8 phat 4 dirichlet min maxes function [0, 1, 0, 0, 2, 0, 2] 
dist 0=[119.90642161335291989   ,119.90642161335291989   ] 
dist 1=[115.87111855163874218   ,122.72297567498273481   ] 
dist 2=[110.20571988480691825   ,123.54789460988886255   ] 
dist 3=[102.37584262598627559   ,123.40967861680869570   ] 
dist 4=[89.729752858864969374  ,122.82349665223512382   ] 
dist 5=[76.638762640939315669  ,117.94631876846785521   ] 
dist 6=[67.033396814567711801  ,116.33762320235003301   ] 
dist 7=[58.278331808372025606  ,108.16218872497100279   ] 
dist 8=[48.553544387591653193  ,95.587532004891047889  ] 
dist 9=[39.074189288090031310  ,80.708910576054271495  ] 
dist 10=[31.281734601452471976  ,76.400717312054671343  ] 
dist 11=[23.280333543647314156  ,71.610260749409311313  ] 
dist 12=[12.946078275350969919  ,69.909659215135825299  ] 
dist 13=[3.1376409531606402214 ,54.523658317021748510  ] 
dist 14=[-2.7768912061451536305 ,52.621431521870127373  ] 
dist 15=[-6.9865590222503121437 ,47.830471548880626302  ] 
dist 16=[-10.003253960556295023  ,43.016316158652854901  ] 
dist 17=[-17.296002245988315328  ,5.6171862830977096609 ] 
dist 18=[-22.339930602996039873  ,2.0373524941392288491 ] 
dist 19=[-26.279106852135889449  ,-4.7198836760749228020 ] 
dist 20=[-29.707069917355596027  ,-6.1496827915326517400 ] 
dist 21=[-32.357600941292448148  ,-7.8152544982423479906 ] 
dist 22=[-33.207476293406453187  ,-5.9996512398405878513 ] 
dist 23=[-33.392893499826566910  ,-4.2482165772805465456 ] 
dist 24=[-33.388356483342370021  ,-2.2233168737382007414 ] 
dist 25=[-29.039382009868481373  ,-.25826951558244269784] 
dist 26=[-28.234742622706714667  ,1.6162750624769956970 ] 
dist 27=[-27.719730439259289620  ,4.3220202945865817543 ] 
dist 28=[-26.740057972124644477  ,7.4326051964435316543 ] 
dist 29=[-6.6933951745770440498 ,10.469748839174801385  ] 
dist 30=[-4.2986397993890844226 ,12.891952511386992103  ] 
dist 31=[1.1878646716952743072 ,15.282319630275120785  ] 
dist 32=[2.1858295364986750156 ,18.202593585643916412  ] 
dist 33=[6.2533612327482812390 ,20.807200035945047901  ] 
dist 34=[5.4248444991115422959 ,21.946788073190697174  ] 
dist 35=[4.2071878091073567225 ,22.447713404064243618  ] 
dist 36=[2.1871578955916064362 ,22.510338423138593233  ] 
dist 37=[.11709792384898313687,20.406634747939590335  ] 
dist 38=[-1.2995844850701407430 ,19.770797113425802579  ] 
dist 39=[-2.4717591775196595801 ,19.321199237962182852  ] 
dist 40=[-3.5732621577601313627 ,19.029057361068912791  ] 
dist 41=[-4.5111882018009290676 ,14.861799974398466172  ] 
dist 42=[-5.0341851037728432715 ,14.300379011964805075  ] 
dist 43=[-5.3395565957130239014 ,13.372331846116969684  ] 
dist 44=[-6.1466483839967088722 ,13.048962035664018296  ] 
dist 45=[-8.7598962486983341695 ,6.1289956143673131902 ] 
dist 46=[-10.401196057626635834  ,5.2868772801752396359 ] 
dist 47=[-11.613388612466856403  ,3.4036411469063168906 ] 
dist 48=[-12.525234818495081594  ,2.9101284434335860142 ] 
dist 49=[-13.170198812803135368  ,.75892379155084136153] 
dist 50=[-13.323433002264712257  ,.3538351513487825597 ] 
dist 51=[-13.543042346292300071  ,-.46278603036996405806] 
dist 52=[-13.651069910539105006  ,-.65869362276063326215] 
dist 53=[-11.722082469174691649  ,-.31899513859324837119] 
dist 54=[-11.314265099102073109  ,.01128972362421359510] 
dist 55=[-10.587825077919351452  ,.29277063599214097996] 
dist 56=[-10.346195252673325677  ,.57198017514298609148] 
dist 57=[-5.6273429101632040113 ,2.6680421028436510055 ] 
dist 58=[-5.1062472969990849348 ,4.8162073174222713485 ] 
dist 59=[-3.5952574462502827405 ,6.5745897974317171291 ] 
dist 60=[-2.5329414546521994547 ,8.2087149228957448564 ] 
dist 61=[-.39428616444551594012,9.6225800225768758858 ] 
dist 62=[-.14345025949563255526,10.467208496467727442  ] 
dist 63=[.43891269363124117298,10.940961285003605322  ] 
dist 64=[.52798453487500040431,11.022327249792705789  ] 
dist 65=[.648918102250943266  ,2.3293190240090169941 ] 
dist 66=[.5296950172332725414 ,2.3645287122554687353 ] 
dist 67=[.36998401376146107748,2.3588052640476090976 ] 
dist 68=[.1181688540634458198 ,2.3579339161915110360 ] 
dist 69=[-.13728781091480336358,2.0073166415620884653 ] 
dist 70=[-.31147940578347655942,1.9165960193013852274 ] 
dist 71=[-.4556822282020302194 ,1.8636406450689203285 ] 
dist 72=[-.60156921994512938235,1.8502860831844166982 ] 
dist 73=[-.73944186409186133651,1.4309888933771899601 ] 
dist 74=[-.8121796541536041265 ,1.3700173481493017573 ] 
dist 75=[-.85207028655098080481,1.2820935429630138137 ] 
dist 76=[-.85962712455548531741,1.2479396605874555220 ] 
dist 77=[-.87251863238836111387,.42384547720811185653] 
dist 78=[-1.0228951519250275986 ,.31613275505051969954] 
dist 79=[-1.1272548390539621313 ,.07327783897023062164] 
dist 80=[-1.1933060399460379306 ,.02181967870104244229] 
dist 81=[-1.2331893002600846055 ,-.24622977932796455036] 
dist 82=[-1.2378079270858750730 ,-.19745344401281187655] 
dist 83=[-1.2780313955678766479 ,-.13434434914356640999] 
dist 84=[-1.2927271738180495106 ,-.03696740636583950374] 
dist 85=[-1.0521722938319654401 ,.06127157130474248068] 
dist 86=[-1.0105103288384862339 ,.12780809928482785967] 
dist 87=[-.94706423705617784519,.18249489380867185245] 
dist 88=[-.92319883537712726088,.23370746306945038701] 
dist 89=[-.35727429646764203728,.2774979736226030621 ] 
dist 90=[-.34215956942827821176,.3443686212584402532 ] 
dist 91=[-.31884577289176998231,.52234197182010729669] 
dist 92=[-.31042376757051875845,.68633755189081121787] 
dist 93=[-.10684184814948213629,.8248232733973143183 ] 
dist 94=[-.07959172511226606102,.90153571185081514251] 
dist 95=[-.01828364392563054030,.94619568622653093233] 
dist 96=[-.00505865860963815931,.95744613742467808851] 
dist 97=[.00576020371680731720,.29139521729778939668] 
dist 98=[-.00479418567113744403,.29310137037874859739] 
dist 99=[-.01871803198177943152,.28732681977854766701] 
dist 100=[-.04047600801127233349,.28587379728942220083] 
dist 101=[-.06251810527113980067,.24268749167424470854] 
dist 102=[-.07757173684165963200,.24177916732866728409] 
dist 103=[-.09007492431745452497,.23151275485979096826] 
dist 104=[-.1019975737398329179 ,.22976450223149221209] 
dist 105=[-.1123384049973528176 ,.18500324140817911788] 
dist 106=[-.11856531204813281704,.17436914157502527924] 
dist 107=[-.12285056652330061695,.16592746706761461075] 
dist 108=[-.12548746819616458911,.1634002722000651399 ] 
dist 109=[-.12886237192985081177,.03163052685686431238] 
dist 110=[-.14638395313047733918,.02036750246573962853] 
dist 111=[-.15779423034424431339,-.00540951306304398087] 
dist 112=[-.16353541367591491425,-.01014051227509892841] 
dist 113=[-.1657957781709071845 ,-.03963976674192406236] 
dist 114=[-.16560869647027647701,-.0443547249638988688 ] 
dist 115=[-.16005400602755518721,-.05303591803680064362] 
dist 116=[-.15863478598375757954,-.05455699010649071149] 
dist 117=[-.13100800419752689853,-.05625987319162251441] 
dist 118=[-.12421976568089845273,-.05538913993136363494] 
dist 119=[-.11781077719405428931,-.05316158693967306162] 
dist 120=[-.11482409777438358663,-.02389630236245967250] 
dist 121=[-.04386918260148934949,.01030177093551358931] 
dist 122=[-.04144380659372090376,.03329085313036883882] 
dist 123=[-.03975602091323120575,.05202193776138572919] 
dist 124=[-.03937471017484584403,.06931635023839865689] 
dist 125=[-.00404339778928036009,.08395469293415525374] 
dist 126=[7.80491425672304820080e-05,.09239139034787629386] 
dist 127=[.00963452528733185332,.09747646318570777709] 
dist 128=[.01105876427298097643,.09865283164043737924] 
dist 129=[.02210488610730340653,.03848070664533189409] 
dist 130=[.02373097485018172254,.03854455617039076548] 
dist 131=[.02662695720911836521,.03734433314640845762] 
dist 132=[.02704600465983760937,.03717010226475905805] 
dist 133=[.02847555328884719218,.03041665828417150448] 
dist 134=[.02537321696354238189,.02877503426559321688] 
dist 135=[.01985627188773426995,.02765944033017560215] 
dist 136=[.01146914204507033203,.02740077375156638598] 
dist 137=[.00303788753542326065,.02310466765754909347] 
dist 138=[-.00265456174306276377,.02208575022698538138] 
dist 139=[-.00732057357008233013,.02053770379143586325] 
dist 140=[-.01167700580831693743,.01997918276382886230] 
dist 141=[-.01539944340113363443,.00662793244759071557] 
dist 142=[-.01754858258598976266,.00484837314787863762] 
dist 143=[-.01891713468014955812,.00086728328068216543] 
dist 144=[-.01954077955811043376,3.05540153012894065910e-06] 
dist 145=[-.01975434712609864721,-.00432319025465881040] 
dist 146=[-.02081703441906092309,-.00507688195794887526] 
dist 147=[-.02180873923115386967,-.00631345670073985131] 
dist 148=[-.02205850373258262349,-.00656321939249666684] 
dist 149=[-.01610447392653001643,-.00663663084195164516] 
dist 150=[-.01540388356756252141,-.00650083587146114458] 
dist 151=[-.01434318792041502493,-.00620670865172162371] 
dist 152=[-.01395674892322825463,-.00266317030475200387] 
dist 153=[-.00515957298857854858,.00239391229776039207] 
dist 154=[-.00488035501538260573,.00578530663114644670] 
dist 155=[-.00464536751626865248,.00854083758734901625] 
dist 156=[-.00456010442087191966,.01107333473589158198] 
dist 157=[-.00063096131188873085,.01320966181146821302] 
dist 158=[-.00016143080593910278,.01439224887828870860] 
dist 159=[.00092906434919619076,.01508084730850918059] 
dist 160=[.00109547669126728536,.01525423385103067287] 
dist 161=[.00237119557900189222,.00466206727412974465] 
dist 162=[.00256044120658858890,.00465642327452849066] 
dist 163=[.00291299602360226269,.00448297534213699204] 
dist 164=[.00296443969694716363,.00445704161721390533] 
dist 165=[.00300802768000886489,.00369245822494874734] 
dist 166=[.00278681826561064683,.00367335164040781288] 
dist 167=[.00208457426066132680,.00351814273282367143] 
dist 168=[.00102329686640474951,.00348247601718896727] 
dist 169=[-4.16166641415931204370e-05,.00284225977371030449] 
dist 170=[-.00075832273720572874,.00268861242545617638] 
dist 171=[-.00134350408552330001,.00253999365617507656] 
dist 172=[-.00188622682683386332,.00247401984967981352] 
dist 173=[-.00234759004871208754,.00060128466814162606] 
dist 174=[-.00260975068246457872,.00040876427491248353] 
dist 175=[-.00277137291221616926,-2.51329881110724194590e-05] 
dist 176=[-.00283357166333704832,-.00011296092378772952] 
dist 177=[-.00284013222928223684,-.00059107957970207643] 
dist 178=[-.00282583897523134972,-.00067143536814008011] 
dist 179=[-.00271210553930797619,-.00080622479636650387] 
dist 180=[-.00268112834431370364,-.00083179274688804836] 
dist 181=[-.00220833064731144033,-.00083772603909172107] 
dist 182=[-.00209348392969399086,-.00081890204117685577] 
dist 183=[-.00197018582847105859,-.00055733371144724810] 
dist 184=[-.00190779574411156591,-4.34595420877246000000e-05] 
dist 185=[-.00070567935008256302,.00047157358372807910] 
dist 186=[-.00061098320744073569,.00081736391283845031] 
dist 187=[-.00058047573487725695,.00109881546294189560] 
dist 188=[-.00057445595915818347,.00135839339626279647] 
dist 189=[-.00013956583336704416,.00157806199034089622] 
dist 190=[-9.54881394426492426970e-05,.00170105398342607661] 
dist 191=[-2.54309565135946378390e-05,.00178000492330555826] 
dist 192=[-7.82397522101726216100e-06,.00179921216345538179] 
dist 193=[.00031586851967936199,.00058701035956481929] 
dist 194=[.00033976967839942276,.00058529428978601879] 
dist 195=[.00038354612835235828,.00056288105165545320] 
dist 196=[.00039017495994657407,.00055817407467103261] 
dist 197=[.00039374964024890865,.00045672868491333711] 
dist 198=[.00036296761177441503,.00044796957189182827] 
dist 199=[.00027531095663599677,.00043211447076610149] 
dist 200=[.00014319241882437881,.00042432081712799486] 
dist 201=[1.07203373013912537450e-05,.00036299232056893592] 
dist 202=[-7.83424389940914988880e-05,.00034727115229357204] 
dist 203=[-.00015097397654464191,.00032080198865230873] 
dist 204=[-.00021820574230263155,.00031227420456640479] 
dist 205=[-.00027528036072867474,.00013008195677912439] 
dist 206=[-.00030758293634800959,.00010803663294219319] 
dist 207=[-.00032733464605480883,6.03497369386016648690e-05] 
dist 208=[-.00033457630302714241,4.74314419153158049030e-05] 
dist 209=[-.00033542351308474057,-1.23296821373527638860e-06] 
dist 210=[-.00034964785066352903,-1.10105108052232414650e-05] 
dist 211=[-.00036475715634272011,-2.53916071320141682630e-05] 
dist 212=[-.00036854389426672714,-2.89930294240174600590e-05] 
dist 213=[-.00027345844374991998,-2.89621817570307342040e-05] 
dist 214=[-.00026228990510355343,-2.37655952568742015450e-05] 
dist 215=[-.00024161353601107635,-1.39046076027717922400e-05] 
dist 216=[-.00023522582156051015,1.06650733620156048170e-05] 
dist 217=[-.00011819304909674851,8.95815429100691669220e-05] 
dist 218=[-.00010551173334758359,.00014247968414272480] 
dist 219=[-6.88272838044930122800e-05,.00018544983608258623] 
dist 220=[-6.66600497080296362210e-05,.00022494531075431688] 
dist 221=[-2.51730719346495939590e-05,.00025828029973971866] 
dist 222=[-2.02798067572477563160e-05,.00027678894595042609] 
dist 223=[-9.53368809616235989170e-06,.00028774853741983402] 
dist 224=[-6.81434909780607836160e-06,.00029057398194270784] 
dist 225=[4.48472950682384024260e-06,6.47092902320589646290e-05] 
dist 226=[6.62934321717381731070e-06,7.01119886379768713700e-05] 
dist 227=[1.00484661923995124950e-05,7.33320667480223408800e-05] 
dist 228=[1.08231246050402259780e-05,7.43257005851250343860e-05] 
dist 229=[1.10900572668159025400e-05,7.41046595615270609380e-05] 
dist 230=[1.00507115939959176100e-05,7.35306262980079874990e-05] 
dist 231=[7.98712163813306632090e-06,7.06422096295227115300e-05] 
dist 232=[-4.32837662146132628480e-06,6.94043403216912073610e-05] 
dist 233=[-1.93629288774179394950e-05,5.87373739747221859080e-05] 
dist 234=[-2.94603615886156110980e-05,5.60569870428599309600e-05] 
dist 235=[-3.76845143041484197190e-05,5.18270568733411353150e-05] 
dist 236=[-4.52809166109716376160e-05,5.03830986908687006530e-05] 
dist 237=[-5.17191132870837532230e-05,1.65297825701316867430e-05] 
dist 238=[-5.53444345113167472400e-05,1.24231731289034307060e-05] 
dist 239=[-5.75373797169502482330e-05,8.10295006951605740540e-06] 
dist 240=[-5.82881329819388714260e-05,6.93163287168066296720e-06] 
dist 241=[-5.83191611856439575880e-05,2.55073095785990421760e-06] 
dist 242=[-5.77515211282759722860e-05,1.62615376186434356450e-06] 
dist 243=[-5.64959895845015370340e-05,3.43677135977797231770e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 1, 0, 1, 2] 
dist 0=[124.92697273212506884   ,124.92697273212506884   ] 
dist 1=[122.96847962009754922   ,126.51953294783662902   ] 
dist 2=[119.11516442428168943   ,128.90720407440180740   ] 
dist 3=[112.73733646587693980   ,130.95604693934352316   ] 
dist 4=[100.74619945589032400   ,131.20659745415293149   ] 
dist 5=[87.995569427324919376  ,130.56837612274036888   ] 
dist 6=[78.595667682496634708  ,129.75262956860995651   ] 
dist 7=[69.994348646014608217  ,109.52914354439950769   ] 
dist 8=[60.401427349663858213  ,106.30638551179325157   ] 
dist 9=[51.035160188982708867  ,96.608112360476641232  ] 
dist 10=[43.320006395929566669  ,95.195834278481605033  ] 
dist 11=[35.384686558787331112  ,74.356017269544944866  ] 
dist 12=[25.116555486046434618  ,70.017163959655725163  ] 
dist 13=[15.275075861393716012  ,65.904761187860217604  ] 
dist 14=[7.9884305848783876841 ,65.067691633030388314  ] 
dist 15=[-2.3129976700061518702 ,15.963314443647225113  ] 
dist 16=[-8.4159984594523173657 ,10.249787566347250730  ] 
dist 17=[-12.633474565335822760  ,-.77583565791178695094] 
dist 18=[-15.423676971764560293  ,-1.6295509296519611911 ] 
dist 19=[-21.286977208345581462  ,-1.8503979347742350001 ] 
dist 20=[-25.570732248449041007  ,-.94154126283323711513] 
dist 21=[-28.436688597636793285  ,.21965218046381591131] 
dist 22=[-30.090056817588485678  ,1.1146745832602179529 ] 
dist 23=[-30.995094122012544815  ,1.9056341511530948321 ] 
dist 24=[-31.082742596544222501  ,2.6680493097602335207 ] 
dist 25=[-30.461332996112556870  ,3.2813786264166296134 ] 
dist 26=[-30.094499095572008321  ,3.4875595890199431459 ] 
dist 27=[-25.884702236430046335  ,3.5339735487893880786 ] 
dist 28=[-24.786293367996257772  ,3.5241145846233035644 ] 
dist 29=[-23.291842151996883468  ,3.5758293220447598275 ] 
dist 30=[-22.676775882300794082  ,5.4572121633929596424 ] 
dist 31=[-8.0215177945864285046 ,7.1441727503770035003 ] 
dist 32=[-6.1406748429004644480 ,8.0608871937653294462 ] 
dist 33=[-1.8859009598740309521 ,10.974977244393168378  ] 
dist 34=[-1.1811406024750773681 ,14.799318929761592413  ] 
dist 35=[-.88812503556130314835,18.035826840205396588  ] 
dist 36=[-.83932053890757640515,19.819388594997175678  ] 
dist 37=[.78741362414131960491,20.846611449003240409  ] 
dist 38=[.97414460305831286563,21.080187799687952154  ] 
dist 39=[.50642635071370247339,7.4628735235976763704 ] 
dist 40=[-1.1316196630084688055 ,7.4396022065539374874 ] 
dist 41=[-2.5214865480566521300 ,7.3069232887103328471 ] 
dist 42=[-3.8895431786385643648 ,7.1972116168646047315 ] 
dist 43=[-5.1009885761532451276 ,6.4480137513652020700 ] 
dist 44=[-5.8702349770607851290 ,6.2433573520367004686 ] 
dist 45=[-6.4467526540346390287 ,5.7289631067469736250 ] 
dist 46=[-6.8943458569445452013 ,5.5348789590229072146 ] 
dist 47=[-7.2147383045710919077 ,3.0772467826647753813 ] 
dist 48=[-7.2867394885134134810 ,2.6821096881940878276 ] 
dist 49=[-7.2416873689554071335 ,1.8466671555836131616 ] 
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dist 211=[-.00023567540229633132,9.11931462904289959430e-05] 
dist 212=[-.00022432632558548151,8.67574755628352470820e-05] 
dist 213=[-.00018173215272630736,8.37259902506665683080e-05] 
dist 214=[-.00011784881464964221,8.27392282661991818000e-05] 
dist 215=[-.00011207868051277377,8.24498403690272274920e-05] 
dist 216=[-.00011113765944635494,8.23992687098670913900e-05] 
dist 217=[-.00010679847059993470,8.25133431156173624120e-05] 
dist 218=[-.00010476375278540953,8.28783345050233333670e-05] 
dist 219=[-8.92317127311920807620e-05,8.33673602282512682360e-05] 
dist 220=[-8.52898841643793111390e-05,8.48845357270238077430e-05] 
dist 221=[-7.85043359912928305940e-05,9.04093303970460481670e-05] 
dist 222=[-7.63857675747648106060e-05,9.22396929846246808670e-05] 
dist 223=[-2.74336123192642471800e-05,9.24109951148936933340e-05] 
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dist 225=[-1.31289443533561362960e-05,8.95234276852086055010e-05] 
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dist 228=[-2.58021718817615049000e-06,7.81401905259900856520e-05] 
dist 229=[-5.24381798643835346730e-07,7.01384600508706431540e-05] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 0, 0, 1, 2] 
dist 0=[121.48472300963908044   ,121.48472300963908044   ] 
dist 1=[120.48870186632970404   ,121.67745072854902148   ] 
dist 2=[116.53225478221588410   ,122.43854236151375823   ] 
dist 3=[109.72428286917075049   ,123.72990017012669733   ] 
dist 4=[97.400526539193432801  ,126.01644827703844580   ] 
dist 5=[84.367483932788360080  ,128.11032024910397409   ] 
dist 6=[74.736723429246427354  ,128.64058085870703527   ] 
dist 7=[65.901045926318842200  ,124.98556873432292437   ] 
dist 8=[56.011222987605092511  ,114.51720228924114032   ] 
dist 9=[46.333495495942878009  ,105.46305219308251786   ] 
dist 10=[38.325580541070686185  ,102.13496162274766484   ] 
dist 11=[30.056494166521102258  ,92.287919700307832053  ] 
dist 12=[19.312920737094549369  ,90.873725692594894987  ] 
dist 13=[9.0557479938592646735 ,70.239661098887522165  ] 
dist 14=[2.7162733130265715174 ,65.978926075697333417  ] 
dist 15=[-1.9823073517769707454 ,61.935641419200200702  ] 
dist 16=[-5.7003518394195550995 ,61.167212963585137122  ] 
dist 17=[-8.5973971116029436450 ,13.601801169524256360  ] 
dist 18=[-10.020341941397788625  ,8.0880858939375850159 ] 
dist 19=[-10.726086774692397716  ,-4.4865701446360472561 ] 
dist 20=[-14.343891156957955607  ,-6.1297160690380532166 ] 
dist 21=[-21.221574415222586036  ,-4.3428529946921327314 ] 
dist 22=[-25.218601644723228703  ,-2.9770246248449150240 ] 
dist 23=[-27.833620536132739804  ,-1.7453896950063479868 ] 
dist 24=[-29.222329435490606412  ,-.47621548826611119327] 
dist 25=[-29.901533794096116730  ,.6412138144607892047 ] 
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dist 27=[-29.223075846102894626  ,1.6559463255539237513 ] 
dist 28=[-28.826362401370642333  ,1.7517768681711535996 ] 
dist 29=[-24.825783704419939373  ,.74774755441001433201] 
dist 30=[-23.785976666640798378  ,1.5677692715785959179 ] 
dist 31=[-22.260991167703069399  ,2.1488428226658390147 ] 
dist 32=[-21.683980593435482629  ,2.5486727563689507463 ] 
dist 33=[-7.7570758609220729459 ,2.8401049216109787259 ] 
dist 34=[-5.9178134377028718115 ,7.1126323002710556541 ] 
dist 35=[-1.7767475301216603928 ,11.157921654698122248  ] 
dist 36=[-.9064753580192369479 ,14.873589024917885343  ] 
dist 37=[1.4217059909371862897 ,18.007155668798350543  ] 
dist 38=[.99875922863130939153,19.741345990310747872  ] 
dist 39=[.60467806128415163477,20.750923298265874081  ] 
dist 40=[.16505828775346003532,21.004923915246418225  ] 
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dist 44=[-1.1929054720678981187 ,6.3440798847948665610 ] 
dist 45=[-1.4852880160373789608 ,5.2927484182017059035 ] 
dist 46=[-1.6310819626836789337 ,5.0436147219561755781 ] 
dist 47=[-1.7059427274351278088 ,4.8069296498479950956 ] 
dist 48=[-1.7163630216399794815 ,4.7283745602770534541 ] 
dist 49=[-1.6137557291904406720 ,1.1118707574576032703 ] 
dist 50=[-1.5749904852772703530 ,.67128951106597616781] 
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dist 59=[-3.6118328759295712387 ,.96565622900320736489] 
dist 60=[-3.5712471170325158796 ,.97939207884017869154] 
dist 61=[-2.9694310539902296142 ,.42385792566146017315] 
dist 62=[-2.8209665767728247104 ,.46244259998870427902] 
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dist 65=[-1.0218714118980933366 ,.57065216565605922322] 
dist 66=[-.89034355708025455399,1.0456132207671896232 ] 
dist 67=[-.60510367993603704805,1.4327033615365053622 ] 
dist 68=[-.52618744533264055295,1.7904426865084126890 ] 
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dist 72=[-.11300662808839066144,2.4069948982403040925 ] 
dist 73=[-.17391919343417054678,.78485738093697659752] 
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dist 90=[-.41176849510886812797,.1902918206439551117 ] 
dist 91=[-.39467982866423406572,.20037629429258966265] 
dist 92=[-.3902547878538661248 ,.20291791556052409888] 
dist 93=[-.31970195446944241183,.15108834493665862666] 
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dist 99=[.00441127020569542875,.19863947876576224876] 
dist 100=[.00805750349187427679,.21367876513114926249] 
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dist 102=[-.03417576381620190912,.24615529111115358747] 
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dist 104=[-.06146246374594338389,.26114739280861607378] 
dist 105=[-.07281339757338328251,.1049251390236529249 ] 
dist 106=[-.07943673962270113873,.10442262182043230846] 
dist 107=[-.08373643293184501326,.10129259694084956603] 
dist 108=[-.08586513968076338697,.09939713885738274913] 
dist 109=[-.08675662142961678786,.08604608566893536628] 
dist 110=[-.08621219634415328126,.08251812134291653964] 
dist 111=[-.08465301767015318347,.07611599368229566665] 
dist 112=[-.08351024029253841297,.07415754591174769665] 
dist 113=[-.07590229688453881714,.02901105250740022509] 
dist 114=[-.07383974605377651203,.02274117219718553407] 
dist 115=[-.06743297116174252743,.00889251392879229266] 
dist 116=[-.06563153484735893049,.00570941519144615825] 
dist 117=[-.04245121472616147687,.00905122949392909309] 
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dist 187=[-1.04199459326266000000e-05,.00080325983298048134] 
dist 188=[-5.59128633805596799850e-06,.00081279850853230851] 
dist 189=[.00015602696044822381,.00031722144551469616] 
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dist 193=[.00011723976019629885,.00024507804749691974] 
dist 194=[9.83751062130505237130e-05,.00023145412300309567] 
dist 195=[7.46081173688877829200e-05,.00022102411885397120] 
dist 196=[3.85655424946433126220e-05,.00021801870065701859] 
dist 197=[2.36232164329214230680e-06,2.39716335549795619110e-05] 
dist 198=[-3.20340914496292409500e-05,1.00957570637894872450e-05] 
dist 199=[-7.03013964244476193410e-05,-1.52569035030092620980e-05] 
dist 200=[-.00010573809984437345,-1.93074525055015819560e-05] 
dist 201=[-.00013582870971259331,-4.91490194733421294930e-05] 
dist 202=[-.00015286970871428851,-5.36448821862005884530e-05] 
dist 203=[-.00016330241739583586,-6.22394929451127298630e-05] 
dist 204=[-.00016715537523061798,-6.34883878943807246170e-05] 
dist 205=[-.00016752913568879790,-6.55998780202425129850e-05] 
dist 206=[-.00016663974550955518,-6.43506815937361354920e-05] 
dist 207=[-.00016015275170446979,-6.14451190749638961600e-05] 
dist 208=[-.00015809178216818365,-5.55974904169719983640e-05] 
dist 209=[-.00013141661259191272,-4.84582119589336781500e-05] 
dist 210=[-.00012486446742855274,-4.04238492495358661470e-05] 
dist 211=[-.00011703351028247522,-3.03587964351495033530e-05] 
dist 212=[-.00011347355946174672,-1.51564883765223003620e-05] 
dist 213=[-3.62954919855761057140e-05,2.03572407229069475460e-05] 
dist 214=[-2.64137911573131214030e-05,4.75841124736606921180e-05] 
dist 215=[-4.34880994550271664460e-06,6.96898918211244512690e-05] 
dist 216=[4.68740536389346089690e-07,8.99877632242284025220e-05] 
dist 217=[2.07703793035224136490e-05,.00010710390996249929] 
dist 218=[2.26343572363420016140e-05,.00011657607543810194] 
dist 219=[2.60775071134053762720e-05,.00012208861921112803] 
dist 220=[2.66485212572759894730e-05,.00012347849434767259] 
dist 221=[2.69792389277010674870e-05,4.18005979275634312320e-05] 
dist 222=[2.61058470527196030840e-05,4.15932012935109183490e-05] 
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dist 224=[2.11618679744622630520e-05,3.95109196281239444110e-05] 
dist 225=[1.72644064655779397140e-05,3.30402241090483493150e-05] 
dist 226=[1.29486316088786332830e-05,3.14373108355178367250e-05] 
dist 227=[7.58593759551703532390e-06,2.94366522235087475110e-05] 
dist 228=[-4.68587707913429684780e-07,2.85635157677735052900e-05] 
dist 229=[-8.53304598666654471820e-06,1.13818235437678286280e-05] 
dist 230=[-1.39352362698565426400e-05,9.99718135986167410540e-06] 
dist 231=[-1.83191336108679691190e-05,7.10164470929538704040e-06] 
dist 232=[-2.23403531653033624120e-05,6.31534940795815878220e-06] 
dist 233=[-2.57279560855870555240e-05,3.39244955407660942660e-06] 
dist 234=[-2.75959898373385725670e-05,2.74767771550570910470e-06] 
dist 235=[-2.86739370013149669700e-05,1.90392909820778056850e-06] 
dist 236=[-2.89243634304493700070e-05,1.66844896158419944270e-06] 
dist 237=[-2.29383185541312896280e-05,1.60846537600867408640e-06] 
dist 238=[-2.27973702731194976170e-05,1.73330171692656959360e-06] 
dist 239=[-2.18153840518796286160e-05,2.01430778232426328490e-06] 
dist 240=[-2.15656396450873059840e-05,2.57448648731063401730e-06] 
dist 241=[-1.76662183315297077590e-05,3.25689502958961207280e-06] 
dist 242=[-1.67278187573048971430e-05,4.02326711668178982050e-06] 
dist 243=[-1.57404222913223452150e-05,4.98249540909538367700e-06] 
dist 244=[-1.52529337529167648610e-05,6.43069769067598911220e-06] 
dist 245=[-5.43162692249322664980e-06,7.88345949961135453730e-06] 
dist 246=[-4.67963366368134420690e-06,8.86081882225726839510e-06] 
dist 247=[-3.07684134088776841070e-06,9.65846758309352614270e-06] 
dist 248=[-2.64055105168392044600e-06,1.08791637549628474310e-05] 
dist 249=[-9.98271364194923787620e-07,1.26098482150245174760e-05] 
dist 250=[-6.53650805418352873220e-07,1.35748114122929900680e-05] 
dist 251=[-1.52046448647873347730e-07,1.41584994028402241650e-05] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 0, 2, 2, 0, 2] 
dist 0=[107.14631439554822290   ,107.14631439554822290   ] 
dist 1=[100.84916035869055310   ,110.53843621018170341   ] 
dist 2=[94.048400068402583714  ,112.37463582234626729   ] 
dist 3=[88.646493752841660983  ,112.73328230178098354   ] 
dist 4=[83.312845903332233859  ,111.94227915166269453   ] 
dist 5=[76.768584353645723617  ,111.24188384683212678   ] 
dist 6=[70.017528091202700386  ,110.28909191411441613   ] 
dist 7=[63.848560271401035162  ,109.58655264512987826   ] 
dist 8=[56.950602654143749738  ,106.41601475011397065   ] 
dist 9=[47.277479410416648993  ,82.349774180623106706  ] 
dist 10=[37.697098462125818326  ,73.143209701948769710  ] 
dist 11=[31.165059563827577039  ,71.764332865056495718  ] 
dist 12=[25.615149133236724223  ,60.288195072233359763  ] 
dist 13=[19.955054025032082447  ,55.050370554782617766  ] 
dist 14=[14.658592794492866290  ,47.262589471634644309  ] 
dist 15=[10.560163793560658903  ,46.438361373395931712  ] 
dist 16=[6.5552526467386405059 ,21.392997496291304388  ] 
dist 17=[-.38428382238139845776,12.914922113815208708  ] 
dist 18=[-6.9158252154101589325 ,6.3362022348819268011 ] 
dist 19=[-13.116899209488480787  ,5.4134002263986047311 ] 
dist 20=[-18.335943076008884674  ,3.3951743795650672707 ] 
dist 21=[-21.292367827645793879  ,2.9657633011585750848 ] 
dist 22=[-23.134643885657412559  ,.4746565486548799794 ] 
dist 23=[-23.927121957672042384  ,-.00634488173650212504] 
dist 24=[-24.175014182718423097  ,-.90111037453333294764] 
dist 25=[-24.080274083863302550  ,-1.1260454057299906345 ] 
dist 26=[-23.365109037376764520  ,-4.6180734443180607540 ] 
dist 27=[-22.953581987420784151  ,-2.8515509485429875011 ] 
dist 28=[-19.850501812072345449  ,-.05191090337710080779] 
dist 29=[-19.046325928306082627  ,2.6336921160714299381 ] 
dist 30=[-17.616551064531797558  ,4.6836191459294784421 ] 
dist 31=[-17.179767945700511277  ,6.6170545475763835208 ] 
dist 32=[-8.3051769989431440571 ,8.8492469661914779200 ] 
dist 33=[-7.6042336434213083294 ,10.837717001097866610  ] 
dist 34=[-4.8092784520709724224 ,11.806163103003125139  ] 
dist 35=[-4.1577871736275314394 ,13.972030762762169486  ] 
dist 36=[-1.6771348298562183850 ,16.401960813241764219  ] 
dist 37=[-1.1738029632679882729 ,17.792812163824177726  ] 
dist 38=[-.33046575635564908174,18.606917663064861463  ] 
dist 39=[-.13477924242997126236,18.783217190811281189  ] 
dist 40=[3.1981345269849051956 ,11.114278960952004444  ] 
dist 41=[3.0828527039107176907 ,6.9293030337164570612 ] 
dist 42=[1.1961319473050392768 ,6.8700425786667676640 ] 
dist 43=[-.45774908711774328099,6.8004114670347785891 ] 
dist 44=[-2.1021109156993739928 ,6.5260004882003796994 ] 
dist 45=[-3.5703755378502838120 ,6.3847585246211838423 ] 
dist 46=[-4.5265650188780107539 ,5.4866154346028382202 ] 
dist 47=[-5.2718938858191408865 ,5.2571607912569795982 ] 
dist 48=[-5.9047495094668254597 ,4.8175164192488824508 ] 
dist 49=[-6.3949298863335861763 ,4.6810666134382209050 ] 
dist 50=[-6.5743319518013631226 ,1.9614950232210490565 ] 
dist 51=[-6.6146080608861075476 ,1.5750770493746688870 ] 
dist 52=[-6.5555807934899119139 ,.74123217905976401783] 
dist 53=[-5.9432120337726693118 ,.51820295199039094832] 
dist 54=[-5.8886115905315617613 ,-.30872703470963853208] 
dist 55=[-5.9654239423350088487 ,-.47362553628688201559] 
dist 56=[-5.9717839945781477122 ,-.68996965554478425742] 
dist 57=[-5.8901677273645870299 ,.43698401549846446363] 
dist 58=[-1.7042194849734689607 ,1.6381448554881561438 ] 
dist 59=[-.71512380239208943852,2.6200136557417948306 ] 
dist 60=[-.65456493170255545483,3.5291707525715908942 ] 
dist 61=[-.64820587562049753467,4.2984126453175183032 ] 
dist 62=[-.510057776115169983  ,4.7251261809070747580 ] 
dist 63=[-.47865683698694162153,4.9737739213333850556 ] 
dist 64=[-.4525257651374345812 ,5.0364343702401292808 ] 
dist 65=[-.44600723962824044395,1.5554876178277008636 ] 
dist 66=[-.03237654194462293739,1.5901181424444849524 ] 
dist 67=[.01606097390921654977,1.5957721381222151445 ] 
dist 68=[.1274498870374240251 ,1.5938159886112124602 ] 
dist 69=[.14421088116848100831,1.3854623522788561786 ] 
dist 70=[.2702166271486285238 ,1.3276862650770389271 ] 
dist 71=[.28884574830157437126,1.2885479989235231398 ] 
dist 72=[.32030269461966845271,1.2693525379214916564 ] 
dist 73=[.17517477342882750222,.34768137807447591676] 
dist 74=[-.07861718288880498597,.34030960865173914374] 
dist 75=[-.28970609482280930745,.3367248310435955621 ] 
dist 76=[-.49147567363417214721,.32141620961340145072] 
dist 77=[-.66681593985558212487,.31550990326693248433] 
dist 78=[-.773047212517230275  ,.26499162992555545866] 
dist 79=[-.84696458160067373064,.25258112376896749873] 
dist 80=[-.89410209565830922047,.23286594851796519283] 
dist 81=[-.92155896341278798527,.22629039273403526082] 
dist 82=[-.92529054518724442873,.08162697437921969996] 
dist 83=[-.90458645849279181468,.06316717499560362797] 
dist 84=[-.89789506661295643383,.02273997321917428134] 
dist 85=[-.75274362586142722962,.01284687873916114605] 
dist 86=[-.71587633184295007964,-.02889901385911499097] 
dist 87=[-.6818727426802637332 ,-.03672234080902712122] 
dist 88=[-.66475189151064613339,-.04823816891531096820] 
dist 89=[-.2647228049761045188 ,.04568584347551283283] 
dist 90=[-.14664416659830553717,.17608085638891196757] 
dist 91=[-.06856526886105149751,.28266915307301086112] 
dist 92=[-.06508274406332935242,.38154799169627631969] 
dist 93=[-.06424494234203430856,.46694438664802730399] 
dist 94=[-.05823933679000083410,.51761551021706412584] 
dist 95=[-.06104091202231626263,.54613253210720083434] 
dist 96=[-.0644069841003402097 ,.55282770104338293542] 
dist 97=[-.06931504046629894359,.21597746522090055526] 
dist 98=[-.07412079651495518530,.21769186238199351986] 
dist 99=[-.07707951414400747860,.21386015717518448192] 
dist 100=[-.07917603752406215466,.21330553058220187233] 
dist 101=[-.08055992092080412967,.17794611085981575565] 
dist 102=[-.08132356724790674266,.16903132042007881869] 
dist 103=[-.08095780443427329799,.16349951462409075578] 
dist 104=[-.07968627626929225898,.16215876682808966194] 
dist 105=[-.07882007728665842455,.12788008821856203366] 
dist 106=[-.07411385598936100328,.1271914690035697976 ] 
dist 107=[-.07321588219177860198,.12583887286890409748] 
dist 108=[-.08383454672173581994,.12169945597145805101] 
dist 109=[-.10662494901538025215,.11942519420820668198] 
dist 110=[-.12007149026379958185,.10551306815816389528] 
dist 111=[-.12899736137136549651,.10190901295350118255] 
dist 112=[-.13384525188665563621,.09274229100301412096] 
dist 113=[-.13622878057700902225,.08933233218348727877] 
dist 114=[-.13595085345337551795,.04995725209982140208] 
dist 115=[-.13323309857204551234,.04348281761080938786] 
dist 116=[-.13103657648478755845,.03032119674195801469] 
dist 117=[-.1160813745579990929 ,.02683343786267669343] 
dist 118=[-.1119748980898268386 ,.01445835016700790988] 
dist 119=[-.10352467410471884017,.01155034994300746292] 
dist 120=[-.08894179614843338610,.01026240803880798038] 
dist 121=[-.04767808200670171264,.01256227611808597654] 
dist 122=[-.02149299821035708145,.03224723336160257535] 
dist 123=[-.00555067669152803006,.04825855634645527576] 
dist 124=[-.00519590477974797952,.06299346068818789384] 
dist 125=[-.00514480427475315775,.07542984959330819133] 
dist 126=[-.00399846508520705206,.08231624706639877262] 
dist 127=[-.00373998458306498070,.08632435448927100530] 
dist 128=[-.00353244043774373041,.08733395146503311528] 
dist 129=[-.00348929798390935199,.02644169955627620148] 
dist 130=[-9.10473809509989034900e-05,.02650518507784489457] 
dist 131=[.00030368533982828327,.02578432198421213134] 
dist 132=[.00121036789778408324,.02562538080898845175] 
dist 133=[.00134518736941079587,.02126827826532181457] 
dist 134=[.00236307727208465778,.02018763826240967729] 
dist 135=[.00251309754960515218,.01931926744240541932] 
dist 136=[.00275344475134094545,.01898190202675420438] 
dist 137=[.00129594465063148762,.00313046677743053483] 
dist 138=[-.00276231350776452350,.00271457615217757812] 
dist 139=[-.00608938541914141306,.00268137876740057873] 
dist 140=[-.00919620337614214408,.00254666984070521450] 
dist 141=[-.01185083755677285593,.00250032072565267298] 
dist 142=[-.01338284780279124351,.00207703891647159617] 
dist 143=[-.01435745087177137111,.00197486699902357002] 
dist 144=[-.01479932890218986033,.00182070288071879066] 
dist 145=[-.01492980761858511233,.00176697868674887677] 
dist 146=[-.01488947114636653354,.00052521764409256448] 
dist 147=[-.01433982700987404468,.00036061717191708438] 
dist 148=[-.01420568001257442918,-3.06701884348294013390e-06] 
dist 149=[-.01167870331510522242,-8.34882095031920265430e-05] 
dist 150=[-.01106349863190918034,-.00046228659635337783] 
dist 151=[-.01047727897612611656,-.00052955462695260166] 
dist 152=[-.01020925697362599431,-.00062393319177832876] 
dist 153=[-.00260792520786561044,.00101284377086271830] 
dist 154=[-.00181998010419887236,.00306829483134332222] 
dist 155=[-.00061205428746860386,.00474134186401418542] 
dist 156=[-.00057608684939368849,.00628376076117391924] 
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dist 162=[-3.22153124653384223020e-05,.00345078057760318353] 
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dist 180=[-.00167330879744615020,-9.27890152783826903810e-06] 
dist 181=[-.00142740259421370934,-1.71386506178275952770e-05] 
dist 182=[-.00136435990587879978,-5.75762544831122018250e-05] 
dist 183=[-.00126891566614275051,-6.44904569423678557010e-05] 
dist 184=[-.00123434823723922170,-7.46303075239345247980e-05] 
dist 185=[-.00041031213031227377,.00021951602686764493] 
dist 186=[-.00030104125611214425,.00052106706421679288] 
dist 187=[-7.42389889982533527550e-05,.00076598998839848428] 
dist 188=[-6.99324312006089153290e-05,.00099098591860019413] 
dist 189=[-6.93100243123351207860e-05,.00118074893019995704] 
dist 190=[-5.43802360989435055200e-05,.00128577859758296724] 
dist 191=[-5.09696091675622533090e-05,.00134691490784526276] 
dist 192=[-4.83026135175529640730e-05,.00136231891699219017] 
dist 193=[-4.77338152021402660620e-05,.00041554667138910791] 
dist 194=[-3.45886744434471358470e-06,.00041453697608649054] 
dist 195=[1.72261240268124990290e-06,.00039798714976596093] 
dist 196=[1.36254863875621176560e-05,.00039552007318134399] 
dist 197=[1.54654374950436638000e-05,.00031996122511049326] 
dist 198=[2.89032310477412103090e-05,.00030339301944894932] 
dist 199=[3.09121313488888431120e-05,.00028838485746798900] 
dist 200=[3.42525014337290495500e-05,.00028526199687378738] 
dist 201=[-5.88255483600064329600e-06,5.60673232799691253410e-05] 
dist 202=[-6.94772856301485082720e-05,3.90677646418975956910e-05] 
dist 203=[-.00012133539135360566,3.86494240464116563310e-05] 
dist 204=[-.00016932783402126458,3.69248913068001922370e-05] 
dist 205=[-.00021005968114405831,3.62111351475817599560e-05] 
dist 206=[-.00023308989332832252,3.05690978291029593860e-05] 
dist 207=[-.00024714108036841797,2.91689899365489014040e-05] 
dist 208=[-.00025222221687323252,2.68198720116151860210e-05] 
dist 209=[-.00025237062594055851,2.60769829665344382710e-05] 
dist 210=[-.00025096154080464431,1.05233241346540215590e-05] 
dist 211=[-.00024056196229582362,8.65634859899476225420e-06] 
dist 212=[-.00023777424533067134,4.65989574942915820280e-06] 
dist 213=[-.00019553012575926241,3.58856227272750522890e-06] 
dist 214=[-.00018530253609298478,-3.80194389047042816120e-07] 
dist 215=[-.00017429980275353313,-1.19094424458782423460e-06] 
dist 216=[-.00016875753439495298,-2.24432969447340088880e-06] 
dist 217=[-6.16873355267497129320e-05,4.25529596911406156810e-05] 
dist 218=[-5.32826964773262265580e-05,7.31989611613423893300e-05] 
dist 219=[-3.53067926871569819650e-05,9.81267824406574591090e-05] 
dist 220=[-3.03940923850269653940e-05,.00012109347290380291] 
dist 221=[-1.17835649559449842280e-05,.00014051485688536876] 
dist 222=[-7.90091926784971770470e-06,.00015136565163832346] 
dist 223=[-7.99537451418269369760e-06,.00015813451037823555] 
dist 224=[-1.00091920566358022530e-05,.00015983539286662830] 
dist 225=[-1.30145090434438934400e-05,5.21330616690141602120e-05] 
dist 226=[-1.60147028233849046130e-05,5.19327267508914526420e-05] 
dist 227=[-1.80081341891226731690e-05,4.98273027451356042840e-05] 
dist 228=[-1.96074810561147837340e-05,4.94015184191941082160e-05] 
dist 229=[-2.10428965910820426310e-05,4.02513606445242174610e-05] 
dist 230=[-2.22292276837681645690e-05,3.80577600789569896780e-05] 
dist 231=[-2.28395110955680913260e-05,3.61426367572260605260e-05] 
dist 232=[-2.31327852701757715110e-05,3.54123527920553051450e-05] 
dist 233=[-2.30602888775697910750e-05,2.55301714964453868400e-05] 
dist 234=[-2.29156467346009016700e-05,2.54083096876228103430e-05] 
dist 235=[-2.29224972393229007880e-05,2.51337133159796229370e-05] 
dist 236=[-2.30406521990287125840e-05,2.44023973807573220120e-05] 
dist 237=[-2.43974168956916215860e-05,2.40003370737849387280e-05] 
dist 238=[-2.72274376664846967590e-05,2.15399210448532467560e-05] 
dist 239=[-2.89422465284589085200e-05,2.09017634069973790210e-05] 
dist 240=[-2.95359374044890860550e-05,1.90345084981872816710e-05] 
dist 241=[-2.95648797084474253110e-05,1.84777723304367057120e-05] 
dist 242=[-2.93611904536056079280e-05,1.17121857390597002560e-05] 
dist 243=[-2.83627942538170675100e-05,1.05278700501289098010e-05] 
dist 244=[-2.78088168944345478880e-05,8.17340901817988877770e-06] 
dist 245=[-2.40049728580297081060e-05,7.54409074563447111860e-06] 
dist 246=[-2.30135506130700131040e-05,5.30893668353477003370e-06] 
dist 247=[-2.11934784620685837350e-05,4.75041271319996592810e-06] 
dist 248=[-1.76599908442207058450e-05,4.25570146040691978740e-06] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 0, 0, 1, 0, 1] 
dist 0=[129.03286758927729799   ,129.03286758927729799   ] 
dist 1=[126.26062329719392566   ,129.62646830685478401   ] 
dist 2=[122.13048867751976334   ,129.20752876148073609   ] 
dist 3=[116.54854092750819408   ,128.65345111165748487   ] 
dist 4=[108.93629597243550959   ,127.37973266391037203   ] 
dist 5=[96.727998353443790957  ,118.12438109246612338   ] 
dist 6=[84.096204253198381151  ,115.96250758443191787   ] 
dist 7=[74.793972608067840588  ,113.51387409122945267   ] 
dist 8=[66.271504103747322547  ,98.294018916223522617  ] 
dist 9=[56.727530911030880562  ,85.307050114737315879  ] 
dist 10=[47.369719980179093456  ,81.229294855137033434  ] 
dist 11=[39.575350877543584487  ,79.651750718670605343  ] 
dist 12=[26.292336203051404248  ,46.229378594664897422  ] 
dist 13=[14.132557038278552373  ,45.119132933605704307  ] 
dist 14=[4.0198035466711089790 ,35.907707681701173707  ] 
dist 15=[-5.7539445825797408899 ,34.273112565206886440  ] 
dist 16=[-14.417430702687062312  ,27.237983313112670609  ] 
dist 17=[-20.120932867943318048  ,-.68947951177167654235] 
dist 18=[-24.698763048169187685  ,-4.6299756064656132725 ] 
dist 19=[-28.897633907025573735  ,-5.0174080084853218798 ] 
dist 20=[-32.260920509768227572  ,-4.3215827283933051529 ] 
dist 21=[-33.518791902696134580  ,-2.0701034223828026979 ] 
dist 22=[-33.962133565777783353  ,.54242062730168554327] 
dist 23=[-34.071325580458897925  ,2.6782379964722338106 ] 
dist 24=[-29.852970655591900576  ,4.7930438460310382235 ] 
dist 25=[-28.789607115476278812  ,7.3354595515601226426 ] 
dist 26=[-28.096801377995893871  ,9.8763346190106922798 ] 
dist 27=[-27.932092607972790161  ,11.992543165088307007  ] 
dist 28=[-7.3705655340508143839 ,14.162649726515142197  ] 
dist 29=[-4.0253910958694304474 ,16.926295981655278950  ] 
dist 30=[1.8126455608174433797 ,19.421898659571714203  ] 
dist 31=[2.7576134414766846716 ,20.530178903899585020  ] 
dist 32=[4.2540367470958273713 ,21.026409793501076865  ] 
dist 33=[10.514078338972350242  ,21.086428832892279575  ] 
dist 34=[12.173310107750895201  ,19.192368930955806711  ] 
dist 35=[12.370018721856327449  ,18.609279144535402186  ] 
dist 36=[11.556235304162178377  ,18.188922363129018397  ] 
dist 37=[8.1893072020232781745 ,17.900276598361984720  ] 
dist 38=[3.2529691474804779063 ,16.343082275724036566  ] 
dist 39=[-.1585225065332884821 ,16.150366718874052516  ] 
dist 40=[-3.0306153626377845114 ,14.278184787056045924  ] 
dist 41=[-5.8283969874113221502 ,13.743004878504822332  ] 
dist 42=[-8.2923946147352008443 ,12.939635056520086759  ] 
dist 43=[-9.8410528903886926955 ,12.625786691349426975  ] 
dist 44=[-10.985883576518245633  ,4.7336670533884153034 ] 
dist 45=[-11.848740740947551499  ,3.6786804286421914723 ] 
dist 46=[-12.459618194603793022  ,1.3247619062919972625 ] 
dist 47=[-12.604648417296326257  ,.77555594734457327868] 
dist 48=[-12.550694768611596486  ,.22904109077808127501] 
dist 49=[-12.390612519665938896  ,-.90746649130538802864] 
dist 50=[-12.248371823430550692  ,-1.0437050831199250075 ] 
dist 51=[-12.398638152735091540  ,-.93171942007820609769] 
dist 52=[-10.002065975532432626  ,-.45794243355864966373] 
dist 53=[-9.7729645897370697786 ,.19563319106794349239] 
dist 54=[-5.6030792950653592671 ,2.2720647424293905881 ] 
dist 55=[-5.1128883774344558713 ,4.3073190989666936537 ] 
dist 56=[-3.3502824058579329403 ,6.0116840689132401295 ] 
dist 57=[-3.0753336185424491874 ,7.7407953104116185963 ] 
dist 58=[-2.9623341818033957109 ,9.1866529135962830454 ] 
dist 59=[-2.9150890329423809412 ,9.9580470243629408563 ] 
dist 60=[-.60095303887373429961,10.367122269580134573  ] 
dist 61=[-.32357708272710914235,10.444335443794273160  ] 
dist 62=[.33123095237718166679,2.1689150933183435927 ] 
dist 63=[.42688644047628446933,2.1973534472201746126 ] 
dist 64=[1.1736491814045360041 ,2.1837132434800676522 ] 
dist 65=[1.3466716900378288735 ,2.1808402650194862720 ] 
dist 66=[1.5550358933608244252 ,2.0431392242301636687 ] 
dist 67=[1.5634081210431221485 ,2.1290600645087808810 ] 
dist 68=[1.2493907365088433798 ,2.1689988663411623303 ] 
dist 69=[.76184644715779719423,2.1698085626904378142 ] 
dist 70=[.26874708366997099564,2.1041859868732547466 ] 
dist 71=[-.06737116054192945149,2.0862469505657097656 ] 
dist 72=[-.34600442740446248682,1.7313687080667911873 ] 
dist 73=[-.6109951660293353015 ,1.6433590257682741161 ] 
dist 74=[-.8405133359766232572 ,1.5600685474615319827 ] 
dist 75=[-.97838563144922331252,1.5200343895003218776 ] 
dist 76=[-1.0729367097141133426 ,.42916069430338431026] 
dist 77=[-1.1305526695413956504 ,.31633420321713783545] 
dist 78=[-1.2170478869298794427 ,.05967985595215973345] 
dist 79=[-1.2796986978751519663 ,.00789258486062203069] 
dist 80=[-1.2954852083411480050 ,-.28425319128531172138] 
dist 81=[-1.2119340731039738518 ,-.33295198093125838892] 
dist 82=[-1.2785119182496614083 ,-.40252806055296016324] 
dist 83=[-1.2939639322934718165 ,-.39452555836976710518] 
dist 84=[-.88748204932080584932,-.36722463383347999827] 
dist 85=[-.86525936747551503833,-.15189802803270457568] 
dist 86=[-.48734874802057036239,.1502868567407396254 ] 
dist 87=[-.48535119783307627067,.35337132529424608845] 
dist 88=[-.39921896562806054921,.51871172271407562607] 
dist 89=[-.38004999778360359462,.67107171733456526064] 
dist 90=[-.36406788373002071254,.79975939314123453332] 
dist 91=[-.36080744148140742192,.87122954719801014037] 
dist 92=[-.11931871239753433891,.91330013351257311494] 
dist 93=[-.08924433290456577609,.92359906885535665518] 
dist 94=[-.02000017877433201885,.25337650306339408955] 
dist 95=[-.00669167465392181603,.25486887428110872134] 
dist 96=[.07522251587926449205,.2849367553735645755 ] 
dist 97=[.08848009070191220134,.31538746006006267101] 
dist 98=[.11526101510724122332,.33496230899063871552] 
dist 99=[.08701978820822397483,.34428451578605474126] 
dist 100=[.03377775812128661073,.3478144724521677265 ] 
dist 101=[-.04731164893857519888,.34608527416366337598] 
dist 102=[-.12885639512524314135,.33804492703224846769] 
dist 103=[-.18390973803187005628,.33242186864049152313] 
dist 104=[-.22902287628372315388,.29542226463111237631] 
dist 105=[-.27110857896614206775,.28543879969157754815] 
dist 106=[-.30703662086337907363,.26243167426878371167] 
dist 107=[-.32770591745495019202,.25413037261980075971] 
dist 108=[-.34077084432351233165,.13288270710413455962] 
dist 109=[-.34651220559851549798,.11417616359848174076] 
dist 110=[-.3477014437067743265 ,.07445795865922077829] 
dist 111=[-.34520079800722180308,.06368644527085100606] 
dist 112=[-.33529737946528987283,.02343748671515777655] 
dist 113=[-.3291516579707701281 ,.01490943479207799043] 
dist 114=[-.29003561305276893712,.00330021160208924605] 
dist 115=[-.26064215584008667895,.00033528121433307734] 
dist 116=[-.10242180435439032386,-.00023986099680294952] 
dist 117=[-.09932446819118019787,.00156600892230519560] 
dist 118=[-.05746698306923971428,.03435490925217044118] 
dist 119=[-.05706027571205723456,.06015926963777324394] 
dist 120=[-.04691937589315867982,.08112577044338453948] 
dist 121=[-.04444852642202737705,.10038903739661849817] 
dist 122=[-.04241140358960671291,.11662944734046757569] 
dist 123=[-.04165239050151643131,.12559478885891809715] 
dist 124=[-.00626666691239187876,.13077808966564758942] 
dist 125=[-.00203737814593224575,.13200304515895503855] 
dist 126=[.00781810327814391945,.02463978186305240644] 
dist 127=[.00930654294141076436,.02676744558343613975] 
dist 128=[.02093571418405411890,.02789701409127077925] 
dist 129=[.02266767909552733635,.03012770845825202537] 
dist 130=[.02584932594655085274,.03219530786998475405] 
dist 131=[.02631051108751707514,.03303067901790197541] 
dist 132=[.02353291355056190680,.03317631407933932222] 
dist 133=[.02012371507329786746,.03304027721806155016] 
dist 134=[.01626630278035137230,.03171976843201294948] 
dist 135=[.01142158526168714493,.03140970404252710477] 
dist 136=[.00409236319128556516,.02571314434017525772] 
dist 137=[-.00325953258169525147,.02433797859469195850] 
dist 138=[-.00819442614471464914,.02301838973475538262] 
dist 139=[-.01220745306504186799,.02242694506358320171] 
dist 140=[-.01589957957075840421,.00555637013289585091] 
dist 141=[-.01901549391406678785,.00381333708561878444] 
dist 142=[-.02074094267800839867,-.00012544988052125878] 
dist 143=[-.02174642403075247112,-.00091597537303219675] 
dist 144=[-.02199921612170434506,-.00529063848542351292] 
dist 145=[-.01848038740931137103,-.00602184086416038831] 
dist 146=[-.01946112513234304977,-.00647953622745535538] 
dist 147=[-.01969246568887481947,-.00621440671916392455] 
dist 148=[-.00764659561181684740,-.00564593304832599008] 
dist 149=[-.00762914994448791052,-.00494116958459407268] 
dist 150=[-.00732707741704305772,-.00413485147362134676] 
dist 151=[-.00728213324380263712,-.00311636226674300522] 
dist 152=[-.00588753733863221240,-.00156914157150623043] 
dist 153=[-.00555537103595491334,-1.42389139065347452120e-05] 
dist 154=[-.00531505865538797101,.00103480194655628460] 
dist 155=[-.00525801966480075843,.00189384049634993712] 
dist 156=[-.00049900478407191948,.00269445178155375833] 
dist 157=[5.65414824071675038870e-05,.00337752977388786858] 
dist 158=[.00134738459794399234,.00376997163736275489] 
dist 159=[.00153666766732214207,.00401739287332781573] 
dist 160=[.00247389740624884687,.00412475563614087903] 
dist 161=[.00258233812692761236,.00415047497244296508] 
dist 162=[.00252241269845737792,.00413474703150419779] 
dist 163=[.00237996615795222020,.00397948596057427439] 
dist 164=[.00209151368375237964,.00393549551153554475] 
dist 165=[.00173879948615187026,.00388234870755181584] 
dist 166=[.00134118074551510520,.00374346208616991658] 
dist 167=[.00084261694130789834,.00368606937849003305] 
dist 168=[8.90840794701594000000e-05,.00311637985104493342] 
dist 169=[-.00066687523503721694,.00297293206336502463] 
dist 170=[-.00117508909083287920,.00276753384167251284] 
dist 171=[-.00158935968229200836,.00268942377599078186] 
dist 172=[-.00197234640918564244,.00087793343765153236] 
dist 173=[-.00229699363004980650,.00063904445297387483] 
dist 174=[-.00247964374331865642,.00016138212173365411] 
dist 175=[-.00260430882936992309,4.75257051200073400250e-05] 
dist 176=[-.00263259966017049467,2.16166855264928199750e-05] 
dist 177=[-.00281763544215749148,-.00068756103430643731] 
dist 178=[-.00295085660914189275,-.00084959381668001439] 
dist 179=[-.00298445236322614769,-.00088295050151995654] 
dist 180=[-.00100232896177096237,-.00080804607661097622] 
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dist 190=[-8.39639373620802647300e-05,.00079755311903997361] 
dist 191=[-5.19850871664504226430e-05,.00083511061454148652] 
dist 192=[8.48510344235529438030e-05,.00084649360949759250] 
dist 193=[.00011041860827233611,.00084538967520391682] 
dist 194=[.00014963934314456441,.00083707016449162842] 
dist 195=[.00013889592274967254,.00081130415868624603] 
dist 196=[.00011225714686368887,.00055009431580908790] 
dist 197=[7.98014443833356611460e-05,.00054668672592751457] 
dist 198=[4.33501958771287830470e-05,.00052324719489422863] 
dist 199=[-2.27383707842695671100e-06,.00051712884666477028] 
dist 200=[-7.11527524174039366380e-05,.00042425031491058906] 
dist 201=[-.00014024378093640513,.00040186290193697319] 
dist 202=[-.00018671137368565874,.00037787220730784353] 
dist 203=[-.00022461816649637663,.00036577571716836078] 
dist 204=[-.00025971978705373465,.00013153930537911721] 
dist 205=[-.00028952176172151668,.00011328907060121567] 
dist 206=[-.00030638705375887417,7.44066791675838404070e-05] 
dist 207=[-.00031669499072764133,6.38289065612026477800e-05] 
dist 208=[-.00032046198127939368,2.40473230461018379950e-05] 
dist 209=[-.00032911588088440865,1.56946951061637255640e-05] 
dist 210=[-.00034318132016021698,3.61025120252407173150e-06] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 1, 0, 0, 0, 1] 
dist 0=[110.76445004531913551   ,110.76445004531913551   ] 
dist 1=[107.26153943954246946   ,112.27029799091574976   ] 
dist 2=[103.23085266985330747   ,112.78160084331870740   ] 
dist 3=[99.618874462272129243  ,112.57694620645236255   ] 
dist 4=[95.660695167696984980  ,110.92436808066931420   ] 
dist 5=[90.240940473810744890  ,108.28402972719318197   ] 
dist 6=[84.333487871764461891  ,106.44913688451756039   ] 
dist 7=[78.424422555175533578  ,105.64517770936348091   ] 
dist 8=[71.398122382739349455  ,101.73049338312421133   ] 
dist 9=[61.026354413407072941  ,80.524111199664517523  ] 
dist 10=[50.511743499449853621  ,69.714143604826949445  ] 
dist 11=[42.916033273666123440  ,68.303310011489652626  ] 
dist 12=[36.018801336459607722  ,53.206938895233967611  ] 
dist 13=[28.299183745213936484  ,50.278434731118869394  ] 
dist 14=[20.048363442678801253  ,45.152929286543312443  ] 
dist 15=[11.328648767016905226  ,44.148844504463825310  ] 
dist 16=[-.24131388558860127122,19.900359091793389462  ] 
dist 17=[-11.207882422720989255  ,18.997373544779135797  ] 
dist 18=[-17.533244757035509271  ,6.3392211500921687622 ] 
dist 19=[-21.692340921134362216  ,4.5546975756930335830 ] 
dist 20=[-24.032176622573464433  ,1.1416834141652798152 ] 
dist 21=[-25.520450929461280512  ,.34337267077026771794] 
dist 22=[-26.440460209831703802  ,-1.9842612555000435443 ] 
dist 23=[-27.670771756951760984  ,-2.3658130414015000576 ] 
dist 24=[-28.224795850971063279  ,-2.1919693057120597396 ] 
dist 25=[-28.323392457566431571  ,-1.2335779893796657075 ] 
dist 26=[-17.179665989556648480  ,-.13899182063981961492] 
dist 27=[-17.106767547145484368  ,.57845632615887395683] 
dist 28=[-14.099646909906360333  ,1.1432284308360516807 ] 
dist 29=[-13.373984732955916447  ,2.6201283666104745776 ] 
dist 30=[-12.865460987056277433  ,5.1094252722876424058 ] 
dist 31=[-12.750654790257005212  ,7.3170791177460235352 ] 
dist 32=[-2.1683535689530384574 ,9.6603064347821710233 ] 
dist 33=[-.93326256224762991051,11.709964357354917422  ] 
dist 34=[.06813656184308281587,12.754821398421645913  ] 
dist 35=[-.33897541992519093204,13.275847852769341981  ] 
dist 36=[-.71335803302127517018,13.355099926905334676  ] 
dist 37=[-1.1240652778402961448 ,12.841641714211655065  ] 
dist 38=[-1.5118566588971491864 ,12.561901150336964412  ] 
dist 39=[-1.7960412619252175256 ,12.114515166181249393  ] 
dist 40=[-2.0514657048158581846 ,11.897259033129768107  ] 
dist 41=[-2.3259640432168310739 ,7.8547937950013898072 ] 
dist 42=[-2.6943831839937751138 ,7.6567203401662469357 ] 
dist 43=[-4.7570589743497991186 ,7.5469379291545386018 ] 
dist 44=[-6.6799298520751583982 ,6.4915992575992324041 ] 
dist 45=[-8.3100257070722158491 ,6.2163976496109172351 ] 
dist 46=[-9.2119157835431372650 ,5.8064756658622772272 ] 
dist 47=[-9.7322044723501685442 ,5.6536492308368611737 ] 
dist 48=[-9.8490465704877718962 ,1.9584665140594275325 ] 
dist 49=[-2.9238003196108887461 ,1.4675899858725563324 ] 
dist 50=[-3.1745608229967737580 ,1.2127570227657659930 ] 
dist 51=[-4.1741895690270875467 ,1.5064942962206995601 ] 
dist 52=[-5.0174208659799402642 ,1.9010842843517405509 ] 
dist 53=[-5.4841499876563606832 ,2.3076551821927732468 ] 
dist 54=[-5.7557267154372650704 ,2.6347405093173939645 ] 
dist 55=[-5.8241229680550734780 ,2.7827425256908790255 ] 
dist 56=[-2.8114613211481062958 ,2.8500954678789448698 ] 
dist 57=[-1.7921049148986396106 ,2.8575443251224290914 ] 
dist 58=[-1.7378078887765245766 ,-.07857171150990074865] 
dist 59=[-1.7265252559615082539 ,.20075504073914364611] 
dist 60=[-1.4267596945017876634 ,.6230147554715318343 ] 
dist 61=[-1.3533604486237424234 ,.99846067363969321421] 
dist 62=[-1.2935566635801228761 ,1.2403782586081362064 ] 
dist 63=[-1.2713498755268567222 ,1.4260271494640852143 ] 
dist 64=[-.21263756184608747948,1.5784467963665196816 ] 
dist 65=[-.08622770847736176584,1.6938407251468732232 ] 
dist 66=[.02108080827191778273,1.7326054832404210033 ] 
dist 67=[.02362705762209292824,1.7378363000099224228 ] 
dist 68=[.02634193445059558940,1.7200375682035246374 ] 
dist 69=[.02587960389080124309,1.5512152809629391659 ] 
dist 70=[.02424196152629805678,1.4984832971155342444 ] 
dist 71=[.02120905476569998949,1.4176955801162338332 ] 
dist 72=[.01668387432166468474,1.3853514859544167791 ] 
dist 73=[-.12875187140708936288,.96431214923053641606] 
dist 74=[-.44411092676184897139,.92723888685478547771] 
dist 75=[-.70174145772810014491,.9184461536042168329 ] 
dist 76=[-.94012196971280659324,.75327396982168024728] 
dist 77=[-1.1417589750376768105 ,.71329414664339831752] 
dist 78=[-1.2535882875524094313 ,.67517132157140019083] 
dist 79=[-1.3187432593751501753 ,.65809875609267124462] 
dist 80=[-1.3351618787647527067 ,.16763217273178928151] 
dist 81=[-.41084414379256605155,.11666392910338259989] 
dist 82=[-.41868826603534994182,.00778570860078158086] 
dist 83=[-.41936334050116119828,.00864457916147430718] 
dist 84=[-.48596740326487747254,.00947629733395233062] 
dist 85=[-.53266946395843221458,.01040119293804479217] 
dist 86=[-.56181524941215720716,.01124325503609096869] 
dist 87=[-.56856956102653772365,.01175332889002635259] 
dist 88=[-.33129728283081613039,.01217553623327077410] 
dist 89=[-.22098981831359247631,.01225253349637418640] 
dist 90=[-.2126922940120503868 ,.02258363191134516166] 
dist 91=[-.21144748344812256789,.07796322088186700462] 
dist 92=[-.17186859000426597191,.13082088839360175548] 
dist 93=[-.1623847250289502958 ,.17670710066380248002] 
dist 94=[-.15552073406765237583,.20442568697171647987] 
dist 95=[-.15381211946486470316,.22361274133257357601] 
dist 96=[-.04316679623509821496,.2356484641055213672 ] 
dist 97=[-.05213811713128320562,.24251541681444657701] 
dist 98=[-.06120131515451016237,.2433866150649315693 ] 
dist 99=[-.06736201380493121486,.23768710535000083081] 
dist 100=[-.07245001251252487156,.23591396886279213756] 
dist 101=[-.07725605936120184464,.19744866426743270509] 
dist 102=[-.08139425111720518161,.18771191932297999481] 
dist 103=[-.08383172409904107669,.17876799415573888535] 
dist 104=[-.08544215687248736104,.17432749402713993131] 
dist 105=[-.08629800248994490818,.11119920805971316436] 
dist 106=[-.08652581367814503725,.107503961526604897  ] 
dist 107=[-.08572245330536809310,.10572822144835151256] 
dist 108=[-.09988850135370879868,.09021589454128337528] 
dist 109=[-.12246542261807277348,.08624092709791214381] 
dist 110=[-.1357565682990786295 ,.08001041419429317812] 
dist 111=[-.14324178558408362218,.07783890869776987622] 
dist 112=[-.14499905055297826917,.02628759930710265881] 
dist 113=[-.06620854230226855727,.01937277181761537191] 
dist 114=[-.05751635988817020728,.01145775635648939071] 
dist 115=[-.06183558199850899179,.01140380642922664940] 
dist 116=[-.07370607106011245696,.01137067661610881197] 
dist 117=[-.08027478661480728019,.01135327441077471423] 
dist 118=[-.08409636304767996042,.01134407167307483262] 
dist 119=[-.0850588086770187819 ,.01134413531729218652] 
dist 120=[-.04272867227830460177,.01134992734443985128] 
dist 121=[-.02556148476573704274,.01136427988621070957] 
dist 122=[-.02453852763768745091,.00264724427630831687] 
dist 123=[-.02434124807833541646,.00977096570280643242] 
dist 124=[-.01981813840333572903,.01649372517926063271] 
dist 125=[-.01873509988438794250,.02228382949420653373] 
dist 126=[-.01781948420166889303,.02570580675425477501] 
dist 127=[-.01749209298188370756,.02798427236625182348] 
dist 128=[-.00235622443043094088,.02923580644778204586] 
dist 129=[-.00054877193106524536,.02986287770287242671] 
dist 130=[.00364342408044265068,.02986631214052418613] 
dist 131=[.00428485704814689286,.02919792911729114854] 
dist 132=[.00916975548571698624,.02877576875788617571] 
dist 133=[.00989468664828864919,.02488435911830106039] 
dist 134=[.01123886849684421897,.02384889489394511419] 
dist 135=[.01143800759309580617,.02227846296850105588] 
dist 136=[.00436787813807445893,.02169698287259517563] 
dist 137=[-.00337568288691314908,.01405223763567951493] 
dist 138=[-.00857476919804375834,.01344556640585245756] 
dist 139=[-.01280360095206649217,.01330813445921017881] 
dist 140=[-.01669539060653850209,.01084563264050967805] 
dist 141=[-.01998019609634553573,.01025630106773516620] 
dist 142=[-.02179934048767950088,.00968665950973814177] 
dist 143=[-.02285964952067302118,.00943651629080331056] 
dist 144=[-.02312611361759776134,.00226018297888513452] 
dist 145=[-.00710024603253064974,.00152135619605830322] 
dist 146=[-.00711674893937376572,-.00014289024078818886] 
dist 147=[-.00690646386352689020,-.00047887376523796264] 
dist 148=[-.00720197955259425692,-.00230833688537165696] 
dist 149=[-.00787305006888724595,-.00261558129224296748] 
dist 150=[-.00827166751806888351,-.00312609501016329422] 
dist 151=[-.00837306493848911511,-.00322373841617182374] 
dist 152=[-.00508300614647971682,-.00167501258946779646] 
dist 153=[-.00323500061836704892,-3.50582510536834028660e-05] 
dist 154=[-.00309329309784234427,.00107209660675751466] 
dist 155=[-.00307125847861037901,.00197943918819806447] 
dist 156=[-.00247037892509147342,.00282617744639994962] 
dist 157=[-.00232853015905333105,.00354931114910613432] 
dist 158=[-.00222067183454013728,.00396596691574108240] 
dist 159=[-.00219293804308012294,.00423016672663273212] 
dist 160=[-.00019942121299536678,.00434808310541924924] 
dist 161=[3.38517103146179835700e-05,.00437976693523103148] 
dist 162=[.00057675804174799519,.00436462210444408632] 
dist 163=[.00065541166340016069,.00420388277784580560] 
dist 164=[.00129001694865737358,.00415781102926284097] 
dist 165=[.00138303187794284162,.00344046370907334077] 
dist 166=[.00142286315088736060,.00326449407603610932] 
dist 167=[.00089676324879305546,.00307657689890220797] 
dist 168=[.0001008641523208485 ,.00298028463285187947] 
dist 169=[-.00069780564220151146,.00166021324618154315] 
dist 170=[-.00123492432181222500,.00159380456886335234] 
dist 171=[-.00167293376723620485,.00157071054188805472] 
dist 172=[-.00207812845086434595,.00131192908521265449] 
dist 173=[-.00242175613888676655,.00124813238896612244] 
dist 174=[-.00261625051113973906,.00116429591723898920] 
dist 175=[-.00274955749535435448,.00112980599945159037] 
dist 176=[-.00277947381240772112,.00035917441802726272] 
dist 177=[-.00097645163366382283,.00025911662497024359] 
dist 178=[-.00097498964018144567,3.61505563723133526800e-05] 
dist 179=[-.00094425859562912369,-1.26734286321540375940e-05] 
dist 180=[-.00108753775180049982,-.00025193244037754809] 
dist 181=[-.00118314322563602599,-.00029391452547533822] 
dist 182=[-.00123876448906726354,-.00035988947178161707] 
dist 183=[-.00125278609803820844,-.00037219063466324864] 
dist 184=[-.00068204391460636876,-.00020564075187050665] 
dist 185=[-.00048079200567584013,2.74691460797969866930e-05] 
dist 186=[-.00047035655274820656,.00018435342232960704] 
dist 187=[-.00046437016572665480,.00031244195533970940] 
dist 188=[-.00042746718219229911,.00043122434033474336] 
dist 189=[-.00041747328877681417,.00053218737179271217] 
dist 190=[-.00038107781615755573,.00058952773554086234] 
dist 191=[-.00037477168092524288,.00062483637637164219] 
dist 192=[-.00027700418948663298,.00063832710022037237] 
dist 193=[-.00025730500522459626,.00063990082774173738] 
dist 194=[-.00022057380931707821,.00063620455626376224] 
dist 195=[-.00021065950383843312,.00061305543394934461] 
dist 196=[-.00017617960690756955,.00060338558514123763] 
dist 197=[-.00016602024864847690,.00050995846432052738] 
dist 198=[-.00015807005214135288,.00048643478327228521] 
dist 199=[-.00015572073687571690,.00036451572242720656] 
dist 200=[-.00015516189591395288,.00025009892642632383] 
dist 201=[-.00015544481244449543,.00024797501098327500] 
dist 202=[-.00015638947821497708,.00023800571787451884] 
dist 203=[-.00015846036152242137,.00023360996113282206] 
dist 204=[-.00016104795275665621,.00019794403001882012] 
dist 205=[-.00016413904332008249,.00018896791938329117] 
dist 206=[-.00018366072681060644,.00017417838352806719] 
dist 207=[-.00019560915161529855,.00016935914759266458] 
dist 208=[-.00020001333915799429,5.73937614210017397260e-05] 
dist 209=[-.00020094067468473234,4.60207794429176372140e-05] 
dist 210=[-.00019928968007520472,2.99289086721167639060e-05] 
dist 211=[-.00019538974695144297,2.55725629816126698640e-05] 
dist 212=[-.00019285427157356171,9.31715413578255107110e-06] 
dist 213=[-.00017649395890949343,5.88035232183884680650e-06] 
dist 214=[-.00017212178727974390,1.19454735080865740360e-06] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 1, 1, 2, 1, 0, 1] 
dist 0=[128.22040415219629444   ,128.22040415219629444   ] 
dist 1=[126.23454346608447302   ,131.23850270212772343   ] 
dist 2=[121.37873635900686195   ,133.87162779715689193   ] 
dist 3=[113.17989502560161994   ,134.27720623171935762   ] 
dist 4=[99.848444493471137001  ,133.73919436120983071   ] 
dist 5=[86.047086252773827896  ,132.78560468599463465   ] 
dist 6=[75.972878041176068244  ,125.80150200104456550   ] 
dist 7=[66.854918377284964450  ,117.52068550136039284   ] 
dist 8=[56.838182279693287377  ,102.13914671741288307   ] 
dist 9=[47.149878090868100049  ,100.77656322572314500   ] 
dist 10=[39.322809124281778900  ,79.559583885328853464  ] 
dist 11=[31.411376369318523533  ,75.100910392357337629  ] 
dist 12=[21.361323412470868268  ,71.014694576555436465  ] 
dist 13=[11.788916355141960893  ,70.227546132611960639  ] 
dist 14=[5.7724790571844659588 ,42.369581802727397584  ] 
dist 15=[1.1958657641461968754 ,36.966755332699988604  ] 
dist 16=[-5.4761556790580102173 ,1.3252035777267185808 ] 
dist 17=[-12.260053305886283994  ,-2.8168986227567931563 ] 
dist 18=[-20.021060701947818139  ,-3.3254540037562444047 ] 
dist 19=[-24.673741677042255032  ,-2.9072252635567577120 ] 
dist 20=[-27.896020338369984741  ,-1.2357639762821335112 ] 
dist 21=[-29.977804045056460399  ,.68005448185357772622] 
dist 22=[-31.286384213927596336  ,2.0736445719541858738 ] 
dist 23=[-31.495300739840913266  ,3.2632048315517350314 ] 
dist 24=[-31.165976753953996662  ,4.3828924405830664705 ] 
dist 25=[-30.796300620684533019  ,5.2925399924407015841 ] 
dist 26=[-26.936627211661879028  ,5.6550501886599400417 ] 
dist 27=[-25.882658936044777729  ,5.7828611948463622083 ] 
dist 28=[-24.343258736316065713  ,5.7716376331979657272 ] 
dist 29=[-23.739878284770476537  ,4.5009297366508256929 ] 
dist 30=[-8.8107990526043419116 ,4.1279350656032585803 ] 
dist 31=[-6.8311345188104615567 ,7.2105055549015834554 ] 
dist 32=[-2.3553741473675971988 ,11.576046925783857319  ] 
dist 33=[-1.4128985129139153617 ,15.594301395201462876  ] 
dist 34=[-1.0327612466260332229 ,18.985900127272574583  ] 
dist 35=[-.71752620396273765661,20.863930417465341284  ] 
dist 36=[-.64359025868049608775,21.956993734512968958  ] 
dist 37=[.4620856512563184502 ,22.232315728202169892  ] 
dist 38=[.60308328231192524906,8.1237978205708438492 ] 
dist 39=[.85587574234833990777,8.0455029703710118871 ] 
dist 40=[.90628235149189449876,6.9116464409119809649 ] 
dist 41=[.80785203933737311964,6.8822142850343930099 ] 
dist 42=[-.39343366468925584023,5.8042195851282066348 ] 
dist 43=[-1.6003033110462530155 ,5.5296683351460668955 ] 
dist 44=[-2.6849080530127050834 ,5.3198578626578386350 ] 
dist 45=[-3.4020432976666538523 ,5.2361827285929979805 ] 
dist 46=[-3.9728609781303154198 ,1.3010091240750732334 ] 
dist 47=[-4.4780735518373211518 ,1.0981423688138556452 ] 
dist 48=[-4.8791639342473598154 ,1.0516734163383485911 ] 
dist 49=[-5.0370817398721048031 ,.74080071301155127166] 
dist 50=[-5.0790356789851413257 ,.68026034989618738904] 
dist 51=[-5.0430435938832308436 ,.56515011292363945978] 
dist 52=[-4.6193318696813799695 ,.53612211451573355029] 
dist 53=[-4.4795688773085207212 ,.51820295199038969991] 
dist 54=[-4.2211583213582982621 ,.57976195468376946857] 
dist 55=[-4.1298662554156711801 ,.62797758750799346167] 
dist 56=[-3.6269198783357067591 ,.72733066547997920798] 
dist 57=[-3.5961102906093006504 ,1.6094919424361231798 ] 
dist 58=[-2.9746783110706651011 ,2.3942743654735254337 ] 
dist 59=[-2.8216843007555196625 ,3.1128769445185644009 ] 
dist 60=[-2.6786531176210859494 ,3.7148535322390133115 ] 
dist 61=[-2.6125716627416905342 ,4.0369011216022484386 ] 
dist 62=[-.70583947276959021819,4.2086126666000580731 ] 
dist 63=[-.50594924310759384263,4.2404847227034901682 ] 
dist 64=[-.05117675548519318624,1.1391986325266557440 ] 
dist 65=[.03843112043569992071,1.5299694856768061016 ] 
dist 66=[.06370223751730789509,1.8607105814187172442 ] 
dist 67=[.06302155776582352085,2.0521581374503380057 ] 
dist 68=[.05428700697375732257,2.1666257324865670740 ] 
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dist 212=[-.00010650532326099405,-1.47936557434619584730e-05] 
dist 213=[-.00010832395422522390,1.45633428130393660960e-05] 
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dist 215=[-.00010719512079626753,5.02134692628141812570e-05] 
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dist 225=[7.44232530536706409900e-06,5.15306900948950163770e-05] 
dist 226=[1.59449504356906062960e-05,5.23266005675956799730e-05] 
dist 227=[1.18271253375953057870e-05,5.54763811338215486080e-05] 
dist 228=[3.78194315524296791490e-06,5.84734113229151151510e-05] 
dist 229=[-4.55672975526566746920e-06,5.92414605296633149050e-05] 
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dist 236=[-2.59256279003758678620e-05,2.06699482494443192650e-05] 
dist 237=[-2.58781531308017162670e-05,2.00849489001842929200e-05] 
dist 238=[-2.56329975118428502270e-05,8.68412095696913438350e-06] 
dist 239=[-2.49004391536306145710e-05,7.05052525274820107600e-06] 
dist 240=[-2.44791724223197426650e-05,3.51076681405128941960e-06] 
dist 241=[-2.18612791809139151290e-05,2.55815052172341114430e-06] 
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dist 243=[-1.93378994470701372810e-05,-1.01033955963998350980e-06] 
dist 244=[-1.75052523616732659500e-05,1.31362253238979405300e-06] 
dist 245=[-1.11666102774635539640e-05,3.64127963828230161970e-06] 
dist 246=[-4.19725847398544941480e-06,5.20228085939852073010e-06] 
dist 247=[-3.76481176893056374530e-06,6.47105974119618778680e-06] 
dist 248=[-3.64265229882666687220e-06,7.82730399082066944090e-06] 
dist 249=[-3.16971916031122182910e-06,9.07600210951818378690e-06] 
dist 250=[-9.03243007038538930700e-07,9.77274295130143261150e-06] 
dist 251=[-5.34319154472125699730e-07,1.01977591118656486460e-05] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 0, 1, 2, 0, 1] 
dist 0=[111.36062979028076864   ,111.36062979028076864   ] 
dist 1=[108.49722325746961054   ,112.41844055728037618   ] 
dist 2=[103.68264350860612969   ,112.98063081836894815   ] 
dist 3=[94.867501915164764355  ,113.86310948219999252   ] 
dist 4=[85.446008769734498180  ,114.63960106635666638   ] 
dist 5=[78.217037874012464981  ,114.78426126211358691   ] 
dist 6=[71.308675853941890351  ,114.48294685420851165   ] 
dist 7=[63.147187419336540821  ,113.93626876563712239   ] 
dist 8=[54.896123827221720496  ,91.606224620679217816  ] 
dist 9=[47.618256762552876775  ,88.464515898013078644  ] 
dist 10=[39.695474768032485795  ,79.915749805081636373  ] 
dist 11=[28.855762528456990560  ,78.401986408516696213  ] 
dist 12=[18.326000255046555300  ,62.538197971405973616  ] 
dist 13=[11.632286559030743826  ,60.703212046961963935  ] 
dist 14=[6.4599991576661603140 ,56.593878781253865781  ] 
dist 15=[1.9943235051459074044 ,53.515831089127802478  ] 
dist 16=[-1.7107297918905628380 ,19.913094463511728838  ] 
dist 17=[-3.8538111368956375866 ,15.768583833731794325  ] 
dist 18=[-7.1832744050095696101 ,6.0740620834215977187 ] 
dist 19=[-13.495858785545328948  ,4.6310924899031187966 ] 
dist 20=[-19.672917980384776124  ,-5.0225726617753918761 ] 
dist 21=[-23.442265280797075636  ,-4.8620861671743274609 ] 
dist 22=[-26.139139759959420923  ,-3.5600785357468546830 ] 
dist 23=[-28.056697754809202033  ,-1.0879912325826424680 ] 
dist 24=[-29.310893580222438116  ,.95701950268013545586] 
dist 25=[-29.566973302742941062  ,2.9938158720225367237 ] 
dist 26=[-29.095464873163442387  ,5.4483495496249729815 ] 
dist 27=[-29.005727752491371106  ,7.8968332998721103356 ] 
dist 28=[-24.349503949599403965  ,9.9180099001479666353 ] 
dist 29=[-23.179046501156544210  ,11.971798013443636451  ] 
dist 30=[-22.372789386611572990  ,14.559411266990669927  ] 
dist 31=[-22.131191014053846259  ,16.889735238941671041  ] 
dist 32=[-4.2761717209211973805 ,17.924759341394406142  ] 
dist 33=[-2.1723994419994640979 ,18.404264970268319343  ] 
dist 34=[1.7417120819227406953 ,18.523768328472011171  ] 
dist 35=[1.4392919301502296007 ,16.695012311123542229  ] 
dist 36=[.36761060299163252301,16.214538214108878756  ] 
dist 37=[-.39540980288286788431,15.931149426252327870  ] 
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dist 39=[-1.7208399060821534564 ,13.761031352767730455  ] 
dist 40=[-2.3156409985164850724 ,14.031591667256039745  ] 
dist 41=[-2.6972146335926136424 ,14.027995172498325178  ] 
dist 42=[-3.7412255640887501502 ,13.652347800120177006  ] 
dist 43=[-5.8444506679801434931 ,13.476310277359975526  ] 
dist 44=[-7.1817008870179387827 ,11.443437279636034054  ] 
dist 45=[-8.1879949914029819293 ,10.922568988651137204  ] 
dist 46=[-8.9792826558928724377 ,10.230668631539207944  ] 
dist 47=[-9.5607144502641396640 ,9.9418329530640635804 ] 
dist 48=[-9.7344209676130378138 ,3.4552273820422109511 ] 
dist 49=[-9.7351623659721741336 ,2.6084303591749210387 ] 
dist 50=[-9.6287629114865461158 ,.68911340591878311072] 
dist 51=[-8.6258092353538806153 ,.29308097471487068601] 
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dist 56=[-3.2393873833040637092 ,2.5375756328483136620 ] 
dist 57=[-3.2575160835085394808 ,3.9722211361531497580 ] 
dist 58=[-3.1840379863010369616 ,5.2984243158930393446 ] 
dist 59=[-3.1728143191565125098 ,6.4198007311458704709 ] 
dist 60=[-2.6314346734800356246 ,7.0418846520319634386 ] 
dist 61=[-2.4970265460846486011 ,7.4043460004085287874 ] 
dist 62=[-2.4083429225086688632 ,7.4954503306527911283 ] 
dist 63=[-2.3859684545419917222 ,2.2833775111026778843 ] 
dist 64=[-.34428988648522644065,2.3156411998545299033 ] 
dist 65=[-.10509019351195497486,2.3112285389256836610 ] 
dist 66=[.34155577003529818697,2.3052314684435863723 ] 
dist 67=[.15778027821341277738,1.9901280207511895048 ] 
dist 68=[-.02868649739059483025,1.9084608964461211589 ] 
dist 69=[-.15517887944430148311,1.8355969116745183189 ] 
dist 70=[-.25903059942018105057,1.8027580395126477223 ] 
dist 71=[-.35571421941571090677,1.6222579169074996119 ] 
dist 72=[-.43769755443157050016,1.6509153796156103257 ] 
dist 73=[-.5563011326306164085 ,1.6490879411642600346 ] 
dist 74=[-.85206995970603075518,1.6079694847221604741 ] 
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dist 76=[-1.2606671457657214899 ,1.3661376930887678292 ] 
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dist 78=[-1.4256729059525002993 ,1.2204448869563101651 ] 
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dist 80=[-1.4592257322479972717 ,.42577914775779532591] 
dist 81=[-1.4212627721255771032 ,.32506941041206537263] 
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dist 86=[-1.2638293838602476490 ,.02477895204110031268] 
dist 87=[-1.2782205351081188603 ,.2142128292369068534 ] 
dist 88=[-.38489821153117204461,.40327378293020106033] 
dist 89=[-.37355653670199928981,.5580789570485069266 ] 
dist 90=[-.36170996199284259435,.70219165790191845835] 
dist 91=[-.35989378327401704285,.82545788910761796032] 
dist 92=[-.30458284405954156503,.90606365227232036927] 
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dist 94=[-.27383415696068064665,.96043388587649648437] 
dist 95=[-.26618045853691528127,.2615230377036470061 ] 
dist 96=[-.13967447494069711414,.26532224498922441057] 
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dist 100=[-.02078944222553699191,.28828298414180660703] 
dist 101=[-.01785208122653314305,.31285272230487896241] 
dist 102=[-.03003211304205910924,.3281473704412839835 ] 
dist 103=[-.06596127563602544977,.33436486490664552242] 
dist 104=[-.11971408234330169893,.3352755749092981368 ] 
dist 105=[-.16391612923975134892,.33311865883751217105] 
dist 106=[-.20540558827708194597,.32191404662873208455] 
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dist 179=[-.00121510083684722552,-9.74087902001088340350e-05] 
dist 180=[-.00145976342658747883,-1.64104359980210140760e-05] 
dist 181=[-.00159562450194070609,5.10544525245041356230e-05] 
dist 182=[-.00167641091798301056,.00010636296133069012] 
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dist 192=[-4.75633464484992268680e-05,.00019451096883435155] 
dist 193=[-4.39164443637515138000e-07,.00018341817381859756] 
dist 194=[8.66015670183457827700e-05,.00017536008550711192] 
dist 195=[3.97112764728237646060e-05,.00022888577592047241] 
dist 196=[-7.31538799617886358620e-06,.00029085600645697914] 
dist 197=[-3.88862438982079040140e-05,.00032557488898114363] 
dist 198=[-6.45686438772993185480e-05,.00034634752492242354] 
dist 199=[-8.82175820061772346990e-05,.00035294167495553042] 
dist 200=[-.00010819368031275500,.00035222088793072946] 
dist 201=[-.00011929438699085942,.00034994211238446196] 
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dist 205=[-.00013062929211980945,.00025733411594095034] 
dist 206=[-.00013412940689012375,.00024169339131175357] 
dist 207=[-.00014018722204733623,.00023399011564159119] 
dist 208=[-.00014728212266513020,7.29188019434949442720e-05] 
dist 209=[-.00015490071111046464,5.25886738989976110060e-05] 
dist 210=[-.00016421658240945385,7.27921779064845665570e-06] 
dist 211=[-.00018592491827442456,-2.63936314957205057370e-06] 
dist 212=[-.00022103789016015467,1.67074975519674127910e-05] 
dist 213=[-.00024046635460926661,2.99568430941355370520e-05] 
dist 214=[-.00025177023598284525,4.07361836861002480870e-05] 
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dist 216=[-8.93544989291686863040e-05,5.90710544139888207020e-05] 
dist 217=[-8.87628284580683918250e-05,6.37646471331466975090e-05] 
dist 218=[-8.53894354533533480330e-05,6.65544114693298823160e-05] 
dist 219=[-8.40136162279149025590e-05,6.73961978374115347950e-05] 
dist 220=[-7.09255886134711770590e-05,6.73392084493963676000e-05] 
dist 221=[-6.76451013540631028810e-05,6.66273416247532081420e-05] 
dist 222=[-6.28167727725995521240e-05,6.52003352138300391890e-05] 
dist 223=[-6.10406165015293566860e-05,6.43709734822262609560e-05] 
dist 224=[-1.88250313525910588790e-05,5.92299155666301185460e-05] 
dist 225=[-1.32416988551526800070e-05,5.78438848209965050270e-05] 
dist 226=[-6.39038636428777020520e-06,5.27659867073431283400e-05] 
dist 227=[-1.05754921320988209870e-05,5.19123130133580240220e-05] 
dist 228=[-1.47754082490437717240e-05,3.98671659644667500080e-05] 
dist 229=[-1.76026608865287019430e-05,4.40399400503202544840e-05] 
dist 230=[-1.99117246725465212580e-05,4.65219580822189326290e-05] 
dist 231=[-2.20542798847909130080e-05,4.72764574213105790480e-05] 
dist 232=[-2.38762862150714909970e-05,4.71135655268121896290e-05] 
dist 233=[-2.49126772639398743400e-05,4.67933644891363512220e-05] 
dist 234=[-2.55529430489184251140e-05,4.47032779990564704920e-05] 
dist 235=[-2.58022233577108863400e-05,4.41884036416837867660e-05] 
dist 236=[-2.58660168940389510710e-05,3.60953195667333683840e-05] 
dist 237=[-2.57698096490223017860e-05,3.41573348518370303100e-05] 
dist 238=[-2.55404767927049854000e-05,3.21332571037872471050e-05] 
dist 239=[-2.52154229115792612010e-05,3.11558430720162138510e-05] 
dist 240=[-2.45069154153476700990e-05,1.08665535996537196110e-05] 
dist 241=[-2.40641719775262787910e-05,9.33178310647732426920e-06] 
dist 242=[-2.31338448531876003870e-05,6.07436269637330453890e-06] 
dist 243=[-2.27269302042420537220e-05,5.19208495403562115630e-06] 
dist 244=[-2.57994305881545190820e-05,1.89750951149399405210e-06] 
dist 245=[-2.77524297284763217680e-05,1.20124037642017386800e-06] 
dist 246=[-2.89016127842828932120e-05,2.47042427787507201990e-07] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 2, 2, 1, 2, 0, 1] 
dist 0=[124.54380986875088318   ,124.54380986875088318   ] 
dist 1=[120.19401595565863663   ,126.25691298257011367   ] 
dist 2=[112.78915590941457189   ,128.69657606612164344   ] 
dist 3=[100.60213912566135978   ,130.77216288807729700   ] 
dist 4=[87.933351203317280703  ,130.98815112199638933   ] 
dist 5=[78.605797326854734867  ,130.33598338856672541   ] 
dist 6=[70.082589430621737098  ,129.46790665472093213   ] 
dist 7=[60.594701284045055495  ,122.13012130808451950   ] 
dist 8=[51.341570346217587567  ,106.84194589902817762   ] 
dist 9=[43.736974257514418267  ,97.272916190358149437  ] 
dist 10=[35.930925651310550314  ,95.899799367774298999  ] 
dist 11=[25.850731009386802378  ,75.115475035144364132  ] 
dist 12=[16.185483024965996921  ,70.780699077542886257  ] 
dist 13=[10.025317296644730758  ,66.749566098889574939  ] 
dist 14=[5.2423410018913591070 ,65.979143933376891704  ] 
dist 15=[1.0674595020529778108 ,34.476925073444386694  ] 
dist 16=[-4.3431858299244038796 ,10.766242111917189988  ] 
dist 17=[-10.378506414906333454  ,-.38522304539927353258] 
dist 18=[-14.505833335579294892  ,-.59247624197069276914] 
dist 19=[-20.096108872283582261  ,.29462541464872411357] 
dist 20=[-24.439634299375306101  ,1.4249565703588821662 ] 
dist 21=[-27.391745008560757362  ,2.2855265510671039332 ] 
dist 22=[-29.189356677112055169  ,3.0334514999893259089 ] 
dist 23=[-30.248885720064904202  ,3.7306419862780274426 ] 
dist 24=[-30.385576899670590698  ,4.2703492273875799873 ] 
dist 25=[-29.928624399262879966  ,4.4075916630133530920 ] 
dist 26=[-29.556022050365501699  ,4.3945813852130952788 ] 
dist 27=[-25.708620634313652970  ,4.3905087162876738467 ] 
dist 28=[-24.677404974186993074  ,2.8260160712667155083 ] 
dist 29=[-23.170571875968438926  ,2.4282391616113184959 ] 
dist 30=[-22.586891650462790334  ,3.9408901967307808153 ] 
dist 31=[-8.2631990792941779497 ,5.9195436002109749094 ] 
dist 32=[-6.3656896277941240115 ,7.6762145003372945916 ] 
dist 33=[-2.1963408097808301718 ,11.206139850383800076  ] 
dist 34=[-1.8406121345883786201 ,15.046105711971864997  ] 
dist 35=[-1.7361304190175836660 ,18.286222201867333695  ] 
dist 36=[.17947774425939194233,20.079974566528713497  ] 
dist 37=[.41966391106205390643,21.123836535528209831  ] 
dist 38=[.90768014392342990527,21.386750886343529291  ] 
dist 39=[1.0221655301589698156 ,8.5298041045606455639 ] 
dist 40=[1.3793330222399105204 ,6.7351425069503679109 ] 
dist 41=[1.1074973001889894003 ,6.6068213000274688800 ] 
dist 42=[-.14443930115617160929,6.5753090990156038036 ] 
dist 43=[-1.4038306130641467161 ,5.5194129892441768341 ] 
dist 44=[-2.5369146724673917665 ,5.2533674351334645488 ] 
dist 45=[-3.2886772827033133415 ,5.0466288797140791535 ] 
dist 46=[-3.8900047057534178397 ,4.9661038487909738309 ] 
dist 47=[-4.4273814337189836881 ,1.8024630525464845336 ] 
dist 48=[-4.8568802060213796557 ,1.4004752090853809596 ] 
dist 49=[-5.0303861214769636294 ,1.3146874390892254673 ] 
dist 50=[-5.0843988627605927120 ,1.1550575406074213810 ] 
dist 51=[-5.0506042889039977855 ,1.1122888842733126966 ] 
dist 52=[-4.6262701421062684010 ,.82152022642730940857] 
dist 53=[-4.4839369571063086775 ,.82771500145963650067] 
dist 54=[-4.2580704228579492217 ,.82882195779285204347] 
dist 55=[-4.1670212227366514047 ,.82120283437642229286] 
dist 56=[-3.5718722599031458494 ,.80702933073079319313] 
dist 57=[-3.4527423374964673665 ,1.3891416719329848483 ] 
dist 58=[-3.4227166521215900331 ,2.1338095957915588118 ] 
dist 59=[-2.8258891918584447602 ,2.8219314770580509123 ] 
dist 60=[-2.6795528643391683240 ,3.4028198171540347268 ] 
dist 61=[-2.5422047436155555046 ,3.7220530266119307022 ] 
dist 62=[-2.4793096579550178604 ,3.9039694548066979045 ] 
dist 63=[-.66231823064870634222,3.9400246429791093444 ] 
dist 64=[-.47206043747043479472,1.1256825016776272395 ] 
dist 65=[-.03974671828050018187,1.1623422406008701331 ] 
dist 66=[-.02222221698236293876,1.4620460581466758122 ] 
dist 67=[-.01863705676844605471,1.7760717580865347578 ] 
dist 68=[.03016577944234216379,1.9556531141725685976 ] 
dist 69=[.03677699328758498336,2.0647776019243760665 ] 
dist 70=[.04652624179311096671,2.0900355043775908110 ] 
dist 71=[.04871067165452398216,.96040089505000978988] 
dist 72=[.04837768800049522181,.82054404206795478309] 
dist 73=[.02012428378925738390,.79457323560150393982] 
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dist 76=[-.40756190022201400454,.61189842374481597261] 
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dist 81=[-.62209068795851125955,.04268982978997171606] 
dist 82=[-.61873572714077856497,.03510382529123814147] 
dist 83=[-.61119730901689579728,.03299462782715815034] 
dist 84=[-.5412834340116912703 ,.03881819912926679695] 
dist 85=[-.52112771663938833395,.04818661537135872907] 
dist 86=[-.49033032875568864437,.05619467800320177058] 
dist 87=[-.47847330783461754846,.06413051341975569044] 
dist 88=[-.40971525791740661911,.07115501112364523164] 
dist 89=[-.39737261964398339296,.1679892130873064812 ] 
dist 90=[-.39119109364235932376,.25885630012190285934] 
dist 91=[-.33497352840691010288,.3427312786427915436 ] 
dist 92=[-.32046245194709315642,.41360885301451555535] 
dist 93=[-.29829303742043551035,.45289046018065518085] 
dist 94=[-.29030715741841766487,.47576667058101548848] 
dist 95=[-.09897336033070414320,.48153026354856387006] 
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dist 97=[-.01626201912363160879,.18276580576198912127] 
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dist 99=[-.01623162683544047650,.27888947840005001243] 
dist 100=[-.02623278401958557163,.3029229335592414075 ] 
dist 101=[-.03304564075853893626,.31655430511177447248] 
dist 102=[-.03867951225055528721,.31915575196863692264] 
dist 103=[-.04400329495892736434,.11300188527648868186] 
dist 104=[-.04858053946184328761,.09511916255675534520] 
dist 105=[-.05125244191631226346,.09167209081608967001] 
dist 106=[-.05298386620707874710,.09098733497677723944] 
dist 107=[-.05382936817318800284,.07451015804220786728] 
dist 108=[-.06434376707549773666,.07052667215490252489] 
dist 109=[-.07366080011152020274,.06720754971566809945] 
dist 110=[-.07990567535137307124,.06599524669395871448] 
dist 111=[-.08341967886958003791,.03501465601832211130] 
dist 112=[-.08513523559829784594,.02957564513627786004] 
dist 113=[-.08521760232732340093,.0282545373004457641 ] 
dist 114=[-.08274421184053059278,.02541142868077861588] 
dist 115=[-.08206238510960032765,.02448641473224042873] 
dist 116=[-.06818215642128624309,.01095668745276884015] 
dist 117=[-.06472683202552247938,.00890406791277064168] 
dist 118=[-.06150262626171150199,.00477034018029144603] 
dist 119=[-.05995669218925493825,.00372075526465243886] 
dist 120=[-.05236555144760337900,.00471112983358079155] 
dist 121=[-.05020035350231568159,.01663240758137487897] 
dist 122=[-.04970060754259115331,.02635944432202822282] 
dist 123=[-.04060682688698069704,.03535926081129580710] 
dist 124=[-.03842022762355674626,.04298673163473947627] 
dist 125=[-.03631630223233850510,.04754794892354008359] 
dist 126=[-.03538302931688806221,.05016361006986449944] 
dist 127=[-.00865347928857663634,.05077512448621573483] 
dist 128=[-.00589406592625682507,.01989084464359329216] 
dist 129=[.00033258266909472443,.01997787565835037661] 
dist 130=[.00158499097061453393,.02222318411477689630] 
dist 131=[.00846863935916172733,.02674957675866485677] 
dist 132=[.00962138458435958883,.02926624771874858944] 
dist 133=[.01157559688921087961,.03078911262157360200] 
dist 134=[.01056303954997695613,.03115666144496394254] 
dist 135=[.00620109770233566997,.01449914208132785987] 
dist 136=[.00180930462728498537,.01203477757709713919] 
dist 137=[-.00116351288160786293,.01153326437649963715] 
dist 138=[-.00360782702064250318,.01146070477418317972] 
dist 139=[-.00590172911738842792,.00923059750970865254] 
dist 140=[-.00786930306747468673,.00870249639763326212] 
dist 141=[-.00901826109979785574,.00832141322838067460] 
dist 142=[-.00976622029663578940,.00823641141219630583] 
dist 143=[-.01014205397205969717,.00072178051462520476] 
dist 144=[-.01030331843580215214,-.00015339007999642061] 
dist 145=[-.01028680753783211298,-.00218438818113076283] 
dist 146=[-.01001726526441271221,-.00248234006978601078] 
dist 147=[-.00986738652153241710,-.00483535003953153655] 
dist 148=[-.00848827993815933722,-.00517956980656103834] 
dist 149=[-.00812677446795806312,-.00579959880823663193] 
dist 150=[-.00757894309832908574,-.00409148626738684823] 
dist 151=[-.00737784015569874181,-.00144473434766897480] 
dist 152=[-.00605084743487550350,.00120918375384241422] 
dist 153=[-.00583247614585786811,.00298996460259557822] 
dist 154=[-.00573767053466971684,.00443761090508208967] 
dist 155=[-.00486672223545565053,.00576895075926397189] 
dist 156=[-.00464658087259896356,.00689232533951403841] 
dist 157=[-.00431407342604156472,.00751431548409287369] 
dist 158=[-.00419448659015747759,.00787666981752469333] 
dist 159=[-.00136402890787863041,.00796781979692367255] 
dist 160=[-.00098921891435913969,.00244496247363761459] 
dist 161=[-.00015316557202917119,.00264746167474626568] 
dist 162=[2.96376131377940785590e-05,.00341623080864472888] 
dist 163=[.00092984714570134911,.00406440904388532325] 
dist 164=[.00108756140444814637,.00442306946485638695] 
dist 165=[.00133850450055649219,.00463174170814475407] 
dist 166=[.00111300781638375083,.00468434752728887144] 
dist 167=[.00055492972176983597,.00172260751726909427] 
dist 168=[-5.59464514448298894120e-06,.00144130644765368580] 
dist 169=[-.00038341547118882451,.00137901683700934891] 
dist 170=[-.00069246771110492500,.00136756034927898258] 
dist 171=[-.00097997689686572418,.00110652995170864893] 
dist 172=[-.00122494631983822071,.00104452618672897073] 
dist 173=[-.00136511316191111473,.00099249844890072256] 
dist 174=[-.00145275972095686020,.00097486102914602611] 
dist 175=[-.00148922168890433952,.00017809296300757306] 
dist 176=[-.00149630213831783680,8.36540988383876721800e-05] 
dist 177=[-.00148993206079216349,-.00013305962042208201] 
dist 178=[-.00143246998619112162,-.00016992629878842825] 
dist 179=[-.00141644116549772642,-.00041720060296635320] 
dist 180=[-.00116929755774839555,-.00045552937201267526] 
dist 181=[-.00110897632184261028,-.00047949549325354140] 
dist 182=[-.00104440565187432307,-.00029980665875158175] 
dist 183=[-.00101151885529961194,-2.85708835966207000000e-05] 
dist 184=[-.00085284158542824221,.00024344256207372965] 
dist 185=[-.00081576287172969714,.00042622416268716400] 
dist 186=[-.00080610894477933567,.00057513891661014608] 
dist 187=[-.00066095740571312324,.00071269096448037856] 
dist 188=[-.00062602160354367214,.00082922044393231604] 
dist 189=[-.00058839494909312203,.00089466890208490416] 
dist 190=[-.00056954474566881702,.00093839535874397281] 
dist 191=[-.00020395141751332515,.00094856573870644699] 
dist 192=[-.00017538624229770683,.00049693477896486661] 
dist 193=[-.00011464714722935798,.00049572899728765158] 
dist 194=[-9.81632514370113677400e-05,.00049102634639683793] 
dist 195=[-3.64052271521212337060e-05,.00048519980740503122] 
dist 196=[-2.33972063780598689690e-05,.00051500743081682628] 
dist 197=[-5.09541308448435500680e-06,.00053650407594142886] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 1, 0, 1, 1, 2] 
dist 0=[121.93386262374356099   ,121.93386262374356099   ] 
dist 1=[120.58831714967286937   ,123.13830259007397616   ] 
dist 2=[118.07912155176558566   ,123.86954801953073106   ] 
dist 3=[112.96033281573724850   ,123.62277261235298921   ] 
dist 4=[104.21294765608131757   ,122.28456533122628402   ] 
dist 5=[94.966976660310843004  ,121.30612976695391935   ] 
dist 6=[87.858539926862612162  ,115.28574211061715519   ] 
dist 7=[81.046080455304530116  ,107.52083125123692227   ] 
dist 8=[69.253310038804413221  ,91.528363053771097068  ] 
dist 9=[58.339297168069685650  ,90.153036192791517044  ] 
dist 10=[48.434772399462948207  ,72.124223237657181233  ] 
dist 11=[37.506323670521198270  ,68.358189100394202572  ] 
dist 12=[26.903478234915127405  ,64.464475733128419929  ] 
dist 13=[18.278479627582125293  ,63.382794597179504604  ] 
dist 14=[9.5071433241307266465 ,45.667204577669501264  ] 
dist 15=[-1.7044750509075991278 ,36.987166730341239662  ] 
dist 16=[-12.230889963160119871  ,14.825367353799249201  ] 
dist 17=[-18.282620764230153422  ,7.8296156288213765465 ] 
dist 18=[-22.237825950941026892  ,6.5206725485328041306 ] 
dist 19=[-24.415262844681700725  ,4.3718066310935225973 ] 
dist 20=[-25.763272951863439489  ,3.9069712610248143238 ] 
dist 21=[-26.700511915172952049  ,3.1475788994483142023 ] 
dist 22=[-28.445345738711812011  ,3.207028014129167885  ] 
dist 23=[-28.855270056423523027  ,3.589156893787167684  ] 
dist 24=[-29.366026174710300944  ,4.451061813881780255  ] 
dist 25=[-29.479718963389598723  ,5.502116586387956347  ] 
dist 26=[-26.982754260931278489  ,6.642980543875192910  ] 
dist 27=[-26.204490652588005911  ,8.039131813767539037  ] 
dist 28=[-22.747728802077515799  ,10.112189814761106096  ] 
dist 29=[-22.384904631000903625  ,12.064362131566254555  ] 
dist 30=[-5.4591554709652003395 ,12.983291780824158477  ] 
dist 31=[-3.4269773980462697663 ,13.440190347015067334  ] 
dist 32=[1.3800837381474844766 ,13.554715063259755035  ] 
dist 33=[2.0778144040242139830 ,13.992993966502334809  ] 
dist 34=[7.9784919549496908303 ,14.395228091341187604  ] 
dist 35=[8.8777411147325919726 ,14.423759128412188875  ] 
dist 36=[6.1188310486910248334 ,13.939268471981788202  ] 
dist 37=[3.0604042906030389783 ,14.577160545699950554  ] 
dist 38=[.9289067223686692884 ,14.881111929175272627  ] 
dist 39=[-.8822013645467935426 ,14.896095439153328373  ] 
dist 40=[-2.6709796080753015795 ,14.432249479554191695  ] 
dist 41=[-4.2606648146650259963 ,14.321741126939264478  ] 
dist 42=[-5.2827286816257890131 ,11.769496711349722594  ] 
dist 43=[-6.0642941018960270911 ,11.143424307796335624  ] 
dist 44=[-6.7257815627675090276 ,10.589045372956277225  ] 
dist 45=[-7.6006325454110306414 ,10.354150243159767268  ] 
dist 46=[-8.0977755938640968309 ,3.0004975989296526229 ] 
dist 47=[-8.2099587117969978966 ,2.2089250321918676030 ] 
dist 48=[-7.2785542491664255074 ,.39055893314307584712] 
dist 49=[-6.5531972698814765995 ,.04560680619511131484] 
dist 50=[-7.4004222225679082105 ,-2.0748504613452746205 ] 
dist 51=[-8.1704540702617838946 ,-2.4172605994312162154 ] 
dist 52=[-8.6045777608012501281 ,-1.4150043160215624324 ] 
dist 53=[-8.7045301661622068904 ,.5654812915901946156 ] 
dist 54=[-3.4789777651604291324 ,1.9013919837675014437 ] 
dist 55=[-3.5051346037172733838 ,2.9925737256483692252 ] 
dist 56=[-3.4399985108155711812 ,4.0020089756203521444 ] 
dist 57=[-3.4303339049221058565 ,4.8557780657158661059 ] 
dist 58=[-2.8591047366040487430 ,5.3292544139474196793 ] 
dist 59=[-2.7157758073490943015 ,5.6051039437872882184 ] 
dist 60=[-2.6248133587091769365 ,5.6746150202718967072 ] 
dist 61=[-2.6024379766673166881 ,1.7433475909921882740 ] 
dist 62=[-.38961924103030215391,1.7724303252345519119 ] 
dist 63=[-.13043080113865699195,1.7872837947292293928 ] 
dist 64=[.47060502163851699065,1.9006926408396743403 ] 
dist 65=[.56274013778527616013,1.9339916995706565774 ] 
dist 66=[1.2580937851497724024 ,1.9334455938542220554 ] 
dist 67=[.99699406747977688083,1.9122977601523082921 ] 
dist 68=[.5892618228710139808 ,1.7115885495982187156 ] 
dist 69=[.1764965625224792234 ,1.7385906527283665606 ] 
dist 70=[-.10514492167233237956,1.7747723042640923121 ] 
dist 71=[-.33884463405133100503,1.7746454744785820804 ] 
dist 72=[-.56138355192968674483,1.7336934397612768579 ] 
dist 73=[-.75424461128917768968,1.7087722761181792733 ] 
dist 74=[-.87018523895214390458,1.4753337925303483324 ] 
dist 75=[-1.0516613489368816193 ,1.4135489425436226285 ] 
dist 76=[-1.2743280890456293630 ,1.3206191567647955671 ] 
dist 77=[-1.3977945281772652429 ,1.2860124974321247675 ] 
dist 78=[-1.4697539583811862204 ,.44749662633467960333] 
dist 79=[-1.4878727674426348034 ,.33627774950800634837] 
dist 80=[-.99475675236148999525,.08601481395742949358] 
dist 81=[-.97937808200052237199,.03221321204585967881] 
dist 82=[-1.1732261711952138763 ,-.24498270963060132882] 
dist 83=[-1.2806008381502175387 ,-.29283747411054604337] 
dist 84=[-1.3432115206272622948 ,-.16425682995984020554] 
dist 85=[-1.3589079861164896023 ,.05066508429710154064] 
dist 86=[-.41886204174397323225,.19549763681081824126] 
dist 87=[-.41956519862716271197,.3138042430148945451 ] 
dist 88=[-.40694924669413519564,.42344171278554159211] 
dist 89=[-.4046978229924123803 ,.51739491344484952252] 
dist 90=[-.33298578908004888891,.57345270898696031129] 
dist 91=[-.31677549985244180712,.60506128581885756039] 
dist 92=[-.30238533258721205712,.61250683727429944245] 
dist 93=[-.29832280066235012832,.24076177371624636318] 
dist 94=[-.06672355670419301942,.25229251435275320423] 
dist 95=[-.03861895085855784727,.26466902241127060501] 
dist 96=[.02654144982949822737,.27128377071453417271] 
dist 97=[.03735277273314508553,.27194549092901464918] 
dist 98=[.11410278528524313845,.26468974615199337463] 
dist 99=[.12582939445820075886,.26277893582881306769] 
dist 100=[.07754910216336033579,.24752258857818037427] 
dist 101=[.02405968846868698533,.25418657985775811417] 
dist 102=[-.01221232946836557721,.25579240199407977329] 
dist 103=[-.04209905359841932044,.25483639384474526672] 
dist 104=[-.07024407104473808579,.2452214198761689733 ] 
dist 105=[-.09444675310515404436,.24255781140920304805] 
dist 106=[-.1086856302034833521 ,.20025812286946458722] 
dist 107=[-.11808657724242466132,.18992266761208356743] 
dist 108=[-.13245747676483106753,.17902757922395611164] 
dist 109=[-.14708928529594069318,.17341412168671357287] 
dist 110=[-.15537545536121432726,.06568058675014209675] 
dist 111=[-.15732139717426222852,.05716466168339890726] 
dist 112=[-.12061521963597129066,.03874469776917601122] 
dist 113=[-.12016848169203843919,.03364967367473745835] 
dist 114=[-.14006044561472850339,.01397240199235299480] 
dist 115=[-.1512597400543972648 ,.00994468727243759166] 
dist 116=[-.15897402554931907609,.00293675085942014024] 
dist 117=[-.16072363756051671544,.01437906287225928500] 
dist 118=[-.04745875346917270953,.03615998079702014716] 
dist 119=[-.04705538603366157671,.05387226921378890845] 
dist 120=[-.00634995595052163471,.07016838830395338493] 
dist 121=[-.00158556955319309643,.08392131137580667073] 
dist 122=[.00945490820107673602,.09153705347267488193] 
dist 123=[.01114924590178341581,.09597490398845640034] 
dist 124=[.02389659134174497698,.09709072953773856034] 
dist 125=[.02579494168627443513,.02977955192364140301] 
dist 126=[.02859549847597435004,.03113876472487250131] 
dist 127=[.02742503125883306675,.03244292475171800439] 
dist 128=[.02491578201392708449,.03305656966342719914] 
dist 129=[.02180508329218124534,.03303405957111892221] 
dist 130=[.01824633855830055438,.03223954133399975116] 
dist 131=[.01375129572796808506,.03176361815245656094] 
dist 132=[.00692288211739348425,.02741486489271360784] 
dist 133=[6.06328258416194470700e-05,.02626466402474435377] 
dist 134=[-.00456897855287398619,.0245116037754404029 ] 
dist 135=[-.00835994492674331202,.02386843586988264696] 
dist 136=[-.01189285344849480529,.00825866198993520729] 
dist 137=[-.01490696942092740312,.00617331723906479876] 
dist 138=[-.01663837611866291566,.00148304533789555231] 
dist 139=[-.01853950398281162416,.00047292724771319225] 
dist 140=[-.02217571509139075474,-.00471463435393273456] 
dist 141=[-.02418898538810291267,-.00561135721899380688] 
dist 142=[-.02536070642266821371,-.00717101096144540661] 
dist 143=[-.02565584696131550548,-.00746614180418368370] 
dist 144=[-.01736527416327530496,-.00774251715900836070] 
dist 145=[-.01435446424280070014,-.00764376128725945259] 
dist 146=[-.01361753948710632129,-.00591638117773399513] 
dist 147=[-.01282974021169717944,-.00371606232922539341] 
dist 148=[-.01242714479279957065,-.0003907190244531488 ] 
dist 149=[-.00587706770746786043,.00294526022533736801] 
dist 150=[-.00561669295850920522,.00518787903737985243] 
dist 151=[-.00551770663352061772,.00701586801548700028] 
dist 152=[-.00241154035065517931,.00870568654689617571] 
dist 153=[-.00099917949001702095,.01013801638782647404] 
dist 154=[-.00070955781145812603,.01094371840915949199] 
dist 155=[-.00020846490372010442,.01149243419174384889] 
dist 156=[-9.41352692833238770250e-05,.01161725682656048014] 
dist 157=[.00290906877174466286,.00395714959926651238] 
dist 158=[.00332819864048487071,.00423816924090635308] 
dist 159=[.00339452436837246162,.00436114434559624428] 
dist 160=[.00331853304824557415,.00439299863303927093] 
dist 161=[.00292523596067566265,.00437892176796585554] 
dist 162=[.00248097158492945589,.00421326259892160380] 
dist 163=[.00192329301719376083,.00417265929428226236] 
dist 164=[.00107965132498383905,.00342827523129339518] 
dist 165=[.00023281502004594586,.00324737939153164102] 
dist 166=[-.00033756868354665271,.00307270222101165893] 
dist 167=[-.00080375708398543437,.00299202592081718307] 
dist 168=[-.00123691248932354606,.00078133584674075417] 
dist 169=[-.00160567895651509729,.00055487870737601094] 
dist 170=[-.00181622778399888803,4.31540677456833688480e-05] 
dist 171=[-.00194732932528607565,-6.13571683114449634680e-05] 
dist 172=[-.00225318903258558329,-.00063155744731863080] 
dist 173=[-.00246553851368636468,-.00072755679112382076] 
dist 174=[-.00259905427145902323,-.00089592963975820930] 
dist 175=[-.00262978544369366188,-.00092658386449643954] 
dist 176=[-.00190620924089641732,-.00095103067224949602] 
dist 177=[-.00163101766169353118,-.00093282400858153524] 
dist 178=[-.00156014766301397880,-.00088916610816250561] 
dist 179=[-.00144743703442600462,-.00070567532326135046] 
dist 180=[-.00140864758119351501,-.00019961170063876126] 
dist 181=[-.00073901373399565664,.00030725877448300574] 
dist 182=[-.00070839127853813261,.00064704717315040028] 
dist 183=[-.00070137045137197476,.00092304791360072854] 
dist 184=[-.00018692155350077082,.00117664694424696516] 
dist 185=[-.00012436030184954834,.00139058611598292218] 
dist 186=[1.88619015220628405820e-05,.00150911456998600780] 
dist 187=[4.54853117276807299590e-05,.00157879901730885247] 
dist 188=[.00021013847086767671,.00159608250434069039] 
dist 189=[.00023657001472806873,.00061306968378736350] 
dist 190=[.00028602389593940509,.00064904383438911787] 
dist 191=[.00029504274245283590,.00066355578818137115] 
dist 192=[.00024101700101188416,.00066673124275437328] 
dist 193=[.00017286143148349611,.00066241499998582810] 
dist 194=[9.68977372649904534890e-05,.00064405790700172689] 
dist 195=[2.18375311352291883600e-06,.00063241901950137678] 
dist 196=[-.00014042644070085647,.00055785853707678182] 
dist 197=[-.00028335795758628556,.00053801246507208456] 
dist 198=[-.00037934984191890419,.00049437091547617867] 
dist 199=[-.00045751861038969105,.00047913726124300011] 
dist 200=[-.00052968284623792749,.00023969125249882015] 
dist 201=[-.00059080737634462445,.00020352348891039702] 
dist 202=[-.00062514253407286823,.00012637316977705529] 
dist 203=[-.00064579821012420248,.00010551035310585939] 
dist 204=[-.00065260783957351755,2.76326699937266376580e-05] 
dist 205=[-.00065140120806273384,1.13889469487562119110e-05] 
dist 206=[-.00064554805606456326,-1.06521743640356217510e-05] 
dist 207=[-.00061985186134500450,-1.56963748478899773000e-05] 
dist 208=[-.00022743147475607840,-1.62479096512456196470e-05] 
dist 209=[-.00019776193437661308,-1.28660762691304056690e-05] 
dist 210=[-.00018989861519334679,-6.03359461375159231000e-06] 
dist 211=[-.00017486674806263179,7.11760831084478490000e-06] 
dist 212=[-.00017009979906356414,2.29924660447036482290e-05] 
dist 213=[-8.76957259644369258180e-05,6.36053315871493545580e-05] 
dist 214=[-8.20994986845538981310e-05,.00010305355122809391] 
dist 215=[-8.00377701213826683700e-05,.00013511554398421620] 
dist 216=[-2.31895788692989235130e-05,.00016461379501284268] 
dist 217=[-1.58438113508580367240e-05,.00018953079091080652] 
dist 218=[8.20572382466417545800e-07,.00020340207559945545] 
dist 219=[4.09588639377893737100e-06,.00021199103748096196] 
dist 220=[2.28207400009867584930e-05,.00021390760800797718] 
dist 221=[2.59132937229928846650e-05,7.68780164163072994020e-05] 
dist 222=[2.70835183161091826540e-05,8.10467216279530492640e-05] 
dist 223=[2.43798790066187480080e-05,8.25209127050598913100e-05] 
dist 224=[1.91987235537086845400e-05,8.25237513163749178290e-05] 
dist 225=[1.29513844505733550110e-05,8.19832417948245781280e-05] 
dist 226=[6.01390292178351004270e-06,7.88584801746807637150e-05] 
dist 227=[-2.62018974852214403140e-06,7.75974232038451365020e-05] 
dist 228=[-1.56046654820465702840e-05,6.54230384877880858030e-05] 
dist 229=[-2.86148850745899965360e-05,6.23751871339856454370e-05] 
dist 230=[-3.73513606290277506980e-05,5.79317564866722410840e-05] 
dist 231=[-4.44655071818302956280e-05,5.62814394382609968810e-05] 
dist 232=[-5.10340073681501250940e-05,1.88334343841902904660e-05] 
dist 233=[-5.65991384426307785350e-05,1.62418489215828936180e-05] 
dist 234=[-5.97292476314861331580e-05,1.07107779728732184000e-05] 
dist 235=[-6.16179128789371781650e-05,9.20281495133144721990e-06] 
dist 236=[-6.22537088290235649820e-05,3.51261972308220402870e-06] 
dist 237=[-6.22415518844919388390e-05,2.32107035583203117680e-06] 
dist 238=[-6.15954227794626093880e-05,5.56443592341930899540e-07] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 2, 2, 2, 0, 2] 
dist 0=[148.61580103217921357   ,148.61580103217921357   ] 
dist 1=[146.12405898708127315   ,149.31187317593899889   ] 
dist 2=[139.72880840002339012   ,148.64680536363822322   ] 
dist 3=[131.49063315689921142   ,147.62769348579064089   ] 
dist 4=[121.67135779197807808   ,139.58384713850729726   ] 
dist 5=[108.99770092903209805   ,132.81407115324485905   ] 
dist 6=[89.412027393536906643  ,129.58603808808355851   ] 
dist 7=[69.493238908804204143  ,126.93834828838759377   ] 
dist 8=[55.489943645474632496  ,118.63219333759551183   ] 
dist 9=[43.355764989448445629  ,98.865832513243744748  ] 
dist 10=[30.851744571242388559  ,98.008155474007177281  ] 
dist 11=[19.261030862840997945  ,46.679497543818079573  ] 
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dist 188=[-.00014575901696403199,.00104997856624406393] 
dist 189=[-1.14025654943761964270e-05,.00110523682280596294] 
dist 190=[1.71072538106828741800e-05,.00111838418987670281] 
dist 191=[.00016312674723391789,.00062578165494148450] 
dist 192=[.00018828985114678028,.00068207161277001080] 
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dist 198=[8.15621409677246848640e-05,.00031883598712553691] 
dist 199=[-3.10500955370455463110e-05,.00023840585965321201] 
dist 200=[-.00010664621607274638,.00023163897723736627] 
dist 201=[-.00016817055997940163,.00021169229905589645] 
dist 202=[-.00022490993032767481,.00020558274217710885] 
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dist 204=[-.00029982661511007243,.00011816730511299021] 
dist 205=[-.00031590975604428813,9.20029794269229961310e-05] 
dist 206=[-.00032098699101450523,8.49224494493282662400e-05] 
dist 207=[-.00032042357093973532,5.91823570896709582480e-05] 
dist 208=[-.00031790211022800560,5.29391025577223219330e-05] 
dist 209=[-.00030638220231131574,4.60652312836574362480e-05] 
dist 210=[-.00028095908748932732,4.42192958659554002370e-05] 
dist 211=[-.00017735140455579199,4.37965931417109028240e-05] 
dist 212=[-.00016925535424848721,4.44656894321001554370e-05] 
dist 213=[-.00015738624301379880,4.60452554840103591860e-05] 
dist 214=[-.00015298042133465436,4.92385658234660196230e-05] 
dist 215=[-.00011704139543635724,5.31437279113358153710e-05] 
dist 216=[-.00011112232087884903,6.46284664193653867010e-05] 
dist 217=[-.00010380496772860799,9.48148916307760876720e-05] 
dist 218=[-.00010061445851856676,.00012253073762693076] 
dist 219=[-2.35758808391404704270e-05,.00014590179449915125] 
dist 220=[-1.37183471926792782050e-05,.00015883631227330130] 
dist 221=[8.49898460715896643140e-06,.00016636430664510137] 
dist 222=[1.28009301835954923380e-05,.00016826750141181275] 
dist 223=[3.34918672068556160910e-05,.00010319711648542133] 
dist 224=[3.59998793949304186020e-05,.00010247579632800651] 
dist 225=[4.05956823782733051470e-05,.00010091276289808709] 
dist 226=[4.12828896312691396330e-05,9.78333383265158899540e-05] 
dist 227=[3.66248833767869645910e-05,4.38796628717856942830e-05] 
dist 228=[3.01547965697916149210e-05,4.18597460032813678200e-05] 
dist 229=[2.16148728343715250700e-05,3.99520186705335824310e-05] 
dist 230=[7.85955953966156805490e-06,3.92070622997120219100e-05] 
dist 231=[-5.91475657368353893090e-06,3.45240524938226307760e-05] 
dist 232=[-1.51514183797975066430e-05,3.32902872947153686560e-05] 
dist 233=[-2.26588724099862629600e-05,3.05381792159616534370e-05] 
dist 234=[-2.95669872476445466240e-05,2.95747792341184611920e-05] 
dist 235=[-3.54033424712312830900e-05,1.50005265766163190490e-05] 
dist 236=[-3.86551254199079480240e-05,1.27808259744810173570e-05] 
dist 237=[-4.05767587388649279080e-05,8.06996764060909397760e-06] 
dist 238=[-4.11314372053901518410e-05,6.79866372821432185130e-06] 
dist 239=[-4.10176871367981927660e-05,2.07432481861781981950e-06] 
dist 240=[-4.06422775296787625470e-05,1.07795519370995017780e-06] 
dist 241=[-3.93284453435754600630e-05,-2.31516735141383432500e-07] 
dist 242=[-3.65650195047341492700e-05,-5.13691247686264502500e-07] 
dist 243=[-2.52094093458583782640e-05,-5.15600977330420755600e-07] 
dist 244=[-2.37778764705482630680e-05,-2.67919327310457532500e-07] 
dist 245=[-2.25268876199541946470e-05,2.04550299059643589400e-07] 
dist 246=[-2.20794957740775177010e-05,1.09531551886159256650e-06] 
dist 247=[-7.02460332148865302290e-06,4.99312704999819148290e-06] 
dist 248=[-6.05270572671142737740e-06,8.53152112207870022440e-06] 
dist 249=[-3.98094287949474457380e-06,1.14083266449737047140e-05] 
dist 250=[-3.41693098073142067550e-06,1.40569856719956045690e-05] 
dist 251=[-1.29337031462889715630e-06,1.62958700965951249740e-05] 
dist 252=[-8.47909571039541045760e-07,1.75455658991086808990e-05] 
dist 253=[-1.98041929277184105660e-07,1.82962513121636750680e-05] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 2, 0, 0, 2] 
dist 0=[60.585096273686765164  ,60.585096273686765164  ] 
dist 1=[54.689242088875581988  ,65.874934485067851651  ] 
dist 2=[46.447741903798418917  ,71.695577575686065908  ] 
dist 3=[37.350521937674560129  ,76.945171832837628001  ] 
dist 4=[28.038228837444835008  ,79.958220186380304560  ] 
dist 5=[16.796981766968699779  ,81.901035000859322178  ] 
dist 6=[0                     ,82.888055655171911785  ] 
dist 7=[50.275884085933401400  ,83.332972525342440572  ] 
dist 8=[54.379586024485670582  ,83.243425445123130930  ] 
dist 9=[61.496951866224784555  ,82.625978942648871956  ] 
dist 10=[61.065404396284848771  ,82.142223367382270951  ] 
dist 11=[52.164198419337324238  ,74.098794335223708229  ] 
dist 12=[45.727443683140267903  ,72.686280753557899313  ] 
dist 13=[39.885612168455587680  ,69.755982484829469085  ] 
dist 14=[33.361340098799519367  ,68.424223813534640247  ] 
dist 15=[26.939792927209079407  ,57.062911513600435217  ] 
dist 16=[21.510907550089821074  ,50.492893164915521692  ] 
dist 17=[15.805372829000074404  ,24.323924956446848691  ] 
dist 18=[8.2854639435229662564 ,22.196212396192226213  ] 
dist 19=[1.0185262795387024384 ,13.854786838734396489  ] 
dist 20=[-3.6786910871158924152 ,12.509607370634601800  ] 
dist 21=[-7.3581194021263258014 ,4.7827326292971213886 ] 
dist 22=[-10.572522034507191106  ,3.5357182898372368474 ] 
dist 23=[-13.577573107494663432  ,.95758719315301044817] 
dist 24=[-15.526913246500822091  ,.52148934101744451037] 
dist 25=[-17.007245235913247907  ,-2.3554762540300418331 ] 
dist 26=[-18.226132449793648992  ,-2.8496186843505078488 ] 
dist 27=[-19.155649090241511470  ,-3.0504837108277511549 ] 
dist 28=[-19.483709022719208792  ,-2.7459965329898070621 ] 
dist 29=[-19.567154001099454711  ,-2.2130142898516484246 ] 
dist 30=[-19.518686460098772455  ,-1.4486390257637533169 ] 
dist 31=[-18.231824434006966541  ,-.3910060738996312053 ] 
dist 32=[-16.951519566318346250  ,1.3144182572156469525 ] 
dist 33=[-8.7101663758855951915 ,2.9997724571185070917 ] 
dist 34=[-8.5573494215004829871 ,3.9803889867175385254 ] 
dist 35=[-.84435122779397228922,4.6237348783309333559 ] 
dist 36=[.06448101991041510266,4.9697760040738261786 ] 
dist 37=[2.1410653983578125516 ,5.1768499228884121707 ] 
dist 38=[2.4615924775235432285 ,5.2674321448935219171 ] 
dist 39=[4.0574767127004559371 ,5.4737286057530585479 ] 
dist 40=[2.9893173789880464441 ,6.0908527166788082716 ] 
dist 41=[1.8538864744795196045 ,6.4437353751896636441 ] 
dist 42=[1.0240350148542057166 ,6.5297939823806417358 ] 
dist 43=[.28299603068640879388,6.3422533139614674450 ] 
dist 44=[-.50195464881687201023,6.2684912584354131675 ] 
dist 45=[-1.2308653577516540155 ,5.9669244113371586144 ] 
dist 46=[-1.7506625601278558855 ,5.8548616508800232856 ] 
dist 47=[-2.2056281719249941259 ,4.8981952003614562924 ] 
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dist 195=[-7.94323643833440798140e-06,.00017754686784866661] 
dist 196=[7.75040894181491834390e-06,.00017670284271120174] 
dist 197=[4.41091967660133237380e-05,.00014453242092686824] 
dist 198=[4.93815250550286528730e-05,.00013671720478470429] 
dist 199=[9.12773788687203823790e-05,.00013138489752484092] 
dist 200=[5.43325274716756012220e-05,.00013013708703792696] 
dist 201=[1.42045662468032446820e-05,.00010904316866315079] 
dist 202=[-1.28877411024374392300e-05,.00011061636239813051] 
dist 203=[-3.50946927836608012600e-05,.00010935164635247851] 
dist 204=[-5.58281357758474605730e-05,.00010836202412185600] 
dist 205=[-7.35438168250917206450e-05,.00010370524405971862] 
dist 206=[-8.37704846962253365430e-05,.00010192010161159617] 
dist 207=[-9.02803339751132533830e-05,8.55866912046534765980e-05] 
dist 208=[-9.32406671478335900090e-05,8.15510525057780505250e-05] 
dist 209=[-9.42482025081929551170e-05,7.54583479932253816710e-05] 
dist 210=[-9.39467525112620861360e-05,7.33003492775126727270e-05] 
dist 211=[-9.11535558569801889560e-05,2.28609378438938619950e-05] 
dist 212=[-8.97447675709537623040e-05,1.61919278666394602280e-05] 
dist 213=[-7.68298967987678245460e-05,1.38821761788443419960e-06] 
dist 214=[-7.34882365067082419290e-05,-1.87568099727195968930e-06] 
dist 215=[-7.31611336195558245610e-05,-1.75550447795729170950e-05] 
dist 216=[-7.95045320545298422570e-05,-1.26294914922946169110e-05] 
dist 217=[-8.31937869895133243410e-05,1.15107330711024099700e-05] 
dist 218=[-8.41226009082974404900e-05,2.76997401279063034520e-05] 
dist 219=[-2.54140713171246233440e-05,4.08534301615641965050e-05] 
dist 220=[-2.52134685507288474150e-05,5.29424350312631657470e-05] 
dist 221=[-2.39084100766380182960e-05,6.31402204978690288010e-05] 
dist 222=[-2.37100180978481758420e-05,6.87850590964427397500e-05] 
dist 223=[-1.88445160520992974440e-05,7.20700362337548364800e-05] 
dist 224=[-1.78085859144663105020e-05,7.28981986244032972300e-05] 
dist 225=[-1.68036511020217885190e-05,2.21837703531371592120e-05] 
dist 226=[-1.65868701713896135970e-05,2.21575590070155870910e-05] 
dist 227=[-2.69534400395716780090e-06,2.13404837581399716650e-05] 
dist 228=[-1.02146388444918933740e-06,2.12125672305316293230e-05] 
dist 229=[2.79540568361100522740e-06,1.72764349951606853410e-05] 
dist 230=[3.45484306810235255590e-06,1.64159516995929144540e-05] 
dist 231=[7.72262796878024444470e-06,1.55871634732971084050e-05] 
dist 232=[4.80951522893577506980e-06,1.54052718533228613800e-05] 
dist 233=[-2.86227685530926493580e-07,1.51022569383509579740e-05] 
dist 234=[-3.71605885316399458940e-06,1.52826920280677985650e-05] 
dist 235=[-6.51680225526178878240e-06,1.51690109668241192350e-05] 
dist 236=[-9.11487414026885100090e-06,1.50451000540700017400e-05] 
dist 237=[-1.13238050841171966270e-05,1.43367734169272322880e-05] 
dist 238=[-1.25795395592016554340e-05,1.41595199042308847790e-05] 
dist 239=[-1.33543718905267866740e-05,1.15538350603990087760e-05] 
dist 240=[-1.36539824024434981980e-05,1.09327044519521999110e-05] 
dist 241=[-1.36871009437079607130e-05,1.02586422553089960290e-05] 
dist 242=[-1.36184223957388374530e-05,9.92601744560623609270e-06] 
dist 243=[-1.30741802946755606400e-05,3.41880955984639070050e-06] 
dist 244=[-1.29230773363078722420e-05,2.91480606862260021900e-06] 
dist 245=[-1.06590957840774213600e-05,1.85452234886279828200e-06] 
dist 246=[-1.01082998281131952280e-05,1.57035300995158100970e-06] 
dist 247=[-9.50993151823516348890e-06,5.27449075218366905150e-07] 
dist 248=[-9.21062590112012564320e-06,3.03583565673602982370e-07] 
dist 249=[-9.51443610380701549160e-06,2.45341653189979141210e-06] 
dist 250=[-9.60410869912031284780e-06,4.10703764860417647930e-06] 
dist 251=[-2.08795797703248842740e-06,5.45144216374493950570e-06] 
dist 252=[-1.83814317517590532420e-06,6.68872986448332691920e-06] 
dist 253=[-9.04826169551268984070e-07,7.73390020573207907020e-06] 
dist 254=[-4.61965341351770329700e-07,8.31550085628818434730e-06] 
dist 255=[-1.24120700003919001710e-07,8.65812751640903446810e-06] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 1, 1, 1, 2] 
dist 0=[135.55523885222342982   ,135.55523885222342982   ] 
dist 1=[130.06187572368199100   ,139.41478389854991935   ] 
dist 2=[122.77389933800501962   ,140.25323911555164891   ] 
dist 3=[112.92693385466468864   ,139.92941904786081631   ] 
dist 4=[97.257369102139416938  ,139.47112114612147499   ] 
dist 5=[81.156314621796683207  ,129.63884452167423624   ] 
dist 6=[69.587248282205835059  ,127.13296841067205579   ] 
dist 7=[59.301953573443019440  ,114.66775663478718652   ] 
dist 8=[48.287612629746781952  ,111.28095021434724603   ] 
dist 9=[37.808526819833033551  ,89.473890572002183777  ] 
dist 10=[29.636380339942989179  ,84.810411510543844020  ] 
dist 11=[21.647775174469715289  ,80.674088700705765680  ] 
dist 12=[11.872128811283097630  ,79.857330343744872704  ] 
dist 13=[2.7034038207481089864 ,40.458390680814120560  ] 
dist 14=[-2.8765198256904199106 ,38.101167066820559161  ] 
dist 15=[-6.9136814225588224581 ,32.257753239135953588  ] 
dist 16=[-10.063813957646627338  ,26.443778373768853129  ] 
dist 17=[-18.760172127558554798  ,-8.8817257925513108015 ] 
dist 18=[-24.105441829209929126  ,-8.8866381629758073408 ] 
dist 19=[-27.967545465945424089  ,-7.3945965727782676743 ] 
dist 20=[-30.777221535881885545  ,-4.1548325358706939472 ] 
dist 21=[-32.746013201591160715  ,-.67571355998848679882] 
dist 22=[-33.266889472377113888  ,1.7717651186791994721 ] 
dist 23=[-33.208914059637907636  ,3.8280214080955402061 ] 
dist 24=[-32.863895665714894242  ,5.7671389181351781144 ] 
dist 25=[-29.175907164682804377  ,7.3888056785004817675 ] 
dist 26=[-28.112543546100735036  ,8.1913116112156498623 ] 
dist 27=[-26.551986415014597854  ,8.5806830864220291764 ] 
dist 28=[-25.923424959466957979  ,8.5893988644940415246 ] 
dist 29=[-10.032294867936666816  ,7.7566325537688143182 ] 
dist 30=[-7.9173441700197964053 ,7.4675378063875798506 ] 
dist 31=[-3.0955749119051835206 ,12.175158533653003569  ] 
dist 32=[-2.1010189638330027532 ,16.513804135131289850  ] 
dist 33=[.716218652613402208  ,20.176651788286441445  ] 
dist 34=[.5008406056910244332 ,22.202142448524654691  ] 
dist 35=[.09876305293785076268,23.376292798051798573  ] 
dist 36=[-.64337684711706908744,23.659869734237104332  ] 
dist 37=[-1.4242244718992215415 ,7.7531842344819540439 ] 
dist 38=[-1.9802294404803613544 ,7.6540048864425783761 ] 
dist 39=[-2.4611527451270194339 ,7.5938437501001458512 ] 
dist 40=[-2.9452568123727311027 ,7.5779376479020893781 ] 
dist 41=[-3.3776371533251132251 ,6.2243729168030843326 ] 
dist 42=[-3.6539421603469790628 ,5.9369711666927304169 ] 
dist 43=[-3.8614552293100910481 ,5.7592000214665411367 ] 
dist 44=[-4.0214899742612813044 ,5.7150958725141919352 ] 
dist 45=[-4.1393518031898484015 ,2.9322699789146516336 ] 
dist 46=[-4.1798243853994531916 ,2.8122405374891892070 ] 
dist 47=[-4.1707695441368053182 ,2.5024935650372103482 ] 
dist 48=[-4.1234514129087548128 ,2.4091543263754002006 ] 
dist 49=[-4.1887519092842262742 ,1.8538530387137622262 ] 
dist 50=[-4.3476712277161641104 ,1.7342285516284741075 ] 
dist 51=[-4.4001185926919183594 ,1.4919234583853304803 ] 
dist 52=[-4.3722750322396228283 ,1.4219093284097974261 ] 
dist 53=[-4.0060737861244557700 ,.41642874611096073422] 
dist 54=[-3.8820675978686417404 ,.26653802914971648332] 
dist 55=[-3.6941069359428555439 ,-.01104165566710290733] 
dist 56=[-3.6143639920894120803 ,-.07356970039623535026] 
dist 57=[-3.0951251612943390331 ,.23657963506052949575] 
dist 58=[-2.9691897262398117056 ,1.0383113298307792265 ] 
dist 59=[-2.7817236975667227982 ,1.6945700030096403633 ] 
dist 60=[-2.7103098420190134467 ,2.3032558274724615028 ] 
dist 61=[-.9599053996231217425 ,2.8186217210123766984 ] 
dist 62=[-.72752288441715890814,3.1046594796694310131 ] 
dist 63=[-.20267297120603954204,3.2714808720847793837 ] 
dist 64=[-.09134496961345917423,3.3134864344299987568 ] 
dist 65=[.4961310219603184044 ,2.3900081781206618520 ] 
dist 66=[.59667344505012455886,2.6137631494541401093 ] 
dist 67=[.77821268521308583395,2.7439806070683971003 ] 
dist 68=[.81129484930111225152,2.7766321368625534950 ] 
dist 69=[.85648726417927826001,.94489951608997817751] 
dist 70=[.78472523304210327485,.90805422958091964205] 
dist 71=[.62844526435157995475,.88346733866866945167] 
dist 72=[.38189857136819309747,.87572041737117709669] 
dist 73=[.1314607863612445817 ,.70171035282189863678] 
dist 74=[-.04029751202596252018,.66581070406087794053] 
dist 75=[-.18365894995221959819,.63936017616787088722] 
dist 76=[-.32145177435017189674,.63068384996298450459] 
dist 77=[-.44165969721229202378,.11563170868391955425] 
dist 78=[-.51526380552763444004,.05450275363248079396] 
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dist 173=[-.00096446744065372626,9.65146616417025956820e-05] 
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dist 182=[-.00095072412630302099,-.00068178397225127312] 
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dist 200=[6.23069097108500892620e-05,.00019961998509361545] 
dist 201=[-3.56455125672683440340e-06,.00015267837921693155] 
dist 202=[-4.78689717717735617780e-05,.00014398006475230260] 
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dist 206=[-.00016203829653376391,1.14110225249241190470e-05] 
dist 207=[-.00017190724941246225,-1.87334549029337386650e-05] 
dist 208=[-.00017556733625973025,-2.38670070979234081970e-05] 
dist 209=[-.00017578916376348998,-5.82319015766940780610e-05] 
dist 210=[-.00017484574707138852,-6.35617191116807301970e-05] 
dist 211=[-.00016768136433994572,-7.31057490703319231630e-05] 
dist 212=[-.00016574999574233609,-7.46357040985003865600e-05] 
dist 213=[-.00013638394630011968,-7.21764895337749420020e-05] 
dist 214=[-.00012926515993665238,-5.52338062756677886910e-05] 
dist 215=[-.00012161603633170111,-3.41259846770054507800e-05] 
dist 216=[-.00011775458705676064,-2.36261363858998000000e-06] 
dist 217=[-9.20536632693321860780e-05,2.94645408738185907800e-05] 
dist 218=[-8.71846639308137142420e-05,5.08260276211288586910e-05] 
dist 219=[-8.19362124698922235340e-05,6.82064156554313320020e-05] 
dist 220=[-7.93099158230932292410e-05,8.42264312969643765730e-05] 
dist 221=[-2.83371748574103112250e-05,9.77776653181348958100e-05] 
dist 222=[-2.43597437458851085910e-05,.00010535560352317289] 
dist 223=[-1.59066578896289651090e-05,.00011014015039441329] 
dist 224=[-1.36136298261929226350e-05,.00011132669889493468] 
dist 225=[-5.02972447854881019530e-06,6.67561149199689844550e-05] 
dist 226=[-3.21983741593758538970e-06,7.18257475989723536440e-05] 
dist 227=[-6.91144499071766632590e-07,7.48120685273290113590e-05] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 0, 0, 0, 2, 0, 1] 
dist 0=[147.14852461560714653   ,147.14852461560714653   ] 
dist 1=[145.67008736083564165   ,147.54860771854374128   ] 
dist 2=[140.21323577270847118   ,147.82092012040045840   ] 
dist 3=[132.79229516564871118   ,147.47825914324626969   ] 
dist 4=[123.66878299879439873   ,136.57680705434208202   ] 
dist 5=[111.72785736589026748   ,134.21769668004147371   ] 
dist 6=[93.105329602840188414  ,128.51967017550513262   ] 
dist 7=[74.105376232805883562  ,126.52218718486614521   ] 
dist 8=[60.658033612875103364  ,102.15768259989899176   ] 
dist 9=[48.912222696254004251  ,97.272758130003549485  ] 
dist 10=[36.660025356115569386  ,93.129703722658999966  ] 
dist 11=[25.207188999175535565  ,92.296833082888660122  ] 
dist 12=[16.624651302322914777  ,32.523744599770697248  ] 
dist 13=[8.5688880399414855541 ,29.851032572281333686  ] 
dist 14=[-.81564010729312669161,26.121562987913261483  ] 
dist 15=[-9.4324087381126360223 ,25.240949044300907145  ] 
dist 16=[-16.341733706020661473  ,-12.081645650659290566  ] 
dist 17=[-22.588961282704386035  ,-15.583388318044675980  ] 
dist 18=[-27.314281789980532398  ,-17.617491340832477771  ] 
dist 19=[-31.150715770043968523  ,-17.809182755629656789  ] 
dist 20=[-34.067289270541040961  ,-16.182296563773452581  ] 
dist 21=[-35.138099538545844706  ,-13.219355467305358222  ] 
dist 22=[-35.405640995763622289  ,-7.8304327035168353443 ] 
dist 23=[-35.113404896968328724  ,-2.2074111575496788404 ] 
dist 24=[-31.728724340377333860  ,1.6900395187217157540 ] 
dist 25=[-30.666525144900528198  ,4.9443209741876534062 ] 
dist 26=[-29.122314546459915337  ,8.0261261287691804572 ] 
dist 27=[-28.466682073618812199  ,10.648188590509548584  ] 
dist 28=[-11.405583633071292398  ,12.083473859722313557  ] 
dist 29=[-9.1305279296459121651 ,12.881942373905251944  ] 
dist 30=[-3.9050444207956404586 ,13.024008962144876700  ] 
dist 31=[-2.8414456131091440835 ,17.183628914850663988  ] 
dist 32=[3.3007377002334074979 ,21.154043022468021795  ] 
dist 33=[4.2800154724500107582 ,23.355362393678086518  ] 
dist 34=[4.3835758035934024640 ,24.637636093942028197  ] 
dist 35=[4.3286944697866653202 ,24.960731159543195630  ] 
dist 36=[4.0045233899067711620 ,7.8721761704191349782 ] 
dist 37=[3.4440216513260381493 ,8.0349630277038781155 ] 
dist 38=[2.4392369763112435977 ,8.0540368536369067874 ] 
dist 39=[1.3858039288465035162 ,8.0430077307369879864 ] 
dist 40=[.63168821943216064268,6.9634714359216010077 ] 
dist 41=[-.02715669120745817413,6.6684269191162615581 ] 
dist 42=[-.70394257183880871819,6.4668454138564402528 ] 
dist 43=[-1.3203251348251353472 ,6.3732290385364735568 ] 
dist 44=[-1.9608436464387724146 ,1.5097403060846615523 ] 
dist 45=[-2.5168123963642870056 ,.92662012576663267548] 
dist 46=[-2.9607475515552883476 ,-.45354175572235694106] 
dist 47=[-3.3559758685245327366 ,-.65590746035753538836] 
dist 48=[-3.6671341869551147988 ,-2.0162071704962191046 ] 
dist 49=[-3.7776961855933395150 ,-2.0814405030412894923 ] 
dist 50=[-4.0659649147216622090 ,-1.9824473309994472581 ] 
dist 51=[-4.2860003880055515871 ,-1.8147716199301009204 ] 
dist 52=[-4.4099192097146137338 ,-1.5700419167986298103 ] 
dist 53=[-4.4253764612435068979 ,-1.2289011648443398264 ] 
dist 54=[-4.3194493029348014204 ,-.6786118934263002105 ] 
dist 55=[-4.2875104379157256758 ,-.11760853304819013839] 
dist 56=[-3.5837497420142251738 ,.26615295843052265832] 
dist 57=[-3.4063578655139989688 ,.63941805427666610655] 
dist 58=[-3.2441035659407321132 ,1.1443579258976380278 ] 
dist 59=[-3.1652111523924252855 ,1.6357876690807453637 ] 
dist 60=[-.90686913417698358285,2.0490397037931374100 ] 
dist 61=[-.66849440461215325365,2.2728400741747809159 ] 
dist 62=[-.12248285564546116052,2.3967261661146152509 ] 
dist 63=[-.01619227018723241836,2.4241824669151111621 ] 
dist 64=[.61587374203982345397,2.1901523826584299714 ] 
dist 65=[.71030356181728741948,2.4305755006121672956 ] 
dist 66=[.67786748242502051403,2.5662941619759994074 ] 
dist 67=[.6266143497172459691 ,2.5982901392839630911 ] 
dist 68=[.55479434474024839044,1.0260714683842508094 ] 
dist 69=[.45598485961560160436,1.0327378640319610453 ] 
dist 70=[.29759340329799831158,1.0112804247199693496 ] 
dist 71=[.13595515833412392396,1.0081459268925226267 ] 
dist 72=[.02423207636943558109,.83745047500886891977] 
dist 73=[-.06987557073712283845,.79485804350235183403] 
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dist 75=[-.24256921609464358091,.76104276209301082927] 
dist 76=[-.32719291802283138507,.1082178870722535559 ] 
dist 77=[-.39145088789618800578,.03180354578791378319] 
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dist 84=[-.52576362030028458435,-.23801661119785094928] 
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dist 86=[-.51266083831260624854,-.06967252136855309597] 
dist 87=[-.50517636289693189637,.03309081300151298508] 
dist 88=[-.43554997354550237856,.10233219867394005235] 
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dist 90=[-.38949685831670930222,.21104328463373581003] 
dist 91=[-.37924336901980781964,.2739755174815212032 ] 
dist 92=[-.13124169475670027863,.33071575939277658168] 
dist 93=[-.09832284394871038094,.36217626838403747559] 
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dist 100=[.06227142787600041026,.12424177661016844773] 
dist 101=[.04812933773505467021,.1243992945169728928 ] 
dist 102=[.02620847923638892231,.12043371657544301582] 
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dist 104=[-.01103480358477560311,.09816767850622868366] 
dist 105=[-.02352007796252460929,.09336914148440825463] 
dist 106=[-.03536041395505384658,.08903201487631555218] 
dist 107=[-.04559157411833503016,.08813071121942556792] 
dist 108=[-.05235957683847792460,.01919911873175529515] 
dist 109=[-.05986185992631088292,.01087136249675814134] 
dist 110=[-.06488320254543640690,-.00842279277703431872] 
dist 111=[-.06769404043891544721,-.01162395146650505364] 
dist 112=[-.06904580729664759120,-.03429363404045478927] 
dist 113=[-.06910719226035096133,-.03447996297182599083] 
dist 114=[-.07330954175012070680,-.03075888248332129676] 
dist 115=[-.07522762176887138134,-.02603133238646254768] 
dist 116=[-.07565318226414710601,-.02048810293990658937] 
dist 117=[-.07535273559928062288,-.01340516065144957918] 
dist 118=[-.07248952091930700100,-.0025646505411690890 ] 
dist 119=[-.07168611519570500430,.00834806474545281728] 
dist 120=[-.05921767136567107591,.01571816087678965277] 
dist 121=[-.05617068769306360337,.02175686175295729868] 
dist 122=[-.05291627957797308760,.02738506788956879346] 
dist 123=[-.05125338695762336476,.03218283203576855512] 
dist 124=[-.01938063785925613564,.03539560738076740496] 
dist 125=[-.01684631684531170001,.03744269857565950612] 
dist 126=[-.01137525886844612368,.03953853543355738924] 
dist 127=[-.00986503583624488813,.04003516628626509571] 
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dist 129=[-.00285763875443012445,.04511911059808780578] 
dist 130=[-.00082515157338588649,.04734820456858804432] 
dist 131=[-.00035322319712359472,.04786299529945846525] 
dist 132=[.01270062624806479649,.01599533949445280906] 
dist 133=[.01088417229264039033,.01597482210829179889] 
dist 134=[.00856959671273326401,.01537446594364416685] 
dist 135=[.00503265078008158738,.01528744810040782782] 
dist 136=[.00147163102403132224,.01239011197220719702] 
dist 137=[-.00093868833148457313,.01169718349410927544] 
dist 138=[-.00292036198804802817,.01120807206325277631] 
dist 139=[-.00477987160905132870,.01109723543461856042] 
dist 140=[-.00637471036089541914,.00108166107017326823] 
dist 141=[-.00730577360470631732,-8.63867820300805849700e-05] 
dist 142=[-.00791159193193911025,-.00279581252419606169] 
dist 143=[-.00821538816776537781,-.00319735143310141476] 
dist 144=[-.00834524136725813157,-.00633260346371444572] 
dist 145=[-.00833167205495219274,-.00679309757559734950] 
dist 146=[-.00811259749160998629,-.00761748788280070119] 
dist 147=[-.00806965139895341048,-.00689409591359380060] 
dist 148=[-.00811371780601988406,-.00588667357887130309] 
dist 149=[-.00807414244838409703,-.00475251405966349166] 
dist 150=[-.00780264493578613321,-.00333155967633640775] 
dist 151=[-.00767872019276139747,-.00118541580724902244] 
dist 152=[-.00653505588983943714,.00096649687128353406] 
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dist 154=[-.00580413069796327013,.00358414384792402594] 
dist 155=[-.00564483098039138950,.00466354184271344115] 
dist 156=[-.00184955749890534028,.00557429992182500258] 
dist 157=[-.00134579976519396746,.00607852068118675622] 
dist 158=[-.00021954876904116208,.00637198775310829664] 
dist 159=[2.48592142635768356500e-05,.00644593649389727533] 
dist 160=[.00124584540981297999,.00540967421423866064] 
dist 161=[.00145864235040327944,.00589108301978403924] 
dist 162=[.00180464401391440445,.00617132032058540362] 
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dist 166=[.00095778651098304336,.00182620019370322442] 
dist 167=[.00051586448416011643,.00181410299432599284] 
dist 168=[7.19809606485095939380e-05,.00146353082905221718] 
dist 169=[-.00022725304837441656,.00138366907271013991] 
dist 170=[-.00047205926328526155,.00131849126012175970] 
dist 171=[-.00069986182377086649,.00130299254516076132] 
dist 172=[-.00089400079342968606,.00017983445300333954] 
dist 173=[-.00100516085770450428,4.68080518095072328860e-05] 
dist 174=[-.00107476904050194193,-.00026159824918669218] 
dist 175=[-.00110394596123784862,-.00030920683249244874] 
dist 176=[-.00111003497991585133,-.00066844441661061241] 
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dist 178=[-.00106199177629089619,-.00082111495117690102] 
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dist 181=[-.00105326287452312034,-.00051564005520164344] 
dist 182=[-.00100699604319283391,-.00036957992598409998] 
dist 183=[-.00099749814412640950,-.00014935580500441688] 
dist 184=[-.00080884973978907027,7.14004775963024159600e-05] 
dist 185=[-.00076393412176757721,.00021957700564525791] 
dist 186=[-.00072319357586356830,.00034012082558742912] 
dist 187=[-.00070717493411158216,.00045116609746756079] 
dist 188=[-.00015947322401240006,.00054502731388652715] 
dist 189=[-.00010501293404330036,.00059734415486715748] 
dist 190=[1.79432094238220169360e-05,.00062992356993695807] 
dist 191=[4.23286271450457293870e-05,.00063779767615234047] 
dist 192=[.00017816198659193116,.00051913959086665571] 
dist 193=[.00020076863149043270,.00056808107843996887] 
dist 194=[.00023872102629147131,.00059739215046098568] 
dist 195=[.00022122212442182635,.00060483897831104207] 
dist 196=[.00019398908168145029,.00024696445327411089] 
dist 197=[.00016339113635318736,.00024586224221312850] 
dist 198=[.00012508451742933022,.00023543628112987397] 
dist 199=[6.72416721564606323270e-05,.00023345799655669772] 
dist 200=[9.21316088132634971540e-06,.00018933024886174453] 
dist 201=[-2.98318422749177488920e-05,.00017881801410595892] 
dist 202=[-6.17038667642720217610e-05,.00016987587370337079] 
dist 203=[-9.12529928381519596480e-05,.00016671531876109569] 
dist 204=[-.00011636697372892839,2.08899094097040258710e-05] 
dist 205=[-.00013062983426816426,3.48273786031081437470e-06] 
dist 206=[-.00013941344810584820,-3.68370987738425323440e-05] 
dist 207=[-.00014277290808333581,-4.30271252557327486730e-05] 
dist 208=[-.00014315797326791476,-8.98107815169382028910e-05] 
dist 209=[-.00014249022653525408,-9.67660115780458334880e-05] 
dist 210=[-.00013666109450754146,-.00010952189710567062] 
dist 211=[-.00013659584689831960,-9.92220032989179114650e-05] 
dist 212=[-.00013627785467807293,-8.49490720745691871080e-05] 
dist 213=[-.00013544038554515798,-6.91008105592209155620e-05] 
dist 214=[-.00012930161407328902,-4.93800406159556453820e-05] 
dist 215=[-.00012803829596291779,-1.97302212563693593230e-05] 
dist 216=[-.00010365422288720794,9.96734519432593675150e-06] 
dist 217=[-9.78660627428562293240e-05,2.98780043353419369190e-05] 
dist 218=[-9.25436624332802624530e-05,4.60539251175344261180e-05] 
dist 219=[-9.04319210170251218510e-05,6.09225088186698195520e-05] 
dist 220=[-1.94954465364878982660e-05,7.34701339521019599510e-05] 
dist 221=[-1.22283198090700944420e-05,8.04304994002063713750e-05] 
dist 222=[4.19970266249553173130e-06,8.45157582352334888830e-05] 
dist 223=[7.38732158267127779230e-06,8.55796929604319646900e-05] 
dist 224=[2.55457643583120851010e-05,6.71981276869430540870e-05] 
dist 225=[2.85381108496729086210e-05,7.36029791856447386970e-05] 
dist 226=[3.24430154508730193210e-05,7.74832311539043656860e-05] 
dist 227=[2.83217438510136682280e-05,7.84369532876687110840e-05] 
dist 228=[2.33689624407484544150e-05,3.44936385369238221620e-05] 
dist 229=[1.78900783381587882900e-05,3.42216422654370319360e-05] 
dist 230=[1.10850301729108230370e-05,3.32447295920203824820e-05] 
dist 231=[8.66191881624493587500e-07,3.26559151334409396790e-05] 
dist 232=[-9.36683327181772591520e-06,2.89409680602521800570e-05] 
dist 233=[-1.62283000020920411010e-05,2.79601515895754679740e-05] 
dist 234=[-2.18045262752417872560e-05,2.56341490003555499760e-05] 
dist 235=[-2.69342393404393710820e-05,2.47906202632165754140e-05] 
dist 236=[-3.12670025683514722240e-05,1.33954222852865012920e-05] 
dist 237=[-3.36787629880469981240e-05,1.16050609854337104440e-05] 
dist 238=[-3.51009005898251017100e-05,7.83965837749109187020e-06] 
dist 239=[-3.55041369260096717520e-05,6.82132149514012977640e-06] 
dist 240=[-3.53801323119031559790e-05,3.04253032587663395810e-06] 
dist 241=[-3.50565016857774597990e-05,2.22493303266346735880e-06] 
dist 242=[-3.38615845912544112170e-05,1.16188867960855159290e-06] 
dist 243=[-3.13506290796960011610e-05,9.01704505218947113860e-07] 
dist 244=[-9.64612119255024709520e-07,8.00441944710310685500e-07] 
dist 245=[-9.60118499864734128760e-07,7.59776613834717814770e-07] 
dist 246=[-9.34574585957628048860e-07,6.54023462505874868850e-07] 
dist 247=[-9.17570213072895874760e-07,6.23668186214718661250e-07] 
dist 248=[-6.66336822685407475760e-07,4.33121594903424709420e-07] 
dist 249=[-6.25345971087019662830e-07,3.92662592254134128660e-07] 
dist 250=[-5.15014319122121750950e-07,3.12549010581328048830e-07] 
dist 251=[-4.94942673870964750440e-07,2.90176125355795874920e-07] 
dist 252=[-3.01497349318411374040e-07,-4.14807482221925245000e-08] 
dist 253=[-2.63970214933778929100e-07,-9.07899209798803370500e-08] 
dist 254=[-2.09987610088828625960e-07,-1.17665322161130189600e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 0, 2] 
dist 0=[100.10379413012071323   ,100.10379413012071323   ] 
dist 1=[98.386731642492037191  ,101.31125181136079442   ] 
dist 2=[96.406410190303690646  ,101.53670652286669975   ] 
dist 3=[93.875589717303411203  ,100.86823352463474301   ] 
dist 4=[89.957105617456809436  ,100.74613393237038369   ] 
dist 5=[85.466430097239812502  ,94.929840170857687648  ] 
dist 6=[80.649175705165831920  ,93.435606277943692997  ] 
dist 7=[74.677562811552969253  ,92.586705303021826263  ] 
dist 8=[65.576160808922185235  ,92.362959325097854608  ] 
dist 9=[56.285377538719712508  ,69.123482379114101898  ] 
dist 10=[49.558993915754896809  ,66.105548322050091440  ] 
dist 11=[43.432538565920666778  ,61.728473733824956163  ] 
dist 12=[36.542734697060954126  ,60.522421270283775211  ] 
dist 13=[29.724107634301785381  ,40.957949254375255518  ] 
dist 14=[23.886880960556596147  ,39.081114548447497740  ] 
dist 15=[17.685666728239376088  ,30.831312088044118028  ] 
dist 16=[9.4224090146141096989 ,30.185241737818665295  ] 
dist 17=[1.4020640979582438711 ,11.481316774607893948  ] 
dist 18=[-5.0846716141240805354 ,9.4821765624704503387 ] 
dist 19=[-10.178210709315762602  ,4.8635192965544588065 ] 
dist 20=[-14.250896385257231084  ,4.1067821083015947799 ] 
dist 21=[-17.408959354637617491  ,-1.7661491779199095766 ] 
dist 22=[-18.860720625604711808  ,-2.7782994095830521171 ] 
dist 23=[-19.549778569936501591  ,-4.3893613160952778868 ] 
dist 24=[-19.646530709896731220  ,-4.7611356496425671724 ] 
dist 25=[-18.605289093052709177  ,-5.9376988133560626649 ] 
dist 26=[-18.583868203583838113  ,-3.1915504534936261346 ] 
dist 27=[-17.885334616229726904  ,-.6085444394884477596 ] 
dist 28=[-17.783931763172033363  ,2.3085752833653078113 ] 
dist 29=[-14.468605193800325577  ,5.1194667610680613224 ] 
dist 30=[-13.684681830366413557  ,7.2889309255832821003 ] 
dist 31=[-13.111913163784678633  ,9.3592803687203186130 ] 
dist 32=[-12.985716665879102113  ,11.786058879676147083  ] 
dist 33=[-2.7432797791885502552 ,13.947826535067839160  ] 
dist 34=[-1.8704133372153170357 ,14.968700002705808509  ] 
dist 35=[.07096313251243191998,15.466466924644488296  ] 
dist 36=[.46598621793770800487,15.546405097099063896  ] 
dist 37=[2.5223691440909996880 ,14.369676409419559745  ] 
dist 38=[2.8708847904311386733 ,13.998254510462619300  ] 
dist 39=[3.4026805906654187470 ,13.724811215737348264  ] 
dist 40=[3.4740195999955495868 ,13.527907428271030767  ] 
dist 41=[2.7287866001337190381 ,8.3812894374293813379 ] 
dist 42=[.19545079748825761267,8.3555540336544827986 ] 
dist 43=[-1.9499851204585791670 ,8.1036600798452842434 ] 
dist 44=[-4.0589432187880486828 ,7.9813855323375322567 ] 
dist 45=[-5.9277752444652761209 ,6.8219475932049346986 ] 
dist 46=[-7.1213618986741629160 ,6.5245736248127424895 ] 
dist 47=[-8.0254593973391292377 ,6.0800314644340911952 ] 
dist 48=[-8.7467492383659252824 ,5.9167328135306121703 ] 
dist 49=[-9.2642469864220344098 ,4.5814083843386580061 ] 
dist 50=[-9.3853767579251105085 ,4.6081088307814630822 ] 
dist 51=[-9.3208562292567395492 ,4.6334890576006234817 ] 
dist 52=[-9.3039056082233798043 ,4.6614933155165669873 ] 
dist 53=[-7.7939429803385143524 ,4.6870605735334724973 ] 
dist 54=[-7.4126345243315785198 ,4.7028814344386988710 ] 
dist 55=[-6.1645937233347912056 ,4.7136444393310541027 ] 
dist 56=[-6.2368600216440761019 ,4.7192519739229969720 ] 
dist 57=[-1.9467506134788085131 ,4.7074380514776752360 ] 
dist 58=[-1.9042608085555498256 ,4.6491403228890639542 ] 
dist 59=[-1.8375684939741694554 ,4.5467401292878434092 ] 
dist 60=[-1.8243863141661784388 ,4.4835584997269365968 ] 
dist 61=[-1.4976431245708733721 ,4.1384510707594316804 ] 
dist 62=[-1.4192157250440089795 ,4.0316221680707612651 ] 
dist 63=[-1.3522903098810149074 ,3.6868006593862393088 ] 
dist 64=[-1.3287376580446600575 ,3.1646551154583985180 ] 
dist 65=[-.34586068288617168005,2.1842946902292706350 ] 
dist 66=[-.25239550632345920257,2.2133692085801609948 ] 
dist 67=[-.04528302159685493715,2.1995137325709799823 ] 
dist 68=[.00088026794908729279,2.1974755860209145384 ] 
dist 69=[.21963359401112299883,1.8612898487817245372 ] 
dist 70=[.2584835151075097677 ,1.7743435781878608600 ] 
dist 71=[.31719420568704037079,1.7236056302419976326 ] 
dist 72=[.32668595266078746932,1.7108117324682390924 ] 
dist 73=[.28764161517353015613,1.0445073842735447984 ] 
dist 74=[-.04861822770484680155,1.0398981872738639134 ] 
dist 75=[-.32742115962906317075,.99797809231117921347] 
dist 76=[-.59265573711735876808,.98782037272348139306] 
dist 77=[-.822442632660030067  ,.809575493082283488  ] 
dist 78=[-.9605855240428492132 ,.76656366963618586151] 
dist 79=[-1.0554606648260561204 ,.72408722044683146491] 
dist 80=[-1.1135604410409235150 ,.7044228268444409286 ] 
dist 81=[-1.1473429397801043463 ,.19211156652764756567] 
dist 82=[-1.1505732865422118977 ,.14071616284415941144] 
dist 83=[-1.1316555341140624336 ,.03582266878381838033] 
dist 84=[-1.1161627398933070250 ,.02555081069623438339] 
dist 85=[-.9729734850146062186 ,-.01588846949886202774] 
dist 86=[-.9339491583608248346 ,-.02383848575685043362] 
dist 87=[-.87458810217088269777,-.03595521900171891788] 
dist 88=[-.8523546333725189372 ,-.03885159054758982859] 
dist 89=[-.30498151007444920908,.11916438429824310796] 
dist 90=[-.27147761920734435978,.32163327494605264388] 
dist 91=[-.26076033281210613731,.48643801675992052521] 
dist 92=[-.25565093368601504235,.6382421011639977957 ] 
dist 93=[-.21810550209246760757,.76641312956169027306] 
dist 94=[-.20857137449881893509,.83740399278890527313] 
dist 95=[-.19167855143476737671,.87873004251367855057] 
dist 96=[-.18656883399738522615,.88914032853714293617] 
dist 97=[-.06931504046629933156,.27042621563577404704] 
dist 98=[-.05314455238321123446,.27173933537581167217] 
dist 99=[-.02820185944333725904,.26579142759849684811] 
dist 100=[-.02393371519287613916,.26436417090021908126] 
dist 101=[-.00821733648251732879,.22107980843170161941] 
dist 102=[-.00486770294784241115,.22015200771926813176] 
dist 103=[-.00072681901676471450,.22698037638962978182] 
dist 104=[0                     ,.22852619591069656992] 
dist 105=[.01623742254788906149,.11707032036941678567] 
dist 106=[-.02559997427237873740,.1164114863365802467 ] 
dist 107=[-.05997744998027677523,.11230784299211843006] 
dist 108=[-.09219973880209130904,.11049209190475159648] 
dist 109=[-.11980926569342279006,.09385191190549661607] 
dist 110=[-.13587687190077030276,.08963481677070352127] 
dist 111=[-.14626774569210554951,.08324682337873522668] 
dist 112=[-.15134431170532091128,.08095249643539995345] 
dist 113=[-.15320783589009386933,.02642090459162687455] 
dist 114=[-.15296252183189525507,.01916213450682759931] 
dist 115=[-.14767496887783815499,.00295607945002557990] 
dist 116=[-.14634473997580371915,-.00056898478313404093] 
dist 117=[-.12068923721905853555,-.01806014961290777516] 
dist 118=[-.11440387056664458724,-.0211149799968004583 ] 
dist 119=[-.10845488610630272682,-.02601277854988220673] 
dist 120=[-.10570115506393036209,-.02179745117265679477] 
dist 121=[-.02762546219565369747,.00974251978148350388] 
dist 122=[-.02698142416743083602,.03093792520033873561] 
dist 123=[-.02585790897331894495,.04820171351515549424] 
dist 124=[-.02564333176405237060,.06413336088700720329] 
dist 125=[-.02082684222815797122,.07761403217553651943] 
dist 126=[-.01967797384620346680,.08531305998097212824] 
dist 127=[-.01870047915975270068,.09001032074680654696] 
dist 128=[-.01835320839714892307,.09109428727450465197] 
dist 129=[-.00239226624144367730,.03550050965785119378] 
dist 130=[-.00048638414995823068,.03553676725778718988] 
dist 131=[.00392909137629546506,.03438068447475541545] 
dist 132=[.00460698388074883443,.03421286903458207715] 
dist 133=[.00973470963738804424,.02793925791253785525] 
dist 134=[.01049691692311683405,.02641974474559574324] 
dist 135=[.01189918523042598680,.02537816068945680906] 
dist 136=[.01046759214316969334,.02513776218925999850] 
dist 137=[.00270427612618924118,.01491014364981325576] 
dist 138=[-.00253391316695443552,.01482163536693819152] 
dist 139=[-.00682432423413057268,.01417009379151400692] 
dist 140=[-.01082500463915710581,.01402347966431099030] 
dist 141=[-.01424023576487177083,.01141659958288309787] 
dist 142=[-.01620644318068095223,.01079394728127054879] 
dist 143=[-.01745152442782023665,.01019046834209785725] 
dist 144=[-.01800395002974949324,.00992632671127613299] 
dist 145=[-.01817922320892824497,.00235958738946297352] 
dist 146=[-.01811498708324733389,.00158161912107217055] 
dist 147=[-.01756182681898731846,-.00016927064318039016] 
dist 148=[-.01728910743464665896,-.00052363102653764070] 
dist 149=[-.01478232800231117627,-.00244316648584902473] 
dist 150=[-.01413590998938116212,-.00276608915307213147] 
dist 151=[-.01315756817800065926,-.00329769852349533067] 
dist 152=[-.01280174274862948420,-.00242801277700385430] 
dist 153=[-.00429339356149582770,.00221853246746276832] 
dist 154=[-.00339298433737576881,.00533417610696287935] 
dist 155=[-.00323956987152766699,.00786533190857748762] 
dist 156=[-.00321730152494065615,.01019123751373741556] 
dist 157=[-.00257715999309909204,.01215315928576638647] 
dist 158=[-.00242677474014016254,.01323914368000513360] 
dist 159=[-.00231603813718720149,.01387141033915907804] 
dist 160=[-.00229139147588593259,.01403065381893305543] 
dist 161=[-.00019162186091735601,.00428531954303985883] 
dist 162=[5.29461573483499105640e-05,.00427832017007308219] 
dist 163=[.00062213860343854269,.00411506887679698608] 
dist 164=[.00070413619108337600,.00409060973266741320] 
dist 165=[.00136889423059940157,.00331876034300124071] 
dist 166=[.00146610678494263676,.00314941871522243259] 
dist 167=[.00163942711086183491,.00299521516626469204] 
dist 168=[.00093265074229323905,.00296300276276290623] 
dist 169=[-4.49993467047299012910e-05,.00173417027029033748] 
dist 170=[-.00070272041620351355,.00172197253988674476] 
dist 171=[-.00123949102816831651,.00165661840339183887] 
dist 172=[-.00173692652879734917,.00162856709787705408] 
dist 173=[-.00215954447400441885,.00137998842526112828] 
dist 174=[-.00239926374976275137,.00131740102904141066] 
dist 175=[-.00254650982319652057,.00122054579041112950] 
dist 176=[-.00260197918786334138,.00118671669918219690] 
dist 177=[-.00260641415094156156,.00040568333526251783] 
dist 178=[-.00259278994295880032,.00030406751061163242] 
dist 179=[-.00248733502516766199,7.90050422555709141190e-05] 
dist 180=[-.00245878349695222994,2.72520634224874837270e-05] 
dist 181=[-.00202402111339958139,-.00021129173718751200] 
dist 182=[-.00191854164394648555,-.00025430480280300657] 
dist 183=[-.00180522910990581059,-.00032054192492732798] 
dist 184=[-.00174797958637845971,-3.74933126298492000000e-05] 
dist 185=[-.00064392504335936468,.00043485597501716780] 
dist 186=[-.00055702790768238136,.00075191979519093050] 
dist 187=[-.00037849220733819468,.00100992587839898362] 
dist 188=[-.00037577806431005027,.00124778563028525760] 
dist 189=[-.00030161133066304168,.00144901856023417132] 
dist 190=[-.00029204685009056230,.00156159672829300473] 
dist 191=[-.00026953633059381040,.00163309292235308233] 
dist 192=[-.00026655387101435705,.00165069722605174235] 
dist 193=[-.00019388152746257363,.00050039988821939497] 
dist 194=[-.00018019672874927956,.00049842218038333965] 
dist 195=[-.00015388622337499648,.00048351941897176841] 
dist 196=[-.00014662613788848130,.00047550841485301923] 
dist 197=[-.00012014525286014973,.00040934930788051131] 
dist 198=[-.00011292496500702825,.00041743447362548627] 
dist 199=[-.00010447299082561869,.00043276535960085506] 
dist 200=[-.00010072313464505251,.00043718855566611082] 
dist 201=[-9.87387244916622428490e-05,.00043558388948024392] 
dist 202=[-.00015448462958137869,.00043169918327996608] 
dist 203=[-.00022554681428054760,.00041639210724439287] 
dist 204=[-.00029125829549906277,.00040774228400670921] 
dist 205=[-.00034699867393415119,.00035430425649643552] 
dist 206=[-.00037846993379294907,.00034036744323080557] 
dist 207=[-.00039761565808048208,.00031199248063695693] 
dist 208=[-.00040441691870431931,.00030267956333676265] 
dist 209=[-.00040495959862314080,.00013630993727763678] 
dist 210=[-.00040164193851432569,.00011201898620290195] 
dist 211=[-.00039073924058877639,6.00054920536303267870e-05] 
dist 212=[-.00038415983712561048,4.60660986118067858310e-05] 
dist 213=[-.00034263401511679220,9.67768399310358288730e-06] 
dist 214=[-.00033167021438997575,6.04844976923854543070e-06] 
dist 215=[-.00029033077620470131,1.18029908073765114870e-06] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 2, 2, 2, 0, 1] 
dist 0=[146.91992550809127721   ,146.91992550809127721   ] 
dist 1=[145.56020522104821255   ,146.99283889626025875   ] 
dist 2=[140.16605975111362646   ,147.27272710223686809   ] 
dist 3=[132.82694905738493568   ,147.47970211954077352   ] 
dist 4=[123.74265215620745672   ,141.64027572078893974   ] 
dist 5=[111.81771872859811016   ,135.61101795065621736   ] 
dist 6=[93.184484163155548166  ,133.16827638193068926   ] 
dist 7=[74.160990214182918233  ,124.51074590949641977   ] 
dist 8=[60.678437431957360028  ,123.26737211497894122   ] 
dist 9=[48.882800325828862342  ,100.79503517120222675   ] 
dist 10=[36.548633749454838203  ,95.899643152307941994  ] 
dist 11=[25.000191326308695413  ,91.720808286404015534  ] 
dist 12=[16.313355462383834912  ,90.883763693073114909  ] 
dist 13=[8.1273773615535553648 ,29.942871859547890555  ] 
dist 14=[-1.4562276296785531878 ,27.410254513841748437  ] 
dist 15=[-10.262228660643022689  ,6.6061395537279732131 ] 
dist 16=[-15.361304162567921198  ,3.9725065788552626855 ] 
dist 17=[-18.745306273257848394  ,-14.072160588726693919  ] 
dist 18=[-23.306713920579519518  ,-16.818797473778458190  ] 
dist 19=[-27.919054727161405595  ,-18.952737697031938026  ] 
dist 20=[-31.595224257490379644  ,-17.334070898483845969  ] 
dist 21=[-34.354586238640665468  ,-14.357189658045140764  ] 
dist 22=[-35.324473443083269412  ,-8.9219399394711464277 ] 
dist 23=[-35.526540557804379414  ,-3.2437058441121344129 ] 
dist 24=[-35.218480830869199244  ,.70313304005270530543] 
dist 25=[-31.709017885685809021  ,4.0108294044194873690 ] 
dist 26=[-30.628014916741860857  ,7.1641409036690744416 ] 
dist 27=[-29.055306585959897869  ,9.8627682120963477758 ] 
dist 28=[-28.394180324032696240  ,11.371795263080424782  ] 
dist 29=[-11.289789384669471048  ,12.255613642290374280  ] 
dist 30=[-9.0103248395407021127 ,12.478799535836138889  ] 
dist 31=[-3.7821353381454078088 ,12.601489515843456592  ] 
dist 32=[-2.7158460240967127235 ,17.297917171300286978  ] 
dist 33=[3.4050246711085604848 ,21.268154989055039722  ] 
dist 34=[4.4240551104944158416 ,23.469075786604227838  ] 
dist 35=[5.1803737535248381815 ,24.751004528234717523  ] 
dist 36=[4.7616619789590115914 ,25.074001178653240426  ] 
dist 37=[4.0733544907253000735 ,7.9020731089484858346 ] 
dist 38=[2.8659310573013860750 ,8.0494727179084828272 ] 
dist 39=[1.6063330954797815679 ,8.0584870452612386132 ] 
dist 40=[.71036075996519261139,8.0450004298439439056 ] 
dist 41=[-.06738616536806330458,6.9464357966003962901 ] 
dist 42=[-.85930503145602609386,6.6486382383167106126 ] 
dist 43=[-1.5767690950843089305 ,6.4424585931745462118 ] 
dist 44=[-2.0599084501342684521 ,6.3483800176767338030 ] 
dist 45=[-2.4538509064965704147 ,1.4827314384554590061 ] 
dist 46=[-2.8183629198459078088 ,.89966783570881283247] 
dist 47=[-3.1107742166723530894 ,-.48022682027179856049] 
dist 48=[-3.2188610175312854327 ,-.68189218160566320131] 
dist 49=[-3.2521142143817123203 ,-2.3725768469616750811 ] 
dist 50=[-3.7225316561427446636 ,-2.4491698787615906101 ] 
dist 51=[-4.0745653717047435033 ,-2.2157098258251245532 ] 
dist 52=[-4.2891824388462662559 ,-1.8944030998503123388 ] 
dist 53=[-4.4078414285177643516 ,-1.4558014742412610785 ] 
dist 54=[-4.4216200097089676638 ,-.75681276965794611509] 
dist 55=[-4.3122108728234511111 ,-.04637923397377469180] 
dist 56=[-4.2798465976058029107 ,.43775275573884545925] 
dist 57=[-3.5736342714402806173 ,.83859589251592111437] 
dist 58=[-3.3960590599861519597 ,1.2496086480039288695 ] 
dist 59=[-3.2332624035288127390 ,1.5947295630717382329 ] 
dist 60=[-3.1545156704178987763 ,1.7803137821558923312 ] 
dist 61=[-.89876241802883056158,1.8844798724154468575 ] 
dist 62=[-.6608211679217723183 ,1.9066639233066577135 ] 
dist 63=[-.11616783895454543932,1.3184748802399271965 ] 
dist 64=[-.01001381557673688701,1.7880656142663414612 ] 
dist 65=[.61921540907708637648,2.1879657497453838217 ] 
dist 66=[.72222645461950819124,2.4278763445606599748 ] 
dist 67=[.70796042829866772025,2.5634250271622155277 ] 
dist 68=[.62532227651635032643,2.5953336574090668928 ] 
dist 69=[.5124363118147823058 ,1.0242884387501381480 ] 
dist 70=[.33224123695097138702,1.0305129714292343242 ] 
dist 71=[.14856583223904790418,1.0081708519887999345 ] 
dist 72=[.02183679627024071841,1.0049094016212464838 ] 
dist 73=[-.08469572720569554481,.83371394774107776183] 
dist 74=[-.18827329564729275895,.7911051264152963245 ] 
dist 75=[-.27938787205812631989,.76367370719653720469] 
dist 76=[-.33649242144937025473,.75709409812798769615] 
dist 77=[-.37851069370997112003,.10624776467732062409] 
dist 78=[-.40979544171912363362,.03008093049595795363] 
dist 79=[-.43180976013077501065,-.14655509901228019535] 
dist 80=[-.43704225850960767209,-.17349722583986454536] 
dist 81=[-.43545304736044514443,-.37786486466656003497] 
dist 82=[-.45505833174121559762,-.37558026972791390198] 
dist 83=[-.49422230757568003978,-.32648249434574516092] 
dist 84=[-.51462236585644665774,-.26807771395154699466] 
dist 85=[-.52400015667219386152,-.19297958453843773034] 
dist 86=[-.5235406847557073581 ,-.07761416795928848351] 
dist 87=[-.5105718916996366912 ,.03854068874988961179] 
dist 88=[-.50308570588048315858,.11677863692830136   ] 
dist 89=[-.43345416495248273398,.18060221850523812009] 
dist 90=[-.41513168805561917861,.23955338553123700362] 
dist 91=[-.38749073625074107168,.28938455095354654183] 
dist 92=[-.37726875467045927833,.31703367946378332899] 
dist 93=[-.13025315769307146328,.33315383289501106665] 
dist 94=[-.09746965614755177100,.3371934057656723557 ] 
dist 95=[-.02378936737651355239,.22294849519450839145] 
dist 96=[-.00790110931567858644,.29063830987236926729] 
dist 97=[.07340436506850527684,.34775748295457721155] 
dist 98=[.08747340441635987005,.37938426632172069818] 
dist 99=[.08219765185290556750,.39780885232287999625] 
dist 100=[.06992211541722818774,.40244392858458267874] 
dist 101=[.05397546801980337711,.12375622675839456902] 
dist 102=[.02929928465563442518,.12388478680023470463] 
dist 103=[.00436816728715503448,.11987380281936114324] 
dist 104=[-.01259237944019905376,.11927102836474006859] 
dist 105=[-.02661755819364823061,.09762988044437849097] 
dist 106=[-.03989973469576741203,.09284011697704638580] 
dist 107=[-.05136540246096631876,.08851184946507696106] 
dist 108=[-.05818176184965608076,.08761231756466205848] 
dist 109=[-.06276827487373027810,.01898036234846427718] 
dist 110=[-.06538489621236317530,.01069016808380218451] 
dist 111=[-.06667064060748808908,-.00850955514746700302] 
dist 112=[-.06669709785647170366,-.01169796758110526529] 
dist 113=[-.06479441270847320126,-.03423050280947225447] 
dist 114=[-.06853914312905263224,-.03470365772091523161] 
dist 115=[-.07299970759186264556,-.02932391402884790696] 
dist 116=[-.07488459680037711772,-.02304014316561421481] 
dist 117=[-.07528464463816934137,-.01502541102193485575] 
dist 118=[-.07497816602022876010,-.0027733305393628740 ] 
dist 119=[-.07211293191877188505,.00955633445199370605] 
dist 120=[-.07131161480068866396,.01787962084553774861] 
dist 121=[-.05889101897053609981,.02469581933001669325] 
dist 122=[-.05585763584077921453,.03104348272432929041] 
dist 123=[-.05261670916635118457,.03645145731705748557] 
dist 124=[-.05096200596156091284,.04002213904105399345] 
dist 125=[-.01923362611304973001,.04203290597961904709] 
dist 126=[-.01671187947414151078,.04247621783595717471] 
dist 127=[-.01127117189441142467,.02880556861024068723] 
dist 128=[-.00977034230164919162,.03573628643947151483] 
dist 129=[-.00399901744825807662,.04160766425544277928] 
dist 130=[-.00281267355549002305,.04490528749237203327] 
dist 131=[-.00080639746897878919,.04711043840163929809] 
dist 132=[-.00033703042670783000,.04762239514206781875] 
dist 133=[.00764356490293352021,.01591256048403951084] 
dist 134=[.00450888967760816421,.01588980428848536653] 
dist 135=[.00135139992726325347,.01528744810040755536] 
dist 136=[-.00078742384994375820,.01520019210878549377] 
dist 137=[-.00254749454116809764,.01231314548508840746] 
dist 138=[-.00420156490252639613,.01162323795059551720] 
dist 139=[-.00562179039067188997,.01113548999473209769] 
dist 140=[-.00645364023220213887,.01102519877280982231] 
dist 141=[-.00699828534921547641,.00106486062185367202] 
dist 142=[-.00727849934965931786,-9.66208840662278040830e-05] 
dist 143=[-.00740425166630182116,-.00279077928018154633] 
dist 144=[-.00739561463689861060,-.00318981278722035861] 
dist 145=[-.00720865842596615678,-.00630719499539017324] 
dist 146=[-.00728771183128060163,-.00612902986819936677] 
dist 147=[-.00781604621385717356,-.00523755790372881731] 
dist 148=[-.00802473519404125366,-.00423173526117453385] 
dist 149=[-.00806637541791113076,-.00297021358073237413] 
dist 150=[-.00802631679295601212,-.00106349766785097027] 
dist 151=[-.00775494684007771974,.00084868282688186609] 
dist 152=[-.00763148858536577306,.00213193677555631362] 
dist 153=[-.00649349080546402292,.00317525792265105809] 
dist 154=[-.00620358277866839206,.00413489511092672899] 
dist 155=[-.00576628468383033312,.00494466657959552367] 
dist 156=[-.00560793889705372949,.00539300482648861022] 
dist 157=[-.00183644144250843853,.00565395721739944326] 
dist 158=[-.00133566458877079726,.00571971923928590756] 
dist 159=[-.00021625375707064857,.00349031346581037610] 
dist 160=[2.67653362002497816610e-05,.00451569178605512770] 
dist 161=[.00123973687482403368,.00538038425608055460] 
dist 162=[.00145120121224776107,.00585891741703200812] 
dist 163=[.00131976084509900840,.00613747700143277722] 
dist 164=[.00111436736067585862,.00620757890700766273] 
dist 165=[.00085526277853155714,.00189692842382655725] 
dist 166=[.00046198836527698451,.00189074861921097270] 
dist 167=[6.68569130696041724160e-05,.00181167288969190881] 
dist 168=[-.00019963293183197891,.00180000466158207244] 
dist 169=[-.00041776928539740909,.00145278974238347658] 
dist 170=[-.00062093828558013168,.00137373992138691571] 
dist 171=[-.00079420051130584184,.00130631842447052701] 
dist 172=[-.00089360745474090398,.00129225638798242251] 
dist 173=[-.00095610927400713757,.00017710598215098741] 
dist 174=[-.00098285969007816949,4.49046170463463861140e-05] 
dist 175=[-.00098902265497992952,-.00026156603719544853] 
dist 176=[-.00098569581827175828,-.00030885170126946722] 
dist 177=[-.00094690181540450044,-.00066571950516483913] 
dist 178=[-.00096841378881128431,-.00065613091920412144] 
dist 179=[-.00103003479016224712,-.00056360973331923388] 
dist 180=[-.00105136032616378142,-.00045984249142605550] 
dist 181=[-.00105094246457604958,-.00033006879153477757] 
dist 182=[-.00104515208690364651,-.00013428509110568569] 
dist 183=[-.00099922105643013906,6.20023065341137530270e-05] 
dist 184=[-.00098970141143973882,.00019377915457049783] 
dist 185=[-.00080282709267829722,.00030100269304650447] 
dist 186=[-.00075832090706377581,.00039980654364932800] 
dist 187=[-.00071767487097104403,.00048333635608448469] 
dist 188=[-.00070150248931502725,.00052991711806780347] 
dist 189=[-.00015898465507424454,.00055909376380855206] 
dist 190=[-.00010485865868401974,.00056613101005983152] 
dist 191=[1.73035595512093096940e-05,.00046214301657246546] 
dist 192=[4.15815135677285122070e-05,.00046415032423938470] 
dist 193=[.00017643255081355761,.00051740186746924539] 
dist 194=[.00019779644539390043,.00056609216285912667] 
dist 195=[.00017345758226408208,.00059521387585851927] 
dist 196=[.00014606456761416795,.00060258968040592457] 
dist 197=[.00011174093157212853,.00024462623843621723] 
dist 198=[5.98819158785763114000e-05,.00024352543961608932] 
dist 199=[7.84728938220950182440e-06,.00023312711986499643] 
dist 200=[-2.71747263403129737060e-05,.00023120234938616723] 
dist 201=[-5.57727267330601161520e-05,.00018726850775068393] 
dist 202=[-8.23018888720601896010e-05,.00017681752120386097] 
dist 203=[-.00010485904571811459,.00016804817931956664] 
dist 204=[-.00011768687767577756,.00016505071492917949] 
dist 205=[-.00012560849491310752,1.98762366937106254530e-05] 
dist 206=[-.00012868646699674108,2.59227775404188348990e-06] 
dist 207=[-.00012907995740474603,-3.74645799054227498880e-05] 
dist 208=[-.00012850724620617482,-4.35699678862937727310e-05] 
dist 209=[-.00012321389423800966,-9.00904826352730543720e-05] 
dist 210=[-.00012389706834883812,-8.80382794313312780000e-05] 
dist 211=[-.00013165634391198275,-7.54847531001084508060e-05] 
dist 212=[-.00013412814093907294,-6.15269345790925071750e-05] 
dist 213=[-.00013382388810960423,-4.41467972122296649770e-05] 
dist 214=[-.00013298884602952467,-1.80040750789794758690e-05] 
dist 215=[-.00012704021352941977,8.18385952723482332220e-06] 
dist 216=[-.00012571878631555539,2.57438025600033954780e-05] 
dist 217=[-.00010217836190560408,4.00118665099600142050e-05] 
dist 218=[-9.65670998756828969040e-05,5.31293485449223405180e-05] 
dist 219=[-9.11439252228887624740e-05,6.42004940974528858030e-05] 
dist 220=[-8.87950660638784040470e-05,7.03434918006184797580e-05] 
dist 221=[-2.00754592606163678140e-05,7.39500571543341347310e-05] 
dist 222=[-1.28403253945092960430e-05,7.48951189635827712570e-05] 
dist 223=[3.49047700855852835600e-06,5.51656871918473855480e-05] 
dist 224=[6.70116960490798608940e-06,5.65603216416246123500e-05] 
dist 225=[2.46956080016136423970e-05,6.81387699084023822820e-05] 
dist 226=[2.56538945352696326960e-05,7.45738706558909039350e-05] 
dist 227=[2.10729722898359823320e-05,7.84690966443806100110e-05] 
dist 228=[1.60038626937691207720e-05,7.94004886404501508750e-05] 
dist 229=[9.70678055986672665290e-06,3.35727526507370498000e-05] 
dist 230=[2.49720138611493256780e-07,3.33133699389690417240e-05] 
dist 231=[-9.22071197224162010790e-06,3.23233454430781089340e-05] 
dist 232=[-1.55709696219065242720e-05,3.17286162658878971620e-05] 
dist 233=[-2.07318206553591558350e-05,2.79802650441351656820e-05] 
dist 234=[-2.54794797227071062120e-05,2.69912091445324908060e-05] 
dist 235=[-2.94895283672638925530e-05,2.47657265875645615510e-05] 
dist 236=[-3.17215399799072322430e-05,2.39820455140647034990e-05] 
dist 237=[-3.30375074356442001440e-05,1.22986274115307988120e-05] 
dist 238=[-3.34101969374531450230e-05,1.05121128017945699580e-05] 
dist 239=[-3.32975159193532836020e-05,6.71959555315978076630e-06] 
dist 240=[-3.29870466390907015090e-05,5.69421217403763589180e-06] 
dist 241=[-3.18989697646628150070e-05,1.87385545193901779460e-06] 
dist 242=[-3.12837457707640136260e-05,1.06779584583065255460e-06] 
dist 243=[-2.74822073523689451770e-05,1.22360382104736493900e-08] 
dist 244=[-2.47001509757397939190e-05,-1.71075162179668834200e-08] 
dist 245=[-3.65905214382982405800e-07,-6.80350491753041759400e-08] 
dist 246=[-4.23165397137537425910e-07,-7.89518191763756828400e-08] 
dist 247=[-4.65116515018683512730e-07,-2.27697218755632075370e-07] 
dist 248=[-4.96379219007269097260e-07,-2.48191281375428450320e-07] 
dist 249=[-5.18574934058573649240e-07,-2.59451546074549825570e-07] 
dist 250=[-5.24461475368944736140e-07,-2.43964826187509606510e-07] 
dist 251=[-5.24142388730375570490e-07,-2.15517519078398293390e-07] 
dist 252=[-5.21655353445832761120e-07,-1.70981347278319572980e-07] 
dist 253=[-4.48853865614291833060e-07,-1.06755906053741362710e-07] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 2, 1, 1, 0, 2] 
dist 0=[129.53911113656602513   ,129.53911113656602513   ] 
dist 1=[128.00432173137247487   ,129.85807896055008649   ] 
dist 2=[123.54683632775758667   ,129.53911113656602513   ] 
dist 3=[117.56539556243145442   ,129.00646697281946372   ] 
dist 4=[109.97669428300275481   ,123.04239847724084643   ] 
dist 5=[99.901128541422915840  ,118.56682588126584656   ] 
dist 6=[84.029245604864495898  ,117.29274350559290560   ] 
dist 7=[67.750499712861052230  ,107.83815300331633126   ] 
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dist 189=[-6.13250187968016537610e-05,.00123003352401307864] 
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dist 191=[.00013822496702231228,.00047878189305211307] 
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dist 200=[-6.87803392391190809710e-05,.00041899382070419764] 
dist 201=[-.00012722133621983720,.00035820192268014509] 
dist 202=[-.00018130718312381944,.00034263379001675531] 
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dist 207=[-.00027545831193792934,5.07062709469416775790e-05] 
dist 208=[-.00027363892085866140,3.74874253465355531530e-05] 
dist 209=[-.00031743200327740289,-1.38766876485754648300e-05] 
dist 210=[-.00034299038708175546,-2.39350294620985277220e-05] 
dist 211=[-.00035804146217043516,-3.89767128295204684570e-05] 
dist 212=[-.00036181728069520189,-4.25475111485331883130e-05] 
dist 213=[-.00019879555942713880,-4.25549450160742513280e-05] 
dist 214=[-.00019343255739195362,1.81414934309199634360e-05] 
dist 215=[-.00010384421654907165,8.12372820254189610080e-05] 
dist 216=[-9.49679378498417487520e-05,.00012353610285285739] 
dist 217=[-7.72677272819089977430e-05,.00015790235523793809] 
dist 218=[-6.93665153251341459470e-05,.00018950034328815950] 
dist 219=[-6.03736465479512745280e-05,.00021617751341149410] 
dist 220=[-5.86029100057860516950e-05,.00023100462508468954] 
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dist 223=[2.52910857809234559000e-06,5.55004359483511919440e-05] 
dist 224=[4.93773988596666825230e-06,5.52582728348939231300e-05] 
dist 225=[1.90383450044698875290e-05,5.30227349213555095300e-05] 
dist 226=[2.13420189588168743180e-05,5.58869785311128267350e-05] 
dist 227=[1.79529884196248954350e-05,5.88822165457300959870e-05] 
dist 228=[1.05752238300686003320e-05,5.98643506611432338340e-05] 
dist 229=[1.40603021036722255910e-06,5.98535411572525976230e-05] 
dist 230=[-1.23694252140578263140e-05,5.93517658095839419400e-05] 
dist 231=[-2.61673231010634952270e-05,5.75883498665658988220e-05] 
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dist 233=[-4.29575794281425689400e-05,5.00343445251272039780e-05] 
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dist 235=[-5.57724992346954305590e-05,4.42667529988595648680e-05] 
dist 236=[-5.90602196067264688210e-05,4.28008366965182598750e-05] 
dist 237=[-6.10236523820064066180e-05,2.30277820799398055760e-05] 
dist 238=[-6.16383301358805997030e-05,1.99212208785329439830e-05] 
dist 239=[-6.14736080259880176210e-05,1.34066661694618453170e-05] 
dist 240=[-6.09289266240785136810e-05,1.16504324427323393050e-05] 
dist 241=[-5.88946067701022007170e-05,5.16954845138544787860e-06] 
dist 242=[-5.77329270873224573330e-05,3.75905150093566852080e-06] 
dist 243=[-5.05306938161538416250e-05,2.01044799746157094050e-06] 
dist 244=[-4.52118683955019495520e-05,1.64701000645941924190e-06] 
dist 245=[-2.32156310530705986280e-05,1.66474206860721234190e-06] 
dist 246=[-2.24957720547517883780e-05,1.99875196761119147310e-06] 
dist 247=[-8.43348695149797797620e-06,6.10223680583213814260e-06] 
dist 248=[-7.25614290620182595010e-06,1.03834955454962108940e-05] 
dist 249=[-4.75117643708840162620e-06,1.38621418387265421600e-05] 
dist 250=[-4.07070476721642263140e-06,1.70614262744655057490e-05] 
dist 251=[-1.51775953208920773630e-06,1.97633676512605397970e-05] 
dist 252=[-9.80417545377526841090e-07,2.12671704413835876460e-05] 
dist 253=[-2.17543350913257487330e-07,2.21646422868801886060e-05] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 2, 0, 1] 
dist 0=[113.48206116700251437   ,113.48206116700251437   ] 
dist 1=[111.58814574952887484   ,114.56944618866580077   ] 
dist 2=[107.59807672302540640   ,115.35101383031581772   ] 
dist 3=[101.38043933626092737   ,116.02820291282468800   ] 
dist 4=[90.634518939133039742  ,116.69039484296202501   ] 
dist 5=[79.308200973611199982  ,117.13118826880647954   ] 
dist 6=[70.779150391652882437  ,116.93301392299361670   ] 
dist 7=[62.787126149383809874  ,112.62909904674319224   ] 
dist 8=[53.580008940239834289  ,102.21496497817373365   ] 
dist 9=[44.408048529369221494  ,93.480044055682203229  ] 
dist 10=[36.541518453128983434  ,90.295553969382387765  ] 
dist 11=[28.168325341973197328  ,81.455608448753803521  ] 
dist 12=[16.955991207947123441  ,80.006686219667407840  ] 
dist 13=[6.201487405007352524  ,62.971573912315757976  ] 
dist 14=[-.355338933211107030  ,59.478926443107286545  ] 
dist 15=[-5.106343024359240663  ,55.579145972003201658  ] 
dist 16=[-8.666507814945692271  ,54.390823537745148894  ] 
dist 17=[-11.401671105100456670  ,17.756704402343445376  ] 
dist 18=[-12.860395523808733847  ,13.339179700387292744  ] 
dist 19=[-13.688487261713681360  ,3.1769054762226503528 ] 
dist 20=[-17.137496258411627055  ,1.5903695883901659349 ] 
dist 21=[-21.533083191905863600  ,1.0700935677174868931 ] 
dist 22=[-24.081249039225458165  ,1.8258140494600051048 ] 
dist 23=[-25.761759629158140434  ,2.7913124667059269648 ] 
dist 24=[-26.695133657426342376  ,4.2182366278527590806 ] 
dist 25=[-27.843147774045545917  ,5.7662732882339982616 ] 
dist 26=[-28.086612187302803716  ,7.2208140084565805611 ] 
dist 27=[-27.662343608673022314  ,8.8516404830720218342 ] 
dist 28=[-27.563338199186048409  ,11.108685514530813549  ] 
dist 29=[-23.241510747362791344  ,13.207226722827069675  ] 
dist 30=[-22.149190036076762078  ,14.211551909531284970  ] 
dist 31=[-21.351178712432174078  ,14.707274223650752014  ] 
dist 32=[-21.071292688773165106  ,14.782511848340330207  ] 
dist 33=[-4.4797448832517942720 ,13.733298327362161634  ] 
dist 34=[-2.5116910661083164465 ,13.389671049083493305  ] 
dist 35=[2.1032524780132203908 ,13.127509614660517555  ] 
dist 36=[2.2474026706301617185 ,12.921487611841187907  ] 
dist 37=[.3368155111484410217 ,10.216033448755899699  ] 
dist 38=[-.9762935989665828871 ,11.849330747867911517  ] 
dist 39=[-2.0667955368118073021 ,12.946032282341825581  ] 
dist 40=[-4.0188952161275791011 ,13.572231428912190179  ] 
dist 41=[-5.8160716520602222775 ,13.905511115777842759  ] 
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dist 180=[-.00109401224166558280,-7.72094214614631430530e-05] 
dist 181=[-.00131403413291523843,.00010280325011379923] 
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dist 195=[-6.07580570515212922840e-05,.00043632339884294219] 
dist 196=[-4.11743101342821577850e-05,.00042346659207497253] 
dist 197=[-8.81039562667002083970e-05,.00026813548599804065] 
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dist 205=[-9.59310146512884381230e-05,.00023904789684143598] 
dist 206=[-9.55760947919685774960e-05,.00022777585879730945] 
dist 207=[-9.26833398600860986180e-05,.00021180742460577029] 
dist 208=[-9.12105803396487692940e-05,.00020571468073683213] 
dist 209=[-7.82075649587400180020e-05,6.32160267135180089440e-05] 
dist 210=[-8.65499537320300074180e-05,4.49711336148195785890e-05] 
dist 211=[-.00012686061687735952,4.25724158099159774510e-06] 
dist 212=[-.00016385762286516382,-4.54122399812708607220e-06] 
dist 213=[-.00019505200527300498,1.19447111207855008330e-05] 
dist 214=[-.00021232110232065517,2.85297504148619669740e-05] 
dist 215=[-.00022241773077543458,4.20382941018400242030e-05] 
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dist 217=[-7.89193519486272099260e-05,6.50832696786227151400e-05] 
dist 218=[-7.82586909355029257990e-05,7.10249267711740732370e-05] 
dist 219=[-7.57110161146177146710e-05,7.46049122205568847990e-05] 
dist 220=[-7.42318273272943193590e-05,7.57974132721154751430e-05] 
dist 221=[-6.50103495835999991730e-05,7.57876356397679224710e-05] 
dist 222=[-6.25922101545059884480e-05,7.51468264394066565060e-05] 
dist 223=[-5.73976894489931148610e-05,7.29233046678659959070e-05] 
dist 224=[-5.56254090479321374170e-05,7.16113523806161102780e-05] 
dist 225=[-2.69413285871387683230e-05,6.33899092164201517830e-05] 
dist 226=[-2.26504444884730846730e-05,6.12287282023414213800e-05] 
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dist 228=[-1.10254596780095091710e-05,5.41656510211226101750e-05] 
dist 229=[-7.43100657237845066150e-06,4.08584562455782839660e-05] 
dist 230=[-1.18960737365073321360e-05,4.48254072299354230390e-05] 
dist 231=[-1.55382197473460765850e-05,4.71635562212258347420e-05] 
dist 232=[-1.89105266042542004060e-05,4.78248082363251455760e-05] 
dist 233=[-2.17736162565099638150e-05,4.75678135245430992120e-05] 
dist 234=[-2.33939594438282226340e-05,4.72431370959298922900e-05] 
dist 235=[-2.43844584600032717950e-05,4.49223184776757822590e-05] 
dist 236=[-2.47468153626285115890e-05,4.45491963206156821470e-05] 
dist 237=[-2.48724358142477831990e-05,3.55394091714964961260e-05] 
dist 238=[-2.49229736560209595290e-05,3.34343289265684024610e-05] 
dist 239=[-2.49278642861823606810e-05,3.17516956890721877550e-05] 
dist 240=[-2.48721859606718684770e-05,3.12905579448157390040e-05] 
dist 241=[-2.47840357631186146490e-05,8.58339649305170986900e-06] 
dist 242=[-2.46599757453237840280e-05,7.38211878502704533150e-06] 
dist 243=[-2.44888045881698868730e-05,4.82785038697081501320e-06] 
dist 244=[-2.42135963777496878220e-05,4.13460979347488154090e-06] 
dist 245=[-2.39317669488123487070e-05,1.53667313380277114190e-06] 
dist 246=[-2.37342641061280915770e-05,9.89674371211104199870e-07] 
dist 247=[-2.35647712225940008610e-05,2.17238856711418723340e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 0, 1, 1, 1, 2] 
dist 0=[130.27502896766659314   ,130.27502896766659314   ] 
dist 1=[129.21212149604836419   ,130.23942150895097334   ] 
dist 2=[125.43449476774471135   ,130.27502896766659314   ] 
dist 3=[120.30638679018888843   ,129.17753530404832259   ] 
dist 4=[113.87014496325042170   ,122.46617338281040297   ] 
dist 5=[105.35315427142255001   ,116.99625252659369584   ] 
dist 6=[91.947351015633162679  ,114.94980132641958077   ] 
dist 7=[78.165878186366798785  ,113.42320566282686344   ] 
dist 8=[68.149761877589802610  ,105.51626808631160650   ] 
dist 9=[59.105112814851141503  ,88.276459962089360791  ] 
dist 10=[49.174685792077579630  ,86.555727218403635761  ] 
dist 11=[31.311430383926521623  ,45.697466208654193268  ] 
dist 12=[18.699193320191417423  ,43.242418908038507156  ] 
dist 13=[8.1281310813734230554 ,38.321634849755314676  ] 
dist 14=[-2.2204816761850705097 ,37.175843247239105863  ] 
dist 15=[-11.480520685268752889  ,29.504247399935147699  ] 
dist 16=[-17.729907123006451327  ,25.323500686896018274  ] 
dist 17=[-22.916909567587619817  ,-.03176998674480993558] 
dist 18=[-27.966071835184218123  ,-.90953311200224875393] 
dist 19=[-32.151489743777400884  ,-9.2283214981764523937 ] 
dist 20=[-33.907014103975316120  ,-8.9683712947593746448 ] 
dist 21=[-34.661410045965370084  ,-7.5228558741873971253 ] 
dist 22=[-34.848466004771721647  ,-4.1986378743106505814 ] 
dist 23=[-31.045132806984222529  ,-.52166139469537712663] 
dist 24=[-30.041967560130087302  ,2.3307690557731639365 ] 
dist 25=[-29.449641424145691805  ,5.0353610079481646293 ] 
dist 26=[-29.299318545591587579  ,8.1379002709587779174 ] 
dist 27=[-7.3559812605888654505 ,11.168497725705286711  ] 
dist 28=[-4.7641073016188279334 ,13.594646469188982363  ] 
dist 29=[1.2432312777944102587 ,15.999062115878563241  ] 
dist 30=[2.2321670571097367385 ,18.951962681549214362  ] 
dist 31=[4.9690909692496481272 ,21.586335261193662815  ] 
dist 32=[5.2775503372024437309 ,22.728302713422857957  ] 
dist 33=[12.059719178080227589  ,23.223044068935313645  ] 
dist 34=[12.329040120982591361  ,23.281523708720770942  ] 
dist 35=[12.699509658428120930  ,21.069477583044515290  ] 
dist 36=[11.792605576260652738  ,20.402372066037402392  ] 
dist 37=[10.429972449631828978  ,19.931551932961225028  ] 
dist 38=[8.5946184279116000639 ,19.627034745138381132  ] 
dist 39=[3.5681988822401499717 ,14.905865595828359512  ] 
dist 40=[-.17532670888374389019,14.364128768897585562  ] 
dist 41=[-3.3229405980676228898 ,13.550976588565671873  ] 
dist 42=[-6.3832690420817366166 ,13.228654295021758382  ] 
dist 43=[-9.0751573256185593628 ,5.0426035220859219694 ] 
dist 44=[-10.761839645667700825  ,4.0434220490060724208 ] 
dist 45=[-12.002842881206050506  ,1.8112045757421219951 ] 
dist 46=[-12.927555187798038460  ,1.4058254118163643176 ] 
dist 47=[-13.576479234083628855  ,.46214585282158991354] 
dist 48=[-13.723176599712035778  ,.29955526483476504948] 
dist 49=[-13.657631627892219422  ,-.79014914508296802265] 
dist 50=[-13.479549306962268365  ,-.90460859627959157468] 
dist 51=[-12.042803960024287224  ,-.7619324256326253483 ] 
dist 52=[-11.618925901091551096  ,-.2380471257240251074 ] 
dist 53=[-10.865089720733521807  ,.47310775882998004531] 
dist 54=[-10.614662708133042152  ,1.3593591190467997208 ] 
dist 55=[-5.9178733108929695459 ,2.5229251078570110243 ] 
dist 56=[-4.6389821140606640380 ,4.6649724870534187646 ] 
dist 57=[-3.1200140834539356444 ,6.4925978078244851308 ] 
dist 58=[-3.0733918233314934698 ,8.3545855288983542468 ] 
dist 59=[-.6480125318526148731 ,9.9277157350583032223 ] 
dist 60=[-.357792261485284784  ,10.771147520425810593  ] 
dist 61=[.3294408116769642357 ,11.224220849644125413  ] 
dist 62=[.42857120762788251092,11.308369122626868754  ] 
dist 63=[1.1979987179087801802 ,2.4181650454627888588 ] 
dist 64=[1.2266245350384147227 ,2.4488970982688380444 ] 
dist 65=[1.6165853770177317975 ,2.4304729139968114596 ] 
dist 66=[1.6486233390875990228 ,2.4277744483142150671 ] 
dist 67=[1.6027366602272814131 ,2.2554281074847483418 ] 
dist 68=[1.4597217091492692766 ,2.2583397515029856431 ] 
dist 69=[1.2734899058341983917 ,2.1938093856830371426 ] 
dist 70=[.85684702154950277311,2.1762046211872425825 ] 
dist 71=[.31147358990211711766,1.8079729267234249671 ] 
dist 72=[-.06017274335899399154,1.7163237528220060960 ] 
dist 73=[-.36815783931469530281,1.6317387198286727492 ] 
dist 74=[-.66091179416124291968,1.5917591073234786841 ] 
dist 75=[-.9143854377735069461 ,.43754054153862685854] 
dist 76=[-1.0664982738132012102 ,.31696937494099387716] 
dist 77=[-1.1706376767220303335 ,.04164661198137543394] 
dist 78=[-1.2337469294155244180 ,-.01235147996637588970] 
dist 79=[-1.2699797017844355607 ,-.32816465766545875891] 
dist 80=[-1.2819106284597297651 ,-.3660607133777319867 ] 
dist 81=[-1.3161274574701659145 ,-.40913517893005514039] 
dist 82=[-1.3323559057875234860 ,-.41173883012636007161] 
dist 83=[-1.0749984085487059188 ,-.40064313062557810042] 
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dist 144=[-.02003442132958367005,-.00634269070809339495] 
dist 145=[-.02061487974502460066,-.00768775223313246265] 
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dist 154=[-.00558202676551369443,.01127548940683339678] 
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dist 156=[4.79490958629208283680e-05,.01464536335706187571] 
dist 157=[.00141395959710675269,.01534439690024037340] 
dist 158=[.00161490069740455696,.01552046502095365979] 
dist 159=[.00320261073721015793,.00473758367485240613] 
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dist 168=[-.00077911700610552387,.00317293923810562482] 
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dist 172=[-.00265421575607164381,.00071543641655874921] 
dist 173=[-.00281674962168453574,.00015794105081711150] 
dist 174=[-.00287767948782206767,3.38940504315911800750e-05] 
dist 175=[-.00288218847744694708,-.00056650806406775646] 
dist 176=[-.00302275178065444213,-.00067259224100201378] 
dist 177=[-.00316469821737519336,-.00084298162552109740] 
dist 178=[-.00320047268161224864,-.00087865910594715447] 
dist 179=[-.00223756021446350076,-.00088340421250047660] 
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dist 182=[-.00193224555445957800,-4.07083745135754000000e-05] 
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dist 184=[-.00070497045551233359,.00083210601017222491] 
dist 185=[-.00066158310931288903,.00111734891749138350] 
dist 186=[-.00065395166569180374,.00138029793227216706] 
dist 187=[-.00026689140456022843,.00160274423456608805] 
dist 188=[-.00021527875119122743,.00172716948930229074] 
dist 189=[-.00010142567126476060,.00180601440619654751] 
dist 190=[-7.30888737251107807020e-05,.00182547573393420469] 
dist 191=[4.82668239744067170210e-05,.00067092693748903823] 
dist 192=[7.10072039476093735800e-05,.00072814656279293034] 
dist 193=[.00010877178236877818,.00076262235066765396] 
dist 194=[.00011689613613119684,.00077411499023713094] 
dist 195=[.00012255577881774062,.00077291170030871841] 
dist 196=[.00011236951070359367,.00076723247401690902] 
dist 197=[9.10849423651631030260e-05,.00073805437291216962] 
dist 198=[-4.61154228162730355060e-05,.00072499716194534353] 
dist 199=[-.00020407572887776081,.00061543757076063464] 
dist 200=[-.00031021819555808688,.00058773567680536100] 
dist 201=[-.00039672237060543506,.00054316241741706080] 
dist 202=[-.00047670732997983961,.00052820453468020834] 
dist 203=[-.00054455146146721026,.00017781578557758850] 
dist 204=[-.00058284959342769440,.00013056864836300246] 
dist 205=[-.00060613940420014080,7.97799611995730841620e-05] 
dist 206=[-.00061439218500791263,6.84851378577243229240e-05] 
dist 207=[-.00061502472595479860,2.59476935910573598870e-05] 
dist 208=[-.00060917734616741648,1.70274264120306723060e-05] 
dist 209=[-.00059587583060182875,3.98967658226163042820e-06] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 1, 0, 1, 0, 2] 
dist 0=[113.42064884768075288   ,113.42064884768075288   ] 
dist 1=[112.19449267071023574   ,114.18856644934558377   ] 
dist 2=[109.09560836607815298   ,115.45556315517992891   ] 
dist 3=[103.92989794956720156   ,116.58883742589322037   ] 
dist 4=[94.486780995806893898  ,116.82879273135709810   ] 
dist 5=[84.419910620192303366  ,116.44854713813164570   ] 
dist 6=[76.770654520641983131  ,115.95961455915804467   ] 
dist 7=[69.532670394477359771  ,94.958571624013532382  ] 
dist 8=[61.086363264599118648  ,91.914343616616640893  ] 
dist 9=[52.606688996176976381  ,83.533590706193100841  ] 
dist 10=[45.222730217873109339  ,82.019251405001468782  ] 
dist 11=[37.265343400422439786  ,65.907721346512437649  ] 
dist 12=[26.481327637263684610  ,62.566164899541619797  ] 
dist 13=[16.041498508731235255  ,58.762865144890828376  ] 
dist 14=[9.4492622622267624378 ,56.912003916163243450  ] 
dist 15=[4.4053771394906249410 ,22.384638126945486271  ] 
dist 16=[.13649909165647605335,18.107320375521442921  ] 
dist 17=[-5.4498029171985238686 ,8.0807170374334559358 ] 
dist 18=[-13.000329665612236523  ,6.5802751046264405962 ] 
dist 19=[-19.542099082844105596  ,-5.5698618005612650736 ] 
dist 20=[-23.591713657775136653  ,-5.7710047743414277535 ] 
dist 21=[-26.557823477783676076  ,-5.6368671813065388266 ] 
dist 22=[-28.797043664065116508  ,-4.1872831322285111484 ] 
dist 23=[-30.341635958820720213  ,-1.3053472589852462753 ] 
dist 24=[-30.689944425066757342  ,1.0220395752643826010 ] 
dist 25=[-30.353500524912866287  ,3.2977978415326723818 ] 
dist 26=[-30.302737092181627020  ,5.9896742753626875785 ] 
dist 27=[-25.535656919622733249  ,8.6523526703992495887 ] 
dist 28=[-24.324566094326277808  ,10.820558493048275110  ] 
dist 29=[-23.572410032109000701  ,12.998625204725649239  ] 
dist 30=[-23.387601485577096723  ,15.710162753923442578  ] 
dist 31=[-4.4348576006003778362 ,18.144706720421569549  ] 
dist 32=[-2.2139847421447029501 ,19.225710845947596458  ] 
dist 33=[1.9681306098271622345 ,19.720422965998229948  ] 
dist 34=[1.7435790716310958999 ,19.821633089473744300  ] 
dist 35=[1.2738608860521964860 ,17.933405213306705008  ] 
dist 36=[.37371806528386783558,17.407712393590041892  ] 
dist 37=[-.57706872826964595312,17.071228677016548320  ] 
dist 38=[-1.2481707488960898105 ,16.922272919849826383  ] 
dist 39=[-1.8200944750886464939 ,14.424883080236350730  ] 
dist 40=[-2.3793239894903367389 ,14.462761261841485991  ] 
dist 41=[-2.9360333085297625441 ,14.210050243581237346  ] 
dist 42=[-4.4802071771621282237 ,14.018052907155273467  ] 
dist 43=[-6.7476989486998003789 ,12.190088205104809619  ] 
dist 44=[-8.1828958330562589976 ,11.697210232544930377  ] 
dist 45=[-9.2555068297901778991 ,10.956267791458425921  ] 
dist 46=[-10.085570608169762709  ,10.676978681756577973  ] 
dist 47=[-10.687322066560578213  ,3.8368671461817962501 ] 
dist 48=[-10.854092508058933927  ,2.9264784713003570616 ] 
dist 49=[-10.835806300264534264  ,1.9750162875624050767 ] 
dist 50=[-10.704501710411729358  ,2.4830531824329951744 ] 
dist 51=[-9.5841530645671934547 ,3.1689844940030521777 ] 
dist 52=[-10.240404730188969456  ,4.2558128719719517054 ] 
dist 53=[-10.751481381342694229  ,5.3601709968757721797 ] 
dist 54=[-10.880070707875101563  ,6.1158059766835387403 ] 
dist 55=[-3.3819056088241814685 ,6.7440673293508240867 ] 
dist 56=[-3.3321102129842845747 ,7.3432183769032439409 ] 
dist 57=[-3.2556284094562745638 ,7.8621164697415104666 ] 
dist 58=[-3.2380728196811940694 ,8.1720451942322577579 ] 
dist 59=[-2.7131044713604440470 ,8.3818981749285755573 ] 
dist 60=[-2.5868156977609422767 ,8.5038138169069645970 ] 
dist 61=[-2.4670267616189803998 ,8.5518694733302820199 ] 
dist 62=[-2.4238018630340872021 ,8.4686336075396495076 ] 
dist 63=[-.56353636490974905762,2.2725605945483286402 ] 
dist 64=[-.33600595064529348361,2.3013147904420087860 ] 
dist 65=[.19407090141221204788,2.2845825304407446712 ] 
dist 66=[.27966367145531554694,2.2813813847999786014 ] 
dist 67=[.25333046185757801756,1.9323004150340256664 ] 
dist 68=[.12737754655013643441,1.8414097313785283918 ] 
dist 69=[-.00114242504313570388,1.9198784893357973988 ] 
dist 70=[-.08877260114939608131,1.9804845620162451729 ] 
dist 71=[-.16104716650478172936,2.0011035895310394800 ] 
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dist 73=[-.36141995673072626502,1.9276034778980499411 ] 
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dist 76=[-1.0205268902937317372 ,1.5087645558655761824 ] 
dist 77=[-1.1186778881809130444 ,1.4204463394837473113 ] 
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dist 80=[-1.2146487244071886312 ,.47814754933241304118] 
dist 81=[-1.1938837111331986715 ,.32651745344730983158] 
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dist 83=[-1.1317559394925644563 ,.12068156174780978344] 
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dist 85=[-1.2876703812684611165 ,.02718940723519434270] 
dist 86=[-1.3011764814435853882 ,.01393254249496722321] 
dist 87=[-.38278490479010396056,.1499602973148078602 ] 
dist 88=[-.38305728592683766413,.36122746232246096829] 
dist 89=[-.37556668846357511368,.53320239645356536953] 
dist 90=[-.37000771626200126519,.69163607057044684842] 
dist 91=[-.32328057084680196869,.82543041238251705481] 
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dist 93=[-.29021729110213716304,.94314343995955638345] 
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dist 95=[-.10934133314064194764,.27063073713873572728] 
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dist 98=[-.02118715000795442330,.26474766308915172021] 
dist 99=[.03083191297061129677,.25617888184455089252] 
dist 100=[.01511244791529403779,.28118087175041378344] 
dist 101=[-.00080812759234014080,.29693343784113883137] 
dist 102=[-.02329886749515154819,.30375714069354207767] 
dist 103=[-.10414377081897909326,.30574503638282589918] 
dist 104=[-.15872724431327683204,.30375810353749737348] 
dist 105=[-.20345987286429023496,.29639237175605204156] 
dist 106=[-.24520021992660104342,.29155000326544253152] 
dist 107=[-.28084188380055255175,.26021086400404214261] 
dist 108=[-.30136466729401938255,.25182786927080792044] 
dist 109=[-.31436114664324333581,.23088448578080268796] 
dist 110=[-.32012590763163465072,.22304273046017103468] 
dist 111=[-.32142062976338446717,.12538779554992114431] 
dist 112=[-.31929210602114601017,.10964121981264639152] 
dist 113=[-.30981938045194653638,.07678652309394392003] 
dist 114=[-.3039017876912974218 ,.06789414126452232292] 
dist 115=[-.26616241250671296656,.03501175121243013041] 
dist 116=[-.25615052555856807245,.02772979357429594827] 
dist 117=[-.21825789059097201415,.01859208152281954130] 
dist 118=[-.15560900097379202074,.01633971932768535395] 
dist 119=[-.04213194919191917269,.02409586595738829243] 
dist 120=[-.03428735121053800570,.04854151478987552273] 
dist 121=[-.01700644063436095133,.06841394216847335615] 
dist 122=[-.01263480014709748600,.08668875828131088784] 
dist 123=[.00743910049164458004,.10210773509186613851] 
dist 124=[.00759186991952006437,.11064215182223337305] 
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dist 126=[.00964588702710005906,.11685157621886141599] 
dist 127=[.00928937769230478506,.03070303713712505465] 
dist 128=[.00840911078292565285,.03075401908167183613] 
dist 129=[.00728521293628511020,.02979545202632635812] 
dist 130=[.00596148439212565573,.02965713869915592018] 
dist 131=[.00426698558110462641,.02426493048513914941] 
dist 132=[.00167124377579880331,.02295448659088365758] 
dist 133=[-.00094050242886420411,.02206606276020851758] 
dist 134=[-.00269863351764781267,.02186216903915562879] 
dist 135=[-.00413208975215789188,.00246231275997146786] 
dist 136=[-.00545526156301271951,.00047294162904438775] 
dist 137=[-.00657344512500624508,-.00117061703557699890] 
dist 138=[-.00927751800423513071,-.00145047702614414633] 
dist 139=[-.01224508635661977165,-.00198130760182620031] 
dist 140=[-.01395839002727748732,-.00208696664899257315] 
dist 141=[-.01504939996144012619,-.00229942355028850705] 
dist 142=[-.01554657446402405971,-.00230839509689518801] 
dist 143=[-.01571717960949627921,-.00224491229454228056] 
dist 144=[-.01566756521567305392,-.00206809123567440382] 
dist 145=[-.01520389647851607288,-.00183717636806362712] 
dist 146=[-.01496844966473056349,-.00155891648011338326] 
dist 147=[-.01281955929287580416,-.00119877350814066814] 
dist 148=[-.01226319466682036892,-.00064277274703593551] 
dist 149=[-.01141673353165696286,-8.13748401498854476710e-05] 
dist 150=[-.01110981937194285362,.00030022727908115572] 
dist 151=[-.00373716352083815422,.00189443201928901617] 
dist 152=[-.00275363508682550424,.00460393150055254823] 
dist 153=[-.00054951246028770256,.00680536553063163447] 
dist 154=[-7.22040425547190572300e-05,.00882853191703700862] 
dist 155=[.00080439910116122599,.01053515212836883500] 
dist 156=[.00082817473562288587,.01147977816850898966] 
dist 157=[.00092736780334805640,.01202944139864475592] 
dist 158=[.00091903623216709583,.01216787925091326942] 
dist 159=[.00087738642368103059,.00366659946366148236] 
dist 160=[.00078062036427586445,.00366179468414709302] 
dist 161=[.00065853080022512395,.00353230671531795286] 
dist 162=[.00051633502847435587,.00350625390540947098] 
dist 163=[.00033520533043722643,.00287514028779347322] 
dist 164=[5.85403537912717000000e-05,.00272212151566326839] 
dist 165=[-.00021982274410551733,.00259474457132854116] 
dist 166=[-.00040770434568309907,.00254766768401949512] 
dist 167=[-.00056154441197873535,.00037075572547174224] 
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dist 169=[-.00088783868625315396,.00010793912534055765] 
dist 170=[-.00130836231733897483,8.27285361454220315530e-05] 
dist 171=[-.00166594533784850623,3.18058710636459300000e-05] 
dist 172=[-.00186931892151788581,1.90959134670396763920e-05] 
dist 173=[-.00199493733856847140,-.00031568679236642908] 
dist 174=[-.00204381287417101934,-.00031369252170896623] 
dist 175=[-.00205021805722991925,-.00030296097571714116] 
dist 176=[-.00204096743697955655,-.00027781712214403985] 
dist 177=[-.00195769045609859702,-.00024602777077392284] 
dist 178=[-.00193823559167597267,-.00020890892322195910] 
dist 179=[-.00158514152771556547,-.00016155863553546246] 
dist 180=[-.00150006742886686506,-8.91457916296877058130e-05] 
dist 181=[-.00141803880320253805,-1.62214386440515538440e-05] 
dist 182=[-.00138128142056897368,3.31626905549000875360e-05] 
dist 183=[-.00034106567447073992,.00015438278434729234] 
dist 184=[-.00023395892071907150,.00043402382845684279] 
dist 185=[7.79913933851289687990e-06,.00066135730843527970] 
dist 186=[5.66016860750304574670e-05,.00087055557229379611] 
dist 187=[.00013090880098953339,.00104725990800385239] 
dist 188=[.00013365239524351885,.00114557524527052405] 
dist 189=[.00014253274426188948,.00120555897520614725] 
dist 190=[.00013914275937059251,.00121981909717009607] 
dist 191=[.00013087310721222637,.00047091686679499470] 
dist 192=[.00011400679770480019,.00046962625380498578] 
dist 193=[9.33482443849595578000e-05,.00045047952799186460] 
dist 194=[7.00210285902460838600e-05,.00044770432556035430] 
dist 195=[4.07505494958098545940e-05,.00036106678254351869] 
dist 196=[-3.50548332123759683410e-06,.00034064569507114800] 
dist 197=[-4.78963040405177482360e-05,.00032573220733893045] 
dist 198=[-7.77027370600835375170e-05,.00032241400862623909] 
dist 199=[-.00010195435569017233,4.75718251547685540520e-05] 
dist 200=[-.00012429226597213994,4.34600080976451322870e-05] 
dist 201=[-.00014316454634072110,2.78418719915492696390e-05] 
dist 202=[-.00016066820824308979,2.43473107793527067810e-05] 
dist 203=[-.00020515260552330716,1.90475174773959578990e-05] 
dist 204=[-.00023033757593434935,1.75224135819641361620e-05] 
dist 205=[-.00024574758159185647,1.61557164911492315200e-05] 
dist 206=[-.00025142079542199101,1.88195630880269530200e-05] 
dist 207=[-.00025210327739527417,2.43641302442193948110e-05] 
dist 208=[-.00025057044973058344,3.51453570681392829250e-05] 
dist 209=[-.00024202618604573640,4.81943018225276084560e-05] 
dist 210=[-.00023768695516301607,6.27437651629173346670e-05] 
dist 211=[-.00020373524335487621,8.08876988126536503010e-05] 
dist 212=[-.00019498551156317436,.00010820957380848534] 
dist 213=[-.00018019476931201315,.00013559221494748893] 
dist 214=[-.00017543366086502431,.00015397778703444794] 
dist 215=[-6.39173066124574922560e-05,.00016894408915895604] 
dist 216=[-4.87059693924260976180e-05,.00018275048528661544] 
dist 217=[-1.50596043726023517530e-05,.00019443677913771777] 
dist 218=[-7.63749411364254024130e-06,.00020098516257441506] 
dist 219=[-6.59341749364836454240e-06,.00020490312660699769] 
dist 220=[-6.30184532574050069530e-06,.00020614525978799628] 
dist 221=[-5.72068814917985462490e-06,.00020566890117283302] 
dist 222=[-6.11714907134458292940e-06,.00020276331296497045] 
dist 223=[-7.08588387010117973880e-06,5.54071237482511811740e-05] 
dist 224=[-9.06278998715134549140e-06,5.51818129320783907360e-05] 
dist 225=[-1.14851039512605025130e-05,5.28423644078688962790e-05] 
dist 226=[-1.42225049472349952570e-05,5.24409224640684340220e-05] 
dist 227=[-1.76594060523501556680e-05,4.25388637313577222550e-05] 
dist 228=[-2.28592512867493542370e-05,4.03199534392271384640e-05] 
dist 229=[-2.80786486731141525990e-05,3.80987060776522978520e-05] 
dist 230=[-3.15933041693096220050e-05,3.75175323229613562480e-05] 
dist 231=[-3.44648552258791447890e-05,1.39049560341309285440e-05] 
dist 232=[-3.71309926297049527820e-05,1.31628930937366680980e-05] 
dist 233=[-3.93993298776686385000e-05,1.05132327727020664650e-05] 
dist 234=[-4.06915335113088053460e-05,9.79751939464260562150e-06] 
dist 235=[-4.15811528031810528780e-05,9.11363865856581742350e-06] 
dist 236=[-4.18098259298481567870e-05,8.89706251805856582260e-06] 
dist 237=[-3.30207739702056200630e-05,8.84296716523138563380e-06] 
dist 238=[-3.36227092090927386810e-05,8.95147857294549891780e-06] 
dist 239=[-3.35703681445386400740e-05,9.19716825557482781780e-06] 
dist 240=[-3.33569576565649356410e-05,9.68781510359565962910e-06] 
dist 241=[-3.19396723957904715690e-05,1.02857949406161574790e-05] 
dist 242=[-3.15472825960177726880e-05,1.09576939689037806230e-05] 
dist 243=[-2.59688246343632358320e-05,1.17988912555083020880e-05] 
dist 244=[-2.46190478903535822510e-05,1.30691176585072804880e-05] 
dist 245=[-2.31097792759618116690e-05,1.43434004763683288630e-05] 
dist 246=[-2.23806249040500778610e-05,1.52007272684559403220e-05] 
dist 247=[-8.18777870678329561940e-06,1.59004465038432034620e-05] 
dist 248=[-7.04620512860813865690e-06,1.65489681842836413200e-05] 
dist 249=[-4.61667316573516700550e-06,1.70999885748164531270e-05] 
dist 250=[-3.95648212953318317710e-06,1.74125909714820320250e-05] 
dist 251=[-1.47835010267266002240e-06,1.91577618201596700800e-05] 
dist 252=[-9.56998298439291308820e-07,2.06163700239860067780e-05] 
dist 253=[-2.13967736469619921200e-07,2.14832104284782090870e-05] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 0, 2, 2, 1, 2] 
dist 0=[130.77336143506607392   ,130.77336143506607392   ] 
dist 1=[129.69461108110435239   ,130.74096082037754723   ] 
dist 2=[125.89167266907676588   ,130.77336143506607392   ] 
dist 3=[120.73473515390624063   ,129.63116684911487799   ] 
dist 4=[114.26869405565836533   ,122.81831092037614968   ] 
dist 5=[105.71610958320211835   ,117.27429927719072710   ] 
dist 6=[92.258486709224270923  ,115.30306673430772113   ] 
dist 7=[78.425947110130043058  ,113.67955091110040776   ] 
dist 8=[68.377232124648309706  ,105.66708376834239657   ] 
dist 9=[59.307956322168211912  ,88.591720931034938488  ] 
dist 10=[49.246146580382895228  ,86.904867234852444518  ] 
dist 11=[31.537432740201090520  ,45.691852316336753928  ] 
dist 12=[18.879464944606629192  ,43.203192071038032238  ] 
dist 13=[8.2719252451749122215 ,38.273689229108303212  ] 
dist 14=[-2.1089897150018910570 ,37.140619534094936347  ] 
dist 15=[-11.395360206339487622  ,29.061594296288563825  ] 
dist 16=[-17.657524877825735097  ,24.794507053409975440  ] 
dist 17=[-22.849559424353478207  ,-.50288014606185736435] 
dist 18=[-27.894305865850065114  ,-1.3940586391417589643 ] 
dist 19=[-32.092310770197019632  ,-8.9517573683933811128 ] 
dist 20=[-33.920363013102182519  ,-8.6724327070234957908 ] 
dist 21=[-34.710941032427049891  ,-7.2056810870928222873 ] 
dist 22=[-34.766318137433832208  ,-3.8527757945964716290 ] 
dist 23=[-31.621160593194416760  ,-.14859292777906833607] 
dist 24=[-30.598498638881258714  ,2.7191830905714722629 ] 
dist 25=[-29.824150215245799160  ,5.4329804257311541391 ] 
dist 26=[-29.227003455429264051  ,8.5383443043666908036 ] 
dist 27=[-9.7843798788255941866 ,11.567236317579062491  ] 
dist 28=[-7.3742070901633850157 ,13.984598141545919712  ] 
dist 29=[-1.5757739977345857679 ,16.373412984890123919  ] 
dist 30=[-.72158506569001917879,19.297539840638682485  ] 
dist 31=[5.3566403444361372957 ,21.890677408866916434  ] 
dist 32=[5.6404014254609628434 ,22.967591555604232382  ] 
dist 33=[9.8272407648742798787 ,23.421462554266494269  ] 
dist 34=[10.156715105888144246  ,23.534742296451828794  ] 
dist 35=[12.841873973970109117  ,20.925361109734222524  ] 
dist 36=[12.109237635020127166  ,20.243279017923858408  ] 
dist 37=[10.961689395909759890  ,19.935244405561042243  ] 
dist 38=[9.3709917424984629115 ,19.753616584493564438  ] 
dist 39=[4.6090388631583600253 ,16.864897591925466466  ] 
dist 40=[.98322879351771111372,16.103046845573920907  ] 
dist 41=[-2.0683529051591710541 ,15.248756061767234653  ] 
dist 42=[-5.0399007409591496669 ,14.812937706206290657  ] 
dist 43=[-7.6566305376287122656 ,6.8621010895060016339 ] 
dist 44=[-9.3013500292283534396 ,6.1274658432233315382 ] 
dist 45=[-10.517490536720297197  ,4.4604368307738810368 ] 
dist 46=[-11.434920447062447018  ,4.0049183127918980526 ] 
dist 47=[-12.088157569834679541  ,1.9686080518926402338 ] 
dist 48=[-12.751234182214732412  ,1.5852330900406244771 ] 
dist 49=[-13.361028119005859131  ,.7067238730872996722 ] 
dist 50=[-13.476778150545737075  ,.52852282466750159955] 
dist 51=[-10.760393561433467081  ,-3.8826491084055235575 ] 
dist 52=[-10.370181466153352224  ,-3.6881704779468918264 ] 
dist 53=[-9.7769735333701609204 ,-3.3932050128043980981 ] 
dist 54=[-9.5445624085930409347 ,-2.2494654496947479114 ] 
dist 55=[-3.6420777846086154338 ,1.0178725397916573512 ] 
dist 56=[-3.2485803792808606645 ,3.2188312600094763207 ] 
dist 57=[-1.0438360605383539067 ,5.0143703413520895749 ] 
dist 58=[-.66438301934231028378,6.6728435970062737550 ] 
dist 59=[.27564021094105016727,8.0746926823270605130 ] 
dist 60=[.38926304313179871681,8.8518137459237969666 ] 
dist 61=[1.1949224167454657473 ,9.3044866731873843358 ] 
dist 62=[1.3179883978721978032 ,9.4184942298881504553 ] 
dist 63=[1.5352844712044582627 ,2.8887882695484222701 ] 
dist 64=[1.5698349141599736133 ,2.9235805584363269969 ] 
dist 65=[2.0348410882604801910 ,2.9044924030919913238 ] 
dist 66=[2.0326823125371919377 ,2.8954813265132725876 ] 
dist 67=[1.9603552781386916808 ,2.4740464122435996457 ] 
dist 68=[1.7758679016421571551 ,2.3635416970564111286 ] 
dist 69=[1.5389607686448464557 ,2.2799469072552149602 ] 
dist 70=[.91626584448222984689,2.2435720360635210314 ] 
dist 71=[.23857891207583702535,1.6594571810402941084 ] 
dist 72=[-.22247142023216751553,1.6197045246585039317 ] 
dist 73=[-.60374419444247295489,.63085476003609324507] 
dist 74=[-.96484688869529372144,.49943968391700394004] 
dist 75=[-1.2766038876820847961 ,.20086618744071529131] 
dist 76=[-1.4620544681378676618 ,.13612932010554067818] 
dist 77=[-1.5870003140294763118 ,-.20623571357765417123] 
dist 78=[-1.6586548775306803581 ,-.26512264977660371945] 
dist 79=[-1.6947027569991268773 ,-.37710517612669364909] 
dist 80=[-1.6968212756577919678 ,-.39973726253851542898] 
dist 81=[-1.6493235441258345042 ,-.44685530402589180273] 
dist 82=[-1.6352773064469750701 ,-.4479930761106623414 ] 
dist 83=[-1.3627632892669250933 ,-.43239358109234271355] 
dist 84=[-1.2945922563034987547 ,-.39041678440018056643] 
dist 85=[-1.2290543759250509740 ,-.33594748421794030347] 
dist 86=[-1.1961507993326668692 ,-.22770598180758296905] 
dist 87=[-.38261139061142238413,.11991230582655076159] 
dist 88=[-.37313575105471087773,.35402665730634574734] 
dist 89=[-.19842030861125521559,.54516351790936132607] 
dist 90=[-.17257414091269551156,.7221885448118653363 ] 
dist 91=[-.11412590162596942883,.872336751195601874  ] 
dist 92=[-.09916436288587484048,.96345882947050114726] 
dist 93=[-.03012798152015905698,1.0154909756498788914 ] 
dist 94=[-.01740007883202344405,1.0275940556976579134 ] 
dist 95=[.00956276054226648366,.42214512620241140382] 
dist 96=[.01598292332101373744,.43448511791474590902] 
dist 97=[.03817277918097685469,.43970698073237255203] 
dist 98=[.03858865364586036770,.43820871486816847862] 
dist 99=[.03145753410661315848,.42614813636362515801] 
dist 100=[.01240349593272018203,.4184175522940774614 ] 
dist 101=[-.01229997926848523934,.36237401016157590012] 
dist 102=[-.04186496581809818925,.34745308882386553353] 
dist 103=[-.09076332903523606716,.32078683810527997955] 
dist 104=[-.15949595266682403734,.31254387100756121156] 
dist 105=[-.2160029676218261607 ,.11894369877160759515] 
dist 106=[-.2690212082126244386 ,.09213971325030647085] 
dist 107=[-.31448945656575626663,.03347529388256945040] 
dist 108=[-.34102725144700116331,.01888476052187116415] 
dist 109=[-.35828746472801254205,-.03527655342070623776] 
dist 110=[-.36692941077312564261,-.04215025756295429868] 
dist 111=[-.37056811291863573542,-.05467792314503205699] 
dist 112=[-.36796540880741372641,-.05699011386053382651] 
dist 113=[-.19485918207661541425,-.06038979820833070934] 
dist 114=[-.19194110956725149565,-.06005899924633558552] 
dist 115=[-.16523524464241693592,-.05811909103609501221] 
dist 116=[-.15822382826209901051,-.05353546643052191974] 
dist 117=[-.147554410436463395  ,-.04773159000682905713] 
dist 118=[-.14365159893273111726,-.02860661817573307594] 
dist 119=[-.04923939893110788322,.02320796077960493091] 
dist 120=[-.04421186450668601749,.0579755734839953848 ] 
dist 121=[-.00831595168376544709,.08623885202433236160] 
dist 122=[-.00220973402700358691,.1122306587213778356 ] 
dist 123=[.00921929572587693240,.13416168038167355179] 
dist 124=[.01081230081358596649,.14630301370665426981] 
dist 125=[.02286247020521541490,.15336871296344423143] 
dist 126=[.02465324720241030411,.15514838531783107012] 
dist 127=[.02781793752849269739,.04687717514717207930] 
dist 128=[.02827720672431689266,.04690046639798902000] 
dist 129=[.03113590251471417770,.04542853219303360437] 
dist 130=[.03049971514260690295,.04512049838067469506] 
dist 131=[.02897783477923285522,.03721839344126451803] 
dist 132=[.02589103885078782969,.03528129677165013156] 
dist 133=[.02211578596308638622,.03369741568185127182] 
dist 134=[.01252032728771251914,.03309789015076165127] 
dist 135=[.00192851134295352444,.02302481850465677827] 
dist 136=[-.00521225499867074084,.02241673710121101227] 
dist 137=[-.01105470704683021760,.00769761648936723192] 
dist 138=[-.01649219516750769591,.00573195528684143509] 
dist 139=[-.02112677105901277859,.00131501146879516236] 
dist 140=[-.02378164698849827336,.00036267356407489437] 
dist 141=[-.02544574884309726042,-.00450749174163473682] 
dist 142=[-.02614696024416980333,-.00535038852669826930] 
dist 143=[-.02630115623505595285,-.00680176283914418693] 
dist 144=[-.02620576618804909468,-.00707947190623306501] 
dist 145=[-.02518582327406465194,-.00730769955004638604] 
dist 146=[-.02494309082736912798,-.00720461755019563413] 
dist 147=[-.02044963011544281089,-.00691531575855732295] 
dist 148=[-.01936167128214847465,-.00630430680885327285] 
dist 149=[-.01831981661676166700,-.00554947287351706100] 
dist 150=[-.01784928337689138852,-.00350497625388398847] 
dist 151=[-.00526479904061892356,.00186671338097092765] 
dist 152=[-.00517120381029938470,.00547199043772595368] 
dist 153=[-.00080633714247347740,.00840461062849221729] 
dist 154=[-.00028437626405242849,.01110562664184977026] 
dist 155=[.00093431040426858641,.01338832782542909712] 
dist 156=[.00111741936895549689,.01466008228847776347] 
dist 157=[.00256273595286844431,.01544989087623308201] 
dist 158=[.00277850074951797281,.01563384460902221129] 
dist 159=[.00317200844041012710,.00606388423806254421] 
dist 160=[.00323405896639502396,.00605435029977771855] 
dist 161=[.00334959819895480067,.00582305170692790609] 
dist 162=[.00327446883326495892,.00578952152175353427] 
dist 163=[.00310943303204964802,.00468759287867088462] 
dist 164=[.00278294862664347400,.00442437723998160459] 
dist 165=[.00238608608505034329,.00423807741521605419] 
dist 166=[.00170586621485989998,.00419589335582933085] 
dist 167=[.00038849387932833377,.00286534614570251365] 
dist 168=[-.00049823799848845154,.00279169936521194431] 
dist 169=[-.00122241147483006728,.00070095619459229236] 
dist 170=[-.00189437338051527243,.00048475766045707997] 
dist 171=[-.00246587286820948868,-4.42256989765492648200e-06] 
dist 172=[-.00279117790513345146,-.00010243602421537903] 
dist 173=[-.00299247230140807108,-.00064806375816607409] 
dist 174=[-.00307161257516892244,-.00073911645534667259] 
dist 175=[-.00308698705494556647,-.00089812723483761750] 
dist 176=[-.00307145216883491721,-.00092689040199144310] 
dist 177=[-.00296739258206389548,-.00094667810535118650] 
dist 178=[-.00291994038312869857,-.00092997006505844399] 
dist 179=[-.00248485037709061047,-.00089085668261790108] 
dist 180=[-.00237397656422967132,-.00081198775449918832] 
dist 181=[-.00220618719677084597,-.00071563582047748174] 
dist 182=[-.00214563524596471293,-.00039483328758500970] 
dist 183=[-.00070660791910460268,.00038997861060636819] 
dist 184=[-.00065686850584277953,.00091593737373783387] 
dist 185=[-8.97674776871050159620e-05,.00134301868005361848] 
dist 186=[3.23877622816900963830e-06,.00173522775079347267] 
dist 187=[.00016382781553716463,.00206597582553080720] 
dist 188=[.00018743745488775768,.00224901823800059878] 
dist 189=[.00037399762183985944,.00235553746628200086] 
dist 190=[.00040131839466841842,.00238238999214276517] 
dist 191=[.00045105537440026457,.00072559830061591397] 
dist 192=[.00045829917136689432,.00072322474111102413] 
dist 193=[.00047516027166305745,.00069303981315992279] 
dist 194=[.00046211164205149988,.00068852278019130759] 
dist 195=[.00043632949325906279,.00055550524428887945] 
dist 196=[.00038709532141788616,.00052641543720852946] 
dist 197=[.00031652529523369201,.00049989726230212143] 
dist 198=[.00015209883087117710,.00049432962326944871] 
dist 199=[-1.27031689510272668550e-05,.00034802728538737028] 
dist 200=[-.00012341543017592186,.00033853731641892900] 
dist 201=[-.00021361206743993299,.00011541458443490707] 
dist 202=[-.00029695534205019762,8.61169826999273257870e-05] 
dist 203=[-.00036760691806578817,2.08510606014652612140e-05] 
dist 204=[-.00040741027012124797,6.23270872858675081690e-06] 
dist 205=[-.00043151074772777295,-6.40475623225786828390e-05] 
dist 206=[-.00043981316027136477,-7.65061116470957348910e-05] 
dist 207=[-.00043953523984749787,-9.65653523259068728630e-05] 
dist 208=[-.00043690954807175866,-.00010077041006096451] 
dist 209=[-.00041843335940153544,-.00010151786322871355] 
dist 210=[-.00041353563404426867,-9.86257033407173086800e-05] 
dist 211=[-.00033967167624468609,-9.27165523520144144740e-05] 
dist 212=[-.00032183115707690118,-8.12982235817503276240e-05] 
dist 213=[-.00030261247592408759,-6.75003494293986511130e-05] 
dist 214=[-.00029296212086383767,-4.56852901742370000000e-06] 
dist 215=[-.00010617678317113639,7.48686228920909419030e-05] 
dist 216=[-9.15446786615912428620e-05,.00012814910786847632] 
dist 217=[-6.03263194357922796750e-05,.00017146686758799228] 
dist 218=[-5.18188477305622676240e-05,.00021134519172540334] 
dist 219=[-1.99167629504953609350e-05,.00024504871259409926] 
dist 220=[-1.66391969624135406260e-05,.00026384821323053178] 
dist 221=[-4.18099888724321838550e-06,.00027531569084411990] 
dist 222=[-1.64703629883949276850e-06,.00027827053443842916] 
dist 223=[2.31877054208476403200e-06,9.79344290458609380950e-05] 
dist 224=[3.30404111717022881210e-06,9.93537268723848426250e-05] 
dist 225=[3.94133563266766197480e-06,9.92207540114610961460e-05] 
dist 226=[2.75763628516429552740e-06,9.84732651710418096810e-05] 
dist 227=[2.59545120004529891300e-07,9.48676317420515301120e-05] 
dist 228=[-4.62047571388345989840e-06,9.30569015806301933800e-05] 
dist 229=[-1.05348921199744824790e-05,7.96781311297288193880e-05] 
dist 230=[-1.71406555931103876420e-05,7.62448562114350699280e-05] 
dist 231=[-2.53865279551103902380e-05,7.01953423360880187390e-05] 
dist 232=[-3.88362522125481959470e-05,6.83409058508134059830e-05] 
dist 233=[-5.14584404377994565800e-05,2.54622099989290570020e-05] 
dist 234=[-6.31092696990683262100e-05,1.95541895138869368620e-05] 
dist 235=[-7.29785433244893985670e-05,9.49803746471109048200e-06] 
dist 236=[-7.85267195497761783980e-05,8.16176411410756807590e-06] 
dist 237=[-8.18709304700284058430e-05,3.11847293045751763310e-06] 
dist 238=[-8.29889647589416546310e-05,2.06270956930825635580e-06] 
dist 239=[-8.29944975411967542530e-05,4.96123820441260068020e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 1, 0, 1, 0, 2] 
dist 0=[112.78366971597702654   ,112.78366971597702654   ] 
dist 1=[109.51911788654927203   ,113.93303747223225244   ] 
dist 2=[103.96767136435719612   ,115.22151246213427201   ] 
dist 3=[94.569208481645110495  ,116.34307326086024820   ] 
dist 4=[84.679302661146989430  ,116.51856101688369872   ] 
dist 5=[77.166658937933281475  ,116.02428023502716052   ] 
dist 6=[70.059521159327107594  ,115.55230347733211978   ] 
dist 7=[61.767594010343787751  ,112.05569768145516092   ] 
dist 8=[53.443297602599157432  ,92.395451024493026781  ] 
dist 9=[46.194418415658182140  ,84.186958896977033197  ] 
dist 10=[38.382069795246635887  ,82.684059135236675722  ] 
dist 11=[27.793463828700447585  ,66.999476206197961774  ] 
dist 12=[17.532875716783831066  ,63.496549235603737556  ] 
dist 13=[11.021491564894301282  ,59.422873134468209660  ] 
dist 14=[6.0024245792180771408 ,57.857987598582370141  ] 
dist 15=[1.6898511619462074395 ,47.734232513040300816  ] 
dist 16=[-1.8742007350440820896 ,19.283382666354011624  ] 
dist 17=[-4.8144499442527293345 ,9.2781630873335001845 ] 
dist 18=[-12.433090390325189141  ,7.7764963662242840710 ] 
dist 19=[-19.050083527747426322  ,-4.5542427962960192310 ] 
dist 20=[-23.175531484459432644  ,-4.8574691247789997214 ] 
dist 21=[-26.231970542018659592  ,-4.6488062952464574855 ] 
dist 22=[-28.604385711497944230  ,-4.2149572446260044380 ] 
dist 23=[-30.289846744442630455  ,-3.4275641360186579619 ] 
dist 24=[-30.670021788771732026  ,-1.6299964991071652023 ] 
dist 25=[-30.493203473126759860  ,1.0092822432213233512 ] 
dist 26=[-30.383513924995351684  ,3.5412634353532431457 ] 
dist 27=[-26.439195079191318667  ,6.4746045702160045774 ] 
dist 28=[-24.904632815305027767  ,9.3463693425472559119 ] 
dist 29=[-23.998144882350783429  ,11.642232171849040143  ] 
dist 30=[-23.572675229350420233  ,13.911199468676458774  ] 
dist 31=[-5.8968301909853011340 ,16.685954003394780485  ] 
dist 32=[-3.7618880989260670578 ,19.157313601934305568  ] 
dist 33=[1.2812167896016936224 ,20.224381826233209393  ] 
dist 34=[1.7775933132404381271 ,20.700441167503208390  ] 
dist 35=[1.4716479116119500240 ,20.819420998201679339  ] 
dist 36=[.429558907907979173  ,18.648671330354173773  ] 
dist 37=[-.32415314441369092048,18.080034188297454887  ] 
dist 38=[-.97416866704199055264,17.745612614896874331  ] 
dist 39=[-1.6258239114767362847 ,17.660892763357060295  ] 
dist 40=[-2.2063629514459826345 ,16.248420743556107796  ] 
dist 41=[-2.5749842461291583246 ,15.868491641778656502  ] 
dist 42=[-2.8491897929956443671 ,15.638924849240978350  ] 
dist 43=[-4.2821795533546455653 ,13.449412842661501280  ] 
dist 44=[-6.6202092420048853420 ,12.873468386546990065  ] 
dist 45=[-8.0994936936063371647 ,12.006990457217082034  ] 
dist 46=[-9.2045372603298676330 ,11.685648947517990176  ] 
dist 47=[-10.058906019035027461  ,5.6444133278249302325 ] 
dist 48=[-10.678894372319454236  ,4.9682297996158649263 ] 
dist 49=[-10.854003248226451548  ,3.4771389047778857995 ] 
dist 50=[-10.842964448445819905  ,3.0570320821364679771 ] 
dist 51=[-10.932053161019674989  ,1.3857570915743511881 ] 
dist 52=[-11.866833373035429054  ,1.0547877841180659786 ] 
dist 53=[-12.367846487871869289  ,.39645147645910159792] 
dist 54=[-12.470400911229270158  ,.23493222447219614061] 
dist 55=[-8.5137271574927101858 ,.12408215754572502242] 
dist 56=[-3.2778300503665997286 ,.86569182723731476759] 
dist 57=[-2.5749084118818920923 ,2.8207188862987638851 ] 
dist 58=[-.96867884160593218526,4.4162009280373035284 ] 
dist 59=[-.63226588107680939606,5.8905425515119495305 ] 
dist 60=[.60669977933294734393,7.1369953821267103948 ] 
dist 61=[.62952162314287054811,7.8280633199795366771 ] 
dist 62=[.6309712693968300533 ,8.2305844082271877087 ] 
dist 63=[.58768341892024581311,8.3319740311677452193 ] 
dist 64=[.52333177288584868477,2.5602807293773329987 ] 
dist 65=[.43707731377468181484,2.5940916351479813423 ] 
dist 66=[.32049447751340867839,2.5836614916678217978 ] 
dist 67=[.13579620074315994863,2.5764918258681770380 ] 
dist 68=[-.05153692258250446221,2.2082519562970343885 ] 
dist 69=[-.17859426418496612334,2.1103748815899892333 ] 
dist 70=[-.28290475583637248016,2.0388926775721545826 ] 
dist 71=[-.3800296487727011517 ,2.0065988515789308932 ] 
dist 72=[-.46241476742118974292,.43793377152722808857] 
dist 73=[-.50849141503934989701,.24954837660748290595] 
dist 74=[-.53558373570900973969,-.07173437980848353678] 
dist 75=[-.83692346108874181633,-.07913584456317096422] 
dist 76=[-1.1149185737234414279 ,-.11975254236107739092] 
dist 77=[-1.2808770550629139363 ,-.12584400472432218509] 
dist 78=[-1.3934100781913722308 ,-.12379976461393885112] 
dist 79=[-1.4594047375420889182 ,-.11025442061083116062] 
dist 80=[-1.4937733022183238742 ,-.09083051692176505266] 
dist 81=[-1.4965360788719697974 ,-.06544903488553979902] 
dist 82=[-1.4561539401483810034 ,-.03144736567606754007] 
dist 83=[-1.4443176829781013434 ,.02219385520290109317] 
dist 84=[-1.2039967900396088415 ,.07667947020501774919] 
dist 85=[-1.1437749370206670561 ,.11403816522697027775] 
dist 86=[-1.0871103888254091340 ,.14520755809867752005] 
dist 87=[-1.0591448064141460855 ,.17514001511349099872] 
dist 88=[-.30799128647071640082,.20122691839958559276] 
dist 89=[-.23005167540676154709,.29609516848049140175] 
dist 90=[-.11171693608115926006,.46648353394168208281] 
dist 91=[-.10813962257437709884,.62433593626487833472] 
dist 92=[-.09041794599290468339,.75902844050436952728] 
dist 93=[-.08679384752457340481,.84033715060530120634] 
dist 94=[-.08667700794531260744,.88613327115152266211] 
dist 95=[-.09127625013840310245,.89688107523092524394] 
dist 96=[-.09837681664942857711,.34647490927472322255] 
dist 97=[-.1081921040195082979 ,.34831679763503267407] 
dist 98=[-.1216403635609646412 ,.34021703403950080919] 
dist 99=[-.14316461644526431771,.33904661040553985117] 
dist 100=[-.16515889193937212796,.28261847896622244718] 
dist 101=[-.18047633919161766436,.27170945005777036341] 
dist 102=[-.19351660607577901924,.25708209193989524198] 
dist 103=[-.20647883747284829175,.25452785971953341971] 
dist 104=[-.21828501180779584701,.03353758275935783633] 
dist 105=[-.23267622566477718166,.00768427654865709496] 
dist 106=[-.23975392828364849907,.00207405039112311674] 
dist 107=[-.24067604499795162674,.00122203820839502771] 
dist 108=[-.13574795427305850106,-.01897286650332195792] 
dist 109=[-.15592490870240843304,-.01933629029757109441] 
dist 110=[-.16913633728131541341,-.01916776792014673410] 
dist 111=[-.17593722166955587528,-.01803129565223788277] 
dist 112=[-.17899738897443442429,-.01643183282977902057] 
dist 113=[-.17879138626992469166,-.01437257285760483659] 
dist 114=[-.1742969999044700483 ,-.01163007235433843137] 
dist 115=[-.17170330119724422264,-.00731832728927196453] 
dist 116=[-.14796015406633218693,-.00294119962955605702] 
dist 117=[-.14170915715171525185,6.12494928051542725600e-05] 
dist 118=[-.13219511677994106649,.00256873315017474254] 
dist 119=[-.12870943284408998707,.00498211317963858227] 
dist 120=[-.04427440433855031787,.02059383490780148422] 
dist 121=[-.03299904302206369684,.05170271819043592800] 
dist 122=[-.00765686364398356436,.07699436825225718790] 
dist 123=[-.00219642093089011825,.10025638721244179829] 
dist 124=[.01032952717730545585,.11988514057687009301] 
dist 125=[.01026587263774320226,.1307523200922277668 ] 
dist 126=[.00986538551902786719,.13707667695532463601] 
dist 127=[.00891287185413309460,.13866963980843838988] 
dist 128=[.00770569154498481323,.04191493081062488842] 
dist 129=[.00629415440973383443,.04195044569402559705] 
dist 130=[.00449330757070476001,.04066622690186806042] 
dist 131=[.00174064668974932641,.04039512781017883325] 
dist 132=[-.00102751100193457716,.03335872517655775561] 
dist 133=[-.00288997156404726750,.03163019320577289608] 
dist 134=[-.00440775381043425185,.03022128950106482432] 
dist 135=[-.00580787851268960749,.02968549080603355731] 
dist 136=[-.00699074380714340285,.00465574097317230401] 
dist 137=[-.00764619277365447915,.00166277668817713148] 
dist 138=[-.00984104390121610038,-.00216100929852823892] 
dist 139=[-.01471441510979655874,-.00226892809915002294] 
dist 140=[-.01887008593894489126,-.00246988712608466321] 
dist 141=[-.0212539236471277242 ,-.00247402106620464712] 
dist 142=[-.02275230947087757508,-.00240515999413122837] 
dist 143=[-.02339278677525509693,-.00222092359216467963] 
dist 144=[-.02354333842567675456,-.00198199041789146576] 
dist 145=[-.02346197790752840160,-.00169595615888828002] 
dist 146=[-.02255752561515929083,-.00132684892635423765] 
dist 147=[-.02234130918233835630,-.00075810094817518618] 
dist 148=[-.01832591469115181793,-.00018413668318134017] 
dist 149=[-.01735272526235891766,.00020571050323667870] 
dist 150=[-.01642163287967336605,.00052751048753104145] 
dist 151=[-.01600017968692527447,.00083140178014751506] 
dist 152=[-.00402043320499422328,.00165716225831794431] 
dist 153=[-.00278101679896412349,.00488699567833576668] 
dist 154=[2.37383438520596072230e-05,.00751453806075368037] 
dist 155=[.00058528169931022285,.00993500535299544253] 
dist 156=[.00116272335559860331,.01198083720816777418] 
dist 157=[.00114843686813869111,.01312094892821450420] 
dist 158=[.00109962618394189866,.01383159751913282161] 
dist 159=[.00099234216109032397,.01399642837128117431] 
dist 160=[.00085861331875989084,.00543091018476814958] 
dist 161=[.00070480504261189977,.00542362971415399406] 
dist 162=[.00051007199922304450,.00521917432282361613] 
dist 163=[.00021386307082361378,.00518954497001032601] 
dist 164=[-8.37438482855024432050e-05,.00420501591913618381] 
dist 165=[-.00028403540531056361,.00396955616743581167] 
dist 166=[-.00044742969174164059,.00380340792564528871] 
dist 167=[-.00059856999936597254,.00376575421412039354] 
dist 168=[-.00072664617537168701,.00036435976598300308] 
dist 169=[-.00080294426421558174,-3.23505206108107944940e-05] 
dist 170=[-.00109049783750770267,-.00030438213496970002] 
dist 171=[-.00169327322881178353,-.00031580465659123848] 
dist 172=[-.00220611036318388425,-.00033369390833380984] 
dist 173=[-.00249833862131710663,-.00033121048563636617] 
dist 174=[-.00267956698813992719,-.00031993216120091247] 
dist 175=[-.00275170508991841515,-.00029403108808502329] 
dist 176=[-.00276667632135424292,-.00026142190845226318] 
dist 177=[-.00275313656152127402,-.00022350755837885272] 
dist 178=[-.00266071906272720671,-.00017524007450832549] 
dist 179=[-.00261828245732307160,-.00010152388518252521] 
dist 180=[-.00222913507285220566,-2.73167863543181233950e-05] 
dist 181=[-.00212985912926666028,2.29026257204416992360e-05] 
dist 182=[-.00197961187112964674,6.41833536916709486330e-05] 
dist 183=[-.00192535394764172310,.00010290745723073828] 
dist 184=[-.00063516940844935860,.00034851910178364771] 
dist 185=[-.00046414787501348449,.00082017890631266483] 
dist 186=[-8.20055851724949496750e-05,.00120318710768681499] 
dist 187=[1.37617418514627510960e-06,.00155494248776495296] 
dist 188=[.00016842749853932022,.00185158339675553373] 
dist 189=[.00016476390469622780,.00201575346451712693] 
dist 190=[.00015620654627653277,.00211129465857200191] 
dist 191=[.00013896379337546188,.00213537747703971739] 
dist 192=[.00011790763854843685,.00065069665175644873] 
dist 193=[9.42086847585203144410e-05,.00064867046021886018] 
dist 194=[6.45200768105220286820e-05,.00062180476284132563] 
dist 195=[1.96821382719613353230e-05,.00061779807178854213] 
dist 196=[-2.52763946407707681270e-05,.00049864603711772112] 
dist 197=[-5.54445097688345138480e-05,.00047253104129950752] 
dist 198=[-7.99704685508992840230e-05,.00044886834254326621] 
dist 199=[-.00010252892793193066,.00044392670574176399] 
dist 200=[-.00012156598398624977,8.54327944461928554820e-05] 
dist 201=[-.00013211134352193355,4.22109925823727460560e-05] 
dist 202=[-.00019122862725135242,-2.83192208695098406700e-05] 
dist 203=[-.00026602836291306142,-2.98631002794168025700e-05] 
dist 204=[-.00032945128721238362,-3.10094004922231376310e-05] 
dist 205=[-.00036520624461978135,-3.00099319449505279220e-05] 
dist 206=[-.00038688641655258273,-2.76495699341426701800e-05] 
dist 207=[-.00039442489686569737,-2.28778052416102635850e-05] 
dist 208=[-.00039426496055508804,-1.70444192610477135520e-05] 
dist 209=[-.00039193833619968053,-1.04685022725378537920e-05] 
dist 210=[-.00037542550574897088,-2.22236738554289535890e-06] 
dist 211=[-.00037103957623900874,1.02429990718822165530e-05] 
dist 212=[-.00030483041439973341,2.27517187580208284870e-05] 
dist 213=[-.00028883181771323481,3.11702384396208169480e-05] 
dist 214=[-.00027160253866652880,3.80434830377005965870e-05] 
dist 215=[-.00026294564701529714,4.44170272641441365820e-05] 
dist 216=[-9.54486268455154270690e-05,6.70281307302603623270e-05] 
dist 217=[-8.23229177235243690380e-05,.00011483520821228336] 
dist 218=[-5.43057134985660835260e-05,.00015370654643951555] 
dist 219=[-4.66665509487312398340e-05,.00018949674750376933] 
dist 220=[-2.31714450699444693960e-05,.00021974830605297645] 
dist 221=[-2.34106639837361581890e-05,.00023662747357287766] 
dist 222=[-2.41775536116817961240e-05,.00024696700346023767] 
dist 223=[-2.58437262681634650370e-05,.00024961878571123903] 
dist 224=[-2.79163993576053328610e-05,7.79341443261622323820e-05] 
dist 225=[-3.02975387457820408240e-05,7.75869672048393483330e-05] 
dist 226=[-3.33120880379601567910e-05,7.48584784816450374370e-05] 
dist 227=[-3.78999670736708001410e-05,7.38386633806064504970e-05] 
dist 228=[-4.25159882894392434340e-05,6.21668172208576232170e-05] 
dist 229=[-4.56424534793049593970e-05,5.92471759222753241490e-05] 
dist 230=[-4.82166859891005675730e-05,5.54560641835660961490e-05] 
dist 231=[-5.06403253417945351800e-05,5.30466719341708888810e-05] 
dist 232=[-5.27260108664040043740e-05,2.82180454131723131940e-06] 
dist 233=[-5.39585817304357422600e-05,1.49847563308565801780e-06] 
dist 234=[-5.49847964352242136180e-05,2.69127055239336221360e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 2, 0, 1] 
dist 0=[121.65711512189548199   ,121.65711512189548199   ] 
dist 1=[120.39947442162881905   ,122.07908672155484328   ] 
dist 2=[116.23634333311624481   ,122.91844577827066811   ] 
dist 3=[109.22728568508371284   ,124.19074171993861790   ] 
dist 4=[96.664000891384528478  ,126.32060488926328155   ] 
dist 5=[83.403351070800099017  ,128.23231673182100073   ] 
dist 6=[73.618755493581352807  ,128.64251463901489317   ] 
dist 7=[64.657251273325646514  ,124.90245149463974743   ] 
dist 8=[54.650925871315832511  ,114.32340520820686193   ] 
dist 9=[44.874747897365524529  ,105.19259944353413463   ] 
dist 10=[36.812623645435163137  ,101.83962680640803899   ] 
dist 11=[28.512541736734572713  ,91.955457350963428228  ] 
dist 12=[17.762622941192656707  ,90.529547003877739941  ] 
dist 13=[7.5178973267214369773 ,69.924134457920370976  ] 
dist 14=[1.2219943834231918859 ,65.674224643235229410  ] 
dist 15=[-3.4028456181815112044 ,61.612300252584715302  ] 
dist 16=[-6.9887323141159932360 ,60.825066828541656915  ] 
dist 17=[-9.7470256259710669512 ,13.571484092627717872  ] 
dist 18=[-11.070137889561133962  ,8.0906530995220038818 ] 
dist 19=[-11.708248559292623750  ,-4.4190174546472766632 ] 
dist 20=[-14.457791414147523074  ,-5.9487256243287892475 ] 
dist 21=[-21.292881782702669665  ,-3.7011849578509587138 ] 
dist 22=[-25.255259756351421989  ,-2.0556898686374489660 ] 
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dist 225=[-2.18516406604692229720e-05,2.84609257431776603000e-05] 
dist 226=[-1.87481887680174744940e-05,2.75419846749982597730e-05] 
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dist 229=[-3.75913124364085902460e-06,5.21664978975320251570e-05] 
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dist 233=[-2.12320639996120648900e-05,2.39216408002989315480e-05] 
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dist 235=[-2.45569794370404781900e-05,2.29693960842366833150e-05] 
dist 236=[-2.49460712298377317830e-05,2.25510764512054136440e-05] 
dist 237=[-2.49102309225122080840e-05,1.99566726869809551090e-05] 
dist 238=[-2.47024144851777060430e-05,1.92783699265295045120e-05] 
dist 239=[-2.38903322355102609660e-05,1.76360761577850232680e-05] 
dist 240=[-2.34191604294369883370e-05,1.70369170177857422060e-05] 
dist 241=[-2.04825030648634407180e-05,9.34652769754094893650e-06] 
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dist 243=[-1.80792783172931453040e-05,5.56997244161883161030e-06] 
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dist 246=[-7.00994820618852281010e-06,6.02870298957078715360e-06] 
dist 247=[-4.10838448341309287920e-06,8.05585403592253543000e-06] 
dist 248=[-2.39427327997327238190e-06,9.92111673448837888950e-06] 
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dist 250=[-5.87307907194053440160e-07,1.23750951031939075360e-05] 
dist 251=[-1.34540302387482155180e-07,1.29027180782738295180e-05] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 1, 1, 1, 0, 2] 
dist 0=[131.32821388676494465   ,131.32821388676494465   ] 
dist 1=[130.47450529099316190   ,131.03991520598093951   ] 
dist 2=[128.08402151245186642   ,131.32821388676494465   ] 
dist 3=[122.27478545840886645   ,129.79863257252754540   ] 
dist 4=[114.86130438509966838   ,122.87648119163986159   ] 
dist 5=[106.09127359722908917   ,117.68795653468130628   ] 
dist 6=[94.802674160304956050  ,115.82520706380877344   ] 
dist 7=[77.374700494447547190  ,113.46967530195503469   ] 
dist 8=[59.626708735029945021  ,96.618338239370802257  ] 
dist 9=[47.060897904442176891  ,92.637821575881346969  ] 
dist 10=[36.067876890813050127  ,90.824880159767885443  ] 
dist 11=[24.559698383772360521  ,55.622085459983062237  ] 
dist 12=[13.766354676998529186  ,41.589929648501167773  ] 
dist 13=[5.6030958851127363242 ,38.325052377185846323  ] 
dist 14=[-2.1354099152558139228 ,33.300163110924371160  ] 
dist 15=[-11.262537398688120485  ,32.144642749499595926  ] 
dist 16=[-19.589794141195539434  ,8.0531567695157348488 ] 
dist 17=[-24.152240384839947581  ,3.3081088668329745143 ] 
dist 18=[-27.527791374288698801  ,2.3997959177211696128 ] 
dist 19=[-32.185182998648101441  ,-9.9865744950635154801 ] 
dist 20=[-34.250093936887067947  ,-11.931701948232942644  ] 
dist 21=[-35.190996081845891503  ,-11.253914557968118511  ] 
dist 22=[-35.360189212569270484  ,-9.3278942513103444047 ] 
dist 23=[-32.048451843669339520  ,-5.3202713902439687790 ] 
dist 24=[-31.082667441923859497  ,-.96732625352965785621] 
dist 25=[-30.432948311883625460  ,2.3359501667789977067 ] 
dist 26=[-30.084286782249611328  ,5.4068400705485461184 ] 
dist 27=[-8.8331765614582942859 ,8.8491557606356832444 ] 
dist 28=[-6.2710274656103754411 ,12.171176740182218276  ] 
dist 29=[-.21112704041253741654,14.771418650928092877  ] 
dist 30=[.72784571024101884084,17.295417894358507614  ] 
dist 31=[6.0611980018851412373 ,20.323160235768792233  ] 
dist 32=[9.2736892217091314256 ,22.990752801614004992  ] 
dist 33=[11.355535299928480379  ,24.086958808694864215  ] 
dist 34=[11.704197746876043576  ,24.541519826915859151  ] 
dist 35=[11.951679732530930403  ,24.655046835629054424  ] 
dist 36=[10.812048183842257887  ,21.883854463801813355  ] 
dist 37=[9.2460625775323068992 ,21.159900643665360140  ] 
dist 38=[7.1105760210771213267 ,20.734869116419359977  ] 
dist 39=[3.7104000360604191487 ,20.627432866480209899  ] 
dist 40=[.25636711938365818721,14.922483656849030645  ] 
dist 41=[-2.0935128943247110485 ,14.251197742657749774  ] 
dist 42=[-4.0303048381547270272 ,13.875769150260035040  ] 
dist 43=[-5.8464090290052010417 ,4.5087991321049514490 ] 
dist 44=[-8.0276617593617778267 ,3.4643881561460220055 ] 
dist 45=[-9.7423723502448930928 ,1.0488211563936568622 ] 
dist 46=[-11.007640203576101777  ,.58555633373800171319] 
dist 47=[-11.957381818704678507  ,-2.2931698042490054097 ] 
dist 48=[-12.631006168921033734  ,-2.7586138923443650385 ] 
dist 49=[-12.800663954853381437  ,-3.6980909934981038603 ] 
dist 50=[-12.764046842116432253  ,-3.8612520949792170654 ] 
dist 51=[-12.617309576548603916  ,-3.7475656384659691710 ] 
dist 52=[-11.227213204170600323  ,-3.4397072388926151922 ] 
dist 53=[-10.818732658408588796  ,-3.0272126130679162217 ] 
dist 54=[-10.198352228633876093  ,-2.4692907011465232276 ] 
dist 55=[-9.9554155351749285789 ,-1.5840764185275491769 ] 
dist 56=[-3.7890583353415823308 ,1.0622978540923372044 ] 
dist 57=[-3.4724197244071751488 ,3.3594806233321739643 ] 
dist 58=[-3.4463689629217965395 ,5.2333741192672933615 ] 
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dist 173=[-.00298953696324995590,3.67460694680199465820e-05] 
dist 174=[-.00320273841672875202,-7.62799449910668732340e-05] 
dist 175=[-.00328617680285145667,-.00067359055202506170] 
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dist 183=[-.00229945900449061347,-.00035879389649711414] 
dist 184=[-.00080932251632479578,.00047564811142665126] 
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dist 186=[-.00073964828806266377,.00148901875960268213] 
dist 187=[-.00025695901429979329,.00190611846824375175] 
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dist 189=[-6.08594530356793456950e-05,.00245265521250812128] 
dist 190=[-3.06905143163648174030e-05,.00256631731358820606] 
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dist 195=[.00020643026083060894,.00080046650804459300] 
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dist 197=[.00015989705191097633,.00077186860867435645] 
dist 198=[.00010007159683794046,.00075853753335296388] 
dist 199=[-8.62450517226061696000e-05,.00067443149080857766] 
dist 200=[-.00029814072536915675,.00065223093381699755] 
dist 201=[-.00044041528817237676,.00059733148417424416] 
dist 202=[-.00055624702828776392,.00057699252310142906] 
dist 203=[-.00066314851758222771,.00032308772850078138] 
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dist 205=[-.00080452505029119026,.00019726337972153289] 
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dist 207=[-.00084515183932400220,8.99587015768490004850e-05] 
dist 208=[-.00084361947686763773,7.12146605195808552320e-05] 
dist 209=[-.00083650084003740778,4.85538677686581781920e-05] 
dist 210=[-.00079995524787338570,4.36621253840928997140e-05] 
dist 211=[-.00035674721915505565,4.38076479896499878250e-05] 
dist 212=[-.00030675420375743991,4.83167708892016229400e-05] 
dist 213=[-.00029380262607496593,5.67869896699286772500e-05] 
dist 214=[-.00027111744099558393,7.26623219459945037790e-05] 
dist 215=[-.00026407252406669890,9.16884305653157848900e-05] 
dist 216=[-.00010638896216463882,.00011267036391823837] 
dist 217=[-8.57184591370918391220e-05,.00013868922348791748] 
dist 218=[-8.34802507761735854410e-05,.00018806939101569132] 
dist 219=[-3.36407338728147938480e-05,.00023633830487764822] 
dist 220=[-2.67226774976698342880e-05,.00027704761903469411] 
dist 221=[-1.14547339544249100020e-05,.00029959484528480725] 
dist 222=[-7.72168377950701594300e-06,.00031280527392429772] 
dist 223=[8.50172416257009461460e-06,.00031612131782358247] 
dist 224=[1.15169219999971601750e-05,9.51860809584667748340e-05] 
dist 225=[1.64087323465123377080e-05,9.96638099238192926210e-05] 
dist 226=[1.74768011916034872950e-05,.00010109128979192453] 
dist 227=[1.78726444834191713740e-05,.00010087044891245200] 
dist 228=[1.63418767258047136510e-05,.00010009049926105242] 
dist 229=[1.33179087933273368190e-05,9.63355561711528352530e-05] 
dist 230=[7.54292895241791458460e-06,9.45260760378640723760e-05] 
dist 231=[-7.45710459815306438440e-06,8.07060212391107251020e-05] 
dist 232=[-2.86302353065930171460e-05,7.71806276083432031980e-05] 
dist 233=[-4.28440347064721113240e-05,7.11154046372403069570e-05] 
dist 234=[-5.44143921135241612390e-05,6.92138708729894466640e-05] 
dist 235=[-6.50911882041009394700e-05,2.51337133120922588190e-05] 
dist 236=[-7.41332297097489120360e-05,1.90965422870565344610e-05] 
dist 237=[-7.92124591510241160650e-05,1.12604627293450880110e-05] 
dist 238=[-8.22689198892464819220e-05,9.63271527702706382510e-06] 
dist 239=[-8.32791710510573850550e-05,3.54431554288359086740e-06] 
dist 240=[-8.32480837918627603540e-05,2.25923104368597439510e-06] 
dist 241=[-8.24444903935437841340e-05,4.77191074215930683950e-07] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 0, 1, 0, 1, 2] 
dist 0=[119.62478323616938329   ,119.62478323616938329   ] 
dist 1=[117.22239999498648501   ,120.40774438972814333   ] 
dist 2=[112.78164562108768813   ,121.10333780597393724   ] 
dist 3=[105.00560276445236919   ,121.34470607911592353   ] 
dist 4=[96.720104292915080722  ,120.90806841962176344   ] 
dist 5=[90.246328997295832277  ,119.49121189017137316   ] 
dist 6=[83.941661183456900664  ,118.58921717814025364   ] 
dist 7=[76.315035069015283619  ,112.06959750239382464   ] 
dist 8=[68.498217767766998178  ,95.990904828385171317  ] 
dist 9=[58.923404847884583732  ,87.184432751816049703  ] 
dist 10=[49.313895394973861252  ,85.832870524640989260  ] 
dist 11=[38.622999236623312683  ,67.888912374552870412  ] 
dist 12=[28.197088122657488844  ,64.177767174924511616  ] 
dist 13=[19.626019777547504458  ,60.411428224248709690  ] 
dist 14=[10.826970555782652250  ,59.478926443107286545  ] 
dist 15=[-.53247641219520592732,32.277371236625841799  ] 
dist 16=[-11.229528193435695395  ,13.823390164698330729  ] 
dist 17=[-17.399628579226140462  ,9.3446281157170908711 ] 
dist 18=[-21.457118958218356869  ,6.5276726085270221535 ] 
dist 19=[-23.741015924467943921  ,5.8297173799560089727 ] 
dist 20=[-25.188926581371931020  ,3.4692995787847243459 ] 
dist 21=[-25.910402329893208701  ,2.9784916310503026036 ] 
dist 22=[-26.276093505880455127  ,2.9044271061698292776 ] 
dist 23=[-27.708553491337137116  ,3.3297667257757826105 ] 
dist 24=[-28.968977925908422844  ,3.9984373956464640912 ] 
dist 25=[-29.351739023164750492  ,4.8981932332017452439 ] 
dist 26=[-29.154456930107522850  ,6.1135669416813309050 ] 
dist 27=[-26.611950612892952863  ,8.0435887829603273349 ] 
dist 28=[-21.558091761777076514  ,9.9051326272874369500 ] 
dist 29=[-20.913916440821862271  ,10.851378888666040510  ] 
dist 30=[-20.755428730708552554  ,11.345150957067521968  ] 
dist 31=[-4.0723699366618465928 ,11.411853637939576879  ] 
dist 32=[-2.1171004396993864624 ,12.155420296092848178  ] 
dist 33=[2.4090861277593699436 ,13.155275061936124652  ] 
dist 34=[3.1138897630483455935 ,13.642126882036593176  ] 
dist 35=[4.5915234521911000794 ,13.705222874494392893  ] 
dist 36=[1.7904270252838577601 ,13.121949817663534904  ] 
dist 37=[-.1636783361044327017 ,12.828356129694585894  ] 
dist 38=[-1.8256386168268644315 ,12.327757384645115379  ] 
dist 39=[-3.4690953679414334932 ,12.597285904227875526  ] 
dist 40=[-4.9304371726715543268 ,12.638793050397508008  ] 
dist 41=[-5.8706829339661154486 ,12.434826701976265656  ] 
dist 42=[-6.5902245747412538214 ,12.270022698878095716  ] 
dist 43=[-7.1768987778228029181 ,10.684882637485397565  ] 
dist 44=[-8.8506134850084107101 ,10.255567699399001770  ] 
dist 45=[-9.7729554085696823266 ,9.6131425130829370406 ] 
dist 46=[-10.299154670781275575  ,9.3691059408093975794 ] 
dist 47=[-10.403378951069852552  ,3.3658307567372052854 ] 
dist 48=[-6.9214926413977207207 ,2.5658332986811998808 ] 
dist 49=[-6.6956715290254187671 ,.75799316417820718677] 
dist 50=[-6.7538035890869389061 ,.37549826683551371468] 
dist 51=[-8.1411948364076588390 ,-.07512204580483621478] 
dist 52=[-8.9095174660535164283 ,1.6732161449189226970 ] 
dist 53=[-9.3567360417353021715 ,2.8660313655586980934 ] 
dist 54=[-9.4693883004264821594 ,3.9766200660532941536 ] 
dist 55=[-2.9127552467591019214 ,5.0577704449694971721 ] 
dist 56=[-2.9272815671360217195 ,5.9550974936121947474 ] 
dist 57=[-2.8633149531099716137 ,6.4199715155677605583 ] 
dist 58=[-2.8482042870210709373 ,6.6576733876461674318 ] 
dist 59=[-2.3818674318872173251 ,6.6940777592648722649 ] 
dist 60=[-2.2648099517866877509 ,1.0979459913643173118 ] 
dist 61=[-2.1729500053022819450 ,1.1755571619297685788 ] 
dist 62=[-2.1368807518514938168 ,1.3528796611777301847 ] 
dist 63=[-.39150630949418970885,1.4990544584856731123 ] 
dist 64=[-.18288575245203487344,1.6100251417205420299 ] 
dist 65=[.30659982450814647313,1.6476915662183743204 ] 
dist 66=[.37894761923518301374,1.6531784548067967870 ] 
dist 67=[.41275340233117371644,1.6364891177230916986 ] 
dist 68=[.16010480605373011439,1.4768153988465126777 ] 
dist 69=[-.01280137644636471338,1.5339329091565623137 ] 
dist 70=[-.15679960994679094073,1.5876624085180729467 ] 
dist 71=[-.29475550739480302794,1.6073482034858687495 ] 
dist 72=[-.41485753641685932074,1.6048099167535240776 ] 
dist 73=[-.4880196727366355768 ,1.5491908751834427866 ] 
dist 74=[-.66747309077645324714,1.5353196251336911036 ] 
dist 75=[-.89426157296483170937,1.2657203261139327041 ] 
dist 76=[-1.0861021645968658189 ,1.1997626817436417647 ] 
dist 77=[-1.1925057659156267777 ,1.1374868726860204360 ] 
dist 78=[-1.2545214574882126702 ,1.1089167738663471136 ] 
dist 79=[-1.2701380016409307414 ,.29103819506683976006] 
dist 80=[-.51117675666452554044,.20576492439093289577] 
dist 81=[-.49966141805246209479,.01215886465382018245] 
dist 82=[-.66639986636578309576,-.02624480883702876507] 
dist 83=[-.80745349373526458236,-.09378261436499006466] 
dist 84=[-.88768588461141933227,.06391627194485581532] 
dist 85=[-.93684968866038099824,.1699645453306266543 ] 
dist 86=[-.94819672567580111158,.25634771403263466965] 
dist 87=[-.37039846947611953595,.33599173730776885833] 
dist 88=[-.37070829178034126643,.40326590620604943555] 
dist 89=[-.35848391481682900551,.44061379240914728038] 
dist 90=[-.35671003049038221844,.46234771020499086425] 
dist 91=[-.29115721361689803257,.46778405603668510875] 
dist 92=[-.27531176302177848799,.17491913767529092723] 
dist 93=[-.26439150903346155878,.2015105384854464728 ] 
dist 94=[-.26188225185684870126,.21992028121380211316] 
dist 95=[-.02946436828113440780,.23147408387696241845] 
dist 96=[-.00233242556821874222,.2380572546740405731 ] 
dist 97=[.06060839408800998535,.23882662901526065095] 
dist 98=[.06254410073390359073,.23327726556746226049] 
dist 99=[.02831531639478697782,.23134034054093365653] 
dist 100=[-.00617613520479073002,.19433530449553726891] 
dist 101=[-.02954312521413137856,.18491808975613037273] 
dist 102=[-.04877149934531749625,.18595335056943829273] 
dist 103=[-.06683602620532463656,.18767456482410823777] 
dist 104=[-.08233908682544286146,.18698380429513044153] 
dist 105=[-.09140048652334213429,.18119469561967625939] 
dist 106=[-.09730816012383992585,.17838199079351018431] 
dist 107=[-.10392416215137042095,.15239773974756236693] 
dist 108=[-.12528662154447514482,.14571351801265168852] 
dist 109=[-.13841803502375865227,.13562404862109554402] 
dist 110=[-.14576071811551827737,.13194964887028344646] 
dist 111=[-.14745824424820115337,.04415999080015482948] 
dist 112=[-.08234456737519268473,.03252281716220581452] 
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dist 174=[-.00219934925784572352,.00196718961456637944] 
dist 175=[-.00222578497812650394,.00060466853493666109] 
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dist 177=[-.00119352027491493960,3.94097979947095470830e-05] 
dist 178=[-.00154625446485576344,-4.42182848348844682160e-05] 
dist 179=[-.00184371752629204406,-.00046685379790897909] 
dist 180=[-.00200843118315815102,-.00054006980261794955] 
dist 181=[-.00210497567252583239,-.00054268314181378160] 
dist 182=[-.00212898874909786879,-.00038200440546795813] 
dist 183=[-.00075829611574638862,-.00013948378525439516] 
dist 184=[-.00075236451024660420,.00010375040012129093] 
dist 185=[-.00072919158730837498,.00026726677868190083] 
dist 186=[-.00071538274088362212,.00040057503871461533] 
dist 187=[-.00062857359851154326,.00052387234007944159] 
dist 188=[-.00060570379037845102,.00062844638198394764] 
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dist 190=[-.00053829140257883678,.00072318215144771765] 
dist 191=[-.00026653222713715150,.00073562681337094755] 
dist 192=[-.00022552331519989901,.00073620340329281846] 
dist 193=[-.00013814955834379513,.00073023250798151410] 
dist 194=[-.00011455383208017989,.00070876672503214406] 
dist 195=[-2.66215168380187969970e-05,.00069593607322102732] 
dist 196=[-8.26558436019665033200e-06,.00061520208424251127] 
dist 197=[1.64635954751705994610e-05,.00059393487210735293] 
dist 198=[2.20014178666168886800e-05,.00048643478327301789] 
dist 199=[-1.53757676721950494000e-06,.00041446584255039569] 
dist 200=[-7.09586569384952905990e-05,.00041161290686936733] 
dist 201=[-.00012813242279840237,.00039299363429030687] 
dist 202=[-.00018915846855218549,.00038851109157759531] 
dist 203=[-.00024522494478676863,.00031656414735789532] 
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dist 205=[-.00031869298165943563,.00028165454450893690] 
dist 206=[-.00033393250408745337,.00027328614733171249] 
dist 207=[-.00033778976231911219,4.51974927154220806520e-05] 
dist 208=[-.00025387044452185758,1.69551087605327472380e-05] 
dist 209=[-.00025312249320259105,-3.07348491621996692690e-05] 
dist 210=[-.00025087062016688681,-3.77851332679617467840e-05] 
dist 211=[-.00024777246879108265,-8.61649985229295911810e-05] 
dist 212=[-.00024005037939669746,-7.50637749295251093220e-05] 
dist 213=[-.00023568170888849453,-6.18459686882112066110e-05] 
dist 214=[-.00022452819310955693,-4.18909477471780034680e-05] 
dist 215=[-.00010915734351399348,-1.17936913893030829180e-05] 
dist 216=[-.00010834085976239784,1.83622702649357277010e-05] 
dist 217=[-.00010461683609609197,3.86018549315515715480e-05] 
dist 218=[-.00010246982046051333,5.50696894207884354080e-05] 
dist 219=[-8.86966220692854720790e-05,7.02496016374637942960e-05] 
dist 220=[-8.50877564167350459450e-05,8.30912964061787413520e-05] 
dist 221=[-7.82460816591946271280e-05,9.02750065247813845030e-05] 
dist 222=[-7.61028038679267683760e-05,9.45575276958028071230e-05] 
dist 223=[-3.15728041284242217110e-05,9.58797410417440115700e-05] 
dist 224=[-2.52756283071437312750e-05,9.57664906883450545200e-05] 
dist 225=[-1.15530407788745102970e-05,9.48608379024396661820e-05] 
dist 226=[-7.98960264686859274610e-06,9.22689028481257465820e-05] 
dist 227=[6.05643985234764561780e-06,9.07648930621577996080e-05] 
dist 228=[8.78343984094772074570e-06,8.13908311162187549080e-05] 
dist 229=[6.48586934571992264970e-06,7.89342520732027717560e-05] 
dist 230=[1.47926937300383375360e-06,6.67438699703223752220e-05] 
dist 231=[-6.06490283067963753810e-06,4.62530055168450077220e-05] 
dist 232=[-1.36268689447360388300e-05,1.65216552164382560920e-05] 
dist 233=[-1.87042346597729776200e-05,1.59886056166054292810e-05] 
dist 234=[-2.28370157660108271700e-05,1.53403072045011027020e-05] 
dist 235=[-2.75855170606933175430e-05,1.50101680373186769010e-05] 
dist 236=[-3.20383931851086028780e-05,6.50941783124233038720e-06] 
dist 237=[-3.45339482622027966380e-05,4.99201882389797166400e-06] 
dist 238=[-3.61232773418280722530e-05,4.97378022530548424050e-07] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 1, 0, 1, 0, 0, 2] 
dist 0=[115.53685541900761161   ,115.53685541900761161   ] 
dist 1=[114.10877593483208161   ,117.40306691154092351   ] 
dist 2=[110.31391950225807485   ,119.09900786684880692   ] 
dist 3=[103.94324390202190778   ,119.50223591587407644   ] 
dist 4=[93.359142440400564995  ,119.08277368468260534   ] 
dist 5=[82.294281940975237313  ,118.62356669760405445   ] 
dist 6=[74.005040918873505411  ,115.28394430714854896   ] 
dist 7=[66.277207940640290289  ,109.88892563575817386   ] 
dist 8=[57.429900833167671224  ,88.653507387224946929  ] 
dist 9=[48.646159969900503306  ,87.146668929713557768  ] 
dist 10=[41.157821392728741989  ,70.970287912716523508  ] 
dist 11=[33.225456515198495866  ,67.570418296665102400  ] 
dist 12=[22.652040386294775497  ,63.414582533759601197  ] 
dist 13=[12.475311072721538495  ,61.789282889144264921  ] 
dist 14=[6.1167175426748084690 ,54.514838330801345835  ] 
dist 15=[1.3277131982944867081 ,50.601243399028179892  ] 
dist 16=[-4.1293727505635266868 ,10.799864982972910686  ] 
dist 17=[-12.210061110943948395  ,9.2152348063386774481 ] 
dist 18=[-19.249995375733445940  ,-3.5908431715567529339 ] 
dist 19=[-23.674608202918167114  ,-5.1048922794250477204 ] 
dist 20=[-26.993399485227918590  ,-6.3415097408297974551 ] 
dist 21=[-29.643305422318915295  ,-5.5038362947643175051 ] 
dist 22=[-31.561734112286682090  ,-4.6496313758370264005 ] 
dist 23=[-32.019484445496459659  ,-3.6865761457266797630 ] 
dist 24=[-31.893577281193474138  ,-1.4002161016421345443 ] 
dist 25=[-31.845890720611762078  ,1.2864359719431212262 ] 
dist 26=[-27.142757914448395526  ,3.8590426421344195126 ] 
dist 27=[-26.912919641392262868  ,6.8343255473129598375 ] 
dist 28=[-25.117451702923409246  ,9.7455263625298457309 ] 
dist 29=[-24.850140200783328545  ,12.071995607374230413  ] 
dist 30=[-5.7515616474234153518 ,14.370819347454309121  ] 
dist 31=[-2.9931787233270946400 ,17.181979381194446492  ] 
dist 32=[2.4067521664975152838 ,19.683861566373681544  ] 
dist 33=[3.0018546327814480177 ,20.757395849735746464  ] 
dist 34=[2.8793184163775381890 ,21.232033678917138253  ] 
dist 35=[2.5418567859538300803 ,21.350121932049185201  ] 
dist 36=[1.8460996189011075594 ,19.101503364462937009  ] 
dist 37=[.64610572048305407888,18.511996062894902921  ] 
dist 38=[-.40324272383613430697,18.164753637029504639  ] 
dist 39=[-1.2933132874922758556 ,18.075314964999660742  ] 
dist 40=[-2.1650775098214937458 ,15.290351872131860329  ] 
dist 41=[-2.9307843352422200636 ,15.112667967260001999  ] 
dist 42=[-3.4007734048517150148 ,12.868748120139659245  ] 
dist 43=[-4.4308315189047347816 ,12.287815281772231789  ] 
dist 44=[-6.8245994696139845889 ,11.554177895806372749  ] 
dist 45=[-8.3374001240724442770 ,11.228537529045498552  ] 
dist 46=[-9.4654883067874687674 ,3.8743610347985167048 ] 
dist 47=[-10.334046569481277171  ,2.9391355321451280504 ] 
dist 48=[-10.962371920386090459  ,.81168430629658082443] 
dist 49=[-11.137294576335979364  ,.37753926638757195469] 
dist 50=[-11.122880076274923531  ,-1.3390213626462535101 ] 
dist 51=[-10.998222129906018665  ,-1.1387725863675718388 ] 
dist 52=[-10.844343483399180191  ,-.7961728480948305526 ] 
dist 53=[-10.948793983551079757  ,-.44058138348090773208] 
dist 54=[-8.9363126573763860019 ,-.18867893526096856461] 
dist 55=[-8.7260125589632905781 ,.02926368452543495590] 
dist 56=[-3.5837497420142267472 ,.91328150208362637865] 
dist 57=[-3.5736342714402806175 ,2.9169034350440550525 ] 
dist 58=[-2.9756399691910436444 ,4.5519647624125768612 ] 
dist 59=[-2.8258512831615918227 ,6.0628057176473163107 ] 
dist 60=[-2.7311104816806482235 ,7.3400859276650553059 ] 
dist 61=[-2.7084064294421080814 ,8.0484198283921978883 ] 
dist 62=[-.39854297153943325023,8.4612492043454910049 ] 
dist 63=[-.12817006629301871836,8.5650362940243805039 ] 
dist 64=[.49841644564400688626,2.6113354124312169880 ] 
dist 65=[.59461427331207283445,2.6456264369375866845 ] 
dist 66=[.57230806904352720519,2.6345092568640956018 ] 
dist 67=[.41605227641102736366,2.6272085794028592771 ] 
dist 68=[.17130360942314858531,2.2598983569642912764 ] 
dist 69=[-.07627237510877885111,2.1659758522344239748 ] 
dist 70=[-.24376925412981357625,2.0814658015236357614 ] 
dist 71=[-.38096550656148501799,2.0456310392534659359 ] 
dist 72=[-.50834598017186601988,1.8018068713918221625 ] 
dist 73=[-.61626423778938336794,1.7756894481126398954 ] 
dist 74=[-.67648091657312808976,1.5337149431525397164 ] 
dist 75=[-.97684727311714661794,1.4696310598874883271 ] 
dist 76=[-1.2668686595343469486 ,1.3725592921771047880 ] 
dist 77=[-1.4396808263857466343 ,1.3366743968877259232 ] 
dist 78=[-1.5564636848108876416 ,.46433711120961616156] 
dist 79=[-1.6241478790824928609 ,.34792542809418457766] 
dist 80=[-1.6585722212677157442 ,.08595941184549407217] 
dist 81=[-1.6597881406938574293 ,.02976940952207077426] 
dist 82=[-1.6152059735759672912 ,-.10020291255936251387] 
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dist 84=[-1.4014878152642183030 ,.00782723237741195266] 
dist 85=[-1.4179139674478520504 ,.07467372132196496843] 
dist 86=[-1.2088977108499730309 ,.12037374296289219909] 
dist 87=[-1.1729667641478398466 ,.15837555704646601255] 
dist 88=[-.49114758855170830269,.24519925100728634047] 
dist 89=[-.4332065724646309141 ,.45957412211109983504] 
dist 90=[-.34481774123537879767,.63503983868692407931] 
dist 91=[-.32715903722318062215,.79828885924218807238] 
dist 92=[-.31288381586837457907,.93726489789507861501] 
dist 93=[-.30743134752541266074,1.0279523021033387621 ] 
dist 94=[-.06398773974048271548,1.0784909201585990158 ] 
dist 95=[-.06503802604181020499,1.0898476022556729218 ] 
dist 96=[-.07199842804913093332,.32230394664893392873] 
dist 97=[-.08198468080174271157,.32469315903354122485] 
dist 98=[-.09505002348714499715,.32266479923935439303] 
dist 99=[-.11257119671668643051,.31851700848286809275] 
dist 100=[-.1402485498648684553 ,.28390626297857093609] 
dist 101=[-.16841457774730372671,.27386325955105450833] 
dist 102=[-.1878791781248698853 ,.25764057525549748046] 
dist 103=[-.20429785751113213098,.25174186480118018734] 
dist 104=[-.22037982437567946206,.2305382716595316986 ] 
dist 105=[-.23468433199881516883,.22836151275245043474] 
dist 106=[-.25075181846219327932,.18750870619254713044] 
dist 107=[-.25876734460807648801,.1775898027890414988 ] 
dist 108=[-.25991590866095964913,.16813082914229436275] 
dist 109=[-.02587468990966981841,.16384324496891848055] 
dist 110=[-.02623306717595570501,.04159138498028058359] 
dist 111=[-.04928962958939247446,.02891635457143307063] 
dist 112=[-.07614678747024849715,.00021463218136933058] 
dist 113=[-.10089313219212862618,-.00551887848957367214] 
dist 114=[-.12181246220714904413,-.01883505815645321468] 
dist 115=[-.1334753139227821903 ,-.01510561516448777108] 
dist 116=[-.14078730219618944974,-.00930076400463501454] 
dist 117=[-.14247232643431880833,-.00342487571819884641] 
dist 118=[-.05538631364007871631,.00058701858242792096] 
dist 119=[-.05533612127112283237,.00391950703912851694] 
dist 120=[-.05330202287979214059,.00709938820848814743] 
dist 121=[-.05300725273888756269,.00986003172383740323] 
dist 122=[-.04301563393717338852,.01152890802534570685] 
dist 123=[-.04062146456183190950,.01268575356486811658] 
dist 124=[-.03893915340330624441,.01341460614999619918] 
dist 125=[-.03855723221542111130,.01385210798378985243] 
dist 126=[-.00387821057747472116,.01390059142538588250] 
dist 127=[.00016699450924776260,.01369606676574197330] 
dist 128=[.00955234211256912379,.01351001516455989739] 
dist 129=[.01012590639002765725,.01711391343182358445] 
dist 130=[.00823839230635156159,.02235137350767698163] 
dist 131=[.00584533896390839878,.0253406736486427162 ] 
dist 132=[.00220241863358982942,.02720097028950486463] 
dist 133=[-.00145735584207269217,.02795610173719500526] 
dist 134=[-.00391742408315899511,.02812861688028601910] 
dist 135=[-.00592051619435014479,.02799754427021883846] 
dist 136=[-.00776637543346546055,.02707123585874453427] 
dist 137=[-.00932514038268030226,.0266420274215617228 ] 
dist 138=[-.01018861444269960402,.02269593949646404640] 
dist 139=[-.01069131316451016850,.02168791740156638455] 
dist 140=[-.01081795198280306650,.02016406292722326194] 
dist 141=[-.00328418376246529468,.01961259467886681891] 
dist 142=[-.00350027288786030199,.00648778652926586690] 
dist 143=[-.00829551625781673948,.00474824375155960157] 
dist 144=[-.01218965731868942580,.00086000217677407636] 
dist 145=[-.01576625679812499614,1.26111782860535628730e-05] 
dist 146=[-.01878253275882240979,-.00220054117129018293] 
dist 147=[-.02045186135018475455,-.00171130158708098156] 
dist 148=[-.02142338687916136149,-.00096153117429475808] 
dist 149=[-.02166825856666210157,-.00020608147441678451] 
dist 150=[-.00661302641775985935,.00030574029708076331] 
dist 151=[-.00659393890838668960,.00072696690585009772] 
dist 152=[-.00632395471420798763,.00112281750667097846] 
dist 153=[-.00628380100893617778,.00146263182463770552] 
dist 154=[-.00507508512853249735,.00166143338902772169] 
dist 155=[-.00480996239800639536,.00179126953141803159] 
dist 156=[-.00457084479736337734,.00185734157915038474] 
dist 157=[-.00452112051180824770,.00188397206403257029] 
dist 158=[-.00087699858722597434,.00188215878635123929] 
dist 159=[-.00043779189725858249,.00181975447926323137] 
dist 160=[.00057281356399206826,.00193061953626312518] 
dist 161=[.00074356309414375453,.00269082374094962997] 
dist 162=[.00091382874187356898,.00333555813085293037] 
dist 163=[.00065853312246226964,.00369932643647506943] 
dist 164=[.00027136661834279854,.00392029663663434559] 
dist 165=[-.00011732305947293484,.00399805305811774825] 
dist 166=[-.00037867525439189367,.00399764104666130680] 
dist 167=[-.00059167707308037265,.00397443926364791289] 
dist 168=[-.00078842377046730353,.00380776266469849350] 
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dist 170=[-.00105172522099013732,.00309256164827586312] 
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dist 172=[-.00112287432090467577,.00275589288123928289] 
dist 173=[-.00045059239085772285,.00266810925160816312] 
dist 174=[-.00067601018176737289,.00097098653065641175] 
dist 175=[-.00116101897833041352,.00083774378458755608] 
dist 176=[-.00155539938995329778,.00055318393321684542] 
dist 177=[-.00191855737407740202,.00047556319890383471] 
dist 178=[-.00222554030247566916,.00018236744993780950] 
dist 179=[-.00239686889464203244,.00012106407924284962] 
dist 180=[-.00250223210450439480,2.94528838937358610690e-05] 
dist 181=[-.00252913254965100384,4.77645934845062592950e-06] 
dist 182=[-.00084856872861946939,5.93109715428490858320e-05] 
dist 183=[-.00084504829481908076,.00011694280193991774] 
dist 184=[-.00080884973978337999,.00017069498464452999] 
dist 185=[-.00080282709267280088,.00021658352007476642] 
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dist 187=[-.00061119936286067538,.00025971267845872566] 
dist 188=[-.00058233040419551527,.00026710070266158406] 
dist 189=[-.00057395379718664063,.00026897265673525757] 
dist 190=[-5.87667945187652661170e-05,.00026816852828137595] 
dist 191=[1.89304644126470967210e-06,.00025761356834817352] 
dist 192=[.00014292696223502352,.00025555126514839227] 
dist 193=[.00014245657989506456,.00028835860235545384] 
dist 194=[.00011842839956479683,.00036773821124907996] 
dist 195=[8.82938281690697365740e-05,.00041229846698687671] 
dist 196=[3.07662057345842283930e-05,.00043907349842255237] 
dist 197=[-2.70788451287163403910e-05,.00044783428376520583] 
dist 198=[-6.58769119095319020170e-05,.00044732007505238417] 
dist 199=[-9.74051554553351756770e-05,.00044448251368041310] 
dist 200=[-.00012638697717992052,.00042596023302231781] 
dist 201=[-.00015083711699904864,.00042047058492571575] 
dist 202=[-.00016437311456853518,.00034755550555804535] 
dist 203=[-.00017225531619801201,.00032981956240479344] 
dist 204=[-.00017424298630789677,.00030905216978287292] 
dist 205=[-.00015154352301210886,.00029946725638590381] 
dist 206=[-.00015459007206205143,7.95238886652195774260e-05] 
dist 207=[-.00015962211885622736,5.36752273022647460510e-05] 
dist 208=[-.00016855611806853248,-4.41192192516587992500e-06] 
dist 209=[-.00021431579290008551,-1.62925330059548575400e-05] 
dist 210=[-.00025690166120826093,-3.20652800324285179760e-05] 
dist 211=[-.00028059735119965213,-2.14609583231216666520e-05] 
dist 212=[-.00029485020065520152,1.08564292197388178090e-06] 
dist 213=[-.00029817373364364331,2.36699060148312195060e-05] 
dist 214=[-.00011124301861257399,3.88160416693322114220e-05] 
dist 215=[-.00011054473860142486,5.11266175528232356990e-05] 
dist 216=[-.00010630600901817577,6.24520197158437149990e-05] 
dist 217=[-.00010469541543197403,7.20167395912850386360e-05] 
dist 218=[-8.79909085290406916390e-05,7.73363125435776146510e-05] 
dist 219=[-8.38314064436876259820e-05,8.04665148657883470810e-05] 
dist 220=[-7.80653715462734094940e-05,8.13380237764273020870e-05] 
dist 221=[-7.58112769703873108700e-05,8.11861458036538202860e-05] 
dist 222=[-2.18097801133246237940e-05,8.02770891612290065010e-05] 
dist 223=[-1.47513196267298980220e-05,7.86064493763232331230e-05] 
dist 224=[-6.61570421159563244960e-06,7.76566140064359696420e-05] 
dist 225=[-8.02266320798757515400e-06,7.18904788963211315030e-05] 
dist 226=[-9.62531734216367288320e-06,7.02421238667732462160e-05] 
dist 227=[-1.16452269971592629590e-05,6.45127352616771111640e-05] 
dist 228=[-1.47089219808188806860e-05,6.20408553529160108060e-05] 
dist 229=[-1.77858014991428384070e-05,4.82586552852373494570e-05] 
dist 230=[-1.98581423557802885040e-05,3.04429719457761767010e-05] 
dist 231=[-2.15512535843716862790e-05,3.02492796076428286610e-05] 
dist 232=[-2.31226145902637050890e-05,2.92640619382361301200e-05] 
dist 233=[-2.44586374571627497410e-05,2.87026747797388765100e-05] 
dist 234=[-2.52174682810906264360e-05,2.12214975330702274090e-05] 
dist 235=[-2.56846642447093614070e-05,1.95660454860965190830e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 0, 0, 0, 2] 
dist 0=[148.61615809230692181   ,148.61615809230692181   ] 
dist 1=[146.12442458752962331   ,149.31221896595967932   ] 
dist 2=[139.72918846181095914   ,148.64714938002722281   ] 
dist 3=[131.49103003592219724   ,147.62799735509193197   ] 
dist 4=[121.67177256587401592   ,139.58404968541376026   ] 
dist 5=[108.99813746926496403   ,132.81420462142162607   ] 
dist 6=[89.412496123707362195  ,129.58635630909547526   ] 
dist 7=[69.493739690059650106  ,126.93849426643904379   ] 
dist 8=[55.490465640903432921  ,118.63221153851785594   ] 
dist 9=[43.356303927189192331  ,98.865938334859902463  ] 
dist 10=[30.852298595149572496  ,98.008372837420884540  ] 
dist 11=[19.261597279434936224  ,46.678874642301383552  ] 
dist 12=[10.744283214146062282  ,43.550183623177174203  ] 
dist 13=[2.9170556098747829362 ,27.255795603622535703  ] 
dist 14=[-5.9550960310847318931 ,24.490518226505462019  ] 
dist 15=[-14.004518486318896969  ,20.323548657497106984  ] 
dist 16=[-20.110959599623077448  ,18.415983833873838002  ] 
dist 17=[-25.285114943803550075  ,-15.630911592809019423  ] 
dist 18=[-29.744398718617882489  ,-17.533550316365449100  ] 
dist 19=[-33.263905857928511353  ,-20.462096992916532529  ] 
dist 20=[-34.704752341231181449  ,-18.349173693158988420  ] 
dist 21=[-35.209423575086142148  ,-14.847976482750485663  ] 
dist 22=[-34.989880277413886601  ,-8.7163636033474103291 ] 
dist 23=[-31.937573687544160111  ,-2.3654179205649705560 ] 
dist 24=[-30.917603058964837937  ,2.0114063569650143293 ] 
dist 25=[-29.504476333006517010  ,5.6494493154821594346 ] 
dist 26=[-28.853986876294758633  ,9.0786989319855788146 ] 
dist 27=[-11.809510105172886782  ,11.993533450901196892  ] 
dist 28=[-9.5676451692933597734 ,13.595061615653433022  ] 
dist 29=[-4.3849273528572793793 ,14.497194099789709921  ] 
dist 30=[-3.3421158102130487002 ,16.558960297495535841  ] 
dist 31=[1.9572612709693644289 ,20.530178903899585020  ] 
dist 32=[2.2918423264728404506 ,22.727603436214399025  ] 
dist 33=[5.5281389359200328057 ,24.000671695422377609  ] 
dist 34=[5.2585914920537073185 ,24.304007813917733839  ] 
dist 35=[4.7480729949889106167 ,8.1720616482757004625 ] 
dist 36=[3.9579423984552623031 ,8.3809590323399625440 ] 
dist 37=[2.8354374941473926026 ,8.4169164069531138977 ] 
dist 38=[1.0056571462606263648 ,8.3379426683400831377 ] 
dist 39=[-.86510002750283497927,7.5541895927878911238 ] 
dist 40=[-2.1506971380979345877 ,7.3077941306419685948 ] 
dist 41=[-3.2227849014057009369 ,6.8928206526107250892 ] 
dist 42=[-4.2473445023456412675 ,6.7411468674889831256 ] 
dist 43=[-5.1337839966107332675 ,2.8483682253496522529 ] 
dist 44=[-5.6583162057614269650 ,2.3157130577726146448 ] 
dist 45=[-6.0064603584993968421 ,1.0941762983547095453 ] 
dist 46=[-6.1934800929574371765 ,1.0097785941548411934 ] 
dist 47=[-6.2850635754591891641 ,.37524920397586093796] 
dist 48=[-6.2546891241523268126 ,.26313540641569972354] 
dist 49=[-6.1450901109181796559 ,.08903596135006258155] 
dist 50=[-5.8494877455345812205 ,.04637458758756983007] 
dist 51=[-4.0259005977653313795 ,.01829007040120693688] 
dist 52=[-4.0526594674419916303 ,.06364621237169929317] 
dist 53=[-4.0178201920748746229 ,.15981931160151761786] 
dist 54=[-3.9681836897054766396 ,.34596748703554147187] 
dist 55=[-3.4896709718728660519 ,.54552116850727110734] 
dist 56=[-3.3553375148937253569 ,.6950288820902943348 ] 
dist 57=[-3.1543282423738585565 ,.83250414382080754256] 
dist 58=[-3.0763320088979808650 ,.98464748259332765532] 
dist 59=[-1.1310461368603057883 ,1.4327234269860905063 ] 
dist 60=[-.87181393923194445043,1.9434953784596112331 ] 
dist 61=[-.28325824127465672382,2.3759444688833013162 ] 
dist 62=[-.15926732978420656633,2.6161909234734043418 ] 
dist 63=[.51035900824577586656,2.7563486985332117186 ] 
dist 64=[.62420947139993309833,2.8948328653259289933 ] 
dist 65=[.83633676148731451186,3.0413536530804602902 ] 
dist 66=[.87440196958277361765,3.0781441482848079103 ] 
dist 67=[.86773304459788809306,1.3762986004056112252 ] 
dist 68=[.81287304426298810325,1.3160262231406477605 ] 
dist 69=[.73486434593386313512,1.2808290343161460230 ] 
dist 70=[.59240122269850639669,1.2719512859067367898 ] 
dist 71=[.23185998642523194144,.79456417511402710652] 
dist 72=[-.01465608713054399672,.75716418138237334979] 
dist 73=[-.21974161848404096047,.72804957992513828326] 
dist 74=[-.41590521142471412222,.72072921579235597382] 
dist 75=[-.58651088350112960443,.14314568570763245137] 
dist 76=[-.69019336908568553765,.07439414566505931386] 
dist 77=[-.76274983813411432324,-.08754085557008911390] 
dist 78=[-.80986369967215861605,-.1114435669345468673 ] 
dist 79=[-.83911296471150183838,-.27952457850025470415] 
dist 80=[-.84293372802195647374,-.28869378336173533751] 
dist 81=[-.83229836553910128393,-.35231824145153117698] 
dist 82=[-.82131575237589599384,-.3541938814887461911 ] 
dist 83=[-.7195654101807089667 ,-.34200230652049884233] 
dist 84=[-.69136799551538299683,-.30787332257344785017] 
dist 85=[-.64844389972326696678,-.2633025124923721398 ] 
dist 86=[-.6322196837325267663 ,-.13827096947134775692] 
dist 87=[-.42901743411799965217,.08359018990846673396] 
dist 88=[-.4151146497922861198 ,.23275900530998990212] 
dist 89=[-.38656415105833567026,.35424339702779486682] 
dist 90=[-.37817600270400640979,.46621852495469905613] 
dist 91=[-.11470932861151275916,.56078660262810412434] 
dist 92=[-.10234325336007516311,.61317576428311033806] 
dist 93=[-.04961770299782710013,.64367700101208046958] 
dist 94=[-.03948426145140146800,.65136084218402593055] 
dist 95=[-.01702962714866672670,.36411048420928823035] 
dist 96=[-.01173886332650909732,.36773636431710339028] 
dist 97=[.11626881206841761305,.30696853727949784854] 
dist 98=[.12034536337111256424,.31087867351194513339] 
dist 99=[.12608599918333466258,.16419685719680028655] 
dist 100=[.1248251106860905945 ,.15628039187078303813] 
dist 101=[.10428283286590752835,.1501772215962007861 ] 
dist 102=[.05899986083829243785,.14767100775734869988] 
dist 103=[.01336576828830302744,.10024748155087136262] 
dist 104=[-.01755672391692174540,.09489487745314528212] 
dist 105=[-.04301009246663683638,.09130173582566222067] 
dist 106=[-.06693649580076531521,.09047209805768028413] 
dist 107=[-.08748101439686744772,.01074449370210818257] 
dist 108=[-.09951117976402907632,.00143099297641901895] 
dist 109=[-.10738332683690608657,-.02015931539607998614] 
dist 110=[-.11142423595997874414,-.02341719003967819432] 
dist 111=[-.11308704181114189395,-.04836172412283471060] 
dist 112=[-.11299834503967193645,-.05205171074217239677] 
dist 113=[-.10929108950770522595,-.05859728958570536692] 
dist 114=[-.10833371873726188882,-.05954580774368883134] 
dist 115=[-.08955380028054354584,-.06419126715595415558] 
dist 116=[-.08493005758141656678,-.05508220164747218102] 
dist 117=[-.08057389890642557890,-.03974274216750107978] 
dist 118=[-.07853579059393232179,-.01647771397995712972] 
dist 119=[-.05264675493658665256,.00687905965957792575] 
dist 120=[-.05037423995645456525,.02258345865369910986] 
dist 121=[-.04692173599176654716,.03538181405558341617] 
dist 122=[-.04566547711531374849,.04720218712395412971] 
dist 123=[-.01543426483771351318,.05720909052293164349] 
dist 124=[-.01140181126710985581,.0630088589323029101 ] 
dist 125=[-.00235939817659926790,.06647815767180395061] 
dist 126=[-.00040475836302101144,.06728206814575658126] 
dist 127=[.00949743019175186445,.04302817556256108043] 
dist 128=[.01121596003000914209,.04690063620421513955] 
dist 129=[.01410988937443986454,.04915400260770745043] 
dist 130=[.01467743215708262627,.04972154672936329876] 
dist 131=[.01500299169126091840,.02082117265010919824] 
dist 132=[.01474625353068881244,.0197031426327010273 ] 
dist 133=[.01361591104394130670,.01894757118868888952] 
dist 134=[.00788667534831381236,.01877196324812679239] 
dist 135=[.00212596849503566559,.01180479500160798035] 
dist 136=[-.00176487823228814963,.01117966547070542997] 
dist 137=[-.00495556573694322053,.01066228211973843915] 
dist 138=[-.00793677672607449596,.01047056767422120545] 
dist 139=[-.01048556086062251237,.00154822022904270532] 
dist 140=[-.01195959999338321368,.00048189119934034046] 
dist 141=[-.01290142265097671986,-.00200142627798870072] 
dist 142=[-.01333743673114953559,-.00237717202634739197] 
dist 143=[-.01349311979085197784,-.00530271160377805306] 
dist 144=[-.01345366672577004016,-.00573808344377678239] 
dist 145=[-.01306120337992323515,-.00653992978703326369] 
dist 146=[-.01286075799743181631,-.00666767158907525144] 
dist 147=[-.01101718063255820359,-.00683174225089269280] 
dist 148=[-.01053938279010360077,-.00666461951589572559] 
dist 149=[-.00981605943888089356,-.00528083973499061643] 
dist 150=[-.00955218793993543490,-.00183153400761771513] 
dist 151=[-.00647871672075811063,.00162533094176279499] 
dist 152=[-.00613145493381137487,.00394376936552874386] 
dist 153=[-.00579783742669576871,.00582765460628988706] 
dist 154=[-.00564866500664955785,.00755921610632627031] 
dist 155=[-.00139239963201604026,.00901995668128501718] 
dist 156=[-.00095297634901508660,.00982858956471976945] 
dist 157=[3.95840651857842512990e-05,.01029947172789557593] 
dist 158=[.00023897925046558978,.01041802351168310274] 
dist 159=[.00133990117617252794,.00426291505340046160] 
dist 160=[.00152404343313522450,.00466510061881625740] 
dist 161=[.00183959170178511560,.00491106263968232384] 
dist 162=[.00189788663777294217,.00496936614650456440] 
dist 163=[.00192495776425889611,.00247877189671542732] 
dist 164=[.00188693485959672790,.00235311082212458513] 
dist 165=[.00142873225451678911,.00223982654837383968] 
dist 166=[.00070321263442173421,.00221640244507994213] 
dist 167=[-2.48890078364020436990e-05,.00148548260717988833] 
dist 168=[-.00051501730668218774,.00140170897712541120] 
dist 169=[-.00091530139064229622,.00134001968679865115] 
dist 170=[-.00128669902818164317,.00132459014288573362] 
dist 171=[-.00160252135049773601,.00012871231633649837] 
dist 172=[-.00178215742315560205,-1.10957466201557339560e-05] 
dist 173=[-.00189312915029482137,-.00033653589066373662] 
dist 174=[-.00193633810708284287,-.00038386561813516219] 
dist 175=[-.00194149307233718694,-.00076433877879490461] 
dist 176=[-.00193193708435787955,-.00082009342480213019] 
dist 177=[-.00185463854463901476,-.00092057533022970359] 
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dist 180=[-.00143218620790387870,-.00061553169315854314] 
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dist 182=[-.00130532618391580713,-3.09138763496145800000e-05] 
dist 183=[-.00078922932688171687,.00032129470334825235] 
dist 184=[-.00075206166075801485,.00055779154281211150] 
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dist 189=[-2.59417697117338415680e-05,.00121673746129935476] 
dist 190=[-5.75981273491109021540e-06,.00122987652137296969] 
dist 191=[.00014842933349206021,.00065276529466958882] 
dist 192=[.00017381270704263515,.00071044602395619490] 
dist 193=[.00021450545686530831,.00074400756513875198] 
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dist 195=[.00022343489210493877,.00034984281223221525] 
dist 196=[.00021798485107397127,.00033323386982229674] 
dist 197=[.00018276287020518920,.00031218848683376414] 
dist 198=[7.55574087393123008910e-05,.00030309830334577335] 
dist 199=[-3.18639197310754785580e-05,.00023508228740479626] 
dist 200=[-.00010396999316731761,.00022805266894000615] 
dist 201=[-.00016264798043379633,.00020861510506578440] 
dist 202=[-.00021675223206623171,.00020172314940387712] 
dist 203=[-.00026253356675053247,.00012353303777515890] 
dist 204=[-.00028816476347144232,.00011022944576124599] 
dist 205=[-.00030347250592527155,8.30694062324855911260e-05] 
dist 206=[-.00030826371785860108,7.57211927526537497360e-05] 
dist 207=[-.00030770707851661161,4.88354212850935956420e-05] 
dist 208=[-.00030522138445469852,4.25399694684724506400e-05] 
dist 209=[-.00029442101546343187,3.52491136816044304220e-05] 
dist 210=[-.00027073561083873937,3.33604538617119696260e-05] 
dist 211=[-.00014087951561589260,3.29908141849363729330e-05] 
dist 212=[-.00013987244316886101,3.38678847617528342950e-05] 
dist 213=[-.00013420502377623522,3.58044604975545650270e-05] 
dist 214=[-.00013213238634679071,3.96426253593009511630e-05] 
dist 215=[-.00011057769826051626,4.43125198995305373160e-05] 
dist 216=[-.00010524734014879346,4.95521627056105548600e-05] 
dist 217=[-9.78771800289218900410e-05,5.61136221717020929650e-05] 
dist 218=[-9.50017824143152841570e-05,7.33477230105514147770e-05] 
dist 219=[-3.30229436686183666420e-05,8.79485004320685525040e-05] 
dist 220=[-2.84309256577278424520e-05,9.61575123177519038510e-05] 
dist 221=[-1.86523420620218944930e-05,.00010110608798139868] 
dist 222=[-1.59935721792203345570e-05,.00010276105624439347] 
dist 223=[-6.00318939062497926920e-06,.00010293471563437419] 
dist 224=[-3.90379413090769411740e-06,.00010200143752898025] 
dist 225=[-8.86792530595104589670e-07,.00010010031115644521] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 1, 1, 2, 0, 2] 
dist 0=[144.56129672257835539   ,144.56129672257835539   ] 
dist 1=[139.57617372829432718   ,145.84588443760216842   ] 
dist 2=[132.71606900309837870   ,145.94578106359616918   ] 
dist 3=[124.11074451622778010   ,145.97196953436568039   ] 
dist 4=[112.74919771853775263   ,144.73924205641038514   ] 
dist 5=[94.930154639142178506  ,133.52462510567304464   ] 
dist 6=[76.713760115202737021  ,131.01074695342906265   ] 
dist 7=[63.766305722714197076  ,122.26707678601400820   ] 
dist 8=[52.400475656689747263  ,120.99392451349768417   ] 
dist 9=[40.454949623920523010  ,98.695867605972819130  ] 
dist 10=[29.231367620104513909  ,93.852722100318109764  ] 
dist 11=[20.720890799728639418  ,89.639860555860272519  ] 
dist 12=[12.633538866939256538  ,88.754744004939224810  ] 
dist 13=[3.0659433178205234128 ,32.261187454770921413  ] 
dist 14=[-5.7790988832481540463 ,29.037543431306903854  ] 
dist 15=[-10.998261857525450064  ,26.645121162577517784  ] 
dist 16=[-14.582368411338177615  ,3.4798130437034909632 ] 
dist 17=[-17.954465421991981168  ,-14.394345957108761396  ] 
dist 18=[-23.952679746071460612  ,-15.393948788715078082  ] 
dist 19=[-28.413664608576472230  ,-14.164406460696936316  ] 
dist 20=[-31.898087317597765311  ,-11.668455927899665583  ] 
dist 21=[-34.470988597677003938  ,-6.9545928026690436870 ] 
dist 22=[-35.310482098936993990  ,-2.0022248144945145146 ] 
dist 23=[-35.430785991853275376  ,1.4457960098490488684 ] 
dist 24=[-35.130033745046660809  ,4.3331953320636091862 ] 
dist 25=[-31.363150843971854968  ,7.0724510269182671698 ] 
dist 26=[-30.241581813842560095  ,9.3997013210808940174 ] 
dist 27=[-28.698779734239347937  ,10.657795180700073294  ] 
dist 28=[-28.021548647098823094  ,11.333478841901168216  ] 
dist 29=[-10.921978741561178243  ,11.456172741288193869  ] 
dist 30=[-8.6937303145026884403 ,11.122087528188669783  ] 
dist 31=[-3.5831704752550779846 ,12.240192988805049433  ] 
dist 32=[-2.5453046562867736590 ,16.851464208847911205  ] 
dist 33=[3.4355689883818594358 ,20.757616548149364127  ] 
dist 34=[3.6496588663936891528 ,22.916023923500100108  ] 
dist 35=[3.4718348221781399507 ,24.164090729182360277  ] 
dist 36=[3.0933168555834002935 ,24.457204959195704556  ] 
dist 37=[2.3617154932059373891 ,8.3984575534256023767 ] 
dist 38=[1.5813759883383050125 ,8.5162310222951954143 ] 
dist 39=[1.0089146201103459273 ,8.4891658301302540378 ] 
dist 40=[-.36331861043617366532,8.3926385375035186803 ] 
dist 41=[-1.8986222608475846945 ,7.5771053194419590365 ] 
dist 42=[-3.1868475445572980407 ,7.3336504867491921372 ] 
dist 43=[-4.4316225833659132058 ,6.8418028011175783445 ] 
dist 44=[-5.5185329751011834875 ,6.6688902086104427111 ] 
dist 45=[-6.1809769520640719260 ,3.1531122836285285595 ] 
dist 46=[-6.6451047073363845620 ,2.6461162494334638080 ] 
dist 47=[-6.9457411092021604479 ,1.5141299473144761888 ] 
dist 48=[-7.1302410076725999395 ,1.2269049688240365470 ] 
dist 49=[-7.1337188188447261020 ,-.04188345478643344829] 
dist 50=[-7.0392000254055406679 ,-.27844331375306257839] 
dist 51=[-6.9462021074892234386 ,-.73136973272234130031] 
dist 52=[-6.2409872200783786703 ,-.80426097065164800876] 
dist 53=[-3.9626654518596832971 ,-.53894226926338650604] 
dist 54=[-3.9787562361158338677 ,.03460029466330940480] 
dist 55=[-3.9225829889148765061 ,.42450753510508095676] 
dist 56=[-3.8709200112177392402 ,.74522633823308381637] 
dist 57=[-3.3817068548944397638 ,1.0444759928250850256 ] 
dist 58=[-3.2475899819781614052 ,1.2984520438476897602 ] 
dist 59=[-3.0454632630069033267 ,1.4396534563536619385 ] 
dist 60=[-2.9687164120691764580 ,1.5220818059674409105 ] 
dist 61=[-1.0721594147618880042 ,1.5428502135718040690 ] 
dist 62=[-.81888168290915153678,1.5099635518968356426 ] 
dist 63=[-.24587948025988164265,1.6487056363645618073 ] 
dist 64=[-.12437141875849584586,2.1630780424694704452 ] 
dist 65=[.50027367043844543313,2.6048794329663254127 ] 
dist 66=[.46443518387354395894,2.8495901080638068541 ] 
dist 67=[.41124775547353920098,2.9920465990865218051 ] 
dist 68=[.33659155135850746192,3.0279325148960282525 ] 
dist 69=[.21553796110844223299,1.4554060902091113538 ] 
dist 70=[.09165079714516095365,1.4154182214685491358 ] 
dist 71=[.00572536293662381051,1.4047711842485911208 ] 
dist 72=[-.06690799854507257729,.90928406628049306669] 
dist 73=[-.13809818220158268869,.76206891412854814656] 
dist 74=[-.25480818281920818976,.72489167517934247911] 
dist 75=[-.47209456713785382928,.69594341627830998551] 
dist 76=[-.66081892069722446587,.68436904858140345066] 
dist 77=[-.77508522929777844808,.12576222857288375709] 
dist 78=[-.85453848083082243506,.05895269858265844396] 
dist 79=[-.9051368207255087351 ,-.09801085927172503071] 
dist 80=[-.9358419954780558455 ,-.12114609808509940351] 
dist 81=[-.93953455582329113032,-.22690771247773701922] 
dist 82=[-.92605852001749328221,-.20102931073785900292] 
dist 83=[-.91392313601981868036,-.16876690922878888745] 
dist 84=[-.79780583059583312963,-.12641126510453785602] 
dist 85=[-.76596178417924550676,-.06046924072717835727] 
dist 86=[-.71850063386848213312,.00617516259563056722] 
dist 87=[-.70025638436032362821,.05132406135734017154] 
dist 88=[-.4962184011105596208 ,.09305130258261544807] 
dist 89=[-.40947058595168534751,.25727579264657278882] 
dist 90=[-.38819965232368457513,.39101752215742334034] 
dist 91=[-.36813299053192146062,.51429511864001600001] 
dist 92=[-.3588619722098574774 ,.61843998034391587666] 
dist 93=[-.09448508582029247878,.67636567173525885283] 
dist 94=[-.06693304301053677936,.7100370855706943239 ] 
dist 95=[-.00433650310863655735,.71839664393630208594] 
dist 96=[.00807642476181932147,.22773803081567570887] 
dist 97=[.07032583240666142687,.26152989758805800028] 
dist 98=[.06350864169162116600,.28765279588004900636] 
dist 99=[.04475213756235834237,.30355263685059079749] 
dist 100=[.02105584128244166128,.30722602393794882049] 
dist 101=[-.01492030190234762616,.17966857324157541006] 
dist 102=[-.0510113221525656115 ,.17119822234485479561] 
dist 103=[-.07516433554967646621,.16658338611244756845] 
dist 104=[-.09470829443569325392,.1156913768387785314 ] 
dist 105=[-.11250423333729116634,.09453862679630795106] 
dist 106=[-.12737467775350125759,.08941308302527309746] 
dist 107=[-.13530562763851460426,.08590203881733917574] 
dist 108=[-.13951132239755191506,.08509231450274739938] 
dist 109=[-.13986267297764799736,.03786825427731146367] 
dist 110=[-.13815558279349906921,.03591898471948999887] 
dist 111=[-.14063540340330918319,.03537929930035040892] 
dist 112=[-.14213449291743568384,.03534775896428915286] 
dist 113=[-.14182196133753100285,.03599536088994118261] 
dist 114=[-.13674650918897564187,.03700350350120601897] 
dist 115=[-.13545269557038279365,.03840344047248319344] 
dist 116=[-.11151368873872157634,.04032373824297784241] 
dist 117=[-.10566119679233107044,.04339756628355297281] 
dist 118=[-.09999645105080765457,.04653489766825115369] 
dist 119=[-.09732475271256555161,.04870772602543782701] 
dist 120=[-.05810808994626855085,.05054332228560642897] 
dist 121=[-.04968217707866131579,.05234319710181010796] 
dist 122=[-.04750999178460353509,.05393694337029410101] 
dist 123=[-.04422800808143516122,.06306778784984854475] 
dist 124=[-.04303233331066788038,.07382295379573609485] 
dist 125=[-.01443781500320090141,.08058973561815933881] 
dist 126=[-.01064620509354930775,.08479163360442145029] 
dist 127=[-.00215616171604270071,.08572474402183611023] 
dist 128=[-.00031212168499867547,.03412949181423144321] 
dist 129=[.00851931853330032173,.04071448933816170764] 
dist 130=[.00758344078700650116,.04435944361594692204] 
dist 131=[.00647457154057501284,.04648146068653923324] 
dist 132=[.00505047254659094647,.04701596586609685498] 
dist 133=[.00286302530869389282,.01438406690519171680] 
dist 134=[.00065757159314615828,.01436074518535332638] 
dist 135=[-.00083813378372971435,.01381254768050751129] 
dist 136=[-.00207054050524550521,.01373080296092516963] 
dist 137=[-.00323093680851618528,.01113850500196024258] 
dist 138=[-.00422849006119737985,.01056834785095678687] 
dist 139=[-.00481455564687822376,.01005375705041510145] 
dist 140=[-.00520039285975192664,.00994683026593735159] 
dist 141=[-.00540322717230585958,.00200458284461290163] 
dist 142=[-.00549076544040065378,.00104665488109744323] 
dist 143=[-.00548866633154646538,-.00116223833378186389] 
dist 144=[-.00580195757619413612,-.00153333507060616705] 
dist 145=[-.00721753083501863026,-.00378708889104369752] 
dist 146=[-.00802032271884472982,-.00327133969238198207] 
dist 147=[-.00851328051346750931,-.00268150525679869985] 
dist 148=[-.00869872007850488302,-.00193677633260369515] 
dist 149=[-.00871330772657388045,-.00080604311492902128] 
dist 150=[-.00866769133355706467,.00032947879292950937] 
dist 151=[-.00831479914505288787,.00109325087359997428] 
dist 152=[-.00821943383067523441,.00171593900594450492] 
dist 153=[-.00676532739946374079,.00229139664522703196] 
dist 154=[-.00641264039335278486,.00277875782380607021] 
dist 155=[-.00603402325164921868,.00306437179614013667] 
dist 156=[-.00584263000844912189,.00323277133369630756] 
dist 157=[-.00215275591461662386,.00327192655307479583] 
dist 158=[-.00186187019092495096,.00250893093555789478] 
dist 159=[-.00123852033635725306,.00337144481226181583] 
dist 160=[-.00106784203886847374,.00416649565515784917] 
dist 161=[-.00041920586482174032,.00483905696307211809] 
dist 162=[-.00028436787103353476,.00521522236276273453] 
dist 163=[-7.38828889906542621990e-05,.00545343106181473021] 
dist 164=[-1.99208375689206778010e-05,.00551226796911355395] 
dist 165=[.00035305538996010001,.00185677813752948399] 
dist 166=[5.43937771826378899060e-05,.00185050502036340115] 
dist 167=[-.00014731670017350729,.00177505116808662576] 
dist 168=[-.00031271235223551568,.00176181804308543171] 
dist 169=[-.00046721088359150313,.00142835419144410212] 
dist 170=[-.00059926113385630431,.00134881373916639097] 
dist 171=[-.00067554127743370773,.00128517426039763933] 
dist 172=[-.00072415921054989722,.00126518107421087629] 
dist 173=[-.00074639648908946749,.00014563481391463308] 
dist 174=[-.00075281913139814458,1.32271552447319011750e-05] 
dist 175=[-.00075110695251037763,-.00029466168049168716] 
dist 176=[-.00072164726197735291,-.00034044739213135005] 
dist 177=[-.00081547747216900617,-.00049543841677269673] 
dist 178=[-.00091434687334782978,-.00042891855391013758] 
dist 179=[-.00097413817259854595,-.00035389634254295088] 
dist 180=[-.00099457587386589122,-.00025957004982074692] 
dist 181=[-.00099432119437307539,-9.07696102240233135810e-05] 
dist 182=[-.00098850906212789361,7.84352061364086111430e-05] 
dist 183=[-.00094687651934556110,.00019193938581244112] 
dist 184=[-.00093588609030135303,.00028418627124474815] 
dist 185=[-.00076860202938040851,.00036899486592552482] 
dist 186=[-.00072819866987883327,.00044054671651250511] 
dist 187=[-.00068488345693248474,.00048016068808669265] 
dist 188=[-.00066302147129793891,.00050323348722626512] 
dist 189=[-.00016541227981191800,.00050904653518686943] 
dist 190=[-.00010914728405573629,.00036945509660556886] 
dist 191=[1.77292433974886929180e-05,.00037533976082978482] 
dist 192=[4.30431627548544321390e-05,.00044914459803282780] 
dist 193=[.00012970706973987244,.00054044691233470200] 
dist 194=[.00011296166540128749,.00059154440922605930] 
dist 195=[9.40175404556557906240e-05,.00062248960474311636] 
dist 196=[6.69417599415320839130e-05,.00062946131807383644] 
dist 197=[9.07154481774981234510e-06,.00025272934665454165] 
dist 198=[-4.89178265467867741080e-05,.00025117853999220807] 
dist 199=[-8.78315695998367998840e-05,.00024220519116264952] 
dist 200=[-.00011948257811669590,.00023812788598488670] 
dist 201=[-.00014863530824775635,.00020256120376538021] 
dist 202=[-.00017327785853068505,.00019352386615915058] 
dist 203=[-.00018702109846056798,.00017937702363454539] 
dist 204=[-.00019515738459029294,.00017446723435321222] 
dist 205=[-.00019753727523115063,5.83769136897412498720e-05] 
dist 206=[-.00019723313996443143,4.28171045741796528450e-05] 
dist 207=[-.00019515594841775364,8.16257559836274271840e-06] 
dist 208=[-.00019059381165096243,4.66953886710380246500e-07] 
dist 209=[-.00018797270439338135,-2.72493220989870221640e-06] 
dist 210=[-.00017168996486211534,2.40543064548096023600e-06] 
dist 211=[-.00016743212345039646,8.20861677597332880740e-06] 
dist 212=[-.00014682966336820901,1.54973990700413640640e-05] 
dist 213=[-6.55900816915826288190e-05,2.65265020827199672200e-05] 
dist 214=[-5.60214375624482991260e-05,3.75950052236406203920e-05] 
dist 215=[-5.49975406716096866390e-05,4.50404795994134757820e-05] 
dist 216=[-5.42852857931699224350e-05,5.11140364182971839330e-05] 
dist 217=[-4.96028133646403156200e-05,5.67358899821372367960e-05] 
dist 218=[-3.43938954916830680490e-05,6.15059737127189929640e-05] 
dist 219=[-3.15592148590479847940e-05,6.41979052756202848480e-05] 
dist 220=[-1.35307480586592865300e-05,6.58329599854066251560e-05] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 1, 2, 1, 0, 0, 2] 
dist 0=[112.60155814164528734   ,112.60155814164528734   ] 
dist 1=[111.73687260082064702   ,112.90878462991198787   ] 
dist 2=[108.61209748367037469   ,113.51903782413043233   ] 
dist 3=[103.32921162743560977   ,114.65688013319426939   ] 
dist 4=[93.834144889254382524  ,115.72025625006256124   ] 
dist 5=[83.734140403886419365  ,116.03817968605082797   ] 
dist 6=[76.042420912232587773  ,115.85716358425653316   ] 
dist 7=[68.748329490093644003  ,113.42267673920786089   ] 
dist 8=[60.214200227875446709  ,92.977877157734439406  ] 
dist 9=[51.634350936742574053  ,89.834591099517408282  ] 
dist 10=[44.144847712814388536  ,81.217207826881611986  ] 
dist 11=[36.058378279205355242  ,79.714990917805004325  ] 
dist 12=[25.080092970550934758  ,63.338854639293717387  ] 
dist 13=[14.459478836151913657  ,60.814053337898315004  ] 
dist 14=[7.7916331985059011592 ,55.947679340817215269  ] 
dist 15=[2.7338198917405823762 ,54.516636990436085534  ] 
dist 16=[-1.4705012805358854014 ,19.845737149548528493  ] 
dist 17=[-5.1503177606896529705 ,15.591689077081203402  ] 
dist 18=[-10.324090583024043068  ,5.6797445673701169081 ] 
dist 19=[-13.924063282146964520  ,4.1847038113031454196 ] 
dist 20=[-19.457427503395620628  ,-4.2879719097559273399 ] 
dist 21=[-23.288897301340093321  ,-2.6224894524767090629 ] 
dist 22=[-26.037798005791802776  ,-.57297266230956173267] 
dist 23=[-28.006473421671976930  ,1.1871376853852155740 ] 
dist 24=[-29.303617091668441986  ,2.9904543256531618600 ] 
dist 25=[-29.577366240481325481  ,5.2265460562937308383 ] 
dist 26=[-29.122314546459915337  ,7.4874489708046388247 ] 
dist 27=[-29.055306585959897583  ,9.3976260307001922438 ] 
dist 28=[-24.350461363355989499  ,11.376784183646722131  ] 
dist 29=[-23.170524878285805155  ,13.921096337461350724  ] 
dist 30=[-22.417133263518731196  ,16.231167878249749325  ] 
dist 31=[-22.237184764869589758  ,17.283059120873620603  ] 
dist 32=[-4.0698669953526689808 ,17.779260930167586800  ] 
dist 33=[-1.9431981149515890410 ,17.878099216480307119  ] 
dist 34=[2.2893393247104968793 ,16.287322596968805573  ] 
dist 35=[1.7089396166755114076 ,15.835051945967626644  ] 
dist 36=[.63519605771045846361,15.538099559596758671  ] 
dist 37=[-.49115736013139034213,15.391095092963840079  ] 
dist 38=[-1.2807778473198195829 ,12.756724853399217197  ] 
dist 39=[-1.9494563696135781599 ,13.421862195842830834  ] 
dist 40=[-2.5979349676848150972 ,13.785237396781970191  ] 
dist 41=[-4.0871758109639178708 ,13.810436466624686686  ] 
dist 42=[-6.1592073718400996105 ,13.544022295762078611  ] 
dist 43=[-7.4755511675846141703 ,13.358640377879575793  ] 
dist 44=[-8.4647704164235823010 ,11.586614922905151359  ] 
dist 45=[-9.2400494122403547886 ,11.112615959097155056  ] 
dist 46=[-9.8070922555575611358 ,10.402747296627476472  ] 
dist 47=[-9.9701591444408172682 ,10.135381303674305801  ] 
dist 48=[-9.9594077837484745508 ,3.5958406701572150385 ] 
dist 49=[-9.8421131594280916713 ,2.7248171665778868187 ] 
dist 50=[-8.8265349625191349246 ,2.0423575036562556781 ] 
dist 51=[-8.5190774844828998576 ,2.6985758380965009713 ] 
dist 52=[-8.9144597383508628386 ,3.7419768033300421118 ] 
dist 53=[-9.7493779998220753339 ,4.8032597615046488358 ] 
dist 54=[-10.235313292993203865  ,5.5305840645507080172 ] 
dist 55=[-10.357713343123337105  ,6.1364439980165711442 ] 
dist 56=[-3.1801472244843222591 ,6.7159930397522488199 ] 
dist 57=[-3.1918699548902524465 ,7.2190346109117435895 ] 
dist 58=[-3.1131857482560138725 ,7.5214403720080968194 ] 
dist 59=[-3.0954707830421104091 ,7.7285830639036496476 ] 
dist 60=[-2.5785812063844751124 ,7.8537606454597802227 ] 
dist 61=[-2.4498685055589365335 ,7.9087214882999120469 ] 
dist 62=[-2.3475925361306154830 ,2.0419985592672452346 ] 
dist 63=[-2.3080968282255888353 ,2.0689210210814606526 ] 
dist 64=[-.40898307718679715187,2.0554522850641577415 ] 
dist 65=[-.18203953733325932593,2.0534579053519170849 ] 
dist 66=[.34952519498779802537,1.7386967888636163812 ] 
dist 67=[.29226670382272104415,1.6572815130733665258 ] 
dist 68=[.14200899035784677106,1.6097564598046320834 ] 
dist 69=[-.01096975710351648010,1.5977296868491909678 ] 
dist 70=[-.11506723719816740033,1.6756365267375831713 ] 
dist 71=[-.20077010187073085756,1.7309545365137725373 ] 
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dist 193=[-7.00383565390475917040e-05,.00045905067065579556] 
dist 194=[-8.16746740237456730170e-05,.00044948681663897778] 
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dist 209=[-.00020818902656492507,2.96445015567768653930e-05] 
dist 210=[-.00020876178104237984,-1.62785395083638362510e-05] 
dist 211=[-.00020932515488524627,-1.22857258432420200440e-05] 
dist 212=[-.00021001500721786482,5.27256771811964147260e-06] 
dist 213=[-.00021065504594011166,2.28680248232900329380e-05] 
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dist 217=[-.00010011776331771635,6.06191635931933586130e-05] 
dist 218=[-9.60219218001760184630e-05,6.47964766708992220510e-05] 
dist 219=[-9.47407787715195640650e-05,6.72740591827451528260e-05] 
dist 220=[-7.86122961578467792450e-05,6.80091329080071259450e-05] 
dist 221=[-7.46697964114021665160e-05,6.79685336950482642710e-05] 
dist 222=[-6.98874625691191348760e-05,6.73662682644654669460e-05] 
dist 223=[-6.77551159646690837210e-05,6.62502635694380461690e-05] 
dist 224=[-1.60037571065925129860e-05,6.54390903876497274830e-05] 
dist 225=[-1.37780457388480742660e-05,6.16810500218719532160e-05] 
dist 226=[-1.43120055962253560460e-05,6.03755812345837509550e-05] 
dist 227=[-1.50120898370077394420e-05,5.64359614369885040790e-05] 
dist 228=[-1.61016181238743682230e-05,5.48596277434459162500e-05] 
dist 229=[-1.72036698001839969780e-05,4.54051543743000027480e-05] 
dist 230=[-1.79535541552475902480e-05,4.30458129357465018520e-05] 
dist 231=[-1.85734237852079220500e-05,3.92957226908088684450e-05] 
dist 232=[-1.91595973560598211520e-05,3.31021943662980848040e-05] 
dist 233=[-1.96646537150327412790e-05,3.29061665898545908480e-05] 
dist 234=[-1.99626594995760945960e-05,3.15169185810709224390e-05] 
dist 235=[-2.01602718365612979380e-05,3.02880492588857516320e-05] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 1, 0, 1, 2] 
dist 0=[119.53813052030565462   ,119.53813052030565462   ] 
dist 1=[118.08445760788791799   ,120.58709326032147983   ] 
dist 2=[115.75395305041875650   ,121.29993671494240290   ] 
dist 3=[112.40602321485696803   ,121.59402461521602483   ] 
dist 4=[104.69064025030447857   ,121.15542031635137817   ] 
dist 5=[96.169911230638904219  ,119.87274122334735114   ] 
dist 6=[85.473852602661505324  ,119.03687365713239210   ] 
dist 7=[71.501115084581202076  ,98.795972078807899863  ] 
dist 8=[61.199499730693283618  ,95.683658671402122059  ] 
dist 9=[51.765983093516519291  ,86.761378934317422726  ] 
dist 10=[41.227552352816517173  ,85.371554833294791073  ] 
dist 11=[30.924280094923279979  ,67.364897771572874413  ] 
dist 12=[22.410598141245731613  ,65.371992738720810687  ] 
dist 13=[13.631017232480544313  ,59.795952110851624404  ] 
dist 14=[2.2434202435146367358 ,58.793521435387639198  ] 
dist 15=[-8.5114210234477558237 ,18.719563311405809459  ] 
dist 16=[-14.779828581697950021  ,16.901049761166289474  ] 
dist 17=[-18.982736428207401889  ,9.3548735264615747630 ] 
dist 18=[-21.511508989013379857  ,7.9842329813386645888 ] 
dist 19=[-23.195837971589217336  ,5.4437447283364195268 ] 
dist 20=[-24.029091744267319640  ,4.8708006599849765894 ] 
dist 21=[-24.435022416353079825  ,3.2631309361164148479 ] 
dist 22=[-26.129292879998155604  ,3.0315522706707333648 ] 
dist 23=[-27.760914884176115493  ,3.1713353668567635516 ] 
dist 24=[-28.832203367065410706  ,3.7983952956810906852 ] 
dist 25=[-29.278637345578502005  ,4.6409201534121077734 ] 
dist 26=[-29.378458641826454923  ,5.6440184758448201304 ] 
dist 27=[-26.834661443804612670  ,6.9292857817591082157 ] 
dist 28=[-24.171928566912923993  ,8.9005660876518241914 ] 
dist 29=[-21.391728628217857879  ,10.774602180863353653  ] 
dist 30=[-21.042894383353457085  ,11.676581346763996250  ] 
dist 31=[-4.8857941999558059470 ,12.136231087616936364  ] 
dist 32=[-2.9482524605281045432 ,12.630136441767419723  ] 
dist 33=[1.6175280192183156295 ,13.066530276259057630  ] 
dist 34=[2.2860410874209816545 ,13.111041875626258360  ] 
dist 35=[7.8393190880612077425 ,12.142148869483198387  ] 
dist 36=[5.6348435076286174771 ,12.286528714991272949  ] 
dist 37=[2.8624208147654882666 ,13.339402463571984995  ] 
dist 38=[.9259114579102474634 ,13.882759619742101398  ] 
dist 39=[-.72350695420160059907,14.110439525036302504  ] 
dist 40=[-2.3583948805830851684 ,14.104586858370529240  ] 
dist 41=[-3.8146385878097355263 ,13.624649753367131910  ] 
dist 42=[-4.7561457786708010067 ,13.512028629210130717  ] 
dist 43=[-5.9892776393415662168 ,11.066874223943742206  ] 
dist 44=[-6.7806467550137470264 ,10.471329782566657336  ] 
dist 45=[-7.2371882484386221038 ,9.9311427579773283013 ] 
dist 46=[-7.3402423927042830076 ,9.7008145410683797968 ] 
dist 47=[-6.7233178301790185962 ,2.8026039367793104868 ] 
dist 48=[-6.6564622986485550327 ,2.0519675077098605500 ] 
dist 49=[-6.0101179574477029335 ,.33131450012768945945] 
dist 50=[-6.2423883092710505560 ,.00318030926149500202] 
dist 51=[-7.1003239879489061171 ,-1.9915092267512327969 ] 
dist 52=[-7.8249492672269887806 ,-1.2934201216870638746 ] 
dist 53=[-8.2327313943834205685 ,.51927697522943447593] 
dist 54=[-8.3266406415762145366 ,1.7424420668043086419 ] 
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dist 58=[-3.2287281321356878173 ,4.8835423175138496531 ] 
dist 59=[-2.6840677613189476045 ,5.1365659065366287410 ] 
dist 60=[-2.5481869108584160760 ,5.2001573029578318856 ] 
dist 61=[-2.4600839258632037928 ,1.5805997331766618096 ] 
dist 62=[-2.4380951145212165666 ,1.6357448063554072698 ] 
dist 63=[-.35859457099066463308,1.7477451855235494361 ] 
dist 64=[-.11498620540083130365,1.7833247577292805430 ] 
dist 65=[.45029521506841479909,1.7859386864387687467 ] 
dist 66=[.53641677438864960389,1.7668837962567286944 ] 
dist 67=[.87128349928140304981,1.5883229107355210720 ] 
dist 68=[.4892062020390097073 ,1.5333923215261575886 ] 
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dist 70=[-.16176700212834424594,1.6433936457448394734 ] 
dist 71=[-.38098010429551489159,1.6748952060301245291 ] 
dist 72=[-.58984736022379846608,1.6738433057818708436 ] 
dist 73=[-.77092926495443265449,1.6337306156660293888 ] 
dist 74=[-.97194718594379149607,1.6095665247972804695 ] 
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dist 80=[-.9933270667208901735 ,.32724816474201967306] 
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dist 86=[-1.2939418195512383277 ,.28288755626874172841] 
dist 87=[-.38231612602048048594,.39265895820238680254] 
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dist 91=[-.3109999880005764362 ,.67290664054077975079] 
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dist 97=[-.0425576638492236611 ,.2436085103625966544 ] 
dist 98=[-.03141062989653108151,.24175255663794287612] 
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dist 100=[-.01572453215549809280,.28127037318359103073] 
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dist 104=[-.18088289235944561592,.30228829459354562149] 
dist 105=[-.2078118598553809745 ,.2918895201994672206 ] 
dist 106=[-.22358276231362834063,.28682043638516936446] 
dist 107=[-.23390634366595956409,.24447160386851630181] 
dist 108=[-.23921333867168049684,.23361725487168754697] 
dist 109=[-.24155919577587823396,.21605729562929102592] 
dist 110=[-.24012725764917576001,.21014546329922819925] 
dist 111=[-.2361407921580353791 ,.07086692063133808874] 
dist 112=[-.23332960525981420989,.05204477983978232657] 
dist 113=[-.21453836496841829079,.01053241265394483397] 
dist 114=[-.20942550775284350199,.00088370408897820350] 
dist 115=[-.19121471967870470774,-.03035518323665894302] 
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dist 118=[-.14020878406481474786,-.01897998775577319344] 
dist 119=[-.04633448479735964682,-.00596084128286228835] 
dist 120=[-.04627939497508236018,.00287183264482221678] 
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dist 122=[-.04429842606275735395,.01701796980568823268] 
dist 123=[-.03590982116537814006,.02292483592919588095] 
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dist 128=[.00023156572090149656,.03056021102311201301] 
dist 129=[.00807848125138389903,.02985154999622984665] 
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dist 177=[-.00097563947590335554,-2.99980466927654158240e-05] 
dist 178=[-.00128174800286829240,-.00010175411053295941] 
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dist 180=[-.00168363482596116287,-.00055868693439400123] 
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dist 182=[-.00179072337481936229,-.00025858348959994943] 
dist 183=[-.00070619179768650343,-4.55396972562431179520e-05] 
dist 184=[-.00070299355988461918,9.79547609669252868930e-05] 
dist 185=[-.00067347352179610439,.00021523320057398411] 
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dist 187=[-.00054281583635690987,.00041694769252707316] 
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dist 190=[-.00047663116579689674,.00051615870565168378] 
dist 191=[-6.54781714501493032550e-05,.00051869975652534661] 
dist 192=[-1.60477051086296314460e-05,.00051653066299638472] 
dist 193=[9.82383144809026823260e-05,.00049679913069888919] 
dist 194=[.00011614284744669045,.00049125780764714154] 
dist 195=[.00024830498351466217,.00040615340232886386] 
dist 196=[.00026212085946733233,.00038535828241122736] 
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dist 198=[7.35319997525770855900e-05,.00039909314995868873] 
dist 199=[-3.99666452211873887140e-05,.00039784238284409401] 
dist 200=[-.00011607056284388024,.00039543773837195659] 
dist 201=[-.00017790361167285641,.00037655430168200438] 
dist 202=[-.00023474014941483503,.00037362138775043868] 
dist 203=[-.00028270019061980137,.00029829593696267633] 
dist 204=[-.00030928905648500212,.00028066292190586332] 
dist 205=[-.00032486558031139750,.00026696815835342014] 
dist 206=[-.00032887733081832640,.00026345603178470858] 
dist 207=[-.00019380988722716432,7.69554909758285031210e-05] 
dist 208=[-.00019473412211700043,5.54804136072380281870e-05] 
dist 209=[-.00019567029712339794,7.60646000560976449700e-06] 
dist 210=[-.00019684894528291646,-2.85970703600918901930e-06] 
dist 211=[-.00023308647092913253,-5.42911731534484395840e-05] 
dist 212=[-.00025359627411769310,-6.33062316373049229120e-05] 
dist 213=[-.00026552988053576476,-5.10079174601965027600e-05] 
dist 214=[-.00026854122198639648,-1.72454578277012950350e-05] 
dist 215=[-.00010765883330111037,1.65801819033785128610e-05] 
dist 216=[-.00010681949057248477,3.92804984470920862730e-05] 
dist 217=[-.00010347148477095968,5.77485362655094031190e-05] 
dist 218=[-.00010148337078381392,7.47694587655990983690e-05] 
dist 219=[-8.89987783305448025220e-05,8.91670765116055199270e-05] 
dist 220=[-8.57115425742154991220e-05,9.72189643964533910300e-05] 
dist 221=[-7.86664684725455403240e-05,.00010201630579234514] 
dist 222=[-7.62603320964852673900e-05,.00010349133119333300] 
dist 223=[-3.69750261691957754880e-05,.00010332403906521849] 
dist 224=[-3.11074345600198068930e-05,.00010239762092365061] 
dist 225=[-1.85647857641299869290e-05,9.92588886292875412590e-05] 
dist 226=[-1.51792003570255532680e-05,9.74450743073871653540e-05] 
dist 227=[-2.55117088498755845310e-06,8.61553580599634421560e-05] 
dist 228=[6.08185914274912056000e-08,8.31989561316329826260e-05] 
dist 229=[3.60458971048594220590e-06,7.21288213971655229520e-05] 
dist 230=[-1.31423379498359968690e-06,5.41042022016206393530e-05] 
dist 231=[-1.05832646489695791540e-05,5.03082014218324661890e-05] 
dist 232=[-1.68115605013834857880e-05,4.99706231949075124150e-05] 
dist 233=[-2.18871764913764163370e-05,4.77191067957756587560e-05] 
dist 234=[-2.65794364049914922770e-05,4.71914418856348905720e-05] 
dist 235=[-3.05586245503561873900e-05,3.84412071605019454310e-05] 
dist 236=[-3.28029547034216764440e-05,3.64031532658542704480e-05] 
dist 237=[-3.41651394667307303220e-05,3.42443780021970196770e-05] 
dist 238=[-3.46417386277506289440e-05,3.32751130295521336160e-05] 
dist 239=[-3.47037724887692353480e-05,1.13837717721558360520e-05] 
dist 240=[-3.44198454718238587470e-05,9.77913590630426284940e-06] 
dist 241=[-3.38347600901572243980e-05,6.37201729197497658790e-06] 
dist 242=[-3.34424104357382835090e-05,5.44874659570122156780e-06] 
dist 243=[-3.13295093089561873600e-05,1.99835981849636651820e-06] 
dist 244=[-3.06594263969507987200e-05,1.26969509509667568490e-06] 
dist 245=[-3.02149179152247591740e-05,2.64865173199683979890e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 0, 2, 0, 1] 
dist 0=[119.10628267723043316   ,119.10628267723043316   ] 
dist 1=[117.67186773597501492   ,120.12601512872008674   ] 
dist 2=[115.35148225682117956   ,120.78915700977932950   ] 
dist 3=[112.02058610946399014   ,121.03853385146180284   ] 
dist 4=[104.51176147635171891   ,120.58526235218539346   ] 
dist 5=[96.115518145646072726  ,119.30602651974265128   ] 
dist 6=[85.346434839273990569  ,118.48346014614118233   ] 
dist 7=[71.512733620926702721  ,98.218517813133312768  ] 
dist 8=[61.303912502805919940  ,95.115285316449469940  ] 
dist 9=[51.945258122171574396  ,86.220363169151181635  ] 
dist 10=[41.474669885912414799  ,84.846653358496117717  ] 
dist 11=[31.227892749697587306  ,66.913272748038569406  ] 
dist 12=[22.744018870885430978  ,65.653205742868547838  ] 
dist 13=[13.979802772851144902  ,59.412163653878835624  ] 
dist 14=[2.5913508533163452779 ,58.450622096750300271  ] 
dist 15=[-8.1653377804461363717 ,18.935220656777442573  ] 
dist 16=[-14.422318728540160327  ,17.117832721808341200  ] 
dist 17=[-18.602177266972092006  ,9.4933208683186135325 ] 
dist 18=[-21.086639640700802804  ,8.1138573645367581875 ] 
dist 19=[-22.739136544018301887  ,5.5176791718602452370 ] 
dist 20=[-23.598877021911214116  ,4.9211193964221299146 ] 
dist 21=[-24.078480501967785595  ,3.1756597589980513032 ] 
dist 22=[-25.590240568449131524  ,2.8987300640566779895 ] 
dist 23=[-27.778426590656645454  ,3.0029897827738979724 ] 
dist 24=[-28.863225415530795018  ,3.5996793449429810479 ] 
dist 25=[-29.317558945431891882  ,4.4182370561345650890 ] 
dist 26=[-29.410444427352839025  ,5.4112420148429389778 ] 
dist 27=[-26.915614352767571264  ,6.6948888390917178692 ] 
dist 28=[-24.277254067391529239  ,8.6758555500255457232 ] 
dist 29=[-21.094471781753876881  ,10.570080731737759682  ] 
dist 30=[-20.839753139957631414  ,11.512137415672110386  ] 
dist 31=[-4.5455520637161216617 ,11.996295095066191211  ] 
dist 32=[-2.6141911890574015731 ,12.069589277574102042  ] 
dist 33=[1.9072926606685951928 ,11.856913831964549561  ] 
dist 34=[2.5826303622318197463 ,11.948005308290374998  ] 
dist 35=[7.7926278912035781646 ,11.557158671098965053  ] 
dist 36=[4.9594136202079940975 ,11.327189782649438447  ] 
dist 37=[2.0482288795938572771 ,12.428049142347378716  ] 
dist 38=[.01850184717005350508,13.084368609802569281  ] 
dist 39=[-1.7068243133395479205 ,13.454474366302024895  ] 
dist 40=[-3.4117514278294607466 ,13.481127268808117772  ] 
dist 41=[-4.9272674589666818379 ,13.242015945561638217  ] 
dist 42=[-5.9019357348657081803 ,13.047927896498444329  ] 
dist 43=[-7.2860532492575591343 ,11.386476541423399885  ] 
dist 44=[-8.1020193098499782457 ,10.935028088573151421  ] 
dist 45=[-8.5783449883121502338 ,10.208064108472320098  ] 
dist 46=[-8.6984627734340788555 ,9.9527111224640042982 ] 
dist 47=[-7.8508552343190069582 ,4.3606617931384600479 ] 
dist 48=[-7.7680314797291958516 ,3.6611257071915479544 ] 
dist 49=[-7.0230234030567309154 ,2.0941453328660082027 ] 
dist 50=[-7.6160840676113633799 ,1.7079427609100428204 ] 
dist 51=[-9.1012228162975496383 ,-.06597342809285284325] 
dist 52=[-9.9147694333317530254 ,.02670732440268818183] 
dist 53=[-10.375827117668569884  ,1.8568089110064140962 ] 
dist 54=[-10.462446299688265944  ,3.0948887987890078939 ] 
dist 55=[-2.9321036307762213177 ,4.1100096413895738638 ] 
dist 56=[-2.7728851041481393427 ,5.0555082183570116515 ] 
dist 57=[-2.6658871035760785096 ,5.8597465975466361610 ] 
dist 58=[-2.6552753455180978125 ,6.3584298441346829588 ] 
dist 59=[-2.1980569577653113928 ,6.6435285169367926709 ] 
dist 60=[-2.0850798331299797552 ,6.6913540106317874198 ] 
dist 61=[-2.0081688594340687954 ,1.5293423942147210036 ] 
dist 62=[-1.9877898375235606727 ,1.6666744188169297176 ] 
dist 63=[-.28834636390320333073,1.7651622471105361679 ] 
dist 64=[-.08903373705381307253,1.7871128171232888795 ] 
dist 65=[.37463380246329267697,1.7783603807892278973 ] 
dist 66=[.44404079407010276095,1.7697323267204093458 ] 
dist 67=[.77784054853735554467,1.5149813799104546356 ] 
dist 68=[.49308075811229169105,1.4465134217664367958 ] 
dist 69=[.20374451228796672553,1.3875845347105075388 ] 
dist 70=[.00508697621103217255,1.3638394100911612080 ] 
dist 71=[-.16098070642834700247,1.3843555143983894163 ] 
dist 72=[-.3210346641325682279 ,1.3820557639924207283 ] 
dist 73=[-.50751710865771776268,1.3431089599058268022 ] 
dist 74=[-.7088449480614778619 ,1.3246208551162899141 ] 
dist 75=[-.89359128413071646942,1.1293670360204766383 ] 
dist 76=[-.99368861317992970328,1.0791313335632843872 ] 
dist 77=[-1.0499944909173719012 ,1.0094733414537481707 ] 
dist 78=[-1.0623920555181621074 ,.98164255559529753652] 
dist 79=[-.67951510446667820856,.32129237207248995843] 
dist 80=[-.67092559851173487876,.23684158164244834584] 
dist 81=[-.59173040735671939211,.04680353347929768025] 
dist 82=[-.7271267968421878398 ,.00656231818692252047] 
dist 83=[-.87255361255811084017,-.20339540874931996776] 
dist 84=[-.95394472194737613583,-.11606236677145127238] 
dist 85=[-1.0010491032683820766 ,.06578929534440152518] 
dist 86=[-1.0123004494990875283 ,.18815487700815770257] 
dist 87=[-.36475458601022957916,.28788342395497579593] 
dist 88=[-.36272471839032698905,.37989010826504149824] 
dist 89=[-.35433410057654329484,.45762296007945794131] 
dist 90=[-.34855349727212785319,.5006973810764673677 ] 
dist 91=[-.31067161117653263154,.52577994784211442204] 
dist 92=[-.30047554046635543132,.53209917539738679959] 
dist 93=[-.27568113490627437073,.35230899199509472781] 
dist 94=[-.26650174212155010612,.36392812176722582437] 
dist 95=[-.14530024224996600797,.36927364158817983658] 
dist 96=[-.12607904181125844221,.36799191050883559926] 
dist 97=[-.08551441031153241041,.35992795165768714553] 
dist 98=[-.07446623618560888647,.35383779092190812804] 
dist 99=[-.03304432492761733850,.31300335038329028688] 
dist 100=[-.02411597789586434365,.30189182262860846393] 
dist 101=[-.01152831571716766886,.25898029708122563452] 
dist 102=[-.01334817175210560032,.22298972123863106456] 
dist 103=[-.03442662683905761938,.22282976931673940222] 
dist 104=[-.06388548213166111446,.2215961174555703157 ] 
dist 105=[-.09715432976421124410,.2114562770187247107 ] 
dist 106=[-.12782610497227981225,.20960199297090296634] 
dist 107=[-.15373226764682043284,.16829977824635566867] 
dist 108=[-.16808486432028589382,.15853661848960791149] 
dist 109=[-.17644140337460420294,.15025091733090833416] 
dist 110=[-.17854661407741938272,.14746536154864160829] 
dist 111=[-.12039052378895451918,.04275599691397605019] 
dist 112=[-.12167894917782450339,.03739205706869480490] 
dist 113=[-.12234993524136913904,.02570624559136678290] 
dist 114=[-.12234861605679133655,.02244990147423601125] 
dist 115=[-.12193233357731021083,.00971646081790510450] 
dist 116=[-.12095550334414029228,.00714547882368301028] 
dist 117=[-.11941106346958242375,.00543754952345584985] 
dist 118=[-.11674133180782466834,.01850486620102430289] 
dist 119=[-.00765258217169409664,.02916230558879480710] 
dist 120=[-.00370345179475174744,.03901657133890314045] 
dist 121=[.00560653598193891679,.04736483699042034272] 
dist 122=[.00696718310048552758,.05229861629875739263] 
dist 123=[.01828141106395614853,.05517392036547657354] 
dist 124=[.01998953684570504597,.05584371173995946151] 
dist 125=[.02182971393156075426,.02954168336484893543] 
dist 126=[.02165052096201039584,.03068747473934027932] 
dist 127=[.02090423123701581816,.03117840519897539722] 
dist 128=[.01921078419668215791,.03116440739007471125] 
dist 129=[.01708448319789476166,.03016564833204093831] 
dist 130=[.01461940772349178608,.02990400136781579030] 
dist 131=[.01148565126870267782,.02474728350215006295] 
dist 132=[.00670430552343858906,.02347455448201992438] 
dist 133=[.00189261426146549685,.02227664445546912561] 
dist 134=[-.00136182227988243927,.02171219269349805856] 
dist 135=[-.00403512000228229848,.00580784101905516122] 
dist 136=[-.00653990645989463920,.00415013110381615445] 
dist 137=[-.00975680087391796852,.00037534142508576775] 
dist 138=[-.01302443488330359113,-.00037144642948135921] 
dist 139=[-.01579159984284383410,-.00466680160448947866] 
dist 140=[-.01740936401241928215,-.00537675421474168771] 
dist 141=[-.01836610205161062091,-.00668365150676163763] 
dist 142=[-.01858826422854892216,-.00692158738224983669] 
dist 143=[-.0109623923578352314 ,-.00725216401979706719] 
dist 144=[-.01079664102632101263,-.00718080086513081077] 
dist 145=[-.00927338836952559502,-.00692386035716637391] 
dist 146=[-.00887576137452418191,-.00635388148392844262] 
dist 147=[-.00827309010728726424,-.00445821768262162090] 
dist 148=[-.00805249055485378610,-.00156117196620809729] 
dist 149=[-.00525993234310924278,.00134316920082836548] 
dist 150=[-.00521107443527612857,.00329164291803823657] 
dist 151=[-.00062514972015260820,.00487535800479116793] 
dist 152=[-.00011832378573486403,.00633154336153700429] 
dist 153=[.00115522360434607645,.00756016026787974997] 
dist 154=[.00134262274703610319,.00824037614180321794] 
dist 155=[.00243266499267996808,.00863659080933827840] 
dist 156=[.00253234269747054623,.00873628754115459279] 
dist 157=[.00260188583163016003,.00358067942040497338] 
dist 158=[.00255854596989461308,.00370587989427220038] 
dist 159=[.00244729118831833295,.00375328362133358149] 
dist 160=[.00221729986146505730,.00374356656559179259] 
dist 161=[.00193460826709050633,.00363766072711349000] 
dist 162=[.00161408646189203685,.00358186796317583607] 
dist 163=[.00121100451776124743,.00307350675011377484] 
dist 164=[.00060048992766676955,.00294120586906332748] 
dist 165=[-1.25194796601181937790e-05,.00273962046368421997] 
dist 166=[-.00042552293295170063,.00266640148325868778] 
dist 167=[-.00076316319088692077,.00091631804968387526] 
dist 168=[-.00110852520018143468,.00068481499875032625] 
dist 169=[-.00163273417761021909,.00016623145696727954] 
dist 170=[-.00211466116713320316,5.26089868178631864580e-05] 
dist 171=[-.00252125696702959142,-.00051468619238432118] 
dist 172=[-.00274637919146672427,-.00061380423650824940] 
dist 173=[-.00287762485944317753,-.00078099664975705962] 
dist 174=[-.00291062006038492889,-.00081397668124499604] 
dist 175=[-.00156565777828996406,-.00083457480377778589] 
dist 176=[-.00154800773168054298,-.00081838819065710811] 
dist 177=[-.00127706615783429289,-.00067946896829722383] 
dist 178=[-.00121103101280047612,-.00052220535599091447] 
dist 179=[-.00114022963107622609,-.00032558678994005704] 
dist 180=[-.00110426785034593743,-2.89980428709020000000e-05] 
dist 181=[-.00062297292154883355,.00026838507547597984] 
dist 182=[-.00061595358046750176,.00046816272993029457] 
dist 183=[-.00024081949213716328,.00063087697401411323] 
dist 184=[-.00020845266895812199,.00078110527191474230] 
dist 185=[-8.43706553387402837280e-05,.00090833145480641872] 
dist 186=[-5.87598644522983444470e-05,.00097971870744719450] 
dist 187=[-1.64280367984656053870e-05,.00102683207972308985] 
dist 188=[-6.25034424903619458250e-06,.00103793796007387774] 
dist 189=[.00020337786223290024,.00061780702704228577] 
dist 190=[.00021122123738828301,.00063052343535648604] 
dist 191=[.00020547997527855978,.00063200454728204107] 
dist 192=[.00016692792871850602,.00062842764208682428] 
dist 193=[.00011997712120824508,.00060495508313616624] 
dist 194=[6.72654738519590160010e-05,.00059594479600871569] 
dist 195=[1.29840410263677831900e-06,.00050068808739272103] 
dist 196=[-9.82875557958607573030e-05,.00047690790409685325] 
dist 197=[-.00019818832199826729,.00044430117716933500] 
dist 198=[-.00026540732323362173,.00043137911475425063] 
dist 199=[-.00032027901670642619,.00013584815626054338] 
dist 200=[-.00037115602608978433,.00011779005459382829] 
dist 201=[-.00041440124529620649,7.89583306999894728160e-05] 
dist 202=[-.00043897170824332132,6.82798396099598447190e-05] 
dist 203=[-.00045411710360585100,2.74308161289581792570e-05] 
dist 204=[-.00045994128538644632,1.89829265775886305550e-05] 
dist 205=[-.00046093404292487539,5.21777666198283601800e-06] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 1, 2, 2, 0, 2] 
dist 0=[101.68974595940899050   ,101.68974595940899050   ] 
dist 1=[98.207227468570251800  ,103.08801748683103941   ] 
dist 2=[94.173939763318451500  ,103.68444136907527670   ] 
dist 3=[90.582413455020761468  ,103.97545527246206053   ] 
dist 4=[86.664695841803585052  ,103.78169281752794705   ] 
dist 5=[81.322385806832288052  ,100.90631169207919754   ] 
dist 6=[75.509597860473569754  ,99.956905276383662431  ] 
dist 7=[69.709860728854328254  ,99.260298112509524458  ] 
dist 8=[62.824462012525344225  ,98.492121104996219703  ] 
dist 9=[52.673557622757292781  ,75.947712663354410969  ] 
dist 10=[42.502697695933227063  ,71.321117553123736794  ] 
dist 11=[35.535992647293120005  ,64.358564401020658716  ] 
dist 12=[29.587716057600304263  ,62.253889540187102404  ] 
dist 13=[23.481857907123963068  ,58.760708635354658500  ] 
dist 14=[17.751122268173752064  ,45.578033644481358094  ] 
dist 15=[13.300302439239115608  ,41.889460574381768226  ] 
dist 16=[5.4670950561263049139 ,40.688390823878893882  ] 
dist 17=[-1.6796041929010887639 ,16.136074180533861468  ] 
dist 18=[-7.2079842773086562450 ,13.059417211499434498  ] 
dist 19=[-11.991611733048131768  ,5.8297173799560091805 ] 
dist 20=[-15.965744204845282432  ,4.7631435382733025419 ] 
dist 21=[-18.269357950067298403  ,-4.5065001546879199932 ] 
dist 22=[-20.394762012698782579  ,-6.0465759220624671196 ] 
dist 23=[-22.360209463874463155  ,-7.0825627829805080186 ] 
dist 24=[-23.653074835582093197  ,-3.8092246470460178426 ] 
dist 25=[-24.421449156710793238  ,-1.2326681535632247823 ] 
dist 26=[-24.545494011370659589  ,1.2300901824020939997 ] 
dist 27=[-23.965095774768583059  ,4.0666117211435714368 ] 
dist 28=[-23.864710509384262851  ,6.8311417666123636769 ] 
dist 29=[-19.836410766671021880  ,9.0164525499496632326 ] 
dist 30=[-18.846243007494495130  ,11.151772186344976742  ] 
dist 31=[-18.134674411283268061  ,13.727495101040668284  ] 
dist 32=[-17.931315144308439863  ,16.025424525855370971  ] 
dist 33=[-4.6304340739436324686 ,17.060542136146716475  ] 
dist 34=[-2.0348642533665773542 ,17.549012697866813505  ] 
dist 35=[-1.7911447820206228251 ,17.671238956063562021  ] 
dist 36=[-1.3425413633691295771 ,15.983422427814164711  ] 
dist 37=[-1.2336638660514356466 ,15.539877382415488264  ] 
dist 38=[-.90390073774678747742,15.278556586162730636  ] 
dist 39=[-.82454518426742014462,15.212408795855897290  ] 
dist 40=[-.80709052439544889827,11.535279399234588356  ] 
dist 41=[-.86679952575552031557,11.767693477867583561  ] 
dist 42=[-1.1851300186325242550 ,11.763027224664669284  ] 
dist 43=[-3.4577886484916282416 ,11.490228984668038314  ] 
dist 44=[-5.4706068225688723422 ,11.318487860806596923  ] 
dist 45=[-6.7547538419597109511 ,9.8020767094487118288 ] 
dist 46=[-7.7261455778687808918 ,9.4003884084555922199 ] 
dist 47=[-8.4992694290564520289 ,8.7686660218152907621 ] 
dist 48=[-9.0723710278704261214 ,8.5445018286074733382 ] 
dist 49=[-9.2502095438078146059 ,3.3042315246764428810 ] 
dist 50=[-9.2591218200051769520 ,2.4111827555682017482 ] 
dist 51=[-9.1604291501593648928 ,.78075631882884141087] 
dist 52=[-8.2191592400611629931 ,.42365456273500054325] 
dist 53=[-8.3268948996127477897 ,-.34811347660298737542] 
dist 54=[-8.7879442749066334819 ,-.46950421426617044238] 
dist 55=[-9.0980895031199802975 ,-.48985940390955091155] 
dist 56=[-9.1592460943295120861 ,.70290420316044979664] 
dist 57=[-2.4620595153033740709 ,2.3758391681903976923 ] 
dist 58=[-2.4720428991099718439 ,3.7417344077577265261 ] 
dist 59=[-2.4075631827085028493 ,5.0046345996155095115 ] 
dist 60=[-2.3982289573859164826 ,6.0725514744232158491 ] 
dist 61=[-1.9777598472324638744 ,6.6646948526669584439 ] 
dist 62=[-1.8744676933513881008 ,7.0096450053991547576 ] 
dist 63=[-1.8059704221712286355 ,7.0965650606293774601 ] 
dist 64=[-1.7900098063199289206 ,2.1846302196670221604 ] 
dist 65=[-.23890714921109389107,2.2171046276919350225 ] 
dist 66=[-.05763086338120212870,2.2147385362455251929 ] 
dist 67=[-.00465943288616040338,2.2095176371910248364 ] 
dist 68=[.03986440802804660711,1.9007316735299031469 ] 
dist 69=[.05045129623473221452,1.8175083573754601217 ] 
dist 70=[.08762249628463550702,1.7588426424837384018 ] 
dist 71=[.09492224422042544792,1.7316903315830903045 ] 
dist 72=[.09643171073814929210,1.2170738433967016735 ] 
dist 73=[-.13321522161536496798,1.2356029946726645585 ] 
dist 74=[-.42394849225199023906,1.2333558257242897915 ] 
dist 75=[-.70038088732704757628,1.2002546855375369821 ] 
dist 76=[-.93970686986875470782,1.1822863083223640715 ] 
dist 77=[-1.0832018917667989994 ,1.0160018283663119134 ] 
dist 78=[-1.1812554535270571229 ,.97259944835997990521] 
dist 79=[-1.2402721224479146118 ,.90692450218920856142] 
dist 80=[-1.2721821839358209187 ,.88284298257761932917] 
dist 81=[-1.2754280648618986711 ,.30154607461222476273] 
dist 82=[-1.2426614304711766089 ,.22408495059440506428] 
dist 83=[-1.2330298127363915714 ,.05020091709595753071] 
dist 84=[-1.0288291505147523574 ,.01274926608450966492] 
dist 85=[-.97751313414184288567,-.01086544538988215366] 
dist 86=[-.93012784951962735354,-.01648614703639199533] 
dist 87=[-.93613646112537166248,-.01733737382962412978] 
dist 88=[-.94701073914379804177,.06319293470392188986] 
dist 89=[-.28706946154750291179,.24257202156311700965] 
dist 90=[-.28707783198792695024,.38905892909473557966] 
dist 91=[-.27774243913779469171,.52475878057543589419] 
dist 92=[-.27582976125807880404,.64058347774166688972] 
dist 93=[-.22712654875309540266,.71000373964102133349] 
dist 94=[-.21523838205526860781,.74918595459790914211] 
dist 95=[-.20549683298311483412,.75840291465613862233] 
dist 96=[-.20187759473550195609,.29809406819181930593] 
dist 97=[-.03235249124662023409,.29989591994046400799] 
dist 98=[-.01901128500151759305,.29340362430481052285] 
dist 99=[-.02121698197069545588,.29245673214630152992] 
dist 100=[-.02308112272663724868,.24262212544521560151] 
dist 101=[-.02489451926698351927,.23019969146795618399] 
dist 102=[-.02647680805349184101,.22224677144263973531] 
dist 103=[-.02742529858000233747,.22033241290800533162] 
dist 104=[-.02806561028463031769,.16036755884574265539] 
dist 105=[-.02842643444982616153,.16117546305501279272] 
dist 106=[-.05229332751563064617,.16053996382063974328] 
dist 107=[-.08700742322029910543,.15424076327772805834] 
dist 108=[-.11684102577069111062,.15270304555530673525] 
dist 109=[-.13436302238969064777,.12534338423749442996] 
dist 110=[-.1458957644152875463 ,.11871977647459951615] 
dist 111=[-.15195701581678760701,.11222830237778209093] 
dist 112=[-.15478343006584346342,.10921430454702406807] 
dist 113=[-.15466519840826959615,.02831151792772902329] 
dist 114=[-.15089600548656099202,.01863256345218075878] 
dist 115=[-.14867783577491616322,-.00029962030218012351] 
dist 116=[-.12821080260146002317,-.00409700921920242625] 
dist 117=[-.1228092095768123156 ,-.02514832204251721158] 
dist 118=[-.11462796610196531701,-.02866496165370124688] 
dist 119=[-.11160988598938814849,-.02222000079742988079] 
dist 120=[-.09729971669974000335,.01775661965648541077] 
dist 121=[-.03651173235774099606,.04458838472507219303] 
dist 122=[-.03644224445955021833,.06640615512632458334] 
dist 123=[-.03502199518088765480,.08647730877920868502] 
dist 124=[-.03481708951777335564,.10341536042275011652] 
dist 125=[-.02815732283351378861,.11279454069105427801] 
dist 126=[-.02657029416420011757,.11825955011536968982] 
dist 127=[-.02544343692492709068,.11963384205188635694] 
dist 128=[-.02519156800331803530,.03669955535882413882] 
dist 129=[-.00236697851068020781,.03674805937030871194] 
dist 130=[.00029334198393286250,.03558216933320652796] 
dist 131=[.00646307099869725906,.03540670108411733040] 
dist 132=[.00737546323228799661,.02901078964045613457] 
dist 133=[.01450977309157623879,.02759602983741169618] 
dist 134=[.01555682780002795002,.02631142662839368256] 
dist 135=[.00850032594795189425,.02604494504404955102] 
dist 136=[5.41347020463746441000e-05,.01835252857613770918] 
dist 137=[-.00564270076335588865,.01843271040269769327] 
dist 138=[-.01030622076846890633,.01833601089984612421] 
dist 139=[-.01465021969689573331,.01770689635201514980] 
dist 140=[-.01835504942578414014,.01742181635176591964] 
dist 141=[-.02048110798253510895,.01482051233470885305] 
dist 142=[-.02181847862539511089,.01415859084796607190] 
dist 143=[-.02239228752613766835,.01315325903324479727] 
dist 144=[-.02252298738634149606,.01279224123160969203] 
dist 145=[-.02243480285660529759,.00419832506953216114] 
dist 146=[-.02158608114605596666,.00305376255538703617] 
dist 147=[-.02134673483681918646,.00049702804107031232] 
dist 148=[-.01763957408979194506,-5.95429121367089216930e-05] 
dist 149=[-.01673289474401368977,-.00282456692434243740] 
dist 150=[-.01576345120677376224,-.00330745918676042059] 
dist 151=[-.01526838326713312536,-.0004732872380748730 ] 
dist 152=[-.01422915286185092696,.00362781706956540850] 
dist 153=[-.00502495695137891956,.00638443004557578070] 
dist 154=[-.00425999462052352676,.00863104674856974626] 
dist 155=[-.00408691994500568047,.01070735530319519349] 
dist 156=[-.00405368340558826898,.01246699413680830018] 
dist 157=[-.00329834327227963437,.01345635475428973103] 
dist 158=[-.00311865308875815899,.01412641656113321738] 
dist 159=[-.00296287351693817033,.01427980194445486302] 
dist 160=[-.00290813851081557434,.00475843525164588404] 
dist 161=[-.00040426586565605942,.00475321091447127958] 
dist 162=[-.00010439149957622226,.00457749589768700845] 
dist 163=[.00059027727171727527,.00455122145047576568] 
dist 164=[.00069794903092112514,.00369457268466843898] 
dist 165=[.00150543200364247775,.00348919196673634380] 
dist 166=[.00162587893012307400,.00334258226688906314] 
dist 167=[.00134206153328284516,.00330727728646390925] 
dist 168=[.00030419116316165410,.00239721012561331681] 
dist 169=[-.00039473628127986068,.00239572648914891507] 
dist 170=[-.00096586150589151862,.00238191401905020463] 
dist 171=[-.00149632325887745165,.00227901040821714940] 
dist 172=[-.00194780868254106702,.00225489635452983847] 
dist 173=[-.00220537737147124828,.00184028529202571722] 
dist 174=[-.00236549378306786908,.00174091107650602382] 
dist 175=[-.00243007113426541055,.00164245943340658629] 
dist 176=[-.00244442210029713881,.00159761973167024797] 
dist 177=[-.00243266064207014894,.00041151986588731876] 
dist 178=[-.00235256564075595800,.00029248193136538441] 
dist 179=[-.00231430665076460639,2.58002346856188166550e-05] 
dist 180=[-.00197535976241714787,-3.07988804001577807280e-05] 
dist 181=[-.00188847660723470653,-.00032101565967694014] 
dist 182=[-.00175378511692429078,-.00037101123015226790] 
dist 183=[-.00170625858009703572,-.00028510898579539609] 
dist 184=[-.00144214649149536082,.00033550252726473617] 
dist 185=[-.00054035081738617670,.00075147037336356323] 
dist 186=[-.00053796229999785525,.00108928007781820056] 
dist 187=[-.00051412930041011635,.00139956013309860826] 
dist 188=[-.00051059352776153483,.00166124245115162266] 
dist 189=[-.00040981453141933163,.00180609044227617051] 
dist 190=[-.00038607288795980060,.00189041679242900214] 
dist 191=[-.00036846701374260256,.00191174547956078824] 
dist 192=[-.00036434737821608225,.00054865944092275151] 
dist 193=[-.00017307235438265344,.00054715998154239892] 
dist 194=[-.00014751586336974558,.00052504656877508517] 
dist 195=[-9.23307854549072291500e-05,.00052167867222864409] 
dist 196=[-7.72388830600516114240e-05,.00043201233986589657] 
dist 197=[-1.97417491006371324750e-05,.00041836227989994626] 
dist 198=[-8.05240919210099171700e-06,.00043446893280614128] 
dist 199=[4.25452661754814285400e-06,.00045368374767285358] 
dist 200=[-.00014292559069683942,.00045999604753183205] 
dist 201=[-.00024179130636547723,.00045983188435173374] 
dist 202=[-.00032232703496220492,.00045560611557502664] 
dist 203=[-.00039672666541613173,.00044354819080217036] 
dist 204=[-.00045978418987833572,.00043646153514930715] 
dist 205=[-.00049528527460147472,.00039210746739174841] 
dist 206=[-.00051674914510792926,.00038045186335686502] 
dist 207=[-.00052407105846016289,.00034742411163938394] 
dist 208=[-.00052348482435517460,.00033651767892596508] 
dist 209=[-.00051943720428965890,.00020929538435857525] 
dist 210=[-.00050116619626356405,.00018739551170641106] 
dist 211=[-.00049087147256601701,.00014314435768813023] 
dist 212=[-.00042399548295768144,.00013122304756978564] 
dist 213=[-.00040654458037690920,8.80688941356803764740e-05] 
dist 214=[-.00037363889328419886,7.77088099674041849690e-05] 
dist 215=[-.00031277440532614561,6.67495913798371749380e-05] 
dist 216=[-.00021521848476415484,6.44086504961595913830e-05] 
dist 217=[-6.06241182908877908650e-05,8.68153575640058272940e-05] 
dist 218=[-6.03045445625881389760e-05,.00012527255168679861] 
dist 219=[-5.76392574661920768560e-05,.00016059721223212408] 
dist 220=[-5.71399819356965977740e-05,.00019039570196530531] 
dist 221=[-4.74091092044952828510e-05,.00020700745549287232] 
dist 222=[-4.59124567361338210850e-05,.00021670096705442487] 
dist 223=[-4.21271375368358311250e-05,.00021906104237217412] 
dist 224=[-4.07034560918358669270e-05,5.63244840552591419940e-05] 
dist 225=[-2.34645425210434741830e-05,5.60350388244929163290e-05] 
dist 226=[-2.06650197603769616510e-05,5.45648142989239078690e-05] 
dist 227=[-1.48000032105040871740e-05,5.35852084140005354420e-05] 
dist 228=[-1.32006979597588954830e-05,4.72207285584628004920e-05] 
dist 229=[-7.21244442161938944590e-06,5.26579155149481440860e-05] 
dist 230=[-5.89773465685591727390e-06,5.65476511596271241040e-05] 
dist 231=[-4.05594578368047460070e-06,5.88542918469399330240e-05] 
dist 232=[-1.27769475265303055720e-05,5.95392293470962806230e-05] 
dist 233=[-2.33190917870257214830e-05,5.93449118091466749180e-05] 
dist 234=[-3.19040431357737484100e-05,5.88360281195259283330e-05] 
dist 235=[-3.98314067996835902170e-05,5.67160002145323012580e-05] 
dist 236=[-4.65485449043526053360e-05,5.55110030029280612600e-05] 
dist 237=[-5.03280956180727047710e-05,4.80518495050586254840e-05] 
dist 238=[-5.26106324672065283060e-05,4.61041305346472545000e-05] 
dist 239=[-5.33836519219560339340e-05,4.23106803639174486730e-05] 
dist 240=[-5.33898845062913930860e-05,4.11035837644761227860e-05] 
dist 241=[-5.29187001503768064670e-05,1.75116271153087143190e-05] 
dist 242=[-5.14932286859922577060e-05,1.41350338171085570750e-05] 
dist 243=[-5.06489993115346774860e-05,6.84464175485919192590e-06] 
dist 244=[-4.53520279356669310010e-05,4.88885991971114093120e-06] 
dist 245=[-4.39580461511908860470e-05,1.72895146647869669580e-06] 
dist 246=[-4.01898730764901333520e-05,1.07209012819073981190e-06] 
dist 247=[-3.64441460359074785870e-05,2.02252440598491724350e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 2, 2, 2, 0, 0, 2] 
dist 0=[144.59433133713358879   ,144.59433133713358879   ] 
dist 1=[139.33678847911428552   ,146.12429599302525033   ] 
dist 2=[132.25060950251947610   ,146.26562395292057351   ] 
dist 3=[123.44850060121583653   ,146.02384009222378050   ] 
dist 4=[111.87630278304501304   ,144.35561725698515398   ] 
dist 5=[93.776374882879841834  ,132.95477931167945939   ] 
dist 6=[75.290916958409114085  ,129.75250758637737008   ] 
dist 7=[62.179970135879047859  ,126.42678930917000892   ] 
dist 8=[50.699344508352720874  ,109.88797966992754250   ] 
dist 9=[38.678512677596686889  ,95.162056844422422661  ] 
dist 10=[27.413014265657697386  ,91.002504985245426575  ] 
dist 11=[18.920617853708218305  ,90.143708580603257235  ] 
dist 12=[10.899426396553004572  ,48.633433291089580185  ] 
dist 13=[1.4813029309118124476 ,33.798641490369744856  ] 
dist 14=[-7.1955234575627378429 ,31.181104859346035831  ] 
dist 15=[-12.274039461275141939  ,27.286355473947166742  ] 
dist 16=[-16.938768317776088240  ,23.445109220828721910  ] 
dist 17=[-23.030705452186266299  ,-12.312598891757286270  ] 
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dist 151=[-.00747018976357588440,-.00210122477960674680] 
dist 152=[-.00690483693628763840,-.0002625396449284609 ] 
dist 153=[-.00577636368322730435,.00158331600545291750] 
dist 154=[-.00546048292738464965,.00282537309649437600] 
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dist 158=[-.00043031454926576277,.00603599409102839280] 
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dist 160=[-7.00765838417868391200e-05,.00641169888624110253] 
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dist 165=[.00164701418801471840,.00184213537910494514] 
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dist 167=[.00107487851862602105,.00175424209590021073] 
dist 168=[.00059150003753825046,.00152733342406202867] 
dist 169=[.00010600608718429557,.00135128085220109993] 
dist 170=[-.00022128398061525485,.00128473206615087723] 
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dist 172=[-.00073828182001390555,.00017117192103575630] 
dist 173=[-.00095071523679206566,4.08415405959567536380e-05] 
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dist 176=[-.00118106164614035799,-.00065990548198492579] 
dist 177=[-.00118852240687958385,-.00071225551661661415] 
dist 178=[-.00118423640490649960,-.00080926374330107916] 
dist 179=[-.00113936474159088166,-.00082384612734900104] 
dist 180=[-.00112765343950487250,-.00083223459402506844] 
dist 181=[-.00102284272258760294,-.00072978975430910808] 
dist 182=[-.00097650967738582816,-.00059495234532714872] 
dist 183=[-.00096801578047259356,-.00042666881201939481] 
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dist 186=[-.00069767100963257873,.00025131717942719215] 
dist 187=[-.00068485144908608048,.00038983035590631225] 
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dist 189=[-.00014899927211339900,.00062477032870075874] 
dist 190=[-2.26399345228076089710e-05,.00068445280068622350] 
dist 191=[4.94259445220257567950e-06,.00071979860475499348] 
dist 192=[.00014115417167400547,.00072869574613007394] 
dist 193=[.00016499276048343821,.00066737418845752873] 
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dist 195=[.00021061126636099080,.00070684296608088442] 
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dist 199=[.00011570776555552895,.00025850291493696476] 
dist 200=[3.57928367693566838190e-05,.00022541873257023539] 
dist 201=[-4.42811378072597024520e-05,.00021667355733523722] 
dist 202=[-9.80191844750304682610e-05,.00019927101930102558] 
dist 203=[-.00014173560552683576,.00019359946866715108] 
dist 204=[-.00018201829753980904,8.61446044960538006720e-05] 
dist 205=[-.00021608383294149671,7.06350692288312343510e-05] 
dist 206=[-.00023511464644758622,3.70255712958326002800e-05] 
dist 207=[-.00024642534417306365,2.79429868914151344980e-05] 
dist 208=[-.00024983757973655524,-6.19292318905706616400e-06] 
dist 209=[-.00024940506187328550,-1.30047784130551906120e-05] 
dist 210=[-.00024705974451422420,-2.28399174806716697960e-05] 
dist 211=[-.00023824099515942142,-2.50288087305910001350e-05] 
dist 212=[-.00013241228129249291,-2.52146054458314219820e-05] 
dist 213=[-.00013156767417709278,-2.35450867681363547330e-05] 
dist 214=[-.00012575455670841100,-2.02348012235718410130e-05] 
dist 215=[-.00012436198075050960,-1.06664554216618145080e-05] 
dist 216=[-.00010148532608087552,1.03046408242200702190e-05] 
dist 217=[-9.60082757189259558680e-05,3.13335385476073350100e-05] 
dist 218=[-9.04383543638042988530e-05,4.54715263505536419960e-05] 
dist 219=[-8.78302059487834397060e-05,5.70005444621645432170e-05] 
dist 220=[-3.04698136038431563930e-05,6.76706223004953883640e-05] 
dist 221=[-2.62193575116454244560e-05,7.67268238580946992940e-05] 
dist 222=[-1.71742784032821656490e-05,8.18480042325910920120e-05] 
dist 223=[-1.47169409274234759660e-05,8.49734609045034521660e-05] 
dist 224=[-5.49524199377574138840e-06,8.61057445670305324020e-05] 
dist 225=[-3.55525901555401069410e-06,8.62989952791508384160e-05] 
dist 226=[-7.93203030121543215270e-07,8.56958952582147702450e-05] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 0, 0, 0, 1, 2] 
dist 0=[131.32727974429149171   ,131.32727974429149171   ] 
dist 1=[130.47359993352041496   ,131.03899548601665921   ] 
dist 2=[128.08317505692765793   ,131.32727974429149171   ] 
dist 3=[122.27404416970334341   ,129.79775618076144880   ] 
dist 4=[114.86068737450200772   ,122.87553994781518641   ] 
dist 5=[106.09079137231337742   ,117.68725208027791881   ] 
dist 6=[94.802357573942600318  ,115.82431907111213194   ] 
dist 7=[77.374630691080683909  ,113.46904666682727684   ] 
dist 8=[59.626885249406317729  ,96.617731913541285766  ] 
dist 9=[47.061238206917659677  ,92.637223982897295938  ] 
dist 10=[36.068348785300578289  ,90.824257067632193708  ] 
dist 11=[24.560288748758249354  ,55.622090398978465404  ] 
dist 12=[13.767043262372438202  ,41.590160275265719709  ] 
dist 13=[5.6038356494737776244 ,38.325332450515520013  ] 
dist 14=[-2.1346446060787600597 ,33.300479601568168308  ] 
dist 15=[-11.261775665216698705  ,32.145003424560701179  ] 
dist 16=[-19.589065864557768921  ,8.0537492464371292827 ] 
dist 17=[-24.151605211559375280  ,3.3087580226185117378 ] 
dist 18=[-27.527595871620986163  ,2.4004604729000437819 ] 
dist 19=[-32.184992348151129296  ,-9.9864824246734465113 ] 
dist 20=[-34.249912672890423143  ,-11.931763533713709408  ] 
dist 21=[-35.190822642399550962  ,-11.254063088473876970  ] 
dist 22=[-35.360014419519339657  ,-9.3281485220236891868 ] 
dist 23=[-32.048332699062241362  ,-5.3206819446272863791 ] 
dist 24=[-31.082558152965474052  ,-.96789221581252715133] 
dist 25=[-30.432840722349747680  ,2.3352819473690575309 ] 
dist 26=[-30.084170141276713131  ,5.4060909169426925134 ] 
dist 27=[-8.8332384795035201896 ,8.8483358709599645264 ] 
dist 28=[-6.2711075625638676110 ,12.170299773175453378  ] 
dist 29=[-.21124361352059725314,14.770514990289898246  ] 
dist 30=[.72772106224694117687,17.294505232784239911  ] 
dist 31=[6.0592186896422780485 ,20.322260760860515502  ] 
dist 32=[9.2735398047880523054 ,22.989894104637142630  ] 
dist 33=[11.355374185455824620  ,24.086200660497094052  ] 
dist 34=[11.704032926485887325  ,24.540826813993010688  ] 
dist 35=[11.948176461214220727  ,24.654253964879759203  ] 
dist 36=[10.808546981618225941  ,21.883791332891093047  ] 
dist 37=[9.2425551234916846935 ,21.159869237131969482  ] 
dist 38=[7.1070552082142864013 ,20.734715050547980496  ] 
dist 39=[3.7068530481167043432 ,20.626916183835341508  ] 
dist 40=[.25279145867863971133,14.922680790330242858  ] 
dist 41=[-2.0971118480925172082 ,14.251316467067455260  ] 
dist 42=[-4.0339271898529088218 ,13.875777284472516763  ] 
dist 43=[-5.8500604935020805032 ,4.5094915806696362024 ] 
dist 44=[-8.0302645197582245666 ,3.4651336643894520116 ] 
dist 45=[-9.7450395482389270923 ,1.0497101174695228422 ] 
dist 46=[-11.010346845212883804  ,.5864274909989561232 ] 
dist 47=[-11.960103014165900161  ,-2.2920949828635043008 ] 
dist 48=[-12.633728499336371354  ,-2.7575259657910358895 ] 
dist 49=[-12.803372447593049821  ,-3.6969708896670915660 ] 
dist 50=[-12.766708701528228446  ,-3.8601607305513985287 ] 
dist 51=[-12.619842348047986781  ,-3.7407657281949041950 ] 
dist 52=[-11.229759184851202456  ,-3.4330129325733758908 ] 
dist 53=[-10.821252251464125942  ,-3.0206070141250201326 ] 
dist 54=[-10.200511954363532502  ,-2.4627768378760351969 ] 
dist 55=[-9.9575609361851997017 ,-1.5776801005216599956 ] 
dist 56=[-3.7932905533552719901 ,1.0662746311826444428 ] 
dist 57=[-3.4713789365878719584 ,3.3635564368914323116 ] 
dist 58=[-3.4457065724963774401 ,5.2375366685955413736 ] 
dist 59=[-.68463381447163771002,6.9683021314509806614 ] 
dist 60=[-.25660762919531403208,8.4312017259638789566 ] 
dist 61=[.51968334492265461481,9.2421358577639863093 ] 
dist 62=[.64171099485255517601,9.7144988715082397929 ] 
dist 63=[1.5376817942947249269 ,9.8334684012842883879 ] 
dist 64=[1.6724056732297247942 ,3.0163481581998666564 ] 
dist 65=[1.9082667464523071105 ,3.0520629694826841729 ] 
dist 66=[1.9426281267766360806 ,3.0308043731338309909 ] 
dist 67=[1.7996274633231044037 ,3.0212131568498886220 ] 
dist 68=[1.5571608493551420207 ,2.5798919146608536949 ] 
dist 69=[1.2714064958052540713 ,2.4643167647624831968 ] 
dist 70=[.90554710807478431382,2.3768529614407507249 ] 
dist 71=[.34507029635520124354,2.3389248598790217542 ] 
dist 72=[-.2188658709683245918 ,1.8637954708877839088 ] 
dist 73=[-.59848690223498903138,1.7455238475889889503 ] 
dist 74=[-.90800354197907138542,1.7011472059167642154 ] 
dist 75=[-1.1937120717923636285 ,.60865902924556247818] 
dist 76=[-1.4351710381130537911 ,.46259211770294515111] 
dist 77=[-1.5692394361290572263 ,.13252944193429181412] 
dist 78=[-1.6546039654970397076 ,.06215557535230269334] 
dist 79=[-1.7288814129796745102 ,-.30818144572751389727] 
dist 80=[-1.7660389221224164460 ,-.37169085505456041617] 
dist 81=[-1.7681216787136399875 ,-.45104299562579127293] 
dist 82=[-1.7691462051370895066 ,-.43471554807869833162] 
dist 83=[-1.7036789082484343806 ,-.39183602894221662599] 
dist 84=[-1.4193231664433701900 ,-.33643600749448111612] 
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8 phat 4 dirichlet min maxes function [0, 0, 0, 2, 2, 1, 0, 0, 1] 
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dist 6=[68.581595780737350818  ,126.73605736523582117   ] 
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dist 8=[49.916303709148797616  ,120.38305828252365797   ] 
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dist 10=[34.208808932363395424  ,99.605012589687096739  ] 
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dist 23=[-26.985854747846507790  ,4.1698144620901127111 ] 
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dist 45=[-1.6455604253578472669 ,4.9662240918641568923 ] 
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dist 60=[-2.8481976778302110649 ,.41783316733234537012] 
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dist 163=[6.30187113499643200740e-05,.00177855650659747246] 
dist 164=[5.01116920472591554510e-05,.00233415080002018593] 
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dist 188=[-.00059416173678837007,.00014962329992087960] 
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dist 200=[-6.12817430318495521030e-05,.00048706582691735181] 
dist 201=[-6.93901961307252366220e-05,.00014814034368774228] 
dist 202=[-7.44337054211272152030e-05,.00014733868875028917] 
dist 203=[-7.64739482711616937740e-05,.00014047988373033406] 
dist 204=[-7.69208818463541514120e-05,.00013946886719755683] 
dist 205=[-7.65661180829956612490e-05,.00011159942725784983] 
dist 206=[-7.39623747029333212980e-05,.00010550539619892420] 
dist 207=[-7.28476105288371030970e-05,.00010007314632426384] 
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dist 209=[-5.89305346175053568900e-05,1.76263824740783540490e-05] 
dist 210=[-5.49090565135255578510e-05,7.84730793599641247020e-06] 
dist 211=[-5.33708062628795921320e-05,-9.83602479462766507800e-06] 
dist 212=[-6.11055479535541033300e-05,9.57696221863327213930e-06] 
dist 213=[-7.52469415885158569560e-05,2.25887590734033935150e-05] 
dist 214=[-8.31377307510612266640e-05,3.31557338881684502410e-05] 
dist 215=[-8.78177090966100220860e-05,4.28614345542317846540e-05] 
dist 216=[-8.92094832477503351340e-05,5.10467496179269087750e-05] 
dist 217=[-8.88712305508170982640e-05,5.55769109844925586240e-05] 
dist 218=[-8.82502189374980573970e-05,5.82134660971588315970e-05] 
dist 219=[-8.43220030867650434590e-05,5.88780529121301162960e-05] 
dist 220=[-8.33101598905629250780e-05,1.99376064098024203370e-05] 
dist 221=[-6.82183728195192723210e-05,1.98353108151828639800e-05] 
dist 222=[-6.45958456846030643370e-05,1.92420619419845719700e-05] 
dist 223=[-6.06823980591584103250e-05,1.88765256243869751960e-05] 
dist 224=[-5.87320402654661368500e-05,1.63973329034705027300e-05] 
dist 225=[-2.08034308460067003870e-05,1.57401738349352638310e-05] 
dist 226=[-1.78474412492344951030e-05,2.62372102622048541500e-05] 
dist 227=[-1.15813245575029632470e-05,3.49425982644570328950e-05] 
dist 228=[-9.88671779903660014890e-06,4.29398846524838311400e-05] 
dist 229=[-7.18580684406444791970e-06,4.96887454851864150570e-05] 
dist 230=[-1.01028283204584972020e-05,5.34367399681638953010e-05] 
dist 231=[-1.27914807287203604920e-05,5.56360903349086968610e-05] 
dist 232=[-1.50660408322458882660e-05,5.62354120025730090820e-05] 
dist 233=[-1.63388352628797673260e-05,2.09384876624390694800e-05] 
dist 234=[-1.70981935619453099040e-05,2.07716904605827107760e-05] 
dist 235=[-1.73340617358066572520e-05,1.99877890420515242640e-05] 
dist 236=[-1.73203577659404507130e-05,1.96078042534464498610e-05] 
dist 237=[-1.71515976706696820200e-05,1.67561196318535723020e-05] 
dist 238=[-1.67257255840235440610e-05,1.60283264596325428950e-05] 
dist 239=[-1.64773673962305520620e-05,1.47608219691367366350e-05] 
dist 240=[-1.49268581157819705570e-05,1.43686665173344842860e-05] 
dist 241=[-1.45200865852976143770e-05,5.29958311385649551280e-06] 
dist 242=[-1.32364763215525699270e-05,4.05413689880321940730e-06] 
dist 243=[-1.29131769648380231190e-05,1.72302260875854216020e-06] 
dist 244=[-8.58230250602927081520e-06,3.06022195793903112940e-06] 
dist 245=[-7.80113232365851515060e-06,3.95710931843278433700e-06] 
dist 246=[-6.26775325690106637110e-06,4.68612380319850397490e-06] 
dist 247=[-5.85660803843730020110e-06,5.35678603316694937580e-06] 
dist 248=[-4.40068695508668089890e-06,6.05936555899759030620e-06] 
dist 249=[-3.66581487220314301800e-06,6.52571482373182433650e-06] 
dist 250=[-3.62328210968516877980e-06,6.81350760599021300070e-06] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 1, 1, 2, 1, 1, 2] 
dist 0=[126.28794064513264355   ,126.28794064513264355   ] 
dist 1=[120.67039222520343494   ,130.07068452718346199   ] 
dist 2=[112.75954887336732570   ,132.52253872518770330   ] 
dist 3=[99.855167216479664814  ,132.85683726274528180   ] 
dist 4=[86.481247254296290555  ,132.27992653651769697   ] 
dist 5=[76.696513405363999826  ,131.34350068880489728   ] 
dist 6=[67.817730106577372415  ,124.57739153488769588   ] 
dist 7=[58.028643591581332144  ,122.20527908871862782   ] 
dist 8=[48.538953715666159408  ,106.97151868888367184   ] 
dist 9=[40.835771189130741067  ,99.174734453617475385  ] 
dist 10=[33.015648202316107827  ,78.208754010382455668  ] 
dist 11=[23.034930604406726718  ,73.810560165664825175  ] 
dist 12=[13.509668515353501731  ,69.758202308290981328  ] 
dist 13=[7.4963841155503319989 ,68.972418283136015133  ] 
dist 14=[2.8919355895393921434 ,44.632330514996473767  ] 
dist 15=[-1.0174498430093275778 ,37.512124565485428517  ] 
dist 16=[-4.2211975441565357461 ,27.238440006374984022  ] 
dist 17=[-12.164057267428414852  ,-2.1095634668487293397 ] 
dist 18=[-19.784593857254778163  ,-1.9122774224493642932 ] 
dist 19=[-24.348337691313697399  ,-.57913741344372264808] 
dist 20=[-27.503610718631594990  ,.99450142943031298588] 
dist 21=[-29.531891317094004965  ,2.1517506747071524586 ] 
dist 22=[-30.800776607158944154  ,3.1412627426300015153 ] 
dist 23=[-30.999534887479293060  ,4.0628055424455008398 ] 
dist 24=[-30.666024616543237117  ,4.7943516375322388599 ] 
dist 25=[-30.296630866776658346  ,5.0375228067288882848 ] 
dist 26=[-26.507123884469397950  ,5.0983939128501994661 ] 
dist 27=[-25.472355097927864306  ,5.1129142711394289094 ] 
dist 28=[-23.945420689504800436  ,3.6077534270876765073 ] 
dist 29=[-23.353580982947013362  ,3.2111968571325062547 ] 
dist 30=[-8.7411820993706477915 ,2.6755041126993889482 ] 
dist 31=[-6.8157734801417573584 ,7.3035050031411505168 ] 
dist 32=[-2.4675456827751247797 ,11.590995209252475300  ] 
dist 33=[-1.8373935867895885590 ,15.534586758775331618  ] 
dist 34=[-1.5871138724552356145 ,18.861305791401516657  ] 
dist 35=[-1.5286179538193312907 ,20.700087685102513471  ] 
dist 36=[-1.3662134961899185045 ,21.765941872886747099  ] 
dist 37=[-1.3321007825836286486 ,22.024155364265377912  ] 
dist 38=[-1.3302370900736971520 ,8.6966871427157463074 ] 
dist 39=[-1.3655174665197041970 ,8.6175918696680158339 ] 
dist 40=[-1.4158610298922355508 ,8.5960870001116023715 ] 
dist 41=[-1.4744234823456947209 ,6.6567225926560374121 ] 
dist 42=[-1.5467699508832098981 ,5.5648562181115363500 ] 
dist 43=[-1.6524673876513452299 ,5.2904750891517172484 ] 
dist 44=[-1.7662737115757826033 ,5.1162187565458029913 ] 
dist 45=[-2.5023891548375063229 ,5.0735972471828680557 ] 
dist 46=[-3.2539181460960944990 ,3.5267288886238348016 ] 
dist 47=[-3.8533895640085011949 ,3.4272100011309656434 ] 
dist 48=[-4.3862787101505087744 ,2.9103070320755343790 ] 
dist 49=[-4.8108429315083911107 ,2.7903230475593433369 ] 
dist 50=[-4.9807129723588546669 ,2.4840018349278769029 ] 
dist 51=[-5.0329705510174705880 ,2.3858632754783100642 ] 
dist 52=[-4.9977733991377428179 ,1.3439747823883013617 ] 
dist 53=[-4.5671419931655720843 ,1.1670849824686191801 ] 
dist 54=[-4.4235435460757941432 ,.82691705386412177136] 
dist 55=[-4.2076938723867750064 ,.74072480565454995737] 
dist 56=[-4.1202113484496083765 ,.46147579087690371419] 
dist 57=[-4.0513866953518584741 ,.39329521626204865968] 
dist 58=[-3.5857046272527318593 ,1.2116930744960564449 ] 
dist 59=[-3.2102249722672865382 ,1.9606455975018127806 ] 
dist 60=[-2.4691930432330718402 ,2.6550445128039246398 ] 
dist 61=[-2.4045265330983880706 ,3.2429063122516102055 ] 
dist 62=[-.8337202742686788698 ,3.5693733456218877029 ] 
dist 63=[-.62570794269891565372,3.7598061646832496878 ] 
dist 64=[-.15716090444486260635,3.8075966736358637002 ] 
dist 65=[-.05745012261750358477,1.7883582984543286657 ] 
dist 66=[.34623791097649252011,2.1479581238942842974 ] 
dist 67=[.22951839296102260919,2.3473592743417590576 ] 
dist 68=[.11005859641246019671,2.4633896092760838734 ] 
dist 69=[.02712844932173008225,2.4924510312146609600 ] 
dist 70=[-.04306641544814918588,1.0342692655585385013 ] 
dist 71=[-.11203454218932361706,1.0003624406532018893 ] 
dist 72=[-.17313408149894671034,.98859080412648236267] 
dist 73=[-.21213160560597676187,.75742954258838397892] 
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dist 75=[-.2708043584142114323 ,.59420495864591549354] 
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dist 77=[-.57003163677764660857,.55833238269416649064] 
dist 78=[-.65492807397766012774,.09811171179767052561] 
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dist 80=[-.75382433221135273665,-.08352195519662205265] 
dist 81=[-.77731325724442013607,-.10288903805777868498] 
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dist 83=[-.76409506015388004735,-.05415543240646308814] 
dist 84=[-.75711583363894068377,.02328901142335710391] 
dist 85=[-.64067341674701982147,.07550674772643684416] 
dist 86=[-.61060580878352006269,.11814338348356530927] 
dist 87=[-.57858940842393012228,.15756916932239267015] 
dist 88=[-.56155899834656629148,.19090943991002069413] 
dist 89=[-.4110898945452009574 ,.20939682413787904344] 
dist 90=[-.33449098952242013732,.2201668442459288281 ] 
dist 91=[-.31609611279805679432,.28537227650394962073] 
dist 92=[-.30034701218563686554,.36214819153974116065] 
dist 93=[-.29451306181764785186,.43200971951441986678] 
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dist 96=[-.01543286434707172837,.50345857178210687522] 
dist 97=[.01219194659559058384,.2580612075343634005 ] 
dist 98=[.03894761137657753416,.26041566599773185065] 
dist 99=[.02298035017310746197,.26047511460827860644] 
dist 100=[.00681730516047124101,.25773823389459037254] 
dist 101=[-.00421182945356956709,.25278567679885439879] 
dist 102=[-.01336470543230120185,.09961143311712656960] 
dist 103=[-.02208277463045541579,.09953371353005790945] 
dist 104=[-.02963977636196941995,.09589775715913702951] 
dist 105=[-.03418551293571911902,.09537327795523031908] 
dist 106=[-.03730879786801356612,.07742171767386945344] 
dist 107=[-.03922156025278991534,.07312014592549610606] 
dist 108=[-.04027915694189100816,.07010408647199098479] 
dist 109=[-.04039722406494842542,.06942574858313751435] 
dist 110=[-.03939530990174365488,.00705432413674934019] 
dist 111=[-.03909339618397626751,-.00021883506040329850] 
dist 112=[-.03266244837031035229,-.01708453685478872782] 
dist 113=[-.03104105960940745386,-.01959028118204897957] 
dist 114=[-.03983993082972900052,-.01485293148348806452] 
dist 115=[-.04520498368986369523,-.00645693339534518741] 
dist 116=[-.04854546125138788092,.00198978938461706350] 
dist 117=[-.0499060561247655323 ,.00768279178638054397] 
dist 118=[-.05022318345403570749,.01233398888566009222] 
dist 119=[-.04999155475682324391,.01664567685329179146] 
dist 120=[-.04834501217949530745,.02035909285595893646] 
dist 121=[-.04757729781241359360,.02256173787110856869] 
dist 122=[-.04054820010304328282,.02380228888339400995] 
dist 123=[-.03875163057180732053,.02409480134790454757] 
dist 124=[-.03602642598162649791,.00947153347756443925] 
dist 125=[-.03504351303679058594,.00953627276315987700] 
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dist 127=[-.00845373028567333847,.01474959029304012221] 
dist 128=[-.00146416144766856142,.02172444486204506818] 
dist 129=[5.32140353606888014000e-05,.02813021492858053160] 
dist 130=[.00515863146625253515,.03353225920339704823] 
dist 131=[.00306883053729982021,.03652173196870814523] 
dist 132=[.00096175664407708718,.03826102398177424574] 
dist 133=[-.00046780272055640360,.03869906272309942785] 
dist 134=[-.00164642994124104054,.01165970736449938169] 
dist 135=[-.00275751504436525068,.01162475008970657559] 
dist 136=[-.00371368957131072192,.01116983545318954039] 
dist 137=[-.00427745313303386447,.01108133827314808189] 
dist 138=[-.00465116496651008987,.00903438018523024422] 
dist 139=[-.00485300623703466004,.00854293383449410562] 
dist 140=[-.00495147208602591128,.00812880334390042120] 
dist 141=[-.00495027028389639540,.00797946812065949281] 
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dist 143=[-.00476517582374777120,.00026368652500549712] 
dist 144=[-.00411655130633198388,-.00164717775644561056] 
dist 145=[-.00417730163944321867,-.00193903659522835660] 
dist 146=[-.00529600593236168261,-.00199538414060603557] 
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dist 148=[-.0063117331414832377 ,.00056559153227148592] 
dist 149=[-.00644814761963449098,.00142660860533823771] 
dist 150=[-.00645099883810803698,.00212686904233382715] 
dist 151=[-.00641635786066155582,.00277123426678422355] 
dist 152=[-.00614222193598174888,.00331507194920985485] 
dist 153=[-.00607976579723627217,.00361624008628180499] 
dist 154=[-.00495806693826436971,.00379176593251269560] 
dist 155=[-.00468926627813609858,.00383588307730374544] 
dist 156=[-.00442958854255070527,.00117718009812059273] 
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dist 159=[-.00070031205790541361,.00137065978834052747] 
dist 160=[6.02191706803668861380e-05,.00208299454144881249] 
dist 161=[.00021367659993799963,.00273781928284240124] 
dist 162=[.00054563932399867302,.00329056851109844040] 
dist 163=[.00027545086417670691,.00359759287900473490] 
dist 164=[3.85684767625016512690e-06,.00378085975705032042] 
dist 165=[-.00017944929535150011,.00382685077401866260] 
dist 166=[-.00032962434813245061,.00148106768840569392] 
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dist 173=[-.00072308611096003094,.00100244630383234094] 
dist 174=[-.00069622799519839137,8.44146908714768006270e-05] 
dist 175=[-.00068856621028677116,-2.26322856668614389600e-05] 
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dist 192=[-1.71950949358421703580e-05,.00032552523701195598] 
dist 193=[5.19780989856293550970e-06,.00041957590969784788] 
dist 194=[6.32222789848589432180e-05,.00049886742392644248] 
dist 195=[1.56708348168495818830e-05,.00054273967458423573] 
dist 196=[-3.19977474537685693900e-05,.00056826382386746630] 
dist 197=[-6.40160199737636597440e-05,.00057469769624510354] 
dist 198=[-9.00914076810388828070e-05,.00019094919346764804] 
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dist 201=[-.00014599448201908767,.00017933571217040953] 
dist 202=[-.00015286546145457180,.00015320337897298893] 
dist 203=[-.00015509917829877288,.00014652437892641191] 
dist 204=[-.00015511173279542135,.00013522679941056100] 
dist 205=[-.00015361687281988556,.00013161293371295336] 
dist 206=[-.00014997477462501500,4.73675539608518325010e-05] 
dist 207=[-.00014781884275094364,3.58784362829260965940e-05] 
dist 208=[-.00013429484775378198,1.04917947035316126330e-05] 
dist 209=[-.00013073857854329345,4.53386975162375974770e-06] 
dist 210=[-.00011909757618203409,4.58906332717784680230e-06] 
dist 211=[-.00011643587858997857,1.65085624877683989710e-05] 
dist 212=[-.00010391431201675887,2.84678291619042181390e-05] 
dist 213=[-.00010563853164897726,3.65143631167689707770e-05] 
dist 214=[-.00010531132635232774,4.30816409273144701890e-05] 
dist 215=[-.00010460026866135549,4.91678234491979833240e-05] 
dist 216=[-9.99890661531393327230e-05,5.43381896179202298260e-05] 
dist 217=[-9.88027445735128816000e-05,5.72694003513825932310e-05] 
dist 218=[-8.09249574497640146600e-05,5.90676065487153454460e-05] 
dist 219=[-7.66299376113710575900e-05,5.97396162712969416360e-05] 
dist 220=[-7.20168349064267506750e-05,5.98918695489088765450e-05] 
dist 221=[-6.97020176804475582310e-05,5.96263871076679675380e-05] 
dist 222=[-2.47556427110535559550e-05,5.90108750562582493450e-05] 
dist 223=[-2.12631641544222397410e-05,5.82730374018376230900e-05] 
dist 224=[-1.38486997083517898130e-05,5.62619568145126010440e-05] 
dist 225=[-1.18399645479036491210e-05,5.52125222732348504320e-05] 
dist 226=[-4.33568701944090872660e-06,5.86563214357254141370e-05] 
dist 227=[-2.75054530561755548900e-06,6.30984773684244704490e-05] 
dist 228=[-5.70326543179385587370e-07,6.57112387378283810630e-05] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 0, 1, 1, 1, 2] 
dist 0=[130.77336143506607198   ,130.77336143506607198   ] 
dist 1=[129.69461108110435051   ,130.74096082037754528   ] 
dist 2=[125.89167266907676414   ,130.77336143506607198   ] 
dist 3=[120.73473515390623899   ,129.63116684911487616   ] 
dist 4=[114.26869405565836382   ,122.81831092037614817   ] 
dist 5=[105.71610958320211705   ,117.27429927719072580   ] 
dist 6=[92.258486709224269889  ,115.30306673430771975   ] 
dist 7=[78.425947110130042284  ,113.67955091110040661   ] 
dist 8=[68.377232124648309116  ,105.66708376834239572   ] 
dist 9=[59.307956322168211469  ,88.591720931034937194  ] 
dist 10=[49.246146580382896246  ,86.904867234852443222  ] 
dist 11=[31.537432740201090330  ,45.691852316336754100  ] 
dist 12=[18.879464944606629276  ,43.203192071038032513  ] 
dist 13=[8.2719252451749125191 ,38.273689229108303546  ] 
dist 14=[-2.1089897150018905591 ,37.140619534094936666  ] 
dist 15=[-11.395360206339486953  ,29.061594296288565116  ] 
dist 16=[-17.657524877825734342  ,24.794507053409976960  ] 
dist 17=[-22.849559424353477396  ,-.5028801460618562858 ] 
dist 18=[-27.894305865850064291  ,-1.3940586391417578676 ] 
dist 19=[-32.092310770197018805  ,-8.9517573683933813888 ] 
dist 20=[-33.920363013102181688  ,-8.6724327070234961466 ] 
dist 21=[-34.710941032427049070  ,-7.2056810870928227306 ] 
dist 22=[-34.766318137433831442  ,-3.8527757945964722162 ] 
dist 23=[-31.621160593194415895  ,-.14859292777906906432] 
dist 24=[-30.598498638881257903  ,2.7191830905714714450 ] 
dist 25=[-29.824150215245798440  ,5.4329804257311532468 ] 
dist 26=[-29.227003455429263513  ,8.5383443043666898411 ] 
dist 27=[-9.7843798788255931634 ,11.567236317579061475  ] 
dist 28=[-7.3742070901633839944 ,13.984598141545918660  ] 
dist 29=[-1.5757739977345847110 ,16.373412984890122844  ] 
dist 30=[-.7215850656900181789 ,19.297539840638681412  ] 
dist 31=[5.3566403444361367931 ,21.890677408866915374  ] 
dist 32=[5.6404014254609624695 ,22.967591555604231373  ] 
dist 33=[9.8272407648742808351 ,23.421462554266493291  ] 
dist 34=[10.156715105888145019  ,23.534742296451827801  ] 
dist 35=[12.841873973970109422  ,20.925361109734221895  ] 
dist 36=[12.109237635020127413  ,20.243279017923857827  ] 
dist 37=[10.961689395909760066  ,19.935244405561040482  ] 
dist 38=[9.3709917424984630083 ,19.753616584493562617  ] 
dist 39=[4.6090388631583593562 ,16.864897591925465377  ] 
dist 40=[.98322879351771050352,16.103046845573919967  ] 
dist 41=[-2.0683529051591716156 ,15.248756061767233603  ] 
dist 42=[-5.0399007409591501862 ,14.812937706206289690  ] 
dist 43=[-7.6566305376287127477 ,6.8621010895060020415 ] 
dist 44=[-9.3013500292283539007 ,6.1274658432233318859 ] 
dist 45=[-10.517490536720297648  ,4.4604368307738812593 ] 
dist 46=[-11.434920447062447467  ,4.0049183127918982360 ] 
dist 47=[-12.088157569834679986  ,1.9686080518926402981 ] 
dist 48=[-12.751234182214733565  ,1.5852330900406245150 ] 
dist 49=[-13.361028119005860249  ,.70672387308729967228] 
dist 50=[-13.476778150545738183  ,.52852282466750157198] 
dist 51=[-10.760393561433467256  ,-3.8826491084055234418 ] 
dist 52=[-10.370181466153352349  ,-3.6881704779468918723 ] 
dist 53=[-9.7769735333701611131 ,-3.3932050128043983330 ] 
dist 54=[-9.5445624085930411011 ,-2.2494654496947475243 ] 
dist 55=[-3.6420777846086153436 ,1.0178725397916574158 ] 
dist 56=[-3.2485803792808604918 ,3.2188312600094761702 ] 
dist 57=[-1.0438360605383541723 ,5.0143703413520892476 ] 
dist 58=[-.6643830193423105832 ,6.6728435970062732666 ] 
dist 59=[.27564021094105176233,8.0746926823270598891 ] 
dist 60=[.38926304313180040737,8.8518137459237962054 ] 
dist 61=[1.1949224167454669327 ,9.3044866731873835682 ] 
dist 62=[1.3179883978721989612 ,9.4184942298881496915 ] 
dist 63=[1.5352844712044587617 ,2.8887882695484234532 ] 
dist 64=[1.5698349141599741215 ,2.9235805584363281574 ] 
dist 65=[2.0348410882604823478 ,2.9044924030919925192 ] 
dist 66=[2.0326823125371941091 ,2.8954813265132736801 ] 
dist 67=[1.9603552781386938781 ,2.4740464122435996272 ] 
dist 68=[1.7758679016421593965 ,2.3635416970564112313 ] 
dist 69=[1.5389607686448487482 ,2.2799469072552148417 ] 
dist 70=[.91626584448222817845,2.2435720360635217910 ] 
dist 71=[.23857891207583508497,1.6594571810402923125 ] 
dist 72=[-.22247142023216963675,1.6197045246585021673 ] 
dist 73=[-.6037441944424752244 ,.63085476003609080697] 
dist 74=[-.96484688869529612675,.49943968391700119909] 
dist 75=[-1.2766038876820873156 ,.20086618744071176115] 
dist 76=[-1.4620544681378702448 ,.13612932010553718449] 
dist 77=[-1.5870003140294789324 ,-.20623571357765877055] 
dist 78=[-1.6586548775306829906 ,-.26512264977660841275] 
dist 79=[-1.6947027569991294868 ,-.37710517612669858077] 
dist 80=[-1.6968212756577945632 ,-.39973726253852039546] 
dist 81=[-1.6493235441258369297 ,-.44685530402589677535] 
dist 82=[-1.6352773064469775164 ,-.44799307611066719024] 
dist 83=[-1.3627632892669268350 ,-.43239358109234734963] 
dist 84=[-1.2945922563035003434 ,-.39041678440018481999] 
dist 85=[-1.2290543759250525745 ,-.33594748421794410085] 
dist 86=[-1.1961507993326685871 ,-.22770598180758123512] 
dist 87=[-.38261139061142541307,.11991230582655203226] 
dist 88=[-.37313575105471390436,.35402665730634670835] 
dist 89=[-.19842030861125469489,.5451635179093620368 ] 
dist 90=[-.17257414091269459023,.72218854481186581557] 
dist 91=[-.11412590162596755961,.87233675119560215975] 
dist 92=[-.09916436288587287552,.96345882947050119117] 
dist 93=[-.03012798152015594516,1.0154909756498789866 ] 
dist 94=[-.01740007883202018365,1.0275940556976580326 ] 
dist 95=[.00956276054227002967,.42214512620241281731] 
dist 96=[.01598292332101728482,.4344851179147473516 ] 
dist 97=[.03817277918098042606,.43970698073237398046] 
dist 98=[.03858865364586386599,.43820871486816989864] 
dist 99=[.03145753410661653530,.42614813636362648554] 
dist 100=[.01240349593272333678,.41841755229407879888] 
dist 101=[-.01229997926848234535,.36237401016157685939] 
dist 102=[-.04186496581809557875,.34745308882386641063] 
dist 103=[-.09076332903523739973,.32078683810528085772] 
dist 104=[-.15949595266682504486,.31254387100756204492] 
dist 105=[-.21600296762182690534,.11894369877160725444] 
dist 106=[-.26902120821262494099,.09213971325030600470] 
dist 107=[-.31448945656575656699,.03347529388256867890] 
dist 108=[-.34102725144700134936,.01888476052187037125] 
dist 109=[-.3582874647280126614 ,-.03527655342070939685] 
dist 110=[-.3669294107731257431 ,-.04215025756295751919] 
dist 111=[-.37056811291863583996,-.05467792314503543474] 
dist 112=[-.36796540880741385166,-.05699011386053722733] 
dist 113=[-.19485918207661450159,-.06038979820833411033] 
dist 114=[-.19194110956725053086,-.06005899924633887845] 
dist 115=[-.16523524464241647677,-.05811909103609811734] 
dist 116=[-.15822382826209865144,-.05353546643052468652] 
dist 117=[-.14755441043646292422,-.04773159000683142326] 
dist 118=[-.14365159893273070088,-.02860661817573141947] 
dist 119=[-.04923939893110928847,.02320796077960647544] 
dist 120=[-.04421186450668824924,.05797557348399685553] 
dist 121=[-.00831595168376768032,.08623885202433377165] 
dist 122=[-.00220973402700581822,.11223065872137918941] 
dist 123=[.00921929572587723095,.13416168038167485816] 
dist 124=[.01081230081358632256,.14630301370665555019] 
dist 125=[.02286247020521653744,.15336871296344549623] 
dist 126=[.02465324720241152593,.15514838531783232966] 
dist 127=[.02781793752849424555,.04687717514716975166] 
dist 128=[.02827720672431861715,.04690046639798670881] 
dist 129=[.03113590251471534972,.04542853219303141794] 
dist 130=[.03049971514260807504,.04512049838067251808] 
dist 131=[.02897783477923402939,.03721839344126248020] 
dist 132=[.02589103885078900783,.03528129677164831535] 
dist 133=[.02211578596308756985,.03369741568184974707] 
dist 134=[.01252032728771042618,.03309789015076012003] 
dist 135=[.00192851134295178295,.02302481850465800258] 
dist 136=[-.00521225499867224757,.02241673710121214475] 
dist 137=[-.01105470704683153381,.00769761648936607488] 
dist 138=[-.01649219516750883749,.00573195528684012367] 
dist 139=[-.02112677105901377240,.00131501146879345120] 
dist 140=[-.02378164698849918558,.00036267356407319662] 
dist 141=[-.02544574884309812462,-.00450749174163698602] 
dist 142=[-.02614696024417065434,-.00535038852670056734] 
dist 143=[-.02630115623505678565,-.00680176283914662463] 
dist 144=[-.02620576618804993290,-.00707947190623550266] 
dist 145=[-.02518582327406536004,-.00730769955004882440] 
dist 146=[-.02494309082736991598,-.00720461755019800073] 
dist 147=[-.02044963011544300756,-.00691531575855956783] 
dist 148=[-.01936167128214855655,-.00630430680885529691] 
dist 149=[-.01831981661676193135,-.00554947287351882307] 
dist 150=[-.01784928337689194056,-.00350497625388297882] 
dist 151=[-.00526479904062111513,.00186671338097104067] 
dist 152=[-.00517120381030167382,.00547199043772546667] 
dist 153=[-.00080633714247362023,.00840461062849124339] 
dist 154=[-.00028437626405239871,.01110562664184835069] 
dist 155=[.00093431040426901350,.01338832782542730124] 
dist 156=[.00111741936895598336,.01466008228847576055] 
dist 157=[.00256273595286938863,.01544989087623093393] 
dist 158=[.00277850074951898464,.01563384460902008223] 
dist 159=[.00317200844041126266,.00606388423806511888] 
dist 160=[.00323405896639617905,.00605435029978027755] 
dist 161=[.00334959819895593701,.00582305170693032010] 
dist 162=[.00327446883326604706,.00578952152175594514] 
dist 163=[.00310943303205065260,.00468759287867272176] 
dist 164=[.00278294862664432837,.00442437723998331309] 
dist 165=[.00238608608505102005,.00423807741521771438] 
dist 166=[.00170586621485817728,.00419589335583102656] 
dist 167=[.00038849387932669557,.00286534614570346178] 
dist 168=[-.00049823799849003239,.00279169936521279901] 
dist 169=[-.00122241147483160271,.00070095619459281302] 
dist 170=[-.00189437338051676521,.00048475766045754647] 
dist 171=[-.00246587286821094605,-4.42256989729644663400e-06] 
dist 172=[-.00279117790513488942,-.00010243602421506518] 
dist 173=[-.00299247230140949782,-.00064806375816584791] 
dist 174=[-.00307161257517034588,-.00073911645534647165] 
dist 175=[-.00308698705494697661,-.00089812723483744215] 
dist 176=[-.00307145216883632063,-.00092689040199128010] 
dist 177=[-.00296739258206520409,-.00094667810535100322] 
dist 178=[-.00291994038313002002,-.00092997006505820897] 
dist 179=[-.00248485037709154791,-.00089085668261757675] 
dist 180=[-.00237397656423052490,-.00081198775449870283] 
dist 181=[-.00220618719677170701,-.00071563582047680497] 
dist 182=[-.00214563524596552907,-.00039483328758326884] 
dist 183=[-.00070660791910559914,.00038997861060762561] 
dist 184=[-.00065686850584416870,.00091593737373876816] 
dist 185=[-8.97674776891774691130e-05,.00134301868005429036] 
dist 186=[3.23877622605359983810e-06,.00173522775079390467] 
dist 187=[.00016382781553494529,.00206597582553103613] 
dist 188=[.00018743745488540044,.00224901823800071609] 
dist 189=[.00037399762183805739,.00235553746628202788] 
dist 190=[.00040131839466663724,.00238238999214279969] 
dist 191=[.00045105537439903480,.00072559830061523370] 
dist 192=[.00045829917136536603,.00072322474111034493] 
dist 193=[.00047516027165995791,.00069303981315930548] 
dist 194=[.00046211164204841361,.00068852278019066865] 
dist 195=[.00043632949325600032,.00055550524428891481] 
dist 196=[.00038709532141486683,.00052641543720608852] 
dist 197=[.00031652529523214986,.00049989726230176183] 
dist 198=[.00015209883087039948,.00049432962326900233] 
dist 199=[-1.27031689510402316050e-05,.00034802728538940626] 
dist 200=[-.00012341543017542376,.00033853731642091120] 
dist 201=[-.00021361206743901916,.00011541458443728700] 
dist 202=[-.00029695534204890306,8.61169827026756924950e-05] 
dist 203=[-.00036760691806417322,2.08510606051571445840e-05] 
dist 204=[-.00040741027011945630,6.23270873226486453900e-06] 
dist 205=[-.00043151074772587873,-6.40475623176220051630e-05] 
dist 206=[-.00043981316026944488,-7.65061116420178262420e-05] 
dist 207=[-.00043953523984558901,-9.65653523205057888420e-05] 
dist 208=[-.00043690954806986696,-.00010077041005555993] 
dist 209=[-.00041843335939971993,-.00010151786322330913] 
dist 210=[-.00041353563404248770,-9.86257033354576249980e-05] 
dist 211=[-.00033967167624317422,-9.27165523470039399520e-05] 
dist 212=[-.00032183115707545750,-8.12982235771902614490e-05] 
dist 213=[-.00030261247592275714,-6.75003494253722785760e-05] 
dist 214=[-.00029296212086254332,-4.56852901742450000000e-06] 
dist 215=[-.00010617678317057848,7.48686228916484119300e-05] 
dist 216=[-9.15446786611149152310e-05,.00012814910786773875] 
dist 217=[-6.03263194354879667320e-05,.00017146686758701439] 
dist 218=[-5.18188477303043491050e-05,.00021134519172420498] 
dist 219=[-1.99167629520805127170e-05,.00024504871259271657] 
dist 220=[-1.66391969642590876820e-05,.00026384821322904617] 
dist 221=[-4.18099889009349443690e-06,.00027531569084257585] 
dist 222=[-1.64703630184654450290e-06,.00027827053443687408] 
dist 223=[2.31877053878241331820e-06,9.79344290437613965220e-05] 
dist 224=[3.30404111383168108940e-06,9.93537268702489343720e-05] 
dist 225=[3.94133562934131587380e-06,9.92207540093528743930e-05] 
dist 226=[2.75763628187383771990e-06,9.84732651689372293620e-05] 
dist 227=[2.59545116771741399800e-07,9.48676317401435156800e-05] 
dist 228=[-4.62047571701460987160e-06,9.30569015786463434490e-05] 
dist 229=[-1.05348921229855872470e-05,7.96781311286025498560e-05] 
dist 230=[-1.71406555959920312320e-05,7.62448562104843383240e-05] 
dist 231=[-2.53865279578320030860e-05,7.01953423349864749670e-05] 
dist 232=[-3.88362522124281042070e-05,6.83409058498052163490e-05] 
dist 233=[-5.14584404381951077940e-05,2.54622100005789663980e-05] 
dist 234=[-6.31092696999383401910e-05,1.95541895157907435440e-05] 
dist 235=[-7.29785433257589638930e-05,9.49803746479316875230e-06] 
dist 236=[-7.85267195512682799790e-05,8.16176411417726464790e-06] 
dist 237=[-8.18709304716518125790e-05,3.11847293048088451620e-06] 
dist 238=[-8.29889647606025852390e-05,2.06270956932194470690e-06] 
dist 239=[-8.29944975428361897350e-05,4.96123820443053589370e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 1, 0, 1, 2, 1, 2] 
dist 0=[111.02047383111048262   ,111.02047383111048262   ] 
dist 1=[108.09900704956594098   ,111.82965002719018175   ] 
dist 2=[103.10191340285808871   ,112.11953721717638038   ] 
dist 3=[94.073804217398973018  ,112.63531743745907571   ] 
dist 4=[84.449139874710795973  ,113.55011686995082654   ] 
dist 5=[77.076548331654281271  ,114.39248690443974377   ] 
dist 6=[70.043280771615337305  ,114.62410831410223691   ] 
dist 7=[61.752795615818532178  ,114.08772152672735836   ] 
dist 8=[53.382353469144853097  ,107.79389969817898054   ] 
dist 9=[46.017648058240037242  ,91.117924587282838649  ] 
dist 10=[38.016152692636578014  ,87.951005618646055329  ] 
dist 11=[27.089095680364466259  ,79.313271065048334474  ] 
dist 12=[16.491800857503155862  ,77.821941931764701491  ] 
dist 13=[9.7980388751959833921 ,61.570306003845646320  ] 
dist 14=[4.6741128154688448955 ,58.240064943416226142  ] 
dist 15=[.33334219953335323495,54.273587915710301609  ] 
dist 16=[-3.2110784329607053528 ,52.890663826029387362  ] 
dist 17=[-5.1638241179176730041 ,18.841802292731222100  ] 
dist 18=[-10.127922390814433351  ,14.672346956498230779  ] 
dist 19=[-13.716583240098532905  ,4.9737355590069487934 ] 
dist 20=[-16.851899937887813921  ,3.5076058783047382168 ] 
dist 21=[-20.207678291877725923  ,-2.5623446638254244183 ] 
dist 22=[-23.172809046500274518  ,-.54601422215139723278] 
dist 23=[-25.461780086479616280  ,1.1881967186503861800 ] 
dist 24=[-27.305541001301246941  ,2.9661558228075536636 ] 
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dist 38=[-.65093670397006587566,13.183513464687124856  ] 
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dist 47=[-9.2768018835613466879 ,10.951940172033769164  ] 
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dist 80=[-1.2577270797949571811 ,-.1102101215585830087 ] 
dist 81=[-1.2476009090789222894 ,-.08440255062799327685] 
dist 82=[-1.0414890878100768189 ,-.04971377630612847674] 
dist 83=[-.98967750045824282455,.00512374604277185594] 
dist 84=[-.94086017671400816592,.06085712319600306194] 
dist 85=[-.91650368828988812007,.09910763256307194211] 
dist 86=[-.27094755195217016601,.13105656069564268899] 
dist 87=[-.20409364022115818193,.25623792599348784146] 
dist 88=[-.09727051557340574318,.40334041066595974242] 
dist 89=[-.09308836966542765669,.53969903802698132537] 
dist 90=[-.08220587973128378270,.65681521102638339593] 
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dist 100=[-.14283437980436638065,.22268138970093585491] 
dist 101=[-.15922515583508452542,.22046259081444602778] 
dist 102=[-.17309735320022636301,.03951552275255441585] 
dist 103=[-.18675358453787898825,.03201103938633222543] 
dist 104=[-.19982283410594376454,.00444643376084728404] 
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dist 107=[-.22107253718926647555,-.00755646455515856315] 
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dist 116=[-.11453872139251903803,-.00322386288027631071] 
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dist 118=[-.03848742705514931616,.01770773526992113314] 
dist 119=[-.02873169847762333467,.04463393553378909805] 
dist 120=[-.00679559685872418776,.06652719899977782615] 
dist 121=[-.00207186510550571110,.08666603048543771818] 
dist 122=[.00929342431409233635,.10366025645836386623] 
dist 123=[.00946611453654930649,.1130692104879110085 ] 
dist 124=[.01166911039076638728,.1185450554590763404 ] 
dist 125=[.01158279525830772578,.11992431056517064051] 
dist 126=[.01112018867362687669,.03625691186216070216] 
dist 127=[.01003722600509457982,.03629930470241968653] 
dist 128=[.00866917156489822544,.03521387209380103535] 
dist 129=[.00707470914258598035,.03498277157123359539] 
dist 130=[.00504356782960141183,.02891944737107237333] 
dist 131=[.00194196016368628772,.02742698266375988044] 
dist 132=[-.00117635827173929518,.02621402010834164347] 
dist 133=[-.00327394164469522637,.02575060693169428909] 
dist 134=[-.00498298249185114640,.00408059409038594596] 
dist 135=[-.00655913564281071335,.00148912995066674667] 
dist 136=[-.00848302960855919874,-.00149903659985036851] 
dist 137=[-.01270835773905422138,-.00183155223175489688] 
dist 138=[-.01631296811107385446,-.00245108699206669981] 
dist 139=[-.01838334049191110654,-.00257067174174411777] 
dist 140=[-.01968802060016248904,-.00278540072162479018] 
dist 141=[-.02025290832166481181,-.00278631661808152595] 
dist 142=[-.02039326306050801353,-.00270588366731690789] 
dist 143=[-.02032598740138372024,-.00249598578093457396] 
dist 144=[-.01954937487313689989,-.00222499645362217241] 
dist 145=[-.01936291722050383446,-.00190199797578580879] 
dist 146=[-.01589035062393977388,-.00148602262503406916] 
dist 147=[-.01504792615158262401,-.00084589400510501370] 
dist 148=[-.01424258833373578448,-.00020013999816339281] 
dist 149=[-.01387725505822622290,.00023820239510077684] 
dist 150=[-.00349887040278633194,.00142550837265458883] 
dist 151=[-.00242474167235626417,.00422531812473665429] 
dist 152=[6.79502840636325998800e-06,.00650328682005034512] 
dist 153=[.00049331262697016363,.00860208764848022832] 
dist 154=[.00117444612592799590,.01037622796545648773] 
dist 155=[.00119841312819848205,.01136519279988706661] 
dist 156=[.00130811866126173117,.01198372257257039946] 
dist 157=[.00129094461812528505,.01212663509456091866] 
dist 158=[.00123524393113288322,.00470677367323142129] 
dist 159=[.00111399404699454448,.00470147223212711743] 
dist 160=[.00096318559819190883,.00452645757552884623] 
dist 161=[.00079012338723344337,.00450108947149654795] 
dist 162=[.00057125021427473474,.00364978350495003481] 
dist 163=[.00023856064746254801,.00344594785378346172] 
dist 164=[-9.56365915033165313370e-05,.00330249345285614655] 
dist 165=[-.00032050449965582576,.00326992282374990129] 
dist 166=[-.00050390552072332827,.00032023341219551548] 
dist 167=[-.00067349419066181208,-1.46472557863005285920e-05] 
dist 168=[-.00094193052938632474,-.00023804275254976831] 
dist 169=[-.00146515361497292259,-.00027491578079573738] 
dist 170=[-.00191045490389172528,-.00034336635658390204] 
dist 171=[-.00216445376428393324,-.00035602462783090388] 
dist 172=[-.00232229706184487198,-.00037511629712117265] 
dist 173=[-.00238583800027927220,-.00037201894876637322] 
dist 174=[-.00239978253376128150,-.00035912981228050444] 
dist 175=[-.00238834618688081056,-.00032988053548642567] 
dist 176=[-.00230886746052545880,-.00029315048353780318] 
dist 177=[-.00227212962776399317,-.00025055709766590457] 
dist 178=[-.00193524070347654578,-.00019640106233027283] 
dist 179=[-.00184920618779211476,-.00011376130694871130] 
dist 180=[-.00171898361637702070,-3.05921535673639683190e-05] 
dist 181=[-.00167193000973675465,2.56688828546825392070e-05] 
dist 182=[-.00055245879078004417,.00030159666784787467] 
dist 183=[-.00040405329872070088,.00071094884494535047] 
dist 184=[-7.23796630532335936220e-05,.00104337532193675817] 
dist 185=[-3.12120184560459973830e-08,.00134869347323276196] 
dist 186=[.00017335203986430694,.00160617910884526248] 
dist 187=[.00017634837409594872,.00174868212605033880] 
dist 188=[.00018996946058830713,.00183161759099249604] 
dist 189=[.00018576925734984847,.00185252102794568402] 
dist 190=[.00017611284060810010,.00056455025389211134] 
dist 191=[.00015674484963077445,.00056287398464249688] 
dist 192=[.00013312054712497247,.00053974441775534556] 
dist 193=[.00010656381626167027,.00053629102680678490] 
dist 194=[7.33153739675268526650e-05,.00043309938276168144] 
dist 195=[2.31216183410099787180e-05,.00041047896718012023] 
dist 196=[-2.72019441308499152080e-05,.00038995372096715162] 
dist 197=[-6.09665322216532417990e-05,.00038566327500504762] 
dist 198=[-8.84134924640351550030e-05,7.45593625134308615220e-05] 
dist 199=[-.00011365504465730979,3.70439336782099739330e-05] 
dist 200=[-.00016572407297931846,-2.06761399777879045640e-05] 
dist 201=[-.00023069450072669340,-2.57428834848989034750e-05] 
dist 202=[-.00028579445971240037,-3.42630464088502909470e-05] 
dist 203=[-.00031687687502257964,-3.59905092138691651310e-05] 
dist 204=[-.00033574893876222346,-3.72089970103163031780e-05] 
dist 205=[-.00034236748828699842,-3.61635855279091062900e-05] 
dist 206=[-.00034230108927698659,-3.36812052406826274550e-05] 
dist 207=[-.00034030426092263386,-2.86550510215168373890e-05] 
dist 208=[-.00032601730231449380,-2.25083382914254299410e-05] 
dist 209=[-.00032221494741241901,-1.55763671646708057350e-05] 
dist 210=[-.00026477258083215627,-6.88195732355740589740e-06] 
dist 211=[-.00025088652981265547,6.26292155812798472090e-06] 
dist 212=[-.00023593508570137570,1.94541499606954753850e-05] 
dist 213=[-.00022841894120236220,2.83328608267590851620e-05] 
dist 214=[-8.30384737631619151860e-05,5.80989648998995267070e-05] 
dist 215=[-7.16421820376333547820e-05,9.96182704937719908370e-05] 
dist 216=[-4.73060492970344526100e-05,.00013338002321497266] 
dist 217=[-4.06672217996745880160e-05,.00016446999348954941] 
dist 218=[-1.65885202928008571120e-05,.00019075129335771832] 
dist 219=[-1.61370424654355809060e-05,.00020541943114266398] 
dist 220=[-1.54840524040078130100e-05,.00021444012941587351] 
dist 221=[-1.57984857661808366330e-05,.00021674340765161913] 
dist 222=[-1.66937083717108497380e-05,6.63926804621270773140e-05] 
dist 223=[-1.85910555401812643820e-05,6.60956835990873894560e-05] 
dist 224=[-2.09376250178486402270e-05,6.39631613048161740560e-05] 
dist 225=[-2.36167284477712245210e-05,6.29550061131993856070e-05] 
dist 226=[-2.69980434720836698890e-05,5.37906485626496394810e-05] 
dist 227=[-3.21330013612543760370e-05,5.14408086181144795070e-05] 
dist 228=[-3.72952805010138819830e-05,4.78686550102842771920e-05] 
dist 229=[-4.07852453651798273510e-05,4.65805665109430425340e-05] 
dist 230=[-4.36518009997268116850e-05,8.48108094646281542210e-06] 
dist 231=[-4.63390675073524875330e-05,6.76598771313870418930e-06] 
dist 232=[-4.86436259697774021740e-05,1.48337984258367347260e-06] 
dist 233=[-4.99908034630746152890e-05,1.03765861311792412320e-06] 
dist 234=[-5.10703825225141902370e-05,2.93500204627344777870e-07] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 1, 1, 2] 
dist 0=[120.47870677193890624   ,120.47870677193890624   ] 
dist 1=[116.36161559787029401   ,123.35925265105687297   ] 
dist 2=[110.60585141773997096   ,124.20388798702765561   ] 
dist 3=[102.66387798420758317   ,124.07357889674186885   ] 
dist 4=[89.849729516111925970  ,123.47524643256258622   ] 
dist 5=[76.590799060613754506  ,118.48428299384854586   ] 
dist 6=[66.873809819868933110  ,116.84035508063014268   ] 
dist 7=[58.029201971571389131  ,108.56323821155601956   ] 
dist 8=[48.224141201437869278  ,96.213752549015724492  ] 
dist 9=[38.678570187401286863  ,80.787539578465226443  ] 
dist 10=[30.852388694132758948  ,76.432457729045975967  ] 
dist 11=[22.835296132144875875  ,72.063947347899139295  ] 
dist 12=[12.506440543272595308  ,70.341703749205273909  ] 
dist 13=[2.7042263313103480210 ,54.265255438428760869  ] 
dist 14=[-3.2227297711439180933 ,52.341933595036687834  ] 
dist 15=[-7.4605165382429129914 ,47.519216858900758382  ] 
dist 16=[-10.533317227688279170  ,42.721222125337166741  ] 
dist 17=[-17.852312337820362497  ,5.3776914833133738804 ] 
dist 18=[-22.922081775483513878  ,1.8014488894655407194 ] 
dist 19=[-26.863689978392807508  ,-4.9296980473815613493 ] 
dist 20=[-30.262418869357662956  ,-6.3467979483882969888 ] 
dist 21=[-32.871391508854633906  ,-6.6756185878587245786 ] 
dist 22=[-33.674773652404703802  ,-4.6384719161449817442 ] 
dist 23=[-33.824630870834741763  ,-2.7124395281815761679 ] 
dist 24=[-33.822011079502315512  ,-.53643563497931845337] 
dist 25=[-29.278077552479972085  ,1.5492295857371228021 ] 
dist 26=[-28.312096111185043262  ,3.1234992690486936470 ] 
dist 27=[-27.780087147705157988  ,4.5854646664117344816 ] 
dist 28=[-26.965244535841252311  ,7.7216112859257585472 ] 
dist 29=[-6.3657254516264158654 ,10.786301136804398488  ] 
dist 30=[-3.9161803368381940877 ,13.219257895187668852  ] 
dist 31=[1.4700093148643809950 ,15.609863568941366145  ] 
dist 32=[2.7004268011750222181 ,18.515920598972053897  ] 
dist 33=[5.4689469652964549834 ,21.092653501765625486  ] 
dist 34=[4.9033923941455350905 ,22.178263147259500397  ] 
dist 35=[4.0090232527336184153 ,22.645881346140977541  ] 
dist 36=[2.4705108025085829289 ,22.762733893457638808  ] 
dist 37=[.88039669373981235667,20.292516302543426614  ] 
dist 38=[-.2192545526877967175 ,19.646399964434754714  ] 
dist 39=[-1.3655174665197080324 ,19.266789899873164643  ] 
dist 40=[-2.5734163972453082737 ,19.170806845462883264  ] 
dist 41=[-3.6220030358968269686 ,14.002850197747646702  ] 
dist 42=[-4.2473445023456442672 ,13.361610041169778235  ] 
dist 43=[-4.6679037053735300865 ,12.624180606621021101  ] 
dist 44=[-4.9045841530433131321 ,12.261879586456711766  ] 
dist 45=[-7.3216889586081458098 ,4.1294853490775953846 ] 
dist 46=[-8.9207987728213348594 ,3.1383678728429999044 ] 
dist 47=[-10.107895941184617762  ,.873348397865483746  ] 
dist 48=[-11.012136251210664192  ,.41972712928795827653] 
dist 49=[-11.660911944101980497  ,-2.1090455604986357690 ] 
dist 50=[-11.834381458521649991  ,-1.8912354948722072988 ] 
dist 51=[-11.811168675771986476  ,-1.5777867003295542748 ] 
dist 52=[-11.677737561298524422  ,-1.0623863521813767485 ] 
dist 53=[-10.411543133667297081  ,-.53288329086729760529] 
dist 54=[-10.036371527773923381  ,-.16334961625318491286] 
dist 55=[-9.4664207226649382469 ,.15122980589130672959] 
dist 56=[-9.2423118375229570025 ,.46292981859280786712] 
dist 57=[-3.5369120932128817475 ,.96180845581994398905] 
dist 58=[-3.1134632267812387702 ,3.0893176994493111335 ] 
dist 59=[-3.0134330568866883341 ,4.8251675979158752632 ] 
dist 60=[-2.9888820216621800118 ,6.4287665226856970816 ] 
dist 61=[-.46094705285413166326,7.7843163454084364296 ] 
dist 62=[-.16476481719350033616,8.5357620976207353101 ] 
dist 63=[.52173772431601470193,8.9734431678464108049 ] 
dist 64=[.62771880864285445695,9.0837222900948016729 ] 
dist 65=[.9869003383481873447 ,2.7911449724658550054 ] 
dist 66=[.81619305443820424777,2.8260245146657580425 ] 
dist 67=[.5936926184497689823 ,2.8104448806984498645 ] 
dist 68=[.24893000394985667725,2.8020006895123597854 ] 
dist 69=[-.09891121878757624447,2.3958572959204635054 ] 
dist 70=[-.33365425617577878113,2.2881844220868928233 ] 
dist 71=[-.52548228233552850961,2.2102920267490406016 ] 
dist 72=[-.7030482975774394235 ,2.1755178325006867819 ] 
dist 73=[-.8532749407960187741 ,1.6909214070528522618 ] 
dist 74=[-.93663943134079906272,1.6208234336902016974 ] 
dist 75=[-.98532075933538810054,1.5151932135929638261 ] 
dist 76=[-.99752212530784189621,1.4757720079597360520 ] 
dist 77=[-1.2059587397694798835 ,.51515247655730165463] 
dist 78=[-1.3852343949834322184 ,.38723096278418018327] 
dist 79=[-1.5063808002184725009 ,.09899909448049871301] 
dist 80=[-1.5765901689503064655 ,.03735270292097335192] 
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dist 225=[3.71312028774535811360e-06,7.77259088782928896820e-05] 
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dist 231=[7.49523511646453270100e-06,8.49056508536040108620e-05] 
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dist 238=[-7.09985968710515496200e-05,1.77230965712565678660e-05] 
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dist 242=[-7.40659170300464211030e-05,1.87676844050776587140e-06] 
dist 243=[-7.22260427943472318020e-05,3.80032841476229191110e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 1, 1, 2, 0, 1] 
dist 0=[130.29683291685195485   ,130.29683291685195485   ] 
dist 1=[129.59580284611399705   ,130.03167608591624446   ] 
dist 2=[126.55893018899145946   ,130.29683291685195485   ] 
dist 3=[122.11517937786488764   ,129.39600489167443510   ] 
dist 4=[116.23553433429718837   ,120.90803298070162485   ] 
dist 5=[108.28406731002691957   ,118.57451337259479928   ] 
dist 6=[95.597323873285601353  ,117.29554494689987497   ] 
dist 7=[82.440598707752100539  ,113.85600014936794170   ] 
dist 8=[65.656266853836013752  ,90.943254718055321750  ] 
dist 9=[53.627619923345330031  ,87.228245152157900828  ] 
dist 10=[42.955185139179162962  ,83.112071864021890865  ] 
dist 11=[31.547988241193416527  ,81.455591787339393469  ] 
dist 12=[20.701304489055375939  ,48.857224301317102882  ] 
dist 13=[12.243860180077961076  ,44.003272623212504086  ] 
dist 14=[3.9773026984568977698 ,42.845996930594816400  ] 
dist 15=[-6.1349820614632094366 ,34.008157832140147332  ] 
dist 16=[-15.493271319617745797  ,4.790228123810332221  ] 
dist 17=[-20.766384330286390278  ,-.1461553060447501385 ] 
dist 18=[-24.962006212214103172  ,-3.075638391891642710  ] 
dist 19=[-29.354008177408266223  ,-5.4635298024325487565 ] 
dist 20=[-32.894449023609728752  ,-6.7009639731607403162 ] 
dist 21=[-34.244462410482468537  ,-5.6832659532528054148 ] 
dist 22=[-34.738736614103226570  ,-2.9523861696800460106 ] 
dist 23=[-34.860720494820204996  ,.1409710708400327235 ] 
dist 24=[-30.614777541427413627  ,2.6043753576717973477 ] 
dist 25=[-29.501142988694042643  ,4.9920338047722314051 ] 
dist 26=[-28.845832772965570534  ,7.7978781437938200627 ] 
dist 27=[-28.680040119534953679  ,10.571207587026290840  ] 
dist 28=[-6.8352837580890883958 ,12.837288805220078338  ] 
dist 29=[-4.7332838119113098086 ,15.123638354787762711  ] 
dist 30=[1.6234801545588461924 ,17.986305828511802394  ] 
dist 31=[2.7430914832338714365 ,20.556195005633542193  ] 
dist 32=[9.6374828821019143656 ,21.682477596047441786  ] 
dist 33=[10.687675414207764450  ,22.178239440676827668  ] 
dist 34=[12.125000774151155157  ,22.238856659596399558  ] 
dist 35=[11.319054249170222441  ,20.172997395403579208  ] 
dist 36=[10.064213771792481454  ,19.546325539581173677  ] 
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dist 38=[5.9645563576899140992 ,18.808702374848006760  ] 
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dist 40=[-1.6400044847929004224 ,14.655297472912584633  ] 
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dist 43=[-8.6650881401646636885 ,12.966120077905168581  ] 
dist 44=[-10.285071990098462560  ,4.8719722495671078076 ] 
dist 45=[-11.479835799404308458  ,3.7896265213736119295 ] 
dist 46=[-12.375274220553486631  ,1.3266766038735221146 ] 
dist 47=[-13.006547424061759153  ,.8103310780307693584 ] 
dist 48=[-13.153142726506716151  ,-.74508413276989814724] 
dist 49=[-13.094027316772020267  ,-.87535995460808717124] 
dist 50=[-12.925037562542909340  ,-.75427926691702269293] 
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dist 53=[-10.425783661777005385  ,1.2519165005748308183 ] 
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dist 58=[-3.0453970302234305906 ,8.0591099750928821795 ] 
dist 59=[-2.9970037619763511085 ,9.5290292191630499854 ] 
dist 60=[-.61033529841010134551,10.334801245706829999  ] 
dist 61=[-.32468386456503614842,10.764639529191053073  ] 
dist 62=[.35021712512412932647,10.845367064078485844  ] 
dist 63=[.44808670581122666392,2.3111330714540352155 ] 
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dist 68=[1.2517275740412717585 ,2.2130014250848908828 ] 
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dist 87=[-.49949595083950479708,.1305887037056254701 ] 
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dist 100=[.11532357006311751119,.26310861633553291038] 
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dist 109=[-.17616870543725894487,.04736951812498207219] 
dist 110=[-.18155506619315932378,.0105862911127420921 ] 
dist 111=[-.18339102108794157105,.00360304536766168245] 
dist 112=[-.18286676676769285121,-.01643055634209487704] 
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dist 117=[-.13041308992427560271,.01397554021929071357] 
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dist 119=[-.05956333920401938549,.04753672479671938316] 
dist 120=[-.04854034153952105498,.06794521081986135957] 
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dist 122=[-.04391023439394296381,.09308968113382815608] 
dist 123=[-.04345331984663266048,.107567574715405415  ] 
dist 124=[-.00908836393725851920,.11714173039690212012] 
dist 125=[-.00493961725142029663,.1226322419783819025 ] 
dist 126=[.00464884478903139908,.12385290257485781399] 
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dist 128=[.0174341658555659516 ,.03677112422609091455] 
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dist 130=[.02239256800008351325,.03676085519524608889] 
dist 131=[.02293534043530645758,.03763685151143933603] 
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dist 253=[-2.54279758022522575920e-07,3.05574164669103123730e-05] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 0, 0, 0, 0, 0, 1] 
dist 0=[4.8798393275945280427 ,4.8798393275945280427 ] 
dist 1=[0                     ,8.0945207515836966483 ] 
dist 2=[4.8798393275945280427 ,10.702391201839472500  ] 
dist 3=[10.203577175078507932  ,13.160875458131439087  ] 
dist 4=[11.210932230254746029  ,15.332741007614010034  ] 
dist 5=[15.177757506463017620  ,16.796981766968699785  ] 
dist 6=[15.893687549101311973  ,18.022373206306636633  ] 
dist 7=[16.965252799866395134  ,19.241339088483574393  ] 
dist 8=[17.204389529380143161  ,20.324478525364266475  ] 
dist 9=[19.973339580195213066  ,21.007925918251741773  ] 
dist 10=[20.310709707283626616  ,21.529536373810850035  ] 
dist 11=[20.142280424721558164  ,21.966837876489202504  ] 
dist 12=[19.347728070943692275  ,22.316856254724701076  ] 
dist 13=[18.203342743932350171  ,22.490190351669493404  ] 
dist 14=[16.586817697522335536  ,22.567780671546850842  ] 
dist 15=[13.908898501234261323  ,22.535822581908387701  ] 
dist 16=[11.154845174208423242  ,22.397683768964979259  ] 
dist 17=[9.2345958204880565944 ,10.664959550568107896  ] 
dist 18=[7.5621350647400444263 ,9.7242993762065554329 ] 
dist 19=[5.7964318402473841467 ,7.6436683134964926912 ] 
dist 20=[4.1114074590286633355 ,7.1483224814837929949 ] 
dist 21=[2.7607661116800359324 ,4.1977970828613707912 ] 
dist 22=[1.3999018118842561205 ,3.6759416762166616364 ] 
dist 23=[-.32585335805810773433,3.0539539047103848867 ] 
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dist 25=[-3.0357736029147500430 ,-.53186140742385775434] 
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dist 27=[-4.5860993931205761392 ,-1.7181331846024190416 ] 
dist 28=[-5.1846129130072257031 ,-1.8923902719132459693 ] 
dist 29=[-5.5149086862543584188 ,-2.3597997934619310652 ] 
dist 30=[-5.7111234930267587787 ,-2.3908097655255540053 ] 
dist 31=[-5.7748823725705198929 ,-2.2345848672937509117 ] 
dist 32=[-5.7804943204211314376 ,-1.8782955194561337330 ] 
dist 33=[-1.7532927430706703567 ,-1.5626655903150084120 ] 
dist 34=[-1.4326973177212408336 ,-1.2910859442956172231 ] 
dist 35=[-1.3767661616810890564 ,-1.0482769801397158183 ] 
dist 36=[-1.0565350048424649941 ,-.78561744741869797518] 
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dist 40=[-.33880012255382547625,.2859974655251460835 ] 
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dist 45=[.63086385051566704752,.94551040029987525935] 
dist 46=[.62965816256540382349,.9782313320596337042 ] 
dist 47=[.59840833270763794602,.9849214149630807848 ] 
dist 48=[.51907597669672249627,.86052717073849906455] 
dist 49=[.43114298383056077303,.63743675197325814058] 
dist 50=[.3656067306105019818 ,.55739130117054484244] 
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dist 53=[.16818915588598624061,.36063542319441434134] 
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dist 55=[-.00024593581626041727,.30902672743778866791] 
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dist 117=[.00084902423463883990,.00280774864393374900] 
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dist 119=[8.29687311771185733920e-05,.00249547278691929994] 
dist 120=[-.00077499742835534753,.00109288912217689424] 
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dist 123=[-.00217984401873559887,-.00049525053863221054] 
dist 124=[-.00250591735618504977,-.00055452273682866226] 
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dist 134=[-.00043598607343550047,-8.45095960310356097870e-05] 
dist 135=[-.00042613303853577248,-1.39332943991627164810e-05] 
dist 136=[-8.42940499474138503520e-05,.00012390357525081340] 
dist 137=[.00015701401768364851,.00024978593120955844] 
dist 138=[.00018483294175011871,.00035067637902651285] 
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dist 148=[9.32025441300262548450e-05,.00027396126878115673] 
dist 149=[6.32246345611125705090e-05,.00025541055781896865] 
dist 150=[3.82433473908152924030e-05,.00022778785870379067] 
dist 151=[1.15165490894683830450e-05,.00021901113135810541] 
dist 152=[-8.43875757716877270680e-05,4.54264285661926035730e-05] 
dist 153=[-.00014784697063466994,1.12255815326144039300e-05] 
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dist 155=[-.00024483474740341344,-4.69456787367372986860e-05] 
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dist 157=[-.00030470722796826020,-5.89853493116545234500e-05] 
dist 158=[-.00031704386035665433,-5.86156517387450101340e-05] 
dist 159=[-.00032014707127677118,-5.47863841613906583680e-05] 
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dist 164=[-5.30824636193101833450e-05,-1.43116076153224345460e-05] 
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dist 169=[1.31332367013936249290e-05,2.39284688667026304920e-05] 
dist 170=[1.49343510477253942650e-05,3.35239269154877770740e-05] 
dist 171=[1.82054471391992664460e-05,4.20247207588529069960e-05] 
dist 172=[1.88281813735829358410e-05,4.90320800258857831000e-05] 
dist 173=[1.97539398327160448660e-05,5.26907164748816442430e-05] 
dist 174=[1.91025830462456822310e-05,5.47033045836947190600e-05] 
dist 175=[1.75685554355552174870e-05,5.51672064053148829700e-05] 
dist 176=[1.44686173287873462050e-05,4.47879391177376606920e-05] 
dist 177=[1.11655454390385775400e-05,4.35759145719704333720e-05] 
dist 178=[8.82116278773000576250e-06,3.96072286236183332450e-05] 
dist 179=[6.76097704286985291010e-06,3.89185329024537586340e-05] 
dist 180=[4.58499299911635078630e-06,2.94528838937322679520e-05] 
dist 181=[2.52673610925500572460e-06,2.74184656655715011770e-05] 
dist 182=[9.32449606651546107500e-07,2.52522474661248173030e-05] 
dist 183=[-6.17720939049122267720e-07,2.45262383401941205290e-05] 
dist 184=[-6.73674257274223583070e-06,3.04780673884927385240e-06] 
dist 185=[-1.21966299626550536660e-05,-6.49825972209926694300e-08] 
dist 186=[-1.65532453175804291330e-05,-2.64798389430584505980e-06] 
dist 187=[-2.04493020043901162340e-05,-3.92705766763329987530e-06] 
dist 188=[-2.36802326815916389470e-05,-4.11323482402186066090e-06] 
dist 189=[-2.53930159487674554520e-05,-4.74447611200878681820e-06] 
dist 190=[-2.63174437325402553190e-05,-4.52682781414397938370e-06] 
dist 191=[-2.65020143692153501850e-05,-4.06573260771207748880e-06] 
dist 192=[-9.57654583818755640290e-06,-3.16438258264179761140e-06] 
dist 193=[-9.22657833558646812090e-06,-2.21511237209067334370e-06] 
dist 194=[-8.13799678148396429090e-06,-1.56262136103174671740e-06] 
dist 195=[-7.98117801908196864380e-06,-1.01125989448268334460e-06] 
dist 196=[-5.59059540454763236570e-06,-4.63411932422955128440e-07] 
dist 197=[-5.09735477414835595510e-06,3.36077193121562402210e-08] 
dist 198=[-4.62195262324757251060e-06,3.83381429667102295980e-07] 
dist 199=[-4.53192834555436795180e-06,6.90372546862808091980e-07] 
dist 200=[4.57638825241067429390e-07,1.01859191856288988010e-06] 
dist 201=[1.30024105392637155910e-06,2.16500214508360701750e-06] 
dist 202=[1.39671911424742599510e-06,3.16928950779457153440e-06] 
dist 203=[1.52064698911623246560e-06,4.07946826262748306680e-06] 
dist 204=[1.51701594707775552560e-06,4.84268901927957814610e-06] 
dist 205=[1.46749571066188224370e-06,5.26286167264674553560e-06] 
dist 206=[1.35837919401607822250e-06,5.50595245012479328130e-06] 
dist 207=[1.18766202962142718590e-06,5.56532920308639427000e-06] 
dist 208=[8.92666034225803221280e-07,4.31422170234010433340e-06] 
dist 209=[5.89503353517877556480e-07,4.18907196015090701990e-06] 
dist 210=[3.86035139616525640860e-07,3.81496235949476560950e-06] 
dist 211=[2.19256175047461696340e-07,3.72417575754146481340e-06] 
dist 212=[6.17212524037796971290e-08,2.89875361205515163150e-06] 
dist 213=[-7.62310212858007541410e-08,2.71827208263273368540e-06] 
dist 214=[-1.65340504122010449970e-07,2.44883181968988266660e-06] 
dist 215=[-2.35675872488132247710e-07,2.36110611968995342880e-06] 
dist 216=[-8.05564036810642940960e-07,4.75589422769606157140e-07] 
dist 217=[-1.46436150230608341200e-06,2.29661959127559945880e-07] 
dist 218=[-1.99442367372828859470e-06,-2.97385043474333283550e-07] 
dist 219=[-2.47555189989841773330e-06,-3.61601903866956195060e-07] 
dist 220=[-2.87930889778237827350e-06,-3.58827090320733033120e-07] 
dist 221=[-3.10187213616020729050e-06,-3.33045354495479393060e-07] 
dist 222=[-3.23093562980879089630e-06,-2.97013034233268634160e-07] 
dist 223=[-3.26309676873564810520e-06,-2.47599875002757414580e-07] 
dist 224=[-9.60171840384356530540e-07,-1.68398346477148150530e-07] 
dist 225=[-9.29374643302170952220e-07,-8.83484620308050943860e-08] 
dist 226=[-8.29790312783513934790e-07,-3.45038566233980428180e-08] 
dist 227=[-8.15280544181936616560e-07,8.74800221576651890550e-09] 
dist 228=[-5.85617052253004709400e-07,4.81258856099627675680e-08] 
dist 229=[-5.39153034740803967570e-07,8.16087980411336146620e-08] 
dist 230=[-4.91319712091737892440e-07,1.01469694000278434550e-07] 
dist 231=[-4.82136592859981838770e-07,1.16348561034342914760e-07] 
dist 232=[2.31520535051706712150e-08,1.31951232366818258580e-07] 
dist 233=[8.05159391632161742090e-08,2.55743561500921394330e-07] 
dist 234=[7.56324744519854681980e-08,3.57016084634399508720e-07] 
dist 235=[6.80319457865691756290e-08,4.44616708846383549220e-07] 
dist 236=[5.53481198307863733950e-08,5.16689247258420468380e-07] 
dist 237=[4.09646665896449394030e-08,5.56252030803738486540e-07] 
dist 238=[2.65559513551731540030e-08,5.78968949931165691660e-07] 
dist 239=[9.71876760068431689950e-09,5.84101216468607643940e-07] 
dist 240=[-1.43822705036478169660e-08,5.19311007370211309130e-07] 
dist 241=[-3.77615920882964427890e-08,5.08333373904741228700e-07] 
dist 242=[-5.17624583708709198150e-08,4.69746064407429086550e-07] 
dist 243=[-6.14202730492948305800e-08,4.62040489440249084680e-07] 
dist 244=[-6.75645201282504339510e-08,3.61253905744229759400e-07] 
dist 245=[-7.15223584494995927720e-08,3.38867219504233924180e-07] 
dist 246=[-7.24893436726011948510e-08,3.13672100775358111640e-07] 
dist 247=[-7.19872724341621698550e-08,3.03100273281836426980e-07] 
dist 248=[-1.22978035760493329540e-07,6.70014652193465795660e-08] 
dist 249=[-1.81518050369668469790e-07,4.99698684552854532430e-08] 
dist 250=[-2.28121546313803691760e-07,3.61803786892997601430e-08] 
dist 251=[-2.69550751075165667800e-07,4.01011707069250451820e-08] 
dist 252=[-3.03679785137206139960e-07,4.41526171587326209900e-08] 
dist 253=[-3.21272267030667441600e-07,4.77395283650272598480e-08] 
dist 254=[-3.30001581232680820520e-07,4.98369936000942558350e-08] 
dist 255=[-3.31379922816360003160e-07,5.11533015933726902020e-08] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 1, 1, 1, 1, 0, 2] 
dist 0=[150.33451506610393667   ,150.33451506610393667   ] 
dist 1=[149.31221896595967982   ,149.95273464488830847   ] 
dist 2=[146.26575598232242090   ,150.33451506610393667   ] 
dist 3=[139.23502039215225357   ,147.62685431730886913   ] 
dist 4=[130.36383741175244891   ,141.66976039842544658   ] 
dist 5=[120.00050936522235136   ,134.37141491544342731   ] 
dist 6=[106.74947830066347701   ,133.30681565536614681   ] 
dist 7=[86.399085710250605076  ,125.09936034584525172   ] 
dist 8=[65.747806244788149875  ,107.01933928631025815   ] 
dist 9=[51.295711668990110977  ,103.08729922963217538   ] 
dist 10=[38.841056135897948944  ,102.23569729039219822   ] 
dist 11=[26.115266105629711358  ,40.684981019779436119  ] 
dist 12=[14.388666057299452066  ,32.216455835534281886  ] 
dist 13=[5.8927225552001963257 ,20.778152411575706995  ] 
dist 14=[-1.7921605731564987833 ,16.160108020819502202  ] 
dist 15=[-11.069241266794566052  ,15.359999850199857548  ] 
dist 16=[-18.020205656638968369  ,-8.8696129004020028314 ] 
dist 17=[-23.532905725849733055  ,-13.845410279020865011  ] 
dist 18=[-28.470983035058020149  ,-14.669644236887729700  ] 
dist 19=[-32.458959736391960784  ,-23.304976635188119214  ] 
dist 20=[-34.197553926218488171  ,-22.322149085720329823  ] 
dist 21=[-34.895071237598934514  ,-19.872390578332422320  ] 
dist 22=[-34.758710742219747596  ,-15.994080008247202441  ] 
dist 23=[-32.018291577116109544  ,-9.3364861387324060055 ] 
dist 24=[-31.048941232390758911  ,-2.4662803138520163217 ] 
dist 25=[-29.726796672761864809  ,2.2608480336273255953 ] 
dist 26=[-29.089753329169992196  ,6.1891241883153004283 ] 
dist 27=[-12.127820697292816511  ,9.8985440259853722433 ] 
dist 28=[-9.9015873272687725844 ,13.075676102072537644  ] 
dist 29=[-4.7317405633149021576 ,14.857834395793127385  ] 
dist 30=[-3.6991688157979657508 ,16.156917338629514411  ] 
dist 31=[2.3602811506322188795 ,20.127933517476135050  ] 
dist 32=[3.5901278687020681430 ,22.325968144528783897  ] 
dist 33=[5.7380701736528593852 ,23.599488488019341175  ] 
dist 34=[6.0908027123140215519 ,23.902397015479032469  ] 
dist 35=[6.2653285456258643574 ,8.2079932930760527587 ] 
dist 36=[5.6671598620197421430 ,8.4674054220235067421 ] 
dist 37=[4.7345583828308749691 ,8.5335648442580117966 ] 
dist 38=[3.4362643897913787185 ,8.4735589682600322313 ] 
dist 39=[1.3439678240046433086 ,7.7740005178779190417 ] 
dist 40=[-.78897244243197667761,7.5447060231228341730 ] 
dist 41=[-2.2490648886071110346 ,7.1083369012135242099 ] 
dist 42=[-3.4615233749279378560 ,6.9526775559726184534 ] 
dist 43=[-4.6127910409183078415 ,3.2443423407757671335 ] 
dist 44=[-5.6046100723377387633 ,2.7216978753815715008 ] 
dist 45=[-6.1848382175891294199 ,1.5297707584433606044 ] 
dist 46=[-6.5619959193886133420 ,1.2535939706641111870 ] 
dist 47=[-6.7484705055753113062 ,.4630381453108707531 ] 
dist 48=[-6.8256185673592670025 ,-.18635236658118859665] 
dist 49=[-6.7785157049130529144 ,-.29629234055759575907] 
dist 50=[-6.6057251218971318567 ,-.44502275428442592386] 
dist 51=[-4.0363099565034732584 ,-.46228014866751622173] 
dist 52=[-4.0698270272048860153 ,-.43172536410519485738] 
dist 53=[-4.0450723220250815876 ,-.33474626348565265277] 
dist 54=[-3.9964951474614753170 ,-.17406869824204201017] 
dist 55=[-3.5275584314887271436 ,.10936764630577590638] 
dist 56=[-3.3941071040709983145 ,.40657302943884584618] 
dist 57=[-3.1941548455650004627 ,.82883860935896546164] 
dist 58=[-3.1160775302089715315 ,1.3448580047111341703 ] 
dist 59=[-1.1581708868843494155 ,1.8233394808715860059 ] 
dist 60=[-.89699020301109363423,2.2284317209319013208 ] 
dist 61=[-.30305141090569690652,2.4534890361159979088 ] 
dist 62=[-.17819967139893412543,2.5847824247122513188 ] 
dist 63=[.50091770231560136873,2.6554899923406776505 ] 
dist 64=[.61614842325210739877,2.9096907914472832215 ] 
dist 65=[.81997656872258188843,3.0577010709355851207 ] 
dist 66=[.81303961061018336476,3.0948771650287557614 ] 
dist 67=[.76124570356274267725,1.7399046674854139970 ] 
dist 68=[.6878171713751728185 ,1.4852876788149027080 ] 
dist 69=[.59285637286891039536,1.4193745646878179106 ] 
dist 70=[.4662060508610101204 ,1.3808884599504139169 ] 
dist 71=[.26697025270190495487,1.3711816734035955941 ] 
dist 72=[.06475497247123201411,.7681045661877325015 ] 
dist 73=[-.07374789570340552931,.73942431127547879466] 
dist 74=[-.24150013676879237396,.73177378433545221469] 
dist 75=[-.45311544156616862486,.14878480561155159797] 
dist 76=[-.63701566697842947372,.07934359414634131317] 
dist 77=[-.74853703573974674282,-.08450422386891178192] 
dist 78=[-.82629354809509394594,-.10855577306584380506] 
dist 79=[-.87622893190034040874,-.27080316743858213104] 
dist 80=[-.90686888430021252963,-.32957745419698694413] 
dist 81=[-.91068662328394558054,-.33120484804853336479] 
dist 82=[-.89850337430813908337,-.31971029608580129066] 
dist 83=[-.88656248869412183646,-.28772308375781076455] 
dist 84=[-.77594742131443522936,-.24599104320317285213] 
dist 85=[-.74539886763243409619,-.19580496727962992565] 
dist 86=[-.69891043327764824281,-.13093693360576605955] 
dist 87=[-.6813685449791340851 ,-.03091728657805220211] 
dist 88=[-.41223805656467771779,.09097771684289433473] 
dist 89=[-.39219614974993061574,.25193420626802863598] 
dist 90=[-.38360187945383178456,.38300440328650764601] 
dist 91=[-.10012121188165301213,.50379870094759876236] 
dist 92=[-.07141410861949965512,.60580937776237150503] 
dist 93=[-.03671581034353074816,.66231937382372956417] 
dist 94=[-.01579641865629906245,.69521893537029030769] 
dist 95=[-.01082442149542967638,.70350687355304621579] 
dist 96=[.09415996030333226748,.29454503771609144776] 
dist 97=[.11702679291472163094,.31111960535151087876] 
dist 98=[.12124366106780393015,.31506758799117941878] 
dist 99=[.12755400397558297167,.2105969683483569289 ] 
dist 100=[.12643808169172251042,.17688866307462188876] 
dist 101=[.12202813821808438564,.1683235650427876547 ] 
dist 102=[.11210329916786781329,.16169684498730733549] 
dist 103=[.06336057687036712836,.15899000328316955984] 
dist 104=[.01414404730179546509,.09646285051274139734] 
dist 105=[-.01919607364314696269,.0928722655182019351 ] 
dist 106=[-.04662988182481103590,.09203870040309327057] 
dist 107=[-.07240318115942493487,.01122875731409188710] 
dist 108=[-.09452436065525823728,.00178561219099273270] 
dist 109=[-.10746219250839378077,-.02010394001715985268] 
dist 110=[-.11590908255938709884,-.02341675184777939580] 
dist 111=[-.12020503410301605437,-.04870429043282080385] 
dist 112=[-.12193783694902438111,-.05244938580696382371] 
dist 113=[-.12182285599822369932,-.05908642864065903403] 
dist 114=[-.11778430098261341705,-.06004857501697366064] 
dist 115=[-.11674694358254659111,-.06509363247623633784] 
dist 116=[-.09646389722690680700,-.06364082303035472355] 
dist 117=[-.09147498322442928444,-.05929914034932055243] 
dist 118=[-.08677070607424736451,-.0427626986745392961 ] 
dist 119=[-.08457454267740876391,-.01769093959324209973] 
dist 120=[-.05122117727029510256,.00747741771691995921] 
dist 121=[-.04772793760749894166,.02439810826251344385] 
dist 122=[-.04645467489513649875,.03818618113658276122] 
dist 123=[-.01576698868166424006,.05091859190085019446] 
dist 124=[-.01167267791151162647,.06169654213010774553] 
dist 125=[-.00248658549159340582,.06792547599727695327] 
dist 126=[-.00050250989983512738,.07166570745407810741] 
dist 127=[.00957486538732363357,.07253171613856573230] 
dist 128=[.01132241445701698982,.04757842722283595992] 
dist 129=[.01428248242441978578,.04986821617707797769] 
dist 130=[.01485920558616703100,.05044494075298371556] 
dist 131=[.01522714832517938086,.02736440228402075557] 
dist 132=[.01497837616786620522,.02240774832257390531] 
dist 133=[.01435038921996272934,.02120154964863252724] 
dist 134=[.01305805773897840489,.02038413905331469521] 
dist 135=[.00847037469108585499,.02019447797725779396] 
dist 136=[.00226587741913658943,.01138181258062381235] 
dist 137=[-.00192388300580444799,.01085975216428882366] 
dist 138=[-.00535888009276695981,.01066526828418357857] 
dist 139=[-.00856709267734085605,.00160015483957699175] 
dist 140=[-.01130914505018711256,.00051664858662208422] 
dist 141=[-.01289356605448826907,-.00200827008795888090] 
dist 142=[-.01390417347859241743,-.00238963097863720889] 
dist 143=[-.01436830907585443018,-.00536908142755753928] 
dist 144=[-.01453062521439944231,-.00581282153281941289] 
dist 145=[-.01448642416348461542,-.00662805132231400322] 
dist 146=[-.01405999078109595214,-.00675804293162621511] 
dist 147=[-.01384373215625948018,-.00694259074003312392] 
dist 148=[-.01185480105692514819,-.00677631442369491299] 
dist 149=[-.01133984546304164366,-.00642672586986115582] 
dist 150=[-.01056033928805128470,-.00567944736116328187] 
dist 151=[-.01027612987779157893,-.00196654412862778327] 
dist 152=[-.00624125958246371030,.00175432434185694148] 
dist 153=[-.00590279371382912748,.00424971571686777604] 
dist 154=[-.00575104843338414469,.00627730618489669066] 
dist 155=[-.00142408240553287367,.00814086000287797038] 
dist 156=[-.00097713939005711572,.00971291634424814360] 
dist 157=[3.28420429878646116390e-05,.01058315669307417207] 
dist 158=[.00023556956192482338,.01108989472187893626] 
dist 159=[.00135736886306215210,.01121748332653223437] 
dist 160=[.00154488041800023480,.00474124110801619314] 
dist 161=[.00186772236235545166,.00499280916675545637] 
dist 162=[.00192704637438310771,.00505214235945564955] 
dist 163=[.00195785043851292683,.00328099056367133327] 
dist 164=[.00192020859327390296,.00266615178773462603] 
dist 165=[.00183713600316409142,.00253071969638687430] 
dist 166=[.00153583433419778917,.00240862188538617237] 
dist 167=[.00075503398032524732,.00238336654165428144] 
dist 168=[-2.84878905118616352020e-05,.00142912636377109937] 
dist 169=[-.00055586093359715809,.00136657034745987794] 
dist 170=[-.00098650189352929798,.00135078643583565025] 
dist 171=[-.00138597153011111415,.00013403644332692748] 
dist 172=[-.00172560538234836918,-8.26184122388703450540e-06] 
dist 173=[-.00191868216837297239,-.00033956085789986862] 
dist 174=[-.00203782594910325682,-.00038776774550084011] 
dist 175=[-.00208392735226298109,-.00077531994723122669] 
dist 176=[-.00208908865414196710,-.00083214029606475967] 
dist 177=[-.00207868292702882390,-.00093454538541281704] 
dist 178=[-.00199524546448961421,-.00094965015852735280] 
dist 179=[-.00197249121231887573,-.00097325959001559924] 
dist 180=[-.00162487723526729973,-.00086281813214084914] 
dist 181=[-.00154041509147936759,-.00066167979529699533] 
dist 182=[-.00144976732337114447,-.00041071630753691345] 
dist 183=[-.00140387340922821026,-3.26757301882152000000e-05] 
dist 184=[-.00076699403466243491,.00034623068193169242] 
dist 185=[-.00071547940611315357,.00060063792003181496] 
dist 186=[-.00069484205806354273,.00080771999674599824] 
dist 187=[-.00025958745384660051,.00099872385480355728] 
dist 188=[-.00016397886629294586,.00116037086232544732] 
dist 189=[-7.06602638195975864370e-05,.00125089225130228722] 
dist 190=[-1.89052064885894430140e-05,.00130913382442364309] 
dist 191=[-5.95067285903520698460e-06,.00132326638339407084] 
dist 192=[.00017658042349860621,.00072332178360925532] 
dist 193=[.00021818603978497807,.00075751989754704512] 
dist 194=[.00022675696711412569,.00076614444315471907] 
dist 195=[.00022755444967513646,.00044621656423755547] 
dist 196=[.00022208810766045896,.00037411630211269679] 
dist 197=[.00021111322403469462,.00035616468683636930] 
dist 198=[.00019003533870101724,.00033396285629530578] 
dist 199=[8.31583057736727360790e-05,.00032414280992372623] 
dist 200=[-3.13287437952993789510e-05,.00023641160204093512] 
dist 201=[-.00010817379005668165,.00021613991394903955] 
dist 202=[-.00017070429259707339,.00020973383823471913] 
dist 203=[-.00022835446578718544,.00013282954805219824] 
dist 204=[-.00027713210129226040,.00011947633855393938] 
dist 205=[-.00030443346395476218,9.24958568212828835990e-05] 
dist 206=[-.00032072916402265569,8.51918306719590940200e-05] 
dist 207=[-.00032580786867520527,5.85857370296810022280e-05] 
dist 208=[-.00032516439097148091,5.21835652286522005440e-05] 
dist 209=[-.00032256900306572319,4.50239984992865992700e-05] 
dist 210=[-.00030698633699600239,4.30905596805775231520e-05] 
dist 211=[-.00014505486360214162,4.26442018954617922020e-05] 
dist 212=[-.00014401898897805854,4.33915814542031058890e-05] 
dist 213=[-.00013825697487245373,4.51371928669578360050e-05] 
dist 214=[-.00013607056236751171,4.86553207813300107860e-05] 
dist 215=[-.00011416266523945443,5.29540965021828778910e-05] 
dist 216=[-.00010872406518024078,5.77999193292754386800e-05] 
dist 217=[-.00010100507596076665,6.38781962317650928240e-05] 
dist 218=[-9.80702350654896923650e-05,7.30712799748865857410e-05] 
dist 219=[-3.37412345036864988250e-05,8.23047666789184986490e-05] 
dist 220=[-2.90616823243107839530e-05,9.14658236513800165070e-05] 
dist 221=[-1.90911029459546884290e-05,.00010032042187559261] 
dist 222=[-1.63783455639479617580e-05,.00010565393255628609] 
dist 223=[-6.17435593071261495990e-06,.00010742804134501151] 
dist 224=[-4.03209135979871486070e-06,.00010760308947641656] 
dist 225=[-9.29374643307289858830e-07,.00010658717205174233] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 0, 2, 0, 1, 2] 
dist 0=[112.95183527365374810   ,112.95183527365374810   ] 
dist 1=[109.66856487125068680   ,114.11061000996550469   ] 
dist 2=[104.08628856305922730   ,115.41771224849957598   ] 
dist 3=[94.641362136672992245  ,116.55598776428878081   ] 
dist 4=[84.704892905889741678  ,116.73491115853913818   ] 
dist 5=[77.161021965614416030  ,116.23494541526937324   ] 
dist 6=[70.028511585423663516  ,115.76421467760761951   ] 
dist 7=[61.713265545654789796  ,112.22175616323291958   ] 
dist 8=[53.369298376384129957  ,92.613937443548224094  ] 
dist 9=[46.109530955766059647  ,84.401569410715110089  ] 
dist 10=[38.290846308724667435  ,82.886368032370841900  ] 
dist 11=[27.700643712919330762  ,67.008205161355813795  ] 
dist 12=[17.439845466281504013  ,63.700730619160309045  ] 
dist 13=[10.927630213733923707  ,59.593468455524530258  ] 
dist 14=[5.9071353489332660684 ,58.027798901292651392  ] 
dist 15=[1.5919822165885939002 ,47.603518885486990851  ] 
dist 16=[-1.9751285206158127316 ,19.466087609412027456  ] 
dist 17=[-5.1264373740717521968 ,9.4355887881637257003 ] 
dist 18=[-12.786971169853413095  ,7.9424573412609149339 ] 
dist 19=[-19.437759890910658471  ,-4.5361953175838818345 ] 
dist 20=[-23.578952524715131934  ,-4.7387522019087929818 ] 
dist 21=[-26.640584157113835372  ,-4.4992438261522467774 ] 
dist 22=[-29.004886313401459131  ,-4.0406962249243476032 ] 
dist 23=[-30.668254289804903223  ,-3.2312241613315298898 ] 
dist 24=[-31.049445269741910348  ,-1.7091765437140988265 ] 
dist 25=[-30.789095154347497641  ,.93807403498791513165] 
dist 26=[-30.729213688978911108  ,3.4764176609280961744 ] 
dist 27=[-26.302189921586797636  ,6.4154116565602545626 ] 
dist 28=[-24.825009373527810091  ,9.2918061579551642800 ] 
dist 29=[-24.033798473189205557  ,11.589968456723203368  ] 
dist 30=[-23.789093873403492438  ,13.859922190921561138  ] 
dist 31=[-5.4147634938226640918 ,16.634091948055875701  ] 
dist 32=[-2.6055444819052807479 ,19.104843103628171793  ] 
dist 33=[1.8131827267110124417 ,20.172803796030459097  ] 
dist 34=[1.7618930059917597670 ,20.649979047762823803  ] 
dist 35=[1.3795560470358224436 ,20.769239476293679322  ] 
dist 36=[.22603449741023204654,18.607983953371618402  ] 
dist 37=[-.58817476334126039678,18.041791400827467166  ] 
dist 38=[-1.2861029294316515395 ,17.708792041859968994  ] 
dist 39=[-1.9796605726962690033 ,17.624428504283396277  ] 
dist 40=[-2.5940026915697901508 ,14.922483656849032800  ] 
dist 41=[-2.9783725509312065646 ,14.575608592150364961  ] 
dist 42=[-3.2577725868655189672 ,14.393736032057540933  ] 
dist 43=[-4.2660198589892320921 ,12.287506895004154677  ] 
dist 44=[-6.5991005207450076699 ,11.740785198896203697  ] 
dist 45=[-8.0755626675711510538 ,11.013182889587246453  ] 
dist 46=[-9.1788528699119831640 ,10.707479773894163711  ] 
dist 47=[-10.032516497727491722  ,3.7586473264022202086 ] 
dist 48=[-10.652350088395575330  ,2.8531394084812876820 ] 
dist 49=[-10.827890860223573833  ,.79769333877308876197] 
dist 50=[-10.817425283962414963  ,.37401932359853898977] 
dist 51=[-10.697523629694322134  ,-.65573753526892046215] 
dist 52=[-10.151946840702136167  ,-.39111266650940038112] 
dist 53=[-10.620122991039921110  ,-.20095042525239063911] 
dist 54=[-10.717915045245732779  ,-.03393321636285636101] 
dist 55=[-8.4952300992005140331 ,.13913613751013405778] 
dist 56=[-3.4773409335002853360 ,.86242179194821414223] 
dist 57=[-3.4062736078581317730 ,2.8129048227404737408 ] 
dist 58=[-3.3959753555649441384 ,4.4046969146106170146 ] 
dist 59=[-2.8225389169245645567 ,5.8756497108591750568 ] 
dist 60=[-2.6794483925560691444 ,7.1192421493251065987 ] 
dist 61=[-2.5880980686588911094 ,7.8087299164504046134 ] 
dist 62=[-2.5663329602659685083 ,8.2103316886239554394 ] 
dist 63=[-.37098026662267725187,8.3114898610443679098 ] 
dist 64=[-.11408750845659852223,2.5540978912161131673 ] 
dist 65=[.45212224605946088135,2.5879283469373789803 ] 
dist 66=[.33080024556551500205,2.5777405672263694165 ] 
dist 67=[.138982413535887068  ,2.5706188611904959415 ] 
dist 68=[-.05547902463841730808,2.2034678838608045602 ] 
dist 69=[-.18731038605993660673,2.1058590532817354732 ] 
dist 70=[-.29549362726042080407,2.0345826382425692057 ] 
dist 71=[-.39616830204930782654,2.0023734527345796795 ] 
dist 72=[-.48154189987516893416,1.7516704305823887352 ] 
dist 73=[-.52919402887051941773,1.7099177892396874776 ] 
dist 74=[-.55723523407105416092,1.6849802091121559567 ] 
dist 75=[-.83485597251853089103,1.4539806926339194376 ] 
dist 76=[-1.1122655921667614573 ,1.3929734277319266095 ] 
dist 77=[-1.2778935969994797407 ,1.3005832311251642924 ] 
dist 78=[-1.3902256979212873356 ,1.2664805127482365539 ] 
dist 79=[-1.4561492570034876103 ,.43855033711837017955] 
dist 80=[-1.4905163932952631017 ,.32808664615765289667] 
dist 81=[-1.4932959250296479125 ,.07961350818820913714] 
dist 82=[-1.4530557771411248564 ,.02628421745961491373] 
dist 83=[-1.4412471130565548311 ,.01996525074351467913] 
dist 84=[-1.2688350160658250811 ,.07549292093874342747] 
dist 85=[-1.3306747528624104222 ,.1135559199860320152 ] 
dist 86=[-1.3462508767245255929 ,.14530392383627267854] 
dist 87=[-1.0569652915192952455 ,.17577935866441232511] 
dist 88=[-.40941089183817124109,.20233258110015722086] 
dist 89=[-.39736049630265528237,.29558843504208109863] 
dist 90=[-.39479477364651503316,.46559859200565875388] 
dist 91=[-.32659436557757721579,.62310307902931544485] 
dist 92=[-.30980259619180286383,.75750094114569117906] 
dist 93=[-.29618816103765994425,.83864137104722632331] 
dist 94=[-.2910110945580475625 ,.88434083503538196429] 
dist 95=[-.08797528625220764012,.89506550580379195769] 
dist 96=[-.09556917495818046831,.34568380462583445416] 
dist 97=[-.10592573235797543455,.34752891024861940187] 
dist 98=[-.12004318168653499018,.33946362617078893135] 
dist 99=[-.1425686633052866389 ,.33829815525630740337] 
dist 100=[-.16556351860687537082,.2822733114615857211 ] 
dist 101=[-.18154757722476423096,.27152344808348442173] 
dist 102=[-.19512467493352389971,.25664462015931942146] 
dist 103=[-.20857218615923824666,.25399281281752989348] 
dist 104=[-.22075080030597024231,.22709036387177905063] 
dist 105=[-.23531302069088442215,.21844570521252120327] 
dist 106=[-.24247115400554736976,.2163731225551845717 ] 
dist 107=[-.24342869849304464297,.17758539120143264101] 
dist 108=[-.13542390179220335281,.16817634952653671896] 
dist 109=[-.15555985151227244451,.15919636501280269843] 
dist 110=[-.16874653821239459328,.15513416133060109137] 
dist 111=[-.17553908996942898401,.03925740970705083719] 
dist 112=[-.17859913640454024763,.02724743647028074090] 
dist 113=[-.1783957383341534879 ,6.01542859380237373510e-05] 
dist 114=[-.17391608790961781942,-.00537398540522418557] 
dist 115=[-.17132866384641280737,-.03573857686542504555] 
dist 116=[-.14764284672537695153,-.04079859270816848786] 
dist 117=[-.14140629126796799503,-.04968007548718519756] 
dist 118=[-.13503822078910584411,-.051276034231768272  ] 
dist 119=[-.12843626672220163861,-.02571272672722874008] 
dist 120=[-.05242199660905685351,.02054282589489031687] 
dist 121=[-.05047262293613563347,.05158397952119239261] 
dist 122=[-.05019000118851676763,.07682066164059757442] 
dist 123=[-.04070377316178490025,.10003223463733516495] 
dist 124=[-.03843307131115659970,.11961845927661602324] 
dist 125=[-.03683319272493678182,.13046210894717509791] 
dist 126=[-.03647013635429176764,.13677277840400302725] 
dist 127=[-.00362941290114611667,.13836229545374186872] 
dist 128=[.00020104405778605728,.04182212593078081354] 
dist 129=[.00908831667685973986,.04185811909254621976] 
dist 130=[.01040514894085126028,.04057795560154785908] 
dist 131=[.02069718939519792796,.04030761969698800989] 
dist 132=[.02220861466750554225,.03328809062048079277] 
dist 133=[.02492286412779747209,.03156369850207778403] 
dist 134=[.02065788645796044938,.03015784385372305574] 
dist 135=[.01124159474959498283,.02962323755343695951] 
dist 136=[.00178110714510566834,.02650697901934784012] 
dist 137=[-.00459899263611883611,.02562314313371080601] 
dist 138=[-.00982108645024723781,.02521601879373811975] 
dist 139=[-.01468432994179988118,.02147322004600326628] 
dist 140=[-.01883143465767390288,.02051801421471852994] 
dist 141=[-.02121047983855075898,.01907410125380859394] 
dist 142=[-.02270600679607980849,.01855184913221842423] 
dist 143=[-.02334559612923868376,.00612825827939595780] 
dist 144=[-.02349628491654751012,.00448176306238272228] 
dist 145=[-.02341520843354915871,.00080214939091457437] 
dist 146=[-.02251295324903624966,1.04468795014824085290e-08] 
dist 147=[-.02229710336197915497,-.00398704457096625870] 
dist 148=[-.01936340752967492126,-.00468351586371476878] 
dist 149=[-.02028269916760635909,-.00581645244886186954] 
dist 150=[-.02051442193464498322,-.00604787949220645539] 
dist 151=[-.01596894410869759993,-.00314316166023666502] 
dist 152=[-.00623878536315398679,.00165828997551042731] 
dist 153=[-.00598178175933601441,.00488122973156139377] 
dist 154=[-.00594338873805803104,.00750317808752746960] 
dist 155=[-.00479910031599858018,.00991851234244005293] 
dist 156=[-.00454850059158090517,.01196001699371206104] 
dist 157=[-.00432094698441757853,.01309773457170272232] 
dist 158=[-.00427331167102240612,.01380698980902286330] 
dist 159=[-.00082597390788197426,.01397148216777672043] 
dist 160=[-.00041034491183773297,.00541780508092349278] 
dist 161=[.00054579475420079745,.00541058613803127761] 
dist 162=[.00070742600727647108,.00520685572071468984] 
dist 163=[.00180687719477553515,.00517721295224677188] 
dist 164=[.00197667610967003339,.00419569404635353359] 
dist 165=[.00228747538670946071,.00396090945854998269] 
dist 166=[.00233884332422250621,.00379494271297946908] 
dist 167=[.00151239318849204702,.00378221069464297931] 
dist 168=[.00033192871170094759,.00376003827024527006] 
dist 169=[-.00046282986211343837,.00360187842896279453] 
dist 170=[-.00111206938555343148,.00355987024315056085] 
dist 171=[-.00171477990218619633,.00292480242721301210] 
dist 172=[-.00222756187186418631,.00277133606271282643] 
dist 173=[-.00251975871273326687,.00260616421758717595] 
dist 174=[-.00270096760750563959,.00252311561678600791] 
dist 175=[-.00277309797483766439,.00091710815372873661] 
dist 176=[-.00278806116474768658,.00079104626970515422] 
dist 177=[-.00277421317621294082,.00052191980788617233] 
dist 178=[-.00268176083245143191,.00044854003333667845] 
dist 179=[-.00263811820636449179,.00017155006641101544] 
dist 180=[-.00226803872822441159,.00011360049460690030] 
dist 181=[-.00236732411109348722,2.74181924735354101110e-05] 
dist 182=[-.00239276477948706335,4.07807062964273988780e-06] 
dist 183=[-.00194293205106389316,-.00031321339101941997] 
dist 184=[-.00071271400659173020,.00039028048725661598] 
dist 185=[-.00069128676251184999,.00086178535876068051] 
dist 186=[-.00067855855681407493,.00124468875955078028] 
dist 187=[-.00058844918371618644,.00159638357231098500] 
dist 188=[-.00056467981702228851,.00189299884274442947] 
dist 189=[-.00052170496232357986,.00205720290912355961] 
dist 190=[-.00050858357123413457,.00215287707740064118] 
dist 191=[-.00020423607964818299,.00217708448774424092] 
dist 192=[-.00016203797523580855,.00064604301700691008] 
dist 193=[-6.84995240329923898020e-05,.00064405414016681493] 
dist 194=[-4.60517452529858630290e-05,.00061740098280305191] 
dist 195=[5.47369845623872248460e-05,.00061345198470267222] 
dist 196=[7.32132583784044900730e-05,.0005717000181198916 ] 
dist 197=[.00010460626716567502,.00059922207180457720] 
dist 198=[.00011107145152622747,.00060850128962927385] 
dist 199=[-4.29499169857630847230e-05,.00060864789895977574] 
dist 200=[-.00021826457800632616,.00060332411518581797] 
dist 201=[-.00033599667861754690,.00058694060549146838] 
dist 202=[-.00043186757599352867,.00057721998115324996] 
dist 203=[-.00052038018677012683,.00051619521392478724] 
dist 204=[-.00059536321553826675,.00050013117624785759] 
dist 205=[-.00063751353902819751,.00045728699169404719] 
dist 206=[-.00066291344109730005,.00044106069150830481] 
dist 207=[-.00067138737715704472,.00026329079537220718] 
dist 208=[-.00067028433490596715,.00023341719011280507] 
dist 209=[-.00066485354373689564,.00017221610296391278] 
dist 210=[-.00064180346943263675,.00015571540161946664] 
dist 211=[-.00062845213323048850,9.55085104733413786090e-05] 
dist 212=[-.00054528455987403750,8.15634877038964385380e-05] 
dist 213=[-.00052349269374904858,6.58181703633820890250e-05] 
dist 214=[-.00041272632416779245,6.23972492942195825290e-05] 
dist 215=[-.00026200181103103926,6.23789515397403720660e-05] 
dist 216=[-9.54415035682237645190e-05,6.70341442589886302610e-05] 
dist 217=[-8.23157187370952282580e-05,.00011484091273612883] 
dist 218=[-5.42988254962255396970e-05,.00015371171754559238] 
dist 219=[-4.66598929100729063240e-05,.00018950094829248003] 
dist 220=[-1.78292349403971226940e-05,.00021975134574002015] 
dist 221=[-1.17942348871918036620e-05,.00023662922098558376] 
dist 222=[-2.83754231040691168680e-06,.00024697027071163239] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 2, 0, 1, 2] 
dist 0=[123.73874371956169796   ,123.73874371956169796   ] 
dist 1=[121.84080133503529248   ,125.22219961008578179   ] 
dist 2=[117.69093252957969089   ,127.71369781763201182   ] 
dist 3=[110.88055371566729417   ,129.95165086567184670   ] 
dist 4=[98.410275886967889516  ,130.43150592316867134   ] 
dist 5=[85.214006674200149578  ,129.94318125945463652   ] 
dist 6=[75.514473861280541783  ,129.27979550589295888   ] 
dist 7=[66.669388260015573300  ,108.35802570109420980   ] 
dist 8=[56.852519690977567499  ,105.11410924277546556   ] 
dist 9=[47.297887990123769637  ,95.392708435979121763  ] 
dist 10=[39.480184042761914163  ,93.993886959615206274  ] 
dist 11=[31.487659257290377533  ,73.250590264069348181  ] 
dist 12=[21.211136537331387624  ,68.945000492684018600  ] 
dist 13=[11.396313267279599873  ,64.891482452107097514  ] 
dist 14=[5.2352285422787096324 ,64.110565873343814077  ] 
dist 15=[.55773381698678323645,15.523440528842465717  ] 
dist 16=[-5.0354408494682844947 ,9.8829094134257472122 ] 
dist 17=[-9.9795484256760837025 ,-2.9252039303171795509 ] 
dist 18=[-13.865252910256471367  ,-3.1829979460325372143 ] 
dist 19=[-20.463643941257569691  ,-2.4353275965612849944 ] 
dist 20=[-24.667792905373481124  ,-.25588920516450192005] 
dist 21=[-27.487343011591558638  ,2.1614714882935077861 ] 
dist 22=[-29.128973228156853282  ,3.8589708987014712617 ] 
dist 23=[-30.045595038247400837  ,5.2554874501361481348 ] 
dist 24=[-30.137501916916433344  ,6.4924530544664557601 ] 
dist 25=[-29.596764552971550144  ,7.4624453338919500413 ] 
dist 26=[-29.212351237402807851  ,7.8083635079818129569 ] 
dist 27=[-25.338820508329213237  ,7.8970640767606199609 ] 
dist 28=[-24.311074693399300928  ,7.8537531108476969129 ] 
dist 29=[-22.792007941312701315  ,5.4778528167632033862 ] 
dist 30=[-22.214545340861614736  ,4.4929127316061562117 ] 
dist 31=[-8.1659412157695583175 ,2.1827944355528171306 ] 
dist 32=[-6.3209158005396355609 ,7.2361293388574318051 ] 
dist 33=[-2.4603481624576569900 ,11.342001668301648754  ] 
dist 34=[-2.2985829028198800309 ,15.114089648341217222  ] 
dist 35=[-1.9212143776957240054 ,18.294634489222385844  ] 
dist 36=[-1.8361063245168869041 ,20.052096204410146825  ] 
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dist 203=[-7.10439257870842410160e-05,.00012006306184999860] 
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dist 211=[-8.07843398665591290740e-05,-2.79191487669841281410e-05] 
dist 212=[-8.92855156604771459400e-05,-9.42203189632356811770e-06] 
dist 213=[-9.43390853338065030610e-05,9.10440989594624890140e-06] 
dist 214=[-9.58686063261859286680e-05,2.15226862089316618210e-05] 
dist 215=[-9.55377231276656292150e-05,3.16081801539346323450e-05] 
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dist 225=[-1.25215763007809620560e-05,3.75308889587286724050e-05] 
dist 226=[-1.06968711909049648300e-05,4.61356635093408623430e-05] 
dist 227=[-3.89055498721015697200e-06,5.33983577794341165710e-05] 
dist 228=[-2.45088596358799825880e-06,5.74336317541923864150e-05] 
dist 229=[-4.07425470929118549760e-06,5.98040300547647732580e-05] 
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dist 233=[-1.54421592891440134030e-05,2.12224225852651444970e-05] 
dist 234=[-1.67018569291692852050e-05,2.08451980891365015120e-05] 
dist 235=[-1.74513937604698935860e-05,1.77012153404986264660e-05] 
dist 236=[-1.76795693871631049510e-05,1.69071599323603141800e-05] 
dist 237=[-1.76626275139971731890e-05,1.56243850558769541220e-05] 
dist 238=[-1.74836767126400493970e-05,1.51961360168928566390e-05] 
dist 239=[-1.70740102374800191830e-05,5.17511543938865854050e-06] 
dist 240=[-1.68360390322648890000e-05,3.82320297446751486080e-06] 
dist 241=[-1.53522886450278436720e-05,8.28381671807355289850e-07] 
dist 242=[-1.49633381138151848760e-05,2.34232911386100284960e-07] 
dist 243=[-1.36220868933652796160e-05,1.02227828599729641500e-06] 
dist 244=[-1.33622504799390303750e-05,2.20912353111403024140e-06] 
dist 245=[-9.30881858124052574730e-06,3.39848584475615406600e-06] 
dist 246=[-8.05153551037665666330e-06,4.19654163927738020620e-06] 
dist 247=[-4.63217227590055204880e-06,4.84554308236774663300e-06] 
dist 248=[-4.59736515666265888040e-06,5.44309646595373351780e-06] 
dist 249=[-4.52226707374529388100e-06,5.94802539564318344200e-06] 
dist 250=[-4.34448620788809760430e-06,6.22926643655175743410e-06] 
dist 251=[-2.78169844533309172540e-06,6.50362602201779309580e-06] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 1, 0, 2, 0, 2] 
dist 0=[120.26352513042077801   ,120.26352513042077801   ] 
dist 1=[117.04283531984631559   ,121.32173721558929152   ] 
dist 2=[111.07375259326232851   ,122.30029266415768030   ] 
dist 3=[99.930364249484740254  ,123.53808412898249027   ] 
dist 4=[88.068435608224998316  ,125.38762516395767382   ] 
dist 5=[79.239895416282081700  ,126.97452924822335760   ] 
dist 6=[71.077269648755077970  ,127.17322534194359801   ] 
dist 7=[61.845584927398973979  ,126.51146623439582719   ] 
dist 8=[52.754652080228677551  ,120.97346971421796675   ] 
dist 9=[45.136624196985233524  ,103.76756525620056857   ] 
dist 10=[37.183545830731660404  ,100.43696208757987366   ] 
dist 11=[26.733857711844760860  ,90.633091502595705122  ] 
dist 12=[16.678180521032564678  ,89.226530819965785557  ] 
dist 13=[10.287713315568126030  ,68.837463940409308879  ] 
dist 14=[3.0952225967449243025 ,64.636624460266795502  ] 
dist 15=[-3.2205186294130309278 ,60.637746577583640687  ] 
dist 16=[-7.7350059735955426715 ,59.882960329873979858  ] 
dist 17=[-11.008951142706767007  ,13.197502792190055640  ] 
dist 18=[-13.466395387620643994  ,7.7882201568381846913 ] 
dist 19=[-14.722725389865849761  ,-1.3789089412846137024 ] 
dist 20=[-15.369936691662603752  ,-.60639403080803616211] 
dist 21=[-20.854319028600679191  ,.03933015155335168230] 
dist 22=[-24.755583738925493078  ,.63943663089352133543] 
dist 23=[-27.299184965068538361  ,1.2455937735757988123 ] 
dist 24=[-28.632226805656523682  ,1.7405293968410754919 ] 
dist 25=[-29.270517658014520588  ,1.9064630096355073268 ] 
dist 26=[-29.280023489682872829  ,1.9416110306588058141 ] 
dist 27=[-28.578504306481699440  ,1.9281810326829724818 ] 
dist 28=[-28.189204079722412186  ,1.3167967693442460518 ] 
dist 29=[-24.251703295973115926  ,3.1000103628657818614 ] 
dist 30=[-23.231240790434457081  ,4.7300804055973824814 ] 
dist 31=[-21.738277506304661111  ,5.6323265717237834289 ] 
dist 32=[-21.172938455041773632  ,6.1671777868669589744 ] 
dist 33=[-7.5185712252474810481 ,6.3381611577007616110 ] 
dist 34=[-5.7130788301360616798 ,6.9279693744594225031 ] 
dist 35=[-1.6478755178336982111 ,10.884082202180583854  ] 
dist 36=[-.79665648323476188681,14.517296322924043715  ] 
dist 37=[.73514856594515972247,17.581106175660096515  ] 
dist 38=[.97583197890698843325,19.276516108762686250  ] 
dist 39=[.91959179079889896696,20.262870564998293771  ] 
dist 40=[.00494024051377205164,20.511270805550264501  ] 
dist 41=[-.93252249188505030437,6.4032787750002675808 ] 
dist 42=[-1.7854877463722293015 ,6.4240787506627028469 ] 
dist 43=[-2.3658805007586476173 ,6.2571871942654594284 ] 
dist 44=[-2.8455902775221406523 ,6.2210925143900776626 ] 
dist 45=[-3.3002658817783396971 ,5.1732983687857375316 ] 
dist 46=[-3.6754691167650431399 ,4.9146020174169693595 ] 
dist 47=[-3.8401471312512066238 ,4.7072117209310607671 ] 
dist 48=[-3.9002313012601500210 ,4.6298941112747055807 ] 
dist 49=[-3.8851096975103859625 ,.85519831779136215491] 
dist 50=[-3.6046898954410716618 ,.41213551612931524255] 
dist 51=[-3.5043232119687637734 ,.38750905767816262255] 
dist 52=[-3.3157903923803520021 ,.35792184720937417539] 
dist 53=[-3.2459233148161217548 ,.39985925803819934792] 
dist 54=[-3.0026562499803330872 ,.49365082572741459702] 
dist 55=[-3.2330590950734426701 ,1.2250226874421694007 ] 
dist 56=[-3.3400894182973944604 ,1.8354390749872472628 ] 
dist 57=[-3.3748216695391318179 ,2.3938940263873944359 ] 
dist 58=[-3.3673370872713821933 ,2.8609037434078734302 ] 
dist 59=[-3.2454016363015490649 ,3.1085556952815151487 ] 
dist 60=[-3.2158854532020395423 ,3.2374138315349233543 ] 
dist 61=[-2.6449393283294712327 ,3.2622708957891202001 ] 
dist 62=[-2.5060664150834257160 ,.02543654777806821614] 
dist 63=[-2.3747646018431383026 ,.05209319515237059891] 
dist 64=[-2.3157113886187496079 ,.07415675504684852337] 
dist 65=[-.60438256037986065502,.19550292556243543378] 
dist 66=[-.42564098948982707778,.65883976008578294275] 
dist 67=[-.02049990209421246013,1.0358494201771594976 ] 
dist 68=[.05043024829903637604,1.3832462107852470253 ] 
dist 69=[.04106503839549988173,1.6769481844301430565 ] 
dist 70=[.03087615248603555003,1.8418223067014401060 ] 
dist 71=[.01749033900953895158,1.9445064285647279020 ] 
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dist 238=[-2.20761083722220695410e-05,1.97162264784328482690e-05] 
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dist 249=[-2.44103692355317410280e-06,8.83267125893684273820e-06] 
dist 250=[-2.28057998300430122460e-06,9.21854399787737701880e-06] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 1, 0, 2, 1, 2] 
dist 0=[116.89158643724158232   ,116.89158643724158232   ] 
dist 1=[114.95463994844685218   ,118.08559452625392148   ] 
dist 2=[112.07065650003544072   ,118.92709080579421233   ] 
dist 3=[107.11003954758251967   ,119.45313202496553617   ] 
dist 4=[99.767949511744087987  ,119.63438089139385601   ] 
dist 5=[87.420720102067486975  ,119.12548663954672521   ] 
dist 6=[74.505947721554091618  ,118.05701799650862949   ] 
dist 7=[64.903460532149062876  ,116.13112556503458920   ] 
dist 8=[56.028468069117280091  ,95.830804854561025966  ] 
dist 9=[45.989242771095885141  ,92.637821575881345993  ] 
dist 10=[36.098461800967755217  ,83.628284484458670968  ] 
dist 11=[27.798722154519376842  ,82.213243240329928986  ] 
dist 12=[19.124855479005349134  ,65.734645452372837448  ] 
dist 13=[7.7196904636738336487 ,60.820532711234800160  ] 
dist 14=[-3.1209525219705746560 ,56.963090015121359748  ] 
dist 15=[-9.5547126285402324012 ,55.930702954779891632  ] 
dist 16=[-14.010159255031505597  ,16.898910759866638144  ] 
dist 17=[-16.970991786702714777  ,12.246281595228088620  ] 
dist 18=[-19.083570590417296206  ,6.6937240185401067140 ] 
dist 19=[-20.154182992612045718  ,4.3295467538970313722 ] 
dist 20=[-20.699157268991323064  ,3.8393544165995075273 ] 
dist 21=[-21.686707626911451008  ,2.7324972804197708335 ] 
dist 22=[-24.355865852542354160  ,2.677529438073157036  ] 
dist 23=[-26.169912397931665663  ,2.964720454093096521  ] 
dist 24=[-27.414915783914244600  ,3.733375636916599243  ] 
dist 25=[-28.479530294943067426  ,4.699457574110459897  ] 
dist 26=[-28.724237493009004870  ,5.778475013229472672  ] 
dist 27=[-28.423481212718954477  ,7.118049111199501331  ] 
dist 28=[-25.737188427509814321  ,9.127260773264565569  ] 
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dist 32=[-4.5295141578841375287 ,12.519755299535755566  ] 
dist 33=[-2.6120009241118665809 ,11.530155386781707034  ] 
dist 34=[1.8997592607849509928 ,11.268579315621254438  ] 
dist 35=[2.5577029510674452849 ,11.113934959889155162  ] 
dist 36=[5.4747147896126456959 ,11.074735704968016475  ] 
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dist 38=[.68399711451487891556,13.053045094030064422  ] 
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dist 43=[-5.5763408328807641265 ,13.140677996055221278  ] 
dist 44=[-6.1875502643833467643 ,10.798813109134462622  ] 
dist 45=[-6.6527148095690815818 ,10.227082530709026001  ] 
dist 46=[-6.8120080688530545861 ,9.6720405698636641658 ] 
dist 47=[-6.8367942743934490875 ,9.4120583622141183197 ] 
dist 48=[-6.7683947800356424349 ,2.7988899847817756742 ] 
dist 49=[-6.1088995451250595353 ,2.0529841394724910202 ] 
dist 50=[-6.1497147292759972172 ,.34797111379484489577] 
dist 51=[-6.4433414834292142893 ,.01800753355575570888] 
dist 52=[-7.1915756655379435464 ,-1.3314322553775145698 ] 
dist 53=[-7.8968459202492137385 ,.5116467051484476956 ] 
dist 54=[-8.2915787360567835594 ,1.7552649853825793127 ] 
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dist 58=[-3.1454053054858666884 ,4.9482223888958274059 ] 
dist 59=[-3.1348382763011749976 ,5.2052601901865646807 ] 
dist 60=[-2.5996300707583473164 ,5.2700326730672517119 ] 
dist 61=[-2.4667377308551972946 ,1.6199791757043236448 ] 
dist 62=[-2.3802813994362435185 ,1.6497973454945849560 ] 
dist 63=[-2.3593824734313792646 ,1.6517143223518648121 ] 
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dist 65=[-.09940427790015988699,1.5537314584761530624 ] 
dist 66=[.44967912869709590212,1.4027234824272783865 ] 
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dist 80=[-.92889317398447359523,.4022546149804506354 ] 
dist 81=[-.77661970960265044451,.30100622362191482004] 
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dist 92=[-.301107495461485439  ,.57156860078298835315] 
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dist 94=[-.2728365660728292159 ,.22635970606697978676] 
dist 95=[-.269366181365975049  ,.2239456492767350466 ] 
dist 96=[-.05897359245907553871,.22122347655584163054] 
dist 97=[-.03342819423393238469,.2170810908920112107 ] 
dist 98=[.02572039935964796386,.18095803212266114358] 
dist 99=[.03555686339498311839,.17186603348665308999] 
dist 100=[.07288942083590502486,.1892355923622687209 ] 
dist 101=[.02287790291048828294,.21114438706499200508] 
dist 102=[-.01104916307231303359,.22486985516862087056] 
dist 103=[-.04005823945510200714,.23064313903569963113] 
dist 104=[-.06537512978230785063,.23183633852779974254] 
dist 105=[-.08863332736725433400,.230883278294815399  ] 
dist 106=[-.10877382018377072843,.22200225954944941108] 
dist 107=[-.12085746846267085682,.21955342767264111797] 
dist 108=[-.12770131029946586296,.18113777849990165737] 
dist 109=[-.1292897462458350757 ,.17176837638875031282] 
dist 110=[-.11730702745414984634,.16183217142447293872] 
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dist 168=[-.00118841375955570254,4.78921947692646558640e-05] 
dist 169=[-.00156603967889729658,-3.95529260087603808840e-05] 
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dist 179=[-.00135522479332884540,-.00047182114093027821] 
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dist 182=[-.00037066365924880893,.00060017469032936810] 
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dist 184=[-7.21689882989976377620e-05,.00109676159963499558] 
dist 185=[2.03281410466488476900e-05,.00129737090341443791] 
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dist 193=[.00015683039585145225,.00054596279335777806] 
dist 194=[.00010162821690267273,.00048316893964339509] 
dist 195=[2.38138087966455622970e-05,.00046641747396997460] 
dist 196=[-.00010608635826125131,.00042848088628735579] 
dist 197=[-.00023629341381613398,.00041499600953549635] 
dist 198=[-.00032375487205865544,.00021403143011577770] 
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dist 200=[-.00046078031662859355,.00011786227682575772] 
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dist 202=[-.00054785470601058080,3.42282356720888253650e-05] 
dist 203=[-.00056673899217104309,2.02988132977945242610e-05] 
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dist 205=[-.00057208281655467522,-2.76071669520690020900e-06] 
dist 206=[-.00022178937679007200,-3.33688295601840123000e-06] 
dist 207=[-.00021473105065665869,-4.91237921458300040000e-07] 
dist 208=[-.00021049060045966384,5.33939553232852234600e-06] 
dist 209=[-.00018257632571348725,1.66167496806419420120e-05] 
dist 210=[-.00017520847097517935,3.02470481598011365020e-05] 
dist 211=[-.00016141990684073624,4.54210465760062246000e-05] 
dist 212=[-.00015711625828604698,6.43288123476837206480e-05] 
dist 213=[-7.47506243120019008480e-05,9.27852418966060119280e-05] 
dist 214=[-5.16539220208997043990e-05,.00012130018499090201] 
dist 215=[-2.31938055844425957530e-05,.00014044064448941567] 
dist 216=[-1.59456234601081265240e-05,.00015601610578301544] 
dist 217=[1.09161327228034179310e-06,.00017179403079885665] 
dist 218=[1.63287010694147661820e-05,.00018491368147255430] 
dist 219=[1.88943848778563874090e-05,.00019287070555187178] 
dist 220=[2.34812911224214629110e-05,.00019463782001929586] 
dist 221=[2.43011710673034240430e-05,7.16011963471715577020e-05] 
dist 222=[2.49853935436704321180e-05,7.16361324952311322810e-05] 
dist 223=[2.38527331375168836560e-05,7.11694891961059303520e-05] 
dist 224=[2.10068756411590516150e-05,6.85155904551381465530e-05] 
dist 225=[1.51652350938962813590e-05,6.73819813933746415170e-05] 
dist 226=[8.67499669926627514970e-06,5.70299136576047939620e-05] 
dist 227=[5.95445785246526299200e-07,5.44214718626171697530e-05] 
dist 228=[-1.15572467024039390870e-05,5.04666676279039204330e-05] 
dist 229=[-2.37346994289307044740e-05,4.90532252535275903190e-05] 
dist 230=[-3.19127206829495534070e-05,1.60289248271361614750e-05] 
dist 231=[-3.85728699012558595830e-05,1.38343248984774123740e-05] 
dist 232=[-4.47233847163478497840e-05,9.14544552754376376370e-06] 
dist 233=[-4.99351542528974614650e-05,7.86546844945205015870e-06] 
dist 234=[-5.28678767316674371320e-05,3.02585394381508686830e-06] 
dist 235=[-5.46392011054667416850e-05,2.01420976910905859840e-06] 
dist 236=[-5.52394837445389339310e-05,4.94387505033694322220e-07] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 2, 2, 2, 0, 1] 
dist 0=[130.49197297255942987   ,130.49197297255942987   ] 
dist 1=[129.65744773299994009   ,130.21848688856387529   ] 
dist 2=[127.31040937945185556   ,130.49197297255942987   ] 
dist 3=[121.58267128819638694   ,129.00783715931004374   ] 
dist 4=[114.26679566587852932   ,122.05713405464050202   ] 
dist 5=[105.60415737942686160   ,117.08260316658049173   ] 
dist 6=[94.448468283365931228  ,115.06198882461176078   ] 
dist 7=[77.219402663706794326  ,112.91970025996471039   ] 
dist 8=[59.669998132312393425  ,95.988954727654621832  ] 
dist 9=[47.235820524066659423  ,92.072982390974331900  ] 
dist 10=[36.347983108076009081  ,90.313295824165303615  ] 
dist 11=[24.933380048556601821  ,55.767388259760712537  ] 
dist 12=[14.216692665680513681  ,41.398801625895738409  ] 
dist 13=[6.0914398155888157324 ,38.685438974673141513  ] 
dist 14=[-1.6308881715014755596 ,33.699592326335602138  ] 
dist 15=[-10.768034502067761407  ,32.562476625040693423  ] 
dist 16=[-19.106754935950246552  ,8.2698938666994012891 ] 
dist 17=[-23.658758861546587108  ,3.5514232712794622631 ] 
dist 18=[-26.763591745829738744  ,2.6340577413671919917 ] 
dist 19=[-31.464740623348778922  ,-9.7213665262318899375 ] 
dist 20=[-33.572761870878512223  ,-11.764508722388434636  ] 
dist 21=[-34.551056451542045002  ,-11.142788530779429880  ] 
dist 22=[-34.741227906359561379  ,-9.2840798475383570171 ] 
dist 23=[-31.565064880670150664  ,-5.3749126353385838971 ] 
dist 24=[-30.649661488004479240  ,-1.1193346642432715478 ] 
dist 25=[-30.043216181909652056  ,2.1209608560813309749 ] 
dist 26=[-29.738174233475101194  ,5.1432641440442354662 ] 
dist 27=[-8.7779715448771741431 ,8.5453719815253485483 ] 
dist 28=[-6.2563079301349907097 ,11.836691758707182067  ] 
dist 29=[-.31624590159970274833,14.426101834546463510  ] 
dist 30=[.62457239744180767718,16.952043528422866157  ] 
dist 31=[6.3676763280491304946 ,19.999822549187971606  ] 
dist 32=[8.9196796308832964978 ,22.702648612806531477  ] 
dist 33=[10.983356170867454949  ,23.861123164151128937  ] 
dist 34=[11.325474114500483371  ,24.353999059589196678  ] 
dist 35=[13.062873752541897983  ,24.407624568116404645  ] 
dist 36=[11.656597797897109011  ,22.043038215096531913  ] 
dist 37=[9.8012269919629356889 ,21.330399304980763769  ] 
dist 38=[7.3102848952392803632 ,20.827604566588895713  ] 
dist 39=[3.3812020119734086494 ,20.502392471107570711  ] 
dist 40=[-.59944145772305599097,15.675286218510363561  ] 
dist 41=[-3.2956384696249729793 ,14.730903830674070606  ] 
dist 42=[-5.5060213864800310645 ,14.392392311193861357  ] 
dist 43=[-7.5599872144854562745 ,6.9620176038660517725 ] 
dist 44=[-9.6135971066696775078 ,6.0555906014583094713 ] 
dist 45=[-11.376264685691161459  ,4.0106009445885422443 ] 
dist 46=[-12.670074180547139143  ,3.4801343215842511039 ] 
dist 47=[-13.628495128930369892  ,1.0824162429844512824 ] 
dist 48=[-14.297868956906699767  ,.63644074398069711658] 
dist 49=[-14.447689269982383534  ,-.29706024463188298925] 
dist 50=[-14.567580011478366927  ,-.53007964794530782229] 
dist 51=[-14.182811678889547536  ,-1.2684545201667409132 ] 
dist 52=[-12.670320101287630939  ,-1.2843610029689118362 ] 
dist 53=[-12.225066970757215106  ,-1.0458001781978510179 ] 
dist 54=[-11.430728767280670132  ,-.4065840510834808596 ] 
dist 55=[-11.168066985164281013  ,.42159653393027178258] 
dist 56=[-6.1474980658135831268 ,2.8489702358991035205 ] 
dist 57=[-5.5860419981770477341 ,5.1725673492739979519 ] 
dist 58=[-3.5610148990967773398 ,7.0763183287986668206 ] 
dist 59=[-1.2774673191883893406 ,8.8487456780674077217 ] 
dist 60=[-.24336812498800304279,10.460493610257839376  ] 
dist 61=[.39332642239524722099,11.366157883093853634  ] 
dist 62=[.49276734258116775633,11.867402410458044341  ] 
dist 63=[1.1355402422732420874 ,11.955494031761319468  ] 
dist 64=[1.3447802561387375083 ,2.5127916093760955038 ] 
dist 65=[1.4372951539541878234 ,2.5474085405019960761 ] 
dist 66=[1.3917690832992384505 ,2.5340222480438058332 ] 
dist 67=[1.2563608059000511639 ,2.5320457722912180910 ] 
dist 68=[1.0778119624830573042 ,2.1475527332312428054 ] 
dist 69=[.86099816510734139297,2.0481072249369137546 ] 
dist 70=[.57955300778083426109,1.9900732366110467181 ] 
dist 71=[.1444205448028718312 ,1.9754393820835418280 ] 
dist 72=[-.29475154971017012538,1.5359882949257261602 ] 
dist 73=[-.59226620143217449035,1.4425198964932469390 ] 
dist 74=[-.83682498139796040507,1.4047991572361788143 ] 
dist 75=[-1.0658570449304276461 ,.48579744977278415321] 
dist 76=[-1.2800700949053698496 ,.3667278633981411173 ] 
dist 77=[-1.4061600534943870863 ,.16701755323047077202] 
dist 78=[-1.4756388270305201599 ,.0733065041068273672 ] 
dist 79=[-1.4899925457111668829 ,.05266090959658865861] 
dist 80=[-1.3286251767906215581 ,-.31568514657918065173] 
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dist 85=[-1.0800349466442753456 ,-.32378343521301305334] 
dist 86=[-1.0116149721096093328 ,-.22895714637537974303] 
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dist 88=[-.41309402027072085179,.13711473059530898075] 
dist 89=[-.38294954012558078475,.37114672289785772137] 
dist 90=[-.37273967217102826246,.56166074809441235285] 
dist 91=[-.17188687997277199691,.73716658422502563954] 
dist 92=[-.14291280944571706916,.8853565218292228643 ] 
dist 93=[-.07913579775477817314,.96743823685376311996] 
dist 94=[-.06238701041076625551,1.0152217063487577476 ] 
dist 95=[.00578620110746933265,1.0272587669607348405 ] 
dist 96=[.01892071140540275489,.44654723928291852595] 
dist 97=[.04138233474466126281,.4427203423061652692 ] 
dist 98=[.04620189575181026155,.42788836322583030547] 
dist 99=[.05292683033137128176,.30575626598975551737] 
dist 100=[.05197227779685353470,.2806065139437281867 ] 
dist 101=[.04735532668681450105,.26980440778461158399] 
dist 102=[.02584912154132698980,.26743129143738425166] 
dist 103=[-.01291886245581558433,.22958621544245694427] 
dist 104=[-.05200439538566398552,.20631433229522810071] 
dist 105=[-.07850222584163912517,.19559629799119495792] 
dist 106=[-.10032401664794807727,.19117785287399153066] 
dist 107=[-.12085032835714926228,.03342361190585081334] 
dist 108=[-.13848145856542951899,.02101333919719526132] 
dist 109=[-.15705343616701885616,-.00759213314433918252] 
dist 110=[-.1691336934798576204 ,-.01261952437804913612] 
dist 111=[-.17509266429025269588,-.04592392491681813472] 
dist 112=[-.17733220290232280721,-.05113879189657452016] 
dist 113=[-.17707483024563909772,-.06103445255229645614] 
dist 114=[-.17101201165829067298,-.06283901850055783094] 
dist 115=[-.16947897027539232875,-.0654523534711804827 ] 
dist 116=[-.13983158252298577339,-.06461832759539172366] 
dist 117=[-.13256122085164761726,-.06216053091829040513] 
dist 118=[-.12568483731188283355,-.05691426459652614910] 
dist 119=[-.12249426583171669432,-.02532343707068094435] 
dist 120=[-.04873599497230693541,.01120647025657280239] 
dist 121=[-.04682238709663828031,.03575788778118328411] 
dist 122=[-.04638524622174959232,.05575749258785411634] 
dist 123=[-.00511186974634409693,.07421705714563491712] 
dist 124=[-.00029361273401894977,.08983842946549499158] 
dist 125=[.01087697325885876082,.09878811210298487635] 
dist 126=[.01255300089605050189,.10422570594865739407] 
dist 127=[.02546146018850661780,.10548154366944167546] 
dist 128=[.02736671320062776893,.04111737514656435391] 
dist 129=[.03075258930035909919,.04116814693388001988] 
dist 130=[.03124293860264459946,.03984806430219364500] 
dist 131=[.03329893120764067279,.03965649068534329657] 
dist 132=[.03168074483622742079,.03327327032977662158] 
dist 133=[.02701362204004040815,.03226344439143857211] 
dist 134=[.02111946996393223449,.03176097908334437633] 
dist 135=[.01216632193410370107,.02916966759079648187] 
dist 136=[.00316830264289489218,.02598647851547199361] 
dist 137=[-.00290432680484414287,.02418523041862728436] 
dist 138=[-.00787952399466636145,.02353287925956539415] 
dist 139=[-.01252081687854639062,.00788436551069833240] 
dist 140=[-.01648422589945597505,.00579748461059421940] 
dist 141=[-.01876827665147896013,.00112309104955570149] 
dist 142=[-.02021744549533436270,.00011027343202307187] 
dist 143=[-.02236028243992923286,-.00499023390789122665] 
dist 144=[-.02436265046989606621,-.00587717190281616561] 
dist 145=[-.02552775612823332091,-.00735266776023304992] 
dist 146=[-.02582119996438777765,-.00764610975684787809] 
dist 147=[-.02005550835242176505,-.00777586274917498131] 
dist 148=[-.01715490704280714055,-.00763052933459703785] 
dist 149=[-.01640609618569200362,-.00729614882076882475] 
dist 150=[-.01527256946580994244,-.00662534713516864192] 
dist 151=[-.01486008410592497332,-.00282348514083977852] 
dist 152=[-.00575902383573120716,.00256720905372611693] 
dist 153=[-.00548730472204574188,.00618200553036971525] 
dist 154=[-.00538749444444857771,.00911880908557171042] 
dist 155=[-.00077281093323241340,.01181762549177238192] 
dist 156=[-.00022123342948534567,.01409415569837238105] 
dist 157=[.00106171032224619843,.01535431025351901173] 
dist 158=[.00125666719267382608,.01608801526915031788] 
dist 159=[.00276333214940264655,.01627278928886107696] 
dist 160=[.00298724589724150241,.0049717042685939973 ] 
dist 161=[.00340192294949319858,.00496432591003224367] 
dist 162=[.00346539338836132362,.00477643194935111326] 
dist 163=[.00353488474893820354,.00474835505056605312] 
dist 164=[.00344475548826811274,.00431980208112043909] 
dist 165=[.00296459902208294971,.00414163551465060050] 
dist 166=[.00221587253649753112,.00410024859368447176] 
dist 167=[.00108493161639067002,.00344212765265174760] 
dist 168=[-4.97101258485802719060e-05,.00317088449046053454] 
dist 169=[-.00081315620612131200,.00299696662672588422] 
dist 170=[-.00143631550008433781,.00291930454722255505] 
dist 171=[-.00201397342028962163,.00071681739978186359] 
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dist 183=[-.00203033837018127340,-4.44355344025653000000e-05] 
dist 184=[-.00074901823542937328,.00050400599791832663] 
dist 185=[-.00068735237861011577,.00087217642572676851] 
dist 186=[-.00068030377657225546,.00117179751384154753] 
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dist 188=[-.00014696045182758779,.00168181423485463773] 
dist 189=[-.00010009464463865361,.00181262371333341380] 
dist 190=[-2.63174437325402553280e-05,.00189603058076756729] 
dist 191=[-7.57322022354064467100e-06,.00191647640371455659] 
dist 192=[.00040248030718061666,.00062371556501553008] 
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dist 194=[.00046195655154888285,.00059787174793616936] 
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dist 197=[.00038382107931747859,.00050781245419767938] 
dist 198=[.00029025576195930724,.00049879297178054020] 
dist 199=[.00014928395873455115,.00042683359451471646] 
dist 200=[7.95087163974325544150e-06,.00040835907729349958] 
dist 201=[-8.70513709053628959820e-05,.00037755535469848089] 
dist 202=[-.00016450881515070551,.00036751338312248503] 
dist 203=[-.00023617974647607005,.00015028065241348632] 
dist 204=[-.00029700480507721766,.00012371992517992315] 
dist 205=[-.00033139842586381459,6.60185912444547173580e-05] 
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dist 207=[-.00037796312716082706,-8.63532398788704142590e-06] 
dist 208=[-.00040814541291927267,-2.03623387336566955420e-05] 
dist 209=[-.00042593384823928696,-3.78850714439932753590e-05] 
dist 210=[-.00043040960628424988,-4.22476920547668384730e-05] 
dist 211=[-.00033973830206958540,-4.23525424085772916390e-05] 
dist 212=[-.00029441620000541735,-3.66176350206668411690e-05] 
dist 213=[-.00028249182452000894,-2.56342341553610385190e-05] 
dist 214=[-.00026011686546551676,-4.89678372010191082000e-06] 
dist 215=[-.00025313443227938664,2.00068362353861425540e-05] 
dist 216=[-.00013172080891595267,.00010123160598732048] 
dist 217=[-.00011895710841523544,.00015764482991369428] 
dist 218=[-7.91224322519643922300e-05,.00020347737635249572] 
dist 219=[-2.76237308920421447320e-05,.00024561668529122258] 
dist 220=[-2.15577435915473918840e-05,.00028119303513542602] 
dist 221=[-8.11015766591103583710e-06,.00030096589789423784] 
dist 222=[-4.93404378345167025330e-06,.00031280822006603499] 
dist 223=[9.48446577170338875320e-06,.00031578850609689709] 
dist 224=[1.21106599022947950110e-05,8.00289536036404665560e-05] 
dist 225=[1.64308762292835452090e-05,8.38555288631267428600e-05] 
dist 226=[1.73430948284691988240e-05,8.50781457795936567050e-05] 
dist 227=[1.77169743568472227220e-05,8.48759034909690925860e-05] 
dist 228=[1.64775618910348619180e-05,8.42458010977546864260e-05] 
dist 229=[1.40114740343472613450e-05,8.09229334276465984960e-05] 
dist 230=[8.37112538872838788560e-06,7.95671251337117850160e-05] 
dist 231=[-7.63102554489698107160e-06,6.71077832102038913190e-05] 
dist 232=[-2.36645346016655001600e-05,6.39923785757240723700e-05] 
dist 233=[-3.44313386645995316040e-05,5.92946187880857365800e-05] 
dist 234=[-4.31991420420120955000e-05,5.76145069228711338610e-05] 
dist 235=[-5.12952701097356454780e-05,1.79508470516250979660e-05] 
dist 236=[-5.81554227608994883270e-05,1.47919429414791948350e-05] 
dist 237=[-6.20155745919522441110e-05,9.67917731748829978380e-06] 
dist 238=[-6.43469916597992781660e-05,8.29077750953030668960e-06] 
dist 239=[-6.51370657718297070400e-05,3.08462259038565467710e-06] 
dist 240=[-6.51594895270610261100e-05,1.98839957384352017620e-06] 
dist 241=[-6.45070630606721995080e-05,4.37883516475859177670e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 1, 0, 1, 0, 2] 
dist 0=[116.87444241650915412   ,116.87444241650915412   ] 
dist 1=[114.46694747923942581   ,117.53437807490393840   ] 
dist 2=[110.28777880207366208   ,117.56716237273367462   ] 
dist 3=[102.58733827498265023   ,117.47873343765383947   ] 
dist 4=[94.250072415059968401  ,117.35834990495778671   ] 
dist 5=[87.530922127151097396  ,117.25869161347265020   ] 
dist 6=[80.794741220723808899  ,117.13557876552358566   ] 
dist 7=[72.375524469869687808  ,116.44241854806881179   ] 
dist 8=[63.605273936543781701  ,91.430634617831005388  ] 
dist 9=[55.460233883384210986  ,87.864853333062966566  ] 
dist 10=[46.255813615980290629  ,81.246660547803748531  ] 
dist 11=[33.249240679903273228  ,79.545323872127618191  ] 
dist 12=[20.444714277156189396  ,73.985365884761681918  ] 
dist 13=[12.040520712240132126  ,72.471223802774199672  ] 
dist 14=[5.2623061217334727363 ,66.346171975952743884  ] 
dist 15=[-1.0621072659587466328 ,55.874340276903444591  ] 
dist 16=[-6.6207204612056601635 ,14.944861158229934283  ] 
dist 17=[-10.348709670992546627  ,6.5130802851019999472 ] 
dist 18=[-13.469881850456333279  ,5.2380171809424063683 ] 
dist 19=[-16.614995104762335149  ,-2.8763342400624975484 ] 
dist 20=[-19.325061944379905226  ,-1.6985753946931609625 ] 
dist 21=[-20.761945043452225104  ,-.49375242934894189094] 
dist 22=[-22.392209917500076108  ,.87868974756418200308] 
dist 23=[-23.472633319233384266  ,2.7389337404314574346 ] 
dist 24=[-23.696634492739164245  ,4.6846763383806896910 ] 
dist 25=[-23.375141788999119094  ,6.4057911915303973891 ] 
dist 26=[-23.289706604944990933  ,8.2488471482982298053 ] 
dist 27=[-19.686305401923100873  ,10.688757778110953002  ] 
dist 28=[-18.772962197228851896  ,12.942012190162857452  ] 
dist 29=[-18.084456882413811278  ,14.047336718389373816  ] 
dist 30=[-17.827973418270574562  ,14.611508276223238134  ] 
dist 31=[-3.9999807598197327610 ,14.712880405772143332  ] 
dist 32=[-2.3550883335438201452 ,13.762556199831864209  ] 
dist 33=[1.5140277593963922042 ,13.456234684964485680  ] 
dist 34=[2.0762051989306922000 ,13.226499248780534916  ] 
dist 35=[6.2551460020523382173 ,13.053858086303033078  ] 
dist 36=[2.7796645529076730512 ,9.9817018733941990616 ] 
dist 37=[.35538404858440870165,10.900344430076566847  ] 
dist 38=[-1.7065314212266902323 ,11.420670032030846240  ] 
dist 39=[-3.7460432092578303888 ,11.694539246065106539  ] 
dist 40=[-5.5602504838920122139 ,11.701407704574104759  ] 
dist 41=[-6.7292565867983977090 ,11.461806281889469944  ] 
dist 42=[-7.6259742914601519613 ,11.285321908760782522  ] 
dist 43=[-8.3610557811369445114 ,9.8251024059453347666 ] 
dist 44=[-8.9150574466975263434 ,9.4319903577191694305 ] 
dist 45=[-9.0934655194615583410 ,8.7843571516449281013 ] 
dist 46=[-9.1028930513151244543 ,8.5637643558925040622 ] 
dist 47=[-9.0088738288704403015 ,3.9942342248510188916 ] 
dist 48=[-8.1444957598299174943 ,3.4412083149806309265 ] 
dist 49=[-7.8771616288199020129 ,2.2099783994095484661 ] 
dist 50=[-7.3984249993477810916 ,1.8837751896750520841 ] 
dist 51=[-7.9993073502448780226 ,.48974893283708053345] 
dist 52=[-8.6982153990136212902 ,1.7663884792389254396 ] 
dist 53=[-9.0897014081872120260 ,3.2642174195616672031 ] 
dist 54=[-9.1598069529942479088 ,4.4906356532335713997 ] 
dist 55=[-2.4866534185693303195 ,5.6300798923100302765 ] 
dist 56=[-2.2308390232951678098 ,6.5972274331820541710 ] 
dist 57=[-2.1680547002678620445 ,7.1668059987963565851 ] 
dist 58=[-2.1589162851800115177 ,7.5028468492967840590 ] 
dist 59=[-1.7753286928536430373 ,7.5670915568213003510 ] 
dist 60=[-1.6817014688174637234 ,1.6330291882744475692 ] 
dist 61=[-1.6184231009705254142 ,1.6727725806893967558 ] 
dist 62=[-1.6037080148218854444 ,1.6811957109031086821 ] 
dist 63=[-.21151072177328487124,1.6832337843151100527 ] 
dist 64=[-.04889313778168267756,1.4537177679796214844 ] 
dist 65=[.32818874823698015401,1.3941823913615447588 ] 
dist 66=[.38489436593494805352,1.3593386107681894214 ] 
dist 67=[.63719378128714305901,1.3503976978117413792 ] 
dist 68=[.25882254500099092544,.9708474339659583957 ] 
dist 69=[-.00074595973823507027,1.0501549784637322829 ] 
dist 70=[-.21752363242145700045,1.0877016169575941535 ] 
dist 71=[-.42613793825118222917,1.1019610625662605742 ] 
dist 72=[-.60833509692828888267,1.0992253537766892673 ] 
dist 73=[-.72031157687935863642,1.0680135663728818736 ] 
dist 74=[-.80013681473719927652,1.0518387803231043711 ] 
dist 75=[-.8547875876356867499 ,.90184712778876400485] 
dist 76=[-.89053273932188434487,.86295634179723093249] 
dist 77=[-.89608736582411074712,.80417041375221773323] 
dist 78=[-.88826505910887116135,.78268282318316815387] 
dist 79=[-.87687253333742140087,.266572351703444059  ] 
dist 80=[-.77249189045134057588,.19794183981210075723] 
dist 81=[-.74298933091267473613,.04408894731087797952] 
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dist 83=[-.72732410177976314224,-.14843380007351248593] 
dist 84=[-.79319040350410914221,.08894377993279515710] 
dist 85=[-.83154271547523530157,.24864824654088051511] 
dist 86=[-.84118319889217249275,.37879101539800599687] 
dist 87=[-.25407910882457840914,.49883810288287728043] 
dist 88=[-.2538827032727561168 ,.60025553917430608097] 
dist 89=[-.24510631962550539691,.65645443894432818678] 
dist 90=[-.24340094214664942695,.68919027122105397795] 
dist 91=[-.20047894775924228684,.69743682986597020152] 
dist 92=[-.19044264805092022879,.2109797422785334862 ] 
dist 93=[-.18070961481603655796,.21279229852130819324] 
dist 94=[-.17738228989720571279,.20979935771536918432] 
dist 95=[-.03566522627794844408,.20896663040624502247] 
dist 96=[-.01837933848814951732,.17716993958671319554] 
dist 97=[.02162005216143811990,.16941460647147459352] 
dist 98=[.02816731164305160198,.16204288630138017466] 
dist 99=[.05660887372078495312,.15946456263080448675] 
dist 100=[.00628603834329836875,.13863137724315804892] 
dist 101=[-.02786095298181585433,.14750602938011743196] 
dist 102=[-.05601433707634978359,.15098994129058822024] 
dist 103=[-.08254875950943299583,.15146856662181939404] 
dist 104=[-.10537527724247772365,.15073271967754464414] 
dist 105=[-.11881206015191840379,.14480196762877827708] 
dist 106=[-.12769031150320922318,.14309027540506466832] 
dist 107=[-.13242428180113176171,.11825254721501745926] 
dist 108=[-.13450382047294061082,.11219266647895142056] 
dist 109=[-.13437318365298388008,.105456005087815721  ] 
dist 110=[-.13030125646665062815,.1021617033350688281 ] 
dist 111=[-.12886450292968693275,.03832252941138706098] 
dist 112=[-.10803152528541324549,.03284917166186650852] 
dist 113=[-.10279520752766155599,.02091765323136413943] 
dist 114=[-.09687913094911119135,.01762227781655978044] 
dist 115=[-.09397688675118139289,.00486370311976120389] 
dist 116=[-.09186937034146678404,.02277947005495936630] 
dist 117=[-.0964754282815759142 ,.03982922096667590287] 
dist 118=[-.09749005501917747471,.05374899506617229878] 
dist 119=[-.03167792890878376402,.06664473252078110585] 
dist 120=[-.03159366118495183547,.07758805974295349267] 
dist 121=[-.03030932312944830069,.08385231589519640044] 
dist 122=[-.03012414586873164922,.08806430707332094445] 
dist 123=[-.02430007375035302779,.08897975247382364840] 
dist 124=[-.02291806745048305728,.02799215543655257749] 
dist 125=[-.02192730774877325781,.02808750887426215313] 
dist 126=[-.02170742140540158785,.02731908808548055564] 
dist 127=[-.00195885068947482109,.02720817337409696692] 
dist 128=[.00034179554746888280,.02238525739756163350] 
dist 129=[.00567778040293555504,.02120121971583073201] 
dist 130=[.00646363609609370431,.02041780416966501337] 
dist 131=[.00860585133700229129,.02023535525039204064] 
dist 132=[.00244300317852770192,.01447102240273666283] 
dist 133=[-.00172509018800803761,.0154903856612567249 ] 
dist 134=[-.00514869431086426019,.01586529760300589863] 
dist 135=[-.00835618813806013873,.01591074281182204462] 
dist 136=[-.01110389774816066304,.01581967140138608500] 
dist 137=[-.01270232608797769275,.01525932365511894189] 
dist 138=[-.01373527690083342966,.01501174531761663733] 
dist 139=[-.01423827177580521534,.01274885997625885901] 
dist 140=[-.01444084036019629230,.01217545330471729151] 
dist 141=[-.01440996151751744046,.01130576869194528276] 
dist 142=[-.01401672925343573791,.01099386935377713458] 
dist 143=[-.01380371674124215240,.00358261028517183900] 
dist 144=[-.01186093660645051662,.00259581381758423787] 
dist 145=[-.01135343199252479569,.00039301581219565549] 
dist 146=[-.01058030438788199775,-8.66112201011671617710e-05] 
dist 147=[-.01063247851854370122,-.00201903167702857457] 
dist 148=[-.01157437021205873092,.00171007809787508901] 
dist 149=[-.01212232083912846574,.00421179853644078730] 
dist 150=[-.01226031668135097988,.00624512059033256067] 
dist 151=[-.00368689613291283616,.00811460323472093935] 
dist 152=[-.00367124050352242688,.00969186546994680948] 
dist 153=[-.00351742460626237297,.01056500323905079675] 
dist 154=[-.00348806287170995995,.01107310775193539320] 
dist 155=[-.00283163361659530931,.01120108430704211002] 
dist 156=[-.00267509947181627613,.00337817592400471193] 
dist 157=[-.00254183206097633052,.00337767002944966123] 
dist 158=[-.00249444614907463985,.00326693958892423628] 
dist 159=[-.00032103099513778368,.00324407191144586327] 
dist 160=[-6.14918873585963974800e-05,.00267042020795865389] 
dist 161=[.00053972963804650664,.00253029092751797229] 
dist 162=[.00063207499230451865,.00241503455376063731] 
dist 163=[.00089020317822230997,.00237167342804013228] 
dist 164=[.00012770874724480139,.00187983896275171015] 
dist 165=[-.00038610029394259595,.00199809016317008488] 
dist 166=[-.00080624899667824303,.00203697992320152120] 
dist 167=[-.00119690045339080042,.00203386080137192630] 
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dist 175=[-.00179678039414216189,.00032034521148854298] 
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dist 177=[-.00139335017095434954,-2.47567827351272336160e-05] 
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dist 179=[-.00128403622698329780,-.00024974510132476600] 
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dist 193=[8.78761943697375575930e-05,.00031810270305500480] 
dist 194=[9.92281165650241612950e-05,.00030457607930301988] 
dist 195=[.00012211807891157979,.00030149534535107360] 
dist 196=[2.71943537000819983950e-05,.00021580934710609042] 
dist 197=[-3.66815215795223174400e-05,.00023008937985820008] 
dist 198=[-8.88298369050476319420e-05,.00023461498010467321] 
dist 199=[-.00013719059479112927,.00023431969805909843] 
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dist 210=[-.00015886698465702256,-2.12440497049672888980e-06] 
dist 211=[-.00015676721458858482,-2.82591814433274052160e-05] 
dist 212=[-.00017050973611287601,2.83214874601664279690e-05] 
dist 213=[-.00017850429271435531,6.62379028275393511200e-05] 
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dist 215=[-5.46841815378703215210e-05,.00012529520896359225] 
dist 216=[-5.43793833617873122700e-05,.00014913501533113747] 
dist 217=[-5.18458041652059573300e-05,.00016232792388474630] 
dist 218=[-5.14572996693570512670e-05,.00017000424160423545] 
dist 219=[-4.12408582775812863950e-05,.00017193944653934721] 
dist 220=[-3.90511269608975413760e-05,5.21826146505158214260e-05] 
dist 221=[-3.69410942531832373370e-05,5.20010380656942536500e-05] 
dist 222=[-3.64803149088510677020e-05,4.98199362250835139030e-05] 
dist 223=[-6.48313524730370099000e-06,4.94823650332646474150e-05] 
dist 224=[-2.86102346243663169880e-06,3.99608964614359006980e-05] 
dist 225=[5.43386518057810880150e-06,3.79039294303795915800e-05] 
dist 226=[6.85213458993368067510e-06,3.59253174199240329040e-05] 
dist 227=[1.08566044918335833810e-05,3.54907149889672394400e-05] 
dist 228=[-1.03089329785716343130e-06,3.08149326700482554890e-05] 
dist 229=[-9.01555339823947214960e-06,3.25436582568689147140e-05] 
dist 230=[-1.55194103604690635000e-05,3.30524258622005669820e-05] 
dist 231=[-2.15272237966715520000e-05,3.29206179225352919750e-05] 
dist 232=[-2.66189344480770726330e-05,3.26884302564670574340e-05] 
dist 233=[-2.94853089144454908300e-05,3.12292931068258880960e-05] 
dist 234=[-3.12180325538099264710e-05,3.08535744447080862970e-05] 
dist 235=[-3.18084765287849430530e-05,2.52615200138220293550e-05] 
dist 236=[-3.17800307282558444840e-05,2.39196081288206252880e-05] 
dist 237=[-3.15872588415918244700e-05,2.24683560314007825580e-05] 
dist 238=[-3.02480188072665455460e-05,2.17460715485560690130e-05] 
dist 239=[-2.98915379492467693120e-05,7.69292848501096602710e-06] 
dist 240=[-2.45576208298667717860e-05,6.59773704776280134940e-06] 
dist 241=[-2.32693468558451337940e-05,4.27710702675452613550e-06] 
dist 242=[-2.18750515071590543690e-05,3.64979726892498671910e-06] 
dist 243=[-2.11784323961485507780e-05,1.31479248703955697370e-06] 
dist 244=[-1.98103670355252583540e-05,5.56570133266979045870e-06] 
dist 245=[-2.06242442481050695360e-05,9.40749216393247446650e-06] 
dist 246=[-2.08448744255217906020e-05,1.25294452790960682480e-05] 
dist 247=[-3.84180632209398259910e-06,1.54010728635367168440e-05] 
dist 248=[-1.59558051526973220410e-06,1.78263671096285325210e-05] 
dist 249=[-1.11835909481376220580e-06,1.91760548760199078130e-05] 
dist 250=[-2.18896810596323731280e-07,1.99715388158104748860e-05] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 1, 1, 1, 2] 
dist 0=[129.19346255052872646   ,129.19346255052872646   ] 
dist 1=[127.40481648263889424   ,129.69394657470894989   ] 
dist 2=[122.33037181963728274   ,129.66128568689680885   ] 
dist 3=[115.67232034250339637   ,129.39550403409132421   ] 
dist 4=[107.58521561255637561   ,124.59591623265406528   ] 
dist 5=[97.048448186413524272  ,120.28615954602542657   ] 
dist 6=[80.648855807656586643  ,117.89274765456725220   ] 
dist 7=[63.897101567077299807  ,115.57745710948916647   ] 
dist 8=[51.954882456338872498  ,110.52594228934600743   ] 
dist 9=[41.421786087101305102  ,88.134931461093866807  ] 
dist 10=[30.258834665746669174  ,86.327650187948722693  ] 
dist 11=[19.701906673293533550  ,60.181448388027831169  ] 
dist 12=[11.565703958946713792  ,57.862013352699954259  ] 
dist 13=[3.7033108153866192173 ,44.055133819624463653  ] 
dist 14=[-5.7880049447844283706 ,41.740020727824701179  ] 
dist 15=[-14.539659759581942208  ,36.736062100845250249  ] 
dist 16=[-19.465282090674729042  ,35.881460357818796091  ] 
dist 17=[-23.342767869850895437  ,1.0161539135938926266 ] 
dist 18=[-28.418780217948092796  ,-.01027135696343660416] 
dist 19=[-32.627716934398047249  ,-8.1846046856908119631 ] 
dist 20=[-34.386322637637821637  ,-9.3710819796652378310 ] 
dist 21=[-35.137708768592656362  ,-11.648675199961368772  ] 
dist 22=[-35.324021621316619460  ,-11.094953784492877497  ] 
dist 23=[-31.445531033262485345  ,-8.7721324984131036496 ] 
dist 24=[-30.422955113324997541  ,-4.7819246862606437152 ] 
dist 25=[-29.819329977492326361  ,-1.1519191469408985133 ] 
dist 26=[-29.666229725578799206  ,2.3657286149952606659 ] 
dist 27=[-7.4171469781813043682 ,5.6969648098972418301 ] 
dist 28=[-4.7894434894654107455 ,8.5227785051421997560 ] 
dist 29=[.25730518704088107778,11.824486060173134286  ] 
dist 30=[1.8790298403940663521 ,14.422247035987573491  ] 
dist 31=[9.3307599681275694793 ,16.955927211712695197  ] 
dist 32=[10.407402418548649651  ,20.011982442834551549  ] 
dist 33=[11.352140642216826281  ,22.720984873532682254  ] 
dist 34=[10.561963912052281001  ,23.878951510892496195  ] 
dist 35=[9.3495907436757788629 ,24.372224174330732283  ] 
dist 36=[7.6919408174962103035 ,24.435596968705833364  ] 
dist 37=[5.4356023799803387864 ,22.030576140133128553  ] 
dist 38=[1.8469324988274838490 ,21.320522611705083639  ] 
dist 39=[-1.7971284022725388662 ,20.831010031609425784  ] 
dist 40=[-4.2739351825926775642 ,20.536904019256425757  ] 
dist 41=[-6.3127624766869420199 ,13.734841582467900914  ] 
dist 42=[-8.2201486204091815109 ,13.407954649386972917  ] 
dist 43=[-9.9131957862645404626 ,5.1103619524202847464 ] 
dist 44=[-10.869909359020737393  ,3.9997227340997470457 ] 
dist 45=[-11.408750160147315721  ,1.4667285488327327220 ] 
dist 46=[-11.501903444463548663  ,.93711755036984615785] 
dist 47=[-12.370991629419189430  ,-.37237697773196161987] 
dist 48=[-13.328330175768995557  ,-.48133779945011059593] 
dist 49=[-13.998879590192111316  ,-.33725741138700380611] 
dist 50=[-14.149825262378197229  ,.18291151255703205564] 
dist 51=[-14.082383179114151996  ,.8875744727099499945 ] 
dist 52=[-13.897715806661226119  ,1.7641994864777007113 ] 
dist 53=[-12.409141639606930824  ,2.9142632029906288028 ] 
dist 54=[-11.970145042538786682  ,4.7044740238024491363 ] 
dist 55=[-11.200751937939664792  ,6.5150901617388324538 ] 
dist 56=[-10.941463840686389161  ,7.7463351429659537125 ] 
dist 57=[-4.5058873507427383763 ,8.7631653803340250367 ] 
dist 58=[-3.6181609055470263561 ,9.7230494906630217718 ] 
dist 59=[-1.6225937830273387439 ,10.548894983214405122  ] 
dist 60=[-1.1614602612786038533 ,11.033879236130584723  ] 
dist 61=[.32154974461908024534,11.352570461426343035  ] 
dist 62=[.42227618103610834339,11.518574667553328332  ] 
dist 63=[1.2742938492812194062 ,11.572709219013021049  ] 
dist 64=[1.4037033400964880956 ,11.447399944642816235  ] 
dist 65=[1.4723108916294597654 ,2.5707578079449557460 ] 
dist 66=[1.3411522420119463224 ,2.6027085134211435640 ] 
dist 67=[1.1698900892072283350 ,2.5826547657516369091 ] 
dist 68=[.96392332928103857333,2.5787946313220895702 ] 
dist 69=[.69779218611937060773,2.2369354713469779475 ] 
dist 70=[.28769977003544364875,2.2183532704245221973 ] 
dist 71=[-.12550128297533530604,2.0184906179003990381 ] 
dist 72=[-.40399795038082185393,2.0005424687606603911 ] 
dist 73=[-.63131237576794501069,1.6646267990128410779 ] 
dist 74=[-.84141137594887749572,1.6219089315337574375 ] 
dist 75=[-1.0190474020983024167 ,.46559296476500977886] 
dist 76=[-1.1175340939543481918 ,.34596785315344705938] 
dist 77=[-1.1749034082113423347 ,.07348291945876656956] 
dist 78=[-1.1893588819500726968 ,.01851015970049296294] 
dist 79=[-1.2668007402108334333 ,-.2930658434674301964 ] 
dist 80=[-1.3334707232045823670 ,-.3449534255631100371 ] 
dist 81=[-1.3714723176109618418 ,-.36121495385483905214] 
dist 82=[-1.3751262795158981984 ,-.33593549079017291756] 
dist 83=[-1.3508405521698929234 ,-.30205921703939054225] 
dist 84=[-1.3313282481107584651 ,-.26027913192457249301] 
dist 85=[-1.1624611702469315344 ,-.20565244769968629333] 
dist 86=[-1.1163194825114151565 ,-.12077313801962154896] 
dist 87=[-1.0431342129952451057 ,-.03491615240631622808] 
dist 88=[-1.0169080255109932731 ,.02359919668710390724] 
dist 89=[-.39128424964912959608,.17459869393154944645] 
dist 90=[-.38650135230821679653,.41383192879961497237] 
dist 91=[-.13737429975964679899,.60858158383615058794] 
dist 92=[-.10606916295842306917,.78801712037611626593] 
dist 93=[-.03410209419519063156,.93956445410845714617] 
dist 94=[-.01979310808862405531,1.0238206804270560795 ] 
dist 95=[.06544156671779125490,1.0732697306121451649 ] 
dist 96=[.07943173191994419513,1.0853810863601964369 ] 
dist 97=[.1079389864005945677 ,.36653216603527707235] 
dist 98=[.11306725632176775804,.37698301606505702525] 
dist 99=[.12923317597442549724,.38119966524896921989] 
dist 100=[.10711398978781292266,.37937282429075867504] 
dist 101=[.07807847774190653974,.37100236729106454715] 
dist 102=[.03374702437648425398,.36501396520026748729] 
dist 103=[-.01083569496160461381,.3253823427793146167 ] 
dist 104=[-.04195944974700724182,.31465666982664789243] 
dist 105=[-.13581460917314800141,.28924575714994298504] 
dist 106=[-.19917734558120321814,.27992903652230621216] 
dist 107=[-.25109791251864658663,.15023335117128658183] 
dist 108=[-.29953177743340373133,.1299505883959240826 ] 
dist 109=[-.34087787751527427477,.08706056979409852423] 
dist 110=[-.36466241375221337772,.07542068375396896846] 
dist 111=[-.37969452361361197024,.03197565734863234373] 
dist 112=[-.38629658928118401877,.02266357409646517965] 
dist 113=[-.38768875526939100969,.01011945751378594039] 
dist 114=[-.38203692373400544113,.00682412159594034747] 
dist 115=[-.15587310173260641804,.00612949628289248990] 
dist 116=[-.15343897647064286127,.00809731073036750163] 
dist 117=[-.13670851866974652649,.01234239016081109086] 
dist 118=[-.13209195025285430429,.02069079620120261974] 
dist 119=[-.12209242755368480045,.03082150324489728573] 
dist 120=[-.11856449403232711921,.04214375489358585258] 
dist 121=[-.06202975359461783596,.05627699753628694169] 
dist 122=[-.05388120515888054487,.07756911766272801075] 
dist 123=[-.03630644691823187208,.09890231716921745687] 
dist 124=[-.03145791557649836131,.11579972588962901284] 
dist 125=[-.01282298167809819540,.13464002324303996147] 
dist 126=[-.00898452738549878265,.14522684755333090419] 
dist 127=[-.00255108475385341843,.1513492675311375009 ] 
dist 128=[-.00102895351675473080,.15280019041140029149] 
dist 129=[.02404588177945093399,.03439587041880922745] 
dist 130=[.02150144541841837467,.03532178640946348445] 
dist 131=[.01838092191485019908,.03550890146205539819] 
dist 132=[.01485310647816344406,.03537334530371378243] 
dist 133=[.01042416354832067998,.03398137999926315051] 
dist 134=[.00372576587492011759,.03365213437931450677] 
dist 135=[-.00299290279912315667,.02757245401544691167] 
dist 136=[-.00750246602443536001,.02610233557234748451] 
dist 137=[-.01116940632810170441,.02469368239922622332] 
dist 138=[-.01454287831347486954,.02405987035686935110] 
dist 139=[-.01738978454727576962,.00599859704695961058] 
dist 140=[-.0189662318500197607 ,.00413125973489220873] 
dist 141=[-.01988483479711501772,-9.09751720537995917700e-05] 
dist 142=[-.02011580925848334724,-.00093742792315053028] 
dist 143=[-.01806440824514649806,-.00563601732505915038] 
dist 144=[-.01977781461400667823,-.00592111368615255023] 
dist 145=[-.02083666339324311617,-.00567703956321154009] 
dist 146=[-.02108469001558073120,-.00515605408837116303] 
dist 147=[-.00818967718051529590,-.00451083421019813783] 
dist 148=[-.00817418068655878031,-.00377344113091345356] 
dist 149=[-.00785724186683707803,-.00284250573864533121] 
dist 150=[-.00781030680690692600,-.00142879512320672440] 
dist 151=[-.00632163815857633731,-8.21456902439971331900e-06] 
dist 152=[-.00596640035520951184,.00095004305122634740] 
dist 153=[-.00571126823584468843,.00173458400591384949] 
dist 154=[-.00565115753999234045,.00246552108929896495] 
dist 155=[-.00054441590980261693,.00308899866688178715] 
dist 156=[5.16738362236926671550e-05,.00344693215316280042] 
dist 157=[.00143621204933422762,.00367226026632859610] 
dist 158=[.00163988141240826742,.00376930619670662797] 
dist 159=[.00235962250520842294,.00379178620006725523] 
dist 160=[.00230410430917441065,.00378891562054479513] 
dist 161=[.00217339109454602291,.00405883965872472982] 
dist 162=[.00190941218672571369,.00416275870030310289] 
dist 163=[.00158683921337509576,.00418009452338369991] 
dist 164=[.00122345872204552289,.00415845636373767525] 
dist 165=[.00076798632840337758,.00401247403060018070] 
dist 166=[7.97467315044262000000e-05,.00395075121009791112] 
dist 167=[-.00061066341337683698,.00334536697244985600] 
dist 168=[-.00107476813691022059,.00319246076292686320] 
dist 169=[-.00145304439752989246,.00297163083519355787] 
dist 170=[-.00180269759493763739,.00288826059154531994] 
dist 171=[-.00209905475339148761,.00094658448688701343] 
dist 172=[-.00226573319489878755,.00069011468170841761] 
dist 173=[-.00237903219451081357,.00011732221078303045] 
dist 174=[-.00240486433572938483,1.91029307418872705840e-05] 
dist 175=[-.00277743272368119894,-.00062705577768306866] 
dist 176=[-.00302337316382851990,-.00073537180535890691] 
dist 177=[-.00316648645676417743,-.00084602152112089698] 
dist 178=[-.00320257098487381024,-.00074564732752479380] 
dist 179=[-.00105934416482017868,-.00062424278155196031] 
dist 180=[-.00105342241035092182,-.00048899662507031062] 
dist 181=[-.00101747900370681553,-.00032042283797774328] 
dist 182=[-.00100025855649173261,-6.66824561268551927250e-05] 
dist 183=[-.00085398196180148819,.00018755687283296993] 
dist 184=[-.00081652961594718816,.00035811486833452104] 
dist 185=[-.00075677723223584824,.00049678443441532556] 
dist 186=[-.00073636425018014829,.00062441128652578587] 
dist 187=[-.00025364323038527683,.00073222287057469369] 
dist 188=[-.00018865933201755736,.00079221561242781251] 
dist 189=[-4.39828633640189484710e-05,.00082755506917254367] 
dist 190=[-1.15268520921473269090e-05,.00083747976534650798] 
dist 191=[9.76976986529102991020e-05,.00083567708155428245] 
dist 192=[9.24131413036937954510e-05,.00082676046047796072] 
dist 193=[8.05275662839329008940e-05,.00080665666780008169] 
dist 194=[5.68416283672332897560e-05,.00076761663304812442] 
dist 195=[2.79915599474965381860e-05,.00059090417474376484] 
dist 196=[-4.40043239933165758400e-06,.00058731479672067852] 
dist 197=[-4.49376265278632230740e-05,.00056229632539461921] 
dist 198=[-.00010613061942192795,.00055573503124130698] 
dist 199=[-.00016751021230826012,.00045612328558674044] 
dist 200=[-.00020878950318463325,.00043209297508864991] 
dist 201=[-.00024246197251569739,.00040632929414945857] 
dist 202=[-.00027363973194570638,.00039333779263786064] 
dist 203=[-.00030010845040935990,.00014189133799327197] 
dist 204=[-.00031508429770280340,.00012227492167832525] 
dist 205=[-.00032423343950801109,8.04500561175437988930e-05] 
dist 206=[-.00032756806310105603,6.90616255930948744410e-05] 
dist 207=[-.00032847757543062297,2.61701386829124407620e-05] 
dist 208=[-.00035364080314907932,1.71759552298622355430e-05] 
dist 209=[-.00036889055509087258,4.02648141287275968200e-06] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 1, 0, 2] 
dist 0=[107.58508141133808215   ,107.58508141133808215   ] 
dist 1=[107.18662182923487051   ,107.37811595277315684   ] 
dist 2=[105.79636847286113033   ,107.58508141133808215   ] 
dist 3=[103.43973458509968176   ,105.24915562165957202   ] 
dist 4=[99.202340029547543543  ,104.69021370106774218   ] 
dist 5=[94.175792682977883360  ,97.741864287182914690  ] 
dist 6=[88.684108435953487776  ,95.966622099126722560  ] 
dist 7=[81.898539583636403516  ,94.066206471796294000  ] 
dist 8=[71.731512614946362656  ,93.068704850335316275  ] 
dist 9=[61.258562184229947873  ,66.622640512882131137  ] 
dist 10=[53.252146502042212803  ,63.125311598379747074  ] 
dist 11=[45.636050971953593380  ,54.394084813288269601  ] 
dist 12=[36.697717901569271553  ,52.833946951017431264  ] 
dist 13=[27.701070818350537966  ,39.028879472639030647  ] 
dist 14=[19.837979139025075105  ,36.355748116831474551  ] 
dist 15=[11.341455218519643587  ,32.550193558964098458  ] 
dist 16=[-.20084234823974004085,31.392473422070980286  ] 
dist 17=[-11.201211985849946966  ,9.1269261899035806421 ] 
dist 18=[-17.547673605759268512  ,6.3272463142378695715 ] 
dist 19=[-21.722644541484388319  ,.29462541464872672068] 
dist 20=[-24.075484644126182508  ,-.9415486464544525218 ] 
dist 21=[-25.573528952901290018  ,-6.8202184787354421309 ] 
dist 22=[-26.337356356264791260  ,-7.8313232083613906234 ] 
dist 23=[-26.764403917226153312  ,-9.1372705300178975292 ] 
dist 24=[-27.084426851344341111  ,-9.1255908473191598827 ] 
dist 25=[-12.219905676433990637  ,-8.8113631867330301507 ] 
dist 26=[-10.419384875037461474  ,-7.9391954253222735900 ] 
dist 27=[-8.3301929021639389409 ,-4.4696576381745624309 ] 
dist 28=[-8.1752303864869827398 ,-.75673570208517044429] 
dist 29=[-6.5624461248570564779 ,2.7098050384616245679 ] 
dist 30=[-6.2015678519749557545 ,5.2091474388059303585 ] 
dist 31=[-5.6967981338293843698 ,7.4256106105977658762 ] 
dist 32=[-5.5167130842867494085 ,9.7779650949760973541 ] 
dist 33=[-1.5158698134140743438 ,11.831800753952175785  ] 
dist 34=[-.99945811064878818206,12.865815117775072764  ] 
dist 35=[.13622691713576047502,13.380582856413627420  ] 
dist 36=[.37346766156098887743,13.445610223907565569  ] 
dist 37=[1.5360059288054531060 ,12.840688780898745975  ] 
dist 38=[1.7368479626068722046 ,12.536440245133891021  ] 
dist 39=[2.0142027329698649617 ,12.141497393277513603  ] 
dist 40=[2.0290667253673171745 ,11.910761186758574087  ] 
dist 41=[.04416726243937413186,5.3103035461972546070 ] 
dist 42=[-2.3670825541531517561 ,4.7035550509091659733 ] 
dist 43=[-4.3528013607774978955 ,4.3865299975060017238 ] 
dist 44=[-6.2079782188677585701 ,4.2678489430149549609 ] 
dist 45=[-7.7831415049972226296 ,3.4707637370873086129 ] 
dist 46=[-8.6587542823737993337 ,3.2819681556704103915 ] 
dist 47=[-9.1692741371886011464 ,2.9267657184489265851 ] 
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