8 phat 2 dirichlet min maxes function [0, 1, 0, 0, 2, 1, 0, 1, 2] 
dist 0=[12.617388140964767411  ,12.617388140964767411  ] 
dist 1=[12.609494983702710602  ,12.619515470722685928  ] 
dist 2=[12.593799520959263793  ,12.620123529660496679  ] 
dist 3=[12.564473269498664195  ,12.618646465604513274  ] 
dist 4=[12.530360299852180055  ,12.616117024822665982  ] 
dist 5=[12.495522659614422499  ,12.608709159208414820  ] 
dist 6=[12.453227812321071193  ,12.604585643258426039  ] 
dist 7=[12.389295860611103406  ,12.575024491355390790  ] 
dist 8=[12.315777751488568001  ,12.512863361964742276  ] 
dist 9=[12.235150711366729448  ,12.492779100763846926  ] 
dist 10=[12.133284575701469705  ,12.485335775536403766  ] 
dist 11=[11.974837476377308051  ,12.470743792444597114  ] 
dist 12=[11.811174656795722424  ,12.465940017328709921  ] 
dist 13=[11.688451065757165103  ,12.458999906992181248  ] 
dist 14=[11.571346531788194275  ,12.410152985631175659  ] 
dist 15=[11.430148795571114545  ,12.108367930470957967  ] 
dist 16=[11.283025517965601978  ,11.975850406770952630  ] 
dist 17=[11.142222509205229441  ,11.955621506549461605  ] 
dist 18=[10.978042269710829705  ,11.902044832558497358  ] 
dist 19=[10.737432269819534969  ,11.894030276203414584  ] 
dist 20=[10.487661822180209304  ,11.796935638723284425  ] 
dist 21=[10.286847742776710641  ,11.776799216444793388  ] 
dist 22=[10.081969297973956687  ,11.757626909138044660  ] 
dist 23=[9.8159429998240305387 ,11.752998086176274571  ] 
dist 24=[9.5285594278570557153 ,11.504623189878972299  ] 
dist 25=[9.2382718429421391892 ,11.471361165516304545  ] 
dist 26=[8.8880765563840541782 ,11.373706268423418191  ] 
dist 27=[8.3611203253929002808 ,11.241401443711378430  ] 
dist 28=[7.8324994263740598039 ,10.547583683112503873  ] 
dist 29=[7.4756460446733957534 ,10.501625466052604549  ] 
dist 30=[7.1737092451337837056 ,10.487863793544944495  ] 
dist 31=[6.8646982569157991717 ,9.6392823998580135766 ] 
dist 32=[6.5720649554402577977 ,9.5614044269744904774 ] 
dist 33=[6.3356206726247583156 ,9.3861692086012684889 ] 
dist 34=[6.0933017373016593437 ,9.3500980858782658497 ] 
dist 35=[5.7771716561505164974 ,9.1282705007813011745 ] 
dist 36=[5.4652799539332919866 ,9.0868659997724415955 ] 
dist 37=[5.2399082842632685081 ,9.0092818688942541224 ] 
dist 38=[5.0330951610875361070 ,8.9899283779522740663 ] 
dist 39=[4.7954171022255876913 ,8.7176894425439912940 ] 
dist 40=[4.5539204692065169575 ,8.6797345259049089669 ] 
dist 41=[4.3318327190805920498 ,8.5876454155410680812 ] 
dist 42=[4.0797290502969757622 ,8.5726766352456220771 ] 
dist 43=[3.7181883038835019211 ,8.4338079944807398084 ] 
dist 44=[3.3580196175429681717 ,8.4068499697385297575 ] 
dist 45=[3.1114007624300773526 ,8.3734939770469610798 ] 
dist 46=[2.8988968776077886579 ,8.3625545343034842976 ] 
dist 47=[2.6751582539210772809 ,6.6004443839355225194 ] 
dist 48=[2.4592688546079531260 ,6.3459242403252242537 ] 
dist 49=[2.2781520305569855973 ,6.3132582346042593204 ] 
dist 50=[2.0864187372264476130 ,6.2374331490769370420 ] 
dist 51=[1.8280638266482460140 ,6.2254340773197409435 ] 
dist 52=[1.5691618837270051077 ,6.1246979647335216205 ] 
dist 53=[1.3752369919428700898 ,6.1064807612051294337 ] 
dist 54=[1.1902701322863232316 ,6.0813941536571347918 ] 
dist 55=[.9671895711929733301 ,6.0740967541099060910 ] 
dist 56=[.73453212012485970196,5.0312078995255616016 ] 
dist 57=[.51125726195807888278,4.9642277629027311399 ] 
dist 58=[.2502915128660778133 ,4.8019253033569079691 ] 
dist 59=[-.13312005014751586273,4.6473979905237040597 ] 
dist 60=[-.51382233079718214472,3.8155099298790703729 ] 
dist 61=[-.76395418243831783748,3.7789483911928323922 ] 
dist 62=[-.9682834523638412466 ,3.7706597008521632322 ] 
dist 63=[-1.1657945353111287592 ,2.7285348134354947701 ] 
dist 64=[-1.3456815696709553051 ,2.6420984315675673963 ] 
dist 65=[-1.4795238097078983057 ,2.4483995437927727165 ] 
dist 66=[-1.6343613288749953613 ,2.4135867132407594058 ] 
dist 67=[-1.8252016214058371692 ,2.1786598585592534542 ] 
dist 68=[-1.9794825015643196758 ,2.1372872995566290874 ] 
dist 69=[-2.1377077037080815644 ,2.0642108266445121694 ] 
dist 70=[-2.3443265319419730456 ,2.0484305537239417849 ] 
dist 71=[-2.5483513033220244233 ,1.8167707965496170382 ] 
dist 72=[-2.6962045282985044596 ,1.7856314371053651864 ] 
dist 73=[-2.8323525064301847021 ,1.7204789420038090916 ] 
dist 74=[-2.9895677657280272095 ,1.7050905793065758438 ] 
dist 75=[-3.1497829933372852608 ,1.6408947866378054050 ] 
dist 76=[-3.2979328477217474270 ,1.6292397584321751488 ] 
dist 77=[-3.4667978641508666690 ,1.6055810828622508802 ] 
dist 78=[-3.7098682498196809212 ,1.5996336679891756824 ] 
dist 79=[-3.9496655454296234667 ,.40317561740975840797] 
dist 80=[-4.1054412610221445313 ,.37924043238620459152] 
dist 81=[-4.2306978381144616127 ,.37682178578163117943] 
dist 82=[-4.3484332316761282432 ,.38114158820165756303] 
dist 83=[-4.4534257735574963783 ,.39574036917607957361] 
dist 84=[-4.5277180373940607503 ,.415883626875930503  ] 
dist 85=[-4.5943363470588041198 ,.44237305862683792157] 
dist 86=[-4.6686396759094196790 ,.47871609318014165979] 
dist 87=[-4.7366239833244758361 ,.53825179934295845721] 
dist 88=[-4.7779694806335484592 ,.59944003199925213595] 
dist 89=[-4.8080482327755244669 ,.64239239791760921182] 
dist 90=[-4.8309687662015228676 ,.68044486781691026331] 
dist 91=[-4.8482377920742226742 ,.7220531570527823555 ] 
dist 92=[-4.8557122511250422758 ,.76305519423614637767] 
dist 93=[-4.8585993442239574799 ,.79868861834448408128] 
dist 94=[-4.8578682376121860428 ,.83743298594242745267] 
dist 95=[-4.7406367147218217526 ,.89087700135961171918] 
dist 96=[-4.7266964388436222979 ,.94487355858689528836] 
dist 97=[-4.6981310818447353723 ,.98582982244352943828] 
dist 98=[-4.6894794152033961403 ,1.0253414103702328212 ] 
dist 99=[-4.6517019955003385130 ,1.0735662318506475911 ] 
dist 100=[-4.6433839405368319749 ,1.1240980674467312247 ] 
dist 101=[-4.6190858314004715373 ,1.1728368625343657686 ] 
dist 102=[-4.6097991133192185986 ,1.2299371290667108237 ] 
dist 103=[-4.5600548849253725944 ,1.3139053329470365744 ] 
dist 104=[-4.3540349746881157067 ,1.3983058243107766329 ] 
dist 105=[-4.3386432700851471900 ,1.4571360946930195495 ] 
dist 106=[-4.3170622720615766033 ,1.5089060239521264204 ] 
dist 107=[-4.3098900984240141633 ,1.5650772215195916127 ] 
dist 108=[-4.1578273630537033572 ,1.6202595640545507598 ] 
dist 109=[-4.1298296556411685163 ,1.6680774415564465265 ] 
dist 110=[-3.9813964086329744787 ,1.7200059321994692741 ] 
dist 111=[-1.9451450149057355235 ,1.7916287379841569628 ] 
dist 112=[-1.8253377709040210922 ,1.8641012823581517029 ] 
dist 113=[-1.5477797614690006095 ,1.9194293481372868878 ] 
dist 114=[-1.5051499661765100545 ,1.9731991185561250539 ] 
dist 115=[-1.1409864352218052772 ,2.0394423237355439722 ] 
dist 116=[-1.0442238414333813597 ,2.1092390627695410311 ] 
dist 117=[-.95226391123732024789,2.1772214156149452021 ] 
dist 118=[-.77177186126114501857,2.2574148995981115718 ] 
dist 119=[-.37992829967763496933,2.3760476578259310397 ] 
dist 120=[.23717869289713794119,2.4934379384486868896 ] 
dist 121=[.24066862819050194082,2.5686634160980332989 ] 
dist 122=[.24675863083757560216,2.6279598478670557695 ] 
dist 123=[.24780231445988750739,2.6816481507901118402 ] 
dist 124=[1.0085182967433288475 ,2.7281030184457877150 ] 
dist 125=[1.0328156923788419604 ,2.7584729154912183440 ] 
dist 126=[1.0860590499487009332 ,2.7831075781628669821 ] 
dist 127=[1.0948982784641035830 ,2.8066288906375166448 ] 
dist 128=[1.1535021606726169351 ,2.8272034150537982564 ] 
dist 129=[1.1629668931552294363 ,2.8400532755607199179 ] 
dist 130=[1.1800964070775810609 ,2.8498097554113295682 ] 
dist 131=[1.1834658102178964224 ,2.8580104191014889538 ] 
dist 132=[1.2129664335264875674 ,2.8646628696467929675 ] 
dist 133=[1.2169120701884729829 ,2.8682263108275377955 ] 
dist 134=[1.2162868618575782133 ,2.8702375653775591131 ] 
dist 135=[1.2092737452774192854 ,2.8706810622239970614 ] 
dist 136=[1.1986383172101206377 ,2.6429185512699641637 ] 
dist 137=[1.1835286125811362478 ,2.6225504984823068767 ] 
dist 138=[1.1621465610136731532 ,2.5803923115575103273 ] 
dist 139=[1.1264313076305017753 ,2.5686866587725369404 ] 
dist 140=[1.0888099118728685053 ,2.5218786435404374458 ] 
dist 141=[1.0598055841090942345 ,2.5123013054408959051 ] 
dist 142=[1.0313666401170737014 ,2.4886110636897460593 ] 
dist 143=[.99600408416080472365,2.4831799273730987430 ] 
dist 144=[.9586026686049437183 ,2.4437193378961819039 ] 
dist 145=[.92201035277978525066,2.4352822920091224369 ] 
dist 146=[.87874640535158292487,2.4217934034368175063 ] 
dist 147=[.81466734907341715886,2.4178049084584137767 ] 
dist 148=[.74790702412189689648,2.4071134570578134784 ] 
dist 149=[.69392135034091511814,2.4034953743891972384 ] 
dist 150=[.63858023991405883266,2.4013491098226497675 ] 
dist 151=[.56639930805542170712,2.4006292322299679379 ] 
dist 152=[.48829702037658419128,1.2603534123748092884 ] 
dist 153=[.40927836696158770849,1.2569391653294055536 ] 
dist 154=[.31389047437188239912,1.2486631816090901642 ] 
dist 155=[.17033368209110287898,1.2460850415559537899 ] 
dist 156=[.02653231730442918225,.91237659107923069792] 
dist 157=[-.06983367399519434107,.88920268824202361074] 
dist 158=[-.15056318716786803107,.83475212311553966765] 
dist 159=[-.2318405180944573235 ,.82617571910182562117] 
dist 160=[-.30792543082765920716,.75142363130114796715] 
dist 161=[-.36789258003626795413,.73768004427311822563] 
dist 162=[-.42795548730971928797,.71951072841801605647] 
dist 163=[-.50442343244778170762,.71422936443469899758] 
dist 164=[-.57891998838521289343,.60639935336265133587] 
dist 165=[-.63110012551515744652,.59256310964897105894] 
dist 166=[-.67728426663059871676,.56364173616537028722] 
dist 167=[-.72780518013172652263,.5559442875017586392 ] 
dist 168=[-.77767390145840679986,.52655724113348573703] 
dist 169=[-.82125023410516069044,.52090627712250728015] 
dist 170=[-.87969981525883787202,.50845568208751465163] 
dist 171=[-.94329252813945323124,.50544694509221806736] 
dist 172=[-1.0021721071734212328 ,.35583798016719511748] 
dist 173=[-1.0475187325875890754 ,.34256648555754546715] 
dist 174=[-1.0919599220363538568 ,.31142739413610525517] 
dist 175=[-1.1472195656291708037 ,.30677851866102438067] 
dist 176=[-1.2004367295008519643 ,.26452268151834965378] 
dist 177=[-1.2367108590699031001 ,.25687260160687783668] 
dist 178=[-1.2677772767221158305 ,.2472730268915174466 ] 
dist 179=[-1.3001703428101810280 ,.24511053531388989163] 
dist 180=[-1.3312204664589537520 ,.1857973740648195533 ] 
dist 181=[-1.3569174009161334353 ,.17842025757086276507] 
dist 182=[-1.3838046493937298861 ,.1632876647921454899 ] 
dist 183=[-1.4196161219852039051 ,.15938358261036524393] 
dist 184=[-1.4542089900712144456 ,.14521079176486442831] 
dist 185=[-1.4762233725460450983 ,.14240581863465607114] 
dist 186=[-1.4933993856861390891 ,.13732012683887235207] 
dist 187=[-1.5086433301648173757 ,.13616047177880153802] 
dist 188=[-1.5216131472648414146 ,.05379055680198267986] 
dist 189=[-1.5296949731182025813 ,.04636305987496154956] 
dist 190=[-1.5358043950746601032 ,.03194421792918669586] 
dist 191=[-1.5408869983657504922 ,.02845105046192616300] 
dist 192=[-1.5447885941571890813 ,.01729534181269881749] 
dist 193=[-1.5461751297678438413 ,.01475670389728214193] 
dist 194=[-1.5463739147203343956 ,.01374626093583173052] 
dist 195=[-1.5458664961018257715 ,.01527981999508236008] 
dist 196=[-1.5407271436810826944 ,.01801560073865312990] 
dist 197=[-1.5389793906509241314 ,.02199715689199740242] 
dist 198=[-1.5358581570437755468 ,.02768114928898617595] 
dist 199=[-1.5346947559372704953 ,.03722485507851338076] 
dist 200=[-1.4635293973210146943 ,.04860244228880252765] 
dist 201=[-1.4555449405802682630 ,.06161969396950370724] 
dist 202=[-1.4367119768782767175 ,.07842482438981647698] 
dist 203=[-1.4324020126191536749 ,.10494896087421247854] 
dist 204=[-1.4044682541671318491 ,.13235643197460288502] 
dist 205=[-1.3987391642154613870 ,.1526938533439530936 ] 
dist 206=[-1.3885030307673677192 ,.17188816345390983812] 
dist 207=[-1.3858284210539564170 ,.19472501868954986738] 
dist 208=[-1.3342299512982769615 ,.21835184467323700709] 
dist 209=[-1.3268314120962004806 ,.24070519176207094887] 
dist 210=[-1.3099283244142084850 ,.26656733315672662695] 
dist 211=[-1.3055890576686639825 ,.30422497349426524257] 
dist 212=[-1.2820452313043758636 ,.34320038987482077835] 
dist 213=[-1.2772024062779272297 ,.37433204422612822001] 
dist 214=[-1.2674568066796232293 ,.40590027819709334054] 
dist 215=[-1.2646239834990265621 ,.44662161164483354751] 
dist 216=[-.85673577825754051537,.4904665782716794982 ] 
dist 217=[-.82917083357233653977,.53452546409861298285] 
dist 218=[-.76312967053325124135,.587499270238315532  ] 
dist 219=[-.73261365910748246688,.66699270042766474475] 
dist 220=[-.6493612846974888588 ,.74656772975262075869] 
dist 221=[-.63419422726648473841,.79986786201629129781] 
dist 222=[-.61318806752686573389,.84449751933224275364] 
dist 223=[-.6070592209833549375 ,.88940165555211612223] 
dist 224=[-.49414586061781512653,.93142519705369408836] 
dist 225=[-.47966996511528645736,.96453614636378451848] 
dist 226=[-.44867627725558255969,.99769413625675738209] 
dist 227=[-.44130095686480379484,1.0399058232787450415 ] 
dist 228=[-.40738585444167535975,1.0810357684681479710 ] 
dist 229=[-.40130886023629527747,1.1098681772833566608 ] 
dist 230=[-.3869203548257120525 ,1.1354152495551424244 ] 
dist 231=[-.38458193703446157361,1.1634080155134849499 ] 
dist 232=[-.24038660250424049157,1.1910707552578057145 ] 
dist 233=[-.22678615570759022563,1.2362571759871623977 ] 
dist 234=[-.19550672342202533176,1.2736609813579714944 ] 
dist 235=[-.19039444931631404953,1.3095098315508570886 ] 
dist 236=[-.149851510445141051  ,1.3419165676529387760 ] 
dist 237=[-.14258111441777480231,1.3655562028093915297 ] 
dist 238=[-.13188383723853104847,1.3874669622757922447 ] 
dist 239=[-.12902694593940816409,1.4129603267203827370 ] 
dist 240=[-.07924461458056333727,1.4366420580153909289 ] 
dist 241=[-.07293361643521811049,1.4513085317206990747 ] 
dist 242=[-.05887705225058079930,1.4622802131362190320 ] 
dist 243=[-.05622213838223156123,1.4711873710979046868 ] 
dist 244=[-.03938215197199680518,1.4781578331464617818 ] 
dist 245=[-.03640683686488855390,1.4813851174369589533 ] 
dist 246=[-.03089615288011204390,1.4828813031567711674 ] 

8 phat 2 dirichlet min maxes function [0, 2, 1, 2, 0, 2, 2, 0, 1] 
dist 0=[11.470022233805996017  ,11.470022233805996017  ] 
dist 1=[11.436290966244120831  ,11.502137097391914069  ] 
dist 2=[11.333516620873140250  ,11.553112655227186333  ] 
dist 3=[11.223502009960949869  ,11.598097014731124696  ] 
dist 4=[11.130379280973550443  ,11.636165419954372559  ] 
dist 5=[11.031111488379216665  ,11.659483785306099423  ] 
dist 6=[10.896522387313578028  ,11.676622448850994502  ] 
dist 7=[10.748305359648243772  ,11.689977220620895743  ] 
dist 8=[10.594539518699282070  ,11.700771490082456580  ] 
dist 9=[10.406103236960435160  ,11.707670164690333247  ] 
dist 10=[10.119239581917815377  ,11.713077133668932577  ] 
dist 11=[9.8301158679880491600 ,11.717905457766570252  ] 
dist 12=[9.6326407739416449478 ,11.722018676865904196  ] 
dist 13=[9.4630630590361722143 ,11.724564612345680308  ] 
dist 14=[9.2854979896488562906 ,11.726453872020736562  ] 
dist 15=[9.1148162154575821070 ,11.727937675674590502  ] 
dist 16=[8.9727622632341010387 ,11.728895705444129382  ] 
dist 17=[8.8234137382168695928 ,11.728680861012125190  ] 
dist 18=[8.6235563469018979361 ,11.727540329517825265  ] 
dist 19=[8.4240004986497160865 ,11.725421385717715191  ] 
dist 20=[8.2758554454091432052 ,11.721162900066074551  ] 
dist 21=[8.1358960956920414925 ,11.718295500599684739  ] 
dist 22=[7.9690723056233806543 ,11.711227372202231446  ] 
dist 23=[7.7962024550518663596 ,11.707816795517498026  ] 
dist 24=[7.6320602777035153620 ,11.688628592305145347  ] 
dist 25=[7.4416012875749808824 ,11.682299343304625377  ] 
dist 26=[7.1634791866874734887 ,11.676003026777179340  ] 
dist 27=[6.8842542121233819061 ,11.672076556937174121  ] 
dist 28=[6.6893825494326158842 ,11.563097193764555587  ] 
dist 29=[6.5175131914152606525 ,11.552288795197790639  ] 
dist 30=[6.3302789121817685015 ,11.459574405149164226  ] 
dist 31=[6.1457526920687494723 ,11.306958857839492006  ] 
dist 32=[5.9847106775601902918 ,9.5710127587975838808 ] 
dist 33=[5.8087660770584084650 ,9.4574473623804436039 ] 
dist 34=[5.5646333883301755581 ,9.1896135998105456412 ] 
dist 35=[5.3167450059533899628 ,9.1489917530728674661 ] 
dist 36=[5.1257770708384591214 ,8.7778806798425137134 ] 
dist 37=[4.9384418430116565116 ,8.7095218040918608686 ] 
dist 38=[4.7050787460457683349 ,8.6246189451335643203 ] 
dist 39=[4.4577265785639572572 ,8.6036309972788779521 ] 
dist 40=[4.2144383398691963720 ,8.1832988805618367651 ] 
dist 41=[3.9255665390538756424 ,8.1419038862225383641 ] 
dist 42=[3.4958954840992348414 ,8.0490753391509578279 ] 
dist 43=[3.0672476118449165206 ,8.0310852307165192356 ] 
dist 44=[2.7824670374368865699 ,7.9165765876969782349 ] 
dist 45=[2.5463320530836134860 ,7.8958465873321831793 ] 
dist 46=[2.3122466758709463575 ,7.8577197556082598771 ] 
dist 47=[2.0951823615009956133 ,7.8487280856575673611 ] 
dist 48=[1.9271238891586439758 ,7.7250024880635879481 ] 
dist 49=[1.7614443231106506637 ,7.7078582368117473371 ] 
dist 50=[1.5538923041156413085 ,7.6571822044145821494 ] 
dist 51=[1.3529788718749857779 ,7.4281124953905776779 ] 
dist 52=[1.2138499234641227269 ,7.4087025587491657099 ] 
dist 53=[1.0922391849348741519 ,7.3925827417251456724 ] 
dist 54=[.96139074795140844072,7.3227687552778800972 ] 
dist 55=[.83334385828538549748,7.1733191712133741470 ] 
dist 56=[.72293593052581331037,5.5522509895701703821 ] 
dist 57=[.60339754609419892677,5.5137722821944067506 ] 
dist 58=[.43882655729335121282,5.4244673358524275687 ] 
dist 59=[.27752248704120704119,5.4084158618603888804 ] 
dist 60=[.17104952811414675557,5.2872512878858687642 ] 
dist 61=[.08349653999806072560,5.2645186340513250319 ] 
dist 62=[-.00213211091564061479,5.2292480745924083793 ] 
dist 63=[-.08081771245290924033,5.2198518851094034061 ] 
dist 64=[-.140601822089051805  ,3.2137347218449163651 ] 
dist 65=[-.1984933475095696801 ,3.0925041540731800030 ] 
dist 66=[-.26961409522659622842,2.8085228927044365093 ] 
dist 67=[-.33785225664237220528,2.7673936426498152752 ] 
dist 68=[-.38421621203258050346,2.3844961804542451218 ] 
dist 69=[-.42383886583084278502,2.3156429848948197649 ] 
dist 70=[-.46511464947721295042,2.2322266767368320780 ] 
dist 71=[-.50475501967479727574,2.2167298446207322575 ] 
dist 72=[-.53784095683319483326,1.6816715196161822949 ] 
dist 73=[-.68035401924858533921,1.6160130035695082244 ] 
dist 74=[-.83847366456512690726,1.4837165044091675061 ] 
dist 75=[-1.0115643386992807926 ,1.4502884522594845100 ] 
dist 76=[-1.1826030066237130591 ,1.3334917754316178477 ] 
dist 77=[-1.3325170154055094206 ,1.3094873521399927171 ] 
dist 78=[-1.4968081025669137982 ,1.2757986449890191068 ] 
dist 79=[-1.7253445448113319411 ,1.2663193525941126965 ] 
dist 80=[-1.9500175854317321020 ,.49705514444503894488] 
dist 81=[-2.0988588063659704992 ,.43251439389226693334] 
dist 82=[-2.2217514414870063025 ,.28708153611108898042] 
dist 83=[-2.3426518793337450073 ,.26197615246236756034] 
dist 84=[-2.4541075081020513359 ,.08342681287388100643] 
dist 85=[-2.5392296418902273336 ,.05202421167074220912] 
dist 86=[-2.6220095999185329782 ,-.00036958115767377680] 
dist 87=[-2.7241009439105358529 ,-.01217640504285591087] 
dist 88=[-2.8220873332365297326 ,-.19596417604719377308] 
dist 89=[-2.8884520455663701224 ,-.21986153196307559417] 
dist 90=[-2.9448669296519157500 ,-.27149402291423559328] 
dist 91=[-3.0030632824696807557 ,-.28183226096780958643] 
dist 92=[-3.0585037595411077828 ,-.32624636837974903943] 
dist 93=[-3.1039000038685306310 ,-.30875920138169621356] 
dist 94=[-3.1510027602117134413 ,-.28883428343946629219] 
dist 95=[-3.2132745729362169202 ,-.26872143085189229076] 
dist 96=[-3.2728274696272018949 ,-.25048019155430374777] 
dist 97=[-3.3090572622860153926 ,-.22999871511744232705] 
dist 98=[-3.3354372941196586032 ,-.20092618760924432772] 
dist 99=[-3.3555939464855043162 ,-.17117335795877941421] 
dist 100=[-3.3711783721026095820 ,-.14797019674362411979] 
dist 101=[-3.3792692058360290658 ,-.12496398668571595225] 
dist 102=[-3.3834916648218376890 ,-.09599626685240383483] 
dist 103=[-3.3838489185628021435 ,-.06516371471196560058] 
dist 104=[-3.3533834799429457213 ,-.03469911772211672421] 
dist 105=[-3.3475049298064210740 ,.00155221513661052438] 
dist 106=[-3.3399752036054321459 ,.05552618541828086497] 
dist 107=[-3.3366159333532028271 ,.10930550802767034016] 
dist 108=[-3.3291538852856289760 ,.14477902238926838852] 
dist 109=[-3.3255244970062814672 ,.17388571771333505918] 
dist 110=[-3.3222667886111245427 ,.20220560052533988625] 
dist 111=[-3.3197532107165109621 ,.22809597947363214149] 
dist 112=[-2.9655013304766096154 ,.24748789046239382462] 
dist 113=[-2.9340425649351242719 ,.26597426192144113444] 
dist 114=[-2.8663300894807118901 ,.28824432688982574382] 
dist 115=[-2.8483284111247479743 ,.30934581121240778021] 
dist 116=[-2.7702410976471971326 ,.32315956255331784208] 
dist 117=[-2.7552994384953046699 ,.33438162213934423163] 
dist 118=[-2.7190805991796770372 ,.3451195943376143534 ] 
dist 119=[-2.7118856078794383107 ,.35482383992965941434] 
dist 120=[-2.6360103368384601396 ,.36191282760448876869] 
dist 121=[-2.6227276221137087274 ,.36850149738343458283] 
dist 122=[-2.5968392745489707417 ,.37620670803771088943] 
dist 123=[-2.5898078804910449582 ,.38340984408074420185] 
dist 124=[-2.5631792842634198029 ,.38799076250948086947] 
dist 125=[-2.5568933086104226113 ,.39156851017428984694] 
dist 126=[-2.5441102028743874266 ,.39475836630078890201] 
dist 127=[-2.5401465364782247109 ,.39748939357331679785] 
dist 128=[-1.0330395882068942681 ,.39923162509947777901] 
dist 129=[-.95045061413279526312,.40059953871813843286] 
dist 130=[-.75673759317573728698,.40183329657219592415] 
dist 131=[-.72896497154825377362,.4027975658737651261 ] 
dist 132=[-.46779654665166615548,.40308742671949644324] 
dist 133=[-.42100805211398850925,.40299502686558260156] 
dist 134=[-.36476589223510134362,.40281100528468855037] 
dist 135=[-.35512451751424323826,.40117003781600308592] 
dist 136=[.00564548189335458182,.40063393903658485681] 
dist 137=[.0494195566393847278 ,.43167861751858305324] 
dist 138=[.1246227935140169406 ,.518127846657431743  ] 
dist 139=[.11710167895171965369,.61297578369607472783] 
dist 140=[.10182309848162923107,.70678538257110909142] 
dist 141=[.07961991130769716445,.78908282694513811967] 
dist 142=[.05697557579202972134,.87930594586444512895] 
dist 143=[.03560008302387402175,1.0048093846289145964 ] 
dist 144=[.01846996370410721533,1.1280856856145810253 ] 
dist 145=[.00105426412200978069,1.2094030654048931754 ] 
dist 146=[-.02146325790245472428,1.2761274139642041432 ] 
dist 147=[-.04355692032341850155,1.3410488678779819420 ] 
dist 148=[-.05927799110578241134,1.4003974479002724770 ] 
dist 149=[-.07344594957324691170,1.4448370870663200087 ] 
dist 150=[-.08932987680510646019,1.4871850588172093889 ] 
dist 151=[-.10523126894569407417,1.5381700106782314262 ] 
dist 152=[-.11946917997181324764,1.5864501456504354136 ] 
dist 153=[-.13531306234574379322,1.6179822891838910019 ] 
dist 154=[-.15763590301891343234,1.6435088420864835047 ] 
dist 155=[-.17966419900211388603,1.6677738707103014940 ] 
dist 156=[-.19433042437078864686,1.6895831839894420843 ] 
dist 157=[-.20650965228358104598,1.7052903057764474285 ] 
dist 158=[-.21859395651050823736,1.7196530192223520964 ] 
dist 159=[-.22979018129698521819,1.7360877124886174320 ] 
dist 160=[-.23841854353850658993,1.7510498019709902734 ] 
dist 161=[-.24687692327212229193,1.7595238768289695221 ] 
dist 162=[-.25739356575853341048,1.7649334293533205307 ] 
dist 163=[-.26751502603138803122,1.7676397354886063750 ] 
dist 164=[-.27439333197978341664,1.7690033865504384930 ] 
dist 165=[-.28025934815290426095,1.7690429895376747652 ] 
dist 166=[-.28633326186373633336,1.7681467261277708813 ] 
dist 167=[-.29212605548642524417,1.7674669825337005446 ] 
dist 168=[-.29686807977429293238,1.7407952592696601802 ] 
dist 169=[-.30178147507479526714,1.7363285237781142746 ] 
dist 170=[-.3082596014381026293 ,1.7276685749172885265 ] 
dist 171=[-.31476567843127514996,1.7250468399143678343 ] 
dist 172=[-.31979092771919262658,1.7138320632704706785 ] 
dist 173=[-.32472891508560594464,1.7110752618393341770 ] 
dist 174=[-.33088624941555993366,1.7036770133821807760 ] 
dist 175=[-.33740983827700993326,1.7013582427408761650 ] 
dist 176=[-.34381250625607272671,1.5367923227830624115 ] 
dist 177=[-.3513995126095942592 ,1.5211445578037953429 ] 
dist 178=[-.36265913953113788771,1.4861817165786737013 ] 
dist 179=[-.37440412722891490785,1.4780241107458032611 ] 
dist 180=[-.38393205889874705826,1.4336333835815479450 ] 
dist 181=[-.39372914617759450351,1.4250781858052969199 ] 
dist 182=[-.40655052137201201251,1.4076347052211160612 ] 
dist 183=[-.42044879757735707371,1.4027753424630888094 ] 
dist 184=[-.43455228797251881723,1.3461995256025211623 ] 
dist 185=[-.45161132250461682984,1.3378003007668339932 ] 
dist 186=[-.47732841416413238342,1.3173592223371355051 ] 
dist 187=[-.50345341470780758982,1.3135656020960763686 ] 
dist 188=[-.52214363491676021305,1.2819116033664402837 ] 
dist 189=[-.53909978886028849326,1.2755610443566323936 ] 
dist 190=[-.55829053844563600305,1.2667174645474251691 ] 
dist 191=[-.57761688271034725614,1.2638525272884695144 ] 
dist 192=[-.59511527964967378425,.73900573752754132577] 
dist 193=[-.61475384847252123133,.71463885561971143326] 
dist 194=[-.64263845994413612912,.65796309789488698057] 
dist 195=[-.67120560527608145684,.64889659360415310922] 
dist 196=[-.69357354201603012102,.57312576334289332717] 
dist 197=[-.71584507171166591216,.55935072806587486259] 
dist 198=[-.7440267110164484314 ,.54027728644314386981] 
dist 199=[-.77410119548666336145,.53472570746166643027] 
dist 200=[-.80394196094523226342,.43283344515419925926] 
dist 201=[-.83954694687447884222,.41979436898503814624] 
dist 202=[-.89267176849841384817,.39186624842424389313] 
dist 203=[-.94575603572249998367,.385276649987775076  ] 
dist 204=[-.98119884968538949899,.35473533526588945097] 
dist 205=[-1.0107560081037347277 ,.34927981004161917766] 
dist 206=[-1.0403043345802151686 ,.33643235079279873769] 
dist 207=[-1.0678392923325743664 ,.3343237429089645604 ] 
dist 208=[-1.0908198043036829556 ,.20689423884631017235] 
dist 209=[-1.1371129761725828612 ,.19486525644653563111] 
dist 210=[-1.1746885493619616620 ,.16727802760299003594] 
dist 211=[-1.2105647631197363350 ,.16272468714104876097] 
dist 212=[-1.2429056191327075795 ,.12721452138501723976] 
dist 213=[-1.2663439982902959062 ,.12085856059641208475] 
dist 214=[-1.2879150826647930883 ,.11132605566640438882] 
dist 215=[-1.3127889565468449306 ,.10884088748409725534] 
dist 216=[-1.3357781087988470124 ,.06606189277853815056] 
dist 217=[-1.3498125512882710495 ,.06063761130664565549] 
dist 218=[-1.3600713442327854840 ,.04841722871140640754] 
dist 219=[-1.3679624221446862504 ,.04624435244385764178] 
dist 220=[-1.3740814050925389540 ,.03119823439231215362] 
dist 221=[-1.3772540098032245975 ,.02853393580392411356] 
dist 222=[-1.3788969346163905386 ,.02393777641760937879] 

8 phat 2 dirichlet min maxes function [2, 2, 1, 0, 1, 2, 2, 1, 2] 
dist 0=[13.115757913332476581  ,13.115757913332476581  ] 
dist 1=[13.112322351171451643  ,13.118004980545267994  ] 
dist 2=[13.100827861076949838  ,13.119956326982856549  ] 
dist 3=[13.080421117805303403  ,13.120954244067765542  ] 
dist 4=[13.043527566569422798  ,13.121452662867962263  ] 
dist 5=[12.998519713824542119  ,13.121401113251061354  ] 
dist 6=[12.945666894290867619  ,13.120983706612002544  ] 
dist 7=[12.876553810533667144  ,13.120014466909835507  ] 
dist 8=[12.766526366228610881  ,13.118426008986225045  ] 
dist 9=[12.648398498398825901  ,13.115641890277349229  ] 
dist 10=[12.546892181403108507  ,13.112522642334676534  ] 
dist 11=[12.437387152792021976  ,13.110536123193406745  ] 
dist 12=[12.287268307925525752  ,13.108866570593830259  ] 
dist 13=[12.121173728612751425  ,13.107138251066235460  ] 
dist 14=[11.947779776185978981  ,13.105456136947528106  ] 
dist 15=[11.734527387644848954  ,13.103973059487012490  ] 
dist 16=[11.409037165183640462  ,13.102319897361316135  ] 
dist 17=[11.080704860073009658  ,13.099957249512673912  ] 
dist 18=[10.856085448158751745  ,13.097484630903146646  ] 
dist 19=[10.662804759947753168  ,13.095392186014893395  ] 
dist 20=[10.459793167086921079  ,13.093142914585557364  ] 
dist 21=[10.264263723771631076  ,13.090044984081396458  ] 
dist 22=[10.100901526814026250  ,13.086585933056127033  ] 
dist 23=[9.9285965326336241133 ,13.082892318673460609  ] 
dist 24=[9.6972998246277860509 ,13.078272865810185556  ] 
dist 25=[9.4660221979062163012 ,13.067381138614730240  ] 
dist 26=[9.2937909513055744839 ,10.841867275691861180  ] 
dist 27=[9.1305468621964749446 ,10.717846519479951428  ] 
dist 28=[8.9352062295756089146 ,10.435302591352236572  ] 
dist 29=[8.7323763783502400975 ,10.384270232865720646  ] 
dist 30=[8.5391778939803768684 ,10.021643612811819210  ] 
dist 31=[8.3145369920764744544 ,9.9554970921707240373 ] 
dist 32=[7.9859565439747800068 ,9.8455622927806420027 ] 
dist 33=[7.6558642803728815619 ,9.8194150426541516375 ] 
dist 34=[7.4251752077260863027 ,9.3713651865308697260 ] 
dist 35=[7.2213885646991206959 ,9.3124947916371391185 ] 
dist 36=[6.9988842315712017031 ,9.1742152790463504845 ] 
dist 37=[6.7793110208667467063 ,9.1514132512487002108 ] 
dist 38=[6.5872437194735328975 ,8.9598083048612559507 ] 
dist 39=[6.3770416222557869671 ,8.9240104310686288211 ] 
dist 40=[6.0849356061970753356 ,8.8749314609846479106 ] 
dist 41=[5.7881632446318970555 ,8.8599905809645619353 ] 
dist 42=[5.5592959013352130470 ,8.4480257660402574073 ] 
dist 43=[5.3345649993678309263 ,8.4000174421789909641 ] 
dist 44=[5.0543324444606768271 ,8.2981988058901674469 ] 
dist 45=[4.7571731979323634659 ,8.2719290114042788077 ] 
dist 46=[4.4647411425074800354 ,8.1621515417532365220 ] 
dist 47=[4.1174206359754778430 ,8.1418240334617717236 ] 
dist 48=[3.6007303825064000774 ,8.1072227237349471017 ] 
dist 49=[3.0849815902446686477 ,8.0843337604702594784 ] 
dist 50=[2.7414254630764588916 ,8.0090683883573003844 ] 
dist 51=[2.4555748451923419837 ,7.9943050404379302666 ] 
dist 52=[2.1706209055947258963 ,7.9788182507793075502 ] 
dist 53=[1.9053814610648287801 ,7.9722251397042676085 ] 
dist 54=[1.6983788610322467517 ,7.8336149317292858444 ] 
dist 55=[1.4663355740099708310 ,7.8093897498347925459 ] 
dist 56=[.87878193054015480246,7.6817593934119105292 ] 
dist 57=[0                     ,7.4382535354763926729 ] 
dist 58=[.8043118270122066284 ,2.3754683884051154360 ] 
dist 59=[.6484464493530346056 ,2.3264540590330215112 ] 
dist 60=[.4781251833883893946 ,1.8701890888422604145 ] 
dist 61=[.3099090513736145334 ,1.7886705526346074422 ] 
dist 62=[.1624613526075332038 ,1.6899565864677801348 ] 
dist 63=[.0007974297215311608 ,1.6727580848960544974 ] 
dist 64=[-.22428194564595808885,1.0511092944357111664 ] 
dist 65=[-.44590477506110436976,.97559728784636254962] 
dist 66=[-.59374486861074289304,.82303951817113433446] 
dist 67=[-.71701087056081420853,.78468694466990099976] 
dist 68=[-.84034604018736904952,.65149287000145819515] 
dist 69=[-.95547550812199784189,.6244650065082872609 ] 
dist 70=[-1.0459228601849135929 ,.58846495915481752717] 
dist 71=[-1.1639766080333767752 ,.58022395159419124323] 
dist 72=[-1.3803652694047136944 ,-.23585289847503483003] 
dist 73=[-1.5234576773473989741 ,-.30291746327729125018] 
dist 74=[-1.6413242810525032645 ,-.45520018165261560444] 
dist 75=[-1.7568293855578298550 ,-.47478686794489923162] 
dist 76=[-1.8630255839436442526 ,-.47060685776015627356] 
dist 77=[-1.9436647298912846544 ,-.46051485135462890852] 
dist 78=[-2.0216437871364792420 ,-.4425009232837370535 ] 
dist 79=[-2.1172044298767772286 ,-.41519308824545906729] 
dist 80=[-2.2086334357541919470 ,-.36795234497814417164] 
dist 81=[-2.2700904156168799348 ,-.31877394798462308056] 
dist 82=[-2.3218349194866368040 ,-.28371650773685807209] 
dist 83=[-2.3744226101805749540 ,-.25214506127662376841] 
dist 84=[-2.4240359146225751386 ,-.21688677512207678487] 
dist 85=[-2.4638880058165180955 ,-.18175275205760229707] 
dist 86=[-2.5045550708542656846 ,-.15067103167919599637] 
dist 87=[-2.5574350536192065860 ,-.11643948675361348688] 
dist 88=[-2.6078034604735531836 ,-.06870810777408833992] 
dist 89=[-2.6384265870356818818 ,-.02030731203185266070] 
dist 90=[-2.6607118353688464149 ,.01660414558422250194] 
dist 91=[-2.6777290294268188115 ,.05238525309071736855] 
dist 92=[-2.6909467711275308076 ,.09627330734863392104] 
dist 93=[-2.6980325733337727915 ,.14234989456574026826] 
dist 94=[-2.7020497145820438386 ,.18688444348984597535] 
dist 95=[-2.7029876091082117000 ,.23911148865469286557] 
dist 96=[-2.6761774116168941996 ,.31594732737149165226] 
dist 97=[-2.6712690446609068509 ,.39312540222446392541] 
dist 98=[-2.6656571973119654888 ,.44672264335151531686] 
dist 99=[-2.6628542407865226549 ,.4936603513246395052 ] 
dist 100=[-2.6584430540034545449 ,.54421476923466070551] 
dist 101=[-2.6566184675362353614 ,.59363857578649536221] 
dist 102=[-2.6554905967943913574 ,.63605822286453383525] 
dist 103=[-2.6550119627135097102 ,.6817674852142632787 ] 
dist 104=[-2.3532667317877125079 ,.74434839832133309676] 
dist 105=[-2.3271140994939334983 ,.80744116811910768726] 
dist 106=[-2.2712095844367604376 ,.85519906719976458775] 
dist 107=[-2.2561206973519746107 ,.90120896814557943859] 
dist 108=[-2.1930472106255074987 ,.95731471596472251032] 
dist 109=[-2.1810475032079896505 ,1.0161168111818436616 ] 
dist 110=[-2.1510400692263494691 ,1.0729112778085748833 ] 
dist 111=[-2.1459886687273433087 ,1.1395386634754875464 ] 
dist 112=[-2.0894524636603549844 ,1.2376649838950274467 ] 
dist 113=[-2.0791634738993671413 ,1.3348935412527354687 ] 
dist 114=[-2.0606427966579678441 ,1.3979315400458665336 ] 
dist 115=[-2.0559587341270430993 ,1.4484516552883486036 ] 
dist 116=[-2.0406951318523960689 ,1.4956211145615434160 ] 
dist 117=[-2.0362189606228694894 ,1.5374425058353192197 ] 
dist 118=[-2.0326592424143289006 ,1.5665761143735548057 ] 
dist 119=[-2.0313233607989910795 ,1.5922122241528844872 ] 
dist 120=[-.75999678169248973658,1.6200484562653802883 ] 
dist 121=[-.69210893281242672813,1.6454419619387840994 ] 
dist 122=[-.53314186962751561482,1.6613094171530603808 ] 
dist 123=[-.51026946712366811226,1.6733574465245887660 ] 
dist 124=[-.29689069199463792268,1.6834751603224750197 ] 
dist 125=[-.25874095020266772758,1.6916690053631201486 ] 
dist 126=[-.21245587914421083298,1.6960225169812422744 ] 
dist 127=[-.20430941108727060258,1.6984286356194419875 ] 
dist 128=[.08654678979585384463,1.6988338744254152295 ] 
dist 129=[.12180488946858312111,1.6081292331208914178 ] 
dist 130=[.19338671573185615856,1.5995720820576314975 ] 
dist 131=[.21141776571163799373,1.5825902608021422853 ] 
dist 132=[.27433048241452162694,1.5778501689964028696 ] 
dist 133=[.28694077690538374334,1.5591490359254836745 ] 
dist 134=[.30424744807436501751,1.5548758275049727072 ] 
dist 135=[.30836099348823208777,1.5450961243912861705 ] 
dist 136=[.6711124313327772789 ,1.5418321930927230646 ] 
dist 137=[.70077453019848579423,1.5266223128149158912 ] 
dist 138=[.76865691649181155033,1.5227332725527691185 ] 
dist 139=[.77845518397160080793,1.5172508339640038680 ] 
dist 140=[.863347883595164651  ,1.5152277413227286891 ] 
dist 141=[.87787445202132522782,1.5106473748380273689 ] 
dist 142=[.89705202029904265457,1.5088462785918468514 ] 
dist 143=[.90041091515632473823,1.5075782110094008544 ] 
dist 144=[.78082768631569573512,1.5066941971955142927 ] 
dist 145=[.64427410573214212472,1.1155701034968140927 ] 
dist 146=[.55242731980740661427,1.1365513736675224128 ] 
dist 147=[.47511387184188114958,1.1570396668800385818 ] 
dist 148=[.39667317424300715419,1.1758244662566223726 ] 
dist 149=[.32285724894061094828,1.1899942605825345856 ] 
dist 150=[.26403623471160171266,1.2036045078435334822 ] 
dist 151=[.20452293105441595857,1.2201531647997022495 ] 
dist 152=[.1279383949752768799 ,1.2356558365669669120 ] 
dist 153=[.05293120715932654201,1.2450833813041406306 ] 
dist 154=[-.00027507948813158379,1.2519387073094357486 ] 
dist 155=[-.04806890885544206700,1.2571541660617175761 ] 
dist 156=[-.10143392623222918195,1.2609707938279809037 ] 
dist 157=[-.15475097390625930963,1.2622315460395360384 ] 
dist 158=[-.20235331532634145184,1.2625539050807218836 ] 
dist 159=[-.25522615839535258322,1.2626171483268746343 ] 
dist 160=[-.32961872236660303072,1.2557650490081104693 ] 
dist 161=[-.40303607454889755952,1.2541504133204964628 ] 
dist 162=[-.45200952785041302866,1.2503478892261430762 ] 
dist 163=[-.49279412907821896396,1.2488785809919404593 ] 
dist 164=[-.5334669254338986814 ,1.2411663016972473077 ] 
dist 165=[-.57129843087215835823,1.2392498051577655795 ] 
dist 166=[-.60072179981785383259,1.2344803025268593253 ] 
dist 167=[-.62982979992874130528,1.2326847291652756690 ] 
dist 168=[-.6664007462579121741 ,1.1505372831054965663 ] 
dist 169=[-.70180403325394536554,1.1420031981786220921 ] 
dist 170=[-.72624314414908564835,1.1222160654590084807 ] 
dist 171=[-.74750338405368144638,1.1179250729155960499 ] 
dist 172=[-.77019550316107919005,1.0902381038758995121 ] 
dist 173=[-.79226956583846058541,1.0847588343011107522 ] 
dist 174=[-.81105883282868031028,1.0748958809555307803 ] 
dist 175=[-.8311790634884756714 ,1.0723908360086500354 ] 
dist 176=[-.85857641289375486598,1.0275243216756454001 ] 
dist 177=[-.88522392360406012539,1.0211898074777205424 ] 
dist 178=[-.90234580055655677983,1.0063575667413022332 ] 
dist 179=[-.91589220185393550198,1.0030864371404682438 ] 
dist 180=[-.92824137479545109371,.98166820951673333988] 
dist 181=[-.93898407700396060589,.97735479522928229839] 
dist 182=[-.94610631423669278133,.96968663408034690732] 
dist 183=[-.95199320756877235366,.96772871084043393646] 
dist 184=[-.95779611745851433508,.62107289881090650846] 
dist 185=[-.96272182687699626105,.59861672851805375523] 
dist 186=[-.96510080064770889616,.54874891942674471014] 
dist 187=[-.96624423218956646958,.54074056745491395947] 
dist 188=[-.96631339406339883488,.47431575645534313603] 
dist 189=[-.96434094151191270339,.46225642086968769834] 
dist 190=[-.96346542338398382679,.44541191199104283377] 
dist 191=[-.96258629100335538769,.44056535596719530819] 
dist 192=[-.96188915996132063739,.35213662501947463632] 
dist 193=[-.92648375582241121916,.34082853472748619149] 
dist 194=[-.92224220055658405207,.3164865238748903025 ] 
dist 195=[-.91207030402486605738,.31088206984194248325] 
dist 196=[-.90968513391081018888,.28391935145590199422] 
dist 197=[-.89386709264772238481,.27910626431738005624] 
dist 198=[-.89054918239823493521,.26810058342284327008] 
dist 199=[-.88472231353933416422,.26603561729049176549] 
dist 200=[-.9393756260725637668 ,.15956345141855904556] 
dist 201=[-.97522199445015912322,.14940064923797343356] 
dist 202=[-1.0044018237907223356 ,.12630436103850371068] 
dist 203=[-1.0324031366051890720 ,.12232294277609200521] 
dist 204=[-1.0577407121878457937 ,.09322726848024911434] 
dist 205=[-1.0762687892618226581 ,.08803852390892582910] 
dist 206=[-1.0934881732458691851 ,.07964252020683317413] 
dist 207=[-1.1135925511735271110 ,.07764467073870801001] 
dist 208=[-1.1323067849493687890 ,.04478364338991545036] 
dist 209=[-1.1439672599235589435 ,.05303014394454363560] 
dist 210=[-1.1527743315724087860 ,.12121406629969804204] 
dist 211=[-1.1600783704023098096 ,.17826868117044797686] 
dist 212=[-1.1659173455602578166 ,.23561204294618901251] 
dist 213=[-1.1688659200484852434 ,.28923629819908644409] 
dist 214=[-1.1703013262587413320 ,.33141925622063735342] 
dist 215=[-1.1705262519424490531 ,.3735980424231135439 ] 
dist 216=[-.4303929670350670629 ,.42720565088732334597] 
dist 217=[-.3644385895116548037 ,.47939592442060886798] 
dist 218=[-.35593153246906990837,.51590719245468330769] 
dist 219=[-.3375409564059778278 ,.54817973301715219994] 
dist 220=[-.33325250189889012958,.58342050947312694539] 
dist 221=[-.31248089535622644904,.61817385833760436231] 
dist 222=[-.30871601462625662439,.64849732718089250266] 
dist 223=[-.30019154469074755456,.68160043314685930072] 
dist 224=[-.29840249249638833415,.72746882959196422455] 
dist 225=[-.21370754959220358341,.77243460793486591904] 
dist 226=[-.20555159310234484465,.801928392126549772  ] 
dist 227=[-.18679027918751901322,.82594043663584122898] 
dist 228=[-.18365749499720969207,.84898620193579966214] 
dist 229=[-.15518268934858640278,.86984026362846417905] 
dist 230=[-.14998943028797638988,.88508827137305911203] 
dist 231=[-.12980969959572733152,.89925679287468717639] 
dist 232=[-.10120030362340792856,.91579427977704803442] 
dist 233=[-.06432337843960952922,.93118397432207855714] 
dist 234=[-.05968046409628635104,.94076277985242021138] 
dist 235=[-.04980419891383192571,.94798496005432425275] 
dist 236=[-.04751105082725636428,.95395113453235147571] 
dist 237=[-.03707861124793828049,.9587019183303768234 ] 
dist 238=[-.03523757604105225837,.96106407384657590861] 
dist 239=[-.03100598334917464189,.96218552142764684244] 

8 phat 2 dirichlet min maxes function [2, 1, 2, 0, 2, 2, 0, 0, 1] 
dist 0=[12.332709979248090606  ,12.332709979248090606  ] 
dist 1=[12.313905805631319703  ,12.340540629345288184  ] 
dist 2=[12.289151392342832895  ,12.343698895127322028  ] 
dist 3=[12.257528292347427463  ,12.343816894297831700  ] 
dist 4=[12.214586537118036292  ,12.340544677953424164  ] 
dist 5=[12.144566064182073844  ,12.319816846172460064  ] 
dist 6=[12.068914368341417494  ,12.311705181178236421  ] 
dist 7=[12.003451289171626394  ,12.299978959185033988  ] 
dist 8=[11.932431031845656583  ,12.290713553332443159  ] 
dist 9=[11.834552749790263074  ,12.258420503709485694  ] 
dist 10=[11.725997722485876433  ,12.250227470943255028  ] 
dist 11=[11.612278336530983574  ,12.231660443674245062  ] 
dist 12=[11.472125147428079888  ,12.224923628848636672  ] 
dist 13=[11.257856301268418191  ,12.127103311978820830  ] 
dist 14=[11.041459188294772317  ,12.111363815859993972  ] 
dist 15=[10.892793727844776910  ,12.073539562707943631  ] 
dist 16=[10.764181249312963422  ,12.063040486298665198  ] 
dist 17=[10.627977056341451118  ,12.001553045841713521  ] 
dist 18=[10.496084695936521841  ,11.987941239815202314  ] 
dist 19=[10.384714074732363498  ,11.962376834286414254  ] 
dist 20=[10.266198611016181465  ,11.954924222908870696  ] 
dist 21=[10.105729501409240736  ,11.612773489181680592  ] 
dist 22=[9.9446060457178861306 ,11.573884979540253320  ] 
dist 23=[9.8234719763123547034 ,11.501438490460762527  ] 
dist 24=[9.7075136064969536652 ,11.483429264051596397  ] 
dist 25=[9.5670866747113497412 ,11.425112431661378350  ] 
dist 26=[9.4203544009811628063 ,11.409683959649238227  ] 
dist 27=[9.2791765244356592554 ,11.334221268998587738  ] 
dist 28=[9.1139162275098117415 ,11.181073191977100174  ] 
dist 29=[8.8708661288690938242 ,10.554585296549073076  ] 
dist 30=[8.6260778172680050855 ,10.476407144210798906  ] 
dist 31=[8.4538644137614890952 ,10.180529586874373886  ] 
dist 32=[8.1336673441745441067 ,9.0565201696720417338 ] 
dist 33=[7.8057665145222029985 ,8.9300646660294982185 ] 
dist 34=[7.5273711364278710476 ,8.9040509223378825819 ] 
dist 35=[7.2409239317067784006 ,8.8512652301540496367 ] 
dist 36=[6.9687042362222516564 ,8.8366529860400373792 ] 
dist 37=[6.7472019114396115963 ,8.2937337348061635605 ] 
dist 38=[6.5187917643711798396 ,8.0889247701345518947 ] 
dist 39=[6.2189431019565860593 ,8.0603120489067334319 ] 
dist 40=[5.9222421350353764462 ,7.9965768389772262507 ] 
dist 41=[5.7064171253131646016 ,7.9829210940728723070 ] 
dist 42=[5.5069148084046822888 ,7.9040685232688089438 ] 
dist 43=[5.2754853925566084509 ,7.8893335533701825744 ] 
dist 44=[5.0391306537145066652 ,7.8605299215772272142 ] 
dist 45=[4.8199272739345247403 ,7.8530239921908398581 ] 
dist 46=[4.5696263794853724212 ,6.8767849066397584137 ] 
dist 47=[4.2089014974774920794 ,6.7806865237854688488 ] 
dist 48=[3.8487938304857529857 ,6.7664315285846561881 ] 
dist 49=[3.6009587863041875383 ,6.6229953863548727052 ] 
dist 50=[3.3860578570969408281 ,6.5956682524823330751 ] 
dist 51=[3.1576577263034986338 ,6.5649333723331874834 ] 
dist 52=[2.8499258737477394467 ,6.5580571074851756161 ] 
dist 53=[2.2645371709957135767 ,5.6257824028380758999 ] 
dist 54=[1.8725368024617405049 ,5.4863686123121027427 ] 
dist 55=[1.5442634763692461660 ,5.4295372763814899651 ] 
dist 56=[1.2137282333237566217 ,4.8516248226622095820 ] 
dist 57=[.90408796924427470443,4.8053298975432712535 ] 
dist 58=[.65937638715122660535,4.7686515001014560784 ] 
dist 59=[.41353185899080390044,4.6994681999263376013 ] 
dist 60=[.0993600990816394856 ,4.3802439959468842932 ] 
dist 61=[-.20754171321898075981,4.2001370702358492591 ] 
dist 62=[-.4243131046814107262 ,3.4842247425614619966 ] 
dist 63=[-.61817496885349003625,3.2868516204580085130 ] 
dist 64=[-.83345888625767936209,2.7078127262016112941 ] 
dist 65=[-1.0479940709381376077 ,2.5805619638985017973 ] 
dist 66=[-1.2388626168401932251 ,2.5549216061821458711 ] 
dist 67=[-1.4504025527478548296 ,2.5120279589177926896 ] 
dist 68=[-1.7476079098729062822 ,2.5021026717117557841 ] 
dist 69=[-2.0410649231506858321 ,1.7086182438475686705 ] 
dist 70=[-2.2376153021366193094 ,1.6406107800210739423 ] 
dist 71=[-2.4022683476488308274 ,1.4862718478315245608 ] 
dist 72=[-2.5681628487009964848 ,1.4600715083565180888 ] 
dist 73=[-2.7236563847746602429 ,1.3428876487722299022 ] 
dist 74=[-2.8467153067181393555 ,1.2743096489063537512 ] 
dist 75=[-2.9705173384961343915 ,1.2620474510838854009 ] 
dist 76=[-3.1289856491357404847 ,1.2370386752679357021 ] 
dist 77=[-3.2839528878758974569 ,1.2305097831951090171 ] 
dist 78=[-3.3937549045873595341 ,1.0055942374203139646 ] 
dist 79=[-3.4923319533135832834 ,.98242170436847684201] 
dist 80=[-3.6024097769411832313 ,.93416562176920613891] 
dist 81=[-3.7124920099292156516 ,.92136510526345013771] 
dist 82=[-3.8110896498067289155 ,.87256126333017774447] 
dist 83=[-3.9209402495510592328 ,.86320742703618500493] 
dist 84=[-4.0760327025750210837 ,.84220850290749821829] 
dist 85=[-4.2279056517309148934 ,.8374277132144685947 ] 
dist 86=[-4.3248814811069050252 ,.81073749519915760819] 
dist 87=[-4.4009620610105047257 ,.80477527897445501055] 
dist 88=[-4.4692653494187906968 ,.80107634498041388043] 
dist 89=[-4.5279867388695095143 ,.80204169298111334579] 
dist 90=[-4.5657464166382494353 ,.80548465493277389504] 
dist 91=[-4.5956891097671378698 ,.81235124199514031121] 
dist 92=[-4.6231512760256189654 ,.82306843303268831524] 
dist 93=[-4.6466931501555077139 ,.84190827969211745623] 
dist 94=[-4.6609559688330976113 ,.8620395208018291093 ] 
dist 95=[-4.6712813658857888292 ,.87792214346531916709] 
dist 96=[-4.6790687193662360799 ,.89382761408501270522] 
dist 97=[-4.6847094411628814864 ,.91405533697026847647] 
dist 98=[-4.6864454951083618789 ,.93567595857952359116] 
dist 99=[-4.6856649988945786072 ,.95715383278239230942] 
dist 100=[-4.6842927283904307163 ,.98279159676552342304] 
dist 101=[-4.3770982587958310350 ,1.0210491042520666884 ] 
dist 102=[-4.3486899612869018154 ,1.0610385892699454063 ] 
dist 103=[-4.2887491470470213388 ,1.0936037333054064970 ] 
dist 104=[-4.2718558964093160180 ,1.1272022693098488706 ] 
dist 105=[-4.2024912400440350278 ,1.1713264028309424538 ] 
dist 106=[-4.0842078082124923034 ,1.2192403040164537812 ] 
dist 107=[-4.0605587885384646579 ,1.2679954998121909450 ] 
dist 108=[-3.9277475413341353341 ,1.3270745527596180402 ] 
dist 109=[-3.6553149760829184217 ,1.4162755716226309076 ] 
dist 110=[-.64155094860215492722,1.5050309603020619532 ] 
dist 111=[-.63566048480411925716,1.5623285011932391311 ] 
dist 112=[-.2872054558877125179 ,1.6079703364374955574 ] 
dist 113=[-.2568404500989486853 ,1.6501142328199752904 ] 
dist 114=[-.1874647690990877745 ,1.6871566479090821012 ] 
dist 115=[-.1766680688848241505 ,1.7123979615567031011 ] 
dist 116=[-.0895209109995060676 ,1.7340175504314953750 ] 
dist 117=[-.0743668672470902310 ,1.7565779247536591665 ] 
dist 118=[-.0524470977654863813 ,1.7768898581336494172 ] 
dist 119=[-.0467270987609272563 ,1.7895177074886500315 ] 
dist 120=[.0463739659043959029 ,1.7990320789715410943 ] 
dist 121=[.0577065734359254747 ,1.8068913099713177789 ] 
dist 122=[.0827070729870953221 ,1.8131572737780022461 ] 
dist 123=[.0866043685858640140 ,1.8162992191013126154 ] 
dist 124=[.1143838446550998274 ,1.8177780550300042957 ] 
dist 125=[.1188153087916166394 ,1.8175701194441878614 ] 
dist 126=[.1263372903474132431 ,1.7030683559052577380 ] 
dist 127=[.1277569037312459532 ,1.6923800476905721598 ] 
dist 128=[.9680703302445328461 ,1.6705513921606842854 ] 
dist 129=[.9962442653771344787 ,1.6644386873316358564 ] 
dist 130=[1.0585700721297200150 ,1.6399047500153270397 ] 
dist 131=[1.0686806493434034097 ,1.6346806512274977337 ] 
dist 132=[1.1394646434984528570 ,1.6218391945754582918 ] 
dist 133=[1.1510981744614895191 ,1.6184197400290095863 ] 
dist 134=[1.1710819302944045594 ,1.5967598992589690285 ] 
dist 135=[1.1750015053691946749 ,1.5919153263289774716 ] 
dist 136=[1.2208105399899937022 ,1.5837771649553071357 ] 
dist 137=[1.1759438105527200281 ,1.5814289889280987023 ] 
dist 138=[1.0965839286758774528 ,1.5737612352504424992 ] 
dist 139=[1.0159318307681796627 ,1.5712102289705214356 ] 
dist 140=[.91830767966493982608,1.5678565046682562521 ] 
dist 141=[.77108219359148742806,1.5663430784050217327 ] 
dist 142=[.62346426653047351301,1.3817392808492608157 ] 
dist 143=[.52427067748297182668,1.3820966738262843058 ] 
dist 144=[.44087344851663404755,1.3757398784092249969 ] 
dist 145=[.35641933030468921234,1.3741020585154660299 ] 
dist 146=[.27704236049151795438,1.3698292203298463072 ] 
dist 147=[.21394664920840834636,1.3680351704776562907 ] 
dist 148=[.15025065272792585188,1.3581843605161916282 ] 
dist 149=[.06847299208806089260,1.3556624222712464949 ] 
dist 150=[-.01153358715057642201,1.3501542476251967569 ] 
dist 151=[-.06814781697271160993,1.3481967688697947782 ] 
dist 152=[-.11886130869231512243,1.3173833594173209212 ] 
dist 153=[-.1752730451560751758 ,1.3124951837515099615 ] 
dist 154=[-.23151255649246480071,1.3009284237780438427 ] 
dist 155=[-.28153766289974070374,1.2976146586431980186 ] 
dist 156=[-.33694940706255328221,1.2794478090393127525 ] 
dist 157=[-.41472890062537977144,1.2754553329549687079 ] 
dist 158=[-.49141260934894303666,1.2675792939027642366 ] 
dist 159=[-.54244278620142174539,1.2652099857079703628 ] 
dist 160=[-.58480682891454767319,.93706540157035556449] 
dist 161=[-.62683727552105285127,.91453755693261235662] 
dist 162=[-.66579183094240382584,.86147532017185163873] 
dist 163=[-.69585645744516413011,.85315909495079749588] 
dist 164=[-.72538028189961600594,.77986558738551203245] 
dist 165=[-.7621727738672173704 ,.76635846116600166226] 
dist 166=[-.79764387536769412953,.74871975212730241267] 
dist 167=[-.82188403470006930816,.7436934942900764414 ] 
dist 168=[-.84271030586877093905,.63623554210429270637] 
dist 169=[-.86453038750392658033,.6224562551641633164 ] 
dist 170=[-.88550953133365749235,.59382243129589939717] 
dist 171=[-.90297352951699346944,.5862313371361923772 ] 
dist 172=[-.92133599136398251427,.55747691727274238506] 
dist 173=[-.94590888044396576644,.5518706890697070326 ] 
dist 174=[-.96967611620165453808,.53989543723776194311] 
dist 175=[-.98481702036371571983,.53660081472347704068] 
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dist 177=[-1.0071776952962233136 ,.35408186166704078564] 
dist 178=[-1.0393207942930288926 ,.31889807428432649044] 
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dist 182=[-1.1465136172067982913 ,.24653861040592474651] 
dist 183=[-1.1703380092472797086 ,.24343060901976232878] 
dist 184=[-1.1924164496563544077 ,.1804723853846568409 ] 
dist 185=[-1.2059887089145713388 ,.17253993349178688313] 
dist 186=[-1.2160199925795148691 ,.15575089630548705574] 
dist 187=[-1.2239393975481053695 ,.15173256073049974083] 
dist 188=[-1.2300275384958702089 ,.13426121121161009409] 
dist 189=[-1.2327363645844015053 ,.13111598763526861784] 
dist 190=[-1.2339314278529424730 ,.12403518855732585182] 
dist 191=[-1.2339666198143043195 ,.12270740726407151681] 
dist 192=[-.96111284367049244449,-.04407449963948226873] 
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dist 195=[-.93532194469063010294,-.06994839631380820340] 
dist 196=[-.92849405982023924782,-.08327208823346850389] 
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dist 199=[-.88554388692235994292,-.09090185907689498022] 
dist 200=[-.87397234083228292503,-.09157586322009127802] 
dist 201=[-.87083552921259537816,-.09021021621425914774] 
dist 202=[-.85527091162713571099,-.08733874361196901076] 
dist 203=[-.85206637598982671421,-.08163837037612394456] 
dist 204=[-.84520038990411217526,-.07450678367743028510] 
dist 205=[-.84310873102199894759,-.06273269976786733007] 
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dist 211=[-.51276633764298252326,.35205052047211738958] 
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dist 214=[-.42718573077394115099,.51268683436931549613] 
dist 215=[-.41055562241437847842,.55223259183300769383] 
dist 216=[-.36778180460848791292,.5871261854496964958 ] 
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dist 228=[-.08987763994761339520,.96169575211831924134] 
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dist 230=[-.05377203826334454850,.99417823362037637575] 
dist 231=[-.04944168098992197748,1.0036859336549910314 ] 
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dist 233=[-.03795914148853822249,1.0159145810840889740 ] 
dist 234=[-.02618836821481944202,1.0199303835487061797 ] 
dist 235=[-.02410503477817340725,1.0217387264237359909 ] 
dist 236=[-.02035589478072036672,1.0224633449493421658 ] 

8 phat 2 dirichlet min maxes function [1, 1, 1, 2, 2, 1, 2, 1, 2] 
dist 0=[7.6630515326805633624 ,7.6630515326805633624 ] 
dist 1=[7.5267153757749720565 ,7.8205199030893391915 ] 
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dist 5=[6.8089017640125478637 ,8.5421267054760168428 ] 
dist 6=[6.6541023534581157694 ,8.7828560362099624111 ] 
dist 7=[6.4623498328514092291 ,8.9409266332049207522 ] 
dist 8=[6.2596705166546244091 ,9.0699122757799146811 ] 
dist 9=[6.0611679424599604624 ,9.1943192157242510806 ] 
dist 10=[5.8261144905107493313 ,9.3074053649280514437 ] 
dist 11=[5.4772470765046459725 ,9.3911150943729488146 ] 
dist 12=[5.1244860460495248408 ,9.4699836485635033124 ] 
dist 13=[4.8738592120827255168 ,9.5637093862980922210 ] 
dist 14=[4.6481078254642666326 ,9.6519236089731152958 ] 
dist 15=[4.3948364227706341928 ,9.7087500419183577930 ] 
dist 16=[4.1408380622289428692 ,9.7539027960953320901 ] 
dist 17=[3.9121780780260683647 ,9.7954298120887355199 ] 
dist 18=[3.6564579435349827600 ,9.8318414342487527856 ] 
dist 19=[3.2942288527197025249 ,9.8565370851454976232 ] 
dist 20=[2.9230923722093507781 ,9.8775825888664748472 ] 
dist 21=[2.6317455356915535112 ,9.8993995065449117770 ] 
dist 22=[2.3407509635637203242 ,9.9186693297514036769 ] 
dist 23=[1.9710222370896937599 ,9.9295275109129383230 ] 
dist 24=[1.5753697007859724703 ,9.9363998319535918360 ] 
dist 25=[1.1806892112553617628 ,9.9397234938278844613 ] 
dist 26=[.70793163410590331796,9.9405951053443140919 ] 
dist 27=[0                     ,9.9401340807447071804 ] 
dist 28=[5.3740243549956613797 ,9.9342484886039745044 ] 
dist 29=[5.4656189638249446127 ,9.9332156147427292391 ] 
dist 30=[5.6768231665818779755 ,9.9027968236037887586 ] 
dist 31=[5.7361190482034436961 ,9.8968182437569273221 ] 
dist 32=[5.9873409992644093678 ,9.8803180753671208131 ] 
dist 33=[6.9574258368465360842 ,9.8758404939229670082 ] 
dist 34=[6.9815281599510158668 ,9.8408905712674605810 ] 
dist 35=[7.0265415173094335315 ,9.8326831516061405382 ] 
dist 36=[7.0365192118693490860 ,9.8204668781376056405 ] 
dist 37=[7.0625281638647547822 ,9.8162320148074204964 ] 
dist 38=[7.0641573136164872681 ,8.9321355230364185818 ] 
dist 39=[6.8810987187675164404 ,8.8739317032750661667 ] 
dist 40=[6.6737524192596258838 ,8.7397576387121834650 ] 
dist 41=[6.4614030164541968928 ,8.7160672852499901046 ] 
dist 42=[6.2601021531634795437 ,8.5384107497941754615 ] 
dist 43=[6.0969458626409061606 ,8.5056330474604141725 ] 
dist 44=[5.9292082601608569523 ,8.4543403664676813529 ] 
dist 45=[5.7095862036394626227 ,8.4410842312472779670 ] 
dist 46=[5.4924059839727823367 ,8.2022417578446084438 ] 
dist 47=[5.3344355307660044074 ,8.1707726399559566455 ] 
dist 48=[5.1883709082110662125 ,8.0998758647990326719 ] 
dist 49=[5.0188093564084546921 ,8.0851312307270733858 ] 
dist 50=[4.8455197877796319778 ,7.9949010667728531268 ] 
dist 51=[4.6845466240690413306 ,7.9779760664776869436 ] 
dist 52=[4.5005012060095995103 ,7.9461608528241096603 ] 
dist 53=[4.2349378333591213695 ,7.9381570780879028825 ] 
dist 54=[3.9696014817988379183 ,6.8137350459981410720 ] 
dist 55=[3.7864647801903726917 ,6.7362367421021437866 ] 
dist 56=[3.6270845553792854340 ,6.5752584191504929661 ] 
dist 57=[3.4567607875418637964 ,6.5337667459478939110 ] 
dist 58=[3.2908618638821670800 ,6.3767162452541581848 ] 
dist 59=[3.1491793541293361749 ,6.3466789901041743450 ] 
dist 60=[2.9970065920376698270 ,6.2536691537030178236 ] 
dist 61=[2.7891549984748545479 ,6.1110720244964709990 ] 
dist 62=[2.5796206586824405475 ,5.4580039798039780725 ] 
dist 63=[2.4207188483013436072 ,5.3777882638019461830 ] 
dist 64=[2.2672687322534121511 ,5.0930736048054323142 ] 
dist 65=[2.0795386279228426778 ,3.2989670100044369303 ] 
dist 66=[1.8823837826288902542 ,3.1606334904604913346 ] 
dist 67=[1.6912421128142226590 ,2.9429409660184153263 ] 
dist 68=[1.4664115687111730478 ,2.9211295818117385682 ] 
dist 69=[1.1345259609079654288 ,2.9160542631350188838 ] 
dist 70=[.8038182949564697713 ,2.2985452645137821207 ] 
dist 71=[.58369887977045362619,2.2029431659973634464 ] 
dist 72=[.40079897228631465108,2.1825880988927088549 ] 
dist 73=[.21894268856562273094,1.6452116069320517253 ] 
dist 74=[.05002901833957741489,1.5795178816302590162 ] 
dist 75=[-.08110975304077779822,1.4432881051897725989 ] 
dist 76=[-.21068677259536196028,1.4101664245922411556 ] 
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dist 78=[-.5308856257841760717 ,1.2568784439077833682 ] 
dist 79=[-.63991846474934348024,1.2121064700697552918 ] 
dist 80=[-.73512112530416793352,1.2020735803520408173 ] 
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dist 100=[-2.0244666076460132780 ,-.27876326167085240024] 
dist 101=[-2.0777390443397669437 ,-.29852964739878823692] 
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dist 103=[-2.1626510250092091592 ,-.30710221007935581286] 
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dist 105=[-2.2117920677378304518 ,-.30638869517302337603] 
dist 106=[-2.2317103447585751209 ,-.30315664115989291125] 
dist 107=[-2.2444265872876455446 ,-.2977839120738130227 ] 
dist 108=[-2.2543971068942506486 ,-.28808037748935290327] 
dist 109=[-2.2633326126358285797 ,-.27628769598291860224] 
dist 110=[-2.2709688966052182447 ,-.26255927808967881983] 
dist 111=[-2.2757434558838880412 ,-.24470858899263606251] 
dist 112=[-2.2793940445811657255 ,-.21643301533308577689] 
dist 113=[-2.2824765606070647801 ,-.18725362645020261579] 
dist 114=[-2.2849831254956073732 ,-.16578736709558446551] 
dist 115=[-2.2863297263390689707 ,-.14573038757820388188] 
dist 116=[-2.2870884338459827392 ,-.1221810029110369577 ] 
dist 117=[-2.2872403811771937210 ,-.09800161911263257826] 
dist 118=[-2.1721931071373043222 ,-.07542284416307745948] 
dist 119=[-2.1619582815574012665 ,-.04953580069323894337] 
dist 120=[-2.1407528598059084353 ,-.01212507745493866884] 
dist 121=[-2.1348820510515728894 ,.02647373047055058154] 
dist 122=[-2.1114510565231102982 ,.05711325002162633126] 
dist 123=[-2.1066891592931786515 ,.08800944053612924237] 
dist 124=[-2.0900962365545919520 ,.12763707275468248701] 
dist 125=[-2.0602872600007772970 ,.17020235602759282501] 
dist 126=[-1.9145385613015976281 ,.21284773290280460098] 
dist 127=[-1.8960630445335727771 ,.26404230226970554114] 
dist 128=[-1.8269423723441550010 ,.3407979593797010826 ] 
dist 129=[-1.1720173110412818113 ,.41730371166573156082] 
dist 130=[-1.1590950118455831813 ,.46749945749770982899] 
dist 131=[-1.1557701236670553867 ,.50840027403327637362] 
dist 132=[-1.1522844388070225192 ,.54773508685997395312] 
dist 133=[-1.1509429778072608242 ,.58340239407246049589] 
dist 134=[-.3521820843514529473 ,.60963696489500132988] 
dist 135=[-.30938791251078357203,.63418282893732845559] 
dist 136=[-.20930200334745359508,.66309784677122645135] 
dist 137=[-.19495010214263487652,.69017365616610291827] 
dist 138=[-.06110051234288108936,.70736479530045765681] 
dist 139=[-.03722805450210642324,.72073755814072926884] 
dist 140=[-.00829244743394031239,.73254364117436681055] 
dist 141=[-.00334071424721491742,.74255226579419631916] 
dist 142=[.17749166659917772931,.74873769489540776797] 
dist 143=[.19934328976852553968,.75336162164033206459] 
dist 144=[.24368218952318890924,.75712794282287248023] 
dist 145=[.25482211378286793983,.76022599161719776114] 
dist 146=[.29353666424003842924,.76217740959394998371] 
dist 147=[.3012905391441325014 ,.76368841636486218398] 
dist 148=[.31157078353853221492,.76502285509757611746] 
dist 149=[.31364669643344159457,.76616444507057459032] 
dist 150=[.53499098297995306873,.7669032912223144788 ] 
dist 151=[.55296612986467237896,.76750017643030958115] 
dist 152=[.59401323740453160985,.76807360127823897016] 
dist 153=[.59994611960197640195,.76855376702344148193] 
dist 154=[.65095184987496375442,.76877720933740479356] 
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dist 158=[.54366403230717597022,.77080542758476938236] 
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dist 161=[.38510224546223320856,.80069878756996136091] 
dist 162=[.34464412763335901849,.80745491718700336193] 
dist 163=[.31040603878531191455,.8113435060808876758 ] 
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dist 223=[-.70575053600737984   ,.00872764982872336012] 
dist 224=[-.71065122604040238176,.00490268982346815794] 
dist 225=[-.71457152172601989042,.03026662503559420299] 
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dist 234=[-.20920051019700442417,.24964181832564233903] 
dist 235=[-.20134489552173851115,.26495012544241938931] 
dist 236=[-.19957713698251309336,.28166029229885818365] 
dist 237=[-.19021133980544205656,.29813438181238271423] 
dist 238=[-.18848159066194112477,.31249870641415167314] 
dist 239=[-.1848446234689778517 ,.32817048985173530368] 
dist 240=[-.18384200539273153414,.34987267518635514654] 
dist 241=[-.14816774328768166385,.37113864019805382768] 
dist 242=[-.14461078924452871974,.38506612701518506091] 
dist 243=[-.13643762898882682616,.39638041663688749066] 
dist 244=[-.133398108058262388  ,.4071970826685866587 ] 
dist 245=[-.12141581527318367833,.41695575945403536321] 
dist 246=[-.07267610802643476429,.42403950059992663632] 
dist 247=[-.06927060466507999120,.43056951195755481353] 
dist 248=[-.06863885949937289916,.43811399636352606036] 
dist 249=[-.04604944611941088740,.44509317096740134456] 
dist 250=[-.04327450942002239651,.4493626910070547377 ] 
dist 251=[-.03768455608410463297,.45249374993591173514] 
dist 252=[-.03627108691166774874,.45492059227131683026] 
dist 253=[-.03133309139849071934,.45675205532926826698] 
dist 254=[-.03031402928589861151,.45750239898183986076] 
dist 255=[-.02889599412942187811,.45779032698268377492] 

8 phat 2 dirichlet min maxes function [0, 2, 1, 1, 1, 0, 2, 1, 2] 
dist 0=[13.458577130221153773  ,13.458577130221153773  ] 
dist 1=[13.450359189531343851  ,13.461838063045965959  ] 
dist 2=[13.434622494722824099  ,13.466662046512225967  ] 
dist 3=[13.395905792800515335  ,13.468700470064257363  ] 
dist 4=[13.346984690053192796  ,13.466935922648435372  ] 
dist 5=[13.288326960268531129  ,13.463358582320082861  ] 
dist 6=[13.210813434661615614  ,13.459222951672994106  ] 
dist 7=[13.086478599338538189  ,13.451171696435553938  ] 
dist 8=[12.958113856141496325  ,13.447196588155330280  ] 
dist 9=[12.864484589397967864  ,13.423674546058281593  ] 
dist 10=[12.777640842445329957  ,13.417328536649045178  ] 
dist 11=[12.676420377752587788  ,13.394095563536274455  ] 
dist 12=[12.572750387316722239  ,13.389967654528765740  ] 
dist 13=[12.476114116389387678  ,13.310358213376350794  ] 
dist 14=[12.299912534440713272  ,12.878352648330019246  ] 
dist 15=[12.127724940588843876  ,12.774163549808080585  ] 
dist 16=[11.966330650731690412  ,12.747935434989180682  ] 
dist 17=[11.775873579982351482  ,12.612703197343032604  ] 
dist 18=[11.579626467479553446  ,12.585805323848085919  ] 
dist 19=[11.395076269669496436  ,12.529255956621003938  ] 
dist 20=[11.182383933846598018  ,12.512680097899029715  ] 
dist 21=[10.873596109319065321  ,12.322596611757158237  ] 
dist 22=[10.554272674455651100  ,12.294012121384564144  ] 
dist 23=[10.299447724691205864  ,12.221116781521556764  ] 
dist 24=[10.041207208413269177  ,12.209238277833000761  ] 
dist 25=[9.7082230970440905050 ,12.085773530884394965  ] 
dist 26=[9.3496675657308330863 ,12.060581099896615869  ] 
dist 27=[8.9891663299613697264 ,12.032602193075763243  ] 
dist 28=[8.5554911750688025860 ,12.023363690168069332  ] 
dist 29=[7.9043131224585613538 ,11.745340747236458716  ] 
dist 30=[7.2516876744804612115 ,10.212209078593775328  ] 
dist 31=[6.8122234705177689368 ,10.189198194856526621  ] 
dist 32=[6.4415936613528955157 ,9.9073444737454329366 ] 
dist 33=[6.0642342334333706398 ,9.8664872064913068395 ] 
dist 34=[5.7081173425403214289 ,9.7702059050567628017 ] 
dist 35=[5.4224343126970740117 ,9.7513926529787575408 ] 
dist 36=[5.1315276817601508153 ,9.6129950386246667880 ] 
dist 37=[4.7545179719723036335 ,9.5858525264590732600 ] 
dist 38=[4.3837680598385507186 ,9.5426633977689088665 ] 
dist 39=[4.1178923608673464765 ,9.5308933777061332254 ] 
dist 40=[3.8759783725554878269 ,7.4901944010932425628 ] 
dist 41=[3.6010489908991117879 ,7.3339387154938777027 ] 
dist 42=[3.3234502944972917530 ,7.3016227746831106078 ] 
dist 43=[3.0708578861076154068 ,7.2499271540479555026 ] 
dist 44=[2.7862900200785394639 ,7.2369991907057650120 ] 
dist 45=[2.3808123356696878951 ,6.1534207914886045509 ] 
dist 46=[1.9780326591020332396 ,6.0609609766543750115 ] 
dist 47=[1.7042521287920570957 ,5.8513264454158032975 ] 
dist 48=[1.4705176073356661158 ,5.8151067805071279561 ] 
dist 49=[1.2278850662828505328 ,5.5527761365029736640 ] 
dist 50=[.99589864985748808486,5.5061298820119644591 ] 
dist 51=[.80473584883457363245,5.4299287619378480483 ] 
dist 52=[.55570749918149533269,5.4120645942846776113 ] 
dist 53=[.32031365029284374834,5.1217115162909887332 ] 
dist 54=[.05867606216711618441,5.0843851384870097938 ] 
dist 55=[-.3098185624420200856 ,4.9986700987256426525 ] 
dist 56=[-.6740107461647583056 ,4.9850574514377271802 ] 
dist 57=[-.91844391018115055734,4.8746771520509855877 ] 
dist 58=[-1.1237527033039517322 ,4.8550018513076968062 ] 
dist 59=[-1.3314833890327406180 ,4.8270355034762536883 ] 
dist 60=[-1.5267419998480525055 ,4.8193331760668544754 ] 
dist 61=[-1.6821759143648117468 ,3.5903899164131252803 ] 
dist 62=[-1.8980941650225717385 ,2.0734069842894469651 ] 
dist 63=[-2.1278697658478928421 ,2.0558216391128682376 ] 
dist 64=[-2.3144251882509424018 ,1.7863539871492114935 ] 
dist 65=[-2.4928446289392338937 ,1.7511155429210148726 ] 
dist 66=[-2.6540725607574341186 ,1.6763628330763809413 ] 
dist 67=[-2.7718715254475816167 ,1.6603540280515671772 ] 
dist 68=[-2.8813640231069202795 ,1.5839471369659228968 ] 
dist 69=[-3.0093758516167107189 ,1.5708949997994793182 ] 
dist 70=[-3.1288630099268718109 ,1.5431159898954861205 ] 
dist 71=[-3.2882356181280429568 ,1.5379746624925216082 ] 
dist 72=[-3.4942576757373564458 ,.0697628664939355477 ] 
dist 73=[-3.6269167984675202615 ,-.0489882896567994998 ] 
dist 74=[-3.7322781471439232022 ,-.0725903904229384531 ] 
dist 75=[-3.8291206356645088430 ,-.1056808157127285684 ] 
dist 76=[-3.9140050834389113574 ,-.1138489397477115776 ] 
dist 77=[-3.9715413572884982322 ,-.7767648007124110845 ] 
dist 78=[-4.0205367172354914836 ,-.8314621100940578042 ] 
dist 79=[-4.0712672142168868014 ,-.9557774180127767340 ] 
dist 80=[-4.1166874698296236368 ,-.9748214582034019895 ] 
dist 81=[-4.1444435579027590783 ,-1.1288013838294760651 ] 
dist 82=[-4.1648183029089189223 ,-1.1553695098514947446 ] 
dist 83=[-4.1807085579019275571 ,-1.1933530515018867123 ] 
dist 84=[-4.1926684435361648934 ,-1.2030755635669095743 ] 
dist 85=[-4.1973196820823358295 ,-1.3632168418917422464 ] 
dist 86=[-4.1981481594892753018 ,-1.3825266771657585293 ] 
dist 87=[-4.1970494644993470640 ,-1.4251410506076823244 ] 
dist 88=[-3.9478348861272964061 ,-1.4315552267660949989 ] 
dist 89=[-3.9237685672328136761 ,-1.4789344721411700493 ] 
dist 90=[-3.8733589551157775932 ,-1.4864608283024977460 ] 
dist 91=[-3.8589562767460289746 ,-1.4985862589431989541 ] 
dist 92=[-3.7992491133160106652 ,-1.5010009285351402227 ] 
dist 93=[-3.7871203396649216001 ,-1.6936908470307095356 ] 
dist 94=[-3.7542802143312536322 ,-1.4022713548770062066 ] 
dist 95=[-3.7486323016729709429 ,-1.2059241503021174220 ] 
dist 96=[-3.6847820149963802757 ,-1.0403069501834217244 ] 
dist 97=[-3.6723608465267544575 ,-.87175850356202252185] 
dist 98=[-3.6474850816690443122 ,-.71284621815704766453] 
dist 99=[-3.6401323718160740189 ,-.58575760252258893893] 
dist 100=[-3.6090641689185454512 ,-.45676718426105911058] 
dist 101=[-3.6019672653368258564 ,-.29024857990778702058] 
dist 102=[-3.5828247957169036073 ,-.12693563734375162248] 
dist 103=[-3.5778336637636467644 ,-.01076205709733562531] 
dist 104=[-2.3251154540777917619 ,.09392177334900750561] 
dist 105=[-2.3177652771258537439 ,.21129399813499818333] 
dist 106=[-2.3013568085501602067 ,.32883040197225078318] 
dist 107=[-2.2964445876339793111 ,.43417212807744216744] 
dist 108=[-2.2742712981746842311 ,.55150203617502294227] 
dist 109=[-2.2695694512579952912 ,.71697641377163552927] 
dist 110=[-2.2588774452057532874 ,.88043044739733407523] 
dist 111=[-2.2554267932049000913 ,.98968247590551152039] 
dist 112=[-2.2190914473866177895 ,1.0809027673883828968 ] 
dist 113=[-2.2134068494832801539 ,1.1722550730541860020 ] 
dist 114=[-2.1981234431581822541 ,1.2574694374248016342 ] 
dist 115=[-2.1927332291523828115 ,1.3241471585368400026 ] 
dist 116=[-2.1650179185721811982 ,1.3904887554333263665 ] 
dist 117=[-2.0824131764923730697 ,1.4743609302192832300 ] 
dist 118=[-2.0716583175234840786 ,1.5558112219170761573 ] 
dist 119=[-2.0235830387047153844 ,1.6124693965758187340 ] 
dist 120=[-1.6201417834902243486 ,1.6622185911910540328 ] 
dist 121=[-1.5853271228767197418 ,1.7160429579432109656 ] 
dist 122=[-1.5147908845836708710 ,1.7688422025934644038 ] 
dist 123=[-1.4680021502261612882 ,1.8144939053129252972 ] 
dist 124=[-1.3247548497953908185 ,1.8639941991977052104 ] 
dist 125=[.65717385603038945513,1.9321867771647803089 ] 
dist 126=[.96227588580983078991,1.9985253808271315996 ] 
dist 127=[.97173062217866799926,2.0406123543318838552 ] 
dist 128=[1.1204624224471104752 ,2.0733016948146464685 ] 
dist 129=[1.1386957776052116028 ,2.1020585125696059727 ] 
dist 130=[1.1772148803859782438 ,2.1263428564158204576 ] 
dist 131=[1.1843062852333743783 ,2.1668897453238064106 ] 
dist 132=[1.2210756868005350639 ,2.2089349806398655491 ] 
dist 133=[1.2270112883151369562 ,2.2427835627972661246 ] 
dist 134=[1.2363810293647300063 ,2.2773634886620130840 ] 
dist 135=[1.2378547869647446404 ,2.3223359974217909973 ] 
dist 136=[1.3881048802990737985 ,2.3652354416223660382 ] 
dist 137=[1.3790504480117566691 ,2.3915257649193179144 ] 
dist 138=[1.3661327204662690901 ,2.4108788260212771548 ] 
dist 139=[1.3486066589919956610 ,2.4260352740626864690 ] 
dist 140=[1.3242288137747558200 ,2.4377692040061630800 ] 
dist 141=[1.2839139968847331671 ,2.4434346926243810495 ] 
dist 142=[1.2415839441196608085 ,2.4460507576011449876 ] 
dist 143=[1.2091475265096232710 ,2.4462130085104329887 ] 
dist 144=[1.1775290379357028870 ,2.4301856763536049318 ] 
dist 145=[1.1384677559193906171 ,2.4265573735094496841 ] 
dist 146=[1.0972832606894265562 ,2.4209321740111668382 ] 
dist 147=[1.0571740369129199242 ,2.4187573784606054376 ] 
dist 148=[1.0098878308038725993 ,2.4106699816469204801 ] 
dist 149=[.94000469501956010409,2.4079188667585187147 ] 
dist 150=[.86725524134126771878,2.4014996290474403952 ] 
dist 151=[.80850725513577873708,2.3989001711853306237 ] 
dist 152=[.74835475093016006412,2.1671999675951409101 ] 
dist 153=[.66998839067803706592,2.1456032821037237085 ] 
dist 154=[.58523345554766077264,2.0983110390109999153 ] 
dist 155=[.49953490755247998416,2.0861904671787107674 ] 
dist 156=[.39611642142772302696,2.0287397182833286770 ] 
dist 157=[.2405052849736691355 ,2.0176006114468974160 ] 
dist 158=[.08461495989081438264,1.9924808689817386938 ] 
dist 159=[-.01992006249248013356,1.9856209367962143931 ] 
dist 160=[-.10757162147159366434,1.9199719492374004272 ] 
dist 161=[-.19595098997389904492,1.9092832078321686846 ] 
dist 162=[-.27877389673671739922,1.8853096624692335844 ] 
dist 163=[-.34420721276743676278,1.8786796787510599929 ] 
dist 164=[-.40989261728478596678,1.8464788994100267989 ] 
dist 165=[-.49372374426408643831,1.8398143904240098479 ] 
dist 166=[-.57549893185141284654,1.8253392298756242668 ] 
dist 167=[-.63296343075025974318,1.8208722790840435158 ] 
dist 168=[-.68402227904426833815,1.0124265802487683783 ] 
dist 169=[-.74018353534865967467,.98279553821304359411] 
dist 170=[-.79580462331856969226,.91358050838847590686] 
dist 171=[-.8447036580161993895 ,.90260067382460879559] 
dist 172=[-.89839213581386453559,.8090346192530617007 ] 
dist 173=[-.97826528502341828622,.79194852708074298014] 
dist 174=[-1.0653026170734701400 ,.76880131267827673555] 
dist 175=[-1.1222341415590154279 ,.76188311842979793907] 
dist 176=[-1.1684053107738209854 ,.63238360968876590941] 
dist 177=[-1.2124153219988699065 ,.61577697056397726593] 
dist 178=[-1.2520334940317596401 ,.5806251214743126265 ] 
dist 179=[-1.2806430135021299190 ,.57183147690556865781] 
dist 180=[-1.3068658987188935158 ,.53469102109903143741] 
dist 181=[-1.3369405192160442545 ,.52788023706651454804] 
dist 182=[-1.3647608783941652884 ,.51194970363655287928] 
dist 183=[-1.3819697188857469065 ,.50913107295764988867] 
dist 184=[-1.3948174086406245636 ,.33203217724290471803] 
dist 185=[-1.4051991621111023896 ,.31570360016467095565] 
dist 186=[-1.4133674937709565878 ,.27753916855075808643] 
dist 187=[-1.4462003322243773135 ,.27181264446433784336] 
dist 188=[-1.4898460102877418306 ,.22054242572575328982] 
dist 189=[-1.5213973271204110181 ,.21130202903829325682] 
dist 190=[-1.5503524059266667292 ,.19951722880899536985] 
dist 191=[-1.5836162554112344577 ,.19679051957381263958] 
dist 192=[-1.6143761442593831728 ,.12674755063085212321] 
dist 193=[-1.6333185453599514653 ,.1180470427852012199 ] 
dist 194=[-1.6473611229133091408 ,.10006127386200873981] 
dist 195=[-1.6585280692487696277 ,.09540181921190641691] 
dist 196=[-1.6672900121184639018 ,.07831880788259051560] 
dist 197=[-1.6717155728772154422 ,.07500854680259529553] 
dist 198=[-1.6738911157520000050 ,.06872965601569482149] 

8 phat 2 dirichlet min maxes function [2, 1, 2, 2, 2, 1, 0, 2] 
dist 0=[12.538178369042073337  ,12.538178369042073337  ] 
dist 1=[12.529940091702925578  ,12.545617190814168334  ] 
dist 2=[12.517241158762886516  ,12.555122920551535970  ] 
dist 3=[12.495397488555586455  ,12.562610750159002687  ] 
dist 4=[12.450597717765662352  ,12.563846965118614225  ] 
dist 5=[12.398770725542465371  ,12.559165727057699422  ] 
dist 6=[12.348824127868969793  ,12.557960584055040135  ] 
dist 7=[12.288771541498584637  ,12.514686106231092142  ] 
dist 8=[12.204332775512407883  ,12.505022908384988223  ] 
dist 9=[12.106459149472397098  ,12.486345957229373951  ] 
dist 10=[12.000484688089093155  ,12.480131462069846294  ] 
dist 11=[11.867490404176760606  ,12.451130311078664102  ] 
dist 12=[11.661565313426493658  ,12.443845951222661842  ] 
dist 13=[11.450171266970258565  ,12.421402704944763741  ] 
dist 14=[11.295305972211277392  ,12.416067230841632911  ] 
dist 15=[11.151077687618042531  ,11.941000133419782354  ] 
dist 16=[10.982218266698888092  ,11.894862844299301241  ] 
dist 17=[10.808945721438151116  ,11.792205507322703140  ] 
dist 18=[10.647067996197811628  ,11.766999022132856968  ] 
dist 19=[10.461329168309034149  ,11.636610707123682076  ] 
dist 20=[10.192634782471132684  ,11.611096230741104690  ] 
dist 21=[9.9151582801252039929 ,11.557369784355736593  ] 
dist 22=[9.6942988268934423532 ,11.541798023260700580  ] 
dist 23=[9.4709933219030958238 ,11.371263327511798964  ] 
dist 24=[9.1837335229401309576 ,11.345369849290561685  ] 
dist 25=[8.8747362662592388169 ,11.281584039472882415  ] 
dist 26=[8.5645011878113351187 ,11.269682325132051123  ] 
dist 27=[8.1916010533405777058 ,11.167838991912811562  ] 
dist 28=[7.6320033259257329019 ,11.147127823065071517  ] 
dist 29=[7.0711927591595068960 ,11.119011911933203815  ] 
dist 30=[6.6934416421342891849 ,11.109513125251402757  ] 
dist 31=[6.3747189371857238684 ,9.9411857444913425273 ] 
dist 32=[6.0499633891850013228 ,9.9068196092080135839 ] 
dist 33=[5.7433161477039058207 ,9.8240312647670079175 ] 
dist 34=[5.4970075322902988604 ,9.8089377270853272603 ] 
dist 35=[5.2458997628990424465 ,9.6842277550282404842 ] 
dist 36=[4.9200572316829591898 ,9.6595696996131117366 ] 
dist 37=[4.5994050411830413417 ,9.6249095045828504019 ] 
dist 38=[4.3690519001474178364 ,9.6139651589403387277 ] 
dist 39=[4.1590352705871786486 ,7.3006935821385121891 ] 
dist 40=[3.9197076357488600146 ,7.2260470003077677888 ] 
dist 41=[3.6776745905536394976 ,7.0742282298483580373 ] 
dist 42=[3.4568354496673244561 ,7.0351507327968051189 ] 
dist 43=[3.2075392189393426414 ,6.8942487466650361984 ] 
dist 44=[2.8516967059028182613 ,6.8657145191796241690 ] 
dist 45=[2.4979160513543104445 ,6.8152754145680130349 ] 
dist 46=[2.2568634762808483656 ,6.8038489948532519252 ] 
dist 47=[2.0504346797540673889 ,5.8943682432504398000 ] 
dist 48=[1.8351189366121709787 ,5.8159047182568348785 ] 
dist 49=[1.6285998636575229390 ,5.6367880474943122762 ] 
dist 50=[1.4573474009351692457 ,5.6069298180406405639 ] 
dist 51=[1.2778094473546620416 ,5.3791915778920835175 ] 
dist 52=[1.0381476321482493792 ,5.3386140345833576670 ] 
dist 53=[.7990124205715571627 ,5.2762385937198877232 ] 
dist 54=[.5438788214343643548 ,5.2605217523787443461 ] 
dist 55=[.1752167603886375584 ,4.9955481860545852409 ] 
dist 56=[-.0747996583918023682 ,4.9619699668472100357 ] 
dist 57=[-.2876346903110647943 ,4.8851980990261418443 ] 
dist 58=[-.5076029838077604678 ,4.8727081873097803818 ] 
dist 59=[-.7173221222568100240 ,4.7749671137344988497 ] 
dist 60=[-.8891712130265508359 ,4.7576375608931870234 ] 
dist 61=[-1.0675076087224831531 ,4.7317253199931614344 ] 
dist 62=[-1.3031761641307317034 ,4.7250327136591981078 ] 
dist 63=[-1.5372031612897611812 ,2.8011960493094655145 ] 
dist 64=[-1.7089772706424935989 ,2.7652781578703711217 ] 
dist 65=[-1.8693591280442066909 ,2.6822590137412180455 ] 
dist 66=[-2.0578287323848155332 ,2.6696458756055798193 ] 
dist 67=[-2.2517213170689705187 ,2.5614522184701973309 ] 
dist 68=[-2.4337961183306360558 ,2.5422546242045051743 ] 
dist 69=[-2.6435372205338409491 ,2.5165113439820780716 ] 
dist 70=[-2.9480864391175469682 ,2.5100799189334966685 ] 
dist 71=[-3.2495352389241445008 ,.5564276149743735031 ] 
dist 72=[-3.4468776940526524599 ,.5053456376243461956 ] 
dist 73=[-3.6072677287697709435 ,.3895607011309531864 ] 
dist 74=[-3.7609244843663262565 ,.3709762895627996183 ] 
dist 75=[-3.8999326049526077587 ,.2276900660544298647 ] 
dist 76=[-4.0017360786761930287 ,.2027493046254148924 ] 
dist 77=[-4.0965859576590267025 ,.1649336928146270620 ] 
dist 78=[-4.2077859721984210977 ,.1555650394209352055 ] 
dist 79=[-4.3117022355868449904 ,-.0811338126990446410 ] 
dist 80=[-4.3774218369092468107 ,-.1082153945012663879 ] 
dist 81=[-4.4282674103256908008 ,-.1591601372487713763 ] 
dist 82=[-4.4726954504531547126 ,-.1709412971005545788 ] 
dist 83=[-4.5100389284316057763 ,-.2048561206278952865 ] 
dist 84=[-4.5325523573750348727 ,-.2105554000547532853 ] 
dist 85=[-4.5487166421155124020 ,-.2081863330290214392 ] 
dist 86=[-4.5606739359100762808 ,-.1942525705605398315 ] 
dist 87=[-4.5695583095681540804 ,-.1755325060860661189 ] 
dist 88=[-4.5734329081619034948 ,-.1540227508530903580 ] 
dist 89=[-4.5744478609983206932 ,-.1262450305951920953 ] 
dist 90=[-4.5733356154017225125 ,-.0824557774791434878 ] 
dist 91=[-4.5672462232564999333 ,-.0314004944945867873 ] 
dist 92=[-4.5646868703882964553 ,.0254315601884244621 ] 
dist 93=[-4.5531894962557049354 ,.0977448252434620081 ] 
dist 94=[-4.5508898760381227628 ,.2106983211951009421 ] 
dist 95=[-4.5110869585706022331 ,.32522649732777249146] 
dist 96=[-4.5035247890748931069 ,.4038377316148074025 ] 
dist 97=[-4.4802212013510586357 ,.471688038952847368  ] 
dist 98=[-4.4765499288822895005 ,.54319688303700225346] 
dist 99=[-4.4227064384842201675 ,.61214496070883432427] 
dist 100=[-4.4106180666263220304 ,.66975974148041396104] 
dist 101=[-4.4004283504952864927 ,.73049083536006525556] 
dist 102=[-4.3973561664438294653 ,.81190235688668871837] 
dist 103=[-1.7582507021705923345 ,.89315794415709399372] 
dist 104=[-1.6397863535153297402 ,.95326760880668097184] 
dist 105=[-1.3665496334959667626 ,1.0098046930128422300 ] 
dist 106=[-1.3236830518977257702 ,1.0767786727722150543 ] 
dist 107=[-.9689596472552880822 ,1.1459032048677936326 ] 
dist 108=[-.90583093090590435239,1.2110417943355228817 ] 
dist 109=[-.81738818469126199391,1.2862011003461994313 ] 
dist 110=[-.79268249448007787777,1.3953976696382483165 ] 
dist 111=[-.36080834835075508414,1.5046459944749239935 ] 
dist 112=[-.30688182730435169963,1.5800135069507523020 ] 
dist 113=[-.18916076227855549881,1.6455214888971830770 ] 
dist 114=[-.16605732494005966193,1.7153460631864433013 ] 
dist 115=[-.03395156281186721718,1.7832048973597808353 ] 
dist 116=[-.01133367210232542252,1.8408541245275317305 ] 
dist 117=[.04316189171314005135,1.9024866847012733253 ] 
dist 118=[.09462358315799005777,1.9862770683867345836 ] 
dist 119=[.4190583922061260380 ,2.0705251014534562811 ] 
dist 120=[.4231715664775997392 ,2.1339892496027129299 ] 
dist 121=[.4481390324877906116 ,2.1948479628559142447 ] 
dist 122=[.4519541195117669903 ,2.2686789987738187702 ] 
dist 123=[.4593402766094318884 ,2.3458734156589562983 ] 
dist 124=[.4604592238235040874 ,2.4201843613883685978 ] 
dist 125=[1.1273196935133160913 ,2.5071844267740504994 ] 
dist 126=[1.1489692029267633265 ,2.6351266997840552912 ] 
dist 127=[1.1958744445123869385 ,2.7615550861714656874 ] 
dist 128=[1.2038706728999550536 ,2.8425017747968146770 ] 
dist 129=[1.2535027024032416870 ,2.9062285299010162369 ] 
dist 130=[1.2613324649410367125 ,2.9637923006606996202 ] 
dist 131=[1.2763410798914918587 ,3.0135051944480153120 ] 
dist 132=[1.2793997646922990317 ,3.0458361761558406916 ] 
dist 133=[1.2951332095411759430 ,3.0718731262466886125 ] 
dist 134=[1.2954515819096406279 ,3.0964179451625201996 ] 
dist 135=[1.2914590982920089684 ,3.1177845941818283887 ] 
dist 136=[1.2805186634753275836 ,3.1311113501661251550 ] 
dist 137=[1.2658606025439839289 ,3.1412100541942554421 ] 
dist 138=[1.2470023943583294067 ,3.1496638938252916427 ] 
dist 139=[1.2213260575517861753 ,3.1564961992953277547 ] 
dist 140=[1.1794054290736458694 ,3.1601084566114975992 ] 
dist 141=[1.1355826492000585687 ,3.1620826159192096471 ] 
dist 142=[1.1022999719506730588 ,3.1623622150014025797 ] 
dist 143=[1.0701402923066101318 ,2.9086197547295215758 ] 
dist 144=[1.0308063387174871563 ,2.8859165841465900867 ] 
dist 145=[.98954010984034829552,2.8388205361433013386 ] 
dist 146=[.94965328155745745771,2.8257358684410701516 ] 
dist 147=[.90285639058712662197,2.7733245460596867145 ] 
dist 148=[.83395892371732930126,2.7626577380110367644 ] 
dist 149=[.76234460898155878842,2.7360960845850867564 ] 
dist 150=[.70468367549186579349,2.7302313052584623778 ] 
dist 151=[.64579900189718226045,2.6855489035494811038 ] 
dist 152=[.5692907412366688289 ,2.6761181155946637276 ] 
dist 153=[.48664781841008120734,2.6607535805761703184 ] 
dist 154=[.40323249267877352316,2.6563259557179623620 ] 
dist 155=[.30267689333891909645,2.6438850455122886309 ] 
dist 156=[.15149580190926148747,2.6395815032945046092 ] 
dist 157=[9.61313827379372800000e-05,2.6368597800238476855 ] 
dist 158=[-.10133361708788864982,2.6355586108871513282 ] 
dist 159=[-.18627799304150098177,1.0733435731774899176 ] 
dist 160=[-.27175859798293273873,.98998802588845923839] 
dist 161=[-.35175609916297496749,.79472396096566440063] 
dist 162=[-.4147755569372335556 ,.7663525675819345596 ] 
dist 163=[-.47786855067385161047,.7160816019809491206 ] 
dist 164=[-.55816021382302598576,.71030668401147877867] 
dist 165=[-.63636992465217841566,.60396390230235974035] 
dist 166=[-.69113796680100365243,.59056503591324863475] 
dist 167=[-.73960090081986287253,.56201392026949823157] 
dist 168=[-.79259871574569454208,.55492885122062923338] 
dist 169=[-.84490510975405619987,.5239157136843265099 ] 
dist 170=[-.89060334472118519828,.51830053247426242276] 
dist 171=[-.94053734686168235522,.50453083070799186185] 
dist 172=[-1.0097812203283122617 ,.50255652613359060602] 
dist 173=[-1.0776757818025771506 ,.35795865582478012998] 
dist 174=[-1.1222143513048511363 ,.34444532699628737163] 
dist 175=[-1.1584782920172232787 ,.31285912790636784665] 
dist 176=[-1.1932853620854344049 ,.30803673969923149232] 
dist 177=[-1.2247812315337873757 ,.26550472007836145084] 
dist 178=[-1.2478047738343011732 ,.25780783250476038056] 
dist 179=[-1.2691913578798374469 ,.24780240448456421187] 
dist 180=[-1.2941415551481756094 ,.24527036821935679898] 
dist 181=[-1.3173509103204871030 ,.18692853239632427086] 
dist 182=[-1.3317764294598824594 ,.17961047536649874371] 
dist 183=[-1.3426278950799162158 ,.16436372307216704378] 
dist 184=[-1.3689345079519519548 ,.16046194571214742181] 
dist 185=[-1.4026097045694874525 ,.14545152187574558608] 
dist 186=[-1.4375941535882891497 ,.14259924716273728973] 
dist 187=[-1.4710487672821104765 ,.1367711479625333123 ] 
dist 188=[-1.4986071919566899967 ,.13526122928350542311] 
dist 189=[-1.5273284921118988812 ,.05905302532441594779] 
dist 190=[-1.5654348733279149163 ,.05190280155097354639] 
dist 191=[-1.6021953657303435155 ,.03839101994886499819] 
dist 192=[-1.6255348240372337793 ,.03520748315084085770] 
dist 193=[-1.6436823053639688405 ,.02572106220430177820] 
dist 194=[-1.6596797540220630849 ,.02385458223515790190] 
dist 195=[-1.6732121440722369041 ,.02403198169144247639] 
dist 196=[-1.6815019096793928598 ,.02704103398332280162] 
dist 197=[-1.6876010675654616748 ,.03131042738020332843] 
dist 198=[-1.6923737065036935237 ,.03652772592497236586] 
dist 199=[-1.6958855646356762858 ,.04347484335440155128] 
dist 200=[-1.6969428093071212340 ,.05466166456865736313] 
dist 201=[-1.6968397890623805528 ,.06781554170822736426] 
dist 202=[-1.6961677030874464128 ,.08262846727346206581] 
dist 203=[-1.6901717735328638912 ,.10160066678986409945] 
dist 204=[-1.6882126217978072571 ,.13138625519133420641] 
dist 205=[-1.6844692731102546514 ,.16210484384514779869] 
dist 206=[-1.6830537518161970849 ,.18480794113403038712] 
dist 207=[-1.6008247434834175979 ,.2061452503166243292 ] 
dist 208=[-1.5917127833754922487 ,.23140276773749518413] 
dist 209=[-1.5703023670303414515 ,.25746468722267388442] 
dist 210=[-1.5654086233699769525 ,.28201874228157505888] 
dist 211=[-1.5339842899751270639 ,.31034748062859618288] 
dist 212=[-1.5275675573826165579 ,.3515034693979818442 ] 
dist 213=[-1.5160259662608624113 ,.39406119700211498292] 
dist 214=[-1.5130035418115615509 ,.42799520422483676623] 
dist 215=[-1.4561165922386036398 ,.46235131433116954783] 
dist 216=[-1.4479633297819412734 ,.50659706786552082571] 
dist 217=[-1.4292070731452166499 ,.55420153375257341455] 
dist 218=[-1.4245328216123965543 ,.60198834579002073378] 
dist 219=[-1.3980691816574600434 ,.65940845960424417534] 
dist 220=[-1.3926391422528513538 ,.74553410076132203865] 
dist 221=[-1.3820217475699434746 ,.83173556629585959751] 
dist 222=[-1.3790117539420362160 ,.889458913269978751  ] 
dist 223=[-.90867522699669339136,.93777610989549274685] 
dist 224=[-.87961407730457860885,.98636481305036922049] 
dist 225=[-.81194830172241190781,1.0318206696012975293 ] 
dist 226=[-.80109776106478853865,1.0676104353777629885 ] 
dist 227=[-.71033416445602669156,1.1034275846598298878 ] 
dist 228=[-.69379825465757477599,1.1489929786000747315 ] 
dist 229=[-.67091451213871725098,1.1933760983219468291 ] 
dist 230=[-.66423167487588918413,1.2244656498117866097 ] 
dist 231=[-.54106927724390488453,1.2519884886964977470 ] 
dist 232=[-.52527981719451151964,1.2821092426233213322 ] 
dist 233=[-.49148786499261210945,1.3118534420309870020 ] 
dist 234=[-.48343295566589881742,1.3378705583146809632 ] 
dist 235=[-.44649872984594424469,1.3663272003923855090 ] 
dist 236=[-.43988133550784702659,1.4058265016196645766 ] 
dist 237=[-.4241771176244746001 ,1.4445809390558501046 ] 
dist 238=[-.42165522598261037228,1.4700590640822137329 ] 
dist 239=[-.26402594913766967149,1.4908677613543003682 ] 
dist 240=[-.24917148148300976587,1.5109502977095284187 ] 
dist 241=[-.21498736625829560807,1.5291982154857214733 ] 
dist 242=[-.20941797902870194036,1.5426707285427919172 ] 
dist 243=[-.16504944962064980738,1.5553202613324109210 ] 
dist 244=[-.15709153179144918621,1.5702773044581345624 ] 
dist 245=[-.14544483356731198504,1.5842984037798519689 ] 
dist 246=[-.14231488019943609815,1.5932053336606772089 ] 
dist 247=[-.08762844939694696070,1.6001332724988329281 ] 
dist 248=[-.08069759920074476469,1.6062408709826554883 ] 
dist 249=[-.06530835139419076176,1.6114045213036950758 ] 
dist 250=[-.06235825009817701465,1.6145578585063175336 ] 
dist 251=[-.04406414672088170284,1.6168642958715799322 ] 
dist 252=[-.04083492951398883399,1.6186414492105952341 ] 
dist 253=[-.03475050488013591804,1.6197370286220993930 ] 

8 phat 2 dirichlet min maxes function [0, 2, 2, 2, 2, 0, 1, 1, 2] 
dist 0=[16.526048163536078942  ,16.526048163536078942  ] 
dist 1=[16.519860491050494635  ,16.525761223421755801  ] 
dist 2=[16.507680898125153488  ,16.526048163536078942  ] 
dist 3=[16.480515813988008305  ,16.516734801376386282  ] 
dist 4=[16.427536612821930603  ,16.503906846816127886  ] 
dist 5=[16.365932938531562065  ,16.497060912658901591  ] 
dist 6=[16.303436830550342753  ,16.460022989055848310  ] 
dist 7=[16.197554794314569526  ,16.398361421681162154  ] 
dist 8=[16.064552267073890855  ,16.298177170821218318  ] 
dist 9=[15.965506307506006226  ,16.267142167943880529  ] 
dist 10=[15.840095799188917001  ,16.253165303322975626  ] 
dist 11=[15.659334927638992816  ,16.243572324429482700  ] 
dist 12=[15.378303236380420576  ,16.235731115406407849  ] 
dist 13=[15.089417947784997379  ,16.221740160796661788  ] 
dist 14=[14.877250268178512017  ,15.575739060984579860  ] 
dist 15=[14.679139271234441124  ,15.565720174742932577  ] 
dist 16=[14.446461535030375506  ,15.053896923401973490  ] 
dist 17=[14.207322195341735843  ,14.985638730122560411  ] 
dist 18=[13.983369890634130839  ,14.858446612959994518  ] 
dist 19=[13.726001618600399210  ,14.826196235185493581  ] 
dist 20=[13.353232880976382228  ,14.718104904399296850  ] 
dist 21=[12.968137918813146382  ,14.689619902090484263  ] 
dist 22=[12.661476834603541756  ,14.660723305703775735  ] 
dist 23=[12.351313460715602956  ,14.649267509154683758  ] 
dist 24=[11.952211059968943697  ,13.930308534885381068  ] 
dist 25=[11.522893340010926394  ,13.857569717121608646  ] 
dist 26=[11.091899509203739414  ,13.839026904909829942  ] 
dist 27=[10.573916075657499050  ,13.808275538120419358  ] 
dist 28=[9.7967305123601137968 ,13.799034116306194456  ] 
dist 29=[9.0181674606479975100 ,13.761664166567929380  ] 
dist 30=[8.4946745526749392923 ,11.980421946805253532  ] 
dist 31=[8.0104467437532729510 ,11.945106249241952155  ] 
dist 32=[7.5468733708854922390 ,11.622491647074115230  ] 
dist 33=[7.0768456046424562492 ,11.568962569855081848  ] 
dist 34=[6.6345482890890928534 ,11.465104588380159172  ] 
dist 35=[6.2818652640335303351 ,11.437963820794083410  ] 
dist 36=[5.9247047504145101969 ,11.340538368858661778  ] 
dist 37=[5.4644983934889293533 ,11.317594199157228814  ] 
dist 38=[5.0132416929022697418 ,11.279091942324723828  ] 
dist 39=[4.6918682795140040985 ,11.268447520474618226  ] 
dist 40=[4.4017637118165230864 ,6.1625174053989028871 ] 
dist 41=[4.0755469743966225280 ,5.8846289351337126330 ] 
dist 42=[3.7481610390765096734 ,5.2350014443377072891 ] 
dist 43=[3.4533769022488564250 ,5.1407968926384300447 ] 
dist 44=[3.1238024428186047695 ,4.8753572188358046984 ] 
dist 45=[2.6572823262681518357 ,4.2581243954642846703 ] 
dist 46=[2.1952500027081566131 ,3.9251429403988228958 ] 
dist 47=[1.8836198871072738191 ,3.8895197065338594433 ] 
dist 48=[1.6202093408187705478 ,3.1030051008616846124 ] 
dist 49=[1.3510077429245445445 ,2.7664257597534822195 ] 
dist 50=[1.0962682705129144269 ,2.7079379045963778864 ] 
dist 51=[.89068872900782963425,2.6283269273509118676 ] 
dist 52=[.68018852942291800148,2.6103183192859962533 ] 
dist 53=[.40576158740892569114,2.2339871873100993138 ] 
dist 54=[.12803061654705494943,2.1891394961762368467 ] 
dist 55=[-.30630655338420039887,2.0913614501431763345 ] 
dist 56=[-.73445128274788576433,2.0750576784491330787 ] 
dist 57=[-1.0198149643079883852 ,1.9695811331297720099 ] 
dist 58=[-1.2573073215681022841 ,1.9528038783310662484 ] 
dist 59=[-1.4940138644929770832 ,1.9217359068376956990 ] 
dist 60=[-1.7142047418342758684 ,1.9155548845834026156 ] 
dist 61=[-1.8856527649383553248 ,1.7756758517356260421 ] 
dist 62=[-2.0555167356018239688 ,-.62564158715434869811] 
dist 63=[-2.2693791725722628640 ,-.63908361927696840441] 
dist 64=[-2.4767887888521194656 ,-1.0430442527349365226 ] 
dist 65=[-2.6208506174562071036 ,-1.0899280996792106598 ] 
dist 66=[-2.7471837291585033937 ,-1.1892348840123762538 ] 
dist 67=[-2.8836980766339350770 ,-1.2073939539002182347 ] 
dist 68=[-3.0175978217576011764 ,-1.3033855773720078767 ] 
dist 69=[-3.1334813487221599358 ,-1.3187876052257038514 ] 
dist 70=[-3.2592938977159344116 ,-1.3445967404756391874 ] 
dist 71=[-3.4329165503551869505 ,-1.3491959852605307855 ] 
dist 72=[-3.6022647857502419014 ,-2.2386604465803898771 ] 
dist 73=[-3.7109844092547446044 ,-2.2975052315930966633 ] 
dist 74=[-3.7969754710332243108 ,-2.3075428259315236047 ] 
dist 75=[-3.8754168435851982166 ,-2.3137092902339009665 ] 
dist 76=[-3.9437679919522380912 ,-2.3056147564618007269 ] 
dist 77=[-3.9894034279254297699 ,-2.2923773372389874587 ] 
dist 78=[-4.0275231028557432975 ,-2.2752802998900002550 ] 
dist 79=[-4.0658196113673703666 ,-2.2520428144627797863 ] 
dist 80=[-4.0993703519447348136 ,-2.2142363572182595762 ] 
dist 81=[-4.1185083092796644904 ,-2.1697106564539600990 ] 
dist 82=[-4.1309314937212279972 ,-2.1196001660757430170 ] 
dist 83=[-4.1376187966259568845 ,-2.0554922354332302018 ] 
dist 84=[-4.1407192456934638609 ,-1.9549959095894358964 ] 
dist 85=[-4.1404260684035426803 ,-1.8480899782990005060 ] 
dist 86=[-4.1353901293228841813 ,-1.7583506820735588713 ] 
dist 87=[-4.1325626411384009876 ,-1.6634152827474322889 ] 
dist 88=[-3.9173070208544526038 ,-1.5357269314805427900 ] 
dist 89=[-3.8944972992642283479 ,-1.3957051712797594216 ] 
dist 90=[-3.8437337589128735830 ,-1.2514531348971318579 ] 
dist 91=[-3.8291684057640548558 ,-1.0754819477337076438 ] 
dist 92=[-3.7621969633994797433 ,-.80863248566875380941] 
dist 93=[-3.7483184476547048233 ,-.54075870164140774266] 
dist 94=[-3.7168977959974325414 ,-.36069058561385650635] 
dist 95=[-3.7069360445462267720 ,-.20927044925894531335] 
dist 96=[-3.6061624666155390665 ,-.0559407588785851520 ] 
dist 97=[-3.5902465066013565517 ,.0881195182640598364 ] 
dist 98=[-3.5493012291486099503 ,.2024779270936944471 ] 
dist 99=[-3.5421264277305927652 ,.3177556829785566123 ] 
dist 100=[-3.4709008122872072282 ,.4654931994381035732 ] 
dist 101=[-3.4560840541195413159 ,.6098493179065850768 ] 
dist 102=[-3.4387148656766379978 ,.7116074795491081376 ] 
dist 103=[-3.4318308217919428417 ,.8023320811662545270 ] 
dist 104=[-2.2096516290511168987 ,.9025720635792296249 ] 
dist 105=[-2.1493450333264875667 ,1.0020869801983469366 ] 
dist 106=[-2.0079920241311254499 ,1.0899131964876518763 ] 
dist 107=[-1.9858277981131232165 ,1.1866071620972718611 ] 
dist 108=[-1.7932402641623418442 ,1.3215805926903861455 ] 
dist 109=[-1.7580023049220227472 ,1.4542626147716511201 ] 
dist 110=[-1.7112909470575179796 ,1.5454583173108577878 ] 
dist 111=[-1.6979608524075832812 ,1.6377856454162977212 ] 
dist 112=[-1.4256467619714267469 ,1.7127216329469046595 ] 
dist 113=[-1.3908646323272968810 ,1.7842308465146129540 ] 
dist 114=[-1.3179814416356417966 ,1.8486437387913155156 ] 
dist 115=[-1.2989884157784363119 ,1.8952049914403531593 ] 
dist 116=[-1.2246714863046230053 ,1.9379213592519995374 ] 
dist 117=[-1.2105766865474395648 ,1.9869601987662525522 ] 
dist 118=[-1.1794645225041338547 ,2.0321592022487910605 ] 
dist 119=[-1.1722542094335631845 ,2.1617515810307890517 ] 
dist 120=[-.78201594381938241542,2.3379884526465427572 ] 
dist 121=[-.74663966316163748273,2.4534338812013081147 ] 
dist 122=[-.66350609905064053043,2.5472492285894285367 ] 
dist 123=[-.65142388392075313705,2.6369939494023957091 ] 
dist 124=[-.53848284922345269075,2.7180011139214754261 ] 
dist 125=[-.51811214266940890474,2.7768775518152772354 ] 
dist 126=[-.4934127050038115146 ,2.8312279670955495098 ] 
dist 127=[-.4886985886900669937 ,2.8941367478324811688 ] 
dist 128=[-.32933821012917314604,2.9523950035400023404 ] 
dist 129=[-.30978753436791043951,2.9881492672274874644 ] 
dist 130=[-.27017736358262728048,3.0145077141205415841 ] 
dist 131=[-.26013088713325248628,3.0351948068409236685 ] 
dist 132=[-.22475516793016629807,3.0512935945215536795 ] 
dist 133=[-.21757622815896359146,3.0593050471071477729 ] 
dist 134=[-.20687556240945530571,3.0630790451844458820 ] 
dist 135=[-.20408254298199698316,3.0635644624651921994 ] 
dist 136=[.63532879208483425477,.72574580843668860557] 
dist 137=[.63375941281161437311,.74312105897838524895] 
dist 138=[.63020049553117099569,.75690885701255807054] 
dist 139=[.62394567337293006104,.76955464173237668604] 
dist 140=[.61447860842640815091,.78061454204519977094] 
dist 141=[.59807579682921765643,.78806016704907903369] 
dist 142=[.58059305503502046448,.79434241336270439429] 
dist 143=[.56680752966484944774,.800750255585005943  ] 
dist 144=[.55300075697724700219,.806321192119380143  ] 
dist 145=[.535431723488663199  ,.80925644599749539263] 
dist 146=[.51664390644316628853,.81084751273225969202] 
dist 147=[.49796316671516740315,.8111779380539304971 ] 
dist 148=[.47565315861737471791,.81072612700981050826] 
dist 149=[.44235306731623046345,.81027487970244626233] 
dist 150=[.4075551154547314317 ,.80963690330276695193] 
dist 151=[.37925549246049950029,.80913908530804928982] 
dist 152=[.35010069080405305135,.77899451761926445464] 
dist 153=[.31188269672826200094,.77542344390612668219] 
dist 154=[.2704355259012228021 ,.76698281735749533233] 
dist 155=[.22836828026248241956,.76486356013125969187] 
dist 156=[.17748999293013036008,.75204785281551690808] 
dist 157=[.10081074589041529109,.74934549160417018294] 
dist 158=[.02395927569939318271,.7443066004427239347 ] 
dist 159=[-.02760777446347425012,.74290314353399996515] 
dist 160=[-.07087980357191793812,.71787485588286899137] 
dist 161=[-.1145628910770056883 ,.71421569379211401765] 
dist 162=[-.15553022868161353024,.70570049353546437268] 
dist 163=[-.18794313335670049097,.70356187684899708288] 
dist 164=[-.22052318018786528987,.69113909116148137232] 
dist 165=[-.26215898519814887949,.68855404211021219481] 
dist 166=[-.30279742281716637302,.68359770389485416527] 
dist 167=[-.33138944543818324337,.68219934891122905904] 
dist 168=[-.3568294486013729021 ,.45918179756167081395] 
dist 169=[-.38486423616209535486,.4442543949598432029 ] 
dist 170=[-.41265874826936373575,.40940532848538488675] 
dist 171=[-.43713806302043209616,.40390141918291408447] 
dist 172=[-.46405063726687155542,.35691065519113856413] 
dist 173=[-.50157499673563116377,.34834984959418804949] 
dist 174=[-.53845612833243760023,.33677611710876279811] 
dist 175=[-.56279669840498425063,.33337709054216010213] 
dist 176=[-.58277886076007502627,.26885722096954100172] 
dist 177=[-.60223226817110441231,.26061437330810893783] 
dist 178=[-.62001891500715300735,.24315888032276260405] 
dist 179=[-.63333631424925876806,.23884153284417610026] 
dist 180=[-.64602323253703569388,.22043487192689568375] 
dist 181=[-.66128887202830077683,.21707729691413473381] 
dist 182=[-.67573470046467863529,.20927633747171328599] 
dist 183=[-.68514350523717247792,.20789106358137867624] 
dist 184=[-.69272900987154536394,.14769717057597695314] 
dist 185=[-.6998841061518676175 ,.14557620984420113121] 
dist 186=[-.70627475399312213117,.1380902152825487976 ] 
dist 187=[-.71080354162158964112,.13653302970297663502] 
dist 188=[-.71486766640063645234,.13419073927362397704] 
dist 189=[-.71940041758981000689,.13356463461327820762] 
dist 190=[-.72346061364803201608,.08083087678034579298] 
dist 191=[-.72563514674089831084,.07639605887427101040] 
dist 192=[-.7268598206936859941 ,.06601190666732711641] 
dist 193=[-.72712170803593671394,.06451091658824873437] 
dist 194=[-.72689500178967540814,.05054613757749705645] 
dist 195=[-.72655483000810503585,.04804179494022728797] 
dist 196=[-.72529966129453317635,.04500038677009669609] 
dist 197=[-.72452479849113563362,.04444452668729582941] 
dist 198=[-.71443859753754991446,.02517481600269214780] 
dist 199=[-.70983732642834873544,.02282199985763587699] 
dist 200=[-.03433367978442802159,.01806272923240581932] 
dist 201=[-.04033827717645205585,.01686102079446434986] 
dist 202=[-.04531904706826711266,.01265890533486910521] 
dist 203=[-.05025695307893301012,.01180603337267226871] 
dist 204=[-.05483370416987388512,.01060408117709204150] 
dist 205=[-.05837014601078334952,.01027285785458039722] 
dist 206=[-.06184840854732827729,-.01574320910510887654] 
dist 207=[-.06619250050039279755,-.01790822001888017787] 
dist 208=[-.07038804905633844293,-.02282303028418201223] 
dist 209=[-.07327225994206707821,-.02361188614810278210] 
dist 210=[-.07576962955057704468,-.02971223460001340044] 
dist 211=[-.07841812033846697399,-.03077496573458226617] 
dist 212=[-.08098518194088912304,-.03238314634401703014] 
dist 213=[-.08315690703053209240,-.03278291116625933572] 
dist 214=[-.08547154690671923490,-.03919188883979067285] 
dist 215=[-.08861017673707402202,-.03998665930633025687] 
dist 216=[-.09166164432215994391,-.04174142127950831028] 
dist 217=[-.09362770074459248330,-.04202930778808548310] 
dist 218=[-.09518968324308995397,-.04401218941485031867] 
dist 219=[-.09662514244171511877,-.04433768294854714033] 
dist 220=[-.09788218112752352004,-.04490834263985257532] 
dist 221=[-.09873060497947225318,-.04501775223509426855] 
dist 222=[-.09944845817561868960,-.06215158142660023135] 
dist 223=[-.10018329681872594212,-.06317529335142155744] 
dist 224=[-.10084104271070016223,-.06532331883367812006] 
dist 225=[-.10125058602245573779,-.06577474391569820782] 
dist 226=[-.10155972729765471152,-.06783837669902490992] 
dist 227=[-.10181596562500925225,-.06819356880996533447] 
dist 228=[-.1020208730255457692 ,-.06883239430635657901] 
dist 229=[-.10212474955817546081,-.06895814358165689228] 
dist 230=[-.10217533011684424386,-.06916085394303488495] 
dist 231=[-.10216712966619015841,-.06900092970645316466] 
dist 232=[-.09720165636703690758,-.06862662593045354977] 
dist 233=[-.09677289785901589885,-.06785863492710304475] 
dist 234=[-.09577755365003465525,-.06688925190701819630] 
dist 235=[-.09554659908783741350,-.06570954590702576134] 
dist 236=[-.09412685304005518655,-.06414087249508010859] 
dist 237=[-.09383887494149388602,-.06161597193181797895] 
dist 238=[-.09330595653857454040,-.05898593775463857697] 
dist 239=[-.09316335625318381643,-.05699681243955625824] 
dist 240=[-.09070849379076826149,-.05508166640346733160] 
dist 241=[-.09035430561209260059,-.05274744462590017892] 
dist 242=[-.08952263109689486564,-.05030127622079864786] 
dist 243=[-.08932963086673112693,-.04793842414330054340] 
dist 244=[-.08810468847213349128,-.0451661552028184877 ] 
dist 245=[-.08746818129340528035,-.04108266524319766373] 
dist 246=[-.08508515497007128092,-.03683394171472276793] 
dist 247=[-.08396553282549556510,-.03340087396103150018] 
dist 248=[-.06599889012855799167,-.02988219958077647046] 
dist 249=[-.06453453364554266277,-.02529110956519957594] 
dist 250=[-.06152549513827047889,-.02031964920567260574] 
dist 251=[-.06069010456320664341,-.01527981701856961827] 
dist 252=[-.05413725723179964329,-.00918609803522570516] 

8 phat 2 dirichlet min maxes function [1, 2, 2, 1, 1, 1, 1, 1, 2] 
dist 0=[11.005364375168949012  ,11.005364375168949012  ] 
dist 1=[10.826214382285171836  ,11.121408671175071804  ] 
dist 2=[10.644813507302055414  ,11.214255244582465586  ] 
dist 3=[10.519766528997215689  ,11.300638933403124053  ] 
dist 4=[10.411168857125067030  ,11.376971684409241384  ] 
dist 5=[10.295543158030896933  ,11.429623637719566298  ] 
dist 6=[10.183236892084252782  ,11.475366146192410266  ] 
dist 7=[10.087910350911364995  ,11.524063876020821231  ] 
dist 8=[9.9860598020125878355 ,11.568120184274055398  ] 
dist 9=[9.8476597929132979481 ,11.595303259180319646  ] 
dist 10=[9.7085134455439273780 ,11.615502770216283631  ] 
dist 11=[9.6036757534707092871 ,11.631640784763105845  ] 
dist 12=[9.5031141068698244909 ,11.644061561256119437  ] 
dist 13=[9.3810642984889979852 ,11.649401556067774169  ] 
dist 14=[9.2534113805766859655 ,11.650917434276157859  ] 
dist 15=[9.1304386030230893738 ,11.650349050704211956  ] 
dist 16=[8.9863869875346964734 ,11.639695903105446623  ] 
dist 17=[8.7744302836318544669 ,11.408817465672997350  ] 
dist 18=[8.5609666218925380061 ,11.365355209477531753  ] 
dist 19=[8.4108864304902268282 ,11.353181259495679985  ] 
dist 20=[8.2773604823987904446 ,11.304715431902109293  ] 
dist 21=[8.1301000030759226044 ,11.293753996954534857  ] 
dist 22=[7.9839031973191860203 ,11.267559196150740151  ] 
dist 23=[7.8546284456844752772 ,11.258803553263526680  ] 
dist 24=[7.7119729872504762860 ,11.215144398235666986  ] 
dist 25=[7.5122566759552313654 ,11.204537875618868342  ] 
dist 26=[7.3086740921155996589 ,11.186115204331229751  ] 
dist 27=[7.1505533137742162751 ,11.180763511426478062  ] 
dist 28=[6.9942132778072034725 ,11.160604959017164467  ] 
dist 29=[6.7977496619012436124 ,11.154361115310068275  ] 
dist 30=[6.5886178672449448059 ,11.142383581627772560  ] 
dist 31=[6.3816079712466589697 ,11.138229414529913997  ] 
dist 32=[6.1348270721236324372 ,11.116385976976682474  ] 
dist 33=[5.7666238346912422128 ,8.9113235368941801784 ] 
dist 34=[5.3985650737801769114 ,8.7953024483201072380 ] 
dist 35=[5.1523613482809483828 ,8.5311484685621200187 ] 
dist 36=[4.9463583942262329606 ,8.4856781958618280851 ] 
dist 37=[4.7390879573010544761 ,8.1509434358927478333 ] 
dist 38=[4.5449008490386353864 ,8.0910507845932327630 ] 
dist 39=[4.3912261838234483697 ,7.9950018978009552128 ] 
dist 40=[4.2365756066012216816 ,7.9718072258640759228 ] 
dist 41=[4.0384845472004199725 ,7.5852183178170953212 ] 
dist 42=[3.8446024542392395345 ,7.5358735202887109680 ] 
dist 43=[3.7067859070137908358 ,7.4200506967887918356 ] 
dist 44=[3.5825629934744544497 ,7.4033646322460156807 ] 
dist 45=[3.4430502369255816081 ,7.2466493319141733592 ] 
dist 46=[3.3030351920428076154 ,7.2184646672411251997 ] 
dist 47=[3.1768026728838967654 ,7.1845968132746744280 ] 
dist 48=[3.0354673945926953995 ,7.1785712288047453022 ] 
dist 49=[2.8350451595365580438 ,6.9517263496844020833 ] 
dist 50=[2.6361259935557330625 ,5.4376291061101212396 ] 
dist 51=[2.5008021778962168692 ,5.2203266154727748522 ] 
dist 52=[2.3850862609168100552 ,5.1666577745090771213 ] 
dist 53=[2.2645924056397869241 ,4.9604517376118200516 ] 
dist 54=[2.1490897242679873475 ,4.9215770227552356669 ] 
dist 55=[2.0533365309075179122 ,4.8490895196084603239 ] 
dist 56=[1.9529391015900616235 ,4.8326080906696200845 ] 
dist 57=[1.8188598494866014877 ,4.7788547774460582526 ] 
dist 58=[1.6849796474707336059 ,4.2554922597579722483 ] 
dist 59=[1.5853778964585384571 ,4.2355757584039507911 ] 
dist 60=[1.4910149221988805510 ,4.1631799046352293891 ] 
dist 61=[1.3780878917521880550 ,4.1481165441517115899 ] 
dist 62=[1.2607538092754618906 ,4.1206892629333890148 ] 
dist 63=[1.1487630516922950137 ,4.1139807503269646677 ] 
dist 64=[1.0183144864841511760 ,2.3877027934862488278 ] 
dist 65=[.82715238950893317489,1.9263259549406185867 ] 
dist 66=[.63687217349323621741,1.3523935072906942203 ] 
dist 67=[.4984397739729400919 ,1.0896815626377923923 ] 
dist 68=[.27105967613086163675,.9654305595902441361 ] 
dist 69=[.09396132355600109562,.94921430277312842715] 
dist 70=[-.08154774785549931740,.80831211628991311909] 
dist 71=[-.30257213033980164549,.78343118404563863984] 
dist 72=[-.51692167402235810578,.75089463241513826746] 
dist 73=[-.66573699550481683937,.74371209162774394444] 
dist 74=[-.79614510251372999415,.56908130120360393828] 
dist 75=[-.93688116673949958657,.54773668413454517472] 
dist 76=[-1.0747623390398140641 ,.50311954999642493838] 
dist 77=[-1.1937536410520248526 ,.49275973198199217975] 
dist 78=[-1.3226012928214036820 ,.44921550215690969139] 
dist 79=[-1.4999007615027600647 ,.44135586643866329609] 
dist 80=[-1.6733665312704137888 ,.42594345783016764569] 
dist 81=[-1.7868828991235810034 ,.42228709668598007618] 
dist 82=[-1.8790593756394737263 ,.24484964771172566641] 
dist 83=[-1.9671832002653090342 ,.22916771152870876711] 
dist 84=[-2.0467485076188563467 ,.19346339081497216644] 
dist 85=[-2.1046985993709961234 ,.18797593499207117376] 
dist 86=[-2.1583514442355366780 ,.14330379989763385214] 
dist 87=[-2.2207331566415090737 ,.13551226640449227862] 
dist 88=[-2.2787467574308348968 ,.12455365538791950403] 
dist 89=[-2.3149301604679915106 ,.12170119297746970762] 
dist 90=[-2.3423214951374351020 ,.07189402986265908797] 
dist 91=[-2.3651704257681890735 ,.06574823703190258007] 
dist 92=[-2.3836401901700147106 ,.05243759897368747995] 
dist 93=[-2.3935187516324626324 ,.04987782330833816339] 
dist 94=[-2.3990713372094373565 ,.03530858036061787069] 
dist 95=[-2.4003823432683978802 ,.03285990034920048990] 
dist 96=[-2.3938166956938664802 ,.02789864639339492177] 
dist 97=[-2.3923785653426066241 ,.02675916427948847225] 
dist 98=[-2.3865131179854994800 ,-.56149174549088951679] 
dist 99=[-2.3849195817840267841 ,-.49516972588899335803] 
dist 100=[-2.3662625353591907236 ,-.42554407816893571075] 
dist 101=[-2.3615907410980091908 ,-.35860729910614912196] 
dist 102=[-2.3565346809846240280 ,-.30303150592199022624] 
dist 103=[-2.3539436902064205511 ,-.24478217378402584788] 
dist 104=[-2.2854936585678194611 ,-.16715261091903717719] 
dist 105=[-2.2755733293923838060 ,-.08991881193594778446] 
dist 106=[-2.2565216855571357657 ,-.03324942715362143668] 
dist 107=[-2.2513172713774398398 ,.01957466328295395661] 
dist 108=[-2.2316182587797202500 ,.08143795838745173113] 
dist 109=[-2.2267738643528403469 ,.14488039667850490733] 
dist 110=[-2.2170491176758997722 ,.20402102118659792275] 
dist 111=[-2.2139811908278932434 ,.27174417512553559811] 
dist 112=[-2.1405281265366700907 ,.36950593610797635681] 
dist 113=[-2.0383784515962878625 ,.46699717734678801585] 
dist 114=[-1.8718964306567123202 ,.53364003991963864512] 
dist 115=[-1.8597782584618413139 ,.59089774909923883676] 
dist 116=[-1.7939537945578959282 ,.65086452075751064504] 
dist 117=[-1.7815412421935186832 ,.70848519703420203822] 
dist 118=[-1.7560694322944687603 ,.75636385695106937473] 
dist 119=[-1.7490668173632467051 ,.80661603830204589984] 
dist 120=[-1.6825381851291223194 ,.87373061746038484704] 
dist 121=[-1.6626863535642046539 ,.94065070816589430579] 
dist 122=[-1.6368332913325651410 ,.99012684636370798546] 
dist 123=[-1.6308053920516763512 ,1.0366555477801320969 ] 
dist 124=[-1.5958555021342706805 ,1.0917917897957774344 ] 
dist 125=[-1.5889223533966746814 ,1.1487383299441325602 ] 
dist 126=[-1.5755012802673186251 ,1.2025085417413410883 ] 
dist 127=[-1.5718362456246570553 ,1.2646586713682040010 ] 
dist 128=[-.97711705610819449758,1.3551199249554394454 ] 
dist 129=[-.78908356858063927268,1.4445143908389936142 ] 
dist 130=[-.71761471929793054174,1.5023991173660021460 ] 
dist 131=[-.70619536051780180666,1.5487122993355219424 ] 
dist 132=[-.61170566444615654049,1.5918307770603434861 ] 
dist 133=[-.59463519675536333261,1.6299822207047881200 ] 
dist 134=[-.57074594611565827127,1.6564321369466400208 ] 
dist 135=[-.56393036787000646128,1.6795768445649549053 ] 
dist 136=[-.44083258418327548714,1.7045118558837094496 ] 
dist 137=[-.42516137533780750019,1.7270987359443042974 ] 
dist 138=[-.39133939918422031923,1.7408528357065579711 ] 
dist 139=[-.38377357859208318375,1.7508773351842336804 ] 
dist 140=[-.3462057194222512326 ,1.7585471583857447334 ] 
dist 141=[-.33954923333232911003,1.7641875208176008829 ] 
dist 142=[-.32467496367740280084,1.7660950327566153961 ] 
dist 143=[-.32170071295535363572,1.7665110844436269772 ] 
dist 144=[-.18292091317874632326,1.7661864368251941442 ] 
dist 145=[-.1695853394509636778 ,1.6857850744885295037 ] 
dist 146=[-.13963700812235724113,1.6774587168258027609 ] 
dist 147=[-.13423831963187350002,1.6600815247118225551 ] 
dist 148=[-.09764264725943437190,1.6550171935326450047 ] 
dist 149=[-.09116600504460740037,1.6335991494299829852 ] 
dist 150=[-.07976529056802558132,1.6291572088248635167 ] 
dist 151=[-.07729863300039971518,1.6166658594293322407 ] 
dist 152=[-.04008174652234675807,1.6145753482362117790 ] 
dist 153=[-.03509802527869796818,1.5885939308380315073 ] 
dist 154=[-.02443559655795432885,1.5836025192586871159 ] 
dist 155=[-.02208617583711611705,1.5727701422921893962 ] 
dist 156=[-.01066576724440494280,1.5709561966044052801 ] 
dist 157=[-.00869180042976302669,1.5752550557457878424 ] 
dist 158=[-.00418389006341939385,1.5774811256763368232 ] 
dist 159=[-.00346807101462117801,1.5779047653955200878 ] 
dist 160=[.56155432731949184047,1.5388445424914976267 ] 
dist 161=[.48849786707993462363,.80109839037420868108] 
dist 162=[.38495188189604699056,.75910852197626717062] 
dist 163=[.29793524901618180195,.66021021959448337148] 
dist 164=[.20987974878775533881,.64597871546873679334] 
dist 165=[.12715785357288816575,.55268385720929032594] 
dist 166=[.06146825198331847356,.55139974272055705905] 
dist 167=[-.00478682120351032186,.55087796475535196443] 
dist 168=[-.08977020789694665188,.54941695147235960079] 
dist 169=[-.17287574289277248315,.54895816144948674535] 
dist 170=[-.23162209825504432366,.54874865849488648725] 
dist 171=[-.28418286822256675048,.54882295812737844215] 
dist 172=[-.34255450578139474357,.54907544741697084288] 
dist 173=[-.40069331142852616667,.54957839723803034562] 
dist 174=[-.45232334365975018958,.55036510014919015468] 
dist 175=[-.50944341409390092452,.5517521600688665536 ] 
dist 176=[-.58953569309772877116,.55324129018467887487] 
dist 177=[-.66846376224129683489,.55443609817178763187] 
dist 178=[-.7209286430977347306 ,.55565248535264477463] 
dist 179=[-.76441910332659829597,.55722784803978447194] 
dist 180=[-.80746110820499918388,.55892684609307884528] 
dist 181=[-.84728449720887450425,.56063755941771104248] 
dist 182=[-.87790479968578712057,.56269652330050333874] 
dist 183=[-.90786519849102077127,.56578796311564897095] 
dist 184=[-.94505024477579096467,.56902579317834898939] 
dist 185=[-.98082507579271528104,.57167007755560137177] 
dist 186=[-1.0051466061289621273 ,.57440407997059645578] 
dist 187=[-1.0259073547254391359 ,.57800062282751544456] 
dist 188=[-1.0474437515266231629 ,.58190669862378219775] 
dist 189=[-1.0680178548941996087 ,.58587833491831926597] 
dist 190=[-1.0849310364168738570 ,.59068636333226172402] 
dist 191=[-1.1025261503090954717 ,.59793667697014525855] 
dist 192=[-1.1258280985338676260 ,.60519939701744767493] 
dist 193=[-1.1481507456184025759 ,.61005702258820964306] 
dist 194=[-1.1618299115061428567 ,.61411533289575384911] 
dist 195=[-1.1718955228521052807 ,.61818203724465462762] 
dist 196=[-1.1797675983924494250 ,.62197571682716928044] 
dist 197=[-1.1859252533581003842 ,.62494234130904676587] 
dist 198=[-1.1891347588652727132 ,.62789127232208918286] 
dist 199=[-1.1908224382819548920 ,.63161416923390324438] 
dist 200=[-1.1910379824320088857 ,.63522435994787467068] 
dist 201=[-1.1816645379886236612 ,.63772262523156952623] 
dist 202=[-1.1797280326887627930 ,.63990126046246895519] 
dist 203=[-1.1774791012318648436 ,.64223341575593743366] 
dist 204=[-1.1763228408450142842 ,.64450444662968286196] 
dist 205=[-1.1740180752978685892 ,.64643864218254738378] 
dist 206=[-1.1728097908372512708 ,.64850938445936552819] 
dist 207=[-1.1716831740442206793 ,.6513262910711304076 ] 
dist 208=[-1.1707879892221269011 ,.654061169740631673  ] 
dist 209=[-1.0200672912938386442 ,.65580391020689801986] 
dist 210=[-1.0073779137697348544 ,.65716456975923866228] 
dist 211=[-.9805692768933688679 ,.65837176502807993977] 
dist 212=[-.97320978696351301574,.65939674518370840739] 
dist 213=[-.94388935017012472901,.66002881227185673581] 
dist 214=[-.93826409702024699641,.66049765448976627417] 
dist 215=[-.92411102316191379458,.6608698969367933335 ] 
dist 216=[-.92179080396458517155,.66112238623339949758] 
dist 217=[-.74906325970097662152,.66111236736554476072] 
dist 218=[-.7310825393841390865 ,.66090707129374773704] 
dist 219=[-.70670222202931022711,.66056622290948026433] 
dist 220=[-.69940766530888201847,.6596771532687710206 ] 
dist 221=[-.60247459123566111251,.65918622637415846803] 
dist 222=[-.60054389003022931658,.65783704716403867357] 
dist 223=[-.59624801173624888724,.65719349153476524596] 
dist 224=[-.5948813544992316965 ,.65338877108422251936] 
dist 225=[-.42260283331610107672,.65242888579676608544] 
dist 226=[-.41076613455621076417,.64984152998320038288] 
dist 227=[-.3830705193392735952 ,.64891448401285981155] 
dist 228=[-.37868423021189930826,.64334183113726356104] 
dist 229=[-.34107527022026550336,.64196343971610425565] 
dist 230=[-.33419304528165382684,.6394533129749011014 ] 
dist 231=[-.32493165602363594779,.63867737708702695645] 
dist 232=[-.32218101663997839248,.62148993447371401273] 
dist 233=[-.269477122719182406  ,.61888237657230161779] 
dist 234=[-.2627154913707245611 ,.61321029438851886986] 
dist 235=[-.24845498660614646631,.61147644746421148237] 
dist 236=[-.24481675963874724074,.60378408778591327904] 
dist 237=[-.22991510670535443724,.60213882992408468506] 
dist 238=[-.22714393542919698987,.59792840742540036969] 
dist 239=[-.22076751487641832247,.59684576798180358492] 
dist 240=[-.21952574058625542769,.5362694099970640888 ] 
dist 241=[-.14519747138214448681,.53022635884883853459] 
dist 242=[-.13838791360323270602,.51616939258862984537] 
dist 243=[-.1223783489692544961 ,.51341081275740009337] 
dist 244=[-.12004625922897305833,.49393470249721152813] 
dist 245=[-.09826078507352009941,.49017855043974990536] 
dist 246=[-.0943255909691038807 ,.48391635440320024368] 
dist 247=[-.08955164255334014550,.48232767283873993186] 
dist 248=[-.08862796088899017730,.45216129809057129658] 
dist 249=[-.05771012797159965517,.41478597465909060141] 
dist 250=[-.05390435217328721381,.40304623824503649976] 
dist 251=[-.04620920260165038845,.40021683714368220088] 
dist 252=[-.0442561390412871985 ,.39295140360785990772] 
dist 253=[-.03738130133014950839,.34962233571609782306] 
dist 254=[-.03597606410144082186,.34240421272951823141] 
dist 255=[-.03390278093585115968,.30286546215717547138] 

8 phat 2 dirichlet min maxes function [1, 0, 2, 1, 1, 1, 0, 1, 2] 
dist 0=[12.159309420628639757  ,12.159309420628639757  ] 
dist 1=[12.116243094393824991  ,12.177176510660008717  ] 
dist 2=[12.049172380036316687  ,12.205561759740310396  ] 
dist 3=[11.940246129751694973  ,12.237518661184233544  ] 
dist 4=[11.828321801732934669  ,12.259476920724278430  ] 
dist 5=[11.749262093150102973  ,12.283160773648039881  ] 
dist 6=[11.678563895914161904  ,12.299924218521605035  ] 
dist 7=[11.600078019935067305  ,12.311779211258795926  ] 
dist 8=[11.521896602072550530  ,12.320298999987665398  ] 
dist 9=[11.452416523052793844  ,12.323725768119762454  ] 
dist 10=[11.375489735067617417  ,12.324088023941239757  ] 
dist 11=[11.267529928353876353  ,12.322847960324347929  ] 
dist 12=[11.157461690248943753  ,12.314358605338428021  ] 
dist 13=[11.072103787177445436  ,12.311304004692097321  ] 
dist 14=[10.987880348136382123  ,12.297817214302260021  ] 
dist 15=[10.882349334813650129  ,12.295459713731214235  ] 
dist 16=[10.770253736590319901  ,11.982566223358556598  ] 
dist 17=[10.659779424903675588  ,11.950633096881702351  ] 
dist 18=[10.528514220618947326  ,11.881000709020047445  ] 
dist 19=[10.333278040973717411  ,11.860939592497003503  ] 
dist 20=[10.134059330192215434  ,11.774200216747471648  ] 
dist 21=[9.9915718035398835282 ,11.756500122214463787  ] 
dist 22=[9.8627427069791625901 ,11.714572269440053516  ] 
dist 23=[9.7174889844116853518 ,11.703257770611887063  ] 
dist 24=[9.5714155476614862463 ,11.585876905072148808  ] 
dist 25=[9.4393065498945457196 ,11.566629533378176781  ] 
dist 26=[9.2910747589692722916 ,11.519662253567979717  ] 
dist 27=[9.0805158271883328172 ,11.509044682673313319  ] 
dist 28=[8.8645360690643531120 ,11.433376507465621948  ] 
dist 29=[8.6946223880484437626 ,11.417438744600561786  ] 
dist 30=[8.5245760976719773366 ,11.391286026554772720  ] 
dist 31=[8.0934122849388925030 ,11.383876533661799468  ] 
dist 32=[7.7827254610649474561 ,9.3319650880626190041 ] 
dist 33=[7.5182295132370901610 ,9.3221517289924874081 ] 
dist 34=[7.2449510976767548896 ,9.3116130051061976484 ] 
dist 35=[6.9845506179330654125 ,9.3078082740924533305 ] 
dist 36=[6.7335919502555355401 ,8.4516341446348407335 ] 
dist 37=[6.4524930681444617346 ,8.3752342643858884946 ] 
dist 38=[6.2149357124708037516 ,8.2862435650529214791 ] 
dist 39=[5.9714434313735416958 ,8.2690400310635801998 ] 
dist 40=[5.7421431455919192189 ,7.6223070680928025815 ] 
dist 41=[5.5561713087875266399 ,7.5411346974326261074 ] 
dist 42=[5.3361607635073390816 ,7.3811067762803773051 ] 
dist 43=[5.1019035913563682446 ,7.3406498238649460310 ] 
dist 44=[4.8694727025063470333 ,7.2008838680918122263 ] 
dist 45=[4.6331011994584271196 ,7.1700579549170441865 ] 
dist 46=[4.2711798285503472412 ,7.1304273755037258396 ] 
dist 47=[3.9094223248651523125 ,7.1175720696098349938 ] 
dist 48=[3.6597131329546185412 ,5.8979418607783174703 ] 
dist 49=[3.4424024384853483682 ,5.8322790793948148582 ] 
dist 50=[3.2102097386390444008 ,5.7720922901459714664 ] 
dist 51=[2.9840855964585045219 ,5.6516482748757738106 ] 
dist 52=[2.7910401035145142906 ,5.2433201678856630347 ] 
dist 53=[2.5837566515237738884 ,5.1938709502728321635 ] 
dist 54=[2.3006828270865256172 ,5.0975030522875476847 ] 
dist 55=[2.0152909108120543092 ,5.0733651305455667917 ] 
dist 56=[1.7987324728926106865 ,4.8067329171519623207 ] 
dist 57=[1.5894446304563942361 ,4.7675471190599095407 ] 
dist 58=[1.3331251106747587958 ,4.6868207287669517036 ] 
dist 59=[1.0637174385729185282 ,4.6654347283111327400 ] 
dist 60=[.80207828124369969241,4.5847256357502569416 ] 
dist 61=[.49391054670658885358,4.5686494555074258985 ] 
dist 62=[.03840245085521506109,4.5347231227555487106 ] 
dist 63=[-.4145667547270016631 ,4.5252016444884559153 ] 
dist 64=[-.71258218906423435139,2.3849148406398177522 ] 
dist 65=[-.95646867592864548752,2.3651410725996301575 ] 
dist 66=[-1.1929457401302735581 ,2.3410387899152811882 ] 
dist 67=[-1.4087993879312794537 ,2.3360309768832791672 ] 
dist 68=[-1.5702031903147172448 ,1.1382822769191217322 ] 
dist 69=[-1.7239205884612064524 ,1.0627505615878412826 ] 
dist 70=[-1.9090378735982939902 ,.89013794506079547104] 
dist 71=[-2.0846250356493141078 ,.86231298660821136769] 
dist 72=[-2.2002286287973879722 ,.64295638941084422406] 
dist 73=[-2.2949616875302470423 ,.60410769197937038105] 
dist 74=[-2.3870774890643085933 ,.5467906772876478167 ] 
dist 75=[-2.4713933377539331417 ,.53178524367056903335] 
dist 76=[-2.5349355131355284253 ,.27742975898101273523] 
dist 77=[-2.5959929944364582986 ,.24554537294270192377] 
dist 78=[-2.6703860232755490130 ,.17414702209661470388] 
dist 79=[-2.7408647343281583992 ,.1617505367937360222 ] 
dist 80=[-2.7862665151039877651 ,.07582913112251209341] 
dist 81=[-2.8224178889227430259 ,.06088572838000157367] 
dist 82=[-2.8558837236257752975 ,.03514625123644515770] 
dist 83=[-2.8854457998665385466 ,.02964485186239050911] 
dist 84=[-2.9059779041258303616 ,-.14242993985140449073] 
dist 85=[-2.9240279691629360527 ,-.16105089079448340974] 
dist 86=[-2.9436604686923670046 ,-.19733106326800274938] 
dist 87=[-2.9612758599051449146 ,-.20603242234759838528] 
dist 88=[-2.9712554187539087695 ,-.23346295952391847245] 
dist 89=[-3.0058415672517621292 ,-.23956237977938779744] 
dist 90=[-3.0366090436966269927 ,-.2410679101725788394 ] 
dist 91=[-3.0686608285451942636 ,-.23602324058309980926] 
dist 92=[-3.0975167237236444011 ,-.22789703183256620922] 
dist 93=[-3.1155029715340234906 ,-.21689943699243643285] 
dist 94=[-3.1291043201176677688 ,-.20162567244697617563] 
dist 95=[-3.1404225445933765763 ,-.17639797781448009572] 
dist 96=[-3.1495034091657058066 ,-.14649271830712221838] 
dist 97=[-3.1541559409546259119 ,-.11251424234837462502] 
dist 98=[-3.1564844059744122590 ,-.06880697832500313459] 
dist 99=[-3.1562689438241029272 ,0                     ] 
dist 100=[-1.7336407790789802666 ,-.9624813919938360325 ] 
dist 101=[-1.7337172294185585945 ,-.86379976908991638826] 
dist 102=[-1.7332774093748673825 ,-.73489103305694338746] 
dist 103=[-1.7324566511294288524 ,-.60778330042222736846] 
dist 104=[-1.7005315211745358958 ,-.5163009210920922564 ] 
dist 105=[-1.6955113467441797700 ,-.4327858883531157574 ] 
dist 106=[-1.6864629704083751662 ,-.33753189836460686232] 
dist 107=[-1.6839589021833049435 ,-.24123240377198088914] 
dist 108=[-1.6746471391726544397 ,-.15353484877082315202] 
dist 109=[-1.6719580093674870389 ,-.05473091585920024788] 
dist 110=[-1.6670074649735314335 ,.08597994958852454468] 
dist 111=[-1.6653942278748903864 ,.22552374822100811424] 
dist 112=[-1.4826959700016489406 ,.319662237194059776  ] 
dist 113=[-1.4661900813299329947 ,.39920726043286339763] 
dist 114=[-1.4299618371415126626 ,.48039978693711882174] 
dist 115=[-1.4211779942041330291 ,.55711607180012996094] 
dist 116=[-1.3774846540933668323 ,.61876399499343304221] 
dist 117=[-1.3691853585383419006 ,.68161598146994585487] 
dist 118=[-1.3510238000813370143 ,.76314947760417437533] 
dist 119=[-1.3458899373544341960 ,.84333260739619850824] 
dist 120=[-1.2989902273257489143 ,.90078633353207355755] 
dist 121=[-1.2914341348358123331 ,.95300091772645844595] 
dist 122=[-1.2750266520036562388 ,1.0122361128419115279 ] 
dist 123=[-1.2702627251157699911 ,1.0719764331600939616 ] 
dist 124=[-1.2501083707175926318 ,1.1262131475980217091 ] 
dist 125=[-1.2460202790891292959 ,1.1872125227070186935 ] 
dist 126=[-1.2360836118831289193 ,1.2739997207151262394 ] 
dist 127=[-1.2336680455806241247 ,1.3593822045462753399 ] 
dist 128=[-.56113511807405527991,1.4147648923850636867 ] 
dist 129=[-.52271470167655298419,1.4591816215025350864 ] 
dist 130=[-.43287566398027273488,1.5007105302213656138 ] 
dist 131=[-.41970150609659583824,1.5375743259543976461 ] 
dist 132=[-.29926173300650324031,1.5633354144178076304 ] 
dist 133=[-.27766987364904425624,1.5860911750902417176 ] 
dist 134=[-.25082631304863121017,1.6109378137547187519 ] 
dist 135=[-.24541517189279454515,1.6334452452826698612 ] 
dist 136=[-.08181368242098502587,1.6468462777366163641 ] 
dist 137=[-.06177934992478830237,1.6562455168840038667 ] 
dist 138=[-.02072495023414556921,1.6627479154439362042 ] 
dist 139=[-.01024692942836127901,1.6672906995356655885 ] 
dist 140=[.02720881079209301059,1.6688530123658302130 ] 
dist 141=[.03457181682010528231,1.6689676214302059122 ] 
dist 142=[.04686972426609475839,1.6683190365957856197 ] 
dist 143=[.04962154404634188671,1.6076562856526872104 ] 
dist 144=[.25388980634543403188,1.6006803224416209411 ] 
dist 145=[.27110824125667296046,1.5855230414365368228 ] 
dist 146=[.31067866654207925676,1.5808870641351715868 ] 
dist 147=[.3164502722802481628 ,1.5603183894554234145 ] 
dist 148=[.36671458106478376784,1.5559307524764695582 ] 
dist 149=[.37542509361766715497,1.5445280924146721499 ] 
dist 150=[.38685317348461189804,1.5417444851811707130 ] 
dist 151=[.38903352786292786353,1.5088775589784921784 ] 
dist 152=[.44609916386017185762,1.5033445086323443496 ] 
dist 153=[.45279803072212037772,1.4891301732963441125 ] 
dist 154=[.46710992405095565958,1.4861619696989002329 ] 
dist 155=[.46969365331802602479,1.4608737177695218754 ] 
dist 156=[.4840906665019832383 ,1.4554345397120813063 ] 
dist 157=[.40444338792599119539,1.4479784963871457290 ] 
dist 158=[.26744664104618721251,1.4453497871745175901 ] 
dist 159=[.13011674939343478985,.9772663273629342365 ] 
dist 160=[.03796050257561605704,.97801579404397818172] 
dist 161=[-.03937762152845528895,.9780587696407484964 ] 
dist 162=[-.11745648537207641499,.97674254290447990612] 
dist 163=[-.19068189068211700507,.97654256133058580618] 
dist 164=[-.24861329418784505828,.96914018399828783904] 
dist 165=[-.30683800300098639556,.96727131655572491716] 
dist 166=[-.38123645968698008537,.96618823504756087624] 
dist 167=[-.45384380028481840741,.96588418053192452603] 
dist 168=[-.50490671216805503473,.93300177723884648352] 
dist 169=[-.55031630400056806117,.9284282872853772999 ] 
dist 170=[-.60031851855965841629,.92034764505877036127] 
dist 171=[-.65259383944470369374,.91831416581651398519] 
dist 172=[-.70157518466354709049,.91182605540367409854] 
dist 173=[-.7550200323405580244 ,.90981280594057302575] 
dist 174=[-.82903306239441485446,.90849939756850156919] 
dist 175=[-.90155106223182509038,.90808663107731045429] 
dist 176=[-.94901785809911161167,.77018207692893409474] 
dist 177=[-.98754640347722772272,.75837182821194865236] 
dist 178=[-1.0243237646137988265 ,.73284013802767066786] 
dist 179=[-1.0574634283216547669 ,.72653630727441716025] 
dist 180=[-1.0814461759198105258 ,.69723044173494520603] 
dist 181=[-1.1034790350152241758 ,.69177005754949985806] 
dist 182=[-1.1288217253673329722 ,.67911784827343921475] 
dist 183=[-1.1522082802205772212 ,.67640119743226987774] 
dist 184=[-1.1664193337663691670 ,.65005795288466131922] 
dist 185=[-1.1767255479966752598 ,.64553459718462301663] 
dist 186=[-1.1844983565205222182 ,.63712516138819422823] 
dist 187=[-1.1904976173326271997 ,.63499334657238132122] 
dist 188=[-1.1937120730801734622 ,.62786567681391932042] 
dist 189=[-1.1955228837279375452 ,.62597148687108975829] 
dist 190=[-1.1959092347993164611 ,.62409671731408689068] 
dist 191=[-.39514461090065366751,.62336504748238351672] 
dist 192=[-.40580094609119358318,.28101665107925582505] 
dist 193=[-.41469552015653947245,.2721438317160300586 ] 
dist 194=[-.4236024390028513516 ,.25147690422505561461] 
dist 195=[-.43191418286736314016,.24820382167579567234] 
dist 196=[-.43842869053484566876,.22049530974132928843] 
dist 197=[-.44492260147167219722,.21545848525468771923] 
dist 198=[-.45315209427902151834,.208590447801370776  ] 
dist 199=[-.46115756199264333355,.20655718048166754185] 
dist 200=[-.46675564151629937991,.16903534615771287864] 
dist 201=[-.47170358702801585511,.16423911894231383302] 
dist 202=[-.47710918836332724862,.15404522040725568688] 
dist 203=[-.48244460534186745222,.15156932561936077246] 
dist 204=[-.48711198003694669941,.14068654152199691909] 
dist 205=[-.49221976847879948666,.13872778307140670826] 
dist 206=[-.49931666937118305956,.13408199332937218106] 
dist 207=[-.5062921807312646426 ,.13334790470423269551] 
dist 208=[-.51091456494066937091,.08481262305292589556] 
dist 209=[-.51473313612440871252,.08030454163050503633] 
dist 210=[-.51849402731659730093,.06986292504480030669] 
dist 211=[-.52196477671573660447,.06823144568285848732] 
dist 212=[-.52462307166742333166,.05449097844309145489] 
dist 213=[-.52721620872020286536,.05202525080323140602] 
dist 214=[-.53042656617882722287,.04864860403749411438] 
dist 215=[-.53351588900102716621,.04770047675408984678] 
dist 216=[-.53562505964105072357,.03009112639349048206] 
dist 217=[-.53743714472865890733,.02787270250866487761] 
dist 218=[-.5418339816661215494 ,.02312504174236159413] 
dist 219=[-.54628162988564520658,.02205842290342588853] 
dist 220=[-.54989884440498357226,.01695055580709630857] 
dist 221=[-.55184375281696841317,.01606215618662873561] 
dist 222=[-.55294822769481684487,.01400639148222000322] 

8 phat 2 dirichlet min maxes function [2, 2, 2, 2, 0, 0, 0, 0, 2] 
dist 0=[3.5173358538358024463 ,3.5173358538358024463 ] 
dist 1=[3.3521256942496565994 ,3.7486917392030193145 ] 
dist 2=[3.2024429833056744429 ,3.9770057805510727906 ] 
dist 3=[3.0331902533350157982 ,4.1300496534402757355 ] 
dist 4=[2.8626871541453512027 ,4.2584459922018324615 ] 
dist 5=[2.7080031973456022305 ,4.3881798027177792275 ] 
dist 6=[2.5340418395935401256 ,4.5100656750914187634 ] 
dist 7=[2.2864364700548983796 ,4.6070732902383239214 ] 
dist 8=[2.0322226972140784070 ,4.7051997686330780731 ] 
dist 9=[1.8318301398528080694 ,4.8315602690550048239 ] 
dist 10=[1.6309018406780701501 ,4.9555395600788612884 ] 
dist 11=[1.3745450036379436442 ,5.0441420145860811373 ] 
dist 12=[1.0996736401965448015 ,5.1244860460495248409 ] 
dist 13=[.82469422378090508751,5.2154349103281606267 ] 
dist 14=[.49474190898427000892,5.3071084234079206066 ] 
dist 15=[0                     ,5.3903504590928804369 ] 
dist 16=[2.5046333477853242171 ,5.4840219101541877353 ] 
dist 17=[3.8491448856087284086 ,5.6174080505799444706 ] 
dist 18=[3.9183087996491964107 ,5.7491120736120387550 ] 
dist 19=[4.0755664739701328694 ,5.8360558292813880096 ] 
dist 20=[4.1001115782680310754 ,5.9075276878447899650 ] 
dist 21=[4.2957626095926788574 ,5.9773514768505582194 ] 
dist 22=[4.3297490771243754118 ,6.0414236055828818177 ] 
dist 23=[4.3791886976455060047 ,6.0898917250423103994 ] 
dist 24=[4.3919887742376831005 ,6.1365912685148316948 ] 
dist 25=[4.6002131075651790990 ,6.1935904337658669033 ] 
dist 26=[4.7186653562632274074 ,6.2480208715090395954 ] 
dist 27=[4.7831438431095823856 ,6.2844469563061656855 ] 
dist 28=[4.7981053155238630789 ,6.3149426901297642603 ] 
dist 29=[4.8460139402485242249 ,6.3456547314962688195 ] 
dist 30=[4.9605604286460421953 ,6.3744484980126126816 ] 
dist 31=[4.9771686671443896525 ,6.3972725541226512828 ] 
dist 32=[5.0683152094582487418 ,6.4202792436919377717 ] 
dist 33=[5.2348328792635712692 ,6.4498047945945431956 ] 
dist 34=[5.2629100117206313440 ,6.4778007615611636138 ] 
dist 35=[5.3214063242309898167 ,6.4946900665424608012 ] 
dist 36=[5.3339710760947488093 ,6.5068127411898285105 ] 
dist 37=[5.3886052944001095113 ,6.5157437855077907100 ] 
dist 38=[5.3981886624373133015 ,6.5223215483095523878 ] 
dist 39=[5.4139976531020395878 ,6.5250310298685370385 ] 
dist 40=[5.4171825480888992722 ,6.5258739118138079454 ] 
dist 41=[5.4189058679249584654 ,6.5254375713040209080 ] 
dist 42=[5.4128722657631633370 ,6.5082332799714022782 ] 
dist 43=[5.3468116388178484138 ,6.5047287734925574766 ] 
dist 44=[5.2493123236462531296 ,6.4980528593081473298 ] 
dist 45=[5.1198711070209509958 ,6.4958368505410936331 ] 
dist 46=[4.9785434841237117463 ,6.4855537050966271137 ] 
dist 47=[4.8335040469437373904 ,6.4829138022171272722 ] 
dist 48=[4.6567987258078232858 ,6.4748902165818909487 ] 
dist 49=[4.3888221592400206876 ,6.4728186241758096345 ] 
dist 50=[4.1198360368762510491 ,6.2963759757374634045 ] 
dist 51=[3.9390930198303147229 ,6.2794909430625463828 ] 
dist 52=[3.7869898553635275392 ,6.2404052262708823708 ] 
dist 53=[3.6325501311944063337 ,6.2322605034943278962 ] 
dist 54=[3.4869813170149497500 ,6.1781919479129216566 ] 
dist 55=[3.3703578623051743959 ,6.1676266971325680484 ] 
dist 56=[3.2516876355563867101 ,6.1489705622090931150 ] 
dist 57=[3.0979329626342711693 ,6.1443867853879445205 ] 
dist 58=[2.9466372333336181302 ,5.9553917018243610992 ] 
dist 59=[2.8378017924521555361 ,5.9333280233774942559 ] 
dist 60=[2.7383850116458144643 ,5.8981005707407850544 ] 
dist 61=[2.6247597286985010454 ,5.8891664463202819031 ] 
dist 62=[2.5096156590940486460 ,5.7345341296707983493 ] 
dist 63=[2.4041247026164978369 ,5.7071295656348297625 ] 
dist 64=[2.2846635800949775283 ,5.5702914019064211260 ] 
dist 65=[2.1136459492137764887 ,3.0500593255988080821 ] 
dist 66=[1.9432989734993902610 ,2.9556352718760926440 ] 
dist 67=[1.8265202785274915360 ,2.7355731604691362892 ] 
dist 68=[1.7257227494537858674 ,2.7033662426436383186 ] 
dist 69=[1.6192927547901596255 ,2.4105030400243081304 ] 
dist 70=[1.5163886826041271242 ,2.3581223034797373932 ] 
dist 71=[1.4296932916855072327 ,2.2929841938128135184 ] 
dist 72=[1.3375867441399077198 ,2.2800047392365055148 ] 
dist 73=[1.2130410757963097173 ,1.8852563415542399554 ] 
dist 74=[1.0880242449503410193 ,1.8368292557698033306 ] 
dist 75=[.9940334495558578944 ,1.7381338034162939096 ] 
dist 76=[.90404233366968943714,1.7130072076080128578 ] 
dist 77=[.79502239491613701288,1.6236430010624064085 ] 
dist 78=[.68107308776096261857,1.6058613442201001280 ] 
dist 79=[.57136724615536982224,1.5769317075463498912 ] 
dist 80=[.44288735742479097114,1.5701755917905078381 ] 
dist 81=[.25385192213762896788,1.2701214734379588224 ] 
dist 82=[.06560703950341596222,1.0059554941778187448 ] 
dist 83=[-.05971100373418339248,.90553170049953168021] 
dist 84=[-.1638851673172494874 ,.88912738140334307826] 
dist 85=[-.26756568623389683729,.76341431007902800635] 
dist 86=[-.36395430181775409048,.74128152006372763387] 
dist 87=[-.43896469119584644979,.70754121394417265329] 
dist 88=[-.5132624435214302977 ,.69909879553416547789] 
dist 89=[-.60680086167698513073,.56012299604029772518] 
dist 90=[-.69754197163254345277,.54277642291199007827] 
dist 91=[-.7606519681351947031 ,.50297198664169012977] 
dist 92=[-.81609006107604656131,.49712986777568108982] 
dist 93=[-.87614763243658452321,.44660465097326914227] 
dist 94=[-.93514207997545563655,.43781698470220521952] 
dist 95=[-.98632824696526302582,.4262658152440702852 ] 
dist 96=[-1.0419997923877262297 ,.42396390944544352061] 
dist 97=[-1.1189333843008752570 ,-.02828234496603592749] 
dist 98=[-1.1943909744382618739 ,-.05693155404944490842] 
dist 99=[-1.2441593134571161388 ,-.1216786313842184294 ] 
dist 100=[-1.2850182717068764633 ,-.13231033699299426262] 
dist 101=[-1.3248431076911787183 ,-.21208299063057528581] 
dist 102=[-1.3613230644692054314 ,-.22602293512136376512] 
dist 103=[-1.3888043260095785242 ,-.24776279283741335149] 
dist 104=[-1.4151694301118766277 ,-.25300765212918357969] 
dist 105=[-1.4471854427277991549 ,-.33674677568953766704] 
dist 106=[-1.4776704538351135133 ,-.347262786035532389  ] 
dist 107=[-1.4979124140362623129 ,-.3708833190573326215 ] 
dist 108=[-1.5146818372458118292 ,-.37465319101886318454] 
dist 109=[-1.5312785983455155292 ,-.40305377571054137334] 
dist 110=[-1.5466487703544079209 ,-.40791720489022257425] 
dist 111=[-1.5585125892421349361 ,-.41544353138590635235] 
dist 112=[-1.5701729375238759894 ,-.41722192738379089894] 
dist 113=[-1.5847295826134385978 ,-.44384469987574697042] 
dist 114=[-1.5984974400456000942 ,-.44752354624680273771] 
dist 115=[-1.6070031320014511281 ,-.45148150499661503808] 
dist 116=[-1.6133484027547119842 ,-.45149639864502523284] 
dist 117=[-1.6184757010086245632 ,-.44985868231495186928] 
dist 118=[-1.6224755723287301581 ,-.4458515290492287741 ] 
dist 119=[-1.6243118573520759601 ,-.43931791941811638786] 
dist 120=[-1.6250662393403008760 ,-.42757607242836678983] 
dist 121=[-1.6250151788960943903 ,-.41449182558303742596] 
dist 122=[-1.6226098872693717206 ,-.40258919262636901295] 
dist 123=[-1.6217849787194268268 ,-.38918869699533053856] 
dist 124=[-1.6193155538583827480 ,-.37011303315633718365] 
dist 125=[-1.6181799700745768411 ,-.34867718343895015909] 
dist 126=[-1.6045539865359707207 ,-.32583751063340726144] 
dist 127=[-1.6014489516613185190 ,-.29742297406101614018] 
dist 128=[-1.5840605210566899918 ,-.25369233208253498297] 
dist 129=[-.67890392866928926184,-.20974840781697808995] 
dist 130=[-.54504735450423226195,-.18048063908418859953] 
dist 131=[-.53375232385197836404,-.15614737246707398915] 
dist 132=[-.50892683907327627574,-.13193648617390997066] 
dist 133=[-.50358910573355614588,-.1094433717076913592 ] 
dist 134=[-.4743550074533627429 ,-.09197932377498440699] 
dist 135=[-.46905598317150747925,-.07472474739415031792] 
dist 136=[-.45815496075787893376,-.05306889027254959061] 
dist 137=[-.45525642896514459549,-.03210291871187099623] 
dist 138=[-.42838345167849862029,-.01760703296693146134] 
dist 139=[-.42419206397865642887,-.00496707503563142277] 
dist 140=[-.41600071017394606431,.00857710762307483157] 
dist 141=[-.41391327547220785502,.02179067397589863107] 
dist 142=[-.40665949093083557724,.03310883486046958895] 
dist 143=[-.4050043466156939276 ,.04529441467986333289] 
dist 144=[-.40278432170250875626,.06197773472491754826] 
dist 145=[-.402046079464037226  ,.07827553563516587891] 
dist 146=[-.07821180808623270303,.08891940061281139719] 
dist 147=[-.06075436324268107754,.09754109753521596529] 
dist 148=[-.02013321665700736937,.10575123234720617755] 
dist 149=[-.01421890154820456864,.1131444623972755549 ] 
dist 150=[.03942615821671157683,.11849895210632599198] 
dist 151=[.04895127700513468387,.12342695499415062963] 
dist 152=[.06086990041258248545,.12911446832717126692] 
dist 153=[.06314897295664472626,.13439481437724251983] 
dist 154=[.12754758932650781253,.15881010195875016182] 
dist 155=[.13043551487727523618,.17720710910122552817] 
dist 156=[.13106576643926783469,.19335242523178345139] 
dist 157=[.13270522588858190652,.21081016179038689323] 
dist 158=[.13276211450237986233,.2279305878324291745 ] 
dist 159=[.13226980385423503986,.24272698651675589116] 
dist 160=[.13090764996103155956,.25876476747944261578] 
dist 161=[.12935092361091819582,.2808495144168311105 ] 
dist 162=[.12808049577591565479,.30245486330760623893] 
dist 163=[.12677641293213022708,.31657552150512258434] 
dist 164=[.125083424355880264  ,.32801894995035146743] 
dist 165=[.12326406115088116299,.33891799411185777671] 
dist 166=[.12145403222925771196,.34872787697159700514] 
dist 167=[.1192962976912520639 ,.35581573285457499597] 
dist 168=[.11608641689812110563,.3623186967823411123 ] 
dist 169=[.11274577182340513256,.36978961034544325964] 
dist 170=[.11006488598943429857,.37671921747335055583] 
dist 171=[.10733894243328700607,.38105747436768136571] 
dist 172=[.10381748085465198508,.38435929694949245622] 
dist 173=[.10002775744353407402,.38714412193133799953] 
dist 174=[.09622894045294824681,.3894071416322710166 ] 
dist 175=[.09167126513847737064,.39062221411193966836] 
dist 176=[.08484721560301851121,.39131065971191605925] 
dist 177=[.07794534221106995966,.39146762757004060784] 
dist 178=[.07307631757691543946,.34946954720415035323] 
dist 179=[.06873241043499729448,.34778677926844136823] 
dist 180=[.06392973919151405667,.34362173769516821383] 
dist 181=[.05916051705796447140,.34286581022380378852] 
dist 182=[.05495007593033085234,.33617287820262496263] 
dist 183=[.05031321315018148632,.33481458883219785528] 
dist 184=[.04383858413567268365,.33303470619234638813] 
dist 185=[.03725467060115979659,.33241087486607138868] 
dist 186=[.03218062777980097984,.3187432445917778166 ] 
dist 187=[.02720494346905095076,.31685778678997283182] 
dist 188=[.02101405948425847584,.31303656590527035893] 
dist 189=[.01446083051795933248,.31198877852325451826] 
dist 190=[.00803597641325238762,.30789521533712774524] 
dist 191=[.00042677953917551906,.30701991589333629796] 
dist 192=[-.01086278548889704025,.30501187335849159174] 
dist 193=[-.02211531483099617835,.30437850586428271262] 
dist 194=[-.02957647288128450013,.26756312886020309493] 
dist 195=[-.03574270053517599450,.26414493108671123525] 
dist 196=[-.04181685421976908699,.25641684967957279062] 
dist 197=[-.04742014878080577943,.25482785484307016085] 
dist 198=[-.05170345759868274982,.24491170136661025744] 
dist 199=[-.05587170725537851350,.24305046371069258427] 
dist 200=[-.06101496982881016548,.23959791341174255883] 
dist 201=[-.06595069971493208229,.23874154859309182739] 
dist 202=[-.06928906738850822291,.22611897347985925099] 
dist 203=[-.07212113973455377795,.22437580802844408156] 
dist 204=[-.07503222866514023297,.2200703219490077988 ] 
dist 205=[-.07779779009140727166,.21942941731408981021] 
dist 206=[-.08004797463317820782,.21272765028966260143] 
dist 207=[-.08236898276647119121,.2114249406082214468 ] 
dist 208=[-.08541796340325997315,.21001064115256216953] 
dist 209=[-.08834804203229124548,.20968620241402394384] 
dist 210=[-.09019357007648036704,.10920774825426514378] 
dist 211=[-.09161220809629680049,.10296009166031777796] 
dist 212=[-.09283498501323985433,.08842393207685170102] 
dist 213=[-.09384977838413952325,.08620196938411794345] 
dist 214=[-.10179783969364723442,.06873428258801506631] 
dist 215=[-.11302226457790119482,.06608265304205840535] 
dist 216=[-.12418538625057569083,.06219651540542765811] 
dist 217=[-.13829404801798816627,.06115118007619965284] 
dist 218=[-.1519957147478037687 ,.04281815990055615533] 
dist 219=[-.16153129322643708033,.04048783141084765369] 
dist 220=[-.16990937412566548674,.03532001526425690046] 
dist 221=[-.17898229236266582493,.03431114891974389152] 
dist 222=[-.18788706875666531474,.02816749490231807598] 
dist 223=[-.19559276266973478711,.02707714196514938081] 
dist 224=[-.20395243037635565178,.02499785873315927021] 
dist 225=[-.21547240034711482259,.02449821605517171093] 
dist 226=[-.22674309665835962604,.01418016470560331862] 
dist 227=[-.23410593697270228785,.01798255296708698834] 
dist 228=[-.24006831846156060981,.02182677404970987388] 
dist 229=[-.24573868139452284002,.02543340432238369537] 
dist 230=[-.25083603787085876521,.02828589969056266401] 
dist 231=[-.25450700783660752579,.03115077480995423895] 
dist 232=[-.25786248812169491067,.0348069196736810552 ] 
dist 233=[-.26169822359639839204,.03837019949221669004] 
dist 234=[-.26522632054841610486,.04086379692739593486] 
dist 235=[-.26735157647151941008,.04306733167424181610] 
dist 236=[-.26887105480158218932,.04547091122173839262] 
dist 237=[-.2699766910998792105 ,.04783804033200148943] 
dist 238=[-.27080458169919859307,.04989584337691642748] 
dist 239=[-.27121337716626448409,.05213470792540447484] 
dist 240=[-.27139621246310280392,.05522574216844593149] 
dist 241=[-.27138610235353064062,.05824679206918712042] 
dist 242=[-.07126329596701091494,.06020584432059527106] 
dist 243=[-.07074255048007281128,.06177450721637707316] 
dist 244=[-.07060684541145375333,.06323471486394435129] 
dist 245=[-.06980628397120462204,.06452454115457837616] 
dist 246=[-.06963580251407439452,.06541197915538979641] 
dist 247=[-.06931228789844688592,.06618016466176736583] 
dist 248=[-.06922022268497190339,.06699316518883829815] 
dist 249=[-.0676314119567484827 ,.06771272089055800509] 
dist 250=[-.06469364156383148222,.06810729455680649400] 
dist 251=[-.06397479350035305710,.06834162329630202742] 
dist 252=[-.06377898314065601226,.06842051620344188533] 
dist 253=[-.06338135247540363420,.06843582961595963305] 
dist 254=[-.06006636355061040214,.06841596562517011676] 
dist 255=[-.05950361267184611702,.06836623412576615056] 

8 phat 2 dirichlet min maxes function [2, 1, 0, 0, 2, 2, 2, 0, 1] 
dist 0=[13.437089305161528928  ,13.437089305161528928  ] 
dist 1=[13.419736618136148003  ,13.451653495150967789  ] 
dist 2=[13.364921675665008272  ,13.471747470498423032  ] 
dist 3=[13.305092462923868476  ,13.481841967663665697  ] 
dist 4=[13.255675932040003314  ,13.487191611896524669  ] 
dist 5=[13.204084721603294964  ,13.488312416792959257  ] 
dist 6=[13.135552709575023338  ,13.486542246231862290  ] 
dist 7=[13.060773517206725669  ,13.484086545267230493  ] 
dist 8=[12.984196886719434922  ,13.381288629148552518  ] 
dist 9=[12.891069898954028472  ,13.364466661208739905  ] 
dist 10=[12.750103250687270715  ,13.333681145506540891  ] 
dist 11=[12.601883279462942124  ,13.324811542814127982  ] 
dist 12=[12.479748376593852726  ,13.289704091194639680  ] 
dist 13=[12.352430740743579362  ,13.280029478207089597  ] 
dist 14=[12.183481969467644624  ,13.258637851715232655  ] 
dist 15=[11.999154677289121767  ,13.250869003021621392  ] 
dist 16=[11.810335661367291092  ,12.737458187653213768  ] 
dist 17=[11.580627320844320377  ,12.710481799840013241  ] 
dist 18=[11.232778646175372948  ,12.700906418213003360  ] 
dist 19=[10.882849161539350154  ,12.395133985396005695  ] 
dist 20=[10.644818409092920031  ,12.319181704910746175  ] 
dist 21=[10.441438690710664686  ,12.256527232387768270  ] 
dist 22=[10.230079908452146378  ,12.227841789214880543  ] 
dist 23=[10.027877905019177011  ,12.201910338318141279  ] 
dist 24=[9.8611150732409652819 ,12.170966400981278592  ] 
dist 25=[9.6871204118771934252 ,12.158163135243328328  ] 
dist 26=[9.4559938953372908392 ,12.071257800500230150  ] 
dist 27=[9.2259814862488088917 ,11.113628546502413088  ] 
dist 28=[9.0564403169302056376 ,11.018552948907420509  ] 
dist 29=[8.8974586147087556504 ,10.892820524509037559  ] 
dist 30=[8.7096724752867418422 ,10.637175616439734314  ] 
dist 31=[8.5159985541296202066 ,10.516384396751181235  ] 
dist 32=[8.1104462718696582989 ,9.3761710605135938419 ] 
dist 33=[7.7028963664595205002 ,9.2754248725316143292 ] 
dist 34=[7.3581483034269318334 ,9.0515381356782189741 ] 
dist 35=[7.0054786309598584067 ,9.0041869772689586783 ] 
dist 36=[6.6716170092540277304 ,8.7307838033416051161 ] 
dist 37=[6.4020793234867138677 ,8.6803870873530742340 ] 
dist 38=[6.1260548439200943432 ,8.5812336664214380505 ] 
dist 39=[5.7662481901376217663 ,8.5555571141500350265 ] 
dist 40=[5.4114302761219494698 ,8.2596374459541507306 ] 
dist 41=[5.1553532387401440508 ,8.2162611621230312037 ] 
dist 42=[4.9206916393177819178 ,8.1196566849056781264 ] 
dist 43=[4.6515108297195529433 ,8.0969426506879560976 ] 
dist 44=[4.3783005446415019293 ,7.9751434936371460118 ] 
dist 45=[4.1275205498958909186 ,7.9516748360658429103 ] 
dist 46=[3.8432342260802855438 ,7.9033547046011253443 ] 
dist 47=[3.4360218036708348743 ,7.8897704066578688645 ] 
dist 48=[3.0305980048178722120 ,6.5931981055224995565 ] 
dist 49=[2.7534620007405712719 ,6.5632283158806282685 ] 
dist 50=[2.5151773294925111793 ,6.5557530733639821241 ] 
dist 51=[2.1977903286491166216 ,5.1314310540998994499 ] 
dist 52=[1.8523774688249881708 ,5.0453738844392387524 ] 
dist 53=[1.5799217216212490716 ,4.8622006120860450418 ] 
dist 54=[1.3067110174747760501 ,4.8221692890360834787 ] 
dist 55=[.95827798874274455638,4.6316999269962156130 ] 
dist 56=[.6182845029426856368 ,4.5989484645955644464 ] 
dist 57=[.37882352592323857266,4.5271608616264790132 ] 
dist 58=[.16539392084131345545,4.5022123812388951010 ] 
dist 59=[-.07049902386873273121,3.8698955353095150176 ] 
dist 60=[-.30490537118251210186,3.8060420945071884830 ] 
dist 61=[-.51239134181531952473,3.7064146412548689403 ] 
dist 62=[-.74146266468287314514,3.5799801526275152797 ] 
dist 63=[-1.0621937237184643301 ,3.2780695432493800766 ] 
dist 64=[-1.3783674373108614853 ,1.2412386791216377881 ] 
dist 65=[-1.5892144478064515723 ,1.1991579374253949191 ] 
dist 66=[-1.7648294111046107858 ,1.1888706190423209038 ] 
dist 67=[-1.9401068131474834135 ,.7503770295206878062 ] 
dist 68=[-2.1054251362907801820 ,.4995830258020567905 ] 
dist 69=[-2.2475885765406422537 ,.4558976328350864830 ] 
dist 70=[-2.3816001902438667674 ,.3860959424415756286 ] 
dist 71=[-2.5410148795070525809 ,.3697918416451227152 ] 
dist 72=[-2.6912304652525031567 ,.1165558302432629715 ] 
dist 73=[-2.7884523331651292501 ,.0843436522386028644 ] 
dist 74=[-2.8753135979230905020 ,.0156494540786520546 ] 
dist 75=[-2.9788302317399102249 ,.0021037662895242518 ] 
dist 76=[-3.0807475976617860432 ,-.0682426029618582055 ] 
dist 77=[-3.1695621531443923895 ,-.0797812164788426109 ] 
dist 78=[-3.2665036274688947548 ,-.1038225938925223223 ] 
dist 79=[-3.4009325892134012464 ,-.1078559729257764158 ] 
dist 80=[-3.5319181510483375735 ,-.4929180846023578841 ] 
dist 81=[-3.6150896600732044423 ,-.5089204236869923359 ] 
dist 82=[-3.6798222181593338718 ,-.5117467684274771009 ] 
dist 83=[-3.7370589384980648088 ,-1.0574031098535427898 ] 
dist 84=[-3.7856554636748420981 ,-1.0918487811609595488 ] 
dist 85=[-3.8158323358769912789 ,-1.1664866721616941531 ] 
dist 86=[-3.8385530422636337207 ,-1.1807619278209723553 ] 
dist 87=[-3.8573332007790065399 ,-1.2620775965920768232 ] 
dist 88=[-3.8726828302646594662 ,-1.2756739252737820989 ] 
dist 89=[-3.8816822326872265226 ,-1.3032307383291085088 ] 
dist 90=[-3.8878502741594881083 ,-1.3094081903845295120 ] 
dist 91=[-3.8918685974547196166 ,-1.3526299890183534376 ] 
dist 92=[-3.8942558191764221359 ,-1.3598742349786475573 ] 
dist 93=[-3.8938967847996345966 ,-1.3623972795531083662 ] 
dist 94=[-3.8915056415191202412 ,-1.3564014363537817346 ] 
dist 95=[-3.8898348441317696210 ,-1.3457881311464542204 ] 
dist 96=[-3.5779980873949165255 ,-1.3291480450791642367 ] 
dist 97=[-3.5491622672347360925 ,-1.3047853421225966670 ] 
dist 98=[-3.4875464800895528587 ,-1.1627829005856627679 ] 
dist 99=[-3.4701077647152614936 ,-1.0102400335676712672 ] 
dist 100=[-3.3981985292292160110 ,-.86603596264051173946] 
dist 101=[-3.3840740443960656911 ,-.75010768544083231962] 
dist 102=[-3.3476394946842952824 ,-.63190279135913081456] 
dist 103=[-3.3412921196685613862 ,-.47859339856465565453] 
dist 104=[-3.2657710548732258584 ,-.32791543890309227436] 
dist 105=[-3.2521638057941710030 ,-.22023079491304588843] 
dist 106=[-3.2245857373883605643 ,-.1226896622995427689 ] 
dist 107=[-3.2166497952073227314 ,-.0125681916332708053 ] 
dist 108=[-3.1838935812243165242 ,.0981346179411333905 ] 
dist 109=[-3.1766965302157292684 ,.1980019985518371614 ] 
dist 110=[-3.1579336132218155043 ,.3097613670331687090 ] 
dist 111=[-3.1531680419468508496 ,.4680172384077550155 ] 
dist 112=[-2.4044623658105041537 ,.6245974573835908049 ] 
dist 113=[-2.3829865982336717445 ,.7296574949931781383 ] 
dist 114=[-2.3202512230103463320 ,.8178149767089426139 ] 
dist 115=[-1.1124676349372584679 ,.9068096757508725386 ] 
dist 116=[-.81236557679734533064,.9902779135273448054 ] 
dist 117=[-.75844968890315752467,1.0563383830689070567 ] 
dist 118=[-.6937581982474382652 ,1.1227661780060162843 ] 
dist 119=[-.68246137715802253445,1.2077054566992401419 ] 
dist 120=[-.26293134553298598177,1.2906556166647904250 ] 
dist 121=[-.21186159319002913678,1.3491307392283609834 ] 
dist 122=[-.10877136534240098252,1.4012901875410852850 ] 
dist 123=[-.08283133358080137004,1.4589872919965493188 ] 
dist 124=[.00722861221088038181,1.5163384042884227642 ] 
dist 125=[.02561991956115058239,1.5671163249194981707 ] 
dist 126=[.04973861153558485490,1.6231841434068282066 ] 
dist 127=[.05508637899620253720,1.7016925047181758509 ] 
dist 128=[.6208892119534167716 ,1.7784873012288839393 ] 
dist 129=[.66720971896569974828,1.8277033428128997691 ] 
dist 130=[.77279534096325750997,1.8665012005801537345 ] 
dist 131=[.78893831235743263527,1.9016330358566579783 ] 
dist 132=[.9204673848622570918 ,1.9320321347677757359 ] 
dist 133=[.94317126450784698479,1.9519039767365586078 ] 
dist 134=[.97552686641973677207,1.9680204374344152011 ] 
dist 135=[.98369689803360664221,1.9834030046878706784 ] 
dist 136=[1.1207503489465541133 ,1.9966991619060754754 ] 
dist 137=[1.1372550834718400443 ,2.0044718201117203003 ] 
dist 138=[1.1731200661537472138 ,2.0097498165989910745 ] 
dist 139=[1.1788524111030695498 ,2.0421236459232116106 ] 
dist 140=[1.2166510179005078933 ,2.0743284573066284377 ] 
dist 141=[1.2224690368776858615 ,2.0990849026195960735 ] 
dist 142=[1.2331531428630068563 ,2.1233115118476994658 ] 
dist 143=[1.2157662363128878119 ,2.1533997211445018729 ] 
dist 144=[1.1811132663335252498 ,2.1816088492768975459 ] 
dist 145=[1.1539667478472584554 ,2.1983214747931880568 ] 
dist 146=[1.1269417967296252156 ,2.2099383948776239178 ] 
dist 147=[1.0927727265336145736 ,2.2177689681075614265 ] 
dist 148=[1.0563426701588125826 ,2.2233014412239524918 ] 
dist 149=[1.0202760335443653423 ,2.2257274246444482072 ] 
dist 150=[.97731616511079541394,2.2263621315111245924 ] 
dist 151=[.91332231877833938348,2.2259775007986743803 ] 
dist 152=[.84650062936253530723,2.1971195301767043336 ] 
dist 153=[.79223288147343705523,2.1920779566977772146 ] 
dist 154=[.73639229647773978764,2.1832699194090440033 ] 
dist 155=[.66328057963000574035,2.1806865934314228317 ] 
dist 156=[.58403351975465953089,2.1706102326860977436 ] 
dist 157=[.50365968057964451781,2.1675377563957674160 ] 
dist 158=[.40649322901215423916,2.1611525850738949431 ] 
dist 159=[.2600987020183628604 ,2.1588202671788239147 ] 
dist 160=[.11339053156104979864,1.9309061675618594929 ] 
dist 161=[.01496975563000918639,1.9099595291328425561 ] 
dist 162=[-.06759809098718131699,1.8640463308656296910 ] 
dist 163=[-.15091677887257645125,1.8525787970596759534 ] 
dist 164=[-.22903482107903076454,1.7970005552022058905 ] 
dist 165=[-.29080745795629245603,1.7863260273315400568 ] 
dist 166=[-.35286794233822261633,1.7625885081524744767 ] 
dist 167=[-.43213721056148177978,1.7559957825934668407 ] 
dist 168=[-.50948848873435247294,1.6942284242535527776 ] 
dist 169=[-.56387977485593799291,1.6842226673644357163 ] 
dist 170=[-.61224304937566159423,1.6620642861044080105 ] 
dist 171=[-.66549071271068652621,1.6558159794412895224 ] 
dist 172=[-.71825399058624888036,1.6270664081452106824 ] 
dist 173=[-.76468054494829649705,1.6211601857657824565 ] 
dist 174=[-.81568606174174787137,1.6077945454898106165 ] 
dist 175=[-.89529750795020839934,1.6035776612743321086 ] 
dist 176=[-.97738328240507270647,.87208099996682274542] 
dist 177=[-1.0310811455887764900 ,.84547791509924429167] 
dist 178=[-1.0746340611103414779 ,.78343204435741480287] 
dist 179=[-1.1161536584581561938 ,.77356723146332622823] 
dist 180=[-1.1535320237988679218 ,.69003491814682631634] 
dist 181=[-1.1805255199375610913 ,.67480807617387462714] 
dist 182=[-1.2052678040252530152 ,.6540347248790619599 ] 
dist 183=[-1.2336441989677109287 ,.64786643524691986014] 
dist 184=[-1.2598846543512956828 ,.53348072237148868171] 
dist 185=[-1.2760860949190147651 ,.518824248087955284  ] 
dist 186=[-1.2881454987058619457 ,.48768296193693964368] 
dist 187=[-1.2978236546470451200 ,.48004258715453670946] 
dist 188=[-1.3054206856671964450 ,.44675410442721712122] 
dist 189=[-1.3091583531282597067 ,.44073327837826285853] 
dist 190=[-1.3110060387906666899 ,.42640040693677650593] 
dist 191=[-1.3111860801976027516 ,.42412307665922771288] 
dist 192=[-1.1639618970345450384 ,.2723573722152590438 ] 
dist 193=[-1.2196429248905627298 ,.25826504724567763891] 
dist 194=[-1.2647881348690981299 ,.22552580202837569467] 
dist 195=[-1.3078051685464982243 ,.22046093614368038418] 
dist 196=[-1.3465232275588076677 ,.1770644468403838818 ] 
dist 197=[-1.3744777911075435688 ,.16926060084250671061] 
dist 198=[-1.4000975034532184138 ,.15877982205609813314] 
dist 199=[-1.4294789189582319727 ,.15596165625265477974] 
dist 200=[-1.4566491522585916050 ,.09912379499174283337] 
dist 201=[-1.4734268831439757932 ,.09198739252650657306] 
dist 202=[-1.4859196520939145904 ,.07686270510305557602] 
dist 203=[-1.4959555018455923594 ,.07331107769510783137] 
dist 204=[-1.5038413066462237062 ,.05754964436656557093] 
dist 205=[-1.5077365361645855465 ,.05474107823920891411] 
dist 206=[-1.5096720599398071267 ,.04843834190133247338] 

8 phat 2 dirichlet min maxes function [2, 0, 1, 2, 2, 1, 2, 0, 1] 
dist 0=[12.453415427222971161  ,12.453415427222971161  ] 
dist 1=[12.430999354785745527  ,12.479717887809472370  ] 
dist 2=[12.367663473437212683  ,12.518258472352396197  ] 
dist 3=[12.291591025732635710  ,12.558042157730843774  ] 
dist 4=[12.209090169417097843  ,12.593052822969820866  ] 
dist 5=[12.105455273388933998  ,12.612506755890286616  ] 
dist 6=[11.944864952464454780  ,12.624415324410882284  ] 
dist 7=[11.781890788102297265  ,12.629258145319804906  ] 
dist 8=[11.668721447069442984  ,12.630664233759909902  ] 
dist 9=[11.569539258769165459  ,12.629137018707044227  ] 
dist 10=[11.462498203959317725  ,12.625053674528870607  ] 
dist 11=[11.357634000920348564  ,12.622215611926576225  ] 
dist 12=[11.267155008939497643  ,12.549517902259802161  ] 
dist 13=[11.169198371074094470  ,12.536511959941797729  ] 
dist 14=[11.034426480355460786  ,12.491318264632208565  ] 
dist 15=[10.898140269949170610  ,12.417617467848501847  ] 
dist 16=[10.794125676393345260  ,12.265789408052375517  ] 
dist 17=[10.693042386597070788  ,12.251229695764150230  ] 
dist 18=[10.568476472733564341  ,12.216597841902090968  ] 
dist 19=[10.437173873627457453  ,12.205885269923566315  ] 
dist 20=[10.309146063662262761  ,12.092998958266233981  ] 
dist 21=[10.157987997716414089  ,12.074903234544444832  ] 
dist 22=[9.9341759530837048659 ,12.026391504104649436  ] 
dist 23=[9.7081499102830180828 ,12.018701126491436872  ] 
dist 24=[9.5481359376679136292 ,11.928253020464514054  ] 
dist 25=[9.4046106573305894853 ,11.909217582913675909  ] 
dist 26=[9.2445280671906290849 ,11.890242723460334874  ] 
dist 27=[9.0845423414765186936 ,11.884416687426533477  ] 
dist 28=[8.9414025757054134896 ,11.660697832569173127  ] 
dist 29=[8.7820549980803351991 ,11.629761371447888742  ] 
dist 30=[8.5572435261465070254 ,11.538638914546005913  ] 
dist 31=[8.3273157382839408523 ,11.414950453251345454  ] 
dist 32=[8.1475039293769082389 ,9.1380667805333674553 ] 
dist 33=[7.9129963070197177098 ,9.0631898759574373381 ] 
dist 34=[7.6306768399933039373 ,8.9787985536748063082 ] 
dist 35=[7.3396004806761845602 ,8.9641070871562036941 ] 
dist 36=[7.0626244629359952784 ,8.8800031653257835700 ] 
dist 37=[6.8366885096846792320 ,8.8566419174986511726 ] 
dist 38=[6.5415726219670216458 ,8.8499816476511609177 ] 
dist 39=[6.1107774814998213007 ,8.0304197245840919968 ] 
dist 40=[5.8209611696149213091 ,7.8953745170773820974 ] 
dist 41=[5.5766734886857277818 ,7.8645196933244402659 ] 
dist 42=[5.3279761077138490641 ,7.8318443693259524279 ] 
dist 43=[5.0931339327167845231 ,7.8254245819770105626 ] 
dist 44=[4.9042628119768910305 ,6.5126846246673906849 ] 
dist 45=[4.7114073602519614030 ,6.4025595337841042784 ] 
dist 46=[4.4606318374936362111 ,6.1604998371118647062 ] 
dist 47=[4.2134342319338666103 ,6.1094936107345652101 ] 
dist 48=[3.8448331874267822989 ,5.8253094313659445720 ] 
dist 49=[3.5868122457092654317 ,5.7741201466858859386 ] 
dist 50=[3.3627833689684562891 ,5.7052586270223960198 ] 
dist 51=[3.1242223763683916602 ,5.6902981233155476682 ] 
dist 52=[2.8923873693485698222 ,5.5088556684836584421 ] 
dist 53=[2.6952527665243833579 ,5.4799179128904776978 ] 
dist 54=[2.4842557252201902867 ,5.3359006653912654740 ] 
dist 55=[2.1969727946756559942 ,5.2486735597599702387 ] 
dist 56=[1.9077289762149492884 ,5.1821922664342668377 ] 
dist 57=[1.6888854292409710646 ,5.1668856059650703553 ] 
dist 58=[1.4780068921785063451 ,5.1492333927327210497 ] 
dist 59=[1.2206124469740033514 ,5.1440655554200929549 ] 
dist 60=[.95053565841083011147,2.7078362839940798406 ] 
dist 61=[.68892868423762927577,2.6536966694431515597 ] 
dist 62=[.38131435536671311983,2.3803185719026733219 ] 
dist 63=[-.07277835828144636558,1.9918931971762831121 ] 
dist 64=[-.52419541555487657098,1.9592923711779326579 ] 
dist 65=[-.82111051714934184066,1.8831862405640199700 ] 
dist 66=[-1.0640082820421031321 ,1.8719406765202695756 ] 
dist 67=[-1.2993796609259599324 ,1.7700358574300661135 ] 
dist 68=[-1.5141265631709365415 ,1.7517154221641383571 ] 
dist 69=[-1.6745374528350284408 ,1.7288147081915209508 ] 
dist 70=[-1.8271473977276861241 ,1.7239693724532569786 ] 
dist 71=[-2.0106999055039848520 ,.65588577632554925098] 
dist 72=[-2.1846862473128789078 ,.58842798290416200391] 
dist 73=[-2.2990382735606745784 ,.43520822018732543465] 
dist 74=[-2.3925264666050268980 ,.40998027921187493072] 
dist 75=[-2.4830682956815876593 ,.21837507183122517786] 
dist 76=[-2.5657045482849531258 ,.18462192102045306585] 
dist 77=[-2.6275794850666071608 ,.13257521989771050761] 
dist 78=[-2.6866467635453227928 ,.11971024034810444968] 
dist 79=[-2.7580686605713841480 ,-.09110646451010331988] 
dist 80=[-2.8255758545403973835 ,-.11748676322256296   ] 
dist 81=[-2.8689859037671372974 ,-.17826566058809889398] 
dist 82=[-2.9034674162058839643 ,-.18702818487904080828] 
dist 83=[-2.9352489303132623299 ,-.26494720009024203671] 
dist 84=[-2.9632314621069055052 ,-.27853608771743689483] 
dist 85=[-2.9825127245822818750 ,-.29581282653788366363] 
dist 86=[-2.9993039812092041826 ,-.29883831569090075672] 
dist 87=[-3.0173250994177105586 ,-.39147384912926947693] 
dist 88=[-3.0333655265377965615 ,-.40317218309181920292] 
dist 89=[-3.0422319227873874888 ,-.4206483957506052444 ] 
dist 90=[-3.0476357753570658098 ,-.4250123775502754096 ] 
dist 91=[-3.0498211491485598735 ,-.42672743699229628747] 
dist 92=[-3.0498111470012849467 ,-.42100056371636288601] 
dist 93=[-3.0488207552316984929 ,-.40927403623731105777] 
dist 94=[-3.0425193534607048501 ,-.38620057231803255881] 
dist 95=[-3.0403754895214843398 ,-.35980551993308708689] 
dist 96=[-3.0474902537948445729 ,-.33479558702804168186] 
dist 97=[-3.0566750895808363316 ,-.30583528306876063432] 
dist 98=[-3.0614094933620950089 ,-.2636415699236374937 ] 
dist 99=[-3.0640264513022665458 ,-.21579749973105951473] 
dist 100=[-3.0647436202620241667 ,-.16424164740199480718] 
dist 101=[-3.0642127107074824268 ,-.09971449049034265970] 
dist 102=[-3.0631561731238743426 ,0                     ] 
dist 103=[-2.2248200164856009431 ,-.70059656476943601582] 
dist 104=[-2.2169722600391678110 ,-.5689256227940152838 ] 
dist 105=[-2.2142149569727919418 ,-.47426474809724400926] 
dist 106=[-2.2093357642512386670 ,-.38795425472711990417] 
dist 107=[-2.2076155025703695220 ,-.28966877057173574617] 
dist 108=[-1.9807310268132950877 ,-.1903916108622666698 ] 
dist 109=[-1.9601953044951591380 ,-.1001138531181923915 ] 
dist 110=[-1.9154507299375050751 ,.00149212161786119985] 
dist 111=[-1.9040677995075087439 ,.14606775935929566644] 
dist 112=[-1.8508027531516760614 ,.28939382306818797796] 
dist 113=[-1.8406016491219757932 ,.38600441684697971605] 
dist 114=[-1.8172762089205158926 ,.46755264330604919352] 
dist 115=[-1.8114449433568696646 ,.5506523527225520428 ] 
dist 116=[-1.7550811768699727456 ,.6290844210212872022 ] 
dist 117=[-1.7457271313847209926 ,.69197016415644776316] 
dist 118=[-1.7259163175028073186 ,.7559557466216551492 ] 
dist 119=[-1.7202142419581227369 ,.83878824884709773396] 
dist 120=[-1.6962964868696902926 ,.92016783617818196408] 
dist 121=[-1.6914941124104270765 ,.9783450800104318037 ] 
dist 122=[-1.6783459012877963881 ,1.0310803396481020656 ] 
dist 123=[-1.6762567778738235981 ,1.0907008519148003414 ] 
dist 124=[-.75489844350609392412,1.1507131371750701449 ] 
dist 125=[-.7028530963173731844 ,1.2050172480635944574 ] 
dist 126=[-.58097224272095252389,1.2659474543259520861 ] 
dist 127=[-.56323782206080622213,1.3524605162818262902 ] 
dist 128=[-.39932127982460582715,1.4375061688120379307 ] 
dist 129=[-.36992275209980616831,1.4925689791708316873 ] 
dist 130=[-.33383884718155898889,1.5366146720821917844 ] 
dist 131=[-.32693325805977115628,1.5776021710627450453 ] 
dist 132=[-.1022232543979836642 ,1.6138516300216685067 ] 
dist 133=[-.07477902293881067947,1.6389500592653797258 ] 
dist 134=[-.01884772841761240141,1.6608759638768142481 ] 
dist 135=[-.00465042453020717472,1.6844396767811371709 ] 
dist 136=[.04555272396287284154,1.7056825025842431360 ] 
dist 137=[.05555364976773270529,1.7183269357814498147 ] 
dist 138=[.07090703352012340527,1.7271916159571560546 ] 
dist 139=[.07470353159437005462,1.7333173016559260524 ] 
dist 140=[.3621291715354141564 ,1.7374843104258597991 ] 
dist 141=[.3860724395280455548 ,1.7385158135808732464 ] 
dist 142=[.44116586676585008468,1.7382908101722948070 ] 
dist 143=[.44912390952507885797,1.7374313469359852301 ] 
dist 144=[.51926472201605641623,1.6633494576362135447 ] 
dist 145=[.53141193709680854139,1.6551952921571756266 ] 
dist 146=[.54712505588969576917,1.6375643124287004909 ] 
dist 147=[.5499165140689903176 ,1.6322658130645341655 ] 
dist 148=[.63010040242492906852,1.6091225337971262431 ] 
dist 149=[.63945274767360216754,1.6042663977279523447 ] 
dist 150=[.65932216423501707803,1.5916145866877340978 ] 
dist 151=[.66296212354731792829,1.5887285548705216796 ] 
dist 152=[.68245809266569676048,1.5543956234468640690 ] 
dist 153=[.6855787178200636828 ,1.5485435625172490864 ] 
dist 154=[.69115749421727753389,1.5340139842810783637 ] 
dist 155=[.64974400771513726371,1.5305789958750446822 ] 
dist 156=[.57529089777902947217,1.5060259496101247185 ] 
dist 157=[.49958457289838074875,1.5007211332701743606 ] 
dist 158=[.40792327268875451076,1.4920948624939093978 ] 
dist 159=[.2696726701436468121 ,1.4895669214757609612 ] 
dist 160=[.13108761234179369714,1.2700437534632599618 ] 
dist 161=[.03808875961689836455,1.2687855027132553410 ] 
dist 162=[-.03995714114190681097,1.2678774476794196594 ] 
dist 163=[-.11875199500716192451,1.2672023157673059411 ] 
dist 164=[-.19265011795082320353,1.2334490381287324331 ] 
dist 165=[-.25111625435724817971,1.2285111928173201044 ] 
dist 166=[-.30988093710200811298,1.2197399607681152207 ] 
dist 167=[-.3849730718201921592 ,1.2174501002245305958 ] 
dist 168=[-.45825959272527790996,1.2096671435505829324 ] 
dist 169=[-.50980450351110285154,1.2073152122785654139 ] 
dist 170=[-.55564743937723735412,1.2045549115298832163 ] 
dist 171=[-.60613426602045033807,1.2032392601946732762 ] 
dist 172=[-.65616795624641625744,1.0422474889827004040 ] 
dist 173=[-.70352173056826252854,1.0280869476972850222 ] 
dist 174=[-.75836441984866048156,.99730190575600662849] 
dist 175=[-.83429928509629356294,.98971712945108837075] 
dist 176=[-.90869509974279128034,.95366093471485555571] 
dist 177=[-.95738370565807473764,.94687664307799924732] 
dist 178=[-.9968960185611624723 ,.93147273966470013273] 
dist 179=[-1.0345993029364263960 ,.92776128110725485638] 
dist 180=[-1.0685646452409957779 ,.8925596272005625242 ] 
dist 181=[-1.0931302971788939838 ,.88667806027896394732] 
dist 182=[-1.1156839459925570749 ,.87488385590589078386] 
dist 183=[-1.1416039234218082598 ,.87166751815321615322] 
dist 184=[-1.1655355638501088947 ,.85924880147200138472] 
dist 185=[-1.1801386399924860039 ,.85652583450207365224] 
dist 186=[-1.1908025813215235046 ,.85053429858008250582] 
dist 187=[-1.1989833428902685080 ,.84864474517260584042] 
dist 188=[-1.2053267583401671561 ,.41612485470099275272] 
dist 189=[-1.2086438224012753738 ,.40300616927918798196] 
dist 190=[-1.2104005157684399755 ,.37244703231173150999] 
dist 191=[-1.2105417852189032752 ,.3675935484666628523 ] 
dist 192=[-.45467355609500876848,.32659874725204704225] 
dist 193=[-.46475431754366823131,.31914114603846710951] 
dist 194=[-.47330516145980201677,.30894268636194862443] 
dist 195=[-.48209102160502648996,.30593031477459830315] 
dist 196=[-.49043313240136574514,.25032244005794707255] 
dist 197=[-.4972094440706710645 ,.24320840486033887182] 
dist 198=[-.50418675059641822867,.22806864165523803279] 
dist 199=[-.51333270770763050579,.22440035572346519877] 
dist 200=[-.52237619900978569723,.2081549537716404418 ] 
dist 201=[-.52894376938259066105,.20523903819029455268] 
dist 202=[-.53500358278111369587,.19826321654046071048] 
dist 203=[-.54201656001145437011,.19720529662631647198] 
dist 204=[-.5861238813060344276 ,.12520776863628402494] 
dist 205=[-.61512504244129479019,.11850225883987144746] 
dist 206=[-.63868315997134682596,.10298479585160267945] 
dist 207=[-.66120632467985346144,.10054321977486920534] 
dist 208=[-.68153035473998750022,.08015953102617571514] 
dist 209=[-.69629457055196448377,.07650114527016706203] 
dist 210=[-.70991760730637665814,.07143757767141870298] 
dist 211=[-.72567824822436857245,.06998753320371625315] 
dist 212=[-.74029565838578214467,.04403384353396119311] 
dist 213=[-.74934714973973243552,.04075598559669289870] 
dist 214=[-.75611701439547255809,.03370085156996527474] 
dist 215=[-.76161071547886399598,.03215145405780853160] 
dist 216=[-.76597991280767424692,.02443491427929489416] 
dist 217=[-.76825313048883860918,.02308907365837606306] 
dist 218=[-.76944130219697045237,.02007376895907498248] 

8 phat 2 dirichlet min maxes function [2, 2, 1, 0, 0, 1] 
dist 0=[12.524969830301971429  ,12.524969830301971429  ] 
dist 1=[12.447864324423507748  ,12.596046758312747540  ] 
dist 2=[12.378398840478246637  ,12.641404319126689514  ] 
dist 3=[12.300726465074835744  ,12.676914972197152049  ] 
dist 4=[12.190797313926176258  ,12.708619477219708456  ] 
dist 5=[12.067552045671339770  ,12.735713855443671892  ] 
dist 6=[11.936626444768472285  ,12.752791741272223265  ] 
dist 7=[11.774015587481804824  ,12.765924843683472302  ] 
dist 8=[11.524059046168822621  ,12.777248047486309859  ] 
dist 9=[11.271226118447757227  ,12.786300576573570880  ] 
dist 10=[11.097111038230206019  ,12.790352740711925770  ] 
dist 11=[10.946058668086848434  ,12.791546465130573731  ] 
dist 12=[10.785450793327108208  ,12.790464719681040026  ] 
dist 13=[10.629562926210136591  ,12.784620690508045872  ] 
dist 14=[10.497383297009917676  ,12.782109911807645447  ] 
dist 15=[10.356264541902679426  ,12.770338995327573690  ] 
dist 16=[10.164624136490725140  ,12.747053382268920333  ] 
dist 17=[9.9719801524065474823 ,12.727373272881273123  ] 
dist 18=[9.8268455713700864772 ,12.718178123874611225  ] 
dist 19=[9.6876318270399341721 ,12.702053799631231056  ] 
dist 20=[9.5186627058108786228 ,12.697169173948307029  ] 
dist 21=[9.3419251504017386454 ,12.677035397891872813  ] 
dist 22=[9.1716405005766099799 ,12.671044416024474667  ] 
dist 23=[8.9721438672046596902 ,12.656900991311200888  ] 
dist 24=[8.6785753531183272827 ,12.651392954887787437  ] 
dist 25=[8.3829036367379493194 ,12.622605568508941717  ] 
dist 26=[8.1749939303353775351 ,12.615022164456339705  ] 
dist 27=[7.9899852828948192055 ,12.599163468081004514  ] 
dist 28=[7.7859000431343290206 ,12.593583822963999140  ] 
dist 29=[7.5832670813727688492 ,12.500172309896501248  ] 
dist 30=[7.4040639623060482939 ,12.486959779164256713  ] 
dist 31=[7.2062987052409616122 ,12.407053574751786605  ] 
dist 32=[6.9294242252235097568 ,12.273098189042832094  ] 
dist 33=[6.6472119478905584297 ,10.611121129655156495  ] 
dist 34=[6.4280964155924102761 ,10.499045711481396599  ] 
dist 35=[6.2115342008867908194 ,10.245507487754442629  ] 
dist 36=[5.9395309092503818105 ,10.197934124701783038  ] 
dist 37=[5.6500848402442912665 ,9.8774370734004405206 ] 
dist 38=[5.3637578765870429418 ,9.8189628009876477751 ] 
dist 39=[5.0225810649078981584 ,9.7160651643772836373 ] 
dist 40=[4.5137589652883081712 ,9.6928556803127141520 ] 
dist 41=[4.0054542918192574265 ,9.3120674396403731471 ] 
dist 42=[3.6663461530160713943 ,9.2613587259463458936 ] 
dist 43=[3.3836349834592060836 ,9.1396440089761902520 ] 
dist 44=[3.1008917373400251125 ,9.1214425662009510472 ] 
dist 45=[2.8371177959839170128 ,8.9449937659135764727 ] 
dist 46=[2.6302744248170074903 ,8.9118215533246831517 ] 
dist 47=[2.4238949005055769701 ,8.8730516791990729392 ] 
dist 48=[2.1619745598377094992 ,8.8640399691393389489 ] 
dist 49=[1.9068164144419574039 ,8.5688087135182588933 ] 
dist 50=[1.7274818361561917431 ,8.5311095567881593832 ] 
dist 51=[1.5679508241192775969 ,8.4556550872277494985 ] 
dist 52=[1.3919972382718503567 ,8.4360576865042251675 ] 
dist 53=[1.2172651349447640504 ,8.2386279770406773222 ] 
dist 54=[1.0626180334462321491 ,8.2077037716744116449 ] 
dist 55=[.89182171817155712808,8.0786049186711083023 ] 
dist 56=[.65249641968782053549,7.8781358041146364227 ] 
dist 57=[.41620880253639682794,6.0243129158128111124 ] 
dist 58=[.25756122550483381523,5.9048236761261143847 ] 
dist 59=[.12416597242161068744,5.6758915384489796255 ] 
dist 60=[-.01112196211457203154,5.6206843132092887347 ] 
dist 61=[-.13856796416453667337,5.0301694740596662195 ] 
dist 62=[-.24059938891611198246,4.9440793412330370529 ] 
dist 63=[-.34437684607108636862,4.5783778274502231972 ] 
dist 64=[-.47880905863560551588,4.0257780284351927712 ] 
dist 65=[-.61113756603742488244,.63065220172488368024] 
dist 66=[-.70650212919654108645,.56268463424612198068] 
dist 67=[-.79381917571625038715,.42478795345846324156] 
dist 68=[-.89396130551349897077,.39005075735624140121] 
dist 69=[-.99568235802657306306,.26875103576754694449] 
dist 70=[-1.0893169232635717253 ,.24444668729190686966] 
dist 71=[-1.1957449086983363353 ,.21045819381513637286] 
dist 72=[-1.3486414173213704585 ,.20173068213766391012] 
dist 73=[-1.4996905641908341494 ,-.05457253193257172916] 
dist 74=[-1.5987299231386365410 ,-.06072874837400857671] 
dist 75=[-1.6794378789018334395 ,-.06999137546316962837] 
dist 76=[-1.7571620974824709981 ,-.07217633567982103280] 
dist 77=[-1.8277858103894111860 ,-.07291765340025769746] 
dist 78=[-1.8800923681225219463 ,-.06998849212864522764] 
dist 79=[-1.9294319381176024315 ,-.06412458831509861953] 
dist 80=[-1.9881889034868581082 ,-.05275158581714711966] 
dist 81=[-2.0436097738124725353 ,-.03990622752656423766] 
dist 82=[-2.0796054533451844728 ,-.02815163264997940096] 
dist 83=[-2.1085622850006895705 ,-.01490837637648580513] 
dist 84=[-2.1358280343113717405 ,.00389730040119224866] 
dist 85=[-2.1601982755930771027 ,.02495354481168351318] 
dist 86=[-2.1775739434188080046 ,.04719813053217252562] 
dist 87=[-2.1933062765102365359 ,.07470105204743699257] 
dist 88=[-2.2111055134425126362 ,.1167821420585098954 ] 
dist 89=[-2.2274288466627602872 ,.15965175829744988792] 
dist 90=[-2.2372579814208888832 ,.19030945376988124992] 
dist 91=[-2.2443048225526884686 ,.21807773565002815598] 
dist 92=[-2.2494978972306480224 ,.2494001936898612843 ] 
dist 93=[-2.2531691877078189270 ,.28085433765915340701] 
dist 94=[-2.2541292783126951060 ,.30915226881128218784] 
dist 95=[-2.2539445143652035972 ,.34074919433211791432] 
dist 96=[-2.2530883512963666020 ,.3853975123613852478 ] 
dist 97=[-2.2454780145324136269 ,.43102136281374147721] 
dist 98=[-2.2435824549341651843 ,.46652094544963143461] 
dist 99=[-2.2371640411157083241 ,.50165076617377930568] 
dist 100=[-2.2358034556759674041 ,.54579894503605018588] 
dist 101=[-2.2148356903604639012 ,.59275516306083712049] 
dist 102=[-2.2101343344916874784 ,.63911576909137859592] 
dist 103=[-2.1918032052950598855 ,.69426339688078908891] 
dist 104=[-2.1592918555836547003 ,.77636020724529288263] 
dist 105=[-1.8997276581282567684 ,.85796515565363835898] 
dist 106=[-1.8774622054934430636 ,.9111465287143904531 ] 
dist 107=[-1.8296903719100973136 ,.95407125798012916567] 
dist 108=[-1.8171336096492743245 ,.99466069695640208906] 
dist 109=[-1.7629051715712206960 ,1.0309962888949002302 ] 
dist 110=[-1.7526517368509254321 ,1.0569105395129966270 ] 
dist 111=[-1.7276017815279978854 ,1.0803444363598312891 ] 
dist 112=[-1.7230309135516575628 ,1.1067622561280099586 ] 
dist 113=[-1.6742764511312166388 ,1.1311289017126068112 ] 
dist 114=[-1.6655663426478290246 ,1.1463601813531548246 ] 
dist 115=[-1.6497169375344544522 ,1.1579286886901476743 ] 
dist 116=[-1.6457025627998359026 ,1.1676468349091377153 ] 
dist 117=[-1.6324934547948267160 ,1.1755172588938574980 ] 
dist 118=[-1.6287442866249979884 ,1.1796961772853320656 ] 
dist 119=[-1.6255041851066052145 ,1.1820012017275705962 ] 
dist 120=[-1.6242517265829093058 ,1.1823773625007067108 ] 
dist 121=[-.59741301866502053574,1.1413367497983049638 ] 
dist 122=[-.54253553866858462455,1.1371337745521260358 ] 
dist 123=[-.41403453976126420044,1.1293244630222575231 ] 
dist 124=[-.39558295187038700559,1.1271282352079658584 ] 
dist 125=[-.22313812944988235288,1.1186651071205684971 ] 
dist 126=[-.19231986471885164027,1.1163907519478639370 ] 
dist 127=[-.15501941672293141848,1.1117377981587910637 ] 
dist 128=[-.14855793556673625708,1.1101659726293604788 ] 
dist 129=[.08644832295441085201,1.1030234198680175181 ] 
dist 130=[.11490657502713111418,1.1008766169847639546 ] 
dist 131=[.1726204382309424339 ,1.0983622863156194238 ] 
dist 132=[.18713693913162097747,1.0971220567190390006 ] 
dist 133=[.23764789994464427526,1.0948785128673329348 ] 
dist 134=[.24779578708724774901,1.0938284279139882609 ] 
dist 135=[.26138910888505373329,1.0929852810849063710 ] 
dist 136=[.264342891182573589  ,1.0921964508244832757 ] 
dist 137=[.48223857982472755789,.60618392458777314995] 
dist 138=[.41737056121900815629,.65628732429758663555] 
dist 139=[.36268824650849316293,.69743005414885842231] 
dist 140=[.30708473422297479907,.73751466174433208618] 
dist 141=[.25468386933888886318,.77419601790247294723] 
dist 142=[.21280733930569512407,.80172979944613336864] 
dist 143=[.17032902960800817731,.82803477925968247641] 
dist 144=[.11552156057971287362,.85980278769064433723] 
dist 145=[.06177767155965525122,.88993863270613364787] 
dist 146=[.02355199408700514355,.90971702107026525913] 
dist 147=[-.01088960029706782594,.92583802962213804814] 
dist 148=[-.04950272270872109825,.94134867104381207734] 
dist 149=[-.08816987455773445537,.95541755824521744785] 
dist 150=[-.12282778430605638418,.96577362023322892397] 
dist 151=[-.16143285295811947308,.97547214843517995365] 
dist 152=[-.21588366466674549776,.9869127831736921851 ] 
dist 153=[-.26967353902218507849,.99751094381475016485] 
dist 154=[-.30563589579480642059,1.0038405578139905804 ] 
dist 155=[-.33567346778610985003,1.0083051931585683679 ] 
dist 156=[-.36577228395075183436,1.0114444976427033341 ] 
dist 157=[-.39386015243392405202,1.0136044544960981897 ] 
dist 158=[-.41585681162792426528,1.0141521135077875563 ] 
dist 159=[-.43775979836643550226,1.0140785937059181874 ] 
dist 160=[-.46547351070723424921,1.0137538135020150299 ] 
dist 161=[-.49239653508149200157,1.0058504477347699316 ] 
dist 162=[-.51113801064589425061,1.0042224704456994104 ] 
dist 163=[-.52760729644721729692,1.0005482715484131919 ] 
dist 164=[-.54544474127194802032,.9992277346605461141 ] 
dist 165=[-.56295203382637272348,.99260175404072848252] 
dist 166=[-.57810151028276767102,.99101323693769885394] 
dist 167=[-.59453671692803436206,.98685854845879409756] 
dist 168=[-.61718614272233807974,.98546736936163485023] 
dist 169=[-.63929469829495940981,.91563997551651945457] 
dist 170=[-.65356716591659023466,.90848728106660776898] 
dist 171=[-.66493500104287525971,.89196693871362424229] 
dist 172=[-.67542803495568286087,.8883923064167809353 ] 
dist 173=[-.68464712835580078809,.8655421763575016458 ] 
dist 174=[-.69092060339662588575,.86104527367021130947] 
dist 175=[-.69628389782418916179,.85289325013156198038] 
dist 176=[-.70186345936172111819,.8508194894899499103 ] 
dist 177=[-.70673228974136606877,.81477617870215823172] 
dist 178=[-.70925339810402986158,.80969433911976744021] 
dist 179=[-.71061485815957139454,.79768589045206111079] 
dist 180=[-.71087467631725343189,.7951595745238418134 ] 
dist 181=[-.71014294385799108034,.77754516745658098206] 
dist 182=[-.70982055653904072934,.77400952027319205605] 
dist 183=[-.70949908250299163715,.76806944294222487875] 
dist 184=[-.70909294227146323705,.76650823513018966931] 
dist 185=[-.68722252853662685621,.48431661775095680061] 
dist 186=[-.68446400646538647315,.46620029609668669754] 
dist 187=[-.67778703770057394008,.4266287019870199296 ] 
dist 188=[-.67616151154625463158,.42027004500124154122] 
dist 189=[-.66546148783728372013,.3676412386864819718 ] 
dist 190=[-.66317658452388248772,.35809356059084588671] 
dist 191=[-.65915241174347425357,.34472543041447962004] 
dist 192=[-.65807484620925775359,.34089299877064844411] 
dist 193=[-.63536315295618046479,.27112853823717284119] 
dist 194=[-.63206615335445529059,.26221171293052929639] 
dist 195=[-.62472536574739774413,.24298885952295393816] 
dist 196=[-.62257462633665410942,.2386003307202785178 ] 
dist 197=[-.61278090829582950292,.21723386261645124368] 
dist 198=[-.6251418739033841254 ,.21342237258636273389] 
dist 199=[-.65684020655719829892,.20478733773203523075] 
dist 200=[-.70071298471076792365,.20310591173755534416] 
dist 201=[-.74370856653570020566,.12033034288767971028] 
dist 202=[-.77189916538105441794,.11240192870169476978] 
dist 203=[-.79484002100896962427,.13565076689902245081] 
dist 204=[-.81684288394482824352,.17785129606720258749] 
dist 205=[-.83674515188127186655,.21731884764004157355] 
dist 206=[-.85128613139163809694,.24837108823128143617] 
dist 207=[-.86478758561738165414,.27942491574825100778] 
dist 208=[-.88053299555645601275,.3188988402642239413 ] 
dist 209=[-.895180339443097443  ,.35733088887855413855] 
dist 210=[-.9042908380857843321 ,.38421856934738272245] 
dist 211=[-.91115320547235948597,.40798581626267221135] 
dist 212=[-.91681069949113977096,.43394016652486498867] 
dist 213=[-.92130726053194825833,.45953572920827827035] 
dist 214=[-.92352728013834918405,.4818683023334118653 ] 
dist 215=[-.92459742818999455171,.50624732828930727554] 
dist 216=[-.92471331189533762291,.54002609295314248968] 
dist 217=[-.17582206046503896015,.57313833456149509436] 
dist 218=[-.16993707976671710024,.59485212868655306449] 
dist 219=[-.15638839203808938495,.61252420169158065264] 
dist 220=[-.15411286463896500586,.6294747439455978632 ] 
dist 221=[-.1364172121901152532 ,.64480598205380285188] 
dist 222=[-.13321268879102742595,.65600291620605348888] 
dist 223=[-.12838929479780637029,.66639404510236448146] 
dist 224=[-.12711745297279519323,.6785030973011144345 ] 
dist 225=[-.09103404939022831814,.68976117147927529324] 
dist 226=[-.08682932144574078084,.69674947913556392801] 
dist 227=[-.07921501914759752675,.7019961108404751045 ] 
dist 228=[-.07749581432945098693,.70628971184136463576] 
dist 229=[-.05463327039565284943,.7096769132844460059 ] 
dist 230=[-.05169277922613989454,.71129910767332522596] 
dist 231=[-.03731650632434723723,.7120491928924524397 ] 

8 phat 2 dirichlet min maxes function [2, 1, 2, 2, 2, 0, 0, 0, 1] 
dist 0=[12.587902515670985265  ,12.587902515670985265  ] 
dist 1=[12.582267690705414939  ,12.588396048721655848  ] 
dist 2=[12.572860012009832831  ,12.587902515670985265  ] 
dist 3=[12.557279863687282621  ,12.583419878808035610  ] 
dist 4=[12.534089115364484735  ,12.566453516405574599  ] 
dist 5=[12.494242978812601881  ,12.559347718938428552  ] 
dist 6=[12.446381889778780097  ,12.543383081210314489  ] 
dist 7=[12.391137745231940554  ,12.536519728948478502  ] 
dist 8=[12.296955457268318560  ,12.506263995888517123  ] 
dist 9=[12.195716848934777849  ,12.502945458444882907  ] 
dist 10=[12.088575775073360839  ,12.441464943862162926  ] 
dist 11=[12.000906600621365867  ,12.426997669296714054  ] 
dist 12=[11.917634656717996738  ,12.419236414945279159  ] 
dist 13=[11.817755857196513472  ,12.387326904404784785  ] 
dist 14=[11.713944208391132826  ,12.204437523368474703  ] 
dist 15=[11.614942971832855013  ,12.084905899843775483  ] 
dist 16=[11.499756477531678412  ,11.845293235988831069  ] 
dist 17=[11.331216796936173229  ,11.729496386675905267  ] 
dist 18=[11.156327968184653710  ,11.564325481655138678  ] 
dist 19=[11.015749553194423320  ,11.539534691370475701  ] 
dist 20=[10.872332306717118852  ,11.476551727087345945  ] 
dist 21=[10.686089146460846532  ,11.466196790939997205  ] 
dist 22=[10.484848056334498968  ,11.360258716683266470  ] 
dist 23=[10.281450890919725734  ,11.338674573056320128  ] 
dist 24=[10.035957758649482754  ,11.314320469436636281  ] 
dist 25=[9.6663671510661445837 ,11.306061962389296816  ] 
dist 26=[9.2953163670705485116 ,11.076493420467309119  ] 
dist 27=[9.0439830430656889777 ,11.043855513829824696  ] 
dist 28=[8.8303677260435633439 ,10.995681727088514030  ] 
dist 29=[8.6101561607171626113 ,10.958719693830621589  ] 
dist 30=[8.3348939852067950594 ,10.717440305306717851  ] 
dist 31=[7.7753899748686675876 ,10.573968269965852324  ] 
dist 32=[7.2145576474998787457 ,9.9134890537908712784 ] 
dist 33=[6.8366278996051502526 ,9.6661718915265070997 ] 
dist 34=[6.5175786838626251489 ,9.6307106418088901930 ] 
dist 35=[6.1922094249183000452 ,9.5450547711210558148 ] 
dist 36=[5.8848075040763003237 ,9.5299508854117967065 ] 
dist 37=[5.6376084015532824287 ,9.4007076599255777108 ] 
dist 38=[5.3853346067226121549 ,9.3752791698858500889 ] 
dist 39=[5.0576353666731891927 ,9.3408625519844521433 ] 
dist 40=[4.7349956416725339331 ,9.3295907197094348970 ] 
dist 41=[4.5029531692541976817 ,7.1838619392638912773 ] 
dist 42=[4.2911302533408968969 ,6.8099420986736698683 ] 
dist 43=[4.0072223958348195456 ,6.4686221166056670101 ] 
dist 44=[3.6461315085709825491 ,6.4184837836700651111 ] 
dist 45=[3.3062669535787349784 ,5.9814554334355704426 ] 
dist 46=[3.0350418520733010054 ,5.8688795851739824021 ] 
dist 47=[2.7601324460061544984 ,5.7659961924489011093 ] 
dist 48=[2.4055320787828795193 ,5.7448482991215194647 ] 
dist 49=[2.0575713252369493092 ,5.6346434525417547159 ] 
dist 50=[1.8092133223660103098 ,5.3746522532646745113 ] 
dist 51=[1.5844232155485941046 ,5.3415280396549734037 ] 
dist 52=[1.3307115257803529306 ,5.2643542351026786169 ] 
dist 53=[1.0755162976199551322 ,5.2528494937707524464 ] 
dist 54=[.8447911962234348003 ,5.1501213607800946737 ] 
dist 55=[.5860433807009287912 ,5.1317247122666299150 ] 
dist 56=[.2187773042205462462 ,5.1081936431738668510 ] 
dist 57=[-.1454707802212434089 ,5.1028731349315110590 ] 
dist 58=[-.3921505342916335187 ,4.0860492963081996228 ] 
dist 59=[-.6017731268554730681 ,4.0215867236835915685 ] 
dist 60=[-.8178242696870949664 ,3.8871177603636123669 ] 
dist 61=[-1.0234354223415520220 ,3.8556441449738862218 ] 
dist 62=[-1.1913088140603054979 ,3.6144840172546309756 ] 
dist 63=[-1.3649731840407882133 ,3.5028665102287041778 ] 
dist 64=[-1.5937487647746268063 ,2.8211179977703673847 ] 
dist 65=[-1.8205946281224986792 ,2.5498104549926122179 ] 
dist 66=[-1.9865442044993470102 ,2.5151035142879935446 ] 
dist 67=[-2.1409340245541062268 ,2.4354791558224719258 ] 
dist 68=[-2.3215525473905921251 ,2.4229811685518821745 ] 
dist 69=[-2.5069236387119665859 ,2.3208722784810508048 ] 
dist 70=[-2.6803250607782246176 ,2.3027456585374941997 ] 
dist 71=[-2.8795505803722580241 ,2.2772593561023025119 ] 
dist 72=[-3.1682103382066844519 ,2.2701929501212289883 ] 
dist 73=[-3.4536901685776117235 ,.4561826232055477235 ] 
dist 74=[-3.6401990568888229806 ,.1787131412067663087 ] 
dist 75=[-3.7913594547894801908 ,.1481017155289897123 ] 
dist 76=[-3.9354622660927828493 ,.0879612019137217572 ] 
dist 77=[-4.0653495903933145618 ,.0733076041952080151 ] 
dist 78=[-4.1596558643341782559 ,.0254889837563488107 ] 
dist 79=[-4.2467032825925075232 ,.0151246392284049069 ] 
dist 80=[-4.3475616870406984265 ,.0081268272006495912 ] 
dist 81=[-4.4411922589250801396 ,.0117258763355970562 ] 
dist 82=[-4.4993330911100568222 ,.0199096160955986402 ] 
dist 83=[-4.5430729982246735569 ,.0332438545614538228 ] 
dist 84=[-4.5791075796450046296 ,.0529489386898320201 ] 
dist 85=[-4.6077926358368679264 ,.0866133592185691700 ] 
dist 86=[-4.6221407513788981029 ,.1269067248230090416 ] 
dist 87=[-4.6297728556218641893 ,.1731184122544080508 ] 
dist 88=[-4.6315843203249519521 ,.23280021464062902067] 
dist 89=[-4.6224642682118138859 ,.3269492628805132040 ] 
dist 90=[-4.6187905907684676567 ,.42268849512373192012] 
dist 91=[-4.6120890576299344434 ,.48873027740812698004] 
dist 92=[-4.6092146942944906625 ,.54606871651375538349] 
dist 93=[-4.5935262244013528631 ,.60701708658946262973] 
dist 94=[-4.5891779939652526966 ,.66608817097496905172] 
dist 95=[-4.5739346970441329789 ,.71592438451621637106] 
dist 96=[-4.5707368748182547993 ,.76886666078027443724] 
dist 97=[-4.5274095182080406397 ,.84036019027271297833] 
dist 98=[-4.5189714076711310919 ,.9119453314639258148 ] 
dist 99=[-4.4956386384990008156 ,.96525613193778171943] 
dist 100=[-4.4902426505990083244 ,1.0157460885626070418 ] 
dist 101=[-4.4421176563131421105 ,1.0760558759100644925 ] 
dist 102=[-4.4311729880771430912 ,1.1385696205720179202 ] 
dist 103=[-4.4149798255571447712 ,1.1978746392268291622 ] 
dist 104=[-4.3754026427178832421 ,1.2666085371179472586 ] 
dist 105=[-1.8267236284889486893 ,1.3668274734087859307 ] 
dist 106=[-1.7078328289607381178 ,1.4672345302237216020 ] 
dist 107=[-1.4331530424113575849 ,1.5367219597439202576 ] 
dist 108=[-1.3903854053059742492 ,1.5973501173574952099 ] 
dist 109=[-1.0323389735918847390 ,1.6623335509325247730 ] 
dist 110=[-.96855269615451307046,1.7257035699257619328 ] 
dist 111=[-.8804214030802189253 ,1.7798819374621098431 ] 
dist 112=[-.85608371291007601455,1.8380986691703882965 ] 
dist 113=[-.41421056453546581161,1.9176202590258054002 ] 
dist 114=[-.20346479740497061399,1.9977443170415545883 ] 
dist 115=[-.07206712513308021414,2.0583717562656179836 ] 
dist 116=[-.04109061127584560711,2.1167724080617635299 ] 
dist 117=[.06054244227396464315,2.1879936962714229879 ] 
dist 118=[.2680088755998183201 ,2.2626566121573098928 ] 
dist 119=[.2739344564363117803 ,2.3348223583901641462 ] 
dist 120=[.3681914131525379742 ,2.4195326927247911245 ] 
dist 121=[.3796776033972742017 ,2.5443653272410250847 ] 
dist 122=[.4041831020269220980 ,2.6677798873102078274 ] 
dist 123=[.4084859978010411669 ,2.7468199945065934202 ] 
dist 124=[.4327180601967218994 ,2.8090716409722168365 ] 
dist 125=[.4365161565679535033 ,2.8653471911597019760 ] 
dist 126=[.4433038033389059377 ,2.9139785804791220194 ] 
dist 127=[.4444804567118319296 ,2.9456611483386981962 ] 
dist 128=[1.1502041840726577031 ,2.9712375121312376720 ] 
dist 129=[1.1728320669182772499 ,2.9954519141227635173 ] 
dist 130=[1.2219500836956254118 ,3.0165674131724561684 ] 
dist 131=[1.2302708231627169577 ,3.0297506072262017254 ] 
dist 132=[1.2825749594468959950 ,3.0397555054096268017 ] 
dist 133=[1.2908533633102504660 ,3.0481573118512462324 ] 
dist 134=[1.3065473763386591774 ,3.0549675834183873036 ] 
dist 135=[1.3097648406802670923 ,3.0586060719776267859 ] 
dist 136=[1.3278564891935275960 ,3.0606469039284995570 ] 
dist 137=[1.3286850782743391760 ,3.0610662616861864691 ] 
dist 138=[1.3250448446892234274 ,2.8158177202159189272 ] 
dist 139=[1.3143374450638666930 ,2.7939010670857902350 ] 
dist 140=[1.2998204906792149572 ,2.7484841993952995282 ] 
dist 141=[1.2809469461886268454 ,2.7358728608648917423 ] 
dist 142=[1.2551380948688661933 ,2.6854124532625765290 ] 
dist 143=[1.2128900923752298568 ,2.6751187924191963427 ] 
dist 144=[1.1686859528964210083 ,2.6495843606686177754 ] 
dist 145=[1.1350548841146721826 ,2.6438384226083821214 ] 
dist 146=[1.1025023610027948636 ,2.6011463870274743297 ] 
dist 147=[1.0626092034483541180 ,2.5920754320273901753 ] 
dist 148=[1.0207153737759118712 ,2.5774782728522176634 ] 
dist 149=[.98016218065246204324,2.5732045405837273116 ] 
dist 150=[.93253851596473603332,2.5615849236639589032 ] 
dist 151=[.86237204696063362798,2.5576420260577301656 ] 
dist 152=[.78941790348324760904,2.5552733127544155896 ] 
dist 153=[.73064698181939174636,2.5544104083515990126 ] 
dist 154=[.67060070885729270704,1.3470422892758095357 ] 
dist 155=[.59254621587872460029,1.3430251522616827116 ] 
dist 156=[.50821527373946101253,1.3250178142374891738 ] 
dist 157=[.4230714078731878063 ,1.3211286988880919290 ] 
dist 158=[.32041455439241532986,1.3120834359915201674 ] 
dist 159=[.1660551667127505899 ,1.3090831654326700938 ] 
dist 160=[.01146800196285542696,.94426962168008344732] 
dist 161=[-.09209978569823244306,.91905702795268598773] 
dist 162=[-.17883704654061387596,.85994115199014134155] 
dist 163=[-.26612508707208340162,.85059684125315888333] 
dist 164=[-.34781565978196089999,.76987819609453605053] 
dist 165=[-.41217073297682343713,.75507057944967467318] 
dist 166=[-.47660233785951213597,.73530061606319727549] 
dist 167=[-.55859905589100163043,.72947359654238080837] 
dist 168=[-.63846973632183436949,.61471694670790708688] 
dist 169=[-.69440012040103268092,.59998848597197181158] 
dist 170=[-.78922332874115284929,.56905060733776243598] 
dist 171=[-.87143596386808114833,.56098787757099502206] 
dist 172=[-.93960141345071624206,.52906265617254148742] 
dist 173=[-1.0070925410880850602 ,.52303187826788737003] 
dist 174=[-1.0695576756426669308 ,.50941461467694755428] 
dist 175=[-1.1176257520114130179 ,.50648169937649949427] 
dist 176=[-1.1646960220481799362 ,.35378057746232112621] 
dist 177=[-1.2231718923734085522 ,.33978338239301516981] 
dist 178=[-1.2794603855680691022 ,.30706535834862566235] 
dist 179=[-1.3177842020982347420 ,.30209285697278254359] 
dist 180=[-1.3505589646574287999 ,.2580646211522298213 ] 
dist 181=[-1.3846584259735608255 ,.25010646438365988317] 
dist 182=[-1.4172980047336566396 ,.23981012461874241858] 
dist 183=[-1.4442357034058344234 ,.23726274512495118317] 
dist 184=[-1.4723551364346350178 ,.17697530304547584764] 
dist 185=[-1.5097218494726404993 ,.1694347477477287053 ] 
dist 186=[-1.5457909825691506848 ,.15374977320854872746] 
dist 187=[-1.5687217486359444520 ,.1497328214496427838 ] 
dist 188=[-1.5865863025253618910 ,.13441676902505897574] 
dist 189=[-1.6023953383945547008 ,.13149701969735877938] 
dist 190=[-1.6158127766342751403 ,.12563460697582459863] 
dist 191=[-1.6241133817484951494 ,.12414587178754199222] 
dist 192=[-1.6303176125080250101 ,.04601418616086660810] 
dist 193=[-1.6353521152915912593 ,.03874257671333901996] 
dist 194=[-1.6391487217134922242 ,.02487408202945158827] 
dist 195=[-1.6404025592750855570 ,.02157808760679173556] 
dist 196=[-1.6404651877010387845 ,.01152796809788459929] 
dist 197=[-1.6398637381951310751 ,.00939539192865120672] 
dist 198=[-1.6341776132098418582 ,.00927642405160049990] 
dist 199=[-1.6322838466442218040 ,.01186738114270643116] 
dist 200=[-1.6288507484362732003 ,.01570954110763361860] 
dist 201=[-1.6275750746777971176 ,.02059393028147028554] 
dist 202=[-1.5507822256559917197 ,.02721104920096991967] 
dist 203=[-1.5421960056333155165 ,.03798227991036028728] 
dist 204=[-1.5219474446362073762 ,.05069361632961739961] 
dist 205=[-1.5173370841314076924 ,.06506877245390581246] 
dist 206=[-1.4873504402429604796 ,.08351959064166370932] 
dist 207=[-1.4812107997559451595 ,.11252828091022237494] 
dist 208=[-1.4702641068176854920 ,.1424611428704236834 ] 
dist 209=[-1.4674145410505458697 ,.16460755490984043711] 
dist 210=[-1.4122463897389181243 ,.18544535664574273771] 
dist 211=[-1.4043455112452490549 ,.21014579934821855637] 
dist 212=[-1.3863070103706747199 ,.23565136631616152427] 
dist 213=[-1.3816787294708154434 ,.25970880345041426932] 
dist 214=[-1.3566069455269537321 ,.28748591625694226473] 
dist 215=[-1.3514548718619136059 ,.32786558341592573766] 
dist 216=[-1.3410729086293040444 ,.36963092236541533157] 
dist 217=[-1.3380541987597659709 ,.40294905437046451299] 
dist 218=[-.90523052517314586384,.43669618821923515679] 
dist 219=[-.87597239061574450597,.48017714295885684146] 
dist 220=[-.80767876991750740781,.52696834855400944409] 
dist 221=[-.79688395809879140441,.57395239257945219682] 
dist 222=[-.69549656733581927296,.63041772603965754525] 
dist 223=[-.67501830562521952429,.71512222591215961839] 
dist 224=[-.65270818443534621609,.79990484550227721376] 
dist 225=[-.64619579107432565722,.85668259143959934597] 
dist 226=[-.52619619599111451975,.90421307517529114844] 
dist 227=[-.51081211541863254774,.95201831047558596843] 
dist 228=[-.47788122110580454174,.99674599564965490296] 
dist 229=[-.4700380639148156322 ,1.0319701741203378513 ] 
dist 230=[-.43402534802838386331,1.0672284358146460541 ] 
dist 231=[-.42757284983347332264,1.1120924510979605440 ] 
dist 232=[-.41227688304216707883,1.1557968909672355939 ] 
dist 233=[-.4098065200169196921 ,1.1895697383801719488 ] 
dist 234=[-.25639340793201290478,1.2642742586700167137 ] 
dist 235=[-.2419302355020133109 ,1.3132591994911391580 ] 
dist 236=[-.20865609356876836532,1.3531238984908651860 ] 
dist 237=[-.20322687410475743156,1.3913588116517464506 ] 
dist 238=[-.16006739177047123678,1.4259411018386255470 ] 
dist 239=[-.15232701694558750466,1.4511998510242270511 ] 
dist 240=[-.14097020756378864209,1.4746436780080589266 ] 
dist 241=[-.13792714850674244854,1.5019685179305371024 ] 
dist 242=[-.08482575530276684036,1.5273769630017993162 ] 
dist 243=[-.07809493791395653696,1.5431575854250704906 ] 
dist 244=[-.06312797502199731982,1.5550158168470159844 ] 
dist 245=[-.06027871788140854971,1.5647395695517933991 ] 
dist 246=[-.04242135983960487897,1.5724260456896236659 ] 
dist 247=[-.03926783295492628337,1.5761376816227428544 ] 
dist 248=[-.0333738141064108836 ,1.5778971868176062040 ] 

8 phat 2 dirichlet min maxes function [2, 2, 0, 1, 2, 1, 2, 1, 2] 
dist 0=[12.937103382715082838  ,12.937103382715082838  ] 
dist 1=[12.893860398317265996  ,12.971572769776849570  ] 
dist 2=[12.835594001689582239  ,12.999022702925907928  ] 
dist 3=[12.741045056498762672  ,13.014197314994229236  ] 
dist 4=[12.639078380565106279  ,13.023384183159616674  ] 
dist 5=[12.551147336180183179  ,13.026897324876424968  ] 
dist 6=[12.456017881352072135  ,13.027748962946218935  ] 
dist 7=[12.325262265929391252  ,13.026293324645673214  ] 
dist 8=[12.180427987161894244  ,13.022858456289246299  ] 
dist 9=[12.028996886537001099  ,13.007578703623361401  ] 
dist 10=[11.842593230308007068  ,13.002972346325289464  ] 
dist 11=[11.557902979977218212  ,12.991861559576072744  ] 
dist 12=[11.270481745661472520  ,12.987161302117373630  ] 
dist 13=[11.073155618056692170  ,12.961209091272813719  ] 
dist 14=[10.902616415913239281  ,12.954469171985215129  ] 
dist 15=[10.722313021242145438  ,12.937679721656713011  ] 
dist 16=[10.547931921827488980  ,12.931210406307770489  ] 
dist 17=[10.401073261642840967  ,12.898331869415161975  ] 
dist 18=[10.245151377354126589  ,12.878080712191027716  ] 
dist 19=[10.034521381123326573  ,12.872574096692560627  ] 
dist 20=[9.8232984542504174018 ,12.854880415192371985  ] 
dist 21=[9.6650028405312966754 ,12.850393149210185845  ] 
dist 22=[9.5139816282789994841 ,12.804742695998532325  ] 
dist 23=[9.3318463050772838608 ,12.793640512110292716  ] 
dist 24=[9.1419598310642060308 ,12.780748560347742484  ] 
dist 25=[8.9599367238788121712 ,12.774748042685435924  ] 
dist 26=[8.7473993041101753630 ,12.766780178896424733  ] 
dist 27=[8.4354737056758144191 ,12.761033564875260820  ] 
dist 28=[8.1216683358809409709 ,12.715397388958096814  ] 
dist 29=[7.9016112726426472722 ,12.604479611054644339  ] 
dist 30=[7.7064264196917150527 ,12.145488944753434236  ] 
dist 31=[7.4920901006674357604 ,12.086614794836597534  ] 
dist 32=[7.2798517253655801833 ,11.852205365771659771  ] 
dist 33=[7.0930543129176308450 ,10.098444722792335130  ] 
dist 34=[6.8876568553614388703 ,9.9565680715273916378 ] 
dist 35=[6.6010251165650707761 ,9.6208367538556280711 ] 
dist 36=[6.3092787274119446821 ,9.5719555655791786280 ] 
dist 37=[6.0834232395088554635 ,9.1052079032336846832 ] 
dist 38=[5.8608267028699342535 ,9.0196839604197037759 ] 
dist 39=[5.5821110241998394216 ,8.9188687860823715649 ] 
dist 40=[5.2859677824740380809 ,8.8991916270240569175 ] 
dist 41=[4.9936670867811400371 ,8.5240084845066919374 ] 
dist 42=[4.6458552159521218435 ,8.5043067666528435896 ] 
dist 43=[4.1276906450143911373 ,8.4985047695573567394 ] 
dist 44=[3.6102256216743663990 ,8.3175386968209208273 ] 
dist 45=[3.2652107030180740579 ,8.2951363011934331978 ] 
dist 46=[2.9777994128416578777 ,8.2593524496326828443 ] 
dist 47=[2.6907218256379393787 ,8.2502370079139505644 ] 
dist 48=[2.4231395380445019145 ,8.2340070018181146744 ] 
dist 49=[2.2136996794544710164 ,8.2070450007741730557 ] 
dist 50=[1.9859447592413773969 ,8.0810465322896942509 ] 
dist 51=[1.4878764474844208999 ,8.0009156129155070227 ] 
dist 52=[.89185733754866029934,7.6614491664313308875 ] 
dist 53=[0                     ,7.5352191069587481508 ] 
dist 54=[1.1432343961506525114 ,5.6135153101029256174 ] 
dist 55=[.9673354458650113486 ,5.5139362470882894236 ] 
dist 56=[.7930185820990990509 ,5.4895851345360928977 ] 
dist 57=[.6392986639826375074 ,5.2031380356749776272 ] 
dist 58=[.4699874619698423231 ,5.1618625434256958179 ] 
dist 59=[.2333082893384589947 ,5.0756379772194273761 ] 
dist 60=[-.0001347529385789583 ,5.0526173538856989153 ] 
dist 61=[-.1565036028704171171 ,4.9643060236400113821 ] 
dist 62=[-.28758362272636742858,4.9472958258810683186 ] 
dist 63=[-.41988067043756034158,4.9090570438144984655 ] 
dist 64=[-.54410559307455913374,4.9002087308173820388 ] 
dist 65=[-.64290116736516365017,2.3798110565640434886 ] 
dist 66=[-.74278946788126735759,2.2384608141625391823 ] 
dist 67=[-.87138812245363217486,1.9083871640469622400 ] 
dist 68=[-.99760794648748025488,1.8609701873770593627 ] 
dist 69=[-1.0879831272636172686 ,1.4206589108775006028 ] 
dist 70=[-1.1701400999436770264 ,1.3421062246124202711 ] 
dist 71=[-1.2634908601771037868 ,1.2467412475882780561 ] 
dist 72=[-1.3578322444818224445 ,1.2301545453055412611 ] 
dist 73=[-1.4439542078977173170 ,.6345893872624427833 ] 
dist 74=[-1.5412787192502321202 ,.56235190566146379289] 
dist 75=[-1.6804339869423412909 ,.41620808573040904897] 
dist 76=[-1.8176944070102304298 ,.379470339885327807  ] 
dist 77=[-1.9074403679407562084 ,.25179247894747797829] 
dist 78=[-1.9803034380651087874 ,.22600771203652105878] 
dist 79=[-2.0500311216354907511 ,.19144041001938838257] 
dist 80=[-2.1131046289954028992 ,.18356800103576962664] 
dist 81=[-2.1593510107731596672 ,-.1166776322511838953 ] 
dist 82=[-2.2025178407188826590 ,-.0973879956378853457 ] 
dist 83=[-2.2532743810875990145 ,-.0687485496919533573 ] 
dist 84=[-2.3008299309463241883 ,-.0389907405513926023 ] 
dist 85=[-2.3311930703730024996 ,-.0152259105661850418 ] 
dist 86=[-2.3550341489385802194 ,.0088225147198143554 ] 
dist 87=[-2.3765010357378068461 ,.0397218333854273286 ] 
dist 88=[-2.3950259521865847162 ,.0728812252918383887 ] 
dist 89=[-2.4070999781604934201 ,.1059691170795950742 ] 
dist 90=[-2.4168742981220074658 ,.1455495005167503612 ] 
dist 91=[-2.4262032972021706981 ,.2046692489907050650 ] 
dist 92=[-2.4341323815454532405 ,.2643848597745137778 ] 
dist 93=[-2.4383073715441719336 ,.3063496439646360996 ] 
dist 94=[-2.4405839685713029754 ,.3436142789439092102 ] 
dist 95=[-2.4409175628158918660 ,.3845417471640303056 ] 
dist 96=[-2.4541116311130959584 ,.4250204551770939812 ] 
dist 97=[-2.4860839785406778719 ,.4604936789463076306 ] 
dist 98=[-2.5046974881848091862 ,.4993389137557596899 ] 
dist 99=[-2.5172592147576213365 ,.5533040723102916615 ] 
dist 100=[-2.5250235309549130539 ,.6080558026513708370 ] 
dist 101=[-2.5303573331694061121 ,.6500481834066751141 ] 
dist 102=[-2.5331947621304044512 ,.6910325601291901733 ] 
dist 103=[-2.5347812254632881569 ,.7417564326084599494 ] 
dist 104=[-2.5351053473278500426 ,.7953101801649171726 ] 
dist 105=[-2.4912223579202407323 ,.8476129453167946790 ] 
dist 106=[-2.4843953068355557585 ,.9094077790101956166 ] 
dist 107=[-2.4741587190354762869 ,1.0009223001987685694 ] 
dist 108=[-2.4707742107195025858 ,1.0917486482014413765 ] 
dist 109=[-2.4626198051277409579 ,1.1507922174284985936 ] 
dist 110=[-2.4597448510021289285 ,1.1982863380204399147 ] 
dist 111=[-2.4580091991491699382 ,1.2429266672398507677 ] 
dist 112=[-2.4573605806917333606 ,1.2827082511138495788 ] 
dist 113=[-2.1575799329714418329 ,1.3107727390509058458 ] 
dist 114=[-2.1317161863165169306 ,1.3358371788383048889 ] 
dist 115=[-2.0761804092711393066 ,1.3636228186289466845 ] 
dist 116=[-2.0616949589189025610 ,1.3891261321952142470 ] 
dist 117=[-1.9985963682515187574 ,1.4050634373455678466 ] 
dist 118=[-1.9866900033098355607 ,1.4171646620699121466 ] 
dist 119=[-1.9577800063730574970 ,1.4273259101748297292 ] 
dist 120=[-1.9524056162441779470 ,1.4355531453253951306 ] 
dist 121=[-1.8957602935713476820 ,1.4399194501852159117 ] 
dist 122=[-1.8856852920000395765 ,1.4423254571556289050 ] 
dist 123=[-1.8673222374027843698 ,1.4427126442784771274 ] 
dist 124=[-1.8626750980065237663 ,1.3788552403906157579 ] 
dist 125=[-1.8473867360384587245 ,1.3726334140400749325 ] 
dist 126=[-1.8430690297915212751 ,1.3605930121233902085 ] 
dist 127=[-1.8393528668742425259 ,1.3572213162003550341 ] 
dist 128=[-1.8379613439609058632 ,1.3440295984793964033 ] 
dist 129=[-.66408979285818138466,1.3408177589614439024 ] 
dist 130=[-.60136477736444356295,1.3337802012530423919 ] 
dist 131=[-.45449473939127990732,1.3314187751389887457 ] 
dist 132=[-.43341197711660483561,1.3205115518734213157 ] 
dist 133=[-.23634642974289261749,1.3175392446718035615 ] 
dist 134=[-.20113239225267216976,1.3136308532124738606 ] 
dist 135=[-.15852279985374785443,1.3120138908742117008 ] 
dist 136=[-.15115990736231781351,1.3086461188469805951 ] 
dist 137=[.1173142423367096483 ,1.3072180451027901694 ] 
dist 138=[.14981870362556676475,1.3061413791273141291 ] 
dist 139=[.2157302110025885285 ,1.3052528644406110562 ] 
dist 140=[.23230487668559823318,.58757763041938990243] 
dist 141=[.28995441191465335086,.54919466468983681661] 
dist 142=[.30153879809574370658,.469808144197821639  ] 
dist 143=[.31700145396610727669,.5330508265511045466 ] 
dist 144=[.2936253521369480048 ,.62099879735598465837] 
dist 145=[.24321702110802579537,.70738360840827737929] 
dist 146=[.19215180096540931176,.76437558926650809851] 
dist 147=[.12635428291564578469,.81115273942075316083] 
dist 148=[.06187370179053947165,.85668994031813050493] 
dist 149=[.01607419304896457437,.89833642043884947831] 
dist 150=[-.02512779442836569949,.92955530606234770213] 
dist 151=[-.07122491980658808328,.95933994780305504998] 
dist 152=[-.11733296939371441976,.99525156978386550883] 
dist 153=[-.15857894592212433926,1.0292878678013751214 ] 
dist 154=[-.20445667671164342322,1.0515735629614501404 ] 
dist 155=[-.26908598714476521447,1.0696792737841729065 ] 
dist 156=[-.33289976313664064095,1.0870005514162896490 ] 
dist 157=[-.37551660558060934759,1.1026452289869321885 ] 
dist 158=[-.4110613357912816551 ,1.1140469015692727386 ] 
dist 159=[-.44659615858080772349,1.1246105654648921588 ] 
dist 160=[-.47970463697693381485,1.1369053630082892998 ] 
dist 161=[-.50554740208245735743,1.1482384441638958790 ] 
dist 162=[-.5312003041087366042 ,1.1549563613439007902 ] 
dist 163=[-.5635500494948821941 ,1.1596327309831721806 ] 
dist 164=[-.59492495647097123338,1.1628008175551414357 ] 
dist 165=[-.61668000032149326367,1.1649049013108878746 ] 
dist 166=[-.63570786724496163176,1.1653257293005718407 ] 
dist 167=[-.65617782310956983063,1.1650970232159779429 ] 
dist 168=[-.67618693182182962608,1.1646029372576655930 ] 
dist 169=[-.69337243167968719891,1.1547247510695874598 ] 
dist 170=[-.71190767297278813416,1.1527465174232467698 ] 
dist 171=[-.73731504669476579218,1.1482899478536652976 ] 
dist 172=[-.76207622774215783523,1.1467106720837584438 ] 
dist 173=[-.77802757205912907966,1.1388605773513184341 ] 
dist 174=[-.79069496441530329548,1.1369931346996005935 ] 
dist 175=[-.80232365395443653101,1.1321401022510886187 ] 
dist 176=[-.81249642230504636092,1.1305203638875055422 ] 
dist 177=[-.81934170174861201621,1.0498366960009326044 ] 
dist 178=[-.82511102724334805432,1.0415761761072686599 ] 
dist 179=[-.83098137123220791729,1.0224831863886996194 ] 
dist 180=[-.83604789736490170349,1.0183765906562095939 ] 
dist 181=[-.83860276852793975433,.99194298519835474593] 
dist 182=[-.83992517502441330663,.98674543791037276499] 
dist 183=[-.84011815707678535093,.97736718105501618106] 
dist 184=[-.83886455764603146142,.97499514620399183657] 
dist 185=[-.83830632218045973372,.93325813074005199836] 
dist 186=[-.83774475554591095321,.92738264457047824466] 
dist 187=[-.83715312740152525651,.91354446782702231912] 
dist 188=[-.80902431387098910708,.9106025812993669728 ] 
dist 189=[-.80556326578662983565,.89044312787097040602] 
dist 190=[-.79722639515800952828,.88639952143701479299] 
dist 191=[-.79523310794170064312,.8794820041887156711 ] 
dist 192=[-.78207645330282346978,.87770208296271760667] 
dist 193=[-.77929165095877762283,.55558491880644581098] 
dist 194=[-.77439083307998127055,.53439218976220021412] 
dist 195=[-.77309026197491915969,.48824203607866856237] 
dist 196=[-.74589278719058447889,.48092532556582860099] 
dist 197=[-.74195747411040274887,.42042848542108039474] 
dist 198=[-.73317199213568656602,.40945443376544128539] 
dist 199=[-.73064394611846882422,.39407139566213455258] 
dist 200=[-.71888519150780776203,.3896675461834454103 ] 
dist 201=[-.7164273951303427003 ,.30954976965767329473] 
dist 202=[-.71093596048880064498,.29930943769868071922] 
dist 203=[-.7091984067335160261 ,.27722009504697832463] 
dist 204=[-.65154671744023305239,.27219035537614045234] 
dist 205=[-.68997372912749323624,.24759759547606194839] 
dist 206=[-.72344167619847404859,.24321001522639205191] 
dist 207=[-.75992878947059269392,.23330371135248533625] 
dist 208=[-.8104288950740892545 ,.25510499990159636481] 
dist 209=[-.85991920595888408981,.29171025500455741902] 
dist 210=[-.89236834772010058458,.32831297090719017682] 
dist 211=[-.91877497454077661551,.37483467350295659571] 
dist 212=[-.94410241163094093942,.42012627456725964064] 
dist 213=[-.96701224781735662241,.45181017626186733379] 
dist 214=[-.983751347205365942  ,.47981427015229820648] 
dist 215=[-.99929453639700652899,.51039137122955921003] 
dist 216=[-1.0174221576947183725 ,.5405436874906395339 ] 
dist 217=[-1.0342862079602965481 ,.56684920226139143246] 
dist 218=[-1.0447766156770511565 ,.59556297040017200099] 
dist 219=[-1.0526797320200108884 ,.63534524577558210602] 
dist 220=[-1.0591976901465512740 ,.6743420654206824425 ] 
dist 221=[-1.0643800501814429710 ,.69991501838226280935] 
dist 222=[-1.0669423624461637215 ,.72072838824992645588] 
dist 223=[-1.0681780400914433536 ,.74069294683501417996] 
dist 224=[-1.0683157768503323027 ,.75875107900691302695] 
dist 225=[-.14846592087159538948,.77194117497559741124] 
dist 226=[-.14275419392512812785,.78418373055278234315] 
dist 227=[-.14126861454784396848,.79845291003434079968] 
dist 228=[-.1152897061786646624 ,.81172082146847993101] 
dist 229=[-.11195338973543622478,.8199595804500415046 ] 
dist 230=[-.10442980900768792547,.82614845207331163469] 
dist 231=[-.10231333322522428387,.83121942409367431806] 
dist 232=[-.09341573982908597293,.83522486092121615364] 
dist 233=[-.07822430144298856984,.83715294741344320806] 
dist 234=[-.07642786077152432337,.83804921661793953426] 

8 phat 2 dirichlet min maxes function [0, 2, 0, 0, 2, 2, 0, 0, 2] 
dist 0=[12.081438282762867017  ,12.081438282762867017  ] 
dist 1=[12.024808202664420934  ,12.126262237380460479  ] 
dist 2=[11.948279284013473809  ,12.162619107950840403  ] 
dist 3=[11.823882242985824194  ,12.185393990012159411  ] 
dist 4=[11.693954436438510029  ,12.202732133371776589  ] 
dist 5=[11.595306872611151452  ,12.217359116453177193  ] 
dist 6=[11.499987930816978845  ,12.230696055391123034  ] 
dist 7=[11.383365572956340260  ,12.253907132179621561  ] 
dist 8=[11.260948526847434138  ,12.276308967661575816  ] 
dist 9=[11.142454236118399361  ,12.294634075221662897  ] 
dist 10=[11.003264275973989321  ,12.303034156753494426  ] 
dist 11=[10.798083789185128753  ,12.306242097077364411  ] 
dist 12=[10.584591653756030097  ,12.305974862564841080  ] 
dist 13=[10.412162066179292898  ,12.295254013020126201  ] 
dist 14=[10.235528030579907069  ,12.290789131361195387  ] 
dist 15=[10.005219731670279492  ,12.281754939049535625  ] 
dist 16=[9.7559451385699042666 ,12.277885892308614789  ] 
dist 17=[9.5034632447616541733 ,12.045144085263037026  ] 
dist 18=[9.1983734908191569432 ,12.018790703426128362  ] 
dist 19=[8.7387176924782165795 ,11.961651787889745938  ] 
dist 20=[8.2773604823987904447 ,11.944822167929848544  ] 
dist 21=[7.9654656746324126549 ,11.872642773015233618  ] 
dist 22=[7.7010774571883137362 ,11.857772861899170221  ] 
dist 23=[7.4296981512577590351 ,11.820647590870479717  ] 
dist 24=[7.1721957251504469915 ,11.811740900110511824  ] 
dist 25=[6.9632994816680794021 ,11.712237566677544899  ] 
dist 26=[6.7484495782945176612 ,11.695485959569956477  ] 
dist 27=[6.4671344218365167981 ,11.636039445503426284  ] 
dist 28=[6.1891006289427175166 ,11.227282725878772244  ] 
dist 29=[5.9873709613194719295 ,11.187782527691910307  ] 
dist 30=[5.8014129581812054679 ,11.145314021058501253  ] 
dist 31=[5.5864482906543278629 ,11.011686781217394880  ] 
dist 32=[5.3673205642675799205 ,10.705481702227771174  ] 
dist 33=[5.1647103761147077110 ,9.6408087684414616446 ] 
dist 34=[4.9338396005154296300 ,9.5273489361306677756 ] 
dist 35=[4.6016872156573607092 ,9.2620940923176770599 ] 
dist 36=[4.2703272763756371708 ,9.2210294061214671411 ] 
dist 37=[4.0426234934328448815 ,8.8623184826938047169 ] 
dist 38=[3.8455436902196508070 ,8.7970057689703945112 ] 
dist 39=[3.6366536285838876204 ,8.7113097135780348998 ] 
dist 40=[3.4342343352275173628 ,8.6880866723452149662 ] 
dist 41=[3.2630292805877424035 ,8.1867200561896158989 ] 
dist 42=[3.0805709381226162333 ,8.1230620582884775084 ] 
dist 43=[2.8331396100276064634 ,8.0051708396799532057 ] 
dist 44=[2.5844584857784607849 ,7.9726684208954456166 ] 
dist 45=[2.3969982795160361372 ,7.9616208692012198137 ] 
dist 46=[2.2170285811021071189 ,7.7980034401562177998 ] 
dist 47=[1.9983003560829609537 ,7.7439005391255825480 ] 
dist 48=[1.7692851264270911512 ,7.7296612646976261074 ] 
dist 49=[1.5481678060338334251 ,7.0132941691020007005 ] 
dist 50=[1.2887009499614632502 ,6.9487733443963229484 ] 
dist 51=[.9062979156592259767 ,6.7982323418936999513 ] 
dist 52=[.5260867291936470274 ,6.7755251394902059389 ] 
dist 53=[.27538460708068468664,6.5740078988085361692 ] 
dist 54=[.06959428028667512103,6.5376997015961371055 ] 
dist 55=[-.13098801980842204085,6.4910069911741376303 ] 
dist 56=[-.31477411449301230911,6.4799008564207205411 ] 
dist 57=[-.45338791183039656376,6.2061036808325439164 ] 
dist 58=[-.58656634331419658858,6.1719425943741808754 ] 
dist 59=[-.74861752690046651145,6.1013157579716304259 ] 
dist 60=[-.90317317355333068333,6.0829683504830245666 ] 
dist 61=[-1.0063743697678115212 ,6.0154133899671993558 ] 
dist 62=[-1.0925488789871110686 ,6.0023124781601505165 ] 
dist 63=[-1.1790059408903186590 ,5.9608952447360189236 ] 
dist 64=[-1.3545733718533429500 ,5.8965876831124892814 ] 
dist 65=[-1.5477766073442410540 ,2.5997430814823222964 ] 
dist 66=[-1.7309289339788845937 ,2.4587979103918849681 ] 
dist 67=[-1.8793026801880235849 ,2.1369085950898563485 ] 
dist 68=[-2.0317512652029344200 ,2.0853884262777986751 ] 
dist 69=[-2.2312038984504259767 ,1.9484144855716895349 ] 
dist 70=[-2.4283341511734995282 ,1.7284186777367114661 ] 
dist 71=[-2.5714970771994844262 ,1.6988952945096385354 ] 
dist 72=[-2.7036373333330321297 ,1.6369780270338279593 ] 
dist 73=[-2.8566875191432056798 ,1.6224974595444828212 ] 
dist 74=[-3.0129178983015714514 ,1.5609456500749017240 ] 
dist 75=[-3.1577805821208546378 ,1.5498597670013714156 ] 
dist 76=[-3.3232147830472530427 ,1.5269779975871038246 ] 
dist 77=[-3.5617255593883891828 ,1.5214787604421615810 ] 
dist 78=[-3.7972277126665062431 ,.60591490367611535187] 
dist 79=[-3.9506301491355664692 ,.5581937682995927516 ] 
dist 80=[-4.0744488354010489955 ,.54808710721760469968] 
dist 81=[-4.1916298280925006030 ,.22477684056774727159] 
dist 82=[-4.2966728667144754262 ,.19028374994999426417] 
dist 83=[-4.3719461938624662794 ,.1212277797643192315 ] 
dist 84=[-4.4404216905395176416 ,.10411508971951908447] 
dist 85=[-4.5182789171941667949 ,.04607641424289730569] 
dist 86=[-4.5898001657969487353 ,.0341603610900248439 ] 
dist 87=[-4.6329351181364171126 ,.02094720520794186310] 
dist 88=[-4.6638768040250154966 ,.02010064407223248181] 
dist 89=[-4.6866295699410787821 ,.02409858658180308152] 
dist 90=[-4.7039528469975372519 ,.03471371005166744836] 
dist 91=[-4.7131781251361187500 ,.05222676992189760127] 
dist 92=[-4.7183159417571922478 ,.08381356709038675847] 
dist 93=[-4.7192894335332169109 ,.12223367140385390956] 
dist 94=[-4.6623165267468204240 ,.16707018813975255305] 
dist 95=[-4.6535872499488366418 ,.22545984257515298907] 
dist 96=[-4.6353231163360552161 ,.3180661296543738898 ] 
dist 97=[-4.6292623559544271530 ,.41236145113133596904] 
dist 98=[-4.6005289389938504601 ,.4775064584488694442 ] 
dist 99=[-4.5939897004661278512 ,.5341615080660553706 ] 
dist 100=[-4.5735229849075460334 ,.59452101439767294112] 
dist 101=[-4.5699420664965683863 ,.65309470955783543783] 
dist 102=[-4.5132000844521612192 ,.70261394082443330591] 
dist 103=[-4.5030537794301015754 ,.75530281776333967872] 
dist 104=[-4.4758480935564183165 ,.82655330802556233614] 
dist 105=[-4.4700646578375581834 ,.89792858030580128708] 
dist 106=[-4.4174540826089972837 ,.95111886802511375551] 
dist 107=[-4.4058308049779139512 ,1.0015252660484551165 ] 
dist 108=[-4.3907736184454991387 ,1.0617735971645169173 ] 
dist 109=[-4.3849920063984496949 ,1.1242390446780283896 ] 
dist 110=[-1.8009608000467982693 ,1.1835132397332340879 ] 
dist 111=[-1.6823778470109305016 ,1.2522193303332871221 ] 
dist 112=[-1.4086343445135920709 ,1.3524017339649586314 ] 
dist 113=[-1.3659922555560839054 ,1.4527609778524824637 ] 
dist 114=[-1.0099633888069085172 ,1.5221756236833688708 ] 
dist 115=[-.9466033322549930268 ,1.5826948636578554687 ] 
dist 116=[-.85882188602951163639,1.6474866822249117554 ] 
dist 117=[-.83452956597088994254,1.7106216968885722378 ] 
dist 118=[-.3979223088328625934 ,1.7645179196072830967 ] 
dist 119=[-.34349275460344628361,1.8223601225357381744 ] 
dist 120=[-.21254010508446503987,1.9012774263861063626 ] 
dist 121=[-.02672890354181934848,1.9807481091391701610 ] 
dist 122=[.06507937163786291410,2.0408048652123984123 ] 
dist 123=[.08717429783802346009,2.0985809630694676854 ] 
dist 124=[.18406628609694243203,2.1689337452931903042 ] 
dist 125=[.35939162041418400837,2.2426293349777981957 ] 
dist 126=[.80628822882183938026,2.3137755174110382861 ] 
dist 127=[.80543373797923796993,2.3972250527614975267 ] 
dist 128=[.80185951495793349161,2.5201258792567732144 ] 
dist 129=[.79446291038850092542,2.6416186975011974370 ] 
dist 130=[.78280401975590306503,2.7194383034495360415 ] 
dist 131=[.76218764290272450733,2.7807410471424420795 ] 
dist 132=[.74007356561978684541,2.8361808890698275130 ] 
dist 133=[.7224257207151366541 ,2.8841064110838729385 ] 
dist 134=[.7045562957777721724 ,2.9153592664840609766 ] 
dist 135=[.68155444007882920629,2.9406229748475706852 ] 
dist 136=[.6568253402212324998 ,2.9645995783217835775 ] 
dist 137=[.63204872963800955758,2.9855084012101234545 ] 
dist 138=[.60232091999392337985,2.9985033864657453039 ] 
dist 139=[.55779384733881224991,3.0082961719473630476 ] 
dist 140=[.51120389649441823118,3.0163957176847996741 ] 
dist 141=[.47322721288648858714,3.0228661855415631879 ] 
dist 142=[.43402628462667101859,3.0261424350876447810 ] 
dist 143=[.38254043255556009739,3.0277325313786134336 ] 
dist 144=[.32665906660340151592,3.0274582044125358916 ] 
dist 145=[.26988213053559781254,2.7900566541310463183 ] 
dist 146=[.20117312837539904606,2.7686434711725986202 ] 
dist 147=[.09758052541987758994,2.7241570712047900207 ] 
dist 148=[-.00623833640004723535,2.7117675905655086996 ] 
dist 149=[-.07585218643537418676,2.6619710329571057432 ] 
dist 150=[-.13421180915714862002,2.6518573198844352753 ] 
dist 151=[-.19303022683187162183,2.6264238232994830402 ] 
dist 152=[-.24812722059791437916,2.6209987770241901901 ] 
dist 153=[-.29160663510375728662,2.5774417159930474644 ] 
dist 154=[-.33520343490188092516,2.5683659745646583384 ] 
dist 155=[-.39076993004762392842,2.5530026514079930104 ] 
dist 156=[-.44492895170833341946,2.5487698944517063890 ] 
dist 157=[-.48289794583256532706,2.5355227093465727495 ] 
dist 158=[-.51653757271751340653,2.5310982978972339218 ] 
dist 159=[-.55338541589714989277,2.5269837728828121567 ] 
dist 160=[-.5897843845278296724 ,2.5243699552947987352 ] 
dist 161=[-.62162922012349618887,1.0483620493696802461 ] 
dist 162=[-.65646033285110028127,.96916782899585783342] 
dist 163=[-.70480023528832984079,.78355185254527562639] 
dist 164=[-.75220587739028958824,.75663502093357843631] 
dist 165=[-.78330129383712412761,.50661890790233748792] 
dist 166=[-.80861437567103161626,.46178238083349696604] 
dist 167=[-.83289888034194136122,.40701841759603148589] 
dist 168=[-.85486305178359444264,.3967869929570879905 ] 
dist 169=[-.87089808462175577158,.31112935141983020148] 
dist 170=[-.88577086770869592803,.30458213675662255322] 
dist 171=[-.90308766947995527053,.30328880798677981832] 
dist 172=[-.91917592266626680077,.25696242728257100999] 
dist 173=[-.92913623791572348758,.25117822263314942794] 
dist 174=[-.93658178743543708815,.23964901959296239336] 
dist 175=[-.94261451668962152858,.23672303796666307862] 
dist 176=[-.94732502887323349772,.22650898495539013622] 
dist 177=[-.94948354983611881603,.22432116045490565331] 
dist 178=[-.95043587676435588402,.22131227878570664553] 
dist 179=[-.97160655371339222527,.22040282341033484975] 
dist 180=[-1.0387308357187730188 ,.14056279155998805186] 
dist 181=[-1.1008362484889851416 ,.13353151528719388721] 
dist 182=[-1.1485936974935622760 ,.12004979605419959089] 
dist 183=[-1.1953275745670528981 ,.11679857691552286933] 
dist 184=[-1.2533406747664836330 ,.10658422923163652325] 
dist 185=[-1.3091614882731721682 ,.10415870983246789701] 
dist 186=[-1.3471292693083581573 ,.10354134842252104587] 
dist 187=[-1.3795590118869803021 ,.10524108283235456813] 
dist 188=[-1.4132348287530047946 ,.10808813932342897509] 
dist 189=[-1.4454288039590963489 ,.11206423642759902437] 
dist 190=[-1.4719336561254071896 ,.11765637009834664687] 
dist 191=[-1.4995433992803602278 ,.12696582206285807619] 
dist 192=[-1.5361571918163468642 ,.13803368488828255436] 
dist 193=[-1.5714526622039055020 ,.1506572830030693557 ] 
dist 194=[-1.5937907908204469177 ,.16692918475538481909] 
dist 195=[-1.6110774302428736194 ,.19258548901904028222] 
dist 196=[-1.6261717024634971644 ,.21908670584537834132] 
dist 197=[-1.6388346402045728889 ,.23873725044106086502] 
dist 198=[-1.6463984368020253447 ,.25726919321524845224] 
dist 199=[-1.6517321921961239542 ,.2792977594680855554 ] 
dist 200=[-1.6554776796717111596 ,.30207750229477573852] 
dist 201=[-1.6580357035948238171 ,.32361333722214761641] 
dist 202=[-1.6586207438854082694 ,.34851723382326280761] 
dist 203=[-1.6581952417981228297 ,.38476502841404347149] 
dist 204=[-1.6574969361984606776 ,.42227521335743906414] 
dist 205=[-1.6518018257707463217 ,.45222714126820165812] 
dist 206=[-1.6500009114718941759 ,.48259052986538936394] 
dist 207=[-1.6458298062914446277 ,.52174617121275790012] 
dist 208=[-1.6441339350067326149 ,.56389960869437541248] 
dist 209=[-1.5549172740458252368 ,.60625045076502448962] 
dist 210=[-1.5453076346503902818 ,.65716456975923866248] 
dist 211=[-1.5230622439763978688 ,.73356033070544923383] 
dist 212=[-1.5178265343385807250 ,.81003159253490430046] 
dist 213=[-1.4863001135433223480 ,.86124764813549897937] 
dist 214=[-1.4799098621056235618 ,.90412659487838622584] 
dist 215=[-1.4678974748606385543 ,.9472600049724148061 ] 
dist 216=[-1.4646410380650156464 ,.98762044989004349736] 
dist 217=[-1.4110816459445114784 ,1.0194110674379800743 ] 
dist 218=[-1.4033497035337665736 ,1.0512375514893529078 ] 
dist 219=[-1.3848855534695773666 ,1.0917414513709735294 ] 
dist 220=[-1.3808986873824600174 ,1.1312011357409250512 ] 
dist 221=[-1.3529194991426800461 ,1.1588520931828212807 ] 
dist 222=[-1.3471995830667289852 ,1.1833412131095590646 ] 
dist 223=[-1.3376751089837428850 ,1.2101575564686730903 ] 
dist 224=[-1.3253522689268113290 ,1.2366475545378873251 ] 
dist 225=[-.85328302418902171529,1.2598317265984987077 ] 
dist 226=[-.8260787795807090342 ,1.2852008662123629280 ] 
dist 227=[-.76272899576404150563,1.3204280225280568706 ] 
dist 228=[-.75257355171772948475,1.3549958915733354225 ] 
dist 229=[-.66757367312575686286,1.3777287188576176074 ] 
dist 230=[-.65208619873357690243,1.3963028995022590200 ] 
dist 231=[-.63066768090187121247,1.4142413990352968432 ] 
dist 232=[-.62440722921461963416,1.4305492697952844921 ] 
dist 233=[-.50897894572155207137,1.4426029864594660738 ] 
dist 234=[-.49418047355142895287,1.4539337164869789074 ] 
dist 235=[-.46252052515576921663,1.4673505644128892371 ] 
dist 236=[-.45496132496350897847,1.4799375594402564968 ] 
dist 237=[-.42038961945460935547,1.4879499242160268408 ] 
dist 238=[-.41419542288164639023,1.4942009473560852473 ] 
dist 239=[-.39946507788081109142,1.4997447847123455020 ] 
dist 240=[-.39712385943821990893,1.5044558120552685788 ] 
dist 241=[-.24903683318031241669,1.5073766508815328654 ] 
dist 242=[-.2350919856195641047 ,1.5095656786891567745 ] 
dist 243=[-.20298439578444210396,1.5113504137454664187 ] 
dist 244=[-.1977672197787179348 ,1.5125125594514882243 ] 
dist 245=[-.15604453582207268534,1.5123696327286918061 ] 
dist 246=[-.14855992068281014558,1.5112661295361199120 ] 
dist 247=[-.13765507935190022817,1.5103063790759399161 ] 
dist 248=[-.13470894993078513813,1.5036241636621892456 ] 
dist 249=[-.08311833342678666798,1.5016487581408095933 ] 
dist 250=[-.07658132691186480767,1.4975679486534809400 ] 
dist 251=[-.06210414784762113869,1.4960409405217302714 ] 
dist 252=[-.05929470905096453740,1.4657592307662509922 ] 
dist 253=[-.04219715824853439317,1.4609331674693464381 ] 
dist 254=[-.03918162101320413809,1.4502571609310422066 ] 
dist 255=[-.03341754233109254613,1.4403934093293657729 ] 

8 phat 2 dirichlet min maxes function [2, 2, 1, 2, 1, 0, 0, 0, 1] 
dist 0=[13.244329592749477802  ,13.244329592749477802  ] 
dist 1=[13.229911062815623482  ,13.254976034341748193  ] 
dist 2=[13.212762528472878465  ,13.264957621618220962  ] 
dist 3=[13.191196613096201470  ,13.276719223070065626  ] 
dist 4=[13.162108258629999825  ,13.288807660284178333  ] 
dist 5=[13.114869113528100314  ,13.300096137295023895  ] 
dist 6=[13.059126732671352374  ,13.313027710772113350  ] 
dist 7=[12.972240484928608154  ,13.331684692309459132  ] 
dist 8=[12.831366220431906418  ,13.349797840292935283  ] 
dist 9=[12.680269819657485969  ,13.360555705161518879  ] 
dist 10=[12.552409702211304448  ,13.368047098641390708  ] 
dist 11=[12.416107039780288694  ,13.373103067956907076  ] 
dist 12=[12.231244291942829680  ,13.376241272179573230  ] 
dist 13=[12.027563611641177089  ,13.376066878115717029  ] 
dist 14=[11.816000990459319809  ,13.373432016046934366  ] 
dist 15=[11.556485962176351419  ,13.370961702801751558  ] 
dist 16=[11.161027082807044377  ,13.358620257514507124  ] 
dist 17=[10.761880690149839749  ,13.353529355672382561  ] 
dist 18=[10.487617110505326561  ,13.341816864260422231  ] 
dist 19=[10.250250906393866302  ,13.336755790348891873  ] 
dist 20=[9.9986670886295462261 ,13.308551234503731076  ] 
dist 21=[9.7548761885819904100 ,13.301253655337341574  ] 
dist 22=[9.5486743732457194366 ,13.280680452353894410  ] 
dist 23=[9.3289175333338934177 ,13.273864526202335594  ] 
dist 24=[9.0309116572710006527 ,13.190582939182529250  ] 
dist 25=[8.7314247926574719004 ,13.147894929247008279  ] 
dist 26=[8.5057429024425430981 ,10.723779012863057025  ] 
dist 27=[8.2891675930895142172 ,10.679788938290650199  ] 
dist 28=[8.0260986535369226110 ,10.262217289792435535  ] 
dist 29=[7.7507665012997237248 ,10.184898226870914151  ] 
dist 30=[7.4851423959245372654 ,10.092895992207406323  ] 
dist 31=[7.1736423441882599795 ,10.072565568252490477  ] 
dist 32=[6.7148269639081897125 ,9.4154046773540128872 ] 
dist 33=[6.2523720937419619870 ,9.3320255990858818695 ] 
dist 34=[5.9263143816616609097 ,9.1664573498413977653 ] 
dist 35=[5.6352156433877131691 ,9.1240906197041792999 ] 
dist 36=[5.3125770141488625306 ,8.9744958360274212644 ] 
dist 37=[4.9912906409535820726 ,8.9420123565948578378 ] 
dist 38=[4.7055977972005273105 ,8.8924222804481696914 ] 
dist 39=[4.3889871037866587895 ,8.8786491388689074005 ] 
dist 40=[3.9440396186895901488 ,8.2580959883888979886 ] 
dist 41=[3.4896929026869237622 ,8.2430962912498511112 ] 
dist 42=[3.1354874154833783445 ,7.7284799976913567839 ] 
dist 43=[2.7840127350146531605 ,7.6756736393195212273 ] 
dist 44=[2.3405853518420738920 ,7.5605046705928531280 ] 
dist 45=[1.8676612845237084070 ,7.5362196800136160725 ] 
dist 46=[1.3982094022436605220 ,7.4047943903146369882 ] 
dist 47=[.83758433220016082371,7.3815004047845316712 ] 
dist 48=[0                     ,7.3329603020744115592 ] 
dist 49=[4.7687852554459923035 ,7.3202728888039724173 ] 
dist 50=[4.4624145790587673235 ,7.2172615711869485058 ] 
dist 51=[4.2280190021752639442 ,7.2005898156304672905 ] 
dist 52=[3.9996451077967769254 ,7.1720723794875783497 ] 
dist 53=[3.7173532205181322563 ,7.1655907918765967151 ] 
dist 54=[3.3704018167910346755 ,7.0624300795220259954 ] 
dist 55=[2.8015501470758242766 ,7.0442869028946427469 ] 
dist 56=[2.2336815390529246296 ,6.9564746133709502988 ] 
dist 57=[1.8544188803548779201 ,6.7956534999044729629 ] 
dist 58=[1.5379089997066870336 ,2.8261535694371008839 ] 
dist 59=[1.2209985296056104830 ,2.7736642972789042278 ] 
dist 60=[.9252564714876760620 ,2.2803268647521954507 ] 
dist 61=[.6934021802580727900 ,2.1919708401511014854 ] 
dist 62=[.4622100725383789558 ,2.0861307002628841078 ] 
dist 63=[.1691156380770846034 ,2.0682532810005537660 ] 
dist 64=[-.1160702773878409859 ,1.3854873073030705634 ] 
dist 65=[-.3156353456831041644 ,1.3024847719106648004 ] 
dist 66=[-.4921722162515285140 ,1.1356248246195570130 ] 
dist 67=[-.6852653048525706608 ,1.0937973369229143843 ] 
dist 68=[-.8759769509643926440 ,.94958395442445510881] 
dist 69=[-1.0429909266530875457 ,.91988877357691221001] 
dist 70=[-1.2259031451995129765 ,.88289966806729391301] 
dist 71=[-1.4801964099971005125 ,.8760621943613610697 ] 
dist 72=[-1.7301324996716395247 ,-.0622397665153838442 ] 
dist 73=[-1.8956202803221749462 ,-.1389501707966081377 ] 
dist 74=[-2.0321596013750681304 ,-.31231604777257314114] 
dist 75=[-2.1663259714364140377 ,-.34053956365387452209] 
dist 76=[-2.2899086930042329390 ,-.55300608731447559069] 
dist 77=[-2.3841232241297573925 ,-.58982646698570889416] 
dist 78=[-2.4755842794547200058 ,-.6473959459163509145 ] 
dist 79=[-2.5881583404377412618 ,-.66107937986209530559] 
dist 80=[-2.6960988539031902442 ,-.87316750548365462361] 
dist 81=[-2.7690309300150317059 ,-.89985103876658395888] 
dist 82=[-2.8308418882449142530 ,-.95628096775515551519] 
dist 83=[-2.8943082930642638583 ,-.96737654212100278947] 
dist 84=[-2.9545878128433103331 ,-1.0227770116156698054 ] 
dist 85=[-3.0036569242226001267 ,-1.0319434590471388025 ] 
dist 86=[-3.0543149589677385028 ,-1.0490603297766325559 ] 
dist 87=[-3.1209568595251336616 ,-1.0304509220538408068 ] 
dist 88=[-3.1846539400691609052 ,-.9458908140269285212 ] 
dist 89=[-3.2235355947570077504 ,-.81304502988386269595] 
dist 90=[-3.2520083629010256645 ,-.67822241471687576762] 
dist 91=[-3.2740718943529432217 ,-.58575599904526894611] 
dist 92=[-3.2913332859630905998 ,-.50605432893505895546] 
dist 93=[-3.3005965270059649079 ,-.42225713786652520052] 
dist 94=[-3.3058573974301000698 ,-.34161284421760264066] 
dist 95=[-3.3071044114445574284 ,-.2745122048653466776 ] 
dist 96=[-3.2775807523118017105 ,-.20405273258985641858] 
dist 97=[-3.2719685354940335677 ,-.10997506352409461526] 
dist 98=[-3.2660044145439803395 ,-.01628830051315678522] 
dist 99=[-3.2627098879237688434 ,.05261099898666499418] 
dist 100=[-3.2580750733355048211 ,.1169959991955075694 ] 
dist 101=[-3.2560745460495072969 ,.19263784854937267928] 
dist 102=[-3.2548435380197233662 ,.27034600067589422326] 
dist 103=[-3.2543335906593843226 ,.34299587205784474693] 
dist 104=[-2.8878792708518241328 ,.42635725035131285759] 
dist 105=[-2.8627963270930772218 ,.54689812131735550734] 
dist 106=[-2.7882399330278538007 ,.66720026182934408342] 
dist 107=[-2.7697785321310595776 ,.74960869116988394715] 
dist 108=[-2.6934128876544344617 ,.82059928330415746793] 
dist 109=[-2.6788592670961865890 ,.89524928614658166279] 
dist 110=[-2.6421913262269058636 ,.96716601900779476996] 
dist 111=[-2.6361914362030191792 ,1.0272297086255295072 ] 
dist 112=[-2.5679152040845464887 ,1.0905423040155704887 ] 
dist 113=[-2.5554107678069631456 ,1.1754539383866299582 ] 
dist 114=[-2.5329989222584171187 ,1.2602843839017172859 ] 
dist 115=[-2.5273378759077002820 ,1.3232742881494988160 ] 
dist 116=[-2.5089821894000257468 ,1.3827820376632731555 ] 
dist 117=[-2.5035286912693217630 ,1.4536907596620646691 ] 
dist 118=[-2.4993849457820796820 ,1.5271406781081440729 ] 
dist 119=[-2.4978896691825940873 ,1.5968131339528598128 ] 
dist 120=[-.99589736104604251968,1.6775909338362078645 ] 
dist 121=[-.86553797783591547134,1.7954550809162312513 ] 
dist 122=[-.64903251526363714651,1.9119187706200490448 ] 
dist 123=[-.62079928873730786419,1.9870969717939614306 ] 
dist 124=[-.35757460807057652366,2.0469796079405416306 ] 
dist 125=[-.3105071431845707611 ,2.1022748632600791057 ] 
dist 126=[-.25335525663599724726,2.1508832348117386040 ] 
dist 127=[-.24324344581801450886,2.1840250369073074870 ] 
dist 128=[.11555573899457022127,2.2124352521487513745 ] 
dist 129=[.15906440505052657625,2.2421235252240760996 ] 
dist 130=[.24743024934615864642,2.2688873624605807034 ] 
dist 131=[.2696999604493627561 ,2.2856022363995475696 ] 
dist 132=[.34747352217233667646,2.2982873986418904462 ] 
dist 133=[.36304973601245020034,2.3089333398192655722 ] 
dist 134=[.38459830767131336292,2.3175528696254761595 ] 
dist 135=[.38986051140221459173,2.3221328590829478297 ] 
dist 136=[.83695265609140633562,2.3246656914241572794 ] 
dist 137=[.87356389302740313   ,2.3250970691422787587 ] 
dist 138=[.95732155462127179099,2.1750487485404980860 ] 
dist 139=[.96944188191034098253,2.1612851532116067233 ] 
dist 140=[1.0741112198416389232 ,2.1333316584735643236 ] 
dist 141=[1.0920213970751641312 ,2.1255471872289594806 ] 
dist 142=[1.1157637819010793138 ,2.0945858647849698599 ] 
dist 143=[1.1200057199649260567 ,2.0879196145684564776 ] 
dist 144=[1.2310754203176498106 ,2.0719931157457716036 ] 
dist 145=[1.2437883014660173767 ,2.0673130316308367509 ] 
dist 146=[1.2714171045477588107 ,2.0417988287175266934 ] 
dist 147=[1.2753856406640346673 ,2.0358191909416502090 ] 
dist 148=[1.3039402142691826374 ,2.0267605839862224161 ] 
dist 149=[1.3081380531722320940 ,2.0237989300128669978 ] 
dist 150=[1.3152368339384885539 ,2.0163841489453926403 ] 
dist 151=[1.3163245766101641275 ,2.0136641637152568941 ] 
dist 152=[1.2144947078243432086 ,2.0118636856985094427 ] 
dist 153=[1.0302054489681797579 ,2.0108302710317351751 ] 
dist 154=[.84540455344606776398,1.5567046598350177864 ] 
dist 155=[.72119506614137471679,1.5634566803029128001 ] 
dist 156=[.61673291486633477775,1.5684576879580449893 ] 
dist 157=[.51089421134670051414,1.5702259624294181252 ] 
dist 158=[.41138498166670308913,1.5707542776462454450 ] 
dist 159=[.33223184786879114763,1.5707948748081669710 ] 
dist 160=[.25227542167410556692,1.5630916410654290589 ] 
dist 161=[.14955359847026692087,1.5611986570076089375 ] 
dist 162=[.04902394181625281617,1.5566506460736038589 ] 
dist 163=[-.02216702246714472922,1.5548550700204772993 ] 
dist 164=[-.08599421187020643155,1.5453123799842485735 ] 
dist 165=[-.15707893656472246746,1.5429184105034063735 ] 
dist 166=[-.2279966144780491717 ,1.5371250357427106899 ] 
dist 167=[-.29115624504315361377,1.5349649434805064519 ] 
dist 168=[-.36118165040893066543,1.4348062372826659580 ] 
dist 169=[-.45955413897469028199,1.4243499722756915433 ] 
dist 170=[-.55657675678052608729,1.4000489781801018629 ] 
dist 171=[-.62120464024871169401,1.3947984466868537512 ] 
dist 172=[-.67492693973535361025,1.3605908253790703933 ] 
dist 173=[-.728341380536718635  ,1.3538086985216140136 ] 
dist 174=[-.77792220607581621334,1.3416832436699301296 ] 
dist 175=[-.81631523445924380095,1.3386194313951653166 ] 
dist 176=[-.85413894418252161297,1.2824792596525438600 ] 
dist 177=[-.90144387308396383381,1.2745574443751811853 ] 
dist 178=[-.9471344800124341388 ,1.2561282623220164087 ] 
dist 179=[-.97850325702576547486,1.2519500516336744665 ] 
dist 180=[-1.0056101595298825662 ,1.2256629328606021634 ] 
dist 181=[-1.0342589401675544871 ,1.2203637591807506802 ] 
dist 182=[-1.0619571549319749460 ,1.2106897855715952765 ] 
dist 183=[-1.0852635906576460678 ,1.2081509305888072960 ] 
dist 184=[-1.1099891840478853810 ,.78152657969132729142] 
dist 185=[-1.1433637338835520952 ,.75318178616028044246] 
dist 186=[-1.1757387709792869780 ,.68965783352838137432] 
dist 187=[-1.1964676233847449391 ,.67963617817440287792] 
dist 188=[-1.2127853281545046132 ,.5965124297798228902 ] 
dist 189=[-1.2275199920909237565 ,.58141765819055008492] 
dist 190=[-1.2402393842918649701 ,.56033262427770660028] 
dist 191=[-1.2484980947364156008 ,.55426422584465832774] 
dist 192=[-1.2551325986615562504 ,.44349012454622530593] 
dist 193=[-1.2613572150924905914 ,.4293210097035810041 ] 
dist 194=[-1.2664990723329072378 ,.39882300716271892537] 
dist 195=[-1.2688035899516264280 ,.3917919393808986489 ] 
dist 196=[-1.2697515560508811785 ,.35801027713089939974] 
dist 197=[-1.2696219862316156117 ,.35197733075055900865] 
dist 198=[-1.2662797292594110711 ,.33816974718744056933] 
dist 199=[-1.2649433870424141021 ,.3355839954905584563 ] 
dist 200=[-1.2632785448992579018 ,.20177840209565608262] 
dist 201=[-1.2623434382602129645 ,.1890092786951847931 ] 
dist 202=[-1.2640790037571661246 ,.15997266904241880574] 
dist 203=[-1.2992841942415078800 ,.15497798085904300601] 
dist 204=[-1.3311447182064421439 ,.11834407478953842565] 
dist 205=[-1.3544500337170815823 ,.11180839371586637598] 
dist 206=[-1.3761165212699979471 ,.10127738642045389091] 
dist 207=[-1.4014237056672191416 ,.09875802661308381161] 
dist 208=[-1.4249864493399948034 ,.05718180848368922418] 
dist 209=[-1.4396772690922502532 ,.05186815800364969126] 
dist 210=[-1.4507840676603677580 ,.03951125367868916758] 
dist 211=[-1.4600150273569606270 ,.03766626373066310091] 
dist 212=[-1.4674096352321071606 ,.02131663461515330003] 
dist 213=[-1.4711732306460215061 ,.01839655723021303112] 
dist 214=[-1.4730228098591985242 ,.01463862095608965149] 
dist 215=[-1.4733291871746443205 ,.01379747771205562592] 
dist 216=[-1.0547652387123393628 ,-.07769312426532987139] 
dist 217=[-1.0522118029940203293 ,-.06895800870703131289] 
dist 218=[-.72685473015726359608,.06460451033408807531] 
dist 219=[-.70456643128694508409,.15401486814749677937] 
dist 220=[-.6550403133803122156 ,.2288245441745691032 ] 
dist 221=[-.64715533434173645262,.30400287101927091776] 
dist 222=[-.58227519981132035794,.37429981904231068145] 
dist 223=[-.57042279807256508925,.42959019112628074372] 
dist 224=[-.55369883298133771025,.48486815757304406426] 
dist 225=[-.54890324132965057547,.55511554375676979708] 
dist 226=[-.46069973852463712764,.62350246243702270848] 
dist 227=[-.44934277955304533932,.67134093114799073536] 
dist 228=[-.4248354917551003953 ,.71362226144043144159] 
dist 229=[-.41911149195080247908,.75978766789590692697] 
dist 230=[-.39160771038786443438,.80531226957650083227] 
dist 231=[-.38663804328084534237,.84503121297126410616] 
dist 232=[-.37530425530411588346,.88838904042629379689] 
dist 233=[-.37302693650939958181,.94846462829112831601] 
dist 234=[-.22391462890256905603,1.0073584511844447699 ] 
dist 235=[-.21208216227963963022,1.0459907132469195839 ] 
dist 236=[-.18466309174715940549,1.0774462669656538644 ] 
dist 237=[-.18034677658855503178,1.1076422808410512845 ] 
dist 238=[-.1441926812996903539 ,1.1349711118415039653 ] 
dist 239=[-.13769133678548622441,1.1549615394924691810 ] 
dist 240=[-.1287192164292417503 ,1.1735451496106556461 ] 
dist 241=[-.12613487815774473229,1.1952484803655798683 ] 
dist 242=[-.07965920729461265688,1.2154523755128438494 ] 
dist 243=[-.07378306464831442496,1.2280401265405757717 ] 
dist 244=[-.06115221050870010019,1.2375458026783263718 ] 
dist 245=[-.05834739725987664454,1.2454252668998250266 ] 
dist 246=[-.04457155726137268811,1.2517206216840464979 ] 
dist 247=[-.04216512933488869159,1.2548918472257545047 ] 
dist 248=[-.03671448331974047271,1.2564127406886162074 ] 

8 phat 2 dirichlet min maxes function [0, 0, 1, 0, 0, 1] 
dist 0=[12.436921663266994038  ,12.436921663266994038  ] 
dist 1=[12.294611784117924590  ,12.570105389765365134  ] 
dist 2=[12.173733716494608040  ,12.654484159980630004  ] 
dist 3=[12.044481000368063575  ,12.719885682559451146  ] 
dist 4=[11.868676323025222574  ,12.777172541474676579  ] 
dist 5=[11.674735644476257390  ,12.825349648713615909  ] 
dist 6=[11.472950168924213065  ,12.854316754859454784  ] 
dist 7=[11.225187555563674425  ,12.874954802277296767  ] 
dist 8=[10.847368217726754287  ,12.889817308978103825  ] 
dist 9=[10.465912586854988058  ,12.901180667949853355  ] 
dist 10=[10.203606285611109510  ,12.907825259492325104  ] 
dist 11=[9.9763756637039502107 ,12.912317138296253697  ] 
dist 12=[9.7351973077641656593 ,12.915077399648216036  ] 
dist 13=[9.5012831609061955886 ,12.916528241040731858  ] 
dist 14=[9.3031025665176201866 ,12.915787167885433270  ] 
dist 15=[9.0916048837475744238 ,12.913294179328269024  ] 
dist 16=[8.8044274381094955842 ,12.910597607268474967  ] 
dist 17=[8.5156522966899858806 ,12.901211218887558071  ] 
dist 18=[8.2977628896589259824 ,12.896460274416293913  ] 
dist 19=[8.0883927802435106312 ,12.887531952107738704  ] 
dist 20=[7.8336869624064155142 ,12.883763835684705083  ] 
dist 21=[7.5669003873773578150 ,12.863189258303667739  ] 
dist 22=[7.3092112908763441059 ,12.857703349829206008  ] 
dist 23=[7.0067808325287640261 ,12.837968200386807212  ] 
dist 24=[6.5610487967086057068 ,12.834447069999813925  ] 
dist 25=[6.1116650843909637191 ,12.779286628524551745  ] 
dist 26=[5.7946282980159232849 ,12.767074308760245351  ] 
dist 27=[5.5113797347994581857 ,12.748721425057732906  ] 
dist 28=[5.1971300673670638784 ,12.742430471965384010  ] 
dist 29=[4.8840156064411563253 ,12.596613239389301259  ] 
dist 30=[4.6053049862054323994 ,12.580543291609336418  ] 
dist 31=[4.2961973511033510538 ,12.463326727949616236  ] 
dist 32=[3.8615050493144657002 ,12.273098189042832094  ] 
dist 33=[3.4175034252774226592 ,10.240846162361280982  ] 
dist 34=[3.0711606988609536865 ,10.110393146217535075  ] 
dist 35=[2.7272980094614991570 ,9.8100772097992865006 ] 
dist 36=[2.2932129104425073532 ,9.7603797214877307682 ] 
dist 37=[1.8301195952275068042 ,9.3688295041510727991 ] 
dist 38=[1.3702335296661497335 ,9.2981526552499095011 ] 
dist 39=[.82089021907704212501,9.1935096654037680007 ] 
dist 40=[0                     ,9.1655179123364838855 ] 
dist 41=[6.9117079884992212805 ,8.6718602433065487589 ] 
dist 42=[6.6613389963972862733 ,8.6086761726515224847 ] 
dist 43=[6.4403661774071127653 ,8.4683499181525498266 ] 
dist 44=[6.1994248210064858177 ,8.4403903061191922053 ] 
dist 45=[5.9618836020429364237 ,8.2718447791131832871 ] 
dist 46=[5.7545106695450540349 ,8.2415676197203417749 ] 
dist 47=[5.5279386590023037498 ,8.1835560381269370343 ] 
dist 48=[5.2136183612442896181 ,8.1693417472123755870 ] 
dist 49=[4.8946317143828332590 ,7.6786770571636594276 ] 
dist 50=[4.6493992537115545266 ,7.6282679127191507577 ] 
dist 51=[4.4093915493946448451 ,7.5179073117548832465 ] 
dist 52=[4.1113015043963125924 ,7.4948727637979932362 ] 
dist 53=[3.7959357576584024268 ,7.3021664676453717863 ] 
dist 54=[3.4868406035396502628 ,7.2668431884189072048 ] 
dist 55=[3.1207703573451647662 ,7.1586986374298264802 ] 
dist 56=[2.5775526559214951941 ,7.0004765267138631372 ] 
dist 57=[2.0353458233771740419 ,5.8240335609625419267 ] 
dist 58=[1.6733184553814466508 ,5.7544300316849655210 ] 
dist 59=[1.3712957997997912997 ,5.6258236136077417137 ] 
dist 60=[1.0690576128058950660 ,5.5964510249143789368 ] 
dist 61=[.78711281002648036746,5.2471856430820583802 ] 
dist 62=[.56624654952298314073,5.2000443700116120454 ] 
dist 63=[.34617003751193090457,4.9871131177961591210 ] 
dist 64=[.06738309325970571467,4.6697991442539164424 ] 
dist 65=[-.20377933285586199398,1.8938985854837801759 ] 
dist 66=[-.39336447398528895612,1.7277970874546828370 ] 
dist 67=[-.56089931085277165509,1.3462270765002529251 ] 
dist 68=[-.74387945613300058709,1.2889272365482525447 ] 
dist 69=[-.9244467728317956788 ,.8013382520236835612 ] 
dist 70=[-1.0823330920691584240 ,.7158567372661507419 ] 
dist 71=[-1.2550452106359665908 ,.6773218828491007130 ] 
dist 72=[-1.4949051651983098903 ,.6706244578746694181 ] 
dist 73=[-1.7305473016388108790 ,.0004825320313277149 ] 
dist 74=[-1.8863922146703686668 ,-.0691879319322278549 ] 
dist 75=[-2.0147782046480456580 ,-.2179783759646277201 ] 
dist 76=[-2.1406073885905685258 ,-.2480266438239885328 ] 
dist 77=[-2.2562974970115701177 ,-.4026613033710523126 ] 
dist 78=[-2.3441364862103483121 ,-.4282284463882282350 ] 
dist 79=[-2.4290636688537107119 ,-.4836118851064846817 ] 
dist 80=[-2.5331116673642920716 ,-.4920463025043188465 ] 
dist 81=[-2.6326359129658252258 ,-.9146578468267300196 ] 
dist 82=[-2.6994730716820491337 ,-.95405441159584599266] 
dist 83=[-2.7556757116374620732 ,-1.0342357269894720051 ] 
dist 84=[-2.8126717033454697862 ,-1.0528558804045840699 ] 
dist 85=[-2.8663600505992658787 ,-1.1204902265536278448 ] 
dist 86=[-2.9093376463659222062 ,-1.1332695146032999492 ] 
dist 87=[-2.9530544899878031663 ,-1.1465657665479990430 ] 
dist 88=[-3.0097065799860402640 ,-1.1445858004241814510 ] 
dist 89=[-3.0635554448333374111 ,-1.1367435735953904297 ] 
dist 90=[-3.0960621284894317847 ,-1.1216696164066125200 ] 
dist 91=[-3.1194335890895329287 ,-1.0983768036805235076 ] 
dist 92=[-3.1367430176174587592 ,-1.0576631541801989739 ] 
dist 93=[-3.1499842538394698590 ,-1.0086047492062529875 ] 
dist 94=[-3.1570817505490017186 ,-.95194563812252745663] 
dist 95=[-3.1611039211821806485 ,-.8785347184301764681 ] 
dist 96=[-3.1620388187925366643 ,-.76250317312596213722] 
dist 97=[-3.1251330579894771504 ,-.6445415228756417442 ] 
dist 98=[-3.1187359158813675423 ,-.5634111748631186274 ] 
dist 99=[-3.1107314468796327955 ,-.4932472774743795047 ] 
dist 100=[-3.1072302237366359359 ,-.4191203076690168260 ] 
dist 101=[-3.1009390725242604285 ,-.3475725510739264618 ] 
dist 102=[-3.0984865926347943547 ,-.2877157456941330279 ] 
dist 103=[-3.0969943571915991939 ,-.2245813391720747421 ] 
dist 104=[-3.0964118593913041249 ,-.1399250876014350837 ] 
dist 105=[-2.8074819909854120028 ,-.0554643527345946746 ] 
dist 106=[-2.8117302391391640018 ,.0068911514951412071 ] 
dist 107=[-2.8137300978003305350 ,.0653983220258217402 ] 
dist 108=[-2.8137581480085786137 ,.1344770999662289362 ] 
dist 109=[-2.8115696772269243139 ,.2056275023492247615 ] 
dist 110=[-2.8103336385220592853 ,.2724207770870043569 ] 
dist 111=[-2.8035341219831689681 ,.3492752900292881286 ] 
dist 112=[-2.7890486263104952209 ,.4606580816424637570 ] 
dist 113=[-2.4829379289010319921 ,.5719193749519472529 ] 
dist 114=[-2.4596220730566913689 ,.6482896973344593084 ] 
dist 115=[-2.4118378753810917642 ,.7142432968468597860 ] 
dist 116=[-2.3991666129154171286 ,.7838556550851057280 ] 
dist 117=[-2.3676454534707402219 ,.8510768694987176035 ] 
dist 118=[-2.3623711973183424388 ,.9074716196216053839 ] 
dist 119=[-2.3582256673481020323 ,.9671382827020898510 ] 
dist 120=[-2.3567239675939631209 ,1.0474463303551319163 ] 
dist 121=[-1.0459341974995622406 ,1.1278083899275448623 ] 
dist 122=[-.9842875901223907773 ,1.1876929684973044912 ] 
dist 123=[-.8450414532547518314 ,1.2444770053886489568 ] 
dist 124=[-.8212034993616724945 ,1.3124433025890794155 ] 
dist 125=[-.6141355808709469744 ,1.3830093685782946131 ] 
dist 126=[-.5771113450236533981 ,1.4501922698476342358 ] 
dist 127=[-.4703497363537521219 ,1.5282739627657406659 ] 
dist 128=[-.3265670623539380626 ,1.6424281461298943406 ] 
dist 129=[.13030166338960789768,1.7552993424062621420 ] 
dist 130=[.17168713285471855552,1.8282511693892200460 ] 
dist 131=[.25570124496032405692,1.8864656528794865430 ] 
dist 132=[.27686061820358779418,1.9404007583536736466 ] 
dist 133=[.35066781096699897644,1.9879391143911378421 ] 
dist 134=[.36546425635659103564,2.0205729917414690713 ] 
dist 135=[.38572080609863661017,2.0487859169171598303 ] 
dist 136=[.39049101294022024792,2.0786463289536709060 ] 
dist 137=[.81625601441411123843,2.1056728407931338220 ] 
dist 138=[.8510549157520466065 ,2.1225524892025940816 ] 
dist 139=[.93068595576113189209,2.1353630080482633849 ] 
dist 140=[.94218033151592204585,2.1461141027159826251 ] 
dist 141=[1.0417374740549883994 ,2.1548183090717112756 ] 
dist 142=[1.0587702357717498724 ,2.1594418237198255261 ] 
dist 143=[1.0812646783702330051 ,2.1619965498842061322 ] 
dist 144=[1.0852047396456773993 ,2.1624261565516902152 ] 
dist 145=[1.1910821261456333620 ,2.0300973091602867985 ] 
dist 146=[1.2031844948896490481 ,2.0178739543696437385 ] 
dist 147=[1.2294273206137516171 ,1.9931842939166696882 ] 
dist 148=[1.2332405797686174302 ,1.9863033022056072029 ] 
dist 149=[1.2601681304343408368 ,1.9589809539216327687 ] 
dist 150=[1.2641124827209703348 ,1.9530124514775220721 ] 
dist 151=[1.2709591149791579646 ,1.9388954720023402865 ] 
dist 152=[1.2720111078603980481 ,1.9344824419878744007 ] 
dist 153=[1.4234479611024044567 ,1.9121396761932126574 ] 
dist 154=[1.4286927826237443348 ,1.9067622964019874055 ] 
dist 155=[1.4373211534194399617 ,1.8987491648290256079 ] 
dist 156=[1.4388672898246460991 ,1.8960527689742728136 ] 
dist 157=[1.3505791258474371267 ,1.8894517334203741810 ] 
dist 158=[1.2568738501143694572 ,1.8869852364786566917 ] 
dist 159=[1.1433446302547968466 ,1.8853208560065047013 ] 
dist 160=[.97201656461898499718,1.8843003008228729278 ] 
dist 161=[.8001931263156674479 ,1.4877060426675485747 ] 
dist 162=[.68468280504114194794,1.4856611558285054802 ] 
dist 163=[.58751225594089345808,1.4808574467580286907 ] 
dist 164=[.48902251412591679437,1.4790350964814984952 ] 
dist 165=[.39639901854766832221,1.4695735499366438155 ] 
dist 166=[.32268516022118224035,1.4672417526658412021 ] 
dist 167=[.24818880836967768963,1.4614995673219019584 ] 
dist 168=[.15243590239169676101,1.4593588150295442823 ] 
dist 169=[.05870555218077269560,1.3616489648790815804 ] 
dist 170=[-.00770356378751451951,1.3514973406538886009 ] 
dist 171=[-.06727745085024853594,1.3279333541712284932 ] 
dist 172=[-.13367639067719359906,1.3228591134444084819 ] 
dist 173=[-.19994846898185813104,1.2898259529982569057 ] 
dist 174=[-.25901547737499313016,1.2832931233095074174 ] 
dist 175=[-.32453996611925263911,1.2716039999880963621 ] 
dist 176=[-.41663415742429474795,1.2686556515480184005 ] 
dist 177=[-.50748296629196487811,1.2149735701257824195 ] 
dist 178=[-.56802775275290610362,1.2074072027654361419 ] 
dist 179=[-.618388046435677452  ,1.1897685300557619932 ] 
dist 180=[-.66851216276743928548,1.1858207747463110264 ] 
dist 181=[-.7150726066205731439 ,1.1605826870150506775 ] 
dist 182=[-.7511830643142360986 ,1.1555028884897017143 ] 
dist 183=[-.78681126080070862663,1.1463267740766961109 ] 
dist 184=[-.83144391214949248275,1.1439470387071227929 ] 
dist 185=[-.87458951443788174529,.73636422024657607541] 
dist 186=[-.9042717065165633574 ,.70933420625004520149] 
dist 187=[-.92998596883319995205,.64800205166439579288] 
dist 188=[-.95726516046912034059,.63848741535859455528] 
dist 189=[-.98370158457455125422,.55967461926521383024] 
dist 190=[-1.0060464245315793189 ,.54536703357322741214] 
dist 191=[-1.0298391278689567880 ,.52535137389608619599] 
dist 192=[-1.0620666273808148763 ,.51960271138792370012] 
dist 193=[-1.0933620947398187142 ,.41478498167502018694] 
dist 194=[-1.1134278965257256045 ,.40137988360879303202] 
dist 195=[-1.1292558722459541709 ,.37250147170770076686] 
dist 196=[-1.1436040870063813915 ,.36587322224500328498] 
dist 197=[-1.1560296035606289257 ,.33381616810233673867] 
dist 198=[-1.1641687817657007839 ,.32809212814728370206] 
dist 199=[-1.1707876660335960718 ,.31505935140243268044] 
dist 200=[-1.1771339314448957924 ,.31256432389225731323] 
dist 201=[-1.1824420044294002830 ,.18684600497573563211] 
dist 202=[-1.1849091256513802244 ,.17482455789809958105] 
dist 203=[-1.2017778922189696948 ,.14753177159609502993] 
dist 204=[-1.2350791469819713802 ,.14280177495223632165] 
dist 205=[-1.2652117839107835146 ,.10849963286199885848] 
dist 206=[-1.2872450828876313010 ,.10238390612446377615] 
dist 207=[-1.3077209487801533964 ,.09239889145474123772] 
dist 208=[-1.3316257206813984643 ,.09004794973822047484] 
dist 209=[-1.3538766674273399274 ,.05159794878290436797] 
dist 210=[-1.3677392124503886035 ,.04665375928473563868] 
dist 211=[-1.3782076115369506094 ,.03526672139841087096] 
dist 212=[-1.3868860349170708917 ,.03347266706873315498] 
dist 213=[-1.3938210250775046722 ,.01872517100245178212] 
dist 214=[-1.3973177766160548386 ,.01609842610143408194] 
dist 215=[-1.3990180700086319849 ,.01240177762211110080] 
dist 216=[-1.3992791880931962089 ,.01137322061151405954] 
dist 217=[-1.0394762897975504334 ,-.07991859114210052947] 
dist 218=[-1.0338127213860960980 ,-.08351989499310845768] 
dist 219=[-1.0211065873103375962 ,-.08939690796280980867] 
dist 220=[-1.0175722305683010958 ,-.09074730267620891637] 
dist 221=[-1.0004665764427707241 ,-.09261033750251264091] 
dist 222=[-.99691813475315100827,-.09171294255016137401] 
dist 223=[-.98919508962074766438,-.08923150182416582482] 
dist 224=[-.98680467192699153848,-.06342155478413797960] 
dist 225=[-.68333386362395363134,.06119202919282247922] 
dist 226=[-.66253302623100575107,.14461333437848358917] 
dist 227=[-.61559082169721557742,.21441342217111270638] 
dist 228=[-.60827564769487793602,.28455948322194223248] 
dist 229=[-.5481944508978320585 ,.3501518915900529067 ] 
dist 230=[-.53721449549873686444,.40174318170597833757] 
dist 231=[-.52168767258578295488,.45332378923819471752] 
dist 232=[-.51724406607920724796,.51887352379944497983] 
dist 233=[-.43552215831585364423,.58268728127029746923] 
dist 234=[-.42499400718797896276,.62732620107050967095] 
dist 235=[-.40225419041708886189,.66677897257729015182] 
dist 236=[-.39695400504971405721,.70985472846910999382] 
dist 237=[-.37135844043617890665,.75233163892885755196] 
dist 238=[-.36672894277165880161,.78938980879442981258] 
dist 239=[-.35506539314928820765,.82984149011328566388] 
dist 240=[-.34310126307903129525,.88588819015722401132] 
dist 241=[-.21251317810056682217,.94083093272394888164] 
dist 242=[-.201396387907595683  ,.97686818417122912758] 
dist 243=[-.17560577393072398575,1.0062070501964709844 ] 
dist 244=[-.17156964967656334701,1.0343646988003580723 ] 
dist 245=[-.13747409786805645327,1.0598442696521226993 ] 
dist 246=[-.13134040401377739409,1.0784742016679583257 ] 
dist 247=[-.12295963314713231161,1.0957851667052957559 ] 
dist 248=[-.12059092046072967104,1.1159905322220185168 ] 
dist 249=[-.07639336217445095360,1.1347936745401960200 ] 
dist 250=[-.07081673154108537801,1.1464975124252902522 ] 
dist 251=[-.05889173087129579406,1.1553224737427567390 ] 
dist 252=[-.05618478366535530757,1.1626137333389680189 ] 
dist 253=[-.04336966114837387671,1.1684204773605169724 ] 
dist 254=[-.04113535803767181979,1.1713092423789144044 ] 
dist 255=[-.03591933163007017320,1.1726844119142589540 ] 

8 phat 2 dirichlet min maxes function [2, 0, 0, 1, 2, 1, 1, 0, 2] 
dist 0=[12.910534707771907252  ,12.910534707771907252  ] 
dist 1=[12.863517927390143758  ,12.956740845191933700  ] 
dist 2=[12.721710922619216040  ,13.029665290179416266  ] 
dist 3=[12.568641631914038567  ,13.096328071288894629  ] 
dist 4=[12.436410242284111518  ,13.154416396337352637  ] 
dist 5=[12.293154927739600841  ,13.193050587282016375  ] 
dist 6=[12.096001840305088537  ,13.225091687190727300  ] 
dist 7=[11.877516085003985795  ,13.256810843662752349  ] 
dist 8=[11.648953669563535434  ,13.286409091082233759  ] 
dist 9=[11.367535001134676749  ,13.309966662937949370  ] 
dist 10=[10.937682906917057520  ,13.333755140191784139  ] 
dist 11=[10.504838305689216648  ,13.364274141776191406  ] 
dist 12=[10.211451984463078869  ,13.397007598198347806  ] 
dist 13=[9.9619562690246688947 ,13.429646667384533385  ] 
dist 14=[9.7046225317038097744 ,13.468662068845716621  ] 
dist 15=[9.4597032506937689175 ,13.526882090792217079  ] 
dist 16=[9.2598488560365730720 ,13.584216084687767644  ] 
dist 17=[9.0532647222706379935 ,13.619689032365032505  ] 
dist 18=[8.7814286309438449143 ,13.646135853566912030  ] 
dist 19=[8.5121723633025650973 ,13.667389069664071861  ] 
dist 20=[8.3159019738440630637 ,13.683811142885143651  ] 
dist 21=[8.1340730497520142469 ,13.690945541664739972  ] 
dist 22=[7.9225638830169164579 ,13.692673367072289137  ] 
dist 23=[7.7062411913009050841 ,13.691745484787143597  ] 
dist 24=[7.5051582045322453067 ,13.678849226191959475  ] 
dist 25=[7.2751933655324880592 ,13.674444013220992930  ] 
dist 26=[6.9433621464043868914 ,13.656021905480058300  ] 
dist 27=[6.6119486542511328949 ,13.652296268800286040  ] 
dist 28=[6.3836516805409370816 ,13.583868492357705969  ] 
dist 29=[6.1854745313569001071 ,13.568128856076016211  ] 
dist 30=[5.9745123500593060799 ,13.503667790514888891  ] 
dist 31=[5.7695409419564348676 ,13.386745386025114226  ] 
dist 32=[5.5953178308020096234 ,11.666060295854601821  ] 
dist 33=[5.4089019522386280713 ,11.546863858376245858  ] 
dist 34=[5.1551603538848257411 ,11.260397820466535084  ] 
dist 35=[4.8997152032994402899 ,11.219068322940294868  ] 
dist 36=[4.7064820866395248804 ,10.803862200364198239  ] 
dist 37=[4.5203159400482620092 ,10.726153369959763786  ] 
dist 38=[4.2931287288625708465 ,10.639395298293017626  ] 
dist 39=[4.0547645146291557565 ,10.623239001362172227  ] 
dist 40=[3.8238904530216666360 ,9.9238892081482796256 ] 
dist 41=[3.5524189022458682766 ,9.8352768617327198298 ] 
dist 42=[3.1516749845825407064 ,9.6634049304622225563 ] 
dist 43=[2.7524940263218332453 ,9.6201559053641767432 ] 
dist 44=[2.4872721127197994041 ,9.4732557705199558146 ] 
dist 45=[2.2673255669808518631 ,9.4391804623202372105 ] 
dist 46=[2.0492292389683553346 ,9.4014044263193109623 ] 
dist 47=[1.8469438613770017445 ,9.3913048150340890577 ] 
dist 48=[1.6902344855059428054 ,7.8827851393137725264 ] 
dist 49=[1.5356494377146492876 ,7.7550540709147255512 ] 
dist 50=[1.3418583370077345262 ,7.4744329584785793785 ] 
dist 51=[1.1541866769178459243 ,7.4142097245514843539 ] 
dist 52=[1.0240761508360590248 ,7.0839983035480551859 ] 
dist 53=[.91018341714850145857,7.0241448501297540955 ] 
dist 54=[.7873762518715941871 ,6.9012397254012587394 ] 
dist 55=[.66703551151389896856,6.8686026399286910846 ] 
dist 56=[.56300544737286265069,6.5637963636150685027 ] 
dist 57=[.45014171837113591367,6.5163843855785883242 ] 
dist 58=[.29446392007739430397,6.4229420820701548794 ] 
dist 59=[.14173344492599321625,6.3988999607371176426 ] 
dist 60=[.04065705828520665462,6.3137242122313873457 ] 
dist 61=[-.04275344341238956474,6.2947191022464861228 ] 
dist 62=[-.12482382243682064269,6.2651584320753642567 ] 
dist 63=[-.2131513183437365898 ,6.2568435769759839470 ] 
dist 64=[-.41159532808850613849,2.5974515098637946073 ] 
dist 65=[-.54719340596111770243,2.3989465664611652809 ] 
dist 66=[-.66379496593211253924,1.9352577060874096678 ] 
dist 67=[-.78626137016381432271,1.8688339626235627943 ] 
dist 68=[-.90432313726407614991,1.2505410037966088915 ] 
dist 69=[-1.0033106577083162409 ,1.1404020828728383804 ] 
dist 70=[-1.1081033250346705269 ,1.0068627340357527339 ] 
dist 71=[-1.2493907174710184925 ,.98420541192393751669] 
dist 72=[-1.3866332827206177568 ,.17065456902579025636] 
dist 73=[-1.4752485279507021280 ,.19610306288267825353] 
dist 74=[-1.5459335767173929676 ,.23847254540565983211] 
dist 75=[-1.6114559718857815709 ,.28188972430179984036] 
dist 76=[-1.6692956506648201843 ,.31152867344743537038] 
dist 77=[-1.7092509529940235059 ,.33684639386668878071] 
dist 78=[-1.7440938990419972668 ,.36300437494389582869] 
dist 79=[-1.7814868984010529480 ,.38781150538935268545] 
dist 80=[-1.9589640396883258113 ,.4077344968120306348 ] 
dist 81=[-2.1311994144778212821 ,.42796952008171397993] 
dist 82=[-2.2721358279543518961 ,.45402501825428725369] 
dist 83=[-2.4086720303303932851 ,.47941766383873710238] 
dist 84=[-2.5331441654941235753 ,.49700470599870938718] 
dist 85=[-2.6258361717317554048 ,.51230829985415076862] 
dist 86=[-2.7136942328049450806 ,.5285771750804245867 ] 
dist 87=[-2.8188375818236485463 ,.54429392709195070864] 
dist 88=[-2.9181421832726506891 ,.55739051979064108722] 
dist 89=[-2.9826517790108197468 ,.57112164772656770595] 
dist 90=[-3.0345116949552874067 ,.58937098326481231513] 
dist 91=[-3.0832301227159828557 ,.60690901945376951493] 
dist 92=[-3.1266592896126190763 ,.6177975287806148493 ] 
dist 93=[-3.1573697013537390623 ,.62593049505439642118] 
dist 94=[-3.1848996987414150748 ,.63245963428061101562] 
dist 95=[-3.2156172414077094201 ,.63749884648022684453] 
dist 96=[-3.2433740423850569765 ,.6396791081953232284 ] 
dist 97=[-3.2590640492907119197 ,.64063139323868147104] 
dist 98=[-3.2690671235810020714 ,.64076629821130399942] 
dist 99=[-3.2740750733844745861 ,.63512726354727182831] 
dist 100=[-3.2765717286502321983 ,.63362845695844539014] 
dist 101=[-3.2765276172594694182 ,.63079067111516604208] 
dist 102=[-3.2748089370667387504 ,.62972784512594385531] 
dist 103=[-3.2734406854230150749 ,.62428700393002429981] 
dist 104=[-3.2255549817000503700 ,.62288238316839689525] 
dist 105=[-3.2174998880266439176 ,.61796482866820226618] 
dist 106=[-3.2015443953770604282 ,.6170867885180152596 ] 
dist 107=[-3.1966435544835828045 ,.39245190330768081645] 
dist 108=[-3.1752169471882490266 ,.37589875004122140437] 
dist 109=[-3.1701419681711694681 ,.33655797147846806047] 
dist 110=[-3.1557517406784011872 ,.33003778580535210717] 
dist 111=[-3.1521023454503580176 ,.27365242003112193373] 
dist 112=[-2.8618569742753564379 ,.26292991603585034648] 
dist 113=[-2.8340673904328392633 ,.24865827911382310285] 
dist 114=[-2.7715736790558813888 ,.24407409236295469795] 
dist 115=[-2.7573400899561681847 ,.15200473530563038004] 
dist 116=[-2.6768116302398768849 ,.13976463146517850981] 
dist 117=[-2.6612858045711748351 ,.1144852263443105452 ] 
dist 118=[-2.6305034941458435502 ,.09629228320148256939] 
dist 119=[-2.6221343120898691593 ,.03888899932558702761] 
dist 120=[-2.5156159630467769275 ,-.54028620908925646954] 
dist 121=[-2.5001966231828610473 ,-.51499242374126634374] 
dist 122=[-2.4618122582780198907 ,-.47771988864981872287] 
dist 123=[-2.4555593838179200014 ,-.44019056444372994953] 
dist 124=[-2.3940009324560274683 ,-.41386978185560709911] 
dist 125=[-2.3817220402221270426 ,-.39052955014161726418] 
dist 126=[-2.3673701961206633656 ,-.3649192248644880975 ] 
dist 127=[-2.3626499258937871076 ,-.2458592188469725726 ] 
dist 128=[-1.4003135528488195753 ,.02882272276797251590] 
dist 129=[-1.3519534149837274367 ,.21259581000180879713] 
dist 130=[-1.2395972154399489515 ,.36625581173820198067] 
dist 131=[-1.2216967287001707990 ,.52052130939720361957] 
dist 132=[-1.0720723157427651626 ,.66468711270526395114] 
dist 133=[-1.0449493345954642120 ,.77796043756354486651] 
dist 134=[-1.0074153186374142951 ,.89110825405411704944] 
dist 135=[-.99652404904376034323,1.0347723602466449780 ] 
dist 136=[-.79768737294826370844,1.1745901679512990443 ] 
dist 137=[-.77231555984381621723,1.2723574233592098966 ] 
dist 138=[-.71792794227361909465,1.3587344508671273618 ] 
dist 139=[-.70527549857643565558,1.4530048834875482418 ] 
dist 140=[-.64583555856660230269,1.5459517823265628840 ] 
dist 141=[-.63527214331371429903,1.6270363442572445416 ] 
dist 142=[-.61062300228071230973,1.7155488786261908599 ] 
dist 143=[-.6065079656249793721 ,1.8381991300524997021 ] 
dist 144=[-.3663948549753489527 ,1.9584664136692969806 ] 
dist 145=[-.34369272909314904597,2.0374499117449599986 ] 
dist 146=[-.29194510551590346922,2.1018707055122331049 ] 
dist 147=[-.28321373656933423029,2.1646489498506267044 ] 
dist 148=[-.21761876553691962602,2.2246849332768040639 ] 
dist 149=[-.20592745889508287233,2.2685390478420030858 ] 
dist 150=[-.18761945046981401074,2.3092489313848355252 ] 
dist 151=[-.18310050865144528649,2.3567116155317720254 ] 
dist 152=[-.10756701320244171927,2.4008572672698322219 ] 
dist 153=[-.09798638674923259628,2.4283028823458021712 ] 
dist 154=[-.07579070922470978843,2.4489609327536210338 ] 
dist 155=[-.07243478929892051141,2.4659642629841407905 ] 
dist 156=[-.04334930255125898780,2.4794560583511897456 ] 
dist 157=[-.03817705863253118484,2.4860720108369113848 ] 
dist 158=[-.03132548206936942504,2.4894158467155054106 ] 
dist 159=[-.02966779811690347941,2.4898233892072618399 ] 
dist 160=[.03553519947562974560,.5243675840820046524 ] 
dist 161=[.03896812699757277773,.52980335054086066519] 
dist 162=[.03958645926052385620,.53557093755622968578] 
dist 163=[.04483501437706840854,.54077761490968473044] 
dist 164=[.04577902556671440019,.54397027207293354109] 
dist 165=[.04646884363540514389,.54632218385453808831] 
dist 166=[.04620647089732014194,.54816656827669253176] 
dist 167=[.04547873582412567429,.54955937815290600437] 
dist 168=[.04410883577033639554,.55010536715970154314] 
dist 169=[.04199720379803008087,.55023613282942065594] 
dist 170=[.03830356655008400347,.55011184779659301213] 
dist 171=[.03441070692643380957,.52576016285186545124] 
dist 172=[.03150236100820545993,.52344709918184113025] 
dist 173=[.02873895751617020603,.51779475155268891322] 
dist 174=[.02542536802038958662,.51662067475013267664] 
dist 175=[.02198385816594601839,.50761311811650180068] 
dist 176=[.01870877833537047996,.50574893367601487928] 
dist 177=[.01490502049473481645,.50291829687796655447] 
dist 178=[.00934931352320183488,.50205864438843816356] 
dist 179=[.00359177449301120473,.48352863850180433029] 
dist 180=[-.00101915550306071189,.48091403369535344047] 
dist 181=[-.00570612341929913099,.4753708785859299699 ] 
dist 182=[-.01176786156665348459,.47377623629930409948] 
dist 183=[-.01830327805624806384,.46709005635377700132] 
dist 184=[-.02488449994969315410,.46574731502798357921] 
dist 185=[-.03280842244823583769,.46210055203220234747] 
dist 186=[-.04471321803254004832,.46150302140463140302] 
dist 187=[-.05679162054612923396,.41205955427685686972] 
dist 188=[-.06540981738769301080,.40727731271518889798] 
dist 189=[-.07320536769503263429,.39621136077234298662] 
dist 190=[-.08199414804293096585,.39409875405812654625] 
dist 191=[-.09082624109003740705,.39195191092015916104] 
dist 192=[-.09879504529848376798,.37621787347253927901] 
dist 193=[-.10771644965914684969,.37149160203488881635] 
dist 194=[-.12035798865167573117,.37030460912455273882] 
dist 195=[-.13329946337754558337,.34827205865965254868] 
dist 196=[-.14342032568979800573,.34528067904864762496] 
dist 197=[-.15348697042910061511,.3384570237029829506 ] 
dist 198=[-.16965331780196976845,.33696557065769618037] 
dist 199=[-.19693038736810657154,.32784420083622564109] 
dist 200=[-.22350187695394029898,.32607154976836317915] 
dist 201=[-.24212422072571724436,.32275448670242291276] 
dist 202=[-.25862162787177767163,.32189386516559651545] 
dist 203=[-.27669588852759754032,.19194992137255869865] 
dist 204=[-.2945576944733453313 ,.18326370307634656143] 
dist 205=[-.31020557434053582529,.16324309271333333446] 
dist 206=[-.32734248415461886454,.15996504638001384546] 
dist 207=[-.35115876522124518146,.13382134224962938486] 
dist 208=[-.37454431050509352937,.12910966145549608336] 
dist 209=[-.38995879816370855951,.1222266971713376194 ] 
dist 210=[-.40259465280449849205,.12036129731140889045] 
dist 211=[-.4148688706072572371 ,.08740229471459792185] 
dist 212=[-.42607634214508483929,.08320147589336798124] 
dist 213=[-.43444646809152848641,.07391554020210581544] 
dist 214=[-.44240126865805298346,.07205191085036201344] 
dist 215=[-.45194799603452632995,.06107338605318915073] 
dist 216=[-.46097275341341887767,.05911733367616161395] 
dist 217=[-.46684030868396827488,.05529454783630946259] 
dist 218=[-.47156045207528379904,.05434641225899091326] 
dist 219=[-.4759969049720458652 ,.02237892664332787460] 
dist 220=[-.47995003936355075387,.01912134957530774586] 
dist 221=[-.48273753802287343644,.01212198858204444387] 
dist 222=[-.48522563872716222637,.01058291459289284999] 
dist 223=[-.48798172231333867751,.00297983664017396361] 
dist 224=[-.49044932913869966486,.00165883943393448154] 
dist 225=[-.49178385543148620201,-.00132310173308979841] 
dist 226=[-.49255401218134344287,-.00183867111657798430] 
dist 227=[-.49276459584430452354,-.00630586194389066703] 
dist 228=[-.4926892818681947555 ,-.00712105266457676653] 
dist 229=[-.49251159490124595609,-.00765253193688620011] 
dist 230=[-.49185013950287036386,-.00736057306221222995] 
dist 231=[-.49146803315185306382,-.00665131123627822101] 
dist 232=[-.48566985669221483572,-.00536884601437498068] 
dist 233=[-.48463474283977976235,-.00341081298170547018] 

8 phat 2 dirichlet min maxes function [1, 1, 1, 0, 2, 1, 2, 0, 2] 
dist 0=[6.6028816776060622337 ,6.6028816776060622337 ] 
dist 1=[6.5890504096316999125 ,6.6204978258899124623 ] 
dist 2=[6.5513442537981082753 ,6.6447675122074822577 ] 
dist 3=[6.4947513135923481444 ,6.6826708038663017760 ] 
dist 4=[6.4004506937957952438 ,6.7420881907189006761 ] 
dist 5=[6.2976872528550243585 ,6.7925042095335626061 ] 
dist 6=[6.2072469506325290048 ,6.8463793767399620673 ] 
dist 7=[6.1077872206948455511 ,6.9196300428367009886 ] 
dist 8=[5.9689506854367699669 ,6.9950123098263682619 ] 
dist 9=[5.8140575905639711237 ,7.0574126234152514045 ] 
dist 10=[5.6503786558387701894 ,7.1227423065393025823 ] 
dist 11=[5.4475846343077923920 ,7.2098416003948126759 ] 
dist 12=[5.1362476565171526214 ,7.3051142052389226382 ] 
dist 13=[4.8189742453829956550 ,7.4031338349443269815 ] 
dist 14=[4.5924369448640098993 ,7.5227275431814241714 ] 
dist 15=[4.3872177018174819670 ,7.7042870311379117374 ] 
dist 16=[4.1552074132614647144 ,7.8859216402527836706 ] 
dist 17=[3.9215057069564954520 ,8.0058160741497020434 ] 
dist 18=[3.7095210915966819963 ,8.1043629977455182571 ] 
dist 19=[3.4711456592833673134 ,8.2006177178697945602 ] 
dist 20=[3.1318906902889369117 ,8.2889305048630170510 ] 
dist 21=[2.7835950861975560905 ,8.3557137070011761816 ] 
dist 22=[2.5090604005411808708 ,8.4200386722976401234 ] 
dist 23=[2.2338110606118510013 ,8.4985203775007629616 ] 
dist 24=[1.8826566896420034876 ,8.5734501081684075976 ] 
dist 25=[1.5061539724717145182 ,8.6235691855648083403 ] 
dist 26=[1.1295207812162802928 ,8.6655006257143095406 ] 
dist 27=[.67760486918525661815,8.7076839640878899605 ] 
dist 28=[0                     ,8.7472035173071535862 ] 
dist 29=[7.4166217584791895762 ,8.7784817942643674407 ] 
dist 30=[7.4191940085879537328 ,8.8099662381812525218 ] 
dist 31=[7.4110394064136464598 ,8.8503122250768423526 ] 
dist 32=[7.3947249739371476906 ,8.8885407281626823873 ] 
dist 33=[7.3628576022152671853 ,8.9115565561903141897 ] 
dist 34=[7.3231228290542823923 ,8.9280203614003219144 ] 
dist 35=[7.2753421282515825856 ,8.9400429595413209525 ] 
dist 36=[7.2121357392201728730 ,8.9488738993345157499 ] 
dist 37=[7.1107060806318475850 ,8.9525709371400167565 ] 
dist 38=[7.0050763953355545318 ,8.9536958685942615671 ] 
dist 39=[6.9250714888806477452 ,8.9531774993906310301 ] 
dist 40=[6.8479001370782288884 ,8.9279207673554890186 ] 
dist 41=[6.7536015686585552398 ,8.9229201145934578736 ] 
dist 42=[6.6546100419376534531 ,8.9135833311811846265 ] 
dist 43=[6.5586682753701535196 ,8.9105529898653410394 ] 
dist 44=[6.4458211713274486867 ,8.8968675825161567447 ] 
dist 45=[6.2792156511670949939 ,8.8932369843751740170 ] 
dist 46=[6.1056024796026780928 ,8.8828181300013644831 ] 
dist 47=[5.9647275981034184257 ,8.8795471888619193281 ] 
dist 48=[5.6868279049699686602 ,8.6309889284131354813 ] 
dist 49=[5.4407639672503993792 ,8.6074075457005175425 ] 
dist 50=[5.2336748348578482432 ,8.5528068957928137363 ] 
dist 51=[5.0233793741732157372 ,8.5415143292945160520 ] 
dist 52=[4.8251473220055220447 ,8.4346505811817170133 ] 
dist 53=[4.5739590705935517127 ,8.3777322609507156757 ] 
dist 54=[4.1882441815009527847 ,4.6875056679782286569 ] 
dist 55=[3.9300266906674958265 ,4.6726219893967059124 ] 
dist 56=[3.7137721560700167587 ,4.1054466874344422683 ] 
dist 57=[3.4958897202240965259 ,4.0355918454612942767 ] 
dist 58=[3.2915943694052646711 ,3.8964541827359888271 ] 
dist 59=[3.1296817496676821250 ,3.8614858131498668419 ] 
dist 60=[2.9665353056677417885 ,3.7410336789265102312 ] 
dist 61=[2.7573047694228274851 ,3.7154380836976673831 ] 
dist 62=[2.5524301665461713445 ,3.6835326247110044040 ] 
dist 63=[2.4067052522709047213 ,3.6759597736976808052 ] 
dist 64=[2.2752709448544142833 ,2.7716651760711094481 ] 
dist 65=[2.1275520527107873346 ,2.6961290088915936005 ] 
dist 66=[1.9792588189306016240 ,2.5279214223469432857 ] 
dist 67=[1.8455269897819382676 ,2.4962287688157417871 ] 
dist 68=[1.6957807534797552907 ,2.2943702790931426668 ] 
dist 69=[1.4834361449520656423 ,2.2585999568058906309 ] 
dist 70=[1.2727437114914173433 ,2.1927756747018177555 ] 
dist 71=[1.1296052499443878594 ,2.1776310519962144544 ] 
dist 72=[1.0074330938002516116 ,1.9828826972852932960 ] 
dist 73=[.88059685461160369931,1.9557085442322715785 ] 
dist 74=[.75926836282953667431,1.8998695588115374388 ] 
dist 75=[.65912459027612583225,1.8854533467762135622 ] 
dist 76=[.55452472564419992435,1.8329368806150893735 ] 
dist 77=[.4153730811932694516 ,1.8226320724807675360 ] 
dist 78=[.27670681397694663435,1.8034799269465801988 ] 
dist 79=[.17404796176367457479,1.7989774664047204329 ] 
dist 80=[.07729885127726137583,.71726084298979030161] 
dist 81=[-.03773115151974814496,.70930374531160892141] 
dist 82=[-.1584722495718949433 ,.64060205371854346902] 
dist 83=[-.30029196363335135407,.62865762574357706398] 
dist 84=[-.43214782248285260528,.61292596183406329779] 
dist 85=[-.59240178965776599628,.60977482735413378244] 
dist 86=[-.78261943086780714739,-.00406582126678634888] 
dist 87=[-.90870098374545791408,-.04296421982212273448] 
dist 88=[-1.0129248654373048326 ,-.13089016676173766834] 
dist 89=[-1.1157196172302433610 ,-.14531357113454838967] 
dist 90=[-1.2107001552530605499 ,-.25369552392612757416] 
dist 91=[-1.2836700078838181034 ,-.27263724060840543097] 
dist 92=[-1.3550690200605127505 ,-.30212292744256378532] 
dist 93=[-1.4437668768659573092 ,-.30925284525318204305] 
dist 94=[-1.5292564645726161004 ,-.42325572348287476125] 
dist 95=[-1.5878235745131118543 ,-.43755981660857170462] 
dist 96=[-1.6383425882022290720 ,-.46975342907876956032] 
dist 97=[-1.6916426317620209818 ,-.47484098441353396242] 
dist 98=[-1.7431614296522195862 ,-.51375295856422278693] 
dist 99=[-1.7865561520168450915 ,-.52042569609334700962] 
dist 100=[-1.8326586902015318908 ,-.53056011091227629297] 
dist 101=[-1.8950079836152017092 ,-.5330117414908772648 ] 
dist 102=[-1.9555947954502583426 ,-.57030162978377599525] 
dist 103=[-1.9946480277059624466 ,-.57540966026430051121] 
dist 104=[-2.0257091012555409435 ,-.5812128152247325972 ] 
dist 105=[-2.0543299067912082163 ,-.58155869595047819049] 
dist 106=[-2.0794600205681700217 ,-.57967771053390736982] 
dist 107=[-2.0965594949402004603 ,-.57457101749095930703] 
dist 108=[-2.1111848919829365169 ,-.56609471729729825892] 
dist 109=[-2.1264195712605333397 ,-.55073759113101795162] 
dist 110=[-2.1401097325650416272 ,-.53358433562803453152] 
dist 111=[-2.1485576887837584374 ,-.51792428533064611561] 
dist 112=[-2.1548493236156655960 ,-.50024929046681875975] 
dist 113=[-2.1599152170674439539 ,-.4750362709612642659 ] 
dist 114=[-2.1638540209104580663 ,-.44668091298512370009] 
dist 115=[-2.1656380191886498149 ,-.4164386753164895227 ] 
dist 116=[-2.1662006790612336428 ,-.37879492152691318506] 
dist 117=[-2.1660538981623659562 ,-.32083981471964977682] 
dist 118=[-1.0661578132142444791 ,-.26260121803519904456] 
dist 119=[-1.0645877280036944871 ,-.22382335507080544867] 
dist 120=[-.98875693839365700845,-.19159579064542343422] 
dist 121=[-.97905876288633172661,-.15955162536549895023] 
dist 122=[-.96043626972470470374,-.12979559866677214464] 
dist 123=[-.95575233716897555038,-.10671803797393362804] 
dist 124=[-.9399703185997325483 ,-.08394184331452333239] 
dist 125=[-.93618061022419555978,-.05539040067336977761] 
dist 126=[-.93231163026854516371,-.02776620314151038694] 
dist 127=[-.93136070225348885936,-.00869781976741748123] 
dist 128=[-.75193271420496719014,.00789603907443816490] 
dist 129=[-.7367806192117689745 ,.02562476087230104512] 
dist 130=[-.70350256731372283269,.04288908481668982830] 
dist 131=[-.69629644173650539472,.05762628420831613423] 
dist 132=[-.65715052822063548152,.07344947321168378449] 
dist 133=[-.65004521451935968306,.09505792320841983264] 
dist 134=[-.63534076775263465744,.11615481999731182157] 
dist 135=[-.6314040602695231056 ,.12993228725444318009] 
dist 136=[-.59550986376170258474,.14109156042509670856] 
dist 137=[-.589875697819400014  ,.15171698513373737576] 
dist 138=[-.57889015079118389984,.16128441689511974864] 
dist 139=[-.57609109655520866526,.16821225265015818179] 
dist 140=[-.56638015289678998326,.17458697586824035775] 
dist 141=[-.5641482777987145953 ,.18194225809169121636] 
dist 142=[-.56119293655343467756,.18875836528808430746] 
dist 143=[-.56019028741206073138,.1929768341547067739 ] 
dist 144=[-.11709683006303373545,.19613311907773713891] 
dist 145=[-.09322015567571321224,.19870152624403810992] 
dist 146=[-.03763926567761236304,.20075029586621302979] 
dist 147=[-.02955699146561931336,.2018280815836330006 ] 
dist 148=[.04391978879381185120,.20240939406322632452] 
dist 149=[.05697096471220372292,.20253150170091050922] 
dist 150=[.07325890032660713579,.19465100116406295704] 
dist 151=[.07634670780459986707,.19413186705861457497] 
dist 152=[.16800001281397964564,.20629849516769805838] 
dist 153=[.16498064242472926397,.23147791906904568721] 
dist 154=[.16184341068283074006,.25358107232686412312] 
dist 155=[.15887227601343066855,.27748927438847885237] 
dist 156=[.15543927190683641972,.30094021835048546634] 
dist 157=[.15045497250525852557,.321214785607727253  ] 
dist 158=[.14531593568312151551,.34319608080618887921] 
dist 159=[.14126383635712473515,.37347226032297194264] 
dist 160=[.13720866702213035545,.40309485915875363907] 
dist 161=[.13205650596921488563,.42246247913921041324] 
dist 162=[.12655437060987606204,.43816586605448322105] 
dist 163=[.12109953111600799169,.45313514830344693133] 
dist 164=[.11459897401834385814,.46661711593642268493] 
dist 165=[.10491549350080826991,.4763727252526645801 ] 
dist 166=[.09514078934703417088,.48533802668630140769] 
dist 167=[.08827525279142446541,.49565958258903596585] 
dist 168=[.08218133865903646608,.50523769343481075962] 
dist 169=[.07549134566721799109,.51122993387815144857] 
dist 170=[.06887554203665209894,.51578574252683424407] 
dist 171=[.06307791085706010636,.51961946063667839438] 
dist 172=[.05672885377228891867,.52272811831468105016] 
dist 173=[.04790770605085048555,.52438434475351747997] 
dist 174=[.03895723715176132444,.52530511863975918192] 
dist 175=[.03209082243387412984,.52550194748510812179] 
dist 176=[.02538750579619446019,.47389515422540190053] 
dist 177=[.01708885252273926023,.4718028290621879569 ] 
dist 178=[.00832623290320681244,.46659641518033215696] 
dist 179=[-.00023268539672609411,.46562990558064409807] 
dist 180=[-.01034528215207953329,.45713208611034771407] 
dist 181=[-.02532124746861437357,.45539078536907387327] 
dist 182=[-.04024058575599282138,.45308961587103001652] 
dist 183=[-.05012682157345234861,.45228281416350958519] 
dist 184=[-.05829023350410352370,.43445663817875915502] 
dist 185=[-.06632008471754762196,.43198468583218178896] 
dist 186=[-.07371976084151840778,.42696908571027441216] 
dist 187=[-.07936317174236985401,.42558727825113759129] 
dist 188=[-.08484237724980009652,.42015515282585054477] 
dist 189=[-.09158551805021564229,.41899382287737008968] 
dist 190=[-.09804767028326161719,.41628301833696385348] 
dist 191=[-.10240326067667022682,.41546017282701826238] 
dist 192=[-.10608178618482535001,.3662577942347174604 ] 
dist 193=[-.10983640832418975853,.36167624194772795438] 
dist 194=[-.1133867081252393257 ,.35131242239345702181] 
dist 195=[-.11624825358232205333,.34917579491079829308] 
dist 196=[-.11917544301982198662,.3358479083353955679 ] 
dist 197=[-.1229885151981078044 ,.33334188675301597944] 
dist 198=[-.12664154050728814614,.32869292366246019208] 
dist 199=[-.12892871618222297553,.32753753527765197061] 
dist 200=[-.13067097567535654582,.31043914868583996998] 
dist 201=[-.13214466012671803518,.30807877236787464468] 
dist 202=[-.13334686425636245242,.30222428421240267251] 
dist 203=[-.13400341022245951924,.30136732578903763737] 
dist 204=[-.13439147011866699374,.29218141148903963152] 
dist 205=[-.13452002895031831854,.29039338508315182136] 
dist 206=[-.13454326748646818963,.28850379232002875566] 
dist 207=[-.13451012379309894053,.28810769409066221854] 
dist 208=[-.13442989322388257189,.15172272036333399472] 
dist 209=[-.13434723600447908679,.14322469880225623615] 
dist 210=[-.13405700127113142525,.12345171167310103774] 
dist 211=[-.13393297663454224616,.12042614542062013746] 
dist 212=[-.13709034314324741558,.09711906596504128587] 
dist 213=[-.15248934660704334943,.09347966714568163759] 
dist 214=[-.16780776061450335864,.08816189022018247199] 
dist 215=[-.18717282141782699509,.08672560806972772394] 
dist 216=[-.20598131630359878475,.06147670354181446746] 
dist 217=[-.21907406858118246482,.05826641376287344140] 
dist 218=[-.23058072162696043268,.05116086882797894746] 
dist 219=[-.24304653305590093838,.04975854920849155723] 
dist 220=[-.25528411322946086206,.04609116689474465451] 
dist 221=[-.26587808819648791307,.05155143321692906084] 
dist 222=[-.27737470308649896048,.05687235004760500515] 
dist 223=[-.29322186902749757503,.06059593136806828478] 
dist 224=[-.30872779586944947183,.06388663138425194469] 
dist 225=[-.31885982273456849066,.06747680944572118035] 
dist 226=[-.32706733384490260906,.07101330159436645143] 
dist 227=[-.33487727475084166447,.07408935721994290066] 
dist 228=[-.34190092716754054148,.07743773256346564082] 
dist 229=[-.34696413272624179429,.08206301416172902256] 
dist 230=[-.35159722969225956327,.08658548547273904319] 
dist 231=[-.35690091134012849487,.08952279736040116281] 
dist 232=[-.36178318554068267344,.09188024687331800846] 
dist 233=[-.36473110732374186753,.09408428988330048907] 
dist 234=[-.36684718790489433599,.09603802245250786304] 
dist 235=[-.36840299509459982488,.09739465751130896392] 
dist 236=[-.369571982100233408  ,.09858235954491530523] 
dist 237=[-.37014120180149700249,.09986061763047033247] 
dist 238=[-.37038390097047133765,.10099939894837811728] 
dist 239=[-.37037799844296678943,.10162943402955216572] 
dist 240=[-.08879004158742268024,.10201117206872376681] 
dist 241=[-.08859226038912321014,.10215722618124479559] 
dist 242=[-.08738986272835263359,.10220811989935873976] 
dist 243=[-.08714291261759317287,.10220939520351838602] 
dist 244=[-.08668221148474315239,.10217438030870201836] 

8 phat 2 dirichlet min maxes function [2, 1, 0, 0, 1, 1, 0, 1] 
dist 0=[12.813627066226084384  ,12.813627066226084384  ] 
dist 1=[12.729510220552156830  ,12.875066030671412087  ] 
dist 2=[12.591689710322207165  ,12.922201561374923963  ] 
dist 3=[12.447362491361144483  ,12.960202711366468606  ] 
dist 4=[12.337224232185844299  ,12.985119419228584747  ] 
dist 5=[12.230270829652912615  ,13.009192077994661021  ] 
dist 6=[12.098672728607205924  ,13.045051089338100430  ] 
dist 7=[11.960154576642654527  ,13.073930985622670233  ] 
dist 8=[11.825525272109848516  ,13.101118495687830167  ] 
dist 9=[11.666972462900596382  ,13.123518550325256753  ] 
dist 10=[11.432783487639256339  ,13.133253372349751546  ] 
dist 11=[11.188931506999005007  ,13.137128652253372532  ] 
dist 12=[10.991735134401015447  ,13.136198148156627730  ] 
dist 13=[10.789515532189076951  ,13.119247245577028864  ] 
dist 14=[10.525572768133494663  ,13.112703685281053735  ] 
dist 15=[10.239772228484075859  ,13.105955541089952810  ] 
dist 16=[9.9501423771889984392 ,13.101445537724278937  ] 
dist 17=[9.6000666727209426161 ,12.879027582229657118  ] 
dist 18=[9.0725430329087381471 ,12.851939648630696453  ] 
dist 19=[8.5431168674793992514 ,12.793101518444560374  ] 
dist 20=[8.1854317756942888245 ,12.775556606818983955  ] 
dist 21=[7.8824885356829117850 ,12.699445484993221446  ] 
dist 22=[7.5719716087476786238 ,12.683569520586192754  ] 
dist 23=[7.2776227501856092088 ,12.643646603700544557  ] 
dist 24=[7.0393330682018083807 ,12.633804383159153062  ] 
dist 25=[6.7947121837924769782 ,12.522709283964474320  ] 
dist 26=[6.4750406454795746771 ,12.480399777190099504  ] 
dist 27=[6.1594136932675037139 ,11.988195402330650999  ] 
dist 28=[5.9309648025379789059 ,11.944581833928494538  ] 
dist 29=[5.7209491268083919550 ,11.914989803158067078  ] 
dist 30=[5.4790338919124287532 ,11.838209370187844889  ] 
dist 31=[5.2329258154497168296 ,11.448557786625880489  ] 
dist 32=[5.0061386337054448768 ,11.211364460317409817  ] 
dist 33=[4.7483390154039488850 ,10.215705950128463050  ] 
dist 34=[4.3782019255570680686 ,10.088685328109532939  ] 
dist 35=[4.0093050122980042636 ,9.7911185444317445079 ] 
dist 36=[3.7564626362526343195 ,9.7454433613782632286 ] 
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dist 38=[3.3082704978065288860 ,9.2675279835010704542 ] 
dist 39=[3.0860319940867563586 ,9.1722971111372605234 ] 
dist 40=[2.8992027695899907805 ,9.1474663181853817817 ] 
dist 41=[2.7010879552637851140 ,8.5752756085095623922 ] 
dist 42=[2.4337078466471165549 ,8.5028433906496211538 ] 
dist 43=[2.1655742856285896827 ,8.3529645088020720507 ] 
dist 44=[1.9644422003577547802 ,8.3136410632053868412 ] 
dist 45=[1.7723180464612141414 ,8.1668391543858814138 ] 
dist 46=[1.5402050996825791637 ,8.1381862709756789187 ] 
dist 47=[1.2979185160891069756 ,8.0797614316429458069 ] 
dist 48=[1.0650997024103390479 ,8.0642985974014364977 ] 
dist 49=[.7927514884283174600 ,7.2239189283084827017 ] 
dist 50=[.3923580979537495723 ,7.1490577181537983433 ] 
dist 51=[-.0054448404357924706 ,6.9754192840474342207 ] 
dist 52=[-.2674344152196992075 ,6.9484227022548802820 ] 
dist 53=[-.4821390754738848048 ,6.7190666286309298988 ] 
dist 54=[-.6908226391000153531 ,6.6778423156318669059 ] 
dist 55=[-.8816403278084762432 ,6.6220074504685153005 ] 
dist 56=[-1.0248907913892490380 ,6.6066647558215371520 ] 
dist 57=[-1.1618750529251477153 ,6.3083542364183648777 ] 
dist 58=[-1.3276355250570378711 ,6.2707468860876052859 ] 
dist 59=[-1.4852644848305942203 ,6.1909558984397210034 ] 
dist 60=[-1.5897282861425902082 ,6.1721764122385916159 ] 
dist 61=[-1.6760916933916614829 ,6.0883953739864211032 ] 
dist 62=[-1.7613282275443572042 ,6.0578856527311229278 ] 
dist 63=[-1.8401756774293940957 ,5.9856694410318349920 ] 
dist 64=[-1.9009900853978057718 ,5.9317094475538947238 ] 
dist 65=[-1.9607743152755754930 ,2.4752082054136744840 ] 
dist 66=[-2.1100347315352421062 ,2.3240689522413201530 ] 
dist 67=[-2.2755696983460562882 ,1.9725692688103859153 ] 
dist 68=[-2.4052245723562115125 ,1.9219502857664390085 ] 
dist 69=[-2.5344088664408129962 ,1.4581430326560210621 ] 
dist 70=[-2.6980662514826960512 ,1.3758344285499986832 ] 
dist 71=[-2.8572936581730010367 ,1.2745934893404118844 ] 
dist 72=[-2.9687639858772226192 ,1.2567075368443926848 ] 
dist 73=[-3.0674446867541762795 ,.6469015586716492379 ] 
dist 74=[-3.1755266551490280051 ,.6160844685498646435 ] 
dist 75=[-3.2824048162918433636 ,.5573684671757787611 ] 
dist 76=[-3.3762757475490466865 ,.5459885159575854720 ] 
dist 77=[-3.4793521739920705115 ,.5287306186370888990 ] 
dist 78=[-3.6230555909012039487 ,.5245633114236929176 ] 
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dist 80=[-3.8522401213297921595 ,.1812032725820844185 ] 
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dist 82=[-3.9827012284949318541 ,-.6140839471010133985 ] 
dist 83=[-4.0346452409934894018 ,-.7519970774155029966 ] 
dist 84=[-4.0668557841197312282 ,-.7731954633725271735 ] 
dist 85=[-4.0910534420517222472 ,-.87531517350357905981] 
dist 86=[-4.1109548846104516577 ,-.77043384784250335266] 
dist 87=[-4.1272082311253037822 ,-.67088569820599877802] 
dist 88=[-4.1368144351266500957 ,-.59023749557907059644] 
dist 89=[-4.1434938869135501884 ,-.50745510042680029195] 
dist 90=[-4.1480340419614889740 ,-.39937132247546974947] 
dist 91=[-4.1509155869265792025 ,-.29283187528402575968] 
dist 92=[-4.1509577433095698189 ,-.21622266129222637932] 
dist 93=[-4.1489365503900357903 ,-.14635992842647563285] 
dist 94=[-4.1471711959772903530 ,-.06679286689055029850] 
dist 95=[-3.8083189173743158362 ,.0135777539447010397 ] 
dist 96=[-3.7771877274358339164 ,.0866552020433012985 ] 
dist 97=[-3.7108459081082908836 ,.1688921978273541801 ] 
dist 98=[-3.6921232657845326178 ,.2858888970831162115 ] 
dist 99=[-3.6151449884084590773 ,.4018509368025323607 ] 
dist 100=[-3.6000790379749111627 ,.4799517560572771608 ] 
dist 101=[-3.5607691923982990876 ,.5458013536270363975 ] 
dist 102=[-3.5543225455521195659 ,.6127779864259853907 ] 
dist 103=[-3.4755668649106335797 ,.6759085176353919153 ] 
dist 104=[-3.4611908777124835010 ,.7263805290171455918 ] 
dist 105=[-3.4326614486512766956 ,.7775995493773990836 ] 
dist 106=[-3.4245705929345383351 ,.8437190532589828165 ] 
dist 107=[-3.3920130724261531536 ,.9085839280504130878 ] 
dist 108=[-3.3845457028038295277 ,.95478724449368610969] 
dist 109=[-3.3665171305106708257 ,.99649372274495621259] 
dist 110=[-3.3604316484067765974 ,1.0433787245403234685 ] 
dist 111=[-2.3418864433131640568 ,1.0904161269620576833 ] 
dist 112=[-2.3314070259821834046 ,1.1327337210074625686 ] 
dist 113=[-2.3077218117183523950 ,1.1800129180040293821 ] 
dist 114=[-2.3018846419288894444 ,1.2468937745131863898 ] 
dist 115=[-2.2702123455458132425 ,1.3124956504194329540 ] 
dist 116=[-2.2638610767191461728 ,1.3546608938463055607 ] 
dist 117=[-2.2510278113717711214 ,1.3880374342648200770 ] 
dist 118=[-2.2473572029849770502 ,1.4184933500926080885 ] 
dist 119=[-2.1990985636775944531 ,1.4450090708170988680 ] 
dist 120=[-2.1843580026858547140 ,1.4626291626920855198 ] 
dist 121=[-2.0585153038412098276 ,1.4772390278753986490 ] 
dist 122=[-2.0512851501857371525 ,1.4917179667985461546 ] 
dist 123=[-2.0438867849201064299 ,1.5044646217393472086 ] 
dist 124=[-2.0231194639776883475 ,1.5121469904438815129 ] 
dist 125=[-1.9221134985213721212 ,1.5176509301693922241 ] 
dist 126=[-1.8597986518772279673 ,1.5216846576977100999 ] 
dist 127=[-1.5973277422496713254 ,1.5245026853527240210 ] 
dist 128=[-1.5218940365201797588 ,1.5251443876679902151 ] 
dist 129=[.8612134451651917636 ,1.5783841827414089205 ] 
dist 130=[.84405454728840869491,1.6659752443820068958 ] 
dist 131=[.82536648258516873373,1.7464618341471018990 ] 
dist 132=[.81002902311275009347,1.8074276221001887182 ] 
dist 133=[.79411144107819844509,1.8662056752451612999 ] 
dist 134=[.77310181868410099654,1.9379449304955422399 ] 
dist 135=[.75025545363561654618,2.0063717264256129222 ] 
dist 136=[.7269927948804732562 ,2.0519043928153507653 ] 
dist 137=[.69880949857580650346,2.0897096632393588952 ] 
dist 138=[.65628732429758663663,2.1272365949584715000 ] 
dist 139=[.61166938335903420093,2.1620417205180467940 ] 
dist 140=[.57510567334846571042,2.1889639339383346566 ] 
dist 141=[.53718856248670750865,2.2154689575154101943 ] 
dist 142=[.48715822050061005351,2.2486080794477039454 ] 
dist 143=[.4327435517036407154 ,2.2797871471444854111 ] 
dist 144=[.37729512119355143953,2.2984543969026190754 ] 
dist 145=[.31007704150983279589,2.3116708865376533531 ] 
dist 146=[.2086004986157517830 ,2.3210514729925853788 ] 
dist 147=[.10684866542113749431,2.3278657779008152339 ] 
dist 148=[.03852965796837733187,2.3308188385902674653 ] 
dist 149=[-.01884440418072932870,2.3316205686781365554 ] 
dist 150=[-.07683247912795875651,2.3313343446559614086 ] 
dist 151=[-.13125626635292834675,2.3061403987959108902 ] 
dist 152=[-.17437846825257555542,2.3014722672961218231 ] 
dist 153=[-.21777919831872081753,2.2931097153828771139 ] 
dist 154=[-.27331691132868067193,2.2905460927068781831 ] 
dist 155=[-.32755565305368508906,2.2797997423762631464 ] 
dist 156=[-.3657624672898912092 ,2.2767069024660761852 ] 
dist 157=[-.39980368334985490128,2.2692059971005054825 ] 
dist 158=[-.43738611366245080634,2.2662938327496836477 ] 
dist 159=[-.47468506949443760089,2.0436933531758476612 ] 
dist 160=[-.50759293741572244327,2.0228405126656412488 ] 
dist 161=[-.54381872812966464243,1.9768476888474141754 ] 
dist 162=[-.60223818514224722962,1.9654905558171101184 ] 
dist 163=[-.66318271144686552479,1.9087774205249222486 ] 
dist 164=[-.70302116196171530259,1.8978257796555273603 ] 
dist 165=[-.73529869703907181338,1.8740474562447528195 ] 
dist 166=[-.76600995954850351974,1.8670676283921073370 ] 
dist 167=[-.79361661330545652728,1.8003445221322290382 ] 
dist 168=[-.81347993639389685571,1.7897965519239817634 ] 
dist 169=[-.83161145836899600627,1.7654585963867815555 ] 
dist 170=[-.85229315179535837979,1.7595590964307133596 ] 
dist 171=[-.87143596386808114771,1.7251420238429089608 ] 
dist 172=[-.88341412918014452675,1.7181201116806128288 ] 
dist 173=[-.89251829245887272566,1.7046557082614012767 ] 
dist 174=[-.90016934431669392907,1.7009190596254406534 ] 
dist 175=[-.90636249438800571073,.95668818744423375277] 
dist 176=[-.90963726277493105152,.92715476810620253995] 
dist 177=[-.91142338606247218147,.8583037046903349497 ] 
dist 178=[-.91174707194321515323,.84734016582900587215] 
dist 179=[-.59306874449432869843,.75474003604999278179] 
dist 180=[-.5978158091552359395 ,.73786510655563363035] 
dist 181=[-.6025384763201020654 ,.71477569053795243376] 
dist 182=[-.66679858850844878787,.70794457611738488703] 
dist 183=[-.75796408627792757027,.58146721788918610782] 
dist 184=[-.82188084155175346728,.56526214674294823378] 
dist 185=[-.87852600520353905236,.5307782858717199977 ] 
dist 186=[-.94061413234407992653,.52237316803811754841] 
dist 187=[-1.0019845703402294302 ,.48532820466416035832] 
dist 188=[-1.0557599381833914612 ,.4786606683613757231 ] 
dist 189=[-1.1146586328457846615 ,.46266477658061695268] 
dist 190=[-1.2043695047490526865 ,.46023743108036978289] 
dist 191=[-1.2959588352184302442 ,.29392438930790407397] 
dist 192=[-1.3558843528983337060 ,.27843496395752837893] 
dist 193=[-1.4045067489893178661 ,.24252635681950843692] 
dist 194=[-1.4508974900559864659 ,.2369078452167932451 ] 
dist 195=[-1.4926931414109473945 ,.18953360572098310192] 
dist 196=[-1.5229407953527714204 ,.1810200733491497845 ] 
dist 197=[-1.5507343785598073783 ,.16936761411944067573] 
dist 198=[-1.5827166667387704224 ,.16607678514077964664] 
dist 199=[-1.6122720290735247618 ,.10499482636433948568] 
dist 200=[-1.6303609139328833512 ,.09729149068218550461] 
dist 201=[-1.6436381135211940223 ,.08080599796157078384] 
dist 202=[-1.6539528120053641827 ,.07708691301728474944] 
dist 203=[-1.6620032484814620760 ,.05934087426218519330] 
dist 204=[-1.6662261801129982926 ,.05624973646536104625] 
dist 205=[-1.6684819080536695454 ,.04907773407714760458] 

8 phat 2 dirichlet min maxes function [1, 1, 1, 2, 0, 1, 2] 
dist 0=[6.7677249742739955907 ,6.7677249742739955907 ] 
dist 1=[6.7047854926040532248 ,6.8292859228843734249 ] 
dist 2=[6.6462663877020685172 ,6.8822899808641841588 ] 
dist 3=[6.5793067579262217027 ,6.9395943932368813252 ] 
dist 4=[6.4826066271704194779 ,7.0183525755410392477 ] 
dist 5=[6.3799201100167520389 ,7.0994821946868549392 ] 
dist 6=[6.2890171134904318972 ,7.1662708606274477488 ] 
dist 7=[6.1886063760720827714 ,7.2358660151613302466 ] 
dist 8=[6.0478939775776710540 ,7.3282212984346716800 ] 
dist 9=[5.8906554006585548513 ,7.4290321239546438326 ] 
dist 10=[5.7241473813223334020 ,7.5324459170870089042 ] 
dist 11=[5.5176057220638408082 ,7.6584021986333657418 ] 
dist 12=[5.2002497763499393743 ,7.8493726879269547900 ] 
dist 13=[4.8768472817887091076 ,8.0403355138663426548 ] 
dist 14=[4.6461219613378263491 ,8.1662614733834964093 ] 
dist 15=[4.4373033039426463770 ,8.2696236108841467088 ] 
dist 16=[4.2015178667554967270 ,8.3703424304136837097 ] 
dist 17=[3.9641822771062806558 ,8.4625909879924333251 ] 
dist 18=[3.7491631479674196491 ,8.5320765903105570944 ] 
dist 19=[3.5075875894476464480 ,8.5987377882693218529 ] 
dist 20=[3.1640362941266699663 ,8.6796909664868330532 ] 
dist 21=[2.8114423992415889554 ,8.7567878801655115780 ] 
dist 22=[2.5336996731742597880 ,8.8080263279497524974 ] 
dist 23=[2.2554017302650497935 ,8.8505319243635469913 ] 
dist 24=[1.9005866429133108040 ,8.8927021083420307769 ] 
dist 25=[1.5202746448103550233 ,8.9318313996754876739 ] 
dist 26=[1.1399985860520742640 ,8.9621757864597046885 ] 
dist 27=[.68383464390153430927,8.9921421490583746805 ] 
dist 28=[0                     ,9.0297617388544312086 ] 
dist 29=[7.3470148567642738095 ,9.0650453349039161495 ] 
dist 30=[7.3591793153464042512 ,9.0856692587599765830 ] 
dist 31=[7.3758244696056194298 ,9.0996709053645728936 ] 
dist 32=[7.3779524075138988606 ,9.1084675988575366418 ] 
dist 33=[7.3747270177383084740 ,9.1144751957170954932 ] 
dist 34=[7.3636651351635168183 ,9.1173198717212551697 ] 
dist 35=[7.3446625592519232525 ,9.1184166166834998923 ] 
dist 36=[7.3096762343833504363 ,9.1176351562617656653 ] 
dist 37=[7.2667562534581902130 ,9.0722790606545755885 ] 
dist 38=[7.2160223939687234381 ,9.0647957613436952339 ] 
dist 39=[7.1494449615503820363 ,9.0526598363971379197 ] 
dist 40=[7.0431588659098819701 ,9.0489175948956657135 ] 
dist 41=[6.9326831054549464977 ,9.0371781949855147818 ] 
dist 42=[6.8493485555873132490 ,9.0330846785339194926 ] 
dist 43=[6.6474554242302681458 ,9.0274725067547726134 ] 
dist 44=[6.2820746238380948883 ,9.0249810318018888592 ] 
dist 45=[5.9152398507473027020 ,8.6966161742381132512 ] 
dist 46=[5.6686219833560654137 ,8.6677379447838322666 ] 
dist 47=[5.4609447394099787754 ,8.6009641009153042412 ] 
dist 48=[5.2498547879630582030 ,8.5877659918020662682 ] 
dist 49=[5.0507490188737723100 ,8.4966505229056861894 ] 
dist 50=[4.8910032395463850146 ,8.4791640102829085585 ] 
dist 51=[4.7282430618330166498 ,8.4493247673078021728 ] 
dist 52=[4.5170815871277766988 ,8.4340624767979804098 ] 
dist 53=[4.3091648317828538496 ,8.1567359491676696813 ] 
dist 54=[4.1593822818225038702 ,8.1234078469991768554 ] 
dist 55=[4.0223420401405396004 ,8.0300090421296367959 ] 
dist 56=[3.8653888821801980997 ,7.9112823525335982212 ] 
dist 57=[3.7061544653204412793 ,4.0619175230341425778 ] 
dist 58=[3.5599907101127334056 ,3.9313235796043420933 ] 
dist 59=[3.3942484790066541560 ,3.8966686909808581572 ] 
dist 60=[3.1567103540927524428 ,3.8898997880842523397 ] 
dist 61=[2.9199964111565967835 ,3.1791168577174236415 ] 
dist 62=[2.7575507268814730857 ,3.1070288194021614408 ] 
dist 63=[2.6171551588704456904 ,3.0169239879044070233 ] 
dist 64=[2.4686309413747614209 ,2.9987755664487637346 ] 
dist 65=[2.3248559966935396083 ,2.4641778193269669357 ] 
dist 66=[2.2034554504549760065 ,2.4274773596286875043 ] 
dist 67=[2.0742422597570354729 ,2.3591278820428705854 ] 
dist 68=[1.8992212723391807121 ,2.3431569372906849722 ] 
dist 69=[1.7234053473399242222 ,2.1462505901688104482 ] 
dist 70=[1.5910130921233544961 ,2.1184465246851311149 ] 
dist 71=[1.4640520969469428840 ,2.0620207072728559263 ] 
dist 72=[1.3099587308796500675 ,2.0475975152699512664 ] 
dist 73=[1.1276117931432866953 ,1.9961249225019597868 ] 
dist 74=[.98512903814330563417,1.9857047429700709457 ] 
dist 75=[.81113733571549575239,1.9683538709972115023 ] 
dist 76=[.54289539407071320426,1.9642949400581453394 ] 
dist 77=[.27571469323242646095,.94989077736158657062] 
dist 78=[.09777282948432193548,.92013388985945180766] 
dist 79=[-.05022617076747274210,.8762628696035442056 ] 
dist 80=[-.19765168751050915933,.86487753502081997439] 
dist 81=[-.33478881945496182934,.67492501892994234459] 
dist 82=[-.44163986085343100067,.65132601993257466931] 
dist 83=[-.54759650949441415843,.59824368494927562375] 
dist 84=[-.68115652372932528213,.58965495189239192986] 
dist 85=[-.81079923558242283182,.5255520550851778545 ] 
dist 86=[-.90108880949630019664,.51453825116416010974] 
dist 87=[-.98053154165841540136,.49721183307229460196] 
dist 88=[-1.0667928307628383939 ,.49317399600474877661] 
dist 89=[-1.1516439265984261535 ,-.04184191391173584042] 
dist 90=[-1.2254466756633046864 ,-.07671628660901991945] 
dist 91=[-1.3058696360603954408 ,-.15508863576778215943] 
dist 92=[-1.4171980003833369488 ,-.16828039066739433389] 
dist 93=[-1.5264701567569471162 ,-.26350852408475683864] 
dist 94=[-1.5986694439460269623 ,-.28010420789217880578] 
dist 95=[-1.6580856881290246455 ,-.3071807918638145457 ] 
dist 96=[-1.7162327212261402534 ,-.31335995999368783587] 
dist 97=[-1.7696502653098775962 ,-.40873249840216404206] 
dist 98=[-1.8101512199370869879 ,-.42097086545249822141] 
dist 99=[-1.8492600812209838726 ,-.44749259798809575073] 
dist 100=[-1.8971101936888931250 ,-.45255365915805852525] 
dist 101=[-1.9428532106933709782 ,-.48157735689579274799] 
dist 102=[-1.9735349350276843693 ,-.48646516920552609611] 
dist 103=[-1.9992936899620222484 ,-.49625299072384235401] 
dist 104=[-2.0253476179538325637 ,-.49860053441356878431] 
dist 105=[-2.0498408449686667779 ,-.51543333674907362354] 
dist 106=[-2.0693578423897399413 ,-.51818034021483200516] 
dist 107=[-2.0891209374486019103 ,-.51832926194099366434] 
dist 108=[-2.1145989015897279923 ,-.51500356358141445915] 
dist 109=[-2.1389410310045065751 ,-.50968727252182248371] 
dist 110=[-2.1541615283759655308 ,-.50187371411387203524] 
dist 111=[-2.1657321294613086503 ,-.49068591391803323196] 
dist 112=[-2.1754765480148556920 ,-.47187486612376547656] 
dist 113=[-2.1833926770444743296 ,-.45135350151410794334] 
dist 114=[-2.1876512833280757906 ,-.43332506613570574502] 
dist 115=[-2.1900807329352690208 ,-.41354308274833266552] 
dist 116=[-2.1906818465557105763 ,-.38600721319375626707] 
dist 117=[-2.1904085554888718619 ,-.35534679548983850314] 
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dist 172=[.03860281952946618765,.57045734270612782751] 
dist 173=[.02992970870822985969,.52809552790242983302] 
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dist 175=[.01470168625211977675,.52175240518248379604] 
dist 176=[.00402068107123170169,.52083490006806714143] 
dist 177=[-.00670856961348689817,.513042027194598455  ] 
dist 178=[-.01476676514760432972,.5113946712613411797 ] 
dist 179=[-.02246855691228760194,.50913411283792438668] 
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dist 181=[-.04147796560668210101,.49063877051688662528] 
dist 182=[-.05078159348238206709,.48814216712425063528] 
dist 183=[-.06164229038388802526,.48304403174738974065] 
dist 184=[-.07757419973361880884,.48161602514628563701] 
dist 185=[-.09340493257550235501,.47587569463551781827] 
dist 186=[-.10386112578522044329,.47465642980573262446] 
dist 187=[-.11245773184031418335,.4716294265063522058 ] 
dist 188=[-.12085204311176079275,.47084797517410714269] 
dist 189=[-.12854737336590724363,.41860241907378273265] 
dist 190=[-.13434882224583575354,.41368667959517420233] 
dist 191=[-.13991674898106451793,.40253698511074117596] 
dist 192=[-.14667836070305503164,.40023014519560522584] 
dist 193=[-.15311325540164144288,.38575879370139348733] 
dist 194=[-.15737470277076457575,.3830227569184566873 ] 
dist 195=[-.16089146444487328173,.37797149404617349517] 
dist 196=[-.16434841046440902735,.37671526516911557498] 
dist 197=[-.16753389241109432214,.3575998911709443311 ] 
dist 198=[-.16996518691779623658,.35495998924623429857] 
dist 199=[-.17232872002727097511,.34842357224065847935] 
dist 200=[-.17524352718827819223,.34743846495960561923] 
dist 201=[-.17797912032181819629,.3371868236194789664 ] 
dist 202=[-.17962599053104861869,.33518324049667423532] 
dist 203=[-.18080394592002568808,.33299412158621485976] 
dist 204=[-.18166408768234983466,.33246051549199677121] 
dist 205=[-.18229003009890877177,.18159019891793692867] 
dist 206=[-.18253126264997003438,.17209836825224212177] 
dist 207=[-.18259453988291950014,.15001370414891434555] 
dist 208=[-.18253461114519569512,.14661779578658344544] 
dist 209=[-.18080216371168106494,.12032681942196900729] 
dist 210=[-.18044726041072429968,.11612781840486270561] 
dist 211=[-.18853293919678074504,.11003321921134176733] 
dist 212=[-.2109807463822757973 ,.10837132977628305169] 
dist 213=[-.23278993774057547801,.07898183098048451971] 
dist 214=[-.24798138275327546758,.07524136879569740263] 
dist 215=[-.26134261920432601922,.06699886577585256169] 
dist 216=[-.27583298937961229961,.06532912238917450641] 
dist 217=[-.29006688584039655025,.05567144424868984942] 
dist 218=[-.30240250988604771651,.05395552722612401103] 
dist 219=[-.31580033331333872506,.05055312849255786630] 
dist 220=[-.33428186009750425732,.04969853569122649885] 
dist 221=[-.3523706014983879884 ,.05348316305925888714] 
dist 222=[-.36419771494219816298,.06014031640976512993] 
dist 223=[-.37378643013625217535,.06681212978045759782] 
dist 224=[-.38292403805822268464,.07530984399840172379] 
dist 225=[-.3911505382960063396 ,.08358738509434700349] 
dist 226=[-.39709582330231154236,.08937886661713145710] 
dist 227=[-.40255118516353001299,.09449697143414823932] 
dist 228=[-.40881852951266862519,.10008208726547015188] 
dist 229=[-.41459971649207819736,.10558571508935384946] 
dist 230=[-.41811098236313795866,.11037800198860993346] 
dist 231=[-.42065636613598099122,.11559987193760567867] 
dist 232=[-.42257508560820743568,.12282115176985875474] 
dist 233=[-.42402802827391892214,.12988883645702079435] 
dist 234=[-.42471082044735097601,.13449656576750451532] 
dist 235=[-.42498331797710033416,.13821512596687922484] 
dist 236=[-.42498168843877783552,.14172753254939756424] 
dist 237=[-.09850059510067135404,.144866630193987622  ] 
dist 238=[-.09797174525521796727,.1470925319842155702 ] 
dist 239=[-.09706488299072878625,.1490905619829612649 ] 
dist 240=[-.09684292185506914886,.15131850214236515565] 
dist 241=[-.09270361470264001881,.15333556348569474557] 
dist 242=[-.09213539219013661598,.15449039581918387623] 
dist 243=[-.09082206797875701625,.15524205105855092583] 
dist 244=[-.08963560745860933233,.15564702497939456524] 
dist 245=[-.08482366619388275718,.15589412317097008645] 
dist 246=[-.08440442080024998288,.15601454954847252631] 
dist 247=[-.08265015802099704051,.15606589569431813379] 

8 phat 2 dirichlet min maxes function [0, 2, 0, 2, 0, 2, 1, 0, 1] 
dist 0=[11.140693525211643689  ,11.140693525211643689  ] 
dist 1=[11.124482261923410372  ,11.167819731967550777  ] 
dist 2=[11.086780983570514480  ,11.197798801334160731  ] 
dist 3=[11.028197226903137845  ,11.214930447124197585  ] 
dist 4=[10.934206355096880714  ,11.226043026643802567  ] 
dist 5=[10.833528671518523511  ,11.231945464513479716  ] 
dist 6=[10.748204623589378940  ,11.242637865870534003  ] 
dist 7=[10.657165816785911535  ,11.251928177033709926  ] 
dist 8=[10.533631282110420582  ,11.258836444336502585  ] 
dist 9=[10.397539638571911608  ,11.263241341458604289  ] 
dist 10=[10.256282827394749934  ,11.266650376334427567  ] 
dist 11=[10.083121593354052674  ,11.269585658973310646  ] 
dist 12=[9.8194413145044504628 ,11.271987677153477008  ] 
dist 13=[9.5536565424099003668 ,11.273268858288406009  ] 
dist 14=[9.3720781102122413842 ,11.273972121369996100  ] 
dist 15=[9.2160944949279446819 ,11.274067578339968381  ] 
dist 16=[9.0526622571650378824 ,11.273770288432677265  ] 
dist 17=[8.8954930092181640424 ,11.272906034557365290  ] 
dist 18=[8.7645532383555681726 ,11.271458805948443048  ] 
dist 19=[8.6267670553714979166 ,11.269139163788036100  ] 
dist 20=[8.4422145955018601532 ,11.265652620638197776  ] 
dist 21=[8.2578498277347198471 ,11.262735462153858418  ] 
dist 22=[8.1208121350638319278 ,11.257362565444400559  ] 
dist 23=[7.9911725436392940435 ,11.254922028687532859  ] 
dist 24=[7.8363909265070156044 ,11.242268615630802476  ] 
dist 25=[7.6758525424477775098 ,11.237412706317497446  ] 
dist 26=[7.5231872462803998975 ,11.232887684160508489  ] 
dist 27=[7.3458603631571039281 ,11.221260372638563497  ] 
dist 28=[7.0866889757502709156 ,11.138828724529021301  ] 
dist 29=[6.8263748714404007802 ,11.082277819557639259  ] 
dist 30=[6.6444761750936566905 ,9.5217474556358926302 ] 
dist 31=[6.4838061887827476981 ,9.4305210883935261294 ] 
dist 32=[6.3083907525314321712 ,9.2207013957406459089 ] 
dist 33=[6.1352803475568683332 ,9.1852467371296932094 ] 
dist 34=[5.9838263326190651183 ,8.9113755106780693710 ] 
dist 35=[5.8180379380355373557 ,8.8616857959552438636 ] 
dist 36=[5.5875937515017522883 ,8.7864663639319774440 ] 
dist 37=[5.3534169472494673950 ,8.7667105838536879067 ] 
dist 38=[5.1726977518594907423 ,8.4177465020455124808 ] 
dist 39=[4.9951134352299801767 ,8.3727171159129784835 ] 
dist 40=[4.7734714288581123995 ,8.2718685976624831052 ] 
dist 41=[4.5383183476887631910 ,8.2519535190811319058 ] 
dist 42=[4.3066929440321505223 ,8.1274945525717711288 ] 
dist 43=[4.0314154985333028365 ,8.1048269837828961026 ] 
dist 44=[3.6216686061254165169 ,8.0626658429224870547 ] 
dist 45=[3.2127691309178486782 ,8.0525223437593248726 ] 
dist 46=[2.9408801098884834693 ,7.6908327801797231646 ] 
dist 47=[2.7151791621275554790 ,7.6531371068101376894 ] 
dist 48=[2.4910138982872541990 ,7.5703430684285550353 ] 
dist 49=[2.2828708970594756893 ,7.5528983525695392185 ] 
dist 50=[2.1212520916438116603 ,7.4561130400701703659 ] 
dist 51=[1.9614774641861336747 ,7.4387452998378261125 ] 
dist 52=[1.7607085517444293730 ,7.4032813701349958323 ] 
dist 53=[1.5660601147354540843 ,7.3940052256006358308 ] 
dist 54=[1.4307641701375118803 ,7.0792997394518510217 ] 
dist 55=[1.3119693818299156610 ,7.0452219312862434340 ] 
dist 56=[1.1833185479428243052 ,6.9929727619719460570 ] 
dist 57=[1.0569264751226741601 ,6.9796707471413044513 ] 
dist 58=[.94716404016348280331,6.7606081267936094312 ] 
dist 59=[.82766328047165935333,6.7230353207638927147 ] 
dist 60=[.66231687276754541832,6.5398461991271054897 ] 
dist 61=[.49990632257602961199,6.2096660217159475911 ] 
dist 62=[.39214709994121863299,3.0889560544249889482 ] 
dist 63=[.30292431117738244913,3.0740700260129157629 ] 
dist 64=[.06865318155649838204,2.5971109299850188891 ] 
dist 65=[-.11557869112502204858,2.5382729706423775371 ] 
dist 66=[-.28091779440842431285,2.4192918284766237428 ] 
dist 67=[-.46542504066889799127,2.3890476162210212166 ] 
dist 68=[-.64982809366579055077,2.2822241322353964946 ] 
dist 69=[-.81475137621476223931,2.2604283418734804707 ] 
dist 70=[-.99825960846410801532,2.2270186305587882629 ] 
dist 71=[-1.2569900507355049840 ,2.2184668366778589615 ] 
dist 72=[-1.5128944000502494026 ,1.5249012217063630700 ] 
dist 73=[-1.6851010089235973053 ,1.4659911325649410294 ] 
dist 74=[-1.8302581284509148687 ,1.3331138827540065079 ] 
dist 75=[-1.9779851601199950932 ,1.3098933932200721408 ] 
dist 76=[-2.1174067266194900897 ,1.1457473583688099136 ] 
dist 77=[-2.2293492028842468998 ,1.1166756156716005080 ] 
dist 78=[-2.3434608525709859949 ,1.0679032530723025053 ] 
dist 79=[-2.4915600878046360465 ,1.0568739406657267851 ] 
dist 80=[-2.6373801775037631538 ,.88223246791613871855] 
dist 81=[-2.7423781649441969470 ,.85947487096615838738] 
dist 82=[-2.8383841382507261626 ,.80891573714262427455] 
dist 83=[-2.9482439382111162541 ,.79958950248975607132] 
dist 84=[-3.0596446570553741732 ,.73983250101336344331] 
dist 85=[-3.1618157591000676681 ,.72943518676307378226] 
dist 86=[-3.2776088948403477306 ,.71025650423542440434] 
dist 87=[-3.4434943257653193549 ,.70592912101818698671] 
dist 88=[-3.6069731664780918815 ,-.08316190291596285787] 
dist 89=[-3.7131418061874247957 ,-.05779839152606500793] 
dist 90=[-3.7984779638368694029 ,-.02576802939984073079] 
dist 91=[-3.8786358843824770649 ,.01307678701501893620] 
dist 92=[-3.9500796813649424396 ,.06456562418972016652] 
dist 93=[-4.0005634406477255584 ,.14714508669011921095] 
dist 94=[-4.0457577884320111746 ,.23146837588765169901] 
dist 95=[-4.0960472075150624802 ,.28993173213455285917] 
dist 96=[-4.1418146007256873932 ,.34097860947639735276] 
dist 97=[-4.1689234100667574896 ,.39566060429500821653] 
dist 98=[-4.1877683767343889097 ,.44888754591042201496] 
dist 99=[-4.2004848173622348668 ,.49412187282536387537] 
dist 100=[-4.2095469496595078754 ,.54244582026695716643] 
dist 101=[-4.2137754025474332942 ,.60802955642715645172] 
dist 102=[-4.2153083713847983654 ,.67381599080942436177] 
dist 103=[-4.2146982314655602521 ,.72295314241895983234] 
dist 104=[-4.1361354010540183134 ,.76962082072903984968] 
dist 105=[-4.1258711820232161155 ,.82553826413243502164] 
dist 106=[-4.1035518290243866015 ,.88357902232514320258] 
dist 107=[-4.0964551376243285860 ,.93873943545784546643] 
dist 108=[-4.0639057385176584552 ,1.0027366438924981615 ] 
dist 109=[-4.0463007698118950639 ,1.0961141046101120893 ] 
dist 110=[-3.7176243418154231950 ,1.1896603798584145866 ] 
dist 111=[-3.6988136331494234012 ,1.2543341529006979142 ] 
dist 112=[-3.6667563981743509955 ,1.3106841043882070329 ] 
dist 113=[-3.6587796532244568488 ,1.3709494802115412457 ] 
dist 114=[-3.6377311976682982645 ,1.4296305789109936211 ] 
dist 115=[-3.6133112208159257745 ,1.4796478090492106999 ] 
dist 116=[-3.5024464190559013721 ,1.5332579590601018447 ] 
dist 117=[-3.4283879241684574054 ,1.6063094816940443049 ] 
dist 118=[-3.1067958286766349023 ,1.6798263062049562632 ] 
dist 119=[-2.9880806817306120377 ,1.7352988905280827670 ] 
dist 120=[-1.5892661017118616327 ,1.7885805920279764612 ] 
dist 121=[-1.4870096711621481169 ,1.8533388082025339977 ] 
dist 122=[-1.2514747790806056541 ,1.9211077991788781617 ] 
dist 123=[-1.2145156674625130203 ,1.9864318281784249079 ] 
dist 124=[-.88019131190445254536,2.0629752041900554976 ] 
dist 125=[-.73376045370686756431,2.1756143367436949704 ] 
dist 126=[-.03973921490047674508,2.2869964459000280739 ] 
dist 127=[-.02828595613950479571,2.3585136981252146529 ] 
dist 128=[-.02577182477133010420,2.4150503797082049039 ] 
dist 129=[-.01445846537400937737,2.4665233499175307297 ] 
dist 130=[-.01248389638389492636,2.5112636466686338471 ] 
dist 131=[-.00855230904035319694,2.5408762543189323941 ] 
dist 132=[-.00761785468845814244,2.5653045061328201999 ] 
dist 133=[-.00480976979724234104,2.5893140675978089503 ] 
dist 134=[-.00477673388736399474,2.6104836100015019343 ] 
dist 135=[-.00573582210637837789,2.6235540297621334546 ] 
dist 136=[-.00829367287843579074,2.6332999679791286146 ] 
dist 137=[-.01169134904261566753,2.6411716229461450552 ] 
dist 138=[-.01600788222717282880,2.6473119643177114151 ] 
dist 139=[-.02184248729408489999,2.6501327319512102697 ] 
dist 140=[-.03130790237394730665,2.6510844614856994696 ] 
dist 141=[-.04097000011305601161,2.6504154059038603375 ] 
dist 142=[-.04759114388167320868,2.4598068909053358288 ] 
dist 143=[-.05328330417418024071,2.4422423010164714140 ] 
dist 144=[-.05923344134122406136,2.4057133469221026952 ] 
dist 145=[-.06492900585854749393,2.3954728312965700068 ] 
dist 146=[-.06960415897037222939,2.3539883967593403347 ] 
dist 147=[-.07445099216394371546,2.3455439671764964511 ] 
dist 148=[-.08083314125301302369,2.3238945176321661328 ] 
dist 149=[-.08713453130549184711,2.3194772187005829122 ] 
dist 150=[-.09165880660338785818,2.2809890496839765935 ] 
dist 151=[-.09577151499705626344,2.2731107223616033816 ] 
dist 152=[-.10042820311056628193,2.2589070966921593635 ] 
dist 153=[-.1051091140604305778 ,2.2550402810983337844 ] 
dist 154=[-.10931884102030758672,2.2409493419684769839 ] 
dist 155=[-.11401343916889816448,2.2368867363660078427 ] 
dist 156=[-.1206326492158555944 ,2.2297960309803466596 ] 
dist 157=[-.12714836932455782457,2.2275701685098793102 ] 
dist 158=[-.13142935607948290776,.97350236299624169308] 
dist 159=[-.13491674299875673183,.90543829361503816227] 
dist 160=[-.13826029135679011493,.74569496064727008344] 
dist 161=[-.1412778371876488156 ,.7226251605234968154 ] 
dist 162=[-.14346211615733862471,.50674156145766891979] 
dist 163=[-.14546649663969140204,.46797889218054207817] 
dist 164=[-.14776491972347356988,.42104031729873837702] 
dist 165=[-.14987669083276278176,.41252150911327644002] 
dist 166=[-.15113495228478224592,.37124392581609835696] 
dist 167=[-.16969979875052354069,.36888533178691778554] 
dist 168=[-.24308447400539892506,.36815573501693556006] 
dist 169=[-.32453823527092563628,.3644962361404200811 ] 
dist 170=[-.40564396566259246888,.36367870791956503387] 
dist 171=[-.47763734821482275685,.36197687957197433446] 
dist 172=[-.55726108493840070298,.3614405287432327769 ] 
dist 173=[-.66887912986802033463,.27928873200140814789] 
dist 174=[-.77886882471217752736,.27339994932555434623] 
dist 175=[-.85198142625007551187,.26200875724841938511] 
dist 176=[-.91258994620628997391,.25918712311618439958] 
dist 177=[-.97257919766924783082,.24986122516542413675] 
dist 178=[-1.0280879706457445639 ,.24768936784578871279] 
dist 179=[-1.0707804680691028458 ,.24594144838077434436] 
dist 180=[-1.1125650613477145185 ,.24608505660273245018] 
dist 181=[-1.1644439723874468082 ,.24708952906261450111] 
dist 182=[-1.2143666810657673925 ,.24923158141687162364] 
dist 183=[-1.2483291936478740029 ,.25263197990285852205] 
dist 184=[-1.2773446434763098851 ,.25866841653387176203] 
dist 185=[-1.3074855149500771308 ,.26599013053691122426] 
dist 186=[-1.3363063698016924570 ,.27453001279143890664] 
dist 187=[-1.3600439591100716953 ,.2856592544148769658 ] 
dist 188=[-1.3847795879101146966 ,.30333495900022047083] 
dist 189=[-1.4175927886366572112 ,.32164078055006541127] 
dist 190=[-1.4491878618517027422 ,.33528972167998415134] 
dist 191=[-1.4690525282750247626 ,.34823581347407778995] 
dist 192=[-1.4842725091364669882 ,.36373138400439528514] 
dist 193=[-1.4972932857954390069 ,.37981284617404689923] 
dist 194=[-1.5080183318341095563 ,.39510184759001413224] 
dist 195=[-1.5140577802685588280 ,.4128480892662492831 ] 
dist 196=[-1.5178666703225017613 ,.43875539876489546206] 
dist 197=[-1.5196721955499119925 ,.46559684473293964952] 
dist 198=[-1.5204638851221111262 ,.48707847861961192746] 
dist 199=[-1.5202184033113886644 ,.50889951469464748473] 
dist 200=[-1.5192533074695827258 ,.53709822900621229599] 
dist 201=[-1.5185561185947943016 ,.56748466067808323967] 
dist 202=[-1.5137342692896435569 ,.59805379648555020476] 
dist 203=[-1.5123155476171089315 ,.63483283704645715147] 
dist 204=[-1.5075162505684070300 ,.69005093603581943838] 
dist 205=[-1.5062145504823293075 ,.74533173818322674829] 
dist 206=[-1.4062946888794684823 ,.78236153046035606397] 
dist 207=[-1.3961059471288587814 ,.81336922292634804462] 
dist 208=[-1.3731232955529165699 ,.84456939501735262233] 
dist 209=[-1.3674314718219697921 ,.87376843776163120502] 
dist 210=[-1.3369112803840390374 ,.89677420099965129142] 
dist 211=[-1.3308127954621299815 ,.91981161354156573611] 
dist 212=[-1.3183510196609235885 ,.94913723248542954919] 
dist 213=[-1.3147677251626501635 ,.97770924705925782353] 
dist 214=[-1.2695518128537851315 ,.99773321901179703594] 
dist 215=[-1.2629099385566134358 ,1.0154696117681194138 ] 
dist 216=[-1.2456843829287762745 ,1.0348942550666371280 ] 
dist 217=[-1.2431554611201610040 ,1.0540835998045930237 ] 
dist 218=[-1.2127061029691647939 ,1.0708791099762421380 ] 
dist 219=[-1.2065258092549415850 ,1.0892578615417168253 ] 
dist 220=[-1.1787103526469547201 ,1.1147781592757791421 ] 
dist 221=[-1.1278320946672030699 ,1.1398193062112291556 ] 
dist 222=[-.72175941232304200141,1.1562820695814922613 ] 
dist 223=[-.6991644995912205207 ,1.1697272133866604703 ] 
dist 224=[-.64651427032290318646,1.1827017357814782228 ] 
dist 225=[-.63808738349336636164,1.1944894561827577183 ] 
dist 226=[-.56732763003573965034,1.2031889060916295611 ] 
dist 227=[-.55442703058372821407,1.2113531380914815572 ] 
dist 228=[-.53665096662810278615,1.2210006659588661386 ] 
dist 229=[-.53142999389366222396,1.2300406241568761379 ] 
dist 230=[-.43493308599684309451,1.2357753498614909293 ] 
dist 231=[-.42255859266558605167,1.2402264454163109816 ] 
dist 232=[-.39613639851332993284,1.2441335162509278250 ] 
dist 233=[-.38976854302374494372,1.2474239607792838952 ] 
dist 234=[-.36106462237889694624,1.2494093301631370703 ] 
dist 235=[-.3559207247175461069 ,1.2508323450743648539 ] 
dist 236=[-.34354591112236604306,1.2518740707697623619 ] 
dist 237=[-.34169091702275917163,1.2524282869743627100 ] 
dist 238=[-.21616520711153570024,1.2521713197779638908 ] 
dist 239=[-.20439285081814283818,1.2509299529459950954 ] 
dist 240=[-.17720411360660903579,1.2500384060387609602 ] 
dist 241=[-.17285398516158975584,1.2440883938110984071 ] 
dist 242=[-.13727629095221278267,1.2423661941125410642 ] 
dist 243=[-.1308872364956204118 ,1.2388599260347372320 ] 
dist 244=[-.12181997869603523686,1.2375728904318184177 ] 
dist 245=[-.11929331085111711197,1.2117774117356771899 ] 
dist 246=[-.07447002597568163113,1.2076863691816861716 ] 
dist 247=[-.06879724831393530559,1.1986510602310633254 ] 
dist 248=[-.05641844277051964393,1.1957980021112603665 ] 
dist 249=[-.05384700111544654815,1.1827854534060974151 ] 
dist 250=[-.03977886713925868030,1.1598281378887724429 ] 
dist 251=[-.03730935557065164874,1.1549937353021912182 ] 
dist 252=[-.03218027586065242595,1.1257499305630767602 ] 

8 phat 2 dirichlet min maxes function [1, 0, 2, 2, 1, 1, 0, 0, 1] 
dist 0=[13.514324508895465332  ,13.514324508895465332  ] 
dist 1=[13.489255178273718405  ,13.528818084392399267  ] 
dist 2=[13.451459066360055829  ,13.537970692330552688  ] 
dist 3=[13.386077862234366265  ,13.541682828862279501  ] 
dist 4=[13.316009458370926836  ,13.542132217049017226  ] 
dist 5=[13.259469526121406520  ,13.540042127873747276  ] 
dist 6=[13.201619663499853103  ,13.533222193134362547  ] 
dist 7=[13.126306949829023656  ,13.527879333311556144  ] 
dist 8=[13.044868201238039578  ,13.482648807277255337  ] 
dist 9=[12.962517488609110862  ,13.385116567487768487  ] 
dist 10=[12.863115047567282646  ,13.356756369999032930  ] 
dist 11=[12.713483830712445262  ,13.346168114612219224  ] 
dist 12=[12.556488743783429675  ,13.329350598315162157  ] 
dist 13=[12.427636337201168711  ,13.323639307696216876  ] 
dist 14=[12.293771617410816896  ,13.299933084499005895  ] 
dist 15=[12.116729350636714676  ,13.289543231608654915  ] 
dist 16=[11.923859222126161281  ,13.215096631351441155  ] 
dist 17=[11.726696180652983103  ,12.706524142151483764  ] 
dist 18=[11.487127480480904156  ,12.681117289380148539  ] 
dist 19=[11.124671954927807994  ,12.670871693339455793  ] 
dist 20=[10.760173507344942949  ,12.350128657502002519  ] 
dist 21=[10.512433933540578823  ,12.309037627787133602  ] 
dist 22=[10.300975324425064746  ,12.238506900091906754  ] 
dist 23=[10.081565939531590992  ,12.221506995660124583  ] 
dist 24=[9.8718760018157407352 ,12.177527311850384442  ] 
dist 25=[9.6992844907455029585 ,12.126786228117923266  ] 
dist 26=[9.5195169151456258640 ,11.899718283722471133  ] 
dist 27=[9.2811255031301435755 ,11.750094852467542615  ] 
dist 28=[9.0440707313062427186 ,11.104880942582510896  ] 
dist 29=[8.6827447023982284424 ,10.867279585355084864  ] 
dist 30=[8.0723948924672832551 ,10.777956883873362397  ] 
dist 31=[7.6605418566084579096 ,10.730314743892843420  ] 
dist 32=[7.3122736400937199333 ,10.718031011184248628  ] 
dist 33=[6.9561950394556797956 ,9.6002672487597959395 ] 
dist 34=[6.6192264396522120543 ,9.5010297586947058174 ] 
dist 35=[6.3473761914109207369 ,9.2802376615435418000 ] 
dist 36=[6.0691609763901845833 ,9.2335432490676818391 ] 
dist 37=[5.7067345992542900565 ,8.9628446990708870078 ] 
dist 38=[5.3494441879016644785 ,8.9128398281428137542 ] 
dist 39=[5.0917652253027956934 ,8.8147918364053673640 ] 
dist 40=[4.8558210826283076785 ,8.7894339197334131871 ] 
dist 41=[4.5854450757990559520 ,8.4918016627006687201 ] 
dist 42=[4.3111769781297026740 ,8.4483701034805313792 ] 
dist 43=[4.0596639084746109156 ,8.3505894284244076577 ] 
dist 44=[3.7747369306669182392 ,8.3284584406303132381 ] 
dist 45=[3.3668363966625800442 ,8.2019167143787131604 ] 
dist 46=[2.9608259996374868389 ,8.1774788929227243766 ] 
dist 47=[2.6834553321053385510 ,8.1294732229808126998 ] 
dist 48=[2.4451478010358708729 ,8.1164962805855840415 ] 
dist 49=[2.1953540685526593043 ,6.3721555664324578254 ] 
dist 50=[1.9550170641297982234 ,6.3434210121040425706 ] 
dist 51=[1.7545244352839213229 ,6.3355971466084510397 ] 
dist 52=[1.5432788182448876066 ,4.9698087980831228786 ] 
dist 53=[1.2599297831759590173 ,4.8864412049087169081 ] 
dist 54=[.97658980179446895746,4.7096667217359608676 ] 
dist 55=[.76537598953031431953,4.6705267120550932271 ] 
dist 56=[.56492028319974229632,4.4893826759686631519 ] 
dist 57=[.32459960625564850357,4.4255623683580255577 ] 
dist 58=[.07473930943445252284,4.2866211200702729342 ] 
dist 59=[-.16387593274439883039,4.1873360333856225294 ] 
dist 60=[-.44187341691167990037,3.7438114154566799072 ] 
dist 61=[-.84925270503800821783,3.6010148402269958657 ] 
dist 62=[-1.2534293548778984995 ,2.4712330998166301151 ] 
dist 63=[-1.5186201483884551140 ,2.4284097544821135588 ] 
dist 64=[-1.7348400930170365617 ,2.4194357422211915824 ] 
dist 65=[-1.9431548890530203577 ,1.2986106001049415914 ] 
dist 66=[-2.1324185782489153781 ,1.2063897628615385775 ] 
dist 67=[-2.2724445148152536992 ,.99835330591076993004] 
dist 68=[-2.4043400682007208372 ,.96341405538406038467] 
dist 69=[-2.5610919006853468583 ,.70870559728818100121] 
dist 70=[-2.7087242196254424374 ,.66429948296203872342] 
dist 71=[-2.8041483404039454050 ,.59216255211209914333] 
dist 72=[-2.8803774053419524723 ,.57560891879538128885] 
dist 73=[-2.9512396584101051434 ,.32041537311419639065] 
dist 74=[-3.0139598297227988383 ,.28768308514841198875] 
dist 75=[-3.0576298571632331548 ,.21837594505579312992] 
dist 76=[-3.0961151322663881363 ,.2041183430187029962 ] 
dist 77=[-3.1381139526611929111 ,.13478053897252747659] 
dist 78=[-3.2232857800220509918 ,.12310381099041801206] 
dist 79=[-3.3263864873815121997 ,.0998179157410828122 ] 
dist 80=[-3.4698602851886908888 ,.09485494276758339553] 
dist 81=[-3.6098108413808604507 ,-.68028989409901187122] 
dist 82=[-3.6988223205740036243 ,-.69555063164964016659] 
dist 83=[-3.7682687725571464620 ,-.69810672108508683672] 
dist 84=[-3.8299668093630887573 ,-1.1968762317315926217 ] 
dist 85=[-3.8825626354906319070 ,-1.2283272394521723997 ] 
dist 86=[-3.9156056543424226866 ,-1.2958793109747859550 ] 
dist 87=[-3.9409341109350684850 ,-1.3091391029546947029 ] 
dist 88=[-3.9626803005990251379 ,-1.3806395528323594524 ] 
dist 89=[-3.9807697744305784888 ,-1.3924473371650928103 ] 
dist 90=[-3.9914722879676589041 ,-1.4175414846046937188 ] 
dist 91=[-3.9989238171336047035 ,-1.4218290033596451973 ] 
dist 92=[-4.0040034992136305804 ,-1.4520704517679999179 ] 
dist 93=[-4.0072382362308264169 ,-1.4561831910739915103 ] 
dist 94=[-4.0073073238147760734 ,-1.4544880011276888931 ] 
dist 95=[-4.0051400406550815646 ,-1.2923522008361060923 ] 
dist 96=[-4.0035024997256025217 ,-1.1422646036817416648 ] 
dist 97=[-3.6891048307741344134 ,-.9889402386162187072 ] 
dist 98=[-3.6599668662302476660 ,-.84403126934645007469] 
dist 99=[-3.5978033362760823152 ,-.72758986644892863028] 
dist 100=[-3.5802034197501689060 ,-.60890982194201665721] 
dist 101=[-3.5076045933871636076 ,-.45504740829846988823] 
dist 102=[-3.4933399853485101022 ,-.30385441096028520276] 
dist 103=[-3.4561951636907919399 ,-.19584653675456289825] 
dist 104=[-3.4499232209159758618 ,-.09805808576888196669] 
dist 105=[-3.3737867041032298559 ,.01227478904326344025] 
dist 106=[-3.3599783886786881053 ,.12315196495435406286] 
dist 107=[-3.3320686546638102350 ,.22311853403954124343] 
dist 108=[-3.3240316034127267162 ,.33494199609705803815] 
dist 109=[-3.2908708812114443504 ,.49323190434153958331] 
dist 110=[-3.2835363075513260262 ,.64982257109155341953] 
dist 111=[-3.2644849786741692391 ,.75485235542202389248] 
dist 112=[-3.2595077821749696129 ,.84294395910624663574] 
dist 113=[-2.4139311294997057205 ,.93180658536192680083] 
dist 114=[-2.3945768836277705073 ,1.0151092590211778718 ] 
dist 115=[-2.3372883704972615267 ,1.0809698924157477487 ] 
dist 116=[-1.1554669903865898258 ,1.1471330380127630377 ] 
dist 117=[-.84601081295263920289,1.2316475430184430584 ] 
dist 118=[-.79040730176633711266,1.3141413350341273434 ] 
dist 119=[-.72377698856978431951,1.3722254471327738284 ] 
dist 120=[-.71220239191402584004,1.4239639950045185418 ] 
dist 121=[-.27907283469039637163,1.4810851761547684136 ] 
dist 122=[-.22635510586111119439,1.5377994716623780827 ] 
dist 123=[-.11999510322506652437,1.5879129583890683773 ] 
dist 124=[-.09324478602272469815,1.6431637547561656102 ] 
dist 125=[-.00046542407265514368,1.7204250631357734886 ] 
dist 126=[.01850854628425864241,1.7959637081012297360 ] 
dist 127=[.04316101538672437620,1.8443263376901345114 ] 
dist 128=[.04845443498340780977,1.8823960987303716266 ] 
dist 129=[.63457296084097903964,1.9167729405402614198 ] 
dist 130=[.68250514990664476093,1.9464507580105316835 ] 
dist 131=[.79170916808800766461,1.9657293245634780674 ] 
dist 132=[.80845820450685696375,1.9812281967048532683 ] 
dist 133=[.94433635057232591875,1.9957922526208905837 ] 
dist 134=[.96778789210146114903,2.0083046707183378187 ] 
dist 135=[1.0013866460285723012 ,2.0155987983841323210 ] 
dist 136=[1.0100043386895885590 ,2.0205267398937904252 ] 
dist 137=[1.1508200059278917072 ,2.0235748121425344919 ] 
dist 138=[1.1678370730464105734 ,2.0252121320768802457 ] 
dist 139=[1.2046715921498192712 ,2.0579457961973826899 ] 
dist 140=[1.2106825682159794451 ,2.0944163193843141178 ] 
dist 141=[1.2131277831847084564 ,2.1282332263276464358 ] 
dist 142=[1.1781687864437880844 ,2.1543769042567387319 ] 
dist 143=[1.1508306133890430430 ,2.1801020735329486518 ] 
dist 144=[1.1236594952794906852 ,2.2122476574666315539 ] 
dist 145=[1.0893663297492785299 ,2.2424593096573669082 ] 
dist 146=[1.0528345321701350039 ,2.2604511671266608093 ] 
dist 147=[1.0167111240937259426 ,2.2730718110012537237 ] 
dist 148=[.97371595408044940702,2.2818031284936820291 ] 
dist 149=[.90970620206632806805,2.2880774348312350544 ] 
dist 150=[.84288250322989662409,2.2908716337351004846 ] 
dist 151=[.78863501867995062699,2.2916740103291390494 ] 
dist 152=[.73283481532250691293,2.2913699105787925014 ] 
dist 153=[.65980154600452337763,2.2634595332143748814 ] 
dist 154=[.58065176592078274072,2.2584888988723340705 ] 
dist 155=[.50039359866184924224,2.2498426731283401912 ] 
dist 156=[.40337900370568776638,2.2472621725785544382 ] 
dist 157=[.25722639550539320592,2.2371390176253646785 ] 
dist 158=[.11076397883452162639,2.2340420906425076073 ] 
dist 159=[.01251039651392530194,2.2274571068010919866 ] 
dist 160=[-.06991495107090407151,2.2250153745691814159 ] 
dist 161=[-.15308657261285283306,1.9934067976502514440 ] 
dist 162=[-.23106495002608960132,1.9720618357008663692 ] 
dist 163=[-.29272466417917751773,1.9252568119194177704 ] 
dist 164=[-.35466958649772472693,1.9135494202428608331 ] 
dist 165=[-.43378863402114974647,1.8567902544556837508 ] 
dist 166=[-.51099245308491262256,1.8458747882008333993 ] 
dist 167=[-.56527921209360202172,1.8216164757837645198 ] 
dist 168=[-.61354882656959649365,1.8148377469209357766 ] 
dist 169=[-.66669246348403530283,1.7513219730064824777 ] 
dist 170=[-.7193523134463681668 ,1.7410455666939989572 ] 
dist 171=[-.76568759794556217937,1.7181820671266904511 ] 
dist 172=[-.8165927540934250249 ,1.7118239959579425039 ] 
dist 173=[-.895327855346039691  ,1.6818332467876739045 ] 
dist 174=[-.97753800368021158017,1.6756715385202134505 ] 
dist 175=[-1.0313151079383888686 ,1.6619769678430738335 ] 
dist 176=[-1.0749300514695375126 ,1.6577063462507604546 ] 
dist 177=[-1.1165051652729035693 ,.90571452896080216417] 
dist 178=[-1.1539311903075559533 ,.87815908755722516931] 
dist 179=[-1.1809552861974971583 ,.81388566946358888965] 
dist 180=[-1.2057218067663013476 ,.80366721619051335577] 
dist 181=[-1.2341204098970140521 ,.71711224765660189909] 
dist 182=[-1.2603843529271633730 ,.70133229287991589936] 
dist 183=[-1.2766151406708857723 ,.6798118023404635611 ] 
dist 184=[-1.2887140575995581991 ,.67341810514693575118] 
dist 185=[-1.2984563421231609350 ,.55480893136220458051] 
dist 186=[-1.3061101544073373385 ,.53960993884230791149] 
dist 187=[-1.3098579497701122624 ,.50732232306499530078] 
dist 188=[-1.3117201573295435009 ,.49939152120653260885] 
dist 189=[-1.3118813951588884161 ,.46489734658439831749] 
dist 190=[-.97631735721709917714,.45865360402725927083] 
dist 191=[-1.0316313024062513044 ,.4438024678074815148 ] 
dist 192=[-1.1163492870687504329 ,.44142912366068886748] 
dist 193=[-1.2043906148050115487 ,.28374882514042750952] 
dist 194=[-1.2619696875982178129 ,.26911279698763611522] 
dist 195=[-1.3086599471223674351 ,.23509811046030933911] 
dist 196=[-1.3531594396625075483 ,.22984503378551604088] 
dist 197=[-1.3932186574661689208 ,.18472106280566977661] 
dist 198=[-1.4221532514984025302 ,.1766053496684853289 ] 
dist 199=[-1.4486829953989378149 ,.16573818095012387365] 
dist 200=[-1.4791256628586736182 ,.16283878023381221372] 
dist 201=[-1.5072761595138547300 ,.10358403274261718322] 
dist 202=[-1.5246400719172090543 ,.09614893302481831741] 
dist 203=[-1.5375465771985696026 ,.08041468711195306950] 
dist 204=[-1.5478731331240128756 ,.07669701225156682106] 
dist 205=[-1.5559821462571370821 ,.06038632353279455813] 
dist 206=[-1.5600212071068787324 ,.05746600591497524732] 
dist 207=[-1.5620190510713387506 ,.05097189575991634857] 

8 phat 2 dirichlet min maxes function [0, 2, 1, 1, 2, 0, 1] 
dist 0=[13.305505901240566942  ,13.305505901240566942  ] 
dist 1=[13.289970576873871327  ,13.318961306517968152  ] 
dist 2=[13.266695661312190096  ,13.333920971990648107  ] 
dist 3=[13.233116485631932380  ,13.352967265910622535  ] 
dist 4=[13.176387198926497597  ,13.382759356931605893  ] 
dist 5=[13.107400955592425989  ,13.411577494835449313  ] 
dist 6=[13.024811690476726731  ,13.426726077927517336  ] 
dist 7=[12.915844479297756203  ,13.434856684654773915  ] 
dist 8=[12.741376476380491152  ,13.435607066215986766  ] 
dist 9=[12.560121887634698807  ,13.432704861079543307  ] 
dist 10=[12.424014212073843006  ,13.429652684204197850  ] 
dist 11=[12.293954113664558831  ,13.418921784951995590  ] 
dist 12=[12.136877415222388839  ,13.413139306236171249  ] 
dist 13=[11.973076790510464436  ,13.101008738576117902  ] 
dist 14=[11.816125421999083396  ,13.067423832103137460  ] 
dist 15=[11.632976868474741533  ,12.993113192993642372  ] 
dist 16=[11.364413207264820715  ,12.971772976146139004  ] 
dist 17=[11.085573058389055785  ,12.875151024039905682  ] 
dist 18=[10.861327806690843753  ,12.855181121535105852  ] 
dist 19=[10.632496529710815170  ,12.809530198907000804  ] 
dist 20=[10.335314284909433324  ,12.795238799761335415  ] 
dist 21=[10.014257523383219567  ,12.652683280878877437  ] 
dist 22=[9.6899512587017087276 ,12.629980699020411730  ] 
dist 23=[9.2987228400902594878 ,12.571774164754904376  ] 
dist 24=[8.7100445701319479758 ,12.561279463403518857  ] 
dist 25=[8.1195857518883189571 ,12.460243282058451744  ] 
dist 26=[7.7212358067804749692 ,12.439145126177040437  ] 
dist 27=[7.3844697036859339646 ,12.413646515510827209  ] 
dist 28=[7.0402811447173186858 ,12.402868107905953886  ] 
dist 29=[6.7146421151889686297 ,10.226241794419253680  ] 
dist 30=[6.4520530434696339937 ,10.092258842252712650  ] 
dist 31=[6.1834233103030324490 ,9.7773087784514278576 ] 
dist 32=[5.8336236054509982196 ,9.7298957396154759724 ] 
dist 33=[5.4888418532960386932 ,9.3523276983919911857 ] 
dist 34=[5.2402766428297556908 ,9.3045557280045729288 ] 
dist 35=[5.0127695203676478806 ,9.2127069591768879071 ] 
dist 36=[4.7521963300175104713 ,9.1892814926326091970 ] 
dist 37=[4.4879455331815833460 ,8.8903957871399067549 ] 
dist 38=[4.2457274292235316446 ,8.8477023951871785288 ] 
dist 39=[3.9714156423205710268 ,8.7478646244989297592 ] 
dist 40=[3.5788122486580095548 ,8.7284898113401820906 ] 
dist 41=[3.1880649161449560401 ,8.5881823875203148048 ] 
dist 42=[2.9211733191695992817 ,8.5609853778587337743 ] 
dist 43=[2.6919233205466117457 ,8.5169328905006103046 ] 
dist 44=[2.4517081090277373943 ,8.5053186869749626862 ] 
dist 45=[2.2206374799508344366 ,6.9847210489476232933 ] 
dist 46=[2.0279543352223992999 ,6.9010006471124191325 ] 
dist 47=[1.8250059735938897648 ,6.7092113077927337168 ] 
dist 48=[1.5528743891615507760 ,6.6774747276087206882 ] 
dist 49=[1.2807903078613135868 ,6.4312378753034772533 ] 
dist 50=[1.0780277417788116720 ,6.3871821867780524071 ] 
dist 51=[.88565182331490431989,6.3207947238619447632 ] 
dist 52=[.65510180046028015653,6.3035893735900734071 ] 
dist 53=[.41544446694870750392,6.0080905839016669360 ] 
dist 54=[.18663828640550378757,5.9705366669273717152 ] 
dist 55=[-.07988156596898817166,5.8859460176315892614 ] 
dist 56=[-.47038408806054148464,5.8707727886240294132 ] 
dist 57=[-.85788284821075067592,5.7663982650904437064 ] 
dist 58=[-1.1123912595672483714 ,5.7478503912883424298 ] 
dist 59=[-1.3201927428305140920 ,5.7156224628434242652 ] 
dist 60=[-1.5208840887258198946 ,5.7085902579716321545 ] 
dist 61=[-1.7035468816281995725 ,2.4238946724604961772 ] 
dist 62=[-1.8392438494843244147 ,2.2765989555158390468 ] 
dist 63=[-1.9676105618891978316 ,1.9339821223100716078 ] 
dist 64=[-2.1209610876265325302 ,1.8845789328335036986 ] 
dist 65=[-2.2657954460672196772 ,1.4321891590373619324 ] 
dist 66=[-2.3601035744176929220 ,1.3518568870984428365 ] 
dist 67=[-2.4362238762981047244 ,1.2529589863211535952 ] 
dist 68=[-2.5808094039103814240 ,1.2353065781424694341 ] 
dist 69=[-2.7543842064273359238 ,.95177414992255241601] 
dist 70=[-2.8765602013356633051 ,.91869824031726777259] 
dist 71=[-2.9854106762765113830 ,.85064070506466596954] 
dist 72=[-3.1056972366311077743 ,.83434856769308336286] 
dist 73=[-3.2252699531353686205 ,.77293851088235896377] 
dist 74=[-3.3312705668178514057 ,.76137778316564227337] 
dist 75=[-3.4484827324798978293 ,.74346414989625415165] 
dist 76=[-3.6129043258733437987 ,.73934172560220352719] 
dist 77=[-3.7736643546943304459 ,-.5403879545095998112 ] 
dist 78=[-3.8762341887842679483 ,-.6002544028875864077 ] 
dist 79=[-3.9566274063544573291 ,-.7363299460352607995 ] 
dist 80=[-4.0286900582265119992 ,-.7573049644653725275 ] 
dist 81=[-4.0905798958817544302 ,-.9260842881367349440 ] 
dist 82=[-4.1302880124600683707 ,-.9552711200540350926 ] 
dist 83=[-4.1616850763280288772 ,-.9972394964548308236 ] 
dist 84=[-4.1903400518617273441 ,-1.0081775113440118376 ] 
dist 85=[-4.2148210287863552734 ,-1.1849315255269796076 ] 
dist 86=[-4.2295232695636841177 ,-1.2063341043972884308 ] 
dist 87=[-4.2400204233312347329 ,-1.2539242202068627419 ] 
dist 88=[-4.2476752144284282811 ,-1.2609556519545791503 ] 
dist 89=[-4.2530100889259021376 ,-1.2779897080340557635 ] 
dist 90=[-4.2542249189406125865 ,-1.1211634658765628575 ] 
dist 91=[-4.2526742017078221311 ,-.98845716612145821962] 
dist 92=[-4.2512150496364855837 ,-.85274184317882298677] 
dist 93=[-3.9304305869889328691 ,-.72438959465395905078] 
dist 94=[-3.9006089663376942018 ,-.62112162076465921352] 
dist 95=[-3.8372680334280296136 ,-.51575308658952762467] 
dist 96=[-3.8193361154142366729 ,-.37899966632418721349] 
dist 97=[-3.7453760581499272591 ,-.24455645705780219304] 
dist 98=[-3.7308491713454034171 ,-.14842379061874893092] 
dist 99=[-3.6920723982140922187 ,-.06129744281579369609] 
dist 100=[-3.6861052709333349047 ,.03713645683579020968] 
dist 101=[-3.6094179893090625354 ,.13612700491928375822] 
dist 102=[-3.5952424127880820212 ,.22548073736358919859] 
dist 103=[-3.5669491358748377826 ,.32551468644359322876] 
dist 104=[-3.5588241415918127354 ,.46721249956062939422] 
dist 105=[-3.5255828237913089867 ,.60742122477448932148] 
dist 106=[-3.5180216621642941110 ,.70150179821314735378] 
dist 107=[-3.4989778034037106225 ,.78044976711228879231] 
dist 108=[-3.4932236305525055514 ,.86015058334096446481] 
dist 109=[-2.3850248422397824242 ,.9349017652293861454 ] 
dist 110=[-2.3739181810634977464 ,.99405923263993119244] 
dist 111=[-2.3486256837147946876 ,1.0535405707669321295 ] 
dist 112=[-2.3425883516617946115 ,1.1295887831557083671 ] 
dist 113=[-2.3082758647735444649 ,1.2038488073647929848 ] 
dist 114=[-2.3014142681712199362 ,1.2561808418874497073 ] 
dist 115=[-2.2879765069485462496 ,1.3028416818427256661 ] 
dist 116=[-2.2842416296010654682 ,1.3544257030773147986 ] 
dist 117=[-2.1327696697648248156 ,1.4056808755157768194 ] 
dist 118=[-2.1154435646092405555 ,1.4510285098412388717 ] 
dist 119=[-2.0893062171816141663 ,1.5010717357839287744 ] 
dist 120=[-2.0822054217104120119 ,1.5711070463901132506 ] 
dist 121=[-1.9555491134460631990 ,1.6395792191835568414 ] 
dist 122=[-1.9423416571440835388 ,1.6833721783219293850 ] 
dist 123=[-1.8544134396667024095 ,1.7177915518207336849 ] 
dist 124=[-1.7189558398823517969 ,1.7487784496136212783 ] 
dist 125=[.68145028146069891106,1.7754618094434319427 ] 
dist 126=[.73309682747685444895,1.7926716245413999611 ] 
dist 127=[.85059084103102812   ,1.8063673746134632138 ] 
dist 128=[.86875508304772760566,1.8189991669722799714 ] 
dist 129=[1.0144281527617887622 ,1.8297904841562200479 ] 
dist 130=[1.0395519778306185878 ,1.8541623442495766902 ] 
dist 131=[1.0760568367574853921 ,1.9158725439087117170 ] 
dist 132=[1.0854226915470233193 ,1.9914029309518122614 ] 
dist 133=[1.1151797937963560210 ,2.0635520305584156578 ] 
dist 134=[1.1045718833128890109 ,2.1117416856685120057 ] 
dist 135=[1.0886158044814222415 ,2.1519512139173241530 ] 
dist 136=[1.0610574104584977408 ,2.1921899383981207968 ] 
dist 137=[1.0317094868487482158 ,2.2297209794105795726 ] 
dist 138=[1.0085974345521594941 ,2.2591040241929579450 ] 
dist 139=[.98547568389705812753,2.2883653917699472593 ] 
dist 140=[.95608704624835567397,2.3254123143879295114 ] 
dist 141=[.92467539633647708792,2.3604187659648113036 ] 
dist 142=[.89346364457745252489,2.3815208117314957024 ] 
dist 143=[.85620279232563726755,2.3966359303266982472 ] 
dist 144=[.80060279586718707221,2.4076997547361192671 ] 
dist 145=[.7425071438127681161 ,2.4159171733419191386 ] 
dist 146=[.69526676755566411214,2.4196486116356138256 ] 
dist 147=[.64660401329077979903,2.4209341184004995800 ] 
dist 148=[.58282007089258924849,2.4207812786076634271 ] 
dist 149=[.51364952530806449824,2.3967936318030971480 ] 
dist 150=[.44344751546975628711,2.3922122885241905644 ] 
dist 151=[.35854385103261298429,2.3842338462639851192 ] 
dist 152=[.2305868923558664381 ,2.3817554819258199515 ] 
dist 153=[.10234376465430388361,2.3715412763318568569 ] 
dist 154=[.01629565751431403079,2.3684517823130961033 ] 
dist 155=[-.05590813525173079184,2.3612100146085850371 ] 
dist 156=[-.12879351123395588789,2.3583924496176885400 ] 
dist 157=[-.19714496016903411883,2.1252765212036047956 ] 
dist 158=[-.25121950504026687494,2.1035371280855526114 ] 
dist 159=[-.3055688761015250452 ,2.0557350890990847849 ] 
dist 160=[-.37501946235521326361,2.0437821471587885726 ] 
dist 161=[-.44280382813594856155,1.9852603483386198810 ] 
dist 162=[-.49049073200615476672,1.9739561658166561119 ] 
dist 163=[-.53291621855445508879,1.9490498600386915616 ] 
dist 164=[-.5796623105111915563 ,1.9417940453136860051 ] 
dist 165=[-.62600393915014894151,1.8742616343824478257 ] 
dist 166=[-.66681227593394227634,1.8634315253494552582 ] 
dist 167=[-.71167215657898835702,1.8387957398766481141 ] 
dist 168=[-.78068230345621422729,1.8324421030663430395 ] 
dist 169=[-.85461621460435695666,1.7985243798419499692 ] 
dist 170=[-.90296417453240283986,1.7915702884844523519 ] 
dist 171=[-.94215851270743145422,1.7774075160807576463 ] 
dist 172=[-.97949023423471330825,1.7732629385091832387 ] 
dist 173=[-1.0130761385574352249 ,.98840618790312326874] 
dist 174=[-1.0372921924365653624 ,.95839462552854533619] 
dist 175=[-1.0594493327922061261 ,.88838679350087149694] 
dist 176=[-1.0848022078316492840 ,.87725293145026202104] 
dist 177=[-1.1082610105861360303 ,.78295108111588418655] 
dist 178=[-1.1228444566913863574 ,.76575554942595500058] 
dist 179=[-1.1338175705740126182 ,.74230114431469299018] 
dist 180=[-1.1428401876076005826 ,.73533233929183704457] 
dist 181=[-1.1499911771148655939 ,.60601737576202016316] 
dist 182=[-1.1534804976997652821 ,.5894437443284583768 ] 
dist 183=[-1.1552623444683058200 ,.55423474552790690597] 
dist 184=[-1.1555854742086439586 ,.5455823580354223426 ] 
dist 185=[-1.0109949009231453831 ,.50795687758465130921] 
dist 186=[-1.0659386982298946050 ,.50114524985726586444] 
dist 187=[-1.1261345876676872232 ,.48493456806805561668] 
dist 188=[-1.2162839260118157566 ,.48234727598215253315] 
dist 189=[-1.3109129249369089425 ,.31018848533075399914] 
dist 190=[-1.3728208569049824395 ,.29420712162854446218] 
dist 191=[-1.4230441975159778409 ,.2570610412535085476 ] 
dist 192=[-1.4709492690674472154 ,.25132590203111491633] 
dist 193=[-1.5141000075191145195 ,.20203192539571766071] 
dist 194=[-1.5453118533730111107 ,.19316517717558678152] 
dist 195=[-1.5739744725339769457 ,.18129992967222362666] 
dist 196=[-1.6069313442879524534 ,.17813807469978792668] 
dist 197=[-1.6373972399991358469 ,.11334986212148508332] 
dist 198=[-1.6560990590277000594 ,.10522095954020251693] 
dist 199=[-1.6698926930603585320 ,.08802363914276436358] 
dist 200=[-1.6807321020631613150 ,.08395428568973271710] 
dist 201=[-1.6892147865854729664 ,.06614517287503010729] 
dist 202=[-1.6935844284018804298 ,.06295314055365015238] 
dist 203=[-1.6958066068268105565 ,.05586725222273462798] 

8 phat 2 dirichlet min maxes function [1, 2, 1, 0, 1, 1, 1, 0, 1] 
dist 0=[12.376105166882774906  ,12.376105166882774906  ] 
dist 1=[12.361538572833223725  ,12.387405661386019347  ] 
dist 2=[12.341704791842569204  ,12.395540492320563866  ] 
dist 3=[12.309334209925275976  ,12.397447877026379416  ] 
dist 4=[12.271102997290550610  ,12.396278129228747222  ] 
dist 5=[12.227829409254021797  ,12.394077378549603437  ] 
dist 6=[12.172254693352123177  ,12.376014343123511195  ] 
dist 7=[12.084828447511370636  ,12.370263240301713639  ] 
dist 8=[11.991565303856150476  ,12.357983078374765021  ] 
dist 9=[11.912646820027984713  ,12.353128765289544294  ] 
dist 10=[11.828537883911035594  ,12.257818746981832149  ] 
dist 11=[11.714514905999678467  ,12.242434322600731548  ] 
dist 12=[11.588937347624153962  ,12.208443067042010276  ] 
dist 13=[11.458618759706475685  ,12.197601624525874945  ] 
dist 14=[11.298870224718642884  ,12.147731645730811663  ] 
dist 15=[11.055596872109467167  ,12.136633861412957914  ] 
dist 16=[10.810279679340202858  ,12.108964152800623703  ] 
dist 17=[10.642356543299190457  ,12.100366355985118459  ] 
dist 18=[10.497735631467998752  ,11.689148386591926289  ] 
dist 19=[10.345605618673003623  ,11.645417387791956691  ] 
dist 20=[10.198917646064406596  ,11.561803556445926755  ] 
dist 21=[10.076058495789995097  ,11.540602487861587620  ] 
dist 22=[9.9461912532226657865 ,11.468518987565629233  ] 
dist 23=[9.7714734672414061051 ,11.450900749631764475  ] 
dist 24=[9.5965557623506424899 ,11.431356101359213443  ] 
dist 25=[9.4658872601896332297 ,11.422988710207537075  ] 
dist 26=[9.3416191762528996331 ,10.561997148700256966  ] 
dist 27=[9.1922958487811252118 ,10.480410492849117609  ] 
dist 28=[9.0368911986179023781 ,10.385258160644278030  ] 
dist 29=[8.8882995321000235640 ,10.351515676741866036  ] 
dist 30=[8.7150720201430316458 ,9.7140879522456674300 ] 
dist 31=[8.4611364079360532572 ,9.6062732940165364908 ] 
dist 32=[8.2057355166726291498 ,9.2794204522605510668 ] 
dist 33=[8.0266464140347932631 ,9.2649437193764509366 ] 
dist 34=[7.7284787497425387133 ,8.3509771185529026687 ] 
dist 35=[7.4427808013526708815 ,8.2681044946675851599 ] 
dist 36=[7.1492504377542290650 ,8.0809349675982687923 ] 
dist 37=[6.8705670207050389490 ,8.0442088476205556327 ] 
dist 38=[6.6442394604660339308 ,7.9077560273703726774 ] 
dist 39=[6.4112439913159661863 ,7.8928707172987408648 ] 
dist 40=[6.1058911445674175443 ,7.6834942853662672123 ] 
dist 41=[5.8039838776727620247 ,7.6646692922508773751 ] 
dist 42=[5.5847648953318559770 ,7.5786845288015619778 ] 
dist 43=[5.3825214057649303411 ,7.5657791669469369201 ] 
dist 44=[5.1484964428598137017 ,7.4793733554864388749 ] 
dist 45=[4.9098156777184396258 ,7.4633411874642717768 ] 
dist 46=[4.5732546093801869834 ,7.4351475135846208364 ] 
dist 47=[4.2357569025766073986 ,7.4286651819864357582 ] 
dist 48=[3.8339782678355698088 ,7.0239958443001289274 ] 
dist 49=[3.2354031908451720507 ,7.0161908820609788727 ] 
dist 50=[2.6370467728862046198 ,5.7243775851643608774 ] 
dist 51=[2.2361427249735331831 ,5.6856538305831481367 ] 
dist 52=[1.9001753356342781263 ,5.4837998103786660453 ] 
dist 53=[1.5615091667702937967 ,5.4491628637196431340 ] 
dist 54=[1.2440091455931247982 ,5.3739763215371800984 ] 
dist 55=[.99268767277093400538,5.3594669544999793607 ] 
dist 56=[.7398346327446007427 ,5.2380219552785472714 ] 
dist 57=[.4162088025363968272 ,4.6753176448778751096 ] 
dist 58=[.0998348382979146017 ,4.5795679929717125330 ] 
dist 59=[-.1240175287953994202 ,4.5548637221339342516 ] 
dist 60=[-.32461667819884133931,4.5210623515500188573 ] 
dist 61=[-.54799856777967626625,4.1626882968933330045 ] 
dist 62=[-.77096056168991916862,4.1052148236664603414 ] 
dist 63=[-.9698816446171823771 ,3.8152241388092024256 ] 
dist 64=[-1.1908038370006734291 ,3.2922297258835013358 ] 
dist 65=[-1.5017540099912654646 ,2.8132778263010060407 ] 
dist 66=[-1.8090253906003695981 ,1.9446961689029091061 ] 
dist 67=[-2.0152362903341749383 ,1.8709459508932761468 ] 
dist 68=[-2.1884290834568070045 ,1.7047556792113706933 ] 
dist 69=[-2.3636559050405516191 ,1.6754208220653200924 ] 
dist 70=[-2.5283630353530266994 ,1.4704625214640551932 ] 
dist 71=[-2.6594870681687409065 ,1.4341253226588258635 ] 
dist 72=[-2.7921201468755706707 ,1.3723102146843690836 ] 
dist 73=[-2.9628655536945608966 ,1.3585339393319626401 ] 
dist 74=[-3.1303076630062137677 ,1.1417011359385187752 ] 
dist 75=[-3.2497318462792490873 ,1.1132418432610004445 ] 
dist 76=[-3.3577585588716312797 ,1.0504268648854330171 ] 
dist 77=[-3.4796215500849377793 ,1.0383785797749148481 ] 
dist 78=[-3.6022015476389176413 ,1.0139431524160809714 ] 
dist 79=[-3.7130990336545967137 ,1.0099744717799439079 ] 
dist 80=[-3.8375587448908007953 ,.92809244874507182855] 
dist 81=[-4.0143850989647295107 ,.92227897349558366018] 
dist 82=[-4.1878788189124697055 ,.87564607655422103331] 
dist 83=[-4.2990113914193422465 ,.86987537323829683001] 
dist 84=[-4.3866008214975766864 ,.85187197909569919675] 
dist 85=[-4.4659346908900655918 ,.84715517077668720396] 
dist 86=[-4.5346384847909018742 ,.84515862616401486068] 
dist 87=[-4.5797149656271396234 ,.84658872824894626738] 
dist 88=[-4.6164811198097535595 ,.84976202121544777875] 
dist 89=[-4.6519529149650689842 ,.85481844086403523964] 
dist 90=[-4.6830799314768333834 ,.86222685831678288091] 
dist 91=[-4.7024683897467477316 ,.87481117377251772722] 
dist 92=[-4.7171399318724674366 ,.88983829757904844357] 
dist 93=[-4.7293942310492012736 ,.90701678563202218963] 
dist 94=[-4.7392797310803956583 ,.92916588703958184413] 
dist 95=[-4.7444729755061226481 ,.96406894518917433051] 
dist 96=[-4.7472612387477941138 ,1.0000562989082888083 ] 
dist 97=[-4.7475225919278893069 ,1.0265426808901693033 ] 
dist 98=[-4.4328754337088650754 ,1.0513118268770222375 ] 
dist 99=[-4.4046166394961921982 ,1.0804370464304299334 ] 
dist 100=[-4.3460923568215073649 ,1.1103747768550976598 ] 
dist 101=[-4.3298156037670963931 ,1.1383954033028194518 ] 
dist 102=[-4.2645907085947858727 ,1.1705779806588565486 ] 
dist 103=[-4.2512467552115351481 ,1.2171610029350402853 ] 
dist 104=[-4.2180425525786726368 ,1.2652653666703413800 ] 
dist 105=[-4.2105514735673449935 ,1.3035330602799259835 ] 
dist 106=[-3.7019519063283549645 ,1.3422015786200736522 ] 
dist 107=[-3.6491020626767483000 ,1.3919110001927761855 ] 
dist 108=[-3.5802373250936728708 ,1.4453656709974995304 ] 
dist 109=[-3.5175668895316386594 ,1.4990129799892176124 ] 
dist 110=[-3.1546487445052466219 ,1.5634841807091082649 ] 
dist 111=[-2.9457102575641322309 ,1.6602260414090899749 ] 
dist 112=[-.59621121590448379161,1.7563237804567880538 ] 
dist 113=[-.2466719248474134932 ,1.8182197264402678906 ] 
dist 114=[-.2162263173092043659 ,1.8673655735124222149 ] 
dist 115=[-.1467587213498678321 ,1.9124749816027142908 ] 
dist 116=[-.1359016467141751743 ,1.9519375246435667552 ] 
dist 117=[-.0489488907443822977 ,1.9785017737214870708 ] 
dist 118=[-.0338492212398792032 ,2.0009048327123683449 ] 
dist 119=[-.0118035726001012941 ,2.0237281129939659283 ] 
dist 120=[-.0061221618584235938 ,2.0441242278256623026 ] 
dist 121=[.0855629433505650187 ,2.0568207344282400757 ] 
dist 122=[.0967634766244283661 ,2.0664074807237531684 ] 
dist 123=[.1211953394600599621 ,2.0743653794682124508 ] 
dist 124=[.1252055678821823408 ,2.0807413491732651619 ] 
dist 125=[.1514495557597889265 ,2.0840008178354414490 ] 
dist 126=[.1555801503652956751 ,2.0856264538866672336 ] 
dist 127=[.1631944800837055229 ,2.0854675914706377848 ] 
dist 128=[.1646714482502719280 ,1.9421929352388195291 ] 
dist 129=[.9961222889119617732 ,1.9290374503335511616 ] 
dist 130=[1.0236505241824462697 ,1.9020316603257598382 ] 
dist 131=[1.0844343138386746626 ,1.8944955252759664994 ] 
dist 132=[1.0943347782037073969 ,1.8642988729116533403 ] 
dist 133=[1.1629427585963821912 ,1.8579661160275232190 ] 
dist 134=[1.1741789611269128714 ,1.8423718865704108248 ] 
dist 135=[1.1937363983954069518 ,1.8384321278033542540 ] 
dist 136=[1.1974907263138738666 ,1.8122843910813386668 ] 
dist 137=[1.2399592408285652816 ,1.8065286475520779617 ] 
dist 138=[1.2457113971913522626 ,1.7970547441519299584 ] 
dist 139=[1.2493511139761871284 ,1.7942891257835684788 ] 
dist 140=[1.2453862462466139770 ,1.7858989787243096144 ] 
dist 141=[1.1589018343933003753 ,1.7829774638187402266 ] 
dist 142=[1.0478034485072221066 ,1.7800910034820984913 ] 
dist 143=[.88033446677828971019,1.7783251378985722333 ] 
dist 144=[.71244221070992524968,1.3770957296536002198 ] 
dist 145=[.59965107040440617154,1.3712020781505706812 ] 
dist 146=[.5048488982995344646 ,1.3696350787570928402 ] 
dist 147=[.40888809339753484222,1.3654347235798117770 ] 
dist 148=[.31872223027797348545,1.3636450905860428497 ] 
dist 149=[.24709182337971842124,1.3537445778598455494 ] 
dist 150=[.17481727437379674934,1.3511961363891004363 ] 
dist 151=[.08207531048461976728,1.3458400308256334382 ] 
dist 152=[-.00863589667369710485,1.3439752166950931126 ] 
dist 153=[-.07279032182426676876,1.3132201140434418876 ] 
dist 154=[-.13022284616031686921,1.3085469357477232793 ] 
dist 155=[-.19405560765701823924,1.2982271761119659524 ] 
dist 156=[-.25766350185154493323,1.2949732994042277794 ] 
dist 157=[-.31419716803371682577,1.2801542091611743224 ] 
dist 158=[-.376781187313037096  ,1.2769032786973410513 ] 
dist 159=[-.46458316404092517056,1.2687844093421545633 ] 
dist 160=[-.55113056023060382472,1.2663778240231707760 ] 
dist 161=[-.60869803956239158114,.93789613389475509219] 
dist 162=[-.65646033285110028294,.91501451521006533764] 
dist 163=[-.70379964955336981041,.86115484928965442151] 
dist 164=[-.74764457636997120402,.85270271898091859147] 
dist 165=[-.78143398681838364311,.77843170671522688053] 
dist 166=[-.81456879124863205109,.76475331858008628959] 
dist 167=[-.85579662984129769677,.74683253532752902554] 
dist 168=[-.89551243638774649266,.74169924895156692051] 
dist 169=[-.92260126369515825251,.63328409966382850574] 
dist 170=[-.94581935333339501357,.61938000961187924559] 
dist 171=[-.97005731224985855247,.59044214813780286447] 
dist 172=[-.9933072557343774113 ,.58276262059900589004] 
dist 173=[-1.0125749887640736071 ,.55361312089839638392] 
dist 174=[-1.0327579361916177994 ,.54795072311941070545] 
dist 175=[-1.0596687367235667788 ,.53575591873577846663] 
dist 176=[-1.0856705198060277730 ,.53251067936455956176] 
dist 177=[-1.1022185808373657849 ,.36514983004859483716] 
dist 178=[-1.1151302906636442682 ,.35003270630448640208] 
dist 179=[-1.1265902123394285927 ,.31476014801963158836] 
dist 180=[-1.1363406381354859742 ,.30933644235584336131] 
dist 181=[-1.1424161728942506732 ,.26204032856991382232] 
dist 182=[-1.1470086116886612456 ,.25349269689075594968] 
dist 183=[-1.1647035014467995953 ,.24222712917284072501] 
dist 184=[-1.1886676859916055165 ,.23927490342964527361] 
dist 185=[-1.2108883976034370591 ,.17532680830014672464] 
dist 186=[-1.2245709495002875744 ,.16730066295536942121] 
dist 187=[-1.2347111084677535941 ,.15043188569023038427] 
dist 188=[-1.2427670987979191947 ,.14628828762563443967] 
dist 189=[-1.2489643191894142899 ,.12918036426189107879] 
dist 190=[-1.2516720144648562224 ,.12603291191189338813] 
dist 191=[-1.2528729463840972931 ,.11926043594283135247] 
dist 192=[-1.2530451985802701962 ,.11771292790574593327] 
dist 193=[-1.0866824552904071078 ,-.02123777508137532204] 
dist 194=[-1.0724433009279481828 ,-.02856877043258000094] 
dist 195=[-1.0692527202382182894 ,-.04338740434559777555] 
dist 196=[-1.0478548837747300952 ,-.04710229507914786003] 
dist 197=[-1.0434639309115808370 ,-.05995021831419618569] 
dist 198=[-1.0358033725798914183 ,-.06254840499085832719] 
dist 199=[-1.0338293904488548596 ,-.06587297068488317608] 
dist 200=[-.99455098130083617028,-.06648257498470509075] 
dist 201=[-.98911842271754205068,-.06604282241823331814] 
dist 202=[-.97743817652105310967,-.06401806685840212715] 
dist 203=[-.97402076055554094535,-.06043122267807432358] 
dist 204=[-.95945585414011732426,-.05374477900693303527] 
dist 205=[-.95647572937911204729,-.04551982016149141026] 
dist 206=[-.94878684383478099266,-.03578083520489070105] 
dist 207=[-.94715558645783464603,-.02299799063766304730] 
dist 208=[-.68719432421003129325,.05214204163602550573] 
dist 209=[-.66881576600759078538,.13506222132623573574] 
dist 210=[-.62583633418757028258,.20441233025983056741] 
dist 211=[-.61896151591693632519,.27405683888348745173] 
dist 212=[-.56057358361463252444,.33914915689361062802] 
dist 213=[-.54986338524545562836,.39029626671788648532] 
dist 214=[-.53530029905815099042,.44138568507681373067] 
dist 215=[-.53092564498312338675,.50624732828930727627] 
dist 216=[-.44875486422250036435,.56936083736502032325] 
dist 217=[-.40572593968851141905,.6134599306038374548 ] 
dist 218=[-.38079991181069834581,.65238336730895194884] 
dist 219=[-.37496127892860689218,.69480077985155024819] 
dist 220=[-.35599410925972644247,.73658118459226679143] 
dist 221=[-.30805716257158925309,.77295739302992923096] 
dist 222=[-.2969651031255851415 ,.81260224831181185885] 
dist 223=[-.29512899125865855976,.86745311472805387829] 
dist 224=[-.1841371401399888365 ,.92118952287209333106] 
dist 225=[-.17365415969288614026,.95637794237751811632] 
dist 226=[-.14956083878749861229,.98496132507694417537] 
dist 227=[-.145606981767803551  ,1.0122858951027736426 ] 
dist 228=[-.11442467693951594927,1.0369389797350682547 ] 
dist 229=[-.10883344930647642449,1.0548397672451042486 ] 
dist 230=[-.10055244141676864767,1.0713478632185517206 ] 
dist 231=[-.09835752650503949147,1.0904318913291841433 ] 
dist 232=[-.06022791150041941597,1.1080940230852458838 ] 
dist 233=[-.05539209233711671413,1.1189163023589355080 ] 
dist 234=[-.04457931196975661001,1.1268744255538925573 ] 
dist 235=[-.04257413640103689400,1.1330835188072834313 ] 
dist 236=[-.02949492691724748311,1.1378227134713090196 ] 
dist 237=[-.02718112878709233233,1.1399031492722331938 ] 
dist 238=[-.02298486748786254801,1.1407779606264899491 ] 

8 phat 2 dirichlet min maxes function [1, 1, 2, 2, 1, 2, 2, 0, 1] 
dist 0=[13.687573254688357573  ,13.687573254688357573  ] 
dist 1=[13.670253240264061218  ,13.704279084512264246  ] 
dist 2=[13.617682156003948111  ,13.727161576735166132  ] 
dist 3=[13.556896827740826333  ,13.743310566576115166  ] 
dist 4=[13.498164927163248470  ,13.754051119217450062  ] 
dist 5=[13.429212052742059993  ,13.756128120318005452  ] 
dist 6=[13.327550266702527478  ,13.753454255124591838  ] 
dist 7=[13.211640358720368661  ,13.751787791637621969  ] 
dist 8=[13.085703337580196901  ,13.715502082069189537  ] 
dist 9=[12.927284624048025666  ,13.706536514879494503  ] 
dist 10=[12.681465503732453684  ,13.687797114434681345  ] 
dist 11=[12.431921613900642312  ,13.681013576299089711  ] 
dist 12=[12.258607033636453498  ,13.646800757762930099  ] 
dist 13=[12.106615890532273462  ,13.638535110131247264  ] 
dist 14=[11.942357809368596729  ,13.605668155575251320  ] 
dist 15=[11.781253724520414707  ,13.533027804208945560  ] 
dist 16=[11.641879776037949743  ,13.139148616904103173  ] 
dist 17=[11.490650421855096486  ,13.090963898661361829  ] 
dist 18=[11.282136260835064878  ,13.022888738583658099  ] 
dist 19=[11.071060862978100800  ,13.009884295148778778  ] 
dist 20=[10.909590548115042172  ,12.950262600200015317  ] 
dist 21=[10.752311856366085991  ,12.937091295240621551  ] 
dist 22=[10.558003337279507569  ,12.905405634343080159  ] 
dist 23=[10.352956615728021061  ,12.894936933199393653  ] 
dist 24=[10.152735729634243141  ,12.785926442638838785  ] 
dist 25=[9.9161616788181892353 ,12.765161602495027924  ] 
dist 26=[9.5657336996840106918 ,12.740581208376028797  ] 
dist 27=[9.2119705397694897257 ,12.730649273455030963  ] 
dist 28=[8.9620596006300063984 ,12.509469250143599964  ] 
dist 29=[8.7385154532173664528 ,12.488560928093153200  ] 
dist 30=[8.4901995400825904214 ,12.319258668626119192  ] 
dist 31=[8.2427120177519540234 ,12.050695144009882619  ] 
dist 32=[8.0224822064970280070 ,9.2263451307839922475 ] 
dist 33=[7.7783746386258410527 ,9.0462865663794180551 ] 
dist 34=[7.4353983187460485241 ,8.8380454631815203126 ] 
dist 35=[7.0854534524316119003 ,8.5651756899290458827 ] 
dist 36=[6.8134786402841723787 ,8.5030734880112792983 ] 
dist 37=[6.5445106449234919593 ,8.4078371418170492026 ] 
dist 38=[6.2065916020502625077 ,8.3866379488684061348 ] 
dist 39=[5.8471118306016877326 ,8.2639472184754725051 ] 
dist 40=[5.4919207767265227411 ,8.2404048518514462690 ] 
dist 41=[5.0691399779945311180 ,8.1945006594216627276 ] 
dist 42=[4.4393621318165627802 ,8.1822490997599609764 ] 
dist 43=[3.8099197840235575535 ,6.7912443761620069007 ] 
dist 44=[3.3884806670536479087 ,6.5762661685099718084 ] 
dist 45=[3.0356362313719967241 ,6.5384654257610326048 ] 
dist 46=[2.6805107695276946849 ,6.4650438748365315338 ] 
dist 47=[2.3479447419304061733 ,6.4472101230237895470 ] 
dist 48=[2.0853172562490589422 ,6.1194081334767455842 ] 
dist 49=[1.8216694788544328861 ,6.0815007215093220857 ] 
dist 50=[1.4850218714843486787 ,5.9977485734094591301 ] 
dist 51=[1.1563104615388563074 ,5.9805617010170495054 ] 
dist 52=[.9243996176590352586 ,5.8811987637313427667 ] 
dist 53=[.7172783851718046464 ,5.8633167856745329090 ] 
dist 54=[.4877023067731397602 ,5.8280199434882737304 ] 
dist 55=[0                     ,5.8190915206342367915 ] 
dist 56=[.0562674373575196589 ,5.5182393988434966712 ] 
dist 57=[-.1682878247807273186 ,5.4866003209348247952 ] 
dist 58=[-.4833693648583170605 ,5.4286643930843749736 ] 
dist 59=[-.7943008810785368648 ,5.4155964743042984539 ] 
dist 60=[-1.0022607161076793984 ,5.2534221921581348323 ] 
dist 61=[-1.1761503480000223786 ,5.2320306352683307641 ] 
dist 62=[-1.3508304387649342705 ,5.1334088257894252842 ] 
dist 63=[-1.5142300163470394749 ,4.9871131177961591193 ] 
dist 64=[-1.6430088996145839187 ,1.1778511811562301087 ] 
dist 65=[-1.7720729548390326459 ,1.1105441476545346114 ] 
dist 66=[-1.9366176846717197973 ,1.0948621512573567916 ] 
dist 67=[-2.0972281439147018061 ,.8500266221733729392 ] 
dist 68=[-2.2105606336313791789 ,.8187966337685962808 ] 
dist 69=[-2.3118327176375333035 ,.7514669334168094225 ] 
dist 70=[-2.4242136089769220518 ,.7385442713976007122 ] 
dist 71=[-2.5362099358843858523 ,.6666905263044255849 ] 
dist 72=[-2.6359488528276886841 ,.6548386925798826494 ] 
dist 73=[-2.7466199291307327729 ,.6302695354292208591 ] 
dist 74=[-2.9023480786443005928 ,.6255972314353081448 ] 
dist 75=[-3.0547714243952299987 ,-.8540869495109755101 ] 
dist 76=[-3.1522267285237165751 ,-.9291747590894584836 ] 
dist 77=[-3.2288526725949889822 ,-1.0975220919436040197 ] 
dist 78=[-3.2979657026345172471 ,-1.1258226002304103982 ] 
dist 79=[-3.3576348440747824110 ,-1.3282069680032932374 ] 
dist 80=[-3.3964903771025734228 ,-1.3631596002857286440 ] 
dist 81=[-3.4278693162755807742 ,-1.4210884842630787021 ] 
dist 82=[-3.4576403634350803756 ,-1.4339008856573022806 ] 
dist 83=[-3.4836076955559318790 ,-1.6236835180768701023 ] 
dist 84=[-3.4997724296177839698 ,-1.6482703421509522324 ] 
dist 85=[-3.5120058875272323182 ,-1.6979106071000079215 ] 
dist 86=[-3.5222417984882725818 ,-1.7098381681679231798 ] 
dist 87=[-3.5305268257657493119 ,-1.7500408556404094552 ] 
dist 88=[-3.5349535680071216928 ,-1.7579095781305015368 ] 
dist 89=[-3.5374430352380062146 ,-1.7640595666827555892 ] 
dist 90=[-3.5379757590013896734 ,-1.7607516431184955574 ] 
dist 91=[-3.4107882380097970668 ,-1.7538550354864289896 ] 
dist 92=[-3.4151755257760339201 ,-1.7434400198865914885 ] 
dist 93=[-3.4157233766507785433 ,-1.7284190606508827008 ] 
dist 94=[-3.4128681757851147297 ,-1.5815771150681287940 ] 
dist 95=[-3.4114968194794498362 ,-1.3385448028325684701 ] 
dist 96=[-3.2207929171978827255 ,-1.0936125794809522827 ] 
dist 97=[-3.2026443541404144695 ,-.92749861978772265121] 
dist 98=[-3.1562834688616623741 ,-.78622408431631002527] 
dist 99=[-3.1493423841379177713 ,-.64060438354469693546] 
dist 100=[-3.0717529086800014372 ,-.50216507658488846429] 
dist 101=[-3.0562236232880977325 ,-.38959767035102741374] 
dist 102=[-3.0402065892640431790 ,-.27365981037491987049] 
dist 103=[-3.0308044566275274290 ,-.12174062016379644104] 
dist 104=[-2.9508126885667427471 ,.02830579316531205400] 
dist 105=[-2.9480629575911573856 ,.13675745129380693701] 
dist 106=[-2.9471185679315197894 ,.23624484645564869889] 
dist 107=[-1.2301826641196597509 ,.35045082178282833164] 
dist 108=[-1.1387269938099318765 ,.46634129295559228835] 
dist 109=[-.92451670538113040337,.57256676827613494059] 
dist 110=[-.89342376619806311222,.69281047634872815144] 
dist 111=[-.60542484287427015044,.86475754683090076484] 
dist 112=[-.55382384549386233872,1.0356236906051379901 ] 
dist 113=[-.4905978699794005307 ,1.1515465239771835034 ] 
dist 114=[-.47871199966492196895,1.2502225009333902511 ] 
dist 115=[-.08517769101072659393,1.3521260261621834434 ] 
dist 116=[-.03724615182162132322,1.4491729528758111239 ] 
dist 117=[.06050372901598641264,1.5284308306485003662 ] 
dist 118=[.08528203305093389809,1.6104072328546947799 ] 
dist 119=[.17274134736427837716,1.7183282807161195938 ] 
dist 120=[.19011381657473778224,1.8252300980670835827 ] 
dist 121=[.21636471199243316664,1.9031326485424830138 ] 
dist 122=[.22292830490483381731,1.9752743296576404227 ] 
dist 123=[.7132372463505968048 ,2.0591418323404598809 ] 
dist 124=[.75393711526312641259,2.1448848513297321084 ] 
dist 125=[.84687334317266322149,2.2245293901547690791 ] 
dist 126=[.86060934474929448994,2.3155653058111579050 ] 
dist 127=[.97637693039852851207,2.4468670274683226093 ] 
dist 128=[.99622016901955645417,2.5761631286208571225 ] 
dist 129=[1.0233544401528186310 ,2.6591794362128508901 ] 
dist 130=[1.0289908807954793992 ,2.7248018716790821758 ] 
dist 131=[1.1497028068052098736 ,2.7845378930969130060 ] 
dist 132=[1.1637953152250724996 ,2.8364532790550515708 ] 
dist 133=[1.1941198930660125089 ,2.8708009134079710267 ] 
dist 134=[1.1988352627293574242 ,2.8991192104547873917 ] 
dist 135=[1.2293001209665858632 ,2.9269250272025758832 ] 
dist 136=[1.2338113077341045350 ,2.9514857578141457628 ] 
dist 137=[1.2419272952430400626 ,2.9668262906013678711 ] 
dist 138=[1.2432493237882118657 ,2.9784738023412066350 ] 
dist 139=[1.6211074032346566184 ,2.9882624027495439201 ] 
dist 140=[1.6333296100777130447 ,2.9962008462107778942 ] 
dist 141=[1.6576895563392106163 ,3.0004476960322012839 ] 
dist 142=[1.6625751621093075297 ,3.0028369279930631232 ] 
dist 143=[1.6791176461041727175 ,3.0033448565482430854 ] 
dist 144=[1.6808493953368379788 ,2.7753338074704882574 ] 
dist 145=[1.6782718856528032827 ,2.7548465839867019686 ] 
dist 146=[1.6691296424707344245 ,2.7126042952698537171 ] 
dist 147=[1.6574093438164880588 ,2.7008693585291320936 ] 
dist 148=[1.6445224722302330126 ,2.6540000249606430469 ] 
dist 149=[1.6282249899782199442 ,2.6443098802942087074 ] 
dist 150=[1.6028655592022950317 ,2.6205188147548072046 ] 
dist 151=[1.5734018565197400978 ,2.6147485322301780832 ] 
dist 152=[1.5406922277599820646 ,2.5754543969590978954 ] 
dist 153=[1.4991050937799093937 ,2.5668908278177511600 ] 
dist 154=[1.4341428542374551786 ,2.5533757324541741156 ] 
dist 155=[1.3672742491209983388 ,2.5492858300088190873 ] 
dist 156=[1.3180638343810552585 ,2.5385414627010296979 ] 
dist 157=[1.2720227333707269745 ,2.5348592440917117080 ] 
dist 158=[1.2178264315156311380 ,2.5326452829232636491 ] 
dist 159=[1.1620697697949128173 ,2.5318349344185549227 ] 
dist 160=[1.0350427533128472834 ,1.5546507958343479353 ] 
dist 161=[.8752292911811815441 ,1.5427635269785139556 ] 
dist 162=[.74093895116381794572,1.5396891651558832722 ] 
dist 163=[.60506102148739759527,1.4804911209392596884 ] 
dist 164=[.47742054945719153897,1.4720376096499829282 ] 
dist 165=[.37606878485295380322,1.4526911406271254988 ] 
dist 166=[.27385000957509374285,1.4478143744713844982 ] 
dist 167=[.14274208639721149144,1.4208554695996985125 ] 
dist 168=[.01453000024130905130,1.4153356255322509742 ] 
dist 169=[-.07610952318808756237,1.4043573803654726521 ] 
dist 170=[-.15721500072449673321,1.4012071794159824239 ] 
dist 171=[-.24730375682662879057,.94627895880509146594] 
dist 172=[-.33704470503950530724,.91594792541665354898] 
dist 173=[-.4167598509935020891 ,.8453211889001906073 ] 
dist 174=[-.50497011751717311469,.83402495691085847648] 
dist 175=[-.62868138677352343278,.73931017362864719224] 
dist 176=[-.75061056379736727751,.72206448867226717188] 
dist 177=[-.83169497024339396677,.69826536087959723427] 
dist 178=[-.89895052040974921268,.69129858011928960996] 
dist 179=[-.96558194373935624571,.56291365636456963283] 
dist 180=[-1.0272775213787559766 ,.54646777161690411727] 
dist 181=[-1.0747962336273981819 ,.5113111578387325196 ] 
dist 182=[-1.1213689811061901392 ,.50291364288698739875] 
dist 183=[-1.1792826218084892631 ,.46463832516176616743] 
dist 184=[-1.2350568979412949888 ,.45779148541993644094] 
dist 185=[-1.2730752112611637276 ,.44145618338506907596] 
dist 186=[-1.3056365122626414624 ,.43892517241738505484] 
dist 187=[-1.3395898694665836692 ,.27483355150697218245] 
dist 188=[-1.3721364624272624677 ,.25940863880329643731] 
dist 189=[-1.4138477627518800567 ,.223898300224507829  ] 
dist 190=[-1.4547604765732249305 ,.21813849878904967418] 
dist 191=[-1.4918239793280551025 ,.17202307761083593837] 
dist 192=[-1.5189976579795065232 ,.16375558108180672401] 
dist 193=[-1.5443223246980141437 ,.15172910528258791257] 
dist 194=[-1.5739920757519767576 ,.14847684890243333654] 
dist 195=[-1.6016624726600219436 ,.09155810938585854895] 
dist 196=[-1.6189921936496244372 ,.08435022496368227635] 
dist 197=[-1.6321852154540654360 ,.06840101974764004023] 
dist 198=[-1.6433139173874259112 ,.06530107501621440384] 
dist 199=[-1.6523554507279295892 ,.04651354353854017058] 
dist 200=[-1.6572023780834529956 ,.04320368144266714675] 
dist 201=[-1.6599373953732749441 ,.03685598567116707092] 
dist 202=[-1.6605339110319445624 ,.03533328796427954341] 
dist 203=[-1.5981318581872870791 ,-.03952152914906153635] 
dist 204=[-1.5926138574812016562 ,-.04493485905027454290] 
dist 205=[-1.5907300018695639172 ,-.05442681118655011183] 
dist 206=[-1.5877064421960099678 ,-.05645043927331284029] 
dist 207=[-1.5864849786004811766 ,-.06088395392868407623] 
dist 208=[-1.5147493447895391515 ,-.06057338115109767976] 
dist 209=[-1.5066109468998133246 ,-.05819788018580202537] 
dist 210=[-1.4872799700621401254 ,-.05236532989684183830] 
dist 211=[-1.4829346455087134908 ,-.04533135506093198866] 
dist 212=[-1.4538387302796936940 ,-.03815153931176085986] 
dist 213=[-1.4478605086888798433 ,-.02943929356205039526] 
dist 214=[-1.4374159991541670992 ,-.01627722029430086161] 
dist 215=[-1.4347254897873715329 ,-.00114635417597304050] 
dist 216=[-1.3797486289703005906 ,.01543868029146533838] 
dist 217=[-1.3718958101399172300 ,.03638575271312630954] 
dist 218=[-1.3542318824642286083 ,.06895925829136449741] 
dist 219=[-1.3494554785476611834 ,.10243634351956546036] 
dist 220=[-1.3256630234952015955 ,.12699667539246639958] 
dist 221=[-1.3207651166769654962 ,.14990041374081821615] 
dist 222=[-1.3102998659288648843 ,.17675346589476767875] 
dist 223=[-1.3071180871881545640 ,.20432202210391833078] 
dist 224=[-.89961286942138617849,.2300870124406943287 ] 
dist 225=[-.87210621398077245394,.25965128811319733831] 
dist 226=[-.80805484511598248746,.30241235598068708207] 
dist 227=[-.79774475184013356951,.36680841573683112587] 
dist 228=[-.71175906535570573044,.45592937123422695813] 
dist 229=[-.69607552424958541838,.52602926924388807118] 
dist 230=[-.67429425075227549319,.59611798112229643906] 
dist 231=[-.65958807890079078882,.68519426192252050681] 
dist 232=[-.53790838572907026451,.7719167369644611485 ] 
dist 233=[-.522518685242304998  ,.83259319675463067183] 
dist 234=[-.48963686481109626624,.8862342764764089856 ] 
dist 235=[-.48173525717432847394,.94482405600966358736] 
dist 236=[-.44594923524256536635,1.0026138837105648121 ] 
dist 237=[-.43953571057623984268,1.0530561867566330810 ] 
dist 238=[-.42416555395030024533,1.1081391663571511804 ] 
dist 239=[-.42181374752997890416,1.1844859610466444404 ] 
dist 240=[-.26631474005658597021,1.2593441581730083600 ] 
dist 241=[-.25171126364983613114,1.3084746128590788618 ] 
dist 242=[-.21801094302699771262,1.3485079227140629240 ] 
dist 243=[-.21259544562698940552,1.3869888643742290823 ] 
dist 244=[-.16857449144414148891,1.4218505303283638520 ] 
dist 245=[-.16067065479742925872,1.4474112458613148201 ] 
dist 246=[-.14937293812596527675,1.4712338161381923868 ] 
dist 247=[-.14625073604295036972,1.4991450753250448131 ] 
dist 248=[-.09104328704098071221,1.5251757539106483498 ] 
dist 249=[-.08405340777640512130,1.5414783442540295484 ] 
dist 250=[-.06874025836209864482,1.5538890475610473582 ] 
dist 251=[-.06561403017047588197,1.5643570169311391147 ] 
dist 252=[-.04802659979240843303,1.5728609966392673300 ] 
dist 253=[-.04493463863091520677,1.5774181891577185457 ] 
dist 254=[-.03865313153466952153,1.5799875360485758973 ] 

8 phat 2 dirichlet min maxes function [0, 1, 1, 1, 0, 1, 2] 
dist 0=[16.235874413637985554  ,16.235874413637985554  ] 
dist 1=[16.223741292568280360  ,16.243282589949284075  ] 
dist 2=[16.197697382644188860  ,16.250428206312847729  ] 
dist 3=[16.156287122029771307  ,16.258772766214724575  ] 
dist 4=[16.082703995664677845  ,16.270965774420863481  ] 
dist 5=[15.992357833857826461  ,16.282470825875307463  ] 
dist 6=[15.883915722288249673  ,16.288065991552817038  ] 
dist 7=[15.740652285199728221  ,16.290410503893144106  ] 
dist 8=[15.511066176597950199  ,16.288931165329562987  ] 
dist 9=[15.272967478927964608  ,16.285085946582340234  ] 
dist 10=[15.095663294112172586  ,16.279749470478385037  ] 
dist 11=[14.927690699232462326  ,16.268279454391862642  ] 
dist 12=[14.726901776145309333  ,16.262302589030305271  ] 
dist 13=[14.518628606566647962  ,15.464136842405166708  ] 
dist 14=[14.320724402755001064  ,15.392525982000223808  ] 
dist 15=[14.091062749653206759  ,15.212832293538365946  ] 
dist 16=[13.755792473932970622  ,15.186462989246501186  ] 
dist 17=[13.408338477241977969  ,14.895991350723678300  ] 
dist 18=[13.129953590601259252  ,14.838566094948859258  ] 
dist 19=[12.846833229390370946  ,14.779615644935518102  ] 
dist 20=[12.480439531103551864  ,14.766950244232038580  ] 
dist 21=[12.085269795085229186  ,14.279298893719461473  ] 
dist 22=[11.687074540662689847  ,14.246082057896435234  ] 
dist 23=[11.207432903590000892  ,14.195689595279918800  ] 
dist 24=[10.486563050478448235  ,14.185239528946283099  ] 
dist 25=[9.7639667772462698706 ,14.151949928575760526  ] 
dist 26=[9.2774200878760022272 ,14.147163319314068876  ] 
dist 27=[8.8671436614580033621 ,14.075630679389175231  ] 
dist 28=[8.4495449097792955592 ,13.946921864787753182  ] 
dist 29=[8.0555586322757212845 ,12.020267482400745631  ] 
dist 30=[7.7397047228864632343 ,11.876554909862429907  ] 
dist 31=[7.4182811065299614628 ,11.563025050406329766  ] 
dist 32=[7.0020175514536750839 ,11.490806726576460502  ] 
dist 33=[6.5928367782939027254 ,11.124906821750074017  ] 
dist 34=[6.2997344913240538704 ,11.057529156029581919  ] 
dist 35=[6.0334012775748208657 ,10.911084918491490450  ] 
dist 36=[5.7312659116532631740 ,10.872944348807665656  ] 
dist 37=[5.4265218172063688370 ,10.535216144835496423  ] 
dist 38=[5.1497519712905062207 ,10.480021352776150629  ] 
dist 39=[4.8383782797858908434 ,10.372217391692934729  ] 
dist 40=[4.3952445520991321619 ,10.344100130678866382  ] 
dist 41=[3.9553279141699619188 ,10.243069024411098285  ] 
dist 42=[3.6568169024618581163 ,10.219751599438109333  ] 
dist 43=[3.4025326166623207755 ,10.180241969350395603  ] 
dist 44=[3.1394801316234331194 ,10.169637134215895080  ] 
dist 45=[2.8885458799383172149 ,5.1913471424442907350 ] 
dist 46=[2.6827193880660134948 ,4.9203988200661052483 ] 
dist 47=[2.4689451908068227626 ,4.2867895790052714981 ] 
dist 48=[2.1862175393318634222 ,4.1954465388953242398 ] 
dist 49=[1.9053540502580141147 ,3.4093831086210201814 ] 
dist 50=[1.6990301585591638323 ,3.3660158059633200118 ] 
dist 51=[1.5062147479099455892 ,3.2777893136459667771 ] 
dist 52=[1.2793687725336233914 ,3.2611323515820793912 ] 
dist 53=[1.0241595178281877083 ,3.1523586027854313839 ] 
dist 54=[.7996111161948570954 ,3.1357662791018647070 ] 
dist 55=[.52377580761556323303,3.1045529653238724292 ] 
dist 56=[.20530763155733065459,3.0980476628629505950 ] 
dist 57=[-.15940398861647930033,2.9414247923924338474 ] 
dist 58=[-.40002435830890504188,2.9245406297469495806 ] 
dist 59=[-.63841556972142551683,2.8799987933979786776 ] 
dist 60=[-1.0460692118869915914 ,2.8270033542668583465 ] 
dist 61=[-1.4473361368584338789 ,-.50350229333222950091] 
dist 62=[-1.7138173881437548036 ,-.6225005962436967884 ] 
dist 63=[-1.9345289710994883637 ,-.89507091439545676361] 
dist 64=[-2.1527619779108138217 ,-.93479427710647824055] 
dist 65=[-2.3546360978180406545 ,-1.2774077084074561480 ] 
dist 66=[-2.5099298290031739824 ,-1.3363799195373028148 ] 
dist 67=[-2.6620050270590256093 ,-1.4145932299757295632 ] 
dist 68=[-2.8510132469734462131 ,-1.4293799260606652128 ] 
dist 69=[-3.0331148522166784535 ,-1.7061539487703230574 ] 
dist 70=[-3.1575726454460855967 ,-1.7224787984241867468 ] 
dist 71=[-3.2645743866588483499 ,-1.7476962435986728741 ] 
dist 72=[-3.3768706607785070864 ,-1.7523561251577723910 ] 
dist 73=[-3.4850320116485037914 ,-1.8215424466252206169 ] 
dist 74=[-3.5755032653517752082 ,-1.8292394142964950209 ] 
dist 75=[-3.6710718177700773884 ,-1.8278593431493248788 ] 
dist 76=[-3.7996310480451515369 ,-1.8138462877102440226 ] 
dist 77=[-3.9240000168987527788 ,-1.7927552680657781124 ] 
dist 78=[-4.0028120843485297134 ,-1.7630673960081514033 ] 
dist 79=[-4.0639788672449461900 ,-1.7212429463487221987 ] 
dist 80=[-4.1177716696944607234 ,-1.6516231001119741165 ] 
dist 81=[-4.1632424743003323261 ,-1.5760360289542681809 ] 
dist 82=[-4.1911256136442209449 ,-1.5103492679390177218 ] 
dist 83=[-4.2117097787848564167 ,-1.4389303438859439645 ] 
dist 84=[-4.2279927365600293363 ,-1.3404168641706693841 ] 
dist 85=[-4.2406531525773361311 ,-1.2312441566804294852 ] 
dist 86=[-4.2467479827123472350 ,-1.1172038429393755484 ] 
dist 87=[-4.2492783213235688775 ,-.97699559699538120134] 
dist 88=[-4.2485832922889269296 ,-.7631953864812304135 ] 
dist 89=[-4.2436137938521680820 ,-.54826602499417494393] 
dist 90=[-4.2412721208768790724 ,-.40354158827316137012] 
dist 91=[-4.2295375457001834254 ,-.28159969623338749034] 
dist 92=[-4.2275923497634938701 ,-.1577575261473949932 ] 
dist 93=[-3.9426361947587695293 ,-.04119745350388919988] 
dist 94=[-3.9140221994484242116 ,.05163033523130565380] 
dist 95=[-3.8501881720936666895 ,.14546579019786645167] 
dist 96=[-3.8335597022960658353 ,.26605630761484773838] 
dist 97=[-3.7508017072554897958 ,.3840155499725902605 ] 
dist 98=[-3.7342251791060054088 ,.46733127562456252696] 
dist 99=[-3.6984654701904869454 ,.5417723574807968067 ] 
dist 100=[-3.6877367175929452145 ,.62424932259064267412] 
dist 101=[-3.5720887788613376603 ,.70624862315385409104] 
dist 102=[-3.5543270534496802730 ,.77878069841525393908] 
dist 103=[-3.5096386897898019803 ,.85876267945473006383] 
dist 104=[-3.5016607382498805973 ,.97055024829184012135] 
dist 105=[-3.4273390352304026394 ,1.0804662558221543119 ] 
dist 106=[-3.4120948049187255618 ,1.1529653744083677071 ] 
dist 107=[-3.3930938409844364080 ,1.2124168128256482947 ] 
dist 108=[-3.3859848849748063062 ,1.2701635811452402997 ] 
dist 109=[-2.1105627336058643136 ,1.3228577692889474808 ] 
dist 110=[-2.0486451090668958994 ,1.3621072753869747080 ] 
dist 111=[-1.9039439629719265370 ,1.3992886524936706219 ] 
dist 112=[-1.8811353504768976070 ,1.4437139556022480201 ] 
dist 113=[-1.6854712721890139425 ,1.4855753410902724935 ] 
dist 114=[-1.6497796344765210915 ,1.5125052866283039444 ] 
dist 115=[-1.6017949794881677014 ,1.5338327974877292346 ] 
dist 116=[-1.5878093814846088568 ,1.5532935031981449170 ] 
dist 117=[-1.3168098909050099045 ,1.5702208478454535717 ] 
dist 118=[-1.2821790837034123548 ,1.5814191086016785759 ] 
dist 119=[-1.2090943129952449367 ,1.5993510062049473348 ] 
dist 120=[-1.1906948734430128234 ,1.7260595347523989906 ] 
dist 121=[-1.1144203326725282427 ,1.8512315575723441458 ] 
dist 122=[-1.1003306647613751615 ,1.9607904041758279824 ] 
dist 123=[-1.0680854935009969911 ,2.0806808408760871305 ] 
dist 124=[-1.0618330184985242401 ,2.2521792507905302551 ] 
dist 125=[-.692191225979086384  ,2.4292981412692668451 ] 
dist 126=[-.65832287978238335197,2.5453451241931853965 ] 
dist 127=[-.57908604426159326872,2.6396804166140138364 ] 
dist 128=[-.56733619972021478073,2.7299799231582489844 ] 
dist 129=[-.4607472457603079279 ,2.8115307853496196538 ] 
dist 130=[-.44155790550361280208,2.8708824774098057973 ] 
dist 131=[-.41748062276840209936,2.9257547994170333904 ] 
dist 132=[-.41227480462776395998,2.9893936707281885811 ] 
dist 133=[-.26581543796717680871,3.0483992763461374732 ] 
dist 134=[-.24771185703803765434,3.0847442885380144630 ] 
dist 135=[-.21057735282933544439,3.1116976318482025723 ] 
dist 136=[-.20103620455882343321,3.1331482982758212607 ] 
dist 137=[-.16658745806959711154,3.1499088801798588670 ] 
dist 138=[-.1597986470225765708 ,3.1581080155553646536 ] 
dist 139=[-.14775278408044670079,3.1620654981841328410 ] 
dist 140=[-.14511691145363330828,3.1624108341214871480 ] 
dist 141=[.61794398383388192999,.76739607984520195894] 
dist 142=[.60524447276253840023,.78030252771381184301] 
dist 143=[.59224651161172863114,.79038033223823395569] 
dist 144=[.57532879966980355534,.79934354071028442726] 
dist 145=[.55704766329351338597,.80698776287291786693] 
dist 146=[.53859731320049999944,.81179069923370239971] 
dist 147=[.51636168280653856834,.81547070461735833923] 
dist 148=[.48294446176890445499,.81862455401537860661] 
dist 149=[.4479319349291944631 ,.82109953645122884455] 
dist 150=[.41931702860434174295,.82206455990250620686] 
dist 151=[.3897112193605018107 ,.82230468794359895401] 
dist 152=[.35073587513328916099,.82208115965429475894] 
dist 153=[.30838665387146912438,.81945115210940714172] 
dist 154=[.2652898145819764942 ,.81852214872005634777] 
dist 155=[.2130846320852805787 ,.81687695874696045382] 
dist 156=[.13431465055969770276,.81625500215340216404] 
dist 157=[.05533639082001838494,.77761232385695420666] 
dist 158=[.00229825746157058220,.77327343371238565444] 
dist 159=[-.04225555743773649847,.76300690974286051375] 
dist 160=[-.08730867031667822573,.76068092837929975248] 
dist 161=[-.12960869330536855452,.74537018553310410757] 
dist 162=[-.16315414272501495276,.74223201236066262131] 
dist 163=[-.19694460608943461255,.73667716560851002949] 
dist 164=[-.24022451388005794715,.73524044859611437448] 
dist 165=[-.28251376230558028311,.70681825249226704285] 
dist 166=[-.31234305934263895503,.7027553886133615746 ] 
dist 167=[-.33896271803634038751,.69352177829947428043] 
dist 168=[-.3684179876246367232 ,.69111920009703795917] 
dist 169=[-.39769108830301297311,.67841910915518077534] 
dist 170=[-.42358244153420818794,.67581111628442862832] 
dist 171=[-.45213877666948499521,.67046302091215483668] 
dist 172=[-.49206833798336880762,.66888802385236439165] 
dist 173=[-.53136256928752468802,.45039226646059732205] 
dist 174=[-.55737850256651923199,.43557294990892226231] 
dist 175=[-.57882805361425268558,.40105713859910893706] 
dist 176=[-.59986297146783028941,.39554155337914027513] 
dist 177=[-.61919698644832822881,.34922823883805198292] 
dist 178=[-.63384528014008368409,.34079460302266976928] 
dist 179=[-.64796901512431869742,.32917477586055492042] 
dist 180=[-.66520562720664828121,.32576672363403647158] 
dist 181=[-.68164074509995738404,.26291536516576499692] 
dist 182=[-.69255963648971626197,.25486493831216069639] 
dist 183=[-.70160426834593232555,.23766811931316077045] 
dist 184=[-.71054490824963253931,.23354851096275991884] 
dist 185=[-.71881025305669275067,.21486689413811792335] 
dist 186=[-.72515471287840068444,.2115262383992629333 ] 
dist 187=[-.73135258730438456567,.20352192030085529835] 
dist 188=[-.73903204844390683041,.20231147479106544047] 
dist 189=[-.74621953399059157718,.12170625836656574462] 
dist 190=[-.75045016607757632744,.11414144006933067738] 
dist 191=[-.75335475611564858597,.09671468416164812801] 
dist 192=[-.75523959150997083314,.09389943292760609827] 
dist 193=[-.75640693030672537288,.07123717617183175648] 
dist 194=[-.75658082256839519282,.06717432145315524265] 
dist 195=[-.75610205242025234369,.06130145763265760871] 
dist 196=[-.75576714547533050643,.05970194755645747800] 
dist 197=[-.74853197807701294266,.03163508458331191314] 
dist 198=[-.74709163099306951902,.02808304668784728265] 
dist 199=[-.74366160696383692182,.02025011330983041366] 
dist 200=[-.74241707256015687357,.01870523854688967833] 
dist 201=[-.72760208862695735517,.00956211298352483462] 
dist 202=[-.72512938441288942843,.00795426487376821643] 
dist 203=[-.71252063788379969399,.00481276115396006841] 
dist 204=[-.69121580505812583283,.00404464929812696474] 
dist 205=[-.03588857056211671340,-.02126836102878841755] 
dist 206=[-.04022096877554093602,-.02378252388962976713] 
dist 207=[-.04379806919549969124,-.02961834520360619571] 
dist 208=[-.04731753566692520116,-.03046886048932246641] 
dist 209=[-.05056262468306948410,-.03812618877366416201] 
dist 210=[-.05304246186832647079,-.03948157234702257793] 
dist 211=[-.05545569722956426295,-.04118955642455603934] 
dist 212=[-.05843452120204448527,-.04151819644722219869] 
dist 213=[-.06129541200864608436,-.05132046280120977197] 
dist 214=[-.06323704427581921282,-.05250416521294211361] 
dist 215=[-.06489212659179364214,-.05495075684832152274] 
dist 216=[-.06660706342549441340,-.05553781834289085585] 
dist 217=[-.06824581370928161146,-.05779755725894531290] 
dist 218=[-.06959628883013952714,-.05822053469395130794] 
dist 219=[-.07100544908723075934,-.05893639716608659981] 
dist 220=[-.07287911015832234757,-.05908676959567959399] 
dist 221=[-.07469971842438020216,-.06907231277542646545] 
dist 222=[-.07589671630949943738,-.06991607894742455398] 
dist 223=[-.07687611484422216475,-.07174051197450068381] 
dist 224=[-.07782630181146021218,-.07207324193530637229] 
dist 225=[-.07894693078366863052,-.07401143681172683661] 
dist 226=[-.07999947074900989079,-.07432324232934117066] 
dist 227=[-.08098452454112308239,-.07495305048939715435] 
dist 228=[-.08214486548459469900,-.07506840407172945017] 
dist 229=[-.08323046750409540552,-.07630364653482936902] 
dist 230=[-.08391660818449553255,-.07566290615025851066] 
dist 231=[-.08444623118562457655,-.07485866866073282533] 
dist 232=[-.08490587783003684885,-.07361380175453884490] 
dist 233=[-.08528887302351393498,-.07216997823730104583] 
dist 234=[-.08551191469711008726,-.07057007273559377583] 
dist 235=[-.08566164212461160776,-.06853758656318368069] 
dist 236=[-.08575133865221740707,-.06536385948829211815] 
dist 237=[-.08581167498492688281,-.06209559007499337448] 
dist 238=[-.08584397559858722785,-.05968499842746712189] 
dist 239=[-.08586157970434453538,-.0574236798018344968 ] 
dist 240=[-.08586321359400642890,-.05475227485572884622] 
dist 241=[-.08585376755249778882,-.05199779568365369180] 
dist 242=[-.08582706940344220794,-.04940421270365132470] 
dist 243=[-.08578191527728376809,-.04641229679520423860] 
dist 244=[-.08575383205955031170,-.04206481129726277790] 
dist 245=[-.08107182546435629913,-.03756651143866510981] 
dist 246=[-.08059537708916272275,-.03397144921420851625] 
dist 247=[-.08006848984538354644,-.03032283241049140437] 
dist 248=[-.07995338856751823378,-.02561032193272560496] 
dist 249=[-.07558101863356666693,-.02053121900001381753] 
dist 250=[-.07521486706486896663,-.01541653173672077948] 
dist 251=[-.07212699642590124507,-.00925711828880298742] 

8 phat 2 dirichlet min maxes function [2, 0, 2, 2, 1, 1, 0, 1, 2] 
dist 0=[12.552584163976275492  ,12.552584163976275492  ] 
dist 1=[12.534872291622823789  ,12.558612963259186937  ] 
dist 2=[12.504890237664033526  ,12.565005320658859447  ] 
dist 3=[12.452556148448893072  ,12.571289597008988611  ] 
dist 4=[12.396278129228747221  ,12.573611196109718417  ] 
dist 5=[12.350524373987374484  ,12.573478992924925983  ] 
dist 6=[12.303398683240043000  ,12.571489250763013402  ] 
dist 7=[12.241629244546116111  ,12.562452058500763640  ] 
dist 8=[12.174625104663838458  ,12.467178375620581945  ] 
dist 9=[12.106563171802767076  ,12.441641676974727633  ] 
dist 10=[12.024181882241224196  ,12.434541752899948332  ] 
dist 11=[11.899911671729205969  ,12.408266693863065898  ] 
dist 12=[11.769408773053308165  ,12.400224694757393781  ] 
dist 13=[11.662101066041370726  ,12.385471655502650717  ] 
dist 14=[11.550436323286083252  ,12.380477518969332972  ] 
dist 15=[11.402506911195187038  ,12.353746420519262405  ] 
dist 16=[11.241222396636882228  ,11.905118272884922148  ] 
dist 17=[11.076147587668094077  ,11.887414706499136199  ] 
dist 18=[10.875416215331840728  ,11.864210597341273955  ] 
dist 19=[10.571534798778140645  ,11.855799711519152889  ] 
dist 20=[10.265805639064564776  ,11.565426960584385896  ] 
dist 21=[10.057683969696191587  ,11.529188371961026694  ] 
dist 22=[9.8796790119738970253 ,11.466025938562843202  ] 
dist 23=[9.6943893727990630865 ,11.451121263923489876  ] 
dist 24=[9.5169284884375371905 ,11.410562792470385577  ] 
dist 25=[9.3702302261712443035 ,11.397041121495701866  ] 
dist 26=[9.2168599068689123787 ,11.317764548745441309  ] 
dist 27=[9.0127131947880582697 ,11.147739215467810548  ] 
dist 28=[8.8093401765290210442 ,10.486764931375809352  ] 
dist 29=[8.6590622893906343559 ,10.404413807411185445  ] 
dist 30=[8.4046328984548978695 ,10.171414226255924888  ] 
dist 31=[7.8801554936490107057 ,10.157371575599844988  ] 
dist 32=[7.5259299130513305430 ,9.2872954096621321432 ] 
dist 33=[7.2260351919824323332 ,9.2077178592435934856 ] 
dist 34=[6.9188248401092049120 ,9.0284398330381876144 ] 
dist 35=[6.6277169882776723754 ,8.9920679995353660747 ] 
dist 36=[6.3922140846426892722 ,8.7649147442490833690 ] 
dist 37=[6.1505969286543628662 ,8.7226457139836825687 ] 
dist 38=[5.8350340079429002103 ,8.6442835952527853606 ] 
dist 39=[5.5235398548140120232 ,8.6250264197323381397 ] 
dist 40=[5.2981915676799633481 ,8.3465999931665479915 ] 
dist 41=[5.0911328358732483537 ,8.3080937281786716728 ] 
dist 42=[4.8527763971150636371 ,8.2145938897009948174 ] 
dist 43=[4.6103689522637829133 ,8.1997427903904424110 ] 
dist 44=[4.3871059642797976570 ,8.0589208691845490404 ] 
dist 45=[4.1333992455453436541 ,8.0316971174318101964 ] 
dist 46=[3.7692366986162555945 ,7.9988429358544941630 ] 
dist 47=[3.4063204554867952569 ,7.9888821621901964927 ] 
dist 48=[3.1575955658775611897 ,6.5396452194265664681 ] 
dist 49=[2.9430363925704190674 ,6.5209640264180353107 ] 
dist 50=[2.6925887076576403558 ,6.4976098394733812186 ] 
dist 51=[2.3388379329330051209 ,6.4919357782839070903 ] 
dist 52=[2.0066730164992845383 ,5.2980968819518639756 ] 
dist 53=[1.7428856523306639249 ,5.2238449886809109377 ] 
dist 54=[1.4766992086434241858 ,5.0660273327615380177 ] 
dist 55=[1.1349388094114978847 ,5.0311068586690239125 ] 
dist 56=[.8003281492897611949 ,4.8675281930547221804 ] 
dist 57=[.5627336341604139494 ,4.8392011701007689076 ] 
dist 58=[.3489522842004270666 ,4.7635101485705323010 ] 
dist 59=[.1095724044949945215 ,4.6651581857438521056 ] 
dist 60=[-.1301195812951524188 ,4.1934035464916535123 ] 
dist 61=[-.3451506418600167240 ,4.1366494362556143257 ] 
dist 62=[-.5849376149167342599 ,3.9470717608537266008 ] 
dist 63=[-.9236352179053903079 ,3.4942140606127500788 ] 
dist 64=[-1.2588408831220185697 ,2.4589957673443597950 ] 
dist 65=[-1.4846640721308506443 ,2.3729688249262083230 ] 
dist 66=[-1.6752753659018145671 ,2.1815804144089371671 ] 
dist 67=[-1.8696633609066185777 ,2.1454435039235739217 ] 
dist 68=[-2.0533624736381350750 ,1.9164882103377697938 ] 
dist 69=[-2.2012287375550656166 ,1.8759899678208939806 ] 
dist 70=[-2.3522927345881526235 ,1.8011101666775955324 ] 
dist 71=[-2.5487843092878597018 ,1.7838163470665201016 ] 
dist 72=[-2.7424421090490983500 ,1.5669901825983779923 ] 
dist 73=[-2.8821753048337196178 ,1.5365434574138325826 ] 
dist 74=[-3.0102309297212611412 ,1.4754883193356095994 ] 
dist 75=[-3.1571897844506027036 ,1.4601757911914716292 ] 
dist 76=[-3.3064434945618026803 ,1.4082556453166478686 ] 
dist 77=[-3.4436808001364241123 ,1.3977845835795439357 ] 
dist 78=[-3.5994915337352632210 ,1.3844169341906534937 ] 
dist 79=[-3.8230343707889475576 ,1.3818328754588623495 ] 
dist 80=[-4.0432609340334351850 ,.62235388257082123845] 
dist 81=[-4.1858096475688173373 ,.63166961665720851214] 
dist 82=[-4.2998514842422763980 ,.64748088830949165068] 
dist 83=[-4.4060643343332986024 ,.67633239532690096911] 
dist 84=[-4.5001102886819182089 ,.70682674282933347954] 
dist 85=[-4.5654914269371820150 ,.72920860774749163282] 
dist 86=[-4.6229131726623443183 ,.75001961352758186449] 
dist 87=[-4.6851283916455926363 ,.77424675115718195242] 
dist 88=[-4.7416209904221847136 ,.7989561993425503262 ] 
dist 89=[-4.7761551930577941463 ,.8217012771665134449 ] 
dist 90=[-4.8014956145532862698 ,.8474882876870409731 ] 
dist 91=[-4.8212150585488732882 ,.8843636933865134373 ] 
dist 92=[-4.8360069290387322440 ,.9221742629319439236 ] 
dist 93=[-4.8416389418208969694 ,.9517032413143828351 ] 
dist 94=[-4.8433650207400428986 ,.9810023384378573262 ] 
dist 95=[-4.8425310689406720027 ,1.0178990812037532499 ] 
dist 96=[-4.6596547375081632832 ,1.0571517422164608254 ] 
dist 97=[-4.6406052178637445820 ,1.0958735577723476378 ] 
dist 98=[-4.6015598311548327892 ,1.1418882363762475735 ] 
dist 99=[-4.5698553843013870108 ,1.2103037867749395831 ] 
dist 100=[-4.3530565986482752785 ,1.2793627249230060779 ] 
dist 101=[-4.3406097141485011133 ,1.3279515629281198072 ] 
dist 102=[-4.3153211917090292188 ,1.3711807417277238614 ] 
dist 103=[-4.3077667378495965581 ,1.4188114239519446618 ] 
dist 104=[-4.2770747322418972029 ,1.4660315185641301573 ] 
dist 105=[-4.2685333635197838030 ,1.5076210911357794986 ] 
dist 106=[-4.2328062473831437227 ,1.5533522771316512999 ] 
dist 107=[-4.1681305180051472344 ,1.6171366569775524255 ] 
dist 108=[-3.7065998016127830567 ,1.6819909859914676720 ] 
dist 109=[-3.6557998724431012092 ,1.7320023048933968942 ] 
dist 110=[-3.5040960356731797952 ,1.7810835375080548117 ] 
dist 111=[-3.2911835467860927819 ,1.8422206908549175999 ] 
dist 112=[-2.0037711783785985248 ,1.9069866390783536698 ] 
dist 113=[-1.8875334606245360629 ,1.9705812773237497097 ] 
dist 114=[-1.6132857964626018833 ,2.0459835166014788668 ] 
dist 115=[-1.3721201121078773294 ,2.1579713753130378782 ] 
dist 116=[.05589167797736592149,2.2689036312636485269 ] 
dist 117=[.07807709491044814796,2.3400851509790343177 ] 
dist 118=[.08364960452130080701,2.3963007166725418567 ] 
dist 119=[.17193839202452072414,2.4473827140539454448 ] 
dist 120=[.18280658497193971831,2.4917113319186508119 ] 
dist 121=[.20593205783513624068,2.5209201750914347949 ] 
dist 122=[.21015288359575723543,2.5448688056937557010 ] 
dist 123=[.23292032602506178347,2.5681633735390639095 ] 
dist 124=[.23655769842583309158,2.5886700722282145845 ] 
dist 125=[.24305910783056677932,2.6014695078767170487 ] 
dist 126=[.24421359190596591728,2.6111769558033479563 ] 
dist 127=[1.0493344809121794575 ,2.6193157424659686182 ] 
dist 128=[1.0744795928205228385 ,2.6259013076152793278 ] 
dist 129=[1.1296236142278878451 ,2.6293958895243819129 ] 
dist 130=[1.1387299507294836248 ,2.6313228970472739726 ] 
dist 131=[1.1995455555294952654 ,2.6316381971605818182 ] 
dist 132=[1.2093686116773594935 ,2.4290958993787179963 ] 
dist 133=[1.2270426315163224872 ,2.4108939690882446713 ] 
dist 134=[1.2304864843169202652 ,2.3732982774318062357 ] 
dist 135=[1.2615802140996447458 ,2.3628511857819290728 ] 
dist 136=[1.2657965922207794837 ,2.3210770412569958158 ] 
dist 137=[1.2652915157537754597 ,2.3124783463065629560 ] 
dist 138=[1.2582263446429550905 ,2.2912609732604750345 ] 
dist 139=[1.2474321311608279866 ,2.2862582245182368581 ] 
dist 140=[1.2320157768562025001 ,2.2509554337101220281 ] 
dist 141=[1.2101582023674966537 ,2.2433405436123294561 ] 
dist 142=[1.1736089530749967804 ,2.2311516160477624100 ] 
dist 143=[1.1350955499234091674 ,2.2275341936097333203 ] 
dist 144=[1.1053837222687812586 ,2.2176968964036911198 ] 
dist 145=[1.0762324619440206369 ,2.2142760713368061518 ] 
dist 146=[1.0399585568547461085 ,2.2121263581390443230 ] 
dist 147=[1.0015802104771797766 ,2.2111289212690608456 ] 
dist 148=[.89387573019759659626,1.3608060496444656518 ] 
dist 149=[.75341065450479274381,1.3561871544131496533 ] 
dist 150=[.63539728749723581111,1.3546031665866921539 ] 
dist 151=[.51601869937298712687,1.3222894815630118433 ] 
dist 152=[.40389614850043986877,1.3172653330036557155 ] 
dist 153=[.31489704535731580359,1.3061271552032149047 ] 
dist 154=[.2251649321999027756 ,1.3026409516993442208 ] 
dist 155=[.11011084485659458659,1.2868604146270350618 ] 
dist 156=[-.00238383912340822294,1.2834191413258396213 ] 
dist 157=[-.08188194174899817947,1.2750377636490888978 ] 
dist 158=[-.15298683416778541091,1.2724438954946576932 ] 
dist 159=[-.2319199661289509628 ,.93395393034740320427] 
dist 160=[-.3105208570564871489 ,.91043734761902511876] 
dist 161=[-.38029759139474521484,.85516055077787380272] 
dist 162=[-.45747484175092123059,.84646215213659592218] 
dist 163=[-.56566891931589018608,.77050468707948315958] 
dist 164=[-.67228519405787988638,.75653484216560300294] 
dist 165=[-.74315344274581914322,.73810502463916032211] 
dist 166=[-.8018988121824397895 ,.73276773859037332203] 
dist 167=[-.8600390618136384271 ,.62292077377456110773] 
dist 168=[-.9138332981508508624 ,.60882835148232299773] 
dist 169=[-.95520036526267043162,.57940097864903130763] 
dist 170=[-.99568101879690415296,.5715744135409081473 ] 
dist 171=[-1.0459313254780074678 ,.54173563566808281757] 
dist 172=[-1.0942816012510264228 ,.53598461124812682996] 
dist 173=[-1.1271647994696434119 ,.52338140092031118601] 
dist 174=[-1.1552476566235408308 ,.52026507480278004861] 
dist 175=[-1.1844028309296529005 ,.35405561681280084636] 
dist 176=[-1.2122705287170634804 ,.33899793145538766233] 
dist 177=[-1.2352056464834120690 ,.30374621569143480866] 
dist 178=[-1.2590895060002763147 ,.29843860442752818313] 
dist 179=[-1.2907523920918551557 ,.25084825165488139843] 
dist 180=[-1.3234639660272400075 ,.24224577252463226718] 
dist 181=[-1.3444750605979411489 ,.2312749127344334498 ] 
dist 182=[-1.3609417201925753150 ,.22868331787774719309] 
dist 183=[-1.3756841676613250970 ,.16294674113880800781] 
dist 184=[-1.3883199487056357410 ,.15476325038336549377] 
dist 185=[-1.3963620935408837759 ,.13782162262453643726] 
dist 186=[-1.4026394267110566985 ,.13342747332129689207] 
dist 187=[-1.4082181092297305267 ,.11823827929653627822] 
dist 188=[-1.4126730063150100599 ,.11536092059416036302] 
dist 189=[-1.4144562948053821219 ,.11021582529803583583] 
dist 190=[-1.4149963060141400594 ,.10907206687703726537] 
dist 191=[-1.4146428150099716688 ,.02592724632600563073] 
dist 192=[-1.4102115654454160732 ,.01849041193074210627] 
dist 193=[-1.4086207813853800581 ,.00386757443532704925] 
dist 194=[-1.4063434288390839004 ,.00028680222516949345] 
dist 195=[-1.4052845874105220170 ,-.01145293032694612577] 
dist 196=[-1.3457212601183550240 ,-.01402089579663755435] 
dist 197=[-1.3388731752380118345 ,-.01574825087881083507] 
dist 198=[-1.3225695288655234660 ,-.01486170141304615401] 
dist 199=[-1.3188690065703112420 ,-.01281293042200542598] 
dist 200=[-1.2941313917139632466 ,-.00940763253743121777] 
dist 201=[-1.2890223380796923993 ,-.00433329540360379155] 
dist 202=[-1.2800904278858792226 ,.00438985194112104819] 
dist 203=[-1.2777792793353779469 ,.01486678828938182133] 
dist 204=[-1.2302563786969340266 ,.02695410891822637814] 
dist 205=[-1.2234524662668140640 ,.04262289732057441411] 
dist 206=[-1.2081774525687678411 ,.06742098088464551185] 
dist 207=[-1.2039902702417922153 ,.09306990674407152941] 
dist 208=[-1.1834608255441877922 ,.11214105504599999702] 
dist 209=[-1.1792215009630437142 ,.13017821721307631232] 
dist 210=[-1.1700697762526067635 ,.15169290037337215248] 
dist 211=[-1.1672615094002126535 ,.17398112421048677095] 
dist 212=[-.80750768715357310558,.19511162276338852046] 
dist 213=[-.78287304725045584899,.21959259871892561245] 
dist 214=[-.72532106490332669688,.2552785555839658372 ] 
dist 215=[-.71620889689977254813,.32732522519795860078] 
dist 216=[-.63838162682180907237,.40595906494634180969] 
dist 217=[-.62416909773424549116,.46776401854133180687] 
dist 218=[-.60497370816824446796,.52951592181819192843] 
dist 219=[-.59278123752054614046,.60793765676601496604] 
dist 220=[-.45986408073494366881,.68425794746828540269] 
dist 221=[-.4463728288470917654 ,.73760672235045489344] 
dist 222=[-.41748092717323981736,.78471745450175014365] 
dist 223=[-.41061089563104286334,.83609340732528935308] 
dist 224=[-.37897506601601605101,.88671974992030615586] 
dist 225=[-.37330580473059311378,.93083298904515252212] 
dist 226=[-.35989813369952647298,.97894017848971011717] 
dist 227=[-.35770527691916314033,1.0455373271641225255 ] 
dist 228=[-.22342502815902830087,1.1107993896941170929 ] 
dist 229=[-.21075384610901877665,1.1535679033655642583 ] 
dist 230=[-.18161920726651382499,1.1883455502741347626 ] 
dist 231=[-.17685040259481468872,1.2216541372045931266 ] 
dist 232=[-.13910933426218602162,1.2517487350870558202 ] 
dist 233=[-.1323417637405173011 ,1.2736744335843799410 ] 
dist 234=[-.12236001561202882526,1.2939690657303707801 ] 
dist 235=[-.11970173512441292091,1.3175414057340178144 ] 
dist 236=[-.07343448193152479114,1.3394169605136628959 ] 
dist 237=[-.06756824620034297913,1.3529265573722994275 ] 
dist 238=[-.05448359016540487669,1.3629873904057852381 ] 
dist 239=[-.05202895521284836844,1.3710721864485617598 ] 
dist 240=[-.03629745227669915187,1.3773331796814882128 ] 
dist 241=[-.03351671524680904181,1.3801010469177089409 ] 
dist 242=[-.02840647967911597100,1.3813508474332910816 ] 

8 phat 2 dirichlet min maxes function [0, 0, 2, 0, 2, 1, 1, 0, 2] 
dist 0=[13.246477204300484573  ,13.246477204300484573  ] 
dist 1=[13.236080892401386299  ,13.256430621947322113  ] 
dist 2=[13.218049653303599610  ,13.266870795578845754  ] 
dist 3=[13.177556402055467241  ,13.279206112308012087  ] 
dist 4=[13.125312075823830480  ,13.291903728511522123  ] 
dist 5=[13.060287817469483720  ,13.303792625351970677  ] 
dist 6=[12.972930967352116772  ,13.317437870625516726  ] 
dist 7=[12.831375696260685181  ,13.337156963604699438  ] 
dist 8=[12.679559502682823113  ,13.356312296560708053  ] 
dist 9=[12.551166723190751916  ,13.367704143456163153  ] 
dist 10=[12.414362562968034458  ,13.375656568110500215  ] 
dist 11=[12.228904666549761426  ,13.381063042647798457  ] 
dist 12=[12.024608855334469192  ,13.384456911189153256  ] 
dist 13=[11.812464839984295101  ,13.384364253989471605  ] 
dist 14=[11.552277471011030728  ,13.381699903374620157  ] 
dist 15=[11.155839786084648901  ,13.379279818607536935  ] 
dist 16=[10.755725044116885892  ,13.366441391750746027  ] 
dist 17=[10.480830944233877045  ,13.361309674123310475  ] 
dist 18=[10.242956512476133208  ,13.349151406832568831  ] 
dist 19=[9.9908933907328753911 ,13.343884289818760118  ] 
dist 20=[9.7466744244824192699 ,13.314493677937772178  ] 
dist 21=[9.5401692860967572055 ,13.306880826214031468  ] 
dist 22=[9.3201403113839130932 ,13.286474596976414282  ] 
dist 23=[9.0218311078708089042 ,13.278895540083249445  ] 
dist 24=[8.7220696435171993495 ,13.191072325758790706  ] 
dist 25=[8.4962305075120224193 ,13.174542201229606393  ] 
dist 26=[8.2795528381224534197 ,13.100856152681095158  ] 
dist 27=[8.0164287906983957539 ,10.703781454989952878  ] 
dist 28=[7.7410759308136089631 ,10.287941626361860145  ] 
dist 29=[7.4754870478260416612 ,10.210921019580203300  ] 
dist 30=[7.1640704410506011112 ,10.119254839108658046  ] 
dist 31=[6.7054272392082498013 ,10.098938123629035169  ] 
dist 32=[6.2431668068207519008 ,9.4438999599833799287 ] 
dist 33=[5.9172815615446505131 ,9.3607599114701839723 ] 
dist 34=[5.6263737679348705285 ,9.2700118757884518136 ] 
dist 35=[5.3040034456279082272 ,9.1534044263922299289 ] 
dist 36=[4.9830173695531887512 ,9.0041377381417318291 ] 
dist 37=[4.6976434034667822494 ,8.9717231685682003137 ] 
dist 38=[4.3814289416928272321 ,8.9220989548514157023 ] 
dist 39=[3.9370911287807617716 ,8.9083525243853898056 ] 
dist 40=[3.4833902056752499947 ,8.2852789541173705194 ] 
dist 41=[3.1297254099117545390 ,8.2237884455312233866 ] 
dist 42=[2.7788223138224301230 ,8.2087329452396511046 ] 
dist 43=[2.3361642670801421430 ,7.6926981326868100593 ] 
dist 44=[1.8640853324831816166 ,7.6397499098983841801 ] 
dist 45=[1.3955081788159585106 ,7.5243586822074432045 ] 
dist 46=[.835954128690933988  ,7.4999732561141665491 ] 
dist 47=[0                     ,7.3685964684911292960 ] 
dist 48=[5.2505704648818824226 ,7.3453285466475441898 ] 
dist 49=[4.9944045025604402294 ,7.2966631820762826860 ] 
dist 50=[4.7280684289763316316 ,7.2841423388232780667 ] 
dist 51=[4.4215891011405674798 ,7.1822195882261050649 ] 
dist 52=[4.1007327895555476996 ,7.1656560824377615195 ] 
dist 53=[3.7765110720824372079 ,7.1374531417568983557 ] 
dist 54=[3.3922970793919512816 ,7.1047069297935544613 ] 
dist 55=[2.8218960787991161508 ,7.0191680973716222272 ] 
dist 56=[2.2524691381862526669 ,6.7668022210662519872 ] 
dist 57=[1.8721507989710853038 ,6.7362911888827433470 ] 
dist 58=[1.5547439829796334198 ,6.6159678385209796802 ] 
dist 59=[1.2369099418572513553 ,2.8021530531707481242 ] 
dist 60=[.9402900385296121163 ,2.3080832813453055120 ] 
dist 61=[.7077216450973259650 ,2.2195886491901951053 ] 
dist 62=[.4757935169944841268 ,2.1135975799958751026 ] 
dist 63=[.1817335738494054755 ,2.0956924994748105210 ] 
dist 64=[-.1044069979836096591 ,1.4116342649690466228 ] 
dist 65=[-.3046647010516490958 ,1.3284677449586075827 ] 
dist 66=[-.4818398494952801041 ,1.1612904272970301576 ] 
dist 67=[-.6756702469188925541 ,1.1193831015372888227 ] 
dist 68=[-.8671329610666775146 ,.97489938120150465303] 
dist 69=[-1.0348402515353065891 ,.9451408592224275437 ] 
dist 70=[-1.2185414196477210932 ,.90808423040973185519] 
dist 71=[-1.4739682116968305351 ,.90123005574238762165] 
dist 72=[-1.7250338556999276200 ,-.0399156545293232444 ] 
dist 73=[-1.8912947074645033425 ,-.1168648774385500098 ] 
dist 74=[-2.0284996122568669614 ,-.29075889647714886888] 
dist 75=[-2.1633657067011144389 ,-.31909116937531482458] 
dist 76=[-2.2876228050927658862 ,-.53218638780522029918] 
dist 77=[-2.3824015689118575840 ,-.56912000649891277154] 
dist 78=[-2.4744584975302192333 ,-.62692813418289501322] 
dist 79=[-2.5878334955079771937 ,-.64065386846732034382] 
dist 80=[-2.6965755196941788636 ,-.85333683919996477127] 
dist 81=[-2.7701057776947353635 ,-.88010930023783502356] 
dist 82=[-2.8324850668253616567 ,-.9367178340813543957 ] 
dist 83=[-2.8966336216035480704 ,-.94786953840403133873] 
dist 84=[-2.9576227016867064601 ,-1.0034275638263792491 ] 
dist 85=[-3.0073697866708989246 ,-1.0126293238194685817 ] 
dist 86=[-3.0588178836428053648 ,-1.0298099906562934601 ] 
dist 87=[-3.1266176596848889239 ,-1.0333145309199655454 ] 
dist 88=[-3.1914626437135232200 ,-1.0461114597924650558 ] 
dist 89=[-3.2310944860121762898 ,-.95994268137361098726] 
dist 90=[-3.2601755040505761927 ,-.82469619629655512568] 
dist 91=[-3.2828192675007356476 ,-.68747329548651855609] 
dist 92=[-3.3005754835375015107 ,-.59339987022441657059] 
dist 93=[-3.3101053852634708165 ,-.51235300134872529454] 
dist 94=[-3.3155188367288293261 ,-.42720250569894876786] 
dist 95=[-3.3168044003514212023 ,-.34529141671236648305] 
dist 96=[-3.2883703736526278272 ,-.27719152792168280077] 
dist 97=[-3.2828812049114880498 ,-.20573008497252736339] 
dist 98=[-3.2772117642938999154 ,-.11037473540156309754] 
dist 99=[-3.2739549460741953993 ,-.01544146444671856673] 
dist 100=[-3.2695586299053549414 ,.05433514826821664842] 
dist 101=[-3.2676252082815124130 ,.11950138666999303275] 
dist 102=[-3.2664330491567475212 ,.19600554183133134937] 
dist 103=[-3.2659340082446777302 ,.27456980990487260664] 
dist 104=[-2.8994489931400860730 ,.34797616984650383879] 
dist 105=[-2.8681251232071829599 ,.43217159117108697985] 
dist 106=[-2.8666871500705124926 ,.55387872738235262086] 
dist 107=[-2.7812984275954231472 ,.67532966991771418777] 
dist 108=[-2.7049541735646840316 ,.7585023089231590974 ] 
dist 109=[-2.6903983884443322887 ,.83012726416921531152] 
dist 110=[-2.6536700827528984513 ,.90540680986321182792] 
dist 111=[-2.6476923349942394199 ,.97790737313826027303] 
dist 112=[-2.5794409221369088751 ,1.0384226243203935725 ] 
dist 113=[-2.5669261265254326344 ,1.1021797314791190199 ] 
dist 114=[-2.5445101065213344852 ,1.1876470143839982660 ] 
dist 115=[-2.5388481894495167272 ,1.2730143143982264623 ] 
dist 116=[-2.5204988777978603161 ,1.3363735773114330682 ] 
dist 117=[-2.5150367117958574276 ,1.3962014683326732320 ] 
dist 118=[-2.5109039903473413763 ,1.4674502278677384898 ] 
dist 119=[-2.5094126184863479482 ,1.5412300892629743056 ] 
dist 120=[-.98891535917279046078,1.6111823284974793043 ] 
dist 121=[-.92462262974776964098,1.6922589462946559232 ] 
dist 122=[-.74841755355211324691,1.8105291833107743474 ] 
dist 123=[-.62539168520898658824,1.9273853111363262567 ] 
dist 124=[-.36119647870495790939,2.0028077378883608592 ] 
dist 125=[-.31395428221278054627,2.0628746842378375111 ] 
dist 126=[-.25658334721927203654,2.1183227519687040324 ] 
dist 127=[-.24642444880764443165,2.1670534476156414981 ] 
dist 128=[.11370752141201880357,2.2002576307651381558 ] 
dist 129=[.1573802867366815036 ,2.2286987980404002701 ] 
dist 130=[.24608425379361785204,2.2583837155689976081 ] 
dist 131=[.26844088896681372684,2.2851343745023096547 ] 
dist 132=[.34652907163214159737,2.3018409133004886756 ] 
dist 133=[.36216654889103809542,2.3145197204075277069 ] 
dist 134=[.38382638125296495009,2.3251603784114624291 ] 
dist 135=[.3891378236028944232 ,2.3337757413271668316 ] 
dist 136=[.83786478829983110991,2.3383538281820407320 ] 
dist 137=[.87461811969881023302,2.3408860637876832689 ] 
dist 138=[.95869857831686779472,2.3413184852728210400 ] 
dist 139=[.97086915302400218715,2.1895560585477754142 ] 
dist 140=[1.0759368178229661501 ,2.1756435502477620968 ] 
dist 141=[1.0939155194879566678 ,2.1473745872822472177 ] 
dist 142=[1.1177590677201448060 ,2.1395027530551526262 ] 
dist 143=[1.1220287721494311404 ,2.1081895085816873437 ] 
dist 144=[1.2334940716312241397 ,2.1014556694805096473 ] 
dist 145=[1.2462542579738519233 ,2.0853540997717854917 ] 
dist 146=[1.2739930571275377182 ,2.0806478267911310529 ] 
dist 147=[1.2779721628328311166 ,2.0548273336275169303 ] 
dist 148=[1.3066641634333917954 ,2.0487893432644864326 ] 
dist 149=[1.3108839790796862360 ,2.0396301076539577448 ] 
dist 150=[1.3179986708134609130 ,2.0366426989658549450 ] 
dist 151=[1.3190744301677143344 ,2.0291504264598930633 ] 
dist 152=[1.3448594880236500370 ,2.0264066919591063586 ] 
dist 153=[1.2218579428237691411 ,2.0245940813763657785 ] 
dist 154=[1.0363103635629930352 ,2.0235610941701798976 ] 
dist 155=[.85024954232812493975,1.5691514938198250950 ] 
dist 156=[.72519543224917525421,1.5742647895766391200 ] 
dist 157=[.6200252585896772584 ,1.5761125297421356004 ] 
dist 158=[.51347285946896972148,1.5766887119480853394 ] 
dist 159=[.4132948526724187499 ,1.5767152249776055410 ] 
dist 160=[.33361331333258510074,1.5692003865015786431 ] 
dist 161=[.25312635124981372771,1.5673301452212440646 ] 
dist 162=[.14972723004451052165,1.5628230300605246395 ] 
dist 163=[.04853667740486310741,1.5610343923973039572 ] 
dist 164=[-.02311923606749737344,1.5515008380570926928 ] 
dist 165=[-.08736014506118337620,1.5491039651351315087 ] 
dist 166=[-.15890091181190246923,1.5433164625432746831 ] 
dist 167=[-.23027087755306739249,1.5411586380207156004 ] 
dist 168=[-.29382921715101579016,1.4409093143201729239 ] 
dist 169=[-.36429333023274129074,1.4304373507892333268 ] 
dist 170=[-.4632780559192069614 ,1.4060961290294572393 ] 
dist 171=[-.560902877574649586  ,1.4008348423518723561 ] 
dist 172=[-.62592934873071929809,1.3665530505739452130 ] 
dist 173=[-.67998020267470619115,1.3597541411935576833 ] 
dist 174=[-.73371679893308850361,1.3476000741464031391 ] 
dist 175=[-.78359376027877405617,1.3445284274702467649 ] 
dist 176=[-.82221129693670788007,1.2881986397057316971 ] 
dist 177=[-.86025165126973462981,1.2802490070628384069 ] 
dist 178=[-.90782127385384370788,1.2617599755032046865 ] 
dist 179=[-.95376449649294020414,1.2575614957370486096 ] 
dist 180=[-.98530162207203596025,1.2311996812783826090 ] 
dist 181=[-1.0125485820920418132 ,1.2258844472891024395 ] 
dist 182=[-1.0413368491412782117 ,1.2161683176699208147 ] 
dist 183=[-1.0691647315742032512 ,1.2136146652541561246 ] 
dist 184=[-1.0925719644728260040 ,.78552176383515208009] 
dist 185=[-1.1173972629839943996 ,.75707283528092452244] 
dist 186=[-1.1508971211714113890 ,.69333672456322523523] 
dist 187=[-1.1833909808173674480 ,.6832730999276766848 ] 
dist 188=[-1.2041936030718727127 ,.59978979196522946166] 
dist 189=[-1.2205667519999598628 ,.58462917534807750692] 
dist 190=[-1.2353469505884588740 ,.56345542446533643157] 
dist 191=[-1.2481024368560815621 ,.55736015941639102951] 
dist 192=[-1.2563788380578886212 ,.44608154621381432518] 
dist 193=[-1.2630210813689399713 ,.4318475955831895955 ] 
dist 194=[-1.2692419982955962116 ,.40121278355004926415] 
dist 195=[-1.2743755656732819626 ,.39414680416098091966] 
dist 196=[-1.2766694651555306573 ,.36022109415629562937] 
dist 197=[-1.2776065133743569489 ,.35416227109076537991] 
dist 198=[-1.2774693588063828633 ,.34028787512493749391] 
dist 199=[-1.2740829069647863154 ,.33769559247100720383] 
dist 200=[-1.2727347471958194574 ,.20317538815552662612] 
dist 201=[-1.2710424084752590940 ,.19034072837990847344] 
dist 202=[-1.2701007891977550555 ,.16115004899017999866] 
dist 203=[-1.3046844653554611338 ,.15613287455652701865] 
dist 204=[-1.3366928477977324474 ,.1192893126365720289 ] 
dist 205=[-1.3601071078134180797 ,.11271575124137593294] 
dist 206=[-1.3818756603507471402 ,.10213867295370946649] 
dist 207=[-1.4073031942140608018 ,.09960395030111407631] 
dist 208=[-1.4309785716082183553 ,.05773412983174441591] 
dist 209=[-1.4457406034314015671 ,.05238639862049401955] 
dist 210=[-1.4569023966711992803 ,.03993747221624933499] 
dist 211=[-1.4661811415543007196 ,.03808953920271605895] 
dist 212=[-1.4736156357454985500 ,.02158135310597852091] 
dist 213=[-1.4774026406739409372 ,.01863212183955899210] 
dist 214=[-1.4792682018000080790 ,.01487305160573061789] 
dist 215=[-1.4795759203905461889 ,.01405973879845224372] 
dist 216=[-1.0693015161878989984 ,-.07732311297182516380] 
dist 217=[-1.0609693715850894533 ,-.08121664095218749908] 
dist 218=[-1.0584010270318937218 ,-.06964386581112155367] 
dist 219=[-.73098865449796509118,.06475504962989846238] 
dist 220=[-.70856104621245970259,.15472520692385865824] 
dist 221=[-.65874188125031170703,.23000317504844112443] 
dist 222=[-.65080244454946753713,.30565198051181807091] 
dist 223=[-.5854586929873706618 ,.37638880626783353208] 
dist 224=[-.57352204681555006991,.43202510436015444265] 
dist 225=[-.55668392748888383667,.487648888764719682  ] 
dist 226=[-.55185431971415598729,.55833572086583223582] 
dist 227=[-.46302221713653058714,.62715046919984993032] 
dist 228=[-.4515850093872866009 ,.67528830506601256182] 
dist 229=[-.42690755692975036058,.71783433301569937252] 
dist 230=[-.4211419905869276767 ,.76428893341702377801] 
dist 231=[-.39345772056592773895,.81009883692445564865] 
dist 232=[-.38845600592373149459,.85006691437713741434] 
dist 233=[-.37704250724956664898,.89369689340865929197] 
dist 234=[-.37475593209504526236,.95414982549128922084] 
dist 235=[-.22502559419157314609,1.0134137227237094877 ] 
dist 236=[-.21312537830234426154,1.0522890657107413452 ] 
dist 237=[-.18555169163034967255,1.0839429175029848312 ] 
dist 238=[-.18120919514886890074,1.1143299285323603236 ] 
dist 239=[-.14485831660615915054,1.1418320604239650836 ] 
dist 240=[-.13832180311956191422,1.1619500225453950911 ] 
dist 241=[-.12929460159016663327,1.1806529684124792998 ] 
dist 242=[-.126696619862367241  ,1.2024968151708566783 ] 
dist 243=[-.07999156011213900563,1.2228321326416282630 ] 
dist 244=[-.07408625995263310550,1.2355028557252135391 ] 
dist 245=[-.06138789474908118818,1.2450724767211419293 ] 
dist 246=[-.05857270811576488338,1.2530072774916301458 ] 
dist 247=[-.04470838788253771270,1.2593486593235775333 ] 
dist 248=[-.04228617973879581420,1.2625466030234461598 ] 
dist 249=[-.03681192017607851692,1.2640813499804168294 ] 

8 phat 2 dirichlet min maxes function [1, 1, 0, 0, 2, 1, 0, 0, 1] 
dist 0=[13.722472952145294172  ,13.722472952145294172  ] 
dist 1=[13.698386517364175853  ,13.739216176920085729  ] 
dist 2=[13.671182819359108879  ,13.753910654315786381  ] 
dist 3=[13.641967507996177248  ,13.769796801236764006  ] 
dist 4=[13.605433992652216217  ,13.782600479932646110  ] 
dist 5=[13.548953709847718469  ,13.785548480901147141  ] 
dist 6=[13.485914063825289472  ,13.783987059934616850  ] 
dist 7=[13.423145762707799177  ,13.783412660723087692  ] 
dist 8=[13.348030910802950682  ,13.747068213389373098  ] 
dist 9=[13.235616828772699071  ,13.737534950948315795  ] 
dist 10=[13.106708579596044858  ,13.731664292614444398  ] 
dist 11=[12.965628078940385924  ,13.729181392150805623  ] 
dist 12=[12.787466718206044981  ,13.539078313895092012  ] 
dist 13=[12.510256278081352043  ,13.513112818649932731  ] 
dist 14=[12.229045365634766710  ,13.459650896236861168  ] 
dist 15=[12.034885964647101426  ,13.444106850422090943  ] 
dist 16=[11.865825247789505091  ,13.378770026617890206  ] 
dist 17=[11.684999348833114608  ,13.364871439793253950  ] 
dist 18=[11.508762301335542233  ,13.326538300149879767  ] 
dist 19=[11.358057413867534408  ,13.318992863669541060  ] 
dist 20=[11.196022510672748252  ,13.240353796473912322  ] 
dist 21=[10.974476375243225172  ,13.224710394946352900  ] 
dist 22=[10.751032123931162500  ,13.191055251236878481  ] 
dist 23=[10.581408292863218835  ,13.180347102698231777  ] 
dist 24=[10.169612023859341906  ,13.131212470264658888  ] 
dist 25=[9.6635833718822338589 ,13.120354519532339808  ] 
dist 26=[9.3206667829262680002 ,13.090175525345974422  ] 
dist 27=[9.0290924970365123781 ,13.078841107387576684  ] 
dist 28=[8.7283801520559424478 ,10.538547210696018923  ] 
dist 29=[8.4421505332773863114 ,10.390894028770487794  ] 
dist 30=[8.2084906163030205405 ,10.049717696924372817  ] 
dist 31=[7.9668539146607962294 ,9.9930765947414010071 ] 
dist 32=[7.6487205510569359842 ,9.5423389095954894982 ] 
dist 33=[7.3334824947416532318 ,9.4602368539752162885 ] 
dist 34=[7.1034218846171228591 ,9.3403041371189678079 ] 
dist 35=[6.8899982996832316636 ,9.3073465314396742145 ] 
dist 36=[6.6412895715668514819 ,8.7116257155565900622 ] 
dist 37=[6.3866558033194728114 ,8.6346469169402205011 ] 
dist 38=[6.1495333515981837606 ,8.4660875511070695827 ] 
dist 39=[5.8780052240333433696 ,8.4288384099517551449 ] 
dist 40=[5.4857714114683691969 ,8.2314242944147617062 ] 
dist 41=[5.0938213261213012812 ,8.1954146153048208672 ] 
dist 42=[4.8234255957361240960 ,8.1196849987056682756 ] 
dist 43=[4.5882741683288962471 ,8.0990128418194444438 ] 
dist 44=[4.3372711204585550334 ,7.7704569010289933096 ] 
dist 45=[4.0929816202383718176 ,7.7576974493079088885 ] 
dist 46=[3.5101871949659102690 ,7.1425389293043611514 ] 
dist 47=[3.0982690150494097772 ,7.1138328418148379212 ] 
dist 48=[2.7536226225780904614 ,6.9026784196094895660 ] 
dist 49=[2.4071110205219561823 ,6.8643819128790510883 ] 
dist 50=[2.0828384539054652936 ,6.8029556530924853038 ] 
dist 51=[1.8271281231081546988 ,6.7878544463102877314 ] 
dist 52=[1.5707627315854523223 ,6.5283881626178977934 ] 
dist 53=[1.2438693459400778830 ,6.4948068305212190280 ] 
dist 54=[.92489532124791134382,6.4167144872067703446 ] 
dist 55=[.7001997360138375126 ,6.4039173792518097860 ] 
dist 56=[.49987911472881278189,6.2991132144915027016 ] 
dist 57=[.27838264930395663809,6.2798910083479420273 ] 
dist 58=[.05821453265710413571,6.2527960650994757261 ] 
dist 59=[-.1411477717595666727 ,6.2449792231521689991 ] 
dist 60=[-.4035000179564366133 ,2.4253779468421812905 ] 
dist 61=[-.6539742925826369586 ,2.4154627568250582725 ] 
dist 62=[-.95156094788529354248,1.3983708104393443595 ] 
dist 63=[-1.1502609580139297695 ,1.3143177399502130667 ] 
dist 64=[-1.3160425423443890216 ,1.1243539087137450177 ] 
dist 65=[-1.4819835451558486896 ,1.0928240289653772598 ] 
dist 66=[-1.6368284991848366180 ,.8592279264063640768 ] 
dist 67=[-1.7582367965764671604 ,.8184887903146010196 ] 
dist 68=[-1.8793299027447567405 ,.7535909138226477223 ] 
dist 69=[-2.0329187076180757761 ,.7383531202489412791 ] 
dist 70=[-2.1824542882236227704 ,.5003265521456228596 ] 
dist 71=[-2.2873399159555918452 ,.4700963793463089635 ] 
dist 72=[-2.3980559596429290401 ,.4050201541492222214 ] 
dist 73=[-2.5541971665245478967 ,.3926116176369863047 ] 
dist 74=[-2.6553216720399859014 ,.3236967314411433024 ] 
dist 75=[-2.7363239727059207040 ,.3124179146680378376 ] 
dist 76=[-2.8119817743688818186 ,.2889674555778388270 ] 
dist 77=[-2.9094002182496436724 ,.2847662552887197450 ] 
dist 78=[-3.0437753095938593576 ,-1.0687448032116530351 ] 
dist 79=[-3.1293507425132191494 ,-1.1375251005407572418 ] 
dist 80=[-3.1962495838649505231 ,-1.2915535966026667979 ] 
dist 81=[-3.2559242400009291664 ,-1.3173650522374831300 ] 
dist 82=[-3.3069749018635729426 ,-1.5016888525640522204 ] 
dist 83=[-3.3393823788571863326 ,-1.5334038336875400508 ] 
dist 84=[-3.3646175237866178118 ,-1.5860795125250292028 ] 
dist 85=[-3.3869867421014373002 ,-1.5976369215666763790 ] 
dist 86=[-3.4060006811368251867 ,-1.5195560869099269755 ] 
dist 87=[-3.4178151415808848173 ,-1.3819792928936354739 ] 
dist 88=[-3.4267382594107849847 ,-1.1701183483858791464 ] 
dist 89=[-3.4341802411685530188 ,-.9563305319416450630 ] 
dist 90=[-3.4401911951151889401 ,-.8110472455712265548 ] 
dist 91=[-3.4433868868155526540 ,-.6871884698580052040 ] 
dist 92=[-3.4451642677529566183 ,-.5590566666375768779 ] 
dist 93=[-3.4454986432150801570 ,-.4369678524389815687 ] 
dist 94=[-3.1491827050029948998 ,-.3372676432089056880 ] 
dist 95=[-3.1229410077242366773 ,-.2342049603568485297 ] 
dist 96=[-3.0680130479890724619 ,-.0986682021941711968 ] 
dist 97=[-3.0527403043475969190 ,.0354107680291802900 ] 
dist 98=[-2.9912969869353314582 ,.1326468063450877628 ] 
dist 99=[-2.9790578201291771511 ,.2221695367662389817 ] 
dist 100=[-2.9480178734902716066 ,.3254107148032311106 ] 
dist 101=[-2.9420564671401465390 ,.4304340018378447710 ] 
dist 102=[-2.8887475718819307438 ,.5270851365402446414 ] 
dist 103=[-2.8779491849669926968 ,.6367957460975158743 ] 
dist 104=[-2.8598923643447391772 ,.7940413906009273538 ] 
dist 105=[-2.8549396069039078415 ,.9504358321290950844 ] 
dist 106=[-2.8405067256792238426 ,1.0567442256280352538 ] 
dist 107=[-2.8357008731819885586 ,1.1474525106195990324 ] 
dist 108=[-2.8328192696622805472 ,1.2414698279019189302 ] 
dist 109=[-2.8317830672062964260 ,1.3312162051772299713 ] 
dist 110=[-1.1644594372524250568 ,1.4048484510281956267 ] 
dist 111=[-1.0756141620099954337 ,1.4813065795942360260 ] 
dist 112=[-.86753004083220900834,1.5823562895785579137 ] 
dist 113=[-.83736673513713176496,1.6826316131620954461 ] 
dist 114=[-.55768649727942321191,1.7559949878025407441 ] 
dist 115=[-.50759338216304103082,1.8242232742748998833 ] 
dist 116=[-.44630454581221669177,1.9039667951842390181 ] 
dist 117=[-.43489396366644110108,1.9857277497464949241 ] 
dist 118=[-.05291023807120079869,2.0620263091988146096 ] 
dist 119=[-.00641969174602721402,2.1495149460645904099 ] 
dist 120=[.08832815552605947031,2.2760292576188595033 ] 
dist 121=[.1123226453321088993 ,2.4007046785335584165 ] 
dist 122=[.19686972913107136845,2.4808404533090041277 ] 
dist 123=[.21368565663439890566,2.5442829777317934310 ] 
dist 124=[.23874801220765500872,2.6022004345042962909 ] 
dist 125=[.24510979719146346766,2.6526511966364549608 ] 
dist 126=[.72085877047251962138,2.6862344216467338521 ] 
dist 127=[.76027204643225123477,2.7141482024064703128 ] 
dist 128=[.8502983144193662897 ,2.7419285555882726219 ] 
dist 129=[.86355835699517738612,2.7665791597129368125 ] 
dist 130=[.97576098078703356942,2.7819764886636070550 ] 
dist 131=[.9949878500818482394 ,2.7936667354303012446 ] 
dist 132=[1.0211464021559969484 ,2.8034892692237067296 ] 
dist 133=[1.0264580748275748850 ,2.8114528201639070917 ] 
dist 134=[1.1438011441984884083 ,2.8157072556342979258 ] 
dist 135=[1.1574543360780282970 ,2.8180924276734445399 ] 
dist 136=[1.1868920410477515921 ,2.8185790386385101428 ] 
dist 137=[1.1914030708498466592 ,2.6099203156082570908 ] 
dist 138=[1.2211754642664801399 ,2.5911129502294356735 ] 
dist 139=[1.2255524864004513881 ,2.5524267352058498352 ] 
dist 140=[1.2335586764347309150 ,2.5416763558661956663 ] 
dist 141=[1.2347381519654212050 ,2.4987705316285683424 ] 
dist 142=[1.5725236526749239846 ,2.4898430569191584594 ] 
dist 143=[1.5835250699464187525 ,2.4680220475263822898 ] 
dist 144=[1.6051999216150460400 ,2.4625525040192406978 ] 
dist 145=[1.6096432596359715433 ,2.4266909578338496992 ] 
dist 146=[1.6231576947791753810 ,2.4187844441363330676 ] 
dist 147=[1.6239237823191386156 ,2.4063918677399343443 ] 
dist 148=[1.6205557299869774761 ,2.4025928271878005733 ] 
dist 149=[1.6106466731485595440 ,2.3927004705354951381 ] 
dist 150=[1.5734920913576905983 ,2.3892738517297831648 ] 
dist 151=[1.4254182009183284876 ,2.3871814204228919159 ] 
dist 152=[1.2022737479391628154 ,2.3863426179570159689 ] 
dist 153=[.97858161463355078142,1.6726930551585804459 ] 
dist 154=[.82831742933762544753,1.6658484156523023376 ] 
dist 155=[.70203244622727277682,1.6637686207059145806 ] 
dist 156=[.57422477909480381671,1.6595365508103049702 ] 
dist 157=[.4541471173593004402 ,1.6579444990742206211 ] 
dist 158=[.35877154810281254132,1.5709425956347707904 ] 
dist 159=[.26255376777828075868,1.5614472708453417650 ] 
dist 160=[.13910784910447317665,1.5391569842904958042 ] 
dist 161=[.01837267751678748458,1.5341700793061511814 ] 
dist 162=[-.06700596818799969983,1.5016895676457706352 ] 
dist 163=[-.14342942512937783673,1.4951079733797693183 ] 
dist 164=[-.22835596487413981345,1.4833664047309016062 ] 
dist 165=[-.31297646011647699256,1.4803398881252860538 ] 
dist 166=[-.3881765661559692711 ,1.4226797182185044843 ] 
dist 167=[-.47141786155951420414,1.4144609020745541335 ] 
dist 168=[-.58819346521703202491,1.3955892752551900456 ] 
dist 169=[-.70330004593781986556,1.3909217277547444776 ] 
dist 170=[-.7798676104697246686 ,1.3644886786733537890 ] 
dist 171=[-.84339871810773002478,1.3590908924238385002 ] 
dist 172=[-.90637618744331036152,1.3485272881023382000 ] 
dist 173=[-.9647115615094411907 ,1.3455421961735881157 ] 
dist 174=[-1.0096804663002326999 ,.90247706849030649448] 
dist 175=[-1.0537904255673405440 ,.87323754604053776891] 
dist 176=[-1.1086917972386228068 ,.80517722585724262654] 
dist 177=[-1.1615895630361393924 ,.79428553283200140286] 
dist 178=[-1.1976879436402738650 ,.70310121049864198893] 
dist 179=[-1.2286486725512920028 ,.68650540604582820873] 
dist 180=[-1.2610025675976329389 ,.66356435461191990046] 
dist 181=[-1.2920587484624249457 ,.6568650604848814628 ] 
dist 182=[-1.3178308831538151179 ,.53358271960739643239] 
dist 183=[-1.3448588361370539749 ,.51779444189797621489] 
dist 184=[-1.3809383247248840330 ,.48401119700083321337] 
dist 185=[-1.4158188247446922896 ,.47598251647525514748] 
dist 186=[-1.4380523748514195995 ,.43911418923520281792] 
dist 187=[-1.4554408960281024524 ,.43252115008639543602] 
dist 188=[-1.4709458904010421635 ,.41688355966721476448] 
dist 189=[-1.4841903608032834423 ,.41439153046076512042] 
dist 190=[-1.4925391300451555470 ,.25810438393724595525] 
dist 191=[-1.4989630737549680480 ,.24338346197893110428] 
dist 192=[-1.5045106523522049266 ,.20955213630489683241] 
dist 193=[-1.5088626533043428277 ,.20401911594653752495] 
dist 194=[-1.5105054434856259548 ,.16025898346925887325] 
dist 195=[-1.5108919007451678385 ,.15241913808273958773] 
dist 196=[-1.5104346035500660878 ,.14085025820993051699] 
dist 197=[-1.5168257382534100006 ,.1377746634932166533 ] 
dist 198=[-1.5433331454099390407 ,.08435238050678714514] 
dist 199=[-1.5599241561145804047 ,.07758321691292787362] 
dist 200=[-1.5725427706044364088 ,.06247915191196828554] 
dist 201=[-1.5831654716103634136 ,.05965991919403921205] 
dist 202=[-1.5917795598408244726 ,.04149306361969916489] 
dist 203=[-1.5963661954461697765 ,.03828487457160707610] 
dist 204=[-1.5989117470809426819 ,.03241262025637400917] 
dist 205=[-1.5993640226474436726 ,.03107767687294014427] 
dist 206=[-1.3703992679204360706 ,-.04608614810044657292] 
dist 207=[-1.3605927712431200043 ,-.05114290565180598706] 
dist 208=[-1.3580633281262305803 ,-.05994739727097428890] 
dist 209=[-1.3062782538243253787 ,-.06183223724356910713] 
dist 210=[-1.2988759993867021056 ,-.06580164693842894078] 
dist 211=[-1.2822347471585019609 ,-.06540132643772160205] 
dist 212=[-1.2777164728006602089 ,-.06303831040272294342] 
dist 213=[-1.2553152714570984318 ,-.05736086526196889559] 
dist 214=[-1.2506996455606666468 ,-.05054492658374934277] 
dist 215=[-1.2408068996244796099 ,-.04362924688177552072] 
dist 216=[-1.2377907798636467726 ,-.03526733303105525343] 
dist 217=[-.85249968561783674502,.06306583828345375551] 
dist 218=[-.82670404672136218168,.17013054244706806311] 
dist 219=[-.76664552665357729474,.25971083780992931274] 
dist 220=[-.75695929666690249072,.34973260772738112283] 
dist 221=[-.67634484669148265882,.43391035111464247611] 
dist 222=[-.66163700534825142402,.50012191040154378994] 
dist 223=[-.64116048613017847778,.56632264007156623375] 
dist 224=[-.63520983847279046363,.65045713124495090168] 
dist 225=[-.52548415844630271314,.73236789870964980943] 
dist 226=[-.51138947707240259082,.78967654451953657617] 
dist 227=[-.48115763742698866502,.84033890023522897044] 
dist 228=[-.47296046304202443507,.89567285670721878426] 
dist 229=[-.44055916451000489094,.95024983924842760504] 
dist 230=[-.4181044854656168361 ,.99788527579311803965] 
dist 231=[-.40354876534102097544,1.0499009621807602207 ] 
dist 232=[-.40134218329770328277,1.1219935182700007459 ] 
dist 233=[-.25382942787177848908,1.1926788539053168157 ] 
dist 234=[-.23998481539838105976,1.2390674244459823217 ] 
dist 235=[-.20801699325662091497,1.2768629114662623084 ] 
dist 236=[-.20289422957991820542,1.3131866259562241318 ] 
dist 237=[-.16108002431809895726,1.3460897374810330702 ] 
dist 238=[-.1535705874288144174 ,1.3702070800904531534 ] 
dist 239=[-.14288844051292705724,1.3926770293796736112 ] 
dist 240=[-.13991932046292384191,1.4189926310735158719 ] 
dist 241=[-.08729012864067784613,1.4435293717675874278 ] 
dist 242=[-.08062787223001509758,1.4588860960756631178 ] 
dist 243=[-.06607162164201414439,1.4705647230947013953 ] 
dist 244=[-.06306309210848565976,1.4803936547417438558 ] 
dist 245=[-.04646277881645298233,1.4883620008467603899 ] 
dist 246=[-.04354674380332627058,1.4926006079077637673 ] 
dist 247=[-.03753155557708494984,1.4949471638573497427 ] 

8 phat 2 dirichlet min maxes function [1, 2, 0, 2, 0, 2, 2, 0, 2] 
dist 0=[11.406491031663754903  ,11.406491031663754903  ] 
dist 1=[11.300812782132213654  ,11.473612685436337031  ] 
dist 2=[11.188079041559827392  ,11.525799378017118497  ] 
dist 3=[11.092740682733638413  ,11.571751095528397665  ] 
dist 4=[10.991197102521210621  ,11.610529634238156689  ] 
dist 5=[10.853644915969719913  ,11.634027193191389626  ] 
dist 6=[10.702230762763664058  ,11.650958082353954878  ] 
dist 7=[10.545251386734157479  ,11.663467361539048036  ] 
dist 8=[10.352951673723476609  ,11.673339405015118803  ] 
dist 9=[10.060289883395917933  ,11.679724577781090624  ] 
dist 10=[9.7654054134937301349 ,11.684780841677915956  ] 
dist 11=[9.5642158229303082760 ,11.689349490711023084  ] 
dist 12=[9.3916827339963283608 ,11.693260160541922872  ] 
dist 13=[9.2113930802625872613 ,11.695690512242448294  ] 
dist 14=[9.0383183624038280608 ,11.697505849654811379  ] 
dist 15=[8.8946354594926296321 ,11.698962192080876289  ] 
dist 16=[8.7438930865346375604 ,11.699962739053941986  ] 
dist 17=[8.5425830631105945834 ,11.699958851891727610  ] 
dist 18=[8.3417653090119574681 ,11.699222373190301101  ] 
dist 19=[8.1929892320159800006 ,11.697298667700490396  ] 
dist 20=[8.0527355302989964278 ,11.694764316394125432  ] 
dist 21=[7.8859963784408962598 ,11.691779540228201713  ] 
dist 22=[7.7134496837660656334 ,11.687346919805532368  ] 
dist 23=[7.5499671229455371788 ,11.684827299858066980  ] 
dist 24=[7.3605461196101342152 ,11.673583267498746398  ] 
dist 25=[7.0842604922272387050 ,11.668735280434250693  ] 
dist 26=[6.8070130897353256722 ,11.664508785579884164  ] 
dist 27=[6.6137437472300861010 ,11.661185593174024166  ] 
dist 28=[6.4435213304760389351 ,11.653576809320915290  ] 
dist 29=[6.2584430885942729819 ,11.560558432776919777  ] 
dist 30=[6.0762561627950662427 ,11.542830809441396385  ] 
dist 31=[5.9175940377245387896 ,11.437216362031228945  ] 
dist 32=[5.7445340781435725344 ,11.223318879464461773  ] 
dist 33=[5.5047594698830286568 ,9.8123946554015583154 ] 
dist 34=[5.2614541507086472687 ,9.7134815962566608196 ] 
dist 35=[5.0742706893900217606 ,9.4856653735148884549 ] 
dist 36=[4.8908896418109333558 ,9.4473929781792268579 ] 
dist 37=[4.6627883596747140923 ,9.1490648846308820602 ] 
dist 38=[4.4211872480871535445 ,9.0949047719639499149 ] 
dist 39=[4.1838099405537040300 ,9.0137613422921514489 ] 
dist 40=[3.9021460210160252461 ,8.9921823708840823420 ] 
dist 41=[3.4834132570532964837 ,8.6088925719099025810 ] 
dist 42=[3.0657070604941647223 ,8.5594630337274046130 ] 
dist 43=[2.7881479247187435587 ,8.4494001056499572986 ] 
dist 44=[2.5579476756720174016 ,8.4270814817607861312 ] 
dist 45=[2.3296577816990993828 ,8.2931536733826081466 ] 
dist 46=[2.1179103262942607948 ,8.2687930278988968817 ] 
dist 47=[1.9538723604088618593 ,8.2220870511915619834 ] 
dist 48=[1.7920654723813056978 ,8.2104808588764150596 ] 
dist 49=[1.5892391815863811217 ,7.8006652595360628514 ] 
dist 50=[1.3928389443140399090 ,7.7585094843454143687 ] 
dist 51=[1.2567326911011307438 ,7.6652302200705184567 ] 
dist 52=[1.1376556269049212128 ,7.6462766832089730160 ] 
dist 53=[1.0093645681174411193 ,7.5352629051653268245 ] 
dist 54=[.8837198299696295302 ,7.4548960246692119669 ] 
dist 55=[.7752248486729217306 ,7.4256880710096888264 ] 
dist 56=[.6576236455397031992 ,7.3281786166414166684 ] 
dist 57=[.4955520164314942187 ,7.1261532648760890374 ] 
dist 58=[.3366273938008874994 ,6.2230196941819877802 ] 
dist 59=[.2316120670260301269 ,6.1627338873370144823 ] 
dist 60=[.1451332356096965749 ,6.0520366648344461061 ] 
dist 61=[.0603501586167857743 ,6.0267470029368708439 ] 
dist 62=[-.0176919029191982831 ,5.7131678544126219491 ] 
dist 63=[-.12303857848748649831,5.6581633944852816326 ] 
dist 64=[-.38893713765797842326,5.4046386213884521618 ] 
dist 65=[-.57542885119366028111,2.5462675226555887533 ] 
dist 66=[-.74084231322647129278,2.3870031613098389814 ] 
dist 67=[-.92244638957331632999,2.0167935634374316133 ] 
dist 68=[-1.1022069864004286430 ,1.9637491262099250493 ] 
dist 69=[-1.2602488912550447802 ,1.7516614112432839441 ] 
dist 70=[-1.4338504111251627300 ,1.7170782083563751409 ] 
dist 71=[-1.6758380153720638938 ,1.7074859626399411087 ] 
dist 72=[-1.9139484011616416517 ,1.2663770578483011314 ] 
dist 73=[-2.0720449131429929720 ,.85469620990816554506] 
dist 74=[-2.2029694803423287339 ,.70549420468646357974] 
dist 75=[-2.3324151169863287549 ,.67931267007188318698] 
dist 76=[-2.4521691034216818424 ,.49615196357085965795] 
dist 77=[-2.5443362044150873565 ,.46381821811797640131] 
dist 78=[-2.6346459629624529936 ,.40885284448031561816] 
dist 79=[-2.7469749048010616175 ,.39666660328286229729] 
dist 80=[-2.8552603561066971691 ,.20714233831885179453] 
dist 81=[-2.9294008426803539597 ,.18226461442498392179] 
dist 82=[-2.9932916458393766036 ,.1283227902433798025 ] 
dist 83=[-3.0605880835159155580 ,.11739227997679838409] 
dist 84=[-3.1255628022332491393 ,.05792202004718287966] 
dist 85=[-3.1801715392544213142 ,.04777277294472208267] 
dist 86=[-3.2380888460362778129 ,.02642246242247912213] 
dist 87=[-3.3163025265137729498 ,.02185922776217974478] 
dist 88=[-3.3916735529296230024 ,-.35794863518598161751] 
dist 89=[-3.4382231084510589576 ,-.33442361229990362632] 
dist 90=[-3.4729504538037322742 ,-.31029019013615532774] 
dist 91=[-3.5010365360194621052 ,-.29283187528402575988] 
dist 92=[-3.5233691699777049025 ,-.27682590104800113079] 
dist 93=[-3.5350829923531083026 ,-.2584939381206367049 ] 
dist 94=[-3.5413600303231219498 ,-.23993763987520582594] 
dist 95=[-3.5426135036204751285 ,-.22303209708468894006] 
dist 96=[-3.5262419754702890527 ,-.20399007485258268094] 
dist 97=[-3.5219768816048292655 ,-.17688909791687011037] 
dist 98=[-3.5183186040659445943 ,-.14912517470018363633] 
dist 99=[-3.5154432902277210986 ,-.12743091984915008052] 
dist 100=[-3.5110385211019154905 ,-.10588206954942729409] 
dist 101=[-3.5082231354504038651 ,-.07869719011368930275] 
dist 102=[-3.5053825572903026329 ,-.04973666259003879463] 
dist 103=[-3.5029764110055406716 ,-.02108614036692177431] 
dist 104=[-3.1462250929923722944 ,.01303212783960978999] 
dist 105=[-3.1144170175303797474 ,.06385830013789344862] 
dist 106=[-3.0461443808981011963 ,.11450929318115209419] 
dist 107=[-3.0275790565009085286 ,.14792758001966327984] 
dist 108=[-2.9491463208389018509 ,.17535626030665525511] 
dist 109=[-2.9340515962238838182 ,.20205636794328783075] 
dist 110=[-2.8967771563008903070 ,.22647364913935017754] 
dist 111=[-2.8897782999182859309 ,.24477412450264096588] 
dist 112=[-2.8133687883323105287 ,.2622312288218291912 ] 
dist 113=[-2.7998176512022099404 ,.2832767752258515681 ] 
dist 114=[-2.7735389579896910721 ,.30322497199122830991] 
dist 115=[-2.7663869973145362028 ,.31629430531427358392] 
dist 116=[-2.7393013198011403252 ,.32692309695981323525] 
dist 117=[-2.7328178127759549191 ,.33711225231842236436] 
dist 118=[-2.7196793023689797731 ,.34633282624310137548] 
dist 119=[-2.7155776958091537892 ,.35308903409248759371] 
dist 120=[-2.0784530787751508913 ,.35938874672988618333] 
dist 121=[-2.0719135205249840275 ,.36678542889715252097] 
dist 122=[-2.0579034904896901336 ,.37369727274326336102] 
dist 123=[-2.0538103899606513966 ,.37805817318299975852] 
dist 124=[-2.0363764284616908204 ,.38142375900016874591] 
dist 125=[-2.0072414946306624576 ,.38435387699706396947] 
dist 126=[-2.0011851864519979910 ,.38681157946329303977] 
dist 127=[-1.9664038178726335686 ,.38828737683642474776] 
dist 128=[-1.8939750334608719063 ,.38934061200488888452] 
dist 129=[.02413347007493763629,.4233061697379492124 ] 
dist 130=[.11792678143281360037,.51509548048585287315] 
dist 131=[.12297115134209600624,.61593297591821092498] 
dist 132=[.12485350214915510914,.71574203180824138651] 
dist 133=[.12496995849158276254,.80341920329901145768] 
dist 134=[.12440979623547189082,.8996366751868024417 ] 
dist 135=[.1228825467214935275 ,1.0335973291985467032 ] 
dist 136=[.12035544708337881715,1.1652295141122508760 ] 
dist 137=[.1157996138485551347 ,1.2521360915850636308 ] 
dist 138=[.10272860242817749217,1.3235318677455279866 ] 
dist 139=[.07612454577926982363,1.3931393792762334748 ] 
dist 140=[.05367494094380612941,1.4568643673118384634 ] 
dist 141=[.03081751321119244662,1.5047372889553145767 ] 
dist 142=[.00926441760468328687,1.5505096303389569149 ] 
dist 143=[-.00797016758309946716,1.6058354418490559292 ] 
dist 144=[-.02545774892191118190,1.6583368760227151607 ] 
dist 145=[-.04802256258818892857,1.6928153470601710686 ] 
dist 146=[-.07014147259009898108,1.7209394570036282275 ] 
dist 147=[-.08584625803503866077,1.7480311975793491033 ] 
dist 148=[-.09996442884225186823,1.7726231744093728725 ] 
dist 149=[-.11573959657218858358,1.7907517984974014963 ] 
dist 150=[-.13150181519474660823,1.8077533335820568490 ] 
dist 151=[-.1455683042686721744 ,1.8278398885224869144 ] 
dist 152=[-.16118313381552702385,1.8463668276830709519 ] 
dist 153=[-.18313634052109527675,1.8571317956142585863 ] 
dist 154=[-.20477969851189187895,1.8643544828312727363 ] 
dist 155=[-.21915566268619022168,1.8687150418736230718 ] 
dist 156=[-.23105638686396946934,1.8714501248134445271 ] 
dist 157=[-.24280274307842642354,1.8721718216244950541 ] 
dist 158=[-.25364571507210031987,1.8717061669115793886 ] 
dist 159=[-.26193435586395072067,1.8710676966976756857 ] 
dist 160=[-.26999534939062515891,1.8465318807805148818 ] 
dist 161=[-.2799281241812928314 ,1.8422548777488445989 ] 
dist 162=[-.2894428147169538874 ,1.8339689585626140280 ] 
dist 163=[-.29583214025323096864,1.8314038867691262247 ] 
dist 164=[-.30119820444589211787,1.8201881886827880876 ] 
dist 165=[-.30662145987999841882,1.8174148537497774659 ] 
dist 166=[-.31171054276613856915,1.8096827171495040416 ] 
dist 167=[-.3157404455998799223 ,1.8074280236636776907 ] 
dist 168=[-.31979373544030521348,1.6379318690759831448 ] 
dist 169=[-.32497633829156203292,1.6217370753255931550 ] 
dist 170=[-.33020217589906159473,1.5855348095948292249 ] 
dist 171=[-.33442843393876227624,1.5770377323789224723 ] 
dist 172=[-.3387611550026953763 ,1.5309372814042545527 ] 
dist 173=[-.34441295974515401446,1.5220260630536674155 ] 
dist 174=[-.35052936738356726195,1.5038293304587694162 ] 
dist 175=[-.35672005599294294143,1.4987407987153415661 ] 
dist 176=[-.3641958706079925535 ,1.4393139307011715761 ] 
dist 177=[-.37545133778480568743,1.4304916259625771538 ] 
dist 178=[-.38725815579797838331,1.4088972436840800883 ] 
dist 179=[-.39693877871402334593,1.4049631250615391860 ] 
dist 180=[-.40698535359587249358,1.3711483410243019910 ] 
dist 181=[-.42025564224546581672,1.3643538011357588457 ] 
dist 182=[-.43470052492720057056,1.3551803883267132813 ] 
dist 183=[-.44944415193303385352,1.3521004248681186116 ] 
dist 184=[-.46733899054570683839,.79556668212769270358] 
dist 185=[-.4943850923617636407 ,.76961029652756168509] 
dist 186=[-.5218868825088601064 ,.70921554299584647942] 
dist 187=[-.54160396736032663434,.69955868888843828775] 
dist 188=[-.55953437075538888352,.61873705713060080496] 
dist 189=[-.57989154403382608371,.60403739302700661068] 
dist 190=[-.60042852865643854265,.58371623939424573298] 
dist 191=[-.61907799475944145603,.57778760894448669847] 
dist 192=[-.690339797873360993  ,.4688228731381988541 ] 
dist 193=[-.74577252139549678899,.45487507276009565424] 
dist 194=[-.79485078328799670178,.42502789354014058986] 
dist 195=[-.8485723594205913014 ,.41795053418228314676] 
dist 196=[-.90163161590398864062,.38538428651203788873] 
dist 197=[-.94976341552267149107,.37956510016155593532] 
dist 198=[-1.0055114003155827936 ,.36578326667153731603] 
dist 199=[-1.0825743824286815511 ,.36358013261014755218] 
dist 200=[-1.1580508235660816622 ,.22619310673500258794] 
dist 201=[-1.2074545562472572054 ,.21324963838459576727] 
dist 202=[-1.2475639422106456567 ,.18351522593799742759] 
dist 203=[-1.2858742315721034975 ,.17864645498924715342] 
dist 204=[-1.3204190973856437370 ,.1402223434639216825 ] 
dist 205=[-1.3454713234962078807 ,.13334013395557271952] 
dist 206=[-1.3685442920416194319 ,.12316056039857437396] 
dist 207=[-1.3951744688549866156 ,.12046232913235058708] 
dist 208=[-1.4197996867517913720 ,.07366371738557076990] 
dist 209=[-1.4348552191934983170 ,.06773336231403981412] 
dist 210=[-1.4458871274585879355 ,.05448362676461253340] 
dist 211=[-1.4544226920553182178 ,.05202690481543270632] 
dist 212=[-1.4610485573958476635 ,.03603822118629679875] 
dist 213=[-1.4644440389163594745 ,.03321341862771136599] 
dist 214=[-1.4661458953621005494 ,.02808199106629632964] 

8 phat 2 dirichlet min maxes function [2, 0, 0, 0, 2] 
dist 0=[15.014095602299645789  ,15.014095602299645789  ] 
dist 1=[14.841184912900628083  ,15.179866206949892525  ] 
dist 2=[14.709586639155340802  ,15.282912470134007676  ] 
dist 3=[14.582139115105327146  ,15.360429361817560145  ] 
dist 4=[14.425818519396155679  ,15.424120322227185134  ] 
dist 5=[14.261546480842812226  ,15.474867766120044556  ] 
dist 6=[14.102298430118661666  ,15.500627566812934277  ] 
dist 7=[13.915071520032905105  ,15.514250401803315395  ] 
dist 8=[13.638912660003960059  ,15.516470374703616489  ] 
dist 9=[13.351542404128591686  ,15.492359427007626740  ] 
dist 10=[13.119480298903970554  ,15.484017427253303447  ] 
dist 11=[12.881814795589284143  ,15.475794117648527230  ] 
dist 12=[12.572033440403143075  ,15.469788368993237556  ] 
dist 13=[12.236828712421753714  ,15.454662220137042152  ] 
dist 14=[11.897495359676725873  ,15.447253764704681139  ] 
dist 15=[11.487623466909519988  ,15.432158142436298821  ] 
dist 16=[10.870338868675609977  ,15.425691227304452723  ] 
dist 17=[10.251094541931928121  ,14.658538761959187419  ] 
dist 18=[9.8333844621494220090 ,14.587089619671307585  ] 
dist 19=[9.4803373716727532698 ,14.438966026212726117  ] 
dist 20=[9.1196728918579213751 ,14.398468979985091502  ] 
dist 21=[8.7785707657262239069 ,14.239265846576141178  ] 
dist 22=[8.5037496216578281845 ,14.207227470316661320  ] 
dist 23=[8.2228352352769210613 ,14.131037960611869970  ] 
dist 24=[7.8573619830110071135 ,14.112862280668897618  ] 
dist 25=[7.4973115821249837943 ,12.979299976386708430  ] 
dist 26=[7.2380803559475456182 ,12.862453764181733356  ] 
dist 27=[7.0011697098873054149 ,12.709860058863799323  ] 
dist 28=[6.7303751016212245407 ,12.667455375315271173  ] 
dist 29=[6.4560808681523092916 ,12.356334237066153361  ] 
dist 30=[6.2051707094293525831 ,12.322870625315530220  ] 
dist 31=[5.9214360385916200010 ,12.286263405949112687  ] 
dist 32=[5.5158672632934195397 ,12.274020322878045158  ] 
dist 33=[5.1124706934540240363 ,10.631407651008986724  ] 
dist 34=[4.8374201423850640045 ,10.490910529375383293  ] 
dist 35=[4.6016872156573607088 ,10.183550271743520858  ] 
dist 36=[4.3555235612578897638 ,10.114482059481086642  ] 
dist 37=[4.1192587821710243772 ,9.7543872563283732315 ] 
dist 38=[3.9231084166798012970 ,9.6884190460655106984 ] 
dist 39=[3.7172723682084221066 ,9.5479720130460643713 ] 
dist 40=[3.4422636965310301240 ,9.5094359026587389259 ] 
dist 41=[3.1677658112868632184 ,9.1773250665291595017 ] 
dist 42=[2.9639678146894721044 ,9.1237962544737508918 ] 
dist 43=[2.7713623984537675396 ,9.0185497010230664152 ] 
dist 44=[2.5416207506224701268 ,8.9911316488743979691 ] 
dist 45=[2.3033854615066985267 ,8.8924102831923866411 ] 
dist 46=[2.0768033227071003628 ,8.8700803940829036263 ] 
dist 47=[1.8135368989708885543 ,8.8316192107615409320 ] 
dist 48=[1.4285721138979935978 ,8.8216683528768348770 ] 
dist 49=[1.0461876344407899718 ,4.9171464325084605043 ] 
dist 50=[.79323925425799509299,4.8285780391721924579 ] 
dist 51=[.58470018500650762193,4.6335415051648313805 ] 
dist 52=[.37993578722468791287,4.5975151239549443177 ] 
dist 53=[.19132658562878384934,4.3742165823038829594 ] 
dist 54=[.04740101404966476898,4.3360971918126672666 ] 
dist 55=[-.09250471069168056286,4.2638651234480276379 ] 
dist 56=[-.26503920126525740746,4.2474326441143764771 ] 
dist 57=[-.43073806858706772734,3.7514169433771965850 ] 
dist 58=[-.54330528470300987382,3.6990554265526219937 ] 
dist 59=[-.63940539663398745955,3.6105836573389435300 ] 
dist 60=[-.73924310815648941688,3.5915254497185729373 ] 
dist 61=[-.83482866040953198687,3.3245329180402576689 ] 
dist 62=[-.9139247220353626472 ,3.2939643669905157450 ] 
dist 63=[-1.0790895447760688876 ,3.1366212808354437062 ] 
dist 64=[-1.4421777612894653038 ,2.9088100171587418542 ] 
dist 65=[-1.7991516555856031191 ,-.3799626257894591906 ] 
dist 66=[-2.0355138740442666582 ,-.50882290904848104617] 
dist 67=[-2.2305037990333170038 ,-.8032628884108820605 ] 
dist 68=[-2.4220283742005290083 ,-.84603306762145603912] 
dist 69=[-2.5983659000052169826 ,-1.0431495293910332067 ] 
dist 70=[-2.7326236230934274649 ,-1.0414895918494322804 ] 
dist 71=[-2.8627724514318278963 ,-1.0310448252314644302 ] 
dist 72=[-3.0226824407652659003 ,-1.0058945705825328319 ] 
dist 73=[-3.1758362310748048299 ,-.97583932361699830867] 
dist 74=[-3.2789686338690429962 ,-.94578005890296296655] 
dist 75=[-3.3659831776749584458 ,-.90981799589688831076] 
dist 76=[-3.4546825540501695357 ,-.85615386626024377452] 
dist 77=[-3.5385093639006715959 ,-.79484200634465824987] 
dist 78=[-3.6060425224429217840 ,-.72830149552539420945] 
dist 79=[-3.6751202344491620245 ,-.64478294302368282841] 
dist 80=[-3.7651348280231977621 ,-.51559394755484424689] 
dist 81=[-3.8512913092036999566 ,-.38526572064472188409] 
dist 82=[-3.9049406846750019270 ,-.2971906665693939069 ] 
dist 83=[-3.9454917300760614927 ,-.22267808062640474577] 
dist 84=[-3.9792576371227446759 ,-.14656596672448978882] 
dist 85=[-4.0064244608974158206 ,-.07469448805095281034] 
dist 86=[-4.0205825161107770477 ,-.01713323769967038285] 
dist 87=[-4.0281068014843308465 ,.04132458660680700667] 
dist 88=[-4.0296875279137423270 ,.11678214205850989529] 
dist 89=[-4.0263275285644073139 ,.19069951793422089322] 
dist 90=[-4.0236006731671916235 ,.24300084545025902945] 
dist 91=[-4.0191291456162929923 ,.28980616212177836022] 
dist 92=[-4.0167847569270471343 ,.34175234956463630483] 
dist 93=[-4.0040678855758012742 ,.39342399954612343512] 
dist 94=[-4.0002950975814384488 ,.4391324825752708742 ] 
dist 95=[-3.9869019506770684148 ,.4895199431684991123 ] 
dist 96=[-3.9838052598709197856 ,.55989858751342257921] 
dist 97=[-3.6700542764367965847 ,.62901411605583187105] 
dist 98=[-3.6394271166000941216 ,.67435181421382972083] 
dist 99=[-3.5710975372741841467 ,.71123468770751577693] 
dist 100=[-3.5541509094560877486 ,.7465479179802627587 ] 
dist 101=[-3.4666060468415909529 ,.77841375071608204355] 
dist 102=[-3.4493914063366897689 ,.80151373114244993607] 
dist 103=[-3.4130860125201528387 ,.8227598203435600486 ] 
dist 104=[-3.4025215070024862415 ,.84721313563861083415] 
dist 105=[-3.2859798162388013063 ,.86975212235753161424] 
dist 106=[-3.2682927156853913998 ,.88334433555209457404] 
dist 107=[-3.2246116345578543390 ,.89306464129789159942] 
dist 108=[-3.2165232043602218946 ,.90012324348326937159] 
dist 109=[-3.1465092593814556334 ,.90533877675468603466] 
dist 110=[-3.1322737134621423410 ,.90769132512614913365] 
dist 111=[-3.1131607597219259559 ,.90844215012283689054] 
dist 112=[-3.1066260622031941698 ,.90832200940804034357] 
dist 113=[-1.8793723734058543572 ,.89096201418476151377] 
dist 114=[-1.8212022382516092796 ,.88780927020462820039] 
dist 115=[-1.6855365222904001512 ,.88142328446486465804] 
dist 116=[-1.6640738312105835286 ,.87927840909999673962] 
dist 117=[-1.4815946052514051708 ,.86901414434975752381] 
dist 118=[-1.4483798487593070950 ,.86663471390559433474] 
dist 119=[-1.4032808115111940223 ,.97044026050520259289] 
dist 120=[-1.3899454911704920807 ,1.1478229270291199846 ] 
dist 121=[-1.1409367949551063942 ,1.3205815035156695699 ] 
dist 122=[-1.1091051883150929086 ,1.4415645216453920784 ] 
dist 123=[-1.0415779505945899497 ,1.5486367062349319322 ] 
dist 124=[-1.0250104280928606266 ,1.6657694213760776171 ] 
dist 125=[-.95336330695220591006,1.7814127928531833052 ] 
dist 126=[-.94037469068451994121,1.8825296635364545914 ] 
dist 127=[-.90988170878900720076,1.9930996381044621695 ] 
dist 128=[-.90475907099817092443,2.1465441224937253178 ] 
dist 129=[-.57778671266923733105,2.2997529173085914902 ] 
dist 130=[-.54753658106522926663,2.4075515233123128581 ] 
dist 131=[-.47733106576614621864,2.4951992233403804443 ] 
dist 132=[-.46648181190063191152,2.5791301441530396443 ] 
dist 133=[-.37370721348743631925,2.6549543976426004838 ] 
dist 134=[-.35705372948037975884,2.7101853651462380425 ] 
dist 135=[-.3346494984782856967 ,2.7612969090794720973 ] 
dist 136=[-.32865729465290201432,2.8206484085270316250 ] 
dist 137=[-.20814732658777249264,2.8757209514470238056 ] 
dist 138=[-.1930368417284030785 ,2.9097218655201060428 ] 
dist 139=[-.16098727319868354633,2.9350313088931141012 ] 
dist 140=[-.15352631011709027736,2.9553485878385227025 ] 
dist 141=[-.12008099322299014146,2.9712712338510837321 ] 
dist 142=[-.11415025281989665934,2.9790077405686983640 ] 
dist 143=[-.10083296529339718614,2.9828069079952790562 ] 
dist 144=[-.09844191399466636441,2.9830755060296085495 ] 
dist 145=[.76159046167210347503,.93355754802132274335] 
dist 146=[.76603305925677449162,.93329419181778460017] 
dist 147=[.77418788902038427598,.93251924586127350719] 
dist 148=[.76360793063412870364,.93194295343974681349] 
dist 149=[.74171469541125553603,.92807134674829220205] 
dist 150=[.71964730676874451572,.92695570178524389252] 
dist 151=[.69307276818755693769,.92381006256494113643] 
dist 152=[.65315687028047717447,.92255727184342274755] 
dist 153=[.61134320192462093366,.90730460340145991059] 
dist 154=[.57717987829507817696,.90469428571009381506] 
dist 155=[.54184187440260938684,.89800949906963511888] 
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dist 175=[-.46590521403903801407,.64347126000499010624] 
dist 176=[-.51438330843181503535,.64191049546784324762] 
dist 177=[-.56212570472628537977,.48045960842888213351] 
dist 178=[-.5937993065834443951 ,.46833643775403271193] 
dist 179=[-.61998542858698725775,.44029447537907451719] 
dist 180=[-.64578527022462986283,.43550348491006455072] 
dist 181=[-.66957851282453896138,.39823599827805914566] 
dist 182=[-.68774099684055049048,.39139741340970180103] 
dist 183=[-.70538495090672796989,.38111185983637323627] 
dist 184=[-.72710496590775007669,.37835094912104454091] 
dist 185=[-.74791062088707749602,.32836364451535132651] 
dist 186=[-.76189843665522427806,.3218537911616055758 ] 
dist 187=[-.7736682095376012704 ,.30739763841827204172] 
dist 188=[-.78560469757045313033,.30430922922272797893] 
dist 189=[-.79683719788794027795,.28669858584117120706] 
dist 190=[-.80579212431843792988,.2834535001085605483 ] 
dist 191=[-.81485865095363650353,.27699692558014652467] 
dist 192=[-.82653785280977096338,.27530843533056139672] 
dist 193=[-.83761967201271868793,.21460948951707127387] 
dist 194=[-.84429746175081866305,.20844339346941015228] 
dist 195=[-.84907547091216997781,.194422537459435698  ] 
dist 196=[-.85256024328275720618,.19184289406467475368] 
dist 197=[-.85506882581777194009,.17393173889386425538] 
dist 198=[-.85594306921700486183,.17066464444291826559] 
dist 199=[-.85611437399655637259,.16507626900831081665] 
dist 200=[-.85581186050522817817,.16379028324399102044] 
dist 201=[-.84871391768004570275,.1420951961232926544 ] 
dist 202=[-.84722005741761483658,.13923975418196291519] 
dist 203=[-.84409968881166851266,.13239320628125778395] 
dist 204=[-.84300768320202800927,.13138625519133420411] 
dist 205=[-.8247047375328839333 ,.12152549769246518315] 
dist 206=[-.82211914756748248336,.11968520975524421059] 
dist 207=[-.80657648894159289102,.11755556495237189262] 
dist 208=[-.78060723158128318778,.11710636768488723025] 
dist 209=[-.15307566634467126715,.09955837610659988215] 
dist 210=[-.1558901012330690933 ,.09748249756085418996] 
dist 211=[-.15806804907049663195,.09256771508869851581] 
dist 212=[-.15997122817330396827,.09177477957672453036] 
dist 213=[-.16157014042901924603,.08483584512741693575] 
dist 214=[-.16253122185114196478,.08353265924754460063] 
dist 215=[-.16321699458824425694,.08182246361534553731] 
dist 216=[-.1637149462415936112 ,.08127710537379121640] 
dist 217=[-.16408460223773584608,.07039071238804557805] 
dist 218=[-.16425727656455521947,.06895925829136449666] 
dist 219=[-.16432079367922925984,.06601002676138208752] 
dist 220=[-.1642791257213873299 ,.06522046535599418294] 
dist 221=[-.16410828961783408015,.06220200072987025759] 
dist 222=[-.16401560012159876617,.06159512630290325390] 
dist 223=[-.1636160416573529404 ,.06026558195769352517] 
dist 224=[-.16350521246129414835,.05988061631084925066] 
dist 225=[-.14024700575638727686,.03917841440278079353] 
dist 226=[-.13854292308895248746,.03728543211168761751] 
dist 227=[-.13440371861002296725,.03293794241153513315] 
dist 228=[-.133790776170078524  ,.03216185845483049511] 
dist 229=[-.12763185787186414126,.02646236769646312363] 
dist 230=[-.12646371915868182687,.02541469054384279368] 
dist 231=[-.12514013651540605534,.02373377257561841360] 
dist 232=[-.12484919849151537924,.02331345445230739232] 
dist 233=[-.11410084564119128926,.01588279890805186119] 
dist 234=[-.11272643092652015138,.01490664398357386873] 
dist 235=[-.11002711988331957436,.01266372286798207328] 
dist 236=[-.10933775246875051731,.01224492947859548178] 
dist 237=[-.10693028093429880716,.00927760063284604506] 
dist 238=[-.10638734631483922151,.00872438557847772237] 
dist 239=[-.10563649443198849088,.00780150003974033281] 
dist 240=[-.10539713378799621257,.00757680502555652862] 
dist 241=[-.08255989660615525442,-.02809009491723709260] 
dist 242=[-.08061040132079837218,-.03043034930606791623] 
dist 243=[-.07624562478337265357,-.03563688888077524316] 
dist 244=[-.07539764408735092815,-.03660599624799097551] 
dist 245=[-.07004983467969874722,-.04279227943158017019] 
dist 246=[-.06908603510302128815,-.04387474276391133635] 
dist 247=[-.06729769480545097120,-.04587497896549576325] 
dist 248=[-.06687438913490389992,-.04632932025069642774] 
dist 249=[-.06129881732831394324,-.04164814105691394966] 
dist 250=[-.06051886332802043272,-.03721224816058299854] 
dist 251=[-.05883418073208142900,-.03287944608588889666] 
dist 252=[-.05843856142495404558,-.02751080167472293515] 
dist 253=[-.05653497915424237596,-.02183819723315434116] 
dist 254=[-.05618816425347018617,-.01628976685296133743] 
dist 255=[-.05530433911796802458,-.00972742455508026050] 

8 phat 2 dirichlet min maxes function [1, 2, 2, 2, 0, 2, 2, 0, 2] 
dist 0=[16.241856649570468289  ,16.241856649570468289  ] 
dist 1=[16.195748442046476102  ,16.279740472761493504  ] 
dist 2=[16.134473913174064439  ,16.310315383249357814  ] 
dist 3=[16.035936088960384903  ,16.327198450752798437  ] 
dist 4=[15.920123571870775106  ,16.337373642430201686  ] 
dist 5=[15.789768141125365599  ,16.341137232507477082  ] 
dist 6=[15.622844281188942404  ,16.340511156545251561  ] 
dist 7=[15.360800271553147623  ,16.337153380302794903  ] 
dist 8=[15.090499583335432477  ,16.323688586943112108  ] 
dist 9=[14.890556870700899045  ,16.315693726679301419  ] 
dist 10=[14.702451851109539117  ,16.266094958991342229  ] 
dist 11=[14.479483252995372768  ,16.250989222390709574  ] 
dist 12=[14.249215596349457480  ,16.234932702679598606  ] 
dist 13=[14.031919844431205634  ,16.225896488363813262  ] 
dist 14=[13.780916727532342055  ,15.983181379132972625  ] 
dist 15=[13.415854771725650749  ,15.936500934947545047  ] 
dist 16=[13.038099059247292412  ,15.675534294563272450  ] 
dist 17=[12.736333338464366435  ,15.174218960821474795  ] 
dist 18=[12.430255812977459316  ,15.084424321068199952  ] 
dist 19=[12.035254920931809748  ,14.893021422317589722  ] 
dist 20=[11.609781977145312699  ,14.840098303478957577  ] 
dist 21=[11.181847669704716094  ,14.624537977879910264  ] 
dist 22=[10.666966101478102760  ,14.583163350736191056  ] 
dist 23=[9.8937961737887713884 ,14.478018547296620239  ] 
dist 24=[9.1190617270026035684 ,14.460960736156490395  ] 
dist 25=[8.5979226220844799750 ,14.262955232219937264  ] 
dist 26=[8.1590399189298872605 ,14.226668375658964540  ] 
dist 27=[7.7132406379884346001 ,14.159950628347457757  ] 
dist 28=[7.2932333375594680986 ,14.142537362191658134  ] 
dist 29=[6.9574887452564260400 ,13.858077618761036026  ] 
dist 30=[6.6167146714200476756 ,13.804234630883785360  ] 
dist 31=[6.1765906258552042223 ,13.528120725786370528  ] 
dist 32=[5.7445340781435725341 ,13.000927120965018228  ] 
dist 33=[5.4360191656791850758 ,11.204447287348903139  ] 
dist 34=[5.1566820911636767480 ,10.872717994551768594  ] 
dist 35=[4.8413032894131377011 ,10.818215803793946768  ] 
dist 36=[4.5240646413407243661 ,10.712111195665737219  ] 
dist 37=[4.2372858286585712005 ,10.684449618566195693  ] 
dist 38=[3.9157378787793554532 ,10.585299279208518006  ] 
dist 39=[3.4594492496763092227 ,10.562200222299355992  ] 
dist 40=[3.0070569520463691013 ,10.523703097720372294  ] 
dist 41=[2.7010879552637851156 ,10.513103711174377155  ] 
dist 42=[2.4415452340896413054 ,6.1809833208474085786 ] 
dist 43=[2.1748123925941344014 ,5.9134044449353107449 ] 
dist 44=[1.9214693109812411751 ,5.8460844978022541196 ] 
dist 45=[1.7154690628216410503 ,5.5903083581635458507 ] 
dist 46=[1.5031290056859764294 ,5.5416931147973778095 ] 
dist 47=[1.2244227327180604662 ,5.4489757108766115378 ] 
dist 48=[.9485475197600803221 ,5.4270303546390774263 ] 
dist 49=[.7475244033924745589 ,4.1650476162300336197 ] 
dist 50=[.5612977893530635997 ,4.0550946481319682876 ] 
dist 51=[.3445906917356590769 ,3.8042111008714648930 ] 
dist 52=[.1228048227793020173 ,3.7654185139520855671 ] 
dist 53=[-.0837419662454940676 ,3.4511433042044436150 ] 
dist 54=[-.3203470105756571125 ,3.3965538730070223605 ] 
dist 55=[-.6623632297439724467 ,3.3182722306547709963 ] 
dist 56=[-1.0007731796417703515 ,3.2976760138480583858 ] 
dist 57=[-1.2229574787337450367 ,2.9612385412028362868 ] 
dist 58=[-1.4042863688754524647 ,2.9204671986268844326 ] 
dist 59=[-1.5792903242554257929 ,2.8294113729091589686 ] 
dist 60=[-1.7385048450579252294 ,2.8160868131116595936 ] 
dist 61=[-1.9102491418478398574 ,2.7082672929190744123 ] 
dist 62=[-2.1176032444596669388 ,2.6906926990385669021 ] 
dist 63=[-2.2778190588273051264 ,2.6394030784157296656 ] 
dist 64=[-2.4353886130573038485 ,2.5744988978992167319 ] 
dist 65=[-2.6321657179327888094 ,-.6604047211216818116 ] 
dist 66=[-2.8222190579111773342 ,-.7791223572023573379 ] 
dist 67=[-2.9529025964556735526 ,-1.0484221929072561842 ] 
dist 68=[-3.0661063094629629908 ,-1.0891010266134176392 ] 
dist 69=[-3.1862593837091427563 ,-1.4198435339113896551 ] 
dist 70=[-3.3028156658339396577 ,-1.4764542670997851005 ] 
dist 71=[-3.4016412490139803050 ,-1.5567375094802216769 ] 
dist 72=[-3.5072014636529861794 ,-1.5757813862442228922 ] 
dist 73=[-3.6507042961569839570 ,-1.8451252519429333573 ] 
dist 74=[-3.7900110091674472652 ,-1.9485332253368515349 ] 
dist 75=[-3.8787913406733941211 ,-2.0341787431815763225 ] 
dist 76=[-3.9482716512358508779 ,-2.0478861794374348767 ] 
dist 77=[-4.0103840144116561300 ,-2.1360156442130324051 ] 
dist 78=[-4.0636195260355777476 ,-2.0893937432079284881 ] 
dist 79=[-4.0975970462020258957 ,-1.9866737725525558274 ] 
dist 80=[-4.1242671072409071982 ,-1.8774224419667102351 ] 
dist 81=[-4.1482808734897978879 ,-1.7857664077108330453 ] 
dist 82=[-4.1682944205535033896 ,-1.6888550092822682976 ] 
dist 83=[-4.1789646162442695967 ,-1.5585841452193292913 ] 
dist 84=[-4.1849466697942931165 ,-1.4157762212646376897 ] 
dist 85=[-4.1862025879590433112 ,-1.2687344274701620484 ] 
dist 86=[-4.1846293001617014266 ,-1.0894260173080880798 ] 
dist 87=[-4.1829761747990566477 ,-.81760312794583762888] 
dist 88=[-4.1737545274612466415 ,-.54483213842114439557] 
dist 89=[-4.1713572521412154179 ,-.36173159993985415687] 
dist 90=[-3.9146956635340994445 ,-.20805473890870341396] 
dist 91=[-3.8884375494875205850 ,-.0529277756989016710 ] 
dist 92=[-3.8298339333586734653 ,.0924996223294749187 ] 
dist 93=[-3.8141352205398000392 ,.2073952519161611926 ] 
dist 94=[-3.7375186810340676688 ,.3227009881923993988 ] 
dist 95=[-3.7220006826234899422 ,.4697691092503004588 ] 
dist 96=[-3.6881420265396225496 ,.6131161937546371516 ] 
dist 97=[-3.6778216767454573623 ,.7135443464541788002 ] 
dist 98=[-3.5673902206032971060 ,.8024320876800934136 ] 
dist 99=[-3.5503455460133836043 ,.8996368763852228578 ] 
dist 100=[-3.5069635942151906781 ,.9955419373131757466 ] 
dist 101=[-3.4994348781475332157 ,1.0792332185780822241 ] 
dist 102=[-3.4257388883234121230 ,1.1705779806588565476 ] 
dist 103=[-3.4105622877538310736 ,1.2970849528780512011 ] 
dist 104=[-3.3925642457056169275 ,1.4209786508566458030 ] 
dist 105=[-3.3855717717376511088 ,1.5018745052997046427 ] 
dist 106=[-2.1417873587286368589 ,1.5672979976231591489 ] 
dist 107=[-2.0804254551084413418 ,1.6293268010489561699 ] 
dist 108=[-1.9368869669291332407 ,1.6849200865477990826 ] 
dist 109=[-1.9142991190806642894 ,1.7246114940397940224 ] 
dist 110=[-1.7197332025995468673 ,1.7605186318541336981 ] 
dist 111=[-1.6842066299156359650 ,1.8009801833695505494 ] 
dist 112=[-1.6366589801750639555 ,1.8380986691703882979 ] 
dist 113=[-1.6228922092531662159 ,1.8606389830026159962 ] 
dist 114=[-1.3515945751684506946 ,1.8769615567811778783 ] 
dist 115=[-1.3169307262158258785 ,1.8892200194341424693 ] 
dist 116=[-1.2439451566753037126 ,1.8984146553669715427 ] 
dist 117=[-1.2253612027401973409 ,1.9024866847012733260 ] 
dist 118=[-1.1497562849051435136 ,1.9039833261258851211 ] 
dist 119=[-1.1356711853660762092 ,1.9234692310458854810 ] 
dist 120=[-1.1038072111035522362 ,2.0432837166405685511 ] 
dist 121=[-1.0972468094485038365 ,2.2230785530750864494 ] 
dist 122=[-.72105585802369076081,2.3992938066638870391 ] 
dist 123=[-.68672822301160092981,2.5147439620349131652 ] 
dist 124=[-.60614398141339067155,2.6085872581749275738 ] 
dist 125=[-.59440571003540889284,2.6984026231622903351 ] 
dist 126=[-.53641311466629150095,2.7795059551379070189 ] 
dist 127=[-.52334417875075427222,2.8385121697011837758 ] 
dist 128=[-.52042429386934922885,2.8930443839220303611 ] 
dist 129=[-.43691853339119211307,2.9562572531837534110 ] 
dist 130=[-.28351131548253761922,3.0148497413833741742 ] 
dist 131=[-.26465234142704594568,3.0509062277661646200 ] 
dist 132=[-.22647637769638622668,3.0776045466389419645 ] 
dist 133=[-.21678862344087183729,3.0987761817919600992 ] 
dist 134=[-.18266946641233164903,3.1152944094024816310 ] 
dist 135=[-.17572480814436024556,3.1233852530921296577 ] 
dist 136=[-.16543380266005933764,3.1272583027099427368 ] 
dist 137=[-.16272156825982800788,3.1276101627243536190 ] 
dist 138=[.38418478834358407867,.7290627872676520343 ] 
dist 139=[.37236238391781728332,.74362292858421921665] 
dist 140=[.35941765115766793223,.75501699024825756203] 
dist 141=[.3461123017282218415 ,.76519376924688170463] 
dist 142=[.32990345954354115507,.77390337082897642363] 
dist 143=[.30534871791664577072,.7794299612446312678 ] 
dist 144=[.27954475816002832352,.78372729024897133134] 
dist 145=[.25834059696805037605,.7875213437628087698 ] 
dist 146=[.23630003994364834195,.79062201186040464208] 
dist 147=[.2071511864576737789 ,.79214628319620261679] 
dist 148=[.1754157920332230833 ,.79282207943517271026] 
dist 149=[.14303259133939616397,.7928209781458845802 ] 
dist 150=[.10374375972331610557,.79179350683491729902] 
dist 151=[.04439569045984255673,.79126886992252505329] 
dist 152=[-.01512537336392063136,.78957381445274653299] 
dist 153=[-.05510604409072702086,.78873117018593176936] 
dist 154=[-.08869937199017349652,.74484187758740513002] 
dist 155=[-.12268049629408734461,.74018281513831349792] 
dist 156=[-.15459058706485243522,.72961339490911492343] 
dist 157=[-.1799028851786256894 ,.72689837434525115518] 
dist 158=[-.20540494309108355231,.71250363715098783495] 
dist 159=[-.23807393349360768587,.70957165651563743329] 
dist 160=[-.26999534939062515791,.70355440646240954894] 
dist 161=[-.29250825365137153826,.70179277692304943042] 
dist 162=[-.31259439488686980808,.67897017518710551558] 
dist 163=[-.33481232355063085471,.67558921363696987952] 
dist 164=[-.35688712465939557021,.666916934868046247  ] 
dist 165=[-.37640104545566070965,.66550715640133082108] 
dist 166=[-.39791379504255391182,.65065163817214713594] 
dist 167=[-.42798121342202280564,.64760935883443569982] 
dist 168=[-.45756131447748983523,.64427076327246549367] 
dist 169=[-.47712551430251535295,.64318054161359494647] 
dist 170=[-.49323253007318088085,.38773613846168173233] 
dist 171=[-.50898874659448448069,.37158126062565878692] 
dist 172=[-.52344409819126683766,.33380397947953277671] 
dist 173=[-.53434949906012319275,.32802663781620571801] 
dist 174=[-.54481871080660650297,.27708101533013907909] 
dist 175=[-.55752997669956519087,.26785174763752260969] 
dist 176=[-.56961606283339304613,.25584683934309519646] 
dist 177=[-.57758545038084314563,.25278186987118432518] 
dist 178=[-.58411996078087986282,.23198142158829795602] 
dist 179=[-.59046854615407866389,.23032531599098344156] 
dist 180=[-.59626479273077433072,.22446890564182007364] 
dist 181=[-.6005907582082208439 ,.2231939998750723409 ] 
dist 182=[-.60469863464177811213,.22125484205866506025] 
dist 183=[-.60962294241106881295,.2207128215769055239 ] 
dist 184=[-.61418116767592815141,.17080632313232911184] 
dist 185=[-.61682521786557759594,.16656150015548292944] 
dist 186=[-.61859162781386814936,.15657819706200421517] 
dist 187=[-.61964038286214912104,.15506636215184436688] 
dist 188=[-.62015580431548576026,.14137543516316883278] 
dist 189=[-.62018341811757789645,.13887282424263125787] 
dist 190=[-.61925921284091734994,.13572311584162567207] 
dist 191=[-.61911827027787307925,.13495360178651232453] 
dist 192=[-.61368045646556284495,.11503560323424846497] 
dist 193=[-.61258074372622467363,.11252061409132162843] 
dist 194=[-.60952082580936550092,.10738340251218818309] 
dist 195=[-.60866215163575144752,.10604869589496544479] 
dist 196=[-.60206771003619176106,.10116347222312357521] 
dist 197=[-.59989015727562617512,.10017970004532465571] 
dist 198=[-.59552205752479427498,.09833281696964873352] 
dist 199=[-.59007411716711941344,.09787905993265979743] 
dist 200=[-.56027450823982907119,.06635399864233472853] 
dist 201=[-.55144526769724262308,.06358773702273165675] 
dist 202=[-.12572471139753325032,.05726708939022063180] 
dist 203=[-.13090632208631775824,.05618889197607613745] 
dist 204=[-.13513858549943576694,.04809390298351613775] 
dist 205=[-.13922637513335975311,.04663832609404059711] 
dist 206=[-.14294518394573617565,.04436035492373246002] 
dist 207=[-.1457018296030557816 ,.04379097357912097814] 
dist 208=[-.14830240750875089382,.03407276937528138877] 
dist 209=[-.15139711163413757654,.03282689809739650976] 
dist 210=[-.15431113280313425417,.02996329396598885158] 
dist 211=[-.1561891385766796314 ,.02948479995377302430] 
dist 212=[-.15768196157385860482,.02576194746277173652] 
dist 213=[-.15905556376884694946,.02508953422898362605] 
dist 214=[-.16026008647626274978,.02408015086478531064] 
dist 215=[-.16107676192906854727,.02381409583195269677] 
dist 216=[-.16177223356450176146,-.01542456149764000982] 
dist 217=[-.16249213928583862647,-.01796148598641274249] 
dist 218=[-.16311776860600930772,-.02362997908267114437] 
dist 219=[-.1634362098701634653 ,-.02464220463009506707] 
dist 220=[-.16359340186283018017,-.03143857419509820211] 
dist 221=[-.16361321032644540824,-.03262467007892281792] 
dist 222=[-.16348285121258833649,-.03473066134950693146] 
dist 223=[-.16339851510596097099,-.03518306556243331196] 
dist 224=[-.16319794552201608736,-.04149556806991647767] 
dist 225=[-.1630992617705095584 ,-.04235078411448282900] 
dist 226=[-.16099393028649213214,-.04403201606029672470] 
dist 227=[-.16064271950360852026,-.04443537830889154119] 
dist 228=[-.15988602220970321919,-.04571221264985238573] 
dist 229=[-.15964392441065440976,-.04598831172411646309] 
dist 230=[-.15852786387045676583,-.04604967756990547424] 
dist 231=[-.15827976065537979206,-.04579549381913795674] 
dist 232=[-.15759349035477034268,-.04540364369417691929] 
dist 233=[-.15743116087621270366,-.04490465746509005062] 
dist 234=[-.12989731972640428044,-.04422763321600465198] 
dist 235=[-.12795537480962734914,-.04312380555013778127] 
dist 236=[-.1232943900974750082 ,-.04181956145902530870] 
dist 237=[-.12261760677858849517,-.04034105410638781806] 
dist 238=[-.11589688588017969686,-.03844024832432017173] 
dist 239=[-.11464368088790842804,-.03544718296461927980] 
dist 240=[-.11321952938264361251,-.03225220454641815460] 
dist 241=[-.11294382218490400932,-.02954392780965330942] 
dist 242=[-.10143326607110026222,-.02665311657403104564] 
dist 243=[-.09999253583260643313,-.02272817080276943926] 
dist 244=[-.09721546246836746859,-.01840242978585890178] 
dist 245=[-.09622506761294160644,-.01390879507902014276] 
dist 246=[-.08874838955930118878,-.00839709640686038377] 

8 phat 2 dirichlet min maxes function [2, 1, 1, 2, 2, 0, 2, 0, 2] 
dist 0=[12.050797287388643641  ,12.050797287388643641  ] 
dist 1=[11.908421291946970259  ,12.151831696274734011  ] 
dist 2=[11.749082602169837931  ,12.242649631808744640  ] 
dist 3=[11.580216305185459944  ,12.344170923941944208  ] 
dist 4=[11.370772822984250732  ,12.438203656475946111  ] 
dist 5=[11.049170761094458240  ,12.499074988084064227  ] 
dist 6=[10.724718868166952132  ,12.547735278070750820  ] 
dist 7=[10.503878339410687235  ,12.592935514789592422  ] 
dist 8=[10.315076888436569571  ,12.632823373004087862  ] 
dist 9=[10.118742759170232968  ,12.660237950175046213  ] 
dist 10=[9.9308787020304112638 ,12.683945435895430219  ] 
dist 11=[9.7759454256687700739 ,12.709004643409548461  ] 
dist 12=[9.6143227333785408845 ,12.731952519214582115  ] 
dist 13=[9.3997032930029782480 ,12.755376738471152715  ] 
dist 14=[9.1862036550490230961 ,12.780447746145809881  ] 
dist 15=[9.0290563142784099340 ,12.797989128994078067  ] 
dist 16=[8.8819385112584838748 ,12.809941541263012253  ] 
dist 17=[8.7085431962783237141 ,12.818491467207301065  ] 
dist 18=[8.5299409239402007446 ,12.822427496420138216  ] 
dist 19=[8.3619959654663484342 ,12.823708644202105056  ] 
dist 20=[8.1684039681240975993 ,12.821752174608464895  ] 
dist 21=[7.8872293956058800020 ,12.817552847597552340  ] 
dist 22=[7.6056171069094226800 ,12.814277110565292554  ] 
dist 23=[7.4102722522989839183 ,12.803284733376368617  ] 
dist 24=[7.2392513284219730060 ,12.797631940741582436  ] 
dist 25=[7.0549129455754735829 ,12.762663380654930324  ] 
dist 26=[6.8744186529079546806 ,12.754321930850346655  ] 
dist 27=[6.7187675173795887537 ,12.730607419808069300  ] 
dist 28=[6.5502918681787460467 ,12.723736485376515414  ] 
dist 29=[6.3185016625952216565 ,12.670712342792565336  ] 
dist 30=[6.0840318917216192925 ,12.658026569638304667  ] 
dist 31=[5.9048362557285342978 ,12.638862937649659787  ] 
dist 32=[5.7304178130137140600 ,12.606720281259473213  ] 
dist 33=[5.5150495147569724608 ,10.643584856813292899  ] 
dist 34=[5.2877553986742307022 ,10.522049843774211675  ] 
dist 35=[5.0656351708725583486 ,10.231430652929717077  ] 
dist 36=[4.8029677298252983474 ,10.189396596996924592  ] 
dist 37=[4.4134965320280439659 ,9.7737113273556822229 ] 
dist 38=[4.0250672064039780900 ,9.6964231791556813128 ] 
dist 39=[3.7665656678556993294 ,9.6087098110321411922 ] 
dist 40=[3.5517290300191554221 ,9.5921718096741832830 ] 
dist 41=[3.3379427869678557272 ,8.9127849606448675159 ] 
dist 42=[3.1391683808587236247 ,8.8270246866050232267 ] 
dist 43=[2.9843728938112019826 ,8.6596802836170209899 ] 
dist 44=[2.8309170352455650846 ,8.6175050456617889527 ] 
dist 45=[2.6374990887237987459 ,8.4733811735122181826 ] 
dist 46=[2.4496895307844716829 ,8.4405709430212237783 ] 
dist 47=[2.3186644312941396619 ,8.4021883550289618316 ] 
dist 48=[2.2031108946290467274 ,8.3911587900831535473 ] 
dist 49=[2.0771812657262921419 ,6.9955465537807783592 ] 
dist 50=[1.9529951392140369912 ,6.8772327969035635734 ] 
dist 51=[1.8444134690828448293 ,6.6166095339137584987 ] 
dist 52=[1.7255800303499152092 ,6.5617316082927149165 ] 
dist 53=[1.5603867335708626832 ,6.2534673883663563814 ] 
dist 54=[1.3978022998103147110 ,6.1977208371276983434 ] 
dist 55=[1.2894027010259490216 ,6.0852888457181619842 ] 
dist 56=[1.1990734004892227846 ,6.0560110378136879127 ] 
dist 57=[1.1087654252898893186 ,5.7665419945450779163 ] 
dist 58=[1.0245002701377392235 ,5.7224100852594748058 ] 
dist 59=[.9583395868491837850 ,5.6341533905986065776 ] 
dist 60=[.8922237521840834302 ,5.6112333933256781666 ] 
dist 61=[.8081347442942286598 ,5.5282950445915803858 ] 
dist 62=[.5879758219584749167 ,5.5104997517797073316 ] 
dist 63=[.3538504443576804997 ,5.4788244422328100384 ] 
dist 64=[.1381078962710725500 ,5.4710488640006525385 ] 
dist 65=[-.0266734826633519915 ,2.2511962308503403843 ] 
dist 66=[-.1869983036275344490 ,2.0753842329387846437 ] 
dist 67=[-.3849204333977507633 ,1.6651274835154750529 ] 
dist 68=[-.5751081645696445315 ,1.6060848012626198509 ] 
dist 69=[-.7045001782977211702 ,1.0603007536601180378 ] 
dist 70=[-.8151694857969551485 ,.96312574636324472635] 
dist 71=[-.9304749190146231263 ,.84434599862149015883] 
dist 72=[-1.0410795392235772444 ,.82344804053587388838] 
dist 73=[-1.1329512317947029258 ,.12798426738862392392] 
dist 74=[-1.2294713704158392460 ,.05316405606712674898] 
dist 75=[-1.3586781257596442711 ,.04033791188485483532] 
dist 76=[-1.4839400707875259671 ,.02220854269671565597] 
dist 77=[-1.5646825241341786614 ,.01788017091777146611] 
dist 78=[-1.6289498796933932238 ,-.05857019868836517324] 
dist 79=[-1.6883077469262505756 ,-.06769921568273584066] 
dist 80=[-1.7405708738834874653 ,-.08786077602488676260] 
dist 81=[-1.9336005228408079088 ,-.09084774891528117258] 
dist 82=[-2.0854103316644405175 ,-.11343776668908868222] 
dist 83=[-2.2093327188269851922 ,-.11705577415569353843] 
dist 84=[-2.3288888532911434103 ,-.12264637274778906249] 
dist 85=[-2.4375531529242127681 ,-.12383230175558669276] 
dist 86=[-2.5179186704525973945 ,-.14328802916237837832] 
dist 87=[-2.5935484423177843502 ,-.14558225015660647601] 
dist 88=[-2.6832762494232544830 ,-.14764119049707543803] 
dist 89=[-2.7676235090820175988 ,-.14689959744679638968] 
dist 90=[-2.8217369481145437332 ,-.14493786971936040767] 
dist 91=[-2.8644737690873303169 ,-.1413451612232592787 ] 
dist 92=[-2.9033256064829303856 ,-.13586532277590446032] 
dist 93=[-2.9370738756815683830 ,-.12635758630865711021] 
dist 94=[-2.9594033713998323378 ,-.11592003533978031996] 
dist 95=[-2.9778335112430594986 ,-.10672149535670523659] 
dist 96=[-2.9959941145204966931 ,-.09662342450410573962] 
dist 97=[-3.0114510530161064357 ,-.08258691005406990417] 
dist 98=[-3.0190692122323492397 ,-.06699500844128161762] 
dist 99=[-3.0227865158452495249 ,-.05067767062469183912] 
dist 100=[-3.0232006052389825159 ,-.03060511009038991715] 
dist 101=[-3.0183253909776689189 ,0                     ] 
dist 102=[-3.0157989288370213018 ,-.25146529980848494142] 
dist 103=[-3.0129766274081994464 ,-.18974103772862716905] 
dist 104=[-3.0110363431817325558 ,-.12662116613022819016] 
dist 105=[-2.9493975179398388620 ,-.06805594381013386971] 
dist 106=[-2.9398548217054534641 ,-.00120911743243817867] 
dist 107=[-2.9215183927458940464 ,.09502649706214249405] 
dist 108=[-2.9162658829501419330 ,.19088052233796251124] 
dist 109=[-2.8952031058865563690 ,.25620287911128389245] 
dist 110=[-2.8899746446702391213 ,.31210829766006304844] 
dist 111=[-2.8778149003731884123 ,.37031089086753970186] 
dist 112=[-2.8735080080615221000 ,.4260202027828738041 ] 
dist 113=[-2.5711692934102671426 ,.47195798937207548918] 
dist 114=[-2.5430376218590230013 ,.51986032904817975643] 
dist 115=[-2.4803973129463919793 ,.58342797558621892226] 
dist 116=[-2.4659533419518447066 ,.64661991742628536588] 
dist 117=[-2.3875655460854155757 ,.69302150380488582229] 
dist 118=[-2.3726143732162898208 ,.73634174706528110774] 
dist 119=[-2.3419906221114569375 ,.78721437359839219648] 
dist 120=[-2.3335021448443417796 ,.83950470245378370188] 
dist 121=[-2.2388656038706401646 ,.88849637317635685717] 
dist 122=[-2.2246778373483946720 ,.94482558203726160712] 
dist 123=[-2.1912223338089104912 ,1.0264618467435448879 ] 
dist 124=[-2.1842477606905503533 ,1.1071328386537363646 ] 
dist 125=[-2.1355405707566624498 ,1.1596025808627092191 ] 
dist 126=[-2.1258132806947515089 ,1.2018470871616994177 ] 
dist 127=[-2.1094853032507648884 ,1.2416262155063634574 ] 
dist 128=[-2.1052126979411867658 ,1.2771323751090231155 ] 
dist 129=[-1.1680717727246062973 ,1.3022892107981275250 ] 
dist 130=[-1.1268866165301993364 ,1.3248733946977116098 ] 
dist 131=[-1.0312635600094742488 ,1.3500924638244992436 ] 
dist 132=[-1.0160222726541891625 ,1.3731651098277172144 ] 
dist 133=[-.8889166820178205823 ,1.3871653921215961464 ] 
dist 134=[-.86589681343288077139,1.3973080103161980320 ] 
dist 135=[-.83396141803373417384,1.4049518511016008450 ] 
dist 136=[-.82473134737765369891,1.4106823794358371954 ] 
dist 137=[-.65667064356960024797,1.4131732036863715970 ] 
dist 138=[-.63523975749024508528,1.4140935898375863038 ] 
dist 139=[-.58922996917176426305,1.4138627745749989182 ] 
dist 140=[-.57862436057427455399,1.3739761187700813808 ] 
dist 141=[-.52816160565570073241,1.3692212234533454406 ] 
dist 142=[-.5192016945634151679 ,1.3842282852989363678 ] 
dist 143=[-.49850074037322249058,1.4590956491431968537 ] 
dist 144=[-.49489471997523990265,1.5628441404433804408 ] 
dist 145=[-.2952478796841922672 ,1.6645835046476508891 ] 
dist 146=[-.27630608620670504414,1.7314167208515352342 ] 
dist 147=[-.23327498849301975134,1.7859481647934797829 ] 
dist 148=[-.22590464918122223533,1.8384946244494283080 ] 
dist 149=[-.17180207739247247787,1.8884766188270739752 ] 
dist 150=[-.16217455128144801157,1.9269048119681867311 ] 
dist 151=[-.14668605281330450096,1.9625312541657159146 ] 
dist 152=[-.14298698451227414298,2.0039993690094933156 ] 
dist 153=[-.08225278489374192073,2.0425342021522436750 ] 
dist 154=[-.07449873935798259327,2.0664308901107318288 ] 
dist 155=[-.05654233231699945376,2.0843463430087790734 ] 
dist 156=[-.05383056348549040972,2.0989631525666381276 ] 
dist 157=[-.03030844665001090329,2.1104980158678939279 ] 
dist 158=[-.02611865002839423762,2.1160893801760781695 ] 
dist 159=[-.0206053962981469255 ,2.1189389334593456417 ] 
dist 160=[-.01929611276692293070,2.1195097229253699648 ] 
dist 161=[.00242599360212592721,.64176162915523198219] 
dist 162=[-.05293930619374124114,.64174853712221204852] 
dist 163=[-.12398915974833579556,.64158446930102802149] 
dist 164=[-.1934835197091640172 ,.64124629032593505551] 
dist 165=[-.24262911183821946534,.64063628953196735078] 
dist 166=[-.28662078108260904456,.64018270122138714917] 
dist 167=[-.33550659186478079916,.63917632759888571854] 
dist 168=[-.38421419924986158568,.63870198185168076156] 
dist 169=[-.42749353893740538766,.63601797819949022533] 
dist 170=[-.47539461062507765705,.63521752914557294183] 
dist 171=[-.54258345149212513505,.6334446299071694227 ] 
dist 172=[-.60880308939563695649,.63276409580126987802] 
dist 173=[-.65282874234890152869,.62920597298024494525] 
dist 174=[-.68933201816986273258,.62832463784045543685] 
dist 175=[-.72547201222295484533,.62580996912053329629] 
dist 176=[-.75891737359117092755,.62507139079328086589] 
dist 177=[-.7846457680618634683 ,.61567815851429511526] 
dist 178=[-.80983088394282218582,.61397071306849226814] 
dist 179=[-.84110419137860049929,.61024080449287346173] 
dist 180=[-.8711981007873808416 ,.60904432273035038492] 
dist 181=[-.89166730892420109063,.60351694878450297652] 
dist 182=[-.90915002115882569539,.60228550649463912473] 
dist 183=[-.92730192847563331573,.59903934199984304704] 
dist 184=[-.94465231661417918641,.59815908351342613843] 
dist 185=[-.95893030016579202108,.58761393254667021139] 
dist 186=[-.97379696022687882559,.58587139825285862292] 
dist 187=[-.99350210693873540217,.58103276747965962853] 
dist 188=[-1.0123696172331242972 ,.58028620802024346782] 
dist 189=[-1.0238868252222047527 ,.57069817577305038188] 
dist 190=[-1.0323079140852893415 ,.56863987105808831198] 
dist 191=[-1.0387941693682763555 ,.5667540800902906662 ] 
dist 192=[-1.0438241002161856007 ,.56623200261018280232] 
dist 193=[-1.0464212491385454433 ,.54042305596161719644] 
dist 194=[-1.0477523318513651619 ,.53704462559354150199] 
dist 195=[-1.0478818186119512711 ,.52983874972011155053] 
dist 196=[-1.0385480069416727817 ,.52776135752197141544] 
dist 197=[-1.0367013340745976792 ,.51903201792472107659] 
dist 198=[-1.0343580753537707751 ,.51727344920644228422] 
dist 199=[-1.0332897041935522945 ,.51263995799678138757] 
dist 200=[-1.0308642771087547778 ,.51178280952466160847] 
dist 201=[-1.0296943416583716232 ,.50120304731726279772] 
dist 202=[-1.0284670987942193354 ,.49932674608797058578] 
dist 203=[-1.0276591136654762508 ,.49510111476188906968] 
dist 204=[-.91326803984827043885,.49377016061212488176] 
dist 205=[-.90305153671418827425,.48771162192343909139] 
dist 206=[-.88107596080553853298,.48637997748532587639] 
dist 207=[-.87518474587287354643,.48334551948312344701] 
dist 208=[-.8498259353901488327 ,.482340660792949158  ] 
dist 209=[-.8449561961819693712 ,.47107159981377160641] 
dist 210=[-.83310085428749260097,.46915030849466833037] 
dist 211=[-.83075433484773209896,.46530016183686177113] 
dist 212=[-.80578708697552417049,.46418563003194739154] 
dist 213=[-.8014139978090051447 ,.45957086063210354375] 
dist 214=[-.79279392672902467533,.45853075657662842756] 
dist 215=[-.78389560789164869974,.45581553815506039696] 
dist 216=[-.75695157148265976277,.45507680645316425112] 
dist 217=[-.67015768556851014889,.44979381647143895439] 
dist 218=[-.65926981442356239751,.44864188169175988408] 
dist 219=[-.61463432617808859301,.44626344771853125663] 
dist 220=[-.31057639520128554691,.44550330362374798619] 
dist 221=[-.30272099632207399428,.44200118048095752397] 
dist 222=[-.28426377245368544514,.44122170125656446791] 
dist 223=[-.28137138308804452814,.43874260381986690111] 
dist 224=[-.2560461646830561964 ,.4383685080257990527 ] 
dist 225=[-.25139457366453242011,.43201248259801931919] 
dist 226=[-.24528099221349897365,.43083615766495052624] 
dist 227=[-.24353961472919691365,.42785229131955995365] 
dist 228=[-.20700833426527695651,.42705092917134777117] 
dist 229=[-.20233152258166374362,.42162755062019122993] 
dist 230=[-.19258193690264960274,.42040009283783167634] 
dist 231=[-.18999479556367051422,.41831645257205020342] 
dist 232=[-.18016659637457356816,.41771033678979854231] 
dist 233=[-.17826739906656938421,.40387837052726224102] 
dist 234=[-.1741570340452299606 ,.40184076429759317461] 
dist 235=[-.17309786637272093738,.3974560659965752519 ] 
dist 236=[-.11799339962648383194,.39614715391490309189] 
dist 237=[-.11301218959333171732,.39046229375865596745] 
dist 238=[-.10137332565251863238,.3892738854938342875 ] 
dist 239=[-.09960535637069675856,.38615986008982635265] 
dist 240=[-.08395942732902364163,.38547068218328194124] 
dist 241=[-.08113334701347484955,.34156723942606602924] 
dist 242=[-.07747453601886156985,.33723712930274775842] 
dist 243=[-.07657008659043419006,.32718121075128660196] 
dist 244=[-.05521847313431431780,.3252289375254726816 ] 
dist 245=[-.05255216600737074865,.31139042341937068207] 
dist 246=[-.04699520608805311577,.30873622459069895654] 
dist 247=[-.04559021072191477299,.3043270169238949945 ] 
dist 248=[-.04013387300429279671,.2994859639444358548 ] 
dist 249=[-.03910326501634486171,.26136907717333735599] 
dist 250=[-.03701235935964259618,.25647241383935731076] 

8 phat 2 dirichlet min maxes function [2, 1, 2, 1, 1, 1, 2, 0, 1] 
dist 0=[10.500409109499356621  ,10.500409109499356621  ] 
dist 1=[10.493902632705188063  ,10.503057877567201796  ] 
dist 2=[10.482442678172851964  ,10.504417205542297882  ] 
dist 3=[10.459981009755112328  ,10.505767767895080794  ] 
dist 4=[10.435289373211198528  ,10.506661981683591008  ] 
dist 5=[10.414910380017115708  ,10.506195841304593101  ] 
dist 6=[10.393621798298916503  ,10.504641429683308567  ] 
dist 7=[10.365292808423227046  ,10.503269487152686055  ] 
dist 8=[10.334323998463615823  ,10.451847429999551884  ] 
dist 9=[10.302477359925115494  ,10.443551315649046018  ] 
dist 10=[10.263626966345268089  ,10.427975650675821929  ] 
dist 11=[10.204645801549439889  ,10.423455900878742376  ] 
dist 12=[10.142493236677096633  ,10.405213985740983323  ] 
dist 13=[10.090958533735673524  ,10.400455626242041993  ] 
dist 14=[9.9885353168935949021 ,10.389313159142051332  ] 
dist 15=[9.8718346807093860867 ,10.385237285632715086  ] 
dist 16=[9.7860002198419600559 ,10.141878801253022430  ] 
dist 17=[9.7056646894887503430 ,10.134373388602171772  ] 
dist 18=[9.6109574296782334649 ,10.113201123276350724  ] 
dist 19=[9.5133430757240945895 ,10.109823316286174419  ] 
dist 20=[9.3997090861136683225 ,9.9064645929310610575 ] 
dist 21=[9.2877517071792300439 ,9.8918803409483257008 ] 
dist 22=[9.1607290368935721644 ,9.8605590135915036083 ] 
dist 23=[9.0006828477166943298 ,9.8514609119183162787 ] 
dist 24=[8.8722103627096928806 ,9.7620113735016473763 ] 
dist 25=[8.7412414513694246262 ,9.7480313815112682805 ] 
dist 26=[8.5712102676028976187 ,9.7151898838155097775 ] 
dist 27=[8.3874122870124274338 ,9.7077703746321130999 ] 
dist 28=[8.2013810202272986473 ,9.6594667940077982024 ] 
dist 29=[7.9765699466614286649 ,9.6495687155874887264 ] 
dist 30=[7.6376665142743106143 ,9.6320447690941766376 ] 
dist 31=[7.2976203688227490392 ,9.6275078502634586306 ] 
dist 32=[7.0682391255706762309 ,9.2694370469182834750 ] 
dist 33=[6.8742129622198798884 ,9.2566873122685366237 ] 
dist 34=[6.6755754060423955503 ,9.2380164859070354045 ] 
dist 35=[6.4872935554703600668 ,9.2323779155365699344 ] 
dist 36=[6.3143567148546308129 ,8.2592674181927479278 ] 
dist 37=[6.0475153814349692601 ,8.1956127023864281213 ] 
dist 38=[5.8231230070315567904 ,8.0552220800503925387 ] 
dist 39=[5.5955306678273381154 ,8.0266826263097829152 ] 
dist 40=[5.3811498275175199305 ,7.8615169005289132735 ] 
dist 41=[5.2095992281406448592 ,7.8320667498242730711 ] 
dist 42=[5.0352130645827065393 ,7.7737501555386842080 ] 
dist 43=[4.8094925545563561315 ,7.7590639675963964781 ] 
dist 44=[4.5874706032869730707 ,7.6121213482749368240 ] 
dist 45=[4.4278780000748356867 ,7.5899534545472964861 ] 
dist 46=[4.2822132633225603743 ,7.5480285663270229709 ] 
dist 47=[4.1158981639311615507 ,7.5379594019888472132 ] 
dist 48=[3.9474503574243910460 ,7.5068830275841205510 ] 
dist 49=[3.7932569742094522520 ,7.4996973232811398374 ] 
dist 50=[3.6187485105616814377 ,7.4733963605324806173 ] 
dist 51=[3.3690515291797838201 ,7.4321344447629990206 ] 
dist 52=[3.1203878327642794563 ,5.9645866674059505954 ] 
dist 53=[2.9500126622775986946 ,5.8810050198109893940 ] 
dist 54=[2.8030531928390760576 ,5.7138010125921587478 ] 
dist 55=[2.6480416098405117796 ,5.6720900733744809328 ] 
dist 56=[2.4982663984127747026 ,5.5297072955719737354 ] 
dist 57=[2.3722506741438528178 ,5.5000287008212984891 ] 
dist 58=[2.2385196583361164114 ,5.4170350709190867665 ] 
dist 59=[2.0578887500149965992 ,5.3104656832973965924 ] 
dist 60=[1.8766777114436359271 ,4.4991619415600015791 ] 
dist 61=[1.7406272149139750593 ,4.4122485444451426701 ] 
dist 62=[1.5640767833978230887 ,4.1705935410336410448 ] 
dist 63=[1.2321332224930694736 ,3.8633750924591190395 ] 
dist 64=[1.0101129584221247962 ,2.2819134030626269011 ] 
dist 65=[.82442108327954392943,2.1661367313295491760 ] 
dist 66=[.63776941986250456984,2.1450492288066552656 ] 
dist 67=[.46306771649605091551,2.1399658580705768410 ] 
dist 68=[.32516850336126040481,1.8068351709169340023 ] 
dist 69=[.18675489637722828819,1.7543090454443598706 ] 
dist 70=[.00999577075068185781,1.7431379361501889336 ] 
dist 71=[-.16268196160169576967,1.4327407518406413574 ] 
dist 72=[-.28477255409046669364,1.3944998854562484446 ] 
dist 73=[-.39411736372042017951,1.3160286849017302674 ] 
dist 74=[-.51581978261016065249,1.2959042772235544406 ] 
dist 75=[-.63729188096128779321,1.2233230564087641945 ] 
dist 76=[-.74571585125940000858,1.2091056165912466782 ] 
dist 77=[-.86619685628654848585,1.1837847341394996443 ] 
dist 78=[-1.0358906009147529470 ,1.1782397405959681705 ] 
dist 79=[-1.2037142926783672728 ,.77815511944212531578] 
dist 80=[-1.3167164226712966892 ,.74367388352446996781] 
dist 81=[-1.4120580401965137927 ,.66485336881947441922] 
dist 82=[-1.5092501776740397186 ,.652274578758417567  ] 
dist 83=[-1.6010958497448918510 ,.55208902502605877581] 
dist 84=[-1.6750551404929026366 ,.53436934125742195702] 
dist 85=[-1.7506532185995144285 ,.50856834453591477876] 
dist 86=[-1.8490541333890339846 ,.50172463043170702341] 
dist 87=[-1.9460923570920143063 ,.38538266441998876037] 
dist 88=[-2.0162409643533396976 ,.37085177352758951895] 
dist 89=[-2.0806691770636936778 ,.33849320867644323914] 
dist 90=[-2.1548296025972131099 ,.33279503814040829542] 
dist 91=[-2.2302807147024232419 ,.2944694594629258418 ] 
dist 92=[-2.2998719834731134101 ,.28783411777326952755] 
dist 93=[-2.3790572542429637000 ,.27610420473173730073] 
dist 94=[-2.4928815179588944044 ,.27363066576689434001] 
dist 95=[-2.6053026445418613769 ,-.31523346668768131645] 
dist 96=[-2.6788760045592277180 ,-.21767538819316827954] 
dist 97=[-2.7386491397006683041 ,-.15045838828408867932] 
dist 98=[-2.7958741346306029592 ,-.09220604252671201112] 
dist 99=[-2.8476149648351950006 ,-.03047960603992907669] 
dist 100=[-2.8854530352801036312 ,.02920562556717617870] 
dist 101=[-2.9206468074667693980 ,.07930165473382865445] 
dist 102=[-2.9618104594898789926 ,.13228122632984121517] 
dist 103=[-3.0002068236473723735 ,.20349910323729910816] 
dist 104=[-3.0243320175877219334 ,.2746297339797292088 ] 
dist 105=[-3.0428025126184832760 ,.32726310136810304858] 
dist 106=[-3.0585817876751695065 ,.3767650858376695134 ] 
dist 107=[-3.0715577047044683142 ,.43538002940108796143] 
dist 108=[-3.0788149017526710327 ,.49584382301255650939] 
dist 109=[-3.0833173952708720950 ,.55274093984584319484] 
dist 110=[-3.0852810062625929615 ,.61831464968614853223] 
dist 111=[-3.0857781045038164918 ,.71347416277796810623] 
dist 112=[-2.7426847206697857544 ,.80858302541623244416] 
dist 113=[-2.7225629970509453125 ,.87395569632735326032] 
dist 114=[-2.6841251603906736940 ,.93050763475116112005] 
dist 115=[-2.6744334224333334298 ,.99034889592221587961] 
dist 116=[-2.6418201913361734367 ,1.0482283514987696418 ] 
dist 117=[-2.6338200290205952878 ,1.0969379605057444455 ] 
dist 118=[-2.6258826171639913626 ,1.1486073433829461473 ] 
dist 119=[-2.6220798072951735242 ,1.2183252116527551221 ] 
dist 120=[-2.2334313302613135407 ,1.2881717681802487428 ] 
dist 121=[-2.1969346194773075167 ,1.3403574967122102473 ] 
dist 122=[-2.1544742364208238980 ,1.3899774762942411252 ] 
dist 123=[-2.1394306935130333659 ,1.4495664828213691662 ] 
dist 124=[-1.8565698971755038607 ,1.5115430861702616433 ] 
dist 125=[-1.8088882731010489316 ,1.5707132637473902361 ] 
dist 126=[-1.5675877368205572604 ,1.6396110320996356723 ] 
dist 127=[-1.1302339535136835909 ,1.7404919739759168499 ] 
dist 128=[-.81069108903204966215,1.8402216541915328197 ] 
dist 129=[-.807537663387648015  ,1.9045162282445353916 ] 
dist 130=[-.80030713136784339873,1.9556386859411104843 ] 
dist 131=[-.79840169180245679526,2.0026914707550651025 ] 
dist 132=[-.31660226335475210997,2.0439491128859624080 ] 
dist 133=[-.30068279132343920295,2.0718966883445754823 ] 
dist 134=[-.26406691194171864082,2.0956593898812822115 ] 
dist 135=[-.25816134374258349104,2.1201830082852649329 ] 
dist 136=[-.2107433969231919369 ,2.1421262301488222815 ] 
dist 137=[-.20225980493336116491,2.1555694162085887492 ] 
dist 138=[-.18997879330612191094,2.1654666389113512637 ] 
dist 139=[-.18664857588472943333,2.1732267420338426342 ] 
dist 140=[-.1284734351893557167 ,2.1790925328997214384 ] 
dist 141=[-.12111896227609469254,2.1814130031173951785 ] 
dist 142=[-.10489185720241601613,2.1817937650872508466 ] 
dist 143=[-.10171886251593577056,2.1812964498835761429 ] 
dist 144=[-.08275562316060622350,2.0497514659173523253 ] 
dist 145=[-.07942257715666557229,2.0371079786601065200 ] 
dist 146=[-.07296612003979517543,2.0107752025981489485 ] 
dist 147=[-.07140330897295540256,2.0032884715948345464 ] 
dist 148=[-.02013321665700736948,1.9724674849515252887 ] 
dist 149=[-.01490120721235688686,1.9661521293424330028 ] 
dist 150=[-.00386942728987654487,1.9493557541914852862 ] 
dist 151=[-.00131684194066321074,1.9461874946977211217 ] 
dist 152=[.00987158677209336299,1.9142654435863071006 ] 
dist 153=[.01186506400229261931,1.9079137345512298665 ] 
dist 154=[.01610288998718985932,1.8954621489678696538 ] 
dist 155=[.01701337156060325815,1.8918158295751581804 ] 
dist 156=[.02117888267495127798,1.8766880892432626383 ] 
dist 157=[.02173168137034055893,1.8730826864166901956 ] 
dist 158=[.02131565417061247191,1.8638793864772339791 ] 
dist 159=[.01946889698488974836,1.8608709289625820331 ] 
dist 160=[.01682946376835431279,.88367638912196240575] 
dist 161=[.01324374550431037285,.8295024036029442554 ] 
dist 162=[.00825388935014897221,.79604839235594200571] 
dist 163=[0                     ,.79631324703136603354] 
dist 164=[.22148595703760559087,.5104647419699431736 ] 
dist 165=[.14342746737286998629,.47927618524224348622] 
dist 166=[.06471862579287435848,.44209214835287426754] 
dist 167=[-.03621116519996406222,.43570025462901419645] 
dist 168=[-.13489981343642133926,.41804916307017120353] 
dist 169=[-.2046472507035617968 ,.41651346019053530868] 
dist 170=[-.26703673721912253276,.41480148948971360221] 
dist 171=[-.33630350839738869394,.4141278180091233319 ] 
dist 172=[-.40528340873345218256,.41392934277068785248] 
dist 173=[-.4665261149342451642 ,.41455350713738644654] 
dist 174=[-.53426967344529288613,.41590446847183145247] 
dist 175=[-.62924516031334018043,.41861225838160601556] 
dist 176=[-.72283760588787552187,.42200905904642413681] 
dist 177=[-.78505093889946457386,.42611514660586190668] 
dist 178=[-.83662399156831463353,.43155688664734996376] 
dist 179=[-.88766894488330565056,.440294475379074517  ] 
dist 180=[-.93490006130866095454,.44937953767973485781] 
dist 181=[-.97122281935869033244,.4562107204416243072 ] 
dist 182=[-1.0067696054682912604 ,.46274641419629093328] 
dist 183=[-1.0508983322828575614 ,.47064999038635406648] 
dist 184=[-1.0933595852721739970 ,.47889570398030631736] 
dist 185=[-1.1222388151611210996 ,.4867995230793203447 ] 
dist 186=[-1.1469032878544423661 ,.49602312249931809139] 
dist 187=[-1.1725110158449762906 ,.50954621693552927913] 
dist 188=[-1.1969885444347772980 ,.52358051262383129427] 
dist 189=[-1.2171341073888067972 ,.53484825287269095801] 
dist 190=[-1.2381132658754271422 ,.54632649647590001161] 
dist 191=[-1.2659253225112930078 ,.56120255756664932098] 
dist 192=[-1.2926436513844726822 ,.57725350500967617412] 
dist 193=[-1.3092492943430863727 ,.593429746140101652  ] 
dist 194=[-1.3217471343951788632 ,.61291240553113923943] 
dist 195=[-1.3320382837989756815 ,.64218464022146864499] 
dist 196=[-1.3402132864170347876 ,.67149385134880841675] 
dist 197=[-1.3442487956016917179 ,.69112437179628241203] 
dist 198=[-1.3463627829494345223 ,.70755917987648604492] 
dist 199=[-1.3468526961246423879 ,.72408979345672830026] 
dist 200=[-1.3437837686572334100 ,.7395553339154111889 ] 
dist 201=[-1.3425561859934797644 ,.75173126432406082518] 
dist 202=[-1.3409212601146807769 ,.76391475996146933376] 
dist 203=[-1.3400117160693178876 ,.77941054462332457618] 
dist 204=[-1.3364795759957960886 ,.79450050211285421577] 
dist 205=[-1.3352166118065246930 ,.80506122418715952393] 
dist 206=[-1.3317105548399431310 ,.81439957444787022558] 
dist 207=[-1.3301702858489166299 ,.82460166328008979432] 
dist 208=[-1.2152854386377286973 ,.83466470091504659008] 
dist 209=[-1.2043532496021930923 ,.84344701950570977843] 
dist 210=[-1.1803893310718113143 ,.85303542168591304335] 
dist 211=[-1.1604183801105318298 ,.866321693302848726  ] 
dist 212=[-1.0417684778737404637 ,.87934426964378810817] 
dist 213=[-1.0351045456591170690 ,.8878782328976418905 ] 
dist 214=[-1.0199195191627654343 ,.89481673718218050649] 
dist 215=[-1.0161549632743071660 ,.90145960235567352749] 
dist 216=[-.99580817621407140678,.90745897414588573214] 
dist 217=[-.99113436556900813605,.91182434732856807132] 
dist 218=[-.97522822253626416146,.91585891040816932287] 
dist 219=[-.94940816717144194208,.9205354389769358155 ] 
dist 220=[-.81850222028306504611,.92486914097283053481] 
dist 221=[-.81565010850147423249,.92753283459701091826] 
dist 222=[-.80947117508043580432,.92950104223314301612] 
dist 223=[-.80755965707125964284,.93105371083062291677] 
dist 224=[-.56156704512857767853,.93223229741590955232] 
dist 225=[-.54472706277018693052,.93270463127958798385] 
dist 226=[-.50542619056892727911,.93275247591376489682] 
dist 227=[-.49916061547333654053,.93238793377199183507] 
dist 228=[-.44613573647004763446,.93139426595668070208] 
dist 229=[-.4364548835072101102 ,.93078304509648051037] 
dist 230=[-.42323326264555793552,.92887271936793357524] 
dist 231=[-.41930433661323603761,.92792359542185964275] 
dist 232=[-.34626923847628544345,.92229006392362896502] 
dist 233=[-.33689803466149140862,.92076408224654170207] 
dist 234=[-.31698254492281739437,.91780776666172327975] 
dist 235=[-.3120758294752664792 ,.9167965219943586774 ] 
dist 236=[-.29074400554380839367,.89569837428061751679] 
dist 237=[-.28687964735195721489,.89241240312809262276] 
dist 238=[-.27764223428039667374,.88519923997261137952] 
dist 239=[-.27618691724372309953,.8829506179566603319 ] 
dist 240=[-.17807710797803025419,.87280434491830835694] 
dist 241=[-.1689616198750390941 ,.87059601413907429904] 
dist 242=[-.14775902797860072326,.86504299504639739562] 
dist 243=[-.14448844275822028311,.86346190376559099965] 
dist 244=[-.11630009895245002355,.7822964725633312973 ] 
dist 245=[-.11122585804268793482,.77413109662094317345] 
dist 246=[-.10445494457372647387,.75511516396314074836] 
dist 247=[-.10265806332667709279,.75135335972263665872] 
dist 248=[-.06542842910088969458,.72487820864787437391] 
dist 249=[-.06075764094388985661,.71975186371367559155] 
dist 250=[-.05088887136341675025,.71118065904407022358] 
dist 251=[-.04853737192710055502,.70680802747645264209] 
dist 252=[-.03836113935377583488,.62524749458276520151] 
dist 253=[-.03652815219497923486,.61542419755101801695] 
dist 254=[-.03248864512279772456,.58790524013334372562] 

8 phat 2 dirichlet min maxes function [0, 2, 1, 1, 2, 1, 2] 
dist 0=[13.057743976776422804  ,13.057743976776422804  ] 
dist 1=[12.996845888853422517  ,13.107545333337042582  ] 
dist 2=[12.922201561374923963  ,13.137819480779037224  ] 
dist 3=[12.822656616133508464  ,13.159787758304490174  ] 
dist 4=[12.662184626407618130  ,13.176387198926497596  ] 
dist 5=[12.495072337708151302  ,13.191237848956549955  ] 
dist 6=[12.368971868563480322  ,13.206215180370838128  ] 
dist 7=[12.247879474382194854  ,13.224273085649559427  ] 
dist 8=[12.100787903096815611  ,13.251437088388805425  ] 
dist 9=[11.946951569398461769  ,13.277308283413824704  ] 
dist 10=[11.798884478781051127  ,13.290193249989591950  ] 
dist 11=[11.625596788234664441  ,13.296110683397408594  ] 
dist 12=[11.370902677883420194  ,13.296667954002397177  ] 
dist 13=[11.106217502884696081  ,13.288947786205695375  ] 
dist 14=[10.892974455524182970  ,13.284745975725258054  ] 
dist 15=[10.675023313699634002  ,13.274523797356689317  ] 
dist 16=[10.391507796471819214  ,13.257657378578435317  ] 
dist 17=[10.084986112326977555  ,12.984618719494326135  ] 
dist 18=[9.7750324220186177876 ,12.953001654966301425  ] 
dist 19=[9.4008788974206346235 ,12.883553089767562038  ] 
dist 20=[8.8376220784497522263 ,12.862917484911056740  ] 
dist 21=[8.2725508967195759447 ,12.773685691039354089  ] 
dist 22=[7.8911406010586321966 ,12.755132403617312900  ] 
dist 23=[7.5684904509899592427 ,12.711222857944248335  ] 
dist 24=[7.2383976877664601502 ,12.698679303569180241  ] 
dist 25=[6.9258849938224145506 ,12.568358262562056525  ] 
dist 26=[6.6735350343501785868 ,12.547194895136865443  ] 
dist 27=[6.4150647275728359219 ,12.488425208448974148  ] 
dist 28=[6.0780726639585456926 ,12.417368757987333874  ] 
dist 29=[5.7457133485201601232 ,12.010626170988679759  ] 
dist 30=[5.5057671363762080412 ,11.966077539821205329  ] 
dist 31=[5.2858050341881173321 ,11.822762241609683323  ] 
dist 32=[5.0333594871732252608 ,11.602044505529244518  ] 
dist 33=[4.7770599177764279612 ,10.174560790476974762  ] 
dist 34=[4.5416813299263343996 ,10.042721247287588232  ] 
dist 35=[4.2747545864201945541 ,9.7332973507981211501 ] 
dist 36=[3.8922838879800749894 ,9.6863444634682248036 ] 
dist 37=[3.5114297447380908856 ,9.2644455979368721630 ] 
dist 38=[3.2509654108999656858 ,9.1875519861700654091 ] 
dist 39=[3.0268798477325434111 ,9.0899103092405690348 ] 
dist 40=[2.7915078854272685604 ,9.0658147543913080442 ] 
dist 41=[2.5647444842108280636 ,8.4620634255978558189 ] 
dist 42=[2.3750822540490963342 ,8.3859690538877961185 ] 
dist 43=[2.1748123925941343986 ,8.2954096787928010889 ] 
dist 44=[1.9056186981830117172 ,8.2837835015105588793 ] 
dist 45=[1.6361694294331830618 ,8.0392595722537396208 ] 
dist 46=[1.4348733609728089205 ,8.0095256539465193140 ] 
dist 47=[1.2433986584354719225 ,7.9522145232323291621 ] 
dist 48=[1.0132229219347313863 ,7.9378392230003282001 ] 
dist 49=[.77357433695644266717,7.0276875183574675046 ] 
dist 50=[.54420757015687552375,6.9476898433643993324 ] 
dist 51=[.27659754489437580294,6.7634590925259524747 ] 
dist 52=[-.1160141302910180174 ,6.7337930050689570201 ] 
dist 53=[-.50579678715632350006,6.4944013124189315628 ] 
dist 54=[-.76209415688950676621,6.4514995410947869646 ] 
dist 55=[-.97167829799435928886,6.3897627055921297631 ] 
dist 56=[-1.1746282174470607580 ,6.3728716115955931536 ] 
dist 57=[-1.3597035584740491738 ,6.0759123091699129448 ] 
dist 58=[-1.4977988699062645764 ,6.0382683245394011802 ] 
dist 59=[-1.6290310877268512969 ,5.9557276134938744203 ] 
dist 60=[-1.7866622937343504999 ,5.9389103892330779135 ] 
dist 61=[-1.9359750271542359902 ,5.8437124246764029126 ] 
dist 62=[-2.0339392067216708970 ,5.8269356487699471046 ] 
dist 63=[-2.1138403172096364452 ,5.7930452278539466607 ] 
dist 64=[-2.1909100641083371090 ,5.7704880711505816771 ] 
dist 65=[-2.2610451117160109826 ,2.3902866033710678020 ] 
dist 66=[-2.3132153621022806997 ,2.2417827012031484333 ] 
dist 67=[-2.4380371289757738810 ,1.8963961233098920024 ] 
dist 68=[-2.6112364956294711612 ,1.8466420759467568478 ] 
dist 69=[-2.7800397649700843685 ,1.3908203967619803840 ] 
dist 70=[-2.8987019062523824227 ,1.3099164259048664904 ] 
dist 71=[-3.0042602441529589111 ,1.2103825754425683200 ] 
dist 72=[-3.1206618366823789043 ,1.1927545410996426305 ] 
dist 73=[-3.2362290480692416907 ,.73506743622527248492] 
dist 74=[-3.3384553228402526160 ,.72389307752391711134] 
dist 75=[-3.4513095577560556730 ,.70863686077158278576] 
dist 76=[-3.6093914222738454491 ,.70567730920180267152] 
dist 77=[-3.7638658446612525720 ,.2062469269158989331 ] 
dist 78=[-3.8622941662562620079 ,.1804723984289686160 ] 
dist 79=[-3.9392914729925868483 ,.1440047868408169310 ] 
dist 80=[-4.0080505673685095978 ,.1347109882220553815 ] 
dist 81=[-4.0669179667708647463 ,-.5885567848821012474 ] 
dist 82=[-4.1043544897621368528 ,-.6483562419520220530 ] 
dist 83=[-4.1335769175943133905 ,-.7842551187129531027 ] 
dist 84=[-4.1595971641752284329 ,-.8051427270475828561 ] 
dist 85=[-4.1816056088117782905 ,-.9735302916424579192 ] 
dist 86=[-4.1947819265002601507 ,-1.0026139881496325751 ] 
dist 87=[-4.2041424210999075368 ,-.93363852931372330039] 
dist 88=[-4.2108816355495877952 ,-.8110176462938747312 ] 
dist 89=[-4.2155045624783098303 ,-.69490730077410552181] 
dist 90=[-4.2163971891676680717 ,-.60126806455574791297] 
dist 91=[-4.2147431913537700600 ,-.50552791576554565187] 
dist 92=[-4.2131959460003931833 ,-.38101501159530137515] 
dist 93=[-3.8872162597670490746 ,-.25849393812063670531] 
dist 94=[-3.8570334646956496531 ,-.17071649451815133402] 
dist 95=[-3.7928705981946150764 ,-.09099237384528318583] 
dist 96=[-3.7747265247602163378 ,-.00066967888096291573] 
dist 97=[-3.6999765213810556643 ,.09030331411671945737] 
dist 98=[-3.6853135756938758053 ,.17262928980186309611] 
dist 99=[-3.6464154208078046422 ,.26496279519433844914] 
dist 100=[-3.6403350808150219885 ,.39595297386963637038] 
dist 101=[-3.5632656995475370163 ,.52564286714394832346] 
dist 102=[-3.5490618784765908760 ,.61277798642598539044] 
dist 103=[-3.5207970100145215086 ,.68601849346672763932] 
dist 104=[-3.5127174709919017249 ,.76015111842010633079] 
dist 105=[-3.4798739241952675155 ,.82980136256564118183] 
dist 106=[-3.4723652176298645618 ,.88511985515382197037] 
dist 107=[-3.4537709034614476338 ,.94092335189166682946] 
dist 108=[-3.4478683651919720991 ,1.0125149105286541797 ] 
dist 109=[-2.3617332981827216197 ,1.0825389437350668761 ] 
dist 110=[-2.3514337435292947638 ,1.1320755164410773673 ] 
dist 111=[-2.3281379496291558644 ,1.1764403925876183394 ] 
dist 112=[-2.3223349241797016247 ,1.2257858518884738062 ] 
dist 113=[-2.2910488763383294358 ,1.2749904209123461506 ] 
dist 114=[-2.2847488030659793568 ,1.3187936461555349099 ] 
dist 115=[-2.2719676656572021181 ,1.3673554441443485352 ] 
dist 116=[-2.2682883976219428428 ,1.4355918024087555016 ] 
dist 117=[-2.2200768856805086193 ,1.5023861062573178812 ] 
dist 118=[-2.2129563883660156120 ,1.5451818340983281874 ] 
dist 119=[-2.1948482252416259567 ,1.5789035608635553781 ] 
dist 120=[-2.1757096877999087766 ,1.6094107913983289554 ] 
dist 121=[-2.0785754499869478497 ,1.6357863570684538983 ] 
dist 122=[-2.0680938154584478950 ,1.6529858902992605650 ] 
dist 123=[-2.0333157316374362634 ,1.6668867557357592660 ] 
dist 124=[-1.9778574804512365930 ,1.6800720975305198515 ] 
dist 125=[-1.6128730382964388565 ,1.6914750054471168286 ] 
dist 126=[-1.5776493750190921779 ,1.6982477783680786166 ] 
dist 127=[-1.4880609199452602704 ,1.7029801314501642678 ] 
dist 128=[-1.3930490608110159808 ,1.7062218367799599200 ] 
dist 129=[1.0120863226198570787 ,1.7713794663981462815 ] 
dist 130=[1.0036896164716279195 ,1.8342587408721540453 ] 
dist 131=[.99051862860013651572,1.8949900658794874820 ] 
dist 132=[.96728260805857449153,1.9692663340137066836 ] 
dist 133=[.94237308254315599025,2.0401895351273048388 ] 
dist 134=[.92251009622051935545,2.0875131413583002785 ] 
dist 135=[.90241098170414427679,2.1269482369319816584 ] 
dist 136=[.87655537931747509204,2.1663273848087588491 ] 
dist 137=[.84876486934691578725,2.2030023142847075532 ] 
dist 138=[.82092809842893581343,2.2316247515925776062 ] 
dist 139=[.78753260089728995477,2.2600441154166307856 ] 
dist 140=[.73751466174433208772,2.2959093794533914063 ] 
dist 141=[.68517724937080380205,2.3297639992999557693 ] 
dist 142=[.64250675933940867269,2.3501433060083314810 ] 
dist 143=[.59845107479376151481,2.3647063488841702587 ] 
dist 144=[.54057409134811574884,2.3753008289867799650 ] 
dist 145=[.47774600406091184488,2.3831315913825726883 ] 
dist 146=[.41389254700796463823,2.3866416361580311431 ] 
dist 147=[.33660417892557231792,2.3877963730593208855 ] 
dist 148=[.2200551275540006527 ,2.3875989573400153598 ] 
dist 149=[.10322608399877384638,2.3635953495428879762 ] 
dist 150=[.02481797936293214367,2.3590343298951730996 ] 
dist 151=[-.04099403002095306838,2.3509954557240078600 ] 
dist 152=[-.10745667672007785354,2.3485187684794790804 ] 
dist 153=[-.16980239556999603721,2.3381566906352334171 ] 
dist 154=[-.21915264317982867349,2.3350809620331324732 ] 
dist 155=[-.26877794268955086965,2.3277309766228636044 ] 
dist 156=[-.33222369427376411972,2.3248643255098057658 ] 
dist 157=[-.39416102902613294207,2.0964431737315784648 ] 
dist 158=[-.43775488154008892403,2.0750889278465223635 ] 
dist 159=[-.47655953032612923105,2.0280741087026928166 ] 
dist 160=[-.51934687107787541525,2.0163692317312540124 ] 
dist 161=[-.56178130779400826725,1.9586256676309555245 ] 
dist 162=[-.59917497715667345836,1.9474692740374248846 ] 
dist 163=[-.6403023207746884081 ,1.9230291755685277613 ] 
dist 164=[-.70463889729028702041,1.9158037972379570486 ] 
dist 165=[-.77298521435499801576,1.8486297915933048336 ] 
dist 166=[-.81767231841138447329,1.8379077504169562407 ] 
dist 167=[-.85389064730663110949,1.8133567052275536461 ] 
dist 168=[-.88837333479946876245,1.8071939757877762573 ] 
dist 169=[-.91938582947708088726,1.7729570729006060008 ] 
dist 170=[-.941728040463543648  ,1.7659507852339496991 ] 
dist 171=[-.96215170903565244178,1.7520657714503759844 ] 
dist 172=[-.98549249359456114435,1.7480947462202535725 ] 
dist 173=[-1.0070925410880850602 ,.97891517826293785982] 
dist 174=[-1.0205556701396446809 ,.94902658032507348306] 
dist 175=[-1.0307271709939465823 ,.87931967540941457708] 
dist 176=[-1.0391654567844797483 ,.86822866183289241306] 
dist 177=[-1.0459118491447993307 ,.77438063242562347804] 
dist 178=[-1.0493182712534322753 ,.75727123315046683751] 
dist 179=[-1.0510726360744456106 ,.73390885300293621828] 
dist 180=[-1.0513321374362264860 ,.72697756038075546984] 
dist 181=[-.7618120344187458945 ,.59845484495873750521] 
dist 182=[-.82667782402786237318,.58198427018451080387] 
dist 183=[-.88417396954227505619,.54697394566984158591] 
dist 184=[-.94720973024375852714,.53839421579756996062] 
dist 185=[-1.0095252441145377336 ,.5009125293554836183 ] 
dist 186=[-1.0641413759017316078 ,.49414046838266186085] 
dist 187=[-1.1239712780311170252 ,.47797865148740731944] 
dist 188=[-1.2141079852804092246 ,.47544323136524306135] 
dist 189=[-1.3077180643830289439 ,.30504434932919467248] 
dist 190=[-1.3689627379183787288 ,.28920856361531717586] 
dist 191=[-1.4186518624509602082 ,.25243334011087622194] 
dist 192=[-1.4660540025306414780 ,.24672959740798370306] 
dist 193=[-1.5087563176423343060 ,.19802351735060925452] 
dist 194=[-1.5396519055154218338 ,.18926520316929542318] 
dist 195=[-1.5680323766831921694 ,.17745491390586725635] 
dist 196=[-1.6006772232987916822 ,.17424318894646035849] 
dist 197=[-1.6308504456474963060 ,.11063648202658680002] 
dist 198=[-1.6493474932674495923 ,.10264209281955666321] 
dist 199=[-1.6629601486786293259 ,.08566394030394344382] 
dist 200=[-1.6736020058696504875 ,.08170947269315563893] 
dist 201=[-1.6819202289397773162 ,.06388696014817270307] 
dist 202=[-1.6862412093084701679 ,.06073114932886727677] 
dist 203=[-1.6884899833097452829 ,.05355931671019087641] 

8 phat 2 dirichlet min maxes function [2, 0, 0, 2, 0, 1, 0, 0, 1] 
dist 0=[14.105604034959329763  ,14.105604034959329763  ] 
dist 1=[14.061376761124138285  ,14.162699062921301951  ] 
dist 2=[14.017811221493376747  ,14.224164126662203034  ] 
dist 3=[13.963360453883238583  ,14.285862775569165252  ] 
dist 4=[13.907440192071045977  ,14.359965968951824931  ] 
dist 5=[13.857996255712776914  ,14.471025640730894147  ] 
dist 6=[13.785940199754744990  ,14.580465854498323907  ] 
dist 7=[13.653116763408617042  ,14.648093682446962865  ] 
dist 8=[13.434080622311494140  ,14.698470921844582144  ] 
dist 9=[13.200642301266503818  ,14.738939735598430841  ] 
dist 10=[13.010226569245516447  ,14.770241711796288962  ] 
dist 11=[12.813489644841206408  ,14.783967691385567491  ] 
dist 12=[12.554769287920830696  ,14.789854319544843625  ] 
dist 13=[12.273692958529497190  ,14.789810986988453867  ] 
dist 14=[11.987554447681274914  ,14.764696387711804222  ] 
dist 15=[11.640780704336670324  ,14.757069462464934253  ] 
dist 16=[11.117227498317638540  ,14.739312947655190522  ] 
dist 17=[10.591518869707538985  ,14.731901116933084540  ] 
dist 18=[10.236124246312720658  ,14.691271839802640360  ] 
dist 19=[9.9349026388670789297 ,14.680795535979976349  ] 
dist 20=[9.6258244499167341728 ,14.652947259408550813  ] 
dist 21=[9.3326562131884334905 ,14.642472557251299866  ] 
dist 22=[9.0950545335305820632 ,14.140033968980541694  ] 
dist 23=[8.8509103127251379314 ,14.086378282654663662  ] 
dist 24=[8.5315740104015148794 ,13.977605921272832885  ] 
dist 25=[8.2161687223157111738 ,13.939685865098934551  ] 
dist 26=[7.9877417343806632811 ,13.630374224537231419  ] 
dist 27=[7.7776162186206687064 ,13.454958635283293609  ] 
dist 28=[7.5353942915789912929 ,12.185042247789471812  ] 
dist 29=[7.2888851144545942300 ,12.169262893681332138  ] 
dist 30=[7.0616102248686941596 ,11.484394631848983395  ] 
dist 31=[6.8031702476417410898 ,11.396676280184834341  ] 
dist 32=[6.4320221384072560128 ,11.227623234745261616  ] 
dist 33=[6.0621067036785660720 ,11.184955133358114435  ] 
dist 34=[5.8085936165304967526 ,11.039926152180191669  ] 
dist 35=[5.5899246060480670849 ,11.005546509577712300  ] 
dist 36=[5.3593526618319595197 ,10.966975011853028299  ] 
dist 37=[5.1366709494052217082 ,10.954867842904497225  ] 
dist 38=[4.9495519462679749447 ,9.3556307531035326681 ] 
dist 39=[4.7512049760410065005 ,9.2193030431135998809 ] 
dist 40=[4.4836115182992916649 ,8.9203236146612730832 ] 
dist 41=[4.2153131191403538004 ,8.8546698535163412984 ] 
dist 42=[4.0141424321391488587 ,8.5032004255576951726 ] 
dist 43=[3.8220651386242569666 ,8.4391167560130725951 ] 
dist 44=[3.5901283679177485509 ,8.3052689532417213731 ] 
dist 45=[3.3480879487081547079 ,8.2689665661470698264 ] 
dist 46=[3.1155952818180843063 ,7.9430218091417082600 ] 
dist 47=[2.8436943841794039172 ,7.8914907408558576965 ] 
dist 48=[2.4440306746778805119 ,7.7895923083138916864 ] 
dist 49=[2.0464592803303452070 ,7.7630866473368609574 ] 
dist 50=[1.7829249563532334582 ,7.6675503747875376333 ] 
dist 51=[1.5650623769634895882 ,7.6463218826484414477 ] 
dist 52=[1.3501602831396703923 ,7.6093878832950073578 ] 
dist 53=[1.1515717038461259464 ,7.6001046460521322940 ] 
dist 54=[.99895597968534780888,5.0012578548561056553 ] 
dist 55=[.84957304436108808924,4.9532408200924822638 ] 
dist 56=[.66391171102827213294,4.8544440856740937408 ] 
dist 57=[.4848988298683925402 ,4.5630335827432824707 ] 
dist 58=[.36210598424051181851,4.5291082455024073345 ] 
dist 59=[.25600711413555667202,4.4052305470370430694 ] 
dist 60=[.14376290155131133449,1.6002298060705150569 ] 
dist 61=[.00636155619793134996,1.5746900876753841058 ] 
dist 62=[-.21697130178242521709,.60875511600594903652] 
dist 63=[-.43408874301686652394,.4919851739290401056 ] 
dist 64=[-.63265738490088429515,.25603041496100090494] 
dist 65=[-.78180418308250896281,.19690323745798503013] 
dist 66=[-.96478164115003448994,-.00735945507415639726] 
dist 67=[-1.1762685216576768946 ,-.04872385733306042021] 
dist 68=[-1.4075263067365796220 ,-.10078425735457256736] 
dist 69=[-1.7285479978908207551 ,-.10944774299614707132] 
dist 70=[-2.0437722522902320862 ,-.44395160156000125636] 
dist 71=[-2.2518464585252470959 ,-.46838647062227148539] 
dist 72=[-2.4227882840592129248 ,-.47222322577529293417] 
dist 73=[-2.5895181406595580008 ,-.49191488489022902705] 
dist 74=[-2.7422585151752762431 ,-.49213868937522658056] 
dist 75=[-2.8572567357353244014 ,-.48630391703287810987] 
dist 76=[-2.9674904917303492322 ,-.47073253778748320721] 
dist 77=[-3.1011807739169115486 ,-.4500628811501669037 ] 
dist 78=[-3.2283481981783200967 ,-.42384485164376281267] 
dist 79=[-3.3124981928548973468 ,-.38843981603409532098] 
dist 80=[-3.3818824217944597169 ,-.3310492556790308837 ] 
dist 81=[-3.4500019861457655281 ,-.27250206026231992535] 
dist 82=[-3.5127339653326172525 ,-.23247092204247979758] 
dist 83=[-3.5605763307447128394 ,-.19815907273064461659] 
dist 84=[-3.6070640828113688310 ,-.16246322419804448553] 
dist 85=[-3.6643877907754746088 ,-.12840668301204665697] 
dist 86=[-3.7181891960210644726 ,-.10064351878518213309] 
dist 87=[-3.7505914091120104108 ,-.07203627838093302190] 
dist 88=[-3.7737996827909733358 ,-.03460366930399713251] 
dist 89=[-3.7908261434611396556 ,.00223648071838643496] 
dist 90=[-3.8033740229175147214 ,.02847710734296837453] 
dist 91=[-3.8086668009787765979 ,.05211238819375662135] 
dist 92=[-3.8103586510907613001 ,.07854103613360085312] 
dist 93=[-3.8096774735902342101 ,.1049120365132789224 ] 
dist 94=[-3.7760965267963057040 ,.12831773467262646038] 
dist 95=[-3.7694088844870721673 ,.15416087213586355862] 
dist 96=[-3.7568050443379704415 ,.19027476369048335219] 
dist 97=[-3.7526909060091696242 ,.22566469380040185602] 
dist 98=[-3.7340079804226654541 ,.24861408901705414182] 
dist 99=[-3.7291019235868093246 ,.26696467536406575726] 
dist 100=[-3.7149716093162846030 ,.28397253217250405804] 
dist 101=[-3.7106550451373502931 ,.29891865376553766077] 
dist 102=[-3.3800962307905196833 ,.30902753008609417079] 
dist 103=[-3.3484603111622461800 ,.3175761567517921665 ] 
dist 104=[-3.2778625958027806581 ,.32628377479185330801] 
dist 105=[-3.2610046302350088504 ,.33401412938948301378] 
dist 106=[-3.1712914291213679281 ,.33865687109478613527] 
dist 107=[-3.1538933438202275093 ,.34194391179330087332] 
dist 108=[-3.1178744446204871388 ,.34425845182555690477] 
dist 109=[-3.1076594728830388644 ,.34578202560181596414] 
dist 110=[-2.9924839497524651160 ,.34597245771087468163] 
dist 111=[-2.9751876240304193335 ,.34549853872282166595] 
dist 112=[-2.9330999092183469393 ,.34486924032040113622] 
dist 113=[-2.9251004646467475312 ,.28284828094828295003] 
dist 114=[-2.8597233856082465971 ,.27661141646284062532] 
dist 115=[-2.8465400079559482753 ,.27536736923101269734] 
dist 116=[-2.8277644137657406785 ,.33565177675089334207] 
dist 117=[-2.8217998002860587626 ,.37922854749949445971] 
dist 118=[-1.6577723953715805027 ,.41922125913392084221] 
dist 119=[-1.6036547009865864898 ,.4651759839547267068 ] 
dist 120=[-1.4776828200040134896 ,.51185537862722277901] 
dist 121=[-1.4576846290374592859 ,.55474797105474850726] 
dist 122=[-1.2890913901835627661 ,.69389630981988006459] 
dist 123=[-1.2584673062737219174 ,.8221544701822203148 ] 
dist 124=[-1.2164922546404526035 ,.9503797189210670106 ] 
dist 125=[-1.2041489943160199617 ,1.1133319143337565762 ] 
dist 126=[-.97714065320363659107,1.2719839236913600582 ] 
dist 127=[-.94814156284752897825,1.3830137653042407720 ] 
dist 128=[-.8863092418837128698 ,1.4812026398051548506 ] 
dist 129=[-.87152489396994520908,1.5885064531700702381 ] 
dist 130=[-.80487318427572160618,1.6943843052337781808 ] 
dist 131=[-.79300624305959470106,1.7868712163066124148 ] 
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dist 172=[-.55878603468144972133,.67137117314690088794] 
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dist 185=[-.82968044969398511962,.44444982510630567305] 
dist 186=[-.84071228324384804238,.41421935417232550942] 
dist 187=[-.85520815055144285539,.40863159855855778911] 
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dist 189=[-.87750720026361377377,.39726917732395819212] 
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dist 195=[-.89399233485835196498,.31800265601766077449] 
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dist 197=[-.88652101236622334122,.31160678715068822103] 
dist 198=[-.88389886698832827667,.26537066069088065463] 
dist 199=[-.88299050742033642274,.26033680774068957444] 
dist 200=[-.87863571467560889635,.24905138800506004144] 
dist 201=[-.87750173812574038358,.24670757560275831315] 
dist 202=[-.87393331712359648982,.23259173111495688507] 
dist 203=[-.87306179583114944109,.22997119649947219916] 
dist 204=[-.79489465250800688441,.22497398972174414966] 
dist 205=[-.78731948139773973769,.22371268042313920102] 
dist 206=[-.77040822042158741046,.20721065883689795737] 
dist 207=[-.76630907410994944162,.20486984240810205697] 
dist 208=[-.74469678665130794549,.19938582820049737692] 
dist 209=[-.73718324090646291349,.19834273112911229112] 
dist 210=[-.72041448689891982938,.19062347939412871602] 
dist 211=[-.7055245801487843525 ,.18913123504300660057] 
dist 212=[-.63267175926181600856,.18677313612688880657] 
dist 213=[-.60685414173330885872,.1861358659386800677 ] 
dist 214=[-.2270161336483492324 ,.17368732683247863936] 
dist 215=[-.22673336197424382915,.17202244641005157643] 
dist 216=[-.22531975163699570171,.16802723661252254445] 
dist 217=[-.22498252811737676654,.16729824201920444915] 
dist 218=[-.22395097686861028139,.16133362070338624485] 
dist 219=[-.22372329952059740155,.16015779402998286161] 
dist 220=[-.17934700930039144131,.15849137516295670477] 
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dist 225=[-.15476958367535403182,.14176581214527520197] 
dist 226=[-.15239231640689322175,.13827448000033448851] 
dist 227=[-.1518567343438776311 ,.13757916524970696705] 
dist 228=[-.13442276324213665227,.1357755714891161111 ] 
dist 229=[-.13220973155392854821,.1354516330861298977 ] 
dist 230=[-.12779968593682777699,.11022959256122564714] 
dist 231=[-.12666819865167125911,.10784075713089678342] 
dist 232=[-.12265672134959653988,.10232569434999436942] 
dist 233=[-.1217902927859312905 ,.1012991625655576684 ] 
dist 234=[-.12044907407418769289,.09389808701498573874] 
dist 235=[-.12008386814533670573,.09250861264503210534] 
dist 236=[-.08695502190219469322,.09023726571801217448] 
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dist 249=[-.04763658373945048947,-.00381632130209301730] 
dist 250=[-.04653468989342833077,-.00980500017875839648] 

8 phat 2 dirichlet min maxes function [2, 2, 2, 1, 0, 0, 1, 2] 
dist 0=[6.7366373540062963997 ,6.7366373540062963997 ] 
dist 1=[6.7144473652028844575 ,6.7596231129450538548 ] 
dist 2=[6.6873010834576996523 ,6.7899492498128858355 ] 
dist 3=[6.6550213529049949696 ,6.8233153339544007261 ] 
dist 4=[6.6122987725992496365 ,6.8584587034759571605 ] 
dist 5=[6.5533860947227654318 ,6.9019152543356696557 ] 
dist 6=[6.4563528122301181763 ,6.9685307647708729052 ] 
dist 7=[6.3510308945939780755 ,7.0389694190751075003 ] 
dist 8=[6.2589673492110171137 ,7.0977172268968567523 ] 
dist 9=[6.1582463591633429452 ,7.1596146930124400299 ] 
dist 10=[6.0182988330171856903 ,7.2426513269850532617 ] 
dist 11=[5.8624655310166842183 ,7.3337314489223465443 ] 
dist 12=[5.6982081607101505906 ,7.4277997687987422777 ] 
dist 13=[5.4949845196610391518 ,7.5428334055105127327 ] 
dist 14=[5.1833021158351937332 ,7.7177661626248109270 ] 
dist 15=[4.8656720081992698772 ,7.8928743880274617104 ] 
dist 16=[4.6386599679759328788 ,8.0086100371519754691 ] 
dist 17=[4.4327831662247558916 ,8.1039074703394085120 ] 
dist 18=[4.1996852736783227336 ,8.1972718806194317883 ] 
dist 19=[3.9646904120962051887 ,8.2831226813837511361 ] 
dist 20=[3.7512262299965634896 ,8.3483691858089078999 ] 
dist 21=[3.5109383814307971680 ,8.4115306216203497837 ] 
dist 22=[3.1686590808742927639 ,8.4890426146761170459 ] 
dist 23=[2.8171264060975801107 ,8.5632750725215741850 ] 
dist 24=[2.5398284899727541028 ,8.6133200711220109520 ] 
dist 25=[2.2616112629763204807 ,8.6556200495135841458 ] 
dist 26=[1.9064013993588699568 ,8.6988760639551675463 ] 
dist 27=[1.5254140765851354907 ,8.7398496327657251495 ] 
dist 28=[1.1440967729958971089 ,8.7730213966919228292 ] 
dist 29=[.68641519898028731299,8.8070986827380747280 ] 
dist 30=[0                     ,8.8516953993272953742 ] 
dist 31=[7.6330899216658408810 ,8.8943812387841888269 ] 
dist 32=[7.6042751570422503306 ,8.9208161088840825735 ] 
dist 33=[7.5674900587369137137 ,8.9406182874610143888 ] 
dist 34=[7.5221889886720360454 ,8.9567755746708998623 ] 
dist 35=[7.4616110984007886952 ,8.9695099630620193146 ] 
dist 36=[7.3637263990944990296 ,8.9756222330502272550 ] 
dist 37=[7.2615313902267518952 ,8.9784225327936822421 ] 
dist 38=[7.1837139441684708562 ,8.9785638760972169209 ] 
dist 39=[7.1082508013388357003 ,8.9729513461945213658 ] 
dist 40=[7.0154703700009626560 ,8.9707754536417419200 ] 
dist 41=[6.9177713875112913739 ,8.9649767105821101152 ] 
dist 42=[6.8226356626425061591 ,8.9623080663389206989 ] 
dist 43=[6.7103980935972609419 ,8.9469773165000929198 ] 
dist 44=[6.5442992358271479008 ,8.9429045838522261654 ] 
dist 45=[6.3075458259400660579 ,8.9336572818015774163 ] 
dist 46=[5.9354522247853329172 ,8.9302194478906784835 ] 
dist 47=[5.5620210167324563595 ,8.7621152214975253142 ] 
dist 48=[5.3112127659101526709 ,8.7442385456980525601 ] 
dist 49=[5.1002728946755826039 ,8.7027330026438839849 ] 
dist 50=[4.8862970403940971498 ,8.6934321911645938014 ] 
dist 51=[4.6847412205017300403 ,8.6043359085792350827 ] 
dist 52=[4.5234759294340429850 ,8.5549028334432017572 ] 
dist 53=[4.3595745772994407770 ,4.5456187524994440123 ] 
dist 54=[4.1474760170564453193 ,4.5301710098432932487 ] 
dist 55=[3.9388915035728155591 ,4.0134737704543693676 ] 
dist 56=[3.7478542144960909619 ,3.9693221163172859798 ] 
dist 57=[3.5417494681461200246 ,3.7491631104454831031 ] 
dist 58=[3.3781707478781822297 ,3.7138469976200883837 ] 
dist 59=[3.2131312028229093217 ,3.5916851444092093793 ] 
dist 60=[3.0011834826635608224 ,3.5659468586331865521 ] 
dist 61=[2.7935109648527325634 ,3.5326327962128232957 ] 
dist 62=[2.6455701132898968395 ,3.5239615329005754118 ] 
dist 63=[2.5119051151824421458 ,2.6351907843680156880 ] 
dist 64=[2.3613293438010410617 ,2.5984414620649894252 ] 
dist 65=[2.2099688853233079166 ,2.4752451582261870481 ] 
dist 66=[2.0731651823327274115 ,2.4505155561277332700 ] 
dist 67=[1.9197317824413071338 ,2.4116090721866945612 ] 
dist 68=[1.7018593359209849343 ,2.4021096957088913128 ] 
dist 69=[1.4855600172821469896 ,2.0636497740075625384 ] 
dist 70=[1.3384182813787805235 ,2.0491331680438781191 ] 
dist 71=[1.2126213888584487518 ,1.8526466924612363590 ] 
dist 72=[1.0816921042127113407 ,1.8256110788774110567 ] 
dist 73=[.9562457176713290737 ,1.7692364397819592226 ] 
dist 74=[.85237784461923708662,1.7551672882296698489 ] 
dist 75=[.74360095898999307449,1.6996437155880295682 ] 
dist 76=[.5985201490244460199 ,1.6892481843524301814 ] 
dist 77=[.4537779860327170817 ,1.6679650752855883916 ] 
dist 78=[.28708631388815467683,1.6624756207019444514 ] 
dist 79=[.03537495627090931901,.88679408870225269733] 
dist 80=[-.13212913249977418514,.87813955835352582345] 
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dist 85=[-.73719422181491681575,.04969922531183802214] 
dist 86=[-.86158760494209390198,.00506511203153509499] 
dist 87=[-.98219628811712664928,-.09638553648890860591] 
dist 88=[-1.0659757542053276165 ,-.11261564261228985505] 
dist 89=[-1.1394630571706065262 ,-.23935329983156530546] 
dist 90=[-1.2189083783132343440 ,-.26156051756856894128] 
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dist 92=[-1.3686353413169121957 ,-.30304676684427270085] 
dist 93=[-1.4603941588578139503 ,-.44211446427639004613] 
dist 94=[-1.5386715155572229159 ,-.45936027317245665949] 
dist 95=[-1.6377515508911618461 ,-.49835755285477055771] 
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dist 100=[-1.8912988288549890906 ,-.57521420411724061281] 
dist 101=[-1.9261638431803636195 ,-.64183590140096779278] 
dist 102=[-1.9696130701894954825 ,-.64965105553195063194] 
dist 103=[-2.0047614461655647246 ,-.66283954953484883967] 
dist 104=[-2.0368648901390200837 ,-.66566251054731594701] 
dist 105=[-2.0656439616686852190 ,-.67005264207353549393] 
dist 106=[-2.0857158465663297274 ,-.66819806319675183855] 
dist 107=[-2.1034101258343250294 ,-.66292033201630511178] 
dist 108=[-2.1226796694680911912 ,-.65155761484725155509] 
dist 109=[-2.1402094806216966781 ,-.63826176566458494952] 
dist 110=[-2.1509455783948362100 ,-.62525245121863978932] 
dist 111=[-2.1588438262546360346 ,-.60987161684940916308] 
dist 112=[-2.1650235872523085388 ,-.5870900917613728446 ] 
dist 113=[-2.1696832994518592055 ,-.56109095472272198039] 
dist 114=[-2.1715022304256928275 ,-.53284194755043675329] 
dist 115=[-2.1720997949701765665 ,-.49732299857409870452] 
dist 116=[-2.1718736935679162934 ,-.44225051116712966169] 
dist 117=[-.9503037474904381445 ,-.38679232572258977998] 
dist 118=[-.94863271778104422257,-.34973054884356691319] 
dist 119=[-.87192506458642161566,-.31878144114442179639] 
dist 120=[-.86219537606284853595,-.28776740956664139293] 
dist 121=[-.84336013928467486994,-.25881300952929157879] 
dist 122=[-.83862316455876841226,-.23610005198755037985] 
dist 123=[-.8225841858465397852 ,-.2134414414803469765 ] 
dist 124=[-.81883197325341555513,-.18470383249338549056] 
dist 125=[-.81484000886244693501,-.15673798594439816369] 
dist 126=[-.81387850585790666192,-.13716540416896462361] 
dist 127=[-.64551352915665798759,-.11984865840793585446] 
dist 128=[-.63133292873392455568,-.1009036941214920254 ] 
dist 129=[-.60009640310812070095,-.08218888516771122112] 
dist 130=[-.59350585093298798858,-.06579209455079204646] 
dist 131=[-.55659516683982748401,-.04782660385881472985] 
dist 132=[-.54992695077993612798,-.02283746220957275312] 
dist 133=[-.53643045430902965681,.00173815993127815819] 
dist 134=[-.53290878929039813049,.01805014181096150505] 
dist 135=[-.49869531148371387271,.03155571066771378375] 
dist 136=[-.49345034379658279411,.04490785334067974771] 
dist 137=[-.4831295364661331406 ,.05726380748648655782] 
dist 138=[-.48049675721030665385,.06678565050097517980] 
dist 139=[-.47129767254137578171,.07613048158850730175] 
dist 140=[-.46924208810526567821,.08777929670089172238] 
dist 141=[-.46636473244258019832,.09903005916457078059] 
dist 142=[-.46546710524628494293,.10678330056630166082] 
dist 143=[-.08011077627658391552,.11352249980618293016] 
dist 144=[-.05930618495208685751,.12071804423690967691] 
dist 145=[-.01095320423853548041,.12773112134789646344] 
dist 146=[-.00388882125215669868,.1337412685970545828 ] 
dist 147=[.05978121322915827211,.14022214114551451688] 
dist 148=[.07107453281915516518,.1491196139831298999 ] 
dist 149=[.08530915523862871626,.15781279254885008702] 
dist 150=[.08809528634410731715,.17357294269035109009] 
dist 151=[.14281594260689231105,.20507008123986667106] 
dist 152=[.14370377124632222773,.22695044530866822011] 
dist 153=[.1480646134647231583 ,.24613558746015935803] 
dist 154=[.14878369431951379789,.26685436488081429301] 
dist 155=[.1500452020615322702 ,.28715818411948590505] 
dist 156=[.1502740356611525955 ,.30468388296844902436] 
dist 157=[.15052044744873189105,.32366187599306331629] 
dist 158=[.15014569420325784879,.34977351205679933309] 
dist 159=[.14936023430084549968,.37531029266052352008] 
dist 160=[.147808547358322601  ,.39198940090313756676] 
dist 161=[.1458751141230343199 ,.40549433340171853892] 
dist 162=[.14356294789624798655,.41833737968856265332] 
dist 163=[.14051764358612197523,.42988422987587362571] 
dist 164=[.13565283057151121872,.43820558777489641643] 
dist 165=[.13061649724449259575,.44581858101118956796] 
dist 166=[.12688513005136879963,.45453262777999961163] 
dist 167=[.12337243200688001278,.4626058880279724332 ] 
dist 168=[.11920965866670054559,.46765634387401374759] 
dist 169=[.11491453492523796243,.47149584772590337103] 
dist 170=[.11087221575304841969,.47472646804544053001] 
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dist 173=[.09246318540901405973,.47951970850342995568] 
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dist 175=[.08127577424627545530,.41746343433001450158] 
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dist 179=[.04909340653049916411,.39870862495998893621] 
dist 180=[.03503676143203553450,.3968517401962158385 ] 
dist 181=[.02098539870242394543,.39449300442976177676] 
dist 182=[.01163459334169729072,.39365478443988782294] 
dist 183=[.00386955468999327646,.37556760185665046042] 
dist 184=[-.00384044107744659425,.3731043177369716701 ] 
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dist 207=[-.08409454804212377103,.1196071500454956337 ] 
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dist 211=[-.12023368611131153234,.07207104332731748958] 
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8 phat 2 dirichlet min maxes function [0, 0, 0, 0, 1, 0, 2] 
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dist 35=[4.6298722058208980109 ,5.0628889885592845983 ] 
dist 36=[4.6334346794034516795 ,5.0888701610687799467 ] 
dist 37=[4.6474596659077628430 ,5.1137921523447533847 ] 
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dist 45=[4.4317182108785971443 ,5.2679222187142522263 ] 
dist 46=[4.3870110354693983681 ,5.2745198328470755277 ] 
dist 47=[4.3434002262109559085 ,5.2795547997770934788 ] 
dist 48=[4.2894202825090541272 ,5.2838340601228217315 ] 
dist 49=[4.2323884775296159998 ,5.2869889308006645634 ] 
dist 50=[4.1765713279975677474 ,5.2876595857053572024 ] 
dist 51=[4.0954963814758516446 ,5.2871921238126843919 ] 
dist 52=[3.9857706162157901140 ,5.2868544133153126382 ] 
dist 53=[3.8661825625377756353 ,5.2777735357741659982 ] 
dist 54=[3.7437577159675260337 ,5.2751769247567938712 ] 
dist 55=[3.5948216081271438057 ,5.2733468667960191480 ] 
dist 56=[3.3692006209097187897 ,5.2721254536984340577 ] 
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dist 60=[2.7338432757162935224 ,5.1772260881045366645 ] 
dist 61=[2.6121036349773517545 ,2.7648821650775584908 ] 
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dist 63=[2.4162178277748551710 ,2.5287604935239022978 ] 
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dist 65=[2.1635231138554508732 ,2.2392675198354937874 ] 
dist 66=[2.0737156003601297681 ,2.1959124180919953465 ] 
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dist 126=[-.4951109583839793383 ,-.3111701748871124666 ] 
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dist 135=[-.40160624344629617494,-.16805011119730266084] 
dist 136=[-.40099272077033303765,-.15526413544913404684] 
dist 137=[-.30520102781390572013,-.1424508882518824016 ] 
dist 138=[-.29716976786574109304,-.13093889005436816034] 
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dist 140=[-.27580864968258814387,-.09991526957790973578] 
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dist 150=[-.20493246478971313759,.00682320167172163581] 
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dist 153=[-.01304460153853933266,.03096423786733972390] 
dist 154=[-.01113700589428425799,.03891169137797632587] 
dist 155=[-.00969869998104683522,.04800144630772290547] 
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dist 249=[-.05393021008945892786,-.00808055587386071783] 
dist 250=[-.05395223366557423741,-.00607203856790452862] 
dist 251=[-.05395105692097844544,-.00364815411750694273] 

8 phat 2 dirichlet min maxes function [0, 2, 2, 1, 0, 1, 0, 0, 2] 
dist 0=[13.161782570477324966  ,13.161782570477324966  ] 
dist 1=[13.136004597057087323  ,13.203309584197210588  ] 
dist 2=[13.074449388860438645  ,13.250596583788233940  ] 
dist 3=[12.979385444642870064  ,13.279890883804923964  ] 
dist 4=[12.825871842404641804  ,13.301815971611378849  ] 
dist 5=[12.660577077036161354  ,13.335143750649779980  ] 
dist 6=[12.518401424229259663  ,13.369663558950123773  ] 
dist 7=[12.364895758388451322  ,13.403769228396317999  ] 
dist 8=[12.154293191778546101  ,13.435773089155697703  ] 
dist 9=[11.921209481804331808  ,13.461885757882341797  ] 
dist 10=[11.677804043497024292  ,13.488847379771595225  ] 
dist 11=[11.378409164537508035  ,13.524243566490115736  ] 
dist 12=[10.921429701331201826  ,13.562621258686660660  ] 
dist 13=[10.461401022088534128  ,13.601500895511753473  ] 
dist 14=[10.149811712097184967  ,13.648436071841954838  ] 
dist 15=[9.8850763577636248464 ,13.719015443382405689  ] 
dist 16=[9.6124087788519121749 ,13.788711141500193802  ] 
dist 17=[9.3531354494607842525 ,13.832113285159069002  ] 
dist 18=[9.1419595303057760483 ,13.864817171988132356  ] 
dist 19=[8.9240246107900055188 ,13.891745293757070083  ] 
dist 20=[8.6377174197906438807 ,13.913082350688835191  ] 
dist 21=[8.3543459858173213223 ,13.923434914447615252  ] 
dist 22=[8.1481481452315100943 ,13.927777204406414210  ] 
dist 23=[7.9574868380436205106 ,13.927289223193188399  ] 
dist 24=[7.7362415894452520402 ,13.918492191991906420  ] 
dist 25=[7.5102608678556998379 ,13.914873259843630813  ] 
dist 26=[7.3006575795512108751 ,13.896927576349623741  ] 
dist 27=[7.0613108951155916469 ,13.894171885686864135  ] 
dist 28=[6.7163762797579380204 ,13.830254787941504026  ] 
dist 29=[6.3720640645268827191 ,13.781784208133079353  ] 
dist 30=[6.1352036963667562931 ,13.555995207307705407  ] 
dist 31=[5.9299375082628078066 ,13.456285380446927003  ] 
dist 32=[5.7119724933003212251 ,11.938998403451373357  ] 
dist 33=[5.5005281868709849573 ,11.820555734068492568  ] 
dist 34=[5.3213351866788137105 ,11.535551646781511029  ] 
dist 35=[5.1300619128806558598 ,11.494398941818707012  ] 
dist 36=[4.8702971530811679202 ,11.079911097982557844  ] 
dist 37=[4.6090569411061244484 ,11.002190107020727740  ] 
dist 38=[4.4118785380739355357 ,10.915625101128009832  ] 
dist 39=[4.2223374550118355626 ,10.899389214234543610  ] 
dist 40=[3.9916359480099139861 ,10.196020860556896208  ] 
dist 41=[3.7499045290765654840 ,10.106766499527792347  ] 
dist 42=[3.5162436214471703328 ,9.9338076304776149296 ] 
dist 43=[3.2418547783632945306 ,9.8902678549729813213 ] 
dist 44=[2.8372216845767760184 ,9.7423732483545276514 ] 
dist 45=[2.4343424464630250977 ,9.7079599533416548229 ] 
dist 46=[2.1669666147828581919 ,9.6697628424575876874 ] 
dist 47=[1.9455682320488712497 ,9.6593090438693049184 ] 
dist 48=[1.7265815034406035213 ,8.1246769232479387766 ] 
dist 49=[1.5238260588699584972 ,7.9946104746805690083 ] 
dist 50=[1.3673458279185300877 ,7.7089345730738417722 ] 
dist 51=[1.2135470824215561226 ,7.6474152976640925207 ] 
dist 52=[1.0215139334780004300 ,7.3113104641225633077 ] 
dist 53=[.83591864292215288313,7.2503361072105181227 ] 
dist 54=[.70786777877760155386,7.1248072167829303162 ] 
dist 55=[.59643124610616165052,7.0913656246605193635 ] 
dist 56=[.47728628481803124063,6.7809378757375064949 ] 
dist 57=[.36113489236306185849,6.7325320283855403005 ] 
dist 58=[.26166903162878716092,6.6370928382462251040 ] 
dist 59=[.1545515330185479161 ,6.6124989014878866884 ] 
dist 60=[.00778979586863413869,6.5251559851736411067 ] 
dist 61=[-.1502521923059592718 ,6.5056748288861996757 ] 
dist 62=[-.3471487066758945314 ,6.4748659387334436443 ] 
dist 63=[-.4816999479469490835 ,6.4663414818887126518 ] 
dist 64=[-.5974130323893726485 ,2.7023569430230679840 ] 
dist 65=[-.7189653049298838036 ,2.4980574546092284778 ] 
dist 66=[-.8361580092967600279 ,2.0207624294094113088 ] 
dist 67=[-.9344373153044157697 ,1.9523959109120555355 ] 
dist 68=[-1.0384985402960399813 ,1.3157047885709730084 ] 
dist 69=[-1.1788239947849854846 ,1.2022656477038065984 ] 
dist 70=[-1.3151329568106131904 ,1.0647939389771489532 ] 
dist 71=[-1.4031300854163477933 ,1.0414835539419551415 ] 
dist 72=[-1.4733051837152920839 ,.18431146056094345871] 
dist 73=[-1.5383265643819322310 ,.08074692034092590583] 
dist 74=[-1.5957048344345628519 ,-.05978101765406028663] 
dist 75=[-1.6353085847086052285 ,-.02461708263175347035] 
dist 76=[-1.6698105064439976115 ,.03234954800167710176] 
dist 77=[-1.7067842099700243769 ,.09039790754856044721] 
dist 78=[-1.7403605184100747584 ,.12988841456447782211] 
dist 79=[-1.7612735018940477553 ,.16351342466103375577] 
dist 80=[-2.0179820510545294326 ,.19812717755725502136] 
dist 81=[-2.1963942406124329448 ,.23091221472125115795] 
dist 82=[-2.3424383063854299973 ,.25723157753931372296] 
dist 83=[-2.4840101025345782419 ,.28397635508030265543] 
dist 84=[-2.6131298119765175059 ,.31846325081784772248] 
dist 85=[-2.7093778565204305918 ,.35214432558826430983] 
dist 86=[-2.8006993792915743298 ,.37566943885933695594] 
dist 87=[-2.9101201859173982657 ,.39636976736420712379] 
dist 88=[-3.0135311821126763567 ,.41876233651567182171] 
dist 89=[-3.0808202178477852547 ,.44065649447957233445] 
dist 90=[-3.1350401102496794675 ,.45936469319661015131] 
dist 91=[-3.1861875766781627565 ,.47941001593378574691] 
dist 92=[-3.2319263484035097607 ,.50664657144452198519] 
dist 93=[-3.2645192195650232126 ,.53305841824949157094] 
dist 94=[-3.2939939297110923826 ,.54980758416963121195] 
dist 95=[-3.3272702460334011336 ,.56275888617428741254] 
dist 96=[-3.3574792479309117076 ,.57399339083286041816] 
dist 97=[-3.3746878027958342764 ,.58331901651373639116] 
dist 98=[-3.3858280840741890188 ,.58864122659998384582] 
dist 99=[-3.3917630931354718887 ,.5920667743193682269 ] 
dist 100=[-3.3949936123244433894 ,.5938108624503254548 ] 
dist 101=[-3.3953140026609829825 ,.59475877055985486817] 
dist 102=[-3.3937844932542869445 ,.5950019936059491658 ] 
dist 103=[-3.3924380407122433632 ,.59476531274555844133] 
dist 104=[-3.3441768943832722830 ,.59422694780505972755] 
dist 105=[-3.3359952411593211082 ,.59240613977704281301] 
dist 106=[-3.3198570187282664036 ,.59154388234796453022] 
dist 107=[-3.3148901648916672071 ,.58861552952438319318] 
dist 108=[-3.2931677520035869552 ,.58739197510427450408] 
dist 109=[-3.2879770166542456009 ,.4019534290461326822 ] 
dist 110=[-3.2733096284390422906 ,.3878547165630205910 ] 
dist 111=[-3.2694756026977459057 ,.3541992876065002631 ] 
dist 112=[-2.9684321281245682771 ,.3485047845483920746 ] 
dist 113=[-2.9396278382609940374 ,.2995381157624316669 ] 
dist 114=[-2.8749162780784060592 ,.2901250562083223495 ] 
dist 115=[-2.8601051393860446887 ,.2760971552464083147 ] 
dist 116=[-2.7768890811789743740 ,.2507111358596538898 ] 
dist 117=[-2.7608403209923292593 ,.1895831886269097908 ] 
dist 118=[-2.7288632833103978011 ,-.43528614742728732796] 
dist 119=[-2.7201282753426140381 ,-.41846408764310418523] 
dist 120=[-2.6105876231600075955 ,-.39843166867673202944] 
dist 121=[-2.5946640106555114109 ,-.37768909131602776562] 
dist 122=[-2.5551545540708416180 ,-.35802688010687699253] 
dist 123=[-2.5485809796949781084 ,-.33524293884836635615] 
dist 124=[-2.4855237296674025207 ,-.30201625259001287453] 
dist 125=[-2.4729329476829847409 ,-.26869749103608704405] 
dist 126=[-2.4578007856113531236 ,-.24554523708370692493] 
dist 127=[-2.4525024441911307808 ,-.2252384296177595936 ] 
dist 128=[-1.4504355940329005887 ,.02576052414816884280] 
dist 129=[-1.4006159754427560364 ,.215304214989887676  ] 
dist 130=[-1.2848489686643204899 ,.37379665164489994542] 
dist 131=[-1.2664101427836039170 ,.53292515278352729188] 
dist 132=[-1.1121722370071373264 ,.6816425074699052168 ] 
dist 133=[-1.0842072921170708267 ,.7985028611039165535 ] 
dist 134=[-1.0455401210225594748 ,.91524352958642353175] 
dist 135=[-1.0343067428900887027 ,1.0634824817840206017 ] 
dist 136=[-.8290824892154686288 ,1.2077583583803189320 ] 
dist 137=[-.80289233124936642455,1.3086515096626195599 ] 
dist 138=[-.74677737230639187297,1.3977990399862552727 ] 
dist 139=[-.73368943187875284741,1.4951064235955533913 ] 
dist 140=[-.67243473120738576908,1.5910551971015370077 ] 
dist 141=[-.6615471686594902011 ,1.6747700067387332985 ] 
dist 142=[-.63606607966774363922,1.7661632037366034329 ] 
dist 143=[-.63186989898513183662,1.8928166854095383906 ] 
dist 144=[-.38298126727421519344,2.0170137795778766230 ] 
dist 145=[-.35947457973869323897,2.0985843558661334484 ] 
dist 146=[-.30584291152367981693,2.1651220255453157620 ] 
dist 147=[-.29683289750486223708,2.2308533349072736109 ] 
dist 148=[-.22869772218166816731,2.2930075639214935520 ] 
dist 149=[-.21654872495482094466,2.3383985669644850495 ] 
dist 150=[-.19766964762419310629,2.3805245746015485061 ] 
dist 151=[-.19296623422317762159,2.4296225924109670357 ] 
dist 152=[-.11398250577521412071,2.4752807925329404045 ] 
dist 153=[-.10396781838875076802,2.5036515414708349123 ] 
dist 154=[-.08088394986701937195,2.5249878885211244579 ] 
dist 155=[-.07728951306737982707,2.5425167244094009306 ] 
dist 156=[-.06709293395395597691,2.5563997500907956897 ] 
dist 157=[-.05727393742293777891,2.5631570598636190312 ] 
dist 158=[-.05592159741964192883,2.5665685699534611585 ] 
dist 159=[-.05346551483545783869,2.5670727289857208126 ] 
dist 160=[-.05288772655279726507,.54788258271012953667] 
dist 161=[-.05121611455208344503,.55137803354864118672] 
dist 162=[-.05086989687406233821,.55373633086369660213] 
dist 163=[-.05088661789399079411,.55518965083459165695] 
dist 164=[-.05139992529967870229,.55613796048132109176] 
dist 165=[-.05213331789460929671,.55647616380679885349] 
dist 166=[-.05303022970249606781,.55643622662294444141] 
dist 167=[-.05422370856757142827,.55629175179092248688] 
dist 168=[-.05614328597775750838,.54862082655217682381] 
dist 169=[-.05839828682818227778,.54731257255248377329] 
dist 170=[-.06093313069086431046,.54489596945827048659] 
dist 171=[-.06417603421056303531,.54417774524374609028] 
dist 172=[-.06926237186360632214,.5412286810675801802 ] 
dist 173=[-.07444872116009952356,.54042796118004406881] 
dist 174=[-.07809161772428685248,.53852635762920840958] 
dist 175=[-.08132622192048610792,.53781391619070601193] 
dist 176=[-.08488014300873232613,.48459495057989851027] 
dist 177=[-.08839733751153239683,.47963120343824897152] 
dist 178=[-.09148520367279946092,.46863005955680965503] 
dist 179=[-.09487202378593665671,.46599963958255917799] 
dist 180=[-.09958479678297034866,.45233052716940842543] 
dist 181=[-.10437083244382478139,.44970666569623620754] 
dist 182=[-.10805069326262939429,.44416500604263177097] 
dist 183=[-.11165133835858653996,.44258093146310134778] 
dist 184=[-.11612071852063282259,.42629795382014540642] 
dist 185=[-.12084636408824983904,.42378914068941137915] 
dist 186=[-.12547187229146276972,.41794136281546001445] 
dist 187=[-.13094440000982103174,.41661860981020469854] 
dist 188=[-.13905732145382731803,.4082348913810039413 ] 
dist 189=[-.14724637149142783216,.40654153732532392782] 
dist 190=[-.1530233735356198522 ,.40346773585409890258] 
dist 191=[-.15818154162605922505,.40266415775188796059] 
dist 192=[-.16389593800380957191,.32517897249186206624] 
dist 193=[-.16958145424265589055,.31152042029121678536] 
dist 194=[-.17462418072909061627,.30894564432988670796] 
dist 195=[-.18019949542910468419,.30471176456167718818] 
dist 196=[-.18801491881439354943,.30364961888866642559] 
dist 197=[-.1959804772781864069 ,.28414063966098198722] 
dist 198=[-.2021562249879435091 ,.2815091811030232352 ] 
dist 199=[-.20824925327876331884,.27550034289622231214] 
dist 200=[-.2158840582642586738 ,.27422280691312882527] 
dist 201=[-.22399546843140818884,.26621208546971724425] 
dist 202=[-.23199451859444070689,.26466729247973271976] 
dist 203=[-.24150410977040598844,.26182343393257905457] 
dist 204=[-.25565636483361023442,.26110341993997115657] 
dist 205=[-.26979660154411626815,.15020251651907792212] 
dist 206=[-.27925814294210841842,.14281092856059235467] 
dist 207=[-.28717320640829322431,.1258079341668533099 ] 
dist 208=[-.30361683717281521053,.12301064320732578707] 
dist 209=[-.31857313482825203968,.10092364513395345448] 
dist 210=[-.33084430256703553037,.09695113156477619947] 
dist 211=[-.3427824803579305334 ,.09108061990819392856] 
dist 212=[-.35369525364290893716,.08951435098720513248] 
dist 213=[-.36186601172442680399,.06209021968906628909] 
dist 214=[-.36965172666301881533,.05859853965651962323] 
dist 215=[-.3790248534860251236 ,.05082244385712175613] 
dist 216=[-.38790062355168640575,.04932593217619759421] 
dist 217=[-.39369751874471620935,.03997333900844638802] 
dist 218=[-.39839042252033871505,.03830810707530247744] 
dist 219=[-.40285151912195900937,.03519533847424467466] 
dist 220=[-.40686111083931675965,.03446200278123129317] 
dist 221=[-.40974859090235211449,.00963027505593414382] 
dist 222=[-.41238852612405552875,.00704898365971581790] 
dist 223=[-.41540843010339672167,.00161623877838143741] 
dist 224=[-.41816212288718625881,.00032327921725083773] 
dist 225=[-.4197375192833748246 ,-.00517180235340725735] 
dist 226=[-.42076335637501898959,-.00616673507353272535] 
dist 227=[-.4213192364703762907 ,-.00827498008427850332] 
dist 228=[-.4215840109501368072 ,-.00875482373792361470] 
dist 229=[-.42156086049173418926,-.01081440721055829440] 
dist 230=[-.42117903392527548069,-.01109037408836488447] 
dist 231=[-.42093103246198764389,-.01087719432798855351] 
dist 232=[-.41694829527194206653,-.00993886167482305253] 
dist 233=[-.41619450386542625086,-.00859678145791168500] 
dist 234=[-.41441447509545554633,-.00676903315981251250] 
dist 235=[-.41255667636876666515,-.00422129698068575099] 

8 phat 2 dirichlet min maxes function [1, 0, 2, 2, 1, 1, 2, 0, 2] 
dist 0=[13.518750677430855357  ,13.518750677430855357  ] 
dist 1=[13.511216470715910603  ,13.525222696741878156  ] 
dist 2=[13.487572108316540096  ,13.532784928626761298  ] 
dist 3=[13.448385966955173815  ,13.537783423569288759  ] 
dist 4=[13.379348556435211888  ,13.542279441673117268  ] 
dist 5=[13.305289620972909833  ,13.547022106823583810  ] 
dist 6=[13.246020963166350697  ,13.548494968768853228  ] 
dist 7=[13.185823337137768929  ,13.536987168105174086  ] 
dist 8=[13.108043759480262038  ,13.443672683504731648  ] 
dist 9=[13.024227465468799828  ,13.426886627229418988  ] 
dist 10=[12.939886238245080206  ,13.399116809487850697  ] 
dist 11=[12.838380148896377721  ,13.390821390664441051  ] 
dist 12=[12.685918956413555140  ,13.363815564702659253  ] 
dist 13=[12.526090377956885612  ,13.354704914729687161  ] 
dist 14=[12.390767086776000508  ,13.341371269627912151  ] 
dist 15=[12.234799053799409243  ,13.324719804953474033  ] 
dist 16=[12.079775574580586314  ,12.803195804523882560  ] 
dist 17=[11.884383414449499798  ,12.698876109021631252  ] 
dist 18=[11.684808273494847007  ,12.677073472924462937  ] 
dist 19=[11.442427336045919255  ,12.651496937657366854  ] 
dist 20=[11.075849541971986816  ,12.641153822411100706  ] 
dist 21=[10.707255615781347056  ,12.319951295389978408  ] 
dist 22=[10.456810954628226976  ,12.278668222700512725  ] 
dist 23=[10.243127717081605147  ,12.208208758468655632  ] 
dist 24=[10.021544345816575668  ,12.191116648614472243  ] 
dist 25=[9.8098598490334940866 ,12.147877231423453415  ] 
dist 26=[9.6357612970180090540 ,12.132618500114077372  ] 
dist 27=[9.4545438949195649180 ,12.040008573703192597  ] 
dist 28=[9.2143867604062259956 ,11.839494620070672734  ] 
dist 29=[8.9756489391902855458 ,11.066001233267743650  ] 
dist 30=[8.8001056234136024925 ,10.969664888699287334  ] 
dist 31=[8.6241027792378151083 ,10.600558580059208386  ] 
dist 32=[8.0087085696829945157 ,9.3762891148352414728 ] 
dist 33=[7.5935226878448666123 ,9.3298172602911894254 ] 
dist 34=[7.2425129465640566685 ,9.0607599968232174214 ] 
dist 35=[6.8837547221776536818 ,9.0110177999067920365 ] 
dist 36=[6.5443277867083228728 ,8.9134053366519664312 ] 
dist 37=[6.2706209850017443013 ,8.8881191243401933567 ] 
dist 38=[5.9906208545885008350 ,8.5914130035078371070 ] 
dist 39=[5.6260226608903415731 ,8.5480990945918626077 ] 
dist 40=[5.2666636808122167987 ,8.4504026608089900026 ] 
dist 41=[5.0076127164693890947 ,8.4283888071084894179 ] 
dist 42=[4.7705342890702761178 ,8.3013407114168641313 ] 
dist 43=[4.4990403820566917838 ,8.2767767491208531742 ] 
dist 44=[4.2237408993987430497 ,8.2288543499008500931 ] 
dist 45=[3.9714395555929058167 ,8.2159680468605848238 ] 
dist 46=[3.5626895234900382046 ,6.5075619502881669614 ] 
dist 47=[3.1146499697639654048 ,6.4248909949780772387 ] 
dist 48=[2.7395339584223057510 ,6.4109997668071526938 ] 
dist 49=[2.3620117375537830636 ,6.3037908341693870239 ] 
dist 50=[2.0085013343375931086 ,6.2843787993822280904 ] 
dist 51=[1.7294096272755595527 ,6.2551569793271577579 ] 
dist 52=[1.4493150240582523344 ,6.2474544724790672704 ] 
dist 53=[1.0917927968923012021 ,4.8718421086684910593 ] 
dist 54=[.7427840255028913545 ,4.7881661595514751027 ] 
dist 55=[.4967345992986608407 ,4.6107687860008177426 ] 
dist 56=[.2771852155936258555 ,4.5715075270235152240 ] 
dist 57=[.0341509626383533644 ,4.3899062253763897200 ] 
dist 58=[-.2075706086820899979 ,4.3583451172802706020 ] 
dist 59=[-.4218720011261478982 ,4.2734516899157504335 ] 
dist 60=[-.6587490643063584021 ,4.1632026966649252726 ] 
dist 61=[-.9907558565962921543 ,3.6434155805863622358 ] 
dist 62=[-1.3181930055799477685 ,3.5811528963504446819 ] 
dist 63=[-1.5367966728965820975 ,3.3743948867075455164 ] 
dist 64=[-1.7191416205655958015 ,1.1247527386218217358 ] 
dist 65=[-1.9015768560235415457 ,1.0507724375893190217 ] 
dist 66=[-2.0717451032926280919 ,.9643441249507690965 ] 
dist 67=[-2.2050347502031376951 ,.9237727223313687238 ] 
dist 68=[-2.3378453981939532913 ,.9136917273513103359 ] 
dist 69=[-2.5061025707991893401 ,.66096240230152494749] 
dist 70=[-2.6698069544613333528 ,.40419850808755626541] 
dist 71=[-2.7844126127512426860 ,.37125141499867659427] 
dist 72=[-2.8858697263893895195 ,.30141242331255866589] 
dist 73=[-2.9969934731546645789 ,.28707854839713748972] 
dist 74=[-3.1068797801630655126 ,.21686709685045825745] 
dist 75=[-3.2033928037489268375 ,.20507153900086202874] 
dist 76=[-3.3093703904828791507 ,.18127842207325863943] 
dist 77=[-3.4571183797619472129 ,.17641380090124786029] 
dist 78=[-3.6013276897938909650 ,-.57634288557899815194] 
dist 79=[-3.6931543225052753211 ,-.63094184467668180729] 
dist 80=[-3.7649191649414306349 ,-.63877895943452235332] 
dist 81=[-3.8288891520197041160 ,-.70531711963999437923] 
dist 82=[-3.8835744888475481798 ,-.71652608985269719296] 
dist 83=[-3.9182062449637854509 ,-.73157828425285615543] 
dist 84=[-3.9450734085961368414 ,-.73406224025929633617] 
dist 85=[-3.9687090543084127991 ,-1.2226298144454924436 ] 
dist 86=[-3.9885809295512860872 ,-1.2534255258063307718 ] 
dist 87=[-4.0003939813462372020 ,-1.3194422417434867884 ] 
dist 88=[-4.0086851638909223231 ,-1.3324767367707726970 ] 
dist 89=[-4.0144637907988251541 ,-1.4019002819536168699 ] 
dist 90=[-4.0182599917485038877 ,-1.4133328204353032242 ] 
dist 91=[-4.0186188527367368548 ,-1.4378955336684424291 ] 
dist 92=[-4.0166425052239245903 ,-1.4418025910567969004 ] 
dist 93=[-4.0150338803796686962 ,-1.4694375746871696451 ] 
dist 94=[-3.7051365031457090979 ,-1.4727911713003716039 ] 
dist 95=[-3.6763476375300527864 ,-1.4704076715989517385 ] 
dist 96=[-3.6149860324890485430 ,-1.4595711922159454654 ] 
dist 97=[-3.5976034311111994750 ,-1.2952562660564692576 ] 
dist 98=[-3.5258610450977315029 ,-1.1428501424603326849 ] 
dist 99=[-3.5117561568673136121 ,-.98721779094337227104] 
dist 100=[-3.4748053125860797059 ,-.84016377757730959997] 
dist 101=[-3.4686780760093387374 ,-.72205547550026236074] 
dist 102=[-3.3933287756108723889 ,-.60172717115647907515] 
dist 103=[-3.3796124204945331404 ,-.44579425557708455214] 
dist 104=[-3.3518900014674782073 ,-.29259604421563353898] 
dist 105=[-3.3438918411909205281 ,-.18320100428649182787] 
dist 106=[-3.3108249360136058224 ,-.08420232434589558684] 
dist 107=[-3.3035035036248400854 ,.02742817452709586230] 
dist 108=[-3.2844076150493284733 ,.13957148980540584818] 
dist 109=[-3.2794535483275492281 ,.24062237808059668592] 
dist 110=[-2.4110796374100665080 ,.35361278703788692356] 
dist 111=[-2.3922656206566392414 ,.51349927527673324046] 
dist 112=[-2.3480230155716874862 ,.67164763324817058143] 
dist 113=[-2.3399635622725353649 ,.77768884557392368079] 
dist 114=[-2.2619315093043556594 ,.86659276412481291836] 
dist 115=[-2.2469331770519788757 ,.95621680767927882636] 
dist 116=[-2.1824025756182906595 ,1.0401966206025534803 ] 
dist 117=[-.72498768654436020475,1.1065325353683015220 ] 
dist 118=[-.29010995517196661709,1.1731176344962547271 ] 
dist 119=[-.23717817630075756204,1.2580960243320857728 ] 
dist 120=[-.13041164108618757839,1.3410068180365683583 ] 
dist 121=[-.10356301798108769251,1.3993253976068294963 ] 
dist 122=[-.01047638334870962096,1.4512113238502852702 ] 
dist 123=[.00857366427957226041,1.5084012326483238876 ] 
dist 124=[.03324171062015680796,1.5651290456713973441 ] 
dist 125=[.03848235059144359470,1.6151691299535911375 ] 
dist 126=[.43658140826742205233,1.6702682810886186899 ] 
dist 127=[.43882476379674062869,1.7472302323343091202 ] 
dist 128=[.78622989687658528592,1.8224487875892684799 ] 
dist 129=[.80310266257682678313,1.8705768618420272375 ] 
dist 130=[.93968220167491086979,1.9084282135933587752 ] 
dist 131=[.9632559863008162897 ,1.9425495138785432400 ] 
dist 132=[.99712168321644958422,1.9719653066289308623 ] 
dist 133=[1.0058825864779243165 ,1.9909995314615946785 ] 
dist 134=[1.1471109851340278871 ,2.0062184679877495638 ] 
dist 135=[1.1642097857756120229 ,2.0254693331871258457 ] 
dist 136=[1.2011666757522812228 ,2.0626558929759911071 ] 
dist 137=[1.2072511220900008549 ,2.0996340891600015175 ] 
dist 138=[1.2455811167869119577 ,2.1339726471638733574 ] 
dist 139=[1.2514500905691709692 ,2.1606047312567091498 ] 
dist 140=[1.2626597026738094418 ,2.1868911471869450271 ] 
dist 141=[1.2645538630494320674 ,2.2198496931178689946 ] 
dist 142=[1.2615835344555797384 ,2.2508648029068892359 ] 
dist 143=[1.2277336412123892361 ,2.2693799056261004346 ] 
dist 144=[1.1918586800220470096 ,2.2824225220011208676 ] 
dist 145=[1.1638665864170431645 ,2.2915523055888812420 ] 
dist 146=[1.1361036029889377112 ,2.2981647241058707456 ] 
dist 147=[1.1011426224462119408 ,2.3011395357340704406 ] 
dist 148=[1.0639394232102940559 ,2.3020430154574638920 ] 
dist 149=[1.0272098050008338500 ,2.3017828063161373479 ] 
dist 150=[.98353561849767097851,2.2745418007740010981 ] 
dist 151=[.91856331615163281408,2.2696456668320221297 ] 
dist 152=[.8507541040069430754 ,2.2611813025309229058 ] 
dist 153=[.79573577467557016264,2.2586219281368278962 ] 
dist 154=[.73916876200733493572,2.2486371305708257129 ] 
dist 155=[.66516611522143301776,2.2455600255123151196 ] 
dist 156=[.58498224494188698721,2.2390041108410856036 ] 
dist 157=[.50369848588289832523,2.2365624868139929486 ] 
dist 158=[.40546046751072270345,2.0045666355206113630 ] 
dist 159=[.25748265359450000754,1.9831789666158069429 ] 
dist 160=[.10919604248073756906,1.9362911180643602501 ] 
dist 161=[.00972308040391839732,1.9245407675966292668 ] 
dist 162=[-.07372078866293673041,1.8676983066869057424 ] 
dist 163=[-.15791338678719849326,1.8567621790476935468 ] 
dist 164=[-.23684503001724002457,1.8324206835709773984 ] 
dist 165=[-.29925249528681051119,1.8256440350101464598 ] 
dist 166=[-.36194325810614347072,1.7620234804090590767 ] 
dist 167=[-.44200793145783690928,1.7517207298403711027 ] 
dist 168=[-.52013155789053946239,1.7288081777532292534 ] 
dist 169=[-.5750609113595685901 ,1.7224170198260056914 ] 
dist 170=[-.6238977144889722702 ,1.6923764246378500633 ] 
dist 171=[-.67765961631608682798,1.6862001370775581483 ] 
dist 172=[-.73092868063108045419,1.6724408891987618248 ] 
dist 173=[-.77779496151403844978,1.6681415036335288265 ] 
dist 174=[-.82927941801427063553,.91183308338774915236] 
dist 175=[-.90862494216601295393,.88417631232701302338] 
dist 176=[-.99173142292890297494,.81965929133543180094] 
dist 177=[-1.0460953830064517350 ,.80940407623976833515] 
dist 178=[-1.0901870132361409250 ,.72249549595835797136] 
dist 179=[-1.1322179031461764849 ,.7066491256222945847 ] 
dist 180=[-1.1700552852256067416 ,.68504973361445260465] 
dist 181=[-1.1973784398347755153 ,.67862772657570059626] 
dist 182=[-1.2224211723472729109 ,.55944388632412380508] 
dist 183=[-1.2511397698043785822 ,.54417023393476355749] 
dist 184=[-1.2776996956075618614 ,.51173347145786261163] 
dist 185=[-1.2941106753204140952 ,.50375432044943003133] 
dist 186=[-1.3063407274996061453 ,.46913210364374028013] 
dist 187=[-1.3161828221125448466 ,.46285866255246068851] 
dist 188=[-1.3239147077220151594 ,.44795735428523905676] 
dist 189=[-1.3277067150567219944 ,.44555550023027107208] 
dist 190=[-1.3295900339907285231 ,.28675066085115968048] 
dist 191=[-1.3297596996618210305 ,.27201851127775365246] 
dist 192=[-1.3127927986625588126 ,.23776451579819833671] 
dist 193=[-1.3575277728027168128 ,.2324869014969933707 ] 
dist 194=[-1.3977992150143938828 ,.18699832491558254775] 
dist 195=[-1.4268874091957285000 ,.17881564482038169649] 
dist 196=[-1.4535582645518899706 ,.16790235854943231942] 
dist 197=[-1.4841632191259095888 ,.16502162732567163512] 
dist 198=[-1.5124643211041200608 ,.10508792528653195131] 
dist 199=[-1.5299226358394243116 ,.09757419324678553902] 
dist 200=[-1.5429010769544884773 ,.08170511897914962340] 
dist 201=[-1.5532884087305361837 ,.07792505343234047935] 
dist 202=[-1.5614459505439567528 ,.06159051105384862410] 
dist 203=[-1.5655079762263808409 ,.05864726049208900544] 
dist 204=[-1.5675182804030797932 ,.05218234057176688747] 

8 phat 2 dirichlet min maxes function [1, 2, 1, 2, 2, 1, 0, 2] 
dist 0=[10.626163057703209216  ,10.626163057703209216  ] 
dist 1=[10.602163454450785875  ,10.641284960933596023  ] 
dist 2=[10.558592813828933093  ,10.649351932161960877  ] 
dist 3=[10.506510890421897233  ,10.657788897912046159  ] 
dist 4=[10.448474092167595463  ,10.674385830710083398  ] 
dist 5=[10.374514866539974317  ,10.691719422736662756  ] 
dist 6=[10.258755471379568326  ,10.703103012514169042  ] 
dist 7=[10.140790897718638693  ,10.716542250844159083  ] 
dist 8=[10.058011779619064012  ,10.730545430915472352  ] 
dist 9=[9.9845436606914022106 ,10.740612241218115777  ] 
dist 10=[9.9038133088160932856 ,10.748041697918705176  ] 
dist 11=[9.8238555420252178829 ,10.753261507974767396  ] 
dist 12=[9.7534753680055290382 ,10.754489777742714502  ] 
dist 13=[9.6760899760942809515 ,10.753813527689588321  ] 
dist 14=[9.5681139422253956136 ,10.751420880244335406  ] 
dist 15=[9.4582358159301059937 ,10.569069250061465256  ] 
dist 16=[9.3732419703056255791 ,10.551168321489947517  ] 
dist 17=[9.2895466461115701359 ,10.513779468797324458  ] 
dist 18=[9.1848597533063840073 ,10.503136905724615129  ] 
dist 19=[9.0736919236188438486 ,10.459128454813745145  ] 
dist 20=[8.9640750166672684527 ,10.450205544964818274  ] 
dist 21=[8.8337276008579239008 ,10.425913706363959074  ] 
dist 22=[8.6396470790877421709 ,10.421835887779457622  ] 
dist 23=[8.4431750722738923220 ,10.373869893916252341  ] 
dist 24=[8.3032621183236160597 ,10.364640348022358541  ] 
dist 25=[8.1769072286037280011 ,10.345241153417822050  ] 
dist 26=[8.0346593431381018509 ,10.339257004706605794  ] 
dist 27=[7.8917280003077902692 ,10.312474953180430117  ] 
dist 28=[7.7626383308100580362 ,10.306656683493379961  ] 
dist 29=[7.6179354750190633207 ,10.289710456213229495  ] 
dist 30=[7.4125566797631115570 ,10.286547641280859388  ] 
dist 31=[7.2019560344770897914 ,8.9164137242178494143 ] 
dist 32=[7.0363671099875504722 ,8.8376945922301536336 ] 
dist 33=[6.8707324788698119153 ,8.6599724434123979687 ] 
dist 34=[6.6599477088884202404 ,8.6274086395789195870 ] 
dist 35=[6.4342141335197702727 ,8.4528416193893838287 ] 
dist 36=[6.2087892269173254177 ,8.4433104014850722413 ] 
dist 37=[5.9385883396383467228 ,8.4268650360671581996 ] 
dist 38=[5.5337669706160861726 ,8.4228013612356542165 ] 
dist 39=[5.1287708529135940511 ,8.0329210637764427551 ] 
dist 40=[4.8578708438709786924 ,8.0000160199677838366 ] 
dist 41=[4.6312219344663895069 ,7.9245830947826700155 ] 
dist 42=[4.4032137062137739346 ,7.9113658121749412023 ] 
dist 43=[4.1896268677094616398 ,7.8132913788073265729 ] 
dist 44=[4.0206581954910960542 ,7.7954030984400852874 ] 
dist 45=[3.8506759859498118847 ,7.7670554632455382169 ] 
dist 46=[3.6330355523600843912 ,7.7599379299139831632 ] 
dist 47=[3.4200770092052989479 ,7.6365191589031936995 ] 
dist 48=[3.2688206756148915105 ,7.6190631601978219882 ] 
dist 49=[3.1326151222617918990 ,7.5912670832575532415 ] 
dist 50=[2.9798540912533702880 ,7.5843607555171726680 ] 
dist 51=[2.8266752136994366906 ,7.4691771077855726654 ] 
dist 52=[2.6887985524540300200 ,7.4566585408228747645 ] 
dist 53=[2.5346189623394907267 ,7.3793887490196692734 ] 
dist 54=[2.3162348107617633271 ,7.2615840116277207639 ] 
dist 55=[2.0996426499249811073 ,6.1229190426145034824 ] 
dist 56=[1.9526303693066554816 ,6.0492395240409754557 ] 
dist 57=[1.8272937225939605012 ,5.9053000607275585104 ] 
dist 58=[1.6973956962818539938 ,5.8701922221433413259 ] 
dist 59=[1.5732751565948734306 ,5.5327750509360602271 ] 
dist 60=[1.4710462214807495050 ,5.4808115457911141245 ] 
dist 61=[1.3644629387277451278 ,5.2793786538694338241 ] 
dist 62=[1.2229267093821590590 ,4.9780281898238164343 ] 
dist 63=[1.0483059293712253148 ,2.6485130359184030593 ] 
dist 64=[.82540885294271535323,2.6182506856504348971 ] 
dist 65=[.61664256217250379914,2.3440358346808626686 ] 
dist 66=[.45165561768044530083,2.2948309808166986369 ] 
dist 67=[.28588151376426687344,2.2333223416401453065 ] 
dist 68=[.07396682522519860154,2.2204738857015251498 ] 
dist 69=[-.1331307906372796821 ,1.8472718384666709567 ] 
dist 70=[-.27964011445877902459,1.8012334337698786721 ] 
dist 71=[-.41092861055028801405,1.7072469569884937212 ] 
dist 72=[-.55715367058649591552,1.6832045491586568015 ] 
dist 73=[-.70314596354360032408,1.5970527701858237106 ] 
dist 74=[-.83350405690421333896,1.5799255955653246219 ] 
dist 75=[-.97838800370363621915,1.5505960320579541643 ] 
dist 76=[-1.1824749471727315998 ,1.5440826855525386873 ] 
dist 77=[-1.3842878704768901144 ,1.0381174551805480635 ] 
dist 78=[-1.5200776381681424802 ,.99471576168162748732] 
dist 79=[-1.6345289977232917281 ,.89597611647680150228] 
dist 80=[-1.7510027465813351329 ,.87964444432726443384] 
dist 81=[-1.8609346820236210303 ,.75535894955571483   ] 
dist 82=[-1.9492237780403948078 ,.73335290364859656478] 
dist 83=[-2.0392507877234326131 ,.69951076107895255539] 
dist 84=[-2.1561348658824598461 ,.69106032498381129531] 
dist 85=[-2.2712501342225340393 ,.55066378294378926039] 
dist 86=[-2.3542038552932639896 ,.53301832379530918264] 
dist 87=[-2.4301229842792893995 ,.4924121874927290972 ] 
dist 88=[-2.5171052368264716099 ,.48632169910065191758] 
dist 89=[-2.6053715715731999236 ,.43416632598385816084] 
dist 90=[-2.6864278343240566992 ,.42498697856532028861] 
dist 91=[-2.7783749586652578986 ,.41277686947083173153] 
dist 92=[-2.9102017924987611934 ,.41001212078452340023] 
dist 93=[-3.0402213037501161522 ,-.2117584342719055773 ] 
dist 94=[-3.1249402599108494926 ,-.12237624049414046088] 
dist 95=[-3.1933519965352872836 ,-.03126635893569134478] 
dist 96=[-3.2581489386607117037 ,.03168224717126955211] 
dist 97=[-3.3162678563486769050 ,.08641631759707466292] 
dist 98=[-3.3579700332258648150 ,.1446940557393891882 ] 
dist 99=[-3.3959580454692127093 ,.20121062339697816686] 
dist 100=[-3.4392216052571093335 ,.24890816685879979159] 
dist 101=[-3.4789715484855922853 ,.29957749810643324505] 
dist 102=[-3.5029063934825429027 ,.36797962595850621274] 
dist 103=[-3.5200210479668165889 ,.43642799439603428806] 
dist 104=[-3.5324928233603381606 ,.48728491652722168843] 
dist 105=[-3.5417586555403490237 ,.53532191124741630369] 
dist 106=[-3.5460517220555659009 ,.59250002616902474385] 
dist 107=[-3.5475580721118761894 ,.65164362422020950947] 
dist 108=[-3.5474605249554090774 ,.70754218000829229046] 
dist 109=[-3.5184566354572185651 ,.77215525451787039061] 
dist 110=[-3.5092884078844372209 ,.86614635284657400114] 
dist 111=[-3.1410057534194714985 ,.96018328615748117743] 
dist 112=[-3.1215367382665839922 ,1.0249811592799831950 ] 
dist 113=[-3.0858890258132482523 ,1.0812093096122650851 ] 
dist 114=[-3.0771417732426429133 ,1.1409822902468086697 ] 
dist 115=[-3.0497926423201274262 ,1.1989636867560548741 ] 
dist 116=[-3.0426901523650805587 ,1.2480301872870928559 ] 
dist 117=[-3.0394168906464046737 ,1.3003150853291726526 ] 
dist 118=[-3.0222993037396546637 ,1.3711691614906293863 ] 
dist 119=[-2.5917241334252356717 ,1.4422949545855169761 ] 
dist 120=[-2.5506945221226987651 ,1.4956681658174911027 ] 
dist 121=[-2.5046980992838727117 ,1.5466453547922584898 ] 
dist 122=[-2.4508492696695669720 ,1.6081922914860355489 ] 
dist 123=[-2.1617580826822239269 ,1.6723820147283806065 ] 
dist 124=[-1.9952603394649671008 ,1.7339299289973518182 ] 
dist 125=[-1.3206578331845475862 ,1.8058001186850080529 ] 
dist 126=[-1.1485988814030949325 ,1.9112724383582587049 ] 
dist 127=[-.48858251924506166345,2.0155559523666062507 ] 
dist 128=[-.48314441782423341443,2.0826728162760858839 ] 
dist 129=[-.47212450344706747168,2.1359104698103001133 ] 
dist 130=[-.46924494854853692526,2.1846893263632787407 ] 
dist 131=[-.45867089647759962733,2.2273063303653830332 ] 
dist 132=[-.45647792131047313947,2.2559026260982361416 ] 
dist 133=[-.45234125476572905106,2.2799228315110887684 ] 
dist 134=[-.45128568032987222508,2.3042414221320998547 ] 
dist 135=[-.08672669655562864875,2.3258779562307429992 ] 
dist 136=[-.07771809429538912234,2.3391720739113356475 ] 
dist 137=[-.05723425357806771491,2.3490068030208736290 ] 
dist 138=[-.05388351078152512508,2.3568062444585544678 ] 
dist 139=[-.02822353093601589734,2.3627747945158021993 ] 
dist 140=[-.02370692043722110037,2.3652862930402756901 ] 
dist 141=[-.01680320993700234334,2.3657661824156507998 ] 
dist 142=[-.01508157795553611164,2.3653200195715919070 ] 
dist 143=[.01318733422038110839,2.2106631130871188086 ] 
dist 144=[.01671175063203010529,2.1960924857831364756 ] 
dist 145=[.02482457200646509433,2.1657650173784824205 ] 
dist 146=[.02598548439421984440,2.1571989197284882070 ] 
dist 147=[.03633636464544013511,2.1221951530010225622 ] 
dist 148=[.03813136511332011719,2.1150454073344619145 ] 
dist 149=[.04041196652783838426,2.0963421041434314610 ] 
dist 150=[.0407903311516206346 ,2.0926877819977365294 ] 
dist 151=[.05298711410823351893,2.0581694553019056655 ] 
dist 152=[.05451449309591195629,2.0512172720430364730 ] 
dist 153=[.05676287573657493267,2.0380686276754767816 ] 
dist 154=[.05733022085863077974,2.0343317537496110752 ] 
dist 155=[.05744917965220105830,2.0195851041127716605 ] 
dist 156=[.05663120475040744336,2.0157981010771036608 ] 
dist 157=[.05500866481319357657,2.0073982691045862682 ] 
dist 158=[.05185176977318838350,2.0044622843459187254 ] 
dist 159=[.04825305517525440188,.91924638810628825376] 
dist 160=[.04486366027381524289,.85963638144023974661] 
dist 161=[.04095548777913297400,.71954143248340843911] 
dist 162=[.03528202658184223758,.69939240118144037854] 
dist 163=[.02885906247657591978,.50941537317212332308] 
dist 164=[.02195372155869072392,.4839493971484742779 ] 
dist 165=[.01332286485837106123,.48458978945984922816] 
dist 166=[-.01136907509656003732,.48468880184311694236] 
dist 167=[-.11691590493070288397,.37755467392831861279] 
dist 168=[-.19150501198215530464,.37292065981249029034] 
dist 169=[-.25822025666510421794,.36402333061059999477] 
dist 170=[-.33228221529781841104,.36178714161056995595] 
dist 171=[-.4060335662180497848 ,.35425998414706734437] 
dist 172=[-.47150713289697572954,.35245320241704255272] 
dist 173=[-.54392650177412105611,.35062013050363045731] 
dist 174=[-.64545273544220885569,.35018001052504769928] 
dist 175=[-.74549963532068230748,.35036685589604849504] 
dist 176=[-.8120037363193937334 ,.35152277479901896458] 
dist 177=[-.86713436746567509554,.35361811102943418548] 
dist 178=[-.92170190239536804989,.35756150348502524037] 
dist 179=[-.97219364513746770794,.36242574251252792628] 
dist 180=[-1.0110264894885805818 ,.36820327168510584897] 
dist 181=[-1.0490323301930132284 ,.37579795800010808592] 
dist 182=[-1.0962176561992956852 ,.38792837519204769936] 
dist 183=[-1.1416223045286947132 ,.40051703760846281168] 
dist 184=[-1.1725079262114186871 ,.40994412893111168625] 
dist 185=[-1.1988909736823629368 ,.4189259200163857014 ] 
dist 186=[-1.2262911860905513152 ,.42973410763151770073] 
dist 187=[-1.2524873521333696745 ,.44098180757100703594] 
dist 188=[-1.2740562259420202858 ,.45172113067762949307] 
dist 189=[-1.2965255909039583789 ,.4642217051620489345 ] 
dist 190=[-1.3263238812439214262 ,.4825121353744962821 ] 
dist 191=[-1.3549790882519265459 ,.5014788776735126485 ] 
dist 192=[-1.3728775754880942468 ,.51668384487895778853] 
dist 193=[-1.3864535978140315389 ,.53215221987553104263] 
dist 194=[-1.3978231434485109400 ,.55217230687767673794] 
dist 195=[-1.4070038223835987496 ,.57376045823589641693] 
dist 196=[-1.4118266886971100004 ,.59549906690751111283] 
dist 197=[-1.4144169714446263764 ,.62166834463835572546] 
dist 198=[-1.4149707948392121717 ,.66097340008610188317] 
dist 199=[-1.4140441220489712604 ,.700326124333624334  ] 
dist 200=[-1.4131445698591381494 ,.72668602564254570368] 
dist 201=[-1.4117943164003720841 ,.74875800623015264594] 
dist 202=[-1.4110003000710130885 ,.77096466509534075279] 
dist 203=[-1.4069134993348860538 ,.79174497678965394545] 
dist 204=[-1.4056496374599699043 ,.80811343867230783923] 
dist 205=[-1.4012264339373960602 ,.82450012725846251851] 
dist 206=[-1.4000905207279578067 ,.84535332621285762124] 
dist 207=[-1.2909771939447016333 ,.86566680069781832093] 
dist 208=[-1.2803212833435550828 ,.87989529761281316645] 
dist 209=[-1.2567133695751780401 ,.8924899245411216252 ] 
dist 210=[-1.2506674659445447504 ,.90627005271526444056] 
dist 211=[-1.2208216591796857100 ,.91987498259457866795] 
dist 212=[-1.2149290486400045842 ,.93176904232434911715] 
dist 213=[-1.1980807625796687767 ,.94477250676300698342] 
dist 214=[-1.1764901935343335921 ,.962813598298680291  ] 
dist 215=[-1.0523618508358557820 ,.98050803495009528409] 
dist 216=[-1.0453418148769216821 ,.99212532766653625464] 
dist 217=[-1.0359360757458335207 ,1.0015954895264887721 ] 
dist 218=[-1.0328514851171168865 ,1.0107042005317524535 ] 
dist 219=[-.97122920681745227961,1.0189593234892643252 ] 
dist 220=[-.96521156512325460084,1.0250162364202466614 ] 
dist 221=[-.92027242178734925394,1.0306650309826518759 ] 
dist 222=[-.90296442283651064304,1.0372881855138901540 ] 
dist 223=[-.62389517215346899863,1.0434666368976591786 ] 
dist 224=[-.60481001008943695096,1.0473371855375842154 ] 
dist 225=[-.56030150184155586668,1.0502845757288526695 ] 
dist 226=[-.55319258843535282326,1.0527715847139734538 ] 
dist 227=[-.49325050700925142292,1.0547922176437853719 ] 
dist 228=[-.48231391856661804791,1.0558746825849010924 ] 
dist 229=[-.46731514203709962191,1.0564840719425215325 ] 
dist 230=[-.46288237247235723929,1.0566129444483176764 ] 
dist 231=[-.38070097106670836766,1.0563565448831256532 ] 
dist 232=[-.37015900044712931992,1.0558966251940115962 ] 
dist 233=[-.34770628536369025288,1.0542779841340980248 ] 
dist 234=[-.34223060179321686265,1.0533601350450252908 ] 
dist 235=[-.31801320216855422756,1.0476400021130423481 ] 
dist 236=[-.31365836243624295318,1.0460448576662308255 ] 
dist 237=[-.30313692220890561544,1.0428842789813020539 ] 
dist 238=[-.30158608304647180574,1.0417668895985712510 ] 
dist 239=[-.19281130331226395567,1.0188916407429687944 ] 
dist 240=[-.18266154696462203303,1.0152984825426536329 ] 
dist 241=[-.15912994758243812286,1.0073882856961133913 ] 
dist 242=[-.15543828120895534186,1.0049073067860204053 ] 
dist 243=[-.12437890569050901913,.99365509584178939876] 
dist 244=[-.11879392958181650651,.99119335268466986266] 
dist 245=[-.11112695684036163027,.98503515702939287504] 
dist 246=[-.10893789253664881832,.9832308807713936233 ] 
dist 247=[-.06888071597422281012,.89279610235938667709] 
dist 248=[-.06382228500246542543,.88367585492421952131] 
dist 249=[-.05297888734176880204,.86242905550847470655] 
dist 250=[-.05054488783939757899,.85821611745280382159] 
dist 251=[-.03881255591284174061,.81802005797745759811] 
dist 252=[-.03676607200986390006,.81022887202571215051] 
dist 253=[-.03205804848933607259,.78496974045377664025] 

8 phat 2 dirichlet min maxes function [0, 2, 1, 0, 1, 2, 1, 0, 1] 
dist 0=[13.111106745161383927  ,13.111106745161383927  ] 
dist 1=[13.098608463888256318  ,13.126198485407666072  ] 
dist 2=[13.085537538973735807  ,13.139970211819911455  ] 
dist 3=[13.062389477649241467  ,13.147184619192847854  ] 
dist 4=[13.019991130507740693  ,13.150992542111435607  ] 
dist 5=[12.974568157872484384  ,13.151134336459748528  ] 
dist 6=[12.935906152135376534  ,13.149141199482034946  ] 
dist 7=[12.863586428627243275  ,13.146288037912890703  ] 
dist 8=[12.764593815303765917  ,13.138383855462115296  ] 
dist 9=[12.680068056634933509  ,13.134060287107155675  ] 
dist 10=[12.589333617459489196  ,13.107426573353761436  ] 
dist 11=[12.465508767105567697  ,13.100026004119140056  ] 
dist 12=[12.328758712799081873  ,13.081982264718940085  ] 
dist 13=[12.186333845723546019  ,13.074862771914961889  ] 
dist 14=[12.011393976722844255  ,12.974465279620877028  ] 
dist 15=[11.744612542836458327  ,12.957857342286322572  ] 
dist 16=[11.475514726588552690  ,12.917897758869890774  ] 
dist 17=[11.291310239231640941  ,12.906207584517406436  ] 
dist 18=[11.132676161772470836  ,12.840258045827657244  ] 
dist 19=[10.965834088303502987  ,12.825422435288915771  ] 
dist 20=[10.804990837184731091  ,12.796971280242538585  ] 
dist 21=[10.670344384685803737  ,12.788445083834385935  ] 
dist 22=[10.528085676089678332  ,12.396054026990867903  ] 
dist 23=[10.336796348825510751  ,12.351708777722292241  ] 
dist 24=[10.145351508274116831  ,12.268244087849467605  ] 
dist 25=[10.002468802725927080  ,12.247252572873786724  ] 
dist 26=[9.8667220973835012870 ,11.963505729405817942  ] 
dist 27=[9.5553153270082174236 ,11.910994072350897571  ] 
dist 28=[9.0116343420134494989 ,11.653576809320915292  ] 
dist 29=[8.4656562789727271403 ,10.327310083172591920  ] 
dist 30=[8.0963739460464637441 ,9.8167139384923877300 ] 
dist 31=[7.7831688736780688679 ,9.8066132320150712318 ] 
dist 32=[7.4614381059843370178 ,9.5074500485844181101 ] 
dist 33=[7.1560321343744741824 ,9.4693425348619432462 ] 
dist 34=[6.9081064486899587756 ,9.3360220706252638547 ] 
dist 35=[6.6529789255836977112 ,9.3061720615967536899 ] 
dist 36=[6.3187680739022359734 ,9.2636524093121542596 ] 
dist 37=[5.9884155753149392379 ,9.2505812358154313394 ] 
dist 38=[5.7487148031658537099 ,8.2740416984565668320 ] 
dist 39=[5.5277576290760307962 ,8.2575509721113362668 ] 
dist 40=[5.2723571111041003019 ,8.0214890648069525390 ] 
dist 41=[5.0120405743163389142 ,7.9891744986195688477 ] 
dist 42=[4.7714193493655026817 ,7.9166122105020011320 ] 
dist 43=[4.4973065938829342971 ,7.9020720856278047048 ] 
dist 44=[4.1030464296111104696 ,7.8112411451992495600 ] 
dist 45=[3.7098191820399962148 ,7.7944579842183818197 ] 
dist 46=[3.4398344772991496207 ,7.7634101902679079497 ] 
dist 47=[3.2064219778942505402 ,7.7558667062964051206 ] 
dist 48=[2.9594502338729287441 ,6.7154739917199570774 ] 
dist 49=[2.7204030074104592807 ,6.6907526993988309274 ] 
dist 50=[2.5186778306632819832 ,6.5926468745285718827 ] 
dist 51=[2.3041002762748384532 ,6.5738119109730090542 ] 
dist 52=[2.0136446788259549333 ,6.5268198975322985145 ] 
dist 53=[1.7219813422014034748 ,6.5188698629754615382 ] 
dist 54=[1.5025692655673617954 ,5.4926253128757132854 ] 
dist 55=[1.2923685271431549182 ,5.4708402020844099265 ] 
dist 56=[1.0375387361941179183 ,4.8019780368042075652 ] 
dist 57=[.77107224581803986997,4.7328671206288829155 ] 
dist 58=[.51432490566728130889,4.6222102707400941490 ] 
dist 59=[.21345711327253368511,4.4884552082166000695 ] 
dist 60=[-.22947876928324006918,4.1629199844586840474 ] 
dist 61=[-.66952641631735031286,2.3579652450806637366 ] 
dist 62=[-.95884485839446587242,2.3103447116722005993 ] 
dist 63=[-1.1953960963108119112 ,2.2993269498573500190 ] 
dist 64=[-1.4243980978255293304 ,1.4437763767472122318 ] 
dist 65=[-1.6331883617153431405 ,1.3708775217054015274 ] 
dist 66=[-1.7889035156439375770 ,1.2051560426148671723 ] 
dist 67=[-1.9368049852873899673 ,1.1779165450028033434 ] 
dist 68=[-2.1143498998034643706 ,.97007871659682611209] 
dist 69=[-2.2824680946310747685 ,.93340679862755917489] 
dist 70=[-2.3926693744284837312 ,.87719047269911292089] 
dist 71=[-2.4824376178071013701 ,.86317008157022223303] 
dist 72=[-2.5688343150345940780 ,.6317896888310487712 ] 
dist 73=[-2.6473296282533782361 ,.6028196623095693990 ] 
dist 74=[-2.7055013815623618717 ,.5361972335223244282 ] 
dist 75=[-2.7604472388490033312 ,.5263825255960398822 ] 
dist 76=[-2.8260554066056294163 ,.4412189309937318709 ] 
dist 77=[-2.8878198647721374029 ,.4263396432648272169 ] 
dist 78=[-2.9273924580995343247 ,.4068189929950814943 ] 
dist 79=[-2.9586676898640274282 ,.4028183201251733122 ] 
dist 80=[-2.9872309822507659377 ,-.3696885970523296133 ] 
dist 81=[-3.0122038652809028133 ,-.41857129528676327113] 
dist 82=[-3.0291131163475264877 ,-.52740029009436213363] 
dist 83=[-3.0435267923410315343 ,-.54653644804559841055] 
dist 84=[-3.0585161037378149860 ,-.67529456832276281943] 
dist 85=[-3.0715971707245978685 ,-.697534809199403685  ] 
dist 86=[-3.1347940934765992890 ,-.73691611374143727299] 
dist 87=[-3.1836873807933469959 ,-.74522998589448617585] 
dist 88=[-3.2206843766815397911 ,-.85845769833176944746] 
dist 89=[-3.2515584701233956231 ,-.87378403724593474651] 
dist 90=[-3.2764454940772550859 ,-.90272371604489747722] 
dist 91=[-3.2894975353426325703 ,-.90927331012366263476] 
dist 92=[-3.2967438474558432743 ,-.92729656126991454858] 
dist 93=[-3.2984015410365300487 ,-.92932081077298616398] 
dist 94=[-3.2957999178858885995 ,-.92623389232658129253] 
dist 95=[-3.2943953894638304695 ,-.9153593798230568645 ] 
dist 96=[-3.2927337350906231502 ,-.90186101991903917971] 
dist 97=[-3.2906393515565586074 ,-.88828044556844413061] 
dist 98=[-3.2875464603464279800 ,-.84906686440758618081] 
dist 99=[-3.2850121158521246643 ,-.74259749592345353614] 
dist 100=[-3.2809986095326012568 ,-.60393894863041326014] 
dist 101=[-3.2790038762812035728 ,-.4674066184532028549 ] 
dist 102=[-2.9734911790486194746 ,-.36943704567282696718] 
dist 103=[-2.9457041676835501025 ,-.28029748646272308479] 
dist 104=[-2.8857686247992349017 ,-.17906873576387952987] 
dist 105=[-2.8742069860100934408 ,-.07697396800973012856] 
dist 106=[-2.8739257257751904692 ,.01563031680705518437] 
dist 107=[-2.8725255319967633687 ,.11966595142569385797] 
dist 108=[-2.8610656908717706503 ,.26747160643549286246] 
dist 109=[-2.8478402865166235134 ,.4139068213454085266 ] 
dist 110=[-2.7774790815222230293 ,.51246371271278938136] 
dist 111=[-2.7482272997230942110 ,.59549301552639357856] 
dist 112=[-2.6340798663532503230 ,.67984141865472312024] 
dist 113=[-2.6266772695475150814 ,.75928778737729928666] 
dist 114=[-2.5962751945482116591 ,.82271724194147128259] 
dist 115=[-2.5898116705474958892 ,.88700961812017921155] 
dist 116=[-2.5729232396487976515 ,.96990894605137298121] 
dist 117=[-2.5690787034443229303 ,1.0511970722817237860 ] 
dist 118=[-1.1534988592632238435 ,1.1090481001447648257 ] 
dist 119=[-1.0744394714844959078 ,1.1612198886954556836 ] 
dist 120=[-.8889766476718502407 ,1.2198001352263412778 ] 
dist 121=[-.8622172556112515494 ,1.2785351223022167596 ] 
dist 122=[-.61185920998926033332,1.3313278334674341027 ] 
dist 123=[-.5669296732492063371 ,1.3902738033996715919 ] 
dist 124=[-.51255840167744446387,1.4736186075378819882 ] 
dist 125=[-.50276061975277136825,1.5554132740847143440 ] 
dist 126=[-.15591874387513738217,1.6081610212493076613 ] 
dist 127=[-.11367102856151745351,1.6501167319729642068 ] 
dist 128=[-.02808167681890866133,1.6887534391132103254 ] 
dist 129=[-.00648285028166955174,1.7226430962415894170 ] 
dist 130=[.06898703697876731057,1.7456155571514182792 ] 
dist 131=[.08424793809633025591,1.7651636514060194173 ] 
dist 132=[.10544681415886674279,1.7853604851174302119 ] 
dist 133=[.11101470549590103904,1.8033443829087514648 ] 
dist 134=[.56702244205026156401,1.8140427119938893198 ] 
dist 135=[.60460559309888778459,1.8215364913054321969 ] 
dist 136=[.69057424870920738572,1.8267034762167843049 ] 
dist 137=[.70341304946941970452,1.8300281294693631258 ] 
dist 138=[.81133790061087098341,1.8306612681027816699 ] 
dist 139=[.82997593626593089898,1.8293441227366181317 ] 
dist 140=[.85553606558444105405,1.8289296805855825298 ] 
dist 141=[.86121773859687502613,1.7278873701339013196 ] 
dist 142=[.97771517298895400705,1.7175263907872602100 ] 
dist 143=[.99144841164750889148,1.7014214944155277111 ] 
dist 144=[1.0217012235306800778 ,1.7280734816295487802 ] 
dist 145=[1.0009749204312453808 ,1.7536207180068836886 ] 
dist 146=[.96849920641536350017,1.7767260653402653712 ] 
dist 147=[.92949462262459975638,1.7936139873457898014 ] 
dist 148=[.8710269521528397123 ,1.8093080073339840297 ] 
dist 149=[.80982960144274102201,1.8276406989131346037 ] 
dist 150=[.75990970280528833152,1.8444010446535417718 ] 
dist 151=[.70834665978675085607,1.8538076036931772919 ] 
dist 152=[.64057812387556122519,1.8597006370250799327 ] 
dist 153=[.56699906005060472317,1.8624096836367755701 ] 
dist 154=[.49220172672418860701,1.8637198540963239310 ] 
dist 155=[.40165505098084067904,1.8640180765133926421 ] 
dist 156=[.2651006402548797544 ,1.8636366645426046022 ] 
dist 157=[.12821824626574726016,1.8628005080334747763 ] 
dist 158=[.03635990148690762239,1.8288788634170916836 ] 
dist 159=[-.04073173072783860457,1.8234672417371802475 ] 
dist 160=[-.11856850592214019299,1.8137976977038958941 ] 
dist 161=[-.19157210704043096007,1.8111088562710703704 ] 
dist 162=[-.24933807597678129511,1.8010758269317885500 ] 
dist 163=[-.30740639103068391341,1.7981302882130773384 ] 
dist 164=[-.3816191975123244825 ,1.7926400485391588922 ] 
dist 165=[-.45405338697816352581,1.7908136596988976726 ] 
dist 166=[-.50500986662480795854,1.5858718621243318438 ] 
dist 167=[-.55034130884999597695,1.5672933748734827377 ] 
dist 168=[-.60028340802787953483,1.5266092279630009489 ] 
dist 169=[-.64978854058951591719,1.5165896004616352801 ] 
dist 170=[-.69337289301676566579,1.4676862374388473757 ] 
dist 171=[-.74322600930823817093,1.4583652124324803794 ] 
dist 172=[-.82085652315744082875,1.4377019384771261843 ] 
dist 173=[-.89690225847174392046,1.4320432517902308672 ] 
dist 174=[-.94665425738283244276,1.3794631054128021314 ] 
dist 175=[-.98701160036746593285,1.3709268847002293931 ] 
dist 176=[-1.0254915571713189786 ,1.3524114127500378514 ] 
dist 177=[-1.0601369195541249400 ,1.3470178556256794309 ] 
dist 178=[-1.0851610812314708463 ,1.3241264755708670369 ] 
dist 179=[-1.1081020908579099603 ,1.3194641419816732208 ] 
dist 180=[-1.1344175559867475901 ,1.3080303044669532496 ] 
dist 181=[-1.1587390053161503180 ,1.3052732307995977992 ] 
dist 182=[-1.1737067237378391804 ,.69181095085993714188] 
dist 183=[-1.1847894031894996007 ,.67015094774234309397] 
dist 184=[-1.1935762837345955507 ,.61968162426467293173] 
dist 185=[-1.2004477852900881340 ,.61164944151970496905] 
dist 186=[-1.2038715383018273225 ,.54387646473611999036] 
dist 187=[-1.2055277284968272760 ,.5315369058044235752 ] 
dist 188=[-1.2057392060170437074 ,.51463723712906322923] 
dist 189=[-.5652376650529286427 ,.50964828148967676015] 
dist 190=[-.57368695261403248918,.41745876123001944426] 
dist 191=[-.59943222305823611137,.4056549789677729925 ] 
dist 192=[-.64084664823969396569,.38052058318996293235] 
dist 193=[-.68628621994481521272,.37442660201940934722] 
dist 194=[-.73122858833444884798,.34738531839052665848] 
dist 195=[-.77065486620293323525,.34253372956496593165] 
dist 196=[-.81582740784964614264,.33087251124935533766] 
dist 197=[-.88680645824099074105,.32913673781419171247] 
dist 198=[-.95628530892905150356,.2091745063809145659 ] 
dist 199=[-1.0016946939433317466 ,.19798810999820480371] 
dist 200=[-1.0384838873606906824 ,.17209792915899472836] 
dist 201=[-1.0734924552681513786 ,.168018229597004695  ] 
dist 202=[-1.1049715567145725940 ,.13399226280061418325] 
dist 203=[-1.1276471436520805017 ,.12788265246067945975] 
dist 204=[-1.1483758146140324818 ,.11941404986914802158] 
dist 205=[-1.1720695215954120567 ,.11699141102218400417] 
dist 206=[-1.1939817486531389214 ,.07361791019967414599] 
dist 207=[-1.2075866872836983609 ,.06813786833516929247] 
dist 208=[-1.2178050363161051019 ,.05633279569634048897] 
dist 209=[-1.2261751845425693746 ,.05374588181913859013] 
dist 210=[-1.2327849650051625915 ,.04080034500760043278] 
dist 211=[-1.2359640803289080537 ,.03854060926458951060] 
dist 212=[-1.2375767990487311016 ,.03349793044504282505] 

8 phat 2 dirichlet min maxes function [1, 2, 0, 0, 0, 0, 0, 2] 
dist 0=[13.247329119194168446  ,13.247329119194168446  ] 
dist 1=[13.219074364595216102  ,13.263703726910670780  ] 
dist 2=[13.164280707482830244  ,13.270980429050417549  ] 
dist 3=[13.104545289285039835  ,13.275833327025613721  ] 
dist 4=[13.056528514912519078  ,13.282514530279580980  ] 
dist 5=[13.007525266557599063  ,13.287982253238087901  ] 
dist 6=[12.943849097993730684  ,13.287984039516347326  ] 
dist 7=[12.875014297792192101  ,13.284602422945719040  ] 
dist 8=[12.805383173368045864  ,13.276537007003530882  ] 
dist 9=[12.721295872470474690  ,13.187606186240756682  ] 
dist 10=[12.594651132514932075  ,13.171512000471134726  ] 
dist 11=[12.461715545742205209  ,13.139610834809098293  ] 
dist 12=[12.352471741485837662  ,13.129711240555169434  ] 
dist 13=[12.238845984960398366  ,13.085923110250440047  ] 
dist 14=[12.088388435507284694  ,13.075570615377022207  ] 
dist 15=[11.827863552819462217  ,13.045450055588642112  ] 
dist 16=[11.634672931084610432  ,13.038315736196134739  ] 
dist 17=[11.455674935966253749  ,12.439037189947852080  ] 
dist 18=[11.243988595251402470  ,12.381167374635266885  ] 
dist 19=[10.929815535992189142  ,12.251879237958551363  ] 
dist 20=[10.703832888388961082  ,12.221193850672034690  ] 
dist 21=[10.497529147179915282  ,12.056164043696233407  ] 
dist 22=[10.262053300096146866  ,12.024096635275733946  ] 
dist 23=[9.9485746386514464225 ,11.958350493336227779  ] 
dist 24=[9.6817455737801674248 ,11.939807686912126201  ] 
dist 25=[9.4126478957770151815 ,11.723019470336404334  ] 
dist 26=[9.0674157974058895311 ,11.690806476227548244  ] 
dist 27=[8.6965387899569340666 ,11.610951424710679188  ] 
dist 28=[8.3248865202582943027 ,11.596982623763763441  ] 
dist 29=[7.8786933321618566292 ,11.468818080741177891  ] 
dist 30=[7.2097264950002784701 ,11.442965163269929785  ] 
dist 31=[6.5396404046378194986 ,11.410355733190479650  ] 
dist 32=[6.0889706033326341657 ,11.398511273238381921  ] 
dist 33=[5.7094859586247275700 ,10.280853408432093974  ] 
dist 34=[5.3240678486984463233 ,10.268900624746742050  ] 
dist 35=[4.9609468729648852222 ,8.4063393994974282683 ] 
dist 36=[4.6706269149048372696 ,8.3538757371909823646 ] 
dist 37=[4.3758939790725951952 ,7.8623832311716919881 ] 
dist 38=[3.9951223221135593320 ,7.7730851269955038945 ] 
dist 39=[3.6212381097492360162 ,7.6652367539162433381 ] 
dist 40=[3.3540464082889559803 ,7.6436145335377661311 ] 
dist 41=[3.0851082620059052378 ,6.9283638384142448140 ] 
dist 42=[2.7019117956055740518 ,6.8396117090637154359 ] 
dist 43=[2.3265595604774127740 ,6.6610120172036029728 ] 
dist 44=[2.0598247350995232020 ,6.6155773742231158385 ] 
dist 45=[1.8196240152114900685 ,6.4554147073513051430 ] 
dist 46=[1.5503808714347994207 ,6.4221568770493621597 ] 
dist 47=[1.2400706357582639820 ,6.3720525604276704628 ] 
dist 48=[.9726189819201258878 ,6.3587086025495052038 ] 
dist 49=[.7452454482057245737 ,5.2420042310546013067 ] 
dist 50=[.3864762938670053466 ,5.1474408180259223810 ] 
dist 51=[.00858743424476704280,4.9334429581384836680 ] 
dist 52=[-.24595870619688360972,4.8964871997753343527 ] 
dist 53=[-.46076895348144234481,4.6303811523682884385 ] 
dist 54=[-.67975085857454709723,4.5832487833938750526 ] 
dist 55=[-.8866306474762465937 ,4.5056953221108083058 ] 
dist 56=[-1.0530458209677260901 ,4.4877616590097757813 ] 
dist 57=[-1.2229574787337450374 ,4.2005748916074065009 ] 
dist 58=[-1.4438266837141674822 ,4.1635216401930166484 ] 
dist 59=[-1.6614480322198255879 ,4.0800799481664505703 ] 
dist 60=[-1.8183742479719222636 ,4.0657510006725116140 ] 
dist 61=[-1.9620903219956230500 ,3.9635556228835814623 ] 
dist 62=[-2.1268855389951706628 ,3.9455956272672504183 ] 
dist 63=[-2.3642954474191008877 ,3.9158586330224936529 ] 
dist 64=[-2.5681382648393664408 ,3.9091061685435982634 ] 
dist 65=[-2.7329754802575466156 ,2.4397975230887527427 ] 
dist 66=[-2.8895137613010748874 ,2.4330775706102725322 ] 
dist 67=[-3.1194082931540934123 ,.8943022928094314912 ] 
dist 68=[-3.2791597377189803330 ,.8525640131925458954 ] 
dist 69=[-3.4071055463084401860 ,.4686692323223693536 ] 
dist 70=[-3.5265313862646833978 ,.4006779409792439187 ] 
dist 71=[-3.6324815510021192939 ,.3174572128961861649 ] 
dist 72=[-3.7065325047116424507 ,.3034004649917154787 ] 
dist 73=[-3.7720012918100589536 ,-.1987182780727796644 ] 
dist 74=[-3.8436326331546032692 ,-.2591787220691499344 ] 
dist 75=[-3.9089445123180939588 ,-.3819148718717926831 ] 
dist 76=[-3.9491376096800863409 ,-.4126838252508373527 ] 
dist 77=[-3.9789652809685715142 ,-.5194413694543061339 ] 
dist 78=[-4.0028120843485297133 ,-.5406746289976924759 ] 
dist 79=[-4.0212301186935933766 ,-.5688043422745909194 ] 
dist 80=[-4.0293413178209913592 ,-.5741837048186223344 ] 
dist 81=[-4.0326100475122106138 ,-1.1667565536629255886 ] 
dist 82=[-4.0319871875790465958 ,-1.2150228165285757587 ] 
dist 83=[-3.8591083751963263511 ,-1.3246505055615765940 ] 
dist 84=[-3.8413184630087638670 ,-1.3411566402994450377 ] 
dist 85=[-3.8049779373579807577 ,-1.4762711166541271502 ] 
dist 86=[-3.7944440266408582501 ,-1.4994263247923883358 ] 
dist 87=[-3.7505914091120104095 ,-1.5320268531166180039 ] 
dist 88=[-3.7410394798637708745 ,-1.5396321774020587067 ] 
dist 89=[-3.7157891417741643680 ,-1.6772710790888305829 ] 
dist 90=[-3.7097608637908429316 ,-1.6936357294518494084 ] 
dist 91=[-3.6608883678215313080 ,-1.7289170552393635693 ] 
dist 92=[-3.6505776911528518310 ,-1.7345414627500237596 ] 
dist 93=[-3.6300027120078487564 ,-1.7706600117583089618 ] 
dist 94=[-3.6237142601267149682 ,-1.6787890285473498007 ] 
dist 95=[-3.5962752771880384835 ,-1.3684702086998860396 ] 
dist 96=[-3.5898816363806667088 ,-1.1596374671413385220 ] 
dist 97=[-3.5716805740302674392 ,-.98374622783781786493] 
dist 98=[-3.5672997698590864136 ,-.80514341926863861339] 
dist 99=[-2.1972587521289220883 ,-.63699358385609671982] 
dist 100=[-2.1964915036118747643 ,-.50289777982579325567] 
dist 101=[-2.1954490606039726584 ,-.36713712657065627095] 
dist 102=[-2.1945696971582968353 ,-.19232862155127620442] 
dist 103=[-2.1918075835266194983 ,-.02108614036692177394] 
dist 104=[-2.1905875087821863144 ,.10041641955477403284] 
dist 105=[-2.1874578654292456378 ,.20958606114952026576] 
dist 106=[-2.1860561960152933460 ,.33151556419595376928] 
dist 107=[-2.1781233152903868328 ,.45334979024136421306] 
dist 108=[-2.1760281446645582131 ,.56213968201373043118] 
dist 109=[-2.1711360357755971889 ,.68298344968230242804] 
dist 110=[-2.1692995078209375969 ,.85301854700968864934] 
dist 111=[-2.1598238194558167165 ,1.0208201811932043013 ] 
dist 112=[-2.1574969099448813152 ,1.1327337210074625685 ] 
dist 113=[-2.1517470746325903435 ,1.2259111144285656360 ] 
dist 114=[-2.1496023131886491375 ,1.3187936461555349099 ] 
dist 115=[-1.6097030674766895121 ,1.4051615434019459962 ] 
dist 116=[-1.5768395942668594783 ,1.4722897982717430417 ] 
dist 117=[-1.5113016477349244487 ,1.5386572814107427697 ] 
dist 118=[-1.4946802801309330961 ,1.6219847490597464624 ] 
dist 119=[-1.4366431480537356751 ,1.7026273298008203632 ] 
dist 120=[-1.4242644753671231122 ,1.7582595579155152849 ] 
dist 121=[-1.4069972459613421623 ,1.8066193543889462876 ] 
dist 122=[-1.3929966533626594174 ,1.8581824006416312292 ] 
dist 123=[-.95708791250687683802,1.9269367315130062076 ] 
dist 124=[-.91527717902836132281,1.9805294763193515953 ] 
dist 125=[-.86460370774702801834,2.0263055261579513056 ] 
dist 126=[-.81411741228283294135,2.0738427921334737741 ] 
dist 127=[-.54081845966345186461,2.1192922513715527619 ] 
dist 128=[-.38645210961112585707,2.1567209442452906978 ] 
dist 129=[1.0997885215031333520 ,2.1957222561393048518 ] 
dist 130=[1.1018871974764470238 ,2.2474633325031442043 ] 
dist 131=[1.4289134963565916404 ,2.2971639231491136888 ] 
dist 132=[1.4369003196693476563 ,2.3280059590412835468 ] 
dist 133=[1.4523157702490710556 ,2.3511672499191914893 ] 
dist 134=[1.4552399305007938926 ,2.3701517041333375494 ] 
dist 135=[1.4695302799766491225 ,2.3852148262162078379 ] 
dist 136=[1.4691280598693618396 ,2.3926938004105358172 ] 
dist 137=[1.4641968070149993107 ,2.3966084111914661829 ] 
dist 138=[1.4517656067383820879 ,2.3974166414417549034 ] 
dist 139=[1.4353624701714615822 ,2.3905692131737257782 ] 
dist 140=[1.4145484672454740913 ,2.3881373972322889228 ] 
dist 141=[1.3863726577310032518 ,2.3851612796803833584 ] 
dist 142=[1.3405327513600469908 ,2.3834110690599232513 ] 
dist 143=[1.2926666778272812291 ,2.3775644831179470285 ] 
dist 144=[1.2563885647164681872 ,2.3752561830577391021 ] 
dist 145=[1.2214055793454963179 ,2.3695978572043307278 ] 
dist 146=[1.1787166422893744465 ,2.3671569472478496464 ] 
dist 147=[1.1339801878092668098 ,2.1481287299324918258 ] 
dist 148=[1.0908091674516846298 ,2.1276094756478243061 ] 
dist 149=[1.0402106387621982037 ,2.0827885021420078664 ] 
dist 150=[.96577362023322892397,2.0710462988600182970 ] 
dist 151=[.88842104319791777046,2.0167439767690385749 ] 
dist 152=[.82616379856704161643,2.0061573145928068917 ] 
dist 153=[.76260497309967128079,1.9818760433386927740 ] 
dist 154=[.68004713734994398378,1.9755061148736002750 ] 
dist 155=[.59087797357367468599,1.9131347786472013978 ] 
dist 156=[.50088225395186685666,1.9028806919874781564 ] 
dist 157=[.39239621062167302633,1.8799457125367526082 ] 
dist 158=[.2292898901280105413 ,1.8734239028108626459 ] 
dist 159=[.06592622684692955677,1.8426481950786081721 ] 
dist 160=[-.04358899032144871696,1.8362305147101382810 ] 
dist 161=[-.13538492569590008079,1.8220315002740375975 ] 
dist 162=[-.22789500853115418058,1.8175738981365433780 ] 
dist 163=[-.31456086220384158819,1.0177235854774802485 ] 
dist 164=[-.38298770968482535783,.98889633123246410303] 
dist 165=[-.45164028535962412046,.921473893927216631  ] 
dist 166=[-.53920894187792927147,.91080128389691301548] 
dist 167=[-.62460948920553530089,.81935907778467151843] 
dist 168=[-.68459256792837876577,.80263802672892479239] 
dist 169=[-.73786028619195165238,.78012098756968138939] 
dist 170=[-.79640830231134021808,.77344645629371572762] 
dist 171=[-.85436960291049633191,.64572185459430837312] 
dist 172=[-.90529135621530268828,.62934530551260678442] 
dist 173=[-.96117280779605105324,.59478954713462443249] 
dist 174=[-1.0436914747900093966 ,.58600923608415444129] 
dist 175=[-1.1338544057764071530 ,.54986052864545363264] 
dist 176=[-1.1928319728189377167 ,.543155204606168309  ] 
dist 177=[-1.2406652350429551021 ,.52770747642680930833] 
dist 178=[-1.2862653499205489827 ,.5247335644718269028 ] 
dist 179=[-1.3273198266514710422 ,.34604205874874266099] 
dist 180=[-1.3569763646838192588 ,.32965935249052822303] 
dist 181=[-1.3841694279126632080 ,.29118795437341514958] 
dist 182=[-1.4153730516724019045 ,.28555526535331430811] 
dist 183=[-1.4456912392962631717 ,.23334121435036350758] 
dist 184=[-1.4768709886432737488 ,.22391518519057516366] 
dist 185=[-1.5054793523315912833 ,.21237725213928970348] 
dist 186=[-1.5383358071353812971 ,.21006862785858116909] 
dist 187=[-1.5687217486359444498 ,.13650764671001479103] 
dist 188=[-1.5874512216355272355 ,.12744028271651167252] 
dist 189=[-1.6013563491108325458 ,.10903735311061232681] 
dist 190=[-1.6124512523037773085 ,.10435047826827775483] 
dist 191=[-1.6211622633793595262 ,.08773493452019722340] 
dist 192=[-1.6255348240372337771 ,.08437098881216426961] 
dist 193=[-1.6276932045681612720 ,.07911899391958128234] 

8 phat 2 dirichlet min maxes function [2, 0, 2, 2, 1, 2, 2, 0, 1] 
dist 0=[12.606078214601116610  ,12.606078214601116610  ] 
dist 1=[12.601449536626333896  ,12.610162280090754858  ] 
dist 2=[12.587010379836218193  ,12.612587635937291663  ] 
dist 3=[12.566823593072100280  ,12.612024021284142924  ] 
dist 4=[12.542336824075645524  ,12.602904873557310493  ] 
dist 5=[12.503977933914148948  ,12.599130899797758093  ] 
dist 6=[12.450608173869860276  ,12.586463922613261767  ] 
dist 7=[12.363219896945224982  ,12.581180999871117007  ] 
dist 8=[12.271678515820027812  ,12.518928285451716336  ] 
dist 9=[12.201699203952823599  ,12.506040286970494448  ] 
dist 10=[12.095199375488366165  ,12.501027178576521200  ] 
dist 11=[11.950701465167276684  ,12.477132101045058168  ] 
dist 12=[11.847376251226637345  ,12.471352159691616093  ] 
dist 13=[11.753612784383280868  ,12.463525753473999472  ] 
dist 14=[11.647363428858642034  ,12.406766045612409313  ] 
dist 15=[11.540208227683848783  ,12.268532417458345450  ] 
dist 16=[11.442825917043986774  ,11.830678628822055462  ] 
dist 17=[11.333187010455590893  ,11.808431530036398784  ] 
dist 18=[11.177017445892009670  ,11.749877300708920838  ] 
dist 19=[11.016693632498981714  ,11.741381795480103120  ] 
dist 20=[10.851180661719961673  ,11.636899294158272406  ] 
dist 21=[10.662833748351683726  ,11.615431253675344503  ] 
dist 22=[10.434850236475892882  ,11.595410010845884666  ] 
dist 23=[10.090882996920069091  ,11.591273859532491590  ] 
dist 24=[9.7452753683515951223 ,11.339279512546397476  ] 
dist 25=[9.5107308891967752142 ,11.305258870204220631  ] 
dist 26=[9.3109047851287214557 ,11.251098377763687912  ] 
dist 27=[9.1041398874610714776 ,11.236790866740945675  ] 
dist 28=[8.9068771790675842004 ,10.975010341453568568  ] 
dist 29=[8.7450503007815135878 ,10.946131449465404480  ] 
dist 30=[8.5769639688881526186 ,10.759135308179027927  ] 
dist 31=[8.0936506222660259127 ,10.467193575460674550  ] 
dist 32=[7.5470911536186622022 ,9.4724261126930696434 ] 
dist 33=[7.1784257119606526156 ,9.3962400086747362419 ] 
dist 34=[6.8668160749679342148 ,9.3768752355913600989 ] 
dist 35=[6.5484217353879998289 ,9.1139689165550612759 ] 
dist 36=[6.2472259711643111292 ,9.0769252438285110216 ] 
dist 37=[6.0043917952903208040 ,8.9871698550383609869 ] 
dist 38=[5.7560033605130818280 ,8.9721277608772065268 ] 
dist 39=[5.4325922354499691996 ,8.8366581363953183885 ] 
dist 40=[5.1138173119738514216 ,8.8102218812454529469 ] 
dist 41=[4.8839671597403975844 ,8.7764011677284392310 ] 
dist 42=[4.6735472599855036005 ,8.7647193281070579818 ] 
dist 43=[4.1976027083593416785 ,6.5785236895383874601 ] 
dist 44=[3.7742569031808787505 ,6.3571300807245802067 ] 
dist 45=[3.4185232616195954483 ,6.3175091847456680242 ] 
dist 46=[3.0583836504361085040 ,6.2534303356696264884 ] 
dist 47=[2.7197729316641886588 ,6.2381008312157750495 ] 
dist 48=[2.4501348308206901863 ,5.9833208875404417386 ] 
dist 49=[2.1773711203676959428 ,5.9506639069992735954 ] 
dist 50=[1.8262591189105652404 ,5.8739332451391166986 ] 
dist 51=[1.4820622491256973386 ,5.8627458508875907187 ] 
dist 52=[1.2369519724202894160 ,5.7583570031495984917 ] 
dist 53=[1.0156772435885033949 ,5.7394960503199629529 ] 
dist 54=[.7668001704851682152 ,5.7165737474399142193 ] 
dist 55=[.5169625149993198153 ,5.7120253320688713884 ] 
dist 56=[.2918444053352665691 ,4.6303266452113226937 ] 
dist 57=[.0400037463604123176 ,4.5620774826376110046 ] 
dist 58=[-.3167048543581474816 ,4.4186064875467976240 ] 
dist 59=[-.6701592876841928629 ,4.3857560362366868620 ] 
dist 60=[-.9089872409029134845 ,4.1310346386227816814 ] 
dist 61=[-1.1113499569559139222 ,4.0855245600971825073 ] 
dist 62=[-1.3189745613419181816 ,3.9488061864319583813 ] 
dist 63=[-1.5159750341616316950 ,3.7526639474578643500 ] 
dist 64=[-1.6758519455807240676 ,2.4453487721003406008 ] 
dist 65=[-1.8403752957420767161 ,2.3727493637889013195 ] 
dist 66=[-2.0559625093109700163 ,2.3567690092143138396 ] 
dist 67=[-2.2691941587950450092 ,2.1088810830211790026 ] 
dist 68=[-2.4242994620384338171 ,2.0762472731891128094 ] 
dist 69=[-2.5677126757947766987 ,2.0052352396462466420 ] 
dist 70=[-2.7341875818368362865 ,1.9909228541870726365 ] 
dist 71=[-2.9043249948848000129 ,1.9113146255310241017 ] 
dist 72=[-3.0623900035784264061 ,1.8975117124653696430 ] 
dist 73=[-3.2431434526043159366 ,1.8692859255949255216 ] 
dist 74=[-3.5040282895185930744 ,1.8621492636290753405 ] 
dist 75=[-3.7616563751094642638 ,.3964762199240481912 ] 
dist 76=[-3.9293859113875269071 ,.32902905917298488362] 
dist 77=[-4.0646722127589974437 ,.31594423756443902474] 
dist 78=[-4.1925429571619072364 ,.29253084320922956753] 
dist 79=[-4.3070581542782980785 ,.28738623862071370337] 
dist 80=[-4.3889296940126448696 ,.27541820649859158505] 
dist 81=[-4.4632149591740866934 ,.27764866284443902678] 
dist 82=[-4.5473917162683849760 ,.28645415915362053037] 
dist 83=[-4.6247763417569797738 ,.30653596082909090196] 
dist 84=[-4.6718965793333030902 ,.33243583642121307959] 
dist 85=[-4.7062441887777378783 ,.36450517150257623334] 
dist 86=[-4.7325421296031236217 ,.40741141355060022803] 
dist 87=[-4.7527684996854711016 ,.47663636099331213289] 
dist 88=[-4.7628317529684683333 ,.54748457705921402038] 
dist 89=[-4.7674625561165791112 ,.59688312785103858222] 
dist 90=[-4.7679354552272795888 ,.6403107491454883408 ] 
dist 91=[-4.6911975508388401669 ,.6872955077134746508 ] 
dist 92=[-4.6807639445211104103 ,.7333128648442176726 ] 
dist 93=[-4.6597541609705869813 ,.7728770486453709527 ] 
dist 94=[-4.6531169052233723100 ,.8155407902880141028 ] 
dist 95=[-4.6231708707905936191 ,.8739545799579621497 ] 
dist 96=[-4.6162248667370773833 ,.9327890557028860075 ] 
dist 97=[-4.5952690891164937417 ,.9771373441101454651 ] 
dist 98=[-4.5910031291102042249 ,1.0196571422064939651 ] 
dist 99=[-4.5413593913212808872 ,1.0711848478429768719 ] 
dist 100=[-4.5315628799984953460 ,1.1249869842608214259 ] 
dist 101=[-4.5077109002413116016 ,1.1766036692895387680 ] 
dist 102=[-4.4994277184355117626 ,1.2368679556734807506 ] 
dist 103=[-4.4568784381144812619 ,1.3252507961269029081 ] 
dist 104=[-4.3250421734838989397 ,1.4139988125737939352 ] 
dist 105=[-4.3084508703526742713 ,1.4757246950791737680 ] 
dist 106=[-4.2382909423082856450 ,1.5299029632069961230 ] 
dist 107=[-1.9108549271038006435 ,1.5884728912712451122 ] 
dist 108=[-1.7916079760283260498 ,1.6458861680304195724 ] 
dist 109=[-1.5155384484091552085 ,1.6954413001299872207 ] 
dist 110=[-1.4729732727808256463 ,1.7490914338231570286 ] 
dist 111=[-1.1113408249800091477 ,1.8228827312664487457 ] 
dist 112=[-1.0468389095494990963 ,1.8974590437505052866 ] 
dist 113=[-.9592768519198081680 ,1.9542498958220344409 ] 
dist 114=[-.9361266518679099560 ,2.0093040805848539619 ] 
dist 115=[-.3562107022604475917 ,2.0769376746035296296 ] 
dist 116=[-.2875391320343135360 ,2.1480993630427772326 ] 
dist 117=[-.1557952210385360442 ,2.2172643831774646341 ] 
dist 118=[-.0592344119352521414 ,2.2987426414870436397 ] 
dist 119=[.18878912784053502438,2.4191487007103022516 ] 
dist 120=[.27937731934780190528,2.5382649382002595515 ] 
dist 121=[.29048790697469266977,2.6145858532066891617 ] 
dist 122=[.31403586857154560105,2.6747337805892216748 ] 
dist 123=[.31834264141954312207,2.7291724683952362512 ] 
dist 124=[.34108485136481945657,2.7762621153790112458 ] 
dist 125=[.34473662704766956389,2.8070211927734228515 ] 
dist 126=[.35076292788454270512,2.8319426955450627705 ] 
dist 127=[.35185403165772967345,2.8556895517139957499 ] 
dist 128=[1.1007252927102538324 ,2.8764477371790156306 ] 
dist 129=[1.1245461250393048188 ,2.8894169353173147533 ] 
dist 130=[1.1765133215456042833 ,2.8992695856623489287 ] 
dist 131=[1.1852135131658678155 ,2.9075612007463030093 ] 
dist 132=[1.2415269318745085778 ,2.9142952626286927917 ] 
dist 133=[1.2505336715716108772 ,2.9179174910345978773 ] 
dist 134=[1.2671761063039591012 ,2.9199825646157924084 ] 
dist 135=[1.2705083585963365141 ,2.9204877722597858318 ] 
dist 136=[1.2946857225733341602 ,2.6877948423494497134 ] 
dist 137=[1.2971038100864410253 ,2.6670077608232071192 ] 
dist 138=[1.2949325501686078089 ,2.6239817206484662175 ] 
dist 139=[1.2859287831489150796 ,2.6120383590667541513 ] 
dist 140=[1.2731515063978219874 ,2.5642944936029775489 ] 
dist 141=[1.2558911096960433966 ,2.5545279332317789868 ] 
dist 142=[1.2319240360520878917 ,2.5303871454775499043 ] 
dist 143=[1.1923300779136251513 ,2.5248469959345355269 ] 
dist 144=[1.1507753333324354043 ,2.4847004542957114711 ] 
dist 145=[1.1189674601028526172 ,2.4761115475340087641 ] 
dist 146=[1.0879956328006839571 ,2.4624319704474271335 ] 
dist 147=[1.0497820710416893152 ,2.4583705942374263088 ] 
dist 148=[1.0095182359579826696 ,2.4476142936269011494 ] 
dist 149=[.9703473865353351962 ,2.4440121952003415673 ] 
dist 150=[.9242000252251667096 ,2.4419331443590740203 ] 
dist 151=[.85603934762674787174,2.4413686195739476527 ] 
dist 152=[.78510247596939800446,1.3482329030979951743 ] 
dist 153=[.72785378411367489633,1.3427666815952288619 ] 
dist 154=[.66927024637934630232,1.3305997147244960443 ] 
dist 155=[.56881710500216590094,1.3268170742898358768 ] 
dist 156=[.4447380657833429005 ,1.3097914411011378150 ] 
dist 157=[.34624260887415477664,1.3060993466349842680 ] 
dist 158=[.24692973723328499114,1.2973402418001544372 ] 
dist 159=[.11958159638833946999,1.2945027690525887352 ] 
dist 160=[-.00494025528071323906,.94105873252383205231] 
dist 161=[-.09295192203382015513,.91657451986571889366] 
dist 162=[-.17168706047242614143,.859104230353342125  ] 
dist 163=[-.25911518596682649978,.85003756758868759311] 
dist 164=[-.34619066257138379452,.77134813026221956805] 
dist 165=[-.4235160777817327364 ,.756896582982113852  ] 
dist 166=[-.50906443482275450522,.73770194746765514329] 
dist 167=[-.62902190131263891182,.73208701100712795026] 
dist 168=[-.74724490934734216763,.61937380074632773645] 
dist 169=[-.82585784885786349743,.60491016469601979919] 
dist 170=[-.89105654948489246163,.57460726743086150303] 
dist 171=[-.95563961260550970766,.56661233133558554813] 
dist 172=[-1.0154322623924317260 ,.53560673515823181311] 
dist 173=[-1.0614756078792069918 ,.52969302370210459445] 
dist 174=[-1.1065934353713546330 ,.51651240250018987141] 
dist 175=[-1.1626858579044766843 ,.5134923131497153953 ] 
dist 176=[-1.2167008042004507291 ,.35177875917793405155] 
dist 177=[-1.2535116344614570845 ,.3378507815557670794 ] 
dist 178=[-1.2850300887872913127 ,.30524439712082441585] 
dist 179=[-1.3178823907468662823 ,.30033610676762936153] 
dist 180=[-1.3493652561436213186 ,.25632331137333176805] 
dist 181=[-1.3754082941765555062 ,.24836768386258864062] 
dist 182=[-1.4026470447981466292 ,.23822632718462832411] 
dist 183=[-1.4389128737751905643 ,.23583783297154669235] 
dist 184=[-1.4739427900124344522 ,.17501171339723934181] 
dist 185=[-1.4962394644946342854 ,.16743263395827611497] 
dist 186=[-1.5136405603459929831 ,.15177076352463991637] 
dist 187=[-1.5290927636867639148 ,.14770620919241027499] 
dist 188=[-1.5422459782340058304 ,.1327742534684753791 ] 
dist 189=[-1.5504534654346187398 ,.1298714666567516365 ] 
dist 190=[-1.5566712952434454931 ,.1243290423370489304 ] 
dist 191=[-1.5618683068744635098 ,.1229935266743475207 ] 
dist 192=[-1.5658654217822932218 ,.04215581266671821313] 
dist 193=[-1.5672848253838420209 ,.03476447953325877140] 
dist 194=[-1.5674979866870445972 ,.02049298734437184854] 
dist 195=[-1.5669769141354899301 ,.01705818579863818314] 
dist 196=[-1.5617038664268444144 ,.00625220680507840519] 
dist 197=[-1.5599110785719086222 ,.00375275201815710664] 
dist 198=[-1.5567960182814592949 ,.00315164003678814449] 
dist 199=[-1.5556362172015364539 ,.00506529118479485526] 
dist 200=[-1.4843129281988065504 ,.00820246592851457504] 
dist 201=[-1.4762816136682810287 ,.01251723568797968353] 
dist 202=[-1.4572978133726575888 ,.01855069312232317284] 
dist 203=[-1.4529759282415517814 ,.02856078488450385475] 
dist 204=[-1.4246895925828597566 ,.04044835735786974818] 
dist 205=[-1.4188843930318966037 ,.05398942241065491402] 
dist 206=[-1.4085791775282885165 ,.07143266856334490653] 
dist 207=[-1.4059019213200824329 ,.09892386729884848839] 
dist 208=[-1.3532680351807226615 ,.12731570311392565619] 
dist 209=[-1.3457295408407108400 ,.14836043118001638286] 
dist 210=[-1.3285900426392842789 ,.16819955858892577464] 
dist 211=[-1.3241164949939580743 ,.19177089683903224356] 
dist 212=[-1.3004857579987566178 ,.21614004233445850353] 
dist 213=[-1.2956233532729944458 ,.23916954540604924431] 
dist 214=[-1.2856549193525662751 ,.26579380515552717825] 
dist 215=[-1.2827149933782153932 ,.30453751673072549401] 
dist 216=[-.87305765362693452333,.34462726523424776975] 
dist 217=[-.84527725450046559536,.37663404984330546043] 
dist 218=[-.7804109143353963302 ,.40907607620049628237] 
dist 219=[-.77015895313787128758,.45090639331310682378] 
dist 220=[-.67378186811667709112,.49593649988916538888] 
dist 221=[-.65610651629493704513,.54117371653183376756] 
dist 222=[-.62516984940972406499,.59555522677094223916] 
dist 223=[-.61892240696595499167,.67715102738459037253] 
dist 224=[-.50382310261314245083,.75882752695403137583] 
dist 225=[-.48906703823452794696,.81353176392071612688] 
dist 226=[-.45747429345922776128,.85933345872960612506] 
dist 227=[-.4499557629164432224 ,.91254697235032722714] 
dist 228=[-.41538763835496520926,.96799072250689324697] 
dist 229=[-.409193696629696735  ,1.0163206562637151850 ] 
dist 230=[-.3945264043048581835 ,1.0690425096417922032 ] 
dist 231=[-.39214433036406430115,1.1420484668278643169 ] 
dist 232=[-.2451433620735775068 ,1.2136004446804778803 ] 
dist 233=[-.23127900820933450947,1.2605081957902297393 ] 
dist 234=[-.19939137975490677827,1.2986711623975288247 ] 
dist 235=[-.19418076950711153575,1.3352549078531649880 ] 
dist 236=[-.15284580986516256829,1.3683309132549351728 ] 
dist 237=[-.14543328361992914516,1.3924672852613466911 ] 
dist 238=[-.13453067486319054694,1.4148470443812403225 ] 
dist 239=[-.13161775185209234916,1.4408987629728636328 ] 
dist 240=[-.08084998403904345120,1.4651059012901893752 ] 
dist 241=[-.07441415829627968618,1.4801096259907656685 ] 
dist 242=[-.06008251208344535617,1.4913476533794621790 ] 
dist 243=[-.05737294110793094024,1.5004966839258908124 ] 
dist 244=[-.04021211302641819923,1.5076767977367837719 ] 
dist 245=[-.03718027844804410093,1.5110415835788823934 ] 
dist 246=[-.03155853418094396941,1.5126117429186174859 ] 

8 phat 2 dirichlet min maxes function [1, 1, 0, 0, 2, 0, 0, 2] 
dist 0=[13.540037668833885103  ,13.540037668833885103  ] 
dist 1=[13.522553390737280554  ,13.550322342582910498  ] 
dist 2=[13.478724940564956427  ,13.565344212560433749  ] 
dist 3=[13.425492207304481109  ,13.583292164686927872  ] 
dist 4=[13.370398215179639032  ,13.605274318106676992  ] 
dist 5=[13.302925448912612921  ,13.626642232647949412  ] 
dist 6=[13.200189433314641446  ,13.642135469998764126  ] 
dist 7=[13.081621283865523968  ,13.656407319277723770  ] 
dist 8=[12.950830739069990586  ,13.672883995891661524  ] 
dist 9=[12.784976342739130156  ,13.686639481106540632  ] 
dist 10=[12.526173201031451304  ,13.690026602264286202  ] 
dist 11=[12.263349799673180971  ,13.689668890555335379  ] 
dist 12=[12.081418234249300727  ,13.688453513733032851  ] 
dist 13=[11.922509084778882082  ,13.657005646587365101  ] 
dist 14=[11.751766521000350542  ,13.647643884202213616  ] 
dist 15=[11.584891924597277332  ,13.633435876533205751  ] 
dist 16=[11.441455392001317758  ,13.602274596196708201  ] 
dist 17=[11.286604078532944321  ,13.415992235250339550  ] 
dist 18=[11.074081407455871216  ,13.387703591440372315  ] 
dist 19=[10.859382699437422069  ,13.328813902251137674  ] 
dist 20=[10.695830909945294409  ,13.311731817814982928  ] 
dist 21=[10.465055437727067016  ,13.239787449625965759  ] 
dist 22=[9.9541712829998092941 ,13.224886454344494634  ] 
dist 23=[9.4409965791730715645 ,13.183099861963435140  ] 
dist 24=[9.0934178738497281207 ,13.176075087593601204  ] 
dist 25=[8.7980732799569701124 ,13.089340559602697618  ] 
dist 26=[8.4937815810711623759 ,13.072676094929178440  ] 
dist 27=[8.2043368525488320289 ,13.036362835808232279  ] 
dist 28=[7.9683633944421758927 ,13.022112752109277657  ] 
dist 29=[7.7246130270696616766 ,12.890645936761358153  ] 
dist 30=[7.4040639623060482931 ,12.807897549900674336  ] 
dist 31=[7.0866028843615314978 ,12.458229456934721174  ] 
dist 32=[6.8551992213396527578 ,12.316407372102236622  ] 
dist 33=[6.6408102203243536614 ,10.381471804464162771  ] 
dist 34=[6.3913887953593055469 ,10.233635771227383528  ] 
dist 35=[6.1362534946261042513 ,9.8917544423458750183 ] 
dist 36=[5.8990101799821335702 ,9.8353207619886039462 ] 
dist 37=[5.6276165243608774953 ,9.3829444069240733616 ] 
dist 38=[5.2359024286650654354 ,9.3005635885959154280 ] 
dist 39=[4.8446093786856230648 ,9.1812336810457295498 ] 
dist 40=[4.5748973198058181414 ,9.1481398861205039055 ] 
dist 41=[4.3405858124218984638 ,8.5482675459945838904 ] 
dist 42=[4.0908646610504703886 ,8.4708364731129352399 ] 
dist 43=[3.7067859070137908357 ,8.3019883706314960434 ] 
dist 44=[3.2958891206225391432 ,8.2641158227371435608 ] 
dist 45=[2.9519537520527969446 ,8.0686083507503985346 ] 
dist 46=[2.6059247656596923037 ,8.0330181119583212851 ] 
dist 47=[2.2819563702943826965 ,7.9566010628394748219 ] 
dist 48=[2.0262432991018212491 ,7.9366822098531411112 ] 
dist 49=[1.7696502703862728642 ,7.2007166671156474127 ] 
dist 50=[1.4421615698656688598 ,7.1282418953962220622 ] 
dist 51=[1.1224606997991621071 ,6.9619669304324701008 ] 
dist 52=[.89701138969047184359,6.9334369495353692943 ] 
dist 53=[.69576752041422683773,6.7176503957125661099 ] 
dist 54=[.47286611907748927746,6.6785336549628787187 ] 
dist 55=[.2510777775929083309 ,6.6177635325582811664 ] 
dist 56=[-.0599749881562123032 ,6.6022819399329660788 ] 
dist 57=[-.3205974531165351673 ,6.3326512341887172635 ] 
dist 58=[-.5775319527099895146 ,6.2978974138815102670 ] 
dist 59=[-.8148397965328765139 ,6.2185450052977655102 ] 
dist 60=[-.9969659600067088675 ,6.2043988495367049359 ] 
dist 61=[-1.1749838955422670421 ,6.1022626036943584721 ] 
dist 62=[-1.3958637181128400743 ,6.0586219869866826804 ] 
dist 63=[-1.6086175654621165890 ,5.9227698878766863348 ] 
dist 64=[-1.7541367112269003831 ,5.8604886943438305735 ] 
dist 65=[-1.8794117108285850422 ,1.0004423661469426706 ] 
dist 66=[-2.0111993963240250262 ,.9851557647274369855 ] 
dist 67=[-2.1383634695383517423 ,.7454358915516317979 ] 
dist 68=[-2.2451489316390041031 ,.7150048409891612143 ] 
dist 69=[-2.3583322556160193198 ,.6491111783535824319 ] 
dist 70=[-2.5110920606113985625 ,.6367929770352470043 ] 
dist 71=[-2.6594870681687409065 ,.5656707701359265074 ] 
dist 72=[-2.7552143340128621343 ,.5539374751464721507 ] 
dist 73=[-2.8314650009658490892 ,.5303492798646228397 ] 
dist 74=[-2.9019587095590547549 ,.5252464828145206182 ] 
dist 75=[-2.9640598447215817670 ,-.9014919422137966391 ] 
dist 76=[-3.0376051602093206795 ,-.9734199132296392835 ] 
dist 77=[-3.1105825545171821113 ,-1.1347530138600591339 ] 
dist 78=[-3.1763332506297027661 ,-1.1617086763416142067 ] 
dist 79=[-3.2330501787869173666 ,-1.3557317709025686660 ] 
dist 80=[-3.2698973207977450079 ,-1.3892011181913359740 ] 
dist 81=[-3.2995587230631621408 ,-1.4442505757751442889 ] 
dist 82=[-3.3275406161877834701 ,-1.4565123049300195235 ] 
dist 83=[-3.3518964453951486074 ,-1.6383684616096764449 ] 
dist 84=[-3.3670541501626037125 ,-1.5801000223527796985 ] 
dist 85=[-3.3785221937180222841 ,-1.4373373471756769874 ] 
dist 86=[-3.3881131283364024408 ,-1.2178278994506701342 ] 
dist 87=[-3.3958735916049486201 ,-.9964196969858302966 ] 
dist 88=[-3.4000166032246995772 ,-.8460629846862080165 ] 
dist 89=[-3.4023421337431081119 ,-.7179869471972830485 ] 
dist 90=[-3.4028295048218317382 ,-.5856588548124116259 ] 
dist 91=[-3.1269001106950706878 ,-.4596701337812543119 ] 
dist 92=[-3.1023317468378623298 ,-.3569379994877223213 ] 
dist 93=[-3.0511633856843338734 ,-.2508754114905706752 ] 
dist 94=[-3.0369264632036738167 ,-.1115668088436549252 ] 
dist 95=[-2.9797409927991752412 ,.0261680200021619466 ] 
dist 96=[-2.9681912003436362940 ,.1259400952777303945 ] 
dist 97=[-2.9392025888144881055 ,.2176833012402868046 ] 
dist 98=[-2.9331247600512006280 ,.3233183003886731195 ] 
dist 99=[-2.8839184667001899554 ,.4306857130355259951 ] 
dist 100=[-2.8736936263677565079 ,.5293585729643029718 ] 
dist 101=[-2.8569384286772038938 ,.6412575410519264805 ] 
dist 102=[-2.8521791659481711912 ,.8015137311424499368 ] 
dist 103=[-2.8388205016058723960 ,.9608540562212403054 ] 
dist 104=[-2.8343372817980231996 ,1.0690922034616396895 ] 
dist 105=[-2.8316594650447669866 ,1.1613698395308495551 ] 
dist 106=[-2.8307204514645707154 ,1.2568916728423374708 ] 
dist 107=[-1.1817004768843084453 ,1.3479993583927101241 ] 
dist 108=[-1.0938538268612780049 ,1.4226282218032371398 ] 
dist 109=[-.8880974113593401081 ,1.5000142347405913728 ] 
dist 110=[-.85823686912592575269,1.6021503692010595559 ] 
dist 111=[-.58161167726204785202,1.7034395090381773022 ] 
dist 112=[-.53205053466839206459,1.7774403855342196735 ] 
dist 113=[-.47133631085604627591,1.8461573342122258815 ] 
dist 114=[-.45993717140553278196,1.9263194147287696626 ] 
dist 115=[-.08195834255984202323,2.0084255700516353411 ] 
dist 116=[-.03592568950571097093,2.0849194088688603480 ] 
dist 117=[.05794288043860647587,2.1725323508906825142 ] 
dist 118=[.08173432198396023083,2.2991080218175946317 ] 
dist 119=[.16569097190883139745,2.4238128670178571684 ] 
dist 120=[.18237084730632618511,2.5039452315433132999 ] 
dist 121=[.20752902169509789894,2.5673596393520274075 ] 
dist 122=[.2138321977586626854 ,2.6252077142175780228 ] 
dist 123=[.68477630234046315272,2.6755672708919827760 ] 
dist 124=[.72385836515284632898,2.7090351067890404844 ] 
dist 125=[.81310642950602054966,2.7367928426460084328 ] 
dist 126=[.82628984518709203862,2.7643194129525915110 ] 
dist 127=[.93747885099362457933,2.7887158228602096237 ] 
dist 128=[.95653708192030327012,2.8039554602245555240 ] 
dist 129=[.98257464766468290339,2.8155274305907458013 ] 
dist 130=[.98796346766386507802,2.8252533812358944805 ] 
dist 131=[1.1039840428702588242 ,2.8331409057368001287 ] 
dist 132=[1.1175211531227473736 ,2.8373592660645556270 ] 
dist 133=[1.1466660216057548795 ,2.8397304900426946108 ] 
dist 134=[1.1511836143447168497 ,2.8402295559878009066 ] 
dist 135=[1.1805198027878763558 ,2.6283620288204806314 ] 
dist 136=[1.1848567240707021441 ,2.6092850754689428363 ] 
dist 137=[1.1926992964523819389 ,2.5700213544832015310 ] 
dist 138=[1.1939450774867870035 ,2.5591122098603023408 ] 
dist 139=[1.5535497931263839387 ,2.5155688329433848440 ] 
dist 140=[1.5652097661610504767 ,2.5065234642313043156 ] 
dist 141=[1.5884339788215510335 ,2.4843943250832230036 ] 
dist 142=[1.5930963336241274700 ,2.4788902489042439293 ] 
dist 143=[1.6087947427606160881 ,2.4424930955212859225 ] 
dist 144=[1.6103982869175977997 ,2.4344899604840863583 ] 
dist 145=[1.6078754260694143104 ,2.4219363372552184429 ] 
dist 146=[1.5990516598759358296 ,2.4180962776896622467 ] 
dist 147=[1.5877612619690286518 ,2.4081041225663081041 ] 
dist 148=[1.5753746053885046051 ,2.4046599046364321109 ] 
dist 149=[1.4340612318269294878 ,2.4025767891241676334 ] 
dist 150=[1.2092558388616922683 ,2.4017865523559791091 ] 
dist 151=[.98390269779838726662,1.6531579304318530864 ] 
dist 152=[.83252755593812972512,1.6511790643313405717 ] 
dist 153=[.70531398591753787315,1.6473152052597790380 ] 
dist 154=[.57657457744024486571,1.6458574331203653181 ] 
dist 155=[.45562647358236327602,1.5629964689610262600 ] 
dist 156=[.35956744276543898067,1.5538683814794415760 ] 
dist 157=[.26266737127618700635,1.5323980161357116818 ] 
dist 158=[.1383556900582061022 ,1.5275594337847431323 ] 
dist 159=[.01677816985519925901,1.4960627096652584587 ] 
dist 160=[-.06918913878690475611,1.4896535549886206032 ] 
dist 161=[-.14613232468306844348,1.4782205392435376108 ] 
dist 162=[-.23162555741383066455,1.4752614688613431469 ] 
dist 163=[-.31680448932702401753,1.4185372300517947546 ] 
dist 164=[-.39249130919290467178,1.4104367550100389757 ] 
dist 165=[-.47626353410895629265,1.3918755795919687441 ] 
dist 166=[-.59377438721816865316,1.3872200165354587572 ] 
dist 167=[-.70960176823889662807,1.3612940070689194911 ] 
dist 168=[-.78664248267076698123,1.3559873341400775799 ] 
dist 169=[-.85055926202011333248,1.3454858474729214837 ] 
dist 170=[-.91390771975009507516,1.3424853775415033812 ] 
dist 171=[-.97257941534388077402,.90562222914908446484] 
dist 172=[-1.0177953647403129810 ,.87656672981624910498] 
dist 173=[-1.0621360479614348569 ,.80891190305282989376] 
dist 174=[-1.1173084785566122655 ,.79809149447687087011] 
dist 175=[-1.1704594788861335729 ,.70736983447619566763] 
dist 176=[-1.2067173069362832512 ,.69085210701639791315] 
dist 177=[-1.2378004360427076955 ,.66805670047974826237] 
dist 178=[-1.2702594196726941147 ,.66138448153241437999] 
dist 179=[-1.3014024085701982627 ,.53844187626738730468] 
dist 180=[-1.3272238434620344871 ,.52269390237896670326] 
dist 181=[-1.3542834132613950154 ,.48902794698474235252] 
dist 182=[-1.3903789997869183593 ,.48098920270067040518] 
dist 183=[-1.4252673758280523495 ,.44433470427288221078] 
dist 184=[-1.4474996646689299015 ,.43777834277754327974] 
dist 185=[-1.4648799901214147125 ,.42214057718889852006] 
dist 186=[-1.4803651279351978647 ,.41971517773471150601] 
dist 187=[-1.4935835958357926533 ,.26269065102109037018] 
dist 188=[-1.5018995918490138080 ,.24792896010503175823] 
dist 189=[-1.5082792902817124541 ,.21394982829876755986] 
dist 190=[-1.5137549916926914361 ,.20843549373615838675] 
dist 191=[-1.5180330509505292304 ,.1643222247387418104 ] 
dist 192=[-1.5196233396637015505 ,.15641425327503973846] 
dist 193=[-1.5199699307512815607 ,.14489962788475302742] 
dist 194=[-1.5194926258308312804 ,.14178948557012342637] 
dist 195=[-1.5326970527493049718 ,.08738834456890448174] 
dist 196=[-1.5492762809785088360 ,.08049914870963308560] 
dist 197=[-1.5618959581065028178 ,.06524656922932701250] 
dist 198=[-1.5725374604432738808 ,.06229025399126413769] 
dist 199=[-1.5811804562061774730 ,.04429811720685877928] 
dist 200=[-1.5858085768444027406 ,.04112797850455337316] 
dist 201=[-1.5884130749392465958 ,.03506768920544996548] 
dist 202=[-1.5889640937615084493 ,.03361910239706218111] 
dist 203=[-1.3836066349401764373 ,-.04045783598163868696] 
dist 204=[-1.3779476187727213937 ,-.04563892188105751825] 
dist 205=[-1.3680603080205035982 ,-.05473747588934950087] 
dist 206=[-1.3655106579503156622 ,-.05668042247939383098] 
dist 207=[-1.3133410195600786723 ,-.06096566730409444217] 
dist 208=[-1.3058856358782447821 ,-.06069229901619198069] 
dist 209=[-1.2891230854392239790 ,-.05844903743756087923] 
dist 210=[-1.2845768334558483749 ,-.05291405772574925762] 
dist 211=[-1.2620111748486031371 ,-.04623221078544436779] 
dist 212=[-1.2573629710790369742 ,-.03940280107005120192] 
dist 213=[-1.2474077438010996960 ,-.03110928534977071579] 
dist 214=[-1.2443747266116227790 ,-.01857256364524232578] 
dist 215=[-.85742505179558728146,.06103603801553329428] 
dist 216=[-.83134225595210119591,.16884468677569352263] 
dist 217=[-.77060589810158569451,.25904809681030413132] 
dist 218=[-.76082364982669603414,.34969720940762574065] 
dist 219=[-.67927901496557985317,.43446237999462429667] 
dist 220=[-.66440303019652690059,.50113743851721324321] 
dist 221=[-.64373143839176514453,.56780298327585337406] 
dist 222=[-.63771223521502351656,.65253016396231082081] 
dist 223=[-.52666803723080451365,.73501899055143645403] 
dist 224=[-.51240772673755224303,.79273394704383378035] 
dist 225=[-.48184726296253569941,.8437574921455154429 ] 
dist 226=[-.4597023589463751489 ,.89948907499949354075] 
dist 227=[-.42566912658733903651,.95446013634789058014] 
dist 228=[-.41956901052246264635,1.0024425764400703631 ] 
dist 229=[-.4049349286129967865 ,1.0548397672451042488 ] 
dist 230=[-.40270618589715560305,1.1274643665310017718 ] 
dist 231=[-.25450700783660752591,1.1986729155025334004 ] 
dist 232=[-.24059358116664609577,1.2454076813639282363 ] 
dist 233=[-.20847500039364732557,1.2834884249670892121 ] 
dist 234=[-.20332157689602849324,1.3200916679066454121 ] 
dist 235=[-.16133438439002844597,1.3532516241380942809 ] 
dist 236=[-.15379458113400207202,1.3775635146301501401 ] 
dist 237=[-.143046103767844846  ,1.4002210306385144484 ] 
dist 238=[-.1400661319378774762 ,1.4267655609833105448 ] 
dist 239=[-.08730044425280282820,1.4515206548882360409 ] 
dist 240=[-.08062031128144296770,1.4670226565355772702 ] 
dist 241=[-.06600757231214961129,1.4788218776250694704 ] 
dist 242=[-.06300365789993780785,1.4887704578779678441 ] 
dist 243=[-.04628621000781352792,1.4968497190863933951 ] 
dist 244=[-.04334847466702525733,1.5011739967133177087 ] 
dist 245=[-.03732932876679492475,1.5036047585035094863 ] 

8 phat 2 dirichlet min maxes function [0, 2, 1, 0, 0, 1, 1, 0, 2] 
dist 0=[12.570931982804415592  ,12.570931982804415592  ] 
dist 1=[12.538555576378456609  ,12.590490984317583456  ] 
dist 2=[12.484844872330474756  ,12.636323881162672328  ] 
dist 3=[12.407482164107955676  ,12.681712196973638944  ] 
dist 4=[12.320131912898449743  ,12.707443958335027118  ] 
dist 5=[12.226478665150687834  ,12.723874387941218558  ] 
dist 6=[12.109562467881491814  ,12.732072496243924795  ] 
dist 7=[11.929180647649914023  ,12.736383784936102902  ] 
dist 8=[11.746423026330025592  ,12.737269828731068701  ] 
dist 9=[11.620004551991728150  ,12.735811205953004192  ] 
dist 10=[11.509726259933642915  ,12.733790455953575112  ] 
dist 11=[11.391511918538560598  ,12.649634608211526897  ] 
dist 12=[11.276180887060958969  ,12.635865851286025421  ] 
dist 13=[11.177430978357461130  ,12.610983554261223982  ] 
dist 14=[11.071166541581071968  ,12.570034594641502157  ] 
dist 15=[10.925780308212643023  ,12.450592880784888158  ] 
dist 16=[10.779127347864779846  ,12.428362005670830115  ] 
dist 17=[10.667795090821630307  ,12.396698742529637849  ] 
dist 18=[10.560172621057768633  ,12.386226687493853945  ] 
dist 19=[10.428353171825814010  ,12.275366123914685984  ] 
dist 20=[10.289827479681817509  ,12.257623561310052355  ] 
dist 21=[10.155382204707986740  ,12.209444725578894375  ] 
dist 22=[9.9971192454847956309 ,12.202049237173520398  ] 
dist 23=[9.7633349515341033235 ,12.110180354413058796  ] 
dist 24=[9.5274679523196942236 ,12.090683133843439244  ] 
dist 25=[9.3608741227116664786 ,12.072492573810698857  ] 
dist 26=[9.2118496158514295045 ,12.067630986206392436  ] 
dist 27=[9.0462476291432181477 ,11.814268764060531138  ] 
dist 28=[8.8811025644749869496 ,11.780718142601653121  ] 
dist 29=[8.7339034547887239015 ,11.722067470174734064  ] 
dist 30=[8.5704943367518541373 ,11.647083780774647487  ] 
dist 31=[8.3405146602392946887 ,11.441961649880546821  ] 
dist 32=[8.1055481544775383847 ,9.3266994707630552387 ] 
dist 33=[7.9221926001090189898 ,9.2434952446158850344 ] 
dist 34=[7.6634284328017787882 ,9.2286662727102770645 ] 
dist 35=[7.3657997235100524158 ,8.7664169859225328936 ] 
dist 36=[7.0827319265686814277 ,8.7059610302703170935 ] 
dist 37=[6.8520595420236294273 ,8.6939741396945605823 ] 
dist 38=[6.6138920435903672489 ,8.6666110900396225056 ] 
dist 39=[6.2950243860085961615 ,8.6597673421035769738 ] 
dist 40=[5.8596337298527009804 ,8.1386196179588670942 ] 
dist 41=[5.5669475950766832609 ,8.1052106669007433150 ] 
dist 42=[5.3204828345978912895 ,8.0977506221500303067 ] 
dist 43=[5.0699604839610580520 ,6.7826409569551822523 ] 
dist 44=[4.8336424927710077410 ,6.6719220675997694465 ] 
dist 45=[4.6439906512749671436 ,6.4286055146918814834 ] 
dist 46=[4.4507079206182465881 ,6.3770505181271638081 ] 
dist 47=[4.1928649890877956522 ,6.0911976075559439279 ] 
dist 48=[3.8139638932391640874 ,6.0396053126410071561 ] 
dist 49=[3.5530938338462712976 ,5.9344876777267360992 ] 
dist 50=[3.3267879988243194816 ,5.9068900157645294722 ] 
dist 51=[3.0861124533878021027 ,5.6460031568847137639 ] 
dist 52=[2.8524110865136142234 ,5.6056721809621198909 ] 
dist 53=[2.6539920627554992111 ,5.5268633689090763236 ] 
dist 54=[2.4418818474145663473 ,5.5068560383100795541 ] 
dist 55=[2.1534174124528965789 ,5.4376941204613307238 ] 
dist 56=[1.8631361862357895712 ,5.4219527983415695316 ] 
dist 57=[1.6437557245681806221 ,5.4016570456506819194 ] 
dist 58=[1.4326006795297779979 ,5.3946623312021539705 ] 
dist 59=[1.1752102043507000757 ,3.1439438320148596405 ] 
dist 60=[.90531830427084139653,2.7207293787525017680 ] 
dist 61=[.64415835192636089808,2.6518335792028347361 ] 
dist 62=[.33727267354666250852,2.4162724452152661922 ] 
dist 63=[-.11550881925499777113,2.0724780381395236022 ] 
dist 64=[-.56556511019994669452,1.7463451077858871225 ] 
dist 65=[-.86155342763159406916,1.7143325633877219035 ] 
dist 66=[-1.1036576418072708452 ,1.6397951374380480683 ] 
dist 67=[-1.3382011503655251563 ,1.6287743071045745253 ] 
dist 68=[-1.5521536691318789974 ,1.5297371778761066642 ] 
dist 69=[-1.7119049548992011816 ,1.5120106145567166904 ] 
dist 70=[-1.8638225201373994292 ,1.4896455369761268208 ] 
dist 71=[-2.0464495774072061501 ,1.4849041955050393582 ] 
dist 72=[-2.2195119204017595831 ,.46877200271412705971] 
dist 73=[-2.3331773847213750921 ,.40456299674570883693] 
dist 74=[-2.4260162014418787762 ,.25912769905517049565] 
dist 75=[-2.5157827709006744216 ,.23495426522236705787] 
dist 76=[-2.5976149055123916663 ,.05443186738905559161] 
dist 77=[-2.6587250654614540987 ,.02271136729479560225] 
dist 78=[-2.7169039712764509819 ,-.02719156625232800180] 
dist 79=[-2.7870274689720523238 ,-.03920529377433244605] 
dist 80=[-2.8532427023098123471 ,-.23260410344237892189] 
dist 81=[-2.8957901353345832354 ,-.25701968825647032859] 
dist 82=[-2.9295519518191572849 ,-.31209976861830768301] 
dist 83=[-2.9606130892677278991 ,-.32092205265785899573] 
dist 84=[-2.9879234603302950788 ,-.38797332571014358718] 
dist 85=[-3.0066778624315423306 ,-.39952506999085850501] 
dist 86=[-3.0229438455879120126 ,-.41731265162675876107] 
dist 87=[-3.0402991634186913850 ,-.42157797496909318604] 
dist 88=[-3.0556918583819034584 ,-.48650580672952506887] 
dist 89=[-3.0641052473919541230 ,-.49551098121981699652] 
dist 90=[-3.0691086772215234993 ,-.50489257234175235534] 
dist 91=[-3.0708566241698663621 ,-.50461000304922484609] 
dist 92=[-3.0704150176777070327 ,-.50019347410651535527] 
dist 93=[-3.0693067807060352548 ,-.4898543557591761046 ] 
dist 94=[-3.0625028825509296633 ,-.47312617045971151568] 
dist 95=[-3.0604628940996605576 ,-.44315952305228301892] 
dist 96=[-2.9971630172351492752 ,-.40978645106530456067] 
dist 97=[-3.0104838538938155442 ,-.37943551209969648072] 
dist 98=[-3.0188280373893272693 ,-.34526908761588738983] 
dist 99=[-3.0226605384366068950 ,-.29663674821027419882] 
dist 100=[-3.0245460707178538790 ,-.24199265127459129004] 
dist 101=[-3.0251025731305844465 ,-.18378519669881120964] 
dist 102=[-3.0247957923696440722 ,-.1113879515957496176 ] 
dist 103=[-3.0236102909904720926 ,0                     ] 
dist 104=[-2.4189828637249663235 ,-.55182052375755997532] 
dist 105=[-2.4141958066312514991 ,-.45607336189531222775] 
dist 106=[-2.4124316999466131882 ,-.36881369084965041488] 
dist 107=[-2.1697542855793813663 ,-.26950842707368562328] 
dist 108=[-2.1477693057173058367 ,-.1692351963176376988 ] 
dist 109=[-2.0999745509942267096 ,-.07810307266139059081] 
dist 110=[-2.0876327208678409771 ,.02442336439570777892] 
dist 111=[-2.0309591822926075556 ,.17025938556341538708] 
dist 112=[-2.0200747683644168207 ,.31481503716296838505] 
dist 113=[-1.9948486150080048474 ,.41222294270233978591] 
dist 114=[-1.9887844842721829652 ,.49441015578172370606] 
dist 115=[-1.9290345594728086740 ,.57810632035721584771] 
dist 116=[-1.9190254916835392822 ,.6570669542977294846 ] 
dist 117=[-1.8979825094955097327 ,.72032019733685687509] 
dist 118=[-1.8919397003805644597 ,.78462829297695014433] 
dist 119=[-1.8666728509086027165 ,.86780945975507727345] 
dist 120=[-1.8615866808650611642 ,.94949896879157477931] 
dist 121=[-1.8473935448895274649 ,1.0078437949264074882 ] 
dist 122=[-1.8452756371785553997 ,1.0606755975941278677 ] 
dist 123=[-.82981723315228422854,1.1203219499807226886 ] 
dist 124=[-.77262136203170649142,1.1803127479450207954 ] 
dist 125=[-.63862292232297884711,1.2345241413066846294 ] 
dist 126=[-.61916589132086501349,1.2952909325502040223 ] 
dist 127=[-.43879071990610203379,1.3814997888087333294 ] 
dist 128=[-.40643583725978658728,1.4662190590397443318 ] 
dist 129=[-.36686110175027250653,1.5210297726589293744 ] 
dist 130=[-.35939629213776834102,1.5648276599218487389 ] 
dist 131=[-.11149092462313452185,1.6055059433188011470 ] 
dist 132=[-.08123434462482907391,1.6414276006159188416 ] 
dist 133=[-.01966226831934541209,1.6662039041401341408 ] 
dist 134=[-.00405581955949327600,1.6877477548801425116 ] 
dist 135=[.05096849635846734239,1.7107440237145003528 ] 
dist 136=[.06196993769685842435,1.7314316230511777545 ] 
dist 137=[.07846141027578789950,1.7437428597564392008 ] 
dist 138=[.08265539995409157763,1.7523708592407658131 ] 
dist 139=[.40184317957769098242,1.7583272724285599491 ] 
dist 140=[.42836475535689549656,1.7623301058415063094 ] 
dist 141=[.48930049267472703838,1.7631453133445313517 ] 
dist 142=[.4981762516480671454 ,1.7627831954289229402 ] 
dist 143=[.57548408771718450749,1.7620761915683668896 ] 
dist 144=[.58886284677772239341,1.6825552259570401842 ] 
dist 145=[.60642440626677889182,1.6739465279781439037 ] 
dist 146=[.60974423669253300823,1.6553600291518808523 ] 
dist 147=[.69689885645059434243,1.6498061823171815319 ] 
dist 148=[.70708926751833243989,1.6256730977202752649 ] 
dist 149=[.72892894139559045365,1.6206374588784073218 ] 
dist 150=[.73273996890770321456,1.6075126027501394932 ] 
dist 151=[.7548512689704902757 ,1.6045865499184534827 ] 
dist 152=[.75828954820584487778,1.5697057240255221285 ] 
dist 153=[.7649056509657808628 ,1.5637346677109018043 ] 
dist 154=[.7195868259780173731 ,1.5490947055272517388 ] 
dist 155=[.65085674043857887544,1.5454829857488492570 ] 
dist 156=[.57622307233402217078,1.5212376032632901961 ] 
dist 157=[.50033927146028057772,1.5159903498782859521 ] 
dist 158=[.40846737929770237541,1.5069218313055390131 ] 
dist 159=[.2699037774588821377 ,1.5044357309877371807 ] 
dist 160=[.13100592178479429889,1.3828273618694364611 ] 
dist 161=[.03779728255698365738,1.3820035217879762521 ] 
dist 162=[-.04042468565978127858,1.3811900548957206479 ] 
dist 163=[-.11939748463906525914,1.3472934739760890454 ] 
dist 164=[-.1934627601976257131 ,1.3422395515255613372 ] 
dist 165=[-.2520618015132987389 ,1.3332496937671327499 ] 
dist 166=[-.31096076794991621668,1.3308730291746214132 ] 
dist 167=[-.3862255693152828771 ,1.3226321845358182010 ] 
dist 168=[-.45968130981924074195,1.3201591054870615827 ] 
dist 169=[-.51134671839851282733,1.3168523632409965987 ] 
dist 170=[-.55729844360360909198,1.3154711113627704810 ] 
dist 171=[-.60790766400489053793,1.1457026395068560499 ] 
dist 172=[-.65806425668084612281,1.1306701982926157273 ] 
dist 173=[-.70368910341653689896,1.0979355111579355552 ] 
dist 174=[-.75899973717319513526,1.0898725005846960429 ] 
dist 175=[-.83557704274355298018,1.0513041986198473785 ] 
dist 176=[-.9106002561217625203 ,1.0440258194194220371 ] 
dist 177=[-.95969665643937580654,1.0275932656012446072 ] 
dist 178=[-.99953685407715875691,1.0235089622716521308 ] 
dist 179=[-1.0375479878283558869 ,.98497680342751632728] 
dist 180=[-1.0717873511683156677 ,.97858458268914488685] 
dist 181=[-1.0965456116948196637 ,.96551189751479904908] 
dist 182=[-1.1192704797821978594 ,.96188439910537325552] 
dist 183=[-1.1453789431142795539 ,.94745167834158194776] 
dist 184=[-1.1694892486320113061 ,.94441448130882480745] 
dist 185=[-1.1842242717615470676 ,.93704841605852652764] 
dist 186=[-1.1950121417751248355 ,.9350952328092307305 ] 
dist 187=[-1.2033395059343801722 ,.46791046211797757796] 
dist 188=[-1.2098073189624179184 ,.4531781058489852555 ] 
dist 189=[-1.2131595169533794825 ,.41885822004888622476] 
dist 190=[-1.2148928739610290994 ,.41340419539762112779] 
dist 191=[-1.2150620622610203636 ,.36735424255344486844] 
dist 192=[-.47695449804307258099,.35897527063089136332] 
dist 193=[-.48677664478689364648,.3475110150995451797 ] 
dist 194=[-.49516420181987247614,.34412576310824341395] 
dist 195=[-.50387237355549908591,.28162217872699228389] 
dist 196=[-.51219711388392772352,.27362425788801413524] 
dist 197=[-.51905134351128047382,.25659988444792879751] 
dist 198=[-.52619185944341683851,.25247540218283665208] 
dist 199=[-.53566150786731984101,.23419141958354565277] 
dist 200=[-.54507621859718446016,.23091063688717920313] 
dist 201=[-.55693382103255433304,.22304977293487758906] 
dist 202=[-.60705992496215790192,.22186572864143276507] 
dist 203=[-.65611995792491834195,.14086552206132065473] 
dist 204=[-.68820674528995609062,.13331817159934534665] 
dist 205=[-.71422797316961626835,.1158535878740210572 ] 
dist 206=[-.73903310710398331152,.1131032545449342886 ] 
dist 207=[-.76136710046440911687,.09016359404266858313] 
dist 208=[-.77750673973594878346,.08604610761155955976] 
dist 209=[-.79231338170850164539,.08034031237579984178] 
dist 210=[-.80931695052306002513,.07870833892443999639] 
dist 211=[-.82506986849425137332,.04950717755997458618] 
dist 212=[-.83487541719370440322,.04581867411143971961] 
dist 213=[-.84226955938960953826,.03787449020250621176] 
dist 214=[-.84837980812831417568,.03613406069787718684] 
dist 215=[-.8532469442123632697 ,.02742864319864821089] 
dist 216=[-.85567014810786090129,.02590974990519665284] 
dist 217=[-.85693913332381193836,.02251875891346980714] 

8 phat 2 dirichlet min maxes function [1, 0, 2, 2, 2, 2, 1, 0, 1] 
dist 0=[13.319724086896591934  ,13.319724086896591934  ] 
dist 1=[13.308418102855396027  ,13.336661407629283181  ] 
dist 2=[13.280132330117398275  ,13.353217816463011476  ] 
dist 3=[13.233154175059714224  ,13.359154733774574600  ] 
dist 4=[13.154544401242174790  ,13.360010666384339100  ] 
dist 5=[13.071856653192630085  ,13.357915135415345200  ] 
dist 6=[13.008570538447043859  ,13.337047322109405120  ] 
dist 7=[12.946883476497674948  ,13.309144532247313815  ] 
dist 8=[12.870596113727631859  ,13.259640683876494002  ] 
dist 9=[12.790042852089874949  ,13.251691060786865190  ] 
dist 10=[12.711298501137636744  ,13.214440734789090800  ] 
dist 11=[12.618188925326250270  ,13.205469117680488167  ] 
dist 12=[12.480189470571835993  ,13.177041461864930839  ] 
dist 13=[12.336237629266234875  ,13.171414663732455031  ] 
dist 14=[12.219325252623884882  ,13.102699161547193669  ] 
dist 15=[12.098954660282535061  ,13.048657744906804506  ] 
dist 16=[11.941175447123785624  ,12.441160869326723500  ] 
dist 17=[11.769973374408262289  ,12.411937893110464033  ] 
dist 18=[11.595925079424480348  ,12.256542095727505433  ] 
dist 19=[11.385135084095808001  ,12.226137212032118474  ] 
dist 20=[11.067001849344873993  ,12.180952807921618660  ] 
dist 21=[10.743527160399086145  ,12.145486658481788417  ] 
dist 22=[10.511376978673872019  ,11.936909786652794350  ] 
dist 23=[10.299972280278361501  ,11.905828106400990743  ] 
dist 24=[10.059460744738156327  ,11.828033711961211960  ] 
dist 25=[9.8164882754648432245 ,11.814776878270834954  ] 
dist 26=[9.5952428392938780663 ,11.687597350024717455  ] 
dist 27=[9.2860655541655876216 ,11.661850736179691495  ] 
dist 28=[8.9183562238069111470 ,11.630834057561566203  ] 
dist 29=[8.5494825353401101628 ,11.619235494443921323  ] 
dist 30=[8.1063376835664399808 ,11.356115360567693080  ] 
dist 31=[7.4416175204319395778 ,11.261112286788708059  ] 
dist 32=[6.7756677258782056043 ,10.250084379832683303  ] 
dist 33=[6.3276047927177228853 ,10.113037649464896451  ] 
dist 34=[5.9501263498662335096 ,10.085980605570430970  ] 
dist 35=[5.5664420280133527072 ,10.045397970969773123  ] 
dist 36=[5.2047634597026260500 ,10.033494987457113276  ] 
dist 37=[4.9152842730086709365 ,7.9311315281828321128 ] 
dist 38=[4.5879021757227791047 ,7.2248895067009586710 ] 
dist 39=[4.1962322445891925049 ,7.1371318363730750944 ] 
dist 40=[3.8002678193496646667 ,6.9604432364521873035 ] 
dist 41=[3.4283616475815070542 ,6.9154369329025575898 ] 
dist 42=[3.1329003032583084658 ,6.7564435116201670045 ] 
dist 43=[2.8346698694152924764 ,6.7234509662188566116 ] 
dist 44=[2.4516878520066828943 ,6.6729193136677703144 ] 
dist 45=[2.0767255685527553339 ,6.6596853503648680419 ] 
dist 46=[1.8105650984678285190 ,5.5507492250310539393 ] 
dist 47=[1.5711880696546948003 ,5.4566376840601326356 ] 
dist 48=[1.3033321736111219798 ,5.2435751670543795789 ] 
dist 49=[1.0352532300609492862 ,5.2067333401187807780 ] 
dist 50=[.7949817765417059417 ,4.9413709775179849679 ] 
dist 51=[.5272465690563428771 ,4.8943117349655173359 ] 
dist 52=[.1493332993955145602 ,4.8169155716729001538 ] 
dist 53=[-.2245273755746490910 ,4.7989774618893193720 ] 
dist 54=[-.4760574766597272740 ,4.5106518355316136879 ] 
dist 55=[-.6879923953286755378 ,4.4734622947691392880 ] 
dist 56=[-.9035088165330279753 ,4.3892741013129037597 ] 
dist 57=[-1.1067760295934633696 ,4.3750836827358874185 ] 
dist 58=[-1.2697275435626249298 ,4.2705063729552773616 ] 
dist 59=[-1.4355937397294254011 ,4.2520426820622624052 ] 
dist 60=[-1.6505234134959941437 ,4.2226440836184650695 ] 
dist 61=[-1.8619692964128449012 ,4.2156168668656986132 ] 
dist 62=[-2.0139064060304812417 ,2.9867128047898042976 ] 
dist 63=[-2.1525078376635628610 ,2.8325643439591643874 ] 
dist 64=[-2.3106254698530660744 ,2.2619528135079448416 ] 
dist 65=[-2.4706926343792913933 ,2.1791980613776331276 ] 
dist 66=[-2.6170968111397810446 ,2.1652104433528650652 ] 
dist 67=[-2.7827083347252781276 ,2.1349964790068164519 ] 
dist 68=[-3.0196042373295179551 ,2.1294966476575796339 ] 
dist 69=[-3.2527891974053404768 ,.4922594233770408386 ] 
dist 70=[-3.4035610622452748285 ,.0063803272752340443 ] 
dist 71=[-3.5240133048526890821 ,-.0886718371298647623 ] 
dist 72=[-3.6359327360161504856 ,-.2156463679109071487 ] 
dist 73=[-3.7348724516300037354 ,-.2475225071488826149 ] 
dist 74=[-3.8034134339534108454 ,-.3583813698276468800 ] 
dist 75=[-3.8633728946501523649 ,-.3804243591534754893 ] 
dist 76=[-3.9279963355774997233 ,-.4102670991234188961 ] 
dist 77=[-3.9866340289269812819 ,-.4166201392963224440 ] 
dist 78=[-4.0226525044405701239 ,-1.0332569161065835739 ] 
dist 79=[-4.0493052834784183558 ,-1.0837291191872079250 ] 
dist 80=[-4.0704763894385578865 ,-1.1983968919836043306 ] 
dist 81=[-4.0867200661181518047 ,-1.2157746839475513815 ] 
dist 82=[-4.0936615162648528664 ,-1.3573717886893269309 ] 
dist 83=[-4.0961016516852907707 ,-1.3817008517792400460 ] 
dist 84=[-4.0953131241210351875 ,-1.3911886544865489194 ] 
dist 85=[-3.8961705888328681095 ,-1.4244864945620403928 ] 
dist 86=[-3.8762141718080097180 ,-1.5698937371888352841 ] 
dist 87=[-3.8350216004328922272 ,-1.5872749094265654533 ] 
dist 88=[-3.8231522057837372062 ,-1.6250936836398113292 ] 
dist 89=[-3.7738232021914704439 ,-1.6309878848668711064 ] 
dist 90=[-3.7633776437564638546 ,-1.6710222562265165077 ] 
dist 91=[-3.7354962112488673334 ,-1.6771840792029121064 ] 
dist 92=[-3.7295901392430605974 ,-1.6881837471570904466 ] 
dist 93=[-3.6755169634522046829 ,-1.6901257007417226801 ] 
dist 94=[-3.6644686024049951108 ,-1.8936001259979826739 ] 
dist 95=[-3.6423864609652890683 ,-1.6906586916544598236 ] 
dist 96=[-3.6357218559104774893 ,-1.3852468471959396078 ] 
dist 97=[-3.6069815944343849543 ,-1.1796425664656804610 ] 
dist 98=[-3.6003359216100208062 ,-1.0063938680074258552 ] 
dist 99=[-3.5817681825040877688 ,-.83035451636671040995] 
dist 100=[-3.5771797071027040709 ,-.66454566896974585942] 
dist 101=[-2.2435498410724402473 ,-.53220260225995545141] 
dist 102=[-2.2403516226758632434 ,-.39811356019436015626] 
dist 103=[-2.2338863485749681323 ,-.22532159352892853313] 
dist 104=[-2.2317911855802163441 ,-.05599365752476950120] 
dist 105=[-2.2221164820239039612 ,.06424522223995453949] 
dist 106=[-2.2198652924507980479 ,.17237582876759543446] 
dist 107=[-2.2128248199811635973 ,.29328929692718186296] 
dist 108=[-2.2115208719946960503 ,.41418995748679088995] 
dist 109=[-2.1941419673858537602 ,.52227063923054267244] 
dist 110=[-2.1907938274890553841 ,.64242769718146126417] 
dist 111=[-2.1822742590844621862 ,.81161914276666760646] 
dist 112=[-2.1798855242456317281 ,.97863732992968737682] 
dist 113=[-2.1641915739043740969 ,1.0901049499348644473 ] 
dist 114=[-2.1485745440183122127 ,1.1829943925202029324 ] 
dist 115=[-2.1438189323738013462 ,1.2757253537358971259 ] 
dist 116=[-2.1183338005604424979 ,1.3620391010822846441 ] 
dist 117=[-1.6146134234323407036 ,1.4292690534436459538 ] 
dist 118=[-1.5810421541083391939 ,1.4958723563502531793 ] 
dist 119=[-1.5137057195018358112 ,1.5796820602543880329 ] 
dist 120=[-1.4965388799242626599 ,1.6608818837563795619 ] 
dist 121=[-1.4336720117358317970 ,1.7170499136455552022 ] 
dist 122=[-1.3120880831348004100 ,1.7660361890717935762 ] 
dist 123=[-1.2909928455179511939 ,1.8185191577907685792 ] 
dist 124=[-1.1752719729458412354 ,1.8864489530424691635 ] 
dist 125=[-.94713085548488920592,1.9646023401957167022 ] 
dist 126=[.77355768398924294341,2.0176066960922509006 ] 
dist 127=[.77566850804134979669,2.0627155224091441853 ] 
dist 128=[1.0924613907258150631 ,2.1092972453485269527 ] 
dist 129=[1.1307590094781602833 ,2.1536704099063117856 ] 
dist 130=[1.1368029550510789695 ,2.1899489638264651915 ] 
dist 131=[1.1477179494108708311 ,2.2275171721273845228 ] 
dist 132=[1.1496782138179577991 ,2.2770503549879011635 ] 
dist 133=[1.4116740995597097737 ,2.3245281711727827157 ] 
dist 134=[1.4276889701073825591 ,2.3538775807026539614 ] 
dist 135=[1.4309662502162946395 ,2.3757845722993028264 ] 
dist 136=[1.4486920402075408802 ,2.3934993038547658668 ] 
dist 137=[1.4492624271026295655 ,2.4074555341625422039 ] 
dist 138=[1.4452279608273754746 ,2.4143313632501791341 ] 
dist 139=[1.4338337344946197736 ,2.4178111569293920392 ] 
dist 140=[1.4184877948721890808 ,2.4181856353163151640 ] 
dist 141=[1.3986514677481174183 ,2.4083965939165420147 ] 
dist 142=[1.3715898095555081490 ,2.4055505701344258640 ] 
dist 143=[1.3273529094620797655 ,2.4016665332239852473 ] 
dist 144=[1.2810859389461243180 ,2.3997674978446810206 ] 
dist 145=[1.2459063743956758339 ,2.3931534555633647475 ] 
dist 146=[1.2118738036801699001 ,2.3906900747126399971 ] 
dist 147=[1.1701915575638054331 ,2.3847703423090548311 ] 
dist 148=[1.1264301179851026339 ,2.3822750314703338208 ] 
dist 149=[1.0840828415120092480 ,2.1584276349741262897 ] 
dist 150=[1.0343613293869194635 ,2.1374973911530187954 ] 
dist 151=[.96111239297326459426,2.0917410554625108550 ] 
dist 152=[.88495310257591787492,2.0798439734613551948 ] 
dist 153=[.8235936966343580212 ,2.0243645397685424582 ] 
dist 154=[.76089507090812290643,2.0135696542715704023 ] 
dist 155=[.67938000157322084786,1.9889513013146909840 ] 
dist 156=[.59130099444153693209,1.9824066318738647927 ] 
dist 157=[.50235501400520817048,1.9188256377955037550 ] 
dist 158=[.39509841212336105764,1.9084061553436621103 ] 
dist 159=[.23380095732654438903,1.8850865968974400058 ] 
dist 160=[.07223827878328526110,1.8785110071245452786 ] 
dist 161=[-.03607901349960862967,1.8472309013008922957 ] 
dist 162=[-.12688033276671388777,1.8407245715144876956 ] 
dist 163=[-.21840254417961758373,1.8264016741726885704 ] 
dist 164=[-.30415137783691381872,1.8219272459328032475 ] 
dist 165=[-.37186697165307803852,1.0174511496328407330 ] 
dist 166=[-.43981732319117518256,.98831115221148627011] 
dist 167=[-.5265050701073725369 ,.92018659444826699766] 
dist 168=[-.61105264945865397933,.90939503589820482126] 
dist 169=[-.67044525330652727114,.81710389763283115156] 
dist 170=[-.72319720584234200132,.80023547301477627445] 
dist 171=[-.7811910465741780492 ,.77747359469084199396] 
dist 172=[-.83861071437078954478,.7707075701930785559 ] 
dist 173=[-.88906686387375827142,.64219761788743269788] 
dist 174=[-.94444558819304026695,.62571958890244856076] 
dist 175=[-1.0263458811301691885 ,.59091266911385578619] 
dist 176=[-1.1158181917666993902 ,.58211487791516727289] 
dist 177=[-1.1743438419023873707 ,.54558023895843241746] 
dist 178=[-1.2218100845293003133 ,.53882964349032991859] 
dist 179=[-1.2670591206497991864 ,.52319740691167569545] 
dist 180=[-1.3077964142086301612 ,.52027107557476403918] 
dist 181=[-1.3372214959169644051 ,.34185032416818590017] 
dist 182=[-1.3641997969365253972 ,.32546168365211101389] 
dist 183=[-1.3951530044489248488 ,.28703668943268416763] 
dist 184=[-1.4237846369725874735 ,.28136427163721804013] 
dist 185=[-1.4625880096313114104 ,.22939010596383153287] 
dist 186=[-1.4939446792421226108 ,.22001250824529070458] 
dist 187=[-1.5227171248945529636 ,.20837489521755158134] 
dist 188=[-1.5557648289529210221 ,.20592273212571182134] 
dist 189=[-1.5863269248883208730 ,.13343385225230363232] 
dist 190=[-1.6051601062701689429 ,.12447625804703319283] 
dist 191=[-1.6191365244578100533 ,.10618634488375724097] 
dist 192=[-1.6302779235375134913 ,.10150182970137319121] 
dist 193=[-1.6390240134138951091 ,.08470534694161098847] 
dist 194=[-1.6434222002230972116 ,.08135450250151299821] 
dist 195=[-1.6455908855309355389 ,.07565941327866925482]