8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 0, 0, 0, 0, 1] 
dist 0=[41.511944735862345073  ,41.511944735862345073  ] 
dist 1=[40.744645561165953298  ,41.930492054543623296  ] 
dist 2=[39.918964477550205337  ,42.174748994557892967  ] 
dist 3=[39.267132859437524785  ,42.245735397526441140  ] 
dist 4=[38.615661114748584138  ,42.250174706410041204  ] 
dist 5=[37.791293502129382804  ,42.228676601731093740  ] 
dist 6=[36.915127553899306558  ,42.183991645620545441  ] 
dist 7=[36.056624663982243317  ,42.127178052059878100  ] 
dist 8=[35.043176854063746137  ,41.931014235951321135  ] 
dist 9=[33.547838719539563419  ,39.734951378495368305  ] 
dist 10=[31.999303769681959154  ,39.143290621638910046  ] 
dist 11=[30.773232925330434159  ,38.978958660030679693  ] 
dist 12=[29.543336736014918274  ,38.361840766102205481  ] 
dist 13=[27.979380833259971999  ,38.190451758717146081  ] 
dist 14=[26.311709961625042231  ,37.873872580404432551  ] 
dist 15=[24.667260762292928943  ,37.774451996855189436  ] 
dist 16=[22.717024675220707790  ,37.283837217763973033  ] 
dist 17=[19.827238166270095861  ,29.312836324568826317  ] 
dist 18=[16.933562455042634895  ,23.567758236026411442  ] 
dist 19=[14.967762078737374106  ,23.234414103629445968  ] 
dist 20=[13.296043653054238318  ,20.262203330852330950  ] 
dist 21=[11.577641741658451455  ,19.281966345900699186  ] 
dist 22=[9.9511022960049231272 ,18.569699821257180679  ] 
dist 23=[8.6465061757685218140 ,18.434992244550139331  ] 
dist 24=[7.3217795706823189034 ,16.604513095359310745  ] 
dist 25=[5.6147987835153039702 ,15.936859405795172199  ] 
dist 26=[3.9484661791330321126 ,11.145798387123863732  ] 
dist 27=[2.7861541693025178496 ,10.809271367744190361  ] 
dist 28=[1.7650276361520367568 ,9.6288738917189110083 ] 
dist 29=[.66282753921588447649,9.3839064945391548340 ] 
dist 30=[-.41371026736119188053,9.0517400586297119986 ] 
dist 31=[-2.1094742402744987380 ,8.9610553614324842948 ] 
dist 32=[-4.6080296894062065108 ,2.8719131143744662383 ] 
dist 33=[-7.0478997283971844856 ,2.8074234039946538737 ] 
dist 34=[-8.5816950466437058349 ,1.8764028030801099057 ] 
dist 35=[-9.7549990762910221657 ,1.7504100612925544023 ] 
dist 36=[-10.754123131805542816  ,1.5597616526999297218 ] 
dist 37=[-11.573745681574062810  ,1.5129616237714297126 ] 
dist 38=[-12.029828887212039808  ,1.4734002651914728807 ] 
dist 39=[-12.311820356767655903  ,1.5092019820694301142 ] 
dist 40=[-12.436189905615864304  ,1.5931015958034703247 ] 
dist 41=[-12.495074921271361441  ,1.7618477626389434739 ] 
dist 42=[-12.515308590593020445  ,1.9501167629443846021 ] 
dist 43=[-12.514081223238221058  ,2.1120620355051402534 ] 
dist 44=[-12.486544972315798918  ,2.2842497666346746462 ] 
dist 45=[-12.446539917512941645  ,2.5136717680058053154 ] 
dist 46=[-12.395172393836481667  ,2.7608186518507911118 ] 
dist 47=[-12.326536916114972965  ,3.0038392514162457452 ] 
dist 48=[-12.280396547899018162  ,3.2894591973841912091 ] 
dist 49=[-7.8668979809504922982 ,3.7066226360311242488 ] 
dist 50=[-4.7643588686701609991 ,4.1216644683512721254 ] 
dist 51=[-3.3822159713141825449 ,4.3988734933065471808 ] 
dist 52=[-3.1688328332320378291 ,4.6274952056471996441 ] 
dist 53=[-1.7969764308777827902 ,4.8487917927308381783 ] 
dist 54=[-1.0742644554543738301 ,5.0478662750733861291 ] 
dist 55=[-1.0154000788095735895 ,5.1878761763581327484 ] 
dist 56=[-.42154424410109649506,5.3111877697975101706 ] 
dist 57=[-.33268951322017586028,5.4436831284852055418 ] 
dist 58=[-.20879226405424803868,5.5592184037479816158 ] 
dist 59=[-.18057132139901918201,5.6148821215232426838 ] 
dist 60=[-.18667293245946704265,5.6373245539954688210 ] 
dist 61=[-.24399050712572240983,5.6269775049984913290 ] 
dist 62=[-.34905988825271169214,5.5794394898557674587 ] 
dist 63=[-.55602277372199249989,5.5538307670634435649 ] 
dist 64=[-.85530749973029019271,5.3965144716433681807 ] 
dist 65=[-1.0623733305042794967 ,3.8326237738610051903 ] 
dist 66=[-1.2408129313098716371 ,3.9921864558746488392 ] 
dist 67=[-1.4259746412887691523 ,4.1021288034806964304 ] 
dist 68=[-1.6005446126201869428 ,4.1828425506111434093 ] 
dist 69=[-1.7367590292518304503 ,4.2256216311427657965 ] 
dist 70=[-1.8705317926776234062 ,4.2491315674028283462 ] 
dist 71=[-2.0353709755235431256 ,4.2527538349542501401 ] 
dist 72=[-2.1905667712106825333 ,3.9057700360331559776 ] 
dist 73=[-2.2858780152669513957 ,3.8953164493542092771 ] 
dist 74=[-2.3552597903729528361 ,3.7596563909986355663 ] 
dist 75=[-2.4070324482058141492 ,3.7307579603494387246 ] 
dist 76=[-2.4432342998069493078 ,3.6330041056490868318 ] 
dist 77=[-2.4504997772040255018 ,3.6182869806904110542 ] 
dist 78=[-2.4465883654062178979 ,3.5454423434037323077 ] 
dist 79=[-2.4382396701240643548 ,3.5324210066054860290 ] 
dist 80=[-2.0707503727338382990 ,3.2713013370249528382 ] 
dist 81=[-2.6755196167601422694 ,3.2601605897942820305 ] 
dist 82=[-3.2730775612390632066 ,.31347010604582782829] 
dist 83=[-3.6601773961966667395 ,.2554935029807112874 ] 
dist 84=[-3.9677260392136271708 ,-.21858357125130060267] 
dist 85=[-4.2476863456630533829 ,-.33701665523547526052] 
dist 86=[-4.4889543810651057574 ,-.45811148132871776799] 
dist 87=[-4.6420346732756766097 ,-.48527043564030706805] 
dist 88=[-4.7600907368610830478 ,-.84223516095012197547] 
dist 89=[-4.8615455733913079398 ,-.9578061491816087716 ] 
dist 90=[-4.9396689239770508460 ,-.92782761766697845946] 
dist 91=[-4.9645751030622881251 ,-.82558900150939077062] 
dist 92=[-4.9667874507773538721 ,-.68472233417562323318] 
dist 93=[-4.9542752760937025927 ,-.5005356957429892795 ] 
dist 94=[-4.8294300083996100967 ,-.24925405763302650586] 
dist 95=[-4.8182174225393957342 ,.15945448821716128583] 
dist 96=[-4.8105643556381848175 ,.5793134772545438280 ] 
dist 97=[-4.7967696775685781984 ,.8751122679151890223 ] 
dist 98=[-3.4485882021634818372 ,1.1368449164121537634 ] 
dist 99=[-3.3058104153361566404 ,1.4207267364687985612 ] 
dist 100=[-2.9643805427716535642 ,1.8343488782552162973 ] 
dist 101=[-2.8968852398182600642 ,2.3615709395000262957 ] 
dist 102=[-2.3986238036060193167 ,2.8429136565683923319 ] 
dist 103=[-2.3021323795197749694 ,3.1962887273831516419 ] 
dist 104=[-2.1426092398684768580 ,3.5238584114073873470 ] 
dist 105=[-2.1015651487118454464 ,3.9021839649213254424 ] 
dist 106=[-1.3282992917644076902 ,4.2503550883009279701 ] 
dist 107=[-1.2866666660626671391 ,4.4575472562397687185 ] 
dist 108=[-1.2251651268461213866 ,4.6012806629380251282 ] 
dist 109=[-1.2113158947179553026 ,4.6961235861234761175 ] 
dist 110=[-1.1750180304192529207 ,4.7620738347023346602 ] 
dist 111=[-1.1647929064239992526 ,4.7904671813640647282 ] 
dist 112=[-.45022456363098843246,4.7967926496423208002 ] 
dist 113=[-.42457949526662540224,4.7902238276192311595 ] 
dist 114=[-.50153823238249746928,2.0056368148153252200 ] 
dist 115=[-.58685474575097135042,2.1579338656767686519 ] 
dist 116=[-.67221225471954495937,2.2883824825053905725 ] 
dist 117=[-.7509053564024300152 ,2.3696384209564253905 ] 
dist 118=[-.80963168829345540843,2.4305288658934221630 ] 
dist 119=[-.86488458813613356363,2.4796783821539186882 ] 
dist 120=[-.9297157246080905426 ,2.5172428132863219510 ] 
dist 121=[-.98928009776793381058,2.5318814296998364650 ] 
dist 122=[-1.0235173710677459098 ,2.5337352907227630006 ] 
dist 123=[-1.0456844420736143593 ,2.5302405636812024184 ] 
dist 124=[-1.0570881377678501549 ,2.4895372079870190843 ] 
dist 125=[-1.0626777120696657533 ,2.4753283827235748230 ] 
dist 126=[-1.0616481404000500430 ,2.4377411108940351401 ] 
dist 127=[-1.0570019190301347782 ,2.4213289735903913320 ] 
dist 128=[-1.0528453590995439468 ,1.6789397390674313437 ] 
dist 129=[-.2462982543467087997 ,1.6046633349237521920 ] 
dist 130=[-.50369647192864429139,1.4171376306818488041 ] 
dist 131=[-.76169193177632798949,1.3900189230490754500 ] 
dist 132=[-1.0005788079865653945 ,1.0908951349481928657 ] 
dist 133=[-1.1816941454931591497 ,1.0335219674661026187 ] 
dist 134=[-1.3553300033605273421 ,.97142175482408854166] 
dist 135=[-1.5643586062339754690 ,.95971615773410779799] 
dist 136=[-1.7600910993549530061 ,.41469015198784089002] 
dist 137=[-1.8806475117789704944 ,.34759546286469687336] 
dist 138=[-1.9693192201433678756 ,.21064751026142373145] 
dist 139=[-2.0377641275262795959 ,.17563971738948799797] 
dist 140=[-2.0902511905391199455 ,.05212880190855361352] 
dist 141=[-2.1152167239913483509 ,.02669676011202711469] 
dist 142=[-2.1256041443919090904 ,-.00681072942984326534] 
dist 143=[-2.1257554210951994596 ,-.01435976785569884305] 
dist 144=[-1.1455168327717989776 ,-.30089470048366661694] 
dist 145=[-1.1428118759518078113 ,-.16353595594745813308] 
dist 146=[-1.1398385305581995563 ,-.06595266879637018827] 
dist 147=[-1.1262865649856783996 ,.02121926148195350435] 
dist 148=[-1.1290951521105512239 ,.11702333982912857845] 
dist 149=[-1.1692504316402997870 ,.21109899876691247603] 
dist 150=[-1.1967205878891015875 ,.29137456506076145651] 
dist 151=[-1.2141176585985666174 ,.37696263454433471663] 
dist 152=[-1.2262424307439964134 ,.49224866877399582944] 
dist 153=[-1.2326634339351337531 ,.60639478352564886541] 
dist 154=[-1.2361525674401479615 ,.6874345287184706238 ] 
dist 155=[-1.2365694468270973388 ,.75979867354670064106] 
dist 156=[-1.2349865726925868734 ,.83931555189522094862] 
dist 157=[-1.2310491949624859083 ,.91742173593147185305] 
dist 158=[-1.2233972966415863729 ,.98415720827530241094] 
dist 159=[-1.2191805652194736936 ,1.0554065888151575076 ] 
dist 160=[-.95448650366617279999,1.1515368907971358721 ] 
dist 161=[-.94479498436653687873,1.2433588601576846127 ] 
dist 162=[-.91818246565737287673,1.2974098878527370630 ] 
dist 163=[-.91043001297482586516,1.3341966162547172465 ] 
dist 164=[-.85475873514423797703,1.3570964312616791582 ] 
dist 165=[-.8417818822823550399 ,1.3722355158243176819 ] 
dist 166=[-.82032263143528055896,1.3780391264099515911 ] 
dist 167=[-.81374034437721627947,1.3781234077910628226 ] 
dist 168=[-.66105057505043548551,1.3757734153049362254 ] 
dist 169=[-.6392294870474117029 ,1.2510640561939921388 ] 
dist 170=[-.59044815379901140701,1.2304816039421108537 ] 
dist 171=[-.5765500533546552591 ,1.1916433654482154925 ] 
dist 172=[-.51280530427792668719,1.1802287203643221569 ] 
dist 173=[-.49990787243515974527,1.1521924118880397388 ] 
dist 174=[-.4699308448861778406 ,1.1518994684262162549 ] 
dist 175=[-.46154623349458096282,1.1492680526815202806 ] 
dist 176=[-.10732597619504970957,1.0845112847312154612 ] 
dist 177=[-.07507215404134752531,1.0110090765877817626 ] 
dist 178=[-.21049727766315212501,.96240569816287311559] 
dist 179=[-.3470411667564755477 ,.95519681763905764615] 
dist 180=[-.4815841906674007426 ,.90183616820018630895] 
dist 181=[-.60467386424371672774,.9018495971790701137 ] 
dist 182=[-.69549430143379521555,.8951914880371496863 ] 
dist 183=[-.7801438744100153194 ,.89303189596875045099] 
dist 184=[-.87859792709672487485,.84305862165848440664] 
dist 185=[-.96980638852390626483,.83351016567225726824] 
dist 186=[-1.0255307671867928776 ,.80792110609560028806] 
dist 187=[-1.0659746409586457250 ,.80067000185206486792] 
dist 188=[-1.0961825177888255654 ,.74959798602942236352] 
dist 189=[-1.1186336382220680167 ,.73788017074163601355] 
dist 190=[-1.1281116430154475393 ,.71808490736571627463] 
dist 191=[-1.1311129236495139010 ,.71223051791813076588] 
dist 192=[-1.1298245497110331634 ,.70222629172716594544] 
dist 193=[-.77605291974757603803,.72278393669579220708] 
dist 194=[-.84372450716661201232,.73591624240665739343] 
dist 195=[-.89599729164540416792,.74233304926275931322] 
dist 196=[-.94099470523256864371,.74528583209248059223] 
dist 197=[-.97792440180649871792,.74459241529665112049] 
dist 198=[-.99798938371792638838,.7416961093380439219 ] 
dist 199=[-1.0095648533330346975 ,.73933482444860022786] 
dist 200=[-1.0126034113547225738 ,.67143688902588327279] 
dist 201=[-1.0116813170228585342 ,.66010617770250011965] 
dist 202=[-1.0088849324118462444 ,.63619046843423701231] 
dist 203=[-1.0014086168583859478 ,.62865061143836712823] 
dist 204=[-.99713406457579913378,.59439644810716048404] 
dist 205=[-.95782148826265609087,.58701320664337550214] 
dist 206=[-.96264106152020940007,.56421062912215103545] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 2, 1, 2] 
dist 0=[52.827770948779295863  ,52.827770948779295863  ] 
dist 1=[51.741024773726698469  ,53.678558672030223503  ] 
dist 2=[50.403837462568560564  ,54.073519442645480512  ] 
dist 3=[48.624391822672671936  ,54.261210234077842104  ] 
dist 4=[45.771378767767159858  ,54.284225893340734067  ] 
dist 5=[42.843312536741793422  ,53.739349766225645875  ] 
dist 6=[40.764033460636605845  ,53.584876119227837281  ] 
dist 7=[38.903747011728486958  ,52.926258196738114073  ] 
dist 8=[36.850010104671507248  ,52.790383153068849611  ] 
dist 9=[34.822835212002095257  ,52.132245514821448148  ] 
dist 10=[33.068411325573071859  ,51.940414404031327446  ] 
dist 11=[31.172756399540989451  ,51.375779907884904794  ] 
dist 12=[28.581157125037834885  ,51.180862831587589963  ] 
dist 13=[25.987010709845593593  ,49.873210178390365521  ] 
dist 14=[24.080966022201964980  ,49.539523336238874347  ] 
dist 15=[22.307506733428617031  ,48.051086576185407112  ] 
dist 16=[20.242607405327980802  ,45.375756431796722437  ] 
dist 17=[18.138527804825400640  ,26.989021100384527934  ] 
dist 18=[16.208173317243528506  ,26.107944715849314877  ] 
dist 19=[14.026824045074450229  ,25.034014622487956449  ] 
dist 20=[10.919347358940254626  ,24.768830466172120538  ] 
dist 21=[7.8525175553050213828 ,17.263915034347351972  ] 
dist 22=[5.8334384776287967245 ,16.325939598857671177  ] 
dist 23=[4.1857104607854891537 ,14.373560442831116089  ] 
dist 24=[2.6027623558446474492 ,13.863512657970385055  ] 
dist 25=[1.1730708039628934447 ,11.981220525011123222  ] 
dist 26=[.1376482579591581467 ,11.614127642018967716  ] 
dist 27=[-1.1868463723356705365 ,10.929868917725963014  ] 
dist 28=[-3.1193079758860231824 ,10.772066355149678811  ] 
dist 29=[-4.9737722774170381503 ,.84898103940843504319] 
dist 30=[-6.5028921859358404595 ,-.01306361801532767183] 
dist 31=[-8.0952634333136429818 ,-1.8234375911941511755 ] 
dist 32=[-10.203675093928956764  ,-2.2135372773992212580 ] 
dist 33=[-12.217799398758271463  ,-3.9369406096121964927 ] 
dist 34=[-13.433705216808005792  ,-4.2388813172922430386 ] 
dist 35=[-14.306912720008153703  ,-4.3531435445347252535 ] 
dist 36=[-14.951329389700923126  ,-4.1199830177915207586 ] 
dist 37=[-15.439301727284795690  ,-3.8471429990223032308 ] 
dist 38=[-15.686982331108612755  ,-3.6196460596900445200 ] 
dist 39=[-15.809280022447125371  ,-3.3843377630386702562 ] 
dist 40=[-15.811302874971093391  ,-3.0797128837044359104 ] 
dist 41=[-15.210709271851198202  ,-2.7559828779430440214 ] 
dist 42=[-15.237162250977962714  ,-2.2859659415350933420 ] 
dist 43=[-15.203533005129394025  ,-1.1470241723153619652 ] 
dist 44=[-15.149309566042055383  ,.6449226349073797423 ] 
dist 45=[-13.485134592652382125  ,2.4596692414187558204 ] 
dist 46=[-13.354571841656295518  ,3.6897474654153760268 ] 
dist 47=[-13.173601719149180472  ,4.7262469155772432285 ] 
dist 48=[-13.095096856235421183  ,5.7686884562746223419 ] 
dist 49=[-3.4130575989927222766 ,6.7347344972001189394 ] 
dist 50=[-2.5976811319065257180 ,7.4664898617871897846 ] 
dist 51=[-1.9862221037888513121 ,8.1668198823828657981 ] 
dist 52=[-1.9716224261872834204 ,9.0076323853788758127 ] 
dist 53=[1.8137488594754061820 ,9.7935407863441647318 ] 
dist 54=[2.1971474962604895538 ,10.274824288348292784  ] 
dist 55=[2.8987091297040100505 ,10.625665376275105988  ] 
dist 56=[3.0492637599700152943 ,10.891021492729074886  ] 
dist 57=[4.1067313693482853999 ,11.082161445902094616  ] 
dist 58=[4.1732705278467181240 ,11.136888324054242341  ] 
dist 59=[4.2596937562350729396 ,11.132190380608416508  ] 
dist 60=[4.2424098421039251784 ,11.092907667040684539  ] 
dist 61=[4.1889248574517447971 ,10.741330851686629262  ] 
dist 62=[4.0922348645755186994 ,10.644865120588956115  ] 
dist 63=[3.9455970307616401021 ,10.389473213605264249  ] 
dist 64=[3.4028755168462587590 ,10.041601761692765043  ] 
dist 65=[2.4826390502854097199 ,4.5100021310208632946 ] 
dist 66=[1.8540101815786951312 ,4.4940386764842733773 ] 
dist 67=[1.3189359476958114430 ,4.4735862433841198977 ] 
dist 68=[.7719777028125062167 ,4.4556560637079440993 ] 
dist 69=[.2594067899368066726 ,1.7520527739206881661 ] 
dist 70=[-.1384871400580218860 ,1.5264057960103386758 ] 
dist 71=[-.5286153144505686713 ,.9858794765492636340 ] 
dist 72=[-1.0102724135941878639 ,.9077461515009473664 ] 
dist 73=[-1.4671268140426609095 ,.1538668570365845326 ] 
dist 74=[-1.7582996167055328368 ,.0190806854011325485 ] 
dist 75=[-1.9841048176264106802 ,-.1475064020872957641 ] 
dist 76=[-2.1800940089910678641 ,-.1771969305785823209 ] 
dist 77=[-2.3423769167428297340 ,-1.1182665704093001362 ] 
dist 78=[-2.4336954130482673347 ,-1.2152303770808746966 ] 
dist 79=[-2.4909516896012222610 ,-1.4176405067958748643 ] 
dist 80=[-2.5173802372975570292 ,-1.4558446191799280438 ] 
dist 81=[-2.5299904485474918099 ,-1.6292896988099666134 ] 
dist 82=[-2.5320983535490315989 ,-1.6585549364827603548 ] 
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dist 134=[-1.2682166267246699216 ,.50222131871504933554] 
dist 135=[-1.2584767683623053485 ,.62983049395968646492] 
dist 136=[-1.2551970605580419226 ,.7561432837465214535 ] 
dist 137=[-1.2005509226696586483 ,.8719885253672457267 ] 
dist 138=[-1.1861037414698880413 ,.9578156417235016541 ] 
dist 139=[-1.1729204616600368803 ,1.0381089748565796334 ] 
dist 140=[-1.1648169639672842890 ,1.1318644515935733881 ] 
dist 141=[-.93626063338784831699,1.2180703597278545346 ] 
dist 142=[-.90425748465829301694,1.2682288260988065051 ] 
dist 143=[-.84093834040976665362,1.3015888775257147934 ] 
dist 144=[-.82376028971581755781,1.3207433322254247731 ] 
dist 145=[-.75917690685983678076,1.3325640248641733145 ] 
dist 146=[-.74409422155776002701,1.3366521872267096784 ] 
dist 147=[-.71567681659924598873,1.3358527347040121332 ] 
dist 148=[-.70767570794341788553,1.3328759036207321973 ] 
dist 149=[-.09083477030278359269,.8282326732066067301 ] 
dist 150=[-.04473922263981136483,.9097353941230772438 ] 
dist 151=[.05708008596607346462,.9847025351596900582 ] 
dist 152=[.07675924746599428410,1.0704372226696915664 ] 
dist 153=[.19204278574056727919,1.1484488144880605475 ] 
dist 154=[.21133106957048817755,1.1925859765075338062 ] 
dist 155=[.25072100400153006051,1.2204009506052750057 ] 
dist 156=[.2334992509695954745 ,1.2332558956075091885 ] 
dist 157=[.1848842528310362876 ,1.2400407496883398393 ] 
dist 158=[.1252552337026825104 ,1.2436221589672924743 ] 
dist 159=[.0461339027739037418 ,1.2455491224839359013 ] 
dist 160=[-.0802867995320667305 ,1.2457227116275077848 ] 
dist 161=[-.2089974822064698392 ,1.0725618451301589816 ] 
dist 162=[-.2972615532880547091 ,1.0748138508020668759 ] 
dist 163=[-.3728174731593615359 ,1.0713350981641418732 ] 
dist 164=[-.4508081796097312864 ,1.0695753498766524650 ] 
dist 165=[-.5244235051491738075 ,.7764191033837074446 ] 
dist 166=[-.5825184162654202921 ,.7586325138550685373 ] 
dist 167=[-.6403975422081502996 ,.7607574853816767817 ] 
dist 168=[-.7131568059173838080 ,.7596217464071315789 ] 
dist 169=[-.7828304165384998437 ,.7445350881741467671 ] 
dist 170=[-.8283954440132909481 ,.7391201162374553658 ] 
dist 171=[-.8650616082323049732 ,.7314321192149713121 ] 
dist 172=[-.8992169379872329394 ,.7278306084609562512 ] 
dist 173=[-.9291958019055459274 ,.62396416382764281699] 
dist 174=[-.9535781206067627706 ,.60848019472818666917] 
dist 175=[-.9906778823579952742 ,.57607215370967389881] 
dist 176=[-1.0337825834615853193 ,.56653694045750845613] 
dist 177=[-1.0724040015146028528 ,.52617289486116377067] 
dist 178=[-1.0916078664404369888 ,.51761616017375644195] 
dist 179=[-1.1012597959327629994 ,.61308201466278579047] 
dist 180=[-1.1023433736544030785 ,.70862527589229819932] 
dist 181=[-1.0901862210670413135 ,.7956527717936679321 ] 
dist 182=[-1.0846672858830953216 ,.8591110642642848470 ] 
dist 183=[-1.0790757034505317883 ,.9174681694093404548 ] 
dist 184=[-1.0742027252652887959 ,.9841324942730718124 ] 
dist 185=[-1.0878641647142888153 ,1.0446460583111088623 ] 
dist 186=[-1.0967320189646837268 ,1.0784516858691415878 ] 
dist 187=[-1.0995358428312821924 ,1.0991636154888748493 ] 
dist 188=[-1.0986940091601996840 ,1.1074133534268103644 ] 
dist 189=[-1.0154713605161714187 ,1.1105433191143336758 ] 
dist 190=[-1.0009554000100348266 ,1.1108208042413843027 ] 
dist 191=[-.98079747184420397248,1.1090555066609623843 ] 
dist 192=[-.97936993031790491433,1.1053795908784208045 ] 
dist 193=[-.96714695899990014567,.1513439791393410326 ] 
dist 194=[-.9627773989941809441 ,.2819103286800998002 ] 
dist 195=[-.9457060511518305080 ,.3901596275036115485 ] 
dist 196=[-.9414401668960996206 ,.4963540872637972255 ] 
dist 197=[-.5665599007002120382 ,.5931848001202332175 ] 
dist 198=[-.53039357564035671482,.6640555515005255683 ] 
dist 199=[-.44241776447231762585,.7295336915950020446 ] 
dist 200=[-.42862559697520342623,.8048389224179037190 ] 
dist 201=[-.29916237676272641591,.8739481041054839461 ] 
dist 202=[-.27500542608104742553,.9146920670541542893 ] 
dist 203=[-.24406308923253258649,.9424901881365678265 ] 
dist 204=[-.23549106246116922353,.9599190870519156491 ] 
dist 205=[-.13650435109415559817,.9716368452544419763 ] 
dist 206=[-.1230548769679527117 ,.9766364031478245927 ] 
dist 207=[-.09414615137364467666,.9776780097561047101 ] 
dist 208=[-.08680389609824250014,.9759547355052683972 ] 
dist 209=[-.05524668412800246723,.8361098244024726930 ] 
dist 210=[-.04943523494392465575,.8447290996812089392 ] 
dist 211=[-.03596503647323080031,.8479071304809169631 ] 
dist 212=[-.03348183053872014777,.8474935432169608742 ] 
dist 213=[-.0609340132472758055 ,.71110358745258081792] 
dist 214=[-.12018252966781638619,.7044665001346254547 ] 
dist 215=[-.19671159970779833746,.6881169190433579778 ] 
dist 216=[-.29964875074071028332,.6819105333012244331 ] 
dist 217=[-.40150001977523329066,.6497442348050357544 ] 
dist 218=[-.47369490617110929957,.6419504613132782380 ] 
dist 219=[-.53803811373194697215,.6242210937597216402 ] 
dist 220=[-.60854708042615000104,.6180340074116195723 ] 
dist 221=[-.67768110563916097129,.5346635212831650283 ] 
dist 222=[-.73653638671881651503,.5217946893209995739 ] 
dist 223=[-.79917761780750348434,.48871049512200422451] 
dist 224=[-.88342604125388288843,.48246571838052551316] 
dist 225=[-.9638643085665778825 ,.4237044225137234112 ] 
dist 226=[-1.0112957863087521847 ,.4116645065384708125 ] 
dist 227=[-1.0436649519660862706 ,.3965249514357359576 ] 
dist 228=[-1.0639747402413814913 ,.3909041214641344133 ] 
dist 229=[-1.0778957014867085149 ,.21806434928773016655] 
dist 230=[-1.0847606865686037858 ,.19735536328407093374] 
dist 231=[-1.0877767324464299258 ,.1566961988028507758 ] 
dist 232=[-1.0863325138459692706 ,.14647896423096851515] 
dist 233=[-.97342981492349396197,.11212456232408955251] 
dist 234=[-.95557617457411848557,.1041948210820803344 ] 
dist 235=[-.94391040938113739414,.09779129828110751262] 
dist 236=[-.94457923528426684494,.09855165398306970645] 
dist 237=[-.94162920718864851673,.10253429470064359056] 
dist 238=[-.93914898817130655751,.11068812386909985468] 
dist 239=[-.92618679029473620055,.12346636134105396956] 
dist 240=[-.89863009113711262837,.1459097495583145074 ] 
dist 241=[-.58560186122005512754,.1728711593365266196 ] 
dist 242=[-.55312171470084317997,.23891117996302896694] 
dist 243=[-.47199635559889012222,.32234470362674806359] 
dist 244=[-.39284266923985720784,.40190408237999595243] 
dist 245=[-.26689356343411114238,.47294926914723202152] 
dist 246=[-.25257041192317900252,.52239487907376797   ] 
dist 247=[-.22669010255504758707,.5655235548413706597 ] 
dist 248=[-.22051326519511977224,.61135249042366337911] 
dist 249=[-.12096777100095582922,.6617170579792649155 ] 
dist 250=[-.10737484229346379111,.7113799200611791174 ] 
dist 251=[-.07688962691961191669,.74820496248046987741] 
dist 252=[-.07061320097981254377,.77717362654933446839] 
dist 253=[-.0336060223519325486 ,.7996223263414454474 ] 
dist 254=[-.0270163613848235359 ,.8104198039822597750 ] 
dist 255=[-.0138261486775998796 ,.8152150641287165179 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 1, 2, 0, 0, 1] 
dist 0=[45.281647665517075090  ,45.281647665517075090  ] 
dist 1=[44.851031100915679083  ,45.546160445858483712  ] 
dist 2=[44.215508157393859043  ,45.764557326034261910  ] 
dist 3=[43.132588977345849569  ,46.010839471013999025  ] 
dist 4=[41.825584221774419335  ,46.324325505451003196  ] 
dist 5=[40.295083442386935200  ,46.810702905046391530  ] 
dist 6=[38.304045519428547281  ,47.282280062034589607  ] 
dist 7=[35.157720900302430811  ,47.536681861055078686  ] 
dist 8=[31.957609050921807413  ,47.680062082223449087  ] 
dist 9=[29.751652755085714568  ,47.708734995997304637  ] 
dist 10=[27.846023424428213648  ,47.661078132213079715  ] 
dist 11=[25.845076234995595691  ,47.612085626120918254  ] 
dist 12=[23.928986339134352804  ,47.333537638762934182  ] 
dist 13=[22.361990768430619289  ,47.264681499751142476  ] 
dist 14=[20.745268908987368438  ,38.581677816088299833  ] 
dist 15=[18.630060111178994701  ,37.754586017102390680  ] 
dist 16=[16.552509401769756456  ,35.682189462790738099  ] 
dist 17=[15.085926763934246544  ,35.368558505252036487  ] 
dist 18=[13.779582861140336986  ,32.054013633941660851  ] 
dist 19=[12.341740620390313576  ,31.405847083948349779  ] 
dist 20=[10.919802005472965325  ,30.691479129418859000  ] 
dist 21=[9.6764838193806306544 ,30.516197016933136953  ] 
dist 22=[8.3176988099785188272 ,24.098623872100087477  ] 
dist 23=[6.4333978136236298398 ,23.273996530976649844  ] 
dist 24=[4.5889289622993150066 ,21.633499155951971941  ] 
dist 25=[3.3891648242029522161 ,21.209638540826874353  ] 
dist 26=[2.4228276368715342881 ,19.702670493691329323  ] 
dist 27=[1.5116497164669969220 ,19.369392954057461058  ] 
dist 28=[.69643881721275246363,18.872972393016212338  ] 
dist 29=[-.91516503773621806568,18.728893821299559097  ] 
dist 30=[-2.4814758281962684913 ,5.6057485387777293957 ] 
dist 31=[-3.7248556375603344901 ,4.5087784040854014362 ] 
dist 32=[-4.8636591888432815397 ,2.0179428869263573867 ] 
dist 33=[-5.8571557737561743717 ,1.6110270960186569501 ] 
dist 34=[-6.5198383019775018842 ,-.54158256411469656897] 
dist 35=[-7.0721812958937688175 ,-.43979131407995592146] 
dist 36=[-7.6249502921205126921 ,-.27402396127413558721] 
dist 37=[-8.8258008371559814510 ,-.03425729644617057000] 
dist 38=[-10.160699227775008069  ,.3032818686436318592 ] 
dist 39=[-10.976508582424667494  ,.85925765510699879392] 
dist 40=[-11.571324416203528469  ,1.4244662115430941563 ] 
dist 41=[-12.023436028584796871  ,1.7989926375455803291 ] 
dist 42=[-12.373360286495235421  ,2.1037250639667348228 ] 
dist 43=[-12.559919542318411442  ,2.3908041668086220028 ] 
dist 44=[-12.663371594221239116  ,2.6429886319858879356 ] 
dist 45=[-12.681143963302417670  ,2.8086358608598062399 ] 
dist 46=[-7.4867314900393358002 ,2.9418559651463290956 ] 
dist 47=[-7.1824030106244193228 ,3.0647455921963416530 ] 
dist 48=[-6.4209266334059658340 ,3.1706939828088018061 ] 
dist 49=[-6.3099616877554785058 ,3.2363409925802187293 ] 
dist 50=[-5.1258985356513468055 ,3.2845494599488234553 ] 
dist 51=[-4.9019082718466415327 ,3.3208995126098935858 ] 
dist 52=[-4.6499200811695288462 ,3.3460804332847025296 ] 
dist 53=[-4.6008613141974455042 ,3.3496644497829432052 ] 
dist 54=[-2.5731826287969742291 ,3.3385475353631379483 ] 
dist 55=[-2.3249655302287002802 ,3.3285588636261223231 ] 
dist 56=[-1.8133199703829072406 ,2.4691813132680603537 ] 
dist 57=[-1.6821834705126653746 ,2.9154306867382241068 ] 
dist 58=[-1.2149598850954240220 ,3.2837509629914208602 ] 
dist 59=[-1.1216926291971032168 ,3.6666150568317866416 ] 
dist 60=[-.9870118754530317846 ,4.1711154934420869489 ] 
dist 61=[-.9516328268141569732 ,4.6550329792741241219 ] 
dist 62=[.0509989643538319891 ,4.9557316496588968401 ] 
dist 63=[-.2165644091057167295 ,5.1809684549537299042 ] 
dist 64=[-.4739202114446371427 ,5.3634563662536568678 ] 
dist 65=[-.64370685742401673075,5.5055662168852628272 ] 
dist 66=[-.78190154695551125471,5.5695357465820816054 ] 
dist 67=[-.91319719086413883918,5.5973065042166753890 ] 
dist 68=[-1.0301603464131007308 ,5.5947012342843725979 ] 
dist 69=[-1.1111776470161531052 ,5.4993349928216958107 ] 
dist 70=[-1.1815507350684240710 ,5.4692918719064836277 ] 
dist 71=[-1.2560794478180366747 ,5.3897473304294505316 ] 
dist 72=[-1.3240461737140757240 ,5.3556108470707581657 ] 
dist 73=[-1.3682337231596124851 ,5.1664561586146049063 ] 
dist 74=[-1.4036910159336931602 ,5.1183634898320052818 ] 
dist 75=[-1.4367787750288659613 ,5.0146440751710284758 ] 
dist 76=[-1.4660567447256290557 ,4.9903486723383206865 ] 
dist 77=[-1.4862958548826532931 ,4.7832500341178322559 ] 
dist 78=[-1.5039407048429958027 ,3.5013941133475447263 ] 
dist 79=[-1.7147782936999250900 ,3.1458120437250383306 ] 
dist 80=[-2.2832564262248761181 ,3.0942405706099390572 ] 
dist 81=[-2.8036790964595446180 ,2.5220663586324882251 ] 
dist 82=[-3.1888777916179425241 ,2.4114970539601188711 ] 
dist 83=[-3.5493665565432225086 ,2.2932947741324881616 ] 
dist 84=[-3.9711390968671805862 ,2.2703824259868370432 ] 
dist 85=[-4.3613441384880789279 ,1.1954450994781181457 ] 
dist 86=[-4.5957903195482528192 ,1.0616910042927695768 ] 
dist 87=[-4.7613794319620602722 ,1.0755729086105154473 ] 
dist 88=[-4.8766410635568204807 ,1.4735054784291769461 ] 
dist 89=[-4.9610588678144184048 ,1.7316780765810256596 ] 
dist 90=[-5.0034960117925149859 ,1.9370817666129356089 ] 
dist 91=[-5.0233739099881751126 ,2.1243710285743861766 ] 
dist 92=[-5.0188985313271035914 ,2.2858444599556501242 ] 
dist 93=[-4.1828893155260337284 ,2.3881982206056023843 ] 
dist 94=[-4.0405001775489846994 ,2.4669386229958429518 ] 
dist 95=[-4.0194905586347464549 ,2.5341577927436025101 ] 
dist 96=[-3.9486817728813270568 ,2.5885043230769077945 ] 
dist 97=[-3.9259127917203621035 ,2.6158575207107076069 ] 
dist 98=[-3.7333341953825645762 ,2.6287221078157297642 ] 
dist 99=[-3.6860917387391377031 ,2.7037961342298472130 ] 
dist 100=[-3.6171219131660145471 ,2.9791923594651757608 ] 
dist 101=[-3.5919005023444314448 ,3.3122730607127906520 ] 
dist 102=[-2.4885675650894430387 ,3.6246048364228248922 ] 
dist 103=[-2.3563011597828010483 ,3.8171861467390863449 ] 
dist 104=[-2.1287723798158272002 ,3.9589680692828657763 ] 
dist 105=[-2.0749626679818553430 ,4.0685397720971704611 ] 
dist 106=[-1.6429858061865067741 ,4.1490543923989392758 ] 
dist 107=[-1.5949900421316705953 ,4.1748589906525264598 ] 
dist 108=[-1.5221288893404064049 ,4.1803704946902883171 ] 
dist 109=[-1.5008837173870329820 ,4.1798717759728108733 ] 
dist 110=[-1.0689449108597481003 ,.7133229662350560562 ] 
dist 111=[-1.2912484190456634878 ,.76594530279078147315] 
dist 112=[-1.5013607408695407688 ,1.0237279820397473959 ] 
dist 113=[-1.6339984630540795557 ,1.2681451796700551541 ] 
dist 114=[-1.7353539528051184457 ,1.4855993598095828632 ] 
dist 115=[-1.8205934757564598315 ,1.6357431557516235782 ] 
dist 116=[-1.8889988323855448342 ,1.7655310488931155237 ] 
dist 117=[-1.9231553468851244681 ,1.9017299036893661111 ] 
dist 118=[-1.9405026632681211417 ,2.0248365269753151229 ] 
dist 119=[-1.9425158403739388496 ,2.1023558010971808514 ] 
dist 120=[-.87578465976190655701,2.1614550594540445137 ] 
dist 121=[-.9631971653249495279 ,2.2110104648717609352 ] 
dist 122=[-1.0327171450946024630 ,2.2507371514566958467 ] 
dist 123=[-1.0961092678778639961 ,2.2705904608619801241 ] 
dist 124=[-1.1508030064236038241 ,2.2797217850242548350 ] 
dist 125=[-1.1855972222246242828 ,2.2772684307477439638 ] 
dist 126=[-1.2125271550388385637 ,1.4001898114793457240 ] 
dist 127=[-1.2358267690850597640 ,1.3247017130724217560 ] 
dist 128=[-1.2533402695651911338 ,1.1510355608616665407 ] 
dist 129=[-1.2573269271216199895 ,1.1137699678653289493 ] 
dist 130=[-1.2562910387002906744 ,.88341287360415357491] 
dist 131=[-1.2549971260234001028 ,.84005565780037841392] 
dist 132=[-1.2109500556668107224 ,.7568842020750519294 ] 
dist 133=[-1.1984139539272124011 ,.73577534158751452658] 
dist 134=[-1.1898786353761671927 ,.45839264813815211597] 
dist 135=[-1.1845700967725979659 ,.41855960519878990986] 
dist 136=[-.9827002377496794075 ,.4443754942359586194 ] 
dist 137=[-.96008824706526358225,.6126945309219535538 ] 
dist 138=[-.90662036595861931267,.7503487025417135530 ] 
dist 139=[-1.0201232143328696146 ,.8822796793309083080 ] 
dist 140=[-1.2008474743630782373 ,1.0005477379079404285 ] 
dist 141=[-1.4527711330772468653 ,1.0836615486333608610 ] 
dist 142=[-1.6977750051384578242 ,1.1570071266117571647 ] 
dist 143=[-1.8508759336498461947 ,1.2362834457652261737 ] 
dist 144=[-1.9661676789276511688 ,1.3075410621111406176 ] 
dist 145=[-2.0602205842096580769 ,1.3488757973604193879 ] 
dist 146=[-2.1350134472055159239 ,1.3762419914927445308 ] 
dist 147=[-2.1734075494327022662 ,1.3917336215885388150 ] 
dist 148=[-2.1929517453566153426 ,1.4001256878012151796 ] 
dist 149=[-2.1963623110118804979 ,1.3999015968239133028 ] 
dist 150=[-2.1274235760650515289 ,1.3941578306181728122 ] 
dist 151=[-2.1105479213016494883 ,1.3885983477525607913 ] 
dist 152=[-2.0900172291642008718 ,1.0347576760808465402 ] 
dist 153=[-2.0792086683909257690 ,.99785923095151056172] 
dist 154=[-2.0512197296549012561 ,.91236126942020205727] 
dist 155=[-2.0384270997585950110 ,.89646242064248626376] 
dist 156=[-2.0191846154798813168 ,.77848840762863906862] 
dist 157=[-2.0108002703629503129 ,.75481763704594005828] 
dist 158=[-.83117860002178995132,.71602438592982592765] 
dist 159=[-.73161250578051113635,.7055450942662527116 ] 
dist 160=[-.49420493118376691443,.49681625570669108255] 
dist 161=[-.45920046974225054353,.46871848962619228719] 
dist 162=[-.1308950228758656361 ,.46177906166460403682] 
dist 163=[-.1284150284020059353 ,.52686783888917959985] 
dist 164=[-.1634893957106619583 ,.6666456707249526833 ] 
dist 165=[-.2298158959233099093 ,.83703319310419292662] 
dist 166=[-.3524150122604688364 ,.99772566215174728465] 
dist 167=[-.5273273151374506511 ,1.0987976500241043517 ] 
dist 168=[-.6998383891083228975 ,1.1756566967643936824 ] 
dist 169=[-.8128524367167553463 ,1.2396825692673866598 ] 
dist 170=[-.9040210193978945102 ,1.2913269919690590165 ] 
dist 171=[-.9893234829560524503 ,1.3187538779517229813 ] 
dist 172=[-1.0644161799436393813 ,1.3337168453139314353 ] 
dist 173=[-1.1148272108068445422 ,1.3368997902213612141 ] 
dist 174=[-1.1568613305462582367 ,1.0862911256970125439 ] 
dist 175=[-1.1985144389746054497 ,1.0868109468577651958 ] 
dist 176=[-1.2338165556738777010 ,1.0027251457242210778 ] 
dist 177=[-1.2504966879842623590 ,.9883338119367011691 ] 
dist 178=[-1.2580318131079064429 ,.9675812782439888270 ] 
dist 179=[-1.2580171401259536808 ,.9599644618452309520 ] 
dist 180=[-1.2404669257869419982 ,.9412652148813671862 ] 
dist 181=[-1.2328468042060508902 ,.9335711786710474943 ] 
dist 182=[-1.2236140089969777086 ,.9276774440952116636 ] 
dist 183=[-1.2181029729932929540 ,.9226927637830917628 ] 
dist 184=[.03699354464433019213,.83584141339788380701] 
dist 185=[.09304961063837566031,.83020859734383632929] 
dist 186=[-.03216508381372299023,.78025922121657092868] 
dist 187=[-.15590671040415069292,.76857825383746748406] 
dist 188=[-.30238374266273441892,.75248599532308672533] 
dist 189=[-.51836438614292427336,.74643563121989468879] 
dist 190=[-.7322459707878353100 ,.69528870667176637648] 
dist 191=[-.8703445235341165202 ,.77735715030250576766] 
dist 192=[-.9794991244716222385 ,.85318506685712519507] 
dist 193=[-1.0778331003541016980 ,.90081304057723982075] 
dist 194=[-1.1617953123506570948 ,.9369408867743672731 ] 
dist 195=[-1.2135769579148364637 ,.9668576365819072443 ] 
dist 196=[-1.2517568613001405975 ,.9905121271298225800 ] 
dist 197=[-1.2814216978410194613 ,1.0016390169694536531 ] 
dist 198=[-1.3049559301515460389 ,1.0060256215556259327 ] 
dist 199=[-1.3186611614131884331 ,1.0059469140760428044 ] 
dist 200=[-1.3278146751429012463 ,.73649824353109398381] 
dist 201=[-1.3331738262942759218 ,.71140164211451352648] 
dist 202=[-1.3356954470831040344 ,.65539782475063689133] 
dist 203=[-1.3335187844779097466 ,.63961300520006947061] 
dist 204=[-1.3275395815598050176 ,.56722348060943861696] 
dist 205=[-1.3237471788120082203 ,.5581844373037634628 ] 
dist 206=[-.67479458841102127462,.5585299212240687326 ] 
dist 207=[-.6187198755267291429 ,.5586341193424864585 ] 
dist 208=[-.49248248211392098917,.5585661312746482620 ] 
dist 209=[-.47042606946722679005,.5582287776533449254 ] 
dist 210=[-.3153468872251499299 ,.5577335079083591590 ] 
dist 211=[-.28696622190176575364,.5570377018801761939 ] 
dist 212=[-.2704488474794351053 ,.5560595164104679223 ] 
dist 213=[-.3704815772239647816 ,.5544401121954738724 ] 
dist 214=[-.4848255831194653674 ,.5527090517433729807 ] 
dist 215=[-.6487213993280394219 ,.5512869755303127345 ] 
dist 216=[-.8094498271663901681 ,.5498259455267832237 ] 
dist 217=[-.9111497282487124517 ,.5479417118863097045 ] 
dist 218=[-.9891632273073646871 ,.5490611396547082635 ] 
dist 219=[-1.0553341943042488315 ,.5754210752870967079 ] 
dist 220=[-1.1092200141457999676 ,.6534876708046548205 ] 
dist 221=[-1.1381909197184705045 ,.7592076236344009474 ] 
dist 222=[-1.1544819814411899949 ,.8616844081304509733 ] 
dist 223=[-1.1582841880194260741 ,.9268045125746286669 ] 
dist 224=[-1.1440573158659936220 ,.9770947178296886259 ] 
dist 225=[-1.1403476354110674446 ,1.0203679344880761513 ] 
dist 226=[-1.1371938169685390339 ,1.0558742029361672089 ] 
dist 227=[-1.1339766773672901509 ,1.0751579989694468780 ] 
dist 228=[-1.1309713086529321092 ,1.0862772834433220962 ] 
dist 229=[-1.1286641787719758364 ,1.0891912103329146635 ] 
dist 230=[-1.1264345180754378990 ,1.0877549272349186155 ] 
dist 231=[-1.1116398627369222589 ,1.0850812432278569169 ] 
dist 232=[-1.1140901664447711326 ,1.0740925397470566642 ] 
dist 233=[-1.1119780935295974724 ,1.0679953117763662828 ] 
dist 234=[-1.1070834186098041578 ,1.0288521195825233051 ] 
dist 235=[-1.1031531172981070800 ,1.0181450651091939580 ] 
dist 236=[-1.0892833257624815863 ,.99917754770251204774] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 0, 0, 2, 0, 1] 
dist 0=[51.308016140953489057  ,51.308016140953489057  ] 
dist 1=[51.046326158733068188  ,51.376055382276804229  ] 
dist 2=[50.556999696288932199  ,51.347412210954512446  ] 
dist 3=[49.579326546687942230  ,51.282112738163047639  ] 
dist 4=[48.505766449269495518  ,51.086340859146468858  ] 
dist 5=[47.633411741530551705  ,51.009774978403059758  ] 
dist 6=[46.737714216796351831  ,50.962575332791509675  ] 
dist 7=[45.571064194698333897  ,50.846031876791366035  ] 
dist 8=[44.314021349270667455  ,46.930342283722394654  ] 
dist 9=[43.057288700759893902  ,46.360899591018717354  ] 
dist 10=[41.555398189926146270  ,45.356880711045051936  ] 
dist 11=[39.319035792277402029  ,45.101034181324666163  ] 
dist 12=[36.996896419441557032  ,44.276462730959778065  ] 
dist 13=[34.385231599223393303  ,44.015407240543972746  ] 
dist 14=[30.075630074746777802  ,43.842557070750487074  ] 
dist 15=[25.739124531634722113  ,43.693677874394127141  ] 
dist 16=[22.779396263537733068  ,33.274672130370869042  ] 
dist 17=[20.252157059412559828  ,32.936344379867849793  ] 
dist 18=[17.643102145110117327  ,32.588007809496455034  ] 
dist 19=[15.170682467856546279  ,32.472056120560255654  ] 
dist 20=[13.189089279498667639  ,16.327484283884553201  ] 
dist 21=[11.180443565313749661  ,15.551927283203965102  ] 
dist 22=[8.5996620268477366654 ,14.379732508322460552  ] 
dist 23=[6.0873957211495863593 ,14.080689469218378691  ] 
dist 24=[4.3522804161569682110 ,9.1464199978323263353 ] 
dist 25=[2.7374132294026946319 ,8.5294434827087026963 ] 
dist 26=[1.0925200315193253074 ,7.2138073999556940427 ] 
dist 27=[-.91676959916714262959,6.9601984988096569316 ] 
dist 28=[-2.8241901891496206576 ,5.6677625068281633138 ] 
dist 29=[-4.0622482161584925746 ,5.4548357023944226885 ] 
dist 30=[-5.0526004454699312401 ,5.0964507243245465561 ] 
dist 31=[-6.4586729207599194461 ,5.0306013051508967628 ] 
dist 32=[-7.5644259522330329102 ,-4.7043714420047427368 ] 
dist 33=[-8.4238754523329333673 ,-4.9072246659269373827 ] 
dist 34=[-9.1801673808008860414 ,-5.2599737331383724240 ] 
dist 35=[-9.8256876786199330126 ,-5.3159390330148477381 ] 
dist 36=[-10.497274084151066045  ,-7.9571871240093546064 ] 
dist 37=[-10.896040419319868959  ,-8.1249351673815269306 ] 
dist 38=[-11.174812798094120427  ,-8.4328817734816979904 ] 
dist 39=[-11.367119776474998106  ,-8.4795885271841043069 ] 
dist 40=[-11.503250671672092680  ,-8.5419727146804509405 ] 
dist 41=[-11.557497059788531872  ,-8.1638685288380332027 ] 
dist 42=[-11.564099940485792122  ,-7.3979059370507881745 ] 
dist 43=[-11.546125794746917792  ,-6.5098069155803517663 ] 
dist 44=[-11.420992983469233066  ,-5.5380181491390901604 ] 
dist 45=[-11.377374145698186788  ,-4.3183928541981740281 ] 
dist 46=[-11.178213692620394950  ,-2.4406762365343880789 ] 
dist 47=[-11.149627425872534887  ,-.54865313021332841828] 
dist 48=[-6.9773255350003398548 ,.72818013592575924958] 
dist 49=[-6.9048224785733144395 ,1.8000063994562806777 ] 
dist 50=[-6.8432173557228219961 ,2.8736759487896313075 ] 
dist 51=[-6.8104157218955558394 ,3.8676782664958280302 ] 
dist 52=[-4.7202156212252017809 ,4.6214977519898982243 ] 
dist 53=[-4.3924793211317242103 ,5.3446288650399699824 ] 
dist 54=[-4.3044538757841420244 ,6.2161676009096745734 ] 
dist 55=[-3.2046366547281891018 ,7.0334941136632302073 ] 
dist 56=[-2.4603172623390745427 ,7.5402037153348327536 ] 
dist 57=[-1.9689814861914886543 ,7.9170990780585236048 ] 
dist 58=[-1.8856465338427125499 ,8.2161466515067184671 ] 
dist 59=[-1.2370402456080676413 ,8.4467930901025671421 ] 
dist 60=[-1.1210426141001390072 ,8.5505723235728586324 ] 
dist 61=[-.93889304474410107668,8.5957007026323209897 ] 
dist 62=[-.8938636066995705505 ,8.5921840663949973148 ] 
dist 63=[.8472610443122096612 ,8.2802462616793554362 ] 
dist 64=[2.6331804067286729408 ,4.4936953730163104337 ] 
dist 65=[2.7906128773018940008 ,4.5849765005878336772 ] 
dist 66=[2.7883016931937318623 ,4.6362476321737763162 ] 
dist 67=[2.5374276583726079459 ,4.6464097473510253157 ] 
dist 68=[2.2694876630869072468 ,3.5651459940916215812 ] 
dist 69=[2.0764863684530935928 ,3.6677000769118171117 ] 
dist 70=[1.9015920966584546843 ,3.7370123461489739325 ] 
dist 71=[1.7058524048589123849 ,3.7794962855867494456 ] 
dist 72=[1.5117585504975233448 ,3.8065069740157559374 ] 
dist 73=[1.3433920686779859155 ,3.8140236454696132417 ] 
dist 74=[1.1615789569447001706 ,3.8088487864101876682 ] 
dist 75=[.91376308282001764771,3.8013787953361309263 ] 
dist 76=[.66702360407447291562,3.7515786283304733128 ] 
dist 77=[.48948115080495767907,3.7358110975662852209 ] 
dist 78=[.32844032536275108756,3.6680304334348176250 ] 
dist 79=[.14754022011465675034,3.6580438657431756144 ] 
dist 80=[-.03263684113840119277,2.2249380535981106757 ] 
dist 81=[-.19082414250290309937,2.0892261170186840676 ] 
dist 82=[-.36353669564112468974,1.7570890285586415195 ] 
dist 83=[-.60176106889343722113,1.7072228363496571335 ] 
dist 84=[-.83551645295072939162,1.2119735175151593693 ] 
dist 85=[-1.0691389941035847438 ,1.1193227122973248495 ] 
dist 86=[-1.3184482906909593505 ,1.0084377581857311525 ] 
dist 87=[-1.5576516848761731331 ,.98289185726901677479] 
dist 88=[-1.8144575671644402873 ,.18920009954772684584] 
dist 89=[-2.0033733481669511472 ,.09185042921927398859] 
dist 90=[-2.1525643179361221752 ,-.11361921193547153408] 
dist 91=[-2.2869099880718647864 ,-.16259806927068376305] 
dist 92=[-2.4017506655104603701 ,-.36486397925160813845] 
dist 93=[-2.4730768853346626263 ,-.40203888136911005279] 
dist 94=[-2.5263878677575870414 ,-.39499202962971106382] 
dist 95=[-2.5693262059678419773 ,-.32437049044629257394] 
dist 96=[-2.6001110147698780639 ,-.23432458085508958148] 
dist 97=[-2.6065670615588194148 ,-.1106855454868686768 ] 
dist 98=[-2.6011382508816590773 ,.06584668635928282142] 
dist 99=[-2.5977398745598036980 ,.33547727930195640289] 
dist 100=[-2.5062941685694603855 ,.60594841747958910231] 
dist 101=[-2.4807282665708183164 ,.78584374849989573706] 
dist 102=[-2.4617240285705095294 ,.93396249348320880329] 
dist 103=[-2.4498883213669209486 ,1.0775912787534043824 ] 
dist 104=[-2.0084868836105775940 ,1.2074822790326098263 ] 
dist 105=[-1.9468667803554750738 ,1.3007670199315372616 ] 
dist 106=[-1.8280457022524562682 ,1.3851997053974379794 ] 
dist 107=[-1.7963383958684817922 ,1.4797650786045808107 ] 
dist 108=[-1.6811520777268062219 ,1.5804085100464789247 ] 
dist 109=[-1.6525456398934705894 ,1.6739531246277598383 ] 
dist 110=[-1.6064426638583702425 ,1.7518839300835548700 ] 
dist 111=[-1.5925294468104452773 ,1.8290039367030990935 ] 
dist 112=[-.15469488277365426811,1.8998206736427250994 ] 
dist 113=[-.03292421155835127405,1.9525930385002553354 ] 
dist 114=[.25932854100974216756,2.0023421425344578573 ] 
dist 115=[.1281391857431544479 ,2.0611003125476564626 ] 
dist 116=[-.17227264041468214793,2.1135610613308388790 ] 
dist 117=[-.37531491862509992051,2.1381706656655924425 ] 
dist 118=[-.54597112277839889942,2.1483851736017433885 ] 
dist 119=[-.71711364239250266596,2.1481993738878857565 ] 
dist 120=[-.87552600200894772894,2.1211705687222663856 ] 
dist 121=[-.99536939486333512933,2.1096386781877494781 ] 
dist 122=[-1.1099466263860884208 ,2.0877841348042802804 ] 
dist 123=[-1.2473383501569446768 ,2.0786446017397690961 ] 
dist 124=[-1.3755837980625723218 ,1.8357992292359076506 ] 
dist 125=[-1.4536527218843609670 ,1.7981745269184282484 ] 
dist 126=[-1.5099323235336081979 ,1.6837422285683586151 ] 
dist 127=[-1.5512036921663678822 ,1.5267146654847651052 ] 
dist 128=[-1.5813984657416430550 ,.59920514729143852289] 
dist 129=[-1.5934651307643323998 ,.58025861692861439662] 
dist 130=[-1.5965369275353138400 ,.55821243823206078548] 
dist 131=[-1.5940302302430184538 ,.55136302145435223253] 
dist 132=[-.31633144959429720272,.01791803587095065098] 
dist 133=[-.45155678374320973264,-.02807289121297900382] 
dist 134=[-.56216925822364732207,-.09353511218521634042] 
dist 135=[-.66826635904202607464,-.11125302943853767565] 
dist 136=[-.76347088606885950852,-.36790024770153954766] 
dist 137=[-.83059917720911772537,-.38677850530795668336] 
dist 138=[-.89009249167833115851,-.42414126767772865327] 
dist 139=[-.95481952789101994475,-.43192750193703826539] 
dist 140=[-1.0132103963938756161 ,-.47725349435047419245] 
dist 141=[-1.0474080784334911560 ,-.48052262904956513829] 
dist 142=[-1.0704770491017499459 ,-.47322758263861937763] 
dist 143=[-1.0844358895532744632 ,-.44963399924826057412] 
dist 144=[-1.0926642474330008949 ,-.41737671526470037144] 
dist 145=[-1.0931792048033540118 ,-.37549600903885180898] 
dist 146=[-1.0896894143296105142 ,-.31853354884819818192] 
dist 147=[-1.0855314732588639484 ,-.22607219219349157642] 
dist 148=[-.96824225323727147092,-.1312056688812470761 ] 
dist 149=[-.96819481364368801126,-.06464054301102138320] 
dist 150=[-.96515123862316738797,-.00603154246938047779] 
dist 151=[-.96225371544757901851,.05708008596607348886] 
dist 152=[-.94120051101105497659,.11829748270568263162] 
dist 153=[-.93509679809848365174,.16934800221524488549] 
dist 154=[-.91772357051029747835,.22276401056934115972] 
dist 155=[-.91087075556830037732,.3230418795369426404 ] 
dist 156=[-.87026944149127972807,.43144627801788219736] 
dist 157=[-.86012436427573696435,.50727028495662463061] 
dist 158=[-.84109779962771162776,.58009210812698829272] 
dist 159=[-.83513514682023624025,.77780944721027579794] 
dist 160=[-.33251487833838850695,.97356530806959761862] 
dist 161=[-.3240249550503811798 ,1.1009449834130351187 ] 
dist 162=[-.3016437948737540596 ,1.2027539497587277783 ] 
dist 163=[-.29821031083059157954,1.2964264537338813379 ] 
dist 164=[.27189783610270914   ,1.3778126661644267693 ] 
dist 165=[.31034304024263864674,1.4305730047342567418 ] 
dist 166=[.39734959101204011003,1.4725271157363926765 ] 
dist 167=[.40980850632093026799,1.5107747901327620512 ] 
dist 168=[.51146113213142007283,1.5416471429058291089 ] 
dist 169=[.52761424470681626776,1.5541570614532521479 ] 
dist 170=[.55177382952277944451,1.5579992531353363927 ] 
dist 171=[.55546799125618523588,1.5556531879191501810 ] 
dist 172=[.60376977080031472682,1.5255087343934522961 ] 
dist 173=[.55645549057670097892,1.5147371762203321609 ] 
dist 174=[.47984305630369571446,1.4983780974022292107 ] 
dist 175=[.19233454919913906299,1.4912289896182128338 ] 
dist 176=[-.09719074666888234033,1.1668173740349279696 ] 
dist 177=[-.29212840248228617826,1.1316283714749334650 ] 
dist 178=[-.45526926286962314529,1.0396390207215516104 ] 
dist 179=[-.61785852000191070005,1.0260995220363680125 ] 
dist 180=[-.76780984004021016105,.8674219361364022259 ] 
dist 181=[-.88049878342253787723,.8358508183424516658 ] 
dist 182=[-.98756908285535733679,.80333459257064306187] 
dist 183=[-1.1150902596431113217 ,.79638774919490448239] 
dist 184=[-1.2338003656365900184 ,.46675379908061059287] 
dist 185=[-1.3056958442511098407 ,.42520913788311419546] 
dist 186=[-1.3571235210469128933 ,.34170395324609417895] 
dist 187=[-1.3941236526586284973 ,.3202430317615005271 ] 
dist 188=[-1.4215016047676886258 ,.24457785065145308223] 
dist 189=[-1.4345161971425937916 ,.22816868710522972735] 
dist 190=[-1.4395096294623513148 ,.20658800962146017394] 
dist 191=[-1.4387022695920454238 ,.20003114091147195399] 
dist 192=[-.74798590047739363924,-.01818958065265137585] 
dist 193=[-.75942378769009814497,-.02280809634640922839] 
dist 194=[-.76498750326557014761,-.02901923323882273753] 
dist 195=[-.76536657372915172068,0                     ] 
dist 196=[-.74172384537501327083,-.34676290342808144267] 
dist 197=[-.7823578152996957337 ,-.35605564663584812499] 
dist 198=[-.81499570176709860368,-.35866401472171828408] 
dist 199=[-.84530073587992761586,-.34915331962596668177] 
dist 200=[-.87120164591624177631,-.33439671566471379808] 
dist 201=[-.88625722872138191241,-.31513683320369814409] 
dist 202=[-.89626722091610002704,-.28887774962915867357] 
dist 203=[-.9020249964280951797 ,-.24617794155584100959] 
dist 204=[-.90461743933335540377,-.19613521897088568006] 
dist 205=[-.90369354054007269695,-.14056158703997285018] 
dist 206=[-.89757906630379514464,-.07024351812467359975] 
dist 207=[-.89324540255026743771,.03866143530967765622] 
dist 208=[-.64941675381217704536,.14861276916020112526] 
dist 209=[-.64797232648153750471,.22310862171498865595] 
dist 210=[-.64009835421786936149,.28596054544038503033] 
dist 211=[-.63776300999626782694,.34942875172901630694] 
dist 212=[-.60796261235128201281,.40850144090920357009] 
dist 213=[-.60035920793444965801,.45380660507969287695] 
dist 214=[-.59235955804483996769,.49774540884215304208] 
dist 215=[-.5880823634432168824 ,.5513645859864573153 ] 
dist 216=[-.47483433217306016915,.60195329695659105391] 
dist 217=[-.45887110504820258226,.63379457878242245256] 
dist 218=[-.42688620595161162865,.65803234164680195355] 
dist 219=[-.41808789757343008385,.67826710376881834003] 
dist 220=[-.38417654556929788104,.69440872954816824587] 
dist 221=[-.37649145408856462757,.70230684663775711958] 
dist 222=[-.36065612859999936833,.70569330838561738519] 
dist 223=[-.35589797115151128451,.70569003648103823852] 
dist 224=[-.03019020367695262399,.69932877749290014884] 
dist 225=[-.04081971207718829006,.7257870679535977938 ] 
dist 226=[-.05701090792093326305,.74457778794968222531] 
dist 227=[-.08503906655550306009,.75633149182621374827] 
dist 228=[-.11450453854009846624,.76391428344902931069] 
dist 229=[-.13643382480311060353,.76605310917174710805] 
dist 230=[-.15705763530110990597,.76507373277955166279] 
dist 231=[-.18131236524698956332,.76344595531061309308] 
dist 232=[-.20606758316477382545,.70298413929730205291] 
dist 233=[-.22868986216732331802,.69258718951463543807] 
dist 234=[-.25410168785791563192,.67147738351018778945] 
dist 235=[-.2899936008087979367 ,.66485424120585130214] 
dist 236=[-.3262993112572020819 ,.6353137577729608427 ] 
dist 237=[-.35336338227177214742,.62846941858629381771] 
dist 238=[-.37886459653480788443,.6087704042307218598 ] 
dist 239=[-.40893164142503414962,.60426010462963194679] 
dist 240=[-.43966659596651651776,.41081435713535429886] 
dist 241=[-.46783461323443830766,.4079749326794371452 ] 
dist 242=[-.4995450730068834751 ,.4010748864827469551 ] 
dist 243=[-.5444227030686800685 ,.39826328529354203597] 
dist 244=[-.58810741886195534612,.3830779406454453764 ] 
dist 245=[-.61505569071815799772,.37926731126571199902] 
dist 246=[-.63493004803425577952,.36978997067099746348] 
dist 247=[-.65037423313548877551,.36623670096284674661] 
dist 248=[-.66180625007661003938,.32366301385493056741] 
dist 249=[-.66566332009513793705,.31683841778687676742] 
dist 250=[-.66638911391584389605,.29867610368048106178] 
dist 251=[-.66531965189868307728,.2954342244574874933 ] 
dist 252=[-.65173391736163542598,.26214940767839796753] 
dist 253=[-.65476976356430307669,.25519983967584911327] 
dist 254=[-.65495904761610863183,.24694000717335086314] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 1, 0, 1, 1, 2] 
dist 0=[51.669381184839920025  ,51.669381184839920025  ] 
dist 1=[51.540914786961666326  ,51.730593592428119754  ] 
dist 2=[51.089210496677375547  ,51.841073330292872858  ] 
dist 3=[50.306112185593202671  ,52.048616045677188550  ] 
dist 4=[48.865356697125273674  ,52.241228114778056387  ] 
dist 5=[47.261480574232137272  ,52.291797824541021283  ] 
dist 6=[45.826777981820630961  ,52.247373142686063862  ] 
dist 7=[44.238493377507961365  ,52.039449117911496068  ] 
dist 8=[42.020955853100758669  ,49.896406920233076226  ] 
dist 9=[39.562270874717437555  ,49.516618366456456447  ] 
dist 10=[37.010712433392809080  ,48.772081552118925322  ] 
dist 11=[33.895865368900283004  ,48.547591129266143514  ] 
dist 12=[29.187266404401552578  ,47.595757415660086860  ] 
dist 13=[24.455263738282962764  ,47.363003319788813736  ] 
dist 14=[21.246800119458504683  ,46.767807485542926853  ] 
dist 15=[18.531405711309939493  ,46.222047841117850328  ] 
dist 16=[15.768436291758194537  ,33.379800858057378942  ] 
dist 17=[13.176372432212519413  ,32.179617021457416216  ] 
dist 18=[11.143289707524681943  ,29.828647185053752387  ] 
dist 19=[9.1233110285228615787 ,29.467154023914146886  ] 
dist 20=[6.5830220082971985031 ,28.984284650275108228  ] 
dist 21=[4.1357521275616277653 ,28.816451852152997896  ] 
dist 22=[2.4870172775013596171 ,23.142624353239010390  ] 
dist 23=[1.1000783651666951156 ,22.858298711712452598  ] 
dist 24=[-.30183360242202148992,17.167714706649182281  ] 
dist 25=[-1.6162260786431820363 ,16.459653191810264125  ] 
dist 26=[-2.6541207309861968051 ,14.910619073040332413  ] 
dist 27=[-3.6964132015097322499 ,14.600216862803694763  ] 
dist 28=[-5.0296314243966006993 ,12.871033491188736176  ] 
dist 29=[-6.2988218654689197821 ,12.576468987778358059  ] 
dist 30=[-7.1415803053374487172 ,11.964464824388220226  ] 
dist 31=[-8.2241649952594776088 ,11.827771122551419380  ] 
dist 32=[-9.0431974301888062464 ,-4.3432303327607381491 ] 
dist 33=[-9.7206798678142867516 ,-4.5635387068853351869 ] 
dist 34=[-10.261006897707931984  ,-5.3141397692290345556 ] 
dist 35=[-10.532126018098397822  ,-5.4535986029613549729 ] 
dist 36=[-10.674613190510910088  ,-5.4454638522905452944 ] 
dist 37=[-10.701166324127217845  ,-5.2391302387351252116 ] 
dist 38=[-8.9569971391886703159 ,-4.9721511218975417310 ] 
dist 39=[-8.8549218121236584813 ,-4.7217864551439412878 ] 
dist 40=[-8.8312849366752448552 ,-4.4388371211745701158 ] 
dist 41=[-8.4130765424141070065 ,-3.5800079852324052060 ] 
dist 42=[-8.3094237518555981081 ,-2.5692070140276762849 ] 
dist 43=[-8.2181657394544693333 ,-1.3393888069001003406 ] 
dist 44=[-8.1753178406605748268 ,.51113550733315928707] 
dist 45=[-6.7789966645266811623 ,2.3572167050002774512 ] 
dist 46=[-6.1298810384073852303 ,3.5694324948510908723 ] 
dist 47=[-5.6688536692201153118 ,4.5501503128970691401 ] 
dist 48=[-5.5455652454039766887 ,5.4722517660976653328 ] 
dist 49=[-5.0693365572493847161 ,6.2870610953849314386 ] 
dist 50=[-4.1004534705051775424 ,6.8395670249281841007 ] 
dist 51=[-3.9341950833413082166 ,7.3064706136567804681 ] 
dist 52=[-3.3881230277183164421 ,7.7796934236618686600 ] 
dist 53=[-3.3472619602742410323 ,8.2009828139951578543 ] 
dist 54=[.1486080519152043067 ,8.4605404097195676493 ] 
dist 55=[.44512049328780414913,8.6518361915155794779 ] 
dist 56=[1.0763517627945205768 ,8.8004069321031614141 ] 
dist 57=[1.2085408346637181575 ,8.9100920913914042158 ] 
dist 58=[1.8374880509538339573 ,8.9459943017897995890 ] 
dist 59=[1.9449992700931827185 ,8.9396494889727304473 ] 
dist 60=[2.1448102903469992900 ,8.9211935140102465178 ] 
dist 61=[2.1860251506837636532 ,5.3777144925021468660 ] 
dist 62=[2.2687157374711339292 ,5.0697999506135820447 ] 
dist 63=[2.2321985053501620306 ,5.1379571742276429094 ] 
dist 64=[2.1343751196043968895 ,5.2982490083021345963 ] 
dist 65=[1.9278753044203997391 ,5.4107181276153969907 ] 
dist 66=[1.6676664526393003034 ,5.4899351790010766336 ] 
dist 67=[1.3553935846128931414 ,5.5174286941366356085 ] 
dist 68=[.94523051204492802213,5.5199201806352511874 ] 
dist 69=[.29422377014639712179,5.5088097766079063211 ] 
dist 70=[-.36628733213362931845,.77118932379376204803] 
dist 71=[-.81442066854587707208,.5152607361268298375 ] 
dist 72=[-1.1929411323506493816 ,.25262833956765088156] 
dist 73=[-1.5756228354011164072 ,-.1396938550120601943 ] 
dist 74=[-1.9319333189525693585 ,-.32067774781904256091] 
dist 75=[-2.2052175218771234886 ,-.48432965450591884401] 
dist 76=[-2.6385481441108003951 ,-.5200424159819988805 ] 
dist 77=[-3.1573891449312034178 ,-1.0664273617242063897 ] 
dist 78=[-3.4957074914695872387 ,-1.2647787881514965196 ] 
dist 79=[-3.7675389639700525945 ,-1.2753888659676413803 ] 
dist 80=[-4.0208436970681636772 ,-1.2311810602372292310 ] 
dist 81=[-4.2438186100120076554 ,-1.1008579781086394625 ] 
dist 82=[-4.3945273408727320639 ,-.92538743540155182353] 
dist 83=[-4.5217150542170105628 ,-.70098105407433789493] 
dist 84=[-4.6507786611798807447 ,-.39790325116179328719] 
dist 85=[-4.7602504530968162302 ,.17448251079498614372] 
dist 86=[-4.8091944788545746576 ,.80812007616919640593] 
dist 87=[-4.8285976253408758843 ,1.2379136380774092492 ] 
dist 88=[-4.8256599679553786776 ,1.6006684822170347094 ] 
dist 89=[-4.7534482952443037808 ,1.9667412995837418986 ] 
dist 90=[-4.7251336208365974678 ,2.3068877595574020673 ] 
dist 91=[-4.6819497335492636898 ,2.5661626699151812719 ] 
dist 92=[-4.6623186874003532097 ,2.8158227807011807334 ] 
dist 93=[-4.2234953358497903078 ,3.1175868020488966141 ] 
dist 94=[-3.4921612022473099630 ,3.4002472411807682290 ] 
dist 95=[-3.3907190854018093455 ,3.7697540356968727194 ] 
dist 96=[-3.2066776441362336299 ,4.1630442643919880481 ] 
dist 97=[-3.1595910403728141191 ,4.5106127708419474337 ] 
dist 98=[-3.0048660721106904055 ,4.7463163403222707482 ] 
dist 99=[-2.9592369722576245335 ,4.9454635102048452785 ] 
dist 100=[-2.9267876685991204996 ,5.1471230011899055049 ] 
dist 101=[-2.9183667595934150081 ,5.3196312618590723882 ] 
dist 102=[-.28427383042796835782,5.4024051808851875755 ] 
dist 103=[-.13323654148435983075,5.4418052406843310207 ] 
dist 104=[.21783026593759139921,5.4431921322963706019 ] 
dist 105=[.2691160032197354587 ,5.3667701545549154835 ] 
dist 106=[.71847175158134217081,5.3339421036536155010 ] 
dist 107=[.79496359065400843235,5.3020079734266815072 ] 
dist 108=[.59994425945259688332,5.2765855826089944748 ] 
dist 109=[-.41436068996830025763,4.6088552998916044917 ] 
dist 110=[-1.0977909243294553104 ,4.5256128423590924545 ] 
dist 111=[-1.6700744360651498402 ,4.2941553344807212890 ] 
dist 112=[-2.2407038790589562464 ,4.2566757858570635467 ] 
dist 113=[-2.7669310527868150898 ,3.8045743911126325556 ] 
dist 114=[-3.1619672006925197811 ,3.7094846145623443494 ] 
dist 115=[-3.5367489168289002392 ,3.5862731651815898124 ] 
dist 116=[-3.9821175784080098457 ,3.2538333450749275626 ] 
dist 117=[-4.3958936741725583898 ,2.4716994473072284608 ] 
dist 118=[-4.6445607827211656896 ,1.5403369613736672098 ] 
dist 119=[-4.8199808603460651576 ,1.3259205964545351880 ] 
dist 120=[-4.9413663825999589501 ,1.2451593653306408494 ] 
dist 121=[-5.0294556376326934232 ,1.2209517860319488162 ] 
dist 122=[-5.0719701020442513888 ,1.1157979993338532199 ] 
dist 123=[-5.0892377700071393170 ,1.0943205510027492307 ] 
dist 124=[-5.0839537609920941988 ,1.0383174328281905595 ] 
dist 125=[-.50833078464325253739,1.0270362270863472671 ] 
dist 126=[-.72433602701797530264,.89524679315004154948] 
dist 127=[-.89866535703529005434,.87183500295771911258] 
dist 128=[-1.0619632645863529602 ,.82486260298328433423] 
dist 129=[-1.2058949334570600197 ,.81172417746428415677] 
dist 130=[-1.3029125694767676416 ,.76012179256556573079] 
dist 131=[-1.3842725094180085400 ,.74832794605626247796] 
dist 132=[-1.4657022506496056429 ,.72288491022240876927] 
dist 133=[-1.5380273823446600557 ,.7148752605228823459 ] 
dist 134=[-1.5830387458849032000 ,-1.4325299555781931189 ] 
dist 135=[-1.7502401514546015227 ,-1.5079786940900761976 ] 
dist 136=[-1.8968243418320968795 ,-1.4686746813709018178 ] 
dist 137=[-2.0257039230897379663 ,-1.4102453243194000998 ] 
dist 138=[-2.1335101170235792821 ,-1.3290557373902837049 ] 
dist 139=[-2.1959650761091878178 ,-1.2156200441827493943 ] 
dist 140=[-2.2372401030094054027 ,-1.0284671270453822311 ] 
dist 141=[-2.2604944036095339337 ,-.83530123017573241212] 
dist 142=[-2.2741713719765626893 ,-.69785882448736105393] 
dist 143=[-2.2772101556083965558 ,-.57484928209638275774] 
dist 144=[-2.2730617485639849172 ,-.43928791507890565999] 
dist 145=[-2.2676781563287346914 ,-.30593305835432051299] 
dist 146=[-2.2371674062129439467 ,-.19172527482321987827] 
dist 147=[-2.2268866104873589826 ,-.06958298753422608286] 
dist 148=[-2.1853149118814870994 ,.09545460894370902885] 
dist 149=[-2.1770055180578351008 ,.25915403089681531138] 
dist 150=[-1.2505936449841295617 ,.37595875806672448447] 
dist 151=[-1.1649172188118700243 ,.48088999601416780566] 
dist 152=[-.95581616800548068496,.59719539275465170498] 
dist 153=[-.92478065625931229358,.71206668611482767256] 
dist 154=[-.61668246285927599638,.81127888969952576515] 
dist 155=[-.5596292117798135943 ,.91814898799182924365] 
dist 156=[-.49105905778532089597,1.0636031668616726869 ] 
dist 157=[-.47633677762565123172,1.2036987754942867494 ] 
dist 158=[-.00167651974437140839,1.3292817386796622830 ] 
dist 159=[.05574565333874827168,1.4412485367122300185 ] 
dist 160=[.17779180222116451024,1.5260527229909720208 ] 
dist 161=[.2048389178720426569 ,1.5960663869346582657 ] 
dist 162=[.32592906239541196828,1.6514842748117667338 ] 
dist 163=[.34731053302245460766,1.6780189065106914776 ] 
dist 164=[.38615873381158254785,1.6913189505857268383 ] 
dist 165=[.39399890580242256114,1.6939023840320666708 ] 
dist 166=[.68539101260155681719,1.3386538253200258702 ] 
dist 167=[.71035055185676459969,1.3140148710171919704 ] 
dist 168=[.74976067005111690488,1.3042802588799199063 ] 
dist 169=[.75791779200161084024,1.2891802164489933121 ] 
dist 170=[.7558151388944623246 ,1.2831182482465019026 ] 
dist 171=[.73715147973146214537,1.2781908144319300929 ] 
dist 172=[.56291940026136161197,1.2735373001848431186 ] 
dist 173=[.3406033123410564458 ,1.0258442345649018866 ] 
dist 174=[.18992071443654981244,1.0303140970561597678 ] 
dist 175=[.06269300137410158300,1.0299977111897796648 ] 
dist 176=[-.06598025274047933142,1.0232139319588665516 ] 
dist 177=[-.18589595129903422867,1.0194198797162299186 ] 
dist 178=[-.2781584235334776411 ,.98280047667250090675] 
dist 179=[-.36792754439427477011,.97268188276968367477] 
dist 180=[-.477885696894326893  ,.95941377660993616577] 
dist 181=[-.58182623332747280418,.95352643061664027376] 
dist 182=[-.6475693145751282953 ,.81175105327626916092] 
dist 183=[-.69797469828899864963,.79705102997227209262] 
dist 184=[-.74068024155075955482,.76313354107439974031] 
dist 185=[-.82019253190016606427,.75209469413623325063] 
dist 186=[-.91594891662301493885,.70063446506855974342] 
dist 187=[-.98222584381457937577,.68925687613821912543] 
dist 188=[-1.0396639144938460844 ,.66321963075087141178] 
dist 189=[-1.1001365888004069854 ,.65463562861406531252] 
dist 190=[-1.1539298944721792288 ,.558015041604634765  ] 
dist 191=[-1.1847028592808080763 ,.54295526738280619241] 
dist 192=[-1.2045380085024532760 ,.50410083526803026392] 
dist 193=[-1.2146633977068828686 ,.4973838038838067068 ] 
dist 194=[-1.2190758556860080502 ,.43072741421381108732] 
dist 195=[-1.2180711505693233830 ,.41719204803819942498] 
dist 196=[-1.2104612792433352563 ,.40069066393788630567] 
dist 197=[-1.2047723219011558412 ,.39455024518806609613] 
dist 198=[-.87451249642596977105,.25708953121120829152] 
dist 199=[-.8405752533110547188 ,.2386798589045705989 ] 
dist 200=[-.75701196010545663067,.2021189421514701195 ] 
dist 201=[-.74221501076900472451,.21463227851876418358] 
dist 202=[-.62480363777087876738,.30542741929727248043] 
dist 203=[-.60704795884330707774,.4109866780334736474 ] 
dist 204=[-.57523747082270592305,.56442797705832468479] 
dist 205=[-.56716802224267599406,.71549650491412510781] 
dist 206=[-.46556010297061563142,.81158417588680502945] 
dist 207=[-.4722401275623232513 ,.88588674051136624214] 
dist 208=[-.48036213988416031112,.94998575716869254967] 
dist 209=[-.48877874353931305231,1.0026944414799441857 ] 
dist 210=[-.49663498763824403984,1.0315256143655322220 ] 
dist 211=[-.50557872833187648964,1.0484198765328652850 ] 
dist 212=[-.54800664204683459238,1.0534762810029444918 ] 
dist 213=[-.64219145349066672462,1.0542949695480687297 ] 
dist 214=[-.74066000058528396912,1.0542711861171613610 ] 
dist 215=[-.80142721655510685429,1.0536350026475363142 ] 
dist 216=[-.84623784271384067471,1.0520059168141491114 ] 
dist 217=[-.88101048346563378429,1.0498668829112154814 ] 
dist 218=[-.90825442047956756176,1.0471931450273511482 ] 
dist 219=[-.92301256304696378657,1.0436131484657841927 ] 
dist 220=[-.93145232702290161844,1.0396493550960748044 ] 
dist 221=[-.93347672512379950511,1.0019226669451049430 ] 
dist 222=[-.87340005127951225736,1.0263996404859243021 ] 
dist 223=[-.86265105833970890922,1.0380257375052967449 ] 
dist 224=[-.84977579461531899588,1.0426315356135994094 ] 
dist 225=[-.84373111510061754618,1.0426912613767017059 ] 
dist 226=[-.83351919718748581644,1.0309693849521397617 ] 
dist 227=[-.82945367124808036671,1.0258106830699834388 ] 
dist 228=[-.8270063922921653506 ,1.0137028090608929318 ] 
dist 229=[-.8261205169450944195 ,1.0082485445081368355 ] 
dist 230=[-.60482872937367063876,.05044925627688185535] 
dist 231=[-.59049235849142055899,-.00991820681125613723] 
dist 232=[-.58548452392664897565,-.04404512418253345388] 
dist 233=[-.55367650353737677744,.02999275835185309154] 
dist 234=[-.54596216059672533702,.10519617623727978198] 
dist 235=[-.58652033266706801428,.19571154820547470496] 
dist 236=[-.6497954322889847435 ,.35735593608429165782] 
dist 237=[-.71034969522827164589,.52431142889015623877] 
dist 238=[-.74759420394382950252,.63215527663211523438] 
dist 239=[-.77493547531333603875,.71741743303669259467] 
dist 240=[-.79595386983754205854,.79422797108964672601] 
dist 241=[-.81136537962441530078,.85977882828666212432] 
dist 242=[-.81632210487093442024,.90009254015232376427] 
dist 243=[-.81745660500929088822,.92965957281929505431] 
dist 244=[-.81760830630617185437,.95230913308592476106] 
dist 245=[-.7879667360055064908 ,.97042753804634483692] 
dist 246=[-.78120176613887893062,.98190652079248201098] 
dist 247=[-.76463706615608024543,.99072127886166848963] 
dist 248=[-.75826430667871415014,.99820560914229780948] 
dist 249=[-.72497146220448601517,1.0042616262858184872 ] 
dist 250=[-.71685363556543288472,1.0073752756848294383 ] 
dist 251=[-.69779978199207488562,1.0089288272735346348 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 0, 0, 1, 2] 
dist 0=[43.404314354079377012  ,43.404314354079377012  ] 
dist 1=[43.221965745435324045  ,43.541284847716659290  ] 
dist 2=[42.662777823010749195  ,43.919071935026086012  ] 
dist 3=[41.765439984107357342  ,44.305116658164997995  ] 
dist 4=[40.232253268216447109  ,44.475165951866810479  ] 
dist 5=[38.629772041858640942  ,44.534994112823754157  ] 
dist 6=[37.455621734485038047  ,44.521209774313071867  ] 
dist 7=[36.366507879195498500  ,43.535613497651504489  ] 
dist 8=[35.103600299248113319  ,43.337710582333345657  ] 
dist 9=[33.820121561022216617  ,42.979580302411531918  ] 
dist 10=[32.648718394718949880  ,42.864800473250256692  ] 
dist 11=[31.330541774526513350  ,42.362435897970677654  ] 
dist 12=[29.460526665545386413  ,42.219854717207507768  ] 
dist 13=[27.555544977473561992  ,41.854549503339645740  ] 
dist 14=[26.097566439409804608  ,41.711283094673007368  ] 
dist 15=[24.681783184675362048  ,31.574277778980713834  ] 
dist 16=[22.945216256539594312  ,30.654476309475356080  ] 
dist 17=[21.125917986010549963  ,28.397618092418141573  ] 
dist 18=[19.379396731121458396  ,28.074478347919485894  ] 
dist 19=[17.343421988430920005  ,25.254353901584413572  ] 
dist 20=[14.367233135331833969  ,25.136775392054445430  ] 
dist 21=[11.401891446093935337  ,23.323563700385858927  ] 
dist 22=[9.4092188256725627034 ,23.199851893504702231  ] 
dist 23=[7.7381090122801567694 ,17.285266794240821328  ] 
dist 24=[6.0578380480785680345 ,16.549537089787318959  ] 
dist 25=[4.4906913688676365387 ,15.922090189356905311  ] 
dist 26=[3.2716439888617044150 ,15.359457851350571106  ] 
dist 27=[2.0682355660531983693 ,13.452460827793491741  ] 
dist 28=[.56353329344508377867,13.174326537376916376  ] 
dist 29=[-1.1868263110646686854 ,12.860841796060944384  ] 
dist 30=[-3.6568452187616074615 ,12.804221143380072940  ] 
dist 31=[-6.0714454078706725815 ,2.4498304991099139547 ] 
dist 32=[-7.6084947358880303503 ,1.6145019658770667690 ] 
dist 33=[-8.8067252892512643890 ,-.08854966368444093760] 
dist 34=[-9.8670981885196314667 ,-.08663050680530253019] 
dist 35=[-10.766930261946409335  ,.02964089692609302548] 
dist 36=[-11.323644070419757781  ,.32830016252089649599] 
dist 37=[-11.740783424123859235  ,.66504468796122346848] 
dist 38=[-12.083191846391331106  ,.93345823300845122181] 
dist 39=[-12.352389767206679631  ,1.2007821698819768524 ] 
dist 40=[-12.476913575913268300  ,1.5336950503115617099 ] 
dist 41=[-12.522511568558114016  ,1.8810291660686674384 ] 
dist 42=[-12.516830475471308400  ,2.2061119943888254891 ] 
dist 43=[-12.387529562285763033  ,2.5759173983794689058 ] 
dist 44=[-12.333655748112921787  ,3.1018344350028294104 ] 
dist 45=[-12.149812446510750404  ,3.6323370106798524890 ] 
dist 46=[-12.075912852134135850  ,4.0205208859610304569 ] 
dist 47=[-7.8863809564244342960 ,4.3779202343628261992 ] 
dist 48=[-7.4698477649438336056 ,4.7857003102054775651 ] 
dist 49=[-7.1133902750093372674 ,5.1937193261792687904 ] 
dist 50=[-7.0528313483149688550 ,5.5521058182170170513 ] 
dist 51=[-6.9664201434917518521 ,5.9421506161500234253 ] 
dist 52=[-6.9309186487535691566 ,6.4764816099419746192 ] 
dist 53=[-4.2848658630712330514 ,6.9924159926008943312 ] 
dist 54=[-4.1827441219607504980 ,7.3090506586962093673 ] 
dist 55=[-2.3926787766750859407 ,7.5397174870267902636 ] 
dist 56=[-2.1605793722892766421 ,7.7126244011481074085 ] 
dist 57=[-1.6788200993476982404 ,7.8344725846478474100 ] 
dist 58=[-1.6277228673521014700 ,7.8613707479896807217 ] 
dist 59=[-1.4486931472352950766 ,7.8524141879217165180 ] 
dist 60=[-1.4110838535660595598 ,7.8313294151436466370 ] 
dist 61=[-1.3547725913453932556 ,7.5181767052483883655 ] 
dist 62=[-1.3394672171560692499 ,7.3179646545926778783 ] 
dist 63=[-1.3154763367931343087 ,3.7639480112368526596 ] 
dist 64=[-1.3105830732929962532 ,3.9752927657190881955 ] 
dist 65=[-1.3114000948759230664 ,4.1442501712649603808 ] 
dist 66=[-1.3188589641111349531 ,4.2283982785910476726 ] 
dist 67=[-1.3288563981783360238 ,4.2721624778865330911 ] 
dist 68=[-1.3398872160719069818 ,4.2797124702786335345 ] 
dist 69=[-1.3531200672795958018 ,4.2237937499885955006 ] 
dist 70=[-1.3719394626173576010 ,4.2365120101106561310 ] 
dist 71=[-1.3897318914535534201 ,4.1903228286459495544 ] 
dist 72=[-1.3989162648602887332 ,4.1753436368484245091 ] 
dist 73=[-1.4031138274166482472 ,4.1609433329943196098 ] 
dist 74=[-1.4011192622835290827 ,4.1439930992571597894 ] 
dist 75=[-1.3949654473405137286 ,4.1270514155360575028 ] 
dist 76=[-1.3875916420668123386 ,4.1126554601517241591 ] 
dist 77=[-1.3674051976739498892 ,4.0975573712734601805 ] 
dist 78=[-1.3567138687259590051 ,4.0817139882649869068 ] 
dist 79=[-1.3700295938097475782 ,3.1546384595331287871 ] 
dist 80=[-1.7720972467158475514 ,3.1245807095104557283 ] 
dist 81=[-2.1845982296027434896 ,2.8026443632431096841 ] 
dist 82=[-2.5649395267205544438 ,2.7361569987717778072 ] 
dist 83=[-2.9950004313413583330 ,2.6601947677428362673 ] 
dist 84=[-3.6060411431499443498 ,2.6333664699987153626 ] 
dist 85=[-4.2041839427572988372 ,.28821869957628983674] 
dist 86=[-4.5827643556489986212 ,.25853161780526473934] 
dist 87=[-4.8734862959231354666 ,-.01123859358148940997] 
dist 88=[-5.1208628151512004608 ,-.06309940005119282855] 
dist 89=[-5.3218638501661522893 ,-.07444571976194709932] 
dist 90=[-5.4274415410899701033 ,-.03239418134385437995] 
dist 91=[-5.4835369828217655446 ,.04046339156230602267] 
dist 92=[-5.4939077005203338586 ,.15240542875896174762] 
dist 93=[-5.4689782389512800489 ,.31440104133163934311] 
dist 94=[-5.4483445192526396242 ,.58706088857745792263] 
dist 95=[-5.4013699198230361169 ,.87023614818011807094] 
dist 96=[-5.3776289424504488425 ,1.0742139971611365520 ] 
dist 97=[-5.2360801705737161038 ,1.2592880260823308800 ] 
dist 98=[-5.1982491665386024354 ,1.4670247060283748179 ] 
dist 99=[-5.1322331301836013719 ,1.6735337210491981500 ] 
dist 100=[-5.1160956272251613146 ,1.8537195238187381545 ] 
dist 101=[-2.8756121738718348058 ,2.0492380587823186286 ] 
dist 102=[-2.6635288371145556736 ,2.3169673009432025552 ] 
dist 103=[-2.1657272332630642445 ,2.5840593831802451100 ] 
dist 104=[-2.0762804081046994563 ,2.7770420554290603240 ] 
dist 105=[-1.5042336147389267562 ,2.9528442500737149643 ] 
dist 106=[-1.4936496304551015779 ,3.1513627031991443804 ] 
dist 107=[-1.4420579920362056873 ,3.3495122640843428713 ] 
dist 108=[-1.4302391123244247564 ,3.5987328907579926102 ] 
dist 109=[-1.3910336774344900084 ,3.9691664612638020431 ] 
dist 110=[-1.3854081794258701059 ,4.1976964881325915375 ] 
dist 111=[.19787914612133840219,4.3662065496175216588 ] 
dist 112=[.24419333388377079024,4.4970396674317966105 ] 
dist 113=[.52650382669678504532,4.5947923430578318853 ] 
dist 114=[.57370698820949835771,4.6312414805614648724 ] 
dist 115=[.6670576166215191633 ,4.6429585607688709479 ] 
dist 116=[.68853826771134379421,4.6419830843854688798 ] 
dist 117=[.84404610571047500886,2.6588416198626882848 ] 
dist 118=[.86544728065249102933,2.7214312622446273872 ] 
dist 119=[.90450475003105918626,2.7708666769887642044 ] 
dist 120=[.91148733756191350226,2.7922627496527494862 ] 
dist 121=[.91874825712457933102,2.7977511851717397070 ] 
dist 122=[.90707364640386526441,2.7955478289808278613 ] 
dist 123=[.88294550287539336213,2.7571778594806279884 ] 
dist 124=[.83552385608095974977,2.7426979320246299716 ] 
dist 125=[.78182384751698192536,2.7029540406530377911 ] 
dist 126=[.60840914652946410062,2.6850432182898985645 ] 
dist 127=[.11307206360026964694,1.8533219642763041506 ] 
dist 128=[-.22185609982071068821,1.7700970891374496682 ] 
dist 129=[-.50367393338054832318,1.5607719373836263268 ] 
dist 130=[-.78699347611183475472,1.5299942729656114678 ] 
dist 131=[-1.0498540747601723557 ,1.1984712877302144007 ] 
dist 132=[-1.2499994932945001448 ,1.1349716523059413829 ] 
dist 133=[-1.4426939240984105641 ,1.0644500214894239918 ] 
dist 134=[-1.6758104272484100790 ,1.0498269412152269741 ] 
dist 135=[-1.8946591070384807325 ,.45502408121903003087] 
dist 136=[-2.0303956837080260672 ,.38159457099413225037] 
dist 137=[-2.1313460808740438123 ,.23045426368126950361] 
dist 138=[-2.2113260437188260126 ,.19153537986509406704] 
dist 139=[-2.2731664764266451430 ,.05218591482817891054] 
dist 140=[-2.3017021202785417188 ,.02407017749067097231] 
dist 141=[-2.3142245037190963090 ,-.01781053864467423974] 
dist 142=[-2.3134119370990726891 ,-.02864774238833447920] 
dist 143=[-.82050193877099675356,-.17361731362128539696] 
dist 144=[-.94478466665107844476,-.17912391456616341285] 
dist 145=[-1.0424495078767267761 ,-.18832541724829165807] 
dist 146=[-1.1294810720179721660 ,-.18445294609489068784] 
dist 147=[-1.2031371751436784620 ,-.17354772387234611383] 
dist 148=[-1.2474030136789886150 ,-.15022128397711547181] 
dist 149=[-1.2786737757124021274 ,-.12453020946205408149] 
dist 150=[-1.3004509046638552633 ,-.10418437078486393505] 
dist 151=[-1.3164161170802587758 ,-.08386685484066900269] 
dist 152=[-1.3244835154777841297 ,-.05828262750722713861] 
dist 153=[-1.3283314166486879164 ,-.03126656947304698357] 
dist 154=[-1.3274485351674292757 ,-.00522992818025757402] 
dist 155=[-1.3236028538756393615 ,.02508958163838444067] 
dist 156=[-1.3193357379574206078 ,.06920628232859183986] 
dist 157=[-1.3062364625576005677 ,.11438372149584529669] 
dist 158=[-1.2993061721299435164 ,.14893995848059948205] 
dist 159=[-1.0193054368763121466 ,.29518166166753114453] 
dist 160=[-1.0039463651903735148 ,.44168807750422346393] 
dist 161=[-.96364674313247647267,.56338654739204802632] 
dist 162=[-.95384883543314578718,.68318477525225999576] 
dist 163=[-.8785547846863284834 ,.7927120527388577039 ] 
dist 164=[-.86199370185673897172,.8734098759787612212 ] 
dist 165=[-.83606793808837807479,.9485178992971501128 ] 
dist 166=[-.82801563953318060747,1.0357333318548984786 ] 
dist 167=[-.64763829460980683138,1.1157972244797920790 ] 
dist 168=[-.62244129120024589717,1.1623569610237553938 ] 
dist 169=[-.56635112148346223558,1.1933407769657250803 ] 
dist 170=[-.55104095509318994846,1.2112249274709301396 ] 
dist 171=[-.51746195193463091253,1.2225184214108775621 ] 
dist 172=[-.52763486862503744311,1.2271888686163743620 ] 
dist 173=[-.53535829777016090606,1.2279091883920782898 ] 
dist 174=[-.53716940101361360863,1.2252415188936625078 ] 
dist 175=[-.53643403069102421089,1.0957143493376476638 ] 
dist 176=[-.53614308555409366964,1.0776492436794815782 ] 
dist 177=[-.51501807604552426499,1.0261428384579632087 ] 
dist 178=[-.50946804186095764875,1.0183233797508915232 ] 
dist 179=[-.50606686729222014481,.92956837793761039191] 
dist 180=[-.50470356804358340183,.92621129854507857838] 
dist 181=[.11182289876437157002,.91661455746897142885] 
dist 182=[.02405568938463213979,.91175005707034344661] 
dist 183=[-.05246982993218336327,.82902913006270538528] 
dist 184=[-.13374163618522541667,.81522472290990479404] 
dist 185=[-.21191979866365534718,.80309573551344695933] 
dist 186=[-.2760959691370205435 ,.80187829945727053624] 
dist 187=[-.34235882484444397049,.77032034652861738166] 
dist 188=[-.42886800993806020573,.76179471036430760095] 
dist 189=[-.51329941448914530242,.75575781079592023147] 
dist 190=[-.57126808346600194129,.75249993344200417397] 
dist 191=[-.62100126534603098777,.76409171732078757013] 
dist 192=[-.6725565600952460146 ,.78255389162827053787] 
dist 193=[-.72139143108798527239,.79331474752159971384] 
dist 194=[-.76026509540868670807,.7963523186451941164 ] 
dist 195=[-.79932368286697529827,.79616745717343244582] 
dist 196=[-.84889804156612104154,.79406794404539180885] 
dist 197=[-.89501204509268241662,.79014899589086420149] 
dist 198=[-.92025673822374731146,.78759359228215304716] 
dist 199=[-.9350728560123492076 ,.69823863772671487823] 
dist 200=[-.94890187698600710225,.68415178462101831988] 
dist 201=[-.96905125822455658451,.65556702243302737736] 
dist 202=[-.99091206052098730702,.64702411520024010224] 
dist 203=[-1.0118243299133807839 ,.61066476758365584937] 
dist 204=[-1.0214006991827803401 ,.60239162076050483049] 
dist 205=[-1.0246181496916735889 ,.60584368344394051611] 
dist 206=[-1.0242767520893085487 ,.65276109187423878855] 
dist 207=[-.76007102738789315559,.69366406697886804942] 
dist 208=[-.75080590250186634364,.73709417099368364244] 
dist 209=[-.71695471836230856791,.77886307090987350772] 
dist 210=[-.70760138335406337343,.81313470698429380355] 
dist 211=[-.69228117738387535985,.84850444174323324546] 
dist 212=[-.68732076456518070685,.89465721675782385798] 
dist 213=[-.09651470222251846635,.93798794180628994643] 
dist 214=[-.08729296765010141499,.96209205456568725326] 
dist 215=[.06921095479540542581,.97674462780508351771] 
dist 216=[.08910520468847426233,.98234454813487939669] 
dist 217=[.13193931744706731901,.98369155271473719408] 
dist 218=[.1403876986680006306 ,.98150262611886331376] 
dist 219=[.18417672847063618561,.97653248470538344471] 
dist 220=[.19141626310125435594,.97319849724063570693] 
dist 221=[.20506564181724103146,.87656293843464743468] 
dist 222=[.20783335957622874572,.86082588621572860672] 
dist 223=[.21291959135979865853,.82735930484904146619] 
dist 224=[.20929951984631937743,.81690440793716744461] 
dist 225=[.20077064493777283789,.76977719630787119304] 
dist 226=[.18331374694911554369,.75971806633544774377] 
dist 227=[.14437056145037459749,.7294327701810445715 ] 
dist 228=[-.02739145503430494776,.72485789715121481516] 
dist 229=[-.21836444464456258931,.52648189387895934908] 
dist 230=[-.34520441031881333371,.51914692162421936334] 
dist 231=[-.4494497409550709968 ,.49795410613500441306] 
dist 232=[-.55022432117073371404,.49431702827045276982] 
dist 233=[-.64114407195379014712,.44988523461283611156] 
dist 234=[-.7060486435766014583 ,.44025204630639625933] 
dist 235=[-.76437553054320395932,.43037198505707552103] 
dist 236=[-.82903696815091223495,.42680698422319183194] 
dist 237=[-.88794233845468468384,.31012358719914700867] 
dist 238=[-.92329072339703030609,.29461077982984381345] 
dist 239=[-.94817706381656310803,.26352235808427097048] 
dist 240=[-.9653173189083040801 ,.25527822075299857411] 
dist 241=[-.97674663269304671913,.2249697267768826065 ] 
dist 242=[-.97888539064776526805,.21821911619448856006] 
dist 243=[-.9774388712796848279 ,.20633930732398370726] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 1, 0, 1, 1, 0, 1] 
dist 0=[48.917392581980223804  ,48.917392581980223804  ] 
dist 1=[48.526527611146156261  ,49.143931852021920423  ] 
dist 2=[47.939555931447811547  ,49.277465638073324621  ] 
dist 3=[46.929521927021098716  ,49.296854199538171606  ] 
dist 4=[45.721052868776681125  ,49.236057504413493505  ] 
dist 5=[44.341348749255790231  ,49.186145169257029011  ] 
dist 6=[42.567479137017411549  ,48.805178641652480963  ] 
dist 7=[39.784409783004675639  ,48.688619397547340846  ] 
dist 8=[36.942361661303981784  ,48.257951706654713621  ] 
dist 9=[34.932841793166480344  ,48.159863123392655716  ] 
dist 10=[33.141873538507728669  ,46.581564535770077611  ] 
dist 11=[31.172756399540989439  ,46.235618174702305081  ] 
dist 12=[29.231708984954654916  ,45.929139185286494784  ] 
dist 13=[27.552765381763486645  ,45.747139749038903907  ] 
dist 14=[25.738209360369729241  ,41.275399522172210136  ] 
dist 15=[23.255231263921831572  ,40.467329278616195037  ] 
dist 16=[20.766323600981044771  ,36.113436484351262376  ] 
dist 17=[18.927962997671419317  ,30.608968879871993248  ] 
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dist 111=[-1.6721474813392252358 ,1.9022733329808275275 ] 
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dist 128=[-.96938740861423416768,1.2639760227638808873 ] 
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dist 130=[-1.2821750685627314009 ,.36617913956415505451] 
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dist 132=[-1.4474802281624317600 ,.21467824289939226024] 
dist 133=[-1.5045631591467090417 ,.18808961742552283616] 
dist 134=[-1.5488995136083623726 ,.09117909389282041639] 
dist 135=[-1.5688286650171536249 ,.07192119841317589058] 
dist 136=[-1.5778342255302245378 ,.03918046362444381059] 
dist 137=[-1.5785643433689923684 ,.03187481184010419269] 
dist 138=[-.49548491085073294697,-.3326335182130701308 ] 
dist 139=[-.57946477042145208495,-.36121232779252867722] 
dist 140=[-.64509150483232844054,-.36656832150942314346] 
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dist 143=[-.7798881042448045437 ,-.35179977713945143994] 
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dist 145=[-.81055276033632468772,-.28829871846270454375] 
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dist 147=[-.82359773420801710835,-.23548060530077040122] 
dist 148=[-.82744887733205931529,-.2020667218734524546 ] 
dist 149=[-.83070842586521463599,-.16672591187678958387] 
dist 150=[-.83335586012629489835,-.13259087500825301778] 
dist 151=[-.83476182060396964901,-.09278673448864257333] 
dist 152=[-.83553585484980539476,-.03481026904594623084] 
dist 153=[-.83565931854049846175,.02457858026891721130] 
dist 154=[-.59801768086874224523,.08071338781934189870] 
dist 155=[-.58390864713700231447,.1692102594787596811 ] 
dist 156=[-.54767615960623632554,.24328125252355407403] 
dist 157=[-.54081221583739589283,.31711303243888755795] 
dist 158=[-.47853858648393902464,.38521447341342931622] 
dist 159=[-.46572490878027130772,.43641134333176293491] 
dist 160=[-.4485918603690170851 ,.48507885354082529915] 
dist 161=[-.44263805836775548559,.54308587153279458726] 
dist 162=[-.31278471193630672197,.5971315451943466496 ] 
dist 163=[-.29537807797049745199,.62998629503653703303] 
dist 164=[-.25800863602051661453,.65364919087504768578] 
dist 165=[-.24758889457022616517,.67990351003485455407] 
dist 166=[-.20551659762156133239,.70131926656020848882] 
dist 167=[-.19745509206056907379,.71760665076344251165] 
dist 168=[-.17737507701196033142,.73119413666542468929] 
dist 169=[-.17403169257770605434,.74146064571361585959] 
dist 170=[.05935311683899939586,.74448886546939489554] 
dist 171=[.08087230822990323044,.7444030818947085342 ] 
dist 172=[.1276960368209871778 ,.74235398613623360007] 
dist 173=[.13686720902721028334,.7242881117215928533 ] 
dist 174=[.18720828834808646902,.71847523235569356562] 
dist 175=[.19540552328615854767,.70998122001926361415] 
dist 176=[.07077473484752383374,.70633929594345481703] 
dist 177=[-.07061879646474817774,.6008551146267939374 ] 
dist 178=[-.16563612272415055352,.57559144338283697249] 
dist 179=[-.24497140037600185479,.57020643722674325525] 
dist 180=[-.32375793578099433634,.55804485111880928252] 
dist 181=[-.39625575752842874942,.55363344170676617076] 
dist 182=[-.45048482068401599841,.53141138381074105673] 
dist 183=[-.50177261894887966643,.52614798965337751294] 
dist 184=[-.56252823987602021355,.51176748638671605635] 
dist 185=[-.61893563275247300731,.50757657160568203372] 
dist 186=[-.65286403784628844527,.39424317469841786566] 
dist 187=[-.67685636245708330273,.39307814937901759886] 
dist 188=[-.69359585179923233355,.38872478560116712572] 
dist 189=[-.7058224423643641969 ,.38641726003302983336] 
dist 190=[-.71179771364247427825,.37182000775811719607] 
dist 191=[-.71434281624405058545,.36783480505792181717] 
dist 192=[-.71370851054919616508,.36078322306809233053] 
dist 193=[-.45426766586476412116,.35852328502765323101] 
dist 194=[-.49564075597878244335,.30205015120161814838] 
dist 195=[-.52137223791625472031,.29366153634884783131] 
dist 196=[-.54059402284532755862,.27507985009974313299] 
dist 197=[-.55597688276790088274,.26943359040606507451] 
dist 198=[-.56771995672986799005,.24457967026839040884] 
dist 199=[-.57240895487625561227,.23939768642730612795] 
dist 200=[-.57395045427595867093,.22655758240177718895] 
dist 201=[-.57313310392728169472,.22329173712331384635] 
dist 202=[-.45287964190577559785,-.12664237036408146002] 
dist 203=[-.4622760827391185773 ,-.1193056934102819416 ] 
dist 204=[-.46710683266422409754,-.10620536070461257673] 
dist 205=[-.46972630253482604014,-.09038622141353131088] 
dist 206=[-.47029518803646972995,-.07219461944754115451] 
dist 207=[-.46947109638516991541,-.04876040772096986172] 
dist 208=[-.46835291246793528482,-.01201037957854235551] 
dist 209=[-.42071788396908574177,.02529703763782615153] 
dist 210=[-.41388554239889388629,.05095679613400372903] 
dist 211=[-.39462106502586645558,.07662350543529164612] 
dist 212=[-.39148753373428809223,.12197251366739649787] 
dist 213=[-.35277005615877059346,.16505549816884795011] 
dist 214=[-.34451915389026693526,.199570638301919852  ] 
dist 215=[-.33624388619154355792,.23445691781640747537] 
dist 216=[-.33361817853899337388,.27902222877916284115] 
dist 217=[-.235593933325773247  ,.32207738027897702487] 
dist 218=[-.22270346637749680375,.35093491564863742688] 
dist 219=[-.19702188093816286776,.37495020868255305162] 
dist 220=[-.19027993997733073482,.39867383824821622034] 
dist 221=[-.16589118559713356763,.42042757006396269305] 
dist 222=[-.16040253645842711164,.43657879511833839909] 
dist 223=[-.15162207336166597784,.45174006277010240478] 
dist 224=[-.14919851390527510912,.46954247962783290637] 
dist 225=[.01573939678804649070,.48547013416648712464] 
dist 226=[.01711569135967102655,.4931467448876968039 ] 
dist 227=[.00400549918752121932,.49695859791213658954] 
dist 228=[-.01096819478848227140,.49745530020912000493] 
dist 229=[-.03241269911039680828,.49029957103131263664] 
dist 230=[-.05639531083802466415,.48788381999033678957] 
dist 231=[-.08150184720335781515,.48592634320591384468] 
dist 232=[-.11226141858182634622,.48408234579827149078] 
dist 233=[-.15881195350731935593,.40975888867301831773] 
dist 234=[-.20550030013580591796,.39902027262871284435] 
dist 235=[-.23681031534561527117,.37888723224802064226] 
dist 236=[-.26287671985157811395,.37349616235707998503] 
dist 237=[-.28863245207977400617,.35410921330688995501] 
dist 238=[-.3122435604490770071 ,.3489242064990499636 ] 
dist 239=[-.32974874994613200351,.3411094482253398882 ] 
dist 240=[-.34614994186980242613,.33843292813303170658] 
dist 241=[-.36535437975338648329,.15818033474795628667] 
dist 242=[-.38306812953356617029,.1550084716754074986 ] 
dist 243=[-.39351858427980699669,.14789843223923439957] 
dist 244=[-.40066095190102846097,.14565372480216612262] 
dist 245=[-.40516859701022717198,.13543936413425534198] 
dist 246=[-.40764629323274244313,.13322990293519128433] 
dist 247=[-.40792332809112180364,.12781771684407524709] 
dist 248=[-.40497145130349371939,.12621393378532227939] 
dist 249=[-.40444209221466849865,.10903840596658848436] 
dist 250=[-.38534740029560678848,.10622127377345605215] 
dist 251=[-.38140940025384467573,.09930325830846550467] 
dist 252=[-.37093931479440234488,.09775019460012395987] 
dist 253=[-.36758360537401589176,.08667019915323662592] 
dist 254=[-.34650081661496141336,.08438314448504786222] 
dist 255=[-.34155003565190078426,.08051118578075907893] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 2, 0, 0, 2] 
dist 0=[48.909619824569948596  ,48.909619824569948596  ] 
dist 1=[48.261537273224711436  ,49.363126569803698607  ] 
dist 2=[47.177000890008232643  ,49.670288609064730919  ] 
dist 3=[45.891713178598663231  ,49.877317130124422182  ] 
dist 4=[44.441693916276545886  ,49.930934806775984236  ] 
dist 5=[42.589332797763307123  ,49.890407600517661321  ] 
dist 6=[39.696921197465898504  ,49.840076382182922542  ] 
dist 7=[36.752082321102137072  ,49.417178491093999340  ] 
dist 8=[34.690224657790518335  ,49.283198783356077392  ] 
dist 9=[32.874488548449905132  ,48.867196538877785393  ] 
dist 10=[30.912523682597223889  ,48.713446245200081409  ] 
dist 11=[28.999304251499436310  ,46.768204368291481589  ] 
dist 12=[27.378087439736514285  ,46.369732336731108027  ] 
dist 13=[25.654676263827746037  ,45.974888054999389925  ] 
dist 14=[23.332919701591972138  ,45.269212144641456287  ] 
dist 15=[21.021963764257435101  ,40.954699895599605944  ] 
dist 16=[19.341508082240843683  ,38.257397005734222825  ] 
dist 17=[17.794415413151297849  ,31.426341177057629134  ] 
dist 18=[16.015939186580553398  ,31.180922145851050717  ] 
dist 19=[14.214998220777611821  ,24.884202949721012800  ] 
dist 20=[12.577812738793113364  ,24.065984240332576507  ] 
dist 21=[10.738702774475603623  ,22.389586574870281405  ] 
dist 22=[8.1303447795267361369 ,21.945392574681331868  ] 
dist 23=[5.5609091704100239197 ,20.286365382006793612  ] 
dist 24=[3.8772192794887353998 ,19.944214230812947976  ] 
dist 25=[2.5108754333614965483 ,19.279601685541695176  ] 
dist 26=[1.2097434550956728937 ,19.106279920385414369  ] 
dist 27=[.04115914937325788070,11.252919139593194006  ] 
dist 28=[-.79552503823218439605,10.795060959319709639  ] 
dist 29=[-2.4993123686052194512 ,8.6298415409842455908 ] 
dist 30=[-4.4657099007114728407 ,7.5898674331041136282 ] 
dist 31=[-6.2425051734305887048 ,4.0268606880290261067 ] 
dist 32=[-7.5251608303433300106 ,2.8826640644608683165 ] 
dist 33=[-8.6961149794440797989 ,-.34058338362261721596] 
dist 34=[-10.026750965443274232  ,-.51769308764450132122] 
dist 35=[-11.252622379183483560  ,-2.7270699585900934059 ] 
dist 36=[-12.005095326980206051  ,-3.0319641984639076316 ] 
dist 37=[-12.557857924599471546  ,-3.5156757341781765233 ] 
dist 38=[-12.985954580281371753  ,-3.6232936109691889370 ] 
dist 39=[-13.307396606270226185  ,-3.5868577019116474229 ] 
dist 40=[-13.434050498701847722  ,-3.3520312988345512529 ] 
dist 41=[-13.479651571578591272  ,-3.1176910039517710653 ] 
dist 42=[-13.477252343836255269  ,-2.7179228670429814552 ] 
dist 43=[-11.002231352808948646  ,-2.1215669009711599390 ] 
dist 44=[-10.965828246598136324  ,-1.6774592670735615227 ] 
dist 45=[-10.750430464691340112  ,-1.2616686458304732493 ] 
dist 46=[-10.687593656468493160  ,-.7778243364995973271 ] 
dist 47=[-10.465931323332393745  ,-.28861296804812336033] 
dist 48=[-10.416031556440877666  ,.1488517831977759024 ] 
dist 49=[-5.6684979130299041642 ,.63176192092107627397] 
dist 50=[-5.2264117691440849608 ,1.3026047858510350715 ] 
dist 51=[-4.2497731812334697273 ,1.9754589284462275086 ] 
dist 52=[-4.0387146357558851257 ,2.7104336192665836571 ] 
dist 53=[-2.9129808429857027311 ,3.6845372805491518624 ] 
dist 54=[-2.5398661713477433098 ,4.3890292769818152192 ] 
dist 55=[-1.8038581362495089772 ,5.0308962896489700228 ] 
dist 56=[-1.2513586301109100002 ,5.7549414506565642711 ] 
dist 57=[-.20478549122316017788,6.4245537972428582942 ] 
dist 58=[-.16437245458189365406,6.8491860392524281656 ] 
dist 59=[1.9337072283571470233 ,7.1756235549893661072 ] 
dist 60=[2.1165223104370236593 ,7.4534865398016997707 ] 
dist 61=[2.4562809370451516382 ,7.6792659701742101194 ] 
dist 62=[2.5287440184826225200 ,7.7979573345768821667 ] 
dist 63=[2.6980324098096946695 ,7.8615279699858547351 ] 
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dist 65=[2.6047579756123028085 ,5.3574067209257935324 ] 
dist 66=[2.4020378503277453721 ,5.1543227013736977341 ] 
dist 67=[2.1613176115477261537 ,5.1601315623741105081 ] 
dist 68=[1.9266556966644101290 ,5.2806820068927446447 ] 
dist 69=[1.6517993798379249345 ,5.3600543140003048225 ] 
dist 70=[1.2504966401555540826 ,5.4046383349853681997 ] 
dist 71=[.63477686180862049013,5.4253901566598389614 ] 
dist 72=[.16674408458857123459,5.4248394120943442505 ] 
dist 73=[-.26475566255389732511,5.3856126376737244267 ] 
dist 74=[-1.1550556913472537832 ,5.3739279357303853572 ] 
dist 75=[-2.0461232929190092642 ,1.2190141744708796589 ] 
dist 76=[-2.6358144272351215626 ,1.1198699757624155021 ] 
dist 77=[-3.1181184105273340253 ,.88642369851466163756] 
dist 78=[-3.5805216510144529427 ,.85589695660677867764] 
dist 79=[-3.9952552478694621205 ,.61110796278608825867] 
dist 80=[-4.2872833216139902465 ,.59593670163259726674] 
dist 81=[-4.5456996923349623783 ,-.26993441880583393677] 
dist 82=[-4.8262940140275261280 ,-.31336124273667584349] 
dist 83=[-5.0750126537882301805 ,-.53781064564023644324] 
dist 84=[-5.2061795498308193039 ,-.57521439114975498336] 
dist 85=[-5.2785755650535891947 ,-.65138829961032310177] 
dist 86=[-5.2939055036929928015 ,-.66605867480851630204] 
dist 87=[-5.2683673330278404647 ,-1.1207471582985908465 ] 
dist 88=[-5.2567728295830690492 ,-1.1612281494598173808 ] 
dist 89=[-5.2450938724876602274 ,-1.2316915444238544728 ] 
dist 90=[-5.2303979594635236624 ,-.75277927271769805957] 
dist 91=[-4.5900844463098800500 ,.19162718998529702272] 
dist 92=[-4.5069535500048153201 ,.8316019829791618617 ] 
dist 93=[-4.2709910284939097292 ,1.3713091117467376541 ] 
dist 94=[-4.2369377194681890185 ,1.9154962613401552254 ] 
dist 95=[-4.1966479971006385787 ,2.4210925823114163460 ] 
dist 96=[-4.1996105074015943253 ,2.8067628617927934916 ] 
dist 97=[-3.5785840652459693720 ,3.1785579438267233057 ] 
dist 98=[-3.5607449262653601244 ,3.6287680395176566297 ] 
dist 99=[-2.3933087767667992824 ,4.0512404886278414331 ] 
dist 100=[-2.2440188291387714249 ,4.3123168028751479645 ] 
dist 101=[-1.9513872439417185472 ,4.5052125720210304665 ] 
dist 102=[-1.8767056867384641304 ,4.6555342695176454089 ] 
dist 103=[-1.6200447128065602352 ,4.7690963636824527406 ] 
dist 104=[-1.5599989788560448361 ,4.8152654595851792911 ] 
dist 105=[-1.4977963396884637032 ,4.8320443435421788394 ] 
dist 106=[-1.4856831203297401098 ,4.8282962652428799700 ] 
dist 107=[-.82741831173994347972,4.4599298214940881046 ] 
dist 108=[-.80469164602232954499,4.5430987445143992281 ] 
dist 109=[-.76015316634035407974,4.5985855910353510445 ] 
dist 110=[-.74787041533535521979,4.6110175481862183125 ] 
dist 111=[-.57167296185874960994,4.6053836028612172568 ] 
dist 112=[-.54650369114061205049,4.5973587262463605323 ] 
dist 113=[-.72856419982662724843,4.5067414262737038320 ] 
dist 114=[-1.2488930035536093954 ,4.4814873080255666636 ] 
dist 115=[-1.6891815946869767771 ,4.3885210598495514076 ] 
dist 116=[-2.1356182999019647276 ,4.3685557171771455073 ] 
dist 117=[-2.5520803941387955666 ,4.1044929621107140746 ] 
dist 118=[-2.8727240386771073619 ,4.0296059372427996937 ] 
dist 119=[-3.1847494369270802021 ,3.9379687828630452537 ] 
dist 120=[-3.5668166260598699834 ,3.7727860724930012101 ] 
dist 121=[-3.9276638290640390125 ,2.8285278769042071766 ] 
dist 122=[-4.1549875631997403339 ,2.4921787308752279076 ] 
dist 123=[-4.3281595121853979269 ,2.2253554696068839099 ] 
dist 124=[-4.4728489724664460987 ,2.1592748208424006355 ] 
dist 125=[-4.5882659635781680977 ,1.9210400072597233018 ] 
dist 126=[-4.6445928622815048336 ,1.8662104882319450169 ] 
dist 127=[-4.6684762549502653852 ,1.7815809775218062880 ] 
dist 128=[-4.6692640028027431941 ,1.7568233992632035163 ] 
dist 129=[-.07937959465181515483,.59641985956876690066] 
dist 130=[-.1059781358506557319 ,.5846277719972467478 ] 
dist 131=[-.28602661468435419184,.62883814293208324293] 
dist 132=[-.43126063429050346843,.66908909313166770234] 
dist 133=[-.56234038947829316268,.71414265450516107691] 
dist 134=[-.7085548995269090768 ,.8113055513065749298 ] 
dist 135=[-.85350505830192893734,.91233241322957826053] 
dist 136=[-.97954518998302651429,.97376115593000882598] 
dist 137=[-1.1160352466384172429 ,1.0179375749418593941 ] 
dist 138=[-1.3027177488064166040 ,1.0501017932909712553 ] 
dist 139=[-1.4829087862035264438 ,1.0744950530610058056 ] 
dist 140=[-1.5934851338098820289 ,1.0876557853125495382 ] 
dist 141=[-1.6743974984312845905 ,1.0950961131447949043 ] 
dist 142=[-1.7361543443909828030 ,1.0966626010125196108 ] 
dist 143=[-1.7840150126531975408 ,1.0034706968473365422 ] 
dist 144=[-1.8094433086080534621 ,.98811374642102453627] 
dist 145=[-1.8233495444431184336 ,.96657997582034744964] 
dist 146=[-1.8251985600572053121 ,.958547958638546061  ] 
dist 147=[-1.7086371006061129845 ,.94094010282618047651] 
dist 148=[-1.6878645795251700666 ,.9343690479370165678 ] 
dist 149=[-1.6599160843667880738 ,.93022714101134258877] 
dist 150=[-1.6485083900442596301 ,.92830167619604569894] 
dist 151=[-1.6233800679910111084 ,-.07440962643207096543] 
dist 152=[-1.6127311844624437085 ,.07125499379760518448] 
dist 153=[-1.6046050724749580413 ,.19203419614370050593] 
dist 154=[-1.5990237158140420183 ,.31055529591119127286] 
dist 155=[-.53936801512075423224,.41865747658164266682] 
dist 156=[-.45390763691101749567,.49784389171269482482] 
dist 157=[-.25095011262691010989,.57107275638451745945] 
dist 158=[-.22173333042394590546,.65539181267266320955] 
dist 159=[.05483277029147950404,.73381212122831683387] 
dist 160=[.10365777435645291609,.78349344514584851395] 
dist 161=[.16498664127753059609,.82167294713759760309] 
dist 162=[.17552079609223802088,.85417934376512923533] 
dist 163=[.52057910732948053043,.88058329900440634514] 
dist 164=[.55998280067939961257,.89440308587425197523] 
dist 165=[.64640742012794996731,.90166721446400888425] 
dist 166=[.65888052748534783447,.93495359024578262118] 
dist 167=[.65112549882611247013,.97749910455629848431] 
dist 168=[.60333902906638336022,.9997513390670092167 ] 
dist 169=[.55534614374144417008,1.0120603926618476242 ] 
dist 170=[.49449037773784195264,1.0149036498237767577 ] 
dist 171=[.42997854119378925881,.78997414611608083714] 
dist 172=[.3673889728161147383 ,.78795108769246603678] 
dist 173=[.29417539611759643812,.78384328432442635247] 
dist 174=[.18725092342570101033,.7812966025100981339 ] 
dist 175=[.07759296258582785060,.76501850065544465446] 
dist 176=[-.00677837521876746573,.76050376608037234117] 
dist 177=[-.09351482216113756631,.74419107485114259489] 
dist 178=[-.20001848385609242384,.74097081009327830178] 
dist 179=[-.31117528497622881659,.68558402112819921607] 
dist 180=[-.41648641812295661209,.67573684051097747782] 
dist 181=[-.53776574432719720607,.64816148792898607809] 
dist 182=[-.71266648716837579293,.64303262210389302296] 
dist 183=[-.8844426263544325729 ,.58749356888086524508] 
dist 184=[-.99324789709722917326,.57547715961095829195] 
dist 185=[-1.0768327703478314703 ,.56177228439068098105] 
dist 186=[-1.1479282826944857376 ,.56157409308136978324] 
dist 187=[-1.2058838083032675018 ,.56684867542814115377] 
dist 188=[-1.2370146390921546879 ,.5712027963772422537 ] 
dist 189=[-1.2544745790445610636 ,.57570101453450609628] 
dist 190=[-1.2586310555254757702 ,.58155289775573290452] 
dist 191=[-1.2457352413179433621 ,.5878095046079863532 ] 
dist 192=[-1.2422551546134360405 ,.59392364318931866395] 
dist 193=[-1.2392409313092634386 ,.60109300564022697395] 
dist 194=[-1.2360612639631708974 ,.61156077691865508229] 
dist 195=[-1.2216846691565246065 ,.62225550158511233772] 
dist 196=[-1.2205134070928385660 ,.63033099772044822498] 
dist 197=[-1.1773757275016489771 ,.63802374251884645189] 
dist 198=[-1.1353260747532315967 ,.6471922117457871308 ] 
dist 199=[-1.0561894493569499147 ,.65659517126580380989] 
dist 200=[-1.0583239285398121744 ,.66522410213855225037] 
dist 201=[-1.0578495833362117094 ,.67493039229186898938] 
dist 202=[-1.0550539514137147522 ,.68863277642093564841] 
dist 203=[-.4618541230121227186 ,.70174271229910130278] 
dist 204=[-.4144544470547949597 ,.70908470913693702207] 
dist 205=[-.30631147793712168916,.71359945054704193019] 
dist 206=[-.28555391227990836959,.7154266275591936002 ] 
dist 207=[-.14876810083918180936,.71537797109943443553] 
dist 208=[-.12428876516905592328,.71358013678528154542] 
dist 209=[-.07910944802977063650,.70805535649448190436] 
dist 210=[-.06873076911128999463,.70473550766604932118] 
dist 211=[.06600620262917671224,.68359429662972613386] 
dist 212=[.08499394460563433431,.67785665045135784714] 
dist 213=[.09244489643858779282,.662872993672785136  ] 
dist 214=[.01500502917804810955,.64274017785613131625] 
dist 215=[-.06949811876988583787,.58558368285817922163] 
dist 216=[-.15502757143653122736,.60549181675104484696] 
dist 217=[-.25774913765622714642,.66440882533486809687] 
dist 218=[-.41088033386263731148,.74245244647456358567] 
dist 219=[-.56307468569600231469,.81737063667130367607] 
dist 220=[-.66205592111969606231,.86381104169308452729] 
dist 221=[-.74106969040585168617,.89833233143610879216] 
dist 222=[-.81355545939761200874,.92566700671017716263] 
dist 223=[-.87634199757207628216,.94632844517124569615] 
dist 224=[-.91663669758766468846,.95420939528190724886] 
dist 225=[-.94818981782387047836,.95686026563154621534] 
dist 226=[-.97607920485840208141,.95663873262734464261] 
dist 227=[-.99910909221901637567,.92976600831701926931] 
dist 228=[-1.0112636132004147907 ,.92291301857592163474] 
dist 229=[-1.0177778936851001107 ,.90539656000754419085] 
dist 230=[-1.0182942596767440305 ,.89831302894883003019] 
dist 231=[-1.0149220352863551732 ,.86024018446367333255] 
dist 232=[-1.0124271749809765458 ,.8507532431039651607 ] 
dist 233=[-.99718837641912499975,.82947915179706755439] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 1, 0, 1, 2] 
dist 0=[46.280380357584094347  ,46.280380357584094347  ] 
dist 1=[45.576932703289943581  ,46.724178365001372495  ] 
dist 2=[44.148059665949277321  ,47.116095117015267101  ] 
dist 3=[42.434124889524607801  ,47.576532756616720205  ] 
dist 4=[40.592304578155223882  ,48.293441455903283763  ] 
dist 5=[38.300197009373059621  ,48.988987319168798840  ] 
dist 6=[34.787813189908164956  ,49.364124355339311273  ] 
dist 7=[31.242830241880268727  ,49.575885230770148524  ] 
dist 8=[28.820376473935501813  ,49.619462195789637896  ] 
dist 9=[26.750664146269685756  ,49.572376129711528582  ] 
dist 10=[24.614097882807682963  ,49.511622145589653398  ] 
dist 11=[22.590981346359216239  ,49.252962142894220912  ] 
dist 12=[20.974053748552241010  ,49.131337493493129369  ] 
dist 13=[19.339670597475523563  ,47.422275157214737936  ] 
dist 14=[17.246276319375757519  ,46.451578215117734399  ] 
dist 15=[15.211215154372206754  ,38.643581585373479450  ] 
dist 16=[13.809513311484647354  ,38.353786000360405752  ] 
dist 17=[12.597015730998372686  ,34.992226621325710751  ] 
dist 18=[11.317299128120207082  ,34.324881192830826877  ] 
dist 19=[10.083005881820860464  ,33.653967784734710126  ] 
dist 20=[9.0513886193730645949 ,33.521577813040194038  ] 
dist 21=[7.9627783673029750687 ,26.477779215218032804  ] 
dist 22=[6.4995799966392016967 ,25.577099327721998022  ] 
dist 23=[5.0785346217340879873 ,23.824325627034953178  ] 
dist 24=[4.1582090921240405754 ,23.379323520495890369  ] 
dist 25=[3.4197016496240049535 ,21.857380217439180736  ] 
dist 26=[2.7258920550691962674 ,21.499823139482942111  ] 
dist 27=[2.1050087928696252137 ,21.114300513120085957  ] 
dist 28=[1.6580978048109651490 ,21.017153177322091534  ] 
dist 29=[1.2476034088921254097 ,10.605912561224651071  ] 
dist 30=[.02278269942473934207,9.4644605567988469033 ] 
dist 31=[-2.1634341152584254704 ,1.4748845270733918010 ] 
dist 32=[-3.5631737954822848932 ,1.4179407121015787534 ] 
dist 33=[-4.6640374505739618333 ,1.4214421422871180167 ] 
dist 34=[-5.6555198255125952086 ,1.5037691736237046157 ] 
dist 35=[-6.8644692661316180754 ,1.6264132753682054418 ] 
dist 36=[-8.5594084067658772437 ,1.7910109524686693868 ] 
dist 37=[-10.151688617087588106  ,2.0152552491720931406 ] 
dist 38=[-11.152012786607772412  ,2.3758688085509290539 ] 
dist 39=[-11.913418718063347790  ,2.7395871601121513208 ] 
dist 40=[-12.551315418701645371  ,2.9763258201813249642 ] 
dist 41=[-13.063421776857674660  ,3.1631075139302767457 ] 
dist 42=[-13.322357195951753954  ,3.3278371280780646343 ] 
dist 43=[-13.456966918181311881  ,3.4634230749519667049 ] 
dist 44=[-13.476330876931133410  ,3.5340104689468504541 ] 
dist 45=[-8.8133677466502258780 ,3.5696375046184150913 ] 
dist 46=[-8.7962548767579985475 ,3.5755111759510464880 ] 
dist 47=[-5.9312278510875672667 ,3.5408518695891170076 ] 
dist 48=[-5.8201689975783037678 ,3.5192192441991297046 ] 
dist 49=[-4.8482797991037833766 ,3.4806131911163344178 ] 
dist 50=[-4.5838607533572061105 ,3.4620678282955845930 ] 
dist 51=[-4.2228955336891162372 ,3.3539380265757142516 ] 
dist 52=[-4.1087142550768257963 ,3.3242968592694894840 ] 
dist 53=[-2.7109752525216426047 ,3.2131794499918308143 ] 
dist 54=[-2.6347947651508030855 ,3.1945026354182979902 ] 
dist 55=[-1.3694912405015680094 ,1.0698978019713702378 ] 
dist 56=[-1.2425533333785762566 ,1.5538456524317848186 ] 
dist 57=[-.79488570573680979832,1.9722346412172042332 ] 
dist 58=[-.70610401455946928623,2.4116952049148438699 ] 
dist 59=[-.58892701161341594193,2.8323618663409781163 ] 
dist 60=[-.56922326295148442718,3.1757969041531941210 ] 
dist 61=[.06152004853623147909,3.5295157789853235478 ] 
dist 62=[.08601915858178646334,3.9914075675575082181 ] 
dist 63=[2.2969354082922705055 ,4.4329764014432018632 ] 
dist 64=[2.3814477270947579438 ,4.7055590921383737720 ] 
dist 65=[2.6276298799519627761 ,4.9076662973340887380 ] 
dist 66=[2.6613289777694737220 ,5.0677055322096943611 ] 
dist 67=[2.6329844806690237102 ,5.1894320020644660398 ] 
dist 68=[2.5134243027239111038 ,5.2385096225299875456 ] 
dist 69=[2.3593411236350088036 ,5.2583036441758781700 ] 
dist 70=[2.1931319223312800908 ,5.2629454087503163083 ] 
dist 71=[1.9865324305111737289 ,5.1249087987986668569 ] 
dist 72=[1.6710941408302846668 ,5.0900055905922741969 ] 
dist 73=[1.3098868667679154739 ,5.0094850872093677311 ] 
dist 74=[.92051765243351149914,4.9781083281096801934 ] 
dist 75=[.43576092325240882234,4.8130497028947928355 ] 
dist 76=[-.30629344101077477083,4.7726639895113691358 ] 
dist 77=[-1.0512689476624620651 ,4.6613924579426471740 ] 
dist 78=[-1.5477151531554365210 ,4.6270258032648988469 ] 
dist 79=[-1.9575615731692655262 ,3.3083593288761081750 ] 
dist 80=[-2.3568544722662372211 ,3.1859575361602576027 ] 
dist 81=[-2.7192575638341552811 ,2.8773746168543718026 ] 
dist 82=[-2.9818599842168705747 ,2.8309190260084713723 ] 
dist 83=[-3.2219663680188604153 ,2.3356171618657697626 ] 
dist 84=[-3.4946017307096447372 ,2.2394383558009533847 ] 
dist 85=[-3.7419157452626112354 ,2.1323223742933153796 ] 
dist 86=[-3.8809519663075755964 ,2.1070327118423384416 ] 
dist 87=[-3.9675945837329637645 ,1.1772565314504013490 ] 
dist 88=[-4.0057547456136298600 ,1.0599560619002967205 ] 
dist 89=[-4.0687821850820360349 ,.82137305984767619081] 
dist 90=[-4.1918810290495510992 ,.75957006161336124294] 
dist 91=[-4.2854787399846947086 ,.53734337552743940221] 
dist 92=[-4.3332988750284550287 ,.49086052690314895664] 
dist 93=[-4.3568160022253234849 ,.44378841229187146343] 
dist 94=[-4.3562904477901649292 ,.89606907311985070882] 
dist 95=[-3.5244844183890075604 ,1.2790418265787701457 ] 
dist 96=[-3.4978794962137988100 ,1.6676099307429108801 ] 
dist 97=[-3.2601508558096879401 ,2.0300920541302740873 ] 
dist 98=[-3.2066659402522624002 ,2.3089516153545662709 ] 
dist 99=[-3.1324250442206667911 ,2.5800128255007534809 ] 
dist 100=[-3.1055859787094564862 ,2.9113751100670051167 ] 
dist 101=[-2.4774854205786046910 ,3.2238833818698364400 ] 
dist 102=[-2.3177478663842249477 ,3.4196929416837565180 ] 
dist 103=[-1.7283980602170872134 ,3.5675594327672412190 ] 
dist 104=[-1.6779822805489249736 ,3.6887081519811044342 ] 
dist 105=[-1.5462558661205184321 ,3.7834493907327880246 ] 
dist 106=[-1.4051718345991730203 ,3.8259141408295125228 ] 
dist 107=[-1.0944809472193228208 ,3.8426524153456925315 ] 
dist 108=[-1.0733940428026399684 ,3.8399988567731308978 ] 
dist 109=[-.92415819084700186811,.48358484875251875015] 
dist 110=[-.92356708955771277407,.74241856875105306831] 
dist 111=[-.40645676857506246379,.95150181069768049582] 
dist 112=[-.36403070458051927934,1.1477067827782434937 ] 
dist 113=[-.26549144400681852679,1.3209149137909755410 ] 
dist 114=[-.24857981977974720598,1.4381915311235704705 ] 
dist 115=[-.11882810077227111922,1.5371304071460484486 ] 
dist 116=[-.09555077352196235731,1.6371389524455104662 ] 
dist 117=[-.05863437098990968492,1.7265533169626794512 ] 
dist 118=[-.04957455756847645791,1.7831954824275377187 ] 
dist 119=[.09993121865585601645,1.8267923154171793418 ] 
dist 120=[.11906528115043053669,1.8641110410999973278 ] 
dist 121=[.15957678880897370663,1.8946265944756984872 ] 
dist 122=[.16807672067971825554,1.9110553093755054567 ] 
dist 123=[.20714075371553850937,1.9203424151312961920 ] 
dist 124=[.21389262217591776006,1.9223381540208506045 ] 
dist 125=[.22475738058831129644,1.0976488585608560736 ] 
dist 126=[.22696546027524556538,1.0287807950863174099 ] 
dist 127=[.62814429091312698327,.8699092316186162743 ] 
dist 128=[.64596884324469618549,.83773281542966663681] 
dist 129=[.5178742713593466214 ,.70122888615181195667] 
dist 130=[.38943567154176421824,.71749315381679627221] 
dist 131=[.24983292565487029145,.72940481617771825941] 
dist 132=[.05834006387073284422,.73569467158892271271] 
dist 133=[-.13290792279465495938,.73907776633223464776] 
dist 134=[-.2715393006083420501 ,.73938509360701572764] 
dist 135=[-.39831246299878434579,.67664806207382464582] 
dist 136=[-.54222921882954883589,.66656056861795044254] 
dist 137=[-.68635444544989999367,.65118503509755970534] 
dist 138=[-.81396801645584208315,.64608583500032308834] 
dist 139=[-.95409773544595140945,.63285861875453725289] 
dist 140=[-1.1482049652504485150 ,.62785177089367777267] 
dist 141=[-1.3366953936937836400 ,.62435876011769789873] 
dist 142=[-1.4544030073835132582 ,.62201602102864250701] 
dist 143=[-1.5429692128413949225 ,.18376927260724396706] 
dist 144=[-1.6151101159011208221 ,.14798415044914058516] 
dist 145=[-1.6724120979774822720 ,.06332108704945022342] 
dist 146=[-1.7017298275322865551 ,.05104355489792046941] 
dist 147=[-1.7165956236826106195 ,-.06347151047834566456] 
dist 148=[-1.7191036003776225432 ,-.08366286128320669983] 
dist 149=[-1.6654614984268204540 ,-.1093404034157759534 ] 
dist 150=[-1.6523801621950298884 ,-.11399491166255231342] 
dist 151=[-1.6360458175810020418 ,-.25163844121892003957] 
dist 152=[-1.6277016322206480500 ,-.26680861368405534764] 
dist 153=[-1.6052192983184946813 ,-.29884640900086536928] 
dist 154=[-1.5952711665139197336 ,-.30430327679135061922] 
dist 155=[-1.5777066986324055329 ,-.33287114110986523174] 
dist 156=[-1.5709471994168626706 ,-.33740456153659337037] 
dist 157=[-.66552457220222644386,-.34012430398144184258] 
dist 158=[-.58878885769966179351,-.15756614238496196628] 
dist 159=[-.40671527615921037448,-.00152471147822364066] 
dist 160=[-.37902843264088496911,.15626144770026340884] 
dist 161=[-.33711949429656170513,.30331132371135614805] 
dist 162=[-.33488571238383781928,.41648916977278113854] 
dist 163=[-.32979322263201644436,.52666442218804917057] 
dist 164=[-.3275050491908158342 ,.6617272606405231287 ] 
dist 165=[-.32560492276464971637,.78951239457945354684] 
dist 166=[-.32397402143966019499,.87063188287322912122] 
dist 167=[-.32217084160896896504,.9331957084604588845 ] 
dist 168=[-.3215383314254618431 ,.98689795702961577403] 
dist 169=[-.32145750099828014011,1.0308673798733967884 ] 
dist 170=[-.32210190733033450075,1.0545732962740417192 ] 
dist 171=[-.32315730364772836364,1.0680028185325371338 ] 
dist 172=[-.32471704682288954973,1.0709443433188805942 ] 
dist 173=[-.32694117410785517148,.63119041988950003841] 
dist 174=[-.33064812351152638743,.63756344244646836984] 
dist 175=[-.33446923918186888048,.64123664429484644799] 
dist 176=[-.33714926733771944561,.64222827460719659206] 
dist 177=[-.33950359366746057729,.64145115428689984432] 
dist 178=[-.34202561509192808375,.63990060472089803032] 
dist 179=[-.34446017411268978086,.63733033701192239783] 
dist 180=[-.34646585553501397852,.66035947746879598107] 
dist 181=[-.34854086238361658094,.67644874137710408766] 
dist 182=[-.35125256066184603664,.68729520661028750499] 
dist 183=[-.35389710889310767002,.69512746993568795654] 
dist 184=[-.35570435441863348162,.69918335731301910166] 
dist 185=[-.35724501019632549717,.7012534884091849777 ] 
dist 186=[-.35882583603175917931,.70115842940111522164] 
dist 187=[-.36031339137649054627,.6996794344606599253 ] 
dist 188=[-.36148206675440246798,.697449745260811947  ] 
dist 189=[-.43944756578111825092,.69169302229552659846] 
dist 190=[-.53981192960062473347,.68859363729309087567] 
dist 191=[-.61976823076991499293,.40280842233819176458] 
dist 192=[-.6928957360191156611 ,.39544536851637078362] 
dist 193=[-.75613054880251020184,.36636389948726162145] 
dist 194=[-.79659357835860737536,.3598706554211678226 ] 
dist 195=[-.82817347959224763296,.34532928199951527763] 
dist 196=[-.85594677703163496413,.34066295840268942599] 
dist 197=[-.8793517540281647127 ,.31985845179763792798] 
dist 198=[-.8934916867505604523 ,.31440933828449498174] 
dist 199=[-.90357609970421180423,.30919787568918188241] 
dist 200=[-.91078667605841511114,.30698822565186355906] 
dist 201=[-.91561024229033273637,.30619689981141881524] 
dist 202=[-.91616278702302195695,.30766659597389192265] 
dist 203=[-.91369057559314173843,.31105791625355680868] 
dist 204=[-.91154078438159284332,.31793580164560573117] 
dist 205=[-.49692232742003091162,.32524304669947590429] 
dist 206=[-.4609747104741200035 ,.33034916091406102891] 
dist 207=[-.51550687357295382256,.4000999668350429231 ] 
dist 208=[-.55198533294117303082,.46818547596799836437] 
dist 209=[-.58016101864504714276,.5219184276241077027 ] 
dist 210=[-.60440053727037331743,.57017681798987632166] 
dist 211=[-.62427430385086874073,.61126920308215596821] 
dist 212=[-.63502203646353193188,.63639422711861899571] 
dist 213=[-.64115028078920074188,.65465382228570565166] 
dist 214=[-.6425832646095094637 ,.66833803601486990057] 
dist 215=[-.6414753120219875308 ,.67894736929434229284] 
dist 216=[-.63987594267068160837,.68493169060251602998] 
dist 217=[-.63289872966316384907,.68867784858318387174] 
dist 218=[-.62961259555800547694,.69035277701505552963] 
dist 219=[-.60458000639744199291,.69056956637012201657] 
dist 220=[-.59788980835992179449,.68881214766325829628] 
dist 221=[-.58747937622075682358,.68483861649827164723] 
dist 222=[-.58371978334337804537,.68238971100259606386] 
dist 223=[-.59259785971085772485,.67492319858595356944] 
dist 224=[-.64353611135093834658,.70697096877908655765] 
dist 225=[-.68664812454539427934,.73362684710078256012] 
dist 226=[-.71249340958731089771,.74879610492040456887] 
dist 227=[-.73064530802112282797,.75848012254248440348] 
dist 228=[-.74304403277591707989,.76323914234341929343] 
dist 229=[-.75212565781900737782,.76485845981516839261] 
dist 230=[-.75703628384625729102,.7639672299513775625 ] 
dist 231=[-.75982440864534564379,.75789064604480434244] 
dist 232=[-.76043604738311143625,.75445233818100503102] 
dist 233=[-.75959417726490775789,.7272668734294328181 ] 
dist 234=[-.7572496221834892429 ,.71976961234062503609] 
dist 235=[-.75201930675504459034,.70842741730403206204] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 0, 0, 0, 1, 2] 
dist 0=[42.439844481530407840  ,42.439844481530407840  ] 
dist 1=[42.118756105808989403  ,42.708700338131520955  ] 
dist 2=[41.105085407327757240  ,43.084694644677081312  ] 
dist 3=[40.022973921721153020  ,43.277588351210713318  ] 
dist 4=[39.193512308460145547  ,43.385103689881186912  ] 
dist 5=[38.387612876422165070  ,43.420120330925417159  ] 
dist 6=[37.399503118782753135  ,43.408832312841900937  ] 
dist 7=[36.365607059656637535  ,43.363888925812857524  ] 
dist 8=[35.376699706892443004  ,41.435631679722733325  ] 
dist 9=[34.227556738085280497  ,41.127550669796703976  ] 
dist 10=[32.553372293759606280  ,40.573845311379465953  ] 
dist 11=[30.829044412447358082  ,40.419524538802562911  ] 
dist 12=[29.479480520908365913  ,39.844434673586315212  ] 
dist 13=[28.140485117876518152  ,39.675838392393608574  ] 
dist 14=[26.458230881738605244  ,39.373740284676593597  ] 
dist 15=[24.675125064139568234  ,39.277926469280657309  ] 
dist 16=[22.933021190329412930  ,28.833874847233257466  ] 
dist 17=[20.879281678449219126  ,28.401346203595054544  ] 
dist 18=[17.850718792908766057  ,28.283029867123337463  ] 
dist 19=[14.824532080747047317  ,24.089332873575464331  ] 
dist 20=[12.780250921201268612  ,20.693183150605911628  ] 
dist 21=[11.054502530649424364  ,20.064235131183770140  ] 
dist 22=[9.3012239681238098230 ,19.281298126345843764  ] 
dist 23=[7.6547764592941323610 ,19.085250184638771505  ] 
dist 24=[6.3559232649607071358 ,16.391676644081193420  ] 
dist 25=[5.0568879530351283338 ,16.195545512759359557  ] 
dist 26=[3.4096607418868037828 ,15.236906729489845476  ] 
dist 27=[1.8141553289310360866 ,11.550498157260650117  ] 
dist 28=[.72175348341875783547,10.242451061594020271  ] 
dist 29=[-.3747869499580997602 ,9.9880805208008211947 ] 
dist 30=[-2.2265448404989870639 ,9.5006853241132686964 ] 
dist 31=[-4.8419064742863918406 ,9.3835883858886283106 ] 
dist 32=[-7.3971647527771711154 ,2.4171759143513116165 ] 
dist 33=[-9.0089264873819172835 ,1.8084306085774519295 ] 
dist 34=[-10.247799742829914458  ,1.3302998543374672239 ] 
dist 35=[-11.312819470690368587  ,1.2662645224557761483 ] 
dist 36=[-12.193595878887720293  ,1.2842570947816417718 ] 
dist 37=[-12.696318577270608987  ,1.3399878530056119935 ] 
dist 38=[-13.023308609698077520  ,1.4578580234272692595 ] 
dist 39=[-13.202283213775486181  ,1.6034213696000186465 ] 
dist 40=[-13.310549317861512453  ,1.7699407155491666653 ] 
dist 41=[-13.354925392348060443  ,1.9818804769582957792 ] 
dist 42=[-13.364007709375459197  ,2.3088243325096357199 ] 
dist 43=[-13.330624389653964497  ,2.6475702577832727960 ] 
dist 44=[-13.274826008022427982  ,2.9067254724623212135 ] 
dist 45=[-13.220340459720107613  ,3.1559022342205444830 ] 
dist 46=[-13.095877369700724900  ,3.4550564311500092119 ] 
dist 47=[-13.035504179300665673  ,3.7620994689992086019 ] 
dist 48=[-7.2590586968690142898 ,4.0428342813680250790 ] 
dist 49=[-7.1888461944866176801 ,4.3572275078492390455 ] 
dist 50=[-7.1598251283771817383 ,4.7985901976104702729 ] 
dist 51=[-4.0585330302206648794 ,5.2319134037037119376 ] 
dist 52=[-2.1466606153668369787 ,5.5142660055908512934 ] 
dist 53=[-1.8035715509797623050 ,5.7394273258872226440 ] 
dist 54=[-1.4186533150537922714 ,5.9446465132734463719 ] 
dist 55=[-1.3489765635037256788 ,6.1207622267554742410 ] 
dist 56=[-.23377386764641599609,6.2298349387359468554 ] 
dist 57=[-.08931878805760098893,6.3104122212628519508 ] 
dist 58=[.20484873278086483909,6.3728473631725611269 ] 
dist 59=[.15913224212576692111,6.4132875173217107736 ] 
dist 60=[-.02848643376378136395,6.4068997588717799287 ] 
dist 61=[-.25372741498505246896,6.3745726441518077881 ] 
dist 62=[-.54905325874745387641,6.3449053566406835385 ] 
dist 63=[-1.0162682552363399562 ,6.1222721372108420770 ] 
dist 64=[-1.4875649930763158812 ,3.7215444494943416231 ] 
dist 65=[-1.7991785781114504761 ,3.9605102017756075352 ] 
dist 66=[-2.0527566572863529602 ,4.1376293525914011258 ] 
dist 67=[-2.2925380935187379853 ,4.2777226749806060647 ] 
dist 68=[-2.5042972549440501208 ,4.3842120444130538123 ] 
dist 69=[-2.6460687914883786331 ,4.4271518027403448247 ] 
dist 70=[-2.7632191470002010523 ,4.4431558779122416965 ] 
dist 71=[-2.8767013273079733023 ,4.4419104136055186262 ] 
dist 72=[-2.9739292035151869756 ,4.3278144671889948746 ] 
dist 73=[-3.0262364149554514348 ,4.2981856671062744137 ] 
dist 74=[-3.0552705967016558388 ,4.2180371464798521310 ] 
dist 75=[-3.0597125419428019088 ,4.1850636754630483582 ] 
dist 76=[-3.0502167335959147528 ,4.0063566819816618547 ] 
dist 77=[-3.0405083576792264205 ,3.9616862390366301847 ] 
dist 78=[-2.9953500295103394952 ,3.8697169975830642494 ] 
dist 79=[-2.9789272977979718638 ,3.8391675735795246615 ] 
dist 80=[-1.0531935341158355102 ,2.0970838333659123376 ] 
dist 81=[-1.4944107728139541150 ,2.0577930756776765979 ] 
dist 82=[-2.1344079624699800762 ,2.0448248310583809953 ] 
dist 83=[-2.7657980428979066176 ,1.4085102802446596873 ] 
dist 84=[-3.1726678662716281612 ,1.0938460517668681927 ] 
dist 85=[-3.4934613252194025170 ,1.0354018546095914563 ] 
dist 86=[-3.7812099244318744431 ,.92906107545102798741] 
dist 87=[-4.0261449382435381613 ,.91093603204875910827] 
dist 88=[-4.1760199071509821524 ,.63436142455965227967] 
dist 89=[-4.2852071680798518389 ,.59630394431730147276] 
dist 90=[-4.3677220775556436933 ,.5092924521351526244 ] 
dist 91=[-4.4296747124858106050 ,.49228904953986188125] 
dist 92=[-4.4567678547913933425 ,.37929311154458939187] 
dist 93=[-4.4636356347442938282 ,.3583127226659656164 ] 
dist 94=[-4.4574528125426298561 ,.32084516595330318294] 
dist 95=[-4.4117681296507562391 ,.31218768552666364964] 
dist 96=[-4.3943350085331401567 ,.16967640767496519582] 
dist 97=[-4.3165821117559922442 ,.1488673251102854530 ] 
dist 98=[-4.3022188954566509930 ,.1096883098495085003 ] 
dist 99=[-2.6260818724920849507 ,.0997737170068620226 ] 
dist 100=[-2.4680199988009154173 ,.0660783512939773214 ] 
dist 101=[-2.0803884193887410423 ,.41785217285703495328] 
dist 102=[-2.0220005282337683862 ,.85921630871678829677] 
dist 103=[-1.6499750549903466688 ,1.2703333485327722079 ] 
dist 104=[-1.6607833761083219387 ,1.5860621495761908590 ] 
dist 105=[-1.6624921446889879500 ,1.8926265192551359800 ] 
dist 106=[-1.6582590928277473571 ,2.2671609681738189005 ] 
dist 107=[-1.6545442318661553233 ,2.6206145311751854680 ] 
dist 108=[-1.6258720842643418895 ,2.8430237824809741200 ] 
dist 109=[-1.6171277819260614844 ,3.0121956104065574633 ] 
dist 110=[-1.5867893948673818147 ,3.1531230140838188217 ] 
dist 111=[-1.5786190889082827572 ,3.2652258865327609291 ] 
dist 112=[-.05971564405259424959,3.3193285466212115204 ] 
dist 113=[.04400961215548980238,3.3464770933737036924 ] 
dist 114=[.2739541198946150991 ,3.3509772204846731882 ] 
dist 115=[.31784760447185814502,1.3661192303507020055 ] 
dist 116=[.58121028942189758931,1.5037247423746925864 ] 
dist 117=[.62544622487186976179,1.6111519274034410107 ] 
dist 118=[.71408433355523999522,1.7057082120352367076 ] 
dist 119=[.73492902630709917476,1.7849301960231474320 ] 
dist 120=[1.1782722779503565344 ,1.8311347913209823228 ] 
dist 121=[1.1016279349228216992 ,1.8620870298322937477 ] 
dist 122=[1.0064148230705299722 ,1.8804167784199296510 ] 
dist 123=[.86093567535159310891,1.8908239920332542788 ] 
dist 124=[.69416576595222630264,1.8966649101445734658 ] 
dist 125=[.51394471885746450463,1.8970950791013114091 ] 
dist 126=[.28919459801909215644,1.8851113931859655617 ] 
dist 127=[-.05535577578990214707,1.8806268438780913222 ] 
dist 128=[-.40057914666895974961,1.8194326496284491056 ] 
dist 129=[-.62802121804775400188,1.7872366728041914260 ] 
dist 130=[-.81295297957672626454,1.7743791342154569286 ] 
dist 131=[-.98847063588481882823,1.4024481676048711036 ] 
dist 132=[-1.1447144253956573263 ,1.3658651507470599837 ] 
dist 133=[-1.2527047695795965736 ,1.2788467838629172475 ] 
dist 134=[-1.3461528557131828444 ,1.2572241283164761472 ] 
dist 135=[-1.4443481635922668250 ,1.1258977063939565553 ] 
dist 136=[-1.5328492619404661252 ,1.0988020945296818283 ] 
dist 137=[-1.5875959909509878931 ,1.0472348934126823539 ] 
dist 138=[-1.7076003556507365422 ,1.0330607185812648780 ] 
dist 139=[-1.8168689949678698048 ,.80171851389419964994] 
dist 140=[-1.8804528056662027903 ,.76916750483680940332] 
dist 141=[-1.9228153689901457654 ,.68746635858206241475] 
dist 142=[-1.9473591540215394817 ,.67458527624334779265] 
dist 143=[-1.9616976128994619619 ,.54443178165464066075] 
dist 144=[-1.9633195261780050730 ,.51917602245382241361] 
dist 145=[-1.9581147398406362058 ,.48908682229022091163] 
dist 146=[-1.9523189483493687080 ,.48046206045956422246] 
dist 147=[-1.5143394248645397207 ,.1951684626733530571 ] 
dist 148=[-1.4674007979767938831 ,.1607615758194943784 ] 
dist 149=[-1.3486422168550379895 ,.0915594693783073943 ] 
dist 150=[-1.3280934387905439646 ,.0739775884256095571 ] 
dist 151=[-1.1389425900315209575 ,.10995876136278135475] 
dist 152=[-1.1148611025285027458 ,.2826156555524535982 ] 
dist 153=[-1.0739672979611835712 ,.40691405076319261191] 
dist 154=[-1.0627491327429181119 ,.51969786609766180093] 
dist 155=[-.82640051596884607763,.64639317874329704519] 
dist 156=[-.79360278914071942658,.77248392415246447272] 
dist 157=[-.8052504043861391649 ,.88285918983426810415] 
dist 158=[-.84554241736297014062,1.0029838179002544693 ] 
dist 159=[-.8849662131357825553 ,1.1680038726506018508 ] 
dist 160=[-.91833493923913827722,1.3273562105818716783 ] 
dist 161=[-.95364207364893041349,1.4248551126232919223 ] 
dist 162=[-1.0592375487379312602 ,1.4958268514022060192 ] 
dist 163=[-1.1735980132836414590 ,1.5492723196313340948 ] 
dist 164=[-1.2423858528253234796 ,1.5904891556679265388 ] 
dist 165=[-1.2909554150167893406 ,1.6126390887975866329 ] 
dist 166=[-1.3246139692618888294 ,1.6250932050381519344 ] 
dist 167=[-1.3493294768795383729 ,1.6275996688909185735 ] 
dist 168=[-1.3622047463970666499 ,1.5110198712262437543 ] 
dist 169=[-1.3688579504056121139 ,1.4910101557387929208 ] 
dist 170=[-1.3687443233595131198 ,1.4642413896983475043 ] 
dist 171=[-1.2429911478271993201 ,1.5231209107736757745 ] 
dist 172=[-1.2225049050422854210 ,1.5609249907775807869 ] 
dist 173=[-1.1906460356879827231 ,1.5833204723112185227 ] 
dist 174=[-1.1802737292608184003 ,1.5906038024814724522 ] 
dist 175=[-1.1516380078726131064 ,1.5912428699275170923 ] 
dist 176=[-1.1406198772392552031 ,1.5871094948146787420 ] 
dist 177=[-1.1316557601308482019 ,1.5789432362843404992 ] 
dist 178=[-1.1246951592171831323 ,1.5739581131904647232 ] 
dist 179=[-.0883507519408140140 ,.26770730047414103876] 
dist 180=[-.22308799483999772176,.08471235195051810978] 
dist 181=[-.32685580082015663783,-.01371640395683104947] 
dist 182=[-.42790841785656964903,-.06721693388433878670] 
dist 183=[-.55180933295766982219,-.07737382193003775652] 
dist 184=[-.66900484450122763665,-.38951630777215222548] 
dist 185=[-.74328985250781873737,-.42574428582416047463] 
dist 186=[-.80044343186890706564,-.50518435910155557749] 
dist 187=[-.84924865531784359095,-.51767778289626146487] 
dist 188=[-.88902329840363226905,-.60143135349041663994] 
dist 189=[-.91012726480691451861,-.61394590819454858885] 
dist 190=[-.9295732839163402205 ,-.63737595874352416404] 
dist 191=[-.9620888579701390977 ,-.64095437323266385592] 
dist 192=[-.9793661848944099577 ,-.63234722953922317039] 
dist 193=[-.9888064352947670969 ,-.59384745598567597911] 
dist 194=[-.9900376915778335032 ,-.55199263805573959556] 
dist 195=[-.7730935740840727635 ,-.49459107970989692901] 
dist 196=[-.75620869139410317045,-.4315476961480295122 ] 
dist 197=[-.75172825352038651769,-.36716888671160881241] 
dist 198=[-.73565371535843959483,-.28943586132935468836] 
dist 199=[-.73231712842301002066,-.17308071562754593224] 
dist 200=[-.6762073490763651234 ,-.05256509849332649018] 
dist 201=[-.6663064148926485661 ,.04177776055322876340] 
dist 202=[-.6382804322020297994 ,.13508780386350453763] 
dist 203=[-.6333378998623839076 ,.25148233280769976105] 
dist 204=[-.57624478827552449254,.37392251751066656527] 
dist 205=[-.56885950791279870418,.49136843651496786079] 
dist 206=[-.58925472733495620528,.62775076232799012173] 
dist 207=[-.62193641409657360247,.82578795722083958348] 
dist 208=[-.65531701139662223103,1.0206100691456054826 ] 
dist 209=[-.67850173718044313286,1.1441580877534010978 ] 
dist 210=[-.69866690592187009713,1.2392543640317265290 ] 
dist 211=[-.71999393732004016015,1.3204951496128970030 ] 
dist 212=[-.74044392156220170216,1.3866893655155497788 ] 
dist 213=[-.75710774404404216198,1.4217189861304065300 ] 
dist 214=[-.77419414003015235447,1.4413045091584973078 ] 
dist 215=[-.79633001408132635284,1.4458428822054814552 ] 
dist 216=[-.81782948067695921896,1.4389506879510266731 ] 
dist 217=[-.83237518365813930028,1.4354293751054726292 ] 
dist 218=[-.84461373624163057804,1.4313420940618261729 ] 
dist 219=[-.8569036231456350685 ,1.3996753521896940349 ] 
dist 220=[-.86828359992040142498,1.4015916733515395659 ] 
dist 221=[-.87688952385179801784,1.4002395817213416580 ] 
dist 222=[-.88510787270367928141,1.3962813561196811085 ] 
dist 223=[-.89493929121187519105,1.3852976724146089585 ] 
dist 224=[-.9035970082603498323 ,1.3792056967733298042 ] 
dist 225=[-.9071302701121046919 ,1.3612645637442695751 ] 
dist 226=[-.9075785166545978228 ,1.3526515310062531940 ] 
dist 227=[-.9056314631784463276 ,.67582413748240112069] 
dist 228=[-.8978972336973978323 ,.61544691957590498202] 
dist 229=[-.8942392330982053490 ,.46957141428464993397] 
dist 230=[-.8802302348729947896 ,.44797954091192601402] 
dist 231=[-.8756474920268254273 ,.23880686990113054903] 
dist 232=[-.8308153654974582257 ,.20065275587201933805] 
dist 233=[-.8213095051580114519 ,.15363609089057368661] 
dist 234=[-.7952130046813313710 ,.14377324212941181894] 
dist 235=[-.7881377456724461554 ,-.00063587773487201782] 
dist 236=[-.7343694039344210970 ,.08794193389269619533] 
dist 237=[-.7220477707086434746 ,.17771252320014306052] 
dist 238=[-.7187477333696647112 ,.28561500721177341717] 
dist 239=[-.7960994801129381872 ,.44657344142411332691] 
dist 240=[-.8701476001817641326 ,.60660605951349729032] 
dist 241=[-.9156506594316044489 ,.71081247721442051111] 
dist 242=[-.9489979762067230408 ,.7941454867783471535 ] 
dist 243=[-.9745189875721184178 ,.8708527436827163240 ] 
dist 244=[-.9931954445323003771 ,.9374836272474538234 ] 
dist 245=[-.9992181084541633956 ,.9805921060445083659 ] 
dist 246=[-1.0005419837341895813 ,1.0147490365184442430 ] 
dist 247=[-1.0004598902371952241 ,1.0456451014049193331 ] 
dist 248=[-.9623963459400909943 ,1.0712735902330453561 ] 
dist 249=[-.9538366737790624437 ,1.0844026712659286993 ] 
dist 250=[-.9331921713781692692 ,1.0908925049343908139 ] 
dist 251=[-.9253354295523004799 ,1.0907659252132507162 ] 
dist 252=[-.8845537647785228229 ,1.0852057527580134264 ] 
dist 253=[-.8746603154910378482 ,1.0816558547343393201 ] 
dist 254=[-.8508279839060978353 ,1.0666741647983392885 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 1, 1, 2, 1, 0, 2] 
dist 0=[51.558159777773250958  ,51.558159777773250958  ] 
dist 1=[51.303549465621309458  ,51.673011735975944904  ] 
dist 2=[50.833902962416741232  ,51.718500502590347343  ] 
dist 3=[49.860351471087818676  ,51.696196687790895662  ] 
dist 4=[48.738510856238673733  ,51.643615070535189939  ] 
dist 5=[47.676466541448477058  ,51.567998216615492909  ] 
dist 6=[46.451901475597444980  ,51.460476077607070809  ] 
dist 7=[44.680752411127593097  ,51.371883004419724132  ] 
dist 8=[42.687230307756372047  ,48.371856333468450577  ] 
dist 9=[40.574332076855816988  ,47.891405118411885343  ] 
dist 10=[37.962623650540198160  ,47.137977226342819918  ] 
dist 11=[33.976529311099461804  ,46.911444947460301160  ] 
dist 12=[29.949697319678491350  ,46.364804756792107895  ] 
dist 13=[27.175197969602017927  ,46.210362909689248385  ] 
dist 14=[24.778093340843452991  ,45.158236585023482953  ] 
dist 15=[22.258646053248536712  ,43.204323207147971586  ] 
dist 16=[19.843322848356237976  ,31.947772527885644469  ] 
dist 17=[17.862011331423161494  ,30.295235899984788012  ] 
dist 18=[15.812165371875705537  ,29.874532966857732495  ] 
dist 19=[13.122809525511979330  ,28.437444805176818955  ] 
dist 20=[10.478772606384145738  ,28.089983812171246626  ] 
dist 21=[8.6098102827384098406 ,27.716782593181017774  ] 
dist 22=[6.9433811974332652653 ,27.606318577863057151  ] 
dist 23=[5.1082077664392278128 ,16.476860221573552474  ] 
dist 24=[3.2951364527494259276 ,12.005556006061749574  ] 
dist 25=[1.7167019202435459361 ,11.426459614233278630  ] 
dist 26=[-2.63979028151534000000e-05,10.258565913388958726  ] 
dist 27=[-2.3662317387099498573 ,9.9766789215397005782 ] 
dist 28=[-4.6746082469071692024 ,9.0687955671753691542 ] 
dist 29=[-6.1603765498444042786 ,8.8853728241886273723 ] 
dist 30=[-7.3361390221417429275 ,8.4055581454232609526 ] 
dist 31=[-8.4055886649803693769 ,7.8421180033951316272 ] 
dist 32=[-9.3324732350757971870 ,-4.3034974960819999386 ] 
dist 33=[-9.9385747421523678436 ,-5.4508491313501028180 ] 
dist 34=[-10.429980117947358571  ,-5.6171335460733318320 ] 
dist 35=[-10.898764841946108356  ,-6.8297722567490182912 ] 
dist 36=[-11.297007564739417239  ,-7.0117398270504491957 ] 
dist 37=[-11.506507219399913893  ,-7.3133957871668665476 ] 
dist 38=[-11.674263317066068672  ,-7.3610910068465625303 ] 
dist 39=[-12.039553735307955551  ,-7.6675075034525151820 ] 
dist 40=[-12.335906550909468375  ,-7.4368286979906176540 ] 
dist 41=[-12.471980360156551224  ,-6.5120940872400382684 ] 
dist 42=[-12.524772157864867270  ,-5.3217382208366093801 ] 
dist 43=[-12.522292955409354394  ,-3.4572557735863468620 ] 
dist 44=[-12.364946855668634159  ,-1.5676581275855844262 ] 
dist 45=[-12.300390153551643416  ,-.27694104846422876871] 
dist 46=[-12.161047440721945200  ,.8230030761427927500 ] 
dist 47=[-12.101505977492165632  ,1.9511303184923405925 ] 
dist 48=[-8.7478697732813106492 ,3.0119894262937861630 ] 
dist 49=[-8.3936501372881367622 ,3.8434398405792670689 ] 
dist 50=[-7.5383458410609974695 ,4.6667492141316620861 ] 
dist 51=[-7.3847175617000904231 ,5.6951405961562355806 ] 
dist 52=[-6.1268924133158684496 ,6.6771178336070578528 ] 
dist 53=[-5.8867703335191057418 ,7.3151378087164719428 ] 
dist 54=[-5.5303808902036119211 ,7.8238899693264390273 ] 
dist 55=[-5.4285322183195564345 ,8.2897894613253743603 ] 
dist 56=[-3.4739387523735712688 ,8.6928246672492486011 ] 
dist 57=[-3.2203933688464627294 ,8.9505847951936063025 ] 
dist 58=[-2.6447218458863074486 ,9.1513425537861153191 ] 
dist 59=[-2.5319630957668656397 ,9.3267557028622075019 ] 
dist 60=[-1.8094792134093380328 ,9.4641134061136893651 ] 
dist 61=[-1.6799619101372152996 ,9.5129329796686600715 ] 
dist 62=[-1.4363988742957974913 ,9.5148555220980567423 ] 
dist 63=[-1.3787122968185784555 ,9.4208250450337005098 ] 
dist 64=[1.5865301246996981022 ,3.9335534975317490600 ] 
dist 65=[1.8789765714472763136 ,4.1013816111112284940 ] 
dist 66=[1.9238652808024939903 ,4.2214600833776100305 ] 
dist 67=[2.2587956093963635963 ,4.3115628909066284046 ] 
dist 68=[2.3123833735261677456 ,4.3596639598112994719 ] 
dist 69=[2.4009082460463549942 ,4.3864728495988423463 ] 
dist 70=[2.4182503346702530167 ,4.3915521613121102127 ] 
dist 71=[2.0695788544237873782 ,4.1988010924936632887 ] 
dist 72=[1.7880852493810809927 ,4.1996561453308097354 ] 
dist 73=[1.5421189587681173332 ,4.1916689661662085734 ] 
dist 74=[1.2803010258255682466 ,4.1574802494236655874 ] 
dist 75=[1.0282309055618334244 ,4.1366793782656516132 ] 
dist 76=[.82114203537585519228,2.9855486145625396998 ] 
dist 77=[.6072012202853860902 ,2.8675963567246363724 ] 
dist 78=[.26509108463154088671,2.5765184207205070639 ] 
dist 79=[-.11044274199726409827,2.5267787617562410258 ] 
dist 80=[-.46856099460485514369,2.0762368452900802701 ] 
dist 81=[-.75766250908338319585,1.9887922507950241968 ] 
dist 82=[-1.0519031949581608654 ,1.8722975402223848069 ] 
dist 83=[-1.4305591850255111219 ,1.8340470857340650913 ] 
dist 84=[-1.7978167067867685350 ,1.0565382839601497505 ] 
dist 85=[-2.0465601823024339836 ,.95598299157331861186] 
dist 86=[-2.2564516386604246732 ,.83348433540605001918] 
dist 87=[-2.4686062402849760181 ,.6851820868685187753 ] 
dist 88=[-2.6663749237213447504 ,.43676578033882179226] 
dist 89=[-2.8188444413965513655 ,.39242753872248772322] 
dist 90=[-2.9676159360531719743 ,.28893443404420432985] 
dist 91=[-3.1506477905034770794 ,.27132349058713069725] 
dist 92=[-3.3196267035288040134 ,.1842777525525828632 ] 
dist 93=[-3.4122939819101200976 ,.20939083885395770276] 
dist 94=[-3.4670374053583581414 ,.26976782042872687387] 
dist 95=[-3.4845842857136571184 ,.3413869557247739359 ] 
dist 96=[-3.4879278581417784938 ,.41138896859130027028] 
dist 97=[-3.4859501995831736864 ,.49358682728656381965] 
dist 98=[-3.4797466245571278872 ,.6139151626353827734 ] 
dist 99=[-3.4680887007688884721 ,.7496049238038131438 ] 
dist 100=[-3.1932920148890815562 ,.89313835776929394728] 
dist 101=[-3.1609301433320956388 ,1.0700103523997429723 ] 
dist 102=[-3.1201455504275148969 ,1.3388019955141340869 ] 
dist 103=[-2.8177475673368193017 ,1.6082214144568325850 ] 
dist 104=[-2.6947624239107217609 ,1.7876043272240497811 ] 
dist 105=[-2.6612798136258251149 ,1.9355310496068483434 ] 
dist 106=[-2.6028939544034368584 ,2.0793773560131777012 ] 
dist 107=[-2.5852962533812208209 ,2.2097399992782565314 ] 
dist 108=[-.60301789946166471165,2.3038408712953162661 ] 
dist 109=[-.43395908056594477142,2.3894901027816859057 ] 
dist 110=[-.05202779316317636216,2.4861166855930598334 ] 
dist 111=[.01661437016242860127,2.5733376767642133320 ] 
dist 112=[.47893478294870337321,2.6214400838988512744 ] 
dist 113=[.55835610653518506408,2.6501544770770488572 ] 
dist 114=[.70324512411402009521,2.6599765888323943138 ] 
dist 115=[.73434037433925048994,2.6588481743955187437 ] 
dist 116=[.96073706137189082018,2.6537035248986087952 ] 
dist 117=[.70890043386814199415,2.6262220560919531594 ] 
dist 118=[.3178483465334133632 ,2.6146628044065582000 ] 
dist 119=[-.07698949903022249518,2.4318367798605352880 ] 
dist 120=[-.34393953414619124991,2.3981659150258582196 ] 
dist 121=[-.56846311525453286037,2.3160701906854091853 ] 
dist 122=[-.79394552575517766678,2.2875185911684292778 ] 
dist 123=[-1.0029218252676139001 ,2.1418945792593444772 ] 
dist 124=[-1.1615571858011675155 ,1.2883217786857683624 ] 
dist 125=[-1.3137806749337458613 ,1.2449817978520458464 ] 
dist 126=[-1.4971622402442680112 ,1.2365542758359144274 ] 
dist 127=[-1.6688436431920739982 ,.75720631614844373314] 
dist 128=[-1.7743623900245055504 ,.69678691929086352826] 
dist 129=[-1.8516712809893480382 ,.57651061127142163809] 
dist 130=[-1.9107443570411723293 ,.54579244133726832732] 
dist 131=[-1.9552471560480072743 ,.43912231347270559031] 
dist 132=[-1.9743942489425992142 ,.41533899889095114491] 
dist 133=[-1.9812783850843861280 ,.38821279462790043139] 
dist 134=[-1.9791244226477880890 ,.38250002595925308577] 
dist 135=[-.51480693934239519497,-.24697838690539460416] 
dist 136=[-.65492467050169566886,-.32008662382812447719] 
dist 137=[-.76745992725071951362,-.33153064572975786138] 
dist 138=[-.87194458934194080816,-.35343324755273065474] 
dist 139=[-.96339452782672360315,-.35770760199423353733] 
dist 140=[-1.0238927602106106888 ,-.37735065994387219115] 
dist 141=[-1.0733778565893167661 ,-.37521225584209801078] 
dist 142=[-1.1208633443577887255 ,-.36565076385274944176] 
dist 143=[-1.1621233524231538793 ,-.34350848805140455456] 
dist 144=[-1.1867541917933674519 ,-.31499799058827770998] 
dist 145=[-1.2039596744141436585 ,-.28000968132788917535] 
dist 146=[-1.2155713370117002834 ,-.23356981027769988963] 
dist 147=[-1.2227219767089123413 ,-.15934096160442212122] 
dist 148=[-1.2224430589424033682 ,-.08056043931135183039] 
dist 149=[-1.2179686504859224888 ,-.01594704719183524129] 
dist 150=[-1.2134817104342295573 ,.05070417783004555381] 
dist 151=[-.8806541927046325943 ,.13762561011229678817] 
dist 152=[-.8466853535475506447 ,.23101171532081603693] 
dist 153=[-.83762712426461213232,.32347415087772812248] 
dist 154=[-.82598318582488510403,.43305571417126312379] 
dist 155=[-.8208160603726511884 ,.5947880444406838574 ] 
dist 156=[-.69300134580163019787,.75546247364472087814] 
dist 157=[-.67908964328773618768,.86082206987892279163] 
dist 158=[-.67595013289793942507,.9459369367306584286 ] 
dist 159=[-.4758614447391564947 ,1.0257912243110385656 ] 
dist 160=[-.44994965102421436051,1.0962455391722470442 ] 
dist 161=[-.39951012867958831711,1.1438348178725529202 ] 
dist 162=[-.38658602894347866436,1.1838398380916837313 ] 
dist 163=[-.34203629667660396958,1.2240183391887507983 ] 
dist 164=[-.33139513230225071723,1.2578178654572577740 ] 
dist 165=[-.31973259282894798883,1.2723566182769358857 ] 
dist 166=[-.31633831766300662226,1.2786302570595323926 ] 
dist 167=[.18841191298552439013,1.2794309659560764883 ] 
dist 168=[.22823172300544106415,1.2499962320555240710 ] 
dist 169=[.31715336061473350448,1.2415497718778042231 ] 
dist 170=[.31284923537953914916,1.2357430663874617970 ] 
dist 171=[.07011028972254333093,1.2320227635640024020 ] 
dist 172=[-.1741745420185365721 ,1.0683207891998423782 ] 
dist 173=[-.33835513806400406086,1.0693638276759458898 ] 
dist 174=[-.47542783451192574448,1.0683047849374651314 ] 
dist 175=[-.61149599998423945467,.98874186324792884469] 
dist 176=[-.73663297454659692338,.97489801157651967317] 
dist 177=[-.830067541867939077  ,.94884975061903314491] 
dist 178=[-.91824892514805269521,.94096081098642948185] 
dist 179=[-1.0224147229566911102 ,.90796444713750893127] 
dist 180=[-1.1189346021037606975 ,.89916857939978608249] 
dist 181=[-1.1765927845603289538 ,.87808463557642391194] 
dist 182=[-1.2168682879823264867 ,.87028980150932503026] 
dist 183=[-1.2439949357588505977 ,.50312223187873648257] 
dist 184=[-1.2632881544622935107 ,.487010664901666001  ] 
dist 185=[-1.2722919025399197104 ,.4489063273132588451 ] 
dist 186=[-1.2754873598415178709 ,.44000568852490582581] 
dist 187=[-1.2739265944873768801 ,.38396832423228597435] 
dist 188=[-.57455353051544721337,.37266086006197456907] 
dist 189=[-.62721845536366458301,.35159626273713526742] 
dist 190=[-.68781552002732623707,.34602435252189416911] 
dist 191=[-.7433795659439994678 ,.2529174853468242286 ] 
dist 192=[-.7759519623002150085 ,.2400277349293434774 ] 
dist 193=[-.79794720075657975284,.2077265333217571917 ] 
dist 194=[-.81128766294112653963,.2029244752372924477 ] 
dist 195=[-.8200998537383159709 ,.1520335832085938616 ] 
dist 196=[-.82401651359525505707,.1422819712385111549 ] 
dist 197=[-.84599577208159737686,.1313037836046975703 ] 
dist 198=[-.86128963170073720703,.1288977022267235148 ] 
dist 199=[-.86851822960723380205,-.21807418151494888612] 
dist 200=[-.8717612922087047564 ,-.18682789109685447274] 
dist 201=[-.87114372639793194278,-.14995651853805879819] 
dist 202=[-.86787423589233321144,-.10187130842315144492] 
dist 203=[-.86545245345589734764,-.02585778234039365077] 
dist 204=[-.67449100921579517204,.05147737763238345456] 
dist 205=[-.65351119928210723015,.10483910344864427108] 
dist 206=[-.60081732501297552921,.15090186992150275937] 
dist 207=[-.59131856161589657759,.19909962611226767028] 
dist 208=[-.53210831552897642817,.24503027756952061428] 
dist 209=[-.52614893670519253012,.28204312784730428702] 
dist 210=[-.5224465892873573459 ,.31964598707965975111] 
dist 211=[-.52085038872013920917,.36793300077076558202] 
dist 212=[-.41585102347319951572,.4299508665702938601 ] 
dist 213=[-.4015025081572879275 ,.48748217379517508592] 
dist 214=[-.37450304388307959671,.53688048467442706648] 
dist 215=[-.36749690559191376339,.58815854505213332313] 
dist 216=[-.34336579974077439669,.63677907855108154849] 
dist 217=[-.33698747693235217852,.67556862511257138126] 
dist 218=[-.32985575794423867471,.71462513275697779585] 
dist 219=[-.32661783123461055542,.76431251208447201693] 
dist 220=[-.02396221785591043156,.81069615537280864817] 
dist 221=[-.01851505907162828496,.83656371654577142411] 
dist 222=[-.01979231357271017273,.85238289279920530793] 
dist 223=[-.02399445565162789523,.85865096884266002545] 
dist 224=[-.03180494285875902210,.86114807452668824106] 
dist 225=[-.04375772842036076762,.86191218621793864752] 
dist 226=[-.06449707672323838663,.86155563613889752523] 
dist 227=[-.08931579804615396534,.85957747466764517747] 
dist 228=[-.11755410817302302896,.7494741936280724869 ] 
dist 229=[-.15372865143832203941,.73300039755085673452] 
dist 230=[-.21022963804858181857,.70785441528328482765] 
dist 231=[-.26757073727952485442,.69535780283057452998] 
dist 232=[-.30709933752006826103,.66753727937471086527] 
dist 233=[-.34118012347928955832,.65929692047569122863] 
dist 234=[-.37677369462375430928,.64866545469548078445] 
dist 235=[-.41064984522477449304,.64410851743735733957] 
dist 236=[-.43787493831476950893,.29558729701376426625] 
dist 237=[-.46546541706183860109,.28406355414166363616] 
dist 238=[-.50080078250036168391,.25853068073788928798] 
dist 239=[-.5349694565781527553 ,.25148431096186420572] 
dist 240=[-.55790267810116687516,.21933878070149167305] 
dist 241=[-.5770179037845505947 ,.21298611807806585237] 
dist 242=[-.5959450616020159745 ,.19806700133421727605] 
dist 243=[-.61332496174986996   ,.19431427073600403494] 
dist 244=[-.62626378092079316507,.15710479721311239875] 
dist 245=[-.63844184114464196953,.15083929530902733061] 
dist 246=[-.65278559869586754153,.13827780018917018543] 
dist 247=[-.66553524240139014518,.13486804985109400108] 
dist 248=[-.6713494504432286556 ,.12193382838970431302] 
dist 249=[-.67320499242910500691,.11902737694353965455] 
dist 250=[-.67289751426279633649,.1133085099748430178 ] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 1, 0, 2, 0, 1] 
dist 0=[48.559251301617114609  ,48.559251301617114609  ] 
dist 1=[48.296519932645770201  ,48.692157526094218334  ] 
dist 2=[47.789900389376463837  ,48.960024114348862582  ] 
dist 3=[46.967439355862051195  ,49.196564802729767325  ] 
dist 4=[45.943864114154645282  ,49.355834004872608837  ] 
dist 5=[44.633940703871523235  ,49.488501062287908303  ] 
dist 6=[42.859662804517852660  ,49.618586688011624871  ] 
dist 7=[39.981515640987776149  ,49.716588646880180154  ] 
dist 8=[37.028781144330974208  ,49.721192058362384487  ] 
dist 9=[34.956555448124178448  ,49.657499771714987441  ] 
dist 10=[33.126927324150396503  ,49.595976797029329754  ] 
dist 11=[31.142928728211318874  ,49.250629812395757252  ] 
dist 12=[28.824039867997538229  ,49.137817142197256536  ] 
dist 13=[26.004744786662421154  ,48.694270636089680719  ] 
dist 14=[23.573876421554128325  ,48.406624484681814994  ] 
dist 15=[21.029096938396869495  ,38.109626071251582527  ] 
dist 16=[18.597509101182596499  ,37.113376105029636016  ] 
dist 17=[16.618426747080411513  ,34.680480901899404682  ] 
dist 18=[14.585596838552680510  ,34.289608326862807195  ] 
dist 19=[11.938831196414890939  ,30.612158110442064736  ] 
dist 20=[9.3468850111945913536 ,29.906354420801912025  ] 
dist 21=[7.5327228076304083446 ,29.025215013464604131  ] 
dist 22=[5.9337205345071274744 ,28.753460973287912058  ] 
dist 23=[4.2007943511513984829 ,22.418223027224997526  ] 
dist 24=[2.5040200592684250448 ,21.597994203894956496  ] 
dist 25=[1.0488900396171711363 ,19.894687499195623823  ] 
dist 26=[-.51661484696655653126,19.440731087663579281  ] 
dist 27=[-2.6554451113068167518 ,17.721178519940116562  ] 
dist 28=[-4.7272661359538046106 ,17.378544545752520867  ] 
dist 29=[-6.0252253252127174637 ,16.673172382351333071  ] 
dist 30=[-7.0142347238454653326 ,16.482649209098716396  ] 
dist 31=[-7.8511563314854443345 ,5.8383736785414209994 ] 
dist 32=[-8.5353785434508564908 ,4.8926904634962234044 ] 
dist 33=[-8.9142417878099118676 ,2.8000461708796769252 ] 
dist 34=[-9.1472098169931387271 ,2.4101129040168952464 ] 
dist 35=[-9.2488859312015890835 ,-.00032779950324388162] 
dist 36=[-9.4136154565001801922 ,-.41065181073022521323] 
dist 37=[-10.505189946740966594  ,-1.1979649244715944338 ] 
dist 38=[-11.728422040035807398  ,-1.3777109747181709540 ] 
dist 39=[-12.847962816213014043  ,-3.0350596037253163429 ] 
dist 40=[-13.525342150280106709  ,-2.9680074360641648628 ] 
dist 41=[-14.011366994376422816  ,-2.5978654789461424979 ] 
dist 42=[-14.366484092118912058  ,-2.2553756960938626682 ] 
dist 43=[-14.622409211746097832  ,-1.8630846263693364972 ] 
dist 44=[-14.712134083094920203  ,-1.4702252163824241208 ] 
dist 45=[-14.729724204383024394  ,-.70399552524013843758] 
dist 46=[-14.697408150654146236  ,.21387714802286312407] 
dist 47=[-7.3292268048539286613 ,1.1338776821242452551 ] 
dist 48=[-6.8457338508363954498 ,1.9843870396631145270 ] 
dist 49=[-5.6743339905317878225 ,2.6249047780124413282 ] 
dist 50=[-5.5014495118487424060 ,3.2339254580329226635 ] 
dist 51=[-3.8160836791295716233 ,3.9586560673258933028 ] 
dist 52=[-3.5087951375711874159 ,4.6360779964539470990 ] 
dist 53=[-3.1311966990245548542 ,5.0563221810485424460 ] 
dist 54=[-3.0534645467002925389 ,5.3684250258903358820 ] 
dist 55=[-1.6984236673994999969 ,5.6144293932000047631 ] 
dist 56=[-.34230869618322438117,5.8034866976054923915 ] 
dist 57=[.2781863139149895268 ,5.8882616879843524208 ] 
dist 58=[.40205686673941011384,5.9240565346083986234 ] 
dist 59=[1.0309094372040880878 ,5.9185211871422017277 ] 
dist 60=[1.1356637745985717836 ,4.0478373157552450172 ] 
dist 61=[1.3299398493162812862 ,4.1094134770999873300 ] 
dist 62=[1.3683841971019967448 ,4.1398046158703610759 ] 
dist 63=[2.5989616497413820650 ,4.1421170917229808103 ] 
dist 64=[2.2878955379307632115 ,3.9203175865589849132 ] 
dist 65=[2.0215855668242545642 ,4.1808916487963911364 ] 
dist 66=[1.7371401134401615463 ,4.4275499858565120955 ] 
dist 67=[1.3535912115647521038 ,4.6478932412992924005 ] 
dist 68=[.97383102797449601913,4.8033354099390273562 ] 
dist 69=[.7044518206110943211 ,4.9418843333478227066 ] 
dist 70=[.46413220691667525474,5.0947634020609196932 ] 
dist 71=[.20029082802652113489,5.2323204626028669289 ] 
dist 72=[-.05899647679864559325,5.3096500158545691091 ] 
dist 73=[-.28120745456326282018,5.3582499471973146839 ] 
dist 74=[-.51935276890073356017,5.3809849363755404063 ] 
dist 75=[-.84237416122935136129,5.3857808799783953061 ] 
dist 76=[-1.1584840878366815011 ,5.3789247877173482261 ] 
dist 77=[-1.3690509459345463404 ,5.3336320932072942393 ] 
dist 78=[-1.9131821952270626584 ,5.3144683597254903745 ] 
dist 79=[-2.9483573046923248155 ,.34577012973341715367] 
dist 80=[-3.6275691581742135717 ,-.27057464270668429824] 
dist 81=[-4.1766733862228823443 ,-.34600693467575704082] 
dist 82=[-4.6924724458401691686 ,-.51327351598759193331] 
dist 83=[-5.1479985388134769808 ,-.54020839458011207012] 
dist 84=[-5.4565096266376218829 ,-.72542999253410081591] 
dist 85=[-5.7167990882799340858 ,-.75449881306725755771] 
dist 86=[-5.9798605175033549804 ,-.80730795776176358722] 
dist 87=[-6.2073746047099829187 ,-.62453354140356067575] 
dist 88=[-6.3257546865336417127 ,-.38250125282540312343] 
dist 89=[-6.3871121651869378430 ,-.12679219469150153563] 
dist 90=[-6.3972041391680599674 ,.18796888565689837274] 
dist 91=[-6.3626427222730641090 ,.66574152157948950656] 
dist 92=[-6.3354561392527036771 ,1.1429265214715793701 ] 
dist 93=[-6.2815281310106654324 ,1.4553529955645923578 ] 
dist 94=[-6.2551914113193750997 ,1.7070440100876941057 ] 
dist 95=[-4.7043754344287480438 ,1.9418016361711888697 ] 
dist 96=[-4.5396897290776863466 ,2.1478364279844505860 ] 
dist 97=[-4.1147553048132698793 ,2.2848811379804458753 ] 
dist 98=[-4.0524557626377039479 ,2.3977159515713283864 ] 
dist 99=[-3.3416729205888838698 ,2.5071217272966711029 ] 
dist 100=[-3.2024332249275451706 ,2.8623776397433031005 ] 
dist 101=[-3.0550361222742620173 ,3.3055072917874886002 ] 
dist 102=[-3.0246060471311814371 ,3.8439657342280318707 ] 
dist 103=[-1.6304781973501813170 ,4.3503253211478650534 ] 
dist 104=[-1.4566739373587398236 ,4.6653272804380420886 ] 
dist 105=[-1.1034923218288825188 ,4.9005943476630519653 ] 
dist 106=[-1.1668591645662449265 ,5.0886773739022876829 ] 
dist 107=[-1.2641808772286420161 ,5.2336337978329806876 ] 
dist 108=[-1.3572109648885278116 ,5.2967519023423899526 ] 
dist 109=[-1.4325701781509640994 ,5.3238116769403876549 ] 
dist 110=[-1.5094406391797352009 ,5.3248378939672230836 ] 
dist 111=[-1.6084935064642002708 ,1.9653076351854627722 ] 
dist 112=[-1.7044262127981053367 ,2.0059015673663851206 ] 
dist 113=[-1.7688370164849012893 ,2.2760358732133747334 ] 
dist 114=[-1.8224808807814101353 ,2.5211035325578745006 ] 
dist 115=[-1.8754302959432589154 ,2.7316492561082503735 ] 
dist 116=[-1.9238312919039796221 ,2.8639644970414577631 ] 
dist 117=[-1.9593118585451799549 ,2.9644940457467714929 ] 
dist 118=[-1.9920658026432822486 ,3.0481504572887359311 ] 
dist 119=[-2.0295659803885810785 ,3.1165738225080218264 ] 
dist 120=[-2.0610670963294139102 ,3.1562876274826932954 ] 
dist 121=[-2.0698734881275674566 ,3.1826693122315875851 ] 
dist 122=[-2.0692769355078188044 ,3.1978556645229939258 ] 
dist 123=[-2.0351820589707531558 ,3.2047494802942181605 ] 
dist 124=[.1158851132358287063 ,3.1988792159258772728 ] 
dist 125=[.0677563697405365580 ,3.1830991501684840646 ] 
dist 126=[.0108062923198449443 ,3.1718773501475596940 ] 
dist 127=[-.23613988945081921492,2.3643173385422549933 ] 
dist 128=[-.56105591633082796339,2.3177290872700913761 ] 
dist 129=[-.83435111482164507253,2.1930470777564677704 ] 
dist 130=[-1.1088880554377835935 ,2.1706328979442229545 ] 
dist 131=[-1.3634300524660885925 ,1.9398934888378542138 ] 
dist 132=[-1.5569142964870228246 ,1.8915505259955692964 ] 
dist 133=[-1.7428772322089113844 ,1.8340794644606828733 ] 
dist 134=[-1.9674057474622744836 ,1.8109781759327600706 ] 
dist 135=[-2.1780081711957079054 ,1.2849747205911484148 ] 
dist 136=[-2.3083840295833457388 ,1.2145939517670562224 ] 
dist 137=[-2.4050883908159858526 ,1.0685759383173494035 ] 
dist 138=[-2.4812800756346436924 ,1.0289300075743584830 ] 
dist 139=[-2.5385914893855239148 ,.92037074262795922424] 
dist 140=[-2.5599336864540923766 ,.9576234023396184422 ] 
dist 141=[-2.5671735703655717532 ,.98049926122810483885] 
dist 142=[-2.5681577101057695334 ,.9971949161153692786 ] 
dist 143=[-2.4859139752900867640 ,1.0097765708796497521 ] 
dist 144=[-2.4683817356718347838 ,1.0178435302145802211 ] 
dist 145=[-2.4060718455675502911 ,1.0189911105807980531 ] 
dist 146=[-2.3958837397828610355 ,1.0127414616171593112 ] 
dist 147=[-2.2994001077400888681 ,1.0110214982647301524 ] 
dist 148=[-2.2988628093593261870 ,.96598643837850831747] 
dist 149=[-2.2913483876972805810 ,.95396125574252128447] 
dist 150=[-2.2840538585755976046 ,.94554243677574408326] 
dist 151=[-2.1458206079453038675 ,.94121449717883227868] 
dist 152=[-2.1417494726035624197 ,-.20255939457970920123] 
dist 153=[-2.1227984855312399088 ,-.02925410088531228828] 
dist 154=[-2.1117597056813367569 ,.1218151553662386614 ] 
dist 155=[-2.0384270997585950115 ,.28219036155279916344] 
dist 156=[-2.0181717230134576485 ,.43641731814580761499] 
dist 157=[-1.9831987208256316847 ,.56294330004582600642] 
dist 158=[-1.9717032563252748961 ,.69350879107012639699] 
dist 159=[-1.6681144125345726291 ,.86386240301850619382] 
dist 160=[-1.6585148007104847231 ,1.0300611888942600174 ] 
dist 161=[-1.6273856298164329347 ,1.1440409021684959219 ] 
dist 162=[-1.6172211534515414954 ,1.2416839918807749394 ] 
dist 163=[-1.5339228239494278219 ,1.3482301814208180822 ] 
dist 164=[-1.5132535955696288715 ,1.4927005673506696404 ] 
dist 165=[-1.4830293894755576378 ,1.6214461001329574450 ] 
dist 166=[-1.4719062792815298306 ,1.7746580613801540852 ] 
dist 167=[-1.1953193149391341275 ,1.9386038345034049166 ] 
dist 168=[-1.1556645350049526526 ,2.0402347423671214681 ] 
dist 169=[-1.0708139659725086987 ,2.1157511539298681058 ] 
dist 170=[-1.0461054160196319673 ,2.1754388713795533243 ] 
dist 171=[-.94162792449956719423,2.2204012350950624824 ] 
dist 172=[-.92074564918780171776,2.2371264172447699283 ] 
dist 173=[-.86304777649050063425,2.2421148756655724556 ] 
dist 174=[-.94384418482654694032,2.2402397460744766768 ] 
dist 175=[-1.0786985300636716266 ,1.8455229463173739525 ] 
dist 176=[-1.2107755275242762968 ,1.5988884743081367523 ] 
dist 177=[-1.3021806788752330430 ,1.5618810442859031884 ] 
dist 178=[-1.3813603348022959416 ,1.4930898599436902009 ] 
dist 179=[-1.4646342357626301844 ,1.4743437485046391055 ] 
dist 180=[-1.5442379684366670697 ,1.4056343859484597698 ] 
dist 181=[-1.6087669384849160464 ,1.3868332287948562019 ] 
dist 182=[-1.6746605911712455917 ,1.3554821865862437433 ] 
dist 183=[-1.7597129116895894510 ,1.3455771605346096559 ] 
dist 184=[-1.8391267082953712092 ,-.04013470102546328872] 
dist 185=[-1.8825115393094569160 ,-.13742169584730454355] 
dist 186=[-1.9078421233415791320 ,-.15246277852330618709] 
dist 187=[-1.9151830870745781479 ,-.27181158293149079251] 
dist 188=[-1.9146550445196810481 ,-.29179092424223912237] 
dist 189=[-1.9090753313989116010 ,-.32261095643148828676] 
dist 190=[-1.8979685909859449809 ,-.32966857596841781341] 
dist 191=[-1.8914057055879851353 ,-.4233563174091203999 ] 
dist 192=[-1.6905703651692365551 ,-.43512931894320377673] 
dist 193=[-1.6583997642165161613 ,-.43373715306525605952] 
dist 194=[-1.5904169396243928091 ,-.41404717787593696873] 
dist 195=[-1.5694395229438051292 ,-.38410845504355488018] 
dist 196=[-1.4760390791473937230 ,-.34180108213557180694] 
dist 197=[-1.4564572673545685663 ,-.28231093209815109101] 
dist 198=[-1.4608914398504267161 ,-.18377742313389888769] 
dist 199=[-1.4587807068678359757 ,.06600005114030221884] 
dist 200=[-1.1039308195935948375 ,.43710070970597876063] 
dist 201=[-1.0692231477490843135 ,.68381580906264022007] 
dist 202=[-.99100293575567479158,.88683085441091967619] 
dist 203=[-.96902396822531845782,1.0834830112749507035 ] 
dist 204=[-.86429329507422664681,1.2611556887360974609 ] 
dist 205=[-.84556820905998848524,1.3884057634163395556 ] 
dist 206=[-.82588732654123680079,1.5031809593759137332 ] 
dist 207=[-.81852161293648896262,1.6310551121166655534 ] 
dist 208=[-.5940644181547871721 ,1.7475083921404161317 ] 
dist 209=[-.56414957482620175397,1.8166915224657665560 ] 
dist 210=[-.50387194455089499914,1.8645433094890560046 ] 
dist 211=[-.48781191769222307641,1.8958408574557202619 ] 
dist 212=[-.42823675369511743017,1.9162144544054396660 ] 
dist 213=[-.41513392559428413855,1.9204584030457734160 ] 
dist 214=[-.39123095596127398326,1.9174455568564749092 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 1, 0, 2, 0, 1] 
dist 0=[53.245948213247371220  ,53.245948213247371220  ] 
dist 1=[52.991210547768255827  ,53.313275163217690074  ] 
dist 2=[52.494665878553740720  ,53.327408119718939892  ] 
dist 3=[51.570418062973026124  ,53.284148084749358516  ] 
dist 4=[50.508512359213490404  ,53.204096338672828903  ] 
dist 5=[49.462137205454916751  ,52.999298598132548990  ] 
dist 6=[48.223986171839092366  ,52.886146136359503330  ] 
dist 7=[46.395965150615965514  ,52.077472526496530291  ] 
dist 8=[44.322232976746473730  ,49.994356861091731226  ] 
dist 9=[42.102580388132205561  ,49.330527878545763334  ] 
dist 10=[39.344277240633185636  ,49.114716411445611256  ] 
dist 11=[35.118942555439538968  ,48.607158384328887207  ] 
dist 12=[30.846473639087285663  ,48.444243834364596481  ] 
dist 13=[27.899838093208531091  ,48.238064050962793862  ] 
dist 14=[25.351471761509267029  ,46.927647105298300557  ] 
dist 15=[22.669687153046591101  ,38.125582060892868311  ] 
dist 16=[20.097285776336116128  ,31.067300419448543170  ] 
dist 17=[17.985691105681813410  ,30.163651862441234700  ] 
dist 18=[15.800175223914834530  ,28.407985366241260749  ] 
dist 19=[12.932220914464858684  ,27.962368268769994237  ] 
dist 20=[10.113215945871561493  ,26.440838418639826675  ] 
dist 21=[8.1230650581588975805 ,26.081366895836001195  ] 
dist 22=[6.3515242908826324974 ,25.700557874528797142  ] 
dist 23=[4.4055444360954866416 ,25.607579575581855130  ] 
dist 24=[2.4863019844861700244 ,12.497955863254633109  ] 
dist 25=[.8212428434164427745 ,11.217180020596278943  ] 
dist 26=[-.98455097978159518091,10.920261949344336399  ] 
dist 27=[-3.4667049638460137650 ,9.8107063979468710494 ] 
dist 28=[-5.8833805184081879942 ,9.6017214895315715109 ] 
dist 29=[-7.4276810180282666857 ,9.3396706684116786956 ] 
dist 30=[-8.6369108624144949072 ,8.9264489313867095693 ] 
dist 31=[-9.7145789086029582371 ,-.63448420836488270063] 
dist 32=[-10.632979397310579667  ,-4.5363512440696257822 ] 
dist 33=[-11.205866298011521293  ,-5.0020511181876940008 ] 
dist 34=[-11.639653224928934387  ,-5.9546826635854944889 ] 
dist 35=[-12.006760192560704753  ,-6.1408046576859027669 ] 
dist 36=[-12.546561165085421152  ,-6.9015951608397795665 ] 
dist 37=[-12.934038057080671312  ,-7.0339402426694773724 ] 
dist 38=[-13.220320886715049252  ,-7.0600209227432116237 ] 
dist 39=[-13.435484425325020352  ,-6.8945352727759585103 ] 
dist 40=[-13.538746540052324879  ,-6.6783089427751618358 ] 
dist 41=[-13.582285287093964713  ,-6.4872553719205466850 ] 
dist 42=[-13.563641215864789822  ,-6.1713482250128650315 ] 
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dist 56=[-1.3294583276838939107 ,8.3130588870260624472 ] 
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dist 59=[-.62296039599098002013,8.5907406262373648967 ] 
dist 60=[-.05984810390087262259,8.5403696997210652806 ] 
dist 61=[.04032171447968598669,8.5039848149484934776 ] 
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dist 65=[.9489902312610152409 ,3.9563990916289052677 ] 
dist 66=[1.1266506602911184277 ,4.1279789430117837800 ] 
dist 67=[1.1581686174495732142 ,4.2626908066364123914 ] 
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dist 100=[-2.0880268113899491002 ,.93622488754864910399] 
dist 101=[-2.0373495959612954637 ,1.0710605867997485653 ] 
dist 102=[-2.0222990484588933416 ,1.2253617006758843116 ] 
dist 103=[-1.7348699779502424869 ,1.4467025702297010394 ] 
dist 104=[-1.7314794962705819512 ,1.6631292957359239269 ] 
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dist 106=[-1.7107750360616570197 ,1.8985353360573064235 ] 
dist 107=[-1.6991083607250890915 ,1.9793358875631652864 ] 
dist 108=[-1.7149084359140571209 ,2.0421674690840713502 ] 
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dist 113=[-1.6431943749512676081 ,1.9937463059165733697 ] 
dist 114=[-1.6210603497637470976 ,1.9606528742107543007 ] 
dist 115=[-1.6119197925145005668 ,1.9489734712047382333 ] 
dist 116=[-1.3617434119770971008 ,2.0875076869786869936 ] 
dist 117=[-1.3245582644383308812 ,2.1981651272623061759 ] 
dist 118=[-1.2466890182807296115 ,2.2832483061612488023 ] 
dist 119=[-1.2237948297348655382 ,2.3558835259368615448 ] 
dist 120=[-1.1267120732034656689 ,2.4151402387296491106 ] 
dist 121=[-1.1062749871244644151 ,2.4468168097843578505 ] 
dist 122=[-1.0505007084351886055 ,2.4644683665734542281 ] 
dist 123=[-1.0397084558837582459 ,2.4677469291410847131 ] 
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dist 126=[-1.2127629366686560819 ,2.2868022024633862422 ] 
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dist 128=[-1.4967886752852240740 ,.9483992674723525638 ] 
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dist 133=[-1.7574165005774478729 ,.6902831629287612598 ] 
dist 134=[-1.7640913508496206384 ,.6682726984873975050 ] 
dist 135=[-1.7624165583045967065 ,.6609877136813729738 ] 
dist 136=[-1.0081101097547645257 ,-.55607656100715033643] 
dist 137=[-1.1279024882678882635 ,-.65325523302929662741] 
dist 138=[-1.2211925665666806191 ,-.67210967662057509414] 
dist 139=[-1.3028654426592863020 ,-.75610946448167373202] 
dist 140=[-1.3709436383452660941 ,-.77046302808802246666] 
dist 141=[-1.4099601781448062279 ,-.77862521544316685482] 
dist 142=[-1.4352200849767593295 ,-.76597617844246952339] 
dist 143=[-1.4483806180527533037 ,-.74583210736882186651] 
dist 144=[-1.4554452221271420836 ,-.72042209087631423554] 
dist 145=[-1.4563675656913367602 ,-.68631879490002181427] 
dist 146=[-1.4529891717487610841 ,-.63146040669463849148] 
dist 147=[-1.4493100665757824688 ,-.56745299622130883904] 
dist 148=[-1.4292185142777199734 ,-.4968219299743164494 ] 
dist 149=[-1.4224517896646014577 ,-.40777816230381842225] 
dist 150=[-1.3960764695014450974 ,-.27026356496586154882] 
dist 151=[-1.3902501734662932652 ,-.12613215397709718239] 
dist 152=[-1.2156111798016550958 ,-.01067079944598606054] 
dist 153=[-1.1972041934282610588 ,.10598032754310603509] 
dist 154=[-1.1890794094543659210 ,.25486729939760564467] 
dist 155=[-1.1434147804393753878 ,.41322511787165427474] 
dist 156=[-1.1316814440000330579 ,.56768815481944231651] 
dist 157=[-1.1062998520594928936 ,.74901711454846462883] 
dist 158=[-1.0973979016467433674 ,1.0146304093992840995 ] 
dist 159=[-.25597809769420847044,1.2775809793553502988 ] 
dist 160=[.02460878154183769098,1.4482815130025400665 ] 
dist 161=[.05907797916698013934,1.5842401292092914262 ] 
dist 162=[.13549658323176226082,1.7084977288850806449 ] 
dist 163=[.14928933244864709718,1.8158525363085852268 ] 
dist 164=[.23579121810116592446,1.8843342402501050800 ] 
dist 165=[.24999019941233847538,1.9375197065067134944 ] 
dist 166=[.27759165707052677401,1.9838123318724750753 ] 
dist 167=[.28366566130891052927,2.0205275659398502598 ] 
dist 168=[.4378326682942617815 ,2.0354788969291559906 ] 
dist 169=[.4532508667117580614 ,2.0392581719503450767 ] 
dist 170=[.4727420026689065705 ,2.0365472358542665811 ] 
dist 171=[.4731626496929062640 ,2.0011924375843680817 ] 
dist 172=[.4661120883852618845 ,1.9885201493098997573 ] 
dist 173=[.4483142313269766322 ,1.9700422214689545017 ] 
dist 174=[.32976585674188941354,1.9607475729157112049 ] 
dist 175=[-.04297119511996585904,1.4129036508148658173 ] 
dist 176=[-.29401518162020004046,1.3560058268100490393 ] 
dist 177=[-.50417515155897833327,1.2122508876119825336 ] 
dist 178=[-.71370312894873323948,1.1902809385249177224 ] 
dist 179=[-.90697297092928598997,.95896637384113088161] 
dist 180=[-1.0522305356791558608 ,.91408685221902550717] 
dist 181=[-1.1902473550287958279 ,.86287390987935735214] 
dist 182=[-1.3546124513609504510 ,.8499881343905092418 ] 
dist 183=[-1.5075915543905089668 ,.70109550706397132262] 
dist 184=[-1.6001554164467130443 ,.70380426381452522689] 
dist 185=[-1.6662563985475158082 ,.70314148635465715183] 
dist 186=[-1.7135951741472943884 ,.70043822001577283647] 
dist 187=[-1.7488112360360781255 ,.69822622753367387871] 
dist 188=[-1.7665176750547677374 ,.6827879470399841395 ] 
dist 189=[-1.7747996491987860139 ,.67825292635749890828] 
dist 190=[-1.7736509467874584030 ,.66502688466038018407] 
dist 191=[-1.1708330407388701688 ,.6599874401436149353 ] 
dist 192=[-1.2061598671708228121 ,.5971733776636932536 ] 
dist 193=[-1.2264879055053713385 ,.5866057070035988329 ] 
dist 194=[-1.2397505831151686739 ,.5582785868937302158 ] 
dist 195=[-1.2468672191439928505 ,.5525807172794603387 ] 
dist 196=[-1.2494999371629460370 ,.4990738699531787101 ] 
dist 197=[-1.2480034856018108813 ,.4876075028470624581 ] 
dist 198=[-1.2381110425831427829 ,.4727011105049719901 ] 
dist 199=[-1.2323287034907114685 ,.4671506676578120189 ] 
dist 200=[-.86951543812534878047,-.40017293330365145236] 
dist 201=[-.89719616792264986836,-.3476347373417562766 ] 
dist 202=[-.92222794659685957816,-.26890670320842664369] 
dist 203=[-.94366056826540580974,-.17928941545177634635] 
dist 204=[-.95697208981344772694,-.08327991629138359808] 
dist 205=[-.96688915039940267248,.03588310143559133587] 
dist 206=[-.97476893392076968007,.21793151052082521273] 
dist 207=[-.97979203836855427144,.4007396224504095791 ] 
dist 208=[-.97951875114844561088,.52293578332701115727] 
dist 209=[-.97439231126260379093,.62422923514234371424] 
dist 210=[-.97003717253631274208,.72359266932523821453] 
dist 211=[-.93989664222269856667,.81420551294268604695] 
dist 212=[-.93112312491112345656,.88056635255740755409] 
dist 213=[-.91576449759085391607,.94192632518473372959] 
dist 214=[-.9106125146698451607 ,1.0125760236474080208 ] 
dist 215=[-.77617744187634521851,1.0770969115499141356 ] 
dist 216=[-.75612810288766049483,1.1139904720914186400 ] 
dist 217=[-.71204714070069159828,1.1377422305610605392 ] 
dist 218=[-.69868464216504926507,1.1498001401594799077 ] 
dist 219=[-.64000557361498717432,1.1562229262809928189 ] 
dist 220=[-.62782415185353964165,1.1574782941141968508 ] 
dist 221=[-.59651351899337683929,1.1551902654645898071 ] 
dist 222=[-.58944746934643936196,1.1523042365165395494 ] 
dist 223=[-.18068108996818126969,1.0306798948356116325 ] 
dist 224=[-.14118453140233469569,1.0133416227329233952 ] 
dist 225=[-.05428430128883543512,.96386564929607280928] 
dist 226=[-.03607497789557594414,.95644988861629155737] 
dist 227=[.06281728121891183248,.8568247776323694562 ] 
dist 228=[.14100382162016045707,.84197610827225957818] 
dist 229=[.16749148588669487911,.8377362413608377072 ] 
dist 230=[.2066479361082185787 ,.83483703132914348553] 
dist 231=[.04675944254362515292,.83300593549494189436] 
dist 232=[-.1146566260643142308 ,.5222781521963309215 ] 
dist 233=[-.22460189753404889387,.45743440993023650995] 
dist 234=[-.31798376753515105351,.44074135800793993145] 
dist 235=[-.4132778389818151237 ,.38251207035089865858] 
dist 236=[-.50259691963327773035,.36894445758798647626] 
dist 237=[-.57212631548962848208,.35257499377723094797] 
dist 238=[-.64053120889718380837,.34708933194052210942] 
dist 239=[-.72536125757064906891,-.22573397493864660172] 
dist 240=[-.8060503949900919518 ,-.2728982117141013677 ] 
dist 241=[-.85792452662932534576,-.37028500679514778533] 
dist 242=[-.89866458256184451069,-.39293164261691393113] 
dist 243=[-.93490578798115380664,-.47968992094142532078] 
dist 244=[-.96551353326315905535,-.55208361872965323901] 
dist 245=[-.98376445524418336987,-.56728002171675745377] 
dist 246=[-.99647225138676412145,-.56136024834293235157] 
dist 247=[-1.0049514744721454812 ,-.547077160410994191  ] 
dist 248=[-1.0094341652849764337 ,-.52304735755271496891] 
dist 249=[-1.0094152122873111246 ,-.48725394194274508496] 
dist 250=[-1.0012588409747559238 ,-.42600961984627601557] 
dist 251=[-.9990269080492370081 ,-.35302748339391717413] 
dist 252=[-.94518362505761195867,-.27037593493861930029] 
dist 253=[-.93176933548656083116,-.16473944149535891852] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 1, 2, 1, 0, 1] 
dist 0=[46.884081580748791924  ,46.884081580748791924  ] 
dist 1=[46.143254931721593763  ,47.309502772646572214  ] 
dist 2=[45.216184578831460456  ,47.586295936726844375  ] 
dist 3=[44.046845994003589025  ,47.733354750942639730  ] 
dist 4=[42.472684885748627066  ,47.812050590128817019  ] 
dist 5=[39.928719710954230835  ,47.815680130004146535  ] 
dist 6=[37.312762957250695786  ,47.764288285429487396  ] 
dist 7=[35.451012724917144564  ,47.707257244855378537  ] 
dist 8=[33.779993878570021018  ,47.463940097294258848  ] 
dist 9=[31.925687194862871674  ,47.341533090182361661  ] 
dist 10=[30.088573421341701835  ,47.221522041990000183  ] 
dist 11=[28.486068544785440724  ,47.125952209900386304  ] 
dist 12=[26.743124264878317185  ,46.915387835451032223  ] 
dist 13=[24.344763364919439169  ,46.799325054518144801  ] 
dist 14=[21.935372710811757733  ,46.590757896024501716  ] 
dist 15=[20.148208341036643969  ,45.906950394291825083  ] 
dist 16=[18.467889473578175198  ,34.214224081974278882  ] 
dist 17=[16.485070757345795438  ,33.146372172459199810  ] 
dist 18=[14.449464835079531754  ,30.535766152777642981  ] 
dist 19=[12.557969684509626209  ,30.157779938203290570  ] 
dist 20=[10.401130608282759596  ,26.257375826451619624  ] 
dist 21=[7.3048791242203175875 ,25.524733931139102643  ] 
dist 22=[4.2439858021371361327 ,24.702546587089869097  ] 
dist 23=[2.2283227494634393909 ,24.547267599420250052  ] 
dist 24=[.5827966964809441323 ,17.967967584461534412  ] 
dist 25=[-.9990401025649334368 ,17.435447751344284308  ] 
dist 26=[-2.4283796350177132415 ,15.512026387999272950  ] 
dist 27=[-3.4646166285797913673 ,15.095404606496838252  ] 
dist 28=[-4.4169944989901531832 ,13.641570977917631477  ] 
dist 29=[-5.8021932105730358506 ,13.332593929831960026  ] 
dist 30=[-7.6797903525351654995 ,12.935596074969393989  ] 
dist 31=[-9.1512493869513547954 ,12.833326035047573116  ] 
dist 32=[-10.464441542373631697  ,2.2309101566199584063 ] 
dist 33=[-11.584609872374173440  ,1.3642191183498256581 ] 
dist 34=[-12.284889478507641361  ,-.56312528761169263914] 
dist 35=[-12.816809457632567236  ,-.89060646846169573071] 
dist 36=[-13.264640553246160506  ,-2.9724567580277854222 ] 
dist 37=[-13.628986733517282255  ,-1.7688724631145554104 ] 
dist 38=[-13.827287620237444901  ,-.53190265166137100462] 
dist 39=[-13.945094342790202881  ,.3265677363350797506 ] 
dist 40=[-13.987314862888589783  ,1.0705593312163402806 ] 
dist 41=[-13.980062118383930175  ,1.8509968049556949816 ] 
dist 42=[-13.949976262955115176  ,2.5937149062374964222 ] 
dist 43=[-13.804078902852821955  ,3.1873112838462526252 ] 
dist 44=[-13.733361206175134939  ,3.7846360460026126674 ] 
dist 45=[-10.395427547328061471  ,4.5423134242615619522 ] 
dist 46=[-10.463600555352850942  ,5.2691486589660595500 ] 
dist 47=[-10.470367540183555425  ,5.7434260156329724810 ] 
dist 48=[-5.8421838216729028952 ,6.1230520252098487047 ] 
dist 49=[-3.9659025953982000270 ,6.4721877780670921775 ] 
dist 50=[-3.6211504767362437768 ,6.7744745923729559822 ] 
dist 51=[-3.3510834460963948019 ,6.9671271937428904526 ] 
dist 52=[-3.1802002597396776145 ,7.1159929984173989812 ] 
dist 53=[-3.1369362646862332852 ,7.2434784882684410075 ] 
dist 54=[-1.4511637716104723824 ,7.3450564069672359306 ] 
dist 55=[-1.3886914941088094458 ,7.3905254606943945348 ] 
dist 56=[-.4425965991752252766 ,7.4032245324958661751 ] 
dist 57=[-.3175103167933028026 ,7.3875416558318978973 ] 
dist 58=[-.1220065505982445342 ,7.3198253679223040607 ] 
dist 59=[-.0861825868963336635 ,7.2872730411127896833 ] 
dist 60=[-.0697321336371785078 ,7.1036782242524419870 ] 
dist 61=[-.1184818149393480098 ,3.8213098637283891252 ] 
dist 62=[-.2168832362587519102 ,4.1118497331626795551 ] 
dist 63=[-.40715644504149150872,4.3227249178357916133 ] 
dist 64=[-.60830544812665589292,4.4812032877647066359 ] 
dist 65=[-.75011442046424067059,4.6033700965062275648 ] 
dist 66=[-.8744215869875121689 ,4.6691859897400630795 ] 
dist 67=[-1.0059295012586800560 ,4.7066658138228747886 ] 
dist 68=[-1.1307884338976232244 ,4.7155781632221971156 ] 
dist 69=[-1.2286388872618163291 ,4.3906428408827459086 ] 
dist 70=[-1.3247385205615878047 ,4.3355162267472588778 ] 
dist 71=[-1.4426369563643516906 ,4.2612860683477022067 ] 
dist 72=[-1.5526129902147020817 ,4.2315604498800739775 ] 
dist 73=[-1.6171412995240240030 ,4.1706692683922143868 ] 
dist 74=[-1.6602433255972676436 ,4.1479885793531497306 ] 
dist 75=[-1.6848197240517253102 ,4.1344794612920531357 ] 
dist 76=[-1.6971760242855572421 ,4.1300233994823961711 ] 
dist 77=[-1.6965664941178422163 ,3.0238120200067397868 ] 
dist 78=[-1.6802857473137520807 ,2.9584530996598623707 ] 
dist 79=[-1.7505322366576652705 ,2.9353016483188535522 ] 
dist 80=[-1.9550907323159248494 ,1.7019575887464054812 ] 
dist 81=[-2.1717706753827644569 ,1.6500807524030718181 ] 
dist 82=[-2.3799918240342522531 ,1.4379170522109776547 ] 
dist 83=[-2.5508109827457296168 ,1.3973789106390742849 ] 
dist 84=[-2.7272437722731159070 ,1.2926260467968560214 ] 
dist 85=[-2.9579265262565293443 ,1.2774787629053291850 ] 
dist 86=[-3.1768691727018460236 ,-.50774406912580822677] 
dist 87=[-3.3064399324070681015 ,-.53711779240480860219] 
dist 88=[-3.3956679496570047015 ,-.99509852057668369378] 
dist 89=[-3.4535237979819105266 ,-1.0511205799704243102 ] 
dist 90=[-3.4914234804550605291 ,-1.1524963136352308881 ] 
dist 91=[-3.5009574921269439855 ,-1.1722892776059833618 ] 
dist 92=[-3.4966414266891801314 ,-1.2052532079276943476 ] 
dist 93=[-3.4872595491430373518 ,-1.1880319095914342820 ] 
dist 94=[-3.2441337526694236038 ,-1.1437503199391798880 ] 
dist 95=[-3.2006012534304107337 ,-1.0512737808996909750 ] 
dist 96=[-3.1067968397371078080 ,-.9497869356088521357 ] 
dist 97=[-3.0759165259183000448 ,-.79156696151028319328] 
dist 98=[-2.9372514643733733918 ,-.62564163557590998891] 
dist 99=[-2.9498069526064275612 ,-.43699900603038527028] 
dist 100=[-2.9536048682613281955 ,-.24820640992736323678] 
dist 101=[-2.9476242314498893339 ,-.08166491175936564744] 
dist 102=[-1.8053452186600324281 ,.50673512232441034381] 
dist 103=[-1.7485770647314294310 ,.94544137372504096832] 
dist 104=[-1.7334102482507888658 ,1.3050083541376826432 ] 
dist 105=[-1.6245643154915927554 ,1.6510502644343705994 ] 
dist 106=[-1.5999231210577610725 ,1.9622861462941929537 ] 
dist 107=[-1.5594757608853366787 ,2.1828964782724218281 ] 
dist 108=[-1.5472616106797216188 ,2.3795632989015307966 ] 
dist 109=[-1.2688145917953824594 ,2.5952053003206587665 ] 
dist 110=[-1.2284135829353074632 ,2.7924104558200770686 ] 
dist 111=[-1.1425822605645651753 ,2.9154752048476788946 ] 
dist 112=[-1.1176752008074111663 ,3.0078983575859339965 ] 
dist 113=[-1.0125607232952570369 ,3.0827872565698132399 ] 
dist 114=[-.99147652092957564409,3.1407706270745720001 ] 
dist 115=[-.93260661320872403679,3.1657121403700039619 ] 
dist 116=[-.92406196748961890454,3.1726703885228809804 ] 
dist 117=[-.80629859244300969843,3.1699049826536394818 ] 
dist 118=[-.78403042444186532219,2.6257808561833199315 ] 
dist 119=[-.74023654687545409715,2.6314539352654474647 ] 
dist 120=[-.72777467616802987866,2.6514315981837914820 ] 
dist 121=[-.67805557192971322365,2.6635003142503930673 ] 
dist 122=[-.6661913132668273731 ,2.6619622202461649622 ] 
dist 123=[-.63948889557795915313,2.6525558553514944960 ] 
dist 124=[-.63054802221834507654,2.6444407880875343080 ] 
dist 125=[.81188509216421589349,2.2387751341018081525 ] 
dist 126=[.57460802978091178732,2.2262245240680661940 ] 
dist 127=[.211454652393419433  ,2.2175256658682796221 ] 
dist 128=[-.15333920966788751652,1.2182265640997786837 ] 
dist 129=[-.39716837775336659281,1.1566163462119097421 ] 
dist 130=[-.59924503015377944117,1.0117694576662354577 ] 
dist 131=[-.79736950864918888357,.9833215399341196281 ] 
dist 132=[-.97796100645038680551,.7820346654779404941 ] 
dist 133=[-1.1100503439518610200 ,.7440056928869756556 ] 
dist 134=[-1.2320151183121435743 ,.6780078637443445953 ] 
dist 135=[-1.3721956367850182433 ,.6623991488646262480 ] 
dist 136=[-1.5014190549364430896 ,.3873491471531858531 ] 
dist 137=[-1.5796418419515233778 ,.3507367794741221721 ] 
dist 138=[-1.6355492885591079472 ,.2658306584659488326 ] 
dist 139=[-1.6756799573925832529 ,.2510283136188754218 ] 
dist 140=[-1.7045991703755627881 ,.1396362246354177126 ] 
dist 141=[-1.7157520746170122524 ,.1196225510145448561 ] 
dist 142=[-1.7179347380672237960 ,.0872484531973293407 ] 
dist 143=[-1.7150986759462424037 ,.0794657600495402316 ] 
dist 144=[-1.3910630438179417473 ,-.53356579709891790053] 
dist 145=[-1.4347218133959203827 ,-.49325474191894875238] 
dist 146=[-1.4611725225318169144 ,-.44078249773985729847] 
dist 147=[-1.4801406183151473578 ,-.36933938620230593359] 
dist 148=[-1.4939275656880616763 ,-.25329317283274449336] 
dist 149=[-1.5023095265220736669 ,-.12941881420750150422] 
dist 150=[-1.5025333520396724812 ,-.02672223871685618670] 
dist 151=[-1.4937451658306172636 ,.08019276483900833961] 
dist 152=[-1.4887761206071219595 ,.22091401743781352881] 
dist 153=[-1.4354645424470486829 ,.37272725741420475162] 
dist 154=[-1.4207032383048740757 ,.52392606011885559797] 
dist 155=[-1.4026613400124564865 ,.70376228169762064687] 
dist 156=[-1.3940175250866912293 ,.96990274263293557656] 
dist 157=[-1.1404125007956657571 ,1.2344169965436557663 ] 
dist 158=[-1.1027278560617248115 ,1.4077629004802106655 ] 
dist 159=[-1.0942496678436376572 ,1.5476651904355624187 ] 
dist 160=[-.51937808950783497766,1.6786703438328820972 ] 
dist 161=[-.46367905119356579059,1.7940638715107516628 ] 
dist 162=[-.33880899573071357529,1.8716442146582040029 ] 
dist 163=[-.31308982658807991528,1.9364550860548227371 ] 
dist 164=[-.16166531609292827776,2.0008741027292280875 ] 
dist 165=[-.13471538863411395195,2.0548744507407268339 ] 
dist 166=[-.08070595494077375243,2.0780928575928193052 ] 
dist 167=[-.06716009189922421056,2.0878637974314359444 ] 
dist 168=[.05959513639029407246,2.0881771356439361953 ] 
dist 169=[.07925018677432326260,2.0419892919682122874 ] 
dist 170=[.10691582928570647811,2.0274997078658292472 ] 
dist 171=[.11393024501438182459,2.0165250256276611284 ] 
dist 172=[.11342808177285244088,2.0074764569906348122 ] 
dist 173=[-.26835524388058518634,1.6960528810656548064 ] 
dist 174=[-.53584549124918325101,1.6572155097026707781 ] 
dist 175=[-.75892910983124641855,1.5536245068800488316 ] 
dist 176=[-.97996208617529233198,1.5367247075959362132 ] 
dist 177=[-1.1829504489496156104 ,1.3484937902046929134 ] 
dist 178=[-1.3339999483418557481 ,1.3097993513176783360 ] 
dist 179=[-1.4760427608422415568 ,1.2673475086087568679 ] 
dist 180=[-1.6430763346480379861 ,1.2538110020221915784 ] 
dist 181=[-1.7974380176010406052 ,.83429894032503725346] 
dist 182=[-1.8888944775984077552 ,.77966349285059758764] 
dist 183=[-1.9518472008946112181 ,.66817755587985266052] 
dist 184=[-1.9924215896819422921 ,.63865697567881581455] 
dist 185=[-2.0207908982200775514 ,.52935295793559482531] 
dist 186=[-2.0350207852646061959 ,.50623878264380320405] 
dist 187=[-2.0416258165197633708 ,.46408898956279234517] 
dist 188=[-2.0395566322991641988 ,.45374384923048882234] 
dist 189=[-.6901451250112589206 ,.37417425019270376797] 
dist 190=[-.80745339577535349422,.46397435883789712623] 
dist 191=[-.9632836135918188249 ,.59895698976630140344] 
dist 192=[-1.1185502078529734432 ,.73351995611888089854] 
dist 193=[-1.2156761353809498123 ,.82164401177453681026] 
dist 194=[-1.2889084459773614322 ,.89266766212498287044] 
dist 195=[-1.3487873642631079877 ,.95896852425333985598] 
dist 196=[-1.3961404802428354302 ,1.0171895278313476429 ] 
dist 197=[-1.4193660176814707443 ,1.0559589690506127783 ] 
dist 198=[-1.4309287425489473762 ,1.0879148395347655453 ] 
dist 199=[-1.4318633545581870360 ,1.1189350939147025941 ] 
dist 200=[-1.3927235899436649685 ,1.1443738719048507087 ] 
dist 201=[-1.3821596460452728302 ,1.1540494648294426205 ] 
dist 202=[-1.3651078368968176764 ,1.1573448097174473201 ] 
dist 203=[-1.3114467310495188292 ,1.1573185041251814387 ] 
dist 204=[-1.1565948850707694221 ,1.1251284763925902211 ] 
dist 205=[-1.0456516770883823345 ,1.1158834330693663418 ] 
dist 206=[-1.0542998509744435012 ,1.1095118825625950751 ] 
dist 207=[-1.0571923565947284523 ,1.1053812282996893619 ] 
dist 208=[-1.0567613386080120197 ,.53837400785809278193] 
dist 209=[-1.0293256121319137918 ,.6236169425418204457 ] 
dist 210=[-1.0208722074558283744 ,.68992346007936124578] 
dist 211=[-1.0145806274759058477 ,.75511318387292165913] 
dist 212=[-1.0095876317483798020 ,.83589861854318127376] 
dist 213=[-.83632767449569542534,.91272074266474170819] 
dist 214=[-.81160853363749632259,.96208898492815129894] 
dist 215=[-.76436678795910879552,1.0008426389122185328 ] 
dist 216=[-.75166867769713099169,1.0352907504659291874 ] 
dist 217=[-.70528678264812784352,1.0643721819344739804 ] 
dist 218=[-.69348613889966361831,1.0817021136500047770 ] 
dist 219=[-.67393719033221015441,1.0937612403296563790 ] 
dist 220=[-.66807069579325334619,1.1018023909543926264 ] 
dist 221=[-.04569634484572487984,1.1059093993928836657 ] 
dist 222=[.00669038710252054784,1.1054499064430815248 ] 
dist 223=[.1259073696539066038 ,1.0967244889880851377 ] 
dist 224=[.14564569801670317097,1.0932748747156300220 ] 
dist 225=[.29109623255630515918,1.0485409771705564915 ] 
dist 226=[.31570165844021110066,1.0365917551213881629 ] 
dist 227=[.35715411244378367996,1.0238913392016733128 ] 
dist 228=[.36587026525489712569,1.0169770588075006414 ] 
dist 229=[.38090807324485955501,.83046619533555304986] 
dist 230=[.3564416364086646386 ,.80398619600356079681] 
dist 231=[.31060748319264441275,.75073975394383626237] 
dist 232=[.25936640359072931469,.73597822067002874139] 
dist 233=[.2133147150964147351 ,.70371953069462014278] 
dist 234=[.16220823067676644972,.71302207103246060571] 
dist 235=[.09078714633088127769,.71718484429584936882] 
dist 236=[-.06106930144458679773,.71739236677094627599] 
dist 237=[-.25195221762283677377,.68558336206075214231] 
dist 238=[-.37977971421638203044,.67939698991902962617] 
dist 239=[-.48600099167741144606,.64727715469256021271] 
dist 240=[-.59062962109230238529,-.12477984271960228335] 
dist 241=[-.68632856696473095463,-.23710958239228641848] 
dist 242=[-.75690159469771843354,-.25659018589153275662] 
dist 243=[-.82264365779070488181,-.29561825453804567278] 
dist 244=[-.89905683625931830883,-.30467298580975631589] 
dist 245=[-.96921848957108058789,-.3304831362087296081 ] 
dist 246=[-1.0100037668299756936 ,-.32807775906819809327] 
dist 247=[-1.0371116188924590328 ,-.31423824617534557292] 
dist 248=[-1.0526714860331020401 ,-.28116228454240637942] 
dist 249=[-1.0625603129105998131 ,-.23821628519371956617] 
dist 250=[-1.0670288745446360694 ,-.18497480508930763403] 
dist 251=[-1.0683857392929117004 ,-.1139476476540293969 ] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 1, 1, 2, 1, 2] 
dist 0=[43.862889116047393820  ,43.862889116047393820  ] 
dist 1=[43.196432094615542998  ,44.296181821706799171  ] 
dist 2=[42.229302356166237226  ,44.612675683174451524  ] 
dist 3=[40.595065905100110075  ,44.812543587101826022  ] 
dist 4=[38.890702749781955277  ,44.965715496865561564  ] 
dist 5=[37.643437262791046280  ,45.095479682681075442  ] 
dist 6=[36.488317378747882112  ,45.169096313536277832  ] 
dist 7=[35.151891015477381060  ,45.168035702572137077  ] 
dist 8=[33.795718982756672821  ,44.886673825556300466  ] 
dist 9=[32.561598875218921819  ,43.999172270328145750  ] 
dist 10=[31.176008417483130683  ,43.777887113162732959  ] 
dist 11=[29.214547917301740512  ,43.410216577662824752  ] 
dist 12=[27.218826834830352342  ,43.290030818383762961  ] 
dist 13=[25.696248938876267519  ,42.844019570963775536  ] 
dist 14=[24.222633764409666236  ,42.698798460443694516  ] 
dist 15=[22.422333628559169431  ,42.403436115607779326  ] 
dist 16=[20.540359631544765239  ,41.810195894949192588  ] 
dist 17=[18.740222934483071274  ,30.995961747971319396  ] 
dist 18=[16.646970640365625351  ,30.002226899550468378  ] 
dist 19=[13.593481456671440538  ,27.591221826008989100  ] 
dist 20=[10.555194340080581490  ,27.234981089183930977  ] 
dist 21=[8.5226264633840255679 ,23.688946901044591018  ] 
dist 22=[6.8281619329179542912 ,23.025491826984119876  ] 
dist 23=[5.1409734558269958815 ,22.253196317389285871  ] 
dist 24=[3.5779928008790314406 ,22.088554337785125481  ] 
dist 25=[2.3798340038628769243 ,16.283501757285158905  ] 
dist 26=[1.2135707373476893993 ,15.559495107390231645  ] 
dist 27=[-.2220738082293331719 ,14.090660933629562115  ] 
dist 28=[-1.5927185145493053454 ,13.713661456104928230  ] 
dist 29=[-4.1060355106148631136 ,12.370746205183519596  ] 
dist 30=[-6.7623525005150334572 ,12.092798082628813909  ] 
dist 31=[-8.4475691435260318879 ,11.668337483064563877  ] 
dist 32=[-9.7537549847657384292 ,11.557303076319980839  ] 
dist 33=[-10.895329113968434561  ,2.5378461011506463042 ] 
dist 34=[-11.852791481389722681  ,1.7845223309965894976 ] 
dist 35=[-12.423361441881470382  ,.1068919722576776931 ] 
dist 36=[-12.824777845607937560  ,.3906128510004625359 ] 
dist 37=[-13.106714645634625753  ,.7359436511583569613 ] 
dist 38=[-13.313556218292343540  ,1.0613677082906241090 ] 
dist 39=[-13.414846246176856768  ,1.4416798210227299162 ] 
dist 40=[-13.461275424409524957  ,1.8257281676496513396 ] 
dist 41=[-13.448341586697032798  ,2.1662787397319050416 ] 
dist 42=[-13.400555489055527229  ,2.5388511711452542232 ] 
dist 43=[-13.354726406243060424  ,3.0507987812437704068 ] 
dist 44=[-13.203529007750991123  ,3.5592680607305694674 ] 
dist 45=[-13.124994961361354337  ,3.9180441627329688497 ] 
dist 46=[-9.5232113188202954735 ,4.2349474963366894404 ] 
dist 47=[-9.5721043124328893343 ,4.5764604488714193824 ] 
dist 48=[-9.5726242501424128737 ,4.9067005865995506801 ] 
dist 49=[-5.8107230136351127202 ,5.1786601723190409628 ] 
dist 50=[-5.7411695176217537658 ,5.4594106161986977796 ] 
dist 51=[-5.7061944685894717473 ,5.8247168677019886715 ] 
dist 52=[-3.3251575645537353264 ,6.1744596860174393916 ] 
dist 53=[-2.4368898628045578644 ,6.3931218516536005225 ] 
dist 54=[-2.2770102334662127613 ,6.5571288535861926954 ] 
dist 55=[-2.0204081515983060635 ,6.6888383161481347767 ] 
dist 56=[-1.9580121761767277846 ,6.7892283936841429162 ] 
dist 57=[-.9292894907815632478 ,6.8282750220814199234 ] 
dist 58=[-.7970118185378308707 ,6.8296019086227892569 ] 
dist 59=[-.6573203538962429534 ,6.8162285280800507652 ] 
dist 60=[-.6471758555205208500 ,6.7058200004688069171 ] 
dist 61=[-.6657902592424686139 ,6.6133465789770521106 ] 
dist 62=[-.72526861095355958538,3.3204945184703757775 ] 
dist 63=[-.82517274735534055835,3.4767120580027757062 ] 
dist 64=[-1.0049468704418385582 ,3.5928787658737160584 ] 
dist 65=[-1.1911891465593571715 ,3.6859318729260473548 ] 
dist 66=[-1.3169075745493115989 ,3.7579250393902243195 ] 
dist 67=[-1.4213134615872710846 ,3.7899372389180833257 ] 
dist 68=[-1.5226759656483008666 ,3.8005878102890747537 ] 
dist 69=[-1.6132376064324072841 ,3.7986734894513135825 ] 
dist 70=[-1.6746022585723369420 ,3.7491346452359199779 ] 
dist 71=[-1.7256861121806293736 ,3.7338733554374358098 ] 
dist 72=[-1.7752316352835671462 ,3.6711058036304224856 ] 
dist 73=[-1.8150209271431750269 ,3.6596059886517841001 ] 
dist 74=[-1.8272084329882248204 ,3.5429366515996589470 ] 
dist 75=[-1.8286982346076343555 ,3.5002680658804044014 ] 
dist 76=[-1.8259633369911382433 ,3.4830084092003897133 ] 
dist 77=[-1.7501296435133411918 ,3.3904761780175106659 ] 
dist 78=[-1.7269786137122183201 ,3.3677081844027574276 ] 
dist 79=[-1.7098258106883897801 ,3.2895713206637553224 ] 
dist 80=[-1.8041653548923369673 ,3.2765793713788267161 ] 
dist 81=[-2.1924344794201130432 ,2.2448166619244574560 ] 
dist 82=[-2.5419328299024099934 ,1.9428262611142156963 ] 
dist 83=[-2.7906208238271214038 ,1.8835109180349514097 ] 
dist 84=[-3.0135288016949938851 ,1.7707420069606336158 ] 
dist 85=[-3.2601241867502938017 ,1.7410707858234553156 ] 
dist 86=[-3.4838423950433837414 ,1.2950777238084758382 ] 
dist 87=[-3.6310908064055542896 ,1.2325733493237465014 ] 
dist 88=[-3.8369270257615706071 ,1.0783292457431555761 ] 
dist 89=[-3.9567622732723533535 ,1.0538830897245841416 ] 
dist 90=[-4.0367615094051008409 ,.81605833588870829795] 
dist 91=[-4.0835716963330480100 ,.77022605655322703141] 
dist 92=[-4.1126465392821089503 ,.71462295110575223433] 
dist 93=[-4.1218360913000979742 ,.69860730873154580229] 
dist 94=[-4.1183131208036064055 ,.27722231832242006088] 
dist 95=[-4.1086653519596881628 ,.22406472632951197782] 
dist 96=[-4.0649082240866870666 ,.10641618524676526012] 
dist 97=[-4.0473016243041582828 ,.08001037408824466755] 
dist 98=[-3.9810121299476751026 ,-.06053490094333939452] 
dist 99=[-3.9613506919232513254 ,-.08606188568986202977] 
dist 100=[-2.2026168473264047692 ,-.14070923552001245553] 
dist 101=[-2.1073189948308436266 ,-.15493238331011842688] 
dist 102=[-1.8316650420112702840 ,.23704407607828012206] 
dist 103=[-1.8593467361282846259 ,.64064685401188623447] 
dist 104=[-1.8756911496001111033 ,1.0169467797881837455 ] 
dist 105=[-1.8840480326779910430 ,1.3066084981128490004 ] 
dist 106=[-1.8835833489711892691 ,1.5885338500056256317 ] 
dist 107=[-1.8718320305034295825 ,1.9339510350318033232 ] 
dist 108=[-1.8650548110873445091 ,2.2604807750544171194 ] 
dist 109=[-1.8011489436726658457 ,2.4670052127106003496 ] 
dist 110=[-1.7834340537132617340 ,2.6253468559467829470 ] 
dist 111=[-1.7598903418276959934 ,2.7595235258241676786 ] 
dist 112=[-1.7495770376518643100 ,2.8680278036053610798 ] 
dist 113=[.3686311600260715004 ,2.9238811284500147205 ] 
dist 114=[.4996652819112382026 ,2.9531000383075596472 ] 
dist 115=[.7807749080229540466 ,2.9581935336819104880 ] 
dist 116=[.8393340758441419939 ,2.4000216815613210317 ] 
dist 117=[1.1264189116302919799 ,2.5137567406598365649 ] 
dist 118=[1.1751694755348416879 ,2.5737743909175761016 ] 
dist 119=[1.2684659985789110900 ,2.6068219488325311848 ] 
dist 120=[1.3144098562798048174 ,2.6138650574360861172 ] 
dist 121=[1.1706144368225108974 ,2.6017309733979341160 ] 
dist 122=[.96607171959355469476,2.6221101861331831238 ] 
dist 123=[.73798204765359582678,2.6350467130609730241 ] 
dist 124=[.4487290749698399383 ,2.6363666414073763294 ] 
dist 125=[0                     ,2.6302242807974908828 ] 
dist 126=[.84830103962748644903,2.5339617712425227231 ] 
dist 127=[.67874105374916909873,2.5040721236025681518 ] 
dist 128=[.4909611352391947056 ,2.4908361516984975195 ] 
dist 129=[.2969403257400336413 ,1.5628258939052444823 ] 
dist 130=[.0610176878515245070 ,1.5416684391832065140 ] 
dist 131=[-.2940441351973022778 ,1.5313915847084047714 ] 
dist 132=[-.6485397101865449554 ,1.2380420520098046648 ] 
dist 133=[-.8822043573577107785 ,1.2020658032836698389 ] 
dist 134=[-1.0723033654298636147 ,1.1197165663562401785 ] 
dist 135=[-1.2528824276451352147 ,1.0972754033778856853 ] 
dist 136=[-1.4137156341913869940 ,.98293558239675286057] 
dist 137=[-1.5249894700739601516 ,.95952567094533414375] 
dist 138=[-1.6213813705928106486 ,.90928276750098774714] 
dist 139=[-1.7228092540521584803 ,.89419443923111730825] 
dist 140=[-1.8134651867872026132 ,.72198213296426233909] 
dist 141=[-1.8668534544784774895 ,.69565951195355346752] 
dist 142=[-1.9032280015745402136 ,.63290866564043719511] 
dist 143=[-1.9259558781595061350 ,.61951688293945927942] 
dist 144=[-1.9386604128169096525 ,.5270341241471387514 ] 
dist 145=[-1.9400133028440141498 ,.5087095701767634655 ] 
dist 146=[-1.9272789818757356760 ,.4765733318287523368 ] 
dist 147=[-1.9236063966115034358 ,.4686413079010407522 ] 
dist 148=[-1.3463719716828821755 ,.3182946825631216482 ] 
dist 149=[-1.2898486005197048520 ,.2963553727330548563 ] 
dist 150=[-1.1520935442534537710 ,.2561666289186760082 ] 
dist 151=[-1.1273658825336778580 ,.2464816284880643062 ] 
dist 152=[-1.1174087740131267919 ,.2174725958130960859 ] 
dist 153=[-1.1011637267721386702 ,.2109163001647811590 ] 
dist 154=[-1.0959239083490679797 ,.2102734053063070446 ] 
dist 155=[-1.0760573084221265407 ,.2175245556918160496 ] 
dist 156=[-1.0712604109480551504 ,.2284006842804911814 ] 
dist 157=[-1.0125378250402250796 ,.2422326541145446716 ] 
dist 158=[-1.0009166025944344051 ,.2609010871383749928 ] 
dist 159=[-.98312804007364089499,.2910899506413481741 ] 
dist 160=[-.97541061677429964449,.5627458040192432251 ] 
dist 161=[-.90362730345162943429,.8325773524838568552 ] 
dist 162=[-.88934235678508404857,1.0078252000425539826 ] 
dist 163=[-.97954750505073535742,1.1474914220348839380 ] 
dist 164=[-1.1332627246147406104 ,1.2752791565125531017 ] 
dist 165=[-1.2286211341115475096 ,1.3857799695509806929 ] 
dist 166=[-1.2995107619741804981 ,1.4564365421285641483 ] 
dist 167=[-1.3555538550677381334 ,1.5115030600590985850 ] 
dist 168=[-1.3996545698493376992 ,1.5597695959174581844 ] 
dist 169=[-1.4228761234338947073 ,1.6000748202860280228 ] 
dist 170=[-1.4352456627508539398 ,1.6233586675222552120 ] 
dist 171=[-1.4365988818660868976 ,1.6386610213386803843 ] 
dist 172=[-1.3607928032199468989 ,1.6470996106284615961 ] 
dist 173=[-1.3458150266549128563 ,1.6504909090544025104 ] 
dist 174=[-1.3272614868597089456 ,1.6478882554459662791 ] 
dist 175=[-1.3185457611286729099 ,1.6372510578114254168 ] 
dist 176=[-1.3001411574058409901 ,1.6299860845881992456 ] 
dist 177=[-1.2912063551271119982 ,1.5470313699691219323 ] 
dist 178=[-1.2833782302322386857 ,1.5399102507183115162 ] 
dist 179=[-1.2767722715767127192 ,1.5346384982967946973 ] 
dist 180=[-.5926956533794608046 ,.67893549021755330854] 
dist 181=[-.5830604795407552706 ,.46770743434712430005] 
dist 182=[-.5789995377749949878 ,.42905381010781503393] 
dist 183=[-.59695976518239790983,.37493528588608725763] 
dist 184=[-.73499728712791934167,.36202209286534331007] 
dist 185=[-.8348319187059248596 ,.13960660725302210126] 
dist 186=[-.9258814101376381798 ,.11028013523257832945] 
dist 187=[-1.0288508435661777012 ,.14282234088163583856] 
dist 188=[-1.1237339146412738890 ,.23427223714858679871] 
dist 189=[-1.1825020924864996675 ,.33185009838666608378] 
dist 190=[-1.2261164952168718779 ,.42744501324376186688] 
dist 191=[-1.2605018685634016836 ,.53995278965112156329] 
dist 192=[-1.2863474786840126284 ,.73451666021628678593] 
dist 193=[-1.2958684096932901958 ,.93276913071483562622] 
dist 194=[-1.2985861514221063581 ,1.0590164651204418755 ] 
dist 195=[-1.2972769447683978230 ,1.1567594346712843540 ] 
dist 196=[-1.1376730030861459947 ,1.2412257448583739066 ] 
dist 197=[-1.1866106648996853157 ,1.3107334087354402287 ] 
dist 198=[-1.2157619766900214621 ,1.3487622873714020931 ] 
dist 199=[-1.2360350421343038198 ,1.3710210950008648745 ] 
dist 200=[-1.2495316130401180722 ,1.3775738237019797045 ] 
dist 201=[-1.2575955388086407096 ,1.3785724466307492485 ] 
dist 202=[-1.2579797384267566219 ,1.3786604375175788255 ] 
dist 203=[-1.2515701762527493973 ,1.3780838405565431100 ] 
dist 204=[-1.2468741786847597112 ,1.3764337189732890650 ] 
dist 205=[-1.2044328413826960160 ,1.3742089173407263749 ] 
dist 206=[-1.1923539313650800194 ,1.3713406842109237872 ] 
dist 207=[-1.1757438567464137971 ,1.3674483430415942781 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 0, 1, 0, 2] 
dist 0=[47.344038493365802325  ,47.344038493365802325  ] 
dist 1=[47.056499567866021473  ,47.581319892002765598  ] 
dist 2=[46.601233671814932458  ,47.835727912552774752  ] 
dist 3=[45.935075185434120993  ,48.151116035123623155  ] 
dist 4=[44.805240977043698112  ,48.631554130310599036  ] 
dist 5=[43.437834000130725495  ,49.093916349078512465  ] 
dist 6=[41.822847036566180151  ,49.337135548630365821  ] 
dist 7=[39.713337476801415033  ,49.465819190558055314  ] 
dist 8=[36.370903568852659826  ,49.471202943696319442  ] 
dist 9=[32.968901786408876218  ,49.396473540848989131  ] 
dist 10=[30.621394540487484472  ,49.336702656373854567  ] 
dist 11=[28.591073770944455067  ,49.015122044921692918  ] 
dist 12=[26.455568108131692496  ,48.942599919574696119  ] 
dist 13=[24.408640601310999774  ,39.558288990632837264  ] 
dist 14=[22.731820284373943753  ,38.663791200360010998  ] 
dist 15=[20.999493050043729231  ,36.440135012885353879  ] 
dist 16=[18.730380842529527161  ,36.094802453700426785  ] 
dist 17=[16.501175907302142559  ,32.596689651313700168  ] 
dist 18=[14.927975303324036140  ,31.915836165842114776  ] 
dist 19=[13.527495019196758365  ,31.129762401542660664  ] 
dist 20=[11.987840388098979938  ,30.915232198551643114  ] 
dist 21=[10.466884056637238466  ,24.372127000452549371  ] 
dist 22=[9.1405979211103865441 ,23.528164524946649471  ] 
dist 23=[7.6946961148972856710 ,21.823792345621511327  ] 
dist 24=[5.6948358893178265096 ,21.378175339137842180  ] 
dist 25=[3.7406884477433877656 ,19.754963142493380319  ] 
dist 26=[2.4772856762973513010 ,19.409081126895684501  ] 
dist 27=[1.4688790044517555807 ,18.801577998361382904  ] 
dist 28=[-.5804921634995360447 ,18.657504966580302886  ] 
dist 29=[-3.0525948836701503204 ,6.0089215084010442441 ] 
dist 30=[-4.6327048078888912482 ,4.9311165982252885470 ] 
dist 31=[-5.8713834891881864287 ,2.5008595549750242310 ] 
dist 32=[-6.9788688180903015740 ,2.0879708809522917165 ] 
dist 33=[-7.9261650469268258743 ,-.84403620542599540221] 
dist 34=[-8.5247373473587006977 ,-1.3459543087594979137 ] 
dist 35=[-8.9874201979745917327 ,-1.8028547254708567338 ] 
dist 36=[-9.9884106575085115792 ,-1.6979131173528176197 ] 
dist 37=[-11.287547006167458736  ,-1.5226667190128128629 ] 
dist 38=[-12.077753615321042505  ,-1.2646381316643572227 ] 
dist 39=[-12.649535282745018334  ,-.8988644026292680791 ] 
dist 40=[-13.076131159883650153  ,-.2935977415320662151 ] 
dist 41=[-13.398883737539637915  ,.3244525172417378127 ] 
dist 42=[-13.555791654420525976  ,.7413554158560036644 ] 
dist 43=[-13.622088975197469693  ,1.0888378435681722705 ] 
dist 44=[-13.622723185052838459  ,1.4301507760119468095 ] 
dist 45=[-7.3038052664833947450 ,1.7393786819781318301 ] 
dist 46=[-6.9167035612895801840 ,1.9588996125257273532 ] 
dist 47=[-5.9674758531892145019 ,2.1534765069640132275 ] 
dist 48=[-5.8264467084602510586 ,2.3631071961786067879 ] 
dist 49=[-4.4180151660656064065 ,2.5543817104929103269 ] 
dist 50=[-4.1569997963075649399 ,2.6757999147945404733 ] 
dist 51=[-3.8429922294900429772 ,2.7684214680867119716 ] 
dist 52=[-3.7754463952146117280 ,2.8451174471512459205 ] 
dist 53=[-1.6018637805774542328 ,2.9054140400905471906 ] 
dist 54=[-1.3385918793734305482 ,2.9328027272393935471 ] 
dist 55=[-.7799968053877327157 ,2.9416095567144959377 ] 
dist 56=[-.6548072965868589360 ,2.9358210639497534952 ] 
dist 57=[-.1027589432190547287 ,3.3663045377799192532 ] 
dist 58=[-.0046355450671486606 ,3.7071870990492941892 ] 
dist 59=[.1732179591373413691 ,4.0434004622049694961 ] 
dist 60=[.2092024363160496731 ,4.4627285027861308388 ] 
dist 61=[.4350319650716562128 ,4.8551822523580009302 ] 
dist 62=[.2426138531908377325 ,5.0841071164081053172 ] 
dist 63=[.0418501334250560109 ,5.2381202552230138476 ] 
dist 64=[-.2226769661353085815 ,5.3313324340652255830 ] 
dist 65=[-.4815387794675596564 ,5.3940617328347260418 ] 
dist 66=[-.6597158282227642743 ,5.4262797540605984391 ] 
dist 67=[-.81292293496705885541,5.4426424588031121660 ] 
dist 68=[-.97215874630755894614,5.4419522960584723884 ] 
dist 69=[-1.1232031863592496383 ,4.8718366669366653174 ] 
dist 70=[-1.2437445407482861124 ,4.9712318358361182635 ] 
dist 71=[-1.3651793152960589587 ,5.0437450568423382353 ] 
dist 72=[-1.5198375181079412336 ,5.0873302731642080806 ] 
dist 73=[-1.6667570976262613606 ,5.1094055746718351264 ] 
dist 74=[-1.7573110393408720790 ,5.1097525538651308698 ] 
dist 75=[-1.8241233388172808378 ,5.0744143658070378797 ] 
dist 76=[-1.8762539839998112318 ,5.0638831620871210773 ] 
dist 77=[-2.1015917070768832820 ,1.5221406017370630474 ] 
dist 78=[-2.6843866825440040366 ,1.2940748257009464899 ] 
dist 79=[-3.1590095531128207407 ,.75282714742418603253] 
dist 80=[-3.6106425593054423249 ,.67388400074031351236] 
dist 81=[-4.0134309190234418207 ,.3212329256072198705 ] 
dist 82=[-4.2930867996797072638 ,.4287327171238927290 ] 
dist 83=[-4.5364355001785194924 ,.5347112675272391721 ] 
dist 84=[-4.7943235352943070584 ,.6663004392417724141 ] 
dist 85=[-5.0213811551700355640 ,.8043066174509356992 ] 
dist 86=[-5.1416536250461483677 ,.9359152707659851953 ] 
dist 87=[-5.2069672877612719693 ,1.0881067125906699663 ] 
dist 88=[-5.2208856700751573845 ,1.3082920678810412386 ] 
dist 89=[-5.2014451641578119840 ,1.5246132183538773324 ] 
dist 90=[-5.1838637467534906324 ,1.6613862915745263058 ] 
dist 91=[-5.1597490118529505692 ,1.7661758378829578126 ] 
dist 92=[-5.1391218804385960305 ,1.8548283268038783905 ] 
dist 93=[-4.1249835033647535548 ,1.9264211784219246096 ] 
dist 94=[-4.0097202452426388400 ,1.9631161245725908479 ] 
dist 95=[-3.7034028576875833829 ,1.9813665321309183294 ] 
dist 96=[-3.6592072212521020962 ,1.9845792607102289458 ] 
dist 97=[-3.1162316758422584351 ,2.1436665426970290059 ] 
dist 98=[-3.0075410238601294429 ,2.5192530986071623543 ] 
dist 99=[-2.8996544641752075378 ,2.8816850502765379893 ] 
dist 100=[-2.8789412981379841174 ,3.3210626243428511060 ] 
dist 101=[-1.7175054519997409987 ,3.7336352719696326471 ] 
dist 102=[-1.5717364461762847273 ,3.9890742475556470854 ] 
dist 103=[-1.2802481112534484176 ,4.1783848192874078831 ] 
dist 104=[-1.2075130645313573233 ,4.3270018162953552380 ] 
dist 105=[-1.0913699570368345448 ,4.4402270003345332348 ] 
dist 106=[-1.0679741296904770011 ,4.4882683848534892105 ] 
dist 107=[-1.0099311784114682011 ,4.5071366241992731701 ] 
dist 108=[-1.0118726577385628600 ,4.5039188759352374647 ] 
dist 109=[-1.2001729389756506853 ,1.2678718283167795760 ] 
dist 110=[-1.3321192671873860785 ,1.5896045488840130081 ] 
dist 111=[-1.4480768316882836244 ,1.8454455892460465957 ] 
dist 112=[-1.5725563844044321209 ,2.0786441223684837848 ] 
dist 113=[-1.6856941572647049885 ,2.2797539413154524006 ] 
dist 114=[-1.7563815690844486746 ,2.4074917681555681932 ] 
dist 115=[-1.8095164215303161263 ,2.5061113992459058825 ] 
dist 116=[-1.8525964514314542474 ,2.5909824150391827569 ] 
dist 117=[-1.8859200063738068758 ,2.6623004375318282325 ] 
dist 118=[-1.9001137587552891209 ,2.7068122423745410859 ] 
dist 119=[-1.9030630272642658985 ,2.7403032062068956084 ] 
dist 120=[-1.9012892585736194154 ,2.7676123734887740897 ] 
dist 121=[.2410228629973635316 ,2.7889312596405398324 ] 
dist 122=[.1655790103630208585 ,2.7985022846225825829 ] 
dist 123=[.0653597504411622366 ,2.8013289580374870236 ] 
dist 124=[-.0949115531719846254 ,2.7957181002672450600 ] 
dist 125=[-.2582127611442967272 ,2.0310422958717564647 ] 
dist 126=[-.3705314286871500853 ,1.9953369899862349316 ] 
dist 127=[-.4976942692520243443 ,1.8948345210840933497 ] 
dist 128=[-.7204062375599366882 ,1.8793961461130225387 ] 
dist 129=[-.9291838175239205748 ,1.6797813581466707738 ] 
dist 130=[-1.0916876315140046513 ,1.6377341337448649438 ] 
dist 131=[-1.2515338640273880353 ,1.5973278465623406659 ] 
dist 132=[-1.4497132276304387277 ,1.5867340358247835738 ] 
dist 133=[-1.6382118621498718596 ,1.0902281510519933412 ] 
dist 134=[-1.7594186793881935342 ,1.0258060029116859948 ] 
dist 135=[-1.8546576890725132741 ,.8984821819854794498 ] 
dist 136=[-1.9394999575124429442 ,.8655092104416054314 ] 
dist 137=[-2.0113008000616416863 ,.7491040460041032797 ] 
dist 138=[-2.0544865274693445673 ,.7224159166564718338 ] 
dist 139=[-2.0850769391808158952 ,.6871089944701748961 ] 
dist 140=[-2.1066141665538432356 ,.6751635336735723560 ] 
dist 141=[-2.1194069276800421870 ,.61088906540355962048] 
dist 142=[-2.1203332991247297501 ,.76772797296541332549] 
dist 143=[-2.1063094615952882512 ,.89728789203191196743] 
dist 144=[-2.1012514800258273564 ,1.0235383009756309744 ] 
dist 145=[-2.1111411531160105624 ,1.1380308638842079466 ] 
dist 146=[-2.1347841867108831042 ,1.2206577628783008202 ] 
dist 147=[-2.1449511581646924110 ,1.2957811167566021936 ] 
dist 148=[-2.1462758195747918822 ,1.3803203054764280182 ] 
dist 149=[-2.0951826194123929838 ,1.4563729508757573393 ] 
dist 150=[-2.0809589757213435804 ,1.4976207624341710769 ] 
dist 151=[-2.0488937020887855234 ,1.5212650611314231329 ] 
dist 152=[-2.0360697151402349541 ,1.5270518323342367620 ] 
dist 153=[-1.9675592610768670601 ,1.5265731571329066522 ] 
dist 154=[-1.9505657560741626512 ,1.5252104921527472326 ] 
dist 155=[-1.9012769080519010613 ,1.5229286406012574109 ] 
dist 156=[-1.8874209463606116593 ,1.5187871620584560713 ] 
dist 157=[-1.3454723831554936639 ,.36425043235060121618] 
dist 158=[-1.3183021284253431772 ,.60052642163064743786] 
dist 159=[-1.2498719259364591659 ,.79756832273839392559] 
dist 160=[-1.2338513074353053086 ,.99284120956750919346] 
dist 161=[-1.1165870383827101943 ,1.1722431852678406745 ] 
dist 162=[-1.0915730978434068848 ,1.3059224698781839795 ] 
dist 163=[-1.0505964484300023879 ,1.4318273333820244762 ] 
dist 164=[-1.0388279077959867661 ,1.5801879580254047280 ] 
dist 165=[-.7860641380914708611 ,1.7174657674294605216 ] 
dist 166=[-.7509612825996814735 ,1.7991236357965265009 ] 
dist 167=[-.6709353075190713358 ,1.8557281727751918751 ] 
dist 168=[-.6514291942696968546 ,1.8929859460853149343 ] 
dist 169=[-.5447352113934739217 ,1.9187978880746452957 ] 
dist 170=[-.5238915621044308996 ,1.9297132535626457422 ] 
dist 171=[-.4807848854403842285 ,1.9318144554662180458 ] 
dist 172=[-.4686511576377080845 ,1.9291588545731681984 ] 
dist 173=[.05163778957590938035,1.5780431576104104312 ] 
dist 174=[-.09269716576403013446,1.5759650965160023780 ] 
dist 175=[-.21938198305060052048,1.5604025770113180433 ] 
dist 176=[-.35522006386983069175,1.5547553465557378328 ] 
dist 177=[-.48665924887268906743,1.4873368182032273936 ] 
dist 178=[-.59578497614942363508,1.4696440101129332027 ] 
dist 179=[-.70954631964440610152,1.4498629890937993639 ] 
dist 180=[-.8594922931672501677 ,1.4397694014189565559 ] 
dist 181=[-1.0064860785379458917 ,1.1712087782789914586 ] 
dist 182=[-1.1084631068897536209 ,1.1331144584083499281 ] 
dist 183=[-1.1970699409591800333 ,1.0558062016456685520 ] 
dist 184=[-1.2906909349165994331 ,1.0342463723039992409 ] 
dist 185=[-1.3804591852216020309 ,.94928837845958631667] 
dist 186=[-1.4536868895462640302 ,.93050385062612752404] 
dist 187=[-1.5288855200045847967 ,.88893407397089578515] 
dist 188=[-1.6265237182762518544 ,.87584893265976317123] 
dist 189=[-1.7180669007173727028 ,-.10199640268350957345] 
dist 190=[-1.7689342071606213362 ,-.12543099767006367652] 
dist 191=[-1.7997888480487229833 ,-.15763312150692978893] 
dist 192=[-1.8114394035178544801 ,-.16494915389029727468] 
dist 193=[-1.8151642099955697414 ,-.16303381331088895497] 
dist 194=[-1.8143782915028378006 ,-.1470269168245296    ] 
dist 195=[-1.8101394840374910098 ,-.11763045266198701434] 
dist 196=[-1.8043802762901126858 ,-.06226330140903322115] 
dist 197=[-1.5875198157593236639 ,-.00029121189345587369] 
dist 198=[-1.5541309778444473535 ,.05547327583780745747] 
dist 199=[-1.4905280994208572354 ,.11740476732687361793] 
dist 200=[-1.4725579808484754183 ,.20399816058587126061] 
dist 201=[-1.4027173186624105181 ,.29989384881387681675] 
dist 202=[-1.3846707270660462010 ,.39896156555385136954] 
dist 203=[-1.3478818041152158695 ,.5194049610121361903 ] 
dist 204=[-1.3358874242234307865 ,.7006340605451290397 ] 
dist 205=[-.82872063648210186189,.88187100218765131535] 
dist 206=[-.80579899707651417861,1.0023463718122087292 ] 
dist 207=[-.74695666206840474357,1.1014726076302664922 ] 
dist 208=[-.73674568866415383198,1.1974840846321107556 ] 
dist 209=[-.63695961756074100339,1.2842316356732079338 ] 
dist 210=[-.61680336076790994179,1.3463766916173238039 ] 
dist 211=[-.59178504683769573101,1.4024511254348665387 ] 
dist 212=[-.58252468319255990943,1.4649657045952554647 ] 
dist 213=[-.38127472797802368998,1.5209669780336164279 ] 
dist 214=[-.35476593763889330793,1.5510405697758695431 ] 
dist 215=[-.2987738320840048654 ,1.5679063504005137274 ] 
dist 216=[-.28354327158621014465,1.5711819078314314504 ] 
dist 217=[-.22422677738403892275,1.5683210208991233040 ] 
dist 218=[-.21260700378412407654,1.5633761079637981242 ] 
dist 219=[-.18683331513037287429,1.5306187965562818634 ] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 1, 0, 2, 1, 2] 
dist 0=[52.137906388750414528  ,52.137906388750414528  ] 
dist 1=[51.967496885791466097  ,52.366939039646912440  ] 
dist 2=[51.516222667709657489  ,52.559062326845312346  ] 
dist 3=[50.733696176564483745  ,52.571883577120697580  ] 
dist 4=[49.399195609082724237  ,52.502366477581225253  ] 
dist 5=[47.921994698636718927  ,52.411625804165252994  ] 
dist 6=[46.569547119016161027  ,51.775913810087737628  ] 
dist 7=[45.047026316220311117  ,50.902697852993198723  ] 
dist 8=[42.890293737270316732  ,49.722492373226683824  ] 
dist 9=[40.484880638167249849  ,49.523061799475702459  ] 
dist 10=[37.969003406317415362  ,48.647869644013226585  ] 
dist 11=[34.883977565746821391  ,48.431386202235155949  ] 
dist 12=[30.205263172794728325  ,47.842883895934325719  ] 
dist 13=[25.497699160297046281  ,47.661883787375014440  ] 
dist 14=[22.297305523711313360  ,39.398881032486337031  ] 
dist 15=[19.579665255008366159  ,39.221206686908343809  ] 
dist 16=[16.799914651791764822  ,32.609382186025073646  ] 
dist 17=[14.183068947861929780  ,31.742574050600488332  ] 
dist 18=[12.115779769591814221  ,30.037628871517929543  ] 
dist 19=[10.048118475198318447  ,29.594627649029242954  ] 
dist 20=[7.4292242224673890188 ,28.017785226661107095  ] 
dist 21=[4.8974816618140407966 ,27.655495826864097430  ] 
dist 22=[3.1776257593748439058 ,27.114940275946098382  ] 
dist 23=[1.7155961735671100249 ,26.951745791238064480  ] 
dist 24=[.21334482209734175234,16.599071435600037769  ] 
dist 25=[-1.2102110079506418002 ,16.291779621063547226  ] 
dist 26=[-2.3584452617787724132 ,14.483129067563273745  ] 
dist 27=[-3.5333451682086014624 ,14.169642501309423209  ] 
dist 28=[-5.0646705282211016244 ,13.547982089027321675  ] 
dist 29=[-6.5298136242592148972 ,13.398092129849307430  ] 
dist 30=[-7.4404315801059373248 ,1.0878886458481880119 ] 
dist 31=[-8.1280695911443753295 ,.84688165461697890324] 
dist 32=[-8.7015121906624375724 ,-2.8402016152276307239 ] 
dist 33=[-9.2071078586557626070 ,-3.3018517618266349849 ] 
dist 34=[-9.9758209648061392740 ,-4.2051380489700484054 ] 
dist 35=[-10.605884588431603048  ,-4.4109729456647876608 ] 
dist 36=[-11.103936776201596465  ,-5.0021670195529194794 ] 
dist 37=[-11.345275143394706035  ,-5.0803807581870360276 ] 
dist 38=[-11.467528090899211406  ,-5.0092203352977510815 ] 
dist 39=[-11.489911893379260543  ,-4.7205677643761602064 ] 
dist 40=[-9.4810217642730072876 ,-4.3751419794519117903 ] 
dist 41=[-9.1224032174005408115 ,-4.0772091256982363930 ] 
dist 42=[-9.0276198400260359263 ,-3.4305404003309013534 ] 
dist 43=[-8.8775350361182862948 ,-2.1618305413809703303 ] 
dist 44=[-8.8247433345179927916 ,-.24366443399625186674] 
dist 45=[-6.6441608093923631375 ,1.6730992085150473364 ] 
dist 46=[-6.4379185871155533639 ,2.9363489867643127992 ] 
dist 47=[-6.3806041851669366086 ,3.9634093414198555398 ] 
dist 48=[-5.2860732015788398294 ,4.9374879549194505466 ] 
dist 49=[-4.6695845599410467854 ,5.8038638602949690832 ] 
dist 50=[-4.5477033974025277414 ,6.4010828636140954481 ] 
dist 51=[-4.1499762939172985645 ,6.9162234693286481138 ] 
dist 52=[-3.5130485641897641896 ,7.4550860987682951041 ] 
dist 53=[-2.9674290611827726165 ,7.9407106266347155476 ] 
dist 54=[-2.7887380096750094018 ,8.2433006440381022273 ] 
dist 55=[-2.7480939360123448446 ,8.4702613984754884921 ] 
dist 56=[.48660678311494654074,8.6537617997284317009 ] 
dist 57=[.76302409086347998823,8.7952228269111715988 ] 
dist 58=[1.3409440430119311855 ,8.8542013505619911946 ] 
dist 59=[1.4686884021711122163 ,8.8635674698154508014 ] 
dist 60=[2.0028178493244230143 ,8.8537462532512417188 ] 
dist 61=[2.0986957042372795689 ,5.4920162296480707614 ] 
dist 62=[2.2356450385666934601 ,5.2024640959471858778 ] 
dist 63=[2.2573825060841575267 ,4.7354674203002514656 ] 
dist 64=[2.2383684240656726488 ,5.0813225176241522612 ] 
dist 65=[2.1604461972778674852 ,5.2871031345642735985 ] 
dist 66=[2.0249345774550017182 ,5.4303044215401660352 ] 
dist 67=[1.7759111263081563657 ,5.5262120120263949806 ] 
dist 68=[1.4732567705007004877 ,5.5908179728526725584 ] 
dist 69=[.79425704526482863018,5.6090034529105958958 ] 
dist 70=[.30771436996945316431,5.6051292921984432399 ] 
dist 71=[-.12466611325807622333,5.5913243440162204140 ] 
dist 72=[-.75025164214622974985,.52639020102063233313] 
dist 73=[-1.2325520580491891910 ,.1652753452902510579 ] 
dist 74=[-1.6367403256211962185 ,-.03356231361102878686] 
dist 75=[-2.0402806111415484164 ,-.20282755425464182622] 
dist 76=[-2.4399577754565826110 ,-.23424015607501909737] 
dist 77=[-2.9918153601117504016 ,-1.2738758100655115298 ] 
dist 78=[-3.3528294786444962809 ,-1.4935614844319428859 ] 
dist 79=[-3.6441549398644406938 ,-1.5304537999008128994 ] 
dist 80=[-3.9176951322998142124 ,-1.7154844897659354870 ] 
dist 81=[-4.1598455346603465998 ,-1.7156186991486440371 ] 
dist 82=[-4.3258168002369292818 ,-1.6558577631870531525 ] 
dist 83=[-4.4683309847823267300 ,-1.4989764987924352449 ] 
dist 84=[-4.6168247689253399404 ,-1.2918782376398383174 ] 
dist 85=[-4.7449742771894166997 ,-1.0316780526664329866 ] 
dist 86=[-4.8062408215551141047 ,-.68286218396908012555] 
dist 87=[-4.8339176824341373003 ,.01946052620043262824] 
dist 88=[-4.8348986072665375150 ,.7349583154727513881 ] 
dist 89=[-4.7782922298976496973 ,1.2198743560537117024 ] 
dist 90=[-4.7528446456861571168 ,1.6287739934673418988 ] 
dist 91=[-4.7150343544966613779 ,2.0408665758425155371 ] 
dist 92=[-4.6963949362806044512 ,2.4234847015370263709 ] 
dist 93=[-4.2667866169303863670 ,2.7147399471154958106 ] 
dist 94=[-4.2448201953559332929 ,3.1476724467005240020 ] 
dist 95=[-4.2389207678575980952 ,3.5597219271553107787 ] 
dist 96=[-3.4044261102752162826 ,3.9498046063874490561 ] 
dist 97=[-3.2910530296304606440 ,4.2962986870066625360 ] 
dist 98=[-3.0817907773713760496 ,4.5343568083832691355 ] 
dist 99=[-3.0283746568488863038 ,4.7388184649577694058 ] 
dist 100=[-2.8514794030236963256 ,4.9512199182507211020 ] 
dist 101=[-2.8018701207260521299 ,5.1347887296405819433 ] 
dist 102=[-2.7645951992467852584 ,5.2241493323458179152 ] 
dist 103=[-2.7566753908870530130 ,5.2688168110909878981 ] 
dist 104=[-.14561943988552928675,5.2739448392952659063 ] 
dist 105=[.00494786545759366616,5.1994672030630973926 ] 
dist 106=[.35396142937283334882,5.1725912927982267443 ] 
dist 107=[.40468700786496712185,5.1496500298013655203 ] 
dist 108=[.50080238958120855613,5.1261594410528448409 ] 
dist 109=[-.4843938794384837333 ,4.6321278489061968626 ] 
dist 110=[-1.1484044836885409370 ,4.5647480134502089064 ] 
dist 111=[-1.7046322542769040608 ,4.3692145259408884603 ] 
dist 112=[-2.2595813779096021732 ,4.3375254007322819223 ] 
dist 113=[-2.7715542629372448750 ,3.9283566418807626537 ] 
dist 114=[-3.1562271058816613860 ,3.8403902316214958966 ] 
dist 115=[-3.5215013823129783982 ,3.7543576185616549895 ] 
dist 116=[-3.9560318235284314066 ,3.7106847497467630427 ] 
dist 117=[-4.3599633291817337842 ,2.6616017661655268032 ] 
dist 118=[-4.6030893852598528448 ,2.5218262169039464621 ] 
dist 119=[-4.7750528327673360547 ,2.0458940917957849267 ] 
dist 120=[-4.8949147737974713138 ,1.3461074710333357610 ] 
dist 121=[-4.9817865049308774403 ,1.2924794784133243107 ] 
dist 122=[-5.0220667124856642750 ,1.1945955858109411753 ] 
dist 123=[-5.0359246032525374018 ,1.1662399723770287473 ] 
dist 124=[-5.0311723268955295808 ,1.0406924888931690955 ] 
dist 125=[-.4132928103792341114 ,1.0154464322987680595 ] 
dist 126=[-.6407195884520455985 ,.95490207645044041539] 
dist 127=[-.82501665855956364114,.93998070326873852676] 
dist 128=[-.9989101125606561149 ,.78782384015693408389] 
dist 129=[-1.1530362023456134932 ,.76197444298336589798] 
dist 130=[-1.2584208005598247211 ,.71028437683572234064] 
dist 131=[-1.3484167092969950587 ,.69624450913581984482] 
dist 132=[-1.4411152850423454070 ,.64312953492836202656] 
dist 133=[-1.5243375899628689427 ,.63104666142333147095] 
dist 134=[-1.5765014337119101428 ,.60774385358745142629] 
dist 135=[-1.6159896902748889531 ,.6011733941749987422 ] 
dist 136=[-1.6485986829790265474 ,-1.4545623810196936124 ] 
dist 137=[-1.7310777018834533807 ,-1.4441795855557177704 ] 
dist 138=[-1.8706400039678996159 ,-1.3709460300810228924 ] 
dist 139=[-1.9922359525368769171 ,-1.2660137343135876049 ] 
dist 140=[-2.0931441816566924964 ,-1.0903483837793063996 ] 
dist 141=[-2.1501162549476777947 ,-.90814309528734714995] 
dist 142=[-2.1858915486029743724 ,-.77710055750627209116] 
dist 143=[-2.2021799711763251890 ,-.65838412423794023728] 
dist 144=[-2.2094307487097899355 ,-.52537251079000467354] 
dist 145=[-2.2091240255364905992 ,-.39325768319425821334] 
dist 146=[-2.2032434465101588728 ,-.27811435045885666033] 
dist 147=[-2.1971239063679139721 ,-.15326521682712283707] 
dist 148=[-2.1684991439427837142 ,.01760339938026646205] 
dist 149=[-2.1581066722175246637 ,.18806493688464796637] 
dist 150=[-2.1211271405126320217 ,.31129360575647434797] 
dist 151=[-2.1099260694186952424 ,.42363439295691522668] 
dist 152=[-1.1558885084994071094 ,.55063689524458557131] 
dist 153=[-1.0689395488229882245 ,.67750836049011886903] 
dist 154=[-.85797062629899701502,.78933216270589679746] 
dist 155=[-.82651457391875304964,.91168645107328211896] 
dist 156=[-.52016724134732021786,1.0806083585343825962 ] 
dist 157=[-.46382578387158586696,1.2442288504176802614 ] 
dist 158=[-.39476103370443309523,1.3454201514098747978 ] 
dist 159=[-.37960437030932640748,1.4203897541065036100 ] 
dist 160=[.07587981213563704422,1.4793212822371182003 ] 
dist 161=[.13076561714281542467,1.5255737573586043822 ] 
dist 162=[.24850872271741638491,1.5499204380717284956 ] 
dist 163=[.27296205283670367072,1.5629174283845648997 ] 
dist 164=[.39293021368387842476,1.5642904048599332106 ] 
dist 165=[.41328456037488806772,1.5833800377960709457 ] 
dist 166=[.45195029434544923683,1.5971744582536566975 ] 
dist 167=[.46008509188254688428,1.6003591328786314193 ] 
dist 168=[.70452388821066227406,1.4389935671408054484 ] 
dist 169=[.72586144558680971595,1.4191378113561005486 ] 
dist 170=[.75588883750583143926,1.4096726053942333558 ] 
dist 171=[.75851911986825193627,1.4014318325218137704 ] 
dist 172=[.59342994030697703142,1.3946284903281492528 ] 
dist 173=[.34986751021413839221,.95501352772315500902] 
dist 174=[.18520888666276432052,.96583727957610703209] 
dist 175=[.04664375259798235637,.97119785469108743429] 
dist 176=[-.09274469454426074819,.97264366617648500583] 
dist 177=[-.22217220658409741738,.97166562961105967712] 
dist 178=[-.32097007306212866873,.96202098652227927595] 
dist 179=[-.41636040493652435698,.95942537020366188239] 
dist 180=[-.53218431195953368115,.91599561755175144012] 
dist 181=[-.64146011795020684851,.90482272216565228134] 
dist 182=[-.71070748352890303324,.89495424912115509532] 
dist 183=[-.76396489973217958141,.88942723891769574303] 
dist 184=[-.80940084081913172121,.76299245414653148462] 
dist 185=[-.84637828568521994567,.74780986814325551837] 
dist 186=[-.86586438860732855647,.7136415463175007054 ] 
dist 187=[-.87666951413324840934,.70281856467982808972] 
dist 188=[-.92150381165806405536,.65345280069798368092] 
dist 189=[-.98489628371779783781,.64277001635048620834] 
dist 190=[-1.0389874056649241587 ,.61671428304785709736] 
dist 191=[-1.0946045419864904979 ,.60890638629980033496] 
dist 192=[-1.1437684341621344260 ,.5258169553880389035 ] 
dist 193=[-1.1720970500687860815 ,.51221453162798675673] 
dist 194=[-1.1906192426521512749 ,.47887007868804961183] 
dist 195=[-1.2006316532645203238 ,.47138138010952803999] 
dist 196=[-1.2049583703202529037 ,.41817918045552460036] 
dist 197=[-1.2044487376968077109 ,.40720066271523361066] 
dist 198=[-1.1946309357434523928 ,.38858089495707639425] 
dist 199=[-1.1910698619334680940 ,.38360025884477027639] 
dist 200=[-.8245477326861739442 ,.28239687654804463647] 
dist 201=[-.78834242263814920353,.2676900527784024430 ] 
dist 202=[-.7004031480005942514 ,.2396803843340253206 ] 
dist 203=[-.68461902948607360785,.33706586070128183111] 
dist 204=[-.56019956803749634231,.50052552061672281586] 
dist 205=[-.54045262328277097658,.66194136317161044952] 
dist 206=[-.50588733249850618675,.76541806527161590489] 
dist 207=[-.49743809504362460509,.84636310921377142025] 
dist 208=[-.49691324359457722826,.91782925820713560248] 
dist 209=[-.49742014819808362105,.9778137988357416646 ] 
dist 210=[-.49863611432732240224,1.0129231194952262112 ] 
dist 211=[-.50059252267903225443,1.0365721093621863845 ] 
dist 212=[-.50405416755497788211,1.0508069502081100857 ] 
dist 213=[-.5078257981431637864 ,1.0604460521401065473 ] 
dist 214=[-.51101973859086527377,1.0657477534479523939 ] 
dist 215=[-.61217684826978872747,1.0689006281767470273 ] 
dist 216=[-.71952026263151569746,1.0699584232638320278 ] 
dist 217=[-.78647750417316201204,1.0695940253169029170 ] 
dist 218=[-.83670198991404440603,1.0670675800223767300 ] 
dist 219=[-.87725061940297949722,1.0624705819951134194 ] 
dist 220=[-.90952991640553430298,1.0589695182019197319 ] 
dist 221=[-.92674535806007147185,.93780191968692300621] 
dist 222=[-.93622642570649954317,.96588954028635938267] 
dist 223=[-.93763404229692510314,.99117531508981797313] 
dist 224=[-.89675309154794098361,1.0116126083347011273 ] 
dist 225=[-.8880665313269696411 ,1.0203440822776223198 ] 
dist 226=[-.8790444909060549971 ,1.0231235856939569583 ] 
dist 227=[-.8737116921685531888 ,1.0220765191907267692 ] 
dist 228=[-.8651826704573999782 ,1.0053314906351243068 ] 
dist 229=[-.8608270075763019292 ,.99909301409539594752] 
dist 230=[-.8571935977652010316 ,.98683521277068261796] 
dist 231=[-.8535913870784833957 ,.98189955642882158864] 
dist 232=[-.52776792371946425149,.00821516882932227200] 
dist 233=[-.50997605999711388276,.08280974224327305638] 
dist 234=[-.511568095898760386  ,.1577472397804970984 ] 
dist 235=[-.55933956517240623529,.24734195884556090294] 
dist 236=[-.63231598888249331088,.40071547160798631833] 
dist 237=[-.70309869823105212607,.55766538986004191529] 
dist 238=[-.74742862053750328961,.65872452417696110941] 
dist 239=[-.78091514225829780092,.73825646242062582707] 
dist 240=[-.80840887984881232687,.80927085869000727753] 
dist 241=[-.82998267092075920883,.86942039259663397726] 
dist 242=[-.83983606070918029512,.90557985485790436804] 
dist 243=[-.8439959304601402502 ,.93110609852912795708] 
dist 244=[-.84360700632564753276,.94880694712219844872] 
dist 245=[-.82975294513185130963,.96218361177845720871] 
dist 246=[-.82517005076192104898,.97044816828597751738] 
dist 247=[-.8122485064953094226 ,.97654835118178288708] 
dist 248=[-.80650325961447556558,.98128706383380051919] 
dist 249=[-.77409166126741182628,.98478582517545019005] 
dist 250=[-.76573014271358746852,.98593736071748495127] 
dist 251=[-.74847634304899596392,.98558910691637068799] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 1, 2, 0, 2] 
dist 0=[43.048743412541910463  ,43.048743412541910463  ] 
dist 1=[42.082627444635184734  ,43.834387111363129384  ] 
dist 2=[40.899859257318043534  ,44.296371051634013820  ] 
dist 3=[39.329115869891301570  ,44.610430042087043785  ] 
dist 4=[36.813509161000862931  ,44.805240977043698116  ] 
dist 5=[34.241950368656893672  ,44.948553106987543536  ] 
dist 6=[32.447652700201649480  ,45.056779302025657330  ] 
dist 7=[30.874742811931848309  ,45.159245199610173327  ] 
dist 8=[29.187080080663395857  ,45.279131608629374547  ] 
dist 9=[27.548902934003478005  ,45.381592578930223919  ] 
dist 10=[26.173370746265781734  ,45.414493585048905606  ] 
dist 11=[24.722088631047407636  ,45.401562119596088788  ] 
dist 12=[22.780894331763988981  ,45.347557195913808691  ] 
dist 13=[20.854463057500480816  ,45.203711933228671302  ] 
dist 14=[19.461894291846436209  ,45.120343068459638728  ] 
dist 15=[18.187673544439680279  ,44.680778083934877797  ] 
dist 16=[16.733649355561460181  ,43.755383090751327469  ] 
dist 17=[15.266042741139781417  ,34.932959401739607412  ] 
dist 18=[13.937109281164260009  ,34.035816166810697241  ] 
dist 19=[12.447168990714277132  ,31.830561096505727768  ] 
dist 20=[10.335388566356507044  ,31.492842651309950881  ] 
dist 21=[8.2550936547561955372 ,28.120528946387150801  ] 
dist 22=[6.8908315292480196987 ,27.473521631167100545  ] 
dist 23=[5.7807153401437719779 ,26.719306665429346738  ] 
dist 24=[4.7163689795735786453 ,26.525523918321017985  ] 
dist 25=[3.7535242251865120844 ,20.523380864403933922  ] 
dist 26=[3.0490553210996571527 ,19.755975371260651333  ] 
dist 27=[2.3612623897697593487 ,18.202754961237959552  ] 
dist 28=[-.2470323680254278738 ,17.798340912703617558  ] 
dist 29=[-2.8020718847994654791 ,16.331089033716483777  ] 
dist 30=[-4.4366341490920355748 ,16.021765026285958115  ] 
dist 31=[-5.7195255171522067602 ,15.488883544604028662  ] 
dist 32=[-6.8690424332150958365 ,15.361806714037181326  ] 
dist 33=[-7.8539491374521134295 ,4.4345348787803522560 ] 
dist 34=[-8.4790749017409733873 ,3.5058806539504967478 ] 
dist 35=[-8.9654134912032045752 ,1.4123746019131504706 ] 
dist 36=[-9.3960179987657908438 ,1.0595242382814258002 ] 
dist 37=[-9.7606049155387977485 ,.36215567169662421786] 
dist 38=[-9.9830507209969016113 ,.41675097376885466438] 
dist 39=[-10.147118057935071221  ,.46794592699898828183] 
dist 40=[-10.277873506296531618  ,.52456555712031488626] 
dist 41=[-10.379602916290526001  ,.57748979661716442627] 
dist 42=[-10.752774797058221940  ,.61410620950056726559] 
dist 43=[-11.231733994467035327  ,.64405053835137667231] 
dist 44=[-11.582038343076409142  ,.6703486262727668048 ] 
dist 45=[-11.845799369399231237  ,.69338730263437772719] 
dist 46=[-11.978981469867024750  ,.71077405502709604051] 
dist 47=[-12.042791755107577544  ,.72725210454215761236] 
dist 48=[-12.039886944021815436  ,.74376848609205471555] 
dist 49=[-6.2269858450273491154 ,.75810650992715029717] 
dist 50=[-5.8773334446218550131 ,.76590547471966065701] 
dist 51=[-5.0241589228958848795 ,.7697442267755840314 ] 
dist 52=[-4.8975334519170923298 ,.76821880718578542259] 
dist 53=[-3.6463538678658019366 ,1.0437012098320467311 ] 
dist 54=[-3.4157290758587620206 ,1.6077219179959242388 ] 
dist 55=[-3.1359032113654549933 ,2.0910240101772544584 ] 
dist 56=[-3.0761432325187273452 ,2.5916570916588294920 ] 
dist 57=[-1.1903397951074684347 ,3.0664040090039001429 ] 
dist 58=[-.9626992529126031235 ,3.4464522930435629269 ] 
dist 59=[-.58728458873368003526,3.8310127058798616260 ] 
dist 60=[-.71434229059377900773,4.3239575922856593065 ] 
dist 61=[-.83820796165804434852,4.7902387215261510063 ] 
dist 62=[-.92222826177587796281,5.0683558644039102925 ] 
dist 63=[-.99303739190575161365,5.2630269701909614738 ] 
dist 64=[-1.0641998253098232413 ,5.3960026311837106967 ] 
dist 65=[-1.1300413237971273541 ,5.4931422896167089877 ] 
dist 66=[-1.1796243650444440615 ,5.5446356240798948619 ] 
dist 67=[-1.2267433765021090416 ,5.5728976274180184006 ] 
dist 68=[-1.2827570271151889726 ,5.5771292244618967315 ] 
dist 69=[-1.3332749877254955234 ,5.0816277498240057680 ] 
dist 70=[-1.3584643563130816760 ,5.0035454330142826123 ] 
dist 71=[-1.3710857440292753936 ,4.8810757566089347501 ] 
dist 72=[-1.3724989614206082193 ,4.8420897125919442568 ] 
dist 73=[-1.3563733887466119823 ,4.7369927599808110395 ] 
dist 74=[-1.3488409944926980495 ,4.6984926968151304471 ] 
dist 75=[-1.3410306290273059533 ,4.6725974233254239181 ] 
dist 76=[-1.3345283509535256580 ,4.6570525039600048789 ] 
dist 77=[-1.1269043581626771106 ,4.3715206170934955472 ] 
dist 78=[-1.0960791294620884977 ,4.3703411350625159487 ] 
dist 79=[-1.0353497261783562863 ,4.3365954301893541206 ] 
dist 80=[-1.1124598958538531790 ,4.3274891244047099919 ] 
dist 81=[-1.8774050372162963729 ,1.1798995141401235229 ] 
dist 82=[-2.3816437176217318610 ,1.2183740896360284387 ] 
dist 83=[-2.7918806584245677763 ,1.2547870459162564376 ] 
dist 84=[-3.1815868879049573993 ,1.2978982882697382250 ] 
dist 85=[-3.5287228279476393616 ,1.3361543271173912584 ] 
dist 86=[-3.7690349295057067831 ,1.3531880618511940076 ] 
dist 87=[-3.9774166334975957097 ,1.3605037950121866902 ] 
dist 88=[-4.1971176076676082116 ,1.3599761565704899959 ] 
dist 89=[-4.3901274942825675096 ,1.3325740208401531453 ] 
dist 90=[-4.4919562009668082376 ,1.3225185026620684812 ] 
dist 91=[-4.5466971837457757794 ,1.3138075549337027174 ] 
dist 92=[-4.5582086281286320886 ,1.3066030913070118598 ] 
dist 93=[-4.5388259666668935870 ,1.3892896881362022063 ] 
dist 94=[-4.5222322086108160715 ,1.4548783012019605664 ] 
dist 95=[-4.4998050600722171698 ,1.5011914527637718498 ] 
dist 96=[-4.4818280761003841642 ,1.5333368574018757069 ] 
dist 97=[-3.5799578022932911122 ,1.5558585814921770962 ] 
dist 98=[-3.4780738540269803264 ,1.5637539918064809926 ] 
dist 99=[-3.2080621665367167521 ,1.5642298029254147767 ] 
dist 100=[-3.1690707126904953559 ,1.5611125205339097124 ] 
dist 101=[-2.6929436955500035442 ,1.8673324202100128961 ] 
dist 102=[-2.5978133297282037577 ,2.1949930016754650400 ] 
dist 103=[-2.5029268982761156538 ,2.5110848009300228266 ] 
dist 104=[-2.4846470144427736176 ,2.8941643777616199928 ] 
dist 105=[-1.4732922449815514290 ,3.2538306145902923168 ] 
dist 106=[-1.3464291708046022153 ,3.4764665375523451641 ] 
dist 107=[-1.0925059746508345753 ,3.6414170117962064319 ] 
dist 108=[-1.1595892644562944369 ,3.7708266695177108088 ] 
dist 109=[-1.2595925960942959129 ,3.8694353623792036236 ] 
dist 110=[-1.3191736488544375457 ,3.9114405339386381644 ] 
dist 111=[-1.3605759330181399404 ,3.9279698765024436464 ] 
dist 112=[-1.3880206129293493433 ,3.9248924468537991884 ] 
dist 113=[-1.4066205331440193000 ,1.1119633603818102432 ] 
dist 114=[-1.4127162532405205226 ,1.3898011703378607568 ] 
dist 115=[-1.4120444024530542426 ,1.6106317719772495002 ] 
dist 116=[-1.4089977092043113123 ,1.8117406596911390050 ] 
dist 117=[.38151572507894050689,1.9850532959221992359 ] 
dist 118=[.38064230002844699976,2.0949165340966827421 ] 
dist 119=[.36435555976659136411,2.1794847545310569404 ] 
dist 120=[.32285185629306741683,2.2518202230197347642 ] 
dist 121=[.26835256222919300249,2.3124494102091003755 ] 
dist 122=[.2001828632308275378 ,2.3502823177999918209 ] 
dist 123=[.108935979030393838  ,2.3787397789945104868 ] 
dist 124=[-.03768801702878019857,2.4019303095517129777 ] 
dist 125=[-.18726130969718453957,2.4200231477475597289 ] 
dist 126=[-.29028579210656803149,2.4281247379287137992 ] 
dist 127=[-.37898316284992507992,2.4304829550147600786 ] 
dist 128=[-.47137390645766369853,2.4256426959031817147 ] 
dist 129=[-.55913098138767619086,1.7592856106688795476 ] 
dist 130=[-.6293374146122000736 ,1.7285105648013290702 ] 
dist 131=[-.70018824817804426878,1.6418838463098149661 ] 
dist 132=[-.79052628554847895366,1.6285205463990698005 ] 
dist 133=[-.87770837349558552016,1.4563657709767656879 ] 
dist 134=[-.9523854980008230090 ,1.4200771643045281352 ] 
dist 135=[-1.0907130590634307844 ,1.3850813183269589093 ] 
dist 136=[-1.2621212500093263595 ,1.3757630756520587191 ] 
dist 137=[-1.4251139894040488347 ,.94720446003946172109] 
dist 138=[-1.5298521494042772618 ,.89154444523902602058] 
dist 139=[-1.6120742214461727121 ,.78147058976206710304] 
dist 140=[-1.6851885602762732012 ,.752936159025330436  ] 
dist 141=[-1.7469695993170176371 ,.65201800374266208346] 
dist 142=[-1.7839559316858470131 ,.67957994349297081358] 
dist 143=[-1.8099449267061253659 ,.7932488059352914727 ] 
dist 144=[-1.8278389335813880808 ,.90411366801724426828] 
dist 145=[-1.8381568021325429367 ,1.0047080433968492199 ] 
dist 146=[-1.8387029448545803682 ,1.0773816134611229571 ] 
dist 147=[-1.8259505367796623973 ,1.1435268458178311017 ] 
dist 148=[-1.8214817099510925146 ,1.2180610138047205040 ] 
dist 149=[-1.8269478955745466783 ,1.2851538825158250917 ] 
dist 150=[-1.8471759673901633069 ,1.3215963249974835354 ] 
dist 151=[-1.8558200163097268529 ,1.3425547252506021486 ] 
dist 152=[-1.8569261407400740724 ,1.3478429163079248178 ] 
dist 153=[-1.8123638705903075496 ,1.3475426027796367228 ] 
dist 154=[-1.8000168302006749597 ,1.3461964495682767181 ] 
dist 155=[-1.7720659436713745946 ,1.3438157216123172020 ] 
dist 156=[-1.7608893666789818624 ,1.3393918780685581876 ] 
dist 157=[-1.7011857092631143283 ,.07621396047145662709] 
dist 158=[-1.6863775857058787790 ,.24411221750907719628] 
dist 159=[-1.6437909395530282648 ,.38635337658571355854] 
dist 160=[-1.6315627891726658119 ,.53092769779634172268] 
dist 161=[-1.1658680396364077497 ,.66607639435495130588] 
dist 162=[-1.1425980141885319842 ,.77069026275278746314] 
dist 163=[-1.0839790413799219719 ,.87305979846324456583] 
dist 164=[-1.0701630496829966885 ,.99924979859379298101] 
dist 165=[-.9695389078120468344 ,1.1189159763887338235 ] 
dist 166=[-.9480358641111293587 ,1.1952422193711162530 ] 
dist 167=[-.9126521088840312674 ,1.2545008991600938566 ] 
dist 168=[-.9025238095717175101 ,1.3709871924112592846 ] 
dist 169=[-.6848622618342500015 ,1.4899196798040222828 ] 
dist 170=[-.6545965361184019592 ,1.5606666222266843640 ] 
dist 171=[-.5855278353166656046 ,1.6097100566873590313 ] 
dist 172=[-.5687034729574829451 ,1.6419959277092689379 ] 
dist 173=[-.4763437347846856150 ,1.6643586485599734887 ] 
dist 174=[-.4582797221101120810 ,1.6737910389972701622 ] 
dist 175=[-.4210278027825445230 ,1.6755646037769787957 ] 
dist 176=[-.4105566314672983201 ,1.6732666436618783814 ] 
dist 177=[-.41474225865931286123,1.3120889965054668774 ] 
dist 178=[-.51144787390409502399,1.2964009198451697898 ] 
dist 179=[-.612451604629042182  ,1.2783992034942435690 ] 
dist 180=[-.74582935848859036215,1.2694868308321577986 ] 
dist 181=[-.87669374009147988231,1.0335488867631403830 ] 
dist 182=[-.96766491905936236639,1.0000608489728741675 ] 
dist 183=[-1.0469023790392797380 ,.93178355092081986814] 
dist 184=[-1.1309268930282539361 ,.91267098951282925143] 
dist 185=[-1.2116775312241164615 ,.83686977059470199189] 
dist 186=[-1.2778467176354169427 ,.82026853236874689789] 
dist 187=[-1.3460639188626488642 ,.78275270078175554725] 
dist 188=[-1.4349921745788123952 ,.77081269584056272292] 
dist 189=[-1.5185287116161711329 ,.1290748779707939232 ] 
dist 190=[-1.5652222121096060708 ,.1108150549015003776 ] 
dist 191=[-1.5939080671659057100 ,.0875285967563219457 ] 
dist 192=[-1.6055562664223160798 ,.0821107787380675472 ] 
dist 193=[-1.6100079717032947077 ,-.07802265811275553157] 
dist 194=[-1.6099645086965876845 ,-.09804935332130780898] 
dist 195=[-1.6066220536839539236 ,-.12485050459784688468] 
dist 196=[-1.6016765811146150270 ,-.13047225495248751612] 
dist 197=[-1.4119642076764971874 ,-.12810601837122422465] 
dist 198=[-1.3826623670213782076 ,-.1136281744240281336 ] 
dist 199=[-1.3270114287060831195 ,-.08750299340926686204] 
dist 200=[-1.3112860091097639945 ,-.03863994830730870175] 
dist 201=[-1.2939813618516970341 ,.01594291123232012908] 
dist 202=[-1.2964390539385408689 ,.06490255371230679363] 
dist 203=[-1.2900068406884834490 ,.1191506709452278848 ] 
dist 204=[-1.2585169588083035024 ,.19484732733619843472] 
dist 205=[-.91172861437710105241,.27860600375768247222] 
dist 206=[-.87489970761814118601,.36503897508060928124] 
dist 207=[-.77773462804749271315,.47005389621518520739] 
dist 208=[-.67125902924673593832,.62799326525262003522] 
dist 209=[-.55853291139908589677,.78591953354601576327] 
dist 210=[-.54003315095617724405,.89088269682093344175] 
dist 211=[-.51722874375594108466,.97722782428000547308] 
dist 212=[-.50895603398125208882,1.0946944169422368536 ] 
dist 213=[-.32599656747109485131,1.2051059045745910876 ] 
dist 214=[-.302011815482553537  ,1.2707617228430463394 ] 
dist 215=[-.25141037938821054578,1.3162530505692015407 ] 
dist 216=[-.23769789157809956588,1.3461666055112304194 ] 
dist 217=[-.18456582925813419919,1.3675062309517191818 ] 
dist 218=[-.17415763672305483068,1.3787704924733142904 ] 
dist 219=[-.15145374246404492514,1.3848201669502270865 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 0, 2, 1, 0, 1] 
dist 0=[46.669189326805466612  ,46.669189326805466612  ] 
dist 1=[46.352879147473421251  ,46.864860375075178195  ] 
dist 2=[45.886864145508984271  ,47.002965027542903085  ] 
dist 3=[45.093054461649009627  ,47.089215874313574797  ] 
dist 4=[44.109844057799934321  ,47.153502410132773934  ] 
dist 5=[42.887252003779810727  ,47.203681927351060338  ] 
dist 6=[41.251285754002114611  ,47.234207521821469004  ] 
dist 7=[38.616945442104275752  ,47.220046249127021718  ] 
dist 8=[35.913186777398753026  ,47.169725811152328162  ] 
dist 9=[33.999901663229870727  ,47.103479611564500734  ] 
dist 10=[32.293506242705811691  ,46.910322938513905904  ] 
dist 11=[30.415992242974380148  ,46.813823997988216574  ] 
dist 12=[28.564743005681138172  ,46.547631010823459230  ] 
dist 13=[26.963110607279717291  ,46.423899089639209179  ] 
dist 14=[25.231904403963159625  ,35.916243371391796541  ] 
dist 15=[22.862794663129585836  ,34.966773491816819755  ] 
dist 16=[20.487897517303522952  ,32.618011798646855809  ] 
dist 17=[18.733418725854223791  ,32.280132199080729245  ] 
dist 18=[17.090537479575077039  ,28.664636703643665678  ] 
dist 19=[15.161230870620366662  ,27.975468866317095442  ] 
dist 20=[13.185246927252983365  ,27.230974862462612167  ] 
dist 21=[11.355603264719773516  ,27.094543019995261547  ] 
dist 22=[9.2740652237467575906 ,20.583584909178424847  ] 
dist 23=[6.2911469878632087334 ,19.768587654506753142  ] 
dist 24=[3.3426321889583274708 ,18.154794694499349229  ] 
dist 25=[1.3984739153547479900 ,17.746191955112274342  ] 
dist 26=[-.19174812189002925835,16.983472237793979874  ] 
dist 27=[-1.7258558985543961601 ,16.241342922203968091  ] 
dist 28=[-3.1158821407892930096 ,15.669547610595976028  ] 
dist 29=[-4.2004739371428875393 ,15.592674998695808934  ] 
dist 30=[-5.9679552246536236136 ,3.6231241096804819151 ] 
dist 31=[-7.3734089515749224746 ,2.6536251849325436325 ] 
dist 32=[-8.6636350663009802263 ,.46088263440199839973] 
dist 33=[-9.7904302404360080760 ,.11004130263830811939] 
dist 34=[-10.542843207490761563  ,-2.5376054250417675691 ] 
dist 35=[-11.170402075105753278  ,-2.9853809328934763644 ] 
dist 36=[-11.798551809093997857  ,-3.6992233237044470267 ] 
dist 37=[-12.341880128914354210  ,-3.6618421769953619351 ] 
dist 38=[-12.630473948181421718  ,-2.8643736793844787190 ] 
dist 39=[-12.791058876395742137  ,-1.5570729890615850685 ] 
dist 40=[-12.822533562964099050  ,-.21657680060091755199] 
dist 41=[-12.801324618824207083  ,.71352163558587961612] 
dist 42=[-12.756536438082296340  ,1.5200235869081639706 ] 
dist 43=[-12.673171076966502261  ,2.3674990719579754508 ] 
dist 44=[-12.629039641355546334  ,3.1755657965427352756 ] 
dist 45=[-10.247325398130506676  ,3.8248912381071092709 ] 
dist 46=[-9.2357952208824578603 ,4.4818763264061827634 ] 
dist 47=[-8.4152342596910365013 ,5.3205759327425032613 ] 
dist 48=[-8.2709961713097225539 ,6.1284142172834921647 ] 
dist 49=[-7.0051896363140711089 ,6.6622512684931001178 ] 
dist 50=[-6.7596352538819468879 ,7.0973289400643214821 ] 
dist 51=[-6.4190801621768395190 ,7.5110170844923324600 ] 
dist 52=[-6.3121933709723510770 ,7.8789008655321723662 ] 
dist 53=[-4.3834207028758863424 ,8.1311442373698781065 ] 
dist 54=[-4.2053043041613111383 ,8.3466471502308993069 ] 
dist 55=[-4.1600770606434590053 ,8.5678186064395942748 ] 
dist 56=[-3.1330479746166438860 ,8.7554460376145415686 ] 
dist 57=[-2.4154935317740176431 ,8.8370522239002416112 ] 
dist 58=[-2.2867563460095745123 ,8.8607008773748401552 ] 
dist 59=[-1.9989406968540051270 ,8.8521913121233951541 ] 
dist 60=[-1.9384052738874191847 ,8.6846977108031436122 ] 
dist 61=[-1.6507285728621939689 ,2.4529817275464615676 ] 
dist 62=[-1.3355074912107215414 ,2.8041762101705276836 ] 
dist 63=[-1.2863862067257889022 ,3.2173166162831138008 ] 
dist 64=[-1.1927332643826481126 ,3.6001573159670421097 ] 
dist 65=[-1.1680581597699095188 ,3.8303816836071920550 ] 
dist 66=[-1.0770737041338379384 ,3.9934380225202669349 ] 
dist 67=[-1.0556348457180082439 ,4.1080890695121444047 ] 
dist 68=[-1.0105857816272228337 ,4.1930249563708164111 ] 
dist 69=[-.99578522908410530131,4.2374036823066019473 ] 
dist 70=[-.9271157372262003242 ,4.2607189758639921260 ] 
dist 71=[-.90884418876598957495,4.2614621691347983436 ] 
dist 72=[-.87427100294524427508,4.1127926017321136274 ] 
dist 73=[-.86269502932986784699,4.1151174343122879980 ] 
dist 74=[-.80812974396246225875,4.1146968398729850198 ] 
dist 75=[-.79431518409664578146,4.1106903961404585116 ] 
dist 76=[-.75054417062368224795,4.1035101845212275000 ] 
dist 77=[-.74068715865184118096,4.0903900435087114163 ] 
dist 78=[-.35348991203572777537,3.2413779963916571368 ] 
dist 79=[-.79519887151563183897,3.2123059905769173049 ] 
dist 80=[-1.2364452751156234745 ,2.6329191011415676111 ] 
dist 81=[-1.5563484826424566696 ,2.5504586866845670000 ] 
dist 82=[-1.8489194949190929591 ,2.3539875165027106029 ] 
dist 83=[-2.1810798136394942671 ,2.3113043139705395576 ] 
dist 84=[-2.5137254152041545923 ,2.0223346330813161323 ] 
dist 85=[-2.8082573936625838631 ,1.9650512708136397708 ] 
dist 86=[-3.1316763158806398728 ,1.8628029296794175507 ] 
dist 87=[-3.5796851330847158436 ,1.8373981681952750542 ] 
dist 88=[-4.0142863671483693062 ,.01723365581743151274] 
dist 89=[-4.2841838174353238205 ,.01385802442011481908] 
dist 90=[-4.4855150272586345639 ,.03588829527042388319] 
dist 91=[-4.6463581950385166578 ,.09453570013138643917] 
dist 92=[-4.7697797300738592887 ,.19114578703997068262] 
dist 93=[-4.8216966687247607503 ,.36470165210721335679] 
dist 94=[-4.8435207250277121940 ,.5484948861091356996 ] 
dist 95=[-4.8467849543309015585 ,.68597645736582432784] 
dist 96=[-4.7022162731477800770 ,.81581807161624855115] 
dist 97=[-4.6658954952856620913 ,.96914550917463014474] 
dist 98=[-4.5888062950303602789 ,1.1258465805445984483 ] 
dist 99=[-4.5596707924901171730 ,1.2691712168171765408 ] 
dist 100=[-4.4090940523833393719 ,1.4301991288443190314 ] 
dist 101=[-4.3838275920649911623 ,1.6575846499003827147 ] 
dist 102=[-4.2549945146314293138 ,1.8874535709789764378 ] 
dist 103=[-4.2324128180354466310 ,2.0584048913520101993 ] 
dist 104=[-2.2023828298708267178 ,2.2190521919957144064 ] 
dist 105=[-2.0081237517399985672 ,2.4078031859145004942 ] 
dist 106=[-1.5577593120034022912 ,2.6003763954842244630 ] 
dist 107=[-1.4753210921871425416 ,2.7762938715765268959 ] 
dist 108=[-1.4162335683542994834 ,2.9738886456623745255 ] 
dist 109=[-1.4101417532694159118 ,3.2530171693654058890 ] 
dist 110=[-.58930135345057094562,3.5252758592096043362 ] 
dist 111=[-.54718415695713267949,3.6954478050246942171 ] 
dist 112=[.13582468950140606246,3.8236150347325100072 ] 
dist 113=[.22643921383442760046,3.9281760012049819748 ] 
dist 114=[.41348739234919149904,4.0097043939672753095 ] 
dist 115=[.45927496552986343858,4.0459183339108424549 ] 
dist 116=[.62356125710911271267,4.0578236535200302732 ] 
dist 117=[.65540438502266751566,4.0551973074102014980 ] 
dist 118=[.69070009675557451723,3.9950845519331549855 ] 
dist 119=[.6886021321725688617 ,3.9379687828630452568 ] 
dist 120=[.67776011512700629341,2.7531634832149947033 ] 
dist 121=[.66526497879917215197,2.7514357744480178142 ] 
dist 122=[.64918597089007223482,2.7151689406185994409 ] 
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dist 124=[.59496046174842695694,2.6628305752379445160 ] 
dist 125=[.56326142612024515444,2.6454874935687460986 ] 
dist 126=[.11539965103478832619,1.8359152544348853451 ] 
dist 127=[-.21374513649830076109,1.7548131231663036886 ] 
dist 128=[-.49080086853656005032,1.5508098733095550436 ] 
dist 129=[-.7694952908247888421 ,1.5206192296922241565 ] 
dist 130=[-1.0281630604962481374 ,1.1972587512443151641 ] 
dist 131=[-1.2252725036633553923 ,1.1352508420004496071 ] 
dist 132=[-1.4151913832203923651 ,1.0659218776333718311 ] 
dist 133=[-1.6451548185574345943 ,1.0510280997865982020 ] 
dist 134=[-1.8611409073934491520 ,.47040633411619422398] 
dist 135=[-1.9952617355761513076 ,.39856468021044935149] 
dist 136=[-2.0951968835766129662 ,.25039783057047837025] 
dist 137=[-2.1747119551225732161 ,.21214017783932505765] 
dist 138=[-2.2362578527273991003 ,.07449371615141778398] 
dist 139=[-2.2644585874402922738 ,.04682934909794366579] 
dist 140=[-2.2769189213998397176 ,.00404117470040152219] 
dist 141=[-2.2758855214550009262 ,-.00658020987709015072] 
dist 142=[-.78070893815235405844,-.06812568873742514589] 
dist 143=[-.90266865282277503942,-.07244883511847819791] 
dist 144=[-.99834951446848459933,-.08421822081149882285] 
dist 145=[-1.0833446573471007336 ,-.08307077846776675219] 
dist 146=[-1.1550894123008520180 ,-.07655408869175713441] 
dist 147=[-1.1978701898070402906 ,-.06101872883249714107] 
dist 148=[-1.2276852219096396936 ,-.04087484582881244050] 
dist 149=[-1.2476678732690431948 ,-.01595960778820357329] 
dist 150=[-1.2621180682815398490 ,.01723450320976681888] 
dist 151=[-1.2698451884290040125 ,.07042839521084917146] 
dist 152=[-1.2741499359016065580 ,.12477653495462212961] 
dist 153=[-1.2749339238708297732 ,.16257936813409589456] 
dist 154=[-1.2734093043094642574 ,.19552478645305563801] 
dist 155=[-1.2695151449654718394 ,.23048423687738364766] 
dist 156=[-1.2610582086872888826 ,.26409294793882232015] 
dist 157=[-1.2563464491964264765 ,.2916476046474545322 ] 
dist 158=[-.96304290210638040125,.32006833092064901113] 
dist 159=[-.94660694744672244215,.38105606160061332543] 
dist 160=[-.90374504556478512887,.49693377470969930654] 
dist 161=[-.89409270744080725552,.61138580173464227107] 
dist 162=[-.81598166435121239756,.71627635207734766125] 
dist 163=[-.79913919769144686643,.79398587447590743514] 
dist 164=[-.7739860229137976653 ,.86673903131177725517] 
dist 165=[-.76589955662018465198,.95184672898075611443] 
dist 166=[-.58593430177789659763,1.0303092955678263058 ] 
dist 167=[-.56108407503000019856,1.0765359074735138168 ] 
dist 168=[-.50636018153965649006,1.1080529533770787722 ] 
dist 169=[-.49126780179548824683,1.1277944115267180948 ] 
dist 170=[-.42388820013962895706,1.1409772673599275360 ] 
dist 171=[-.4679210871890607461 ,1.1463086546841364665 ] 
dist 172=[-.514137059138201406  ,1.1469171947644568014 ] 
dist 173=[-.54713201900303644993,1.1449809747110621034 ] 
dist 174=[-.57677682856477371548,1.0381604179359575727 ] 
dist 175=[-.60961882171072279094,1.0228017554040768201 ] 
dist 176=[-.63889946729360895155,.9778441586854106691 ] 
dist 177=[-.65432768983311483353,.97121018904194706471] 
dist 178=[-.66284562520927570235,.88309528409264014098] 
dist 179=[-.66461239019919495627,.88150230730162165351] 
dist 180=[-.66131025237713262656,.87545406526243277743] 
dist 181=[-.65991570906036515131,.87156306404159864809] 
dist 182=[-.6585728513797008444 ,.80526532758269051756] 
dist 183=[-.65694660248379737823,.80382430569920065831] 
dist 184=[.00597769116861334019,.79509990924388032671] 
dist 185=[-.07638817955972651607,.79235063642518936155] 
dist 186=[-.14728085349836105727,.75764868647917322739] 
dist 187=[-.22113468713436854681,.74871150675968669433] 
dist 188=[-.29131500032946520472,.73917330127681198835] 
dist 189=[-.34754247750436318665,.73411963837921197806] 
dist 190=[-.40436678870027005267,.69935273064334872647] 
dist 191=[-.47692967923631942106,.71120874084481641132] 
dist 192=[-.54699187933925196424,.71706683584404571179] 
dist 193=[-.59383306701266820445,.71802798072411413467] 
dist 194=[-.63267338664325317126,.71256610349793047281] 
dist 195=[-.6707950202870701817 ,.70919745097642554982] 
dist 196=[-.71052731161930850379,.7037245912800628543 ] 
dist 197=[-.76040903054345898254,.70101121903610577572] 
dist 198=[-.80947509250338447547,.6152006834866047018 ] 
dist 199=[-.8515759011184673123 ,.60187450612863874042] 
dist 200=[-.8838649897420306464 ,.57414792392492808998] 
dist 201=[-.91126242585561246726,.56581194739024938322] 
dist 202=[-.93346521026944352615,.52977702913464848232] 
dist 203=[-.94501750875865369447,.52197492819187481692] 
dist 204=[-.95100631998072089504,.50012604586147996882] 
dist 205=[-.95100186487662073265,.49577190171581738178] 
dist 206=[-.79943434524431387535,.42659301069737105148] 
dist 207=[-.79581709697396203116,.49388402994711285021] 
dist 208=[-.6688449976433574828 ,.55965565089237159846] 
dist 209=[-.65050234032479083521,.60497420481271913009] 
dist 210=[-.61571007272733777316,.64402597722885760055] 
dist 211=[-.60633067037085692243,.6847802856138769174 ] 
dist 212=[-.57207239999252936026,.7235508676368363087 ] 
dist 213=[-.56317819963118785341,.7546836428621252591 ] 
dist 214=[-.54847301755850804336,.7862114346149289874 ] 
dist 215=[-.54397662417432337805,.82655935918975000321] 
dist 216=[.05308458387169623850,.86412769332448052232] 
dist 217=[.06002383955194534634,.88455911288637180688] 
dist 218=[.10608860814750478633,.89636651883523016383] 
dist 219=[.11373944353948775196,.89950662408999537319] 
dist 220=[.1279267999246381914 ,.89904937115208394424] 
dist 221=[.13089522575903805214,.89649565578000914536] 
dist 222=[.15774315175260747193,.89191521425062014204] 
dist 223=[.1602330090261163371 ,.88905014013173126148] 
dist 224=[.1575835244553873941 ,.78992956017121193691] 
dist 225=[.14723619249384349094,.77433102983656547933] 
dist 226=[.13272993771547596171,.74236301673409484818] 
dist 227=[.11347697506835762929,.73276560467036980313] 
dist 228=[.08704740268244251106,.69160693985405892349] 
dist 229=[.04389119684362023876,.68239995204003046284] 
dist 230=[-.00227587368973863325,.65748090248218065205] 
dist 231=[-.04072554827449170689,.65384388353215823945] 
dist 232=[-.15986075201393713451,.4681698490805492762 ] 
dist 233=[-.27229792413008812719,.45076179480793564725] 
dist 234=[-.36509898452204198022,.41152233243833471798] 
dist 235=[-.45546798830985630095,.40120085911580236212] 
dist 236=[-.53744221209292345115,.34356266643739708776] 
dist 237=[-.59673093210246141602,.33426197806990616777] 
dist 238=[-.65080479181864841472,.32568239318916417132] 
dist 239=[-.71196128820743230159,.32389247040865610738] 
dist 240=[-.76794473038409491754,.21483588689861077772] 
dist 241=[-.80136729503559347834,.20086035466544687513] 
dist 242=[-.82468984311918086516,.17345990469985637184] 
dist 243=[-.84035265742452301955,.1664558560479725475 ] 
dist 244=[-.85099512025468418318,.14229708746448839924] 
dist 245=[-.85427611909560662054,.13665815916323613591] 
dist 246=[-.85384169912015491893,.13050595572265232157] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 2, 1, 1, 2] 
dist 0=[51.126995026469397521  ,51.126995026469397521  ] 
dist 1=[50.275238875972611409  ,51.790354126192094706  ] 
dist 2=[48.942005091539211320  ,52.370880488229452227  ] 
dist 3=[47.397887964654816323  ,52.828960753853751268  ] 
dist 4=[45.703749506209677189  ,53.003363395865022838  ] 
dist 5=[43.571106031005364969  ,53.040033201420189021  ] 
dist 6=[40.275504544400043172  ,52.991984249498482788  ] 
dist 7=[36.933118109030814363  ,52.459332889409625198  ] 
dist 8=[34.613607218043324694  ,52.275358452360973422  ] 
dist 9=[32.593606476055367956  ,51.935912374170767906  ] 
dist 10=[30.447532492268250294  ,51.806409818165286307  ] 
dist 11=[28.378739093772170864  ,48.519865104139164301  ] 
dist 12=[26.667479249085474194  ,47.962387706665070651  ] 
dist 13=[24.886645740559003290  ,47.294825103148895714  ] 
dist 14=[22.540151232847478478  ,46.451578215117734384  ] 
dist 15=[20.235256910605280549  ,41.187320762229478151  ] 
dist 16=[18.620624194020421230  ,37.980431552628214324  ] 
dist 17=[17.199366892617726253  ,35.463115547354951339  ] 
dist 18=[15.666785554242325558  ,35.280176230623331200  ] 
dist 19=[14.176753737234571960  ,27.797756173314355147  ] 
dist 20=[12.923466407668584231  ,26.835196087241814425  ] 
dist 21=[11.399620007088093439  ,24.931457690502572815  ] 
dist 22=[9.2811492686548699684 ,24.440978727654456965  ] 
dist 23=[7.2008608960500826506 ,22.711819780505244625  ] 
dist 24=[5.7534430974965437268 ,22.322089992655842096  ] 
dist 25=[3.2228704777789605050 ,21.781897968383052494  ] 
dist 26=[1.5389830564597625455 ,21.610279859062978444  ] 
dist 27=[.1457452012410797149 ,6.5190394615580323671 ] 
dist 28=[-1.2244168940693923570 ,6.0326721393335646052 ] 
dist 29=[-2.4848734819926946676 ,3.9172468090273208888 ] 
dist 30=[-4.2508176456661977372 ,2.9916173195868904686 ] 
dist 31=[-6.3842741434887870721 ,.1089397325533282606 ] 
dist 32=[-7.9748121083298978129 ,-.40837385190416116719] 
dist 33=[-9.4770465178277081462 ,-.91925060642581900862] 
dist 34=[-11.257724325319472327  ,-.99443741817212965403] 
dist 35=[-12.917159519320893381  ,-1.5279228309365233025 ] 
dist 36=[-13.935085990393567335  ,-1.6090731654137872664 ] 
dist 37=[-14.680896719952114400  ,-1.7432237501136863420 ] 
dist 38=[-15.253400818261692929  ,-1.7670087737836631649 ] 
dist 39=[-15.693805202515131710  ,-1.9433219050314454796 ] 
dist 40=[-15.912027755815926902  ,-1.9571235717085342555 ] 
dist 41=[-16.010114559241865979  ,-1.9404457868683995492 ] 
dist 42=[-16.017666441145559863  ,-1.8799857932004464608 ] 
dist 43=[-7.1428441468846028002 ,-1.7975967262592497280 ] 
dist 44=[-6.7265014068260105556 ,-1.6931758194646282686 ] 
dist 45=[-6.3735066043681050330 ,-1.2705294570893663982 ] 
dist 46=[-6.2878935387677903094 ,-.39283103337078465237] 
dist 47=[-6.0962075343334434564 ,.45130481731514714243] 
dist 48=[-6.0320998870246624835 ,1.1409702414500619345 ] 
dist 49=[-3.0708685105498142156 ,1.8490565161541444702 ] 
dist 50=[-3.0605671592638015789 ,2.7668764462252998408 ] 
dist 51=[-2.9447048433349508791 ,3.6578647941188308542 ] 
dist 52=[-2.9178053750436086313 ,4.2589575484663619163 ] 
dist 53=[-2.8863884658683702001 ,4.7627959039541398806 ] 
dist 54=[-2.8723401486759506925 ,5.2657502085703372178 ] 
dist 55=[.13730632069823487953,5.7300074610049225292 ] 
dist 56=[.31166250512366476462,6.0926156502454937383 ] 
dist 57=[.67663883715646335866,6.6730358395430488335 ] 
dist 58=[.75826891970394955759,7.0100337544763259195 ] 
dist 59=[1.0983304669711835830 ,7.2328892153410200787 ] 
dist 60=[1.1596460328861902290 ,7.3577232446604121461 ] 
dist 61=[1.2507916561871087377 ,7.4330411476810372230 ] 
dist 62=[1.2691075243731507708 ,7.4530603441830039063 ] 
dist 63=[1.2616625869370190318 ,7.3024971444973070543 ] 
dist 64=[0                     ,7.0513457654735601137 ] 
dist 65=[1.1320311216064896423 ,4.8803237810918840894 ] 
dist 66=[.97649706684030079332,5.0088121365408902655 ] 
dist 67=[.78655034794916360544,5.1212858350034362781 ] 
dist 68=[.56579138528110240705,5.1793265647143154976 ] 
dist 69=[.28011502053395993363,5.2091822131075068800 ] 
dist 70=[-.16900189524290373289,5.2089994419724908085 ] 
dist 71=[-.66196320340399466033,5.1916159749505336626 ] 
dist 72=[-1.0559410676370041220 ,5.1786260608672256366 ] 
dist 73=[-1.3867813095060732116 ,5.1142126132072399629 ] 
dist 74=[-2.0557363640778357038 ,5.0981897603921503799 ] 
dist 75=[-3.0332780114119432150 ,3.5222245623591444274 ] 
dist 76=[-3.6731638973319022136 ,3.5041049631588372266 ] 
dist 77=[-4.1887900444175706623 ,3.4903396498412270242 ] 
dist 78=[-4.6703011336935927179 ,3.4789335524986264152 ] 
dist 79=[-5.0936099274446223358 ,2.9375909186712916426 ] 
dist 80=[-5.3769091593164442072 ,2.8598756231006840526 ] 
dist 81=[-5.6122687324635982358 ,2.7157001237710263986 ] 
dist 82=[-5.8442380973528376799 ,2.6774927665966426806 ] 
dist 83=[-6.0425845302721376868 ,2.5428478544724332645 ] 
dist 84=[-6.1437162150293324208 ,2.5058648411028569809 ] 
dist 85=[-6.1932359566738783362 ,2.4568516048167263552 ] 
dist 86=[-6.2001739348113218732 ,2.4374360618114643790 ] 
dist 87=[-6.1553721301483129554 ,.28393880850041341284] 
dist 88=[-6.1276016162638734908 ,.14828507818004000579] 
dist 89=[-6.0673096993960805548 ,-.08914398961265078797] 
dist 90=[-6.0385926074198421969 ,-.12490002714014910043] 
dist 91=[-4.6566502623337882639 ,-.18190998387408960672] 
dist 92=[-4.5156079388504639798 ,.55894251229454305502] 
dist 93=[-4.1476907253835158188 ,1.1835390662831549272 ] 
dist 94=[-4.0927231745002546399 ,1.8131536688943514049 ] 
dist 95=[-3.4618776811313723865 ,2.3981276109641027706 ] 
dist 96=[-3.3367167618084601986 ,2.8445328950475356582 ] 
dist 97=[-3.2043520320735530065 ,3.2751259643156404939 ] 
dist 98=[-3.1741504093721844995 ,3.7969808292346287369 ] 
dist 99=[-1.8040696066582411866 ,4.2870540733304057018 ] 
dist 100=[-1.6346315341669415488 ,4.5907823105221631296 ] 
dist 101=[-1.1957173964680370144 ,4.8162840390316263303 ] 
dist 102=[-1.1965708881896969742 ,4.9940958511865114364 ] 
dist 103=[-1.0738870074298989851 ,5.1307472573280303644 ] 
dist 104=[-1.0582643943735753582 ,5.1919490062488101836 ] 
dist 105=[-1.0260527379747246897 ,5.2176550288062625348 ] 
dist 106=[-1.0158341807610528110 ,5.2137444324636567168 ] 
dist 107=[-.96957693737817072964,1.0479265259962916822 ] 
dist 108=[-.95910595541426996625,1.2719555577560858067 ] 
dist 109=[-.92786483900740814646,1.4490943686346121827 ] 
dist 110=[-.92182682356945834369,1.6088984801424092200 ] 
dist 111=[-.85081259987291954776,1.7456123366817973740 ] 
dist 112=[-.83670999174734472877,1.8305690109536886504 ] 
dist 113=[-.80595491044363907   ,1.8940381986868485947 ] 
dist 114=[-.79614979883286439576,1.9449761176904622384 ] 
dist 115=[-.75120101790228951531,1.9861584152608101802 ] 
dist 116=[-.74144284648369969294,2.0106774923539927761 ] 
dist 117=[-.71426323232770461928,2.0277785410682496619 ] 
dist 118=[-.70851510154084999779,2.0393292151276122985 ] 
dist 119=[1.0345105320366523164 ,2.0464969122679933722 ] 
dist 120=[1.1213891374042090377 ,2.0460912558020873269 ] 
dist 121=[1.3064609447948905747 ,2.0400805832671325203 ] 
dist 122=[1.0720715800884622351 ,2.0344935811567526863 ] 
dist 123=[.7881841452676688480 ,1.7129155628228854571 ] 
dist 124=[.5919093369781731789 ,1.7676230070306315119 ] 
dist 125=[.4221157935453975254 ,1.8069488930194986146 ] 
dist 126=[.2439277263498319386 ,1.8356258000313027782 ] 
dist 127=[.07383391975783675342,1.8561572326313873382 ] 
dist 128=[-.06365605746198004810,1.8629644434613712457 ] 
dist 129=[-.20371125521489238035,1.8615875759082147676 ] 
dist 130=[-.38405746861163896537,1.8583238504299089010 ] 
dist 131=[-.55895050389006772944,1.8274633771508154996 ] 
dist 132=[-.67724239633973334483,1.8172949991051716963 ] 
dist 133=[-.77685613755008035959,1.7865225970337084425 ] 
dist 134=[-.87719110737374817971,1.7755333823245492554 ] 
dist 135=[-.97048305334212012295,1.1625472346071814312 ] 
dist 136=[-1.0419887492539465490 ,1.1023605039709617958 ] 
dist 137=[-1.1113632132506405822 ,.95191343620319952882] 
dist 138=[-1.1961650362079634257 ,.93031440963426830619] 
dist 139=[-1.2749260276267635019 ,.69595960052979333618] 
dist 140=[-1.3201842022816926630 ,.65153980439570288423] 
dist 141=[-1.3496859373370955660 ,.60284441054308462638] 
dist 142=[-1.3655256740721239701 ,.59416617856144607842] 
dist 143=[-1.3747010830613693241 ,.18545302994848127092] 
dist 144=[-1.3775882879007290557 ,.13561126254236842895] 
dist 145=[-1.4033165148436097914 ,.03338112388826188970] 
dist 146=[-1.4542670358072420401 ,.00832851579204008973] 
dist 147=[-1.4935770790511046272 ,-.08444764916323570269] 
dist 148=[-1.5125106716160914157 ,-.10300456773148161351] 
dist 149=[-1.5207063111821856028 ,-.12707894359060489962] 
dist 150=[-1.5210868441644016368 ,-.13142906835000261605] 
dist 151=[-1.1450101271399214776 ,-.4580409571770856738 ] 
dist 152=[-1.1362452740180195878 ,-.48573711804303877356] 
dist 153=[-1.1096091076018121015 ,-.4890373917442322344 ] 
dist 154=[-1.1027233692259649184 ,-.2625856301566177169 ] 
dist 155=[-.90007634426596615326,-.03580125321486979133] 
dist 156=[-.93059771585424938925,.11604447799255667733] 
dist 157=[-.95349161814579064415,.24223265411454466224] 
dist 158=[-.97199333391945457057,.36658753632281343812] 
dist 159=[-.98603668684805039477,.48041527788040976394] 
dist 160=[-.99113200442709512254,.56457902259707834964] 
dist 161=[-.99149542463021816929,.64323888895662592588] 
dist 162=[-.98975535010408815654,.73509945294269476493] 
dist 163=[-.9717663886145651952 ,.82029208038679697825] 
dist 164=[-.96567622747427925741,.87233139149766572723] 
dist 165=[-.95135722462630498498,.91012633652821911837] 
dist 166=[-.94539946743964436844,.93844479245069174729] 
dist 167=[-.81323918185185442709,.95973841829426388486] 
dist 168=[-.80734175916129250583,.96948700858582135229] 
dist 169=[-.79145058448513786379,.97301444668646048175] 
dist 170=[-.78491286377921470508,.97266540175677351345] 
dist 171=[-.74943486558456011436,.77519769004159611024] 
dist 172=[-.74051932513851110172,.83475431260211971694] 
dist 173=[-.7224880065472893271 ,.88826746613787494922] 
dist 174=[-.71652445244557086822,.94759011806194992064] 
dist 175=[-.61028099693375409762,1.0008605491954296306 ] 
dist 176=[-.59431597663736650464,1.0302126589182487983 ] 
dist 177=[-.55589887310815705513,1.0476903941788313291 ] 
dist 178=[-.54661931309977615249,1.0535562509060514806 ] 
dist 179=[-.48729295795145550051,1.0549705503728317020 ] 
dist 180=[-.47503833740069986402,1.0546771247534695020 ] 
dist 181=[-.45245657077102157172,1.0530784665921798627 ] 
dist 182=[-.44641899068395909265,1.0494480112334323248 ] 
dist 183=[-.44636405080667227899,.8644848619489395749 ] 
dist 184=[-.52354891413846744623,.84211833546514779639] 
dist 185=[-.60983525002962465075,.78376298122623216591] 
dist 186=[-.73123000030817046296,.77402156975006859674] 
dist 187=[-.84939641978088314415,.71349345063170662728] 
dist 188=[-.92279577470196315854,.70367847449627990685] 
dist 189=[-.97754016180195063482,.68290428342126806116] 
dist 190=[-1.0212303143534653266 ,.67612014252512905486] 
dist 191=[-1.0556686353583750924 ,.57450935881283127142] 
dist 192=[-1.0734761608195091230 ,.55924738258427910208] 
dist 193=[-1.0825349482341486943 ,.52059518619507702699] 
dist 194=[-1.0838554036012869283 ,.5234049947280869572 ] 
dist 195=[-1.0355861105164250831 ,.54492975684265432097] 
dist 196=[-1.0254554257394981616 ,.56253334991589607472] 
dist 197=[-1.0122869027556487935 ,.59011059353041068678] 
dist 198=[-1.0062421347146876875 ,.63779997326867889942] 
dist 199=[-.99108000346678990823,.70228799653682104942] 
dist 200=[-.98420869807169020691,.74109755674723696907] 
dist 201=[-.97530803658315949357,.76854600947734756987] 
dist 202=[-.970646005894201121  ,.78768181840017938038] 
dist 203=[-.84363579122016086082,.80731350389649017591] 
dist 204=[-.88924191277542315869,.83336761725369647425] 
dist 205=[-.92638708954607412   ,.8513674826552000745 ] 
dist 206=[-.96174366873150532246,.86308870208778105649] 
dist 207=[-.99199068438258209866,.87002949960701424563] 
dist 208=[-1.0087378518092246670 ,.87105273778672986849] 
dist 209=[-1.0188181807567753063 ,.86578649887033753555] 
dist 210=[-1.0224491003992421719 ,.86443204913937640723] 
dist 211=[-1.0218353755446932383 ,.81880290783920193756] 
dist 212=[-1.0201591105757136902 ,.80975771454020368241] 
dist 213=[-1.0076324903027909639 ,.78518038704490304389] 
dist 214=[-1.0051264102066994163 ,.77798178718387115307] 
dist 215=[-.23374745219828984169,.72749751128367542561] 
dist 216=[-.18108289354812743848,.71578048624150926226] 
dist 217=[-.05892815512535287822,.71371064647153249648] 
dist 218=[-.18152700791553660441,.74489994415534137343] 
dist 219=[-.37556305468257544058,.7730044375233802953 ] 
dist 220=[-.50287031223660021491,.7875290232573120815 ] 
dist 221=[-.60575394236995782157,.7949522151505480450 ] 
dist 222=[-.70229247239702572344,.7963519831078309023 ] 
dist 223=[-.78742858427979778226,.7913631504595070432 ] 
dist 224=[-.84479402839879648209,.7878098559576643189 ] 
dist 225=[-.89283254588959586251,.7829565714186755338 ] 
dist 226=[-.94073476170562088726,.7800033908944270675 ] 
dist 227=[-.98314165136284286437,.6847254441409874677 ] 
dist 228=[-1.0092433757345775982 ,.6701125950615212501 ] 
dist 229=[-1.0284082462312681335 ,.6401067383542064094 ] 
dist 230=[-1.0431256493505403362 ,.6312269853505293947 ] 
dist 231=[-1.0538615207678874661 ,.5936849701947720790 ] 
dist 232=[-1.0571334089513459547 ,.5853670773851359832 ] 
dist 233=[-1.0558562778286030977 ,.5634516778103037700 ] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 0, 2, 1, 2] 
dist 0=[47.251622872495230866  ,47.251622872495230866  ] 
dist 1=[46.899650652325445271  ,47.654647016625596484  ] 
dist 2=[46.484878831830342601  ,48.272873423214821839  ] 
dist 3=[45.819765599449088159  ,48.869018111233937092  ] 
dist 4=[44.467944827892793259  ,49.183869081854192715  ] 
dist 5=[42.840911843000650983  ,49.352646649867024276  ] 
dist 6=[41.076682538961571144  ,49.365804897643267794  ] 
dist 7=[38.869846345282887029  ,49.293780017150956233  ] 
dist 8=[35.474952681619288443  ,49.228787927185270645  ] 
dist 9=[32.040954464861662905  ,48.942368190699430488  ] 
dist 10=[29.677807456756330288  ,48.836668233830029949  ] 
dist 11=[27.640490199102108683  ,47.231449901511174002  ] 
dist 12=[25.507563952831448734  ,46.897948356155913694  ] 
dist 13=[23.468877263663157513  ,45.697623298877810551  ] 
dist 14=[21.807693198824264422  ,43.688086077280171203  ] 
dist 15=[20.099278802354269981  ,34.553918592791491622  ] 
dist 16=[17.871472297425067880  ,33.910091614523293708  ] 
dist 17=[15.687095666293618649  ,33.202156782968629917  ] 
dist 18=[14.151891251017807352  ,33.018428913518417235  ] 
dist 19=[12.791663073607616814  ,26.514802509226075798  ] 
dist 20=[11.305880588059576833  ,25.673736244872957680  ] 
dist 21=[9.8435256893134402208 ,24.001123702476872290  ] 
dist 22=[8.5763999076921967614 ,23.567289146691328206  ] 
dist 23=[7.2015458549156995984 ,22.017062181232285608  ] 
dist 24=[5.3077896043227844134 ,21.672936098252094883  ] 
dist 25=[3.4569740442722170034 ,21.143046574142387569  ] 
dist 26=[2.2535611712180841494 ,20.993490841799249722  ] 
dist 27=[1.2850930411840349107 ,13.253648617650239230  ] 
dist 28=[.37359151889430784871,12.842150998384685746  ] 
dist 29=[-.44048587112693510963,11.665043037694141431  ] 
dist 30=[-2.3144120473055279620 ,11.001963481246812757  ] 
dist 31=[-4.1848586866791269302 ,-.24645020522291169902] 
dist 32=[-5.5658011079955704583 ,-.80148794348362832109] 
dist 33=[-6.8575027333530911867 ,-1.2771359496019743949 ] 
dist 34=[-8.3714902122802311721 ,-1.3226809593910866541 ] 
dist 35=[-9.7789351763534312647 ,-1.2715855191572842157 ] 
dist 36=[-10.645049644314446485  ,-1.0793468798241269635 ] 
dist 37=[-11.283688298804651149  ,-.81453850679791803194] 
dist 38=[-11.782456839895151685  ,-.47356902067920477792] 
dist 39=[-12.170698660129642609  ,-.01355277238679323810] 
dist 40=[-12.367769014224457926  ,.72642409218536106512] 
dist 41=[-12.463424826146134256  ,1.4761440194571563812 ] 
dist 42=[-12.475177988964925044  ,1.9751803853062919770 ] 
dist 43=[-10.184684515211404920  ,2.3846378852405911314 ] 
dist 44=[-10.228485665919619193  ,2.7772013832690880092 ] 
dist 45=[-10.252371792443028202  ,3.1276022871632085340 ] 
dist 46=[-10.256022310309815350  ,3.3689424129746211482 ] 
dist 47=[-5.6200456156042689409 ,3.5760344294427427037 ] 
dist 48=[-5.3992222503275029125 ,3.7898618747068385644 ] 
dist 49=[-5.1606530809252985198 ,3.9802348340633007173 ] 
dist 50=[-5.1171718503876951233 ,4.0937422719749220349 ] 
dist 51=[-3.0248294190648995257 ,4.1722996888761681932 ] 
dist 52=[-2.7679122632578600434 ,4.2231462001247146040 ] 
dist 53=[-2.2440088440707766288 ,4.2515811291399946110 ] 
dist 54=[-2.1103963828750432500 ,4.2536364088555947152 ] 
dist 55=[-1.6407329785952730323 ,4.2198014403470678299 ] 
dist 56=[-1.5439474391547711090 ,4.2091533001762478647 ] 
dist 57=[-1.4202000092180208897 ,2.6169125810473536291 ] 
dist 58=[-1.3957852631993398505 ,2.4684152938647467014 ] 
dist 59=[1.1194057968334134230 ,2.8607719803312198766 ] 
dist 60=[1.1888415975312634359 ,3.2399477628223865074 ] 
dist 61=[1.3025809203219637416 ,3.6262130848405552145 ] 
dist 62=[1.1595695766571031942 ,4.1248573828228425436 ] 
dist 63=[.88285491393932036265,4.5986942804146468732 ] 
dist 64=[.50953476176430007275,4.8859218820176142920 ] 
dist 65=[.13980165704017054849,5.0925958948987983146 ] 
dist 66=[-.12262764939335106952,5.2446689752760235037 ] 
dist 67=[-.3568754826896594931 ,5.3591445549571587985 ] 
dist 68=[-.61416208285335099351,5.4156081938820009911 ] 
dist 69=[-.86691685758663881585,5.4407303754281442684 ] 
dist 70=[-1.0831147114100931218 ,5.4400027952314306598 ] 
dist 71=[-1.3142842365239638789 ,5.1006204532489730709 ] 
dist 72=[-1.6268736000897000781 ,5.0403301882472557695 ] 
dist 73=[-1.9310682321700732384 ,5.0174609099104011367 ] 
dist 74=[-2.1287343123723788143 ,5.0152536906238528007 ] 
dist 75=[-2.2866212932457353961 ,4.7950573560874155766 ] 
dist 76=[-2.4319748786623368210 ,4.7579488029857691548 ] 
dist 77=[-2.5585440077332042675 ,4.6916895431260862859 ] 
dist 78=[-2.6414264621814783490 ,4.6691228512048062891 ] 
dist 79=[-2.7084002835431815048 ,1.9249953158063852361 ] 
dist 80=[-2.7951512071093179308 ,1.6918633633179537647 ] 
dist 81=[-3.0689305392645205547 ,1.1436228691320905830 ] 
dist 82=[-3.3899960906941208465 ,1.0586485853320063324 ] 
dist 83=[-3.6866494793864054264 ,.3233856813669056983 ] 
dist 84=[-3.8629915357497255552 ,.23282722753471559374] 
dist 85=[-3.9852972998551131389 ,.47613990364804927736] 
dist 86=[-4.0662447312339740828 ,.7240224073057438615 ] 
dist 87=[-4.1208167242479716609 ,1.0229009873960330942 ] 
dist 88=[-4.1377974564420034432 ,1.4698039567293207776 ] 
dist 89=[-4.1353364586459302858 ,1.9152917925670792461 ] 
dist 90=[-4.1267403965445685703 ,2.2085268665925205121 ] 
dist 91=[-3.9391447804273044815 ,2.4466054111105784520 ] 
dist 92=[-3.9028323872163538200 ,2.6719112662646270688 ] 
dist 93=[-3.7870425672994116309 ,2.8719733582968790877 ] 
dist 94=[-3.7655043814848834188 ,3.0092812237936060227 ] 
dist 95=[-3.4875504166950708198 ,3.1270345686155007642 ] 
dist 96=[-3.4248405445579679306 ,3.2490394329372784233 ] 
dist 97=[-3.3615755398600580425 ,3.3533390569846046828 ] 
dist 98=[-3.3354739188559601632 ,3.4004120587394112471 ] 
dist 99=[-2.5281702133314979315 ,3.4226968029816257236 ] 
dist 100=[-2.4195027020331862558 ,3.4280352010313268145 ] 
dist 101=[-2.2015328230374585653 ,3.5636388446851433384 ] 
dist 102=[-2.1432767383800177186 ,3.7039176531638555865 ] 
dist 103=[-1.9270382033056076785 ,3.8186887666176174591 ] 
dist 104=[-1.8786726470950759522 ,3.8801931518356605377 ] 
dist 105=[-1.7910281694688042954 ,3.9144814881994657152 ] 
dist 106=[-1.7684248430106969476 ,3.9206285181002587515 ] 
dist 107=[-1.3136579423423212902 ,3.0449856331037190675 ] 
dist 108=[-1.6792781912393385087 ,3.0292873121202012438 ] 
dist 109=[-2.0155227965273564152 ,2.8115891219975969193 ] 
dist 110=[-2.2665027753245131111 ,2.7619591856745109060 ] 
dist 111=[-2.5032579902004557631 ,2.7151132756804616855 ] 
dist 112=[-2.7827121648546077854 ,2.6967164218785773019 ] 
dist 113=[-3.0414498680327664553 ,2.0362590443044898503 ] 
dist 114=[-3.1955025756393202431 ,1.9474905493717269509 ] 
dist 115=[-3.3024462462125584230 ,1.8745523404854789207 ] 
dist 116=[-3.3731229235474728571 ,1.9534869046072208084 ] 
dist 117=[-3.4227987601868257855 ,2.0140779414159307855 ] 
dist 118=[-3.4459127106927071298 ,2.0656124435273327340 ] 
dist 119=[-3.4539999739312857161 ,2.1074750428864385875 ] 
dist 120=[-3.4491245071995790452 ,2.1294468644044792029 ] 
dist 121=[-.4763297588018175836 ,2.1410880069494079129 ] 
dist 122=[-.47158219828505543694,2.1417008879185859626 ] 
dist 123=[-.47127697190229291618,1.9462659061567775760 ] 
dist 124=[-.4777893712691039698 ,1.9521094272897680230 ] 
dist 125=[-.49049731772686941795,1.9520684994847873798 ] 
dist 126=[-.51492406375102381264,1.9477834311822544057 ] 
dist 127=[-.54064129722738405193,1.0694319176959084119 ] 
dist 128=[-.55850471276497607869,.99467619699233500018] 
dist 129=[-.57401166257066213814,.8196940105365729531 ] 
dist 130=[-.59033392014697109817,.78787357670141889143] 
dist 131=[-.60592396734786984692,.55082372438801400376] 
dist 132=[-.61851495367178815368,.50727948385957769052] 
dist 133=[-.63133001836886809647,.43558695969794495851] 
dist 134=[-.64782339584807852887,.41819761997394062999] 
dist 135=[-.76862804217344943495,.29658468466745421967] 
dist 136=[-.93482107154161046323,.28223683634045100515] 
dist 137=[-1.1202624691151254732 ,.26049091592701995683] 
dist 138=[-1.3807464000316326164 ,.25457547881766261117] 
dist 139=[-1.6347351408650335847 ,.24333716291193563392] 
dist 140=[-1.7942480970309729404 ,.34745508893816019993] 
dist 141=[-1.9152882928578669886 ,.47171683921267016135] 
dist 142=[-2.0156790053015804655 ,.68250130660776965301] 
dist 143=[-2.0961313913814086481 ,.89576483130280299538] 
dist 144=[-2.1375678247502834656 ,1.0329482193260319154 ] 
dist 145=[-2.1594105007629030006 ,1.1407121058157125918 ] 
dist 146=[-2.1632285025884262582 ,1.2365406811680165434 ] 
dist 147=[-2.1149020048252181086 ,1.3173762619947484850 ] 
dist 148=[-2.1005673782244685002 ,1.3652899874598428047 ] 
dist 149=[-2.0856707477621134718 ,1.3982523330871259905 ] 
dist 150=[-2.0757600603441724075 ,1.4193998809657326910 ] 
dist 151=[-2.0523080678403313902 ,1.4342895897506207956 ] 
dist 152=[-2.0404228975680364916 ,1.4422731734770974570 ] 
dist 153=[-2.0199142237444648394 ,1.4466971558161816060 ] 
dist 154=[-2.0115025404271777027 ,1.4473865780714357183 ] 
dist 155=[-1.4532769906925657711 ,1.4455972856901633652 ] 
dist 156=[-1.4383559655652724059 ,1.4408294796505087472 ] 
dist 157=[-1.4179486582176628974 ,1.4314616309554887725 ] 
dist 158=[-1.4092936269182612006 ,1.4262583296652932069 ] 
dist 159=[-.17421228502450162513,.3492519802465592977 ] 
dist 160=[-.1164660017506565721 ,.49343298413586935288] 
dist 161=[-.04261791560526710007,.63380312930539116156] 
dist 162=[-.02687799510365365084,.80587068005236060587] 
dist 163=[.39709735774580299489,.9686128928894602577 ] 
dist 164=[.44695654440832795382,1.0717534113461332390 ] 
dist 165=[.55682257585940253708,1.1510868513470044658 ] 
dist 166=[.57438503019109518838,1.2187837003260161470 ] 
dist 167=[.6929473504508961006 ,1.2738951685382606256 ] 
dist 168=[.71110529906804944395,1.3029836613620412444 ] 
dist 169=[.74477018597590615614,1.3190096815619248653 ] 
dist 170=[.75095447944549301159,1.3224088111221137062 ] 
dist 171=[.84855453917477959008,1.2864251364037030213 ] 
dist 172=[.85243029519339130511,1.2967717625816500054 ] 
dist 173=[.84283022396781199145,1.2996145135402124414 ] 
dist 174=[.81502631747013237458,1.2988216630404500056 ] 
dist 175=[.72770198746743283844,.89656246449828794583] 
dist 176=[.63204412315143911353,.89782992627548152017] 
dist 177=[.54331188865674514879,.89580669416865839624] 
dist 178=[.44073118803340361298,.89384394421981996801] 
dist 179=[.33699556998489651714,.88617991365178126502] 
dist 180=[.24365281476945699231,.88243883334846039444] 
dist 181=[.13996534932040796628,.87545970874598796401] 
dist 182=[-.00506721480741182983,.87216845701631980959] 
dist 183=[-.15114990634180128818,.85322862906410901731] 
dist 184=[-.25902946131720344837,.84808437603529716825] 
dist 185=[-.35967265556680892253,.82908193095554382441] 
dist 186=[-.54209326366519398152,.82583555017226960884] 
dist 187=[-.78010617875719259609,.77165876615972869899] 
dist 188=[-.93447713510477222163,.760160221385375977  ] 
dist 189=[-1.0572791456217118430 ,.73915978197303628649] 
dist 190=[-1.1692635531701799146 ,.73301134773360239895] 
dist 191=[-1.2658453946174253177 ,.70853479294998758364] 
dist 192=[-1.3271581647219180921 ,.70160867563038325663] 
dist 193=[-1.3744363544344336513 ,.68688346183485462655] 
dist 194=[-1.4149909385091935033 ,.68166633288188176046] 
dist 195=[-1.4486156782195902405 ,.65696308378806243652] 
dist 196=[-1.4742625393390867882 ,.64971242001113478706] 
dist 197=[-1.4874773658487536004 ,.64003880124813449099] 
dist 198=[-1.4896768192553000150 ,.63589757464730571214] 
dist 199=[-1.4312988209152819898 ,.625827047818414451  ] 
dist 200=[-1.4183434868091361807 ,.62125709292072731879] 
dist 201=[-1.3625274483046311524 ,.61627700211451273719] 
dist 202=[-1.2977644339083026379 ,.61318365523147825314] 
dist 203=[-1.2551104119380705654 ,.6060008726854558267 ] 
dist 204=[-1.2517464816790143892 ,.60294835668371583408] 
dist 205=[-1.2489660670703181424 ,.60068099941815378084] 
dist 206=[-1.2462461588586793840 ,.5988739315590178147 ] 
dist 207=[-.44215868250139352891,.59748800266657703096] 
dist 208=[-.37675075550693779517,.59690367193539708835] 
dist 209=[-.29547890407339016469,.59678995133100505625] 
dist 210=[-.2837197580325440073 ,.5972845990321257101 ] 
dist 211=[-.08487834055453996272,.59806783138536504014] 
dist 212=[-.05855533421069952558,.59910743773733211959] 
dist 213=[-.05615409803231565028,.60053712815641248919] 
dist 214=[-.14574557089370309335,.60287951830808919012] 
dist 215=[-.24153321842342843974,.60564118791031870259] 
dist 216=[-.33567248265220411137,.608746455412872591  ] 
dist 217=[-.44670052358366417327,.64065052639713648974] 
dist 218=[-.60990539476103833842,.75643979538277825432] 
dist 219=[-.77118807026647757394,.86901758927728663469] 
dist 220=[-.87454223749800816379,.94110505292823621696] 
dist 221=[-.95531547040199038756,.99740379284731418371] 
dist 222=[-1.0264564418781665154 ,1.0469505262157134473 ] 
dist 223=[-1.0860039188648450013 ,1.0884222230038435848 ] 
dist 224=[-1.1204961018697926804 ,1.1124845643963016050 ] 
dist 225=[-1.1432526327461405389 ,1.1284287564393370524 ] 
dist 226=[-1.1559505416345688209 ,1.1374927571991241900 ] 
dist 227=[-1.1637196436716923637 ,1.1417844430618628171 ] 
dist 228=[-1.1668007949598613782 ,1.1410829415884975961 ] 
dist 229=[-1.1670300956231226668 ,1.1332765266642691799 ] 
dist 230=[-1.1639491838422657752 ,1.1284149982617297212 ] 
dist 231=[-1.1575969497181652358 ,1.0887325069211961887 ] 
dist 232=[-1.1529011032144747039 ,1.0776359547316571351 ] 
dist 233=[-1.1396107381637723493 ,1.0612467660830372120 ] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 0, 0, 1, 2] 
dist 0=[41.587797596010233584  ,41.587797596010233584  ] 
dist 1=[41.339777035455999262  ,41.796850780166759022  ] 
dist 2=[40.509098965506104355  ,42.471732386388398438  ] 
dist 3=[39.214592973889007020  ,43.190180358686439921  ] 
dist 4=[37.114166711244188033  ,43.573011469436544269  ] 
dist 5=[34.958702594549998714  ,43.782930054538610997  ] 
dist 6=[33.444294416761127121  ,43.828385015923922808  ] 
dist 7=[32.105728253880911602  ,43.771018829191567128  ] 
dist 8=[30.652271098850676777  ,43.713557547540466102  ] 
dist 9=[29.230939525665369516  ,43.630480589919951869  ] 
dist 10=[28.020426458324809992  ,43.564358035685708962  ] 
dist 11=[26.728205466228802460  ,43.320628186970956560  ] 
dist 12=[24.980073090381742218  ,43.224224540714485042  ] 
dist 13=[23.235784043034379934  ,42.944289960622312629  ] 
dist 14=[21.958673056549512540  ,42.817929671056834196  ] 
dist 15=[20.773485686603319944  ,33.381666822662025990  ] 
dist 16=[19.396081508444871174  ,32.516649231765144785  ] 
dist 17=[17.991566305492244211  ,30.390709858834644180  ] 
dist 18=[16.697649853149833332  ,30.069181500456150383  ] 
dist 19=[15.229054624320713355  ,26.823011169663955002  ] 
dist 20=[13.125793093850214225  ,26.201505620549355506  ] 
dist 21=[11.045360845290585592  ,25.486980028555380770  ] 
dist 22=[9.6678754529330763761 ,25.313493892926334373  ] 
dist 23=[8.5325218411925122692 ,19.537253068701217294  ] 
dist 24=[7.4200341222532153680 ,18.801543674354349649  ] 
dist 25=[6.3980113004670245039 ,17.320228958390586542  ] 
dist 26=[5.6242203787475621596 ,16.936742093397158817  ] 
dist 27=[4.7970591622847898208 ,15.559917034464401266  ] 
dist 28=[3.1729909445703288002 ,15.266334377766647354  ] 
dist 29=[1.3562811152076555630 ,14.794621312210755831  ] 
dist 30=[-1.2120737418620792658 ,14.672651657763908996  ] 
dist 31=[-3.7269868919154450603 ,4.0746993724621390654 ] 
dist 32=[-5.3302846016921661344 ,3.1821325388725576094 ] 
dist 33=[-6.5823868750289916517 ,1.9743521339907289955 ] 
dist 34=[-7.6936651069582011643 ,1.8821748095883093753 ] 
dist 35=[-8.6383961299497943457 ,1.7058913072451833587 ] 
dist 36=[-9.2249912707237446097 ,1.6697217629511972103 ] 
dist 37=[-9.6665450734606423876 ,.7566135659061090332 ] 
dist 38=[-10.031990730547011728  ,.66788074517250264603] 
dist 39=[-10.332928108893829897  ,.47379379652834004964] 
dist 40=[-10.516614141163350598  ,.44379452036850982598] 
dist 41=[-10.652642724931281597  ,.22140411572679816567] 
dist 42=[-10.762562996493588699  ,.1832264244120519572 ] 
dist 43=[-10.849619108425178812  ,.12787500072507633876] 
dist 44=[-10.924070172474034035  ,.11373076114876666561] 
dist 45=[-11.000481516078346352  ,-.1184321992536692507 ] 
dist 46=[-11.015186797847642773  ,-.14848302608677541756] 
dist 47=[-5.7524613147975672392 ,-.21033632855546538825] 
dist 48=[-5.4445345015257160555 ,-.22684776471468697358] 
dist 49=[-4.6912529459400186262 ,-.29124604183986958056] 
dist 50=[-4.5792735420606003632 ,-.30368773125070431615] 
dist 51=[-3.9644025110250136011 ,-.33512593782113704869] 
dist 52=[-3.7009061024985492626 ,-.34068853052941201792] 
dist 53=[-3.0132069899779096165 ,-.66736145691353961089] 
dist 54=[-2.9596025669390860066 ,.20529978005988297828] 
dist 55=[-1.2583721088356269638 ,1.0547364649655469646 ] 
dist 56=[-1.0523405828416708024 ,1.6354603220158498626 ] 
dist 57=[-.92719746391456612921,2.1314778115683302333 ] 
dist 58=[-.97613095736001121362,2.6428189970012448673 ] 
dist 59=[-1.0261981814300824595 ,3.1262580852732433882 ] 
dist 60=[-1.0906592097148125180 ,3.5109695119457093608 ] 
dist 61=[-1.1526499165390279594 ,3.8981903540033350965 ] 
dist 62=[-1.1928598833020660457 ,4.3918326787036410301 ] 
dist 63=[-1.2246449474816705518 ,4.8581003301721862932 ] 
dist 64=[-1.2530278276718643481 ,5.1360362430618394262 ] 
dist 65=[-1.2768389949255608533 ,5.3304061142117168145 ] 
dist 66=[-1.2903777987132583500 ,5.4628781971225779766 ] 
dist 67=[-1.2988288618594266001 ,5.5595740905478878472 ] 
dist 68=[-1.3023167552279517407 ,5.6109998183606948588 ] 
dist 69=[-1.3014913682730917786 ,5.6394655874720190899 ] 
dist 70=[-1.2990588798569471768 ,5.6443323681034730042 ] 
dist 71=[-1.2830626752894004136 ,5.1447500120728563027 ] 
dist 72=[-1.2786701824450341666 ,5.0662867098379355375 ] 
dist 73=[-1.2130163382620748620 ,4.9437054052639438397 ] 
dist 74=[-1.1961249639752339960 ,4.9045597964622932042 ] 
dist 75=[-1.1804545503181426018 ,4.8004294745028555737 ] 
dist 76=[-1.1712475841433316254 ,4.7627180412325389390 ] 
dist 77=[-.91115126903566099519,4.7379618964563993630 ] 
dist 78=[-.90624010400705772418,4.7243307526064236626 ] 
dist 79=[-1.5853121374335518117 ,1.5410782493448831199 ] 
dist 80=[-2.0335546843606395771 ,1.5034664960908340106 ] 
dist 81=[-2.3989061929043652657 ,1.5175463104490202480 ] 
dist 82=[-2.7470934054515277239 ,1.5204203480875232284 ] 
dist 83=[-3.0579996612117459822 ,1.5174813620410279486 ] 
dist 84=[-3.2745406825035941774 ,1.5132254279329594634 ] 
dist 85=[-3.4636940502320859557 ,1.3923945001303396743 ] 
dist 86=[-3.6652977931339179067 ,1.3733324158786863167 ] 
dist 87=[-3.8431058408768639989 ,1.3163450575210937460 ] 
dist 88=[-3.9372652225595558957 ,1.3075743357641366664 ] 
dist 89=[-3.9883676938868972429 ,1.1830737761191268729 ] 
dist 90=[-3.9996365097577331427 ,1.1560280317982474696 ] 
dist 91=[-3.9842674488180705884 ,1.1317782418948135533 ] 
dist 92=[-3.9719590286645185680 ,1.1252656156894971361 ] 
dist 93=[-3.9556653849306608100 ,1.1137572564356832409 ] 
dist 94=[-3.9394946897847106780 ,1.1965047795277918716 ] 
dist 95=[-3.2010555448374251367 ,1.2651714069494358042 ] 
dist 96=[-3.1156750897978232250 ,1.3326095880123338052 ] 
dist 97=[-2.8872424918049315157 ,1.3941251288456491368 ] 
dist 98=[-2.8544382968721621729 ,1.4391505503363774068 ] 
dist 99=[-2.4444238673602207405 ,1.6776985024118450102 ] 
dist 100=[-2.3619870028558253004 ,1.9654817128366389566 ] 
dist 101=[-2.2813716473417493980 ,2.2429355828202768155 ] 
dist 102=[-2.2662431218143469512 ,2.5789375258124181531 ] 
dist 103=[-1.3737261785626971510 ,2.8942571335751248096 ] 
dist 104=[-1.2615780749566136049 ,3.0891567371969634061 ] 
dist 105=[-1.0556908469870250917 ,3.2332125997408765118 ] 
dist 106=[-1.0282434518268275672 ,3.3455864987258242613 ] 
dist 107=[-1.0830756533356102692 ,3.4309124400043847332 ] 
dist 108=[-1.1864111230567267979 ,3.4670044614233520680 ] 
dist 109=[-1.2836603502282727580 ,3.4807973598552778148 ] 
dist 110=[-1.3442455427797057869 ,3.4771177998884696978 ] 
dist 111=[-1.3895832891745006213 ,1.1461161283417783758 ] 
dist 112=[-1.4259672878896067121 ,1.2102888346054156141 ] 
dist 113=[-1.4537933855693916520 ,1.4115325964011695454 ] 
dist 114=[-1.4649674329690836885 ,1.5950026576289947508 ] 
dist 115=[-1.4679402755809907383 ,1.7532518178889143326 ] 
dist 116=[-1.4656686275245703708 ,1.8538097906576686667 ] 
dist 117=[.36838235073426377874,1.9314950976731909836 ] 
dist 118=[.37760730171210186419,1.9984373915412433037 ] 
dist 119=[.39407818739012250194,2.0548709584964051888 ] 
dist 120=[.38438724397425079859,2.0906020736122339493 ] 
dist 121=[.36009062896609191824,2.1180826389870722626 ] 
dist 122=[.30957674353638994544,2.1415692946726415854 ] 
dist 123=[.2461039704737241599 ,2.1607502052453078139 ] 
dist 124=[.17007027312705542138,2.1710369233866684636 ] 
dist 125=[.0702571908013420680 ,2.1768024292996422778 ] 
dist 126=[-.0881445412748787726 ,2.1779296405758270212 ] 
dist 127=[-.2490876631185748319 ,1.5651567944021148991 ] 
dist 128=[-.3590501120871764800 ,1.5387775532972151005 ] 
dist 129=[-.4527764802962921369 ,1.4633348910877875033 ] 
dist 130=[-.5489157674416367265 ,1.4522650014850273745 ] 
dist 131=[-.67332510240419203421,1.2991745530428703878 ] 
dist 132=[-.7976508486247733638 ,1.2668439067709653045 ] 
dist 133=[-.92064762435337908131,1.2376207854285795090 ] 
dist 134=[-1.0741172457258482437 ,1.2312367890840644818 ] 
dist 135=[-1.2205718787005436188 ,.84117951324289710104] 
dist 136=[-1.3155695223947088445 ,.79088654456061798473] 
dist 137=[-1.3911547624318619033 ,.69265652199924209083] 
dist 138=[-1.4601206397446177702 ,.6675133993585782388 ] 
dist 139=[-1.5196608437549417628 ,.58084163631397789992] 
dist 140=[-1.5576250766970468650 ,.56035096034490249526] 
dist 141=[-1.5871324297892372267 ,.53826011768535983211] 
dist 142=[-1.6129258487114151292 ,.53269162312889049812] 
dist 143=[-1.6320894900987089472 ,.47768923639496078069] 
dist 144=[-1.6358414268224821836 ,.62089034934029798329] 
dist 145=[-1.6325708888653668999 ,.73960695143386555478] 
dist 146=[-1.6499586067853533983 ,.85598088195504807513] 
dist 147=[-1.6914361687744949199 ,.96196573507137972093] 
dist 148=[-1.7085334878714408118 ,1.0392136157268108402 ] 
dist 149=[-1.7154451442405029940 ,1.1102159851476082702 ] 
dist 150=[-1.7162549999784302680 ,1.1912697538339794422 ] 
dist 151=[-1.6629300418530808936 ,1.2648110926553596636 ] 
dist 152=[-1.6498022072463300885 ,1.3058266924187394342 ] 
dist 153=[-1.6217624428753970029 ,1.3308647407378227698 ] 
dist 154=[-1.6112157152953711218 ,1.3406311564821235852 ] 
dist 155=[-1.5568596445684196634 ,1.3442485255988376730 ] 
dist 156=[-1.5437494046983379066 ,1.3447441481538498795 ] 
dist 157=[-1.5020645130980561164 ,1.3430385259354895001 ] 
dist 158=[-1.4936626753977097366 ,1.3384877840820618244 ] 
dist 159=[-1.0197349045427603657 ,.28153391858117261359] 
dist 160=[-.99519684563598850241,.46774151393685568876] 
dist 161=[-.93460516217432052955,.6227258072396164782 ] 
dist 162=[-.92082816209530369624,.77582046648551242203] 
dist 163=[-.82207935716944369139,.91614739243129421774] 
dist 164=[-.80148433374464603824,1.0201583903616165598 ] 
dist 165=[-.76694045219876460772,1.1175769382277907166 ] 
dist 166=[-.75748468040217954907,1.2315823247264009828 ] 
dist 167=[-.56088821794420684438,1.3366606474987539820 ] 
dist 168=[-.53376476417294577968,1.3984390193795553789 ] 
dist 169=[-.47087900466961299638,1.4403685292209963051 ] 
dist 170=[-.45692680219338320276,1.4662048060491511812 ] 
dist 171=[-.37062921349530255746,1.4836073287114088124 ] 
dist 172=[-.3539468763055539158 ,1.4918713319951611975 ] 
dist 173=[-.32220664596069684506,1.4950299159829687315 ] 
dist 174=[-.31399751090511603799,1.4921798028324664172 ] 
dist 175=[.11279965030187391254,1.2595231200252642650 ] 
dist 176=[-.00712707431220602777,1.2524282800660502822 ] 
dist 177=[-.11260087410183304273,1.2278900383304076882 ] 
dist 178=[-.22602293570745891088,1.2212089050479911251 ] 
dist 179=[-.33596637989052243847,1.1534660870162318786 ] 
dist 180=[-.42755488774042516038,1.1370401726007911058 ] 
dist 181=[-.52330611434960849891,1.1166509926629898852 ] 
dist 182=[-.64986853848702171079,1.1078321784582583139 ] 
dist 183=[-.77410313447389077227,.88577440300331360071] 
dist 184=[-.86056252794804418275,.8545907389405606892 ] 
dist 185=[-.93597295395428177028,.78982911752743311793] 
dist 186=[-1.0161012069189507970 ,.77160168049070438568] 
dist 187=[-1.0932067450296040210 ,.69827132006661702069] 
dist 188=[-1.1565515722119133959 ,.68287347029043281971] 
dist 189=[-1.2220033159316289326 ,.64616657307069769012] 
dist 190=[-1.3075217301933562588 ,.63617061727828426748] 
dist 191=[-1.3879593261979314990 ,-.01355982879465138179] 
dist 192=[-1.4331284729266577617 ,-.03370668788593529222] 
dist 193=[-1.4611513040975046357 ,-.06418021491705620249] 
dist 194=[-1.4731388363749785812 ,-.07188253075528927451] 
dist 195=[-1.4783771430158206699 ,-.07627346396240326675] 
dist 196=[-1.4794560424552875396 ,-.06728058380734417216] 
dist 197=[-1.4776980201666807566 ,-.04818300115375754506] 
dist 198=[-1.4731722843754101549 ,-.01029546225307394283] 
dist 199=[-1.2950730818040482652 ,.03273508008895998681] 
dist 200=[-1.2677488933808757715 ,.07236434874837977215] 
dist 201=[-1.2170524763471308134 ,.1171166018507872665 ] 
dist 202=[-1.2050852378937359457 ,.18059999145310467798] 
dist 203=[-1.1506521082057252109 ,.25132229209155044483] 
dist 204=[-1.1362574827129958442 ,.3249733557931324197 ] 
dist 205=[-1.1103317511812537163 ,.41493444555149290021] 
dist 206=[-1.1023978470265458987 ,.55076766240441283508] 
dist 207=[-.65484802925150693654,.68679947888861680939] 
dist 208=[-.63334225144716641268,.77755384507010274107] 
dist 209=[-.57959453659054093474,.85258837890427877548] 
dist 210=[-.56995237932839768608,.92586671431963408776] 
dist 211=[-.48368266181641967333,.99247404466678200984] 
dist 212=[-.46655399639035364302,1.0408781581712307118 ] 
dist 213=[-.44336494462174114242,1.0852566590258128790 ] 
dist 214=[-.43569944069972845245,1.1357943461747469136 ] 
dist 215=[-.27591781590682313063,1.1816486707084271453 ] 
dist 216=[-.25492915976408334909,1.2073313368309281138 ] 
dist 217=[-.20918310384704361668,1.2231773050729898755 ] 
dist 218=[-.19782382457972192182,1.2297633736320353677 ] 
dist 219=[-.14521856272763353978,1.2309747215324881630 ] 
dist 220=[-.13561369909510639607,1.2290202168991076770 ] 
dist 221=[-.11267025455347900512,1.2104894831248225041 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 0, 1, 0, 1, 0, 1] 
dist 0=[45.893782026217945764  ,45.893782026217945764  ] 
dist 1=[44.661881147523324201  ,46.670129010894716105  ] 
dist 2=[43.228707190347262004  ,47.262175659643574443  ] 
dist 3=[41.648370562277843216  ,47.757715936353247284  ] 
dist 4=[39.654021220679319293  ,48.153809410659889774  ] 
dist 5=[36.567227895468814225  ,48.348734111805415030  ] 
dist 6=[33.438538550568791315  ,48.432940633980563134  ] 
dist 7=[31.276730317815234109  ,48.413604247174938405  ] 
dist 8=[29.403872077164012340  ,48.265150480293631279  ] 
dist 9=[27.428923779422414028  ,48.192351327209603202  ] 
dist 10=[25.532672218828898486  ,47.836252487675946156  ] 
dist 11=[23.973858926096922414  ,47.769392508089761069  ] 
dist 12=[22.358481311275561211  ,46.387198391852326575  ] 
dist 13=[20.235832652590717348  ,46.078374934782805685  ] 
dist 14=[18.147061778100317715  ,45.655379757352470733  ] 
dist 15=[16.666738087159044413  ,44.428091187260121428  ] 
dist 16=[15.342329567620841190  ,41.206924544567999296  ] 
dist 17=[13.876005330235752120  ,31.695170265295205440  ] 
dist 18=[12.421293966173276259  ,30.951922993791411648  ] 
dist 19=[11.142795564948263919  ,30.757451422664275959  ] 
dist 20=[9.7405183235422428338 ,24.833347814068964289  ] 
dist 21=[7.7903044192666676452 ,23.515970613374669683  ] 
dist 22=[5.8791442591380332692 ,21.858627514897166212  ] 
dist 23=[4.6327752083479243824 ,21.427530339311216942  ] 
dist 24=[3.6258145709672195114 ,19.873840733895709869  ] 
dist 25=[2.6717662226227297607 ,19.537040759666543947  ] 
dist 26=[1.8156645370162739479 ,18.985899759717678592  ] 
dist 27=[1.2001678352104310620 ,18.843119287509296527  ] 
dist 28=[.6374909442605422150 ,13.679030475148627586  ] 
dist 29=[-.0077687506935062115 ,11.929489725699181177  ] 
dist 30=[-1.4383704828714687315 ,8.0822225327709889832 ] 
dist 31=[-3.3726803560286754292 ,7.6570863770571196094 ] 
dist 32=[-5.1342143949854757267 ,6.0465079194638216860 ] 
dist 33=[-6.4294404341922205085 ,-.2103954491712097561 ] 
dist 34=[-7.6357872958859918734 ,-.1787641837437366188 ] 
dist 35=[-9.0423205677245018103 ,-.0664715261728964398 ] 
dist 36=[-10.345746730718631143  ,.1237978680829089119 ] 
dist 37=[-11.140228240713720350  ,.4665658943286397588 ] 
dist 38=[-11.717079539767771456  ,.8214445974145760563 ] 
dist 39=[-12.151140788248577254  ,1.0601551162779899035 ] 
dist 40=[-12.483199456836548544  ,1.2573192655441110860 ] 
dist 41=[-12.652530407112831256  ,1.4469248482273016485 ] 
dist 42=[-12.735930855337288064  ,1.6152581900930958005 ] 
dist 43=[-12.738379964013953266  ,1.7277403551168632157 ] 
dist 44=[-10.756573518181878496  ,1.8199027487595864046 ] 
dist 45=[-10.813946963975847365  ,1.9072705005789212298 ] 
dist 46=[-10.834241899395091101  ,1.9840773427861310195 ] 
dist 47=[-10.832034545175543196  ,2.0341479451745121821 ] 
dist 48=[-10.802492097239335303  ,2.0736138644904379693 ] 
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dist 50=[-5.0300991714216227821 ,2.1360214748561990193 ] 
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dist 55=[-1.7359584299189723508 ,.7477037846071251499 ] 
dist 56=[-1.6386309276037530307 ,.76841549165338114791] 
dist 57=[-.3401874178944046378 ,1.5964336270752667713 ] 
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dist 59=[-.1423634828939074624 ,2.6229240704098700000 ] 
dist 60=[-.31620561432556364687,3.0922678104853493386 ] 
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dist 63=[-.9182866760754093463 ,4.1833205827757821822 ] 
dist 64=[-1.0476602667638268292 ,4.5780887139722685003 ] 
dist 65=[-1.1801127579886211914 ,4.9452436271863675937 ] 
dist 66=[-1.3044562577118827734 ,5.1577082805085550787 ] 
dist 67=[-1.4014848674007481412 ,5.2986050402255817501 ] 
dist 68=[-1.4971684289531637380 ,5.3798555276726257890 ] 
dist 69=[-1.6161744015481700997 ,5.4322508199284138125 ] 
dist 70=[-1.7275831521019592968 ,5.4578455178137162648 ] 
dist 71=[-1.7929489393937534483 ,5.4690358382392714340 ] 
dist 72=[-1.8372230461215932160 ,5.4638012285919683160 ] 
dist 73=[-1.8644325952964875294 ,4.8908556980670726343 ] 
dist 74=[-1.8807872762572660962 ,4.8055129812688004337 ] 
dist 75=[-1.8821762246632175666 ,4.7975072092369377087 ] 
dist 76=[-1.8762806087347518283 ,4.6093671146461613252 ] 
dist 77=[-2.3199438912233204168 ,4.4711546932230505312 ] 
dist 78=[-2.7558331613709674303 ,4.4263605468571260885 ] 
dist 79=[-3.1724053118430399929 ,4.3804624751647870315 ] 
dist 80=[-3.5451218039914886540 ,4.3544147051118967799 ] 
dist 81=[-3.8059609526385276473 ,1.4668720780383799346 ] 
dist 82=[-4.0351036365664875732 ,1.2349209932383737006 ] 
dist 83=[-4.2813251087840352435 ,1.2145260846587523607 ] 
dist 84=[-4.4992213177119597768 ,1.3308632173222321497 ] 
dist 85=[-4.6152894867759728636 ,1.4942627473750247470 ] 
dist 86=[-4.6792092694174302950 ,1.6528007265062246394 ] 
dist 87=[-4.6935823557214304094 ,1.7497360848391859843 ] 
dist 88=[-4.6795042355514125302 ,1.8201731881167946038 ] 
dist 89=[-4.6672901024052465490 ,1.8729379572427222445 ] 
dist 90=[-4.6507506733799326756 ,1.9116362983532486399 ] 
dist 91=[-4.6316718419224763117 ,1.9259220651029919316 ] 
dist 92=[-3.7976658197622254056 ,1.9295485773349548023 ] 
dist 93=[-3.6999446030875730377 ,1.9256954787050549527 ] 
dist 94=[-3.4369952647506832176 ,1.9316112087555447322 ] 
dist 95=[-3.3993164576557738805 ,1.9966118378919863775 ] 
dist 96=[-3.0341381211271355189 ,2.0422623071159843776 ] 
dist 97=[-2.8261550056184906158 ,2.3187417886032447214 ] 
dist 98=[-2.7329820517688686924 ,2.6448684356179368322 ] 
dist 99=[-2.7156578918110256814 ,3.0399656089833822286 ] 
dist 100=[-1.8598188917425957037 ,3.4107898100602948819 ] 
dist 101=[-1.6993258348729580387 ,3.6400309872619220069 ] 
dist 102=[-1.6650405595559239041 ,3.8094995935490374327 ] 
dist 103=[-1.6204736820901044841 ,3.9417407065314202985 ] 
dist 104=[-1.6039248742984217153 ,4.0420859277598398020 ] 
dist 105=[-1.2277997007512558535 ,4.0842412559418855594 ] 
dist 106=[-1.2085105046383834067 ,4.1002443500218184295 ] 
dist 107=[-1.3402370390275844177 ,4.0962060107223923731 ] 
dist 108=[-1.4584084120718171533 ,1.1132302512016542574 ] 
dist 109=[-1.5890234671277117851 ,1.4161652071676187432 ] 
dist 110=[-1.7080134410565156734 ,1.6572637182637029758 ] 
dist 111=[-1.7797824347398425354 ,1.8773706281019027552 ] 
dist 112=[-1.8307202562656031095 ,2.0674295403488961019 ] 
dist 113=[-1.8665612546270990403 ,2.1885723071504630659 ] 
dist 114=[-1.8905425302685521792 ,2.2825869221218777084 ] 
dist 115=[-1.8954814103511923640 ,2.3644037529073281213 ] 
dist 116=[-1.8909848373681225297 ,2.4336734854771332560 ] 
dist 117=[-1.8879970084987167376 ,2.4775757715529538005 ] 
dist 118=[.34052194322843107545,2.5113944510845027868 ] 
dist 119=[.37868097985849181536,2.5403941175066261062 ] 
dist 120=[.38778857122517468258,2.5641442898645296662 ] 
dist 121=[.38755687573670702679,2.5769980349121656196 ] 
dist 122=[.37056483522156090401,2.5843519178779793967 ] 
dist 123=[.33845121755072499713,2.5861364317742189183 ] 
dist 124=[.0285699884274104989 ,1.8614324992163534848 ] 
dist 125=[-.2003697799250758733 ,1.8299492891194639916 ] 
dist 126=[-.3956016189002389825 ,1.7397742546911418322 ] 
dist 127=[-.5960142409024781841 ,1.7362620427363921359 ] 
dist 128=[-.7845560521102603077 ,1.7328528226953933920 ] 
dist 129=[-.9324084336707527824 ,1.5048397996306601868 ] 
dist 130=[-1.0788743530512896774 ,1.4703068756832539328 ] 
dist 131=[-1.2618916206514520075 ,1.4631562091545106914 ] 
dist 132=[-1.4366677127389672686 ,.9959255653731382926 ] 
dist 133=[-1.5502407267696726879 ,.9358048644248718663 ] 
dist 134=[-1.6408350472278284041 ,.8186206012903523807 ] 
dist 135=[-1.7238873915569820434 ,.7887064064253202780 ] 
dist 136=[-1.7958636074038780880 ,.6861313440770332932 ] 
dist 137=[-1.8422498538955671524 ,.6617504024748868288 ] 
dist 138=[-1.8788677852312416618 ,.6367856250339285528 ] 
dist 139=[-1.9118649252384808640 ,.6315238013492322929 ] 
dist 140=[-1.9369929302599692160 ,-.37428647247927770255] 
dist 141=[-1.9422298714728913110 ,-.25448918751743962737] 
dist 142=[-1.9402110599831509378 ,-.123508066715527299  ] 
dist 143=[-1.9717633002639506664 ,.04080131644745978245] 
dist 144=[-2.0216753114495537625 ,.29363153896725102947] 
dist 145=[-2.0424183926067261136 ,.54788185358072759626] 
dist 146=[-2.0508646404438132866 ,.71785962647403668662] 
dist 147=[-2.0516798580236158198 ,.85870961820043846921] 
dist 148=[-1.9872397517957589767 ,.99669347398900335652] 
dist 149=[-1.9714330246775828862 ,1.1223197278324779173 ] 
dist 150=[-1.9380121448989901721 ,1.2138423772947885015 ] 
dist 151=[-1.9255094402743187314 ,1.2979344775774777293 ] 
dist 152=[-1.8612882161001058456 ,1.3938988119237268134 ] 
dist 153=[-1.8458406974321574512 ,1.4809717164650531620 ] 
dist 154=[-1.7956776354027860278 ,1.5295718785139228407 ] 
dist 155=[-1.7863102267039509968 ,1.5592965983252904952 ] 
dist 156=[-1.2101810849553639574 ,1.5710257699419055920 ] 
dist 157=[-1.1801501361563765919 ,1.5755639637377424944 ] 
dist 158=[-1.1061094536614819831 ,1.5765867188501963078 ] 
dist 159=[-1.0894606126174855278 ,1.5752211914992562686 ] 
dist 160=[-1.0573419013733711307 ,1.5702314427335425344 ] 
dist 161=[-.9445734017314773233 ,1.2112253473794736624 ] 
dist 162=[-.9029703095311053323 ,1.3270936388291229235 ] 
dist 163=[-.8915715560932611281 ,1.4626025000350210097 ] 
dist 164=[-.6554190647485843041 ,1.5874531435542641342 ] 
dist 165=[-.6229190470319665694 ,1.6607698694334331792 ] 
dist 166=[-.5475744582753970083 ,1.7104223349640825226 ] 
dist 167=[-.5309837616362569429 ,1.7407989090790251994 ] 
dist 168=[-.4277877686520562063 ,1.7612038885182227393 ] 
dist 169=[-.4078919975395591906 ,1.7710522950192789257 ] 
dist 170=[-.3701652909596147361 ,1.7750611009050447743 ] 
dist 171=[-.3604664010275843426 ,1.7721682939034193628 ] 
dist 172=[.30216268725459823241,1.4325064337625540477 ] 
dist 173=[.31124427609118988805,1.4683060830678859591 ] 
dist 174=[.30474972174991307343,1.4838254088988718109 ] 
dist 175=[.28901574624681173945,1.4899397133427507603 ] 
dist 176=[.25657120643961916692,1.4883493718963487190 ] 
dist 177=[.1169775638209425527 ,1.4584077141253664868 ] 
dist 178=[-.02327662843947418529,1.4500407425378631911 ] 
dist 179=[-.14641014441925082082,1.4211000985488659986 ] 
dist 180=[-.27848830988863706082,1.4134359338766261927 ] 
dist 181=[-.4063189464025261813 ,1.3337889124158480024 ] 
dist 182=[-.51249766644515979559,1.3145424965134410544 ] 
dist 183=[-.62323078386453151448,1.2911472458594800992 ] 
dist 184=[-.7692441123452208230 ,1.2808227234066822832 ] 
dist 185=[-.9124123358328873703 ,1.0205098356691270028 ] 
dist 186=[-1.0117886424648979570 ,.98402767007539765532] 
dist 187=[-1.0981930882031165591 ,.90858794973285591698] 
dist 188=[-1.1895786224916051386 ,.88744870596861751556] 
dist 189=[-1.2772607824110477104 ,.80298670254717180026] 
dist 190=[-1.3488824243673080509 ,.78511284140453488539] 
dist 191=[-1.4225190200175490100 ,.74340535695730333601] 
dist 192=[-1.5182470606638847669 ,.73118815641483982512] 
dist 193=[-1.6080740004477530037 ,-.09738623901601737202] 
dist 194=[-1.6581533471593172671 ,-.07615096236491197808] 
dist 195=[-1.6887498346225170140 ,-.03310018202823250497] 
dist 196=[-1.7007988603616126789 ,.01607548223282601383] 
dist 197=[-1.7052912657853793681 ,.06176226020469615851] 
dist 198=[-1.7057206003152279138 ,.11367044617434923878] 
dist 199=[-1.7032591102794407168 ,.18768431904928961681] 
dist 200=[-1.6977973256836150842 ,.27030828520386754836] 
dist 201=[-1.4878463180368964699 ,.35658923530418875334] 
dist 202=[-1.4557983216055567760 ,.46214154181378688938] 
dist 203=[-1.3962366638474444239 ,.62169817341938435612] 
dist 204=[-1.3798010525126341802 ,.78154482496853053163] 
dist 205=[-1.3185588349409906861 ,.8882555040223720763 ] 
dist 206=[-1.3017962546147075701 ,.9765563591793228298 ] 
dist 207=[-1.2717957113703574558 ,1.0629113977612994227 ] 
dist 208=[-1.2626945417030991158 ,1.1414839867571353720 ] 
dist 209=[-.75044825284510424511,1.1987177506550281623 ] 
dist 210=[-.72703039654332930976,1.2513270212722032966 ] 
dist 211=[-.66850666355119438068,1.3114395605848826324 ] 
dist 212=[-.65770602730830263798,1.3660906647921553646 ] 
dist 213=[-.5633707171457271947 ,1.3968981857606488989 ] 
dist 214=[-.54452191908315864313,1.4161654951928520547 ] 
dist 215=[-.51836542414775645329,1.4247480381373106593 ] 
dist 216=[-.50989590496750838547,1.4269751851241627590 ] 
dist 217=[-.33314172088189855607,1.4250408755337422615 ] 
dist 218=[-.30978641000989061586,1.4126053082194655003 ] 
dist 219=[-.25852312543519957348,1.4062064578425572098 ] 
dist 220=[-.24592657802147007101,1.3067949590513120395 ] 
dist 221=[-.18561842806560148306,1.2887826957436470107 ] 
dist 222=[-.17450990217648368411,1.2429175178454252986 ] 
dist 223=[-.14872169173537794581,1.2266084148511039345 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 1, 1, 0, 1] 
dist 0=[55.113925881915739365  ,55.113925881915739365  ] 
dist 1=[54.866889871642557963  ,55.228715031475999604  ] 
dist 2=[54.325683889688984919  ,55.241889989212589489  ] 
dist 3=[53.464573513406350768  ,55.183004521342265432  ] 
dist 4=[51.939753577661925930  ,55.102207909696487586  ] 
dist 5=[50.260200508039794196  ,54.832083880702943923  ] 
dist 6=[48.780999758687117373  ,54.749218359751043316  ] 
dist 7=[47.161709600520427712  ,53.641030594879173274  ] 
dist 8=[44.922465696452235663  ,51.445493127186827049  ] 
dist 9=[42.448784892127159662  ,49.740595962671632430  ] 
dist 10=[39.893033400613451375  ,49.049706922084963291  ] 
dist 11=[36.780484005137373034  ,47.867414655381298088  ] 
dist 12=[32.082763886587385163  ,47.560642324492736884  ] 
dist 13=[27.362177035362805562  ,46.682288849224510640  ] 
dist 14=[24.158196713533178160  ,46.439620955627531770  ] 
dist 15=[21.442594096225408055  ,45.143002095017960796  ] 
dist 16=[18.672473658374942918  ,42.805220905372974152  ] 
dist 17=[16.069089332967667220  ,34.129596443317089909  ] 
dist 18=[14.019252319744853376  ,33.733650164234156708  ] 
dist 19=[11.975359581552281095  ,33.183835979873215885  ] 
dist 20=[9.3952995246576954407 ,32.997466724549770664  ] 
dist 21=[6.9058543701529911649 ,14.264410139182163501  ] 
dist 22=[5.2236838825630437851 ,12.924506703475244273  ] 
dist 23=[3.8037321281104589559 ,11.674238635970216848  ] 
dist 24=[1.9949985078864845434 ,11.361596382614370984  ] 
dist 25=[-.54947184833513785307,5.7493562580438734112 ] 
dist 26=[-2.4439471069304892289 ,5.0734281673220681432 ] 
dist 27=[-4.2306811993932443440 ,3.6752572693007139066 ] 
dist 28=[-6.3447883525572610521 ,3.4036337061225790624 ] 
dist 29=[-8.3214233412070637972 ,2.2435128004717292449 ] 
dist 30=[-9.5591000392553338116 ,2.0432878181236160475 ] 
dist 31=[-10.496252345818931539  ,1.5973320326589462498 ] 
dist 32=[-11.272655222563848951  ,1.2258506463113536499 ] 
dist 33=[-11.890843827542082392  ,-5.1672480979364787529 ] 
dist 34=[-12.195988692648631831  ,-5.4831540031305313554 ] 
dist 35=[-12.355432105061427660  ,-6.0558613684408157945 ] 
dist 36=[-12.391680446110556872  ,-6.0108234606196930524 ] 
dist 37=[-9.7629572349834629539 ,-5.7597186848649449333 ] 
dist 38=[-9.5829056132145277034 ,-5.5199076125477189464 ] 
dist 39=[-9.0890507414808031677 ,-5.2459613281505310459 ] 
dist 40=[-9.0044486431773052177 ,-4.8577538693861749102 ] 
dist 41=[-8.0741656617166438153 ,-4.4287030323620020443 ] 
dist 42=[-7.8817767865992456778 ,-3.9913416632428813851 ] 
dist 43=[-7.6601362195532538337 ,-3.4653788101285254172 ] 
dist 44=[-7.5815555911991396622 ,-2.6823656291731241286 ] 
dist 45=[-6.9429410278792991899 ,-1.8753282153253096103 ] 
dist 46=[-6.8752130721610131473 ,-1.2532612870854265636 ] 
dist 47=[-6.7832588263950084234 ,-.4460271989204186952 ] 
dist 48=[-6.7455875808964020128 ,1.1174745752227199403 ] 
dist 49=[-5.7986701940740101991 ,2.6745052255534664260 ] 
dist 50=[-5.6611685282180128376 ,3.6925145746579224823 ] 
dist 51=[-5.2593692317695725061 ,4.5112234979442969093 ] 
dist 52=[-4.7331786217923495206 ,5.2727827202187360671 ] 
dist 53=[.1172592851086186003 ,5.9401528714096330882 ] 
dist 54=[.4416853935758951634 ,6.3829446465947218756 ] 
dist 55=[1.1211920987741388469 ,6.7466592072568570626 ] 
dist 56=[1.2748665258531123387 ,7.0984771352536896256 ] 
dist 57=[1.9123524628033163653 ,7.4059245827314515063 ] 
dist 58=[1.9563903025414655395 ,7.5924817580738947121 ] 
dist 59=[1.9965694295259259725 ,7.7266255067821194312 ] 
dist 60=[1.9782358725068500507 ,7.8246268169694391849 ] 
dist 61=[1.9449490662472146465 ,7.8917627819384609968 ] 
dist 62=[1.9081905782237794799 ,7.9025328622895666946 ] 
dist 63=[1.8624787160932863929 ,7.7909421255455478201 ] 
dist 64=[1.7598685513046095434 ,7.4599173050793804959 ] 
dist 65=[1.4253777585625608249 ,6.9347020710786595379 ] 
dist 66=[1.0346485390052494544 ,6.9492837978680502269 ] 
dist 67=[.5278692870920642175 ,6.9424422450466381697 ] 
dist 68=[-.2699239161603459289 ,6.9267170992606024913 ] 
dist 69=[-1.0781438768790704291 ,2.4546561073881980313 ] 
dist 70=[-1.6265781180816008468 ,2.2748025656947998236 ] 
dist 71=[-2.0899825431277874287 ,2.0167694115365390001 ] 
dist 72=[-2.5588255701993604030 ,1.9437350455467625715 ] 
dist 73=[-2.9956361688663811460 ,1.1608380003434606283 ] 
dist 74=[-3.3312042531747552245 ,1.1408526328709697108 ] 
dist 75=[-3.6571692352460173563 ,1.0886093990076813006 ] 
dist 76=[-4.0556927445624208346 ,1.0806118352795444990 ] 
dist 77=[-4.4322005077584224667 ,.44865973623351913891] 
dist 78=[-4.6703011336935927048 ,.38900824531100524163] 
dist 79=[-4.8529490847403336802 ,.25200123986840962667] 
dist 80=[-5.0081083247886199345 ,.22833440186600352125] 
dist 81=[-5.1341681829248772642 ,.05208796458855321617] 
dist 82=[-5.2677028805034712329 ,.02057256218062036352] 
dist 83=[-5.3829474046625227226 ,-.03024228802537086611] 
dist 84=[-5.4884463200539319719 ,.68482267426712346292] 
dist 85=[-5.5699816204714751495 ,1.6304566858782830268 ] 
dist 86=[-5.5895661186042301258 ,2.2656719835734140800 ] 
dist 87=[-5.5865984501769266314 ,2.7952072422271492747 ] 
dist 88=[-5.5779992208936187537 ,3.3190350695999894302 ] 
dist 89=[-5.3918530727107846950 ,3.7991484447925698154 ] 
dist 90=[-5.3376642183412360824 ,4.1542014328585174769 ] 
dist 91=[-5.2914961364277636021 ,4.4856656139976127494 ] 
dist 92=[-5.2581825240001046149 ,4.8716205298235375033 ] 
dist 93=[-4.3134015624577196453 ,5.2258332038870143407 ] 
dist 94=[-4.1985469077943989980 ,5.4305985662593462852 ] 
dist 95=[-4.1695162426062791804 ,5.5650744896237230349 ] 
dist 96=[-4.1566669249221430742 ,5.6387317923872032513 ] 
dist 97=[-3.5731811117764722327 ,5.6819144060395706364 ] 
dist 98=[-3.5088438643445166076 ,5.6947577413950125030 ] 
dist 99=[-3.3867404582360149493 ,5.6877950293357279309 ] 
dist 100=[-3.3515544700833519707 ,5.6739852746994927829 ] 
dist 101=[-.74558388679526596916,4.2861553460669684196 ] 
dist 102=[-.53932822368770657177,4.4502011096795794928 ] 
dist 103=[-.09233033335683690232,4.5763692560593986921 ] 
dist 104=[.0051493235290924947 ,4.6840745750005033626 ] 
dist 105=[.17168322991591530824,4.7682359513572852698 ] 
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dist 173=[-.10301341862903615259,.4815754130795763558 ] 
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dist 175=[-.15550901020368748856,.4681485860064255532 ] 
dist 176=[-.17843451562854877685,.4647397104739376656 ] 
dist 177=[-.19912227910676558556,.22262644259729096166] 
dist 178=[-.21388377484368819953,.20063973865619425696] 
dist 179=[-.22713854254831696625,.1478878457520961561 ] 
dist 180=[-.24181302801745899782,.13994251535292533237] 
dist 181=[-.25489871365566995806,.0652490214980009231 ] 
dist 182=[-.26181203231285034042,.0516362428063270657 ] 
dist 183=[-.26566244592577954739,.0344244786937363278 ] 
dist 184=[-.26652066324649967492,.0304522656189115511 ] 
dist 185=[-.30350422853337248667,-.01001725143267070866] 
dist 186=[-.32669437317396547546,.00433918057864478527] 
dist 187=[-.34389392445338301648,.02274972406353438837] 
dist 188=[-.35746253908842739208,.05151000469968539300] 
dist 189=[-.36794829831151074344,.08053967995847907196] 
dist 190=[-.37283748406081795354,.10002575311558537881] 
dist 191=[-.37500659800710635148,.1162556697401339427 ] 
dist 192=[-.37493232130372879162,.1322889823341277474 ] 
dist 193=[-.26631553008162438928,.1469723608572077791 ] 
dist 194=[-.26005985076937924515,.1578143414546687981 ] 
dist 195=[-.24366373136571770268,.16869016807217829126] 
dist 196=[-.24082645316713375928,.1862541983449465773 ] 
dist 197=[-.21195115781286967202,.2023682776232256740 ] 
dist 198=[-.20605595223567151421,.2122077719743423647 ] 
dist 199=[-.19895066161492450611,.2193324092400669110 ] 
dist 200=[-.19631306864428112661,.2246128180278748618 ] 
dist 201=[-.13558209559041524762,.2283206043984931781 ] 
dist 202=[-.12759690635598876348,.2292175963076796691 ] 
dist 203=[-.11082239659745392763,.2290655921890153302 ] 
dist 204=[-.10627924203119507543,.2289830161554904860 ] 
dist 205=[-.08873337736144393089,.1859385162677859751 ] 
dist 206=[-.09471205330465912967,.1831436320685455627 ] 
dist 207=[-.11671133993207746197,.17563261092174591265] 
dist 208=[-.13772575285896988355,.17378131428807121195] 
dist 209=[-.15649255249354777853,.15913620058200808414] 
dist 210=[-.1695213846978044386 ,.15588075186683727771] 
dist 211=[-.1808386314443031103 ,.15088938571305762344] 
dist 212=[-.1927740649465153613 ,.16674473068496905878] 
dist 213=[-.2034034225772660412 ,.18516631037880020758] 
dist 214=[-.2095081388576894731 ,.19857457753595254896] 
dist 215=[-.2134649736241369036 ,.21089461561184037784] 
dist 216=[-.2155226271926601429 ,.22497107866432228149] 
dist 217=[-.2164202736594832748 ,.23777531710166289204] 
dist 218=[-.2162459668745714212 ,.24501576571019744193] 
dist 219=[-.2145701734232329731 ,.2495742473421614466 ] 
dist 220=[-.2134549708905145797 ,.25167040975418857943] 
dist 221=[-.00382705494046216241,.25261210630796595607] 
dist 222=[-.01865176760304983038,.2525620176462810988 ] 
dist 223=[-.03193477614985381397,.25177688979543571303] 
dist 224=[-.06065914065522446800,.25111097650045982704] 
dist 225=[-.09732417792759305046,-.00900628860923114333] 
dist 226=[-.12167509201412512613,-.02306655054739430391] 
dist 227=[-.14167623142143269693,-.03998021983983911674] 
dist 228=[-.16097923726269163541,-.03685635232485589951] 
dist 229=[-.17836374011145161711,-.03241269911039686635] 
dist 230=[-.19070732029111064508,-.02702095255650007507] 
dist 231=[-.20172729041802538615,-.01989601778327298558] 
dist 232=[-.21382894783616520287,-.00853419465288436513] 
dist 233=[-.22456487951840927873,.00469303309079266334] 
dist 234=[-.23013336146632598278,.01926417884163115618] 
dist 235=[-.2332022900533720461 ,.03762143948170922217] 
dist 236=[-.23396080105378823207,.06596211951304900273] 
dist 237=[-.23192217526520205118,.09452325476815229312] 
dist 238=[-.23139492274505489217,.11376032818190168537] 
dist 239=[-.23108054624551601702,.12986262967916343693] 
dist 240=[-.23097640937421131282,.14590974955831449223] 
dist 241=[-.22939495213230943162,.16070316314326765611] 
dist 242=[-.22896453255368641847,.17180046558735599606] 
dist 243=[-.22593183405255732761,.18232047487716038997] 
dist 244=[-.22535648560654235096,.19480873849315732779] 
dist 245=[-.21322360397113409635,.20640120441194107365] 
dist 246=[-.21021713261003546469,.21334502449443927212] 
dist 247=[-.20795984615216346277,.21821369798169918434] 
dist 248=[-.20705873974534290516,.22152228721188008649] 
dist 249=[-.16077934265552133286,.22357059645121174437] 
dist 250=[-.1545345029964485987 ,.22393618254872474825] 
dist 251=[-.14248878087054296747,.2226741491138714659 ] 
dist 252=[-.13933849197755397123,.22244464158074112021] 
dist 253=[-.12821930981674925112,.21164554435654988833] 
dist 254=[-.12546847065400650079,.20954465567279636119] 
dist 255=[-.12181643449897214258,.20261536251069271967] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 1, 0, 2] 
dist 0=[53.625937573012143581  ,53.625937573012143581  ] 
dist 1=[53.522893048008733056  ,53.621890637652737642  ] 
dist 2=[53.196178949335104499  ,53.625937573012143581  ] 
dist 3=[52.642260580260746466  ,53.369639149030118364  ] 
dist 4=[51.631870460688670096  ,53.257545207379872441  ] 
dist 5=[50.480043377567583949  ,52.617496438456384648  ] 
dist 6=[49.361205897004889892  ,52.524453801263649969  ] 
dist 7=[48.049400529693716215  ,51.051344417691440445  ] 
dist 8=[46.126691770683828056  ,49.579003451855407124  ] 
dist 9=[43.951809162227312162  ,49.000706437705935279  ] 
dist 10=[41.632692384868417262  ,48.786829237978647259  ] 
dist 11=[38.756933363812478461  ,48.639028486624872775  ] 
dist 12=[34.358601323437308182  ,48.542363863497032824  ] 
dist 13=[29.914465958345439173  ,40.059154963487548639  ] 
dist 14=[26.855685666576441999  ,39.418149522579430304  ] 
dist 15=[24.217096612357848297  ,38.702333774696056309  ] 
dist 16=[21.451176883427132556  ,38.490930537633424879  ] 
dist 17=[18.804786632559825311  ,31.867435406479438675  ] 
dist 18=[16.643478513410779287  ,31.000273168724056559  ] 
dist 19=[14.416387910551550794  ,29.267375496757674541  ] 
dist 20=[11.506932103533133488  ,28.813064053183884184  ] 
dist 21=[8.6532267734347212606 ,27.161797451197754379  ] 
dist 22=[6.6486539259934841030 ,26.797961756370477614  ] 
dist 23=[4.8746973567143748330 ,26.173573255952065915  ] 
dist 24=[2.9419559096490627854 ,26.016144598857127447  ] 
dist 25=[1.0449261674076085275 ,11.443949818155354862  ] 
dist 26=[-.58672151046406729171,10.206561585363067817  ] 
dist 27=[-2.3445362972938864208 ,9.4210122941417535651 ] 
dist 28=[-4.7463285814622735762 ,9.3258387197042410769 ] 
dist 29=[-7.0790388786311493168 ,3.2935319852293850832 ] 
dist 30=[-8.5609698140245599298 ,2.6637178841020596223 ] 
dist 31=[-9.7117053473872947504 ,1.7348471506020542671 ] 
dist 32=[-10.720858163651733801  ,1.4974010742064066071 ] 
dist 33=[-11.569494871585883245  ,-2.3048411060764065118 ] 
dist 34=[-12.078890501355910580  ,-2.7725453007964918099 ] 
dist 35=[-12.441551553786453123  ,-3.7517249968526126444 ] 
dist 36=[-12.704177927519207815  ,-3.9411151434309984439 ] 
dist 37=[-12.897731558801396769  ,-4.8357580718672034490 ] 
dist 38=[-12.984347148155973413  ,-4.9852483999235554964 ] 
dist 39=[-13.011705259856038011  ,-5.1819055952882623046 ] 
dist 40=[-12.992783641094015698  ,-5.1847101498107512763 ] 
dist 41=[-12.883750996540324491  ,-5.1401033928448733268 ] 
dist 42=[-12.836380876416397956  ,-5.0686735663818309958 ] 
dist 43=[-12.623787815913952736  ,-4.9663065950751014228 ] 
dist 44=[-12.580002390140252836  ,-4.2721586159364718500 ] 
dist 45=[-7.6773422326323196482 ,-2.1193248790599330600 ] 
dist 46=[-7.2274530748604171442 ,-.66106809260507619786] 
dist 47=[-6.3806041851669366005 ,.56842266548251234647] 
dist 48=[-6.3171893710132601525 ,1.8081451677951927394 ] 
dist 49=[-4.4200012450333631332 ,2.9605449650200642645 ] 
dist 50=[-4.2914237767263455502 ,3.8414997904405363271 ] 
dist 51=[-4.1334639818342041698 ,4.6930217717870167648 ] 
dist 52=[-4.1087142550768257961 ,5.7279760334639090303 ] 
dist 53=[-3.8161432046453370406 ,6.7022132428263449443 ] 
dist 54=[-3.7549396890333047198 ,7.3113608987702135396 ] 
dist 55=[-3.6944564304420466380 ,7.7702562837391845375 ] 
dist 56=[-3.6783841614325793929 ,8.1446633556556649589 ] 
dist 57=[-2.9508630029147444972 ,8.4402224261848959286 ] 
dist 58=[-2.8601814188661150967 ,8.5843363923555982734 ] 
dist 59=[-2.6271963396538345052 ,8.6553739824518427445 ] 
dist 60=[-2.5933299605071111051 ,8.6602036288830295722 ] 
dist 61=[-2.1961966519558116819 ,3.6002626896808020595 ] 
dist 62=[-2.1161439433723936053 ,3.9344121182792391178 ] 
dist 63=[-2.0381405437250864184 ,4.2445070522606756283 ] 
dist 64=[-2.0221891785493615494 ,4.6042404522977665056 ] 
dist 65=[-1.1412026447218208732 ,4.9359405410391176347 ] 
dist 66=[-1.0271434697133691222 ,5.1341181022867614970 ] 
dist 67=[-.8080518827802249229 ,5.2733280341163475384 ] 
dist 68=[-.7524857281721432329 ,5.3695475470770825147 ] 
dist 69=[-.5641691808043505115 ,5.4330337334427038939 ] 
dist 70=[-.5181760253054576225 ,5.4461283860429945896 ] 
dist 71=[-.4727049758418194823 ,5.4322421582359419946 ] 
dist 72=[-.4623760827824058443 ,5.4252796440123795660 ] 
dist 73=[2.3486227450803159579 ,4.4340471868252202948 ] 
dist 74=[2.1030004903702169625 ,4.4105673334332939936 ] 
dist 75=[1.7959577157223597598 ,4.3322358018454191157 ] 
dist 76=[1.2801476091228132908 ,4.3090576113299612131 ] 
dist 77=[.53137027283104516945,2.8892412336414321712 ] 
dist 78=[.02553871677894335524,2.8336072121368828149 ] 
dist 79=[-.399716987010027222  ,2.7739621983405161782 ] 
dist 80=[-.82682772590807409564,2.7517940832054335512 ] 
dist 81=[-1.2230270977633661604 ,2.0990275719490267278 ] 
dist 82=[-1.5248885133815185028 ,2.0121640803268053580 ] 
dist 83=[-1.8158456482874540737 ,1.8365559753021009183 ] 
dist 84=[-2.1685349806955940876 ,1.7897088338337632357 ] 
dist 85=[-2.5003913848646019249 ,1.6151831548745951469 ] 
dist 86=[-2.7081848014994055040 ,1.5771931341862176381 ] 
dist 87=[-2.8652223957896919775 ,1.5062097037760000122 ] 
dist 88=[-2.9944459620286955696 ,1.4876013000738561006 ] 
dist 89=[-3.0962433209189473875 ,.01877319600873006765] 
dist 90=[-3.1437968837551622860 ,-.10810956501948350787] 
dist 91=[-3.1670222616764208372 ,-.37812698076405292678] 
dist 92=[-3.1716267165953526577 ,-.43651126789521168279] 
dist 93=[-3.1072096007402836666 ,-.70578701968655340561] 
dist 94=[-3.0909557870954800782 ,-.75261748087302930399] 
dist 95=[-3.0310204027268678132 ,-.83934261348545194296] 
dist 96=[-3.0174094256298575327 ,-.85729270512769617335] 
dist 97=[-2.8465310558251365180 ,-.89281960390805256228] 
dist 98=[-2.8057676288061129080 ,-.87566953117382783267] 
dist 99=[-2.7628897353799526769 ,-.83068568143311899317] 
dist 100=[-2.7409996683103774271 ,-.73601397766788080834] 
dist 101=[-2.5878302919387185784 ,-.61662329545308422233] 
dist 102=[-2.6028553352218518145 ,-.47294854824465384855] 
dist 103=[-2.6111114139039500138 ,-.28387435766993163991] 
dist 104=[-2.6122500073471460877 ,.01676397126976839554] 
dist 105=[-1.7451598638925259432 ,.32324730898860602902] 
dist 106=[-1.7090983339618360691 ,.53566031086581727741] 
dist 107=[-1.6368903753210787873 ,.7200030668597618795 ] 
dist 108=[-1.6160545329526028101 ,.91443332534262293569] 
dist 109=[-.54131362406337681383,1.1006577220488684491 ] 
dist 110=[-.50270712636873419654,1.2522455689584269612 ] 
dist 111=[-.41309510399459472585,1.4076282189474452485 ] 
dist 112=[-.39607862414408507356,1.6090068040399499976 ] 
dist 113=[-.27538710561745706153,1.8048910687260662996 ] 
dist 114=[-.25289203027837574808,1.9383420389585414910 ] 
dist 115=[-.21451650940898699916,2.0819172373688829688 ] 
dist 116=[-.20541317188071998107,2.2783014492457866667 ] 
dist 117=[-.04668233338562888455,2.4589466940612741450 ] 
dist 118=[-.02575373938156926074,2.5647342647303875099 ] 
dist 119=[.02351388619126972663,2.6360635466358357092 ] 
dist 120=[.03139246432040459589,2.6791326020147367734 ] 
dist 121=[.09837988900897342085,2.7074862107998141595 ] 
dist 122=[.11046743469258780831,2.7200666091498955446 ] 
dist 123=[.12749133612176247672,2.7235226240453816722 ] 
dist 124=[.13230573489671338751,2.7154562153944566502 ] 
dist 125=[.47430883790112411545,.67934164252391155321] 
dist 126=[.2731158600907798218 ,.6470082256505503058 ] 
dist 127=[.06607825663835356573,.57025247628374010666] 
dist 128=[-.14202870619471916889,.55566830553596101331] 
dist 129=[-.33510700543980890508,.44673798795904042714] 
dist 130=[-.48215351682991551381,.42609100710745132557] 
dist 131=[-.62378201437438127306,.39224571144519584722] 
dist 132=[-.79523872622885035257,.38367006860488599012] 
dist 133=[-.95647337152830785443,.22748907175200418603] 
dist 134=[-1.0572949288356456718 ,.20717870573444863616] 
dist 135=[-1.1332742891969145480 ,.15873986203563638745] 
dist 136=[-1.1953304564770612199 ,.1515544763571001245 ] 
dist 137=[-1.2449838598587789324 ,.08440869029670685551] 
dist 138=[-1.2714496580737511194 ,.07235506963880923486] 
dist 139=[-1.2860360686314236025 ,.05738554370923599162] 
dist 140=[-1.2885636152681630176 ,.11383819201614620217] 
dist 141=[-1.2215543078727230188 ,.17298824447849747944] 
dist 142=[-1.2100622755927096298 ,.21629150502291903033] 
dist 143=[-1.1882211955083822638 ,.25627015704380222945] 
dist 144=[-1.1807610384693192288 ,.30215529607506247925] 
dist 145=[-1.1492048704432842508 ,.34832360263202623026] 
dist 146=[-1.1605199084795331805 ,.38943518431900332322] 
dist 147=[-1.1648549962965062878 ,.43472215264640424016] 
dist 148=[-1.1644847093848952469 ,.49755915273754782615] 
dist 149=[-1.0861597130430913819 ,.56056701877955935396] 
dist 150=[-1.0721245578878572151 ,.60653769904314999304] 
dist 151=[-1.0474700097573222429 ,.648846816378959448  ] 
dist 152=[-1.0401154466921169908 ,.69724195433127247475] 
dist 153=[-1.0112325524014198265 ,.74587228395465216003] 
dist 154=[-1.0023645539498408385 ,.78912228910249389045] 
dist 155=[-.98440476289835788027,.83674002096301461509] 
dist 156=[-.97799879676707768366,1.1032704808669882102 ] 
dist 157=[-.09394184360572015098,1.3769214693841950479 ] 
dist 158=[-.02858301551316590652,1.5534411359465821856 ] 
dist 159=[.12195393042033378778,1.6927768413257562535 ] 
dist 160=[.1452296695179316002 ,1.8179832377366383110 ] 
dist 161=[.28311620469738423599,1.9246682606023601124 ] 
dist 162=[.30230628396405982059,1.9900643876730625437 ] 
dist 163=[.34367188997040948314,2.0378087901084680365 ] 
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dist 165=[.39081499692101516305,2.1008002724021786837 ] 
dist 166=[.39289492644200895005,2.1108327754641429386 ] 
dist 167=[.38397382613251636033,2.1107541876681490064 ] 
dist 168=[.3577194970433249219 ,2.1078043467745717984 ] 
dist 169=[.31663896616745924394,2.0758620627806675549 ] 
dist 170=[.22627695759066628687,2.0649129889803551805 ] 
dist 171=[.11423422677699360196,2.0305104416685647628 ] 
dist 172=[-.09850159126452922871,2.0168622299067133784 ] 
dist 173=[-.32164997665067671154,1.3224184164070624959 ] 
dist 174=[-.46878266813982892622,1.2543282451972113135 ] 
dist 175=[-.58850612555336227551,1.0840592859348906359 ] 
dist 176=[-.70223725868719796546,1.0596085051044837743 ] 
dist 177=[-.80349800199232388991,.8074891682280227540 ] 
dist 178=[-.91555579445140675296,.7996283072869149460 ] 
dist 179=[-1.0598043950851933871 ,.7921435632345754291 ] 
dist 180=[-1.2339209984134778081 ,.7873485037967397963 ] 
dist 181=[-1.3971958547968643681 ,.6526208478598663256 ] 
dist 182=[-1.4981632292955239447 ,.6333802875861948808 ] 
dist 183=[-1.5729047348634966034 ,.5952090921516722935 ] 
dist 184=[-1.6314832390413930390 ,.5846851995948681140 ] 
dist 185=[-1.6767893270364818501 ,.5442155219182279386 ] 
dist 186=[-1.6985455147539360750 ,.5347910194222196447 ] 
dist 187=[-1.7081018132013821475 ,.5156361349299480449 ] 
dist 188=[-1.7084650242271076591 ,.5098274412463000003 ] 
dist 189=[-.71950649579374838877,-.51426462553700444224] 
dist 190=[-.80822845194260744174,-.54515620153022082343] 
dist 191=[-.8782521614456668035 ,-.60155128706643467599] 
dist 192=[-.94116360557692479273,-.61301102805053754138] 
dist 193=[-.99476275253465296203,-.63520837244494796523] 
dist 194=[-1.0276099672235936792 ,-.6283778794709485021 ] 
dist 195=[-1.0515814402393325945 ,-.60720829854523626609] 
dist 196=[-1.0697475794696004590 ,-.56092609838592702893] 
dist 197=[-1.0830988116458171826 ,-.50703178860831197909] 
dist 198=[-1.0878479343311725798 ,-.4554731894020619084 ] 
dist 199=[-1.0875859432034093525 ,-.39571398738439171893] 
dist 200=[-1.0858281131477324552 ,-.30908013106947013008] 
dist 201=[-1.0771420939147791496 ,-.21171506340944148027] 
dist 202=[-1.0737146092038908559 ,-.10911488219057696762] 
dist 203=[-1.0582813267948060970 ,.01705965343376039278] 
dist 204=[-1.0539782370796778114 ,.20853667018284278045] 
dist 205=[-.87412096169821250074,.40031703432869160722] 
dist 206=[-.86604320942744552427,.52770320042050997667] 
dist 207=[-.84499075129515958267,.63241626767227815063] 
dist 208=[-.83704575576035756703,.73368447246387200485] 
dist 209=[-.79442040530757783143,.82508779896870370378] 
dist 210=[-.78404450415590485716,.89042016521870838953] 
dist 211=[-.7633894423020743996 ,.94922442818144166904] 
dist 212=[-.75677670200829040071,1.0145684069914907676 ] 
dist 213=[-.63901576744521647333,1.0733532361525746996 ] 
dist 214=[-.62149243666759491807,1.1059726739356175517 ] 
dist 215=[-.57922409306433060465,1.1257012252773027822 ] 
dist 216=[-.56938299372217849849,1.1330227273615781404 ] 
dist 217=[-.50420209339658419834,1.1354204879408090045 ] 
dist 218=[-.49084880338146246823,1.1354929321939271623 ] 
dist 219=[-.46676490210174477996,1.1338790271844309204 ] 
dist 220=[-.4605032874110146602 ,1.1301309803368977594 ] 
dist 221=[-.19503341750241400965,.9309885180864607161 ] 
dist 222=[-.16658060963946908893,.90703878363660058749] 
dist 223=[-.10586538780080880081,.84448186131038905051] 
dist 224=[-.09083038589030840150,.83408351184840269266] 
dist 225=[-.02713532437438594471,.72480628444482093501] 
dist 226=[-.01541804835825210305,.70262189986575174654] 
dist 227=[.00972048033873245907,.67694099354911149733] 
dist 228=[.01550108214195041463,.66830466233229693123] 
dist 229=[.04046945492070007127,.62561801805909359309] 
dist 230=[.04349750675180496710,.63900765055062037222] 
dist 231=[.04031029375066454491,.64764581998885105279] 
dist 232=[.02779583407999314724,.652076434395430256  ] 
dist 233=[.01021630665965458806,.65355266684953804611] 
dist 234=[-.04204422467916410777,.65313761324584593503] 
dist 235=[-.12295526285677021635,.64655482594875758263] 
dist 236=[-.25685435083733105476,.66853395448599968937] 
dist 237=[-.3903954181187747564 ,.73549968839112149046] 
dist 238=[-.47989556206861973439,.77584079309665925186] 
dist 239=[-.55434921092575325979,.80441793817586428407] 
dist 240=[-.62782336178067765535,.82442387831763858984] 
dist 241=[-.69512023342825853096,.83895971016110935855] 
dist 242=[-.74491391705877185698,.84570175454201749183] 
dist 243=[-.79146762574482684356,.848023721830668917  ] 
dist 244=[-.8458310394302977169 ,.84728050804206570406] 
dist 245=[-.89589237346856486404,.78051197554838316557] 
dist 246=[-.92527199833900250442,.76901880320059945952] 
dist 247=[-.94515626109190190264,.74866036118786769392] 
dist 248=[-.95731105138952228665,.74275536568002736735] 
dist 249=[-.96442636415627549001,.71986875389646721847] 
dist 250=[-.96496254836401782523,.71293446904163066286] 
dist 251=[-.96119817699391585284,.69936246958716448417] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 1, 1, 0, 0, 1] 
dist 0=[51.274938496229810983  ,51.274938496229810983  ] 
dist 1=[51.010773154433566666  ,51.344909054459065869  ] 
dist 2=[50.483895392886823198  ,51.360415895795788689  ] 
dist 3=[49.457304710567434247  ,51.322072918643274266  ] 
dist 4=[48.336519764135365285  ,51.250014582590522669  ] 
dist 5=[47.433369267278569083  ,51.072469071073511171  ] 
dist 6=[46.512867120839352215  ,51.010138582531912852  ] 
dist 7=[45.322934006189309994  ,50.867796594208602911  ] 
dist 8=[44.045230463719212081  ,49.660261351940355717  ] 
dist 9=[42.363560983882873528  ,46.845711683463195275  ] 
dist 10=[40.173283161334847903  ,46.265367202078598837  ] 
dist 11=[37.900150332878436720  ,45.271035747947388372  ] 
dist 12=[35.123510175807025179  ,45.011274174417477835  ] 
dist 13=[30.921860690992922231  ,44.248668028974427016  ] 
dist 14=[26.690433371114261829  ,44.022761417015329673  ] 
dist 15=[23.794786073191535828  ,43.781225973421621964  ] 
dist 16=[21.313833014348156034  ,42.432720960814075981  ] 
dist 17=[18.738834693853491826  ,32.585940559030966143  ] 
dist 18=[16.289952729721754964  ,32.236119108890475603  ] 
dist 19=[14.312661347979978278  ,32.120987252173249180  ] 
dist 20=[12.295010746959961377  ,20.143411801949172932  ] 
dist 21=[9.6846520532883583710 ,15.754800190297806338  ] 
dist 22=[7.1351028149198102090 ,14.980879964077892987  ] 
dist 23=[5.3602267078830065894 ,13.790095697888106475  ] 
dist 24=[3.8058243326928178953 ,13.494607250431440617  ] 
dist 25=[2.1368337906836145243 ,8.7314402667370311262 ] 
dist 26=[.51265540382778473251,8.1317425245884087973 ] 
dist 27=[-1.1098368220789199722 ,6.8916069651875990755 ] 
dist 28=[-2.9958063753555852571 ,6.6249538239524273039 ] 
dist 29=[-4.3061620533162173617 ,5.5578687614601764302 ] 
dist 30=[-6.2239374581933621373 ,5.3650458577282542561 ] 
dist 31=[-7.4442697481867688579 ,5.1442573211864599776 ] 
dist 32=[-8.3945588090747873885 ,4.7773117443644522381 ] 
dist 33=[-9.2330439672843747645 ,-5.1349615562392969429 ] 
dist 34=[-9.9421373383413493019 ,-5.4875026005023404368 ] 
dist 35=[-10.375381305445462365  ,-5.5425569248987298375 ] 
dist 36=[-10.693100581508780189  ,-7.9695168341788797872 ] 
dist 37=[-10.940764536203774255  ,-8.1258743574180831264 ] 
dist 38=[-11.130838876768659634  ,-8.4065520010141290843 ] 
dist 39=[-11.218386963034756708  ,-8.4505749523120822807 ] 
dist 40=[-11.249626246979999804  ,-8.4747357448458465156 ] 
dist 41=[-11.239291456407430480  ,-8.3728559798099742363 ] 
dist 42=[-11.267202515319451527  ,-7.6091963733721127308 ] 
dist 43=[-11.263798003501192899  ,-6.7087482913514072567 ] 
dist 44=[-11.241779183610135943  ,-5.5625325554359488886 ] 
dist 45=[-11.035576575134914172  ,-3.7801774557916200711 ] 
dist 46=[-10.969048603006893509  ,-1.9768587856310492910 ] 
dist 47=[-10.805305980460475353  ,-.74686453431583621409] 
dist 48=[-10.737690764161482466  ,.29987439826562125494] 
dist 49=[-7.3711660312888495150 ,1.3716455520475810596 ] 
dist 50=[-7.0251201128331545821 ,2.3788558935245267259 ] 
dist 51=[-6.6978991439666036840 ,3.1678764337441403056 ] 
dist 52=[-6.0529632579960868364 ,3.9490909188379043225 ] 
dist 53=[-4.8918302691333473990 ,4.9251617641860909755 ] 
dist 54=[-4.6735771294197095040 ,5.8578610020712190300 ] 
dist 55=[-4.3295513796899299823 ,6.4659160967159959622 ] 
dist 56=[-4.2393389664078575481 ,6.9532956575604451242 ] 
dist 57=[-2.5898483796081828569 ,7.4041793474261236640 ] 
dist 58=[-2.3769075148478928842 ,7.7976262167602781536 ] 
dist 59=[-1.8762236086519963089 ,8.0556660007790497615 ] 
dist 60=[-1.7970208539984730394 ,8.3429733352505831653 ] 
dist 61=[-1.1226010639619367920 ,8.5645968305837620516 ] 
dist 62=[-1.0022129590896370829 ,8.6685623308449316465 ] 
dist 63=[-.83137377110950794423,8.7119785229014891692 ] 
dist 64=[-.78413608014154366191,8.7110274087648133700 ] 
dist 65=[2.9602736876319671463 ,4.5199506546419935866 ] 
dist 66=[2.8243629025359431035 ,4.5697654764895789032 ] 
dist 67=[2.5574818965447276732 ,4.5806311214456620477 ] 
dist 68=[2.2736548690208643515 ,3.7391538988989802661 ] 
dist 69=[2.0700692364215100028 ,3.8070955950898391980 ] 
dist 70=[1.8864324585518574230 ,3.8582716213374729041 ] 
dist 71=[1.6821596100262366962 ,3.8808007930708351896 ] 
dist 72=[1.4803044086495957357 ,3.8868300584689791211 ] 
dist 73=[1.3062769209098591136 ,3.8820508756499048221 ] 
dist 74=[1.1192477485690821901 ,3.8459357317587805529 ] 
dist 75=[.86544675192004385017,3.8320933500284166259 ] 
dist 76=[.61324245931434425777,3.7702610038034555533 ] 
dist 77=[.43256126854256626616,3.7588476441916462531 ] 
dist 78=[.26947815734432225949,2.3629083527785837215 ] 
dist 79=[.087491011230255142  ,2.2293862408924388410 ] 
dist 80=[-.09308090083817015565,1.9025461088366167544 ] 
dist 81=[-.31054145770792492191,1.8521165519615131733 ] 
dist 82=[-.64388897146938414047,1.4142790049724211443 ] 
dist 83=[-.90480857737776655358,1.3977133765669724267 ] 
dist 84=[-1.1629820934661153516 ,1.1575780760027464357 ] 
dist 85=[-1.4853837445773003459 ,1.1279577737481193608 ] 
dist 86=[-1.7934938555764563995 ,.33928076666548561172] 
dist 87=[-1.9946163977334498912 ,.24139656147348106648] 
dist 88=[-2.1561854665695146495 ,.03285912277236016045] 
dist 89=[-2.3063843766698370877 ,-.01605750209089758222] 
dist 90=[-2.4381104634945618573 ,-.22987237404011044789] 
dist 91=[-2.5259369596503172403 ,-.26835629203849944424] 
dist 92=[-2.5986409252274924942 ,-.30646099400566353028] 
dist 93=[-2.6700146860976725890 ,-.28906187029776984073] 
dist 94=[-2.7287028261977320660 ,-.25059686671602502317] 
dist 95=[-2.7507605843241066734 ,-.17340963053700403908] 
dist 96=[-2.7582089790122907422 ,-.07725438341657635215] 
dist 97=[-2.7585212330062010460 ,.03694227654248298529] 
dist 98=[-2.6946496666112746706 ,.18627616342380623735] 
dist 99=[-2.6891546399537773412 ,.4227086428979274009 ] 
dist 100=[-2.6480834106444109351 ,.66333179214567617436] 
dist 101=[-2.6399619780107224810 ,.84968570551592453698] 
dist 102=[-2.1783204871450148387 ,1.0028552829417156707 ] 
dist 103=[-2.1140228182063112044 ,1.1509428089053775231 ] 
dist 104=[-1.9932530458947227569 ,1.2845771710393740990 ] 
dist 105=[-1.9615743248929828618 ,1.3800567036099266548 ] 
dist 106=[-1.8508954185726841912 ,1.4708794850675704201 ] 
dist 107=[-1.8214333765250738906 ,1.6087868726663674269 ] 
dist 108=[-1.7847470520910668993 ,1.7412336583202004115 ] 
dist 109=[-1.7696704641240055662 ,1.8286339650231831655 ] 
dist 110=[-.15282921466680357021,1.8998652960004759770 ] 
dist 111=[-.01839643793568382912,1.9677674572653793851 ] 
dist 112=[.27807952399149657027,2.0284409397289206932 ] 
dist 113=[.3347093401153081914 ,2.0708192086589080881 ] 
dist 114=[.45982117273629272258,2.1079881785207391228 ] 
dist 115=[.14805321773064426955,2.1478756287521172471 ] 
dist 116=[-.16686484520866126081,2.1815095056420978470 ] 
dist 117=[-.37970705626675909834,2.1937140330738008911 ] 
dist 118=[-.55860166030056037419,2.1953563132569004714 ] 
dist 119=[-.73801642847827917642,2.1912304444845100697 ] 
dist 120=[-.90409913207709744953,2.1485132244573981205 ] 
dist 121=[-1.0297779939290887999 ,2.1340899332146886000 ] 
dist 122=[-1.1499699146319262395 ,2.1052181543133006912 ] 
dist 123=[-1.2941506008129595451 ,2.0805122053401276137 ] 
dist 124=[-1.4287698974950451310 ,1.8415089582476330552 ] 
dist 125=[-1.5107962813379952590 ,1.7486825922737505520 ] 
dist 126=[-1.5700248838895270372 ,.70160320210421716855] 
dist 127=[-1.6136440788699815431 ,.67719745627516380116] 
dist 128=[-1.6456680788717354736 ,.59238489247292990774] 
dist 129=[-1.6586133380481047962 ,.57264374694073932178] 
dist 130=[-1.6620887371502228407 ,.54977447285013341595] 
dist 131=[-1.6595970349149723710 ,.54297289693646209187] 
dist 132=[-.34358355792634160249,-.0421516621172339665 ] 
dist 133=[-.48164230369810558795,-.05956764575332085004] 
dist 134=[-.59432705594339901599,-.2561569755217241458 ] 
dist 135=[-.70200288763611795592,-.27573111856788824942] 
dist 136=[-.79835024357819781169,-.3927582281756552214 ] 
dist 137=[-.86581056527122829996,-.41161164686701106707] 
dist 138=[-.92510611549006422689,-.44975928761857381231] 
dist 139=[-.98886092423919637439,-.45674377067564880609] 
dist 140=[-1.0461927115869341911 ,-.49661329694102843513] 
dist 141=[-1.0798458620647634115 ,-.49788493166268294957] 
dist 142=[-1.1026427673296026637 ,-.48830820825282886379] 
dist 143=[-1.1166301866052250071 ,-.46144617905593413401] 
dist 144=[-1.1247462886924563926 ,-.42553281800586696578] 
dist 145=[-1.1254038403059188404 ,-.37982290425529989079] 
dist 146=[-1.1204091536821024609 ,-.31816746923159553101] 
dist 147=[-1.1163444785710889452 ,-.21860169466040900072] 
dist 148=[-.97056854148946996187,-.11662506002158015981] 
dist 149=[-.96896483331947732616,-.04534420154760206118] 
dist 150=[-.95433780078312873293,.01713376509314191045] 
dist 151=[-.94934521419658028022,.08397511922255725346] 
dist 152=[-.93410693239567671731,.1485512915622175119 ] 
dist 153=[-.92782341360247936539,.20198992180920784682] 
dist 154=[-.88849972721527394529,.31229137099655837763] 
dist 155=[-.87848236920321076721,.42568134842325453239] 
dist 156=[-.86030716256962110181,.55883109309859853577] 
dist 157=[-.85466206447472024406,.75393125287659978541] 
dist 158=[-.39770824717336659134,.9472321974061044603 ] 
dist 159=[-.38676156591955395414,1.0732006811269969131 ] 
dist 160=[-.34254773230169251411,1.1740896200180234820 ] 
dist 161=[-.33366449220925864627,1.2672684070438533058 ] 
dist 162=[-.31188844453030543027,1.3484704622958227961 ] 
dist 163=[-.30715958220607828685,1.4015467593848915628 ] 
dist 164=[.26489620222721981037,1.4442430946986123902 ] 
dist 165=[.30428031794303665637,1.4840084539016502161 ] 
dist 166=[.39327956600773530746,1.5164307049099902503 ] 
dist 167=[.40624856902257832089,1.5298115612954351749 ] 
dist 168=[.50999739210737383641,1.5343560311003902567 ] 
dist 169=[.52652266805870596249,1.5321646252276371444 ] 
dist 170=[.55184103415673715375,1.5022336005915055702 ] 
dist 171=[.55633018412245716054,1.4914002840246410597 ] 
dist 172=[.45697289039911446789,1.4772480117628085444 ] 
dist 173=[.17262516137467321567,1.4700114987779270827 ] 
dist 174=[-.11369594951398951435,1.1708419560272283571 ] 
dist 175=[-.30642631333796151622,1.1377407726923246042 ] 
dist 176=[-.46766357341983564132,1.0506305017761946321 ] 
dist 177=[-.62826134686291886876,1.0377224476043844110 ] 
dist 178=[-.77631296990393264047,.88529182731227767172] 
dist 179=[-.88746485704877739818,.87930663577152378485] 
dist 180=[-.99296675884299269483,.8234702379698623217 ] 
dist 181=[-1.1184631488830050346 ,.81653163340785717104] 
dist 182=[-1.2352051389538776236 ,.49317506436817048079] 
dist 183=[-1.3057585434191144417 ,.45224761115545991983] 
dist 184=[-1.3560437029816653327 ,.37008917470813050438] 
dist 185=[-1.3918726015148634661 ,.3489337539347554818 ] 
dist 186=[-1.4182331851282685750 ,.27419390108932005046] 
dist 187=[-1.4307196458773851861 ,.25790107751605966508] 
dist 188=[-1.4354416270670481844 ,.23610302643651410734] 
dist 189=[-1.4344766532553595862 ,.22920221510056252918] 
dist 190=[-.71287278222054911273,.02969444682044304644] 
dist 191=[-.74138255054131654296,.02286459982554551634] 
dist 192=[-.763633409904039025  ,-.00225298913516932873] 
dist 193=[-.77480521421689892866,-.00722383868324775164] 
dist 194=[-.78001093568918121279,-.01610977687217861614] 
dist 195=[-.78073945087381187814,0                     ] 
dist 196=[-.81582964251542276117,-.34783751105991561325] 
dist 197=[-.84953550031964270588,-.34084036776482246898] 
dist 198=[-.87867986113183306023,-.32864545327177704531] 
dist 199=[-.89555953894094896771,-.31132577288295499428] 
dist 200=[-.90670448457296134794,-.28692491299325725749] 
dist 201=[-.91295462135533606009,-.24645962751625603639] 
dist 202=[-.91558884239970868151,-.19872503679964979016] 
dist 203=[-.91490819696142429822,-.14530357279845987583] 
dist 204=[-.90753510794139936618,-.07743801699968737215] 
dist 205=[-.90428713824116510833,.02795963304829215992] 
dist 206=[-.64777642874318005702,.13447982871289415257] 
dist 207=[-.64679719043679282346,.20682720854846687745] 
dist 208=[-.63973432433850573748,.26805640334889271473] 
dist 209=[-.63775535851199944209,.33019240128803183035] 
dist 210=[-.60823069627491010718,.38821962733063181548] 
dist 211=[-.60065696023698556832,.43304681386680335806] 
dist 212=[-.5934904869483518033 ,.47683100133246849623] 
dist 213=[-.58928341463296809518,.53069560362979916123] 
dist 214=[-.47364715470037030668,.58173265715920911206] 
dist 215=[-.45742735435559446731,.61422941365577059182] 
dist 216=[-.42544220907005603724,.63940016102943538457] 
dist 217=[-.41677489590725895067,.66119118728078542425] 
dist 218=[-.38424854434992834343,.67917198415402157532] 
dist 219=[-.37661311015336116146,.68913251047899022374] 
dist 220=[-.36226516421845726922,.6951415939639625122 ] 
dist 221=[-.35821943992949760264,.69734947088361371856] 
dist 222=[-.02699666613032089204,.72757082797665815598] 
dist 223=[-.03193477614985380816,.75574221806319235655] 
dist 224=[-.04054666532909554504,.77472533269824537668] 
dist 225=[-.05385093555099464468,.78616361000139873439] 
dist 226=[-.07314989498507721453,.79337248546921528823] 
dist 227=[-.10569292537082040661,.79547025219933902136] 
dist 228=[-.13961388341305415804,.79430251836029742696] 
dist 229=[-.16441386302486930435,.7928275587721910125 ] 
dist 230=[-.18729956693521727766,.72455390529240696478] 
dist 231=[-.21357937974110489857,.71312144220682350275] 
dist 232=[-.2400544122278875471 ,.69046643593881388021] 
dist 233=[-.26371991695952843613,.68355209263999027018] 
dist 234=[-.28987997192009185858,.65379023317092856001] 
dist 235=[-.32631403901409614489,.64662300876187637243] 
dist 236=[-.36294499554751379184,.62767704247180433174] 
dist 237=[-.38989137272878378441,.62183442876548778712] 
dist 238=[-.41492769764219428797,.40176341080605695921] 
dist 239=[-.4439339413999957138 ,.39733613973519781983] 
dist 240=[-.47330496480243917136,.38696824486865231303] 
dist 241=[-.49979796158878097027,.3832509575965739568 ] 
dist 242=[-.52928313205066664199,.36466087618485980773] 
dist 243=[-.57060009365100721163,.36027411845194881413] 
dist 244=[-.61064555066959644174,.34961679363482909794] 
dist 245=[-.63505479211585466888,.34580362830792351993] 
dist 246=[-.6527077127908941367 ,.30250541985339625662] 
dist 247=[-.6657805122581817568 ,.29566443362217584142] 
dist 248=[-.67492386021285759889,.27701465207956882115] 
dist 249=[-.67698108092996206694,.27425549192995921136] 
dist 250=[-.6763757445807449629 ,.2392856915311447007 ] 
dist 251=[-.67561832130445684431,.23208748716115105865] 
dist 252=[-.65582249899725750708,.22514185031248229943] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 1, 0, 2, 0, 1] 
dist 0=[44.805529826660296656  ,44.805529826660296656  ] 
dist 1=[44.216071960942713856  ,45.170316663660123077  ] 
dist 2=[43.072635813871159487  ,45.416492660261046846  ] 
dist 3=[41.699176071416837532  ,45.677992919821021995  ] 
dist 4=[40.191040027551906748  ,46.103622721680706884  ] 
dist 5=[38.291912942641349955  ,46.523742274341582027  ] 
dist 6=[35.356773487054324897  ,46.763152643633411700  ] 
dist 7=[32.374257730746007940  ,46.915417348481217766  ] 
dist 8=[30.285781960529793293  ,46.987726335146642019  ] 
dist 9=[28.446950196025439399  ,47.002143596373572639  ] 
dist 10=[26.461191963077364895  ,46.966482657088118756  ] 
dist 11=[24.525827858205956207  ,46.812452661297045383  ] 
dist 12=[22.887991520269374993  ,46.715343225080836832  ] 
dist 13=[21.148792624556568567  ,46.100881066749540352  ] 
dist 14=[18.808075960982873327  ,45.501789860770077685  ] 
dist 15=[16.478775889572914211  ,35.788193977448319728  ] 
dist 16=[14.784913293622463040  ,35.383110743028156976  ] 
dist 17=[13.225015513496821870  ,32.992604265628671274  ] 
dist 18=[11.430500935772315610  ,32.529985072085289470  ] 
dist 19=[9.6116748585525522469 ,31.629624466709036694  ] 
dist 20=[7.9541919924178465465 ,31.389218060143607490  ] 
dist 21=[6.0881178459706120337 ,28.157083717548104786  ] 
dist 22=[3.4350004972901812700 ,27.692923541862070434  ] 
dist 23=[.83052415498669912225,26.612680285667911412  ] 
dist 24=[-.84135891884481027094,26.393015550753533396  ] 
dist 25=[-2.1605897783368569926 ,24.919605235199357311  ] 
dist 26=[-3.3556365939385850593 ,24.466732994676274858  ] 
dist 27=[-4.3896925221144625556 ,23.713120975819518174  ] 
dist 28=[-5.0656731864739628297 ,22.969951115395753667  ] 
dist 29=[-5.6148960821059993268 ,12.864013502344009892  ] 
dist 30=[-6.1428612273607923801 ,12.708819635688720147  ] 
dist 31=[-6.6009664788000098733 ,4.6979616077580218872 ] 
dist 32=[-6.8709162004211868097 ,3.9834516141723957554 ] 
dist 33=[-7.0588756497671873836 ,2.3997207127472972836 ] 
dist 34=[-7.1885768953712667683 ,2.1113689353542640928 ] 
dist 35=[-7.2738384095048463901 ,.27560336617257964287] 
dist 36=[-7.2838156538101701867 ,-.03758612769441383410] 
dist 37=[-7.7378299721441661712 ,-.62210815794241218341] 
dist 38=[-8.6184796721002383198 ,-.75153412507875257351] 
dist 39=[-9.4221426662143907358 ,-1.6730899413411980870 ] 
dist 40=[-9.9109234220744604286 ,-.86535219162361458693] 
dist 41=[-10.265216498678778073  ,-.1838176840369745022 ] 
dist 42=[-10.531472637237101304  ,.50212269516923366311] 
dist 43=[-10.724155885563263964  ,1.1373388717040850434 ] 
dist 44=[-10.784445222178172856  ,1.6166036309901057028 ] 
dist 45=[-10.796024012487841809  ,2.0730293781104854273 ] 
dist 46=[-10.793977610951649816  ,2.6172460654404716454 ] 
dist 47=[-5.8364430302314027011 ,3.1286387974702925416 ] 
dist 48=[-5.4981555745637177738 ,3.4540848996338980305 ] 
dist 49=[-4.6773521615928793122 ,3.7054769112389567906 ] 
dist 50=[-4.5535284352861244760 ,3.9212346738400019599 ] 
dist 51=[-3.3648464655962394649 ,4.0970857753961258482 ] 
dist 52=[-3.1466139944001113574 ,4.1891200696034391819 ] 
dist 53=[-2.8734540885272616713 ,4.2368320502049394229 ] 
dist 54=[-2.8099941746446928516 ,4.2453132755509956665 ] 
dist 55=[-1.0746420790596209109 ,3.4399605762300598796 ] 
dist 56=[-.86461836641143365096,3.3677246601006582784 ] 
dist 57=[-.41186350002894881738,3.1747492038830472580 ] 
dist 58=[-.31965427323983044498,3.1409217270031803216 ] 
dist 59=[.15131164752433502912,2.7904291972330173757 ] 
dist 60=[.23000685047773976396,2.7183118742271356271 ] 
dist 61=[.38743221243176460997,2.6316026989067461992 ] 
dist 62=[.41975327615097820128,2.5987993433317833696 ] 
dist 63=[1.5927283405030998721 ,2.5377106590022679916 ] 
dist 64=[1.3319630027873448381 ,2.8330541350044075268 ] 
dist 65=[1.0822127922054249692 ,3.0713439926972834803 ] 
dist 66=[.78196653481367319406,3.2955547037878651152 ] 
dist 67=[.47185675011332059364,3.4948122771673711594 ] 
dist 68=[.18267950897559303822,3.6334189415019129175 ] 
dist 69=[-.14696784507961951769,3.7548661205866889775 ] 
dist 70=[-.61871692848506561905,3.8855974675270746629 ] 
dist 71=[-1.0855366260033824312 ,4.0013278804899099322 ] 
dist 72=[-1.3955171549363770934 ,4.0628454278783451865 ] 
dist 73=[-1.6504925396272074197 ,4.0968899188688907417 ] 
dist 74=[-1.8976826431087586892 ,4.1028374008454517938 ] 
dist 75=[-2.1214750850277683581 ,4.0947184326101333779 ] 
dist 76=[-2.2830275221463713496 ,4.0844992372913510070 ] 
dist 77=[-2.4302295083102163055 ,4.0469488220040035324 ] 
dist 78=[-2.5967267465188925542 ,4.0264222222700386951 ] 
dist 79=[-2.7475089679214100934 ,-.79480705307966611034] 
dist 80=[-2.8319607866774716406 ,-.73345992841188377496] 
dist 81=[-2.8841667966620230385 ,-.6462752512716142307 ] 
dist 82=[-3.0581457086614058014 ,-.50113515425555908826] 
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dist 85=[-3.7673050960408213105 ,.10466618115142519551] 
dist 86=[-3.9616952094898624625 ,.48172625779173579201] 
dist 87=[-4.1315627955337347073 ,.86201754766635554631] 
dist 88=[-4.2187835226965006092 ,1.1179674116066582359 ] 
dist 89=[-4.2644821518162021498 ,1.3319717580466247830 ] 
dist 90=[-4.2723166485565705203 ,1.5448373669230502128 ] 
dist 91=[-4.2382056841706046237 ,1.7408293391734862264 ] 
dist 92=[-4.2206762999800200838 ,1.8874861451956496926 ] 
dist 93=[-4.2014627330504204818 ,2.0262013461544193417 ] 
dist 94=[-4.1829576493870167736 ,2.1905053219512321028 ] 
dist 95=[-3.5814024638682307166 ,2.3430289554060453216 ] 
dist 96=[-3.5097643883364140697 ,2.4347247196787224320 ] 
dist 97=[-3.3104693405076156363 ,2.4995298685638589881 ] 
dist 98=[-3.2814810136596942539 ,2.5447141375063113758 ] 
dist 99=[-2.8967927419164572212 ,2.5742959681963914088 ] 
dist 100=[-2.8172034652433228012 ,2.6130371983798818773 ] 
dist 101=[-2.7426514199438818094 ,2.7016494019757001355 ] 
dist 102=[-2.7272060971102626491 ,2.9246255603183735961 ] 
dist 103=[-1.8090904374015922940 ,3.2592616697098507619 ] 
dist 104=[-1.6921340812417592542 ,3.4643864042072674046 ] 
dist 105=[-1.4610135728910185870 ,3.6139776323374501453 ] 
dist 106=[-1.4907603445726512297 ,3.7269399335788620188 ] 
dist 107=[-1.7414798282517285656 ,3.8116525448140326809 ] 
dist 108=[-1.9304330479293640797 ,3.8484825243820261156 ] 
dist 109=[-2.1104032462690604475 ,3.8611895733639096679 ] 
dist 110=[-2.3252572276561529996 ,3.8575110126569681596 ] 
dist 111=[-2.5253287210568468440 ,2.3639799445284214746 ] 
dist 112=[-2.6462873701273376339 ,2.2939780277150269142 ] 
dist 113=[-2.7324726491998590532 ,2.1661212590993842590 ] 
dist 114=[-2.7937345911772840496 ,2.1333201208227565035 ] 
dist 115=[-2.8369438986039055670 ,2.0244243406160763828 ] 
dist 116=[-2.8510736710894912644 ,1.9930147711564203770 ] 
dist 117=[-2.8518949992433396203 ,1.9673424368105149271 ] 
dist 118=[-2.8447741829979538783 ,1.9582110642842510567 ] 
dist 119=[.1584500869878642701 ,1.3542542928827820161 ] 
dist 120=[-.02141533120158162559,1.3922880302418863206 ] 
dist 121=[-.17074359502757671194,1.4210325796748872948 ] 
dist 122=[-.31761361313726323309,1.4447038094833885293 ] 
dist 123=[-.45181674207060119728,1.4633634426155876984 ] 
dist 124=[-.55058077586155909943,1.4720947604823588815 ] 
dist 125=[-.64239709773709770086,1.4752460391053533596 ] 
dist 126=[-.74886985774857745292,1.4727064774943764510 ] 
dist 127=[-.84799683798992180058,.83919906625124620257] 
dist 128=[-.91048825410715614307,.78524572983071187613] 
dist 129=[-.9581806527281680081 ,.65952765098789031877] 
dist 130=[-.9982234441992643594 ,.63535880930893745724] 
dist 131=[-1.0303374526907827438 ,.46581221222471864914] 
dist 132=[-1.0463747211014093796 ,.43441902411501849192] 
dist 133=[-1.0538637189471513677 ,.37918328695539027505] 
dist 134=[-1.0548206463648254891 ,.36664065179653828556] 
dist 135=[-.82299360960746679701,.15697477840543970079] 
dist 136=[-.80078544961913636905,.12879465432407402754] 
dist 137=[-.75245110973933741614,.06825466025685395237] 
dist 138=[-.73801966510189445129,.05458024055076199054] 
dist 139=[-.67554752872480153134,-.00887912377342101208] 
dist 140=[-.67790989721456420476,-.02002280418570720746] 
dist 141=[-.77212349794145473575,-.04315679939554226081] 
dist 142=[-.90060565015199666206,-.04822378911240862135] 
dist 143=[-1.0245601686509165144 ,-.06997702901253797306] 
dist 144=[-1.1006994507699858107 ,.02756018342086342373] 
dist 145=[-1.1565076497666950718 ,.12195165939630948669] 
dist 146=[-1.1992881581507815846 ,.2368331342832602305 ] 
dist 147=[-1.2324714683004899449 ,.35621821163554829395] 
dist 148=[-1.2499594308417833880 ,.46859243229402403052] 
dist 149=[-1.2593291807973907176 ,.59746509118069289381] 
dist 150=[-1.2600925739693343539 ,.78271978397719919053] 
dist 151=[-1.1838090006142145448 ,.96489050132129543462] 
dist 152=[-1.1699158959998429537 ,1.0814526870905000214 ] 
dist 153=[-1.1509751985609983327 ,1.1723914441662770523 ] 
dist 154=[-1.1432965579153584566 ,1.2522678341146969086 ] 
dist 155=[-1.1254304150401140701 ,1.3190182022387181086 ] 
dist 156=[-1.1175362243945031669 ,1.3575556842366400035 ] 
dist 157=[-1.1131249149827815472 ,1.3828517891135859178 ] 
dist 158=[-1.1102702118495883921 ,1.3967416970559418843 ] 
dist 159=[-.38062648361316465479,1.4047318992842456051 ] 
dist 160=[-.3212620275923815392 ,1.4064745786267090614 ] 
dist 161=[-.18060810588611406185,1.4039861567958559318 ] 
dist 162=[-.16006956492254634816,1.4005413276388475401 ] 
dist 163=[.03072833289859299362,1.3827279983134587959 ] 
dist 164=[.06440814157424760758,1.3763909769342248908 ] 
dist 165=[.10763170227844407791,1.3529406953201760552 ] 
dist 166=[.11584558298005391117,1.3466545631686465127 ] 
dist 167=[.18562093071725820001,.75573735474526698401] 
dist 168=[.02275829780653656906,.70137840617847144395] 
dist 169=[-.11460415012926033158,.61078492668031057245] 
dist 170=[-.2532450531628075434 ,.64711725851288350748] 
dist 171=[-.38224025887579082912,.67680037403529216122] 
dist 172=[-.4810958896522346553 ,.6926647409521938788 ] 
dist 173=[-.57689387839233478162,.70149139608456425507] 
dist 174=[-.69368282179987421162,.70353762047620461891] 
dist 175=[-.80379565735309678761,.52763230135952053862] 
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dist 177=[-.92537903492575546722,.52181203044044831071] 
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dist 186=[-.60295363494440748487,.42864629981943094513] 
dist 187=[-.62542240285862649645,.39462744420452857546] 
dist 188=[-.63894965224172208886,.38719108859855980934] 
dist 189=[-.64853562762228787675,.37707698249293370523] 
dist 190=[-.65526984815100367396,.37342877814450449137] 
dist 191=[-.6592187175737948707 ,.3453311965650205019 ] 
dist 192=[-.65962722135346249121,.34219032043682438111] 
dist 193=[-.65491831475421054034,.34017603286911176614] 
dist 194=[-.67231756438585488539,.33915042439894297472] 
dist 195=[-.71585412673276936849,.33881898703539927268] 
dist 196=[-.74101785107239866829,.33957619105528795628] 
dist 197=[-.75757285222661624557,.34126339349859061934] 
dist 198=[-.76674347150130351493,.34464364088109926618] 
dist 199=[-.77260824954325884108,.34846281199784266351] 
dist 200=[-.77596529677498845119,.41310163176503027926] 
dist 201=[-.77814040375968854079,.48679693850871314234] 
dist 202=[-.77928373177670474583,.5565181253304456711 ] 
dist 203=[-.77968277258999887286,.61841955480467303058] 
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dist 207=[-.37438447695397317489,.76844131490480133431] 
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dist 209=[-.34134979999476980438,.79971400533052851453] 
dist 210=[-.33679226345019819978,.8058265712023911325 ] 
dist 211=[-.29631204175175330175,.80821087435767430745] 
dist 212=[-.28798593522066895952,.80749495481426866535] 
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dist 215=[-.18927955635343272983,.56443370252997059818] 
dist 216=[-.17777169563946841963,.54084254138665141726] 
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dist 218=[-.14954365992046987958,.47293164336637582547] 
dist 219=[-.12951988593856232108,.40159753636412724333] 
dist 220=[-.12477622024814299601,.39630112988363472636] 
dist 221=[-.16257671415576377021,.43656313254212874124] 
dist 222=[-.27641257021973485772,.49001875836461950089] 
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dist 225=[-.52585463454789461296,.59732759468976340877] 
dist 226=[-.57875412323328934588,.61658366932644727707] 
dist 227=[-.62374986831803223034,.63138453147065019633] 
dist 228=[-.65114314019915830989,.63753814209334500579] 
dist 229=[-.67089830547451910517,.63986664024109723332] 
dist 230=[-.685402204382566885  ,.63939400922853790923] 
dist 231=[-.69671358619246862102,.62486625156613549252] 
dist 232=[-.7037246643046672088 ,.62076867180671378643] 
dist 233=[-.70892599312464521506,.60985947207261583797] 
dist 234=[-.71301468915824496772,.6052777907328639553 ] 
dist 235=[-.71607280273983113561,.62540682721700479929] 
dist 236=[-.71716102079413755588,.63643788981842771929] 
dist 237=[-.71701325510886741006,.64254787446087407137] 
dist 238=[-.7151383757267944752 ,.64354185323062427661] 
dist 239=[-.72378666612579333667,.61028002427207903482] 
dist 240=[-.73029230636064787288,.60374101223706672436] 
dist 241=[-.73243400099027944974,.59631266063025635096] 
dist 242=[-.7318196650563125744 ,.59245989537630782709] 
dist 243=[-.72054699708970811791,.5857895590574093223 ] 
dist 244=[-.71625545591981392733,.58267910470420050251] 
dist 245=[-.70737272095877488407,.58026280671388265283] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 0, 2, 0, 2, 0, 1] 
dist 0=[46.618527260673241997  ,46.618527260673241997  ] 
dist 1=[46.192977051194906680  ,47.073378682027390255  ] 
dist 2=[44.948689803066665217  ,47.713471325613203916  ] 
dist 3=[43.443690288067481735  ,48.266943871007408981  ] 
dist 4=[41.791141397941906548  ,48.716917392775408886  ] 
dist 5=[39.710278901732115301  ,48.943703552212809758  ] 
dist 6=[36.494547145848891003  ,49.049832606441439919  ] 
dist 7=[33.237064389245584200  ,49.036021133928106077  ] 
dist 8=[30.989322629890171642  ,48.906891895319668367  ] 
dist 9=[29.045264574567250800  ,48.835295441982855823  ] 
dist 10=[27.000365680901247793  ,48.488983083942237958  ] 
dist 11=[25.040114130744576800  ,48.413459065323213229  ] 
dist 12=[23.433865494505490885  ,46.964493637401649529  ] 
dist 13=[21.773981126917049987  ,46.645821077195375950  ] 
dist 14=[19.599026283917170229  ,45.471322275828436680  ] 
dist 15=[17.461764275940949020  ,43.461307043185655164  ] 
dist 16=[15.952168978658652190  ,32.999143070604675315  ] 
dist 17=[14.606880300563840571  ,32.336012053818467438  ] 
dist 18=[13.125576959142242838  ,31.586628202914413093  ] 
dist 19=[11.660759717812314182  ,31.388439233009058395  ] 
dist 20=[10.380841075608522208  ,24.891727839456941558  ] 
dist 21=[8.9832071054372463780 ,24.053822425385849175  ] 
dist 22=[7.0470973002699092345 ,22.373234514455409736  ] 
dist 23=[5.1523249298748891536 ,21.935733879562874686  ] 
dist 24=[3.9197196056375127925 ,20.357239327906085764  ] 
dist 25=[2.9272388138724555110 ,20.014900328684718986  ] 
dist 26=[1.9924443583771309323 ,19.450985934465866139  ] 
dist 27=[1.1572195841458859756 ,19.305741925372232297  ] 
dist 28=[.5626872333968659238 ,11.873248325132935626  ] 
dist 29=[.0250898292748229168 ,11.528928692946429634  ] 
dist 30=[-1.4488136331902909932 ,10.128928907587927903  ] 
dist 31=[-3.4265280408134154144 ,7.8612043654999616639 ] 
dist 32=[-5.2274508141420696287 ,-.4663203307047672556 ] 
dist 33=[-6.5513000166138234054 ,-.5998527729667148743 ] 
dist 34=[-7.7839276140303708637 ,-.5769216475748739814 ] 
dist 35=[-9.2204942180278150246 ,-.4926337004374010534 ] 
dist 36=[-10.551709902410356854  ,-.32892857652780399219] 
dist 37=[-11.363512499067467021  ,-.07818422573431705588] 
dist 38=[-11.953373743060044400  ,.35343661654001446645] 
dist 39=[-12.398011885578490509  ,.79668677825119589227] 
dist 40=[-12.738115241494182949  ,1.0939504572021047336 ] 
dist 41=[-12.910342366079462627  ,1.3390730506411929856 ] 
dist 42=[-12.993428699317764477  ,1.5745886890959087989 ] 
dist 43=[-12.996316906679675928  ,1.7836846557614959735 ] 
dist 44=[-10.777173655706610682  ,1.9234713967339756056 ] 
dist 45=[-10.795367234205603884  ,2.0384304080216368112 ] 
dist 46=[-10.790408983376830427  ,2.1528281353703333869 ] 
dist 47=[-10.761083203364093765  ,2.2544590971211787455 ] 
dist 48=[-5.4736985717678437907 ,2.3206104702800843785 ] 
dist 49=[-5.0337291506973633823 ,2.3728893151656563595 ] 
dist 50=[-4.0097183660341302525 ,2.4191787151134226077 ] 
dist 51=[-3.9465557529877803517 ,2.4572866839828457564 ] 
dist 52=[-2.3716150614966288719 ,2.4768809259840325503 ] 
dist 53=[-2.1102845946275552393 ,2.4860095585713912934 ] 
dist 54=[-1.7548197813176680650 ,2.4822326368257349397 ] 
dist 55=[-1.6595616062318158221 ,1.0630320177273499071 ] 
dist 56=[-.4505082974686436346 ,1.6492382093707754068 ] 
dist 57=[-.3557605886114815341 ,2.2040835991951435197 ] 
dist 58=[-.1857574841901396804 ,2.6688501267528328112 ] 
dist 59=[-.1512137781198411935 ,3.1334057041433591010 ] 
dist 60=[-.02269475731347929155,3.5635877652822898953 ] 
dist 61=[-.21239443256495945953,3.8912060814333986393 ] 
dist 62=[-.46123816007042408574,4.2075093836317251476 ] 
dist 63=[-.70422255702868361553,4.5926939933594932658 ] 
dist 64=[-.87055673813567226533,4.9503032491341917738 ] 
dist 65=[-1.0125949384821936340 ,5.1565145951176561505 ] 
dist 66=[-1.1586379775264153276 ,5.2923608346589208652 ] 
dist 67=[-1.2961614963913280747 ,5.3688686649626295729 ] 
dist 68=[-1.4042189249500168003 ,5.4171535742451873553 ] 
dist 69=[-1.5114992901213211004 ,5.4402226674957315059 ] 
dist 70=[-1.6459587850523008496 ,5.4495605415058509639 ] 
dist 71=[-1.7724969254249978278 ,5.4429039293441398054 ] 
dist 72=[-1.8481660047322843096 ,4.9487498967861859058 ] 
dist 73=[-1.9012180897929971179 ,4.9513931431691452876 ] 
dist 74=[-1.9374631468980093786 ,4.9205707196618628355 ] 
dist 75=[-1.9613500787542041263 ,4.9122654620245566180 ] 
dist 76=[-1.9658181351763068842 ,4.4383243421704314875 ] 
dist 77=[-2.3768337707415328236 ,4.3931622536965432380 ] 
dist 78=[-2.8233460040259027125 ,4.3433829408491932569 ] 
dist 79=[-3.2500517853609116675 ,4.3173995625142209036 ] 
dist 80=[-3.6318203901999654257 ,1.4943801652689238717 ] 
dist 81=[-3.8989657744256182471 ,1.2669792199915578162 ] 
dist 82=[-4.1336170860896015003 ,.91644273997059077961] 
dist 83=[-4.3857076073303477731 ,1.0446327003971396383 ] 
dist 84=[-4.6087894170617134123 ,1.1631724604272266108 ] 
dist 85=[-4.7276379829585425751 ,1.2974057307410509395 ] 
dist 86=[-4.7931131917783145656 ,1.4882547704275255571 ] 
dist 87=[-4.8078107513048155983 ,1.6744233959346675794 ] 
dist 88=[-4.7935217289240657073 ,1.7899787495392305221 ] 
dist 89=[-4.7809625575185810769 ,1.8760176402235404852 ] 
dist 90=[-4.7638938200432407044 ,1.9443645490006619825 ] 
dist 91=[-4.7443797849325201446 ,1.9963045388445924894 ] 
dist 92=[-3.8875406073825658070 ,2.0168485518476820128 ] 
dist 93=[-3.7872487248234464004 ,2.0247675081637095733 ] 
dist 94=[-3.5174858335269482175 ,2.0263082204051058280 ] 
dist 95=[-3.4788188564719465478 ,2.0347269105487687527 ] 
dist 96=[-2.9898795191389765185 ,2.0994058926527027693 ] 
dist 97=[-2.8912389762727486531 ,2.3724214682712000939 ] 
dist 98=[-2.7956575083235425347 ,2.7065146133662524419 ] 
dist 99=[-2.7778582466931932017 ,3.1112970833828744708 ] 
dist 100=[-1.7147389461884276103 ,3.4912284157126329033 ] 
dist 101=[-1.6803612605114747962 ,3.7261283571895889966 ] 
dist 102=[-1.6354923962919599116 ,3.8998142789010318931 ] 
dist 103=[-1.6188841591905558605 ,4.0354089965129682109 ] 
dist 104=[-1.2412473701818100529 ,4.1383223826093874314 ] 
dist 105=[-1.1900718755248559849 ,4.1815599388725285869 ] 
dist 106=[-1.0810944475618394393 ,4.1980048903337904163 ] 
dist 107=[-1.2559825287356270493 ,4.1939787690665522412 ] 
dist 108=[-1.3927470210098911739 ,1.1412847529326395395 ] 
dist 109=[-1.5143369001500437985 ,1.4511684403226393936 ] 
dist 110=[-1.6470517104396103411 ,1.6977997813128867975 ] 
dist 111=[-1.7678335285251894273 ,1.9229620461001301591 ] 
dist 112=[-1.8417922089055493431 ,2.1173891567119171965 ] 
dist 113=[-1.8956295353846836993 ,2.2413215411438798741 ] 
dist 114=[-1.9360969124535360074 ,2.3375072338238196772 ] 
dist 115=[-1.9648765989694327381 ,2.4211711634763047609 ] 
dist 116=[-1.9720621637189342267 ,2.4919738960149845148 ] 
dist 117=[-1.9708904133488487752 ,2.5368138354660547890 ] 
dist 118=[-1.9663126700771550594 ,2.5713112975300877839 ] 
dist 119=[.38601424203115778404,2.6008138762001944136 ] 
dist 120=[.38605999017953229342,2.6249213374013947941 ] 
dist 121=[.36905333414902655895,2.6378750973512806128 ] 
dist 122=[.33680494249926344513,2.6451695767679795446 ] 
dist 123=[.27538244677073547714,2.6466792434394094532 ] 
dist 124=[.0270509210229034196 ,1.9065097139131918903 ] 
dist 125=[-.2077960418597744822 ,1.8741645635726782966 ] 
dist 126=[-.4080293765521630747 ,1.7816237355977031024 ] 
dist 127=[-.6135186846191073204 ,1.7681569016241367860 ] 
dist 128=[-.8068004111966441051 ,1.5804339459732905674 ] 
dist 129=[-.9583101179425748293 ,1.5408300577604018451 ] 
dist 130=[-1.1083432856998962126 ,1.5053031927691782149 ] 
dist 131=[-1.2957411319057950390 ,1.4978385703344997213 ] 
dist 132=[-1.4746627989206872501 ,1.0198454321876858091 ] 
dist 133=[-1.5908650721658086287 ,.95831649915523342079] 
dist 134=[-1.6834838281817233546 ,.83829520295492885712] 
dist 135=[-1.7682674732099123787 ,.80763361962816367467] 
dist 136=[-1.8416568740596225520 ,.70232862819662019406] 
dist 137=[-1.8887978323853303837 ,.677350538287316879  ] 
dist 138=[-1.9258346242028529643 ,.65137732825515163371] 
dist 139=[-1.9589046246539831138 ,.64559938641240643107] 
dist 140=[-1.9839060410025813212 ,-.25311388592068018323] 
dist 141=[-1.9890300768207262713 ,-.12029478832186398999] 
dist 142=[-1.9863664997766955072 ,.04625198373131209327] 
dist 143=[-2.0141825644078687292 ,.30245226090742786679] 
dist 144=[-2.0653803474615720588 ,.56006812098928701146] 
dist 145=[-2.0866451403633748857 ,.73226527866999841775] 
dist 146=[-2.0953368405725245344 ,.87492187854590692689] 
dist 147=[-2.0963348062263587266 ,1.0146234271755934436 ] 
dist 148=[-2.0314907004537633677 ,1.1417803871736234880 ] 
dist 149=[-2.0154800125085945595 ,1.2343631701749452047 ] 
dist 150=[-1.9815298377046647948 ,1.3193745696677653435 ] 
dist 151=[-1.9687815373821473962 ,1.4163073774976297708 ] 
dist 152=[-1.9031472018769584138 ,1.5042167313956812365 ] 
dist 153=[-1.8873302598453833371 ,1.5532091357700848269 ] 
dist 154=[-1.8362520819466177944 ,1.5830760497853199287 ] 
dist 155=[-1.8264798951768418601 ,1.5946434516372789658 ] 
dist 156=[-1.2408751473289014138 ,1.5989603847089749654 ] 
dist 157=[-1.2104024323939895755 ,1.5998878480939812404 ] 
dist 158=[-1.1351888772732583217 ,1.5985009899429531864 ] 
dist 159=[-1.1182520707749874184 ,1.5935852653033478864 ] 
dist 160=[-.9960273394610080227 ,1.1126514094877940335 ] 
dist 161=[-.9706100387072143471 ,1.2393387775909172175 ] 
dist 162=[-.9282389106318609752 ,1.3579797602061428583 ] 
dist 163=[-.9165933521073535246 ,1.4967958318760831961 ] 
dist 164=[-.6748214248844653870 ,1.6247274016667615703 ] 
dist 165=[-.6415349191847045650 ,1.6999133921305696697 ] 
dist 166=[-.5644560471646457469 ,1.7509067107805406946 ] 
dist 167=[-.5473721335998196499 ,1.7822546309663015125 ] 
dist 168=[-.4420098513086923753 ,1.8033580575293356605 ] 
dist 169=[-.4216835694930980123 ,1.8134579651221079124 ] 
dist 170=[-.3829184615742933267 ,1.8174391871804266344 ] 
dist 171=[-.3728894399506373244 ,1.8141310616697890511 ] 
dist 172=[.31363130560589417699,1.4951340735065322231 ] 
dist 173=[.30753154282000120001,1.5116228857240351680 ] 
dist 174=[.2921596205853218777 ,1.5182573302257533567 ] 
dist 175=[.26012744969862908173,1.5170583068658990430 ] 
dist 176=[.1132097777445485092 ,1.4890897620881732757 ] 
dist 177=[-.02964728343774903943,1.4809869756933785409 ] 
dist 178=[-.15504269247206529482,1.4524134290241459074 ] 
dist 179=[-.28951125656642540899,1.4447677341001084627 ] 
dist 180=[-.41963421527873025555,1.3645506531809575443 ] 
dist 181=[-.52768330401159259737,1.3450814355653766761 ] 
dist 182=[-.64033743720400829712,1.3215760573799486643 ] 
dist 183=[-.78884527780654005228,1.3110935374805299869 ] 
dist 184=[-.93444169480560362075,1.0458457748898715250 ] 
dist 185=[-1.0354742706396606368 ,1.0086493859826314435 ] 
dist 186=[-1.1232880178250449681 ,.931860061117585814  ] 
dist 187=[-1.2161158356856263666 ,.91035850906475954057] 
dist 188=[-1.3051524710350405630 ,.82458340410318540615] 
dist 189=[-1.3778328802699731414 ,.80636539070968894494] 
dist 190=[-1.4525152729820165904 ,.76409096532650786917] 
dist 191=[-1.5495460146278447984 ,.75141773039277421517] 
dist 192=[-1.6405686759641574037 ,-.11386091123799957203] 
dist 193=[-1.6912667504079025092 ,-.10406320399642384465] 
dist 194=[-1.7221782330518309833 ,-.08204797616903424841] 
dist 195=[-1.7342104555292723601 ,-.03759809918348517420] 
dist 196=[-1.7385688050818128115 ,.01312067474365058605] 
dist 197=[-1.7388450607010042997 ,.06016233041494806978] 
dist 198=[-1.7361871407425596970 ,.11354774116510071165] 
dist 199=[-1.7305985486752772431 ,.18959320341975336099] 
dist 200=[-1.5165377366367085054 ,.27445130835240193554] 
dist 201=[-1.4838594266244126965 ,.36301809528220149948] 
dist 202=[-1.4230154161973652295 ,.47133362438588764068] 
dist 203=[-1.4062024872605151988 ,.63503015157340828687] 
dist 204=[-1.3433800674827259632 ,.79900870573221519181] 
dist 205=[-1.3262614507112859968 ,.90845071978301525899] 
dist 206=[-1.2953491113306441912 ,.99898196588128483216] 
dist 207=[-1.2859247289195667013 ,1.0874691658193892502 ] 
dist 208=[-.766558751774713829  ,1.1679494702178177691 ] 
dist 209=[-.74295158908383786772,1.2265176590532838617 ] 
dist 210=[-.68385334250132138296,1.2802980351759713979 ] 
dist 211=[-.67295751560394619956,1.3416663573479829044 ] 
dist 212=[-.57733231359553695279,1.3974151548854435617 ] 
dist 213=[-.55819920585576286491,1.4287627034450909220 ] 
dist 214=[-.53177488250076168038,1.4482654819873139513 ] 
dist 215=[-.52316081197540036251,1.4567299281580467492 ] 
dist 216=[-.34284657272587068313,1.4587406678196818862 ] 
dist 217=[-.31901220184778005943,1.4566117231376770543 ] 
dist 218=[-.26680384595158935793,1.4439842701033323672 ] 
dist 219=[-.2538501217630426598 ,1.4370796964104731831 ] 
dist 220=[-.19271578591368779815,1.3333479564138233423 ] 
dist 221=[-.18144767211006700671,1.3146873946317547806 ] 
dist 222=[-.15500611675987405875,1.2671914016598107196 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 2, 1, 1, 2] 
dist 0=[46.183950826623719265  ,46.183950826623719265  ] 
dist 1=[45.253550805062130242  ,46.946486887737883093  ] 
dist 2=[43.849179442788591736  ,47.680125521789658065  ] 
dist 3=[42.244292087046918422  ,48.305116623718475644  ] 
dist 4=[40.512909124802300564  ,48.633777714036255887  ] 
dist 5=[38.353240407184259020  ,48.807931231985731432  ] 
dist 6=[35.037695556082790451  ,48.820437208822063445  ] 
dist 7=[31.687029156890711964  ,48.741998789354665705  ] 
dist 8=[29.386949871167277947  ,48.670905668741093152  ] 
dist 9=[27.410169601362133215  ,48.414456438386507429  ] 
dist 10=[25.350439531016635691  ,48.278117457664341590  ] 
dist 11=[23.387744931021548618  ,46.520721151309907963  ] 
dist 12=[21.798246996805680263  ,46.171071673437970215  ] 
dist 13=[20.172265002450514489  ,45.685894948875676922  ] 
dist 14=[18.063346583802212644  ,45.162088183262657653  ] 
dist 15=[16.000500875059172231  ,41.499217514896551179  ] 
dist 16=[14.558272046243688464  ,39.195519354715868736  ] 
dist 17=[13.288061163118563703  ,33.529178027060684874  ] 
dist 18=[11.911982394474978264  ,33.371861050127388122  ] 
dist 19=[10.563767923394068741  ,26.796715964720367272  ] 
dist 20=[9.4043630205315911306 ,25.948552564011507863  ] 
dist 21=[8.1532823829119897802 ,24.281387273955972145  ] 
dist 22=[6.4377429869540242671 ,23.852875117519421339  ] 
dist 23=[4.7615155943142038652 ,22.351219844423115413  ] 
dist 24=[3.6673852031296332789 ,22.007506727707500084  ] 
dist 25=[2.7813798741332625207 ,21.549656781140372197  ] 
dist 26=[1.9373921584316782503 ,21.395969956882121860  ] 
dist 27=[1.1760963795022854170 ,13.759905381307638178  ] 
dist 28=[.62067003562346123701,13.487016470143904446  ] 
dist 29=[.10425133335720530801,11.610113847032231878  ] 
dist 30=[-1.6935143691336160828 ,10.789522108383678605  ] 
dist 31=[-3.5960634331984966168 ,8.2146240161788459082 ] 
dist 32=[-5.0133394267295720956 ,7.2868814882987633157 ] 
dist 33=[-6.3514096224528993232 ,.27022050419883899168] 
dist 34=[-7.9375619800060852892 ,.38141409484057930812] 
dist 35=[-9.4171127688456606937 ,.54991145007997349703] 
dist 36=[-10.329349117623304068  ,.78195477516576444273] 
dist 37=[-11.003845173293631606  ,1.1027353778047057378 ] 
dist 38=[-11.533707989559976208  ,1.6253810810948617686 ] 
dist 39=[-11.950266624344957464  ,2.1545037230460305881 ] 
dist 40=[-12.172141127147280043  ,2.5012661317220533206 ] 
dist 41=[-12.294815670765360383  ,2.7790914927794862526 ] 
dist 42=[-12.315068945798486377  ,3.0334846524829798630 ] 
dist 43=[-9.4586438434214495562 ,3.2518309274741372742 ] 
dist 44=[-9.5429614060761153046 ,3.3859626369474168940 ] 
dist 45=[-9.5921927810013590613 ,3.4833562100642996769 ] 
dist 46=[-9.5880731242715462335 ,3.5551930915411967544 ] 
dist 47=[-9.5499954986097300966 ,3.6102602327779279910 ] 
dist 48=[-9.5152533391006372546 ,3.6407609860795990964 ] 
dist 49=[-5.8467703284050630360 ,3.6586202048373706662 ] 
dist 50=[-5.5205221148396283628 ,3.6632307068315913165 ] 
dist 51=[-4.7314066732899878804 ,3.6581977936337870845 ] 
dist 52=[-4.6072783488767567719 ,3.6463379035649337869 ] 
dist 53=[-3.4668463658526410950 ,3.6100067798115980176 ] 
dist 54=[-3.2563373020391843066 ,3.5888037727731610480 ] 
dist 55=[-2.9792610292351401095 ,1.6401620342239055056 ] 
dist 56=[-2.9014556502037114692 ,1.4702371506665856706 ] 
dist 57=[-1.6791666968971400728 ,1.8741568318006921696 ] 
dist 58=[-1.6430670960459504915 ,2.3726411784508551087 ] 
dist 59=[-.60417166886762991029,2.7924047921670850217 ] 
dist 60=[-.52217057373398399375,3.2156747759398948794 ] 
dist 61=[-.06921854497467232996,3.6101192058123646027 ] 
dist 62=[-.36167375374390852716,3.9148841482737281328 ] 
dist 63=[-.64191525633441945232,4.2134086091020412410 ] 
dist 64=[-.82511794070811623803,4.5831190044013865499 ] 
dist 65=[-.97238852511234800564,4.9297426365850318981 ] 
dist 66=[-1.1092437088907561551 ,5.1360989530594896950 ] 
dist 67=[-1.2291118187023896739 ,5.2803288449437878353 ] 
dist 68=[-1.3086091131585691566 ,5.3787498312765581519 ] 
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dist 72=[-1.5292617879961312267 ,5.4459310987767726734 ] 
dist 73=[-1.5574585411712648314 ,5.1497400716307690890 ] 
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dist 76=[-1.6191208999270441822 ,4.9219764394814491742 ] 
dist 77=[-1.6307684394720714024 ,4.7082937334976683374 ] 
dist 78=[-1.6420304720199501789 ,4.6593251360443609834 ] 
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dist 81=[-2.6184692223440751048 ,3.0984938992295154886 ] 
dist 82=[-2.9589777072551142052 ,2.9581667450893316962 ] 
dist 83=[-3.2770362846354041950 ,2.6119652177173755915 ] 
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dist 85=[-3.6148184072290905312 ,2.0293322348894907887 ] 
dist 86=[-3.7237576510915981739 ,1.9285288489145084281 ] 
dist 87=[-3.8039236669172467927 ,1.8078874622247859355 ] 
dist 88=[-3.8317241087106775161 ,1.9337180304842601316 ] 
dist 89=[-4.0779024971298036491 ,2.1571868765083320724 ] 
dist 90=[-4.2877236648394806771 ,2.3604094742764020247 ] 
dist 91=[-4.4405968723058805476 ,2.5352514901009648090 ] 
dist 92=[-4.5560878508136535801 ,2.6454313471480525107 ] 
dist 93=[-4.6416624086331121879 ,2.7294493612973458625 ] 
dist 94=[-4.6750819619924385278 ,2.7998635767293586841 ] 
dist 95=[-4.6851078103304741210 ,2.8562484182635892871 ] 
dist 96=[-4.6772603915630193714 ,2.8842609517896405754 ] 
dist 97=[-3.4947107744385982998 ,2.9593318728063199926 ] 
dist 98=[-3.4745116983365413830 ,3.2520500657983403967 ] 
dist 99=[-2.9687257131297664521 ,3.5243543437857548158 ] 
dist 100=[-2.8945996723227307290 ,3.6883170988280297041 ] 
dist 101=[-2.7290945855033869159 ,3.8043160449729272395 ] 
dist 102=[-2.6790091999940675240 ,3.8851834040805160846 ] 
dist 103=[-2.4594804621577310818 ,3.9410126122590828384 ] 
dist 104=[-2.3539261512699895993 ,3.9570696187487746873 ] 
dist 105=[-1.9867823975064693002 ,3.9555313807669588409 ] 
dist 106=[-1.8061823238561200295 ,3.9438367107231847659 ] 
dist 107=[-.77166425020244080157,.92836956309501301726] 
dist 108=[-.97670423517970981157,.85630397285499784396] 
dist 109=[-1.1764338698827196998 ,1.0090353110413711158 ] 
dist 110=[-1.4212974536823778174 ,1.2638264382543761401 ] 
dist 111=[-1.6527278061263405457 ,1.4909471446330623404 ] 
dist 112=[-1.7988342864876426160 ,1.6485144475150740281 ] 
dist 113=[-1.9104993876238367398 ,1.7855088604210062972 ] 
dist 114=[-2.0044451165899786497 ,1.9305090030479097217 ] 
dist 115=[-2.0798680049799972297 ,2.0619198040896611598 ] 
dist 116=[-2.1175926499242619787 ,2.1446614034604922968 ] 
dist 117=[-2.1367908369517204149 ,2.2077298378888252087 ] 
dist 118=[-2.1390835852568585496 ,2.2605866764504672155 ] 
dist 119=[-.95961279345391238157,2.3029359652559136063 ] 
dist 120=[-1.0535675623644286975 ,2.3240484485307687370 ] 
dist 121=[-1.1281277858452735843 ,2.3336821700455426676 ] 
dist 122=[-1.1958404429528470908 ,2.3314383989735034128 ] 
dist 123=[-1.2540708177259906286 ,1.4536434789929167785 ] 
dist 124=[-1.2907754098926768166 ,1.3778082551980019005 ] 
dist 125=[-1.3187946284052441718 ,1.2035584602410339840 ] 
dist 126=[-1.3423527011428422322 ,1.1655692345212561378 ] 
dist 127=[-1.3597108869029886592 ,.93455602018266263309] 
dist 128=[-1.3634200763061892152 ,.89092478673778396285] 
dist 129=[-1.3614066891603942159 ,.80630152271814562917] 
dist 130=[-1.3594399746934766265 ,.78451030446853407093] 
dist 131=[-1.3121131585196309248 ,.50580960447020505723] 
dist 132=[-1.2986311548957366495 ,.46544119252843386229] 
dist 133=[-1.2880674851611462634 ,.38118663395196200158] 
dist 134=[-1.2809080420812085950 ,.35885936743636659461] 
dist 135=[-1.0608187596908090986 ,.48194866330348340966] 
dist 136=[-1.0459451943598819543 ,.66490661087176740088] 
dist 137=[-1.2354290423486738702 ,.81449819966437854268] 
dist 138=[-1.5000844813703508592 ,.95781564172350166285] 
dist 139=[-1.7576259329512601186 ,1.0862569607074724457 ] 
dist 140=[-1.9187113719519480653 ,1.1764651067534995062 ] 
dist 141=[-2.0401871351391954364 ,1.2560155095204586955 ] 
dist 142=[-2.1395902165708540968 ,1.3419144071973481022 ] 
dist 143=[-2.2187504285830581034 ,1.4191177515933755494 ] 
dist 144=[-2.2594051095756405505 ,1.4639551854942582631 ] 
dist 145=[-2.2802362729434400683 ,1.4937093752742187322 ] 
dist 146=[-2.2838658134377307242 ,1.5106961842566797272 ] 
dist 147=[-2.2156800661526814401 ,1.5199552179973038347 ] 
dist 148=[-2.1985243214072225885 ,1.5198222517237590594 ] 
dist 149=[-2.1780900621607829264 ,1.5134493212815342695 ] 
dist 150=[-2.1669684371934952260 ,1.5072941000579259254 ] 
dist 151=[-2.1385041220897879550 ,1.1203204228732573372 ] 
dist 152=[-2.1253053289693660080 ,1.0800957075762130061 ] 
dist 153=[-2.1037476021028363537 ,.98041697179046151046] 
dist 154=[-2.0950954878352519208 ,.96258104711379285142] 
dist 155=[-.87173886813104750308,.83598440136038684311] 
dist 156=[-.76840956646607937895,.81061011196947579394] 
dist 157=[-.52184126864486694577,.76909358736199067491] 
dist 158=[-.48555280522112290455,.75785895431675435647] 
dist 159=[-.1439580290433927752 ,.53398845519715404146] 
dist 160=[-.09716012584590460796,.54761099817157488298] 
dist 161=[-.11371978054044079033,.69321312063588094311] 
dist 162=[-.14220397796717505882,.87068572560393199302] 
dist 163=[-.17622082552362171522,1.0380463503905654953 ] 
dist 164=[-.24306768084286644859,1.1432783195439801711 ] 
dist 165=[-.3742608403274805712 ,1.2232587063420707078 ] 
dist 166=[-.56143599953779844579,1.2898066482325246523 ] 
dist 167=[-.74604185831165230295,1.3434696671106234686 ] 
dist 168=[-.86697907824973999005,1.3720081500471573472 ] 
dist 169=[-.96454084166692506749,1.3876316508341293096 ] 
dist 170=[-1.0558299337727432630 ,1.3909028767018469603 ] 
dist 171=[-1.1361979137008147994 ,1.1480125234169376009 ] 
dist 172=[-1.1901622960829674597 ,1.1625643749042460288 ] 
dist 173=[-1.2351734449371794543 ,1.1703809951792134521 ] 
dist 174=[-1.2798011803696388830 ,1.1710468650577404567 ] 
dist 175=[-1.3176420079441323251 ,1.0812359889893203674 ] 
dist 176=[-1.3355588641469681106 ,1.0658295426925294992 ] 
dist 177=[-1.3436756467233376180 ,1.0438028011433559132 ] 
dist 178=[-1.3437024446343705177 ,1.0356232796911151236 ] 
dist 179=[-1.3251616287677628644 ,1.0158736514513660404 ] 
dist 180=[-1.3170697855292816815 ,1.0077552489298947589 ] 
dist 181=[-1.3072170390607057928 ,1.0015823678244139223 ] 
dist 182=[-1.3013533502469545087 ,.99644358725040077119] 
dist 183=[-.04134058430463706298,.82191104412937074988] 
dist 184=[-.1720964566475656381 ,.80967507179554240994] 
dist 185=[-.32690872100532151968,.79300693885935477161] 
dist 186=[-.55521464580698763436,.78664796102265223127] 
dist 187=[-.78130834006476165406,.71362262380840943396] 
dist 188=[-.92729035228934298413,.70335377805282349793] 
dist 189=[-1.0426724749126829993 ,.7385909407894516903 ] 
dist 190=[-1.1466081275245636509 ,.82642146010870362284] 
dist 191=[-1.2353452362394831203 ,.90758771027379708973] 
dist 192=[-1.2900539251425616724 ,.95852921465183884257] 
dist 193=[-1.3303696249290989623 ,.99712466999860993366] 
dist 194=[-1.3616507117519515806 ,1.0290026781702257530 ] 
dist 195=[-1.3864269654446579790 ,1.0541445642452055495 ] 
dist 196=[-1.4007740795014256847 ,1.0658473057222002358 ] 
dist 197=[-1.4102530222426371606 ,1.0704412767942225836 ] 
dist 198=[-1.4155909245613076095 ,1.0702186510113854499 ] 
dist 199=[-1.4178697219462025582 ,.78720132910614060485] 
dist 200=[-1.4151339603815176369 ,.76070581475976645918] 
dist 201=[-1.4085319470235397196 ,.70153322616478413452] 
dist 202=[-1.4042394847882271409 ,.68481964261288541837] 
dist 203=[-.71862611210691177262,.60809611329997017933] 
dist 204=[-.6592149086882339931 ,.59845014810263510588] 
dist 205=[-.51904223721261398448,.59758178912105138345] 
dist 206=[-.49516107713461036106,.59639353977881159474] 
dist 207=[-.33294156721326965763,.59507860260328749057] 
dist 208=[-.30325954212428537105,.59370712815930430326] 
dist 209=[-.25115590676555759032,.5920284422547971862 ] 
dist 210=[-.2394611505198799328 ,.58953930477436593974] 
dist 211=[-.28335502620596057195,.58685980883553545564] 
dist 212=[-.39006750144668583601,.58481472243340600373] 
dist 213=[-.51209026865580231976,.58281308693386887446] 
dist 214=[-.68704444760198753372,.58035849991910454572] 
dist 215=[-.85864148523396127098,.57781795178192368875] 
dist 216=[-.96726268468206023927,.60136756159687715572] 
dist 217=[-1.0506369389942458523 ,.68350675412731498199] 
dist 218=[-1.1214467372215362656 ,.79480568573344616201] 
dist 219=[-1.1791391823049180349 ,.90271199759752388734] 
dist 220=[-1.2101486014580139128 ,.97130810484082652635] 
dist 221=[-1.2275749613456084942 ,1.0243114017989257913 ] 
dist 222=[-1.2316847366629778859 ,1.0699686255355540032 ] 
dist 223=[-1.2179141366962537694 ,1.1074668765579792124 ] 
dist 224=[-1.2142582523100302869 ,1.1278988176274173373 ] 
dist 225=[-1.2111161535469770519 ,1.1397688161846747865 ] 
dist 226=[-1.2078568117666218839 ,1.1430882055872319266 ] 
dist 227=[-1.2047780613850560322 ,1.1418292964604107416 ] 
dist 228=[-1.2023581335907819258 ,1.1391080690873742945 ] 
dist 229=[-1.1701476139698049506 ,1.1277381365380344273 ] 
dist 230=[-1.1678204491324510605 ,1.1213825241562769045 ] 
dist 231=[-1.1620510708789685495 ,1.0803960586050936507 ] 
dist 232=[-1.1578289185299927571 ,1.0691678674779700085 ] 
dist 233=[-1.1428611924316135378 ,1.0493256113936182451 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 2, 0, 0, 0, 0, 2] 
dist 0=[37.319903217196324244  ,37.319903217196324244  ] 
dist 1=[36.510569505023680333  ,37.794678561663640093  ] 
dist 2=[35.660928282946970311  ,38.116160482721380863  ] 
dist 3=[35.025025984444414932  ,38.313050968779957874  ] 
dist 4=[34.422009604280965829  ,38.441064070068372599  ] 
dist 5=[33.703488830717559500  ,38.487511915847427574  ] 
dist 6=[32.962323831417639332  ,38.482995230896925021  ] 
dist 7=[32.268646560593685873  ,38.459994803616367425  ] 
dist 8=[31.473731731985485682  ,38.270544963679269600  ] 
dist 9=[30.327792637581114141  ,37.078572968148700864  ] 
dist 10=[29.150603563046036333  ,36.717743917528027709  ] 
dist 11=[28.230666806504219256  ,36.612733067556466030  ] 
dist 12=[27.318108188792731348  ,36.198459889525417886  ] 
dist 13=[26.170192299216059113  ,36.078531689609757853  ] 
dist 14=[24.950637218923374896  ,35.828058030584026360  ] 
dist 15=[23.751553629695603880  ,35.739787216465990168  ] 
dist 16=[22.330333872373706919  ,35.264205970873754199  ] 
dist 17=[20.222571789319979218  ,27.027403017215346706  ] 
dist 18=[18.111530020497663606  ,24.768854014862955404  ] 
dist 19=[16.677161129949127786  ,24.504219881195450059  ] 
dist 20=[15.454937762564333021  ,21.755976664556035599  ] 
dist 21=[14.192051058853137563  ,21.235304501344149964  ] 
dist 22=[12.990215597318860067  ,20.661006713237398814  ] 
dist 23=[12.012083220843080970  ,20.550635561083120474  ] 
dist 24=[11.004389583875257858  ,18.504605442431268441  ] 
dist 25=[9.6843962968711544252 ,17.757053951654446545  ] 
dist 26=[8.3822917390287640918 ,13.927158345098663498  ] 
dist 27=[7.4461268412221672346 ,13.623308916354445229  ] 
dist 28=[6.5930586597903568765 ,12.573293437663301080  ] 
dist 29=[5.1485762199741337887 ,12.340243918234372328  ] 
dist 30=[3.6437514188411334424 ,12.059860159835320292  ] 
dist 31=[1.9317322247689651274 ,11.985804170645835269  ] 
dist 32=[-.52432083903231192787,6.2009757655593602947 ] 
dist 33=[-2.9389496408937159590 ,6.1346768684240463180 ] 
dist 34=[-4.4855403726764958374 ,1.9307283684828344558 ] 
dist 35=[-5.7020052422047849390 ,1.5671509868236800515 ] 
dist 36=[-6.7970987825821076522 ,.75039881034063537072] 
dist 37=[-7.7394208814840089415 ,.61488773638495480591] 
dist 38=[-8.3453668789045411762 ,-.36391829756690971169] 
dist 39=[-8.8259561511124188973 ,-.53114621263162080943] 
dist 40=[-9.2675701978264062286 ,-.80822146014408188543] 
dist 41=[-9.6446184237509219688 ,-.8685354803269284065 ] 
dist 42=[-9.8671090607236966164 ,-1.7240238233025648712 ] 
dist 43=[-10.022081534866286718  ,-1.8350963856289312943 ] 
dist 44=[-10.128828881930721173  ,-2.0377751517856668565 ] 
dist 45=[-10.198746485462866995  ,-2.0800233313744023816 ] 
dist 46=[-10.206310516885799889  ,-2.1714990026331682388 ] 
dist 47=[-10.179530527312472567  ,-2.1592017706046187854 ] 
dist 48=[-10.151530241948800115  ,-2.1016265008074857342 ] 
dist 49=[-6.6077863659667974162 ,-1.9675402505918866203 ] 
dist 50=[-5.7499475775388357316 ,-1.8213215195144158737 ] 
dist 51=[-4.8976151246467855351 ,-1.7152491276684032261 ] 
dist 52=[-4.7604388274285180703 ,-1.6182212160521003812 ] 
dist 53=[-3.5845695154763566600 ,-1.2090263242898009254 ] 
dist 54=[-3.4600141309920238582 ,-.59230824998934191108] 
dist 55=[-3.4359615901171595465 ,.03621909485019914732] 
dist 56=[-2.9212923639404628802 ,.84612924351109373928] 
dist 57=[-2.1224429820301883920 ,1.6323877082033471594 ] 
dist 58=[-1.8295022978538387072 ,2.1665731820934876682 ] 
dist 59=[-1.7547193648072097414 ,2.6193167162119041751 ] 
dist 60=[-1.4931635000342249195 ,3.0805153551733420582 ] 
dist 61=[-1.4369733670504221064 ,3.5132361982782285948 ] 
dist 62=[-1.3673013441556332594 ,3.8523809265244281102 ] 
dist 63=[-1.3510033375341384932 ,4.1890936969780530282 ] 
dist 64=[-.64083273131673609407,4.6123039357542469637 ] 
dist 65=[-.63274042704623204007,5.0113927807106603032 ] 
dist 66=[-.00924651935723579736,5.2518101342154325826 ] 
dist 67=[.04424127965662091331,5.4232447993951134247 ] 
dist 68=[.16138268202621136641,5.5467498657292420140 ] 
dist 69=[.18345316814813864928,5.6346277119432997921 ] 
dist 70=[.31330020506150914503,5.6637027713403772291 ] 
dist 71=[.33485539088595183347,5.6677380700278152048 ] 
dist 72=[.37815792857280117208,5.6555297041755917241 ] 
dist 73=[.38783878757670793255,5.3881148014602451384 ] 
dist 74=[.45240213300761686691,5.3346563388135634996 ] 
dist 75=[.46271167103643721412,5.2134345297599713195 ] 
dist 76=[.46268404747000972145,5.1707863892551686112 ] 
dist 77=[.44865973623351915045,5.0267377889263791668 ] 
dist 78=[.42677031926286971309,5.0057228891148435328 ] 
dist 79=[.39532831301655314885,4.9228505605378374641 ] 
dist 80=[.04493521165118937897,4.9059382529073785302 ] 
dist 81=[-.39143796787417518849,3.0071863550084885273 ] 
dist 82=[-1.0704666944828325748 ,2.8300396594029545240 ] 
dist 83=[-1.6321212558369207642 ,2.3977206097570135888 ] 
dist 84=[-2.1816291917292937271 ,2.3335007368336138488 ] 
dist 85=[-2.6822980965930210935 ,1.6943072690386314362 ] 
dist 86=[-3.0489583684451725231 ,1.5753384029438320969 ] 
dist 87=[-3.3882823467537865730 ,1.4337955559120753805 ] 
dist 88=[-3.7798194200887396071 ,1.4030945810755390284 ] 
dist 89=[-4.1418023087579709276 ,.42492144758850900198] 
dist 90=[-4.3631169811198462014 ,.33956117609285486699] 
dist 91=[-4.5241411857093840166 ,.17336694374844728924] 
dist 92=[-4.6453643129362919177 ,.13335954504871408944] 
dist 93=[-4.7356146762442211894 ,.13049477380448843382] 
dist 94=[-4.7729698996294657130 ,.34339254601090032795] 
dist 95=[-4.7850016998478265134 ,.67688026577541931966] 
dist 96=[-4.7790397695454786781 ,1.0141227303424992730 ] 
dist 97=[-2.7427731965507215384 ,1.2420120737150275128 ] 
dist 98=[-2.8106918629616313254 ,1.4334173568778975283 ] 
dist 99=[-2.8549637318114305328 ,1.6250526046124516386 ] 
dist 100=[-2.8838545782217334390 ,1.8021571557828369408 ] 
dist 101=[-2.8903367163521939135 ,1.9355717626005443419 ] 
dist 102=[-2.8866118485581864768 ,2.0625377442608287554 ] 
dist 103=[-2.8786120477042706909 ,2.2139093838838055527 ] 
dist 104=[-2.7020140514267844145 ,2.3547170706624851415 ] 
dist 105=[-2.2295138888049062735 ,2.4395217964584942574 ] 
dist 106=[-2.1357320565858216586 ,2.4995552574711016725 ] 
dist 107=[-2.1046463350044738606 ,2.5414959243682440643 ] 
dist 108=[-2.0554969611842424942 ,2.5686151144723854297 ] 
dist 109=[-1.5713660534109825018 ,2.5739818635997476407 ] 
dist 110=[-1.5317523728822257184 ,2.5629421812039283901 ] 
dist 111=[-1.5187910567974802588 ,2.5603861120566719367 ] 
dist 112=[-.58829262315959701971,.45668205804288179104] 
dist 113=[-.58537975349519379086,.45479510856864258972] 
dist 114=[-.25415816960936782646,.25485955853160012254] 
dist 115=[-.23039558544934632239,.4394154294445466677 ] 
dist 116=[-.17469622403958656689,.60810690964853438403] 
dist 117=[-.16533651190754126238,.73240225612710004197] 
dist 118=[-.09047971132095751560,.84812680905738846274] 
dist 119=[-.07698949903022249535,.98260852693639279838] 
dist 120=[-.05645721417003550193,1.1076738249679740730 ] 
dist 121=[-.05114534714447503322,1.1858055321540360505 ] 
dist 122=[.03905854034646696571,1.2446223838612122317 ] 
dist 123=[.05042055814908172022,1.2925705647300003022 ] 
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dist 128=[.06019015212820391204,1.0962034329318054362 ] 
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dist 130=[-.08404734857512485518,1.0112649669849703403 ] 
dist 131=[-.13545715562513778218,.99339854095033811946] 
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dist 141=[-.65519471678062167312,.62203313887570190161] 
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dist 154=[-1.7951435897573391938 ,-.30562344417668644033] 
dist 155=[-1.7911901802986399119 ,-.29828463126561200339] 
dist 156=[-1.7605457154474381931 ,-.28452872098226694551] 
dist 157=[-1.7511628604634507338 ,-.25840794789181614853] 
dist 158=[-1.7175158385920769965 ,-.2263117724200036786 ] 
dist 159=[-1.7091729182535252736 ,-.18051164875067614513] 
dist 160=[-1.0662369558858512110 ,-.11207293238846306522] 
dist 161=[-1.0053058338905152008 ,.09162494894519131382] 
dist 162=[-.85468001962222329927,.27189688762686645925] 
dist 163=[-.83263544504131117917,.45287005982870326922] 
dist 164=[-.60371859487963711869,.62064629576644023978] 
dist 165=[-.56073400200264003892,.74823336044750112456] 
dist 166=[-.51144378353198297117,.87093852803774981261] 
dist 167=[-.50159750170997446884,1.0192254928000939423 ] 
dist 168=[-.43003856612633793234,1.1583986470275180711 ] 
dist 169=[-.42850511779698202151,1.2447194726236252618 ] 
dist 170=[-.32133601985451348019,1.3089347154640182326 ] 
dist 171=[-.30719043726901244305,1.3598571813031958292 ] 
dist 172=[-.28011064956422907233,1.3995272182646041398 ] 
dist 173=[-.27316232022351338288,1.4188196583941586413 ] 
dist 174=[-.24939197689038317898,1.4276657004888226314 ] 
dist 175=[-.24342413575787129665,1.4282587307960841719 ] 
dist 176=[-.23725160361553125866,.81753796257928441799] 
dist 177=[-.23528547838501815059,.81513886878585453998] 
dist 178=[.45953641802149536737,.71185126879603202944] 
dist 179=[.49426350496870662223,.75583793159570160279] 
dist 180=[.52935818460688219245,.79249059867545895738] 
dist 181=[.51952675666752348505,.81346524399711060976] 
dist 182=[.49820219200943328548,.82699892334746363191] 
dist 183=[.4556065540948838632 ,.83394511585087810811] 
dist 184=[.40712930383829679196,.83747766355186750368] 
dist 185=[.36232350253752663035,.83738270294522681297] 
dist 186=[.31159171770589083702,.8346172732861652105 ] 
dist 187=[.23945485905474495302,.83258900209402294926] 
dist 188=[.15900210027766421057,.81827168709859791801] 
dist 189=[.0750707512571645403 ,.81402480666308384028] 
dist 190=[-.02756262513223100314,.79762701395760587174] 
dist 191=[-.18267816687520272428,.79456668253574008404] 
dist 192=[-.33782324771397613595,.7375315881281058784 ] 
dist 193=[-.44057521782185841637,.73474413219712839583] 
dist 194=[-.52471595609560369368,.64239815273525797623] 
dist 195=[-.60556270607108159882,.63568054423372324347] 
dist 196=[-.67819285474707518076,.60190540773898690935] 
dist 197=[-.72953232849520970274,.59390786983933316309] 
dist 198=[-.77515841869877125626,.57666581663632723702] 
dist 199=[-.82498128858865546329,.57094436565048585328] 
dist 200=[-.86962118703732670659,.48797654519736930559] 
dist 201=[-.8945558489102366995 ,.47540580182291435188] 
dist 202=[-.90985695203560034596,.44340257649684680825] 
dist 203=[-.91603615915744699348,.437327036344996924  ] 
dist 204=[-.91818964942915324661,.38329069199597882685] 
dist 205=[-.91741928947711860695,.37224638252279178198] 
dist 206=[-.91436211510095546362,.35717241723971110643] 
dist 207=[-.91170727417482313912,.35208493346394084416] 
dist 208=[-.7238879717316302113 ,.18345422105627025925] 
dist 209=[-.70268023483504235377,.16405045185636531116] 
dist 210=[-.64834612596068234144,.12271821681300732582] 
dist 211=[-.63924054679278132206,.1119738819133256472 ] 
dist 212=[-.54800664204683459261,.06821503766212028447] 
dist 213=[-.52975027839069789825,.05998150133010837871] 
dist 214=[-.50766173254873118604,.04173584944152600238] 
dist 215=[-.50005410994719748924,.03764713468553595168] 
dist 216=[-.38898481226749860522,.01689995134815952810] 
dist 217=[-.4043955114018052999 ,.01331136110592147317] 
dist 218=[-.42163783451611078349,.01387555314375790468] 
dist 219=[-.43211651622446047006,.02026240672960524314] 
dist 220=[-.43966413391957130761,.02992274364003023571] 
dist 221=[-.44520526058254482027,.05480758312784183972] 
dist 222=[-.44905032621874994639,.12774559810763566227] 
dist 223=[-.48916469065704484538,.23138835984982547236] 
dist 224=[-.54858471342672742977,.33391917886156308165] 
dist 225=[-.58505057998547428278,.40241858469626119546] 
dist 226=[-.61169717687560093884,.4591698649804158212 ] 
dist 227=[-.63192057558141126493,.51480037138127916542] 
dist 228=[-.64732878464023096546,.56551623284947427205] 
dist 229=[-.6547545989624776121 ,.60264781525097731493] 
dist 230=[-.65775366394749272722,.63697769061678020504] 
dist 231=[-.65784564833191883212,.67650964717340913162] 
dist 232=[-.61892393714446332478,.71263082047655774752] 
dist 233=[-.61154221122959745761,.73334456297830393515] 
dist 234=[-.59914723417942908969,.74676245015796699441] 
dist 235=[-.59512435099657306162,.75375721434076038612] 
dist 236=[-.57997622777002454194,.75714826735921215295] 
dist 237=[-.57509173065436921383,.75658748134973028   ] 
dist 238=[-.56505499760755642446,.75319256132867681928] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 2, 0, 1, 2] 
dist 0=[46.967455343045239769  ,46.967455343045239769  ] 
dist 1=[46.520987237111543634  ,47.270328292218095486  ] 
dist 2=[45.760315085726107322  ,47.457290827096271812  ] 
dist 3=[44.812543587101826023  ,47.583216321124459996  ] 
dist 4=[43.618712547243096491  ,47.642174787260806972  ] 
dist 5=[42.012344681449717718  ,47.662784249566778645  ] 
dist 6=[39.416827191447905387  ,47.635336570229858492  ] 
dist 7=[36.750026488882414544  ,47.587101753692514306  ] 
dist 8=[34.858895419746222076  ,47.524736026619495792  ] 
dist 9=[33.168297480529075651  ,47.439223564093470777  ] 
dist 10=[31.302325476751928483  ,47.360933500986460306  ] 
dist 11=[29.459243263494365968  ,47.133609967229991050  ] 
dist 12=[27.859920453130237883  ,47.026260394928613622  ] 
dist 13=[26.127315433135220778  ,46.758323280443476952  ] 
dist 14=[23.751564668246450332  ,46.571100781603207195  ] 
dist 15=[21.368205226483233922  ,35.475913009802769741  ] 
dist 16=[19.605048232659928706  ,34.476360679230525273  ] 
dist 17=[17.951761879252870639  ,32.022608540040478820  ] 
dist 18=[16.007076874950870426  ,31.661619544285653337  ] 
dist 19=[14.013768146830147058  ,27.946873536958731137  ] 
dist 20=[12.165938850235199675  ,27.242507889192449249  ] 
dist 21=[10.062128076188875168  ,26.448520654888295995  ] 
dist 22=[7.0455602866366439958 ,26.282251781514240614  ] 
dist 23=[4.0642237730948175986 ,19.827040091407237907  ] 
dist 24=[2.1010905460151409430 ,19.017038791630598611  ] 
dist 25=[.49839643373051760966,17.390991332955801764  ] 
dist 26=[-1.0425851770112704775 ,16.974844869564173085  ] 
dist 27=[-2.4353904242702721478 ,15.507726384930029470  ] 
dist 28=[-3.4460341446277008426 ,15.194146771765575769  ] 
dist 29=[-5.2182729208955499418 ,14.754549994648786970  ] 
dist 30=[-6.9891738532421933101 ,14.624529582038893857  ] 
dist 31=[-8.3788432191081523463 ,3.5235196116006743381 ] 
dist 32=[-9.6227388635340228748 ,2.6042023561555847350 ] 
dist 33=[-10.686871291270896167  ,.53995323382035726631] 
dist 34=[-11.358302474307909943  ,.1967194568584481726 ] 
dist 35=[-11.875744151706674561  ,-2.2534717014722589843 ] 
dist 36=[-12.324910493395146792  ,-2.6670605758683420401 ] 
dist 37=[-12.693964952260847398  ,-3.1597612968181781785 ] 
dist 38=[-12.891253063016725665  ,-2.0276279097168733832 ] 
dist 39=[-13.003663182193454473  ,-.86200658942160082069] 
dist 40=[-13.033087283557338021  ,-.04930544574701881328] 
dist 41=[-13.009238022815333922  ,.65903223691619307057] 
dist 42=[-12.981168438042643781  ,1.4084718553809125478 ] 
dist 43=[-12.804633141662547810  ,2.1257149792164285348 ] 
dist 44=[-12.767301133624488766  ,2.7056943092251858648 ] 
dist 45=[-10.789372903839919918  ,3.2955825991006768985 ] 
dist 46=[-10.796321845560466414  ,4.0524565862178537676 ] 
dist 47=[-6.0991182295937576474 ,4.7829139748646184995 ] 
dist 48=[-5.9187268611653578429 ,5.2674160744701838107 ] 
dist 49=[-4.4153193547473331373 ,5.6641584322089201058 ] 
dist 50=[-4.2932691809968111799 ,6.0444124306472296165 ] 
dist 51=[-3.5536770073052321917 ,6.3845582138403057931 ] 
dist 52=[-3.4398048999437471975 ,6.6212309827590401600 ] 
dist 53=[-3.2442469018404216108 ,6.8271526754430903398 ] 
dist 54=[-3.2049997739326314596 ,7.0445357439798268878 ] 
dist 55=[-1.7139014855627477989 ,7.2359779056580661777 ] 
dist 56=[-1.5998143719695859154 ,7.3383656717921980744 ] 
dist 57=[-1.4352195493664816391 ,7.3948286201113786553 ] 
dist 58=[-1.3991595891086657866 ,7.4030106452053210997 ] 
dist 59=[-1.3111937955468086713 ,7.3791704679352723567 ] 
dist 60=[-1.3065506855169345678 ,7.3078288424494903504 ] 
dist 61=[-1.3318162762315608696 ,2.7589571609045495003 ] 
dist 62=[-1.4027703549947384795 ,3.0493819480808838104 ] 
dist 63=[-1.4809858855765896588 ,3.2808087905004079945 ] 
dist 64=[-1.5352294092018890731 ,3.4934737740563173673 ] 
dist 65=[-1.5810096795689034239 ,3.6788116981537155944 ] 
dist 66=[-1.6256716068739310304 ,3.8410319781174566610 ] 
dist 67=[-1.6648672626851503140 ,4.0261844606213072010 ] 
dist 68=[-1.6889142093731075522 ,4.1263281679814448688 ] 
dist 69=[-1.7056826962177953088 ,4.1841842560787845000 ] 
dist 70=[-1.7158518560249795779 ,4.2005198806547287337 ] 
dist 71=[-1.7187018789687683201 ,4.1996377000006586710 ] 
dist 72=[-1.7160008321679475447 ,4.1887079516782219067 ] 
dist 73=[-1.6914219416340622407 ,4.1688390296548082419 ] 
dist 74=[-1.6845330642244343052 ,4.1565637161364384160 ] 
dist 75=[-1.5716446536946820432 ,4.0877044479648048789 ] 
dist 76=[-1.5420359614436779168 ,4.0669047095548714816 ] 
dist 77=[-1.5165548180324195606 ,3.9930888977247092764 ] 
dist 78=[-1.5015340500897403250 ,3.9756173589639227881 ] 
dist 79=[-1.5842953691612952637 ,3.0513710006073256497 ] 
dist 80=[-2.0062434387560067936 ,3.0094657247777542280 ] 
dist 81=[-2.3926502684425093444 ,2.6804084849156208190 ] 
dist 82=[-2.6787630241733712740 ,2.6129445577485872878 ] 
dist 83=[-2.9466121192248310372 ,2.5096142087178825947 ] 
dist 84=[-3.2601272613185152370 ,2.4788275446592767510 ] 
dist 85=[-3.5495895520787077325 ,1.8323611387823811712 ] 
dist 86=[-3.7214173969315363877 ,1.7442460204715422917 ] 
dist 87=[-3.8402996953948356971 ,1.5475761829923995339 ] 
dist 88=[-3.9183801775091763432 ,1.4982907928415994223 ] 
dist 89=[-3.9725499605016858415 ,1.2507761680896320230 ] 
dist 90=[-3.9959474421651890050 ,1.2032724363194086601 ] 
dist 91=[-4.0013472813638884134 ,1.0983559502011428684 ] 
dist 92=[-3.9959802916187811639 ,1.0687151461390400643 ] 
dist 93=[-3.6514812650916503360 ,-.0446197623166287986 ] 
dist 94=[-3.6012664843855284493 ,-.1535257060437903986 ] 
dist 95=[-3.4557308100582029614 ,-.4000840535997796618 ] 
dist 96=[-3.4318801662208472992 ,-.4428446674487929831 ] 
dist 97=[-3.2228505322502681984 ,-.7424391895659263048 ] 
dist 98=[-3.2088949023668296158 ,-.7936792371178368891 ] 
dist 99=[-3.1677298266527832263 ,-.8843592293311618331 ] 
dist 100=[-3.1502902377698021345 ,-.9028925505063947877 ] 
dist 101=[-3.1126448510109134043 ,-.89142941514875355156] 
dist 102=[-3.0966782740295871873 ,-.61451141845321397763] 
dist 103=[-1.8722415689604747673 ,-.3301598324179886453 ] 
dist 104=[-1.9004877503348766120 ,-.11166108822625134857] 
dist 105=[-1.9190578855496905065 ,.10057452015445859615] 
dist 106=[-1.9295397115155049368 ,.359948940473905499  ] 
dist 107=[-1.9342750937280588623 ,.6450533615323345026 ] 
dist 108=[-1.9319599100147436586 ,.88506964619555711789] 
dist 109=[-1.9216196464174177408 ,1.1781731829951869422 ] 
dist 110=[-1.9106210454877462306 ,1.6002789204932653061 ] 
dist 111=[.47277137268914261969,2.0155852227877795096 ] 
dist 112=[.54723025736585453932,2.2815500641446545053 ] 
dist 113=[.71394123826154282944,2.4893384400333475179 ] 
dist 114=[.7389896648565606364 ,2.6723894141822684586 ] 
dist 115=[.92801152120436590513,2.8257877051264569615 ] 
dist 116=[.95768977264236453117,2.9151976912516437390 ] 
dist 117=[1.0066642956341982477 ,2.9749860093815150295 ] 
dist 118=[1.0159397813444287094 ,3.0101351419589893064 ] 
dist 119=[1.1467585480732260081 ,3.0577606595682170175 ] 
dist 120=[1.0922481795056820420 ,3.1258108719751611583 ] 
dist 121=[.91249561323426152473,3.1743849937412368142 ] 
dist 122=[.7024410628574820228 ,3.1894396926794609187 ] 
dist 123=[.42976291370983978494,3.1909340706282596925 ] 
dist 124=[0                     ,3.1853639266694411579 ] 
dist 125=[.97670513989431463843,2.9479900512259042982 ] 
dist 126=[.8576256426524458938 ,2.9311582848662706044 ] 
dist 127=[.50434459662853870928,1.5838594387160150866 ] 
dist 128=[.15828262810801760528,1.4612135865389283708 ] 
dist 129=[-.13434941255613785831,1.2038571948784347516 ] 
dist 130=[-.43090116873403541632,1.1975929377533370999 ] 
dist 131=[-.7075625643330244673 ,1.1276367357353997814 ] 
dist 132=[-.92079153381445389616,1.1111052845655214391 ] 
dist 133=[-1.1285699579689845579 ,1.0923027171110205018 ] 
dist 134=[-1.3834733933973973875 ,1.0835353931812960214 ] 
dist 135=[-1.6245871788476258734 ,.8772443510578112945 ] 
dist 136=[-1.7773162665969392544 ,.85150419683035197117] 
dist 137=[-1.8946724106643131921 ,.79712904628266936127] 
dist 138=[-1.9945737143613802808 ,.7813702750977560704 ] 
dist 139=[-2.0757023844679093509 ,.71532629542202013524] 
dist 140=[-2.1181161972089450226 ,.70180783524631844315] 
dist 141=[-2.1405015297841478338 ,.66544210099836430766] 
dist 142=[-2.1450438766613098753 ,.65889158913311529569] 
dist 143=[-1.5910987096360827775 ,.58989479664897642011] 
dist 144=[-1.6209839746690865671 ,.5761723815551569552 ] 
dist 145=[-1.6420292620422423310 ,.55120681117668698938] 
dist 146=[-1.6565613174009372148 ,.54449208415950850229] 
dist 147=[-1.6658198194790591611 ,.52050435505868467406] 
dist 148=[-1.6658080501703484547 ,.51362290268639330133] 
dist 149=[-1.6604427034138381665 ,.5032909460340742339 ] 
dist 150=[-1.6554994659728700163 ,.4995514605410814557 ] 
dist 151=[-1.3199267580584976493 ,.4890288383422380637 ] 
dist 152=[-1.3198632524714418781 ,.4857777019613101089 ] 
dist 153=[-1.3099664675454492530 ,.4843000323495586324 ] 
dist 154=[-1.3066143809930546841 ,.4848262948490706048 ] 
dist 155=[-1.2523986211824519659 ,.4865838567328731998 ] 
dist 156=[-1.2380245641775860716 ,.4900259614679084147 ] 
dist 157=[-1.2248242981660050280 ,.4953613925228739349 ] 
dist 158=[-1.2165867275307509335 ,.5046824315058624191 ] 
dist 159=[-1.0020358124175186907 ,.58709221893180046393] 
dist 160=[-.97556484045139991555,.77586241521524637494] 
dist 161=[-.91560872422471507812,.92897602685747987167] 
dist 162=[-.89785865024321357847,1.0736394455347736558 ] 
dist 163=[-.81533265917183603865,1.2019460888141675598 ] 
dist 164=[-.79809819708617010774,1.2897636913719674962 ] 
dist 165=[-.75887187481367742031,1.3648219691410811764 ] 
dist 166=[-.74646097110064788557,1.4421955089280083366 ] 
dist 167=[-.91446460299334733815,1.5108660790140735170 ] 
dist 168=[-1.0325877695791185092 ,1.5511809215346542432 ] 
dist 169=[-1.1241473043688741107 ,1.5784878613971378997 ] 
dist 170=[-1.2034399009400655276 ,1.5952252794441551630 ] 
dist 171=[-1.2688010929149750152 ,1.6039056109109720107 ] 
dist 172=[-1.3047482067960958665 ,1.6046535431633748071 ] 
dist 173=[-1.3275177967640995667 ,1.5915224378878320327 ] 
dist 174=[-1.3383514636214790966 ,1.5895763353640859031 ] 
dist 175=[-1.3436118719287619202 ,1.3914450513608750950 ] 
dist 176=[-1.3450201611149472966 ,1.3923205165061867348 ] 
dist 177=[-1.3438569526633956794 ,1.3858793607328301269 ] 
dist 178=[-1.3397298979641164549 ,1.3811967334088921103 ] 
dist 179=[-1.3317547619448892309 ,1.3340682041114022710 ] 
dist 180=[-1.3259215322192127861 ,1.3206817857948811319 ] 
dist 181=[-1.3114043125277437823 ,1.3035780136965279562 ] 
dist 182=[-1.3044291275221644899 ,1.2956507791520566986 ] 
dist 183=[-.36578390300312273485,.38033832206108564051] 
dist 184=[-.54814871882137142881,.34670909316194424888] 
dist 185=[-.6974513043266191362 ,.33032304126690246614] 
dist 186=[-.84082751111245998313,.41681843333903671785] 
dist 187=[-.96955184640649003503,.50740257458982596541] 
dist 188=[-1.0603647895543474806 ,.59365864247641854794] 
dist 189=[-1.1408726216220361464 ,.6933137097990014175 ] 
dist 190=[-1.2284605537982054861 ,.83871876655790218143] 
dist 191=[-1.3078222647426360264 ,.98184200589711647913] 
dist 192=[-1.3554901687524687762 ,1.0713025144820132260 ] 
dist 193=[-1.3891087928772622579 ,1.1386174944282153913 ] 
dist 194=[-1.4123816596289481507 ,1.1933403718293548164 ] 
dist 195=[-1.4274851158419681538 ,1.2368277566870698188 ] 
dist 196=[-1.4304634364526312085 ,1.2592942919691110601 ] 
dist 197=[-1.4252796678889407982 ,1.2706667303043932899 ] 
dist 198=[-1.4235409342479847116 ,1.2727221715468757263 ] 
dist 199=[-1.3352859262098282332 ,1.2350816412006140645 ] 
dist 200=[-1.3474743001219550266 ,1.2258164682234825787 ] 
dist 201=[-1.3520140762170573115 ,1.2133196935019238249 ] 
dist 202=[-1.3530546357526969617 ,1.2071962856656274934 ] 
dist 203=[-1.3137447594021485986 ,1.1868634547348427062 ] 
dist 204=[-1.3037097806436442994 ,1.1790452235735709351 ] 
dist 205=[-1.2978304257357993123 ,1.1616636068747949188 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 2, 0, 2] 
dist 0=[46.200351729487002912  ,46.200351729487002912  ] 
dist 1=[45.360140013075161109  ,46.864115583234472038  ] 
dist 2=[44.342384689109728332  ,47.177000890008232643  ] 
dist 3=[42.996956551269491458  ,47.329913966347091729  ] 
dist 4=[40.847860236623859133  ,47.355025177375178671  ] 
dist 5=[38.641354805372111370  ,46.971469407912652595  ] 
dist 6=[37.066533303190259902  ,46.841058806789961913  ] 
dist 7=[35.648371287478263169  ,46.596570171176078824  ] 
dist 8=[34.067419021573288958  ,46.497955832007505038  ] 
dist 9=[32.496720285367351563  ,45.975629091568034122  ] 
dist 10=[31.119343375093484749  ,45.835731324589877332  ] 
dist 11=[29.614924090993300462  ,45.355855390664392946  ] 
dist 12=[27.536461542124298814  ,45.256759120554191016  ] 
dist 13=[25.443978774935403360  ,43.998641958832798145  ] 
dist 14=[23.883385614199084653  ,43.690793605550699380  ] 
dist 15=[22.407309955768894783  ,42.515121610652719318  ] 
dist 16=[20.652216501340111310  ,40.428269327806744033  ] 
dist 17=[18.842507736393836427  ,27.907026771581011181  ] 
dist 18=[17.147940699082039539  ,27.246416232963252251  ] 
dist 19=[15.204860233368979976  ,26.407587403911603460  ] 
dist 20=[12.401691483982781663  ,26.149111923146672574  ] 
dist 21=[9.6246896352185976418 ,20.384124635053452661  ] 
dist 22=[7.7860798667987049535 ,19.639704263381717635  ] 
dist 23=[6.2735010268682011719 ,18.083960405402650631  ] 
dist 24=[4.7994450594199162409 ,17.668432254395758270  ] 
dist 25=[3.4536221116938024404 ,16.084832887740568178  ] 
dist 26=[2.4534476111576736782 ,15.774676828464674712  ] 
dist 27=[1.5093056068389299961 ,15.118636706540103108  ] 
dist 28=[.38722255251056399126,14.938786951236965401  ] 
dist 29=[-.66594014992893303516,5.7932097158519361993 ] 
dist 30=[-2.2340879223926024218 ,4.9724938402353960674 ] 
dist 31=[-3.9700020459145727524 ,3.1586827846534550648 ] 
dist 32=[-5.6262317401097725654 ,2.8187361194547137771 ] 
dist 33=[-7.3470094281997899456 ,.73317953759528997109] 
dist 34=[-8.6896019583889640985 ,.37751573759123585933] 
dist 35=[-9.7069580649442981794 ,-.30761896698890418909] 
dist 36=[-10.557347508861371785  ,-.46526870133188254565] 
dist 37=[-11.244301840914193677  ,-1.9110501046456832809 ] 
dist 38=[-11.700403841227063026  ,-2.1290155123287846054 ] 
dist 39=[-12.123689798084784518  ,-2.3934003671263745625 ] 
dist 40=[-12.442411784128956461  ,-2.4188791152045666961 ] 
dist 41=[-12.672637334218955159  ,-2.3526018170638260548 ] 
dist 42=[-12.742335274402026386  ,-2.1565476226058950507 ] 
dist 43=[-12.754324236641202602  ,-1.8299099181821903828 ] 
dist 44=[-12.753920938438526898  ,-1.2424486209910235898 ] 
dist 45=[-11.548299066846488236  ,-.62455978863317730321] 
dist 46=[-11.484463706325920162  ,-.17633959504851388297] 
dist 47=[-11.327055721642632211  ,.23194202462246096336] 
dist 48=[-11.258662861843887867  ,.69084658527142306333] 
dist 49=[-5.3664996955358111903 ,1.1461040324573994495 ] 
dist 50=[-4.8473250572735958306 ,1.5400400774398848585 ] 
dist 51=[-3.6809791927461507856 ,1.9641852955020185332 ] 
dist 52=[-3.4531871393848576577 ,2.5402257878422486157 ] 
dist 53=[-2.0573685568221714550 ,3.1122956773621798879 ] 
dist 54=[-1.8157525557949701103 ,3.5207130075921415076 ] 
dist 55=[-1.3401740918520835512 ,4.1762182158109951079 ] 
dist 56=[-1.0647121375200205436 ,5.0133270503969749022 ] 
dist 57=[.41765717671818115792,5.7941562899689104314 ] 
dist 58=[.51138107955522519375,6.2860840066649067418 ] 
dist 59=[.69236892963259944243,6.6605920059883369817 ] 
dist 60=[.7312123360945828034 ,6.9729147434502444973 ] 
dist 61=[2.1839380914000674146 ,7.2217819064749951256 ] 
dist 62=[2.3142650528447140349 ,7.3431382281846468246 ] 
dist 63=[2.5270778242385549575 ,7.3985989352462894523 ] 
dist 64=[2.5710492375167248475 ,7.4031316784110946644 ] 
dist 65=[2.5968065131787267097 ,5.2372579487304189983 ] 
dist 66=[2.3384874729620594449 ,5.0738512406995395752 ] 
dist 67=[1.8971606257699450386 ,4.6514793732986646060 ] 
dist 68=[1.2072202638403183220 ,4.6087700131115766312 ] 
dist 69=[.50906399998402225982,4.7462122742771462497 ] 
dist 70=[.03492946064875930808,4.8215155789311491644 ] 
dist 71=[-.36607041180483818673,4.8662546914051695280 ] 
dist 72=[-.77231138211531584304,4.8815588839207026554 ] 
dist 73=[-1.1510253671416424874 ,4.8787640028553535847 ] 
dist 74=[-1.4421533840866059353 ,4.8710434913299929655 ] 
dist 75=[-1.7250136322158159353 ,4.8209052603086880748 ] 
dist 76=[-2.0707318994048241110 ,4.8072534590461339796 ] 
dist 77=[-2.3969085640247881490 ,1.2344847546505560406 ] 
dist 78=[-2.9515287081800918671 ,1.1665672861246752807 ] 
dist 79=[-3.4122046444818965463 ,1.0606023780183673569 ] 
dist 80=[-3.8477134129893549861 ,1.0336702350512956695 ] 
dist 81=[-4.2342395127867701163 ,-.09032189886355182113] 
dist 82=[-4.4993914123353360466 ,-.13090709953728183339] 
dist 83=[-4.7267522846309164521 ,-.20271223537773658419] 
dist 84=[-4.9624486711336280255 ,-.21737002415310635872] 
dist 85=[-5.1678170975966407860 ,-.96843796263923694415] 
dist 86=[-5.2741046185065420582 ,-1.0316197828836452987 ] 
dist 87=[-5.3290382965646622215 ,-1.1557288244509397542 ] 
dist 88=[-5.3394492549436836570 ,-1.1835803914007267450 ] 
dist 89=[-5.3041586688431961080 ,-1.2601028281487208624 ] 
dist 90=[-5.2798167256646480715 ,-1.2651616368867348222 ] 
dist 91=[-5.2491425922601812607 ,-1.2463806570287795129 ] 
dist 92=[-5.2277040253367435924 ,-.92595869779837140513] 
dist 93=[-4.2873053521624612016 ,.02210066860534937686] 
dist 94=[-4.1796862412451418335 ,.6641271448115920768 ] 
dist 95=[-4.0679848534658298951 ,1.2051591585399537823 ] 
dist 96=[-4.0575040470901286475 ,1.7500895106380578922 ] 
dist 97=[-3.3200527466475963634 ,2.2560541050492200709 ] 
dist 98=[-3.2132624538129111263 ,2.6415496347688996254 ] 
dist 99=[-3.1100252730902031383 ,3.0127724095682977544 ] 
dist 100=[-3.0903856581918387350 ,3.4617634201814039751 ] 
dist 101=[-1.9173012352828562148 ,3.8828952806178359181 ] 
dist 102=[-1.7695180266271357212 ,4.1429122903709585398 ] 
dist 103=[-1.4756431473724434674 ,4.3347769105152202090 ] 
dist 104=[-1.4006526012777954317 ,4.4838649369575819667 ] 
dist 105=[-1.1407506619895059497 ,4.5971682551395775653 ] 
dist 106=[-1.0826112277589699523 ,4.6461942774740995015 ] 
dist 107=[-1.0172391080814525766 ,4.6651032086015335968 ] 
dist 108=[-1.0038566568611754700 ,4.6599227400470951241 ] 
dist 109=[-.65714097742475710964,4.0977608437511882859 ] 
dist 110=[-.622932384581953417  ,4.1277150378512514726 ] 
dist 111=[-.54429276682074627402,4.1484545059067647526 ] 
dist 112=[-.52711650639294307399,4.1576217856978524084 ] 
dist 113=[-.95580397469878304614,4.1517334028699259298 ] 
dist 114=[-1.4293741596104191847 ,4.1426930584187076561 ] 
dist 115=[-1.8278718396269053278 ,4.0934190570043822264 ] 
dist 116=[-2.2283137256347470384 ,4.0773422691639530685 ] 
dist 117=[-2.5995442463970256361 ,3.8900034632986175562 ] 
dist 118=[-2.8814443631514723310 ,3.8419218634707011814 ] 
dist 119=[-3.1520203040869711830 ,3.7873483200981948255 ] 
dist 120=[-3.4780537047552017232 ,3.7513468377318590638 ] 
dist 121=[-3.7833013815357501132 ,2.7068652008266684945 ] 
dist 122=[-3.9709096960808303817 ,2.5752830715016195285 ] 
dist 123=[-4.1083599048390899552 ,2.2287031003493364542 ] 
dist 124=[-4.2133941159355258421 ,2.1707931556771963381 ] 
dist 125=[-4.2896206960521449823 ,1.9740121017744379411 ] 
dist 126=[-4.3120822526525067551 ,1.9242434975268110857 ] 
dist 127=[-4.3149580083884450037 ,1.8765529355589571480 ] 
dist 128=[-4.3129916854750749193 ,1.8642614348097080844 ] 
dist 129=[.1453855579819644608 ,.8837184762646268746 ] 
dist 130=[.05471373921021022157,.88856012436333721865] 
dist 131=[-.08240776150829736738,.88976679368620585851] 
dist 132=[-.30844438434002883855,.93479996969229755538] 
dist 133=[-.53389871494431768532,.98687031644714155385] 
dist 134=[-.68241870287719150637,1.0156553977532410590 ] 
dist 135=[-.80316427068677668185,1.0328586810017909858 ] 
dist 136=[-.91773871570751654781,1.0387042979284489741 ] 
dist 137=[-1.0197133644403382371 ,1.0401523684603163752 ] 
dist 138=[-1.0901594442179030813 ,1.0398071827328727346 ] 
dist 139=[-1.1510782558596101723 ,1.0380593524211703411 ] 
dist 140=[-1.2150212096869112319 ,1.0344635708494978673 ] 
dist 141=[-1.3335947591578749577 ,.89980988073136630901] 
dist 142=[-1.4050951374622484417 ,.87935076609046772815] 
dist 143=[-1.4551506786909242779 ,.84162042968009188567] 
dist 144=[-1.4891554913084942098 ,.83129856033268682918] 
dist 145=[-1.5136984831059856140 ,.79337313936857797848] 
dist 146=[-1.5259741425870309456 ,.78282215015033187015] 
dist 147=[-1.5316457109187998912 ,.76488746267122327709] 
dist 148=[-1.5299050579717314077 ,.75925712512863625414] 
dist 149=[-1.3974879265786705712 ,-.27185493044494255543] 
dist 150=[-1.3757116201140872726 ,-.13709522004504364567] 
dist 151=[-1.3397233185349253507 ,-.02347989470784849113] 
dist 152=[-1.3298418714940142563 ,.09109336081004799933] 
dist 153=[-1.3084770096560731210 ,.19760759428657042236] 
dist 154=[-1.3001203923867372709 ,.27905166675817582249] 
dist 155=[-1.2830247577090639438 ,.35778671511071959472] 
dist 156=[-1.2762682388845868888 ,.45348664685379674389] 
dist 157=[-.5441988559797821636 ,.54358654333521071391] 
dist 158=[-.48092156722911040192,.59996681839638943717] 
dist 159=[-.32944724081749824893,.64248248470536430248] 
dist 160=[-.3071934161566115347 ,.67723642832492897183] 
dist 161=[-.09518415519185377448,.70508492537541787527] 
dist 162=[-.05700402034371844756,.72003389312879120557] 
dist 163=[-.00937325974376366604,.72840613071120936779] 
dist 164=[.00013348619284259549,.72999830246338991009] 
dist 165=[.28838193889278035419,.75057514664764583929] 
dist 166=[.3223443647416717016 ,.81470947228749204908] 
dist 167=[.39605691288064771167,.86222028080259976921] 
dist 168=[.40920341600348358767,.89956351455887345815] 
dist 169=[.38942661751383893662,.9289061638412413865 ] 
dist 170=[.33748962717586880934,.94447264656046743442] 
dist 171=[.27447393310457320066,.95295053958426221384] 
dist 172=[.17980801094700182771,.95398097368295775346] 
dist 173=[.08162561874666710139,.74064600693968689892] 
dist 174=[.00457114689617103664,.73151378056389391185] 
dist 175=[-.07181872772031972000,.70940075647147529562] 
dist 176=[-.16734994092864473808,.701590125956709764  ] 
dist 177=[-.26796427105765760022,.6629578909734763943 ] 
dist 178=[-.3646472956958779162 ,.65397360343759806532] 
dist 179=[-.47704798341323089507,.6342364456058416472 ] 
dist 180=[-.6404093175354613281 ,.62769293765711082184] 
dist 181=[-.80154471608985476545,.53913618883368195153] 
dist 182=[-.9050597841673116539 ,.52574856257335797226] 
dist 183=[-.98626984860526802372,.49071703745619706636] 
dist 184=[-1.0583625149367709322 ,.4850081412135002192 ] 
dist 185=[-1.1209463223976554579 ,.42373551540331937592] 
dist 186=[-1.1646675538336997703 ,.41132113982127454211] 
dist 187=[-1.1958492470454880637 ,.3972561581734103885 ] 
dist 188=[-1.2180864545553357305 ,.42305852425978259036] 
dist 189=[-1.2347680035976207497 ,.45876895315221257471] 
dist 190=[-1.2437720894296742207 ,.48436268968177733047] 
dist 191=[-1.2488735068943958537 ,.50744682160844742104] 
dist 192=[-1.2499792848079180083 ,.53314121959085612531] 
dist 193=[-1.2484290287426473374 ,.5585474215497774638 ] 
dist 194=[-1.2446913683052482295 ,.58048152338108036817] 
dist 195=[-1.2351514854605496488 ,.60407438540554361881] 
dist 196=[-1.2161784878110885345 ,.6361013712193082335 ] 
dist 197=[-.90149545478063158655,.66789241777524544418] 
dist 198=[-.9153641936794468486 ,.69054366937198817209] 
dist 199=[-.92408448498826295179,.71083905631985920286] 
dist 200=[-.92807851187364450051,.73322724268829349027] 
dist 201=[-.92874023916213184152,.75524888319250318574] 
dist 202=[-.92731008278452995633,.77408128538371502297] 
dist 203=[-.91844697185786827149,.79418587982239077761] 
dist 204=[-.91460542690469923423,.82128514571106841872] 
dist 205=[-.27108659796961541593,.84692955714283540301] 
dist 206=[-.22491909701771818674,.86122710003274303037] 
dist 207=[-.12164577514065093863,.86994961433036199104] 
dist 208=[-.10137590056230465797,.87334163286739815797] 
dist 209=[.02144461466955747913,.87304166855593888226] 
dist 210=[.04275237591464762823,.87167595637311019036] 
dist 211=[.08481639683226083145,.86058956087331128934] 
dist 212=[.09490451274872766199,.83403543237994287385] 
dist 213=[.18398169711962168752,.60261655355660410418] 
dist 214=[.19785297974027376895,.61901649040257839212] 
dist 215=[.19806541865104537074,.63150684863373808454] 
dist 216=[.12655544701040856005,.64194943761368299188] 
dist 217=[.04716680464089537864,.65029817654667213061] 
dist 218=[-.03511944666942870530,.66283378174254825542] 
dist 219=[-.13534657673898608165,.70388315740813981986] 
dist 220=[-.28635284857288226907,.75579867354677439603] 
dist 221=[-.43708500378138886919,.80457281451920331708] 
dist 222=[-.53621750461698401877,.83308188951404739535] 
dist 223=[-.61659595109778189349,.85223911061504798172] 
dist 224=[-.6924632260525585176 ,.86367847746675251578] 
dist 225=[-.75967505114044220996,.870526674531370412  ] 
dist 226=[-.80550116604544301164,.87135403738823673213] 
dist 227=[-.84446176895471561763,.86918408785556620314] 
dist 228=[-.88426583596860287251,.86647316670995115736] 
dist 229=[-.91907761730914519033,.7996413669108760166 ] 
dist 230=[-.93810946059909611238,.78794875389040016695] 
dist 231=[-.94923154854140228837,.7625921052557715885 ] 
dist 232=[-.95246954195548345654,.75430623618973719788] 
dist 233=[-.95181292706386463855,.71556923511128885002] 
dist 234=[-.94936843788354206257,.70699520200140888345] 
dist 235=[-.94141592828143094415,.6822282381299061809 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 1, 2, 1, 0, 1] 
dist 0=[53.178815922553249256  ,53.178815922553249256  ] 
dist 1=[52.910876188288667828  ,53.308628932845703646  ] 
dist 2=[52.498896614836413885  ,53.362855829206670002  ] 
dist 3=[51.793606597385217965  ,53.328721629353545900  ] 
dist 4=[50.735190576776122922  ,53.256788312392796739  ] 
dist 5=[48.912461811178400088  ,53.159910136962629873  ] 
dist 6=[46.994514328704293135  ,53.025676906498393349  ] 
dist 7=[45.555746145911057024  ,52.687797865841211773  ] 
dist 8=[44.187058258248635664  ,49.795508451784042334  ] 
dist 9=[42.549229850408531346  ,49.285949474758096479  ] 
dist 10=[40.856564480788473005  ,48.506266221061882821  ] 
dist 11=[39.072139817347067065  ,48.264602906311676118  ] 
dist 12=[34.867854536817066059  ,47.733326829489805489  ] 
dist 13=[30.619938294904355026  ,47.580245421408027013  ] 
dist 14=[27.694073300280363091  ,47.383045510496504040  ] 
dist 15=[25.167527387565391852  ,45.911899756955230237  ] 
dist 16=[22.514531383755409340  ,30.787447117715854912  ] 
dist 17=[19.973087372135476161  ,30.343137362216792834  ] 
dist 18=[17.891993808425544348  ,28.735914249475490598  ] 
dist 19=[15.742463578977962128  ,28.375583907398523644  ] 
dist 20=[12.927384800121039765  ,27.777551094753026704  ] 
dist 21=[10.162743989662582803  ,27.618822579020147300  ] 
dist 22=[8.2145375597272621819 ,15.787124803202320937  ] 
dist 23=[5.8718463607038948993 ,15.483264665739572667  ] 
dist 24=[3.5195531800819990167 ,10.916409006846310447  ] 
dist 25=[1.2296442329972175367 ,10.127637642154874685  ] 
dist 26=[-.8544441757500089639 ,8.9887659372002941871 ] 
dist 27=[-2.3845481948656811798 ,8.6159350452184482644 ] 
dist 28=[-3.8073514360232140078 ,8.3916153819612610914 ] 
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dist 33=[-9.9796160274667203142 ,-3.5200719756070012436 ] 
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dist 40=[-13.369795181385401922  ,-5.3854963166036370553 ] 
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dist 44=[-13.151971549413990053  ,-4.4205310057284632288 ] 
dist 45=[-13.090307098701763580  ,-2.5522278397281140508 ] 
dist 46=[-12.879948252355065803  ,-1.2755978035163422064 ] 
dist 47=[-12.807099399704016231  ,-.18723775016873006868] 
dist 48=[-6.9750167643134411101 ,.9296077934418673534 ] 
dist 49=[-6.4427625165957518486 ,1.9801906746058021484 ] 
dist 50=[-5.1774502232421150720 ,2.8040838215133743807 ] 
dist 51=[-4.9734151471917721121 ,3.6203738036618240999 ] 
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dist 53=[-4.1744978682323186317 ,5.6152803936222261728 ] 
dist 54=[-2.9455836376159399988 ,6.2493305366020867659 ] 
dist 55=[-2.8127351846649494470 ,6.7558827872324653736 ] 
dist 56=[-2.4836968350583576646 ,7.2215124619484799381 ] 
dist 57=[-2.4344416242215916362 ,7.6256743517649733305 ] 
dist 58=[-1.9212351657347280102 ,7.8868273482159475160 ] 
dist 59=[-1.8220038652514055836 ,8.0934312473717818007 ] 
dist 60=[-1.7118066604307890990 ,8.3179444948582001844 ] 
dist 61=[-1.6860057453140554464 ,8.4635631754961717795 ] 
dist 62=[-.7306684841063697707 ,8.5395291532744405075 ] 
dist 63=[-.6095269914882762359 ,8.5492328721930744642 ] 
dist 64=[-.3656695630808464503 ,4.9540559351733273928 ] 
dist 65=[-.3026927883458049043 ,5.0968444295081829255 ] 
dist 66=[-.0776542501526206854 ,5.2078143523299302824 ] 
dist 67=[-.0295411210976310291 ,5.2576743194682442963 ] 
dist 68=[.0452117102579147128 ,5.2747246347757407729 ] 
dist 69=[0                     ,5.2723497802721614462 ] 
dist 70=[3.1142021246531462171 ,4.3583222452822409561 ] 
dist 71=[2.9917885677043765925 ,4.3515535985650160186 ] 
dist 72=[2.8501725140743936678 ,4.3433367869551030942 ] 
dist 73=[2.7168041887629957779 ,4.2801362684595572032 ] 
dist 74=[2.5058688360870790518 ,4.2601735246695252684 ] 
dist 75=[2.0508649610584346159 ,4.1833441118969321658 ] 
dist 76=[1.3485633201932614841 ,4.1669199022766881334 ] 
dist 77=[.64013803363604583659,2.8542847934619783374 ] 
dist 78=[.16067215016890405098,2.6617517481478017549 ] 
dist 79=[-.24336269783838678105,2.6470900738361731299 ] 
dist 80=[-.65066426265354630741,1.9917304102402433768 ] 
dist 81=[-1.0294250645977915686 ,1.9465029068437918239 ] 
dist 82=[-1.3195305781241932798 ,1.7755971862700709673 ] 
dist 83=[-1.6006116127522122186 ,1.7382497865564688394 ] 
dist 84=[-1.9433661897033016418 ,1.6650553662331247170 ] 
dist 85=[-2.2668655983313239454 ,1.6447091483224670741 ] 
dist 86=[-2.4710823614083010562 ,.16093942774812599079] 
dist 87=[-2.6273388962827144616 ,.03155041576254287837] 
dist 88=[-2.7593688616090821576 ,-.21762878071102110756] 
dist 89=[-2.8660478939107479112 ,-.30522418942177140614] 
dist 90=[-2.9211061855253950074 ,-.47709105475432770978] 
dist 91=[-2.9493273729136759014 ,-.53839529180081017991] 
dist 92=[-2.9546450076697691225 ,-.55308413320888797417] 
dist 93=[-2.9326882142787725184 ,-.76263524617961547397] 
dist 94=[-2.9228892374394527865 ,-.83167680942625432125] 
dist 95=[-2.8800573657653866335 ,-.8271683817190230004 ] 
dist 96=[-2.8682916357195248282 ,-.79463174386530771311] 
dist 97=[-2.7268026368479394838 ,-.71541804207844556138] 
dist 98=[-2.6916872328467147162 ,-.61226332325351901161] 
dist 99=[-2.6529218042180103492 ,-.48414230167738019269] 
dist 100=[-2.6335918055783469804 ,-.31312353349304257728] 
dist 101=[-2.6247446861219465937 ,-.03871010543094090651] 
dist 102=[-2.0625888710007929098 ,.24179292244617249067] 
dist 103=[-1.9201774848458075347 ,.43712700571149531932] 
dist 104=[-1.8808157928279553410 ,.60761702425241630184] 
dist 105=[-1.7273457736436778856 ,.78894833239178745294] 
dist 106=[-1.6936064627040739722 ,.96353939681042111704] 
dist 107=[-1.6211189681797247354 ,1.1071263908044198385 ] 
dist 108=[-1.5989773532672758884 ,1.2556259985071953547 ] 
dist 109=[-.60576461713894266364,1.4498344756125368412 ] 
dist 110=[-.58560241323945442131,1.6395670088297805742 ] 
dist 111=[-.5793512252402734214 ,1.7702010672889453473 ] 
dist 112=[-.50520446545127841408,1.8826855020227930021 ] 
dist 113=[-.49304042242074066271,1.9999657143439817633 ] 
dist 114=[-.46709673826182973716,2.1115047236505595866 ] 
dist 115=[-.45926253384345248403,2.2010733996665309181 ] 
dist 116=[-.42484291325403715158,2.2918129586457793562 ] 
dist 117=[-.41751458226263602112,2.4080344968267421761 ] 
dist 118=[-.39780195273962080272,2.5161230351677747671 ] 
dist 119=[-.39345627635760054803,2.5743952918330991556 ] 
dist 120=[-.33906878470113154745,2.6074206440375127131 ] 
dist 121=[-.32972745354937956502,2.6147141265513689473 ] 
dist 122=[-.3059683573284496698 ,2.6120057286230495796 ] 
dist 123=[-.3006249392044030184 ,2.6030235160209181757 ] 
dist 124=[-.2589530096206235194 ,2.5095649526865288346 ] 
dist 125=[-.2500189084182160808 ,1.1518416991583908301 ] 
dist 126=[-.2363762819048973730 ,1.1407857763699794295 ] 
dist 127=[-.2321194364667900266 ,1.1356105796870681604 ] 
dist 128=[-.04272804959259369691,.57147322921087410726] 
dist 129=[-.22943049893593297085,.53218239600399381868] 
dist 130=[-.37308834912038803141,.43865532902258933044] 
dist 131=[-.51286223291530237521,.42307590664263191164] 
dist 132=[-.6840670811689289626 ,.29216683138849676408] 
dist 133=[-.84593417193600124555,.26812469454506308632] 
dist 134=[-.9484341860579587873 ,.23337598606256755354] 
dist 135=[-1.0271900672825966193 ,.22361190535829287329] 
dist 136=[-1.0942707068924666664 ,.04709416023294876896] 
dist 137=[-1.1488333345848549678 ,.02517589303383375399] 
dist 138=[-1.1776207923306301184 ,-.02543914587345541237] 
dist 139=[-1.1935370260454795876 ,-.03285757719015047032] 
dist 140=[-1.1969362726865766778 ,-.09638063239000739448] 
dist 141=[-1.1910878690916288192 ,-.10706470894504527442] 
dist 142=[-1.1864422636180221167 ,-.10435566722316747327] 
dist 143=[-1.1801540121961877079 ,-.02529132224649428720] 
dist 144=[-1.1757632941904218115 ,.05696072340685510108] 
dist 145=[-1.1583195247606356647 ,.11636879075340036492] 
dist 146=[-1.1518756053093219080 ,.17042468832501759056] 
dist 147=[-1.1335147179071596946 ,.23131787197219907413] 
dist 148=[-1.1254142115052820718 ,.29196077419397879534] 
dist 149=[-1.1128495906140221894 ,.3450202916215593633 ] 
dist 150=[-1.1113857101168817298 ,.40270480316239952778] 
dist 151=[-1.1089768683153213169 ,.48181180617623919146] 
dist 152=[-1.0337178811364482651 ,.56074522365719850994] 
dist 153=[-.98930065844069434456,.61773853879359968037] 
dist 154=[-.97898163369191478627,.66960179320554349324] 
dist 155=[-.95065203016383466902,.78774913454532697311] 
dist 156=[-.9429056385228603424 ,1.0581101609310469644 ] 
dist 157=[-.88991074469304061719,1.3252012309949274951 ] 
dist 158=[-.86609110805297102983,1.4978934105929277392 ] 
dist 159=[-.85766089044136880693,1.6346644911139008380 ] 
dist 160=[.05001739872180228916,1.7583529978634658365 ] 
dist 161=[.11512849716243319845,1.8643053736435142999 ] 
dist 162=[.26452642419404415944,1.9302718896833854399 ] 
dist 163=[.28700190564086059429,1.9796498093136395337 ] 
dist 164=[.41751223522750986237,2.0193803554433624184 ] 
dist 165=[.43412799842437352799,2.0497178793141465787 ] 
dist 166=[.46419960158598765044,2.0615968587509573469 ] 
dist 167=[.46990947441309351296,2.0630426385667997140 ] 
dist 168=[.47755100134519385682,2.0602723339956451056 ] 
dist 169=[.4684594859298020211 ,2.0277033590218324727 ] 
dist 170=[.44878717467110014432,2.0163018526287369015 ] 
dist 171=[.40953076335985503389,1.9852636476924939770 ] 
dist 172=[.36066800765981931869,1.9715819508981366378 ] 
dist 173=[.05742463110189876560,1.3481165934852146243 ] 
dist 174=[-.19172141710675892202,1.2857376644947641117 ] 
dist 175=[-.40095801457043648381,1.1285571339240379682 ] 
dist 176=[-.6106692718891463744 ,1.1059206495612933799 ] 
dist 177=[-.8048365418185323775 ,.8564254872969333886 ] 
dist 178=[-.95202049209208675139,.80870608622555356232] 
dist 179=[-1.0930974684790372557 ,.757064638443749777  ] 
dist 180=[-1.2628854986323509254 ,.74759812840740245464] 
dist 181=[-1.4218439021098642678 ,.6919799493155267157 ] 
dist 182=[-1.5196881363728486236 ,.6825763775669313392 ] 
dist 183=[-1.5915786107184426133 ,.6800796282056059517 ] 
dist 184=[-1.6469272344501568346 ,.5108224191022152115 ] 
dist 185=[-1.6893652983739665533 ,.4884886207601602661 ] 
dist 186=[-1.7097152354606940090 ,.4456122250735399360 ] 
dist 187=[-1.7181749422732370573 ,.4345915589675677127 ] 
dist 188=[-1.7184822470239117382 ,.3967389542448122712 ] 
dist 189=[-1.1283181087025294941 ,.3873042871515134227 ] 
dist 190=[-1.1285114173737115407 ,.3772127489523099885 ] 
dist 191=[-1.1259120170313133478 ,.3738111635050969664 ] 
dist 192=[-.92405720724225417529,-.56100798004200982307] 
dist 193=[-.98196313329852102062,-.59146813079790623047] 
dist 194=[-1.0174244187929169476 ,-.58895569947288157279] 
dist 195=[-1.0432722933384845121 ,-.57278680061988234406] 
dist 196=[-1.0628004724125354746 ,-.53374941920877335373] 
dist 197=[-1.0774953048639671658 ,-.48726128364460998966] 
dist 198=[-1.0840472412710597956 ,-.44134759562204896707] 
dist 199=[-1.0858995008705029109 ,-.38702879578973248114] 
dist 200=[-1.0843804978220201707 ,-.30698483886361982163] 
dist 201=[-1.0742988426733326293 ,-.21645127315262547364] 
dist 202=[-1.0703568198981267830 ,-.1202561053339039616 ] 
dist 203=[-1.0515302034411190284 ,-.00140691800631091560] 
dist 204=[-1.0486950411256431324 ,.17956434881235276661] 
dist 205=[-1.0147758224825746581 ,.36106091271738898342] 
dist 206=[-.99787402990513980499,.48200774044756913161] 
dist 207=[-.99248773083504299215,.58185872356471392764] 
dist 208=[-.84033271801995183428,.67913975872425052673] 
dist 209=[-.79936129784312779143,.76741907683701602256] 
dist 210=[-.78921102195456791376,.83133519442231701476] 
dist 211=[-.77036967304784363792,.8897014443918236765 ] 
dist 212=[-.76453349657120098904,.95582658304688783072] 
dist 213=[-.64074290569755721582,1.0156512340328502489 ] 
dist 214=[-.62253341334805291451,1.0488659220446190895 ] 
dist 215=[-.5804257806654871875 ,1.0689805563326342346 ] 
dist 216=[-.5690941834448653247 ,1.0765088611442019510 ] 
dist 217=[-.5091417729890122369 ,1.0793204667715465912 ] 
dist 218=[-.49681094826317469833,1.0806043119903173462 ] 
dist 219=[-.47101919954475618359,1.0810178775363906326 ] 
dist 220=[-.46339074518186992292,1.0803511499283010362 ] 
dist 221=[-.16134661129941194341,.92804227763904706736] 
dist 222=[-.13051091274218901384,.90834349443239801441] 
dist 223=[-.06371872516165038996,.8550336416059059702 ] 
dist 224=[-.04854844801042907650,.84652373314397752805] 
dist 225=[.02451854640028994454,.74725214805872880156] 
dist 226=[.03722761889003552429,.72671739249768916504] 
dist 227=[.06625077914356806371,.70512630331717498375] 
dist 228=[.07081757772149203521,.69868523755142420795] 
dist 229=[.10523578956258843543,.58113320363365528634] 
dist 230=[.11038277210566171358,.59367741732958322455] 
dist 231=[.10878120546595658746,.60244850813693685896] 
dist 232=[.09754142641379842459,.60837504582069571534] 
dist 233=[.08094084245679316917,.61202364639136148477] 
dist 234=[.03464734126810809174,.61196241766855399477] 
dist 235=[-.05422196155262555905,.60965236005851050285] 
dist 236=[-.18844475380564186104,.65053380984535432972] 
dist 237=[-.322655991282170703  ,.70303561220181673534] 
dist 238=[-.41147943929194742338,.73415496591893540632] 
dist 239=[-.48414280759808874806,.7555780800085951245 ] 
dist 240=[-.55384064659740851291,.76937443669844302181] 
dist 241=[-.61852140139037373084,.77867798590201320426] 
dist 242=[-.67005832174593655855,.78216735986584036252] 
dist 243=[-.71913035581320589149,.7820616886205171803 ] 
dist 244=[-.7777307707848773157 ,.78089975711195027514] 
dist 245=[-.83237194319926127291,.71471599195870836964] 
dist 246=[-.86563852709799173925,.70351581443929655884] 
dist 247=[-.88964961939750009916,.6821298489591529989 ] 
dist 248=[-.90734185381697433339,.67570085431535131066] 
dist 249=[-.919641225224763812  ,.6488426181892185069 ] 
dist 250=[-.92237989246945876751,.64190275466175797134] 
dist 251=[-.92126389353910997748,.6250889463707166194 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 0, 2, 1, 2] 
dist 0=[54.324208549356002975  ,54.324208549356002975  ] 
dist 1=[53.781540790960866095  ,54.611910123899443608  ] 
dist 2=[52.716393392598511341  ,54.658828041572923816  ] 
dist 3=[51.501145916380105130  ,54.581881052435271565  ] 
dist 4=[50.359011375032903332  ,54.374581857797387825  ] 
dist 5=[49.049167327127907977  ,54.225638941078903935  ] 
dist 6=[47.163885141582566712  ,54.126648797004804660  ] 
dist 7=[45.046985010357580503  ,54.054361744856300308  ] 
dist 8=[42.811930283295268490  ,53.320044872914697050  ] 
dist 9=[40.056028905813438339  ,48.773435348298463185  ] 
dist 10=[35.858683029269055227  ,48.240957268088897286  ] 
dist 11=[31.625945150878775944  ,47.669001760389873010  ] 
dist 12=[28.728583953895162917  ,47.574983907595110586  ] 
dist 13=[26.246433814748036542  ,46.218399898751336840  ] 
dist 14=[23.671921246035281793  ,43.788358078808968838  ] 
dist 15=[21.225539554021890475  ,41.695768694308754844  ] 
dist 16=[19.254963319664382064  ,41.526208869410749966  ] 
dist 17=[17.248826988133055640  ,34.278593769658608454  ] 
dist 18=[14.660006684161379792  ,33.330907720904161600  ] 
dist 19=[12.134907894232827398  ,31.480628645120336703  ] 
dist 20=[10.383080394915107481  ,31.002895810500102797  ] 
dist 21=[8.8550954407869432104 ,29.325792469447104804  ] 
dist 22=[7.2064863051503882837 ,28.932410287199205985  ] 
dist 23=[4.6387080196795780577 ,28.404910269387066849  ] 
dist 24=[2.9167075075026301201 ,28.224539319441500433  ] 
dist 25=[1.4773060126282229779 ,10.696375018940148264  ] 
dist 26=[.0379290436899999961 ,9.2419259592105372024 ] 
dist 27=[-1.3010217025142395615 ,5.9206594115099312391 ] 
dist 28=[-2.3398352331412709636 ,5.3855604957695533739 ] 
dist 29=[-3.3655451833262065664 ,4.4122751717957043538 ] 
dist 30=[-4.6533948822381774146 ,3.6746900820031027524 ] 
dist 31=[-5.9139466008037835582 ,-.5603804593308994923 ] 
dist 32=[-7.8711609947871685863 ,-.8212400740546383114 ] 
dist 33=[-9.6977532691524169849 ,-4.7112150380649965800 ] 
dist 34=[-10.826611630536666810  ,-5.1113634035604182363 ] 
dist 35=[-11.664125200074174840  ,-5.6831377734585662576 ] 
dist 36=[-12.327113629606049881  ,-5.7282539674353338077 ] 
dist 37=[-12.849529236681500380  ,-5.6688769832892336871 ] 
dist 38=[-13.125478684115980941  ,-5.4544018600195895418 ] 
dist 39=[-13.274685974552131319  ,-5.1588666249214704569 ] 
dist 40=[-13.294305951046614501  ,-4.7756635425828539117 ] 
dist 41=[-8.7355633707041075899 ,-4.2558428451682788402 ] 
dist 42=[-8.4703838981897944305 ,-3.4148103323521435225 ] 
dist 43=[-7.7869795391185900409 ,-2.5550484271076146714 ] 
dist 44=[-7.6823915097705070398 ,-1.9603379644468928024 ] 
dist 45=[-7.5175570428070019994 ,-1.2188054624150929608 ] 
dist 46=[-7.4656525561431888097 ,.53480253231849121547] 
dist 47=[-6.0770104039365301470 ,2.2835403424872561324 ] 
dist 48=[-6.0142659660989865723 ,3.4299912604037068583 ] 
dist 49=[-4.7988309311273306789 ,4.3550739701761347898 ] 
dist 50=[-4.6822535406061100135 ,5.2201845901669885497 ] 
dist 51=[-4.2850108639124690351 ,5.9806195307941273660 ] 
dist 52=[-4.0459859490675784420 ,6.4878346711621126329 ] 
dist 53=[-3.2303010157830160081 ,6.9065612905200765078 ] 
dist 54=[-2.7029949631475618495 ,7.3136748272185802646 ] 
dist 55=[-2.0964015784956956882 ,7.6729867675531387833 ] 
dist 56=[-2.0559515818768931024 ,7.9009446858766810116 ] 
dist 57=[-.16660462458029807564,8.0761714772777939276 ] 
dist 58=[-.1443601135118297608 ,8.2252229020195440362 ] 
dist 59=[1.7495456268486740152 ,8.3463891357879043789 ] 
dist 60=[1.8712984360267871657 ,8.4104717535622659700 ] 
dist 61=[2.2351457726544153966 ,8.4456090520825393764 ] 
dist 62=[2.2889166238198331742 ,8.4515006964762298248 ] 
dist 63=[2.4812553694982899433 ,4.4616410563222113068 ] 
dist 64=[2.4522864772097428841 ,4.8001720521292944320 ] 
dist 65=[2.3832124394112891000 ,5.1121219977776499317 ] 
dist 66=[2.2703012262467502591 ,5.2980025907069206216 ] 
dist 67=[1.9524691247188859294 ,5.4278469837903939984 ] 
dist 68=[1.4782439137086118428 ,5.5159618598922951897 ] 
dist 69=[.9944691647268027350 ,5.5736099834126974002 ] 
dist 70=[.3709428654792412496 ,5.5842217667427416828 ] 
dist 71=[-.2336170372781600139 ,5.5725108199181431146 ] 
dist 72=[-.6417445556067533842 ,5.5606735572791938154 ] 
dist 73=[-.9845129746567471084 ,3.1583861101923429410 ] 
dist 74=[-1.3569458546312682463 ,3.1321286571476533761 ] 
dist 75=[-1.7745293839685591782 ,2.3648845543084398472 ] 
dist 76=[-2.1867353243240603556 ,2.2907093099056645826 ] 
dist 77=[-2.5643361028630770572 ,2.1050551273795236266 ] 
dist 78=[-2.8438167549299128737 ,2.0734886703045020207 ] 
dist 79=[-3.1052760891141682974 ,1.7751455828944337633 ] 
dist 80=[-3.4109977705186576842 ,1.7160997327603436320 ] 
dist 81=[-3.6931453101154723859 ,1.6413680691365288498 ] 
dist 82=[-3.8605231280722416363 ,1.6148546297286218748 ] 
dist 83=[-3.9867694953748638807 ,1.0530033686636003775 ] 
dist 84=[-4.0864611356371995156 ,.97918439431059073261] 
dist 85=[-4.1571383500936981722 ,.82345449791969731402] 
dist 86=[-4.1862946804195782809 ,.78117939562403795505] 
dist 87=[-4.1912362664471255356 ,.61662274939244866677] 
dist 88=[-4.1864791960717833739 ,.58452229492007133275] 
dist 89=[-3.8458209003204031739 ,.67912956993856557043] 
dist 90=[-3.7941459089606636428 ,1.1795003024950683349 ] 
dist 91=[-3.6842998384098638925 ,1.5995628503481556204 ] 
dist 92=[-3.6778064613400585412 ,2.0197891302074520991 ] 
dist 93=[-3.6549531410947977848 ,2.4079030076754873387 ] 
dist 94=[-3.6401686108642089567 ,2.6998018153960702368 ] 
dist 95=[-3.1775278592248799917 ,2.9770984712641624402 ] 
dist 96=[-3.1490448674265407032 ,3.3069321872086353797 ] 
dist 97=[-2.5089557287978226922 ,3.6132357268876619211 ] 
dist 98=[-2.3403425260801007928 ,3.9149618822550392527 ] 
dist 99=[-1.8904672154543516449 ,4.2548476218369443998 ] 
dist 100=[-1.8310788858839811401 ,4.4787611117025148617 ] 
dist 101=[-1.6208204818803935642 ,4.6608420622508242658 ] 
dist 102=[-1.5726259586617203176 ,4.8337570022398351702 ] 
dist 103=[-1.5078401680142747865 ,4.9799306261625689960 ] 
dist 104=[-1.4862661535666098064 ,5.0552593456165390081 ] 
dist 105=[.78057955321793868074,5.0932601611184414831 ] 
dist 106=[.95503057851308798954,5.0960435357779786988 ] 
dist 107=[1.3485521134769530840 ,5.0684957446554159760 ] 
dist 108=[1.4075819068610686396 ,5.0495256227817250817 ] 
dist 109=[1.8657341644150317966 ,4.9888857249828764297 ] 
dist 110=[1.3023398799124385310 ,4.9578655162032248584 ] 
dist 111=[.4280546042790148132 ,3.4108175408507518852 ] 
dist 112=[-.1653718800766436103 ,3.2552390475134121289 ] 
dist 113=[-.66696697151598428668,2.8638384478361188389 ] 
dist 114=[-1.1746915994414486294 ,2.8060302089405023720 ] 
dist 115=[-1.6477690989860599712 ,2.5748667478718358220 ] 
dist 116=[-2.0110645048439848451 ,2.6170964273255064865 ] 
dist 117=[-2.3636916789956427436 ,2.6482513953992874076 ] 
dist 118=[-2.7941859349425060730 ,2.6586106567643068406 ] 
dist 119=[-3.2000760691227159250 ,2.6568637656162867236 ] 
dist 120=[-3.4544904852346274292 ,2.6519543386024655513 ] 
dist 121=[-3.6467777469995571775 ,1.6173455402399092479 ] 
dist 122=[-3.8046724516304985502 ,1.5258807104769860281 ] 
dist 123=[-3.9284453025137614636 ,1.3103605404600045061 ] 
dist 124=[-3.9845262628765720400 ,1.2694058981182034551 ] 
dist 125=[-4.0110111563939625406 ,.96993756686964729743] 
dist 126=[-4.0166453300570509593 ,.91379536006681232247] 
dist 127=[-1.5029468828183933596 ,.81942257824200537481] 
dist 128=[-1.7258893071244030337 ,.79649060346679175222] 
dist 129=[-1.9029970875791437699 ,.39320924594296752672] 
dist 130=[-2.0641435338784213174 ,.34016191258365965065] 
dist 131=[-2.2029251696118953236 ,.21948673499638114066] 
dist 132=[-2.2907480279440287596 ,.1976500293791580462 ] 
dist 133=[-2.3581813569594187766 ,.04841481775396941098] 
dist 134=[-2.4155678873522909962 ,.02245295782695528735] 
dist 135=[-2.4611981079779970829 ,-.02445822871861517214] 
dist 136=[-2.4816966220732416185 ,-.03456153117129789507] 
dist 137=[-2.4877671681519902296 ,-1.2764877558454854395 ] 
dist 138=[-2.4863052301769306956 ,-1.0912466011736881157 ] 
dist 139=[-2.4562834580329909804 ,-.8792359647370954514 ] 
dist 140=[-2.4444333265677782009 ,-.6506353103592471704 ] 
dist 141=[-2.4087685081135502663 ,-.3659496101356377465 ] 
dist 142=[-2.3921642567421456669 ,.0699526095797411238 ] 
dist 143=[-2.3237631176411855258 ,.5078546696865932239 ] 
dist 144=[-2.3251562986629558447 ,.8005268577360040112 ] 
dist 145=[-2.1391897615748213837 ,1.0430492289073725492 ] 
dist 146=[-2.1082115747280324285 ,1.2807623824568171671 ] 
dist 147=[-2.0624625237970496192 ,1.4973860227477711952 ] 
dist 148=[-2.0463510274335346492 ,1.6557247501063162867 ] 
dist 149=[-2.0244124083161286067 ,1.8018153695499149946 ] 
dist 150=[-2.0127219685267283056 ,1.9695523009214793163 ] 
dist 151=[-1.9967434331274745359 ,2.1227441317417042194 ] 
dist 152=[-1.9882705367514078686 ,2.2107708711621221651 ] 
dist 153=[-.92881507685736037349,2.2679921001937861315 ] 
dist 154=[-.9023012206388356373 ,2.2982011027992710607 ] 
dist 155=[-.75370851721845770672,2.3163277018838458163 ] 
dist 156=[-.72503808275349801836,2.3253173258720403019 ] 
dist 157=[-.6664926065541601619 ,2.3293545072039578831 ] 
dist 158=[-.6503436772973656641 ,2.3277222173003182803 ] 
dist 159=[-.0534200932863662250 ,1.9979611813581932373 ] 
dist 160=[.0074040203166236873 ,1.9563474152687030197 ] 
dist 161=[.1343445888706415669 ,1.8441317420425891378 ] 
dist 162=[.1657417143119620645 ,1.8254819693211202310 ] 
dist 163=[.2849356627715898742 ,1.6764210676746316559 ] 
dist 164=[.3076488133947132821 ,1.6533333159857825381 ] 
dist 165=[.3440839273024933068 ,1.6130342643243300543 ] 
dist 166=[.3522921925624336735 ,1.6011384180110445740 ] 
dist 167=[.3578467349192481144 ,1.3659720408536889233 ] 
dist 168=[.3448056584816270633 ,1.3689965892615741710 ] 
dist 169=[.3179674179207833128 ,1.2995769700769794494 ] 
dist 170=[.2652404153395476465 ,1.3285817547373146308 ] 
dist 171=[.1998221026138838133 ,1.3527774637316773843 ] 
dist 172=[.0827938687595521241 ,1.3665862065167913151 ] 
dist 173=[-.1309041405041549213 ,1.3753983884457365071 ] 
dist 174=[-.4723688063965406995 ,1.4509392615410728476 ] 
dist 175=[-.8113263020714364669 ,1.5374625041366225180 ] 
dist 176=[-1.0348404105808058619 ,1.5857372794136407794 ] 
dist 177=[-1.2167848513956164460 ,1.6152064472453585684 ] 
dist 178=[-1.3897925044811662953 ,1.6266691997243687344 ] 
dist 179=[-1.5439993714370428169 ,1.6309299489247994457 ] 
dist 180=[-1.6508903930504602815 ,1.6316562066656549824 ] 
dist 181=[-1.7436961624251294860 ,1.6299069948733658078 ] 
dist 182=[-1.8416764369312153221 ,1.6245050161836401657 ] 
dist 183=[-1.9285429884112324586 ,1.4160644051998549228 ] 
dist 184=[-1.9769812715017537884 ,1.3843587971745939059 ] 
dist 185=[-2.0065999823096399176 ,1.3264055176895797569 ] 
dist 186=[-2.0183326282355159820 ,1.3106455441418284183 ] 
dist 187=[-2.0212587730885602264 ,1.2535085710557512401 ] 
dist 188=[-2.0171652707525024002 ,1.2372353464764964577 ] 
dist 189=[-2.0054594883403101619 ,1.2115426505835998072 ] 
dist 190=[-1.9976768826257104487 ,1.2027326735782836649 ] 
dist 191=[-1.8868188192926052481 ,.95780134153352846064] 
dist 192=[-1.8917533683282049227 ,.99627800530658284227] 
dist 193=[-1.8481688064992656348 ,1.0342035455441205706 ] 
dist 194=[-1.8369791078783250718 ,1.0607773116074228446 ] 
dist 195=[-1.8275461246247546406 ,1.0841234940136706811 ] 
dist 196=[-1.8183865934698272997 ,1.1091665635669915658 ] 
dist 197=[-1.8092359903321887626 ,1.1333801417748543768 ] 
dist 198=[-1.8025359207398635529 ,1.1534150895932499668 ] 
dist 199=[-1.7960957248351756000 ,1.1742227454524472768 ] 
dist 200=[-1.7883177505907990046 ,1.2015192069764854376 ] 
dist 201=[-.64497280038406334719,1.2269304699463117103 ] 
dist 202=[-.55056858368649201908,1.2402133518708340180 ] 
dist 203=[-.32830587959340166892,1.2471478961872023909 ] 
dist 204=[-.29384186684619609709,1.2472211429759620477 ] 
dist 205=[-.05481406348885061171,1.2428647443839668031 ] 
dist 206=[-.02211670345119836954,1.2394362214484940136 ] 
dist 207=[.04120349841119466200,1.2214133988934383783 ] 
dist 208=[.05625891445966685765,1.2172212694542822799 ] 
dist 209=[.20786103265267783657,1.1488096411626411887 ] 
dist 210=[.23063342283276409089,1.1354787576894976679 ] 
dist 211=[.20919581668527022446,1.0950754350148763348 ] 
dist 212=[.10169696476723318764,1.0878919975433102392 ] 
dist 213=[-.01687044849727552006,.9967988603984138275 ] 
dist 214=[-.13867703097859738356,.9765846922666910223 ] 
dist 215=[-.28627014911323901994,1.0204917495941477099 ] 
dist 216=[-.57907769257174222795,1.1112977471178816113 ] 
dist 217=[-.88594835652484824   ,1.1974724901640805689 ] 
dist 218=[-1.0853030948609843004 ,1.2492254130934950710 ] 
dist 219=[-1.2441916825141719014 ,1.2857274208790242987 ] 
dist 220=[-1.3895261000818526545 ,1.3110179193029189224 ] 
dist 221=[-1.5151180996752219448 ,1.3282839548033239554 ] 
dist 222=[-1.5951967389396351923 ,1.3327499291029464840 ] 
dist 223=[-1.6573116034450036280 ,1.3318206588792327113 ] 
dist 224=[-1.7111928832516743846 ,1.3276592815599117526 ] 
dist 225=[-1.7563321538195002507 ,1.2509665603037074148 ] 
dist 226=[-1.7835498462166480534 ,1.2360484948184939653 ] 
dist 227=[-1.8028590370398609750 ,1.2024432722237547739 ] 
dist 228=[-1.8164296569605796120 ,1.1907831126143321656 ] 
dist 229=[-1.8252711488920819079 ,1.1337958082338016727 ] 
dist 230=[-1.8257025156495597866 ,1.1206533524039820892 ] 
dist 231=[-1.8200481243088611874 ,1.0855218090859018172 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 0, 1] 
dist 0=[46.300132857026378818  ,46.300132857026378818  ] 
dist 1=[46.075623645420524407  ,46.443807739694869428  ] 
dist 2=[45.656328280752683249  ,46.540203098982499693  ] 
dist 3=[45.012888584931647297  ,46.620423644553880990  ] 
dist 4=[43.893086795387481751  ,46.699412924900601502  ] 
dist 5=[42.548871136113527581  ,46.771164726449785599  ] 
dist 6=[41.009073395494092686  ,46.822382633890078908  ] 
dist 7=[39.026657690227063219  ,46.867799468634655800  ] 
dist 8=[35.914538490405388189  ,46.916175983002436099  ] 
dist 9=[32.740958527442402843  ,46.955356599608369462  ] 
dist 10=[30.512995968222127635  ,46.964090523843195609  ] 
dist 11=[28.544748324797151611  ,46.951540595851227458  ] 
dist 12=[26.408339551551836943  ,46.906055673403616069  ] 
dist 13=[24.319314861036752236  ,44.291449227441608571  ] 
dist 14=[22.540151232847478478  ,44.057028694524173773  ] 
dist 15=[20.641166235789890748  ,41.747924273107918636  ] 
dist 16=[18.073201965314802664  ,37.935362265855142590  ] 
dist 17=[15.513158551636340733  ,34.996560015151624662  ] 
dist 18=[13.645628707558234894  ,33.996961081534367458  ] 
dist 19=[11.920543003363857907  ,31.538899460484707263  ] 
dist 20=[9.9292532802824035158 ,31.185144172596854426  ] 
dist 21=[7.9086822484853518538 ,27.457844509258383799  ] 
dist 22=[6.0662778212955462298 ,26.752672686591403487  ] 
dist 23=[3.9926194990319037880 ,25.979214219861153420  ] 
dist 24=[1.0474833401959919157 ,25.837980058562876705  ] 
dist 25=[-1.8497353828881772422 ,19.330315851105833130  ] 
dist 26=[-3.7320503962137175090 ,18.519517611334839093  ] 
dist 27=[-5.2409892824917469658 ,16.905925734612158716  ] 
dist 28=[-6.6461227909655382710 ,16.497269631094400507  ] 
dist 29=[-7.8863208175248082714 ,15.085261111573567398  ] 
dist 30=[-8.7362516156955052188 ,14.777188520838359428  ] 
dist 31=[-9.4684169525184561010 ,14.413539408055601007  ] 
dist 32=[-10.238313685475930921  ,14.334411918999038544  ] 
dist 33=[-10.918835618752297708  ,2.9953570639405704782 ] 
dist 34=[-11.293869092913454758  ,2.0759180243975782699 ] 
dist 35=[-11.520378104031442939  ,.00653887326911213045] 
dist 36=[-11.607132628366391886  ,-.32946429564955464043] 
dist 37=[-11.634480450708279930  ,-2.7950332514378199922 ] 
dist 38=[-11.623490383220033303  ,-3.2099688022560991445 ] 
dist 39=[-11.583442845360651091  ,-3.8933644237709601186 ] 
dist 40=[-11.543980900613447699  ,-2.5505896579980473428 ] 
dist 41=[-10.193755830261198919  ,-.57716715530734552265] 
dist 42=[-10.030700813122262673  ,.76334308633882445998] 
dist 43=[-9.5655553181316634073 ,1.8964700008185262457 ] 
dist 44=[-9.5037695700250640623 ,3.0423503849162456011 ] 
dist 45=[-9.8554878999125241923 ,4.1084630515499569839 ] 
dist 46=[-10.035491739156987112  ,4.9232907477529730834 ] 
dist 47=[-10.127979115172601500  ,5.7100512920522374621 ] 
dist 48=[-10.143903849342538211  ,6.6641912314221240364 ] 
dist 49=[-5.8161185130174888739 ,7.5599535042447221580 ] 
dist 50=[-5.5168320379630090937 ,8.1137201602431656509 ] 
dist 51=[-4.9262845784014256860 ,8.5230011678875373530 ] 
dist 52=[-4.7737941071090747374 ,8.8420568757636671370 ] 
dist 53=[-4.2384459918470649892 ,9.0849592627288372340 ] 
dist 54=[-4.1151797391722513803 ,9.1902892632517263999 ] 
dist 55=[-3.9609420366535591835 ,9.2313303263036552303 ] 
dist 56=[-3.9082639000822305294 ,9.2204377889574087239 ] 
dist 57=[-1.9580009238076363775 ,.65573530786997063139] 
dist 58=[-1.8453116149816064011 ,1.1380142731552779465 ] 
dist 59=[-1.6047229060968631060 ,1.5348712605142825805 ] 
dist 60=[-1.5496416122614962552 ,1.9201347489531064739 ] 
dist 61=[-1.2968426548060943997 ,2.2695048446839039156 ] 
dist 62=[-1.2524885306974736655 ,2.5230319743025427821 ] 
dist 63=[-1.1513494571602071383 ,2.7555179904453086608 ] 
dist 64=[-1.1348602085966822992 ,3.0208802895893461790 ] 
dist 65=[-1.0010066282596408764 ,3.2632313917547231841 ] 
dist 66=[-.97527031551280953239,3.4038268927152303678 ] 
dist 67=[-.93798365617629965331,3.4972002896048946368 ] 
dist 68=[-.92671184746819177938,3.5509641919902066390 ] 
dist 69=[-.90418053857487202432,3.5856510498019964058 ] 
dist 70=[-.89615905699845512556,3.6028324563383636043 ] 
dist 71=[-.89066949192634150764,3.6105850874138430760 ] 
dist 72=[-.8861401785278897467 ,3.6076007677987116312 ] 
dist 73=[-.8814093563736497773 ,3.5567882116965180570 ] 
dist 74=[-.87517255315579434882,3.5475146458387684160 ] 
dist 75=[-.86609243257309212891,3.5382631235247659631 ] 
dist 76=[-.86044026303708222661,3.5271458243335857256 ] 
dist 77=[-.83057901214537431418,3.5160958913854329123 ] 
dist 78=[-.8214364138073230471 ,3.5070702506180999933 ] 
dist 79=[-.78670677388183198996,3.4980073070952020494 ] 
dist 80=[-1.0768721538391525801 ,3.4867760169927306938 ] 
dist 81=[-1.4269710270511203295 ,1.8759226118290170686 ] 
dist 82=[-1.6738535615782303600 ,1.7967098499861277233 ] 
dist 83=[-1.8927061758344801747 ,1.6210633600488706932 ] 
dist 84=[-2.1309137785970196118 ,1.5754572169955602708 ] 
dist 85=[-2.3637412445197990637 ,1.3578980963702534891 ] 
dist 86=[-2.5611287299684087214 ,1.3160083386409367359 ] 
dist 87=[-2.7706823526833799891 ,1.2200344792370649849 ] 
dist 88=[-3.0521098899107750322 ,1.1958254338016326480 ] 
dist 89=[-3.3221234612680063987 ,-.08224764467251793953] 
dist 90=[-3.4861095978355914966 ,-.13652698479707507319] 
dist 91=[-3.6041289294082497233 ,-.2098113599762248588 ] 
dist 92=[-3.6906016113768459923 ,-.22495358816975253551] 
dist 93=[-3.7529663876841260911 ,-.21841819087804722736] 
dist 94=[-3.7747226023180692779 ,-.17924718699173246462] 
dist 95=[-3.7787099059682142137 ,-.10878197692704154841] 
dist 96=[-3.7701175125208011138 ,.02265671477516134980] 
dist 97=[-3.5850267483838860992 ,.16327687894685970824] 
dist 98=[-3.5473423010277400107 ,.27039830326740464803] 
dist 99=[-3.4656674148067593804 ,.37342207157452312071] 
dist 100=[-3.4372491736005422363 ,.49771866578213336395] 
dist 101=[-3.2980877652798935853 ,.62615545057425438781] 
dist 102=[-3.2773790156517149292 ,.74572295442510843488] 
dist 103=[-3.2483777151904939151 ,.88172357425488524081] 
dist 104=[-3.1629849923774766176 ,1.0757747998981337863 ] 
dist 105=[-1.5945073139877038746 ,1.2727993819946429461 ] 
dist 106=[-1.4447519056962334929 ,1.4206798276650705976 ] 
dist 107=[-1.2295502703612491320 ,1.5609792643368695519 ] 
dist 108=[-1.2192438646867669616 ,1.7277572211212410505 ] 
dist 109=[-1.1732297481384632449 ,1.9149324138346555065 ] 
dist 110=[-1.1624738514126114690 ,2.1515580789255135523 ] 
dist 111=[-1.1319676066293801640 ,2.3635935345319545797 ] 
dist 112=[-1.1245491976411475860 ,2.5978088729323390112 ] 
dist 113=[.13699813591570776774,2.8128960048915531603 ] 
dist 114=[.2020027912031491141 ,2.9485660260245585722 ] 
dist 115=[.32877836899156294849,3.0521774759708386578 ] 
dist 116=[.3588296901246956485 ,3.1392802791134110303 ] 
dist 117=[.45009894229990820905,3.2092169021854976114 ] 
dist 118=[.46682718796892072308,3.2442985256301089004 ] 
dist 119=[.46334706688895101463,3.2606136034283604948 ] 
dist 120=[.43139915026462841935,3.2556335497003362192 ] 
dist 121=[.39318985014550119625,2.3821294716287551036 ] 
dist 122=[.36471101465555478872,2.3983599514497664902 ] 
dist 123=[.33789014764606996768,2.4017535543188113783 ] 
dist 124=[.30629564648928045023,2.3995299881233264900 ] 
dist 125=[.27401847029389575326,2.3683099998477894918 ] 
dist 126=[.2444696929809885321 ,2.3567048768355097703 ] 
dist 127=[.21122886336916841376,2.3198259531602214060 ] 
dist 128=[.16420888270891302171,2.3042746446255123370 ] 
dist 129=[.11659029961526088271,1.5380928328429533016 ] 
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dist 180=[-.51983135073791250624,.77991939843962251669] 
dist 181=[-.52054317298808243303,.6956210446789136639 ] 
dist 182=[-.52066806891730217079,.68594589891341937684] 
dist 183=[-.52038612659142315234,.6787075570685945271 ] 
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dist 186=[-.06932629435444126671,.61570121762161567344] 
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dist 191=[-.30190798866805146948,.56823512434650221793] 
dist 192=[-.35461585187805479361,.56647339239960939978] 
dist 193=[-.40572206831990874639,.56995281142529011154] 
dist 194=[-.44025706789643224568,.5851022390201834356 ] 
dist 195=[-.46929568869055157922,.59424030375527712054] 
dist 196=[-.49845879430032620956,.59753565938706656194] 
dist 197=[-.52549652799342000639,.59828992043882104943] 
dist 198=[-.54604966155301700316,.59728749283007593225] 
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dist 201=[-.69235456585464254011,.52684721671653087948] 
dist 202=[-.72363079892728475083,.51637329911475672558] 
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dist 205=[-.77923248862733026544,.46295887268227776611] 
dist 206=[-.78460399114956207447,.45683004334297833801] 
dist 207=[-.7858681189256988901 ,.44110646653047885413] 
dist 208=[-.7845082448184518194 ,.43626673810144251208] 
dist 209=[-.51224349714193202995,.45254025978887235917] 
dist 210=[-.49801606713930838565,.48461935116375436992] 
dist 211=[-.47190798466245320977,.51180800318242041272] 
dist 212=[-.46507902650841139067,.53946640393271119225] 
dist 213=[-.44163051001928243709,.56534136724292296666] 
dist 214=[-.43498414893892932587,.58541040167466340147] 
dist 215=[-.42760801884986926409,.60509011250385079514] 
dist 216=[-.42405255167866372709,.62941123460335917758] 
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dist 220=[.09174622415593189554,.67007664971917806706] 
dist 221=[.12619427196380505348,.66607236609288060815] 
dist 222=[.13171182568958952044,.66322468939107843133] 
dist 223=[.14236212315108012785,.65809016911159023809] 
dist 224=[.14460318807349361816,.65566043840208588141] 
dist 225=[.15689713090146431707,.58051491650830131707] 
dist 226=[.15661409527111267297,.56875484668661133129] 
dist 227=[.15257184518044049546,.54387907382985595801] 
dist 228=[.14234942310767315344,.53629731802089216607] 
dist 229=[.12893461774982677192,.5029127109301753903 ] 
dist 230=[.11214739631834917389,.49586132098584486913] 
dist 231=[.08072504718382178060,.47517959126484013618] 
dist 232=[-.02579861509070898502,.47193815868451931499] 
dist 233=[-.15308438400330946202,.34649187142430069784] 
dist 234=[-.2376420928964574488 ,.33510712089871598462] 
dist 235=[-.30716284097403949431,.31010156001838123127] 
dist 236=[-.37441975545711436762,.30273876513555396649] 
dist 237=[-.43514087687648929839,.26311012683193631928] 
dist 238=[-.47857032200016124174,.25746170723615710674] 
dist 239=[-.51768828439168008089,.25229055286358714621] 
dist 240=[-.56119804289558746457,.25081135470835348049] 
dist 241=[-.60081802591984848876,.17979978665719864392] 
dist 242=[-.62440747811261699164,.17047336785730869623] 
dist 243=[-.64079180502710287325,.15221353516470338575] 
dist 244=[-.65164729511369639174,.1474760316027515165 ] 
dist 245=[-.6587652777609969857 ,.13078474866361900211] 
dist 246=[-.660229080810307346  ,.12685129174325693541] 
dist 247=[-.65925006273061051327,.12167694991002682549] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 2, 0, 1, 0, 1] 
dist 0=[47.272008784540269160  ,47.272008784540269160  ] 
dist 1=[46.941498553709256095  ,47.661133979416659959  ] 
dist 2=[46.572364648047429092  ,48.167633253112486925  ] 
dist 3=[46.001122160292082379  ,48.966440144795811338  ] 
dist 4=[44.474731234936192734  ,49.745128380095577938  ] 
dist 5=[42.647489818811530032  ,50.171295234391671538  ] 
dist 6=[40.691491766770650724  ,50.420442308786091076  ] 
dist 7=[38.262464383711541229  ,50.492673887788816354  ] 
dist 8=[34.545959294417957984  ,50.467970599501653200  ] 
dist 9=[30.797332246618132816  ,50.412701815336911592  ] 
dist 10=[28.239863580735709649  ,50.166617308834367306  ] 
dist 11=[26.059291148543366002  ,50.040924467368384087  ] 
dist 12=[23.815535148146014463  ,48.283336969686854053  ] 
dist 13=[21.695529095641607312  ,47.294825103148895725  ] 
dist 14=[20.008869888492045067  ,39.490011328951968381  ] 
dist 15=[18.311139577986775507  ,39.196632913003548567  ] 
dist 16=[16.146343837257728619  ,35.784658535140702419  ] 
dist 17=[14.046694019852654972  ,35.106012982817109033  ] 
dist 18=[12.608847034872996723  ,34.424605864022854983  ] 
dist 19=[11.374012534131895162  ,34.288531445838426496  ] 
dist 20=[10.084844033778769386  ,27.097119176557468996  ] 
dist 21=[8.8500172523620508867 ,26.176764605884141029  ] 
dist 22=[7.8316701314297732554 ,24.385291102220215953  ] 
dist 23=[6.7689454370361307721 ,23.930123141894205287  ] 
dist 24=[5.3555746078639471887 ,22.371616949905663889  ] 
dist 25=[3.9881247961887761392 ,22.005523645554128038  ] 
dist 26=[3.1087318560189859946 ,21.606837658596796997  ] 
dist 27=[2.4097205499701401002 ,21.502688504492417495  ] 
dist 28=[1.7637869974471323377 ,11.763951342558735970  ] 
dist 29=[.39842838300512228309,11.147734286528396154  ] 
dist 30=[-1.7713652531851348540 ,1.3377518707852274023 ] 
dist 31=[-3.1620946746132911659 ,1.0502570512482057284 ] 
dist 32=[-4.2576297138507448794 ,1.0070801996287115835 ] 
dist 33=[-5.7336350205488422448 ,.82109783208631781364] 
dist 34=[-7.1833530392249742453 ,.82411054574418188394] 
dist 35=[-8.9248925752905314840 ,.88522076314825473739] 
dist 36=[-10.560484136063968045  ,1.0371397686356798965 ] 
dist 37=[-11.586972541512265435  ,1.2319039178576116124 ] 
dist 38=[-12.367017533901839018  ,1.4642110566418847047 ] 
dist 39=[-13.018175090335366971  ,1.7660387453925449694 ] 
dist 40=[-13.539060231557342815  ,2.2382089687118103624 ] 
dist 41=[-13.798734496654603482  ,2.7127325864695905636 ] 
dist 42=[-13.932757042081785246  ,3.0240559818396867229 ] 
dist 43=[-13.951735699695139107  ,3.2733289013669342367 ] 
dist 44=[-8.4842229798350919165 ,3.5005693663841883734 ] 
dist 45=[-8.4675714651383201191 ,3.6940555456159219898 ] 
dist 46=[-6.0100138924193636515 ,3.8087226995722861035 ] 
dist 47=[-5.8923663440772595633 ,3.8862313542237486500 ] 
dist 48=[-4.6415824064919378738 ,3.9313839122112031993 ] 
dist 49=[-4.4202226182186742193 ,3.9571771024965788415 ] 
dist 50=[-4.1433357745608294706 ,3.9575342525408801092 ] 
dist 51=[-4.0962947033118237722 ,3.9398323400005159288 ] 
dist 52=[-2.7361099606380021433 ,3.9256931761260631338 ] 
dist 53=[-2.6636568226198387251 ,3.8214583632204888143 ] 
dist 54=[-1.3423025645190744915 ,3.7900704772037637392 ] 
dist 55=[-1.1784460355610726027 ,3.6830514018970921788 ] 
dist 56=[-.80137154738673150628,3.6536867253563608629 ] 
dist 57=[-.74508930468912346782,2.2797532280925576279 ] 
dist 58=[-.45267264348616286231,2.6918587058520784922 ] 
dist 59=[-.42826587061368545034,3.0302432207914090108 ] 
dist 60=[-.08301552741408172229,3.3804916334042889761 ] 
dist 61=[-.05887071629674916730,3.8401288033116710758 ] 
dist 62=[2.3926619299904715859 ,4.2803852709379097859 ] 
dist 63=[2.4741051878472780470 ,4.5532600989350077674 ] 
dist 64=[2.7017111867749869095 ,4.7568741316783713598 ] 
dist 65=[2.7249059867204849264 ,4.9204544292006733434 ] 
dist 66=[2.6837524824265670681 ,5.0467488521953250048 ] 
dist 67=[2.5448987385969316266 ,5.1014348239884820289 ] 
dist 68=[2.3708143163180530380 ,5.1249358095095676542 ] 
dist 69=[2.1889695302566792276 ,5.1265576308656698398 ] 
dist 70=[1.9669367699344516059 ,5.0189626251251530325 ] 
dist 71=[1.6323015282345517313 ,4.9886677286709728310 ] 
dist 72=[1.2509355541353393196 ,4.9156917755180927962 ] 
dist 73=[.8422918380459376066 ,4.8859110880684261153 ] 
dist 74=[.33520181163144244002,4.7251451354887772171 ] 
dist 75=[-.43922433046776124337,4.6850325770104293617 ] 
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dist 86=[-4.1992773897258689858 ,1.3182616564868431356 ] 
dist 87=[-4.2278719395878799304 ,1.2028925927416056094 ] 
dist 88=[-4.2370419793007765389 ,.96928753524171581837] 
dist 89=[-4.2411904084275868346 ,.90870588618639736904] 
dist 90=[-4.2716273354935520054 ,.69105072969503462052] 
dist 91=[-4.3178464678523746876 ,.64486156624620561281] 
dist 92=[-4.3394038906980007554 ,.57329010751063081188] 
dist 93=[-4.3389081286996901819 ,.84531240482160337836] 
dist 94=[-3.6220810440165703698 ,1.2489693449530720804 ] 
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dist 97=[-3.2591625137717811978 ,2.3376991910756825093 ] 
dist 98=[-3.1786017596990480798 ,2.6255713455048664187 ] 
dist 99=[-3.1489420819047238656 ,2.9784733774469128251 ] 
dist 100=[-2.4627396176240467326 ,3.3118064353261771572 ] 
dist 101=[-2.2904436577041722852 ,3.5215729832305697104 ] 
dist 102=[-1.7099596542074769172 ,3.6810473543581508689 ] 
dist 103=[-1.6560857681265471436 ,3.8136435338917463798 ] 
dist 104=[-1.5106192464407730204 ,3.9188620071071350188 ] 
dist 105=[-1.3654389163927123443 ,3.9690616537667469410 ] 
dist 106=[-1.0411491095919703947 ,3.9902426304329680277 ] 
dist 107=[-1.0179215023375866736 ,3.9907153344815226957 ] 
dist 108=[-.94402995903657544381,.54070784989875650952] 
dist 109=[-.94312048129931712827,.80126259207229463923] 
dist 110=[-.45075841585090939221,1.0113676218581098709 ] 
dist 111=[-.40995850792972622862,1.2079127974494515882 ] 
dist 112=[-.31566971070389268398,1.3810005134659779496 ] 
dist 113=[-.29856579231965651005,1.4974597067937245740 ] 
dist 114=[-.17507587803792069145,1.5949148263179244996 ] 
dist 115=[-.15273049961310973325,1.6921425742481253608 ] 
dist 116=[-.11484908002714137156,1.7786746452560781068 ] 
dist 117=[-.1061355016236798738 ,1.8334278038939261953 ] 
dist 118=[.03547798652446227601,1.8755011401677837304 ] 
dist 119=[.05416933112997646621,1.9113968423245325165 ] 
dist 120=[.09343235123038533225,1.9406637048502647288 ] 
dist 121=[.10246667401754795688,1.9562650673374463825 ] 
dist 122=[.13985760758122596665,1.9648763843225742804 ] 
dist 123=[.14666852066603618353,1.9662289367972176725 ] 
dist 124=[.15776233396434002667,1.1054799814074239510 ] 
dist 125=[.1601192211245567122 ,1.0336004843034024113 ] 
dist 126=[.67575384337469461356,.86737512501495353338] 
dist 127=[.64972940186006561118,.83437134934814111097] 
dist 128=[.49879107136315259693,.75184435638022700005] 
dist 129=[.36776684632812631618,.7758844611606658482 ] 
dist 130=[.226135047030694907  ,.79435166019192434004] 
dist 131=[.03283920259220858778,.80410565908666848281] 
dist 132=[-.15977419233840802663,.80935398335976500766] 
dist 133=[-.29868810103411660162,.80983230828662583207] 
dist 134=[-.42500648595787800251,.75720100589493798486] 
dist 135=[-.56734560189556805089,.74796599366571620551] 
dist 136=[-.70929409762426928572,.73513323959868462855] 
dist 137=[-.83406170114435078218,.73014644291454380796] 
dist 138=[-.97031131378490098136,.71853030073548076427] 
dist 139=[-1.1581143738417158868 ,.71362007876855702203] 
dist 140=[-1.3401736472342894744 ,.70979793962943076036] 
dist 141=[-1.4534942582822210208 ,.70644956135414396311] 
dist 142=[-1.5392435788119368856 ,.24424481667763151488] 
dist 143=[-1.6088420517240787746 ,.20656722913237240694] 
dist 144=[-1.6639734038914624191 ,.11746296820735901125] 
dist 145=[-1.6924736285783062971 ,.10421908689222800885] 
dist 146=[-1.7069686453304353430 ,-.01648379332848930942] 
dist 147=[-1.7094590645883397696 ,-.03786063746024741944] 
dist 148=[-1.6462536746359768044 ,-.06585278803188604493] 
dist 149=[-1.6321186358795936636 ,-.07180938119232406003] 
dist 150=[-1.6145956802983271847 ,-.22030006262833888788] 
dist 151=[-1.6058725240244197286 ,-.23765300454168145923] 
dist 152=[-1.5844253243045416208 ,-.27562956218711332621] 
dist 153=[-1.5743945303108504411 ,-.28143543945498685802] 
dist 154=[-1.5603461806973849529 ,-.32101142612099923433] 
dist 155=[-1.5534563937848821948 ,-.32683589216268558463] 
dist 156=[-.62489408540612938555,-.33752334632779374806] 
dist 157=[-.54692695818513555666,-.16575679554031842057] 
dist 158=[-.37263159034535952605,-.01140207523892591266] 
dist 159=[-.37403901667820052598,.14447124381879875512] 
dist 160=[-.37511470103466652197,.28961029045455519072] 
dist 161=[-.37601552568794685705,.40110928979996960828] 
dist 162=[-.3767308955776621061 ,.50945439881589515381] 
dist 163=[-.37706611306727113853,.64200238231514545169] 
dist 164=[-.37718345688842113745,.76727771544261833061] 
dist 165=[-.37702855351268204144,.84658712243102886486] 
dist 166=[-.37672262691059229303,.90750655561920734968] 
dist 167=[-.37623700223676480028,.95936014521836404238] 
dist 168=[-.37552179362619588566,1.0014902635917598158 ] 
dist 169=[-.37429963330728696807,1.0235889746047459543 ] 
dist 170=[-.37283766997052836895,1.0357812601718079799 ] 
dist 171=[-.37118256578539372648,1.0383582412594627154 ] 
dist 172=[-.36901141003171183573,.64611737998457981634] 
dist 173=[-.36763482373420426678,.6491295573104813306 ] 
dist 174=[-.36217465682009489243,.64988691922881476027] 
dist 175=[-.35973622228387749603,.64867777688123433207] 
dist 176=[-.35756804923068741143,.64408621197517834467] 
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dist 181=[-.34722486027999100123,.69146074463755426035] 
dist 182=[-.34294815006588370241,.70464608479413889131] 
dist 183=[-.34087872220817874592,.71193093514813511203] 
dist 184=[-.33900413934999822597,.71629482682283357571] 
dist 185=[-.33737997471137373377,.71781941646794140161] 
dist 186=[-.33481384091042797132,.71740394602086632766] 
dist 187=[-.33299109158053340683,.71571125939728980536] 
dist 188=[-.44866831490709877197,.70959469836014381541] 
dist 189=[-.54870760706718910243,.70601181347214664782] 
dist 190=[-.62819170020848906912,.39459636941458739764] 
dist 191=[-.70052340406860858904,.3729902836134379624 ] 
dist 192=[-.76281546142290586041,.34453314658008711885] 
dist 193=[-.80221955637559493265,.33805352293951474846] 
dist 194=[-.83245223717221965334,.32473080424544717258] 
dist 195=[-.85813188219874966394,.32070548275120111807] 
dist 196=[-.87952305597300238434,.30420358512905472778] 
dist 197=[-.89263448281404601705,.2996695422326736511 ] 
dist 198=[-.9022148180498140825 ,.29756703079321594523] 
dist 199=[-.9095050397731620522 ,.29820717949243039663] 
dist 200=[-.91477787107365638225,.30053873268613377691] 
dist 201=[-.9163018240051914405 ,.30518825414123196697] 
dist 202=[-.91537051147441974988,.31241264019121072798] 
dist 203=[-.91305376156083352827,.32502118402397421528] 
dist 204=[-.47521230857238361071,.3380445505349807481 ] 
dist 205=[-.45485784618043447446,.34692571451352785981] 
dist 206=[-.52138212549770939358,.42300519842909939437] 
dist 207=[-.56389452374018032108,.48751222953372586522] 
dist 208=[-.59698900191826849908,.53822291334438110868] 
dist 209=[-.62591704312941744834,.58342415600319252577] 
dist 210=[-.64997697732072652721,.62166767237845206303] 
dist 211=[-.66363807963835670101,.64460191156151319435] 
dist 212=[-.67230772905477556295,.66073119660183082422] 
dist 213=[-.67644200364979663251,.67180796119795517689] 
dist 214=[-.67779827015601339239,.67989756227637089294] 
dist 215=[-.6768953018932777459 ,.68410176542906526246] 
dist 216=[-.67174315322469831337,.68626710772868278629] 
dist 217=[-.66829678810810448577,.68621799181176325535] 
dist 218=[-.64575435293401194332,.68474886996098308139] 
dist 219=[-.63938489785207741159,.68257261764916341028] 
dist 220=[-.62819679509191473716,.67672081401122895679] 
dist 221=[-.62453603878859425785,.67356179745583945316] 
dist 222=[-.59209895481118748147,.69529210329135024685] 
dist 223=[-.64622042604462771795,.72513406319663252406] 
dist 224=[-.69238426901760489275,.74953792997025916537] 
dist 225=[-.72071820504137841983,.76264879085616797635] 
dist 226=[-.74142475074763541191,.77002056283667331526] 
dist 227=[-.7571387260212694616 ,.77151417493387646461] 
dist 228=[-.76934945439069250244,.76996919092434376043] 
dist 229=[-.77607161712225700589,.76792400807848299332] 
dist 230=[-.78005422005688465796,.75976428764063280038] 
dist 231=[-.78133166841537633829,.75547788696175745989] 
dist 232=[-.78076516082269418248,.72730464703311323015] 
dist 233=[-.77864829211307415087,.7196730535915161497 ] 
dist 234=[-.77260941248130773398,.70634808502896761496] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 0, 1, 0, 1] 
dist 0=[46.662628981313035120  ,46.662628981313035120  ] 
dist 1=[46.457372159977272001  ,46.766122015501947024  ] 
dist 2=[45.814464900454225018  ,47.002391251993661052  ] 
dist 3=[44.936683938195404782  ,47.270776337692929572  ] 
dist 4=[43.793365968291392883  ,47.502281812536568306  ] 
dist 5=[42.233079365829773799  ,47.692095586423959228  ] 
dist 6=[39.689922404557295374  ,47.793892798144758066  ] 
dist 7=[37.074321303593582943  ,47.850081241786288750  ] 
dist 8=[35.224643960437885502  ,47.857542114277929421  ] 
dist 9=[33.576529446327665161  ,47.835452436444675609  ] 
dist 10=[31.765826227542104920  ,47.773694515846178562  ] 
dist 11=[28.668592614583471944  ,47.670171053773165671  ] 
dist 12=[26.055522722950039954  ,47.597814416785221721  ] 
dist 13=[23.794022637431495078  ,47.252600423010397750  ] 
dist 14=[21.412949538718631339  ,46.905055735231124339  ] 
dist 15=[19.129192737568530198  ,45.019564852897800017  ] 
dist 16=[17.256092460577995060  ,43.501951633634957994  ] 
dist 17=[15.319050577301067904  ,36.227199666940698208  ] 
dist 18=[12.779415993432074246  ,35.256184081509811647  ] 
dist 19=[10.283765309378897731  ,32.890208724542077667  ] 
dist 20=[8.5221287317855054738 ,32.514648133040802473  ] 
dist 21=[6.9537380023708326521 ,28.962482454147194532  ] 
dist 22=[5.2296112113078394063 ,28.283845713828764538  ] 
dist 23=[3.5269825103744206305 ,27.443278551585468600  ] 
dist 24=[2.0439580547258713589 ,27.194678926328782275  ] 
dist 25=[.4290567017932581545 ,21.142003548529145657  ] 
dist 26=[-1.8014728142873205938 ,20.362071541512077131  ] 
dist 27=[-3.9707685044105345185 ,18.747956517582194974  ] 
dist 28=[-5.3411837332916933945 ,18.319858469544586426  ] 
dist 29=[-6.3982632949211565601 ,16.710434371568037926  ] 
dist 30=[-7.3151546970989897832 ,16.388127097546212370  ] 
dist 31=[-8.0809767029165780361 ,15.741852696442842605  ] 
dist 32=[-8.5344210354120053261 ,15.571763354404460330  ] 
dist 33=[-8.8512007307271961272 ,5.4708938533260653931 ] 
dist 34=[-9.0713334184235836834 ,4.5804010575663460733 ] 
dist 35=[-9.2308080614640592387 ,2.5996912739370947221 ] 
dist 36=[-9.3050719270296102175 ,2.2403653224844830522 ] 
dist 37=[-9.3346078574895482483 ,-.07290462403979081819] 
dist 38=[-9.3183627847840833124 ,-.467724400608010123  ] 
dist 39=[-9.2952775304566983856 ,-1.2013015431941950696 ] 
dist 40=[-10.436673480692058359  ,-1.3625447869135052481 ] 
dist 41=[-11.483334196559901084  ,-3.0866301889436319033 ] 
dist 42=[-12.119995902562607870  ,-2.8754872637726517722 ] 
dist 43=[-12.581002272744792674  ,-1.2225589341743186908 ] 
dist 44=[-12.925910269212260461  ,-.11223379847150487903] 
dist 45=[-13.178667759829185279  ,.81278342399129693275] 
dist 46=[-13.271491602604409510  ,1.7261855081213960735 ] 
dist 47=[-13.296430794855531692  ,2.5616782160029690570 ] 
dist 48=[-13.277912976121260618  ,3.1757402569333907180 ] 
dist 49=[-7.1486227323936170406 ,3.7447891702197295360 ] 
dist 50=[-6.7418897287612882375 ,4.4005483126660131916 ] 
dist 51=[-5.7492928541707625553 ,5.0105530364763874660 ] 
dist 52=[-5.6031055712093461391 ,5.3970321608170737066 ] 
dist 53=[-4.1481736085660445249 ,5.6934971786490621311 ] 
dist 54=[-3.8803429660054897194 ,5.9444531816243436953 ] 
dist 55=[-3.5581580187722819750 ,6.1471505048792235092 ] 
dist 56=[-3.4923187531310899196 ,6.2511577211565904287 ] 
dist 57=[-1.2996172144289184542 ,6.3032825148664683115 ] 
dist 58=[-1.0357925800968386740 ,6.3062550089859354582 ] 
dist 59=[-.4761763435276013746 ,4.4961915434197288611 ] 
dist 60=[-.3532906526744654621 ,4.6529494326371114362 ] 
dist 61=[.19628514366764420589,4.7618465575457022987 ] 
dist 62=[.29309424796329732706,4.8345576459847826375 ] 
dist 63=[.46465817610639970401,4.8848432689630049639 ] 
dist 64=[.49761778121967203008,4.9041884453097693232 ] 
dist 65=[2.2785505938470614528 ,4.9048666318660361087 ] 
dist 66=[2.0439215611715555423 ,4.8955826026058472676 ] 
dist 67=[1.5949195985367787484 ,4.8421992172484753474 ] 
dist 68=[1.2685564739764455364 ,4.8223366452601559049 ] 
dist 69=[.96928127316311341846,4.7368528769597630033 ] 
dist 70=[.62833612048264082488,4.7203446890672157313 ] 
dist 71=[.28614400952697344462,4.3686158560727459713 ] 
dist 72=[-.0181723877798584009 ,4.5542951242162773573 ] 
dist 73=[-.3535835436587531994 ,4.7240167893114745635 ] 
dist 74=[-.83005113751079811282,4.8235774582609117736 ] 
dist 75=[-1.2798382088769176237 ,4.8913806256856831891 ] 
dist 76=[-1.6191208999270441968 ,4.9341959515432551915 ] 
dist 77=[-1.9515772961951169821 ,4.9580873553217020730 ] 
dist 78=[-2.3574906549140651280 ,4.9582900105417414374 ] 
dist 79=[-2.7405102587940283917 ,4.9325730961205679361 ] 
dist 80=[-2.9815736398435153682 ,4.9169043350084590065 ] 
dist 81=[-3.1650218205906752774 ,-.21658984213396235033] 
dist 82=[-3.3180326593736330368 ,-.27069574564527284142] 
dist 83=[-3.4399205689012481874 ,-.53551971125997067929] 
dist 84=[-3.5887306842864025593 ,-.58068219849311410611] 
dist 85=[-3.9942827315520490657 ,-.67078690843943379064] 
dist 86=[-4.2775710257564106537 ,-.6908090476947359205 ] 
dist 87=[-4.5259130420979581915 ,-.8782890356480815269 ] 
dist 88=[-4.7919934005646852453 ,-.5594765707299618552 ] 
dist 89=[-5.0270801338407311530 ,-.1608591188237350398 ] 
dist 90=[-5.1516913095239791686 ,.4512236384109227081 ] 
dist 91=[-5.2195942226987484201 ,1.0671950795029396817 ] 
dist 92=[-5.2348120064565203396 ,1.4813465583904573317 ] 
dist 93=[-5.2153290782970089630 ,1.8272556341733611672 ] 
dist 94=[-5.2008785398029838178 ,2.1708148757191017170 ] 
dist 95=[-5.1822283163761607167 ,2.4868778306213240843 ] 
dist 96=[-5.1609706254472537348 ,2.7230293137817876606 ] 
dist 97=[-4.3277957968922709465 ,2.9460702748453279908 ] 
dist 98=[-4.2272602427578591574 ,3.2098072295665529253 ] 
dist 99=[-3.9556934264099234406 ,3.4543954458428772200 ] 
dist 100=[-3.9146802761221813631 ,3.6009987202499125026 ] 
dist 101=[-3.4153979076046632556 ,3.7040513757818470681 ] 
dist 102=[-3.3134632764861800505 ,3.7747865333139132373 ] 
dist 103=[-3.2105649438316535106 ,3.8223124111277884342 ] 
dist 104=[-3.1856327493414218047 ,3.8327051175121325593 ] 
dist 105=[-2.0625016455080078047 ,3.8490645387130416739 ] 
dist 106=[-1.9190188263031653997 ,4.0625940293896151779 ] 
dist 107=[-1.6314532392027355462 ,4.2616993269159783313 ] 
dist 108=[-1.5570472253822621408 ,4.4233677712379113002 ] 
dist 109=[-1.4980778663415803659 ,4.5486209159030245327 ] 
dist 110=[-1.8633086355815908555 ,4.6023660818772263180 ] 
dist 111=[-2.2039189234794729534 ,4.6252008839268608914 ] 
dist 112=[-2.4659983451173473232 ,4.6270826307254113614 ] 
dist 113=[-2.7208791628230025517 ,3.4994273320066504862 ] 
dist 114=[-3.0327617977312937768 ,3.4741333782192178571 ] 
dist 115=[-3.3272271513856681699 ,2.7720182953825150090 ] 
dist 116=[-3.5125860799884286217 ,2.6740344910283753370 ] 
dist 117=[-3.6536267222011527030 ,2.4802199804757851848 ] 
dist 118=[-3.7711877547081453500 ,2.4277646466543211295 ] 
dist 119=[-3.8647616391588241840 ,2.2310432940713366275 ] 
dist 120=[-3.9100557449103713561 ,2.1573068283330874887 ] 
dist 121=[-3.9287152961039822364 ,1.9948020213519098880 ] 
dist 122=[-3.9288745572483379756 ,2.0177014638387967679 ] 
dist 123=[.0112720969966848877 ,2.0543838352572852614 ] 
dist 124=[.0225284884213917586 ,2.0829122032452979485 ] 
dist 125=[.0332462494662912435 ,2.1040905748513177243 ] 
dist 126=[.0330557303153520143 ,2.1114227804855767073 ] 
dist 127=[.02820224433417856116,2.1100382277904200340 ] 
dist 128=[.01704507914624651929,2.1062578950668936559 ] 
dist 129=[-.00089071211940670888,1.2192530895461838816 ] 
dist 130=[-.03281147783415695360,1.1422713018439975385 ] 
dist 131=[-.07135444780188829327,.96112617918542287279] 
dist 132=[-.15142753374775604146,.92770688747398672847] 
dist 133=[-.29463233261834523829,.87625769242699292877] 
dist 134=[-.50263815962899447887,.97201913046246162183] 
dist 135=[-.72988219428796207212,1.0750557046289382859 ] 
dist 136=[-.87877694736565897358,1.1370077132009628062 ] 
dist 137=[-.99894801830287109814,1.1807073548670097964 ] 
dist 138=[-1.1115199071003805481 ,1.2108911757334715039 ] 
dist 139=[-1.2107405716158478867 ,1.2329847237979230602 ] 
dist 140=[-1.2776113414465888927 ,1.2443953062384068788 ] 
dist 141=[-1.3336742844334843841 ,1.2501469657093372964 ] 
dist 142=[-1.3897507720577985706 ,1.2496610520551812321 ] 
dist 143=[-1.4381883662610558584 ,1.1350306319941870212 ] 
dist 144=[-1.4637544355838534504 ,1.1162732389363901088 ] 
dist 145=[-1.4999474418489401298 ,1.0867947949529495760 ] 
dist 146=[-1.5934905001948957626 ,1.0773085765357867166 ] 
dist 147=[-1.6603026060038684218 ,1.0503431883613494368 ] 
dist 148=[-1.7082519700303720317 ,1.0401920368910193058 ] 
dist 149=[-1.7442038565219679686 ,1.0309477485370061236 ] 
dist 150=[-1.7631132721489516166 ,1.0245876197748107340 ] 
dist 151=[-1.7731966793159266011 ,-.18328016053940824429] 
dist 152=[-1.7739072051881839786 ,-.02265123558922416131] 
dist 153=[-1.6310734178621260631 ,.11149801074136428705] 
dist 154=[-1.6073585383947745018 ,.24472225666586601318] 
dist 155=[-1.5718172238438682154 ,.36727280801969465829] 
dist 156=[-1.5595524416155300332 ,.45881254725021702202] 
dist 157=[-1.5333323972491129910 ,.54523655888874165323] 
dist 158=[-1.5237374896643788021 ,.64736508671915889081] 
dist 159=[-1.5120586133676087178 ,.74289362980833351034] 
dist 160=[-1.5053165231672655753 ,.80297077821328950969] 
dist 161=[-.57812132292487090189,.84862865364303443662] 
dist 162=[-.50033422081899515208,.88659632356827554422] 
dist 163=[-.3142092346786534146 ,.91675191098121630771] 
dist 164=[-.28751783250676555364,.93122488878393931702] 
dist 165=[-.0282928232641667547 ,.93826842199836848008] 
dist 166=[.0180637280556138900 ,.93876277816422223321] 
dist 167=[.0745985191284873512 ,.78619855503175925489] 
dist 168=[.0841149302342908666 ,.76988821481346967231] 
dist 169=[.4314775016687077769 ,.77131112053688755939] 
dist 170=[.4717325848239852040 ,.84893826879459201424] 
dist 171=[.45902276436903867548,.90790713889694797646] 
dist 172=[.39282787573037032143,.95694141246274400916] 
dist 173=[.31439470628589111668,.9962365494039295092 ] 
dist 174=[.19867945293181153317,1.0163204830846390284 ] 
dist 175=[.07951830751182914033,1.0269405340124062921 ] 
dist 176=[-.01267217691429429443,1.0286315980595273668 ] 
dist 177=[-.1028309899596788864 ,.8266415265766126151 ] 
dist 178=[-.2138837748436881861 ,.81971715605798660508] 
dist 179=[-.32997768165469531916,.80356824246820608066] 
dist 180=[-.44026238832557781699,.79743990920858400159] 
dist 181=[-.5675094567227553394 ,.76570200489537703311] 
dist 182=[-.75132017583699828241,.75803752155621570751] 
dist 183=[-.9322266384370867539 ,.73783264561316664965] 
dist 184=[-1.0506815686201742507 ,.73112149054848886975] 
dist 185=[-1.1519311702922159031 ,.65337475873829312878] 
dist 186=[-1.2406964954282211565 ,.6407274975700282578 ] 
dist 187=[-1.3147074661913155282 ,.60614387557800768125] 
dist 188=[-1.3570564217834076422 ,.60069840161024721888] 
dist 189=[-1.3843417620861444131 ,.53512268735942044764] 
dist 190=[-1.3982162772021719162 ,.52147761135608155424] 
dist 191=[-1.4062024622581103599 ,.52181619394007776177] 
dist 192=[-1.4099819510016554174 ,.54958595941180359716] 
dist 193=[-1.4113970267950739066 ,.57842959988116123344] 
dist 194=[-1.4099480563147338442 ,.59916767220618628543] 
dist 195=[-1.4067637536433674035 ,.61793727653372018518] 
dist 196=[-1.4014410646976288380 ,.63892478690160915667] 
dist 197=[-1.3929828428245571102 ,.65972911848208198543] 
dist 198=[-1.3881421580310793512 ,.6777677646928619116 ] 
dist 199=[-.9916911130187110311 ,.6972341105095489592 ] 
dist 200=[-1.0223529874848358342 ,.72373668392171226414] 
dist 201=[-1.0478711842603156593 ,.75007294373668541904] 
dist 202=[-1.0628453966960813823 ,.76887551542809685335] 
dist 203=[-1.0729839929449159922 ,.78575883447918758974] 
dist 204=[-1.0791964854522710929 ,.8044350134391604522 ] 
dist 205=[-1.0824240768164161557 ,.82283203142520964662] 
dist 206=[-1.0808028039801216555 ,.83860105507684938935] 
dist 207=[-1.0759758601790661047 ,.85546357053767979973] 
dist 208=[-1.0722617913945429802 ,.87822456977002653085] 
dist 209=[-.38942798806783524589,.8997290188033759575 ] 
dist 210=[-.33784339764878543393,.9115760652338877651 ] 
dist 211=[-.2214543250547128778 ,.9186135371415221350 ] 
dist 212=[-.19881434164481095335,.9209214154104947178 ] 
dist 213=[-.05650574192174914270,.9200043774892957199 ] 
dist 214=[-.03145500852900299133,.9141697806938674458 ] 
dist 215=[.01652682402435606360,.58366252936436395932] 
dist 216=[.02782726571776175200,.61058867727455794946] 
dist 217=[.14800196242825799888,.63632088136246523917] 
dist 218=[.16577637013347088571,.65308562520828659806] 
dist 219=[.16314558949731400538,.66651128187873590281] 
dist 220=[.08034636732203711942,.67891526760366482986] 
dist 221=[-.01075973894632979194,.68973939898887964316] 
dist 222=[-.10405065241115097666,.70774872845001772107] 
dist 223=[-.21687655163007635967,.76191138232566321957] 
dist 224=[-.38596391174986840169,.83215317567370869494] 
dist 225=[-.55439018360061922878,.89892986127323090566] 
dist 226=[-.66457663608161858159,.93925984961773505757] 
dist 227=[-.75326933333236227131,.9679828603045526624 ] 
dist 228=[-.83589381090984511464,.98842211460378351346] 
dist 229=[-.90834970992599889028,1.0026421894423727276 ] 
dist 230=[-.95644962719514203958,1.0065361920829937317 ] 
dist 231=[-.99594458306041031091,1.0062517363001939765 ] 
dist 232=[-1.0340487564669700577 ,1.0037897582420356226 ] 
dist 233=[-1.0666588779875695835 ,.95077858215662263993] 
dist 234=[-1.0842219922889713357 ,.94018590601946850903] 
dist 235=[-1.0941293849736158720 ,.91591526101851141987] 
dist 236=[-1.0961798145169603922 ,.9073165484173103986 ] 
dist 237=[-1.0939181117828508053 ,.86468204174569560272] 
dist 238=[-1.0910989118370566869 ,.85472421232062821495] 
dist 239=[-1.0785183414392325621 ,.82896262869023904002] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 2, 1, 2, 2, 1, 2] 
dist 0=[48.917392581980223818  ,48.917392581980223818  ] 
dist 1=[48.526527611146156270  ,49.143931852021920435  ] 
dist 2=[47.939555931447811559  ,49.277465638073324632  ] 
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dist 60=[-.69033281798023172061,10.739999544569840357  ] 
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dist 89=[-1.8251986152657881574 ,.64454635692703197313] 
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dist 93=[-2.3441599557311755138 ,.19049574487009409628] 
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dist 99=[-2.5554892131302200824 ,.22905000858873165825] 
dist 100=[-2.5502106006173204346 ,.32020471190144192694] 
dist 101=[-2.4845318321766506368 ,.44154492711802303557] 
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dist 103=[-2.4406315642222770072 ,.70509446878280959372] 
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dist 105=[-2.0701592196797799872 ,1.0970413256737725771 ] 
dist 106=[-2.0180802986494428061 ,1.3302022409807972010 ] 
dist 107=[-1.9124558134122055739 ,1.4835783634074017250 ] 
dist 108=[-1.8824739929777021825 ,1.6080466607507355291 ] 
dist 109=[-1.7618789821980223697 ,1.7257991669619517206 ] 
dist 110=[-1.7349652947323351211 ,1.8303818704988442621 ] 
dist 111=[-1.6721474813392252440 ,1.9022733329808275566 ] 
dist 112=[-1.6513837426667059814 ,1.9640743153367812694 ] 
dist 113=[-.44838614251954771528,2.0283754585809544710 ] 
dist 114=[-.33995846191959789841,2.0835141624803201302 ] 
dist 115=[-.09904056289471842601,2.1087363680988933004 ] 
dist 116=[-.05184072197830596477,2.1198960747702217634 ] 
dist 117=[.22894320640177096758,2.1189484754840141887 ] 
dist 118=[.2771741468517716795 ,2.0856955806349718212 ] 
dist 119=[.37358972885517948899,2.0722396775704105947 ] 
dist 120=[.39682128566037830135,2.0597529052321784273 ] 
dist 121=[.43058225466382642188,2.0502427681481525048 ] 
dist 122=[.094060012717380084  ,1.7579433742494479693 ] 
dist 123=[-.13379122968704985269,1.7173804872596003077 ] 
dist 124=[-.32582621812332740041,1.6178277374424917459 ] 
dist 125=[-.51937273064927143936,1.5949368570858993749 ] 
dist 126=[-.69923663348760812725,1.4353183956955149872 ] 
dist 127=[-.83665177333942627233,1.4022335867872715832 ] 
dist 128=[-.96938740861423415798,1.2639760227638808846 ] 
dist 129=[-1.1305713825283483639 ,.76214277533617272213] 
dist 130=[-1.2821750685627313862 ,.36617913956415502429] 
dist 131=[-1.3766664321812506591 ,.31689985935154769643] 
dist 132=[-1.4474802281624317428 ,.21467824289939222891] 
dist 133=[-1.5045631591467090233 ,.18808961742552280488] 
dist 134=[-1.5488995136083623533 ,.09117909389282038410] 
dist 135=[-1.5688286650171536054 ,.07192119841317585874] 
dist 136=[-1.5778342255302245182 ,.03918046362444378021] 
dist 137=[-1.5785643433689923478 ,.03187481184010416298] 
dist 138=[-.49548491085073298105,-.33263351821307014186] 
dist 139=[-.57946477042145211906,-.36121232779252868797] 
dist 140=[-.64509150483232847413,-.36656832150942315431] 
dist 141=[-.70295316366380630735,-.37347435281079931668] 
dist 142=[-.75148999274823763763,-.36682177016487465902] 
dist 143=[-.77988810424480457367,-.35179977713945145095] 
dist 144=[-.799017801133056747  ,-.32147168803730608865] 
dist 145=[-.81055276033632471308,-.28829871846270455477] 
dist 146=[-.81855853177356399996,-.26191867596671992975] 
dist 147=[-.8235977342080171289 ,-.23548060530077041144] 
dist 148=[-.82744887733205933407,-.20206672187345246451] 
dist 149=[-.83070842586521465494,-.16672591187678959416] 
dist 150=[-.83335586012629491704,-.13259087500825302861] 
dist 151=[-.8347618206039696682 ,-.09278673448864258325] 
dist 152=[-.83553585484980541451,-.03481026904594624093] 
dist 153=[-.83565931854049848355,.02457858026891720057] 
dist 154=[-.59801768086874222604,.08071338781934188602] 
dist 155=[-.58390864713700229612,.16921025947875966434] 
dist 156=[-.54767615960623630775,.24328125252355405425] 
dist 157=[-.54081221583739587574,.31711303243888753488] 
dist 158=[-.47853858648393900815,.38521447341342929026] 
dist 159=[-.4657249087802712911 ,.43641134333176290623] 
dist 160=[-.4485918603690170699 ,.48507885354082526799] 
dist 161=[-.44263805836775546969,.54308587153279455341] 
dist 162=[-.31278471193630670775,.59713154519434661325] 
dist 163=[-.29537807797049743737,.62998629503653699468] 
dist 164=[-.25800863602051660081,.65364919087504764633] 
dist 165=[-.24758889457022615215,.6799035100348545445 ] 
dist 166=[-.20551659762156132054,.70131926656020847908] 
dist 167=[-.19745509206056906265,.71760665076344250245] 
dist 168=[-.17737507701196032212,.73119413666542468184] 
dist 169=[-.1740316925777060444 ,.74146064571361585297] 
dist 170=[.05935311683899940882,.74448886546939488915] 
dist 171=[.08087230822990324339,.7444030818947085282 ] 
dist 172=[.12769603682098719098,.74235398613623359415] 
dist 173=[.13686720902721029641,.72428811172159284721] 
dist 174=[.18720828834808647929,.71847523235569356008] 
dist 175=[.19540552328615855825,.70998122001926360874] 
dist 176=[.07077473484752382529,.70633929594345481199] 
dist 177=[-.07061879646474818605,.60085511462679398004] 
dist 178=[-.165636122724150561  ,.57559144338283701288] 
dist 179=[-.24497140037600186258,.5702064372267432948 ] 
dist 180=[-.32375793578099434357,.55804485111880932068] 
dist 181=[-.3962557575284287562 ,.55363344170676620833] 
dist 182=[-.45048482068401600545,.5314113838107410915 ] 
dist 183=[-.50177261894887967248,.52614798965337754777] 
dist 184=[-.56252823987602021938,.51176748638671608935] 
dist 185=[-.61893563275247301357,.50757657160568206668] 
dist 186=[-.65286403784628845131,.39424317469841789664] 
dist 187=[-.67685636245708330836,.39307814937901763057] 
dist 188=[-.6935958517992323396 ,.38872478560116715916] 
dist 189=[-.70582244236436420264,.38641726003302986712] 
dist 190=[-.71179771364247428359,.37182000775811722931] 
dist 191=[-.71434281624405059099,.3678348050579218504 ] 
dist 192=[-.71370851054919617122,.36078322306809236375] 
dist 193=[-.45426766586476409479,.35852328502765326544] 
dist 194=[-.49564075597878241521,.30205015120161817429] 
dist 195=[-.52137223791625469134,.29366153634884785663] 
dist 196=[-.54059402284532752963,.27507985009974315692] 
dist 197=[-.55597688276790085443,.26943359040606509822] 
dist 198=[-.56771995672986796308,.24457967026839043378] 
dist 199=[-.57240895487625558646,.23939768642730615284] 
dist 200=[-.573950454275958646  ,.22655758240177721176] 
dist 201=[-.5731331039272816685 ,.22329173712331387115] 
dist 202=[-.45287964190577560885,-.12664237036408144791] 
dist 203=[-.46227608273911858552,-.11930569341028192961] 
dist 204=[-.46710683266422410389,-.10620536070461256463] 
dist 205=[-.46972630253482604391,-.09038622141353129837] 
dist 206=[-.47029518803646973305,-.07219461944754114157] 
dist 207=[-.46947109638516991865,-.04876040772096984836] 
dist 208=[-.46835291246793528805,-.01201037957854234176] 
dist 209=[-.42071788396908572834,.02529703763782616518] 
dist 210=[-.41388554239889387079,.05095679613400374311] 
dist 211=[-.39462106502586643587,.07662350543529162427] 
dist 212=[-.39148753373428807216,.12197251366739647582] 
dist 213=[-.35277005615877057001,.1650554981688479287 ] 
dist 214=[-.34451915389026691084,.19957063830191983048] 
dist 215=[-.3362438861915435321 ,.23445691781640745382] 
dist 216=[-.33361817853899334713,.2790222287791628193 ] 
dist 217=[-.23559393332577322183,.32207738027897700292] 
dist 218=[-.22270346637749677853,.35093491564863740546] 
dist 219=[-.19702188093816284186,.37495020868255303017] 
dist 220=[-.19027993997733070899,.39867383824821619879] 
dist 221=[-.16589118559713353977,.42042757006396267191] 
dist 222=[-.16040253645842708438,.43657879511833837777] 
dist 223=[-.15162207336166594792,.45174006277010238374] 
dist 224=[-.1491985139052750782 ,.46954247962783288577] 
dist 225=[.01573939678804646034,.48547013416648710402] 
dist 226=[.01711569135967099506,.49314674488769678489] 
dist 227=[.00400549918752118729,.49695859791213657022] 
dist 228=[-.01096819478848230447,.49745530020911998512] 
dist 229=[-.03241269911039684122,.49029957103131261932] 
dist 230=[-.05639531083802469727,.48788381999033677252] 
dist 231=[-.08150184720335784793,.48592634320591382736] 
dist 232=[-.11226141858182637876,.48408234579827147264] 
dist 233=[-.15881195350731938848,.40975888867301831002] 
dist 234=[-.20550030013580595029,.39902027262871283798] 
dist 235=[-.23681031534561530281,.37888723224802063657] 
dist 236=[-.2628767198515781445 ,.37349616235707997951] 
dist 237=[-.28863245207977403543,.35410921330688994888] 
dist 238=[-.31224356044907703476,.34892420649904995826] 
dist 239=[-.3297487499461320303 ,.34110944822533987982] 
dist 240=[-.34614994186980245058,.33843292813303169827] 
dist 241=[-.36535437975338650434,.15818033474795630614] 
dist 242=[-.38306812953356618751,.15500847167540752034] 
dist 243=[-.39351858427980701123,.14789843223923442677] 
dist 244=[-.40066095190102847327,.14565372480216615042] 
dist 245=[-.40516859701022718028,.13543936413425537502] 
dist 246=[-.40764629323274244753,.13322990293519131754] 
dist 247=[-.4079233280911218068 ,.12781771684407528268] 
dist 248=[-.40497145130349371706,.12621393378532231459] 
dist 249=[-.40444209221466849836,.10903840596658852058] 
dist 250=[-.3853474002956067698 ,.10622127377345608799] 
dist 251=[-.38140940025384465381,.09930325830846553916] 
dist 252=[-.3709393147944023179 ,.09775019460012399585] 
dist 253=[-.36758360537401586349,.08667019915323665690] 
dist 254=[-.34650081661496137746,.08438314448504789229] 
dist 255=[-.34155003565190074716,.08051118578075911102] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 0, 1, 1, 0, 1] 
dist 0=[47.526052813302593175  ,47.526052813302593175  ] 
dist 1=[47.210125471491618160  ,47.660013847714507169  ] 
dist 2=[46.714305628420797268  ,47.878870410346348936  ] 
dist 3=[46.059826091805449384  ,48.104674527886921851  ] 
dist 4=[45.158127710933173772  ,48.330105170805049173  ] 
dist 5=[43.696630094031385251  ,48.537747941024628364  ] 
dist 6=[41.949347334950833218  ,48.692423346746148950  ] 
dist 7=[38.991613306171140941  ,48.837394830352192582  ] 
dist 8=[35.962112822250533823  ,49.006067156012740146  ] 
dist 9=[33.798213753980210266  ,49.148775336896846438  ] 
dist 10=[29.940503333777422738  ,49.190125692645974230  ] 
dist 11=[27.280644555360731791  ,49.164463064471288296  ] 
dist 12=[24.982536353315942084  ,49.107715006418336021  ] 
dist 13=[22.569275262158445623  ,48.845066412616445071  ] 
dist 14=[20.258728922914435728  ,46.639767403813650778  ] 
dist 15=[18.370565421307141490  ,46.194657678630580507  ] 
dist 16=[16.424230710263203401  ,43.382699979017169717  ] 
dist 17=[13.880842777621128963  ,37.696970166002927193  ] 
dist 18=[11.385622122028204329  ,36.706631865565535769  ] 
dist 19=[9.6313897997851100561 ,34.286768769076430109  ] 
dist 20=[8.0770012479479967476 ,33.900731208607965218  ] 
dist 21=[6.3796338744773446831 ,30.240309993203230591  ] 
dist 22=[4.7100150898945739600 ,29.538162279247873077  ] 
dist 23=[3.2659422857756854490 ,28.669510383844657507  ] 
dist 24=[1.7018840042224796357 ,28.408037731989423006  ] 
dist 25=[-.4481629273520092387 ,22.084115723019074244  ] 
dist 26=[-2.5367942924323610549 ,21.267126299903519302  ] 
dist 27=[-3.8556468083425088698 ,19.576434733689506688  ] 
dist 28=[-4.8725463640621421554 ,19.127350206328553541  ] 
dist 29=[-5.7542327510557431066 ,17.436232139142668759  ] 
dist 30=[-6.4907352237385504603 ,17.096873362175318734  ] 
dist 31=[-6.9275085992054508803 ,16.413527856720394899  ] 
dist 32=[-7.2337268732991712701 ,16.232445202630734174  ] 
dist 33=[-7.4489520169046115791 ,5.5119991519047696447 ] 
dist 34=[-7.6083870437304159719 ,4.5659090790637612856 ] 
dist 35=[-7.6915242208598846792 ,2.4671969254311422822 ] 
dist 36=[-7.7382431088059148906 ,2.0814173141372834561 ] 
dist 37=[-7.9710355742256328340 ,-.35073084968396717878] 
dist 38=[-9.1684393916490606393 ,-.76488078225481898216] 
dist 39=[-10.253838128494239772  ,-1.5476322417637668893 ] 
dist 40=[-11.475923411261501267  ,-1.7230032163242054898 ] 
dist 41=[-12.595778932451524523  ,-2.8309153486661697433 ] 
dist 42=[-13.272816628020643083  ,-1.4736389163814778931 ] 
dist 43=[-13.757956662919312281  ,-.55389818309165676839] 
dist 44=[-14.111209713510436182  ,.22064798574683920057] 
dist 45=[-14.367084254675000013  ,.99857033691984221654] 
dist 46=[-14.463167657331249792  ,1.7182565697570311084 ] 
dist 47=[-14.485224989248053574  ,2.2603987776040921707 ] 
dist 48=[-14.457686218509128397  ,2.7757262627065357630 ] 
dist 49=[-7.2086354247226108063 ,3.3883335170481332988 ] 
dist 50=[-6.7388360764195762337 ,3.9608639337760158517 ] 
dist 51=[-5.6003786028668367605 ,4.3162958395584909034 ] 
dist 52=[-5.4322568722633446798 ,4.5803676312023800896 ] 
dist 53=[-3.7930250921107813092 ,4.7884971170281370919 ] 
dist 54=[-3.4939606152332300644 ,4.9475838408510032871 ] 
dist 55=[-3.1266092564124939398 ,5.0158981407893532303 ] 
dist 56=[-3.0506937190008069446 ,5.0435196578199909764 ] 
dist 57=[-.6885552511347259222 ,5.0403411281901393234 ] 
dist 58=[-.40641860861584808119,4.1209387459948590440 ] 
dist 59=[.1989126431101307446 ,4.2763817047825370948 ] 
dist 60=[.32059579783628790485,4.3955205539762718942 ] 
dist 61=[.93340995932722662294,4.4566161924529452156 ] 
dist 62=[1.0358595253046259805 ,4.4871737892086000158 ] 
dist 63=[1.2258641206077254834 ,4.4881647194311156835 ] 
dist 64=[1.2636073400078817710 ,4.1936301258236666546 ] 
dist 65=[1.0100576384631053126 ,4.1406557954362935294 ] 
dist 66=[.68192674720099344063,4.0590275977649691428 ] 
dist 67=[.45115850950803920916,4.0660723397824623613 ] 
dist 68=[.24742598479107105995,4.3123555715323175718 ] 
dist 69=[.02714424556224707147,4.5324941860523855541 ] 
dist 70=[-.18722660609105643864,4.6879852888227157553 ] 
dist 71=[-.36741922452509620946,4.8267638682482975237 ] 
dist 72=[-.55743190158068670934,4.9801599019027832513 ] 
dist 73=[-.81109417264798002586,5.1182933596194408728 ] 
dist 74=[-1.0584034378814206395 ,5.1960907676511026322 ] 
dist 75=[-1.2230703062878639010 ,5.2451584632072492445 ] 
dist 76=[-1.3591885718755062017 ,5.2684721060003856243 ] 
dist 77=[-1.4924878891549655752 ,5.2738658472322903354 ] 
dist 78=[-1.6142764880699107754 ,5.2675635233298061387 ] 
dist 79=[-1.9233389045052869230 ,5.2230089786183314800 ] 
dist 80=[-2.2322342258176479561 ,5.2052458653918752017 ] 
dist 81=[-2.8217874349271311996 ,-.58408383463160302305] 
dist 82=[-3.4805940143730880886 ,-.77285700224868441428] 
dist 83=[-4.0135422192880839189 ,-.80064753060580125739] 
dist 84=[-4.5147421632824106967 ,-.82607278064535305134] 
dist 85=[-4.9577724146952129959 ,-.63779545815497217241] 
dist 86=[-5.2585233684254151340 ,-.41098007698410039872] 
dist 87=[-5.5130273690328361889 ,-.17267143109003786357] 
dist 88=[-5.7714751373681801706 ,.11975708066186525221] 
dist 89=[-5.9953896764467001125 ,.56262027421235662431] 
dist 90=[-6.1120327329706109088 ,1.0045681835658515505 ] 
dist 91=[-6.1726808367432004312 ,1.2933518232488856239 ] 
dist 92=[-6.1830168551056845797 ,1.5253508625392581617 ] 
dist 93=[-6.1499712073447079642 ,1.7406397899835508652 ] 
dist 94=[-6.1234841326053351425 ,1.9288161265876728133 ] 
dist 95=[-6.0732495314001840914 ,2.0525943580095403102 ] 
dist 96=[-6.0488233529371118683 ,2.1529653147047850688 ] 
dist 97=[-4.5802910864704888689 ,2.2477124138056256091 ] 
dist 98=[-4.4234353140824612216 ,2.3293200042366709087 ] 
dist 99=[-4.0176631369806108635 ,2.3772427211900699914 ] 
dist 100=[-3.9582587172905886955 ,2.4097022728263544971 ] 
dist 101=[-3.2759390904671885965 ,2.4295822887555424960 ] 
dist 102=[-3.1420007394295256030 ,2.7914492156585393992 ] 
dist 103=[-3.0010688751370165299 ,3.2197501392909734789 ] 
dist 104=[-2.9721609685168384321 ,3.7400052547452043144 ] 
dist 105=[-1.6224309025397808467 ,4.2291463277586281797 ] 
dist 106=[-1.4540420749954274442 ,4.5332508355035825974 ] 
dist 107=[-1.1124421201137095407 ,4.7601571828074042273 ] 
dist 108=[-1.0247057187881058209 ,4.9411481188583114230 ] 
dist 109=[-1.0639682466414705568 ,5.0804593426143850746 ] 
dist 110=[-1.1252988811546174934 ,5.1409926522070454185 ] 
dist 111=[-1.2090366421916516556 ,5.1667099421027048309 ] 
dist 112=[-1.2923450623528475658 ,5.1670500866490553201 ] 
dist 113=[-1.4377540653160963118 ,1.5976675618604714207 ] 
dist 114=[-1.5881210670125597003 ,1.9320080746791226876 ] 
dist 115=[-1.6773305511212104216 ,2.1972486224528625009 ] 
dist 116=[-1.7388491752211371255 ,2.4379603914310904602 ] 
dist 117=[-1.7786979026901438824 ,2.6448216348475285515 ] 
dist 118=[-1.8065708303315212712 ,2.7749236748280799004 ] 
dist 119=[-1.8202840335968970168 ,2.8738900469864409411 ] 
dist 120=[-1.8262488016793734121 ,2.9564570112096272151 ] 
dist 121=[-1.8231722239954867605 ,3.0241902849959117411 ] 
dist 122=[.1113127455031383948 ,3.0639353100481680817 ] 
dist 123=[.0568944478739019419 ,3.0908811461989469519 ] 
dist 124=[.0004679632509863346 ,3.1075052295663015055 ] 
dist 125=[-.0523880326874508717 ,3.1162884391631049519 ] 
dist 126=[-.1127806133043817298 ,3.1119261575163269547 ] 
dist 127=[-.1993009143663455373 ,3.0987060846475064806 ] 
dist 128=[-.2873377977355996449 ,3.0891419771913419402 ] 
dist 129=[-.3537894784825146891 ,2.2940229975278827051 ] 
dist 130=[-.51745361745510029049,2.2494366852799211549 ] 
dist 131=[-.78035471937922050034,2.1294320798718812211 ] 
dist 132=[-1.0449376371828388399 ,2.1082149833096720056 ] 
dist 133=[-1.2905609953417863269 ,1.8842444799553716324 ] 
dist 134=[-1.4777842629414752451 ,1.8372852850049934363 ] 
dist 135=[-1.6582284878642407683 ,1.7827690030463767985 ] 
dist 136=[-1.8768012310724558826 ,1.7615989200858141584 ] 
dist 137=[-2.0821746708304744188 ,1.2452673025919125926 ] 
dist 138=[-2.2099330691355908709 ,1.1764481833355706434 ] 
dist 139=[-2.3054286087293143975 ,1.0345411398253629131 ] 
dist 140=[-2.3820145922824100411 ,.9962291252182448406 ] 
dist 141=[-2.4407191721963829196 ,1.0127264218487550260 ] 
dist 142=[-2.4648399085330846532 ,1.0383331435358402179 ] 
dist 143=[-2.4739522518521011585 ,1.0619554190957676891 ] 
dist 144=[-2.4727133247928232896 ,1.0804192358802828199 ] 
dist 145=[-2.4106808373133065414 ,1.0854367651262783605 ] 
dist 146=[-2.3958647635492496841 ,1.0857421903384119694 ] 
dist 147=[-2.3408404619123996331 ,1.0854077271601326292 ] 
dist 148=[-2.3314520666494337326 ,1.0455918403188472082 ] 
dist 149=[-2.2470300088508866279 ,1.0350177163667930356 ] 
dist 150=[-2.2489194715412143127 ,1.0284324404084718423 ] 
dist 151=[-2.2432697297790708704 ,1.0255501790852095092 ] 
dist 152=[-2.2365671169456255781 ,-.15763074176449513699] 
dist 153=[-2.1178323811871922604 ,.01750305953354192402] 
dist 154=[-2.1122927701434062556 ,.16944956834581703983] 
dist 155=[-2.0915171742007401782 ,.32963646720519718029] 
dist 156=[-2.0799245396619998862 ,.48300618996812466965] 
dist 157=[-2.0082079177734998242 ,.60773895391298814279] 
dist 158=[-1.9885861994858292699 ,.73548183931435885667] 
dist 159=[-1.9516461767675297631 ,.90086888479092317829] 
dist 160=[-1.9393050550813364324 ,1.0616225959870332981 ] 
dist 161=[-1.6058326755438351326 ,1.1708694224636196141 ] 
dist 162=[-1.5938843424665193532 ,1.2633922174889288540 ] 
dist 163=[-1.5579037048018170342 ,1.3573833122615797941 ] 
dist 164=[-1.5470137830699426692 ,1.4452146147493517928 ] 
dist 165=[-1.4599437454731489854 ,1.5131477331863194009 ] 
dist 166=[-1.4389022090803747523 ,1.5795725736057385175 ] 
dist 167=[-1.4074560882376882268 ,1.6613837585860951039 ] 
dist 168=[-1.3963686431359124246 ,1.7364302148567434137 ] 
dist 169=[-1.1262905457218152702 ,1.8891822005150086109 ] 
dist 170=[-1.0877176718641753602 ,1.9869879158842502050 ] 
dist 171=[-1.0044575155247353298 ,2.0590793252961191002 ] 
dist 172=[-.98013649000906710073,2.1149891321187650758 ] 
dist 173=[-.8769288193601235121 ,2.1562330063231468330 ] 
dist 174=[-.90075437153439882089,2.1697706456716562700 ] 
dist 175=[-1.0374906128354548178 ,2.1730283958204332840 ] 
dist 176=[-1.1714550498719514211 ,2.1732500954653523327 ] 
dist 177=[-1.2642430613896593730 ,1.4889358464162261290 ] 
dist 178=[-1.3447025889356330651 ,1.4191637405032882982 ] 
dist 179=[-1.4294528287253599874 ,1.4000612579835826034 ] 
dist 180=[-1.5105488416101905650 ,1.3290403257594555460 ] 
dist 181=[-1.5764214057721695322 ,1.3103277324773341859 ] 
dist 182=[-1.6438092499149134447 ,1.2768568678432784932 ] 
dist 183=[-1.7309552565052177978 ,1.2669873723265073167 ] 
dist 184=[-1.8124176527131218753 ,.38492026354370951588] 
dist 185=[-1.8571166706328472026 ,.06005420102334746347] 
dist 186=[-1.8834772889395116643 ,.01916558473352119081] 
dist 187=[-1.8917322366547785926 ,-.07513041970506789471] 
dist 188=[-1.8921041543352982646 ,-.08950581259813707526] 
dist 189=[-1.8869955434266716956 ,-.20801567552943446302] 
dist 190=[-1.8770614735924917514 ,-.22811938561683633933] 
dist 191=[-1.8711157403811639059 ,-.25773840501327495225] 
dist 192=[-1.6691899029075800207 ,-.26484426350812808013] 
dist 193=[-1.6370267807722535477 ,-.36990619187128462266] 
dist 194=[-1.5701434808159511283 ,-.3844988766882618154 ] 
dist 195=[-1.5497533648747428457 ,-.38647708602670513596] 
dist 196=[-1.4605111140827473568 ,-.37074331794558206966] 
dist 197=[-1.4508833914695412266 ,-.34500593022673806192] 
dist 198=[-1.4540551776988176071 ,-.26834677042208984579] 
dist 199=[-1.4520191585644360263 ,.02484621071018550784] 
dist 200=[-1.0870041948208426925 ,.38702951812476278898] 
dist 201=[-1.0513484209593987931 ,.62814170182255602789] 
dist 202=[-.97020530643570993858,.82690614124544037473] 
dist 203=[-.94855483789208730321,1.0200391275337366746 ] 
dist 204=[-.83863774951248516183,1.1949306466509245137 ] 
dist 205=[-.79426813057660580147,1.3208761595419891970 ] 
dist 206=[-.77248228350563904863,1.4351785454892884027 ] 
dist 207=[-.76371567614596022653,1.5635918344316738858 ] 
dist 208=[-.54911535696220976113,1.6808229244720561387 ] 
dist 209=[-.52038020788545225104,1.7504859885698800762 ] 
dist 210=[-.46127165073683891826,1.7986922375901795509 ] 
dist 211=[-.4452909834347237597 ,1.8302666461414029146 ] 
dist 212=[-.38427296176948638835,1.8511498776757436646 ] 
dist 213=[-.37148142343490692435,1.8566774363462975522 ] 
dist 214=[-.3454089713226932742 ,1.8545948807800713527 ] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 2, 2, 1, 2, 0, 2] 
dist 0=[59.040057776341528113  ,59.040057776341528113  ] 
dist 1=[58.509768519818193144  ,59.279859148771254408  ] 
dist 2=[57.768494118383906356  ,59.353573583119656631  ] 
dist 3=[56.686017758993775032  ,59.319443218772850365  ] 
dist 4=[55.142991718754684188  ,59.016682780296332212  ] 
dist 5=[52.562234916795990330  ,58.847858779039228460  ] 
dist 6=[49.874689863882496381  ,58.553454988614666509  ] 
dist 7=[47.905146038065167488  ,58.166601268539514461  ] 
dist 8=[46.078959100560758025  ,55.127964703801625852  ] 
dist 9=[43.964010306279746384  ,54.204139055136284730  ] 
dist 10=[41.818149999560022715  ,53.927804991425110234  ] 
dist 11=[39.868479114294016448  ,53.377203578305278366  ] 
dist 12=[37.683526833720543408  ,53.185147258527122606  ] 
dist 13=[33.959079748598350061  ,52.347030112661342051  ] 
dist 14=[30.568697229960402979  ,52.024964511255298120  ] 
dist 15=[27.653611643541963106  ,49.862508759896601537  ] 
dist 16=[24.614517615518156192  ,28.906783195486711459  ] 
dist 17=[21.718388782839490077  ,28.369908331870139695  ] 
dist 18=[18.931211133546722166  ,26.488781903310903725  ] 
dist 19=[15.447007642142401627  ,26.067552401615615933  ] 
dist 20=[12.180514778574487703  ,25.517994192370171304  ] 
dist 21=[9.6258460261588429026 ,25.334169411280348832  ] 
dist 22=[6.6616276530782270553 ,11.244658429337380342  ] 
dist 23=[3.7209628814116444806 ,10.247049408971553852  ] 
dist 24=[.89080655340201680872,8.9236059340832319898 ] 
dist 25=[-1.1297399935571141218 ,6.8300157299891465918 ] 
dist 26=[-3.3332233430404830041 ,6.4953818482941651727 ] 
dist 27=[-4.9852327780960142485 ,5.8042332563315231502 ] 
dist 28=[-6.5510145994126346073 ,5.6951110012249043126 ] 
dist 29=[-8.4149046496455615130 ,2.0237654754669817950 ] 
dist 30=[-10.155756301511653224  ,1.6673942151632478669 ] 
dist 31=[-11.230026118585806681  ,.55281201788888809413] 
dist 32=[-12.024612687410951898  ,-3.7898165539846545201 ] 
dist 33=[-12.648270176463910941  ,-3.5415674239204279828 ] 
dist 34=[-13.128194559885335439  ,-3.1133932643556729926 ] 
dist 35=[-13.348807912809452206  ,-2.4666832024695824356 ] 
dist 36=[-13.443771603172568774  ,-1.5409890491681126872 ] 
dist 37=[-13.437302575140956367  ,0                     ] 
dist 38=[-12.327614504776000904  ,-3.4173214503112484439 ] 
dist 39=[-12.307942533292808643  ,-2.3928807942747190550 ] 
dist 40=[-11.109628100688378278  ,-1.4783278622291278029 ] 
dist 41=[-10.916141985309808964  ,-.47776711667923870081] 
dist 42=[-10.520246224649836032  ,.49934410039765905639] 
dist 43=[-10.400160639809714555  ,1.3206771977991924583 ] 
dist 44=[-10.084336187033127104  ,2.1844351199606102446 ] 
dist 45=[-9.7668284932341409435 ,3.3312211391736659990 ] 
dist 46=[-9.4589085924769581110 ,4.4576634114763968340 ] 
dist 47=[-9.3686172680479083838 ,5.2404259076617561423 ] 
dist 48=[-3.5877896471384278354 ,5.9216263914525880531 ] 
dist 49=[-3.0589501675140169940 ,6.6429650520978613293 ] 
dist 50=[-1.9616037549477293822 ,7.3360987066673574219 ] 
dist 51=[-1.6837771115346241852 ,7.9049466536677449570 ] 
dist 52=[-.58698817264811027986,8.4930742732004776749 ] 
dist 53=[1.2285374782409157732 ,9.2635608882827208229 ] 
dist 54=[1.4463908716352524541 ,9.9931268320011199639 ] 
dist 55=[1.9186782944596835137 ,10.417964135336066952  ] 
dist 56=[1.9978027471546402978 ,10.702718426309799590  ] 
dist 57=[2.4753988887910519706 ,10.872879322050214977  ] 
dist 58=[2.5488809458160054176 ,10.975817682963626384  ] 
dist 59=[2.6712007406215030971 ,10.992030806072523492  ] 
dist 60=[2.6896454863558412615 ,10.964274261681539107  ] 
dist 61=[4.3414033882312106683 ,10.891514407893680665  ] 
dist 62=[4.4192808119125727555 ,9.9904005147095655913 ] 
dist 63=[4.5368826843837859436 ,9.5772818886541082360 ] 
dist 64=[3.4952829826892939684 ,5.0102592658468015968 ] 
dist 65=[2.5734586878881984205 ,5.0605606507514151892 ] 
dist 66=[1.7872163187681512026 ,5.0699120227432210514 ] 
dist 67=[.98050161614854535323,5.0619806022931385537 ] 
dist 68=[.22225573255287449262,5.0459188956452287380 ] 
dist 69=[-.37060493068248367436,4.7470930890600388942 ] 
dist 70=[-.95610436037550866295,4.6911289764273586648 ] 
dist 71=[-1.6850718446834904744 ,4.5638618742361385903 ] 
dist 72=[-2.3798447308830033433 ,4.5202064524718085432 ] 
dist 73=[-2.8289037946622918062 ,4.3086269310667262397 ] 
dist 74=[-3.1844273651386474872 ,4.2602842259484588955 ] 
dist 75=[-3.5058905226893644840 ,4.1352777484852145741 ] 
dist 76=[-3.7815976689914349410 ,4.0973739544132179856 ] 
dist 77=[-3.9545418383846641845 ,2.1931227025853563372 ] 
dist 78=[-4.0859726758254107459 ,2.0048880486789257202 ] 
dist 79=[-4.1961081598689495746 ,1.5680817473292378274 ] 
dist 80=[-4.2849005428239463076 ,1.4878270172200860703 ] 
dist 81=[-4.3311432565541825276 ,.90714840660486375324] 
dist 82=[-4.3557899047280713777 ,.80093308692690350037] 
dist 83=[-4.3582617260668966142 ,.6215461988439205338 ] 
dist 84=[-4.3470224629192031059 ,.57951350200548956509] 
dist 85=[-4.3347324225956509500 ,-.12305393976868520943] 
dist 86=[-4.2838258605482030902 ,-.21558010205933483487] 
dist 87=[-4.2606585667157228033 ,-.41711902829207886017] 
dist 88=[-4.0840090069259412468 ,-.31427072221078336783] 
dist 89=[-4.1353246743478138675 ,.09098357825535830338] 
dist 90=[-4.1782689230955317964 ,.49222854496964261106] 
dist 91=[-4.2001527480360533744 ,.99303348586638321401] 
dist 92=[-4.1991724438689505181 ,1.5198004161450163017 ] 
dist 93=[-3.6428386996510121552 ,2.0247303644169845681 ] 
dist 94=[-3.5489253863066199955 ,2.6107416266895714047 ] 
dist 95=[-3.5203826062684138924 ,3.4612378664815090764 ] 
dist 96=[-2.1602977310976196859 ,4.2988877583307502119 ] 
dist 97=[-1.8498153157249032092 ,4.8336350742724596026 ] 
dist 98=[-1.7872738042923279236 ,5.2493681495267821955 ] 
dist 99=[-1.6442431993126255252 ,5.6119158208673483183 ] 
dist 100=[-1.6068293205626580522 ,5.9129653903981398583 ] 
dist 101=[-1.4169504464961301222 ,6.0832059101235340400 ] 
dist 102=[-1.3717487784835373772 ,6.1904616421629920711 ] 
dist 103=[-1.3500175606655686864 ,6.2400969974331573362 ] 
dist 104=[-1.3626340854630065085 ,6.2625277185698089820 ] 
dist 105=[-1.3950514556164240766 ,6.2611785283200831705 ] 
dist 106=[-1.4543795262451752716 ,6.2422666564358991363 ] 
dist 107=[-1.5448020005923990199 ,6.2384392968887275158 ] 
dist 108=[-1.7013414922651114908 ,6.2552911291869519390 ] 
dist 109=[-1.8655728107654643470 ,6.2445509756590560382 ] 
dist 110=[-1.9867010243442366032 ,6.2150036364016802502 ] 
dist 111=[-2.0995029559545718765 ,6.1929931730011735179 ] 
dist 112=[-2.2305023403198375774 ,3.1102933296261654129 ] 
dist 113=[-2.3632515708320355872 ,2.8470204337221451598 ] 
dist 114=[-2.4830411348996024668 ,2.2233537060414809966 ] 
dist 115=[-2.6163478336365874228 ,2.1193425076256908871 ] 
dist 116=[-2.8030575267661621464 ,1.9367469792183620569 ] 
dist 117=[-2.9911482248375397096 ,1.9939659108115070161 ] 
dist 118=[-3.1299688960227233168 ,2.0233302087824741261 ] 
dist 119=[-3.3219641523921832874 ,2.0379950489878667038 ] 
dist 120=[-3.7627045038054401949 ,2.0394661697899853672 ] 
dist 121=[-4.0371794769343102340 ,2.0280093508353513716 ] 
dist 122=[-4.2425563301981042356 ,2.0204267730694299925 ] 
dist 123=[-4.4074680899542215361 ,1.9993738278887084782 ] 
dist 124=[-4.5348279262727750032 ,1.9888263587946509385 ] 
dist 125=[-4.5903061625514585548 ,-.747112468295158485  ] 
dist 126=[-4.6144464537480170350 ,-.88925695481696546834] 
dist 127=[-4.6167111005141111305 ,-1.1961541409682273537 ] 
dist 128=[-1.8589644484561841908 ,-1.2536203809447820755 ] 
dist 129=[-2.0235419376554995834 ,-1.5569631348707674571 ] 
dist 130=[-2.1376776927269212513 ,-1.5888400009492996661 ] 
dist 131=[-2.2368200786699409472 ,-1.5842468796750742629 ] 
dist 132=[-2.3415515557050696478 ,-1.5657394165826407687 ] 
dist 133=[-2.4326441529915004988 ,-1.5279370074052821821 ] 
dist 134=[-2.4773404422423531741 ,-1.4687896394369781355 ] 
dist 135=[-2.5002699440893958319 ,-1.3650701770634027134 ] 
dist 136=[-2.5044633351552659030 ,-1.2515460642831665822 ] 
dist 137=[-2.4685985318354219782 ,-1.1532535504861191369 ] 
dist 138=[-2.4574865391230582525 ,-.99489991721558559989] 
dist 139=[-2.4491862496366412347 ,-.6987356376138694043 ] 
dist 140=[-2.4425746502689743407 ,-.24035957382204218568] 
dist 141=[-2.0717069245350834573 ,.22192876044294198007] 
dist 142=[-2.0254504333176856071 ,.53371063860703022339] 
dist 143=[-1.8998829870222441090 ,.79511947487555942632] 
dist 144=[-1.8807448176982905630 ,1.0563282089447359471 ] 
dist 145=[-1.6471032763498523468 ,1.2975850476909162620 ] 
dist 146=[-1.5990930808251442337 ,1.4793495019747954188 ] 
dist 147=[-1.5507598896329503998 ,1.6524459808239438294 ] 
dist 148=[-1.5385271512159787963 ,1.8591013196202726825 ] 
dist 149=[-1.0029257137348614950 ,2.0516293140600512599 ] 
dist 150=[-.93422061929757100528,2.1683316513391712956 ] 
dist 151=[-.79658347580814834434,2.2518951752577185703 ] 
dist 152=[-.76088270231795396634,2.3121385545465831921 ] 
dist 153=[-.63365093316784136659,2.3562673064500354401 ] 
dist 154=[-.60558626239008405618,2.3755041663549746109 ] 
dist 155=[-.56554790593535321172,2.3807711451050952662 ] 
dist 156=[-.55347545830067467404,2.3789186028871545684 ] 
dist 157=[.25458220343301229351,1.4046276779940261353 ] 
dist 158=[.19612164999798099233,1.4051409170464925418 ] 
dist 159=[.09722352444012476943,1.4031913728142487653 ] 
dist 160=[-.00523192023689115602,1.1335579131347348190 ] 
dist 161=[-.07789458903082944071,1.2502560298237610351 ] 
dist 162=[-.14264433033320471955,1.3256072189622223739 ] 
dist 163=[-.21352468697793291964,1.3851704239174114679 ] 
dist 164=[-.28293531177244750018,1.4388434432414737733 ] 
dist 165=[-.34182453547862875446,1.4848118772295977596 ] 
dist 166=[-.40430933964775101175,1.5136174429611280130 ] 
dist 167=[-.48807989328687395882,1.5354002706616214494 ] 
dist 168=[-.57083881566174022499,1.5533306392186756792 ] 
dist 169=[-.62928981109847902072,1.5674366831033433380 ] 
dist 170=[-.6811737752493566957 ,1.5739510588213426510 ] 
dist 171=[-.7377244225921547644 ,1.5761592150838822610 ] 
dist 172=[-.79302367046534638768,1.5730729511823757875 ] 
dist 173=[-.84502969827944806168,1.2000959382152785144 ] 
dist 174=[-.92198555169729818811,1.1953745247540951013 ] 
dist 175=[-1.0247153482355647713 ,1.1738003592573311366 ] 
dist 176=[-1.1228768061268197649 ,1.1702261456454218168 ] 
dist 177=[-1.1815975062340840176 ,1.0995911885220446161 ] 
dist 178=[-1.2227586606272718782 ,1.0826752330576565818 ] 
dist 179=[-1.2508165209287734376 ,1.0700562679988416054 ] 
dist 180=[-1.2706902808718209385 ,1.0659337989853715016 ] 
dist 181=[-1.2791749350275344688 ,.94859650340168249545] 
dist 182=[-1.2809659083422633508 ,.9935422402922943732 ] 
dist 183=[-1.2795908061974139062 ,1.0425558767953288202 ] 
dist 184=[-1.1772632678749699746 ,1.0857635384236603201 ] 
dist 185=[-1.1811865068254579780 ,1.1075345590103043653 ] 
dist 186=[-1.2073145394388409927 ,1.1189120827419633254 ] 
dist 187=[-1.2277384558246716125 ,1.1206413314357356038 ] 
dist 188=[-1.2457685127078856514 ,1.1082406512171465083 ] 
dist 189=[-1.2590377508268915264 ,1.1036276595013102927 ] 
dist 190=[-1.2613955678770640351 ,1.0995870999213545196 ] 
dist 191=[-1.2578441543534145558 ,1.0952632746361936813 ] 
dist 192=[-1.2671604668279685977 ,.01729881393147666505] 
dist 193=[-1.2982796212926567780 ,.17166216857863303474] 
dist 194=[-1.3105329745137169982 ,.30220660648269328593] 
dist 195=[-1.3152483322760053568 ,.43449769433639130115] 
dist 196=[-1.3162736092453236182 ,.55789521792014369176] 
dist 197=[-1.2761215244023207736 ,.65293837657280611586] 
dist 198=[-1.2661277307862941790 ,.74548405151758085417] 
dist 199=[-1.2436776854907481956 ,.85891388727513745442] 
dist 200=[-1.2350372353203873701 ,.96614405576027239149] 
dist 201=[-1.1909484729442130109 ,1.0339419036748906142 ] 
dist 202=[-1.1803827173099366789 ,1.0858920282342084708 ] 
dist 203=[-1.1519504912254450638 ,1.1298595081378577454 ] 
dist 204=[-1.1417978326728200091 ,1.1653801694912552392 ] 
dist 205=[-.81489744812658280352,1.1836122808664810922 ] 
dist 206=[-.80127844778600800224,1.1926973989702002514 ] 
dist 207=[-.76743311905388909671,1.1937275490041116509 ] 
dist 208=[-.75794160162437728166,1.1858577086679718885 ] 
dist 209=[-.69963435169222555892,1.1817069055152349579 ] 
dist 210=[-.68674877126970249375,1.1652000466628991650 ] 
dist 211=[-.66270074211352898825,1.1591954011008494776 ] 
dist 212=[-.65581196330267998734,1.1058984296813655786 ] 
dist 213=[-.52616075450745290437,1.0922628289347220967 ] 
dist 214=[-.50757668440144092685,1.1224351953769390065 ] 
dist 215=[-.55860711650571152563,1.1546657884170139558 ] 
dist 216=[-.67757600519861891179,1.1740292042564707860 ] 
dist 217=[-.76154289883340530144,1.1867813708110917326 ] 
dist 218=[-.83600432584123080115,1.1926207466710759759 ] 
dist 219=[-.91702902222449395184,1.1945183618154548341 ] 
dist 220=[-.99613734088044134472,1.1920864975827801808 ] 
dist 221=[-1.0629493792701753689 ,.81577740986934974707] 
dist 222=[-1.1335982270749341496 ,.78502283637301917374] 
dist 223=[-1.2280237997732536388 ,.71231117751721834643] 
dist 224=[-1.3176727022578001792 ,.69644015305539622037] 
dist 225=[-1.3692535222146205877 ,.59150729934507850649] 
dist 226=[-1.4028604749876887644 ,.57086326079724444231] 
dist 227=[-1.4207582930763224998 ,.5333714415217811418 ] 
dist 228=[-1.4313084285266106053 ,.52395518775072683541] 
dist 229=[-1.4355834816826045033 ,.36171142144442126051] 
dist 230=[-1.4360830392398539260 ,.33961650667599041713] 
dist 231=[-1.4324103373980607453 ,.28550260966124416539] 
dist 232=[-1.2697643051742126986 ,.27722277267993979051] 
dist 233=[-1.2444430170591685113 ,.19642177823297168416] 
dist 234=[-1.1985926079335915502 ,.18128516409622688609] 
dist 235=[-1.1859988483511677616 ,.16271207067924449664] 
dist 236=[-1.1602238412524205696 ,.15806504508901545567] 
dist 237=[-1.1612967201101234816 ,.03086571550225849299] 
dist 238=[-1.1553770381919126594 ,.01394291553648467845] 
dist 239=[-1.1524491048413849442 ,-.00979020782315755784] 
dist 240=[-.76497993427369514788,.13322383125384836083] 
dist 241=[-.72832086904440595373,.25357497680482364579] 
dist 242=[-.64058971060221638752,.35326876358758336359] 
dist 243=[-.62409518424193484627,.45093293243854705231] 
dist 244=[-.49689391147822589714,.57558868311071918676] 
dist 245=[-.47257178308345627584,.67296448180045245812] 
dist 246=[-.43409925569303646004,.76574304784794909843] 
dist 247=[-.42384462659236789464,.87659459145553257615] 
dist 248=[-.24765834324033020993,.9799396566938103502 ] 
dist 249=[-.22866488820945442739,1.0427524011090556837 ] 
dist 250=[-.18314601394879281553,1.0879429222375340306 ] 
dist 251=[-.17590581436649980671,1.1209403865355467497 ] 
dist 252=[-.11138887368750494826,1.1457320361625135333 ] 
dist 253=[-.09955565888944350340,1.1581653917972138961 ] 
dist 254=[-.08352724009136658661,1.1639334613245289398 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 2, 1, 1, 2, 1, 2] 
dist 0=[44.780970218585261553  ,44.780970218585261553  ] 
dist 1=[43.998612841047928190  ,45.391269526535325880  ] 
dist 2=[42.938456028861193114  ,45.853825638725833545  ] 
dist 3=[41.218472088020146710  ,46.046157737863691852  ] 
dist 4=[39.442901086559437733  ,46.119270536730841415  ] 
dist 5=[38.160619979201395144  ,46.105595858482476466  ] 
dist 6=[36.990495544154578723  ,45.662124319595818027  ] 
dist 7=[35.662703392100013910  ,45.523160261222374102  ] 
dist 8=[34.329938928398652392  ,44.789797530960964744  ] 
dist 9=[33.139771231799113029  ,44.663452032316822552  ] 
dist 10=[31.821761092706078603  ,44.042466383793468185  ] 
dist 11=[29.978018843728895038  ,43.887638896900603695  ] 
dist 12=[28.111211713129516392  ,43.384312279671757948  ] 
dist 13=[26.700893468024652774  ,43.282825885609167320  ] 
dist 14=[25.348980726364296317  ,42.046115491672055899  ] 
dist 15=[23.715260899191429202  ,41.743401629811097718  ] 
dist 16=[22.016122311250815648  ,40.111421200768822728  ] 
dist 17=[20.402557761556322448  ,29.594239007077103793  ] 
dist 18=[18.534448066615457788  ,26.181120850280777342  ] 
dist 19=[15.817735635840196263  ,25.533340542624249056  ] 
dist 20=[13.116573987156043498  ,24.722873342428492863  ] 
dist 21=[11.310537514495361117  ,24.485384715920323765  ] 
dist 22=[9.8050498861987173769 ,18.827223661299241888  ] 
dist 23=[8.3050915689961550532 ,18.100879976706352344  ] 
dist 24=[6.9139831457462453036 ,16.590369587995874514  ] 
dist 25=[5.8435040450374334434 ,16.189486163161956866  ] 
dist 26=[4.4324948234028415300 ,14.677412687786244903  ] 
dist 27=[2.9168650894504872749 ,14.378738927201770940  ] 
dist 28=[1.2706283441614006401 ,13.770367967017826357  ] 
dist 29=[-.3438847799980270721 ,13.609378708905811362  ] 
dist 30=[-1.7333371971014445584 ,4.6766785627905243163 ] 
dist 31=[-3.2327248597605061964 ,3.8841646702738129403 ] 
dist 32=[-5.2875653577161602665 ,2.1413501776586789257 ] 
dist 33=[-7.2755936590152830323 ,1.8113296935880127002 ] 
dist 34=[-8.5082163168023591582 ,-.1594461527732264792 ] 
dist 35=[-9.4328826393724148548 ,-.22839290769070384629] 
dist 36=[-10.189933535241689614  ,-1.1494354763214716483 ] 
dist 37=[-10.793132418847720894  ,-1.3032098860641366184 ] 
dist 38=[-11.102568208201487375  ,-2.5185074688679138502 ] 
dist 39=[-11.491952835893568452  ,-2.7101658746740368352 ] 
dist 40=[-11.893649405281653257  ,-2.8740723332719345446 ] 
dist 41=[-12.183938624158031561  ,-2.8230671754995940425 ] 
dist 42=[-12.391921861035571898  ,-2.6767829063791532706 ] 
dist 43=[-12.464764082694814379  ,-2.4042408988333967940 ] 
dist 44=[-12.477445804760869415  ,-1.9887977903180631912 ] 
dist 45=[-12.449141367015775961  ,-1.2721452260114151348 ] 
dist 46=[-10.656143528886576259  ,-.52674156712492433155] 
dist 47=[-10.514645593557654692  ,.00358215808249662366] 
dist 48=[-10.457829886001338814  ,.47663988092952999398] 
dist 49=[-4.8994496833699885619 ,.99384746575839522166] 
dist 50=[-4.8737580821893265917 ,1.4989538379320223965 ] 
dist 51=[-4.8624480336226869186 ,1.9238972965129929312 ] 
dist 52=[-2.6504898237709082731 ,2.3712532817470310492 ] 
dist 53=[-2.5038818545849557190 ,2.9659997594229285436 ] 
dist 54=[-1.0884441221037332153 ,3.5509001270725331345 ] 
dist 55=[-.62519693824885543767,4.0937536494018828069 ] 
dist 56=[-.5126306743717935403 ,4.9183250132749773765 ] 
dist 57=[.3565821546357128045 ,5.6870818572558870537 ] 
dist 58=[.890443830578243224  ,6.1630951748958405251 ] 
dist 59=[.97747795745535898873,6.5158418411057009395 ] 
dist 60=[1.1455626035331046487 ,6.7927394526324895111 ] 
dist 61=[1.1803569458072154003 ,7.0043445819035142214 ] 
dist 62=[2.1849279958784016000 ,7.0964297088523051988 ] 
dist 63=[1.9107159566103065746 ,7.1338776834314098671 ] 
dist 64=[1.5822900753100916724 ,7.1274980116213936954 ] 
dist 65=[1.2088201094086196003 ,4.3916836389916490461 ] 
dist 66=[.73079664966328233284,4.3941748273396347517 ] 
dist 67=[-.0149833319757638479 ,4.3866417194094627115 ] 
dist 68=[-.76876365844640842862,4.2123568234114644251 ] 
dist 69=[-1.2787349571909202329 ,4.2753204564891962768 ] 
dist 70=[-1.7078864121090081636 ,4.3761679049365003734 ] 
dist 71=[-2.1390882011037611084 ,4.4297923303572633714 ] 
dist 72=[-2.5387481689675272359 ,4.4595806699952350060 ] 
dist 73=[-2.8420076618163431376 ,4.4651545487178645994 ] 
dist 74=[-3.1328358704009276191 ,4.4553933220701826354 ] 
dist 75=[-3.4828844635839565713 ,4.4467932423981380237 ] 
dist 76=[-3.8103795115046053337 ,4.3926054813713264753 ] 
dist 77=[-4.0111857676365179106 ,4.3835557096735497965 ] 
dist 78=[-4.1577222560159890199 ,2.5801661601790774882 ] 
dist 79=[-4.2685933723221436323 ,2.5192877539620723531 ] 
dist 80=[-4.3489110646420704908 ,2.2740795766942167422 ] 
dist 81=[-4.3734842269746253502 ,2.2233696354105377319 ] 
dist 82=[-4.3774285312007567039 ,2.1017843088454930122 ] 
dist 83=[-4.5050340091514602730 ,2.0706998061644756520 ] 
dist 84=[-4.7142983445965451687 ,.1968034202034778068 ] 
dist 85=[-4.9251966829038352175 ,.0233148974097811863 ] 
dist 86=[-5.1071235115982668475 ,-.3312996520350704322 ] 
dist 87=[-5.2007281037970703088 ,-.4207539710484056615 ] 
dist 88=[-5.2477687880313015623 ,-.7310113038914198111 ] 
dist 89=[-5.2556892537925188594 ,-.7937011970775456844 ] 
dist 90=[-5.2205840328947210906 ,-.8649579437997608585 ] 
dist 91=[-5.1967722594585202621 ,-.8676927045571723110 ] 
dist 92=[-5.1524619730655154265 ,-.7233097173491315453 ] 
dist 93=[-5.1316278901104988471 ,-.4313932549618885923 ] 
dist 94=[-4.1059487719456698587 ,-.11954460920372944931] 
dist 95=[-3.9943244095193924950 ,.50709344531885568775] 
dist 96=[-3.6984733008835888793 ,1.0358185380803493680 ] 
dist 97=[-3.6547920748978310865 ,1.5694701041599401312 ] 
dist 98=[-3.1197529123172914966 ,2.0657150060433034231 ] 
dist 99=[-2.8321336871763139027 ,2.4451240113475274462 ] 
dist 100=[-2.3406046808769283448 ,2.8117763077021106162 ] 
dist 101=[-2.2915184653333811840 ,3.2570976638957885113 ] 
dist 102=[-1.2915748473993489690 ,3.6757695038869782902 ] 
dist 103=[-1.1629731760773947357 ,3.9360424353633884756 ] 
dist 104=[-.8833121287982203921 ,4.1302152687667822672 ] 
dist 105=[-.8178237468846212702 ,4.2850307496202154771 ] 
dist 106=[-.5048234348756829176 ,4.4041172955488104992 ] 
dist 107=[-.4497075560962758945 ,4.4556726192154596765 ] 
dist 108=[-.3195027563445939690 ,4.4774486618168656087 ] 
dist 109=[-.3002061267487608715 ,4.4776664658542119332 ] 
dist 110=[.88242691903806787408,3.3524652138369574520 ] 
dist 111=[.98960376440407439146,3.3294820646767310492 ] 
dist 112=[.72185093637256780086,3.3173920579453458402 ] 
dist 113=[.13846416392562882973,2.5256046877459457107 ] 
dist 114=[-.25757344103729858376,2.4400056233517577171 ] 
dist 115=[-.59230562201952976746,2.2173717559456476161 ] 
dist 116=[-.93099559951957170011,2.1852027032110903550 ] 
dist 117=[-1.2464007856995595931 ,1.8072944877571514889 ] 
dist 118=[-1.4881931799661388802 ,1.8071818399193492198 ] 
dist 119=[-1.7224318339678996689 ,1.8364386670207940250 ] 
dist 120=[-2.0076868922198834860 ,1.8565371356005746767 ] 
dist 121=[-2.2761779666421196829 ,1.8694803868143095587 ] 
dist 122=[-2.4435030120351365434 ,1.8768909895936414267 ] 
dist 123=[-2.5688002893615767284 ,1.8748950406535471148 ] 
dist 124=[-2.6695364963318201284 ,1.8674816386749504036 ] 
dist 125=[-2.7472289096607153085 ,1.8613051385847484424 ] 
dist 126=[-2.7805457227771328913 ,1.0336559123256244251 ] 
dist 127=[-2.7948845777889935247 ,.96102483096353169293] 
dist 128=[-2.7968280458485047026 ,.78703963695043272519] 
dist 129=[-.92616700702185006695,.75863056945442376461] 
dist 130=[-1.1155785150432171006 ,.51164202228484931876] 
dist 131=[-1.2669802216901304707 ,.46612690981654113487] 
dist 132=[-1.4063094483570866646 ,.40267863124326331582] 
dist 133=[-1.5273908700701146545 ,.38403514246980608851] 
dist 134=[-1.6059460060472617234 ,.04054356434714712140] 
dist 135=[-1.6684896422925737618 ,-.00200502749966853622] 
dist 136=[-1.7256553740301134372 ,-.09876373238583761838] 
dist 137=[-1.7736957270013778286 ,-.11420663733042569259] 
dist 138=[-1.7998088666339195006 ,-.23111511183424418752] 
dist 139=[-1.8149119153451866489 ,-.25060873168509000735] 
dist 140=[-1.8189919221251861923 ,-.28244884698127262233] 
dist 141=[-1.8157027020426510154 ,-.28923115264271451058] 
dist 142=[-1.8121567748097708593 ,-.54795236883155932698] 
dist 143=[-1.7869691364825388736 ,-.3655965264162182489 ] 
dist 144=[-1.7832939637305825828 ,-.0832087588844087783 ] 
dist 145=[-1.3891649961323871336 ,.2016121547690365355 ] 
dist 146=[-1.3649606584892816259 ,.3936832541281258759 ] 
dist 147=[-1.3680553689017348870 ,.5546949767201539213 ] 
dist 148=[-1.3669749896467102832 ,.7155375096593761137 ] 
dist 149=[-1.3639218295351712840 ,.8640723847626686411 ] 
dist 150=[-1.2285352570787784058 ,.9759577169780207368 ] 
dist 151=[-1.2069516516093153322 ,1.0824997838799400675 ] 
dist 152=[-1.1679608253160431701 ,1.2097108344736427073 ] 
dist 153=[-1.1626668163150252788 ,1.3282856811041593129 ] 
dist 154=[-1.1339144873072057884 ,1.4003558815840366212 ] 
dist 155=[-1.1265078544710687341 ,1.4522248728282046339 ] 
dist 156=[-1.0999935716567223127 ,1.4901614500421009912 ] 
dist 157=[-1.0956421503546999683 ,1.5176816754303538821 ] 
dist 158=[-.58673497877871981198,1.5279651968148013280 ] 
dist 159=[-.53895951717641908036,1.5302045704591782840 ] 
dist 160=[-.4761400775734871805 ,1.5271273820180842276 ] 
dist 161=[-.40634715072700255973,1.4398113031877094745 ] 
dist 162=[-.2435955557839612315 ,1.4248777877644019983 ] 
dist 163=[-.2136701234976346704 ,1.3768511605798425503 ] 
dist 164=[-.1738312111611487844 ,1.3698485929977456304 ] 
dist 165=[-.1624985996211473253 ,1.3252048397667005942 ] 
dist 166=[.0681037738704829100 ,1.3172900340215191112 ] 
dist 167=[.0965395392740515392 ,1.3019670851785486589 ] 
dist 168=[.1594513627878343884 ,1.2957366026856890194 ] 
dist 169=[.1710576064338192961 ,1.1395082773426542268 ] 
dist 170=[.2421634575898317303 ,1.1197636551543945726 ] 
dist 171=[.2539018010150653932 ,1.1249098484509318572 ] 
dist 172=[.2770971760196813524 ,1.1241106017834048800 ] 
dist 173=[.2823490478400174758 ,1.1053488377907638343 ] 
dist 174=[.28929782518615439642,1.0979615260076891088 ] 
dist 175=[.11390908323971775208,1.0898272619762107296 ] 
dist 176=[-.14601924118349029772,1.0846937715860928200 ] 
dist 177=[-.40493886727311737323,1.0581089874653145910 ] 
dist 178=[-.57630203403655906556,1.0600855601675897441 ] 
dist 179=[-.71648204456360526771,1.0576388237006172132 ] 
dist 180=[-.85091731754553223918,1.0548730611732510825 ] 
dist 181=[-.97150451317067032565,1.0199849889992870191 ] 
dist 182=[-1.0564031023127584167 ,1.0097985848532892597 ] 
dist 183=[-1.1314941714665855170 ,.9985943715763294613 ] 
dist 184=[-1.2129312646267112874 ,.9924087522909204023 ] 
dist 185=[-1.2863674932204854552 ,.8202389671537394738 ] 
dist 186=[-1.3295184462226320960 ,.7953720095922055912 ] 
dist 187=[-1.3587905370335909074 ,.7453262723304135244 ] 
dist 188=[-1.3768188743845291510 ,.7312704297404401056 ] 
dist 189=[-1.3874802102767074403 ,.6755913738614058444 ] 
dist 190=[-1.3883687591102443686 ,.6630036885165626525 ] 
dist 191=[-1.3831268194343868309 ,.6348716424569613384 ] 
dist 192=[-1.3775092597892394335 ,.6258058868601529263 ] 
dist 193=[-1.2159801169006341522 ,.50497083623300429497] 
dist 194=[-1.2519333537865641092 ,.54532197453094065338] 
dist 195=[-1.2709171979139990618 ,.57962444026771395502] 
dist 196=[-1.2811249594875950987 ,.6160758819372760958 ] 
dist 197=[-1.2820412159834724898 ,.66500490212025284364] 
dist 198=[-1.2015985932900212809 ,.7133428477158380517 ] 
dist 199=[-1.1868489610310247210 ,.7474350933334845191 ] 
dist 200=[-1.1670574175435939262 ,.7776306065574627096 ] 
dist 201=[-1.1588583464141841663 ,.8104147307649085056 ] 
dist 202=[-1.1402970745295673013 ,.8423650950982600249 ] 
dist 203=[-1.1320987727484427702 ,.8692326598966355800 ] 
dist 204=[-1.1254646817869586727 ,.8975310722385720859 ] 
dist 205=[-1.1194804945826453469 ,.9351926893813217109 ] 
dist 206=[-.24532168943028028346,.9707106779103996325 ] 
dist 207=[-.17665583712265276555,.9904524940699687105 ] 
dist 208=[-.01540530874438617323,1.0024220191582464316 ] 
dist 209=[.00817545307337808825,1.0069159915760804001 ] 
dist 210=[.1511468798205646295 ,1.0070203968625020556 ] 
dist 211=[.1706487029858778689 ,1.0051652519061446490 ] 
dist 212=[.2115725351461372620 ,.9947519244771608720 ] 
dist 213=[.21985410457088101122,.9902112317944247158 ] 
dist 214=[.27843689986396237905,.9179735672237312701 ] 
dist 215=[.26860039371867537909,.9049307030290672832 ] 
dist 216=[.18307781450051286777,.8709077452531331486 ] 
dist 217=[.09327647730196426603,.8616578686867877104 ] 
dist 218=[.02107545595465218262,.7975840434683691105 ] 
dist 219=[-.05210945288292819695,.7832032870846916806 ] 
dist 220=[-.14584018167811987854,.7584323922851345470 ] 
dist 221=[-.25586344924930383913,.78774524393071264825] 
dist 222=[-.48020569865049263427,.81804046491965049826] 
dist 223=[-.62743824956093334239,.83372176303158679108] 
dist 224=[-.7464650560855952624 ,.84177686093442110665] 
dist 225=[-.85821381885795646071,.84330652248703112218] 
dist 226=[-.95680383096757527845,.83804371987242907712] 
dist 227=[-1.0233024393453607548 ,.83423648774677835487] 
dist 228=[-1.0790636981141880864 ,.8293438400835858868 ] 
dist 229=[-1.1347909187295868871 ,.82616899507789564819] 
dist 230=[-1.1839033159272413780 ,.72325367939275212023] 
dist 231=[-1.2132590066088115802 ,.70750120955256269482] 
dist 232=[-1.2337757695229439789 ,.67538582345384748507] 
dist 233=[-1.2476048537637097688 ,.66593561936499947141] 
dist 234=[-1.2560783418471367495 ,.62632902350152339731] 
dist 235=[-1.2564234943158361785 ,.6174407530581418084 ] 
dist 236=[-1.2332534803996943025 ,.59459981893165994536] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 0, 0, 1] 
dist 0=[59.035658853838320264  ,59.035658853838320264  ] 
dist 1=[58.806018205374039763  ,59.114421760818305797  ] 
dist 2=[58.043245036219488772  ,59.274778433634464501  ] 
dist 3=[57.080019429521456687  ,59.378531056285297312  ] 
dist 4=[56.049783105543202426  ,59.231382100191818795  ] 
dist 5=[54.448412746275128401  ,58.993511276314236183  ] 
dist 6=[51.617426849508782188  ,58.824306067873952346  ] 
dist 7=[48.683740367036160017  ,58.452653772492194160  ] 
dist 8=[46.557513209418889900  ,58.121035284589554019  ] 
dist 9=[44.609552787601770739  ,54.785164343432380136  ] 
dist 10=[40.340653178588551324  ,54.164860449389559563  ] 
dist 11=[35.567506681634191239  ,53.364787397968524668  ] 
dist 12=[32.280165902961802666  ,53.062544078681924818  ] 
dist 13=[29.443539884128750926  ,52.725624529250018276  ] 
dist 14=[26.470303556285570003  ,51.664400100219482653  ] 
dist 15=[23.627211248151057334  ,46.113916566219377723  ] 
dist 16=[21.310179530368130466  ,42.495439795330719718  ] 
dist 17=[18.927962997671419333  ,26.883060681147414815  ] 
dist 18=[15.824168793759999917  ,26.281147385452486307  ] 
dist 19=[12.785666389233295553  ,24.393746837832909632  ] 
dist 20=[10.664018154772274726  ,23.971414674032574509  ] 
dist 21=[8.8004399404394047391 ,23.463479661869425305  ] 
dist 22=[6.7924050424789415048 ,23.323589086134677112  ] 
dist 23=[4.8352578474872596161 ,11.135251861330115006  ] 
dist 24=[2.7797800738064168918 ,10.764111498017389893  ] 
dist 25=[.4347628582758946374 ,7.7151297257283377671 ] 
dist 26=[-1.8835241085442841520 ,7.6066936420218960808 ] 
dist 27=[-4.0159889850961154821 ,3.2756280498690025304 ] 
dist 28=[-5.6186203348986742478 ,2.9953677189491520754 ] 
dist 29=[-7.1449532621778633153 ,2.5537439930311017920 ] 
dist 30=[-8.9725110150781377587 ,2.0125651403037534811 ] 
dist 31=[-10.684896021559306947  ,.1035104823216196779 ] 
dist 32=[-11.751118187313434062  ,-.7430053910357969601 ] 
dist 33=[-12.551018482062022771  ,-4.6827405193134283559 ] 
dist 34=[-13.199554253717825941  ,-4.2895020330178957667 ] 
dist 35=[-13.702804412474504174  ,-3.7071514454085284663 ] 
dist 36=[-13.922321605741219057  ,-2.9092010046564282488 ] 
dist 37=[-14.020281355862977619  ,-1.8048236449380118656 ] 
dist 38=[-14.038306295212522586  ,0                     ] 
dist 39=[-12.978308020016240423  ,-2.6961206639657668527 ] 
dist 40=[-12.957903703355803313  ,-1.5956106113282040555 ] 
dist 41=[-11.634795074711275408  ,-.6243066559291413263 ] 
dist 42=[-11.423947055720679142  ,.4218821382934772345 ] 
dist 43=[-11.012369787426748658  ,1.4343022974349947310 ] 
dist 44=[-10.891948374775340423  ,2.2711700365111241938 ] 
dist 45=[-10.404944247180639758  ,3.1391234817967959141 ] 
dist 46=[-10.281905238807614300  ,4.2759432566914003948 ] 
dist 47=[-10.011885575312950395  ,5.3857177002739723898 ] 
dist 48=[-9.9201974966697099019 ,6.1459117926916299362 ] 
dist 49=[-3.2631962206479699553 ,6.7959900032535667079 ] 
dist 50=[-2.6746407839233035561 ,7.4664898617871897852 ] 
dist 51=[-1.4395593766986321228 ,8.1000507043905993912 ] 
dist 52=[-1.1436181181230982392 ,8.6029003773967937602 ] 
dist 53=[1.1064244621122779935 ,9.1076813370308289528 ] 
dist 54=[1.4925038185724770478 ,9.7493351156785955847 ] 
dist 55=[1.9507929703025890095 ,10.349077390064290883  ] 
dist 56=[2.0226715380006257106 ,10.686607969264156344  ] 
dist 57=[2.1457263750968812499 ,10.898447745572625084  ] 
dist 58=[2.1665731820934876683 ,10.996230020253693520  ] 
dist 59=[4.3815099578998587860 ,11.035490056647702583  ] 
dist 60=[4.4826143526830512351 ,11.018393955398760957  ] 
dist 61=[4.6623773204902589273 ,10.959180686843797820  ] 
dist 62=[4.6923246379734558246 ,10.869069808279431370  ] 
dist 63=[4.7055065292676280996 ,9.8432917173397007690 ] 
dist 64=[4.6375846678292541144 ,9.4016227648594179976 ] 
dist 65=[3.3339626214018462687 ,5.2340637475521670987 ] 
dist 66=[2.4293198363310349998 ,5.2223794841634760091 ] 
dist 67=[1.6586188652539635847 ,4.9480765881800711544 ] 
dist 68=[.8692844151677574425 ,4.8942962808050510841 ] 
dist 69=[.1282878120843146160 ,4.7783323519744402390 ] 
dist 70=[-.4495528875167194403 ,4.7386757422308059122 ] 
dist 71=[-1.0187729170216595661 ,4.5469191108144855387 ] 
dist 72=[-1.7254613035534734910 ,4.5032211163245183366 ] 
dist 73=[-2.3979941207707931878 ,4.3708440971351489898 ] 
dist 74=[-2.8309286664690842654 ,4.3451332164139111518 ] 
dist 75=[-3.1716980915665093025 ,2.2101247029994837491 ] 
dist 76=[-3.4763911181934493830 ,2.0057529391968040328 ] 
dist 77=[-3.7352838730815466456 ,1.5285003708767115597 ] 
dist 78=[-3.8932959830428561201 ,1.4447609337687269443 ] 
dist 79=[-4.0082872607236941148 ,.8041236982637720672 ] 
dist 80=[-4.0955873598908521559 ,.6875277696815665747 ] 
dist 81=[-4.1620381936541763748 ,.5019501831529075722 ] 
dist 82=[-4.1938128123241552390 ,.4557225154628777503 ] 
dist 83=[-4.2069610120987074499 ,-.3313460045683757291 ] 
dist 84=[-4.2003674801761014930 ,-.4323575545541531543 ] 
dist 85=[-4.1786563542033851972 ,-.6546947009360028085 ] 
dist 86=[-4.1638857318694535541 ,-.6964855659441074727 ] 
dist 87=[-4.1064038581215153609 ,-.9442643946514456075 ] 
dist 88=[-4.0842602036192838439 ,-.8193526063019931664 ] 
dist 89=[-4.0767924872100401768 ,-.3109681565844695244 ] 
dist 90=[-4.0767745374898311450 ,.0868790274340810386 ] 
dist 91=[-3.7507674811857411324 ,.4799838365055693588 ] 
dist 92=[-3.7146305435758615758 ,.9695148309013306309 ] 
dist 93=[-3.5138902245811347443 ,1.4838466389991069061 ] 
dist 94=[-3.4670201283066516516 ,1.9760002110139528052 ] 
dist 95=[-3.3741276364511025039 ,2.5465269701843890224 ] 
dist 96=[-3.3452883507349167896 ,3.3737761554990153536 ] 
dist 97=[-1.7833984766504096977 ,4.1881996500041987945 ] 
dist 98=[-1.7477396798661332341 ,4.7075446778891463007 ] 
dist 99=[-1.5636267392234801355 ,5.1106435006853454341 ] 
dist 100=[-1.5198451926480862095 ,5.4610151254443081419 ] 
dist 101=[-1.4909656613517237294 ,5.7511016015876679521 ] 
dist 102=[-1.4939118797999300920 ,5.9135500755031804086 ] 
dist 103=[-1.5139995201926173224 ,6.0138366298519318364 ] 
dist 104=[-1.5583275178807430539 ,6.0557937107723139146 ] 
dist 105=[-1.6289143569338035735 ,6.0715768278881367414 ] 
dist 106=[-1.7538207087882012112 ,6.0673731056813693178 ] 
dist 107=[-1.8857910332779727997 ,6.0478357287558079322 ] 
dist 108=[-1.9845767932610551191 ,6.0686054651971958961 ] 
dist 109=[-2.0780112304193907789 ,6.0855993979450545691 ] 
dist 110=[-2.1886242487748365861 ,6.0781642197608054230 ] 
dist 111=[-2.3018769490131010757 ,6.0521165072515421423 ] 
dist 112=[-2.4058504393267824487 ,6.0347277420456730554 ] 
dist 113=[-2.5229960693045157818 ,2.9384969947906984191 ] 
dist 114=[-2.6888310341977955446 ,2.6784492642763109861 ] 
dist 115=[-2.8566524163956332717 ,2.0628964954782498853 ] 
dist 116=[-2.9817283181406838876 ,2.0095919129670895524 ] 
dist 117=[-3.0995144631913219056 ,2.0275818151597137232 ] 
dist 118=[-3.2382375108813968580 ,2.0299542298398158818 ] 
dist 119=[-3.3798987323408153673 ,2.0227561904651649912 ] 
dist 120=[-3.5094139843951325752 ,2.0158088729458700348 ] 
dist 121=[-3.6549157628944865929 ,1.9973370153607154868 ] 
dist 122=[-3.8603925761571415384 ,1.9877413227645707507 ] 
dist 123=[-4.0599899952899012245 ,-.6498036845556549522 ] 
dist 124=[-4.1845897535263957813 ,-.7875505799223611285 ] 
dist 125=[-4.3105044456236611474 ,-1.0852801796412916578 ] 
dist 126=[-4.3650790216824575264 ,-1.1413017402952117278 ] 
dist 127=[-4.3894898877162099571 ,-1.3792160845244255128 ] 
dist 128=[-4.3949963968024316034 ,-1.3988970304885728234 ] 
dist 129=[-2.1152817649908663479 ,-1.5491377860527370641 ] 
dist 130=[-2.2210435564105107251 ,-1.5675055977643982180 ] 
dist 131=[-2.3135844065026485345 ,-1.5855553597305294449 ] 
dist 132=[-2.3593306407270205725 ,-1.5723727814167921328 ] 
dist 133=[-2.3833974100533552358 ,-1.5140911615505836013 ] 
dist 134=[-2.3893825922290999657 ,-1.3414919729530223387 ] 
dist 135=[-2.3541336740593919437 ,-1.1392393440139114135 ] 
dist 136=[-2.3451712228749068631 ,-.9147658732628035084 ] 
dist 137=[-2.3399510218606231110 ,-.6308899438246514966 ] 
dist 138=[-2.3384638135422495402 ,-.1915140634781886959 ] 
dist 139=[-2.0267112035722944425 ,.25158723970232505075] 
dist 140=[-1.9861574716984843707 ,.55033472666343962003] 
dist 141=[-1.8743926227537926106 ,.80070559569737306932] 
dist 142=[-1.8570827467582366492 ,1.0506978137735666560 ] 
dist 143=[-1.6430533779667399811 ,1.2814667352491615927 ] 
dist 144=[-1.5985449997666570216 ,1.4551020751423359927 ] 
dist 145=[-1.5540220357929287693 ,1.6202311430924170904 ] 
dist 146=[-1.5420193485588513394 ,1.8170441405298666948 ] 
dist 147=[-1.0342011764283910293 ,2.0002234090263969554 ] 
dist 148=[-.96863203193646888629,2.1109290666810026243 ] 
dist 149=[-.83744723631899212721,2.1897964295648432448 ] 
dist 150=[-.80330703290177706022,2.2458833428288978921 ] 
dist 151=[-.68115858325722454463,2.2866147444207080470 ] 
dist 152=[-.6540582703843592098 ,2.3041862009219960297 ] 
dist 153=[-.61427091292956385497,2.3084849150979889709 ] 
dist 154=[-.60252601223106032312,2.3065666158501076301 ] 
dist 155=[.2145465672321141334 ,1.3853938688232739308 ] 
dist 156=[.2776210598956031310 ,1.4100722330542594541 ] 
dist 157=[.2757581440125476380 ,1.4264390132079688675 ] 
dist 158=[.2286697730724113259 ,1.4330198883887962425 ] 
dist 159=[.1620144801583857253 ,1.4337004428917367066 ] 
dist 160=[.0512440275674618226 ,1.4311302863116219721 ] 
dist 161=[-.0629147396091871243 ,1.3533203532956942024 ] 
dist 162=[-.1430975183642677799 ,1.4120755763061878844 ] 
dist 163=[-.2137496493222653748 ,1.4630136594363231778 ] 
dist 164=[-.2898752025869701346 ,1.4946061775887174543 ] 
dist 165=[-.3637126600595023511 ,1.5181121427708499051 ] 
dist 166=[-.4252372976767473926 ,1.5367655148349131986 ] 
dist 167=[-.4895524931804156179 ,1.5508961712706265773 ] 
dist 168=[-.5745362184592882495 ,1.5563457555351413490 ] 
dist 169=[-.6579286274341776965 ,1.5564858916061469510 ] 
dist 170=[-.7158958651692101609 ,1.5531717781820319987 ] 
dist 171=[-.7663849584226198690 ,1.1724093370834784112 ] 
dist 172=[-.8199318026365072495 ,1.1688982241170969624 ] 
dist 173=[-.8714202491345817307 ,1.1498201183235968152 ] 
dist 174=[-.9188830889595242864 ,1.1470819986114355573 ] 
dist 175=[-.9898342821065839652 ,1.0790073949008141769 ] 
dist 176=[-1.0829427716962810157 ,1.0625907102116123365 ] 
dist 177=[-1.1712633360429437972 ,1.0519889132468055934 ] 
dist 178=[-1.2231027485197462719 ,1.0495132838498409179 ] 
dist 179=[-1.2582276981228603555 ,.7978093325443233349 ] 
dist 180=[-1.2798181895760677935 ,.8428726946845500622 ] 
dist 181=[-1.2939626729354478772 ,.9223646092785512910 ] 
dist 182=[-1.2993575916512087940 ,.9790928887696487894 ] 
dist 183=[-1.2993985719385647502 ,1.0300091718126631135 ] 
dist 184=[-1.2970549938378203492 ,1.0863003490706156146 ] 
dist 185=[-1.1813146549146081757 ,1.1363679895212823530 ] 
dist 186=[-1.2068058509852211465 ,1.1624426283961112927 ] 
dist 187=[-1.2277394690414672884 ,1.1765382573850550431 ] 
dist 188=[-1.2345738098423057758 ,1.1791980335934802141 ] 
dist 189=[-1.2507353794208824901 ,1.1712209081065587850 ] 
dist 190=[-1.2907135841509300562 ,1.1676221712476626933 ] 
dist 191=[-1.3209088158373294967 ,1.1639765555433955651 ] 
dist 192=[-1.3330114079183841935 ,1.1593060616356525132 ] 
dist 193=[-1.3374341153505732271 ,.05026471358197468471] 
dist 194=[-1.3369691952491003423 ,.20691641786957633564] 
dist 195=[-1.2872806675715505169 ,.33893620713208304517] 
dist 196=[-1.2758689017504393450 ,.47198094229956566978] 
dist 197=[-1.2515003405073223186 ,.5956113647661015393 ] 
dist 198=[-1.2425926649677279146 ,.6900509831295921281 ] 
dist 199=[-1.2034623098250052272 ,.7812643488987840630 ] 
dist 200=[-1.1936046280362698043 ,.8920177754740871840 ] 
dist 201=[-1.1659669673685610362 ,.9961967495078318094 ] 
dist 202=[-1.1565437462878771556 ,1.0611661011525434276 ] 
dist 203=[-.7835777409542361772 ,1.1099068891894933410 ] 
dist 204=[-.7672980422231385160 ,1.1493027920676615803 ] 
dist 205=[-.7276896452445114728 ,1.1797214231218231907 ] 
dist 206=[-.7172526981281431420 ,1.1926265691487944920 ] 
dist 207=[-.6531341069109875587 ,1.1979027036396309795 ] 
dist 208=[-.6394064632769100135 ,1.1978607833059370908 ] 
dist 209=[-.6136459930762660879 ,1.1686938779229697755 ] 
dist 210=[-.6064229077380117691 ,1.1612642045584761107 ] 
dist 211=[-.4774524631130653811 ,1.1374842216777560041 ] 
dist 212=[-.4591372132805903650 ,1.1302749585458810638 ] 
dist 213=[-.4143817259264511452 ,1.1358204375601331086 ] 
dist 214=[-.4058873262428743584 ,1.1524525983912699817 ] 
dist 215=[-.4133262274021781494 ,1.1629329010701336051 ] 
dist 216=[-.5360108527248905121 ,1.1685311054435499650 ] 
dist 217=[-.6571829014544617045 ,1.1716290175913552688 ] 
dist 218=[-.7427156351073790412 ,1.1721327767778786678 ] 
dist 219=[-.8185773648367067812 ,.83346869743007591557] 
dist 220=[-.9011444034629695051 ,.80601427371006910093] 
dist 221=[-.9817701940021631064 ,.74095628489492813913] 
dist 222=[-1.0498832820429788280 ,.72605194652967536562] 
dist 223=[-1.1219252455167971076 ,.63064068134530813487] 
dist 224=[-1.2182358976893315414 ,.61154335596461089767] 
dist 225=[-1.3096927421467949929 ,.57620245790148019988] 
dist 226=[-1.3623587381695015894 ,.5669983413928489891 ] 
dist 227=[-1.3967304356734999562 ,.41236452478594614979] 
dist 228=[-1.4151569340043961101 ,.39109567296131012689] 
dist 229=[-1.4262010561229858501 ,.33800955998476434833] 
dist 230=[-1.4311023046031312196 ,.3302366806153035184 ] 
dist 231=[-1.4324455311458305861 ,.24765147083467737877] 
dist 232=[-1.4292855340561839009 ,.23196759845193246464] 
dist 233=[-1.2630162425447907862 ,.21436264449106355368] 
dist 234=[-1.2373792852260302158 ,.21081853957084975951] 
dist 235=[-1.1917535777889711005 ,.06825221985616202196] 
dist 236=[-1.1794436544621451655 ,.04975723920872450784] 
dist 237=[-1.1694666303869797685 ,.02100834026474310948] 
dist 238=[-1.1699555369161710143 ,.01378758986182524842] 
dist 239=[-1.1618406904663130169 ,.00652887037087482905] 
dist 240=[-1.1592426796052001480 ,.01247845903657733524] 
dist 241=[-.76498572991829812583,.1407042800607426372 ] 
dist 242=[-.72755052413437087332,.26287073605877059198] 
dist 243=[-.63737323178935749541,.36378070235586106274] 
dist 244=[-.62107444291498880103,.46216307190375795658] 
dist 245=[-.48890427963388110994,.551473217194081143  ] 
dist 246=[-.45136292831297952022,.6298410455917090030 ] 
dist 247=[-.40495615800530994   ,.7231134809580794379 ] 
dist 248=[-.39530581466505718104,.8354064021209219229 ] 
dist 249=[-.23095576601949505995,.9405321187670197396 ] 
dist 250=[-.20957455960496636526,1.0051931192065619274 ] 
dist 251=[-.1620315092203047606 ,1.0526370670443983389 ] 
dist 252=[-.15155412798787838644,1.0890326171146804324 ] 
dist 253=[-.09465739046221516770,1.1168625596744219130 ] 
dist 254=[-.08442769297597758562,1.1301130283582906563 ] 
dist 255=[-.06267664863319427690,1.1355139538513889663 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 2, 2, 0, 0, 2] 
dist 0=[45.621164692587043238  ,45.621164692587043238  ] 
dist 1=[44.639209820618051496  ,46.437397299573104048  ] 
dist 2=[43.345695924112601583  ,47.085913460257160376  ] 
dist 3=[41.285009590052066653  ,47.397887964654816331  ] 
dist 4=[39.169618647446495592  ,47.545859281014095160  ] 
dist 5=[37.657595258529983802  ,47.551109982870845637  ] 
dist 6=[36.294559669914391530  ,47.246084180674188823  ] 
dist 7=[34.774253860746428725  ,47.126748681346172828  ] 
dist 8=[33.265211145257775148  ,46.861134103500786099  ] 
dist 9=[31.947217108583160485  ,46.744457589586478580  ] 
dist 10=[30.513970191875610265  ,46.089363811641847843  ] 
dist 11=[28.544748324797151602  ,45.920503650351107118  ] 
dist 12=[26.573006729398325454  ,45.408949645309533036  ] 
dist 13=[25.129730315434907432  ,45.268340686661879496  ] 
dist 14=[23.794394144622927426  ,43.437812515554322992  ] 
dist 15=[22.253726746020729508  ,43.051002747502462789  ] 
dist 16=[20.695456556904601235  ,41.120102944930847212  ] 
dist 17=[19.289855140203672043  ,32.121715213164273345  ] 
dist 18=[17.724233461588422780  ,28.576498226760012777  ] 
dist 19=[15.527000618962230692  ,27.894731891760466211  ] 
dist 20=[13.343738780457021330  ,27.087874637402477753  ] 
dist 21=[11.833801828714933681  ,26.868367601186167429  ] 
dist 22=[10.513672006914303866  ,20.560894145759053047  ] 
dist 23=[9.1435870194220138182 ,19.752791818858562715  ] 
dist 24=[7.0624170539193278287 ,18.102507267990473902  ] 
dist 25=[4.6690980866965473236 ,17.669801346160185341  ] 
dist 26=[3.0339327664231706913 ,16.078673602367804582  ] 
dist 27=[1.6340732788721689046 ,15.749857086725487686  ] 
dist 28=[.1801474476063905288 ,15.147463821811937563  ] 
dist 29=[-1.2073666137148553049 ,15.001626422454411311  ] 
dist 30=[-2.3425904122401625987 ,3.9860099088579766529 ] 
dist 31=[-3.5189333816702759521 ,3.0375684306131778079 ] 
dist 32=[-5.0720866378199442695 ,1.7614951494857242185 ] 
dist 33=[-6.5540007704434597613 ,1.6290935531297534627 ] 
dist 34=[-7.7667708702556674509 ,1.3996208180416736556 ] 
dist 35=[-8.9558068421716176006 ,1.3550708333408848613 ] 
dist 36=[-10.051839137568727016  ,-1.2223250706191477080 ] 
dist 37=[-11.312604160331613776  ,-1.4415881583214540760 ] 
dist 38=[-12.471862684998897103  ,-1.8884996691009809397 ] 
dist 39=[-13.162450211391248650  ,-1.9857672940571053036 ] 
dist 40=[-13.644424199704470597  ,-2.3566563064500411393 ] 
dist 41=[-13.970462403602543996  ,-2.4244021709991137101 ] 
dist 42=[-14.204628747398697255  ,-2.4808829855658029458 ] 
dist 43=[-14.319559675439191750  ,-2.4518863108519938964 ] 
dist 44=[-14.369707822328618412  ,-2.3911101620892019628 ] 
dist 45=[-14.353430923053290403  ,-1.5758713696528235531 ] 
dist 46=[-7.7182536784405454684 ,-.37328265039027160029] 
dist 47=[-7.6760471577584834038 ,.45331964805486207874] 
dist 48=[-7.6595869844112837046 ,1.1616147032952003016 ] 
dist 49=[-4.7905463857978383456 ,1.8923146309307465696 ] 
dist 50=[-4.7831690626037495662 ,2.5805329022587366490 ] 
dist 51=[-4.7720559845391209482 ,3.1194109928521780255 ] 
dist 52=[-1.8348405512522399788 ,3.6516954035641379575 ] 
dist 53=[-1.7441593187630513943 ,4.3137065029510110827 ] 
dist 54=[-.22025199283935558784,4.9430682132816036439 ] 
dist 55=[-.1231421235219074456 ,5.3451091868094011453 ] 
dist 56=[.34613131975237850431,5.6575633375979678207 ] 
dist 57=[.4266176069222406175 ,5.9294579354317665209 ] 
dist 58=[.59204737997615464158,6.1546513006181571170 ] 
dist 59=[.62649684975106721741,6.2807806154623197693 ] 
dist 60=[.75575767160502486962,6.3587895436640762408 ] 
dist 61=[.75678457735122187507,6.3920415745501671992 ] 
dist 62=[.71419865914142151893,6.3934199097789400551 ] 
dist 63=[.60137354935518580113,6.3781145325876145954 ] 
dist 64=[0                     ,6.2491215996377514247 ] 
dist 65=[.26537455272923196479,4.6257386269921643552 ] 
dist 66=[.01491363945445717495,4.7542955988922155983 ] 
dist 67=[-.38739193213731137685,4.8322809619988023087 ] 
dist 68=[-.79762408266603337922,4.8889078472251259678 ] 
dist 69=[-1.0797387395736230986 ,4.9321724367655281524 ] 
dist 70=[-1.3618548320690789286 ,4.9613578540094780761 ] 
dist 71=[-1.6619573117099545414 ,4.9617288683194193505 ] 
dist 72=[-1.9416829413508471316 ,4.9480068253371406658 ] 
dist 73=[-2.1564317121349551954 ,4.9332993736798975610 ] 
dist 74=[-2.3647158908546581008 ,4.8265069575543582125 ] 
dist 75=[-2.6186360499282090391 ,4.7950232157888788287 ] 
dist 76=[-2.8576529002696700644 ,4.7200966284204184476 ] 
dist 77=[-3.0064494595559752950 ,4.6905231572291736057 ] 
dist 78=[-3.5859296066173762567 ,3.2504351414723826897 ] 
dist 79=[-4.1965317259745331579 ,3.2141910486182096247 ] 
dist 80=[-4.6847169976880581053 ,3.0864255806422460167 ] 
dist 81=[-5.1341681829248772650 ,3.0490760414840045170 ] 
dist 82=[-5.5249166164582654619 ,3.0000824221470754696 ] 
dist 83=[-5.7787675919479924089 ,2.9796003016639652936 ] 
dist 84=[-5.9813069671180458630 ,.61786257018284988667] 
dist 85=[-6.1672446544385689801 ,.41480711180592689937] 
dist 86=[-6.3205455112679704641 ,-.00380873461749012025] 
dist 87=[-6.3927904885815640658 ,-.05801798866157649604] 
dist 88=[-6.4207179587735471051 ,-.45787868896620885643] 
dist 89=[-6.4205444648453361617 ,-.52667730776186435062] 
dist 90=[-6.3438766286076479539 ,-.62249223901106910877] 
dist 91=[-6.3107614821342625379 ,-.6432862453211456594 ] 
dist 92=[-6.2317388800947334846 ,-.70928079455390161214] 
dist 93=[-6.1962162909345012486 ,-.66057817725956974379] 
dist 94=[-4.7212328990053090714 ,-.08183565982106850770] 
dist 95=[-4.5701665142614173780 ,.69855850496156207978] 
dist 96=[-4.1773569777640289115 ,1.3539681959338611627 ] 
dist 97=[-4.1197051998393579805 ,2.0106632613559120136 ] 
dist 98=[-3.4512651439090717988 ,2.6183457306024410513 ] 
dist 99=[-3.1039452624821245861 ,3.0781055672319308280 ] 
dist 100=[-2.3963505822478418513 ,3.5178115223313375350 ] 
dist 101=[-2.3365334521341670057 ,4.0454391432026373377 ] 
dist 102=[-1.2571067705027338328 ,4.5383523590086105317 ] 
dist 103=[-1.2448053239735937359 ,4.8394817971157435484 ] 
dist 104=[-1.1889214118310237818 ,5.0579251792489174771 ] 
dist 105=[-1.1762333376261587431 ,5.2207656274777234001 ] 
dist 106=[-1.1384661538795228042 ,5.3439630287538742076 ] 
dist 107=[-1.1310522720379083054 ,5.4041609411301565500 ] 
dist 108=[-1.0456735913444199519 ,5.4297467283773385223 ] 
dist 109=[-1.0286227504618138538 ,5.4290607479429512268 ] 
dist 110=[-.99208141001283320275,1.0449194652525245600 ] 
dist 111=[-.98057922138656915618,1.2388325653696970563 ] 
dist 112=[-.92841514159758533182,1.3914297718863185986 ] 
dist 113=[-.91722710137932711396,1.5278455453734819885 ] 
dist 114=[-.88415563352653638246,1.6436685211542956779 ] 
dist 115=[-.87868739240593253331,1.7140529794628748597 ] 
dist 116=[1.2372127493140221556 ,1.7647659540514803864 ] 
dist 117=[1.3420322055600495415 ,1.8020608331932058617 ] 
dist 118=[1.5652641301868220378 ,1.8307787843108040653 ] 
dist 119=[1.6048538616979915088 ,1.9363613918874469482 ] 
dist 120=[1.6817324093737459125 ,2.0467227287180630777 ] 
dist 121=[1.5940105032937041714 ,2.1139379850918389896 ] 
dist 122=[1.4853281471109370798 ,2.1624962129799318784 ] 
dist 123=[1.3569430143321920650 ,2.1983769484750779852 ] 
dist 124=[1.1894673878706287682 ,2.2243931535390474044 ] 
dist 125=[.9247329295931637469 ,2.2335693092187641319 ] 
dist 126=[.6555583977059940765 ,2.2325550499478328851 ] 
dist 127=[.47035361578482972528,2.2290457725145263887 ] 
dist 128=[.31107458876706107603,2.1939314476894865375 ] 
dist 129=[.14538555798196446625,2.1821613009698436501 ] 
dist 130=[-.01189114025626726789,2.1452918975806372523 ] 
dist 131=[-.13759497011431740226,2.1309442620845820530 ] 
dist 132=[-.26435758732789075224,1.3924281832369509297 ] 
dist 133=[-.42587114563781927179,1.3201389806651802711 ] 
dist 134=[-.58169528718443139222,1.1397648687577830474 ] 
dist 135=[-.6857502806276179105 ,1.1136733942595968434 ] 
dist 136=[-.80967731306082582643,.83372088999798306448] 
dist 137=[-.96855439203255274994,.78070598634207227411] 
dist 138=[-1.1212928601622641964 ,.72186690735985622907] 
dist 139=[-1.3057731314915465401 ,.71086146198898729309] 
dist 140=[-1.4788389461690401903 ,.2267218121463661887 ] 
dist 141=[-1.5860094163269489232 ,.1676145769986835569 ] 
dist 142=[-1.6655235666254667687 ,.04587475204699897848] 
dist 143=[-1.7281813126320965160 ,.01473883323226152823] 
dist 144=[-1.7767181861823993765 ,-.09573280992223515538] 
dist 145=[-1.7998591839400321321 ,-.11784014744974225314] 
dist 146=[-1.8101279014011029838 ,-.14844075161672458643] 
dist 147=[-1.8103305167502698246 ,-.15546454454975567868] 
dist 148=[-1.2115912287941590257 ,-.54460656016710978306] 
dist 149=[-1.2081931279454762651 ,-.57713422387211842836] 
dist 150=[-1.0829924529219639895 ,-.63675362456052999555] 
dist 151=[-1.0632630509097893713 ,-.64893712576747302912] 
dist 152=[-1.0325511384992150805 ,-.67312504259592819814] 
dist 153=[-1.0665425626478625203 ,-.66641836146252524837] 
dist 154=[-1.0913242937379041221 ,-.5905725515508092622 ] 
dist 155=[-1.1100572420335184111 ,-.4848938489421721225 ] 
dist 156=[-1.1238075944334432833 ,-.3453271510645088020 ] 
dist 157=[-1.1286975374787690819 ,-.13642347702793967628] 
dist 158=[-1.1284007853527216584 ,.07237413057530395123] 
dist 159=[-1.1265886411010056206 ,.21151984545000346555] 
dist 160=[-1.1082949380411424551 ,.32643712265492913987] 
dist 161=[-1.1021469615533792790 ,.43851006093074531994] 
dist 162=[-1.0841097851687710547 ,.54033103258934726253] 
dist 163=[-1.0760803828793159231 ,.61432204978332574372] 
dist 164=[-.90799570142706125725,.68219299164508002981] 
dist 165=[-.89878739234588525516,.75958617787248498281] 
dist 166=[-.87488739607004786951,.83082630759848806512] 
dist 167=[-.86645611820625933988,.87413215432868555559] 
dist 168=[-.81919589263630574218,.90533420324841480308] 
dist 169=[-.80789920719726652285,.9282462311115994269 ] 
dist 170=[-.78591517957588428169,.97859436092230792523] 
dist 171=[-.77905391341424964339,1.0475312027785905658 ] 
dist 172=[-.65246450701757270349,1.1096338311780328312 ] 
dist 173=[-.63378451676568437832,1.1441830536060757380 ] 
dist 174=[-.58906247140621937149,1.1651965727310146552 ] 
dist 175=[-.57854912735721987909,1.1732615028410776482 ] 
dist 176=[-.5107460119161852026 ,1.1761693369605125914 ] 
dist 177=[-.49691557467994339462,1.1765950929926519817 ] 
dist 178=[-.47152557070364748547,1.1752880495182000254 ] 
dist 179=[-.4648388772796859823 ,1.1714299573962398316 ] 
dist 180=[-.18576746904638394847,.96998495094154699856] 
dist 181=[-.15605421416537690952,.94558284296610706421] 
dist 182=[-.20373171897524187525,.881633064055724013  ] 
dist 183=[-.28092917700588351996,.87102393921303756126] 
dist 184=[-.35238292329757369031,.79311928972188884083] 
dist 185=[-.43476378825676895089,.78319898316316032735] 
dist 186=[-.51795753622708502443,.76223265551630024727] 
dist 187=[-.5926594751846572334 ,.75526246577003299032] 
dist 188=[-.6755270804043628938 ,.64650248953507590547] 
dist 189=[-.79132428711674970518,.63008362992619211438] 
dist 190=[-.90369084075985672739,.58907170184305502953] 
dist 191=[-.97286363924112227235,.5979357226784455142 ] 
dist 192=[-1.0237176153403394755 ,.61482808375504404122] 
dist 193=[-1.0629503811586068173 ,.62747609325017051646] 
dist 194=[-1.0933748739717253164 ,.63943922857767986094] 
dist 195=[-1.1090630669192395706 ,.69701968986246977478] 
dist 196=[-1.1169812954468525041 ,.76372440803617481535] 
dist 197=[-1.1175290356715666845 ,.80370417949020916758] 
dist 198=[-1.0521269182868509654 ,.83177495420772115773] 
dist 199=[-1.0398227172772747269 ,.8509413849546751757 ] 
dist 200=[-1.0222003549104495061 ,.86464771308020978064] 
dist 201=[-1.0153411324130675415 ,.8709235724632127113 ] 
dist 202=[-.99681462183582421044,.87295521923931246126] 
dist 203=[-1.0091402502439768982 ,.87198054896746612655] 
dist 204=[-1.0437353432857055830 ,.7990862929491992539 ] 
dist 205=[-1.0632167573117719276 ,.82960824625445759555] 
dist 206=[-1.0753773382600532407 ,.8736675292040945542 ] 
dist 207=[-1.0807450326700052915 ,.89944890924902609979] 
dist 208=[-1.0814352653829024248 ,.91678747567339899662] 
dist 209=[-1.0801735408195880372 ,.92714575601104074468] 
dist 210=[-1.0676946229223875467 ,.93269387580384374554] 
dist 211=[-1.0655264182768805550 ,.93296450236765855056] 
dist 212=[-.27437042534015740938,.92689302623627280701] 
dist 213=[-.22010844282134600476,.92415655901982208261] 
dist 214=[-.09404113167178439207,.86786328108321684212] 
dist 215=[-.07370810455892533896,.85716839122614512235] 
dist 216=[.08993003718658191089,.82947024072126643658] 
dist 217=[.1185627911127114547 ,.82085848073155961521] 
dist 218=[.16198595835599079447,.76796096861811597732] 
dist 219=[.11622351371469391286,.75573966599233118194] 
dist 220=[.01805180575559684436,.73304804345643203921] 
dist 221=[-.17472937553859514287,.74052856640234320425] 
dist 222=[-.37857266850915841357,.76262605934119316667] 
dist 223=[-.51249693708593716317,.7730870253735004918 ] 
dist 224=[-.62093647376785764214,.7778646895979972222 ] 
dist 225=[-.72304576573811782199,.7778868289838429497 ] 
dist 226=[-.81334498256464837307,.7671234133016684124 ] 
dist 227=[-.87463880339467449868,.7624310891283952931 ] 
dist 228=[-.92645929841311705654,.7570836242703555075 ] 
dist 229=[-.97894026615926156401,.7536852115464783263 ] 
dist 230=[-1.0255954348180249252 ,.6496640684993637070 ] 
dist 231=[-1.0541596900050147898 ,.6341351663773612238 ] 
dist 232=[-1.0749542787507290173 ,.6027256848745121688 ] 
dist 233=[-1.0905947121562567347 ,.5936754035517690877 ] 
dist 234=[-1.1017304392284256354 ,.5567138350844504944 ] 
dist 235=[-1.1045431385720612372 ,.5483479553785482971 ] 
dist 236=[-1.1029228735162798429 ,.5281757311942557737 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 2, 1, 0, 2, 0, 1] 
dist 0=[47.587608886170737476  ,47.587608886170737476  ] 
dist 1=[47.357171998588816654  ,47.722644606405779359  ] 
dist 2=[46.897901429039455941  ,48.031302487232317289  ] 
dist 3=[46.179556652904773203  ,48.302104084908105142  ] 
dist 4=[45.279175690504765370  ,48.481439282414171506  ] 
dist 5=[44.092766172224904387  ,48.627614109617083945  ] 
dist 6=[42.466032907880265690  ,48.765770330976305985  ] 
dist 7=[39.807018628074270749  ,48.866727439981432008  ] 
dist 8=[37.074672745989965794  ,48.864417022129382846  ] 
dist 9=[35.155003313779974191  ,48.787363701002542464  ] 
dist 10=[33.457611530204165203  ,48.730336430154039051  ] 
dist 11=[31.537037576569190493  ,48.317012567486263282  ] 
dist 12=[27.468745234838226978  ,48.193956572990160422  ] 
dist 13=[24.677022058404613109  ,47.744423283661670988  ] 
dist 14=[22.279097049296259247  ,47.538000164637318771  ] 
dist 15=[19.783234733795878564  ,38.216080032498357689  ] 
dist 16=[17.407129957025741685  ,37.296180252653752867  ] 
dist 17=[15.487201028004840933  ,35.024332063747857540  ] 
dist 18=[13.527583696225414264  ,34.669460434144685005  ] 
dist 19=[10.992423286349789132  ,31.148730463262957813  ] 
dist 20=[8.5168801373222911840 ,30.467589354855539086  ] 
dist 21=[6.7950825261930906362 ,29.664558050183298564  ] 
dist 22=[5.2885834247364076742 ,29.440496847150970070  ] 
dist 23=[3.6726130230801992465 ,23.040173754187164088  ] 
dist 24=[2.0996515836822453051 ,22.215527699827622426  ] 
dist 25=[.7643968253842130407 ,20.537804288557707493  ] 
dist 26=[-.6610806750684677931 ,20.097427011819912727  ] 
dist 27=[-2.5956543058449668361 ,18.478489142836683591  ] 
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dist 30=[-6.5321131185001820397 ,17.370306629227303503  ] 
dist 31=[-7.2900952999884146413 ,5.5655127785304779678 ] 
dist 32=[-7.9120317121424971270 ,4.5505809421948058125 ] 
dist 33=[-8.2618426874393665883 ,2.2830956239598019522 ] 
dist 34=[-8.4845216750556933364 ,1.8821748095883093700 ] 
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dist 36=[-8.6595670770121745277 ,-1.2422347496444298026 ] 
dist 37=[-9.1383564714523174651 ,-2.0671506698448239881 ] 
dist 38=[-10.465877458853292113  ,-2.2418646683111261549 ] 
dist 39=[-11.690427235001107331  ,-3.7191699664508224387 ] 
dist 40=[-12.434187881842217736  ,-3.5791159971167073154 ] 
dist 41=[-12.971042980930635085  ,-3.4447527213475171827 ] 
dist 42=[-13.369093947551308987  ,-3.2907947912794281282 ] 
dist 43=[-13.666715903934560490  ,-1.9456114844429475630 ] 
dist 44=[-13.802334014990684934  ,-.3143867833294656361 ] 
dist 45=[-13.850647335705299676  ,.7775374283546067057 ] 
dist 46=[-13.845355690439891128  ,1.6831502125344357965 ] 
dist 47=[-7.3732269012902655362 ,2.5708218816504658247 ] 
dist 48=[-6.9695236644863587601 ,3.3785796496379655537 ] 
dist 49=[-5.9793021869515709291 ,3.9652274449440897216 ] 
dist 50=[-5.8356854079129394104 ,4.5018934852478137171 ] 
dist 51=[-4.3686619772968448357 ,5.1100806450446774943 ] 
dist 52=[-4.0977973296768805225 ,5.6712221951452572980 ] 
dist 53=[-3.7807987903933010139 ,6.0201603085034760868 ] 
dist 54=[-3.7217572751589383624 ,6.2802124642892402322 ] 
dist 55=[-2.8581980465010042749 ,6.4868001193118979561 ] 
dist 56=[-1.1828217122198270150 ,6.6434246109882902143 ] 
dist 57=[-.6118271098187121214 ,6.7042117123520873960 ] 
dist 58=[-.4798747926365693334 ,6.7213490622060681890 ] 
dist 59=[.0594318820623399291 ,6.7068040954814869104 ] 
dist 60=[.1581882049128572855 ,4.0293377293168163517 ] 
dist 61=[.3115761194094111727 ,4.2419897122528498409 ] 
dist 62=[.3458880183041124328 ,4.4241882965722014088 ] 
dist 63=[2.3713804272074522984 ,4.6132126661826828074 ] 
dist 64=[1.9581113092425549083 ,4.7762011319160833173 ] 
dist 65=[1.6154864851782777789 ,4.8544322355360476979 ] 
dist 66=[1.2590296207388560601 ,4.8937713574164217330 ] 
dist 67=[.7904610907356161411 ,4.9013934727356951736 ] 
dist 68=[.3319963436267285695 ,4.8247765525725475674 ] 
dist 69=[.0158171122613052103 ,4.8024390031805657063 ] 
dist 70=[-.2569047529787021684 ,4.7868491427172225903 ] 
dist 71=[-.5419739457955449077 ,4.7764852943442078194 ] 
dist 72=[-.8136603488640418862 ,4.7556202883882511257 ] 
dist 73=[-1.0330270067329410545 ,4.8419305073149026954 ] 
dist 74=[-1.3600093258892697158 ,4.9079914269240178850 ] 
dist 75=[-1.8655196622327772014 ,4.9564058598470765334 ] 
dist 76=[-2.3358050805228486506 ,4.9721966601996741340 ] 
dist 77=[-2.6961549904818448663 ,4.9688871342758236454 ] 
dist 78=[-3.0453246148948327078 ,4.9609724422387685312 ] 
dist 79=[-3.4709781704208538073 ,3.2442205704929429324 ] 
dist 80=[-3.8723252374588682103 ,2.3159773336710515642 ] 
dist 81=[-4.1244571986082094590 ,2.1929267507726443820 ] 
dist 82=[-4.3157900485531043059 ,1.9423830881624046905 ] 
dist 83=[-4.4744093494802261521 ,1.8754461168290851790 ] 
dist 84=[-4.5999999253235739006 ,1.6247802233230194694 ] 
dist 85=[-4.6594698837510022938 ,1.5712394835782859459 ] 
dist 86=[-4.7305990100134003157 ,1.4694364671961912434 ] 
dist 87=[-4.9855600475751886389 ,1.4428056641685588704 ] 
dist 88=[-5.1230674093934281235 ,-.1896873481705634138 ] 
dist 89=[-5.2011230184218346953 ,.1384172078191524635 ] 
dist 90=[-5.2189659539213911622 ,.5359633603555201828 ] 
dist 91=[-5.2145821314247228033 ,1.1325055033394786232 ] 
dist 92=[-5.2059900681406495501 ,1.7270402426184242934 ] 
dist 93=[-5.1925696724141528268 ,2.1165867375532802244 ] 
dist 94=[-5.1721312691430957529 ,2.4308188566937468929 ] 
dist 95=[-4.4461407226864554888 ,2.7247201154384338385 ] 
dist 96=[-4.3605701841448865145 ,2.9833202745015910085 ] 
dist 97=[-4.1292228673535897640 ,3.1566449896381097168 ] 
dist 98=[-4.0889256322579518240 ,3.3008633170501792403 ] 
dist 99=[-3.6564090059933397808 ,3.4432927158157400832 ] 
dist 100=[-3.4904948561526459485 ,3.5657186945863919348 ] 
dist 101=[-3.3790345804789374175 ,3.6300847414359065738 ] 
dist 102=[-2.9977050684330873356 ,3.6643526407784579024 ] 
dist 103=[-2.1458598862801903817 ,3.7356543719535135145 ] 
dist 104=[-1.7060663462772280051 ,4.0041519781283535956 ] 
dist 105=[-1.4222188582745557007 ,4.2119663422339645960 ] 
dist 106=[-1.3462454112955978525 ,4.3914295491540846036 ] 
dist 107=[-1.0575831759824265225 ,4.5426285494471639383 ] 
dist 108=[-1.0003439400900148292 ,4.6248133663674738127 ] 
dist 109=[-.8844039953178459340 ,4.6711832973185188517 ] 
dist 110=[-.8540114778155598176 ,4.6807583008023783395 ] 
dist 111=[-.88654483113734825677,2.1287564875361765648 ] 
dist 112=[-1.2276045478227181326 ,1.6913036886718447156 ] 
dist 113=[-1.4894840462693280378 ,1.6069233999711219115 ] 
dist 114=[-1.7436161562464601747 ,1.5428616334417666035 ] 
dist 115=[-2.0537520796408709776 ,1.7289302758054937038 ] 
dist 116=[-2.3460561831750754524 ,1.8527616863808542237 ] 
dist 117=[-2.5290103471763019171 ,1.9548970038492384345 ] 
dist 118=[-2.6669618725057781972 ,2.0543587009566305564 ] 
dist 119=[-2.7796314967903139319 ,2.1416504327659004661 ] 
dist 120=[-2.8674626350830157258 ,2.1951982795997949253 ] 
dist 121=[-2.9062671361674303848 ,2.2343935843739375709 ] 
dist 122=[-2.9241523227996825720 ,2.2643714372716223406 ] 
dist 123=[-2.9284823573948720018 ,2.2862114158873310035 ] 
dist 124=[-1.0754656785074541544 ,2.2929105913463788819 ] 
dist 125=[-1.2508928606983370797 ,2.2898251566545121843 ] 
dist 126=[-1.3908041700471376687 ,2.2857212282661892563 ] 
dist 127=[-1.5190369037552359489 ,1.3298289337275883303 ] 
dist 128=[-1.6301189598242862227 ,1.2464391281337279238 ] 
dist 129=[-1.7015625728051511790 ,1.0496084177266150195 ] 
dist 130=[-1.7577440472350117800 ,1.0137456871515933502 ] 
dist 131=[-1.8079008931733006091 ,.74082465987951129531] 
dist 132=[-1.8489216429275640170 ,.69012587341464004556] 
dist 133=[-1.8686295103439599427 ,.60843866309369929609] 
dist 134=[-1.8765445737156030889 ,.58784246018925032937] 
dist 135=[-1.8762036354078369521 ,.22494953989378106192] 
dist 136=[-1.8583052418304127332 ,.17804305497196718024] 
dist 137=[-1.8501694610613300182 ,.07163658116442063284] 
dist 138=[-1.8250963880985342818 ,.05306790652856918353] 
dist 139=[-1.8130400125554790548 ,.0259418524228344338 ] 
dist 140=[-1.4427887162742204646 ,.3471171164820880982 ] 
dist 141=[-1.4137902442242758906 ,.5622168949344157119 ] 
dist 142=[-1.4608921892062197731 ,.7409333258133933149 ] 
dist 143=[-1.6202309582814512940 ,.9168748472709041136 ] 
dist 144=[-1.7161260824075418115 ,1.0777013898815113862 ] 
dist 145=[-1.7840586528580581505 ,1.1960837508850434691 ] 
dist 146=[-1.8317510940466475867 ,1.3061327111178905885 ] 
dist 147=[-1.8670463627192915617 ,1.4336983511801896053 ] 
dist 148=[-1.8854797636395071129 ,1.5506489698525711511 ] 
dist 149=[-1.8951311641339755416 ,1.6183260449427736814 ] 
dist 150=[-1.8953599143058063415 ,1.6629317315676313345 ] 
dist 151=[-1.7346160143938432013 ,1.6877850672840162197 ] 
dist 152=[-1.7082879708830407945 ,1.7033991033128528960 ] 
dist 153=[-1.6694984622404575853 ,1.7111176594767754230 ] 
dist 154=[-1.6608769832315497402 ,1.7145395218896304549 ] 
dist 155=[-1.6393544558780396380 ,1.7129860977529180333 ] 
dist 156=[-1.6292215645400000842 ,1.5057635315971709020 ] 
dist 157=[-1.6132700490695232478 ,1.4781081513698589507 ] 
dist 158=[-1.6062775492763125929 ,1.4016497701792479510 ] 
dist 159=[-.64576921920838299848,1.3891287899202523055 ] 
dist 160=[-.56435356946965313925,1.3027394138167906550 ] 
dist 161=[-.36925332543451200329,1.2865772582079446304 ] 
dist 162=[-.34118358690550290067,1.2578957818105720670 ] 
dist 163=[-.0681673019019080074 ,1.2492331040814922432 ] 
dist 164=[-.0191825956235550836 ,1.0444128497281099022 ] 
dist 165=[.0404811456095458905 ,1.0145499375816377892 ] 
dist 166=[.0507982257346775027 ,1.0182450877122942606 ] 
dist 167=[.2585884117688391349 ,1.0378719207581311532 ] 
dist 168=[.20690910114748440171,1.0533389862974694576 ] 
dist 169=[.10897805825621941499,1.0604794229046225887 ] 
dist 170=[-.07188986201497343350,1.0628654771484478937 ] 
dist 171=[-.3369523119272259592 ,1.1094752029858607308 ] 
dist 172=[-.6002221484250251199 ,1.1636607983660426157 ] 
dist 173=[-.7739350804275487853 ,1.1927145694808314607 ] 
dist 174=[-.9154549423710036470 ,1.2088955517146956944 ] 
dist 175=[-1.0502082102199222628 ,1.2126411635192883347 ] 
dist 176=[-1.1704363431357015018 ,1.2098679440361784805 ] 
dist 177=[-1.2539717483971421084 ,1.2075354566670245050 ] 
dist 178=[-1.3267043099306457396 ,1.2043707957676374076 ] 
dist 179=[-1.4038089916293985986 ,1.1996487884709944601 ] 
dist 180=[-1.4723426282288755200 ,1.0334119578643982840 ] 
dist 181=[-1.5108586610891943157 ,1.0085083206691096698 ] 
dist 182=[-1.5348021293501262161 ,.9620745643207220096 ] 
dist 183=[-1.5451578849444461462 ,.9494037940357310400 ] 
dist 184=[-1.5485772772788034068 ,.9027576971082871711 ] 
dist 185=[-1.5459346472898022083 ,.8901153884518656840 ] 
dist 186=[-1.5373411194772174256 ,.8683995673190248307 ] 
dist 187=[-1.5313091154354701266 ,.8617803154458642344 ] 
dist 188=[-.5573690979111140048 ,.53971995026962614323] 
dist 189=[-.6902328016142826117 ,.52370310936235788281] 
dist 190=[-.8813227157022206829 ,.53174614498457805929] 
dist 191=[-1.0685899346941043200 ,.56682740930442093775] 
dist 192=[-1.1861943048978004890 ,.59204199203795003211] 
dist 193=[-1.2753940059256747080 ,.61485244734830757158] 
dist 194=[-1.3492669918156314455 ,.64033931734359457175] 
dist 195=[-1.4088388017236165004 ,.66559051653726823501] 
dist 196=[-1.4409455824911481471 ,.68746072942955788331] 
dist 197=[-1.4591115513807933133 ,.71104023641349848487] 
dist 198=[-1.4630266707292175280 ,.75255053181139529802] 
dist 199=[-1.4197612298255290634 ,.79318644403958446278] 
dist 200=[-1.4096487721486113081 ,.82572865929934661569] 
dist 201=[-1.4015884592593961527 ,.84253853739134731328] 
dist 202=[-1.3942270369229821339 ,.85134090227188060634] 
dist 203=[-1.3878805239588927111 ,.8626580981659906646 ] 
dist 204=[-1.3838694914881579767 ,.8815765634167493735 ] 
dist 205=[-1.3807993562589985980 ,.9017708752242676857 ] 
dist 206=[-1.3782061461784419795 ,.9289837903730271628 ] 
dist 207=[-.46716503141046408389,.9546874299802245793 ] 
dist 208=[-.39300607245641845566,.9688576487734111026 ] 
dist 209=[-.21862695799723420811,.9772891290008630015 ] 
dist 210=[-.19174547745725789691,.9800876840171784190 ] 
dist 211=[-.0205891452788797751 ,.9790432761522858951 ] 
dist 212=[.0055257695226207664 ,.9771335291870526292 ] 
dist 213=[.02583703321094408887,.9647277829076067534 ] 
dist 214=[-.06422562807163495866,.9616850311229968453 ] 
dist 215=[-.17701655653906982982,.9098379803287285714 ] 
dist 216=[-.29588915637041865225,.8997430541103469319 ] 
dist 217=[-.41023101431734042847,.8679957846381001269 ] 
dist 218=[-.54324538577499359961,.8630208792336765841 ] 
dist 219=[-.7366603130951690054 ,.78881315122053357336] 
dist 220=[-.9274397503998495920 ,.77247908281304433483] 
dist 221=[-1.0499335734383233816 ,.82613793998732728855] 
dist 222=[-1.1459552975608824813 ,.8949661301183024967 ] 
dist 223=[-1.2310574342246345897 ,.96005960069657163644] 
dist 224=[-1.3027015273929442084 ,.99880959954454072944] 
dist 225=[-1.3449985039345367619 ,1.0257263116957899007 ] 
dist 226=[-1.3739297250985881029 ,1.0435787911165754665 ] 
dist 227=[-1.3922177086850844830 ,1.0553470531205255801 ] 
dist 228=[-1.4043226238957990707 ,1.0579732913598980611 ] 
dist 229=[-1.4085713061840602140 ,1.0565530165866203315 ] 
dist 230=[-1.4078848128393340870 ,1.0532479567735212004 ] 
dist 231=[-1.4048174286941062446 ,.98524873864321530083] 
dist 232=[-1.3888341036537879384 ,.97258543300691222133] 
dist 233=[-1.3827858945121522785 ,.94445538046295030519] 
dist 234=[-1.3438325569148038391 ,.93491227235169761538] 
dist 235=[-1.2438052592524216431 ,.88901832258412019359] 
dist 236=[-1.1411887444521610679 ,.87858697959230533896] 
dist 237=[-1.1299459200384570156 ,.84997944790074303252] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 0, 0, 1, 0, 1] 
dist 0=[45.197373022787602622  ,45.197373022787602622  ] 
dist 1=[44.407287359086106858  ,45.789406795998405316  ] 
dist 2=[43.318609154854100680  ,46.236545911360275313  ] 
dist 3=[41.533824401963344397  ,46.447935902113920216  ] 
dist 4=[39.683481439171925353  ,46.527643902422547719  ] 
dist 5=[38.332873860665631462  ,46.527814518002902164  ] 
dist 6=[37.085699574956861821  ,46.308417569329410145  ] 
dist 7=[35.648371287478263186  ,46.213396102969069909  ] 
dist 8=[34.193171877011030299  ,45.523375321811920604  ] 
dist 9=[32.874488548449905151  ,44.566455712015125444  ] 
dist 10=[31.398635829864274550  ,44.092955023837700172  ] 
dist 11=[29.315403836193200110  ,43.939015696330598002  ] 
dist 12=[27.198964964037141098  ,43.621966084148444996  ] 
dist 13=[25.590336649762436242  ,43.504838552153347628  ] 
dist 14=[24.039516355938187549  ,42.966617835854226541  ] 
dist 15=[22.153818720427279327  ,42.767287952327379186  ] 
dist 16=[20.187659805998717587  ,41.454228044404297528  ] 
dist 17=[18.315166682975109997  ,27.577004787133199104  ] 
dist 18=[16.144342227847895965  ,26.076947305718775484  ] 
dist 19=[12.985861161280128413  ,24.818218048733259197  ] 
dist 20=[9.8463187494311472234 ,22.820147093679356486  ] 
dist 21=[7.7510969347551537944 ,22.164757096075074175  ] 
dist 22=[6.0102635461367613477 ,19.312501132334557243  ] 
dist 23=[4.2868208297961375355 ,18.171961844233543718  ] 
dist 24=[2.6968864858809124103 ,17.965137336503996209  ] 
dist 25=[1.4894837107639755296 ,16.298276277368780866  ] 
dist 26=[.32520705119301799291,15.994538773069515629  ] 
dist 27=[-1.0925584509260739912 ,14.799692124580664969  ] 
dist 28=[-2.4385168442737367704 ,11.279834360224018587  ] 
dist 29=[-3.3159503530072007910 ,11.186555970579870602  ] 
dist 30=[-4.0230124916840534217 ,5.4189676688299830317 ] 
dist 31=[-4.6882927532337461851 ,3.8339261391054144048 ] 
dist 32=[-5.7961853521622343482 ,.54449086718614257386] 
dist 33=[-8.5294044296062066736 ,-1.0183490022088032615 ] 
dist 34=[-10.254250354044002237  ,-1.1215287433756065404 ] 
dist 35=[-11.580306015761311464  ,-.57879833864577432684] 
dist 36=[-12.719905748955549676  ,.00229313997932210673] 
dist 37=[-13.661394102916439699  ,.431188453156654642  ] 
dist 38=[-14.195944205595684171  ,.8282065503185070528 ] 
dist 39=[-14.539644474110786946  ,1.2826054082160944726 ] 
dist 40=[-14.718982954016733890  ,1.7367714227453515276 ] 
dist 41=[-14.822213109262942519  ,2.1330700040269414210 ] 
dist 42=[-14.861745436916330871  ,2.5616048246538579827 ] 
dist 43=[-14.865127921441343812  ,3.1445264654399192048 ] 
dist 44=[-14.823297864180429932  ,3.7213244334396334202 ] 
dist 45=[-14.757843493282094068  ,4.1255019429565643493 ] 
dist 46=[-14.696031020812781309  ,4.4797580405684652532 ] 
dist 47=[-14.556424415352602648  ,4.8574665675115354200 ] 
dist 48=[-14.489290962511314990  ,5.2204398611812813776 ] 
dist 49=[-6.9235217458636763070 ,5.5159291649174143072 ] 
dist 50=[-6.2674087590574337156 ,5.8180036272907679294 ] 
dist 51=[-5.1555542210115984947 ,6.2072375272909107121 ] 
dist 52=[-4.4659517231645707242 ,6.5805238497420333010 ] 
dist 53=[-2.3191252110413881329 ,6.8189763205757235131 ] 
dist 54=[-1.9335391607577351267 ,7.0038411894120314996 ] 
dist 55=[-1.4086163711492832264 ,7.1633555775928725653 ] 
dist 56=[-1.2702413662557861367 ,7.2939314079605756232 ] 
dist 57=[.36922026390423067862,7.3633405469534568700 ] 
dist 58=[.33599759730992172052,7.4010116947304846637 ] 
dist 59=[.24763566855544081422,7.4049404750959759046 ] 
dist 60=[.10283243395040672138,7.3871940717479423407 ] 
dist 61=[-.15548029724605472934,7.3595978177616591445 ] 
dist 62=[-.4244483996651499167 ,7.2767478583750357483 ] 
dist 63=[-.61178044022821732225,7.2311950028064670129 ] 
dist 64=[-.77417455339431141216,6.9337964705524025290 ] 
dist 65=[-.94379136067434618961,4.2783851974833900898 ] 
dist 66=[-1.1040397830231690384 ,4.3587783060761179769 ] 
dist 67=[-1.2291118187023896643 ,4.4018975393158967806 ] 
dist 68=[-1.3517721609627840310 ,4.4087595496036150794 ] 
dist 69=[-1.5024189125947249488 ,4.3948669772804309755 ] 
dist 70=[-1.6436224479656215726 ,4.3800058451306024203 ] 
dist 71=[-1.7286342371293038489 ,4.3453571086348021027 ] 
dist 72=[-1.7883483079172589629 ,4.3275850704043570098 ] 
dist 73=[-1.8286822009476102469 ,3.9138021600875076006 ] 
dist 74=[-1.8546006851193509242 ,3.8475996285612965426 ] 
dist 75=[-1.8587790240552218806 ,3.6983275970520345888 ] 
dist 76=[-1.8507948701649704516 ,3.6507481579619309227 ] 
dist 77=[-1.8437548678586835971 ,3.4327853692558406663 ] 
dist 78=[-.97620711550532553574,3.3856254316525665388 ] 
dist 79=[-1.2986072113554858484 ,3.2686051320899748206 ] 
dist 80=[-1.6244355590733965455 ,3.2350628478616783661 ] 
dist 81=[-1.9173855960300479467 ,1.6265736540494035347 ] 
dist 82=[-2.2427048538609710550 ,1.4674667286718034007 ] 
dist 83=[-2.6978049916217126851 ,1.1229518888488594723 ] 
dist 84=[-3.1404711063221277657 ,1.0377155298936615886 ] 
dist 85=[-3.4161615441908231806 ,.60592121452063459089] 
dist 86=[-3.6227161692988776510 ,.52872165264963570548] 
dist 87=[-3.7893615297579585441 ,.37438561534057374756] 
dist 88=[-3.9207860092496560026 ,.33553283223216567756] 
dist 89=[-3.9867149572204148856 ,-.04018955359679233021] 
dist 90=[-4.0190867187208341694 ,-.09786872103945716141] 
dist 91=[-4.0233717281499272754 ,-.19087373498492746265] 
dist 92=[-3.8787696155088849874 ,-.21278988183607658973] 
dist 93=[-3.8450992360098391630 ,-.24041190608437104913] 
dist 94=[-3.7966179538755779353 ,-.22486262003614538372] 
dist 95=[-3.7758679220999365673 ,-.18387285250183903767] 
dist 96=[-3.7292757494063159241 ,-.0976222523628582175 ] 
dist 97=[-3.6887790314874594216 ,-.00357990212113337593] 
dist 98=[-3.6785671255945892515 ,.06852599410599854582] 
dist 99=[-3.6659448336001497653 ,.13831260197537726953] 
dist 100=[-1.6436588168047265677 ,.22313285112898426816] 
dist 101=[-1.4743633771773704615 ,.31113774017482188665] 
dist 102=[-1.0721505847778150294 ,.39365835139828785058] 
dist 103=[-1.0328164836894949053 ,.6395420055332633943 ] 
dist 104=[-.95896035434882621491,.98359030931601060892] 
dist 105=[-.94597560311856539935,1.2400565328570397538 ] 
dist 106=[-.82434761685037322292,1.4816995769566870010 ] 
dist 107=[-.80006399228387168863,1.7665738034904291695 ] 
dist 108=[-.76855394462639946063,2.0333963346778707129 ] 
dist 109=[-.8276582347535568206 ,2.2029744131242491197 ] 
dist 110=[-1.0015212483708557356 ,2.3339285707533890713 ] 
dist 111=[-1.2108597340673816905 ,2.4465567692258203472 ] 
dist 112=[-1.5232687518718426879 ,2.5388773691937826840 ] 
dist 113=[-1.8330501609407493380 ,2.5887582201646402657 ] 
dist 114=[-2.0318973153552038532 ,2.6171244459802846784 ] 
dist 115=[-2.1874815432196358496 ,2.6235505293459260894 ] 
dist 116=[-2.3245958614317897435 ,2.5859942751771663860 ] 
dist 117=[-2.4392285567078525340 ,2.6795147653492663697 ] 
dist 118=[-2.5050809619081683356 ,2.7299820505428705739 ] 
dist 119=[-2.5477231061862722187 ,2.7587006852628128437 ] 
dist 120=[-2.5697058433383156951 ,2.7654062625181383228 ] 
dist 121=[-2.5805644419772102591 ,2.7608109815845636057 ] 
dist 122=[-2.5788086213358102034 ,2.7535100477018905924 ] 
dist 123=[-2.5685566653725132795 ,2.7250612168728018355 ] 
dist 124=[-2.5607202108003356682 ,2.7091152549554634140 ] 
dist 125=[-2.5054293846110056630 ,2.6103535306431679761 ] 
dist 126=[-2.4891412998102207373 ,2.5833457228595485530 ] 
dist 127=[-2.4353202299212074502 ,2.5337707716635013568 ] 
dist 128=[-2.4198677065311579720 ,2.5175554263705159937 ] 
dist 129=[-.7499335167378848212 ,.6222506824210604947 ] 
dist 130=[-.90662981402096444933,.49023414947848943844] 
dist 131=[-1.0178575070799574056 ,.48226937601668688461] 
dist 132=[-1.1171718202112240215 ,.3313631361311003154 ] 
dist 133=[-1.2263152797379000704 ,.3154260477964196718 ] 
dist 134=[-1.3263467659461022521 ,.11803940545830011824] 
dist 135=[-1.3892848402285178894 ,.08964267225559591836] 
dist 136=[-1.4371580912746415540 ,.03588464586159358409] 
dist 137=[-1.4770417934338416319 ,.02334364362167233659] 
dist 138=[-1.5087570902673503668 ,-.01289926739497708666] 
dist 139=[-1.5240152207613319232 ,-.01876438457415974266] 
dist 140=[-1.5301250576932624819 ,-.01576336052036731905] 
dist 141=[-1.5295422529017307111 ,0                     ] 
dist 142=[-1.1967808271005016983 ,-.10929609990608580438] 
dist 143=[-1.2004425218489162497 ,-.06172044078007157717] 
dist 144=[-1.1987495976646827304 ,-.00506316307733461186] 
dist 145=[-1.1963305317691789832 ,.05899244997984254575] 
dist 146=[-1.1926795548204452351 ,.1407618936917015923 ] 
dist 147=[-1.1882197181704427856 ,.26813002514693272523] 
dist 148=[-.96537142136148047435,.39685214956739684208] 
dist 149=[-.95955657866158080123,.48402788190483764799] 
dist 150=[-.8158594751852456873 ,.55750341357747373365] 
dist 151=[-.7946205311518559231 ,.63154049040097050333] 
dist 152=[-.7470242697864200571 ,.70031786026472980636] 
dist 153=[-.7325157281759561110 ,.75279990349333851219] 
dist 154=[-.6684991145410943046 ,.80342933679542878563] 
dist 155=[-.6551512671602520930 ,.86481459990532689031] 
dist 156=[-.6233611113880603894 ,.92250763892163490914] 
dist 157=[-.6144062695465903732 ,.95839995618442262167] 
dist 158=[-.21820218628559219033,.98522684202380116205] 
dist 159=[-.17876448334518915694,1.0067338119605122635 ] 
dist 160=[-.09571504226108057321,1.0232102254332752956 ] 
dist 161=[-.07485011183578250563,1.0387910418848751534 ] 
dist 162=[-.00783451341383299317,1.0651091164675170681 ] 
dist 163=[-.21068065433155297234,1.0914861001449300765 ] 
dist 164=[-.41438220285983110087,1.1132920834221234750 ] 
dist 165=[-.55022779944401330287,1.1213634778270330603 ] 
dist 166=[-.66244290604593163336,1.1234765663329388441 ] 
dist 167=[-.77181757049245024969,1.1214896972128216679 ] 
dist 168=[-.87105010208699603533,1.0990803503654927732 ] 
dist 169=[-.94278000015133327918,1.1091574985884911644 ] 
dist 170=[-1.0081299213598033140 ,1.1138908583890703696 ] 
dist 171=[-1.0818940307001451568 ,1.1129447381264987642 ] 
dist 172=[-1.1484619276776546892 ,1.1075592009818938470 ] 
dist 173=[-1.1850863261229113787 ,1.1031287784202816413 ] 
dist 174=[-1.2067982103704346898 ,.82523512959505761686] 
dist 175=[-1.2138401124126444146 ,.81100651337788645295] 
dist 176=[-1.2156425408418599831 ,.75375827040804537791] 
dist 177=[-1.2164403200404823081 ,.74092747965534783491] 
dist 178=[-1.2166507752884311523 ,.71107272639502909198] 
dist 179=[-1.2161093956605139672 ,.70120332433816260136] 
dist 180=[-.5652592212389311523 ,.18557157301184378476] 
dist 181=[-.62161362107913468472,.14910961884015804896] 
dist 182=[-.6763120221057476097 ,.06842515566854487745] 
dist 183=[-.7133505488118131649 ,.05197473110356768535] 
dist 184=[-.7445764548530643212 ,-.04113370545031944319] 
dist 185=[-.78102830944727289577,-.05715063490670075763] 
dist 186=[-.8470433113453180282 ,-.02766247083767607275] 
dist 187=[-.92201234748664476569,.06084293021136790353] 
dist 188=[-.99039336925048972878,.17001335524419440183] 
dist 189=[-1.0301097769953227835 ,.33600481814181582882] 
dist 190=[-1.0564564404198123039 ,.50222345649300256543] 
dist 191=[-1.0714688247247332087 ,.61230032017369916649] 
dist 192=[-1.0806986501400138839 ,.70238239176301995364] 
dist 193=[-1.0839611877101735454 ,.78878640171162323236] 
dist 194=[-1.0834759749912532832 ,.86625628035652189178] 
dist 195=[-1.0720527846174337656 ,.92067491445875593939] 
dist 196=[-.89655702031054791731,.9686507892926243465 ] 
dist 197=[-.89131251840606699307,1.0204013784938824979 ] 
dist 198=[-.80531532175798248946,1.0660788819822268746 ] 
dist 199=[-.79105569753789191047,1.0898123917065844367 ] 
dist 200=[-.75671114015469345543,1.1026041741463132254 ] 
dist 201=[-.74638662930601420129,1.1049830660117029781 ] 
dist 202=[-.72452779353819353911,1.0974379812001270608 ] 
dist 203=[-.72269186997971166106,1.0940290446858906625 ] 
dist 204=[-.65651627854560535691,1.0905743330706921718 ] 
dist 205=[-.6458229544310769455 ,1.0861454171774869967 ] 
dist 206=[-.62303899624357086761,.4243393014375844167 ] 
dist 207=[-.61607507132321747921,.4662109573133746497 ] 
dist 208=[-.58531217370878718172,.5083098521895717142 ] 
dist 209=[-.57835940132801010803,.54580952864736050923] 
dist 210=[-.5584924577358226265 ,.58715274816742337036] 
dist 211=[-.55418179273438238344,.64459604134605711139] 
dist 212=[-.04916416178598318114,.70016422706503890121] 
dist 213=[-.04205933408048639089,.73402220688535947938] 
dist 214=[.05771505466591635121,.75848714923362079786] 
dist 215=[.07150104238201254033,.77655791679064736001] 
dist 216=[.09700559433762648957,.78945826179742670628] 
dist 217=[.10261018770860947854,.79328252013276101761] 
dist 218=[.11645121633009254242,.79360900797972589291] 
dist 219=[.11649730302664159188,.79254586970815536069] 
dist 220=[.11122827100986372367,.75585545169624838316] 
dist 221=[.09733056625586761597,.74816096861494127422] 
dist 222=[.08110586770919331726,.73012059524267549338] 
dist 223=[.0665474795740096526 ,.72351911599363079016] 
dist 224=[.0504161754119819739 ,.69007992372635114992] 
dist 225=[.0279112478563366481 ,.68212750265717840748] 
dist 226=[.0030159879392199013 ,.66227669398335222432] 
dist 227=[-.0226580086167188646 ,.65966170179782259308] 
dist 228=[-.16710417984850316636,.35145857719554809043] 
dist 229=[-.27244132218472039617,.32803710162535181231] 
dist 230=[-.35838414079914381313,.27622236345564156657] 
dist 231=[-.44041439026033524232,.26377468159673012644] 
dist 232=[-.51371949511978723761,.2015105906210279151 ] 
dist 233=[-.56483165677754378056,.1795285876011655360 ] 
dist 234=[-.60951175663796198282,.1300104524813119747 ] 
dist 235=[-.65714014129140969441,.0906843620065101550 ] 
dist 236=[-.70034563933488650163,.00900752985476217599] 
dist 237=[-.72736959988168847311,-.00311221750492579256] 
dist 238=[-.74773371520250428169,-.02254465931283959687] 
dist 239=[-.76435311486802811828,-.02717021186414607386] 
dist 240=[-.77730571524449323893,-.03253679320945842346] 
dist 241=[-.78303193016817020612,-.02880714875592120046] 
dist 242=[-.78456384255781825216,-.01946154230909236810] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 0, 1, 2, 1, 2] 
dist 0=[48.487179088888694506  ,48.487179088888694506  ] 
dist 1=[48.267771902307541371  ,48.649020016129199452  ] 
dist 2=[47.996046321523741176  ,48.799463631363905200  ] 
dist 3=[47.625121614210976276  ,48.973167805879961043  ] 
dist 4=[46.660062603400070361  ,49.119194289818294244  ] 
dist 5=[45.401848687604277966  ,49.159137449834327334  ] 
dist 6=[43.968139774988898703  ,49.128495037374629277  ] 
dist 7=[42.127178052059878100  ,49.075910843972926367  ] 
dist 8=[39.242181144645699136  ,48.799793596942012484  ] 
dist 9=[36.299871575707265229  ,48.700607130035660124  ] 
dist 10=[34.229903817062255778  ,48.305066239595176899  ] 
dist 11=[32.396472442979254649  ,48.214716862054967902  ] 
dist 12=[30.398806538783786411  ,47.008400287528092676  ] 
dist 13=[28.440752368426616909  ,46.110218678649688961  ] 
dist 14=[26.765389151236579411  ,35.033445006763334376  ] 
dist 15=[24.970433180696540972  ,34.696885600742829227  ] 
dist 16=[22.534385132313017376  ,31.051833706361234662  ] 
dist 17=[20.101748156796570613  ,30.351183222673796569  ] 
dist 18=[18.320256125357432903  ,29.600981414796275868  ] 
dist 19=[16.667689505335127603  ,29.458037532329746559  ] 
dist 20=[14.749841983074969741  ,22.693265910366475421  ] 
dist 21=[12.598032986325169857  ,21.841996386395457401  ] 
dist 22=[9.8493937198162774588 ,20.159249618343660625  ] 
dist 23=[7.8871781001351307247 ,19.732148864358927225  ] 
dist 24=[6.1150531226620815458 ,18.274252438749453545  ] 
dist 25=[3.2778428528164886364 ,17.928595509981135576  ] 
dist 26=[1.4124558495891492817 ,17.543694470602170026  ] 
dist 27=[-.10751352116807063259,17.448896794048315581  ] 
dist 28=[-1.5643546087055102509 ,13.664867684509223630  ] 
dist 29=[-4.1817576633385342897 ,11.929489725699181167  ] 
dist 30=[-6.7960987040972056536 ,1.1171363163239285981 ] 
dist 31=[-8.4575918205174175806 ,.73657261189498847475] 
dist 32=[-9.7485901081301994094 ,-2.1459601704890107485 ] 
dist 33=[-10.882313468487647131  ,-2.6347083346760910291 ] 
dist 34=[-11.836957659346620948  ,-3.4111350522587232510 ] 
dist 35=[-12.412447586395297813  ,-3.5864940631562038184 ] 
dist 36=[-12.825231650639944594  ,-4.7360880686574377388 ] 
dist 37=[-13.130091887740445605  ,-4.3912124093521323939 ] 
dist 38=[-13.360018065426178295  ,-3.8973877085049018452 ] 
dist 39=[-13.473325115730523499  ,-3.2016929488432045045 ] 
dist 40=[-13.525830552117668291  ,-2.0510049775198733597 ] 
dist 41=[-13.512281371867151585  ,-.86849586565088071782] 
dist 42=[-13.459447357528463273  ,-.04565737007239899401] 
dist 43=[-13.415612415552445122  ,.67007123895575873053] 
dist 44=[-13.245071086972434511  ,1.4253906526476054520 ] 
dist 45=[-13.172037345443085686  ,2.1473526807120759583 ] 
dist 46=[-7.3442093622922234254 ,2.7300725594030323671 ] 
dist 47=[-6.8145524268427124989 ,3.3219311933060638500 ] 
dist 48=[-6.0789337764476984236 ,4.0804456743334540751 ] 
dist 49=[-5.3446818507526758877 ,4.8123726976163962920 ] 
dist 50=[-4.2581694305152261312 ,5.2981540006211792917 ] 
dist 51=[-3.8375566531916108872 ,5.6963947624211238567 ] 
dist 52=[-3.7273936187365993447 ,6.0789701358847910256 ] 
dist 53=[-3.3295973237702042075 ,6.4218957555511175877 ] 
dist 54=[-3.2417273351165824792 ,6.6618867403189604192 ] 
dist 55=[-3.1063578888845429413 ,6.8722128055801661277 ] 
dist 56=[-3.0684063623607641800 ,7.0967040118702009046 ] 
dist 57=[-1.9493489904407910710 ,7.2965301737495564564 ] 
dist 58=[-1.8306907842056962073 ,7.4084104405970984356 ] 
dist 59=[-1.8129779593872479711 ,7.4770308572685957530 ] 
dist 60=[-1.6196164729290079631 ,7.5042278390205320956 ] 
dist 61=[-1.5831478210784868307 ,7.5023930493089215156 ] 
dist 62=[-1.5204350404422657343 ,3.7086479322129445122 ] 
dist 63=[-1.5042398872715786922 ,4.0027071619460437876 ] 
dist 64=[-1.4484775571284270194 ,4.2451621723556122712 ] 
dist 65=[-1.4316380936807774949 ,4.3806186684058609355 ] 
dist 66=[-1.4012150129351875588 ,4.4644144205303787974 ] 
dist 67=[-1.3906392468103305602 ,4.5006089350518759099 ] 
dist 68=[-1.3408159867413708146 ,4.5175236075911349253 ] 
dist 69=[-1.3248447943210013942 ,4.5243098545553531930 ] 
dist 70=[-1.2924987361674566831 ,4.5254660888370224255 ] 
dist 71=[-1.2800408269951975297 ,4.5198050993109600654 ] 
dist 72=[-1.2145674741374544166 ,4.5106390641995147349 ] 
dist 73=[-1.1981608437431693159 ,4.4977577041993611642 ] 
dist 74=[-1.1442370974764340202 ,4.4799045397883388302 ] 
dist 75=[-1.1331814253753774786 ,4.4647046214826850330 ] 
dist 76=[-.7391775043080547170 ,3.9799110593148931708 ] 
dist 77=[-1.0945154833076963686 ,3.7284297552082700408 ] 
dist 78=[-1.3850334440305916703 ,3.6700473198560990657 ] 
dist 79=[-1.6839028155724744139 ,3.6106481249623034117 ] 
dist 80=[-2.0726105417168025093 ,3.5829065298992902951 ] 
dist 81=[-2.4513091010668721661 ,2.8036752649238400541 ] 
dist 82=[-2.7102386771187505900 ,2.6973295988634639566 ] 
dist 83=[-2.9312728561831281003 ,2.4839638149791381302 ] 
dist 84=[-3.1587121244702648982 ,2.4264509497084967577 ] 
dist 85=[-3.3732190609042282287 ,2.2102780367225635038 ] 
dist 86=[-3.5426478348431180689 ,2.1618734453191397933 ] 
dist 87=[-3.7117935422248506884 ,2.0693781503757528988 ] 
dist 88=[-3.9252122940671081981 ,2.0438173032328453580 ] 
dist 89=[-4.1242232195703043681 ,-.65182919947189934555] 
dist 90=[-4.2358538653945567814 ,-.65593897112415301874] 
dist 91=[-4.3051244121200796261 ,-.62599210725384124977] 
dist 92=[-4.3349950697012061215 ,-.5828775090185829166 ] 
dist 93=[-4.3455242119885727700 ,-.5336086103912452789 ] 
dist 94=[-4.3379582999570056899 ,-.4705109957283026629 ] 
dist 95=[-4.3181809086652368276 ,-.3721572269034454774 ] 
dist 96=[-4.3036645028634944678 ,-.2587080491561501763 ] 
dist 97=[-3.9034614559969062672 ,-.1353330484568856034 ] 
dist 98=[-3.8376544718135833321 ,.0189789253173154997 ] 
dist 99=[-3.6961145972834173563 ,.2559424880902207538 ] 
dist 100=[-3.6514176131825126055 ,.5037609529082261707 ] 
dist 101=[-3.4481337901958603289 ,.7014161639480452682 ] 
dist 102=[-3.4043621097019775805 ,.9003177871726478716 ] 
dist 103=[-3.2767934071420909975 ,1.1531289599670162629 ] 
dist 104=[-3.2542225677133866542 ,1.4215161302400128604 ] 
dist 105=[-1.9839205821762742978 ,1.6826101094954372083 ] 
dist 106=[-1.8714646745153694064 ,1.9886282962879237070 ] 
dist 107=[-1.5649240056986280561 ,2.4363743135922132158 ] 
dist 108=[-.8693812274851108568 ,2.8794897233627679317 ] 
dist 109=[-.86111454780759064542,3.1670239033877710233 ] 
dist 110=[-.60036779297347545798,3.3959338624159270293 ] 
dist 111=[-.56935214064031159437,3.6050041053124859496 ] 
dist 112=[-.49834712321622783543,3.7855579051557594874 ] 
dist 113=[-.48276666680918832993,3.9006213745841700598 ] 
dist 114=[-.38782074659811708379,3.9898544879281096307 ] 
dist 115=[-.3695280237142887467 ,4.0672847016495399146 ] 
dist 116=[-.3347839376965986239 ,4.1260632322092149617 ] 
dist 117=[-.3257947915271124482 ,4.1408337989075637386 ] 
dist 118=[-.1955612144592237886 ,4.1393571503870287176 ] 
dist 119=[-.1772556610687580704 ,4.1079645821456657578 ] 
dist 120=[-.1330384085235682084 ,3.9233442636931761303 ] 
dist 121=[-.1254668945354367217 ,3.2031902689387859222 ] 
dist 122=[-.0600792862405681885 ,3.1523391421832492422 ] 
dist 123=[-.0475906317457288536 ,3.1320955197768119891 ] 
dist 124=[-.0303036575006500478 ,2.0618780299431851650 ] 
dist 125=[-.16656047261345042868,1.9570010828709957040 ] 
dist 126=[-.49221782636917810205,1.6955076430538137033 ] 
dist 127=[-.82001672509991980414,1.6571781384489096038 ] 
dist 128=[-1.1243974356326361629 ,1.2516726539641234747 ] 
dist 129=[-1.3565695903115323796 ,1.1748121548731361359 ] 
dist 130=[-1.5804916866675651584 ,1.0880485240805656998 ] 
dist 131=[-1.8519387660368670242 ,1.0704788073327029213 ] 
dist 132=[-2.1070442962844167900 ,.3953814371482678287 ] 
dist 133=[-2.2657304965363673563 ,.38533242683326919348] 
dist 134=[-2.3842925804803613878 ,.20363896542650304095] 
dist 135=[-2.4792208066713983888 ,.18024700721965251757] 
dist 136=[-2.5531152360703712654 ,.12504181940931450053] 
dist 137=[-2.5877086985411704615 ,.11677870980196417367] 
dist 138=[-2.6035225879502562334 ,.04240420866306312097] 
dist 139=[-2.6031091661003356455 ,.02924734804118040329] 
dist 140=[-1.0278306428568926424 ,.04261239942868362381] 
dist 141=[-1.1590812468241744600 ,.12513088485540349201] 
dist 142=[-1.2623139814560076103 ,.21087636487653519026] 
dist 143=[-1.3544696648367381452 ,.27262903719026891299] 
dist 144=[-1.4325820712156233730 ,.32863436509195501967] 
dist 145=[-1.4797498343051110394 ,.39144415433329279435] 
dist 146=[-1.5133454902061983332 ,.45383294987448201165] 
dist 147=[-1.5372757279668263835 ,.50816066105267872125] 
dist 148=[-1.5543754990823637705 ,.56700445195807767255] 
dist 149=[-1.5607013503001770692 ,.64742258467858005396] 
dist 150=[-1.5603678229925684174 ,.72753472077193408932] 
dist 151=[-1.5578704387453130735 ,.78515887723923380868] 
dist 152=[-1.5369492433452401857 ,.83737067505116830598] 
dist 153=[-1.5298219734526319510 ,.89588116796704260567] 
dist 154=[-1.5026305763675227030 ,.95400198947309941835] 
dist 155=[-1.4958650135602760494 ,1.0046605797220797161 ] 
dist 156=[-1.2019169919802576026 ,1.0595898428846508145 ] 
dist 157=[-1.1832316729350480069 ,1.1347616899844675295 ] 
dist 158=[-1.1360941711945842056 ,1.2068463336174857332 ] 
dist 159=[-1.1231157061396210341 ,1.2494525865284049132 ] 
dist 160=[-1.0397306837250623176 ,1.2786553608995278534 ] 
dist 161=[-1.0212504152813715586 ,1.2972341025071714589 ] 
dist 162=[-.98768388196858459781,1.3086179065201416150 ] 
dist 163=[-.97826107094243577528,1.3409814199955265898 ] 
dist 164=[-.7875626475551944823 ,1.4299136550449342593 ] 
dist 165=[-.7603372019477251517 ,1.4801924304981845330 ] 
dist 166=[-.6962079151453733093 ,1.5118329382174696125 ] 
dist 167=[-.6814780243569357098 ,1.5263554974436503475 ] 
dist 168=[-.5887977248886575978 ,1.5336318304269723097 ] 
dist 169=[-.5703429944249015681 ,1.5363448122554971949 ] 
dist 170=[-.5357765618990795864 ,1.5362438269143440121 ] 
dist 171=[-.5267052932926918521 ,1.5322907789907806504 ] 
dist 172=[-.1633356173735174925 ,1.2862198826542037943 ] 
dist 173=[-.1250692403396220867 ,1.2560887923100522292 ] 
dist 174=[-.39408941768875657298,1.1762150022607060445 ] 
dist 175=[-.57366478393928038692,1.1630995071413390019 ] 
dist 176=[-.7198797411848852495 ,1.0751331961612045142 ] 
dist 177=[-.85893779087707696128,1.0636214123113483805 ] 
dist 178=[-.98286370138449475199,1.0390996350645327596 ] 
dist 179=[-1.0686707748405478458 ,1.0306374627942933475 ] 
dist 180=[-1.1430442457878747849 ,.89280606977972502527] 
dist 181=[-1.2213260995274223833 ,.8869628053416428162 ] 
dist 182=[-1.2918388718076797403 ,.81970369672880737559] 
dist 183=[-1.3351982250478483846 ,.8145520606045650653 ] 
dist 184=[-1.3669944811404844973 ,.82584658086503016924] 
dist 185=[-1.3913486602486200243 ,.83168008214791662442] 
dist 186=[-1.4090680989009640517 ,.83461727328616520656] 
dist 187=[-1.4143790642010003009 ,.8965882065238153622 ] 
dist 188=[-1.4135911743189461077 ,.96991017688464380952] 
dist 189=[-1.4101317162687897933 ,1.0131775750513574527 ] 
dist 190=[-.87169658667644470944,1.0427118162916455765 ] 
dist 191=[-.98581352742066981795,1.0612163209909959266 ] 
dist 192=[-1.0862169010793383755 ,1.0736084171395326340 ] 
dist 193=[-1.1535327738318314590 ,1.0787456633900568426 ] 
dist 194=[-1.2095704297592616397 ,1.0795415871160090330 ] 
dist 195=[-1.2649509579015020976 ,1.0776688182010444877 ] 
dist 196=[-1.3132737946181241307 ,.9762892416233798947 ] 
dist 197=[-1.3411355463433455804 ,.9596542118614320782 ] 
dist 198=[-1.3593763229177495323 ,.9291689225316028533 ] 
dist 199=[-1.3692876990334874319 ,.9204057043808837007 ] 
dist 200=[-1.3730983823003348911 ,.8862308985685272021 ] 
dist 201=[-1.3659399687835019982 ,.8766097061988998293 ] 
dist 202=[-1.2863834739063875738 ,.8571519689114895517 ] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 1, 1, 0, 1] 
dist 0=[43.447784426697239396  ,43.447784426697239396  ] 
dist 1=[42.636494918619942212  ,43.974159712780402002  ] 
dist 2=[41.221614984133062386  ,44.251183742910336442  ] 
dist 3=[39.737004318944837226  ,44.430726606817044329  ] 
dist 4=[38.647169272141188486  ,44.567722773285771237  ] 
dist 5=[37.634940725676934712  ,44.839484527292697028  ] 
dist 6=[36.460074997703113717  ,44.964390434931948009  ] 
dist 7=[35.266106351193916414  ,44.987698405418025735  ] 
dist 8=[34.177385122494170737  ,44.885407973038334825  ] 
dist 9=[32.953344446220467588  ,43.590102161897773582  ] 
dist 10=[31.218540287392987260  ,43.339714767804388962  ] 
dist 11=[29.452353228988723938  ,42.880653116026990346  ] 
dist 12=[28.102776398272078732  ,42.740000464927742210  ] 
dist 13=[26.794347902953170270  ,42.148471127686938960  ] 
dist 14=[25.192300072929288271  ,41.984132892050202727  ] 
dist 15=[23.515103546416409623  ,41.589063872691694166  ] 
dist 16=[21.906156696119825579  ,41.401290738350768601  ] 
dist 17=[20.030997754540347538  ,30.286592604502689857  ] 
dist 18=[17.289637160122566137  ,29.278448993041633048  ] 
dist 19=[14.559211227371597052  ,26.870639061757873868  ] 
dist 20=[12.727678598169598343  ,26.480992079083386365  ] 
dist 21=[11.194601219542460749  ,23.041824176352738988  ] 
dist 22=[9.6181635128099679341 ,22.398719218376479775  ] 
dist 23=[7.1990697248561834004 ,21.541948079952771004  ] 
dist 24=[5.4855742160001009866 ,21.272417118076592987  ] 
dist 25=[3.9538743632957637454 ,16.045900407622358471  ] 
dist 26=[2.2605477611521636050 ,15.374287871081726598  ] 
dist 27=[.58262969929377047531,13.939308782648415198  ] 
dist 28=[-.88804444017481424392,13.586198283315977509  ] 
dist 29=[-2.4973257359325053065 ,12.042503900666524506  ] 
dist 30=[-4.7300567730028656958 ,11.762482309614352180  ] 
dist 31=[-6.8968413115406643846 ,11.111924840086405304  ] 
dist 32=[-8.2428200000017431785 ,10.998593207060950632  ] 
dist 33=[-9.2547655392790813439 ,4.1172001258256761209 ] 
dist 34=[-10.086466158594856027  ,3.4777641767522047655 ] 
dist 35=[-10.754934087038155368  ,2.1012377988679189847 ] 
dist 36=[-11.114198106925748509  ,1.8143376280550410456 ] 
dist 37=[-11.319043372346673308  ,.34272130844692740378] 
dist 38=[-11.369535076454487061  ,.09526714594668775354] 
dist 39=[-11.117441143486201048  ,-.45409348570500444006] 
dist 40=[-11.054191664704104497  ,-.53897214949473990914] 
dist 41=[-11.416743992904735781  ,-1.2135944315301750000 ] 
dist 42=[-11.847989208284918327  ,-1.3318430344183214822 ] 
dist 43=[-12.150726147724547850  ,-1.3402929640794447945 ] 
dist 44=[-12.359682735508993344  ,-1.2042300460663960147 ] 
dist 45=[-12.496579242433137885  ,-.98832061488525197166] 
dist 46=[-12.524459333123611753  ,-.67791061167739203885] 
dist 47=[-12.488225957581493442  ,-.24038665081109424222] 
dist 48=[-12.473349771964180380  ,.48288783052684042241] 
dist 49=[-5.5809874664721635190 ,1.2251063490347861601 ] 
dist 50=[-5.1151120074960315662 ,1.7383527408831132589 ] 
dist 51=[-3.9983947281325197549 ,2.1810488179352752967 ] 
dist 52=[-3.8345786796320826015 ,2.6419963040626300344 ] 
dist 53=[-2.2730739290386991867 ,3.0785900434399868012 ] 
dist 54=[-1.9928323130204985486 ,3.4242391024788287944 ] 
dist 55=[-1.6413839966607294688 ,4.1186213625803613817 ] 
dist 56=[-1.5721329348733664153 ,4.6593823394993771018 ] 
dist 57=[.51413181768731701086,5.0705320555643314903 ] 
dist 58=[.75896289854578166255,5.4119102187891558405 ] 
dist 59=[1.2914474555221362910 ,5.6845395727331908648 ] 
dist 60=[1.3835093835244928632 ,5.8213715464625094852 ] 
dist 61=[1.4924427038734058270 ,5.8916035213486045504 ] 
dist 62=[1.4328861837389857485 ,5.9004040048553086943 ] 
dist 63=[1.3365996044357869353 ,3.5074142883736774925 ] 
dist 64=[1.1953990192046400964 ,3.3941539441259476251 ] 
dist 65=[.95560902443784467106,3.4992682962784661936 ] 
dist 66=[.41213355169895500673,3.6758277333427845810 ] 
dist 67=[-.13709589599880166353,3.8156092254367070703 ] 
dist 68=[-.50741741825250055786,3.9431418770844919520 ] 
dist 69=[-.81751355974442223647,4.0542293292658653861 ] 
dist 70=[-1.1263845080460670884 ,4.1282916629217121805 ] 
dist 71=[-1.4107251091015357298 ,4.1901045735324129453 ] 
dist 72=[-1.6229168280009241513 ,4.2522688356582043140 ] 
dist 73=[-1.8228259210508162452 ,4.3054803635054770296 ] 
dist 74=[-2.0581349237227748210 ,4.3315088409910010641 ] 
dist 75=[-2.2760736325172850586 ,4.3430611595942906630 ] 
dist 76=[-2.4066554858119791101 ,4.3383735642306853980 ] 
dist 77=[-2.4981774902753054293 ,4.3239385707366974337 ] 
dist 78=[-2.5602333566723121004 ,4.3113470471607617955 ] 
dist 79=[-2.6046851007417459052 ,4.2669494733882976797 ] 
dist 80=[-2.6259479813705033964 ,4.2438858594206818152 ] 
dist 81=[-3.0650372714556597244 ,1.6499326984812028656 ] 
dist 82=[-3.6721945531049429540 ,1.6315101744753228784 ] 
dist 83=[-4.1595150756892922227 ,.02040788193814472300] 
dist 84=[-4.6113771257180766038 ,-.01767399180043468342] 
dist 85=[-5.0064433774855402824 ,-.01438673723455944286] 
dist 86=[-5.2670428345278328138 ,.03380981334395497512] 
dist 87=[-5.4793986465672533746 ,.09404937303254989243] 
dist 88=[-5.6819014062728109584 ,.15624718009633978889] 
dist 89=[-5.8529698383311680520 ,.2315465550173500309 ] 
dist 90=[-5.9398330576347944861 ,.34413550872564496764] 
dist 91=[-5.9818586705856564493 ,.47187351587320616619] 
dist 92=[-5.9855542258252582042 ,.60766442817431478764] 
dist 93=[-5.9444172993788575509 ,.77527818645423101515] 
dist 94=[-5.9197858616926706537 ,1.0300535995044693881 ] 
dist 95=[-5.8517600535179340542 ,1.2832602410277498039 ] 
dist 96=[-5.8182020340123811149 ,1.4446264957704250856 ] 
dist 97=[-4.1121382136868521524 ,1.5696011626929351282 ] 
dist 98=[-3.9386349015782076847 ,1.6775764816015967959 ] 
dist 99=[-3.4999708596496723827 ,1.7663758284084641945 ] 
dist 100=[-3.4349493887875097972 ,1.8148256331205485638 ] 
dist 101=[-2.7322244233378226611 ,2.0641066022428010553 ] 
dist 102=[-2.5969235023108308131 ,2.4913461942970860685 ] 
dist 103=[-2.4464607930213030504 ,2.9050657630879242065 ] 
dist 104=[-2.4138547501916916068 ,3.4088007547296886065 ] 
dist 105=[-1.9043317253165223074 ,3.8831156342120981686 ] 
dist 106=[-1.9015334518642527209 ,4.1793969884106546621 ] 
dist 107=[-1.8547466228030091354 ,4.4021472406664093324 ] 
dist 108=[-1.8417621640846008020 ,4.5829409672194473636 ] 
dist 109=[-1.8048867738742351114 ,4.7236016505625950838 ] 
dist 110=[-1.7897563439788610462 ,4.7861475824662097403 ] 
dist 111=[-1.7029360986476769312 ,4.8146999443798002205 ] 
dist 112=[-1.6810995434560543605 ,4.8196676378102077652 ] 
dist 113=[-1.6393455886138733224 ,1.6507520669455286265 ] 
dist 114=[-1.6260321721581292356 ,1.9250247123013312101 ] 
dist 115=[-.96623889366288842056,2.1419130117875435992 ] 
dist 116=[-.89663875408429266279,2.3375656755072708289 ] 
dist 117=[-.72954596912773589179,2.5048884552709094087 ] 
dist 118=[-.70123600399637188737,2.6086757219229410949 ] 
dist 119=[-.46056950927949793763,2.6859485318853566201 ] 
dist 120=[-.41550350527854988769,2.7474230622871754806 ] 
dist 121=[-.35141149810684159513,2.7957796214771630939 ] 
dist 122=[-.33263211630303631336,2.8206802300445202768 ] 
dist 123=[-.06139401011868263897,2.8332390481616227826 ] 
dist 124=[-.22667778515837403067,2.8323141703065198599 ] 
dist 125=[-.41770012948330808201,2.8228348823085534304 ] 
dist 126=[-.69405060450978703612,2.8146743483932872290 ] 
dist 127=[-.96672930011280007566,2.7787977289784674601 ] 
dist 128=[-1.1430987838582851497 ,2.7659422576877224569 ] 
dist 129=[-1.2828853388382271293 ,2.1091156240647746294 ] 
dist 130=[-1.4095162380763767581 ,2.0633067946381378598 ] 
dist 131=[-1.5181792718663461864 ,1.9456633420415481583 ] 
dist 132=[-1.5862357693846848380 ,1.9218547260244968743 ] 
dist 133=[-1.6376775219443932397 ,1.7177427170751259062 ] 
dist 134=[-1.6800163834639346826 ,1.6751932294648708711 ] 
dist 135=[-1.8028109066118883323 ,1.6149576294831576333 ] 
dist 136=[-1.9976506684823284720 ,1.5950507810053430080 ] 
dist 137=[-2.1777705480578177756 ,1.1611254853644515891 ] 
dist 138=[-2.2847200541347258013 ,1.1023679366312598863 ] 
dist 139=[-2.3586639885544159966 ,.97409033289653574406] 
dist 140=[-2.4070287367855599271 ,.93942849448438500601] 
dist 141=[-2.4404747810405636321 ,.78723558234123314446] 
dist 142=[-2.4548552798056158317 ,.75821013539209665785] 
dist 143=[-2.4580413180331233732 ,.68705126877048180367] 
dist 144=[-2.4545252535013726102 ,.67382723339788557511] 
dist 145=[-2.2338437572075720164 ,-.08729093502666017730] 
dist 146=[-2.2018632711306387312 ,.07546117692769027680] 
dist 147=[-2.1079232803745672648 ,.22889206154654242033] 
dist 148=[-2.0936177371609491687 ,.34977408806922363159] 
dist 149=[-1.9465600864083946659 ,.47006090287693340119] 
dist 150=[-1.9343047641816441517 ,.62112167797772678488] 
dist 151=[-1.9105113501037057698 ,.76576589406542913458] 
dist 152=[-1.9011055583320504790 ,.86044067357726744208] 
dist 153=[-1.6720461528570800840 ,.9367315393281451368 ] 
dist 154=[-1.6682617129995462892 ,1.0079897079305967325 ] 
dist 155=[-1.6697707761111837274 ,1.0706609164030916907 ] 
dist 156=[-1.6676551785327562749 ,1.1126764327190734417 ] 
dist 157=[-1.6223920901176192288 ,1.1476768331423033529 ] 
dist 158=[-1.6083127476673797414 ,1.1823524252818392122 ] 
dist 159=[-1.5961456463738884649 ,1.2117295716254386676 ] 
dist 160=[-1.5872059075430371907 ,1.2255778318979978969 ] 
dist 161=[-1.5769933957307534515 ,1.2311937650294438831 ] 
dist 162=[-1.5946505701742288031 ,1.2311755279171572170 ] 
dist 163=[-1.6019201318117545843 ,1.2166060685586075331 ] 
dist 164=[-1.6005634725950210401 ,1.2360072758793836758 ] 
dist 165=[-1.5721007451299453423 ,1.4104289381564480926 ] 
dist 166=[-1.5609964168118089288 ,1.5327470310370840861 ] 
dist 167=[-1.5491943033050763753 ,1.6404477946597691043 ] 
dist 168=[-1.5415077102398583108 ,1.7565184330037330235 ] 
dist 169=[-1.3100846993045844377 ,1.8611077952012169742 ] 
dist 170=[-1.2757551963862696267 ,1.9229732744622146806 ] 
dist 171=[-1.2072599755487889705 ,1.9654606561006533922 ] 
dist 172=[-1.1877790049078605628 ,1.9926853029979809216 ] 
dist 173=[-1.1097482441649209628 ,2.0248413104417995233 ] 
dist 174=[-1.0916626831104062583 ,2.0457346845666367836 ] 
dist 175=[-1.0503196907431357860 ,2.0536871309581381925 ] 
dist 176=[-1.0365412045014167104 ,2.0532763319983754486 ] 
dist 177=[-.63952254361355697551,.69402619583556756465] 
dist 178=[-.76105645046909842444,.6392541365261006768 ] 
dist 179=[-.86973777916612906194,.55293751499756585916] 
dist 180=[-.9457010937295629016 ,.53559112609826495079] 
dist 181=[-1.0123252732679462381 ,.5066741225314794117 ] 
dist 182=[-1.0837272342806352780 ,.49899859363237869661] 
dist 183=[-1.1480198820809597310 ,.34639140477355610877] 
dist 184=[-1.1862623507604506472 ,.32570286596124604276] 
dist 185=[-1.2127932929934624106 ,.27720825599057697734] 
dist 186=[-1.2303271329685248728 ,.26760039634926985067] 
dist 187=[-1.2410652098210266996 ,.20044391852711324744] 
dist 188=[-1.2427913632274316009 ,.18773705124058269596] 
dist 189=[-1.2366528886183654766 ,.16544879957002154144] 
dist 190=[-1.2345577985103663072 ,.16023179871714051163] 
dist 191=[-.91966601523075332419,-.44477484380963673034] 
dist 192=[-.97113568392738665614,-.32882975852260664447] 
dist 193=[-1.0185358172765797783 ,-.22324665019958821811] 
dist 194=[-1.0483809808194355545 ,-.10410471478022775831] 
dist 195=[-1.0711212238036782040 ,.01473247441339229748] 
dist 196=[-1.0901562929285205181 ,.11910021500065548128] 
dist 197=[-1.1053895411119897285 ,.23293374153290481184] 
dist 198=[-1.1129524718167090928 ,.38955939416776675016] 
dist 199=[-1.1163644821654271161 ,.54615448314493785392] 
dist 200=[-1.1150281696166856561 ,.65986675141555108763] 
dist 201=[-1.1110427213705098861 ,.76402651072248818141] 
dist 202=[-1.1070827637458019839 ,.88248916399144198193] 
dist 203=[-1.0955771097384562484 ,1.0011893665687511700 ] 
dist 204=[-1.0896501531801907312 ,1.1062983524521389354 ] 
dist 205=[-1.0540474480350111765 ,1.2216676423125482657 ] 
dist 206=[-1.0444928856539240586 ,1.3813285506007020271 ] 
dist 207=[-1.0223380203246421608 ,1.5352545692717438269 ] 
dist 208=[-1.0140557740663600247 ,1.6277303959331347132 ] 
dist 209=[-.66073017603011509842,1.6929713565348797518 ] 
dist 210=[-.74082825893736555231,1.7381748620364373254 ] 
dist 211=[-.81810208624211576161,1.7714494772010607035 ] 
dist 212=[-.88187680457360958567,1.7890695140231647264 ] 
dist 213=[-.948018381772976906  ,1.7986101851670419840 ] 
dist 214=[-1.0347401689616802257 ,1.7996305623209053303 ] 
dist 215=[-1.1195231684689884857 ,1.7202213930954866154 ] 
dist 216=[-1.1779251619653353370 ,1.7627239599789150316 ] 
dist 217=[-1.2282216435768730365 ,1.7966280522493969069 ] 
dist 218=[-1.2806481477777202066 ,1.8108217282222337025 ] 
dist 219=[-1.3304679775793400379 ,1.8147159586980877023 ] 
dist 220=[-1.3703586201713566665 ,1.8126440852622072255 ] 
dist 221=[-1.4106388773065628488 ,1.7827258894571116664 ] 
dist 222=[-1.4620133549637957722 ,1.7717810354789709239 ] 
dist 223=[-1.5095917204210988600 ,1.7480090890612055695 ] 
dist 224=[-1.5347181657668813975 ,1.7381273795810804928 ] 
dist 225=[-1.5482195982718873713 ,1.1934888876769434505 ] 
dist 226=[-1.5496063456886980149 ,1.1362181733090700397 ] 
dist 227=[-1.5446924752754959911 ,.99629149214278513976] 
dist 228=[-1.5396093039890141535 ,.97250367976540987686] 
dist 229=[-1.5232492221972673075 ,.76179273156945054829] 
dist 230=[-1.5145623402836142624 ,.7215032463522879852 ] 
dist 231=[-1.3794263496628950741 ,.66644348759756333416] 
dist 232=[-1.3564149215929196338 ,.64916065556734054054] 
dist 233=[-1.3007539707262071627 ,.30819412917398795289] 
dist 234=[-1.2834783773177739663 ,.26456075664663940072] 
dist 235=[-1.1913596574167982994 ,.16787516744851588613] 
dist 236=[-1.1564994812955996410 ,.14748997489284028006] 
dist 237=[-1.0682035807956569491 ,.03445898747897038953] 
dist 238=[-1.0049017432842945013 ,.19223904733239031606] 
dist 239=[-1.0216398806745921063 ,.38341505873456107089] 
dist 240=[-1.0267110539987233109 ,.51098716785209391421] 
dist 241=[-1.0272174213299841436 ,.61648463652358480262] 
dist 242=[-1.0257303789307933863 ,.71953948097975030085] 
dist 243=[-.99544877214297824954,.8132192701187666378 ] 
dist 244=[-.98621749994410244999,.88129176894857971564] 
dist 245=[-.9780303266545812229 ,.94368939647515153743] 
dist 246=[-.9722323761471927015 ,1.0147150500036270444 ] 
dist 247=[-.80568707642738060274,1.0791206708362505511 ] 
dist 248=[-.78179093942509129599,1.1150912652165860449 ] 
dist 249=[-.73482682237268357443,1.1371416958898647082 ] 
dist 250=[-.72192397997878319324,1.1459784830576036005 ] 
dist 251=[-.67274458519387347118,1.1496599097738610717 ] 
dist 252=[-.66103334568246534677,1.1511304743472922381 ] 
dist 253=[-.63799869301060436764,1.1512626653156163669 ] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 1, 1, 2, 0, 2] 
dist 0=[40.588515878948467342  ,40.588515878948467342  ] 
dist 1=[40.230643173218123682  ,41.159748482829557715  ] 
dist 2=[39.372748014468231232  ,41.802118519031052049  ] 
dist 3=[38.042280637806399710  ,42.188062473617849726  ] 
dist 4=[35.899036172466847989  ,42.460586422016172637  ] 
dist 5=[33.705393432694754720  ,42.652268770802725780  ] 
dist 6=[32.173544719945305755  ,42.935264248849259023  ] 
dist 7=[30.829316777215583391  ,43.072146735247608993  ] 
dist 8=[29.384708846082087719  ,43.140715044863414691  ] 
dist 9=[27.980813497462767999  ,43.150936377924108502  ] 
dist 10=[26.798918458508646759  ,43.119031921177136829  ] 
dist 11=[25.548957312866379018  ,43.069060787588433892  ] 
dist 12=[23.872713736589618026  ,42.884381944502177899  ] 
dist 13=[22.206278687970985267  ,42.803736026365326831  ] 
dist 14=[20.995239667106873732  ,42.536841637409127486  ] 
dist 15=[19.880135049808529926  ,42.426075840253661790  ] 
dist 16=[18.596598654964560050  ,33.770374572818252758  ] 
dist 17=[17.294054712562606744  ,32.968184884378811786  ] 
dist 18=[16.102566863396602268  ,30.971817783376127993  ] 
dist 19=[14.756360153791781079  ,30.680164801326682119  ] 
dist 20=[12.834737549017727018  ,27.548167606251442866  ] 
dist 21=[10.933960234918626950  ,26.943391790449632350  ] 
dist 22=[9.6709451975367323598 ,26.292960169635818570  ] 
dist 23=[8.6242389026246111705 ,26.160356756131113464  ] 
dist 24=[7.5883386086155551143 ,20.268024705913166856  ] 
dist 25=[6.6292882347852019281 ,19.520803056215635032  ] 
dist 26=[5.8898024235289635229 ,18.047144775805759606  ] 
dist 27=[4.6491993405043344892 ,17.671795168397039055  ] 
dist 28=[2.8901536712304923912 ,16.370288530896450660  ] 
dist 29=[.39582187901304362385,16.077320357296559104  ] 
dist 30=[-2.0515536075498262887 ,15.717774164148026561  ] 
dist 31=[-3.6230795209599978482 ,15.608429225574582706  ] 
dist 32=[-4.8635375803316302717 ,3.8318763736544413352 ] 
dist 33=[-5.9876280259863635620 ,2.8669984024071634025 ] 
dist 34=[-6.9599817298655407398 ,2.7209171523649721648 ] 
dist 35=[-7.5940591183948734390 ,2.5869711281168760882 ] 
dist 36=[-8.1068228539090379530 ,2.5645138993500437979 ] 
dist 37=[-8.5946206594507434959 ,1.9243334564166006788 ] 
dist 38=[-9.0179909726097391384 ,1.8477755662177669508 ] 
dist 39=[-9.2732075168865938183 ,1.6755103070204519654 ] 
dist 40=[-9.4572684894443065142 ,1.6444862040309391291 ] 
dist 41=[-9.5958029451240958426 ,1.4197020155216245932 ] 
dist 42=[-9.6968419862228114451 ,1.3768007859890744816 ] 
dist 43=[-9.9823781773172500255 ,1.3120030527408731442 ] 
dist 44=[-10.338949290197601378  ,1.2938430136404541877 ] 
dist 45=[-10.512803191825471280  ,.93573047349475211753] 
dist 46=[-10.601270443914958707  ,.88647368194515804532] 
dist 47=[-10.616685093866654473  ,.78135717559243789493] 
dist 48=[-6.5275273669636048354 ,.75139519203809257462] 
dist 49=[-6.3805143003407271879 ,.62667987584632331281] 
dist 50=[-6.0000241385416135563 ,.6014492547264366475 ] 
dist 51=[-5.8761587668338808213 ,.53881435878847998187] 
dist 52=[-5.2736514699727375457 ,.5244755539831760481 ] 
dist 53=[-3.9283814972540714309 ,.26212923660142723968] 
dist 54=[-3.7315246394855032270 ,1.0516127172979195892 ] 
dist 55=[-3.6944564304420466379 ,1.5997533367966551516 ] 
dist 56=[-2.0971207530039812452 ,2.0769559107213544611 ] 
dist 57=[-1.9017266836914732884 ,2.5833111460049447206 ] 
dist 58=[-1.5004234466269453954 ,3.0710170610269442255 ] 
dist 59=[-1.3978652635108213700 ,3.4738523344417608449 ] 
dist 60=[-1.0345528526984806088 ,3.8928258710138614886 ] 
dist 61=[-.96142194871348794767,4.4451422327435380947 ] 
dist 62=[-.86053580262843409432,4.9743219927553113203 ] 
dist 63=[-.83676586399300706681,5.3009297598903328906 ] 
dist 64=[1.2160566277569540679 ,5.5428914820391741292 ] 
dist 65=[1.3843480770644271071 ,5.7339657683016576103 ] 
dist 66=[1.7279041260472771117 ,5.8802197854229123824 ] 
dist 67=[1.8053265968737776658 ,5.9431335827607438554 ] 
dist 68=[2.0860936088769335289 ,5.9697501980900123588 ] 
dist 69=[2.1389753241029744662 ,5.9709843379754495345 ] 
dist 70=[2.1693186735295125560 ,5.7897033720101465723 ] 
dist 71=[2.1312848251277797449 ,5.7460540442817771284 ] 
dist 72=[2.0659632516835733560 ,5.6549320047548754135 ] 
dist 73=[1.9757155114589778378 ,5.6213590321244265214 ] 
dist 74=[1.8502231516286958105 ,5.4506716827767068123 ] 
dist 75=[1.6254824628714004798 ,5.4100478339287218710 ] 
dist 76=[1.3525350846287570589 ,5.2732193708259418354 ] 
dist 77=[1.0518411918632433051 ,5.2515534897795921662 ] 
dist 78=[.19407641078127338027,3.6885252909484044071 ] 
dist 79=[-.49821351467431647411,3.6864227313538556038 ] 
dist 80=[-1.0764758295867273707 ,2.7757665527886496262 ] 
dist 81=[-1.6514825502902498914 ,2.7133783395494615053 ] 
dist 82=[-2.1814016047380199403 ,2.0751841143985630809 ] 
dist 83=[-2.5796441959698437609 ,1.9547145597850890482 ] 
dist 84=[-2.9583038144174802664 ,1.8150981933300732352 ] 
dist 85=[-3.4100380658021726598 ,1.7845122333293951434 ] 
dist 86=[-3.8314764583085825107 ,.71171606320131138308] 
dist 87=[-4.0891711528705266813 ,.57920749217294735327] 
dist 88=[-4.2766523046359126333 ,.30476482459681753673] 
dist 89=[-4.4177374972293090824 ,.23380589794447229875] 
dist 90=[-4.5262508401886474153 ,-.02302292508422516073] 
dist 91=[-4.5836761648579693175 ,-.07378307952564813768] 
dist 92=[-4.6147557810028126068 ,-.15735516015852375139] 
dist 93=[-4.6180722449575027871 ,-.1764397421085134624 ] 
dist 94=[-3.1606988154760299770 ,-.25394044078377446005] 
dist 95=[-3.1561904698849110489 ,.25682200980709813821] 
dist 96=[-3.1850885950311464872 ,.77362446449766921485] 
dist 97=[-3.1887362527742777829 ,1.1237182617557116752 ] 
dist 98=[-3.1820427046917758403 ,1.4187578423302857421 ] 
dist 99=[-3.1710790747941938541 ,1.7158292862273153823 ] 
dist 100=[-3.0879722285021531479 ,1.9915025288469156178 ] 
dist 101=[-3.0630257458907945952 ,2.2011393745365494547 ] 
dist 102=[-3.0191564637967519794 ,2.4025845605002701262 ] 
dist 103=[-3.0042057934990632222 ,2.6455674138054687371 ] 
dist 104=[-2.1671392256371108101 ,2.8730773899381485187 ] 
dist 105=[-2.0678896265474639822 ,3.0127665368354392602 ] 
dist 106=[-1.9074678214639637476 ,3.1149049176590155909 ] 
dist 107=[-1.8083131428544779007 ,3.1925362860842585252 ] 
dist 108=[-1.4145542259928512048 ,3.2484997858500318317 ] 
dist 109=[-1.3783870557580130350 ,3.2641547491538417640 ] 
dist 110=[-1.3191186722411560150 ,3.2655127212677078738 ] 
dist 111=[-1.3029964287670193028 ,3.2643967484838244828 ] 
dist 112=[-.18538007283946043828,.20160408677417669654] 
dist 113=[-.1670826147657232509 ,.44947633624341785754] 
dist 114=[.00295985710234128296,.65202149130666377263] 
dist 115=[.03308277816469752750,.84598403620369743326] 
dist 116=[.07147076492428957776,1.0198593014089769571 ] 
dist 117=[.07881579746807027322,1.1422137669021705427 ] 
dist 118=[.2925718088858012422 ,1.2504244054119645346 ] 
dist 119=[.3173833432563334291 ,1.3678420235848298297 ] 
dist 120=[.37173280686773264032,1.4750303902272135445 ] 
dist 121=[.38020153559991959144,1.5424019917925644966 ] 
dist 122=[.43747828371572562137,1.5936189250503496537 ] 
dist 123=[.44603982983699321466,1.6363019365345090523 ] 
dist 124=[.46189391384123457408,1.6703161486700168962 ] 
dist 125=[.46446010665474629264,1.6869188291340919674 ] 
dist 126=[.49980606715243622435,1.6939740798158007721 ] 
dist 127=[.50213322586953511461,1.6930436648293809557 ] 
dist 128=[.49981211410623891962,1.1193595673419171098 ] 
dist 129=[.49057048904640249596,1.0688489103352363321 ] 
dist 130=[.47759541783941753128,.95344398292205857334] 
dist 131=[.46036463847020002135,.92656689511221469994] 
dist 132=[.43670221827247620749,.77398214718702230143] 
dist 133=[.39804492538261740111,.74472494596535719039] 
dist 134=[.28698466513210472079,.68534246434858266869] 
dist 135=[.10761288054165731164,.66915825500117974203] 
dist 136=[-.07313548340143415151,.48321038897078839648] 
dist 137=[-.20676233504764656139,.45529952916051035056] 
dist 138=[-.33158731813319545485,.40994131217706587746] 
dist 139=[-.47720484069640015427,.4030883822626727191 ] 
dist 140=[-.6252354806664344443 ,.38817856246730234298] 
dist 141=[-.75970078730194390742,.38497563865254033911] 
dist 142=[-.91014663320032985663,.28369951994217239354] 
dist 143=[-1.1219866033881458757 ,.27684024590905783029] 
dist 144=[-1.3289200149145387496 ,.18502688064702188321] 
dist 145=[-1.4597791829804008414 ,.1778368767161308471 ] 
dist 146=[-1.5601356054317256642 ,.12916373819058618644] 
dist 147=[-1.6452879620749037280 ,.12005559741905695585] 
dist 148=[-1.7142870373187726925 ,.10380754063004337283] 
dist 149=[-1.7501533637036961731 ,.10001173340280080975] 
dist 150=[-1.7694052091352577979 ,.03722282038018668760] 
dist 151=[-1.7730652116369912578 ,.02874263990387151613] 
dist 152=[-1.7616000099888450468 ,.00921842651232689534] 
dist 153=[-1.7538684714216368420 ,.00563309954513555685] 
dist 154=[-1.7437210718511981213 ,-.01976539469487726490] 
dist 155=[-1.7372949843809747914 ,-.02436041042819363853] 
dist 156=[-1.7098950289727684755 ,-.03230189319623462571] 
dist 157=[-1.7003929121864151105 ,-.03408805436061213297] 
dist 158=[-1.6719279039151722053 ,-.26708248612386822736] 
dist 159=[-1.6602483722264168756 ,-.22523428352320616979] 
dist 160=[-.86674427582065987226,-.1862367653635120489 ] 
dist 161=[-.79586913619530142893,-.04851706327773695442] 
dist 162=[-.6248328246888286084 ,.12250523267646361678] 
dist 163=[-.59925365080149036624,.29484174751911457531] 
dist 164=[-.35424466044329509248,.4550505625558956525 ] 
dist 165=[-.30946925324377727989,.57765516797060982214] 
dist 166=[-.2536756884420686433 ,.69632662682948146551] 
dist 167=[-.24125702101066674692,.84083331527372514358] 
dist 168=[-.14406324501651681112,.97704077482807896337] 
dist 169=[-.13998132169387777916,1.0625788478724655766 ] 
dist 170=[-.12404884617418797163,1.1274695465522901584 ] 
dist 171=[-.13796633541348450973,1.1812452270209418516 ] 
dist 172=[-.15834001186226822456,1.2240839747306875526 ] 
dist 173=[-.19175473397278418541,1.2453099703969743425 ] 
dist 174=[-.22616706598449462329,1.2562491674026531290 ] 
dist 175=[-.25052337601712663294,1.2580196785276850767 ] 
dist 176=[-.27218770114752327856,.67367007826010287128] 
dist 177=[-.29585532729397035586,.70093694865278324787] 
dist 178=[-.31901323781819387243,.72228439345629100109] 
dist 179=[-.33864355022999585776,.73377322871318898697] 
dist 180=[-.35946090555891852386,.74025390524123064148] 
dist 181=[-.38735808385245756837,.74160625464675241282] 
dist 182=[-.41491371405670398297,.73158670972060129059] 
dist 183=[-.4343680883590145342 ,.73139718431449920102] 
dist 184=[-.45162680326260773419,.72130813562767806912] 
dist 185=[-.47041818968034248694,.71788004935731299026] 
dist 186=[-.4887740672196512367 ,.70663504857426179259] 
dist 187=[-.50429481664923177927,.70235433457832554668] 
dist 188=[-.52072501259998863024,.67134380818655326073] 
dist 189=[-.54271231064599250814,.66348185615299613629] 
dist 190=[-.56361395391084086859,.65065975619882454264] 
dist 191=[-.57571031294849180479,.64641098391193005946] 
dist 192=[-.58368410185318872884,.56058597507136222116] 
dist 193=[-.58812782572715960673,.55001536449536832142] 
dist 194=[-.59173681915778534877,.52719247132080059265] 
dist 195=[-.67013511421238880091,.52009058855534355663] 
dist 196=[-.73920098772147203955,.48817228333629427748] 
dist 197=[-.7856721097747749327 ,.4813627709057683249 ] 
dist 198=[-.82454230885783176771,.46217954175664512269] 
dist 199=[-.86326548328978326537,.45852003382573168187] 
dist 200=[-.89713127858749167365,.4097098431542077326 ] 
dist 201=[-.91660944471130716786,.40099557489307721853] 
dist 202=[-.92930352583634284067,.38096409070109093753] 
dist 203=[-.93608299900804898479,.374659101712931536  ] 
dist 204=[-.93856751257838794435,.34530090068513125188] 
dist 205=[-.93815661742103178501,.33892183255138951069] 
dist 206=[-.92868404388555611431,.32462176790973571211] 
dist 207=[-.92726098582748092205,.40291763174352743591] 
dist 208=[-.61675329853719350446,.47359581442118144845] 
dist 209=[-.58687946122435845268,.53874627342427012027] 
dist 210=[-.53290509709818066626,.59541939147437995586] 
dist 211=[-.53241326615698759467,.63225496914526622129] 
dist 212=[-.52733181933675721443,.66164274505838292823] 
dist 213=[-.52576917537320608673,.68858320142429283328] 
dist 214=[-.50119227795523081378,.71185513896043110718] 
dist 215=[-.49629881987922398316,.72659769968542908697] 
dist 216=[-.48038665947080209896,.73792658002270983422] 
dist 217=[-.47804142227262479383,.74757070126835912281] 
dist 218=[-.4394521595773016671 ,.75540133860183616723] 
dist 219=[-.43085238318728945491,.75949050004732190242] 
dist 220=[-.4239418484611907592 ,.76162386319333836221] 
dist 221=[-.42233355999241964828,.76164649952095035554] 
dist 222=[-.33971565375282976385,.30762842376112796438] 
dist 223=[-.42543706310812573184,.39506658636275962948] 
dist 224=[-.51585185388816273384,.48439273534552565229] 
dist 225=[-.5727803781117468452 ,.54286595172795301493] 
dist 226=[-.6161079177877178275 ,.58999535817259761032] 
dist 227=[-.65222895255509865248,.63403453988924360032] 
dist 228=[-.68145490516200877944,.67277309911592451737] 
dist 229=[-.69725883037078630152,.69874169640550783151] 
dist 230=[-.70626160020111130384,.72036031312758872799] 
dist 231=[-.70834057383402755802,.7417340872780814398 ] 
dist 232=[-.68946688401230993079,.75940588531396035383] 
dist 233=[-.68517421840198052812,.76624573301399919408] 
dist 234=[-.68181407573053005768,.76878963081605644641] 
dist 235=[-.67883373277764881561,.76930759135253457604] 
dist 236=[-.67631620850579888202,.74756689195295410246] 
dist 237=[-.67480525151346219037,.74192596419110068667] 
dist 238=[-.67373978694972751384,.73853482778869793994] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 1, 2, 2, 2, 0, 1] 
dist 0=[38.362624332755892189  ,38.362624332755892189  ] 
dist 1=[37.985720414559478935  ,38.703236921857572260  ] 
dist 2=[36.821133999848021484  ,39.215035456300950664  ] 
dist 3=[35.606772432733818017  ,39.589773987945632046  ] 
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dist 31=[-.80610741637794210993,12.168195369531761573  ] 
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dist 49=[-5.9749352250254512425 ,-1.2795876286244208242 ] 
dist 50=[-5.7837676344207762302 ,-1.2130531336213322824 ] 
dist 51=[-4.0956694957282204996 ,-1.1380272719289475238 ] 
dist 52=[-3.3206482335480454687 ,-1.0796456522563830498 ] 
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dist 61=[-.90727666601666111731,3.4268117413585023894 ] 
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dist 88=[-2.8901384372825160279 ,1.0054383207542473057 ] 
dist 89=[-3.1602712529135404383 ,.9786937204131765923 ] 
dist 90=[-3.3673150628134418506 ,.96903460383723181658] 
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dist 99=[-2.1406199649665883429 ,1.2066397822825360712 ] 
dist 100=[-2.0031886389848321240 ,1.4251921653571207334 ] 
dist 101=[-1.9712151793526773162 ,1.5872222250326066298 ] 
dist 102=[-1.9401095742297739780 ,1.7388801040651193308 ] 
dist 103=[-1.9263940299593886628 ,1.9160313478284676244 ] 
dist 104=[-1.6645035291865848739 ,2.0788926587255496887 ] 
dist 105=[-1.6411026971396521750 ,2.1735131788053202035 ] 
dist 106=[-1.5835010302395852618 ,2.2362469240785355620 ] 
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dist 111=[-1.3911336208145426877 ,2.3072451733065765401 ] 
dist 112=[-1.1033073469282971668 ,.82748198482352569406] 
dist 113=[-1.1029248317517061120 ,1.0708973271881330906 ] 
dist 114=[-1.1011651568124967863 ,1.2663249450637834897 ] 
dist 115=[-.86609108661444211079,1.4477327430139243511 ] 
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dist 117=[-.73550328405522485449,1.7118116156966187554 ] 
dist 118=[-.68067609015237440512,1.7981613760371590876 ] 
dist 119=[-.67182965469348589176,1.8815055041058205603 ] 
dist 120=[-.56759566006729948008,1.9543013733542387916 ] 
dist 121=[-.54829908166003494031,1.9985354432146531607 ] 
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dist 123=[-.50626483103624344749,2.0538865381630911759 ] 
dist 124=[-.48135942981623206492,2.0702129319528937849 ] 
dist 125=[-.47444448103916173266,2.0735726710778742021 ] 
dist 126=[-.47181246183985498586,2.0693370572844217224 ] 
dist 127=[-.47424873343400904391,2.0644307111704886526 ] 
dist 128=[-.47826880122717035566,1.2403369647441428765 ] 
dist 129=[-.48196343803475938464,1.1677086164198640859 ] 
dist 130=[-.48608392639712902333,.99542653819333580203] 
dist 131=[-.49181821637692358775,.96461541356523252771] 
dist 132=[-.49812775748199317217,.72288491022240876548] 
dist 133=[-.50455279053214389222,.6778172455183911376 ] 
dist 134=[-.51229534643710868825,.60774385358745142332] 
dist 135=[-.52387438499665976001,.58926649411060788466] 
dist 136=[-.53589994797832930101,.31095166346588629226] 
dist 137=[-.54543068627284194827,.27813438772425837036] 
dist 138=[-.5549938455293371323 ,.24407061687224929377] 
dist 139=[-.56715567629310780833,.31782967365516727329] 
dist 140=[-.69345391039151431985,.39743418506951165211] 
dist 141=[-.80608286933433260869,.47665951965980156329] 
dist 142=[-.92960681787091694412,.57078242767852515123] 
dist 143=[-1.1004885033336548368 ,.76047095222842701086] 
dist 144=[-1.2660065785533321077 ,.9575396273595214419 ] 
dist 145=[-1.3681187882208792692 ,1.0831616451899013089 ] 
dist 146=[-1.4434583512431045691 ,1.1805241979184350825 ] 
dist 147=[-1.5020898207242154241 ,1.2647906189362534851 ] 
dist 148=[-1.5480265915985942134 ,1.3341799971233106207 ] 
dist 149=[-1.5726824190787403942 ,1.3721558960439606434 ] 
dist 150=[-1.5865013831950170129 ,1.3943667337248317196 ] 
dist 151=[-1.5891683586277691664 ,1.4008198940065111019 ] 
dist 152=[-1.5758862813065557022 ,1.4016671082206649195 ] 
dist 153=[-1.5805492878761321811 ,1.4015021125948817834 ] 
dist 154=[-1.5793663856547089907 ,1.4005236913035154760 ] 
dist 155=[-1.5771303659892070543 ,1.3981350144344834394 ] 
dist 156=[-1.5251721902471521123 ,1.3949922440784651792 ] 
dist 157=[-1.5101518806202977335 ,1.3910097962210632105 ] 
dist 158=[-1.4980752832646222137 ,1.3856400880930612500 ] 
dist 159=[-1.4895191068344888068 ,1.3802065878750850910 ] 
dist 160=[-.48159241031423428414,.06410801811050534243] 
dist 161=[-.40776903122447351424,.23433075798230842935] 
dist 162=[-.23201848380671813137,.37419751196800154758] 
dist 163=[-.206832563696523757  ,.50937361972476336502] 
dist 164=[.03416185961539977474,.6313301718609738239 ] 
dist 165=[.07682589562340389091,.71842425746359582405] 
dist 166=[.12979089199425568722,.79674259429940347107] 
dist 167=[.1385945059568693054 ,.88366794296014040577] 
dist 168=[.44504662397138039114,.96369329730214856623] 
dist 169=[.48006602423426997077,1.0144657293725185119 ] 
dist 170=[.5566140276294472467 ,1.0535838677491785984 ] 
dist 171=[.56810754120801745688,1.0870803662778472209 ] 
dist 172=[.64699360099062358064,1.1144356214653466358 ] 
dist 173=[.65853992598204653723,1.1290349968631556007 ] 
dist 174=[.67870361449346579906,1.1370956413164531350 ] 
dist 175=[.67918497161506745086,1.1383445547962482616 ] 
dist 176=[.65858355420092056383,.77247581481830325324] 
dist 177=[.63592773124080461472,.74057770582332960024] 
dist 178=[.60742003222107684278,.70860555885639958255] 
dist 179=[.52984686843161873873,.70700897907245736474] 
dist 180=[.44414405587549418897,.70074688454837265831] 
dist 181=[.36394886287054530309,.6978823085901040749 ] 
dist 182=[.27236256693295846619,.68751727358817493362] 
dist 183=[.14118468400941198607,.68379747777065508155] 
dist 184=[.00771579228104429867,.65186996904718027755] 
dist 185=[-.09301696187872925529,.64489941738260303436] 
dist 186=[-.18914388961972220363,.62628322261476747107] 
dist 187=[-.30422676042795935795,.62067725832808384993] 
dist 188=[-.42280602959225202782,.62058386435605954918] 
dist 189=[-.53289152136348760591,.6266528990988407448 ] 
dist 190=[-.65793709683468417078,.63485474910824694995] 
dist 191=[-.83623937215430691881,.64811760337125615813] 
dist 192=[-1.0107608998236529847 ,.66170863045354282249] 
dist 193=[-1.1207132973753032142 ,.67122011417459416502] 
dist 194=[-1.2045121975779298667 ,.67956804079269827782] 
dist 195=[-1.2746253338414199945 ,.68851406860350673364] 
dist 196=[-1.3312902539007304242 ,.69716190126487344967] 
dist 197=[-1.3614022865069346739 ,.70431908401729092242] 
dist 198=[-1.3778523205269105618 ,.71175540797988494603] 
dist 199=[-1.3814544496737994477 ,.72151661611297274854] 
dist 200=[-1.3249967728462632148 ,.73105190147799140273] 
dist 201=[-1.3145262846529641415 ,.7375860694860810162 ] 
dist 202=[-1.3071364734960268205 ,.74317099306077002157] 
dist 203=[-1.3020082374300323618 ,.74891704294770436693] 
dist 204=[-1.2760023517666000265 ,.7543215831133859522 ] 
dist 205=[-1.2695046454745014114 ,.75854277590042194524] 
dist 206=[-1.2577651951731742592 ,.76270020882504599181] 
dist 207=[-1.2526802585792559840 ,.76784881358934957548] 
dist 208=[-.53880279646470728924,.77240589329428013881] 
dist 209=[-.47784364511271126759,.7742020976525115295 ] 
dist 210=[-.33983917260666951176,.77431180507540857807] 
dist 211=[-.31993406892721551484,.77215237424769206684] 
dist 212=[-.18643752967481724979,.76865214216591113532] 
dist 213=[-.16233095495567735982,.76553172955193033044] 
dist 214=[-.11845440926146732442,.75758730971575473097] 
dist 215=[-.10843581065786977226,.75366759950896387726] 
dist 216=[.03215674801904686729,.73073865500416372269] 
dist 217=[.05165937142686314428,.72434775782526110706] 
dist 218=[.02960278826383305390,.70962880101113960893] 
dist 219=[-.04926854422732055561,.70406441603462476483] 
dist 220=[-.13455348352120632992,.67529677668245459886] 
dist 221=[-.2197703872981059642 ,.66834053671559130104] 
dist 222=[-.32132272338641189154,.64390245791424847097] 
dist 223=[-.47181752578607145311,.71629109848949042374] 
dist 224=[-.62106193411729503933,.79684396066164262989] 
dist 225=[-.71762247990666249514,.84734982293276491864] 
dist 226=[-.7941452645209994135 ,.88556203164143094355] 
dist 227=[-.86339947015278806173,.91703693665076383638] 
dist 228=[-.92273124615306481364,.94180616223629875481] 
dist 229=[-.95964370063414649863,.95324860121974359014] 
dist 230=[-.98722293542846357614,.95813404644635370722] 
dist 231=[-1.0092959912554173105 ,.95782839480112709667] 
dist 232=[-1.0266199625656213308 ,.94285411352804064409] 
dist 233=[-1.0352409261899467621 ,.93777361318752050373] 
dist 234=[-1.0391378859592471917 ,.92335752357890099923] 
dist 235=[-1.0379490503332624624 ,.91689031329724417916] 
dist 236=[-1.0326885805599771674 ,.88024978547934582694] 
dist 237=[-1.0294588105048602527 ,.87076826424529001496] 
dist 238=[-1.0138281796567933711 ,.85122550481413179225] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 2, 2, 0, 0, 2] 
dist 0=[54.273102851306641726  ,54.273102851306641726  ] 
dist 1=[53.720736890171567192  ,54.570490271000543883  ] 
dist 2=[52.614955424923602617  ,54.658240190703461208  ] 
dist 3=[51.353434736995788840  ,54.642684953224570580  ] 
dist 4=[50.178947963662304580  ,54.527713374391120621  ] 
dist 5=[48.840625893404277164  ,54.395708878034976153  ] 
dist 6=[46.924552400533707806  ,54.311887141927854373  ] 
dist 7=[44.777589298335199695  ,54.246696279347085861  ] 
dist 8=[42.516968425459393617  ,53.686369477623219200  ] 
dist 9=[39.733804362121519194  ,49.912280269091158637  ] 
dist 10=[35.499619906304350566  ,49.282512711417495375  ] 
dist 11=[31.231516634847306734  ,48.312933869478065203  ] 
dist 12=[28.312778622101791313  ,48.024840306800739811  ] 
dist 13=[25.815333434904672362  ,47.434826011306193542  ] 
dist 14=[23.229751581119454821  ,46.483120750496864214  ] 
dist 15=[20.775821236107685139  ,41.861277863546559821  ] 
dist 16=[18.804014385292440788  ,38.822791589977060035  ] 
dist 17=[16.801037198148573263  ,32.059840544602093614  ] 
dist 18=[14.222204535773314870  ,31.584651885046796063  ] 
dist 19=[11.709648534334995931  ,29.920367661844253695  ] 
dist 20=[9.9711876900850243508 ,29.527469297771659096  ] 
dist 21=[8.4597797695381364484 ,29.010129438964331179  ] 
dist 22=[6.8539060488968753780 ,28.828920778302471188  ] 
dist 23=[5.3005762694473668361 ,12.331898769427286674  ] 
dist 24=[3.9986428024853031440 ,12.011829394666892301  ] 
dist 25=[2.6237868634303927021 ,7.5598947183169308956 ] 
dist 26=[.29601303710701791849,7.4627552247541629498 ] 
dist 27=[-2.0649139402822606322 ,5.2981149507316452535 ] 
dist 28=[-3.8268411022975407644 ,5.0466367580110223834 ] 
dist 29=[-5.4928207609689565871 ,4.4429935147134444938 ] 
dist 30=[-7.4704658107965962056 ,3.9973553002941152963 ] 
dist 31=[-9.3170817211727317118 ,2.6704296864142563902 ] 
dist 32=[-10.459721594491536277  ,2.0763628674531989893 ] 
dist 33=[-11.309100412767266065  ,-5.0247925265183463168 ] 
dist 34=[-11.984469356498269573  ,-5.0890506757473765537 ] 
dist 35=[-12.517828262811114581  ,-5.5905919737705470237 ] 
dist 36=[-12.799903281830833849  ,-5.6200493742345535501 ] 
dist 37=[-12.952886617113854931  ,-5.5486921164540218380 ] 
dist 38=[-12.974274575974682830  ,-5.3240391853895148133 ] 
dist 39=[-8.6761888561188212381 ,-5.0201878718227263099 ] 
dist 40=[-8.4643393930144658346 ,-4.6324384632327448459 ] 
dist 41=[-8.4029662461737836402 ,-4.1099133500725867486 ] 
dist 42=[-8.3729670143735826964 ,-3.2679147339408119511 ] 
dist 43=[-8.2444606950314848340 ,-2.4082565593440360205 ] 
dist 44=[-8.2079982089488534274 ,-1.8151146332948250015 ] 
dist 45=[-7.8024028939640828757 ,-1.3038769245678266810 ] 
dist 46=[-7.7034474790576476116 ,-.7709447817377252112 ] 
dist 47=[-7.5842550669797876578 ,-.2647703572600658744 ] 
dist 48=[-7.5307815795290202088 ,.5959265617020084637 ] 
dist 49=[-5.5739487500117381562 ,2.3650035695958603071 ] 
dist 50=[-5.3418253981524253464 ,3.5238126482783474116 ] 
dist 51=[-4.8828781582047266030 ,4.4578570514393856464 ] 
dist 52=[-4.7224028615200270978 ,5.3297349904959606201 ] 
dist 53=[-3.4988116641849307358 ,6.0950905459013645354 ] 
dist 54=[-2.8656252825498041576 ,6.6038907795602034665 ] 
dist 55=[-.2505582996180776537 ,7.0221098708235122298 ] 
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