,-4.0081722974138034106 ] 
dist 39=[-8.4621320089520756686 ,-2.2942970290906019071 ] 
dist 40=[-9.3763528008812499944 ,-.5660495465193691074 ] 
dist 41=[-10.393833199626330586  ,.6109591485410051998 ] 
dist 42=[-11.025881604669553146  ,1.6075363891008348721 ] 
dist 43=[-11.499126033055507716  ,2.6161800480843076166 ] 
dist 44=[-11.882058605259670793  ,3.5538011367952870462 ] 
dist 45=[-12.179307374301471694  ,4.2671659913817242124 ] 
dist 46=[-12.310174295764563192  ,4.9522763587913679627 ] 
dist 47=[-12.362443760913913825  ,5.7773527200704022756 ] 
dist 48=[-12.351691853174603234  ,6.5486133079932398736 ] 
dist 49=[-1.7046650005114221295 ,7.0190650741944692840 ] 
dist 50=[-1.2038100370167899637 ,7.3593411887446330526 ] 
dist 51=[-.0516246036869681629 ,7.6112130693008633593 ] 
dist 52=[.1229069734962618703 ,7.7917147002642654823 ] 
dist 53=[1.5517168084240577426 ,7.8470968572507074637 ] 
dist 54=[1.7267753873671897179 ,7.8538693453311637247 ] 
dist 55=[1.0179380608998015219 ,7.8404129007362599857 ] 
dist 56=[.2911812232427015646 ,3.2680866728004607358 ] 
dist 57=[-.1978146393321240908 ,3.7861462107154522539 ] 
dist 58=[-.6057409814119273177 ,4.1067122131291655039 ] 
dist 59=[-1.0090740002659505993 ,4.3445747986053164460 ] 
dist 60=[-1.3781566274295903129 ,4.5324086384259583672 ] 
dist 61=[-1.6494555841823102021 ,4.6741741518522773107 ] 
dist 62=[-1.9009399497748576937 ,4.7280935138671055752 ] 
dist 63=[-2.1910133096418150079 ,4.7465066243647121558 ] 
dist 64=[-2.4581971529900544139 ,4.7465239236914430306 ] 
dist 65=[-2.6183499218862884554 ,3.3956344286020705569 ] 
dist 66=[-2.7307789664867575404 ,3.2663462480859187300 ] 
dist 67=[-2.8074876773550495425 ,2.9425909865134752758 ] 
dist 68=[-2.8612646611043188788 ,2.8848932437152101323 ] 
dist 69=[-2.8821867906321958992 ,2.3730864765392126849 ] 
dist 70=[-2.8842457267547781420 ,2.2736900307441013971 ] 
dist 71=[-2.8792332704077077976 ,2.1335558228280065523 ] 
dist 72=[-2.2461776727691830193 ,2.0903117543797212224 ] 
dist 73=[-2.1768650107289626440 ,1.2341091868619708909 ] 
dist 74=[-1.9941748538410218104 ,1.1254621935186299928 ] 
dist 75=[-1.9655935718037756973 ,.8755428368984981458 ] 
dist 76=[-1.6469562187943118841 ,.8324912919825873936 ] 
dist 77=[-1.8352004449053614610 ,.57222127497269290124] 
dist 78=[-2.0232100958327304381 ,.76503615669875190445] 
dist 79=[-2.2109459458391893179 ,1.0083274217674342245 ] 
dist 80=[-2.4479237448149327709 ,1.2410636527745985069 ] 
dist 81=[-2.6702727367964378976 ,1.3917801550532375339 ] 
dist 82=[-2.7996392242923383393 ,1.5111612302573133516 ] 
dist 83=[-2.8861210673878997629 ,1.6188892488313353489 ] 
dist 84=[-2.9372214998360577144 ,1.7108759263545564231 ] 
dist 85=[-2.9698318609717240066 ,1.7674694009211269149 ] 
dist 86=[-2.9824638469284992867 ,1.8090611679293823995 ] 
dist 87=[-3.0303205365030383231 ,1.8412311834615441672 ] 
dist 88=[-3.1107757052901358172 ,1.8633826615495367577 ] 
dist 89=[-3.1748516209515146181 ,1.8673025552924619262 ] 
dist 90=[-3.1986577069613891192 ,1.8599888876415615628 ] 
dist 91=[-3.2047633997880066920 ,1.8556502666255865511 ] 
dist 92=[-3.1981325919030759111 ,1.7772265801689080605 ] 
dist 93=[-3.1203964255158342332 ,1.7554823240497885879 ] 
dist 94=[-3.0941977876095585460 ,1.8189318113261028482 ] 
dist 95=[-3.0620644688641115553 ,1.9321955194928991274 ] 
dist 96=[-3.0451437050238406203 ,2.0363149662132131225 ] 
dist 97=[-2.2075637608331176909 ,2.0969826945941885369 ] 
dist 98=[-2.1124090491211903206 ,2.1374588162589405772 ] 
dist 99=[-1.8789580949184093922 ,2.1609675226745820536 ] 
dist 100=[-1.8367715117098934958 ,2.1728421770980898219 ] 
dist 101=[-1.4778737500582838220 ,2.1729200805309722338 ] 
dist 102=[-1.4078457690402118524 ,2.1562463044171312507 ] 
dist 103=[-1.3080799072166632807 ,2.1494151130607561726 ] 
dist 104=[-1.2774917916798516572 ,2.2665894843881415098 ] 
dist 105=[-1.0561298626723452955 ,2.4271315418942900084 ] 
dist 106=[-1.2849653297394830801 ,2.5258489824747047865 ] 
dist 107=[-1.5007368310273300809 ,2.5982870614972161838 ] 
dist 108=[-1.6916019886610481952 ,2.6539155525259337327 ] 
dist 109=[-1.8210419690220949994 ,2.6945590481848018929 ] 
dist 110=[-1.9303086168516251608 ,2.7071738812003660646 ] 
dist 111=[-2.0406747414048422985 ,2.7060888628754483550 ] 
dist 112=[-2.1374259976582761188 ,2.6986628290036630029 ] 
dist 113=[-2.1923540788708766844 ,1.6444969341248958228 ] 
dist 114=[-2.2272143581974914553 ,1.5508863688692663206 ] 
dist 115=[-2.2438575266859936118 ,1.3169931082219544357 ] 
dist 116=[-2.2488250855114332210 ,1.2834360465320866330 ] 
dist 117=[-2.2461932690285627510 ,.9219228481688117791 ] 
dist 118=[-2.2219591538589277568 ,.8540283111863170314 ] 
dist 119=[-2.2134039303769389103 ,.7781173781309949267 ] 
dist 120=[-1.4082510800062728061 ,.7648162224165075905 ] 
dist 121=[-1.3301653493669464284 ,.1605875946374484791 ] 
dist 122=[-1.1344618383401214042 ,.0880238926276699704 ] 
dist 123=[-1.1063769723000877216 ,-.0636180313037637620 ] 
dist 124=[-.80148034316136114894,-.1000734736272397856 ] 
dist 125=[-.7439753942151694956 ,-.2403381505606478520 ] 
dist 126=[-.6801856774034750586 ,-.2668127935898289836 ] 
dist 127=[-.6689441137588112146 ,-.3037248630488485756 ] 
dist 128=[-.75585360467048177641,-.1448097908005394834 ] 
dist 129=[-.89582013446530773466,-.0160668038281277370 ] 
dist 130=[-.99059904820089306603,.0967675024960216328 ] 
dist 131=[-1.0705358486954756114 ,.2173784731105675118 ] 
dist 132=[-1.1512475699476222106 ,.3337723628924625864 ] 
dist 133=[-1.2263965604407885444 ,.4297868649910675699 ] 
dist 134=[-1.2841253849451776939 ,.5293008692558296955 ] 
dist 135=[-1.3402225489911394403 ,.6596801788728405266 ] 
dist 136=[-1.4088585133094835595 ,.78674713441621233559] 
dist 137=[-1.4737436495667358315 ,.8730437484843911268 ] 
dist 138=[-1.5148658124878222513 ,.94606362201110137257] 
dist 139=[-1.5465085043537247157 ,1.0201307521960769270 ] 
dist 140=[-1.5735460608061852611 ,1.0892693831405049031 ] 
dist 141=[-1.5955955675330125803 ,1.1426152396754987140 ] 
dist 142=[-1.6073230141931940691 ,1.1946519222783997907 ] 
dist 143=[-1.6137502927237967545 ,1.2585650800111412576 ] 
dist 144=[-1.6146383928128150236 ,1.3190564681577414248 ] 
dist 145=[.4718803487960277283 ,1.3574334649642789576 ] 
dist 146=[.3542426601440861504 ,1.4116927211473257425 ] 
dist 147=[.1908576295044133407 ,1.5991467072443336329 ] 
dist 148=[.0106242003356460570 ,1.7665299534527156090 ] 
dist 149=[-.1742608507247802846 ,1.9090146493513954985 ] 
dist 150=[-.3979322017209028550 ,1.9944684405570244091 ] 
dist 151=[-.73296840373050545207,2.0545080684858118301 ] 
dist 152=[-1.0657154093426334423 ,2.0955651123059064682 ] 
dist 153=[-1.2802524500818649367 ,2.1258154640760270584 ] 
dist 154=[-1.4492477594294752297 ,2.1427252549929666358 ] 
dist 155=[-1.6002595818451855899 ,2.1531129243579886005 ] 
dist 156=[-1.7289587903805568468 ,2.1573322670322714263 ] 
dist 157=[-1.8062751465220741134 ,2.1572825117749156542 ] 
dist 158=[-1.8607501632078250725 ,2.1506323801568581812 ] 
dist 159=[-1.8982901224778174835 ,2.1378896820036491714 ] 
dist 160=[-1.9260380170134623472 ,2.1303177969846051851 ] 
dist 161=[-1.9414329878645088189 ,.88988401319455104479] 
dist 162=[-1.9507333776882033747 ,.78403733628546509819] 
dist 163=[-1.9541575269785194953 ,.53175360681891163832] 
dist 164=[-1.9535547505862025696 ,.49290724506745834557] 
dist 165=[-1.9470455093348136325 ,.14385366746287273605] 
dist 166=[-1.9346908646576650426 ,.08123153443591380056] 
dist 167=[-1.9274097120957771089 ,-.00326469492929424990] 
dist 168=[-.8145599258121978818 ,-.02471950694523704645] 
dist 169=[-.92643373819575163532,-.2420628657162555665 ] 
dist 170=[-1.0262358283855721540 ,-.0558515722403135482 ] 
dist 171=[-1.1022590286243709268 ,.1316104550605801037 ] 
dist 172=[-1.1656850119978253580 ,.3054573758871571613 ] 
dist 173=[-1.2161433531457688672 ,.4373341177294597824 ] 
dist 174=[-1.2404131726138075409 ,.5636888987155061390 ] 
dist 175=[-1.2527792115524591812 ,.71550103286053722284] 
dist 176=[-1.2557294558656077895 ,.85820692895486070715] 
dist 177=[-.91205972699611425962,.94822008792695765667] 
dist 178=[-.88623157177990714822,1.0168523842697878474 ] 
dist 179=[-.82369874771036304523,1.0742279691960802433 ] 
dist 180=[-.80865430089128851955,1.1199604619187244176 ] 
dist 181=[-.71135330476993878254,1.1421257056254448557 ] 
dist 182=[-.6913179704322063034 ,1.1533499113864544972 ] 
dist 183=[-.6544392108807992265 ,1.1554169127958121835 ] 
dist 184=[-.6446514532793588244 ,.83707380893333488684] 
dist 185=[-.4701698508328098566 ,.81274855222521379043] 
dist 186=[-.4461136604238623566 ,.75427962471795794742] 
dist 187=[-.3862155828337159694 ,.73999636036417757245] 
dist 188=[-.3769851673021246886 ,.65032594162505918964] 
dist 189=[-.2841588646325438566 ,.63189349266083632658] 
dist 190=[-.2665060433789049766 ,.59731200363346324196] 
dist 191=[-.2452408240742351991 ,.58798563833153321517] 
dist 192=[-.23974305452193766003,.58821899854413122739] 
dist 193=[-.06604901001869505083,.75666087572801682212] 
dist 194=[-.04404461090280666666,.8667332858844313849 ] 
dist 195=[-.0887314053728973613 ,.9551111551523730613 ] 
dist 196=[-.1959356285403429375 ,1.0369704689182474031 ] 
dist 197=[-.2951857980843577707 ,1.1083954279694551556 ] 
dist 198=[-.4075979900140414550 ,1.1556783374902909774 ] 
dist 199=[-.5673339459070765994 ,1.1938276409042459628 ] 
dist 200=[-.72461463623781535831,1.2294889718295677079 ] 
dist 201=[-.82722885716491178025,1.2582689147945415433 ] 
dist 202=[-.9094304985526964315 ,1.2689545913412585998 ] 
dist 203=[-.98524541981314618382,1.2720207831884128740 ] 
dist 204=[-1.0511704947250000022 ,1.2703880822318314224 ] 
dist 205=[-1.0944504395931849639 ,1.2335838089570394758 ] 
dist 206=[-1.1289245321218184771 ,1.2216132844253813100 ] 
dist 207=[-1.1603939399757337471 ,1.2109259634158261330 ] 
dist 208=[-1.1854572520369085730 ,1.2031793299613123906 ] 
dist 209=[-1.1943647628226245682 ,.1469402070693027956 ] 
dist 210=[-1.1964372791733622614 ,.1870500480144462845 ] 
dist 211=[-1.1942197269813070043 ,.2437805932866548626 ] 
dist 212=[-1.1596676623083374031 ,.3068276637805351306 ] 
dist 213=[-1.1484533386994133690 ,.3721472911528166083 ] 
dist 214=[-1.1367808457862777287 ,.4516228869609021496 ] 
dist 215=[-1.1295871783096414357 ,.57118960127674954013] 
dist 216=[-1.2000801503844895550 ,.69274779743854927401] 
dist 217=[-1.2814163812789633523 ,.7703705179494829894 ] 
dist 218=[-1.3281476251576353424 ,.8306515446002451250 ] 
dist 219=[-1.3584629019586294022 ,.8830016013213290651 ] 
dist 220=[-1.3742855276821793100 ,.9262296016170680101 ] 
dist 221=[-1.3823962274115191677 ,.96558581571250357537] 
dist 222=[-1.3819341745497895398 ,1.0436885369709167956 ] 
dist 223=[-1.3764505813275673948 ,1.1300003352326549271 ] 
dist 224=[-1.3716144457804736423 ,1.2079477720893569064 ] 
dist 225=[-1.0141296404643444474 ,1.2526696144377441824 ] 
dist 226=[-.97625764183045713726,1.2816014442129063690 ] 
dist 227=[-.87922425068146306625,1.2965334135210012554 ] 
dist 228=[-.86374660429301953644,1.3042086266558241647 ] 
dist 229=[-.70239299952665109589,1.3041796675572707571 ] 
dist 230=[-.67056285925058788109,1.2992043316757521354 ] 
dist 231=[-.63335195682060310335,1.2950866445830635062 ] 
dist 232=[-.62237203306597582974,.9699966366179796981 ] 
dist 233=[-.31243466015726669496,.9351652075688250522 ] 
dist 234=[-.423132077742616344  ,.9568112468268355335 ] 
dist 235=[-.53000710549802023314,.9841136779591969379 ] 
dist 236=[-.62618768093196955528,1.0031502835472064937 ] 
dist 237=[-.6942134996090248622 ,1.0154927365108824345 ] 
dist 238=[-.75461580653102690997,1.0179971598231320532 ] 
dist 239=[-.82037158759195941721,1.0133203293826272431 ] 
dist 240=[-.87995857849860681104,1.0123069443855756487 ] 
dist 241=[-.91574248109517460422,.27663658100466546352] 
dist 242=[-.9409267850071742617 ,.19836227242005793596] 
dist 243=[-.95821379501037286721,.17754577519671133371] 
dist 244=[-.96922549419753376975,.09905767062123434984] 
dist 245=[-.97132681827873586023,.08371599062236355131] 
dist 246=[-.96643870632603281069,.05363429702428045375] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 1, 2, 2, 1, 2] 
dist 0=[60.134992656379028302  ,60.134992656379028302  ] 
dist 1=[59.189778052672415604  ,60.894036166227308892  ] 
dist 2=[57.926159180747352951  ,61.488607035634166665  ] 
dist 3=[55.895490560784049164  ,61.777102492447077368  ] 
dist 4=[53.523137518024089263  ,61.896432823574241076  ] 
dist 5=[50.895029798350158644  ,61.856008401565088858  ] 
dist 6=[47.571500823902136501  ,61.612508879405593004  ] 
dist 7=[42.422135095503959392  ,61.495292628574301871  ] 
dist 8=[37.208975062191392938  ,60.898886571121306664  ] 
dist 9=[33.630589058634138388  ,60.804113156254336190  ] 
dist 10=[30.557840106277681253  ,58.718072433161780516  ] 
dist 11=[27.363505325611834956  ,58.233206650126976058  ] 
dist 12=[24.327409744568027168  ,57.706474243376353773  ] 
dist 13=[21.886273803661734158  ,57.444823922252883793  ] 
dist 14=[19.407509655955879067  ,50.996862108652638330  ] 
dist 15=[16.220643666561405113  ,49.807964720896687255  ] 
dist 16=[13.122910980010090212  ,43.402637064404641867  ] 
dist 17=[10.999800755768163992  ,33.234881068982315456  ] 
dist 18=[9.1773290807005339132 ,29.385001102002735228  ] 
dist 19=[7.2798046235107349787 ,24.679633152486016839  ] 
dist 20=[5.4696643625020225740 ,23.911400068694327434  ] 
dist 21=[3.9956056828780453139 ,20.295132122268703212  ] 
dist 22=[2.4774512545889848372 ,17.989513928620317048  ] 
dist 23=[.48994832054746230653,17.533129303669028317  ] 
dist 24=[-1.4259066361410450710 ,16.650975758424795741  ] 
dist 25=[-2.6579943844026561856 ,16.433154847646725370  ] 
dist 26=[-3.6336648448031615731 ,7.5923766103320062381 ] 
dist 27=[-5.3537459539615913206 ,6.0429726603550810491 ] 
dist 28=[-7.6257370491312427342 ,5.6969450303834029379 ] 
dist 29=[-9.8281049116999236746 ,3.0376686056527950445 ] 
dist 30=[-11.824866515035843821  ,2.6208997164375300274 ] 
dist 31=[-13.275741234710637717  ,1.1976120888518176148 ] 
dist 32=[-14.609221266123294925  ,-.76635992791644531256] 
dist 33=[-16.137321151774342198  ,-3.8224218896002694828 ] 
dist 34=[-17.536083116427752188  ,-3.3417105549563001910 ] 
dist 35=[-18.353082823857977923  ,-2.5974058700491490509 ] 
dist 36=[-18.903813350371873346  ,-1.7451296082966804378 ] 
dist 37=[-19.239161160451324995  ,-.83333299184869311815] 
dist 38=[-19.447984550020138788  ,.29369193027561115436] 
dist 39=[-19.493245509979252296  ,2.0048093864996386903 ] 
dist 40=[-19.451555431247169744  ,3.7146296380166764002 ] 
dist 41=[-19.392149103983534731  ,4.8366309747970787808 ] 
dist 42=[-11.795692498537831112  ,5.7403367436368941233 ] 
dist 43=[-11.517768867016430020  ,6.5795333909325159460 ] 
dist 44=[-11.428288306980880695  ,7.3109433840401181707 ] 
dist 45=[-11.145658550678827769  ,7.7847543718041856244 ] 
dist 46=[-11.044965262034922256  ,8.1597484868880054433 ] 
dist 47=[-10.929232535498410949  ,8.4970296483694545906 ] 
dist 48=[-10.867590857707736253  ,8.7756281541836929982 ] 
dist 49=[-3.2506662757864985528 ,8.9165010718427884042 ] 
dist 50=[-2.6579306692777368004 ,8.9831850352703608720 ] 
dist 51=[-2.5858143388249248877 ,8.9802445865457108106 ] 
dist 52=[-2.3044635782655451693 ,8.9041975925814505161 ] 
dist 53=[-2.2432826383480341577 ,8.7953656077500577672 ] 
dist 54=[-2.1123126630766131609 ,8.0949600912244700560 ] 
dist 55=[-2.0728156654519695676 ,7.4676958931766710826 ] 
dist 56=[-1.9000899813222716294 ,5.4119003777497471094 ] 
dist 57=[-1.8644245088624908906 ,6.3230638019009438492 ] 
dist 58=[-1.7612951624311708714 ,6.8877476774461230766 ] 
dist 59=[-1.7459043524945197039 ,7.3071164456951874350 ] 
dist 60=[-1.5324040739008578167 ,7.6382240371927745812 ] 
dist 61=[-1.4870166297305443364 ,7.8922414512980055161 ] 
dist 62=[-1.4457051315952826641 ,8.0038982108801363067 ] 
dist 63=[-1.4359783498497946479 ,8.0504674123207543588 ] 
dist 64=[-.88502588660843576087,8.0446362471715530530 ] 
dist 65=[-.81425385081333126996,1.6187454465133123805 ] 
dist 66=[-.67399562461691336556,1.3050866029014617776 ] 
dist 67=[-.63783196078117018687,.57035409531759929783] 
dist 68=[-.51116349740929600633,.45994452636925712187] 
dist 69=[-.6896320543200771074 ,-.00406781264382898365] 
dist 70=[-1.0045073542939569383 ,.19387376891293467503] 
dist 71=[-1.3118700692332723679 ,.47518942340014517178] 
dist 72=[-1.7006733552007683862 ,.75506198265419192551] 
dist 73=[-2.0848751970003483870 ,.94724686980908355652] 
dist 74=[-2.3255426249780764755 ,1.1117967467533601348 ] 
dist 75=[-2.5070505200236147092 ,1.2814128094734363439 ] 
dist 76=[-2.6551639858907854265 ,1.4411060703264993454 ] 
dist 77=[-2.7703974678469495514 ,1.5660707168743023727 ] 
dist 78=[-2.8206894944459576333 ,1.6894307137270749305 ] 
dist 79=[-2.8428946550512103585 ,1.8427340762202898779 ] 
dist 80=[-2.8460689555639302287 ,1.9883611211468778944 ] 
dist 81=[-2.6824586848373323053 ,2.0810968836798989600 ] 
dist 82=[-2.6637054491259616679 ,2.1528126753467761773 ] 
dist 83=[-2.5944669238686473913 ,2.2145700147699718170 ] 
dist 84=[-2.5792675606744301788 ,2.2652217592619011793 ] 
dist 85=[-2.3862608878491312244 ,2.2926313667863251034 ] 
dist 86=[-2.3412239471026575224 ,2.3083239456744508612 ] 
dist 87=[-2.2925961924088499677 ,2.3122400330275193361 ] 
dist 88=[-2.2688499935517078706 ,1.9084011331402280624 ] 
dist 89=[-1.8619850951962212792 ,2.0585757852103216686 ] 
dist 90=[-2.1267352643177914504 ,2.1456224571456157243 ] 
dist 91=[-2.3723536108076735602 ,2.2027358345122749869 ] 
dist 92=[-2.5865577478903427554 ,2.2335332392053019224 ] 
dist 93=[-2.7259535977820825266 ,2.2497374671068374764 ] 
dist 94=[-2.8370797279763416068 ,2.2486553122140931196 ] 
dist 95=[-2.9384717070605981286 ,2.2381994121861625827 ] 
dist 96=[-3.0222824732516064253 ,2.2282788508394600469 ] 
dist 97=[-3.0632563611823985201 ,1.7251935993856505782 ] 
dist 98=[-3.0806176955048776996 ,1.9456553041216366867 ] 
dist 99=[-3.0802077741591015115 ,2.1200636560946822381 ] 
dist 100=[-3.0473991268027173006 ,2.2772310664056282666 ] 
dist 101=[-3.0317326410955137885 ,2.4113323393209314344 ] 
dist 102=[-2.9822700386742457257 ,2.4936938086373975710 ] 
dist 103=[-2.9581928353922117042 ,2.5539965643738140015 ] 
dist 104=[-1.7488186176149536101 ,2.6000820387869886766 ] 
dist 105=[-1.6263059682326739443 ,2.6318478323073998243 ] 
dist 106=[-1.3344114433157306155 ,2.6369334061374385738 ] 
dist 107=[-1.2811776888515320264 ,2.6279830065854680157 ] 
dist 108=[-.86737730353040342652,2.6191199429048317462 ] 
dist 109=[-.78994167182621186927,2.5150545805882625316 ] 
dist 110=[-.66710822959624208592,2.4850981858982005627 ] 
dist 111=[-.63529926985118268644,2.4498986825464917099 ] 
dist 112=[-.06554899262785306196,2.4319233692625696838 ] 
dist 113=[.00785765077106506716,1.6510900189665244324 ] 
dist 114=[.17318274261742566986,1.5601074946211587635 ] 
dist 115=[.20271565873858573434,1.4735101925260476102 ] 
dist 116=[.31302656863233835057,1.5305149440890744291 ] 
dist 117=[.20463782999282549406,1.5570324245304052392 ] 
dist 118=[.11647189736640347838,1.5697039086155276877 ] 
dist 119=[.02628754177421399714,1.5714664529142510288 ] 
dist 120=[-.09017497518881694889,1.0333568599355655299 ] 
dist 121=[-.20303988586245158667,.99633554432718818502] 
dist 122=[-.27887791608099394816,.89972136234694521333] 
dist 123=[-.34212471335468362469,.88568422038069325807] 
dist 124=[-.4047544600763319414 ,.72067459308244379944] 
dist 125=[-.46226516274703300306,.68817083789458961256] 
dist 126=[-.50509720602002566172,.65449830993539368297] 
dist 127=[-.54546978714385809952,.64786409158738138643] 
dist 128=[-.5931937771646697795 ,.31668903161670112672] 
dist 129=[-.63735306907399659073,.27559860325668883585] 
dist 130=[-.66349972891434415596,.19190403353257020637] 
dist 131=[-.68207921190611957667,.17042366674742547231] 
dist 132=[-.69766482320845088477,.09448823226445738301] 
dist 133=[-.70856331831217852564,.07860188090919244682] 
dist 134=[-.7111885016680455106 ,.05786049879503175105] 
dist 135=[-.71097256645176510297,.05290848657575363223] 
dist 136=[-.7105153942376565933 ,-.44024114908036199324] 
dist 137=[-.67981813839987713351,-.48074074274237690979] 
dist 138=[-.67333078873762835454,-.4840604459786225551 ] 
dist 139=[-.69714249300611904838,-.43556098133462585247] 
dist 140=[-.76519500859817969967,-.3680238276655200673 ] 
dist 141=[-.81787920724689633394,-.29288647681550737621] 
dist 142=[-.8693991231600913661 ,-.21616769445644241518] 
dist 143=[-.93280512987612739281,-.12357001928922888784] 
dist 144=[-.99280030743402628068,.01495783677823032223] 
dist 145=[-1.0307068762401786729 ,.15305192256585871911] 
dist 146=[-1.0596948254761137408 ,.24392172614201395795] 
dist 147=[-1.0840935012597982176 ,.31764727995339851065] 
dist 148=[-1.1036772353033083929 ,.38731059357420580019] 
dist 149=[-1.1134476390070196950 ,.44908926801835967196] 
dist 150=[-1.1179025752712192413 ,.49134530175467413866] 
dist 151=[-1.1162712858888232507 ,.5274362546952414961 ] 
dist 152=[-.12056440422658333945,.67805050119269188157] 
dist 153=[-.02959097518624341266,.82903722584984277049] 
dist 154=[-.01690121003776801044,.94868724448084574689] 
dist 155=[.00992455009898839497,1.0591436295459431405 ] 
dist 156=[.01669750146580638885,1.1534134565147728040 ] 
dist 157=[.04387539644394704725,1.2112316364143853703 ] 
dist 158=[.04898226874129859152,1.2534028310638263978 ] 
dist 159=[.05927960215734639834,1.2852276870696218411 ] 
dist 160=[.06184956571968595119,1.3101276192383980343 ] 
dist 161=[.22129743136345635529,1.3246625147170995328 ] 
dist 162=[.16372969362146640118,1.3343860253676813737 ] 
dist 163=[.11333749189171680539,1.3400847447368387876 ] 
dist 164=[.05959253842670178513,1.3427628243398684448 ] 
dist 165=[.00782625352283267725,1.3404319012473226146 ] 
dist 166=[-.03467249936518473174,1.3339908085335055872 ] 
dist 167=[-.07851669051320259188,1.3294967363320327233 ] 
dist 168=[-.13565716532214817843,.56280068483355263392] 
dist 169=[-.19130463274531181519,.49762276309171618403] 
dist 170=[-.22919252778938849295,.34160792868833859889] 
dist 171=[-.26133446932025831805,.31796666984415838623] 
dist 172=[-.29405208627233262178,.10012552345170727881] 
dist 173=[-.3246578927209027551 ,.06096700957722806514] 
dist 174=[-.3483746073506875618 ,.00954420250179331209] 
dist 175=[-.44208145255193051555,-.00256050199840476943] 
dist 176=[-.540424167564847472  ,-.04149924879595133104] 
dist 177=[-.60276629208709604627,-.01339072820012691315] 
dist 178=[-.65065502145464605258,.00735940973404601211] 
dist 179=[-.69131621066816495726,.02665398135774319317] 
dist 180=[-.72420186691336816471,.04896110722453289056] 
dist 181=[-.74105952875307271986,.07146100854186282073] 
dist 182=[-.74991465062791661317,.09152876450090908555] 
dist 183=[-.75136294797744053749,.11364077158364437668] 
dist 184=[-.59131734465191709324,.14430278427131068134] 
dist 185=[-.57814329647114045534,.17500168082086867123] 
dist 186=[-.5452591724999238455 ,.19726359761285378379] 
dist 187=[-.53706971008634097341,.2176037398159522604 ] 
dist 188=[-.48170693392599267274,.24063732276653746494] 
dist 189=[-.46991470555881582188,.26364675404334190335] 
dist 190=[-.44890076303829248825,.28389419004939812131] 
dist 191=[-.44331545597324735378,.3071761907052846534 ] 
dist 192=[-.3611747497361337081 ,.35047094610683284781] 
dist 193=[-.3146038479013637579 ,.39249659374180677672] 
dist 194=[-.27988658790145124967,.41806397165136503176] 
dist 195=[-.27395854248155255669,.43648336853700790216] 
dist 196=[-.21939482905051256395,.44997858553234927237] 
dist 197=[-.20878795139765244895,.45993618053699798923] 
dist 198=[-.1947225556069573199 ,.46423457175224489887] 
dist 199=[-.19007261387325846519,.47247289146574552887] 
dist 200=[-.05894197835600052557,.50587547129624899033] 
dist 201=[-.04311193941227039075,.53581259511051530268] 
dist 202=[-.01570535717590247535,.57750436223500917551] 
dist 203=[-.00965021239836080606,.63213832700087883898] 
dist 204=[.00263670119421556492,.68188754922677053551] 
dist 205=[.00112413237990934812,.71563417109062880215] 
dist 206=[-.00673722310660707102,.74411191602180241679] 
dist 207=[-.02530848638612242274,.77283387369198309088] 
dist 208=[-.04728073168955298956,.79697214178309426869] 
dist 209=[-.12420403450768138021,.80715705936789164631] 
dist 210=[-.1816309431289569693 ,.8114481456466419454 ] 
dist 211=[-.22865524114638481677,.8120642086531168263 ] 
dist 212=[-.2737795984281421389 ,.78923775785111469055] 
dist 213=[-.31423058236437791946,.78286539786863257119] 
dist 214=[-.34260237922716954244,.77863176020026375332] 
dist 215=[-.36756127037373872378,.77621258534020434246] 
dist 216=[-.45779982588808538587,.30588004749226703959] 
dist 217=[-.51752925154936684507,.18809000568873315854] 
dist 218=[-.56398207057301378716,.1727307056203582313 ] 
dist 219=[-.60443056829873046886,.14076718440248983549] 
dist 220=[-.6379012548187309131 ,.13219833986308644977] 
dist 221=[-.66065981947302693561,.09969538373569596689] 
dist 222=[-.71102877517333008719,.09311526181382302172] 
dist 223=[-.765653676543213001  ,.07997871310373572124] 
dist 224=[-.81473797876333360606,.07652678839901607763] 
dist 225=[-.8429955265481128767 ,.07711026607729810756] 
dist 226=[-.86139819281846597842,.09607079749762729846] 
dist 227=[-.87115312556358055084,.11450868230307708343] 
dist 228=[-.87600826904555231459,.13703857828819979369] 
dist 229=[-.87533944306122892766,.16046030672782235417] 
dist 230=[-.87091937096287466048,.18245809527760396166] 
dist 231=[-.86704185223352844643,.20761695879312611648] 
dist 232=[-.61812682955218530463,.24365479592275786766] 
dist 233=[-.59482504209990162746,.28025150058170622414] 
dist 234=[-.53533799582696160482,.30764123196076540782] 
dist 235=[-.5257022177729951155 ,.34228961946411896477] 
dist 236=[-.42738344242628950003,.40442861582231940718] 
dist 237=[-.40799899601879596074,.44816551995719790259] 
dist 238=[-.38483297857322780805,.48677995728398061   ] 
dist 239=[-.37764733684624344024,.52847597359309034821] 
dist 240=[-.19095896326198224632,.56621756565283192493] 
dist 241=[-.16718224213890450793,.58905079931787322895] 
dist 242=[-.11674265468881316725,.6053253573098569001 ] 
dist 243=[-.10363577015884849931,.61689316054047219269] 
dist 244=[-.05183519359984391536,.62454343329116834082] 
dist 245=[-.04197670402438120059,.6260002133189849816 ] 
dist 246=[-.02176177269200124704,.62361819204069102309] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 2, 0, 0, 0, 1] 
dist 0=[57.568134718296276588  ,57.568134718296276588  ] 
dist 1=[57.281178642174780874  ,57.770605517418034032  ] 
dist 2=[56.859504126110702506  ,57.950170402192567013  ] 
dist 3=[56.119041669643752235  ,58.145479931218027474  ] 
dist 4=[54.915335072831754968  ,58.335593649878052568  ] 
dist 5=[53.065764624131943865  ,58.494240549920239660  ] 
dist 6=[50.771801376876678300  ,58.659533577079729500  ] 
dist 7=[47.943011436539195003  ,58.875857252676360834  ] 
dist 8=[43.318625983697603959  ,59.071050575296396633  ] 
dist 9=[38.606106695678885079  ,59.152015369800894052  ] 
dist 10=[34.178421981010578579  ,59.163907521691491732  ] 
dist 11=[30.500933639081142290  ,59.083757607810610435  ] 
dist 12=[27.331915626066985357  ,58.950201429750995097  ] 
dist 13=[24.019869936068497587  ,58.417827117477803512  ] 
dist 14=[20.861051571201631659  ,55.099255785246243550  ] 
dist 15=[18.303603833337573208  ,52.592008296858452234  ] 
dist 16=[15.690682778046370742  ,40.915231527089916672  ] 
dist 17=[12.309794324928600653  ,39.372487529407223966  ] 
dist 18=[9.0132447873883431900 ,35.652855611500968265  ] 
dist 19=[6.7368109785551930695 ,35.062838208200084585  ] 
dist 20=[4.7645319595026251068 ,29.658954089081228638  ] 
dist 21=[2.6822071254923371506 ,28.647588698085223915  ] 
dist 22=[.67816495375744995347,27.340616774985734176  ] 
dist 23=[-.98208104205622318404,26.958530512516839385  ] 
dist 24=[-2.7171129817015899988 ,18.600079984815548765  ] 
dist 25=[-5.0211524767390405631 ,17.542050313099756418  ] 
dist 26=[-7.2414020524708893916 ,15.285412177958650929  ] 
dist 27=[-8.6418897146229205130 ,14.740806745928834749  ] 
dist 28=[-9.7192942704179115254 ,12.367432341282847683  ] 
dist 29=[-10.648182087268060042  ,11.937713832886443580  ] 
dist 30=[-11.419236019904011157  ,11.000037114362790906  ] 
dist 31=[-11.865944476677852189  ,10.803492073666497239  ] 
dist 32=[-12.165428138312138709  ,.78977722576715248196] 
dist 33=[-12.348513368194180464  ,-.12946669183733287185] 
dist 34=[-12.456442669111870894  ,-2.0157617438029553499 ] 
dist 35=[-13.027944380992337674  ,-2.4672484941989710035 ] 
dist 36=[-14.716970724174885246  ,-4.1055599676207414773 ] 
dist 37=[-15.912542070044568261  ,-4.4186222671130681569 ] 
dist 38=[-16.979723599408911999  ,-4.7910000106837851333 ] 
dist 39=[-18.156179237494543962  ,-4.2762920572504153392 ] 
dist 40=[-19.209193823377424765  ,-2.5693231898050832768 ] 
dist 41=[-19.783442449148464740  ,.01746534204512116651] 
dist 42=[-20.119907744064747821  ,2.6062184169468993987 ] 
dist 43=[-20.223261828690941548  ,4.3211883328541436095 ] 
dist 44=[-20.233278472343062827  ,5.7228935611284868298 ] 
dist 45=[-20.196780160686603790  ,7.0618044159268583988 ] 
dist 46=[-20.119982210205755461  ,8.2567200985934912892 ] 
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dist 167=[-.22499517337112557301,.8094164080944574818 ] 
dist 168=[-.2565433172820505622 ,.80616623695266909326] 
dist 169=[-.2868529868585163023 ,.80344278162365036271] 
dist 170=[-.30570160663905739454,.33529664199667899087] 
dist 171=[-.32002205041464922448,.2957121944050601426 ] 
dist 172=[-.3317519134632616564 ,.20096192576847127363] 
dist 173=[-.34091938742625153255,.18665647069588704789] 
dist 174=[-.3450415791765672401 ,.05445648297382886376] 
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dist 181=[-.4101383217379136048 ,.155134470320721726  ] 
dist 182=[-.43024315815572764721,.17323165776982522029] 
dist 183=[-.44058944805900609193,.1968865473579244809 ] 
dist 184=[-.44608147430235834553,.23207368820141893472] 
dist 185=[-.44701168977443197439,.26652671273694210283] 
dist 186=[-.35880001211093402911,.28790815526397694002] 
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dist 192=[-.27798825985686482629,.37105790810382445587] 
dist 193=[-.27455306115898983355,.39383615772506281403] 
dist 194=[-.21083633300720567377,.40663693469937055939] 
dist 195=[-.2023686180265120669 ,.4145800445248883138 ] 
dist 196=[-.18127289544238618304,.41797076136539609748] 
dist 197=[-.17755902067033326969,.41926104341899285708] 
dist 198=[-.14420607802814624845,.4188207595274008468 ] 
dist 199=[-.13767420405540004683,.4170284064159279215 ] 
dist 200=[-.12878528704500105747,.41573970167015127758] 
dist 201=[-.12590630651996243699,.31519640378878898576] 
dist 202=[-.11527698708030031328,.30408980884169779761] 
dist 203=[-.15056743486715564382,.32025666842655800117] 
dist 204=[-.18456854687988757876,.3574323250631945389 ] 
dist 205=[-.21513365574365203369,.39248036277604255326] 
dist 206=[-.23671067744458293227,.42344402264412742987] 
dist 207=[-.25583395922140592583,.44434900124177319781] 
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dist 209=[-.29536433881913730614,.47938996369432530156] 
dist 210=[-.30645113816583327682,.49406386548167519321] 
dist 211=[-.31404072151426074466,.50028791620700920334] 
dist 212=[-.31884162840966571987,.50286188920802266677] 
dist 213=[-.32171335578762053201,.50296867442526667999] 
dist 214=[-.32203648179062231363,.48962289439357661266] 
dist 215=[-.32048797319674256157,.48553687671447713849] 
dist 216=[-.31934829765950146616,.48251912074290793494] 
dist 217=[-.22383334174699435304,.480171948537114896  ] 
dist 218=[-.2791207992209934263 ,.04498074872221022709] 
dist 219=[-.31448549676805940132,.05609617883437429806] 
dist 220=[-.34201193781836642295,.06993282544666961447] 
dist 221=[-.36601941262188510227,.08445024401822012125] 
dist 222=[-.38591366549908223922,.09828299962955963535] 
dist 223=[-.40151605473245204808,.11425743110348841524] 
dist 224=[-.43322205888932323299,.137322378355218499  ] 
dist 225=[-.46791681275759783983,.1608220252082428322 ] 
dist 226=[-.4991729395099607019 ,.17853160569477584017] 
dist 227=[-.51715614441999992077,.19538539253944842618] 
dist 228=[-.52885344597973696047,.21547024306529639094] 
dist 229=[-.53502365506346165614,.23608809450736692436] 
dist 230=[-.53816787658793179472,.25506945116799963639] 
dist 231=[-.53778912036753211536,.27648347148647815428] 
dist 232=[-.535541700573633878  ,.30681048003523162109] 
dist 233=[-.53344291899891876577,.33623589380768084883] 
dist 234=[-.38685325550943166977,.35405188238028554528] 
dist 235=[-.37137002769040337842,.366772082624276401  ] 
dist 236=[-.334357985534921008  ,.37586049770358495477] 
dist 237=[-.32839024481241311961,.38220502560837657376] 
dist 238=[-.26737345817673658037,.38397453358838132858] 
dist 239=[-.25533212076683723534,.38387892887180716916] 
dist 240=[-.24096706898441496922,.38277956917629269735] 
dist 241=[-.23650869541859408772,.35930015649155704519] 
dist 242=[-.12022244217413448822,.35462264338567980577] 
dist 243=[-.1054074423547552698 ,.36635897843993621923] 
dist 244=[-.07399709456121284749,.37636747081665865886] 
dist 245=[-.06580522288627017324,.38347801334230644898] 
dist 246=[-.03359846021233598770,.38817732037178148622] 
dist 247=[-.02745344993906418597,.38905184296890663822] 
dist 248=[-.01488200980062300980,.38757423939456773017] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 0, 0, 0, 2] 
dist 0=[47.234210483353633390  ,47.234210483353633390  ] 
dist 1=[46.268719433105925188  ,47.901471246549770269  ] 
dist 2=[44.641241001751806805  ,48.337826363165033368  ] 
dist 3=[42.940827277860180933  ,48.638110176438485960  ] 
dist 4=[41.683963138044472623  ,48.762025170171235267  ] 
dist 5=[40.508361287254781636  ,48.780647207933104600  ] 
dist 6=[39.132290530261014817  ,48.748176017243250516  ] 
dist 7=[37.728087316852405207  ,48.503514067623493966  ] 
dist 8=[36.439953238962970597  ,48.000886982610659982  ] 
dist 9=[34.986147682974569997  ,45.811212612467873405  ] 
dist 10=[32.919958478334858599  ,45.631701889043933205  ] 
dist 11=[30.815865469275918387  ,44.918678593852745271  ] 
dist 12=[29.210496740989033889  ,44.714421297853051491  ] 
dist 13=[27.657348196109392931  ,44.283727302910661360  ] 
dist 14=[25.761591594978998476  ,44.131616899242340129  ] 
dist 15=[23.781553931268842719  ,43.450122931395206109  ] 
dist 16=[21.891436994171697865  ,42.605186859358177216  ] 
dist 17=[19.697035487726457535  ,26.995493761494207731  ] 
dist 18=[16.500869006255140119  ,26.877255287117795116  ] 
dist 19=[13.322570752787941978  ,21.553091214922325432  ] 
dist 20=[11.199474569466404817  ,20.787275666586058712  ] 
dist 21=[9.4334309847532185851 ,19.834213210259971558  ] 
dist 22=[7.6818373381890927828 ,19.605905556353120792  ] 
dist 23=[6.0639783095291755590 ,14.489700017469654050  ] 
dist 24=[4.8322465218045667576 ,14.287081415756745770  ] 
dist 25=[3.6415367316314582386 ,12.745970507846578856  ] 
dist 26=[2.1874120041039528946 ,11.948115628858206113  ] 
dist 27=[.75381086835086835384,9.0429994087182059510 ] 
dist 28=[-1.1092679114057429609 ,8.7478674120690077154 ] 
dist 29=[-2.9356622859167812973 ,8.1814388764731291802 ] 
dist 30=[-4.5041229082993731688 ,8.0494956493671299575 ] 
dist 31=[-6.1927914488855746429 ,.98849867361199020446] 
dist 32=[-8.5005440113846784893 ,.36832727920448585644] 
dist 33=[-10.726625693556454715  ,-.92042760316281390883] 
dist 34=[-12.089207376902060826  ,-1.2044666698275703554 ] 
dist 35=[-13.089547544848159459  ,-1.9855795014322908003 ] 
dist 36=[-13.867905290740434368  ,-2.0453609751734274648 ] 
dist 37=[-14.476271385376136007  ,-2.0750962887237177575 ] 
dist 38=[-14.796988684273068646  ,-2.0236840052336814169 ] 
dist 39=[-14.971690159385622003  ,-1.9357815761589597718 ] 
dist 40=[-14.995776720860507269  ,-1.8064667813366370049 ] 
dist 41=[-14.095923165587655577  ,-1.6237590627135299613 ] 
dist 42=[-13.924904262891921175  ,-1.3225333996282357158 ] 
dist 43=[-13.691008217092099144  ,-1.0022614160463854932 ] 
dist 44=[-13.593074035294681921  ,-.74335419978659769018] 
dist 45=[-13.360341499306338267  ,-.05165256213415701569] 
dist 46=[-13.259456722007407159  ,1.2474279074412421840 ] 
dist 47=[-13.179919726589309632  ,2.5630040461472125254 ] 
dist 48=[-13.109876210196039560  ,3.4610423714128296372 ] 
dist 49=[-4.1915485641082187378 ,4.2241945894022690851 ] 
dist 50=[-4.1687557210623556530 ,5.0017057061085812413 ] 
dist 51=[-1.0415244053477132275 ,5.7282410121791955038 ] 
dist 52=[-.73442049399692480568,6.2880860636880097726 ] 
dist 53=[1.4812944297019924254 ,6.8328649141958241274 ] 
dist 54=[1.8624573756515037383 ,7.4994179972243020961 ] 
dist 55=[2.5203456396094681999 ,8.1283303570417695175 ] 
dist 56=[2.6583336012787733970 ,8.5229576342843343894 ] 
dist 57=[3.2198071793532427534 ,8.8217819066140499338 ] 
dist 58=[3.1496325151683070424 ,9.0684154837593995296 ] 
dist 59=[3.0448707698641170183 ,9.2632769666768386133 ] 
dist 60=[2.9139929106589226499 ,9.3555607903250168517 ] 
dist 61=[2.7392643328543066195 ,9.3910660761857781575 ] 
dist 62=[2.4594211201652067678 ,9.3774438536901860153 ] 
dist 63=[2.1337706182235199849 ,9.2979788417146529177 ] 
dist 64=[1.7761912809929067637 ,9.2139500828185740722 ] 
dist 65=[1.3269298908020412476 ,4.3255864009678514036 ] 
dist 66=[.63535052600860701299,4.3160765316651849071 ] 
dist 67=[-.06011933088219246197,2.6917761994440953042 ] 
dist 68=[-.52491989099026801404,2.5384682146599528564 ] 
dist 69=[-.90959596741522545328,2.2201018104915267897 ] 
dist 70=[-1.2852992695538800933 ,2.1775273535275336993 ] 
dist 71=[-1.6262993540793758418 ,1.5517770310012602654 ] 
dist 72=[-1.8724746861800206019 ,1.4631757185437455679 ] 
dist 73=[-2.0962228360283379232 ,1.2872315060984413214 ] 
dist 74=[-2.3477059921895051731 ,1.2458252063621962551 ] 
dist 75=[-2.5791135746344004530 ,1.0100254513874972903 ] 
dist 76=[-2.7227458505960987918 ,.97150265302981471773] 
dist 77=[-2.8295090540107342930 ,.88291967252819340761] 
dist 78=[-2.9137996295340114922 ,.86727214925864754682] 
dist 79=[-3.1426367969357741057 ,-.13593604396322908501] 
dist 80=[-3.4534922121474951748 ,-.12319645130372814036] 
dist 81=[-3.6875512556267327555 ,-.08430040697177141466] 
dist 82=[-3.8785362690248633913 ,0                     ] 
dist 83=[-4.0296285070361680264 ,-1.0955815198728639836 ] 
dist 84=[-4.1343559575260457716 ,-1.0172357544665986054 ] 
dist 85=[-4.2024458717439933586 ,-.91910650994565553043] 
dist 86=[-4.2292351222452669619 ,-.80275085491788641559] 
dist 87=[-4.2372966390316223044 ,-.65106748863061838745] 
dist 88=[-4.2306230671333025236 ,-.41190794429963187333] 
dist 89=[-4.2120017705992004073 ,-.16007854340756640996] 
dist 90=[-4.1989282930895065905 ,.04220582710069555781] 
dist 91=[-4.1223694021922070516 ,.24678032138298314315] 
dist 92=[-4.0990883864140349253 ,.50781737303426233701] 
dist 93=[-4.0106407516483833133 ,.78513122037543975013] 
dist 94=[-3.9929467106673390594 ,1.0547127605670680826 ] 
dist 95=[-2.5764593731552413563 ,1.3703343626934760650 ] 
dist 96=[-2.5574371268696765715 ,1.8314633048794942931 ] 
dist 97=[-1.8432185811047823248 ,2.2853535196804197684 ] 
dist 98=[-1.8233041950866277100 ,2.5720971648624190493 ] 
dist 99=[-1.1203501404152124993 ,2.7914685553810749303 ] 
dist 100=[-1.0339801139264441310 ,2.9764419017680885339 ] 
dist 101=[-.86330508221957993936,3.1318624248415412401 ] 
dist 102=[-.81969705359202735492,3.3304296624700013634 ] 
dist 103=[-.66900384869079237392,3.4939668605581456423 ] 
dist 104=[-.63451624389179511443,3.6525420193869692978 ] 
dist 105=[-.59722633811409693786,3.7891353656526529268 ] 
dist 106=[-.58969720129099527959,3.8649340712275217187 ] 
dist 107=[-.59496058380783288064,3.9107595838995891028 ] 
dist 108=[-.61958783549959883534,3.9277124083348644198 ] 
dist 109=[-.66309360011648258038,3.9263716177535950689 ] 
dist 110=[-.74370265990313607031,3.8991763971816361513 ] 
dist 111=[-.84194973112520196235,3.6591324826492565159 ] 
dist 112=[-.95584838212389777579,3.4461146497795350998 ] 
dist 113=[-1.1029881742527069705 ,2.3933177429424243903 ] 
dist 114=[-1.3338977766231356977 ,2.1018821345576634198 ] 
dist 115=[-1.5666665640331198574 ,1.1433069747237369289 ] 
dist 116=[-1.7212263704270859822 ,1.0799007346470826076 ] 
dist 117=[-1.8480391092415075930 ,.98512986914975062942] 
dist 118=[-1.9700722202147361743 ,.95840684306120494077] 
dist 119=[-2.0796311514967304499 ,.45316595080064173706] 
dist 120=[-2.1566598118432330530 ,.38870455171807058701] 
dist 121=[-2.2245751972250244937 ,.2386451555315336095 ] 
dist 122=[-2.2977613397329229421 ,.21436086860281787294] 
dist 123=[-2.3617544063998803302 ,.01911907004175840354] 
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dist 127=[-2.3811484919475225771 ,-.13047345341018483876] 
dist 128=[-2.3380486028128084165 ,-.10885471518809054529] 
dist 129=[-1.7945548979240383582 ,-.07982945749652051384] 
dist 130=[-1.8996483128131693267 ,-.03326417011714049   ] 
dist 131=[-2.0050409563449876297 ,.02087855978144498329] 
dist 132=[-2.0745462768214360850 ,.08015618471518392776] 
dist 133=[-2.1311352393789116710 ,.15447301620436618234] 
dist 134=[-2.1849786386698375200 ,.26864455617160245594] 
dist 135=[-2.2282015958631858704 ,.3878077605719811675 ] 
dist 136=[-2.2424000331853991535 ,.48205403030583753524] 
dist 137=[-2.2449624381253803295 ,.57605025115760251451] 
dist 138=[-2.2417225751319768841 ,.69423092509682521354] 
dist 139=[-2.1723348179333061739 ,.81888650013792355398] 
dist 140=[-2.1508397079099172352 ,.93873456451959982429] 
dist 141=[-2.1317476439145465632 ,1.0780189075501546667 ] 
dist 142=[-2.1181427242935226645 ,1.2802603016517846269 ] 
dist 143=[.10798223269308024405,1.5274013375227258224 ] 
dist 144=[.11180197516314519916,1.7354685262846438449 ] 
dist 145=[.14640798217840439207,1.8970603049689896686 ] 
dist 146=[.15042124972845372174,2.0374783918465389504 ] 
dist 147=[.14847201403858470844,2.1535470085796990188 ] 
dist 148=[.13794775080130692362,2.2179576935900252345 ] 
dist 149=[.12277829892980533396,2.3228149783344947430 ] 
dist 150=[.10228502175539455269,2.4500850459482833646 ] 
dist 151=[.07400196867631388857,2.5617808101664884422 ] 
dist 152=[.02774011412217750837,2.6266778813120409961 ] 
dist 153=[-.02165474232480442906,2.6697191036644611644 ] 
dist 154=[-.06244529884679109846,2.6941852772518093579 ] 
dist 155=[-.10472274799129069216,2.7048393732249279927 ] 
dist 156=[-.16005927963967167302,2.7039636653602505221 ] 
dist 157=[-.21954251691557176106,2.6764247835147114496 ] 
dist 158=[-.27837453776400066074,2.6701302273603851633 ] 
dist 159=[-.3479987687008831598 ,1.7834551211373318938 ] 
dist 160=[-.46286298610530008794,1.7202590305401439434 ] 
dist 161=[-.66946293839738608184,1.5564957224830932745 ] 
dist 162=[-.87228646211314431708,1.5314823425893444987 ] 
dist 163=[-1.0571073036200732960 ,1.2536572135323047003 ] 
dist 164=[-1.1918560742715855959 ,1.1986572676988586121 ] 
dist 165=[-1.3157013447037427692 ,1.1384547471615779722 ] 
dist 166=[-1.4570026126366770075 ,1.1233080809962197429 ] 
dist 167=[-1.5865079793490477028 ,.56871041698290498555] 
dist 168=[-1.6632760479239762757 ,.4988714877279698201 ] 
dist 169=[-1.7160909728631794965 ,.3548278672636153875 ] 
dist 170=[-1.7500037787476065782 ,.31721147337513424521] 
dist 171=[-1.7725141985934346875 ,.18000977871163766487] 
dist 172=[-1.7828069533613011190 ,.15205247981419477914] 
dist 173=[-1.7877090858491867881 ,.10519014195576874926] 
dist 174=[-1.7874216633926940723 ,.09421887485822662766] 
dist 175=[-.93373023658174182767,-.31377628463421782543] 
dist 176=[-.92815386251492979076,-.17033116488095359128] 
dist 177=[-.6195885856875705432 ,-.02595749558187338659] 
dist 178=[-.58853254615846999924,.07123713644833776854] 
dist 179=[-.51003050651059574006,.15246651817670110134] 
dist 180=[-.49858787699887914051,.23312236674570925924] 
dist 181=[-.37326241636230823968,.30721533041198349108] 
dist 182=[-.34926014186602736691,.36225184009868704752] 
dist 183=[-.32287334254487322188,.4138577617116209561 ] 
dist 184=[-.31767386561270493031,.47425859235263888843] 
dist 185=[-.16483822180810857753,.53024212729085128577] 
dist 186=[-.15999962187768005099,.56421883321668964878] 
dist 187=[-.14271455882800713856,.5885737159569112924 ] 
dist 188=[-.13866239574490450684,.60776706971656106172] 
dist 189=[-.13273967802528068757,.62721406155519235804] 
dist 190=[-.13087878926928157499,.63668070527936310756] 
dist 191=[-.12802862528469389525,.64081301637273058404] 
dist 192=[-.12877502893092760686,.64110733404727369738] 
dist 193=[-.13146773339155006537,.60364908852461677755] 
dist 194=[-.13749693122626787936,.63009016801240908462] 
dist 195=[-.14518894612028108034,.65969371751070427576] 
dist 196=[-.15451957428042266714,.67580933537385266258] 
dist 197=[-.16682573404304205794,.68513842064983236243] 
dist 198=[-.1863941608585418894 ,.68765772031472579887] 
dist 199=[-.20708317052847806923,.68705428778166852762] 
dist 200=[-.223862760134632782  ,.68486034176239792633] 
dist 201=[-.24098412722897511378,.67929360909161081549] 
dist 202=[-.26303959810753617332,.67609841860895593686] 
dist 203=[-.2865735080709611991 ,.6561517297280621616 ] 
dist 204=[-.30959696625569561262,.65068026194938415642] 
dist 205=[-.33665572678349382338,.63493277183568162736] 
dist 206=[-.37629694258277307353,.62940996228949613761] 
dist 207=[-.41528477804757076373,.24411153310903773467] 
dist 208=[-.43973642519875168918,.24024887789950908873] 
dist 209=[-.45822460639218544322,-.02654164982131014405] 
dist 210=[-.47341139396107417189,-.01952510910434542094] 
dist 211=[-.48531793397177078913,-.01275050594095743924] 
dist 212=[-.49071447167301624902,-.00455365490873347639] 
dist 213=[-.53441185252390078993,.00391354824867136276] 
dist 214=[-.59347338641548649393,.01176813460412677342] 
dist 215=[-.6477511982517065644 ,.02066859104619320835] 
dist 216=[-.67922549977649344717,.03331035547576227986] 
dist 217=[-.70001451248792778857,.04609015578146607670] 
dist 218=[-.71164712363400373707,.05554226578104243240] 
dist 219=[-.71924124874428217183,.06436016050432423302] 
dist 220=[-.72344582402174415359,.07461053362444718179] 
dist 221=[-.72419622438221054194,.08499232209335297154] 
dist 222=[-.71259345099620776892,.13538500824487167902] 
dist 223=[-.62651665487085958376,.25238382603789334777] 
dist 224=[-.59675832697916790375,.32915298098995930735] 
dist 225=[-.22833957855399861558,.39113387873831693843] 
dist 226=[-.21829281409731475184,.44911366100079640904] 
dist 227=[-.17771984952943444673,.50006344622995876433] 
dist 228=[-.16991560595687035672,.53398800452972437719] 
dist 229=[-.15064536623724310768,.56192849792686872894] 
dist 230=[-.14728741224825113305,.58899610933341038896] 
dist 231=[-.11770434793006089026,.61242666113716712693] 
dist 232=[-.11168791728431087435,.62585195375123668667] 
dist 233=[-.10653115757459284529,.6345150214280067165 ] 
dist 234=[-.10647257745447605963,.6389402074198695956 ] 
dist 235=[-.10883857090779165805,.64030120416157216912] 
dist 236=[-.1146800352597660576 ,.6355986528749464471 ] 
dist 237=[-.12417851610313084288,.58986206859788906535] 
dist 238=[-.14113813329072910717,.55163618076770114538] 
dist 239=[-.1583552578482661905 ,.20735003215015441428] 
dist 240=[-.16888158943253468333,.20654425167341712246] 
dist 241=[-.1765125510653266597 ,.17215374888267154827] 
dist 242=[-.18217619230581075551,.16754982722918713789] 
dist 243=[-.18634710429932335274,.15554221226913339318] 
dist 244=[-.18802155623938585306,.1533429585289254115 ] 
dist 245=[-.18847959014369198369,.13221036565951937744] 
dist 246=[-.18814013482447876466,.12786227973885638656] 
dist 247=[-.17581963814904882554,.12231504780123808922] 
dist 248=[-.17341227220616761846,.12028574804845240789] 
dist 249=[-.16855617382490961996,.07569504267760001417] 
dist 250=[-.16694298382381956317,.06979573791158338888] 
dist 251=[-.15940393031494032556,.05713619717926749733] 
dist 252=[-.1548591160695490023 ,.05369281976408161101] 
dist 253=[-.14215064989080307925,.03974921949267247570] 
dist 254=[-.14413974629332868624,.03709280401169524038] 
dist 255=[-.14498106933222748178,.03081706141915106183] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 1, 2, 0, 1] 
dist 0=[60.286432615067179720  ,60.286432615067179720  ] 
dist 1=[60.144282973503380287  ,60.324766028501035148  ] 
dist 2=[59.801052465374298900  ,60.286432615067179720  ] 
dist 3=[59.162891631300871727  ,60.145121014004080994  ] 
dist 4=[57.843162909085623133  ,60.034483367267261494  ] 
dist 5=[56.324715782510509042  ,59.900492542743147679  ] 
dist 6=[54.892873540513361478  ,59.768300344948452754  ] 
dist 7=[52.774074042625290263  ,55.337139217748488906  ] 
dist 8=[50.874990548964028290  ,54.643579753565077147  ] 
dist 9=[48.210461570964789461  ,53.567413095799539064  ] 
dist 10=[45.397620317803972904  ,53.259835253460027291  ] 
dist 11=[41.930589862523480648  ,52.859908073625296286  ] 
dist 12=[36.653316162893355690  ,52.683467143860971147  ] 
dist 13=[31.338568807000196949  ,52.330248875251680560  ] 
dist 14=[27.721777843427128283  ,51.345203988111159153  ] 
dist 15=[24.647424938195724618  ,35.578807567682151815  ] 
dist 16=[21.498816290418021604  ,34.494000901544111306  ] 
dist 17=[18.533366759494285825  ,32.349535656997354198  ] 
dist 18=[16.190271710159513573  ,31.793493109562666009  ] 
dist 19=[13.478842062758952410  ,29.817823827736238823  ] 
dist 20=[10.882034106227880455  ,29.369408283445715903  ] 
dist 21=[8.0192175549877811583 ,28.717521450714136620  ] 
dist 22=[5.6294264705276020939 ,28.518294290418231412  ] 
dist 23=[2.7699730138725971109 ,9.8621300245378043284 ] 
dist 24=[.88535161540242559902,8.3040724634072068587 ] 
dist 25=[-.65331757920475563034,4.8102306510684013023 ] 
dist 26=[-2.5591243867239535200 ,4.2041792129308563490 ] 
dist 27=[-5.1061673042529168038 ,2.8771143754865137870 ] 
dist 28=[-7.0020781088835652777 ,2.7705837692695406907 ] 
dist 29=[-8.7896075841377788202 ,.91027470675419144188] 
dist 30=[-10.903737601796099628  ,.44302235783201780687] 
dist 31=[-12.871357355138003782  ,-5.2490316876824980689 ] 
dist 32=[-14.073694818959473841  ,-5.6779237003641805637 ] 
dist 33=[-14.949122616631459827  ,-6.2220232374464486716 ] 
dist 34=[-15.611011302569578362  ,-6.2637069150685407812 ] 
dist 35=[-16.117767429489195372  ,-6.1146353684321358791 ] 
dist 36=[-16.373619372829013928  ,-5.6947744573416209028 ] 
dist 37=[-16.495748698367204119  ,-4.9995909692109481362 ] 
dist 38=[-16.499786706487112592  ,-3.7518030991292360784 ] 
dist 39=[-7.5363101615150658230 ,-2.4504042220011157519 ] 
dist 40=[-7.3662343979103028232 ,-1.5410564455843933382 ] 
dist 41=[-7.1123864050931353156 ,-.74759540554242123529] 
dist 42=[-7.0740858092060690059 ,.09199887799140981697] 
dist 43=[-7.0256071499444964773 ,.89472294935826945606] 
dist 44=[-6.9965184508379226564 ,1.5413705623380896443 ] 
dist 45=[-6.4598801283942088734 ,2.1966248678790332001 ] 
dist 46=[-6.4143071612211431303 ,3.0340031027987513638 ] 
dist 47=[-1.7519211392444058901 ,3.8409755702969978288 ] 
dist 48=[-1.6197101899889460868 ,4.3750602497558268770 ] 
dist 49=[-.5829687497213761300 ,4.8115837238159970528 ] 
dist 50=[-.4011427131266812079 ,5.2294222034378073053 ] 
dist 51=[-.1165764050250045118 ,5.6041172167132881053 ] 
dist 52=[-.0478566851544301072 ,5.8686501916986604137 ] 
dist 53=[1.0241184591843624048 ,6.1042250035097886812 ] 
dist 54=[1.1602437736934407727 ,6.3636976759938334862 ] 
dist 55=[1.4218651227744113260 ,6.5908000589649846664 ] 
dist 56=[1.4800872699549709241 ,6.6972186658640051741 ] 
dist 57=[1.6352607691249481495 ,6.7431611634837658997 ] 
dist 58=[1.6447145315468793766 ,6.7432917338620590137 ] 
dist 59=[1.6048303806573197801 ,6.6349687128577199173 ] 
dist 60=[1.4882798969838751352 ,6.5891750265672909582 ] 
dist 61=[1.3564057520895147333 ,6.3610686039326444067 ] 
dist 62=[1.2553400218157225250 ,5.8947948155840532228 ] 
dist 63=[1.1582059264156611960 ,4.0914370385100786666 ] 
dist 64=[.6922282700022939064 ,4.0807277055677176422 ] 
dist 65=[.23285684027812315597,4.0645027461757857201 ] 
dist 66=[-.22168637148626618253,4.0505903088406217035 ] 
dist 67=[-.63818760278027844336,4.0055497970174646953 ] 
dist 68=[-1.0801668951886688828 ,3.9858053619675839283 ] 
dist 69=[-1.7456629919650815818 ,3.9370187450109322851 ] 
dist 70=[-2.7214628490248110834 ,3.9157212765551406698 ] 
dist 71=[-3.6844091083853933793 ,.7381037241910798846 ] 
dist 72=[-4.2986339900072628419 ,.7288099207138908903 ] 
dist 73=[-4.7753204085368907032 ,.7138360511030772841 ] 
dist 74=[-5.1892821513943577940 ,.7163390128945654489 ] 
dist 75=[-5.5370430151883084776 ,.7272523272131479478 ] 
dist 76=[-5.7800898966634364594 ,.7519805154864315427 ] 
dist 77=[-5.9529834009588621578 ,.7779854409639527129 ] 
dist 78=[-6.0755942790491795302 ,.79397865226316467151] 
dist 79=[-6.1667044903331130462 ,.80525678732843340988] 
dist 80=[-6.2138640107890493051 ,.81250553393661938929] 
dist 81=[-6.2380161075834933201 ,.81627897563534430331] 
dist 82=[-6.2372749335752395618 ,.81638024495274056155] 
dist 83=[-6.2207589781132490582 ,.80982780661752762614] 
dist 84=[-6.1987428595357046648 ,.80818742463584015528] 
dist 85=[-6.1340287348913865333 ,.76091337760461978258] 
dist 86=[-6.0992669947273069295 ,.75101680674894889139] 
dist 87=[-2.8485050118700250283 ,.72718516711027540891] 
dist 88=[-2.5613322273591920794 ,.71827938643712622149] 
dist 89=[-1.8733755999728446651 ,.67242572951117997013] 
dist 90=[-1.7669203418506187584 ,.67181852815475864098] 
dist 91=[-1.6763267212556847831 ,1.1990313295817719627 ] 
dist 92=[-1.6665229616630998869 ,1.6047176511743375223 ] 
dist 93=[-.9213789900344546638 ,1.9872619003683978746 ] 
dist 94=[-.8843796024228713261 ,2.4382209068637610051 ] 
dist 95=[-.8059171503511183270 ,2.8603126100848706757 ] 
dist 96=[-.7839241207686210307 ,3.1276499195273701438 ] 
dist 97=[-.6949634515078226670 ,3.3328364197071892099 ] 
dist 98=[-.6773270317332558801 ,3.5068698685245241446 ] 
dist 99=[-.6334572984348380934 ,3.6475740775065001171 ] 
dist 100=[-.6247983526244334062 ,3.7197364672904578192 ] 
dist 101=[-.5539651217425453649 ,3.7555236883637113766 ] 
dist 102=[-.5392695446439583387 ,3.7613305065146461561 ] 
dist 103=[-.5207448063213643584 ,2.6940864075526073539 ] 
dist 104=[-.5139237888753835532 ,2.6076547692141214042 ] 
dist 105=[-.50960843694804720527,2.3912565020441656666 ] 
dist 106=[-.51276204891671910281,2.3496116806411192692 ] 
dist 107=[-.52134181632033249242,1.9995985523649407511 ] 
dist 108=[-.53948066669072247275,1.9294855868492458913 ] 
dist 109=[-.55937497612010406536,1.8271021716293606144 ] 
dist 110=[-.57496540191397137018,1.7956885773805095315 ] 
dist 111=[-.59034021247279685929,1.1499485500135737482 ] 
dist 112=[-.6093906875789257366 ,1.0648470111460412642 ] 
dist 113=[-.62932103666960730549,.8723646823621763186 ] 
dist 114=[-.64821760604021138661,.83096422375787188667] 
dist 115=[-.72613585268937469958,.58963604753913769192] 
dist 116=[-.9513726817926054171 ,.5455975152964355226 ] 
dist 117=[-1.2004953637579848039 ,.45669905846713812334] 
dist 118=[-1.5474062757662328500 ,.43370455220586228622] 
dist 119=[-1.8869727168850950237 ,.00021715965969280469] 
dist 120=[-2.1067882603106188882 ,-.03421898021124332282] 
dist 121=[-2.2810375886306832744 ,-.06854247960577516655] 
dist 122=[-2.4726946112520380350 ,-.06755608704208140569] 
dist 123=[-2.6636530282430929014 ,-.05121138451143868794] 
dist 124=[-2.7964081384683936758 ,-.01313732415660903031] 
dist 125=[-2.9119929863562458638 ,.04806219939718484072] 
dist 126=[-3.0344273833196970800 ,.15670364039350787988] 
dist 127=[-3.1405170151540033209 ,.27586759050065044438] 
dist 128=[-3.1908672169817710916 ,.37906869335191427457] 
dist 129=[-3.2143069849313604817 ,.49027030390357184528] 
dist 130=[-3.2145017437456510902 ,.64137966829679636207] 
dist 131=[-3.1632791847581477420 ,.80650864145559250378] 
dist 132=[-3.1410982522127424581 ,.97367126671005258207] 
dist 133=[-3.1193798083888124009 ,1.1743060733360746768 ] 
dist 134=[-3.1031308415056635166 ,1.4730329425213794769 ] 
dist 135=[-.05216478941655997367,1.8576357228386840490 ] 
dist 136=[-.0347411532844087949 ,2.1480943408880755577 ] 
dist 137=[.0012440173669606504 ,2.3758368779219025053 ] 
dist 138=[.0102368950451227363 ,2.5774708501666199731 ] 
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dist 140=[.0482776051558765850 ,2.8639791277445110436 ] 
dist 141=[.0558275271749182741 ,3.0425861814445778769 ] 
dist 142=[.0563688037482936248 ,3.2241943132193659415 ] 
dist 143=[.0544938920925875330 ,3.3845377465922464945 ] 
dist 144=[.0496796388513488191 ,3.4782787414875192222 ] 
dist 145=[.04184726634636559437,3.5411643729138206930 ] 
dist 146=[.02791605608540059987,3.5783648933042011269 ] 
dist 147=[.01118786169318977127,3.5961996492807593714 ] 
dist 148=[-.00781219877099521759,3.5962812769688053728 ] 
dist 149=[-.03208398217467988264,3.5610569293759866723 ] 
dist 150=[-.06985516355487311018,3.5535942585332876997 ] 
dist 151=[-.32743558483984951644,2.3542638471169979000 ] 
dist 152=[-.65838006288114922425,2.2663357887477926521 ] 
dist 153=[-.93177741026785769792,2.0402289636772141660 ] 
dist 154=[-1.1979886612620630211 ,2.0050082580624741703 ] 
dist 155=[-1.4390886522459402877 ,1.6270530001581752783 ] 
dist 156=[-1.6122682128177305490 ,1.5525497285776241640 ] 
dist 157=[-1.7687953421741939466 ,1.4680538934395981592 ] 
dist 158=[-1.9434339968939377891 ,1.4451312304986132483 ] 
dist 159=[-2.1027782702765055083 ,.71126790773329755436] 
dist 160=[-2.1982681083931351009 ,.61869403706245088917] 
dist 161=[-2.2652271231116099555 ,.42548675723156321135] 
dist 162=[-2.3107140225578959824 ,.37460842108312280953] 
dist 163=[-2.3407379250647240424 ,.18589984715027467441] 
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dist 165=[-2.3417165199984884501 ,.07984617514555122803] 
dist 166=[-2.3376683422258123530 ,.06416354572199297188] 
dist 167=[-.77716904994840016181,-.5071500408870387461 ] 
dist 168=[-.80179024779956724698,-.4741551054888712020 ] 
dist 169=[-.81688206996943265461,-.4353321664540331257 ] 
dist 170=[-.82291354189013350948,-.3784264905624626490 ] 
dist 171=[-.82485759043830488143,-.3142725320438117983 ] 
dist 172=[-.82363552756206302328,-.2465201869880786107 ] 
dist 173=[-.81985930131687121671,-.1631690652210950227 ] 
dist 174=[-.81720716590770106697,-.0367587797564589520 ] 
dist 175=[-.61505701498799487934,.0899417727213763769 ] 
dist 176=[-.59274125055095966136,.1744518935103136440 ] 
dist 177=[-.53490262861227488868,.24422370630825793176] 
dist 178=[-.52613614668283807933,.31210366374674271807] 
dist 179=[-.42805203546447640968,.3735547983104039105 ] 
dist 180=[-.40865680271335442102,.41766915618766369078] 
dist 181=[-.38759273685991432668,.45752401851682586176] 
dist 182=[-.38246485333411656407,.50197545927345393085] 
dist 183=[-.1867523328390287152 ,.54248680064699345428] 
dist 184=[-.1621716546646767929 ,.56661696529512043392] 
dist 185=[-.11154711645067537527,.5833645048000536299 ] 
dist 186=[-.09836026147900857532,.61791527547844905151] 
dist 187=[-.05047102890330189897,.65954743091299446446] 
dist 188=[-.04068632456217669493,.68640083887767125433] 
dist 189=[-.02819954676921353094,.70757402844856091714] 
dist 190=[-.04862843299192525341,.72653712191825811346] 
dist 191=[-.07193907308991645833,.74153895030949512445] 
dist 192=[-.09348207477282343042,.7469023373786381166 ] 
dist 193=[-.11784343113167400159,.74803975966770591575] 
dist 194=[-.15240388038085901198,.74617307551283607898] 
dist 195=[-.19085923050818990003,.72631683163580024986] 
dist 196=[-.23076590781862772993,.7196746097379344232 ] 
dist 197=[-.27936781978952787206,.71122605135985738399] 
dist 198=[-.352526365367112122  ,.70696068760140711893] 
dist 199=[-.42513847534465485756,.40059803472818271975] 
dist 200=[-.47156016990674323982,.38697954157285854781] 
dist 201=[-.50767489249105005019,.35468231795912126887] 
dist 202=[-.539153155906169241  ,.34699020592942645162] 
dist 203=[-.56523367773117160152,.29932860944345250927] 
dist 204=[-.57980692117254292592,.28971638288802336447] 
dist 205=[-.62163017518943002775,.27149041106683411303] 
dist 206=[-.67533771648269402756,.26660942267080472093] 
dist 207=[-.72398147109991506092,.07139340070175263712] 
dist 208=[-.75219868291261617441,.05046889951181588881] 
dist 209=[-.77084936720577688244,.01042421500570410375] 
dist 210=[-.78131333989496961428,.00092637266053405772] 
dist 211=[-.78723299688726281699,.00264760953452340248] 
dist 212=[-.78774760869902988914,.01026704881570353475] 
dist 213=[-.78519037566488522106,.01773786390790883100] 
dist 214=[-.78261868385985360984,.02694766080298751674] 
dist 215=[-.58433237370370533085,.1231660794641540402 ] 
dist 216=[-.56301430214705087093,.2069914614825472073 ] 
dist 217=[-.50884100862514454198,.2757306411327571249 ] 
dist 218=[-.49974936153199373646,.3418192514844252134 ] 
dist 219=[-.39882128563007600022,.4011160570714800362 ] 
dist 220=[-.3789591436647857226 ,.4427497652418606550 ] 
dist 221=[-.31489279890270576948,.47940243977783941156] 
dist 222=[-.21784312446709554133,.51882001337898573656] 
dist 223=[-.0348873322111467130 ,.55443700043385480823] 
dist 224=[-.0247079834941069390 ,.57592211231671160558] 
dist 225=[-.0077865557658362755 ,.59116009836873226877] 
dist 226=[-.0038781729185699215 ,.60184644560244040281] 
dist 227=[.0023198043121227810 ,.60878293054142786355] 
dist 228=[.0002956246889585345 ,.61005683737158219679] 
dist 229=[-.0061044747800389667 ,.60732255362481371375] 
dist 230=[-.0201378929718590471 ,.60624920409189517192] 
dist 231=[-.0349777858499983997 ,.0454779781996354248 ] 
dist 232=[-.04459642207690462967,.0457186763028880112 ] 
dist 233=[-.05222181954887953551,.0458591033043360735 ] 
dist 234=[-.05910853143011807815,.0458996728876597266 ] 
dist 235=[-.06498373149536402923,.0458718166799278815 ] 
dist 236=[-.06857308180591129177,.0457385787840600096 ] 
dist 237=[-.07117103741243650701,.0455005315552544264 ] 
dist 238=[-.07309039329501815546,.0453312676353636902 ] 
dist 239=[-.07459963438600339467,.0445576462682720208 ] 
dist 240=[-.07556112823045134570,.04422693237055511527] 
dist 241=[-.07630362063262928991,.04365247257265340729] 
dist 242=[-.07693891994356448360,.04342505935282368376] 
dist 243=[-.07745416175599018130,.04227221121504365378] 
dist 244=[-.07771745765496248301,.04193584590602850147] 
dist 245=[-.07784474136044667283,.04086554858451222870] 
dist 246=[-.07785060729837729243,.04055327324798206888] 
dist 247=[-.07898836379918303280,.03773678705278358028] 
dist 248=[-.07932463425047287221,.03713781959211238302] 
dist 249=[-.07924365162655814145,.03564860971697030893] 
dist 250=[-.07901798691236232235,.03514045769868574919] 
dist 251=[-.07702752205802680889,.03245195989322950712] 
dist 252=[-.07638997262139739574,.03182571235363268540] 
dist 253=[-.07487584395503140877,.03055472866539247577] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 0, 0, 2] 
dist 0=[48.528024157527889421  ,48.528024157527889421  ] 
dist 1=[47.388599363537426199  ,49.447789088951868441  ] 
dist 2=[46.039589330242543257  ,49.919454502899490658  ] 
dist 3=[44.275744357168691359  ,50.169424568782560531  ] 
dist 4=[41.479522635824824433  ,50.210443600371896077  ] 
dist 5=[38.620557596634207820  ,50.004278024120075728  ] 
dist 6=[36.606042209456820665  ,49.886133358373269795  ] 
dist 7=[34.819643952899057002  ,49.725922849846401657  ] 
dist 8=[32.871502483419235979  ,49.631271186672171871  ] 
dist 9=[30.962298267078679117  ,49.223302068995879750  ] 
dist 10=[29.331209731437476775  ,49.084106032974904659  ] 
dist 11=[27.586622393887711199  ,48.666174655421627740  ] 
dist 12=[25.223765166748557399  ,48.497893371579127333  ] 
dist 13=[22.868065417759711845  ,47.473328291642296602  ] 
dist 14=[21.151858436215886971  ,47.189621303170717777  ] 
dist 15=[19.569376783189387636  ,45.983255936631949099  ] 
dist 16=[17.747496845712284769  ,43.774204818257335278  ] 
dist 17=[15.901969312681911337  ,28.291240644701153133  ] 
dist 18=[14.224634430064706414  ,27.318788302496491788  ] 
dist 19=[12.341319505007154116  ,26.351935700390089196  ] 
dist 20=[9.6721762960133404468 ,26.054577127105535270  ] 
dist 21=[7.0422926647203618884 ,19.775415967161469090  ] 
dist 22=[5.3157121268956825087 ,18.969295468455083140  ] 
dist 23=[3.9113729363811274927 ,17.264426682156064666  ] 
dist 24=[2.5692493621171612611 ,16.822864731915162861  ] 
dist 25=[1.3610195579489104729 ,15.049827378182741885  ] 
dist 26=[.49166079211888962272,14.715680566102601362  ] 
dist 27=[-.30122742155042491038,13.982439931940674848  ] 
dist 28=[-1.2041343433787358375 ,13.812693429337103921  ] 
dist 29=[-2.0350759804016905986 ,4.9108893451477257001 ] 
dist 30=[-3.6907902102523288150 ,4.1005747866194117075 ] 
dist 31=[-5.4225964485903649619 ,2.6124155414851449868 ] 
dist 32=[-7.0653520516703690638 ,1.9792589233782979193 ] 
dist 33=[-8.5328371660858722012 ,-.04309440036424038494] 
dist 34=[-9.7693808875937562835 ,-.38765043952659212382] 
dist 35=[-10.858107845161107715  ,-1.0657727362038568011 ] 
dist 36=[-11.758790496937498884  ,-1.2258707715075835083 ] 
dist 37=[-12.482637985079916463  ,-.92034205667349021279] 
dist 38=[-12.912135479702067232  ,-.62013883904524567413] 
dist 39=[-13.274250320286041348  ,-.36015080897216477537] 
dist 40=[-13.504325585262870266  ,-.09131806765681567095] 
dist 41=[-13.653299273573731263  ,.15932144461858831216] 
dist 42=[-13.691343131117437792  ,.34706115778394102062] 
dist 43=[-13.673066956990761889  ,.52305386492690094703] 
dist 44=[-13.637276538775368821  ,.72707229623262823817] 
dist 45=[-12.649728214246600294  ,.91298041889468420236] 
dist 46=[-12.586065591366279091  ,1.0168385658328601883 ] 
dist 47=[-12.520135076538735830  ,1.0796434351154676930 ] 
dist 48=[-12.466035602762334176  ,1.1018779014876328205 ] 
dist 49=[-4.8296217651685380174 ,1.1079846892165041442 ] 
dist 50=[-4.1936945976600576064 ,1.1065839864905322438 ] 
dist 51=[-2.7156088573048606572 ,1.0993761829634917006 ] 
dist 52=[-2.4745373526121278062 ,1.5659340630891998393 ] 
dist 53=[-.55554155744195677098,2.3638841848347022390 ] 
dist 54=[-.21941406936168549818,2.8688571040058698935 ] 
dist 55=[.29792318278550646539,3.2565668401056388263 ] 
dist 56=[.42502853911649207494,3.8168978033433053556 ] 
dist 57=[1.3896885891386224153 ,4.7368096446533589477 ] 
dist 58=[1.4183336773902191497 ,5.3076625708217337997 ] 
dist 59=[1.4640603123719020581 ,5.7324079157773884303 ] 
dist 60=[1.4665116764533349038 ,6.0691202829384797283 ] 
dist 61=[1.4543597055409096082 ,6.3342427585079473412 ] 
dist 62=[1.4220750966027036385 ,6.4732417658612540978 ] 
dist 63=[1.3689418714888358518 ,6.5466402885152149064 ] 
dist 64=[1.2735618953131024213 ,6.5555065792263699474 ] 
dist 65=[1.1584032047401706618 ,3.9458816152779121551 ] 
dist 66=[1.0263231651159271210 ,3.9201160709297381452 ] 
dist 67=[.85659443329275532263,3.8433681468204872042 ] 
dist 68=[.59117175311111321372,3.8139723455416159283 ] 
dist 69=[.32243274124367813162,3.6289820255289830205 ] 
dist 70=[.13946620294708392367,3.5847922304275535845 ] 
dist 71=[-.01566327966118739252,3.4958586495049247792 ] 
dist 72=[-.48338281964148786293,3.4675831534487741751 ] 
dist 73=[-1.0453779771288963814 ,3.3416031017174915394 ] 
dist 74=[-1.5823847733411120148 ,3.3111456314253103966 ] 
dist 75=[-2.2041550399621919985 ,3.2278033462562259804 ] 
dist 76=[-3.1045841166412451166 ,3.2038711839676730240 ] 
dist 77=[-3.9897682649575247307 ,1.5979215536422590825 ] 
dist 78=[-4.5507132921074607494 ,1.5891478947278023232 ] 
dist 79=[-4.9819309700295996071 ,1.5933814129175030409 ] 
dist 80=[-5.3492818007214158697 ,1.6154075213480486685 ] 
dist 81=[-5.6491195266023958833 ,1.6397131775009064562 ] 
dist 82=[-5.8775193578170163717 ,1.6530250327978273417 ] 
dist 83=[-6.0380184167745989536 ,1.6599695294337766517 ] 
dist 84=[-6.1480577530660510496 ,1.6590042919364620080 ] 
dist 85=[-6.2272937504021823522 ,1.6521195737321592043 ] 
dist 86=[-6.2648386512343845049 ,1.6468995107114126162 ] 
dist 87=[-6.2791681549243777692 ,1.6189927312422720234 ] 
dist 88=[-6.2657275299310391505 ,1.6128325073589779373 ] 
dist 89=[-6.2356159176562500513 ,1.5020892714150110293 ] 
dist 90=[-6.2111970611011003658 ,1.4800529181178095554 ] 
dist 91=[-6.1278330220161813405 ,1.4140539674892313603 ] 
dist 92=[-6.0852367443823793469 ,1.4004314089407200923 ] 
dist 93=[-2.9855155720198877501 ,1.2493475184433111197 ] 
dist 94=[-2.9683544289329504120 ,1.2149470224330449673 ] 
dist 95=[-2.9514535857521931835 ,1.1764154802817431145 ] 
dist 96=[-2.9374737471250705054 ,1.1586672068201228222 ] 
dist 97=[-.99119512922976515679,1.4347166711329065128 ] 
dist 98=[-.8298893198516368329 ,1.8370734716487614388 ] 
dist 99=[-.71987655974633366925,2.2123892390205713875 ] 
dist 100=[-.79132963957126687127,2.6489849290827844710 ] 
dist 101=[-.8631250424595118844 ,3.0564411401595543038 ] 
dist 102=[-.91081515828877261541,3.3154590707858309249 ] 
dist 103=[-.94998085938840970274,3.5153977109962627692 ] 
dist 104=[-.98776490127455845541,3.6870429058417307139 ] 
dist 105=[-1.0218041439311216399 ,3.8274029824851770402 ] 
dist 106=[-1.0460331591292312616 ,3.9024691361344770516 ] 
dist 107=[-1.0677642824386607509 ,3.9440969204773574306 ] 
dist 108=[-1.0918508774718172206 ,3.9509901696330263490 ] 
dist 109=[-1.1134908911825578093 ,2.8294143507399170951 ] 
dist 110=[-1.1254638600462476806 ,2.7346450508818393331 ] 
dist 111=[-1.1327355209118261155 ,2.4966614858576613600 ] 
dist 112=[-1.1356143478034747934 ,2.4527936100040746721 ] 
dist 113=[-1.1355932295346966713 ,2.0675002247595009568 ] 
dist 114=[-1.1317401149371996630 ,1.9907884582694423877 ] 
dist 115=[-1.1237511752367183230 ,1.8837383937768735368 ] 
dist 116=[-1.1190488675157101964 ,1.8494174202910927846 ] 
dist 117=[.05096095589291515334,1.5068793353480261910 ] 
dist 118=[-.18081531472937245147,1.4964741856178574949 ] 
dist 119=[-.39333464428374823644,1.4584859760192081732 ] 
dist 120=[-.635096699337015388  ,1.4519706097888824607 ] 
dist 121=[-.87715209280110365906,1.3340999589107493007 ] 
dist 122=[-1.0908579027094451007 ,1.3125535062183606418 ] 
dist 123=[-1.3247660475394446452 ,1.2565658169885323764 ] 
dist 124=[-1.6474763763954733279 ,1.2428084365030346873 ] 
dist 125=[-1.9623626211289045810 ,1.1409513966867280558 ] 
dist 126=[-2.1650488278503887166 ,1.1188356909115702830 ] 
dist 127=[-2.3244317389417696284 ,1.0824406764287041665 ] 
dist 128=[-2.5191859539719688345 ,1.0718705885424152026 ] 
dist 129=[-2.7166130940203667677 ,-.02686053590192521271] 
dist 130=[-2.8556839851530388500 ,.02219691207270693293] 
dist 131=[-2.9786821362628779930 ,.09365976764118013843] 
dist 132=[-3.1119649930890870209 ,.21426561015675753367] 
dist 133=[-3.2291724360628213554 ,.3444225015199741414 ] 
dist 134=[-3.2880107022544430901 ,.45401059589511713566] 
dist 135=[-3.3165331104021239579 ,.56945228662454271991] 
dist 136=[-3.3203534616199746592 ,.72298690066696157787] 
dist 137=[-3.2866123170128352710 ,.88919829649351459589] 
dist 138=[-3.2681775192645532947 ,1.0552426987186520084 ] 
dist 139=[-3.2395330034419025795 ,1.2529426154090248942 ] 
dist 140=[-3.2251552492043578847 ,1.5455036965879283506 ] 
dist 141=[-2.3799124748085794564 ,1.9395371996905829797 ] 
dist 142=[-2.3705460960916790269 ,2.2600432492719632182 ] 
dist 143=[-2.3336385897241180544 ,2.5118238602668530870 ] 
dist 144=[-2.3205676614692634674 ,2.7355836655672973565 ] 
dist 145=[-1.4135340852230304506 ,2.9241651455526327140 ] 
dist 146=[-1.3244518423084510506 ,3.0491377913756462954 ] 
dist 147=[-1.1062963799238298880 ,3.2257276712152017527 ] 
dist 148=[-1.0719366871022597802 ,3.4002924710364168066 ] 
dist 149=[-.74570529407764902564,3.5531589922888626868 ] 
dist 150=[-.68440422375503535552,3.6431517847363790495 ] 
dist 151=[-.6064450998473007374 ,3.7043052127984102474 ] 
dist 152=[-.58451165571081867093,3.7420740023899492824 ] 
dist 153=[-.07173165385168839784,3.7619127330741451235 ] 
dist 154=[-.00821922527830394831,3.7609053629639628815 ] 
dist 155=[.13026540515650887477,3.7322050944309277050 ] 
dist 156=[.15900305570185060021,3.7165316765087790747 ] 
dist 157=[-.31842941521826285174,2.3914533483284194745 ] 
dist 158=[-.65165563029758019292,2.3040684191269200959 ] 
dist 159=[-.92732285385916111397,2.0784531542303391201 ] 
dist 160=[-1.1963934685333699827 ,2.0436748497635904590 ] 
dist 161=[-1.4405227891112565896 ,1.6636874773671476190 ] 
dist 162=[-1.6166496046817925672 ,1.5886382975004862568 ] 
dist 163=[-1.7766333543247774052 ,1.5050543971162616995 ] 
dist 164=[-1.9563335185750207210 ,1.4832620305236391636 ] 
dist 165=[-2.1205019264719942529 ,.98917380276417128863] 
dist 166=[-2.2185005680533665060 ,.95219256333004941061] 
dist 167=[-2.2867553012537526104 ,.91553397646989745472] 
dist 168=[-2.3322242719861388027 ,.90809663898064332774] 
dist 169=[-2.3622244970323884013 ,.50829524749029804027] 
dist 170=[-2.3687442482124258114 ,.45807541807365290536] 
dist 171=[-2.3769065061607469468 ,.35708954514334509614] 
dist 172=[-2.3757214185814069438 ,.33118065594458421433] 
dist 173=[-.71932243477047800897,.24024830979392582625] 
dist 174=[-.70726482602289811908,.2204697733624800759 ] 
dist 175=[-.68892748750173269246,.19608204607637535424] 
dist 176=[-.68268494028937200002,.19009728860730953137] 
dist 177=[-.70781926758174340089,-.06144549863216897098] 
dist 178=[-.74869158710472899349,-.04366877822696482683] 
dist 179=[-.77898305674816921889,-.02422881966472746669] 
dist 180=[-.85550531239035921934,.00250418429946926516] 
dist 181=[-.95068234458242436251,.03182821828978730980] 
dist 182=[-1.0244476895568857343 ,.06161291031613611619] 
dist 183=[-1.0966570943293357734 ,.10823131262548974618] 
dist 184=[-1.1856242925817265211 ,.24211750803982116322] 
dist 185=[-1.2698458321120315051 ,.38320528107224094642] 
dist 186=[-1.3231143657476365794 ,.51864649957279415765] 
dist 187=[-1.3639103150372233312 ,.67587423544030460874] 
dist 188=[-1.3983510491002312043 ,.90391445667650947644] 
dist 189=[-1.4260701452658599908 ,1.1280967942253025958 ] 
dist 190=[-1.4400386327518746992 ,1.2699282739473887255 ] 
dist 191=[-1.4466097208025468585 ,1.3785756564550810541 ] 
dist 192=[-1.4448227089260470734 ,1.4703194561191098667 ] 
dist 193=[-.7712613670113226696 ,1.5443874819610346692 ] 
dist 194=[-.77915281158261627129,1.5824895413002223931 ] 
dist 195=[-.78659317217655465757,1.6031154440223617166 ] 
dist 196=[-.7953489276677560781 ,1.6074352046453720381 ] 
dist 197=[-.80341224154673065249,1.5823561592870846729 ] 
dist 198=[-.80808985349062473457,1.5728860190885284648 ] 
dist 199=[-.81117624241692822159,1.5631813659824922894 ] 
dist 200=[-.81289085320628517958,1.5553473598600809892 ] 
dist 201=[-.81358842553660127359,1.5530568632072559391 ] 
dist 202=[-.81261693265499102816,1.5738721665374570663 ] 
dist 203=[-.8102368038192599195 ,1.5893129969911461879 ] 
dist 204=[-.80708041766111829352,1.6014528621800509220 ] 
dist 205=[-.79990994024969876621,1.6105407330341373555 ] 
dist 206=[-.79561012408199365104,1.6138015267256413540 ] 
dist 207=[-.79129983042079058259,1.6134202576761664953 ] 
dist 208=[-.78728676896715238078,1.6080875927440394933 ] 
dist 209=[-.78010245249760627168,.80422990312769574417] 
dist 210=[-.7753140153185126582 ,.77822003480625811784] 
dist 211=[-.76814743669294893486,.70936963535550340894] 
dist 212=[-.76452638848278728399,.6994364888833450248 ] 
dist 213=[-.74934576435968863062,.57819859664680155719] 
dist 214=[-.74310926427896200524,.55399633767917978782] 
dist 215=[-.73543146155804273662,.52983161498918242443] 
dist 216=[-.73125446218033770273,.5251906543384415588 ] 
dist 217=[-.71916504274828573908,.26866294807935226885] 
dist 218=[-.71693360591532123117,.23663033419080021973] 
dist 219=[-.75038731698370968719,.17209019988559263777] 
dist 220=[-.77495632168192052202,.15557371885881847926] 
dist 221=[-.79322684879054939499,.09774990442900113106] 
dist 222=[-.80154224730024827883,.08527123422930014816] 
dist 223=[-.80424097338651657383,.07021362263985284153] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 2, 2, 0, 2] 
dist 0=[47.420255742870699563  ,47.420255742870699563  ] 
dist 1=[46.575935254924287162  ,47.954677951924909502  ] 
dist 2=[45.084895935562968213  ,48.208075310801370595  ] 
dist 3=[43.506901434866939487  ,48.352278594877872029  ] 
dist 4=[42.315281762422120972  ,48.450536617430687391  ] 
dist 5=[41.175298868911043591  ,48.560463245121238846  ] 
dist 6=[39.803446677807829028  ,48.652477502921729213  ] 
dist 7=[38.382708408185412691  ,48.677966916228478099  ] 
dist 8=[37.047377273755852220  ,48.394153363190644320  ] 
dist 9=[35.514729824198517734  ,46.156996378240478660  ] 
dist 10=[33.305711003746661180  ,45.764394125565051455  ] 
dist 11=[31.043442834122487437  ,45.082731599569646766  ] 
dist 12=[29.297996264343680692  ,44.893390628407921247  ] 
dist 13=[27.591107881161482148  ,44.236392042292059362  ] 
dist 14=[25.482675273988613905  ,44.027343367026251318  ] 
dist 15=[23.268293839890046027  ,43.741058773195965889  ] 
dist 16=[21.137972713513040906  ,43.363077147031418141  ] 
dist 17=[18.653057342863586338  ,28.656857195962395342  ] 
dist 18=[15.021771832139926752  ,27.928607492140922341  ] 
dist 19=[11.413865174151297496  ,24.353233110843419226  ] 
dist 20=[9.0222502971273679067 ,23.911852652149243377  ] 
dist 21=[7.0542933381785480174 ,19.618636617625448800  ] 
dist 22=[5.1389091974642103038 ,18.835952732844496447  ] 
dist 23=[3.3942884395367224548 ,17.900204136428525332  ] 
dist 24=[2.1084198465192755623 ,17.722836007719896346  ] 
dist 25=[.90636483014365061773,13.774073845108950824  ] 
dist 26=[-.50375215758019066903,12.425988368436091864  ] 
dist 27=[-2.1994104288105602974 ,9.0684653886653851563 ] 
dist 28=[-4.0121786240074232462 ,8.6723285822745572179 ] 
dist 29=[-6.0030775097407056340 ,7.2290551115074239136 ] 
dist 30=[-8.7713878011559491473 ,6.9500283486408458208 ] 
dist 31=[-11.457578797666682923  ,6.5243068145987711765 ] 
dist 32=[-13.120603010330810924  ,6.4223036482492103832 ] 
dist 33=[-14.362146830729109203  ,-.57692992321141830667] 
dist 34=[-15.364159513655620969  ,-1.1583848724019962186 ] 
dist 35=[-16.161991655905613055  ,-2.3908329226243104474 ] 
dist 36=[-16.587423232745093710  ,-2.6316117307086346782 ] 
dist 37=[-16.824840105059173916  ,-3.0473887182547864976 ] 
dist 38=[-16.870684599359805983  ,-2.7014522111109470424 ] 
dist 39=[-16.208242847969505646  ,-2.3210570043659491568 ] 
dist 40=[-16.058542218451146443  ,-1.9367296000966673258 ] 
dist 41=[-15.907000830414639988  ,-1.4775538071798208925 ] 
dist 42=[-15.810814657545449710  ,-.79832001204755334999] 
dist 43=[-15.657647438966860630  ,-.1020030727373842452 ] 
dist 44=[-15.581771812283962118  ,.42546100623531832484] 
dist 45=[-15.522327910770095804  ,.92910505497322389921] 
dist 46=[-15.470569695097390830  ,1.5305658590954442418 ] 
dist 47=[-9.1507873028029764683 ,2.1477214617998664516 ] 
dist 48=[-9.1379127730960048399 ,2.7140759958111128623 ] 
dist 49=[-2.3467157231905933099 ,3.3509920898806589058 ] 
dist 50=[-2.3202280968613187986 ,4.2497672095348126667 ] 
dist 51=[.8666709470014266242 ,5.1412021626993527435 ] 
dist 52=[1.0054631337662304162 ,5.7488648553359579540 ] 
dist 53=[1.8972639050660121885 ,6.2644809503395793246 ] 
dist 54=[2.0401341303132975970 ,6.7886737323844383508 ] 
dist 55=[2.3139084510906858207 ,7.2778070696629053206 ] 
dist 56=[2.3708995509366490658 ,7.7885289399506952734 ] 
dist 57=[2.7055647567053206651 ,8.4001027690842588244 ] 
dist 58=[2.7253893847097288818 ,8.9131899919213430555 ] 
dist 59=[2.6668236651607353183 ,9.3240943037922706098 ] 
dist 60=[2.4868346994339707035 ,9.5278190862929685115 ] 
dist 61=[2.2435235925349363053 ,9.6315053119494868169 ] 
dist 62=[1.9322633636729376598 ,9.6430233015824342687 ] 
dist 63=[1.5123923169218670999 ,4.6653665381103078111 ] 
dist 64=[.83572223818091631583,4.6677917887306345155 ] 
dist 65=[.1477191436407561216 ,3.4279244547257998280 ] 
dist 66=[-.317398429718010426  ,3.4001964809528933371 ] 
dist 67=[-.7074770627309673266 ,3.1001181447056675148 ] 
dist 68=[-1.0961546483969525742 ,3.0562555646186783590 ] 
dist 69=[-1.4533860893682548926 ,2.6561810245713156851 ] 
dist 70=[-1.7180303297985478172 ,2.5751039859785353627 ] 
dist 71=[-1.9651224559988438479 ,2.4646119490271163109 ] 
dist 72=[-2.2523480215075671907 ,2.4275797032498280447 ] 
dist 73=[-2.5176923803747511851 ,1.6419940064604913846 ] 
dist 74=[-2.6774822770540071064 ,1.5385282912911071565 ] 
dist 75=[-2.7902915811846605198 ,1.3109521052411069591 ] 
dist 76=[-2.8681684367826626052 ,1.2556590221816967874 ] 
dist 77=[-2.9229432890801227962 ,.9888808949896028344 ] 
dist 78=[-2.9435924630802215795 ,.94040205110855406615] 
dist 79=[-2.9453763501270807826 ,.82717552505952476398] 
dist 80=[-2.9394092321557231438 ,.80622474467796092933] 
dist 81=[-2.7600646689449614408 ,-.4313832184667926127 ] 
dist 82=[-2.7598107615840165639 ,-.2858870608050193980 ] 
dist 83=[-2.5892879421604297896 ,-.1330249666087014531 ] 
dist 84=[-2.6993161775220863722 ,-.01342229682986412654] 
dist 85=[-2.8015078467238936167 ,.22708169322153325456] 
dist 86=[-2.9202163592447966755 ,.47413212986408384338] 
dist 87=[-3.0297643118279890621 ,.70595453667792802272] 
dist 88=[-3.0953709926221306540 ,.88573027361017032361] 
dist 89=[-3.1416185338833692857 ,1.0615431372666216425 ] 
dist 90=[-3.1738362136305498773 ,1.2775860726208571259 ] 
dist 91=[-3.1947866177753477917 ,1.4814035466092504444 ] 
dist 92=[-3.1960310022524200006 ,1.6084569532232284896 ] 
dist 93=[-3.1864169001714692890 ,1.7035072308368908812 ] 
dist 94=[-3.1767398909194394666 ,1.7796595472458676140 ] 
dist 95=[-1.1171506128051770691 ,2.0852038066196995617 ] 
dist 96=[-1.1051553450887352236 ,2.5116295447001761190 ] 
dist 97=[-.34770629359982027588,2.8452744841134597739 ] 
dist 98=[-.53435474166818940221,3.1395744971094050837 ] 
dist 99=[-.72046859393597602277,3.3953556725000132054 ] 
dist 100=[-.84002154267739664761,3.5703166161282340927 ] 
dist 101=[-.9333246456768177159 ,3.6994928390595610134 ] 
dist 102=[-1.0147454150506739023 ,3.8000285452030627462 ] 
dist 103=[-1.0819239442802409945 ,3.8797340158438188522 ] 
dist 104=[-1.1184177263925253991 ,3.9257736844441532504 ] 
dist 105=[-1.1392311017878965656 ,3.9560277013796237520 ] 
dist 106=[-1.1438656785696858636 ,3.9727225615605512067 ] 
dist 107=[-1.1425580344165259737 ,3.9794940477529056300 ] 
dist 108=[-1.1397811079050840570 ,3.9701406157718417175 ] 
dist 109=[-1.1352846192459290112 ,3.9486067109324329983 ] 
dist 110=[-1.1295626732541067172 ,3.9345297294912757843 ] 
dist 111=[-1.1172203666987130261 ,1.7496885725776711342 ] 
dist 112=[-1.1096570290518513176 ,1.5622299645982073284 ] 
dist 113=[-1.0925252307525620737 ,1.1110604722629347447 ] 
dist 114=[-1.0846692203513553602 ,1.0437718499189532365 ] 
dist 115=[-.45887889328201375829,.40544259688195835205] 
dist 116=[-.7178860818294901347 ,.32437217200900350443] 
dist 117=[-.96597014608464455363,.26140766151834847304] 
dist 118=[-1.2639258997194416558 ,.25018579694544760544] 
dist 119=[-1.5444248403102461717 ,.16438316284403101919] 
dist 120=[-1.7228430931886490882 ,.14870889406913059584] 
dist 121=[-1.8606197613846239609 ,.12338976529542078524] 
dist 122=[-1.9789189328674339796 ,.11715810695363986119] 
dist 123=[-2.0756196690017665566 ,.01172341199169237451] 
dist 124=[-2.1271978169341028489 ,-.0019255071005282837 ] 
dist 125=[-2.1555966149177311762 ,-.0310078118248889569 ] 
dist 126=[-2.1608096907403858109 ,-.0372133042130068939 ] 
dist 127=[-1.7460340916907368961 ,-.0660309831612483671 ] 
dist 128=[-1.7097775184366402601 ,-.0710210370807461318 ] 
dist 129=[-1.6143059988957394905 ,-.0799880336895354901 ] 
dist 130=[-1.5944120049846017396 ,-.0817450608506924844 ] 
dist 131=[-1.4206336378601611489 ,-.0845607932269310415 ] 
dist 132=[-1.3838651658222037366 ,-.0824812762195834166 ] 
dist 133=[-1.3320552285443354209 ,-.07759024703163574638] 
dist 134=[-1.3146010563585664289 ,-.06762845186831729950] 
dist 135=[-.92943956442316681907,-.05520697466826557391] 
dist 136=[-.87749270861921584459,-.04049584674661510183] 
dist 137=[-.76296489087865194997,-.02131019738792174486] 
dist 138=[-.73329481631161516099,.05431029753184404434] 
dist 139=[-.59527081200481295764,.22225903979911006837] 
dist 140=[-.56922695625260554929,.37766427614018945588] 
dist 141=[-.50764987487168930077,.55363031120838410801] 
dist 142=[-.4948757833089511989 ,.8036481977177062183 ] 
dist 143=[-.42630218975061531052,1.0499884073727297238 ] 
dist 144=[-.41973106902158786423,1.2112796915839979549 ] 
dist 145=[-.41449585489577485719,1.3411565807777758741 ] 
dist 146=[-.41232898288758685086,1.4802306187199817802 ] 
dist 147=[.05758157500558617309,1.6191016707275753286 ] 
dist 148=[.05077776543061671016,1.7181792173392516648 ] 
dist 149=[.02879231019932111250,1.8070835045868654550 ] 
dist 150=[-.01960087912326653466,1.9053555452941350298 ] 
dist 151=[-.07589130029180627723,1.9928097292506543415 ] 
dist 152=[-.12939647297830321397,2.0385399414184197745 ] 
dist 153=[-.19106624581049629973,2.0624757303593546903 ] 
dist 154=[-.27994791164587349916,2.0672706828943726771 ] 
dist 155=[-.37946745342652337424,2.0549738074525638971 ] 
dist 156=[-.48359570031866026763,2.0452135613141378495 ] 
dist 157=[-.61100863110234130193,2.0322853632073906869 ] 
dist 158=[-.80345899234924220115,2.0235572206980821774 ] 
dist 159=[-1.0652290259766437789 ,.61100452815699028361] 
dist 160=[-1.2521130201702873868 ,.60942921237535599734] 
dist 161=[-1.3996020677122049443 ,.60481289014832890515] 
dist 162=[-1.5318211947440455902 ,.60194063271802050572] 
dist 163=[-1.6440551342738941210 ,.42248051582386198102] 
dist 164=[-1.7431593754200313126 ,.40374917764494742405] 
dist 165=[-1.8552699407445620630 ,.35576980906806424494] 
dist 166=[-1.9695675052322414574 ,.3488518963866613261 ] 
dist 167=[-2.0706608357176144812 ,.27000866888734737821] 
dist 168=[-2.1300756444738195843 ,.25472721740043746493] 
dist 169=[-2.1703191625164990958 ,.23855847218539388204] 
dist 170=[-2.1949025455083287917 ,.23554456475813017838] 
dist 171=[-2.2075286845156521932 ,.08604354579377478992] 
dist 172=[-2.2079222440577241767 ,.06767000511354043095] 
dist 173=[-2.1880621556711014537 ,.03004289272654238871] 
dist 174=[-2.1826707798823720614 ,.02041160373230210965] 
dist 175=[-1.4249891100669782555 ,.2210503162253644937 ] 
dist 176=[-1.3701187380487238820 ,.42196267792404165083] 
dist 177=[-1.2296459597456068737 ,.58735718763891381068] 
dist 178=[-1.2074889628425568777 ,.74742000592512415139] 
dist 179=[-.97467937409190540297,.89171535346984329389] 
dist 180=[-.9288942928749030422 ,.99418454798144461808] 
dist 181=[-.8758179558405464986 ,1.0855907000741288665 ] 
dist 182=[-.86075874346359015272,1.1857341121972597633 ] 
dist 183=[-.41621719410073492939,1.2767521313931434398 ] 
dist 184=[-.3600587003251716996 ,1.3317412877530927876 ] 
dist 185=[-.32414826487084009795,1.3708394060880111575 ] 
dist 186=[-.3207706869675796508 ,1.3984428663399208920 ] 
dist 187=[-.24433300538201191031,1.4165459672507590546 ] 
dist 188=[-.23365469462976490423,1.4203934258825778361 ] 
dist 189=[-.20952351202586904975,1.4141363086060512918 ] 
dist 190=[-.20326958284124735424,1.4131734154368739316 ] 
dist 191=[-.1716736158217124835 ,.35278232219539830756] 
dist 192=[-.16547736909949137098,.3470618950817476912 ] 
dist 193=[-.15186206116828830756,.33344626547999938923] 
dist 194=[-.14784008101812325017,.32877598081118520013] 
dist 195=[-.0016309444017888017 ,.30615263904442513373] 
dist 196=[.0132544492639765058 ,.30100134027048484792] 
dist 197=[.01003868768027102604,.32977886600333049292] 
dist 198=[.00444194421475740291,.36884729969430146863] 
dist 199=[-.00116509512822463785,.40396737281727041832] 
dist 200=[-.00610454911174700653,.42874615972952868189] 
dist 201=[-.01149505821995176424,.45068854763621495804] 
dist 202=[-.01890280062288061520,.47448925934244918312] 
dist 203=[-.04792221445167851804,.49540464561496283545] 
dist 204=[-.09418862041986757205,.50583217514341392334] 
dist 205=[-.14754821034410847413,.51120165463359617353] 
dist 206=[-.22452365987658795554,.51193021701788239865] 
dist 207=[-.30054914379618989061,.50518511578716677595] 
dist 208=[-.35011785033793522574,.5026584059259393166 ] 
dist 209=[-.38978828672164068608,.50043816466127831527] 
dist 210=[-.42631028153899437189,.49805627524533052423] 
dist 211=[-.45800413869937824533,.05656055932480770236] 
dist 212=[-.47840585978191916996,.05637038971312976258] 
dist 213=[-.49444021808024466375,.05938187812750191999] 
dist 214=[-.50870455910506599915,.06754245600835250660] 
dist 215=[-.52014985147804847327,.07746264268901894629] 
dist 216=[-.5249335021093322738 ,.08749668039528641801] 
dist 217=[-.52630891449112274284,.09952859954283834292] 
dist 218=[-.52559770104284388321,.11742279619722521333] 
dist 219=[-.5154198395594694382 ,.13770471561313126602] 
dist 220=[-.51170992782213573538,.15926599579943361997] 
dist 221=[-.50414677556793608137,.18588510582518419344] 
dist 222=[-.49460283210273131405,.22635223381188524712] 
dist 223=[-.42469371477119621194,.26664065459134036561] 
dist 224=[-.42216028670688393839,.29254684525853954475] 
dist 225=[-.41459217860173528855,.31286861168011009867] 
dist 226=[-.41114027524458027459,.3308710742020392056 ] 
dist 227=[-.24369527495105759748,.3459968270983843017 ] 
dist 228=[-.22678314724796213544,.35483851629103204372] 
dist 229=[-.18679966672878633513,.36076805895536037111] 
dist 230=[-.17939847851020186883,.36427253180868745082] 
dist 231=[-.12370394229725921816,.36599445829285569394] 
dist 232=[-.11332755438733285869,.36581219150156484928] 
dist 233=[-.09633192889236310620,.36279644761136152014] 
dist 234=[-.09211083544550522443,.36120824436296512919] 
dist 235=[-.02920877207093202057,.34545205802721322236] 
dist 236=[-.02653491116356341328,.3411375586281582899 ] 
dist 237=[-.02089077568281408085,.33556786929470439951] 
dist 238=[-.01936519048637871099,.3312541717563500295 ] 
dist 239=[-.01348266664166127219,.22212348497266968463] 
dist 240=[-.01232937810684518319,.20936177366295204196] 
dist 241=[-.00988000490942584052,.18094459375189783563] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 1, 2] 
dist 0=[27.440391309720743916  ,27.440391309720743916  ] 
dist 1=[24.956355639597513513  ,29.747777110564330846  ] 
dist 2=[22.828893718069430891  ,31.169633008360708177  ] 
dist 3=[20.547695450033712884  ,32.220235788317648981  ] 
dist 4=[17.449802263537547073  ,33.044466046298527216  ] 
dist 5=[14.051456039412651761  ,33.684502852672067365  ] 
dist 6=[10.570186942238392092  ,33.999369289111136981  ] 
dist 7=[6.3499889838266041792 ,34.143693953683586772  ] 
dist 8=[0                     ,34.158669944334845759  ] 
dist 9=[28.063951880706133700  ,33.123754716321638806  ] 
dist 10=[28.703105305369816459  ,32.944942595986479043  ] 
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dist 134=[-.9481722223798089071 ,-.45624562097758999696] 
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dist 139=[-.59691451855428828369,-.02436616799445803   ] 
dist 140=[-.58091142366427001126,.04222930070501151353] 
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dist 142=[-.51195803777645471721,.15337813549355599203] 
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dist 145=[.1743932245793816018 ,.3159326612437487614 ] 
dist 146=[.19963348771254288388,.35113862837598566516] 
dist 147=[.21817812483761901133,.4220616349559972711 ] 
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dist 157=[.03441674364474494477,1.0738851335428153701 ] 
dist 158=[.01379424860875003698,1.0872023813748310036 ] 
dist 159=[-.00733898690529091379,1.0932580147756078439 ] 
dist 160=[-.18375888280925094331,1.0927593954781317843 ] 
dist 161=[-.37158296358695895164,.01419340809093394950] 
dist 162=[-.49391299470487028273,.01058548701553727948] 
dist 163=[-.59162744569778488814,.00806676254388378167] 
dist 164=[-.68125223514887406733,.00947574522136790977] 
dist 165=[-.76121735160795589811,.01277576799600245217] 
dist 166=[-.81199056175258251821,.01857766642542611146] 
dist 167=[-.85107767010329891495,.02729149296780557586] 
dist 168=[-.8844090147464707584 ,.04220266885578291213] 
dist 169=[-.91240280206659134104,.05756180960936347875] 
dist 170=[-.93018999479063997895,.06806235954299449495] 
dist 171=[-.94390171395926429087,.07696925143490745004] 
dist 172=[-.95563155855262440496,.08597518971422412610] 
dist 173=[-.96518794032574155111,.09430724979150349971] 
dist 174=[-.97022630421171047561,.10052736002983791318] 
dist 175=[-.97292204097793595763,.1063630456852408752 ] 
dist 176=[-.97313049153561377053,.11316165341278401887] 
dist 177=[-.40121259326122508798,.11934596359460704868] 
dist 178=[-.35540193934777292466,.12273199415474867167] 
dist 179=[-.24510093064139171995,.12469714555046706229] 
dist 180=[-.22889900702004452564,.12521586656443421825] 
dist 181=[-.15936465061342098589,.12506311144004670911] 
dist 182=[-.15725884950076330739,.12457866342443557982] 
dist 183=[-.15450424787665493598,.16238473145396363811] 
dist 184=[-.15334930778724603086,.23935040864148195173] 
dist 185=[.00268436503447381841,.31229353192355117573] 
dist 186=[.01464962639792025902,.35864774144341564534] 
dist 187=[.04149904355956699899,.39437249529143556281] 
dist 188=[.04600126167473409823,.42489752272609741726] 
dist 189=[.07710605475098842365,.44974302308978205256] 
dist 190=[.08217908855329534359,.46280354130284936051] 
dist 191=[.09137811708555014484,.4700696763543303335 ] 
dist 192=[.09318209781600387347,.47179208140198488472] 
dist 193=[.10955611834723940653,.42942728759445055761] 
dist 194=[.11148609781237156851,.42888091905424692819] 
dist 195=[.10752826817263355472,.42476993903386188464] 
dist 196=[.09673464548884197394,.42256614597573235812] 
dist 197=[.08359638241731195812,.40389675593401064623] 
dist 198=[.06841052386189053021,.39880819935411076497] 
dist 199=[.04883443694985682162,.39140473170380185966] 
dist 200=[.01817779579083192669,.38849292743729244502] 
dist 201=[-.01272645624970888886,.31282386263531969709] 
dist 202=[-.03329113965658997511,.301933026546071056  ] 
dist 203=[-.05019920484386476673,.27844307009283320716] 
dist 204=[-.06651404142055140635,.27166016455606572494] 
dist 205=[-.08118127319576087700,.24397467774148192748] 
dist 206=[-.09151595121311983762,.23815734059855781603] 
dist 207=[-.10064941987311379244,.22513733049708772171] 
dist 208=[-.12579287920380125218,.22105593685550361891] 
dist 209=[-.20746387288995038481,.06207460581244856717] 
dist 210=[-.261740594495279646  ,.05456200354770123427] 
dist 211=[-.30632041265130356032,.04548344113994685581] 
dist 212=[-.3492939589037264062 ,.04376715715454987701] 
dist 213=[-.38983646593812934235,.03152611015952542957] 
dist 214=[-.4200027075884080474 ,.02927910219980885450] 
dist 215=[-.44757578214572015635,.02534999170980902032] 
dist 216=[-.47880144130108284908,.02446114771995932165] 
dist 217=[-.50697262899491022939,-.00743545003252189827] 
dist 218=[-.52235621383781757201,-.01087247418884434973] 
dist 219=[-.53131126882487353568,-.00409743375183475154] 
dist 220=[-.53382800218581259864,.01578867152041519433] 
dist 221=[-.53379386339065329419,.03936393792345809996] 
dist 222=[-.53256922644699727292,.06584067563269708902] 
dist 223=[-.5302392654678162757 ,.09949861573235882818] 
dist 224=[-.52813194891716036309,.16425067832103207171] 
dist 225=[-.11027396900378581   ,.23328545665955467177] 
dist 226=[-.11284899494535564855,.27798609044272606407] 
dist 227=[-.11425063445975486326,.31339253038543766605] 
dist 228=[-.11454640314001690521,.34533889461025323444] 
dist 229=[-.11400299140316827557,.37259066067816413051] 
dist 230=[-.11369283833553965429,.40165109491405429405] 
dist 231=[-.11333231651071291598,.43125633160812367031] 
dist 232=[-.11286372996283630332,.46252417681602780597] 
dist 233=[-.10340851449871296292,.49047190907039508508] 
dist 234=[-.10649511955256143367,.50682790950691648752] 
dist 235=[-.10838037949958142726,.51781657786429603807] 
dist 236=[-.10910229232893327376,.52434492610909414726] 
dist 237=[-.1093038357177780526 ,.52775262063101586107] 
dist 238=[-.10911386483595817893,.52789116539661946339] 
dist 239=[-.10859529423800453377,.52356342011636460835] 
dist 240=[-.10823366322360511703,.52194250234714496752] 
dist 241=[-.09492871547723708511,.34447932157118638715] 
dist 242=[-.12137877441373303794,.33033659525717319692] 
dist 243=[-.16175608787288116663,.29459841579085610677] 
dist 244=[-.20018635037473111382,.28870430578733950465] 
dist 245=[-.23439383352206125001,.23088171980863497497] 
dist 246=[-.25791966550789183973,.21956378388221115231] 
dist 247=[-.27811111063076398547,.2054776129374617308 ] 
dist 248=[-.29901214549795576262,.20086566855470239766] 
dist 249=[-.31776051367669149762,.09561751227455895379] 
dist 250=[-.32936162938826459248,.08219958832257922962] 
dist 251=[-.33794062673715406469,.05326984546499042759] 
dist 252=[-.34462947676391543803,.04630667547704556363] 
dist 253=[-.34958580151275427378,.01534394910575430622] 
dist 254=[-.35125133106182558366,.01225698231943149297] 
dist 255=[-.35103810762111805751,.00539028413941560915] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 1, 1, 0, 2] 
dist 0=[61.815300861928583539  ,61.815300861928583539  ] 
dist 1=[61.664857221435152863  ,61.834217187254017439  ] 
dist 2=[61.154910100263309720  ,61.818864343298620043  ] 
dist 3=[60.252832908233239564  ,61.789486015631977265  ] 
dist 4=[58.536194852565456385  ,61.752447432788890903  ] 
dist 5=[56.681580002509002938  ,61.702813660141179633  ] 
dist 6=[55.228487761150044747  ,61.623132523233668692  ] 
dist 7=[53.787502268660757796  ,56.490296912846242369  ] 
dist 8=[51.981310675420292716  ,55.734826829054649809  ] 
dist 9=[50.073057880633446073  ,54.380537069672067474  ] 
dist 10=[48.224482283706675241  ,54.023595750360121339  ] 
dist 11=[44.915816513781985957  ,52.798747771880099530  ] 
dist 12=[41.476405790736136252  ,52.431038273902074586  ] 
dist 13=[37.289061862667634650  ,52.012390332269915782  ] 
dist 14=[30.974330019776841390  ,51.807787721176510949  ] 
dist 15=[24.642854391798158172  ,36.758497013787797419  ] 
dist 16=[20.388533564760690945  ,36.198535213812058308  ] 
dist 17=[16.831906029916941852  ,34.277229528447637576  ] 
dist 18=[13.286374264781687006  ,33.812779873428058498  ] 
dist 19=[10.009034443777038488  ,33.307731714844214011  ] 
dist 20=[7.5231346993292361226 ,33.154621099038864252  ] 
dist 21=[5.1339328462321658916 ,11.619575265184247022  ] 
dist 22=[2.2421702310862739608 ,11.313935477082289466  ] 
dist 23=[-.48568516859724428116,5.8851349641859296832 ] 
dist 24=[-2.2206205321317320697 ,5.2283984324873427358 ] 
dist 25=[-3.5673335249542728749 ,.40569450349279823694] 
dist 26=[-4.7451198940641282990 ,-.05775427029016186752] 
dist 27=[-5.7331223592412742518 ,-1.7749742451345298434 ] 
dist 28=[-8.0394496382213146289 ,-2.0682420751320838413 ] 
dist 29=[-10.289972560063456205  ,-2.9443482025843634743 ] 
dist 30=[-11.704451330907212707  ,-3.0382465168671000028 ] 
dist 31=[-12.781297910856949678  ,-6.2713716666779875928 ] 
dist 32=[-13.683339390340232344  ,-6.5313688529662673061 ] 
dist 33=[-14.407268611308170776  ,-7.0363713550573563092 ] 
dist 34=[-14.772784089016659722  ,-7.0252244096003082070 ] 
dist 35=[-14.956383266715300056  ,-6.1787862545816306540 ] 
dist 36=[-14.983365494821736150  ,-4.6732581307395404859 ] 
dist 37=[-7.5203506848904243776 ,-3.1075353120356000605 ] 
dist 38=[-7.5270646616852536228 ,-2.0206499958563371219 ] 
dist 39=[-6.6110390423890100652 ,-1.0802401123730440905 ] 
dist 40=[-6.4762739272804672762 ,-.09820826390724450460] 
dist 41=[-6.2358424328401812552 ,.83217105535068667891] 
dist 42=[-6.1725749531995118193 ,1.5668479868977202868 ] 
dist 43=[-5.9615987480065112057 ,2.2974198936654796898 ] 
dist 44=[-5.8944493750870338411 ,3.2117564546408415629 ] 
dist 45=[-5.8461438611391967874 ,4.0827258873369976514 ] 
dist 46=[-5.8267255834239173282 ,4.6404385890452675150 ] 
dist 47=[-1.3624339431295757347 ,5.0751954556350867782 ] 
dist 48=[-1.0000144595453280617 ,5.4557621090477032641 ] 
dist 49=[-.18838189300324000447,5.7729326932457239092 ] 
dist 50=[-.04317608978935045021,5.9549072913728519742 ] 
dist 51=[.90766843284593358871,6.0736515575013810820 ] 
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dist 65=[-2.3160647118068226313 ,2.0521721657372720592 ] 
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dist 67=[-3.2231206579297354594 ,1.9398274619218908336 ] 
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dist 96=[-.74365840615340545385,3.3049349951283976061 ] 
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dist 100=[-.27850521804042496135,3.3573135145155308216 ] 
dist 101=[-.03645823856478461120,1.7497012597326268864 ] 
dist 102=[-.35326025505204876535,1.6109954776332094602 ] 
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dist 109=[-1.6315884250542234486 ,2.0083102946204558788 ] 
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dist 119=[-2.5267178272307676276 ,2.7175978932722815006 ] 
dist 120=[-2.5261709123080613284 ,2.6666414682616579642 ] 
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dist 122=[-2.4958065294409336831 ,2.5549150337894388077 ] 
dist 123=[-2.3850035023303297103 ,2.4673996788521067373 ] 
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dist 127=[-1.5575910512012718485 ,.00043053399826630550] 
dist 128=[-1.4741251224035304440 ,.03214770281943133273] 
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dist 130=[-1.2346789129128456222 ,.08561280475535978274] 
dist 131=[-.9111010288890028199 ,.11025323522631982948] 
dist 132=[-.84990687560709319519,.12854849525208282381] 
dist 133=[-.77915005771069028509,.14565938004427041418] 
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dist 135=[-.21872971803059079676,.18382423883077632354] 
dist 136=[-.15233603513679919942,.20007536879253894258] 
dist 137=[-.09018125001026934567,.21974294501720366145] 
dist 138=[-.08695367061838320752,.23712187724622979792] 
dist 139=[-.06596951208938408241,.37126803378140142979] 
dist 140=[-.06215724530113024998,.48340335640781666637] 
dist 141=[-.05514547689553801798,.60093348435899985434] 
dist 142=[-.05351785630212351104,.75663154553108729651] 
dist 143=[-.09834374275006703263,.90852981051430413618] 
dist 144=[-.13058829085706744036,1.0108976180971023817 ] 
dist 145=[-.1567589424424395456 ,1.0966552004223198861 ] 
dist 146=[-.18139745029105950825,1.1822487110337290834 ] 
dist 147=[-.2030876727222483713 ,1.2612609407307875543 ] 
dist 148=[-.21749455267048198258,1.3207481200575011157 ] 
dist 149=[-.22927703170952549482,1.3773748374990975021 ] 
dist 150=[-.24049257688567945133,1.4449710001059097179 ] 
dist 151=[-.25027958566650659259,1.5079870637320467753 ] 
dist 152=[-.25636330216293819651,1.5463310830228002540 ] 
dist 153=[-.26086256340357586742,1.5739834508693568918 ] 
dist 154=[-.26433416470795610467,1.5943186977823460161 ] 
dist 155=[-.26684816976751005027,1.6084282398594723500 ] 
dist 156=[-.26752982087409807748,1.6112286025995922207 ] 
dist 157=[-.46453745150522475866,1.6073735210784185593 ] 
dist 158=[-.81571705561985471383,1.6030277401974109790 ] 
dist 159=[-1.1642426684277800339 ,-.26576544919740270384] 
dist 160=[-1.3880781410981374864 ,-.28082631289147960122] 
dist 161=[-1.5634074259426492578 ,-.29366671256546570863] 
dist 162=[-1.7183436398721135105 ,-.28851536863262126891] 
dist 163=[-1.8660925105536733816 ,-.27514438186399523349] 
dist 164=[-1.9578611472279038779 ,-.25059445060199337945] 
dist 165=[-2.0255658998037544232 ,-.21316426076662275704] 
dist 166=[-2.0781185562261373270 ,-.14839210709584673226] 
dist 167=[-2.1194833790143455720 ,-.07786323440854647047] 
dist 168=[-2.1425379428121735928 ,-.01745971885780323479] 
dist 169=[-2.1565977075638824889 ,.04706643906989125517] 
dist 170=[-2.1620650566518630388 ,.13404757131195716838] 
dist 171=[-2.1616032183719377992 ,.22875528303222257681] 
dist 172=[-2.1553421370167290077 ,.32411584765634570303] 
dist 173=[-2.1376358942586480511 ,.43817461823754457206] 
dist 174=[-2.1270981583989880833 ,.60750105385991379759] 
dist 175=[-.98304911188890972829,.77494105790246525757] 
dist 176=[-.88286953385957418381,.88147150413654562303] 
dist 177=[-.88701996474808485148,.96373129882151918163] 
dist 178=[-.89767111405227831769,1.0343142004288683100 ] 
dist 179=[-.90314513752158714409,1.0919414705611435716 ] 
dist 180=[-.90352391403203823277,1.1224988830661182477 ] 
dist 181=[-.89526060940408644089,1.1393592287887882062 ] 
dist 182=[-.89365652849986617626,1.1430326507926815532 ] 
dist 183=[-.83970900192951227147,1.1374491267653046421 ] 
dist 184=[-.82920568134008808761,1.1334546618524591230 ] 
dist 185=[-.79940557559861067114,1.1282429204918233012 ] 
dist 186=[-.7920948640924915687 ,1.1860644767644330808 ] 
dist 187=[-.72863619937380072097,1.2377994993667578871 ] 
dist 188=[-.71424538575353884735,1.2654452993930867389 ] 
dist 189=[-.69388011802338536826,1.2807324077861542093 ] 
dist 190=[-.68662460904868864168,1.2831440340686844104 ] 
dist 191=[-.39860256209434080066,.98139547087890259072] 
dist 192=[-.36526705420871192295,.95528981865730791284] 
dist 193=[-.29788246331345793702,.88922515566493542045] 
dist 194=[-.28030843552182063142,.8754530759284929924 ] 
dist 195=[-.21699630900613913705,.76443727575638390252] 
dist 196=[-.20330553628790959856,.74155571784783123279] 
dist 197=[-.27860489923867881312,.70680893151063534089] 
dist 198=[-.41361271061915990744,.69630160281130474796] 
dist 199=[-.54594350040430938453,.47522024096999991491] 
dist 200=[-.63730680116827706841,.44553592587183217832] 
dist 201=[-.71612534297722709159,.48868249802168752433] 
dist 202=[-.79839289491011798247,.5872938713330538575 ] 
dist 203=[-.8765480960230550616 ,.68724643254034010675] 
dist 204=[-.93895564564108438421,.77730778471921401448] 
dist 205=[-1.0017625992435463415 ,.87733608142439364571] 
dist 206=[-1.0815130651440171701 ,1.0170629474190912765 ] 
dist 207=[-1.1564410515758179367 ,1.1524076760007441865 ] 
dist 208=[-1.2000020103230277651 ,1.2349473954701574587 ] 
dist 209=[-1.2289153425033921268 ,1.2945732562423916813 ] 
dist 210=[-1.2453849501310191758 ,1.3384741238430193732 ] 
dist 211=[-1.2546064965440365221 ,1.3712959592167025906 ] 
dist 212=[-1.2545936715944318041 ,1.3867081655369744055 ] 
dist 213=[-1.2500935653130363830 ,1.3923085597179500906 ] 
dist 214=[-1.2451719290524106926 ,1.3918102463295056151 ] 
dist 215=[-1.1359944668125573581 ,1.2843855592551556523 ] 
dist 216=[-1.1441558186056045097 ,1.2650044269865860406 ] 
dist 217=[-1.1459059848370198993 ,1.2304856529613676741 ] 
dist 218=[-1.1437287182558459621 ,1.2201523199937427284 ] 
dist 219=[-1.1102570756645525107 ,1.1785842225348310313 ] 
dist 220=[-1.0994714206768522658 ,1.1661537974391066062 ] 
dist 221=[-1.0882045955744029275 ,1.1398451369964780693 ] 
dist 222=[-1.0813098149527958989 ,1.1303316393044389122 ] 
dist 223=[-.90119574126459057432,.66732978964477122462] 
dist 224=[-.89713780101030507713,.74218731408537374696] 
dist 225=[-.88439761399166767594,.80032713939618921606] 
dist 226=[-.87805544481579144215,.85083122795439721924] 
dist 227=[-.84046973495383440011,.89254718866748684374] 
dist 228=[-.83047740896069278398,.92267726926488413217] 
dist 229=[-.81031343645078107523,.99695834668525492039] 
dist 230=[-.80340998924037374012,1.0788354239996143685 ] 
dist 231=[-.67276369597141287736,1.1527570449984445768 ] 
dist 232=[-.65311515076799025295,1.1952889089593674713 ] 
dist 233=[-.60614454484249208559,1.2229583638592358129 ] 
dist 234=[-.59437350729581070846,1.2375659989777538158 ] 
dist 235=[-.52281812707602765123,1.2452024869911494787 ] 
dist 236=[-.50804675282401539578,1.2450507585518408518 ] 
dist 237=[-.47980195896954067478,1.2402980497299928056 ] 
dist 238=[-.47202355840046788206,1.2360630755679670672 ] 
dist 239=[-.1565555906567263807 ,.91552739110590454022] 
dist 240=[-.28682347672211726983,.88110163707079268513] 
dist 241=[-.39398803743624320949,.79313994131030323512] 
dist 242=[-.49758598793204576679,.7789844461985585936 ] 
dist 243=[-.59091403502855787704,.63341600947719723093] 
dist 244=[-.65709263472744507224,.60472073269199076315] 
dist 245=[-.716032260140278009  ,.57071757995706452507] 
dist 246=[-.78046995514257069821,.56038458897289688595] 
dist 247=[-.83897533982987475929,.22349793165405181435] 
dist 248=[-.87424018269004099163,.18279898279410929472] 
dist 249=[-.89921886331605230377,.10336434550802655804] 
dist 250=[-.91667493914680184206,.08392777975743668468] 
dist 251=[-.92801887483135571725,-.04025544570479931996] 
dist 252=[-.93034096783082699604,-.03607061141503168492] 
dist 253=[-.92612894352778965284,-.02454313963459881204] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 0, 0, 0, 1, 0, 1] 
dist 0=[61.281137524484264269  ,61.281137524484264269  ] 
dist 1=[60.812041623881881002  ,61.393942132466418057  ] 
dist 2=[59.957652197396133683  ,61.375470687347650864  ] 
dist 3=[58.350681809006441285  ,61.307154250137442416  ] 
dist 4=[56.613456464174092869  ,61.186413511342247283  ] 
dist 5=[55.238868245908683947  ,61.042360585969182739  ] 
dist 6=[53.862908213232358831  ,60.953291985395333231  ] 
dist 7=[52.120317545001600987  ,60.762599280512495081  ] 
dist 8=[50.269860301064611800  ,58.949968594087254918  ] 
dist 9=[48.463143748070049897  ,54.801667863340065245  ] 
dist 10=[46.337743524666018353  ,53.947057584360252828  ] 
dist 11=[43.214535692501930602  ,52.527080506091243059  ] 
dist 12=[39.572071366787408898  ,52.144952138555357643  ] 
dist 13=[33.839118199775475432  ,51.228730720486039365  ] 
dist 14=[28.078715165333037280  ,50.897905497288911431  ] 
dist 15=[24.175083838750158053  ,50.596130403379740480  ] 
dist 16=[20.875068566139444266  ,48.483279917049455572  ] 
dist 17=[17.525476971702043492  ,34.246508929192522905  ] 
dist 18=[14.391468236457338837  ,33.751201755869287390  ] 
dist 19=[11.952531349747885994  ,33.600318803728594931  ] 
dist 20=[9.5504696470673785765 ,16.099112971319998612  ] 
dist 21=[6.5638947930750133641 ,11.969307901146055976  ] 
dist 22=[3.7134392591316593607 ,8.5013792767439043424 ] 
dist 23=[1.3716891626619497119 ,7.0278015453995765645 ] 
dist 24=[-1.3919795126250968525 ,6.7584106266356510579 ] 
dist 25=[-3.4826503834774342996 ,.85755015487540877363] 
dist 26=[-5.4863840679067605958 ,-1.1578554005404010367 ] 
dist 27=[-7.9028504897502926870 ,-1.4761190810358201192 ] 
dist 28=[-10.175387003485295581  ,-2.0513714199336497056 ] 
dist 29=[-11.604285848840898642  ,-2.1518299694740102159 ] 
dist 30=[-12.692749891024928418  ,-4.8019612353186701239 ] 
dist 31=[-13.605623966279962638  ,-4.9862428989597859552 ] 
dist 32=[-14.339064161950981699  ,-5.5278453981203469199 ] 
dist 33=[-14.710926095944535141  ,-6.3509285656502271158 ] 
dist 34=[-14.898994313694623118  ,-6.3867169191497227097 ] 
dist 35=[-14.928067302603453609  ,-4.9322725240328700603 ] 
dist 36=[-7.3798946074235674051 ,-3.4157826014005861362 ] 
dist 37=[-6.9292249133830773177 ,-2.3584452742030511636 ] 
dist 38=[-6.8139884172997509595 ,-1.4388085831445654574 ] 
dist 39=[-6.7414856012412454030 ,-.47099340062017027967] 
dist 40=[-6.7208509539549088123 ,.45047542991557540741] 
dist 41=[-5.8414747997369151321 ,1.1855531818410951424 ] 
dist 42=[-5.6704571740549411660 ,1.9234166519601959793 ] 
dist 43=[-5.6134880989160687249 ,2.8563390005000792790 ] 
dist 44=[-5.5673577374146867254 ,3.7496302207633867351 ] 
dist 45=[-5.5414158882534048004 ,4.3295425781031103273 ] 
dist 46=[-3.4918236732646436164 ,4.7906371649708293693 ] 
dist 47=[-3.3874471844639665886 ,5.2100385649459061387 ] 
dist 48=[-3.3685711645373471800 ,5.5710583799578874904 ] 
dist 49=[-.36721083766398788685,5.7993801655175052572 ] 
dist 50=[.51906375451418419854,5.9751351263965050654 ] 
dist 51=[.66961824456317345038,6.1267294008086083977 ] 
dist 52=[.93944850479426864778,6.2403314794345654746 ] 
dist 53=[.9949614838258027266 ,6.2664587724270568381 ] 
dist 54=[1.0631376836762121404 ,6.2586686238672999898 ] 
dist 55=[.92070082116851659637,6.2522231933805617527 ] 
dist 56=[.76094160976819868854,5.9692066216540137291 ] 
dist 57=[.59543239338418170028,5.8907914768835831117 ] 
dist 58=[.39484350793877258002,5.8395606860669767411 ] 
dist 59=[.09502939039312438806,5.8126619209999762497 ] 
dist 60=[-.21337168292628716638,4.2646543426799609591 ] 
dist 61=[-.44830254100744674282,4.0638144635761963240 ] 
dist 62=[-.67388461462321636409,3.6896994631244921487 ] 
dist 63=[-.94513312847080729768,3.2798238197920432165 ] 
dist 64=[-1.2246521043763221409 ,2.6441906520853536041 ] 
dist 65=[-1.4833347958456358483 ,2.5922087633933075704 ] 
dist 66=[-1.8499743437814914020 ,2.5363011083508331369 ] 
dist 67=[-2.3753152664436997940 ,2.5158635638946776364 ] 
dist 68=[-2.8575873829821753891 ,-.0455667469762071539 ] 
dist 69=[-3.2750441192997234293 ,-.0658729721817362736 ] 
dist 70=[-3.5417832749545209624 ,-.31431537086784848588] 
dist 71=[-3.7492461540375442117 ,-.3488946790193720928 ] 
dist 72=[-3.9302308836989683252 ,-.38319166951908162787] 
dist 73=[-4.0834340498110490536 ,-.37528324528429394847] 
dist 74=[-4.1800358964579538313 ,-.34933892743169844046] 
dist 75=[-4.2538931300319170294 ,-.29893701062733158454] 
dist 76=[-4.3162688888835149327 ,-.22128655296542970214] 
dist 77=[-4.3666768310401508491 ,-.08668386185801857979] 
dist 78=[-4.3927415645340059804 ,.05251985165075561448] 
dist 79=[-4.4060410445783483988 ,.14852572266441318526] 
dist 80=[-4.4054719758324029984 ,.23084318241535492702] 
dist 81=[-3.9829016666497945139 ,.31548522697965735589] 
dist 82=[-3.9579187133098356579 ,.39469081255336863037] 
dist 83=[-3.9415988493553307503 ,.45533714940271154483] 
dist 84=[-2.9019228700908388460 ,.51373517701336610971] 
dist 85=[-2.7861526672166692562 ,.58397515436511418405] 
dist 86=[-2.4936201641913656553 ,.93119180188236665124] 
dist 87=[-2.4455677141945627555 ,1.3183025701782378953 ] 
dist 88=[-1.9718870740030547108 ,1.6701303001402717062 ] 
dist 89=[-1.8790528657498562050 ,1.9249863395376902507 ] 
dist 90=[-1.7645138266354898015 ,2.1575708638528007572 ] 
dist 91=[-1.7274380056478213069 ,2.4205420793305714113 ] 
dist 92=[-.85702638716902104813,2.6619600169773905691 ] 
dist 93=[-.74572576621231403365,2.8085296604763623494 ] 
dist 94=[-.50778312895334613682,2.9137003484112298097 ] 
dist 95=[-.44785636691572895505,2.9898786768117261222 ] 
dist 96=[-.19665539026233777006,3.0433953783744913639 ] 
dist 97=[-.15006435986042964258,3.0581272729526136535 ] 
dist 98=[-.04995592666609375754,3.0577254361216513271 ] 
dist 99=[-.02650355303473880311,3.0508260736343092387 ] 
dist 100=[-.2175912501596342987 ,2.2372060883562809861 ] 
dist 101=[-.4891278709317824891 ,2.1556777116221005222 ] 
dist 102=[-.7129121357836336158 ,1.9452675534844076748 ] 
dist 103=[-.9296254123012020194 ,1.9131125871203611405 ] 
dist 104=[-1.1248423544673381206 ,1.5606972789740525272 ] 
dist 105=[-1.2628508090327637051 ,1.4915020178007386236 ] 
dist 106=[-1.3851682364899322529 ,1.4143111416430539428 ] 
dist 107=[-1.5177647364021075251 ,1.3949848384822413114 ] 
dist 108=[-1.6381253141402928494 ,.80489488625341389227] 
dist 109=[-1.7116256739710313117 ,.80202059160884342103] 
dist 110=[-1.7647411097114228168 ,.5673750059527248778 ] 
dist 111=[-1.8037917508896565526 ,.60105465812360730244] 
dist 112=[-1.8307579147142398516 ,.6604119791968517899 ] 
dist 113=[-1.8357049789417798270 ,.72198948931660023609] 
dist 114=[-1.8322676088305754256 ,.76452307091377315191] 
dist 115=[-1.9264826066184723654 ,.80103735090830560268] 
dist 116=[-2.0156527626080544266 ,.83862490727549408116] 
dist 117=[-2.0841932870105778818 ,.87379662829395350007] 
dist 118=[-2.1143625866261759623 ,.90068197032804863536] 
dist 119=[-2.1270826725947894265 ,.92651068125873829885] 
dist 120=[-2.1259832545583226927 ,.95746962170782025282] 
dist 121=[-2.0300528758267682684 ,.98607806455106255402] 
dist 122=[-2.0078887915285945173 ,1.0025362483151476843 ] 
dist 123=[-2.0238760475534176436 ,1.0131564978635537118 ] 
dist 124=[-2.1368530214918034769 ,1.0184919103749950140 ] 
dist 125=[-2.2054822006039315156 ,1.0199666285419143375 ] 
dist 126=[-2.2548058738580413192 ,1.0172382512295110349 ] 
dist 127=[-2.2907222258601663214 ,1.0076367878523509622 ] 
dist 128=[-2.3153040057936760582 ,1.0014849325632512556 ] 
dist 129=[-2.3193849788141343004 ,.18347153750605168299] 
dist 130=[-2.3142709149757488900 ,.48605315394617301698] 
dist 131=[-2.3057905818969628482 ,.94321319806910050462] 
dist 132=[-.3914882424327883507 ,1.3977374732434500088 ] 
dist 133=[-.3942003315884923149 ,1.6898029377270309338 ] 
dist 134=[-.3953099068892464822 ,1.9187183435992376680 ] 
dist 135=[-.3946930456721486776 ,2.1212164811960249346 ] 
dist 136=[-.39294565842277594863,2.2911714612177566481 ] 
dist 137=[-.39161641102846217861,2.4120891628807328323 ] 
dist 138=[-.3826410704393923787 ,2.5090269514295595301 ] 
dist 139=[-.38007364214788319235,2.5894745681838788190 ] 
dist 140=[-.37257779995010417084,2.6553068816429839301 ] 
dist 141=[-.36984971331579828926,2.6939165434184511991 ] 
dist 142=[-.22296410486075662878,2.7199804747380623397 ] 
dist 143=[-.20841964418192441334,2.7357429425318902651 ] 
dist 144=[-.17246443921905159536,2.7436880391035585711 ] 
dist 145=[-.16719796805540644677,2.7385537380301570083 ] 
dist 146=[-.11237203108516267283,2.7246354863604218587 ] 
dist 147=[-.10204042599184790591,2.7146466652793416751 ] 
dist 148=[-.09510094548181514750,1.2470593576955935548 ] 
dist 149=[-.09854567129684080644,1.1205869202142948878 ] 
dist 150=[-.10150059483302887288,.81504485381527015117] 
dist 151=[-.1027001684972556703 ,.76979808710380020116] 
dist 152=[-.31146136278255233015,.33365044905470818208] 
dist 153=[-.49219755735598845927,.29372257502458132509] 
dist 154=[-.66637438702934940973,.2895398019030460900 ] 
dist 155=[-.8770627363900011668 ,.2920506403970693324 ] 
dist 156=[-1.0756387348408082751 ,.2927957869800171895 ] 
dist 157=[-1.2014777212963480020 ,.2923481781922846272 ] 
dist 158=[-1.2980957975753699102 ,.23930574251603585126] 
dist 159=[-1.3800530625244074301 ,.23397771688613045995] 
dist 160=[-1.4462782238372348677 ,.23449090737900293531] 
dist 161=[-1.4801102157957176040 ,.24309853429771310723] 
dist 162=[-1.4979442664635244495 ,.2562347764734327654 ] 
dist 163=[-1.5007273728215815264 ,.2748206418297793952 ] 
dist 164=[-1.3033537979424967761 ,.30094258853973058515] 
dist 165=[-1.2828001430476040859 ,.3441527832165032849 ] 
dist 166=[-1.2268733577616875628 ,.3904817712719964260 ] 
dist 167=[-1.2139595541672993061 ,.4290501777814345155 ] 
dist 168=[-1.1039610274295759064 ,.4692955767543999378 ] 
dist 169=[-1.0797497999529303131 ,.5223180753456020430 ] 
dist 170=[-1.0448739003901268978 ,.5794583399377079032 ] 
dist 171=[-1.0329915237662233608 ,.6361369333352472954 ] 
dist 172=[-.7622561886742304702 ,.70330282987782329323] 
dist 173=[-.91678524143174129284,.80229488201076378226] 
dist 174=[-1.0777460941639827427 ,.89988188915171549571] 
dist 175=[-1.1778066331365596628 ,.96144107478363084438] 
dist 176=[-1.2523801702763343204 ,1.0083650382578329793 ] 
dist 177=[-1.3116259088267712055 ,1.0475483436055539127 ] 
dist 178=[-1.3579229965503744288 ,1.0787316071247600825 ] 
dist 179=[-1.3808210552334793864 ,1.0937304841073056494 ] 
dist 180=[-1.3914035825651482253 ,1.0998507430253839883 ] 
dist 181=[-1.3925036901682737952 ,1.1001141390832833339 ] 
dist 182=[-1.3213312829209954125 ,1.0855590919951043686 ] 
dist 183=[-1.3062503860173996067 ,1.1223999139940623435 ] 
dist 184=[-1.2826593144017257468 ,1.2335428487048594498 ] 
dist 185=[-1.2738507270474297979 ,1.3131443167741308090 ] 
dist 186=[-1.2425869158433135179 ,1.3848711758713583424 ] 
dist 187=[-1.2317245550604602300 ,1.4645894991238807027 ] 
dist 188=[-1.2093341958577005991 ,1.5357424412840190956 ] 
dist 189=[-1.2008344530659432340 ,1.5732863480721910698 ] 
dist 190=[-.3430151151506630809 ,1.5934008616160444500 ] 
dist 191=[-.2677867012965342860 ,1.5975299803178028461 ] 
dist 192=[-.30832409933365365423,1.5898620578131459934 ] 
dist 193=[-.38414295538281980849,1.5831311795358825499 ] 
dist 194=[-.47692647836500065897,1.5739467066330737974 ] 
dist 195=[-.61707593973578913557,1.5672058251746027627 ] 
dist 196=[-.75628747239860289664,.31206290469308053615] 
dist 197=[-.84532873659201469437,.30278021525385239276] 
dist 198=[-.91463873307672102012,.27106446001355955914] 
dist 199=[-1.0685012141655928032 ,.26726163919700914857] 
dist 200=[-1.2175732832574545206 ,.27231100281478814441] 
dist 201=[-1.3194969501243417154 ,.29075975158489539166] 
dist 202=[-1.4063601043978356755 ,.31639850038252887717] 
dist 203=[-1.4953280247261119502 ,.35014032637795057454] 
dist 204=[-1.5742136932694203264 ,.3962629129979397963 ] 
dist 205=[-1.6208408215785823114 ,.47130842355073034735] 
dist 206=[-1.6527457568804433381 ,.54815436453149093628] 
dist 207=[-1.6728794225631396514 ,.60146173920016715839] 
dist 208=[-1.6838945929493553206 ,.64770513514579483725] 
dist 209=[-1.6845370777795774064 ,.69636143416758547634] 
dist 210=[-1.6710147601837445929 ,.74281043600524415594] 
dist 211=[-1.6664190347748754566 ,.7802453087899774525 ] 
dist 212=[-1.1041920798091500062 ,.8182254029967340075 ] 
dist 213=[-1.0642246614366548248 ,.8668500479972050204 ] 
dist 214=[-.96089155496809162592,.9137412031076575252 ] 
dist 215=[-.94483050852843482473,.9448035577446330317 ] 
dist 216=[-.77021757740618625815,.9702011694159295215 ] 
dist 217=[-.73566551485473117159,.9944864974557569021 ] 
dist 218=[-.69690549122006406733,1.0161796122143007545 ] 
dist 219=[-.68647741625983740664,1.0312326120339082597 ] 
dist 220=[-.342011937818366422  ,1.0442946946278119249 ] 
dist 221=[-.29854945777497971337,1.0580425880579345788 ] 
dist 222=[-.20805016946591131056,1.0689260719502448467 ] 
dist 223=[-.1842485020757954291 ,1.0705572478419457427 ] 
dist 224=[-.09623943321635186587,1.0709300807964380872 ] 
dist 225=[-.07868229236642363379,1.0733163353687802931 ] 
dist 226=[-.04694029785566792403,1.0688815349910223635 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 2, 0, 2, 0, 0, 2] 
dist 0=[52.548206084871759540  ,52.548206084871759540  ] 
dist 1=[51.471917925131352699  ,53.109062825519019704  ] 
dist 2=[50.143821678438262584  ,53.410443352028724436  ] 
dist 3=[48.577231684710525875  ,53.468873387989459964  ] 
dist 4=[46.532151407470003731  ,53.366100346008421076  ] 
dist 5=[43.293010060466121683  ,53.181828169184284079  ] 
dist 6=[39.981046613288928991  ,53.031673909246570452  ] 
dist 7=[37.645054636982670894  ,52.929188608066198302  ] 
dist 8=[35.570967532565589985  ,52.521619020823803158  ] 
dist 9=[33.304824567921174058  ,52.372492193003727938  ] 
dist 10=[31.081362553402076610  ,51.938884309032585097  ] 
dist 11=[29.177565378225248087  ,51.746128712742334086  ] 
dist 12=[27.137739772411705595  ,50.694920993613999016  ] 
dist 13=[24.370676143568613683  ,50.395947821374440337  ] 
dist 14=[21.610578562847799250  ,50.084525363689065314  ] 
dist 15=[19.598390461081240228  ,48.480731615411438892  ] 
dist 16=[17.741997183528584355  ,44.497980132084265057  ] 
dist 17=[15.603895172055412019  ,29.608571915795220047  ] 
dist 18=[13.438393774837245471  ,27.990701395164429456  ] 
dist 19=[11.472198711590528695  ,26.862925203488819531  ] 
dist 20=[9.2669913035208013113 ,23.670229370878114761  ] 
dist 21=[6.1460207647209289072 ,19.305249963570236163  ] 
dist 22=[3.0777721620848074067 ,18.545041796331775171  ] 
dist 23=[1.0830694947831268872 ,17.101375204996416202  ] 
dist 24=[-.51636740430468291404,16.767683353198090268  ] 
dist 25=[-2.0052690299774867747 ,13.810819203494036126  ] 
dist 26=[-3.3181017103572987375 ,13.332710211283350200  ] 
dist 27=[-4.2141422833677763138 ,13.204656158615640682  ] 
dist 28=[-4.9816334623693378619 ,10.963944540226255072  ] 
dist 29=[-5.7811628656879559919 ,8.7453681202583087126 ] 
dist 30=[-6.5007422542136584216 ,3.2831706896444930477 ] 
dist 31=[-6.9487717487138888294 ,2.6852535352489906409 ] 
dist 32=[-8.3821895636226700218 ,.5996671747989494805 ] 
dist 33=[-10.918531315728207033  ,-4.4523640614635420664 ] 
dist 34=[-12.489118957146195979  ,-5.1840344468727140048 ] 
dist 35=[-13.662347601236767215  ,-5.3410587048685250219 ] 
dist 36=[-14.610814062766239179  ,-5.8528143432602985332 ] 
dist 37=[-15.366620948755587087  ,-4.9757999764996867560 ] 
dist 38=[-15.769747563901840826  ,-4.0557249540266300350 ] 
dist 39=[-15.994933324840946892  ,-3.3757218958243110050 ] 
dist 40=[-16.039012475778023040  ,-2.7644876765555571843 ] 
dist 41=[-15.445100973926391034  ,-2.0890476451935064815 ] 
dist 42=[-15.308198757105089987  ,-1.4253662419361229221 ] 
dist 43=[-15.174105307774114375  ,-.8609161497677324934 ] 
dist 44=[-15.085181391491169933  ,-.26172285286844188756] 
dist 45=[-14.949026965290123655  ,.5407055773197350478 ] 
dist 46=[-14.880543488569409310  ,1.3310964733525571294 ] 
dist 47=[-14.826966632665235957  ,1.8822943831856365808 ] 
dist 48=[-14.780499131307222672  ,2.3634092693409912555 ] 
dist 49=[-4.8058450707473932038 ,2.8741532949320360337 ] 
dist 50=[-3.9912046280757766517 ,3.3643832062660457748 ] 
dist 51=[-2.1010614585242383641 ,3.7636315389737682681 ] 
dist 52=[-1.7967510403676765853 ,4.2097737863361226242 ] 
dist 53=[.63960376419994481953,4.7004343237402466218 ] 
dist 54=[1.0632744507172211035 ,5.2155641719193693064 ] 
dist 55=[1.7117739890642072854 ,5.5726810456028035303 ] 
dist 56=[1.8704629722679495988 ,5.8821087089887949147 ] 
dist 57=[1.7396176077975727471 ,6.2069630973976921930 ] 
dist 58=[1.2906227788561874355 ,6.8670123188752881947 ] 
dist 59=[.55462103765230245594,7.4335325676231942899 ] 
dist 60=[-.19693194858572324028,7.9094210752327494395 ] 
dist 61=[-.70800157012681253126,8.2910434255529437899 ] 
dist 62=[-1.1395600923349021929 ,8.4812821599381861883 ] 
dist 63=[-1.5740033986135744242 ,8.5805989344347458196 ] 
dist 64=[-1.9758576792948495805 ,8.5992490419250678341 ] 
dist 65=[-2.2774458985974516471 ,4.2471400479056791066 ] 
dist 66=[-2.5627030124456503183 ,4.1354843872979624645 ] 
dist 67=[-2.8994349647926449135 ,4.1083208812174204525 ] 
dist 68=[-3.2097656609741797061 ,3.4356816687884910053 ] 
dist 69=[-3.3897130759395770344 ,2.8515424809740736583 ] 
dist 70=[-3.5082614344325690134 ,2.5587636257874688914 ] 
dist 71=[-3.5736647053380317037 ,2.4816009849070647494 ] 
dist 72=[-3.6142711284895968748 ,2.2501595129160312974 ] 
dist 73=[-3.6338861929432987649 ,2.1387808814402369455 ] 
dist 74=[-3.6417779227154162062 ,2.0427025420991237997 ] 
dist 75=[-3.6355728527229903003 ,2.0141040260794233510 ] 
dist 76=[-1.9282113300150131087 ,.2656704096002740443 ] 
dist 77=[-2.1590893297730230067 ,-.0683708421181281398 ] 
dist 78=[-2.3359622172202200225 ,-.1306514101547201679 ] 
dist 79=[-2.4856748140807477666 ,-.2290691028489471819 ] 
dist 80=[-2.6067631577934039012 ,-.2511111994265512498 ] 
dist 81=[-2.6693887294994258090 ,-.7123076374716748519 ] 
dist 82=[-2.7015844759476624187 ,-.5776147431488706401 ] 
dist 83=[-2.7077510403447234708 ,-.36392508172288819662] 
dist 84=[-2.6861482538554308698 ,-.06275634440786380189] 
dist 85=[-2.6727605159541110227 ,.40470534330784760146] 
dist 86=[-2.7731284184492111806 ,.87555440769108239187] 
dist 87=[-2.9024135417933013828 ,1.1902449521489521566 ] 
dist 88=[-3.0560328261027588490 ,1.4503247929910095495 ] 
dist 89=[-3.1993632284521432008 ,1.7033079155639767612 ] 
dist 90=[-3.2875607752342342990 ,1.9319039852311270588 ] 
dist 91=[-3.3525177953937583638 ,2.0946936561377061260 ] 
dist 92=[-3.4030283532547861327 ,2.2402204461374890788 ] 
dist 93=[-3.4405943764109412753 ,2.3999490992996471036 ] 
dist 94=[-3.4538547206303135912 ,2.5415950702395783966 ] 
dist 95=[-3.4519288776130274520 ,2.6149744886424438856 ] 
dist 96=[-3.4458202935898225514 ,2.6548668061880952480 ] 
dist 97=[-.32684460645171762799,2.6629121725949126628 ] 
dist 98=[-.20175787669665794662,2.6360264542578861211 ] 
dist 99=[-.1724677158665177784 ,2.8749767070263180091 ] 
dist 100=[.06646520181846072610,3.1927266631356841824 ] 
dist 101=[.10708702929213306179,3.4697257151403119792 ] 
dist 102=[.14713618695291133332,3.6507050488905352070 ] 
dist 103=[.14519614047563786127,3.7837266885890852261 ] 
dist 104=[.09233712060710483752,3.8861373728817483544 ] 
dist 105=[-.06018040630096966279,3.9671839490196855773 ] 
dist 106=[-.20398301674009027608,4.0149395132019090080 ] 
dist 107=[-.31657598823793722568,4.0475105646299514531 ] 
dist 108=[-.42767702825015482248,4.0679460864746673685 ] 
dist 109=[-.56554629317944780694,4.0790847523574019618 ] 
dist 110=[-.69622473773978684447,4.0745489723939965259 ] 
dist 111=[-.77864850727025971583,4.0577094083714835171 ] 
dist 112=[-.84142083747841436117,4.0442981104821495574 ] 
dist 113=[-.89371236423162332222,1.7258582309216393361 ] 
dist 114=[-.935267783848389462  ,1.5294903100244392359 ] 
dist 115=[-.95522203064997527599,1.0575597043221545842 ] 
dist 116=[-.964649162018820192  ,.98749839586404069862] 
dist 117=[-.96504186191031513749,.32301743761707541304] 
dist 118=[-.64730294980290009736,.20339756269929577507] 
dist 119=[-.90583027895593113139,.05139481847798127293] 
dist 120=[-1.2188375233610931388 ,.01929919789617732384] 
dist 121=[-1.5139921200443590204 ,-.34369270055148673479] 
dist 122=[-1.7012748756971376128 ,-.3008967495425636057 ] 
dist 123=[-1.8453592700240976621 ,-.2620161208763433842 ] 
dist 124=[-1.9681129177675980515 ,-.2185822258311416464 ] 
dist 125=[-2.0677274303930641394 ,-.1576123649584645548 ] 
dist 126=[-2.1194660358266545463 ,-.0962436720905061127 ] 
dist 127=[-2.1469965907835628354 ,-.0512159923037425608 ] 
dist 128=[-2.1521540575458898650 ,-.0095528067300532214 ] 
dist 129=[-1.7473995723038330267 ,.0383923973931905107 ] 
dist 130=[-1.7136561526463305187 ,.0866938483858185510 ] 
dist 131=[-1.6251264463051497951 ,.1297816307219350202 ] 
dist 132=[-1.6052097959273971411 ,.1773006686535030257 ] 
dist 133=[-1.4433243235053044981 ,.2432913540442512451 ] 
dist 134=[-1.4086193155602769311 ,.3081457947320312282 ] 
dist 135=[-1.3562753684409087278 ,.3511310234774684578 ] 
dist 136=[-1.3397178599368796791 ,.3863320010685642045 ] 
dist 137=[-.9758865145436132681 ,.4201181871755515269 ] 
dist 138=[-.9262556804829596752 ,.45041535626799189914] 
dist 139=[-.8147114574815289853 ,.47169145789675314343] 
dist 140=[-.7870760623020248995 ,.49044044344889044295] 
dist 141=[-.6453865585499273674 ,.51065259358436009991] 
dist 142=[-.6183409941592683580 ,.5283701000471015556 ] 
dist 143=[-.5590521758776720954 ,.53716267838160831209] 
dist 144=[-.5421820091005778263 ,.80685985883101238718] 
dist 145=[-.10178672532876506272,1.0791504008777617225 ] 
dist 146=[-.0684433444152695249 ,1.2578902305303154844 ] 
dist 147=[-.1156932000594041134 ,1.4023175053533669734 ] 
dist 148=[-.1731526880182134757 ,1.5479313941455731465 ] 
dist 149=[-.2595487469644903891 ,1.6899534479842593517 ] 
dist 150=[-.3452683107467497562 ,1.7900334156736201329 ] 
dist 151=[-.4000286288809402874 ,1.8785553803661204522 ] 
dist 152=[-.4425838148613822987 ,1.9744524186457537655 ] 
dist 153=[-.4795941417411189042 ,2.0587102299198294177 ] 
dist 154=[-.51106429822357670495,2.1007804387923368577 ] 
dist 155=[-.54691640346135962288,2.1221613377475250038 ] 
dist 156=[-.57679418026497088884,2.1246352696670454499 ] 
dist 157=[-.6063165316939355748 ,2.0986126154627997541 ] 
dist 158=[-.6319975586893190245 ,2.0873244128808662989 ] 
dist 159=[-.6465452717304113043 ,2.0762581101100355881 ] 
dist 160=[-.82087255390315803591,2.0656290547184942291 ] 
dist 161=[-1.0824583879448802527 ,-.43563119304709698737] 
dist 162=[-1.2608403993963609464 ,-.39217461794400091368] 
dist 163=[-1.4015181422473727579 ,-.34320170051642615331] 
dist 164=[-1.5274503046182356972 ,-.28082475610265695618] 
dist 165=[-1.6342144507392467492 ,-.18387457478496759518] 
dist 166=[-1.7383799594391068268 ,-.08591603734831021582] 
dist 167=[-1.8589067641238667023 ,-.01951484990042029184] 
dist 168=[-1.9849785108907491114 ,.03646155498188548693] 
dist 169=[-2.0972903424439474153 ,.09281633517164516215] 
dist 170=[-2.1629041352358096064 ,.1483276566435799674 ] 
dist 171=[-2.2068530169620837487 ,.1923712930105550179 ] 
dist 172=[-2.2327038290880394390 ,.2346055782788451171 ] 
dist 173=[-2.2456976886541996285 ,.2853926852596549133 ] 
dist 174=[-2.2460602287277340137 ,.3329231876578475577 ] 
dist 175=[-2.2262427727583243498 ,.3621611358964981508 ] 
dist 176=[-2.2203479010723204224 ,.3835887505983446003 ] 
dist 177=[-1.4987450016933588149 ,.3999492913886719507 ] 
dist 178=[-1.4404246668296830634 ,.4550848015134485824 ] 
dist 179=[-1.2914456137080517979 ,.62947639819639892931] 
dist 180=[-1.2677793799334984172 ,.79787204420986744933] 
dist 181=[-1.0218606721845890121 ,.94942603357179410504] 
dist 182=[-.97353767707648402701,1.0566059290351438261 ] 
dist 183=[-.91687717839788679639,1.1517538710141930534 ] 
dist 184=[-.90039991384329153487,1.2552895418655992743 ] 
dist 185=[-.43438736770629324875,1.3492500556840860705 ] 
dist 186=[-.37543720543002966795,1.4061863299201502881 ] 
dist 187=[-.25099034174584255179,1.4468730642935657932 ] 
dist 188=[-.21840320240986217964,1.4759886910551511393 ] 
dist 189=[-.09332204232528057472,1.4954198633928076201 ] 
dist 190=[-.06924033281900344727,1.4993406214049787764 ] 
dist 191=[-.0931175627406740875 ,1.4940609194885319850 ] 
dist 192=[-.1188630014905328971 ,1.4917805336279770608 ] 
dist 193=[-.1498115889600185293 ,.25527812751884495739] 
dist 194=[-.1817245258383845582 ,.24802623987639237312] 
dist 195=[-.2113193994986782618 ,.23238292948047517496] 
dist 196=[-.2448776852613336794 ,.22770080181412460287] 
dist 197=[-.2926093520184224051 ,.20739735121472574162] 
dist 198=[-.3390301611481662824 ,.21016399250001427427] 
dist 199=[-.3673573449447836515 ,.22673486649628442425] 
dist 200=[-.3878500706864343401 ,.24004518423644745309] 
dist 201=[-.4132700667553409286 ,.25236762828786602357] 
dist 202=[-.4467049081197083261 ,.26309664492605653107] 
dist 203=[-.4691725054085416092 ,.27004852125643213972] 
dist 204=[-.4879022675528665999 ,.27555686704100706879] 
dist 205=[-.5064203536824947552 ,.28052532197547263928] 
dist 206=[-.5219416475750993153 ,.28431212612860253662] 
dist 207=[-.5287117164179771450 ,.2851052039495143140 ] 
dist 208=[-.5315226555408354915 ,.2846451917626678246 ] 
dist 209=[-.5312432207674428518 ,.2835183774370674624 ] 
dist 210=[-.5190650079957805502 ,.2744889464827651927 ] 
dist 211=[-.5146782054465852413 ,.2716907465327713571 ] 
dist 212=[-.5109340952578747621 ,.2672630901934568895 ] 
dist 213=[-.5078722234478528363 ,.2655501016124090312 ] 
dist 214=[-.44781502052966034961,.2756980078398387694 ] 
dist 215=[-.45504764096989539139,.3100711429712274363 ] 
dist 216=[-.45758671417217900772,.3370883219475040911 ] 
dist 217=[-.4579785452620672899 ,.3611147598967383632 ] 
dist 218=[-.45664526734416678758,.3813679574174024115 ] 
dist 219=[-.45396732642021877966,.4031139568600573204 ] 
dist 220=[-.45225968539320927765,.4370917511316730202 ] 
dist 221=[-.44124601092151189743,.4747253039613407247 ] 
dist 222=[-.43817067017694442578,.5087832907675689534 ] 
dist 223=[-.42705694208838840018,.5284917704591940036 ] 
dist 224=[-.4248282300778104008 ,.5414546907301932927 ] 
dist 225=[.03885138414165250337,.5485925052107004964 ] 
dist 226=[.07001887052065463405,.5525354093353308176 ] 
dist 227=[.07421334915630008300,.5527481602488874245 ] 
dist 228=[.03639256524707940286,.5508203844195658586 ] 
dist 229=[-.02389943612983258356,.5489609706788583915 ] 
dist 230=[-.08520050829897586640,.4776030649334185800 ] 
dist 231=[-.13669293749472942964,.4825479896621222750 ] 
dist 232=[-.18364537855451490147,.4842781847264575295 ] 
dist 233=[-.22872401544267270417,.4837740906057979352 ] 
dist 234=[-.2691229665058761522 ,.4708027812674336603 ] 
dist 235=[-.2973999080385520929 ,.4663846657742771246 ] 
dist 236=[-.3222000210314182058 ,.4625117694090062053 ] 
dist 237=[-.3487237389527277465 ,.4595927410896346130 ] 
dist 238=[-.3726706710960456921 ,.37341397991975539614] 
dist 239=[-.3871874751762563088 ,.36098567634253720062] 
dist 240=[-.3975697012678094150 ,.31363211348241209352] 
dist 241=[-.4050166441134689628 ,.07027038678850782250] 
dist 242=[-.4100021849989441947 ,.03597685952641772624] 
dist 243=[-.4108743860402554500 ,.02949273658865346787] 
dist 244=[-.4095867040078600019 ,.01597069444376478697] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 1, 1, 2, 2, 0, 2] 
dist 0=[60.734858222831461212  ,60.734858222831461212  ] 
dist 1=[59.782560731793168570  ,61.195466383129639054  ] 
dist 2=[58.654470417672569837  ,61.399599746105687444  ] 
dist 3=[57.491867241963681336  ,61.411294977707219382  ] 
dist 4=[56.079047535798121696  ,61.050857153941951939  ] 
dist 5=[53.951583679599947136  ,60.830536572776380704  ] 
dist 6=[51.521840635711315524  ,60.488451335900284203  ] 
dist 7=[48.901779584183573540  ,60.341543183352842777  ] 
dist 8=[45.634461362638411981  ,59.396891793782449713  ] 
dist 9=[40.619757550470260649  ,55.612104665846510488  ] 
dist 10=[35.554888733015313477  ,54.686319609434112965  ] 
dist 11=[32.087139175186063192  ,54.357371643613943529  ] 
dist 12=[29.117293654915742693  ,53.924807321127124445  ] 
dist 13=[26.040651437862625439  ,52.786424896094950329  ] 
dist 14=[23.121464406061652497  ,46.929139390549987159  ] 
dist 15=[20.780212110230296152  ,43.113465529494713863  ] 
dist 16=[18.407292586888504289  ,40.507515704619220413  ] 
dist 17=[15.361187766938451207  ,31.374343620557932096  ] 
dist 18=[12.400625723700339378  ,30.215229024323066292  ] 
dist 19=[10.369096387808847364  ,27.936510785265877574  ] 
dist 20=[8.6219638579538830847 ,27.356929898762935256  ] 
dist 21=[6.7969243425804698243 ,25.361576900075430083  ] 
dist 22=[5.0517099179608452039 ,24.904949747170493350  ] 
dist 23=[3.5768776592492228648 ,24.396983253947184976  ] 
dist 24=[.58213009984827885416,24.277940380308204213  ] 
dist 25=[-1.3751927463087941463 ,6.2801442302094733237 ] 
dist 26=[-2.9546942724337196660 ,3.9707361609020267027 ] 
dist 27=[-4.4410005075365251440 ,1.2263803900707852756 ] 
dist 28=[-5.7635886577096755348 ,.6898818982187631258 ] 
dist 29=[-6.6899106617733492734 ,.1521863571911836451 ] 
dist 30=[-7.5113501200641420637 ,-1.5775020468557111152 ] 
dist 31=[-8.7745220549135846574 ,-2.2848779649111103985 ] 
dist 32=[-10.821349360993420781  ,-5.8183361642529277414 ] 
dist 33=[-12.748177726882580924  ,-5.8805156767056593514 ] 
dist 34=[-13.964834987008608228  ,-6.3481182064350565174 ] 
dist 35=[-14.898015298267788838  ,-6.3526357568851106423 ] 
dist 36=[-15.692577137247715686  ,-6.2514568825140039514 ] 
dist 37=[-16.340470222865687485  ,-5.9828268293932495202 ] 
dist 38=[-16.687862357881760570  ,-5.6295872070930882512 ] 
dist 39=[-16.883153003024674148  ,-5.1904281178113037406 ] 
dist 40=[-16.923627598365966503  ,-3.3009224261763191321 ] 
dist 41=[-8.2746770887718735344 ,-1.2417302814134912242 ] 
dist 42=[-7.8230331220618992160 ,.16174548465188318891] 
dist 43=[-7.6944110085279929679 ,1.3510866051208053649 ] 
dist 44=[-7.1829985772717476851 ,2.5562830658728374812 ] 
dist 45=[-7.0639456394053807776 ,3.6773865552884729474 ] 
dist 46=[-6.8112844738815434632 ,4.5314111297353167010 ] 
dist 47=[-6.7327738246238201858 ,5.3525582644030611894 ] 
dist 48=[-1.1566019208411170467 ,6.3427258608563272994 ] 
dist 49=[-.66341872018344438988,7.2688620465933029856 ] 
dist 50=[.39572087854097821624,7.8346201494445042626 ] 
dist 51=[.62737987077128663521,8.2448376290636794908 ] 
dist 52=[1.2186602893805257871 ,8.5504129190461165191 ] 
dist 53=[1.2713453992788067267 ,8.7736329116413269666 ] 
dist 54=[1.6306360793196684163 ,8.8550877099549887834 ] 
dist 55=[1.6845198683763311723 ,8.8749358690172338951 ] 
dist 56=[1.7843755671553867576 ,8.8523573177628639893 ] 
dist 57=[1.8008824424301801379 ,8.2785301486585255546 ] 
dist 58=[1.7985074989059918204 ,8.1734868649683240448 ] 
dist 59=[1.4636511959026516139 ,7.8515225771402657282 ] 
dist 60=[1.0829789860721070855 ,7.7889418166646487415 ] 
dist 61=[.7034713629868134531 ,7.0562389358125805574 ] 
dist 62=[.3731327525499017914 ,6.8935582501895358546 ] 
dist 63=[-.2345636363826912188 ,6.1070007613515926243 ] 
dist 64=[-1.2468811300293993481 ,3.3196678853290199441 ] 
dist 65=[-1.9068463730768366357 ,2.4892385573311523678 ] 
dist 66=[-2.4345746630316732332 ,2.3777164513401542094 ] 
dist 67=[-2.9192763203404312859 ,2.1131700409026245567 ] 
dist 68=[-3.3389260630978052526 ,2.0638606513674244545 ] 
dist 69=[-3.6071142738004824090 ,1.8658878455232978250 ] 
dist 70=[-3.8157152345848070956 ,1.7402357083579660636 ] 
dist 71=[-3.9976550238580710702 ,1.7126957061928539233 ] 
dist 72=[-4.1514938674780599739 ,1.6714731261585090553 ] 
dist 73=[-4.2479619363666657048 ,1.6580568656051760252 ] 
dist 74=[-4.3210664847849580816 ,1.1021263073680871567 ] 
dist 75=[-4.3816129567514007844 ,1.0399011174834863421 ] 
dist 76=[-4.4296093570538326506 ,.89475951177400589822] 
dist 77=[-4.4525996153935752808 ,.86587608438166695881] 
dist 78=[-4.4617328341673047471 ,.6657007450188214384 ] 
dist 79=[-4.4543957142969374582 ,.62755740380751273168] 
dist 80=[-4.3506321355310145930 ,.56111578575510361358] 
dist 81=[-4.5017217958957107779 ,.54530778588009799048] 
dist 82=[-4.5731256294737931871 ,.26019319443496483915] 
dist 83=[-4.6066831713030224369 ,.22226210484798706879] 
dist 84=[-4.6067040860480790393 ,.2946763672519583523 ] 
dist 85=[-4.5323420633558827184 ,.6162781508936999478 ] 
dist 86=[-4.5022620651097867475 ,.93485400471509823428] 
dist 87=[-4.4744173091442754917 ,1.3319252493328323484 ] 
dist 88=[-4.4511819627793334466 ,1.7090679201356551506 ] 
dist 89=[-3.3635967011047269018 ,1.9481390232058890269 ] 
dist 90=[-3.2363112789339175053 ,2.1314959345040191408 ] 
dist 91=[-2.9173620592954328354 ,2.2863596159842606955 ] 
dist 92=[-2.8615218779732748635 ,2.4107669061093444160 ] 
dist 93=[-2.3490446928465742608 ,2.4726124223743740815 ] 
dist 94=[-2.2477821563475364152 ,2.6470823584403695649 ] 
dist 95=[-2.1138314060785509815 ,2.9005031682617348373 ] 
dist 96=[-2.0686382825836737326 ,3.1761161304892631259 ] 
dist 97=[-1.1278220196295738344 ,3.4262480362662643368 ] 
dist 98=[-1.0052980112793666241 ,3.5779724652513859096 ] 
dist 99=[-.73862420729061266836,3.6867550075997900463 ] 
dist 100=[-.67364052550296058094,3.7654726030888103106 ] 
dist 101=[-.37128752048496620512,3.8189013142135875963 ] 
dist 102=[-.31704896633194275168,3.8301370754108887772 ] 
dist 103=[-.18675032332688220512,3.8197813162081699594 ] 
dist 104=[-.3000512368314983612 ,3.8141769489222099259 ] 
dist 105=[-.4775686778228743465 ,2.5434117517548387168 ] 
dist 106=[-.6407898729353499061 ,2.4233998311021198506 ] 
dist 107=[-.8686160156772937375 ,2.1226070136628245095 ] 
dist 108=[-1.1432333459521651454 ,2.0760436294227681482 ] 
dist 109=[-1.3903050876761291744 ,1.6032304906281418336 ] 
dist 110=[-1.5645762419873210135 ,1.5127668281703864672 ] 
dist 111=[-1.7186877023556098758 ,1.4044473050829380739 ] 
dist 112=[-1.8853139839792863533 ,1.3760093525987052757 ] 
dist 113=[-2.0364674431034444990 ,1.0258489834392170783 ] 
dist 114=[-2.1493875234896360806 ,1.0384928342461275686 ] 
dist 115=[-2.2385231528781993538 ,1.0426407083797421780 ] 
dist 116=[-2.3061334848821545059 ,1.0544937136657768393 ] 
dist 117=[-2.3356498683228471336 ,1.0934998165908498816 ] 
dist 118=[-2.3468788504861275956 ,1.1307568787978246607 ] 
dist 119=[-2.3440924810254895813 ,1.1751966680691260265 ] 
dist 120=[-2.2098190229333883320 ,1.2162708092822215766 ] 
dist 121=[-2.1817842766415523218 ,1.2401025244751084947 ] 
dist 122=[-2.1264621990343363715 ,1.2557721531404875200 ] 
dist 123=[-2.1077552540848492496 ,1.2642923697046124799 ] 
dist 124=[-2.0198645869688737991 ,1.2674856262980258630 ] 
dist 125=[-2.1119841103846250654 ,1.2650579444651051394 ] 
dist 126=[-2.2162154351161796418 ,1.2531431907498279684 ] 
dist 127=[-2.3132898385627854977 ,1.2451439418140796874 ] 
dist 128=[-2.4260857272876670716 ,-.8042878877377082711 ] 
dist 129=[-2.5296512475028676832 ,-.77340808087836479143] 
dist 130=[-2.5898813944060230768 ,-.61060806418887436479] 
dist 131=[-2.6299628085917724489 ,-.42899133216803506698] 
dist 132=[-2.6530975293181812358 ,-.17432289427664849415] 
dist 133=[-2.6636233793431730891 ,.10771466838316204962] 
dist 134=[-2.6623560547594597635 ,.39857133159228720098] 
dist 135=[-2.6383071644026278634 ,.75153783960633740575] 
dist 136=[-2.6295934871862878059 ,1.2814670399929266253 ] 
dist 137=[-1.4409244569214528682 ,1.8072275659530294253 ] 
dist 138=[-.8436454723722850787 ,2.1435607777355287574 ] 
dist 139=[-.8170703236500437168 ,2.4054847212722582662 ] 
dist 140=[-.7467456314210227806 ,2.6342780864673439003 ] 
dist 141=[-.7366518311727662318 ,2.8242191541229788813 ] 
dist 142=[-.61274676326312269949,2.9767133201722439208 ] 
dist 143=[-.58798403942873056788,3.0968824952289337932 ] 
dist 144=[-.56350364105076930317,3.1988987009608691174 ] 
dist 145=[-.55892664785712538224,3.2828434454459867714 ] 
dist 146=[-.29478323549899549746,3.3308901358419766262 ] 
dist 147=[-.26173013187512742756,3.3618455137514695339 ] 
dist 148=[-.19552896032821622774,3.3775788060236570070 ] 
dist 149=[-.17863113804085013422,3.3823396115771416604 ] 
dist 150=[-.11984063106639343801,3.3749385334304820189 ] 
dist 151=[-.10696136302226252857,3.3487567926033196376 ] 
dist 152=[-.09212874366193428629,3.3318095897493938954 ] 
dist 153=[-.08928564302873125434,1.6329909926342593594 ] 
dist 154=[.4132934045032990112 ,1.4830600820008787412 ] 
dist 155=[.09886951010063799624,1.1197011355942307518 ] 
dist 156=[-.21783342885799763629,1.0655244621412044431 ] 
dist 157=[-.51163321493065885274,.5417817612324353625 ] 
dist 158=[-.73465724269414030481,.46240688595774158509] 
dist 159=[-.94848722452992638468,.4774627528656055627 ] 
dist 160=[-1.2056001037911571023 ,.50003387623236256981] 
dist 161=[-1.4473265946436719773 ,.53874194864329255486] 
dist 162=[-1.5997518920472378015 ,.58075271747234257802] 
dist 163=[-1.7159151306299969105 ,.61650368664526456663] 
dist 164=[-1.8129203009211721621 ,.65449307723139920774] 
dist 165=[-1.8901527396767945311 ,.70543698290546793356] 
dist 166=[-1.9274031261075522763 ,.76077079980587685209] 
dist 167=[-1.9462746565442131896 ,.81627873722727420841] 
dist 168=[-1.9501601937606070782 ,.8825128787977191646 ] 
dist 169=[-1.6668686768746436742 ,.9806506745305718409 ] 
dist 170=[-1.6372543911553754087 ,1.0775848225115562260 ] 
dist 171=[-1.5561636019476996557 ,1.1390158239842415069 ] 
dist 172=[-1.6211383419825991407 ,1.1861668232569593848 ] 
dist 173=[-1.7040837128174566424 ,1.2261156072586448271 ] 
dist 174=[-1.7695110708469996059 ,1.2583465396656621157 ] 
dist 175=[-1.8037304950025136691 ,1.2746988810744107643 ] 
dist 176=[-1.8216318406111441283 ,1.2825407280843023709 ] 
dist 177=[-1.8239108828164980812 ,1.2820012399662407633 ] 
dist 178=[-1.7223466748324976319 ,1.2735135995979821485 ] 
dist 179=[-1.7018029576039102966 ,1.2689829708474899122 ] 
dist 180=[-1.6755750902307056046 ,1.2455773493649303213 ] 
dist 181=[-1.6635005062179103710 ,1.2414665123333885942 ] 
dist 182=[-1.6355952493528819183 ,1.1591633800779234086 ] 
dist 183=[-1.6222200314407211886 ,1.1392157733630020076 ] 
dist 184=[-1.6088185139567513524 ,1.1240819072015602181 ] 
dist 185=[-1.5996097715197220016 ,1.1186152625105352376 ] 
dist 186=[-.37286461820922496427,1.0850741657547678644 ] 
dist 187=[-.26953316893890873549,1.1898436697409963104 ] 
dist 188=[-.0433002140602986209 ,1.3272139661559151575 ] 
dist 189=[.00358783018609955893,1.4651330595056750538 ] 
dist 190=[-.00851458152956148139,1.5659843714588076113 ] 
dist 191=[-.03304601418728021338,1.6589811384778925292 ] 
dist 192=[-.08091762599876250850,1.7655555473867113922 ] 
dist 193=[-.13493420622410307614,1.8624498859284352814 ] 
dist 194=[-.1932945611965053593 ,1.9168147400416713017 ] 
dist 195=[-.3357685661511521118 ,1.9504349655620807432 ] 
dist 196=[-.47176658047465845864,1.9645383812581223305 ] 
dist 197=[-.63441459247449727649,1.9686984335453457080 ] 
dist 198=[-.8016756510344506467 ,1.9646471834685564620 ] 
dist 199=[-.9560847946333920000 ,1.9513818668179724479 ] 
dist 200=[-1.1306041472859077657 ,1.9423530279794440772 ] 
dist 201=[-1.3781234830125804816 ,.67009809869795926615] 
dist 202=[-1.6196810285111623123 ,.73859289917904701116] 
dist 203=[-1.7704082536649732525 ,.78644573820336185664] 
dist 204=[-1.8834145588633120069 ,.82831637647386472241] 
dist 205=[-1.9744335520677846143 ,.8729380783755808463 ] 
dist 206=[-2.0456695473337609634 ,.91588246971521247667] 
dist 207=[-2.0797244939954679989 ,.9510593213431497719 ] 
dist 208=[-2.0956607281821771145 ,.98726357737947922478] 
dist 209=[-2.0960307166067246109 ,1.0343075366137846319 ] 
dist 210=[-2.0113057865221204873 ,1.0800046830007218912 ] 
dist 211=[-1.9911789918166872689 ,1.1108341163243001266 ] 
dist 212=[-1.9565114818662683570 ,1.1366577352289586951 ] 
dist 213=[-1.9443467686501879914 ,1.1623783865118376749 ] 
dist 214=[-1.7261619529338134095 ,1.1860431917890998552 ] 
dist 215=[-1.7194586645686378403 ,1.2036624175779185502 ] 
dist 216=[-1.7143620992422980846 ,1.2202146987072515586 ] 
dist 217=[-1.2954415303591361668 ,1.2396210591463321148 ] 
dist 218=[-1.2492146580183127436 ,1.2559430215788120413 ] 
dist 219=[-1.1293279304538873593 ,1.2601864204722017985 ] 
dist 220=[-1.1108835294367187609 ,1.2585229460823787738 ] 
dist 221=[-.90718484633357805351,1.2546012088201374239 ] 
dist 222=[-.86683333075955648712,1.2216288665794328336 ] 
dist 223=[-.82228407341897026013,1.2112195407731805485 ] 
dist 224=[-.81075805683164934196,1.1891015589131252510 ] 
dist 225=[-.40495720793132377278,1.1805366763955569859 ] 
dist 226=[-.3538441296716710733 ,1.1794372220398873965 ] 
dist 227=[-.24792764228266009865,1.2140096928436675344 ] 
dist 228=[-.22018289692969592423,1.2372497187512475258 ] 
dist 229=[-.11838021249958079793,1.2522980898481676683 ] 
dist 230=[-.09784881404338301825,1.2548059315511668449 ] 
dist 231=[-.06212502444147899239,1.2512786865319015297 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 1, 1, 0, 0, 2] 
dist 0=[49.058905312984869267  ,49.058905312984869267  ] 
dist 1=[48.674754268266718111  ,49.682569207274937191  ] 
dist 2=[47.764496015250148534  ,50.333329668887537863  ] 
dist 3=[46.309727518293996217  ,50.643752193286663289  ] 
dist 4=[43.953281383611671671  ,50.779546100895951235  ] 
dist 5=[41.525483778489109741  ,50.782694597119882168  ] 
dist 6=[39.785654698556819040  ,50.463356403393522012  ] 
dist 7=[38.212587667877176821  ,50.080330214954904292  ] 
dist 8=[36.450543349248062504  ,49.027754325862891864  ] 
dist 9=[34.696148255821985593  ,48.888290953792491093  ] 
dist 10=[33.153409409949947915  ,48.348612234884908216  ] 
dist 11=[31.465514988242876405  ,48.172322678219063225  ] 
dist 12=[29.130998223253432180  ,47.770690776257313631  ] 
dist 13=[26.781225240107084430  ,47.613794762579395553  ] 
dist 14=[25.032183258262985521  ,46.846882320638614299  ] 
dist 15=[23.381916133277381360  ,45.961835973289095138  ] 
dist 16=[21.426380736014148145  ,29.416607647168688622  ] 
dist 17=[19.414401338171960175  ,28.975962211544399994  ] 
dist 18=[17.538292817949849840  ,24.585588907113044772  ] 
dist 19=[15.393751907913243667  ,23.769378078816163850  ] 
dist 20=[12.308715765854802238  ,23.084865426277406278  ] 
dist 21=[9.2522431346663616481 ,22.619758063691463158  ] 
dist 22=[7.2217251850490629940 ,16.286708297110805625  ] 
dist 23=[5.5441764688751302936 ,15.959660387895706397  ] 
dist 24=[3.8982233254922444196 ,13.563032470993848576  ] 
dist 25=[2.3886792950005900326 ,13.163788873020702786  ] 
dist 26=[1.2561819325884279638 ,12.762009684094518011  ] 
dist 27=[-.11451810749761966022,11.676938566239753618  ] 
dist 28=[-2.1092401195056002192 ,10.092165894811165456  ] 
dist 29=[-3.8345693245019039264 ,9.9665964523629052615 ] 
dist 30=[-5.7019802547214820275 ,2.9597173503703943510 ] 
dist 31=[-8.2653512045519924702 ,.74895179886094492502] 
dist 32=[-10.744702198351844085  ,-2.0449271069319462345 ] 
dist 33=[-12.276634137366858860  ,-2.3411860247784742138 ] 
dist 34=[-13.417424462775253642  ,-2.3041789468856886094 ] 
dist 35=[-14.333668568846428249  ,-2.1436181067101068751 ] 
dist 36=[-15.062261323776787264  ,-1.7765924126917819428 ] 
dist 37=[-15.452916012155453144  ,-1.3711298550000369636 ] 
dist 38=[-15.674105213047184729  ,-1.0570053561209691619 ] 
dist 39=[-15.724776338100426577  ,-.75204192265217103159] 
dist 40=[-15.055412242376118644  ,-.38259682390224125329] 
dist 41=[-14.912369169398025386  ,-.00210571729938905076] 
dist 42=[-14.768594549175639260  ,.34717237660212252656] 
dist 43=[-14.678143700613635965  ,.73940153361665389285] 
dist 44=[-14.546968582552482674  ,1.2914561305125566173 ] 
dist 45=[-14.487083616537388462  ,1.8465146792896369603 ] 
dist 46=[-14.447537156326269478  ,2.2508310244380705790 ] 
dist 47=[-14.426239952445685243  ,2.6215644713787772422 ] 
dist 48=[-4.7736940154551979026 ,3.0427433664812163625 ] 
dist 49=[-4.4686283751072163838 ,3.4636548519567914233 ] 
dist 50=[-4.4058797529001295782 ,3.8333874510327961471 ] 
dist 51=[-4.2349730694567038822 ,4.2362441636904336131 ] 
dist 52=[-4.2040329195045179996 ,4.7894039947663756492 ] 
dist 53=[1.3444386203550098384 ,5.3352980724486861362 ] 
dist 54=[1.9795417614060831847 ,5.7091775334170237224 ] 
dist 55=[2.1358399849727669688 ,6.0285639033857267729 ] 
dist 56=[3.8839385624710901975 ,6.3569883803968931110 ] 
dist 57=[3.6432890286713998306 ,6.6660112767031394245 ] 
dist 58=[3.3173690754589459350 ,7.1310197974366549671 ] 
dist 59=[2.8993902649004784878 ,7.6200451564402497190 ] 
dist 60=[2.3348435574910805708 ,8.0203454322939279855 ] 
dist 61=[1.4241295096502614711 ,8.2357796808826963245 ] 
dist 62=[.49755600438192711946,8.3573109523726962964 ] 
dist 63=[-.13029273090173126197,8.3827838462621739450 ] 
dist 64=[-.65847394764402498934,3.8848021004778273765 ] 
dist 65=[-1.1874525343096190193 ,3.6814256375660116920 ] 
dist 66=[-1.6753744068370254238 ,3.1768362575356050700 ] 
dist 67=[-2.0397690297430026064 ,3.0995420053695015906 ] 
dist 68=[-2.3828579384442875408 ,2.4915886220118891359 ] 
dist 69=[-2.7857806077317118273 ,2.4358557115810839155 ] 
dist 70=[-3.1602329800600011112 ,2.0073653741255896369 ] 
dist 71=[-3.3897354081151106108 ,1.9632284916507509808 ] 
dist 72=[-3.5566033598195726262 ,.83293025115502985705] 
dist 73=[-3.6811641419394888349 ,.76387230015648135447] 
dist 74=[-3.7729671366093213492 ,.39865694226395744991] 
dist 75=[-3.8091475415451380514 ,.335659826459848468  ] 
dist 76=[-3.8188816275926319397 ,.19633623636451083808] 
dist 77=[-3.8106135874181769624 ,.17100000859179461115] 
dist 78=[-2.9445293550002707802 ,-.33345909248466865022] 
dist 79=[-3.1715733550056125313 ,-.35942287787124438977] 
dist 80=[-3.3448325533876278748 ,-1.2844763190597363014 ] 
dist 81=[-3.4901973729765635843 ,-1.3171625504266316176 ] 
dist 82=[-3.6067169600460574470 ,-1.5548899486008853882 ] 
dist 83=[-3.6648505557569666225 ,-1.5896333775885117797 ] 
dist 84=[-3.6915077165930031702 ,-1.6202343340865110128 ] 
dist 85=[-3.6936869317906272645 ,-1.5661700308323489109 ] 
dist 86=[-3.6565272986162841178 ,-1.4620045693118465496 ] 
dist 87=[-3.6400998628597403071 ,-1.2626741508902400570 ] 
dist 88=[-3.5768498680207624129 ,-1.0393905394447370577 ] 
dist 89=[-3.5552903579378248592 ,-.839601165981961188  ] 
dist 90=[-3.3587623978212439353 ,-.61899624910315586252] 
dist 91=[-3.3092621019027060392 ,-.3125760514406988624 ] 
dist 92=[-3.2980337033056003168 ,.02536106668616388432] 
dist 93=[-3.2935771511039282230 ,.82781328372262724749] 
dist 94=[-3.2594673752517447386 ,1.6945549047413246834 ] 
dist 95=[-3.2465072785820010207 ,2.2653165094274816773 ] 
dist 96=[-1.6310354803316177721 ,2.7282744848895654296 ] 
dist 97=[-1.5522750729706586148 ,3.1648083864932608131 ] 
dist 98=[-1.2305686093954114258 ,3.5506633772475685408 ] 
dist 99=[-1.1693641230710309943 ,3.8113776433068287361 ] 
dist 100=[-1.0204874082494783362 ,4.0302141706526749006 ] 
dist 101=[-.99438632011762217419,4.2489457227129140554 ] 
dist 102=[-.77496172638692064395,4.4399757508913873641 ] 
dist 103=[-.73003333745401879664,4.5482635155323305895 ] 
dist 104=[-.69959861230091689739,4.6166087722270878286 ] 
dist 105=[-.70836798922097834815,4.6482415761654387244 ] 
dist 106=[-.7371195516759299901 ,4.6555710987254052895 ] 
dist 107=[-.79329809193139552384,4.6269295778945615331 ] 
dist 108=[-.88019175882448581624,4.3338333603741208378 ] 
dist 109=[-1.0314943143708230421 ,4.0729656161641630821 ] 
dist 110=[-1.1883735307406824469 ,3.5078900285657792638 ] 
dist 111=[-1.2975228032328696592 ,3.4999451996382116514 ] 
dist 112=[-1.3924321991129281371 ,1.1147612525080114791 ] 
dist 113=[-1.4925105855583980820 ,.92007055117352290666] 
dist 114=[-1.5880744675015667722 ,.46890766880595720485] 
dist 115=[-1.6649798113064841346 ,.39380227756105545056] 
dist 116=[-1.7428507513172786928 ,.3706685487696049914 ] 
dist 117=[-1.8422772627380767287 ,.3644141394050370285 ] 
dist 118=[-1.9379614201276774715 ,.30353771614787939558] 
dist 119=[-2.0009059187611110747 ,.29380425966098166816] 
dist 120=[-2.0518721701169147674 ,.27361240504891969737] 
dist 121=[-2.0997697091506754383 ,.26807166135270050129] 
dist 122=[-2.1420152252032458515 ,.24635558118617590602] 
dist 123=[-2.1704369168831780852 ,.24188565598804206891] 
dist 124=[-2.1941977737415329840 ,.23159036269021576587] 
dist 125=[-2.2178608113475023584 ,.22873985952657132275] 
dist 126=[-2.2368382158870251418 ,.21356821926053453925] 
dist 127=[-2.2419041045904187287 ,.21000429473595804088] 
dist 128=[-1.1580223847130038781 ,.20472399443628061076] 
dist 129=[-1.1046059362698353915 ,.2029443834196460659 ] 
dist 130=[-.96899506481190730167,.19811267081279600831] 
dist 131=[-.94925976915667731249,.19624204332716626206] 
dist 132=[-.73133257431897275578,.19349589165606243493] 
dist 133=[-.68956323133392457917,.19229667518918142954] 
dist 134=[-.64376705297985384107,.18763618339223793501] 
dist 135=[-.63484976058758834825,.18578318201346943154] 
dist 136=[-.54285449299823604735,.18260103189469096503] 
dist 137=[-.54059108293936859851,.18136838084834877902] 
dist 138=[-.53574219802082012736,.17517345207738664853] 
dist 139=[-.53284223630533035654,.17337069743190422897] 
dist 140=[-.5272277020115533073 ,.16760265861497648025] 
dist 141=[-.52479793105014849249,.24923230811205992696] 
dist 142=[-.10783780337751277295,.33904541687518709187] 
dist 143=[-.07653084392524136076,.46001728473085855305] 
dist 144=[-.00585353697231647282,.57863684669601756473] 
dist 145=[.00666264651907902973,.6590640259085262906 ] 
dist 146=[.09124564706149074086,.72696310775824264771] 
dist 147=[.10555176638101693162,.79557359474226279289] 
dist 148=[.13178029732169416831,.85944126859403936799] 
dist 149=[.13730950508924331974,.90840855793509559136] 
dist 150=[.19611830670023304712,.95587248336217058402] 
dist 151=[.20456591604775492202,1.0137401598143044580 ] 
dist 152=[.20543512962926362016,1.0682869426383984783 ] 
dist 153=[.19346854761694838162,1.1024946179430708456 ] 
dist 154=[.176218964171276048  ,1.1283793778089396749 ] 
dist 155=[.15287469373980677254,1.1497019134449150523 ] 
dist 156=[.04193715729166090283,1.1664810959495216924 ] 
dist 157=[-.09725992161181340651,1.1742294981086465021 ] 
dist 158=[-.26664900059740625313,1.1768557342661583713 ] 
dist 159=[-.52148466220841159337,1.1747381602462497080 ] 
dist 160=[-.77477755041076435258,.39377789933236745259] 
dist 161=[-.93801116375714314787,.39210260406988107406] 
dist 162=[-1.0665024404255613910 ,.36989232202802372991] 
dist 163=[-1.1858240538269293852 ,.36559150636510943105] 
dist 164=[-1.2883250739260531446 ,.35848665249431974412] 
dist 165=[-1.3509753763234348944 ,.3560753860185538369 ] 
dist 166=[-1.3964211709581910972 ,.29532003503604529238] 
dist 167=[-1.4302603095996661687 ,.28651628212605093589] 
dist 168=[-1.4564647410892673241 ,.2668922055694010768 ] 
dist 169=[-1.4714409580824498152 ,.26099951148603449028] 
dist 170=[-1.4810631907309518528 ,.23535956988080588043] 
dist 171=[-1.4859001663662366842 ,.23010679480441565459] 
dist 172=[-1.4872998182739145609 ,.21741488653871138691] 
dist 173=[-1.4832044184396871245 ,.21418483968736204773] 
dist 174=[-1.4746909895196745628 ,-.1129497088137875472 ] 
dist 175=[-1.4693500865529750230 ,-.13558444499137699607] 
dist 176=[-.63416534289234709272,-.1839259107070180737 ] 
dist 177=[-.56258683284895541863,-.19357852753328146964] 
dist 178=[-.39417186844102924036,-.06495526702658803957] 
dist 179=[-.39498362679687566078,.07582848066640650519] 
dist 180=[-.39469499280592466714,.2064280464319116799 ] 
dist 181=[-.40568691603682075452,.30555269373887278005] 
dist 182=[-.42795911067895192669,.40057429840394505998] 
dist 183=[-.43998851403998348043,.51480164806835117846] 
dist 184=[-.44682281863278242461,.62227098282262832463] 
dist 185=[-.44841373831826089648,.69032276280063263012] 
dist 186=[-.44802200031777329521,.74251414440066528793] 
dist 187=[-.44737816248066284789,.78668578597320712776] 
dist 188=[-.44638550611005537316,.82230635902842483536] 
dist 189=[-.44465382222865291301,.84037109839193060453] 
dist 190=[-.36650620666470349785,.84969016758267393608] 
dist 191=[-.36055434034548311836,.85104128961854472732] 
dist 192=[-.34378323206267346256,.64735115777108317862] 
dist 193=[-.34070864670698011025,.63094959200219523748] 
dist 194=[-.30656843041800054074,.59003385238730213409] 
dist 195=[-.29917056464548488006,.58066661225311835205] 
dist 196=[-.29091838428814138756,.51299440810924255047] 
dist 197=[-.28749636654193024916,.49889548345686746199] 
dist 198=[-.20041312582359612183,.47510317367969597259] 
dist 199=[-.18871500999013238889,.46864172309101901596] 
dist 200=[-.1647557323052717618 ,.37792871334899541842] 
dist 201=[-.15828200864038868803,.37984715118758605102] 
dist 202=[-.13365206749106069116,.38002030507984413288] 
dist 203=[-.12842059970765253655,.37904151311136503216] 
dist 204=[-.11795514296017507396,.37631802441880127925] 
dist 205=[-.1741981939842706297 ,.37463464275454468407] 
dist 206=[-.25500648903084789371,.18263887661581844512] 
dist 207=[-.37028478317134055222,.17822104837385183034] 
dist 208=[-.48396627562976016762,.05033017648097090002] 
dist 209=[-.5584024821155811421 ,.03459037303762205249] 
dist 210=[-.61833155699753743249,.00847256960724316993] 
dist 211=[-.67411567457357074579,.00242363686442909191] 
dist 212=[-.7246167430441616563 ,-.00714446000322917795] 
dist 213=[-.76018154003029796469,-.00404247403721782310] 
dist 214=[-.79037578722960518904,.00580167688843452742] 
dist 215=[-.82112849146106473919,.03088854562860628908] 
dist 216=[-.84703073204193519778,.06988407485298109994] 
dist 217=[-.85786704636520706995,.12267020080369262927] 
dist 218=[-.86248344715097498034,.18024962224196573581] 
dist 219=[-.86356139726263452955,.23837340540007329795] 
dist 220=[-.83789647175304821962,.30800005710764691399] 
dist 221=[-.83131680910224587297,.41148332645202891664] 
dist 222=[-.82743834074293332127,.5138524418818582763 ] 
dist 223=[-.82623649701304994821,.57903268304821603443] 
dist 224=[-.62596487940118698189,.62941852611636080638] 
dist 225=[-.63748987412310665495,.67274782469959345596] 
dist 226=[-.64484990392847492   ,.70819370080508522315] 
dist 227=[-.6460738795069581907 ,.72711908811514651225] 
dist 228=[-.64371493278109172129,.7375540980219932037 ] 
dist 229=[-.641913646234213752  ,.73978045366808658195] 
dist 230=[-.60125162552870664503,.77470249994255516928] 
dist 231=[-.59332290877782084319,.83081218616208894623] 
dist 232=[-.57351652754755442527,.88103826786741973373] 
dist 233=[-.56635333177858411274,.90997396929494286417] 
dist 234=[-.52993770260689817024,.92884624170568372831] 
dist 235=[-.52134390048927266651,.93891016099882379411] 
dist 236=[-.50344230826008242901,.94373875123811160457] 
dist 237=[-.49767438765769251632,.94309949210973975858] 
dist 238=[-.24152704223398314885,.93706859449394352996] 
dist 239=[-.21442444608358119646,.93222790342291414127] 
dist 240=[-.15865163948045142287,.65274596765251621737] 
dist 241=[-.20878565427333689293,.62784180639238249828] 
dist 242=[-.28531573829669211888,.5643458952833975523 ] 
dist 243=[-.35912549768352455236,.55407582547673884305] 
dist 244=[-.42550030687610137355,.44944022139842623642] 
dist 245=[-.47235867034867935374,.42883870655068439998] 
dist 246=[-.51387532275479898955,.40419326362961647956] 
dist 247=[-.55893189259602460562,.39658293772831726268] 
dist 248=[-.59977567598611452918,.19882874676727484215] 
dist 249=[-.62447999060710902825,.17366186144124085868] 
dist 250=[-.64208134010737722769,.12025551546510927888] 
dist 251=[-.65457930078138106207,.10642799397297709865] 
dist 252=[-.66283337759943099213,.05155359869063554963] 
dist 253=[-.66447357465054399372,.04113266799953952646] 
dist 254=[-.66185486045676089903,.01976019509861032086] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 2, 0, 2] 
dist 0=[53.475661698953228996  ,53.475661698953228996  ] 
dist 1=[52.234332017741896378  ,54.458096486316279820  ] 
dist 2=[50.716011938819073796  ,54.942637500268888264  ] 
dist 3=[48.701206102314394263  ,55.184943538680986527  ] 
dist 4=[45.477212004169772450  ,55.207551222978820191  ] 
dist 5=[42.173078222615184412  ,54.813920336545950454  ] 
dist 6=[39.838157842359628877  ,54.694281658068273957  ] 
dist 7=[37.761521852168851449  ,54.145743333675275264  ] 
dist 8=[35.488563279703634970  ,53.709626640787115685  ] 
dist 9=[33.257225254349233230  ,53.203479908716162576  ] 
dist 10=[31.346574817704322916  ,53.016823463217169956  ] 
dist 11=[29.300022332198645540  ,52.588164250796060800  ] 
dist 12=[26.525567900672873577  ,52.412960783490335323  ] 
dist 13=[23.760298581497399033  ,51.532522735528556987  ] 
dist 14=[21.750195327922951669  ,51.300513317488725172  ] 
dist 15=[19.902095866588035086  ,49.911857150742073259  ] 
dist 16=[17.783488723741791937  ,47.341239888606517629  ] 
dist 17=[15.643610551209987494  ,28.926669198877265770  ] 
dist 18=[13.710111716989943754  ,27.176445244482912722  ] 
dist 19=[11.549222858527191456  ,23.666254316890748664  ] 
dist 20=[8.5002074327678250204 ,23.448446427604199816  ] 
dist 21=[5.4998344876219978924 ,17.815560209318751645  ] 
dist 22=[3.5331221724242884472 ,17.003545930250955389  ] 
dist 23=[1.9377634709054534983 ,15.461327438520865801  ] 
dist 24=[.42121719293570552809,15.108231809716331724  ] 
dist 25=[-.93787402615396978669,11.508347642412402065  ] 
dist 26=[-1.9042020031607793370 ,10.975537037489275986  ] 
dist 27=[-2.7734605620023175906 ,9.5952621318511614210 ] 
dist 28=[-3.7450278444390260123 ,9.2472460023495525374 ] 
dist 29=[-4.6329007279532606029 ,1.1526683597899457543 ] 
dist 30=[-5.6950695688876360126 ,.5398942038677453030 ] 
dist 31=[-7.4693776405964361475 ,-1.0762823990204571408 ] 
dist 32=[-9.8422411537168044604 ,-2.9596944727219199305 ] 
dist 33=[-12.120084438396001525  ,-3.8699256185412077184 ] 
dist 34=[-13.515013521687676907  ,-3.5491322580984600783 ] 
dist 35=[-14.539438357779629908  ,-3.0585589202030204803 ] 
dist 36=[-15.336624078262925395  ,-2.2126429217363594825 ] 
dist 37=[-15.954881394800406986  ,-1.3392848347080835561 ] 
dist 38=[-16.264049863867335798  ,-.73902851597613807372] 
dist 39=[-16.409350172692842814  ,-.2266524781803523909 ] 
dist 40=[-16.430758080926959518  ,.2965986902390939421 ] 
dist 41=[-15.548289674990403604  ,.7843858434037367093 ] 
dist 42=[-15.370105147777157983  ,1.1555027388261003883 ] 
dist 43=[-15.074106040062543062  ,1.5110867665513256890 ] 
dist 44=[-14.972159106013685831  ,1.9370905696741501331 ] 
dist 45=[-14.593817236813674822  ,3.2757309724061346847 ] 
dist 46=[-14.467906090984893720  ,4.5483729956010007803 ] 
dist 47=[-14.220675765794445952  ,5.6152151697964939490 ] 
dist 48=[-14.131742737250258901  ,6.6786184475181410230 ] 
dist 49=[-4.6356105035306173493 ,7.6574261834831911806 ] 
dist 50=[-3.8149479317053583846 ,8.3868267914997723427 ] 
dist 51=[-1.9532241257685182264 ,9.0729351518092620261 ] 
dist 52=[-1.6129574722686080339 ,9.8791525561302111191 ] 
dist 53=[.56870924986077286394,10.623136025398869275  ] 
dist 54=[.68734923472958421848,11.060965225127810366  ] 
dist 55=[.91169974401999674579,11.358661839886285230  ] 
dist 56=[.9616721309303008852 ,11.543476471649312210  ] 
dist 57=[1.0934372384273001086 ,11.649467273465185883  ] 
dist 58=[1.1019412546819861139 ,11.660223534822708375  ] 
dist 59=[1.0681316172936363264 ,11.579019985770802895  ] 
dist 60=[.9683747054983362010 ,11.539484066758330842  ] 
dist 61=[.7534467772843775320 ,10.696368433453221559  ] 
dist 62=[.5324150737421541805 ,10.534591643084679646  ] 
dist 63=[.3265026048830313594 ,10.132254690154922792  ] 
dist 64=[.0876403943806672812 ,9.6671036235546008567 ] 
dist 65=[-.1539951835685082286 ,2.7694450313496151103 ] 
dist 66=[-.3710266732229141219 ,2.8694197598146855288 ] 
dist 67=[-.73766035730154939177,2.9694679311550455030 ] 
dist 68=[-1.2870227140003092735 ,3.0956053233686935544 ] 
dist 69=[-1.8115937222602087914 ,3.2105650849791049265 ] 
dist 70=[-2.1498446922096764012 ,3.2659850105428103209 ] 
dist 71=[-2.4161949944870455957 ,3.2929664903711935059 ] 
dist 72=[-2.6539411996762505371 ,3.2944899012263263451 ] 
dist 73=[-2.8552453717038808479 ,3.2426092082404402646 ] 
dist 74=[-2.9762529622312895684 ,3.2226115242160446888 ] 
dist 75=[-3.0619576840384370076 ,3.2046477143699679436 ] 
dist 76=[-3.1225261142908141702 ,3.1873388821169905469 ] 
dist 77=[-3.1639736500729143763 ,2.6394068185666573728 ] 
dist 78=[-3.1733821931883537533 ,2.5589909342851459807 ] 
dist 79=[-3.1683526161991790957 ,2.4047548558235387826 ] 
dist 80=[-3.1573573932353768627 ,2.3624542565716426312 ] 
dist 81=[-3.0682804570230663562 ,2.2036339759840686730 ] 
dist 82=[-3.0409976733881015137 ,2.1633940333157603141 ] 
dist 83=[-3.0372917955304578788 ,2.0891711518295470214 ] 
dist 84=[-3.1042701740689920654 ,2.0673778841310881205 ] 
dist 85=[-3.1598328172194798260 ,2.3499572444910975084 ] 
dist 86=[-3.1820089774504974175 ,2.7099259847308155716 ] 
dist 87=[-3.1863216005332350885 ,2.9896024604510055589 ] 
dist 88=[-3.1817522469000093254 ,3.2323692446907955318 ] 
dist 89=[-3.1253430915138806320 ,3.4324855504762526460 ] 
dist 90=[-3.1053037492790627771 ,3.5419823828818642383 ] 
dist 91=[-3.0579169846902305933 ,3.6059272809741332310 ] 
dist 92=[-3.0378968164185628162 ,3.6242831241879450720 ] 
dist 93=[-2.6799735777946704710 ,3.6254926397049987784 ] 
dist 94=[-2.6226011232866502686 ,3.6210142788810600461 ] 
dist 95=[-2.4844780255665673124 ,3.6114576343058631034 ] 
dist 96=[-2.4448014830378432364 ,3.5962375397494286921 ] 
dist 97=[-2.2216739652205656100 ,3.5685313371242175761 ] 
dist 98=[-2.1729061776724584954 ,3.5486410167321425094 ] 
dist 99=[-2.0766848059761975467 ,3.5062902260591501966 ] 
dist 100=[-2.0481925582291739853 ,3.4866465724041828765 ] 
dist 101=[-1.5885002692907555985 ,3.3773359079835211891 ] 
dist 102=[-1.5218608096497740793 ,3.4575456833546935751 ] 
dist 103=[-1.3553184835404443636 ,3.4997106020950783776 ] 
dist 104=[-1.3251854802563044011 ,3.5074901526260667759 ] 
dist 105=[-1.0578241734161705552 ,3.4600849150558526870 ] 
dist 106=[-1.0048258395035611843 ,3.4443637028104779320 ] 
dist 107=[-.93191883555320111227,3.4319095141276624939 ] 
dist 108=[-.90827999482849009568,3.4208143693284907428 ] 
dist 109=[.8498326643983645614 ,2.6542086641051674636 ] 
dist 110=[.7157132447235008845 ,2.6409907329509188847 ] 
dist 111=[.5643314742775214347 ,2.6071580366834507390 ] 
dist 112=[.3499135028671871839 ,2.5913033510339633768 ] 
dist 113=[.1114765990635203616 ,2.0305819229972221230 ] 
dist 114=[-.1357725712618864305 ,2.0490039916129984641 ] 
dist 115=[-.43677633013936875026,2.0595136225254038475 ] 
dist 116=[-.8897560659966500506 ,2.0619837257386677364 ] 
dist 117=[-1.3401780265877576358 ,.2271093184187402066 ] 
dist 118=[-1.6309770172192472531 ,.1522846181760331885 ] 
dist 119=[-1.8604794912993348288 ,.0449441898120505054 ] 
dist 120=[-2.0662685774598497207 ,.0153689322374284217 ] 
dist 121=[-2.2410157633990835140 ,-.4953603503096077416 ] 
dist 122=[-2.3466313862052769871 ,-.5583185898598849178 ] 
dist 123=[-2.4218190485914508799 ,-.6937761727355430046 ] 
dist 124=[-2.4751308506556289119 ,-.7185361822303489068 ] 
dist 125=[-2.5154268147637073422 ,-.85310743769507032731] 
dist 126=[-2.5386689098202855085 ,-.87472997645117800568] 
dist 127=[-2.5538793137947268885 ,-.90937445724828437273] 
dist 128=[-2.5621201182080093277 ,-.91473767659436423445] 
dist 129=[-2.5652682129607371768 ,-1.0291879951680948932 ] 
dist 130=[-2.5601541634349336349 ,-.9224091405219020656 ] 
dist 131=[-2.5480251805697322739 ,-.8229356145012940609 ] 
dist 132=[-2.5390707947284088762 ,-.7075471093747529333 ] 
dist 133=[-1.0454553098544475963 ,-.5908602331457242123 ] 
dist 134=[-.91891406407357226365,-.39108045176642929351] 
dist 135=[-.61696616290642030352,-.14992586469745382992] 
dist 136=[-.57850647138465800023,.09390549658554679205] 
dist 137=[-.3457892425100905274 ,.32068566644048070438] 
dist 138=[-.3143024335677925054 ,.49379454178858316929] 
dist 139=[-.24216167513070237437,.66068655417066984918] 
dist 140=[-.22846494448539402825,.86266021017996869373] 
dist 141=[-.13644647933683790649,1.0528883175578772053 ] 
dist 142=[-.11995376942103288271,1.1729064158743810993 ] 
dist 143=[-.08992063565534051218,1.2644451394475456230 ] 
dist 144=[-.08314200618848633935,1.3410146897244404811 ] 
dist 145=[.00899083251104812868,1.4021547311097246766 ] 
dist 146=[.02333619487625366703,1.4321164955946421000 ] 
dist 147=[.03276230098127173180,1.4476608058652069532 ] 
dist 148=[.02750805930424535868,1.4512605426973347591 ] 
dist 149=[.01498339880763515442,1.3128156321195009281 ] 
dist 150=[-.00724628354970265171,1.3510817084583212169 ] 
dist 151=[-.04127218838445263536,1.3788514026793223326 ] 
dist 152=[-.10103364472017720394,1.3989689588385712584 ] 
dist 153=[-.16576088895330579314,1.4121339757284639423 ] 
dist 154=[-.22060866308457567678,1.4137402323985045077 ] 
dist 155=[-.27868975611218221248,1.4076255296975146719 ] 
dist 156=[-.35632948742511744263,1.4026328771849039241 ] 
dist 157=[-.44057018549791005311,1.3500915237130444322 ] 
dist 158=[-.52500079297770368152,1.3350799898436668797 ] 
dist 159=[-.62572965701370917779,1.3163058734862312385 ] 
dist 160=[-.77502329915224484336,1.3073736236318153106 ] 
dist 161=[-.9224347862206968887 ,.38794710081968813169] 
dist 162=[-1.0156540543350928812 ,.36718731038125909278] 
dist 163=[-1.0870235325576771976 ,.34091478823616850596] 
dist 164=[-1.1472320675698957678 ,.3326614526938413357 ] 
dist 165=[-1.1956631006987784774 ,.09709040217725907920] 
dist 166=[-1.2245872597229506470 ,.06815589989979328910] 
dist 167=[-1.3174296260725696925 ,.01977063104988508951] 
dist 168=[-1.4191705577070906796 ,.00865605134503603563] 
dist 169=[-1.5107128684198980561 ,-.00984045296547964471] 
dist 170=[-1.5628526178044731108 ,-.00469542543187792375] 
dist 171=[-1.5961052391206395986 ,.01316194727101842410] 
dist 172=[-1.6122692186659343807 ,.05380959505665824612] 
dist 173=[-1.6197913804280801125 ,.1008806168702238720 ] 
dist 174=[-1.6185538613710443707 ,.1453732528405292894 ] 
dist 175=[-1.6116415758556233140 ,.1964712806406165457 ] 
dist 176=[-1.6062471586851281860 ,.2699060017430531600 ] 
dist 177=[-1.4826914704022351694 ,.3520373272652950371 ] 
dist 178=[-1.4689139540304671148 ,.43784333263596959292] 
dist 179=[-1.4563902897886308354 ,.54274226442994883486] 
dist 180=[-1.4473282256661200454 ,.701071364704451819  ] 
dist 181=[-.82534627425761357724,.85828078245425075336] 
dist 182=[-.78775140466824680507,.95871220619245370482] 
dist 183=[-.74467914397123239865,1.0367476543801226415 ] 
dist 184=[-.73267467257933969233,1.1045802092619617278 ] 
dist 185=[-.36407411567666223355,1.1606343212223437569 ] 
dist 186=[-.31778494633635114446,1.2110587670404076936 ] 
dist 187=[-.22125195448920737551,1.3093573509252542570 ] 
dist 188=[-.19558823286563989637,1.4178816521186031484 ] 
dist 189=[-.09877078171399013035,1.5158717526878704452 ] 
dist 190=[-.07994806198473726166,1.5721302724209861768 ] 
dist 191=[-.04394767232833630633,1.6085730908196703307 ] 
dist 192=[-.03564181390238571074,1.6274818940637305342 ] 
dist 193=[-.04282496176232290343,1.6372265326088884575 ] 
dist 194=[-.07643063168173993303,1.6370966217316086136 ] 
dist 195=[-.1102959380964885892 ,1.6307897232676849246 ] 
dist 196=[-.15333244898207244482,1.6254581474908468464 ] 
dist 197=[-.21085655984516280782,1.2084648360834857158 ] 
dist 198=[-.37995416762312576433,1.1634391254654696169 ] 
dist 199=[-.51890289648618098968,1.0478273079840333558 ] 
dist 200=[-.65295423159337621351,1.0295681839794076949 ] 
dist 201=[-.77352793609655967923,.83669728300173962315] 
dist 202=[-.85868983290102667109,.7986550104921241796 ] 
dist 203=[-.93418503543360288719,.75475614450454069058] 
dist 204=[-1.0161801805368801201 ,.74224041891664438029] 
dist 205=[-1.0905040382519718684 ,.36986956815535134597] 
dist 206=[-1.1353848677247531764 ,.32305668459142571983] 
dist 207=[-1.1672717598100206369 ,.22509609220143573606] 
dist 208=[-1.1897407259638308541 ,.19931832850090498468] 
dist 209=[-1.2044233739932958040 ,.10003983451014805882] 
dist 210=[-1.2073620079777883715 ,.08092920554591052465] 
dist 211=[-1.2020142180601069113 ,.04371553719648347993] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 0, 0, 1, 2] 
dist 0=[49.071357589004592345  ,49.071357589004592345  ] 
dist 1=[48.847094753231589869  ,49.221013225309653443  ] 
dist 2=[48.078009053683445083  ,49.692032976837743445  ] 
dist 3=[46.842750492060119786  ,50.185151155498349255  ] 
dist 4=[44.756632661914249128  ,50.423127141232358478  ] 
dist 5=[42.582317055458930873  ,50.520316306434041572  ] 
dist 6=[40.994791154141566215  ,50.510027242597710134  ] 
dist 7=[39.529058183807067511  ,48.771503212976327479  ] 
dist 8=[37.841040963837756861  ,48.460131254523131886  ] 
dist 9=[36.133647637304989473  ,47.950001742118980825  ] 
dist 10=[34.590401748396625998  ,47.785553308837424169  ] 
dist 11=[32.867191976234033472  ,47.220434953030572280  ] 
dist 12=[30.440790127134424220  ,47.029449665895732652  ] 
dist 13=[27.980376059298313412  ,46.690074174339917434  ] 
dist 14=[26.121178401457032272  ,46.573779624394712017  ] 
dist 15=[24.340212472138875808  ,31.711199575124106227  ] 
dist 16=[22.192059056759826835  ,30.430873091392110648  ] 
dist 17=[19.962756530651514995  ,27.343879324971286129  ] 
dist 18=[17.857374655625284097  ,26.894968476526241120  ] 
dist 19=[15.431215173232620591  ,24.994280377118000626  ] 
dist 20=[11.920004817058562414  ,24.864801139067768681  ] 
dist 21=[8.4429670439174414692 ,20.677591804753047919  ] 
dist 22=[6.1532129559847893142 ,20.494062111299147900  ] 
dist 23=[4.2853317143873713726 ,15.110163592741468007  ] 
dist 24=[2.4937387885011660272 ,14.831897480725298279  ] 
dist 25=[.87875445950045022162,14.227403318018623386  ] 
dist 26=[-.28367375216316951159,13.557957154113734467  ] 
dist 27=[-2.0054393043141112683 ,10.985406411660464012  ] 
dist 28=[-3.8382862462508609159 ,9.5893696916750996472 ] 
dist 29=[-5.8399235218511856039 ,8.4292882798459375337 ] 
dist 30=[-8.6090666832636733093 ,8.3136902352907436167 ] 
dist 31=[-11.293233143089305797  ,-.09357829437369187659] 
dist 32=[-12.955583520185350291  ,-.78972595736106702063] 
dist 33=[-14.197308534773062651  ,-2.2803752340073805005 ] 
dist 34=[-15.200711397679369804  ,-2.5652718523185839286 ] 
dist 35=[-16.000753113701925910  ,-4.0891338646573657874 ] 
dist 36=[-16.429634757809810110  ,-4.3324010939469843849 ] 
dist 37=[-16.672061460694464206  ,-3.8174476157473469769 ] 
dist 38=[-16.726334487254284069  ,-3.4156367289988175420 ] 
dist 39=[-16.067488608033347342  ,-3.0223464488030418058 ] 
dist 40=[-15.920368940481890065  ,-2.5408521890196125130 ] 
dist 41=[-15.780836425617349398  ,-2.0419141954467638212 ] 
dist 42=[-15.685746553955008210  ,-1.5787876240445903893 ] 
dist 43=[-15.554968218415605845  ,-1.0545029026195259633 ] 
dist 44=[-15.491889815629552821  ,-.31137363843390191692] 
dist 45=[-15.447965963542961478  ,.4379938105844142223 ] 
dist 46=[-15.419434714418005068  ,.9872634102423257242 ] 
dist 47=[-4.7460370341074135369 ,1.4942499604480913915 ] 
dist 48=[-3.8803141176483165213 ,2.0750222150527163217 ] 
dist 49=[-1.8811262569710556603 ,2.6578643037899219399 ] 
dist 50=[-1.5538281877084762166 ,3.1731615223827706074 ] 
dist 51=[-1.0332600717770103004 ,3.7371079304612921702 ] 
dist 52=[-1.0085629978802590045 ,4.5141036588557391909 ] 
dist 53=[2.1295684961270349004 ,5.2811874544196070346 ] 
dist 54=[2.2927442618806148797 ,5.8056038815375474350 ] 
dist 55=[2.7396743591356275319 ,6.5983982232300395535 ] 
dist 56=[2.7846824130094529134 ,7.3986266036207978626 ] 
dist 57=[2.7313501290033064650 ,8.0133415303760663215 ] 
dist 58=[2.5460733467692795470 ,8.5359978578529762703 ] 
dist 59=[2.2912134443606523621 ,8.9597981133509144982 ] 
dist 60=[1.9602111222188694113 ,9.1799279184969391800 ] 
dist 61=[1.5109157288915555237 ,9.2950654201280763242 ] 
dist 62=[.7840797936815802654 ,9.3171933302785768200 ] 
dist 63=[.04434557581568139056,4.1167483468215902840 ] 
dist 64=[-.45644231952650443299,3.9049970273960431069 ] 
dist 65=[-.87712948699894793948,3.6878175215504889014 ] 
dist 66=[-1.2973583475546907924 ,3.6475349387314043509 ] 
dist 67=[-1.6842023334078015068 ,3.2397250115012015243 ] 
dist 68=[-1.9717264016479322116 ,3.1544513296064230758 ] 
dist 69=[-2.2410747089576652324 ,3.0486391431090294979 ] 
dist 70=[-2.5554280187041653874 ,3.0081188179817009574 ] 
dist 71=[-2.8453531447148721436 ,2.1000631091858507272 ] 
dist 72=[-3.0172396692764486675 ,1.9795641926327652472 ] 
dist 73=[-3.1352697974103722554 ,1.7231715294919220964 ] 
dist 74=[-3.2102980115369977606 ,1.6527634784698448238 ] 
dist 75=[-3.2610786866351843673 ,1.3755701226373623619 ] 
dist 76=[-3.2823831933892440026 ,1.3214420800530847980 ] 
dist 77=[-3.2861215504530923420 ,1.1995253008325613282 ] 
dist 78=[-3.2789637089970699589 ,1.1701107086520277343 ] 
dist 79=[-2.6423758269225580454 ,-.6303922134939411524 ] 
dist 80=[-2.7058169536021969401 ,-.6048685725122951452 ] 
dist 81=[-2.7484866570841665315 ,-.5529393636919835152 ] 
dist 82=[-2.7665432381910530113 ,-.4666153553585528254 ] 
dist 83=[-2.7700540179552138136 ,-.3388370557467249790 ] 
dist 84=[-2.7638741922346025406 ,-.1215210809956767617 ] 
dist 85=[-2.8565771535734876886 ,.10755225611067524123] 
dist 86=[-2.9918879009656099206 ,.41403320688890964335] 
dist 87=[-3.1174098169055223939 ,.67274800876190645115] 
dist 88=[-3.1935485151821033300 ,.9332869725594281091 ] 
dist 89=[-3.2483552288580353125 ,1.1745444958905116610 ] 
dist 90=[-3.2886735203304319886 ,1.3563517273431998424 ] 
dist 91=[-3.3168064523931269173 ,1.5291693975087428389 ] 
dist 92=[-3.3229460331459719872 ,1.7345839609127920658 ] 
dist 93=[-3.3159687216661924785 ,1.9249069306675709389 ] 
dist 94=[-3.3079719912609165347 ,2.0375248210689112523 ] 
dist 95=[-.38879049124648704858,2.1146887086852829238 ] 
dist 96=[-.28019272158971485952,2.5116778626311415836 ] 
dist 97=[-.04755186592272294295,2.8558362414573338972 ] 
dist 98=[.00614708958495131227,3.1603598009134876186 ] 
dist 99=[.07507993349612046080,3.4256203333560490092 ] 
dist 100=[-.14525176814950628074,3.6040764147804066901 ] 
dist 101=[-.36678408193152640203,3.7358097112506729172 ] 
dist 102=[-.51321152253912259908,3.8382858128898376797 ] 
dist 103=[-.63227297022762499011,3.9196457647004545402 ] 
dist 104=[-.74465763395373140408,3.9671019890901161420 ] 
dist 105=[-.84377031591670232886,3.9988685479607323957 ] 
dist 106=[-.90989467374706967019,4.0176011594328865890 ] 
dist 107=[-.9643216176745378189 ,4.0265909694454099950 ] 
dist 108=[-1.0167726138191616251 ,4.0194708325520934801 ] 
dist 109=[-1.0619458188177080118 ,3.9992337811187351187 ] 
dist 110=[-1.0873433962396138841 ,3.9862594092624331536 ] 
dist 111=[-1.1030131214444682473 ,1.7447237092130097706 ] 
dist 112=[-1.1093879358325391554 ,1.5534779674132712555 ] 
dist 113=[-1.1092199100781233073 ,1.0933372902461383223 ] 
dist 114=[-1.1070205269691631135 ,1.0249220587024736515 ] 
dist 115=[-1.0876256623385849417 ,.37481221722018899263] 
dist 116=[-1.0845373841699772817 ,.25751467486610448752] 
dist 117=[-.93609521428884962981,.10877041332077280203] 
dist 118=[-1.2405080125270538068 ,.07705773925343827220] 
dist 119=[-1.5273119779608021122 ,.04835640845971515170] 
dist 120=[-1.7096099273035964727 ,.04249231383372329703] 
dist 121=[-1.8502268288384342684 ,.01203382898121534354] 
dist 122=[-1.9706839240388518109 ,.00680242805972628816] 
dist 123=[-2.0689346703276498677 ,-.00489508693357483803] 
dist 124=[-2.1209276582371000856 ,-.00687122723662469256] 
dist 125=[-2.1489882596103160209 ,-.0227370464792338742 ] 
dist 126=[-2.1545852834418386449 ,-.0253800603233153660 ] 
dist 127=[-1.7521677739729084878 ,-.0253383961786509260 ] 
dist 128=[-1.7173967399348515826 ,-.0216390812784890107 ] 
dist 129=[-1.6256510597747453138 ,-.0158936910934564486 ] 
dist 130=[-1.6059687681670655411 ,-.0076877605470027704 ] 
dist 131=[-1.4375973049696076900 ,.0038717338948464692 ] 
dist 132=[-1.4017249356665312049 ,.0229972354085191238 ] 
dist 133=[-1.3501545257342237687 ,.0426193599173117307 ] 
dist 134=[-1.3330509332682998565 ,.0561611516091089138 ] 
dist 135=[-.95491147784457297917,.0678183082308249800 ] 
dist 136=[-.9036796876321836582 ,.0799236197342801911 ] 
dist 137=[-.79016311573882621086,.0913688589607527165 ] 
dist 138=[-.76094985021051253333,.10039400687008191913] 
dist 139=[-.62202818226236936667,.1947343754037823239 ] 
dist 140=[-.5956767416849913033 ,.35568133604957027117] 
dist 141=[-.53449602948347280491,.53844203218071142279] 
dist 142=[-.52057567714363842908,.79873397513990185188] 
dist 143=[-.19460719315065325458,1.0553929854611559393 ] 
dist 144=[-.19205868247044903685,1.2236575655492713746 ] 
dist 145=[-.1818786942873738503 ,1.3593873386189257620 ] 
dist 146=[-.17934708950184582238,1.5015680996829710674 ] 
dist 147=[-.17379631483526512954,1.6424702908041456611 ] 
dist 148=[-.17192780830144996497,1.7426790694161452191 ] 
dist 149=[.03735534395674378329,1.8322703641681778836 ] 
dist 150=[-.00936469049463526498,1.9308008524351739820 ] 
dist 151=[-.06434094719776689051,2.0182054187570529894 ] 
dist 152=[-.11747989533367930989,2.0633933386469447707 ] 
dist 153=[-.17940710538479725861,2.0868458862745099197 ] 
dist 154=[-.26946333787573679145,2.0911502009631360139 ] 
dist 155=[-.37065482602236895798,2.0751752837770566475 ] 
dist 156=[-.47702524399826852845,2.0650752777167288542 ] 
dist 157=[-.60752494396338971027,2.0527673274972441073 ] 
dist 158=[-.80501743266329069971,2.0434665984665465932 ] 
dist 159=[-1.0680067723874503598 ,.25054394830656824869] 
dist 160=[-1.2525646013739491969 ,.25814368048506313304] 
dist 161=[-1.3982236481755850780 ,.26381566584240009547] 
dist 162=[-1.5288094880094722092 ,.26580080822197817799] 
dist 163=[-1.6396602554926661888 ,.26629718135940901619] 
dist 164=[-1.7416594375161816278 ,.26603034979987694856] 
dist 165=[-1.8566860186654381592 ,.25705465368051171869] 
dist 166=[-1.9750165270851417015 ,.25499948606799946864] 
dist 167=[-2.0799482201758651094 ,.24795855841502830405] 
dist 168=[-2.1415026880174885603 ,.24654128052559171877] 
dist 169=[-2.1830497517362631714 ,.22791945936044568716] 
dist 170=[-2.2081349680917975039 ,.22357767163186303   ] 
dist 171=[-2.2207085630180461471 ,.21924669317287292724] 
dist 172=[-2.2213582019266171450 ,.21724498643920737704] 
dist 173=[-2.1998264432070721376 ,.15867628051469434038] 
dist 174=[-2.1959862534954594579 ,.1507112844954799037 ] 
dist 175=[-1.4488475222339879479 ,.22902168500666259848] 
dist 176=[-1.3927667781053830638 ,.43361300703864153201] 
dist 177=[-1.2493338591401886455 ,.60193906004342993624] 
dist 178=[-1.2266435444012313908 ,.764675031132615559  ] 
dist 179=[-.98935646241084512316,.9112688925471393654 ] 
dist 180=[-.94271027167921091947,1.0151747540753542912 ] 
dist 181=[-.88837224033703008963,1.1076594347662181761 ] 
dist 182=[-.8727963984660999202 ,1.2086722698857781072 ] 
dist 183=[-.42125787287103133585,1.3004192921127130453 ] 
dist 184=[-.36418698027635410877,1.3559267120937102613 ] 
dist 185=[-.24396299757672523892,1.3954870328201667244 ] 
dist 186=[-.21222620977098115695,1.4235959623104446863 ] 
dist 187=[-.20493988520198117647,1.4421755361299920105 ] 
dist 188=[-.20395541746755330787,1.4460428777711456664 ] 
dist 189=[-.1855137311602234074 ,1.4402141493680178053 ] 
dist 190=[-.1820783020907949212 ,1.4387288070262732995 ] 
dist 191=[-.1734123721636172408 ,.32172075688679586798] 
dist 192=[-.1710470915246717355 ,.31592298482245659654] 
dist 193=[-.1558100830401417223 ,.30006256506028532757] 
dist 194=[-.1524578178959416776 ,.29689921965247289095] 
dist 195=[-.1463438369180796527 ,.26611332820947267733] 
dist 196=[-.1446364525483738606 ,.25950702635314838904] 
dist 197=[-.1110921540758523390 ,.25108056288097722697] 
dist 198=[-.1059351827251271313 ,.26780684527166959302] 
dist 199=[-.0970746408781807452 ,.29769275350581508658] 
dist 200=[-.0948810282302429226 ,.32478619997216097627] 
dist 201=[-.0973236158395518831 ,.34799735205877959269] 
dist 202=[-.1059575391764543515 ,.36238995474460560645] 
dist 203=[-.1137746416999545625 ,.3730736003858635552 ] 
dist 204=[-.1225119780511201105 ,.38148328150642329475] 
dist 205=[-.1303480564850498591 ,.38786230826754104771] 
dist 206=[-.1345687590043320902 ,.39044194908017212689] 
dist 207=[-.16003013133039843389,.39073147663479582549] 
dist 208=[-.19534348554253309875,.39021053597941731145] 
dist 209=[-.22465620016014676317,.38390792834247408801] 
dist 210=[-.25343748328684205047,.38166334720134010366] 
dist 211=[-.27966930357757812271,.37440545452039346984] 
dist 212=[-.29880708752309952838,.37157958012411457717] 
dist 213=[-.31641152096102366541,.0430177240917887360 ] 
dist 214=[-.33652386114130988788,.0517006144864534518 ] 
dist 215=[-.3547766679500390166 ,.0588237619860868761 ] 
dist 216=[-.36495964120893708822,.0656728319851241920 ] 
dist 217=[-.37118058271413850089,.0718147843195124534 ] 
dist 218=[-.37362061841498062733,.0789928870557351631 ] 
dist 219=[-.37420891725824160219,.0870355392811160462 ] 
dist 220=[-.37332735914405987213,.0960066904535594840 ] 
dist 221=[-.37086950275412513437,.1041975738882316216 ] 
dist 222=[-.36924254022256726151,.13481385542643327379] 
dist 223=[-.23853895664615990277,.19190971083222636546] 
dist 224=[-.237775294049815674  ,.22874463681087737572] 
dist 225=[-.23144483096798250287,.25777691194851463103] 
dist 226=[-.22945467289074472509,.28373442268254538245] 
dist 227=[-.22528690626075512842,.3057162802490967189 ] 
dist 228=[-.22368746852362836219,.3188828681264512603 ] 
dist 229=[-.19161662580087888211,.32810943222224483538] 
dist 230=[-.18655492883495495861,.3343680045204616754 ] 
dist 231=[-.17556524068848451971,.33888655934682758513] 
dist 232=[-.17221294461632725051,.34116900453172328913] 
dist 233=[-.1574158510946243976 ,.34225103020647051514] 
dist 234=[-.1543354108145465486 ,.34197822259792221979] 
dist 235=[-.1458505692419803523 ,.34085543065633145986] 
dist 236=[-.1442889106092831402 ,.33952959961408984026] 
dist 237=[-.1241847068855037908 ,.33574172217722831964] 
dist 238=[-.1205492973489225656 ,.33265388239141306334] 
dist 239=[-.1129531817389047311 ,.14705035554197955844] 
dist 240=[-.1107205249850536962 ,.13055474217909723981] 
dist 241=[-.1013052742069035658 ,.09184729616359983173] 
dist 242=[-.0992945949308418376 ,.08529509873060439550] 
dist 243=[-.0939986255730500977 ,.0333999798767728481 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 2, 0, 0, 1] 
dist 0=[57.714634728983550450  ,57.714634728983550450  ] 
dist 1=[57.270909056710862098  ,57.941459722369887040  ] 
dist 2=[56.413871882196936097  ,57.958990567258643258  ] 
dist 3=[55.401474391078948368  ,57.812361782155187694  ] 
dist 4=[54.337271697556198480  ,57.704906954694947122  ] 
dist 5=[53.028703755363201264  ,57.358044016420474586  ] 
dist 6=[51.040273123445507368  ,57.178448032296349956  ] 
dist 7=[48.760727568046517249  ,56.186104810247662976  ] 
dist 8=[46.289437423124335818  ,54.784940742275961087  ] 
dist 9=[43.197843533191242756  ,53.425398674610974730  ] 
dist 10=[38.440809304039921956  ,53.173637093444770532  ] 
dist 11=[33.627328230797256878  ,52.750304616218163629  ] 
dist 12=[30.310228427476312530  ,52.652460606630298145  ] 
dist 13=[27.445497207635183182  ,51.339246127257310852  ] 
dist 14=[24.438598845123362274  ,48.872364152433118065  ] 
dist 15=[21.560453272736136241  ,37.974450246898839521  ] 
dist 16=[19.209791953148226575  ,37.819285614381754273  ] 
dist 17=[16.788320334828904375  ,29.644659221399272174  ] 
dist 18=[13.627032447062333836  ,28.612101518288209172  ] 
dist 19=[10.529141682089479660  ,26.580354678467144567  ] 
dist 20=[8.3606938219103114721 ,26.064899994940476695  ] 
dist 21=[6.4504278517703651965 ,24.294592616395033697  ] 
dist 22=[4.3834909827396665124 ,23.891858242627663589  ] 
dist 23=[2.3639907486281645462 ,23.449627224190147376  ] 
dist 24=[.6428148016258301753 ,23.355083207975454281  ] 
dist 25=[-1.1975109109697395810 ,7.9846798386067190955 ] 
dist 26=[-3.6937821138178716609 ,7.7461593347889977631 ] 
dist 27=[-6.1128729379400696665 ,6.6580405461878574325 ] 
dist 28=[-7.6449911476019277663 ,6.4973542611996959389 ] 
dist 29=[-8.8289851419758116940 ,5.8726621460409171069 ] 
dist 30=[-9.8569323900655482640 ,5.1375101288927812185 ] 
dist 31=[-10.713524459067085049  ,-2.9580642370744618806 ] 
dist 32=[-11.212899593015047739  ,-3.1683072888255187530 ] 
dist 33=[-12.188538373061612098  ,-5.9312400882812626506 ] 
dist 34=[-12.976425511976997166  ,-6.2946456175187717362 ] 
dist 35=[-13.601485034390125236  ,-6.8051864156819816220 ] 
dist 36=[-13.933845245847416561  ,-6.8812848463316078334 ] 
dist 37=[-14.118270907762529225  ,-6.8015383344107460004 ] 
dist 38=[-14.151574828884446341  ,-6.4958307350455926288 ] 
dist 39=[-13.563500678976032056  ,-5.9688051712197735304 ] 
dist 40=[-13.435676956811024178  ,-5.0057129853832781045 ] 
dist 41=[-13.296405729173111280  ,-3.9989409706489938722 ] 
dist 42=[-13.216280348838835798  ,-3.2973876972935541761 ] 
dist 43=[-13.075978671802966497  ,-2.6870701813082443232 ] 
dist 44=[-13.008679705659738791  ,-2.0438860784512977500 ] 
dist 45=[-12.955729523576110676  ,-1.1409808629285366788 ] 
dist 46=[-12.909336359697922828  ,-.08202314434769137115] 
dist 47=[-4.2094098720045615567 ,.8969850442654195341 ] 
dist 48=[-3.4973586294524961106 ,1.6353987053867783380 ] 
dist 49=[-1.8317990381375947106 ,2.3392745558757532652 ] 
dist 50=[-1.5733285067227742641 ,3.1805572699994400057 ] 
dist 51=[.27368000729206050023,3.9706138855799514004 ] 
dist 52=[.32105709392143247276,4.4700460821743950800 ] 
dist 53=[.40164575432758583413,4.8526380599957845523 ] 
dist 54=[.36719976858765803696,5.1762731026952084879 ] 
dist 55=[.27250403939758928927,5.4375950840008010610 ] 
dist 56=[.07278947893776080856,5.8476380487540245556 ] 
dist 57=[-.14208793532714007149,6.3354509408196858696 ] 
dist 58=[-.29727749052036527493,6.7468652107942721855 ] 
dist 59=[-.43691918570460784373,7.0784033086847913454 ] 
dist 60=[-.59000272083729172901,7.2473877820111964216 ] 
dist 61=[-.73839865043769147865,7.3365612012949869638 ] 
dist 62=[-.85942940135103714914,7.3505518732633158660 ] 
dist 63=[-.98264045118123475082,3.6570854496769670812 ] 
dist 64=[-1.1397678033405076645 ,3.4767473157241932354 ] 
dist 65=[-1.2892567082709797784 ,3.2490927294639530186 ] 
dist 66=[-1.3820472446469613722 ,3.2043350926178410920 ] 
dist 67=[-1.4504068164362506252 ,2.4211806414970518779 ] 
dist 68=[-1.5025529734639952376 ,2.3849947857252170214 ] 
dist 69=[-1.5397524159939140874 ,2.2512592502302148933 ] 
dist 70=[-1.5485434663279249590 ,2.2179488323376784633 ] 
dist 71=[-1.5473540449207411773 ,2.1629744477177921873 ] 
dist 72=[-1.5448112432409810921 ,2.1467309531851975966 ] 
dist 73=[-.83424711200100592112,1.2112616497867998610 ] 
dist 74=[-1.4957128003950118396 ,1.1793800848331212185 ] 
dist 75=[-2.1488075801228484731 ,.27059328595188197378] 
dist 76=[-2.5813699038119948077 ,.20724125253823226781] 
dist 77=[-2.9354442763051793615 ,.12038732135572256578] 
dist 78=[-3.2752509187114186248 ,.1007215279705839429 ] 
dist 79=[-3.5801368604867769967 ,-.30502142612905494014] 
dist 80=[-3.7948293322910337529 ,-.35863892020897354266] 
dist 81=[-3.9847496439168506270 ,-.41760639275302176416] 
dist 82=[-4.1907734105764047219 ,-.41844748033223419483] 
dist 83=[-4.3723245764477016724 ,-.3954919126845569564 ] 
dist 84=[-4.4645632991316252502 ,-.33904507819396909149] 
dist 85=[-4.5120775578612355996 ,-.24755756420333927095] 
dist 86=[-4.5193111085656949997 ,-.04786181753847639923] 
dist 87=[-4.4755846968575987898 ,.24377313492167374844] 
dist 88=[-4.4536559231370595211 ,.55627566817970276084] 
dist 89=[-4.4299386500955463016 ,.94380836082441644228] 
dist 90=[-4.4091036341740463217 ,1.5349072971647255744 ] 
dist 91=[-3.6491825397824411876 ,2.1245332133417658175 ] 
dist 92=[-3.6063190173417127356 ,2.5061973608394986614 ] 
dist 93=[-3.5727869537673036652 ,2.8085296604763623327 ] 
dist 94=[-3.5521520791135632374 ,3.0815539212812526371 ] 
dist 95=[-.85918131205261042314,3.3147936541460290968 ] 
dist 96=[-.84170417842491353456,3.4996486413201986052 ] 
dist 97=[-.45723373723417124883,3.7457617104950580190 ] 
dist 98=[-.4088587095104614961 ,4.0013358298901859891 ] 
dist 99=[-.30296981025244727875,4.2290378470083768322 ] 
dist 100=[-.28020292298333508596,4.3639157387397968206 ] 
dist 101=[-.16215889714096838224,4.4566173571264009687 ] 
dist 102=[-.14203159212867985445,4.5159898951880880424 ] 
dist 103=[-.09690505812165143192,4.5493926621644979422 ] 
dist 104=[-.08969074079932775536,4.5528450107437355142 ] 
dist 105=[.64907757404880611932,4.5167927852444030233 ] 
dist 106=[.69093695887341425146,4.5074562212303022490 ] 
dist 107=[.00400753659827811247,4.3235463591503049292 ] 
dist 108=[-.47252041313201008106,4.3164150562925411183 ] 
dist 109=[-.86697868389879660475,4.2952171525780104193 ] 
dist 110=[-1.2523051368740008680 ,4.2783948020139501021 ] 
dist 111=[-1.6020447683696550272 ,3.1011268695765245303 ] 
dist 112=[-1.8544847145342244642 ,2.9760781950075816853 ] 
dist 113=[-2.0838756645582322981 ,2.6551230673232595828 ] 
dist 114=[-2.3416305823597589057 ,2.6067017564521351865 ] 
dist 115=[-2.5790375391075507513 ,2.0745679184839903929 ] 
dist 116=[-2.7272255634554956366 ,1.9704919127377435260 ] 
dist 117=[-2.8383615543993866918 ,1.8555336573874622120 ] 
dist 118=[-2.9279071827457869448 ,1.8282473817215283041 ] 
dist 119=[-2.9966666989582471205 ,1.1952600035535397918 ] 
dist 120=[-3.0248530329500458975 ,1.1894370705369491639 ] 
dist 121=[-3.0332152602482112510 ,.8974008614679385482 ] 
dist 122=[-3.0283060445232634073 ,.87726829021624895592] 
dist 123=[-3.0301765441032700768 ,.82344879898426376836] 
dist 124=[-3.0409313940715387847 ,.81463108309089453166] 
dist 125=[-3.0378643280693539598 ,.71570752401169617285] 
dist 126=[-3.0270468025645614431 ,.69517450047030925451] 
dist 127=[-.82475253341801411119,.67305330415243309141] 
dist 128=[-.9116330315515611461 ,.66587372164554324982] 
dist 129=[-.9924772592882124411 ,.43740167372504124016] 
dist 130=[-1.0415145786647821645 ,.40736713078243179551] 
dist 131=[-1.0767287914440085914 ,.3468735099132025063 ] 
dist 132=[-1.1023958797529610962 ,.33089647414100925777] 
dist 133=[-1.1202572234883608797 ,.27226070744824444363] 
dist 134=[-1.1244596358000911266 ,.25944999693796839003] 
dist 135=[-1.1236683236253713688 ,.23691660705775249351] 
dist 136=[-1.1228433792567551567 ,.23142322975356665655] 
dist 137=[-.2359820718708455522 ,.06540975728918215879] 
dist 138=[-.2315893208807265542 ,.16174360889125670992] 
dist 139=[-.0300129289423361610 ,.25732232323775165518] 
dist 140=[-.0100422683210405505 ,.32080876600906923052] 
dist 141=[.02918895739705045559,.37294798741608393647] 
dist 142=[.03863853709866769046,.42323761602796568706] 
dist 143=[.06826024122330245340,.46849398084904698758] 
dist 144=[.07448119340315817317,.5005446253193992397 ] 
dist 145=[.07482182859510796439,.52906470276997285142] 
dist 146=[.06724858857192168175,.56023049708951165793] 
dist 147=[.05615128181754307563,.58777222371818852587] 
dist 148=[.04242734165354752873,.60182785474924063586] 
dist 149=[.02416969517767253993,.60937838432438533242] 
dist 150=[-.00502333871716629647,.61095532813442471363] 
dist 151=[-.03898454594591957343,.60419144200570352354] 
dist 152=[-.07627210819251750333,.60206305627751904138] 
dist 153=[-.12311697475564461482,.60044922656620044115] 
dist 154=[-.19522005361851116589,.59912049869199480448] 
dist 155=[-.26729922728291472399,.3703282465515110268 ] 
dist 156=[-.31404955048134322381,.36788020173895795336] 
dist 157=[-.35117622236658634604,.34565710626422038091] 
dist 158=[-.3848512762162194831 ,.34027714970089689726] 
dist 159=[-.41371282298804351394,.33282203022242850065] 
dist 160=[-.43163102031800274956,.32996346517623412265] 
dist 161=[-.44495968866446351688,.25973995730056809349] 
dist 162=[-.46653779332587383017,.24992554547876132391] 
dist 163=[-.49818961358533316325,.22865359713127374985] 
dist 164=[-.51742864789884234187,.22251606237167923247] 
dist 165=[-.53125800751907283674,.19680594154208171109] 
dist 166=[-.54131883084246463974,.19177019722985528189] 
dist 167=[-.54818541538629526865,.17843171460094445222] 
dist 168=[-.54934522163778962975,.1763785767415718048 ] 
dist 169=[-.54815071876301257015,-.1575313545858992835 ] 
dist 170=[-.54625467390421135237,-.0656928830410916064 ] 
dist 171=[-.34112805204370035887,.0266692078933423325 ] 
dist 172=[-.3221152684144682701 ,.0882528589797845546 ] 
dist 173=[-.32603956641386816257,.1390567017706652004 ] 
dist 174=[-.35156321091074575827,.1883984067865756652 ] 
dist 175=[-.37516091117036257541,.2329932014978879320 ] 
dist 176=[-.40229847618700047382,.2648525154826883998 ] 
dist 177=[-.42701650183879453491,.2934660794321732152 ] 
dist 178=[-.44095587860001070094,.32510642007981262141] 
dist 179=[-.44966159204458783198,.3541274307605373732 ] 
dist 180=[-.45348922084832922929,.37228791339435252128] 
dist 181=[-.45505758913584009182,.38595712559558991552] 
dist 182=[-.45474782746802414103,.39705610953644920404] 
dist 183=[-.45300157651383935849,.40564329832478440034] 
dist 184=[-.45162702008788464394,.40928941122187091443] 
dist 185=[-.39821088760842001718,.41027603241850723443] 
dist 186=[-.3904953107610271186 ,.40980343037714490333] 
dist 187=[-.36868122063828037873,.39001928245391486815] 
dist 188=[-.36527349524470634583,.40211016284914788617] 
dist 189=[-.32148673002081975408,.40929501799315837919] 
dist 190=[-.31221789281810367865,.41166417700736531458] 
dist 191=[-.30322287314192247578,.41207314200732304101] 
dist 192=[-.30071277299624323342,.41143416763666131486] 
dist 193=[-.19086769838967878609,.40990522533634781898] 
dist 194=[-.17662860176104678542,.40839448301237009939] 
dist 195=[-.14819853924183352202,.3535641864511556344 ] 
dist 196=[-.14079073854555824688,.3451505734008304629 ] 
dist 197=[-.11429924421465278307,.34342669186525087142] 
dist 198=[-.10836808681082112977,.34308058281788463985] 
dist 199=[-.09978640307306301616,.3419584683883558709 ] 
dist 200=[-.09719144226617804555,.34073971227367293854] 
dist 201=[-.07065739939184771466,.00084188689217778719] 
dist 202=[-.08750279164120659212,.00061788176348824250] 
dist 203=[-.10073614391588773254,-.00171681260800842472] 
dist 204=[-.11248917142754682782,-.00209973876571466145] 
dist 205=[-.12238436299231206575,-.00216147086518995463] 
dist 206=[-.12820443835016220317,-.00180319232871045486] 
dist 207=[-.13215320579861408038,-.00120552228887623882] 
dist 208=[-.13458177418524839936,-.00031219234664569235] 
dist 209=[-.1362585943590282088 ,.00096562349089643267] 
dist 210=[-.13720757058577614839,.00309704427925231535] 
dist 211=[-.13780854978613948223,.00538112399830577312] 
dist 212=[-.13809603670050434481,.00726797944326324960] 
dist 213=[-.1381641087402439768 ,.00922036129957432658] 
dist 214=[-.13788927461720965647,.01176603145035033566] 
dist 215=[-.1373134087861785797 ,.01449086517513501692] 
dist 216=[-.13674476720909902632,.01715801452845200488] 
dist 217=[-.04554601961222580497,.02028771327639854474] 
dist 218=[-.03788725972396187125,.02777112583404154598] 
dist 219=[-.02028393806008938338,.03967094271839933897] 
dist 220=[-.01716163750594401650,.04781555961355866752] 
dist 221=[.00511038263037199569,.05475201121898249713] 
dist 222=[.00899921802296344631,.06183284760433795675] 
dist 223=[.01584602515736614722,.06844719892012942396] 
dist 224=[.01728053012739175892,.0735230938333711597 ] 
dist 225=[.0326076654058805980 ,.0784345572177312072 ] 
dist 226=[.0296945649446834962 ,.0843933554532589850 ] 
dist 227=[.0263758236732768435 ,.0899708746290653573 ] 
dist 228=[.0233193120588602739 ,.0933615332213645288 ] 
dist 229=[.0198735109541273269 ,.0966461702852739867 ] 
dist 230=[.0150019056007340708 ,.0981910027924216216 ] 
dist 231=[.0095955108463441128 ,.0988645502554360970 ] 
dist 232=[.0040162835596328706 ,.0988915236041340695 ] 
dist 233=[-.0027494254331501489 ,.03157774088274998921] 
dist 234=[-.01288914652311371474,.03118264504879524060] 
dist 235=[-.02303525429521194899,.0165908382163703184 ] 
dist 236=[-.02982627293722823918,.0151840492914227406 ] 
dist 237=[-.03544878832078740454,.0096025999753040706 ] 
dist 238=[-.04093279124910835355,.0085416915258469441 ] 
dist 239=[-.04589535127857118694,.0064175255879362793 ] 
dist 240=[-.04943720871702886490,.0058901893663029543 ] 
dist 241=[-.05260875904037443725,.0042347445833016542 ] 
dist 242=[-.05609327421233856925,.0026756635973331257 ] 
dist 243=[-.05918240281601183524,-.0219522109547593022 ] 
dist 244=[-.06077657902367246412,-.0239424579770216099 ] 
dist 245=[-.06163328647500015388,-.0263636799550254571 ] 
dist 246=[-.06178105663918815360,-.0284305541754292395 ] 
dist 247=[-.06114932035493528484,-.02627815663882364355] 
dist 248=[-.06090084000999284904,-.02007097009204041097] 
dist 249=[-.06067361448326585426,-.01219713548731507337] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 0, 1, 1, 0, 1] 
dist 0=[51.785830166612447500  ,51.785830166612447500  ] 
dist 1=[51.191387814895137720  ,52.104181307765913921  ] 
dist 2=[50.280151841658507607  ,52.313704360399044330  ] 
dist 3=[48.696695053815923994  ,52.473552302550727688  ] 
dist 4=[46.799026567454124892  ,52.627293959395152114  ] 
dist 5=[44.633044782245491968  ,52.812450087549836152  ] 
dist 6=[41.851711479023041234  ,53.003121764022528657  ] 
dist 7=[37.496796365374169688  ,53.178845620528570126  ] 
dist 8=[33.077897060980824483  ,53.376822337577825772  ] 
dist 9=[30.040945626756180243  ,53.656206757179816340  ] 
dist 10=[27.428984321044482981  ,53.916639912110909169  ] 
dist 11=[24.706832109604099887  ,54.039020436497089778  ] 
dist 12=[22.114845644087712752  ,54.083336944926206786  ] 
dist 13=[20.022353210446153590  ,54.017722704773901734  ] 
dist 14=[17.889406684920607970  ,50.986054564798731448  ] 
dist 15=[15.135281650713823308  ,50.371623681591009052  ] 
dist 16=[12.450828433152190515  ,46.721426808030602976  ] 
dist 17=[10.595791969993457228  ,39.500933543330973302  ] 
dist 18=[8.9863453632281554340 ,38.255458378156152595  ] 
dist 19=[7.2822737882530657728 ,35.191959410815271581  ] 
dist 20=[5.6378113844749594956 ,34.741740524294023466  ] 
dist 21=[4.2658208650227616073 ,30.097353399854858009  ] 
dist 22=[2.8221734341943058880 ,29.218808790013717516  ] 
dist 23=[.89016140234830667569,28.223840417374092876  ] 
dist 24=[-.97646357849428597868,28.017517576666407564  ] 
dist 25=[-2.1590554797949483430 ,20.043027767941664691  ] 
dist 26=[-3.0762890826426621761 ,19.049831547303524726  ] 
dist 27=[-3.8820189048630063072 ,17.036701690725869297  ] 
dist 28=[-5.1609336376279579027 ,16.520667600834106624  ] 
dist 29=[-6.3734319652373777404 ,14.690550978611760052  ] 
dist 30=[-7.4135097530015078308 ,14.309134530703102579  ] 
dist 31=[-8.0752360689189162289 ,13.756430828209740359  ] 
dist 32=[-8.5917012093800569248 ,13.603022376058314094  ] 
dist 33=[-9.0516872868935200724 ,1.1970599677758700951 ] 
dist 34=[-9.4416167182037643171 ,.16681964347519741407] 
dist 35=[-9.6780722385752216446 ,-2.0544715924646635884 ] 
dist 36=[-9.8507027116188671468 ,-2.4838452025002727030 ] 
dist 37=[-9.9850243247612746640 ,-1.8611413858630637150 ] 
dist 38=[-10.086987498452207729  ,-1.0031911590543674774 ] 
dist 39=[-10.454477502157749157  ,.30664323745897456729] 
dist 40=[-11.800614179219789865  ,1.6226467887390173653 ] 
dist 41=[-13.053358320644536712  ,2.5053803933924713732 ] 
dist 42=[-13.821473247238179537  ,3.2371551125513536492 ] 
dist 43=[-14.384465313409401875  ,3.9512881859994566994 ] 
dist 44=[-14.817740442071352011  ,4.5972434672531831411 ] 
dist 45=[-15.139993132573364695  ,5.0572019566312242751 ] 
dist 46=[-15.259515257525338289  ,5.4680523614816639268 ] 
dist 47=[-15.297418762381519550  ,5.9182536866816141386 ] 
dist 48=[-15.293514112575677111  ,6.3161356566757413934 ] 
dist 49=[-2.5717864808286507908 ,6.5182707485184340137 ] 
dist 50=[-1.9447942576776571492 ,6.6270617751200019206 ] 
dist 51=[-.49045551278263237246,6.6525757886205212848 ] 
dist 52=[-.55705038450244876346,6.5407739425907287618 ] 
dist 53=[-.71132214228561372668,6.5103757890755285901 ] 
dist 54=[-.93659538892282011622,6.4910326936201688878 ] 
dist 55=[-1.3170516045939806766 ,6.4821248193918640365 ] 
dist 56=[-1.7028182593656774596 ,3.7541196510073266495 ] 
dist 57=[-1.9492825522848186158 ,4.4365150538288005535 ] 
dist 58=[-2.1404232984997742772 ,4.8631531032895977328 ] 
dist 59=[-2.3055001768853399863 ,5.1847654489228759340 ] 
dist 60=[-2.4407980144031226845 ,5.4478317161142853057 ] 
dist 61=[-2.5131439679496430268 ,5.6536323064506430130 ] 
dist 62=[-2.5530798937676474420 ,5.7466049037513168573 ] 
dist 63=[-2.5618057643153392425 ,5.7866694541776996232 ] 
dist 64=[-2.5524052602675972653 ,5.7818455886722420215 ] 
dist 65=[-2.5417682428978915900 ,4.2319767873357142170 ] 
dist 66=[-2.5261756232585257574 ,4.0851543407233801243 ] 
dist 67=[-2.5146077950261324282 ,3.9893424223934616042 ] 
dist 68=[-2.4683153815001880854 ,3.8977146349391452741 ] 
dist 69=[-2.4510799429834581718 ,3.8633605531843217742 ] 
dist 70=[-2.3996922499529970515 ,3.6868018310184455432 ] 
dist 71=[-2.3769821699689012314 ,3.6445206840559834262 ] 
dist 72=[-.84137700445964860687,3.5504617791632113465 ] 
dist 73=[-.70195243487449105436,3.5183175441440431883 ] 
dist 74=[-.77817996172725544639,2.0722827760296900967 ] 
dist 75=[-1.1433320660315415705 ,1.9240028990037479138 ] 
dist 76=[-1.5490733165978964106 ,1.5763308996605061166 ] 
dist 77=[-1.9500016778240097989 ,1.6754581683177017228 ] 
dist 78=[-2.2960486957647094736 ,1.8756892686676827586 ] 
dist 79=[-2.6685192133222644847 ,2.1112977294167177584 ] 
dist 80=[-3.1750727927354409784 ,2.3284027493801060400 ] 
dist 81=[-3.6636242347911145653 ,2.4548011338731265083 ] 
dist 82=[-3.9642646996492426957 ,2.5387944207118678470 ] 
dist 83=[-4.1853660771313403850 ,2.5867021439780139343 ] 
dist 84=[-4.3563571580236687155 ,2.6177258633852577754 ] 
dist 85=[-4.4878553960097247874 ,2.6343513353471112002 ] 
dist 86=[-4.5664379327831385861 ,2.6435692417025208113 ] 
dist 87=[-4.6728962614151151152 ,2.6450359498208823820 ] 
dist 88=[-4.7474395828667621271 ,.31744800608529593377] 
dist 89=[-4.7989329527125214159 ,.18488362782711530037] 
dist 90=[-4.8133751405907342506 ,-.11669630386038491146] 
dist 91=[-4.8063865976715968029 ,-.16897222830481979385] 
dist 92=[-4.7953639583248142661 ,-.50350105278322929966] 
dist 93=[-4.7003052346870081509 ,-.24775441095512471786] 
dist 94=[-4.6701615797381362431 ,-.00357642065512999700] 
dist 95=[-4.5826603067193767832 ,.19345994022204100225] 
dist 96=[-4.5454800138261321300 ,.39369853956901244272] 
dist 97=[-2.7371961569130338763 ,.65067997796518366729] 
dist 98=[-2.5556779299171178746 ,.89913816289768650655] 
dist 99=[-2.1199877289053168139 ,1.1358429087514586477 ] 
dist 100=[-2.0454476374394350896 ,1.6000661068987262569 ] 
dist 101=[-1.7336959919544806198 ,2.0170848417837144840 ] 
dist 102=[-1.7524565854461884261 ,2.3112117981114412686 ] 
dist 103=[-1.7792869630364323225 ,2.5717520485700564964 ] 
dist 104=[-1.7983942959751861547 ,2.8547492002817837644 ] 
dist 105=[-1.8015457774691156500 ,3.1135329177788510569 ] 
dist 106=[-1.7911740524985050892 ,3.2774315520462714659 ] 
dist 107=[-1.7875757719600980557 ,3.4033353697694992938 ] 
dist 108=[-1.7003528215436222583 ,3.5104418426464877373 ] 
dist 109=[-1.6767487921359966447 ,3.5973609534061304581 ] 
dist 110=[-1.6590819218592873648 ,3.6426752264644234085 ] 
dist 111=[-1.6490392118744741808 ,3.6662205280743900496 ] 
dist 112=[-1.2536813573256486771 ,3.6662353485417747882 ] 
dist 113=[-1.1992213858106481117 ,2.2041835753345485751 ] 
dist 114=[-1.0930789288380722374 ,2.1900288768698655250 ] 
dist 115=[-1.0736591975613426137 ,2.1931249405353151275 ] 
dist 116=[-.96191063595842831992,2.1867462793569793422 ] 
dist 117=[-.94349402670486260005,2.1787460485202737092 ] 
dist 118=[-1.0699000260926847145 ,2.1072115925996273549 ] 
dist 119=[-1.1840054005942379932 ,2.0861052989148401641 ] 
dist 120=[-1.3109961395965785732 ,2.0565305852883458478 ] 
dist 121=[-1.4888529853337116320 ,2.0438607337781937891 ] 
dist 122=[-1.7281457965939611938 ,.24820286112676582266] 
dist 123=[-1.9587177062840911860 ,.05373494781442989492] 
dist 124=[-2.1368530214918034859 ,.01450096785290122441] 
dist 125=[-2.2900507459374890373 ,-.20127597064376309622] 
dist 126=[-2.4155364926699681842 ,-.23719086226610168573] 
dist 127=[-2.4830658357321678022 ,-.31469129179102510935] 
dist 128=[-2.5390835658549740815 ,-.32755571089242803065] 
dist 129=[-2.6497407521285277858 ,-.86596069349757274369] 
dist 130=[-2.7447922757448524794 ,-.91817263403939265098] 
dist 131=[-2.8001413511762832848 ,-.98666309559771950697] 
dist 132=[-2.8370185886908355165 ,-.99361486305600210791] 
dist 133=[-2.8583418769488568192 ,-.97702712675446491764] 
dist 134=[-2.8680428542790429693 ,-.92604478528871305835] 
dist 135=[-2.8650691871498441895 ,-.80951899139218054898] 
dist 136=[-2.8427788537027262908 ,-.56293238608903870184] 
dist 137=[-2.8275681249334261115 ,-.19062722724391517021] 
dist 138=[-2.3484858845988422481 ,.18277521393394572895] 
dist 139=[-2.3669275870775282584 ,.43374199365276734347] 
dist 140=[-2.3675494527320483934 ,.64308512791780647733] 
dist 141=[-2.3579123835517220048 ,.85035541600998839458] 
dist 142=[-2.3500333570821534769 ,1.0404204969991997361 ] 
dist 143=[-2.3173243431534902410 ,1.1810913233065304217 ] 
dist 144=[-2.3045265413088138793 ,1.3125115049595106000 ] 
dist 145=[-1.1750656861687470992 ,1.7325593017023021784 ] 
dist 146=[-.61008260622749012244,2.0184494318291247454 ] 
dist 147=[-.53910892347440999616,2.2398120164465912017 ] 
dist 148=[-.39477319303605875401,2.4309675391731028009 ] 
dist 149=[-.35747125286507467762,2.5880702520066409438 ] 
dist 150=[-.22429209334341367015,2.7185349993353270828 ] 
dist 151=[-.19621312052523229328,2.8357257614593565094 ] 
dist 152=[-.1559739596550652361 ,2.9402158595246472172 ] 
dist 153=[-.1445258506797989565 ,3.0277377268790930429 ] 
dist 154=[.59879187047324007741,3.0772080293371393443 ] 
dist 155=[.54943781245137240879,3.1082823705720060670 ] 
dist 156=[.49620746720660339722,3.1223855059629325808 ] 
dist 157=[.42379998776374323721,3.1245164742149632426 ] 
dist 158=[.34463682966237347496,3.1183410589176972157 ] 
dist 159=[.26444346848289865478,3.0861634559992919494 ] 
dist 160=[.16815732393611937617,3.0685653835773875727 ] 
dist 161=[.02476730337031044030,1.6283089515070196877 ] 
dist 162=[-.12320862926570871131,1.4976236567707810689 ] 
dist 163=[-.23779781476253065468,1.1784817648778838903 ] 
dist 164=[-.3498492765735947427 ,1.1311784497955516798 ] 
dist 165=[-.561506875158881497  ,.66210687474051484084] 
dist 166=[-.76865541170828950852,.64319157204087067327] 
dist 167=[-.96729791975549897609,.68266965023099275722] 
dist 168=[-1.2062093866593211252 ,.73186927497335438384] 
dist 169=[-1.4304404351094920802 ,.80714147238212761931] 
dist 170=[-1.5704949974219415278 ,.88238382526461333151] 
dist 171=[-1.6756817594654515960 ,.93146469638422075997] 
dist 172=[-1.7607546751250530246 ,.97073759986499621067] 
dist 173=[-1.8276767885176206400 ,1.0068438615858346085 ] 
dist 174=[-1.8604249733628470648 ,1.0381127351213629891 ] 
dist 175=[-1.8761620847216102617 ,1.0580834034237829324 ] 
dist 176=[-1.8773686849995384024 ,1.0735860018765105828 ] 
dist 177=[-1.8020959602076627864 ,1.0870264700364311722 ] 
dist 178=[-1.6913737481697333100 ,1.0969230406981057714 ] 
dist 179=[-1.6700256404825109665 ,1.0982846387923889580 ] 
dist 180=[-1.6431808762854976268 ,1.0951373893454613024 ] 
dist 181=[-1.6308898403797834306 ,1.0914021979825694488 ] 
dist 182=[-1.6052008563691728590 ,1.0628175508935573008 ] 
dist 183=[-1.5933100057075942802 ,1.0541427473152645463 ] 
dist 184=[-1.5834517601303046841 ,1.0323703605773842514 ] 
dist 185=[-1.5742292672683776105 ,1.0234728222873107943 ] 
dist 186=[-.81561294002661831485,.89616365722742132288] 
dist 187=[-.70592959957438560461,.8741152603291946229 ] 
dist 188=[-.67671785307963658772,.83171025411094038156] 
dist 189=[-.56812955065675757895,.81973137544805525868] 
dist 190=[-.5447783595676749015 ,.77312046850719223712] 
dist 191=[-.50217439466855974845,.76126592110465712797] 
dist 192=[-.49155059275557851869,.89139818039712536692] 
dist 193=[-.02623351957190367912,1.0829750375557155160 ] 
dist 194=[-.01147542791758698999,1.2669539508686274629 ] 
dist 195=[-.05370113910244320161,1.3876732433524923351 ] 
dist 196=[-.1834679637065112443 ,1.4851315176561219856 ] 
dist 197=[-.34370470383381637375,1.5762760353284502650 ] 
dist 198=[-.51120182936931068389,1.6563388548374422765 ] 
dist 199=[-.66994560452278064853,1.7095692240043904116 ] 
dist 200=[-.85263687878256664172,1.7533090757596543456 ] 
dist 201=[-1.1157077493890838602 ,1.7954924254398826529 ] 
dist 202=[-1.3740298788313552198 ,1.8296724927840317323 ] 
dist 203=[-1.5377700679180764727 ,1.8414713673383294254 ] 
dist 204=[-1.6635355269330809388 ,1.8432102909785445759 ] 
dist 205=[-1.7703046051635502519 ,1.8382655273361678791 ] 
dist 206=[-1.8566519520925602933 ,1.7291791706934682466 ] 
dist 207=[-1.9009167046981594226 ,1.7015921471935244072 ] 
dist 208=[-1.9245145600773717880 ,1.5314984338950605110 ] 
dist 209=[-1.9283809870022575537 ,.85201209101110488247] 
dist 210=[-1.9086439930672455929 ,.87720935464995720414] 
dist 211=[-1.8977758290563079511 ,.89578645342015283187] 
dist 212=[-1.8830423497871004170 ,.913055453717162666  ] 
dist 213=[-1.8744152937442503388 ,.93303320686245274033] 
dist 214=[-1.8381988248318999956 ,.95320188230917796657] 
dist 215=[-1.8256584410328246611 ,.97123282521248900369] 
dist 216=[-1.7893119619762507174 ,.99113591583542207959] 
dist 217=[-1.7734840809116377023 ,1.0187751355312414000 ] 
dist 218=[-1.3763027295432565854 ,1.0442789731482961062 ] 
dist 219=[-1.4052088918603005714 ,1.0556605802620470843 ] 
dist 220=[-1.4175601258723007068 ,1.0595228472010216850 ] 
dist 221=[-1.4225173573064713238 ,1.0587361413891874722 ] 
dist 222=[-1.4219147864049992172 ,1.0410856032301177865 ] 
dist 223=[-1.4171239554763029083 ,1.0341973251402115930 ] 
dist 224=[-1.4124344899400541823 ,1.0189774355222355491 ] 
dist 225=[-1.0826212284398422753 ,1.0124769914981830439 ] 
dist 226=[-1.0454677605054179872 ,.87915037787969202614] 
dist 227=[-.94810104344896592244,.85814154795972608011] 
dist 228=[-.93361425554521224895,.80946092827229546461] 
dist 229=[-.76518678951137253654,.79421173480129996241] 
dist 230=[-.73171172606497221653,.72200001503241187487] 
dist 231=[-.69659294592276961966,.76886710427984352867] 
dist 232=[-.68871932999284929871,.84686579337850528634] 
dist 233=[-.34316539453273361694,.91809763791579464758] 
dist 234=[-.29989514568563831838,.96039175968426448133] 
dist 235=[-.2114625818838444056 ,.9895671785268532718 ] 
dist 236=[-.18858132870543949798,1.0084469299519370417 ] 
dist 237=[-.10661410948746431333,1.0207106804583769947 ] 
dist 238=[-.08954085867817648155,1.0234827081244426538 ] 
dist 239=[-.06464052748500611244,1.0217049402135288576 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 1, 2, 0, 1, 2] 
dist 0=[53.578915741221153564  ,53.578915741221153564  ] 
dist 1=[53.159412942194366944  ,53.720628241432332678  ] 
dist 2=[52.412805399913991675  ,53.866888090924135371  ] 
dist 3=[51.099788475361552566  ,54.009163327787047394  ] 
dist 4=[49.493821654435979857  ,54.127980957417187681  ] 
dist 5=[47.577364072437204354  ,54.251945312383214583  ] 
dist 6=[45.062574352557891370  ,54.414515183338090794  ] 
dist 7=[41.067287072267082852  ,54.561298786844360036  ] 
dist 8=[36.992858197119682753  ,54.622246253728273139  ] 
dist 9=[34.161953427182549388  ,54.631328352616251336  ] 
dist 10=[31.694209501757331704  ,54.571323556159326086  ] 
dist 11=[29.069754146454647989  ,54.471126686608442817  ] 
dist 12=[26.538256279060971069  ,54.357506279969574587  ] 
dist 13=[24.441485522132793685  ,54.122092744894849021  ] 
dist 14=[22.256148755069519875  ,53.310861545541343279  ] 
dist 15=[19.370517743534808781  ,38.756906699040914766  ] 
dist 16=[16.528773680879382333  ,37.422226532141257784  ] 
dist 17=[14.518443559980207933  ,34.178806803453149679  ] 
dist 18=[12.725638726510171932  ,33.688453417502763825  ] 
dist 19=[10.752262326406036018  ,28.907305331739916343  ] 
dist 20=[8.8041855759169888347 ,28.012183412126938642  ] 
dist 21=[7.1119162191873422146 ,26.934389797448617039  ] 
dist 22=[5.2747104220715127791 ,26.676617871981509135  ] 
dist 23=[2.7466595258530443813 ,18.981600754872748316  ] 
dist 24=[.2827529281287987942 ,18.021274688332794066  ] 
dist 25=[-1.2983700150540451076 ,16.031906853708300301  ] 
dist 26=[-2.5445916134513437149 ,15.514174078764853593  ] 
dist 27=[-4.0520366572699055466 ,13.617371586191434192  ] 
dist 28=[-6.6738583539563011252 ,13.243447927133275584  ] 
dist 29=[-8.3292639653928534508 ,12.566680692509792362  ] 
dist 30=[-9.6032193884696364804 ,12.415292921132101006  ] 
dist 31=[-10.700696283262417340  ,1.9392297926894134568 ] 
dist 32=[-11.609753173892975824  ,1.0386040974471398278 ] 
dist 33=[-12.130931359581878154  ,-.8938036509928573023 ] 
dist 34=[-12.472807870412999561  ,-1.2773473212336287817 ] 
dist 35=[-12.665881754157213654  ,-3.2827291858275147042 ] 
dist 36=[-12.786617914400496525  ,-3.6123664768597804498 ] 
dist 37=[-12.839383899870602651  ,-3.6157961073087010169 ] 
dist 38=[-12.855638878751196574  ,-2.7621472553179664795 ] 
dist 39=[-12.918456746381357542  ,-1.4204686130356544446 ] 
dist 40=[-13.525391203014772418  ,-.06151391079959726554] 
dist 41=[-13.938135948120955528  ,.86123852462266099619] 
dist 42=[-14.197032402173826817  ,1.6381376991833741253 ] 
dist 43=[-14.370376303758049209  ,2.4156577374239478544 ] 
dist 44=[-14.441277818308891067  ,3.1314251150118972656 ] 
dist 45=[-14.451544570918140917  ,3.6621682746300257333 ] 
dist 46=[-14.427930790752338416  ,4.1577718315900553553 ] 
dist 47=[-3.5015119993707224087 ,4.7335262721051652087 ] 
dist 48=[-1.8028657240955395013 ,5.2595865998760984514 ] 
dist 49=[-1.3383748293937061890 ,5.5570249482842922022 ] 
dist 50=[-.8349884956546130444 ,5.7435710823824315920 ] 
dist 51=[-.7089246608195992827 ,5.8273224016373652588 ] 
dist 52=[.52240223322164213201,5.8685086419257119486 ] 
dist 53=[.44116043231013341551,5.8851868950056603365 ] 
dist 54=[.28867919771593018263,6.1743249762345990974 ] 
dist 55=[0                     ,6.4945270506456724423 ] 
dist 56=[2.6549751509035593375 ,6.7427703428079968808 ] 
dist 57=[2.7343330921054325750 ,6.8583843916362587216 ] 
dist 58=[2.7421573555900706027 ,6.9100945970481026968 ] 
dist 59=[2.6452449054157120281 ,6.9080348211067085223 ] 
dist 60=[2.5171124619529393780 ,6.0948478344305584880 ] 
dist 61=[2.3976174406234669336 ,6.1256472932339566420 ] 
dist 62=[2.2626755355257567400 ,6.1293876359322647099 ] 
dist 63=[2.0726479843836435481 ,4.6846249900200448255 ] 
dist 64=[1.8627457646807892722 ,4.5395164840768082901 ] 
dist 65=[1.6483666588741922497 ,4.1790818684160323910 ] 
dist 66=[1.3901181218661907019 ,4.1044298286537998304 ] 
dist 67=[1.0050317787072368355 ,3.5320736483022730226 ] 
dist 68=[.6078731059654643906 ,3.4178243382521321721 ] 
dist 69=[.1911293699373856903 ,3.2316743657377158579 ] 
dist 70=[-.4130397688738615538 ,3.1813331566327514221 ] 
dist 71=[-1.0116607355117343208 ,2.3305572885161931829 ] 
dist 72=[-1.4347539771769392490 ,2.3914966042614630470 ] 
dist 73=[-1.8100286991686493394 ,2.4609262994907004049 ] 
dist 74=[-2.2179342122752404685 ,2.5493159892000072990 ] 
dist 75=[-2.6156009070588491132 ,2.6857407574175570036 ] 
dist 76=[-2.9501029781002637562 ,2.8194422357764116458 ] 
dist 77=[-3.3026179309161723557 ,2.8969419041481641552 ] 
dist 78=[-3.7723139457286968290 ,2.9473274871558645572 ] 
dist 79=[-4.2223482321427139450 ,2.9729370036549750600 ] 
dist 80=[-4.4964090832591129724 ,2.9834624854208199176 ] 
dist 81=[-4.6944341444269281081 ,2.9800210142346909320 ] 
dist 82=[-4.8409170171489564329 ,2.9568786430559411676 ] 
dist 83=[-4.9485546387225406860 ,2.9400892674041025394 ] 
dist 84=[-4.9914995456991100286 ,2.6847606643073445320 ] 
dist 85=[-5.0034275558445249620 ,2.6378002395488271823 ] 
dist 86=[-4.9945796425678093852 ,2.5288459174457785888 ] 
dist 87=[-5.0162318065345808682 ,2.4913970251747248290 ] 
dist 88=[-5.0592915671763990471 ,2.3094427003499875376 ] 
dist 89=[-5.0719220740363833138 ,2.2676021890335502247 ] 
dist 90=[-5.0630183845253894818 ,2.1681408218316008190 ] 
dist 91=[-4.9534407696050601215 ,2.1335894583361879833 ] 
dist 92=[-4.9148744944815889486 ,1.7783890970861403076 ] 
dist 93=[-4.8557743916486854487 ,2.2877122432518501282 ] 
dist 94=[-4.8303834769291831588 ,2.7076968413636952037 ] 
dist 95=[-3.4032077587599982571 ,3.1152381750359712394 ] 
dist 96=[-3.2450215038272483836 ,3.4833684657468515409 ] 
dist 97=[-2.8625553639044504354 ,3.7460996618071572141 ] 
dist 98=[-2.7908834551566681494 ,3.9818863573239467537 ] 
dist 99=[-2.2219778535385236153 ,4.2425258921933941155 ] 
dist 100=[-2.1120470206216599517 ,4.4745174907346233406 ] 
dist 101=[-1.9432563509651497580 ,4.5959942446539081347 ] 
dist 102=[-1.8961708924584992819 ,4.6622357296397799133 ] 
dist 103=[-.9881649147809950458 ,4.6754530458135630839 ] 
dist 104=[-.8698720049103103352 ,4.6446336202104416828 ] 
dist 105=[-.5952989484609386083 ,4.6303711805768687855 ] 
dist 106=[-.5460071693541332086 ,4.6157105521041503465 ] 
dist 107=[-.1847292840602033172 ,4.5930725861430247280 ] 
dist 108=[-.1197815399608564621 ,4.3164150562925411233 ] 
dist 109=[-.0099664960757903736 ,4.3196600313385750641 ] 
dist 110=[.0151503649868775118 ,4.3128313172269353829 ] 
dist 111=[1.4122549148816782090 ,2.5765415554454867772 ] 
dist 112=[1.3303194493093558341 ,2.4255759379616278130 ] 
dist 113=[1.2268734477703513754 ,2.0491025252368070642 ] 
dist 114=[1.0879617905191960207 ,1.9950442100760156839 ] 
dist 115=[.8644664165511612472 ,1.6519669843140311930 ] 
dist 116=[.6270856635273557845 ,1.6646117472937681638 ] 
dist 117=[.4327437074098401855 ,1.6722425184157385163 ] 
dist 118=[.2327664750896839951 ,1.6777545663850695865 ] 
dist 119=[-.0271288458286783861 ,1.6819202343027715599 ] 
dist 120=[-.3056307457983133267 ,1.6849764550062008604 ] 
dist 121=[-.5798851195620363826 ,1.6860485501187833111 ] 
dist 122=[-.9035792650159809350 ,1.6859003214934398420 ] 
dist 123=[-1.3794251777478938880 ,1.6840735297239120930 ] 
dist 124=[-1.8497415498929528958 ,-.4779207209806718256 ] 
dist 125=[-2.1513703105730928853 ,-.5372321922067633360 ] 
dist 126=[-2.3872340711896840382 ,-.5475338679616883782 ] 
dist 127=[-2.5971887744322171436 ,-1.4367974767783399408 ] 
dist 128=[-2.7734433517471062701 ,-1.5093743172320991630 ] 
dist 129=[-2.8760457657495434822 ,-1.6153448527124182696 ] 
dist 130=[-2.9443688143598171878 ,-1.6334902528675056242 ] 
dist 131=[-2.9838065682804561790 ,-1.6199403335036286609 ] 
dist 132=[-3.0088455565461065660 ,-1.5589868679631662648 ] 
dist 133=[-3.0196995420955622155 ,-1.4517428085672027887 ] 
dist 134=[-3.0222654965890701034 ,-1.2534405435323517797 ] 
dist 135=[-3.0142242442639470772 ,-1.0331036977652944579 ] 
dist 136=[-3.0000149469774232534 ,-.8379102172013825661 ] 
dist 137=[-2.9870207759710745723 ,-.62384649207162180912] 
dist 138=[-2.9525094851493705585 ,-.32817733195488645788] 
dist 139=[-2.9353023502931391738 ,-.00277427747264088833] 
dist 140=[-2.5711904795109048556 ,.32997031671151917196] 
dist 141=[-2.5807446165786032986 ,.73177497058516168518] 
dist 142=[-2.5813489507649010294 ,1.3328136002713760096 ] 
dist 143=[-.7589516166107424429 ,1.9295176048470019634 ] 
dist 144=[-.2899378543205122514 ,2.3140268159431350995 ] 
dist 145=[-.2054892495294032149 ,2.6166869580149022088 ] 
dist 146=[-.0854876656340352710 ,2.8888538079785998450 ] 
dist 147=[-.0519829716009230235 ,3.1195371253907145769 ] 
dist 148=[.5310561623358179962 ,3.2578804582533583467 ] 
dist 149=[.6027353811332004601 ,3.3550683206274702490 ] 
dist 150=[.7577751345781888338 ,3.4215002349151135210 ] 
dist 151=[.7854560892978671969 ,3.4703346139855948437 ] 
dist 152=[.9423069160844061974 ,3.4972903047784307130 ] 
dist 153=[.9671496110014787483 ,3.5133972953174277162 ] 
dist 154=[1.0097918161686174270 ,3.5189332573238850731 ] 
dist 155=[1.0170968899604580657 ,3.5172781183504261819 ] 
dist 156=[1.2505092871803034780 ,3.5054030963210686433 ] 
dist 157=[1.1405756775367457985 ,3.4826758531030642275 ] 
dist 158=[1.0353379574508813969 ,3.4694206963047967280 ] 
dist 159=[.83037128224110841345,1.4667270224379722721 ] 
dist 160=[.4325460058741160955 ,1.2950421856391393320 ] 
dist 161=[.0972530428598169484 ,.88596290440536569579] 
dist 162=[-.2402127613634087994 ,.82265204367901775458] 
dist 163=[-.5531219036095239801 ,.78238457911082366522] 
dist 164=[-.7904155630535215802 ,.5208303356133334502 ] 
dist 165=[-1.0177061738564921451 ,.48463770384551022904] 
dist 166=[-1.2906998802098095465 ,.4012615962108826326 ] 
dist 167=[-1.5472725702668070459 ,.3853980808903549402 ] 
dist 168=[-1.7090293223583801464 ,.2748611634370055601 ] 
dist 169=[-1.8322757379614166790 ,.2543883056754587062 ] 
dist 170=[-1.9351541121842840346 ,.2181373282665553283 ] 
dist 171=[-2.0170403271271988148 ,.2099051171858540486 ] 
dist 172=[-2.0565075369146706802 ,.07580726824707739997] 
dist 173=[-2.0764356565858145977 ,.05534379003970197707] 
dist 174=[-2.0803413770012123255 ,.03657107211715931630] 
dist 175=[-1.6026011439172961238 ,.03800028700784973309] 
dist 176=[-1.6926707000836269154 ,.0485818385205555869 ] 
dist 177=[-1.7490690682239555148 ,.0720647023337897049 ] 
dist 178=[-1.7912130363401225906 ,.1094666932557667165 ] 
dist 179=[-1.8249421138023074494 ,.1756007847158950575 ] 
dist 180=[-1.8492717579696187605 ,.2480948430301571971 ] 
dist 181=[-1.8539014233290884943 ,.3108816793998222400 ] 
dist 182=[-1.8509427494727395638 ,.3785546527265301963 ] 
dist 183=[-1.8449804092543591286 ,.4705545241376154132 ] 
dist 184=[-1.7821891028334814415 ,.5711205702264295215 ] 
dist 185=[-1.7634023489250926068 ,.6729842225593982694 ] 
dist 186=[-1.7397714368036022953 ,.7952907994718758571 ] 
dist 187=[-1.7283196462976227422 ,.98455647935073720805] 
dist 188=[-.41713643853372867921,1.1728669122895558422 ] 
dist 189=[-.38516157325742177474,1.2922893821358713194 ] 
dist 190=[-.37947829159932195908,1.3840978481640970155 ] 
dist 191=[-.10823942831267677494,1.4622021676719078178 ] 
dist 192=[-.07331131757939200656,1.5255067899295400693 ] 
dist 193=[-.02034305497128695352,1.5887640932089981738 ] 
dist 194=[-.00670119626153817184,1.7222405352792213193 ] 
dist 195=[.00352364016962805846,1.8392419862562142930 ] 
dist 196=[-.00988896565114618591,1.9468627731444436125 ] 
dist 197=[-.04001082014504236146,2.0167518086928868392 ] 
dist 198=[-.10077117966909921128,2.0615293619099986680 ] 
dist 199=[-.16995981404455269574,2.0837257006073807114 ] 
dist 200=[-.2337197594152767668 ,2.0977544037449618449 ] 
dist 201=[-.30568090288557398456,2.1021194534778824237 ] 
dist 202=[-.40760407345936691606,2.0992555876698250376 ] 
dist 203=[-.5209404158996127209 ,2.0793431501649522302 ] 
dist 204=[-.6384527687623298335 ,2.0167355384096265136 ] 
dist 205=[-.7814969474132351781 ,1.9987390665331997630 ] 
dist 206=[-1.0038389854937717241 ,1.9858309643158187039 ] 
dist 207=[-1.2255675891834979621 ,1.3453755560598883549 ] 
dist 208=[-1.3670918592102368444 ,1.1079396170132705010 ] 
dist 209=[-1.4769234297328990726 ,1.0607912910360533863 ] 
dist 210=[-1.5721716579889546220 ,1.0059968623055045596 ] 
dist 211=[-1.6507231328051456610 ,.9894692372619760515 ] 
dist 212=[-1.7146883054626638203 ,.5228337833030660896 ] 
dist 213=[-1.8502528219169999786 ,.4633423340550108577 ] 
dist 214=[-1.9991856304805156411 ,.3384425469533704738 ] 
dist 215=[-2.1334623031293733146 ,.3052251392681093131 ] 
dist 216=[-2.2105363366099036102 ,.1800674100818317090 ] 
dist 217=[-2.2604422454190425444 ,.1554777707159298599 ] 
dist 218=[-2.2862946624608376954 ,.1074096124160800310 ] 
dist 219=[-2.2993842767717363749 ,.0955103415413544195 ] 
dist 220=[-2.2983553720079197219 ,.09147910241910803071] 
dist 221=[-2.2890688571040615440 ,.13646858048060917019] 
dist 222=[-2.2809459008305886714 ,.1820026494348538755 ] 
dist 223=[-1.6824086981046759834 ,.28539168311412569463] 
dist 224=[-1.6198829872326688004 ,.52222243515162947618] 
dist 225=[-1.4596727764168986334 ,.71707296630633589252] 
dist 226=[-1.4340734431469160052 ,.905471286605053836  ] 
dist 227=[-1.1675561166476383824 ,1.0752116986671775657 ] 
dist 228=[-1.1149567426562504738 ,1.1956011271760764884 ] 
dist 229=[-1.0533822553253600642 ,1.3028481475971676404 ] 
dist 230=[-1.0351054804464197054 ,1.4201382694812998416 ] 
dist 231=[-.52274225498511366039,1.5266190288006064534 ] 
dist 232=[-.45768112310857404701,1.5907280055389863675 ] 
dist 233=[-.32059148409647087685,1.6360474229002125617 ] 
dist 234=[-.28413960043736044749,1.6675442673648560254 ] 
dist 235=[-.1466130867531486052 ,1.6879460286938405551 ] 
dist 236=[-.11987218595061662572,1.6920252940683996432 ] 
dist 237=[-.06725237718081118048,1.6844254203348618294 ] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 2, 2, 2, 2, 0, 2] 
dist 0=[58.300316838375277351  ,58.300316838375277351  ] 
dist 1=[58.149091591438637862  ,58.297620698754643380  ] 
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dist 11=[43.034180863299397820  ,47.100185911588458756  ] 
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dist 18=[13.337416714093271635  ,19.525034357988911720  ] 
dist 19=[10.067907874795231064  ,18.905373860235889580  ] 
dist 20=[6.8732724314096179315 ,13.971252851277354055  ] 
dist 21=[3.9624557881368962314 ,13.100884492013227255  ] 
dist 22=[1.8264223193768010216 ,11.792139217940077522  ] 
dist 23=[-.1561419555492051859 ,11.458690995887705186  ] 
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dist 36=[-5.7609141016977648051 ,-4.3058721227845948113 ] 
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dist 38=[-4.7286614902935883688 ,-2.9610871593072786523 ] 
dist 39=[-4.5431433816530072587 ,-2.3823173048196885468 ] 
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dist 55=[1.7560781057664055713 ,5.0771629253345403913 ] 
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dist 57=[1.5513019594110628229 ,5.1141065049420010688 ] 
dist 58=[1.3680336111415229801 ,3.9606475491341007069 ] 
dist 59=[1.1852963717003400128 ,4.0369321989035871754 ] 
dist 60=[.96858004380645809227,4.1124044629353278085 ] 
dist 61=[.64956378043785706991,4.1570061676592157191 ] 
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dist 64=[-.55594031264378677457,4.1473409890110045935 ] 
dist 65=[-1.2622189438779872360 ,4.1392035632889517183 ] 
dist 66=[-1.9650186446828369279 ,-1.2610666042568604383 ] 
dist 67=[-2.4174318477309062378 ,-1.6960561437354986304 ] 
dist 68=[-2.7729143887645083373 ,-2.1165618756299085102 ] 
dist 69=[-3.0888972095198756284 ,-2.3889962775893527973 ] 
dist 70=[-3.3681379281795927755 ,-3.0404899980665943523 ] 
dist 71=[-3.6206268406651624019 ,-3.1405469185431935332 ] 
dist 72=[-3.8745351831643178575 ,-3.3246387347725506051 ] 
dist 73=[-4.0978909657614803789 ,-3.3580271679798118209 ] 
dist 74=[-4.2284538568131171411 ,-3.5029197312719258125 ] 
dist 75=[-4.3163226144296613082 ,-3.4712021551451958414 ] 
dist 76=[-4.3692176863382235433 ,-3.2571554803265890150 ] 
dist 77=[-4.3958275846205731607 ,-2.9796781716160595577 ] 
dist 78=[-4.3961765129335830796 ,-2.6378935688204492015 ] 
dist 79=[-4.3518886076730668044 ,-2.1842311623097220642 ] 
dist 80=[-4.3393819942290144617 ,-1.4603688460162549376 ] 
dist 81=[-4.0237255991602230702 ,-.72577349943580869974] 
dist 82=[-2.2917163051774907096 ,-.22927293875674063391] 
dist 83=[-1.9755549115987747122 ,.18707979797214616054] 
dist 84=[-1.8003291779106576798 ,.60193176922453936674] 
dist 85=[-1.4983851742355321509 ,.98322468828750913045] 
dist 86=[-1.1044307352514024577 ,1.2656927979597848040 ] 
dist 87=[-.93727906647606601008,1.5293859094703306958 ] 
dist 88=[-.89348310327640780789,1.8357678250215547653 ] 
dist 89=[-.60820021981784765467,2.1209411707333934921 ] 
dist 90=[-.02646030691037206713,2.3000309160871236506 ] 
dist 91=[.18856280438337096415,2.4354221215597677472 ] 
dist 92=[.22883591850387477462,2.5462931091113300665 ] 
dist 93=[.46456489890563253297,2.6327986686681660684 ] 
dist 94=[.50281989397599364915,2.6710101608075484442 ] 
dist 95=[.5814016464338974972 ,2.6859483495103778730 ] 
dist 96=[.59550600666902744777,2.6829439158698782268 ] 
dist 97=[.68354888076291484371,2.5133559084089767811 ] 
dist 98=[.69459335949406221438,1.8657840044474411013 ] 
dist 99=[.6176911471232740148 ,1.8233123575841419458 ] 
dist 100=[.45549127651725879577,1.7048809489131279602 ] 
dist 101=[.28214911169502660063,1.6877580772870177827 ] 
dist 102=[.11516062580688027195,1.4592907166698782225 ] 
dist 103=[-.02170180127819247660,1.4122335205093065090 ] 
dist 104=[-.16257826185466860021,1.3679572189709035250 ] 
dist 105=[-.34560222011333944321,1.3591527692919875033 ] 
dist 106=[-.52333872369607830376,1.1228370980969625533 ] 
dist 107=[-.64312714864277844804,1.1774667418379139344 ] 
dist 108=[-.74334740101534895097,1.2445330145871370526 ] 
dist 109=[-.84301378039063044011,1.3143065090211293867 ] 
dist 110=[-.93469541265989264841,1.3796999220542506295 ] 
dist 111=[-1.0030677141046177240 ,1.4542053114889728819 ] 
dist 112=[-1.0675081360028785382 ,1.5602745269753498403 ] 
dist 113=[-1.2160450668665148937 ,1.6621400030939804824 ] 
dist 114=[-1.3893837625363732457 ,1.7198598923450700562 ] 
dist 115=[-1.5248294285211000994 ,1.7560036892266307919 ] 
dist 116=[-1.6441285183050009541 ,1.7718044317236812688 ] 
dist 117=[-1.7440785949090491926 ,1.7783942669688895250 ] 
dist 118=[-1.8023009758402906918 ,1.7778123995775642392 ] 
dist 119=[-1.8412316779124224082 ,1.7717623055858270934 ] 
dist 120=[-1.8641996608226159185 ,1.7657894129640931403 ] 
dist 121=[-1.8775528938708449081 ,1.5345212095389360887 ] 
dist 122=[-1.8781057051769909041 ,1.4978240834386658112 ] 
dist 123=[-1.8714382692935562247 ,1.4266466309449975863 ] 
dist 124=[-1.8650630120480186885 ,1.4058824400257234224 ] 
dist 125=[-1.8453662038571162868 ,1.3213574437499927789 ] 
dist 126=[-1.8860462904453735345 ,1.3003313396190256177 ] 
dist 127=[-1.9074591394936984825 ,1.2516744384709430850 ] 
dist 128=[-1.9188634635264936226 ,1.2346931313209855366 ] 
dist 129=[-1.9195955892371036860 ,.57015715237196333438] 
dist 130=[-.91235549552399381852,.94533702745990556903] 
dist 131=[-.72824786252813691239,1.1881871270897396895 ] 
dist 132=[-.70172299050895685333,1.3805177863018631159 ] 
dist 133=[-.4305268641057297754 ,1.5565965810098126516 ] 
dist 134=[-.38078020219435215116,1.7074931579590368961 ] 
dist 135=[-.3223084207086432442 ,1.8007450844179764809 ] 
dist 136=[-.3119641604769032091 ,1.8695984006521979460 ] 
dist 137=[.09526504533641392210,1.9231265445550704690 ] 
dist 138=[.14329521137221350016,1.9659529717333205310 ] 
dist 139=[.24584216659550369029,1.9920982059997805964 ] 
dist 140=[.26654982494033635381,2.0110299176883447984 ] 
dist 141=[.36695812126393774881,2.0250680733692402594 ] 
dist 142=[.38394973268814801988,2.0348917398714067684 ] 
dist 143=[.41091967909283840226,2.0370044917281602527 ] 
dist 144=[.4161713797028207234 ,2.0338819243773052557 ] 
dist 145=[.6527669474755482513 ,2.0270009431173875431 ] 
dist 146=[.64201165701815648327,.81381258167637264679] 
dist 147=[.42401641519758102505,.75106415425655765332] 
dist 148=[.23881351650616335   ,.78507831332544645787] 
dist 149=[.05007702928126888037,.81643049480283222973] 
dist 150=[-.12636871909475431519,.84005298680403279214] 
dist 151=[-.26252489066193250805,.86259587024315488056] 
dist 152=[-.39518123315873794155,.88963862265738976601] 
dist 153=[-.5576627325102277629 ,.9149961648625009243 ] 
dist 154=[-.71131511558404770075,.93080936060617998475] 
dist 155=[-.80873769794885260088,.94270223717906743931] 
dist 156=[-.88358551303640255141,.95240264311160766759] 
dist 157=[-.94714801982741936972,.95998634247667244432] 
dist 158=[-.99857531978718966357,.96342561697150942094] 
dist 159=[-1.0249950682512314341 ,.96450114653000896651] 
dist 160=[-1.0394181088148175027 ,.96264507160688245006] 
dist 161=[-1.0429687599116480749 ,-.8431235308359525125 ] 
dist 162=[-1.0028377482650048474 ,-.85316911188417517927] 
dist 163=[-1.1232957048453780768 ,-.82221930344066729606] 
dist 164=[-1.2325515936030408620 ,-.78708755623464610636] 
dist 165=[-1.3250658497614387959 ,-.73711207766844059007] 
dist 166=[-1.3801231502989801894 ,-.68146854343947151938] 
dist 167=[-1.4182895119470853964 ,-.62371463354241319434] 
dist 168=[-1.4433904170282912132 ,-.55338835676215899169] 
dist 169=[-1.4612219393321920472 ,-.44756974155272338695] 
dist 170=[-1.4703753779654316896 ,-.33796857054200387823] 
dist 171=[-1.4749340766637576383 ,-.25254535192972834162] 
dist 172=[-1.4744272092271755877 ,-.16851294937213739149] 
dist 173=[-1.4707179052737178368 ,-.06445905120461567960] 
dist 174=[-1.4651814081810494519 ,.04445110801865044778] 
dist 175=[-1.4515705318890320892 ,.14786595285251848054] 
dist 176=[-1.4443112729990550578 ,.26702775751552229889] 
dist 177=[-.6338184082286755338 ,.43878380735515492398] 
dist 178=[-.5631689092537252199 ,.60872728189941488847] 
dist 179=[-.3950519950252097486 ,.72065620422036400454] 
dist 180=[-.3685915637981313299 ,.8114873677608236231 ] 
dist 181=[-.1362028393939383273 ,.8972331776931761488 ] 
dist 182=[-.0943574464950777181 ,.97430036250648952149] 
dist 183=[-.0364592736513423431 ,1.0273469260120411145 ] 
dist 184=[-.0203090183414405891 ,1.0726615705083440605 ] 
dist 185=[-.00531251800507511103,1.1192561086284267294 ] 
dist 186=[-.03211381358369197100,1.1589874455062685851 ] 
dist 187=[-.06024490221593017450,1.1769122327103995908 ] 
dist 188=[-.09471961984036534631,1.1851887888577789342 ] 
dist 189=[-.14683865937133448856,1.1864138493732319687 ] 
dist 190=[-.2062794976639554598 ,1.1582218205219460256 ] 
dist 191=[-.26997473838710653974,1.1499741553703924555 ] 
dist 192=[-.34895899139588187881,1.1441786167967000307 ] 
dist 193=[-.4778113188545895931 ,1.1402202577324920118 ] 
dist 194=[-.60740526553105928443,.60391397383838852804] 
dist 195=[-.69080103362564224334,.55136100834215861679] 
dist 196=[-.75628747239860289707,.53928782518148943453] 
dist 197=[-.81441093700544310275,.46171541384431405602] 
dist 198=[-.86332088172747281923,.44621084278191623598] 
dist 199=[-.91707651190249686351,.41742799411593031151] 
dist 200=[-.99074863087765573548,.40994076057859344263] 
dist 201=[-1.0713698698975227237 ,.28582402917485495797] 
dist 202=[-1.1440548755494587984 ,.26867981955740245478] 
dist 203=[-1.1860555590485464531 ,.22910961824474401011] 
dist 204=[-1.2136046007352229015 ,.2220060626869214789 ] 
dist 205=[-1.2286164053958886877 ,.16817928200184625455] 
dist 206=[-1.2365389003401938217 ,.15802283039835668874] 
dist 207=[-1.2358500618585607717 ,.14158584181465460473] 
dist 208=[-1.2307583182626586888 ,.13738318110068061167] 
dist 209=[-1.2257077371876771040 ,.06227644902874239493] 
dist 210=[-.88534841322575725903,.16268895631931089052] 
dist 211=[-.85145712454976218901,.28748976626828088611] 
dist 212=[-.76494831633300917732,.38983152780704956644] 
dist 213=[-.8058986079150350636 ,.48821043908574092349] 
dist 214=[-.8356400526665843718 ,.57645270587146441248] 
dist 215=[-.8586185929672659134 ,.63834167169404939027] 
dist 216=[-.8783816880465148234 ,.69274779743854927327] 
dist 217=[-.8934663051963383882 ,.75112755527410864903] 
dist 218=[-.8977727479112485483 ,.8039052416372526816 ] 
dist 219=[-.8977294069730086330 ,.8359551806473245285 ] 
dist 220=[-.8954511233130435384 ,.8589417571804537899 ] 
dist 221=[-.8669260256669397824 ,.8755510246581163899 ] 
dist 222=[-.8581047334189181452 ,.8867787285173831015 ] 
dist 223=[-.8480050106527614509 ,.8887969567325366675 ] 
dist 224=[-.8425039522983970159 ,.8863655469362138741 ] 
dist 225=[-.01458362960352096288,.8838848315103524217 ] 
dist 226=[.02065141817271460850,.6039540834170617955 ] 
dist 227=[.00352833803278259381,.6488950265308275577 ] 
dist 228=[-.01473259873240889840,.6874712996840461951 ] 
dist 229=[-.03930156328809722829,.7189945753664990669 ] 
dist 230=[-.06602600235476136106,.74535774831482167306] 
dist 231=[-.0928898747310353980 ,.8045874009202624685 ] 
dist 232=[-.1249876676789280213 ,.8699912859565603408 ] 
dist 233=[-.1726003827899654954 ,.9290053559788051037 ] 
dist 234=[-.2216432849923242874 ,.9627340085416810613 ] 
dist 235=[-.2594492883488662278 ,.9843889883003483414 ] 
dist 236=[-.2962493518415592548 ,.9952185312493021817 ] 
dist 237=[-.3412788321008253448 ,1.0005778499693026484 ] 
dist 238=[-.3881332172766812478 ,1.0004016026394179151 ] 
dist 239=[-.4322169511598077801 ,.9964590991908113822 ] 
dist 240=[-.4827017317220629132 ,.9934084430395885881 ] 
dist 241=[-.5551028093072267557 ,.7478586414474972986 ] 
dist 242=[-.62571526229446732934,.7229132910067332533 ] 
dist 243=[-.66906219071676224299,.6584792482662510214 ] 
dist 244=[-.70072527518074692995,.6479385821665153007 ] 
dist 245=[-.72470901311343605007,.5385098493303062846 ] 
dist 246=[-.74262513529112711226,.5166528271722127013 ] 
dist 247=[-.75007279719432604691,.4909359360847781362 ] 
dist 248=[-.75251791917227211312,.4827096698150262801 ] 
dist 249=[-.7513554862995066666 ,.26497696374289209618] 
dist 250=[-.70798565534571359158,.23703354796042229333] 
dist 251=[-.7185261466735564157 ,.17818536455928847944] 
dist 252=[-.7322829367417092848 ,.16244488412935690453] 
dist 253=[-.7412018150539885017 ,.10262146829377822973] 
dist 254=[-.7428024562754165359 ,.09091177612301952492] 
dist 255=[-.7403048191051672836 ,.06726469233998298780] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 2, 0, 1] 
dist 0=[56.080825000676545227  ,56.080825000676545227  ] 
dist 1=[55.682175524417410795  ,56.409326195671628516  ] 
dist 2=[55.207804196410878285  ,56.603439622986634677  ] 
dist 3=[54.586308563022574289  ,56.735906221901465884  ] 
dist 4=[53.599865712395700830  ,56.818109889822797070  ] 
dist 5=[52.360192031282078121  ,56.851587188796861920  ] 
dist 6=[50.727365768806650757  ,56.789554478414952994  ] 
dist 7=[48.489923754319140046  ,56.645017225784999850  ] 
dist 8=[44.835806225499574490  ,56.553705537848667877  ] 
dist 9=[41.085430121023144945  ,55.978802821545360429  ] 
dist 10=[38.463540720838927359  ,55.813553376314352271  ] 
dist 11=[36.160421736898424033  ,55.158775553927886799  ] 
dist 12=[33.453663701200899869  ,55.056124218019881616  ] 
dist 13=[27.892303912420789063  ,41.422637143340534620  ] 
dist 14=[24.098568388932986505  ,40.132662100628228115  ] 
dist 15=[20.866080412709726057  ,36.937684613012594573  ] 
dist 16=[17.545540641024931643  ,36.480110950429468666  ] 
dist 17=[14.413854987163283212  ,31.572901782090277790  ] 
dist 18=[11.935164604405001892  ,30.642650128872176434  ] 
dist 19=[9.4537072153582265082 ,29.631160606438532700  ] 
dist 20=[6.3103298606376582241 ,29.453028864425994111  ] 
dist 21=[3.2757873691299568292 ,20.816853760391456381  ] 
dist 22=[1.2286012736441272689 ,19.749809685987077880  ] 
dist 23=[-.49464545494083149788,17.610433334687358933  ] 
dist 24=[-2.2359685111309514783 ,17.068806074595356188  ] 
dist 25=[-3.8660887269566351569 ,15.194559375502492267  ] 
dist 26=[-5.1458975206833564168 ,14.793209893854529917  ] 
dist 27=[-6.4228928329277725186 ,14.325074348604148180  ] 
dist 28=[-8.0432841600601208256 ,14.244002010944760606  ] 
dist 29=[-9.5729636108712672187 ,.46480684948794544212] 
dist 30=[-10.487775354587417917  ,-.64700891227915231756] 
dist 31=[-11.136579813039682729  ,-2.8939778682708151031 ] 
dist 32=[-11.602672823682422777  ,-2.9967421468506582465 ] 
dist 33=[-11.944602857193399448  ,-4.9790800611320434575 ] 
dist 34=[-12.096725817039172151  ,-5.2091812490513532174 ] 
dist 35=[-12.147686540344746997  ,-5.5532826776125130660 ] 
dist 36=[-12.139629832073043055  ,-5.6011217542475664539 ] 
dist 37=[-12.935557526994543998  ,-5.5468668328708208430 ] 
dist 38=[-13.807438276576289415  ,-5.3463165132885892788 ] 
dist 39=[-14.471260395768085850  ,-5.0026179519128440737 ] 
dist 40=[-15.027560054722384011  ,-4.3770286063163863187 ] 
dist 41=[-15.473880300350612422  ,-3.7186006766268589634 ] 
dist 42=[-15.698297312702368678  ,-3.2436786149716530577 ] 
dist 43=[-15.803395065509633213  ,-2.8140424991744152575 ] 
dist 44=[-15.813425223453562350  ,-1.1004452069623655101 ] 
dist 45=[-3.1628151357515242965 ,1.0854876101144458592 ] 
dist 46=[-2.6405563427833105067 ,2.5582087635882420245 ] 
dist 47=[-2.4276334778034504582 ,3.7906573922431037730 ] 
dist 48=[-2.3714755593958282780 ,5.0194132217630276259 ] 
dist 49=[-1.3561292396630840176 ,6.1448985451797904608 ] 
dist 50=[-1.2256385022741059374 ,6.9748917975836621258 ] 
dist 51=[-.93391325284809907264,7.7472974527800443108 ] 
dist 52=[-.88062214304105867999,8.6431563662769892186 ] 
dist 53=[-.54416411105258531453,9.4642134407143435106 ] 
dist 54=[-.48857295256343506211,9.9381754335420704630 ] 
dist 55=[-.38006784499961137018,10.249131278143777433  ] 
dist 56=[-.35594410224450452649,10.419697430708743121  ] 
dist 57=[1.8091757404542439112 ,10.518396327193838343  ] 
dist 58=[1.4392110109492663241 ,10.542417541660604633  ] 
dist 59=[.91432667291644018568,10.299674828045207426  ] 
dist 60=[.04174240078878870900,9.6705717343792736589 ] 
dist 61=[-.84466844211015265142,4.6584926536278245029 ] 
dist 62=[-1.4247678912088231857 ,4.4777110322196061552 ] 
dist 63=[-1.8909719081890670404 ,4.0208687834960464073 ] 
dist 64=[-2.3229796276068725281 ,3.9439848987911483497 ] 
dist 65=[-2.6995298555918165995 ,3.9255584226368497571 ] 
dist 66=[-2.9444875713081843760 ,3.9127224874058843688 ] 
dist 67=[-3.1398808785755902268 ,3.8885625207798271412 ] 
dist 68=[-3.3187174691441677782 ,3.8750478021589703048 ] 
dist 69=[-3.4729479662145513690 ,3.7917059359608219967 ] 
dist 70=[-3.5701603255903459278 ,3.7689062269920567992 ] 
dist 71=[-3.6443337444461127833 ,3.6811158057599494328 ] 
dist 72=[-3.7065837846373866241 ,3.6678060668842080029 ] 
dist 73=[-3.7564929005233284215 ,1.9421466286450389257 ] 
dist 74=[-3.7813948053611398895 ,1.7794380199661204547 ] 
dist 75=[-3.7927733355346044443 ,1.3915536464234793648 ] 
dist 76=[-3.7886879056330178100 ,1.3280342583897351141 ] 
dist 77=[-3.6579502585017932470 ,.7835649673199146411 ] 
dist 78=[-3.7696512770433271061 ,.68364503136961109807] 
dist 79=[-3.8332069752699332598 ,.54262893222343288281] 
dist 80=[-3.8483811327798191389 ,.50197182500283404595] 
dist 81=[-3.8462064586072754035 ,.16608316072973359726] 
dist 82=[-3.8802369757323745199 ,.43580901516631624984] 
dist 83=[-4.0169389433235940781 ,.70343732880139706552] 
dist 84=[-4.1530114164718159977 ,1.0375597434442356069 ] 
dist 85=[-4.2662142282737588950 ,1.3550915892231150232 ] 
dist 86=[-4.3116188849653981066 ,1.5565329336593465336 ] 
dist 87=[-4.3297417579138379689 ,1.7111748539636677031 ] 
dist 88=[-4.3339866681945149408 ,1.8419993317083306276 ] 
dist 89=[-4.2075222888183544754 ,1.9472156876991189927 ] 
dist 90=[-4.1751705662575937364 ,1.9996906938519837117 ] 
dist 91=[-4.1561238978836223650 ,2.0274996840936563578 ] 
dist 92=[-4.1501742361578136177 ,2.0343255977746661452 ] 
dist 93=[-3.2898115008580768126 ,1.0870717549334224675 ] 
dist 94=[-3.1816820012199703896 ,1.3930493912755783779 ] 
dist 95=[-2.9104011846549043273 ,1.8437574305431572135 ] 
dist 96=[-2.8596528596502419925 ,2.2721729101946561569 ] 
dist 97=[-2.4170609759348162527 ,2.6535752325064121286 ] 
dist 98=[-2.3279679659593530362 ,2.9166606633371511017 ] 
dist 99=[-2.2042403815026044671 ,3.1435826285058740632 ] 
dist 100=[-2.1639018621338936522 ,3.3806811374426329364 ] 
dist 101=[-1.3147576235428219638 ,3.5929116395170754813 ] 
dist 102=[-1.2022251941645743740 ,3.7205793077741896670 ] 
dist 103=[-.95509513874665353612,3.8108932037278380182 ] 
dist 104=[-.89385155357379034714,3.8740024243617486592 ] 
dist 105=[-.89826339788701770539,3.9149081007294070980 ] 
dist 106=[-1.0793222893649098599 ,3.9208784433530058457 ] 
dist 107=[-1.2817935993137979468 ,3.9048879805553610843 ] 
dist 108=[-1.5661550569929617303 ,3.8924067079369634872 ] 
dist 109=[-1.8433112516083458511 ,2.4272674182998251606 ] 
dist 110=[-2.0170369493654928077 ,2.2918065581173812059 ] 
dist 111=[-2.1481108620852364056 ,1.9575366241203003925 ] 
dist 112=[-2.2550852476153848344 ,1.9054509363588379546 ] 
dist 113=[-2.3382913439532220356 ,1.8804380388527455485 ] 
dist 114=[-2.3745312683359248218 ,1.9104505897828360671 ] 
dist 115=[-2.3906623441396718551 ,1.9248487099762261774 ] 
dist 116=[-2.3936146369905462354 ,1.9263447615143274059 ] 
dist 117=[-2.3200450691898970615 ,1.9114386096973399512 ] 
dist 118=[-2.2996397649756868205 ,1.9027359843020886319 ] 
dist 119=[-2.2546302644087739298 ,1.8806087998930205331 ] 
dist 120=[-2.2368175844892710634 ,1.8698726689594515587 ] 
dist 121=[-1.9184954358153905938 ,1.1766019698094820759 ] 
dist 122=[-1.8896117247730639049 ,1.1786539239686089874 ] 
dist 123=[-1.8269551056252988064 ,1.1758431353883710086 ] 
dist 124=[-1.8137959914102107148 ,1.1722321885424145648 ] 
dist 125=[-1.9151322168654776095 ,-1.0335614507504991771 ] 
dist 126=[-1.9854809949357872853 ,-1.0939279599533892387 ] 
dist 127=[-2.0574998141996932086 ,-1.1758491045905289049 ] 
dist 128=[-2.1454319814062222555 ,-1.1862931996320085254 ] 
dist 129=[-2.2206495516642149023 ,-1.1698786866169411025 ] 
dist 130=[-2.2652712327917199941 ,-1.1139031780521506665 ] 
dist 131=[-2.3231124860079410833 ,-1.0183268206600332795 ] 
dist 132=[-2.4118772978003808077 ,-.84385896270118830265] 
dist 133=[-2.4919157555335418730 ,-.65075870690354472826] 
dist 134=[-2.5359709983259102457 ,-.48081164266733643217] 
dist 135=[-2.5621765330352321029 ,-.29536131538470349612] 
dist 136=[-2.5709581108485618490 ,-.04036791721312761181] 
dist 137=[-2.5681255163972830419 ,.23973206903629607381] 
dist 138=[-2.5633241524247065912 ,.52539486977762694136] 
dist 139=[-2.5270266659038500350 ,.86980658131012550323] 
dist 140=[-2.5210644142054990004 ,1.3843894882421157033 ] 
dist 141=[-.98539940530675427379,1.8940962094797801543 ] 
dist 142=[-.94190078617683994492,2.2190509468495195510 ] 
dist 143=[-.89509880222535055597,2.4708665960163872414 ] 
dist 144=[-.88397710926644182383,2.6886706802075017497 ] 
dist 145=[-.44264321337509799463,2.8689309934878300359 ] 
dist 146=[-.38723350239343644756,3.0271297416160591086 ] 
dist 147=[-.27350004130665706319,3.1494799926682557222 ] 
dist 148=[-.24394368167526254131,3.2548799748462731095 ] 
dist 149=[-.1371163445274424039 ,3.3418900157193443484 ] 
dist 150=[-.11511528856486132789,3.3908459429491636268 ] 
dist 151=[-.08056219422971842422,3.4213062683352762595 ] 
dist 152=[-.07182836931692181210,3.4345003046735783168 ] 
dist 153=[.59666973552810082348,3.4356044872672961994 ] 
dist 154=[.56690919320075771449,3.4278251342162462951 ] 
dist 155=[.52885698584533569515,3.3941058750706882924 ] 
dist 156=[.46956288854292526299,3.3735360357980243256 ] 
dist 157=[.40117866121615905425,1.7260735323001016385 ] 
dist 158=[.3268477894957348285 ,1.5779674674947698102 ] 
dist 159=[.00943812329326448177,1.2182493922566537446 ] 
dist 160=[-.31427263770569734269,1.1642961994258222384 ] 
dist 161=[-.61401858733123101809,.679640027338542425  ] 
dist 162=[-.84064861050321764024,.70740429908332486409] 
dist 163=[-1.0570686076669242360 ,.73728039057456280601] 
dist 164=[-1.3160726780687161971 ,.77782451956729711351] 
dist 165=[-1.5591227965256636364 ,.82209148121227576484] 
dist 166=[-1.7118724979376945187 ,.86682338366542832006] 
dist 167=[-1.8276966070301408341 ,.92043470318371802498] 
dist 168=[-1.9233760663029588158 ,1.0001348074400213720 ] 
dist 169=[-1.9987831637322531195 ,1.0789474985201438356 ] 
dist 170=[-2.0337018782967038356 ,1.1290174372827665430 ] 
dist 171=[-2.0507732807139412340 ,1.1675870016103280163 ] 
dist 172=[-2.0549493445851712377 ,1.2005071492456316393 ] 
dist 173=[-1.8663357388791162980 ,1.2272467031432174365 ] 
dist 174=[-1.9062245168729738481 ,1.2411523102486731700 ] 
dist 175=[-1.9288028220680566183 ,1.2483080474706118403 ] 
dist 176=[-1.9336527824203779564 ,1.2481116671832786972 ] 
dist 177=[-1.8219375439546223749 ,1.2434426325866980678 ] 
dist 178=[-1.8000665292588480576 ,1.2391724696468792108 ] 
dist 179=[-1.7765771790497423906 ,1.2213968788442909916 ] 
dist 180=[-1.7635558859830980234 ,1.2140917544742698095 ] 
dist 181=[-1.7439163572254175522 ,1.1537143712073777516 ] 
dist 182=[-1.7351423683904284166 ,1.1379864913945117940 ] 
dist 183=[-1.7292084104859784417 ,1.1147933334825822884 ] 
dist 184=[-1.7256159524878718322 ,1.1060544229286363856 ] 
dist 185=[-.56545921055294795169,.88488821511330085682] 
dist 186=[-.54045335315410277238,.8523958764290368561 ] 
dist 187=[-.48671119442434457838,.78844480475763668725] 
dist 188=[-.47141761384840289619,.77523056523860248826] 
dist 189=[-.04523794221825468492,.96057678466594930495] 
dist 190=[-.02529471077318289288,1.0810031690569858837 ] 
dist 191=[-.00156752035972850569,1.1769273147781062660 ] 
dist 192=[.00209616891742730051,1.3092415289145082618 ] 
dist 193=[-.08172368718299510617,1.4495303730183917418 ] 
dist 194=[-.22698151844964394721,1.5535619644960780184 ] 
dist 195=[-.3675516184557325991 ,1.6509425549095131134 ] 
dist 196=[-.53840861188827736564,1.7646893586250934969 ] 
dist 197=[-.71558739461687188077,1.8692503195761272932 ] 
dist 198=[-.88138771829173503316,1.9299710103487368321 ] 
dist 199=[-1.0705569840415612631 ,1.9702017737021829702 ] 
dist 200=[-1.3409989419679143275 ,1.9929876958371133202 ] 
dist 201=[-1.6057104671651621400 ,2.0045261418721888885 ] 
dist 202=[-1.7720107013474103354 ,2.0042008445128746637 ] 
dist 203=[-1.8980137080345996294 ,1.9901088705796380197 ] 
dist 204=[-2.0019045989535320263 ,1.9430903211873687814 ] 
dist 205=[-2.0842707186047177466 ,.93679163077287914476] 
dist 206=[-2.1243711381897657010 ,.96480501027816472889] 
dist 207=[-2.1444514881292599551 ,.99401898169591696505] 
dist 208=[-2.1469200945707656086 ,1.0324878223539425830 ] 
dist 209=[-2.0856498176922822792 ,1.0700953218332066292 ] 
dist 210=[-2.0682379745426330851 ,1.0958716289884003719 ] 
dist 211=[-2.0408327965793772948 ,1.1179017540247617162 ] 
dist 212=[-2.0294057282384647151 ,1.1405591765823080380 ] 
dist 213=[-1.9820817017354587075 ,1.1618661470499438610 ] 
dist 214=[-1.9665592555641410462 ,1.1785066043237925405 ] 
dist 215=[-1.9009251799286910576 ,1.1949024811733977229 ] 
dist 216=[-1.7798574064495173892 ,1.2152323548716321284 ] 
dist 217=[-1.6872395523976586749 ,1.2327440365457354205 ] 
dist 218=[-1.6866839281114397889 ,1.2378932821081843288 ] 
dist 219=[-1.6802179621146615585 ,1.2369346744706985275 ] 
dist 220=[-1.6751144242012337143 ,1.2333964198980269047 ] 
dist 221=[-1.2693361262276098889 ,1.2022618051423285241 ] 
dist 222=[-1.2243971205081444357 ,1.1922656019910057442 ] 
dist 223=[-1.1076654453951493247 ,1.1710658155388681018 ] 
dist 224=[-1.0898068790823957040 ,1.1627991829028658527 ] 
dist 225=[-.89091279480688940481,.99822318143421652234] 
dist 226=[-.85149118496746436448,.97272310633139738201] 
dist 227=[-.80834312482760368323,.93188503383907778908] 
dist 228=[-.79742471050194571317,1.0227714856165778150 ] 
dist 229=[-.39915160596300359508,1.1056222107082802091 ] 
dist 230=[-.34903022653827023353,1.1550527064949686851 ] 
dist 231=[-.24544426187907077661,1.1894451199475661155 ] 
dist 232=[-.21836900002280348417,1.2122837553340189664 ] 
dist 233=[-.11944042089200438306,1.2271255944319457841 ] 
dist 234=[-.09936742786628849445,1.2296040131179547637 ] 
dist 235=[-.06543369859902874036,1.2270908529034623335 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 2, 1, 0, 0, 2] 
dist 0=[62.432333304881842024  ,62.432333304881842024  ] 
dist 1=[62.317932501960536736  ,62.379227845161715542  ] 
dist 2=[62.039242381392044880  ,62.432333304881842024  ] 
dist 3=[61.411294977707219391  ,62.105399297021422183  ] 
dist 4=[60.154214155531847437  ,61.782368025648024016  ] 
dist 5=[58.706437444757876638  ,61.639899764211190853  ] 
dist 6=[56.894694969308418748  ,61.239072765105090937  ] 
dist 7=[55.131940159495934567  ,60.078433049026714145  ] 
dist 8=[53.124315000901013193  ,56.970663504831875784  ] 
dist 9=[50.252983848174144705  ,55.925460113178285048  ] 
dist 10=[47.039578407080275992  ,55.608643046685032429  ] 
dist 11=[43.665856041621064122  ,55.065298367196754323  ] 
dist 12=[38.648133219769101917  ,54.886147151727296044  ] 
dist 13=[33.157218431947237052  ,54.017722704773901734  ] 
dist 14=[26.911634816023164791  ,43.770092314399088408  ] 
dist 15=[22.645811427228527654  ,43.604444727887787846  ] 
dist 16=[19.059358914671023248  ,34.368657659713908958  ] 
dist 17=[15.451723352165235002  ,33.189264370789098631  ] 
dist 18=[12.096577151386577396  ,30.886119352566331274  ] 
dist 19=[9.5180888607679860225 ,30.300513772984202777  ] 
dist 20=[7.0077467781257893355 ,28.293504249461309584  ] 
dist 21=[3.9241097676133408680 ,27.824486206759352435  ] 
dist 22=[.99300115859922453367,27.322952688864660954  ] 
dist 23=[-.90855474302233447166,27.206975965776875798  ] 
dist 24=[-2.4272984249401810514 ,7.0149801542820896778 ] 
dist 25=[-3.8300131282823091248 ,5.3780247571295038284 ] 
dist 26=[-5.0605079721592751698 ,3.4907818260354849280 ] 
dist 27=[-5.8921049618907770637 ,2.8925612159507421344 ] 
dist 28=[-6.5985043849373482135 ,2.7836477275964639695 ] 
dist 29=[-7.3304826532437713648 ,-.5461328704537148713 ] 
dist 30=[-8.2720254188003756074 ,-4.6054004407851773196 ] 
dist 31=[-10.483396980916801734  ,-5.4638533619751853429 ] 
dist 32=[-12.566064806316990640  ,-5.8595543930919917291 ] 
dist 33=[-13.881983105189388095  ,-6.9181628870722001945 ] 
dist 34=[-14.892102991647555883  ,-7.0708996794666675679 ] 
dist 35=[-15.753374576766036972  ,-7.3120934836100254540 ] 
dist 36=[-16.456351646594521924  ,-7.3277207868617061011 ] 
dist 37=[-16.834258192491587207  ,-6.9974846825198275840 ] 
dist 38=[-17.047896346035411409  ,-5.9670352719972373294 ] 
dist 39=[-17.094862342037127115  ,-4.0678804804773614444 ] 
dist 40=[-7.3936287773674824466 ,-2.1171535505302420543 ] 
dist 41=[-7.3708538135957520188 ,-.78295347720426612264] 
dist 42=[-7.3498690644193992886 ,.3522747124087531759 ] 
dist 43=[-7.3268555703034626056 ,1.5095846059231691907 ] 
dist 44=[-7.2971531094154939478 ,2.5902196053394057202 ] 
dist 45=[-5.3380468411857461701 ,3.4197646462951218991 ] 
dist 46=[-2.5708631535285405127 ,4.2233294071835158707 ] 
dist 47=[-1.7275623991301210746 ,5.2005740550710317873 ] 
dist 48=[-1.5954735508095317282 ,6.1186240098847916086 ] 
dist 49=[-.48080024553185125431,6.6861179970602891820 ] 
dist 50=[-.28497892789756837721,7.1055414814575170211 ] 
dist 51=[-.00313257182073627373,7.4328692288746809123 ] 
dist 52=[.07189350204280826972,7.6792951494128662000 ] 
dist 53=[1.3006329196504676143 ,7.7757656328477878388 ] 
dist 54=[1.4511820234886537290 ,7.8103598426803185251 ] 
dist 55=[1.7572117959049547481 ,7.8099190783873450379 ] 
dist 56=[1.8222422198141801856 ,7.4194894919290693721 ] 
dist 57=[1.8609922982898803755 ,7.3423947403906658540 ] 
dist 58=[1.5732396361865242182 ,7.0837759463303328776 ] 
dist 59=[1.1029464491009761656 ,7.0391028420614326852 ] 
dist 60=[.4869444352254620987 ,6.3925064867110539558 ] 
dist 61=[-.4881652381537603428 ,5.9748815844903527005 ] 
dist 62=[-1.4686983476706699291 ,3.4865072471852976401 ] 
dist 63=[-2.1063814078788822700 ,3.4523572229312264475 ] 
dist 64=[-2.6145621114428414259 ,2.8111915408006709095 ] 
dist 65=[-3.0783839033669953263 ,2.7210051416014025825 ] 
dist 66=[-3.4779298602779026441 ,2.4946042891050299003 ] 
dist 67=[-3.7296631178571333022 ,2.4573149434917163368 ] 
dist 68=[-3.9213444772020758810 ,2.1000191620416039414 ] 
dist 69=[-4.0813213680464791698 ,2.0311069899562982815 ] 
dist 70=[-4.2138200652416831088 ,1.9427710032285736688 ] 
dist 71=[-4.2958524628476477987 ,1.9143268775378917451 ] 
dist 72=[-4.3568189251737773467 ,1.2584828892713549843 ] 
dist 73=[-4.4051952273410219939 ,1.1422024143302361613 ] 
dist 74=[-4.4419387858702741909 ,1.1188259312615279605 ] 
dist 75=[-4.4564524552878286571 ,1.0801844266875576791 ] 
dist 76=[-4.4575244691613374054 ,1.0698288238341961820 ] 
dist 77=[-4.4421000871722055300 ,.86013098379026265396] 
dist 78=[-4.2907996624099867791 ,.83054365827444773753] 
dist 79=[-4.4716420443535829283 ,.76491812678639346563] 
dist 80=[-4.6256647620268948772 ,.74661646504681177542] 
dist 81=[-4.7006982794268635493 ,.66055488671671374605] 
dist 82=[-4.7355654713058504840 ,.64277248565392043026] 
dist 83=[-4.7381084136961310058 ,.8288676210999779762 ] 
dist 84=[-4.6782918477572672243 ,1.1523835851853619574 ] 
dist 85=[-4.6499143610119306853 ,1.5535560104503693993 ] 
dist 86=[-4.6073913763793996168 ,1.9336351731844676862 ] 
dist 87=[-4.5862088281736956237 ,2.1729974769427546956 ] 
dist 88=[-3.3005747302954642883 ,2.3547796138854843173 ] 
dist 89=[-3.1583288369591362716 ,2.5051301057632082909 ] 
dist 90=[-2.8045380936030999316 ,2.6242773714719703267 ] 
dist 91=[-2.7442503269990185366 ,2.6815716890248084763 ] 
dist 92=[-2.1882991903177718624 ,2.7100620813343610045 ] 
dist 93=[-2.0800205406826263143 ,2.7142861355960686537 ] 
dist 94=[-1.9374949077479995694 ,2.7397578289544673628 ] 
dist 95=[-1.8898928776944268639 ,3.0320746839086692477 ] 
dist 96=[-.91653509959567441392,3.2989093993866820828 ] 
dist 97=[-.79111421911383767662,3.4621370365661417573 ] 
dist 98=[-.51732311463435902884,3.5807977587566301280 ] 
dist 99=[-.45374728634570864193,3.6697359296150201153 ] 
dist 100=[-.14418052525379946375,3.7328041789693017802 ] 
dist 101=[-.2563705883704638884 ,3.7482003897272544061 ] 
dist 102=[-.4961674201831689091 ,3.7463755098115692550 ] 
dist 103=[-.6666446317709822631 ,3.7407163330385301948 ] 
dist 104=[-.8187769677879036252 ,2.5397118397031733762 ] 
dist 105=[-.98539459914685156375,2.4265979331161098322 ] 
dist 106=[-1.1504196468605533814 ,2.1415640925590880584 ] 
dist 107=[-1.3064495612920141186 ,2.0974215441527761524 ] 
dist 108=[-1.4765732158620642774 ,1.6437664238871060763 ] 
dist 109=[-1.7102873355498878692 ,1.5564764122549001631 ] 
dist 110=[-1.9355985615999056518 ,1.4531000630305097204 ] 
dist 111=[-2.0721978694851421629 ,1.4258881065751543291 ] 
dist 112=[-2.1699300045256340874 ,.99419822962742431409] 
dist 113=[-2.2401428764434823802 ,1.0673465258743263620 ] 
dist 114=[-2.2913256012378105526 ,1.1343601563628822452 ] 
dist 115=[-2.3131127820893819120 ,1.1835310351813499222 ] 
dist 116=[-2.3186646212007750110 ,1.2289169967380904098 ] 
dist 117=[-2.3159357571176884202 ,1.2808260119609318468 ] 
dist 118=[-2.1234685385610919734 ,1.3277007506892961663 ] 
dist 119=[-2.0888411903457038836 ,1.3530028865089222405 ] 
dist 120=[-2.0219104960325691808 ,1.3672529497222503140 ] 
dist 121=[-2.0009882580068918364 ,1.3700413828845112615 ] 
dist 122=[-1.9100293625510381485 ,1.3659649913536156866 ] 
dist 123=[-1.9262635355114141917 ,1.3617313964114534818 ] 
dist 124=[-2.0721006619702100685 ,1.3391207924672738076 ] 
dist 125=[-2.1801035858101894784 ,1.3327333525605682653 ] 
dist 126=[-2.2811495031875903396 ,-.44301387244820069164] 
dist 127=[-2.3992211945337609182 ,-.54196178581365057052] 
dist 128=[-2.5079602396722594540 ,-.56163038121817875076] 
dist 129=[-2.5717539513506116527 ,-.63214985471144441239] 
dist 130=[-2.6148979786857316306 ,-.45520143213729966773] 
dist 131=[-2.6412075991736451439 ,-.20552626441104430595] 
dist 132=[-2.6547335580322022698 ,.07168750671814551731] 
dist 133=[-2.6543289846545645086 ,.35855141166542006748] 
dist 134=[-2.6332917891023188502 ,.70736438365902860275] 
dist 135=[-2.6241620068424179680 ,1.2318265239459972528 ] 
dist 136=[-1.2479779815006276884 ,1.7523860556998949700 ] 
dist 137=[-1.2511723901081313353 ,2.0856275488070011115 ] 
dist 138=[-1.2501641705363316838 ,2.3454065400109852249 ] 
dist 139=[-1.2458832190662935457 ,2.5727789052587622982 ] 
dist 140=[-1.2419650372646235333 ,2.7618671957567310497 ] 
dist 141=[-.7246436376040711961 ,2.9091577901617047721 ] 
dist 142=[-.7037074251716718363 ,3.0275265260529813210 ] 
dist 143=[-.6481356910277043708 ,3.1280081491082761726 ] 
dist 144=[-.6399039910363277370 ,3.2107720551301893700 ] 
dist 145=[-.54091069981203404767,3.2584303136832561212 ] 
dist 146=[-.5209408843510412314 ,3.2895029199337089308 ] 
dist 147=[-.50078823339932992007,3.3060734242032103437 ] 
dist 148=[-.49631617314998903091,3.3120690805815883684 ] 
dist 149=[-.28088147307530402123,3.3050243761533632175 ] 
dist 150=[-.25357935439453073514,3.2814459379911245765 ] 
dist 151=[-.19883791644434394081,3.2657566657688125296 ] 
dist 152=[-.18474242415448660794,1.5854643048125358657 ] 
dist 153=[-.13502198225484794535,1.4378526000172377013 ] 
dist 154=[-.12412307880789372928,1.0801348130719266532 ] 
dist 155=[-.18419392905180712399,1.0269761469453261707 ] 
dist 156=[-.47150422344488607211,.7651620248056067460 ] 
dist 157=[-.69000243691095916987,.42078567461689837273] 
dist 158=[-.89987700582291563631,.40840320787928596805] 
dist 159=[-1.1527767903459393957 ,.4018338428214335819 ] 
dist 160=[-1.3906903384517076342 ,.40416477216013124067] 
dist 161=[-1.5407573206964101693 ,.41159666356062107479] 
dist 162=[-1.6551747783017320384 ,.42605672330957637618] 
dist 163=[-1.7508119731822763138 ,.44842177325427627816] 
dist 164=[-1.8270225004396676552 ,.48739911314289824562] 
dist 165=[-1.8639083909292620076 ,.52991984157536432452] 
dist 166=[-1.8827582766445415875 ,.56642535609653533757] 
dist 167=[-1.8869906466726783801 ,.60549090478113500586] 
dist 168=[-1.6279729661713619167 ,.65822854415535488517] 
dist 169=[-1.6005136204411901550 ,.71567732060815703802] 
dist 170=[-1.5249113360921307182 ,.77354345884449739613] 
dist 171=[-1.5093742293680779899 ,.84276358748926701441] 
dist 172=[-1.3601603901250455533 ,.945521707003403078  ] 
dist 173=[-1.3488877974708028021 ,1.0470975276255554850 ] 
dist 174=[-1.4804681383405533659 ,1.1115998273641538866 ] 
dist 175=[-1.5783505485952975803 ,1.1612579636594363984 ] 
dist 176=[-1.6557894059764611573 ,1.2035973017876973842 ] 
dist 177=[-1.7166040952600132572 ,1.2379594932672913369 ] 
dist 178=[-1.7481417905492069038 ,1.2557843917333238284 ] 
dist 179=[-1.7642633112710543923 ,1.2648980475761606541 ] 
dist 180=[-1.7661414067765951844 ,1.2646623781747906418 ] 
dist 181=[-1.6635005062179103813 ,1.2583594592383305441 ] 
dist 182=[-1.6430736548118037705 ,1.2543524896323924717 ] 
dist 183=[-1.6155082111590314593 ,1.2314940143078468872 ] 
dist 184=[-1.6036818095693904405 ,1.2281606885792248971 ] 
dist 185=[-1.5736232861406393248 ,1.1447590365027416178 ] 
dist 186=[-1.5603420759007149989 ,1.1641823128089502935 ] 
dist 187=[-1.5445630088812635942 ,1.3016659718779805868 ] 
dist 188=[-1.5356468167191848244 ,1.4375508798680609472 ] 
dist 189=[-.3604991525704107046 ,1.5367287762160012920 ] 
dist 190=[-.2610002919847562865 ,1.6279959057583408239 ] 
dist 191=[-.07410316234545229809,1.7323120071701420116 ] 
dist 192=[-.1259171819147893445 ,1.8270065336109101575 ] 
dist 193=[-.17336701505462791158,1.8798753657406621995 ] 
dist 194=[-.22667915612828470447,1.9122294487364127056 ] 
dist 195=[-.30189246078779789349,1.9250507158110075800 ] 
dist 196=[-.38538856103745723485,1.9282652911135779530 ] 
dist 197=[-.47175814687771994417,1.9237930402577566976 ] 
dist 198=[-.57674577682772432188,1.9111145092005257336 ] 
dist 199=[-.73454604783661895457,1.9026760511648188471 ] 
dist 200=[-.89101996831047392069,.48031854872945173502] 
dist 201=[-.99071543485850478604,.50181624736615432528] 
dist 202=[-1.1558148832896280940 ,.5312514272285725564 ] 
dist 203=[-1.3539114390894264636 ,.57212358624630568032] 
dist 204=[-1.5284012036999023315 ,.63926153185637136807] 
dist 205=[-1.6452748274757501424 ,.70824235353730328742] 
dist 206=[-1.7422792195078269216 ,.75646857940665783024] 
dist 207=[-1.8407458248372696413 ,.79869943183770039938] 
dist 208=[-1.9278770053668575162 ,.84375493888451804675] 
dist 209=[-1.9959049120823556214 ,.88714495331785586248] 
dist 210=[-2.0282507190576464196 ,.92272932493463055036] 
dist 211=[-2.0431851399968031326 ,.95938989595354109962] 
dist 212=[-2.0433417104713385182 ,1.0070742771741207471 ] 
dist 213=[-1.9575485998966633458 ,1.0534138597674104254 ] 
dist 214=[-1.9375367546138096712 ,1.0847077516617420596 ] 
dist 215=[-1.8196867420705221185 ,1.1109535085286638796 ] 
dist 216=[-1.2737078300270699743 ,1.1371479457448681427 ] 
dist 217=[-1.2282947658448974945 ,1.1612828751983007017 ] 
dist 218=[-1.1104667017607597414 ,1.1793097734404467802 ] 
dist 219=[-1.0923598748331968383 ,1.1963019668703118669 ] 
dist 220=[-.89200942387090799893,1.2163073078730954833 ] 
dist 221=[-.8523162313763264182 ,1.2332493961336279897 ] 
dist 222=[-.80857152189877161851,1.2380171551263600129 ] 
dist 223=[-.79730581030561480102,1.2367778598733930758 ] 
dist 224=[-.39775353318325693165,1.2331159277700743728 ] 
dist 225=[-.3474418974339281676 ,1.2014847109747821787 ] 
dist 226=[-.24322751844112031116,1.1913989762787612545 ] 
dist 227=[-.21594009723668580745,1.2131562910528381487 ] 
dist 228=[-.11589429355039381832,1.2278691714361918431 ] 
dist 229=[-.09569901125194718555,1.2303411537910317141 ] 
dist 230=[-.06075750348826130303,1.2266884721876283949 ] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 1, 2, 1, 0, 2] 
dist 0=[54.117263340727854071  ,54.117263340727854071  ] 
dist 1=[53.726200564387091681  ,54.463319577599464474  ] 
dist 2=[52.510773554510815543  ,54.904045247090345472  ] 
dist 3=[50.971675617404890858  ,55.101584754346482373  ] 
dist 4=[49.107781742595816202  ,55.198856830654977590  ] 
dist 5=[46.645521714747146621  ,55.239104843631643719  ] 
dist 6=[42.717067353929203165  ,55.244713603799618185  ] 
dist 7=[38.704108160507894680  ,55.203425092206821554  ] 
dist 8=[35.904331246620717476  ,55.145345516504991519  ] 
dist 9=[33.451914590239232961  ,55.083929310357709315  ] 
dist 10=[30.825777501704493956  ,55.007474767690385058  ] 
dist 11=[28.282249645559542663  ,54.890879370450092650  ] 
dist 12=[26.159468319913454256  ,54.753836499640755058  ] 
dist 13=[23.933152481949654309  ,54.614509186695643542  ] 
dist 14=[20.975730872023111754  ,53.825035927909432504  ] 
dist 15=[18.055910329622578644  ,52.084406374185497118  ] 
dist 16=[15.979490619068628236  ,37.262351446582795633  ] 
dist 17=[14.116871958130666314  ,35.801914518116213442  ] 
dist 18=[12.050507101570874767  ,32.268979715142185480  ] 
dist 19=[10.001753793727587040  ,31.743505554371383159  ] 
dist 20=[8.2089588051616127720 ,26.613879161177313619  ] 
dist 21=[6.2520901595160964490 ,25.664150376708825931  ] 
dist 22=[3.5469499220901720860 ,24.522495227243763003  ] 
dist 23=[.90366362905358141559,24.272647790965776013  ] 
dist 24=[-.80627323489479896765,16.332798649310528788  ] 
dist 25=[-2.1689909241350188114 ,15.355752612728950523  ] 
dist 26=[-3.4247419139667477266 ,13.325279004973160801  ] 
dist 27=[-5.3044761278219294654 ,12.806615346162682976  ] 
dist 28=[-7.9257137715490677615 ,10.892814077150122728  ] 
dist 29=[-9.5759997510020017429 ,10.522594582955431101  ] 
dist 30=[-10.840609535607301498  ,9.8755732824045085741 ] 
dist 31=[-11.920621750267385763  ,9.7396641172736389957 ] 
dist 32=[-12.808409949670523820  ,.21194857664267041193] 
dist 33=[-13.305054842966082661  ,-.59995794359573442799] 
dist 34=[-13.615353765719493759  ,-2.3047796542046204318 ] 
dist 35=[-13.759042443973658083  ,-2.6612242019461808032 ] 
dist 36=[-13.827360489479633430  ,-2.9158426688199194408 ] 
dist 37=[-13.836441649699855423  ,-1.9362308907080953645 ] 
dist 38=[-13.807079163489683252  ,-.40147744750043710363] 
dist 39=[-13.763251373849411133  ,1.1478198400925816423 ] 
dist 40=[-13.607855000447687925  ,2.1856362768543079302 ] 
dist 41=[-13.537779086750281194  ,3.0442265063201419329 ] 
dist 42=[-13.358417490443525141  ,3.8789531478484950731 ] 
dist 43=[-13.606379027520994776  ,4.6315865904434111003 ] 
dist 44=[-13.771888780195691926  ,5.1628683050154351038 ] 
dist 45=[-13.817240879007450411  ,5.6324079493457694651 ] 
dist 46=[-13.805584843688024084  ,6.1388814349711243346 ] 
dist 47=[-13.769201914371554733  ,6.5908033350738209498 ] 
dist 48=[-2.0462880128377155549 ,6.8427450213769735723 ] 
dist 49=[-1.7119577514424682433 ,6.9958106888581314378 ] 
dist 50=[-1.1418388256645617802 ,7.0532191215249519383 ] 
dist 51=[-1.0144458738362854285 ,7.0653419135172059005 ] 
dist 52=[-.4704732686992316254 ,7.1837036963123149018 ] 
dist 53=[-.44795054517419527048,7.7451425374913877534 ] 
dist 54=[-.47957936038720883986,8.1552276473393992428 ] 
dist 55=[-.52258553282012620052,8.4662141306701573763 ] 
dist 56=[-.54907064990020468133,8.6981083082151568274 ] 
dist 57=[-.56819472426049409194,8.7924948417534656312 ] 
dist 58=[-.58189229210705272935,8.8231906634340207200 ] 
dist 59=[-.59157362032240566391,8.8059696872995724373 ] 
dist 60=[-.59470988642457694292,7.3766489193148404551 ] 
dist 61=[-.59463495591683797275,7.4212331309161952086 ] 
dist 62=[-.59291398865510086   ,7.4230359426909850829 ] 
dist 63=[-.54539845202724976334,7.4004514621848926637 ] 
dist 64=[-.53637386593133376906,4.6304808301657454715 ] 
dist 65=[-.51807933945253781225,4.3763836248804445977 ] 
dist 66=[-.51205264261394784617,3.7431505602153506828 ] 
dist 67=[-.48389946449828564741,3.6456640255893262887 ] 
dist 68=[-.61185828488291082382,2.6702389291102968821 ] 
dist 69=[-.96735062410613012529,2.4864487220836114797 ] 
dist 70=[-1.2785047726639483738 ,2.2607242526575377087 ] 
dist 71=[-1.5752223145352916833 ,2.2031178950061661777 ] 
dist 72=[-1.9975139221468646012 ,2.1980663327272491949 ] 
dist 73=[-2.3771031823736679244 ,2.4352873484597985746 ] 
dist 74=[-2.6804881027007424799 ,2.7267504125258837873 ] 
dist 75=[-3.1501120798758166847 ,3.1674048668544519830 ] 
dist 76=[-3.6629404024182535075 ,3.6031890700719722256 ] 
dist 77=[-3.9831368261261336968 ,3.8751935965806093595 ] 
dist 78=[-4.2240911182357624297 ,4.0784575696718311110 ] 
dist 79=[-4.4205731788974647776 ,4.2400245294628223897 ] 
dist 80=[-4.5740516783483564024 ,4.3640390510901944510 ] 
dist 81=[-4.6433488691787036180 ,4.4175297513551722725 ] 
dist 82=[-4.6745006251947066070 ,4.4388872004566551786 ] 
dist 83=[-4.6755782191632922350 ,4.4347576397606126218 ] 
dist 84=[-4.5690043279502872157 ,4.2305240391868187595 ] 
dist 85=[-4.5366359581916009830 ,4.1831654867375244478 ] 
dist 86=[-4.4573940179111635284 ,4.0924150691209275817 ] 
dist 87=[-4.4243575456833726824 ,4.0606181541284311375 ] 
dist 88=[-4.3640324249401784429 ,3.9071990697713385514 ] 
dist 89=[-4.4261800301424214976 ,3.8675108197054346323 ] 
dist 90=[-4.4563766920247581514 ,3.7441613584355027045 ] 
dist 91=[-4.4568645650407061152 ,3.7136882439086065889 ] 
dist 92=[-4.4277736174584872862 ,3.4392193729353163952 ] 
dist 93=[-4.4100790011161439970 ,3.9918533263321692228 ] 
dist 94=[-4.3464110989975622987 ,4.4204562100262313546 ] 
dist 95=[-4.3169667833620143016 ,4.7914586805123600594 ] 
dist 96=[-3.9195381064043996105 ,5.0967767949136125624 ] 
dist 97=[-3.8487067960608322082 ,5.2632746701657742112 ] 
dist 98=[-3.6769644211901215160 ,5.3599066438084246516 ] 
dist 99=[-3.6221155257973269909 ,5.3864394793006524985 ] 
dist 100=[-3.3333752963475164801 ,5.3871518477467270636 ] 
dist 101=[-3.2681567916225511827 ,5.3807393443021995195 ] 
dist 102=[-3.1345192951235609922 ,5.3679161662029614830 ] 
dist 103=[-3.0929990529257687863 ,5.3447462397649891060 ] 
dist 104=[-2.4579972217364703171 ,5.3121959297983288264 ] 
dist 105=[-2.3646533066164814189 ,5.2830352691440922971 ] 
dist 106=[-2.1273062607285593821 ,5.1199475146936532571 ] 
dist 107=[-2.0860381919529035470 ,4.7657805136918735717 ] 
dist 108=[-1.6927965514854306916 ,4.2888312606456137818 ] 
dist 109=[-1.6143637742830474528 ,4.2707694883171116473 ] 
dist 110=[-1.5137802789188389208 ,4.2569119682445254775 ] 
dist 111=[-1.4783204223276120785 ,4.2452997426355274626 ] 
dist 112=[-.04377942037003583988,2.0644162343468751641 ] 
dist 113=[-.00672699306609312371,2.0994651327960096200 ] 
dist 114=[-.00089973276284130703,2.1293669099230337522 ] 
dist 115=[.03772024405296918479,2.1602334137331824629 ] 
dist 116=[.04429540530738377573,2.1867462793569793603 ] 
dist 117=[.05655058883627747132,2.1992641203837045118 ] 
dist 118=[.05921401325356879682,2.2040210445949375004 ] 
dist 119=[-.11040521887134343211,2.1995371999040972925 ] 
dist 120=[-.41777076332663809613,2.1895373395079861661 ] 
dist 121=[-.7223792378455951115 ,2.1812907980086347878 ] 
dist 122=[-1.0833223993722191969 ,2.1537401346927525764 ] 
dist 123=[-1.6155488148100900097 ,2.1396752037289214078 ] 
dist 124=[-2.1414007686125054706 ,.51707265699375274836] 
dist 125=[-2.4769067915297148007 ,.5120788801151667704 ] 
dist 126=[-2.7372577134322233655 ,.5097202781714142663 ] 
dist 127=[-2.9631464254513897428 ,.43648277013044458974] 
dist 128=[-3.1552985717403038767 ,.42524803549705628806] 
dist 129=[-3.2956087798402199799 ,.40134137083301589774] 
dist 130=[-3.3976157623145876795 ,.39411975171032606067] 
dist 131=[-3.4740357180965960174 ,.36260018519946218921] 
dist 132=[-3.5324404264497811619 ,.35602218022425528022] 
dist 133=[-3.5625456368337231145 ,.33711407158607823037] 
dist 134=[-3.5777030166604381320 ,.33411704000048161394] 
dist 135=[-3.5764493976599103261 ,.06472790583650955511] 
dist 136=[-3.5647739741679750842 ,.03920463987615717501] 
dist 137=[-3.5524553091854247394 ,.00726985401571663375] 
dist 138=[-3.5085745825921857927 ,.00447746722281007439] 
dist 139=[-3.4850900435507662867 ,-.00828799771943441857] 
dist 140=[-1.7085039476959427729 ,-.01055310206683667658] 
dist 141=[-1.5485442109189094035 ,-.01528028781734218984] 
dist 142=[-1.1648029927265589492 ,.15095321987150860885] 
dist 143=[-1.1047003441644625591 ,.49192466486429556973] 
dist 144=[-.63923193840073387405,.8049435306040712166 ] 
dist 145=[-.65149773395909372324,1.0371312842569837080 ] 
dist 146=[-.65535048227614086236,1.2545501550966020263 ] 
dist 147=[-.65602306903887214986,1.5086330857153060527 ] 
dist 148=[-.6555988647224570084 ,1.7461030961435809659 ] 
dist 149=[-.65428858343744912855,1.8972199637378176567 ] 
dist 150=[-.65159488076032064284,2.0140139979467157431 ] 
dist 151=[.01900624469598224995,2.1144954072160192262 ] 
dist 152=[.02607027792086161085,2.1967923968035749128 ] 
dist 153=[.03590344756987419956,2.2410091516020000253 ] 
dist 154=[.03748352055816900727,2.2657960671965432766 ] 
dist 155=[.04519478126397855434,2.2705451272679922187 ] 
dist 156=[.04648069158034293193,1.6771942038745354054 ] 
dist 157=[.04784170335631131739,1.6252972692212094106 ] 
dist 158=[.04739845303540163449,1.4955710859100931853 ] 
dist 159=[.04627625759715330054,1.4697789100031100982 ] 
dist 160=[.04436168902516923326,1.2592703373525862256 ] 
dist 161=[.04150365422880303002,1.2167701559922517911 ] 
dist 162=[.03661722285549921068,1.1530236791797709429 ] 
dist 163=[.03081067323145394739,1.1338840236500131526 ] 
dist 164=[.02428164895180658595,.73948760964789549768] 
dist 165=[-.04029213602863529674,.68710352163271435187] 
dist 166=[-.17643514601048137552,.56783118591556412164] 
dist 167=[-.33474272755310216174,.54228018010003893979] 
dist 168=[-.49515281153998110364,.38956414456567516735] 
dist 169=[-.63969188234337783883,.36140619252355521723] 
dist 170=[-.80027996783481871902,.30572478012121932897] 
dist 171=[-1.0247496901264312118 ,.29147341103006744054] 
dist 172=[-1.2446206843195728497 ,.1663505646235356156 ] 
dist 173=[-1.3868568418072256866 ,.14623388210110648947] 
dist 174=[-1.4994623221139484859 ,.14082445176323752811] 
dist 175=[-1.6301200554430925169 ,.04219917356534792770] 
dist 176=[-1.7557235942092946153 ,.03060956166549753272] 
dist 177=[-1.8430016633951607876 ,.04746208327044541407] 
dist 178=[-1.9189193640723481966 ,.08806164801099976770] 
dist 179=[-1.9991850896975104741 ,.15890216667596131041] 
dist 180=[-2.0685889300011841130 ,.2362253163138954152 ] 
dist 181=[-2.1011566331793803523 ,.30269917016933221316] 
dist 182=[-2.1161971523857997062 ,.37392540374841178885] 
dist 183=[-2.1158879785960876866 ,.47022060456619872323] 
dist 184=[-2.0795631103311921176 ,.57522543361655955827] 
dist 185=[-2.0646817092640460607 ,.6812147292926609918 ] 
dist 186=[-2.0507511504675557110 ,.80820392597648569853] 
dist 187=[-2.0396557819532881315 ,.99702271969735203002] 
dist 188=[-.60131269777739754027,1.2542087040672742667 ] 
dist 189=[-.65023460878559838409,1.4443675696182704296 ] 
dist 190=[-.72216448905561643895,1.5931816635199592190 ] 
dist 191=[-.79600157328734655126,1.7244260829903860980 ] 
dist 192=[-.85253559438655134512,1.8342922377787706785 ] 
dist 193=[-.90720335222394175651,1.8980837173906240334 ] 
dist 194=[-.97359362747574544867,2.0169512020985947630 ] 
dist 195=[-1.0424151940502418035 ,2.1382032845167127663 ] 
dist 196=[-1.1067868610784579379 ,2.2453414301569850865 ] 
dist 197=[-1.1802125701771951168 ,2.3078813691163470767 ] 
dist 198=[-1.2851692177558471147 ,2.3497117241308582980 ] 
dist 199=[-1.3874022832013692488 ,2.3741993281348122163 ] 
dist 200=[-1.4499587428550271309 ,2.3856556140641419700 ] 
dist 201=[-1.4954155789764806490 ,2.3857379107619425032 ] 
dist 202=[-1.5294053244503051166 ,2.3613838762628076225 ] 
dist 203=[-1.5534131155272944138 ,2.3572012833837257743 ] 
dist 204=[-1.5590329281732370990 ,1.5713293775732311665 ] 
dist 205=[-1.5577422846592461084 ,1.5151574330201442111 ] 
dist 206=[-1.5541697054843524775 ,1.3701171760590890908 ] 
dist 207=[-1.4955171382855109560 ,1.3474377767889627019 ] 
dist 208=[-1.4819415643500494370 ,1.1027103828292835005 ] 
dist 209=[-1.4404325128398315219 ,1.0542524833381710250 ] 
dist 210=[-1.4293831007273120981 ,.99954176863359090443] 
dist 211=[-1.3299860401523429885 ,.98447555321093349138] 
dist 212=[-1.4041791378746051481 ,.50185736926993029606] 
dist 213=[-1.4662363526118045120 ,.44080116227850906896] 
dist 214=[-1.5094846470895477456 ,.31361342108819308788] 
dist 215=[-1.5383474178919245553 ,.28010030104980828905] 
dist 216=[-1.5571156076674413243 ,.15581585367199116415] 
dist 217=[-1.5600957228858089335 ,.13103142633473984504] 
dist 218=[-1.5568457929538619414 ,.08561367950255511460] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 0, 1, 0, 1, 2] 
dist 0=[53.594228954609271557  ,53.594228954609271557  ] 
dist 1=[53.229689580454736928  ,53.881170031721195281  ] 
dist 2=[52.060994624808162863  ,54.239846085949763979  ] 
dist 3=[50.613398607246752348  ,54.315894285188401078  ] 
dist 4=[48.922272324040352126  ,54.278090702548954720  ] 
dist 5=[46.724970201297221691  ,54.202929223346433601  ] 
dist 6=[43.255803891413048247  ,54.083414370844119056  ] 
dist 7=[39.713742826573206528  ,53.985596094459136353  ] 
dist 8=[37.225238689473066624  ,53.615480866671836132  ] 
dist 9=[35.026108543196973097  ,53.470308530102133915  ] 
dist 10=[32.639528356198365702  ,53.040507731956032032  ] 
dist 11=[30.307639879123491531  ,52.845513496113559243  ] 
dist 12=[28.326744921647777029  ,51.770287233684879011  ] 
dist 13=[26.217896639273165060  ,51.457609809623367525  ] 
dist 14=[23.374633922073678248  ,50.122739909289896089  ] 
dist 15=[20.546558063917197440  ,47.648518698965676136  ] 
dist 16=[18.498162106372666456  ,30.179697347309264420  ] 
dist 17=[16.621806781615840621  ,28.551024067711625805  ] 
dist 18=[14.480580481963139769  ,27.562118340279883183  ] 
dist 19=[12.322913725196902338  ,27.371373785570354848  ] 
dist 20=[10.380499581880512479  ,19.554482122613932226  ] 
dist 21=[8.2152411469028806447 ,18.761912941775554625  ] 
dist 22=[5.1666325207603396888 ,17.287491260849635693  ] 
dist 23=[2.1746142811910853977 ,16.954272691712543143  ] 
dist 24=[.23530610293032040293,14.344337734157367448  ] 
dist 25=[-1.3134402189220371543 ,13.977892110262708640  ] 
dist 26=[-2.7448659542516673060 ,13.482136289134653272  ] 
dist 27=[-4.0002769241516544102 ,13.346450242731509764  ] 
dist 28=[-4.8458303369694971298 ,8.6541788064101348489 ] 
dist 29=[-5.5582266718355381397 ,8.2070320741143543516 ] 
dist 30=[-6.2819258953880760052 ,6.2515945948507041725 ] 
dist 31=[-8.3501019504442060118 ,3.0043693447481299712 ] 
dist 32=[-10.877932352697370260  ,-4.1731897546018095137 ] 
dist 33=[-12.444517071661415746  ,-4.5389633575179896492 ] 
dist 34=[-13.616296687334206573  ,-5.2856559008140825211 ] 
dist 35=[-14.566438373871325137  ,-5.4218958076677965690 ] 
dist 36=[-15.323890354341577735  ,-6.2683628007277583276 ] 
dist 37=[-15.725446126306208002  ,-5.9779048153285735857 ] 
dist 38=[-15.946410344603288405  ,-5.0182886155468352922 ] 
dist 39=[-15.989171527582011873  ,-3.9903463782197133504 ] 
dist 40=[-15.450085720657055282  ,-3.2610456841360854055 ] 
dist 41=[-15.319413427315198399  ,-2.6122204556099081536 ] 
dist 42=[-15.189228565397231283  ,-1.9051359990466956435 ] 
dist 43=[-15.102985728237820516  ,-1.2158770331971854600 ] 
dist 44=[-14.956349119275661329  ,-.6380593429165717362 ] 
dist 45=[-14.878125263920661996  ,.0411648390276502045 ] 
dist 46=[-14.809837370285979428  ,.85727105819315548603] 
dist 47=[-14.739237833961143480  ,1.6568042046716017106 ] 
dist 48=[-5.0047210453929031843 ,2.3842257045055317959 ] 
dist 49=[-4.2021537828030006641 ,2.9451928279746980120 ] 
dist 50=[-2.3365471365330706954 ,3.4520083373712415698 ] 
dist 51=[-2.0367123736255905682 ,4.0141799716062827854 ] 
dist 52=[.38172375246129141258,4.5298445986540167313 ] 
dist 53=[.80366169712900774148,4.8510723455799184406 ] 
dist 54=[1.4437261508036822184 ,5.0917605033119396622 ] 
dist 55=[1.6027092348244758195 ,5.2858772145524358641 ] 
dist 56=[2.4805845741213056510 ,6.2159934572346419787 ] 
dist 57=[2.5163384172289955980 ,6.9388302586688995344 ] 
dist 58=[2.3859432745293099004 ,7.4856465387869160242 ] 
dist 59=[1.5932920319800365903 ,7.9357825470571518438 ] 
dist 60=[.78234038503782021779,8.2934424287903576549 ] 
dist 61=[.22798539987776518593,8.4711105617471923092 ] 
dist 62=[-.24328398984333112187,8.5614348937963880368 ] 
dist 63=[-.7228568061548407656 ,8.5710326877092307241 ] 
dist 64=[-1.1697671286602057722 ,4.3558108147546444834 ] 
dist 65=[-1.5107661567674870953 ,4.1417870838266849457 ] 
dist 66=[-1.8387573463784461606 ,3.6054314704354561814 ] 
dist 67=[-2.2337915399241573691 ,3.5260540910368697194 ] 
dist 68=[-2.6029773520136022582 ,2.6908852334726654647 ] 
dist 69=[-2.8278553831830709198 ,2.5331344799753790948 ] 
dist 70=[-2.9895951550046027116 ,2.3508577694004670178 ] 
dist 71=[-3.1068998802530456167 ,2.3123084846087454979 ] 
dist 72=[-3.1946692129651265123 ,.9115818122171694551 ] 
dist 73=[-3.2385948866348044557 ,.7414225509698198884 ] 
dist 74=[-3.2586867152648109666 ,.3820568672257838783 ] 
dist 75=[-3.2561293714308141580 ,.2975741162616892816 ] 
dist 76=[-2.2441140894886493050 ,-.0511095570540941093 ] 
dist 77=[-2.4338988808665392574 ,-.1151239241064235124 ] 
dist 78=[-2.5731094552881609793 ,-.2244046430260241919 ] 
dist 79=[-2.6799861780158480656 ,-.2467666849615942729 ] 
dist 80=[-2.7609326769474042837 ,-.35046643773346822504] 
dist 81=[-2.7966285127660530594 ,-.30984383594664896086] 
dist 82=[-2.8103383656148413892 ,-.22551671215413966291] 
dist 83=[-2.8075056129996113559 ,-.11980809079571475202] 
dist 84=[-2.7950691502474584571 ,.00614493746357547902] 
dist 85=[-2.9361583619003596232 ,.17084758753748944747] 
dist 86=[-3.0685350295319999377 ,.43118366746605268465] 
dist 87=[-3.2241108614593841081 ,.69284834385792725273] 
dist 88=[-3.3683783828142585933 ,.99936583845133183846] 
dist 89=[-3.4555988501165701776 ,1.2892154876237874125 ] 
dist 90=[-3.5179916806534403682 ,1.5766564347977710514 ] 
dist 91=[-3.5631047912454531435 ,1.8401262179383308466 ] 
dist 92=[-3.5938684557338619069 ,2.0343412809146407141 ] 
dist 93=[-3.5989574289710286201 ,2.2148059563436648966 ] 
dist 94=[-3.5905356676397285471 ,2.4234236762994257986 ] 
dist 95=[-3.5799569167344974030 ,2.6137529162887021139 ] 
dist 96=[-.13247718279833557682,2.7212515899738242172 ] 
dist 97=[-.08063475048715594012,2.7885729311529154190 ] 
dist 98=[.00150781975094527197,3.0010310476260158946 ] 
dist 99=[.02132099905012366194,3.3226402822715320850 ] 
dist 100=[.3346582595883179548 ,3.5948194157766545044 ] 
dist 101=[.3748052388075331584 ,3.7885405424068036151 ] 
dist 102=[.16626293627006709328,3.9331018132933773096 ] 
dist 103=[-.13024827542028114612,4.0484254000899796489 ] 
dist 104=[-.3302880939540793393 ,4.1411730793775390063 ] 
dist 105=[-.4976168552903799177 ,4.1956319953524671878 ] 
dist 106=[-.66363708806228704357,4.2325276542603076571 ] 
dist 107=[-.81576100598264737696,4.2551707270287898959 ] 
dist 108=[-.92765515727456612377,4.2669863567738666457 ] 
dist 109=[-1.0313230843106603696 ,4.2606666290893801526 ] 
dist 110=[-1.1506329010281716465 ,4.2398989418180293591 ] 
dist 111=[-1.2595063532982094787 ,4.2264594671202302662 ] 
dist 112=[-1.3215381522766246751 ,1.8713853170417560588 ] 
dist 113=[-1.3610326138582484410 ,1.6703598499991728551 ] 
dist 114=[-1.3799883361858936592 ,1.1857524864102572222 ] 
dist 115=[-1.3900466771194214649 ,1.1141493632559214932 ] 
dist 116=[-1.3940473280348007339 ,.42651414982397650177] 
dist 117=[-1.3943707478940450295 ,.30228625020442621568] 
dist 118=[-1.3897707056930935351 ,.3008517109903759991 ] 
dist 119=[-1.2792787207157704390 ,.30604366966083360157] 
dist 120=[-1.5815219443052604433 ,.31375096547625169511] 
dist 121=[-1.7741342649088917130 ,.32430829456563700792] 
dist 122=[-1.9232868892090713139 ,.33887720610736191765] 
dist 123=[-2.0520798364077022422 ,.36256357801952805415] 
dist 124=[-2.1578866053045729982 ,.38623997817120752449] 
dist 125=[-2.2152991492985637604 ,.40076588663602059474] 
dist 126=[-2.2482342175733028398 ,.41123477004438763739] 
dist 127=[-2.2563474810627761111 ,.41874123918834470803] 
dist 128=[-1.8945141082855214523 ,.42362613409859700832] 
dist 129=[-1.8610796772667828288 ,.42459694148860787895] 
dist 130=[-1.7709535980468275671 ,.4223250266824403835 ] 
dist 131=[-1.7514624339442532740 ,.42193609239600480139] 
dist 132=[-1.5791394071997843108 ,.39913675155151571341] 
dist 133=[-1.5419156530141888978 ,.39424518868259387043] 
dist 134=[-1.4899989292957938476 ,.38143319349286094782] 
dist 135=[-1.4719723349055896603 ,.37672577064638732334] 
dist 136=[-1.0652550982371296260 ,.35045098215168788825] 
dist 137=[-1.0099912827637806680 ,.34405887781624450697] 
dist 138=[-.8890155210497974530 ,.33166780550050778115] 
dist 139=[-.8560788482396307116 ,.32776552196297210468] 
dist 140=[-.7118180002020994589 ,.19616886077294285187] 
dist 141=[-.6842928496400315799 ,.36379680019347329603] 
dist 142=[-.6164392370713963142 ,.55428333190779060153] 
dist 143=[-.6041170621452976137 ,.82573974633424793333] 
dist 144=[-.09357036958032423491,1.0934560634229366051 ] 
dist 145=[-.05340723109551744388,1.2690189261654470539 ] 
dist 146=[-.0138302131576332401 ,1.4106861488853629376 ] 
dist 147=[-.0075304167401282913 ,1.5687897894394417115 ] 
dist 148=[.06227994363433006184,1.7238173979167272009 ] 
dist 149=[.05796683499001106051,1.8350258918918799205 ] 
dist 150=[.03742362492909285345,1.9354308831221774430 ] 
dist 151=[-.01058058942332242462,2.0473451125004829972 ] 
dist 152=[-.06718875955568630957,2.1474458684783450313 ] 
dist 153=[-.12207181159494603085,2.2007039058559588179 ] 
dist 154=[-.18615738806142741339,2.2298587608051089669 ] 
dist 155=[-.27949872817842223354,2.2356198124416964537 ] 
dist 156=[-.3844444937666346263 ,2.2280505342003214552 ] 
dist 157=[-.49484550414891085191,2.2188286191190432238 ] 
dist 158=[-.63034681899487297402,2.2052808997961866443 ] 
dist 159=[-.83546838015873817641,2.1963104311018852249 ] 
dist 160=[-1.0970576848999232411 ,.37809526972987436549] 
dist 161=[-1.2980643003511677009 ,.3787641855565223425 ] 
dist 162=[-1.4574146475198713353 ,.37793549365832011555] 
dist 163=[-1.6015055648190253256 ,.37661408171955037519] 
dist 164=[-1.7247051534866296570 ,.36595639797838551318] 
dist 165=[-1.8511004426754944701 ,.36322414568000289087] 
dist 166=[-1.9713879703395389270 ,.35418316745947633609] 
dist 167=[-2.0940550616473265377 ,.35208728903756165438] 
dist 168=[-2.2026347635919846867 ,.32888933947778730911] 
dist 169=[-2.2667024233213914826 ,.32346890428898241881] 
dist 170=[-2.3104094031472863154 ,.31714332470295188437] 
dist 171=[-2.3377337494368682145 ,.31429828601566407697] 
dist 172=[-2.3524243138530984633 ,-.10509356735709398633] 
dist 173=[-2.3530624554922958420 ,-.10494110326784822495] 
dist 174=[-2.3336634561648209137 ,-.1034851088295020387 ] 
dist 175=[-2.3270518028627898872 ,-.08358579396582817223] 
dist 176=[-1.5200428118957282882 ,.23533221459342616954] 
dist 177=[-1.4619858079886039060 ,.44762033790461566996] 
dist 178=[-1.3130240593906703651 ,.62235753697580927887] 
dist 179=[-1.2896584527112743747 ,.79141856272824517126] 
dist 180=[-1.0417764140147762945 ,.94379138289224288244] 
dist 181=[-.99298428977000702481,1.0519292831034295422 ] 
dist 182=[-.93694788391857164113,1.1483197004398252088 ] 
dist 183=[-.92136508981851185181,1.2538094192077058450 ] 
dist 184=[-.56979918774976456416,1.3496510777777828581 ] 
dist 185=[-.56873218075264266265,1.4075389486844383444 ] 
dist 186=[-.5608958794556017491 ,1.4486777621459690508 ] 
dist 187=[-.5594307951965516962 ,1.4776812939330936619 ] 
dist 188=[-.34026312073529627661,1.4966463405205329355 ] 
dist 189=[-.3193193024769127359 ,1.5006624683056169321 ] 
dist 190=[-.26753798796731178389,1.5054560682662741570 ] 
dist 191=[-.25971556544113844846,1.5038446110807673627 ] 
dist 192=[-.18079467507765972411,.38460713252432243895] 
dist 193=[-.16591176244020109619,.38503945959529686097] 
dist 194=[-.14820092690836388693,.38390726165488903778] 
dist 195=[-.14402270547382074347,.38282483461386135312] 
dist 196=[-.08289580325928141795,.3745199618397862580 ] 
dist 197=[-.08093028212881531818,.3720073492280013078 ] 
dist 198=[-.07635475176195556238,.3640477096807081426 ] 
dist 199=[-.07493425284413967881,.3614175120657474236 ] 
dist 200=[-.06795705107194544927,.3585989149191172639 ] 
dist 201=[-.06642697187995704753,.36233751769246954105] 
dist 202=[-.06313114501038787563,.36372247962170278187] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 0, 0, 0, 1] 
dist 0=[57.728031488453414865  ,57.728031488453414865  ] 
dist 1=[56.527568309125655150  ,58.374147870239141083  ] 
dist 2=[55.156295606058093177  ,58.738598365745980640  ] 
dist 3=[53.828072167068889364  ,58.814473835839778715  ] 
dist 4=[52.274733446664456855  ,58.765324511480285377  ] 
dist 5=[50.004278024120075728  ,58.662043929105296207  ] 
dist 6=[47.440923129391343281  ,58.433272390508389678  ] 
dist 7=[44.717785976445204250  ,58.307031456203159777  ] 
dist 8=[41.350050445408662825  ,57.405089205361794438  ] 
dist 9=[36.212359472597090291  ,54.504877567675499584  ] 
dist 10=[31.036398159590789450  ,53.632318725156481517  ] 
dist 11=[27.515710890706621175  ,53.359584822394271521  ] 
dist 12=[24.525458351436190834  ,52.684874585631756343  ] 
dist 13=[21.467563684260619893  ,51.741921561313127890  ] 
dist 14=[18.590975821506196953  ,47.122110753403473453  ] 
dist 15=[16.324521516490579237  ,43.969337417077325410  ] 
dist 16=[14.064418413006418142  ,40.591295647560807045  ] 
dist 17=[11.212672778004991833  ,32.546011967651473670  ] 
dist 18=[8.4639020973498633009 ,31.501541349068175726  ] 
dist 19=[6.6147699524801152370 ,29.410302607408351553  ] 
dist 20=[5.0635741879528754506 ,28.864182823642806939  ] 
dist 21=[3.5043600425054115665 ,26.890214597442317869  ] 
dist 22=[2.0497523507805961706 ,26.457448619061291755  ] 
dist 23=[.91579857927472856278,25.746248248022597422  ] 
dist 24=[-.20818199796887840068,25.560378531184820748  ] 
dist 25=[-1.6242128478469294090 ,8.7224520994144559459 ] 
dist 26=[-2.9648190849800936097 ,7.2987125776410512526 ] 
dist 27=[-3.7876255785562634215 ,6.0930702070092088342 ] 
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dist 30=[-8.1052736009564786535 ,3.2711529093022350693 ] 
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dist 32=[-11.645710772707955623  ,-2.2279357815404914363 ] 
dist 33=[-13.413209843735251676  ,-5.0033974803198056653 ] 
dist 34=[-14.477970930130559960  ,-5.2000244000469874420 ] 
dist 35=[-15.235255852118171264  ,-5.0123050146954016011 ] 
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dist 38=[-16.390497460665721722  ,-3.9093426682020793193 ] 
dist 39=[-16.505753833565480817  ,-3.4195379087017436321 ] 
dist 40=[-16.519113275921445948  ,-2.8137920431499063474 ] 
dist 41=[-9.3384852555195751458 ,-1.8407691530942174283 ] 
dist 42=[-9.2370939745812957226 ,-.83217012735352122156] 
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dist 44=[-9.0783046239447965876 ,.45356463257368074539] 
dist 45=[-9.0304413839548060027 ,1.0654257295426013858 ] 
dist 46=[-8.9936156566156511512 ,1.6417889551934292766 ] 
dist 47=[-8.9628184576058197363 ,2.0932540656379273732 ] 
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dist 50=[-1.5914329982697942336 ,3.6182785841492200980 ] 
dist 51=[-1.4127052897932784448 ,3.9489333410064331669 ] 
dist 52=[-.0145654947073417100 ,4.1996213652427280466 ] 
dist 53=[.22795926182130774238,4.4055610048854006056 ] 
dist 54=[.60818358108179280007,4.5655702429218713908 ] 
dist 55=[.69838736656435171555,4.6328398059857519301 ] 
dist 56=[1.7538772414312639513 ,4.6608286614616986640 ] 
dist 57=[1.2539784927085295348 ,4.6645880162057441018 ] 
dist 58=[.7421687717351508050 ,4.1032787357255179934 ] 
dist 59=[.3967037126996522238 ,4.3054120601509250740 ] 
dist 60=[.1072466395007942500 ,4.5199944455266705673 ] 
dist 61=[-.18113282524727213121,4.6249016578674709826 ] 
dist 62=[-.44658552567654583791,4.6788831742955357344 ] 
dist 63=[-.64459932424351907449,4.6901456332223479402 ] 
dist 64=[-.83115707233288784886,4.2216425726906435655 ] 
dist 65=[-1.0509619714182794800 ,4.1795131901522793796 ] 
dist 66=[-1.2554302496310602252 ,4.1566110438384899275 ] 
dist 67=[-1.3807894120416290303 ,4.1229785736124662262 ] 
dist 68=[-1.4723329813488894791 ,4.1061794111875796438 ] 
dist 69=[-1.5417998391810238368 ,4.0389964491690806082 ] 
dist 70=[-1.5946316675415675381 ,4.0155842990696648374 ] 
dist 71=[-1.9549738550061936141 ,3.9561503760275779348 ] 
dist 72=[-2.9629784221564266974 ,3.9314228175048034769 ] 
dist 73=[-3.9568551395423290738 ,.8142449131145125624 ] 
dist 74=[-4.5899069522536370629 ,.7087906009504404558 ] 
dist 75=[-5.0801944939046250541 ,.6824074105896345802 ] 
dist 76=[-5.5042207161248967391 ,.5832791984277407187 ] 
dist 77=[-5.8549485301884227382 ,.5643549517663987540 ] 
dist 78=[-6.1062714733662282244 ,.5305019603761056691 ] 
dist 79=[-6.2842935896723417783 ,.5229821191285823112 ] 
dist 80=[-6.4090883994269700810 ,.5022962855739203777 ] 
dist 81=[-6.5009789512324320330 ,.4966691643623078209 ] 
dist 82=[-6.5476636964145351684 ,.4935646639760971245 ] 
dist 83=[-6.5703324884917808766 ,.5334821916660071692 ] 
dist 84=[-6.5663464161021975304 ,.62047115886436585803] 
dist 85=[-6.5457045246337390240 ,.71073997229066977746] 
dist 86=[-6.5218971677054493279 ,.79627632660048148408] 
dist 87=[-6.4497809651705315357 ,.86441258651273649051] 
dist 88=[-6.4115961167501506705 ,.93298311669309380109] 
dist 89=[-3.0206494898431498414 ,1.0203098706577968392 ] 
dist 90=[-2.7199339968686007046 ,1.1024643271713041927 ] 
dist 91=[-1.9994635751965842397 ,1.1503983160519137836 ] 
dist 92=[-1.8877763723156852196 ,1.1826438754266490340 ] 
dist 93=[-1.5424626756407657607 ,1.3111757947878897673 ] 
dist 94=[-1.5107336636655155151 ,1.7371799816472261987 ] 
dist 95=[-1.4999933077998481156 ,2.1380211777073572976 ] 
dist 96=[-.5709961903798924406 ,2.6093220876690296501 ] 
dist 97=[-.5028760977799151445 ,3.0502088347828811010 ] 
dist 98=[-.3475451662931951608 ,3.3296684322083004953 ] 
dist 99=[-.3196484910961603634 ,3.5444213528998297088 ] 
dist 100=[-.12629019132051610406,3.7270457381477841252 ] 
dist 101=[-.09254696676136308095,3.8750632973504777455 ] 
dist 102=[-.03228674527238831671,3.9516912373053259336 ] 
dist 103=[-.01946035596553876374,3.9907144217404726980 ] 
dist 104=[.15394643654133529872,3.9964797122069931463 ] 
dist 105=[.12654150641354462029,2.8669848577317416466 ] 
dist 106=[-.09398586695549547333,2.7745221214819551368 ] 
dist 107=[-.24083563030404056316,2.5429495838972677432 ] 
dist 108=[-.36199485805438474371,2.4986397357925716493 ] 
dist 109=[-.4799534025387503952 ,2.1240717242082361322 ] 
dist 110=[-.5869711367473430108 ,2.0490991987267867748 ] 
dist 111=[-.6644475905839999338 ,1.9402834597802739710 ] 
dist 112=[-.7351939481849517164 ,1.9066975503558068208 ] 
dist 113=[-.8153367036993230419 ,1.2156951524513779331 ] 
dist 114=[-.8893344021931042199 ,1.1247031318936134677 ] 
dist 115=[-.9355471988481692151 ,.91937503172246270195] 
dist 116=[-.9702879274469636806 ,.87487271278685433978] 
dist 117=[-.9984903063511661270 ,.63893479685274269   ] 
dist 118=[-1.0356222957572208356 ,.60658703511184616231] 
dist 119=[-1.2949246640634070815 ,.59559470609779851123] 
dist 120=[-1.6553392409531130478 ,.45230485275822384704] 
dist 121=[-2.0079016215113264025 ,.33680833032999235533] 
dist 122=[-2.2358705913792831582 ,.2715612671034389791 ] 
dist 123=[-2.4162922553319899627 ,.25677233165295050876] 
dist 124=[-2.6203875294225664992 ,.18118773412366129228] 
dist 125=[-2.8233175550499410805 ,.16778557307394789664] 
dist 126=[-2.9646656170053033509 ,.13772656013695311619] 
dist 127=[-3.0880165875181417726 ,.13180367965037932598] 
dist 128=[-3.2191229809235425606 ,.17912753080210969769] 
dist 129=[-3.3329834520145593827 ,.30732156551037406756] 
dist 130=[-3.3875031819808076762 ,.41762551030406729088] 
dist 131=[-3.4130622938098067886 ,.53587566119764508024] 
dist 132=[-3.4138124633443545061 ,.69579927416989834113] 
dist 133=[-3.3622696297699716011 ,.87020122559466417114] 
dist 134=[-3.3391722567643098041 ,1.0462437941061795969 ] 
dist 135=[-3.3154628929069131288 ,1.2571714821819736936 ] 
dist 136=[-3.2985622679528776913 ,1.5708112977958037599 ] 
dist 137=[-.94299871396557749803,1.9682033124387060170 ] 
dist 138=[-.95002714876596574601,2.2792958777731516591 ] 
dist 139=[-.95177692125981746463,2.5234833121960543305 ] 
dist 140=[-.93115664934745651076,2.7401457632918114213 ] 
dist 141=[-.92596568813375164452,2.9224908074868579834 ] 
dist 142=[-.92297994917466922322,3.0534239484376450853 ] 
dist 143=[-.92219833166292423054,3.2418601207390252618 ] 
dist 144=[-.74367403880633268261,3.4326858637634034836 ] 
dist 145=[-.7212091387452451363 ,3.6009899678216696233 ] 
dist 146=[-.66297049026384376967,3.6995436056431308353 ] 
dist 147=[-.65322636743325300506,3.7658560143208800706 ] 
dist 148=[-.55273769680787634647,3.8054864799174369360 ] 
dist 149=[-.53239635739127794541,3.8249237729694340888 ] 
dist 150=[-.50848303473376835441,3.8248907086394928666 ] 
dist 151=[-.5002869517369057988 ,3.7891498005801977846 ] 
dist 152=[-.29173948915562203371,3.7797740043853706785 ] 
dist 153=[-.34299310829894549522,2.4963051603261580933 ] 
dist 154=[-.69259250071211968887,2.4037197346992605500 ] 
dist 155=[-.98150608933576402681,2.1653021875621018926 ] 
dist 156=[-1.2630017799857422807 ,2.1283004315274982756 ] 
dist 157=[-1.5180626000680159517 ,1.7287257335866877927 ] 
dist 158=[-1.7014757854736387313 ,1.6499104638687314634 ] 
dist 159=[-1.8674634049606991446 ,1.5610857623553661768 ] 
dist 160=[-2.0529771195769130317 ,1.5373195897295044881 ] 
dist 161=[-2.2222953505516223830 ,.75791685244352739442] 
dist 162=[-2.3236494536750377148 ,.65965711146304766907] 
dist 163=[-2.3945834075765951847 ,.56976642470064788275] 
dist 164=[-2.4425043742510639179 ,.48656764873649165992] 
dist 165=[-2.4741194149218034417 ,.46986016158398228776] 
dist 166=[-2.4799778114765741370 ,.44449597498632626014] 
dist 167=[-2.4818477991090303217 ,.43702395160418378934] 
dist 168=[-2.4805156567715245798 ,.2845407182872963415 ] 
dist 169=[-.5906264235351203608 ,.2642833268606454422 ] 
dist 170=[-.57710105486935363838,.2179880739770535377 ] 
dist 171=[-.54586443982365227783,.2082538164278849258 ] 
dist 172=[-.53595104343771472697,.1484526881640195567 ] 
dist 173=[-.49000636107015976571,.1374198305712896190 ] 
dist 174=[-.48007859390317066547,.1160450931332671893 ] 
dist 175=[-.45752320427777412243,.1106813796626240730 ] 
dist 176=[-.45931102222094760923,-.0744062776078464073 ] 
dist 177=[-.52943240498540366368,-.05820417347028291215] 
dist 178=[-.5865998645431809824 ,-.02979612126771873902] 
dist 179=[-.64103520497102634848,-.00026003141238702261] 
dist 180=[-.68954963830829983067,.05362923213891186667] 
dist 181=[-.72308645099439624508,.1366987000401007602 ] 
dist 182=[-.7520788999231675554 ,.21498005491489828566] 
dist 183=[-.78245748639402332589,.30474746721680853593] 
dist 184=[-.80857728676392930941,.43366249125321508392] 
dist 185=[-.82057267724338516851,.56069010409974626194] 
dist 186=[-.82602710910518694942,.64292525623794924044] 
dist 187=[-.82603749676796833498,.70809888066639588525] 
dist 188=[-.81012140236466074249,.76703041303683388205] 
dist 189=[-.80429084079371725995,.81744125649754658238] 
dist 190=[-.79924925057306210072,.84860725171909196199] 
dist 191=[-.7947927243215566859 ,.87164768177043963444] 
dist 192=[-.16934564717475845708,.88962832766111174132] 
dist 193=[-.1896874601798935089 ,.90305042193836694483] 
dist 194=[-.20852000159216783438,.90789675537039540883] 
dist 195=[-.22984053723643565598,.9079192126628956979 ] 
dist 196=[-.26011326024801145777,.90622893423589657316] 
dist 197=[-.29380559608251486282,.88886764861721741862] 
dist 198=[-.32877414860645809813,.88301466097556412661] 
dist 199=[-.37136164231304384001,.86718484366097826391] 
dist 200=[-.43546084923290679019,.86030419435150144414] 
dist 201=[-.49903944037560471034,.78069273169997077036] 
dist 202=[-.53954977283952139901,.78148302334240425824] 
dist 203=[-.57090577253101871726,.78046984956164943286] 
dist 204=[-.59795156442341950409,.76749441434428024329] 
dist 205=[-.62014684053253799355,.762872541633069597  ] 
dist 206=[-.6321457934630550476 ,.74946956744652718731] 
dist 207=[-.63897219718088083215,.74343427440226422986] 
dist 208=[-.64052571507713621247,.44885883194043412953] 
dist 209=[-.63916692508574301987,.41905805628432588146] 
dist 210=[-.63736664855542158556,.34795743675149380166] 
dist 211=[-.62904929372290773157,.33526004288358391273] 
dist 212=[-.62559783923273520948,.2341652489497834197 ] 
dist 213=[-.59545567098022805375,.2152470537098309749 ] 
dist 214=[-.58754733470452599924,.1861419804463643889 ] 
dist 215=[-.57640202265452621768,.1783398347720998854 ] 
dist 216=[-.57197009030882070135,.09369312006602008485] 
dist 217=[-.37148360329384560747,.08906325250295253940] 
dist 218=[-.34867300941661465098,.07873371582280263058] 
dist 219=[-.29862050333286102743,.07599133346220716697] 
dist 220=[-.2856481079744275066 ,.06286303086873498574] 
dist 221=[-.2263359138921339089 ,.06029784803922554834] 
dist 222=[-.2152359377043694736 ,.05444190377770483174] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 0, 2, 0, 1, 2] 
dist 0=[59.623776939608034497  ,59.623776939608034497  ] 
dist 1=[59.200596722096575437  ,59.793047898322366450  ] 
dist 2=[58.446214681232353493  ,59.864175127078572266  ] 
dist 3=[56.954584290778195282  ,59.895550025917394882  ] 
dist 4=[55.259126553546053508  ,59.894411099127462263  ] 
dist 5=[53.690684305796632216  ,59.835519357318985871  ] 
dist 6=[51.911939367989323627  ,59.722490389121180251  ] 
dist 7=[49.376474242365814331  ,59.609578402876231157  ] 
dist 8=[46.542022251153141131  ,55.587920973139235141  ] 
dist 9=[43.569169415367390100  ,54.949740428687227526  ] 
dist 10=[39.918843749910033199  ,53.882381816457874688  ] 
dist 11=[34.378752129618324127  ,53.582765329259952552  ] 
dist 12=[28.808087180059478562  ,52.697492455120968646  ] 
dist 13=[25.035548907073946708  ,52.395233439410545016  ] 
dist 14=[21.849166659333576035  ,51.092930870786769552  ] 
dist 15=[18.619114430632519461  ,48.633550310947793009  ] 
dist 16=[15.598335913380324147  ,34.836751979448376231  ] 
dist 17=[13.247442042240701621  ,32.720338459996607242  ] 
dist 18=[10.930192647945031526  ,32.170387967219733196  ] 
dist 19=[8.0432424936038722087 ,30.209805196779395564  ] 
dist 20=[5.2782098809280837168 ,29.765049732034417517  ] 
dist 21=[3.4475799656639742659 ,29.102849708380833010  ] 
dist 22=[1.9438126587246485947 ,28.905206730650128767  ] 
dist 23=[.4838673940912135205 ,13.856279387897932919  ] 
dist 24=[-.84562978207001462487,8.7895551191912158883 ] 
dist 25=[-1.8289546196957424223 ,6.1167279793924573985 ] 
dist 26=[-2.7545366898930870060 ,4.6939533978514450066 ] 
dist 27=[-4.8544909777474612943 ,4.0419120737421864161 ] 
dist 28=[-6.7472868634450538066 ,2.2026443846008411048 ] 
dist 29=[-8.5292375917628469707 ,1.9260457721585776446 ] 
dist 30=[-10.633020208559589585  ,1.3979870819547792531 ] 
dist 31=[-12.589231864881219656  ,1.1999307593006959729 ] 
dist 32=[-13.781762042329315551  ,-5.4287597873327543830 ] 
dist 33=[-14.646735363000962313  ,-6.0610217697031638122 ] 
dist 34=[-15.294635835194316869  ,-6.1746700557650232349 ] 
dist 35=[-15.790040420330877393  ,-5.9895882227519065896 ] 
dist 36=[-16.045951430533221676  ,-5.6539005809958180139 ] 
dist 37=[-16.176531677993909421  ,-5.1596848168566544115 ] 
dist 38=[-16.177609245800624294  ,-4.0499434167976443486 ] 
dist 39=[-9.1780390559344440011 ,-2.8871056551946204089 ] 
dist 40=[-8.6808146054407346444 ,-2.0729280192646672982 ] 
dist 41=[-8.5854230215984903132 ,-1.3610912078830996152 ] 
dist 42=[-8.4449271485887588396 ,-.6059930785158252433 ] 
dist 43=[-8.3903656277051754848 ,.11683706251355638763] 
dist 44=[-8.2389781712183404321 ,.70022865958746543495] 
dist 45=[-8.1770534138089504741 ,1.2922846199722265476 ] 
dist 46=[-8.1123791782222287980 ,2.0499978627810104709 ] 
dist 47=[-8.0721374279278091163 ,2.7806264453460711343 ] 
dist 48=[-2.8989772578911634264 ,3.2647684354537352956 ] 
dist 49=[-2.4685611262879614722 ,3.6611112347921121518 ] 
dist 50=[-1.4808795808020111869 ,4.0415704541511376615 ] 
dist 51=[-1.3141953521265555622 ,4.3835348157024382050 ] 
dist 52=[-.0733749439951691023 ,4.6264415700897753831 ] 
dist 53=[.1414897149219974979 ,4.9236751394439217694 ] 
dist 54=[.4978000403930264222 ,5.1402232593478095388 ] 
dist 55=[.5768507376791497924 ,5.3012149344393769763 ] 
dist 56=[1.7220445154734969388 ,5.4056486733232390633 ] 
dist 57=[1.8717406400229053061 ,5.4542921239992844935 ] 
dist 58=[2.1267516113939838608 ,5.4590538990495793262 ] 
dist 59=[1.6470559607513132115 ,5.3691446873726805554 ] 
dist 60=[.97535699965352522351,4.5906470214769734972 ] 
dist 61=[.52340509064835235808,4.6783900621910120880 ] 
dist 62=[.14619484247166976181,4.7221785580989856819 ] 
dist 63=[-.22731683156524199808,4.7269891788849964569 ] 
dist 64=[-.56972707003234272226,4.1954241385860982092 ] 
dist 65=[-.82287645474004340326,4.1920593453999089251 ] 
dist 66=[-1.0591842135079766246 ,4.1804337746937650821 ] 
dist 67=[-1.3344663865913890430 ,4.1553118922295302244 ] 
dist 68=[-1.5904212259805283468 ,4.1383081277873393327 ] 
dist 69=[-1.7496031390515474980 ,4.0971787904202066418 ] 
dist 70=[-2.6383433804256749739 ,4.0779050663078659248 ] 
dist 71=[-3.6170659726289158111 ,1.1108057178291693829 ] 
dist 72=[-4.2421239044342718082 ,.5985316744924387164 ] 
dist 73=[-4.7280698285048078266 ,.5304476275895756684 ] 
dist 74=[-5.1515336451831243450 ,.3867124215449379508 ] 
dist 75=[-5.5088290473891091170 ,.3533825183504736210 ] 
dist 76=[-5.7554170057306016612 ,.3596326016561029766 ] 
dist 77=[-5.9314043344387033282 ,.3894001488414866403 ] 
dist 78=[-6.0572976420284752310 ,.4405985260989335026 ] 
dist 79=[-6.1515653958459946536 ,.5338005397069472302 ] 
dist 80=[-6.2013213986415185237 ,.6307460716618300811 ] 
dist 81=[-6.2281535702955882792 ,.6968690180121677491 ] 
dist 82=[-6.2309040183255496449 ,.75254468568106268494] 
dist 83=[-6.2181312805778160601 ,.80787001139909522399] 
dist 84=[-6.1968035532129656727 ,.85814215508445443744] 
dist 85=[-6.1372158547756031668 ,.89367335136560756682] 
dist 86=[-6.1046032448368969160 ,.92483273679048948789] 
dist 87=[-2.8178714885555556338 ,.95764937184213027087] 
dist 88=[-2.5290848239818851217 ,.98529710891340125753] 
dist 89=[-2.1339184198491571978 ,.99584965538535542745] 
dist 90=[-2.1012547838909828821 ,1.0398123700772851699 ] 
dist 91=[-2.0868037487944702010 ,1.1994601165178492128 ] 
dist 92=[-2.0056148478495972492 ,1.5350024059751932763 ] 
dist 93=[-1.9848663766302574407 ,1.9190903278345264456 ] 
dist 94=[-1.9363355212168610788 ,2.3733989161929844821 ] 
dist 95=[-1.9186765306472591466 ,2.7989946655902978029 ] 
dist 96=[-.6595964224422888856 ,3.0684929261252710969 ] 
dist 97=[-.5988503479907294105 ,3.2752610400666380175 ] 
dist 98=[-.4642714941808307587 ,3.4504888235512106929 ] 
dist 99=[-.4354775834476139995 ,3.5920402736988085228 ] 
dist 100=[-.2777014603549158507 ,3.6644003814873779108 ] 
dist 101=[-.2498799497077134001 ,3.7001432095893513322 ] 
dist 102=[-.1908938859212891289 ,3.7061845491433850358 ] 
dist 103=[-.1767332312962128100 ,2.6782870860277186432 ] 
dist 104=[-.0642724294962632009 ,2.5953483459163748182 ] 
dist 105=[-.0454014257603830190 ,2.3873187000175382883 ] 
dist 106=[-.0261733981842576815 ,2.3467424131613729278 ] 
dist 107=[-.0265902785035623946 ,2.0081924413857784484 ] 
dist 108=[-.03541185122842442756,1.9400648792377609487 ] 
dist 109=[-.05606234393480960103,1.8398383811175017842 ] 
dist 110=[-.15813589198233880485,1.8091943039045905224 ] 
dist 111=[-.3086434088355759977 ,1.1770420681552200626 ] 
dist 112=[-.44724424873078984723,1.0934646609675569043 ] 
dist 113=[-.55109109952103321837,.90415106323828193208] 
dist 114=[-.6494617989567750843 ,.86324444451032092329] 
dist 115=[-.7661931422244940218 ,.62451113621479123414] 
dist 116=[-.9049971122506074546 ,.58076084724493140365] 
dist 117=[-1.1590912246579581717 ,.49259904166562227077] 
dist 118=[-1.5140036259481195833 ,.46974030413763202632] 
dist 119=[-1.8617529228697495770 ,.01601846112754341720] 
dist 120=[-2.0872637821342087320 ,-.02161202476598079926] 
dist 121=[-2.2664696694573706219 ,-.06449959805937414089] 
dist 122=[-2.4602741331424906034 ,-.06887111728664360227] 
dist 123=[-2.6525369121097596652 ,-.05746453592865640752] 
dist 124=[-2.7861531269479705724 ,-.02308075109688420139] 
dist 125=[-2.9024361981095428906 ,.03463797200386033153] 
dist 126=[-3.0255251260411844814 ,.13917673381613884478] 
dist 127=[-3.1321267256516521860 ,.25455128176480316291] 
dist 128=[-3.1826064632487182666 ,.35552148550539266146] 
dist 129=[-3.2061887897351202091 ,.46520655127676377898] 
dist 130=[-3.2062552758798409990 ,.61537692914518998669] 
dist 131=[-3.1539623070783208556 ,.78000774778418477848] 
dist 132=[-3.1320435252227385643 ,.94741267203941867669] 
dist 133=[-3.1111339269220475100 ,1.1488755428408844201 ] 
dist 134=[-3.0946761258554552496 ,1.4494410901628519089 ] 
dist 135=[-.0093492480075147787 ,1.8329201420172457124 ] 
dist 136=[-.0085998488487913280 ,2.1187829563317999880 ] 
dist 137=[-.0128316159062232289 ,2.3429887920186142350 ] 
dist 138=[-.0212787166017798330 ,2.5416034922088963785 ] 
dist 139=[-.0376308452479743578 ,2.7085222364244768164 ] 
dist 140=[-.0551592037574482436 ,2.8288348706213161043 ] 
dist 141=[-.0683003296472680872 ,3.0081217678206481656 ] 
dist 142=[-.0807004387097400176 ,3.1913651007347208257 ] 
dist 143=[-.09527964569200885863,3.3534055503102654701 ] 
dist 144=[-.11010107057763250746,3.4480733778192651663 ] 
dist 145=[-.12347165580822190233,3.5114976242895429302 ] 
dist 146=[-.13831788184616948711,3.5488462539148831919 ] 
dist 147=[-.15903150616554406301,3.5665660615042039807 ] 
dist 148=[-.17980606469679322983,3.5668949054494619214 ] 
dist 149=[-.19489820982504923885,3.5307705264586687577 ] 
dist 150=[-.20870838132103396807,3.5246660236380651810 ] 
dist 151=[-.33163500552318327046,2.3463183545660099618 ] 
dist 152=[-.66184529439516123882,2.2582453707200109170 ] 
dist 153=[-.93450269327749181524,2.0319557374573757886 ] 
dist 154=[-1.1997681073644441496 ,1.9966237625170639262 ] 
dist 155=[-1.4398586944515879937 ,1.6189618763929537608 ] 
dist 156=[-1.6120450048870110257 ,1.5445467606052445585 ] 
dist 157=[-1.7673987616651440314 ,1.4598100771681051870 ] 
dist 158=[-1.9403094719778837122 ,1.4366228254607901433 ] 
dist 159=[-2.0979981865702663609 ,.70550062987894130805] 
dist 160=[-2.1926037177315421900 ,.61324310375605279185] 
dist 161=[-2.2590733231205416472 ,.42044002110195205515] 
dist 162=[-2.3044808872583861269 ,.36961728957278754508] 
dist 163=[-2.3344325327203672875 ,.18074869810519619375] 
dist 164=[-2.3398136782911385991 ,.14342558378439316782] 
dist 165=[-2.3347394781729360964 ,.07436098161817407437] 
dist 166=[-2.3289378850545791176 ,.05844629690984572013] 
dist 167=[-.51691870012201533577,-.1151506956534211214 ] 
dist 168=[-.52289025590067450034,-.0697132430437202135 ] 
dist 169=[-.52504460431482373639,-.0239978770285690737 ] 
dist 170=[-.52481457567847938658,.0306671660862658794 ] 
dist 171=[-.52373137804762808785,.1118242002758470447 ] 
dist 172=[-.4681799149010715156 ,.1925380887050974699 ] 
dist 173=[-.4600245329503841877 ,.2454350660992201172 ] 
dist 174=[-.4370162549602316256 ,.2880754696468322770 ] 
dist 175=[-.4329271545489780834 ,.3278555115948208017 ] 
dist 176=[-.38633958653570625676,.36274330929209991651] 
dist 177=[-.37632503635498402125,.385858919691551116  ] 
dist 178=[-.36535408248909351442,.40477489326501500748] 
dist 179=[-.36108863735343570552,.42290226390213146531] 
dist 180=[-.24413533640371123823,.43844995690999484252] 
dist 181=[-.22859783849433435231,.44707058100415144139] 
dist 182=[-.19671288918252555299,.4522684038984865228 ] 
dist 183=[-.18814171545434821954,.45415580522538470489] 
dist 184=[-.15574972070813387307,.45387091086288549353] 
dist 185=[-.14891047292657172916,.45302118452813818996] 
dist 186=[-.13558992573165861312,.46445882020330620938] 
dist 187=[-.13204855653728231829,.50130581945872582231] 
dist 188=[-.1321465321622153992 ,.52702726096868685122] 
dist 189=[-.14196735021820597546,.54952816159876479603] 
dist 190=[-.14918998017751923829,.57352226715736595428] 
dist 191=[-.15474337233947543613,.59439439796896353506] 
dist 192=[-.15890967783108874044,.6044351350790168267 ] 
dist 193=[-.16059764695045616159,.6092038364892419593 ] 
dist 194=[-.1611655702545328409 ,.60938981736690540541] 
dist 195=[-.16086293492744104668,.60023887970459204126] 
dist 196=[-.15212436797294476752,.59619345688715064017] 
dist 197=[-.18319303889654928999,.59216889251235389544] 
dist 198=[-.26978664953900465815,.58911154078539802644] 
dist 199=[-.35585143975401755333,.3166041306573832839 ] 
dist 200=[-.41104418854316660668,.2772644973887122126 ] 
dist 201=[-.45417603666742386537,.2690164875603015135 ] 
dist 202=[-.49210755754356335217,.2608044057860198696 ] 
dist 203=[-.52378101870616050131,.2585122285529887176 ] 
dist 204=[-.54193810266528761923,.1633101946558398789 ] 
dist 205=[-.57251165079048668923,.1507955831584542100 ] 
dist 206=[-.60695977245945415518,.1274263402510782318 ] 
dist 207=[-.63738971118390171818,.1217544408612950853 ] 
dist 208=[-.6551800841525762497 ,.1228893821315693034 ] 
dist 209=[-.66711508808477399098,.1357037899221124287 ] 
dist 210=[-.67417618923254864494,.1474851222631046515 ] 
dist 211=[-.67756191006884867633,.1609224594803562275 ] 
dist 212=[-.67759604707284534126,.1731057172708938091 ] 
dist 213=[-.6709102721012029149 ,.1798827766359356935 ] 
dist 214=[-.66498125642788055672,.1839907812489869593 ] 
dist 215=[-.41190275325304221396,.1855236978344417150 ] 
dist 216=[-.3875645647890170014 ,.1860870813882078299 ] 
dist 217=[-.32727187519205756754,.18839741385565688606] 
dist 218=[-.30720789032370194311,.21652407719621724692] 
dist 219=[-.21654022272458078761,.25993998202271396415] 
dist 220=[-.0449861105709261757 ,.30346514613704330575] 
dist 221=[-.0566429060999930443 ,.33202774942790810671] 
dist 222=[-.0663980128561080778 ,.35509213589463750428] 
dist 223=[-.0760975759627051257 ,.37667390355637822858] 
dist 224=[-.0850093107911052029 ,.39564223552391350107] 
dist 225=[-.0916204926276947375 ,.40943827869447931211] 
dist 226=[-.0980620149620450449 ,.42378691277721450998] 
dist 227=[-.1091422841717597718 ,.43454405935829638371] 
dist 228=[-.1193102409909602535 ,.43873524277450041496] 
dist 229=[-.1256847675612268192 ,.44013256433015255753] 
dist 230=[-.1304972823180731511 ,.43911713560436487949] 
dist 231=[-.1344315311451871805 ,.0945499555912468480 ] 
dist 232=[-.1374957385156668960 ,.0897250031497093947 ] 
dist 233=[-.1388359597372975203 ,.07836543320337828707] 
dist 234=[-.1392258220137551433 ,.07599773590681263387] 
dist 235=[-.1390996769235426932 ,.06005909767208446311] 
dist 236=[-.10678745845890348058,.05701104417822436527] 
dist 237=[-.10489366065480869187,.05962668466510129431] 
dist 238=[-.09979287937728249953,.07256793337658492634] 
dist 239=[-.09863338808782256235,.08469532161977543084] 
dist 240=[-.08878170391310365244,.09536168323332209902] 
dist 241=[-.08662766720427695823,.1024725103778911885 ] 
dist 242=[-.08352244952717410626,.1083357236852134031 ] 
dist 243=[-.08247148461870797737,.1140232248313134503 ] 
dist 244=[-.05867731915665139242,.1189714223944114226 ] 
dist 245=[-.05542397432327234459,.1218844701779040950 ] 
dist 246=[-.04823235107585724131,.1238623978728355903 ] 
dist 247=[-.04631214333194888426,.1250793311771345931 ] 
dist 248=[-.03749616955271879352,.1257135904388471845 ] 
dist 249=[-.03580372701738503464,.1256364864372532238 ] 
dist 250=[-.03178465017121130130,.1246922438649725382 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 1, 0, 0, 1, 2] 
dist 0=[53.314406671625833784  ,53.314406671625833784  ] 
dist 1=[53.003862573196811461  ,53.496813881268771932  ] 
dist 2=[52.449246359632278905  ,53.629217060841897949  ] 
dist 3=[51.292091972825351746  ,53.739954061577937403  ] 
dist 4=[49.832853714632605401  ,53.827981829894331833  ] 
dist 5=[48.071867274079320988  ,53.869594559554562814  ] 
dist 6=[45.748518086986114475  ,53.884593707938639543  ] 
dist 7=[42.043474515913396332  ,53.866131338207603910  ] 
dist 8=[38.254734215522769635  ,53.833230621715492220  ] 
dist 9=[35.597074559800152852  ,53.790608809891484766  ] 
dist 10=[33.253066489987397873  ,53.731946821325224842  ] 
dist 11=[30.716700149576052694  ,53.635314236830641308  ] 
dist 12=[28.243142463158335606  ,53.521361008824074348  ] 
dist 13=[26.149753391692282508  ,53.395123760706060016  ] 
dist 14=[23.928065102582907758  ,52.299540893443663182  ] 
dist 15=[20.941718516396332042  ,49.495475451579666752  ] 
dist 16=[17.975673163316785467  ,37.216644218949429178  ] 
dist 17=[15.834837495685306908  ,35.853798825818200759  ] 
dist 18=[13.881445965278285516  ,32.537620665874120005  ] 
dist 19=[11.575290036661467888  ,32.054000316455387261  ] 
dist 20=[9.3405782478521890470 ,27.170400649186699591  ] 
dist 21=[7.3343950662205177531 ,26.261239850635397146  ] 
dist 22=[5.1057015268972733959 ,25.210973875479266275  ] 
dist 23=[2.1088483206635818837 ,25.005196902166804584  ] 
dist 24=[-.93863076835981444723,17.136777731912160107  ] 
dist 25=[-2.8954221551987391057 ,16.168837091582937441  ] 
dist 26=[-4.4375430844911796535 ,14.192188301986085403  ] 
dist 27=[-6.9613550812335794249 ,13.687172201728042446  ] 
dist 28=[-8.7628566852062094596 ,11.896900882411686171  ] 
dist 29=[-10.145805455059281082  ,11.533702297501328315  ] 
dist 30=[-11.330323365218649419  ,11.008229253452975572  ] 
dist 31=[-12.305755411246820680  ,10.867253165781174405  ] 
dist 32=[-12.853413825281895016  ,.11817618651261836839] 
dist 33=[-13.197626345615939983  ,-.77188654744930420348] 
dist 34=[-13.360672539647207924  ,-2.6769974817748216250 ] 
dist 35=[-13.448878147527176840  ,-3.0475183103903249655 ] 
dist 36=[-13.493988116784517146  ,-4.9893156348227201736 ] 
dist 37=[-13.519319689954145723  ,-5.3068196462952053913 ] 
dist 38=[-13.527785887323039805  ,-5.9392169852231563602 ] 
dist 39=[-13.527266168656958329  ,-5.7138940478963683373 ] 
dist 40=[-13.516343210717018125  ,-4.2636231417423594495 ] 
dist 41=[-13.496688979076740086  ,-3.2600897146927305801 ] 
dist 42=[-13.460949442423906465  ,-2.3927188458203707905 ] 
dist 43=[-13.012262761523648205  ,-1.4856086354766345913 ] 
dist 44=[-13.296182118442314323  ,-.6232373800650623470 ] 
dist 45=[-13.408210076678841936  ,.0656945159550669342 ] 
dist 46=[-13.445162583277980439  ,.7591525888422145682 ] 
dist 47=[-13.429024133317717437  ,1.6396708262028278720 ] 
dist 48=[-.65149035754988546668,2.4857336025546773985 ] 
dist 49=[-.04324405869504380983,3.0417094242185361680 ] 
dist 50=[.90147788708475803511,3.4914882400205718483 ] 
dist 51=[1.5580072827176319496 ,4.4119274365246100579 ] 
dist 52=[2.7876375297712410978 ,5.0566174674656198004 ] 
dist 53=[2.8594092914987239567 ,5.5502562174451779085 ] 
dist 54=[2.9449472577369988128 ,5.9671635740515044054 ] 
dist 55=[2.9260156155920616592 ,6.3032083022402749605 ] 
dist 56=[2.8797833755924507125 ,6.4741127418332983867 ] 
dist 57=[2.8195942019984680965 ,6.5663180049964570975 ] 
dist 58=[2.7385674105082020528 ,6.5881483498687102320 ] 
dist 59=[2.6090106187251335288 ,6.3335495314771704123 ] 
dist 60=[2.4591170784052262091 ,6.4893858865184437020 ] 
dist 61=[2.2968617641303973121 ,6.5596613028571787173 ] 
dist 62=[2.0950257899204372487 ,6.5808137265376049330 ] 
dist 63=[1.7871371590475342396 ,6.5749502819792645825 ] 
dist 64=[.937218539500688323  ,4.3306567029208748334 ] 
dist 65=[.2632678417266218708 ,4.1420113760886910912 ] 
dist 66=[-.30710179869603025159,3.6665589689261979024 ] 
dist 67=[-.88378103461532667867,3.5895911421831019295 ] 
dist 68=[-1.4191487539068955787 ,2.8331527497071786033 ] 
dist 69=[-1.8247266836225245760 ,2.6873885855965879273 ] 
dist 70=[-2.2122182913163687906 ,2.5043499881089272980 ] 
dist 71=[-2.6754423668529538234 ,2.4483263018387182311 ] 
dist 72=[-3.1082106654264626082 ,1.1485511115563863010 ] 
dist 73=[-3.3741969477050440167 ,.9856413297581691222 ] 
dist 74=[-3.5684880676669866974 ,.6302155273306346215 ] 
dist 75=[-3.7152121191677808819 ,.5530645606962897884 ] 
dist 76=[-3.8261196175203230508 ,.1625739710078384913 ] 
dist 77=[-3.8775232176716787459 ,.0960390765171465528 ] 
dist 78=[-3.8963176542793976332 ,-.0516634833383497849 ] 
dist 79=[-3.8949888900214572556 ,-.0752127349358481153 ] 
dist 80=[-2.9401196717147663748 ,-.22734609353216801573] 
dist 81=[-3.0158474602891685375 ,-.17334551265157244071] 
dist 82=[-3.1503648372466398979 ,-.09782237317834291926] 
dist 83=[-3.2470993082746852110 ,.02655627088639728531] 
dist 84=[-3.3169744370473753294 ,.17256418044089451441] 
dist 85=[-3.3442649466315905576 ,.33441593981813412411] 
dist 86=[-3.3705748733671601786 ,.5386922758627787418 ] 
dist 87=[-3.4213737672606791214 ,.8540089211642809071 ] 
dist 88=[-3.4398673994483975648 ,1.1688030125373411308 ] 
dist 89=[-3.4405610640653963727 ,1.3710042489915885586 ] 
dist 90=[-3.4343743274690376349 ,1.6985909856386101713 ] 
dist 91=[-2.9290200753265665404 ,2.0490970714771686129 ] 
dist 92=[-2.7872152181992849718 ,2.3690502986592125756 ] 
dist 93=[-2.7542244928478243987 ,2.6028462182751395362 ] 
dist 94=[-2.6547758383701433684 ,2.8181119756092980203 ] 
dist 95=[-2.6344885019828747284 ,3.0641343484054286617 ] 
dist 96=[-.87463579966400583357,3.2871914530141767362 ] 
dist 97=[-.70995707201913850129,3.4108229183183287964 ] 
dist 98=[-.35457637863907521384,3.4852204617924953573 ] 
dist 99=[-.30515644456546021072,3.5118215312472468094 ] 
dist 100=[-.00204521134123065007,3.5198226589521214596 ] 
dist 101=[.05092285346970867860,3.5199926676710942055 ] 
dist 102=[.14024298995446706496,3.5144563831269530763 ] 
dist 103=[.15993957456553415567,3.5185243499938845634 ] 
dist 104=[-.16961753990102123963,3.5233695337139943910 ] 
dist 105=[-.44174926497094027955,3.5172023447488880054 ] 
dist 106=[-.66930067046673971378,3.5062952671880837522 ] 
dist 107=[-.89508905377270516933,2.6281672699137917645 ] 
dist 108=[-1.1021112975242932380 ,2.2691120496568949591 ] 
dist 109=[-1.2547909696063315588 ,2.1949057457323018972 ] 
dist 110=[-1.3967147264796813528 ,1.9520126056956755202 ] 
dist 111=[-1.5608250754985469092 ,1.5821479549789571822 ] 
dist 112=[-1.7109889471646501410 ,.50788981231990782478] 
dist 113=[-1.7972672359536822154 ,.46737859264213481171] 
dist 114=[-1.8531628271756094159 ,.37140117059805778765] 
dist 115=[-1.8820985431254866611 ,.35537227786550933031] 
dist 116=[-1.8988994469063314456 ,.2242015478941376371 ] 
dist 117=[-1.9063795165996101360 ,.2116231835632994456 ] 
dist 118=[-1.9084552478576044582 ,.1846006224209111407 ] 
dist 119=[-1.9037011806814687697 ,.1801002782453401522 ] 
dist 120=[-1.7116275828738855336 ,.1452815000863831780 ] 
dist 121=[-1.7383721292067315606 ,.1389361865496117658 ] 
dist 122=[-1.7441217073426218231 ,.13855093535811176885] 
dist 123=[-1.5591980504739933220 ,.14615860642999492505] 
dist 124=[-1.5432663052426032072 ,.15823763152797921767] 
dist 125=[-1.4953303934016717979 ,.17568049230136957217] 
dist 126=[-1.4834536047333864490 ,.20029148979222019603] 
dist 127=[-1.3727392456814871199 ,.2409471364006329308 ] 
dist 128=[-1.3471988486210195803 ,.28224087327823156175] 
dist 129=[-1.3130009225417204835 ,.30939536176742685081] 
dist 130=[-1.2998787447964746077 ,.33125173715562798353] 
dist 131=[-.9851117105711969981 ,.35142285167175751629] 
dist 132=[-.9415798135973411864 ,.36881821618493684979] 
dist 133=[-.8481234350870318211 ,.37960483300852592622] 
dist 134=[-.8215198037771094821 ,.38752814524561580661] 
dist 135=[-.7119215691060544401 ,.393498315173088249  ] 
dist 136=[-.6903974543748789130 ,.39742770969426567134] 
dist 137=[-.6349178509534219252 ,.3978430492305351808 ] 
dist 138=[-.6255294036282611127 ,.5595537598781091396 ] 
dist 139=[-.5365802620330787764 ,.7936083331918477761 ] 
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dist 143=[-.4995347517984407747 ,1.3485105942732854962 ] 
dist 144=[-.15379470418169172159,1.4472005339354590070 ] 
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dist 147=[-.04415060830861968562,1.7328881295647541506 ] 
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dist 153=[-.4270450730667462237 ,1.8109135667829091124 ] 
dist 154=[-.5943280138218584203 ,1.8045911266222818098 ] 
dist 155=[-.8095972666773772602 ,.46926124287240015221] 
dist 156=[-.9725936045189570490 ,.4716085823182724249 ] 
dist 157=[-1.1024829302474994729 ,.47104616360932221676] 
dist 158=[-1.2210770231058704872 ,.46877307693532511126] 
dist 159=[-1.3300283859184663342 ,.46681697681540440355] 
dist 160=[-1.4432079116360285198 ,.29958334694352141367] 
dist 161=[-1.5395696303707778954 ,.29770410861035637305] 
dist 162=[-1.6381122037984192338 ,.29343730633070071366] 
dist 163=[-1.7254824912354862842 ,.29160589214862747347] 
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dist 165=[-1.8128539830684992087 ,.27892399466571566102] 
dist 166=[-1.8356498099845986966 ,.27114251654228827447] 
dist 167=[-1.8484617981768163772 ,.26917828698748589912] 
dist 168=[-1.8492412745573122794 ,.24226952186542094533] 
dist 169=[-1.8353208042143894732 ,.23763537281252385444] 
dist 170=[-1.8295892658937729466 ,.22556727538976351608] 
dist 171=[-1.1849144096686038101 ,.22296528241676454692] 
dist 172=[-1.1387026442446962824 ,.35962912353001789869] 
dist 173=[-1.0204264803482015761 ,.49551867693159487898] 
dist 174=[-1.0017625332444688546 ,.62645882098687837043] 
dist 175=[-.8059244332507020176 ,.74410507209705633927] 
dist 176=[-.76743830052399216737,.82694249383367846227] 
dist 177=[-.72272267060342960767,.90009749000187413379] 
dist 178=[-.71002515344298999386,.97910296142451491493] 
dist 179=[-.3699535395373698348 ,1.0506781095742419566 ] 
dist 180=[-.3996975362659939558 ,1.0941815155876490513 ] 
dist 181=[-.4188790803385873851 ,1.1254242399138032735 ] 
dist 182=[-.4339971956225619598 ,1.1480735930153034555 ] 
dist 183=[-.4475201314805067124 ,1.1634489397972173275 ] 
dist 184=[-.4586714785935899013 ,1.1663525964883980664 ] 
dist 185=[-.4643236986693965344 ,1.1705172752178063584 ] 
dist 186=[-.46702670477255650244,1.1703095258229590336 ] 
dist 187=[-.46689331008836968774,.31435274486887008063] 
dist 188=[-.46401244602132419847,.3216764568324774751 ] 
dist 189=[-.46234361757911573677,.32631084090170622764] 
dist 190=[-.45525515721977708853,.32849875061293289802] 
dist 191=[-.45301438799906551843,.3290381088249843167 ] 
dist 192=[-.2762530671977790544 ,.3286771864199514000 ] 
dist 193=[-.25904300222726189952,.3247921358967454585 ] 
dist 194=[-.21619171185489711576,.3239248627311423436 ] 
dist 195=[-.20998904298662421192,.3026888143704246320 ] 
dist 196=[-.14386639023843123714,.2987381188421740015 ] 
dist 197=[-.13139514084026881782,.2872950286185272919 ] 
dist 198=[-.1174200610238131433 ,.2849698274132928003 ] 
dist 199=[-.11480174404319931068,.2604922671357504953 ] 
dist 200=[-.07772795401572789527,.2550630429614015980 ] 
dist 201=[-.07603749821408588544,.2486282663838573756 ] 
dist 202=[-.07219893241421552551,.25720872751704853094] 
dist 203=[-.07095410144375527016,.26516207714819668059] 
dist 204=[-.06515981535685251320,.27132175779417183874] 
dist 205=[-.06387508302324513532,.27397550420171657214] 
dist 206=[-.06084597469602297176,.27480291245930168115] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 0, 2, 2, 2, 0, 1] 
dist 0=[48.304129410006157784  ,48.304129410006157784  ] 
dist 1=[47.685095218124813134  ,48.854188538889871958  ] 
dist 2=[45.763554601258657771  ,49.669016394138304665  ] 
dist 3=[43.755555276788919170  ,50.228958277303211629  ] 
dist 4=[42.294303067205727905  ,50.630224070529320719  ] 
dist 5=[40.951505534460121812  ,50.811550741847233153  ] 
dist 6=[39.416434224415499227  ,50.866477421452266741  ] 
dist 7=[37.872267220742249274  ,50.839701325904115273  ] 
dist 8=[36.493111071799748251  ,48.762836280407324160  ] 
dist 9=[34.961599933475534532  ,48.402747319466272729  ] 
dist 10=[32.815884031192252228  ,47.776813399517701560  ] 
dist 11=[30.645873128560670724  ,47.592752879894351778  ] 
dist 12=[29.015355147197533199  ,46.895600329741799627  ] 
dist 13=[27.462169244941633585  ,46.678910923531922774  ] 
dist 14=[25.600682233632692669  ,46.263987184993072071  ] 
dist 15=[23.674324640011726470  ,46.120790655531097505  ] 
dist 16=[21.861614940551660932  ,30.350994536547427460  ] 
dist 17=[19.776755457367393936  ,28.976684204811980108  ] 
dist 18=[16.762485646845765088  ,26.164953002692585326  ] 
dist 19=[13.771228123854082503  ,25.196383254771125054  ] 
dist 20=[11.778195206857269855  ,20.635459701641233454  ] 
dist 21=[10.125237812185760958  ,19.798545969371287424  ] 
dist 22=[8.4929366729657703828 ,18.681138359697955413  ] 
dist 23=[6.5937728319779818742 ,18.359961267950010901  ] 
dist 24=[3.6630709510647083596 ,11.967129949361112696  ] 
dist 25=[1.6188845242511002085 ,11.615465518732243852  ] 
dist 26=[-.17443347537345633785,10.253743295622666421  ] 
dist 27=[-2.1036588890012270165 ,8.9981006205654947039 ] 
dist 28=[-3.9830023873037973162 ,7.0847760360465016282 ] 
dist 29=[-5.5776922933517481183 ,6.7593167117755091288 ] 
dist 30=[-7.2780952052626834002 ,6.0311203948631316408 ] 
dist 31=[-9.5809546759965202973 ,5.9153680358825092986 ] 
dist 32=[-11.800290354593521370  ,-.06649643938698981486] 
dist 33=[-13.167208111074980528  ,-.39908110240445784124] 
dist 34=[-14.180887211962004066  ,-.44011292482736085109] 
dist 35=[-14.988412695018307715  ,-1.8407843480356671346 ] 
dist 36=[-15.617272979809193264  ,-1.9609967117520580079 ] 
dist 37=[-15.916699683232969445  ,-2.1739571768288653752 ] 
dist 38=[-16.061542564600437791  ,-2.2143230333178424379 ] 
dist 39=[-16.072229425804367709  ,-2.2783177989094246823 ] 
dist 40=[-15.539252624955747031  ,-2.2464072027371364900 ] 
dist 41=[-15.404765650998059084  ,-2.0937588727149637166 ] 
dist 42=[-15.148371230295654844  ,-1.6222704487320203581 ] 
dist 43=[-15.172409258771123804  ,-.88412173415498365923] 
dist 44=[-15.000851051984232082  ,-.03291423055758708601] 
dist 45=[-14.935759168518955359  ,.89001417522579752875] 
dist 46=[-14.878280201888081645  ,2.0413137139613280211 ] 
dist 47=[-14.816432622005295727  ,3.8041145150720076790 ] 
dist 48=[-6.0871325765771922215 ,5.5721416648928273365 ] 
dist 49=[-5.3601534637765435889 ,6.7444037340981476692 ] 
dist 50=[-3.7031735619243675046 ,7.7042586220232169479 ] 
dist 51=[-3.3925548800642573290 ,8.6247158322414930574 ] 
dist 52=[-1.3171049522521554979 ,9.4491985856849343416 ] 
dist 53=[-.95017825036891433451,10.026103132689944952  ] 
dist 54=[-.27785940204901431377,10.532220976992649665  ] 
dist 55=[-.12734448373289195688,11.074300933237442605  ] 
dist 56=[1.7570862152705321588 ,11.547664114314023116  ] 
dist 57=[1.8730722771946590628 ,11.779569681520268732  ] 
dist 58=[1.8932110257481300339 ,11.893100984696463985  ] 
dist 59=[1.9616883040161915370 ,11.902272746192884271  ] 
dist 60=[1.9415775102418211801 ,11.726860467396619334  ] 
dist 61=[1.8855717499702335004 ,11.647490038406254887  ] 
dist 62=[1.7663495346518720917 ,11.197587796556764238  ] 
dist 63=[1.6159790488198732407 ,10.253912617351240204  ] 
dist 64=[1.4356364377602071916 ,2.4149316875173780506 ] 
dist 65=[1.1603847876824286503 ,2.4209560557896025888 ] 
dist 66=[.8240696481918577862 ,2.4158075561000768832 ] 
dist 67=[.44391065010780507099,1.2664820275680940010 ] 
dist 68=[.18650859928643982299,1.1744937027011181668 ] 
dist 69=[-.03007649177594381366,.9542131952832456762 ] 
dist 70=[-.24736975972810643217,.9178252762547663223 ] 
dist 71=[-.44832182330840448604,.60695777378478963038] 
dist 72=[-.5997042021199011662 ,.55000238659679959203] 
dist 73=[-.74368900906384768381,.46827113758491223964] 
dist 74=[-.91512777992971343352,.44519076082230621222] 
dist 75=[-1.0757183906954271862 ,.03062113485952450534] 
dist 76=[-1.1764120934826559030 ,-.02066579198530784285] 
dist 77=[-1.2524657173627981340 ,-.1368702692909919397 ] 
dist 78=[-1.3147193743826347809 ,-.15487006404197851704] 
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dist 80=[-1.3849982128253790489 ,-.31515446725658450146] 
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dist 83=[-1.0849311650396966690 ,-.45033977161204754534] 
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dist 86=[-1.1736929022849050083 ,-.41501445668948237854] 
dist 87=[-1.1888486965332315453 ,-.28746331659996461262] 
dist 88=[-1.1919249716201781907 ,-.15643584242812098143] 
dist 89=[-1.1880020330438876005 ,-.05650281788900958614] 
dist 90=[-1.1862620147559143025 ,.03966833474946692671] 
dist 91=[-1.1331989465970758151 ,.15573638284495252181] 
dist 92=[-1.1219255167254654307 ,.27568738486622803348] 
dist 93=[-1.0887089794504784468 ,.38739180451528328635] 
dist 94=[-1.0800816661791219453 ,.51451387493843090538] 
dist 95=[-1.0048274093043525515 ,.6960500806992961746 ] 
dist 96=[-.98738107914839170583,.87353590080048265209] 
dist 97=[-.96280538149310648603,.98450221701049850163] 
dist 98=[-.95384845845666035704,1.1056812075833870544 ] 
dist 99=[-.59139136445735045262,1.2206482709964988159 ] 
dist 100=[-.54985028952041130646,1.3200965576875299506 ] 
dist 101=[-.46202623586260540013,1.3837374881332762286 ] 
dist 102=[-.43813109994352385321,1.4334007181786057210 ] 
dist 103=[-.34515807154137052413,1.4770582589709994473 ] 
dist 104=[-.32691165746124947392,1.5125654571540674800 ] 
dist 105=[-.28685848767908249584,1.5296942036695989793 ] 
dist 106=[-.27635987567590617451,1.5366835424144856410 ] 
dist 107=[-.23072832341778598921,1.5361196260640042586 ] 
dist 108=[-.22171570438040207901,1.5211632829828090368 ] 
dist 109=[-.22149255084623888379,1.5142890860979439809 ] 
dist 110=[-.2331813941806562843 ,1.4842469802942822940 ] 
dist 111=[-.25160342253557281791,1.4006756737205180116 ] 
dist 112=[-.27825161841086749024,.91525074145757622212] 
dist 113=[-.31600349232157737766,.85892278321288346272] 
dist 114=[-.37873692131455936657,.70034449208803699359] 
dist 115=[-.44310597224459510986,.06061295811556443567] 
dist 116=[-.48738576398021734056,.04828473075721229106] 
dist 117=[-.52539602079834367712,.02022638650617968157] 
dist 118=[-.56474716731478413455,.01542208817940546220] 
dist 119=[-.60191154331034025337,-.01648675100448296614] 
dist 120=[-.63119553931397325815,-.02161202476598080452] 
dist 121=[-.66029267688861121648,-.03138512029568751266] 
dist 122=[-.70430147211240596751,-.03353584258503526404] 
dist 123=[-.74717543286022142593,-.05202459539380743630] 
dist 124=[-.78222473682374641013,-.05485168837595465478] 
dist 125=[-.80094687060942769042,-.05545622621635236512] 
dist 126=[-.81130078653208138031,-.05245651008039519275] 
dist 127=[-.81308435635908118169,-.04751210747657129136] 
dist 128=[-.29317399651734299686,-.04017164624847369441] 
dist 129=[-.26971408438722827989,-.02969367537030471590] 
dist 130=[-.21253425424261125186,-.01223321264763864030] 
dist 131=[-.20424352858256655292,.00569366053983804732] 
dist 132=[-.131737111237688221  ,.01803278201470815215] 
dist 133=[-.13009656637150202242,.02861120953376228557] 
dist 134=[-.12983666514263775464,.03951601430843728957] 
dist 135=[-.1222667943480048498 ,.04976429736475784452] 
dist 136=[-.12039737941616058532,.05772441007432655727] 
dist 137=[-.11916575917835960491,.06825444100119938681] 
dist 138=[-.11881503569558121444,.09200321701783379361] 
dist 139=[-.08964055884888752898,.11514475756706778583] 
dist 140=[-.08579171044434188951,.13614648664134442962] 
dist 141=[-.07836890400655548447,.15136042734742365764] 
dist 142=[-.07645556517396962789,.1652772206674737633 ] 
dist 143=[-.06987561972062989878,.18111162728697873612] 
dist 144=[-.06823716109453903134,.19589385647726624596] 
dist 145=[-.06659056306746770365,.2056124066486216693 ] 
dist 146=[-.06615205445030181191,.21352380331441926552] 
dist 147=[.01208566562693122569,.22108704483074853138] 
dist 148=[.01837764239647046062,.22789219595709626838] 
dist 149=[.03223505933688323756,.23277571268439286535] 
dist 150=[.03469107131249663761,.23721450289200738499] 
dist 151=[.04990673299632318752,.24224448157522079473] 
dist 152=[.05233662978872191422,.24684578828268927847] 
dist 153=[.05713168014296157867,.24957194327227287772] 
dist 154=[.04672622693853813579,.25146707119990652282] 
dist 155=[.01350568376486959757,.25274668853386371166] 
dist 156=[-.02240875818612592000,.25354966359018666444] 
dist 157=[-.05822439005116573726,.25353986741154421397] 
dist 158=[-.1008279937586022469 ,.25293940655787731457] 
dist 159=[-.16383814955606164612,.2521904436812314728 ] 
dist 160=[-.22619067579306598254,.09796221369095065727] 
dist 161=[-.26617054987942750143,.09793636953922630031] 
dist 162=[-.29742343790957507729,.09788720385767781963] 
dist 163=[-.32566587176918777881,.08160201233778927004] 
dist 164=[-.35043675809699712357,.07951340814107909761] 
dist 165=[-.36524805942078484603,.07407253045136105280] 
dist 166=[-.3756039907486567144 ,.07310329391900340501] 
dist 167=[-.3825929046151188991 ,.06361071817100486441] 
dist 168=[-.38763601529730396286,.06167278625464052216] 
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dist 171=[-.39138714593482354283,.03865885416083561359] 
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dist 201=[-.06509669652554312426,.06640411988374566634] 
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dist 211=[-.17114364683145686732,-.00368015487336773139] 
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dist 214=[-.1956423411344226121 ,.00279577344499175607] 
dist 215=[-.2020399440069885799 ,.00985974940718325653] 
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dist 220=[-.20338808697862670631,.05430494451705359789] 
dist 221=[-.20154963373472262323,.06610440550462637481] 
dist 222=[-.20035833657413281474,.08034496322812881066] 
dist 223=[-.1997399518625789674 ,.10391058428075665328] 
dist 224=[-.12235243487253024566,.13120495071303395342] 
dist 225=[-.12915169136791120337,.14858878963657136124] 
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dist 229=[-.1567190154527539737 ,.18824539456853596134] 
dist 230=[-.15905793539744167912,.19889105175566927014] 
dist 231=[-.16042852665226884369,.2121008677728889384 ] 
dist 232=[-.16059298073639806008,.22385867136489258766] 
dist 233=[-.15960974817402420777,.23062538853584298793] 
dist 234=[-.15917615462340302351,.23503061335469473215] 
dist 235=[-.14899526788470785042,.23736365502878779884] 
dist 236=[-.14703098063625266577,.23840339841385159357] 
dist 237=[-.14190240353084400111,.2382422726184989611 ] 
dist 238=[-.14029487884166567789,.236344349017921204  ] 
dist 239=[-.13036583773134681821,.23520283937568072586] 
dist 240=[-.12806906367131217705,.16255441420011455804] 
dist 241=[-.12380271601228957375,.15628727236923846595] 
dist 242=[-.12254512832825184328,.14030560303016386479] 
dist 243=[-.08669117766204548054,.13774993201757743627] 
dist 244=[-.10361539602422800984,.1114337093341731823 ] 
dist 245=[-.11569039909355351419,.10626086801444346466] 
dist 246=[-.12652134107986025502,.10014591432638501791] 
dist 247=[-.13848043010017915721,.09832566284150820298] 
dist 248=[-.14936955635157274544,.04857024964341781629] 
dist 249=[-.15593044162023728067,.04225849313873146874] 
dist 250=[-.16057438205899921065,.02891873563312493616] 
dist 251=[-.16381355090597282574,.02542554815901014877] 
dist 252=[-.16595070226958576428,.01192770890503871575] 
dist 253=[-.16637782662147180037,.00933526980265636994] 
dist 254=[-.16583721283588451378,.00416131679793273706] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 0, 1, 2, 1, 2] 
dist 0=[56.699999469857742763  ,56.699999469857742763  ] 
dist 1=[56.400134143704765769  ,56.870887014740785223  ] 
dist 2=[56.025583981018909276  ,56.979760699784482448  ] 
dist 3=[55.556337152441495454  ,57.031905047979533452  ] 
dist 4=[54.487555842873764729  ,57.038613031425197744  ] 
dist 5=[52.917027357122840237  ,56.966113340243767142  ] 
dist 6=[51.092939514386163153  ,56.821176025782489195  ] 
dist 7=[48.729595014955968070  ,56.724790786761475973  ] 
dist 8=[45.005416468888212267  ,56.189514036232049347  ] 
dist 9=[41.206124340137439157  ,56.025010418170754435  ] 
dist 10=[38.542723482715444539  ,55.417957771527083709  ] 
dist 11=[36.195225579907551139  ,55.283493719567105310  ] 
dist 12=[33.657348554588596921  ,53.558096321848669356  ] 
dist 13=[31.183566170043864179  ,52.266887432365531863  ] 
dist 14=[28.685313551555024229  ,36.690456368658558099  ] 
dist 15=[24.907864154179163520  ,36.217111510814477007  ] 
dist 16=[21.675743932279978393  ,31.321295045476891345  ] 
dist 17=[18.333523191233407484  ,30.396896144324151536  ] 
dist 18=[15.167245989048916706  ,29.351473704579246519  ] 
dist 19=[12.637404050321944345  ,29.139942784382191586  ] 
dist 20=[10.082595763605099126  ,20.782743163485743383  ] 
dist 21=[6.8160080359911106811 ,19.744969233280771360  ] 
dist 22=[3.6478776606225396979 ,17.640235616321498223  ] 
dist 23=[1.4859259965987006951 ,17.101584587137556925  ] 
dist 24=[-.36054338434644596312,16.251262108339860868  ] 
dist 25=[-2.2691788655879785344 ,14.799360781077175469  ] 
dist 26=[-4.0824718095115247277 ,14.238089931136212780  ] 
dist 27=[-5.5488001310609690861 ,14.079315484455861553  ] 
dist 28=[-7.0507182454623574774 ,7.2982628293562101383 ] 
dist 29=[-9.0075718370975024113 ,5.0344745083118974008 ] 
dist 30=[-10.869159688686096091  ,-1.9945241795324338925 ] 
dist 31=[-11.990723486406422150  ,-2.4308745019066044917 ] 
dist 32=[-12.794438188230608106  ,-4.8209650732502649082 ] 
dist 33=[-13.385527649028508605  ,-5.2068322375465008041 ] 
dist 34=[-13.832962008529846342  ,-6.0229306239656904524 ] 
dist 35=[-14.062132130754797153  ,-6.1432963013428295183 ] 
dist 36=[-14.178566984503952669  ,-6.3046494270873063429 ] 
dist 37=[-14.180589013024531084  ,-5.9268941141778103476 ] 
dist 38=[-13.979612406784904515  ,-5.3934370011732990921 ] 
dist 39=[-14.441608882180154401  ,-4.6461954532110045439 ] 
dist 40=[-14.793174746930243237  ,-3.4151793162885004051 ] 
dist 41=[-14.934607682057305302  ,-2.1547111988621528890 ] 
dist 42=[-14.984791586190669452  ,-1.2897573642421152146 ] 
dist 43=[-14.971728145078737784  ,-.55070986174042640197] 
dist 44=[-11.817924254446575280  ,.20772462681278660248] 
dist 45=[-11.749353575783461558  ,1.0302161515324085636 ] 
dist 46=[-5.0920696284106990472 ,2.0051989611250479209 ] 
dist 47=[-4.8273193601884098391 ,2.9497917934922692565 ] 
dist 48=[-4.7385091279065896825 ,3.8022436123893323112 ] 
dist 49=[-2.8685605218823883571 ,4.4096358292944392526 ] 
dist 50=[-2.6245925738525415439 ,4.9897179935565263779 ] 
dist 51=[-2.0843849664354669938 ,5.6194745170995388458 ] 
dist 52=[-1.9603429650990148353 ,6.1927738587967536566 ] 
dist 53=[-1.3215552223632080117 ,7.0616008779725749205 ] 
dist 54=[-1.2064831330809577589 ,8.0887869166874024823 ] 
dist 55=[-.95113772354427011239,8.7169220512886135421 ] 
dist 56=[-.89471543088696978384,9.1729679629213322259 ] 
dist 57=[2.6028822277510563629 ,9.5132067432612996801 ] 
dist 58=[2.2544477339147165176 ,9.7696093932562971527 ] 
dist 59=[1.7722416790594675589 ,9.8910879449818131080 ] 
dist 60=[1.0474442657258856039 ,9.9370265539768151155 ] 
dist 61=[0                     ,9.9352429397622523211 ] 
dist 62=[-.3411862693858104073 ,4.0466611316147696979 ] 
dist 63=[-.98400633221376219686,3.9719115923250520126 ] 
dist 64=[-1.5803741827927517235 ,3.9339086267541127476 ] 
dist 65=[-2.0314176753111307492 ,2.9679860829991339644 ] 
dist 66=[-2.4615915190087902866 ,2.8359554285928903545 ] 
dist 67=[-2.9747095535364244744 ,2.5974681971277510569 ] 
dist 68=[-3.4541491817228248611 ,2.4897176340297785714 ] 
dist 69=[-3.7499632929527153055 ,2.2022017134700087502 ] 
dist 70=[-3.9673778266911704650 ,2.1408710155997869736 ] 
dist 71=[-4.1340347171287642576 ,2.0143862373944396212 ] 
dist 72=[-4.2603073380577792639 ,1.9783403233288104506 ] 
dist 73=[-4.3166143274728677766 ,-.04683259245502565129] 
dist 74=[-4.3374616491282830602 ,-.21194261772305007805] 
dist 75=[-4.3334512436217051439 ,-.23713634724451796773] 
dist 76=[-3.3327442306431693540 ,-1.0225678991564705136 ] 
dist 77=[-3.5357245996946293807 ,-1.3503305596804907802 ] 
dist 78=[-3.6854699506609179498 ,-1.4180342975748938541 ] 
dist 79=[-3.8020126115962876240 ,-1.4454026847363951453 ] 
dist 80=[-3.9967303000729092915 ,-1.3915726832042691960 ] 
dist 81=[-4.2860334643250540536 ,-1.3028226208812259413 ] 
dist 82=[-4.4570777749101060134 ,-1.1824085075342325487 ] 
dist 83=[-4.5743504449423401182 ,-1.0159789190954614044 ] 
dist 84=[-4.6490458301583870569 ,-.74356001713815913058] 
dist 85=[-4.6938029398655087418 ,-.4241998790574397491 ] 
dist 86=[-4.6993403794294267838 ,-.07042736965378912856] 
dist 87=[-4.6742666307701836252 ,.37604694222582941241] 
dist 88=[-4.6588244811080193672 ,1.0653596830452901099 ] 
dist 89=[-3.3396328373965170886 ,1.7596579792759652888 ] 
dist 90=[-3.2496398379289011399 ,2.3829412221464367241 ] 
dist 91=[-3.2205550764808601837 ,2.8915129519110668381 ] 
dist 92=[-1.8724072551613734541 ,3.3758905448185082567 ] 
dist 93=[-1.7217070468263654884 ,3.8071469085834955687 ] 
dist 94=[-1.4032387481539541438 ,4.1037501165218118665 ] 
dist 95=[-1.3169380911924204512 ,4.3582781832853596694 ] 
dist 96=[-.98318435985577655952,4.6216429961498561379 ] 
dist 97=[-.91767562874358278193,4.8531489837661374538 ] 
dist 98=[-.77733400248840781706,4.9805480818102576818 ] 
dist 99=[-.73850535086038254939,5.0559746189523332976 ] 
dist 100=[-.59200305227075637299,5.0800859341857637167 ] 
dist 101=[-.56648454930738342633,5.0786235047505767046 ] 
dist 102=[-.57332229921477502547,5.0636874065267684443 ] 
dist 103=[-.6259781605649631751 ,5.0018704660391421355 ] 
dist 104=[-.70387241481277017282,4.7733825350038334526 ] 
dist 105=[-.81141771907771031411,3.2921651867787248043 ] 
dist 106=[-.96109420225771019784,3.1172273369884149612 ] 
dist 107=[-1.2070930544031479837 ,2.6134300882797142696 ] 
dist 108=[-1.4576510681423992563 ,.78559897605100010602] 
dist 109=[-1.6255237878104516844 ,.29374125450784721603] 
dist 110=[-1.7647411097114228238 ,.17081535313361463085] 
dist 111=[-1.9009781466250891561 ,.14948164313862709609] 
dist 112=[-2.0246543736323951774 ,.00839698912645649643] 
dist 113=[-2.1137618026469291256 ,-.01542972474307222575] 
dist 114=[-2.1945075604796337230 ,-.06017843808345424527] 
dist 115=[-2.2848296778419440489 ,-.07005478694295557734] 
dist 116=[-2.3656388048144857811 ,-.17016746454848417044] 
dist 117=[-2.4084325177793757573 ,-.18492543913885880463] 
dist 118=[-2.4315474944965726842 ,-.19567737199146411454] 
dist 119=[-2.4338437630183975422 ,-.18847830562471973562] 
dist 120=[-2.4226292972767925763 ,-.17284869410179966738] 
dist 121=[-1.0020918665369558556 ,-.14613190350992362219] 
dist 122=[-.97472503926162601966,-.10628773580889177824] 
dist 123=[-.9009481315421235683 ,-.03830182488971335921] 
dist 124=[-.89000357691461223174,.03188501006194952751] 
dist 125=[-.75547143064476587551,.08050936963119270552] 
dist 126=[-.72822240346082342434,.12249184316013897774] 
dist 127=[-.70082589949541412376,.16619502923813159528] 
dist 128=[-.6947218165442754414 ,.20749002045944335957] 
dist 129=[-.56181989143605624428,.23987030251778145035] 
dist 130=[-.55667506913522934709,.27182046728104412691] 
dist 131=[-.5533924695721457156 ,.31140106914292345889] 
dist 132=[-.43505274366302338292,.34877099144520483524] 
dist 133=[-.41879843095619789651,.37190492667887509063] 
dist 134=[-.386461309240778554  ,.3889690857249855301 ] 
dist 135=[-.37775174363240559591,.40213180104954097852] 
dist 136=[-.34539526210245950598,.41172397186541314942] 
dist 137=[-.33788008118030850808,.41454746820507213821] 
dist 138=[-.32457412873586655919,.48818778844364114142] 
dist 139=[-.32111743671179700241,.5632714570285728861 ] 
dist 140=[.11570580860519240072,.6395874567684835821 ] 
dist 141=[.14806258483937065191,.71085522425099997338] 
dist 142=[.22016537769760545643,.76579087111874251722] 
dist 143=[.23163038196788163585,.81928699972184258732] 
dist 144=[.31230792017715035253,.88481018818906284988] 
dist 145=[.32496704771487537162,.9466528297432644868 ] 
dist 146=[.34768752593025301866,.98545931787331554671] 
dist 147=[.29709272158807845316,1.0148261340927904474 ] 
dist 148=[.20286294963411008969,1.0389928113209290925 ] 
dist 149=[.09624135757944176807,1.0579712243718898845 ] 
dist 150=[-.01687163065346051074,1.0666306589784969662 ] 
dist 151=[-.15636491986396194281,1.0693929498672857355 ] 
dist 152=[-.36826839463467095087,1.0680375797070994079 ] 
dist 153=[-.57936562836889090969,.47322253036465132375] 
dist 154=[-.71564227922093657527,.46680189488237617563] 
dist 155=[-.82316144951326140876,.46494660047234780802] 
dist 156=[-.92591728290520330471,.27992586583188072034] 
dist 157=[-1.0144608508957058663 ,.26195357406599142975] 
dist 158=[-1.0695930968369608467 ,.21941041471116562768] 
dist 159=[-1.1107889365362480607 ,.21159300755692765449] 
dist 160=[-1.1437151717256672152 ,.15247196635161918904] 
dist 161=[-1.1702624471067521033 ,.1415152118341258552 ] 
dist 162=[-1.1860012725163477406 ,.12357203217173126501] 
dist 163=[-1.1968332084984593683 ,.11914408363385724182] 
dist 164=[-1.2037984089803053966 ,.04240896169741994166] 
dist 165=[-1.2077466399314389958 ,.03241687097694791456] 
dist 166=[-1.2065389529609740221 ,.01037559361445445050] 
dist 167=[-1.2013282586840650801 ,.00607714703700415280] 
dist 168=[-1.1974597309647179808 ,-.01881562378084247780] 
dist 169=[-.51686642708075075576,-.02300714124846654249] 
dist 170=[-.45901705138417187739,-.03157754518052631556] 
dist 171=[-.32208163369798113549,-.03349978863299787347] 
dist 172=[-.29920116396966513066,.02021574773379177737] 
dist 173=[-.23763866791601793021,.12477702677902766618] 
dist 174=[-.23091826606556769467,.2045459619918299999 ] 
dist 175=[-.22924710247381076564,.2813975907000990322 ] 
dist 176=[-.213725566740199245  ,.37431811508028539795] 
dist 177=[-.21015374635051319026,.46195303190680710512] 
dist 178=[-.20532760538862703654,.51771138855874763781] 
dist 179=[-.20349758882820566752,.56077556362018863375] 
dist 180=[-.16244530795147144407,.5977504803021670114 ] 
dist 181=[-.16428422761286520659,.62796270630057550137] 
dist 182=[-.16513257652778969035,.64403830583970243019] 
dist 183=[-.16518114436703127269,.65283038082706459238] 
dist 184=[-.16409389245284771495,.6545892343840440623 ] 
dist 185=[-.1635004496741175196 ,.53955859113639372614] 
dist 186=[-.16182680096131142993,.52933977347422686191] 
dist 187=[-.16101047165671932971,.50267856267927999768] 
dist 188=[-.15536698958919917143,.49636949304250638587] 
dist 189=[-.16153242708130826508,.44763822468904294794] 
dist 190=[-.16566150562120875412,.43709515378458867105] 
dist 191=[-.16804805563464792558,.42046077089772479993] 
dist 192=[-.16951745038086994268,.41541379503249053788] 
dist 193=[-.169990044357487173  ,.30482048000712596581] 
dist 194=[-.16980806767565287451,.28961428117368853713] 
dist 195=[-.16941136817370471327,.2572988463058884053 ] 
dist 196=[-.15106232865127606488,.25180400878730159881] 
dist 197=[-.14804294032337067801,.21747060372860526827] 
dist 198=[-.14243242909134209611,.22141341984399095203] 
dist 199=[-.16681019564574903287,.22278460209950263457] 
dist 200=[-.2632301400831704883 ,.22309442377800882651] 
dist 201=[-.35855727040154090883,.22279801911791882108] 
dist 202=[-.42124207191414296796,.22200620817853923433] 
dist 203=[-.47200187139994976631,.22123518684747934212] 
dist 204=[-.51973785210238612925,.00641615184523904635] 
dist 205=[-.56436273283830662352,-.00823441917482718623] 
dist 206=[-.59664320187377231334,-.00872307726689297134] 
dist 207=[-.62504319845545041584,-.00380837364019610778] 
dist 208=[-.6555587140119415997 ,.00975720114890694661] 
dist 209=[-.6822037162655243433 ,.02631091322273152107] 
dist 210=[-.69515694961607922999,.04315103573262075611] 
dist 211=[-.70158944055206761052,.06341680268950521927] 
dist 212=[-.70221158645494330058,.09364251732500055862] 
dist 213=[-.69116132263337490622,.12794132581735267205] 
dist 214=[-.68705238109435021327,.16446251437705643255] 
dist 215=[-.68346192529626448661,.2095929051992049238 ] 
dist 216=[-.67968333000472274285,.29966565003025669403] 
dist 217=[-.38936407627268425547,.39198527404364471776] 
dist 218=[-.40869091203948937241,.45103681006955016831] 
dist 219=[-.4352702333080776951 ,.49699515356337651988] 
dist 220=[-.46073982682178878939,.53706478422443265484] 
dist 221=[-.47563788511665867198,.57025544191157058994] 
dist 222=[-.48564538934542855678,.58876246467110011979] 
dist 223=[-.49159626989194219555,.62625623870623679514] 
dist 224=[-.4946904987927182464 ,.66926509580939090992] 
dist 225=[-.49482655237421121384,.70760168341250780274] 
dist 226=[-.49077880395908370377,.72976876682204259231] 
dist 227=[-.4893828850322730392 ,.74432899565144601654] 
dist 228=[-.45692163017734727016,.75230740983119178052] 
dist 229=[-.45073544729541416441,.75605934040336612086] 
dist 230=[-.43410823528735694785,.75572951163644139268] 
dist 231=[-.42945515248364621802,.74966902197799665146] 
dist 232=[-.39632492792632971405,.74632867534829468149] 
dist 233=[-.38877547238505406863,.50298107129068574773] 
dist 234=[-.37603417066847545702,.48343075333653574268] 
dist 235=[-.37228324299204800795,.43378433857221603915] 
dist 236=[-.28435615932697342182,.42564937400164960172] 
dist 237=[-.33541907243567601549,.34443956551806536068] 
dist 238=[-.37119777378684532673,.32847379505088237049] 
dist 239=[-.40261641354274356332,.30897036959367375289] 
dist 240=[-.43627902647833713723,.30270213127283498932] 
dist 241=[-.46670581402607014764,.15140245577671463165] 
dist 242=[-.48521107572855855183,.1320937929797398314 ] 
dist 243=[-.49851826394631554881,.09082398557359182879] 
dist 244=[-.50820120235847292166,.08043538031543822083] 
dist 245=[-.51480750894582790496,.03698637430238274297] 
dist 246=[-.51598403658056759158,.02892246384551183845] 
dist 247=[-.51481548164351800338,.01169778622690479374] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 0, 1, 2, 0, 1] 
dist 0=[58.088758514616659610  ,58.088758514616659610  ] 
dist 1=[57.829332289014604732  ,58.157115622959261029  ] 
dist 2=[57.298896495663599809  ,58.170668649402867647  ] 
dist 3=[56.304961306768729192  ,58.100002923175530485  ] 
dist 4=[55.150291520741578462  ,58.006729305172570536  ] 
dist 5=[53.977913376727223288  ,57.704312834906641446  ] 
dist 6=[52.565222044947116187  ,57.539208598473128856  ] 
dist 7=[50.450706008409087788  ,56.366004690811042721  ] 
dist 8=[48.040325661138987987  ,54.419585610514659574  ] 
dist 9=[45.445950383274965500  ,53.698685056492698219  ] 
dist 10=[42.213149892986512582  ,53.448667122814319922  ] 
dist 11=[37.252922409759441769  ,52.919161592897808113  ] 
dist 12=[32.239822506705232199  ,52.755279054439006860  ] 
dist 13=[28.795787196363055932  ,52.527274258872604903  ] 
dist 14=[25.832832411007349297  ,50.935355520948769730  ] 
dist 15=[22.740956863784672686  ,38.803502183736209061  ] 
dist 16=[19.792648252314955010  ,30.639524771781927609  ] 
dist 17=[17.402909774570706429  ,29.605510277494032997  ] 
dist 18=[14.957541503964919647  ,27.575054322678857794  ] 
dist 19=[11.786692619992273565  ,27.059696282182217063  ] 
dist 20=[8.6894559677181454454 ,25.290708784052036180  ] 
dist 21=[6.5378948253877174292 ,24.885557766356035347  ] 
dist 22=[4.6595956912658544115 ,24.442502100810615477  ] 
dist 23=[2.6535253102396582507 ,24.344530599841588828  ] 
dist 24=[.70881479804051492514,9.7458367020354581268 ] 
dist 25=[-.92480693694230662916,8.2161549088431000514 ] 
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dist 28=[-7.2041246246726019658 ,6.3311923543623782087 ] 
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dist 36=[-13.584981516572102802  ,-6.8448316316113545292 ] 
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dist 44=[-13.100210945481499538  ,-1.7896427991741339085 ] 
dist 45=[-13.001243564126716860  ,-1.3052945914807790138 ] 
dist 46=[-12.944433921758527608  ,-.81029792999633422482] 
dist 47=[-5.0133050515330596444 ,-.17183884045100752394] 
dist 48=[-4.3461777142336986554 ,.83387566821590755633] 
dist 49=[-2.7701120138196919776 ,1.6034298871821396762 ] 
dist 50=[-2.5293289434721710381 ,2.3472537676549234229 ] 
dist 51=[-.39853458536923386131,3.2510654708725069490 ] 
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dist 53=[.05636743936869910084,4.6329496329463969728 ] 
dist 54=[-.00610142683549609802,5.0327083178822894876 ] 
dist 55=[-.15505035538661434534,5.3581402667343338276 ] 
dist 56=[-.31836011137216942734,5.8343571015300767724 ] 
dist 57=[-.43811960069951436459,6.2663467029469236258 ] 
dist 58=[-.54734435048203578155,6.6092129385988901273 ] 
dist 59=[-.66887143883250186191,6.8796331570699521635 ] 
dist 60=[-.78736689638058883838,7.0224163939590476126 ] 
dist 61=[-.88459097533410248297,7.0993043380997914457 ] 
dist 62=[-.98388212021910060152,7.1087823380483989376 ] 
dist 63=[-1.1106569151372428214 ,4.3292182241798320539 ] 
dist 64=[-1.2309376931884414432 ,4.1601460390261193060 ] 
dist 65=[-1.3043771338109781294 ,3.7377919192064605941 ] 
dist 66=[-1.3568876312613913460 ,3.6656981861320424806 ] 
dist 67=[-1.3938064562957870095 ,3.0006822379757072444 ] 
dist 68=[-1.4175422348004744588 ,2.8717630309014728396 ] 
dist 69=[-1.4221116456916624065 ,2.6998866843529182121 ] 
dist 70=[-1.4109339452404115153 ,2.6435741261487305938 ] 
dist 71=[-1.4085128914102022147 ,2.3608553392756992271 ] 
dist 72=[-.44027712786005205494,1.3614286436015397166 ] 
dist 73=[-.79087832284776719986,1.0401992737655245057 ] 
dist 74=[-1.1814167637718764192 ,.97108686651401476915] 
dist 75=[-1.7288874879216845643 ,.72958832684780913287] 
dist 76=[-2.2665407358096285730 ,.5351465664487029086 ] 
dist 77=[-2.6179119199275323002 ,.39472435594508266244] 
dist 78=[-2.9004056746633356713 ,.36567604019749112927] 
dist 79=[-3.1631177200362214893 ,-.32359585917658379158] 
dist 80=[-3.3933419522660851653 ,-.38602307816326286175] 
dist 81=[-3.5461604688458982439 ,-.37350141389724006878] 
dist 82=[-3.6717707750173458612 ,-.32508491981554603869] 
dist 83=[-3.7934103501138478436 ,-.21536427622927350655] 
dist 84=[-3.8933474987854951501 ,-.08715528965051245829] 
dist 85=[-3.9323265014693144489 ,.03506710090454367621] 
dist 86=[-3.9550888009348384704 ,.1761234242232516224 ] 
dist 87=[-4.0953154994913067939 ,.37954548102013103345] 
dist 88=[-4.1656322443340455941 ,.60732571437669748848] 
dist 89=[-4.1990720471321674017 ,.84562132712287040799] 
dist 90=[-4.2036974030613481026 ,1.1371919117358701122 ] 
dist 91=[-4.1640191164546594640 ,1.5776217274441568914 ] 
dist 92=[-4.1423237665797095741 ,2.0155462711082521155 ] 
dist 93=[-4.1021631723879492839 ,2.2971301167818523862 ] 
dist 94=[-4.0842208682371252728 ,2.5180945056468425595 ] 
dist 95=[-.95488998314702146764,2.7140925044651453805 ] 
dist 96=[-.60095518696730299132,2.8790628370096577897 ] 
dist 97=[-.55538402613212908894,3.0589645919928790892 ] 
dist 98=[-.45289517702265616104,3.3389709611391264880 ] 
dist 99=[-.43200785265321992909,3.5777979853137385857 ] 
dist 100=[-.30767145683589234697,3.8135114443022844173 ] 
dist 101=[-.28568488764899310689,4.0350334545469575318 ] 
dist 102=[-.24175084087270306909,4.2543698654569829593 ] 
dist 103=[-.23087897442205108612,4.4462107980209568690 ] 
dist 104=[.68375139569522131919,4.5579983859907640000 ] 
dist 105=[.73349809392224946675,4.6325640841529490476 ] 
dist 106=[.8329284386818584035 ,4.6758470350501797123 ] 
dist 107=[.245923795661582219  ,4.6957329263054637532 ] 
dist 108=[-.39244915018568003524,4.6937093649835262493 ] 
dist 109=[-.81741639031339870684,4.6492944426125200911 ] 
dist 110=[-1.1672559307783469285 ,4.6340066179606209079 ] 
dist 111=[-1.5058092401940146961 ,2.7228637684578374986 ] 
dist 112=[-1.8109972496357747079 ,2.5453210078724888249 ] 
dist 113=[-2.0276805130722724285 ,2.1065557270358795906 ] 
dist 114=[-2.2209174307166712385 ,2.0412362568209208752 ] 
dist 115=[-2.4325298887356985951 ,1.6287486716935420517 ] 
dist 116=[-2.6252153035840915927 ,1.3843990418652438222 ] 
dist 117=[-2.7429200360700389722 ,1.3801660142844852911 ] 
dist 118=[-2.8281683011005130215 ,1.3592640499711103527 ] 
dist 119=[-2.8913378849568062479 ,1.3551173330133026958 ] 
dist 120=[-2.9354428343978022076 ,.9870564865847032011 ] 
dist 121=[-2.9446657494920643712 ,.9633948741677576515 ] 
dist 122=[-2.9411588288677430781 ,.90032152412409184129] 
dist 123=[-2.9348550023041602231 ,.89025998749072475933] 
dist 124=[-2.8537121662321083272 ,.77548313410526390618] 
dist 125=[-2.8654513872246389288 ,.75184823605290967464] 
dist 126=[-2.8677078179033362832 ,.72678919540433407717] 
dist 127=[-.9298240639584017197 ,.71929884364569738258] 
dist 128=[-1.0206393958718858057 ,.45863545572749575353] 
dist 129=[-1.0766438493004516503 ,.42467902735181674429] 
dist 130=[-1.1179572357748529518 ,.35637910852338058249] 
dist 131=[-1.1501317455753804631 ,.33845350116943155499] 
dist 132=[-1.1740817830144464544 ,.2732959492983108824 ] 
dist 133=[-1.1825711872037352512 ,.25904290601191694615] 
dist 134=[-1.1845677634249354913 ,.2355039983613940536 ] 
dist 135=[-1.1825670618338972031 ,.2293987695927308241 ] 
dist 136=[-.3575117001817670587 ,-.1444614037825092073 ] 
dist 137=[-.3011339228147960401 ,-.08086342367098091641] 
dist 138=[-.2870873364552636442 ,-.02538924262193406420] 
dist 139=[-.2213497185952056835 ,.03347893372759552138] 
dist 140=[-.2093050960326321839 ,.10796616339420988351] 
dist 141=[-.1806724415178932054 ,.19648727297231296091] 
dist 142=[-.1755760895584089750 ,.32180097900699730876] 
dist 143=[.08633803816362421421,.44555846270405787715] 
dist 144=[.1165849470472994909 ,.52787030451008203345] 
dist 145=[.1198650690193577713 ,.59560321087438876032] 
dist 146=[.1162761662152262997 ,.66117100258996974841] 
dist 147=[.1024094187755334150 ,.72034955282483741736] 
dist 148=[.0830418257443409662 ,.76258120048115287731] 
dist 149=[.0575020755751746664 ,.80050211542429006904] 
dist 150=[.0225909943745020889 ,.84247641181052723065] 
dist 151=[-.0341700141014442466 ,.87988801944786902466] 
dist 152=[-.0921443852230729654 ,.89959770779518280219] 
dist 153=[-.1318986828016514222 ,.9101273662936101494 ] 
dist 154=[-.16587065003411688052,.91207581874779586363] 
dist 155=[-.20077732403977322656,.90791895111441901949] 
dist 156=[-.23356989184285813926,.90386105719294615594] 
dist 157=[-.25910934119349291745,.89715276904391802153] 
dist 158=[-.36099875637211140863,.8935948867660610721 ] 
dist 159=[-.49640671619093582058,.5566291996590913017 ] 
dist 160=[-.5835127817567116844 ,.47112754465037706932] 
dist 161=[-.65189124494518126027,.45848524073036136528] 
dist 162=[-.71256089449753507116,.43383197147290126539] 
dist 163=[-.76361288610144004949,.42695368462548692824] 
dist 164=[-.79360957857617933376,.4004008707037389084 ] 
dist 165=[-.816121446134556838  ,.39388746159226557543] 
dist 166=[-.8626492998034084094 ,.38078542565267773089] 
dist 167=[-.90353751025437007284,.37670231361019431753] 
dist 168=[-.92792849839799543576,-.1097291925894941167 ] 
dist 169=[-.9449051515377590668 ,-.1457918529974366698 ] 
dist 170=[-.95620178860389005411,-.2223139393025537456 ] 
dist 171=[-.96298327275776653728,-.2386105526559753920 ] 
dist 172=[-.96306430159795731002,-.3125182643877049120 ] 
dist 173=[-.95794463964639455819,-.3254111639828611757 ] 
dist 174=[-.95316342700666706442,-.2523663675386878232 ] 
dist 175=[-.54153623965595190218,-.0992475854164164771 ] 
dist 176=[-.55736486804114423252,.0040297183102009162 ] 
dist 177=[-.58830693573109420764,.0905379462871718383 ] 
dist 178=[-.61133523676001433828,.1767331346259622205 ] 
dist 179=[-.62956564160788014552,.2560877927441167668 ] 
dist 180=[-.6432932550457839454 ,.3152957049674603528 ] 
dist 181=[-.64834829723711690086,.3710595723831667362 ] 
dist 182=[-.64967223986730145976,.43666798470789261515] 
dist 183=[-.6485165466158864688 ,.49785718242734217251] 
dist 184=[-.62949591726099471678,.53598478279922567318] 
dist 185=[-.62486343651256215745,.56450136969807652814] 
dist 186=[-.60831840005963518138,.58733650084627843587] 
dist 187=[-.60518897541243120651,.60482069544983111496] 
dist 188=[-.55983774928298633375,.61198255209299386966] 
dist 189=[-.54923941019798125977,.61488707973625686896] 
dist 190=[-.53945981746971073651,.61538254205628651344] 
dist 191=[-.5353508597926505094 ,.59087979762655814478] 
dist 192=[-.38905460448746686986,.59305987547972835477] 
dist 193=[-.36931548717225778338,.59230563346278148738] 
dist 194=[-.33021031872390584993,.59182731723921745896] 
dist 195=[-.31981935185905227583,.58392921856963340112] 
dist 196=[-.28180649902623428559,.57823537682723747095] 
dist 197=[-.27302195998774577194,.57561203245818481821] 
dist 198=[-.2583174752632497139 ,.56606757943209830746] 
dist 199=[-.25432337000510238429,.56241991422499470909] 
dist 200=[-.23174212109458456045,.06658043322315055837] 
dist 201=[-.24844352147968832919,.05515389808437451384] 
dist 202=[-.26063136776284677673,.05321287552744240635] 
dist 203=[-.26983484865903414674,.03688192805654356980] 
dist 204=[-.27668455152509898424,.03384892331350807765] 
dist 205=[-.27947962352133620776,.02944367359347841963] 
dist 206=[-.28035526096590913375,.02819550022232228526] 
dist 207=[-.27985150209690189672,.00556499303178835524] 
dist 208=[-.26276263388229674579,.00236607382940818192] 
dist 209=[-.2593034021762926096 ,-.00129576691383412580] 
dist 210=[-.25225835440309447915,-.00172683662139361874] 
dist 211=[-.24987446065760235406,-.00083264481656411523] 
dist 212=[-.23854289351868574138,.00200373599647422076] 
dist 213=[-.23585616899852607349,.00679988363434911548] 
dist 214=[-.2331325213632480019 ,.01551472482558377258] 
dist 215=[-.2367868663116478969 ,.02513956705405017250] 
dist 216=[-.2375719753879464554 ,.0662824218705813841 ] 
dist 217=[-.2371818627711356566 ,.1061986968842702086 ] 
dist 218=[-.2367736561576139134 ,.1394488872750827766 ] 
dist 219=[-.2269509299389036341 ,.1722585290099526491 ] 
dist 220=[-.2241555029262098310 ,.2022424639297257417 ] 
dist 221=[-.2219418633153377419 ,.2242169308094680822 ] 
dist 222=[-.2204465094982685343 ,.2445156215574312102 ] 
dist 223=[.02943858193265703948,.2678124496301037617 ] 
dist 224=[.04044376414140422053,.2889841285991046372 ] 
dist 225=[.04115195435004102806,.3008025790002797795 ] 
dist 226=[.03862268236299085862,.3080229442867226901 ] 
dist 227=[.03101597697677452839,.3108463837925117530 ] 
dist 228=[.02073502757993070437,.3120053587645097293 ] 
dist 229=[.00753458364120320263,.3125839343521516450 ] 
dist 230=[-.01032235781345708923,.3128473891380297846 ] 
dist 231=[-.03918434762952154777,.3127492142109093606 ] 
dist 232=[-.0685227569670876011 ,.1882868878526922942 ] 
dist 233=[-.0882807534510864654 ,.1850728054522096107 ] 
dist 234=[-.1047884403242181810 ,.1838739402295765908 ] 
dist 235=[-.1211569143839115071 ,.1789840666336733355 ] 
dist 236=[-.1361661610177669915 ,.1774087929094258684 ] 
dist 237=[-.1472499758944181657 ,.1735718589407647243 ] 
dist 238=[-.1575714817886363724 ,.1720342952568256737 ] 
dist 239=[-.1695386793903324446 ,.05228955062181944448] 
dist 240=[-.1804764916576879608 ,.04163603131847038159] 
dist 241=[-.1866903234949946189 ,.01815388981851552002] 
dist 242=[-.1906275503068891431 ,.01322036243631288680] 
dist 243=[-.1924808862823272640 ,-.01347821131196740927] 
dist 244=[-.1932597440547488280 ,-.01804085391783082895] 
dist 245=[-.1929351276727510129 ,-.02795968816082010023] 
dist 246=[-.1919170405831661088 ,-.02981375538572546597] 
dist 247=[-.1911087558287902443 ,-.04384673444295899348] 
dist 248=[-.16997847034025561542,-.04604792678712574086] 
dist 249=[-.16666348527354043184,-.04581795971393950785] 
dist 250=[-.15788219900798140675,-.04221148966096145601] 
dist 251=[-.15590066373568723997,-.03671620253751410281] 
dist 252=[-.13949002561454861483,-.02894934421053843961] 
dist 253=[-.13594268338005917502,-.01803890107701924637] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 2, 1, 1, 2] 
dist 0=[58.560628885617034199  ,58.560628885617034199  ] 
dist 1=[58.072302601764140719  ,58.813568365659598149  ] 
dist 2=[56.948057544617602819  ,58.998006585930732384  ] 
dist 3=[55.620773800440683534  ,59.119184150058710575  ] 
dist 4=[54.321512743619638156  ,59.119611646251981691  ] 
dist 5=[52.791250159413500073  ,59.052708127714550100  ] 
dist 6=[50.541288069609714357  ,58.944059187267053362  ] 
dist 7=[47.994522718951389606  ,58.699284984622542998  ] 
dist 8=[45.278840604916468232  ,58.402197022901105357  ] 
dist 9=[41.912705613907460095  ,55.333311243768425322  ] 
dist 10=[36.768120670755689543  ,54.767749934109004586  ] 
dist 11=[31.578740819739987600  ,53.910571564856623365  ] 
dist 12=[28.033609810297563884  ,53.635591248253105798  ] 
dist 13=[25.005463928476080431  ,53.000296160337898719  ] 
dist 14=[21.880578064640150440  ,52.045967749867698939  ] 
dist 15=[18.922668411350598471  ,47.323087894771671248  ] 
dist 16=[16.561157646744972272  ,44.113089739652410482  ] 
dist 17=[14.177250861789527878  ,29.948180155513879698  ] 
dist 18=[11.129439911537542709  ,28.444777035892224815  ] 
dist 19=[8.1724005177818279429 ,26.616712291712944926  ] 
dist 20=[6.1507801158368291404 ,26.189724991700881704  ] 
dist 21=[4.4198771416145708790 ,25.750249252361064520  ] 
dist 22=[2.6236548648915680531 ,25.665045535572078551  ] 
dist 23=[.9129531129628102362 ,15.193184140031587525  ] 
dist 24=[-.47685007224024838589,14.816410376420208839  ] 
dist 25=[-1.9057130007493683235 ,8.6305332251269852160 ] 
dist 26=[-3.7735098165113599920 ,7.8628929369573352617 ] 
dist 27=[-5.5625256125658160519 ,6.2691173551931326511 ] 
dist 28=[-6.6767911419251234144 ,5.9410546977587335364 ] 
dist 29=[-7.5182837823882830622 ,4.5694171689885885725 ] 
dist 30=[-8.2169145703598075487 ,4.0453939059398557133 ] 
dist 31=[-10.068610364018952420  ,3.0299399781796597077 ] 
dist 32=[-11.246992614021500984  ,2.4986010241375927744 ] 
dist 33=[-12.152570608868907414  ,-7.7252676451874731478 ] 
dist 34=[-12.926675937539897797  ,-7.7086538693396236763 ] 
dist 35=[-13.562093924174923515  ,-7.5065996750301214319 ] 
dist 36=[-13.906185584251445380  ,-7.0474625736806851425 ] 
dist 37=[-14.102963980586149399  ,-6.3150167471658216586 ] 
dist 38=[-14.150816520913889750  ,-5.0221618982968123120 ] 
dist 39=[-12.170449051699947000  ,-3.6809462741280271074 ] 
dist 40=[-12.192303464151064252  ,-2.7552927871247953867 ] 
dist 41=[-11.896154310507975746  ,-1.9590417488349821597 ] 
dist 42=[-11.810651223462331894  ,-1.1337022303966591673 ] 
dist 43=[-11.687475228216879297  ,-.3545722528620447589 ] 
dist 44=[-11.629809073186091629  ,.2575350600590106223 ] 
dist 45=[-11.427391547365412779  ,.8638818752919442197 ] 
dist 46=[-11.352291684762642667  ,1.6202869708239647987 ] 
dist 47=[-11.190858448321489592  ,2.3407279255056771919 ] 
dist 48=[-11.127237807440347175  ,2.8036915009111868073 ] 
dist 49=[-4.7961986674500794803 ,3.1668852604832932738 ] 
dist 50=[-4.2458382682543885336 ,3.5499049305168562511 ] 
dist 51=[-2.9486192213121631100 ,3.9831906603212043679 ] 
dist 52=[-2.7442068324857922623 ,4.3102600660555312804 ] 
dist 53=[-.99217521622535105951,4.6230533285096756467 ] 
dist 54=[-.67952184354028578707,4.9996224026315704538 ] 
dist 55=[-.75631225778208448215,5.3452899811614949957 ] 
dist 56=[-1.0674955814013010080 ,5.5347803539048992874 ] 
dist 57=[-1.3377188816394381296 ,5.6473552812694102546 ] 
dist 58=[-1.6207866098029589839 ,5.6858696343232262920 ] 
dist 59=[-1.8888198871211226292 ,5.9721456446084618106 ] 
dist 60=[-2.0991542301449835872 ,6.2489872778361588387 ] 
dist 61=[-2.3065861895850400070 ,6.4628262469100116720 ] 
dist 62=[-2.5630923565678225582 ,6.5601163606283319906 ] 
dist 63=[-2.8046656291953520028 ,6.6028948586756719893 ] 
dist 64=[-2.9525772274245289601 ,6.5990628703244634412 ] 
dist 65=[-3.0596460831725055363 ,4.5015674556945505958 ] 
dist 66=[-3.1383870160635250052 ,4.4342713957103831505 ] 
dist 67=[-3.1925686583181848249 ,4.1663162413595666749 ] 
dist 68=[-3.2032112690077693786 ,4.1026266337957644382 ] 
dist 69=[-3.1949365238147287071 ,3.9632341169551730295 ] 
dist 70=[-3.1855107326715198118 ,3.9176298794065792119 ] 
dist 71=[-1.1631210623080731562 ,2.0243784937232590731 ] 
dist 72=[-1.6275936591087420558 ,1.9958280711261175096 ] 
dist 73=[-2.0057885013328176159 ,.7451775584246376529 ] 
dist 74=[-2.3651192138461026851 ,.5942425106936468668 ] 
dist 75=[-2.6848928425372307879 ,.2788334319708053644 ] 
dist 76=[-2.9052353656151559434 ,.2018989245482923144 ] 
dist 77=[-3.0950610677810248922 ,-.0911603205601682919 ] 
dist 78=[-3.2930816434607353138 ,-.1468451421666404752 ] 
dist 79=[-3.4670465209505487674 ,-.1666700647946569071 ] 
dist 80=[-3.5608649045951226906 ,-.0693259220381063485 ] 
dist 81=[-3.6141085288439529736 ,.0530474728078415618 ] 
dist 82=[-3.6260972917836447189 ,.2411901452241118650 ] 
dist 83=[-3.6206456929967806858 ,.4371772565757185037 ] 
dist 84=[-3.6064242287365059897 ,.59085746590741156417] 
dist 85=[-3.5784292352742768828 ,.7426876324649685449 ] 
dist 86=[-3.5630248075981697622 ,.93131446285597620056] 
dist 87=[-2.5520218507991438733 ,1.1287766697425051256 ] 
dist 88=[-2.6938307194683366083 ,1.3158677320988575586 ] 
dist 89=[-2.8270195382882005834 ,1.5309126095092791770 ] 
dist 90=[-2.9104340165220188294 ,1.8399118186204813818 ] 
dist 91=[-2.9735812780648266895 ,2.1433509190321039421 ] 
dist 92=[-3.0258254692701495708 ,2.3362119975864639540 ] 
dist 93=[-3.0672389252089366569 ,2.4847215485527811055 ] 
dist 94=[-3.0871301181346469479 ,2.6111998791485628216 ] 
dist 95=[-3.0951303555361160704 ,2.7135614757661247522 ] 
dist 96=[-3.0895984526897182106 ,2.7658406181803319158 ] 
dist 97=[-.4995847829294078203 ,2.7913014656606223758 ] 
dist 98=[-.4689639277263889052 ,2.7944863458098126671 ] 
dist 99=[-.2000538441149485381 ,2.7686432178153959670 ] 
dist 100=[-.1521780962892672369 ,2.9037628618905431538 ] 
dist 101=[-.0854772914868278617 ,3.1590236363427358386 ] 
dist 102=[-.0674897763687505521 ,3.3167648466041197951 ] 
dist 103=[.36286853570791691071,3.4305495247691783238 ] 
dist 104=[.41457328526405595184,3.5141468798313733527 ] 
dist 105=[.49495780782509132245,3.5787916514165892344 ] 
dist 106=[.08421276180393572350,3.6169349607298253808 ] 
dist 107=[-.40240033797561548055,3.6430203951760648137 ] 
dist 108=[-.72600587414990156007,3.6595337091458299468 ] 
dist 109=[-.99196061689448774281,3.6686903202583271586 ] 
dist 110=[-1.2485237741186467498 ,3.6654124439298611021 ] 
dist 111=[-1.4792172743005065162 ,3.6524392960135776487 ] 
dist 112=[-1.6419433068433303462 ,3.6398277577420689269 ] 
dist 113=[-1.7859583645835569290 ,1.4946474514592274742 ] 
dist 114=[-1.9419925760803531419 ,1.4083855743520232851 ] 
dist 115=[-2.0833810625723731592 ,.88194260142259457977] 
dist 116=[-2.1689475939611619547 ,.81728561749749390883] 
dist 117=[-2.2299585725975029715 ,.2644062985821964281 ] 
dist 118=[-2.2733372651350172332 ,.1058793555058928554 ] 
dist 119=[-2.3019712646517272852 ,-.03411287186451107813] 
dist 120=[-2.3076217028072787023 ,-.06490662146742674239] 
dist 121=[-2.2982434227154085904 ,-.85022247261822972359] 
dist 122=[-2.2948317349726684466 ,-.94226284430938374588] 
dist 123=[-1.6827152058417392770 ,-1.1457339454679473762 ] 
dist 124=[-1.7928106447138485207 ,-1.1762427737225110644 ] 
dist 125=[-1.8811736576619526110 ,-1.2173549955866091766 ] 
dist 126=[-1.9254650858631006342 ,-1.0619282301999361993 ] 
dist 127=[-1.9489248112054695394 ,-.9081763043754438783 ] 
dist 128=[-1.9541469257921239876 ,-.7755315259588828591 ] 
dist 129=[-1.5222822465830038306 ,-.6330112887852990845 ] 
dist 130=[-1.4896236241774178519 ,-.4398355717544650579 ] 
dist 131=[-1.4068619038084718763 ,-.2483458084230862964 ] 
dist 132=[-1.3870553302967847477 ,-.1125459207992310167 ] 
dist 133=[-1.2444864052345351416 ,.0084376864022724156 ] 
dist 134=[-1.2141668725923832408 ,.1408093368196151467 ] 
dist 135=[-1.1628681973174940377 ,.2703760251101967559 ] 
dist 136=[-1.1487002536075840585 ,.3801761706528831667 ] 
dist 137=[-.8499894917336654972 ,.4965592157819639933 ] 
dist 138=[-.8088665342465087037 ,.6524175154504572745 ] 
dist 139=[-.7123468846669804534 ,.8050095981965333283 ] 
dist 140=[-.6920375456947536041 ,.9083597100937493568 ] 
dist 141=[-.5572569038052281766 ,.99548763514596850017] 
dist 142=[-.5314484350791789728 ,1.0833252199019574079 ] 
dist 143=[-.4842761810321471947 ,1.1649582435303389558 ] 
dist 144=[-.4727102915779843343 ,1.2273197093299826204 ] 
dist 145=[-.10415352305733039264,1.2875481801703250352 ] 
dist 146=[-.06388902626985741178,1.3606682102074979978 ] 
dist 147=[.00744932201330519297,1.4294325801822350834 ] 
dist 148=[.02281185163736843964,1.4884025553703859916 ] 
dist 149=[.05710695048350638020,1.6115973794945694078 ] 
dist 150=[.05491367895388862900,1.6959371675904494171 ] 
dist 151=[.0207961104924219645 ,1.7679683493762539501 ] 
dist 152=[-.1664297005981887383 ,1.8420425144294922991 ] 
dist 153=[-.3937605256571653313 ,1.9049532719902573002 ] 
dist 154=[-.7352024784675707386 ,1.9324312129201807147 ] 
dist 155=[-1.0744113461568475014 ,1.9448803786614178161 ] 
dist 156=[-1.2928319989408373912 ,1.9478044837603937294 ] 
dist 157=[-1.4645590052263960749 ,1.8948554042694969707 ] 
dist 158=[-1.6174140808418164554 ,1.8812328830755789624 ] 
dist 159=[-1.7520925124370736169 ,1.8731629612966481364 ] 
dist 160=[-1.8367861343839109012 ,1.8705762075678800393 ] 
dist 161=[-1.8983135556159150445 ,-.46342342053177290252] 
dist 162=[-1.9443003008543358120 ,-.59423017048693783396] 
dist 163=[-1.9799323745738476939 ,-.88299949089648755847] 
dist 164=[-2.0001348389298357779 ,-.93297648532383206817] 
dist 165=[-2.0129072901455340526 ,-1.2496551552226662497 ] 
dist 166=[-2.0188864154321911814 ,-1.2995909297930991018 ] 
dist 167=[-2.0200522928441011139 ,-1.3001818346487397901 ] 
dist 168=[-2.0141302567783738825 ,-1.2476935393389241330 ] 
dist 169=[-2.0015721633634560499 ,-1.1504292118563515044 ] 
dist 170=[-1.9937257239292475936 ,-.82136020073162787111] 
dist 171=[-2.0255163369041599968 ,-.4880774760359812232 ] 
dist 172=[-2.0496917156184960580 ,-.2622960210830664387 ] 
dist 173=[-2.0621356526011057038 ,-.0721046520726113426 ] 
dist 174=[-2.0613471685758839178 ,.1191460034926774656 ] 
dist 175=[-2.0496103087689914088 ,.2963594218094427978 ] 
dist 176=[-2.0394252829742433562 ,.4305321191539359476 ] 
dist 177=[-1.4478970844777597010 ,.5588333712296313771 ] 
dist 178=[-1.3916368290315959664 ,.7126175464204761700 ] 
dist 179=[-1.2480380419477319365 ,.8572306353593698268 ] 
dist 180=[-1.2251182994830232714 ,.9489317775525029977 ] 
dist 181=[-.98836047880745932477,1.0194115105267474166 ] 
dist 182=[-.94182959686761293698,1.0793312802672287208 ] 
dist 183=[-.88694094697604684174,1.1278578362351322400 ] 
dist 184=[-.87071864310523191345,1.2192097485514746376 ] 
dist 185=[-.42301167221231442813,1.3096282692755657416 ] 
dist 186=[-.36629859975081089632,1.3644318720205128357 ] 
dist 187=[-.24636991963657801989,1.4036119102065283094 ] 
dist 188=[-.21512212739305306072,1.4316831858913589951 ] 
dist 189=[-.09376823741182342396,1.4504479908314249622 ] 
dist 190=[-.07052200176510206836,1.4541823667468267318 ] 
dist 191=[-.02428150697546432450,1.4492170154507666832 ] 
dist 192=[-.01282528486189725090,1.4467697535101962068 ] 
dist 193=[.08834369278062319635,.66303337840193362714] 
dist 194=[.06347037603757968667,.65353817616093991383] 
dist 195=[.03697470200254725708,.49055013268623602883] 
dist 196=[.0013708134757642196 ,.46777418876420177998] 
dist 197=[-.0373309557093358807 ,.41065709210494632115] 
dist 198=[-.1079165132950424986 ,.40173378092080250325] 
dist 199=[-.2173007712540939417 ,.31153579276525752886] 
dist 200=[-.3190314604240894002 ,.29419731923445642766] 
dist 201=[-.4346169930662651852 ,.27337622478390161462] 
dist 202=[-.5992978600282312152 ,.26767705860015127219] 
dist 203=[-.7613780369232126475 ,.2604982564111052266 ] 
dist 204=[-.8665853581956256449 ,.3111417636385867196 ] 
dist 205=[-.9502582790539665727 ,.3665063973462572705 ] 
dist 206=[-1.0268895601345650455 ,.42257626108778422271] 
dist 207=[-1.1004067981932702074 ,.48987646066452795288] 
dist 208=[-1.1487387386724550400 ,.59005655243398968929] 
dist 209=[-1.1878713851909991227 ,.68922065547776804408] 
dist 210=[-1.2246762268437450791 ,.75246567168212471961] 
dist 211=[-1.2545657351206506422 ,.80147616833966869524] 
dist 212=[-1.2660997299923475158 ,.84383401777465772671] 
dist 213=[-1.2697024706433763892 ,.87863981361469088457] 
dist 214=[-1.2679364286681527971 ,.8975115974564840976 ] 
dist 215=[-1.2333541758550698138 ,.9083086087419698673 ] 
dist 216=[-1.2217733221393545095 ,.9108888046501995146 ] 
dist 217=[-1.2106828289892247945 ,.9092958336573849566 ] 
dist 218=[-1.2031180926081757125 ,.90648902459433012429] 
dist 219=[-.92605034705086717172,.89630018054427068372] 
dist 220=[-.91841032917701178788,.89055773015007207477] 
dist 221=[-.88459542131637652902,.8579185869387598464 ] 
dist 222=[-.87550849725581170289,.9141510499113563621 ] 
dist 223=[-.85153810564154457488,.9608705513208187084 ] 
dist 224=[-.8424432302764081768 ,1.0088886165510438719 ] 
dist 225=[-.26543782777012860271,1.0913020561635719527 ] 
dist 226=[-.2125965208892007277 ,1.1824345744596538811 ] 
dist 227=[-.1004357944847629925 ,1.2647714850769519016 ] 
dist 228=[-.0728711097839891463 ,1.3120832318670666986 ] 
dist 229=[.0404098499494340945 ,1.3427806022755161211 ] 
dist 230=[.0614452234897145623 ,1.3588124923454543821 ] 
dist 231=[.1022647910316984216 ,1.3671727940272398919 ] 
dist 232=[.1118214264680440859 ,1.3672540779691998001 ] 
dist 233=[.13825093916509072443,1.3621146608309147013 ] 
dist 234=[.03618662224951260540,1.3577563323139506368 ] 
dist 235=[-.17656794860775211479,1.0393244645086747344 ] 
dist 236=[-.31804592543134973307,1.0090248222585843493 ] 
dist 237=[-.43434915226125522014,.9295481110090018269 ] 
dist 238=[-.5466361864214826897 ,.9163599665121252019 ] 
dist 239=[-.6476895901455361569 ,.7768025671837053130 ] 
dist 240=[-.7191614152717326284 ,.7017251746907065404 ] 
dist 241=[-.7826217541300334711 ,.63547852862362775764] 
dist 242=[-.8517023924870830150 ,.62452733203412714375] 
dist 243=[-.9143376539601572986 ,.31627260636237569371] 
dist 244=[-.9520759294326022024 ,.27712432058736131103] 
dist 245=[-.9787862338179445770 ,.19466608430507457666] 
dist 246=[-.9974120314559219391 ,.17274366107671451791] 
dist 247=[-1.0094063332602866226 ,.09006851826623000096] 
dist 248=[-1.0118575525114870548 ,.07397542013758255996] 
dist 249=[-1.0067053015338893439 ,.04237553282930288785] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 2, 2, 2, 0, 2] 
dist 0=[59.422943231303204812  ,59.422943231303204812  ] 
dist 1=[58.798508730643098113  ,59.750567755024906821  ] 
dist 2=[57.528561285862614818  ,59.835034597795329738  ] 
dist 3=[56.128409686326277442  ,59.785348009504538906  ] 
dist 4=[54.983967955687898148  ,59.577188284828734611  ] 
dist 5=[53.804626246800405934  ,59.350083067010811120  ] 
dist 6=[52.265109307079129515  ,59.224758448433301860  ] 
dist 7=[50.606910027256886352  ,59.149817449640407831  ] 
dist 8=[48.953554629787008491  ,58.387620945167384111  ] 
dist 9=[46.982626260668790224  ,53.436594524718170499  ] 
dist 10=[44.056026118678504414  ,52.635311534380239202  ] 
dist 11=[41.024930549660507454  ,51.213860445761522332  ] 
dist 12=[38.636612592035900036  ,50.851866132220467257  ] 
dist 13=[36.255338427108381121  ,49.682891646157590801  ] 
dist 14=[30.428129169012269342  ,49.318324510609248656  ] 
dist 15=[24.577245314006342043  ,49.079065514313659708  ] 
dist 16=[20.639319046385081284  ,48.275431704656165828  ] 
dist 17=[17.339176543234533025  ,35.269243002713461146  ] 
dist 18=[14.035197026551515233  ,35.103860547134023553  ] 
dist 19=[10.971193906108728974  ,18.269261179911275213  ] 
dist 20=[8.6292075313150738384 ,17.604601266999303203  ] 
dist 21=[6.0983870576056416130 ,11.453798710882431348  ] 
dist 22=[3.1489520749354025720 ,10.374529494514981403  ] 
dist 23=[.43130544598775347641,8.9993748185482116158 ] 
dist 24=[-1.6169777097835144147 ,8.7551737982686844104 ] 
dist 25=[-3.5728540967944254529 ,1.3256065054276338618 ] 
dist 26=[-5.9213645072668412131 ,.60896391788001903788] 
dist 27=[-8.1246369189786394666 ,-1.3864873332659277290 ] 
dist 28=[-9.5003991306606923823 ,-1.6562211581303410724 ] 
dist 29=[-10.537037950339549157  ,-3.5874927043353142242 ] 
dist 30=[-11.385813115452985636  ,-3.8666734484179615136 ] 
dist 31=[-12.059277226966389837  ,-4.3610854131118755797 ] 
dist 32=[-12.395802673405933455  ,-4.4347142137068210567 ] 
dist 33=[-12.567108539635486825  ,-5.3056760449262881403 ] 
dist 34=[-12.588164019051756293  ,-4.5038534130593393516 ] 
dist 35=[-8.1001086113183429261 ,-3.6379787812005156419 ] 
dist 36=[-8.1957064802913905407 ,-3.0044338729410881438 ] 
dist 37=[-8.2402649055870443019 ,-2.4238575738375479862 ] 
dist 38=[-8.2538245143722885787 ,-1.7684242790417488043 ] 
dist 39=[-8.2493860854245258566 ,-1.1185373177663554842 ] 
dist 40=[-8.2211069438195313632 ,-.55966137020585864103] 
dist 41=[-7.0881476205993372018 ,.03796388172751813624] 
dist 42=[-6.9215566422631301167 ,.84284387116995209507] 
dist 43=[-6.5995418861300105167 ,1.6368177412897465654 ] 
dist 44=[-6.5108923019540517678 ,2.1911451747572063104 ] 
dist 45=[-6.1789367882479867111 ,2.6756347425179330879 ] 
dist 46=[-6.0942961072298431220 ,3.1912238601859864264 ] 
dist 47=[-5.9469317766937373234 ,3.6877028192942685258 ] 
dist 48=[-5.9047397580057836892 ,4.0961602674101558434 ] 
dist 49=[-1.4247557619390476166 ,4.5191631951892308374 ] 
dist 50=[-1.0428034198477068391 ,5.0740605316515129059 ] 
dist 51=[-.20175303556814338484,5.5998670314123031872 ] 
dist 52=[-.03731048738056120832,5.9068223009141701663 ] 
dist 53=[.90774615416156052598,6.1135353617700694703 ] 
dist 54=[1.0659761834054052643 ,6.2390703472303317382 ] 
dist 55=[1.3930350045140697751 ,6.3211802030492448372 ] 
dist 56=[1.4611464456605146747 ,6.3543969147407974027 ] 
dist 57=[1.9314940216910962166 ,6.3586015426867304819 ] 
dist 58=[1.7948426009119427380 ,6.3450578073787702130 ] 
dist 59=[1.5073116220528554940 ,5.6444726573813100300 ] 
dist 60=[1.2541854313146545715 ,5.6302297188459646401 ] 
dist 61=[.97834683736315601038,5.7490256024654666812 ] 
dist 62=[.6000274907077109345 ,5.7963723166889455517 ] 
dist 63=[.18524169557806643852,5.8073998205045024686 ] 
dist 64=[-.23621182294320395761,5.7975553106117656407 ] 
dist 65=[-.74309933157728070253,3.4066271073053904703 ] 
dist 66=[-1.4989366906071319575 ,3.4012983793811801238 ] 
dist 67=[-2.2494501159691268882 ,-.51615238855455174859] 
dist 68=[-2.7351188905645096110 ,-.6093379144121059334 ] 
dist 69=[-3.1197659463162576685 ,-1.2022738459510001991 ] 
dist 70=[-3.4671032496538335760 ,-1.2602058871299297642 ] 
dist 71=[-3.7638994860737089468 ,-1.4130490793552370197 ] 
dist 72=[-3.9468411529162948696 ,-1.4407867040451056687 ] 
dist 73=[-4.0814717757727926333 ,-1.4914524304420045221 ] 
dist 74=[-4.1854699720276490426 ,-1.4587456704226862289 ] 
dist 75=[-4.2660920832111333563 ,-1.3799524331566722235 ] 
dist 76=[-4.3074284454000394899 ,-1.2179138034528757944 ] 
dist 77=[-4.3279962026856245396 ,-1.0151349429718458372 ] 
dist 78=[-4.3257190531314345852 ,-.77378834812338777573] 
dist 79=[-4.3090530989179332972 ,-.45834150480713101857] 
dist 80=[-4.2936748297766053698 ,.04008631983284141428] 
dist 81=[-4.2326777720887309679 ,.54370812377975311435] 
dist 82=[-4.2053855722917397359 ,.87988106180931336936] 
dist 83=[-2.4770866922442501364 ,1.1572869972743847894 ] 
dist 84=[-2.4554369395190790084 ,1.4264454527286331872 ] 
dist 85=[-2.2306285976312633875 ,1.6692126373570268464 ] 
dist 86=[-2.1808753222201339546 ,1.8413220062796059728 ] 
dist 87=[-2.1201615619256096799 ,1.9943644709989567403 ] 
dist 88=[-2.0952538790128697614 ,2.1610515626321755014 ] 
dist 89=[-1.5066451267202322969 ,2.3113083570107703094 ] 
dist 90=[-1.4269688886358142190 ,2.3987954620219548963 ] 
dist 91=[-1.2586699896259227467 ,2.4568861008753864102 ] 
dist 92=[-1.2120222652483259318 ,2.5988736233500145393 ] 
dist 93=[-1.0269433018113877993 ,2.7358889099465182234 ] 
dist 94=[-.98981188630383249856,2.8455304613203833250 ] 
dist 95=[-.90475655902932176853,2.9291175482451564632 ] 
dist 96=[-.88294488092047871488,2.9621457933190279663 ] 
dist 97=[1.2614438352690145777 ,2.9745963205758898701 ] 
dist 98=[1.2744192670568933098 ,2.9760772224829756544 ] 
dist 99=[1.5393083903813176498 ,2.3316771675302823018 ] 
dist 100=[1.4136364897354591495 ,2.3956698710751005445 ] 
dist 101=[1.2964076272746433727 ,2.4387578502487023939 ] 
dist 102=[1.1602658881781947736 ,2.4602031700141124176 ] 
dist 103=[1.0225652998116223780 ,2.4705071713738837990 ] 
dist 104=[.89910009613268948065,2.4691177839848746337 ] 
dist 105=[.76251074478286490918,2.4593621611630152256 ] 
dist 106=[.57241966483106704738,2.4523843142302338248 ] 
dist 107=[.38180778957056696285,2.4031959600950733334 ] 
dist 108=[.24312940917079963252,2.3888629922230196089 ] 
dist 109=[.11598370742094000052,2.3362508868701250743 ] 
dist 110=[-.02862031822523885582,2.3251995549323052466 ] 
dist 111=[-.17336941990823290084,1.2732835439391194150 ] 
dist 112=[-.30110819566924172857,1.1723326409999376691 ] 
dist 113=[-.48406501684466762301,.93183499949892218562] 
dist 114=[-.72273460968490620811,.89137102968930482503] 
dist 115=[-.9381929471695082366 ,.55332191607571025617] 
dist 116=[-1.0920255365467416162 ,.49099095942060035847] 
dist 117=[-1.2302425835805576973 ,.40032424936912245233] 
dist 118=[-1.3833882078590229947 ,.37490475959335567345] 
dist 119=[-1.5242482799194567700 ,-.08668275012576034502] 
dist 120=[-1.6134294413312516980 ,-.14412608162884923788] 
dist 121=[-1.6819002060309592942 ,-.2774012111031330682 ] 
dist 122=[-1.7400837189612545664 ,-.29666162022307127218] 
dist 123=[-1.7872530261794971398 ,-.43189498193292631828] 
dist 124=[-1.8117545746334179832 ,-.3466575567625549413 ] 
dist 125=[-1.8243612779309520702 ,-.24944804045021923036] 
dist 126=[-1.8240457124364440398 ,-.11055824256145365462] 
dist 127=[-1.6125122633314570509 ,.04442662729986425607] 
dist 128=[-1.6115650142470468729 ,.20587667492339103971] 
dist 129=[-1.5944288953116347493 ,.40294226092713118771] 
dist 130=[-1.5905266993864195734 ,.70007352314754421908] 
dist 131=[-.66862490476054309955,.99522526908222834642] 
dist 132=[-.62842166207780276714,1.1843935844273733981 ] 
dist 133=[-.57264617538162218778,1.3321115689214702534 ] 
dist 134=[-.55563153334940767385,1.4618390581026380887 ] 
dist 135=[-.22774841066199176603,1.5700463296043935471 ] 
dist 136=[-.18634990921939176213,1.6558694993390900688 ] 
dist 137=[-.09289152969565644693,1.7309864803571377410 ] 
dist 138=[-.07578197825507569391,1.7982164199470402236 ] 
dist 139=[.03680172030904753301,1.8548541490146202665 ] 
dist 140=[.05607362398162685419,1.8876985940422431162 ] 
dist 141=[.09207065991666261252,1.9094036259160248688 ] 
dist 142=[.09999644007261129838,1.9215842502452420032 ] 
dist 143=[.10732727953462848161,1.9267179965564546955 ] 
dist 144=[.08267932873073586189,1.9235443451788211170 ] 
dist 145=[.05604059195921891002,1.9091641331558634838 ] 
dist 146=[.01982396775269329692,1.8992250598049791552 ] 
dist 147=[-.01968976749056968872,1.1178128659265029886 ] 
dist 148=[-.05949445707775650352,1.1589390889293462869 ] 
dist 149=[-.10708736982156638852,1.1939351625844472609 ] 
dist 150=[-.17768901343184180122,1.2297706001526931865 ] 
dist 151=[-.27155784581491878891,1.2601636621962920731 ] 
dist 152=[-.39925383465807516418,1.2734360904885903378 ] 
dist 153=[-.52252674308759130083,1.2781614236937339087 ] 
dist 154=[-.67194130679158391846,1.2769382016569438578 ] 
dist 155=[-.81253428468133333843,1.2541903432737112370 ] 
dist 156=[-.9006020298514226352 ,1.2455503115834381041 ] 
dist 157=[-.96703325347498193848,1.2298969950662211954 ] 
dist 158=[-1.0212763134060528250 ,1.2237679957863647801 ] 
dist 159=[-1.0643469791914719909 ,-.40985491211106572839] 
dist 160=[-1.0861911857453239869 ,-.48797293517245998181] 
dist 161=[-1.1336361769198694933 ,-.56476087144895198965] 
dist 162=[-1.2250917938592730656 ,-.57079091973171376792] 
dist 163=[-1.3009373789576663012 ,-.55672283528795928799] 
dist 164=[-1.3434930229589623196 ,-.51903972380763085147] 
dist 165=[-1.3846654436759711485 ,-.48162236775089442045] 
dist 166=[-1.4474158842790801900 ,-.43483353297753043913] 
dist 167=[-1.5014764447490009242 ,-.38564622047770738012] 
dist 168=[-1.5332446290854070710 ,-.33865444100693499536] 
dist 169=[-1.5547699263971648540 ,-.28429875656461046362] 
dist 170=[-1.5679481454439798866 ,-.20572133173885479524] 
dist 171=[-1.5747543010218917626 ,-.12563597229681650443] 
dist 172=[-1.5733887835106550588 ,-.06526058070862242811] 
dist 173=[-1.5629125549815016119 ,-.00778535419696357098] 
dist 174=[-1.5548975093129472480 ,.06072922107487464352] 
dist 175=[-.98039436309004178034,.13107111197719363488] 
dist 176=[-.94639274493131564762,.23820353345180627351] 
dist 177=[-.8578812685698507317 ,.35158927918286825629] 
dist 178=[-.84457362978340302091,.46346265860330933435] 
dist 179=[-.6932123139780187954 ,.56578006046156003049] 
dist 180=[-.66320122949180656092,.64102566488127217092] 
dist 181=[-.63113857598024626897,.71083720189619656739] 
dist 182=[-.62359315324015469834,.79146437406321286548] 
dist 183=[-.31713451008553119162,.8655535953208645853 ] 
dist 184=[-.27863748492376140345,.90927197759909974604] 
dist 185=[-.19980266531626198717,.93910329580677063505] 
dist 186=[-.17933864280148757848,.95777155594235477953] 
dist 187=[-.10557346262976010178,1.0150198204956990612 ] 
dist 188=[-.09028931381398323326,1.0550229141007974600 ] 
dist 189=[-.11324789312939369474,1.0833235101821756251 ] 
dist 190=[-.15197319629420931898,1.1030496375209558575 ] 
dist 191=[-.19495117642430517778,1.1157563922538165986 ] 
dist 192=[-.23938927545054817596,1.1181692696017013885 ] 
dist 193=[-.293392257747553994  ,1.1127634147333534856 ] 
dist 194=[-.37454350327478652422,1.1112293350580001683 ] 
dist 195=[-.50403517707501491924,.31725150686633801383] 
dist 196=[-.62608048481582814008,.31738516697364130515] 
dist 197=[-.72353174131723777029,.32089742331358634662] 
dist 198=[-.81285430780155989983,.32993394611054174818] 
dist 199=[-.89964038212342782472,.34081148196709106664] 
dist 200=[-.96025179213794807097,.35167002916096903085] 
dist 201=[-1.0082357349518433535 ,.36458438276607542344] 
dist 202=[-1.0515030017404068812 ,.38366546262981353161] 
dist 203=[-1.0884490624842113827 ,.40522989971667759772] 
dist 204=[-1.1112063611676529119 ,.42805374052490246167] 
dist 205=[-1.1279178746337620599 ,.45615236765111961141] 
dist 206=[-1.1407370264532182027 ,.49876495192681146148] 
dist 207=[-1.1500663134890017604 ,.54121817600065517919] 
dist 208=[-1.1528509002130846030 ,.56868094943330033967] 
dist 209=[-1.1513740366451022576 ,.59039877544909187763] 
dist 210=[-1.1482594055559513159 ,.60992788913263371367] 
dist 211=[-.65474636172246812175,.62653476260480658416] 
dist 212=[-.63150701486431500452,.6365919341667200134 ] 
dist 213=[-.57101851796229367028,.64376859083968351722] 
dist 214=[-.56184724482712041387,.64888127914369672692] 
dist 215=[-.45847761904210382001,.65186106739862484105] 
dist 216=[-.43799174278672881433,.65114926246606375234] 
dist 217=[-.41582646624572730752,.6472646752388677273 ] 
dist 218=[-.41042591290323388104,.64417924619923331874] 
dist 219=[-.20260388209461560998,.62313963474347793872] 
dist 220=[-.17651546231735721661,.6170877833180233267 ] 
dist 221=[-.1227335505159810925 ,.60505372612317593363] 
dist 222=[-.10871960587925426081,.61672920648058195498] 
dist 223=[-.05780206147728043048,.62447389939632171516] 
dist 224=[-.04741476211159108985,.63246187977433669427] 
dist 225=[-.03056097399762891341,.6356915996636808012 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 0, 0, 1, 2, 0, 2] 
dist 0=[59.738134307240445288  ,59.738134307240445288  ] 
dist 1=[59.606573842096166976  ,59.773083815091731168  ] 
dist 2=[59.282986983415530660  ,59.742649947565139784  ] 
dist 3=[58.604326674384943639  ,59.646398390889559276  ] 
dist 4=[57.353183155885168012  ,59.418477328527799399  ] 
dist 5=[55.926060069931291020  ,59.288179967858659730  ] 
dist 6=[54.544608820140276683  ,58.571363936326418950  ] 
dist 7=[52.929188608066198298  ,57.350714455145594183  ] 
dist 8=[50.567537583672913736  ,54.653306932601356771  ] 
dist 9=[47.900315540189548207  ,54.380281089613370804  ] 
dist 10=[45.064463867028032935  ,53.671103736301482288  ] 
dist 11=[41.555118568452587414  ,53.429638906325004226  ] 
dist 12=[36.198069014773669164  ,53.289097607837003430  ] 
dist 13=[30.797179641376878170  ,53.113058609259978344  ] 
dist 14=[27.112650009726618919  ,41.474949674429756074  ] 
dist 15=[23.970968257667036677  ,41.324975055345406055  ] 
dist 16=[20.737843177044659712  ,32.690755551321055304  ] 
dist 17=[17.683112899108164387  ,31.591888062497560326  ] 
dist 18=[15.253657390528876649  ,29.448269454219637231  ] 
dist 19=[12.809783301218536723  ,28.904828868887450149  ] 
dist 20=[9.6969955885481517789 ,27.050682376647263072  ] 
dist 21=[6.6825464809509012633 ,26.617029234939575022  ] 
dist 22=[4.6311703022556480071 ,26.170033397439047248  ] 
dist 23=[2.8849523558576683163 ,26.081678198020428432  ] 
dist 24=[1.0889816362493209204 ,7.4043242650959573829 ] 
dist 25=[-.61158974685317394487,6.3429062076539571209 ] 
dist 26=[-1.9772687164318544163 ,4.6659780560881511253 ] 
dist 27=[-3.3671915079947842214 ,4.3976697185815208859 ] 
dist 28=[-5.1657175740656518814 ,3.9741672594658601974 ] 
dist 29=[-6.8813694853525327420 ,3.8944308094667587239 ] 
dist 30=[-7.9403496679104701820 ,-3.9305104050576899499 ] 
dist 31=[-8.8668662080015395041 ,-4.1678575406320407368 ] 
dist 32=[-10.373204811921329249  ,-7.1090522463107430177 ] 
dist 33=[-11.575284184915106820  ,-7.5021936946083932724 ] 
dist 34=[-12.498723128127924965  ,-7.9566226555815169208 ] 
dist 35=[-13.287440170145022791  ,-7.9336068844966926994 ] 
dist 36=[-13.932136831387459107  ,-7.7206564756217541756 ] 
dist 37=[-14.280298806608551209  ,-7.2450046420018144964 ] 
dist 38=[-14.479057711133090397  ,-6.4887926817329834643 ] 
dist 39=[-14.526996508673675726  ,-5.1560987095962664357 ] 
dist 40=[-11.202917146129454320  ,-3.7739517188497036312 ] 
dist 41=[-11.154353082482204967  ,-2.8201705010780496631 ] 
dist 42=[-10.984912430003111174  ,-1.9998032323158804675 ] 
dist 43=[-10.918672620801815440  ,-1.1495375183935447139 ] 
dist 44=[-10.764425620468886929  ,-.3468816727780038424 ] 
dist 45=[-10.700520678332092072  ,.2837557961516549669 ] 
dist 46=[-4.8231819152792107605 ,.9085193206220083219 ] 
dist 47=[-4.3084257753964399009 ,1.6880006707361888008 ] 
dist 48=[-3.0871756455793930393 ,2.4304849648541374834 ] 
dist 49=[-2.8981334846772212036 ,2.9077444453414425514 ] 
dist 50=[-1.2219531200096665655 ,3.2823029929362096409 ] 
dist 51=[-.92106312939133882362,3.6755343070235702001 ] 
dist 52=[-.51292531576489884546,4.1200711363763494764 ] 
dist 53=[-.40643777761506107792,4.4555328810006322064 ] 
dist 54=[.11723039016531608038,4.7762492986350121012 ] 
dist 55=[-.3294408728043668182 ,5.2085420227372984285 ] 
dist 56=[-.79438349200924746267,5.5387599596304308119 ] 
dist 57=[-1.1182940389397552486 ,5.8057175046497609602 ] 
dist 58=[-1.3992844190836666769 ,6.0123978688107426046 ] 
dist 59=[-1.6932176098690590225 ,6.1019771546136240145 ] 
dist 60=[-1.9713123884498473504 ,6.1420381156168375439 ] 
dist 61=[-2.1892075129463454954 ,6.1509777507593992352 ] 
dist 62=[-2.4037961463956751303 ,5.8460775437628251010 ] 
dist 63=[-2.6687520020963718935 ,5.8234485467780436432 ] 
dist 64=[-2.9181027682445264228 ,5.0006159476550965505 ] 
dist 65=[-3.0704897842358299390 ,4.8774954916095195860 ] 
dist 66=[-3.1804591251065796805 ,4.6330647601201257893 ] 
dist 67=[-3.2606953919135829559 ,4.5635073512873018268 ] 
dist 68=[-3.3153455481679236761 ,4.2871790652461021492 ] 
dist 69=[-3.3261004971253260326 ,4.2213659015543487692 ] 
dist 70=[-3.3153740438788769462 ,4.0782647723256501733 ] 
dist 71=[-3.3066254467671361640 ,4.0316277369781752479 ] 
dist 72=[-1.2398515832972672474 ,.4274850022564501220 ] 
dist 73=[-1.7254138439629620528 ,.3504093008425793789 ] 
dist 74=[-2.1209994564634106292 ,.0741146476611828636 ] 
dist 75=[-2.4972094164361744376 ,.0199681668758012088 ] 
dist 76=[-2.8322349477325113814 ,-.0550621265742340495 ] 
dist 77=[-3.0634747377879015454 ,-.0698757103123696499 ] 
dist 78=[-3.2630937963686724556 ,-.4834327552228600823 ] 
dist 79=[-3.4719622067973918942 ,-.4173629235676062714 ] 
dist 80=[-3.6555242428300129901 ,-.3194339423239968328 ] 
dist 81=[-3.7541444751313320258 ,-.2089163303530023912 ] 
dist 82=[-3.8095977173405396271 ,-.0926012143274301692 ] 
dist 83=[-3.8208362438205028276 ,.0499551908600797977 ] 
dist 84=[-3.8139481470397159759 ,.2651813247290184722 ] 
dist 85=[-3.7981714318908883623 ,.4878699527581260712 ] 
dist 86=[-3.7698610533018386905 ,.66021202821212791121] 
dist 87=[-3.7546291823846283234 ,.82837928027243678197] 
dist 88=[-2.9274962386181522518 ,1.0344349021354286141 ] 
dist 89=[-2.9849809573130641964 ,1.2486971310701184395 ] 
dist 90=[-3.0311683855474651156 ,1.4496198897665620820 ] 
dist 91=[-3.0545237427460426099 ,1.6789832614451323650 ] 
dist 92=[-3.0656875917875710732 ,2.0067317684663811057 ] 
dist 93=[-3.0631879968887549726 ,2.3280278769964976735 ] 
dist 94=[-1.5718565047808008091 ,2.5316469551070298455 ] 
dist 95=[-1.5365526699200966696 ,2.6877940806462265435 ] 
dist 96=[-.8656192562127025613 ,2.8196712295862354008 ] 
dist 97=[-.7784787012722383750 ,2.9255977644405056506 ] 
dist 98=[-.5713818270327398460 ,3.0156194734875472447 ] 
dist 99=[-.5390561560720572355 ,3.1689255745268389789 ] 
dist 100=[-.2547221593670622373 ,3.2797666529885205444 ] 
dist 101=[-.2039244331828635499 ,3.3616777393293700989 ] 
dist 102=[-.1332974694901621432 ,3.4253375643154979424 ] 
dist 103=[-.1140024139862079861 ,3.4633369816739271701 ] 
dist 104=[.34921900850937554155,3.4898631205887516848 ] 
dist 105=[.40491962811499232613,3.5077252944192294498 ] 
dist 106=[.49169985894272721808,3.5187068474479124647 ] 
dist 107=[.51231954771307527299,3.5177699681600102934 ] 
dist 108=[.09757961347143856336,3.5079613237079339869 ] 
dist 109=[-.43102107895141722825,3.4958047942593001837 ] 
dist 110=[-.78237447184263066679,2.1195571876116559398 ] 
dist 111=[-1.0709597962088972128 ,1.9594188067272252556 ] 
dist 112=[-1.3490875082991529879 ,1.9245634845329330142 ] 
dist 113=[-1.5990126691105173071 ,1.6740561745845470683 ] 
dist 114=[-1.7750590757311200429 ,1.6234584887634237726 ] 
dist 115=[-1.9306197544824034497 ,1.5371185227887587362 ] 
dist 116=[-2.0988036993279933877 ,1.4302784774162868877 ] 
dist 117=[-2.2511531314921755385 ,.6201002847549154801 ] 
dist 118=[-2.3435205448656412958 ,.5195873269014669706 ] 
dist 119=[-2.4095927642771746083 ,.1895814638748542981 ] 
dist 120=[-2.4569875402276569574 ,-1.1284225730426059867 ] 
dist 121=[-2.4886617645470527026 ,-1.1578229741723004344 ] 
dist 122=[-2.4948198717931063713 ,-1.3646079779633150816 ] 
dist 123=[-2.4861954862961095381 ,-1.3951629000212905600 ] 
dist 124=[-2.4815561743450540492 ,-1.4505784081065956121 ] 
dist 125=[-1.8444655376254301777 ,-1.4595974734804158498 ] 
dist 126=[-1.5415487557232892398 ,-1.3873187547119674754 ] 
dist 127=[-1.4208651869084437173 ,-1.3028468342583281400 ] 
dist 128=[-1.3463223011258745713 ,-1.1344805908084280375 ] 
dist 129=[-1.3278802997152703033 ,-.9681981231034059621 ] 
dist 130=[-1.1979976452407079137 ,-.8251647685832623287 ] 
dist 131=[-1.1701128937480408244 ,-.6718397299694418036 ] 
dist 132=[-1.1220064748629817356 ,-.4644711855901617918 ] 
dist 133=[-1.1088920282739949252 ,-.2591137012244072775 ] 
dist 134=[-.8312786432298873148 ,-.1138057686844229550 ] 
dist 135=[-.7928368668409682785 ,.0153126434847781448 ] 
dist 136=[-.7022068759453499387 ,.1560724809708789123 ] 
dist 137=[-.6831652103458802713 ,.2935515160085266390 ] 
dist 138=[-.5550588025874093576 ,.4095883742940191316 ] 
dist 139=[-.5303998948639963544 ,.5321801406638726761 ] 
dist 140=[-.4857689492561200815 ,.6958409240250602345 ] 
dist 141=[-.4748817636101058184 ,.8560012814241071607 ] 
dist 142=[-.11001344684221212171,.9907594988436477901 ] 
dist 143=[-.06938787912672317136,1.1604726001614993512 ] 
dist 144=[.00367644617250380376,1.2977991737421498967 ] 
dist 145=[.01972434331235644382,1.4268091703268412080 ] 
dist 146=[.05814495870661404351,1.5441190795871518226 ] 
dist 147=[.05820960163203233255,1.6254197817666349362 ] 
dist 148=[.04304345476959534627,1.6947371974674846322 ] 
dist 149=[.00317412910371731358,1.7658293573578131460 ] 
dist 150=[-.04500137491801402413,1.8262078858038828139 ] 
dist 151=[-.09331830096471099749,1.8527673220876519437 ] 
dist 152=[-.15095395350772486754,1.8647979943357436040 ] 
dist 153=[-.23632484488007833077,1.8671860883911288020 ] 
dist 154=[-.33293795530172400662,1.8183275908566958701 ] 
dist 155=[-.43544258409328946089,1.8051608702905533790 ] 
dist 156=[-.7849240188488017747 ,1.7968163388367526686 ] 
dist 157=[-1.1521737320069430681 ,1.7928856685753050352 ] 
dist 158=[-1.3888275270085705035 ,-.43913610143404517371] 
dist 159=[-1.5750927292253160539 ,-.56526246901969836212] 
dist 160=[-1.7412418647373721103 ,-.84387586374977015662] 
dist 161=[-1.8874204932426329487 ,-.89200358310973997045] 
dist 162=[-1.9766770388300702410 ,-1.1981446932340806000 ] 
dist 163=[-2.0408623516514527126 ,-1.2464638983671504122 ] 
dist 164=[-2.0876029741182550521 ,-1.2432446230599532781 ] 
dist 165=[-2.1233329173930153771 ,-1.1935641324486684159 ] 
dist 166=[-2.1435750927751017711 ,-1.1305700954053407254 ] 
dist 167=[-2.1563534628073840613 ,-1.0632878850112977013 ] 
dist 168=[-2.1622954391363201966 ,-.98001171372623765508] 
dist 169=[-2.1634007553158814250 ,-.85318843252954600236] 
dist 170=[-2.1568768026696168085 ,-.70814875875512563221] 
dist 171=[-2.1441376708115124990 ,-.55217493873915789376] 
dist 172=[-2.1362258862715784886 ,-.35838396744786859735] 
dist 173=[-1.9442881810573596186 ,-.06242515634816408573] 
dist 174=[-1.3892191330515565511 ,.23440991690803613108] 
dist 175=[-1.3349898334767913252 ,.43169782341018282473] 
dist 176=[-1.1966845256493937757 ,.59375687255165380081] 
dist 177=[-1.1745578611234819835 ,.75000201582071863643] 
dist 178=[-.94687127818937014489,.8904589464432463585 ] 
dist 179=[-.90213960614359987315,.9895105690445648486 ] 
dist 180=[-.84916299412951224593,1.0771521957350541495 ] 
dist 181=[-.83338357613858941224,1.1720732498148285499 ] 
dist 182=[-.40409733712899953052,1.2581189001192924892 ] 
dist 183=[-.34969637306238371461,1.3103413840104184499 ] 
dist 184=[-.23449716739074578572,1.3477592496079561695 ] 
dist 185=[-.20465149516041439197,1.3747259216685169952 ] 
dist 186=[-.08753129380906943070,1.3928935415428954516 ] 
dist 187=[-.06520116742498474581,1.3964220112365667846 ] 
dist 188=[-.02042945743695254680,1.3922265271524220652 ] 
dist 189=[-.00925668550290878090,1.3893352040736976552 ] 
dist 190=[.06156428229221775573,.9195610114773315590 ] 
dist 191=[.03705008606047079779,.8598839825986047539 ] 
dist 192=[.01066228783960325900,.8448141081531833210 ] 
dist 193=[-.0251486498902497255 ,.75098776900978681336] 
dist 194=[-.0642440265753206778 ,.73139323126069549336] 
dist 195=[-.1037409449517690515 ,.69452702659109433752] 
dist 196=[-.1510746474798677194 ,.68441944352402507937] 
dist 197=[-.2214463140558217215 ,.51126934683170488976] 
dist 198=[-.2939927547305450703 ,.48712386017376270073] 
dist 199=[-.3500066784518336254 ,.42650006728140910537] 
dist 200=[-.4046139266840469552 ,.41717937719476144877] 
dist 201=[-.4715486970073942125 ,.3319130366215998912 ] 
dist 202=[-.5412563280709175047 ,.3945434829794997115 ] 
dist 203=[-.6069310473230949098 ,.45762250089657487965] 
dist 204=[-.6822113698645587365 ,.53308449881614495377] 
dist 205=[-.8013609199335197795 ,.64513051509382335178] 
dist 206=[-.9151454437566768025 ,.75593466984129008915] 
dist 207=[-1.0059638403223913205 ,.82644004372920289485] 
dist 208=[-1.0891595020881765137 ,.88089086972749533772] 
dist 209=[-1.1646030973339196854 ,.92762518136916243617] 
dist 210=[-1.2151522513786745308 ,.96578678259364347052] 
dist 211=[-1.2559648233922057331 ,.98602552880938606777] 
dist 212=[-1.2941563336572648628 ,.99699377814505739321] 
dist 213=[-1.3250686594702035474 ,.99853148761060892716] 
dist 214=[-1.3368304201733480093 ,.99481921292703562556] 
dist 215=[-1.3403550736276003113 ,.9910304719222444309 ] 
dist 216=[-1.3383909071085767912 ,.97952469596564490909] 
dist 217=[-1.3013900389827897680 ,.97342643461771496952] 
dist 218=[-1.2890849904595542335 ,.93639599170039592488] 
dist 219=[-1.2771601880082564698 ,.92639925647738636204] 
dist 220=[-1.2691512105374099699 ,.9038863799776751324 ] 
dist 221=[-.89166705873166376636,.8955837973117714595 ] 
dist 222=[-.3063276091763320124 ,.8424665464793604413 ] 
dist 223=[-.2518362947633892435 ,.9103006727455031269 ] 
dist 224=[-.1363983690297129484 ,.9695299286097487760 ] 
dist 225=[-.1075126991347510187 ,1.0186728107336990146 ] 
dist 226=[.0086749549263979718 ,1.0694744907206800220 ] 
dist 227=[.0304847682161268852 ,1.1566234424588172587 ] 
dist 228=[.0727513852375656960 ,1.2529920232855174068 ] 
dist 229=[.0827082479380996520 ,1.3400482225776599261 ] 
dist 230=[.1105447282094791347 ,1.3900331127128753958 ] 
dist 231=[.10829374636061070474,1.4224158133739912490 ] 
dist 232=[.09368357760034855486,1.4392247927695235246 ] 
dist 233=[.05839491917689468086,1.4479329651554304382 ] 
dist 234=[.01253309576019530222,1.4479866029013011752 ] 
dist 235=[-.04427210824147976978,1.4425103653652382964 ] 
dist 236=[-.11995039667767776392,1.4379358030615188546 ] 
dist 237=[-.24113009667522437334,1.0912045351890479124 ] 
dist 238=[-.36454363996618680251,1.0336667500957021412 ] 
dist 239=[-.45808110408696682894,.93220168491575650781] 
dist 240=[-.5770194150539958340 ,.91602643781279661662] 
dist 241=[-.6840980816116432778 ,.74667014085458737757] 
dist 242=[-.7598998157134529480 ,.71321289954822863679] 
dist 243=[-.8272756786139596330 ,.67425240912456902015] 
dist 244=[-.9007277712672409566 ,.66277887605312407851] 
dist 245=[-.9673488999729129936 ,.33547269525743311272] 
dist 246=[-1.0074638990197793232 ,.29392633685518352566] 
dist 247=[-1.0358262570694208784 ,.20651295565636075416] 
dist 248=[-1.0555459918303305184 ,.18329534652361942788] 
dist 249=[-1.0682513833197090152 ,.09588809734872147203] 
dist 250=[-1.0708097852049599913 ,.07883432833557311638] 
dist 251=[-1.0655567052042104660 ,.04558471871217173133] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 2, 0, 1, 0, 2] 
dist 0=[54.137742290420620235  ,54.137742290420620235  ] 
dist 1=[53.810172063541645812  ,54.269645180131353786  ] 
dist 2=[53.187712290469869355  ,54.468668122795548082  ] 
dist 3=[52.118554821825110779  ,54.625694435598880208  ] 
dist 4=[50.790054113828719628  ,54.698251166392231527  ] 
dist 5=[49.131853957962524010  ,54.722271164385495207  ] 
dist 6=[46.910637108766065768  ,54.685280264991912881  ] 
dist 7=[43.333725401900322279  ,54.622134201111255017  ] 
dist 8=[39.668431257635602856  ,54.541754815297769478  ] 
dist 9=[37.094197088969366945  ,54.432551484213258577  ] 
dist 10=[34.820390959608523807  ,54.325747679133025365  ] 
dist 11=[32.354673051460026814  ,54.045736907580828234  ] 
dist 12=[29.946764027085042837  ,53.902364871339228079  ] 
dist 13=[27.903614669017342806  ,53.565663675216895082  ] 
dist 14=[25.691209802366553298  ,52.811812684314739785  ] 
dist 15=[22.680905767884218460  ,38.249879813988646188  ] 
dist 16=[19.791407070785850068  ,36.907725750592049492  ] 
dist 17=[17.420097537591943870  ,33.638564446614452622  ] 
dist 18=[14.967700837451564113  ,33.154696255280267884  ] 
dist 19=[11.753867450596504442  ,28.317797696225007845  ] 
dist 20=[8.5993524962776385132 ,27.413132141629625061  ] 
dist 21=[6.3835761808002823371 ,26.354963599056275502  ] 
dist 22=[4.4235807239850613393 ,26.128253148207055431  ] 
dist 23=[2.2902407584073253963 ,18.255995699069302235  ] 
dist 24=[.19787037166694812645,17.280231259089699881  ] 
dist 25=[-1.5990281564546650348 ,15.279972477199537331  ] 
dist 26=[-3.5326992004545144658 ,14.765123114604279021  ] 
dist 27=[-6.1725227179854045627 ,12.917227643958007475  ] 
dist 28=[-8.7259624796411473163 ,12.544486345770777529  ] 
dist 29=[-10.314730674053967141  ,11.951549859099720863  ] 
dist 30=[-11.510731375329883661  ,11.807482240489657325  ] 
dist 31=[-12.494611756774782148  ,.78924240824018981564] 
dist 32=[-13.285852972406090355  ,-.13597314469860976786] 
dist 33=[-13.711790096001552037  ,-2.1186222881438868346 ] 
dist 34=[-13.955040874954243148  ,-2.5084107559476403714 ] 
dist 35=[-14.015496542085795081  ,-4.5441002945137600900 ] 
dist 36=[-13.661907903383046900  ,-4.8781778718382245989 ] 
dist 37=[-13.576628150361169070  ,-5.5561990521794964131 ] 
dist 38=[-13.504984678354035280  ,-5.6801675266107194023 ] 
dist 39=[-13.436639680111281738  ,-5.2731272699673932503 ] 
dist 40=[-13.377957228216312819  ,-4.1085856504367014039 ] 
dist 41=[-13.615872285561756776  ,-3.3020189210659938812 ] 
dist 42=[-13.967701601886534303  ,-2.6049806096324203421 ] 
dist 43=[-14.220986795270957968  ,-1.8771183021408830753 ] 
dist 44=[-14.302598575275120965  ,-1.1864954816882745162 ] 
dist 45=[-14.316629623197424917  ,-.63786386811336830683] 
dist 46=[-14.299794929224824028  ,-.08867090122885295908] 
dist 47=[-1.5227115130546093483 ,.60439248885120124116] 
dist 48=[-.22794502336289819627,1.2684070024077548321 ] 
dist 49=[.62690118121567147854,2.2017564396863758403 ] 
dist 50=[1.0998207445594513661 ,3.1277905237902598654 ] 
dist 51=[1.1809067493831660426 ,4.2688408905693463508 ] 
dist 52=[1.6981008074523840896 ,5.3495211929167128552 ] 
dist 53=[1.7786498282341897706 ,6.0345897165369848685 ] 
dist 54=[1.9369054891689850753 ,6.5611683056812708862 ] 
dist 55=[1.9632246303771085673 ,7.0092119354121422364 ] 
dist 56=[3.2513385166007907459 ,7.3724291859095371580 ] 
dist 57=[3.2860216252395379594 ,7.5603924218926027690 ] 
dist 58=[3.3164380902089108695 ,7.6605933000874802617 ] 
dist 59=[3.2809448094520586493 ,7.6784888468689416583 ] 
dist 60=[3.0994849839553763959 ,7.1078799113101902764 ] 
dist 61=[2.5520375511469197368 ,7.1483772700593583047 ] 
dist 62=[1.4507112727637552579 ,7.1429278177585834654 ] 
dist 63=[.33193379727127921766,4.8627504636795091119 ] 
dist 64=[-.42354684067055966683,4.6789422819869616629 ] 
dist 65=[-1.0563103145975621849 ,4.2160134888566673275 ] 
dist 66=[-1.6855321089314192939 ,4.1346806415800765290 ] 
dist 67=[-2.2630442545406037512 ,3.3911055063726825182 ] 
dist 68=[-2.6895173767346363733 ,3.2454429454566392535 ] 
dist 69=[-3.0863144723295594976 ,3.0480771880878605317 ] 
dist 70=[-3.5454270152129826022 ,2.9838283740898547566 ] 
dist 71=[-3.9704624143109147398 ,2.0084287409500111070 ] 
dist 72=[-4.2313029004451556081 ,1.5092183460722718555 ] 
dist 73=[-4.4213444205182795898 ,1.1348247301211133431 ] 
dist 74=[-4.5639184306117218701 ,1.0567400979074225214 ] 
dist 75=[-4.6673089503553088493 ,.61272931356897635664] 
dist 76=[-4.7010265563867618998 ,.53514656644870292561] 
dist 77=[-4.7067057303363562936 ,.37341273137456290694] 
dist 78=[-4.6982460819863011571 ,.3337305212674397964 ] 
dist 79=[-3.7197652588261492347 ,-.32651545616906191646] 
dist 80=[-3.9846152921607709185 ,-.26205871028709297101] 
dist 81=[-4.1763925797335093029 ,-.17904680627977368102] 
dist 82=[-4.3188210639188142493 ,-.06688398449553729703] 
dist 83=[-4.4241824925112475411 ,.11392472345160474033] 
dist 84=[-4.4679994912250944434 ,.30554578559743496257] 
dist 85=[-4.4812844528536097388 ,.46088467592383384245] 
dist 86=[-4.4745684367488759946 ,.61914336786529153198] 
dist 87=[-4.1798681482508835532 ,.82247728979808046184] 
dist 88=[-4.1228792246699823058 ,1.0390123196457353133 ] 
dist 89=[-4.0085760634679755759 ,1.2499889912274279403 ] 
dist 90=[-3.9709082261820999608 ,1.4972173642603186493 ] 
dist 91=[-3.7968029027064987110 ,1.8584683866316920948 ] 
dist 92=[-3.7546477844369073235 ,2.2127049379951660801 ] 
dist 93=[-3.6297746456341455912 ,2.4319545482214018302 ] 
dist 94=[-3.5999998038841231516 ,2.5943038004909127622 ] 
dist 95=[-1.2093995418368224725 ,2.9743871642103347665 ] 
dist 96=[-.98738107914839171372,3.3571155619121691072 ] 
dist 97=[-.50553600877302409246,3.6339180362632913554 ] 
dist 98=[-.45474901250902728379,3.8860159466162190412 ] 
dist 99=[-.15410491210220365147,4.1701594089688098490 ] 
dist 100=[-.10056735956957639419,4.4258002770249298041 ] 
dist 101=[-.02678336146518413171,4.5641533873331069716 ] 
dist 102=[-.00771550122115119720,4.6430287433845998669 ] 
dist 103=[.35573037013489348069,4.6613099214545714347 ] 
dist 104=[.3995379982230111250 ,4.6577545251802572978 ] 
dist 105=[.3565087656233472514 ,4.6494843412212025214 ] 
dist 106=[.1643177348575596279 ,4.6361841595308247987 ] 
dist 107=[-.0318966943106454768 ,4.6156965880561474999 ] 
dist 108=[-.2154539798950285699 ,3.8773908115059204356 ] 
dist 109=[-.43274882126106192899,3.7765510607363242012 ] 
dist 110=[-.7525528177137974289 ,3.4656609993010662769 ] 
dist 111=[-1.0758624132700740412 ,.70865465262532479719] 
dist 112=[-1.3763722513175126252 ,.69493175097959499271] 
dist 113=[-1.6051970071249262181 ,.66020923682682823476] 
dist 114=[-1.8251594125291966731 ,.65193034237079747842] 
dist 115=[-2.0903049785856599891 ,.5950989616993284556 ] 
dist 116=[-2.3380432744860173420 ,.5910717436170994773 ] 
dist 117=[-2.4885430565700743008 ,.5778303080434671177 ] 
dist 118=[-2.5965140981581363234 ,.5750183971878238014 ] 
dist 119=[-2.6745438541045521616 ,.54087956984960867907] 
dist 120=[-2.7308940378142671914 ,.53404142277897779752] 
dist 121=[-2.7523563819574441028 ,.51783223816183437588] 
dist 122=[-2.7565606063810786992 ,.51230505375564141176] 
dist 123=[-2.7506894151544326722 ,.48560152968357355123] 
dist 124=[-.99235160205583030403,.4794457969205093248 ] 
dist 125=[-.98770946580438321368,.46601499729983931134] 
dist 126=[-.98298274350177130986,.46161630561563573234] 
dist 127=[-.97797172915225819775,.40126184350124856476] 
dist 128=[-.81358817708995002892,.39152209128660473543] 
dist 129=[-.78946776864611031425,.36987565222317780523] 
dist 130=[-.7426892662680694208 ,.36313268154164996788] 
dist 131=[-.72976666095483855619,.33273262802373131972] 
dist 132=[-.68066604843587553116,.32614038544302333976] 
dist 133=[-.67733913718468428661,.31036814270374697456] 
dist 134=[-.68917373796087087513,.30536536973504097085] 
dist 135=[-.69752066781823796167,.25269482914614896659] 
dist 136=[-.70256048774399783562,.26083573845154499668] 
dist 137=[-.70619497899311445195,.3687087251928586964 ] 
dist 138=[-.70892185228752669753,.4582095413170437382 ] 
dist 139=[-.71090374664545541282,.55989001505638027183] 
dist 140=[-.71155955227670929234,.66023381053230803026] 
dist 141=[-.7113919340081251173 ,.73620898302387976598] 
dist 142=[-.7100827323271617983 ,.808851384841891252  ] 
dist 143=[-.28435128974479462328,.89589723394463894896] 
dist 144=[-.24951894536667176959,.97702408704900387438] 
dist 145=[-.16717131479217745407,1.0260463808369831841 ] 
dist 146=[-.15439514756200733751,1.0609233137020286649 ] 
dist 147=[-.04293199517508146417,1.0856006024556092542 ] 
dist 148=[-.02314623989061828150,1.1024000875942533073 ] 
dist 149=[-.01847876824466426650,1.1058850656146988939 ] 
dist 150=[-.07777986362900198842,1.1044459795678678330 ] 
dist 151=[-.17148222093251448228,1.1019692233581788226 ] 
dist 152=[-.30790127326418891149,.39301968302273793426] 
dist 153=[-.40931946436976234365,.41248292009022660896] 
dist 154=[-.49151812562756008806,.42655741772596204028] 
dist 155=[-.59169011505850967978,.43702311045046052358] 
dist 156=[-.68036804069925161348,.4420787591157634972 ] 
dist 157=[-.74035782102324540571,.44414773366955028934] 
dist 158=[-.7907768261769894134 ,.44390774899260021876] 
dist 159=[-.84126306121790821643,.4061019363720110669 ] 
dist 160=[-.88591980410609260057,.4003775383177402605 ] 
dist 161=[-.91307679855879053168,.3843064105445910533 ] 
dist 162=[-.93259534659153309117,.3808256903690429604 ] 
dist 163=[-.94677209912461064196,.3804257284922777975 ] 
dist 164=[-.95641892968995671689,.3805900712825177896 ] 
dist 165=[-.95786170891247071817,.37939128018078199236] 
dist 166=[-.9552154417499245994 ,.37832184215235893404] 
dist 167=[-.95170525330284451651,.37051077359906615617] 
dist 168=[-.56664985001485346502,.36804950447507548758] 
dist 169=[-.54292845587892209804,.36140619252355523238] 
dist 170=[-.48265179422466110752,.35860178909643495179] 
dist 171=[-.47296933711529505123,.34318882209380425938] 
dist 172=[-.37465594781880540047,.36965948334419642559] 
dist 173=[-.35543465932637292998,.40620552703215026682] 
dist 174=[-.35268284650505741045,.43715333162857836456] 
dist 175=[-.4147457596452351825 ,.46850768298756856119] 
dist 176=[-.4649811635350565106 ,.49650252669296734456] 
dist 177=[-.5032428402257920219 ,.5140450842997866706 ] 
dist 178=[-.5351762137957263813 ,.5272709574616529854 ] 
dist 179=[-.5609355736048139248 ,.5380427509993775748 ] 
dist 180=[-.5745545223441870263 ,.55318411043860724441] 
dist 181=[-.5818913340165580501 ,.56077613284775752424] 
dist 182=[-.5834734018941155124 ,.56379957028196648988] 
dist 183=[-.56844681264480195485,.56366396756211024664] 
dist 184=[-.5671225758316882959 ,.24608643668103928732] 
dist 185=[-.5711760667648852696 ,.2672718307460202007 ] 
dist 186=[-.5732553771664656286 ,.28496430841786409505] 
dist 187=[-.5739102102057190032 ,.30251369426769157538] 
dist 188=[-.5725091664431106433 ,.31862895624200772189] 
dist 189=[-.5691532376397267913 ,.3305987842901909901 ] 
dist 190=[-.5669656499995226383 ,.34182825511063869346] 
dist 191=[-.3369903211766051388 ,.3549905195729586863 ] 
dist 192=[-.3275653881310156525 ,.3671321068936937245 ] 
dist 193=[-.3023518237707690762 ,.3742886575692270934 ] 
dist 194=[-.29871312756310867823,.3791723838355926987 ] 
dist 195=[-.25324931108759376735,.3822431466453694886 ] 
dist 196=[-.24406428943643870696,.3839279514230551190 ] 
dist 197=[-.23512533296757441496,.3835012823131138825 ] 
dist 198=[-.2333816906434565868 ,.3815075288026682129 ] 
dist 199=[-.13285351611532369832,.3798953817879516461 ] 
dist 200=[-.12017714594523873211,.3690204401849951598 ] 
dist 201=[-.09494156567397272479,.3657169586704619940 ] 
dist 202=[-.08849362127707447992,.3591860584474890111 ] 
dist 203=[-.06609011598106793134,.3568211699834820404 ] 
dist 204=[-.06109223946763400627,.3563391037623136206 ] 
dist 205=[-.05534863912068153465,.3572737418357417866 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 0, 2, 0, 0, 1] 
dist 0=[55.013758157961048325  ,55.013758157961048325  ] 
dist 1=[53.962986766024775277  ,55.504973704374834127  ] 
dist 2=[52.640731873877289155  ,55.758875859751796460  ] 
dist 3=[51.065373980074951084  ,55.861859186268593961  ] 
dist 4=[48.999291488197106917  ,55.867724492237202336  ] 
dist 5=[45.717197087842903619  ,55.550012902672231349  ] 
dist 6=[42.358745213322856274  ,55.398162335042275761  ] 
dist 7=[39.987641022564862430  ,55.127363933710245402  ] 
dist 8=[37.880227090584951339  ,55.009605521580517191  ] 
dist 9=[35.574687454489145834  ,54.365979627434760838  ] 
dist 10=[33.311113080185070020  ,54.183377853330004163  ] 
dist 11=[31.371117782840857828  ,53.557555876872436280  ] 
dist 12=[29.291119085358333560  ,53.411860598192521892  ] 
dist 13=[26.468068327649929701  ,51.752089807516310794  ] 
dist 14=[23.651898494508649655  ,51.336915641278036753  ] 
dist 15=[21.599187079180717815  ,49.073427804988905442  ] 
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dist 166=[-.41133866924065700183,-.05425878639376796067] 
dist 167=[-.36576902714043430275,-.06580263586086835528] 
dist 168=[-.33762119235671032501,-.06838057664065810898] 
dist 169=[-.34533923705954959895,.00331725092275822369] 
dist 170=[-.34894346890402101305,.08550205915193246402] 
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dist 176=[-.13528940407840478924,.43012381002755445998] 
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dist 178=[-.1108418908084107602 ,.48401379704853325547] 
dist 179=[-.10331276640054129079,.49720225994066992797] 
dist 180=[-.10137633356872743216,.50476539464049453032] 
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dist 182=[-.06896042105272399450,.43206281802367208048] 
dist 183=[-.05988363025947890887,.4249841789324568356 ] 
dist 184=[-.05794426296659762877,.40593470877675725925] 
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dist 187=[-.04008018351018001219,.35639856545402029201] 
dist 188=[-.03901473792596794100,.3442445676363991695 ] 
dist 189=[-.05069309412067388665,.34027725904171957512] 
dist 190=[-.06418172986975681069,.25077531139300590988] 
dist 191=[-.07514208808809626153,.23846245293147877969] 
dist 192=[-.08547320125044468303,.21329049549673079718] 
dist 193=[-.09456827728682676528,.20879999518031484938] 
dist 194=[-.10059699004649367644,.17523994048604362794] 
dist 195=[-.10550825852212587042,.17574820004104679564] 
dist 196=[-.11694879597986703601,.1774594797508458501 ] 
dist 197=[-.19344277493849403056,.17827661403802062107] 
dist 198=[-.26914806327360151164,.17809752841362456625] 
dist 199=[-.31901805766675440587,.17706856613710548019] 
dist 200=[-.35949725273527794113,.17625591054815032344] 
dist 201=[-.39772535922387330935,.1707289569313137759 ] 
dist 202=[-.43398193463471071518,.16914607655209809597] 
dist 203=[-.46070744438151654812,.16568054233348591336] 
dist 204=[-.48460823083273324171,.1643881297264854833 ] 
dist 205=[-.51088897605044937253,.00288025064392230454] 
dist 206=[-.53417416884687540508,.01455704963399014905] 
dist 207=[-.54612011933957977655,.02689181192227860972] 
dist 208=[-.55231167384851717891,.04206391310180120697] 
dist 209=[-.55334570619508928882,.06506453107397513460] 
dist 210=[-.54835332891368383598,.09132439310111298650] 
dist 211=[-.54563117031259784402,.11950375158280117759] 
dist 212=[-.54253860474652376621,.15447517896226303661] 
dist 213=[-.53993241446888278755,.22845810224341728094] 
dist 214=[-.26077988349263951439,.30462165244090495678] 
dist 215=[-.27326434045015456918,.35336107150829322268] 
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dist 217=[-.300670774123804726  ,.42444648573069989361] 
dist 218=[-.31232728311548061679,.45191427413993876949] 
dist 219=[-.32479370839394739502,.46727509196020907088] 
dist 220=[-.34162636611464009195,.49395022918010926685] 
dist 221=[-.35762657821377158685,.52647450772466967207] 
dist 222=[-.36677078863487289453,.55536771899974778946] 
dist 223=[-.37264551550967314095,.57211206998890707162] 
dist 224=[-.375596595026245341  ,.58315809436828888316] 
dist 225=[-.37655988648590077221,.58930981939021305878] 
dist 226=[-.3762253254589546642 ,.5921443466355897176 ] 
dist 227=[-.37193254268885246424,.59196976832808751714] 
dist 228=[-.37085903597384367708,.58655234458259743548] 
dist 229=[-.3454612356350006227 ,.58456554416165357944] 
dist 230=[-.34069712638279250604,.38398636115875561344] 
dist 231=[-.327271621389135144  ,.36887573050386847128] 
dist 232=[-.32418597022344538275,.33059731441151363557] 
dist 233=[-.29618066740869600514,.32428138072858572889] 
dist 234=[-.2899217776575107974 ,.26195758979603528551] 
dist 235=[-.28645800384906645834,.24971774563692483363] 
dist 236=[-.31028561564609800985,.23458791430292755966] 
dist 237=[-.33565173863561510881,.22962400102187983947] 
dist 238=[-.35854736373993696694,.11454676645807336102] 
dist 239=[-.37251586858838578693,.09983874094014907206] 
dist 240=[-.38261298142386484242,.06827135801009125130] 
dist 241=[-.39005917115847872043,.06045855754259514832] 
dist 242=[-.39522675199400402295,.02676701454094512060] 
dist 243=[-.39623071667675167639,.02059556726326647335] 
dist 244=[-.39555587789307452343,.00711387565711421700] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 1, 0, 2, 0, 2] 
dist 0=[60.030483165296089043  ,60.030483165296089043  ] 
dist 1=[59.550408211880719816  ,60.184227980915290255  ] 
dist 2=[58.738598365745980651  ,60.199503367912671428  ] 
dist 3=[57.260295324320301505  ,60.126594582416023845  ] 
dist 4=[55.596106920559916358  ,59.974475973903667407  ] 
dist 5=[54.041981583679971720  ,59.870890686800445289  ] 
dist 6=[52.268056387744135799  ,59.389320287179245282  ] 
dist 7=[49.725922849846401660  ,59.119848510246929230  ] 
dist 8=[46.878109563026700772  ,57.008466040117332582  ] 
dist 9=[43.883352398105869790  ,54.305100840109479832  ] 
dist 10=[40.200777857786681455  ,53.431139387012727009  ] 
dist 11=[34.606036337034731064  ,53.129798873857718376  ] 
dist 12=[28.978868432624331683  ,52.893859014203210247  ] 
dist 13=[25.166676041979183755  ,52.212838025636374946  ] 
dist 14=[21.945459896236425795  ,44.322021848710221407  ] 
dist 15=[18.678116754125333336  ,43.502556609505187004  ] 
dist 16=[15.621354313105251921  ,43.282132490550553180  ] 
dist 17=[13.240827053027754212  ,34.943376119735433752  ] 
dist 18=[10.892908043360554241  ,33.859545966041447579  ] 
dist 19=[7.9658169048522711914 ,31.710890991282835323  ] 
dist 20=[5.1615003662249941675 ,31.152821010193883143  ] 
dist 21=[3.3036097667114106562 ,29.161957558091895368  ] 
dist 22=[1.7760928604137990170 ,28.713609361461698510  ] 
dist 23=[.29086321967513071344,28.042319922280943020  ] 
dist 24=[-1.0631309329613791595 ,27.844591982666397965  ] 
dist 25=[-2.0670814659746627147 ,9.4565981630485406061 ] 
dist 26=[-3.0145663273095630707 ,7.9167223039185588541 ] 
dist 27=[-4.1443627559182907917 ,4.4653940425496381545 ] 
dist 28=[-5.1914263709591754523 ,3.8649469218441486546 ] 
dist 29=[-5.8085760690818281968 ,2.3468612759881177456 ] 
dist 30=[-7.5298460298346725728 ,-.90816879967290638024] 
dist 31=[-9.2958426125987530161 ,-2.1496448997301046682 ] 
dist 32=[-11.380096365759870350  ,-2.4061730687608924491 ] 
dist 33=[-13.317808517004552992  ,-5.4617373308536356046 ] 
dist 34=[-14.498492960252585282  ,-5.8851593243426904561 ] 
dist 35=[-15.354194580059574623  ,-6.3475844479491255925 ] 
dist 36=[-15.993872440966861149  ,-6.0054326656841540109 ] 
dist 37=[-16.481165075346289092  ,-5.6747273846423052115 ] 
dist 38=[-16.728247325072648226  ,-5.2913927104234882681 ] 
dist 39=[-16.847758206995342116  ,-4.7385489815712779400 ] 
dist 40=[-16.848174132307320821  ,-3.9677441065622179068 ] 
dist 41=[-8.1096205129964019705 ,-2.6793975654600863496 ] 
dist 42=[-8.0089237125785329370 ,-1.7839825515136862262 ] 
dist 43=[-7.9575728670064748236 ,-1.0075818700191420098 ] 
dist 44=[-7.9071580309498045374 ,-.19356208907496108739] 
dist 45=[-7.8711635162843835678 ,.58024345015413021573] 
dist 46=[-3.0323563455189437287 ,1.1964680432346683627 ] 
dist 47=[-2.6294643715299449261 ,1.8622106285464627819 ] 
dist 48=[-1.6973010056141267488 ,2.5956242299872508057 ] 
dist 49=[-1.5439892537042058641 ,3.3444193822243981585 ] 
dist 50=[-.3479287095021933500 ,3.8334084074001666352 ] 
dist 51=[-.1393226433407562748 ,4.2258385607459014060 ] 
dist 52=[.1885274029246237104 ,4.6558193902984224970 ] 
dist 53=[.2667008701304952211 ,5.0015758559871215224 ] 
dist 54=[1.4649758851561748556 ,5.2561566696560544136 ] 
dist 55=[1.6173237747989637689 ,5.4518797071583811116 ] 
dist 56=[1.9028793142218385493 ,5.5983044471605527371 ] 
dist 57=[1.9639740097883111613 ,5.6562758253549409565 ] 
dist 58=[2.0891214099167012642 ,5.6741029834954066103 ] 
dist 59=[1.4077348447143290081 ,5.6612926583140549886 ] 
dist 60=[.7138401370976700304 ,4.1358973540471891404 ] 
dist 61=[.2479858135778601072 ,4.1812874011280811762 ] 
dist 62=[-.1396941922175581325 ,4.2020258369674422030 ] 
dist 63=[-.52170476532114171111,4.2096194479795989374 ] 
dist 64=[-.87067634159408097133,4.2025225189118551165 ] 
dist 65=[-1.1265637381097065540 ,4.1895277808010278014 ] 
dist 66=[-1.3633218065003974244 ,4.1735187771619239210 ] 
dist 67=[-1.6360353704804281608 ,4.1529049152798932834 ] 
dist 68=[-1.8881645063342064956 ,4.1378000258227297295 ] 
dist 69=[-2.0427804677194850168 ,4.0857646139987077625 ] 
dist 70=[-2.1557488311057587998 ,4.0645719647286090157 ] 
dist 71=[-2.2416067576023012490 ,4.0123469392661588751 ] 
dist 72=[-2.8488060879314626816 ,3.9899546800997285342 ] 
dist 73=[-3.8403789824341799717 ,.7473242500447187873 ] 
dist 74=[-4.4726323284826129821 ,.6943352950736835729 ] 
dist 75=[-4.9630531725784070965 ,.6821789677217028245 ] 
dist 76=[-5.3884993304524602435 ,.6739610434777761366 ] 
dist 77=[-5.7413486959929758607 ,.6759326149820999804 ] 
dist 78=[-5.9908648017838621237 ,.6798858774099288443 ] 
dist 79=[-6.1678534923511279455 ,.6814842086054439188 ] 
dist 80=[-6.2923991034461708505 ,.6810826105535513675 ] 
dist 81=[-6.3844689552034139606 ,.6800813860134852881 ] 
dist 82=[-6.4318311724577978683 ,.6715766141160966014 ] 
dist 83=[-6.4556740646064403773 ,.6681550350595172298 ] 
dist 84=[-6.4538488105518068340 ,.6579249553183142509 ] 
dist 85=[-6.4358376804852611134 ,.76571745193310240708] 
dist 86=[-6.4127970191151467404 ,.87929949268270692374] 
dist 87=[-6.3451423805568403526 ,.99266479701174726809] 
dist 88=[-6.3089858632572259336 ,1.0972919188960809049 ] 
dist 89=[-2.9465779646775923023 ,1.1760433365543631773 ] 
dist 90=[-2.6494543801816254665 ,1.2510826211030940328 ] 
dist 91=[-1.9377543535449888100 ,1.3409661635581244864 ] 
dist 92=[-1.8275838667427918896 ,1.4231982017978400527 ] 
dist 93=[-1.2528693266295075411 ,1.4677086586907300369 ] 
dist 94=[-.8658871492304659190 ,1.6685934090022157945 ] 
dist 95=[-.8257399232554821668 ,2.0642571568656811861 ] 
dist 96=[-.7325599207648122251 ,2.5305289520022959598 ] 
dist 97=[-.7131532680437137948 ,2.9669204381111011837 ] 
dist 98=[-.5865384688720219847 ,3.2433339814818041704 ] 
dist 99=[-.5625044525097288762 ,3.4555122815510912944 ] 
dist 100=[-.51834452992381457859,3.6355251163714457128 ] 
dist 101=[-.50751636352952120158,3.7811031450721338945 ] 
dist 102=[-.33992928950977021307,3.8558442668382102434 ] 
dist 103=[-.31681633321624426574,3.8930238658937749499 ] 
dist 104=[-.26389276314116772807,3.8989964962774369419 ] 
dist 105=[-.25348133779641843334,2.7943199410566963331 ] 
dist 106=[-.18505888809166818247,2.7047202202032092336 ] 
dist 107=[-.17252947803884743699,2.4805537825781733575 ] 
dist 108=[-.14957365719949281463,2.4372781415687433318 ] 
dist 109=[-.177412063403252004  ,2.0751076719134251085 ] 
dist 110=[-.32002032157877829967,2.0025503460557585877 ] 
dist 111=[-.4628554127660241858 ,1.8961572585563538799 ] 
dist 112=[-.5950547488952686593 ,1.8636593110705969418 ] 
dist 113=[-.6951952264668949199 ,1.1963149631385187111 ] 
dist 114=[-.7911009255404291812 ,1.1083156305743919793 ] 
dist 115=[-.9063810685246910531 ,.90900557622836468815] 
dist 116=[-1.0141513121476789287 ,.86632694932000185597] 
dist 117=[-1.0800692158962076333 ,.6155523764203678146 ] 
dist 118=[-1.1279509065990966053 ,.5697554085071141906 ] 
dist 119=[-1.2543978489584641373 ,.4778606509789216675 ] 
dist 120=[-1.6133951402944318995 ,.4542132814397811553 ] 
dist 121=[-1.9647393711401420329 ,.0505564970048565533 ] 
dist 122=[-2.1921165701144109947 ,-.0081714500955559178 ] 
dist 123=[-2.3722890148670154243 ,0                     ] 
dist 124=[-2.5725513340306886568 ,-.0387952521966649983 ] 
dist 125=[-2.7707788277740531059 ,-.0427975064513754127 ] 
dist 126=[-2.9084278964309068889 ,-.01091075749134607107] 
dist 127=[-3.0281063284150042009 ,.05324956626883488186] 
dist 128=[-3.1546158527188995571 ,.16678110970472676812] 
dist 129=[-3.2640889021296991436 ,.29118459868360818214] 
dist 130=[-3.3157720820195448040 ,.39874133750257380631] 
dist 131=[-3.3397283182563669678 ,.51448282893455672527] 
dist 132=[-3.3396240491668534051 ,.67156759041781853838] 
dist 133=[-3.2848361337807544162 ,.84313512192219118003] 
dist 134=[-3.2616397953924229007 ,1.0166864226716044761 ] 
dist 135=[-3.2393290423657751748 ,1.2248959233746807082 ] 
dist 136=[-3.2222620200982827067 ,1.5347951540113715230 ] 
dist 137=[-.59071634820995606098,1.9217491618582271857 ] 
dist 138=[-.59437492722969515993,2.2217076153750993845 ] 
dist 139=[-.59474157049621836556,2.4570836194076770992 ] 
dist 140=[-.5902437055327729956 ,2.6658020278372157344 ] 
dist 141=[-.58932880757094020664,2.8413698420276669377 ] 
dist 142=[-.55980504391693737518,2.9694546849038520806 ] 
dist 143=[-.55392698139746613507,3.1554817377053342961 ] 
dist 144=[-.53559130506703854887,3.3449065709749629510 ] 
dist 145=[-.53206075506143754955,3.5122397445171145127 ] 
dist 146=[-.48835244973041270127,3.6101003905195576369 ] 
dist 147=[-.47838210749552938044,3.6757904493601238869 ] 
dist 148=[-.46820523590151830387,3.7147320701294317278 ] 
dist 149=[-.463685017387604721  ,3.7334905457030702452 ] 
dist 150=[-.33350862198701866294,3.7336895287962180890 ] 
dist 151=[-.31579641155323561021,3.6971792959892422654 ] 
dist 152=[-.28034891809255280382,3.6896277702264383271 ] 
dist 153=[-.33915484482340026516,2.4525076582538214922 ] 
dist 154=[-.6830449997866980581 ,2.3612468468814264119 ] 
dist 155=[-.96717921161050362487,2.1263786587684892114 ] 
dist 156=[-1.2439148749155437376 ,2.0898722100047034700 ] 
dist 157=[-1.4945925392866649471 ,1.6966832761868143799 ] 
dist 158=[-1.6747305904659116125 ,1.6191501377724581885 ] 
dist 159=[-1.8376276379193123374 ,1.5315373277408156069 ] 
dist 160=[-2.0194949293321850181 ,1.5079610950022760913 ] 
dist 161=[-2.1854521533969801157 ,.74254921029174259145] 
dist 162=[-2.2848548205305123188 ,.64603294190342823997] 
dist 163=[-2.3544964017832296933 ,.44481373938324820842] 
dist 164=[-2.4016866551049029022 ,.39187258400471644557] 
dist 165=[-2.4328209546853791222 ,.3163811897005421575 ] 
dist 166=[-2.4383847096062105565 ,.2286252514576295664 ] 
dist 167=[-2.4385036903793513833 ,.2163025170814749388 ] 
dist 168=[-2.4372340076068225486 ,.1862469081462406244 ] 
dist 169=[-.54222070102057667713,.1811931314020781952 ] 
dist 170=[-.52859114749572190888,.1362679044748197120 ] 
dist 171=[-.4950452677912163759 ,.1277301070646126162 ] 
dist 172=[-.48700868289499780515,.1160963593401543882 ] 
dist 173=[-.43279815996107715124,.1124585402093631025 ] 
dist 174=[-.43406908091638099998,.0420261367812786999 ] 
dist 175=[-.49178255548094020599,.0322352976943265307 ] 
dist 176=[-.53777617853554390645,.0184858761158251172 ] 
dist 177=[-.5798000244573314413 ,.0145625932574355372 ] 
dist 178=[-.61605748354728670807,.0382645566625359286 ] 
dist 179=[-.63903742953924036054,.0622090332101157209 ] 
dist 180=[-.6566969520883380638 ,.0859395885844666330 ] 
dist 181=[-.67172152920377073898,.1155494917082123371 ] 
dist 182=[-.68322014498638285302,.1437154536625038087 ] 
dist 183=[-.68680665963944147365,.20636216079974083822] 
dist 184=[-.68695861358122726999,.30713295316164077341] 
dist 185=[-.684876634674475569  ,.40654750305493749375] 
dist 186=[-.6659849703043637151 ,.47170983345984800586] 
dist 187=[-.65985438848489718668,.52426757764858722987] 
dist 188=[-.65100946854446700749,.57337319089696000412] 
dist 189=[-.64714938252783502273,.61650776297047394811] 
dist 190=[.0177257502326880805 ,.64523322596577449692] 
dist 191=[.0088646222279319220 ,.66890912236998616652] 
dist 192=[-.01078677908038771394,.6918894401245085668 ] 
dist 193=[-.03369613554805491944,.71097925344085711869] 
dist 194=[-.05555984938457607635,.719127201162844902  ] 
dist 195=[-.08083056075937295244,.72231434638735931292] 
dist 196=[-.11733842297326456642,.72160301274328781017] 
dist 197=[-.15825467206134613471,.70555665695027405619] 
dist 198=[-.20111942016159890062,.69970391461856365148] 
dist 199=[-.25360512967694957466,.69412544478099890134] 
dist 200=[-.33291793433320846594,.69016727850437753175] 
dist 201=[-.41171098810185704369,.56265556773651350062] 
dist 202=[-.46212299061417145573,.54073920125420527987] 
dist 203=[-.5013812082095182548 ,.53450744718499506479] 
dist 204=[-.53566203470213177063,.52952915652532350657] 
dist 205=[-.56410603343283159441,.52612968471953300781] 
dist 206=[-.5800710170707118021 ,.38565066847394553795] 
dist 207=[-.58994918815829205952,.36862118574779741991] 
dist 208=[-.59410276200690363666,.3287033045024688556 ] 
dist 209=[-.59546570656513716774,.31975594443832648217] 
dist 210=[-.59420640847619468432,.2632890255228536550 ] 
dist 211=[-.59109354749700289911,.2522299709054159456 ] 
dist 212=[-.58895390609247328201,.2314551301875329675 ] 
dist 213=[-.57471079157797333559,.2260881057781901832 ] 
dist 214=[-.57065559546774710758,.1434400439288560270 ] 
dist 215=[-.55680495711575747484,.1318898964562702834 ] 
dist 216=[-.55067412770207921571,.1048898142010152483 ] 
dist 217=[-.28540161895338858906,.0997230045091933929 ] 
dist 218=[-.25936566891959793   ,.0795772816901779270 ] 
dist 219=[-.2001222845276596548 ,.0793233915660973324 ] 
dist 220=[-.1832293551322028393 ,.0778877619114012529 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 1, 2, 0, 1] 
dist 0=[56.805532096633947630  ,56.805532096633947630  ] 
dist 1=[56.416529865281275529  ,57.118874906582296416  ] 
dist 2=[55.928984726873467485  ,57.304167382266845015  ] 
dist 3=[55.275080024480975950  ,57.430763411816456228  ] 
dist 4=[54.221520319255571224  ,57.509580445642807100  ] 
dist 5=[52.901842443388228046  ,57.541955865607334285  ] 
dist 6=[51.185176350948021833  ,57.483170701206840884  ] 
dist 7=[48.845059653819992327  ,57.345680543398092143  ] 
dist 8=[45.035771948027100883  ,57.249755460433737104  ] 
dist 9=[41.129637872454072904  ,56.711020191742313960  ] 
dist 10=[38.402727595023593554  ,56.544616698847312274  ] 
dist 11=[36.011684071870178893  ,55.920332919402756206  ] 
dist 12=[33.446578977326915080  ,55.786889122946010443  ] 
dist 13=[28.524946980875041616  ,41.427648176508913799  ] 
dist 14=[24.673974624519510814  ,40.083647659524469350  ] 
dist 15=[21.389331308644884146  ,36.763633947396747037  ] 
dist 16=[18.009955825449600418  ,36.287552404201826943  ] 
dist 17=[14.819663357695639962  ,31.222986923837781649  ] 
dist 18=[12.289730907768819865  ,30.266312823943253371  ] 
dist 19=[9.7526250845508738869 ,29.216864682763461876  ] 
dist 20=[6.5330551509273709355 ,29.031060991402149971  ] 
dist 21=[3.4226291631755612266 ,20.256729976134061800  ] 
dist 22=[1.3210280439925493210 ,19.173518360503648330  ] 
dist 23=[-.4513146665534739336 ,16.996242220258633877  ] 
dist 24=[-2.2472933779689778294 ,16.444496666792537980  ] 
dist 25=[-3.9314430783829914913 ,14.530226976994304537  ] 
dist 26=[-5.2578489326980191693 ,14.123267223042994134  ] 
dist 27=[-6.5849105882740341756 ,13.640475627572760491  ] 
dist 28=[-8.2731772242601554766 ,13.555871473245951457  ] 
dist 29=[-9.8694637256673409387 ,-.0116070061135685530 ] 
dist 30=[-10.829279820874803982  ,-1.1048538993898009034 ] 
dist 31=[-11.515869683843893619  ,-3.3114449231455553411 ] 
dist 32=[-12.019757911226134395  ,-3.3997558596848205301 ] 
dist 33=[-12.392787035398266019  ,-5.2934499888338268762 ] 
dist 34=[-12.555972027169439604  ,-5.5098610560249613565 ] 
dist 35=[-12.614211748120844368  ,-5.8118465101841010987 ] 
dist 36=[-12.602038468085884175  ,-5.8291588547920365150 ] 
dist 37=[-13.048793083990608208  ,-5.7442834836200666584 ] 
dist 38=[-13.904360777574271751  ,-5.5166224866413490821 ] 
dist 39=[-14.556996821637910537  ,-5.1431932600353764022 ] 
dist 40=[-15.106200249850472367  ,-4.4765248956935078992 ] 
dist 41=[-15.548621928305461218  ,-3.7786441153492320437 ] 
dist 42=[-15.774618446260367822  ,-3.2804808892124951236 ] 
dist 43=[-15.885636535996873169  ,-2.8350263842667578562 ] 
dist 44=[-15.893358805264010938  ,-.65762781870261650135] 
dist 45=[-3.7231296622301860237 ,1.6222019353081829821 ] 
dist 46=[-3.1331772199944499402 ,3.1535815135166523303 ] 
dist 47=[-1.8340055949798925456 ,4.4284409338351374190 ] 
dist 48=[-1.6612091961711865482 ,5.6848744307220471800 ] 
dist 49=[-.57427191821777709751,6.8321981764479321665 ] 
dist 50=[-.43849373328489801237,7.6717946353847007019 ] 
dist 51=[-.14507987148719701223,8.4464515741578625638 ] 
dist 52=[-.08963491653654292111,9.3348078823306436996 ] 
dist 53=[.2061367988717051274 ,10.143183735079623475  ] 
dist 54=[.25434646029171402144,10.598744404836677648  ] 
dist 55=[.33506980452197048261,10.883423509069113515  ] 
dist 56=[.349786692158296345  ,11.009921765707758649  ] 
dist 57=[1.5789073634652808088 ,11.068448496974315063  ] 
dist 58=[1.2451791097438930583 ,11.081752292106432819  ] 
dist 59=[.76181236806148228166,10.742000237589691737  ] 
dist 60=[-.0512429003452492644 ,9.9579827446121404460 ] 
dist 61=[-.88205876142104726896,4.6593060232654731907 ] 
dist 62=[-1.4363412899678854439 ,4.4243019095330694719 ] 
dist 63=[-1.8936348309233309382 ,3.8349589795175074666 ] 
dist 64=[-2.3375147444794979061 ,3.7445302065772602455 ] 
dist 65=[-2.7384152567234086588 ,3.1423017789384162818 ] 
dist 66=[-3.0242593924076970252 ,3.1138579038036638687 ] 
dist 67=[-3.2804906878561124113 ,3.0583177824052143758 ] 
dist 68=[-3.5633013585631779013 ,3.0389023608031188739 ] 
dist 69=[-3.8162140374639298420 ,2.9458011870175756944 ] 
dist 70=[-3.9531435558965022536 ,2.9218783042890994681 ] 
dist 71=[-4.0314402801963505147 ,2.8496015387688123701 ] 
dist 72=[-4.0503178055748233228 ,2.8307749187866239790 ] 
dist 73=[-4.0481936190794973830 ,1.3094964942378009960 ] 
dist 74=[-4.0426814428814648425 ,1.1693939970253796406 ] 
dist 75=[-4.0337850144830215929 ,.84206744395042029986] 
dist 76=[-4.0182134208483858237 ,.78618052466963861843] 
dist 77=[-3.6875779551290543785 ,.6907013209270122409 ] 
dist 78=[-3.7416465643657183628 ,1.2241124076502307189 ] 
dist 79=[-3.7648195645640914150 ,1.6592793006517038692 ] 
dist 80=[-3.7644055782769821647 ,2.0732992982258383507 ] 
dist 81=[-3.7055795459985018435 ,2.4413421367509874815 ] 
dist 82=[-3.6809009343546326999 ,2.6930683632992988761 ] 
dist 83=[-3.7762818291057340040 ,2.9074424448283461753 ] 
dist 84=[-3.8935680894580253311 ,3.1264514648021004094 ] 
dist 85=[-3.9933820935520198397 ,3.3228847850152363607 ] 
dist 86=[-4.0377707690250790545 ,3.4471809169832703598 ] 
dist 87=[-4.0546173032698036246 ,3.5422241513646398398 ] 
dist 88=[-4.0514813471890071744 ,3.6219347351236176094 ] 
dist 89=[-3.9822560961118913434 ,3.6854510998639489963 ] 
dist 90=[-3.9552184155415775758 ,3.7158698856335734940 ] 
dist 91=[-3.9096117884240469719 ,3.7277196975182838000 ] 
dist 92=[-3.8908911699594906906 ,3.7207209701416418217 ] 
dist 93=[-3.3409099076303702575 ,1.8421727041267613761 ] 
dist 94=[-3.2602257580767330875 ,2.1702683941065185886 ] 
dist 95=[-3.0609344993603964111 ,2.6153577197659292521 ] 
dist 96=[-3.0126524530787582360 ,3.0232763593574364923 ] 
dist 97=[-2.6839949959265264714 ,3.3761234362194663689 ] 
dist 98=[-2.6143927120970462766 ,3.6014402909317946490 ] 
dist 99=[-2.4918031648111613643 ,3.7765935437715018648 ] 
dist 100=[-2.4595731735908337717 ,3.9292746319526418063 ] 
dist 101=[-1.7890043270554153163 ,4.0576413122929538015 ] 
dist 102=[-1.6955106553277399104 ,4.1357529898647865327 ] 
dist 103=[-1.4750913748359068288 ,4.1921634378346897113 ] 
dist 104=[-1.4281581397776006612 ,4.2338755233566840419 ] 
dist 105=[-1.3546616951932341230 ,4.2630608600449622543 ] 
dist 106=[-1.5005366700447412422 ,4.2694519766484376914 ] 
dist 107=[-1.6446267712040887979 ,4.2604018450226016145 ] 
dist 108=[-1.8240499910594243763 ,4.2481206040657927746 ] 
dist 109=[-2.0288726776602200893 ,3.1039930506228590175 ] 
dist 110=[-2.2487678626142253888 ,3.3028288126186910271 ] 
dist 111=[-2.4226784482970687233 ,3.4432915391267766415 ] 
dist 112=[-2.5792854881243973478 ,3.5406073753802706556 ] 
dist 113=[-2.7128004261976704593 ,3.6113187472022367986 ] 
dist 114=[-2.7945598123535770473 ,3.6456210757751958372 ] 
dist 115=[-2.8541115172872618168 ,3.6597678354659994953 ] 
dist 116=[-2.8990133423426268678 ,3.6554356658603852720 ] 
dist 117=[-2.9287761719806416107 ,3.3003043133165666928 ] 
dist 118=[-2.9333531089174656956 ,3.2407477429482198499 ] 
dist 119=[-2.9178262356104624089 ,3.1391332722106732334 ] 
dist 120=[-2.9108012912928082664 ,3.1090932113550600343 ] 
dist 121=[-2.7802250817877336527 ,3.0041062733248270026 ] 
dist 122=[-2.7444932969102975081 ,2.9699704394190674985 ] 
dist 123=[-2.7133098592253171441 ,2.9164384388509633373 ] 
dist 124=[-2.6931416130786877737 ,2.8963684148196831135 ] 
dist 125=[-1.9206557062963617200 ,-1.2251033626085543079 ] 
dist 126=[-1.8302870283603902393 ,-1.2659745102350013801 ] 
dist 127=[-1.6009543812182345615 ,-1.3423612130596058180 ] 
dist 128=[-1.6539834200106534322 ,-1.2779151993648526285 ] 
dist 129=[-1.7515792044524876622 ,-1.1790635661439694894 ] 
dist 130=[-1.8070137860202478612 ,-1.0146523355789095502 ] 
dist 131=[-1.8421802061673788208 ,-.8375078763260242868 ] 
dist 132=[-1.8588831010299909977 ,-.5967749375772920794 ] 
dist 133=[-1.8659794217454814010 ,-.3578595339241995343 ] 
dist 134=[-1.8632288783565863627 ,-.1879587479471293957 ] 
dist 135=[-1.8539817082287801667 ,-.0361117902429634365 ] 
dist 136=[-1.8466319823863256050 ,.1307674617390485734 ] 
dist 137=[-1.3738362131021777526 ,.2945428110270866545 ] 
dist 138=[-1.3238366032691865084 ,.4340156684582730818 ] 
dist 139=[-1.1949663607243272779 ,.58243770238466040115] 
dist 140=[-1.1750660607750703144 ,.78195265222597622399] 
dist 141=[-.9586189538519955891 ,.97756737527407871194] 
dist 142=[-.91588338517251002705,1.1104265977774944814 ] 
dist 143=[-.86815413790337980623,1.2228260744092516665 ] 
dist 144=[-.8556124183535704087 ,1.3367713714233163063 ] 
dist 145=[-.43038731251365546129,1.4430612871445094550 ] 
dist 146=[-.37674884748269808386,1.5249029265625494766 ] 
dist 147=[-.26552078182168333765,1.6045560874101314048 ] 
dist 148=[-.2363469122598426633 ,1.7021109976753918215 ] 
dist 149=[-.12900984615636587853,1.7942651170165575508 ] 
dist 150=[-.10741712661534182289,1.8523596328407602660 ] 
dist 151=[-.06907734485730165224,1.8966624876117894480 ] 
dist 152=[-.06059787826236591627,1.9337628117069895302 ] 
dist 153=[-.02579334085553605530,1.9634183331888387081 ] 
dist 154=[-.1791117140896111035 ,1.9780029255986334329 ] 
dist 155=[-.47003230850412196404,1.9843490221074603622 ] 
dist 156=[-.90743270561694765892,1.9811181112715199566 ] 
dist 157=[-1.3422014049300745468 ,-.07398718486087954549] 
dist 158=[-1.6226213419775501833 ,-.05906524163944858656] 
dist 159=[-1.8436170251017317272 ,-.03207922521528794163] 
dist 160=[-2.0412255353865073720 ,.01841875802395944254] 
dist 161=[-2.2086227828587679765 ,.07475633978678109915] 
dist 162=[-2.3090467362062325590 ,.12504517180599651442] 
dist 163=[-2.3796252992191528159 ,.18051136076922761666] 
dist 164=[-2.4329052610704926809 ,.25750811635436868912] 
dist 165=[-2.4745049139378548822 ,.3424018915996374028 ] 
dist 166=[-2.4983117660159006689 ,.42938095518260587955] 
dist 167=[-2.5136504637554363423 ,.5344984142598678691 ] 
dist 168=[-2.5214532023541580740 ,.69177397444039543927] 
dist 169=[-2.5238283214401262793 ,.84773808366260705255] 
dist 170=[-2.5175058546322790083 ,.94762144652145153647] 
dist 171=[-2.5036148042897544333 ,1.0254904943730980490 ] 
dist 172=[-2.4950153716945146671 ,1.0936037408312311375 ] 
dist 173=[-1.2191792274182918004 ,1.1501751731433496615 ] 
dist 174=[-1.2254455966423179965 ,1.1819847015630960789 ] 
dist 175=[-1.2253511024053276695 ,1.2017207838416043756 ] 
dist 176=[-1.2220446190413173978 ,1.2101102327754711008 ] 
dist 177=[-1.1315688671441499927 ,1.2127493650603658774 ] 
dist 178=[-1.1148225922819636522 ,1.2099957864739158309 ] 
dist 179=[-1.0792881754218997742 ,1.2027651043490874335 ] 
dist 180=[-1.0675059633980287739 ,1.1977422289898486358 ] 
dist 181=[-1.0118285928129085274 ,1.1645623520812178697 ] 
dist 182=[-.99942280997450511767,1.1787970649025603784 ] 
dist 183=[-.96043700959415636781,1.2682567299944921053 ] 
dist 184=[-.95433702115498658801,1.3424758556448792134 ] 
dist 185=[-.34399526115220330831,1.4015882779522110338 ] 
dist 186=[-.28529545334479418799,1.4307592090485330212 ] 
dist 187=[-.16238984142501636967,1.4456848010356464865 ] 
dist 188=[-.13018473227656768653,1.4479437540995263007 ] 
dist 189=[-.01132925774821141377,1.1007755559517853167 ] 
dist 190=[.01189988221221652279,1.0734726984157885412 ] 
dist 191=[-.0728635635468118381 ,1.0071050067042707832 ] 
dist 192=[-.22536614770519274504,.9901085927326760531 ] 
dist 193=[-.37745179446428562497,.88442666933515663967] 
dist 194=[-.48678893169121295193,.86219400217495029519] 
dist 195=[-.58571000375529497864,.86215023117924894152] 
dist 196=[-.69622762760818696764,.9667569724683706192 ] 
dist 197=[-.80569160298047093557,1.0690514364290590083 ] 
dist 198=[-.90040817887722064629,1.1554927628351858011 ] 
dist 199=[-1.0024302663702523710 ,1.2468417948563167472 ] 
dist 200=[-1.1410498600768370665 ,1.3687204500602428628 ] 
dist 201=[-1.2746962873717392506 ,1.4845433153578845437 ] 
dist 202=[-1.3568709804620775715 ,1.5517246909955621584 ] 
dist 203=[-1.4170466075220772731 ,1.5961079996830732041 ] 
dist 204=[-1.4628969591153539734 ,1.6209492036364799245 ] 
dist 205=[-1.4968203723268232325 ,1.6359968992602432730 ] 
dist 206=[-1.5093979113152752376 ,1.6412966397563933121 ] 
dist 207=[-1.5129285270868335969 ,1.6404654129661701891 ] 
dist 208=[-1.5107466461554023878 ,1.6361851281889761232 ] 
dist 209=[-1.4347478102015167362 ,1.4416500466846703962 ] 
dist 210=[-1.4184256880464458934 ,1.4107687828041784583 ] 
dist 211=[-1.4513481185032258547 ,1.3524916476450109399 ] 
dist 212=[-1.4973087303466314754 ,1.3357991068642246515 ] 
dist 213=[-1.5347877007057859602 ,1.2702675010557159582 ] 
dist 214=[-1.5495099675108592027 ,1.2528781501168854007 ] 
dist 215=[-1.5543354513264993228 ,1.2169936293070712303 ] 
dist 216=[-1.5523138854099955214 ,1.2050125723291433495 ] 
dist 217=[-1.5108994670972957442 ,.35501973008162641672] 
dist 218=[-1.4968897614924560970 ,.44103214132831042587] 
dist 219=[-1.4836332515725921813 ,.54633347132393056684] 
dist 220=[-1.4744370584176940685 ,.7054465049449016673 ] 
dist 221=[-1.1137853389390084998 ,.8635629003367382212 ] 
dist 222=[-1.1001930345198149211 ,.9648875404090636054 ] 
dist 223=[-1.0728450858748999130 ,1.0439825648501017823 ] 
dist 224=[-1.0635582161774573778 ,1.1133842661908651408 ] 
dist 225=[-.88833260326759985392,1.1712178160676986430 ] 
dist 226=[-.86204295588800587356,1.2214219225443014233 ] 
dist 227=[-.79908819548743845084,1.3214794220395537352 ] 
dist 228=[-.78351607502505325243,1.4319393633441995679 ] 
dist 229=[-.68747735686638975243,1.5317552628660790240 ] 
dist 230=[-.66770218719718438334,1.5893341166358034130 ] 
dist 231=[-.63022011517018340829,1.6269789913849723888 ] 
dist 232=[-.6199995422437588826 ,1.6472414991681032420 ] 
dist 233=[-.2005976232956932972 ,1.6580943242565204976 ] 
dist 234=[-.15557802455860595398,1.6581865247534165772 ] 
dist 235=[-.06825823929798982916,1.6520582706552342926 ] 
dist 236=[-.04714562527720366562,1.6463856563045450735 ] 
dist 237=[-.21949725186745152829,1.2182420645677681314 ] 
dist 238=[-.39241161406012445291,1.1723304112550023905 ] 
dist 239=[-.5344392131138341035 ,1.0551397336003279765 ] 
dist 240=[-.67136850820686267823,1.0361710942530398738 ] 
dist 241=[-.79447180694173943128,.84254388583505489692] 
dist 242=[-.8813221557840641754 ,.80437430954354629823] 
dist 243=[-.95821379501037286839,.75878993211218163707] 
dist 244=[-1.0415730966812171477 ,.74468181759999771515] 
dist 245=[-1.1171016146901126520 ,.29363936135979699323] 
dist 246=[-1.1627422274412411229 ,.23922656713971873014] 
dist 247=[-1.1952090766811440189 ,.09788238188377565460] 
dist 248=[-1.2181647148272292380 ,-.01891824152833204062] 
dist 249=[-1.2332368733373884089 ,-.03737986449886768215] 
dist 250=[-1.2362092189287571463 ,-.03575720201807757878] 
dist 251=[-1.2310376220713908692 ,-.02528064749309617504] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 2, 1, 1, 2, 0, 1] 
dist 0=[50.619301881043646874  ,50.619301881043646874  ] 
dist 1=[49.693794567927328000  ,50.995229996526284847  ] 
dist 2=[48.207921810987544470  ,51.570700515024459598  ] 
dist 3=[45.770960007168644089  ,52.176767892730840124  ] 
dist 4=[43.251271427322786892  ,52.475539814742722746  ] 
dist 5=[41.434952446035462554  ,52.606814490446440307  ] 
dist 6=[39.782475796079677580  ,52.603411231345450889  ] 
dist 7=[37.916842588902629353  ,52.358869503498558053  ] 
dist 8=[36.051807689787522578  ,50.461673548721490258  ] 
dist 9=[34.401517643136959661  ,49.939922601120365360  ] 
dist 10=[32.588148736707748147  ,49.761509058447353247  ] 
dist 11=[30.071500912803479977  ,49.185079127617944460  ] 
dist 12=[27.536705351758126281  ,48.979501033045280672  ] 
dist 13=[25.650652488616021229  ,48.637653749235308274  ] 
dist 14=[23.872771214563074777  ,48.510581474915583249  ] 
dist 15=[21.769685371119139472  ,47.878437035222586657  ] 
dist 16=[19.609262175156851988  ,30.517979956680753135  ] 
dist 17=[17.601983411961642036  ,27.108557569316319044  ] 
dist 18=[15.314281676527241126  ,26.608223023729878867  ] 
dist 19=[12.033004333005109875  ,23.533145976169380241  ] 
dist 20=[8.7903656848371419695 ,20.872526030061228734  ] 
dist 21=[6.6568842672551962470 ,19.802129478590491994  ] 
dist 22=[4.9180722686664834862 ,19.586349828311323691  ] 
dist 23=[3.2522835353637426401 ,15.511468422252300521  ] 
dist 24=[1.7514667912804125310 ,12.987134521391538436  ] 
dist 25=[.67165375509342793622,12.565319780115339098  ] 
dist 26=[-.31235127326837910169,11.398425514747305355  ] 
dist 27=[-1.4307431021531911330 ,9.9200127401424441995 ] 
dist 28=[-3.4825204050512431983 ,7.2955419202556662379 ] 
dist 29=[-5.2401701908794491334 ,6.7561228558558952039 ] 
dist 30=[-7.1252229822248009186 ,6.6425728107355369320 ] 
dist 31=[-9.6904151776973771243 ,-.70832818606884058155] 
dist 32=[-12.164494712790302819  ,-1.3301946450937388359 ] 
dist 33=[-13.685774311749946538  ,-2.5906627796724510503 ] 
dist 34=[-14.809695182842506294  ,-2.8792005669156412131 ] 
dist 35=[-15.695912676764171656  ,-3.1845683574819183769 ] 
dist 36=[-16.390345617701320628  ,-2.7925284930228499456 ] 
dist 37=[-16.747677920651592589  ,-2.4985454249183192884 ] 
dist 38=[-16.929760522954804158  ,-2.2234995187843783862 ] 
dist 39=[-16.958538521770570083  ,-1.9062881354287169891 ] 
dist 40=[-16.108719328484235403  ,-1.5892964432660993577 ] 
dist 41=[-15.932949433877796891  ,-1.3148007144920346694 ] 
dist 42=[-15.677824392838201934  ,-1.0203875673608544645 ] 
dist 43=[-15.573919884721302676  ,-.6236786080246763382 ] 
dist 44=[-15.268168149238092702  ,-.23355327219055463546] 
dist 45=[-15.146194898015226633  ,.26554627938288091092] 
dist 46=[-14.968549157449118583  ,1.9185041020164243661 ] 
dist 47=[-14.889578676712739228  ,3.5846333093715982470 ] 
dist 48=[-4.6302989327030599094 ,4.7134651802833987084 ] 
dist 49=[-3.7628538920994059746 ,5.6637189510766809198 ] 
dist 50=[-1.7848572275251774363 ,6.6174393581432674259 ] 
dist 51=[-1.4353217793388957265 ,7.4995615669945158299 ] 
dist 52=[1.0154352154221630843 ,8.1642198603236095292 ] 
dist 53=[1.4396376902865628246 ,8.7966411186161283440 ] 
dist 54=[1.6798373060690119908 ,9.5502680060545967062 ] 
dist 55=[1.7015331100161747299 ,10.251195542604165658  ] 
dist 56=[1.7271287927369968263 ,10.673375602429554508  ] 
dist 57=[1.6967641453781407301 ,10.972470695260120817  ] 
dist 58=[1.6317334275305981349 ,11.182249328620739438  ] 
dist 59=[1.5031544459158107527 ,11.319284413112941974  ] 
dist 60=[1.3586034262951446434 ,11.340349526026258430  ] 
dist 61=[1.2298053829344458456 ,11.292905014304970857  ] 
dist 62=[1.0883607029349047397 ,11.230663201523080394  ] 
dist 63=[.88778540092293880689,10.754534663323702289  ] 
dist 64=[.61919630706198428747,3.9015884283481806939 ] 
dist 65=[.34138275393384182121,3.3976803696834457192 ] 
dist 66=[.00394290683418012691,3.3239839469692731547 ] 
dist 67=[-.5026125213501627512 ,2.5221910658014427761 ] 
dist 68=[-1.0070647727325169704 ,2.3696974930926794053 ] 
dist 69=[-1.3361331897306018522 ,2.1985603223171320063 ] 
dist 70=[-1.6494832680025306833 ,2.1648620937638775265 ] 
dist 71=[-2.0950114894098923860 ,1.4193075367429027531 ] 
dist 72=[-2.3750178901405311467 ,1.2168149100569322029 ] 
dist 73=[-2.5872956958094915278 ,1.1758852175419105772 ] 
dist 74=[-2.7626384907438270946 ,1.0934904468228166731 ] 
dist 75=[-2.9023184723941508409 ,1.0702055508507271905 ] 
dist 76=[-2.9722457929744456336 ,.7585748342742779444 ] 
dist 77=[-3.0082782460034073091 ,.7131003013160980306 ] 
dist 78=[-3.0127383001175431528 ,.60453410627817483754] 
dist 79=[-2.9220064421712877482 ,.58328719261627006375] 
dist 80=[-2.9028151397041767780 ,.42610439567013966018] 
dist 81=[-2.8267152892879696109 ,.39592625443791465639] 
dist 82=[-2.8157396231598044817 ,.34581679783791634537] 
dist 83=[-2.5969824138013307328 ,.33311460422345480202] 
dist 84=[-2.6990954805323713662 ,-.22503026168999183356] 
dist 85=[-2.8110956599172321752 ,.09997260742024645962] 
dist 86=[-2.9381742525236983845 ,.37946811437988617724] 
dist 87=[-3.0533366015780122801 ,.66947465388840947874] 
dist 88=[-3.1177382226732287758 ,.9436772763981977173 ] 
dist 89=[-3.1573268790963127653 ,1.1601351798496852200 ] 
dist 90=[-3.1733887527228275238 ,1.3755771032987244348 ] 
dist 91=[-3.1753812789504654360 ,1.6457572124885211705 ] 
dist 92=[-3.1700376108713139121 ,1.9036419428099784876 ] 
dist 93=[-3.1381857224029808150 ,2.0700374235157572708 ] 
dist 94=[-3.1238673046059039878 ,2.2012366879701623988 ] 
dist 95=[-2.8922228666695522754 ,2.3186932626797811275 ] 
dist 96=[-2.8508909907587814633 ,2.4184018808125964318 ] 
dist 97=[-2.7353710702553048251 ,2.4838448962379863482 ] 
dist 98=[-2.7099162979511267975 ,2.7346261344088375726 ] 
dist 99=[-2.4709366665347567500 ,2.9489925364978940015 ] 
dist 100=[-2.4175185193537358719 ,3.1301928225845824725 ] 
dist 101=[-2.3483421615789043201 ,3.2739500479048766751 ] 
dist 102=[-2.3215120611242420770 ,3.3794900820006021691 ] 
dist 103=[-1.6857160898718940315 ,3.4605760251101149479 ] 
dist 104=[-1.5979523422052196624 ,3.5234159465431973972 ] 
dist 105=[-1.4130632364464735908 ,3.5561286610736438743 ] 
dist 106=[-1.3611477431035704155 ,3.5731030169890968740 ] 
dist 107=[-1.1516827447591364404 ,3.5731197190721396708 ] 
dist 108=[-1.1092671334738993560 ,3.5623124555584585116 ] 
dist 109=[-1.0064279906893114257 ,3.5505488584349676303 ] 
dist 110=[-.98273418703212857511,3.5066536599779430768 ] 
dist 111=[1.2383540115614189248 ,3.4830400008440973906 ] 
dist 112=[.63575713269588195255,1.8995789435998023607 ] 
dist 113=[.23009693468184176816,1.6112126429936031059 ] 
dist 114=[-.10890466557986941731,1.5663454566701020927 ] 
dist 115=[-.44547667804399210671,1.1504875075191935376 ] 
dist 116=[-.75466577307648947057,1.0509990050151193462 ] 
dist 117=[-.98438946916849407998,.94883396684319444505] 
dist 118=[-1.1998895184068243622 ,.92153471577096450973] 
dist 119=[-1.4523242185044847779 ,.34971045155635964356] 
dist 120=[-1.6882686042313930616 ,.15544814866373203632] 
dist 121=[-1.8379559627782367743 ,-.02709109331999211040] 
dist 122=[-1.9531375368391577456 ,-.06454876480391403122] 
dist 123=[-2.0513576932112227222 ,-.26155569164047298305] 
dist 124=[-2.1311644442301722768 ,-.29435592392392526345] 
dist 125=[-2.1728516246307040595 ,-.36451170050494511045] 
dist 126=[-2.1945991532105555043 ,-.3760116555848342618 ] 
dist 127=[-2.1974349181010635951 ,-.88443829927902107877] 
dist 128=[-1.6574247079461647636 ,-.93239988153028146631] 
dist 129=[-1.6093592395003583515 ,-.96005207026199707073] 
dist 130=[-1.7157624070089096885 ,-.85775012882466168565] 
dist 131=[-1.8124879523140153002 ,-.73886403199325990601] 
dist 132=[-1.8818330650948462645 ,-.61852722922923545958] 
dist 133=[-1.9444821703221584108 ,-.51042586004255102082] 
dist 134=[-2.0144838182204719111 ,-.39064061209517917231] 
dist 135=[-2.0773544835045165578 ,-.22366495318042841691] 
dist 136=[-2.1115383505202564914 ,-.05606716500803042649] 
dist 137=[-2.1313182622842882640 ,.06620767651935941723] 
dist 138=[-2.1366866733557320151 ,.17867033955788394035] 
dist 139=[-2.1326661815130848987 ,.30711895222833748272] 
dist 140=[-2.1280842889843659776 ,.45959003025479665936] 
dist 141=[-2.0969277468756926529 ,.74799691682483571741] 
dist 142=[-2.0915613602314780834 ,1.1784052517960645459 ] 
dist 143=[-.28007138069416025485,1.6045981606263353514 ] 
dist 144=[.01812931176433889462,1.8761845868544135856 ] 
dist 145=[.03278892352104874856,2.0865045641077442453 ] 
dist 146=[.04157994695760570648,2.2681783026338241297 ] 
dist 147=[.03525920519060478523,2.4240117757699981751 ] 
dist 148=[.02130988824506590293,2.5565599581470156778 ] 
dist 149=[-.00272594376238055966,2.6590212762454097991 ] 
dist 150=[-.03870774684205095004,2.7471984455036077996 ] 
dist 151=[-.1003355028713771468 ,2.8198924134013322914 ] 
dist 152=[-.16716350635109267794,2.8605601305803007818 ] 
dist 153=[-.22390309947784574709,2.8855598843583331570 ] 
dist 154=[-.284081816590251028  ,2.8957231662537405056 ] 
dist 155=[-.36464391655570743634,2.8955882579985874513 ] 
dist 156=[-.45210870628641989788,2.8888447067079103188 ] 
dist 157=[-.5398410836384921226 ,2.8588591107417126635 ] 
dist 158=[-.64455737464068593034,2.8408466299812757794 ] 
dist 159=[-.79981123054099522531,1.8411608588317369617 ] 
dist 160=[-1.0446348180309711638 ,1.3383900489256479893 ] 
dist 161=[-1.2415993518857521110 ,1.0363101996582215773 ] 
dist 162=[-1.3968348592472692951 ,.99082898269112493464] 
dist 163=[-1.5356592500630512465 ,.5523965319110207213 ] 
dist 164=[-1.6532728869682195488 ,.47194909284112630419] 
dist 165=[-1.7271210412641403481 ,.37134818996892148035] 
dist 166=[-1.8183929262013575918 ,.34825939233080963803] 
dist 167=[-1.9046521210253468398 ,-.28909239913707620525] 
dist 168=[-1.9791888103593488365 ,-.36533994202809761055] 
dist 169=[-2.0236768242803756041 ,-.53227182272178742711] 
dist 170=[-2.0546653130856906557 ,-.56255566365320582652] 
dist 171=[-2.0753251283080467565 ,-.74165814100198583935] 
dist 172=[-2.0877598797351601235 ,-.66771178800669924397] 
dist 173=[-2.0864538202690754581 ,-.5292337061882160083 ] 
dist 174=[-2.0772077898686607500 ,-.35806781379778674579] 
dist 175=[-2.0685243270962698186 ,-.09760371145778500970] 
dist 176=[-1.4278032243215546548 ,.16372098972011977986] 
dist 177=[-1.3466066238117410763 ,.33832153107725144006] 
dist 178=[-1.3319878461117320710 ,.48277739548838456741] 
dist 179=[-1.1773207765543324032 ,.62379677381645481487] 
dist 180=[-1.1447263374182041365 ,.75175454953757413359] 
dist 181=[-1.1065004428107834020 ,.84408186982320141032] 
dist 182=[-1.0912000427416237237 ,.92795733173854613941] 
dist 183=[-.77577881560018940057,1.0221826023885627679 ] 
dist 184=[-.68441679325995208355,1.1082764795681989601 ] 
dist 185=[-.58467246926698222689,1.1597008259994845348 ] 
dist 186=[-.55757512960426507441,1.1955544630435748431 ] 
dist 187=[-.45290498215391623298,1.2195105589626963322 ] 
dist 188=[-.43176770444016356783,1.2353451766986425649 ] 
dist 189=[-.38701356755574219086,1.2387865642550039490 ] 
dist 190=[-.37447799091320770214,1.2380673533460317307 ] 
dist 191=[-.04131971324694228376,1.2379854589880032892 ] 
dist 192=[-.01859140426305044090,.91199525898024597628] 
dist 193=[8.44626555314940532000e-05,.99188697468561599357] 
dist 194=[.00235725591084743874,1.1006336808703019788 ] 
dist 195=[-.00210048272261474544,1.2173907427506049618 ] 
dist 196=[-.01644320743206172265,1.3041004461844587668 ] 
dist 197=[-.04075202408673985768,1.3853929052517146137 ] 
dist 198=[-.08498432345112509388,1.4805310224900180077 ] 
dist 199=[-.13389257605749633644,1.5680793896827304780 ] 
dist 200=[-.17686424557888916869,1.6190815799703710986 ] 
dist 201=[-.22369323893490699015,1.6530748001837511640 ] 
dist 202=[-.28799949334256800938,1.6727403474817752054 ] 
dist 203=[-.35858973904703515327,1.6828891087354708796 ] 
dist 204=[-.45598175920772002869,1.6829271396141315577 ] 
dist 205=[-.58800869411477987379,1.6707356097251933262 ] 
dist 206=[-.74217642825350224232,1.6642186545971333972 ] 
dist 207=[-.9668078521665102294 ,.86922710169772889627] 
dist 208=[-1.1873487299975966860 ,.92545265423326229338] 
dist 209=[-1.3251919083550162964 ,.96085811583682789892] 
dist 210=[-1.4288104465106446242 ,.98777124536977222426] 
dist 211=[-1.5127655438677984633 ,1.0101070469803887027 ] 
dist 212=[-1.5798882660731578552 ,1.0277725546207489724 ] 
dist 213=[-1.6163304640871161417 ,1.0360481451975931476 ] 
dist 214=[-1.6564756553741863742 ,1.0390229627842159010 ] 
dist 215=[-1.7181108818513000948 ,1.0374207561465955138 ] 
dist 216=[-1.7553511021045320567 ,1.0286759627146304069 ] 
dist 217=[-1.7818408682880211166 ,1.0240099166311512415 ] 
dist 218=[-1.8005723113924790059 ,1.0076639822599675315 ] 
dist 219=[-1.8128746811187582130 ,1.0005613491935519779 ] 
dist 220=[-1.8137067979829621181 ,.95140514800711220622] 
dist 221=[-1.8074229841493354470 ,.93861645303878948159] 
dist 222=[-1.8018105689490744432 ,.91693938800915708185] 
dist 223=[-1.0611921838534136903 ,.9099358103913046326 ] 
dist 224=[-1.0233357683567276239 ,.73781982548565675641] 
dist 225=[-.92521079155804817833,.71187388393828183743] 
dist 226=[-.91010941456899812313,.66152957907914213696] 
dist 227=[-.74354163899416434786,.64792087460748703324] 
dist 228=[-.71055194434280463173,.71644185138268297999] 
dist 229=[-.67410140132462964577,.78498292403991962409] 
dist 230=[-.66465614123202003686,.86137649354096689603] 
dist 231=[-.33309364781528106248,.93101384478619497235] 
dist 232=[-.29131986619771998618,.9725921850466005106 ] 
dist 233=[-.20476946351746521142,1.0015600911421882515 ] 
dist 234=[-.18209600655094668764,1.0208731537335948742 ] 
dist 235=[-.09889170203704235090,1.0334458611878894033 ] 
dist 236=[-.08210622678888208121,1.0355139406741541045 ] 
dist 237=[-.05285443720228986206,1.0348371096519671310 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 1, 1, 1, 0, 1] 
dist 0=[60.646675505843982859  ,60.646675505843982859  ] 
dist 1=[59.327280412887116137  ,61.284540097151380192  ] 
dist 2=[57.866403070220749970  ,61.614512845057544323  ] 
dist 3=[56.663530010120457994  ,61.704557727066378231  ] 
dist 4=[55.417250096652460438  ,61.651696435471870265  ] 
dist 5=[53.782883935828002987  ,61.145884640324612564  ] 
dist 6=[52.020205723464511488  ,60.995699000932371659  ] 
dist 7=[50.261425269020910833  ,60.900433953833627089  ] 
dist 8=[48.164849188931333041  ,60.716672358415140278  ] 
dist 9=[45.053069653692850447  ,54.691822685607093618  ] 
dist 10=[41.833047228465246705  ,53.820591754648352132  ] 
dist 11=[39.304106683330722283  ,52.263756948116318486  ] 
dist 12=[36.791264809681203020  ,51.864491339239793618  ] 
dist 13=[33.635358406597909253  ,50.553849007253634009  ] 
dist 14=[30.298100244513674457  ,50.154371926056956454  ] 
dist 15=[27.060831731956226421  ,49.843250171458129722  ] 
dist 16=[22.793245153357807943  ,49.620225807310652264  ] 
dist 17=[17.713205059358459317  ,35.872500156054834101  ] 
dist 18=[12.180659011569522912  ,21.684428219092345647  ] 
dist 19=[8.4781942110948965474 ,16.749025196333569741  ] 
dist 20=[5.3978764229324290601 ,16.017535516169445108  ] 
dist 21=[2.3502690754831504215 ,9.5018219894067111769 ] 
dist 22=[-.45216525611835692884,8.3613134033487455040 ] 
dist 23=[-2.5532104178249930398 ,6.8449144743253181926 ] 
dist 24=[-4.5479717942977766303 ,6.5298236423983391393 ] 
dist 25=[-6.9258353325455514633 ,2.1727134618100816146 ] 
dist 26=[-9.1463642750526034120 ,-1.1737209661973272305 ] 
dist 27=[-10.512735205510051147  ,-1.6398307622227781926 ] 
dist 28=[-11.518119788537578212  ,-2.2521834427067495715 ] 
dist 29=[-12.296952693768936332  ,-2.3303374468516051118 ] 
dist 30=[-12.898359926097722339  ,-2.2145582334905693811 ] 
dist 31=[-13.195298138697531722  ,-1.8268330587951953271 ] 
dist 32=[-13.327217259705532664  ,-1.1737079201907509037 ] 
dist 33=[-13.340389930971165420  ,0                     ] 
dist 34=[-7.4964050412391557415 ,-3.0349811497546200476 ] 
dist 35=[-7.4771821429712443933 ,-1.9976629069796332852 ] 
dist 36=[-7.4722842796297854774 ,-1.0991844800439421558 ] 
dist 37=[-7.0935478652676385673 ,-.16055817493367682449] 
dist 38=[-6.9946167158640087525 ,.72807097534832039923] 
dist 39=[-6.9332337103667698843 ,1.4275029967779159143 ] 
dist 40=[-6.9129244419922614194 ,2.1204849916368237229 ] 
dist 41=[-5.2832624122975330621 ,2.9837645655714045912 ] 
dist 42=[-5.0698558750737258881 ,3.8035102229579274094 ] 
dist 43=[-4.6497258817016982241 ,4.3230048262095652335 ] 
dist 44=[-4.5404641458539506673 ,4.7215826398419775911 ] 
dist 45=[-4.1569826536274521917 ,5.0591232928808209638 ] 
dist 46=[-4.0658794488233225933 ,5.3320736077374753197 ] 
dist 47=[-3.9606363995396270313 ,5.4731334167217079086 ] 
dist 48=[-3.9272584646303005956 ,5.5455472963913894725 ] 
dist 49=[.06258465555146327928,5.5584250269482419925 ] 
dist 50=[.38923354254165011338,5.5090610464595102875 ] 
dist 51=[1.0810608373436311977 ,5.4865276285843225804 ] 
dist 52=[1.2278314867403289201 ,5.3760535005319690880 ] 
dist 53=[1.8961956725044707871 ,5.3542041060078679983 ] 
dist 54=[2.0122806920112625292 ,4.9822207055006037566 ] 
dist 55=[2.2041101653589687749 ,4.8930833763154814328 ] 
dist 56=[2.2423076513533884513 ,4.8150126149217882412 ] 
dist 57=[2.1418331162026913153 ,4.7826114491639410865 ] 
dist 58=[1.9633520668516460108 ,4.6764806270825170029 ] 
dist 59=[1.6570312514857309382 ,4.8865740214540661114 ] 
dist 60=[1.2925989320012409857 ,5.0601123381875265483 ] 
dist 61=[.88213892003499219879,5.1972392459430623700 ] 
dist 62=[.3597018285415030284 ,5.2619398322478075418 ] 
dist 63=[-.45166548727438422459,5.2867747109944684256 ] 
dist 64=[-1.2650713820686373673 ,5.2866476287317338942 ] 
dist 65=[-1.7956860271287378559 ,-.73669615258726487812] 
dist 66=[-2.2205548815793933318 ,-1.0074760385251324656 ] 
dist 67=[-2.6120174755896809993 ,-1.6237740999970837088 ] 
dist 68=[-2.9520462384852638283 ,-1.7128694830188437489 ] 
dist 69=[-3.1717008772927116988 ,-2.4421900681557858588 ] 
dist 70=[-3.3454005695321200149 ,-2.5587446517612956209 ] 
dist 71=[-3.5021091109354135071 ,-2.7344660187776087695 ] 
dist 72=[-3.6340249665492011407 ,-2.7635793347403764973 ] 
dist 73=[-3.7087840187654930215 ,-3.1743820837919365966 ] 
dist 74=[-3.7562685623543782384 ,-3.0641785703465812996 ] 
dist 75=[-3.7792675747326399313 ,-2.8420325157885526202 ] 
dist 76=[-3.7850176756517767695 ,-2.5656656351918173882 ] 
dist 77=[-3.7776560689570078556 ,-2.2391041553603132082 ] 
dist 78=[-3.7350647652871694081 ,-1.8138680028856416282 ] 
dist 79=[-3.7121563630482490412 ,-1.1437956023751434177 ] 
dist 80=[-3.5765076351442660126 ,-.46492906101184699534] 
dist 81=[-1.6357042958406838639 ,-.00459127692361438093] 
dist 82=[-1.3487662492186316540 ,.38308013966010195493] 
dist 83=[-1.1581612105957933923 ,.77205229094961937542] 
dist 84=[-.88447450833349659979,1.1313289592463708463 ] 
dist 85=[-.54036980229385740606,1.4005324306701229960 ] 
dist 86=[-.37120455762937946818,1.6548825398986789585 ] 
dist 87=[-.33366128383697902211,1.9549005974064493065 ] 
dist 88=[-.05112215716294528697,2.2333565066573414293 ] 
dist 89=[.28175628256990252269,2.4016889528137050643 ] 
dist 90=[.41613445385722745896,2.5213405983554362457 ] 
dist 91=[.44440175593607672336,2.6055994410270731004 ] 
dist 92=[.5047117895796795779 ,2.6665244989319387962 ] 
dist 93=[.49608830384382333395,2.6930772280520508559 ] 
dist 94=[.45660328906065554721,2.6994882360456776697 ] 
dist 95=[.36514045213648722919,2.6965528586503997185 ] 
dist 96=[.26470596822220179842,1.8071726492409934921 ] 
dist 97=[.18942245469878133966,1.4790577422185434748 ] 
dist 98=[.11852515374816678223,1.4779687174473339612 ] 
dist 99=[.03552486213763895376,1.4591962701385411167 ] 
dist 100=[-.09860187408471228438,1.4563302777265834913 ] 
dist 101=[-.25631675700545179323,1.3681119909329092848 ] 
dist 102=[-.41285281953053902489,1.3461351355117861402 ] 
dist 103=[-.60840724780309179325,1.3324254279762417482 ] 
dist 104=[-.79447989262204383702,1.3286553946494318915 ] 
dist 105=[-.91320333324531146054,.97918138953508247941] 
dist 106=[-1.0052314856897121954 ,.9329343712158878064 ] 
dist 107=[-1.0848179302900955255 ,.8445033172771704597 ] 
dist 108=[-1.1503490000677980225 ,.8217853391652190294 ] 
dist 109=[-1.1863220518199721004 ,.7443204556226535658 ] 
dist 110=[-1.2076543756949997362 ,.7246159711928598928 ] 
dist 111=[-1.2148173748391050705 ,.82714108066067879646] 
dist 112=[-1.2148765493421940669 ,.99876696585516979741] 
dist 113=[-1.2115882102456026278 ,1.1066731010317309860 ] 
dist 114=[-1.2063298155363183754 ,1.1882646180058068873 ] 
dist 115=[-1.2355010962757790689 ,1.2549172210330309291 ] 
dist 116=[-1.2552092293854549150 ,1.3078991787823308846 ] 
dist 117=[-1.2593618827975082571 ,1.3349658264538238562 ] 
dist 118=[-1.2577449312488977802 ,1.3483279580001521372 ] 
dist 119=[-1.2544038694041800461 ,1.3504694630041386966 ] 
dist 120=[-1.1916919750901900581 ,1.2867169790927633703 ] 
dist 121=[-1.3099727585914756651 ,1.2720340715794925520 ] 
dist 122=[-1.3850813884406442490 ,1.2535823076728770727 ] 
dist 123=[-1.4429371393468683642 ,1.2444805740860257890 ] 
dist 124=[-1.4923610956317175613 ,1.2206063001738585632 ] 
dist 125=[-1.5325725236201842928 ,1.2099438838554010549 ] 
dist 126=[-1.5536607521650937491 ,1.1923144369904195674 ] 
dist 127=[-1.5647765031989030398 ,1.1850782553820730544 ] 
dist 128=[-1.5651874828728824723 ,.27587155967599641721] 
dist 129=[-.42331358537542307869,.55053518675799177836] 
dist 130=[-.30239829006982470725,.72915801628907068198] 
dist 131=[-.28490735503179827933,.87153315977512642279] 
dist 132=[-.11492423527442177275,1.0029040612407842646 ] 
dist 133=[-.08451202685964805936,1.1168815584578127250 ] 
dist 134=[-.04685995397277870335,1.1888280395638459190 ] 
dist 135=[-.04013398214695297506,1.2437254244062500543 ] 
dist 136=[.18518610207762082089,1.2896681849395985049 ] 
dist 137=[.2111251988943651801 ,1.3279369778765514810 ] 
dist 138=[.26811941825519739264,1.3522109614967475448 ] 
dist 139=[.27676883826846169905,1.3708738040224694063 ] 
dist 140=[.33660677603023614238,1.3867503961154626674 ] 
dist 141=[.34539027829707082205,1.3996172207393606242 ] 
dist 142=[.36149842032598844534,1.4062693681801298232 ] 
dist 143=[.36382427885367467519,1.4096449633307772357 ] 
dist 144=[.38782360414354832913,1.4094370174117459926 ] 
dist 145=[.38574509741259927913,.54711903977427715555] 
dist 146=[.35960143544410434894,.47806106928970996955] 
dist 147=[.23653354913819695351,.42605135072303377707] 
dist 148=[.1100401130483082063 ,.42912237673559796744] 
dist 149=[-.0088742257421696421 ,.43079739833244854431] 
dist 150=[-.1016978053573656360 ,.43181872851426017554] 
dist 151=[-.1931288084044260217 ,.43228035416157293197] 
dist 152=[-.30648642826452934345,.43242202539995155391] 
dist 153=[-.41413129405744243304,.43216336072557573531] 
dist 154=[-.48276516146158588238,.43159766803166698143] 
dist 155=[-.53592224039454793083,.43050547918786175196] 
dist 156=[-.58180548172836157648,.42918830528028942499] 
dist 157=[-.61946144200422464333,.42772028076980672409] 
dist 158=[-.63978644821666620881,.42587243294458838659] 
dist 159=[-.6513380957972896373 ,.42422582655817122004] 
dist 160=[-.65413605187781524015,-.47242700133841554331] 
dist 161=[-.61408431804655961466,-.51274850097568729422] 
dist 162=[-.61337281979242976984,-.58053964156440590391] 
dist 163=[-.66812692505156122155,-.56809914907077348892] 
dist 164=[-.71419831788548038786,-.5451762020969640676 ] 
dist 165=[-.74130461473655485915,-.51730002203074826496] 
dist 166=[-.75971763116493975894,-.48509147363143249248] 
dist 167=[-.77109198714387292531,-.44356522304772173367] 
dist 168=[-.77868846692228399958,-.37850435054687922773] 
dist 169=[-.78202299191794828911,-.31008444056232573239] 
dist 170=[-.78288194969982056381,-.25515238128903238199] 
dist 171=[-.78083233712656715804,-.19961234627879146344] 
dist 172=[-.77647929428929959374,-.12876408470721595586] 
dist 173=[-.77315117350764018726,-.05354234809696872448] 
dist 174=[-.76301824868575012822,.01945216010507466269] 
dist 175=[-.75795352208429771367,.10476233517384934055] 
dist 176=[-.34977686953607254694,.22913376811514296921] 
dist 177=[-.31332751855052247366,.35263836104384044115] 
dist 178=[-.22671252186758422855,.43448972295480819451] 
dist 179=[-.2127861416313974817 ,.5014675480068633015 ] 
dist 180=[-.0930647719861423515 ,.56561618406089895563] 
dist 181=[-.0714147725373460812 ,.62450334170696335256] 
dist 182=[-.0407642223457253259 ,.66618954757939095545] 
dist 183=[-.0321221093612391090 ,.70312117908106614572] 
dist 184=[.02433834944772785888,.74319799747148169173] 
dist 185=[.01327296263602196660,.77841316521250759329] 
dist 186=[-.00122490967217519689,.79594334082469498221] 
dist 187=[-.02100239212107512774,.80514995615168809883] 
dist 188=[-.05313781342096050087,.80714771608288568554] 
dist 189=[-.09073369898883284048,.79476381449202962208] 
dist 190=[-.13230244048218951265,.79122585580588859547] 
dist 191=[-.18472044135349184924,.78880843568686578595] 
dist 192=[-.27630312089035263631,.78729165437851622419] 
dist 193=[-.36801613631563204544,.31423405303312525216] 
dist 194=[-.42736118661613524761,.28074626844393074823] 
dist 195=[-.47432493109577365266,.27347539071731496156] 
dist 196=[-.51662983547172791356,.22573906317487070955] 
dist 197=[-.55267131398742806035,.21645291846142536887] 
dist 198=[-.59705871516529441164,.19938786636062188366] 
dist 199=[-.64534314660101405762,.19511222762280731085] 
dist 200=[-.6978982632376129724 ,.12566064335590985288] 
dist 201=[-.74525074754184982332,.11609138535009051051] 
dist 202=[-.77277337344924800403,.09738189543324033343] 
dist 203=[-.79102689337138083675,.09289064167320390417] 
dist 204=[-.80138921756491352128,.07165708269313661153] 
dist 205=[-.806998944458761853  ,.06773621675173251859] 
dist 206=[-.80685997458541177712,.05854742351115187843] 
dist 207=[-.80290637600091424813,.05673912092422111485] 
dist 208=[-.79912097216465225449,.03972020110991842104] 
dist 209=[-.56336964470053930361,.11237268894111423717] 
dist 210=[-.54123207847776673769,.19196050217648236923] 
dist 211=[-.48493953283160219314,.25700735829492529778] 
dist 212=[-.47576083346411504584,.31916319998733897248] 
dist 213=[-.4503897411447135942 ,.37465851031443280237] 
dist 214=[-.4605662179316849376 ,.41312553386044759848] 
dist 215=[-.4683994290687541270 ,.44646280313277763579] 
dist 216=[-.4738512592999092176 ,.48148682569973134868] 
dist 217=[-.4747188245576980809 ,.51299695921275798597] 
dist 218=[-.4734245888412501693 ,.53231169537781077816] 
dist 219=[-.4718076475703589870 ,.5463793241434583642 ] 
dist 220=[-.4550177444029596548 ,.55695082068992136867] 
dist 221=[-.4500919684494254223 ,.56445748659637870935] 
dist 222=[-.4438573720125883939 ,.5662949048602871693 ] 
dist 223=[-.4408866935970181788 ,.56549964368959478256] 
dist 224=[-.00180109188376041225,.56356986809380553422] 
dist 225=[.03633287115556240220,.33597687193793490775] 
dist 226=[.02818919877678598992,.35946445372980142263] 
dist 227=[.01904741151491249340,.37931444822838769062] 
dist 228=[.00616394789523029253,.39530447735875968462] 
dist 229=[-.00812791551429144546,.40724039147492510803] 
dist 230=[-.02289080628304346623,.43891838102964358798] 
dist 231=[-.04081841344725412015,.47387200517232349324] 
dist 232=[-.06774037062891005172,.5053769616628502177 ] 
dist 233=[-.09560539557260502378,.52329157757695313675] 
dist 234=[-.11729693132839305372,.53467683458158542282] 
dist 235=[-.13861131500134753142,.5401236862476294637 ] 
dist 236=[-.16497184196116734988,.5426694862188723372 ] 
dist 237=[-.19254680389524256957,.5424767105020916393 ] 
dist 238=[-.21870820935287399747,.5402557225067702772 ] 
dist 239=[-.2488365751888444926 ,.5386839759714573457 ] 
dist 240=[-.29224358280718655877,.40866491679916017697] 
dist 241=[-.33465782194700894173,.39651191651019699774] 
dist 242=[-.3608243802671009907 ,.36487016063710017352] 
dist 243=[-.38009191834650553971,.35951438214435778529] 
dist 244=[-.39497324026341766497,.30460754352651648177] 
dist 245=[-.40632953534195099463,.29349168605908609523] 
dist 246=[-.41152895709837682981,.28022005802251881124] 
dist 247=[-.41360194857318567673,.27555587380417769494] 
dist 248=[-.41340269977163089915,.16252275075665085126] 
dist 249=[-.38997006420817686408,.14782647855192310438] 
dist 250=[-.38946309595899849412,.11681951729151773756] 
dist 251=[-.39694338899313227187,.10845485826343977596] 
dist 252=[-.40181455411099135169,.07629308128807511622] 
dist 253=[-.40260784629993039022,.06998513734536315241] 
dist 254=[-.40179034892667795947,.05671534352622981748] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 2, 1, 2, 0, 1] 
dist 0=[56.332842487400640643  ,56.332842487400640643  ] 
dist 1=[55.962155785385869166  ,56.628139962305999618  ] 
dist 2=[54.777283729679578083  ,56.982393039394686269  ] 
dist 3=[53.296661880554708319  ,57.050939137509434187  ] 
dist 4=[51.562315065807708443  ,56.966787773282863069  ] 
dist 5=[49.306124733789557020  ,56.853238370473496572  ] 
dist 6=[45.741439748014467670  ,56.645582505977089637  ] 
dist 7=[42.102068532480974468  ,56.537086881710100321  ] 
dist 8=[39.547537972379418476  ,55.883911302969539338  ] 
dist 9=[37.292812737346999077  ,55.704276398639820011  ] 
dist 10=[34.850551197850893509  ,55.017731226800284548  ] 
dist 11=[32.467422773045961231  ,54.909010989136968345  ] 
dist 12=[30.448668151964960720  ,52.946062775392598624  ] 
dist 13=[28.304702246020318104  ,52.485499473362628815  ] 
dist 14=[25.421174346629174526  ,50.749848996036838358  ] 
dist 15=[22.557010214512795799  ,47.707184624329745377  ] 
dist 16=[20.490174253929170879  ,31.065345932718538363  ] 
dist 17=[18.605017704795921226  ,30.139459957113337318  ] 
dist 18=[16.466162383110810128  ,29.097102046861213633  ] 
dist 19=[14.318210293286507246  ,28.890822751221046173  ] 
dist 20=[12.396313736073340686  ,20.507393565548237840  ] 
dist 21=[10.263685785029790963  ,19.467452089699063357  ] 
dist 22=[7.2731731259293197144 ,17.361760676527138135  ] 
dist 23=[4.3356580899060348654 ,16.823849237544615944  ] 
dist 24=[1.4758375794764997787 ,14.927469982168786481  ] 
dist 25=[-.66653678987249820508,14.531581419193418941  ] 
dist 26=[-2.4739068777204475631 ,13.989144817628103210  ] 
dist 27=[-4.3060476716586754305 ,13.833402316997720660  ] 
dist 28=[-6.0240274515296307111 ,3.3966231113321271749 ] 
dist 29=[-7.3761084072289474844 ,2.9535130721671678775 ] 
dist 30=[-8.7274743130049002570 ,1.0258000399888870581 ] 
dist 31=[-10.444012319662090658  ,-2.0848766290744876487 ] 
dist 32=[-12.058922672228159234  ,-5.0778652590726007267 ] 
dist 33=[-13.004539820465056709  ,-5.3733342578897585633 ] 
dist 34=[-13.649792642846202818  ,-5.3682884501957535598 ] 
dist 35=[-14.064084347283607001  ,-5.2503416221911984095 ] 
dist 36=[-14.353543934209164432  ,-4.9772911260882152630 ] 
dist 37=[-14.499480651756342732  ,-4.5410142218178837409 ] 
dist 38=[-14.571348514397662571  ,-3.7716721692202771932 ] 
dist 39=[-14.563737839847461070  ,-2.9698436112710827572 ] 
dist 40=[-14.569929279850335112  ,-2.4037553409364327892 ] 
dist 41=[-14.753414533977738615  ,-1.9041064485283714190 ] 
dist 42=[-14.827498318559428251  ,-1.3669250114687371950 ] 
dist 43=[-14.829635061235950780  ,-.84852779242843419099] 
dist 44=[-11.408960573494477504  ,.8529103674759789700 ] 
dist 45=[-11.265312332014919160  ,2.3369803521242316565 ] 
dist 46=[-11.110699313109862773  ,3.5988268252588348880 ] 
dist 47=[-11.028929596835279745  ,4.8857577898689400948 ] 
dist 48=[-1.5390381457767291787 ,6.0892148453250547292 ] 
dist 49=[-.9638423439733315913 ,7.0180695724028793103 ] 
dist 50=[-.8961633893421923261 ,7.9232377775124123702 ] 
dist 51=[-.4866311712400968862 ,9.0323020140641896778 ] 
dist 52=[-.4185277104617544335 ,10.078813405752654631  ] 
dist 53=[-.2819081351684906048 ,10.734403803145887764  ] 
dist 54=[-.2509619783760471895 ,11.229184637623293965  ] 
dist 55=[2.1911057346552639865 ,11.633978222827778818  ] 
dist 56=[2.3523281874508972895 ,11.950264644620019294  ] 
dist 57=[2.6712066240607630870 ,12.091879737071372325  ] 
dist 58=[2.7426031881141395452 ,12.138621881498992541  ] 
dist 59=[2.8812956018015032741 ,12.129925550637025925  ] 
dist 60=[2.1063596924852763162 ,11.909110397967700708  ] 
dist 61=[1.5664523980771246986 ,11.837518819639490755  ] 
dist 62=[1.0966154148798853378 ,11.567370756368236589  ] 
dist 63=[0                     ,11.094544456205135403  ] 
dist 64=[.12812333469344728659,3.6739906429327942739 ] 
dist 65=[-.25164738093344749643,3.6851308068616206939 ] 
dist 66=[-.63531356431036682095,3.6857764575597504978 ] 
dist 67=[-1.1239063196524071301 ,3.5773720568539523163 ] 
dist 68=[-1.5934892491140912206 ,3.5470911075593360294 ] 
dist 69=[-1.9013649620596210840 ,3.5269449926098295162 ] 
dist 70=[-2.1495570709826136598 ,3.5153229055812247017 ] 
dist 71=[-2.3810743131318263728 ,2.7426285211015602487 ] 
dist 72=[-2.5842961364546902404 ,2.6474951077311455871 ] 
dist 73=[-2.7196589135995998499 ,2.4112370529646631165 ] 
dist 74=[-2.8315768640958700999 ,2.3667350212717254815 ] 
dist 75=[-2.9413882625785424427 ,1.9898807467897430566 ] 
dist 76=[-3.0331702833023817325 ,1.9146060532045404886 ] 
dist 77=[-3.0731487424407237318 ,1.8070057049141882436 ] 
dist 78=[-3.0896803331315201256 ,1.7733010809050806681 ] 
dist 79=[-3.0876900287214462940 ,1.0758934823638399903 ] 
dist 80=[-3.0891753668890541330 ,.98351501716184630256] 
dist 81=[-3.1663184340552607370 ,.7784912828867742595 ] 
dist 82=[-3.2214823972784090084 ,.7300464164774152496 ] 
dist 83=[-3.2583987083187766529 ,.4821340370790364722 ] 
dist 84=[-3.2638948486709573302 ,.4364671154128945479 ] 
dist 85=[-3.2902758306224309147 ,.3354342364439439343 ] 
dist 86=[-3.3073565093513209188 ,.3107892529921500799 ] 
dist 87=[-3.3051904366780115217 ,.40016401610423433693] 
dist 88=[-3.2472793857602098571 ,.76192311428931619367] 
dist 89=[-3.2242012851995682797 ,1.0665086382465082197 ] 
dist 90=[-3.1991929147458246231 ,1.3723150003580331861 ] 
dist 91=[-3.1830724596660639060 ,1.6552071573499313970 ] 
dist 92=[-2.6916188858135706957 ,1.8683763574185265682 ] 
dist 93=[-2.6230979672914873496 ,2.0711765598213029596 ] 
dist 94=[-2.4493180785305583266 ,2.3127212011669608124 ] 
dist 95=[-2.4133489235669658397 ,2.5371422958866608994 ] 
dist 96=[-2.1177140981534202580 ,2.6716255014025199036 ] 
dist 97=[-2.0561774306599623051 ,2.7659912356147053176 ] 
dist 98=[-1.9657837358578504851 ,2.8303366703497416534 ] 
dist 99=[-1.9371476504472625035 ,2.8743481037822313839 ] 
dist 100=[-1.3196948451630450989 ,3.0176383514029219068 ] 
dist 101=[-1.2358963063780966540 ,3.1032634576947472513 ] 
dist 102=[-1.0503903862434039352 ,3.1622873965254351004 ] 
dist 103=[-1.0026229835540536450 ,3.2005913479221738370 ] 
dist 104=[-.7750255948968201512 ,3.2227496110495127368 ] 
dist 105=[-.7316789810680666956 ,3.2234967182488108431 ] 
dist 106=[-.6315503649276445757 ,3.2029972626635166115 ] 
dist 107=[-.6079868798787193072 ,3.1896995035029676281 ] 
dist 108=[1.1935268953583858458 ,1.8805797255468291597 ] 
dist 109=[1.1149904687104314355 ,1.7611174347506067559 ] 
dist 110=[.96793027557144328637,1.7211504921030345643 ] 
dist 111=[.80393540108766591491,1.8015883684968926176 ] 
dist 112=[.65780517960776755068,1.8526512394143059272 ] 
dist 113=[.49685053718885897114,1.8920344263568562468 ] 
dist 114=[.27367442906187485443,1.9258413783162628060 ] 
dist 115=[.02765757976959707951,1.9535232702987708733 ] 
dist 116=[-.22446463231692860049,1.9684521963748554515 ] 
dist 117=[-.52930932907918126431,1.9769151914653720464 ] 
dist 118=[-.98575465367104605844,1.9787818362455950166 ] 
dist 119=[-1.4390365914043123238 ,-.2537526725452977881 ] 
dist 120=[-1.7312595053936754548 ,-.4240797715509678561 ] 
dist 121=[-1.9616188387597909740 ,-.4551017960712152971 ] 
dist 122=[-2.1675890704300697537 ,-.4994318918926624324 ] 
dist 123=[-2.3420098951298114662 ,-.5064708216102295188 ] 
dist 124=[-2.4465762512905611758 ,-1.1012794701245646178 ] 
dist 125=[-2.5199928711020337560 ,-1.1496787125651496812 ] 
dist 126=[-2.5700955580682157138 ,-1.2142015153016877191 ] 
dist 127=[-2.6069567361443301015 ,-1.2189502163566497184 ] 
dist 128=[-2.6275261722060974944 ,-1.2009733401337258704 ] 
dist 129=[-2.6401140158205906361 ,-1.1500274462954006597 ] 
dist 130=[-2.6451192754107218175 ,-1.0652633898262427451 ] 
dist 131=[-2.6448889694149559178 ,-.9123117436955850528 ] 
dist 132=[-2.6365818863148233239 ,-.7436232071912816145 ] 
dist 133=[-2.6207859499356734736 ,-.5960448753553759928 ] 
dist 134=[-2.6114948965949313469 ,-.4357393501004959909 ] 
dist 135=[-1.8039735983070191125 ,-.2162384490809027779 ] 
dist 136=[-1.8266297042178576958 ,.0244487673736154155 ] 
dist 137=[-1.8388286398471994683 ,.2693203051585195647 ] 
dist 138=[-1.8457225559407480659 ,.5641288490662945634 ] 
dist 139=[-1.8471959936761591096 ,1.0041302355651347803 ] 
dist 140=[-.09980853123786505256,1.4407306011900167584 ] 
dist 141=[.00397385149365167511,1.7219689592855147601 ] 
dist 142=[.03052474417156144955,1.9434269586988208460 ] 
dist 143=[.57068969753618257987,2.1410271979463209830 ] 
dist 144=[.63546889024651849956,2.3080722910903642654 ] 
dist 145=[.77623350229088905457,2.4077041238684363691 ] 
dist 146=[.79974846195062783643,2.4770347199636987340 ] 
dist 147=[.94285079578019218449,2.5231467998734438530 ] 
dist 148=[.96483794090930628124,2.5564112011508942456 ] 
dist 149=[1.0017155622449562119 ,2.5744659117140455574 ] 
dist 150=[1.0075150133167816525 ,2.5848519473878308217 ] 
dist 151=[1.1166910957790487143 ,2.5875091083230712884 ] 
dist 152=[1.0461790450252021063 ,2.5850185747347092238 ] 
dist 153=[.97529983526840157204,2.5759211805865496425 ] 
dist 154=[.8854607314316670763 ,2.5581271113913932404 ] 
dist 155=[.79037743919803758498,2.5480487398761823861 ] 
dist 156=[.5962328852469301199 ,1.0751146313812573260 ] 
dist 157=[.3025163232430991161 ,.9486809276669038310 ] 
dist 158=[.0550662362585068179 ,.7915420071388394644 ] 
dist 159=[-.1938338795580855890 ,.6009548493544242396 ] 
dist 160=[-.4245297468009541975 ,.55080305162250658359] 
dist 161=[-.5993312366994064963 ,.47759007824387910483] 
dist 162=[-.7666268899831019742 ,.46679593306727650284] 
dist 163=[-.9673721380248940914 ,.35139868400949462852] 
dist 164=[-1.1559491409836613455 ,.32941486052189257654] 
dist 165=[-1.2746829416833529365 ,.30459234850540198219] 
dist 166=[-1.3649724720907274494 ,.29937698149468785317] 
dist 167=[-1.4400280070184526630 ,.08593452345160339696] 
dist 168=[-1.4995310283792921170 ,.05876295012987489842] 
dist 169=[-1.5277505040980416420 ,.01654179865190098192] 
dist 170=[-1.5418645613267030072 ,.00597115896320190702] 
dist 171=[-1.5450722808738660186 ,-.00424530339378654595] 
dist 172=[-1.4416453476453367727 ,.00484162829727165878] 
dist 173=[-1.4882283920805900460 ,.02656505912201668193] 
dist 174=[-1.5312786846649921380 ,.07118348822528779830] 
dist 175=[-1.5658130851035806462 ,.1222323423070665241 ] 
dist 176=[-1.5784092951040381684 ,.169620126394674953  ] 
dist 177=[-1.5817251961531469806 ,.22337646242651231313] 
dist 178=[-1.5792182120698919106 ,.29984472956001381072] 
dist 179=[-1.5337318885980461274 ,.38502446958991607379] 
dist 180=[-1.5189198401062645094 ,.47354907736576147795] 
dist 181=[-1.5044891422651663164 ,.5820330651411659160 ] 
dist 182=[-1.4949397915026126539 ,.7457569056483265836 ] 
dist 183=[-.4265492268273711539 ,.9082569433650543616 ] 
dist 184=[-.3152027619454042597 ,1.0120827364188119886 ] 
dist 185=[-.2940972785256535255 ,1.0927801005773266996 ] 
dist 186=[-.2696364354860090919 ,1.1629782487155958630 ] 
dist 187=[-.2642127290539598817 ,1.2210315525936965616 ] 
dist 188=[-.07652075566240389553,1.2745959218083794704 ] 
dist 189=[-.05188241789324744950,1.3772468011450941619 ] 
dist 190=[-.01586040387870173146,1.4904905499271783482 ] 
dist 191=[-.00617695057393751801,1.5927186663334987505 ] 
dist 192=[-.00189393765969733268,1.6514078871252247541 ] 
dist 193=[-.0130777258889448607 ,1.6894225050617354785 ] 
dist 194=[-.0365009599668022839 ,1.7091414921593140560 ] 
dist 195=[-.0827197640921212617 ,1.7192767211818320401 ] 
dist 196=[-.1350367163169737968 ,1.7190437824970471270 ] 
dist 197=[-.1827985424983155746 ,1.7123904896864553952 ] 
dist 198=[-.2363458415558864703 ,1.7067343841262291563 ] 
dist 199=[-.3117556929605781842 ,1.5404754320341524449 ] 
dist 200=[-.3954144424285204600 ,1.4943893750247523574 ] 
dist 201=[-.5402565102030925636 ,1.4796844772668661611 ] 
dist 202=[-.68183798402382227742,1.4642605128126020022 ] 
dist 203=[-.8093677068972012108 ,1.4549048257860968436 ] 
dist 204=[-.9043974528285866431 ,.84021669472310577284] 
dist 205=[-1.0050636115148499091 ,.7938715337565177433 ] 
dist 206=[-1.0831434466576317547 ,.78016118083581676055] 
dist 207=[-1.1507845316582521772 ,.39356313533787634453] 
dist 208=[-1.2065194310721300855 ,.34448560314436041994] 
dist 209=[-1.2558530879676183259 ,.24111529596843562916] 
dist 210=[-1.3565919477897553677 ,.21364017872122475118] 
dist 211=[-1.4677643442747368724 ,.11005511632352698025] 
dist 212=[-1.5681130848449457384 ,.08989716189898802685] 
dist 213=[-1.6256562272865099697 ,.05034892583863950553] 
dist 214=[-1.6628438175235608469 ,.04061834753361284358] 
dist 215=[-1.6819564090665225165 ,.03356129761980342444] 
dist 216=[-1.6916936219800689364 ,.06489443274908354592] 
dist 217=[-1.6914650505354763047 ,.09724467993192540390] 
dist 218=[-1.6849035765047329751 ,.1394090616059087342 ] 
dist 219=[-1.6794640838161724411 ,.1846239958566364115 ] 
dist 220=[-1.2515355104774536865 ,.2291498982109319180 ] 
dist 221=[-1.2052272850946659553 ,.39119071774633825798] 
dist 222=[-1.0870469913408621288 ,.53550062776626481693] 
dist 223=[-1.0681814123692578933 ,.6750073391586478059 ] 
dist 224=[-.8711424348331969909 ,.80068300247133412693] 
dist 225=[-.8322171607541659994 ,.88979505528399289549] 
dist 226=[-.7867914471018372626 ,.96915486765874770509] 
dist 227=[-.7733390544218892875 ,1.0559100936605778661 ] 
dist 228=[-.3928823390256159794 ,1.1346454132418161360 ] 
dist 229=[-.3445591241522487637 ,1.1819993079138516131 ] 
dist 230=[-.2428530193734064423 ,1.2154135874516885710 ] 
dist 231=[-.2158237813225588275 ,1.2385196711435637763 ] 
dist 232=[-.1139691346122581648 ,1.2534257378417307111 ] 
dist 233=[-.0941091930536740287 ,1.2563444186602916526 ] 
dist 234=[-.0552270898781849928 ,1.2506590139725144792 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 2, 0, 2, 0, 1] 
dist 0=[54.619381784506297482  ,54.619381784506297482  ] 
dist 1=[54.177235338055751501  ,54.996025177789397631  ] 
dist 2=[52.788483822736244919  ,55.491272067297757783  ] 
dist 3=[51.083641029901686087  ,55.707627851226575696  ] 
dist 4=[49.122294533838715676  ,55.802338849751924623  ] 
dist 5=[46.593611325120014987  ,55.811852114579184430  ] 
dist 6=[42.623160236241249933  ,55.760211550188763688  ] 
dist 7=[38.581724091001460099  ,55.669501814023338960  ] 
dist 8=[35.769484338429564514  ,55.409839414051693196  ] 
dist 9=[33.313541646861191054  ,55.274225904613497689  ] 
dist 10=[30.694691807363865100  ,54.885518595967729814  ] 
dist 11=[28.164499549786273682  ,54.701503061739479202  ] 
dist 12=[26.062378695825060910  ,53.673664818995959082  ] 
dist 13=[23.865896987722190121  ,53.359230594812882156  ] 
dist 14=[20.958467297314229782  ,52.006854252599253006  ] 
dist 15=[18.092406213249118824  ,49.457531199728535228  ] 
dist 16=[16.060889190520749989  ,31.293839396911186513  ] 
dist 17=[14.245294073381582728  ,29.570760970454427848  ] 
dist 18=[12.241205041720206129  ,27.848295069666336150  ] 
dist 19=[10.259938437114876552  ,27.598867805642180336  ] 
dist 20=[8.5350097630648373335 ,20.033007267984883240  ] 
dist 21=[6.6595153245751814334 ,19.170626418403039640  ] 
dist 22=[4.0758573269055146681 ,17.643848332153500583  ] 
dist 23=[1.5537113117478908414 ,17.318346588527142077  ] 
dist 24=[-.07620900720276617397,14.308671317990335362  ] 
dist 25=[-1.3733931146902657740 ,13.930172758110374882  ] 
dist 26=[-2.5658696471017736790 ,13.266346382678892691  ] 
dist 27=[-3.6083716310667672664 ,13.122713523130766808  ] 
dist 28=[-4.3063677197684820145 ,7.9059958464372312890 ] 
dist 29=[-4.8907224491518129656 ,7.4653377772614856434 ] 
dist 30=[-5.4794901933382918259 ,5.6673489961742809878 ] 
dist 31=[-7.8267270555365516705 ,2.7965806565925978630 ] 
dist 32=[-10.255720863227299185  ,-2.9898504688678725388 ] 
dist 33=[-11.756797688971073241  ,-3.3262330117843266809 ] 
dist 34=[-12.874750834962867353  ,-4.0432211747060828469 ] 
dist 35=[-13.772752084976621182  ,-3.6436729213446537291 ] 
dist 36=[-14.486815986694191424  ,-3.0432973900734210121 ] 
dist 37=[-14.869499732381516147  ,-2.2526705139675829515 ] 
dist 38=[-15.085892912745993838  ,-1.0009694180347364322 ] 
dist 39=[-15.134721562143967322  ,.26762891382423637457] 
dist 40=[-14.481569103878313818  ,1.1258485944309634798 ] 
dist 41=[-14.342123974239526658  ,1.8445275532499493135 ] 
dist 42=[-14.199402279754817677  ,2.5569413067865800166 ] 
dist 43=[-14.111367216610640183  ,3.2079469654689682818 ] 
dist 44=[-13.978842445650833948  ,3.6818732324678779785 ] 
dist 45=[-13.918029807399835922  ,4.1155058044156757388 ] 
dist 46=[-13.876468240519570843  ,4.6059546623549410960 ] 
dist 47=[-13.850976124773033519  ,5.0489079358621784318 ] 
dist 48=[-4.2265581936817334901 ,5.2931076857833742498 ] 
dist 49=[-3.4460523329883725941 ,5.4378571808439719269 ] 
dist 50=[-1.6569711372267676376 ,5.4840161667524765171 ] 
dist 51=[-1.3551941834189973384 ,5.4933335025551100316 ] 
dist 52=[.21004589761431166686,5.4911782870413735418 ] 
dist 53=[.18026498340420874535,5.4802534580829248996 ] 
dist 54=[.07840458680598486880,5.7755303940892700484 ] 
dist 55=[-.03531680437545479334,5.9969703924060585167 ] 
dist 56=[-.11241582464213991544,6.1604062079061766702 ] 
dist 57=[-.17712626142868914103,6.8057513537831304026 ] 
dist 58=[-.24147220866800677752,7.3635090868738754217 ] 
dist 59=[-.3003627382480076676 ,7.8368954274318351401 ] 
dist 60=[-.3433316545755841342 ,8.2199284542739959116 ] 
dist 61=[-.3827226171125042657 ,8.4170322358495450320 ] 
dist 62=[-.4273577252218648493 ,8.5186415051667999250 ] 
dist 63=[-.4681348683075513794 ,8.5364219742361237420 ] 
dist 64=[-.4921426339585698149 ,3.7277184979130064216 ] 
dist 65=[-.5412755736501646763 ,3.5997753286929150150 ] 
dist 66=[-.9722402136344617372 ,3.4400492872054851740 ] 
dist 67=[-1.5324018889497382703 ,3.3822472510660421758 ] 
dist 68=[-2.0760810889145368585 ,2.1376456219597990732 ] 
dist 69=[-2.4413360020269264762 ,1.9776227269606791000 ] 
dist 70=[-2.7455285899011261556 ,1.6292325372394445095 ] 
dist 71=[-3.0456403666473073195 ,1.5467043714631859132 ] 
dist 72=[-3.3201156104601364139 ,1.1587020851577998266 ] 
dist 73=[-3.5220825645921120882 ,1.0900225040943698559 ] 
dist 74=[-3.7098011746984012067 ,.9298701409117254872 ] 
dist 75=[-3.9275448925064666522 ,.9047651845764305757 ] 
dist 76=[-4.1243688186871583118 ,.4468355057091611788 ] 
dist 77=[-4.2286141896517655962 ,.51691717001714732563] 
dist 78=[-4.2853762438189591483 ,.63839468064958181037] 
dist 79=[-4.2965862659533777409 ,.86072805249184186977] 
dist 80=[-4.3685539566806119075 ,1.0941008628234831691 ] 
dist 81=[-4.6546442508499810016 ,1.2596224106503916273 ] 
dist 82=[-4.8584679476537500999 ,1.4062989103126653432 ] 
dist 83=[-5.0038680100251715859 ,1.5646000939904927064 ] 
dist 84=[-5.1086408720143738900 ,1.7173843812293506306 ] 
dist 85=[-5.1502598817276577983 ,1.8542276931662569564 ] 
dist 86=[-5.1591891363342081595 ,1.9944820130600821013 ] 
dist 87=[-5.1503952866979254749 ,2.1725170054783347309 ] 
dist 88=[-4.7633803978836138649 ,2.3425113335268312683 ] 
dist 89=[-4.6928271432051031032 ,2.4507030335851878815 ] 
dist 90=[-4.5590625897650616055 ,2.5339220165851843524 ] 
dist 91=[-4.5422922792731296912 ,2.6043321150751374158 ] 
dist 92=[-4.2901375837590266107 ,2.6607309564286237344 ] 
dist 93=[-4.2403394214208767361 ,2.6880689449116041152 ] 
dist 94=[-4.0935889725719898921 ,2.6991642671592651019 ] 
dist 95=[-4.0610001548149603802 ,2.8360886758719936959 ] 
dist 96=[-3.2513636136863962531 ,3.2478566185985321788 ] 
dist 97=[-3.1696424451654723917 ,3.5301084927043899646 ] 
dist 98=[-3.0489140685624633160 ,3.7716043127384020434 ] 
dist 99=[-3.0101115021101214444 ,4.0207439884109058946 ] 
dist 100=[-2.1565466757651456194 ,4.2418196758997352121 ] 
dist 101=[-2.0398486146541749488 ,4.4022593672591884306 ] 
dist 102=[-1.7815267655724684661 ,4.5111773962750524088 ] 
dist 103=[-1.7134126898455794106 ,4.5655533376290564713 ] 
dist 104=[-1.3949125121553513768 ,4.5935669609033323072 ] 
dist 105=[-1.3337220361154104419 ,4.5972372013675526734 ] 
dist 106=[-1.1906639668943659274 ,4.5838306987607557230 ] 
dist 107=[-1.1574573750676648670 ,4.5704005058958044272 ] 
dist 108=[-.2887869574718480153 ,2.8451122611970655521 ] 
dist 109=[-.3013588986119224505 ,2.6888059138978507993 ] 
dist 110=[-.3140285830760550139 ,2.2998304741019747176 ] 
dist 111=[-.3247930099532275519 ,2.2415790151307911232 ] 
dist 112=[-.3297602364685848311 ,1.6427627038506132236 ] 
dist 113=[-.3320464297723870100 ,1.5298162406555862807 ] 
dist 114=[-.3321055337621392731 ,1.3969024200198983548 ] 
dist 115=[-.3257741918660961550 ,1.3669442757177527317 ] 
dist 116=[-.3234863726546209383 ,.3754690854772190325 ] 
dist 117=[-.3215315422559919087 ,.2546295397499809756 ] 
dist 118=[-.3197446772272437199 ,.20920651038160874144] 
dist 119=[-.4853453662529403332 ,.1730411956189191747 ] 
dist 120=[-.73150856943985963433,.1954578265818175512 ] 
dist 121=[-.93666658581743778771,.2125443967977035638 ] 
dist 122=[-1.1511708928426378485 ,.2268121646716442120 ] 
dist 123=[-1.4346771487266005302 ,.2382604858410874575 ] 
dist 124=[-1.7109335496062640482 ,.2440957759264975315 ] 
dist 125=[-1.8965085596595044440 ,.24716974776493796023] 
dist 126=[-2.0513376601787741686 ,.24763678320844610115] 
dist 127=[-2.2048595627509034190 ,.24142582276304272144] 
dist 128=[-2.3459462989168991451 ,.23945743628907807896] 
dist 129=[-2.4511370531186179614 ,.23719659630620573535] 
dist 130=[-2.5502789880522826682 ,.23582198733195890104] 
dist 131=[-2.6672241411870767317 ,.23196536931883439339] 
dist 132=[-2.7755555678638545322 ,.23024691734265319636] 
dist 133=[-2.8403127138140362968 ,.22683302217818256078] 
dist 134=[-2.8856275239716525646 ,.23731121265639338197] 
dist 135=[-2.9163434687199868397 ,.28924313117115254162] 
dist 136=[-2.9353895676417816921 ,.32246975980371480865] 
dist 137=[-2.9345546832437171963 ,.46820720333725872983] 
dist 138=[-2.9232821430872053151 ,.89096973061623734775] 
dist 139=[-2.9117428720457529363 ,1.5236794325471297023 ] 
dist 140=[-.1232533502603723038 ,2.1513156946281224051 ] 
dist 141=[-.1420824995332388175 ,2.5538344316154632713 ] 
dist 142=[-.1647705663533676182 ,2.8684794477855134683 ] 
dist 143=[-.1859622239647830208 ,3.1454079839718974583 ] 
dist 144=[-.1988204680008806914 ,3.3791932228803677517 ] 
dist 145=[-.2080263875734513490 ,3.5486795836714197860 ] 
dist 146=[-.2146444300332433807 ,3.6746200034752771226 ] 
dist 147=[-.2194611365562690278 ,3.7740456808414696265 ] 
dist 148=[-.2214791378043619731 ,3.8530252190342249391 ] 
dist 149=[-.2219706197377780420 ,3.8973651731595410352 ] 
dist 150=[-.2216753923595881521 ,3.9248314551979522460 ] 
dist 151=[-.22849772275892470423,3.9364678081120336894 ] 
dist 152=[-.24403278880760713659,3.9370621703927716482 ] 
dist 153=[-.25642029509663289122,3.9262124055942517884 ] 
dist 154=[-.2677625343431577717 ,3.8949496215139166257 ] 
dist 155=[-.2775729618764595258 ,3.8759900147027119898 ] 
dist 156=[-.2890474663880074706 ,1.8115149404284905953 ] 
dist 157=[-.3183611553064582417 ,1.6307178984199705107 ] 
dist 158=[-.3521869387655818295 ,1.1958280338729797126 ] 
dist 159=[-.3831974131372093624 ,1.1296315925104571604 ] 
dist 160=[-.6380100419832150614 ,.51346300619578938063] 
dist 161=[-.8956366442372405312 ,.40167132849633482508] 
dist 162=[-1.1405437096764928977 ,.25651900129768533059] 
dist 163=[-1.4320478198194945746 ,.22149418005214466176] 
dist 164=[-1.7058178834560646736 ,.1248441078127548938 ] 
dist 165=[-1.8799506848962309967 ,.1259268960297751055 ] 
dist 166=[-2.0144090201324325623 ,.1261422635080307101 ] 
dist 167=[-2.1298371305588943008 ,.1844480010003211175 ] 
dist 168=[-2.2241644514014050429 ,.2307895977969176006 ] 
dist 169=[-2.2744086927604665432 ,.2675042610728990641 ] 
dist 170=[-2.3019686661154701943 ,.3006720449551365179 ] 
dist 171=[-2.3063614016767393818 ,.3290172674546345549 ] 
dist 172=[-1.8365558482277066285 ,.3464858462553888421 ] 
dist 173=[-1.7935739141510046357 ,.3593340760330637147 ] 
dist 174=[-1.6833561938243725991 ,.3692409800390975312 ] 
dist 175=[-1.6597789799407301576 ,.37711377796684293407] 
dist 176=[-1.4684528038481476354 ,.38184379818714681366] 
dist 177=[-1.4283910914599176812 ,.38518276041964003357] 
dist 178=[-1.3680002409710196404 ,.38750208173542132643] 
dist 179=[-1.3493033203038010429 ,.38899215288744133666] 
dist 180=[-.9479996805546095261 ,.38902057703936032301] 
dist 181=[-.8937297091040966208 ,.38798457332333062942] 
dist 182=[-.7712261772562218865 ,.3866956645751494007 ] 
dist 183=[-.7422457626820281770 ,.38780199471237270035] 
dist 184=[-.5861437687451460262 ,.40743783988154331626] 
dist 185=[-.5566741099492199867 ,.53749726025256681092] 
dist 186=[-.4941873717498120807 ,.7255467763724749559 ] 
dist 187=[-.4767657861128351415 ,.9917219646558197698 ] 
dist 188=[-.09130912391821861423,1.2535411104209976739 ] 
dist 189=[-.05991321463136359943,1.4242076029808931114 ] 
dist 190=[-.01548443863440402185,1.5607621120854150908 ] 
dist 191=[-.1231767825607619991 ,1.7157935913108270960 ] 
dist 192=[-.2336685435597249871 ,1.8633728783840282437 ] 
dist 193=[-.3471681348517250740 ,1.9670692706774604015 ] 
dist 194=[-.4943963662819443180 ,2.0584673421899525545 ] 
dist 195=[-.65197633390812099137,2.1569667158905850923 ] 
dist 196=[-.80678706888173832519,2.2431960915329113894 ] 
dist 197=[-.98916706192387643891,2.2856255150834670859 ] 
dist 198=[-1.2567699450517342298 ,2.3066226083065470001 ] 
dist 199=[-1.5202102983842737502 ,2.3084433797675526837 ] 
dist 200=[-1.6859777816024891804 ,2.2772823978989183175 ] 
dist 201=[-1.8118761252674608257 ,2.2635908788077124951 ] 
dist 202=[-1.9162051738490740358 ,2.2500312190894860035 ] 
dist 203=[-1.9993341144232427500 ,2.2384324278218786489 ] 
dist 204=[-2.0406271882270950583 ,1.6533415114768856644 ] 
dist 205=[-2.0617516597818206939 ,1.6553029083138168009 ] 
dist 206=[-2.0643912443127484460 ,1.6514489918636338366 ] 
dist 207=[-2.0087487967143692620 ,1.6005419717791976446 ] 
dist 208=[-1.9923266813081795794 ,1.5875291411492940517 ] 
dist 209=[-1.9773704768207256216 ,1.5477201269416802280 ] 
dist 210=[-2.1070582975632762797 ,1.5355055859250282329 ] 
dist 211=[-2.2407496088558862889 ,1.4379652017224096740 ] 
dist 212=[-2.3593396428272078916 ,1.4144650122021693319 ] 
dist 213=[-2.4287605949063527367 ,1.3787927989827165093 ] 
dist 214=[-2.4754339091707847397 ,1.3664569085687289718 ] 
dist 215=[-2.5032417078160706899 ,.81803989896480850671] 
dist 216=[-2.5168192377397861795 ,.7555644819476380136 ] 
dist 217=[-2.5174745934503800104 ,.62701063134576237158] 
dist 218=[-2.4922381082371603070 ,.59282417634313597997] 
dist 219=[-2.4884731496476978211 ,.4653067650634831960 ] 
dist 220=[-1.6702192376392371440 ,.4387511547574621033 ] 
dist 221=[-1.6095959564465803558 ,.4959900533987648613 ] 
dist 222=[-1.4532954466876188181 ,.68644226457510308765] 
dist 223=[-1.4287792545883370535 ,.8711139714072503415 ] 
dist 224=[-1.1658712062312141467 ,1.0378451371628279144 ] 
dist 225=[-1.1138729848804835578 ,1.1566991129477588120 ] 
dist 226=[-1.0547708936776611573 ,1.2631957616450141700 ] 
dist 227=[-1.0383196229277485514 ,1.3806096282226211278 ] 
dist 228=[-.52315822894224956823,1.4873794553072148078 ] 
dist 229=[-.45799758381969811324,1.5513979390416122557 ] 
dist 230=[-.32189317664973064122,1.5963306957313187986 ] 
dist 231=[-.28597587551127669956,1.6269350892603075746 ] 
dist 232=[-.15235120384048181324,1.6467618076340907462 ] 
dist 233=[-.1258719351511176408 ,1.6503284177941472051 ] 
dist 234=[-.07671066477528468699,1.6446402988053122493 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 0, 2, 0, 2] 
dist 0=[48.924324667453222958  ,48.924324667453222958  ] 
dist 1=[47.794604650745231284  ,49.829144267574098148  ] 
dist 2=[46.446007556981171917  ,50.279480722216906810  ] 
dist 3=[44.675853341854383843  ,50.515933606653846616  ] 
dist 4=[41.862507542590130923  ,50.566850087239719985  ] 
dist 5=[38.983479263882071696  ,50.235221608655854596  ] 
dist 6=[36.950923448157513982  ,50.097301530806208250  ] 
dist 7=[35.144516540256456048  ,49.915321523283310139  ] 
dist 8=[33.168454355202985888  ,49.812229765691678551  ] 
dist 9=[31.228382436810574589  ,49.413661490641745174  ] 
dist 10=[29.565522066817038911  ,49.269961290223240068  ] 
dist 11=[27.782413767365489812  ,48.879572138076526011  ] 
dist 12=[25.361750176090024335  ,48.710480759749487363  ] 
dist 13=[22.946181601077438139  ,47.808189213827986496  ] 
dist 14=[21.183221187743090151  ,47.557115919175530201  ] 
dist 15=[19.554634588554499229  ,46.367698508406715464  ] 
dist 16=[17.675473330804213792  ,44.175474886286928719  ] 
dist 17=[15.769854194776152742  ,28.653050197903290106  ] 
dist 18=[14.035197026551515233  ,27.178406701756727077  ] 
dist 19=[12.085599240433841336  ,25.692036490617132747  ] 
dist 20=[9.3205989448217325001 ,25.398860604514918279  ] 
dist 21=[6.5966553868179522845 ,19.311987624750161494  ] 
dist 22=[4.8109643891832422204 ,18.628323295356957962  ] 
dist 23=[3.3617857483705831331 ,17.307978634335243065  ] 
dist 24=[1.9825614819820261781 ,16.997174570023497891  ] 
dist 25=[.74503116261040410765,14.321054118645315601  ] 
dist 26=[-.13803523578036918706,13.989167468065204564  ] 
dist 27=[-.93584540533647908387,13.268845464802969267  ] 
dist 28=[-1.8329889815410225392 ,13.100879821392400866  ] 
dist 29=[-2.6556864352419266567 ,4.6492464183067321243 ] 
dist 30=[-3.6830382067091548559 ,4.0751378518661527680 ] 
dist 31=[-5.3443038873989001177 ,2.5253211337963790857 ] 
dist 32=[-6.9181691607543179001 ,1.6908442282835192306 ] 
dist 33=[-8.9482202151520694213 ,-.2272399560764821472 ] 
dist 34=[-10.463863809450166010  ,-.5524459802548520542 ] 
dist 35=[-11.608063027197398318  ,-1.2019901730410894796 ] 
dist 36=[-12.555363845820973290  ,-1.3571998209824411623 ] 
dist 37=[-13.316729794475838822  ,-1.1059478063485573252 ] 
dist 38=[-13.717659986688024768  ,-.73408723916137681374] 
dist 39=[-13.937974754078113103  ,-.41272482959096960544] 
dist 40=[-13.986415367347135507  ,-.08051362869355461734] 
dist 41=[-13.778997511862973070  ,.22993218246827128572] 
dist 42=[-13.708456739149457463  ,.46478883586481516718] 
dist 43=[-13.638613068306068946  ,.68762071810048666656] 
dist 44=[-13.573870234283990325  ,.95033589896951073534] 
dist 45=[-13.470444784112091738  ,1.1916910361971114407 ] 
dist 46=[-13.398734222333193285  ,1.3294185966133164478 ] 
dist 47=[-13.323269778148212242  ,1.4167670704432579091 ] 
dist 48=[-13.265447856746300225  ,1.4572300370932610570 ] 
dist 49=[-5.1187329663491712297 ,1.4779064228466028444 ] 
dist 50=[-4.4385775240749349778 ,1.4864458990679555398 ] 
dist 51=[-2.8609147993345782005 ,1.4876880123042278645 ] 
dist 52=[-2.6006998324501096834 ,1.6872672013149699897 ] 
dist 53=[-.5619837063693714955 ,2.4320512339188669711 ] 
dist 54=[-.2051800098149988696 ,2.9034793292722297901 ] 
dist 55=[.3543756908239573525 ,3.3105204576246165722 ] 
dist 56=[.4887875753566393986 ,4.3623423923478162150 ] 
dist 57=[1.3972664106912089607 ,5.3494013812040935692 ] 
dist 58=[1.3864202098462620058 ,5.9597885018803938617 ] 
dist 59=[1.3407373335394209991 ,6.4113612527801760418 ] 
dist 60=[1.2357442451738568714 ,6.7644981748360283750 ] 
dist 61=[1.1124229463958724290 ,7.0417565607164657372 ] 
dist 62=[.99358064069955899641,7.1904739089718803212 ] 
dist 63=[.8553562259131637103 ,7.2736587182299851424 ] 
dist 64=[.6546578834681496145 ,7.2894027476063495596 ] 
dist 65=[.4292554915325620287 ,4.0461167005152240481 ] 
dist 66=[.1924256276867882753 ,3.8636056302787920833 ] 
dist 67=[-.0980822793324846405 ,3.4349474582034636686 ] 
dist 68=[-.5377247160690450587 ,3.3448422711217808405 ] 
dist 69=[-.9763339363407654057 ,3.0931772612039284615 ] 
dist 70=[-1.2627198765219043260 ,3.0467180905848683247 ] 
dist 71=[-1.4923825258078803665 ,2.9601899163303894218 ] 
dist 72=[-1.7046029405386412006 ,2.9354579880618501892 ] 
dist 73=[-1.8892893314142305735 ,2.8402544155206241401 ] 
dist 74=[-2.0090570029338073329 ,2.8136500051832058003 ] 
dist 75=[-2.1041494597976472228 ,2.7639455773829188139 ] 
dist 76=[-2.8354921247930311511 ,2.7481919833750572117 ] 
dist 77=[-3.6689651770778898245 ,1.5705594023369857645 ] 
dist 78=[-4.1988933893224758796 ,1.6039136876667732045 ] 
dist 79=[-4.6083201164033677516 ,1.6620041214270929177 ] 
dist 80=[-4.9607796419371282294 ,1.7681109934801870962 ] 
dist 81=[-5.2500106125179580527 ,1.8777907619842033278 ] 
dist 82=[-5.4384160802152874534 ,1.9501171862982552682 ] 
dist 83=[-5.5629703466818634397 ,2.0081487980732510682 ] 
dist 84=[-5.6330577860195193503 ,2.0608913569688924298 ] 
dist 85=[-5.6761700144007753084 ,2.1053322968481679745 ] 
dist 86=[-5.6930476872641702936 ,2.1302683643093741478 ] 
dist 87=[-5.6940816123897966838 ,2.1451476983368472604 ] 
dist 88=[-5.6778798798812805438 ,2.1494457354720532235 ] 
dist 89=[-5.6418728958609934753 ,2.1453722376615392517 ] 
dist 90=[-5.6167267332472194936 ,2.1395474466183148767 ] 
dist 91=[-5.5448636119006732539 ,2.1068249591797161050 ] 
dist 92=[-5.5096823858852430445 ,2.0967893546049851356 ] 
dist 93=[-4.1808572536860884923 ,1.9681670187587418245 ] 
dist 94=[-4.1408808733872452762 ,1.9348235086750163843 ] 
dist 95=[-4.0483290097567807755 ,1.9006170920391137750 ] 
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dist 134=[-3.0044106220476872130 ,.42991019043071583203] 
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dist 138=[-2.8781704918695362835 ,1.0273076208862013625 ] 
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dist 148=[-1.2336436358529429051 ,3.0532404835094747635 ] 
dist 149=[.77304141328006793275,3.2212128561129364943 ] 
dist 150=[.87027053411651872908,3.3183529272968114517 ] 
dist 151=[1.0830458607772654132 ,3.3821907222449747296 ] 
dist 152=[1.1176483225276339735 ,3.4172543198861705270 ] 
dist 153=[1.2541946224202797157 ,3.4335570703487357217 ] 
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dist 155=[.66290979330530631452,3.4039599074857436799 ] 
dist 156=[.16573428692276940875,3.3902394032711316809 ] 
dist 157=[-.33295642305851183322,2.3606266309381066035 ] 
dist 158=[-.66580459185482406597,2.2729093412539468815 ] 
dist 159=[-.94081411868881688436,2.0474232789231505264 ] 
dist 160=[-1.2086740949983744893 ,2.0121949841300368730 ] 
dist 161=[-1.4513311919287832343 ,1.6677936030708294652 ] 
dist 162=[-1.6257564994231643284 ,1.6641724382861862504 ] 
dist 163=[-1.7835462600997163521 ,1.6457836838941529101 ] 
dist 164=[-1.9598090407335424704 ,1.6365248922672616393 ] 
dist 165=[-2.1206599033119768262 ,.8619932407772566316 ] 
dist 166=[-2.2169427384042586330 ,.7915400304761597117 ] 
dist 167=[-2.2843278187344349621 ,.6202169899427163227 ] 
dist 168=[-2.3298556398073918447 ,.5942975767495849515 ] 
dist 169=[-2.3598800282545379310 ,.3446122304949162585 ] 
dist 170=[-2.3653917282482981966 ,.2986708674130390873 ] 
dist 171=[-2.3611967129469690944 ,.2411247046362662614 ] 
dist 172=[-2.3573247919540663557 ,.2275878976311904043 ] 
dist 173=[-.7869359791723951014 ,-.1387605189499491984 ] 
dist 174=[-.8603660793333566752 ,-.1827452130783068682 ] 
dist 175=[-.9159272294987091948 ,-.18968188648843071474] 
dist 176=[-.9616086396837844589 ,-.1353754437582038110 ] 
dist 177=[-.9974274623206656840 ,-.0793270850397845629 ] 
dist 178=[-1.0136273212127751515 ,-.0273118545302193784 ] 
dist 179=[-1.0213248689841087441 ,.0316847685097428172 ] 
dist 180=[-1.0232121398623393211 ,.1155976538678379059 ] 
dist 181=[-.8489723220802076031 ,.2005515348866750337 ] 
dist 182=[-.83053512615786920621,.2637047183213585468 ] 
dist 183=[-.78539330752343153728,.3229624332681968846 ] 
dist 184=[-.77316598354696093204,.3923734583179527184 ] 
dist 185=[-.69912306251726336947,.4629814445764475467 ] 
dist 186=[-.68320427774147761871,.5270188872290968273 ] 
dist 187=[-.6528823552397944933 ,.5985021442550373946 ] 
dist 188=[-.64427482547708539131,.6988302579638947455 ] 
dist 189=[-.49574401086223324969,.7959795899136571510 ] 
dist 190=[-.47473394847443165784,.85477750302547376258] 
dist 191=[-.49718365286907101819,.89674189372133881241] 
dist 192=[-.53005557637467061257,.92670822612845903611] 
dist 193=[-.55958596305872104825,.94908140372415103735] 
dist 194=[-.58034661006896383616,.96074002506433636856] 
dist 195=[-.59863747674143937802,.96678636850262266618] 
dist 196=[-.61831215540996154464,.96675697246837062322] 
dist 197=[-.63547681637531734575,.87381412100813827067] 
dist 198=[-.64375185816620970724,.85845620694771165671] 
dist 199=[-.6470876227811687450 ,.89114685239918036271] 
dist 200=[-.6470880477841568719 ,.9582400021794703625 ] 
dist 201=[-.6395687086443422392 ,1.0305938550349641735 ] 
dist 202=[-.6361383660413980807 ,1.0786266706860747114 ] 
dist 203=[-.6265886493464000382 ,1.1180327681115051445 ] 
dist 204=[-.6220815914937702571 ,1.1559591176381190158 ] 
dist 205=[-.5521856525749392274 ,1.1872419073416697480 ] 
dist 206=[-.5402154636107421386 ,1.2001341423009897445 ] 
dist 207=[-.5142832241921634083 ,1.2048629054387542798 ] 
dist 208=[-.5061598031628212354 ,1.2035644110779743022 ] 
dist 209=[-.4092271332466304519 ,1.1735652799737305521 ] 
dist 210=[-.4752305127111011150 ,1.1630544226929546043 ] 
dist 211=[-.5579905375111145107 ,1.1533358226040945572 ] 
dist 212=[-.6632217945050406059 ,1.1463280722884743676 ] 
dist 213=[-.7643999967916640407 ,-.09238702911878046073] 
dist 214=[-.8309846277731932686 ,-.16045280600192613675] 
dist 215=[-.8849567619713474632 ,-.30791160309768607417] 
dist 216=[-.9357998971918303093 ,-.31563620210163936194] 
dist 217=[-.9807163005788764752 ,-.2585057560267887769 ] 
dist 218=[-1.0110353282014236254 ,-.1895783386154085066 ] 
dist 219=[-1.0364552737162123174 ,-.09883337393705571596] 
dist 220=[-1.0893169126627292751 ,.04536693829855492034] 
dist 221=[-1.1662450349551183521 ,.19183188461638934274] 
dist 222=[-1.2108150926594808067 ,.29161488626275635704] 
dist 223=[-1.2402007573298831399 ,.3762719311526686837 ] 
dist 224=[-1.2565302368355525110 ,.4623727989440055659 ] 
dist 225=[-1.2655646254046224747 ,.5427709193648555600 ] 
dist 226=[-1.2658367648434720369 ,.6046698723394877155 ] 
dist 227=[-1.2613549241598740314 ,.6648505380116998077 ] 
dist 228=[-1.2568523381717852174 ,.7383920090458275259 ] 
dist 229=[-.92611896672000994623,.8076663043730383465 ] 
dist 230=[-.89086961023005669809,.8508177853994542628 ] 
dist 231=[-.80126012842247994578,.8830832522029274789 ] 
dist 232=[-.78653035148363634562,.9089137221616574132 ] 
dist 233=[-.63950847421318899527,.9286224411715947079 ] 
dist 234=[-.61054901778776326943,.9364575291139484742 ] 
dist 235=[-.57517032843843227903,.9384466144211433116 ] 
dist 236=[-.56369057615037484734,.9367685038518259215 ] 
dist 237=[-.28810736087940396457,.91566879443724620874] 
dist 238=[-.25286789987126667982,.90918878013894984881] 
dist 239=[-.17761713992790071581,.9193814039006107553 ] 
dist 240=[-.15850665112386404563,.9368814102362171207 ] 
dist 241=[-.07936047759169934277,.9486092251662052846 ] 
dist 242=[-.06459867073366683297,.9507467286528118469 ] 
dist 243=[-.03303806324807640119,.9477726669935909191 ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 2, 0, 0, 2] 
dist 0=[54.601966647231261462  ,54.601966647231261462  ] 
dist 1=[53.112017765700054113  ,55.808184131042608283  ] 
dist 2=[51.355096289367765744  ,56.431996789675594544  ] 
dist 3=[49.063322195595053655  ,56.764392242142534376  ] 
dist 4=[45.437525035556796913  ,56.823721222324656834  ] 
dist 5=[41.738792406868508369  ,56.589588555275514251  ] 
dist 6=[39.155637176397739753  ,56.441953454700602026  ] 
dist 7=[36.890329494550056684  ,56.250537381983028328  ] 
dist 8=[34.460495337625046889  ,56.129587466658317233  ] 
dist 9=[32.104534215645585244  ,55.619147859050847373  ] 
dist 10=[30.133925804671607377  ,55.441255532513085402  ] 
dist 11=[28.063131134646924918  ,54.909566170624289871  ] 
dist 12=[25.306570686646260069  ,54.688974976439643912  ] 
dist 13=[22.581462784688166287  ,53.386387686689666238  ] 
dist 14=[20.635984318455139250  ,53.021804301499176474  ] 
dist 15=[18.882584145622259587  ,51.473826699101338146  ] 
dist 16=[16.924183221479958051  ,48.636083041623730114  ] 
dist 17=[14.974045984367887509  ,28.794033929044236795  ] 
dist 18=[13.253117891890304228  ,27.405988327185722876  ] 
dist 19=[11.361994725803321070  ,26.192742451849252297  ] 
dist 20=[8.7309628285064132250 ,25.848351930508484266  ] 
dist 21=[6.1525327636600656374 ,17.931161103136561951  ] 
dist 22=[4.4713963354167136851 ,16.931396970225814472  ] 
dist 23=[3.1161607168478995646 ,14.809982233139987795  ] 
dist 24=[1.8402024486602282747 ,14.287717787719329166  ] 
dist 25=[.70336690277852466626,12.095724004660703227  ] 
dist 26=[-.09597770343065363899,11.692523930579478391  ] 
dist 27=[-.81559503753617798256,10.838317430559555338  ] 
dist 28=[-2.8012578401026413153 ,10.634977964832392954  ] 
dist 29=[-5.6284133727529806875 ,.94614922150636680073] 
dist 30=[-7.9047767139947589154 ,.06551268736474564274] 
dist 31=[-9.7621183057373236323 ,-1.7418180596032726777 ] 
dist 32=[-11.541037898653284880  ,-2.1719866520933653094 ] 
dist 33=[-13.139975417043081376  ,-3.1735491313012050475 ] 
dist 34=[-14.278498361445539764  ,-3.1180562831000183794 ] 
dist 35=[-15.301636721527358924  ,-2.9626457936631983362 ] 
dist 36=[-16.439886870996743500  ,-2.6345380661637727549 ] 
dist 37=[-17.464036611818568579  ,-2.2809503926422251243 ] 
dist 38=[-18.031522340284316166  ,-2.0236840052336814237 ] 
dist 39=[-18.375830663447550222  ,-1.7902147765400017632 ] 
dist 40=[-18.508637975936122496  ,-1.5310120466627393278 ] 
dist 41=[-18.550015868039239652  ,-1.2772326408154444801 ] 
dist 42=[-18.529027128924017460  ,-.64850671339650760932] 
dist 43=[-18.459028592950571299  ,.74278216453364442668] 
dist 44=[-18.398310562621703771  ,2.9072842388496824875 ] 
dist 45=[-13.902881585742680519  ,5.0845496690388962016 ] 
dist 46=[-13.773497029430937553  ,6.5269156355272486203 ] 
dist 47=[-13.351890376761242785  ,7.7063437655844559552 ] 
dist 48=[-13.281452141766994513  ,8.8344631912008172699 ] 
dist 49=[-6.2440258948377065955 ,9.8428379470589233279 ] 
dist 50=[-5.5732717052102669740 ,10.544497713093124132  ] 
dist 51=[-4.0572524660456831743 ,11.155902494326969710  ] 
dist 52=[-3.7545877486697089162 ,11.804231064749607138  ] 
dist 53=[-1.8827030766898299078 ,12.367721103412439622  ] 
dist 54=[-1.5492954812498383054 ,12.640528638141271141  ] 
dist 55=[-.90407313107803176065,12.779953639406704591  ] 
dist 56=[-.74839228591721916203,12.811033781480812697  ] 
dist 57=[.89905402974485344203,12.552771941274064566  ] 
dist 58=[.90126190056149173944,12.482559018865971268  ] 
dist 59=[.89078804558131830223,12.437747225632959066  ] 
dist 60=[.86080887276485352546,12.416443301571698690  ] 
dist 61=[.82470860947903347002,9.6292625679168824856 ] 
dist 62=[.7897670519287930379 ,9.2764541051792211983 ] 
dist 63=[.74115309170128095769,8.4358436194368173834 ] 
dist 64=[.6715547942068203317 ,7.6289170619689132846 ] 
dist 65=[.48644285066259043689,.80737260747722255495] 
dist 66=[.17407442027100450325,.79904339177977636864] 
dist 67=[-.08318514011369169393,.78368283609880565218] 
dist 68=[-.33211588901754650869,.77895352991794941196] 
dist 69=[-.5564353424058108071 ,.27209400463397832051] 
dist 70=[-.71553467617036672043,.23040321550695932759] 
dist 71=[-.85733097873667333214,.13497113667329813739] 
dist 72=[-1.0126709078168613012 ,.12094507276954322238] 
dist 73=[-1.1549907654808301166 ,-.00611856554175126195] 
dist 74=[-1.2448378672910239239 ,-.02841606939355192812] 
dist 75=[-1.3135821015542963605 ,-.05756098513397654932] 
dist 76=[-1.3716456058282607777 ,-.06331842516602302988] 
dist 77=[-1.4185041204090011750 ,-.21441921360996728261] 
dist 78=[-1.4425092014245420901 ,-.2319201627200595883 ] 
dist 79=[-1.4544058657636054999 ,-.2704993042452677896 ] 
dist 80=[-1.4535459696297057854 ,-.27606268918078421185] 
dist 81=[-.76609668683402036185,-.30901167760980086406] 
dist 82=[-.70914433794545364743,-.28530604013283350116] 
dist 83=[-.56921138664496155908,-.25069284560129542095] 
dist 84=[-.54816760537936606313,-.19229986758834380252] 
dist 85=[-.34195420168456495593,-.13241490577251657005] 
dist 86=[-.30423106816914400998,-.09184206128260117585] 
dist 87=[-.26557307765948224023,-.05170005473992676849] 
dist 88=[-.2620828143851701858 ,.05877841334602642211] 
dist 89=[-.24087055770556874034,.16421133853897437778] 
dist 90=[-.23649341597846699899,.23174607637355377198] 
dist 91=[-.22804492638906896768,.28424770977715021328] 
dist 92=[-.22569912780709728174,.33190838390820674224] 
dist 93=[-.18905340592810113877,.37253114373476136035] 
dist 94=[-.18389436267735221375,.39703902977302925525] 
dist 95=[-.17095544516399948321,.41455980555560341158] 
dist 96=[-.16897066749337829539,.42735679618687662681] 
dist 97=[-.14847548401325826796,.43649969625248588835] 
dist 98=[-.14450537479090688036,.4394438762732986256 ] 
dist 99=[-.13994777629463363314,.43988418863020875757] 
dist 100=[-.13877163844602517997,.43896176009915202139] 
dist 101=[-.10093805330014854767,.42568610435289837991] 
dist 102=[-.09605922714422610357,.42165751689289910558] 
dist 103=[-.08636599917489125989,.41683996847621458686] 
dist 104=[-.08386534845944779310,.41435814391001526402] 
dist 105=[-.07497575758525479091,.34616379526431159895] 
dist 106=[-.07301493288894672617,.3365099957837421149 ] 
dist 107=[-.06999947183716521604,.31605691868669163258] 
dist 108=[-.06915317544640818310,.31020586322258345452] 
dist 109=[-.06778369802843005070,.29180725538004733325] 
dist 110=[-.06816810549111573705,.28856169948291246296] 
dist 111=[-.06949454314401518731,.2782570126984368328 ] 
dist 112=[-.07245639053521403303,.26631926878832846522] 
dist 113=[-.07625629195301381016,.13288684354718353353] 
dist 114=[-.08844656216472038645,.12009328183976102771] 
dist 115=[-.12354604274098026374,.08997021509790315120] 
dist 116=[-.1573445419847273149 ,.06389887362620390802] 
dist 117=[-.18779392537850369353,-.02568922707028804651] 
dist 118=[-.20952747667947375907,-.03380054469135123196] 
dist 119=[-.22909513854620906797,-.04844661927070152461] 
dist 120=[-.25090616450409138394,-.05162478547575711458] 
dist 121=[-.27056735042400001   ,-.06555352354103555063] 
dist 122=[-.2815521991164873691 ,-.06547280353144051199] 
dist 123=[-.28833604543075749067,-.06436061673036159735] 
dist 124=[-.29121712996293312112,-.06157256652342094985] 
dist 125=[-.29257223562597534072,-.05826395690488291099] 
dist 126=[-.29326071780454219884,-.05507306292739888841] 
dist 127=[-.29361500957744315591,-.05127370038703266158] 
dist 128=[-.29363503452015105948,-.04578352548331546323] 
dist 129=[-.06144140154839005495,-.01954568490200318793] 
dist 130=[-.06090984191176591866,.01120207307062026461] 
dist 131=[-.0593775211238403047 ,.03644297635166477691] 
dist 132=[-.05893669596773085427,.06072701371387569855] 
dist 133=[-.02595370965016383516,.08250903525644973124] 
dist 134=[-.02293184729383117263,.09776904463661747201] 
dist 135=[-.01588128630281917448,.11116542424197268058] 
dist 136=[-.01468353182628852636,.12551497945427083037] 
dist 137=[-.00531623592798997358,.13859098132371173067] 
dist 138=[-.00363401939570732969,.14690605442823298601] 
dist 139=[-.00101390426704666905,.1533285054110375629 ] 
dist 140=[-.00035666494132117648,.15885005671917813311] 
dist 141=[.01060225123109978601,.16337186081874085729] 
dist 142=[.01199424759825437784,.16580375419341655383] 
dist 143=[.01496472263777628150,.16717111879260613764] 
dist 144=[.01556278525775979298,.16744373697389801011] 
dist 145=[.01850528850174593702,.08268649323523887282] 
dist 146=[.01900005290687196667,.07580650725643348042] 
dist 147=[.01987251331270435539,.05896863094968089845] 
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dist 189=[-.00126698348953311992,.05896329261790592956] 
dist 190=[-.00205390208516396849,.05891463679910390903] 
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dist 200=[-.02195192844785611551,.00708830123172748524] 
dist 201=[-.02566233728234665838,.00711540921036781434] 
dist 202=[-.02793775436337626744,.00710097959439327544] 
dist 203=[-.02959769018571064222,.00705400954013840173] 
dist 204=[-.03085155310685391630,.00701870779640640799] 
dist 205=[-.03179515144261662840,.00616497787241677809] 
dist 206=[-.03221706977680172625,.00602119561006369919] 
dist 207=[-.03236802325639035902,.00577869026706428989] 
dist 208=[-.03234141085201043755,.00576126266803517256] 
dist 209=[-.02617276392951423548,.00548002870796706786] 
dist 210=[-.02549441184707372731,.00540135868215521307] 
dist 211=[-.02372584921640329284,.00532855319728669949] 
dist 212=[-.02339522077429145612,.00528142178643919642] 
dist 213=[-.02032496535548072908,-.00138751566091858406] 
dist 214=[-.01970181113594645598,.00079688674197252986] 
dist 215=[-.01885812862716013599,.00309288109118696151] 
dist 216=[-.01857284521816457992,.00613706747685689715] 
dist 217=[-.01346196533333071633,.00911990012026778478] 
dist 218=[-.01283574863640689816,.01117142355275470784] 
dist 219=[-.01136112048336191448,.01293200166714628125] 
dist 220=[-.01108446667534301480,.01475443646077600111] 
dist 221=[-.01084638403697687720,.01647714788037084624] 
dist 222=[-.01146110934773029769,.01784027418665938799] 
dist 223=[-.01202872156741564131,.01920236575600578129] 
dist 224=[-.01268053235874750850,.02092178822156644532] 
dist 225=[-.01333663726379797220,.02252762745776237490] 
dist 226=[-.01392137294173811129,.02343650241771054948] 
dist 227=[-.01456583971142155251,.02401123309950658365] 
dist 228=[-.01546032519065548733,.02428293992167658463] 
dist 229=[-.01632088014328525068,.02442298100310739420] 
dist 230=[-.01682991450064375334,.02447196392205225031] 
dist 231=[-.01717887220806996975,.02446466458643064561] 
dist 232=[-.01740052121235138597,.02438657703992266076] 
dist 233=[-.01752650666043157689,.02397094352045833763] 
dist 234=[-.01754191717256345779,.02433796047432464724] 
dist 235=[-.01742158232402092449,.02450952555482351282] 
dist 236=[-.01739140787940383127,.02452560928688453473] 
dist 237=[-.01643475328357585130,.02425984154814001396] 
dist 238=[-.01624676141482040015,.02412899944955927754] 
dist 239=[-.01573219998530222276,.02391714593376292103] 
dist 240=[-.01558741405548015672,.02381827216030421392] 
dist 241=[-.01452501328870919384,.01754248562695541526] 
dist 242=[-.01427964641956262535,.01685541079133429691] 
dist 243=[-.01388087171934076763,.01511133070505997462] 
dist 244=[-.01375709653840736698,.01484239684075296815] 
dist 245=[-.01058310412335380128,.01200098586236605768] 
dist 246=[-.01229411488167959675,.01144564080128723984] 
dist 247=[-.01394310449693711488,.01081412706932577153] 
dist 248=[-.01593954759787031228,.01064931368123194504] 
dist 249=[-.01781426989414752175,.00526660485697760808] 
dist 250=[-.01897758717386180509,.00458622958864242985] 
dist 251=[-.01984380567439300856,.00318059895815376175] 
dist 252=[-.02053284400715765343,.00281244448408300365] 
dist 253=[-.02105748436055957278,.00146095656326106292] 
dist 254=[-.02126772985059820692,.00118747671066582025] 
dist 255=[-.02133670102967779817,.00070396972563044075] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 0, 1, 2, 0, 1] 
dist 0=[54.194248711822624702  ,54.194248711822624702  ] 
dist 1=[53.878716106416156989  ,54.322014041967697028  ] 
dist 2=[53.305529278263973907  ,54.366548468230009192  ] 
dist 3=[52.148708669484276223  ,54.349476291462396564  ] 
dist 4=[50.714875325139995091  ,54.300770258206334195  ] 
dist 5=[49.035384176043833689  ,54.219012820855925699  ] 
dist 6=[46.850060930530885487  ,54.096845442327626012  ] 
dist 7=[43.395962464624850819  ,53.997912546491489217  ] 
dist 8=[39.866091969197358989  ,53.636309838233026189  ] 
dist 9=[37.378083018363863921  ,53.491893456244162944  ] 
dist 10=[35.170599301910981259  ,53.077208539911068144  ] 
dist 11=[32.760959553563289144  ,52.890009263673435811  ] 
dist 12=[30.397940458059738030  ,51.864224023855050218  ] 
dist 13=[28.376504248783221582  ,51.550996993420552820  ] 
dist 14=[26.212232023198649115  ,49.691041688377871900  ] 
dist 15=[23.278447626533094129  ,34.174083414247754468  ] 
dist 16=[20.353202013220008443  ,29.524584007950526059  ] 
dist 17=[18.222863543218995749  ,28.651602138562054778  ] 
dist 18=[16.259872085777783316  ,27.681467280752219632  ] 
dist 19=[14.002779292609078904  ,27.508672264902952513  ] 
dist 20=[11.719193719073619731  ,19.654303236690975991  ] 
dist 21=[9.6500402193050451672 ,18.686253614834658735  ] 
dist 22=[7.3331083592123987676 ,17.624274082648123438  ] 
dist 23=[4.0590797903469636702 ,17.482693229029443535  ] 
dist 24=[.84365555721841948095,14.527078083385872495  ] 
dist 25=[-1.2392774866607228241 ,14.164796815807781327  ] 
dist 26=[-2.9007089398798268506 ,13.722350802674797042  ] 
dist 27=[-4.4320385721713120876 ,13.635957010075622826  ] 
dist 28=[-5.7714400773574751273 ,9.1929670980358040953 ] 
dist 29=[-6.6661528486126457902 ,8.7635916016784675800 ] 
dist 30=[-8.3917478691085116481 ,6.7974575628807920412 ] 
dist 31=[-11.036197021782941077  ,-1.8875785736940680134 ] 
dist 32=[-12.676065862027497603  ,-4.2067132993487921571 ] 
dist 33=[-13.903405896683887198  ,-4.5834713309965719971 ] 
dist 34=[-14.899453413997529053  ,-5.3244565606068946188 ] 
dist 35=[-15.695294441330539030  ,-5.4854996068360048561 ] 
dist 36=[-16.122404031787624382  ,-6.4727872505363916404 ] 
dist 37=[-16.364397666613605418  ,-6.6014787039381488817 ] 
dist 38=[-16.419833499888431459  ,-6.5505652094241675228 ] 
dist 39=[-15.827639167887970166  ,-5.9288336241299617582 ] 
dist 40=[-15.690464249557643949  ,-4.6738747565159110799 ] 
dist 41=[-15.569964983955002202  ,-3.8013833108639830211 ] 
dist 42=[-15.479410652395859886  ,-3.0437396386905160027 ] 
dist 43=[-15.366615804729960246  ,-2.2466980884809497656 ] 
dist 44=[-15.309954471386174874  ,-1.4867060123845772248 ] 
dist 45=[-15.270606348544474801  ,-.7179949331745568656 ] 
dist 46=[-15.245142550556922068  ,.0534202007031353212 ] 
dist 47=[-4.8704845495357838512 ,.81501363091156224158] 
dist 48=[-4.0298478227363014819 ,1.6502584788696185119 ] 
dist 49=[-2.0841556629409366268 ,2.3016830745773207196 ] 
dist 50=[-1.7686369902810394675 ,2.8642274156301110740 ] 
dist 51=[.72232204777292071828,3.4522628019362010116 ] 
dist 52=[1.1542753676580239850 ,4.0114028966020112697 ] 
dist 53=[1.8263440987285427217 ,4.4586182837863027946 ] 
dist 54=[1.9871089430768780341 ,5.0252790461617094547 ] 
dist 55=[2.1853295147339047637 ,6.2506623546034702999 ] 
dist 56=[2.8164788793493464840 ,7.0254133504191813395 ] 
dist 57=[2.5732187649916669155 ,7.6187147568131175815 ] 
dist 58=[2.2153113856646526370 ,8.1197953457289494653 ] 
dist 59=[1.6090299315300797606 ,8.5233682511243516372 ] 
dist 60=[.9837442614010773162 ,8.7274300700133975515 ] 
dist 61=[.5499905115752593691 ,8.8357480648082317358 ] 
dist 62=[.17472252071551088784,8.8572007531662794608 ] 
dist 63=[-.21735626614481479592,4.0920961801456078417 ] 
dist 64=[-.58895704336748881396,3.8980366572340322562 ] 
dist 65=[-.88257842014937163408,3.4122574050635827750 ] 
dist 66=[-1.1745757004673845787 ,3.3383836191176670753 ] 
dist 67=[-1.5397254963169801958 ,3.1031881430078162339 ] 
dist 68=[-1.8866328910003749819 ,2.8945647321936743212 ] 
dist 69=[-2.1058738813919367200 ,2.8485577563403283926 ] 
dist 70=[-2.2730761288227761795 ,2.7307482914578679774 ] 
dist 71=[-2.4124120637187577803 ,2.6994408338207241638 ] 
dist 72=[-2.5227655886175370143 ,.8063877059412207430 ] 
dist 73=[-2.5743580859241326437 ,.5208851378327091172 ] 
dist 74=[-2.5991177333237295298 ,.4581739676509811861 ] 
dist 75=[-2.6024425966724033562 ,.4469713041373668822 ] 
dist 76=[-2.6361403888399202754 ,.0048467078318831233 ] 
dist 77=[-2.9120416566256458769 ,-.1088389788161661864 ] 
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dist 79=[-3.4596546490074597218 ,-.67677157113747305172] 
dist 80=[-3.7264084464474753853 ,-.75382624665971211562] 
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dist 86=[-4.0416696756128813117 ,.0708922731650784931 ] 
dist 87=[-4.0279534940830293198 ,.49017913491845575685] 
dist 88=[-3.3316999760568339309 ,.91425103091360119863] 
dist 89=[-3.3822980393517884502 ,1.1965772446082231266 ] 
dist 90=[-3.4122136089914914411 ,1.4289467814946648463 ] 
dist 91=[-3.4267762115591826358 ,1.6536773465011100908 ] 
dist 92=[-3.4253800651630931807 ,1.8561384875256141694 ] 
dist 93=[-3.3986099782008321904 ,2.0653091044772043075 ] 
dist 94=[-3.3861533389604898574 ,2.2749559066337986968 ] 
dist 95=[-.3155931040276776819 ,2.5035441268361525588 ] 
dist 96=[-.0252930165459031050 ,2.7116444000044367965 ] 
dist 97=[.0253419809902762847 ,2.8395327039534958949 ] 
dist 98=[.1085674002584606433 ,3.1244927502336904455 ] 
dist 99=[.1274195505887703027 ,3.4376405903096949765 ] 
dist 100=[.40672938173250810873,3.6386424344097623580 ] 
dist 101=[.44315225698240117557,3.7959761239766903220 ] 
dist 102=[.47005364281675859178,3.9348501484730224630 ] 
dist 103=[-.02657871925508921066,4.0505662428904990573 ] 
dist 104=[-.52539553022826937727,4.1154781483236897377 ] 
dist 105=[-.85499202160502174519,4.1556322258660325748 ] 
dist 106=[-1.1234824829116456658 ,4.1725386657343544967 ] 
dist 107=[-1.3784626983497504688 ,4.1732608638795767644 ] 
dist 108=[-1.6049787552237770437 ,4.1641781259335229041 ] 
dist 109=[-1.7598849145735071218 ,4.1182358469990366873 ] 
dist 110=[-1.8918637027116714813 ,4.0943758577911804004 ] 
dist 111=[-2.0268868358000560618 ,2.1238302331175228289 ] 
dist 112=[-2.1475339795467805690 ,1.9447180594669519879 ] 
dist 113=[-2.2221466902262901252 ,1.5100421010874155875 ] 
dist 114=[-2.2772468951006177400 ,1.4437225180875559308 ] 
dist 115=[-2.3200345638891428376 ,.8130731707225059627 ] 
dist 116=[-2.3515662874290281914 ,.6971936815813769808 ] 
dist 117=[-2.3617516720400053625 ,.5498619353546067592 ] 
dist 118=[-2.3594429408310404101 ,.5138146217265904835 ] 
dist 119=[-2.3540923965894055641 ,.32123724845143083766] 
dist 120=[-2.2315842236489640590 ,.09900305526181542552] 
dist 121=[-2.3276952275677028076 ,.09115384120205476861] 
dist 122=[-2.4008489246271563707 ,.07925620354204489588] 
dist 123=[-2.4685055937310512667 ,.08609816043496701404] 
dist 124=[-2.5154886288932021701 ,.09732601468564468781] 
dist 125=[-2.5379556300667670088 ,.106425340710028199  ] 
dist 126=[-2.5414289705087059200 ,.11553710310702505687] 
dist 127=[-1.2045514852953897637 ,.1268473090697721394 ] 
dist 128=[-1.1694937561389612702 ,.15038734217663573853] 
dist 129=[-1.0772848533946870066 ,.17116709859519121798] 
dist 130=[-1.0624931926084991647 ,.19190403353257018613] 
dist 131=[-.9009617385046578154 ,.21784267276757957395] 
dist 132=[-.8684648289246271515 ,.24231959845803360136] 
dist 133=[-.8317877997892636061 ,.25722496622916282826] 
dist 134=[-.8207893692837627595 ,.26786429381816599687] 
dist 135=[-.69517924614431269696,.27532900727523875301] 
dist 136=[-.66550033688101644333,.28061227185057806424] 
dist 137=[-.65846918083970381657,.28256125112570644034] 
dist 138=[-.63812148982704836068,.28266630324570916531] 
dist 139=[-.63301288208370961935,.28201903191914408484] 
dist 140=[-.2262131144912736463 ,.1072760722862246988 ] 
dist 141=[-.1929130822938794156 ,.22302376869248371011] 
dist 142=[-.1848880745822662664 ,.3855132118706782046 ] 
dist 143=[.07992908842983789299,.54610319263785594618] 
dist 144=[.1116813429572035767 ,.65427232003941938332] 
dist 145=[.1168854426825428285 ,.74478370895903167434] 
dist 146=[.1145114684272151026 ,.8348941911359726198 ] 
dist 147=[.1012065227101528829 ,.9178798172844096147 ] 
dist 148=[.0835203776292283663 ,.97995321776484954699] 
dist 149=[.0636621155368385275 ,1.0386164449059002540 ] 
dist 150=[.0384405082384044903 ,1.1079916232025677637 ] 
dist 151=[-.0006516937305151578 ,1.1722663941880675363 ] 
dist 152=[-.0456192983255241452 ,1.2105716440013472994 ] 
dist 153=[-.0942882893478109917 ,1.2372037366145057532 ] 
dist 154=[-.1549495026023933270 ,1.2548847511503753909 ] 
dist 155=[-.2477731026067722537 ,1.2654696825483028284 ] 
dist 156=[-.3406053636305440913 ,1.2668637440093603003 ] 
dist 157=[-.4013023503936059873 ,1.2587565194003612947 ] 
dist 158=[-.47319048613890968937,1.2560511978950096766 ] 
dist 159=[-.70316572309226509146,.68207099875896567364] 
dist 160=[-.85110004058350513051,.68262461659074325591] 
dist 161=[-.96722214303575970469,.68146431881971355501] 
dist 162=[-1.0702404334545386461 ,.6788325493213351851 ] 
dist 163=[-1.1569168752994155740 ,.67631446673961774156] 
dist 164=[-1.2078222141311246916 ,.58525647287247103194] 
dist 165=[-1.2424225618765920754 ,.57123686955182636812] 
dist 166=[-1.2898578047823327239 ,.54366264916426472645] 
dist 167=[-1.3297194600038723341 ,.53571018127976563042] 
dist 168=[-1.3537619259447004884 ,.50365636961256679313] 
dist 169=[-1.3708225871170056946 ,.49589320948373664424] 
dist 170=[-1.3828187527557114636 ,.47837251071693564023] 
dist 171=[-1.3906452072777441012 ,.47246238247729611157] 
dist 172=[-1.3910641570945182909 ,.0712089445524765160 ] 
dist 173=[-1.3861411144636366804 ,.0352115619790709576 ] 
dist 174=[-1.3822304785476028854 ,-.0407309955492522107 ] 
dist 175=[-.64317659670533287245,-.0590157767399620932 ] 
dist 176=[-.58019017559654947017,-.1330855735794194170 ] 
dist 177=[-.42720025011600028521,-.1098682898070496565 ] 
dist 178=[-.40510238522906711712,.0168477996397603517 ] 
dist 179=[-.3998977733215864992 ,.1354688909773178289 ] 
dist 180=[-.4752293227840013578 ,.2272882620378449725 ] 
dist 181=[-.5268773597263938438 ,.3170217694999167861 ] 
dist 182=[-.57104522775691010242,.4273163995734409026 ] 
dist 183=[-.61652123464996959853,.5315202848819173498 ] 
dist 184=[-.65932061054520499505,.5969468196446544214 ] 
dist 185=[-.69280333084171929102,.6464665023976992609 ] 
dist 186=[-.72584304203119550269,.68719144471610426084] 
dist 187=[-.76686854688428661553,.71995332853710870422] 
dist 188=[-.80459902156274622569,.73769367857606326219] 
dist 189=[-.82448811935858719416,.74781554709508247938] 
dist 190=[-.83511558737757724763,.75017042756559593162] 
dist 191=[-.83736865073647246368,.7766662666109364727 ] 
dist 192=[-.83288916883659006938,.8031268271361455356 ] 
dist 193=[-.82962336313844492131,.81490619952619448801] 
dist 194=[-.82540623821108709363,.82019881606724573571] 
dist 195=[-.82171813338457850284,.82076939977074552721] 
dist 196=[-.69773616245368265438,.79255663269802008441] 
dist 197=[-.67902161069565987124,.78537461486741499288] 
dist 198=[-.64220323380806391959,.77108894100272944328] 
dist 199=[-.63171744405820919112,.7658073693820503917 ] 
dist 200=[-.59001573071027853371,.73915347430894793972] 
dist 201=[-.57997354315537280316,.73248939598796536347] 
dist 202=[-.55793101169898510683,.71035152359866137849] 
dist 203=[-.55065999394140865653,.70615012255803080257] 
dist 204=[-.5178779287646268109 ,.15291431701646855544] 
dist 205=[-.5298965798072369602 ,.14211364838575311226] 
dist 206=[-.53662268375258256891,.13866175931266190414] 
dist 207=[-.53787952103121927251,.0409916305319328786 ] 
dist 208=[-.53667230898601817168,.02900724466454637523] 
dist 209=[-.5346600381839710036 ,.00891405100920946865] 
dist 210=[-.52942507739360849961,.00430966183250914218] 
dist 211=[-.5376068693900685802 ,-.00348732270047535299] 
dist 212=[-.5619813312034745704 ,-.00144323512698577024] 
dist 213=[-.5818956518926944924 ,.00564421483170680394] 
dist 214=[-.6009251379136985091 ,.02145428724986931645] 
dist 215=[-.6164723892920138424 ,.03990914206600292087] 
dist 216=[-.6224898418930396799 ,.05755162074373010357] 
dist 217=[-.6244855038786926477 ,.07796479859235721093] 
dist 218=[-.6239810474294771806 ,.10747800270619233361] 
dist 219=[-.6057307366167692301 ,.1405614276171047656 ] 
dist 220=[-.5997831417459356220 ,.2579675538515038823 ] 
dist 221=[-.5951165539379393732 ,.3373869147418907251 ] 
dist 222=[-.5912051277678496189 ,.4028107462266719631 ] 
dist 223=[-.03203414504462641873,.4661857684643886936 ] 
dist 224=[.01311619959387588115,.5233475351853914210 ] 
dist 225=[.02235897321026860957,.5639766416741230313 ] 
dist 226=[.03420790520392555893,.6002524505939977124 ] 
dist 227=[.03640198244344813627,.6400417511220638230 ] 
dist 228=[.03481286517714617961,.6753794118284050968 ] 
dist 229=[.02748014713191086927,.6938904283677115351 ] 
dist 230=[.01453859704722518073,.7040444476646377461 ] 
dist 231=[-.00943294550979008936,.7060413650846405462 ] 
dist 232=[-.03864446056847856718,.7011750360567381277 ] 
dist 233=[-.07249653539750566920,.6992069401037263069 ] 
dist 234=[-.11621333347811551776,.6973844795795775844 ] 
dist 235=[-.1847908647587461757 ,.6896416963845724590 ] 
dist 236=[-.2538287941463384492 ,.4618537213148809299 ] 
dist 237=[-.2993827438449580194 ,.4496855436878327530 ] 
dist 238=[-.3364310031784765770 ,.4466896036246045738 ] 
dist 239=[-.3715259381276151127 ,.2184492929990985576 ] 
dist 240=[-.4026523490290159384 ,.1962357325952974800 ] 
dist 241=[-.4238636082076046087 ,.14624908879443606654] 
dist 242=[-.4418601194795293201 ,.13568393988656698382] 
dist 243=[-.4601573315253929004 ,.07437960989587005429] 
dist 244=[-.4756476433976733851 ,.06338769252925705617] 
dist 245=[-.4824429959514942312 ,.04101695899451800275] 
dist 246=[-.4854338994681741021 ,.03529303656116015373] 
dist 247=[-.4857426712290541781 ,-.01654333798725676233] 
dist 248=[-.4732830268612077769 ,-.02472073276482149308] 
dist 249=[-.4695508338082348987 ,-.03556842568170404899] 
dist 250=[-.4668570570689690187 ,-.03781146805903742968] 
dist 251=[-.4604846790847406074 ,-.03678401515102057220] 
dist 252=[-.35199631072806823314,-.03080175345964445469] 
dist 253=[-.33810004995456681498,-.02005190418744560793] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 2, 0, 0, 1, 0, 2] 
dist 0=[50.873051440133160988  ,50.873051440133160988  ] 
dist 1=[49.948547417027264243  ,51.222425354124919210  ] 
dist 2=[48.471534559333963994  ,51.692976061277384467  ] 
dist 3=[46.003401411842351614  ,52.220206078561132598  ] 
dist 4=[43.443483665536067024  ,52.533930034226676172  ] 
dist 5=[41.599894998165776068  ,52.812707740734696153  ] 
dist 6=[39.924513601085275508  ,52.950274945234291181  ] 
dist 7=[38.036049072750835275  ,52.945976170896749198  ] 
dist 8=[36.150052568150285633  ,51.073127380989998102  ] 
dist 9=[34.484308009009446864  ,50.732755273051246952  ] 
dist 10=[32.656585984080209152  ,50.203849929597464508  ] 
dist 11=[30.123359784577126906  ,50.020868793013412247  ] 
dist 12=[27.573423717741905417  ,49.450037777413688727  ] 
dist 13=[25.678748047281385077  ,49.241512175450264664  ] 
dist 14=[23.895350579721323325  ,48.920872031200719436  ] 
dist 15=[21.789510718368521217  ,48.790746306822101217  ] 
dist 16=[19.628255331251193783  ,31.774333317989574204  ] 
dist 17=[17.623118696729540640  ,30.323130096964038205  ] 
dist 18=[15.340073360143275224  ,26.837309550459199676  ] 
dist 19=[12.067975555069356927  ,26.328324796281332796  ] 
dist 20=[8.8325036864858701048 ,21.372893039033424719  ] 
dist 21=[6.6956437192766290463 ,20.468108354215474348  ] 
dist 22=[4.9449809271506112106 ,19.381103642332652071  ] 
dist 23=[3.2525629506975111010 ,19.168906916914771460  ] 
dist 24=[1.7175550841483385392 ,12.600082382189382520  ] 
dist 25=[.59571771421233692543,12.172264663467122943  ] 
dist 26=[-1.2911814040172968868 ,11.008661440484544418  ] 
dist 27=[-3.3352955935034639691 ,8.7475677014574818193 ] 
dist 28=[-5.0790643900471171438 ,6.9919908944002049564 ] 
dist 29=[-6.9455242682153422226 ,6.6694704448099226273 ] 
dist 30=[-9.4808967066470789064 ,6.1436095946041778183 ] 
dist 31=[-11.925966544298165882  ,6.0289519826909553015 ] 
dist 32=[-13.431889653566711896  ,-1.3463366552073183157 ] 
dist 33=[-14.547577081732666570  ,-1.9659473886555718987 ] 
dist 34=[-15.433206371251990521  ,-2.5457463711953026529 ] 
dist 35=[-16.127241605987816420  ,-2.0286271233880646961 ] 
dist 36=[-16.477094177041579624  ,-1.4779711900440663938 ] 
dist 37=[-16.649865406339663693  ,-1.0841283599236387128 ] 
dist 38=[-16.676750884537136205  ,-.73311826975649850305] 
dist 39=[-15.951371299707116772  ,-.3526662318685383235 ] 
dist 40=[-15.790409163340539664  ,.0145698260504257976 ] 
dist 41=[-15.538191379260032561  ,.3131577146860923564 ] 
dist 42=[-15.440957758236381323  ,.6171344183312886933 ] 
dist 43=[-15.096658570479300215  ,1.0061009851904087381 ] 
dist 44=[-14.975286944277552620  ,1.3792309404760784461 ] 
dist 45=[-14.734983418910393743  ,1.6201740849022679879 ] 
dist 46=[-14.645918066921663908  ,1.8097797851301395274 ] 
dist 47=[-11.475546638026624609  ,2.0906613590654302490 ] 
dist 48=[-4.1839162946872905795 ,3.8810043117766798654 ] 
dist 49=[-2.2889838714903701382 ,5.0875182861829876297 ] 
dist 50=[-1.9462043462496796484 ,6.0962880670022772700 ] 
dist 51=[-1.5638183772043576753 ,7.0977179624502776484 ] 
dist 52=[.6150279912002000705 ,8.0169934186732866920 ] 
dist 53=[.78690260464021662478,8.6980328301729290271 ] 
dist 54=[1.1378449632493470859 ,9.3347821331885813121 ] 
dist 55=[1.2192079270340456718 ,10.077456057106095782  ] 
dist 56=[1.5048164947247432161 ,10.759982614413225017  ] 
dist 57=[1.5597222814543130104 ,11.156763344111245606  ] 
dist 58=[1.5884876056218652589 ,11.420490994514787639  ] 
dist 59=[1.5469501974118033235 ,11.572081292057530169  ] 
dist 60=[1.3991504926864901738 ,11.649445117875616331  ] 
dist 61=[1.2100521135288463138 ,11.649680675409211972  ] 
dist 62=[1.0199115159220249850 ,11.394859945436481392  ] 
dist 63=[.7789647257891847636 ,6.7379358199622386611 ] 
dist 64=[.5240267406310491060 ,3.6513008746052880403 ] 
dist 65=[.2780050771459810295 ,3.3833745965022744024 ] 
dist 66=[-.0085295975347299338 ,3.1844903891614681719 ] 
dist 67=[-.4252017447943590324 ,3.1859731280371127666 ] 
dist 68=[-.93749735393299418869,3.1747574177950511869 ] 
dist 69=[-1.2991042251250874701 ,3.1655880696164654305 ] 
dist 70=[-1.5951065543038068847 ,3.1165034024241141951 ] 
dist 71=[-1.8788218928337921380 ,3.1051029486001788914 ] 
dist 72=[-2.1328566812567945463 ,2.9250784949115126363 ] 
dist 73=[-2.3104287375409042918 ,2.8802297654071528425 ] 
dist 74=[-2.4660206154404623652 ,2.8399791933215787212 ] 
dist 75=[-2.6323669796041192828 ,2.8193606617704844144 ] 
dist 76=[-2.7796330427060762465 ,2.1481755865246988021 ] 
dist 77=[-2.8590774223660643407 ,2.0557089411946046959 ] 
dist 78=[-2.9041280992607319043 ,1.8737109899360569541 ] 
dist 79=[-2.9141006526237636200 ,1.8249580846559263559 ] 
dist 80=[-2.9103985840134523068 ,1.6452464537040101935 ] 
dist 81=[-2.9008724644488834625 ,1.6028634403134760558 ] 
dist 82=[-2.8853236489302717362 ,1.5291847402577120338 ] 
dist 83=[-2.8734333266832847868 ,1.5094912172136465106 ] 
dist 84=[-2.6581032164703146493 ,1.8681528059905820887 ] 
dist 85=[-2.6272549951759654617 ,2.1966097070407027235 ] 
dist 86=[-2.5640277137453418123 ,2.4535130377877890387 ] 
dist 87=[-2.5425476049292647095 ,2.6794701272828446042 ] 
dist 88=[-2.5426869347860067444 ,2.8678836928529273527 ] 
dist 89=[-2.5468775914540625265 ,2.9749882623955058494 ] 
dist 90=[-2.5411661568220337782 ,3.0428888089237670367 ] 
dist 91=[-2.5347002743706998013 ,3.0748737216442244562 ] 
dist 92=[-2.4833209412924701948 ,3.0917489749364200960 ] 
dist 93=[-2.4673560405444932482 ,3.0993549331165678077 ] 
dist 94=[-2.4211232432729845680 ,3.1015548428944108558 ] 
dist 95=[-2.4018008796952657661 ,3.0968439238049657244 ] 
dist 96=[-2.1654543807216706700 ,3.0879087069061933789 ] 
dist 97=[-2.1239172847586170182 ,3.0736420405833474315 ] 
dist 98=[-2.0266949584965413291 ,3.0514130141108368199 ] 
dist 99=[-1.9943824212175803566 ,3.0385469970507908638 ] 
dist 100=[-1.8411675210553507894 ,2.6413244624308950707 ] 
dist 101=[-1.8065779956743326601 ,2.7548161558166181256 ] 
dist 102=[-1.7308252289907563185 ,2.8910891196551341363 ] 
dist 103=[-1.7062611584279190842 ,3.0285278904694398887 ] 
dist 104=[-1.3874228831577824838 ,3.1458405456301558289 ] 
dist 105=[-1.3392062258323479575 ,3.2017891297904524326 ] 
dist 106=[-1.2122750436368375930 ,3.2282055250461213061 ] 
dist 107=[-1.1924848403222350023 ,3.2288134532279334826 ] 
dist 108=[-.96871394481638156012,3.1748644789103217239 ] 
dist 109=[-.92358177034987566843,3.1518752097792166735 ] 
dist 110=[-.87477128831940706677,3.1297316213878304789 ] 
dist 111=[-.86125142281114145075,3.1122718068469916787 ] 
dist 112=[.1718733180040262085 ,2.0823989934968108449 ] 
dist 113=[-.0696448378348228813 ,2.1025165922293490101 ] 
dist 114=[-.3652404534232663000 ,2.1135043035322707939 ] 
dist 115=[-.81181948658919488986,2.1149154940627216140 ] 
dist 116=[-1.2562886311502731052 ,.13598559354880419866] 
dist 117=[-1.5434671644930834028 ,.02699061692956881058] 
dist 118=[-1.7703506986921039892 ,-.00374243524153429419] 
dist 119=[-1.9741874144041490310 ,-.53829682682212067848] 
dist 120=[-2.1475485833189871336 ,-.60367992133768337928] 
dist 121=[-2.2528072956408395633 ,-.74507992898010235897] 
dist 122=[-2.3283186845976634714 ,-.76994672082796161494] 
dist 123=[-2.3829625674262838147 ,-.91253007276446649772] 
dist 124=[-2.4258808396680742253 ,-.93496906217747919913] 
dist 125=[-2.4515756632974943307 ,-.97267520861447057398] 
dist 126=[-2.4691905862214783885 ,-.97921051599830362125] 
dist 127=[-2.4803971446016023923 ,-1.0569249490296132615 ] 
dist 128=[-2.4866423986698099165 ,-.95784554634536984731] 
dist 129=[-2.4844570190481753795 ,-.86444399678493719789] 
dist 130=[-2.4756917965141785995 ,-.75449364506256059562] 
dist 131=[-2.4670950358413448577 ,-.64242248922061399257] 
dist 132=[-1.0057778128355536136 ,-.54054802066654295486] 
dist 133=[-.88284735263466297711,-.42668476206800142148] 
dist 134=[-.6452180545658205656 ,-.19784269699058892594] 
dist 135=[-.5446738176312573950 ,.03674523000809270569] 
dist 136=[-.3780219296406123538 ,.25540441736126134647] 
dist 137=[-.30287323304093422603,.42309041539622953671] 
dist 138=[-.2902721247265353532 ,.58549116161056416943] 
dist 139=[-.18643492227791494917,.78306174387324595352] 
dist 140=[-.1674898281999580968 ,.96940914038161312022] 
dist 141=[-.13948128568941332336,1.0870211918269485919 ] 
dist 142=[-.1318731115747958482 ,1.1767682184745237203 ] 
dist 143=[.00032673950739246456,1.2519104641875252241 ] 
dist 144=[.01743403968607603496,1.3121777212130986656 ] 
dist 145=[.03379725811443237448,1.3425615005745466860 ] 
dist 146=[.03263640875069345477,1.3585745869160582934 ] 
dist 147=[.02372524146076242515,1.3614890894793430521 ] 
dist 148=[.00392579022854748821,1.3593101403006577845 ] 
dist 149=[-.02760043907976041757,1.3926250128924926978 ] 
dist 150=[-.08331497808179568141,1.4199015224713538253 ] 
dist 151=[-.14434435089140312838,1.4398312384616675614 ] 
dist 152=[-.19708530269631756007,1.4438224436223810357 ] 
dist 153=[-.25382128208424077329,1.4418890531753922165 ] 
dist 154=[-.33080250416385475483,1.4381621353691368590 ] 
dist 155=[-.41487359879314498577,1.3873388127496967712 ] 
dist 156=[-.49990974447900854477,1.3723855326567832676 ] 
dist 157=[-.60192434842979891298,1.3562958708240955069 ] 
dist 158=[-.75376200005739150839,1.3471670723148429528 ] 
dist 159=[-.90389904177554655985,.51429759059781929307] 
dist 160=[-.99912854859598313254,.41254903160724257566] 
dist 161=[-1.0723643053811029789 ,.39281291584327961129] 
dist 162=[-1.1347247793793490379 ,.36552584648908871231] 
dist 163=[-1.1853218937263821066 ,.35693269535244431637] 
dist 164=[-1.2246847771853030673 ,.10431870050758710945] 
dist 165=[-1.3183076610634846762 ,.07580072766308191771] 
dist 166=[-1.4206602450234024099 ,.02723355273136585144] 
dist 167=[-1.5127805158432039471 ,.01630575859167426469] 
dist 168=[-1.5655666153780657618 ,-.00394797882904089765] 
dist 169=[-1.5996367885662116317 ,-9.83040936110580600000e-05] 
dist 170=[-1.6170627618693950491 ,.01548208291106648427] 
dist 171=[-1.6256277863493636782 ,.0511187112054220507 ] 
dist 172=[-1.6243336131687828578 ,.0929654081228234200 ] 
dist 173=[-1.6174883010907509028 ,.1333297941943811359 ] 
dist 174=[-1.6114745300345314894 ,.1803128050635541896 ] 
dist 175=[-1.4737344832514922181 ,.2485756739589621034 ] 
dist 176=[-1.4364319368954779871 ,.3569724505876443478 ] 
dist 177=[-1.4234645931607511386 ,.49675618783618138907] 
dist 178=[-1.4127042283515052109 ,.63208854692373517102] 
dist 179=[-1.4040061092597400470 ,.75414839989483579014] 
dist 180=[-.78563333547679648564,.84096257641109059188] 
dist 181=[-.74222900115531782011,.91855694880084408471] 
dist 182=[-.7300508991537907173 ,1.0038208142937871735 ] 
dist 183=[-.36094602675487092095,1.0813612807070958240 ] 
dist 184=[-.31428562303535165845,1.1281326070249511970 ] 
dist 185=[-.21652451336614005237,1.1613056494467967921 ] 
dist 186=[-.19068712052215269747,1.2402200471256510159 ] 
dist 187=[-.09421425461137694114,1.3445371031557472008 ] 
dist 188=[-.07525210823113433519,1.4388114353367944973 ] 
dist 189=[-.0394523901940218002 ,1.4931832086219473506 ] 
dist 190=[-.03100830653270010371,1.5287165415907026934 ] 
dist 191=[-.02466795509446033844,1.5478102907795930286 ] 
dist 192=[-.05491664956415495011,1.5580277491599537740 ] 
dist 193=[-.08584479607063664493,1.5581374023719164257 ] 
dist 194=[-.12575070104879463944,1.5523600368283044819 ] 
dist 195=[-.16833977114450131791,1.5470454203849225031 ] 
dist 196=[-.20997774633553235588,1.1563010796081808333 ] 
dist 197=[-.36538491056198592608,1.1140089848148483192 ] 
dist 198=[-.49786948118918495458,1.0052456540929813738 ] 
dist 199=[-.62553663287880312789,.98799742473796931398] 
dist 200=[-.74026601341381327074,.80585446906097688647] 
dist 201=[-.8211185446459709684 ,.76985305917322603335] 
dist 202=[-.89260344475934642201,.72826660111299279314] 
dist 203=[-.96994801997699100438,.71623796363152583378] 
dist 204=[-1.0399986419016086870 ,.36249362829687000716] 
dist 205=[-1.0823751911673419095 ,.31765568576354564854] 
dist 206=[-1.1125742002879602398 ,.22350827359779002531] 
dist 207=[-1.1340282201559748606 ,.19855317759140392197] 
dist 208=[-1.1482060765833898291 ,.10494832669525084853] 
dist 209=[-1.1509486343995130450 ,.08660750489052476388] 
dist 210=[-1.1464867649434226257 ,.05138577075214144900] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 1, 1, 1, 1, 2] 
dist 0=[48.266969394452035828  ,48.266969394452035828  ] 
dist 1=[47.329974398495392764  ,48.718586942706199592  ] 
dist 2=[46.296738594791410216  ,48.961506962781065962  ] 
dist 3=[45.460849437560144996  ,49.064953587117286797  ] 
dist 4=[44.607639899493330849  ,49.096107251884605684  ] 
dist 5=[43.505363550984035816  ,48.976657974067847064  ] 
dist 6=[42.324806046610085402  ,48.897722287582504101  ] 
dist 7=[41.159085300173448933  ,48.799610530321075852  ] 
dist 8=[39.778903647046347648  ,48.706356912609645604  ] 
dist 9=[37.742077345016022172  ,45.550967519262246812  ] 
dist 10=[35.641248156717710001  ,45.069580823636037566  ] 
dist 11=[34.005535595723128657  ,44.155957727934832058  ] 
dist 12=[32.394674725078963280  ,43.899966913698874170  ] 
dist 13=[30.393100692412751196  ,42.914364600914747441  ] 
dist 14=[28.289703075079266554  ,42.659306021043669606  ] 
dist 15=[26.272283656438000881  ,42.150079015363241080  ] 
dist 16=[22.063842193300162771  ,41.987075250519534751  ] 
dist 17=[19.034469713625835872  ,31.516923768074371053  ] 
dist 18=[16.425731789886070637  ,25.918515358938488505  ] 
dist 19=[13.701884414947407948  ,22.831903530879266332  ] 
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