8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 0, 1, 0, 1, 2] 
dist 0=[81.197780615276130428  ,81.197780615276130428  ] 
dist 1=[80.406739480042099168  ,81.806337996862653946  ] 
dist 2=[77.859405186592075133  ,82.539461821412520880  ] 
dist 3=[74.663558623017716168  ,82.697002682418547975  ] 
dist 4=[70.848269411700033336  ,82.380766455275710291  ] 
dist 5=[65.852442951670378586  ,82.144584597204060992  ] 
dist 6=[57.945306435046214102  ,81.532323500167928710  ] 
dist 7=[49.907549021693186064  ,81.217166885974573163  ] 
dist 8=[44.390088837181756566  ,79.566370148877643867  ] 
dist 9=[39.665546402037140058  ,79.259562266510923821  ] 
dist 10=[34.791119972221711349  ,78.940694984717646050  ] 
dist 11=[30.194406515010471144  ,78.662145359867198204  ] 
dist 12=[26.577277325535295058  ,78.144243660648397858  ] 
dist 13=[22.983217846118046894  ,77.991739364013267579  ] 
dist 14=[18.477015639804042944  ,75.454728445586442312  ] 
dist 15=[14.162269203438958598  ,70.468703322235475358  ] 
dist 16=[11.331461075492245866  ,33.128781828756969381  ] 
dist 17=[9.039123677164243210  ,29.583229427402307409  ] 
dist 18=[5.707496040964759616  ,21.363949936082188370  ] 
dist 19=[.073908928347650470  ,20.057124324266109391  ] 
dist 20=[-5.3166640358089580447 ,9.5101922616059487993 ] 
dist 21=[-8.8209817008574080889 ,7.6847785399715156379 ] 
dist 22=[-11.613620031226489656  ,4.9200638625656314708 ] 
dist 23=[-14.163845588659161762  ,4.2400228236546724514 ] 
dist 24=[-16.361798322248157613  ,-.4551345455637253137 ] 
dist 25=[-17.748500694933976984  ,-1.2434239375397074708 ] 
dist 26=[-18.805809652088321834  ,-1.3557755509657650087 ] 
dist 27=[-19.689130291153764651  ,-1.9786754951698207569 ] 
dist 28=[-20.392701968063844731  ,-2.0672267980821672125 ] 
dist 29=[-20.732894009283279778  ,-2.1297158018018935534 ] 
dist 30=[-20.872607493443486622  ,-2.0603284273478575084 ] 
dist 31=[-20.776861638691771637  ,-1.9531564212640055770 ] 
dist 32=[-6.6777133910799766929 ,-1.8146204165651914823 ] 
dist 33=[-6.0386644203503595029 ,-1.4200853872793174887 ] 
dist 34=[-4.4532878130241624903 ,-.8501000595983362404 ] 
dist 35=[-4.2255586006991651080 ,-.1171806789951196315 ] 
dist 36=[-1.8968622073081786832 ,.5860695613847070280 ] 
dist 37=[-1.7930434390204436429 ,1.0381314849597662826 ] 
dist 38=[-1.7848567862959703453 ,1.3896841917476693760 ] 
dist 39=[-.8770985970618185950 ,1.6925612545891970067 ] 
dist 40=[-.4994384328420347787 ,2.1093250503855742129 ] 
dist 41=[-.3333449314415469395 ,2.7769758643912654629 ] 
dist 42=[-.2946353576576284324 ,3.2995211491771646715 ] 
dist 43=[-.1798692132909836355 ,3.7570422580493398031 ] 
dist 44=[-.155253163647772719  ,4.1351943681332135795 ] 
dist 45=[-.152267573746567127  ,4.3413867205870178847 ] 
dist 46=[-.175970575951846000  ,4.4601819774529317804 ] 
dist 47=[-.208391876395465412  ,4.4899470466355508749 ] 
dist 48=[-.240243980912688038  ,2.4397819962699270628 ] 
dist 49=[-.276440961895908106  ,2.2719014675085597335 ] 
dist 50=[-.326473261386993137  ,1.8502966201127311517 ] 
dist 51=[-.380327041399116440  ,1.7750454622788767195 ] 
dist 52=[-.431914686580087591  ,1.1213715484027326999 ] 
dist 53=[-.491141125269237480  ,.9982389774474656507 ] 
dist 54=[-.5756104922839736138 ,.8125695350630949728 ] 
dist 55=[-.6572910823817302684 ,.7612592754906235401 ] 
dist 56=[-.7181156799743913100 ,.18989550148827956068] 
dist 57=[-.9988612859143554815 ,.12388456365787128793] 
dist 58=[-1.2382372951617888389 ,.11313475781085703968] 
dist 59=[-1.4500579816733358333 ,.0302413290398961529 ] 
dist 60=[-1.6259294250967508923 ,.0161319231627847343 ] 
dist 61=[-1.7221426141536532790 ,-.0067561314905459779 ] 
dist 62=[-1.7776898296452337651 ,-.0118319085001488913 ] 
dist 63=[-1.7916022796298529715 ,-.0821889289769762507 ] 
dist 64=[-.49336521919499597865,-.0912083472272003004 ] 
dist 65=[-.4548297861385177982 ,-.07203298867321977172] 
dist 66=[-.3554987283918422333 ,-.03061029530635194905] 
dist 67=[-.3408691919577844537 ,.02272814904350326023] 
dist 68=[-.2123652899434208061 ,.07406667595582555449] 
dist 69=[-.2161695747441688957 ,.10753654927737630529] 
dist 70=[-.2169178028264544590 ,.13401766517005253039] 
dist 71=[-.1097816515838095127 ,.15753558099229099496] 
dist 72=[-.0469457286886655704 ,.17709254639360521827] 
dist 73=[-.0308535300827769974 ,.1978622478516358498 ] 
dist 74=[-.0281479087957363902 ,.2415176029055596144 ] 
dist 75=[-.0072947825180920405 ,.2795801634875853509 ] 
dist 76=[-.0036860310799510673 ,.3107379404839911636 ] 
dist 77=[.0022672444978021710 ,.3269022473338094260 ] 
dist 78=[.0035945905590752555 ,.3352409058113576195 ] 
dist 79=[.0225571811314201524 ,.3367196503763347682 ] 
dist 80=[.0250297340174732705 ,.21489224985834263408] 
dist 81=[.0288131039278827459 ,.20393834604072901544] 
dist 82=[.01734989802408945390,.17409793258589240295] 
dist 83=[-.00632494093208103336,.16941026993585823772] 
dist 84=[-.02942467525321902493,.1154907688559815743 ] 
dist 85=[-.04452551801974781447,.1048839650073773281 ] 
dist 86=[-.05650454471301160075,.0925278010054003160 ] 
dist 87=[-.06718001824508650459,.0892588722862785981 ] 
dist 88=[-.07607059951941998598,.0434829152103462693 ] 
dist 89=[-.08094562314239381998,.0400160622299073401 ] 
dist 90=[-.09135542857313590898,.0388703789799863012 ] 
dist 91=[-.10672029529625012754,.0334780389643654307 ] 
dist 92=[-.11918001756871899148,.0322923351938669396 ] 
dist 93=[-.12544982215607918588,.0293300515003945089 ] 
dist 94=[-.1287687752040532176 ,.0284569704131294562 ] 
dist 95=[-.1294819842807240131 ,.0190676679158639506 ] 
dist 96=[-.0519390723955237344 ,.0175013730602708560 ] 
dist 97=[-.0493021990428380922 ,.0139807587426188364 ] 
dist 98=[-.0425855345245269158 ,.0129441428654131710 ] 
dist 99=[-.0411492459786131273 ,.0083517390049245526 ] 
dist 100=[-.0301479715681802158 ,.0074407043432498381 ] 
dist 101=[-.0279768294008133760 ,.00863069095086472427] 
dist 102=[-.0217864666630468967 ,.01081061273021009155] 
dist 103=[-.01072516451722415153,.01272238326246029316] 
dist 104=[.01124992455519514432,.01429162079350180059] 
dist 105=[.01185397470359168474,.01633221312563766139] 
dist 106=[.01145137616676571814,.02029677492970934623] 
dist 107=[.01020712311795916256,.02383029375469451409] 
dist 108=[.00878215644223232928,.02677317146428451076] 
dist 109=[.00766033395145366279,.02838692520199740553] 
dist 110=[.00656073203026227454,.02932022482672477210] 
dist 111=[.00522354888058309168,.02955470199174238946] 
dist 112=[.00385633040387206795,.01763256458933184588] 
dist 113=[.00263687936288186887,.01663016935967367803] 
dist 114=[.00130656393193512930,.0140286935712942108 ] 
dist 115=[-.00050213084806276537,.01353542409765798244] 
dist 116=[-.00226344392741172292,.00917034599182455177] 
dist 117=[-.00340534304365463825,.00831653101630325483] 
dist 118=[-.00429976066941368214,.00703713540810935497] 
dist 119=[-.00507633881842570880,.00666537029503905069] 
dist 120=[-.00570777060084471059,-.00040950266840971809] 
dist 121=[-.00705660067066548134,-.00132103161176771543] 
dist 122=[-.00893975270129340728,-.00283832295215115954] 
dist 123=[-.01062113285028069999,-.00249686250614135790] 
dist 124=[-.01202251466923464735,-.00210124355485116417] 
dist 125=[-.01279140051914311347,-.00180107127178332113] 
dist 126=[-.01323624023691013296,-.00151736195869360132] 
dist 127=[-.01334801588092264655,-.00118709205530556180] 
dist 128=[-.00368821309895326027,-.00085728214977829860] 
dist 129=[-.00343660408959168335,-.00057532008583540996] 
dist 130=[-.00277017481464579832,-.00027781498840891444] 
dist 131=[-.00267089899910505834,.00011392427984799597] 
dist 132=[-.00154117279926478695,.00049338358101537868] 
dist 133=[-.00132683897759603145,.00074205637602302779] 
dist 134=[-.00107478047337006599,.00093977767913703787] 
dist 135=[-.00102178493775788163,.00111650468144653974] 
dist 136=[.00083055730399438139,.00126385065988797284] 
dist 137=[.00104797965745671181,.00140109471795360388] 
dist 138=[.00109630858236526390,.00174879613932593211] 
dist 139=[.00098764757147807693,.00205387656405472484] 
dist 140=[.00086162402303637983,.00230424471430759545] 
dist 141=[.00075987627498277944,.00243422720894426575] 
dist 142=[.00065778470355458353,.00250245852122213561] 
dist 143=[.00053034924046329751,.00251419866436250128] 
dist 144=[.00039834692467773712,.00168796923757692453] 
dist 145=[.00027806212812329457,.00161116849347597760] 
dist 146=[.00014479049742019307,.00139603243060720253] 
dist 147=[-3.89051050232242910000e-05,.00136164285058411557] 
dist 148=[-.00021874699920114561,.00095256804738436482] 
dist 149=[-.00033669397259499785,.00087058022071784302] 
dist 150=[-.00043054184876682503,.00077678623893484476] 
dist 151=[-.00051450188902121618,.00075057418545342704] 
dist 152=[-.00058452826324099547,-6.03219287181631640000e-05] 
dist 153=[-.00062293704266506313,-.00015704431558456160] 
dist 154=[-.00070990068622467980,-.00024028299708709990] 
dist 155=[-.00083692201943946854,-.00021256373123867396] 
dist 156=[-.00094019711517271179,-.00017968200526753553] 
dist 157=[-.00099194124132927890,-.00015443357710161894] 
dist 158=[-.00101947285890501532,-.00013028016052121648] 
dist 159=[-.00102638923035298119,-.00010174447004117682] 
dist 160=[-.00034421116749511750,-7.30225354508663390000e-05] 
dist 161=[-.00032124999152810628,-4.81225038541056760000e-05] 
dist 162=[-.00025972299458506557,-2.15606919935500990000e-05] 
dist 163=[-.00025086350058710613,1.37784915459708010000e-05] 
dist 164=[-.00014452361108987157,4.80056535864739250000e-05] 
dist 165=[-.00012427675136093815,7.01452153213955310000e-05] 
dist 166=[-.00010158730629845509,8.74155338485332000000e-05] 
dist 167=[-9.75919005361317300000e-05,.00010227022618195205] 
dist 168=[8.28699196315369000000e-05,.00011426984231909829] 
dist 169=[8.52717277675288520000e-05,.00012517491936034450] 
dist 170=[8.18360806411729240000e-05,.00015795499983943680] 
dist 171=[7.17275446358993680000e-05,.00018726124939881247] 
dist 172=[6.02003184027171600000e-05,.00021169333076270856] 
dist 173=[5.11199796382200330000e-05,.00022507947769658623] 
dist 174=[4.22146756972763280000e-05,.00023279099237806705] 
dist 175=[3.13804424630159660000e-05,.00023467497342786721] 
dist 176=[2.03054371641431110000e-05,.00014539123190974749] 
dist 177=[1.04404432787905750000e-05,.00013776178734142260] 
dist 178=[-3.04941687179719000000e-07,.00011764135976442587] 
dist 179=[-1.48843284303539000000e-05,.00011376880208890226] 
dist 180=[-2.90489329433307810000e-05,7.88138595428572100000e-05] 
dist 181=[-3.81448798547480750000e-05,7.18779511106346400000e-05] 
dist 182=[-4.51643243858013110000e-05,6.16457417109559400000e-05] 
dist 183=[-5.10680849258358960000e-05,5.85729666805268400000e-05] 
dist 184=[-5.57337342244109070000e-05,-1.01081029023345000000e-06] 
dist 185=[-5.78272181994731030000e-05,-8.59017005262358001000e-06] 
dist 186=[-7.31987730980697400000e-05,-5.66954311806432391000e-06] 
dist 187=[-8.73698182681418600000e-05,0                     ] 
dist 188=[-9.91907553228659200000e-05,-2.10802105364344800000e-05] 
dist 189=[-.00010567471663680574,-1.88391711030027200000e-05] 
dist 190=[-.00010941843433301102,-1.64635005197694500000e-05] 
dist 191=[-.00011033650582808163,-1.33248739362569100000e-05] 
dist 192=[-3.26761806152876000000e-05,-9.98507669975784000000e-06] 
dist 193=[-3.07705515560392500000e-05,-6.80867264891141000000e-06] 
dist 194=[-2.57315664109620200000e-05,-3.18305904505417000000e-06] 
dist 195=[-2.48500494710517200000e-05,1.94425241617213000000e-06] 
dist 196=[-1.61677932555690500000e-05,7.01841568151451000000e-06] 
dist 197=[-1.44749763726765800000e-05,1.04327012067024300000e-05] 
dist 198=[-1.21734787456633800000e-05,1.32446270837128700000e-05] 
dist 199=[-1.14309339555120300000e-05,1.59223253406644800000e-05] 
dist 200=[5.63842263047290000000e-07,1.82701614260765500000e-05] 
dist 201=[7.09639333624290000000e-07,1.97696751932589300000e-05] 
dist 202=[5.16077635848420000000e-07,2.09169990498749800000e-05] 
dist 203=[-1.87382741810550000000e-07,2.18634849455417900000e-05] 
dist 204=[-1.00114695135463000000e-06,2.26126715898577700000e-05] 
dist 205=[-1.63355343135493000000e-06,2.29750350781860710000e-05] 
dist 206=[-2.24570939109986000000e-06,2.31187853718739670000e-05] 
dist 207=[-2.97912474077719100000e-06,2.29983788108525000000e-05] 
dist 208=[-3.72271182074595600000e-06,1.53610458089039180000e-05] 
dist 209=[-4.37544673264589800000e-06,1.47436970151400480000e-05] 
dist 210=[-5.07840728713385000000e-06,1.29838918793493160000e-05] 
dist 211=[-6.02191875037681000000e-06,1.26827717186226160000e-05] 
dist 212=[-6.93363024079538000000e-06,9.21073278091374300000e-06] 
dist 213=[-7.51013511659182000000e-06,8.50095759767821700000e-06] 
dist 214=[-7.94471857368284000000e-06,7.65947870754015800000e-06] 
dist 215=[-8.29187098404216000000e-06,7.37737297985907500000e-06] 
dist 216=[-8.55155316475371000000e-06,1.99387949781937000000e-07] 
dist 217=[-8.63818440974110000000e-06,-6.73742566185341000000e-07] 
dist 218=[-8.61842417042886000000e-06,-1.48261818506487410000e-06] 
dist 219=[-8.84403423597399900000e-06,-1.66348123849343540000e-06] 
dist 220=[-9.64214637845271600000e-06,-1.74712038849542150000e-06] 
dist 221=[-9.99996399630676500000e-06,-1.49528762982245266000e-06] 
dist 222=[-1.01653237370091500000e-05,-9.85599062766854730000e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 2, 1, 2, 0, 1] 
dist 0=[85.225927254808528136  ,85.225927254808528136  ] 
dist 1=[84.579247526250782818  ,85.796408925853743142  ] 
dist 2=[82.568620037064876184  ,86.383893805810788871  ] 
dist 3=[79.861235870553835587  ,86.433227454543206719  ] 
dist 4=[76.392190332818366211  ,86.122185141676154578  ] 
dist 5=[71.701071422678391615  ,85.923672512228952407  ] 
dist 6=[64.116685540492828684  ,84.815484546617856742  ] 
dist 7=[56.324620592647233336  ,84.626907740240410890  ] 
dist 8=[50.804861950521679149  ,80.556242203093047067  ] 
dist 9=[45.894499713431555324  ,79.611439992823150672  ] 
dist 10=[40.534846334615445366  ,78.471939079622603102  ] 
dist 11=[35.300155481605952211  ,77.963350464736606109  ] 
dist 12=[30.888771619617073243  ,77.262590209101231289  ] 
dist 13=[26.238527032617484702  ,77.089322768678475553  ] 
dist 14=[20.050985807049569623  ,74.257440073378762831  ] 
dist 15=[13.974546371048510574  ,68.861583604100143236  ] 
dist 16=[9.7677489566356150497 ,28.699942689006286345  ] 
dist 17=[6.1283268342294071210 ,24.920223910585809894  ] 
dist 18=[2.3159616233821008852 ,16.125801590632726097  ] 
dist 19=[-1.3117875030772510741 ,14.831830601255457202  ] 
dist 20=[-5.1452996189053549688 ,8.8962304446855701348 ] 
dist 21=[-7.7612060966507711239 ,7.7513894416023541682 ] 
dist 22=[-10.856961166436064133  ,7.4827853975481654693 ] 
dist 23=[-14.400722569674928326  ,1.6980714102621799032 ] 
dist 24=[-16.633834817469565786  ,1.0670523108292449691 ] 
dist 25=[-18.333889468466001927  ,-.3095413374937301046 ] 
dist 26=[-19.751428434856914206  ,-.5131922696610644323 ] 
dist 27=[-20.881963069202918054  ,-1.9820003410122920784 ] 
dist 28=[-21.437623375339941740  ,-2.2096047312275920420 ] 
dist 29=[-21.683401771544064168  ,-2.5788344535912129333 ] 
dist 30=[-21.670260445324541994  ,-2.6483871062498623616 ] 
dist 31=[-21.296468051073273747  ,-3.2716872583020002325 ] 
dist 32=[-9.1694153017038475995 ,-3.3454782037415981707 ] 
dist 33=[-8.2486494689561009965 ,-2.3519794502255964727 ] 
dist 34=[-5.9782623531387681647 ,-1.2311247126446762736 ] 
dist 35=[-5.6484195763845248320 ,.2620008305970646800 ] 
dist 36=[-3.9849646462973736257 ,1.7098008910311629564 ] 
dist 37=[-3.9761128691394723348 ,2.6504504147540397870 ] 
dist 38=[-3.9630527009760719559 ,3.3922054972909913166 ] 
dist 39=[-1.8198556147304939687 ,4.0480314659579559426 ] 
dist 40=[-1.6337547378287424540 ,4.5923589897865490127 ] 
dist 41=[-1.2008589190326620263 ,4.8900786530329197125 ] 
dist 42=[-1.1231504552501515638 ,5.0619636991400854360 ] 
dist 43=[-.5590230112657073074 ,5.6650010540023798550 ] 
dist 44=[-.4590503807715210865 ,6.1852273999097614787 ] 
dist 45=[-.2854071185453822004 ,6.4603471829342485900 ] 
dist 46=[-.2476615476961102925 ,6.6074089782321741867 ] 
dist 47=[.3149947009279328064 ,6.6281041017854403745 ] 
dist 48=[.3905808670775628191 ,3.6689961838370391578 ] 
dist 49=[.4012476071753984150 ,3.4179860565680865995 ] 
dist 50=[.2003827907163606548 ,2.7913728738055921650 ] 
dist 51=[-.0605818665644304448 ,2.6768504285764568381 ] 
dist 52=[-.3120343595387077443 ,1.9059011675918737972 ] 
dist 53=[-.4750868080671320822 ,1.9160107178028370043 ] 
dist 54=[-.6030831393578859022 ,1.9147985327758366547 ] 
dist 55=[-.7247883381416629955 ,1.1740307086762113537 ] 
dist 56=[-1.4034600449587062913 ,.25602801573449413411] 
dist 57=[-1.8405049504258397091 ,.1596564914782862035 ] 
dist 58=[-2.1807985096388899933 ,.1458286859536886158 ] 
dist 59=[-2.4741790420531048633 ,.0146811271482177220 ] 
dist 60=[-2.7122349561176875907 ,-.0079472058351897643 ] 
dist 61=[-2.8321970438928317421 ,-.0377076493129150059 ] 
dist 62=[-2.8934415037009239762 ,-.0425127049024238092 ] 
dist 63=[-2.9008872694976614800 ,-.1828704727376943652 ] 
dist 64=[-.6771702713349151922 ,-.1989967267643827142 ] 
dist 65=[-.6218794800040336072 ,-.1500661735667967413 ] 
dist 66=[-.4797260040376487373 ,-.0764449091828321311 ] 
dist 67=[-.4592094813224694976 ,.023203322171646699  ] 
dist 68=[-.2876366319122831571 ,.120116374122782221  ] 
dist 69=[-.2930699439542784343 ,.182864648900711983  ] 
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dist 85=[-.051392604733079534  ,.12332760357522522839] 
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dist 100=[-.0249426247960696441 ,.0500700215277987394 ] 
dist 101=[-.0254129730346203344 ,.0559528969479668502 ] 
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dist 113=[-.0091893374390691788 ,.0207983130257548817 ] 
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dist 115=[-.0133039467684066321 ,.0165749971577402340 ] 
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dist 120=[-.0204941694178063073 ,.00277491938778452811] 
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dist 122=[-.0213770754959239064 ,.0019764400783755826 ] 
dist 123=[-.0215315015443335416 ,.0008896000782496644 ] 
dist 124=[-.0215412851078350787 ,.0006909024394567423 ] 
dist 125=[-.0214121747813060752 ,.0004526212329934934 ] 
dist 126=[-.0209714901175366021 ,.0004123514925712972 ] 
dist 127=[-.0199885658265359471 ,0                     ] 
dist 128=[-.00238662185638941231,-.0013202443436508185 ] 
dist 129=[-.00218869815783941930,-.00112870400131710114] 
dist 130=[-.00202696921595552101,-.00059907386793297354] 
dist 131=[-.0022314958706441908 ,.0001275245585740056 ] 
dist 132=[-.0023433293103278885 ,.0008369482042394290 ] 
dist 133=[-.0024077790153214810 ,.0012982934706686204 ] 
dist 134=[-.0024236108961294648 ,.0016608697159579285 ] 
dist 135=[-.00134054546287459114,.0019773705040394616 ] 
dist 136=[-.00125076057590669412,.0022356396433819303 ] 
dist 137=[-.00102425196267668166,.0023665527875319663 ] 
dist 138=[-.00098267862925169866,.0024365325658458881 ] 
dist 139=[-.00062524381496827405,.0024523509734205669 ] 
dist 140=[-.00055706673708131086,.00083833852081838361] 
dist 141=[-.00045320071519752763,.00078680716346488139] 
dist 142=[-.00042440575359230410,.0006464754285333585 ] 
dist 143=[.00010111097086139726,.0006262723728515617 ] 
dist 144=[.00016884387201237115,.00060893065683590021] 
dist 145=[.00025313178885106954,.00074891437195871425] 
dist 146=[.00013462607039216967,.00087319640232522760] 
dist 147=[-2.30443525198667500000e-05,.00097651213260082754] 
dist 148=[-.00017620321508909519,.00103302373570110575] 
dist 149=[-.00027677110701714843,.00106557312311571988] 
dist 150=[-.00035688215307612429,.00107348589500604664] 
dist 151=[-.00042866005545463611,.00028662394412203793] 
dist 152=[-.0004885656583260685 ,.00026371904844515535] 
dist 153=[-.0005214448888041614 ,.00020442776160316844] 
dist 154=[-.0005404456079226731 ,.00019589153462475798] 
dist 155=[-.0005451361422722945 ,.00010000324760563984] 
dist 156=[-.00034692576701409336,8.21819084688030900000e-05] 
dist 157=[-.00032986924407586650,6.13675606507466000000e-05] 
dist 158=[-.00028432228836390710,5.77638896347833600000e-05] 
dist 159=[-.00027540113564267113,-8.34026381517416500000e-05] 
dist 160=[-.0001942825660508710 ,-9.94142733573863300000e-05] 
dist 161=[-.0001780294680311699 ,-.00011721509790879727] 
dist 162=[-.00018863793596627099,-6.37100866104752200000e-05] 
dist 163=[-.00020649220261224890,1.05036845355388300000e-05] 
dist 164=[-.00021492960976039657,8.32855698393960400000e-05] 
dist 165=[-.00021910798179505655,.00013109733501216825] 
dist 166=[-.00022000675497093943,.00016919950240303592] 
dist 167=[-.00014777054499513361,.00020335640756748040] 
dist 168=[-.00014063986024463093,.00023186928193806628] 
dist 169=[-.00012127010200612275,.00024751868484383923] 
dist 170=[-.00011803574955877020,.00025655977538209395] 
dist 171=[-8.28511419275263600000e-05,.00025878306269170102] 
dist 172=[-7.58500554640227200000e-05,7.66353787658658800000e-05] 
dist 173=[-6.72783882528412500000e-05,7.24198904687880900000e-05] 
dist 174=[-6.45367475883355700000e-05,6.09921915006973300000e-05] 
dist 175=[1.88155493445538000000e-06,5.91156342378134400000e-05] 
dist 176=[9.94925974684847000000e-06,7.11630013354206160000e-05] 
dist 177=[2.10029709480334300000e-05,8.20025983327973600000e-05] 
dist 178=[1.03513247534727300000e-05,9.08636893411350000000e-05] 
dist 179=[-3.93470580742004000000e-06,9.77922037463628600000e-05] 
dist 180=[-1.78008193087723300000e-05,.00010093889927216959] 
dist 181=[-2.67827585210026500000e-05,.00010232347764430290] 
dist 182=[-3.37987123005449900000e-05,.00010223771954939693] 
dist 183=[-3.98442128934460800000e-05,3.73152089515576100000e-05] 
dist 184=[-4.47936539226702000000e-05,3.53558067761840000000e-05] 
dist 185=[-4.76002074746210100000e-05,3.07772679174400000000e-05] 
dist 186=[-4.92190526252727100000e-05,2.93981168933542000000e-05] 
dist 187=[-4.96141871762303200000e-05,2.28013246081114000000e-05] 
dist 188=[-4.41102039617521000000e-05,2.14489893244712000000e-05] 
dist 189=[-4.32000419951536000000e-05,1.83008523117167000000e-05] 
dist 190=[-4.05268666354312000000e-05,1.73962324483113000000e-05] 
dist 191=[-3.96804454123657000000e-05,8.79430267304280000000e-06] 
dist 192=[-3.36548459311015000000e-05,7.34578179398220000000e-06] 
dist 193=[-3.22684086703243000000e-05,4.87428772796130000000e-06] 
dist 194=[-2.97796755387451000000e-05,4.28222482099550000000e-06] 
dist 195=[-2.90847475997760000000e-05,5.49942847436250000000e-06] 
dist 196=[-1.42028600471593000000e-05,1.12437347170630910000e-05] 
dist 197=[-1.21658974028991000000e-05,1.49422739173874720000e-05] 
dist 198=[-6.84191664103060000000e-06,1.78057729449623700000e-05] 
dist 199=[3.33243125152426800000e-06,2.02285032293805200000e-05] 
dist 200=[3.70703753234696130000e-06,2.21479176278944700000e-05] 
dist 201=[3.21500670365555730000e-06,2.30093403111190600000e-05] 
dist 202=[2.13750293705042783000e-06,2.34129621647192800000e-05] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 0, 1, 1, 2] 
dist 0=[87.158568860276366130  ,87.158568860276366130  ] 
dist 1=[86.569050919714326716  ,87.451478314490777767  ] 
dist 2=[85.423106171551778900  ,87.414233464498322875  ] 
dist 3=[83.948748876338140317  ,87.166609430572155612  ] 
dist 4=[82.048722624069977688  ,86.940367624567537961  ] 
dist 5=[79.475743144412006391  ,86.036284625451917719  ] 
dist 6=[75.315587315048783324  ,85.638542605160003637  ] 
dist 7=[70.458119969804098061  ,82.652317309688489261  ] 
dist 8=[62.133364136642397599  ,81.826725722288868195  ] 
dist 9=[53.566424574170272487  ,80.979209320532515700  ] 
dist 10=[47.549852020420947474  ,80.506455787592305594  ] 
dist 11=[37.489260384749599599  ,80.035106775697220490  ] 
dist 12=[30.419825418450861824  ,79.917937591443202441  ] 
dist 13=[24.494948115265204500  ,77.117830977982628944  ] 
dist 14=[18.586097444376838352  ,71.702646679882543502  ] 
dist 15=[13.140734425812914293  ,31.182828976263295919  ] 
dist 16=[9.0647505240826381318 ,27.927730404270742723  ] 
dist 17=[5.209443745674734260  ,18.454732012679695067  ] 
dist 18=[.643262763672297021  ,17.118807992727003108  ] 
dist 19=[-3.6373136262850612153 ,10.348140455601468217  ] 
dist 20=[-6.3529188340101116310 ,9.7970793909695528108 ] 
dist 21=[-8.4459423761239212614 ,5.5721598472884016488 ] 
dist 22=[-10.240671358129924782  ,4.8677981572334675049 ] 
dist 23=[-12.793141254227125502  ,3.7601025532525425886 ] 
dist 24=[-15.568135507679831109  ,3.5137352330055851146 ] 
dist 25=[-17.662014330235340637  ,.1709094232504548057 ] 
dist 26=[-19.374256837562258769  ,-.2319360225044076106 ] 
dist 27=[-20.713167573466467782  ,-1.0710955730266386821 ] 
dist 28=[-21.318096359027749154  ,-1.2024816432281558452 ] 
dist 29=[-21.576703771397133140  ,-1.969188102644418029  ] 
dist 30=[-21.548769434983206701  ,-2.082862010704417330  ] 
dist 31=[-8.7676449819750104235 ,-2.270497004384757745  ] 
dist 32=[-7.9091158024212373622 ,-2.300597285624091010  ] 
dist 33=[-5.7824178653605977995 ,-1.3378285023839760365 ] 
dist 34=[-5.4769628896210447523 ,.0554957653033818257 ] 
dist 35=[-2.791432159500864913  ,1.4075503448663688739 ] 
dist 36=[-2.791141573248588040  ,2.2847289292833279641 ] 
dist 37=[-2.755473533039070517  ,2.9743664303973796751 ] 
dist 38=[-2.741879022275634575  ,3.5798208213767491664 ] 
dist 39=[-2.690950661868200471  ,4.0787314500169735567 ] 
dist 40=[-2.676264706639677237  ,4.3441490215753682873 ] 
dist 41=[-1.5376394895385222331 ,4.5652485691341823919 ] 
dist 42=[-1.4231478796073955756 ,5.1749655253548198448 ] 
dist 43=[-1.1630365898948601401 ,5.6789757476049664650 ] 
dist 44=[-1.1046165177995977530 ,5.9538275848896807602 ] 
dist 45=[-.7664154147862721989 ,6.1122015159186398692 ] 
dist 46=[-.7020291660915676274 ,6.1519119999644651664 ] 
dist 47=[-.574399534063697667  ,3.3142956487292125831 ] 
dist 48=[-.540708541490484147  ,3.0819801979066063774 ] 
dist 49=[-.123976359888884856  ,2.5003802548410284896 ] 
dist 50=[-.062973308145323109  ,2.3965789195989524657 ] 
dist 51=[-.2399070910359504736 ,1.5002913494641770095 ] 
dist 52=[-.3916489418508273507 ,1.3317727085637635388 ] 
dist 53=[-.5118851922987843910 ,1.0766059733078541281 ] 
dist 54=[-.6188652797179768585 ,1.0065759165811626855 ] 
dist 55=[-.9842810310806566251 ,.7611766704588625914 ] 
dist 56=[-1.3984738843368443310 ,.7588195799565838889 ] 
dist 57=[-1.7251911819919342752 ,.3152225190353048498 ] 
dist 58=[-2.0142181491599119586 ,.2767791212430756222 ] 
dist 59=[-2.2541673428790674506 ,.1833798294612159495 ] 
dist 60=[-2.3854331807897406621 ,.1699271112176259647 ] 
dist 61=[-2.4612263141958044640 ,.0386248582564974010 ] 
dist 62=[-2.4802406031175009261 ,.0156070357262988052 ] 
dist 63=[-.67477612764692386095,-.0140560715730621393 ] 
dist 64=[-.62055676627193119307,-.0190310064886845601 ] 
dist 65=[-.4814593770479118026 ,-.0916858434744695452 ] 
dist 66=[-.4608943162033728894 ,.0083695493271732077 ] 
dist 67=[-.2402627743788577220 ,.1062112612648860332 ] 
dist 68=[-.2594797947103909454 ,.1703030239911605548 ] 
dist 69=[-.2788137174072454362 ,.2212406790760400079 ] 
dist 70=[-.2892452157406793704 ,.2667439697679092615 ] 
dist 71=[-.2951150580494775153 ,.3046773385223162521 ] 
dist 72=[-.2962620411554286035 ,.3254927000122950459 ] 
dist 73=[-.1500810532940837829 ,.3430187418767793064 ] 
dist 74=[-.1380433278000697817 ,.3952146347181580950 ] 
dist 75=[-.1085942157422056780 ,.4378850081143253890 ] 
dist 76=[-.1033323569532301654 ,.4599253808454915386 ] 
dist 77=[-.06008954782872546829,.4712352667613392621 ] 
dist 78=[-.05208995521676959623,.4731553211247768030 ] 
dist 79=[-.03951081361508441264,.3003108386141739169 ] 
dist 80=[-.03626764086663344039,.2847462410588909214 ] 
dist 81=[.0165845107691465092 ,.2425691069566109640 ] 
dist 82=[-.0016555104819761659 ,.2359064024819075464 ] 
dist 83=[-.0193424029051206959 ,.1603315456220870251 ] 
dist 84=[-.0308706382687083198 ,.1454924953517833633 ] 
dist 85=[-.0399651372440614773 ,.1280227145044944749 ] 
dist 86=[-.0479691652244132898 ,.1234939769809899499 ] 
dist 87=[-.0753244054037660828 ,.1267491799119745743 ] 
dist 88=[-.1071554296235947586 ,.1273369729977104042 ] 
dist 89=[-.1319250339488066159 ,.03029645943614629382] 
dist 90=[-.1531941762504392478 ,.02727079261616458833] 
dist 91=[-.1704054257287981808 ,.0196964406204109445 ] 
dist 92=[-.1790214514150602054 ,.0186034096944473151 ] 
dist 93=[-.1835458434574133340 ,.0072150041620902137 ] 
dist 94=[-.1844688007608002533 ,.0051629332485389426 ] 
dist 95=[-.06006700870372732649,.0026258228493332941 ] 
dist 96=[-.0555977597818488844 ,.0021885794660676794 ] 
dist 97=[-.0438815137746112613 ,-.0051967497019861656 ] 
dist 98=[-.0421972039363886568 ,.0008623122847906014 ] 
dist 99=[-.0361223029021764810 ,.0079691726192564368 ] 
dist 100=[-.0383606644335924867 ,.0125912268570951210 ] 
dist 101=[-.0399690563349221615 ,.0162245928749312932 ] 
dist 102=[-.0405454171601704088 ,.0193982745855719988 ] 
dist 103=[-.0406258930292504754 ,.0256298025170440515 ] 
dist 104=[-.0404164704744539643 ,.0327029199291133337 ] 
dist 105=[-.0343721232418273041 ,.0380236827692438327 ] 
dist 106=[-.0333060175128782859 ,.0422661481927262505 ] 
dist 107=[-.0306223446505001810 ,.0455851232264016842 ] 
dist 108=[-.0297425511863090618 ,.0472305800374077652 ] 
dist 109=[-.0250028159658845400 ,.0479508427261427279 ] 
dist 110=[-.0239486402020919778 ,.0480222265729972221 ] 
dist 111=[-.0217361662693003392 ,.0345285170818325861 ] 
dist 112=[-.0210581220918940650 ,.0329366031930134062 ] 
dist 113=[-.0116519629742891307 ,.0289944706864590650 ] 
dist 114=[-.0102462761916307023 ,.0279607386282609401 ] 
dist 115=[-.0071462720207014047 ,.02163435852104126886] 
dist 116=[-.0063257138872217349 ,.02033980185390682822] 
dist 117=[-.0034002646939560493 ,.01776781781625663624] 
dist 118=[-.0041070099859697486 ,.01662334287732781519] 
dist 119=[-.0067620524463281149 ,.0135324313537270649 ] 
dist 120=[-.0101002386368721211 ,.0135794385820172036 ] 
dist 121=[-.0127510793641745620 ,-.00416103836464710562] 
dist 122=[-.0151167859594846106 ,-.00378469056470261716] 
dist 123=[-.0170881456991924633 ,-.00333921285165177893] 
dist 124=[-.0181696014985271098 ,-.00297134631242492619] 
dist 125=[-.0187952198004368471 ,-.00259518977523455120] 
dist 126=[-.0189524131638692757 ,-.00211653740855634542] 
dist 127=[-.00520701210869943865,-.00161652948714511863] 
dist 128=[-.00484435400313738044,-.00115531611798024528] 
dist 129=[-.00388736441976347850,-.00064014760349644968] 
dist 130=[-.00374484692377783033,7.45970836921396700000e-05] 
dist 131=[-.0021338587590957973 ,.00077559248222742991] 
dist 132=[-.0018289791491796177 ,.00123610305626660571] 
dist 133=[-.0014689410035830095 ,.00160309874885740243] 
dist 134=[-.0013933818462221794 ,.00193209655022661984] 
dist 135=[.00086267422139451241,.00220673480793789253] 
dist 136=[.00091436510015625502,.0023574820640720130 ] 
dist 137=[.00090485231354106834,.0025196084969851611 ] 
dist 138=[.00080964842589561089,.0029498348280950321 ] 
dist 139=[.00069414514139625877,.0033027602893723695 ] 
dist 140=[.00060387478438859826,.0034858128622209727 ] 
dist 141=[.00051610085575848259,.0035816459336365018 ] 
dist 142=[.00041048238252108016,.0035980231429160858 ] 
dist 143=[.00030323477325473671,.0024011202337852965 ] 
dist 144=[.00020895571136667352,.0022901900260773462 ] 
dist 145=[.00010735017486621531,.0019807242088768829 ] 
dist 146=[-2.90666781414623700000e-05,.0019312971369129176 ] 
dist 147=[-.00016151849516963416,.0013467715356310240 ] 
dist 148=[-.00024736023925046593,.0012298541247850894 ] 
dist 149=[-.00031445991561003786,.0010956661290949052 ] 
dist 150=[-.00037235800747595291,.0010582327672645332 ] 
dist 151=[-.0005482380862865177 ,-9.23268820344463100000e-05] 
dist 152=[-.0008128885306171297 ,-.00022957201049048614] 
dist 153=[-.0010201185115574982 ,-.00030549567114065687] 
dist 154=[-.0011999000769196766 ,-.00027068558038611100] 
dist 155=[-.0013460033346583562 ,-.00023035645069836114] 
dist 156=[-.0014192180695661456 ,-.00019800011111664177] 
dist 157=[-.0014581106638863928 ,-.00016574870007788423] 
dist 158=[-.0014676349698124225 ,-.00012582269735436015] 
dist 159=[-.00048945162729534276,-8.46803696272975600000e-05] 
dist 160=[-.00045614673982772860,-4.75829977769109500000e-05] 
dist 161=[-.00036721529138167093,-6.82817554177734400000e-06] 
dist 162=[-.00035442166356064291,4.88705618034163000000e-05] 
dist 163=[-.00020171803525812972,.00010310913275801924] 
dist 164=[-.0001727141139792229 ,.00013805882647916055] 
dist 165=[-.0001401095439281094 ,.00016514742290712196] 
dist 166=[-.0001344091339512712 ,.00018811746162478895] 
dist 167=[3.37189535356102070000e-05,.00020635430023937073] 
dist 168=[2.93905089408417375000e-05,.00021461578096572537] 
dist 169=[1.96019903317462186000e-05,.0002299329040544579 ] 
dist 170=[0                     ,.0002714478032713703 ] 
dist 171=[5.91796817809904100000e-05,.0003060021946774100 ] 
dist 172=[5.02892585170939000000e-05,.0003248392686276157 ] 
dist 173=[4.16835285703211000000e-05,.0003355666920374442 ] 
dist 174=[3.13805880791096000000e-05,.0003378514634304582 ] 
dist 175=[2.09457438988186000000e-05,.0002086314312779175 ] 
dist 176=[1.18133894765399000000e-05,.0001974927666451358 ] 
dist 177=[2.00560460498440000000e-06,.0001683273193039062 ] 
dist 178=[-1.11179613395659000000e-05,.0001626292962132658 ] 
dist 179=[-2.37767051672229000000e-05,.00011255702084804373] 
dist 180=[-3.17361224449653000000e-05,.00010263830769431747] 
dist 181=[-3.76799980967249000000e-05,8.76500977351925400000e-05] 
dist 182=[-4.23210976091214000000e-05,8.32760287898229000000e-05] 
dist 183=[-5.79319160039906000000e-05,-1.13587554851595900000e-06] 
dist 184=[-8.63409432491197000000e-05,-1.18883913471714000000e-05] 
dist 185=[-.0001089158060862539 ,-1.63373891881317000000e-05] 
dist 186=[-.0001290622467757295 ,-1.07899590159045000000e-05] 
dist 187=[-.0001458299667368034 ,-4.75742445522504000000e-06] 
dist 188=[-.0001549615467871906 ,-1.35175517424240000000e-07] 
dist 189=[-.0001601476545536860 ,4.27587132865384000000e-06] 
dist 190=[-.0001612167529424882 ,9.46962437247136000000e-06] 
dist 191=[-4.41049122523771000000e-05,1.46843552015189000000e-05] 
dist 192=[-4.12702706146976700000e-05,1.91795414893199000000e-05] 
dist 193=[-3.36268761448346600000e-05,2.39499842702286000000e-05] 
dist 194=[-3.25258403140557100000e-05,3.02602975982290000000e-05] 
dist 195=[-1.91450620834088000000e-05,3.63106517902471000000e-05] 
dist 196=[-1.65830447400637300000e-05,4.00473359348358000000e-05] 
dist 197=[-1.37409556582260900000e-05,4.27591375116040000000e-05] 
dist 198=[-1.32367602994233000000e-05,4.47329506563560000000e-05] 
dist 199=[-2.54409245247797000000e-06,4.60537406057639000000e-05] 
dist 200=[-2.07604126116865000000e-06,4.62880555111827000000e-05] 
dist 201=[-2.13934428211029000000e-06,4.58818339370877000000e-05] 
dist 202=[-2.94272257640622383000e-06,4.56084540137067000000e-05] 
dist 203=[-3.92207446711012000000e-06,2.83480127680178300000e-05] 
dist 204=[-4.68538581625714000000e-06,2.97737990376574600000e-05] 
dist 205=[-5.42591702073926000000e-06,3.05069383062694100000e-05] 
dist 206=[-6.31492118555490000000e-06,3.06545488543185200000e-05] 
dist 207=[-7.21661736138430000000e-06,2.20467281218062000000e-05] 
dist 208=[-8.00777620891120000000e-06,2.11469293963779900000e-05] 
dist 209=[-8.85908904139850000000e-06,1.85944917296673800000e-05] 
dist 210=[-1.00002062382232000000e-05,1.81568860923268800000e-05] 
dist 211=[-1.11011547506484000000e-05,1.31584575223825800000e-05] 
dist 212=[-1.17927573203997000000e-05,1.21385864904029300000e-05] 
dist 213=[-1.23084996899826000000e-05,1.09212139278131400000e-05] 
dist 214=[-1.27099835753923000000e-05,1.05106705534821600000e-05] 
dist 215=[-1.30017102853558000000e-05,2.61683377870330000000e-07] 
dist 216=[-1.30809096121389600000e-05,-9.86754922246360000000e-07] 
dist 217=[-1.30190709452016500000e-05,-2.20901905567415300000e-06] 
dist 218=[-1.29461026478868100000e-05,-2.46839632335239400000e-06] 
dist 219=[-1.39433054302513200000e-05,-2.56483488230896100000e-06] 
dist 220=[-1.44557854593832800000e-05,-2.18950297268015670000e-06] 
dist 221=[-1.46920774444397200000e-05,-1.44074396298478703000e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 0, 0, 1, 1, 0, 1] 
dist 0=[83.720718020657734802  ,83.720718020657734802  ] 
dist 1=[82.809967547684088174  ,83.947489791710466576  ] 
dist 2=[81.153346397169821924  ,83.941485230920239851  ] 
dist 3=[78.049387470218486943  ,83.858246409801377471  ] 
dist 4=[74.257234814081502988  ,83.648715910442192023  ] 
dist 5=[69.854239174280558852  ,83.373583452019583290  ] 
dist 6=[64.164467440609417253  ,83.079429570610919822  ] 
dist 7=[55.237259912542213225  ,82.563014640101706786  ] 
dist 8=[46.189624005211994202  ,82.319258090606786887  ] 
dist 9=[40.018968032584133150  ,81.839525033141146749  ] 
dist 10=[34.777942596022889419  ,80.846937719152990968  ] 
dist 11=[29.439233172414087534  ,80.521432255859393198  ] 
dist 12=[24.447960589020885145  ,80.346444340888614663  ] 
dist 13=[20.592601487305245026  ,79.984203722543030108  ] 
dist 14=[16.829566041668986507  ,68.796561846053419314  ] 
dist 15=[12.205184091568331239  ,66.728293968031296834  ] 
dist 16=[7.823925058235152425  ,55.186185751911949337  ] 
dist 17=[3.7584979584358617711 ,33.331722381774129152  ] 
dist 18=[-1.9609802960745990247 ,29.628838844238226954  ] 
dist 19=[-5.7338513649475468417 ,21.038792646019894775  ] 
dist 20=[-8.8017771321559099846 ,19.682235496766745562  ] 
dist 21=[-11.708162743813778558  ,8.657543349795120427  ] 
dist 22=[-14.287393789369654514  ,6.753257326574308603  ] 
dist 23=[-16.049898968357901569  ,3.887843371518643349  ] 
dist 24=[-17.551837744831777811  ,3.179853749203085624  ] 
dist 25=[-19.091526132167552990  ,0                     ] 
dist 26=[-20.443419740524185833  ,-2.7536814284356497142 ] 
dist 27=[-21.196240162179009943  ,-2.587118645608118003  ] 
dist 28=[-21.656523797676206964  ,-2.354274286805621990  ] 
dist 29=[-21.841616559744788749  ,-2.072917987901851554  ] 
dist 30=[-21.841321388861920421  ,-1.712849704807925410  ] 
dist 31=[-21.757980034656162797  ,-1.165574892439574809  ] 
dist 32=[-21.032113002659425474  ,-.617571803842886209  ] 
dist 33=[-7.3921990077894445784 ,-.253855575738086020  ] 
dist 34=[-6.6691008604934660460 ,.036995287356245044  ] 
dist 35=[-4.8830180341183634151 ,.296097041409396692  ] 
dist 36=[-4.6249391627186411216 ,.509102468343128361  ] 
dist 37=[-2.024494630023694116  ,.617000052202911650  ] 
dist 38=[-1.561850491548789349  ,.673533592790574099  ] 
dist 39=[-.977315000173410716  ,.682577501108492965  ] 
dist 40=[-.876805633539717572  ,1.295777015262221773  ] 
dist 41=[-.5200127230267161481 ,2.444254511971107700  ] 
dist 42=[-.5787517904546101128 ,3.182936706553258833  ] 
dist 43=[-.6766011773959651843 ,3.759455906167360432  ] 
dist 44=[-.788664870791412900  ,4.261653385104062698  ] 
dist 45=[-.904176028773905252  ,4.675141153633450703  ] 
dist 46=[-1.041998078400612964  ,4.898097741694785423  ] 
dist 47=[-1.243006514808327757  ,5.023456043902513828  ] 
dist 48=[-1.443382104242123673  ,5.047941042789202926  ] 
dist 49=[-1.578806346285958746  ,2.7951699924561280111 ] 
dist 50=[-1.690684569690848269  ,2.6130963451526574315 ] 
dist 51=[-1.797553295847208262  ,2.1691102045397476070 ] 
dist 52=[-1.891514901626725363  ,2.0797961568735624516 ] 
dist 53=[-1.952140864484112081  ,1.2095712906683823840 ] 
dist 54=[-1.999464303073880243  ,1.0696883400773702164 ] 
dist 55=[-2.040625970952678789  ,.8538330709328701099 ] 
dist 56=[-2.0708120494775505968 ,.7957896001229735888 ] 
dist 57=[-2.0744779906005754559 ,-.01905886035525595858] 
dist 58=[-2.0597394705184130325 ,-.04383336526927321174] 
dist 59=[-2.0471315611217968958 ,-.04740408751346443269] 
dist 60=[-1.9594467644097659695 ,-.0671428149290342620 ] 
dist 61=[-1.9336309393804465950 ,-.0700024916810629625 ] 
dist 62=[-1.8286466997376486487 ,-.0703442346412038316 ] 
dist 63=[-1.7805090596474436867 ,-.0659263085443962067 ] 
dist 64=[-1.4974917658846684949 ,-.0602800898352385174 ] 
dist 65=[-.55079311995807800585,-.05520963333217644120] 
dist 66=[-.50305041014928272871,-.04979875561336147723] 
dist 67=[-.3814499010558808196 ,-.04283037574297894869] 
dist 68=[-.3639740182249507921 ,-.03559601640342956920] 
dist 69=[-.1745020406047907364 ,-.02909463360302671876] 
dist 70=[-.1398793978186335869 ,-.02196345437015165019] 
dist 71=[-.0983048341219495635 ,-.01218377023878724518] 
dist 72=[-.0912870672389526268 ,.0861725107558348868 ] 
dist 73=[-6.35291955733095300000e-05,.1803267723269272858 ] 
dist 74=[.0066095493535233611 ,.2415070280433531879 ] 
dist 75=[.0075986182035443062 ,.2897621389751049759 ] 
dist 76=[.0141839732948954257 ,.3324453140086546253 ] 
dist 77=[.0151396134401975671 ,.3678781731128948113 ] 
dist 78=[.0167629183979587776 ,.3872587457128738628 ] 
dist 79=[.0170078737688024173 ,.3984451978166026203 ] 
dist 80=[.0170002315645018328 ,.4012425621845884827 ] 
dist 81=[.0166055562478780544 ,.22464364353972758319] 
dist 82=[.0159242600559536644 ,.21003443162974752228] 
dist 83=[.0147237741475471439 ,.1729904568695399784 ] 
dist 84=[.0133220452486775726 ,.16621289325763289862] 
dist 85=[.0118330698518412862 ,.10725706053330353416] 
dist 86=[.0099898421551159258 ,.0959937733695639077 ] 
dist 87=[.00702220171723852282,.0789769909006968325 ] 
dist 88=[-.0214063990025608920 ,.0742061396038178073 ] 
dist 89=[-.0661927397888337740 ,.0056539033083564305 ] 
dist 90=[-.0953905881382340049 ,.0036282822191765016 ] 
dist 91=[-.1184922587704501410 ,.0032626512873796735 ] 
dist 92=[-.1390098833350658317 ,.0009355234006507791 ] 
dist 93=[-.1560709803076332573 ,.0005453464999777979 ] 
dist 94=[-.1654115827521471373 ,-.0001911391574016000 ] 
dist 95=[-.1708028619880878119 ,-.0003510168975440840 ] 
dist 96=[-.1721401707163040022 ,-.0018895367791828703 ] 
dist 97=[-.04695826375667381364,-.0021088638470732172 ] 
dist 98=[-.04338143986723323842,-.0025285041459022784 ] 
dist 99=[-.03409555644871381551,-.0026304497440021754 ] 
dist 100=[-.0327323227536780011 ,-.0029705681214503159 ] 
dist 101=[-.0176254952146379641 ,-.0030436849732699352 ] 
dist 102=[-.0148075669000123981 ,-.00295399660093571181] 
dist 103=[-.0114535461950115639 ,-.00212541520742635861] 
dist 104=[-.0108034512800893523 ,.00575106722262954710] 
dist 105=[-.0075161026631417249 ,.01417049581013218531] 
dist 106=[-.0076985821261979244 ,.01962806226582118641] 
dist 107=[-.0079982320158485308 ,.02390904971321889437] 
dist 108=[-.0083409936302146722 ,.02764499768287059928] 
dist 109=[-.0086951971396274657 ,.03070228421327588623] 
dist 110=[-.0091184085390633046 ,.03228168224295003882] 
dist 111=[-.0097357815186575230 ,.03309733377472163825] 
dist 112=[-.0103489379288580328 ,.03323383476858007748] 
dist 113=[-.0107556165987962940 ,.02151113119698443193] 
dist 114=[-.0110822928238227257 ,.02044397731458585617] 
dist 115=[-.0113777977261601087 ,.01751986155501313517] 
dist 116=[-.0116255059571446845 ,.01705975167883714965] 
dist 117=[-.0117624152695932101 ,.01171200236239483221] 
dist 118=[-.0118429986255239489 ,.01065463860730536844] 
dist 119=[-.0118671187011464233 ,.00943365426606968863] 
dist 120=[-.0118626173910197884 ,.00910859556731530102] 
dist 121=[-.01182946092685933397,.00065749624331239111] 
dist 122=[-.01177047713087987486,.00044565490687968068] 
dist 123=[-.01166309965102629276,.00041065387538497327] 
dist 124=[-.01153576925785358677,.00013613744149174354] 
dist 125=[-.01208570123258641843,8.88113835327564900000e-05] 
dist 126=[-.01271420135742857942,1.21383788286519400000e-05] 
dist 127=[-.01304526163957035479,-5.22096171834976000000e-06] 
dist 128=[-.01310720274501855917,-.00025393759603702978] 
dist 129=[-.00434790230142622589,-.00028593480812139604] 
dist 130=[-.00402814178293388095,-.00033710643158791486] 
dist 131=[-.00318713130805958159,-.00034788702008358059] 
dist 132=[-.00306623228325270525,-.00035109494853665117] 
dist 133=[-.00166439858633322636,-.00033307547197652381] 
dist 134=[-.00140116910139190761,-.00029819147817534586] 
dist 135=[-.00109949304568368363,-.00023170055042225887] 
dist 136=[-.00104744054499851461,.00042870429470872436] 
dist 137=[-.00013841727267924387,.00121146849915883693] 
dist 138=[-8.21179877898199600000e-05,.00172343369651985335] 
dist 139=[-7.38557761927115900000e-05,.00212977010295077694] 
dist 140=[1.53585649037886000000e-06,.00249215404871898466] 
dist 141=[1.44377936316503900000e-05,.00279404490919483414] 
dist 142=[3.22441435952074500000e-05,.00295962278115406467] 
dist 143=[3.55937186675667900000e-05,.00305539598437831417] 
dist 144=[.00011006627538075122,.00307945892146439354] 
dist 145=[.00011879500249086711,.00183158872914898707] 
dist 146=[.00013275008207547836,.00172655604878033655] 
dist 147=[.00013553093467422946,.00145452466979458622] 
dist 148=[.00013478188183249358,.00140279960709813869] 
dist 149=[.00012841195656532593,.00094757238435594064] 
dist 150=[.00011687607277258417,.00085852492955642473] 
dist 151=[9.54405807695951940000e-05,.00072457819614167823] 
dist 152=[-.00012452094461043988,.00068582097596619465] 
dist 153=[-.00050345251795673335,8.44496890414577600000e-05] 
dist 154=[-.00075155306566252181,6.66520768362661430000e-05] 
dist 155=[-.00094866301238844333,6.39153808947576090000e-05] 
dist 156=[-.00112468267588892867,3.70190207368086860000e-05] 
dist 157=[-.00127140066285469402,3.20669153216645860000e-05] 
dist 158=[-.00135190391086186060,2.56870892012833470000e-05] 
dist 159=[-.00139848093916914616,2.41147774341628720000e-05] 
dist 160=[-.00141018465856528880,-1.43287375356782840000e-05] 
dist 161=[-.00038579830803951854,-1.88935774535753410000e-05] 
dist 162=[-.00035899099421392207,-2.89181857097938140000e-05] 
dist 163=[-.00028818478130166295,-3.05372326533676300000e-05] 
dist 164=[-.00027762987422143527,-3.54232149575027300000e-05] 
dist 165=[-.00015813589684153851,-3.41305418413069490000e-05] 
dist 166=[-.00013549139075925591,-3.11043518400078970000e-05] 
dist 167=[-.00010878678080145805,-2.49678396087926400000e-05] 
dist 168=[-.00010315145976832020,3.42423438763788100000e-05] 
dist 169=[-1.62319277495726600000e-05,.00010577550200725853] 
dist 170=[-1.07872916829292300000e-05,.00015231355601319286] 
dist 171=[-1.00053786862739000000e-05,.00018894887953577471] 
dist 172=[-2.23313886284455000000e-06,.00022107651033151773] 
dist 173=[-8.65951377864090000000e-07,.00024742963427226776] 
dist 174=[8.82219038780210000000e-07,.00026108609397427202] 
dist 175=[1.16880809024315000000e-06,.00026823635316832452] 
dist 176=[1.03678662313413000000e-05,.00026944377919839288] 
dist 177=[1.14266679702541500000e-05,.00018028248906198534] 
dist 178=[1.33456943361072300000e-05,.00017199261473133165] 
dist 179=[1.37082248972110700000e-05,.00014884327209743773] 
dist 180=[1.42135518932508200000e-05,.00014513971117675909] 
dist 181=[1.37818420807328100000e-05,.00010131519427061672] 
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dist 188=[-9.06170341937931600000e-05,3.28014846750639800000e-06] 
dist 189=[-.00010161591688176224,2.79940601110386800000e-06] 
dist 190=[-.00010712645258004192,2.05097148739978700000e-06] 
dist 191=[-.00011005215073412654,1.85769671351871300000e-06] 
dist 192=[-.00011076537355598199,-1.41621329563310800000e-06] 
dist 193=[-3.68587590341898180000e-05,-1.83772307425705300000e-06] 
dist 194=[-3.43437733865573800000e-05,-2.63108744202123000000e-06] 
dist 195=[-2.76282793169595400000e-05,-2.79906822047346800000e-06] 
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dist 205=[-3.17420136255160000000e-07,2.31976227553812100000e-05] 
dist 206=[-1.55052753189140000000e-07,2.46383853746336200000e-05] 
dist 207=[-1.23892952771910000000e-07,2.54705178549026700000e-05] 
dist 208=[8.01809134928431000000e-07,2.56755577558469800000e-05] 
dist 209=[9.03978159334463000000e-07,1.57426078582332410000e-05] 
dist 210=[1.08795607055212400000e-06,1.48965491011515374000e-05] 
dist 211=[1.12294920115816000000e-06,1.26800123839043040000e-05] 
dist 212=[1.17205153896102700000e-06,1.22503801681377620000e-05] 
dist 213=[1.13127655892951500000e-06,8.44354025467266200000e-06] 
dist 214=[1.03746362481205300000e-06,7.69011075838804200000e-06] 
dist 215=[8.48168707644746000000e-07,6.56084073179501300000e-06] 
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dist 219=[-8.07278672197103000000e-06,7.98055440913722000000e-07] 
dist 220=[-9.61363385620128000000e-06,5.36392210750467000000e-07] 
dist 221=[-1.08987738977730300000e-05,4.85782669362776000000e-07] 
dist 222=[-1.16036022013779300000e-05,4.21669911864129000000e-07] 
dist 223=[-1.20104970024064500000e-05,4.02127915734914000000e-07] 
dist 224=[-1.21101916318524800000e-05,-4.37261998164010000000e-08] 
dist 225=[-3.37373828682342900000e-06,-9.77971611092210000000e-08] 
dist 226=[-3.15690288657939700000e-06,-2.19443636863624000000e-07] 
dist 227=[-2.57210380634197900000e-06,-2.23916342982459100000e-07] 
dist 228=[-2.48796048575227500000e-06,-2.04581864730929800000e-07] 
dist 229=[-1.46346908448125100000e-06,-1.65476793767876470000e-07] 
dist 230=[-1.26783746146067000000e-06,-1.04883448056718410000e-07] 
dist 231=[-1.05004248250611500000e-06,0                     ] 
dist 232=[-1.01174852555327400000e-06,3.17717781449916000000e-07] 
dist 233=[-6.47118637801710000000e-07,9.52877288314961000000e-07] 
dist 234=[-6.55662654962430000000e-07,1.36342417703286200000e-06] 
dist 235=[-6.68826901351570000000e-07,1.68335429939053500000e-06] 
dist 236=[-6.83603718088500000000e-07,1.95798263473765400000e-06] 
dist 237=[-6.98564699569220000000e-07,2.17954967133458600000e-06] 
dist 238=[-7.16240393061830000000e-07,2.28837045544906200000e-06] 
dist 239=[-7.41813098050730000000e-07,2.34424223715700100000e-06] 
dist 240=[-7.67124821207020000000e-07,2.35512743050534700000e-06] 
dist 241=[-7.83768885751670000000e-07,1.69523750968810500000e-06] 
dist 242=[-7.96976361935300000000e-07,1.62609180575467000000e-06] 
dist 243=[-8.08639485256030000000e-07,1.42990331021350100000e-06] 
dist 244=[-8.18201994422280000000e-07,1.39632877881145500000e-06] 
dist 245=[-8.23067030969160000000e-07,1.01194091695359700000e-06] 
dist 246=[-8.25365296292200000000e-07,9.33499022074292000000e-07] 
dist 247=[-8.24735048105760000000e-07,8.40102188929601000000e-07] 
dist 248=[-8.22973028104900000000e-07,8.08731950034346000000e-07] 
dist 249=[-8.20774421666360000000e-07,1.92820406468280000000e-08] 
dist 250=[-8.17897583048647000000e-07,-7.68102618696270000000e-08] 
dist 251=[-8.76170548394685000000e-07,-1.73405340178999700000e-07] 
dist 252=[-9.86881240458631000000e-07,-1.93258617270948400000e-07] 
dist 253=[-1.07423016671327300000e-06,-1.99418267816130300000e-07] 
dist 254=[-1.11340352042153900000e-06,-1.69955668133084030000e-07] 
dist 255=[-1.13140374275095100000e-06,-1.11715290861350470000e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 1, 0, 1, 0, 2] 
dist 0=[85.036837227869785101  ,85.036837227869785101  ] 
dist 1=[84.431826048555774060  ,85.623867739390109582  ] 
dist 2=[82.604279811103950420  ,86.223186987472308665  ] 
dist 3=[80.079489377381379514  ,86.352595534016517360  ] 
dist 4=[76.772180012564503414  ,86.187988658533026493  ] 
dist 5=[72.259015586650015256  ,86.028957478615840912  ] 
dist 6=[64.921800148211818079  ,85.034637708558426323  ] 
dist 7=[57.376442885163983387  ,84.848086772025305376  ] 
dist 8=[52.032755974627655329  ,80.989813882616905243  ] 
dist 9=[47.280701768170168287  ,80.087533752930437733  ] 
dist 10=[42.096909985929029874  ,78.916282737104966737  ] 
dist 11=[37.036430941700621644  ,78.428661494891848281  ] 
dist 12=[31.881114800327515162  ,77.524702266636248675  ] 
dist 13=[24.630076885920352119  ,77.203153069742827790  ] 
dist 14=[18.586810348149538589  ,74.609588125156385683  ] 
dist 15=[12.617374272995817970  ,69.568768363251586711  ] 
dist 16=[7.157617372022684624  ,31.045724449545906982  ] 
dist 17=[3.148398927436918815  ,27.399313917507925828  ] 
dist 18=[-.562851175600130905  ,18.859316150941379852  ] 
dist 19=[-4.833390820235533143  ,17.630526387325756536  ] 
dist 20=[-8.804802885065635028  ,10.017615565104344774  ] 
dist 21=[-11.322702908798402157  ,8.5545810496040979704 ] 
dist 22=[-13.256955289205347944  ,8.2435929845071627509 ] 
dist 23=[-14.900429550373980798  ,1.674238664362276270  ] 
dist 24=[-16.234176738192548212  ,-9.7390588704027024067 ] 
dist 25=[-16.933483320470251841  ,-11.049459973598631423  ] 
dist 26=[-17.307020173664830853  ,-11.876601342114283907  ] 
dist 27=[-17.342680601842358161  ,-9.9226939164648489636 ] 
dist 28=[-17.594272661847506874  ,-7.8265122977394517366 ] 
dist 29=[-18.326603440444102134  ,-6.3226786097918406842 ] 
dist 30=[-18.730506160240839889  ,-4.982817222212949153  ] 
dist 31=[-18.793090252705568799  ,-3.537473470702642454  ] 
dist 32=[-9.9396582017405145367 ,-2.152109129523184247  ] 
dist 33=[-9.2070782149766029896 ,-1.050065904586731090  ] 
dist 34=[-7.3976452580196160546 ,.046478617672646143  ] 
dist 35=[-7.0788787215767237168 ,1.410944804276678345  ] 
dist 36=[-4.3799426359005020279 ,2.706694006805968707  ] 
dist 37=[-3.8795442452154055407 ,3.529806219684999449  ] 
dist 38=[-3.1123208596538092498 ,4.159425750653787324  ] 
dist 39=[-2.9082174688900369147 ,4.684321841085290514  ] 
dist 40=[.6444917167414845439 ,5.098382308202626751  ] 
dist 41=[1.0995101017362030163 ,5.286409318030249387  ] 
dist 42=[1.914424222155793388  ,5.375153390087315308  ] 
dist 43=[2.078585612185150820  ,5.984553076104203558  ] 
dist 44=[1.9014241619031980722 ,6.627082394091479648  ] 
dist 45=[1.4124753106300970817 ,6.968213979820146217  ] 
dist 46=[.959950346195962971  ,7.151942730971639881  ] 
dist 47=[.446335307158887761  ,7.187397214445937133  ] 
dist 48=[-.060330214254151826  ,1.8488430980015833699 ] 
dist 49=[-.485426073530596409  ,1.6978092996236631996 ] 
dist 50=[-.927932425997842964  ,1.4417304806598567214 ] 
dist 51=[-1.504143967643627166  ,1.3773171065821456716 ] 
dist 52=[-2.056222124493601873  ,.6378287171281115752 ] 
dist 53=[-2.402732900459397861  ,.5261190316045180019 ] 
dist 54=[-2.662112782234605220  ,.3924688840472784406 ] 
dist 55=[-2.867327057428877998  ,.3698709741941691720 ] 
dist 56=[-3.020239506495056113  ,-.5100905502810170165 ] 
dist 57=[-3.071410123644000823  ,-.6115189499209133788 ] 
dist 58=[-3.084554872493662984  ,-.60438617233771256717] 
dist 59=[-3.085920174055944214  ,-.52375602613180373883] 
dist 60=[-1.1238312542235684347 ,-.42745035894286289936] 
dist 61=[-1.1868186870329414527 ,-.3566431423284017017 ] 
dist 62=[-1.2231787680514853814 ,-.2918442788641920236 ] 
dist 63=[-1.2322887566285095204 ,-.2193965995953699312 ] 
dist 64=[-.70309636554359930633,-.1485776130951748882 ] 
dist 65=[-.65927917130633620126,-.0902309337687441854 ] 
dist 66=[-.5473279696289885707 ,-.0304507004651911174 ] 
dist 67=[-.52680120759458480641,.0461065934753129852 ] 
dist 68=[-.34604616312548879278,.1196841454022811909 ] 
dist 69=[-.31135834241437253211,.1676121491661228044 ] 
dist 70=[-.25935958823800634772,.2054997568397115335 ] 
dist 71=[-.24457660140682522451,.2391053270262880685 ] 
dist 72=[.02927217586231693287,.2670297854754677255 ] 
dist 73=[.06439673918031025920,.2822985105566312879 ] 
dist 74=[.1346768625435423428 ,.3520281325323767089 ] 
dist 75=[.1511393119583264598 ,.4157980294744754284 ] 
dist 76=[.16873543652273811625,.4688473275062034737 ] 
dist 77=[.1462707578069683826 ,.4979094410126893381 ] 
dist 78=[.12446385161375096665,.5147027955671721663 ] 
dist 79=[.0982172583710080669 ,.5189083148022536060 ] 
dist 80=[.0714951048205196854 ,.14375715043306273035] 
dist 81=[.0477879486731901649 ,.13331386919536172993] 
dist 82=[.0220064007579089214 ,.10602101937211824459] 
dist 83=[-.0129793962033949957 ,.10197642563211654833] 
dist 84=[-.0470824033446527626 ,.05701285355962139108] 
dist 85=[-.0693527015759011771 ,.0485854895250852215 ] 
dist 86=[-.0869993767372250454 ,.0385144397286825737 ] 
dist 87=[-.1026995025163962213 ,.0364606632713629329 ] 
dist 88=[-.1157612194399106188 ,-.0333184584338807170 ] 
dist 89=[-.1229059598640814581 ,-.0414857649037683208 ] 
dist 90=[-.1270166618386947412 ,-.04740749727815839757] 
dist 91=[-.1280010398401204797 ,-.04096295251284861841] 
dist 92=[-.0896064950743015314 ,-.03355585906115811583] 
dist 93=[-.0943594336420836521 ,-.0279988563684340405 ] 
dist 94=[-.0968231455598561880 ,-.0228036504641992878 ] 
dist 95=[-.0971848734220246727 ,-.0168332319859210921 ] 
dist 96=[-.0643733902603197559 ,-.0109081405269233335 ] 
dist 97=[-.0613135254489853895 ,-.0058916372330349720 ] 
dist 98=[-.0528691211499721118 ,-.0006363747220041920 ] 
dist 99=[-.0515063250759061335 ,.0062406406999446895 ] 
dist 100=[-.0358502915006115212 ,.0128475742455580595 ] 
dist 101=[-.0327350994866417319 ,.0170285466296633757 ] 
dist 102=[-.0290744072561423382 ,.0201905746583439480 ] 
dist 103=[-.0280192082018948395 ,.0227423262719355001 ] 
dist 104=[.0020306775709413095 ,.0247586347861309511 ] 
dist 105=[.0056317414532764805 ,.0257897111495089291 ] 
dist 106=[.0112156073087492937 ,.0287171063461898169 ] 
dist 107=[.0095193914611045244 ,.0332973362286444985 ] 
dist 108=[.0064992308996558604 ,.0369912298446301616 ] 
dist 109=[.0042354594230252069 ,.0388009656574843776 ] 
dist 110=[.0021213842709498914 ,.0397354092918779834 ] 
dist 111=[-.0003042274495778968 ,.0399456875105762550 ] 
dist 112=[-.0027084657102097371 ,.01274062257202566553] 
dist 113=[-.0047381046629463635 ,.01185960075033364982] 
dist 114=[-.0068585740699464754 ,.0103281004209146192 ] 
dist 115=[-.0096249030305368368 ,.0099440196778794127 ] 
dist 116=[-.0122680812575344207 ,.00519964282125167412] 
dist 117=[-.0138987629632458186 ,.00444680814105435773] 
dist 118=[-.0150831771589171109 ,.00359406115603436920] 
dist 119=[-.0159506583078521796 ,.00344605837509314603] 
dist 120=[-.0165519554969415903 ,-.00312950640081767822] 
dist 121=[-.0166844207724457561 ,-.00388942519890906619] 
dist 122=[-.0166358690092241647 ,-.00425282789887555805] 
dist 123=[-.0165761260115443876 ,-.00371879434062973087] 
dist 124=[-.00778787365680753779,-.00310302843752503454] 
dist 125=[-.00827364225823080337,-.00263982128071722303] 
dist 126=[-.00855469067254399176,-.00220560467211709483] 
dist 127=[-.00862531119697645118,-.00170498902619310613] 
dist 128=[-.00524236109111611802,-.00120746135204281633] 
dist 129=[-.00495624748340176705,-.00078542011744288473] 
dist 130=[-.00420825145053308627,-.00034277557646396833] 
dist 131=[-.00406474593765691875,.00023685362606447678] 
dist 132=[-.00278913178785357575,.00079749473320259859] 
dist 133=[-.00253783330569572419,.00116461880297078627] 
dist 134=[-.00216205208890795563,.00145632546782335436] 
dist 135=[-.00205175053960991140,.00171685775549760726] 
dist 136=[6.87837162700808000000e-05,.00193403248625670070] 
dist 137=[.00034222372335525843,.00206590627751673156] 
dist 138=[.00089818294317047041,.00263189250463912766] 
dist 139=[.00103134301823784617,.00313794904782796433] 
dist 140=[.00129363142023571839,.00355998406804071041] 
dist 141=[.00113585751812340444,.00379164051406009751] 
dist 142=[.00097888950006139336,.00392570421083087243] 
dist 143=[.00078467820805636364,.00395939475705701578] 
dist 144=[.00058429495466998774,.00109957579996186165] 
dist 145=[.00040273688846840777,.00102735220458914738] 
dist 146=[.00020234472846601986,.00083462073589532396] 
dist 147=[-7.30109346479481400000e-05,.00080586381689936752] 
dist 148=[-.00034236752460488023,.00047433230629181410] 
dist 149=[-.00051890009611169091,.00041107763162981887] 
dist 150=[-.00065928188573433532,.00033731977479691162] 
dist 151=[-.00078479454215811414,.00032166791636119840] 
dist 152=[-.00088946656660118831,-.00023427206115018914] 
dist 153=[-.00094692086894008778,-.00029955134173102274] 
dist 154=[-.00098017050555434641,-.00036784121064292250] 
dist 155=[-.00098852619008719082,-.00032411354110773344] 
dist 156=[-.00067752140097940692,-.00027270692483095524] 
dist 157=[-.00071669662192275969,-.00023359802563093535] 
dist 158=[-.00073735243274753610,-.00019651297792836485] 
dist 159=[-.00074089610283522815,-.00015314444734818459] 
dist 160=[-.00050404447593388957,-.00010971295505455992] 
dist 161=[-.00048182671162204821,-7.23695880158378800000e-05] 
dist 162=[-.00041907100262472203,-3.27814218343758000000e-05] 
dist 163=[-.00040900373972819822,1.95898740046932000000e-05] 
dist 164=[-.00028798926368775293,7.03126222866935200000e-05] 
dist 165=[-.00026362162878382207,.00010334411715407182] 
dist 166=[-.00023590665834700724,.00012937194107069174] 
dist 167=[-.00022808507851666128,.00015222785417534604] 
dist 168=[1.55788950530410310000e-05,.00017098859812937629] 
dist 169=[4.46573257318019280000e-05,.00018072175538642412] 
dist 170=[9.22489389567534900000e-05,.00020987117898710243] 
dist 171=[.00010330637332068481,.00024822278921946477] 
dist 172=[.00010590846663746474,.00027944946523660947] 
dist 173=[9.26286716423082600000e-05,.00029516030156424041] 
dist 174=[7.95149900536011200000e-05,.00030353092517256778] 
dist 175=[6.34275146594730200000e-05,.00030554972068517335] 
dist 176=[4.69042889718465700000e-05,.00010297613870579035] 
dist 177=[3.20545504439365100000e-05,9.63064733691859000000e-05] 
dist 178=[1.57660753711857400000e-05,7.83223951175580900000e-05] 
dist 179=[-6.48381951903974000000e-06,7.57353600805590100000e-05] 
dist 180=[-2.81793222002676800000e-05,4.42883744430853200000e-05] 
dist 181=[-4.22628970795110900000e-05,3.82757674150813200000e-05] 
dist 182=[-5.33076216249325100000e-05,3.15960499932803800000e-05] 
dist 183=[-6.29126100000451300000e-05,3.04227681457048400000e-05] 
dist 184=[-7.07270361303915300000e-05,-2.38646447569070600000e-05] 
dist 185=[-7.46476311718755400000e-05,-3.01436461687128700000e-05] 
dist 186=[-7.67338689762451000000e-05,-3.48695570296331500000e-05] 
dist 187=[-7.72490186764696000000e-05,-3.07143373054288500000e-05] 
dist 188=[-6.25651279214367100000e-05,-2.58882342108751000000e-05] 
dist 189=[-6.66078953724074300000e-05,-2.22153872194258700000e-05] 
dist 190=[-6.89436183883100800000e-05,-1.87316528117403300000e-05] 
dist 191=[-6.95197336487357800000e-05,-1.46567835916719600000e-05] 
dist 192=[-4.34190897824976430000e-05,-1.05763555671099900000e-05] 
dist 193=[-4.11840527869114354000e-05,-7.06987561470945000000e-06] 
dist 194=[-3.52795755613856490000e-05,-3.35507938377021000000e-06] 
dist 195=[-3.41242213267811920000e-05,1.55480729482651000000e-06] 
dist 196=[-2.38114373087771570000e-05,6.31584435578877000000e-06] 
dist 197=[-2.17571852764034670000e-05,9.43864662275884000000e-06] 
dist 198=[-1.86909569885204600000e-05,1.19235306532564900000e-05] 
dist 199=[-1.77783498809747000000e-05,1.41465381882242000000e-05] 
dist 200=[2.95647416440200000000e-08,1.60002978543824400000e-05] 
dist 201=[2.32934744947738000000e-06,1.70160512008062600000e-05] 
dist 202=[7.01059451917903500000e-06,2.17808190800607800000e-05] 
dist 203=[8.14025840404250100000e-06,2.60552958761094400000e-05] 
dist 204=[1.09321729513171220000e-05,2.96221507238191200000e-05] 
dist 205=[9.64685886326460000000e-06,3.15792112762328900000e-05] 
dist 206=[8.35227771640584000000e-06,3.27095044878764400000e-05] 
dist 207=[6.72916354860983000000e-06,3.29870375641051900000e-05] 
dist 208=[5.04406856238415000000e-06,9.27152313202093000000e-06] 
dist 209=[3.50270916133864000000e-06,8.70215946577126600000e-06] 
dist 210=[1.79037948757543000000e-06,7.15333908637163100000e-06] 
dist 211=[-5.75104034563980000000e-07,6.92966374961593800000e-06] 
dist 212=[-2.89234139409437000000e-06,4.17367984423300300000e-06] 
dist 213=[-4.41279107019226000000e-06,3.64274704396514100000e-06] 
dist 214=[-5.62303061710155000000e-06,3.05845721746935900000e-06] 
dist 215=[-6.70611134481449000000e-06,2.95283978353949500000e-06] 
dist 216=[-7.60935544101050000000e-06,-1.71424147051409700000e-06] 
dist 217=[-8.10410754026286000000e-06,-2.24983374925551800000e-06] 
dist 218=[-8.38877441414400000000e-06,-3.02360779326348300000e-06] 
dist 219=[-8.45616835059488000000e-06,-2.65830690666412000000e-06] 
dist 220=[-5.82518821415922400000e-06,-2.22625473962867000000e-06] 
dist 221=[-6.12962735736049700000e-06,-1.89351036441167000000e-06] 
dist 222=[-6.28697755679504400000e-06,-1.57412958542278000000e-06] 
dist 223=[-6.31601811636766200000e-06,-1.19515153927650000000e-06] 
dist 224=[-4.60655910972062000000e-06,-8.12746097784500000000e-07] 
dist 225=[-4.42516541971267900000e-06,-4.79680727371920000000e-07] 
dist 226=[-3.90525616418563600000e-06,-1.23095070298790000000e-07] 
dist 227=[-3.81588091005646800000e-06,3.52933589078610000000e-07] 
dist 228=[-2.78080375748938400000e-06,8.12524915684120000000e-07] 
dist 229=[-2.56856298326886200000e-06,1.10373444105535000000e-06] 
dist 230=[-2.31737372919852400000e-06,1.32396939776171000000e-06] 
dist 231=[-2.23237878745142500000e-06,1.50119875285628000000e-06] 
dist 232=[-7.29714313040890000000e-08,1.64195348612734000000e-06] 
dist 233=[1.89760338742878000000e-07,1.97079453005598800000e-06] 
dist 234=[4.20225519278407500000e-07,2.33433481889358200000e-06] 
dist 235=[4.74790154786980900000e-07,2.64054596290549600000e-06] 
dist 236=[4.31252457199030000000e-07,2.88260682101600400000e-06] 
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dist 238=[1.52235144932120000000e-07,3.04120621575659800000e-06] 
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dist 240=[-1.67557683755990000000e-07,9.03411792702570000000e-07] 
dist 241=[-3.05504920893960000000e-07,8.45716489606360000000e-07] 
dist 242=[-4.51898084823300000000e-07,7.64018653638810000000e-07] 
dist 243=[-6.45655507288020000000e-07,7.36796254915640000000e-07] 
dist 244=[-8.31674166171250000000e-07,1.70191957943210000000e-07] 
dist 245=[-9.47290545072710000000e-07,1.38531532621270000000e-07] 
dist 246=[-1.03213203522396000000e-06,5.14665490011500000000e-08] 
dist 247=[-1.09572723362377000000e-06,-5.02257749944100000000e-08] 
dist 248=[-1.14026351068936000000e-06,-1.33669270360105400000e-07] 
dist 249=[-1.15072066382505000000e-06,-1.14486521001907400000e-07] 
dist 250=[-1.14665772074845000000e-06,-7.55023066385762300000e-08] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 2, 1, 2, 2, 0, 2] 
dist 0=[86.161407849087763818  ,86.161407849087763818  ] 
dist 1=[85.262937925792186465  ,86.605667712042444270  ] 
dist 2=[84.048487572905214464  ,86.800158254352213219  ] 
dist 3=[82.343342307407935164  ,86.702441284920651541  ] 
dist 4=[79.955174211127643788  ,86.423199471939998806  ] 
dist 5=[76.014689242413103087  ,86.175137693382122706  ] 
dist 6=[71.382726052271984614  ,85.317137239793082239  ] 
dist 7=[66.234923021905107678  ,84.870432102387156114  ] 
dist 8=[59.727033627322922156  ,82.236002902320565201  ] 
dist 9=[49.667181373872233753  ,81.454208466840465615  ] 
dist 10=[39.518758258805336199  ,80.744237861302569538  ] 
dist 11=[32.657084444848741024  ,80.294430068830571806  ] 
dist 12=[26.892276633083373171  ,79.992400405756746557  ] 
dist 13=[21.120343666830459089  ,78.164702382672613931  ] 
dist 14=[15.786564790209185354  ,67.921086794379431304  ] 
dist 15=[11.769520114420617607  ,61.072911721039085085  ] 
dist 16=[7.9458615286034178631 ,31.243748700810749490  ] 
dist 17=[3.3823202392284078062 ,27.430024807187181537  ] 
dist 18=[-.9051305347806351285 ,18.564230952303974130  ] 
dist 19=[-3.6270608715842008349 ,17.223124924704379954  ] 
dist 20=[-5.7272466648510827635 ,7.7536071788914574301 ] 
dist 21=[-7.5321734922785434186 ,3.9171079348947873176 ] 
dist 22=[-9.4453088935254981658 ,3.1474351442052711280 ] 
dist 23=[-11.781997263565855650  ,2.0002218969267805120 ] 
dist 24=[-14.579664102284824034  ,1.7831188754772274411 ] 
dist 25=[-17.195049825350622600  ,-.68573070135515152209] 
dist 26=[-18.804642686527141536  ,-.99249475298545821556] 
dist 27=[-19.985480575625027372  ,-1.6090445212379690763 ] 
dist 28=[-20.934510634883968409  ,-1.7032327649222659950 ] 
dist 29=[-21.553061954142673362  ,-2.1737054958568502204 ] 
dist 30=[-21.764745798451921930  ,-2.2438404413807576440 ] 
dist 31=[-21.691679444943253995  ,-2.2624914086124435463 ] 
dist 32=[-8.5855339290490226155 ,-1.5639211734962918816 ] 
dist 33=[-7.7345899672804343408 ,-.3559964265937566532 ] 
dist 34=[-5.6319332486821538802 ,.8217787741882533112 ] 
dist 35=[-5.3281370194790451855 ,1.5908150850189079557 ] 
dist 36=[-2.2635286042484073205 ,2.2000146494708496369 ] 
dist 37=[-2.0659541339773581083 ,2.7417468206493368865 ] 
dist 38=[-2.0408144842089773069 ,3.1924542806423967034 ] 
dist 39=[-1.9781791260018087304 ,3.4393560314685208382 ] 
dist 40=[-1.9591712042715291649 ,3.5820012802792761712 ] 
dist 41=[-.8093576210368552710 ,3.8926683293591459945 ] 
dist 42=[-.7055984578207160072 ,4.5751365380966370166 ] 
dist 43=[-.4729925344929385315 ,5.1696935491276544636 ] 
dist 44=[-.4304403705406945690 ,5.6589045619192223505 ] 
dist 45=[-.1556649321092738207 ,5.9214752097100220638 ] 
dist 46=[-.1087463911327035193 ,6.0671303883703618122 ] 
dist 47=[-.0209346829421649386 ,6.0902873010969277263 ] 
dist 48=[-.0015646347435289567 ,3.3376161680391779327 ] 
dist 49=[.0624799163269224939 ,3.1075705428665846615 ] 
dist 50=[-.1308575069012664125 ,2.5323865864430225987 ] 
dist 51=[-.2563774819323394964 ,2.4284192923643357372 ] 
dist 52=[-.3548289652923537800 ,1.5427794099054935716 ] 
dist 53=[-.4404872469092960315 ,1.3759296906690474000 ] 
dist 54=[-.5102425821452591386 ,1.1282721607312584195 ] 
dist 55=[-.5454219095281953963 ,1.1157026334917434123 ] 
dist 56=[-1.1587902899326647987 ,1.1126024090227798684 ] 
dist 57=[-1.5638854084725077998 ,.09900534641471204167] 
dist 58=[-1.8808221289221474578 ,.07723375149061446104] 
dist 59=[-2.1566962433910972913 ,.02712915597324282465] 
dist 60=[-2.3824630060374426681 ,.01994803361949110569] 
dist 61=[-2.4998445263571482467 ,-.04105244205469373410] 
dist 62=[-2.5613822037122333371 ,-.0509993959321532717 ] 
dist 63=[-2.5724433004921830115 ,-.0652690149802143695 ] 
dist 64=[-.6392380917252691080 ,-.03875372662145946897] 
dist 65=[-.5876020896454306102 ,.0318380268584978407 ] 
dist 66=[-.4546027106398909415 ,.10070970139693847197] 
dist 67=[-.4354295191662714353 ,.14529908880085974162] 
dist 68=[-.2232944677813161702 ,.1801002569085687852 ] 
dist 69=[-.1841615189538327682 ,.2100436171133160353 ] 
dist 70=[-.1442805662953941579 ,.2341616862369005065 ] 
dist 71=[-.1458103675310062039 ,.2457938848715217713 ] 
dist 72=[-.1461923420051304774 ,.2515226272607605359 ] 
dist 73=[-.06092967291150741018,.2603364091515373335 ] 
dist 74=[-.05410853092295650024,.3169627298454496811 ] 
dist 75=[-.03806527475587679293,.3670949003278354417 ] 
dist 76=[-.03537000277034885679,.4086958386716809640 ] 
dist 77=[-.01419963801756719518,.4313538919205999896 ] 
dist 78=[-.01049599977888450283,.4442865324790869891 ] 
dist 79=[-.00451764068577973211,.4471620055604936737 ] 
dist 80=[-.00312911474781116638,.2582948461254481131 ] 
dist 81=[-.0080483967360848549 ,.2424509185870438978 ] 
dist 82=[-.0226597032836390840 ,.2019327591625758879 ] 
dist 83=[-.0318908718433359744 ,.1943759446681931068 ] 
dist 84=[-.0388371874059080675 ,.1285861496613153183 ] 
dist 85=[-.0443625436529795714 ,.11589455106471273331] 
dist 86=[-.0487343384871185152 ,.09666199466439806068] 
dist 87=[-.0510912705543979179 ,.09122798226318479779] 
dist 88=[-.0749424585549852414 ,.0581662802986127887 ] 
dist 89=[-.1086468949668354647 ,.01342875490682448603] 
dist 90=[-.1353286981173708860 ,.01169520886207616393] 
dist 91=[-.1590289668515700171 ,.00751645305553998058] 
dist 92=[-.1787226921441447095 ,.0082173047293628679 ] 
dist 93=[-.1894564021507321376 ,.0138715718765340269 ] 
dist 94=[-.1955821020341868883 ,.0195202604252881716 ] 
dist 95=[-.1969327595321436623 ,.0243352733144840305 ] 
dist 96=[-.05220317592867419344,.0293957578918114874 ] 
dist 97=[-.0483254503009171912 ,.0360222383357612424 ] 
dist 98=[-.0381757481598221918 ,.0423404664352795134 ] 
dist 99=[-.0367034428631492807 ,.0461754682237864411 ] 
dist 100=[-.0199504280561164672 ,.0488777024309458254 ] 
dist 101=[-.0168147672851166834 ,.0506906794416055883 ] 
dist 102=[-.0131588140398641953 ,.0517675248830026101 ] 
dist 103=[-.01328544878221955602,.0519296599045696450 ] 
dist 104=[-.01330793072214785554,.0510032786004766920 ] 
dist 105=[-.00729752321647218739,.0508339639200146948 ] 
dist 106=[-.00678100566337615153,.0252871482670886746 ] 
dist 107=[-.0055861191554145334 ,.0295408897956064957 ] 
dist 108=[-.0063252203157972444 ,.0330685359208421067 ] 
dist 109=[-.0072842309023561250 ,.0349766290085029671 ] 
dist 110=[-.0082939702533072166 ,.0360458450943477266 ] 
dist 111=[-.0092352139645511482 ,.0362345517724493866 ] 
dist 112=[-.0102937026460660426 ,.0217394225285387311 ] 
dist 113=[-.0117701702173099160 ,.0204907839325937757 ] 
dist 114=[-.0132207567873780193 ,.0172648128313084042 ] 
dist 115=[-.0141764676588216914 ,.0166442897181448207 ] 
dist 116=[-.0149410020721205645 ,.0112682918476260514 ] 
dist 117=[-.0156312762285560282 ,.0102167171408347808 ] 
dist 118=[-.0162112543655817244 ,.0086105973459304270 ] 
dist 119=[-.0165371431080446586 ,.0081537600672219454 ] 
dist 120=[-.0167359568603909090 ,.00501189722766842833] 
dist 121=[-.0168105808601804372 ,.00148350599358026993] 
dist 122=[-.0168001784004236169 ,.00132674799707629484] 
dist 123=[-.0166698571908275037 ,.00093694182725590684] 
dist 124=[-.0164145491833648997 ,.00088094533231220720] 
dist 125=[-.0162654983096354834 ,.00030374018843600351] 
dist 126=[-.0153351376986663910 ,.00020043136726870170] 
dist 127=[-.0146784199264174605 ,7.20935858183963500000e-05] 
dist 128=[-.00437636947668928630,5.07567325394608900000e-05] 
dist 129=[-.00406017736047184531,-.00069573408221485452] 
dist 130=[-.00322589973740342937,-.00078178433962177674] 
dist 131=[-.00310596255673899320,-.00094399849722057076] 
dist 132=[-.00170673772776230802,-.00097693378693891369] 
dist 133=[-.0014433882973906916 ,-.00104192076745353982] 
dist 134=[-.00126799685967299386,-.0004197305399549089 ] 
dist 135=[-.00129830509976229309,.0003967036358688143 ] 
dist 136=[-.00130572306870538925,.0011854578448008598 ] 
dist 137=[-.00067995832006257474,.0017015548165849015 ] 
dist 138=[-.00062863790949712656,.0021113308782148064 ] 
dist 139=[-.00050149487314753911,.0024769679789377265 ] 
dist 140=[-.00047871178574655166,.0027816342105101114 ] 
dist 141=[-.00028658330894838627,.0029487603502595468 ] 
dist 142=[-.00025065401432601802,.0030454387271680305 ] 
dist 143=[-.00019526500831382828,.0030697292819994401 ] 
dist 144=[-.00018046459014852166,.00183782412728913633] 
dist 145=[7.99402129326667100000e-05,.00173395601956312079] 
dist 146=[.00011349512333294369,.00146423494564070460] 
dist 147=[.00017813174752925270,.00141277612116416901] 
dist 148=[.00019241592566440598,.00095887452240241879] 
dist 149=[.00022922103777633270,.00086988051913845695] 
dist 150=[.00022948814079052124,.00073618150517981199] 
dist 151=[-.00011707949364399243,.00069734326002104811] 
dist 152=[-.00049791540582886902,.00056473431941500667] 
dist 153=[-.00074735261477701428,.00014603415629127741] 
dist 154=[-.0009455917804144445 ,.00013284972973915570] 
dist 155=[-.0011226976560684325 ,9.93793609810516410000e-05] 
dist 156=[-.0012703483546053179 ,9.45585875844927940000e-05] 
dist 157=[-.0013513742141104727 ,4.26015235676802960000e-05] 
dist 158=[-.0013982575297407749 ,3.31025192866066760000e-05] 
dist 159=[-.0014100380159630471 ,2.16841367845152940000e-05] 
dist 160=[-.00038703174279766987,1.97233892238641800000e-05] 
dist 161=[-.00036054800858147700,-5.16110694568838400000e-05] 
dist 162=[-.00029039887542033990,-5.96583240157380600000e-05] 
dist 163=[-.00027993759074258528,-7.47012274164612000000e-05] 
dist 164=[-.00016090570674877853,-7.77622473177656000000e-05] 
dist 165=[-.00013830269654153906,-8.37345973317315400000e-05] 
dist 166=[-.00011797147003914619,-4.23522481387200400000e-05] 
dist 167=[-.00011995937832846346,3.18784737848695300000e-05] 
dist 168=[-.00012026731240213332,.00010371016471196478] 
dist 169=[-7.78099628596782190000e-05,.00015045822281154942] 
dist 170=[-7.37159081133607810000e-05,.00018727071553373638] 
dist 171=[-6.28247564297950930000e-05,.00021956757014012709] 
dist 172=[-6.10248743092116980000e-05,.00024606465146435236] 
dist 173=[-4.19974274323237800000e-05,.00025979852304520947] 
dist 174=[-3.82621276103669000000e-05,.00026700275499782104] 
dist 175=[-3.36122689237244700000e-05,.00026821839845569987] 
dist 176=[-3.21573220457648200000e-05,.00018039121977951414] 
dist 177=[2.07792719388385000000e-06,.00017219820790821184] 
dist 178=[6.23411936121760000000e-06,.00014924669089475318] 
dist 179=[1.41538369260597470000e-05,.00014556983795633835] 
dist 180=[1.42538390009053599000e-05,.00010188759623485892] 
dist 181=[1.33141240987884476000e-05,9.31251838759656300000e-05] 
dist 182=[1.08965942171901606000e-05,8.30940844774800200000e-05] 
dist 183=[-1.03132034182989000000e-05,8.02701807775537100000e-05] 
dist 184=[-4.11143423104491600000e-05,5.53103373587099860000e-05] 
dist 185=[-6.10926273015753800000e-05,1.42840500003515200000e-05] 
dist 186=[-7.67456006501153800000e-05,1.29937513755807100000e-05] 
dist 187=[-9.03369854318842900000e-05,9.74022744938018000000e-06] 
dist 188=[-.00010138469220769605,9.23938378266179000000e-06] 
dist 189=[-.00010691620524365459,4.23955889052345000000e-06] 
dist 190=[-.00010985459845408039,3.32365914360020000000e-06] 
dist 191=[-.00011058401267057566,2.12408483013010000000e-06] 
dist 192=[-3.68747570737702100000e-05,1.83284187562930000000e-06] 
dist 193=[-3.43918488339505300000e-05,-4.97998919431810000000e-06] 
dist 194=[-2.77455453090539400000e-05,-5.79948427773450000000e-06] 
dist 195=[-2.67894902677320200000e-05,-7.33548643858210000000e-06] 
dist 196=[-1.53195888666316000000e-05,-7.64946807768100000000e-06] 
dist 197=[-1.31365883384492000000e-05,-8.27131005137560000000e-06] 
dist 198=[-1.17503176119325000000e-05,-4.15442216983813000000e-06] 
dist 199=[-1.19545697144166000000e-05,2.85606435467377000000e-06] 
dist 200=[-1.19786706761682000000e-05,9.64597293935938000000e-06] 
dist 201=[-7.43320782095920000000e-06,1.40868645902914700000e-05] 
dist 202=[-6.99260594581811000000e-06,1.76072023052435000000e-05] 
dist 203=[-5.89662400716484000000e-06,2.07343927664118000000e-05] 
dist 204=[-5.65978124619227000000e-06,2.33268569887867000000e-05] 
dist 205=[-3.94124811373744600000e-06,2.47195596497774900000e-05] 
dist 206=[-3.60492023864377000000e-06,2.54847560330933800000e-05] 
dist 207=[-3.00251562124866000000e-06,2.56261188614707800000e-05] 
dist 208=[-2.85815576701708000000e-06,1.61234479857706300000e-05] 
dist 209=[-3.21127636839110000000e-07,1.52813876472320700000e-05] 
dist 210=[2.76559432528400000000e-08,1.30790568121667200000e-05] 
dist 211=[6.94255855517300000000e-08,1.26379039273041700000e-05] 
dist 212=[-1.19083012151410000000e-07,8.85091782381579000000e-06] 
dist 213=[-4.05709445003030000000e-07,8.09740447956912000000e-06] 
dist 214=[-8.02617929385950000000e-07,7.10256301915600000000e-06] 
dist 215=[-1.86338242135286000000e-06,7.18108274077740000000e-06] 
dist 216=[-5.17229218694012000000e-06,7.16477496784420000000e-06] 
dist 217=[-7.33355854224157000000e-06,6.54629285899130000000e-07] 
dist 218=[-9.04318792961063000000e-06,5.42235991138920000000e-07] 
dist 219=[-1.05552039443299400000e-05,3.07064302692650000000e-07] 
dist 220=[-1.18035433915648700000e-05,2.45908282254280000000e-07] 
dist 221=[-1.24640801914301600000e-05,2.71952436811700000000e-08] 
dist 222=[-1.28131760596471100000e-05,-1.76194946553600000000e-08] 
dist 223=[-1.28806652260207400000e-05,-6.98083483114100000000e-08] 
dist 224=[-3.34098862932058500000e-06,-7.36632364522200000000e-08] 
dist 225=[-3.12622843245999400000e-06,-5.92733843978700000000e-08] 
dist 226=[-2.54761931305774000000e-06,-2.08585109108000000000e-08] 
dist 227=[-2.46351231339181000000e-06,4.16766715856400000000e-08] 
dist 228=[-1.53205777856151000000e-06,1.52084276020070000000e-07] 
dist 229=[-1.58334490075073000000e-06,2.82765751772930000000e-07] 
dist 230=[-1.59485767103287000000e-06,4.25985694466140000000e-07] 
dist 231=[-1.59026005997590000000e-06,6.03861371755140000000e-07] 
dist 232=[-1.57740313775895000000e-06,1.12472765793063000000e-06] 
dist 233=[-1.34133324582683480000e-06,1.52393205435205000000e-06] 
dist 234=[-1.29517908551598600000e-06,1.82729332532234000000e-06] 
dist 235=[-1.19827426566253000000e-06,2.07405640135999000000e-06] 
dist 236=[-1.16707083383535000000e-06,2.27053425931466000000e-06] 
dist 237=[-1.02582379350499000000e-06,2.37384212419624000000e-06] 
dist 238=[-9.93414183978200000000e-07,2.42755180645267000000e-06] 
dist 239=[-9.03562910465630000000e-07,2.43355581920257000000e-06] 
dist 240=[-8.81819083818490000000e-07,1.90777233751643000000e-06] 
dist 241=[-7.03400357536600000000e-07,1.84074823485703000000e-06] 
dist 242=[-6.64358388389560000000e-07,1.65122117707725000000e-06] 
dist 243=[-6.07955518887160000000e-07,1.61300219109842000000e-06] 
dist 244=[-5.89078625765770000000e-07,1.23611295741681000000e-06] 
dist 245=[-5.57113092040990000000e-07,1.15723235367253000000e-06] 
dist 246=[-5.53545452414610000000e-07,1.03773177075842000000e-06] 
dist 247=[-5.61921528139880000000e-07,8.01108821991520000000e-07] 
dist 248=[-5.88649683319660000000e-07,2.18445659946750000000e-07] 
dist 249=[-7.37608150215054000000e-07,-7.33084450226000000000e-08] 
dist 250=[-8.70472933863209000000e-07,-1.65925164519647000000e-07] 
dist 251=[-9.82188853152295000000e-07,-1.85836107863712000000e-07] 
dist 252=[-1.07042669316758600000e-06,-1.94250452229947600000e-07] 
dist 253=[-1.10988185563515600000e-06,-1.66074333648530600000e-07] 
dist 254=[-1.12812583304356100000e-06,-1.09393925277367680000e-07] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 2, 0, 0, 2, 1, 2] 
dist 0=[78.380774697609483658  ,78.380774697609483658  ] 
dist 1=[77.631304330717949664  ,79.399848408844784612  ] 
dist 2=[75.659223273565728678  ,80.479439261878087963  ] 
dist 3=[72.457818399703261938  ,81.022693845745436755  ] 
dist 4=[67.104028903891141480  ,81.277176842316935609  ] 
dist 5=[61.531594105876546150  ,81.204254138254510830  ] 
dist 6=[57.457771144931240856  ,80.973109544304377541  ] 
dist 7=[53.703514082801915494  ,79.919946432552677881  ] 
dist 8=[49.406737630226301497  ,73.024419750477519672  ] 
dist 9=[45.093742445096210155  ,71.838440595631393370  ] 
dist 10=[41.275014706090105095  ,70.053945550155700097  ] 
dist 11=[37.090080198127167360  ,69.482867590189436181  ] 
dist 12=[31.316046329326229497  ,68.822197250185091197  ] 
dist 13=[25.552394380917888413  ,68.493910133367915562  ] 
dist 14=[21.408947590025052595  ,67.941348484881273522  ] 
dist 15=[17.662653482878167493  ,66.148201067783355057  ] 
dist 16=[13.483703868353822618  ,25.291169855608599090  ] 
dist 17=[9.351118958294698255  ,21.247552913480985929  ] 
dist 18=[5.789759043998021500  ,20.539647155785236428  ] 
dist 19=[1.967723399270639776  ,19.057832852370586811  ] 
dist 20=[-3.205200149787193292  ,18.697187205780110812  ] 
dist 21=[-8.2312542754469175150 ,6.4396586723675358698 ] 
dist 22=[-11.467580939927135479  ,5.2650500418233739173 ] 
dist 23=[-14.011446970931391968  ,2.5939367682931314578 ] 
dist 24=[-16.275228220072780871  ,2.2118305539329820294 ] 
dist 25=[-18.188380072211992728  ,-1.0049642086143602855 ] 
dist 26=[-19.334011989128293164  ,-1.5346040957812228635 ] 
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dist 236=[2.57336870307066137000e-07,2.70386044763563100000e-06] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 0, 0, 2, 1, 2] 
dist 0=[79.990307791972072070  ,79.990307791972072070  ] 
dist 1=[79.495166649852287682  ,80.409924361888966353  ] 
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dist 6=[62.502904476280485779  ,81.758757731964767590  ] 
dist 7=[59.166240186512362407  ,80.859626516834638765  ] 
dist 8=[55.248179965750499914  ,74.064658509352860950  ] 
dist 9=[51.257385474982664665  ,72.902127116312440891  ] 
dist 10=[47.631123267886441714  ,70.825262932210630057  ] 
dist 11=[43.579592824515361234  ,70.265179818890243516  ] 
dist 12=[37.892481422348803170  ,68.295696890445506570  ] 
dist 13=[31.486873485940500120  ,67.694193719046191617  ] 
dist 14=[21.101440985088332756  ,66.933558256976372255  ] 
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dist 22=[-15.284853000027189479  ,1.459186522786853480  ] 
dist 23=[-17.229048698023770607  ,1.079199422386843007  ] 
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dist 34=[-6.5782763811102605616 ,-2.263497694586217760  ] 
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dist 40=[.5540894230434155216 ,5.690397964211598660  ] 
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dist 43=[1.795363940065564305  ,7.153399049694604704  ] 
dist 44=[2.0092039681582674379 ,7.276172030897804272  ] 
dist 45=[1.9146491650875490522 ,7.280875612379451185  ] 
dist 46=[1.6566819006418984722 ,6.509295375630207768  ] 
dist 47=[1.1136721019919825430 ,6.537388131896644671  ] 
dist 48=[.5267087038399607188 ,3.3523844810476274212 ] 
dist 49=[.0935956608819392685 ,3.2193634539462958342 ] 
dist 50=[-.3046307696108192427 ,2.1643155614512153816 ] 
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dist 60=[-3.761545478026614723  ,-.8597569754701856393 ] 
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dist 72=[.02807638149247228152,.3315114951071900272 ] 
dist 73=[.05874396739805845104,.3820223589694071762 ] 
dist 74=[.1199558740854540830 ,.4239722879418715213 ] 
dist 75=[.1342492910430905804 ,.4469124894127086697 ] 
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dist 185=[-.00010329839938897353,-2.68190101725128000000e-05] 
dist 186=[-.00011592963523258511,-3.82101514027349200000e-05] 
dist 187=[-.00012225592261414261,-4.05074497274858100000e-05] 
dist 188=[-.00012561720827650125,-4.87691638442845900000e-05] 
dist 189=[-.00012645039256608453,-4.95838293277685800000e-05] 
dist 190=[-6.09325651361762700000e-05,-4.21628158356043100000e-05] 
dist 191=[-6.14388993165346000000e-05,-3.60576330258944600000e-05] 
dist 192=[-3.82548315922037460000e-05,-3.02905624355614200000e-05] 
dist 193=[-3.62715473510540214000e-05,-2.35774710763039000000e-05] 
dist 194=[-3.10393246759425580000e-05,-1.68714319700408400000e-05] 
dist 195=[-3.00173537555493740000e-05,-1.11314105641676200000e-05] 
dist 196=[-2.09044171432946060000e-05,-5.06868021521178000000e-06] 
dist 197=[-1.90912057429232790000e-05,2.92239412216534000000e-06] 
dist 198=[-1.63833023629918400000e-05,1.06656239966614700000e-05] 
dist 199=[-1.55787860298740500000e-05,1.57425833092217500000e-05] 
dist 200=[9.52728512318200000000e-08,1.97812111674885000000e-05] 
dist 201=[2.11975806410770900000e-06,2.33931228456964100000e-05] 
dist 202=[6.23638628663633900000e-06,2.64050540195477000000e-05] 
dist 203=[7.22871621025072000000e-06,2.80564187433888700000e-05] 
dist 204=[1.03342070620682150000e-05,2.90092079034191400000e-05] 
dist 205=[1.08536635078989170000e-05,2.92415114362224100000e-05] 
dist 206=[1.06594650650872610000e-05,2.88604062051609100000e-05] 
dist 207=[9.44448128309717360000e-06,2.91044992113725700000e-05] 
dist 208=[7.99834573692872000000e-06,1.45426522072532600000e-05] 
dist 209=[6.88447841709704100000e-06,1.40534044778406800000e-05] 
dist 210=[5.81539888878635600000e-06,9.71711466827837000000e-06] 
dist 211=[4.54710330015520300000e-06,8.85742055190196000000e-06] 
dist 212=[2.86713486283420000000e-06,7.56857327545146400000e-06] 
dist 213=[-9.94139788709590000000e-07,7.18875982865005900000e-06] 
dist 214=[-4.77516385762388000000e-06,2.66907106680149100000e-06] 
dist 215=[-7.25533851399439000000e-06,2.57521654663759200000e-06] 
dist 216=[-9.22905740507781000000e-06,-1.53261415154060900000e-06] 
dist 217=[-1.09950840742953700000e-05,-2.00417717933582200000e-06] 
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dist 219=[-1.32753966232924800000e-05,-3.17336127537302500000e-06] 
dist 220=[-1.37409422282355700000e-05,-3.79190501491941000000e-06] 
dist 221=[-1.38535843957490000000e-05,-3.83217430151193500000e-06] 
dist 222=[-5.55786097067793100000e-06,-3.68005241051112900000e-06] 
dist 223=[-5.58365421447446100000e-06,-3.17661100307551000000e-06] 
dist 224=[-4.06324634301529700000e-06,-2.65592335804764000000e-06] 
dist 225=[-3.90229829680629800000e-06,-2.04141305001573000000e-06] 
dist 226=[-3.44176696769749200000e-06,-1.42302235268186000000e-06] 
dist 227=[-3.36266342907160300000e-06,-8.86817989193750000000e-07] 
dist 228=[-2.44825131940223100000e-06,-3.14676229009330000000e-07] 
dist 229=[-2.26090639429864700000e-06,4.46773751883210000000e-07] 
dist 230=[-2.03896132429529400000e-06,1.18312683740052000000e-06] 
dist 231=[-1.96396604227303500000e-06,1.65544770714733000000e-06] 
dist 232=[-6.13759128888530000000e-08,2.01936145136487000000e-06] 
dist 233=[1.70227337970645000000e-07,2.32441418997541000000e-06] 
dist 234=[3.77272650227405700000e-07,2.56913337630835000000e-06] 
dist 235=[4.25326007596580400000e-07,2.69300968106390000000e-06] 
dist 236=[4.52238794946601300000e-07,2.75454237063909000000e-06] 
dist 237=[3.88199952974305610000e-07,2.76243699920021000000e-06] 
dist 238=[2.56381790586649500000e-07,2.68634129426483800000e-06] 
dist 239=[0                     ,2.69578917340554800000e-06] 
dist 240=[2.72803167213950000000e-07,1.76459608608260000000e-06] 
dist 241=[1.14543787395520000000e-07,1.72269356878429000000e-06] 
dist 242=[-3.66842760143700000000e-08,1.27907885165326000000e-06] 
dist 243=[-2.15147883524120000000e-07,1.18749008044612000000e-06] 
dist 244=[-3.94666696639050000000e-07,1.07034043728982000000e-06] 
dist 245=[-6.16170388699930000000e-07,1.02746502254725000000e-06] 
dist 246=[-9.21836076108240000000e-07,1.11276568864090000000e-07] 
dist 247=[-1.11561652013508000000e-06,-2.93186121283000000000e-09] 
dist 248=[-1.26230820923601000000e-06,-1.94089600437735300000e-07] 
dist 249=[-1.38064250856604000000e-06,-2.16844874431650800000e-07] 
dist 250=[-1.47052053639326000000e-06,-2.25220366441382800000e-07] 
dist 251=[-1.50399576513411000000e-06,-1.92253542452636530000e-07] 
dist 252=[-1.51520073145735000000e-06,-1.26507600476841190000e-07] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 0, 0, 0, 1, 0, 1] 
dist 0=[71.197859788854246074  ,71.197859788854246074  ] 
dist 1=[68.835253032971127477  ,72.977526709005478400  ] 
dist 2=[65.596216982514629601  ,74.349177471584551916  ] 
dist 3=[60.318731563723404440  ,75.083673835011735013  ] 
dist 4=[54.898821970773311286  ,75.490279662996232346  ] 
dist 5=[51.091035278848652902  ,75.554120058226979454  ] 
dist 6=[47.737128674583956323  ,75.405501336413971950  ] 
dist 7=[44.127644171617006224  ,75.271183481893544984  ] 
dist 8=[40.630092870014442984  ,74.028887869966339790  ] 
dist 9=[37.722100754744596399  ,70.880109881756817276  ] 
dist 10=[34.686961034273628952  ,70.113704203537216821  ] 
dist 11=[30.680581621587250394  ,69.133344363951630249  ] 
dist 12=[26.745406863570176011  ,68.725599512479247694  ] 
dist 13=[23.993724607704723927  ,68.025399075425110431  ] 
dist 14=[21.576016890034195848  ,67.793551537034604746  ] 
dist 15=[18.972987974372691300  ,67.418911160927575973  ] 
dist 16=[16.438170800635291528  ,64.596061701527717391  ] 
dist 17=[14.279418259166305752  ,29.171855169788431150  ] 
dist 18=[9.2946711439146066972 ,26.093287500652483714  ] 
dist 19=[5.4040886989651766848 ,18.980116408981793970  ] 
dist 20=[1.5683859757809406734 ,17.835164597311547395  ] 
dist 21=[-3.1970284435213599194 ,8.7635668672715733201 ] 
dist 22=[-7.7295991327708545847 ,7.1928091552516954851 ] 
dist 23=[-10.635802710873215220  ,4.7711578393840225717 ] 
dist 24=[-12.907716739742858808  ,4.1870683464683213981 ] 
dist 25=[-14.908485749071909045  ,-.2432522177690172209 ] 
dist 26=[-16.581972392533714103  ,-.9050222534309522575 ] 
dist 27=[-17.547526396650107172  ,-1.0435037531138428469 ] 
dist 28=[-18.179344071375258764  ,-2.7698940148562264734 ] 
dist 29=[-18.520707583754957500  ,-2.9882909198554472853 ] 
dist 30=[-18.706945582886880553  ,-3.2460826013617644637 ] 
dist 31=[-18.719800753449452358  ,-3.2464824437436579810 ] 
dist 32=[-18.608697919201644498  ,-3.1570445967252486708 ] 
dist 33=[-5.8752455054133437721 ,-2.4836078414928896370 ] 
dist 34=[-5.9490632449971821262 ,-1.6583324115897476959 ] 
dist 35=[-5.9622904752596627690 ,-.9911770461565472670 ] 
dist 36=[-3.4081027436869268441 ,-.3168901935777641052 ] 
dist 37=[-1.6729488466138669852 ,.5374235636305305803 ] 
dist 38=[-1.2650112110896185153 ,1.3513412184989737934 ] 
dist 39=[-1.1688568745210909836 ,1.8648414309555171336 ] 
dist 40=[-.7079033114060583689 ,2.2540016752086549395 ] 
dist 41=[-.6264576891212269833 ,2.5723953816227347597 ] 
dist 42=[-.4341340071737411994 ,2.8268939298806041444 ] 
dist 43=[-.4048965793920136941 ,2.9614570877684727552 ] 
dist 44=[-.1288489646322031644 ,3.0504472775071947604 ] 
dist 45=[-.0768195427075155064 ,3.3545558191850061363 ] 
dist 46=[-.0375878461660077102 ,3.5202742862519843164 ] 
dist 47=[-.0464569948299745005 ,3.6156564812212203618 ] 
dist 48=[-.0775486890883860192 ,3.6393682673553243594 ] 
dist 49=[-.1375290167134317679 ,2.3342925571582971146 ] 
dist 50=[-.2292253472437456288 ,1.9671718209289169034 ] 
dist 51=[-.3868016830023055022 ,1.7523787232742550526 ] 
dist 52=[-.5475255565430158230 ,1.4312576484806006076 ] 
dist 53=[-.6518386014082678408 ,.90173159085657954328] 
dist 54=[-.7340094263234471515 ,.80211372576419545461] 
dist 55=[-.8066152798660254493 ,.65176016423992973708] 
dist 56=[-.8670562099143829176 ,.61031765998158210883] 
dist 57=[-.9008225859649917090 ,.19183785327460142549] 
dist 58=[-.9215084233478590960 ,.13670291094976263178] 
dist 59=[-1.0027317720345811641 ,.12276609118147661324] 
dist 60=[-1.1731820377493950187 ,-.10705389627743196192] 
dist 61=[-1.3146615045502313390 ,-.1365512907099198471 ] 
dist 62=[-1.3920124015621751821 ,-.19166276975326170384] 
dist 63=[-1.4366148725940316510 ,-.20335929332478148562] 
dist 64=[-1.4476644995975385152 ,-.22975984036082354448] 
dist 65=[-.5126433316087128425 ,-.22498299569857953519] 
dist 66=[-.5264209598282229807 ,-.1472927942706596764 ] 
dist 67=[-.5298771432062046577 ,-.0840072966296705286 ] 
dist 68=[-.27362656228618986068,-.0197631359889987914 ] 
dist 69=[-.14507141185822451775,.0617778950630828865 ] 
dist 70=[-.12129147030214888801,.1399418733339424951 ] 
dist 71=[-.09250265857282856780,.1907502605369798905 ] 
dist 72=[-.0869070958525469185 ,.2308296675186497834 ] 
dist 73=[-.02382598241515976968,.2662721450260997340 ] 
dist 74=[-.01240110222388934728,.2956751468304419493 ] 
dist 75=[-.01016984666838024030,.3117043417400001461 ] 
dist 76=[.05302758029593429825,.3208808606560746291 ] 
dist 77=[.06042668066423002134,.3229934192103346093 ] 
dist 78=[.07438673251620036610,.26944905346210872315] 
dist 79=[.07724783077992763248,.27531386973114493983] 
dist 80=[.08309458097862911321,.27625223487179939684] 
dist 81=[.08150925744812100471,.18374374584466961578] 
dist 82=[.07506645201914448413,.17478681173986328357] 
dist 83=[.04951203755806996384,.15049358972470253813] 
dist 84=[.02188840502547786229,.14641791775473336599] 
dist 85=[-.01540538272075387371,.10253584911966610091] 
dist 86=[-.05170370417595505316,.09383257409776049416] 
dist 87=[-.0753673045108884431 ,.08303553746320761686] 
dist 88=[-.0940840189370199939 ,.07954753270498282522] 
dist 89=[-.1106903190873001200 ,.028200034478547503  ] 
dist 90=[-.1244825546385601473 ,.02420949758219547709] 
dist 91=[-.1319967456546291665 ,.02317732488771384531] 
dist 92=[-.1362833583394756273 ,-.00578604775487784132] 
dist 93=[-.1372262515353127888 ,-.00922905113284611409] 
dist 94=[-.12131444898231280013,-.01648796300598704589] 
dist 95=[-.123188352402433489  ,-.01353285942084896798] 
dist 96=[-.12339202771757986556,0                     ] 
dist 97=[-.04019548148030349736,-.02036722342533893984] 
dist 98=[-.04110435765035248781,-.01399812072113851547] 
dist 99=[-.04122450170362157826,-.00862972732960532633] 
dist 100=[-.0297545965672520564 ,-.00302444307380954901] 
dist 101=[-.0202690234903395662 ,.00492845061668688209] 
dist 102=[-.0184257216438314093 ,.01359055043777059528] 
dist 103=[-.0153418814788003148 ,.01921833401024450237] 
dist 104=[-.0145561054673758860 ,.02364512188595577852] 
dist 105=[-.00312383402963149109,.02752705038462091847] 
dist 106=[-.00212640542990873946,.03071554235163846560] 
dist 107=[-.00195757545785079092,.03238220854822676520] 
dist 108=[.00459627048146359038,.03325886468626264971] 
dist 109=[.00535254459823673148,.03342224059829210200] 
dist 110=[.0065628786055185295 ,.03280073093937745076] 
dist 111=[.0048285060630691800 ,.0324436214571400635 ] 
dist 112=[.0032039899202261777 ,.0314792181777108582 ] 
dist 113=[.0013319769962986613 ,.01541968515535764892] 
dist 114=[-.0005292088553652367 ,.01104086412963430280] 
dist 115=[-.0021111301201749297 ,.01015745681340249614] 
dist 116=[-.0037739699652195705 ,.00918377904600586405] 
dist 117=[-.00595771667223752460,.00892653070566154261] 
dist 118=[-.00805302323888448393,.00428334515157227202] 
dist 119=[-.00936408780205711270,.00411266862648051607] 
dist 120=[-.01033879781225510282,.00263782764834355004] 
dist 121=[-.01109554655279619032,.00235596464311391069] 
dist 122=[-.01165006750043346911,.00192805730902786617] 
dist 123=[-.01181982864085288994,.00180868840626046039] 
dist 124=[-.01184848674548866373,-.00037921705259841942] 
dist 125=[-.01184137618819721007,-.00066095895053906877] 
dist 126=[-.00374877152796481206,-.00121683089509688188] 
dist 127=[-.00356978084407925352,-.00134472172738147018] 
dist 128=[-.00399871195761989029,-.00170781029666483631] 
dist 129=[-.00423337545914933419,-.00174106130035020365] 
dist 130=[-.00436857585374375372,-.0014319629036957145 ] 
dist 131=[-.00440151653889653723,-.0009201696635694763 ] 
dist 132=[-.00118645609286181170,-.0003848490386517221 ] 
dist 133=[-.00109391531611569402,.0003143658850863676 ] 
dist 134=[-.00085355495041937377,.0009902064459258761 ] 
dist 135=[-.00081892042429141611,.0014325562981277288 ] 
dist 136=[-.00042766542180750171,.0017838777825107867 ] 
dist 137=[-.00035477365739861981,.0020974713835658161 ] 
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dist 147=[.00048084098602083476,.00088902841639724715] 
dist 148=[.00023842868264517498,.00063445477821544072] 
dist 149=[-9.42035854479576100000e-05,.00060134864310783262] 
dist 150=[-.00041946452994855714,.00049399571479246151] 
dist 151=[-.00063255828648715977,.00048098592306736871] 
dist 152=[-.00080195573149510431,.00033856153801010442] 
dist 153=[-.0009533427769811562 ,.00031016737087004217] 
dist 154=[-.0010795686531814165 ,.00027553023431981541] 
dist 155=[-.0011488430085816907 ,.00026445433248014916] 
dist 156=[-.0011889276898694313 ,-6.33861791307246000000e-06] 
dist 157=[-.0011989964076743125 ,-3.92178209640397600000e-05] 
dist 158=[-.00033022370084539964,-8.57250164360617380000e-05] 
dist 159=[-.00036422427010329592,-9.01732839488367468000e-05] 
dist 160=[-.00039276626079197570,-8.69589186956223931000e-05] 
dist 161=[-.00040571494147489177,-7.23340313311987305000e-05] 
dist 162=[-.00041146860507900109,-4.67645262916478649500e-05] 
dist 163=[-.00041137135438257184,0                     ] 
dist 164=[-.00011449889826038168,-3.79391524346600200000e-05] 
dist 165=[-.00010583495323594250,2.53720841996170200000e-05] 
dist 166=[-8.31799763901179200000e-05,8.66617760777181300000e-05] 
dist 167=[-7.98953752273119600000e-05,.00012656070963291512] 
dist 168=[-4.25055402551727000000e-05,.00015798901258146987] 
dist 169=[-3.55014427540424000000e-05,.00018557391137672148] 
dist 170=[-2.73560181929062000000e-05,.00020821065464609584] 
dist 171=[-2.58785280135728000000e-05,.00021994962600718047] 
dist 172=[3.32294919685513000000e-05,.00022611734355025821] 
dist 173=[4.00864940383061000000e-05,.00022716158714010634] 
dist 174=[5.38999083231867000000e-05,.00015337935614850098] 
dist 175=[5.68767885607278000000e-05,.00014648204026946849] 
dist 176=[6.56120407185988000000e-05,.00012710586472801142] 
dist 177=[6.59238751974832000000e-05,.00012400257764967020] 
dist 178=[5.63845909245730300000e-05,8.69580317900475750000e-05] 
dist 179=[3.83860040845598700000e-05,8.34277271488919000000e-05] 
dist 180=[1.86703908109976200000e-05,7.10256751385781370000e-05] 
dist 181=[-8.23018949590304000000e-06,6.86381548277354060000e-05] 
dist 182=[-3.44516134454322400000e-05,4.02438746534694865000e-05] 
dist 183=[-5.14660484896949700000e-05,3.89000987794820700000e-05] 
dist 184=[-6.48028841489014900000e-05,2.62000356893495600000e-05] 
dist 185=[-7.63920537369997400000e-05,2.37120266228132000000e-05] 
dist 186=[-8.58156292286062700000e-05,2.02218132988849900000e-05] 
dist 187=[-9.05356285618194900000e-05,1.91284734793141600000e-05] 
dist 188=[-9.30457783903250400000e-05,-2.22644985940272000000e-06] 
dist 189=[-9.36763387986601900000e-05,-4.92449757426383000000e-06] 
dist 190=[-3.27755233884031100000e-05,-1.00815904367364000000e-05] 
dist 191=[-3.07333229629411100000e-05,-1.12881790228604600000e-05] 
dist 192=[-3.35877260671722000000e-05,-1.49128340599778500000e-05] 
dist 193=[-3.56155681400022000000e-05,-1.53997008892577200000e-05] 
dist 194=[-3.67369320322915000000e-05,-1.27202474165644200000e-05] 
dist 195=[-3.69644146656854000000e-05,-8.46376743925770000000e-06] 
dist 196=[-1.42380904493272400000e-05,-3.96002028457717000000e-06] 
dist 197=[-1.35956449603873600000e-05,2.28072047660667000000e-06] 
dist 198=[-1.21587109755865500000e-05,8.65662939646453000000e-06] 
dist 199=[-1.17055841248729200000e-05,1.27518612355739200000e-05] 
dist 200=[-9.65796324117173000000e-06,1.59142454049375200000e-05] 
dist 201=[-9.23534876527489000000e-06,1.85785168521007200000e-05] 
dist 202=[-8.05274163178939000000e-06,2.07357649290488200000e-05] 
dist 203=[-7.85852921757549000000e-06,2.18808659815412400000e-05] 
dist 204=[-5.35707974695275000000e-06,2.24915721102041600000e-05] 
dist 205=[-4.88154355976885000000e-06,2.25999251009863600000e-05] 
dist 206=[-4.18660313318212000000e-06,1.87684905585245320000e-05] 
dist 207=[-3.97482612493065000000e-06,1.82558718122702400000e-05] 
dist 208=[-3.71845299679165000000e-06,1.67707141989151200000e-05] 
dist 209=[-3.79071817837218000000e-06,1.64136969882329800000e-05] 
dist 210=[-4.04890930684684000000e-06,1.32677507673997100000e-05] 
dist 211=[-4.62380457755035000000e-06,1.14156620066135400000e-05] 
dist 212=[-5.23714933490918000000e-06,6.47535274472670000000e-06] 
dist 213=[-5.64840370481595000000e-06,6.27820237895356000000e-06] 
dist 214=[-5.98542043869623000000e-06,5.72732922730108000000e-06] 
dist 215=[-6.30353583983916000000e-06,5.59312535608098000000e-06] 
dist 216=[-6.75874564449340000000e-06,4.48543720186923000000e-06] 
dist 217=[-8.06363433812929000000e-06,4.24589167624734100000e-06] 
dist 218=[-9.15150230026113000000e-06,3.86692859983352100000e-06] 
dist 219=[-9.74687760174350000000e-06,3.75236012375502900000e-06] 
dist 220=[-1.00888074688198300000e-05,1.31667142994991000000e-06] 
dist 221=[-1.01682913668093600000e-05,9.95970139808630000000e-07] 
dist 222=[-5.08340037999029700000e-06,2.54982192246160000000e-07] 
dist 223=[-4.87770441458223200000e-06,1.19307496028730000000e-07] 
dist 224=[-4.40891916189489800000e-06,-7.96496708783940000000e-07] 
dist 225=[-4.25660000505986700000e-06,-9.49053049789470000000e-07] 
dist 226=[-3.55167106724404000000e-06,-1.13024781874925000000e-06] 
dist 227=[-3.20785016580584000000e-06,-7.35018141984520000000e-07] 
dist 228=[-1.65121430184492000000e-06,-3.12196025913530000000e-07] 
dist 229=[-1.57261839867158000000e-06,2.51897618507590000000e-07] 
dist 230=[-1.38375085088316000000e-06,7.98305795811740000000e-07] 
dist 231=[-1.32777926996255000000e-06,1.15078776619390000000e-06] 
dist 232=[-1.03756036631647000000e-06,1.44088193283768000000e-06] 
dist 233=[-9.77336962231780000000e-07,1.68604513122735000000e-06] 
dist 234=[-8.44476978014170000000e-07,1.88487399905911600000e-06] 
dist 235=[-8.04422147310720000000e-07,1.99277140367951500000e-06] 
dist 236=[-3.81300970110240000000e-07,2.05351501084982900000e-06] 
dist 237=[-3.13570798366910000000e-07,2.06469774749975000000e-06] 
dist 238=[-1.91009696713770000000e-07,1.82978225690749000000e-06] 
dist 239=[-1.63134869978240000000e-07,1.78954859950863000000e-06] 
dist 240=[-9.24152495510300000000e-08,1.67664751846116000000e-06] 
dist 241=[-8.86338654060400000000e-08,1.63797710206231000000e-06] 
dist 242=[-1.10046225018570000000e-07,1.39518563860607000000e-06] 
dist 243=[-1.71068349998590000000e-07,1.24375070216132000000e-06] 
dist 244=[-2.39502648626590000000e-07,7.63896227361230000000e-07] 
dist 245=[-2.90410630429770000000e-07,7.43310569992770000000e-07] 
dist 246=[-4.76917694366172000000e-07,1.14940782312400000000e-08] 
dist 247=[-6.16550253666952000000e-07,-7.54093706591700000000e-08] 
dist 248=[-7.23380274389625000000e-07,-1.53621852461982000000e-07] 
dist 249=[-8.11574388970761000000e-07,-1.69957576116336000000e-07] 
dist 250=[-8.80870286700523000000e-07,-1.72064189820006900000e-07] 
dist 251=[-9.12513607144507000000e-07,-1.45933094235839500000e-07] 
dist 252=[-9.26657561970110000000e-07,-9.56068833493750500000e-08] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 0, 2, 1, 2] 
dist 0=[87.088058634448766899  ,87.088058634448766899  ] 
dist 1=[86.562000040571480709  ,87.349284738433511903  ] 
dist 2=[85.537446669107259460  ,87.317209525034886430  ] 
dist 3=[84.182104934321523104  ,87.099548630084616810  ] 
dist 4=[82.336059306018359598  ,86.864287846527455422  ] 
dist 5=[79.030722000873439430  ,86.071661672821343225  ] 
dist 6=[74.943186888191268194  ,85.649554537839773011  ] 
dist 7=[69.523146727613031990  ,83.149396059119223533  ] 
dist 8=[60.870776754574381851  ,82.392113192498573963  ] 
dist 9=[52.031165939485754486  ,81.684676314371100723  ] 
dist 10=[45.864000098550633583  ,81.235917819156366671  ] 
dist 11=[36.844315564105820330  ,80.853688138586344358  ] 
dist 12=[29.542983713572304737  ,80.744705297028693963  ] 
dist 13=[23.389258301258035631  ,78.021042984214344848  ] 
dist 14=[17.198101563002300169  ,72.701643821080120673  ] 
dist 15=[11.461906795449506048  ,32.768066613147562377  ] 
dist 16=[7.1238957637208922673 ,29.003464965682927459  ] 
dist 17=[2.9825375652709527637 ,20.170630134234557025  ] 
dist 18=[-1.9687239952236586818 ,18.903818979445392674  ] 
dist 19=[-6.6117342739005273556 ,8.325893496575342975  ] 
dist 20=[-9.5232902411954426689 ,7.779542720232417715  ] 
dist 21=[-11.722725616339324809  ,3.8166572839266353925 ] 
dist 22=[-13.525014159258280558  ,3.1722226558480498477 ] 
dist 23=[-14.936565142814068376  ,2.0908019490785592370 ] 
dist 24=[-15.577685111000523881  ,1.8768708261150114841 ] 
dist 25=[-15.882375705122322449  ,-.6039968217617815283 ] 
dist 26=[-16.338038659400060624  ,-.9048227608430557423 ] 
dist 27=[-17.789331109045773027  ,-1.4902702872087245762 ] 
dist 28=[-18.572158654079041862  ,-1.5910789802738457165 ] 
dist 29=[-19.016255278937738050  ,-1.973729023639996993  ] 
dist 30=[-19.115107182235302746  ,-2.024769176807781448  ] 
dist 31=[-10.138007265262547894  ,-1.997769776684019671  ] 
dist 32=[-9.4049051531855300043 ,-1.5425138076761005346 ] 
dist 33=[-7.5834549258146498667 ,-.6489833630273620968 ] 
dist 34=[-7.2682210873263329657 ,.4742742424696943817 ] 
dist 35=[-4.521507024045444651  ,1.5475950339769216919 ] 
dist 36=[-4.011387966101771392  ,2.2425391064868432684 ] 
dist 37=[-3.251079273800465896  ,2.7887231115663708209 ] 
dist 38=[-3.041828316891302007  ,3.2695041267409590192 ] 
dist 39=[-2.051212289135396536  ,3.6677744528177334696 ] 
dist 40=[-2.0449239770950090494 ,3.9612411383900688512 ] 
dist 41=[-1.5290543587893503767 ,4.8776715934612650508 ] 
dist 42=[-1.4602032617027948775 ,5.6805283605679610077 ] 
dist 43=[-1.3209040420144713449 ,6.3426527038200197301 ] 
dist 44=[-1.2813766868539045855 ,6.6984245527634052603 ] 
dist 45=[-1.118908947944526315  ,6.8956925261271934980 ] 
dist 46=[-1.084193524566960194  ,6.9351268841000348297 ] 
dist 47=[-.988876149796567648  ,2.2228666558774723603 ] 
dist 48=[-.969588691325177533  ,2.0897281343231182764 ] 
dist 49=[-.769760047375035664  ,1.7498766069941291384 ] 
dist 50=[-.730285747864376591  ,1.6920055460639076972 ] 
dist 51=[-.637504107550557648  ,1.152862699934802670  ] 
dist 52=[-.8712768375944421568 ,1.051669390778674933  ] 
dist 53=[-1.1025889304794036205 ,.907073738836444269  ] 
dist 54=[-1.3079992170801911860 ,.793417375348381882  ] 
dist 55=[-1.4787958059481619243 ,.6290766854149412642 ] 
dist 56=[-1.5723079036921279996 ,.6214808922050260431 ] 
dist 57=[-1.6262952963853555953 ,.2892891412498432237 ] 
dist 58=[-1.6397263373304148913 ,.2531115262732081290 ] 
dist 59=[-1.1828365745259411249 ,.1654815503132910254 ] 
dist 60=[-1.2496762703765203292 ,.1528738508344460733 ] 
dist 61=[-1.2882722835459807486 ,.0305839096839866625 ] 
dist 62=[-1.2979627951479909954 ,.0092188174542840027 ] 
dist 63=[-.74289128380935427398,-.0184220861751203781 ] 
dist 64=[-.69690410179318258424,-.0230122830260731622 ] 
dist 65=[-.57926179999840125616,-.0436143044659308212 ] 
dist 66=[-.55765582701735580017,.0414640003042879390 ] 
dist 67=[-.36718229615541238857,.1234244069904324924 ] 
dist 68=[-.33058577035170687748,.1762999930935635752 ] 
dist 69=[-.27575708020428001017,.2174760640493959022 ] 
dist 70=[-.2696699992809238827 ,.2528713473608926359 ] 
dist 71=[-.2750675163124820733 ,.2814342302065821101 ] 
dist 72=[-.2762054374515166546 ,.2954149805606250374 ] 
dist 73=[-.1384403543904475390 ,.3712612645390112241 ] 
dist 74=[-.1271425544951290264 ,.4388214513296232845 ] 
dist 75=[-.0995494717976508723 ,.4950326026824861899 ] 
dist 76=[-.0946540038961304088 ,.5258337621981841584 ] 
dist 77=[-.05433014466051005452,.5436386872030519754 ] 
dist 78=[-.04689272974260594668,.5481110273522170723 ] 
dist 79=[-.03523828350011379225,.1520222730509176974 ] 
dist 80=[-.03223286774340919046,.14103748205136502783] 
dist 81=[-.00206297041354654198,.11230241309258779546] 
dist 82=[-.0359667079315826359 ,.10803990396628822166] 
dist 83=[-.06879967122882081612,.0863462822661048098 ] 
dist 84=[-.08981862500438698440,.0983592409803851500 ] 
dist 85=[-.10599012135163437597,.1082885762650497215 ] 
dist 86=[-.1195337428803128159 ,.1136674451507613223 ] 
dist 87=[-.13022546741308283601,.1167101127018386680 ] 
dist 88=[-.13504669996755961294,.1173315670247324241 ] 
dist 89=[-.13729090689974275291,.02869837094583479705] 
dist 90=[-.1377263068189132090 ,.02587125311902603031] 
dist 91=[-.0939340146146141379 ,.01879238398240350515] 
dist 92=[-.0991055869710560168 ,.01776970629240106044] 
dist 93=[-.1018024497749172575 ,.0071122746847667147 ] 
dist 94=[-.1022811145723851832 ,.0051889173539443929 ] 
dist 95=[-.06703292370876074818,.0028152416008960598 ] 
dist 96=[-.06381691369129258763,.0024032463571135428 ] 
dist 97=[-.05492495467115432254,.0024548559299756539 ] 
dist 98=[-.05351546047550627258,.0102203072682486092 ] 
dist 99=[-.03700928274632876655,.0176595032566082392 ] 
dist 100=[-.03373075934343189252,.0222939259701176804 ] 
dist 101=[-.0317139062902889537 ,.0257113536396422649 ] 
dist 102=[-.0323351919582529529 ,.0283070509174934772 ] 
dist 103=[-.0325217605672582082 ,.0303140920765082122 ] 
dist 104=[-.0324543346052534338 ,.0313893205873114269 ] 
dist 105=[-.0262964421510455784 ,.0319774554246259171 ] 
dist 106=[-.0253478130615149008 ,.0330439362916269193 ] 
dist 107=[-.0229267614344783358 ,.0370524881790153173 ] 
dist 108=[-.0222538827861489326 ,.0390645340751499218 ] 
dist 109=[-.0180159652001026778 ,.0401339442958593521 ] 
dist 110=[-.0171083622192860096 ,.0403908964283832989 ] 
dist 111=[-.0153647743972507058 ,.01656330275458909788] 
dist 112=[-.0148775865695795778 ,.01573554446351701966] 
dist 113=[-.0067818403932627966 ,.01394073764738838711] 
dist 114=[-.0056318502754220318 ,.01339893044479963814] 
dist 115=[-.0030918679323785524 ,.00748892346319066244] 
dist 116=[-.0024763753991915719 ,.00867275746870141873] 
dist 117=[.0003992344306136964 ,.00965367051687062388] 
dist 118=[-.00091312059523751705,.0101847860144076602 ] 
dist 119=[-.00334165982168722464,.0104834627971484935 ] 
dist 120=[-.00493171100201447124,.0105393350894074905 ] 
dist 121=[-.00619487936185803686,.00263719990565090403] 
dist 122=[-.00732265788460953267,.00240246877974668541] 
dist 123=[-.00826249653396028088,.0018043286951020242 ] 
dist 124=[-.00877776632719777847,.0017183894080584587 ] 
dist 125=[-.00907532863998724454,.0007833202868930139 ] 
dist 126=[-.00914877438130253529,.0006120611154389005 ] 
dist 127=[-.00557319913588698017,.0004073688027746673 ] 
dist 128=[-.00527018522687023090,.0003727663460135511 ] 
dist 129=[-.00447733709945903135,-.0009751019430903281 ] 
dist 130=[-.00432524354378833127,-.0011306714375962583 ] 
dist 131=[-.00297080918997945798,-.0014356456957285484 ] 
dist 132=[-.00270382021369411229,-.0015016784158327205 ] 
dist 133=[-.00230523254582531973,-.00088889586709673358] 
dist 134=[-.00218794410862666454,.00028953289650066823] 
dist 135=[-.0020739571495125026 ,.00144237396716215426] 
dist 136=[-.0020880718537050015 ,.00219790791243024775] 
dist 137=[-.00115897961661920509,.00279866256833224223] 
dist 138=[-.00108197107072070582,.00333564774810157067] 
dist 139=[-.00088748469006318623,.00378334864436024713] 
dist 140=[-.00085166366152815915,.00402883482164989727] 
dist 141=[-.00054387859305978727,.00417055318135517831] 
dist 142=[-.00048507864685248079,.00420534056070993181] 
dist 143=[-.00039540047465015789,.00118057895865538645] 
dist 144=[-.00037052367497801210,.00110459007306910234] 
dist 145=[8.43603221742672200000e-05,.00090000223184101758] 
dist 146=[.00014303499713765371,.00087049674733171548] 
dist 147=[.00025891268479041639,.0006455848577838493 ] 
dist 148=[.00028562285428842173,.0007537761398119922 ] 
dist 149=[.00012642715474068285,.0008437715314220287 ] 
dist 150=[-.00010044796427670508,.0008930760050226918 ] 
dist 151=[-.00031998149804622255,.0009215726201561387 ] 
dist 152=[-.00046189082257763914,.0009287267807289620 ] 
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dist 156=[-.00078184866665299011,.00016693470632103567] 
dist 157=[-.00080117944525709392,8.52156155809407000000e-05] 
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dist 162=[-.00047416363229305331,-8.89961379867055000000e-05] 
dist 163=[-.00034289607495497557,-.0001174118191429992 ] 
dist 164=[-.00031616621450902624,-6.34836454831896570000e-05] 
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dist 172=[-9.31518714140621500000e-05,.00037442447791839014] 
dist 173=[-6.33104093549391100000e-05,.00038060704252664291] 
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dist 176=[-4.86559902869422380000e-05,.00010357481814138158] 
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dist 178=[1.36476480314959700000e-05,8.15588499648546000000e-05] 
dist 179=[2.64079318948200300000e-05,5.37055646760808000000e-05] 
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dist 181=[1.53904139358579000000e-05,6.91232071721038000000e-05] 
dist 182=[-5.62292204959050000000e-06,7.25908694222000000000e-05] 
dist 183=[-2.60096159424311000000e-05,7.44134004573284000000e-05] 
dist 184=[-3.93696745700537000000e-05,7.47640688609994000000e-05] 
dist 185=[-4.99862749239954000000e-05,2.54243939515938400000e-05] 
dist 186=[-5.94580874894459000000e-05,2.35890458152147100000e-05] 
dist 187=[-6.73370017820620000000e-05,1.88708001557794100000e-05] 
dist 188=[-7.16160612910690000000e-05,1.80935567484645100000e-05] 
dist 189=[-7.40294388686314000000e-05,1.04617267677018000000e-05] 
dist 190=[-7.44853115239448000000e-05,9.01884708647440000000e-06] 
dist 191=[-4.76926691711364200000e-05,7.07826308471130000000e-06] 
dist 192=[-4.53449714983283500000e-05,6.47989437580330000000e-06] 
dist 193=[-3.90405054266276410000e-05,-5.01105372337190000000e-06] 
dist 194=[-3.78551728144992070000e-05,-6.43381695160140000000e-06] 
dist 195=[-2.65470741097964300000e-05,-9.23973078866600000000e-06] 
dist 196=[-2.42854064395379200000e-05,-9.86933789600540000000e-06] 
dist 197=[-2.11115190137319300000e-05,-7.91799732691764000000e-06] 
dist 198=[-2.00955314408119300000e-05,1.88661139629850000000e-06] 
dist 199=[-1.90521952030770000000e-05,1.14876392721623000000e-05] 
dist 200=[-1.91195837030650000000e-05,1.77776622199172000000e-05] 
dist 201=[-1.54481773744703600000e-05,2.27728061389907000000e-05] 
dist 202=[-1.49655800614510600000e-05,2.72224015072471000000e-05] 
dist 203=[-1.36571427358148200000e-05,3.09177099140505000000e-05] 
dist 204=[-1.33116480514632500000e-05,3.29119937056836000000e-05] 
dist 205=[-1.07721601281227000000e-05,3.40193915507719000000e-05] 
dist 206=[-1.02198354796723000000e-05,3.42425673948517000000e-05] 
dist 207=[-9.25717077071200000000e-06,1.30076652617016800000e-05] 
dist 208=[-8.99470476895630000000e-06,1.24956040708263000000e-05] 
dist 209=[-3.54305263653450000000e-06,1.12875174707937800000e-05] 
dist 210=[-2.80509715938070000000e-06,1.08864193231494400000e-05] 
dist 211=[-1.11390893267420000000e-06,8.99926379423680000000e-06] 
dist 212=[-7.76369340515300000000e-07,8.59569340517540000000e-06] 
dist 213=[1.29958319373370000000e-06,7.59759372630980000000e-06] 
dist 214=[-5.78905376630700000000e-07,7.92756301711173000000e-06] 
dist 215=[-2.60113150102170000000e-06,8.18965922844299000000e-06] 
dist 216=[-3.90199103129690000000e-06,8.25002727868919000000e-06] 
dist 217=[-4.90831336173480000000e-06,4.29551147312615400000e-06] 
dist 218=[-5.75874164005580000000e-06,4.10894454450472800000e-06] 
dist 219=[-6.44834350566850000000e-06,3.69890540045107000000e-06] 
dist 220=[-6.81485375431740000000e-06,3.56967625362845000000e-06] 
dist 221=[-7.01081572855690000000e-06,2.98759080464903000000e-06] 
dist 222=[-7.04618551793950000000e-06,2.86564180444185000000e-06] 
dist 223=[-5.85980939915306000000e-06,2.51719097949051000000e-06] 
dist 224=[-5.70104977787166000000e-06,2.46085263128575000000e-06] 
dist 225=[-5.23351296431577000000e-06,1.76780231532398000000e-06] 
dist 226=[-5.12547776638796000000e-06,1.62952524516809000000e-06] 
dist 227=[-4.11757422222743000000e-06,1.43828593869459000000e-06] 
dist 228=[-3.89810065496697100000e-06,1.37484866830701000000e-06] 
dist 229=[-3.58302489044626300000e-06,1.31224725608287000000e-06] 
dist 230=[-3.27750032373599900000e-06,1.33699170617070000000e-06] 
dist 231=[-1.75262992868283000000e-06,1.41562954166350000000e-06] 
dist 232=[-1.76144341069332000000e-06,1.58699465345400000000e-06] 
dist 233=[-1.52761412361856000000e-06,1.76847148177090000000e-06] 
dist 234=[-1.48950493264987000000e-06,1.88736365081370000000e-06] 
dist 235=[-1.38860681410677000000e-06,1.98173843079290000000e-06] 
dist 236=[-1.35267032674897000000e-06,2.10533157329980000000e-06] 
dist 237=[-1.15282709547503000000e-06,2.18064378190250000000e-06] 
dist 238=[-1.10661877131176000000e-06,2.19809578548020000000e-06] 
dist 239=[-1.01201816165868000000e-06,1.46941020277919000000e-06] 
dist 240=[-9.82839706660340000000e-07,1.40473517963509000000e-06] 
dist 241=[-5.28567728614240000000e-07,1.24483390710356000000e-06] 
dist 242=[-4.62078974393100000000e-07,1.19922245691232000000e-06] 
dist 243=[-3.11487625590780000000e-07,9.39438197625080000000e-07] 
dist 244=[-2.75330042809060000000e-07,8.85252000800650000000e-07] 
dist 245=[-8.98969491029200000000e-08,7.72588685312490000000e-07] 
dist 246=[-5.67397423148600000000e-08,7.57000641486160000000e-07] 
dist 247=[2.02976358833400000000e-08,7.67483848684890000000e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 1, 0, 0, 2] 
dist 0=[89.256184533536817095  ,89.256184533536817095  ] 
dist 1=[88.633005067628059273  ,89.504391972613313025  ] 
dist 2=[87.338101233255299272  ,89.416530910431016076  ] 
dist 3=[85.690980144608576023  ,88.832206316272106582  ] 
dist 4=[83.662503503501863626  ,88.569414658831207926  ] 
dist 5=[80.970166005218310804  ,87.231396864242016708  ] 
dist 6=[76.673484118340115000  ,87.036781868871749183  ] 
dist 7=[71.680651443159914424  ,82.603810184176225388  ] 
dist 8=[64.613405214989414941  ,81.873092521690021995  ] 
dist 9=[56.027430225664614010  ,80.994285365260442875  ] 
dist 10=[48.795401044685538141  ,80.665937533256577564  ] 
dist 11=[38.163967440545156209  ,79.316428757811978534  ] 
dist 12=[30.980329851830377700  ,79.020315627940070341  ] 
dist 13=[24.951139432260248291  ,75.786153065133472388  ] 
dist 14=[18.925866868956037615  ,69.771410945850031158  ] 
dist 15=[13.366741480508345154  ,30.704504625269675320  ] 
dist 16=[9.1969885405647990958 ,29.980631464763213857  ] 
dist 17=[5.245534078412930375  ,17.170265960333649583  ] 
dist 18=[.556076972559303675  ,15.545803275156405322  ] 
dist 19=[-3.8428589358132684839 ,11.861966738076883680  ] 
dist 20=[-6.6350515038157750774 ,11.251498807472002355  ] 
dist 21=[-9.7411799466280554555 ,6.7973291856772181898 ] 
dist 22=[-14.515609236942453879  ,6.0427521112312980519 ] 
dist 23=[-18.905285311239085959  ,4.7781928425739963206 ] 
dist 24=[-21.521893915099610056  ,4.5101817629494799336 ] 
dist 25=[-23.340912570154875915  ,.8458163692646814813 ] 
dist 26=[-24.549139090930707078  ,.3887545572456356418 ] 
dist 27=[-25.374808797830214949  ,-.5895024584087179246 ] 
dist 28=[-25.667004526319263061  ,-.7414503810545006269 ] 
dist 29=[-25.661876710069192197  ,-1.732148560659851097  ] 
dist 30=[-25.301266443562908234  ,0                     ] 
dist 31=[-4.2378319118105352999 ,-2.152743061764415805  ] 
dist 32=[-3.8596358250288940311 ,-2.200192016400288054  ] 
dist 33=[-3.329104242497938274  ,-1.3652618184440803511 ] 
dist 34=[-3.166810489250902350  ,.0789811623230910379 ] 
dist 35=[-3.133398767723083030  ,1.4804148527374140344 ] 
dist 36=[-3.173985024786453863  ,2.3894511903592962458 ] 
dist 37=[-3.191697121247928253  ,3.1039072071829111773 ] 
dist 38=[-3.191145649872281456  ,3.7307219974300246844 ] 
dist 39=[-3.155934098718917608  ,4.2468964550664238785 ] 
dist 40=[-3.146735711849700292  ,4.5208262362743595597 ] 
dist 41=[-1.8365277561806263490 ,4.6684980699226757706 ] 
dist 42=[-1.7066252484139741001 ,4.6998898079527312185 ] 
dist 43=[-1.4033584405466147803 ,1.9125902247854934036 ] 
dist 44=[-1.3393059734832591717 ,1.8526014879613937942 ] 
dist 45=[-.9205651315774780501 ,1.7014910630723839190 ] 
dist 46=[-.8404385718784647433 ,1.6552947423429805949 ] 
dist 47=[-.693169439434001839  ,1.403198215511104299  ] 
dist 48=[-.657072202002434110  ,1.350256417079665590  ] 
dist 49=[-.086489856640541220  ,1.235380790905594509  ] 
dist 50=[-.0134182875118511879 ,1.200785990070029699  ] 
dist 51=[-.2564950842334281726 ,.812654002325105184  ] 
dist 52=[-.4152325169685431298 ,.8303241832581354964 ] 
dist 53=[-.5410132504981037061 ,.86949078004343864356] 
dist 54=[-.6529272467931743989 ,.8898797519839570524 ] 
dist 55=[-.7460628048456832957 ,.9008393066522951488 ] 
dist 56=[-.7970986127345212093 ,.9023898317050716835 ] 
dist 57=[-.8265939639172886689 ,.37611079643236789919] 
dist 58=[-.8339803707071881313 ,.33323294659530674281] 
dist 59=[-.51356136309914788826,.2281294914027774773 ] 
dist 60=[-.48662829995856233872,.2130349254269399914 ] 
dist 61=[-.41543499254167177747,.0621378776413588004 ] 
dist 62=[-.40195885890518251714,.0354435225712216866 ] 
dist 63=[-.2789018094701081775 ,.0016890948396050196 ] 
dist 64=[-.2546757052769552122 ,-.0038835583096071791 ] 
dist 65=[-.2190744459311763042 ,-.09522918475956115135] 
dist 66=[-.2313976571343547901 ,.01002199928744923605] 
dist 67=[-.2639586897087482562 ,.1129371701878162010 ] 
dist 68=[-.2924882656259944387 ,.1803468746584317551 ] 
dist 69=[-.3160722695198277567 ,.2339168365771058217 ] 
dist 70=[-.3289218269230793874 ,.2817650671076630138 ] 
dist 71=[-.3363070710494565102 ,.3216494650068150118 ] 
dist 72=[-.3381111040416389547 ,.3435294869240366420 ] 
dist 73=[-.17402299349390113474,.3561816090599219834 ] 
dist 74=[-.16058767569902933038,.3593431160130232120 ] 
dist 75=[-.12744911916241412098,.10399179758361812598] 
dist 76=[-.12156176048418917459,.09766771007348841087] 
dist 77=[-.07199796451520157071,.08051959274855727619] 
dist 78=[-.06277112452110697137,.07800664177013113485] 
dist 79=[-.0485738150125285607 ,.0477972816569451567 ] 
dist 80=[-.0447930771687580286 ,.0420067411974381620 ] 
dist 81=[.01713761406587399623,.0631309744878368123 ] 
dist 82=[-.00212156617333394898,.0853474610319782189 ] 
dist 83=[-.02079379315216481882,.1028421661066126677 ] 
dist 84=[-.03295994242367773612,.1182831006688955639 ] 
dist 85=[-.04255318930051307476,.1310871956545434356 ] 
dist 86=[-.05098875499298592110,.1380788150634517550 ] 
dist 87=[-.05792189363871348075,.1421023785945991583 ] 
dist 88=[-.06153712028143619490,.1430835999284261596 ] 
dist 89=[-.06345823124000757362,.03792121864079934633] 
dist 90=[-.06380012834457052173,.03457223480497847187] 
dist 91=[-.04405890017863575222,.02612477116958461551] 
dist 92=[-.04220261444277233411,.02485481209433707212] 
dist 93=[-.03688095862554706717,.0118609106409604397 ] 
dist 94=[-.03603713408874662677,.0094799599709784651 ] 
dist 95=[-.02557188279542895670,.0064643401024666018 ] 
dist 96=[-.02345775327088243639,.0058049402435636550 ] 
dist 97=[-.02110114340917390215,-.00665645210625809113] 
dist 98=[-.02046234239463667984,.00101549783878485851] 
dist 99=[-.02237499882033887984,.00850295471792757410] 
dist 100=[-.02527744046501497020,.01336914937866265834] 
dist 101=[-.02763556114046248905,.01719076643751416457] 
dist 102=[-.02882920700851446770,.02052266372696260948] 
dist 103=[-.02942653415213412278,.02323930550684441865] 
dist 104=[-.02950626105421265207,.02461320735394869418] 
dist 105=[-.0193601148444852858 ,.02534841229428997604] 
dist 106=[-.0183935767576318128 ,.02552354024558682943] 
dist 107=[-.0158551674571053423 ,.01424220481461814737] 
dist 108=[-.0153744767732723641 ,.01392379103352615454] 
dist 109=[-.0109666867406395325 ,.0132543087937455490 ] 
dist 110=[-.0100859605528707083 ,.0130151882671709588 ] 
dist 111=[-.0088325346670203814 ,.0118493751490696335 ] 
dist 112=[-.0084379095514472603 ,.0115679202991990837 ] 
dist 113=[-.0004955255745678758 ,.0107287530468158541 ] 
dist 114=[-.00014816978029430090,.0105358595581915380 ] 
dist 115=[-.00175188424229124551,.0087000047591432399 ] 
dist 116=[-.00280478121044016086,.00951056848252661952] 
dist 117=[-.00364342027873209823,.01048495491938406505] 
dist 118=[-.00439477526340003611,.01098288071375563687] 
dist 119=[-.00502191160554254726,.01124114226705812733] 
dist 120=[-.00536636066121858601,.01127890348450720741] 
dist 121=[-.00556577943468299309,.00372968434431150539] 
dist 122=[-.00561590205399170240,.00342097237773027936] 
dist 123=[-.00357065828851208701,.00262508117857551701] 
dist 124=[-.00339530970736287266,.00251071035093419715] 
dist 125=[-.00292722855238489711,.00123543125665627988] 
dist 126=[-.00283514156403501216,.00099951192285872305] 
dist 127=[-.00200268127502657799,.00072226853937027527] 
dist 128=[-.00183599543024052676,.00067501974228147290] 
dist 129=[-.00158895214624876431,-.00067933642246119286] 
dist 130=[-.00169150764014855064,8.32191685711026600000e-05] 
dist 131=[-.00203693085551945647,.00083105100790803566] 
dist 132=[-.00234396086521040139,.00132233502748732023] 
dist 133=[-.00259937614286772704,.00171388088113777156] 
dist 134=[-.00273931832016386879,.00206495405708016107] 
dist 135=[-.00282020837317497851,.00235808427280647914] 
dist 136=[-.00284052626554962710,.00251912366808992678] 
dist 137=[-.00162066740177277189,.00261237275499737052] 
dist 138=[-.00151893980005830914,.00263581188446942064] 
dist 139=[-.00125964679803088697,.00074753215399033033] 
dist 140=[-.00121125471751815971,.00070345933205516735] 
dist 141=[-.00079204789410293972,.00058325022604139162] 
dist 142=[-.00071119167464244562,.00056525715822294728] 
dist 143=[-.00058844191738059287,.00035008310062172451] 
dist 144=[-.00055383673986300201,.00030844576059001156] 
dist 145=[8.90918515314913400000e-05,.00049078230294671454] 
dist 146=[-1.69315262766458400000e-05,.00070810245664256907] 
dist 147=[-.00015634391316019814,.00088039231447850784] 
dist 148=[-.00024736247076654333,.00103382578862748713] 
dist 149=[-.00031926437740172456,.00116156929147573196] 
dist 150=[-.00038263191453904318,.00123160185237228562] 
dist 151=[-.00043474800825241867,.00127209828632100068] 
dist 152=[-.00046189082257765002,.00128227177271025786] 
dist 153=[-.00047636930297285908,.00034282107515346350] 
dist 154=[-.00047888082375443863,.00031665214422692962] 
dist 155=[-.00033679822463119611,.00024866588113455935] 
dist 156=[-.00032316494870149616,.00023855266847424792] 
dist 157=[-.00028373130998933428,.00012748366410116079] 
dist 158=[-.00027735724567582367,.00010669140308562594] 
dist 159=[-.00019841413840502536,8.16854779614630400000e-05] 
dist 160=[-.00018233547942826657,7.64760140906331300000e-05] 
dist 161=[-.00016433767418632055,-5.18457830702987800000e-05] 
dist 162=[-.00015916438928222587,8.07191922511734000000e-06] 
dist 163=[-.00018199105816402824,6.66576814442256200000e-05] 
dist 164=[-.00021021715996688642,.00010481889926114486] 
dist 165=[-.00023332836745154103,.00013486299089135670] 
dist 166=[-.00024526313138117218,.00016116077725161010] 
dist 167=[-.00025143239817796792,.00018265707231698356] 
dist 168=[-.00025245296332801427,.00019360157912753334] 
dist 169=[-.00016407655193128229,.00019945838646325902] 
dist 170=[-.00015598323734161644,.00020071392447265385] 
dist 171=[-.00013378696072066722,6.89473943599058090000e-05] 
dist 172=[-.00013025473258407724,6.48758410581766400000e-05] 
dist 173=[-8.95043154930100410000e-05,5.36851756804161200000e-05] 
dist 174=[-8.14239739528236350000e-05,5.20753586192310400000e-05] 
dist 175=[-7.20211055245114500000e-05,3.18302745103582900000e-05] 
dist 176=[-6.94194407706820257000e-05,2.79133415836671400000e-05] 
dist 177=[8.35620558328416200000e-06,4.11187654840931800000e-05] 
dist 178=[-1.12116442808116000000e-06,5.89688878687502400000e-05] 
dist 179=[-1.38419887212924500000e-05,7.29006062708853000000e-05] 
dist 180=[-2.22041213167663100000e-05,8.49196315058445000000e-05] 
dist 181=[-2.88723477334887600000e-05,9.46671868511381200000e-05] 
dist 182=[-3.48551980878242900000e-05,9.95586107193747800000e-05] 
dist 183=[-3.98513666611542900000e-05,.00010213963638682291] 
dist 184=[-4.25946794587865900000e-05,.00010269187643683585] 
dist 185=[-4.41804526491915600000e-05,3.35307689616793040000e-05] 
dist 186=[-4.45719224176309600000e-05,3.10554164580685500000e-05] 
dist 187=[-2.87492256362913150000e-05,2.45402694543652200000e-05] 
dist 188=[-2.73787904688988333000e-05,2.36035257300350900000e-05] 
dist 189=[-2.37024530254117750000e-05,1.27148202604047100000e-05] 
dist 190=[-2.29687763845237490000e-05,1.06667794526686300000e-05] 
dist 191=[-1.63476958129835460000e-05,8.32674388814971000000e-06] 
dist 192=[-1.50129775408839500000e-05,7.92169659102819000000e-06] 
dist 193=[-1.30320627368353060000e-05,-5.51019050343852300000e-06] 
dist 194=[-1.37758310154442900000e-05,6.99096463365517000000e-07] 
dist 195=[-1.69583615336024400000e-05,6.79443145740956700000e-06] 
dist 196=[-1.97981547764557100000e-05,1.08022925823944110000e-05] 
dist 197=[-2.21641024934943100000e-05,1.39990632845434900000e-05] 
dist 198=[-2.34608701976964100000e-05,1.68681372290418200000e-05] 
dist 199=[-2.42094318177907400000e-05,1.92643077627841700000e-05] 
dist 200=[-2.43936339727020400000e-05,2.05799688669888800000e-05] 
dist 201=[-1.45381967354517850000e-05,2.13403030827703600000e-05] 
dist 202=[-1.37053546922896667000e-05,2.15274458194670800000e-05] 
dist 203=[-1.15488894340152250000e-05,6.14611916458429300000e-06] 
dist 204=[-1.11370464166377510000e-05,5.79818645234947700000e-06] 
dist 205=[-7.52394361099815400000e-06,4.83456480412933300000e-06] 
dist 206=[-6.81598947811707000000e-06,4.69580929019266900000e-06] 
dist 207=[-5.74896484001209400000e-06,2.92697613802915400000e-06] 
dist 208=[-5.44033519535093300000e-06,2.58266090196628400000e-06] 
dist 209=[4.36574334966006000000e-07,4.11992464477493300000e-06] 
dist 210=[-2.73689743600648000000e-07,6.10305697066278900000e-06] 
dist 211=[-1.43827948984273600000e-06,7.67876297888721000000e-06] 
dist 212=[-2.19317013385695800000e-06,9.08587869932128000000e-06] 
dist 213=[-2.78317780588007800000e-06,1.02585353800901300000e-05] 
dist 214=[-3.29192056453884600000e-06,1.09012324811613200000e-05] 
dist 215=[-3.70450424350251400000e-06,1.12720181604217400000e-05] 
dist 216=[-3.91203016475816100000e-06,1.13626052957728200000e-05] 
dist 217=[-4.02028476083418400000e-06,3.15312800288539400000e-06] 
dist 218=[-4.03796719788282700000e-06,2.93904153539082600000e-06] 
dist 219=[-3.01490331160738600000e-06,2.37165735876808000000e-06] 
dist 220=[-2.90341645775163600000e-06,2.28692856453215000000e-06] 
dist 221=[-2.57796414956617500000e-06,1.32127084642492000000e-06] 
dist 222=[-2.52150931268603200000e-06,1.13742103076167000000e-06] 
dist 223=[-1.85491585675622800000e-06,9.22160260312690000000e-07] 
dist 224=[-1.71705884351765000000e-06,8.76248890680790000000e-07] 
dist 225=[-1.55552975188947500000e-06,-5.17260770099217000000e-08] 
dist 226=[-1.50003987795730400000e-06,4.45998951709230000000e-07] 
dist 227=[-1.64202358621922200000e-06,9.30973561005061700000e-07] 
dist 228=[-1.89364271879355400000e-06,1.24366544816241700000e-06] 
dist 229=[-2.09601500222028600000e-06,1.48616780084196900000e-06] 
dist 230=[-2.19398131455673900000e-06,1.69196470781637200000e-06] 
dist 231=[-2.24377292823801600000e-06,1.85540270727083700000e-06] 
dist 232=[-2.25443245751647300000e-06,1.92942210246795400000e-06] 
dist 233=[-1.59121593119611400000e-06,1.96425727415782100000e-06] 
dist 234=[-1.52295672697616400000e-06,1.97180921164499400000e-06] 
dist 235=[-1.33195202606662500000e-06,1.00653557648294000000e-06] 
dist 236=[-1.29948920774656800000e-06,9.86080264309340000000e-07] 
dist 237=[-9.33707402993072000000e-07,9.48987843900960000000e-07] 
dist 238=[-8.59594458816950000000e-07,9.35698953583280000000e-07] 
dist 239=[-7.70602399797525000000e-07,8.73424974632890000000e-07] 
dist 240=[-7.41077846922196000000e-07,8.54968421444240000000e-07] 
dist 241=[-3.10866227745900000000e-08,8.07627824958910000000e-07] 
dist 242=[5.35279624194300000000e-08,7.89160134020720000000e-07] 
dist 243=[1.87416681762991000000e-07,8.43799517886431000000e-07] 
dist 244=[2.05390348124737400000e-07,9.45073713950328000000e-07] 
dist 245=[2.03740133152409900000e-07,1.02475549402421700000e-06] 
dist 246=[1.71851129004929240000e-07,1.06061069499236000000e-06] 
dist 247=[1.12179700670063890000e-07,1.07685685783467400000e-06] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 2, 0, 0, 1] 
dist 0=[84.323885181931405094  ,84.323885181931405094  ] 
dist 1=[84.080949963230042746  ,84.313353220034646545  ] 
dist 2=[83.226771265522619134  ,84.323885181931405094  ] 
dist 3=[81.690656037191412097  ,83.918438242264164830  ] 
dist 4=[78.727350403607107306  ,83.643426068102146952  ] 
dist 5=[75.078691696945952508  ,83.189637644992805200  ] 
dist 6=[70.807375744115497688  ,82.902284815289510847  ] 
dist 7=[65.265966399770449575  ,82.598070860749074435  ] 
dist 8=[56.548648814177147422  ,82.301256502074786049  ] 
dist 9=[47.706885492927990552  ,81.952508454531292833  ] 
dist 10=[41.668492785956277134  ,81.678251542847030851  ] 
dist 11=[36.530848502677297273  ,80.957639640657823374  ] 
dist 12=[31.282734667279486116  ,80.717618847816677884  ] 
dist 13=[26.366456796502518552  ,78.087102423949951400  ] 
dist 14=[22.552203291817792663  ,72.898826003567089024  ] 
dist 15=[16.753271587150383030  ,34.304811529419854531  ] 
dist 16=[12.134923360731348811  ,30.647410683771144866  ] 
dist 17=[7.5059999777011723612 ,22.157461590072152375  ] 
dist 18=[1.6541806324327322873 ,20.815407083372370454  ] 
dist 19=[-3.9554151215108212434 ,9.8923317818995913496 ] 
dist 20=[-7.6175395813857596665 ,8.0018013357185781984 ] 
dist 21=[-10.552875261050328344  ,5.1635579837256822912 ] 
dist 22=[-13.261924222995946672  ,4.4583927932459057019 ] 
dist 23=[-15.616472943809932174  ,.2460396708235169834 ] 
dist 24=[-17.137035158840297671  ,.1281788074722927521 ] 
dist 25=[-18.336990908202831118  ,-2.2152544859587428595 ] 
dist 26=[-19.412028162437574568  ,-2.4012742103225669412 ] 
dist 27=[-20.302138461085410710  ,-2.6806797196689498786 ] 
dist 28=[-20.764346916763953537  ,-2.6891782938447905990 ] 
dist 29=[-21.002162835523015129  ,-2.6195809943703446738 ] 
dist 30=[-20.997566506567929852  ,-2.4631343508240626701 ] 
dist 31=[-6.9921829795752223031 ,-1.9926548182155639664 ] 
dist 32=[-6.3335239103000891687 ,-1.4851834642872006491 ] 
dist 33=[-4.6975632023707441014 ,-.9547544996432689996 ] 
dist 34=[-4.4608327170446502184 ,-.2621067080414005191 ] 
dist 35=[-2.0506185565981596298 ,.4045713652975293761 ] 
dist 36=[-1.6198327449853281318 ,.8318876500836186728 ] 
dist 37=[-1.0783991835422906205 ,1.1621584123910174302 ] 
dist 38=[-.9840530140195856210 ,1.4424949034976236396 ] 
dist 39=[-.4860760762203594486 ,2.1781186052861705910 ] 
dist 40=[-.4662867247796367663 ,2.8814739514531713981 ] 
dist 41=[.1525032317742984481 ,3.4306518208034958242 ] 
dist 42=[.2073406690006223884 ,3.9090477983931639217 ] 
dist 43=[.3179456867850997617 ,4.3025819498837363505 ] 
dist 44=[.3338638874958320236 ,4.5135434703139151331 ] 
dist 45=[.4131265793153223177 ,4.6302391746602737036 ] 
dist 46=[.4227027858294662676 ,4.6480456523597776277 ] 
dist 47=[.3522063178222254106 ,2.6144713566980018404 ] 
dist 48=[.2219045465634998635 ,2.4438432969071283630 ] 
dist 49=[.08205371648111048215,2.0071050363099000483 ] 
dist 50=[-.1048739919099512229 ,1.9331838045896936712 ] 
dist 51=[-.28520208863167915775,1.2310039059879599160 ] 
dist 52=[-.3988495515564551176 ,1.0977143100874828236 ] 
dist 53=[-.48412025275171211478,.9136310428057299291 ] 
dist 54=[-.55157876178726698735,.8570008834117793059 ] 
dist 55=[-.70151504212389025459,.2689719866769993714 ] 
dist 56=[-1.0073238250891580347 ,.2663267819537258390 ] 
dist 57=[-1.2476786508364452516 ,.07007373949137480621] 
dist 58=[-1.4588027695002637184 ,.05434403048879339001] 
dist 59=[-1.6330195020070021670 ,.0199115528604816353 ] 
dist 60=[-1.7264023820344878829 ,.0148068724246244791 ] 
dist 61=[-1.7777949155084625711 ,-.0213363251002438859 ] 
dist 62=[-1.7883719087298304419 ,-.0268398947634004487 ] 
dist 63=[-.5200603453407711641 ,-.0360417095336015000 ] 
dist 64=[-.4795703711808682428 ,-.0376550725687781508 ] 
dist 65=[-.3746531726343168030 ,-.0505527552053393032 ] 
dist 66=[-.3595465947122820323 ,-.0520365733867974788 ] 
dist 67=[-.1902442353633592245 ,-.0544463534101134055 ] 
dist 68=[-.1588815984884375206 ,-.0548683490164831367 ] 
dist 69=[-.1219883488183970904 ,-.0398893130176827583 ] 
dist 70=[-.1156307954470450388 ,.0531393901560437685 ] 
dist 71=[-.0897271404406540699 ,.1425779648620511402 ] 
dist 72=[-.0894512112296680041 ,.2008352580004429081 ] 
dist 73=[-.0222388225185170443 ,.2468832545018287068 ] 
dist 74=[-.0177122093650469335 ,.2877152211037345252 ] 
dist 75=[-.0077596749835152038 ,.3216327970332522089 ] 
dist 76=[-.0059373035651138067 ,.3401518240049653706 ] 
dist 77=[.0048727470750069244 ,.3507778091345778299 ] 
dist 78=[.0066092648624217737 ,.3532677886988870793 ] 
dist 79=[.0101301121084694597 ,.20733907620578957692] 
dist 80=[.0107615430146598121 ,.19511562154992344408] 
dist 81=[.0146480922789963418 ,.1635713190117077167 ] 
dist 82=[.0152245620430326115 ,.1577452310871192828 ] 
dist 83=[.0151420442834161502 ,.1056341922248182483 ] 
dist 84=[.0141870673909677724 ,.0955331102265708438 ] 
dist 85=[.0127875464702694714 ,.0805952721042290458 ] 
dist 86=[-.0140956459355901719 ,.0762343267444266569 ] 
dist 87=[-.0551744394209519286 ,.0369350871206688078 ] 
dist 88=[-.0819853388486816230 ,.0368055507699089780 ] 
dist 89=[-.1032096319662771677 ,.03257235935676354652] 
dist 90=[-.1220533708827928245 ,.03174715777777399458] 
dist 91=[-.1376984475496222630 ,.0302304469814781590 ] 
dist 92=[-.1461911564097014822 ,.0297547023571548108 ] 
dist 93=[-.1509886544263667447 ,.0276866465855626881 ] 
dist 94=[-.1519249602219957024 ,.0271226254368032843 ] 
dist 95=[-.0472296314387643235 ,.0256181797509569829 ] 
dist 96=[-.0445544381126255930 ,.0250471774566129394 ] 
dist 97=[-.0375095014257934406 ,.0217878777649342781 ] 
dist 98=[-.0363245091116986172 ,.0210127683014652360 ] 
dist 99=[-.0243773536240127678 ,.0192873225359979989 ] 
dist 100=[-.0220774440213140809 ,.0186938774239479025 ] 
dist 101=[-.0190142889095767024 ,.0158147278457598704 ] 
dist 102=[-.0161452660118947819 ,.0151660545399691949 ] 
dist 103=[-.0137264193465653439 ,.0133425688881797483 ] 
dist 104=[-.0135286558230384311 ,.0165978872310966487 ] 
dist 105=[-.01099007869139538782,.0205857026024672474 ] 
dist 106=[-.01051152110718526021,.0240338490852168491 ] 
dist 107=[-.0096884415692784354 ,.0268290684108530039 ] 
dist 108=[-.0094591312112860075 ,.0282180053907096521 ] 
dist 109=[-.0087293672618872705 ,.0289433542833001303 ] 
dist 110=[-.0084853503548094942 ,.0290977574464738391 ] 
dist 111=[-.0082815404597517778 ,.02112786105101249655] 
dist 112=[-.0081539935078686315 ,.02033302297326620287] 
dist 113=[-.0080764471726400867 ,.0180043399566175673 ] 
dist 114=[-.0080909915021398605 ,.0176643583828979487 ] 
dist 115=[-.0081726183365298295 ,.0129452103871817661 ] 
dist 116=[-.0083627545241482049 ,.0119867608989661031 ] 
dist 117=[-.0086030821746741435 ,.0110256837245587813 ] 
dist 118=[-.0088848651459379860 ,.0094901536355558885 ] 
dist 119=[-.0092470943546528501 ,.00276507388577439136] 
dist 120=[-.0098080400674686274 ,.00276700233008284897] 
dist 121=[-.0103522958910249732 ,.00142972366776600145] 
dist 122=[-.0106483048307843461 ,.00131653450479371772] 
dist 123=[-.0108164798139289353 ,.00103534939937729269] 
dist 124=[-.0108521124460714646 ,.00099214555983904245] 
dist 125=[-.0108005348110927295 ,.00057000488144660896] 
dist 126=[-.0106217442053275843 ,.00049246730207311281] 
dist 127=[-.00414891805682284477,.00039225229175249423] 
dist 128=[-.00385010074311121167,.00036762053021630118] 
dist 129=[-.00306122953953871149,-.00022956266853729113] 
dist 130=[-.00294781886122480002,-.00030047144613747191] 
dist 131=[-.0016233739225756088 ,-.00045606205774056488] 
dist 132=[-.0013740065143855500 ,-.00048121039821677162] 
dist 133=[-.0010895258583259182 ,-.0004040879695495573 ] 
dist 134=[-.0010403288389338556 ,.0003697947723002074 ] 
dist 135=[-.00101843651913433091,.0011175143420784181 ] 
dist 136=[-.00102111136791766666,.0016067907188406965 ] 
dist 137=[-.00028925944368220789,.0019952931147202659 ] 
dist 138=[-.00025454858228795004,.0023419728665847555 ] 
dist 139=[-.00016956522761731907,.0026308516936448788 ] 
dist 140=[-.00015736048741179055,.0027893212337524439 ] 
dist 141=[-3.61381956959309700000e-05,.0028809935486021531 ] 
dist 142=[-1.48146436585348000000e-05,.0029040270715356563 ] 
dist 143=[1.24459146937774300000e-05,.00174046533089885021] 
dist 144=[1.69167423747095100000e-05,.00164233645378432674] 
dist 145=[.00016042909374324800,.00138740239260650272] 
dist 146=[.00017695236445115138,.00133874296146203726] 
dist 147=[.00020696744476042434,.00090932650798953832] 
dist 148=[.00021266303593037824,.00082510358138056636] 
dist 149=[.00022082112667748941,.00069860841294121167] 
dist 150=[-.00010947806986303735,.00066183696068963967] 
dist 151=[-.00047017518204588655,.00027507610001656971] 
dist 152=[-.0007064343563077464 ,.00027646642957804986] 
dist 153=[-.0008942095136186252 ,.00013654373917974877] 
dist 154=[-.0010619774677904025 ,.00012516592525497080] 
dist 155=[-.0012018470173015512 ,9.73496619364670570000e-05] 
dist 156=[-.0012786044508323086 ,9.24644010629216230000e-05] 
dist 157=[-.0013230187102509517 ,5.18430592830061500000e-05] 
dist 158=[-.0013341792999712026 ,4.43751858074542800000e-05] 
dist 159=[-.00036646795619555814,3.27585985721377000000e-05] 
dist 160=[-.00034145733207769793,2.97503012586736400000e-05] 
dist 161=[-.00027517795997301132,-2.13797424264262900000e-05] 
dist 162=[-.00026529355386368361,-2.79628187908813500000e-05] 
dist 163=[-.00015272582530903963,-4.03850047722440500000e-05] 
dist 164=[-.00013134340069053371,-4.30289395770193500000e-05] 
dist 165=[-.00010757786722544782,-4.05572832237962600000e-05] 
dist 166=[-.00011296922307062398,2.97184590410885500000e-05] 
dist 167=[-.00011606398025852445,9.77287048431361800000e-05] 
dist 168=[-.00011680560793372031,.00014199346549544358] 
dist 169=[-2.93760384606761870000e-05,.00017685378377954594] 
dist 170=[-2.64352850863477080000e-05,.00020744279473039624] 
dist 171=[-1.90788225853402490000e-05,.00023254160702917036] 
dist 172=[-1.80200342831708580000e-05,.00024555528324583418] 
dist 173=[-6.97186254829325100000e-06,.00025238448636976773] 
dist 174=[-4.98074112981323900000e-06,.00025354084421624222] 
dist 175=[-2.53034328337670000000e-06,.00017061698830726152] 
dist 176=[-2.11555759591483000000e-06,.00016288117866491169] 
dist 177=[1.21178245178035400000e-05,.00014119882526938027] 
dist 178=[1.37127328800859500000e-05,.00013772595914994231] 
dist 179=[1.66045310231337600000e-05,9.64246799055396900000e-05] 
dist 180=[1.71617384125641700000e-05,8.81380765211122130000e-05] 
dist 181=[1.80045318960414200000e-05,7.86581772489320520000e-05] 
dist 182=[-9.55322820185680000000e-06,7.59913084230187920000e-05] 
dist 183=[-3.87015632143144000000e-05,2.56723312649656200000e-05] 
dist 184=[-5.76101468036987400000e-05,2.57031643553187500000e-05] 
dist 185=[-7.24273350863831000000e-05,1.60647099431744460000e-05] 
dist 186=[-8.52967114556888700000e-05,1.51531110032430000000e-05] 
dist 187=[-9.57591912603548500000e-05,1.27688272254210800000e-05] 
dist 188=[-.00010099922630748549,1.23784793954252280000e-05] 
dist 189=[-.00010378441960387931,8.35125346148381000000e-06] 
dist 190=[-.00010447887276043665,7.57050090091687000000e-06] 
dist 191=[-3.49339902331302300000e-05,6.58417660538675000000e-06] 
dist 192=[-3.25923423489414200000e-05,6.28232026321630000000e-06] 
dist 193=[-2.63221203937046700000e-05,-6.39807958113490000000e-07] 
dist 194=[-2.54180269697612900000e-05,-1.47944803861747000000e-06] 
dist 195=[-1.45880815064869100000e-05,-3.36844387383313000000e-06] 
dist 196=[-1.25256865858828300000e-05,-3.34785497454259030000e-06] 
dist 197=[-1.12851638087064700000e-05,-3.07155384950784350000e-06] 
dist 198=[-1.15911001046798700000e-05,2.33348284395119000000e-06] 
dist 199=[-1.17159994169392000000e-05,8.73810583549968000000e-06] 
dist 200=[-1.17059677322674300000e-05,1.29444372399602900000e-05] 
dist 201=[-3.43906911041792000000e-06,1.62890245542015300000e-05] 
dist 202=[-3.16602678888581000000e-06,1.92776153972551000000e-05] 
dist 203=[-2.49853186744345000000e-06,2.17678206291898000000e-05] 
dist 204=[-2.37111931074902000000e-06,2.31293843331166000000e-05] 
dist 205=[-1.38653634695210000000e-06,2.39112856521004500000e-05] 
dist 206=[-1.20256219125910000000e-06,2.41056809539037600000e-05] 
dist 207=[-8.92356897269900000000e-07,1.49993147814340890000e-05] 
dist 208=[-8.17562943893700000000e-07,1.42183855509331500000e-05] 
dist 209=[4.39756717608100000000e-07,1.21547009546297300000e-05] 
dist 210=[6.07868801496900000000e-07,1.17593576112870100000e-05] 
dist 211=[9.15284321724500000000e-07,8.15958983739333000000e-06] 
dist 212=[9.79596330714700000000e-07,7.44442929105226000000e-06] 
dist 213=[1.11309901234220000000e-06,6.39884587571134000000e-06] 
dist 214=[-7.81693334426220000000e-07,6.08127351766304000000e-06] 
dist 215=[-3.90236706523926000000e-06,3.12549870805770000000e-06] 
dist 216=[-5.94964477277105000000e-06,3.13776597809770000000e-06] 
dist 217=[-7.57910936617872000000e-06,2.95789806863156000000e-06] 
dist 218=[-9.03747289379298000000e-06,2.90779611463154000000e-06] 
dist 219=[-1.02539914081267500000e-05,2.79699564861060900000e-06] 
dist 220=[-1.09212305828017500000e-05,2.75262796622399000000e-06] 
dist 221=[-1.13064137938124300000e-05,2.51608314022398000000e-06] 
dist 222=[-1.14006962273357800000e-05,2.45871812901886000000e-06] 
dist 223=[-3.58287165066451000000e-06,2.27789110691718000000e-06] 
dist 224=[-3.39745700928018000000e-06,2.24022946393859000000e-06] 
dist 225=[-2.91531510516716000000e-06,1.69445438245120000000e-06] 
dist 226=[-2.81629254113863000000e-06,1.59593320046810000000e-06] 
dist 227=[-1.99511640256990000000e-06,1.37447344069700000000e-06] 
dist 228=[-1.83188203467394000000e-06,1.30590934430690000000e-06] 
dist 229=[-1.57061115722602000000e-06,1.00063616634510000000e-06] 
dist 230=[-1.39077889343864000000e-06,9.38464077464600000000e-07] 
dist 231=[-1.13725903727048000000e-06,8.82172804874670000000e-07] 
dist 232=[-1.13171783867503000000e-06,1.27035877547198000000e-06] 
dist 233=[-9.85016926403480000000e-07,1.57294006660481000000e-06] 
dist 234=[-9.53823969180590000000e-07,1.83276325561892000000e-06] 
dist 235=[-8.94898030800720000000e-07,2.04251256393830000000e-06] 
dist 236=[-8.76593640828820000000e-07,2.14587609249085000000e-06] 
dist 237=[-7.99393705325870000000e-07,2.19904118097659000000e-06] 
dist 238=[-7.78162042243970000000e-07,2.20905889571304000000e-06] 
dist 239=[-7.30268247499670000000e-07,1.59810861738827000000e-06] 
dist 240=[-7.13230876992110000000e-07,1.53375683250385000000e-06] 
dist 241=[-6.32664644534540000000e-07,1.35047724852282800000e-06] 
dist 242=[-6.09646820211120000000e-07,1.31911716153890200000e-06] 
dist 243=[-5.87214544805250000000e-07,9.79667682386260000000e-07] 
dist 244=[-5.75026526068010000000e-07,9.10760267197450000000e-07] 
dist 245=[-5.68017416297180000000e-07,8.28062517752020000000e-07] 
dist 246=[-5.69984565395700000000e-07,7.67111115135780000000e-07] 
dist 247=[-5.78852691653550000000e-07,9.13165231180200000000e-08] 
dist 248=[-6.95766757464977000000e-07,-7.04774137365600000000e-08] 
dist 249=[-8.20498716153425000000e-07,-1.58608529622299000000e-07] 
dist 250=[-9.25128207849892000000e-07,-1.77350871628955000000e-07] 
dist 251=[-1.00771384626792000000e-06,-1.84609357201619000000e-07] 
dist 252=[-1.04474281157351000000e-06,-1.57669566779251000000e-07] 
dist 253=[-1.06178977198529000000e-06,-1.03785755869307660000e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 2, 0, 2] 
dist 0=[80.415613292987446036  ,80.415613292987446036  ] 
dist 1=[78.437883964959933748  ,81.906513937283621182  ] 
dist 2=[75.674401227317382628  ,82.727207468894210997  ] 
dist 3=[71.806995678005412171  ,83.213919255705452368  ] 
dist 4=[65.423926015886483056  ,83.371888340005623780  ] 
dist 5=[58.824155711414786583  ,83.294039573900750537  ] 
dist 6=[54.092096810255139649  ,83.148832067279602282  ] 
dist 7=[49.824582200823931228  ,82.068051112474007549  ] 
dist 8=[45.078972648764300172  ,79.547039097628515558  ] 
dist 9=[40.393515172511584394  ,77.467049789720549017  ] 
dist 10=[36.366270447548505773  ,76.503021412208048037  ] 
dist 11=[32.053247349017322181  ,75.075247318796524679  ] 
dist 12=[26.227686453755870226  ,74.577667732177178264  ] 
dist 13=[20.468307147935026630  ,73.357251665159329816  ] 
dist 14=[16.419425766162935629  ,72.899883175891343367  ] 
dist 15=[12.851949970871058840  ,70.468674070274690964  ] 
dist 16=[8.945097046830534950  ,65.750245492793993954  ] 
dist 17=[3.752286520402550023  ,29.158110843195120005  ] 
dist 18=[-.011511108985394429  ,25.683267166569474366  ] 
dist 19=[-3.452134930285023587  ,17.552099925033276863  ] 
dist 20=[-7.3569547202484715624 ,16.381134440457734758  ] 
dist 21=[-10.972736328276317678  ,5.828795443000204352  ] 
dist 22=[-13.259633297920156860  ,4.027013432295469431  ] 
dist 23=[-15.014695727299306057  ,1.620236461794149554  ] 
dist 24=[-16.505596628730187597  ,1.217000883015849591  ] 
dist 25=[-17.711514290929368331  ,-1.4470406669064971551 ] 
dist 26=[-18.327605604184720702  ,-1.8309248115841989829 ] 
dist 27=[-18.625389856941169234  ,-2.3812603846015881509 ] 
dist 28=[-18.648990130988967748  ,-2.4662872830848855703 ] 
dist 29=[-16.995785466223165700  ,-4.1608744436399604083 ] 
dist 30=[-17.683209285146944927  ,-4.3540835584267134400 ] 
dist 31=[-18.059082316332357966  ,-4.5880561717837269002 ] 
dist 32=[-18.109383529287207371  ,-3.667771680736551677  ] 
dist 33=[-9.5524533322059657665 ,-2.127566960803528668  ] 
dist 34=[-8.8422260974550060794 ,-.912859718013848156  ] 
dist 35=[-7.0913663639666342034 ,.286996414280388810  ] 
dist 36=[-6.7824722047551681733 ,1.769009367084907155  ] 
dist 37=[-4.1807221152012273707 ,3.173951095420984889  ] 
dist 38=[-3.6988163686461974444 ,4.067037870679903161  ] 
dist 39=[-2.9568485180825483296 ,4.751320330838571578  ] 
dist 40=[-2.7606333262532940069 ,5.324281702906057377  ] 
dist 41=[-.69768821822952479147,5.778468322725174699  ] 
dist 42=[-.5603316649688296984 ,5.989463209786783126  ] 
dist 43=[-.34196428731067217801,6.088953065031510669  ] 
dist 44=[-.28943410283787557547,6.098745271638947408  ] 
dist 45=[.53148896987683804105,6.478373037658989161  ] 
dist 46=[.63710196271259983346,6.801226348420499338  ] 
dist 47=[.82764526786835358493,6.972214378426480689  ] 
dist 48=[.640897487331249066  ,7.005609437045834972  ] 
dist 49=[.073428922729866824  ,1.9643978660795441888 ] 
dist 50=[-.402405306453129840  ,2.0201730098905767458 ] 
dist 51=[-.897693241321821579  ,2.0692357501460342807 ] 
dist 52=[-1.542857419552868331  ,2.0815209985166892106 ] 
dist 53=[-2.161492217232789697  ,.5978632230273740724 ] 
dist 54=[-2.551237254180063103  ,.4901856066164953529 ] 
dist 55=[-2.844803085917544550  ,.3610072932316413868 ] 
dist 56=[-3.080511907518635599  ,.3392028975837571527 ] 
dist 57=[-3.258991036821080601  ,.09955667936819462003] 
dist 58=[-3.324705412722816381  ,.06435651854021137253] 
dist 59=[-3.346077357233131134  ,.01833366843419913736] 
dist 60=[-3.347843658283354293  ,.00946056175369830688] 
dist 61=[-1.0915470639306400732 ,-.22777732400351399995] 
dist 62=[-1.1518293690760269094 ,-.25553608144602442596] 
dist 63=[-1.1866326782923815832 ,-.30666366097939794882] 
dist 64=[-1.1953702988891704080 ,-.25280496993321229078] 
dist 65=[-.67816191442765602583,-.16781539914451564594] 
dist 66=[-.63538025761936232859,-.09818133746272358676] 
dist 67=[-.52630919384553581431,-.02715566387456654649] 
dist 68=[-.50635011739824536425,.06340995208717502975] 
dist 69=[-.33103644729294689921,.15033867143206382028] 
dist 70=[-.29745179967032685888,.20689605915139388915] 
dist 71=[-.2470334586331995592 ,.25154613118261318715] 
dist 72=[-.23275189325326647942,.29106633233941252679] 
dist 73=[-.12083277160655589336,.32385860386794874478] 
dist 74=[-.10779348446119233099,.34171979785905267938] 
dist 75=[-.09171756475675197684,.35191673065959409928] 
dist 76=[-.08753018643002583145,.4037976765691091288 ] 
dist 77=[.02473478261252038758,.4549069548967691602 ] 
dist 78=[.03810432871620427947,.4829071004312331344 ] 
dist 79=[.06678457554167220886,.4990908177718572950 ] 
dist 80=[.07085243578378215321,.5031557230481502772 ] 
dist 81=[.08000155599533401996,.15563682379232371506] 
dist 82=[.05317141260261621676,.16222654800382579168] 
dist 83=[.02226500711077928825,.16559752422505514102] 
dist 84=[-.01955865347450282732,.16596816761572010154] 
dist 85=[-.06029009017036261278,.05437858608226716589] 
dist 86=[-.08685177859309248392,.04632680215532458743] 
dist 87=[-.10786263900658240367,.03638142535179553060] 
dist 88=[-.12649948404311033855,.03437492957315232296] 
dist 89=[-.14196834668443180943,.0145444221077938577 ] 
dist 90=[-.15036867693495152914,.0112228226019952837 ] 
dist 91=[-.15512178153126854331,.0072125084016300585 ] 
dist 92=[-.15607171986972580962,.0065378975118034936 ] 
dist 93=[-.08682293351765899456,-.01522773480683340495] 
dist 94=[-.09153124848735386939,-.01745452571705241086] 
dist 95=[-.09398046272875302890,-.02038529945818267246] 
dist 96=[-.09441396112986519431,-.01286492501356883615] 
dist 97=[-.06152181525218598560,-.00500857097075385865] 
dist 98=[-.05852919082808191768,.00163531570736576909] 
dist 99=[-.05028411736210446030,.00859105964162281552] 
dist 100=[-.04897853142933635719,.01769083095355001241] 
dist 101=[-.03376537604066952348,.02640848349474658791] 
dist 102=[-.03168147154409490122,.03184425300424994068] 
dist 103=[-.02768790208082155197,.03586413557769739758] 
dist 104=[-.02658084147708889060,.03894687421573428383] 
dist 105=[-.02058940530213684768,.04128540151179123822] 
dist 106=[-.01937005413475614490,.04234264249900927430] 
dist 107=[-.01675585211408660506,.04271796140913920354] 
dist 108=[-.01599153515852697143,.04265366698247460993] 
dist 109=[-.00754128254333660595,.03636902399234480519] 
dist 110=[-.00621820645478544747,.03598685197112120019] 
dist 111=[-.00375464612685879091,.03696247306838597795] 
dist 112=[-.00317587913504136797,.03719190227189068844] 
dist 113=[-.00154973423778051187,.02638627203374106444] 
dist 114=[-.00132693751280541866,.02522298487024433242] 
dist 115=[-.00155448045892934466,.02139958119895447637] 
dist 116=[-.0034030715614508127 ,.0175055886474834327 ] 
dist 117=[-.00697792197421554972,.00500579472372437658] 
dist 118=[-.00930620682614173690,.00426989468499256387] 
dist 119=[-.01114310697283282556,.0034340431348741074 ] 
dist 120=[-.01276244630518754848,.0032889202409569919 ] 
dist 121=[-.01409819453169731876,.00159942009570260040] 
dist 122=[-.01480649271017255410,.00131287537981832855] 
dist 123=[-.01518410288296364283,.00096297986541291456] 
dist 124=[-.01524409481975980869,.00089137695466668933] 
dist 125=[-.00764687727289260914,-.00140290444239054061] 
dist 126=[-.00811862225282365366,-.00167212273508383837] 
dist 127=[-.00839102322350373946,-.00220386598335566610] 
dist 128=[-.00845824688273932127,-.00232109431956650418] 
dist 129=[-.00512618475982491524,-.00262294335324778692] 
dist 130=[-.00484421725904227865,-.00261590858411653364] 
dist 131=[-.00410804868260137517,-.00249260041389647927] 
dist 132=[-.00396721713757336702,-.00218052365712138138] 
dist 133=[-.00271533603216971328,-.00183271045435031726] 
dist 134=[-.00246901598932781296,-.00156712958360700554] 
dist 135=[-.00210092875658068892,-.00079997042546360560] 
dist 136=[-.00199294782622932001,.00028276166022057314] 
dist 137=[-.00117441407203841243,.00134167226787200542] 
dist 138=[-.00106477967782404873,.00203545284315954539] 
dist 139=[-.00093590361283066814,.00258695897028795735] 
dist 140=[-.00090091310196494816,.00307975364333281451] 
dist 141=[.00013239598711122078,.00349055095939342454] 
dist 142=[.00025554553861598208,.00371577466192840330] 
dist 143=[.00049014539378353951,.00384578166853959831] 
dist 144=[.00053394659895833652,.00387768155499309427] 
dist 145=[.00065649870924832686,.00128146945127500628] 
dist 146=[.00066535372824049147,.00134586610538176056] 
dist 147=[.00063620460359829049,.00137973638586397743] 
dist 148=[.00054809296023723414,.00138634240959793252] 
dist 149=[.00041711550499775370,.00046801249791482870] 
dist 150=[.00026862825395415475,.00041542256630189788] 
dist 151=[.00011107281597036141,.00033465722248941652] 
dist 152=[-9.75396489542386100000e-05,.00032214112477906609] 
dist 153=[-.00029932377249489482,.00016375834594750223] 
dist 154=[-.00042972194778376416,.0001360557207623249 ] 
dist 155=[-.00053134400054769663,.0001037797057478886 ] 
dist 156=[-.00061863109783927744,9.80006041906037000000e-05] 
dist 157=[-.00068902120927172786,-.0001342254327910171 ] 
dist 158=[-.00072341297217442964,-.0001611398464875985 ] 
dist 159=[-.00074108075581685761,-.0002152315295655771 ] 
dist 160=[-.00074491972918917747,-.0002269371244063449 ] 
dist 161=[-.00053147747487076980,-.0002606172897958109 ] 
dist 162=[-.00050940479967170487,-.0002615409793422099 ] 
dist 163=[-.00044701592214378096,-.00024717098767464480] 
dist 164=[-.00043640549193993392,-.00018198460295210415] 
dist 165=[-.00031511015228831609,-.00011560066235203976] 
dist 166=[-.00029044246479584400,-5.68168377283914530000e-05] 
dist 167=[-.00026105380223813259,6.94481064006828300000e-06] 
dist 168=[-.00025132487087949226,9.31451918670298000000e-05] 
dist 169=[-.00010140308374479312,.00017679840251440072] 
dist 170=[-9.16321899424408600000e-05,.00023043004871426315] 
dist 171=[-7.77297567789617800000e-05,.00027173445554625806] 
dist 172=[-7.34570868240575700000e-05,.00030634310829527395] 
dist 173=[7.70934258553833000000e-06,.00033365687743083412] 
dist 174=[1.77332695674484400000e-05,.00034593550530710350] 
dist 175=[3.49533316684790219400e-05,.00035159910732142752] 
dist 176=[0                     ,.00035259246805119169] 
dist 177=[5.64910413722986900000e-05,.00013692386698436825] 
dist 178=[5.82862591098640460000e-05,.00014536324356126562] 
dist 179=[5.63884544871135590000e-05,.00015022912162424147] 
dist 180=[4.89889429010977780000e-05,.00015141407305528746] 
dist 181=[4.04584188986601310000e-05,5.32778612699387900000e-05] 
dist 182=[3.12251679792135000000e-05,5.06303263498345200000e-05] 
dist 183=[1.51228452977170000000e-05,4.44822573649566400000e-05] 
dist 184=[-6.61777777631140000000e-06,4.25339191111532200000e-05] 
dist 185=[-2.77025599709802000000e-05,3.36929820310984100000e-05] 
dist 186=[-4.11963967059844000000e-05,3.18596553833092600000e-05] 
dist 187=[-5.15597761715115000000e-05,2.74169124322557500000e-05] 
dist 188=[-6.01891952174188000000e-05,2.62599304353219000000e-05] 
dist 189=[-6.71779997045576000000e-05,1.46954078222243000000e-05] 
dist 190=[-7.10140810451278000000e-05,1.27000410344278000000e-05] 
dist 191=[-7.32354199577516000000e-05,9.43463082922220000000e-06] 
dist 192=[-7.37927484477851000000e-05,8.60343950266780000000e-06] 
dist 193=[-6.43692784988399200000e-05,7.12835837198180000000e-06] 
dist 194=[-6.28817700509229100000e-05,7.30150241377640000000e-06] 
dist 195=[-5.85754020812060320000e-05,8.25826721279260000000e-06] 
dist 196=[-5.27500326674181200000e-05,1.05177506462726000000e-05] 
dist 197=[-2.33195832478243400000e-05,1.29641673261064000000e-05] 
dist 198=[-2.25095709886492500000e-05,1.46650703951907000000e-05] 
dist 199=[-2.02930552304748000000e-05,1.61252450392394000000e-05] 
dist 200=[-1.97797586056671200000e-05,1.76144569576455000000e-05] 
dist 201=[-1.55137869897842300000e-05,1.89879742036864000000e-05] 
dist 202=[-1.46094580286955500000e-05,1.99882274338828000000e-05] 
dist 203=[-1.31857383515569400000e-05,2.08963440997588000000e-05] 
dist 204=[-1.27608727951386300000e-05,2.19038427446879000000e-05] 
dist 205=[-3.90773595910287000000e-06,2.27878439679781400000e-05] 
dist 206=[-2.74443819484630000000e-06,2.32047338624273800000e-05] 
dist 207=[-1.09904241614200000000e-07,2.33570225827978600000e-05] 
dist 208=[4.01334190655870000000e-07,2.31880812196163300000e-05] 
dist 209=[2.79354201998045930000e-06,1.83626980392476100000e-05] 
dist 210=[2.34592138111837000000e-06,1.77129179318616400000e-05] 
dist 211=[1.52669613496578055000e-06,1.62371730571488200000e-05] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 1, 0, 0, 1, 2] 
dist 0=[83.871079172753922431  ,83.871079172753922431  ] 
dist 1=[82.976396224336364176  ,84.075113607645054297  ] 
dist 2=[81.373913454650770781  ,84.000474995078554578  ] 
dist 3=[78.346281182707122398  ,83.783678918105846799  ] 
dist 4=[74.639503535392080252  ,83.547476818456171515  ] 
dist 5=[70.326590285755143283  ,83.349061200879339571  ] 
dist 6=[64.747682445812850779  ,83.071068657984333855  ] 
dist 7=[55.988591320539273221  ,82.737637339552247061  ] 
dist 8=[47.108827049667036141  ,82.408625447421520349  ] 
dist 9=[41.047994368073070338  ,81.964173449335348898  ] 
dist 10=[35.894970155879661884  ,81.698602503788039329  ] 
dist 11=[30.637051202703920421  ,80.684487330301110004  ] 
dist 12=[25.715290474113470849  ,80.355080421377014804  ] 
dist 13=[21.902917869564811837  ,79.855131928547498792  ] 
dist 14=[18.171352399073468184  ,76.359403186552491599  ] 
dist 15=[13.570501254035317687  ,67.527390223426931044  ] 
dist 16=[9.203200404824073413  ,33.418768219254591862  ] 
dist 17=[6.402861466974107436  ,29.741888758679722739  ] 
dist 18=[3.128694152973823769  ,21.209676949710241922  ] 
dist 19=[-2.532614055892666783  ,19.868386435269406137  ] 
dist 20=[-6.2525196238275487985 ,8.9137454397303899440 ] 
dist 21=[-9.2610176626802164413 ,7.0223927762437475851 ] 
dist 22=[-12.083173917810036904  ,4.1938130841228697206 ] 
dist 23=[-14.567663477638044789  ,3.4904821109135329070 ] 
dist 24=[-16.228569716718595073  ,-2.3535256706664532471 ] 
dist 25=[-17.603227744609927050  ,-2.5126174970494129498 ] 
dist 26=[-18.945318754890681867  ,-2.7138020658705105710 ] 
dist 27=[-20.102927577090236872  ,-2.6734862728395814536 ] 
dist 28=[-20.741622822929321257  ,-2.5584350236048922394 ] 
dist 29=[-21.122928628536981135  ,-2.367198363857372373  ] 
dist 30=[-21.254178841674024317  ,-2.094054771002289898  ] 
dist 31=[-21.218172573471335149  ,-1.651842237040543537  ] 
dist 32=[-7.2687063388114343691 ,-1.201982123356763592  ] 
dist 33=[-6.5684177760827692855 ,-.897600934453571034  ] 
dist 34=[-4.8320213349416170652 ,-.647677388306710768  ] 
dist 35=[-4.5826120517357150051 ,-.0950728653434648353 ] 
dist 36=[-2.0344361274694152822 ,.2654226945366289666 ] 
dist 37=[-1.5800583968128173021 ,.5503352466525715094 ] 
dist 38=[-1.0125874179630369189 ,.8029503798928310288 ] 
dist 39=[-.9186714123082165431 ,1.2126233450146065298 ] 
dist 40=[.0143635027488829936 ,2.3444288513934548461 ] 
dist 41=[.0618618739553249954 ,3.0739766063852509510 ] 
dist 42=[.1316589174825029001 ,3.6449973442580138690 ] 
dist 43=[.1475400214989192719 ,4.1450034874654393269 ] 
dist 44=[.1467650651736100904 ,4.5582886702684702164 ] 
dist 45=[.123831379844123842  ,4.7836536863024036521 ] 
dist 46=[.081925461567841441  ,4.9135112916656165278 ] 
dist 47=[.005532708733851322  ,4.9460818788830859349 ] 
dist 48=[-.075128186906520465  ,2.6810443812195547705 ] 
dist 49=[-.134151237157801680  ,2.4955875587514514193 ] 
dist 50=[-.187226166400432367  ,2.0302713529367359415 ] 
dist 51=[-.244483860360913914  ,1.9472156006752925940 ] 
dist 52=[-.298910992916867032  ,1.2270489497751081586 ] 
dist 53=[-.3422876796797603300 ,1.0914643226668172615 ] 
dist 54=[-.4100519627881656382 ,.8867579993205863390 ] 
dist 55=[-.4641167358733427539 ,.8303041773962499918 ] 
dist 56=[-.7728992518597639758 ,.03009382703437420189] 
dist 57=[-1.1067804588765407758 ,.01509321298529787865] 
dist 58=[-1.3701954276111758709 ,-.01707222882701373262] 
dist 59=[-1.6032765884579026899 ,-.02188179768763076571] 
dist 60=[-1.7967994530804143257 ,-.05280231260901416756] 
dist 61=[-1.9026776705153176329 ,-.05730594315765778998] 
dist 62=[-1.9638188052495337258 ,-.06453075727214123608] 
dist 63=[-1.9791675404408891239 ,-.0654731337105798493 ] 
dist 64=[-.54269241794100085706,-.0611819520701140695 ] 
dist 65=[-.49990207607274057984,-.0381691991098347305 ] 
dist 66=[-.3898097713887457060 ,-.0075446850314877987 ] 
dist 67=[-.3735414536148443409 ,.0221816242281258810 ] 
dist 68=[-.1979545996745943282 ,.0416277049904813549 ] 
dist 69=[-.1654673219976532604 ,.0570491331530829367 ] 
dist 70=[-.1258801559692942638 ,.0707637089446723032 ] 
dist 71=[-.1179572967659242245 ,.0821510627277990878 ] 
dist 72=[-.01041363116644793890,.1588325635703062224 ] 
dist 73=[-.00660086585070838742,.2202400324802788310 ] 
dist 74=[.00191194603064210487,.2683565855728837984 ] 
dist 75=[.00315105840864220367,.3103076192435603581 ] 
dist 76=[.0125460924410613166 ,.3446494124944991866 ] 
dist 77=[.0139884857153920784 ,.3624698393393227186 ] 
dist 78=[.0163205241392193931 ,.3716535553855260634 ] 
dist 79=[.0167223372216712363 ,.3732887380455378849 ] 
dist 80=[.0202561288621304070 ,.23749433466808283243] 
dist 81=[.01299064383835697962,.22530231754353880256] 
dist 82=[.0009370083838567686 ,.1921519097811300059 ] 
dist 83=[-.0108692007000064578 ,.18693488199702040467] 
dist 84=[-.0185994437226415244 ,.12722019526033819236] 
dist 85=[-.0247315917042457041 ,.11548291545627178577] 
dist 86=[-.0301810185685700958 ,.1017569072226595790 ] 
dist 87=[-.0346971726892090526 ,.0981018756015355888 ] 
dist 88=[-.05652211627300064418,.00957552446180247025] 
dist 89=[-.08185480547644185737,.00846669646668998823] 
dist 90=[-.10160327412684272459,.00586717122283536019] 
dist 91=[-.11862010083680965795,.00547495264132110114] 
dist 92=[-.13241852899937283907,.00210697398041983696] 
dist 93=[-.13935568410958238183,.00152923423795532538] 
dist 94=[-.14302818925289043541,.00070811096477613837] 
dist 95=[-.14383081472164059478,.00052261696089371445] 
dist 96=[-.04887724876696474236,-.00285370421028701089] 
dist 97=[-.0454215754900970563 ,-.0023937643170004950 ] 
dist 98=[-.0364196834351588489 ,.0018453909928740472 ] 
dist 99=[-.0350164425756426377 ,.0069696344419395348 ] 
dist 100=[-.0201858499447974863 ,.0105860506589020081 ] 
dist 101=[-.0173867295909512550 ,.0137492714575399201 ] 
dist 102=[-.0138677638135377888 ,.01707026617524154885] 
dist 103=[-.0129703118624552285 ,.02019181302195313049] 
dist 104=[-.0088237738758049990 ,.02256126451105288700] 
dist 105=[-.0090033204521167666 ,.02480560389860306890] 
dist 106=[-.0094459733542547464 ,.0274288632807605635 ] 
dist 107=[-.0099167572732663252 ,.0298679957561945799 ] 
dist 108=[-.0102081287924557478 ,.0314623331495066704 ] 
dist 109=[-.0104184694322803886 ,.0330064119858422951 ] 
dist 110=[-.0105671578441858379 ,.0337979973876666289 ] 
dist 111=[-.0106605586316874434 ,.0339314736055302076 ] 
dist 112=[-.0106510483530549212 ,.01955448055306803482] 
dist 113=[-.0105631742021433776 ,.01843766279560434231] 
dist 114=[-.0104847546964911450 ,.01554177132323999750] 
dist 115=[-.0100855042850381701 ,.01499310998997798928] 
dist 116=[-.0099206110481616749 ,.01014260510758525727] 
dist 117=[-.0095737857048689126 ,.00919446210988012397] 
dist 118=[-.0094317476552878422 ,.00777289436116368523] 
dist 119=[-.00866722154465946509,.00736038347740184979] 
dist 120=[-.00848063387084716358,.00103913526118362587] 
dist 121=[-.0078566595760582531 ,.00093079860079988916] 
dist 122=[-.0099445131262651409 ,.00067318353160216810] 
dist 123=[-.0118084442550780658 ,.00062969402570937745] 
dist 124=[-.0133619006894196839 ,.00028062446542062984] 
dist 125=[-.0142141934579273914 ,.00021889921021120128] 
dist 126=[-.0147072764786978631 ,.00012062581000639500] 
dist 127=[-.0148311723388376683 ,9.70854996751118000000e-05] 
dist 128=[-.00409219366594327057,-.00026724392021482601] 
dist 129=[-.00381156760651262484,-.00031410000877884345] 
dist 130=[-.00306898199338863504,-.00039696658180700396] 
dist 131=[-.00295837090008638482,-.00041290591253037963] 
dist 132=[-.0017017573296646638 ,-.00043550251042715176] 
dist 133=[-.0014634989864960957 ,-.00041949322089027388] 
dist 134=[-.0011830161700734790 ,-.00038109769099014090] 
dist 135=[-.0011240746977727359 ,.0003215720467151358 ] 
dist 136=[-.00022631758285564119,.0010745841904868754 ] 
dist 137=[-.00019843480197492180,.0015645213528682945 ] 
dist 138=[-.00013055485349840565,.0019502657687486595 ] 
dist 139=[-.00012079275886642054,.0022886687971692593 ] 
dist 140=[-2.52230826179597000000e-05,.0025663561485306562 ] 
dist 141=[-8.49597891942833000000e-06,.0027104896667247746 ] 
dist 142=[1.30945690067905800000e-05,.0027860994737647195 ] 
dist 143=[1.66631965341697900000e-05,.0027990891223951587 ] 
dist 144=[.00012341797009534827,.00187639138590615978] 
dist 145=[.00013522338048152447,.00179068883246084254] 
dist 146=[.00015449081223880169,.00155086499539376159] 
dist 147=[.00015833205071416603,.00151253809521813145] 
dist 148=[.00015865642078552508,.00105728296571574253] 
dist 149=[.00015083302907984803,.00096608546778232108] 
dist 150=[.00013617689142146846,.00086167380509791796] 
dist 151=[-.0001017774566366959 ,.00083250997987570254] 
dist 152=[-.0004214034785372330 ,.00013084513882567448] 
dist 153=[-.0006286961527222066 ,.00012232828209253704] 
dist 154=[-.0007911023714816144 ,.00010067858110507269] 
dist 155=[-.0009321293778882813 ,9.71893441534856500000e-05] 
dist 156=[-.0010467792007519717 ,6.27613065610407100000e-05] 
dist 157=[-.0011042262671649026 ,5.62419967901761300000e-05] 
dist 158=[-.0011347785796897213 ,4.77732527676711300000e-05] 
dist 159=[-.0011424083618211322 ,4.52849053063582100000e-05] 
dist 160=[-.00038282619938421977,-8.77337443114689000000e-06] 
dist 161=[-.00035718913410333014,-1.53206567989759200000e-05] 
dist 162=[-.0002885534147761661 ,-2.99933173702520300000e-05] 
dist 163=[-.0002786643234395206 ,-3.23198714468608600000e-05] 
dist 164=[-.0001602251814246125 ,-2.97875456361785483000e-05] 
dist 165=[-.0001376855976490040 ,-2.38253632291695285000e-05] 
dist 166=[-.0001123867287994693 ,-1.49775363874918862100e-05] 
dist 167=[-.0001079170239398648 ,2.43105083391843600000e-05] 
dist 168=[-2.89022482305074800000e-05,9.41342423262632000000e-05] 
dist 169=[-2.63720895484225400000e-05,.0001399151535071246 ] 
dist 170=[-2.03541942463076000000e-05,.0001763616134607941 ] 
dist 171=[-1.91519709379801000000e-05,.0002089311785264762 ] 
dist 172=[-1.08011733859246000000e-05,.0002360746155191717 ] 
dist 173=[-9.26474658779240000000e-06,.0002509306406617892 ] 
dist 174=[-6.44328603493120000000e-06,.0002595308712679659 ] 
dist 175=[-5.79229632696990000000e-06,.0002616505947832366 ] 
dist 176=[3.48740111252560000000e-06,.00016239934308983073] 
dist 177=[4.78987423244380000000e-06,.00015391434613728331] 
dist 178=[6.98265390298040000000e-06,.00013151966614808255] 
dist 179=[7.45703854988930000000e-06,.00012722098627864297] 
dist 180=[8.06015326907690000000e-06,8.82610512856970000000e-05] 
dist 181=[7.62641190289620000000e-06,8.05279534869837000000e-05] 
dist 182=[6.57300854549420000000e-06,6.91684103857384000000e-05] 
dist 183=[-8.13726309436822000000e-06,6.57396168368688000000e-05] 
dist 184=[-4.18857458777745400000e-05,2.84399386295111200000e-05] 
dist 185=[-6.40233648486050600000e-05,2.80371295345624000000e-05] 
dist 186=[-8.16410345880647500000e-05,2.72808385139182610000e-05] 
dist 187=[-9.74063401439779400000e-05,2.69663981338400200000e-05] 
dist 188=[-.00011055644797388911,2.52842041401651000000e-05] 
dist 189=[-.00011776895920260573,2.48268707001270500000e-05] 
dist 190=[-.00012193283855400829,2.32933022636895000000e-05] 
dist 191=[-.00012295296993098283,2.29498948305867000000e-05] 
dist 192=[-3.78184409555673500000e-05,1.89180104238570000000e-05] 
dist 193=[-3.58016858763755000000e-05,1.80923983237082000000e-05] 
dist 194=[-3.04786444311639100000e-05,1.62600529662861000000e-05] 
dist 195=[-2.94850011804518400000e-05,1.56680621249209000000e-05] 
dist 196=[-2.02757401478896000000e-05,1.29361138849846000000e-05] 
dist 197=[-1.84622719327062000000e-05,1.23572520310000000000e-05] 
dist 198=[-1.29057873778522000000e-05,1.06987500983963000000e-05] 
dist 199=[-1.11237130469697900000e-05,1.04144210499071000000e-05] 
dist 200=[-9.84882113654828000000e-06,9.37981069990120000000e-06] 
dist 201=[-9.55171916302850000000e-06,1.35646396606678600000e-05] 
dist 202=[-9.02548121418657000000e-06,1.68273313706310800000e-05] 
dist 203=[-8.86405665087535000000e-06,1.96303829847858500000e-05] 
dist 204=[-8.22076655744570000000e-06,2.18936303937885700000e-05] 
dist 205=[-8.02164273049720000000e-06,2.30087192403022000000e-05] 
dist 206=[-7.62825925997920000000e-06,2.35829280743066400000e-05] 
dist 207=[-7.49164367361960000000e-06,2.36940668419216100000e-05] 
dist 208=[-6.87950774496330000000e-06,1.71290558000632700000e-05] 
dist 209=[-6.67572256266530000000e-06,1.64390820441217300000e-05] 
dist 210=[-6.53273582687020000000e-06,1.44735474929289000000e-05] 
dist 211=[-6.44938605663320000000e-06,1.41374924033770000000e-05] 
dist 212=[-6.40896821375197000000e-06,1.02636938468505300000e-05] 
dist 213=[-6.44016894965610000000e-06,9.47206205002858000000e-06] 
dist 214=[-6.52917620455593000000e-06,8.53365909988130000000e-06] 
dist 215=[-6.71894985008172000000e-06,8.21957831305864000000e-06] 
dist 216=[-6.92280950496104000000e-06,2.17874754178900000000e-07] 
dist 217=[-7.40832733658586300000e-06,-7.55252450075800000000e-07] 
dist 218=[-8.74716432990230000000e-06,-1.67150888632779500000e-06] 
dist 219=[-9.87109234271473000000e-06,-1.87286234018056600000e-06] 
dist 220=[-1.07585541157449000000e-05,-1.96007679744050450000e-06] 
dist 221=[-1.11565897783546100000e-05,-1.67612699120865030000e-06] 
dist 222=[-1.13402972467652600000e-05,-1.10417942496708019000e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 2] 
dist 0=[84.797482153096319803  ,84.797482153096319803  ] 
dist 1=[84.062779952170534473  ,85.239689378796142376  ] 
dist 2=[82.710551202033911731  ,85.424761477966508935  ] 
dist 3=[80.650237753380846457  ,85.454519314327354294  ] 
dist 4=[77.089437535785980108  ,85.277547371273365420  ] 
dist 5=[72.841712605063649879  ,84.979691267693177529  ] 
dist 6=[68.039933692801668366  ,84.697259187682113410  ] 
dist 7=[61.916568496341306086  ,83.992191686588675295  ] 
dist 8=[52.394639566765151296  ,83.642034472353419744  ] 
dist 9=[42.770110882514688625  ,81.687164072443969296  ] 
dist 10=[36.236964909382287187  ,81.044613207915263391  ] 
dist 11=[30.720693137096688078  ,80.609993511298270947  ] 
dist 12=[25.153354723941188336  ,80.347121186959523639  ] 
dist 13=[19.980477195152250764  ,68.479290964083718729  ] 
dist 14=[16.037570364703342107  ,67.435861965584783239  ] 
dist 15=[12.238831373602428813  ,58.101911751574453313  ] 
dist 16=[7.6397571621027895447 ,43.339225133639108260  ] 
dist 17=[3.080962906280671219  ,32.152004603580937564  ] 
dist 18=[-.869001761051365372  ,28.387023577063805151  ] 
dist 19=[-4.146776771618840044  ,19.641385960656849639  ] 
dist 20=[-7.3612051489254015055 ,18.296586656943466052  ] 
dist 21=[-10.286164216779445062  ,7.0803134799731858056 ] 
dist 22=[-12.408750941061677605  ,5.1545965304597390670 ] 
dist 23=[-14.348536972346159896  ,2.3409343624030659890 ] 
dist 24=[-16.543981942512547021  ,1.6404905663147358565 ] 
dist 25=[-18.555603855412821483  ,-1.8899696840305660510 ] 
dist 26=[-19.762109004674427032  ,-1.9909674590069079004 ] 
dist 27=[-20.609980613374166680  ,-2.1196199009552964989 ] 
dist 28=[-21.191304987609741247  ,-2.0953374930489182795 ] 
dist 29=[-21.560261679803372594  ,-2.024095672668770140  ] 
dist 30=[-21.584837795655492736  ,-1.904793138342461771  ] 
dist 31=[-21.415002525409876850  ,-1.5758536956155088492 ] 
dist 32=[-20.613335404054249425  ,-.6943506592608196458 ] 
dist 33=[-8.0881895743391491910 ,.1721107472663648949 ] 
dist 34=[-7.2957908608338332311 ,.7405450997711274158 ] 
dist 35=[-5.3343120535849071759 ,1.1919636308578749685 ] 
dist 36=[-5.0525958258618333892 ,1.5933354169633317374 ] 
dist 37=[-2.1835538905025507577 ,1.9259779770418076439 ] 
dist 38=[-1.6725669851139580889 ,2.1041266828404301978 ] 
dist 39=[-1.0332833580440784996 ,2.2013147753172567645 ] 
dist 40=[-.9275761417775307586 ,2.2192189778164112232 ] 
dist 41=[-.1670177655648727480 ,2.7255405506652829687 ] 
dist 42=[-.1187355481300770698 ,3.5422116129676180241 ] 
dist 43=[-.0278209872597653739 ,4.1813663283419238961 ] 
dist 44=[-.0069919517148661051 ,4.7409730709804223012 ] 
dist 45=[.054416642527400336  ,5.2035011468930083827 ] 
dist 46=[.068467179274847100  ,5.4557105055583835264 ] 
dist 47=[.073067145650389825  ,5.6010330020908624199 ] 
dist 48=[.066482219988269553  ,5.6374815329798776477 ] 
dist 49=[.056949755135709983  ,3.0384904743017089001 ] 
dist 50=[.049425041603882984  ,2.8257520211942116890 ] 
dist 51=[.042792246923086406  ,2.2930887456564911277 ] 
dist 52=[.036553428138751690  ,2.1980795056796311543 ] 
dist 53=[.031563929178282652  ,1.3771131458890825263 ] 
dist 54=[.029754324548631788  ,1.2227710255140980675 ] 
dist 55=[.029935373397557230  ,.9892196562610036069 ] 
dist 56=[-.3128609318244238015 ,.92508307376537701068] 
dist 57=[-.8960899317985124253 ,.0548904225106366140 ] 
dist 58=[-1.2750849040339752785 ,.0418256978626690730 ] 
dist 59=[-1.5740275814280419211 ,.0119114004752379952 ] 
dist 60=[-1.8384720942429359447 ,.0075794725006590356 ] 
dist 61=[-2.0580094448248823407 ,-.0284421381045260620 ] 
dist 62=[-2.1781094413601595868 ,-.0342993723662588760 ] 
dist 63=[-2.2474581407679164331 ,-.0428715586221693516 ] 
dist 64=[-2.2648639463915073995 ,-.0443226347479478665 ] 
dist 65=[-.61754503118380678848,-.0698321675759687499 ] 
dist 66=[-.56811762253624852476,-.0727919691400315902 ] 
dist 67=[-.44125623778669500159,-.0758071512638141473 ] 
dist 68=[-.42250005846566167814,-.0747801080357335786 ] 
dist 69=[-.2211106978896827714 ,-.0721180975459359910 ] 
dist 70=[-.1839099499867453161 ,-.0673569961767907964 ] 
dist 71=[-.1384198483041441250 ,-.0343695877358988559 ] 
dist 72=[-.1292921314559681402 ,.0782789358813855551 ] 
dist 73=[-.0391088775385453040 ,.1864401670332295728 ] 
dist 74=[-.0348791033845562604 ,.2564230360586902922 ] 
dist 75=[-.0249541024075176137 ,.3112308527081325155 ] 
dist 76=[-.0232294843829780318 ,.3589745458892547183 ] 
dist 77=[-.01012826429268621056,.3980334313142668775 ] 
dist 78=[-.00781872756594563452,.4182618039857629863 ] 
dist 79=[-.00395827252455665345,.4286578000269268549 ] 
dist 80=[-.00308755737648609534,.4304747826277955131 ] 
dist 81=[.00994785866115170942,.2730035957497022259 ] 
dist 82=[.01166458722464503063,.2588628416358185781 ] 
dist 83=[.0137230847457910355 ,.2205151196635149270 ] 
dist 84=[.0139142211762327529 ,.2144724569589907781 ] 
dist 85=[.0134794133397646932 ,.1456936002674089170 ] 
dist 86=[.0121589824761442023 ,.1321897805056509831 ] 
dist 87=[.00995738308129134577,.1163379284392004400 ] 
dist 88=[-.0218321327257609604 ,.1120957652630025171 ] 
dist 89=[-.0668315738360393728 ,.00751106518463344726] 
dist 90=[-.0958582737801146141 ,.00642620531396421889] 
dist 91=[-.1184645290307544667 ,.00386772626011084427] 
dist 92=[-.1379084514690716219 ,.00346000677512704603] 
dist 93=[-.1536606247747822901 ,.0001049756316885348 ] 
dist 94=[-.1615709279079576208 ,-.0004705201572146767 ] 
dist 95=[-.1657438757076957340 ,-.0013630634502653612 ] 
dist 96=[-.1666181649388032596 ,-.0007738593105647864 ] 
dist 97=[-.05470969678493671816,.0013359985252184038 ] 
dist 98=[-.05065800309969631550,.0032001815957871253 ] 
dist 99=[-.04002859756718673639,.0052139823152591370 ] 
dist 100=[-.03850050198742053677,.0079203074124857701 ] 
dist 101=[-.0238547337597564454 ,.01082031735502562507] 
dist 102=[-.0239470459725531280 ,.01360525427944235466] 
dist 103=[-.0238283851680638626 ,.01680367590990938144] 
dist 104=[-.0236238107273516628 ,.0213491358912919458 ] 
dist 105=[-.0218578914520028828 ,.0258517166797307194 ] 
dist 106=[-.0213875237629932162 ,.0288799178276858236 ] 
dist 107=[-.0202878036753683618 ,.0313724456498662569 ] 
dist 108=[-.0198759253753146092 ,.0337445490577191557 ] 
dist 109=[-.0177662108207141443 ,.0370508055742651517 ] 
dist 110=[-.0172725821922611867 ,.0387654753169349660 ] 
dist 111=[-.0159208211532613287 ,.0396275746998846688 ] 
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dist 113=[-.0111069287486655988 ,.0256144224354917269 ] 
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dist 180=[8.50919333466526000000e-06,.00014609848502404755] 
dist 181=[9.81737889637812000000e-06,.00010085728316416124] 
dist 182=[9.67142808424699000000e-06,9.19008258118302400000e-05] 
dist 183=[9.00400600475032000000e-06,7.84998007117085400000e-05] 
dist 184=[-9.90367911007092000000e-06,7.45480016758865100000e-05] 
dist 185=[-4.91135183383701700000e-05,5.82856078987494100000e-06] 
dist 186=[-7.48292565889479900000e-05,5.25324877693887000000e-06] 
dist 187=[-9.52913286019922300000e-05,3.80696076123272000000e-06] 
dist 188=[-.00011359843070106903,3.59913154682166000000e-06] 
dist 189=[-.00012886755974113630,1.40406980181263000000e-06] 
dist 190=[-.00013724215293292932,1.00704127735845000000e-06] 
dist 191=[-.00014207723294808759,5.22165964302250000000e-07] 
dist 192=[-.00014326301169237973,4.40816670910160000000e-07] 
dist 193=[-4.00255569010702510000e-05,-2.50570401219513000000e-06] 
dist 194=[-3.74724505401867070000e-05,-2.84382632965342000000e-06] 
dist 195=[-3.05807075285597600000e-05,-3.48297758282005000000e-06] 
dist 196=[-2.95865997232386140000e-05,-3.61389697921877000000e-06] 
dist 197=[-1.74956401495333240000e-05,-3.87936981900432000000e-06] 
dist 198=[-1.51783310933591350000e-05,-3.80248988509263000000e-06] 
dist 199=[-1.26080780314989880000e-05,-3.56309475348627000000e-06] 
dist 200=[-1.21482362304087780000e-05,3.52795491899224700000e-06] 
dist 201=[-2.75828592842640000000e-06,1.10497615308169480000e-05] 
dist 202=[-2.56439901169783000000e-06,1.59128026777085420000e-05] 
dist 203=[-2.08268803505277000000e-06,1.97037183430935680000e-05] 
dist 204=[-1.99199407000924000000e-06,2.29599646700261170000e-05] 
dist 205=[-1.25420453872378000000e-06,2.55881683341072040000e-05] 
dist 206=[-1.11439489162993000000e-06,2.68803824495372780000e-05] 
dist 207=[-8.90401449457150000000e-07,2.75450708404639320000e-05] 
dist 208=[-8.32179397470050000000e-07,2.76763708269176170000e-05] 
dist 209=[1.98382075797390800000e-07,1.99450266794210360000e-05] 
dist 210=[3.33433105241219100000e-07,1.91350457485452070000e-05] 
dist 211=[5.32155825112650000000e-07,1.68333154935308590000e-05] 
dist 212=[5.73360243042210000000e-07,1.64395440307484140000e-05] 
dist 213=[6.27883501599550000000e-07,1.19203355135256400000e-05] 
dist 214=[5.89223110569920000000e-07,1.09977505607204350000e-05] 
dist 215=[-2.56445557176065000000e-07,9.90070665021055800000e-06] 
dist 216=[-3.50121689524580000000e-06,9.53276497171898300000e-06] 
dist 217=[-6.65239422373013500000e-06,5.67153316764351000000e-07] 
dist 218=[-8.67429604882454800000e-06,5.16921392213683000000e-07] 
dist 219=[-1.02328144043489340000e-05,3.89085364396460000000e-07] 
dist 220=[-1.15404856819381990000e-05,3.70449534101980000000e-07] 
dist 221=[-1.25727996736803420000e-05,1.70737298264730000000e-07] 
dist 222=[-1.30357674952201910000e-05,1.34086199005590000000e-07] 
dist 223=[-1.32492353969178940000e-05,8.96076326186200000000e-08] 
dist 224=[-1.32888860117432300000e-05,1.44445198021880000000e-07] 
dist 225=[-3.74404847022502000000e-06,3.05814127892650000000e-07] 
dist 226=[-3.49167269471651000000e-06,4.40312445149170000000e-07] 
dist 227=[-2.82067812491788000000e-06,5.79019943695020000000e-07] 
dist 228=[-2.71864679257538000000e-06,7.57161736190870000000e-07] 
dist 229=[-1.60250271285268000000e-06,9.44068242796878000000e-07] 
dist 230=[-1.62244420688798000000e-06,1.11765213102190300000e-06] 
dist 231=[-1.62206679723418000000e-06,1.31241234536715000000e-06] 
dist 232=[-1.61411120201152000000e-06,1.58355904019628000000e-06] 
dist 233=[-1.53616920554156000000e-06,1.85119400279619000000e-06] 
dist 234=[-1.50972960801074000000e-06,2.03199803078712000000e-06] 
dist 235=[-1.44737052062036000000e-06,2.18154201137744000000e-06] 
dist 236=[-1.42191520203445000000e-06,2.32486299422436000000e-06] 
dist 237=[-1.28494531377539000000e-06,2.48475484470790000000e-06] 
dist 238=[-1.25180229896075000000e-06,2.61509643802040000000e-06] 
dist 239=[-1.15650338377657000000e-06,2.68244399112120000000e-06] 
dist 240=[-1.13105372330224000000e-06,2.69131969469527000000e-06] 
dist 241=[-8.14739726370630000000e-07,1.80501134238513000000e-06] 
dist 242=[-7.59650698554420000000e-07,1.71796739889665000000e-06] 
dist 243=[-6.39560795679890000000e-07,1.49193033511104000000e-06] 
dist 244=[-6.04063470413150000000e-07,1.44197040761611100000e-06] 
dist 245=[-4.54042780191720000000e-07,1.05303506820905100000e-06] 
dist 246=[-4.23412326391430000000e-07,9.74405563657215000000e-07] 
dist 247=[-3.47036070641320000000e-07,7.31356167095800000000e-07] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 0, 1, 0, 0, 2] 
dist 0=[87.230571970959631858  ,87.230571970959631858  ] 
dist 1=[86.628872517730378228  ,87.531377145136215397  ] 
dist 2=[85.461867637612888336  ,87.498135955292373021  ] 
dist 3=[83.965388041198488090  ,87.251679710231105927  ] 
dist 4=[82.048953906540061516  ,87.026606502694397356  ] 
dist 5=[79.460776929467309028  ,86.115650018775836475  ] 
dist 6=[75.283318388020992893  ,85.723348340627770032  ] 
dist 7=[70.408742365965652997  ,82.696856801838976148  ] 
dist 8=[62.241106144314168108  ,81.865887142466166054  ] 
dist 9=[53.672523265428815446  ,81.003874870948712225  ] 
dist 10=[47.653419038556031753  ,80.529136318331862341  ] 
dist 11=[37.371781559631900110  ,80.041587089623809913  ] 
dist 12=[30.289880881594197229  ,79.917937591443202438  ] 
dist 13=[24.355077461990701912  ,77.115941464722513123  ] 
dist 14=[18.437354907906890616  ,71.698113045004659378  ] 
dist 15=[12.984638845746558636  ,31.144324885691188705  ] 
dist 16=[8.904779638218933620  ,27.997453688648880511  ] 
dist 17=[5.047492085031625709  ,18.407648294644983505  ] 
dist 18=[.481510133928627529  ,17.069358907177897381  ] 
dist 19=[-3.797248048343586776  ,10.318300287877830856  ] 
dist 20=[-6.508392518843856096  ,9.7673145426615427329 ] 
dist 21=[-8.594167598372666089  ,5.5059458383203208695 ] 
dist 22=[-10.376003511261633300  ,4.7955677699263377518 ] 
dist 23=[-12.854495854072892545  ,3.6890281926074919351 ] 
dist 24=[-15.627402464852982352  ,3.4402246099287141907 ] 
dist 25=[-17.718073346250247928  ,.04418603921151789528] 
dist 26=[-19.424797856270926165  ,-.36159092530035237001] 
dist 27=[-20.757213557266183591  ,-1.2178989993095098392 ] 
dist 28=[-21.355045268246228057  ,-1.3399574327365335652 ] 
dist 29=[-21.608951485899383488  ,-2.1559084435738754633 ] 
dist 30=[-21.576571020960487571  ,-2.2730884734567058251 ] 
dist 31=[-8.6560691236283973077 ,-2.4712256823841864060 ] 
dist 32=[-7.7904764323980369582 ,-1.977012084593316776  ] 
dist 33=[-5.6642746177449504794 ,-.916182038473552577  ] 
dist 34=[-5.3470991508869106213 ,.500246698553027374  ] 
dist 35=[-2.5943706871694342486 ,1.873409694613365673  ] 
dist 36=[-2.5867556478439444653 ,2.762314192662951482  ] 
dist 37=[-2.5776040865449074222 ,3.459028174481068525  ] 
dist 38=[-2.5714760704934463380 ,4.067086032647950023  ] 
dist 39=[-2.5675079287070831514 ,4.565648478632802970  ] 
dist 40=[-2.5664425841698021421 ,4.826399865426758177  ] 
dist 41=[-.93042410322958498455,4.962632042927524227  ] 
dist 42=[-.79964520568492169616,5.424420872217036774  ] 
dist 43=[-.50102739455158975319,5.894329879822674548  ] 
dist 44=[-.45178360136954424176,6.125071914550651874  ] 
dist 45=[-.2219375658010875003 ,6.235891477109498287  ] 
dist 46=[-.563604508904503832  ,6.244642072918826239  ] 
dist 47=[-.905351683559779567  ,3.650364493554878374  ] 
dist 48=[-1.198496000024247741  ,3.4146459603912546269 ] 
dist 49=[-1.508863828709503993  ,2.8268529509633378272 ] 
dist 50=[-1.919365874356800872  ,2.7132003409719245506 ] 
dist 51=[-2.314929260312109902  ,1.8043392469870970646 ] 
dist 52=[-2.565916811936618102  ,1.6308097566613092203 ] 
dist 53=[-2.756729030096038207  ,1.3475265099386971549 ] 
dist 54=[-2.912815215727038401  ,1.2748003769291518980 ] 
dist 55=[-3.033135950944856222  ,1.0096260045031051211 ] 
dist 56=[-3.081615121141260522  ,1.0140609970869072202 ] 
dist 57=[-3.089231776145465783  ,.2243995849909070928 ] 
dist 58=[-3.079608271286324732  ,.19192619782992138872] 
dist 59=[-2.961699580333839773  ,.1148471783707570222 ] 
dist 60=[-2.917938979363073766  ,.10353768075763599167] 
dist 61=[-2.8168380042992562330 ,.00109705309898535314] 
dist 62=[-2.6803227236226371805 ,-.01644901744020337489] 
dist 63=[-.57355676677247456356,-.04056722159380481905] 
dist 64=[-.52484945040767262197,-.04512394656450413439] 
dist 65=[-.40037712006505297537,-.08797313298153965143] 
dist 66=[-.38246791840766034592,.0050342446652317181 ] 
dist 67=[-.20162875557480476268,.0960109979262257482 ] 
dist 68=[-.21718045412464232103,.1556219191635371501 ] 
dist 69=[-.22959472397832459087,.2030100790770035886 ] 
dist 70=[-.23565471523987567631,.2453557395652728924 ] 
dist 71=[-.23828377815696554929,.2806613727956247695 ] 
dist 72=[-.23849782190811272292,.3000366230552320990 ] 
dist 73=[-.12914128262539976941,.3112477934808194747 ] 
dist 74=[-.11969045314805320554,.3420714690675430801 ] 
dist 75=[-.09596440277682659764,.37914475348410057943] 
dist 76=[-.09226688296630055324,.39938572567408051757] 
dist 77=[-.05564926074979432401,.41101412598471964766] 
dist 78=[-.04882549215515415670,.41378789751660343031] 
dist 79=[-.04008016211721083531,.23385331850655435041] 
dist 80=[-.03779973442324331170,.21889386404746447973] 
dist 81=[.01616507176114070594,.18089511328615405886] 
dist 82=[-.0007243223191691699 ,.17388245920731162386] 
dist 83=[-.0171100553933537055 ,.11311969562351082833] 
dist 84=[-.0277941700414923402 ,.1014775869404553249 ] 
dist 85=[-.0362259908117094666 ,.08637410862611041754] 
dist 86=[-.0436510606531920554 ,.08937330548362871012] 
dist 87=[-.06981452214929251170,.09084144749055908350] 
dist 88=[-.10027556047700156844,.09099090028949297054] 
dist 89=[-.12437085498458474858,.02610695496732081855] 
dist 90=[-.14575450935542642103,.02331076388400594344] 
dist 91=[-.16351910219821783037,.0163798534707188401 ] 
dist 92=[-.17320699283659463209,.0153845624600034530 ] 
dist 93=[-.17874644140482011661,.0051920931678267085 ] 
dist 94=[-.17999536259257936677,.0033725420997637562 ] 
dist 95=[-.04738988817375813592,.0011042296464259935 ] 
dist 96=[-.04368738118171610698,.0007284974868874369 ] 
dist 97=[-.03413008529547028453,-.00611087033766612747] 
dist 98=[-.03269376444629242401,.00059020544616288013] 
dist 99=[-.02989268809073347508,.00713506515173770375] 
dist 100=[-.03127073954831465426,.01139395547843505598] 
dist 101=[-.03220159509119247690,.01474397320136110061] 
dist 102=[-.03260204959552762806,.01767330727255973030] 
dist 103=[-.03269050353544228219,.02257127564312722564] 
dist 104=[-.03255404832303961770,.02838121592239937477] 
dist 105=[-.02514837553078427679,.03268121431784920141] 
dist 106=[-.02404115610012982866,.03598362393154712288] 
dist 107=[-.02153429138214336293,.03854882716020176227] 
dist 108=[-.02074373682819130179,.03991463020861445161] 
dist 109=[-.01716818307913540762,.04065163459619720048] 
dist 110=[-.01642502163884077456,.04071527729268025447] 
dist 111=[-.01447617721438620030,.03179470309958020659] 
dist 112=[-.01406542465540174313,.03061739986693317458] 
dist 113=[-.00939228957003662802,.02746405236376999823] 
dist 114=[-.00855224438486892415,.02675591004063236130] 
dist 115=[-.00709919614570103972,.02095166159732628195] 
dist 116=[-.00673866885505952237,.01974269292282055271] 
dist 117=[-.00581528538346365063,.01781547757711206595] 
dist 118=[-.00567646418281320246,.01637368774724610093] 
dist 119=[-.00834504330373254462,.0097801823680388354 ] 
dist 120=[-.01086798131421528923,.0098508118874089671 ] 
dist 121=[-.01283140230921570464,.00252798984534139393] 
dist 122=[-.01451622881877327094,.00229733484377118128] 
dist 123=[-.01587324654677911912,.00171520891337690158] 
dist 124=[-.01653204728355697446,.00162904309272262267] 
dist 125=[-.01685223243897711612,.00073496166120838367] 
dist 126=[-.01686597298001175112,.00057176350297361849] 
dist 127=[-.00173640704294291463,.0003677276169368507 ] 
dist 128=[-.00159439232124517346,.0003265688665725821 ] 
dist 129=[-.00138481823088912182,-.00059935686786380025] 
dist 130=[-.00132106964212286610,5.32083222732854100000e-05] 
dist 131=[-.0015379042323233769 ,.00069343753851607616] 
dist 132=[-.0017381924921704826 ,.00111416238845358192] 
dist 133=[-.0019015470855850448 ,.00144955134455764104] 
dist 134=[-.0019853767226769371 ,.00175033019458199166] 
dist 135=[-.0020274378651227246 ,.00200145343654208921] 
dist 136=[-.0020342144904529877 ,.00213931313825207661] 
dist 137=[-.00124552792429916903,.00221898476742628576] 
dist 138=[-.00117530304603932048,.00223862734906550667] 
dist 139=[-.00098868904573297164,.00064545162023305423] 
dist 140=[-.00095933545079607470,.00060907095085831225] 
dist 141=[-.00063612793805031813,.00050834200547556636] 
dist 142=[-.00057333128364767324,.00049380805146014040] 
dist 143=[-.00049822650541344840,.00030929420956921800] 
dist 144=[-.00047815187282345636,.00027343009216954484] 
dist 145=[9.52359392189985870000e-05,.00035711767329422395] 
dist 146=[-2.16168725421195200000e-05,.00048789444969196312] 
dist 147=[-.00014236023682527301,.00058923057953516739] 
dist 148=[-.00022064585297965449,.0006756053618079577 ] 
dist 149=[-.00028186630375769585,.0007453530055557396 ] 
dist 150=[-.00033472872584361712,.0007804858942713329 ] 
dist 151=[-.00037761016445489552,.0007988003199048344 ] 
dist 152=[-.00039912952044644235,.0008015818822608921 ] 
dist 153=[-.00041038559610776184,.00025399328121675534] 
dist 154=[-.00041243673852464057,.00023259367146297095] 
dist 155=[-.00030651599889048433,.00017760629803158742] 
dist 156=[-.00029510642577507400,.00016965482568348708] 
dist 157=[-.00026181627546959829,8.20876289698389000000e-05] 
dist 158=[-.00025607372091406928,6.59150481160889000000e-05] 
dist 159=[-.00018806776617711985,4.67010268854110000000e-05] 
dist 160=[-.00017403178905233432,4.32984221408813000000e-05] 
dist 161=[-.00015761304517726426,-7.88766776046784400000e-06] 
dist 162=[-.00015204672581483321,4.27150631399308000000e-05] 
dist 163=[-.0001429746541162862 ,9.20155104102175440000e-05] 
dist 164=[-.0001638735692254027 ,.00012380713396593698] 
dist 165=[-.0001811994818853871 ,.00014847159522051294] 
dist 166=[-.0001905851121775232 ,.00016942378730589534] 
dist 167=[-.0001958686238172502 ,.00018608447642958875] 
dist 168=[-.00019691710068698846,.00019367930911772357] 
dist 169=[-.00011376138928884354,.00019727473455027303] 
dist 170=[-.00010672372162119886,.00019802325337045439] 
dist 171=[-8.86099659498832900000e-05,6.22903100711636000000e-05] 
dist 172=[-8.53647172842123100000e-05,5.90186335001350600000e-05] 
dist 173=[-5.55966795252170500000e-05,5.01137584148197000000e-05] 
dist 174=[-4.98496919695133300000e-05,4.86003451252140000000e-05] 
dist 175=[-4.16039532315861700000e-05,3.24966259546681000000e-05] 
dist 176=[-3.91252816947368500000e-05,2.93213708453432000000e-05] 
dist 177=[6.88066363871193000000e-06,3.47588809569057400000e-05] 
dist 178=[-7.93872006854300000000e-07,4.96710871852282800000e-05] 
dist 179=[-1.30950160479262000000e-05,6.14850204319021600000e-05] 
dist 180=[-2.10401463187569000000e-05,7.19944783395604400000e-05] 
dist 181=[-2.72207380029092000000e-05,8.07382173406771900000e-05] 
dist 182=[-3.25034860370011000000e-05,8.55234974013789900000e-05] 
dist 183=[-3.68133625873387000000e-05,8.82803686073727400000e-05] 
dist 184=[-3.91234625798416000000e-05,8.89495612254576300000e-05] 
dist 185=[-4.03840188098338000000e-05,3.04219887936596400000e-05] 
dist 186=[-4.06321426860692000000e-05,2.87207154543756300000e-05] 
dist 187=[-3.71711423520903500000e-05,2.47955546391998400000e-05] 
dist 188=[-3.65057920187360800000e-05,2.36064441107372200000e-05] 
dist 189=[-3.44440576536157150000e-05,1.81356941629989000000e-05] 
dist 190=[-3.37877055213130240000e-05,1.70238743900866000000e-05] 
dist 191=[-2.88062005869307200000e-05,1.43598792873992000000e-05] 
dist 192=[-2.76465988678451600000e-05,1.36821534040959000000e-05] 
dist 193=[-2.56651117731501600000e-05,7.01435004963690000000e-06] 
dist 194=[-2.50798499874379900000e-05,5.86363670432320000000e-06] 
dist 195=[-1.35920675039474500000e-05,5.13533149762113000000e-06] 
dist 196=[-1.54789392554535800000e-05,7.46741870885788000000e-06] 
dist 197=[-1.69883941136829000000e-05,9.26819462281798000000e-06] 
dist 198=[-1.77816530530837050000e-05,1.07808362329919500000e-05] 
dist 199=[-1.81909461777586720000e-05,1.20034073034953000000e-05] 
dist 200=[-1.82647730881837730000e-05,1.26506124447898400000e-05] 
dist 201=[-1.34657495618961600000e-05,1.29923236047529500000e-05] 
dist 202=[-1.29455141737170000000e-05,1.30476291602528800000e-05] 
dist 203=[-1.15491695893811900000e-05,1.06666203832932000000e-05] 
dist 204=[-1.12361643651140000000e-05,1.03326471283000300000e-05] 
dist 205=[-8.64910594463500000000e-06,9.57234787771463000000e-06] 
dist 206=[-8.10865343636140000000e-06,9.31283363774263000000e-06] 
dist 207=[-7.25626279893090000000e-06,8.06658359971035000000e-06] 
dist 208=[-7.00592957133550000000e-06,7.79501382750822000000e-06] 
dist 209=[-1.87048967841590000000e-06,7.01721037515441000000e-06] 
dist 210=[-1.19633673868630000000e-06,6.86730569737811000000e-06] 
dist 211=[3.19743095716950000000e-07,6.79358158446276500000e-06] 
dist 212=[6.18829369811330000000e-07,7.54416089738066000000e-06] 
dist 213=[1.79275484762342370000e-06,8.13180310614136000000e-06] 
dist 214=[1.49116293218590850000e-06,8.39823846968298000000e-06] 
dist 215=[9.64078656023102470000e-07,8.51606184495532000000e-06] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 2, 1, 2, 0, 1] 
dist 0=[84.928817393494653046  ,84.928817393494653046  ] 
dist 1=[84.248790242471930201  ,85.547689830567626737  ] 
dist 2=[82.153774930149252621  ,86.210633473426216296  ] 
dist 3=[79.344459102383980200  ,86.333427782260192817  ] 
dist 4=[75.760712538237906873  ,86.155452823055614720  ] 
dist 5=[70.924704998060579390  ,85.970875013513261037  ] 
dist 6=[63.118029862435641839  ,85.051367290233891042  ] 
dist 7=[55.110150913131836997  ,84.754914922964328599  ] 
dist 8=[49.471314445956258490  ,81.406978591297418246  ] 
dist 9=[44.491038312914950241  ,80.556840205926902589  ] 
dist 10=[39.111571116737328127  ,79.544549990989091510  ] 
dist 11=[33.891828271322034599  ,79.071210583070807784  ] 
dist 12=[29.549169672194303117  ,78.338462398059258496  ] 
dist 13=[25.020735867711160945  ,78.084379673987291803  ] 
dist 14=[19.059939178522420928  ,75.454890444897433430  ] 
dist 15=[13.236998380182068730  ,70.332030581058150928  ] 
dist 16=[8.2326638784414378807 ,31.392132926130592845  ] 
dist 17=[4.1141541803858193911 ,27.711401183483524770  ] 
dist 18=[.2596961630357882237 ,19.080560528140297350  ] 
dist 19=[-4.2380656371902597418 ,17.844357656692226511  ] 
dist 20=[-8.4335504262947254513 ,7.4892279224142161426 ] 
dist 21=[-11.082058326448489700  ,6.3809930308907186196 ] 
dist 22=[-13.103542854024297021  ,6.1355177393769344402 ] 
dist 23=[-14.797868757228808550  ,1.7091420421808126906 ] 
dist 24=[-16.154994307498908866  ,.4868492440776458039 ] 
dist 25=[-16.831798660473781973  ,-.6968477795011223201 ] 
dist 26=[-17.144584916228087160  ,-.8710906561560110855 ] 
dist 27=[-17.182770074922485962  ,-2.0737889458952083586 ] 
dist 28=[-17.744344726637870403  ,-2.2548486470380752128 ] 
dist 29=[-18.506953365306405114  ,-2.5587353249495622316 ] 
dist 30=[-18.944647681152568120  ,-2.6105079621463532281 ] 
dist 31=[-19.054253584976255640  ,-2.9502423497703338374 ] 
dist 32=[-9.9046454026367065428 ,-2.3780272036798366126 ] 
dist 33=[-9.1620978798724025842 ,-1.3434797801613232220 ] 
dist 34=[-7.3271888109457009387 ,-.3136724529331992070 ] 
dist 35=[-7.0083806199141136500 ,.9682086378045614372 ] 
dist 36=[-4.2737732121059779193 ,2.1889517603707011643 ] 
dist 37=[-3.7681427983290392349 ,2.9755042191748460489 ] 
dist 38=[-3.3408253011733315988 ,3.5898515178148356188 ] 
dist 39=[-2.7972995100020134099 ,4.1245224210533649126 ] 
dist 40=[-1.2925939306764586255 ,4.5633504662564429724 ] 
dist 41=[-.9193055577484350130 ,4.7958069200046675623 ] 
dist 42=[-.8534313532383667899 ,4.9203273482751574318 ] 
dist 43=[-.3786021872480144526 ,5.7054860388247667799 ] 
dist 44=[-.2956121799481728235 ,6.3745021547673234379 ] 
dist 45=[-.1510751287343035277 ,6.7399391682666973830 ] 
dist 46=[-.1203667681737050846 ,6.9507423279284278081 ] 
dist 47=[.32017069251860999422,7.0036345022881406151 ] 
dist 48=[.37935137855580908977,1.9366466344678628992 ] 
dist 49=[.3754347322643203374 ,1.7791479543612420775 ] 
dist 50=[.0485766372686997998 ,1.4600554678411860534 ] 
dist 51=[-.4967961579376287292 ,1.5250017372864166239 ] 
dist 52=[-1.0247404063243033311 ,1.5509794734470634316 ] 
dist 53=[-1.3651334616084002719 ,1.5601048554390154909 ] 
dist 54=[-1.6303467348739290912 ,1.5576999832333372870 ] 
dist 55=[-1.8589741964638793038 ,.4022666153396132070 ] 
dist 56=[-2.0442289214333030483 ,.2135194995122562127 ] 
dist 57=[-2.1367467336683172789 ,.1288515970473313262 ] 
dist 58=[-2.1839000238670667778 ,.1165725062035094834 ] 
dist 59=[-2.1886818533319177256 ,.0035268643558609521 ] 
dist 60=[-1.1955793299281643129 ,-.0158342525034763617 ] 
dist 61=[-1.2568948079690014888 ,-.0420043646835549409 ] 
dist 62=[-1.2883847816709212575 ,-.0465627508543109420 ] 
dist 63=[-1.2941259553538770577 ,-.1610346093948565671 ] 
dist 64=[-.81311480615326740137,-.1743026133188672152 ] 
dist 65=[-.77031287555846832833,-.1215657143226578031 ] 
dist 66=[-.6546144304696116070 ,-.0499177469396641007 ] 
dist 67=[-.6364881152623780600 ,.0425458851133171356 ] 
dist 68=[-.4305640029534974807 ,.1316043969975512135 ] 
dist 69=[-.3902880612602386667 ,.1897103802142779281 ] 
dist 70=[-.3429683916914945843 ,.2357181887997492175 ] 
dist 71=[-.3305670214971809166 ,.2766193610029755872 ] 
dist 72=[-.11709907681461603069,.3106466912557246015 ] 
dist 73=[-.0908552400822156535 ,.3292908124115327805 ] 
dist 74=[-.0866149922501850602 ,.3435824869816597731 ] 
dist 75=[-.0477698860301390777 ,.4010696193833664840 ] 
dist 76=[-.0406508762363043328 ,.4476665182539649541 ] 
dist 77=[-.0307313623260028372 ,.4711088880038760929 ] 
dist 78=[-.0278353714410584177 ,.4835256934579356412 ] 
dist 79=[.0236904129620323132 ,.4862273996165064667 ] 
dist 80=[.0300514529601005337 ,.1653938165791857025 ] 
dist 81=[.0408170550033594897 ,.1537175701081466919 ] 
dist 82=[.0300011398483162694 ,.1232247251071502501 ] 
dist 83=[-.0118745042343091296 ,.1185927489238815448 ] 
dist 84=[-.0527471466545406689 ,.0955222638306515399 ] 
dist 85=[-.0794761753092097061 ,.0976307707522264187 ] 
dist 86=[-.1006870255272110331 ,.0980103203341222504 ] 
dist 87=[-.1195988152202735817 ,.0445997445557968025 ] 
dist 88=[-.1353518851824673219 ,.0424322114280140271 ] 
dist 89=[-.1439911932137125499 ,.0383675676997584026 ] 
dist 90=[-.1489880227688735520 ,.0372601433994817303 ] 
dist 91=[-.1502434413611253360 ,.0332302934655219157 ] 
dist 92=[-.1012608586249563327 ,.0321239767388676403 ] 
dist 93=[-.1064834641789702202 ,.0304573383320881082 ] 
dist 94=[-.1092133433488314266 ,.0298752134204911725 ] 
dist 95=[-.1098291085172817464 ,.0283652552587651533 ] 
dist 96=[-.08062193309107568097,.0280205549205989567 ] 
dist 97=[-.07767884188736540975,.0280310415680686196 ] 
dist 98=[-.0691076614627691177 ,.0285139803477036078 ] 
dist 99=[-.0677826447813752356 ,.0292455631096717515 ] 
dist 100=[-.0504845022708835489 ,.0302475171725826860 ] 
dist 101=[-.0469561589693759599 ,.0316246916848633058 ] 
dist 102=[-.0314882919976120668 ,.0338517528044398620 ] 
dist 103=[-.02444996578474857395,.0360520919687066157 ] 
dist 104=[-.02125166511855345637,.0373238764034222158 ] 
dist 105=[-.0195726244547740161 ,.0381477155229766702 ] 
dist 106=[-.0190948795313322989 ,.0385659327100009092 ] 
dist 107=[-.0159124826843773543 ,.0389114458629727785 ] 
dist 108=[-.0152093812754497428 ,.0440437900770656599 ] 
dist 109=[-.0139175111989544909 ,.0468592419266942258 ] 
dist 110=[-.0135596741806814705 ,.0484879445643311188 ] 
dist 111=[-.0065754025019997743 ,.0488971745137838947 ] 
dist 112=[-.0056138129509432976 ,.01915046200470572390] 
dist 113=[-.0033029832606076221 ,.01813413115266534030] 
dist 114=[-.0028962616954425323 ,.0157218731652861877 ] 
dist 115=[-.0009586565915554935 ,.0150507915700733657 ] 
dist 116=[-.0041257211847284581 ,.0115305824117201577 ] 
dist 117=[-.0061789840053667338 ,.0108258683425057129 ] 
dist 118=[-.0077871491273246979 ,.0083015058777086682 ] 
dist 119=[-.0091831620770694671 ,.0037529077751348125 ] 
dist 120=[-.0103180496798488795 ,-.0030207735741535043 ] 
dist 121=[-.0108871088343697732 ,-.0038155547957476794 ] 
dist 122=[-.0111900208117114128 ,-.00512191558841949858] 
dist 123=[-.0112657991868105443 ,-.00450185125047886293] 
dist 124=[-.0083971809859499370 ,-.00378435894170924817] 
dist 125=[-.0088722185631068891 ,-.00324047165799264736] 
dist 126=[-.0091215403411723618 ,-.00272679411834388925] 
dist 127=[-.0091648252568887080 ,-.00212924997202683244] 
dist 128=[-.0061393035805603610 ,-.0015327010384582672 ] 
dist 129=[-.0058588088155791048 ,-.0010228478740471074 ] 
dist 130=[-.0050737894283966614 ,-.0004849942944018109 ] 
dist 131=[-.0049484713699362966 ,.0002231047425635871 ] 
dist 132=[-.0034587477509619086 ,.0009089894754655999 ] 
dist 133=[-.0031604546698914288 ,.0013585009709610125 ] 
dist 134=[-.0028190496679231448 ,.0017159334052828507 ] 
dist 135=[-.0027240532962172534 ,.0020354421154546321 ] 
dist 136=[.00022035182755945257,.0023018419904956047 ] 
dist 137=[.00057142395017258930,.0024479502841284698 ] 
dist 138=[.0011553440938312425 ,.0025698678086048284 ] 
dist 139=[.0012876843557713370 ,.0030308362681860305 ] 
dist 140=[.00156561614337856198,.0034056357107329968 ] 
dist 141=[.00138001393412547196,.0035935155676024268 ] 
dist 142=[.00119390696199275399,.0036935176538075958 ] 
dist 143=[.00096173307507787594,.0037185944133952361 ] 
dist 144=[.00072128386663740494,.00124824815769561724] 
dist 145=[.00050221354845895425,.00116500913088658089] 
dist 146=[.00025950970675101834,.00094197407312119473] 
dist 147=[-7.50078874461528200000e-05,.00090988484328186211] 
dist 148=[-.00040250504829367827,.0005246051131707546 ] 
dist 149=[-.00061728999225065769,.0004512827556979835 ] 
dist 150=[-.00078819066465579956,.0003691208028031778 ] 
dist 151=[-.00094108690084138335,.0003547308694122986 ] 
dist 152=[-.0010686093917135750 ,-.0002979318154303509 ] 
dist 153=[-.0011385531778440476 ,-.0003734000767785305 ] 
dist 154=[-.0011789394593119473 ,-.00043847718514614775] 
dist 155=[-.0011888551962312826 ,-.00038753631955919093] 
dist 156=[-.0007631523186164106 ,-.00032719926394656090] 
dist 157=[-.0008115354303694196 ,-.00028092063535665906] 
dist 158=[-.0008394298017809150 ,-.00023669097051913727] 
dist 159=[-.0008461846880106872 ,-.00018448823746475225] 
dist 160=[-.0005229995770646262 ,-.00013196694820985124] 
dist 161=[-.0004954049471167407 ,-8.64604444717487900000e-05] 
dist 162=[-.0004228478266286076 ,-3.79364968122014800000e-05] 
dist 163=[-.0004087554640841833 ,2.65995927814040000000e-05] 
dist 164=[-.00028333179235102941,8.90978691437621600000e-05] 
dist 165=[-.00025846085816094915,.00012951755359411151] 
dist 166=[-.00022127404138494361,.00016104025650654757] 
dist 167=[-.00021028027630192366,.00018814134115788230] 
dist 168=[2.89938282491704300000e-06,.00021002723103337884] 
dist 169=[3.04248072120511370000e-05,.00022080124847701604] 
dist 170=[8.59514624344254000000e-05,.0002639507357644083 ] 
dist 171=[9.92706738273347000000e-05,.0003149058414451761 ] 
dist 172=[.00011009179812664168,.0003573961221259505 ] 
dist 173=[9.33673306008758200000e-05,.0003806781342014174 ] 
dist 174=[7.69832330285545700000e-05,.0003940887407943615 ] 
dist 175=[5.70727303311770500000e-05,.0003973024629278912 ] 
dist 176=[3.67296002835820400000e-05,.00011105902704441530] 
dist 177=[1.86212674403639600000e-05,.00010406876669002622] 
dist 178=[-1.09401143508920900000e-06,8.51608422216745900000e-05] 
dist 179=[-2.78333759264527000000e-05,8.24248808990914400000e-05] 
dist 180=[-5.38083438425711910000e-05,4.91310603084717100000e-05] 
dist 181=[-7.04837689755354600000e-05,4.27410930592316100000e-05] 
dist 182=[-8.33473222875936400000e-05,3.56437574195632800000e-05] 
dist 183=[-9.41575646872272500000e-05,3.43505924964699400000e-05] 
dist 184=[-.00010269758516747251,-1.84852442321010000000e-05] 
dist 185=[-.00010652877743069219,-1.59229324253062873000e-05] 
dist 186=[-.00010830310612599709,-1.04991590714396008500e-05] 
dist 187=[-.00010865972154460823,0                     ] 
dist 188=[-7.46042754522167000000e-05,-1.71522298428601000000e-05] 
dist 189=[-7.81468707423145000000e-05,-1.13709133245557000000e-05] 
dist 190=[-7.99182697000128000000e-05,-5.85300378875120000000e-06] 
dist 191=[-8.01777150513501000000e-05,6.48528984398500000000e-07] 
dist 192=[-6.16583851629783000000e-05,7.18272799363050000000e-06] 
dist 193=[-5.93903076118912000000e-05,1.28315921520344000000e-05] 
dist 194=[-5.29822092679678000000e-05,1.88432823314857000000e-05] 
dist 195=[-5.17185105866100000000e-05,2.68219530914930000000e-05] 
dist 196=[-3.90407382380054000000e-05,3.44926077803321000000e-05] 
dist 197=[-3.64011367064256000000e-05,3.92793747578516000000e-05] 
dist 198=[-3.28544554622340000000e-05,4.28148118734319000000e-05] 
dist 199=[-3.16145850011109000000e-05,4.55076010184597000000e-05] 
dist 200=[-5.20957193777250000000e-06,4.74174067518149000000e-05] 
dist 201=[-1.87736845425750000000e-06,4.78704337674588000000e-05] 
dist 202=[5.23883970156681700000e-06,4.77599591881219000000e-05] 
dist 203=[5.88734946273983800000e-06,4.76841028217896000000e-05] 
dist 204=[6.20913118029432400000e-06,4.26875568638164000000e-05] 
dist 205=[5.31923637075398730000e-06,4.15103572450451000000e-05] 
dist 206=[3.50825991907613085000e-06,3.91162528719970400000e-05] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 1, 1, 0, 0, 2] 
dist 0=[78.140222412218277124  ,78.140222412218277124  ] 
dist 1=[77.416819247151110328  ,79.047441837219775041  ] 
dist 2=[75.436954693387786515  ,80.049210308574134730  ] 
dist 3=[72.235683004536714416  ,80.622154838598455865  ] 
dist 4=[66.833559799577831647  ,80.990639575405970206  ] 
dist 5=[61.205088131692305844  ,81.176282996954445929  ] 
dist 6=[57.100668392478349657  ,81.198257364315552043  ] 
dist 7=[53.328870121337905960  ,80.459018115651218934  ] 
dist 8=[49.028103489389688399  ,74.671741864554543910  ] 
dist 9=[44.720383796772662068  ,73.638261670033891693  ] 
dist 10=[40.921066734578758959  ,71.939785959104807212  ] 
dist 11=[36.769731650472656606  ,71.429165708591334510  ] 
dist 12=[31.057577974221224666  ,69.881199244401732244  ] 
dist 13=[25.362812958346116803  ,69.333104957931148862  ] 
dist 14=[21.280912110449259400  ,68.833634857436105156  ] 
dist 15=[16.785589518263417018  ,67.619914699312827212  ] 
dist 16=[11.068704208496377220  ,27.768676136554696767  ] 
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dist 182=[-6.85018088100026010000e-05,4.68056121872249700000e-05] 
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dist 186=[-.00012734401929650689,1.72574859132085300000e-05] 
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dist 193=[-4.22280307665768000000e-05,-1.25473212983011500000e-05] 
dist 194=[-4.36651315411602000000e-05,-5.66278433618340000000e-06] 
dist 195=[-4.43572871784327000000e-05,2.31547040811400000000e-07] 
dist 196=[-4.43598100431143000000e-05,6.45849102605820000000e-06] 
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dist 198=[-3.52449710381745000000e-05,2.25405249371662000000e-05] 
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dist 200=[-3.11434326495940000000e-05,3.10193773701611000000e-05] 
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dist 206=[-5.62844367639508000000e-06,3.01871341813151800000e-05] 
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dist 208=[-8.35539901278660000000e-07,2.64984956437156800000e-05] 
dist 209=[3.30584417260828250000e-06,2.56349287851402200000e-05] 
dist 210=[2.78488736602000000000e-06,2.15467095742154900000e-05] 
dist 211=[1.81626260207191920000e-06,2.06645914899553500000e-05] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 1, 1, 2, 1, 2] 
dist 0=[77.410669157431157784  ,77.410669157431157784  ] 
dist 1=[75.315533595900300371  ,78.783577239484321279  ] 
dist 2=[72.290437578339986577  ,79.751476408936152098  ] 
dist 3=[67.206313760371579128  ,80.230310163081856111  ] 
dist 4=[61.904133378140507184  ,80.442709969084873865  ] 
dist 5=[58.008959124180212086  ,80.347264763334267164  ] 
dist 6=[54.400292699476292472  ,80.111985869969600057  ] 
dist 7=[50.241846677192125561  ,79.843855666464381358  ] 
dist 8=[46.051724077376789922  ,77.464211331874903177  ] 
dist 9=[42.316897539504141970  ,71.897603183874749834  ] 
dist 10=[38.203257060395285661  ,70.686886261725084936  ] 
dist 11=[32.501777516277004233  ,68.843059276798884915  ] 
dist 12=[26.798941188665795759  ,68.266270498490662534  ] 
dist 13=[22.679947149931533738  ,67.342126590193206950  ] 
dist 14=[18.936063339244366474  ,66.714357236726511712  ] 
dist 15=[14.729983671870407270  ,66.269676597001440673  ] 
dist 16=[10.553312735313617127  ,62.696610133748410842  ] 
dist 17=[6.9267080462857768889 ,21.767542445961874861  ] 
dist 18=[3.0114444135714375405 ,20.257371230067381570  ] 
dist 19=[-2.3172249968746832172 ,19.925050387963373588  ] 
dist 20=[-7.5032626966040472680 ,9.045875926639446918  ] 
dist 21=[-10.849719112964864757  ,5.6502145481063724462 ] 
dist 22=[-13.488200033947500912  ,2.8456362733053986316 ] 
dist 23=[-15.850034395385145205  ,2.4374116924467342433 ] 
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dist 32=[-18.567333330123181321  ,-5.7107729050509282175 ] 
dist 33=[-9.6033954448459963334 ,-4.4399954146273945308 ] 
dist 34=[-8.6119044122170524481 ,-3.1076292376732012088 ] 
dist 35=[-7.3390741223674199270 ,-1.9805576251676609053 ] 
dist 36=[-5.8178562187138374122 ,-.7971879510097300437 ] 
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dist 44=[.4608152416558669851 ,6.0761660646474859621 ] 
dist 45=[.6181244710828368178 ,6.6309274780313650976 ] 
dist 46=[.8221605698739831997 ,6.9330138380164296891 ] 
dist 47=[.8139172222788439363 ,7.1064954913135218634 ] 
dist 48=[.7520590963035924978 ,7.1485723121042735388 ] 
dist 49=[.6173882695078803241 ,3.6420747297961973544 ] 
dist 50=[.4056685343975056957 ,3.3542174045821807516 ] 
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dist 52=[-.3512284555350540627 ,2.5239305339595949011 ] 
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dist 63=[-3.5570528047685822270 ,-.31468996256885689521] 
dist 64=[-3.5699748049945309699 ,0                     ] 
dist 65=[-.5250249950252168673 ,-.3212114684344241322 ] 
dist 66=[-.5267686719112004751 ,-.23075851037869378875] 
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dist 68=[-.2844064491188532373 ,-.06760315358786111718] 
dist 69=[-.2742472523816283004 ,.0454408482671780341 ] 
dist 70=[-.20954115730689885034,.15503984821182208908] 
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dist 73=[-.1072501635858031596 ,.3282982009379443817 ] 
dist 74=[-.0856541521838798398 ,.3667730642737191855 ] 
dist 75=[-.0795306187275885643 ,.3861312339937074952 ] 
dist 76=[.0309844970565786535 ,.3963926408614915614 ] 
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dist 80=[.0922840591507454800 ,.1972738867698281877 ] 
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dist 90=[-.0876193501156196793 ,.0307462572815640095 ] 
dist 91=[-.0923698402996137574 ,.0288903049173818055 ] 
dist 92=[-.0950410944454076928 ,.0121018308432887405 ] 
dist 93=[-.0955305438828272920 ,.0093349961384516928 ] 
dist 94=[-.08501346253498042785,.0049183671358730925 ] 
dist 95=[-.08324633151256228436,.0038091879199479859 ] 
dist 96=[-.07817940927233151287,.0023291822993417283 ] 
dist 97=[-.0765814482373921825 ,.0029514061259461601 ] 
dist 98=[-.0655326938534901282 ,.0047582219434355453 ] 
dist 99=[-.0586767154289719769 ,.0086220164455960657 ] 
dist 100=[-.03348050910141790703,.0127494552419288156 ] 
dist 101=[-.03212475416658274567,.0156066816310207524 ] 
dist 102=[-.0284476163637724504 ,.0180494716609518444 ] 
dist 103=[-.0277326765876590456 ,.02114135602472785542] 
dist 104=[-.0209232285005284855 ,.02681562310452624668] 
dist 105=[-.0195274524548905929 ,.0318803226578028540 ] 
dist 106=[-.0176011457703093241 ,.0361010356112345946 ] 
dist 107=[-.0169571742216707776 ,.0384165500151509077 ] 
dist 108=[-.0034619948013346916 ,.0397561046080555927 ] 
dist 109=[-.0017595102882185263 ,.0400926891695732869 ] 
dist 110=[.0021983403496067045 ,.02361763809886372427] 
dist 111=[.0028255031200789417 ,.02272672118283992450] 
dist 112=[.0077233390981402659 ,.0208184255368308735 ] 
dist 113=[.00619457593828556791,.0202172526919928543 ] 
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dist 117=[-.00079919494651934923,.00602101281813304607] 
dist 118=[-.00283620830625528890,.00468569999241636094] 
dist 119=[-.00416163651041860583,.00449377962602115037] 
dist 120=[-.00520529474636510342,.0023194842794220103 ] 
dist 121=[-.00612107693824994468,.0019148180855827268 ] 
dist 122=[-.00687273847011799907,.0014439963877671319 ] 
dist 123=[-.00726329594130056383,.0013633593759656247 ] 
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dist 128=[-.0043696131738339797 ,-.00316752444531691494] 
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dist 149=[-5.90043006364470000000e-05,.00054383627928957545] 
dist 150=[-.00024552195811068102,.00043143851689379757] 
dist 151=[-.00036780950851377395,.00041470897978951424] 
dist 152=[-.00046508444103463283,.00022852628975531827] 
dist 153=[-.00055208200259203198,.00019349293728767868] 
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dist 156=[-.00068742030942927709,-.00015201078144089015] 
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dist 159=[-.00040607984835466244,-.00027174322673749278] 
dist 160=[-.00038744943406453889,-.00031586781547224729] 
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dist 162=[-.00041867777978224248,-.00019735646222348184] 
dist 163=[-.00042046967536965762,-.00013759754495014914] 
dist 164=[-.00027665372331258818,-7.13050652246045220000e-05] 
dist 165=[-.00026340899036451992,2.01650579936250500000e-05] 
dist 166=[-.00022680563105824101,.00010974252312862588] 
dist 167=[-.00022097029069087435,.00016850815700344704] 
dist 168=[-.00015289064102011877,.00021528020948738429] 
dist 169=[-.00013933608972787931,.00025714038849235044] 
dist 170=[-.00012366273729833902,.00029205916458188247] 
dist 171=[-.00011930756190110777,.00031121358185498743] 
dist 172=[1.25256743174482330000e-05,.00032227419700989459] 
dist 173=[2.82540728687299760000e-05,.00032498943055106185] 
dist 174=[5.63024695423850400000e-05,.00012057532119640729] 
dist 175=[6.20847204689518500000e-05,.00014105284313073125] 
dist 176=[6.47624378167324460000e-05,.00015767609121790156] 
dist 177=[5.05322086344753420000e-05,.00016601267302977725] 
dist 178=[3.62009661652571900000e-05,.00017042497011488379] 
dist 179=[2.37625261605023400000e-05,.00017143089816300611] 
dist 180=[1.04820124925388500000e-05,5.65945289059869000000e-05] 
dist 181=[-7.20182421505563000000e-06,5.25726006239448000000e-05] 
dist 182=[-2.43324638487563500000e-05,4.19250331518754900000e-05] 
dist 183=[-3.54129211236459800000e-05,4.03869074807961300000e-05] 
dist 184=[-4.40550890188268500000e-05,2.23851467133450800000e-05] 
dist 185=[-5.14850533477964700000e-05,1.89830375984183700000e-05] 
dist 186=[-5.74868916405814900000e-05,1.51055037957031200000e-05] 
dist 187=[-6.04473699014153900000e-05,1.44130033532596800000e-05] 
dist 188=[-6.19746184718029100000e-05,-1.51782686690051800000e-05] 
dist 189=[-6.22738186377401400000e-05,-1.86061938393772500000e-05] 
dist 190=[-4.50782729673483660000e-05,-2.55878209597459200000e-05] 
dist 191=[-4.32705323338452910000e-05,-2.56059271816666100000e-05] 
dist 192=[-3.81139321433024360000e-05,-2.11265704640044670000e-05] 
dist 193=[-3.86850509281699600000e-05,-1.56744023478588970000e-05] 
dist 194=[-3.99220698577921100000e-05,-1.00993074826265880000e-05] 
dist 195=[-4.01982077049299300000e-05,-5.13013141463726700000e-06] 
dist 196=[-2.46028252059050210000e-05,2.85143477524951000000e-07] 
dist 197=[-2.32659121706894400000e-05,7.63576692437010000000e-06] 
dist 198=[-1.97518072111054900000e-05,1.47779792585532490000e-05] 
dist 199=[-1.90947837989691000000e-05,1.93644357000739670000e-05] 
dist 200=[-1.30436151045969900000e-05,2.29035813284331880000e-05] 
dist 201=[-1.18501499913714700000e-05,2.58793542449105970000e-05] 
dist 202=[-1.01287388501569800000e-05,2.82304673647788920000e-05] 
dist 203=[-9.60207050984342000000e-06,2.92843797549495440000e-05] 
dist 204=[5.29138233867530000000e-07,2.97725200210690870000e-05] 
dist 205=[0                     ,2.98727093535870600000e-05] 
dist 206=[4.36547800160397500000e-06,1.26200353230092300000e-05] 
dist 207=[4.97580689001925600000e-06,1.49777330845854800000e-05] 
dist 208=[6.83847641976721800000e-06,1.69432272409006400000e-05] 
dist 209=[5.60421668152036000000e-06,1.80207018538373300000e-05] 
dist 210=[4.14713607181750000000e-06,1.86424006218009100000e-05] 
dist 211=[2.83679966281020000000e-06,1.87942563451179000000e-05] 
dist 212=[1.39928689139560000000e-06,6.19146180953028000000e-06] 
dist 213=[-5.63955386771700000000e-07,5.86881656507691000000e-06] 
dist 214=[-2.47691708519210000000e-06,5.07678079458250000000e-06] 
dist 215=[-3.71448218748400000000e-06,4.87158149207830000000e-06] 
dist 216=[-4.67987571784060000000e-06,3.62947823391527000000e-06] 
dist 217=[-5.51008585223860000000e-06,3.37816040235286000000e-06] 
dist 218=[-6.18435709317300000000e-06,2.87378300070097000000e-06] 
dist 219=[-6.52933009173950000000e-06,2.73488580481658000000e-06] 
dist 220=[-6.71077456967890000000e-06,8.93855027522400000000e-07] 
dist 221=[-6.73645311658380000000e-06,6.19763214762000000000e-07] 
dist 222=[-6.32195850972209000000e-06,1.12605791717900000000e-07] 
dist 223=[-6.21867161720169000000e-06,-2.18274732290000000000e-09] 
dist 224=[-5.92841210577443800000e-06,-2.96357166991100000000e-07] 
dist 225=[-5.80438915341262500000e-06,-3.08224006950100000000e-07] 
dist 226=[-5.12131690530433000000e-06,-2.14633957004700000000e-07] 
dist 227=[-4.66667843076515000000e-06,4.56823591604000000000e-08] 
dist 228=[-2.71296710684186000000e-06,3.36041246155700000000e-07] 
dist 229=[-2.61338579645603000000e-06,6.56219949676450000000e-07] 
dist 230=[-2.33473288582316000000e-06,1.18597312301917000000e-06] 
dist 231=[-2.27818540909715000000e-06,1.52104565763548000000e-06] 
dist 232=[-1.73250761372941000000e-06,1.77371686346868000000e-06] 
dist 233=[-1.61862631213389000000e-06,1.97568073152917000000e-06] 
dist 234=[-1.46090633945702000000e-06,2.13354809702914000000e-06] 
dist 235=[-1.40745573475811000000e-06,2.21077757653773000000e-06] 
dist 236=[-2.73528157010830000000e-07,2.24414205694815000000e-06] 
dist 237=[-1.29464277156460000000e-07,2.24617799902847000000e-06] 
dist 238=[1.97165266762550000000e-07,1.93191772071416000000e-06] 
dist 239=[2.55465363438440000000e-07,1.87398958061452000000e-06] 
dist 240=[3.23908657297291200000e-07,1.75221554020981000000e-06] 
dist 241=[2.74431850930299500000e-07,1.73642930238387600000e-06] 
dist 242=[1.79678617529278260000e-07,1.76369784262588300000e-06] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 2, 2, 0, 2, 0, 1] 
dist 0=[81.207445212251630541  ,81.207445212251630541  ] 
dist 1=[80.417107195407702381  ,81.816016977852731688  ] 
dist 2=[77.872583931138988872  ,82.548828864361957113  ] 
dist 3=[74.679378301096890592  ,82.705840529712374202  ] 
dist 4=[70.866089613423456901  ,82.391553127781503991  ] 
dist 5=[65.872147327238970581  ,82.155772274511411886  ] 
dist 6=[57.967183677218320853  ,81.543023866237434012  ] 
dist 7=[49.931619438706269977  ,81.227397604954596296  ] 
dist 8=[44.416123315459872445  ,79.556543110434880441  ] 
dist 9=[39.693715532355491904  ,79.250103085960616852  ] 
dist 10=[34.822163490084849141  ,78.932338439799328344  ] 
dist 11=[30.228523108885755808  ,78.653582582698441179  ] 
dist 12=[26.614320204117999864  ,78.140868885030063797  ] 
dist 13=[23.023596913379833158  ,77.990203415135582911  ] 
dist 14=[18.522099362446038750  ,75.454439815838475006  ] 
dist 15=[14.211990764880862373  ,70.470528194699362792  ] 
dist 16=[11.384253716358048313  ,33.138406400004793284  ] 
dist 17=[9.0943877700200522996 ,29.593437181624539827  ] 
dist 18=[5.6816542108127496731 ,21.374921252525849487  ] 
dist 19=[.0508769334840205333 ,20.068595216051932570  ] 
dist 20=[-5.3366719685156179007 ,9.5206925836129525013 ] 
dist 21=[-8.8385538251163483821 ,7.6950022468257510984 ] 
dist 22=[-11.628747622731921203  ,4.9313956560119119966 ] 
dist 23=[-14.175911848567076568  ,4.2511402483845236076 ] 
dist 24=[-16.370675082843486586  ,-.57042214927070278944] 
dist 25=[-17.754421057417030680  ,-1.3580725679563935223 ] 
dist 26=[-18.808401899696912236  ,-1.4756096713657009333 ] 
dist 27=[-19.687051132181697914  ,-2.0627234388518479081 ] 
dist 28=[-20.386140222254864138  ,-2.1488664278734206920 ] 
dist 29=[-20.723754619344518857  ,-2.1673884094107624651 ] 
dist 30=[-20.861804704621869004  ,-2.0555090761545664408 ] 
dist 31=[-20.765214409280113464  ,-1.9089723108805772969 ] 
dist 32=[-6.6985091856904392966 ,-1.7746172118382833733 ] 
dist 33=[-6.0603676286850265349 ,-1.3499300540123613712 ] 
dist 34=[-4.4791702386810596477 ,-.7755277723900957958 ] 
dist 35=[-4.2497349104230620154 ,-.0386276791338381848 ] 
dist 36=[-1.9312312112822184563 ,.6680257489541570751 ] 
dist 37=[-1.8777008669356103357 ,1.1222180292556280044 ] 
dist 38=[-1.8718100502239603544 ,1.4751698678897339891 ] 
dist 39=[-.9013902303045247817 ,1.7786438206852870421 ] 
dist 40=[-.1576590869802214202 ,2.1367923287169544537 ] 
dist 41=[.0529823946528255292 ,2.8108264516254902200 ] 
dist 42=[.0835260509343095575 ,3.3363080484272008532 ] 
dist 43=[.3105124265878303946 ,3.7927716352811922553 ] 
dist 44=[.3452318298606856232 ,4.1674000679607692596 ] 
dist 45=[.4010101378891940221 ,4.3667173027517418469 ] 
dist 46=[.4104319946400838991 ,4.4749508853310163668 ] 
dist 47=[.4911066861448686286 ,4.4910986697983686155 ] 
dist 48=[.4963064737167909011 ,2.5517725827243897642 ] 
dist 49=[.37362623303605232386,2.3878720924795665630 ] 
dist 50=[.20630162456192151283,1.9662397383364370843 ] 
dist 51=[-.0172187533872137742 ,1.8962522269286158759 ] 
dist 52=[-.23333727553747106333,1.2121198498109805855 ] 
dist 53=[-.37125074753205762046,1.0820367107236955559 ] 
dist 54=[-.47688718140895822144,.9075751631062485081 ] 
dist 55=[-.56456740461692631856,.8521898631448636595 ] 
dist 56=[-.67840427976429643161,.24076056905053544255] 
dist 57=[-.96803640232133823387,.1784877701719445452 ] 
dist 58=[-1.1950332184562682659 ,.1686740955650638653 ] 
dist 59=[-1.3933465618114183581 ,.0855760329122976209 ] 
dist 60=[-1.5562417608926202918 ,.0709449778262443819 ] 
dist 61=[-1.6421943046377467694 ,.0497847519408904657 ] 
dist 62=[-1.6883132796605015000 ,.0441653852578086391 ] 
dist 63=[-1.6977622105811792217 ,-.0485627212759951055 ] 
dist 64=[-.5067398720709952325 ,-.0598787437835691431 ] 
dist 65=[-.4670384887134821080 ,-.0843257729869850740 ] 
dist 66=[-.3643169926930771352 ,-.0517181539585058897 ] 
dist 67=[-.3494993686181239471 ,.0006333406438887543 ] 
dist 68=[-.2383096330593036325 ,.0513323250990296849 ] 
dist 69=[-.2394502203498345085 ,.0845187912388896284 ] 
dist 70=[-.2388984027011814090 ,.1108753590104575364 ] 
dist 71=[-.1111712154618914232 ,.1343976714916214535 ] 
dist 72=[-.0488776932684212502 ,.1539988706835734814 ] 
dist 73=[-.0317144534903786772 ,.1975743784354208672 ] 
dist 74=[-.0288651923015579079 ,.2424180470735385794 ] 
dist 75=[-.0065847464020496504 ,.2821287417611208503 ] 
dist 76=[-.0027369148365402976 ,.3150795922986802063 ] 
dist 77=[.0035171027535990800 ,.3330091372024957764 ] 
dist 78=[.0049313213753735255 ,.3432155609133654606 ] 
dist 79=[.0251833548132253154 ,.3454149034700001559 ] 
dist 80=[.0278032849580848487 ,.2037997850184908541 ] 
dist 81=[.0317564180694019101 ,.19187436443716853349] 
dist 82=[.02100105957674321109,.16100051242329988439] 
dist 83=[-.00147931783417847150,.1553674180503319048 ] 
dist 84=[-.02349165886962348134,.1040856697177965803 ] 
dist 85=[-.03792989274164421603,.0941393335687209674 ] 
dist 86=[-.04941932160659295178,.0796852263580086412 ] 
dist 87=[-.05970005416526748212,.0753794427403987377 ] 
dist 88=[-.0682765271019799882 ,.04426773488309353970] 
dist 89=[-.0797683590303913690 ,.0403469125799005251 ] 
dist 90=[-.1002921941125514416 ,.0390607979124856417 ] 
dist 91=[-.1184747143685412869 ,.0330429415581158834 ] 
dist 92=[-.1335437917855373631 ,.0317279776431492260 ] 
dist 93=[-.1416750984277086685 ,.0286851238659851717 ] 
dist 94=[-.1462034189869601833 ,.0276976182713309563 ] 
dist 95=[-.1471066445076777014 ,.0172397924759065255 ] 
dist 96=[-.0503181070355471327 ,.0155657769513538138 ] 
dist 97=[-.0478348093796426614 ,.0117546924640889822 ] 
dist 98=[-.0415568840305392166 ,.0107453549788392161 ] 
dist 99=[-.0401428931090833944 ,.0057167517036615737 ] 
dist 100=[-.0299459483560854699 ,.0047441838360141899 ] 
dist 101=[-.0279221392908408002 ,.00683219939052889941] 
dist 102=[-.0201335131553706197 ,.00889844390256199195] 
dist 103=[-.01368611501881429991,.01071901022167273800] 
dist 104=[-.01299651624347190173,.01221704276318193406] 
dist 105=[-.0116057384572955077 ,.0167868583927988816 ] 
dist 106=[-.0112067128130368166 ,.0207419105556792776 ] 
dist 107=[-.0096122188896427473 ,.0241138289386934443 ] 
dist 108=[-.0092367059093200382 ,.0268366355990142466 ] 
dist 109=[-.0084396271555267960 ,.0282083496518752624 ] 
dist 110=[-.0081897888269183076 ,.0289175816446020527 ] 
dist 111=[-.0071308236293447923 ,.0290031661832601337 ] 
dist 112=[-.0068357987767617128 ,.02235446187396983149] 
dist 113=[-.0066931561132220827 ,.02161691862874472280] 
dist 114=[-.0067199240867739541 ,.0194636458114103335 ] 
dist 115=[-.0068501828900657138 ,.0190869473419096209 ] 
dist 116=[-.0071198047474268830 ,.0146634743864604985 ] 
dist 117=[-.0075390468853179474 ,.0137436074707680894 ] 
dist 118=[-.0082651920275460894 ,.0096650562901722957 ] 
dist 119=[-.0089960074883383544 ,.00386528239997183332] 
dist 120=[-.0094340507415989246 ,-.00240198486802626398] 
dist 121=[-.0097370771610667466 ,-.00251531878581709463] 
dist 122=[-.0099307462270728317 ,-.00247463870594803407] 
dist 123=[-.0100377320708540901 ,-.00221445439865479086] 
dist 124=[-.0100077570265115143 ,-.00190366095156736493] 
dist 125=[-.00987963117299722264,-.00166163545321501517] 
dist 126=[-.00977706394920075149,-.00142722997781612033] 
dist 127=[-.00908263580623749735,-.00114659717655037249] 
dist 128=[-.00432786890305012767,-.00086248450863019286] 
dist 129=[-.00401510115551774847,-.00061415554958705595] 
dist 130=[-.00318990952165615788,-.00034774876492243159] 
dist 131=[-.00307127853194215403,8.35847355422318000000e-06] 
dist 132=[-.0016874754185972863 ,.00035469156662575738] 
dist 133=[-.0014270431867175028 ,.00058224651476286299] 
dist 134=[-.0011297246766173244 ,.00076361914349409753] 
dist 135=[-.0010783257690052534 ,.00092624513953187182] 
dist 136=[.00094165162870222390,.0011723162508544914 ] 
dist 137=[.00096629943213462237,.0016825990141233207 ] 
dist 138=[.00094730561107575457,.0020877532352675078 ] 
dist 139=[.00086427959087988162,.0024492599669967689 ] 
dist 140=[.00076531604298033964,.0027504823296360177 ] 
dist 141=[.00068291966258552812,.0029157184219000776 ] 
dist 142=[.00059808283673792127,.0030113031329750132 ] 
dist 143=[.00048936924975150500,.0030353189389870191 ] 
dist 144=[.00037544846564378232,.00181701344533027471] 
dist 145=[.00026987609240342705,.00171429762450513873] 
dist 146=[.00015158728072815367,.00144757774687487025] 
dist 147=[-1.29387460534477900000e-05,.00139669780602136147] 
dist 148=[-.00017441025563935024,.00094788910738479308] 
dist 149=[-.00028055693585235513,.00085989846763778777] 
dist 150=[-.00036520151562175722,.00072771098941918338] 
dist 151=[-.00044114400172576945,.00068931278914411592] 
dist 152=[-.00050456066441030751,-4.31054191062263700000e-05] 
dist 153=[-.00073881048320835327,-.00013760591756154300] 
dist 154=[-.00093477542444347242,-.00020621412654478444] 
dist 155=[-.0011098474093831816 ,-.00018517796459519152] 
dist 156=[-.0012558017533650372 ,-.00015945301418399987] 
dist 157=[-.0013358964666715135 ,-.00013922230087193912] 
dist 158=[-.0013822409743028903 ,-.00011943707490752054] 
dist 159=[-.0013938862781103358 ,-9.54741162351624350000e-05] 
dist 160=[-.00038263797989715152,-7.10644097654781200000e-05] 
dist 161=[-.00035645307934661968,-4.94967774593717800000e-05] 
dist 162=[-.00028709555741521360,-2.61663605395299000000e-05] 
dist 163=[-.00027675386631882439,5.26066578151211000000e-06] 
dist 164=[-.00015906806620854561,3.58007463519943500000e-05] 
dist 165=[-.00013672131048235844,5.56051068852053900000e-05] 
dist 166=[-.00011045674270892086,7.10939678122546700000e-05] 
dist 167=[-.00010490473895194978,8.44685058166744700000e-05] 
dist 168=[7.04808034355842400000e-05,.00010248102316813091] 
dist 169=[7.19506289392226000000e-05,.00014869007861273781] 
dist 170=[6.97510566182201000000e-05,.00018507923556131109] 
dist 171=[6.20182709599550300000e-05,.00021700676892743563] 
dist 172=[5.30091832906162400000e-05,.00024320250218766932] 
dist 173=[4.57325560325323000000e-05,.00025678350234817175] 
dist 174=[3.84365867378919450000e-05,.00026390798857326027] 
dist 175=[2.93474034058551710000e-05,.00026511354664224082] 
dist 176=[1.99539101941922670000e-05,.00017825842784109209] 
dist 177=[1.14458217336934930000e-05,.00017015959985273226] 
dist 178=[2.06967450257060100000e-06,.00014747193105876500] 
dist 179=[-1.07783291706207200000e-05,.00014383884305002332] 
dist 180=[-2.32997437101958210000e-05,.00010066094697239178] 
dist 181=[-3.13775518423396430000e-05,9.20002676043491000000e-05] 
dist 182=[-3.76474312080870870000e-05,8.20890576267975590000e-05] 
dist 183=[-4.29779630728140110000e-05,7.93024675009733550000e-05] 
dist 184=[-4.72192035294013650000e-05,-6.47593705304323900000e-06] 
dist 185=[-6.02780450739611800000e-05,-6.53018785704800020000e-06] 
dist 186=[-7.57498937987857100000e-05,-4.37180711943317172000e-06] 
dist 187=[-8.91857230316351000000e-05,0                     ] 
dist 188=[-.00010010811243701126,-1.53909171383328600000e-05] 
dist 189=[-.00010557881533212519,-1.35358072098123400000e-05] 
dist 190=[-.00010848612761823990,-1.17026826206391000000e-05] 
dist 191=[-.00010920851247631986,-9.45573522659214000000e-06] 
dist 192=[-3.66162438336349500000e-05,-7.15253548776360000000e-06] 
dist 193=[-3.41660508641619000000e-05,-5.09523586062440000000e-06] 
dist 194=[-2.76161498641764800000e-05,-2.85135698101080000000e-06] 
dist 195=[-2.66613228814197000000e-05,1.94421515857500000000e-07] 
dist 196=[-1.53714547419806700000e-05,3.15943432796500000000e-06] 
dist 197=[-1.32203708076492000000e-05,5.08220490700570000000e-06] 
dist 198=[-1.07769183544417800000e-05,6.58582554774070000000e-06] 
dist 199=[-1.03155092291712600000e-05,7.88361209358370000000e-06] 
dist 200=[6.63740749115680000000e-06,9.29504600009139000000e-06] 
dist 201=[6.84214369639680000000e-06,1.37203491664233100000e-05] 
dist 202=[6.70593213943851000000e-06,1.72294286721301300000e-05] 
dist 203=[6.07185081306231000000e-06,2.03485011591479300000e-05] 
dist 204=[5.31966653352658000000e-06,2.29356701779101500000e-05] 
dist 205=[4.71368194543796000000e-06,2.43283805680244800000e-05] 
dist 206=[4.10747287671191000000e-06,2.50975967610411400000e-05] 
dist 207=[3.35419374572899700000e-06,2.52413298345982600000e-05] 
dist 208=[2.57684099729044000000e-06,1.61399520163127540000e-05] 
dist 209=[1.87477937103879000000e-06,1.53358855320714600000e-05] 
dist 210=[1.10292355859706000000e-06,1.31652336469528100000e-05] 
dist 211=[4.78799571995100000000e-08,1.27747662679208500000e-05] 
dist 212=[-9.81174909867340000000e-07,8.86041685927165000000e-06] 
dist 213=[-1.64971343013753000000e-06,8.08011432002087000000e-06] 
dist 214=[-2.31367529426089000000e-06,7.03611435288462000000e-06] 
dist 215=[-3.19932458605352000000e-06,6.68504181749495000000e-06] 
dist 216=[-4.08508883822176000000e-06,-1.46487899281280000000e-07] 
dist 217=[-6.22386034970417000000e-06,-9.67364270428110000000e-07] 
dist 218=[-7.92603822039318000000e-06,-2.40684451879218000000e-06] 
dist 219=[-9.44933348800915000000e-06,-2.24462954201744000000e-06] 
dist 220=[-1.07199412161469900000e-05,-2.03647511428706000000e-06] 
dist 221=[-1.14167503574265500000e-05,-1.84572586006336000000e-06] 
dist 222=[-1.18188858257057500000e-05,-1.63387220862043000000e-06] 
dist 223=[-1.19170495951347400000e-05,-1.34169251746224000000e-06] 
dist 224=[-3.59091587282988200000e-06,-1.02498734877946000000e-06] 
dist 225=[-3.37620084407594100000e-06,-7.15532705542880000000e-07] 
dist 226=[-2.80680028716443200000e-06,-3.56100712105530000000e-07] 
dist 227=[-2.71048752783317800000e-06,1.59452770638130000000e-07] 
dist 228=[-1.72744746175551000000e-06,6.72414823489140000000e-07] 
dist 229=[-1.53645717896993000000e-06,1.02155268910006000000e-06] 
dist 230=[-1.28568457734761000000e-06,1.31329500221956000000e-06] 
dist 231=[-1.20323706043247000000e-06,1.59794139710370000000e-06] 
dist 232=[-1.47339405358040000000e-07,1.85202214383114000000e-06] 
dist 233=[-1.30056636280190000000e-07,2.02217216220893000000e-06] 
dist 234=[-1.42341077664750000000e-07,2.16135788990965000000e-06] 
dist 235=[-1.97930163864930000000e-07,2.29225417690403000000e-06] 
dist 236=[-2.63412425947411500000e-07,2.40352033820021000000e-06] 
dist 237=[-3.15048010313259000000e-07,2.46461699905871000000e-06] 
dist 238=[-3.65692952311220000000e-07,2.49993547934671000000e-06] 
dist 239=[-4.27252085942600000000e-07,2.50866434850004000000e-06] 
dist 240=[-4.90077957431040000000e-07,1.67569510340776100000e-06] 
dist 241=[-5.45770404490690000000e-07,1.60840331372497700000e-06] 
dist 242=[-6.06156695749020000000e-07,1.41642695102383600000e-06] 
dist 243=[-6.87661264194640000000e-07,1.38377771752628500000e-06] 
dist 244=[-7.66509249981620000000e-07,1.00458435683347000000e-06] 
dist 245=[-8.16333605905330000000e-07,9.27067447494030000000e-07] 
dist 246=[-8.53814824248860000000e-07,8.35825773528330000000e-07] 
dist 247=[-8.83572550829980000000e-07,8.05666629394730000000e-07] 
dist 248=[-9.05658365833170000000e-07,1.91738737088200000000e-08] 
dist 249=[-9.12627565268110000000e-07,-7.62757595809000000000e-08] 
dist 250=[-9.09798371447440000000e-07,-1.67579399593172000000e-07] 
dist 251=[-9.66229852088089000000e-07,-1.87122912570341000000e-07] 
dist 252=[-1.05211750443318800000e-06,-1.94082143257268500000e-07] 
dist 253=[-1.09067285581308500000e-06,-1.65613389220489800000e-07] 
dist 254=[-1.10838683328383500000e-06,-1.08950032443038280000e-07] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 0, 2] 
dist 0=[85.681165646601939474  ,85.681165646601939474  ] 
dist 1=[85.403195715064277243  ,85.668799130983874507  ] 
dist 2=[84.336106532934222731  ,85.681165646601939474  ] 
dist 3=[82.487216554494269134  ,85.410517065932399439  ] 
dist 4=[79.089388283858052346  ,85.146855900009722964  ] 
dist 5=[74.958341914884221366  ,84.715708275623190919  ] 
dist 6=[70.183437206882428383  ,84.378571324320223849  ] 
dist 7=[64.024897914742079162  ,83.731207236119969299  ] 
dist 8=[54.372195070161676093  ,83.437695796302268630  ] 
dist 9=[44.576882349682636346  ,81.939479709842257790  ] 
dist 10=[37.849296123172277700  ,81.465319340406907437  ] 
dist 11=[32.084463240631983630  ,81.190770100682114282  ] 
dist 12=[26.131387605522191498  ,81.117733339036117773  ] 
dist 13=[20.518082469485877383  ,68.975863031442585545  ] 
dist 14=[16.109294817269909693  ,67.991357944633167635  ] 
dist 15=[11.741911359205949616  ,58.535206730330659359  ] 
dist 16=[6.294038033371223018  ,43.606973684568943138  ] 
dist 17=[1.111797580288603860  ,32.291852972824443799  ] 
dist 18=[-2.195563635226682290  ,28.502188834989204623  ] 
dist 19=[-4.759951015651816049  ,19.615165378421058724  ] 
dist 20=[-6.977510916790194353  ,18.340930164197338289  ] 
dist 21=[-8.7999070672956089444 ,6.747409648469521582  ] 
dist 22=[-9.7874973377990998961 ,4.764078210680982244  ] 
dist 23=[-10.351819370302482537  ,2.140328634688638116  ] 
dist 24=[-10.485300476105110678  ,1.715334686047428552  ] 
dist 25=[-10.415844282115753192  ,-3.5873535449559290053 ] 
dist 26=[-13.087723648912535436  ,-3.2887081456378691569 ] 
dist 27=[-15.147984686060265970  ,-2.9584295747653383576 ] 
dist 28=[-16.916410409046748676  ,-2.516259012219667090  ] 
dist 29=[-18.364788029261806005  ,-2.050593619432582227  ] 
dist 30=[-19.147178643481204666  ,-1.625326177074198867  ] 
dist 31=[-19.592631988164712685  ,-1.156176598580064685  ] 
dist 32=[-19.695745845352595302  ,-.514679334711711282  ] 
dist 33=[-10.267675673005540119  ,.110157955707123909  ] 
dist 34=[-9.4992804167915612729 ,.513562068254113017  ] 
dist 35=[-7.6013973568376213156 ,.827562342195717559  ] 
dist 36=[-7.2702754537782543762 ,1.097094814853059869  ] 
dist 37=[-4.4431598825153581835 ,1.315388127486362721  ] 
dist 38=[-3.9201577466362303918 ,1.425461972276331925  ] 
dist 39=[-3.1252243848618225451 ,1.484175361388138084  ] 
dist 40=[-2.9122498138853077665 ,1.498140570888472639  ] 
dist 41=[-.1615817247577795949 ,2.973570647234279107  ] 
dist 42=[-.2947382840276302344 ,4.180975380155884268  ] 
dist 43=[-.4245466079855418146 ,5.129612142075196209  ] 
dist 44=[-.579573802731089402  ,5.964306014274874074  ] 
dist 45=[-.735082476094524482  ,6.655545863681334959  ] 
dist 46=[-.866979910139429962  ,7.032662612540619720  ] 
dist 47=[-1.004479463694197213  ,7.2496362768976176214 ] 
dist 48=[-1.182401818489443598  ,7.3028160883696133420 ] 
dist 49=[-1.350272972902631233  ,1.9748910886110134945 ] 
dist 50=[-1.447866899375047668  ,1.8118397832431541287 ] 
dist 51=[-1.511194137537019699  ,1.3946816693737442682 ] 
dist 52=[-1.542856774334430154  ,1.3347204439343281697 ] 
dist 53=[-1.554124032174717290  ,.6797512290967945991 ] 
dist 54=[-1.549861980665315140  ,.5597857084978285477 ] 
dist 55=[-1.511310442406453771  ,.4162330550128099583 ] 
dist 56=[-1.494049650877078462  ,.3919719805534046898 ] 
dist 57=[-.5565479070310454851 ,.00154471739307951778] 
dist 58=[-.7701531582161985586 ,-.0067137764996028601 ] 
dist 59=[-.9385875903092262399 ,-.0244569210566992616 ] 
dist 60=[-1.0875197005831177159 ,-.0270005940369453759 ] 
dist 61=[-1.2111374016736787392 ,-.0441947691874103145 ] 
dist 62=[-1.2787548031920195974 ,-.0466516512401485661 ] 
dist 63=[-1.3177963736306874671 ,-.0506905767429550885 ] 
dist 64=[-1.3275983924112924188 ,-.0369840024581228736 ] 
dist 65=[-.75646731836023394816,-.0095552457621090782 ] 
dist 66=[-.70918715785857942771,.0085492288101840147 ] 
dist 67=[-.58844987986203055386,.0230088712517470704 ] 
dist 68=[-.56631622252021745423,.0359559029757618878 ] 
dist 69=[-.37156118093151620819,.0467136794767674544 ] 
dist 70=[-.33419773148443775876,.0524752097557162350 ] 
dist 71=[-.27816207692344157839,.0557283504956632861 ] 
dist 72=[-.26224508979196042789,.0565127610291290348 ] 
dist 73=[-.0147214115954975953 ,.2051529250674633909 ] 
dist 74=[-.0120450051402903080 ,.3027216182166741515 ] 
dist 75=[-.00602563139516617132,.3799682938881023925 ] 
dist 76=[-.00505600783914216626,.4486339483676248360 ] 
dist 77=[.00188464949671722943,.5057573688086303802 ] 
dist 78=[.00300949966801612549,.5370554031873958174 ] 
dist 79=[.00496933896387233859,.5551464131123031390 ] 
dist 80=[.00533825872891669541,.5596904968040903731 ] 
dist 81=[-.0021523517164780471 ,.15491471555780061081] 
dist 82=[-.0083270300735342897 ,.1436188819313511355 ] 
dist 83=[-.0132723250565006163 ,.11411954114672872127] 
dist 84=[-.0177212718677291154 ,.10974458538491707626] 
dist 85=[-.0214286710824517266 ,.0612079273417583091 ] 
dist 86=[-.0234275536585891568 ,.0521139641926884490 ] 
dist 87=[-.0245296085112984155 ,.0412292582264034665 ] 
dist 88=[-.0247720464827954290 ,.0390008783671362967 ] 
dist 89=[-.0417052748221347787 ,.00339594855292428620] 
dist 90=[-.0596608912901720621 ,.00269596970517474749] 
dist 91=[-.0737676043955794060 ,.00107292238079322310] 
dist 92=[-.0861105413641665174 ,.00083769427192715670] 
dist 93=[-.0962307590855563318 ,-.0011407368585201603 ] 
dist 94=[-.1014901627317900811 ,-.0013903448795228582 ] 
dist 95=[-.1042295733750262803 ,-.0017569371267974535 ] 
dist 96=[-.1047151586278846389 ,-.0007385338384825837 ] 
dist 97=[-.06843828942018151075,.0011587162743357786 ] 
dist 98=[-.06513293636034113438,.0023948698607751203 ] 
dist 99=[-.05600961317222069998,.0033647837862136292 ] 
dist 100=[-.05456418635083105583,.0042044437741125974 ] 
dist 101=[-.03767787026520410703,.0048928573041732488 ] 
dist 102=[-.03432698127817646482,.0052613986704198870 ] 
dist 103=[-.03045328303938318166,.0054604284108466218 ] 
dist 104=[-.02940006983304621041,.0055027848680810805 ] 
dist 105=[-.0044612942536830240 ,.0155557751117639991 ] 
dist 106=[-.0042267051723817534 ,.0229853565428941778 ] 
dist 107=[-.0036737496273950363 ,.0287933653790902544 ] 
dist 108=[-.0035153759356282675 ,.0338202775572823411 ] 
dist 109=[-.0026966061724162664 ,.0379027888693455127 ] 
dist 110=[-.0025272078853146081 ,.0399521924085541231 ] 
dist 111=[-.0021591079722387930 ,.0410409186958220854 ] 
dist 112=[-.0020490719868719835 ,.0412999575368219006 ] 
dist 113=[-.0008222740500653255 ,.01379839516089977593] 
dist 114=[-.0007649520207451941 ,.01284040167610560451] 
dist 115=[-.0011625388611427882 ,.0102957559370275605 ] 
dist 116=[-.0015238693555026621 ,.0099297754115307985 ] 
dist 117=[-.0018272568689805871 ,.0056095291999681176 ] 
dist 118=[-.0019946088415885611 ,.0047929457105517733 ] 
dist 119=[-.0020917682538488611 ,.0038670326454260897 ] 
dist 120=[-.0021162130354765157 ,.0037061237460292679 ] 
dist 121=[-.00344827679542070700,-.00069058719331766856] 
dist 122=[-.0050704965372883157 ,-.00065296995633372278] 
dist 123=[-.0063590298799101283 ,-.0006055500822179812 ] 
dist 124=[-.0075092344866813660 ,-.0005340621835795855 ] 
dist 125=[-.0084676842306264442 ,-.0004545435183255168 ] 
dist 126=[-.0089931253318108712 ,-.0003751373649964641 ] 
dist 127=[-.0092965479397613378 ,-.0002821237609737444 ] 
dist 128=[-.0093714346615938059 ,-.0001484598405879644 ] 
dist 129=[-.00569539461497605870,-1.62121544417414000000e-05] 
dist 130=[-.00538407719860016814,7.12033008256348000000e-05] 
dist 131=[-.00457032503275901502,.0001410943199642755 ] 
dist 132=[-.00441442190658799068,.0002037181171574085 ] 
dist 133=[-.00302720425873820807,.0002558069048595829 ] 
dist 134=[-.00275398516792855816,.0002838451053908281 ] 
dist 135=[-.00234591857144184234,.0002996435808638214 ] 
dist 136=[-.00222600966117904688,.00030413167436922371] 
dist 137=[7.96320612152997300000e-05,.00148146586046197220] 
dist 138=[.0002236202549957069 ,.00225295216418261301] 
dist 139=[.0002066515874872091 ,.00286631638447162735] 
dist 140=[.0001803932873766665 ,.00341448577708104612] 
dist 141=[.0001508513183721735 ,.00387148030745454510] 
dist 142=[.0001208144744051476 ,.00412204861672682281] 
dist 143=[8.52187917516091000000e-05,.00426669397935888291] 
dist 144=[3.35688668724249000000e-05,.00430219386274762684] 
dist 145=[-1.76653078958729000000e-05,.00120653878706999672] 
dist 146=[-5.16175084257023000000e-05,.00112846278875692358] 
dist 147=[-7.88605569591116000000e-05,.00091848380120879657] 
dist 148=[-.0001034408232607616 ,.00088820098579700681] 
dist 149=[-.0001239586762734974 ,.00052264836064213891] 
dist 150=[-.0001350613137510826 ,.00045281747642603070] 
dist 151=[-.0001412293591563210 ,.00037490622746710401] 
dist 152=[-.0001425529911643508 ,.00036102465354175705] 
dist 153=[-.00032944699993445813,-5.43967487822812100000e-05] 
dist 154=[-.00047439454272644656,-5.11161532200873000000e-05] 
dist 155=[-.00058737377188023972,-4.70974331068821000000e-05] 
dist 156=[-.00068443999179358910,-4.11539200373164000000e-05] 
dist 157=[-.00076273883689225544,-3.45837285431937000000e-05] 
dist 158=[-.00080104686616034548,-2.80697483227845000000e-05] 
dist 159=[-.00082074427061451416,-2.04709512914146000000e-05] 
dist 160=[-.00082498535253080136,-9.58500636401610000000e-06] 
dist 161=[-.00058973655286246768,1.16476215567510000000e-06] 
dist 162=[-.00056536544205822648,8.22431214966580000000e-06] 
dist 163=[-.00049638540218810314,1.38176351568244000000e-05] 
dist 164=[-.00048464605600123384,1.87415205728984000000e-05] 
dist 165=[-.00035023565061337597,2.28163230612769000000e-05] 
dist 166=[-.00032288162722129797,2.50364724752779000000e-05] 
dist 167=[-.00029031932785833100,2.62908055261371000000e-05] 
dist 168=[-.00027952645998324610,.0001023929419296932 ] 
dist 169=[-5.60358358336548000000e-06,.00019531300350402654] 
dist 170=[1.43615571449724400000e-05,.00025490257947059613] 
dist 171=[1.25170138547003000000e-05,.00030081183776290131] 
dist 172=[9.84108233915160000000e-06,.00033930473610084525] 
dist 173=[6.89908477986050000000e-06,.00036969147822062266] 
dist 174=[3.99598709153390000000e-06,.00038334737886546091] 
dist 175=[6.17193635404700000000e-07,.00038965377121724849] 
dist 176=[-4.21626312876300000000e-06,.00039079805932514036] 
dist 177=[-8.98295789148940000000e-06,.00011247170329877507] 
dist 178=[-1.20969217015913000000e-05,.0001051235002026567 ] 
dist 179=[-1.45459304963086000000e-05,8.53929922990261000000e-05] 
dist 180=[-1.66704606766521000000e-05,8.25104331139658000000e-05] 
dist 181=[-1.83821639335382000000e-05,4.82329844003000000000e-05] 
dist 182=[-1.91906557067343000000e-05,4.16844288480777000000e-05] 
dist 183=[-1.95508003977092000000e-05,3.42605457674188000000e-05] 
dist 184=[-1.95377052962548000000e-05,3.28417513321815000000e-05] 
dist 185=[-2.73958188801346000000e-05,9.22393575681260000000e-06] 
dist 186=[-4.09849938763935000000e-05,1.09544348870125500000e-05] 
dist 187=[-5.17622648188241000000e-05,1.27624896580415000000e-05] 
dist 188=[-6.13413206829456000000e-05,1.51126551244278000000e-05] 
dist 189=[-6.92845614718304000000e-05,1.75900483090812000000e-05] 
dist 190=[-7.35536703883532000000e-05,1.99045835494075000000e-05] 
dist 191=[-7.59019984053205000000e-05,2.25111372764196000000e-05] 
dist 192=[-7.63446707986933000000e-05,2.61504210465347000000e-05] 
dist 193=[-4.85681848902984000000e-05,2.97240272981812000000e-05] 
dist 194=[-4.60915369523110400000e-05,3.20695987663912000000e-05] 
dist 195=[-3.95840457614064300000e-05,3.39347146559318000000e-05] 
dist 196=[-3.82641977990168100000e-05,3.55976483962819000000e-05] 
dist 197=[-2.69592336205325600000e-05,3.69782194225417000000e-05] 
dist 198=[-2.46990568216670800000e-05,3.77204394569785000000e-05] 
dist 199=[-2.11951543097740400000e-05,3.81286537882505000000e-05] 
dist 200=[-2.01916505031121300000e-05,3.81809797268962000000e-05] 
dist 201=[-4.00056414514410000000e-06,3.80233943622973000000e-05] 
dist 202=[-4.41613668111250000000e-06,3.76764906724538000000e-05] 
dist 203=[-4.78295265595330000000e-06,3.69540962828232000000e-05] 
dist 204=[-5.17092581036020000000e-06,3.65643015804327000000e-05] 
dist 205=[-5.53512331247820000000e-06,3.41910621208369000000e-05] 
dist 206=[-5.80740535800690000000e-06,3.35684230271769000000e-05] 
dist 207=[-6.05994681895880000000e-06,3.12262240110929000000e-05] 
dist 208=[-6.34559317807440000000e-06,2.74616502772671000000e-05] 
dist 209=[-6.59461155718150000000e-06,9.29108202373440000000e-06] 
dist 210=[-6.70153388969320000000e-06,8.66025272565158000000e-06] 
dist 211=[-6.72275565175370000000e-06,7.01529172749949000000e-06] 
dist 212=[-6.69554883777050000000e-06,6.74330983166280000000e-06] 
dist 213=[-6.47953399141760000000e-06,3.70283765821280000000e-06] 
dist 214=[-6.40101838136317000000e-06,3.12682187899300000000e-06] 
dist 215=[-6.06650654536276000000e-06,1.36727538174370000000e-06] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 2, 2, 0, 0, 0, 1] 
dist 0=[84.307083117760196344  ,84.307083117760196344  ] 
dist 1=[84.055591997867878138  ,84.331534332408274207  ] 
dist 2=[83.078019029285004486  ,84.315373123148556934  ] 
dist 3=[81.342088322194563745  ,84.241220281055815332  ] 
dist 4=[78.153237957872100893  ,84.107787154967903181  ] 
dist 5=[74.279778460924666595  ,83.855758383110245650  ] 
dist 6=[69.811620746987960788  ,83.544987432395990427  ] 
dist 7=[64.056162885020128002  ,83.228484387595899059  ] 
dist 8=[55.045366886949004552  ,82.697800147173485173  ] 
dist 9=[45.918332221799348653  ,82.439685663594221203  ] 
dist 10=[39.698651147707227079  ,81.199285568149559050  ] 
dist 11=[34.421206442643357024  ,80.792155237046797266  ] 
dist 12=[29.053422274487275111  ,80.552030636195019207  ] 
dist 13=[24.039666249633777923  ,78.912071870505946552  ] 
dist 14=[19.785388837255993279  ,68.863064596130291041  ] 
dist 15=[15.165187257976136998  ,62.199215871372601618  ] 
dist 16=[10.494282579292521397  ,33.265622928822921198  ] 
dist 17=[4.5352643349351257024 ,29.557686482479922886  ] 
dist 18=[-1.2024500488135082720 ,20.950718794427054283  ] 
dist 19=[-4.9900533905826152710 ,19.604577537581379861  ] 
dist 20=[-8.0725942489068567358 ,8.554797785838275608  ] 
dist 21=[-10.996521777248551277  ,6.649333810997010753  ] 
dist 22=[-13.592568193174532497  ,3.815355433239537941  ] 
dist 23=[-15.366591329854473535  ,3.107497232624460608  ] 
dist 24=[-16.877037205803138457  ,-2.020666238044368825  ] 
dist 25=[-18.421181765956458547  ,-2.8209418446426419046 ] 
dist 26=[-19.780267674671344509  ,-2.8906359771430931107 ] 
dist 27=[-20.552468502932464116  ,-2.8437549580311611253 ] 
dist 28=[-21.042997063767100737  ,-2.645956019812058163  ] 
dist 29=[-21.278848804697549816  ,-2.384158343009712153  ] 
dist 30=[-21.336506084943748188  ,-2.0260653382715250122 ] 
dist 31=[-21.116691690576031639  ,-1.6862484903828021907 ] 
dist 32=[-7.4962563407813176595 ,-1.126607407570302165  ] 
dist 33=[-6.7755122631602405062 ,-.554421735334981966  ] 
dist 34=[-4.9910424306621135600 ,-.175387040053809860  ] 
dist 35=[-4.7329248261915175136 ,.127267467861525189  ] 
dist 36=[-2.121162571939160007  ,.396514255577165464  ] 
dist 37=[-1.655465780225734550  ,.617862442694097311  ] 
dist 38=[-1.068345867253109334  ,.730364776480643640  ] 
dist 39=[-.966569090275596288  ,1.243605696580042651  ] 
dist 40=[-.425704666180152969  ,2.411080394146568043  ] 
dist 41=[-.4528636735821759745 ,3.162263858608950064  ] 
dist 42=[-.4980844771107332442 ,3.748677676022438317  ] 
dist 43=[-.5624859862818275448 ,4.259526059678665048  ] 
dist 44=[-.6664141998443391345 ,4.680004158236995532  ] 
dist 45=[-.784293058341784611  ,4.906260227708295914  ] 
dist 46=[-.904419316054037828  ,5.032777788308359343  ] 
dist 47=[-1.046824457523874947  ,5.055748601462054639  ] 
dist 48=[-1.253523110008771425  ,2.8001885318832782180 ] 
dist 49=[-1.459240580433860354  ,2.6183552126795137030 ] 
dist 50=[-1.597861343379478187  ,2.1749842808808211856 ] 
dist 51=[-1.711956844375159649  ,2.0851196152896749206 ] 
dist 52=[-1.820267240336984298  ,1.433253531936003014  ] 
dist 53=[-1.915055629978496208  ,1.1005430580563194638 ] 
dist 54=[-1.975450040744541186  ,.8836826365371969279 ] 
dist 55=[-2.021729930006659090  ,.8252057682075208661 ] 
dist 56=[-2.060485009150483265  ,.1263627988748310490 ] 
dist 57=[-2.0880261655651821953 ,-.01858412555455593432] 
dist 58=[-2.0896995818957514149 ,-.02969529577104039252] 
dist 59=[-2.0730872522082478884 ,-.05210786074124773040] 
dist 60=[-2.0599647975854514537 ,-.05540776399185274405] 
dist 61=[-1.9684573059936601022 ,-.0710727476581098700 ] 
dist 62=[-1.9418689454683006009 ,-.0727939560463750813 ] 
dist 63=[-1.8009620097566816241 ,-.0712572743714681802 ] 
dist 64=[-.55210788227250239141,-.0588489598572294468 ] 
dist 65=[-.50490793127732376011,-.0374778960457848184 ] 
dist 66=[-.38442667525220917902,-.0163048610234605368 ] 
dist 67=[-.36711236131331923703,-.0022963709843188133 ] 
dist 68=[-.17852668606879763857,.0089206261280766153 ] 
dist 69=[-.14400387839453939613,.0190048869120300821 ] 
dist 70=[-.10267667048576040131,.0274270283863815979 ] 
dist 71=[-.09569463266772498439,.08233205391602728437] 
dist 72=[-.0374042556576169458 ,.17678869392956601794] 
dist 73=[-.00059081232811097412,.23819104488842340605] 
dist 74=[.00231220941376556657,.2866410138646499485 ] 
dist 75=[.0085021982029059604 ,.32952018592826616671] 
dist 76=[.0094404829694751301 ,.3651250904742282938 ] 
dist 77=[.0151852663309450926 ,.38460632015346845651] 
dist 78=[.0160321645106942895 ,.39585678797625177015] 
dist 79=[.0170962148620129553 ,.39868162867411450626] 
dist 80=[.01496848248389762544,.22422892697077444095] 
dist 81=[.00826405952223183957,.20978761014112629836] 
dist 82=[.00158350095134297618,.17311020619758559987] 
dist 83=[-.00286893721875295218,.16638317021910256806] 
dist 84=[-.00646475063392823607,.10779795785492336382] 
dist 85=[-.00974402619733294031,.09658771355940813845] 
dist 86=[-.01250410263539540222,.07965724808427537918] 
dist 87=[-.02054109930441895854,.07489994389064884016] 
dist 88=[-.06533472694064831522,.0162473493399428555 ] 
dist 89=[-.09454803941647696885,.00567953501908903400] 
dist 90=[-.11767072191118543114,.00483064037835268206] 
dist 91=[-.13821845464513278102,.00290514342522768026] 
dist 92=[-.15531007921406125514,.00262079195307884818] 
dist 93=[-.16467378349417215565,.0003621547892196846 ] 
dist 94=[-.17008592018193764466,-4.22278164523330000000e-06] 
dist 95=[-.17144530456917269023,-.0005565301959895215 ] 
dist 96=[-.04657593975642231366,-.0006670339193234961 ] 
dist 97=[-.04302197207586569714,-.00209548362566884459] 
dist 98=[-.03380537647940670959,-.00128926633013001969] 
dist 99=[-.03243815959849895778,-.00046307429574708664] 
dist 100=[-.01746726403471025594,.00020826983481842603] 
dist 101=[-.01467432009417426116,.00082796875641681833] 
dist 102=[-.01130507484592244288,.00135626575763755697] 
dist 103=[-.01061455908532643095,.00549507608098429954] 
dist 104=[-.00653445119354754359,.01389055946510921365] 
dist 105=[.00180875441720739533,.01933574798746711012] 
dist 106=[.00204152760748809053,.02360996957274002198] 
dist 107=[.00201990145510845638,.02734446265693877818] 
dist 108=[.00193977266434529509,.03040335236425086180] 
dist 109=[.00176430518104438154,.03198824723322316407] 
dist 110=[.00154786840308871852,.03280814857725464905] 
dist 111=[.00130466005689346126,.03294980707582152556] 
dist 112=[.00100102146738335998,.02128063791812166408] 
dist 113=[.00054425837645153493,.02022087216507818380] 
dist 114=[8.68700295147847430000e-05,.01731919583158259058] 
dist 115=[-.00021940667335152423,.01685969394307563796] 
dist 116=[-.00046780822383620801,.01155825955165201695] 
dist 117=[-.00069547145544761321,.01051006859191892575] 
dist 118=[-.00088728652364480780,.00929002328883830423] 
dist 119=[-.00157665002199873716,.00895817575451898844] 
dist 120=[-.00513451502274504194,-.00034609404948947945] 
dist 121=[-.00743393758454791977,-.00036525727538428221] 
dist 122=[-.00922852525861841030,-.00040511792461088339] 
dist 123=[-.01077722867669846530,-.00040789890387380147] 
dist 124=[-.01203357005604492835,-.00039901624606255797] 
dist 125=[-.01266450860370999064,-.00037293180654096780] 
dist 126=[-.01299832247388850689,-.00033906262309537274] 
dist 127=[-.01307203662613255997,-.00029917704099720315] 
dist 128=[-.00431004404794412652,-.00024827927785798372] 
dist 129=[-.00399693715246083130,-.00017059496656236485] 
dist 130=[-.00317166492485015875,-9.24215529608381310000e-05] 
dist 131=[-.00305299151358642824,-3.95352295604639320000e-05] 
dist 132=[-.00167164101300458899,3.96534770292421300000e-06] 
dist 133=[-.00141184295567711930,4.49177423723882760000e-05] 
dist 134=[-.00111481065232004687,8.03081805241208530000e-05] 
dist 135=[-.00106340364218172692,.00040213929296266205] 
dist 136=[9.29769049824565190000e-05,.00117878452362654276] 
dist 137=[9.59702043176791950000e-05,.00168683515337193423] 
dist 138=[.00012309628280491686,.00209010970866906509] 
dist 139=[.00012437928990245792,.00244978020178482225] 
dist 140=[.00012155880042323555,.00274937774250967733] 
dist 141=[.00011271111847957125,.00291357272725138162] 
dist 142=[.00010108059938296394,.00300836276708626686] 
dist 143=[8.71860110346665793000e-05,.00303173132710573530] 
dist 144=[6.93316107172226680000e-05,.00181389667506698298] 
dist 145=[4.19564787666238162000e-05,.00171110475105289826] 
dist 146=[1.44011385576931960000e-05,.00144426893405339385] 
dist 147=[-5.34740921802343540000e-06,.00139345955906316845] 
dist 148=[-2.13509524975610457000e-05,.00094480073389356701] 
dist 149=[-3.59526127767563933000e-05,.00085687924738712476] 
dist 150=[-4.81877938270647217000e-05,.00072496435512866427] 
dist 151=[-.00011989049811800293,.00068660953447641460] 
dist 152=[-.00049474753010989776,-2.03296772571677208000e-05] 
dist 153=[-.00074020337667671030,-2.15583794408137446000e-05] 
dist 154=[-.00093521596077060763,-2.74385976641514228000e-05] 
dist 155=[-.00110934415518661038,-2.81169930837936004000e-05] 
dist 156=[-.00125445364116228080,-2.82921212309214961000e-05] 
dist 157=[-.00133398850469024096,-2.69917878274927973000e-05] 
dist 158=[-.00137988423699234707,-2.50726383499802250000e-05] 
dist 159=[-.00139112537895084770,-2.25589520407320787000e-05] 
dist 160=[-.00038582610723748073,-1.92011128395705958000e-05] 
dist 161=[-.00035981121406427783,-1.37937586753117850000e-05] 
dist 162=[-.00029038369894801203,-8.22685382952581600000e-06] 
dist 163=[-.00028037279533007431,-4.39205580062782200000e-06] 
dist 164=[-.00016117615783938219,-1.16672529183057400000e-06] 
dist 165=[-.00013851539454557715,1.98484424986556700000e-06] 
dist 166=[-.00011302541777310162,4.78512320638415100000e-06] 
dist 167=[-.00010850216351619631,4.13376384353146014000e-05] 
dist 168=[4.42600743510377500000e-06,.00011315635716420924] 
dist 169=[4.65944713766732200000e-06,.00015952686605248556] 
dist 170=[7.81477084010816500000e-06,.00019562861967737175] 
dist 171=[8.06270445761238400000e-06,.00022658647720850110] 
dist 172=[8.13621695767707500000e-06,.00025151128879841180] 
dist 173=[7.70654272812227950000e-06,.00026360698433461720] 
dist 174=[7.06463373165608840000e-06,.00026978537390538881] 
dist 175=[6.21762882825324190000e-06,.00027116169962728440] 
dist 176=[5.08478775470034693000e-06,.00019176086345041360] 
dist 177=[3.17982942103376610000e-06,.00018360378593826947] 
dist 178=[1.08693620353711900000e-06,.00016070655729937869] 
dist 179=[-3.26031102333468400000e-07,.00015682055200076558] 
dist 180=[-1.48056446163904800000e-06,.00011278912725337902] 
dist 181=[-2.54855108224756930000e-06,.00010386259618715459] 
dist 182=[-4.80891407884960914000e-06,9.31765117820313488000e-05] 
dist 183=[-3.57719566813982080000e-05,8.96488870419097422000e-05] 
dist 184=[-6.57899931453599908600e-05,1.08113457431535090000e-06] 
dist 185=[-8.50043058491420750500e-05,-1.22053690613800950000e-06] 
dist 186=[-9.97711868970105671000e-05,-1.80462129280115318000e-06] 
dist 187=[-.00011209373353453214,-1.87675958804154440000e-06] 
dist 188=[-.00012180344132472609,-1.94814710442710850000e-06] 
dist 189=[-.00012617342845687785,-1.88987671567599780000e-06] 
dist 190=[-.00012817205043290533,-1.78288905811601560000e-06] 
dist 191=[-.00012844582322771858,0                     ] 
dist 192=[-3.67603798391455909000e-05,-1.39742922537181370000e-06] 
dist 193=[-3.42683913133597585000e-05,1.13426244913134680000e-06] 
dist 194=[-2.76229517800618850000e-05,3.95515571915555270000e-06] 
dist 195=[-2.66488921544763270000e-05,6.05138732154291510000e-06] 
dist 196=[-1.52401248872890600000e-05,7.99112090679809240000e-06] 
dist 197=[-1.30681605527851590000e-05,1.01898017885449153000e-05] 
dist 198=[-1.14899243411481650000e-05,1.23522815875983993300e-05] 
dist 199=[-1.15559370400409600000e-05,1.41481589212186854000e-05] 
dist 200=[-1.15662407345518070000e-05,1.59966478518035867000e-05] 
dist 201=[-1.15025522990953650000e-05,1.83685213148027860000e-05] 
dist 202=[-1.14008487022425280000e-05,2.06485939975911390000e-05] 
dist 203=[-1.12778882459714200000e-05,2.21320064317023210000e-05] 
dist 204=[-1.10633103817960360000e-05,2.34723458633842690000e-05] 
dist 205=[-1.09580500339121470000e-05,2.48632742146654360000e-05] 
dist 206=[-1.03676000542980940000e-05,2.56216687316505370000e-05] 
dist 207=[-1.01953142451371560000e-05,2.57628136414043500000e-05] 
dist 208=[-9.61323310651707100000e-06,1.53861042596555087000e-05] 
dist 209=[-9.46716708704499300000e-06,1.45536285668023220000e-05] 
dist 210=[-7.92036211341381900000e-06,1.23604747829870235000e-05] 
dist 211=[-7.59432355877351000000e-06,1.19533168062618402000e-05] 
dist 212=[-6.89584543668742000000e-06,8.16775395280644980000e-06] 
dist 213=[-6.67441129240655300000e-06,7.42207341338914550000e-06] 
dist 214=[-5.67863091910325870000e-06,6.35320329208053150000e-06] 
dist 215=[-5.46018703689250840000e-06,5.44837325740079740000e-06] 
dist 216=[-4.85059972487971200000e-06,1.56119197130194370000e-06] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 2, 2, 0, 1, 0, 2] 
dist 0=[84.017299331184186410  ,84.017299331184186410  ] 
dist 1=[83.194434011250992574  ,84.203391889468918126  ] 
dist 2=[81.689230178276348661  ,84.122955201457379534  ] 
dist 3=[78.862382629927338533  ,83.944673167517261212  ] 
dist 4=[75.380264387641005236  ,83.695482153114933878  ] 
dist 5=[71.260298376743944598  ,83.201546191090699985  ] 
dist 6=[65.888173114174372231  ,82.947433142663484635  ] 
dist 7=[57.408982322394060340  ,82.004960181484372451  ] 
dist 8=[48.799806916025596024  ,81.707709460062336043  ] 
dist 9=[42.908591970518025265  ,81.460397838341806954  ] 
dist 10=[37.883820163663047852  ,81.201676692118200848  ] 
dist 11=[32.731368496926125321  ,80.917696375061988865  ] 
dist 12=[27.892466349897344942  ,80.549936767740350926  ] 
dist 13=[24.118102462769852490  ,80.152675360945595372  ] 
dist 14=[20.399038739690993192  ,76.706833723448414123  ] 
dist 15=[15.779242744309290282  ,34.938831319110618733  ] 
dist 16=[11.377094581631137543  ,31.329378674444070694  ] 
dist 17=[8.525784768279601695  ,22.950308531557901699  ] 
dist 18=[5.5185959063528553632 ,21.615938597533253098  ] 
dist 19=[-.2419662519999564990 ,11.213501408932247013  ] 
dist 20=[-5.7471017438344589179 ,8.944258841748400761  ] 
dist 21=[-9.3128336130401738336 ,6.113456822180966529  ] 
dist 22=[-12.139444809857938933  ,5.412436884447225098  ] 
dist 23=[-14.694795726660677324  ,1.833604623419279873  ] 
dist 24=[-16.878784333532067836  ,-1.2639536997571421428 ] 
dist 25=[-18.223322422418403158  ,-1.5212186408854375771 ] 
dist 26=[-19.209741385865396392  ,-1.9803594791121892979 ] 
dist 27=[-19.964516488466534053  ,-2.0559751168089684678 ] 
dist 28=[-20.535009364095433353  ,-2.186434577543395066  ] 
dist 29=[-20.794101620044977200  ,-2.129478418609063657  ] 
dist 30=[-20.852442891661197852  ,-1.991124473047863270  ] 
dist 31=[-6.6691260004502519890 ,-1.719618841843815037  ] 
dist 32=[-6.0617198949769828395 ,-1.433543038455503095  ] 
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dist 68=[-.1505475093683043698 ,.05008198061800202001] 
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dist 70=[-.1562741163768305098 ,.10687472695027632926] 
dist 71=[-.1567918373751065066 ,.1558671963114769037 ] 
dist 72=[-.03180275808089926806,.2113239141968485023 ] 
dist 73=[-.02607502258934568625,.2550740229052475509 ] 
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dist 75=[-.01077494785723281685,.3258872748548348534 ] 
dist 76=[.00604105266804215042,.3434165051702184696 ] 
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dist 79=[.0135994239902870441 ,.20195485421187127121] 
dist 80=[.02742359517220935841,.18915672816728137662] 
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dist 83=[-.0013938487009924957 ,.09803177304511409463] 
dist 84=[-.02023859852677937036,.08795766098661762805] 
dist 85=[-.03248713386274611034,.07292060769240225473] 
dist 86=[-.04211040801644811212,.06862883947611675997] 
dist 87=[-.05781598349104177056,.0395040034654943583 ] 
dist 88=[-.0839018623511452697 ,.01965035909483460284] 
dist 89=[-.1045409007535079097 ,.01798002497928254813] 
dist 90=[-.1228654075677213190 ,.01388417978924953771] 
dist 91=[-.1380948679363531289 ,.01325708231709334326] 
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dist 93=[-.1511855698698985370 ,.00620296059751323974] 
dist 94=[-.1523025317053418834 ,.00477904241359146054] 
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dist 100=[-.0164193017212872984 ,.0076284474849347152 ] 
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dist 107=[-.00211485741085061952,.02922901630271151197] 
dist 108=[-.00272522219572081148,.03068908553517401837] 
dist 109=[-.00342111478210972010,.03151752259996604280] 
dist 110=[-.00409107001580030483,.03168802119218775166] 
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dist 113=[-.00638109982367372301,.01765163389280557844] 
dist 114=[-.00711814823899337622,.01724791786717292410] 
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dist 116=[-.00903154717369571374,.01122984154818515886] 
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dist 118=[-.01003277148108588003,.00984681940196536009] 
dist 119=[-.01034202694574480926,.00390352957169546409] 
dist 120=[-.01055135193972140206,.00190919575742803000] 
dist 121=[-.01057563452714337719,.00174721119540324968] 
dist 122=[-.01174346925445758081,.00135239303164024131] 
dist 123=[-.01267083977621847579,.00128329743273211610] 
dist 124=[-.01309902289126820073,.00071096360900146940] 
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dist 130=[-.00120484626629221196,-.0003261051190218706 ] 
dist 131=[-.00137065104250110341,1.31705036518542000000e-05] 
dist 132=[-.00150783577445416186,.0003430883092238201 ] 
dist 133=[-.00158257997536376812,.0005585573431219784 ] 
dist 134=[-.00162548075842962948,.0007288426996249732 ] 
dist 135=[-.00163577078460890140,.0008790276725643482 ] 
dist 136=[-.00041145784964686430,.0010026220150321188 ] 
dist 137=[-.00037001387252224760,.0010671297540618862 ] 
dist 138=[-.00026651015545499664,.0011016452878206360 ] 
dist 139=[-.00025161129896791302,.0011077541957223278 ] 
dist 140=[-9.67132477250604500000e-05,.00078373288513685530] 
dist 141=[-6.88337090856658100000e-05,.00075260155962129641] 
dist 142=[-3.44465397891563500000e-05,.00066201500202717525] 
dist 143=[-2.86243673787474100000e-05,.00064738184795536750] 
dist 144=[.00016961453041981838,.00046457669581253829] 
dist 145=[.00019184856506601240,.00042728100873975606] 
dist 146=[.00012790910237789860,.00038571475054901934] 
dist 147=[-1.15651590827313100000e-05,.00037380945809745068] 
dist 148=[-.00014799820347597213,.00034197408447544016] 
dist 149=[-.0002369234479216937 ,.00035310333285949099] 
dist 150=[-.0003069885241391982 ,.00035828781704003779] 
dist 151=[-.0003684034095734079 ,.00035869723989269783] 
dist 152=[-.0004186640416706637 ,.00022397521265627510] 
dist 153=[-.0004443607737850664 ,.00021124099491318361] 
dist 154=[-.0004581393524985412 ,.00017794672281847130] 
dist 155=[-.0004609855046953323 ,.00017249833410143208] 
dist 156=[-.00016037700630406423,.00011630096882807121] 
dist 157=[-.00015126042794590490,.00010540884342656706] 
dist 158=[-.00012606475471929498,9.16496124594790100000e-05] 
dist 159=[-.00012240181962022175,8.74441015466025200000e-05] 
dist 160=[-9.98334822983478100000e-05,-9.07406116361619000000e-06] 
dist 161=[-.00012020693036957617,-2.07802681919791700000e-05] 
dist 162=[-.00013543387617524000,-2.98762885223881200000e-05] 
dist 163=[-.00014745748827066088,2.81860389038960000000e-07] 
dist 164=[-.00015673235742966437,2.98450112694499000000e-05] 
dist 165=[-.00016101072431369455,4.92681727195186000000e-05] 
dist 166=[-.00016276626817904703,6.47264958825204000000e-05] 
dist 167=[-.00016261712216635800,7.85417833049332000000e-05] 
dist 168=[-4.38948747073794600000e-05,9.00382145882810000000e-05] 
dist 169=[-3.99948461566305000000e-05,9.62725457659738000000e-05] 
dist 170=[-3.02220174428917000000e-05,9.97712100659464000000e-05] 
dist 171=[-2.86807101337031000000e-05,.00010060804044263114] 
dist 172=[-1.38008616355929000000e-05,6.76611734608468900000e-05] 
dist 173=[-1.10705761712057000000e-05,6.47207920376721400000e-05] 
dist 174=[-7.39191558648030000000e-06,5.65949194726154600000e-05] 
dist 175=[-6.40540849880700000000e-06,5.50507775954403300000e-05] 
dist 176=[1.36802988554096000000e-05,3.97159773768365000000e-05] 
dist 177=[1.61294733413462000000e-05,3.65978380379009900000e-05] 
dist 178=[1.29742628897268420000e-05,3.23466564372244000000e-05] 
dist 179=[-1.01980836880409000000e-06,3.13809289430239000000e-05] 
dist 180=[-1.48910279303478800000e-05,3.40725838553330000000e-05] 
dist 181=[-2.40149028496439000000e-05,3.53573245597634000000e-05] 
dist 182=[-3.12945495766164800000e-05,3.59770975019870000000e-05] 
dist 183=[-3.78303443133459500000e-05,3.60208261313209000000e-05] 
dist 184=[-4.32895583877532300000e-05,2.54856673306690600000e-05] 
dist 185=[-4.62869637031433900000e-05,2.43527587191742900000e-05] 
dist 186=[-4.80187394614980200000e-05,2.13790182042320580000e-05] 
dist 187=[-4.84435922661312300000e-05,2.07523917998332440000e-05] 
dist 188=[-1.97934852078978500000e-05,1.55040135383639500000e-05] 
dist 189=[-1.92601286839307600000e-05,1.44306293950614600000e-05] 
dist 190=[-1.80521671776083700000e-05,1.27721230388067300000e-05] 
dist 191=[-1.76273549145437500000e-05,1.22841067227493100000e-05] 
dist 192=[-1.55458754981290000000e-05,2.41439454073190000000e-06] 
dist 193=[-1.50870583388294000000e-05,1.13145235614890000000e-06] 
dist 194=[-1.36990785296524000000e-05,-1.78170565190600000000e-06] 
dist 195=[-1.34668974114662000000e-05,4.27821018025820000000e-07] 
dist 196=[-1.01722888265008000000e-05,3.06793442285082000000e-06] 
dist 197=[-1.04975448304168000000e-05,4.78008297102520000000e-06] 
dist 198=[-1.07733983057365000000e-05,6.21278138307201000000e-06] 
dist 199=[-1.08250803535180000000e-05,7.44188726527699800000e-06] 
dist 200=[-6.89641859022281000000e-06,8.44609410837873500000e-06] 
dist 201=[-6.52687705823381000000e-06,8.99757966942402700000e-06] 
dist 202=[-5.67329247179258000000e-06,9.31670768156706800000e-06] 
dist 203=[-5.40908802460866000000e-06,9.39694626949213000000e-06] 
dist 204=[-4.20758203281866000000e-06,8.42188073980714000000e-06] 
dist 205=[-3.96100422096076000000e-06,8.25686326368317000000e-06] 
dist 206=[-3.36736672447497000000e-06,7.75749644721500000000e-06] 
dist 207=[-3.21448551347335000000e-06,7.60370419598410000000e-06] 
dist 208=[-1.69739270890667000000e-06,6.43956916772630000000e-06] 
dist 209=[-1.43595760780422000000e-06,6.17164255872090000000e-06] 
dist 210=[-1.00648953408333000000e-06,5.71220638569350000000e-06] 
dist 211=[-9.34292573992510000000e-07,5.57826959833390000000e-06] 
dist 212=[-2.02032461732291000000e-06,2.64446503961220000000e-06] 
dist 213=[-2.72109058908093700000e-06,2.24821494918690000000e-06] 
dist 214=[-3.26505668754918000000e-06,1.32583067603520000000e-06] 
dist 215=[-3.72745309536467000000e-06,5.54447774407020000000e-07] 
dist 216=[-4.09518448272104000000e-06,-6.38285412131812600000e-07] 
dist 217=[-4.26263879006820000000e-06,-5.60545824515585000000e-07] 
dist 218=[-4.34178230475747000000e-06,-3.75680489289225320000e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 2, 1, 2, 1, 2] 
dist 0=[79.678868420041764427  ,79.678868420041764427  ] 
dist 1=[77.287550152873552564  ,80.794612004589396189  ] 
dist 2=[74.264388030319111840  ,81.388283114564975236  ] 
dist 3=[70.626934912731665753  ,81.698252932215369183  ] 
dist 4=[65.846649354390443348  ,81.836480943576497777  ] 
dist 5=[58.262646384527422937  ,81.534066663203894867  ] 
dist 6=[50.546823181010559323  ,81.310925462034888900  ] 
dist 7=[45.240114826578879798  ,80.657733282373581727  ] 
dist 8=[40.685062745109312376  ,80.317941880539183222  ] 
dist 9=[35.967919382881097724  ,78.346998869742304198  ] 
dist 10=[31.508428322641959560  ,77.709887680774027293  ] 
dist 11=[27.980741391474256698  ,77.328231492480958962  ] 
dist 12=[24.458174502539518484  ,76.925628064267945419  ] 
dist 13=[20.017574703506904928  ,76.721729045533723881  ] 
dist 14=[15.753683570784091302  ,76.359873059355686558  ] 
dist 15=[12.935529049839340044  ,73.031958749253988318  ] 
dist 16=[10.630299137404514284  ,64.810495201590158603  ] 
dist 17=[8.4125787841709782137 ,32.520601023253090270  ] 
dist 18=[5.3063068749980359457 ,29.027364958603161219  ] 
dist 19=[-.2291734760914613942 ,20.933934657259778074  ] 
dist 20=[-5.5239614798125185157 ,19.645512655773752418  ] 
dist 21=[-8.9634895367861610210 ,9.2738528265531772592 ] 
dist 22=[-11.701817830710733781  ,7.4794478727777402439 ] 
dist 23=[-14.198043740250897824  ,4.7546654438818319271 ] 
dist 24=[-16.346488232937966517  ,4.0867812890847941900 ] 
dist 25=[-17.696786018835017992  ,-.9970247518810606457 ] 
dist 26=[-18.720384918044862276  ,-1.8171052710524933045 ] 
dist 27=[-19.564931715290191090  ,-1.9373237497912245003 ] 
dist 28=[-20.232497497102162351  ,-2.0883975767267901276 ] 
dist 29=[-20.550013151499427650  ,-2.0725076862994719752 ] 
dist 30=[-20.672469460599841664  ,-2.0148808133460535785 ] 
dist 31=[-20.611273659649960016  ,-1.9333236128323341423 ] 
dist 32=[-20.314465935056557664  ,-1.8248001839338377451 ] 
dist 33=[-6.5305768812816528175 ,-1.2952890322565612869 ] 
dist 34=[-5.8971459274024760918 ,-.7219603627438098694 ] 
dist 35=[-4.3363589037502881541 ,.0109131526175385046 ] 
dist 36=[-4.1049621005249095836 ,.7131400724606036900 ] 
dist 37=[-2.3874957078394457431 ,1.1646519896511147028 ] 
dist 38=[-1.4390883639929687341 ,1.5157951601473885502 ] 
dist 39=[-.9119468658302526020 ,1.8182900705249626400 ] 
dist 40=[-.8055549058430075923 ,2.0640086652544658656 ] 
dist 41=[-.0088446334775502509 ,2.2422759692988892539 ] 
dist 42=[.2661900462362527425 ,2.9071344969837893227 ] 
dist 43=[.3095352137242312808 ,3.4208053698147484272 ] 
dist 44=[.3765229586732778606 ,3.8589028249527469429 ] 
dist 45=[.3882870416961110469 ,4.2125640612711334902 ] 
dist 46=[.5340342003358176424 ,4.3897199864794176761 ] 
dist 47=[.5510822865929219534 ,4.4765755282829123154 ] 
dist 48=[.53776613330345462007,4.4870347072730874996 ] 
dist 49=[.37687581473827521309,2.6682450190655065628 ] 
dist 50=[.20460175481605419137,2.5052124854737686658 ] 
dist 51=[-.0256013579835625283 ,2.0866200880186202726 ] 
dist 52=[-.24829873389646776917,2.0137908471637200500 ] 
dist 53=[-.39074557275081955549,1.3328878787627717548 ] 
dist 54=[-.50026618467771215627,1.2023339070569045222 ] 
dist 55=[-.59193367868943595714,1.0193876465480816633 ] 
dist 56=[-.66606402811902132407,.9633674724776855605 ] 
dist 57=[-1.0129763578990405670 ,.1912544325784873003 ] 
dist 58=[-1.2937011583226728160 ,.0939881489914213888 ] 
dist 59=[-1.5097645079052323284 ,.0767544792301902857 ] 
dist 60=[-1.6916939940288559616 ,.0533989075419254591 ] 
dist 61=[-1.8362092097795582643 ,.0479242767496039154 ] 
dist 62=[-1.9032910337550894497 ,-.0686018512881339637 ] 
dist 63=[-1.9352683053868992487 ,-.0824112198229465559 ] 
dist 64=[-1.9399130381491476568 ,0                     ] 
dist 65=[-.2084300528411446498 ,-.0898151512226924350 ] 
dist 66=[-.2199602705862416142 ,-.0498017073663360157 ] 
dist 67=[-.2258433116504886714 ,.0028471242469870783 ] 
dist 68=[-.2287441862136015453 ,.0538038567810338343 ] 
dist 69=[-.2291126164145342331 ,.0870925898282838173 ] 
dist 70=[-.0653356010761925346 ,.1134619200724648957 ] 
dist 71=[-.0569808028821936895 ,.1368842112563934197 ] 
dist 72=[-.0370376062388310977 ,.1563262498600437043 ] 
dist 73=[-.0339718085740226211 ,.1668553550612989700 ] 
dist 74=[-.0070097663996630654 ,.1727655893932821984 ] 
dist 75=[-.0023274107166286769 ,.1738744322306894795 ] 
dist 76=[.0044037605389377698 ,.11239253099902306169] 
dist 77=[.0060405894915311104 ,.10703583271125187299] 
dist 78=[.0336429539475582978 ,.09252064398747441466] 
dist 79=[.0370086404165678129 ,.0898605625522205572 ] 
dist 80=[.0427005482778353583 ,.0636182146297335612 ] 
dist 81=[.03600141721158602072,.0583856344958005184 ] 
dist 82=[.0200166975131279875 ,.0617634454297252418 ] 
dist 83=[-.0019479387556918079 ,.0631963264768433382 ] 
dist 84=[-.0234200199146826574 ,.0637962096510108013 ] 
dist 85=[-.0374470112848092528 ,.0639105645751731749 ] 
dist 86=[-.0485461163784277688 ,.04014249269850026774] 
dist 87=[-.0583695944939245114 ,.03781210539827857657] 
dist 88=[-.0664872704840743081 ,.03199083919396980940] 
dist 89=[-.0707993423755109614 ,.0308476412491749601 ] 
dist 90=[-.0731217427999131014 ,.0216476589339128857 ] 
dist 91=[-.0736088382808315638 ,.0198475807811285575 ] 
dist 92=[-.0323769278385497779 ,.0170050240425538380 ] 
dist 93=[-.0315634153091796360 ,.0162260438014547003 ] 
dist 94=[-.0296796380649266461 ,.0013751965611475269 ] 
dist 95=[-.0290148628509617788 ,-.0005519970918480188 ] 
dist 96=[-.0257527813441042661 ,-.0049056754767949524 ] 
dist 97=[-.0250359131701560760 ,-.0057069412679887986 ] 
dist 98=[-.0235851106644386644 ,-.0041098213565100385 ] 
dist 99=[-.0247376517895169423 ,.0005453433828206667 ] 
dist 100=[-.0254019981285531091 ,.0050666282093932257 ] 
dist 101=[-.0255686780562230585 ,.0079754655043786702 ] 
dist 102=[-.01048720596402068018,.0102286469093900747 ] 
dist 103=[-.00977364289139485994,.0121416131855184866 ] 
dist 104=[-.0081672402038895845 ,.0136983182555919983 ] 
dist 105=[-.0077076850403651811 ,.0145336650946107071 ] 
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dist 108=[-.0042624463203265627 ,.01377487069517304739] 
dist 109=[-.0040672515429384321 ,.01353373231939198080] 
dist 110=[-.0020638573776542869 ,.0127665076854099348 ] 
dist 111=[-.0017014893405184634 ,.0125498123128068856 ] 
dist 112=[-.0012305215993284747 ,.0106774423373884036 ] 
dist 113=[-.0010863032741462680 ,.0102483332172567896 ] 
dist 114=[-.0010658260266569116 ,.0095871251843644372 ] 
dist 115=[-.0012372444893418114 ,.0089880413246097386 ] 
dist 116=[-.00189966697225983629,.00543600700970740598] 
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dist 118=[-.00326294193967400384,.00318681659220027558] 
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dist 120=[-.00425005778755407386,.00247358235601442170] 
dist 121=[-.00448942330497666832,.00239321258571840555] 
dist 122=[-.00461820333718270891,.00153757343540776899] 
dist 123=[-.00463930868419316910,.00137392886834514117] 
dist 124=[-.00256305208729452716,.00117411101644214600] 
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dist 130=[-.00195512497407461461,-.0003200567865663487 ] 
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dist 140=[-8.48322496426351800000e-05,.00106048959486891659] 
dist 141=[-7.61694020503911900000e-05,.00100360630855050374] 
dist 142=[.00025247591063748697,.00085442984986313932] 
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dist 147=[-5.11177072645643300000e-05,.00050651316378374878] 
dist 148=[-.00027186184582461691,.00052010491174821823] 
dist 149=[-.00041661563198369985,.00052344141817532292] 
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dist 151=[-.0006348286068326646 ,.00026645920303371718] 
dist 152=[-.0007207853032417555 ,.00021711758045754213] 
dist 153=[-.0007679765047045183 ,.00020810589196583177] 
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dist 156=[-.00022291614729552751,9.38536376493125000000e-05] 
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dist 158=[-.00016983935502693160,-2.40161941765447800000e-05] 
dist 159=[-.00016406968063151701,-3.84131815718812800000e-05] 
dist 160=[-.00016205910942917124,-6.66171145007382390000e-05] 
dist 161=[-.00018845370026791382,-6.17653789139608800000e-05] 
dist 162=[-.00021038654197888385,-2.95384518451049700000e-05] 
dist 163=[-.00022237905579412486,1.32312232985055700000e-05] 
dist 164=[-.00022928400633459802,5.46905108806793900000e-05] 
dist 165=[-.00023095972140940049,8.17061684073530400000e-05] 
dist 166=[-6.11919143962752100000e-05,.00010300694221894957] 
dist 167=[-5.61629700687412720000e-05,.00012172863556969094] 
dist 168=[-4.32041166331404170000e-05,.00013710360288471120] 
dist 169=[-4.13372657139307600000e-05,.00014508850156871851] 
dist 170=[-2.05744934947110630000e-05,.00014930501327592644] 
dist 171=[-1.67297241312905390000e-05,.00015002512700286577] 
dist 172=[-1.22070212016627000000e-05,.00010260222281317467] 
dist 173=[-1.14229089291794600000e-05,9.81348904796140300000e-05] 
dist 174=[1.86879057349842000000e-05,8.54759962754074000000e-05] 
dist 175=[2.20998139412039700000e-05,8.34418361178620300000e-05] 
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dist 177=[2.67534299675297900000e-05,5.39446575370691280000e-05] 
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dist 179=[-4.54271562784784000000e-06,4.67469979419827900000e-05] 
dist 180=[-2.21900462783429400000e-05,4.76268634620493400000e-05] 
dist 181=[-3.36555578017044900000e-05,4.78050236420648100000e-05] 
dist 182=[-4.26559699049452000000e-05,3.18281078051010940000e-05] 
dist 183=[-5.04960720064500100000e-05,3.02601276497790230000e-05] 
dist 184=[-5.68823838475046100000e-05,2.60227043704809000000e-05] 
dist 185=[-6.00988922470210000000e-05,2.53168636924267200000e-05] 
dist 186=[-6.18130878016559400000e-05,1.76915637307407300000e-05] 
dist 187=[-6.22216989128724300000e-05,1.61791011292928900000e-05] 
dist 188=[-2.10721602925186100000e-05,1.43198646438688300000e-05] 
dist 189=[-1.97277067316041000000e-05,1.37281279814036200000e-05] 
dist 190=[-1.60981500741962400000e-05,-5.05540563659250000000e-07] 
dist 191=[-1.55777493371709190000e-05,-2.23430492118296000000e-06] 
dist 192=[-1.78904772418698470000e-05,-5.05006052768586200000e-06] 
dist 193=[-1.97726912487829820000e-05,-5.20720126076702590000e-06] 
dist 194=[-2.12419269860477490000e-05,-2.96489893883842000000e-06] 
dist 195=[-2.19106197224597420000e-05,1.01835546912804000000e-06] 
dist 196=[-2.22022596912629330000e-05,4.91137048970414000000e-06] 
dist 197=[-2.21704982252079500000e-05,7.46218691798707000000e-06] 
dist 198=[-6.28606335574541000000e-06,9.48852802228186000000e-06] 
dist 199=[-5.80841055699343000000e-06,1.12949546614822900000e-05] 
dist 200=[-4.58257072597907000000e-06,1.27963659195857700000e-05] 
dist 201=[-4.38755915254378000000e-06,1.36091919708384900000e-05] 
dist 202=[-2.41988601439600000000e-06,1.40640429271332000000e-05] 
dist 203=[-2.05074503048790000000e-06,1.41642162107035000000e-05] 
dist 204=[-1.56882909010640000000e-06,9.15998101356713400000e-06] 
dist 205=[-1.43595107469750000000e-06,8.71939823651560000000e-06] 
dist 206=[1.49981968144070000000e-06,7.52789191436203000000e-06] 
dist 207=[1.85702882027260000000e-06,7.30637773440290000000e-06] 
dist 208=[2.56056503080860000000e-06,5.14369826827764000000e-06] 
dist 209=[2.71711221725170000000e-06,4.70999358603768000000e-06] 
dist 210=[1.52098618752771700000e-06,4.44773169048360000000e-06] 
dist 211=[-3.75518173747950000000e-07,4.64849695286170000000e-06] 
dist 212=[-2.24575081469188000000e-06,4.74904766205990000000e-06] 
dist 213=[-3.47370066643025000000e-06,4.75949009143280000000e-06] 
dist 214=[-4.45179739229376000000e-06,3.58119463091546000000e-06] 
dist 215=[-5.32804891419791000000e-06,3.44720313592170000000e-06] 
dist 216=[-6.05928296414177000000e-06,3.08173293844771900000e-06] 
dist 217=[-6.46044884407118000000e-06,3.00333049810708500000e-06] 
dist 218=[-6.69204434161506000000e-06,2.31050455818853000000e-06] 
dist 219=[-6.74865245841132000000e-06,2.16564919403441000000e-06] 
dist 220=[-2.68361620865541000000e-06,1.95070088661156000000e-06] 
dist 221=[-2.59429761642718000000e-06,1.88308759197349000000e-06] 
dist 222=[-2.39661672033708000000e-06,4.67346006941670000000e-07] 
dist 223=[-2.33088780352056000000e-06,2.84693270575600000000e-07] 
dist 224=[-2.02169921946789000000e-06,-1.34510788890100000000e-07] 
dist 225=[-1.95520495662481000000e-06,-2.08756486118000000000e-07] 
dist 226=[-1.75456149424626000000e-06,-2.32450417157150000000e-07] 
dist 227=[-1.72427897318021000000e-06,1.38144153170870000000e-07] 
dist 228=[-1.45254956536758000000e-06,4.97496897981080000000e-07] 
dist 229=[-1.46074137598704000000e-06,7.30012804562750000000e-07] 
dist 230=[-9.71304433012840000000e-07,9.25602882141972000000e-07] 
dist 231=[-9.25215618905490000000e-07,1.09186520627527500000e-06] 
dist 232=[-8.17679546507130000000e-07,1.22710375749647300000e-06] 
dist 233=[-7.83231161850590000000e-07,1.30005511784561200000e-06] 
dist 234=[-6.25517564531260000000e-07,1.34053728707458700000e-06] 
dist 235=[-5.92503491951400000000e-07,1.34757408456199500000e-06] 
dist 236=[-5.12904346462470000000e-07,1.16110824303435000000e-06] 
dist 237=[-4.91182605613630000000e-07,1.13345828342091000000e-06] 
dist 238=[-2.75013982541930000000e-07,1.05413586460491000000e-06] 
dist 239=[-2.38039590589990000000e-07,1.03092284984689000000e-06] 
dist 240=[-1.74547097114150000000e-07,8.60135017530950000000e-07] 
dist 241=[-1.59230462890650000000e-07,8.21633118208190000000e-07] 
dist 242=[-1.25173970026100000000e-07,7.54224131345370000000e-07] 
dist 243=[-1.57572177380600000000e-07,7.07726266058890000000e-07] 
dist 244=[-3.07582978974348000000e-07,3.31500222134330000000e-07] 
dist 245=[-4.03974373346625000000e-07,2.24402967156090000000e-07] 
dist 246=[-4.78400055684044000000e-07,-8.61446266107610000000e-08] 
dist 247=[-5.41031082365256000000e-07,-9.73247609656830000000e-08] 
dist 248=[-5.90527794955976000000e-07,-1.04053577912193100000e-07] 
dist 249=[-6.12701593900244000000e-07,-8.94365059343205000000e-08] 
dist 250=[-6.22968676583305000000e-07,-5.91187704278987000000e-08] 

8 phat 4 dirichlet min maxes function [0, 1, 0, 2, 0, 1, 2, 0, 1] 
dist 0=[87.467560701252709401  ,87.467560701252709401  ] 
dist 1=[86.815286659638967803  ,87.642665906248765420  ] 
dist 2=[85.494588466643452585  ,87.689332911447114263  ] 
dist 3=[83.033924064723646525  ,87.517277224021567147  ] 
dist 4=[79.930745574584108959  ,87.311386204445967651  ] 
dist 5=[76.045987228348857564  ,86.476030373929934430  ] 
dist 6=[70.846158411286627174  ,86.064623731352389630  ] 
dist 7=[62.494938581679034463  ,83.228478626640277469  ] 
dist 8=[53.944568996596849126  ,82.427623251463942050  ] 
dist 9=[47.950109747398094086  ,81.558403821886151119  ] 
dist 10=[42.683093911802719367  ,81.097022946480160164  ] 
dist 11=[37.036059736017685794  ,80.493612403728763469  ] 
dist 12=[31.581698184462009374  ,80.278951815010687006  ] 
dist 13=[27.083802152110247329  ,79.855101153382108234  ] 
dist 14=[20.973966518085361569  ,76.362789600294797556  ] 
dist 15=[14.745641248089366244  ,32.819425741987740080  ] 
dist 16=[9.002113559700448503  ,29.076870566899836790  ] 
dist 17=[4.703991129974339307  ,20.299990904554672421  ] 
dist 18=[.644654200344635428  ,19.037648473670337104  ] 
dist 19=[-4.145848852962887878  ,9.9227931635835139155 ] 
dist 20=[-8.623629442270172020  ,5.619633517176648354  ] 
dist 21=[-11.435335695094777322  ,4.8769130794564634399 ] 
dist 22=[-13.563921117341463303  ,3.8304453019742050516 ] 
dist 23=[-15.316704767804684321  ,3.6288216340971986362 ] 
dist 24=[-16.696556888326208826  ,-.0003169897052850593 ] 
dist 25=[-17.337893327248603429  ,-.4177877067926361812 ] 
dist 26=[-17.630128547422082641  ,-1.2943400552638858961 ] 
dist 27=[-17.621399754942410651  ,-1.4192818758750132365 ] 
dist 28=[-18.251385958457066181  ,-2.2392712501394411751 ] 
dist 29=[-18.675892599861645520  ,-2.3555782366223141627 ] 
dist 30=[-18.746582517977880197  ,-2.5555670893832780773 ] 
dist 31=[-10.002255292268957461  ,-2.5841299690819043103 ] 
dist 32=[-9.2793114789095738931 ,-2.124404610321755102  ] 
dist 33=[-7.4869543578506751176 ,-1.087160786598226125  ] 
dist 34=[-7.1708260315528036304 ,-.051966871318418784  ] 
dist 35=[-4.4768190488210051049 ,1.240149757198042845  ] 
dist 36=[-3.9760485787985298102 ,2.468039709918391765  ] 
dist 37=[-3.2113581212817385379 ,3.247692596820001804  ] 
dist 38=[-3.0063472849323359567 ,3.843525968882994158  ] 
dist 39=[-2.5587097236498994484 ,4.339139087409969009  ] 
dist 40=[-.91348170588987105232,4.729394643645800925  ] 
dist 41=[-.78204015972577663788,5.117045171061024247  ] 
dist 42=[-.48264703152628041151,5.907791237569892842  ] 
dist 43=[-.43350243908279439433,6.558248358590311760  ] 
dist 44=[-.0702024482089994671 ,6.904711086186767872  ] 
dist 45=[-.0090394775981638330 ,7.092780532901764648  ] 
dist 46=[.0934102885042495645 ,7.128937657707078583  ] 
dist 47=[.1149312080185301282 ,2.4900745581260854191 ] 
dist 48=[-.104031787156252011  ,1.7709508435590804068 ] 
dist 49=[-.500505861427220014  ,1.6303075167737962174 ] 
dist 50=[-.913400319568144605  ,1.3904849462680816438 ] 
dist 51=[-1.451175421118099772  ,1.3302531169047675890 ] 
dist 52=[-1.966314725206645108  ,.9476970712910414094 ] 
dist 53=[-2.289178392107374087  ,.9773148313350979685 ] 
dist 54=[-2.530266571228054453  ,.9941851402028438265 ] 
dist 55=[-2.719880607509506132  ,.9982018296126182813 ] 
dist 56=[-2.860236281652591975  ,.22104064168544905232] 
dist 57=[-2.905242830151589852  ,.18877823677871541769] 
dist 58=[-2.915172534674640562  ,.1121401648405710133 ] 
dist 59=[-2.915730940888748668  ,.1010566848496462528 ] 
dist 60=[-1.1738885291562635770 ,-.0008711403804037945 ] 
dist 61=[-1.2103744157801280359 ,-.0183030827469575627 ] 
dist 62=[-1.2193703721710928704 ,-.0418139018108569799 ] 
dist 63=[-.70165214595551460824,-.0458333020919053536 ] 
dist 64=[-.65868533425880132612,-.13925884713395144788] 
dist 65=[-.54850964509609592292,-.0866557006917990595 ] 
dist 66=[-.52830990638320119234,-.0326033121743445671 ] 
dist 67=[-.3491149582654309467 ,.0368132358456821464 ] 
dist 68=[-.3146399094066704442 ,.1035815263186303231 ] 
dist 69=[-.2632685828016466093 ,.1471011842231786356 ] 
dist 70=[-.2485234176056265668 ,.1815271290777629488 ] 
dist 71=[-.2386956205692555558 ,.2120940648801753568 ] 
dist 72=[-.13524215569434401812,.2756483297524981852 ] 
dist 73=[-.12585042093132236793,.3470987789474020627 ] 
dist 74=[-.10230344656662781042,.4106055772126468289 ] 
dist 75=[-.09849973404340131078,.4634215314292555064 ] 
dist 76=[-.0620827750765737076 ,.4923144465786425687 ] 
dist 77=[-.0552501921504290444 ,.5089511313528875235 ] 
dist 78=[-.0461821221662148118 ,.5129749903154778399 ] 
dist 79=[-.0434849698383032708 ,.14677549463402227751] 
dist 80=[.0112420441793314161 ,.13671858613348628328] 
dist 81=[.0179042117587395129 ,.1102640786855432220 ] 
dist 82=[.02145460955396346291,.1063114296323175635 ] 
dist 83=[-.00999297558023860130,.09636691385695024323] 
dist 84=[-.04066372346628868236,.10129857612797158407] 
dist 85=[-.06070634878572443208,.1035794528082449976 ] 
dist 86=[-.07660007218408789587,.10443957076065695412] 
dist 87=[-.09075813675536576652,.10437484466572152569] 
dist 88=[-.1025469087203809439 ,.0428879594548294846 ] 
dist 89=[-.10901027547790246338,.0406944231915591871 ] 
dist 90=[-.1127478796689910764 ,.0362470717875342085 ] 
dist 91=[-.1136868547380724163 ,.0349735396203413643 ] 
dist 92=[-.0929871108584982508 ,.0298632002692321198 ] 
dist 93=[-.0954892550535157265 ,.0286851238659851919 ] 
dist 94=[-.0958758260238700769 ,.0260945611006368090 ] 
dist 95=[-.0694835103669719502 ,.0252664965112953226 ] 
dist 96=[-.0670452060158132762 ,.0216354410274848165 ] 
dist 97=[-.0600582365405853755 ,.0206431208201256901 ] 
dist 98=[-.0588334671964354023 ,.0199147910024432143 ] 
dist 99=[-.0449193699114534291 ,.0197172453485839233 ] 
dist 100=[-.0420565493460519031 ,.0198095606653486475 ] 
dist 101=[-.0380163317035363062 ,.0203283385976912142 ] 
dist 102=[-.0289945558409471069 ,.0212507287718217716 ] 
dist 103=[-.0081637016436213234 ,.0229517986753303681 ] 
dist 104=[.0061882513155837977 ,.0247261109457761648 ] 
dist 105=[.01261428188744191320,.0259408809099379909 ] 
dist 106=[.01392481664296477792,.03033146921530359635] 
dist 107=[.01383859139807725373,.03395262124153397558] 
dist 108=[.01185900372942298697,.03580061746905242320] 
dist 109=[.01030939353897915997,.03677319652354065368] 
dist 110=[.00879806788153200622,.0369103468649337339 ] 
dist 111=[.00697004119734960859,.01290110270398876617] 
dist 112=[.00510548944755706920,.01201393780699207869] 
dist 113=[.00344840454489419177,.00965303901240013404] 
dist 114=[.00164516688177398090,.00931356709642058214] 
dist 115=[-.00080138649270195749,.00614690865664796590] 
dist 116=[-.00318233257239643086,.0045303642011512404 ] 
dist 117=[-.00472464745782813515,.0036693601619868029 ] 
dist 118=[-.00593148704116848210,.0035198253418283527 ] 
dist 119=[-.00697749787627377984,-.00301857866126285696] 
dist 120=[-.00782739209513788134,-.00390741243731488152] 
dist 121=[-.00825377310173854242,-.00401645890107743877] 
dist 122=[-.00848040473759918752,-.00388890142590596696] 
dist 123=[-.00853536821264128450,-.00340787010197549970] 
dist 124=[-.0083584988384394340 ,-.00285377669340895945] 
dist 125=[-.0086434814460288829 ,-.00243545317556656217] 
dist 126=[-.0087150903825573976 ,-.00204193027767471289] 
dist 127=[-.00530690697860458325,-.00158632527564069994] 
dist 128=[-.00501849498549779627,-.00113257261761000840] 
dist 129=[-.00426388665461316979,-.00074631589204116574] 
dist 130=[-.00411895002673230753,-.00034010465616042577] 
dist 131=[-.00282987435320118039,.00019315624243180413] 
dist 132=[-.00257574564728479333,.00070928682247615354] 
dist 133=[-.00219583834337577277,.00104737048569758839] 
dist 134=[-.00208420614151072560,.00131606857044519486] 
dist 135=[6.40585320283375600000e-05,.00155610481996592951] 
dist 136=[.00034108910705244846,.00208729575129280136] 
dist 137=[.00090462308651970244,.0026607763777925012 ] 
dist 138=[.00103968464316477307,.0031736006236838718 ] 
dist 139=[.00136040457374141043,.0036013031281914118 ] 
dist 140=[.00118289672147401254,.0038360797298684606 ] 
dist 141=[.00104041795981859356,.0039719524049962032 ] 
dist 142=[.00089816838229687243,.0040060972005563302 ] 
dist 143=[.00072151655007090898,.00111318332939016964] 
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dist 145=[.00037312855348901899,.00084582440777620740] 
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dist 147=[-6.24281611773231800000e-05,.00048169199757060091] 
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dist 152=[-.00081075946637442002,-.00030187992448498198] 
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dist 163=[-.00029192563893061600,2.19727569063446100000e-05] 
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dist 168=[4.49479870672386800000e-05,.00016773981850135784] 
dist 169=[9.30278957606119800000e-05,.00021237327460893158] 
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dist 171=[9.95917104612132100000e-05,.00028287134669079177] 
dist 172=[8.32027268171658200000e-05,.00029879305881840761] 
dist 173=[7.03605918854491770000e-05,.00030727544126251574] 
dist 174=[5.78254766478637450000e-05,.00030931416166548137] 
dist 175=[4.26536181022211980000e-05,.00010424704753649740] 
dist 176=[2.71817320322580790000e-05,9.75123503259740900000e-05] 
dist 177=[1.34505904885298940000e-05,7.93434656150523100000e-05] 
dist 178=[-1.46726830652597400000e-06,7.67293945353910500000e-05] 
dist 179=[-2.16629884142041400000e-05,5.91237947266890600000e-05] 
dist 180=[-4.12700000491541260000e-05,3.88456539132751100000e-05] 
dist 181=[-5.38465856972756040000e-05,3.20912183335033700000e-05] 
dist 182=[-6.35378296676977600000e-05,3.09032910254757400000e-05] 
dist 183=[-7.16656846877172560000e-05,-1.38888947389367800000e-05] 
dist 184=[-7.80820156698271110000e-05,-1.44348135872477598000e-05] 
dist 185=[-8.09634811570787750000e-05,-1.23218440416933651000e-05] 
dist 186=[-8.22933645810195750000e-05,-8.10732813084008109000e-06] 
dist 187=[-8.25363540499761250000e-05,0                     ] 
dist 188=[-6.76836406822595100000e-05,-2.26058566265691300000e-05] 
dist 189=[-6.99450792001047000000e-05,-1.91563722805439600000e-05] 
dist 190=[-7.03628128361911800000e-05,-1.58741763361420000000e-05] 
dist 191=[-4.45275107445379000000e-05,-1.20208416642168700000e-05] 
dist 192=[-4.22603102727686700000e-05,-8.15514534443083000000e-06] 
dist 193=[-3.62812043067475400000e-05,-4.82316939865610000000e-06] 
dist 194=[-3.50902289763623800000e-05,-1.28517319432120000000e-06] 
dist 195=[-2.46559538794567200000e-05,3.40078699987970000000e-06] 
dist 196=[-2.25725330323038800000e-05,7.92413209142760000000e-06] 
dist 197=[-1.94084459656549800000e-05,1.08153830894267000000e-05] 
dist 198=[-1.84824101479291800000e-05,1.30312619810958000000e-05] 
dist 199=[-4.60710274635147900000e-07,1.48676703955742000000e-05] 
dist 200=[1.88002899279456400000e-06,1.85949477141970700000e-05] 
dist 201=[6.28118130987179000000e-06,2.34151959796367200000e-05] 
dist 202=[7.30865099626582000000e-06,2.77118117670224300000e-05] 
dist 203=[7.36283859999370000000e-06,3.12822195980066300000e-05] 
dist 204=[5.41721065486134000000e-06,3.32133215067769100000e-05] 
dist 205=[3.90489829689905400000e-06,3.42914556272786900000e-05] 
dist 206=[2.44032548456785800000e-06,3.44904401155826500000e-05] 
dist 207=[6.84173648095180000000e-07,1.02223686724185900000e-05] 
dist 208=[-1.09755936714724000000e-06,8.77578556696361100000e-06] 
dist 209=[-2.66414298948676000000e-06,7.33152806410494000000e-06] 
dist 210=[-4.35364155616582000000e-06,6.98280458514746000000e-06] 
dist 211=[-6.62461758116226000000e-06,6.11631425608608000000e-06] 
dist 212=[-8.82103009954781000000e-06,3.65868721860544000000e-06] 
dist 213=[-1.02139979643304600000e-05,3.06867445198724000000e-06] 
dist 214=[-1.12689381773802000000e-05,2.96303977246141000000e-06] 
dist 215=[-1.21206336292146000000e-05,1.09208262371050000000e-07] 
dist 216=[-1.27649846750997000000e-05,-7.30120873088950000000e-07] 
dist 217=[-1.29950862223453000000e-05,-8.77273319830050000000e-07] 
dist 218=[-1.30457336518574000000e-05,-8.28645654134240000000e-07] 
dist 219=[-1.29759654218041000000e-05,-5.01064515521576000000e-07] 
dist 220=[-6.19836954106555000000e-06,-1.10496261325140000000e-07] 
dist 221=[-6.35780959641105000000e-06,1.88727732095240000000e-07] 
dist 222=[-6.38795981066873000000e-06,4.74400620557630000000e-07] 
dist 223=[-4.70584276668061000000e-06,8.11143705501690000000e-07] 
dist 224=[-4.52527521695234000000e-06,1.14967120830807000000e-06] 
dist 225=[-4.00835941991972000000e-06,1.44248881312968000000e-06] 
dist 226=[-3.91630751298135000000e-06,1.75424484054847000000e-06] 
dist 227=[-2.88496752046856000000e-06,2.16816216124580000000e-06] 
dist 228=[-2.67247043105091000000e-06,2.56613419954460000000e-06] 
dist 229=[-2.41331504187999000000e-06,2.81447687638993000000e-06] 
dist 230=[-2.31856457625441000000e-06,2.99787589643194000000e-06] 
dist 231=[-1.65025848360750000000e-07,3.13749928846683000000e-06] 
dist 232=[1.00121262735360000000e-07,3.23645024292391000000e-06] 
dist 233=[4.21179353711529000000e-07,3.25805417009920000000e-06] 
dist 234=[4.76558028255723000000e-07,3.24520103512949000000e-06] 
dist 235=[5.11393639599533400000e-07,3.21678888542331000000e-06] 
dist 236=[4.39932771137674100000e-07,3.03295497601308200000e-06] 
dist 237=[2.90965004003167050000e-07,3.08414034014557000000e-06] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 0, 0, 0, 2, 0, 1] 
dist 0=[21.375973071737962698  ,21.375973071737962698  ] 
dist 1=[16.934708329202620446  ,23.496238342655280106  ] 
dist 2=[10.211569039780343157  ,27.515720410314245528  ] 
dist 3=[0                     ,32.044685825570275274  ] 
dist 4=[31.807305095718742438  ,35.092106984388461922  ] 
dist 5=[33.313112582228595157  ,37.636550234626907168  ] 
dist 6=[35.535701216574223319  ,40.158990252223633896  ] 
dist 7=[36.040126747192180740  ,42.399615034015585181  ] 
dist 8=[41.958303323646422138  ,43.819550436606126441  ] 
dist 9=[42.673502192674792691  ,44.910753872334307908  ] 
dist 10=[41.997948285674657322  ,45.839175936166573762  ] 
dist 11=[40.343273373923086807  ,46.592229362771200061  ] 
dist 12=[37.965955693650122853  ,46.983432862047452497  ] 
dist 13=[34.611080055775163090  ,47.184620418068487854  ] 
dist 14=[29.056833335657981683  ,47.179233618602512557  ] 
dist 15=[23.345750471420894675  ,46.951853843220318281  ] 
dist 16=[19.365134189516614032  ,22.424641580956451872  ] 
dist 17=[15.899569547919116395  ,20.443964669362398113  ] 
dist 18=[12.242757480577045286  ,16.079132570807940941  ] 
dist 19=[8.7537766570358099900 ,15.007417366025345325  ] 
dist 20=[5.9575904093608761040 ,8.7430625503034248051 ] 
dist 21=[3.1401350692071915289 ,7.5902114770888532259 ] 
dist 22=[-.43371773324509665746,6.6538411205751117411 ] 
dist 23=[-3.8532911745112739978 ,5.4920296783001779223 ] 
dist 24=[-6.0553965553240439276 ,-1.3305783824574954380 ] 
dist 25=[-7.7822123156682275250 ,-2.4096342506689663774 ] 
dist 26=[-9.3060349896832521334 ,-3.4911283384645094316 ] 
dist 27=[-10.578444059541445196  ,-4.4951482750445781236 ] 
dist 28=[-11.302471206049874300  ,-4.8128499360557798388 ] 
dist 29=[-11.761843822936689844  ,-4.6639042293677833547 ] 
dist 30=[-12.023274581341016555  ,-4.0766739234660021160 ] 
dist 31=[-12.077503002121549981  ,-3.4010738795561026179 ] 
dist 32=[-3.7514215792915058233 ,-2.8996072459089362983 ] 
dist 33=[-3.4609952103775219597 ,-2.4376617216170697883 ] 
dist 34=[-2.7193771777072364545 ,-1.9183005772596818946 ] 
dist 35=[-2.6109000304003976597 ,-1.4096738491574600670 ] 
dist 36=[-1.4543260463449827092 ,-.98993840553413368714] 
dist 37=[-1.2428888069556560641 ,-.55925923720557249919] 
dist 38=[-1.0212160648441281056 ,-.00658051754488595560] 
dist 39=[-.93444449563958427538,.52390883154426628074] 
dist 40=[.60988187922575951711,.86638189644318534113] 
dist 41=[.88939410061108900299,1.1494679453736097539 ] 
dist 42=[1.0281325149334719608 ,1.4456909053863683366 ] 
dist 43=[1.2715786770616334636 ,1.7037582602503576764 ] 
dist 44=[1.2971493652731274496 ,1.9155164309083594162 ] 
dist 45=[1.2594923985302641337 ,2.0272694013719575376 ] 
dist 46=[1.1274499599024416949 ,2.0864950028551700904 ] 
dist 47=[.97461707957109935592,2.0978450394389625365 ] 
dist 48=[.8541559493446027503 ,1.3136196378941219499 ] 
dist 49=[.73633447278392719754,1.2450830754615340956 ] 
dist 50=[.59381076145481888755,1.0595876657113129256 ] 
dist 51=[.44870908916050292032,1.0298840995561751541 ] 
dist 52=[.32053100636583847583,.700009921882980386  ] 
dist 53=[.18175782162323208864,.63556584595756681653] 
dist 54=[-.00559791196310351093,.55753586189764846547] 
dist 55=[-.18763976126860175603,.53562717599195396045] 
dist 56=[-.30529868331722962548,-.04977188626174300854] 
dist 57=[-.40551495649762223202,-.10854316135779000929] 
dist 58=[-.51759629986439774936,-.20486960657551489205] 
dist 59=[-.61530750311974835328,-.25536734385344142449] 
dist 60=[-.69524660249529137095,-.291946900691530363  ] 
dist 61=[-.73658636033664398066,-.28606182240589677395] 
dist 62=[-.75881524732793569473,-.25493446047263865447] 
dist 63=[-.76265619188133158215,-.21816056875328269016] 
dist 64=[-.25350011015831572843,-.18979920842706350904] 
dist 65=[-.23679960359711977678,-.16263318187076841742] 
dist 66=[-.19218122689272094248,-.1305782655333179632 ] 
dist 67=[-.18576145943145104736,-.09839112758814564003] 
dist 68=[-.10951411213080822434,-.07067980964968011856] 
dist 69=[-.09509878546618677287,-.04129514679577016751] 
dist 70=[-.07873334234284117999,-.00243114932087736839] 
dist 71=[-.07589129656755129379,.03524937289819750216] 
dist 72=[.04738748737564486016,.05993163094450957651] 
dist 73=[.06436307619939903184,.07954688929646548012] 
dist 74=[.07853409843476194203,.10159633456146264418] 
dist 75=[.09862403413521220387,.12182261443417185283] 
dist 76=[.10123464323632541951,.13866833271821591476] 
dist 77=[.09917173676653570526,.14790393046667195953] 
dist 78=[.09026967263061569648,.15324218547995467083] 
dist 79=[.07969438700439241845,.15457569454674905577] 
dist 80=[.07097313472173337500,.09537835616597280959] 
dist 81=[.06207779285605257303,.09037941217347971986] 
dist 82=[.05080135188936300041,.07718276062101474795] 
dist 83=[.03905040945916045358,.07466713631449867141] 
dist 84=[.02826293375424741387,.05183685931783615299] 
dist 85=[.01625537416140702541,.04733078157021370204] 
dist 86=[-.00035363749847258662,.04068634024468958000] 
dist 87=[-.01662922454931788966,.03870126235060905915] 
dist 88=[-.02731187441050640653,.00027979955842289923] 
dist 89=[-.03581790433952869752,-.00464565683030696915] 
dist 90=[-.04458173536991979738,-.01306687672382780733] 
dist 91=[-.05359211323173793838,-.01715782796539034541] 
dist 92=[-.06110520324236087313,-.02109666980200722387] 
dist 93=[-.06522756331431018216,-.02095596294605020955] 
dist 94=[-.06761137129389996582,-.01886014068645203098] 
dist 95=[-.06820626370063160270,-.01629311520991828232] 
dist 96=[-.01967352640311231273,-.01427758629514918384] 
dist 97=[-.01847970227729667536,-.01231182458551510089] 
dist 98=[-.01523277139676327518,-.00994097338800768495] 
dist 99=[-.01476375032972954724,-.00753253946093255761] 
dist 100=[-.00901037627728311222,-.00541632098291111865] 
dist 101=[-.00790592834258049849,-.00313698068166564947] 
dist 102=[-.00668090046518565693,-7.86897365764552960000e-05] 
dist 103=[-.00646034054094339139,.00289418772033970094] 
dist 104=[.00329157313323953319,.00483408812923507909] 
dist 105=[.00453381445449934697,.00637446525567438331] 
dist 106=[.00567972338199483628,.00820145204027994929] 
dist 107=[.00722301713080421933,.00980734970316597251] 
dist 108=[.00743422735382199520,.01112644805070625768] 
dist 109=[.00728947967539897572,.01181232799369993191] 
dist 110=[.00662575212817897438,.01217666150318782416] 
dist 111=[.00583541740292138019,.01223943650675919069] 
dist 112=[.00518697431931112132,.00849669879339287810] 
dist 113=[.00452827889182845187,.00814202569546042252] 
dist 114=[.00369668705575579770,.00712171819042726527] 
dist 115=[.00283193203156460133,.00696087518710448070] 
dist 116=[.00204106992645934224,.00494274749218260027] 
dist 117=[.00116339616062256863,.00453437883538469128] 
dist 118=[-4.69236310115262254000e-05,.00408386333729645709] 
dist 119=[-.00123028403880945670,.00396390765158817988] 
dist 120=[-.00200081522207028153,-.00020647414624248177] 
dist 121=[-.00260711470597401371,-.00063767969406325152] 
dist 122=[-.00331731351088815409,-.00123258634321800756] 
dist 123=[-.00395847604067009783,-.00161672200852497644] 
dist 124=[-.00448115373534412347,-.00183170248684895433] 
dist 125=[-.00474519496727870978,-.00180776057240073663] 
dist 126=[-.00488646437523505262,-.00162562477956234134] 
dist 127=[-.00492062116543638525,-.00140617398971129642] 
dist 128=[-.00171750261518925392,-.00123378736962021184] 
dist 129=[-.00161396067448904774,-.00106550274702353064] 
dist 130=[-.00133098752728969339,-.00086225295342825371] 
dist 131=[-.00129028384514005092,-.00065561817151637988] 
dist 132=[-.00078421030385368384,-.00047380766166309135] 
dist 133=[-.00068676493807757924,-.00027781158324397730] 
dist 134=[-.00057980914818097127,-1.46889880457616708000e-05] 
dist 135=[-.00056095237468107457,.00024150794006841275] 
dist 136=[.00032466566263323369,.00040997840768923103] 
dist 137=[.00044085751233034731,.00054479039589499777] 
dist 138=[.00053826527104338309,.00070807748648494617] 
dist 139=[.00068161031156249225,.00085442744052605095] 
dist 140=[.00070181152707695781,.00097660231524571637] 
dist 141=[.00069014313735123694,.00104371413488888392] 
dist 142=[.00063226361573475943,.00108257171201701083] 
dist 143=[.00056256728329518534,.00109233864049386897] 
dist 144=[.00050389265408868766,.00069719748770342508] 
dist 145=[.00044293670752678512,.00066324781388872738] 
dist 146=[.00036413398862250242,.00057250121545718227] 
dist 147=[.00028124210637787432,.00055457969595577431] 
dist 148=[.00020400434531290670,.00039264937036217082] 
dist 149=[.00011715336424256830,.00036016763353234299] 
dist 150=[-3.99195462183410230000e-06,.00031200534267919564] 
dist 151=[-.00012298201384145685,.00029745794795727532] 
dist 152=[-.00020126663019092395,1.06265985660052325000e-05] 
dist 153=[-.00026374430130484647,-2.63913984643545848000e-05] 
dist 154=[-.00033512797818672943,-9.10793797205724491000e-05] 
dist 155=[-.00040395463587090886,-.00012122371423847470] 
dist 156=[-.00046143036963582414,-.00015093240536836587] 
dist 157=[-.00049300979276375253,-.00015048897925439222] 
dist 158=[-.00051129703843085511,-.00013602197135659616] 
dist 159=[-.00051589386515647390,-.00011809493810447858] 
dist 160=[-.00014633810414638830,-.00010388828469588555] 
dist 161=[-.00013779037680395176,-8.98995462127566747000e-05] 
dist 162=[-.00011443129167042941,-7.28316435235896176000e-05] 
dist 163=[-.00011093262398569629,-5.53861264866681550000e-05] 
dist 164=[-6.89608772713592378000e-05,-3.98913670226278806000e-05] 
dist 165=[-6.08264901469518190000e-05,-2.30680265907111164000e-05] 
dist 166=[-5.15732058802756317000e-05,-3.33996951876527000000e-07] 
dist 167=[-4.95681712599246406000e-05,2.18101598863584808000e-05] 
dist 168=[2.48781614545365848000e-05,3.62888069514188670000e-05] 
dist 169=[3.40187898802242052000e-05,4.81955910364395330000e-05] 
dist 170=[4.27576286564032848000e-05,6.23130267479494726000e-05] 
dist 171=[5.45622351679776590000e-05,7.47579125758490129000e-05] 
dist 172=[5.62436130120976155000e-05,8.49938279318065723000e-05] 
dist 173=[5.52664393967150255000e-05,9.03240356016679038000e-05] 
dist 174=[5.04306872211633487700e-05,9.31701499435267881000e-05] 
dist 175=[4.46294306750903432990e-05,9.36620603996574763000e-05] 
dist 176=[3.98118010851281218400e-05,6.61461784572652534000e-05] 
dist 177=[3.48635527685124178000e-05,6.34955704291008671000e-05] 
dist 178=[2.85405414704364404000e-05,5.58077690454512131000e-05] 
dist 179=[2.19262752454772471000e-05,5.45632811801218317000e-05] 
dist 180=[1.58184095641094508000e-05,3.91037065036999702700e-05] 
dist 181=[8.99431778419780480000e-06,3.59501892581566865400e-05] 
dist 182=[-4.69823381778721900000e-07,3.24262392563814931600e-05] 
dist 183=[-9.73935016947241960000e-06,3.14093147064363521700e-05] 
dist 184=[-1.57898578165831283000e-05,-1.08508200720406346000e-06] 
dist 185=[-2.05645459237515451000e-05,-4.50890732353023910000e-06] 
dist 186=[-2.64314196315906349000e-05,-9.25863237055936650000e-06] 
dist 187=[-3.16146431028595011000e-05,-1.23176283603517735000e-05] 
dist 188=[-3.58534041508464131000e-05,-1.39957920765011611000e-05] 
dist 189=[-3.80142139929898585000e-05,-1.38466487629455949300e-05] 
dist 190=[-3.91709058130118170000e-05,-1.24827408900876300000e-05] 
dist 191=[-3.94150328711490654000e-05,-1.08277776250233362700e-05] 
dist 192=[-1.35632274060524834000e-05,-9.52093772170429240000e-06] 
dist 193=[-1.27712440304583138000e-05,-8.23817571066963410000e-06] 
dist 194=[-1.05891551584975594000e-05,-6.67839518120790620000e-06] 
dist 195=[-1.02752763526451984000e-05,-5.08683540390630470000e-06] 
dist 196=[-6.31016813536355590000e-06,-3.67736383117988800000e-06] 
dist 197=[-5.54177483970129510000e-06,-2.15051190437656840000e-06] 
dist 198=[-4.70844708206307160000e-06,-9.17723844880568000000e-08] 
dist 199=[-4.56061274683352780000e-06,1.91518651601783980000e-06] 
dist 200=[2.56101234816263720000e-06,3.23620638926604330000e-06] 
dist 201=[3.48401884630622280000e-06,4.32760879452238670000e-06] 
dist 202=[4.23744206154191790000e-06,5.64229188201365810000e-06] 
dist 203=[5.37527402993305630000e-06,6.82223001093025780000e-06] 
dist 204=[5.53903806801350440000e-06,7.80770842771725720000e-06] 
dist 205=[5.45294953740864570000e-06,8.34887121989932860000e-06] 
dist 206=[5.00542293860320820000e-06,8.66170950315635500000e-06] 
dist 207=[4.46416370640381990000e-06,8.73893598091825840000e-06] 
dist 208=[4.00525478719912840000e-06,5.66284774381302313000e-06] 
dist 209=[3.52550509633936092000e-06,5.39586665134047363800e-06] 
dist 210=[2.90118141573808311000e-06,4.67814859831087307000e-06] 
dist 211=[2.24238722202002066100e-06,4.53440930114244386000e-06] 
dist 212=[1.62544634397895377000e-06,3.23610580387788490000e-06] 
dist 213=[9.29375811851865990000e-07,2.97389755370741220000e-06] 
dist 214=[-4.42288653724211000000e-08,2.58488326699927580000e-06] 
dist 215=[-1.00122220516865820000e-06,2.46662632746822710000e-06] 
dist 216=[-1.63125951260267940000e-06,1.15911197226909200000e-07] 
dist 217=[-2.13438388433587290000e-06,-1.87238165203591100000e-07] 
dist 218=[-2.75051098638107710000e-06,-7.19277763439869910000e-07] 
dist 219=[-3.31718952736415350000e-06,-9.64266549610735280000e-07] 
dist 220=[-3.79052847161008590000e-06,-1.20014684936681302000e-06] 
dist 221=[-4.05045286105362470000e-06,-1.19725636336946353000e-06] 
dist 222=[-4.20068034062775590000e-06,-1.08205439073089000000e-06] 
dist 223=[-4.23766865539883240000e-06,-9.38921557210652000000e-07] 
dist 224=[-1.21214088272799979000e-06,-8.24937946168104480000e-07] 
dist 225=[-1.14436812721581063000e-06,-7.12146316406057630000e-07] 
dist 226=[-9.56114941302140490000e-07,-5.73710955548404470000e-07] 
dist 227=[-9.29036046754099630000e-07,-4.31766653852917820000e-07] 
dist 228=[-5.81731958929198280000e-07,-3.04995865284106880000e-07] 
dist 229=[-5.14014091537443960000e-07,-1.66788567608431970000e-07] 
dist 230=[-4.41434670608890230000e-07,2.06651404937113800000e-08] 
dist 231=[-4.28483861115867570000e-07,2.03146536788115780000e-07] 
dist 232=[1.85679224839914000000e-07,3.21586466823584800000e-07] 
dist 233=[2.56202824097292800000e-07,4.28352925892525200000e-07] 
dist 234=[3.26344245473805800000e-07,5.44896646749220110000e-07] 
dist 235=[4.11660855332781900000e-07,6.45415850191792090000e-07] 
dist 236=[4.22020079826731600000e-07,7.26972763240491470000e-07] 
dist 237=[4.10781009008606200000e-07,7.68093993169160320000e-07] 
dist 238=[3.67368631349339100000e-07,7.89570342705923610000e-07] 
dist 239=[3.16270183943398800000e-07,7.92982039517904580000e-07] 
dist 240=[2.74460658087956670000e-07,5.94493508970503000000e-07] 
dist 241=[2.32056502272241070000e-07,5.72745448648270630000e-07] 
dist 242=[1.78578787498810930000e-07,5.09059561838941080000e-07] 
dist 243=[1.22991562289822640000e-07,4.97991533631379630000e-07] 
dist 244=[7.21898147316907700000e-08,3.66915232615856580000e-07] 
dist 245=[1.58556886831247600000e-08,3.39766442977065610000e-07] 
dist 246=[-6.17425766537000000000e-08,3.08004259695306540000e-07] 
dist 247=[-1.37487229179924760000e-07,2.97057093576107910000e-07] 
dist 248=[-1.86452491629990770000e-07,1.46869607928080300000e-08] 
dist 249=[-2.43963300294892230000e-07,-1.11038179758271000000e-08] 
dist 250=[-2.91931753233559360000e-07,-3.40050906216919010000e-08] 
dist 251=[-3.32690137119752070000e-07,-4.18105304719342900000e-08] 
dist 252=[-3.65092698154468930000e-07,-3.70371927013285790000e-08] 
dist 253=[-3.79826578542923330000e-07,-2.49596718099889147000e-08] 
dist 254=[-3.86775446521732380000e-07,0                     ] 

8 phat 4 dirichlet min maxes function [2, 2, 0, 0, 0, 1, 0, 1] 
dist 0=[82.211496697798027703  ,82.211496697798027703  ] 
dist 1=[80.794612004589396190  ,82.991130131984431675  ] 
dist 2=[78.009299749754390145  ,83.234418068263935362  ] 
dist 3=[74.562713502760280428  ,83.239889710758514413  ] 
dist 4=[70.506698645236479262  ,83.071116185519824144  ] 
dist 5=[65.231396193136095366  ,82.803782212429153025  ] 
dist 6=[56.918876924066946678  ,82.537877591469652612  ] 
dist 7=[48.481382147993531678  ,81.937571687267891032  ] 
dist 8=[42.706978760519800864  ,81.641824352679341531  ] 
dist 9=[37.780936267885294210  ,80.347982895909971292  ] 
dist 10=[32.728042824982422670  ,80.077521502346433583  ] 
dist 11=[27.981355328998269719  ,79.250251979423900546  ] 
dist 12=[24.276434300744412425  ,78.991912302451255274  ] 
dist 13=[20.623303092194854356  ,78.885641347977444931  ] 
dist 14=[16.081732077709291879  ,77.258808858202671027  ] 
dist 15=[11.751952852563068750  ,67.607331597717408243  ] 
dist 16=[8.9432250499612258247 ,61.155250633118632024  ] 
dist 17=[6.7042977761126816402 ,33.022405301547889051  ] 
dist 18=[1.8504122613834168262 ,29.410540319597238576  ] 
dist 19=[-3.6799333082761831792 ,21.035441934491392030  ] 
dist 20=[-7.2994914942886883328 ,19.712365487018278747  ] 
dist 21=[-10.211143292765127861  ,8.9721965804754097787 ] 
dist 22=[-12.916251124253391153  ,7.1169166259999071000 ] 
dist 23=[-15.279937227397986939  ,4.3242031048861000204 ] 
dist 24=[-16.828981887556844777  ,3.6343847903893388652 ] 
dist 25=[-18.077036288978011472  ,-2.0595479156176993799 ] 
dist 26=[-19.239461502998109547  ,-2.1331085942764117454 ] 
dist 27=[-20.219906576298028882  ,-2.3577707344361784786 ] 
dist 28=[-20.741962651544007817  ,-2.3297186409864794471 ] 
dist 29=[-21.028659402410326792  ,-2.2123804611851151290 ] 
dist 30=[-21.070632241329791054  ,-1.9581697425738164507 ] 
dist 31=[-20.955534179777854456  ,-1.6807399330946957258 ] 
dist 32=[-20.616132265234009905  ,-1.4699919342047408062 ] 
dist 33=[-6.9801300766662682824 ,-.9966989670441912972 ] 
dist 34=[-6.2994928399287468767 ,-.3460328891475139784 ] 
dist 35=[-4.6219887574152454990 ,.2811444084537277410 ] 
dist 36=[-4.3741204488329261701 ,.6850888362876045491 ] 
dist 37=[-1.9409734787814032195 ,.9994697698274107084 ] 
dist 38=[-1.5079176378575344015 ,1.2700997464631886563 ] 
dist 39=[-.9436623468728161893 ,1.4900551849375305534 ] 
dist 40=[-.8319337782362151566 ,1.6027111921306129072 ] 
dist 41=[.1963878166130224998 ,2.4206539560842338458 ] 
dist 42=[.2184435283487820035 ,3.1319976650859028146 ] 
dist 43=[.3611454881851202301 ,3.6823567751673940734 ] 
dist 44=[.3816341142087544119 ,4.1530951130080798300 ] 
dist 45=[.4121723141367883318 ,4.5341004497855185537 ] 
dist 46=[.4133635834074814102 ,4.7268338823132642023 ] 
dist 47=[.4071204308000351739 ,4.8214295630289832331 ] 
dist 48=[.34333107838069344543,4.8347851470975506249 ] 
dist 49=[.21518681153399134029,2.8262774397283992106 ] 
dist 50=[.0420771973445706973 ,2.6481150689842838911 ] 
dist 51=[-.1259803341802619567 ,2.1942907497549877094 ] 
dist 52=[-.23407493783813398461,2.1138418887785639717 ] 
dist 53=[-.31767333198325283843,1.3866433471192022451 ] 
dist 54=[-.4157328200716704588 ,1.2477249962996808429 ] 
dist 55=[-.5455057742657301835 ,1.0465063219419297189 ] 
dist 56=[-.63838276545586060901,.9873718072599077959 ] 
dist 57=[-1.0953542614697032505 ,.0776269709434504779 ] 
dist 58=[-1.4031515323972181180 ,.0707870847651914775 ] 
dist 59=[-1.6409302747836289633 ,.0156274006745857765 ] 
dist 60=[-1.8426971549806488769 ,.0064592553589880898 ] 
dist 61=[-2.0041373640284438070 ,-.0071452156911243530 ] 
dist 62=[-2.0813355096693946125 ,-.0101450458027808788 ] 
dist 63=[-2.1186571261063840337 ,-.0555891366680365954 ] 
dist 64=[-2.1212215075417000615 ,0                     ] 
dist 65=[-.12223455519067017825,-.0564589952322257299 ] 
dist 66=[-.12646296933353203012,-.0139917097893010591 ] 
dist 67=[-.12946428011749479777,.0273203025096883642 ] 
dist 68=[-.1310132987991803343 ,.0544055142047385690 ] 
dist 69=[-.1318565487656694245 ,.0759370429517131415 ] 
dist 70=[-.1320219546495645354 ,.0951570889492511097 ] 
dist 71=[-.0330546485663761651 ,.1111527593750769538 ] 
dist 72=[-.0272787199559191444 ,.1198564330594230431 ] 
dist 73=[-.0139244616887525381 ,.1247875943763584675 ] 
dist 74=[-.0118553415944221687 ,.1257728887630113639 ] 
dist 75=[.0047129719421524402 ,.08609600374936820681] 
dist 76=[.0074735906730948058 ,.08257840943242671883] 
dist 77=[.0117886092820331255 ,.07272046119980144550] 
dist 78=[.0127544770047707766 ,.0708320411090557453 ] 
dist 79=[.0254165183378610566 ,.0519284540090784021 ] 
dist 80=[.0269961466753378754 ,.0480787947632640009 ] 
dist 81=[.0189752853396443671 ,.0428094220507509306 ] 
dist 82=[.0018469334118687155 ,.0410432886117007786 ] 
dist 83=[-.0149544747206527666 ,.0406315311368732855 ] 
dist 84=[-.0259682020694780634 ,.0410888398045149550 ] 
dist 85=[-.0347129583044584268 ,.0411889814035360414 ] 
dist 86=[-.0424901704368527893 ,.0412068322046540641 ] 
dist 87=[-.0489334912879994342 ,.02435942504906058272] 
dist 88=[-.0523725570492257675 ,.02270330051405720525] 
dist 89=[-.0542288076063892915 ,.0187653893068746265 ] 
dist 90=[-.0546301890423627276 ,.0179206684755485000 ] 
dist 91=[-.0232938272685037073 ,.0122903578124640162 ] 
dist 92=[-.0228244351480061165 ,.0112068834904762802 ] 
dist 93=[-.0215746304140039273 ,.0092116216576142332 ] 
dist 94=[-.0210903114070500084 ,.0087230488709943384 ] 
dist 95=[-.0185712499510842948 ,.0009521849806342332 ] 
dist 96=[-.0179935132609060472 ,-.0001230547683011101 ] 
dist 97=[-.0166641710835171649 ,-.0024857924728398224 ] 
dist 98=[-.0162240527248073344 ,-.0006638215139532927 ] 
dist 99=[-.0146933785088726305 ,.0027161348831155408 ] 
dist 100=[-.0153028509050356290 ,.0049049843673302701 ] 
dist 101=[-.0156532358384362606 ,.0066149905784762913 ] 
dist 102=[-.0157410495725925498 ,.0080906399302781365 ] 
dist 103=[-.00664609445547266828,.0092998988145063373 ] 
dist 104=[-.00614459239519207084,.0099499260997172388 ] 
dist 105=[-.0050491895212075535 ,.0103074318095832028 ] 
dist 106=[-.0047345201055184204 ,.0103847279110617278 ] 
dist 107=[-.0034311701571636011 ,.00970585416565502129] 
dist 108=[-.0031767657463049263 ,.00956628368439418972] 
dist 109=[-.0025361160699481184 ,.0090668483490212954 ] 
dist 110=[-.0024243795730939687 ,.0089402740673126332 ] 
dist 111=[-.0014045337531215896 ,.0075896434707933532 ] 
dist 112=[-.0011974492469168851 ,.0072799489369173664 ] 
dist 113=[-.0009974574574570521 ,.0068707068816255637 ] 
dist 114=[-.0009673334194350595 ,.0067121613772349421 ] 
dist 115=[-.00122334341658376165,.00340443385917925897] 
dist 116=[-.00182649433205155002,.00351306826178267098] 
dist 117=[-.00230479650310016935,.00356388506265882794] 
dist 118=[-.00272784340181202408,.00357031452245348260] 
dist 119=[-.00307619301313015300,.00196127310554836974] 
dist 120=[-.00325774063965662302,.00182310102108569161] 
dist 121=[-.00335016842458260695,.00147249748405143409] 
dist 122=[-.00336553461577804249,.00141825142101495957] 
dist 123=[-.00180310873523616220,.00086603151424083195] 
dist 124=[-.00168944001262714914,.00076256247386783186] 
dist 125=[-.00138161119644167561,.00063251604160278296] 
dist 126=[-.00133733742337985696,.00059967068778995108] 
dist 127=[-.0007957263758866947 ,-.00025082612834548216] 
dist 128=[-.00090050846362637025,-.00035191930685281012] 
dist 129=[-.00104652878235922246,-.0002773654213862562 ] 
dist 130=[-.00116758499631921039,5.92417058446138000000e-05] 
dist 131=[-.00126432744354656968,.0003858636189703578 ] 
dist 132=[-.00131344848685020267,.0006001726446250069 ] 
dist 133=[-.00133829527442664069,.0007707752792028230 ] 
dist 134=[-.00134184733906415029,.0009235126999244259 ] 
dist 135=[-.00039699222162849358,.0010509605034301010 ] 
dist 136=[-.00035493575033052009,.0011209448155606760 ] 
dist 137=[-.00025036229893185033,.0011614564033721019 ] 
dist 138=[-.00023533981591904357,.0011716379101501377 ] 
dist 139=[-8.05849940448262500000e-05,.00073550068038854356] 
dist 140=[-5.29023933257228900000e-05,.00069824196363187785] 
dist 141=[-1.84734711543830600000e-05,.00059942539526202686] 
dist 142=[-1.27527932207046000000e-05,.00058010638870954823] 
dist 143=[.00018678005332773303,.00040651636499623900] 
dist 144=[.00020977955832024875,.00037190948133885796] 
dist 145=[.00013320202757837276,.00032044721009317378] 
dist 146=[-2.37787151850702400000e-05,.00030505289948779215] 
dist 147=[-.00017763214430752892,.00032561396065866641] 
dist 148=[-.00027864649233470364,.00033968341173922678] 
dist 149=[-.0003591098470131664 ,.00034777777844462631] 
dist 150=[-.0004312061659811180 ,.00034975889436357064] 
dist 151=[-.0004913859074804755 ,.00018141905153890708] 
dist 152=[-.0005244403445315756 ,.00016762706331235276] 
dist 153=[-.0005435776555573246 ,.00013348330630071779] 
dist 154=[-.0005483875720109191 ,.00012737832450772326] 
dist 155=[-.00015433619910506060,7.59001349052146900000e-05] 
dist 156=[-.00014492516577015620,6.62871048196935700000e-05] 
dist 157=[-.00011943268042693973,5.14660313606951800000e-05] 
dist 158=[-.00011562013242617245,4.75130431056671600000e-05] 
dist 159=[-7.05351579004926200000e-05,-2.18568620897108500000e-05] 
dist 160=[-8.98840383672292300000e-05,-3.07926930258437600000e-05] 
dist 161=[-.00010834504765713154,-2.41022447649156300000e-05] 
dist 162=[-.00012464773366086616,5.53212166803820000000e-06] 
dist 163=[-.00013816854577093751,3.43101811143622800000e-05] 
dist 164=[-.00014554955332255481,5.30864180893459500000e-05] 
dist 165=[-.00014979302457120638,6.79094235382955100000e-05] 
dist 166=[-.00015081657990977715,8.09608087859157800000e-05] 
dist 167=[-3.89098421807441680000e-05,9.16891759931262300000e-05] 
dist 168=[-3.53599583796174800000e-05,9.72705024011562200000e-05] 
dist 169=[-2.63607638945082360000e-05,.00010023735323674163] 
dist 170=[-2.50648545759588830000e-05,.00010074847669672580] 
dist 171=[-1.11410189616897590000e-05,7.01762019383573900000e-05] 
dist 172=[-8.59932180496281800000e-06,6.72613459951422100000e-05] 
dist 173=[-5.53651772268248000000e-06,5.88926376614436200000e-05] 
dist 174=[-5.01186502547335000000e-06,5.75425759182396700000e-05] 
dist 175=[1.39829758964785200000e-05,4.09768311426554600000e-05] 
dist 176=[1.61235853636679400000e-05,3.76137942686051790000e-05] 
dist 177=[1.02487744734889600000e-05,3.38310853399493780000e-05] 
dist 178=[-2.19803050956718000000e-06,3.27484368365290000000e-05] 
dist 179=[-1.43595785541646000000e-05,3.05311560194904400000e-05] 
dist 180=[-2.22743303687610500000e-05,3.16286512965850400000e-05] 
dist 181=[-2.84993239306232400000e-05,3.21548582842498900000e-05] 
dist 182=[-3.39390292360613100000e-05,3.22314230863953500000e-05] 
dist 183=[-3.83801542141234400000e-05,2.07569466606058500000e-05] 
dist 184=[-4.06327279852228800000e-05,1.96538884204302380000e-05] 
dist 185=[-4.18363923134044300000e-05,1.67259676456721590000e-05] 
dist 186=[-4.21043546698246800000e-05,1.62428319887450710000e-05] 
dist 187=[-1.44222666968697700000e-05,1.11503183958003400000e-05] 
dist 188=[-1.35498104578169000000e-05,1.01523194967543600000e-05] 
dist 189=[-1.11688424359814900000e-05,8.90774046169435000000e-06] 
dist 190=[-1.08228503862634500000e-05,8.51974906565893000000e-06] 
dist 191=[-8.76501984476026300000e-06,-5.87295772340580000000e-07] 
dist 192=[-1.07001628264929880000e-05,-1.69265235335280000000e-06] 
dist 193=[-1.21566855919317960000e-05,-2.32681582646895000000e-06] 
dist 194=[-1.33232350526981650000e-05,3.98838849885750000000e-07] 
dist 195=[-1.42282285548653470000e-05,3.06896054064686000000e-06] 
dist 196=[-1.46432276314560700000e-05,4.82061492299347000000e-06] 
dist 197=[-1.48185347570348700000e-05,6.21357826742701000000e-06] 
dist 198=[-1.48008247245729000000e-05,7.45715350821969000000e-06] 
dist 199=[-4.08401463574750000000e-06,8.49147714629962000000e-06] 
dist 200=[-3.74526387820327000000e-06,9.05200626546971000000e-06] 
dist 201=[-2.88793339702973000000e-06,9.36623544891910000000e-06] 
dist 202=[-2.75193884108288000000e-06,9.43931378949686000000e-06] 
dist 203=[-1.41663458696570000000e-06,6.21849302708273800000e-06] 
dist 204=[-1.16916539616160000000e-06,5.93314224869625000000e-06] 
dist 205=[-8.39544825352000000000e-07,5.15420455555124000000e-06] 
dist 206=[-7.49391481599800000000e-07,5.00754231236080000000e-06] 
dist 207=[1.13463477894750000000e-06,3.56840672663926000000e-06] 
dist 208=[1.36442741746870000000e-06,3.27780107641187000000e-06] 
dist 209=[1.10413619240090000000e-06,2.87900163866023000000e-06] 
dist 210=[-1.85670116318480000000e-07,2.79658950738840000000e-06] 
dist 211=[-1.46077474098125000000e-06,3.05184009640470000000e-06] 
dist 212=[-2.29876205009197000000e-06,3.17669655189930000000e-06] 
dist 213=[-2.96683094871526000000e-06,3.23794831124640000000e-06] 
dist 214=[-3.56601975702304000000e-06,3.24159314489720000000e-06] 
dist 215=[-4.06628813861809000000e-06,2.36720967664890000000e-06] 
dist 216=[-4.34085328534599000000e-06,2.27030763994775000000e-06] 
dist 217=[-4.49941856913582000000e-06,2.01208337904079400000e-06] 
dist 218=[-4.53823067604600000000e-06,1.95672423194365800000e-06] 
dist 219=[-1.81810990551167000000e-06,1.48683844591970000000e-06] 
dist 220=[-1.76293185755788000000e-06,1.38965380547954000000e-06] 
dist 221=[-1.63881328761890000000e-06,1.24082697712647000000e-06] 
dist 222=[-1.59643817570954000000e-06,1.19609837277295000000e-06] 
dist 223=[-1.39300666087076000000e-06,2.77918859003800000000e-07] 
dist 224=[-1.34884750312840000000e-06,1.58675298800300000000e-07] 
dist 225=[-1.21654884438283000000e-06,-1.13480692548000000000e-07] 
dist 226=[-1.19508967419070000000e-06,7.06814748966800000000e-08] 
dist 227=[-9.06805940669860000000e-07,3.15076317337040000000e-07] 
dist 228=[-9.54819165120320000000e-07,4.73371730295950000000e-07] 
dist 229=[-9.80152670040470000000e-07,6.03843384388386000000e-07] 
dist 230=[-9.85180283768060000000e-07,7.17228878221670000000e-07] 
dist 231=[-6.44122682924030000000e-07,8.09670439132522000000e-07] 
dist 232=[-6.11515421059790000000e-07,8.59891768595994000000e-07] 
dist 233=[-5.36049665721490000000e-07,8.88233812825578000000e-07] 
dist 234=[-5.12224431847520000000e-07,8.93658612800650000000e-07] 
dist 235=[-4.04421368847750000000e-07,7.83557603688150000000e-07] 
dist 236=[-3.82091007861270000000e-07,7.66413401000030000000e-07] 
dist 237=[-3.27858568382350000000e-07,7.15964516640570000000e-07] 
dist 238=[-3.13862108418000000000e-07,7.01059807850140000000e-07] 
dist 239=[-1.73255523255600000000e-07,5.88370521576450000000e-07] 
dist 240=[-1.48982053209770000000e-07,5.62769261943720000000e-07] 
dist 241=[-1.08553144713780000000e-07,5.18894510392920000000e-07] 
dist 242=[-9.86874646211600000000e-08,5.06231790638560000000e-07] 
dist 243=[-2.00331017480037000000e-07,2.31715339319090000000e-07] 
dist 244=[-2.65768529553012000000e-07,1.94655610709980000000e-07] 
dist 245=[-3.16416347852004000000e-07,1.08813099954480000000e-07] 
dist 246=[-3.59231435118835000000e-07,3.76525188933400000000e-08] 
dist 247=[-3.93123317398553000000e-07,-6.57258867036728000000e-08] 
dist 248=[-4.08275184639530000000e-07,-5.69855179683166000000e-08] 
dist 249=[-4.15347586322130000000e-07,-3.78818716336761200000e-08] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 1, 1, 0, 0, 1, 2] 
dist 0=[83.866554768689929159  ,83.866554768689929159  ] 
dist 1=[82.969149953887520078  ,84.070171368115165465  ] 
dist 2=[81.362492727431302226  ,83.994546039807157926  ] 
dist 3=[78.329501536467057536  ,83.778214051286149429  ] 
dist 4=[74.617093728775177004  ,83.557149210186124120  ] 
dist 5=[70.298925847134237776  ,83.361613222246318986  ] 
dist 6=[64.714094177409519876  ,83.083946911790416239  ] 
dist 7=[55.946709464113474384  ,82.756062829726940197  ] 
dist 8=[47.058530569098597992  ,82.427632700211116990  ] 
dist 9=[40.991291457550193232  ,81.987035086951354975  ] 
dist 10=[35.832174613775885912  ,81.721431251763328575  ] 
dist 11=[30.567087436412525366  ,80.712489331417069368  ] 
dist 12=[25.638104846135862289  ,80.383863855892127547  ] 
dist 13=[21.819424586351856074  ,79.884342415470553836  ] 
dist 14=[18.081074414634305347  ,76.390764762318762319  ] 
dist 15=[13.471100761491842988  ,67.561191935646579488  ] 
dist 16=[9.094930056381761016  ,33.456194762805756766  ] 
dist 17=[6.288811821720995726  ,29.779504437036641534  ] 
dist 18=[3.0998660404724020479 ,21.247336421532687311  ] 
dist 19=[-2.5628926655501715700 ,19.905917635235340310  ] 
dist 20=[-6.2831122818015989153 ,8.949559716356247078  ] 
dist 21=[-9.2911301825717335619 ,7.057667469327178280  ] 
dist 22=[-12.111575523001938574  ,4.228543409205342342  ] 
dist 23=[-14.593686220074545444  ,3.524871098423259994  ] 
dist 24=[-16.251452649336072948  ,-2.1274919361176234616 ] 
dist 25=[-17.621821631677224976  ,-2.2778984152893955499 ] 
dist 26=[-18.956956963920421928  ,-2.4504304323130201415 ] 
dist 27=[-20.107517427523883500  ,-2.3953708655640537520 ] 
dist 28=[-20.741556962544834205  ,-2.268034387218277903  ] 
dist 29=[-21.119098421711643938  ,-2.070056989704036444  ] 
dist 30=[-21.246857207023874161  ,-1.793011364769782639  ] 
dist 31=[-21.207847431728228029  ,-1.349811585706142707  ] 
dist 32=[-7.3016514499351300378 ,-.900922147004949927  ] 
dist 33=[-6.6052413618707202844 ,-.600431531915947070  ] 
dist 34=[-4.8782347915708596548 ,-.358520262136959896  ] 
dist 35=[-4.6298224458758931333 ,-.0252270093727351831 ] 
dist 36=[-2.094025275766588679  ,.3365829261263168368 ] 
dist 37=[-1.641500270889155859  ,.6226583764276793980 ] 
dist 38=[-1.076199304373139016  ,.8763957651793172514 ] 
dist 39=[-.981884001998499388  ,1.146689772491757179  ] 
dist 40=[-.5759456282623275271 ,2.2770194582416914265 ] 
dist 41=[-.5827659045142632699 ,3.0058704860099644591 ] 
dist 42=[-.6137062673738869803 ,3.5762150841242634698 ] 
dist 43=[-.6825141222495261621 ,4.0755275877257664426 ] 
dist 44=[-.767181965195452373  ,4.4881408058803157252 ] 
dist 45=[-.861442647796156087  ,4.7128550646457350088 ] 
dist 46=[-.978562430817194647  ,4.8418018478739498945 ] 
dist 47=[-1.154349214031394398  ,4.872573663108562608  ] 
dist 48=[-1.331178782011417460  ,2.8001468454151579734 ] 
dist 49=[-1.452574901521020297  ,2.6296239880336465147 ] 
dist 50=[-1.554762154863314330  ,2.2084265918134849724 ] 
dist 51=[-1.655368856123100248  ,2.1251071777076285593 ] 
dist 52=[-1.745751444005888146  ,1.289228237936397804  ] 
dist 53=[-1.807377180295928952  ,1.132133876539396735  ] 
dist 54=[-1.859206383306790059  ,.8141900023670856521 ] 
dist 55=[-1.910756475134422194  ,.7580201144785505558 ] 
dist 56=[-1.9523447725095203518 ,.04468798268693164702] 
dist 57=[-1.9645577562008551915 ,.02876651673404051748] 
dist 58=[-1.9578323243706837551 ,-.00575266090834334691] 
dist 59=[-1.9470708604032451911 ,-.01098886594622678348] 
dist 60=[-1.8761192485866967497 ,-.04583612769123660070] 
dist 61=[-1.8532427388648196818 ,-.0509602443033283297 ] 
dist 62=[-1.7589816537149009809 ,-.0602424530279271884 ] 
dist 63=[-1.5942707438382379436 ,-.0617277534346907430 ] 
dist 64=[-.54652547733761874154,-.0657956983425237541 ] 
dist 65=[-.49979639575178894483,-.05594399387037103692] 
dist 66=[-.3805306889889972583 ,-.02645093629655131235] 
dist 67=[-.3633849131486909837 ,.00244702168324180499] 
dist 68=[-.1767449095817084730 ,.02142057688130117416] 
dist 69=[-.1425804135596870836 ,.03650057929653553101] 
dist 70=[-.1016583768575685604 ,.04991916831015385213] 
dist 71=[-.0947287844559143448 ,.0815233953640006956 ] 
dist 72=[-.01396130695889731806,.1750171619192735734 ] 
dist 73=[-.00993386118160180393,.2357871383595318601 ] 
dist 74=[-.0008470633392129043 ,.2837313447794964634 ] 
dist 75=[.0004777808865200007 ,.3261517317283963136 ] 
dist 76=[.0108721231696323253 ,.3613680437338567523 ] 
dist 77=[.0125079976806744086 ,.3806229866002455833 ] 
dist 78=[.0150579181554605822 ,.3917246828140144345 ] 
dist 79=[.0155050668264247395 ,.3944695783319736056 ] 
dist 80=[.0208490708438787222 ,.22212097698923794122] 
dist 81=[.01580185605813033639,.20783864307715770088] 
dist 82=[.00554690505930773475,.17155652513312739165] 
dist 83=[-.00455871873320750553,.16490354313793502278] 
dist 84=[-.01120788001951200821,.1069212073062648946 ] 
dist 85=[-.01650405907283038782,.0958242892583383321 ] 
dist 86=[-.02123181493724054828,.0790773058164172584 ] 
dist 87=[-.02515455241825285672,.0743666769367038660 ] 
dist 88=[-.0648643779982467056 ,.01122400993170119223] 
dist 89=[-.0937443222946348746 ,.01005012254667337068] 
dist 90=[-.1165976575860577702 ,.00725500350567590762] 
dist 91=[-.1368966498821154632 ,.00683992911001599422] 
dist 92=[-.1537746816264926716 ,.00306550893335820331] 
dist 93=[-.1630089637085911139 ,.00240580294476923016] 
dist 94=[-.1683297847281487667 ,.00151944090845441330] 
dist 95=[-.1696272921781593517 ,.00133561310640549950] 
dist 96=[-.04641647536623530962,-.00297014851346701757] 
dist 97=[-.04293236201850426098,-.00347121174750438669] 
dist 98=[-.03384872089790957944,-.00180916407034844363] 
dist 99=[-.0325300594350208107 ,.00017849394011502101] 
dist 100=[-.0176401505543369710 ,.00149301123668649798] 
dist 101=[-.0148578591750027191 ,.00254704527340782971] 
dist 102=[-.0116034497294821218 ,.00349932527941692239] 
dist 103=[-.0110108763221397914 ,.00647793685348372261] 
dist 104=[-.00824383066081399719,.01489129291689487617] 
dist 105=[-.0081819817195616095 ,.02030800480995874736] 
dist 106=[-.0081959336651916658 ,.02451467508103816772] 
dist 107=[-.0083116648174358701 ,.02811153138846994467] 
dist 108=[-.0084770987815098132 ,.03100014193757802010] 
dist 109=[-.0086889609473252071 ,.03238757820865736323] 
dist 110=[-.0089696381793554058 ,.03308653947378094424] 
dist 111=[-.0094088606915545361 ,.03323451990459490575] 
dist 112=[-.0098549469130929025 ,.02261039479509731707] 
dist 113=[-.0101631760629671822 ,.02155914163526046967] 
dist 114=[-.0104236588406748209 ,.01867796127523277922] 
dist 115=[-.0106804836282599849 ,.01819314822192022552] 
dist 116=[-.0109103914299339095 ,.01288118276494417208] 
dist 117=[-.0110642109033423096 ,.01181928297579304972] 
dist 118=[-.0111900195639111966 ,.01052036939493137613] 
dist 119=[-.0113090275994620998 ,.01009825864955787894] 
dist 120=[-.0114046138234130416 ,.00117750651811900468] 
dist 121=[-.01143738759482971075,.00106105779805216541] 
dist 122=[-.01201573692774527958,.00078253324516713950] 
dist 123=[-.01341962811981273377,.00073502934802937206] 
dist 124=[-.01452214941119542430,.00035125534249263791] 
dist 125=[-.01502177154631347254,.00028275208400305837] 
dist 126=[-.01524720811576308731,.00017411119918441680] 
dist 127=[-.01525842202913787404,.00014763177115135842] 
dist 128=[-.0005565786356729241 ,-.00027205720352195902] 
dist 129=[-.0007004566200619116 ,-.00025922633515791298] 
dist 130=[-.0008126342151149823 ,-.00010685969818242240] 
dist 131=[-.0009103479026520254 ,4.28904913795481300000e-05] 
dist 132=[-.0009909300629671103 ,.00014088455842506938] 
dist 133=[-.0010347969193191561 ,.00021827037258815458] 
dist 134=[-.0010600450245640682 ,.00028611165995253532] 
dist 135=[-.0010663750394826175 ,.00034200784400032649] 
dist 136=[-.00025242847317744380,.00037191921553615208] 
dist 137=[-.00022224222808854385,.00038825670423853307] 
dist 138=[-.00014868547669598564,.00039179746919007135] 
dist 139=[-.00013786050698566172,.00033384471844122344] 
dist 140=[-3.38537252234126100000e-05,.00032603277269387597] 
dist 141=[-1.55671606599393000000e-05,.00029912737494070201] 
dist 142=[8.64115591291795000000e-06,.00029420974351259993] 
dist 143=[1.33144841630336000000e-05,.00022682307793569041] 
dist 144=[9.45056160368116570000e-05,.00021219399566678706] 
dist 145=[5.35372400676414240000e-05,.00019620211506472842] 
dist 146=[-4.70455315735230000000e-06,.0001942961071594588 ] 
dist 147=[-6.21123485071148240000e-05,.0002131029529434344 ] 
dist 148=[-9.97743214183406570000e-05,.0002283130117337721 ] 
dist 149=[-.00012962215227449391,.0002359993968506371 ] 
dist 150=[-.00015597577895246525,.0002396207453984535 ] 
dist 151=[-.00017761021496361957,.0002401244635126259 ] 
dist 152=[-.00018870279676931765,.00013389827010306440] 
dist 153=[-.00019429998965974365,.00012473617554460177] 
dist 154=[-.00019513790615142726,.00010135084185014241] 
dist 155=[-6.51371049108140300000e-05,9.77246929114938700000e-05] 
dist 156=[-6.30824503655080700000e-05,6.04222709103178500000e-05] 
dist 157=[-5.64312477607022000000e-05,5.33980467802489900000e-05] 
dist 158=[-5.54467545929141000000e-05,4.46271802591483540000e-05] 
dist 159=[-4.02736640109364000000e-05,4.23938477447239590000e-05] 
dist 160=[-4.75438286810622700000e-05,-1.62262791684969000000e-05] 
dist 161=[-6.07541408622444900000e-05,-2.25025409991015000000e-05] 
dist 162=[-7.08452852690856800000e-05,-1.00575833164571000000e-05] 
dist 163=[-7.92345774725437200000e-05,2.20099436014990000000e-06] 
dist 164=[-8.59469063142462100000e-05,1.02996988446418000000e-05] 
dist 165=[-8.93556615267194700000e-05,1.67802663937769000000e-05] 
dist 166=[-9.10842637829856900000e-05,2.26073573407918000000e-05] 
dist 167=[-9.13296199637272300000e-05,2.74630762848478000000e-05] 
dist 168=[-2.76081826188448000000e-05,3.00824660925558000000e-05] 
dist 169=[-2.47772067813281500000e-05,3.15491538511001000000e-05] 
dist 170=[-1.77633384906790100000e-05,3.18766967805808000000e-05] 
dist 171=[-1.67038021687407200000e-05,2.62223086729542300000e-05] 
dist 172=[-6.35268290670780000000e-06,2.56072630831355300000e-05] 
dist 173=[-4.49019541616180000000e-06,2.35568495575902126000e-05] 
dist 174=[-2.03533542481210000000e-06,2.31376595920168230000e-05] 
dist 175=[-1.48831654730570000000e-06,1.81288934995833100000e-05] 
dist 176=[1.09723186412847900000e-05,1.70359505801879200000e-05] 
dist 177=[7.32201057862746000000e-06,1.67847983759616000000e-05] 
dist 178=[2.09118516852075000000e-06,1.92998531604543000000e-05] 
dist 179=[-3.07848620900450000000e-06,2.14358776641607000000e-05] 
dist 180=[-6.48620318929310000000e-06,2.31482673320672000000e-05] 
dist 181=[-9.20298350393260000000e-06,2.39761280814063000000e-05] 
dist 182=[-1.16267290920166000000e-05,2.43700468880129000000e-05] 
dist 183=[-1.36312983946422000000e-05,2.43864362564475000000e-05] 
dist 184=[-1.46820319757202000000e-05,1.45270800873444300000e-05] 
dist 185=[-1.52486374255662000000e-05,1.36184600495694800000e-05] 
dist 186=[-1.53492957613365000000e-05,1.12515658648888200000e-05] 
dist 187=[-9.24244256160888000000e-06,1.08657890871997900000e-05] 
dist 188=[-9.38560833400689000000e-06,6.89603664966702000000e-06] 
dist 189=[-9.44940533315649000000e-06,6.12812579336265000000e-06] 
dist 190=[-9.42670313727483000000e-06,5.16024096958263000000e-06] 
dist 191=[-9.35717100027888000000e-06,4.87171973782612000000e-06] 
dist 192=[-9.26936093572450000000e-06,-1.50079024973901000000e-06] 
dist 193=[-9.07394115636610000000e-06,-1.91041600794950000000e-06] 
dist 194=[-8.97873562705570000000e-06,-6.92725821281750000000e-07] 
dist 195=[-8.55843854950702000000e-06,5.13230772387320000000e-07] 
dist 196=[-9.48814846299224000000e-06,1.31769192845431000000e-06] 
dist 197=[-9.99546716293184000000e-06,1.97103971985649000000e-06] 
dist 198=[-1.02868047280438100000e-05,2.57639990867111000000e-06] 
dist 199=[-1.03562585091512900000e-05,3.09528491884026000000e-06] 
dist 200=[-3.57724594996207100000e-06,3.40497489400517000000e-06] 
dist 201=[-3.32030603292749200000e-06,3.61751187751485000000e-06] 
dist 202=[-2.70995136301145000000e-06,3.75038130387063000000e-06] 
dist 203=[-2.56532172694928000000e-06,3.83025503670405000000e-06] 
dist 204=[-1.69512034712400000000e-06,3.83349927209427000000e-06] 
dist 205=[-1.52743004019393000000e-06,3.79967893372367000000e-06] 
dist 206=[-1.18928838358391000000e-06,3.76050735548339000000e-06] 
dist 207=[-1.09950592906874000000e-06,3.47669218508376500000e-06] 
dist 208=[-4.18149764257100000000e-08,3.39618372854939800000e-06] 
dist 209=[1.13351171514160000000e-07,3.22193702301215050000e-06] 
dist 210=[-2.04372175470690000000e-07,3.15884647398199980000e-06] 
dist 211=[-5.16409006090280000000e-07,2.07126626108004000000e-06] 
dist 212=[-7.19023036485080000000e-07,2.12109660331061000000e-06] 
dist 213=[-8.77234946455340000000e-07,2.19528592265902000000e-06] 
dist 214=[-1.01282964551411000000e-06,2.23064129638402000000e-06] 
dist 215=[-1.12179090288217000000e-06,2.23742380564316000000e-06] 
dist 216=[-1.17408890759199000000e-06,1.45658409301338000000e-06] 
dist 217=[-1.20007008277898000000e-06,1.38281378749923000000e-06] 
dist 218=[-1.20447910801927000000e-06,1.19135528056020000000e-06] 
dist 219=[-1.12332400604911000000e-06,1.15318075768806000000e-06] 
dist 220=[-1.10197115093632000000e-06,8.25904255829230000000e-07] 
dist 221=[-1.05482899802752000000e-06,7.60316519502640000000e-07] 
dist 222=[-1.03668465505510000000e-06,6.61081349722040000000e-07] 
dist 223=[-9.42697254612370000000e-07,6.31805901569800000000e-07] 
dist 224=[-9.20824124107430000000e-07,5.14105972037800000000e-08] 
dist 225=[-8.48783257950350000000e-07,-2.34615757669700000000e-08] 
dist 226=[-8.39309035072891000000e-07,-1.89588593666900000000e-07] 
dist 227=[-9.17703861258550000000e-07,-2.22078544218030000000e-07] 
dist 228=[-9.78374683267230000000e-07,-2.54314476903530200000e-07] 
dist 229=[-1.00639135642199000000e-06,-2.07368293734741300000e-07] 
dist 230=[-1.01805758732203000000e-06,-1.32199510402322650000e-07] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 2, 0, 1, 1, 2] 
dist 0=[87.187114849174576369  ,87.187114849174576369  ] 
dist 1=[86.663687807555282579  ,87.443156691818749191  ] 
dist 2=[85.638931549231712546  ,87.401123319391489910  ] 
dist 3=[84.282261900934391498  ,87.171324093703930794  ] 
dist 4=[82.434370566922531062  ,86.933503808674224214  ] 
dist 5=[79.124724541487677606  ,86.120694943492789136  ] 
dist 6=[75.032926447293871884  ,85.689593443051196898  ] 
dist 7=[69.607406672372115584  ,83.136122497366246824  ] 
dist 8=[60.946563767917062556  ,82.368845407549388151  ] 
dist 9=[52.098068487326816790  ,81.648240908106593947  ] 
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dist 90=[-.1187604770764190929 ,.02477232232817356453] 
dist 91=[-.03935451137278534429,.01790055208214321481] 
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dist 93=[-.02955385418465823877,.0066133785153642357 ] 
dist 94=[-.02852888265310770233,.0047595759079605483 ] 
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dist 97=[-.0219366884862234072 ,.0021497765182593154 ] 
dist 98=[-.0255034253556454897 ,.0099726793649950036 ] 
dist 99=[-.0280566511563898868 ,.0174704723133056604 ] 
dist 100=[-.0298669151905437061 ,.0221528906096492469 ] 
dist 101=[-.0311815010262255707 ,.0256191727957452394 ] 
dist 102=[-.0317607643614289125 ,.0282768875262475430 ] 
dist 103=[-.0319101110560167437 ,.0303381925326071744 ] 
dist 104=[-.0318429738683528820 ,.0314314275238487079 ] 
dist 105=[-.0258933856487692437 ,.0320142775594048286 ] 
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dist 107=[-.0226106224149474597 ,.0245340000187629527 ] 
dist 108=[-.0219447704046522788 ,.0235292681429823557 ] 
dist 109=[-.0178304149268989025 ,.0210666555007978440 ] 
dist 110=[-.0169467261493320068 ,.0203339641357250058 ] 
dist 111=[-.0152305970212720992 ,.01637171826059920762] 
dist 112=[-.0147457239820286813 ,.01553815981385312404] 
dist 113=[-.0068872532044926180 ,.01375328111578640400] 
dist 114=[-.0057640263090284704 ,.01322030752531838510] 
dist 115=[-.00403850759580925117,.00727240711378540265] 
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dist 117=[-.00792391596648398253,.00936750627338593331] 
dist 118=[-.00946312694141616963,.0098836301597676881 ] 
dist 119=[-.01074685514023376093,.0101763789466308301 ] 
dist 120=[-.01145152691462221318,.0102366746236462770 ] 
dist 121=[-.01185934376236222874,.00252415387470430215] 
dist 122=[-.01196183024978337004,.00229673093191932171] 
dist 123=[-.00333793746257366350,.00171830548612333927] 
dist 124=[-.00312157246749329004,.00163520191039988583] 
dist 125=[-.00254276100569967610,.00073463593603698819] 
dist 126=[-.00245640293476555334,.00056997590236961217] 
dist 127=[-.00145654422612409529,.00037260961971331653] 
dist 128=[-.00126553291000577352,.00033929364124655527] 
dist 129=[-.00104332243401249478,-.00044846000024521994] 
dist 130=[-.0012471743472765196 ,.00018816950973358570] 
dist 131=[-.0014777290726029254 ,.00080511819832379909] 
dist 132=[-.0016820085769499817 ,.00120706198265485148] 
dist 133=[-.0018517172185956423 ,.00152393971739623999] 
dist 134=[-.0019446081443871458 ,.00180243230857362016] 
dist 135=[-.0019982662571566562 ,.00203116897079813260] 
dist 136=[-.0020117403482828092 ,.00215007374199467395] 
dist 137=[-.00111129613102556336,.00221286277213577196] 
dist 138=[-.00103673916638718294,.00222371372041089793] 
dist 139=[-.00084873159881148235,.00151712122840096073] 
dist 140=[-.00081417830220056142,.00145078105160837898] 
dist 141=[-.00051771718762816958,.00126296009345934012] 
dist 142=[-.00046117345798901125,.00123282837325087147] 
dist 143=[-.00037486089217114676,.00086939668118050077] 
dist 144=[-.00035098675042174511,.00079615298082439816] 
dist 145=[8.43223187680326100000e-05,.00071299277469011195] 
dist 146=[-6.46582180100478600000e-05,.00068953470938593753] 
dist 147=[-.00032508155201271501,.00062170534671268893] 
dist 148=[-.00049425401079610011,.00072519469885582696] 
dist 149=[-.00062703785998136607,.00081126578724462609] 
dist 150=[-.00074269000245218261,.00085841581890880673] 
dist 151=[-.00083689992508834246,.00088566651299452239] 
dist 152=[-.00088437468704460218,.00089251093357012494] 
dist 153=[-.00090968793791354134,.00023511595414739971] 
dist 154=[-.00091571447874563341,.00021592775770748420] 
dist 155=[-.00030953766889687691,.00016663085215089761] 
dist 156=[-.00028969929841209869,.00015931176425928345] 
dist 157=[-.00023609986587392926,8.06290542888393700000e-05] 
dist 158=[-.00022838958242784329,6.60370356070815000000e-05] 
dist 159=[-.00013434466520281626,4.82309357979232200000e-05] 
dist 160=[-.00011634389501946524,4.45661055879928600000e-05] 
dist 161=[-9.63830317606603900000e-05,-4.42739683997913800000e-05] 
dist 162=[-.00010948473457784622,1.41714143248575200000e-05] 
dist 163=[-.00013140361699467921,7.08850624329171900000e-05] 
dist 164=[-.00015051136135819508,.00010810294296722723] 
dist 165=[-.00016613550755297643,.00013773424003176919] 
dist 166=[-.00017418644901293581,.00016426508447041433] 
dist 167=[-.00017830519931064735,.00018640121779539729] 
dist 168=[-.00017898062540185401,.00019854787326747173] 
dist 169=[-.00011370784930170463,.00020556603859282417] 
dist 170=[-.00010779913047644319,.00020729755594325702] 
dist 171=[-9.17975060607007300000e-05,.00012987309726062113] 
dist 172=[-8.92627172971025800000e-05,.00012323864116635681] 
dist 173=[-6.05466966808650200000e-05,.00010568326074611451] 
dist 174=[-5.48969351066323100000e-05,.00010224429185691817] 
dist 175=[-4.82523301100362200000e-05,7.14896406830003700000e-05] 
dist 176=[-4.64378694191994800000e-05,6.53575122049817500000e-05] 
dist 177=[6.87537671584122000000e-06,5.62147748028212700000e-05] 
dist 178=[-5.30135657490945000000e-06,5.34874041771927400000e-05] 
dist 179=[-3.25991492035882500000e-05,5.17918381871785900000e-05] 
dist 180=[-5.05209030301601300000e-05,5.99512072472498700000e-05] 
dist 181=[-6.47952016515174400000e-05,6.65577401469584600000e-05] 
dist 182=[-7.75823845226042800000e-05,6.98778398463796800000e-05] 
dist 183=[-8.82533851212938700000e-05,7.16215728045581000000e-05] 
dist 184=[-9.41086902334417600000e-05,7.19532090380199000000e-05] 
dist 185=[-9.74906203708467800000e-05,2.31788279379575050000e-05] 
dist 186=[-9.83213300404527100000e-05,2.13694471317726500000e-05] 
dist 187=[-2.77092072225414980000e-05,1.66538394796774100000e-05] 
dist 188=[-2.60222903426171360000e-05,1.59757271322518100000e-05] 
dist 189=[-2.14249220787827190000e-05,8.24820133579605000000e-06] 
dist 190=[-2.07614389590780730000e-05,6.80577709358966000000e-06] 
dist 191=[-1.25554957782479000000e-05,5.13526631040596000000e-06] 
dist 192=[-1.09731745463374430000e-05,4.84744457855588000000e-06] 
dist 193=[-9.23606763335981700000e-06,-3.44976143314789800000e-06] 
dist 194=[-1.01197453937962000000e-05,1.93856108266417200000e-06] 
dist 195=[-1.23011820239391300000e-05,7.16328562664102600000e-06] 
dist 196=[-1.42406916279771700000e-05,1.05448487027933030000e-05] 
dist 197=[-1.58528110798124100000e-05,1.31838167865408370000e-05] 
dist 198=[-1.67311518547593000000e-05,1.54543369278248490000e-05] 
dist 199=[-1.72316372978835900000e-05,1.72905562759943190000e-05] 
dist 200=[-1.73397593255147500000e-05,1.82018040000699170000e-05] 
dist 201=[-1.01755709579858300000e-05,1.86733522467245620000e-05] 
dist 202=[-9.56797009661194000000e-06,1.87601929498015500000e-05] 
dist 203=[-8.00837850766974000000e-06,1.37078524422196710000e-05] 
dist 204=[-7.71171936269185000000e-06,1.31709621910394380000e-05] 
dist 205=[-5.14595464764903000000e-06,1.16295705545420200000e-05] 
dist 206=[-4.64657356498571000000e-06,1.13645095706378320000e-05] 
dist 207=[-3.88550148518393000000e-06,8.28822097307739000000e-06] 
dist 208=[-3.66969129805940000000e-06,7.65702932061594800000e-06] 
dist 209=[-7.16314983803700000000e-09,6.91085941650704300000e-06] 
dist 210=[-2.25052888852809000000e-06,6.65832623704062100000e-06] 
dist 211=[-4.43209144639116300000e-06,5.58536697590224000000e-06] 
dist 212=[-5.83461156472433300000e-06,6.55090741756152000000e-06] 
dist 213=[-6.91838528239272800000e-06,7.35352299351444000000e-06] 
dist 214=[-7.83197194969256800000e-06,7.79036825311884000000e-06] 
dist 215=[-8.55439745094373300000e-06,8.03854324032460000000e-06] 
dist 216=[-8.87767508016265600000e-06,8.09025840304233000000e-06] 
dist 217=[-9.02795662951568000000e-06,2.16083672463005300000e-06] 
dist 218=[-9.06215895739969900000e-06,2.00440781160933000000e-06] 
dist 219=[-2.34193605020788000000e-06,1.59201227088328000000e-06] 
dist 220=[-2.16302968596491000000e-06,1.53258167076854000000e-06] 
dist 221=[-1.71445260345335000000e-06,8.40472040351380000000e-07] 
dist 222=[-1.62864769370120000000e-06,7.09959396515470000000e-07] 
dist 223=[-9.33199476082110000000e-07,5.61162374765230000000e-07] 
dist 224=[-8.89655347551970000000e-07,5.34978338921870000000e-07] 
dist 225=[-1.35159978309135000000e-06,9.07694273171300000000e-08] 
dist 226=[-1.64059792610034000000e-06,6.33772913114150000000e-07] 
dist 227=[-1.85518176586635000000e-06,1.15621522280665000000e-06] 
dist 228=[-2.02101249461924000000e-06,1.48265856701214000000e-06] 
dist 229=[-2.14677904817174000000e-06,1.72419908616587000000e-06] 
dist 230=[-2.20193212138095000000e-06,1.90890408066765000000e-06] 
dist 231=[-2.22108740410861000000e-06,2.05243483737551000000e-06] 
dist 232=[-2.21574894365665000000e-06,2.13015949348606000000e-06] 
dist 233=[-1.89279045165003000000e-06,2.17365127179763000000e-06] 
dist 234=[-1.83632574037004000000e-06,2.18092802242726000000e-06] 
dist 235=[-1.68594921481257000000e-06,1.72631150843288000000e-06] 
dist 236=[-1.64090739031434000000e-06,1.66013177302943000000e-06] 
dist 237=[-1.35196173343954000000e-06,1.49871061744191000000e-06] 
dist 238=[-1.28797433341396000000e-06,1.44547224312454100000e-06] 
dist 239=[-1.16630912150005000000e-06,1.18184683548340700000e-06] 
dist 240=[-1.13179312208623000000e-06,1.12480022311341900000e-06] 
dist 241=[-5.17277701550240000000e-07,9.96272795399430000000e-07] 
dist 242=[-4.30550280507910000000e-07,9.55940353071650000000e-07] 
dist 243=[-2.37715401603170000000e-07,6.00814109282828000000e-07] 
dist 244=[-1.91966804843510000000e-07,6.70517180489668000000e-07] 
dist 245=[2.84926093711900000000e-08,7.25256422791233000000e-07] 
dist 246=[6.76952918997900000000e-08,7.49946320575256000000e-07] 
dist 247=[8.21078397860178200000e-08,7.61033602146880000000e-07] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 1, 1, 2] 
dist 0=[80.371810265206830103  ,80.371810265206830103  ] 
dist 1=[78.396165798526983586  ,81.861329653787903218  ] 
dist 2=[75.635671861111403134  ,82.681833426349112069  ] 
dist 3=[71.772448408748351281  ,83.169196387609471827  ] 
dist 4=[65.396209571912936478  ,83.329130623206119630  ] 
dist 5=[58.803747153545319865  ,83.253328976741573406  ] 
dist 6=[54.077768638891191939  ,83.109428279987861093  ] 
dist 7=[49.816522728579296317  ,82.034381239326356312  ] 
dist 8=[45.078972648764300158  ,79.524390159761743887  ] 
dist 9=[40.401990282830242357  ,77.452744061341636234  ] 
dist 10=[36.382669231545182302  ,76.491969699606663660  ] 
dist 11=[32.078590645514373289  ,75.069117245502000871  ] 
dist 12=[26.265567774603539789  ,74.572884520540878098  ] 
dist 13=[20.518563921631703169  ,73.353739666165975390  ] 
dist 14=[16.477980136850649124  ,72.895343703392112032  ] 
dist 15=[12.917310170469980503  ,70.470921747275456495  ] 
dist 16=[8.9579078488665848955 ,65.762751977184969472  ] 
dist 17=[3.7629287678502677506 ,29.222918368822012618  ] 
dist 18=[-.0052581747544498459 ,25.753055554629381891  ] 
dist 19=[-3.4526936224954892907 ,17.624378626925976372  ] 
dist 20=[-7.3693183630330654491 ,16.460142399962169973  ] 
dist 21=[-10.996521777248551278  ,5.8827633868797974697 ] 
dist 22=[-13.288704580207264707  ,4.0754615701067639590 ] 
dist 23=[-15.045514913547526260  ,1.6841068595483288058 ] 
dist 24=[-16.533758589940401933  ,1.3002806674001753514 ] 
dist 25=[-17.734432235546534311  ,-1.5059275093463817232 ] 
dist 26=[-18.341977364699489410  ,-1.8834611554063346532 ] 
dist 27=[-18.627257377881319236  ,-2.4482504269030904425 ] 
dist 28=[-18.651786955629196311  ,-2.5525166830378614232 ] 
dist 29=[-16.859282470475058021  ,-4.0940431989778143946 ] 
dist 30=[-17.570487801257241540  ,-4.2758987654178897485 ] 
dist 31=[-17.978642403219983156  ,-4.4607897555880484120 ] 
dist 32=[-18.080836415232540123  ,-3.8449989491481232213 ] 
dist 33=[-9.3535396928745487141 ,-2.3230891939384082206 ] 
dist 34=[-8.6454391219170418772 ,-1.1249252462438170177 ] 
dist 35=[-6.8984098567270031744 ,.0567012713152430052 ] 
dist 36=[-6.5951023606099727628 ,1.5137035788671035803 ] 
dist 37=[-4.0002564849846678357 ,2.8970996285953791365 ] 
dist 38=[-3.5210783733143861709 ,3.7857454597509564542 ] 
dist 39=[-2.7949356267832261111 ,4.4773135495174105271 ] 
dist 40=[-2.6001647729878526812 ,5.0753989986080798175 ] 
dist 41=[-.8758689407798956069 ,5.5639179701503607354 ] 
dist 42=[-.7358861425090759645 ,5.8188449710777835336 ] 
dist 43=[-.5026584647527769133 ,5.9502571830001246200 ] 
dist 44=[-.4486959301504421030 ,5.9713924707189715949 ] 
dist 45=[.3954325182464049057 ,6.0667062127035689034 ] 
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dist 177=[2.75489495166559945000e-05,.00012699017139744265] 
dist 178=[2.29723557046931970000e-05,.00013122340580666643] 
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dist 182=[2.74207755051761400000e-05,4.84492734095584500000e-05] 
dist 183=[1.18689236559477200000e-05,4.29362607546311000000e-05] 
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dist 187=[-5.19069422367775700000e-05,2.73187565282296000000e-05] 
dist 188=[-6.05880739008629600000e-05,2.62688368016339000000e-05] 
dist 189=[-6.75977624203125600000e-05,1.54535883881370000000e-05] 
dist 190=[-7.10494196154109500000e-05,1.35746703956064000000e-05] 
dist 191=[-7.31261532416877900000e-05,1.03959775795785000000e-05] 
dist 192=[-7.35297792378601900000e-05,9.60869804132400000000e-06] 
dist 193=[-6.18136422510548000000e-05,7.91774987757430000000e-06] 
dist 194=[-6.02223040177307000000e-05,7.88915481475810000000e-06] 
dist 195=[-5.56972863761902000000e-05,8.54762323647090000000e-06] 
dist 196=[-4.97891976275605000000e-05,1.03046800446051000000e-05] 
dist 197=[-3.16366294984729900000e-05,1.22644866859324900000e-05] 
dist 198=[-2.91936108486260400000e-05,1.37299942842915700000e-05] 
dist 199=[-2.62952252404726000000e-05,1.50969614514993100000e-05] 
dist 200=[-2.53253838981333400000e-05,1.66650515328664480000e-05] 
dist 201=[-6.59754645042340000000e-07,1.82208598811482900000e-05] 
dist 202=[2.34023743239738000000e-06,2.27863033431244200000e-05] 
dist 203=[5.11535177906102700000e-06,2.69221289433600700000e-05] 
dist 204=[5.73758458007970300000e-06,3.03959102692871100000e-05] 
dist 205=[6.02129356215315550000e-06,3.31394673192885500000e-05] 
dist 206=[5.15221749895486300000e-06,3.43700157519103700000e-05] 
dist 207=[3.39544849911177116000e-06,3.49389046410580800000e-05] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 2, 2, 2, 0, 2] 
dist 0=[70.518720881377558485  ,70.518720881377558485  ] 
dist 1=[68.234712638693245098  ,71.699937668855134887  ] 
dist 2=[65.733307246148408529  ,72.331372201598608047  ] 
dist 3=[63.684605664740019355  ,72.443519410281992860  ] 
dist 4=[61.576390507065450246  ,72.244390584637564200  ] 
dist 5=[58.837752512133683753  ,71.830240857510680325  ] 
dist 6=[55.906271554080625718  ,71.635451261567542178  ] 
dist 7=[53.028689143169641076  ,71.390826811617285843  ] 
dist 8=[49.642092678978085320  ,70.878089437156004241  ] 
dist 9=[44.679639163032636996  ,61.997927146095706983  ] 
dist 10=[39.597977026301392767  ,59.709206801104168693  ] 
dist 11=[35.735706494549872929  ,59.085252011981030053  ] 
dist 12=[32.030614167932865402  ,56.776687729213971014  ] 
dist 13=[27.576002255352983248  ,56.176449264486472819  ] 
dist 14=[22.985257226696278014  ,55.145704925568954950  ] 
dist 15=[18.736811394671103536  ,54.841578639918386825  ] 
dist 16=[13.928671571125450336  ,53.534903915075975839  ] 
dist 17=[7.104293999961685159  ,33.044063772763541564  ] 
dist 18=[.383328683732266977  ,12.886132431824345690  ] 
dist 19=[-4.012514955744332921  ,11.962239197738129655  ] 
dist 20=[-7.545176133028681639  ,6.5747970107941525173 ] 
dist 21=[-10.822534295334857472  ,5.9737155290129047984 ] 
dist 22=[-13.686868793164702079  ,.70612181160681208872] 
dist 23=[-15.572281211031479915  ,.149992516465326303  ] 
dist 24=[-17.105980272862579247  ,-1.3800170268153081952 ] 
dist 25=[-18.568605377143871058  ,-1.5707209767699504965 ] 
dist 26=[-19.780268674397331407  ,-6.4641398803460614043 ] 
dist 27=[-20.312212523550532377  ,-7.0235961772949465465 ] 
dist 28=[-20.535073227033940686  ,-7.9826427411368887430 ] 
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dist 30=[-18.932652732977898396  ,-8.2659541133241442147 ] 
dist 31=[-18.490473727729040059  ,-7.9594150673411544164 ] 
dist 32=[-15.633561991600068923  ,-6.9179517304454319378 ] 
dist 33=[-10.236968285556387225  ,-5.6701284721229655490 ] 
dist 34=[-8.7821506291244360162 ,-4.5336920876415311797 ] 
dist 35=[-6.3026474514041089406 ,-3.266853228246695904  ] 
dist 36=[-5.9330836411788161193 ,-2.025965756644093763  ] 
dist 37=[-3.3380177486801585277 ,-.992323991399279216  ] 
dist 38=[-2.2900335170546517181 ,.079890853140858114  ] 
dist 39=[-2.1341283943366576718 ,1.474972339305835323  ] 
dist 40=[-1.1903252236438188532 ,2.817318174405003585  ] 
dist 41=[-1.0844610602171415631 ,3.965886215215654114  ] 
dist 42=[.68283123762474480562,4.988850131734541428  ] 
dist 43=[.90896712332130027606,5.776780895218629431  ] 
dist 44=[1.3367021078919239473 ,6.444611125076156266  ] 
dist 45=[1.4291506411432335988 ,6.980616701462035365  ] 
dist 46=[1.3471855194145958041 ,7.243151753733556051  ] 
dist 47=[.83439712514382610719,7.368183421448626950  ] 
dist 48=[.2837925107693302858 ,7.377364569780382285  ] 
dist 49=[-.1214235639460187211 ,4.2888299928781891047 ] 
dist 50=[-.4931075522256996309 ,4.0092205096452591041 ] 
dist 51=[-.9105250085822631043 ,3.3138513278865388004 ] 
dist 52=[-1.320193985758665966  ,3.1801379217588958340 ] 
dist 53=[-1.661192181755992491  ,2.1113963810908783325 ] 
dist 54=[-2.014010391533471137  ,1.9078658162087947298 ] 
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dist 56=[-2.907897720513016729  ,1.4909511783130747911 ] 
dist 57=[-3.181518709579168573  ,.12793568479406717316] 
dist 58=[-3.385707209141526864  ,-.2181484131601802693 ] 
dist 59=[-3.546249338340074892  ,-.38728520054388658105] 
dist 60=[-3.665146296144736797  ,-.48757409522124901641] 
dist 61=[-3.703525351307838825  ,-.50805649201441102711] 
dist 62=[-3.701318476497258873  ,-.54907542118065443776] 
dist 63=[-3.681204988125730498  ,-.53717556045308857671] 
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dist 67=[-.4673335967281705696 ,-.26768359278215180678] 
dist 68=[-.4466283881300156468 ,-.2079957746032346245 ] 
dist 69=[-.379882811479270004  ,-.14035400988948955371] 
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dist 71=[-.23511098700700245927,.04705890215389937341] 
dist 72=[-.20518358931418624118,.15259298875126838582] 
dist 73=[-.19578384271774751214,.22131693252921296975] 
dist 74=[.01493364109957135240,.2856363554200001468 ] 
dist 75=[.04059771251814635918,.3445894436680830020 ] 
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dist 77=[.08242080178301038615,.4401766677832835096 ] 
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dist 80=[.04123470810556302714,.4810663770406680699 ] 
dist 81=[0                     ,.33877929540091931808] 
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dist 86=[.00847547704287612128,.11819701233242655469] 
dist 87=[-.01321997170577035747,.09772418413292582149] 
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dist 90=[-.1143412952431990739 ,-.00161455839439746828] 
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dist 92=[-.1675481422647079923 ,-.01582908261555477802] 
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dist 100=[-.03953491562225913647,.00059313782973158275] 
dist 101=[-.02908166904502619271,.00523995715415814438] 
dist 102=[-.02629638588269376160,.01012562876024606994] 
dist 103=[-.02559293539695209716,.01654296213825699140] 
dist 104=[-.01312303800335490841,.02270023940107720047] 
dist 105=[.00319717520340585630,.02655147792841314042] 
dist 106=[.01041990433780020706,.02941253252778457858] 
dist 107=[.01149023655570176476,.03162920012449337089] 
dist 108=[.01535654875998477262,.03327096435257109439] 
dist 109=[.01555388724607632166,.03684398718822224537] 
dist 110=[.01490854666166390264,.03877644604746250536] 
dist 111=[.01295769436019902809,.03977742567289355835] 
dist 112=[.01075502240904104479,.03995008543296727630] 
dist 113=[.00910734220604118493,.02589114877611685677] 
dist 114=[.0075714859724092046 ,.02461170158105684716] 
dist 115=[.0058130171385292530 ,.02110197012365008817] 
dist 116=[.0040716769455234187 ,.02054567215797560396] 
dist 117=[.0026035554456853793 ,.01411127407559117600] 
dist 118=[.0010711207022565123 ,.01283750619702302309] 
dist 119=[-.0009266000436285279 ,.01135706718923935450] 
dist 120=[-.0028564751147941027 ,.01095325823751380282] 
dist 121=[-.00621486312010152355,-.00127246637549994799] 
dist 122=[-.00901864135959369446,-.00272900488700671579] 
dist 123=[-.01120763022084161366,-.0050519105456368338 ] 
dist 124=[-.01309776090890301119,-.00584784720550790634] 
dist 125=[-.01463136917135980496,-.0059822708438070516 ] 
dist 126=[-.01540137497690662998,-.0057770229063430182 ] 
dist 127=[-.01580893264366303447,-.00516584876893769803] 
dist 128=[-.01589994749682621683,-.00446667103430249604] 
dist 129=[-.00524817983975141832,-.00391118150181779969] 
dist 130=[-.00486938254033677310,-.00336161233484598575] 
dist 131=[-.00386968684718728996,-.00268576594084493628] 
dist 132=[-.00372592874643546359,-.00199041816973393126] 
dist 133=[-.00212252156523222107,-.00136312878648802803] 
dist 134=[-.00179790528616860774,-.00067283811428585821] 
dist 135=[-.00170346328266945053,.0002733250636573004 ] 
dist 136=[-.0013095594200917462 ,.0011982393703778559 ] 
dist 137=[.00033133039468050746,.0018040154082283541 ] 
dist 138=[.00080195357578400950,.0022854374203147349 ] 
dist 139=[.00091407231639056135,.0027155162581661563 ] 
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dist 151=[-7.34002394551902000000e-05,.00088768291662106516] 
dist 152=[-.0002474205837422593 ,.00084094448421219733] 
dist 153=[-.00060107533579396303,-5.17377245370744900000e-05] 
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dist 164=[-.00034245044757133785,-.0001593876084496354 ] 
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dist 166=[-.00020080898813243186,-5.23982353265075000000e-05] 
dist 167=[-.00019401697772291532,2.38287923613703000000e-05] 
dist 168=[-.00013327034052997523,9.81158716119343000000e-05] 
dist 169=[4.03042349145918300000e-05,.0001463078013649372 ] 
dist 170=[8.22889132886062000000e-05,.00019395292359057732] 
dist 171=[9.16660266849267000000e-05,.00023803929687470691] 
dist 172=[.00011980382044425610,.00027584948395231938] 
dist 173=[.00012345314007044524,.00030629838560502735] 
dist 174=[.00011977068344848729,.00032109390128220104] 
dist 175=[.00010519157619205171,.00032865614738009674] 
dist 176=[8.83197354842744300000e-05,.00033032003359348137] 
dist 177=[7.55141732270897100000e-05,.00023402563440663556] 
dist 178=[6.34003621177505700000e-05,.00022411429567969148] 
dist 179=[4.92764883245410900000e-05,.00019626144525655110] 
dist 180=[3.51566164294582000000e-05,.00019153055922483343] 
dist 181=[2.30564024626508000000e-05,.00013786440945724722] 
dist 182=[1.02644905647751000000e-05,.00012697721636695998] 
dist 183=[-6.60987089892810000000e-06,.00011395184902194439] 
dist 184=[-4.34459152707438000000e-05,.00010964472640657493] 
dist 185=[-8.01122845815963470000e-05,1.46140213194356000000e-06] 
dist 186=[-.00010358739915717664,-1.16925337696744300000e-05] 
dist 187=[-.00012163378344077854,-2.56441127466291690000e-05] 
dist 188=[-.00013670049472490016,-2.83659101354333330000e-05] 
dist 189=[-.00014857445479358502,-2.86829440585877192000e-05] 
dist 190=[-.00015391654390066165,-2.43195088499657503000e-05] 
dist 191=[-.00015636140356348555,-1.59295633542261854200e-05] 
dist 192=[-.00015670709897976570,0                     ] 
dist 193=[-4.37542711663312600000e-05,-3.08969255648513200000e-05] 
dist 194=[-4.06895617017552900000e-05,-2.63135380841571200000e-05] 
dist 195=[-3.26223506233287000000e-05,-2.06211335122851700000e-05] 
dist 196=[-3.13828384577244000000e-05,-1.47385423277644200000e-05] 
dist 197=[-1.96139968334373700000e-05,-9.39776596068016000000e-06] 
dist 198=[-1.68086921009642100000e-05,-3.49612685289450000000e-06] 
dist 199=[-1.60103473770326500000e-05,4.61861645585040000000e-06] 
dist 200=[-1.13563301370193000000e-05,1.25527321685014000000e-05] 
dist 201=[1.38086643308479200000e-06,1.77359858164415000000e-05] 
dist 202=[4.81524984236187000000e-06,2.18370270160808000000e-05] 
dist 203=[5.55637032196210000000e-06,2.54655108093542000000e-05] 
dist 204=[7.40168301443002000000e-06,2.84623217295006000000e-05] 
dist 205=[7.36791064412786000000e-06,3.00501739583962000000e-05] 
dist 206=[6.59953245460329000000e-06,3.09556090453613000000e-05] 
dist 207=[4.64161989322830300000e-06,3.16977217753156000000e-05] 
dist 208=[2.44558599021565000000e-06,3.18227740922789000000e-05] 
dist 209=[7.29774222494660000000e-07,2.12481149741708400000e-05] 
dist 210=[-9.40641232056800000000e-07,2.01952957817798400000e-05] 
dist 211=[-2.95654542434298000000e-06,1.74847528502446800000e-05] 
dist 212=[-5.00928673887350000000e-06,1.68775061511199300000e-05] 
dist 213=[-6.82651593131710000000e-06,1.22835072793976500000e-05] 
dist 214=[-8.79698474056610000000e-06,1.13568374580572900000e-05] 
dist 215=[-1.14596531876818000000e-05,9.74944238982012000000e-06] 
dist 216=[-1.40420627643587000000e-05,9.34002686058190000000e-06] 
dist 217=[-1.56933286655196000000e-05,1.64794054483207000000e-06] 
dist 218=[-1.69597004303070000000e-05,6.02906710023390000000e-07] 
dist 219=[-1.80108595172726000000e-05,-1.48587334784738000000e-06] 
dist 220=[-1.88290047272720000000e-05,-1.98805986509731000000e-06] 
dist 221=[-1.91683603501852000000e-05,-2.65850078123376000000e-06] 
dist 222=[-1.92288113610713000000e-05,-2.38611108408836000000e-06] 
dist 223=[-1.91722183395613000000e-05,-1.79189328188148000000e-06] 
dist 224=[-1.84193232773233000000e-05,-1.14278303269471000000e-06] 
dist 225=[-4.53596176630351000000e-06,-6.51993655439800000000e-07] 
dist 226=[-4.08203396302222000000e-06,-1.89565412885750000000e-07] 
dist 227=[-3.98432254938618000000e-06,3.46844452351320000000e-07] 
dist 228=[-3.08087897051088000000e-06,8.81455434330320000000e-07] 
dist 229=[-2.89012312881491000000e-06,1.33679758757680000000e-06] 
dist 230=[-2.61486225962001000000e-06,1.81564759281800000000e-06] 
dist 231=[-2.52471821227709000000e-06,2.44385501356765000000e-06] 
dist 232=[-6.12021422045510000000e-07,3.04451580642296000000e-06] 
dist 233=[-3.66108893289210000000e-07,3.41380799761896000000e-06] 
dist 234=[1.89280901912050000000e-07,3.68008192921309000000e-06] 
dist 235=[2.92976965331620000000e-07,3.87092099217475000000e-06] 
dist 236=[4.57945522852419200000e-07,3.99902143739225000000e-06] 
dist 237=[3.92121531964840300000e-07,4.02528969785230000000e-06] 
dist 238=[2.58551799332425420000e-07,3.99629010323090000000e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 0, 0, 1, 1, 2] 
dist 0=[91.225948873726659072  ,91.225948873726659072  ] 
dist 1=[90.523060597841995940  ,91.608675229260614954  ] 
dist 2=[88.105452230032163334  ,92.202169208225617516  ] 
dist 3=[84.174016486235323779  ,93.712288425643448446  ] 
dist 4=[77.214016006640243413  ,95.225970388603047531  ] 
dist 5=[69.893813742662339997  ,95.758821128954553458  ] 
dist 6=[64.525109373428927821  ,95.798978442353015201  ] 
dist 7=[59.574361148774605504  ,95.348418970743650758  ] 
dist 8=[53.920087894926256205  ,88.851157908775795427  ] 
dist 9=[48.265393260983730093  ,87.613683975577966079  ] 
dist 10=[43.040349425733996670  ,85.040749244718406787  ] 
dist 11=[32.397146442739456389  ,84.197521447930387385  ] 
dist 12=[19.456381134296610432  ,80.261475807057686360  ] 
dist 13=[0                     ,79.371412670758273112  ] 
dist 14=[18.197502169263304592  ,76.569060253328854661  ] 
dist 15=[13.681348847359092126  ,76.112755800256830424  ] 
dist 16=[8.8247852292340502415 ,30.944025961561372192  ] 
dist 17=[4.1310314933680436696 ,26.829247174416466886  ] 
dist 18=[.2637101045968746166 ,17.149546825782859221  ] 
dist 19=[-3.7340297998358370439 ,15.753185719581971736  ] 
dist 20=[-8.9491507082478973296 ,15.084441887474117979  ] 
dist 21=[-13.962074854091787270  ,4.7185777050703943712 ] 
dist 22=[-17.153684565241587857  ,3.6684166867862756121 ] 
dist 23=[-19.621537973400991504  ,1.3313859569254994356 ] 
dist 24=[-21.747555818863615609  ,.9885249622692719370 ] 
dist 25=[-23.495264875831928999  ,-1.6590018834995327201 ] 
dist 26=[-24.454662648448150274  ,-2.0827630682335912719 ] 
dist 27=[-25.026731454708330080  ,-2.7274313075792058985 ] 
dist 28=[-25.231062472092830379  ,-2.8501564455275808144 ] 
dist 29=[-25.200228500904688110  ,-4.4827327725460254050 ] 
dist 30=[-25.094853723037129610  ,-4.6768616064616720603 ] 
dist 31=[-24.166915414599627011  ,-4.8559657667572091367 ] 
dist 32=[-11.266006154481725973  ,-4.7717507404063092002 ] 
dist 33=[-10.155883467702607818  ,-4.5794999393149046072 ] 
dist 34=[-7.4092312025202892761 ,-4.2525376194204966078 ] 
dist 35=[-7.0092561111118914522 ,-3.7685755862736093199 ] 
dist 36=[-6.0029698326076015924 ,-2.8015321540677174323 ] 
dist 37=[-2.8632104586891440946 ,-1.2123518248233301488 ] 
dist 38=[-2.5931152630385506643 ,.3493803639597717925 ] 
dist 39=[-1.9567898003495645294 ,2.2680965817105919081 ] 
dist 40=[-1.8432961460950027348 ,4.0884622581705382573 ] 
dist 41=[-.9890245899146248025 ,5.2586332078318718725 ] 
dist 42=[-.8361456113586188233 ,6.1703810489204338324 ] 
dist 43=[-.5786119562631095240 ,6.9609272197912154506 ] 
dist 44=[-.5198306959419302904 ,7.6082159638555333273 ] 
dist 45=[.3930775640143667044 ,7.9490360110716944272 ] 
dist 46=[.5139005214410646817 ,8.1289927922255077338 ] 
dist 47=[.6056143472840257146 ,8.1555289342794226996 ] 
dist 48=[.5303963086109759904 ,4.5634805027162725961 ] 
dist 49=[.4122099082726747533 ,4.2566903786359807145 ] 
dist 50=[.2455092545540809844 ,3.4892661322726686962 ] 
dist 51=[.0137135583205724949 ,3.3479084874942121393 ] 
dist 52=[-.36378042006198015534,2.7137716501658880873 ] 
dist 53=[-.7551813883909643828 ,1.9367161334920438896 ] 
dist 54=[-1.0424445841558675351 ,1.5869697199939294667 ] 
dist 55=[-1.3055327048718190524 ,1.4931702441349085681 ] 
dist 56=[-1.7803853773493691882 ,.25929319350949717437] 
dist 57=[-2.3238125735975451620 ,.0668597322621965689 ] 
dist 58=[-2.7466564793236018410 ,.0332072441976302766 ] 
dist 59=[-3.1105972411703991070 ,-.0101627699700056644 ] 
dist 60=[-3.4053801513031337985 ,-.0172501396489959135 ] 
dist 61=[-3.5528201889111485166 ,-.2388497457291455045 ] 
dist 62=[-3.6273975318979420446 ,-.2643316495606467618 ] 
dist 63=[-3.6353746795341511724 ,-.3108260845098488512 ] 
dist 64=[-.83513057945537196467,-.3197354336550163808 ] 
dist 65=[-.76764977396084059891,-.3333564910165629507 ] 
dist 66=[-.59370443765251099003,-.32402567139815654859] 
dist 67=[-.56869889732378455157,-.30181937006698994981] 
dist 68=[-.4165226417731662841 ,-.25659609210434736117] 
dist 69=[-.2394892358368815023 ,-.1644492560904503480 ] 
dist 70=[-.19188568659546577721,-.0467884840257701330 ] 
dist 71=[-.1685953526913008981 ,.1034763363384370883 ] 
dist 72=[-.14322167544159181945,.2477907392239390478 ] 
dist 73=[-.08249954040195237118,.3417787403473459737 ] 
dist 74=[-.07131230211851728057,.4160713498818004596 ] 
dist 75=[-.05399254697613408024,.4819717191462731328 ] 
dist 76=[-.04947096068210165093,.5367433309791498157 ] 
dist 77=[.02791146663737932865,.5667257856814360628 ] 
dist 78=[.03785792446033309603,.5840383338283190013 ] 
dist 79=[.05673850353113698676,.5883604604738477960 ] 
dist 80=[.06085820528492657545,.33796632786066658173] 
dist 81=[.07099474658913879893,.31713162166153557458] 
dist 82=[.07066003525463509832,.26382563560025417377] 
dist 83=[.06624151316686436833,.25394414993878116599] 
dist 84=[.05517424780648457693,.1705400597931040494 ] 
dist 85=[.04302733700898518987,.15066434556126780639] 
dist 86=[.03430672919572808162,.12553314024387202114] 
dist 87=[-.0269795372183220821 ,.11838612338138723983] 
dist 88=[-.0950131082583921344 ,.02763489291340698260] 
dist 89=[-.1394390554077994117 ,.01194174941356976091] 
dist 90=[-.1746439846710306006 ,.00910145800793844637] 
dist 91=[-.2059748181802405828 ,.00552926696295692058] 
dist 92=[-.2320504294995602107 ,.00483746039538154473] 
dist 93=[-.2463367852361696559 ,-.01526653198169592192] 
dist 94=[-.2545882095381337419 ,-.01760503808483935724] 
dist 95=[-.2566404436244813942 ,-.02191395797305264178] 
dist 96=[-.07013759452576131283,-.02277216031504518709] 
dist 97=[-.06499681776076017034,-.02430368684073445176] 
dist 98=[-.05156293433376191494,-.02362646101913785892] 
dist 99=[-.04957175165017627410,-.02180586028543247440] 
dist 100=[-.0357297574229600179 ,-.01798019933287759340] 
dist 101=[-.02325644584203704687,-.01384653734584658635] 
dist 102=[-.0218078203522040814 ,-.0051215246530802623 ] 
dist 103=[-.0185512099977759618 ,.0081768962975936995 ] 
dist 104=[-.0179911358358203605 ,.0209948423068822023 ] 
dist 105=[-.0124127574612926971 ,.0292809736314082279 ] 
dist 106=[-.0113200780791391902 ,.0357507077009879451 ] 
dist 107=[-.0098820466550741398 ,.0413393319013498186 ] 
dist 108=[-.0093987035687880400 ,.0458667739404127811 ] 
dist 109=[.00030103059818456805,.0481127988795958679 ] 
dist 110=[.00150084111911483400,.0492633813936392863 ] 
dist 111=[.0027623099377202201 ,.0494308235268140797 ] 
dist 112=[.0025117873873764644 ,.0333986762368857431 ] 
dist 113=[.00197383547843269680,.0318465015211616563 ] 
dist 114=[.00107086355596054665,.0275717775761871249 ] 
dist 115=[-.00025896290713373159,.0268604706634890918 ] 
dist 116=[-.00249573781900972190,.0189274618569674104 ] 
dist 117=[-.00483496791031284073,.0173416244907298847 ] 
dist 118=[-.00657280525486525502,.0154276194382749748 ] 
dist 119=[-.00818213375915698381,.0148244833482686401 ] 
dist 120=[-.0107010811766504884 ,.00277663830144995162] 
dist 121=[-.0141426316567928190 ,.00132561581382039902] 
dist 122=[-.0167952010257417281 ,.00105871109574013713] 
dist 123=[-.0190245938851337684 ,.00074192696032869376] 
dist 124=[-.0207985213323959040 ,.00068819390632470319] 
dist 125=[-.0216383810069972549 ,-.00144378012082532006] 
dist 126=[-.0220445768470081071 ,-.00168987572403473653] 
dist 127=[-.0220926374710417741 ,-.00217578096379319643] 
dist 128=[-.00644397546439290169,-.00228217282368102469] 
dist 129=[-.00599093850933062979,-.00255208993247811996] 
dist 130=[-.00478940694205339334,-.00254105178216845283] 
dist 131=[-.00461666133074443892,-.00242239452017525391] 
dist 132=[-.00320665769197988581,-.00212791210188390837] 
dist 133=[-.00219663035878918757,-.00161276242344747543] 
dist 134=[-.00176052615632214877,-.00069213907522820907] 
dist 135=[-.00168488791447789509,.00051271149895730197] 
dist 136=[-.00133590688377610066,.00167792147785923888] 
dist 137=[-.00086314938046480646,.00244087803657695485] 
dist 138=[-.00077248320172296443,.00304706234945717353] 
dist 139=[-.00063473667926950978,.00358842091519184821] 
dist 140=[-.00059618846527633876,.00403967210310647985] 
dist 141=[.00011377239980134772,.00428727515993772725] 
dist 142=[.00020529702661647763,.00443053327351937626] 
dist 143=[.00038692001653867502,.00446653090763117821] 
dist 144=[.00042904533041809123,.00270139862153978721] 
dist 145=[.00055020628204338167,.00255212570526740043] 
dist 146=[.00056256170984104694,.00216292220838278076] 
dist 147=[.00054024771029571446,.00208823106622997292] 
dist 148=[.00046519784579661471,.00142745882359862095] 
dist 149=[.00037991407869149911,.00129741882710228528] 
dist 150=[.00031685802986496477,.00110235340241280260] 
dist 151=[-.00015615526686480422,.00104535973872096698] 
dist 152=[-.00071789244027684834,.00026173241249763409] 
dist 153=[-.00108603005260041891,.00013717922243893337] 
dist 154=[-.00137876748783552478,.00011396610894773200] 
dist 155=[-.00164048531701206987,8.58689346644311900000e-05] 
dist 156=[-.00185874196375304418,8.00645245199922900000e-05] 
dist 157=[-.00197854095095038884,-.00010946700651978749] 
dist 158=[-.00204786972833929766,-.00013171727540227621] 
dist 159=[-.00206529213037516837,-.00017596548267561732] 
dist 160=[-.00056917635918467184,-.00018582022302394546] 
dist 161=[-.00053109856792919602,-.00021189422592094626] 
dist 162=[-.00042980552330064562,-.00021195142109872419] 
dist 163=[-.00041468770610419523,-.00020252917768713446] 
dist 164=[-.00028146523277603321,-.00017787095364598074] 
dist 165=[-.00020835735864922190,-.00015015811524692632] 
dist 166=[-.00017178063702337604,-6.74816729800082000000e-05] 
dist 167=[-.00016153097614287780,4.18615043985011600000e-05] 
dist 168=[-.00014289101664707897,.00014775484916114650] 
dist 169=[-9.76029568271042400000e-05,.00021671018619444023] 
dist 170=[-8.86581764836668100000e-05,.00027104133150738779] 
dist 171=[-7.82023751345086000000e-05,.00031874630291631631] 
dist 172=[-7.53366535352634400000e-05,.00035790088399867224] 
dist 173=[9.93583468664975800000e-06,.00037820990170775739] 
dist 174=[2.01037890602606840000e-05,.00038889336375877829] 
dist 175=[3.91591645128726000000e-05,.00039070233405571763] 
dist 176=[4.28136929915668700000e-05,.00026471972349328134] 
dist 177=[5.31885421707096200000e-05,.00025291366100181313] 
dist 178=[5.40631593114420410000e-05,.00021967972364022067] 
dist 179=[5.18275401577072640000e-05,.00021434738577076659] 
dist 180=[4.48026606176645500000e-05,.00015058053803362470] 
dist 181=[3.68559615142826270000e-05,.00013775591884615125] 
dist 182=[3.09511752827594000000e-05,.00012312935438210282] 
dist 183=[-1.37512022038283500000e-05,.00011899539187769307] 
dist 184=[-5.91201488867292700000e-05,2.57347649980795700000e-05] 
dist 185=[-8.85699318733462700000e-05,1.36538344547801020000e-05] 
dist 186=[-.00011166402599529952,1.13894864001104990000e-05] 
dist 187=[-.00013174582630554407,8.78522101371766000000e-06] 
dist 188=[-.00014808274949706757,8.33490823994793000000e-06] 
dist 189=[-.00015627701189320183,-1.09020636992275200000e-05] 
dist 190=[-.00016063674608147287,-1.31256560975120100000e-05] 
dist 191=[-.00016171529720672949,-1.76139946484224900000e-05] 
dist 192=[-5.41841029396928560000e-05,-1.85708089800074400000e-05] 
dist 193=[-5.06057550408433410000e-05,-2.14369616358314600000e-05] 
dist 194=[-4.09906806707428800000e-05,-2.15469508016721100000e-05] 
dist 195=[-3.96074493866753400000e-05,-2.07278820275115620000e-05] 
dist 196=[-2.69745045863560400000e-05,-1.84409871254834560000e-05] 
dist 197=[-1.97062438515229900000e-05,-1.47756010356020090000e-05] 
dist 198=[-1.61511896187925100000e-05,-7.00123863661175000000e-06] 
dist 199=[-1.55272388433075500000e-05,3.27282722685309000000e-06] 
dist 200=[-1.21441736411224400000e-05,1.32353965623540400000e-05] 
dist 201=[-8.15088276010946000000e-06,1.97708822285256300000e-05] 
dist 202=[-7.37121441083770400000e-06,2.49724277348112600000e-05] 
dist 203=[-6.19502933820882900000e-06,2.96277506028516100000e-05] 
dist 204=[-5.85650158128712300000e-06,3.35112382500942400000e-05] 
dist 205=[5.56403509727329400000e-07,3.56418673093503700000e-05] 
dist 206=[1.38435478160135120000e-06,3.68727126976628900000e-05] 
dist 207=[3.04077306666755000000e-06,3.71761646792641900000e-05] 
dist 208=[3.43142289711508000000e-06,2.30728591691890420000e-05] 
dist 209=[4.59986150641081000000e-06,2.18668219392934223000e-05] 
dist 210=[4.75491747037459200000e-06,1.86908037318710250000e-05] 
dist 211=[4.60634072871907300000e-06,1.80706987670471330000e-05] 
dist 212=[4.00720481587462000000e-06,1.25561585633382030000e-05] 
dist 213=[3.31438209540375300000e-06,1.14598354607087500000e-05] 
dist 214=[2.79295161602300700000e-06,9.81971865406289400000e-06] 
dist 215=[-1.13165800278683900000e-06,9.33380972796782400000e-06] 
dist 216=[-5.98621950865514600000e-06,2.43789881404619100000e-06] 
dist 217=[-9.17215548787263800000e-06,1.36568501427831600000e-06] 
dist 218=[-1.17087871050148680000e-05,1.16272126330537800000e-06] 
dist 219=[-1.39801166544013380000e-05,9.31711689814835000000e-07] 
dist 220=[-1.58751824374759560000e-05,8.89982380398328000000e-07] 
dist 221=[-1.69148309509006900000e-05,-7.86009648781880000000e-07] 
dist 222=[-1.75151831722049000000e-05,-9.77576395382480000000e-07] 
dist 223=[-1.76624518246578600000e-05,-1.35283582834366100000e-06] 
dist 224=[-4.93334795576928910000e-06,-1.43546121930746900000e-06] 
dist 225=[-4.62450045060534900000e-06,-1.64496470238444630000e-06] 
dist 226=[-3.78769386036126700000e-06,-1.63759941945818300000e-06] 
dist 227=[-3.66663674944879900000e-06,-1.54675838342492800000e-06] 
dist 228=[-2.49768395025147000000e-06,-1.31982606588713000000e-06] 
dist 229=[-1.90326561128533800000e-06,-1.06691855429495000000e-06] 
dist 230=[-1.70366932827469000000e-06,-5.53010006043995000000e-07] 
dist 231=[-1.53119836420482900000e-06,4.10291873737311000000e-07] 
dist 232=[-1.45481040219766000000e-06,1.34369961776261800000e-06] 
dist 233=[-1.05208302753413000000e-06,1.94743262312871500000e-06] 
dist 234=[-9.70352812258930000000e-07,2.41823136952231600000e-06] 
dist 235=[-8.68933708954960000000e-07,2.82277455420288800000e-06] 
dist 236=[-8.32784099924790000000e-07,3.14956600504525400000e-06] 
dist 237=[-3.28815762274500000000e-08,3.31104130893702400000e-06] 
dist 238=[6.55753844933300000000e-08,3.39426441395023800000e-06] 
dist 239=[1.38120028050700000000e-07,3.40971380189120200000e-06] 
dist 240=[1.36296295872160000000e-07,2.47617309866978090000e-06] 
dist 241=[1.13645261830060000000e-07,2.37745122969201900000e-06] 
dist 242=[6.19983265088700000000e-08,2.09557327453253600000e-06] 
dist 243=[-2.00035633187530000000e-08,2.04715491204236900000e-06] 
dist 244=[-1.63416168784350000000e-07,1.48917297458311800000e-06] 
dist 245=[-3.15227112619935000000e-07,1.37493332196764600000e-06] 
dist 246=[-4.30649609570930000000e-07,1.23936494755002000000e-06] 
dist 247=[-5.40051897691750000000e-07,1.19351750752251200000e-06] 
dist 248=[-8.20706321592251000000e-07,3.55405421073950000000e-08] 
dist 249=[-1.07280139997636900000e-06,-1.05458310726883000000e-07] 
dist 250=[-1.26731682948743100000e-06,-2.37357358232162600000e-07] 
dist 251=[-1.43081759350033400000e-06,-2.66546694855555900000e-07] 
dist 252=[-1.55995906043499300000e-06,-2.80571678752623500000e-07] 
dist 253=[-1.61777782366857200000e-06,-2.40277501489393290000e-07] 
dist 254=[-1.64448816533616400000e-06,-1.58447353069759703000e-07] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 2, 1, 0, 0, 1, 2] 
dist 0=[86.298666283087869513  ,86.298666283087869513  ] 
dist 1=[85.655321011243469958  ,86.672422226925959637  ] 
dist 2=[84.431315444229754014  ,86.863777260834842778  ] 
dist 3=[81.740337505358467384  ,86.779290135648352051  ] 
dist 4=[78.313842007992434362  ,86.524477003858704968  ] 
dist 5=[74.154667312192542870  ,86.273187711333488494  ] 
dist 6=[68.664150619885878362  ,85.481145097988746033  ] 
dist 7=[59.924694309639924076  ,85.068648978206241726  ] 
dist 8=[51.005314287238009379  ,82.658828462862033802  ] 
dist 9=[44.796868796029798542  ,81.915010208910645476  ] 
dist 10=[39.388806009889839906  ,81.277244327557936000  ] 
dist 11=[33.663755964654810726  ,80.856534468682129495  ] 
dist 12=[28.178053462691142226  ,80.569811475224607236  ] 
dist 13=[23.725323745656460815  ,80.152680116044360893  ] 
dist 14=[18.701617134555450016  ,76.464652833661230400  ] 
dist 15=[13.015384813123790259  ,67.453114459072860270  ] 
dist 16=[7.664774290675701867  ,32.289158591029010318  ] 
dist 17=[3.896749362307772025  ,28.518701402388007850  ] 
dist 18=[-.4560754273853074161 ,19.675443921424641583  ] 
dist 19=[-5.1488309408980148477 ,18.407533595022240672  ] 
dist 20=[-8.0901055938318746629 ,6.865713448004099709  ] 
dist 21=[-10.310184431424400515  ,4.890629286174949648  ] 
dist 22=[-12.126010850642931665  ,2.279315678632928197  ] 
dist 23=[-13.553755573784882813  ,1.856270796783344949  ] 
dist 24=[-14.224988754382258233  ,-.9276676716565903023 ] 
dist 25=[-14.551278171398573913  ,-1.1788885805678795033 ] 
dist 26=[-14.968493181729760850  ,-1.6465476989824022737 ] 
dist 27=[-16.732767356396537617  ,-1.7308545376152781408 ] 
dist 28=[-18.177639833259565873  ,-1.951918930595175070  ] 
dist 29=[-18.957849954225572599  ,-1.945968807665568178  ] 
dist 30=[-19.401603851058236694  ,-1.865977704603579422  ] 
dist 31=[-19.503108303500201558  ,-1.673625419758308984  ] 
dist 32=[-10.258453855922736661  ,-1.458519220185271801  ] 
dist 33=[-9.5047263207776609174 ,-.8209188756386228578 ] 
dist 34=[-7.6376542063428568638 ,.2118123527989747047 ] 
dist 35=[-7.3140870785183225463 ,1.2010190517328784443 ] 
dist 36=[-4.515966282838460627  ,1.8424160241063301343 ] 
dist 37=[-3.997365941700043795  ,2.3471856613157062428 ] 
dist 38=[-3.219545054930865294  ,2.7922783327191921032 ] 
dist 39=[-3.007519413369281604  ,3.1612709071726852444 ] 
dist 40=[-1.3791165873243005405 ,3.3629193379822576194 ] 
dist 41=[-1.3264950785058580177 ,4.0796068576744333082 ] 
dist 42=[-1.2293121160202122762 ,5.0116817250130044368 ] 
dist 43=[-1.2028266713241180838 ,5.8286945705199280027 ] 
dist 44=[-1.101558526259915417  ,6.5029204745940182375 ] 
dist 45=[-1.075781190036626012  ,6.8661332296710169608 ] 
dist 46=[-1.015282849138724338  ,7.0688354733918274910 ] 
dist 47=[-.992782777490424154  ,7.1087638305654994553 ] 
dist 48=[-.875927678245593212  ,2.1993987662698306209 ] 
dist 49=[-.847194476249096120  ,2.0585735109588074302 ] 
dist 50=[-.778559845785215366  ,1.6971250665201647838 ] 
dist 51=[-.753216871441235180  ,1.6400842890726249062 ] 
dist 52=[-.7372621783855918105 ,1.064659759797026585  ] 
dist 53=[-.9438041673797580893 ,.957601295455119017  ] 
dist 54=[-1.1275052235862516642 ,.646753255078080203  ] 
dist 55=[-1.2803617807762263733 ,.53787691105665359939] 
dist 56=[-1.3641247599119103384 ,.25607395352594849992] 
dist 57=[-1.4125463118093492684 ,.22331953773768711671] 
dist 58=[-1.4247092490564636990 ,.1441847594125714832 ] 
dist 59=[-1.0896005496684912411 ,.1328148720445968893 ] 
dist 60=[-1.2136610748036993358 ,.0230664054537346809 ] 
dist 61=[-1.2815178689437061328 ,.0039476601287855205 ] 
dist 62=[-1.3206916304136304882 ,-.0208521283462749571 ] 
dist 63=[-1.3305105733889862743 ,-.0249231551481803174 ] 
dist 64=[-.75877939111040301519,-.1111294233549937169 ] 
dist 65=[-.71143540804769468718,-.0545123712860810210 ] 
dist 66=[-.59049392935661778795,.0196903975876165997 ] 
dist 67=[-.56831884966130597198,.0913711530540310798 ] 
dist 68=[-.3730881795331574662 ,.1379619537977309118 ] 
dist 69=[-.3356222320714953348 ,.1746184655761337262 ] 
dist 70=[-.2794583937901869141 ,.2067641897388808744 ] 
dist 71=[-.2634913730712745961 ,.2331617688476387811 ] 
dist 72=[-.12340306291494400166,.2469408527545481703 ] 
dist 73=[-.11320745931062743124,.3034686688701820718 ] 
dist 74=[-.08829453848935983605,.3809674553679228388 ] 
dist 75=[-.08393870564142016566,.4498582545808618193 ] 
dist 76=[-.04754733482610683721,.5071681903894715877 ] 
dist 77=[-.0408502171715225305 ,.5385647855371274508 ] 
dist 78=[-.0305196357288218523 ,.5567073598877960298 ] 
dist 79=[-.0278153521743080402 ,.5612511340724941703 ] 
dist 80=[.0184780131383910919 ,.15573211366124104192] 
dist 81=[.0227935670611739687 ,.14443246102573532578] 
dist 82=[-.0066736882946950043 ,.11487016166504605974] 
dist 83=[-.0353663770086832329 ,.1105139035124734933 ] 
dist 84=[-.0539698924413300827 ,.0951226747840028522 ] 
dist 85=[-.0685445725725021535 ,.0999124957551124270 ] 
dist 86=[-.0812064782603990726 ,.1026470701933903944 ] 
dist 87=[-.0915095496627897244 ,.1032667399207012539 ] 
dist 88=[-.0966980065401623656 ,.02781870427806161770] 
dist 89=[-.0994682019584177144 ,.02530381309010417002] 
dist 90=[-.1001462474647904422 ,.0190918253334808863 ] 
dist 91=[-.08641655933492246609,.0180770484711716968 ] 
dist 92=[-.09657032769344005074,.0088751690246769431 ] 
dist 93=[-.10184134593249580919,.0071949731192811710 ] 
dist 94=[-.10458672857956095873,.0047985828478257057 ] 
dist 95=[-.10506737097022488747,.0041201738389131352 ] 
dist 96=[-.06882142858285391557,-.0076624064850291246 ] 
dist 97=[-.06551245348946621342,-.0048506992064155299 ] 
dist 98=[-.05636552295671374478,.0014379008614201146 ] 
dist 99=[-.05492134086046094138,.0075301805624290654 ] 
dist 100=[-.03795218510926072222,.0115222689388560626 ] 
dist 101=[-.03458328304226060927,.0146960479495794925 ] 
dist 102=[-.03070873082635550562,.0175323603131865750 ] 
dist 103=[-.02966725997399052201,.0198969735027563393 ] 
dist 104=[-.0181682994373297794 ,.0211938106118023219 ] 
dist 105=[-.0175589658326023033 ,.02303898655542674338] 
dist 106=[-.0160249574847898387 ,.02885460620468192569] 
dist 107=[-.0155600426958104843 ,.03388448743157799641] 
dist 108=[-.0128863413632567589 ,.03796900592985006818] 
dist 109=[-.0123013898753951277 ,.04002220170590128605] 
dist 110=[-.0111236906241607577 ,.04111210491701167779] 
dist 111=[-.0107764667224140925 ,.04136275295675776548] 
dist 112=[-.0055152497469571896 ,.01778123549120379593] 
dist 113=[-.0047495486625053832 ,.01698613722266602775] 
dist 114=[-.0030191292154662748 ,.0150254851112732308 ] 
dist 115=[-.00336557807560815031,.0144896874656938425 ] 
dist 116=[-.00522586432184189958,.0113597265717329733 ] 
dist 117=[-.00670608716710424610,.0107167748855781187 ] 
dist 118=[-.00803037668876419839,.00976150187229731426] 
dist 119=[-.0091349057132932476 ,.00975707419895467194] 
dist 120=[-.0097407545836864142 ,-.0034376642712609477 ] 
dist 121=[-.0100906308792916774 ,-.00376799659505675543] 
dist 122=[-.0101766655590194405 ,-.00334028109463370239] 
dist 123=[-.0075475224282050234 ,-.00283104573877476310] 
dist 124=[-.0085117751414414935 ,-.00243896629213329330] 
dist 125=[-.0090408308577359631 ,-.00206302201305428415] 
dist 126=[-.0093469149184294811 ,-.00161778541175166904] 
dist 127=[-.0094238124621474940 ,-.00116917320995373152] 
dist 128=[-.0057199901934308261 ,-.00077969491679430090] 
dist 129=[-.0054068107314634445 ,-.00036379953620122833] 
dist 130=[-.00458857522524928537,.00019001933049558319] 
dist 131=[-.00443165735149000110,.00072655739211191077] 
dist 132=[-.00303794374996595309,.00107373792926275244] 
dist 133=[-.00276349079447394630,.00134469162831850273] 
dist 134=[-.00235287879160071762,.00157796325183272943] 
dist 135=[-.00223247414972632661,.00176651722124232619] 
dist 136=[8.06921112760090000000e-05,.00185956587906090394] 
dist 137=[.0003789956278170275 ,.0022616358842386731 ] 
dist 138=[.0009852031403607281 ,.0028792416135457174 ] 
dist 139=[.00094005263573142245,.0034314143442303569 ] 
dist 140=[.00080027619362116945,.0038918949921462620 ] 
dist 141=[.00066286593338934477,.0041446468977084914 ] 
dist 142=[.00049528040196723063,.0042909136905975799 ] 
dist 143=[.00032378925830518761,.0043276628137126347 ] 
dist 144=[.00017080897627587054,.00120027142415783289] 
dist 145=[4.00742805654608400000e-06,.00112111337833603941] 
dist 146=[-.0002225020057710488 ,.00091002946516366225] 
dist 147=[-.00044263278075489948,.00087853701129229251] 
dist 148=[-.00058407089963122714,.0005159086712889646 ] 
dist 149=[-.00069330435861702921,.0004467517940063557 ] 
dist 150=[-.00078531972543367663,.0003660545543505670 ] 
dist 151=[-.00085808948440836408,.0003489380665796611 ] 
dist 152=[-.00089075300806987460,-.00013066528211078095] 
dist 153=[-.00090597851327206255,-8.64067546420110559000e-05] 
dist 154=[-.00090937065307207130,0                     ] 
dist 155=[-.0006602775724656759 ,-.00026435190336447946] 
dist 156=[-.0007425384501367101 ,-.0002283538866075569 ] 
dist 157=[-.0007852010356275329 ,-.0001938852126810361 ] 
dist 158=[-.0008076754590047388 ,-.0001531298371588106 ] 
dist 159=[-.0008114697616616364 ,-.0001121048688023573 ] 
dist 160=[-.0005520005481404893 ,-7.65559034998833000000e-05] 
dist 161=[-.0005276223974477143 ,-3.86594307150966000000e-05] 
dist 162=[-.0004588269222845920 ,1.17125088763804000000e-05] 
dist 163=[-.0004477739797196133 ,6.06075059355415000000e-05] 
dist 164=[-.0003152772801427538 ,9.26311023846358000000e-05] 
dist 165=[-.0002886019103735768 ,.0001180500368986389 ] 
dist 166=[-.0002581979176102392 ,.0001406701646484044 ] 
dist 167=[-.0002495760938064778 ,.0001594385164712601 ] 
dist 168=[1.68601513865522900000e-05,.0001695337335802702 ] 
dist 169=[4.86742697468615700000e-05,.0001833585940272141 ] 
dist 170=[.0001004967743450994 ,.0002314898532229819 ] 
dist 171=[.00010565413892394569,.0002733523375869328 ] 
dist 172=[9.28179663109421900000e-05,.0003074134062887571 ] 
dist 173=[7.98259049631862400000e-05,.0003245055801971730 ] 
dist 174=[6.34602733589525800000e-05,.0003335915836266018 ] 
dist 175=[4.64397444037362000000e-05,.0003357945959782806 ] 
dist 176=[3.08400817835064000000e-05,.00011259226230137337] 
dist 177=[1.34913530871909000000e-05,.00010526654634351943] 
dist 178=[-1.04895017131069000000e-05,8.55289265366949200000e-05] 
dist 179=[-3.39737222901696000000e-05,8.26905266951360300000e-05] 
dist 180=[-4.93476246315479000000e-05,4.82264197261849000000e-05] 
dist 181=[-6.15408432872772000000e-05,4.16404280478884000000e-05] 
dist 182=[-7.23720669614987000000e-05,3.43196510253980000000e-05] 
dist 183=[-8.13432842008667000000e-05,3.30365739869862000000e-05] 
dist 184=[-8.61370823298709000000e-05,-2.24157966865349600000e-05] 
dist 185=[-8.87337087319844000000e-05,-2.06525949036646800000e-05] 
dist 186=[-8.92131833847105000000e-05,-1.55695373010558611800e-05] 
dist 187=[-6.56097522047054000000e-05,-9.78413608472916000000e-06] 
dist 188=[-7.29529241962410000000e-05,-5.22677155755410000000e-06] 
dist 189=[-7.64816066229453000000e-05,-7.57646694638500000000e-07] 
dist 190=[-7.82763332872533000000e-05,4.67820578196290000000e-06] 
dist 191=[-7.87206949598980000000e-05,1.02329768745807000000e-05] 
dist 192=[-5.38523938551676000000e-05,1.51759737636853000000e-05] 
dist 193=[-5.12945718793963000000e-05,2.05549747666040000000e-05] 
dist 194=[-4.46858174432849000000e-05,2.78450489832332000000e-05] 
dist 195=[-4.31648894824241000000e-05,3.49206323778455000000e-05] 
dist 196=[-3.18384290822677800000e-05,3.94467010375231000000e-05] 
dist 197=[-2.95358339033146300000e-05,4.29183330941548000000e-05] 
dist 198=[-2.54816727468096800000e-05,4.57994050467749000000e-05] 
dist 199=[-2.44581115618985900000e-05,4.80404424739627000000e-05] 
dist 200=[-5.14143575752081000000e-06,4.89660387028628000000e-05] 
dist 201=[-2.50222093123026800000e-06,4.91602085607938000000e-05] 
dist 202=[2.79269434276779000000e-06,4.90007428644324000000e-05] 
dist 203=[4.07550423503178000000e-06,4.68834018647445000000e-05] 
dist 204=[4.05936231162204000000e-06,4.61232440466684000000e-05] 
dist 205=[2.73811042106838000000e-06,4.42513354102026000000e-05] 
dist 206=[1.13499284235658000000e-06,4.34616015020225000000e-05] 
dist 207=[-5.00932689143740000000e-07,3.90195681778097000000e-05] 
dist 208=[-1.95290076283254800000e-06,9.91098317006980000000e-06] 
dist 209=[-3.52962401307819000000e-06,9.27432632894994000000e-06] 
dist 210=[-5.66203102617693000000e-06,7.57605265931917000000e-06] 
dist 211=[-7.72899365410795000000e-06,7.31234397972283000000e-06] 
dist 212=[-9.04546712994628000000e-06,4.38040955875390000000e-06] 
dist 213=[-1.00484563566803000000e-05,3.81777844179253000000e-06] 
dist 214=[-1.08684315387423000000e-05,3.13614533941587000000e-06] 
dist 215=[-1.14964249913330000000e-05,2.96500649451185000000e-06] 
dist 216=[-1.17357404223765000000e-05,-7.28504038090660000000e-07] 
dist 217=[-1.18017161923125000000e-05,-6.70408019965320000000e-07] 
dist 218=[-1.17400222195727000000e-05,-3.50758917426304360000e-07] 
dist 219=[-5.74920938082220000000e-06,2.83413592150900000000e-08] 
dist 220=[-6.41491244490980000000e-06,3.22943769193170000000e-07] 
dist 221=[-6.74443625370610000000e-06,6.08067611340110000000e-07] 
dist 222=[-6.91368081544550000000e-06,9.49549532905280000000e-07] 
dist 223=[-6.94169148417800000000e-06,1.29562109690590000000e-06] 
dist 224=[-5.04164912371520000000e-06,1.59904898357480000000e-06] 
dist 225=[-4.83845258552840000000e-06,1.92545186688270000000e-06] 
dist 226=[-4.26609432701500000000e-06,2.36296458375050000000e-06] 
dist 227=[-4.16142462599760000000e-06,2.78525278915870000000e-06] 
dist 228=[-3.04604436637619000000e-06,3.05111556690680000000e-06] 
dist 229=[-2.81726139118757000000e-06,3.25011129619350000000e-06] 
dist 230=[-2.52595038719242000000e-06,3.40642305221430000000e-06] 
dist 231=[-2.41948471175629000000e-06,3.52117541032620000000e-06] 
dist 232=[-1.60427139267630000000e-07,3.55486190592090000000e-06] 
dist 233=[1.20724463870670000000e-07,3.54641725506700000000e-06] 
dist 234=[4.37490596898927000000e-07,3.52303867744390000000e-06] 
dist 235=[4.98379284045101000000e-07,3.32272795949330000000e-06] 
dist 236=[5.43677574152702000000e-07,3.25441275069810000000e-06] 
dist 237=[4.69525185224970700000e-07,3.34057008362114000000e-06] 
dist 238=[3.11340984393130210000e-07,3.40013311460391000000e-06] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 2, 1, 0, 1, 2] 
dist 0=[87.546567873420495345  ,87.546567873420495345  ] 
dist 1=[86.931075957053566283  ,87.703618992673609506  ] 
dist 2=[85.666515450722249790  ,87.714773854123981610  ] 
dist 3=[83.290218375365433453  ,87.492740725413298163  ] 
dist 4=[80.282263288361474614  ,87.284669976769033940  ] 
dist 5=[76.496783451033124833  ,86.344570879219619091  ] 
dist 6=[71.417238023662030285  ,86.004045369129686567  ] 
dist 7=[63.245033484983801979  ,82.720886590480031788  ] 
dist 8=[54.867451751332032152  ,81.861674414834101217  ] 
dist 9=[48.968461520396695645  ,80.903590764627487356  ] 
dist 10=[43.757702769945734132  ,80.420127015011444634  ] 
dist 11=[38.127114197765518560  ,79.856101874786942786  ] 
dist 12=[32.661503731043945190  ,79.621814031818544422  ] 
dist 13=[28.109398164153943385  ,79.213828923827172408  ] 
dist 14=[22.657526958494462786  ,75.555828164138232581  ] 
dist 15=[16.662872756353108053  ,31.026140500111758800  ] 
dist 16=[10.974708541236483434  ,27.202907029367274710  ] 
dist 17=[6.783609326379494720  ,18.300739821002367086  ] 
dist 18=[3.153832569780240260  ,16.973288859005657489  ] 
dist 19=[-1.4184167003958118240 ,11.282661606637930684  ] 
dist 20=[-5.6960760969902050441 ,6.8324515412743722799 ] 
dist 21=[-8.3984919349247171895 ,6.0824563098390852768 ] 
dist 22=[-10.468221541614069554  ,5.0129664315340709766 ] 
dist 23=[-12.616125545057420716  ,4.8013480540235611947 ] 
dist 24=[-15.506111991793573339  ,.6915725426662382718 ] 
dist 25=[-17.417723526634764662  ,.2131854037445951457 ] 
dist 26=[-19.123669097527661733  ,-.8015982975605694844 ] 
dist 27=[-20.468440012339811366  ,-.9585763302608788286 ] 
dist 28=[-21.097377411478804255  ,-1.952433098240624137  ] 
dist 29=[-21.366706658145618868  ,-2.100634524359285851  ] 
dist 30=[-21.362686851458408317  ,-2.369658608177721271  ] 
dist 31=[-8.8634647846576789289 ,-2.416923559664779860  ] 
dist 32=[-8.0003207903825416183 ,-2.5213893128387883210 ] 
dist 33=[-5.8601827928787344199 ,-1.4290405409525747626 ] 
dist 34=[-5.5527856836960791183 ,-.2775275285266059950 ] 
dist 35=[-3.406023898887588104  ,1.2411442945895887958 ] 
dist 36=[-3.209025918737282646  ,2.7066148734652446564 ] 
dist 37=[-3.203036756261147314  ,3.6466022528115455903 ] 
dist 38=[-3.156861010508158529  ,4.3741997732533333157 ] 
dist 39=[-3.146832886938397270  ,4.9940162339214910334 ] 
dist 40=[-1.8124762593619068812 ,5.4916956097621517631 ] 
dist 41=[-1.6811499878603748108 ,5.7329454660646723722 ] 
dist 42=[-1.3766976448451165946 ,5.8514339367260772796 ] 
dist 43=[-1.3129426569336835573 ,5.8600588332697535956 ] 
dist 44=[-.9008473911979128421 ,5.9979959203057354783 ] 
dist 45=[-.8226476940730525363 ,6.1583515951477550079 ] 
dist 46=[-.678150736687965284  ,6.1985571751285692990 ] 
dist 47=[-.642772662703005418  ,3.3446663426106097399 ] 
dist 48=[-.101563687626457064  ,3.1109658109014495648 ] 
dist 49=[-.026576719405729316  ,2.5255691176443995146 ] 
dist 50=[.143270868714363474  ,2.4210231668438855858 ] 
dist 51=[.178152188885071886  ,1.5177474941258650184 ] 
dist 52=[.390219875991680118  ,1.3478252106732862312 ] 
dist 53=[.3168663972759154915 ,1.0906112654711072049 ] 
dist 54=[-.3468356771101554676 ,1.0199505134206511810 ] 
dist 55=[-.9904583125421788899 ,.9021834880779428683 ] 
dist 56=[-1.4087562808114782185 ,.3684034607551780133 ] 
dist 57=[-1.7387435737265859465 ,.3245059456363049933 ] 
dist 58=[-2.0306998415147078781 ,.2175752430800270640 ] 
dist 59=[-2.2730936764653843701 ,.2021762626829425933 ] 
dist 60=[-2.4057014905703248371 ,.0509505890323927191 ] 
dist 61=[-2.4822706325280942309 ,.0243741565148394772 ] 
dist 62=[-2.5014778236970386190 ,-.0097309134034993689 ] 
dist 63=[-.68083079801331386082,-.0154497404044818143 ] 
dist 64=[-.62625583531806057643,-.1936661249520826611 ] 
dist 65=[-.4861832486702996833 ,-.2142262306576154835 ] 
dist 66=[-.4654728731935323676 ,-.2518082423147725444 ] 
dist 67=[-.2959172919690152703 ,-.2279614493343509552 ] 
dist 68=[-.3185307426979148977 ,-.1333263407543634460 ] 
dist 69=[-.3307459902124144866 ,-.0362485440143837423 ] 
dist 70=[-.3376358458039405551 ,.0882722158410865863 ] 
dist 71=[-.3390187548994782199 ,.2078311462074462786 ] 
dist 72=[-.1728022465395748957 ,.2851688389481179198 ] 
dist 73=[-.1591168048954331815 ,.3457123751696287471 ] 
dist 74=[-.1255596053908964754 ,.3984078990299657565 ] 
dist 75=[-.1195681895808022107 ,.4414833021282555155 ] 
dist 76=[-.07004076442986940406,.4637236266040110314 ] 
dist 77=[-.06086218368281504659,.4751381057497016089 ] 
dist 78=[-.04650060896410956263,.4770654718801467414 ] 
dist 79=[-.04276870725276043537,.3031332715380326948 ] 
dist 80=[.02149530855762906640,.2874554477231512438 ] 
dist 81=[.02980377644006085580,.2449549110425334427 ] 
dist 82=[.0449480540121236028 ,.2382366002526447735 ] 
dist 83=[.0481261476346055143 ,.1620236548471330030 ] 
dist 84=[.0552870635383465604 ,.1470543771765186607 ] 
dist 85=[.0250169442182635037 ,.1406441197847003081 ] 
dist 86=[-.0263856296758087846 ,.1444098499149651191 ] 
dist 87=[-.0762203776688327722 ,.1451099388956655896 ] 
dist 88=[-.1083460960464727814 ,.03536713300124338370] 
dist 89=[-.1333432887469400118 ,.03195019455257210886] 
dist 90=[-.1548041044185854812 ,.0233823999373383756 ] 
dist 91=[-.1721674964284461867 ,.0221315986866447600 ] 
dist 92=[-.1808538322991825938 ,.0091836595056853735 ] 
dist 93=[-.1854115890409365417 ,.0068409329251853473 ] 
dist 94=[-.1863397060175472061 ,.0039208582454777220 ] 
dist 95=[-.06060293717815203998,.0033788596112532405 ] 
dist 96=[-.05609982408091097723,-.0065706002811630692 ] 
dist 97=[-.04429169891163558529,-.0072888273676198458 ] 
dist 98=[-.04259417510633879937,-.0070308946186871009 ] 
dist 99=[-.0413920646920540399 ,-.0053915104132619357 ] 
dist 100=[-.0432171736479090598 ,-.00302765417581885374] 
dist 101=[-.0439338107603660115 ,.0037172286448090673 ] 
dist 102=[-.0440756249136831820 ,.0156011094386359626 ] 
dist 103=[-.0439076456597473902 ,.0269749587858964333 ] 
dist 104=[-.0369060504047563297 ,.0341158458137784459 ] 
dist 105=[-.0357233917417715906 ,.0394517084010043307 ] 
dist 106=[-.0327168722244575627 ,.0436408417016994166 ] 
dist 107=[-.0317873137325924629 ,.0469015507171605265 ] 
dist 108=[-.0264449383466147540 ,.0485424991135968760 ] 
dist 109=[-.0252706172576364513 ,.0492967556030685049 ] 
dist 110=[-.0228960338905224188 ,.0493363986277596125 ] 
dist 111=[-.0221922523180993711 ,.0359401534649448063 ] 
dist 112=[-.0116084220659010840 ,.0343087999952581132 ] 
dist 113=[-.0100618358909946587 ,.0303020441365646037 ] 
dist 114=[-.0066318344936430678 ,.0292080011206390534 ] 
dist 115=[-.0057684940879206721 ,.02284424986140898760] 
dist 116=[-.0017770148407505036 ,.02153482846817264956] 
dist 117=[-.0010514974601098199 ,.01885073681712525604] 
dist 118=[-.00167009505636017709,.01608998306090033508] 
dist 119=[-.00681820913843556007,.0135105578026678761 ] 
dist 120=[-.01018730392599554116,.00312416310516097862] 
dist 121=[-.01286276451141911756,.00285076491796337125] 
dist 122=[-.01525053062467080014,.00215228667786599589] 
dist 123=[-.01724030382043264645,.00205192721063916403] 
dist 124=[-.0183318738859909816 ,.00095403012337810680] 
dist 125=[-.0189633486439111321 ,.00075250832588156400] 
dist 126=[-.0191220155628857415 ,.0005125241498778548 ] 
dist 127=[-.00525418231147930850,.0004718865197900484 ] 
dist 128=[-.00488856021428621557,-.0011262739883246610 ] 
dist 129=[-.00392358254097563502,-.0013107497119304546 ] 
dist 130=[-.00377986972159749458,-.0016735836404173460 ] 
dist 131=[-.00215487383021602419,-.0017525481481898647 ] 
dist 132=[-.0022479390197471184 ,-.00131221438139822441] 
dist 133=[-.0023635578840848317 ,-.00055114271469927905] 
dist 134=[-.0024303591951527781 ,.00044937105954202871] 
dist 135=[-.0024471351091152102 ,.00141673118950222400] 
dist 136=[-.00136657634900192728,.00204593459326002918] 
dist 137=[-.00127691033990865161,.00254116934257434144] 
dist 138=[-.00104999423402183575,.00297541943946004537] 
dist 139=[-.00100809201171579563,.00333165699117925963] 
dist 140=[-.00064730766682513967,.00351644161371293330] 
dist 141=[-.00057824315890697768,.00361319380945850682] 
dist 142=[-.00047303740044940763,.00362973883380047228] 
dist 143=[-.00044374518716590851,.00242290114708085765] 
dist 144=[9.37555516306422600000e-05,.00231103890827784355] 
dist 145=[.00016308787324059434,.00199891435221608759] 
dist 146=[.00030031366442318031,.00194906267739546663] 
dist 147=[.00033203596043480481,.00135932867611739014] 
dist 148=[.00042251842246249508,.00124135789718401943] 
dist 149=[.00028249969897160703,.00110598922855788207] 
dist 150=[-.00014058317565294834,.0010823763497511884 ] 
dist 151=[-.00055263625461054962,.0010908418527778926 ] 
dist 152=[-.00081975619469742469,.00028895792026046677] 
dist 153=[-.00102892910672795258,.00026590410672457886] 
dist 154=[-.00121041006606201512,.00020645718901701314] 
dist 155=[-.00135790079691041958,.00019762622554859226] 
dist 156=[-.00143181751486633732,.00010200916584895666] 
dist 157=[-.00147108852797392195,8.42216527379345100000e-05] 
dist 158=[-.00148071302744408899,6.26213160446455700000e-05] 
dist 159=[-.00049400985884460745,5.81594716243271300000e-05] 
dist 160=[-.00046042117008035691,-8.61592631544193500000e-05] 
dist 161=[-.00037071463543068962,-.00010310563143553085] 
dist 162=[-.00035781273196705032,-.00013670337799062642] 
dist 163=[-.00020372421172343842,-.00014415230658673108] 
dist 164=[-.00020137205619039058,-.00012950332453229666] 
dist 165=[-.00021131736957935040,-5.87257531224767800000e-05] 
dist 166=[-.00021642371428490643,3.44008098825265900000e-05] 
dist 167=[-.00021726447191534040,.00012459541493280559] 
dist 168=[-.00013907039845180461,.00018371175629155414] 
dist 169=[-.00013196656568064159,.00023072296663193472] 
dist 170=[-.00011264903744897406,.00027275192401067991] 
dist 171=[-.00010958464457201082,.00030779665832749026] 
dist 172=[-7.46584664968098300000e-05,.00032701723144147294] 
dist 173=[-6.77693462685325800000e-05,.00033811857819896788] 
dist 174=[-5.96956169619163300000e-05,.00034085553725404109] 
dist 175=[-5.74819400128225400000e-05,.00020913664878968081] 
dist 176=[7.95346686702814000000e-06,.00019792328792759179] 
dist 177=[1.57577798618350700000e-05,.00016852679703434417] 
dist 178=[3.06195899127848700000e-05,.00016283586616459194] 
dist 179=[3.34035610179261300000e-05,.00011231120432793841] 
dist 180=[4.12393593099678600000e-05,.00010231304702578824] 
dist 181=[3.34119653791755540000e-05,8.73479009390077300000e-05] 
dist 182=[-1.12594281170053600000e-05,8.72118146779836400000e-05] 
dist 183=[-5.49905977096377400000e-05,8.76385673228142000000e-05] 
dist 184=[-8.36699112485492300000e-05,2.83607687129749740000e-05] 
dist 185=[-.00010648881131873042,2.61878294171634800000e-05] 
dist 186=[-.00012690303022945519,2.05065310465154500000e-05] 
dist 187=[-.00014392906635699762,1.96895183936408100000e-05] 
dist 188=[-.00015326699111688671,1.03194446152304900000e-05] 
dist 189=[-.00015865808277560991,8.56605251218643000000e-06] 
dist 190=[-.00015997999363633943,6.54409046236903000000e-06] 
dist 191=[-4.46512931129294980000e-05,6.19500760241882000000e-06] 
dist 192=[-4.17928759288677880000e-05,-8.58566966223042000000e-06] 
dist 193=[-3.40825205924260130000e-05,-1.02921000382766100000e-05] 
dist 194=[-3.29701453111078050000e-05,-1.37204685918295100000e-05] 
dist 195=[-1.94600745309155880000e-05,-1.44634329394974300000e-05] 
dist 196=[-1.91990008774852700000e-05,-1.11834142822954500000e-05] 
dist 197=[-2.02735446601138900000e-05,-4.65897844881879000000e-06] 
dist 198=[-2.08830908732769300000e-05,4.01008303773932000000e-06] 
dist 199=[-2.10080499178197600000e-05,1.24028946426731900000e-05] 
dist 200=[-1.24415301560696300000e-05,1.78285994654690800000e-05] 
dist 201=[-1.17109885731786300000e-05,2.20577285191288800000e-05] 
dist 202=[-9.83155090398739000000e-06,2.56898112023228300000e-05] 
dist 203=[-9.47177586059133000000e-06,2.86209036442014600000e-05] 
dist 204=[-6.36271777079179000000e-06,3.00610869488366100000e-05] 
dist 205=[-5.75588785760429000000e-06,3.08014904042562500000e-05] 
dist 206=[-4.82956665626611000000e-06,3.09481671168279800000e-05] 
dist 207=[-4.56655223901287000000e-06,2.22823263066394860000e-05] 
dist 208=[3.93207463882986400000e-07,2.13751533085849880000e-05] 
dist 209=[1.03590534320294010000e-06,1.87991237767170090000e-05] 
dist 210=[2.25806948292414000000e-06,1.83585318963423550000e-05] 
dist 211=[2.53899942300148000000e-06,1.33065726160037140000e-05] 
dist 212=[2.36156094994844600000e-06,1.22755680501367850000e-05] 
dist 213=[-3.12756003717972000000e-07,1.10489987475911400000e-05] 
dist 214=[-3.93613602805540000000e-06,1.06377515319276700000e-05] 
dist 215=[-7.45464596579022800000e-06,9.88879839726807000000e-06] 
dist 216=[-9.71187855510334600000e-06,2.63456778307659600000e-06] 
dist 217=[-1.14514304066785830000e-05,2.44670477328800500000e-06] 
dist 218=[-1.29104067000933940000e-05,1.94992330934856000000e-06] 
dist 219=[-1.40619868672054370000e-05,1.87843755359434000000e-06] 
dist 220=[-1.45785095529702890000e-05,1.03985825786395000000e-06] 
dist 221=[-1.48164750728096560000e-05,8.81407240565270000000e-07] 
dist 222=[-1.48597777326932130000e-05,7.01724900691630000000e-07] 
dist 223=[-3.92022417688342000000e-06,6.70340655701560000000e-07] 
dist 224=[-3.62442179090054000000e-06,-1.09704662199240000000e-07] 
dist 225=[-2.87272284754732000000e-06,-1.77578889111070000000e-07] 
dist 226=[-2.73862626173219000000e-06,-1.82104959307690000000e-07] 
dist 227=[-2.79223093374600000000e-06,-1.01663809622200000000e-07] 
dist 228=[-2.95433438658230000000e-06,2.54277414584570000000e-08] 
dist 229=[-3.01588717523010000000e-06,2.06509204485490000000e-07] 
dist 230=[-3.03408343757160000000e-06,8.81892601214000000000e-07] 
dist 231=[-3.02364332962860000000e-06,1.71306046377880000000e-06] 
dist 232=[-2.66580574091610000000e-06,2.23689390847810000000e-06] 
dist 233=[-2.59484247217250000000e-06,2.62981389541970000000e-06] 
dist 234=[-2.40767848830500000000e-06,2.94012735131800000000e-06] 
dist 235=[-2.34358326666880000000e-06,3.18376659833520000000e-06] 
dist 236=[-1.97966685929874000000e-06,3.31143768964710000000e-06] 
dist 237=[-1.89666820406824000000e-06,3.37720855155110000000e-06] 
dist 238=[-1.72799522797344000000e-06,3.38049349434450000000e-06] 
dist 239=[-1.67670620786744000000e-06,2.56315904141041000000e-06] 
dist 240=[-8.78217457349730000000e-07,2.45619659827276000000e-06] 
dist 241=[-7.61495264712850000000e-07,2.19133227096487000000e-06] 
dist 242=[-5.02216405205510000000e-07,2.11333374040594000000e-06] 
dist 243=[-4.36689524747010000000e-07,1.67769425404560100000e-06] 
dist 244=[-1.36022489969770000000e-07,1.58572496090391000000e-06] 
dist 245=[-8.11120239016600000000e-08,1.39287178604786000000e-06] 
dist 246=[4.24561653993800000000e-08,1.19377808112019000000e-06] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 0, 1, 0, 1] 
dist 0=[84.402651635375158530  ,84.402651635375158530  ] 
dist 1=[84.208215727316804454  ,84.344155743481789689  ] 
dist 2=[83.373998565345114751  ,84.402651635375158530  ] 
dist 3=[81.849658489744949227  ,83.944673167517261197  ] 
dist 4=[78.998055631275216786  ,83.488548385405751051  ] 
dist 5=[75.486988207442498399  ,83.250966090375436590  ] 
dist 6=[71.331146219667056605  ,82.471739553902875533  ] 
dist 7=[65.911191275100931961  ,82.179800669359042754  ] 
dist 8=[57.355350453228858142  ,81.904390280311867006  ] 
dist 9=[48.668983073633814628  ,81.684626397491700687  ] 
dist 10=[42.727776557035504944  ,81.462888309364356610  ] 
dist 11=[37.663370398777839064  ,81.180028273533472012  ] 
dist 12=[32.475058950797225158  ,80.929067030799056043  ] 
dist 13=[27.605459684668670707  ,79.298103350137319684  ] 
dist 14=[23.812061997910249688  ,35.541949542082617117  ] 
dist 15=[20.078845280349936215  ,31.938045848555890482  ] 
dist 16=[14.296757526940223696  ,23.723168213248531283  ] 
dist 17=[9.682959115537821605  ,22.233252968880804881  ] 
dist 18=[5.093860543438419879  ,11.461587734245219198  ] 
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dist 65=[-.3196912846614662287 ,-.0741499802867067783 ] 
dist 66=[-.1750192317683150053 ,-.0296381331616889968 ] 
dist 67=[-.1481141811405457804 ,.0275859184964576220 ] 
dist 68=[-.1314810333551985100 ,.0826307325867972236 ] 
dist 69=[-.1368192716442686058 ,.1184758990701421164 ] 
dist 70=[-.1396522165712590012 ,.1467951517713664087 ] 
dist 71=[-.1412549509076918654 ,.1753340165861247921 ] 
dist 72=[-.1416539556673168135 ,.21586834531588633895] 
dist 73=[-.02767563058623494013,.25126238180005231722] 
dist 74=[-.02226779307309073937,.28026164911618928317] 
dist 75=[-.00974755009050047615,.2953376331215634188 ] 
dist 76=[-.00791652017749546450,.30315587957795244212] 
dist 77=[.0075687416309184529 ,.3045633879583647814 ] 
dist 78=[.0101176736283047345 ,.19620764561664929929] 
dist 79=[.0138403051632294798 ,.18643328293804951535] 
dist 80=[.0145189838093713454 ,.15965135074847756421] 
dist 81=[.0263384712081002602 ,.15543317230928048672] 
dist 82=[.01773168292379048971,.10655603934526952489] 
dist 83=[-.0074752874708142030 ,.09691044860027644046] 
dist 84=[-.0320486062998297448 ,.08571057893827302701] 
dist 85=[-.0480870198150229737 ,.08272423408423119948] 
dist 86=[-.0607832339005723300 ,.0363858593756187669 ] 
dist 87=[-.0720547421230870682 ,.0366380007527436095 ] 
dist 88=[-.08217627937542291853,.0366180322704382585 ] 
dist 89=[-.09636247772996222910,.01779794166262792973] 
dist 90=[-.10787622524026751977,.01622103462349465454] 
dist 91=[-.11366378846271966187,.01238022749785416073] 
dist 92=[-.11673629081771354345,.01179342397344748961] 
dist 93=[-.1174428602624561875 ,.00628621633787909927] 
dist 94=[-.04235531658457001014,.00529384470879303680] 
dist 95=[-.0396765344773542659 ,.00397650046906723431] 
dist 96=[-.0327566483245352426 ,.00366001910724771818] 
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dist 99=[-.0179587714374593988 ,.0034663374437376685 ] 
dist 100=[-.0148129485919340879 ,.0103248148908593246 ] 
dist 101=[-.0138762823375158230 ,.0149019935518872906 ] 
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dist 103=[-.0131964734124780486 ,.02213914506484207899] 
dist 104=[-.0132234523660458629 ,.02518011611165833410] 
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dist 106=[-.00316457151895337888,.02847212513065739978] 
dist 107=[-.00201539912432499383,.0298116820608147506 ] 
dist 108=[-.0018504057667453762 ,.0305775926881802603 ] 
dist 109=[-.0018593499412679075 ,.0306835489326319413 ] 
dist 110=[-.0028071664244440732 ,.01596572452658071786] 
dist 111=[-.0038554204455073118 ,.01507797913859761351] 
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dist 113=[-.0056944506193792860 ,.01232372453316328217] 
dist 114=[-.0065223873011785213 ,.00840820719312432441] 
dist 115=[-.0075614935858046723 ,.00763974318995810801] 
dist 116=[-.0085353536475232989 ,.00649082423011099535] 
dist 117=[-.0091038192240358726 ,.00615489668813464693] 
dist 118=[-.0094785294062551071 ,.00355647544629200356] 
dist 119=[-.00968149456735391772,.00362575460011367083] 
dist 120=[-.00976068021855808596,.00364261747429955065] 
dist 121=[-.00974936067523915499,.00175327625018575003] 
dist 122=[-.0108034033301961241 ,.00160014526579281190] 
dist 123=[-.0115023069916351638 ,.00122830465070602769] 
dist 124=[-.0119067084497259957 ,.00116357569368707109] 
dist 125=[-.0120083268783810905 ,.00062983668321591677] 
dist 126=[-.00333589134484249037,.00053251932887358224] 
dist 127=[-.00311354834620617928,.00038038926935543835] 
dist 128=[-.00252205406263404176,.00034162304813637106] 
dist 129=[-.00243389654508975015,-.00030563645150789687] 
dist 130=[-.0014229067323496863 ,-.00038895463716909700] 
dist 131=[-.0012305270050409204 ,-.00054450247154108051] 
dist 132=[-.00127572742675040834,-.0004131632602599552 ] 
dist 133=[-.00140048216792109592,.0002213420325637887 ] 
dist 134=[-.00146841375872844903,.0008356387875511192 ] 
dist 135=[-.00150738330375199679,.0012355793792327561 ] 
dist 136=[-.00151671006852302742,.0015506688310716736 ] 
dist 137=[-.00037839796019845033,.0018273418722108812 ] 
dist 138=[-.00033918299688730577,.0020544885921458245 ] 
dist 139=[-.00024162522668587813,.0021725054047821821 ] 
dist 140=[-.00022758509619427403,.0022346307207960765 ] 
dist 141=[-8.28851575395086100000e-05,.0022453641333909142 ] 
dist 142=[-5.69437417246993700000e-05,.00151824896223263605] 
dist 143=[-2.47424496384485900000e-05,.00145038729264968098] 
dist 144=[-1.93115910314303800000e-05,.00125938333144847986] 
dist 145=[.00016250856596230752,.00122881009386214423] 
dist 146=[.00018286336435061494,.00086278315109499630] 
dist 147=[.00021942121822897788,.00078924605399168621] 
dist 148=[.00019384500860174132,.00070541591887397990] 
dist 149=[-7.23740076895927400000e-05,.00068191036291753133] 
dist 150=[-.0003319146683097171 ,.00033064018394872154] 
dist 151=[-.0005003798873367466 ,.00033530315186260088] 
dist 152=[-.0006324923760609348 ,.00033556806428151679] 
dist 153=[-.0007473967603755018 ,.00020762892922708705] 
dist 154=[-.0008409069441371797 ,.00019559059578892094] 
dist 155=[-.0008878967993034942 ,.00016424963683339352] 
dist 156=[-.0009129267273084476 ,.00015913253439640046] 
dist 157=[-.0009190503808914105 ,.00010669022018077386] 
dist 158=[-.00031000127900939840,9.65591536215289100000e-05] 
dist 159=[-.00028977373895770922,8.37108405284155000000e-05] 
dist 160=[-.00023537334999805743,7.98055082859232700000e-05] 
dist 161=[-.0002275165229275447 ,-9.16497377175838000000e-06] 
dist 162=[-.0001328351318643289 ,-1.99537434203864500000e-05] 
dist 163=[-.00012695568478540246,-4.42071973536043700000e-05] 
dist 164=[-.00013792818841109732,-4.18406287153870200000e-05] 
dist 165=[-.00014637467290496547,1.64773611219146500000e-05] 
dist 166=[-.00015028013621168252,7.31284437305883000000e-05] 
dist 167=[-.00015186490525526136,.0001103251219290972 ] 
dist 168=[-.00015174060337035301,.0001398974191034139 ] 
dist 169=[-4.26267945676959300000e-05,.0001663110326340888 ] 
dist 170=[-3.89958680125655300000e-05,.0001883090161741579 ] 
dist 171=[-3.00327556285635000000e-05,.0002003124765262174 ] 
dist 172=[-2.84730764483573000000e-05,.0002071599223967475 ] 
dist 173=[-1.51212118141832000000e-05,.00020886224132364041] 
dist 174=[-1.26557878140572000000e-05,.00013173754472813051] 
dist 175=[-8.90643136460340000000e-06,.00012508559471282713] 
dist 176=[-7.90488014504030000000e-06,.00010737295655326960] 
dist 177=[9.36019647287130000000e-06,.00010399675115850072] 
dist 178=[1.15712544322231000000e-05,7.26860940005670300000e-05] 
dist 179=[1.56837547064992000000e-05,6.64441019510328000000e-05] 
dist 180=[1.65443441156867000000e-05,5.74571934909331000000e-05] 
dist 181=[-5.81125208491487000000e-06,5.46704613923753000000e-05] 
dist 182=[-3.30353639721802600000e-05,3.56936028522438000000e-05] 
dist 183=[-5.09011810934418000000e-05,3.64261116260334000000e-05] 
dist 184=[-6.51251482041287600000e-05,3.64859788589576000000e-05] 
dist 185=[-7.78603705550696500000e-05,3.12526625580436500000e-05] 
dist 186=[-8.84854028610391200000e-05,3.03992044726417000000e-05] 
dist 187=[-9.43138763172073400000e-05,2.83053869619945420000e-05] 
dist 188=[-9.76790189838396200000e-05,2.75507280934363300000e-05] 
dist 189=[-9.85033198072675700000e-05,2.37786375621255400000e-05] 
dist 190=[-3.30282264663886400000e-05,2.29129706194855000000e-05] 
dist 191=[-3.15315372043243300000e-05,2.09131230385566000000e-05] 
dist 192=[-2.77214934636088000000e-05,2.02460347227608000000e-05] 
dist 193=[-2.67766524571010500000e-05,1.24376061667150000000e-05] 
dist 194=[-2.03774119995873000000e-05,1.12063672631141000000e-05] 
dist 195=[-1.90699602258697000000e-05,8.42484756740880000000e-06] 
dist 196=[-1.66150394035776000000e-05,7.67785024447970000000e-06] 
dist 197=[-1.59719891742356000000e-05,4.14241190254990000000e-06] 
dist 198=[-1.19233733965108100000e-05,7.31177163029622000000e-06] 
dist 199=[-1.20093632411233600000e-05,1.06852164361509800000e-05] 
dist 200=[-1.19868669392688000000e-05,1.33165287734302800000e-05] 
dist 201=[-9.68180733986477000000e-06,1.55786790092387200000e-05] 
dist 202=[-9.30461317528486000000e-06,1.74068505892283000000e-05] 
dist 203=[-8.52154818743184000000e-06,1.83116609700001000000e-05] 
dist 204=[-8.27795574018279000000e-06,1.87788821755957200000e-05] 
dist 205=[-7.21183169443534000000e-06,1.88660024100651100000e-05] 
dist 206=[-6.96618660966949000000e-06,1.42733190464991000000e-05] 
dist 207=[-6.32617001448580000000e-06,1.38109448694985000000e-05] 
dist 208=[-6.14434155299570000000e-06,1.24707372603399000000e-05] 
dist 209=[-4.98052325364730000000e-06,1.22052725201267000000e-05] 
dist 210=[-4.70993005888230000000e-06,9.44397739797170000000e-06] 
dist 211=[-4.36941882950780000000e-06,8.86196619121910000000e-06] 
dist 212=[-4.23494998687400000000e-06,8.10163994475530000000e-06] 
dist 213=[-4.10698774347834000000e-06,7.82431409612090000000e-06] 
dist 214=[-4.47366696596339400000e-06,1.79950052200160000000e-06] 
dist 215=[-5.86955251792770700000e-06,1.04286723838080000000e-06] 
dist 216=[-6.94695489983789000000e-06,-9.14475087209700000000e-07] 
dist 217=[-7.85315847981198000000e-06,-1.43758336735323500000e-06] 
dist 218=[-8.56922751761123000000e-06,-1.52733153922218500000e-06] 
dist 219=[-8.89019345374297000000e-06,-1.31075322600888730000e-06] 
dist 220=[-9.03885386692476000000e-06,-8.65519174625601230000e-07] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 0, 1, 1, 1, 2] 
dist 0=[86.161312425751397657  ,86.161312425751397657  ] 
dist 1=[85.262945849174303514  ,86.605504518309745015  ] 
dist 2=[84.048601512252403608  ,86.799941246391339654  ] 
dist 3=[82.343534624644321233  ,86.702176433786811881  ] 
dist 4=[79.955438612073199284  ,86.422895016767777382  ] 
dist 5=[76.015034603789259833  ,86.174821573544316098  ] 
dist 6=[71.383150456421021431  ,85.316800422405552655  ] 
dist 7=[66.235411860557685054  ,84.870092924236180882  ] 
dist 8=[59.727587548859526784  ,82.235671586773840537  ] 
dist 9=[49.667816875018206932  ,81.453878930799877588  ] 
dist 10=[39.519474398528067537  ,80.743944388228793332  ] 
dist 11=[32.657861922937144191  ,80.294177720209286092  ] 
dist 12=[26.893112075723103777  ,79.992196780578439699  ] 
dist 13=[21.121246366336762162  ,78.164501860464167442  ] 
dist 14=[15.787534319627852461  ,67.920827439094433597  ] 
dist 15=[11.770545928304715666  ,61.072647518099277450  ] 
dist 16=[7.9469458575122819725 ,31.243539504713849174  ] 
dist 17=[3.3834802847292378645 ,27.429825945951159617  ] 
dist 18=[-.9039105260058714633 ,18.564058572861314155  ] 
dist 19=[-3.6258449935288684872 ,17.222958927648656033  ] 
dist 20=[-5.7260825785577894532 ,7.7536331665430990905 ] 
dist 21=[-7.5311389894118533417 ,3.9169956030073240295 ] 
dist 22=[-9.4451340048410123368 ,3.1474845283860362204 ] 
dist 23=[-11.781815041628484224  ,2.0002826426592902856 ] 
dist 24=[-14.579478991757703756  ,1.7831834385022156152 ] 
dist 25=[-17.194864106569670198  ,-.68569543234189879743] 
dist 26=[-18.804458703900022653  ,-.99246207695359034246] 
dist 27=[-19.985300356681843470  ,-1.6090188668474804498 ] 
dist 28=[-20.934364817660649002  ,-1.7032080465665884473 ] 
dist 29=[-21.552898322616889260  ,-2.1736935384938196756 ] 
dist 30=[-21.764592603576650017  ,-2.2438302226879281421 ] 
dist 31=[-21.691539498830782089  ,-2.2624901846970905144 ] 
dist 32=[-8.5855360117470827274 ,-1.5672923623925906349 ] 
dist 33=[-7.7345952308892285705 ,-.3594549966974668487 ] 
dist 34=[-5.6319515257532854517 ,.8182479894505087080 ] 
dist 35=[-5.3281522033817020331 ,1.5872594922019067698 ] 
dist 36=[-2.2635750331238033136 ,2.1964643531120875988 ] 
dist 37=[-2.0659778734648118560 ,2.7382439552674499598 ] 
dist 38=[-2.0408389171692257349 ,3.1890209501125233360 ] 
dist 39=[-1.9782054324044317793 ,3.4360158308114154096 ] 
dist 40=[-1.9591969511477350529 ,3.5787875206016993216 ] 
dist 41=[-.8093638300958629488 ,3.8927351260256456422 ] 
dist 42=[-.7056030043945324218 ,4.5752054148578692068 ] 
dist 43=[-.4729945892351579537 ,5.1697564439271497530 ] 
dist 44=[-.4304407362650654053 ,5.6589568630387995577 ] 
dist 45=[-.1556660672941110451 ,5.9215112516226767949 ] 
dist 46=[-.1087477400657437869 ,6.0671431367896859374 ] 
dist 47=[-.0209335540439130312 ,6.0902614832541694492 ] 
dist 48=[-.0015621824462593334 ,3.3378155739780691681 ] 
dist 49=[.0773723404550512642 ,3.1077770155475979138 ] 
dist 50=[-.1146329614283953769 ,2.5325909981094652761 ] 
dist 51=[-.2399081699966077291 ,2.4286342569099898092 ] 
dist 52=[-.3388671138964846816 ,1.5429321215109149711 ] 
dist 53=[-.4261851629323625479 ,1.3760686254193977565 ] 
dist 54=[-.4981860946267766770 ,1.1283161437389856256 ] 
dist 55=[-.5362028746115354963 ,1.1157460504654184348 ] 
dist 56=[-1.1587435425593172702 ,1.1126474143694623297 ] 
dist 57=[-1.5638076662258758105 ,.09895166108368638618] 
dist 58=[-1.8807173372671299362 ,.07717733151471343638] 
dist 59=[-2.1565632423141780574 ,.02707271265973259476] 
dist 60=[-2.3823037040036051219 ,.01988737221653518851] 
dist 61=[-2.4996657702729061258 ,-.04109336406853484462] 
dist 62=[-2.5611927623963448615 ,-.05103605242531428256] 
dist 63=[-2.5722462508304981795 ,-.06531518229478659787] 
dist 64=[-.63980345551058714971,-.06754165160925941175] 
dist 65=[-.5881905936971738817 ,-.0114804688659298958 ] 
dist 66=[-.45516600639185414556,.0574615768095206937 ] 
dist 67=[-.4360426101885018717 ,.1024444662976528792 ] 
dist 68=[-.22363160691272890824,.1379433576300133113 ] 
dist 69=[-.18444136001248460871,.1691654256753311356 ] 
dist 70=[-.1443463752882819774 ,.1948078215353681590 ] 
dist 71=[-.1458548425600761917 ,.2081131499103803605 ] 
dist 72=[-.1462030426195545909 ,.2153091894987543313 ] 
dist 73=[-.06104622818809712186,.25916902774641471553] 
dist 74=[-.05422318042794208740,.31583486787720280314] 
dist 75=[-.03817749929235380028,.36608733938210370112] 
dist 76=[-.03547766134971274375,.40784922637355654586] 
dist 77=[-.01430677225958956406,.43070846080073205938] 
dist 78=[-.01060218560591454683,.4439075400446812469 ] 
dist 79=[-.00461135902566386417,.4472034895238497025 ] 
dist 80=[-.00322239441764085499,.25691477550755877101] 
dist 81=[.0041813688904877365 ,.24108720697523864523] 
dist 82=[-.0097244475632143243 ,.20058763559992152611] 
dist 83=[-.0188702536036480353 ,.19308238187331257086] 
dist 84=[-.0261661983212588537 ,.12730223039459621534] 
dist 85=[-.0327147672973455078 ,.1146239505991997943 ] 
dist 86=[-.0381843086006194299 ,.09553493494060721841] 
dist 87=[-.0411883554130474818 ,.09010794870079648442] 
dist 88=[-.07179938661138687475,.05838866945868200989] 
dist 89=[-.10551574874126258634,.01334041143077482250] 
dist 90=[-.13223313732633227525,.01160791870067250444] 
dist 91=[-.1560097852328374784 ,.00742842522612454845] 
dist 92=[-.17579854122964888204,.00681848195033405078] 
dist 93=[-.18664193260263513654,.00105095866920388914] 
dist 94=[-.19290707073840933653,4.84468488733925100000e-05] 
dist 95=[-.19447095857649235629,-.00128770757213498489] 
dist 96=[-.05297828793835625359,-.00153179910554194368] 
dist 97=[-.04907717539141081866,-.00049589954951360688] 
dist 98=[-.03890466910753340832,.00556985720820824210] 
dist 99=[-.03738259638824514244,.00956245337149759306] 
dist 100=[-.02066772136295815402,.0127499856017941132 ] 
dist 101=[-.01753363550322462635,.0156139917032863788 ] 
dist 102=[-.01397376373202460580,.0180071213600916111 ] 
dist 103=[-.01406239818985987093,.0193218405783015190 ] 
dist 104=[-.01402744120379403547,.0200822313600908843 ] 
dist 105=[-.00884098568317895296,.02239550741212379196] 
dist 106=[-.00831139735291029206,.02728080143217744596] 
dist 107=[-.00697790037295145869,.03147450202569224564] 
dist 108=[-.00673378710107476305,.03485266604160396216] 
dist 109=[-.00461926722166235640,.03649202811471754137] 
dist 110=[-.00421135753436896077,.03732518553410732485] 
dist 111=[-.00360712911495403943,.03749444002950577169] 
dist 112=[-.00343200881341649368,.02559275374771328167] 
dist 113=[-9.98299078816881700000e-05,.02441429578726610408] 
dist 114=[-.00102328927103535283,.02117866291749713882] 
dist 115=[-.00175188424229123922,.02062413247247407505] 
dist 116=[-.00232328556912587404,.01463257999140557890] 
dist 117=[-.00281902260365504703,.01343163804037803742] 
dist 118=[-.00322289273899799429,.01193813901369995239] 
dist 119=[-.0048981095617207499 ,.01143090547685111986] 
dist 120=[-.00896250811546214700,.00768861446834856593] 
dist 121=[-.01156298099129039598,.0014428358302684954 ] 
dist 122=[-.01356191450117140579,.0012887393158512739 ] 
dist 123=[-.01523256677153503856,.0009060830127385375 ] 
dist 124=[-.01654958762190401322,.0008511247650928851 ] 
dist 125=[-.01714112290277378183,.0002863522877882275 ] 
dist 126=[-.01741388773172416255,.0001854187288595760 ] 
dist 127=[-.01746225894023274995,5.97533547275370000000e-05] 
dist 128=[-.00144463366176110847,3.89115579378128000000e-05] 
dist 129=[-.00139605371378231897,.0002874298166727603 ] 
dist 130=[-.0008545173889164092 ,.00073206108571790377] 
dist 131=[-.0009831093540145190 ,.00102000356056798231] 
dist 132=[-.0010962425381776632 ,.00124460537600911767] 
dist 133=[-.0011899430148801686 ,.00143734999790697452] 
dist 134=[-.0012411087916733453 ,.00159196839054882904] 
dist 135=[-.0012706110216220426 ,.00166495041042441112] 
dist 136=[-.0012779908329621435 ,.00170024235148179270] 
dist 137=[-.0006617629403302178 ,.00170492281283247944] 
dist 138=[-.00061131968558393272,.0005225058926644806 ] 
dist 139=[-.00048652594803758560,.0004956775645354963 ] 
dist 140=[-.00046419463617537801,.0004196371821456274 ] 
dist 141=[-.0002762749085822201 ,.0004086809743486648 ] 
dist 142=[-.0002411903442734272 ,.0002640770196898782 ] 
dist 143=[-.0001870111451245332 ,.0002356523810264409 ] 
dist 144=[-.0001725907464979940 ,.0002055322305071820 ] 
dist 145=[1.81640795046051000000e-05,.0002422263715922014 ] 
dist 146=[-7.81924013834895000000e-05,.0003279483366615060 ] 
dist 147=[-.0001416564618159808 ,.0003955063995398276 ] 
dist 148=[-.0001923542302265776 ,.0004552038681038194 ] 
dist 149=[-.0002379406809138531 ,.0005047403308305165 ] 
dist 150=[-.0002760407126768903 ,.0005318278893737931 ] 
dist 151=[-.0002969644868228214 ,.0005474612372188706 ] 
dist 152=[-.0003090499326968903 ,.0005513741128320880 ] 
dist 153=[-.0003119977834763397 ,.00014089480019248786] 
dist 154=[-.0002108665773339250 ,.00012785211028004832] 
dist 155=[-.00020194791972537755,9.49329474875524000000e-05] 
dist 156=[-.00017735284009720985,9.01062460452972000000e-05] 
dist 157=[-.00017234283045959089,3.95842733047109000000e-05] 
dist 158=[-.0001258108026508171 ,3.03762800708509000000e-05] 
dist 159=[-.0001162776750652271 ,1.89778379152719000000e-05] 
dist 160=[-.0001023853986336908 ,1.67973375715900000000e-05] 
dist 161=[-9.80145093639914000000e-05,-1.36280074516610000000e-06] 
dist 162=[-7.47752506204480000000e-05,4.33805020883251000000e-05] 
dist 163=[-8.76434363658111000000e-05,7.28527446873069000000e-05] 
dist 164=[-9.87908912239888000000e-05,9.63971746513537000000e-05] 
dist 165=[-.0001078740775368743 ,.0001175665391650987 ] 
dist 166=[-.0001125214859002848 ,.0001352561177981134 ] 
dist 167=[-.0001148421840988030 ,.0001449614603192479 ] 
dist 168=[-.0001152041078682026 ,.0001505537619182851 ] 
dist 169=[-7.01852123690424000000e-05,.0001518851892504223 ] 
dist 170=[-6.61795857870314000000e-05,4.61549954902576700000e-05] 
dist 171=[-5.55558466259585000000e-05,4.39840472336543300000e-05] 
dist 172=[-5.38945790640251000000e-05,3.78644093713568000000e-05] 
dist 173=[-3.55707382139726200000e-05,3.68692534685519000000e-05] 
dist 174=[-3.20175851993302600000e-05,2.51830610234149000000e-05] 
dist 175=[-2.77826269013545700000e-05,2.28510993492720000000e-05] 
dist 176=[-2.66735405360744160000e-05,2.00960628928871000000e-05] 
dist 177=[9.54890299554700000000e-07,2.05674347329996000000e-05] 
dist 178=[-7.50744597899110000000e-06,2.78660170562769000000e-05] 
dist 179=[-1.30829777427693000000e-05,3.35119021692726000000e-05] 
dist 180=[-1.76084956717030000000e-05,3.83090302452499000000e-05] 
dist 181=[-2.15038205683327000000e-05,4.21793486763171000000e-05] 
dist 182=[-2.47023669808621000000e-05,4.41347912479950000000e-05] 
dist 183=[-2.64561135084452000000e-05,4.51506925628339000000e-05] 
dist 184=[-2.74657332075121000000e-05,4.52798252174942000000e-05] 
dist 185=[-2.77025599709793000000e-05,1.94742268199806700000e-05] 
dist 186=[-2.53303801900997000000e-05,1.83383846984423000000e-05] 
dist 187=[-2.48988958349086000000e-05,1.57755565253436000000e-05] 
dist 188=[-2.34961773992399000000e-05,1.49942035991010000000e-05] 
dist 189=[-2.30849449653513000000e-05,1.15614443713834000000e-05] 
dist 190=[-1.95609653474551000000e-05,1.08695582573141000000e-05] 
dist 191=[-1.87473844995735000000e-05,9.10454625775430000000e-06] 
dist 192=[-1.74780430002811000000e-05,8.75046159508560000000e-06] 
dist 193=[-1.70659690122164000000e-05,4.89143100673580000000e-06] 
dist 194=[-7.79641072992290000000e-06,4.19214802490020000000e-06] 
dist 195=[-8.30697291545870000000e-06,5.58734882227645000000e-06] 
dist 196=[-9.48245399419870000000e-06,7.26682385562550000000e-06] 
dist 197=[-1.04553798473091000000e-05,8.77908574669120000000e-06] 
dist 198=[-1.09798830683233000000e-05,1.00136680496765000000e-05] 
dist 199=[-1.12718426644000000000e-05,1.06463167769651000000e-05] 
dist 200=[-1.13189132481070000000e-05,1.09839553305270000000e-05] 
dist 201=[-6.50971060916120000000e-06,1.10452893045686000000e-05] 
dist 202=[-6.10082718931357700000e-06,4.39869829360767000000e-06] 
dist 203=[-5.04918391799792000000e-06,4.18407699711136000000e-06] 
dist 204=[-4.86322948661660000000e-06,3.58645176057761000000e-06] 
dist 205=[-3.13970021998416000000e-06,3.48691740054844000000e-06] 
dist 206=[-2.80781658855367000000e-06,2.36513391924060000000e-06] 
dist 207=[-2.33702933955712000000e-06,2.14184448755080000000e-06] 
dist 208=[-2.19411918311232000000e-06,1.86901403308010000000e-06] 
dist 209=[6.12446912129000000000e-08,1.98172658399820000000e-06] 
dist 210=[-8.04524758783300000000e-07,2.80515164481114000000e-06] 
dist 211=[-1.36416389608300000000e-06,3.45519678612840000000e-06] 
dist 212=[-1.79969236838490000000e-06,4.02982696464580000000e-06] 
dist 213=[-2.17190008994810000000e-06,4.50556085996220000000e-06] 
dist 214=[-2.47642038903070000000e-06,4.76191023146280000000e-06] 
dist 215=[-2.64270088494170000000e-06,4.90436291406010000000e-06] 
dist 216=[-2.73750589259110000000e-06,4.93274274361660000000e-06] 
dist 217=[-2.75758686235400000000e-06,1.81638787788055000000e-06] 
dist 218=[-2.49011436383602000000e-06,1.71690454034609000000e-06] 
dist 219=[-2.44347056556142300000e-06,1.49754529306695000000e-06] 
dist 220=[-2.29134363442462000000e-06,1.43091016520632000000e-06] 
dist 221=[-2.25213123076997000000e-06,1.13950937945205000000e-06] 
dist 222=[-1.87472631104716000000e-06,1.08067821193000000000e-06] 
dist 223=[-1.78914713439245000000e-06,9.17915604284500000000e-07] 
dist 224=[-1.66772971987052000000e-06,8.93266453715800000000e-07] 
dist 225=[-1.62459952111117000000e-06,5.86890520849100000000e-07] 
dist 226=[-7.49181996710880000000e-07,5.26705623335600000000e-07] 
dist 227=[-8.83169813608760000000e-07,4.47529266787500000000e-07] 
dist 228=[-9.90580716802070000000e-07,5.66249092678180000000e-07] 
dist 229=[-1.07566606549341000000e-06,6.88815774693990000000e-07] 
dist 230=[-1.12078934630025000000e-06,7.90724916247010000000e-07] 
dist 231=[-1.14485545702452000000e-06,8.45359143405180000000e-07] 
dist 232=[-1.14702706202602000000e-06,8.75060809033420000000e-07] 
dist 233=[-9.14439512140990000000e-07,8.81480111452580000000e-07] 
dist 234=[-8.83758664137990000000e-07,6.49620934459630000000e-07] 
dist 235=[-7.97459396510530000000e-07,6.25817510586720000000e-07] 
dist 236=[-7.79255239353330000000e-07,5.74230106527290000000e-07] 
dist 237=[-6.07003677233880000000e-07,5.57555522223100000000e-07] 
dist 238=[-5.70491964890890000000e-07,4.81533187242400000000e-07] 
dist 239=[-5.19544464875090000000e-07,4.64784034442770000000e-07] 
dist 240=[-5.02168539356200000000e-07,4.17942107932700000000e-07] 
dist 241=[-1.26429455475030000000e-07,4.08170213424630000000e-07] 
dist 242=[-7.86369280113800000000e-08,3.17328032054130000000e-07] 
dist 243=[3.43107097786500000000e-08,3.49730534555530000000e-07] 
dist 244=[5.17019102184900000000e-08,3.73524459675470000000e-07] 
dist 245=[1.32415611263035000000e-07,3.91008518313850000000e-07] 
dist 246=[1.06282752537015300000e-07,4.00022898135050000000e-07] 
dist 247=[6.69558708247012000000e-08,4.04506592270080000000e-07] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 1, 0, 1] 
dist 0=[80.382890251962063047  ,80.382890251962063047  ] 
dist 1=[78.408586614986172449  ,81.871139876674051598  ] 
dist 2=[75.648760593233145724  ,82.691258623839926913  ] 
dist 3=[71.785833596239313704  ,83.178814377032637102  ] 
dist 4=[65.409457368153374758  ,83.339778502671171446  ] 
dist 5=[58.816613150798429252  ,83.265132908752563307  ] 
dist 6=[54.089958406569097787  ,83.121521811345329501  ] 
dist 7=[49.827699138460436003  ,82.046658408818685030  ] 
dist 8=[45.088425489712589952  ,79.535682595327875581  ] 
dist 9=[40.409418926655071433  ,77.463113120540230826  ] 
dist 10=[36.387888099753767242  ,76.502034897589391328  ] 
dist 11=[32.081065338915505275  ,75.077521753318800902  ] 
dist 12=[26.263891630374050144  ,74.581171742263318448  ] 
dist 13=[20.512655946484099536  ,73.358929711151583730  ] 
dist 14=[16.469005851361924033  ,72.898826003567089023  ] 
dist 15=[12.905570142776453228  ,70.475353113883028508  ] 
dist 16=[8.9342306038213150625 ,65.768342862472084706  ] 
dist 17=[3.7420317943287466916 ,29.227571463465738716  ] 
dist 18=[-.0223422022596823947 ,25.757397898548700048  ] 
dist 19=[-3.4645171969289979612 ,17.627890196209117143  ] 
dist 20=[-7.3726014727791555567 ,16.463534718536806043  ] 
dist 21=[-10.991443575584306942  ,5.8847261793067067264 ] 
dist 22=[-13.279079296558025657  ,4.0771525852387657414 ] 
dist 23=[-15.033311358268606988  ,1.6854938083018832052 ] 
dist 24=[-16.521029670640115700  ,1.3016150828523321976 ] 
dist 25=[-17.722540967168386841  ,-1.4999003439071802847 ] 
dist 26=[-18.332932728738671980  ,-1.8781746527817622118 ] 
dist 27=[-18.623044338098290548  ,-2.4421213825719690523 ] 
dist 28=[-18.646996568621542732  ,-2.5449384074416519472 ] 
dist 29=[-16.862072384813409886  ,-4.1004471655242983051 ] 
dist 30=[-17.573456905819779316  ,-4.2834269573970217399 ] 
dist 31=[-17.981715605828008585  ,-4.4725759306438034769 ] 
dist 32=[-18.083936725677734475  ,-3.7812710191005940927 ] 
dist 33=[-9.3555340013238126609 ,-2.2693038198085365139 ] 
dist 34=[-8.6473403428113205786 ,-1.0847541276950421190 ] 
dist 35=[-6.9000479156715364537 ,.0780286694052167233 ] 
dist 36=[-6.5967018832291844537 ,1.5042578370189512022 ] 
dist 37=[-4.0013523081573881502 ,2.8576899173669127855 ] 
dist 38=[-3.5220739311152087830 ,3.7307219974300246764 ] 
dist 39=[-2.7958261920435705458 ,4.4142996986732856672 ] 
dist 40=[-2.6010092943578866560 ,5.0128069699151814388 ] 
dist 41=[-.8633765667366557631 ,5.5071563082217493174 ] 
dist 42=[-.7234967589437063891 ,5.7756521463077946472 ] 
dist 43=[-.4913713197249395531 ,5.9288614664985600218 ] 
dist 44=[-.4374716762890268198 ,5.9637396066375713536 ] 
dist 45=[.4060060888850272237 ,6.0676145067058352194 ] 
dist 46=[.5168963529603543631 ,6.4126563466350253226 ] 
dist 47=[.6258358467568269684 ,6.6116792841220129892 ] 
dist 48=[.5963573897967015280 ,6.6616073448963168421 ] 
dist 49=[.5280213787909013491 ,2.3066181406883549171 ] 
dist 50=[.4104009321793772566 ,2.3710118821915908846 ] 
dist 51=[-.0403093409927478424 ,2.4003080392301910053 ] 
dist 52=[-.7314164447297218591 ,2.3993219917981719416 ] 
dist 53=[-1.4018317997098555100 ,.6430374804088738438 ] 
dist 54=[-1.8371591404147862961 ,.5329870105916568366 ] 
dist 55=[-2.1799707013999256696 ,.3972178908734718919 ] 
dist 56=[-2.4820004410977311021 ,.3705640545281061399 ] 
dist 57=[-2.7316407276400901570 ,.0738260950412632079 ] 
dist 58=[-2.8658263108980896382 ,.0413369111308248115 ] 
dist 59=[-2.9400040958990309456 ,-.0005489045340933856 ] 
dist 60=[-2.9516262050911915815 ,0                     ] 
dist 61=[-1.1441977528385156799 ,-.2251186248898142820 ] 
dist 62=[-1.2022156714883449218 ,-.2502417680602863760 ] 
dist 63=[-1.2319571908957064036 ,-.2964014140564327006 ] 
dist 64=[-1.2373550740070190884 ,-.3053803213794298447 ] 
dist 65=[-.77500891062088917325,-.3201431203573152999 ] 
dist 66=[-.73390529748958118859,-.3117184097204047181 ] 
dist 67=[-.6230009013367306334 ,-.2907564163340275049 ] 
dist 68=[-.6056346622145973459 ,-.2475397367967770442 ] 
dist 69=[-.4088720658084779713 ,-.2010152316315713346 ] 
dist 70=[-.3704269924581132010 ,-.1668674760619589735 ] 
dist 71=[-.3251961124211150611 ,-.07297727473098178695] 
dist 72=[-.3133596253149895541 ,.0576625658356581822 ] 
dist 73=[-.0881203866138740992 ,.18423740192627178235] 
dist 74=[-.0768521215582758909 ,.26583482478527716218] 
dist 75=[-.0606416279311591988 ,.32935854090651372005] 
dist 76=[-.0559857849857973884 ,.3839882484302009172 ] 
dist 77=[.0278554866650429904 ,.4282569861851469024 ] 
dist 78=[.0383754757763105437 ,.4505321167430803466 ] 
dist 79=[.0575683980633718656 ,.4623203076697645477 ] 
dist 80=[.0617018034843246547 ,.4648373445674793013 ] 
dist 81=[.0721552607673060535 ,.1601735772215266364 ] 
dist 82=[.07204474308268030864,.1560235217360264070 ] 
dist 83=[.06793749219452235235,.1600911954768889709 ] 
dist 84=[.05737525668345594685,.1609315568773485798 ] 
dist 85=[.04571390255300487911,.0679662315193151031 ] 
dist 86=[.0359819481966447306 ,.0590096889730551639 ] 
dist 87=[.0143032159251572109 ,.0501637324067624516 ] 
dist 88=[-.0138690942541086704 ,.0479274996469116510 ] 
dist 89=[-.0434127757130033673 ,.0384156151205596493 ] 
dist 90=[-.0623642367440582179 ,.0364889526840734067 ] 
dist 91=[-.0770012583622783660 ,.0314491563823726382 ] 
dist 92=[-.0893712973950890032 ,.0305196450134804558 ] 
dist 93=[-.0993576677460688615 ,.0217998782418177365 ] 
dist 94=[-.1045073217378060792 ,.0200061401711639504 ] 
dist 95=[-.1071613496588781101 ,.0179626797821361846 ] 
dist 96=[-.1075991763090673496 ,.0173237379597885925 ] 
dist 97=[-.08645823751337163237,.0172635206093091779 ] 
dist 98=[-.08392296371485964637,.0180949938811862772 ] 
dist 99=[-.0766207498496091523 ,.0197237653889172674 ] 
dist 100=[-.0673863232105409912 ,.0228386802492048007 ] 
dist 101=[-.03209907430446844490,.0260738477809661430 ] 
dist 102=[-.02907435456805355198,.0281822583526967119 ] 
dist 103=[-.02454359820434652996,.0298472753252812035 ] 
dist 104=[-.0236845318995229938 ,.0313188382940772125 ] 
dist 105=[-.0187264768417885547 ,.0325382892776988449 ] 
dist 106=[-.0176828377813065970 ,.0332006810395656769 ] 
dist 107=[-.0159871617361777455 ,.0335791203147860196 ] 
dist 108=[-.0155019240603019881 ,.0373476863188465518 ] 
dist 109=[-.0055008319825212638 ,.0422519780171717489 ] 
dist 110=[-.0041802911027058714 ,.0449421585515322794 ] 
dist 111=[-.0011068351631048070 ,.0464983296727202548 ] 
dist 112=[-.0005603312303656599 ,.0468893290038133259 ] 
dist 113=[.0033423536265344604 ,.02254210743938158968] 
dist 114=[.0040037034608751808 ,.02154689538074472994] 
dist 115=[.0052196080448476808 ,.0192565385902328653 ] 
dist 116=[.0054710842635011705 ,.0170522582627871894 ] 
dist 117=[.00508595061107446367,.00538727513659499239] 
dist 118=[.00331337678748283817,.00495401961369136750] 
dist 119=[.00144681158431912966,.00383213640089383000] 
dist 120=[-.00100727262263339278,.00367090265720892223] 
dist 121=[-.00338010508589065789,.0018578045153576892 ] 
dist 122=[-.00492351689634817522,.0015213313295362692 ] 
dist 123=[-.00613841004830487681,.0011279543331658076 ] 
dist 124=[-.00720394457145242098,.0010607409302166816 ] 
dist 125=[-.00807830606282265338,-.0017085591295654242 ] 
dist 126=[-.00853242222667704634,-.0020283776878781752 ] 
dist 127=[-.00877053038170255386,-.0026672417746104233 ] 
dist 128=[-.00881180372934173521,-.0028066522355661644 ] 
dist 129=[-.00588879639171429375,-.0031883608269916351 ] 
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dist 136=[-.00260395437565141375,.00031510520732104914] 
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dist 150=[.00032130122745271887,.00045072673472085257] 
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dist 152=[-7.43916397773109400000e-05,.00034191151744201882] 
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dist 155=[-.00054867162003727374,.00012169501125324193] 
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dist 160=[-.00081478565169275495,-.00022931550453296778] 
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dist 172=[-9.86272060225998520000e-05,.00030196255463442157] 
dist 173=[1.10253075505266260000e-05,.00034277670123669065] 
dist 174=[2.41065834172882470000e-05,.00036516295148794221] 
dist 175=[4.77700736243770600000e-05,.00037808873207203306] 
dist 176=[5.25499669641723400000e-05,.00038126086955745453] 
dist 177=[6.64202729164945600000e-05,.00013209385549334705] 
dist 178=[6.78407037955657700000e-05,.00013901073748419360] 
dist 179=[6.53193862861037000000e-05,.00014266707838258984] 
dist 180=[5.68048021805792500000e-05,.00014347841271456983] 
dist 181=[4.20369793305777700000e-05,4.72211586216897600000e-05] 
dist 182=[2.74428391198954900000e-05,4.38156792615369300000e-05] 
dist 183=[1.18793062738749400000e-05,3.48274860819935100000e-05] 
dist 184=[-8.82224532756703000000e-06,3.35265131741266600000e-05] 
dist 185=[-2.88703469429041800000e-05,1.84158304420279200000e-05] 
dist 186=[-4.18350581031959000000e-05,1.55654040633286000000e-05] 
dist 187=[-5.19445852657493400000e-05,1.22980663347049400000e-05] 
dist 188=[-6.06331852699932600000e-05,1.17085073632085100000e-05] 
dist 189=[-6.76489551539558400000e-05,-1.29124233698605000000e-05] 
dist 190=[-7.11031252523445800000e-05,-1.57669439332771000000e-05] 
dist 191=[-7.28829083220703200000e-05,-2.15653868407200000000e-05] 
dist 192=[-7.32363745876914500000e-05,-2.27878741943513000000e-05] 
dist 193=[-5.28686232398525140000e-05,-2.66442640222380000000e-05] 
dist 194=[-5.07332614805760790000e-05,-2.68743563365651000000e-05] 
dist 195=[-4.46543671731812010000e-05,-2.46820662161755600000e-05] 
dist 196=[-4.36144717750985440000e-05,-1.82691030585538230000e-05] 
dist 197=[-3.16486530153095200000e-05,-1.17173704063305750000e-05] 
dist 198=[-2.92044495731246000000e-05,-5.88572468666893900000e-06] 
dist 199=[-2.63022147380021800000e-05,4.63254335183150000000e-07] 
dist 200=[-2.53296061288666400000e-05,9.07408257979090000000e-06] 
dist 201=[-1.09406576804513100000e-05,1.74385619404695500000e-05] 
dist 202=[-9.93155632266517000000e-06,2.28078291679125390000e-05] 
dist 203=[-8.49868055602278000000e-06,2.69490076698197750000e-05] 
dist 204=[-8.05306056588132000000e-06,3.04277863538352230000e-05] 
dist 205=[5.15533422258530000000e-07,3.31754029395417430000e-05] 
dist 206=[1.57733780026752000000e-06,3.44075732325303000000e-05] 
dist 207=[3.39726675988929748000e-06,3.49773593335629800000e-05] 
dist 208=[0                     ,3.50896345010189500000e-05] 
dist 209=[5.76260569850172200000e-06,1.42219836782640100000e-05] 
dist 210=[5.98509969914344700000e-06,1.51205763160995000000e-05] 
dist 211=[5.82281265840988800000e-06,1.56389511970508900000e-05] 
dist 212=[5.09588503138905000000e-06,1.57653983154539700000e-05] 
dist 213=[4.24846379008586000000e-06,5.53500767160156000000e-06] 
dist 214=[3.18584303570890000000e-06,5.27020798597942000000e-06] 
dist 215=[1.56645929067530000000e-06,4.64881716199194000000e-06] 
dist 216=[-6.27892899028800000000e-07,4.45056631535289000000e-06] 
dist 217=[-2.75852405736100000000e-06,3.53404658501302000000e-06] 
dist 218=[-4.12450365268130000000e-06,3.34241299738054000000e-06] 
dist 219=[-5.17611799206210000000e-06,2.88698145679245000000e-06] 
dist 220=[-6.05613705438510000000e-06,2.75803009321948000000e-06] 
dist 221=[-6.76946083024990000000e-06,1.50053642417480000000e-06] 
dist 222=[-7.15784733596490000000e-06,1.28696004224090000000e-06] 
dist 223=[-7.37820590693950000000e-06,9.24732914313400000000e-07] 
dist 224=[-7.42286098922240000000e-06,8.36730399759500000000e-07] 
dist 225=[-6.53478494411698000000e-06,6.56288177503400000000e-07] 
dist 226=[-6.38789905232525000000e-06,6.63830209220800000000e-07] 
dist 227=[-5.96357993399419400000e-06,7.53539623462100000000e-07] 
dist 228=[-5.38463590294248000000e-06,9.77255864032500000000e-07] 
dist 229=[-2.42477110050511000000e-06,1.22160152961440000000e-06] 
dist 230=[-2.34318612795671000000e-06,1.39341412147480000000e-06] 
dist 231=[-2.11717062431147000000e-06,1.54288307143250000000e-06] 
dist 232=[-2.06498429108456000000e-06,1.69838805006870000000e-06] 
dist 233=[-1.62127843844366000000e-06,1.84364647305230000000e-06] 
dist 234=[-1.52683402996546000000e-06,1.95238447070780000000e-06] 
dist 235=[-1.38078085949922000000e-06,2.05399668876790000000e-06] 
dist 236=[-1.33614922020108000000e-06,2.17095353377553000000e-06] 
dist 237=[-3.98080398323240000000e-07,2.27562674269686000000e-06] 
dist 238=[-2.75312080505270000000e-07,2.32838168424344000000e-06] 
dist 239=[2.85946027349000000000e-09,2.35279172564949000000e-06] 
dist 240=[5.63768906392700000000e-08,2.34468517522894000000e-06] 
dist 241=[2.76601983484849900000e-07,1.88282575349503000000e-06] 
dist 242=[2.33843113346799100000e-07,1.81784468513902000000e-06] 
dist 243=[1.52880331899665980000e-07,1.67147065329652000000e-06] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 0, 0, 1, 2, 0, 2] 
dist 0=[84.034424549076943124  ,84.034424549076943124  ] 
dist 1=[83.204409706309217419  ,84.211540715086081348  ] 
dist 2=[81.709784422652509955  ,84.087720609550000203  ] 
dist 3=[78.920189899612025714  ,83.819318374960021110  ] 
dist 4=[75.481191525133742184  ,83.606581248103430458  ] 
dist 5=[71.395216872829110154  ,83.091129469572775792  ] 
dist 6=[66.056903963426157412  ,82.339871934007147307  ] 
dist 7=[57.620123084894228900  ,82.030416009950538059  ] 
dist 8=[49.051272083917658378  ,81.726147181091998207  ] 
dist 9=[43.185546568010168968  ,81.446385839555775113  ] 
dist 10=[38.180282023559566048  ,81.235127447544491776  ] 
dist 11=[33.044276410070652182  ,81.032910919597975040  ] 
dist 12=[28.218592778301171533  ,80.789664061800983900  ] 
dist 13=[24.450853468509672945  ,80.273915257291947980  ] 
dist 14=[20.734850940073346203  ,35.548527481072510352  ] 
dist 15=[16.114050664267255161  ,31.964747246478104603  ] 
dist 16=[11.708573482342571704  ,26.021503165046553844  ] 
dist 17=[8.851046540172129465  ,22.312212533278853610  ] 
dist 18=[6.573702605258341183  ,13.698520079812693142  ] 
dist 19=[4.482742710732970512  ,10.899911514689763636  ] 
dist 20=[-1.1423734842485881252 ,10.201363106549495778  ] 
dist 21=[-6.5940262524581812393 ,6.172807462266917245  ] 
dist 22=[-10.108445308241694632  ,2.284491133164988449  ] 
dist 23=[-13.082674395405798438  ,2.150613294996858753  ] 
dist 24=[-15.575594550943633832  ,-1.1504035824426226245 ] 
dist 25=[-17.650949284677835009  ,-1.4233576314011407847 ] 
dist 26=[-19.306960479315155624  ,-1.9208811259661537880 ] 
dist 27=[-20.126559622531420814  ,-2.0006402700066683192 ] 
dist 28=[-20.549531782389224273  ,-2.187718729992780402  ] 
dist 29=[-20.622421916306734514  ,-2.151256996110487454  ] 
dist 30=[-6.4273541230770323785 ,-2.032938160938461513  ] 
dist 31=[-5.8552762163496428662 ,-1.786064964159934992  ] 
dist 32=[-4.4260429446030267855 ,-1.523263145001623676  ] 
dist 33=[-4.2186964484889808656 ,-1.340641044032775210  ] 
dist 34=[-2.088125061438450676  ,-1.189157139952097189  ] 
dist 35=[-1.705598282313541388  ,-.6588766897287823035 ] 
dist 36=[-1.3091314032538625705 ,.1523253327807207336 ] 
dist 37=[-1.181022164640830122  ,.9279616956864116373 ] 
dist 38=[-1.103406002311255286  ,1.7403796531506211938 ] 
dist 39=[-1.088002001740422311  ,2.3800920250856037329 ] 
dist 40=[-.6648349118154471532 ,2.8789476103908057084 ] 
dist 41=[-.6111355227048034192 ,3.3123596799865484502 ] 
dist 42=[-.5599750286286995329 ,3.6678869574789312758 ] 
dist 43=[-.5581497882394538123 ,3.8562859858781248321 ] 
dist 44=[-.575593524579409923  ,3.9572911707720783873 ] 
dist 45=[-.616780074493833523  ,3.9749930311462591289 ] 
dist 46=[-.681344758853168997  ,2.5081918032651088232 ] 
dist 47=[-.791955005900005853  ,2.3819484232307067794 ] 
dist 48=[-.907449338949555997  ,2.0596266874535189768 ] 
dist 49=[-.991590237834107592  ,1.9976438732065131420 ] 
dist 50=[-1.067201395149756046  ,1.4746850780710854347 ] 
dist 51=[-1.149026380803942269  ,1.321892468896160479  ] 
dist 52=[-1.227135566206015242  ,1.122631319469254800  ] 
dist 53=[-1.288117033931904133  ,.907094136419154741  ] 
dist 54=[-1.347642028935966969  ,.4457246691213143390 ] 
dist 55=[-1.420144501831047445  ,.4453374042636978900 ] 
dist 56=[-1.4856087984120367891 ,.14401037024995526304] 
dist 57=[-1.5171684399037227126 ,.12018870672104720825] 
dist 58=[-1.5300030057676225274 ,.06628825127856672039] 
dist 59=[-1.5247530040283796515 ,.05764040674739626843] 
dist 60=[-1.4989513985406952772 ,-.00577075293017074426] 
dist 61=[-1.4607110808226608373 ,-.01617181219381495237] 
dist 62=[-.47546847546608234427,-.0337967755970508573 ] 
dist 63=[-.43571375433552004825,-.0372968480599291025 ] 
dist 64=[-.3339013940066699506 ,-.0781741915081566930 ] 
dist 65=[-.3192612116375432501 ,-.0834891465023607144 ] 
dist 66=[-.1588514242143634779 ,-.08945944404048673743] 
dist 67=[-.1515795628546817010 ,-.04710872667694794966] 
dist 68=[-.1592437492090586609 ,.0092878547398352779 ] 
dist 69=[-.1633444813076511274 ,.0648763262673061553 ] 
dist 70=[-.1656731075664696106 ,.1461308141432067400 ] 
dist 71=[-.1662398139865899863 ,.1989681421206477436 ] 
dist 72=[-.03473484509897553372,.2406700364236494402 ] 
dist 73=[-.02879861076838738681,.2775845782496875671 ] 
dist 74=[-.01486804248772739595,.3082349781486930312 ] 
dist 75=[-.01286690883634606520,.3249920091828936523 ] 
dist 76=[.0050077956940261863 ,.3346488213439204012 ] 
dist 77=[.0080017589510900747 ,.3370229492645805029 ] 
dist 78=[.0121386077879235963 ,.19128297077764148599] 
dist 79=[.0128020345066647657 ,.1791874695956866063 ] 
dist 80=[.0282165420451550389 ,.14836520385536378505] 
dist 81=[.0299762488691570459 ,.14270460541258022315] 
dist 82=[.0324323036406622410 ,.09312921334669051635] 
dist 83=[.01857076945197180846,.08361878723780539880] 
dist 84=[-.00340117453895611049,.0693156101068968731 ] 
dist 85=[-.02481017308520550166,.0652657515457229287 ] 
dist 86=[-.0546547249278780064 ,.04147792226970671073] 
dist 87=[-.0795141198100822115 ,.04148112664635120183] 
dist 88=[-.0991911325201930544 ,.02100950771160213896] 
dist 89=[-.1166738714142905710 ,.01927773120116521990] 
dist 90=[-.1312110221441807856 ,.01500433213323545916] 
dist 91=[-.1391619292859413487 ,.01435638938598441620] 
dist 92=[-.1437386986914702549 ,.00803799602091134587] 
dist 93=[-.1448430205008355713 ,.00688533703142271157] 
dist 94=[-.04017175673101929753,.00540502891120910783] 
dist 95=[-.03724410606126639556,.00506174990743789749] 
dist 96=[-.02958074535630405046,-.00370286317972883738] 
dist 97=[-.02846547260623879275,-.00473576064109137685] 
dist 98=[-.0158024081100832069 ,-.00701338346183198556] 
dist 99=[-.0134287196296333468 ,-.00408539826131323127] 
dist 100=[-.01427588390667524861,.00055075088418489014] 
dist 101=[-.01473546723701344360,.00523869037659607305] 
dist 102=[-.01496471156659569863,.01247800861459336159] 
dist 103=[-.01499993615565318450,.01713905052232130062] 
dist 104=[-.00932661296161397237,.02075847968073632295] 
dist 105=[-.00897181485059539954,.02385186930709965098] 
dist 106=[-.0084224545862887375 ,.02633464586716764341] 
dist 107=[-.0082462486776751054 ,.02752356042148081582] 
dist 108=[-.0077962411005286183 ,.02812386586821334392] 
dist 109=[-.0076365538617244635 ,.02826363902307419369] 
dist 110=[-.0075350206345937238 ,.01942322930041563967] 
dist 111=[-.0074827566593501296 ,.01854128440391101094] 
dist 112=[-.0074614813616695250 ,.01610660525181878654] 
dist 113=[-.0074834882059198639 ,.01570079350777847845] 
dist 114=[-.0075382362408514576 ,.01115992868892514912] 
dist 115=[-.0076480698937270415 ,.01024972031028273345] 
dist 116=[-.0077813695705675056 ,.00915587689392753030] 
dist 117=[-.0079299918072763344 ,.00880966388317498811] 
dist 118=[-.0081163106444707258 ,.0040809320315839889 ] 
dist 119=[-.00871215465286707147,.0041018880990707388 ] 
dist 120=[-.01015466412959143610,.00201994018562491582] 
dist 121=[-.01134443686306852792,.00185084126046455581] 
dist 122=[-.01227849077358404914,.00143797920677677602] 
dist 123=[-.01270322245730474420,.00136546964132553131] 
dist 124=[-.01289429152772967376,.00076426544360097152] 
dist 125=[-.01289835652110152873,.00065383937790701788] 
dist 126=[-.00196564372005358971,.00048173454626116828] 
dist 127=[-.00162780011008711843,.00043731389491199698] 
dist 128=[-.00157905889270832227,-.00031586993359490016] 
dist 129=[-.0010622966925016507 ,-.00041289339998370239] 
dist 130=[-.0012634589955092645 ,-.00059584238035471419] 
dist 131=[-.0014404014285597115 ,-.00030322873382637411] 
dist 132=[-.0015869402492589804 ,9.59596634978252800000e-05] 
dist 133=[-.0016669625613003025 ,.00048314656477470252] 
dist 134=[-.0017131147812234091 ,.00073393797800655668] 
dist 135=[-.0017246917180285578 ,.00092988690710436976] 
dist 136=[-.00042987938185052699,.00109890090255812914] 
dist 137=[-.00038631794138251031,.00123576457341044588] 
dist 138=[-.00027794294214580249,.00130381632610811682] 
dist 139=[-.00026195390870829985,.00133926328374420801] 
dist 140=[-.00010088028601798553,.00134639945662377328] 
dist 141=[-7.19038160994066800000e-05,.00098526620074793184] 
dist 142=[-3.49012911517527000000e-05,.00094710849881323539] 
dist 143=[-2.76024362259484000000e-05,.00083700593175430507] 
dist 144=[.00018094009990251973,.00081815155068973705] 
dist 145=[.00020539050824430754,.00059718758097745667] 
dist 146=[.00013592591548882986,.00055184402990422068] 
dist 147=[1.72826181530517260000e-05,.00049852310697069085] 
dist 148=[-.0001444287758318626 ,.00048069684342892754] 
dist 149=[-.00030177549882126663,.0003606062259976582 ] 
dist 150=[-.00040306635525739706,.0003673878550431473 ] 
dist 151=[-.00048148700280760333,.0003684466106315352 ] 
dist 152=[-.00054785962280181280,.00021747544086165705] 
dist 153=[-.00060048407856456947,.00020421704310184539] 
dist 154=[-.00062421603671465942,.00016957491797059042] 
dist 155=[-.00063539064832620792,.00016416131788224144] 
dist 156=[-.00063804797592204861,.00010613466692959106] 
dist 157=[-.00018933832832275093,9.49993872908938900000e-05] 
dist 158=[-.00017809172823339245,8.14610130106986360000e-05] 
dist 159=[-.0001472919735007679 ,7.79187482175357800000e-05] 
dist 160=[-.0001428209715229295 ,-2.03602892391225530000e-05] 
dist 161=[-9.03259292929610000000e-05,-3.20578166959143730000e-05] 
dist 162=[-.0001075060627958207 ,-5.80953876860682800000e-05] 
dist 163=[-.0001220146485189721 ,-3.25598243394099000000e-05] 
dist 164=[-.0001336913594349732 ,3.28987270209770000000e-06] 
dist 165=[-.0001395926595854729 ,3.81478875680639000000e-05] 
dist 166=[-.0001426383328924522 ,6.10186981812672000000e-05] 
dist 167=[-.0001430229852029721 ,7.92122881037162000000e-05] 
dist 168=[-4.61547054073867700000e-05,9.54644816046838000000e-05] 
dist 169=[-4.21314119298936900000e-05,.0001089886980870137 ] 
dist 170=[-3.20504003898741900000e-05,.0001163300950258422 ] 
dist 171=[-3.04377346220222200000e-05,.0001204620955046835 ] 
dist 172=[-1.50650454526035000000e-05,.0001212533927434169 ] 
dist 173=[-1.22367041741571000000e-05,8.01773414187693200000e-05] 
dist 174=[-8.37270989212030000000e-06,7.65294645665991100000e-05] 
dist 175=[-7.28174010255900000000e-06,6.65640906656555350000e-05] 
dist 176=[1.34876000583598000000e-05,6.46720098903149200000e-05] 
dist 177=[1.60417769650641000000e-05,4.62337130425423600000e-05] 
dist 178=[2.09115462174960000000e-05,4.25068495786731400000e-05] 
dist 179=[1.46827727693897500000e-05,3.73521423752521700000e-05] 
dist 180=[-1.71999229465410000000e-06,3.56570589288705200000e-05] 
dist 181=[-1.78018801632288000000e-05,3.70281613517011000000e-05] 
dist 182=[-2.83455849039258000000e-05,3.76918906771431000000e-05] 
dist 183=[-3.67219906082551000000e-05,3.77368764910840000000e-05] 
dist 184=[-4.41829157621313000000e-05,2.76895324912779500000e-05] 
dist 185=[-5.03739116290384000000e-05,2.65534478778897900000e-05] 
dist 186=[-5.36987024330127000000e-05,2.35806087905247600000e-05] 
dist 187=[-5.55209125599528000000e-05,2.29001620321399500000e-05] 
dist 188=[-5.58990086747168000000e-05,1.76137272659254800000e-05] 
dist 189=[-2.26423687768068600000e-05,1.65149796633478000000e-05] 
dist 190=[-2.19330154504802700000e-05,1.46975877072469000000e-05] 
dist 191=[-2.02718563113767600000e-05,1.41940972297987000000e-05] 
dist 192=[-1.96995336569720100000e-05,4.04261962561190000000e-06] 
dist 193=[-1.69342190449673000000e-05,2.69429860453730000000e-06] 
dist 194=[-1.63306826832118000000e-05,-3.69965400317000000000e-07] 
dist 195=[-1.47109662829541000000e-05,-9.66509779773900000000e-07] 
dist 196=[-1.45640783091133400000e-05,4.57654266649000000000e-07] 
dist 197=[-1.53892825157332400000e-05,3.86786801658390000000e-06] 
dist 198=[-1.58620902074093400000e-05,6.06085093192390000000e-06] 
dist 199=[-1.59713172652770900000e-05,7.75575607762440000000e-06] 
dist 200=[-7.53788972488324700000e-06,9.18451091876370000000e-06] 
dist 201=[-7.14673322440297000000e-06,1.03469183796923000000e-05] 
dist 202=[-6.27310688337210000000e-06,1.09823453196933000000e-05] 
dist 203=[-6.00389361845760000000e-06,1.13462368460784000000e-05] 
dist 204=[-4.81052254109391000000e-06,1.14287490125022000000e-05] 
dist 205=[-4.56844477484799000000e-06,1.00178304544479800000e-05] 
dist 206=[-3.90839531640071000000e-06,9.79772616391450000000e-06] 
dist 207=[-3.79926468774360000000e-06,9.12373424380661000000e-06] 
dist 208=[-2.44925039408808000000e-06,8.95082982643388000000e-06] 
dist 209=[-2.19361248281083000000e-06,7.39863033596816100000e-06] 
dist 210=[-1.83388747418741000000e-06,7.05124684031190000000e-06] 
dist 211=[-1.72055769953429000000e-06,6.53350321311349800000e-06] 
dist 212=[-1.61840737978203000000e-06,6.36118260483971830000e-06] 
dist 213=[-1.67784944586218000000e-06,3.36525297714929000000e-06] 
dist 214=[-1.87573038288217000000e-06,3.43827606700558000000e-06] 
dist 215=[-2.40131486393712000000e-06,3.44870670965586000000e-06] 
dist 216=[-2.86716690732888000000e-06,2.76061611000365000000e-06] 
dist 217=[-3.25155895420342000000e-06,2.67037339988544000000e-06] 
dist 218=[-3.45303203493207000000e-06,2.43708247893225000000e-06] 
dist 219=[-3.56083420325703000000e-06,2.36833855615663000000e-06] 
dist 220=[-3.58022972223952000000e-06,1.94363606736745000000e-06] 
dist 221=[-2.57105932551754000000e-06,1.85062708838915000000e-06] 
dist 222=[-2.47025485741368000000e-06,1.67055699246246000000e-06] 
dist 223=[-2.22217750233216000000e-06,1.61909183818895000000e-06] 
dist 224=[-2.14476752884853000000e-06,7.54629618782960000000e-07] 
dist 225=[-1.73817419672551000000e-06,6.31556503767180000000e-07] 
dist 226=[-1.65148240410541000000e-06,3.54868945916640000000e-07] 
dist 227=[-1.46232744335372000000e-06,2.90616249197840000000e-07] 
dist 228=[-1.46103014878029000000e-06,-4.05612282852400000000e-08] 
dist 229=[-1.50516055079820000000e-06,-9.84995090284700000000e-08] 
dist 230=[-1.52366550130147000000e-06,-1.90579452573702980000e-07] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 0, 2, 0, 2] 
dist 0=[85.202632867551410403  ,85.202632867551410403  ] 
dist 1=[84.222785778858954671  ,85.692834792029731484  ] 
dist 2=[81.831972354451006639  ,86.129551644905774731  ] 
dist 3=[78.718209908394535569  ,86.439622269783883478  ] 
dist 4=[74.853364753416988610  ,86.424419863692723832  ] 
dist 5=[69.699763985749618304  ,86.201612768906907428  ] 
dist 6=[61.442999835623435460  ,85.982566060457813576  ] 
dist 7=[52.996486889741328385  ,85.119506269358862121  ] 
dist 8=[47.085762007019618907  ,84.714261779204918374  ] 
dist 9=[41.903882078518548883  ,81.867887566905505118  ] 
dist 10=[36.366243564856316008  ,81.068477891275795710  ] 
dist 11=[31.028498184583165912  ,80.241997333328718896  ] 
dist 12=[26.644522074075561672  ,79.782224343534054343  ] 
dist 13=[22.123052287878650980  ,79.291999541193959790  ] 
dist 14=[16.236908570807075745  ,77.484166633852987402  ] 
dist 15=[10.517294532867706860  ,67.551367560068469824  ] 
dist 16=[6.6130620555052758335 ,60.868578386669730809  ] 
dist 17=[2.6224925595300214163 ,31.674010465221717577  ] 
dist 18=[-2.1112823110078066616 ,27.950026548996909424  ] 
dist 19=[-6.5436477332802104869 ,19.217360639176725142  ] 
dist 20=[-9.3317226315878139975 ,17.966568209720378813  ] 
dist 21=[-11.448032488935107894  ,6.5757307247802122356 ] 
dist 22=[-13.200695902165000293  ,4.6273752203305209322 ] 
dist 23=[-14.588044801364903802  ,2.0534048390337586230 ] 
dist 24=[-15.247477635865678710  ,1.6399641811898982562 ] 
dist 25=[-15.558510195761861752  ,-1.3158790395017480692 ] 
dist 26=[-15.565942399612615149  ,-1.4395492958235538049 ] 
dist 27=[-14.879257970018572769  ,-2.1809948209428666569 ] 
dist 28=[-16.615481780698662299  ,-2.2881852905675798935 ] 
dist 29=[-18.038893994954466667  ,-2.4376557717415421222 ] 
dist 30=[-18.810464318134876293  ,-2.4354506307494256099 ] 
dist 31=[-19.253314721857642800  ,-2.3935557480948906206 ] 
dist 32=[-19.364228740382628543  ,-1.4875259447695055995 ] 
dist 33=[-10.056983685244463291  ,-.5753557486984889364 ] 
dist 34=[-9.3016552971728956314 ,.5709925572001751959 ] 
dist 35=[-7.4357943758974509378 ,1.6657525983032490919 ] 
dist 36=[-7.1116545512278478632 ,2.3727569309288544542 ] 
dist 37=[-4.3328005992908562964 ,2.9263700033915829330 ] 
dist 38=[-3.8191058569256456197 ,3.4101325263146160326 ] 
dist 39=[-3.0417253192718681043 ,3.8082683994315855411 ] 
dist 40=[-2.8326157475075741547 ,4.0207546341855435892 ] 
dist 41=[-.5524402055488674836 ,4.1366365234601932634 ] 
dist 42=[-.5035510053641346869 ,4.1560941690081710858 ] 
dist 43=[-.1663566873091007131 ,4.9816287863788393876 ] 
dist 44=[-.1088311704536220920 ,5.8015443599143391210 ] 
dist 45=[-.0057281789324801016 ,6.4808123845004296130 ] 
dist 46=[.0156002422797104926 ,6.8518484214840892362 ] 
dist 47=[.28003567776989592727,7.0658853298733980325 ] 
dist 48=[.3043301170968534260 ,7.1196026975439816440 ] 
dist 49=[.1212308109781432026 ,1.9675258584464237146 ] 
dist 50=[-.3495233129099813476 ,1.8072329390877108706 ] 
dist 51=[-.8060368570596434408 ,1.3982466712996033716 ] 
dist 52=[-1.1010653793144212120 ,1.3379358824175904290 ] 
dist 53=[-1.3315702875526044690 ,1.1429329511662589367 ] 
dist 54=[-1.5312266448405137132 ,1.1402381229668549771 ] 
dist 55=[-1.6935857760807542475 ,.4354940777065601778 ] 
dist 56=[-1.7756029241897570535 ,.4069230679632302451 ] 
dist 57=[-1.8179554511123126018 ,.06657990009876929468] 
dist 58=[-1.8231401212541037298 ,.05741281540216048815] 
dist 59=[-.9495059707145456622 ,-.02426348157041074970] 
dist 60=[-1.0960989501107674639 ,-.03792798596091913877] 
dist 61=[-1.2160144789226525977 ,-.05678927027337295805] 
dist 62=[-1.2783057436435316221 ,-.05977500301230548075] 
dist 63=[-1.3102904924141088211 ,-.13217075660796398844] 
dist 64=[-1.3161259598620412185 ,-.11573036182921829224] 
dist 65=[-.8264858543610334628 ,-.05432805820987842716] 
dist 66=[-.7829274928501580955 ,.02547989370762169599] 
dist 67=[-.66522255798018091455,.10249878320623147904] 
dist 68=[-.64677784705615047007,.15281181191536911812] 
dist 69=[-.43739850150587001278,.19269507966946471814] 
dist 70=[-.39645318710060472954,.22820355858439240147] 
dist 71=[-.34831888613449849979,.25776227001379439668] 
dist 72=[-.33569371804104587988,.2739635633879882552 ] 
dist 73=[-.05552265434882357421,.28332873801330249126] 
dist 74=[-.05211765332547254706,.28567538429206430113] 
dist 75=[-.02481916740588425796,.3494994452799501423 ] 
dist 76=[-.01995727829881929439,.4079406167048110872 ] 
dist 77=[-.01222167488701481604,.4553101444924476567 ] 
dist 78=[-.01034892596952581329,.4791384180176821855 ] 
dist 79=[.01917820405001887879,.4917596896506457212 ] 
dist 80=[.02298281611242297495,.4945115673248771520 ] 
dist 81=[.02765090531289571846,.1641272334570777852 ] 
dist 82=[-.00802213419783228776,.1520659173355800286 ] 
dist 83=[-.04287746619647827604,.1204201751106311503 ] 
dist 84=[-.06569392421191588704,.1158692285469877821 ] 
dist 85=[-.08381665757452780781,.07503441908435507159] 
dist 86=[-.09999421535080836523,.07546663938733698000] 
dist 87=[-.11347642255096823018,.0423500898541334310 ] 
dist 88=[-.1208728981054752449 ,.0404006369390573755 ] 
dist 89=[-.12515172052622786232,.01083131866536423881] 
dist 90=[-.1262263999758595924 ,.01007916329824150449] 
dist 91=[-.0766460053158293480 ,.00279557418317984889] 
dist 92=[-.0899391115683651554 ,.00151199092691576609] 
dist 93=[-.1010029018852382608 ,-.00017108457953848035] 
dist 94=[-.1070631139743654254 ,-.00048936483554179824] 
dist 95=[-.1105608736399559547 ,-.00856720905513628680] 
dist 96=[-.1114245246223545316 ,-.00910413515396511685] 
dist 97=[-.06626469371125343546,-.00402211376615806601] 
dist 98=[-.06247100820669428133,.00268694869696704687] 
dist 99=[-.05263406854155415082,.00917318310069746768] 
dist 100=[-.05077969025390784148,.01336914937866264226] 
dist 101=[-.03432437123102325349,.01664516456438677961] 
dist 102=[-.03111245675482823834,.01947085700453251372] 
dist 103=[-.02631249562756083791,.02175422747744822754] 
dist 104=[-.02491677226477307744,.02287221702723706700] 
dist 105=[-.00810013049979494495,.02344945607993992835] 
dist 106=[-.00782505218383594252,.0263420626908311443 ] 
dist 107=[-.00521000889536129410,.0333509032801047328 ] 
dist 108=[-.00470765727290290655,.0396029733601938646 ] 
dist 109=[-.00402545702525973148,.0448110008309049517 ] 
dist 110=[-.00380869175052984273,.0476648603320365424 ] 
dist 111=[.00040216512354785206,.0493116676216301225 ] 
dist 112=[.00092402176029851384,.0497157746581917539 ] 
dist 113=[2.25194657141550070000e-05,.01392691353744910419] 
dist 114=[-.0027355235729413100 ,.01299123033355420766] 
dist 115=[-.00541385735179170581,.01049546251920717620] 
dist 116=[-.00713515640758137234,.01013561689782750390] 
dist 117=[-.00846584315271370551,.00795753390932415350] 
dist 118=[-.00959008334318707462,.00794109059448933628] 
dist 119=[-.01048099743073960531,.00413365421201667319] 
dist 120=[-.01088335854157484073,.00397158732135977762] 
dist 121=[-.01107276314904805588,.0012235579051483050 ] 
dist 122=[-.01111610576214025171,.0011566866140231004 ] 
dist 123=[-.00682803298927733262,.0004539517079676638 ] 
dist 124=[-.00793140921647039616,.0003271276943424181 ] 
dist 125=[-.00881995743664969156,.0001717310269237303 ] 
dist 126=[-.00925049756465198777,.0001457460456672652 ] 
dist 127=[-.00947101986472089766,-.0008003706714841513 ] 
dist 128=[-.00952371590292390492,-.0009094868339431516 ] 
dist 129=[-.00671014705725761814,-.0011184672265113912 ] 
dist 130=[-.00642327764532277030,-.0011620522640587891 ] 
dist 131=[-.00561825112033087128,-.0012570259150326017 ] 
dist 132=[-.00548220115002604256,-.0012376612915296422 ] 
dist 133=[-.00393711661906654245,-.0011672449952880566 ] 
dist 134=[-.00362437918937684922,-.00069464844334391180] 
dist 135=[-.00325051284300746622,.00010940862694348988] 
dist 136=[-.00312844997044137524,.0011927571720483793 ] 
dist 137=[-.00062823890394620018,.00224303334639724832] 
dist 138=[-.00060094235295039953,.00291556313735579130] 
dist 139=[-.0003689144648020856 ,.00343278701029878097] 
dist 140=[-.0003252002063267007 ,.00386512828709251058] 
dist 141=[-.0002581409267561527 ,.00420610797051017626] 
dist 142=[-.0002399602682499803 ,.00435977958036616041] 
dist 143=[8.45334445185791000000e-05,.00443054111644873446] 
dist 144=[0                     ,.00444160257574519873] 
dist 145=[.0002076103694737098 ,.0012798379126449134 ] 
dist 146=[.0002259565209221766 ,.0011945235077680060 ] 
dist 147=[.0002752959269067686 ,.0009659107280505164 ] 
dist 148=[.00027753604694743317,.0009330222107471331 ] 
dist 149=[.00026323049869749427,.0006808931633634774 ] 
dist 150=[.00022284934773549501,.0006858986438005325 ] 
dist 151=[.0001648350014907430 ,.0003786654590544002 ] 
dist 152=[-7.55653811232603000000e-05,.0003639235655962838 ] 
dist 153=[-.0003085053177946035 ,.0001237469924336548 ] 
dist 154=[-.0004612159543359248 ,.0001179897885038969 ] 
dist 155=[-.0005826825538012664 ,5.57108976277637000000e-05] 
dist 156=[-.0006913075221083871 ,4.42650050584927000000e-05] 
dist 157=[-.0007818947355170842 ,3.04864303821317000000e-05] 
dist 158=[-.0008315896557333415 ,2.79937822588878000000e-05] 
dist 159=[-.0008603043661843540 ,-6.09183292563490000000e-05] 
dist 160=[-.0008674093118429555 ,-7.12244707183510000000e-05] 
dist 161=[-.0005358206794960231 ,-9.12680435086109000000e-05] 
dist 162=[-.00050756588011884815,-9.55844841171056000000e-05] 
dist 163=[-.00043322131544123012,-.0001059566799745969 ] 
dist 164=[-.00041882336860566848,-.0001049908139477414 ] 
dist 165=[-.0002901821412232921 ,-9.94084182136987000000e-05] 
dist 166=[-.0002646746700478990 ,-8.61576575514150600000e-05] 
dist 167=[-.0002266745303178014 ,-7.15429652900949910000e-05] 
dist 168=[-.0002153953479673621 ,2.49845551205160000000e-05] 
dist 169=[-7.00169570928581500000e-05,.0001368094564762822 ] 
dist 170=[-6.80220709460686300000e-05,.0002101638734712156 ] 
dist 171=[-4.54821214663328200000e-05,.0002685423122374938 ] 
dist 172=[-4.10817257771885600000e-05,.0003207837906190622 ] 
dist 173=[-3.59282689514017100000e-05,.0003643596197119502 ] 
dist 174=[-3.45956930557212190000e-05,.0003882599208754820 ] 
dist 175=[6.38709350713916000000e-06,.0004020577456626874 ] 
dist 176=[1.12466123778746800000e-05,.0004054376113716113 ] 
dist 177=[2.10844609879724000000e-05,.00011518645277570977] 
dist 178=[2.27386909861472000000e-05,.0001080719739561779 ] 
dist 179=[2.71692497407642900000e-05,8.88567905163415000000e-05] 
dist 180=[2.73166234607667000000e-05,8.60092335585227000000e-05] 
dist 181=[2.59408863514740200000e-05,5.52370690276422000000e-05] 
dist 182=[2.21500636663199860000e-05,5.54155680266757000000e-05] 
dist 183=[1.53661298720374000000e-05,3.82747072494672000000e-05] 
dist 184=[-6.51044199911580000000e-06,3.67453254706468000000e-05] 
dist 185=[-2.77279860844140000000e-05,2.92964004212953000000e-05] 
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dist 187=[-5.24280361064454000000e-05,2.64542152085196000000e-05] 
dist 188=[-6.19707091768007000000e-05,2.57733784127080000000e-05] 
dist 189=[-6.97892452350657000000e-05,2.44535556175315000000e-05] 
dist 190=[-7.38123296247350000000e-05,2.40075396130345000000e-05] 
dist 191=[-7.59377419660084000000e-05,2.20601022411366000000e-05] 
dist 192=[-7.62616636093763000000e-05,2.14171305097617000000e-05] 
dist 193=[-5.42790819666782000000e-05,2.10029583968616000000e-05] 
dist 194=[-5.22807705957501000000e-05,2.07948288658662000000e-05] 
dist 195=[-4.64667526979215000000e-05,2.07342180017821000000e-05] 
dist 196=[-4.54992141693785000000e-05,2.09076755102846000000e-05] 
dist 197=[-3.36940008800545000000e-05,2.12826990152282000000e-05] 
dist 198=[-2.84354540213910500000e-05,2.20249160724930000000e-05] 
dist 199=[-2.56628364267133900000e-05,2.28079432740325000000e-05] 
dist 200=[-2.49588137683963410000e-05,2.33456631162341000000e-05] 
dist 201=[-6.58637248534041000000e-06,2.38015304322866000000e-05] 
dist 202=[-6.37493070695229000000e-06,2.42589721200710000000e-05] 
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dist 204=[-3.79933497248199000000e-06,2.52838498919932000000e-05] 
dist 205=[-3.25379419025745000000e-06,2.84664855458066000000e-05] 
dist 206=[-3.07407175008995000000e-06,3.00793928078061000000e-05] 
dist 207=[6.10199962218650000000e-07,3.09354051214536000000e-05] 
dist 208=[1.06470560036345000000e-06,3.11067082599273000000e-05] 
dist 209=[1.85671758294419000000e-06,1.11208314779226000000e-05] 
dist 210=[2.03970720136574000000e-06,1.04342093057695500000e-05] 
dist 211=[2.56894791872376000000e-06,8.58700675431291000000e-06] 
dist 212=[2.62280952479108000000e-06,8.30460253763640000000e-06] 
dist 213=[2.52579783156780000000e-06,5.75041941416750000000e-06] 
dist 214=[2.19918593191803660000e-06,5.78006899819220000000e-06] 
dist 215=[1.61696160450970000000e-06,3.70778669803910000000e-06] 
dist 216=[-5.55490986560800000000e-07,3.53376701860760000000e-06] 
dist 217=[-2.66443044786000000000e-06,2.73790846253268000000e-06] 
dist 218=[-4.03484334092950000000e-06,2.68575709478987000000e-06] 
dist 219=[-5.11066353975320000000e-06,2.54463350602730000000e-06] 
dist 220=[-6.04757429948980000000e-06,2.48711296786290000000e-06] 
dist 221=[-6.81023587510040000000e-06,2.43541813244850000000e-06] 
dist 222=[-7.19279099109130000000e-06,2.39816079234910000000e-06] 
dist 223=[-7.39545852777860000000e-06,2.35192195084750000000e-06] 
dist 224=[-7.44249590026970000000e-06,2.33979579177030000000e-06] 
dist 225=[-5.52371003358303000000e-06,2.34339954860310000000e-06] 
dist 226=[-5.32676317102143400000e-06,2.36895389685820000000e-06] 
dist 227=[-4.73738209459780000000e-06,2.40593186889110000000e-06] 
dist 228=[-4.64843906757053000000e-06,2.45503340542800000000e-06] 
dist 229=[-3.41139630073486000000e-06,2.52169533587660000000e-06] 
dist 230=[-2.72221690790472000000e-06,2.62859324290810000000e-06] 
dist 231=[-1.60570352118317700000e-06,2.73223060253650000000e-06] 
dist 232=[-1.51095493882325000000e-06,2.78594856801340000000e-06] 
dist 233=[-1.33896718870923000000e-06,2.81281293343120000000e-06] 
dist 234=[-1.30888131423534000000e-06,2.80963884026920000000e-06] 
dist 235=[-1.12954339414054000000e-06,2.78763516712430000000e-06] 
dist 236=[-1.08702028669606000000e-06,2.76224647830590000000e-06] 
dist 237=[-1.00399491014985000000e-06,2.68293876487660000000e-06] 
dist 238=[-9.78745292024270000000e-07,2.64134737593870000000e-06] 
dist 239=[-5.23736995671000000000e-07,2.39245614048347000000e-06] 
dist 240=[-4.59154551226130000000e-07,2.28209316795151000000e-06] 
dist 241=[-3.05504920885720000000e-07,1.31426408531483000000e-06] 
dist 242=[-2.75285443274130000000e-07,1.24772396140696000000e-06] 
dist 243=[-6.45557989116500000000e-08,1.08697115951338000000e-06] 
dist 244=[-2.66388990803600000000e-08,1.04171303274251000000e-06] 
dist 245=[4.41267830013900000000e-08,7.95514733773820000000e-07] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 2, 2, 1, 2, 0, 2] 
dist 0=[79.761953897116553727  ,79.761953897116553727  ] 
dist 1=[77.357057834842764354  ,81.037295806991150100  ] 
dist 2=[74.367438300580099573  ,81.727351139546380051  ] 
dist 3=[70.758844352903836618  ,81.859668925503546494  ] 
dist 4=[66.009515320973249891  ,81.595320093051019541  ] 
dist 5=[58.467427397079359286  ,81.378530016926760822  ] 
dist 6=[50.792182854705252091  ,80.735804894739425275  ] 
dist 7=[45.511097225142122268  ,80.397933942963901477  ] 
dist 8=[40.975619933903288095  ,78.567138412220265083  ] 
dist 9=[36.274915114640666634  ,78.084379742188198279  ] 
dist 10=[31.828585503712983543  ,77.782409367703005368  ] 
dist 11=[28.307393375746755367  ,77.489788620590288050  ] 
dist 12=[24.787679594644243130  ,77.209141878913973681  ] 
dist 13=[20.345706574068596952  ,76.824093315445640030  ] 
dist 14=[16.078083772297849811  ,76.434872365121679380  ] 
dist 15=[13.253369937798598032  ,73.088854830671582633  ] 
dist 16=[10.938253685798386756  ,32.753231106981309769  ] 
dist 17=[8.7035244471089401147 ,29.270444110128128508  ] 
dist 18=[6.6783413430267539488 ,21.199304878376953279  ] 
dist 19=[4.8062452712205631257 ,19.912822126146594774  ] 
dist 20=[-.7070015004226426367 ,10.281238047273111159  ] 
dist 21=[-5.9758270889869341173 ,7.7663919733258629481 ] 
dist 22=[-9.3907691787105441045 ,5.0433494789553357625 ] 
dist 23=[-12.100891770427858129  ,4.3751695965204249672 ] 
dist 24=[-14.556701239428598086  ,-.7690179427768478539 ] 
dist 25=[-16.660077140601950107  ,-.9208340098636536914 ] 
dist 26=[-17.963600885247164504  ,-1.7871449934975280899 ] 
dist 27=[-18.930289963453828248  ,-1.9142075441807807225 ] 
dist 28=[-19.689319004066437229  ,-2.0903685216887633172 ] 
dist 29=[-20.271731666338694166  ,-2.0921240573258153151 ] 
dist 30=[-20.555985012763934123  ,-2.0506152157273696277 ] 
dist 31=[-20.611958848255192869  ,-1.9783209831009448270 ] 
dist 32=[-6.4946554715108211320 ,-1.8758170128171530001 ] 
dist 33=[-5.8769225342993799947 ,-1.7109549521359478756 ] 
dist 34=[-4.3465242284621340772 ,-1.2648277215105379424 ] 
dist 35=[-4.1241744426480450653 ,-.66651189890633811962] 
dist 36=[-2.5151916182704545178 ,.09532789544956852918] 
dist 37=[-2.5132843207243302073 ,.8244943919809486916 ] 
dist 38=[-.9732063678182930828 ,1.2929082169007752848 ] 
dist 39=[-.8824851959719808221 ,1.6568350583423047660 ] 
dist 40=[-.0609690608724322575 ,2.0649296201140384530 ] 
dist 41=[-.0244108674444486084 ,2.7181589269335899414 ] 
dist 42=[.2625992618335121146 ,3.2271374041705434381 ] 
dist 43=[.3080389803914848995 ,3.6687799021315619090 ] 
dist 44=[.3775318008005580071 ,4.0308968975588350007 ] 
dist 45=[.3895419594731556670 ,4.2229160921853924800 ] 
dist 46=[.5442508426370169500 ,4.3263116322269354023 ] 
dist 47=[.5616319305441308605 ,4.3420803419325693108 ] 
dist 48=[.5671145275137432918 ,2.4839520763296877914 ] 
dist 49=[.5476674177948236270 ,2.3263675294226167084 ] 
dist 50=[.3828738024017203923 ,1.9196949944586371294 ] 
dist 51=[.20037145490176063089,1.8527543093432774401 ] 
dist 52=[-.0427206553100757206 ,1.1890118947796052383 ] 
dist 53=[-.27766985791084774949,1.0626273053230336833 ] 
dist 54=[-.427807253398157604  ,.89548264082694874855] 
dist 55=[-.54312141113037038907,.8437287133549931558 ] 
dist 56=[-.65348406803463074234,.2392849900418553064 ] 
dist 57=[-.93153228676423221861,.2276250199474258910 ] 
dist 58=[-1.1491664501482335794 ,.1254796571231617238 ] 
dist 59=[-1.3388084634380980166 ,.1071576419018016994 ] 
dist 60=[-1.4942248373317635445 ,.0813061515978676449 ] 
dist 61=[-1.5755640792015964533 ,.0740675192085750553 ] 
dist 62=[-1.6191403396446524385 ,-.0510228695152947814 ] 
dist 63=[-1.6274155595070114452 ,-.0662944790969720873 ] 
dist 64=[-.4923950423211281114 ,-.0995535777245410196 ] 
dist 65=[-.4538629262487655107 ,-.1051904799770038701 ] 
dist 66=[-.3541660631371716328 ,-.0912515947563060830 ] 
dist 67=[-.3397720976482179941 ,-.0487125286277892329 ] 
dist 68=[-.2907511995964488626 ,.0069931761460452152 ] 
dist 69=[-.2903417688236441180 ,.0608589738018089899 ] 
dist 70=[-.1145135121865088036 ,.0960849762115930394 ] 
dist 71=[-.1083632082938677216 ,.1240366821233031879 ] 
dist 72=[-.0415696823491221970 ,.1489544434147651559 ] 
dist 73=[-.0383085118798325717 ,.1918253414154263843 ] 
dist 74=[-.0113031072147704297 ,.2353961673275110453 ] 
dist 75=[-.0065847464020496495 ,.2739597379536631286 ] 
dist 76=[.0006648599112021506 ,.3059442101331980112 ] 
dist 77=[.0024430155178967390 ,.3233205796221722616 ] 
dist 78=[.0295901478156449690 ,.3331753664591432197 ] 
dist 79=[.0330206997904545439 ,.3352108506435781081 ] 
dist 80=[.0387006258851207044 ,.19853980274716989768] 
dist 81=[.0398498978049184640 ,.18699846262947888092] 
dist 82=[.03887893469498898089,.1570567708291590854 ] 
dist 83=[.02126902226622377567,.1516221872196193930 ] 
dist 84=[-.00294116371575469539,.1017041508727470161 ] 
dist 85=[-.02662619598068422945,.0920152756111552714 ] 
dist 86=[-.04214866362180909758,.0780551782606559448 ] 
dist 87=[-.05449131743523933463,.0738533385604344505 ] 
dist 88=[-.06552454794757550322,.04402427628011686721] 
dist 89=[-.0771549777474872217 ,.0426230212515706312 ] 
dist 90=[-.0970020436967471507 ,.0347578708367974554 ] 
dist 91=[-.1145682261322564679 ,.0330913043450530148 ] 
dist 92=[-.1291144142886436725 ,.0296918007033277100 ] 
dist 93=[-.1369409325739656074 ,.0286998074781271404 ] 
dist 94=[-.1412689112016421423 ,.0148148014539651739 ] 
dist 95=[-.1421454897033030858 ,.0127741824327366938 ] 
dist 96=[-.0507746854582696846 ,.0081135723240585612 ] 
dist 97=[-.0484334480474764438 ,.0070375214072171672 ] 
dist 98=[-.0426350395980058579 ,.0010615458644115519 ] 
dist 99=[-.0411497966848236105 ,-3.44357924456911000000e-05] 
dist 100=[-.0319390206546427162 ,.00060700910955504367] 
dist 101=[-.0274237539868790593 ,.00494079935614550297] 
dist 102=[-.01461911162227030202,.00776582595691342594] 
dist 103=[-.01384642988558402227,.00999453669729035861] 
dist 104=[-.0122289392295219062 ,.01195584192888781376] 
dist 105=[-.0117564900082424488 ,.0165052975204344987 ] 
dist 106=[-.0098035214740703337 ,.0203737536224938230 ] 
dist 107=[-.0093759575573746570 ,.0236507614559023883 ] 
dist 108=[-.0083654572971992981 ,.0262958753446315482 ] 
dist 109=[-.0080521116931721748 ,.0276495135741134694 ] 
dist 110=[-.0065549695761969048 ,.0283461696336526105 ] 
dist 111=[-.0061804152017028594 ,.0284500796032903497 ] 
dist 112=[-.0058892914118351170 ,.02247636965761856667] 
dist 113=[-.0058438188913433187 ,.02178116801462602177] 
dist 114=[-.0059236630987584741 ,.0197529196806790678 ] 
dist 115=[-.0061837261158985305 ,.0193680396031578389 ] 
dist 116=[-.0066214711317399632 ,.0151659962208303552 ] 
dist 117=[-.0074088665797410803 ,.0127828042511072812 ] 
dist 118=[-.0082103105415298547 ,.00371644773219962085] 
dist 119=[-.0087041840907176627 ,.00345149287672823076] 
dist 120=[-.0090621903204153286 ,-.00195636918274226850] 
dist 121=[-.0093231290729698429 ,-.00267625589437566847] 
dist 122=[-.0094991624516534037 ,-.00279030738025292263] 
dist 123=[-.00951942083199027824,-.00273504147008428334] 
dist 124=[-.00944667339358206169,-.00243582795493367926] 
dist 125=[-.00937650914981131818,-.00208173707388946273] 
dist 126=[-.00885857446951456752,-.00180812945940838765] 
dist 127=[-.00856074686884863654,-.00154502239766394089] 
dist 128=[-.00432440917220461396,-.00123254602106732068] 
dist 129=[-.00401188347611785359,-.00091741171684086373] 
dist 130=[-.00318733518994403599,-.00064364614657625016] 
dist 131=[-.00306879667509575730,-.00035127467826046465] 
dist 132=[-.00168608909990363965,3.79638545191504000000e-05] 
dist 133=[-.0014258643513718741 ,.00041611427097562492] 
dist 134=[-.0011287799936562416 ,.00066440521818563086] 
dist 135=[-.0010774217507682261 ,.00086217932626954178] 
dist 136=[.00085062045366332487,.0011713921838324826 ] 
dist 137=[.00105032565730979838,.0016812598712232049 ] 
dist 138=[.00107461010217712759,.0020860840618972576 ] 
dist 139=[.00105065931752084491,.0024472957601423310 ] 
dist 140=[.00095519603476824787,.0027482720835950941 ] 
dist 141=[.00084235099881199248,.0029133731045823636 ] 
dist 142=[.00074924778933804317,.0030088796124415448 ] 
dist 143=[.00065409976570527218,.0030328756752122747 ] 
dist 144=[.00053307565838555485,.00181553134994285456] 
dist 145=[.00040666270691411703,.00171289701199643960] 
dist 146=[.00029005409124932405,.00144638963530455401] 
dist 147=[.00015979619120853993,.00139555076181609661] 
dist 148=[-2.09371544689350500000e-05,.00094710366887496661] 
dist 149=[-.00019819829832102198,.00085918435254825579] 
dist 150=[-.00031465211290262644,.00072710428171083267] 
dist 151=[-.00040746167419263255,.00068873740237188195] 
dist 152=[-.00049183116961915552,-4.30790642362831000000e-05] 
dist 153=[-.00073820510387383932,-.00013750181934438310] 
dist 154=[-.00093400777521974067,-.00023176200577636814] 
dist 155=[-.0011089345877017357 ,-.00022923355645794124] 
dist 156=[-.0012547678268932297 ,-.00020498338412790996] 
dist 157=[-.0013347960353638006 ,-.00017560199181819349] 
dist 158=[-.0013811020254327019 ,-.00015266002158974627] 
dist 159=[-.0013927375879320083 ,-.00013036788934500044] 
dist 160=[-.00038232549237946820,-.00010356088801553722] 
dist 161=[-.00035616176075725737,-7.63464203749306900000e-05] 
dist 162=[-.00028686028990459676,-5.24277208545474400000e-05] 
dist 163=[-.00027652713795873590,-2.66533306539351100000e-05] 
dist 164=[-.00015893663288651282,7.94876673116550000000e-06] 
dist 165=[-.00013660803230352334,4.15437681067445000000e-05] 
dist 166=[-.00011036524409685458,6.33140478900352200000e-05] 
dist 167=[-.00010481831304509152,8.03281545162486500000e-05] 
dist 168=[6.43820717318570100000e-05,.00010239725543813842] 
dist 169=[7.90115251989678000000e-05,.00014856795349670916] 
dist 170=[8.04112959676418600000e-05,.00018492687370176351] 
dist 171=[7.77288038191489100000e-05,.00021682783857366267] 
dist 172=[6.88316178150447700000e-05,.00024300175564545013] 
dist 173=[5.85334120095764000000e-05,.00025657142800405614] 
dist 174=[5.02774236266296050000e-05,.00026368995654307228] 
dist 175=[4.20529087861479120000e-05,.00026489449482799833] 
dist 176=[3.18765315332059860000e-05,.00017811032642430935] 
dist 177=[2.13920255370398580000e-05,.00017001814296986050] 
dist 178=[1.19400241170641380000e-05,.00014734911735063885] 
dist 179=[1.55723714829508700000e-06,.00014371905805251537] 
dist 180=[-1.26315984224014100000e-05,.00010057680252841721] 
dist 181=[-2.64479809857260370000e-05,9.19232935782948040000e-05] 
dist 182=[-3.53499612022441780000e-05,8.20203762083940610000e-05] 
dist 183=[-4.22486129508158080000e-05,7.92362197412551450000e-05] 
dist 184=[-4.80964634133964260000e-05,-6.47110219706025800000e-06] 
dist 185=[-6.02273693830034600000e-05,-8.64797263358861540000e-06] 
dist 186=[-7.56861310869064500000e-05,-7.53056200072562020000e-06] 
dist 187=[-8.91105656106989600000e-05,-5.01953424347782650000e-06] 
dist 188=[-.00010002368817704016,0                     ] 
dist 189=[-.00010548977041345931,-1.69989605878138900000e-05] 
dist 190=[-.00010839462416166085,-1.48880002516989200000e-05] 
dist 191=[-.00010911634487951971,-1.28175363899760900000e-05] 
dist 192=[-3.66059069872671800000e-05,-1.03003141230428300000e-05] 
dist 193=[-3.41583925108818300000e-05,-7.73013936804092000000e-06] 
dist 194=[-2.76166734949652900000e-05,-5.44859055659690000000e-06] 
dist 195=[-2.66615370226281500000e-05,-2.97130725275090000000e-06] 
dist 196=[-1.53873280940438000000e-05,3.77925176158600000000e-07] 
dist 197=[-1.32389469319530200000e-05,3.63590603134710000000e-06] 
dist 198=[-1.07944542429227800000e-05,5.75036445602060000000e-06] 
dist 199=[-1.03288941277724000000e-05,7.40619017245860000000e-06] 
dist 200=[5.98705727119430000000e-06,9.30084081422143000000e-06] 
dist 201=[7.57460840321430000000e-06,1.37270247844711700000e-05] 
dist 202=[7.78480601828250000000e-06,1.72354139164603900000e-05] 
dist 203=[7.61347557683232000000e-06,2.03514812769756800000e-05] 
dist 204=[6.88031510037067000000e-06,2.29344335296438800000e-05] 
dist 205=[6.01553868572954000000e-06,2.43216318562671000000e-05] 
dist 206=[5.32065530744011000000e-06,2.50833960901709800000e-05] 
dist 207=[4.62694364852231000000e-06,2.52275960206387100000e-05] 
dist 208=[3.76660472401713700000e-06,1.62039494847890870000e-05] 
dist 209=[2.87933289440108000000e-06,1.54037717025044200000e-05] 
dist 210=[2.07837777644442000000e-06,1.32364463548684600000e-05] 
dist 211=[1.19788498461122000000e-06,1.28499520108982400000e-05] 
dist 212=[-5.86378614785000000000e-09,8.92135389848923000000e-06] 
dist 213=[-1.17899628809039000000e-06,8.13761206943415000000e-06] 
dist 214=[-1.93776088120280000000e-06,7.10226334809097000000e-06] 
dist 215=[-2.52880616700898000000e-06,6.74890710459384000000e-06] 
dist 216=[-4.08145654442856000000e-06,-1.46562857657600000000e-07] 
dist 217=[-6.21831995426226000000e-06,-9.66815260048090000000e-07] 
dist 218=[-7.91896983166525000000e-06,-2.62343899999279000000e-06] 
dist 219=[-9.44088189144253000000e-06,-2.60933377562559000000e-06] 
dist 220=[-1.07103248491715000000e-05,-2.42139940030679000000e-06] 
dist 221=[-1.14064750663976000000e-05,-2.18342476476004000000e-06] 
dist 222=[-1.18082035105751100000e-05,-1.97026027280602000000e-06] 
dist 223=[-1.19062047325041600000e-05,-1.73739410221779000000e-06] 
dist 224=[-3.61992923141882700000e-06,-1.42096998840269000000e-06] 
dist 225=[-3.40501956349820600000e-06,-1.08014650012967000000e-06] 
dist 226=[-2.83636516262183500000e-06,-7.50177881199330000000e-07] 
dist 227=[-2.73852415105324200000e-06,-3.69178344712160000000e-07] 
dist 228=[-1.75898955342010000000e-06,1.74689318771740000000e-07] 
dist 229=[-1.56840410692183000000e-06,7.14778753439660000000e-07] 
dist 230=[-1.31351878334928000000e-06,1.08076296253368000000e-06] 
dist 231=[-1.22996619054260000000e-06,1.38486708163399000000e-06] 
dist 232=[-1.91507202481570000000e-07,1.67879634634558000000e-06] 
dist 233=[-6.71723738201500000000e-08,1.93935906626228000000e-06] 
dist 234=[-4.92452625885900000000e-08,2.11072591499790000000e-06] 
dist 235=[-6.45154690685500000000e-08,2.24750217928462000000e-06] 
dist 236=[-1.28774066368720000000e-07,2.37045150298265000000e-06] 
dist 237=[-2.04030005588489300000e-07,2.47251232856908000000e-06] 
dist 238=[-2.63045405506237000000e-07,2.54284935949353000000e-06] 
dist 239=[-3.20639936712920000000e-07,2.55407300547092000000e-06] 
dist 240=[-3.90262695343360000000e-07,1.67508949875183300000e-06] 
dist 241=[-4.61134214807390000000e-07,1.60787894688723100000e-06] 
dist 242=[-5.23705732877160000000e-07,1.41606691666780000000e-06] 
dist 243=[-5.91354290297010000000e-07,1.38347460062642100000e-06] 
dist 244=[-6.82430357227780000000e-07,1.00442438796678000000e-06] 
dist 245=[-7.70463420791050000000e-07,9.26931996544960000000e-07] 
dist 246=[-8.26012861745260000000e-07,8.35827877442940000000e-07] 
dist 247=[-8.67719033929720000000e-07,8.05780042708440000000e-07] 
dist 248=[-9.00692840455950000000e-07,1.90369829059300000000e-08] 
dist 249=[-9.25060558324360000000e-07,-7.64087177541800000000e-08] 
dist 250=[-9.32537671643030000000e-07,-1.67646239099031000000e-07] 
dist 251=[-9.65167109824374000000e-07,-1.87165669445588000000e-07] 
dist 252=[-1.05090706879393000000e-06,-1.94040973000584600000e-07] 
dist 253=[-1.08940493830150000000e-06,-1.65560211539069800000e-07] 
dist 254=[-1.10708582515122500000e-06,-1.08907053006593500000e-07] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 0, 0, 0, 0, 2] 
dist 0=[63.485438773841302713  ,63.485438773841302713  ] 
dist 1=[61.117801901292130931  ,64.798952034939311066  ] 
dist 2=[58.603259256640477647  ,65.589853210364551310  ] 
dist 3=[56.703109441419504370  ,65.871486064339665794  ] 
dist 4=[54.889779701674636744  ,65.968693999913568788  ] 
dist 5=[52.720995870195593417  ,66.023680124525297106  ] 
dist 6=[50.488390579829001196  ,66.056907540031520897  ] 
dist 7=[48.419711376199626306  ,66.067894628121303276  ] 
dist 8=[46.072435056154892640  ,65.903710884151512425  ] 
dist 9=[42.726799197012909554  ,59.715462544711719138  ] 
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dist 152=[-.00039555836296763223,.00066288052918946523] 
dist 153=[-.00051177109419085329,-4.31673530233029500000e-05] 
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dist 166=[-.00013149425121061758,-2.69997514610265500000e-05] 
dist 167=[-.00010616685419505783,1.49604277529679900000e-05] 
dist 168=[-.00010086717344643062,5.56031227828974900000e-05] 
dist 169=[6.75054529005060800000e-05,9.92841627347740200000e-05] 
dist 170=[9.50733361733579400000e-05,.00014382939151547442] 
dist 171=[.00010073045944240249,.00017890401349372239] 
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dist 176=[9.24660871849484000000e-05,.00025601267109383599] 
dist 177=[8.13970017643635000000e-05,.00017201598472825349] 
dist 178=[7.03307442646681900000e-05,.00016418604141989478] 
dist 179=[5.65669182691049610000e-05,.00014225925409491243] 
dist 180=[4.23316313756073510000e-05,.00013875275200286908] 
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dist 188=[-8.60350094721544500000e-05,-2.64503136670103000000e-05] 
dist 189=[-9.65511378937496100000e-05,-2.76589380031254400000e-05] 
dist 190=[-.00010182066820197582,-2.71191232957066470000e-05] 
dist 191=[-.00010462029529709509,-2.40629803873871514000e-05] 
dist 192=[-.00010530834243716687,-2.04396674876741470000e-05] 
dist 193=[-3.77322269895519300000e-05,-1.76431141264868300000e-05] 
dist 194=[-3.54320428930225500000e-05,-1.49529523586118600000e-05] 
dist 195=[-2.94150229304106200000e-05,-1.17520371140961100000e-05] 
dist 196=[-2.83525969880174900000e-05,-8.51688289142052000000e-06] 
dist 197=[-1.81911489638858900000e-05,-5.69001975257112000000e-06] 
dist 198=[-1.62215843004112200000e-05,-2.65532574970578000000e-06] 
dist 199=[-1.34751731292942800000e-05,2.85136540485827000000e-06] 
dist 200=[-1.26191911783033800000e-05,8.71810594280975000000e-06] 
dist 201=[-3.46405974346063000000e-06,1.26680025806357700000e-05] 
dist 202=[-1.54131231998709000000e-06,1.59246343082400600000e-05] 
dist 203=[-1.10318526560759000000e-06,1.95600364542975600000e-05] 
dist 204=[3.38320203055600000000e-08,2.27628032964042500000e-05] 
dist 205=[9.73957452410900000000e-08,2.53525553351987800000e-05] 
dist 206=[-2.33179998476500000000e-07,2.67084586587735600000e-05] 
dist 207=[-1.18195730624872000000e-06,2.74055012912142100000e-05] 
dist 208=[-2.24266702632759000000e-06,2.75390633578246000000e-05] 
dist 209=[-3.01860204670651000000e-06,1.50781036135584990000e-05] 
dist 210=[-3.72439174242545000000e-06,1.42828752109368783000e-05] 
dist 211=[-4.50626490121568000000e-06,1.21880191836629560000e-05] 
dist 212=[-5.26505156992379000000e-06,1.17850902487239830000e-05] 
dist 213=[-5.87911711932009000000e-06,8.15166294047030600000e-06] 
dist 214=[-6.49716179821280000000e-06,7.43089926866734100000e-06] 
dist 215=[-7.27190709606628000000e-06,6.36760887669996800000e-06] 
dist 216=[-7.99598855681883000000e-06,6.04838527117141900000e-06] 
dist 217=[-8.41253537279212000000e-06,5.85051846646920000000e-07] 
dist 218=[-8.67887323592594600000e-06,-7.93207876108410000000e-07] 
dist 219=[-8.80542108978529900000e-06,-1.01158126686272000000e-06] 
dist 220=[-9.07190962132234000000e-06,-2.68528536238316000000e-06] 
dist 221=[-1.02875720493313800000e-05,-2.95096835256235000000e-06] 
dist 222=[-1.09520133612440500000e-05,-3.25280049334043400000e-06] 
dist 223=[-1.13325093303572600000e-05,-2.95714111276229590000e-06] 
dist 224=[-1.14184084165458500000e-05,-2.60433827989037900000e-06] 
dist 225=[-3.43403077875734300000e-06,-2.30905243655248700000e-06] 
dist 226=[-3.23537766300907000000e-06,-2.00319361675703000000e-06] 
dist 227=[-2.71602532380362400000e-06,-1.60824754785690000000e-06] 
dist 228=[-2.61947907136035600000e-06,-1.19234921595607000000e-06] 
dist 229=[-1.73728293668507000000e-06,-8.03090991861970000000e-07] 
dist 230=[-1.56463591020716000000e-06,-3.63589468799090000000e-07] 
dist 231=[-1.31293943249988000000e-06,2.52240270485450000000e-07] 
dist 232=[-1.23748348086359000000e-06,8.59293599372870000000e-07] 
dist 233=[-1.71234599630970000000e-07,1.26389183840384000000e-06] 
dist 234=[6.49153244123400000000e-08,1.59292478491912000000e-06] 
dist 235=[1.19832017445240000000e-07,1.89934315386973000000e-06] 
dist 236=[2.73693394569280000000e-07,2.16340345790537000000e-06] 
dist 237=[2.89143221437550000000e-07,2.37748403603091600000e-06] 
dist 238=[2.58711043505440000000e-07,2.50387753298978700000e-06] 
dist 239=[1.58261277095560000000e-07,2.57006062885934500000e-06] 
dist 240=[4.34823478961210000000e-08,2.58353630573638800000e-06] 
dist 241=[-4.39592898454410000000e-08,1.71347165492981400000e-06] 
dist 242=[-1.26976890636743000000e-07,1.65107012687876600000e-06] 
dist 243=[-2.24179007140053000000e-07,1.46514143046430100000e-06] 
dist 244=[-3.21544555655515000000e-07,1.43702313391784900000e-06] 
dist 245=[-4.05224924303283120000e-07,1.04862266050152100000e-06] 
dist 246=[-4.93864355633160000000e-07,9.68705378239904000000e-07] 
dist 247=[-6.10971608131419000000e-07,8.87622091011747000000e-07] 
dist 248=[-7.23305562201884000000e-07,8.68768387314460000000e-07] 
dist 249=[-7.92961359426424000000e-07,2.45772196212000000000e-10] 
dist 250=[-8.43883537776668000000e-07,-1.02046377298762000000e-07] 
dist 251=[-8.81694001132677000000e-07,-1.86127734247468700000e-07] 
dist 252=[-9.07686897193609000000e-07,-2.03596503710132600000e-07] 
dist 253=[-9.78555598339875000000e-07,-2.01699006947262700000e-07] 
dist 254=[-1.01289578426653600000e-06,-1.70002029021715400000e-07] 
dist 255=[-1.02792270513195300000e-06,-1.10901615001022750000e-07] 

8 phat 4 dirichlet min maxes function [2, 0, 1, 2, 2, 1, 1, 1, 2] 
dist 0=[83.852687846307731677  ,83.852687846307731677  ] 
dist 1=[82.872414280746522599  ,84.085900094493094047  ] 
dist 2=[81.160602116872883019  ,84.051792462210595750  ] 
dist 3=[78.007639860856386385  ,83.965381744415999249  ] 
dist 4=[74.174869568406776840  ,83.821498259474477070  ] 
dist 5=[69.749986042024083773  ,83.563677363712887238  ] 
dist 6=[64.047958178216793875  ,83.237879934842882905  ] 
dist 7=[55.118375459575415870  ,82.919952663972810080  ] 
dist 8=[46.072437048144400689  ,82.374971072459444682  ] 
dist 9=[39.905718408021363363  ,82.117600199643640523  ] 
dist 10=[34.670731941425391494  ,80.858195793277971205  ] 
dist 11=[29.342128023282548701  ,80.448079285478922265  ] 
dist 12=[24.362413510427114443  ,80.208461587826442931  ] 
dist 13=[20.518894476054005957  ,79.831543320720904259  ] 
dist 14=[16.769909016094499154  ,68.531427030061515594  ] 
dist 15=[12.165894250131425748  ,66.446466214435936406  ] 
dist 16=[7.804823997016586802  ,54.873558580092760085  ] 
dist 17=[4.5726311018677757335 ,33.015685272196408373  ] 
dist 18=[-1.1482415165968801988 ,29.317103973064950887  ] 
dist 19=[-4.9265961881285893694 ,20.733253687045108473  ] 
dist 20=[-8.0037198017410070954 ,19.391149649834555686  ] 
dist 21=[-10.926086355955296902  ,8.376699123296605488  ] 
dist 22=[-13.523198723455646491  ,6.477979607840876469  ] 
dist 23=[-15.302282827689744817  ,3.653600293738711804  ] 
dist 24=[-16.821691900880678781  ,2.948616672505753986  ] 
dist 25=[-18.382469421016304014  ,-2.7192513474629806217 ] 
dist 26=[-19.758862641802703484  ,-2.7223817723166009192 ] 
dist 27=[-20.542714786090432813  ,-2.558817352934385770  ] 
dist 28=[-21.042969157922136141  ,-2.329522890377501663  ] 
dist 29=[-21.288440812281833774  ,-2.051979777599397228  ] 
dist 30=[-21.354885370648521847  ,-1.696563180299326136  ] 
dist 31=[-21.290785280804578282  ,-1.156174551913128115  ] 
dist 32=[-20.686741195611321451  ,-.615038544062948559  ] 
dist 33=[-7.5093750105919048864 ,-.255900349391626176  ] 
dist 34=[-6.7851187522552043300 ,.031254588123294059  ] 
dist 35=[-4.9924341692018069481 ,.286992204539316936  ] 
dist 36=[-4.7334488238733174016 ,.497176337799684129  ] 
dist 37=[-2.111129353938717640  ,.603534421626416492  ] 
dist 38=[-1.643686986272277844  ,.659190052762898097  ] 
dist 39=[-1.055114382826515504  ,.7403869627032459127 ] 
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dist 188=[-.00011334605400011648,-1.80264409705052900000e-06] 
dist 189=[-.00012315856015717027,-1.77670648626332330000e-06] 
dist 190=[-.00012757497066175926,-1.70224841144416560000e-06] 
dist 191=[-.00012959449220195624,-1.57002505625382260000e-06] 
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dist 193=[-3.71333114365281564000e-05,1.14928146570416600000e-06] 
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dist 200=[-1.18166037372769790000e-05,1.60669247817540038000e-05] 
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dist 203=[-1.15025738452579980000e-05,2.23039017299233150000e-05] 
dist 204=[-1.12728530839658430000e-05,2.34930346760804750000e-05] 
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dist 207=[-1.03662448144784910000e-05,2.58944942587401290000e-05] 
dist 208=[-9.76172135609431000000e-06,2.60363216907230030000e-05] 
dist 209=[-9.61723562748913200000e-06,1.56132541664197910000e-05] 
dist 210=[-8.00789330088949100000e-06,1.47701625078142260000e-05] 
dist 211=[-7.67215052595021600000e-06,1.25507332574477474000e-05] 
dist 212=[-6.95199022805550600000e-06,1.21364973278097340000e-05] 
dist 213=[-6.72438352188644200000e-06,8.30854782685026490000e-06] 
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dist 215=[-5.48011530266552780000e-06,6.37309615379478950000e-06] 
dist 216=[-4.85930298181888760000e-06,4.36623005232721160000e-06] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 0, 1, 0, 2, 0, 1] 
dist 0=[87.588027192994664446  ,87.588027192994664446  ] 
dist 1=[86.975134340886253360  ,87.743133095840311131  ] 
dist 2=[85.714131062125182967  ,87.749150436230131951  ] 
dist 3=[83.341614250453122885  ,87.520429078311106373  ] 
dist 4=[80.337418112126335466  ,87.311380907520880219  ] 
dist 5=[76.555408276071331141  ,86.359215892110476010  ] 
dist 6=[71.479730245378999285  ,86.024922754340983405  ] 
dist 7=[63.312857768132703674  ,82.696615234903144810  ] 
dist 8=[54.940300102750538558  ,81.831617166809219970  ] 
dist 9=[49.043950532902132982  ,80.864179134492112294  ] 
dist 10=[43.834537166406059611  ,80.378701111748034098  ] 
dist 11=[38.203823297856853847  ,79.846403965053022471  ] 
dist 12=[32.737129525105390204  ,79.585201064373459336  ] 
dist 13=[28.182559655481266069  ,79.177552639804212272  ] 
dist 14=[22.699171274109338889  ,75.505403288684024244  ] 
dist 15=[16.716971623153276918  ,30.935137062808334832  ] 
dist 16=[11.029556244446221699  ,27.110203514551613794  ] 
dist 17=[6.8323742105325579199 ,18.208427189110361210  ] 
dist 18=[3.2498260072122333409 ,16.879421738353863261  ] 
dist 19=[-1.279445731669640505  ,11.264114101390858667  ] 
dist 20=[-5.527412463258577640  ,6.7777816305270733499 ] 
dist 21=[-8.218876404807080711  ,6.0216161894674225776 ] 
dist 22=[-10.289351455622064556  ,4.9559457906955867124 ] 
dist 23=[-12.678913155075669245  ,4.7553852367754558173 ] 
dist 24=[-15.517610554771027893  ,.56495682769027082558] 
dist 25=[-17.464601140760541769  ,.08231720259767971202] 
dist 26=[-19.160880574245486104  ,-.95328905853601021967] 
dist 27=[-20.495722710538167857  ,-1.1010248388838800060 ] 
dist 28=[-21.115718174638278115  ,-2.1470850200834260756 ] 
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dist 30=[-21.370523977007510502  ,-2.5537418206432269094 ] 
dist 31=[-8.7220445515956109060 ,-2.5904997675937220683 ] 
dist 32=[-7.8509355017445392986 ,-2.8869187006770759202 ] 
dist 33=[-5.7116851073764198086 ,-1.951052517932012273  ] 
dist 34=[-5.3910673228191404548 ,-.787918242481778842  ] 
dist 35=[-3.0272251917582391735 ,.755206123798379327  ] 
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dist 38=[-3.0528999476105788369 ,3.970064446344743789  ] 
dist 39=[-3.0539553851820683771 ,4.629207201641512374  ] 
dist 40=[-1.1660197831872564974 ,5.169692572528114342  ] 
dist 41=[-1.0148477895254335859 ,5.453125833841401632  ] 
dist 42=[-.66690525217624704979,5.601256632432742559  ] 
dist 43=[-.60915261692076035489,5.969689782160895983  ] 
dist 44=[-.17371528534980744957,6.197543895093571954  ] 
dist 45=[-.09916776380243510328,6.306283445171255754  ] 
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dist 47=[-.524409448225858639  ,3.733446938562714105  ] 
dist 48=[-.898220501128821724  ,3.4961148846438538125 ] 
dist 49=[-1.215809643478142860  ,2.9041818366254048707 ] 
dist 50=[-1.549603840534878091  ,2.7886460673239977089 ] 
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dist 58=[-3.212145643328523789  ,.14769712629494716902] 
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dist 60=[-3.049075451853668320  ,.01467022641432062631] 
dist 61=[-2.999610768911426691  ,-.00603815392827881233] 
dist 62=[-2.8698685701268972780 ,-.03418409842902298283] 
dist 63=[-.56485694694021000271,-.03954114054727364323] 
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dist 65=[-.3952599196604414928 ,-.1677803332324152611 ] 
dist 66=[-.3777318172752907041 ,-.0896707815088812280 ] 
dist 67=[-.24866585584049645478,.0170345808387845823 ] 
dist 68=[-.26420630170666594173,.1212406304964955605 ] 
dist 69=[-.27198189282403300494,.1894151721732232344 ] 
dist 70=[-.27555480313205299217,.2435328597070917441 ] 
dist 71=[-.27595826535325091858,.2918011562251721237 ] 
dist 72=[-.15050528461517255947,.3320114209321643621 ] 
dist 73=[-.13973282102409139103,.3540604482734191751 ] 
dist 74=[-.11251395306072353989,.3668065850567135818 ] 
dist 75=[-.10830577531354561561,.3713257804234814311 ] 
dist 76=[-.06575809577277411280,.3913358586731679138 ] 
dist 77=[-.05780143597109681705,.4028827752588062557 ] 
dist 78=[-.04777817124163282734,.4057578267361934297 ] 
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dist 80=[.01979402234052388388,.2146343168476440200 ] 
dist 81=[.02752645824548481145,.1774257779423906327 ] 
dist 82=[.0147988073497846491 ,.17056931196204028037] 
dist 83=[-.0048611840213174947 ,.11096684979567741172] 
dist 84=[-.0238832569274684449 ,.09954317584069760089] 
dist 85=[-.0362283714381860712 ,.10064859939855346338] 
dist 86=[-.0459124498067403298 ,.10255126547323473825] 
dist 87=[-.0668217418385090625 ,.10281015258818691541] 
dist 88=[-.0967847554013216974 ,.03073392832834828167] 
dist 89=[-.1205059440329182486 ,.02755323707349920884] 
dist 90=[-.1415904492468836004 ,.01963409594074443441] 
dist 91=[-.1591291914735628389 ,.01849652138174041242] 
dist 92=[-.1687349295982640252 ,.00673214048979659193] 
dist 93=[-.1742820171934647515 ,.00462271883789305004] 
dist 94=[-.1756627252968986250 ,.00201096874530967146] 
dist 95=[-.04695475569103031372,.00157615654281827121] 
dist 96=[-.04332523433612241261,-.01378290451975781975] 
dist 97=[-.03396731965001868107,-.0091855854571953701 ] 
dist 98=[-.03254038033739784341,-.0034017284030227834 ] 
dist 99=[-.02248605649677886189,.0044598038756363486 ] 
dist 100=[-.02447442570874472780,.0121087810774856359 ] 
dist 101=[-.02555949377408869269,.0170475877710810144 ] 
dist 102=[-.02618391546892779760,.0208913768602233881 ] 
dist 103=[-.02633693484188170044,.0241837895928700394 ] 
dist 104=[-.01387877593843433923,.0268284617947232705 ] 
dist 105=[-.01285526124113266657,.0280948807851777282 ] 
dist 106=[-.01031208162326426089,.0297375091228346427 ] 
dist 107=[-.00985484014627689742,.0326259997089815477 ] 
dist 108=[-.00598387586501792107,.0340125159085497375 ] 
dist 109=[-.00525749792546132926,.0346915373540813680 ] 
dist 110=[-.00414104833964553426,.0347634837773962766 ] 
dist 111=[-.00384047322246512996,.0242362221646814465 ] 
dist 112=[-.0050848316267003273 ,.0231287687401317528 ] 
dist 113=[-.0069097815091254033 ,.0201313777741435971 ] 
dist 114=[-.0088440274788195268 ,.0195790828005497791 ] 
dist 115=[-.0114020170939940344 ,.0141184654905253298 ] 
dist 116=[-.0138596116453319460 ,.0130190238277888390 ] 
dist 117=[-.0153946500707220625 ,.0115384761667093670 ] 
dist 118=[-.0165310176747975106 ,.01128612934754049750] 
dist 119=[-.0174025259802813639 ,.01136527937831425684] 
dist 120=[-.0180266527450901490 ,.00297472792076568463] 
dist 121=[-.0181788442565692814 ,.00271520589326950583] 
dist 122=[-.0181391413248437248 ,.00205340860668663814] 
dist 123=[-.0179991416305485518 ,.00195809018903215994] 
dist 124=[-.0166340797508761969 ,.00092079454013454184] 
dist 125=[-.0162493336803038222 ,.00073038715656996314] 
dist 126=[-.01605796804529001100,.00050309159767176180] 
dist 127=[-.00287009920017672255,.00046396101786135744] 
dist 128=[-.00201409211761765858,-.00098499042351155741] 
dist 129=[-.00184339335092233979,-.00114885968712074291] 
dist 130=[-.00183839241073318274,-.00066787712071227120] 
dist 131=[-.00206521910807460160,.00010587285173851140] 
dist 132=[-.00224612057972271974,.00086421851047870268] 
dist 133=[-.00233105070095436661,.0013621191978511956 ] 
dist 134=[-.00237231651940029569,.0017587204388086159 ] 
dist 135=[-.00237933745983584612,.0021140733129365585 ] 
dist 136=[-.00155543827911311552,.0024106870627927658 ] 
dist 137=[-.00147556187383272017,.0025736010553594040 ] 
dist 138=[-.00126180669146493422,.0026679170858527902 ] 
dist 139=[-.00122640561629839415,.0026916108563341999 ] 
dist 140=[-.00084879350234527937,.00076086213567071942] 
dist 141=[-.00077438457555986593,.00071491371896858247] 
dist 142=[-.00068226030848466608,.00059019922092479736] 
dist 143=[-.00065331758489024159,.00057157946079174001] 
dist 144=[3.55991781517829300000e-05,.00062853681661939642] 
dist 145=[.00011922354378725636,.00077565792365791854] 
dist 146=[.00012216155689209929,.00088693148924663184] 
dist 147=[-2.34860990203440800000e-05,.00097695167286330381] 
dist 148=[-.00016494488945720594,.00104705674053674753] 
dist 149=[-.00025724780362227054,.00107903836576476632] 
dist 150=[-.00033012445548699805,.00109283793928865087] 
dist 151=[-.00039430268638629045,.00109126707790432424] 
dist 152=[-.00044706569907266668,.00029562733684763511] 
dist 153=[-.00047452935235995481,.00027120564733541214] 
dist 154=[-.00048914268772570583,.00020826041540323142] 
dist 155=[-.00049167218288008220,.00019915313737225695] 
dist 156=[-.00034321164929523531,9.82688146664111000000e-05] 
dist 157=[-.00032904686903521203,7.95880676422292000000e-05] 
dist 158=[-.00028829520517079532,5.74783318288556000000e-05] 
dist 159=[-.00028172764771650478,5.35434287540797000000e-05] 
dist 160=[-.00020083355615194957,-9.83890141768730000000e-05] 
dist 161=[-.00018440178092528389,-9.53253762160379800000e-05] 
dist 162=[-.00016596334105820197,-5.11136820170010500000e-05] 
dist 163=[-.0001880319494993557 ,9.72461993078827000000e-06] 
dist 164=[-.0002082529806998457 ,6.91760676184682000000e-05] 
dist 165=[-.0002192013613314823 ,.00010787368043398435] 
dist 166=[-.0002253549079547580 ,.00013831571285978343] 
dist 167=[-.0002264875611031846 ,.00016492695879246050] 
dist 168=[-.00013205388496273972,.00018665947346169613] 
dist 169=[-.00012403036956553523,.00019769379819381228] 
dist 170=[-.00010331426529689925,.00020359370687368635] 
dist 171=[-9.95931798935818370000e-05,.00020489862323587482] 
dist 172=[-6.53179186860904200000e-05,7.40099038193173300000e-05] 
dist 173=[-5.86824574373624400000e-05,6.99166443184198700000e-05] 
dist 174=[-4.91900093403610200000e-05,5.88819306702993700000e-05] 
dist 175=[-4.63182945727024700000e-05,5.70233563059245400000e-05] 
dist 176=[8.53030059561362000000e-06,3.86550355459740600000e-05] 
dist 177=[1.53404566776592000000e-05,5.56021513830772000000e-05] 
dist 178=[1.16823754561688800000e-05,6.90014019480103000000e-05] 
dist 179=[-2.18784668938174000000e-06,8.08730938076240000000e-05] 
dist 180=[-1.67513631968740100000e-05,9.07145530209725000000e-05] 
dist 181=[-2.61232148377611600000e-05,9.60325577164884000000e-05] 
dist 182=[-3.33767755687388200000e-05,9.90054066113128000000e-05] 
dist 183=[-3.95141476690429700000e-05,9.95923257591870000000e-05] 
dist 184=[-4.45088551848445100000e-05,3.55643545739453800000e-05] 
dist 185=[-4.72161667047668700000e-05,3.36484505010018900000e-05] 
dist 186=[-4.87353155403434400000e-05,2.92440117113349600000e-05] 
dist 187=[-4.90010632157375800000e-05,2.78720846611787600000e-05] 
dist 188=[-4.39863645834832300000e-05,2.17343910958020500000e-05] 
dist 189=[-4.31064851166222600000e-05,2.04777170536894200000e-05] 
dist 190=[-4.04427015673111000000e-05,1.73992584798959100000e-05] 
dist 191=[-3.96489488824741500000e-05,1.66566190102686700000e-05] 
dist 192=[-3.34604500057197800000e-05,9.11696933709100000000e-06] 
dist 193=[-3.20424932179600400000e-05,7.79866699236700000000e-06] 
dist 194=[-2.96738939932983300000e-05,5.72780357206880000000e-06] 
dist 195=[-2.89654789506333500000e-05,5.17404600240160000000e-06] 
dist 196=[-2.00347138424666400000e-05,6.98432409868365000000e-06] 
dist 197=[-2.09644096722072500000e-05,1.10389182090564900000e-05] 
dist 198=[-2.14309511732976100000e-05,1.42701491043914800000e-05] 
dist 199=[-2.14909507609823800000e-05,1.71659259797004200000e-05] 
dist 200=[-1.64441317605498700000e-05,1.95818350645204500000e-05] 
dist 201=[-1.58564868706228500000e-05,2.09041862369586200000e-05] 
dist 202=[-1.42370727591327200000e-05,2.16630268376517700000e-05] 
dist 203=[-1.38871916883580400000e-05,2.18372751809740900000e-05] 
dist 204=[-1.07595661447292950000e-05,1.22538103798926590000e-05] 
dist 205=[-1.01016720375773300000e-05,1.18254786092775610000e-05] 
dist 206=[-9.13388456144201500000e-06,1.08798810379286600000e-05] 
dist 207=[-8.82473094259454250000e-06,1.05690259514774900000e-05] 
dist 208=[-2.29591407760044000000e-06,9.12054914276059000000e-06] 
dist 209=[-1.45476845552903000000e-06,8.80992366232680000000e-06] 
dist 210=[4.83664037531480000000e-07,7.88548760199553000000e-06] 
dist 211=[-3.34599733234030000000e-07,7.74104869216401000000e-06] 
dist 212=[-1.53847561216451000000e-06,6.01753828817478000000e-06] 
dist 213=[-2.39138048877152000000e-06,6.37203268893511000000e-06] 
dist 214=[-3.06726404266365000000e-06,6.57016384639053000000e-06] 
dist 215=[-3.65141401034314000000e-06,6.60828051804405000000e-06] 
dist 216=[-4.12766811584660400000e-06,4.05702634457004000000e-06] 
dist 217=[-4.37429910195312900000e-06,3.83924174076197000000e-06] 
dist 218=[-4.50587067858287000000e-06,3.31011028466245000000e-06] 
dist 219=[-4.52723049320779500000e-06,3.17095899832213000000e-06] 
dist 220=[-4.26582873810765000000e-06,2.35757178718679000000e-06] 
dist 221=[-4.19958755758631000000e-06,2.19333011314542000000e-06] 
dist 222=[-4.00735448965688000000e-06,1.85664077873707000000e-06] 
dist 223=[-3.92374115612682000000e-06,1.76240639220706000000e-06] 
dist 224=[-3.45925880404417000000e-06,5.93539749972720000000e-07] 
dist 225=[-3.34485260749315000000e-06,4.16502315019120000000e-07] 
dist 226=[-3.10600281636633000000e-06,9.24608953515200000000e-08] 
dist 227=[-3.02833920386113000000e-06,4.90957109696700000000e-07] 
dist 228=[-1.78437470880193000000e-06,9.62858689747276000000e-07] 
dist 229=[-1.60167143554923000000e-06,1.26484941581296000000e-06] 
dist 230=[-1.17875958822850000000e-06,1.49649104328935900000e-06] 
dist 231=[-8.14105509258000000000e-07,1.68857533041112000000e-06] 
dist 232=[2.48880950768350000000e-07,1.83981059777076000000e-06] 
dist 233=[2.87624663507066300000e-07,1.90896206514861000000e-06] 
dist 234=[1.89930881389928360000e-07,1.94012865979174000000e-06] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 1, 1, 2, 1, 2] 
dist 0=[82.196182314260275642  ,82.196182314260275642  ] 
dist 1=[80.778600430968487295  ,82.976384468141751950  ] 
dist 2=[77.992599927618022018  ,83.219848354667210503  ] 
dist 3=[74.545396298953337051  ,83.225646744644357293  ] 
dist 4=[70.488969124876383048  ,83.058039076326662986  ] 
dist 5=[65.213338852753234316  ,82.792292401853487279  ] 
dist 6=[56.900542791725761383  ,82.526630885856425380  ] 
dist 7=[48.462703288065609586  ,81.929320152009638991  ] 
dist 8=[42.687702541773180272  ,81.634953388330265820  ] 
dist 9=[37.760785347345621441  ,80.346215212774743804  ] 
dist 10=[32.706441523107214549  ,80.075837465413221896  ] 
dist 11=[27.958082333781636830  ,79.254435155167319086  ] 
dist 12=[24.251405146447615095  ,78.997582111399417007  ] 
dist 13=[20.596150088135155764  ,78.892023942467816552  ] 
dist 14=[16.051444015444456351  ,77.266436971828464138  ] 
dist 15=[11.718522725800865793  ,67.619914699312827227  ] 
dist 16=[8.907642419867148420  ,61.169798788227214288  ] 
dist 17=[6.666906201989116428  ,33.042098370537326868  ] 
dist 18=[1.859146613873458195  ,29.430784519550841532  ] 
dist 19=[-3.6695398215593006703 ,21.055734631029664316  ] 
dist 20=[-7.2880082336808722724 ,19.733207797598358462  ] 
dist 21=[-10.198790170976421755  ,8.9888954883199180809 ] 
dist 22=[-12.903117366219012604  ,7.1326208131244842480 ] 
dist 23=[-15.266160069457633252  ,4.3409369827901780714 ] 
dist 24=[-16.814883610931747019  ,3.6505109542012271666 ] 
dist 25=[-18.062807615633023391  ,-1.9715667020741869854 ] 
dist 26=[-19.225352564191360684  ,-2.0486222596734039262 ] 
dist 27=[-20.206102523766574819  ,-2.2627958213463504024 ] 
dist 28=[-20.728766232439727308  ,-2.234016721320257495  ] 
dist 29=[-21.016422493160324048  ,-2.122772245487596633  ] 
dist 30=[-21.060099882891801998  ,-1.883740803022855549  ] 
dist 31=[-20.947060985424920936  ,-1.627598602149326367  ] 
dist 32=[-20.610030182425549559  ,-1.447357194918624113  ] 
dist 33=[-7.0251018725933275746 ,-1.0624477044576324410 ] 
dist 34=[-6.3472974003818259104 ,-.4269962506979832291 ] 
dist 35=[-4.6672745904196329252 ,.1858715523568209323 ] 
dist 36=[-4.4259624213166064555 ,.5822569635247286317 ] 
dist 37=[-1.9625108783828398776 ,.8928155015348981553 ] 
dist 38=[-1.5233797680493595294 ,1.1639154606331906986 ] 
dist 39=[-.9746756534813600644 ,1.3863481279152505376 ] 
dist 40=[-.8838798280202848816 ,1.5030512382701395324 ] 
dist 41=[-.0836338799939461656 ,2.2660625022463051203 ] 
dist 42=[-.0575517122393162256 ,2.9702326721964957113 ] 
dist 43=[.0038963939089538292 ,3.5213296564232453345 ] 
dist 44=[.006787616324521380  ,4.0038182795885094836 ] 
dist 45=[-.010459283786259498  ,4.4025969121968968529 ] 
dist 46=[-.057522069759537925  ,4.6200355202221384635 ] 
dist 47=[-.111155284935787309  ,4.7453136704346546801 ] 
dist 48=[-.154686361483301114  ,4.7767150814296729232 ] 
dist 49=[-.197800346131456785  ,2.5884464662960625628 ] 
dist 50=[-.250068073137097787  ,2.4092887860238591092 ] 
dist 51=[-.303042077532050398  ,1.9598241372910058123 ] 
dist 52=[-.349135356865526665  ,1.8796290968259181034 ] 
dist 53=[-.4241289565633312741 ,1.1841985580764612551 ] 
dist 54=[-.4977561442563681649 ,1.0532928773272767283 ] 
dist 55=[-.5562877494031568403 ,.8556830560078441812 ] 
dist 56=[-.5866267410379184816 ,.8011872294967537025 ] 
dist 57=[-.7457336333435213728 ,.05465618856705732842] 
dist 58=[-1.0678363181690537210 ,.04695308158194202858] 
dist 59=[-1.3219454110121579025 ,-.0100861289109688946 ] 
dist 60=[-1.5467749944441972461 ,-.0193685297899985301 ] 
dist 61=[-1.7334384706939284763 ,-.0348572856152079833 ] 
dist 62=[-1.8355544456536026615 ,-.0379472053945284514 ] 
dist 63=[-1.8945120464270583366 ,-.0733630016858122748 ] 
dist 64=[-1.9092881678885820189 ,-.06562342468299851937] 
dist 65=[-.52420532311481382089,-.03488891663083224138] 
dist 66=[-.4829437503134813060 ,.00522799630753717815] 
dist 67=[-.3767379403302580699 ,.04398338948604526350] 
dist 68=[-.3610739133320367354 ,.06930666008261509838] 
dist 69=[-.1915577294539413821 ,.08938421941542908685] 
dist 70=[-.1601897228622785610 ,.10726302781548203135] 
dist 71=[-.1220710144454044500 ,.12214747532129032212] 
dist 72=[-.1145199836277476138 ,.13030696492781357083] 
dist 73=[-.0178563114490778657 ,.1531485724382203775 ] 
dist 74=[-.0157157113734825507 ,.2123929486859819636 ] 
dist 75=[-.0016355204183136831 ,.2588109506582785853 ] 
dist 76=[.0007350808495398243 ,.2992753886025629462 ] 
dist 77=[.0051973701598397101 ,.3323965285826635088 ] 
dist 78=[.0061596247891696230 ,.3495771733665939468 ] 
dist 79=[.0153193083939483420 ,.3584310159301124436 ] 
dist 80=[.0166583989523616969 ,.3600011126838986964 ] 
dist 81=[.01499394259804832084,.22921736309396016621] 
dist 82=[-.00219124986102643375,.21746934802048217572] 
dist 83=[-.01899380741274026854,.18551224605436736549] 
dist 84=[-.02999930184057416987,.1804888214972648977 ] 
dist 85=[-.03874537990050116634,.1228846028023201434 ] 
dist 86=[-.04655778058655096962,.1115606364753568488 ] 
dist 87=[-.05307032598562312951,.0983405007686938050 ] 
dist 88=[-.05664392628114820710,.0948343310117068792 ] 
dist 89=[-.05871158465049374717,.0363067533686643864 ] 
dist 90=[-.07887303496690598709,.0356517541923996975 ] 
dist 91=[-.09789460468796593017,.0325534899371783546 ] 
dist 92=[-.11427861108430396809,.0318208879375716365 ] 
dist 93=[-.12756299263691012345,.0295145220403302167 ] 
dist 94=[-.1342460448263413155 ,.0290797368333173142 ] 
dist 95=[-.1377824960743056904 ,.0234633327335601761 ] 
dist 96=[-.1385409937371859753 ,.0223553635011928943 ] 
dist 97=[-.0523055461866402629 ,.0198615954228070902 ] 
dist 98=[-.0493442539059081894 ,.0190549067049418135 ] 
dist 99=[-.0416669313847613029 ,.0153231595439063354 ] 
dist 100=[-.0402689580063669314 ,.0145247999975180910 ] 
dist 101=[-.0275191432157428409 ,.0124072248527920658 ] 
dist 102=[-.0213870592908342335 ,.0119241233967718124 ] 
dist 103=[-.01186321067523944229,.00962790221513871965] 
dist 104=[-.01131760199667478560,.01022207062879191183] 
dist 105=[.00786628796624803177,.01222947881442362024] 
dist 106=[.00708104361187706004,.01756329686621304695] 
dist 107=[.00616549504631618926,.02179424648179546625] 
dist 108=[.00543049858515924149,.02556468261320074905] 
dist 109=[.00469762241863610114,.02870469777440537518] 
dist 110=[.00379001337100888073,.03042648239857469687] 
dist 111=[.00285429391887897511,.03142223387047514499] 
dist 112=[.00200931927704816236,.03167239870496573938] 
dist 113=[.00107960751296915710,.01885766942090590100] 
dist 114=[-.00019349606291723785,.01778070001311188870] 
dist 115=[-.00143587549363530560,.01498809086104976012] 
dist 116=[-.00224344901235848984,.01445903057951055611] 
dist 117=[-.00287788720019417088,.00978148301102740056] 
dist 118=[-.00343147780180797905,.00886716166890212157] 
dist 119=[-.00388322416605766363,.00749637328330613976] 
dist 120=[-.00411247839316375142,.00709858117636802937] 
dist 121=[-.00503965072850597461,-.00046344041126014395] 
dist 122=[-.00757416524589611588,-.00143777362260490164] 
dist 123=[-.00958735648461028897,-.00146338690851838847] 
dist 124=[-.01138462375522947975,-.00126893212566460209] 
dist 125=[-.01288251734652445808,-.00108242559540237266] 
dist 126=[-.01370432488696147382,-.00086160597613935988] 
dist 127=[-.01417977095803690675,-.00063926036287933501] 
dist 128=[-.01429923615644728161,-.00044661962278467334] 
dist 129=[-.00394592964011629332,-.00024130350402318347] 
dist 130=[-.00367538346174632033,3.15333315626547900000e-05] 
dist 131=[-.00295945462352737165,.00029646434237133670] 
dist 132=[-.00285281402790179077,.00047035098447932581] 
dist 133=[-.00164127174576117025,.00060880940397302386] 
dist 134=[-.00141155798388235665,.00073279697186084083] 
dist 135=[-.00114113517441959253,.00083625314695049694] 
dist 136=[-.00108430794201761700,.00089302808040184022] 
dist 137=[.00073788315437019523,.00103547267379130873] 
dist 138=[.00066994116384103244,.00150784168611234179] 
dist 139=[.00058985466219565827,.00187975498909153600] 
dist 140=[.00052401237677247203,.00220602628497677194] 
dist 141=[.00045692888111298860,.00247376033178430360] 
dist 142=[.00037187159408766812,.00261273150679829588] 
dist 143=[.00028315562899231770,.00268563531114935060] 
dist 144=[.00020149993725559455,.00269816386065969078] 
dist 145=[.00011042107229594119,.00180876902445343708] 
dist 146=[-1.57987331275833600000e-05,.00172616187028483407] 
dist 147=[-.00013955266982597738,.00149499382794448253] 
dist 148=[-.00022082816520839809,.00145805067499758582] 
dist 149=[-.00028558201343752801,.00101921270188054730] 
dist 150=[-.00034361158887914258,.00093130369196999133] 
dist 151=[-.00039204598817750398,.00083065883892923110] 
dist 152=[-.00041862801875366374,.00080254855825699345] 
dist 153=[-.00043398623725615452,-6.58365289610209490000e-05] 
dist 154=[-.00060587385286473905,-.00014356701042665671] 
dist 155=[-.00076242867120073487,-.00012276789847780036] 
dist 156=[-.00089837648956076088,-.00010656864378498573] 
dist 157=[-.00100889774120465676,-9.08664469195157670000e-05] 
dist 158=[-.00106427607236555801,-7.20368581464984050000e-05] 
dist 159=[-.00109372899012447782,-5.29477282784972330000e-05] 
dist 160=[-.00110108741599524161,-3.62088913090523360000e-05] 
dist 161=[-.00036878108775130958,-1.82020553680751570000e-05] 
dist 162=[-.00034406280478182691,5.93548882739521500000e-06] 
dist 163=[-.00027787902035186924,2.93612620254314370000e-05] 
dist 164=[-.00026835542922296225,4.45381441507994970000e-05] 
dist 165=[-.00015413731490028657,5.63969695641545500000e-05] 
dist 166=[-.00013240357803536883,6.66235186430978610000e-05] 
dist 167=[-.00010804211863757058,7.49080795199658570000e-05] 
dist 168=[-.00010377108711101575,7.90418134611830060000e-05] 
dist 169=[5.44006215406961900000e-05,9.06748633255754100000e-05] 
dist 170=[4.81072687251676200000e-05,.00013479518415398917] 
dist 171=[4.08385637745205900000e-05,.00016988917525274478] 
dist 172=[3.50270810751238340000e-05,.00020127319301751434] 
dist 173=[2.92519091443084480000e-05,.00022744517244411006] 
dist 174=[2.21251929819890320000e-05,.00024180068133484647] 
dist 175=[1.47919707895717690000e-05,.00025009252957678660] 
dist 176=[8.19402029080835600000e-06,.00025213676833605047] 
dist 177=[9.56428748143720000000e-07,.00015564569778082026] 
dist 178=[-8.92256622011551000000e-06,.00014741876992292793] 
dist 179=[-1.85387545793708200000e-05,.00012576722843448475] 
dist 180=[-2.47314630548802360000e-05,.00012158903424568101] 
dist 181=[-2.95276798578245890000e-05,8.41117534241263000000e-05] 
dist 182=[-3.35889881107895920000e-05,7.66818962760785900000e-05] 
dist 183=[-3.68095583523427480000e-05,6.56589574824964700000e-05] 
dist 184=[-3.82615061314739340000e-05,6.23725695900275200000e-05] 
dist 185=[-4.03518297292406100000e-05,-1.23595302890567000000e-06] 
dist 186=[-6.16863925343913500000e-05,0                     ] 
dist 187=[-7.86651404250112000000e-05,-1.57711897892909200000e-05] 
dist 188=[-9.38589755417339300000e-05,-1.43911295822290500000e-05] 
dist 189=[-.00010653259467597695,-1.28038078815165600000e-05] 
dist 190=[-.00011348409307468584,-1.05471989223315600000e-05] 
dist 191=[-.00011749772246826499,-8.06929699816039000000e-06] 
dist 192=[-.00011848207366924033,-5.60131800045943000000e-06] 
dist 193=[-3.41984583381968300000e-05,-2.69920543608124000000e-06] 
dist 194=[-3.21215826356851100000e-05,1.50606221888153000000e-06] 
dist 195=[-2.65745397206412800000e-05,5.70970946676656000000e-06] 
dist 196=[-2.56846646023225000000e-05,8.60546324693864000000e-06] 
dist 197=[-1.60387651538529800000e-05,1.10628319841772500000e-05] 
dist 198=[-1.41728747298100400000e-05,1.35224538805424700000e-05] 
dist 199=[-1.18584386905407500000e-05,1.57588597211587100000e-05] 
dist 200=[-1.12063587600574700000e-05,1.73281393026856300000e-05] 
dist 201=[-3.22051707366614000000e-06,1.86899318362574100000e-05] 
dist 202=[-3.58782588506719000000e-06,2.01007055673159200000e-05] 
dist 203=[-4.02065865798494000000e-06,2.13578280171542200000e-05] 
dist 204=[-4.36322131567802000000e-06,2.21083546679577590000e-05] 
dist 205=[-4.70034154330223800000e-06,2.26220401364218750000e-05] 
dist 206=[-5.11166689508382700000e-06,2.29371479646422700000e-05] 
dist 207=[-5.53230240189130100000e-06,2.30958956097885200000e-05] 
dist 208=[-5.90653014022571000000e-06,2.29876612780360500000e-05] 
dist 209=[-6.31346642108952000000e-06,1.64935253984012170000e-05] 
dist 210=[-6.86428045434984000000e-06,1.58284703955547460000e-05] 
dist 211=[-7.39805281870152000000e-06,1.39345569537118300000e-05] 
dist 212=[-7.73723864601172000000e-06,1.36104882290364820000e-05] 
dist 213=[-7.99466220446273000000e-06,9.87961793274207900000e-06] 
dist 214=[-8.20324087754192000000e-06,9.11725733724264400000e-06] 
dist 215=[-8.36149727847288000000e-06,8.21251754446592600000e-06] 
dist 216=[-8.41877445223692000000e-06,7.90911626343107100000e-06] 
dist 217=[-8.41253537279149000000e-06,2.08509306226480000000e-07] 
dist 218=[-8.35386942513004000000e-06,-7.28328806749480000000e-07] 
dist 219=[-8.42683910680693700000e-06,-1.60627046058910220000e-06] 
dist 220=[-9.51089471143126100000e-06,-1.80035921313715160000e-06] 
dist 221=[-1.03669596120262770000e-05,-1.88579736720960550000e-06] 
dist 222=[-1.07507898018434560000e-05,-1.61293771600167980000e-06] 
dist 223=[-1.09280573225462280000e-05,-1.06269621662191191000e-06] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 2, 1, 0, 1] 
dist 0=[86.901975624822438755  ,86.901975624822438755  ] 
dist 1=[86.308293692014722572  ,87.207002874670126746  ] 
dist 2=[85.165353013478659110  ,87.198043453554055602  ] 
dist 3=[83.689300903764151138  ,86.988477698731339577  ] 
dist 4=[81.766338500229928336  ,86.767774037957033313  ] 
dist 5=[79.148490193629622286  ,85.940955383119685429  ] 
dist 6=[74.899509140864821341  ,85.505632664955762951  ] 
dist 7=[69.929958116982688870  ,82.826525273015893332  ] 
dist 8=[61.864371925491490129  ,82.045089780163128118  ] 
dist 9=[53.331698713928362160  ,81.262844448726953787  ] 
dist 10=[46.822414178178082698  ,80.807937691307646974  ] 
dist 11=[36.040839598850667074  ,80.344502977101582202  ] 
dist 12=[28.740932039411829654  ,80.202196332017307974  ] 
dist 13=[22.597893929034970388  ,77.501384600464541133  ] 
dist 14=[16.433269498855541678  ,72.229494078124050478  ] 
dist 15=[10.732363217323298412  ,32.546107616198499630  ] 
dist 16=[6.440055162946546684  ,28.802493582944432317  ] 
dist 17=[2.361358595156803674  ,20.024070867847156718  ] 
dist 18=[-2.486806188823653537  ,18.762110402976432535  ] 
dist 19=[-7.026998398713423670  ,10.684629625236423215  ] 
dist 20=[-9.877050691220254194  ,10.166107661932366837  ] 
dist 21=[-12.032991542322961193  ,5.8278383620492787865 ] 
dist 22=[-13.804595439400938874  ,5.1077223555042087867 ] 
dist 23=[-15.196094891349777336  ,4.0413122784328306140 ] 
dist 24=[-15.836342482467049773  ,3.7956444542137559905 ] 
dist 25=[-16.133175414568789494  ,-10.069693980183506421  ] 
dist 26=[-16.271028014633537725  ,-8.5181999121756607625 ] 
dist 27=[-17.703740396621438354  ,-6.8223663834925273523 ] 
dist 28=[-18.470326919278217548  ,-5.5909654567229094433 ] 
dist 29=[-18.896935793851086627  ,-4.4810834220041154036 ] 
dist 30=[-18.972300376989733382  ,-3.266834139255202438  ] 
dist 31=[-10.075278276775581313  ,-2.094727764292687847  ] 
dist 32=[-9.3414544370570052241 ,-1.151565760484473914  ] 
dist 33=[-7.5240832036247510886 ,-.204082481652118642  ] 
dist 34=[-7.2041848120338310032 ,.986238337670702866  ] 
dist 35=[-4.4789710053240961822 ,2.119048162626997138  ] 
dist 36=[-3.9729277810883644823 ,2.837782950843480284  ] 
dist 37=[-3.2005550863810445646 ,3.386124074155087768  ] 
dist 38=[-2.9936389095300449197 ,3.840232355491984410  ] 
dist 39=[.6237820441931212498 ,4.198229379369580306  ] 
dist 40=[1.0864737570573445285 ,4.363754703080539460  ] 
dist 41=[1.918371152665011450  ,5.143099305559232576  ] 
dist 42=[1.9690882438669834218 ,5.942895314499415330  ] 
dist 43=[1.4248243951787524133 ,6.601471232793911643  ] 
dist 44=[1.0187998094554210728 ,6.953579165514483090  ] 
dist 45=[.6417316905851017576 ,7.146530823216881357  ] 
dist 46=[.212297315411121019  ,7.183299965095446125  ] 
dist 47=[-.211771204667558677  ,1.8759919220349986296 ] 
dist 48=[-.567701124857646003  ,1.7240283990268320199 ] 
dist 49=[-.938107063669919271  ,1.3340732922446291786 ] 
dist 50=[-1.420014129376174491  ,1.2780149569496861325 ] 
dist 51=[-1.881129399495812896  ,.6621864407051528167 ] 
dist 52=[-2.168849114795414538  ,.5491519231370163190 ] 
dist 53=[-2.382112948062553770  ,.4143361947944999412 ] 
dist 54=[-2.546866885978080074  ,.3915082009231567279 ] 
dist 55=[-2.666415003217409820  ,-.40669048227071401003] 
dist 56=[-2.699673650973958776  ,-.45072661415843169013] 
dist 57=[-2.703082489347518345  ,-.45228214338392864388] 
dist 58=[-2.703800897539989622  ,-.39652467872763807221] 
dist 59=[-1.1302992468720313934 ,-.32749766927453417123] 
dist 60=[-1.1945537540061584945 ,-.2762163910964614108 ] 
dist 61=[-1.2316512504815478045 ,-.2288101768962929273 ] 
dist 62=[-1.2409518940631560253 ,-.1751567401660820671 ] 
dist 63=[-.71176748473626961358,-.1223863220809753758 ] 
dist 64=[-.6679128405139682551 ,-.0784685551230562222 ] 
dist 65=[-.55563188957028991036,-.0331079182599550153 ] 
dist 66=[-.53500271878573715325,.0254318308911457415 ] 
dist 67=[-.35291603177511595292,.0818114163179546178 ] 
dist 68=[-.31791219286907617665,.1185821957560596814 ] 
dist 69=[-.2655100053289560798 ,.1476825652713226548 ] 
dist 70=[-.25056041711143623131,.1735298886195653741 ] 
dist 71=[.02719807699601899310,.1950187665210591665 ] 
dist 72=[.06282160895840190196,.2812391040084361171 ] 
dist 73=[.1342296233690198296 ,.3539814423012865575 ] 
dist 74=[.14674605042420612373,.4186666434393750807 ] 
dist 75=[.12617238923980694473,.4724861872331376716 ] 
dist 76=[.10998318275410049286,.5019747833536986620 ] 
dist 77=[.09412028424932143207,.5190174793468417021 ] 
dist 78=[.0748336431080786190 ,.5232894912146131011 ] 
dist 79=[.0551068821451864425 ,.14540126275204990832] 
dist 80=[.0374863940776039982 ,.1349591657548187286 ] 
dist 81=[.0182337528971564024 ,.10761355351339026967] 
dist 82=[-.0079944139885410086 ,.10355935838596774318] 
dist 83=[-.0335879603420816209 ,.05832910784643297444] 
dist 84=[-.0503169563349116170 ,.0498390874798869527 ] 
dist 85=[-.0635838069378200402 ,.0397146316220022324 ] 
dist 86=[-.0753989181348825633 ,.0376447023411639591 ] 
dist 87=[-.0852315695669686945 ,-.0331011405248315617 ] 
dist 88=[-.0906082754080851931 ,-.03564192601534297813] 
dist 89=[-.0936974848986193592 ,-.03451351220364973805] 
dist 90=[-.0944254301284773541 ,-.02992383229072528301] 
dist 91=[-.0897803779576964108 ,-.02460682588791945441] 
dist 92=[-.0946341563152333755 ,-.0205834153883212279 ] 
dist 93=[-.0971579113657155227 ,-.0167906022029201684 ] 
dist 94=[-.0975516926203088482 ,-.0123887189376710404 ] 
dist 95=[-.0646203848184250228 ,-.0079986747418304591 ] 
dist 96=[-.0615631339283713079 ,-.0042516408043167404 ] 
dist 97=[-.0531055693449827172 ,-.0003017000773905034 ] 
dist 98=[-.0517465141429041663 ,.0048971454939289133 ] 
dist 99=[-.0360106081436696553 ,.0098912752818529036 ] 
dist 100=[-.0328779153404774642 ,.0130270235383395852 ] 
dist 101=[-.0292195200562495439 ,.0153689711346891959 ] 
dist 102=[-.0281793814721288404 ,.0172042388493330432 ] 
dist 103=[.0021488708515176067 ,.0186450457872961993 ] 
dist 104=[.0057769180185575935 ,.0228121787462466666 ] 
dist 105=[.00751323270640658485,.0282187708254648544 ] 
dist 106=[.0053305195914735299 ,.0328738665022180529 ] 
dist 107=[.0029714573900049163 ,.0366365903180884082 ] 
dist 108=[.0012124542606411140 ,.0384917419884708851 ] 
dist 109=[-.0004205023346896202 ,.0394585570568561186 ] 
dist 110=[-.0022789479196936931 ,.0396858243634169791 ] 
dist 111=[-.0041116658310494551 ,.01285337964497710763] 
dist 112=[-.0056427495390335896 ,.01197256722446284895] 
dist 113=[-.0072278543919491079 ,.00962716752298831950] 
dist 114=[-.0092760445696457239 ,.00928992042806368963] 
dist 115=[-.0112227405979441350 ,.00528985306433348620] 
dist 116=[-.0124042248088020942 ,.00453258723350862251] 
dist 117=[-.0132389333561343234 ,.00367652711740970840] 
dist 118=[-.0138059487457776937 ,.00352780204712901739] 
dist 119=[-.0141632042593891174 ,-.00258523347904306999] 
dist 120=[-.0142232477792288901 ,-.00290785070898929346] 
dist 121=[-.0140556206595864590 ,-.00304970281855183768] 
dist 122=[-.0139854917917932354 ,-.00268050960483851771] 
dist 123=[-.00781403412381713758,-.00225070437177335791] 
dist 124=[-.00830477009306054754,-.00192530397157010882] 
dist 125=[-.00858870636446263125,-.00161837440444027017] 
dist 126=[-.00866005396064412509,-.00126190623411825067] 
dist 127=[-.00528030819016261585,-.00090633714861036847] 
dist 128=[-.00499421339707692769,-.00060290058181661829] 
dist 129=[-.00424523356155629114,-.00028317765549360193] 
dist 130=[-.00410129717942748360,.00013728115914091143] 
dist 131=[-.00282035250159115730,.00054443466554181358] 
dist 132=[-.00256771724843131644,.00081124511603737752] 
dist 133=[-.00219017748725217594,.00102339024416283332] 
dist 134=[-.00207914468292033547,.00121303046585223970] 
dist 135=[5.90396715385283400000e-05,.00137116949058698140] 
dist 136=[.00033476135914697865,.00207161016302270644] 
dist 137=[.00089586742026419679,.00264232011201127924] 
dist 138=[.00103041711736540487,.00315270517857217350] 
dist 139=[.00093086154921020165,.00357838691375016796] 
dist 140=[.00082002857917478509,.00381205987095452650] 
dist 141=[.00070906178720760509,.00394729616983918086] 
dist 142=[.00057085149029467960,.00398128196776905517] 
dist 143=[.00042782250307622777,.00110736621397234553] 
dist 144=[.00029765958816968111,.00103517533493399604] 
dist 145=[.00015356651453009931,.00084225078647879031] 
dist 146=[-4.49106785067372400000e-05,.00081345903346962832] 
dist 147=[-.00023919262633137267,.00048069060227362901] 
dist 148=[-.00036660197142672994,.00041713713074514410] 
dist 149=[-.00046797952141814091,.00034314743515111644] 
dist 150=[-.00055868770949035329,.00032742766190441625] 
dist 151=[-.00063435836981009796,-.00023278579963444180] 
dist 152=[-.00067590351595390648,-.00026734386678789663] 
dist 153=[-.00069994994220494375,-.00026206782670809519] 
dist 154=[-.00070599321247880697,-.00023182431068831851] 
dist 155=[-.00067946637140032829,-.00019602372957484093] 
dist 156=[-.00071897284503128139,-.00016863583810751291] 
dist 157=[-.00073982147455131362,-.00014252763247571048] 
dist 158=[-.00074340144386275505,-.00011180773115283642] 
dist 159=[-.00050694126822028758,-8.09500405995146600000e-05] 
dist 160=[-.00048472734492105135,-5.42878622914116300000e-05] 
dist 161=[-.00042188204716470968,-2.59187358445045400000e-05] 
dist 162=[-.00041179526570639870,1.17362164718663500000e-05] 
dist 163=[-.00029029344198373953,4.82388391044249800000e-05] 
dist 164=[-.00026580792040044721,7.20252641140524100000e-05] 
dist 165=[-.00023799038814020022,9.07802455055402900000e-05] 
dist 166=[-.00023012985212344436,.00010726452445939542] 
dist 167=[1.51836866582916190000e-05,.00012080179675281388] 
dist 168=[4.44600765023334910000e-05,.00016610514701585667] 
dist 169=[9.21159491217810500000e-05,.00021048203911438799] 
dist 170=[8.74208153818463820000e-05,.00024912689218148234] 
dist 171=[7.57662525417006800000e-05,.00028060156936137088] 
dist 172=[6.64668078089726900000e-05,.00029645143774189493] 
dist 173=[5.72343452293221500000e-05,.00030489897382907395] 
dist 174=[4.58430659555312800000e-05,.00030691901925235644] 
dist 175=[3.41123892967383100000e-05,.00010358243320099843] 
dist 176=[2.35279222389275800000e-05,9.69168626268195600000e-05] 
dist 177=[1.18861269982374900000e-05,7.89205494492714900000e-05] 
dist 178=[-4.05285726346927000000e-06,7.63317678070503800000e-05] 
dist 179=[-1.96052031289966500000e-05,4.47891671524504700000e-05] 
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dist 181=[-3.76409098380855800000e-05,3.20575617242542900000e-05] 
dist 182=[-4.45493927070717300000e-05,3.08807855038664500000e-05] 
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dist 186=[-5.52873560887442300000e-05,-2.18471205401964700000e-05] 
dist 187=[-6.27053587960118400000e-05,-1.84909604216001200000e-05] 
dist 188=[-6.67757842981296100000e-05,-1.59247325301282400000e-05] 
dist 189=[-6.91275759534222200000e-05,-1.34796548489236500000e-05] 
dist 190=[-6.97076920197379100000e-05,-1.06046290418267800000e-05] 
dist 191=[-4.36369415858296020000e-05,-7.71818121862622000000e-06] 
dist 192=[-4.14027641617675671000e-05,-5.22720396634748000000e-06] 
dist 193=[-3.54943832280586370000e-05,-2.57976750035648000000e-06] 
dist 194=[-3.43366999208210030000e-05,9.29612791527290000000e-07] 
dist 195=[-2.39950634453280700000e-05,4.33519986106564000000e-06] 
dist 196=[-2.19333241486543520000e-05,6.56986576158633000000e-06] 
dist 197=[-1.88571919698511300000e-05,8.34865039944162000000e-06] 
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dist 199=[-2.96735139291000000000e-08,1.12681076035941900000e-05] 
dist 200=[2.28314617010676200000e-06,1.70423158617810800000e-05] 
dist 201=[6.99456892556874700000e-06,2.18425218269743400000e-05] 
dist 202=[8.13243947434485400000e-06,2.61426337553658100000e-05] 
dist 203=[7.76575588971811500000e-06,2.97311061078962500000e-05] 
dist 204=[6.86627589339740000000e-06,3.17001302721578800000e-05] 
dist 205=[5.95615173650808000000e-06,3.28373860857567700000e-05] 
dist 206=[4.80966549807797000000e-06,3.31166793596884800000e-05] 
dist 207=[3.61690546053341000000e-06,9.31903202939862700000e-06] 
dist 208=[2.52255267831585000000e-06,8.75004646772490200000e-06] 
dist 209=[1.30434017259013000000e-06,7.20032601409919500000e-06] 
dist 210=[-3.81307458000700000000e-07,6.97658327348815800000e-06] 
dist 211=[-2.03328362503918000000e-06,4.21292860303761200000e-06] 
dist 212=[-3.11758956177905000000e-06,3.68012375261308300000e-06] 
dist 213=[-3.98090024713897000000e-06,3.09474903080867800000e-06] 
dist 214=[-4.75369713347163000000e-06,2.98904499049812200000e-06] 
dist 215=[-5.39816490082172000000e-06,-1.70376817412523200000e-06] 
dist 216=[-5.75093591757332000000e-06,-2.15859814367898000000e-06] 
dist 217=[-5.95354021054076000000e-06,-2.11298948549644800000e-06] 
dist 218=[-6.00057771355780000000e-06,-1.85637845728252000000e-06] 
dist 219=[-5.83711086471812400000e-06,-1.55201145599968000000e-06] 
dist 220=[-6.14372676111655300000e-06,-1.31640639599383000000e-06] 
dist 221=[-6.30231314460149100000e-06,-1.08917215234699000000e-06] 
dist 222=[-6.33133043458512300000e-06,-8.18039321628330000000e-07] 
dist 223=[-4.62546395103605300000e-06,-5.43704670272360000000e-07] 
dist 224=[-4.44412840745118600000e-06,-3.03696985288870000000e-07] 
dist 225=[-3.92372864619468800000e-06,-4.58823015541800000000e-08] 
dist 226=[-3.83421363940402100000e-06,2.99329377621320000000e-07] 
dist 227=[-2.79608797149036200000e-06,6.32534243017000000000e-07] 
dist 228=[-2.58309222516289300000e-06,8.42599544445960000000e-07] 
dist 229=[-2.33119209588078400000e-06,1.00022049192192000000e-06] 
dist 230=[-2.24586631589808800000e-06,1.12480127579763000000e-06] 
dist 231=[-7.58186069087100000000e-08,1.50055853039438600000e-06] 
dist 232=[1.83977002702955000000e-07,1.97366014345994000000e-06] 
dist 233=[4.16330357002351500000e-07,2.33920119388829000000e-06] 
dist 234=[3.10920998183720000000e-07,2.64726968065040900000e-06] 
dist 235=[1.65934069458510000000e-07,2.89084762097731600000e-06] 
dist 236=[5.64311925714300000000e-08,2.99982594873363500000e-06] 
dist 237=[-4.65945240533700000000e-08,3.05044773647656100000e-06] 
dist 238=[-1.65844705336470000000e-07,3.06186812166934200000e-06] 
dist 239=[-2.84510766217240000000e-07,7.19638990418210000000e-07] 
dist 240=[-3.85229214626180000000e-07,6.77565696704030000000e-07] 
dist 241=[-4.90817536447390000000e-07,6.13116735094470000000e-07] 
dist 242=[-6.28873903407270000000e-07,5.93126208132670000000e-07] 
dist 243=[-7.60601020678000000000e-07,2.37592571541080000000e-07] 
dist 244=[-8.41019099889260000000e-07,2.03348841558980000000e-07] 
dist 245=[-8.98310008107460000000e-07,1.21439288400100000000e-07] 
dist 246=[-9.38041324856060000000e-07,4.99453531971600000000e-08] 
dist 247=[-9.63155624118960000000e-07,-9.20131505891544000000e-08] 
dist 248=[-9.67808727610380000000e-07,-7.91067965115330100000e-08] 
dist 249=[-9.54420904124780000000e-07,-5.22997252969671100000e-08] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 0, 0, 1, 0, 2] 
dist 0=[82.449310267481029182  ,82.449310267481029182  ] 
dist 1=[81.037170033183006532  ,83.219254667223398381  ] 
dist 2=[78.382123403426531302  ,83.382571197285681253  ] 
dist 3=[75.099954054357863727  ,83.125976097657644169  ] 
dist 4=[71.185370150623360782  ,82.890452305906901834  ] 
dist 5=[66.061785128886651285  ,82.334914857003439047  ] 
dist 6=[57.954748971253907151  ,82.045666989176681576  ] 
dist 7=[49.716148756399539975  ,81.020921205988539107  ] 
dist 8=[44.067165790244362415  ,80.691856235344559291  ] 
dist 9=[39.236777010825586362  ,80.324654649930009593  ] 
dist 10=[34.263959870428930624  ,80.056028105164234882  ] 
dist 11=[29.581225397512659860  ,79.786059422472715174  ] 
dist 12=[25.907601873838049405  ,79.502445855258528962  ] 
dist 13=[22.267848244954266450  ,79.139885337513486102  ] 
dist 14=[17.718706020100703641  ,77.484190360264720175  ] 
dist 15=[13.369820398623010796  ,34.104125200666705036  ] 
dist 16=[10.528431049740759516  ,30.540943935882417446  ] 
dist 17=[8.2406636788249035425 ,22.275234531140350097  ] 
dist 18=[6.1003301610419197501 ,20.957992103274365866  ] 
dist 19=[4.2051084624814407854 ,11.421832919641866726  ] 
dist 20=[-.5400735764684269737 ,10.734932101134637616  ] 
dist 21=[-5.9548995431924048835 ,5.6903730032645831629 ] 
dist 22=[-9.4619150287274625095 ,5.0017562833207205565 ] 
dist 23=[-12.241940980361212037  ,-.61855083380721243984] 
dist 24=[-14.755339927657598566  ,-.97242077504666455286] 
dist 25=[-16.903742950502288216  ,-1.6649523826430369409 ] 
dist 26=[-18.227071266618541284  ,-1.7667926016920129799 ] 
dist 27=[-19.588703838543126478  ,-2.2230138480133039404 ] 
dist 28=[-20.371188552150574085  ,-2.2744046705252343585 ] 
dist 29=[-20.763525498692906190  ,-2.2326393689665395048 ] 
dist 30=[-20.819651785127343953  ,-2.0651869792049272242 ] 
dist 31=[-6.5788409974953448097 ,-1.8669360917901671321 ] 
dist 32=[-5.9645633351644787300 ,-1.7015009638733145240 ] 
dist 33=[-4.4387249914599383140 ,-1.5345478326540802747 ] 
dist 34=[-4.2169570595142827470 ,-1.3286066618194870872 ] 
dist 35=[-1.9681778079780724673 ,-.71879110544632178435] 
dist 36=[-1.6502141298519628688 ,.06422533390994514943] 
dist 37=[-1.6005943560054608708 ,.81406090670604841158] 
dist 38=[-1.5932533063175699890 ,1.2960399410925427540 ] 
dist 39=[-.1759470670223044735 ,2.0164342667739931163 ] 
dist 40=[-.0870521881670016665 ,2.6778402292686927910 ] 
dist 41=[.1070095790849471346 ,3.1933854377685579965 ] 
dist 42=[.1351795422246461060 ,3.6409397112067813487 ] 
dist 43=[.3368997011220954642 ,4.0079722962110416775 ] 
dist 44=[.3670478502630686974 ,4.2026034033183200733 ] 
dist 45=[.4172746184230101153 ,4.3073814416547909678 ] 
dist 46=[.4257693411804113663 ,4.3236991791255383542 ] 
dist 47=[.4754621993747829476 ,2.4894636962879657087 ] 
dist 48=[.4765174349120685726 ,2.3336666987607112720 ] 
dist 49=[.4670947620941462708 ,1.9303719596749610518 ] 
dist 50=[.39997033695541778179,1.8640446552735790675 ] 
dist 51=[.21295032866526330454,1.2019533725197954453 ] 
dist 52=[-.0366265538618383822 ,1.0756481077566699211 ] 
dist 53=[-.27800259186989775264,.90944015446427150867] 
dist 54=[-.43242982300074469439,.85816391285803481961] 
dist 55=[-.64235040363819394336,.21555435883604639455] 
dist 56=[-.9208343823212900462 ,.19087454022654701246] 
dist 57=[-1.1388693733872356363 ,.1331166703782478947 ] 
dist 58=[-1.3289263466077564727 ,.1243938684597069206 ] 
dist 59=[-1.4847042031585441182 ,.0494763021661034368 ] 
dist 60=[-1.5662361658464975382 ,.0365647443625686439 ] 
dist 61=[-1.6099368080774772408 ,.0183628676979674274 ] 
dist 62=[-1.6182277776538596892 ,.0142092683329666807 ] 
dist 63=[-.4921617535371875018 ,-.0632025647696129640 ] 
dist 64=[-.4541130399452196868 ,-.0723719462074827403 ] 
dist 65=[-.3554456914608542174 ,-.0918772638691883867 ] 
dist 66=[-.3412100884568214785 ,-.0945416176167338744 ] 
dist 67=[-.1817289106644765645 ,-.0513375846932944626 ] 
dist 68=[-.1763365829511070847 ,.0053301518451300623 ] 
dist 69=[-.1781195682649146505 ,.0601500411540605220 ] 
dist 70=[-.1781743724885142817 ,.0960099078383696983 ] 
dist 71=[-.0508168617461588192 ,.1335358189914143817 ] 
dist 72=[-.0438245448562994852 ,.1887067003218007420 ] 
dist 73=[-.0275534485024179779 ,.2322936825683371324 ] 
dist 74=[-.0248423752075259679 ,.2709033821308574109 ] 
dist 75=[-.0040759809285718618 ,.3029439753783014919 ] 
dist 76=[-.0005164950508409529 ,.3203770732776003926 ] 
dist 77=[.0053840509814280118 ,.3302974179057375219 ] 
dist 78=[.0066737575064847175 ,.3324250342946146952 ] 
dist 79=[.0244978660604397373 ,.19707008074327235825] 
dist 80=[.0268238795816209172 ,.18565538942724322169] 
dist 81=[.0301268941108562309 ,.1560571058093296731 ] 
dist 82=[.0306344916000401733 ,.1506382742550044865 ] 
dist 83=[.0219472171389415785 ,.1013076448457128527 ] 
dist 84=[-.0026055847491852550 ,.0917250177567121217 ] 
dist 85=[-.0266319070288370877 ,.0777875677060228235 ] 
dist 86=[-.0423817934323136589 ,.0736325361354980760 ] 
dist 87=[-.0549080626609786486 ,.04331080756514320509] 
dist 88=[-.0768115969359633737 ,.04170148997841004680] 
dist 89=[-.0966850941741370426 ,.0379750476889304120 ] 
dist 90=[-.1142936672064443700 ,.0367628809311574578 ] 
dist 91=[-.1288866241168787517 ,.0311266596583518213 ] 
dist 92=[-.1367572845740859716 ,.0299004814922569393 ] 
dist 93=[-.1411346297036596241 ,.0270054576063907320 ] 
dist 94=[-.1420081092849566845 ,.0260585610260634384 ] 
dist 95=[-.0482975794476562542 ,.0165121933472289530 ] 
dist 96=[-.0459310127923329523 ,.0149589849576214285 ] 
dist 97=[-.0399171301238237750 ,.0114282104442237323 ] 
dist 98=[-.0385838647310280837 ,.0104698137285795323 ] 
dist 99=[-.0287374624026882985 ,.0057920070559685281 ] 
dist 100=[-.0267843476747571286 ,.0048783571751315015 ] 
dist 101=[-.0209122031499562563 ,.0048985613636199647 ] 
dist 102=[-.0206375473073756694 ,.0077619117813404907 ] 
dist 103=[-.01247345813330443160,.0121614196330761842 ] 
dist 104=[-.01178585714929446690,.0171002475084515955 ] 
dist 105=[-.0104632751886464217 ,.0208934369589238441 ] 
dist 106=[-.0101028312541219490 ,.0240591406958197056 ] 
dist 107=[-.0087794984035476352 ,.0266024662258096186 ] 
dist 108=[-.0084353436120288946 ,.0279187704783236283 ] 
dist 109=[-.0079109675277031593 ,.0285798990728913474 ] 
dist 110=[-.0077373597524121593 ,.0286962399351351384 ] 
dist 111=[-.0073257959760800017 ,.02278308105847374182] 
dist 112=[-.0072703399774650002 ,.02207729197382066628] 
dist 113=[-.0073451858546703816 ,.0199387254225902591 ] 
dist 114=[-.0076127095082598533 ,.0196037284178931834 ] 
dist 115=[-.0079767959273133500 ,.0150151674581932531 ] 
dist 116=[-.0084363045563497272 ,.0140589429434142604 ] 
dist 117=[-.0090472805925327825 ,.0108581229990363936 ] 
dist 118=[-.0100145376295917852 ,.0059542670904319845 ] 
dist 119=[-.0109535283775044188 ,.00257502986163658504] 
dist 120=[-.0114522272973262357 ,.00240516078219653558] 
dist 121=[-.0117185804810063362 ,.00196856421506113094] 
dist 122=[-.0117422736880812859 ,.00190072030012929808] 
dist 123=[-.0116255739701552781 ,.00119382518809954000] 
dist 124=[-.0115197250335467640 ,.00105991939771768563] 
dist 125=[-.01088132977037405597,.00089416338332665534] 
dist 126=[-.00949913665101535500,.00085163335322565514] 
dist 127=[-.00163182111283144190,-.00028645072530712684] 
dist 128=[-.0015821733988756094 ,-.00042181017912964586] 
dist 129=[-.0013204485417356473 ,-.00072194994462955519] 
dist 130=[-.0014856165854526938 ,-.00065793435752121793] 
dist 131=[-.0016180975902928388 ,-.00036288905716963078] 
dist 132=[-.0016851774460547888 ,3.03508378574866700000e-05] 
dist 133=[-.0017194847798078540 ,.00041250257064441745] 
dist 134=[-.0017240658391471855 ,.00066346867214444012] 
dist 135=[-.00052184757208232008,.00086340939365840417] 
dist 136=[-.00047031007701851579,.00104257852332448434] 
dist 137=[-.0003409425063900042 ,.00119212255242667203] 
dist 138=[-.0003223493275020526 ,.00127420726862330590] 
dist 139=[-.0001267018593618472 ,.0013216506751157855 ] 
dist 140=[-9.13676899068197000000e-05,.0013333771397471373 ] 
dist 141=[-4.80972532723656000000e-05,.00085313586657019952] 
dist 142=[-4.08374125443393000000e-05,.00081178772787429763] 
dist 143=[.0002233375585999733 ,.00070112795933372469] 
dist 144=[.0002538153359037072 ,.00067928428533810942] 
dist 145=[.0003121988296990606 ,.00048139650288814920] 
dist 146=[.00029442760902814315,.00044167972671205647] 
dist 147=[.00016308892062842725,.00040806049916278287] 
dist 148=[-1.92672410159054800000e-05,.00042686828214502570] 
dist 149=[-.00019815279056953986,.0004376968693970314 ] 
dist 150=[-.00031569413566910239,.0004403504714005609 ] 
dist 151=[-.00040938565479286850,.00023494471839320591] 
dist 152=[-.00049339921038396448,.00021803766543558511] 
dist 153=[-.00056353935804987784,.00017581006782221726] 
dist 154=[-.00060204192600592482,.00016820999352017546] 
dist 155=[-.00062429105929791476,.0001031859386138657 ] 
dist 156=[-.00062977213297327540,9.09307871652843000000e-05] 
dist 157=[-.00018072239655175898,7.22509266495685000000e-05] 
dist 158=[-.00017038960099482392,6.71476442915459000000e-05] 
dist 159=[-.00014186070543200540,-2.37578501490577800000e-05] 
dist 160=[-.00013774904633981023,-3.54568690838077400000e-05] 
dist 161=[-.00013645256791316130,-5.81803992793231500000e-05] 
dist 162=[-.00015785412706407082,-5.34376837909245200000e-05] 
dist 163=[-.00017562216730242866,-2.74713699843712000000e-05] 
dist 164=[-.00018533005544231408,7.42098840444451000000e-06] 
dist 165=[-.00019091553615553784,4.13063159536495300000e-05] 
dist 166=[-.00019226667123349480,6.32688832790176400000e-05] 
dist 167=[-5.16653483099607200000e-05,8.04366200610037900000e-05] 
dist 168=[-4.73350103726740100000e-05,9.52489545981920100000e-05] 
dist 169=[-3.63707320801178400000e-05,.00010725792232453219] 
dist 170=[-3.46651469301857100000e-05,.00011327455283189303] 
dist 171=[-1.76008420885694000000e-05,.00011641498571987511] 
dist 172=[-1.44456177366614000000e-05,.00011698155818803054] 
dist 173=[-1.03333636805900000000e-05,8.67240325768616520000e-05] 
dist 174=[-9.28868009182930000000e-06,8.34686301744485600000e-05] 
dist 175=[1.49423226162265000000e-05,7.39975548940883400000e-05] 
dist 176=[1.78623381459750000000e-05,7.23637886105337100000e-05] 
dist 177=[2.17300256552121500000e-05,5.30904727239053100000e-05] 
dist 178=[1.22219866042152810000e-05,4.91157905827650200000e-05] 
dist 179=[1.76840011300917600000e-06,4.44572381695264300000e-05] 
dist 180=[-1.25278335875376000000e-05,4.28761984612558900000e-05] 
dist 181=[-2.64520474390242760000e-05,4.03080752924127300000e-05] 
dist 182=[-3.54265857376427810000e-05,4.04330181749065600000e-05] 
dist 183=[-4.23844614035095500000e-05,2.86527184893258000000e-05] 
dist 184=[-4.82872328598379100000e-05,2.74120870227038000000e-05] 
dist 185=[-5.29752292496082800000e-05,2.41959864217834000000e-05] 
dist 186=[-5.51011907688065300000e-05,2.34577356109230000000e-05] 
dist 187=[-5.61040634012373400000e-05,1.78496024878091000000e-05] 
dist 188=[-5.63237020337986600000e-05,1.66920600094159000000e-05] 
dist 189=[-2.41134444426445800000e-05,1.47317913888353000000e-05] 
dist 190=[-2.34388031476638500000e-05,1.42065566129519000000e-05] 
dist 191=[-2.18377069062118000000e-05,3.81352543063490000000e-06] 
dist 192=[-2.12691552275958000000e-05,2.42142427739710000000e-06] 
dist 193=[-1.84635091508985000000e-05,-6.68098647024500000000e-07] 
dist 194=[-1.78389312000380000000e-05,-1.32713683582830000000e-06] 
dist 195=[-1.79120496232850400000e-05,-4.35584434850780540000e-06] 
dist 196=[-1.84555687757977800000e-05,-3.57826100068998220000e-06] 
dist 197=[-1.86890567364447500000e-05,-2.29332131101593685000e-06] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 0, 1, 1, 2, 1, 2] 
dist 0=[77.007806456418668926  ,77.007806456418668926  ] 
dist 1=[74.942598597664376581  ,78.290912118985841439  ] 
dist 2=[71.909516202094151560  ,79.186289843069517221  ] 
dist 3=[66.763999659923862806  ,79.704163704680156817  ] 
dist 4=[61.393101417356973689  ,80.044580633981557535  ] 
dist 5=[57.460715692414455035  ,80.231594833663376981  ] 
dist 6=[53.831153513190674553  ,80.270901741670345252  ] 
dist 7=[49.669016599376567890  ,80.128227301526150753  ] 
dist 8=[45.486826232189595358  ,78.312692402079206071  ] 
dist 9=[41.777443977802615607  ,73.668667280146593580  ] 
dist 10=[37.707041199097645778  ,72.631037432571699633  ] 
dist 11=[32.084456317801096553  ,70.899831021945039679  ] 
dist 12=[26.468987135511482744  ,70.391070710371513772  ] 
dist 13=[22.427014406309452915  ,68.801944333313956188  ] 
dist 14=[18.767245733881338684  ,68.253604345203448100  ] 
dist 15=[14.676807794565767959  ,67.561191935646579490  ] 
dist 16=[10.574559119350531183  ,64.867729058122537112  ] 
dist 17=[5.0924406746949821084 ,27.376899062543721173  ] 
dist 18=[.1325475792061127718 ,24.109727102213570902  ] 
dist 19=[-3.4264249279178614638 ,19.606160264239698596  ] 
dist 20=[-6.6896118306032609601 ,15.367270362764246665  ] 
dist 21=[-10.242029608413809771  ,5.7611583484060017350 ] 
dist 22=[-13.549578115223167618  ,3.7667959149813152707 ] 
dist 23=[-15.606513191764079255  ,2.6369939316491341425 ] 
dist 24=[-17.145121141800780893  ,1.1238900379220247327 ] 
dist 25=[-18.381684920404205169  ,-1.1465805152432441953 ] 
dist 26=[-19.328663577137736128  ,-1.9416520782546956096 ] 
dist 27=[-19.709934395609670270  ,-2.1091192605827046980 ] 
dist 28=[-19.833220681319892525  ,-4.6302646396969899984 ] 
dist 29=[-19.752716623674143682  ,-4.9332246731285318180 ] 
dist 30=[-16.664257387543719939  ,-5.3599832333738202556 ] 
dist 31=[-17.012954591965210415  ,-5.4001916352707814298 ] 
dist 32=[-17.053709616435351345  ,-5.3034027096205036894 ] 
dist 33=[-9.2176617597722448008 ,-4.0670880510629065973 ] 
dist 34=[-8.5654241435959440328 ,-2.4099592526247322468 ] 
dist 35=[-7.1634916149085497625 ,-1.1142613141201448232 ] 
dist 36=[-6.6601718385124439491 ,.1559298596409817566 ] 
dist 37=[-4.1544137947119028270 ,1.7124094237707084844 ] 
dist 38=[-3.6875156425491158514 ,3.1890208761903301993 ] 
dist 39=[-3.0859609012743164241 ,4.1412437592613626394 ] 
dist 40=[-2.8407939653235234893 ,4.8868712039679990677 ] 
dist 41=[-1.8215170200462670648 ,5.5401425230744373491 ] 
dist 42=[-1.5544801477187856176 ,6.0802450313405302819 ] 
dist 43=[-1.4711113430337698995 ,6.3748199072447282111 ] 
dist 44=[.1803192659943060473 ,6.5445804142950198842 ] 
dist 45=[.3820308715374768840 ,6.5871682851472662645 ] 
dist 46=[.846459759429223905  ,5.8384880669319476848 ] 
dist 47=[.913484433608716769  ,5.9886259682271362597 ] 
dist 48=[1.4307971550349997890 ,6.0140516854197917424 ] 
dist 49=[1.3864185628159356076 ,2.8171793616638655905 ] 
dist 50=[1.2777594580971302824 ,2.7291681073939675736 ] 
dist 51=[.8594311605322043679 ,2.5382565175064805920 ] 
dist 52=[.3299352384918291914 ,1.1903811421938814656 ] 
dist 53=[-.3753804791833493431 ,1.0771608937862314765 ] 
dist 54=[-1.0593358316565994553 ,.53185159296895752385] 
dist 55=[-1.5038359167934230217 ,.50263091070341378671] 
dist 56=[-1.8544871688344588088 ,.3328884535198654443 ] 
dist 57=[-2.1647206666886172768 ,.1464181561047756053 ] 
dist 58=[-2.4222888769875944801 ,.0793487902620008561 ] 
dist 59=[-2.5632029603459912457 ,.0681542521403139583 ] 
dist 60=[-2.6445757736941409570 ,-.3267797489113786161 ] 
dist 61=[-2.6650068211971542236 ,-.3722885880052914152 ] 
dist 62=[-1.1740468628889114405 ,-.4593717317933097441 ] 
dist 63=[-1.2091986947015337077 ,-.4775248884704478386 ] 
dist 64=[-1.2179830012084490570 ,-.4887322392016930951 ] 
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dist 153=[-.00163587590402863455,-.0002453321359284785 ] 
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dist 171=[9.40891410481326000000e-05,.0003563987549808071 ] 
dist 172=[.0001049909313370580 ,.0003679837613304037 ] 
dist 173=[.0001373817227536964 ,.0003702655348550643 ] 
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dist 175=[.00013663651589018313,.0003129953124313944 ] 
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dist 177=[9.85944689929486000000e-05,.00017840903579986258] 
dist 178=[8.30819028893870000000e-05,.00012361110993615892] 
dist 179=[6.53769751340808000000e-05,.00011275613659892297] 
dist 180=[3.00800940830359000000e-05,9.62184807103023900000e-05] 
dist 181=[-1.84829327465737000000e-05,9.14360728620576700000e-05] 
dist 182=[-6.59931507217136000000e-05,3.82136280023818000000e-05] 
dist 183=[-9.71027213156282000000e-05,3.13442700677316000000e-05] 
dist 184=[-.0001218024649083030 ,3.01358062746496000000e-05] 
dist 185=[-.0001438096683954934 ,-2.00967681483545000000e-05] 
dist 186=[-.0001621010791447206 ,-2.56197325991678000000e-05] 
dist 187=[-.0001720163178944214 ,-3.59254666816799000000e-05] 
dist 188=[-.0001775857163618859 ,-3.80570121144002000000e-05] 
dist 189=[-.0001786089729440551 ,-4.23681598141766000000e-05] 
dist 190=[-7.70324654593319000000e-05,-3.50817784919262200000e-05] 
dist 191=[-7.85067555113449000000e-05,-2.69360371950124000000e-05] 
dist 192=[-7.87021837113215000000e-05,-1.91023380989963000000e-05] 
dist 193=[-5.75795273747568000000e-05,-9.78373118092300000000e-06] 
dist 194=[-5.50470717910262000000e-05,-3.66303475267500000000e-07] 
dist 195=[-4.86700928353017000000e-05,7.86186898759600000000e-06] 
dist 196=[-4.69603799640338000000e-05,1.66944859807297000000e-05] 
dist 197=[-3.63009890753584400000e-05,2.85180932692592000000e-05] 
dist 198=[-3.40859157364000000000e-05,3.99370635616865000000e-05] 
dist 199=[-2.97363606427331800000e-05,4.71603551298758000000e-05] 
dist 200=[-2.85344860094394800000e-05,5.26111995985802000000e-05] 
dist 201=[-1.07089344117493040000e-05,5.69786302162795000000e-05] 
dist 202=[-8.11272175228684800000e-06,6.02578055833889000000e-05] 
dist 203=[-3.02311400402591000000e-06,6.13791280714789000000e-05] 
dist 204=[-1.78862779206198000000e-06,6.16720918551660000000e-05] 
dist 205=[2.01213848421170000000e-06,6.16545979503475000000e-05] 
dist 206=[2.70869984385596000000e-06,5.61827311055183000000e-05] 
dist 207=[2.54150941692795000000e-06,5.49084235724648000000e-05] 
dist 208=[1.15525511964227500000e-06,5.09972385480034000000e-05] 
dist 209=[-5.22541896626870000000e-07,1.65022367154182600000e-05] 
dist 210=[-1.84968571230410000000e-06,1.18103334087920100000e-05] 
dist 211=[-3.15674769938989000000e-06,1.08702159151207000000e-05] 
dist 212=[-4.75503454422352000000e-06,9.28015484828230000000e-06] 
dist 213=[-6.39341303011806000000e-06,8.86632746231630000000e-06] 
dist 214=[-8.66044506847145000000e-06,3.47362753378498000000e-06] 
dist 215=[-1.14250418875843000000e-05,2.84057116057643000000e-06] 
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dist 217=[-1.54979794426048000000e-05,-1.48712288281685000000e-06] 
dist 218=[-1.70493318862649000000e-05,-1.98129446838393000000e-06] 
dist 219=[-1.78386346509541000000e-05,-2.91097473861113000000e-06] 
dist 220=[-1.82240705022648000000e-05,-3.10709042581662000000e-06] 
dist 221=[-1.82785405506661000000e-05,-3.33220385764333700000e-06] 
dist 222=[-6.89124681531740000000e-06,-2.48736499573294000000e-06] 
dist 223=[-7.05135454664220000000e-06,-1.84137257477992000000e-06] 
dist 224=[-7.06537229629590000000e-06,-1.22570166683147000000e-06] 
dist 225=[-5.55780601059460000000e-06,-5.01321049620300000000e-07] 
dist 226=[-5.35876090762490000000e-06,2.26327252225700000000e-07] 
dist 227=[-4.80583024659860000000e-06,8.55092163427500000000e-07] 
dist 228=[-4.68486541509520000000e-06,1.52409543442630000000e-06] 
dist 229=[-3.60590531942800000000e-06,2.41192660434850000000e-06] 
dist 230=[-3.37897968239420000000e-06,3.26561138348520000000e-06] 
dist 231=[-3.04080120777070000000e-06,3.79880859059500000000e-06] 
dist 232=[-2.93432748109510000000e-06,4.19320838223140000000e-06] 
dist 233=[-7.06452701079120000000e-07,4.49472604836890000000e-06] 
dist 234=[-4.17645494229440000000e-07,4.71368718844430000000e-06] 
dist 235=[2.25119834614140000000e-07,4.77962364083750000000e-06] 
dist 236=[3.53320737579280000000e-07,4.78708923713440000000e-06] 
dist 237=[4.96645661647219000000e-07,4.77342284109020000000e-06] 
dist 238=[4.31153690960233800000e-07,4.19737049543083000000e-06] 
dist 239=[2.86885882191337400000e-07,4.07489206368747000000e-06] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 2, 0, 2, 1, 2] 
dist 0=[83.873062463601462139  ,83.873062463601462139  ] 
dist 1=[81.862110043061719699  ,84.959553970708057397  ] 
dist 2=[79.280830039910848412  ,85.576579928728036042  ] 
dist 3=[75.918342798280042100  ,85.713999315928995652  ] 
dist 4=[71.340857248015446488  ,85.557803299417241696  ] 
dist 5=[63.910928763833323177  ,85.395851301661489039  ] 
dist 6=[56.274486557540261039  ,84.433704687277147629  ] 
dist 7=[50.872986289874614889  ,84.217907007898962490  ] 
dist 8=[46.077122602340958474  ,80.522299833897160479  ] 
dist 9=[40.857895622659861629  ,79.639747562369460270  ] 
dist 10=[35.770471049882069055  ,78.507838501543084904  ] 
dist 11=[31.500802278856723596  ,78.027163216811924362  ] 
dist 12=[27.015839298831484752  ,77.148355423916505192  ] 
dist 13=[21.069568300345010077  ,76.830942824570640814  ] 
dist 14=[15.241014452537083776  ,76.354893183299831326  ] 
dist 15=[11.225848222681065039  ,73.038354133872142215  ] 
dist 16=[7.7737789916290382987 ,30.899692042894955677  ] 
dist 17=[4.1921200635017879024 ,27.269815266564998780  ] 
dist 18=[.8053307820992059006 ,18.760032621265948048  ] 
dist 19=[-1.8691989867677014048 ,17.541057368138515996  ] 
dist 20=[-5.2012648593508206768 ,8.3877717945912835589 ] 
dist 21=[-9.1992368454076974788 ,8.1412007435769893572 ] 
dist 22=[-11.731223370746767554  ,2.0427724882766656751 ] 
dist 23=[-13.673326364042885740  ,1.6397552508356892584 ] 
dist 24=[-15.318345634762948297  ,-.2066137825112878910 ] 
dist 25=[-16.649384620108027296  ,-.4158732966746572625 ] 
dist 26=[-17.339469638025157748  ,-1.9388927915700028093 ] 
dist 27=[-17.696968773844414718  ,-2.1750207314508382502 ] 
dist 28=[-17.719696027404722553  ,-2.5524325048737088169 ] 
dist 29=[-18.259869892737794833  ,-2.6246029119209419199 ] 
dist 30=[-18.689994520626701102  ,-3.2922887391155647999 ] 
dist 31=[-18.796879604148645191  ,-3.3733658622191006547 ] 
dist 32=[-9.7666700473243356770 ,-3.3691012194566683095 ] 
dist 33=[-9.0335421123428324756 ,-2.3631196537652887181 ] 
dist 34=[-7.2224263146333868456 ,-1.2703569167543515701 ] 
dist 35=[-6.9076509371255192426 ,-.1865732571795353191 ] 
dist 36=[-4.2100477822063851863 ,1.1575159720500842063 ] 
dist 37=[-3.9597757391665461242 ,2.4360552190509739474 ] 
dist 38=[-2.9562683186262008639 ,3.2589874668490223037 ] 
dist 39=[-2.7532510153624781922 ,3.9009744533839857190 ] 
dist 40=[-1.1608361321670668579 ,4.4585675227243720869 ] 
dist 41=[-1.0841301337153277169 ,4.9155307917306106394 ] 
dist 42=[-.5202594543725951724 ,5.1565280552946216637 ] 
dist 43=[-.4207594670974876189 ,5.6406955442406399853 ] 
dist 44=[-.2502373129655715922 ,6.2998790237902959138 ] 
dist 45=[-.2128171945462721126 ,6.6597545670250510151 ] 
dist 46=[.3432796902127727294 ,6.8671018943401165758 ] 
dist 47=[.41741544823725271328,6.9185494723146312268 ] 
dist 48=[.4430797309693254389 ,2.2707884040483921232 ] 
dist 49=[.3846228617792604391 ,1.7507773547334331632 ] 
dist 50=[.2988674691341505791 ,1.7675163040444684652 ] 
dist 51=[.0031388562643119844 ,1.8038338519003823045 ] 
dist 52=[-.5768676581721427873 ,1.8182019273163654148 ] 
dist 53=[-1.1379049044498278515 ,1.8158891548981499769 ] 
dist 54=[-1.4992116011201972787 ,.4193476207123583787 ] 
dist 55=[-1.7803082224818697872 ,.3919120719425469005 ] 
dist 56=[-2.0219860993750919570 ,.16815496576809605546] 
dist 57=[-2.2173995163200131500 ,.1540693280541913969 ] 
dist 58=[-2.3142793348170405254 ,.01996395549802202005] 
dist 59=[-2.3632528687590675079 ,-.00321446303897369738] 
dist 60=[-2.3678860057276997937 ,-.0336187605344982274 ] 
dist 61=[-1.2664580469220341060 ,-.0385339231562581013 ] 
dist 62=[-1.2937114300828044069 ,-.1834522752282880333 ] 
dist 63=[-1.2972687170970868024 ,-.2001028782507657663 ] 
dist 64=[-.85054125416794362405,-.2295248665545856031 ] 
dist 65=[-.8078172118072343664 ,-.1952791049281551242 ] 
dist 66=[-.6927364133914263520 ,-.1210972464738520781 ] 
dist 67=[-.6735256049316853801 ,-.0447017447828524797 ] 
dist 68=[-.4685021346139931270 ,.0536218632990504892 ] 
dist 69=[-.4280601953196382178 ,.1482221272071839815 ] 
dist 70=[-.3775965124886442966 ,.209808721122500442  ] 
dist 71=[-.3614867138893568173 ,.258432293774784283  ] 
dist 72=[-.10205592180275275157,.301430090503741110  ] 
dist 73=[-.09677932310368493908,.38038451567240619042] 
dist 74=[-.05326557613799329903,.4441861249367297393 ] 
dist 75=[-.04532229335136170071,.4970386313762974438 ] 
dist 76=[-.03292356598941401453,.5385948184520264902 ] 
dist 77=[-.02975395383682538736,.5574240156679450437 ] 
dist 78=[.02336670224421525992,.5660514572632289128 ] 
dist 79=[0                     ,.5669925164671593126 ] 
dist 80=[.04304499073659237690,.1674148316464721126 ] 
dist 81=[.04579626813874205920,.1407014154026436248 ] 
dist 82=[.05217417088276959980,.1126307736202274614 ] 
dist 83=[.0221053852959611738 ,.1182351003848046790 ] 
dist 84=[-.0226818572001677213 ,.1214662956402141609 ] 
dist 85=[-.0663335664183815268 ,.1222770585217963636 ] 
dist 86=[-.0947930160603688810 ,.0358967313052633843 ] 
dist 87=[-.1172840139204073618 ,.0327604101795223551 ] 
dist 88=[-.1371821509527147235 ,.01998151009600300375] 
dist 89=[-.1536497916473632867 ,.01884446502822568719] 
dist 90=[-.1624872505088630270 ,.00743058139160479174] 
dist 91=[-.1673426318593108697 ,.00537975415963107224] 
dist 92=[-.1682522025557901339 ,.00275589648458447250] 
dist 93=[-.110077731282584155  ,.00223835922710532363] 
dist 94=[-.112236610805477477  ,-.01247746491646372516] 
dist 95=[-.112591948828557408  ,-.0091078604218607604 ] 
dist 96=[-.0754247453601330364 ,.0006452405711299930 ] 
dist 97=[-.0715732944345040107 ,.0104282555264938216 ] 
dist 98=[-.0618444434245451718 ,.0188701286983074786 ] 
dist 99=[-.0596021159749845601 ,.0278490227088301649 ] 
dist 100=[-.04370608104790565350,.0397716969262666716 ] 
dist 101=[-.04052124921913128158,.0512619251528079969 ] 
dist 102=[-.03471906310291243540,.0585209632623634106 ] 
dist 103=[-.03327078751965118734,.0639950694230103339 ] 
dist 104=[-.01185464937583036707,.0683827151505675032 ] 
dist 105=[-.01147907987359643070,.0716849496013775127 ] 
dist 106=[-.00744283617898191984,.0728400170901425073 ] 
dist 107=[-.00666780724052386246,.0730459423111060290 ] 
dist 108=[-.00572721733774539382,.0725819884366696801 ] 
dist 109=[-.00548165890943947217,.0678596294482025607 ] 
dist 110=[.00137355059265126633,.0665233583942170267 ] 
dist 111=[.00218921730400760659,.0626388963353453141 ] 
dist 112=[.00395460392920051320,.0163299581480507113 ] 
dist 113=[.0016895081121667552 ,.0118993237450890902 ] 
dist 114=[-.0008916427887517691 ,.0110088951088613258 ] 
dist 115=[-.0036679218682835112 ,.00959835458402866959] 
dist 116=[-.0073932862970437109 ,.00981290150441077551] 
dist 117=[-.0109993808190724251 ,.00983927636250061401] 
dist 118=[-.0133013235073700078 ,.00307540524771859803] 
dist 119=[-.0150639847777201909 ,.00280094113652777054] 
dist 120=[-.0165242800395490532 ,.00210203436092007472] 
dist 121=[-.0176603145295756019 ,.00200159130389594518] 
dist 122=[-.0181327362145533983 ,.00091086896850729835] 
dist 123=[-.0183121791256583054 ,.00071126511106232674] 
dist 124=[-.0182819828210299213 ,.00047226279517178422] 
dist 125=[-.00283812037811598835,.00043182239680638756] 
dist 126=[-.00264428581063635315,-.00113399804858328434] 
dist 127=[-.00212748844046662460,-.00131471068336417613] 
dist 128=[-.00205317946334242578,-.00158011962033365179] 
dist 129=[-.00202731441666654098,-.00112955202509509480] 
dist 130=[-.00223362720394978690,-.0007459222258569812 ] 
dist 131=[-.00234644675517267171,-.0003424068883479783 ] 
dist 132=[-.00241146964716618500,.0001873951784159794 ] 
dist 133=[-.00242744696058708461,.0007002083676434988 ] 
dist 134=[-.00134671172722863465,.0010361593734822070 ] 
dist 135=[-.00125707796173575753,.0013032055295055049 ] 
dist 136=[-.00103071678046899721,.0015418378578314498 ] 
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dist 138=[-.00063111346646712985,.0018499924736618472 ] 
dist 139=[-.00056276230674570359,.0019131754264116565 ] 
dist 140=[-.00045871640920610537,.0019290511209636138 ] 
dist 141=[-.00042981397397890874,.00117802235146182063] 
dist 142=[9.85696091688518300000e-05,.00111436510919362035] 
dist 143=[.00016666555265824700,.00094766691090734972] 
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dist 146=[.00037292025371373784,.00097782360500021335] 
dist 147=[.00019090794871630474,.00103464269321367793] 
dist 148=[-5.95914126734866100000e-05,.00106737203704521749] 
dist 149=[-.00030474011522428433,.00107533236096715514] 
dist 150=[-.00046547310869468947,.00028759861837390640] 
dist 151=[-.0005933399182171670 ,.00026476379548695828] 
dist 152=[-.0007077196932852491 ,.00020560029401019168] 
dist 153=[-.0008031271260678077 ,.00019707513678889296] 
dist 154=[-.0008555037639172001 ,.00010121537082427236] 
dist 155=[-.0008858174521089934 ,8.33853740624159130000e-05] 
dist 156=[-.0008934345576238378 ,6.25657100133283340000e-05] 
dist 157=[-.00024774826790469112,5.89400622418964200000e-05] 
dist 158=[-.00023157064469764415,-8.26596915855140100000e-05] 
dist 159=[-.00018833847604251071,-9.87367230894918100000e-05] 
dist 160=[-.00018188359099537211,-.00012974081094561083] 
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dist 162=[-.00020615012303588960,-6.77750747478728200000e-05] 
dist 163=[-.00021463567228702892,-3.19091073774227800000e-05] 
dist 164=[-.00021884451983682984,1.56490956234292100000e-05] 
dist 165=[-.00021975803468154020,6.17387402962987700000e-05] 
dist 166=[-.00014787090985377619,9.17642477317547800000e-05] 
dist 167=[-.00014076730271413398,.00011543151521567883] 
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dist 170=[-8.30579186564978800000e-05,.00016214870370649204] 
dist 171=[-7.60565017343933600000e-05,.00016681963800419735] 
dist 172=[-6.74921574331479600000e-05,.00016760942295752051] 
dist 173=[-6.47507869516408200000e-05,.00011442057022956147] 
dist 174=[1.78016791577426000000e-06,.00010941098633303578] 
dist 175=[9.86142700974148000000e-06,9.52404246913978100000e-05] 
dist 176=[2.20106291556432550000e-05,9.29620743110829000000e-05] 
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dist 178=[2.20216693598002123000e-05,9.76394009875121030000e-05] 
dist 179=[1.46730220540431600000e-05,.00010079823475597112] 
dist 180=[-5.46804544763235000000e-06,.00010219112388713714] 
dist 181=[-2.51160350056870600000e-05,.00010211927110807556] 
dist 182=[-3.78767876680632100000e-05,2.78395121527069700000e-05] 
dist 183=[-4.78894377597121000000e-05,2.56465961658109200000e-05] 
dist 184=[-5.66041300501019500000e-05,1.99604628785589900000e-05] 
dist 185=[-6.36981099814971300000e-05,1.91221692609863800000e-05] 
dist 186=[-6.72626659566738400000e-05,9.88295908684427000000e-06] 
dist 187=[-6.91593755156922100000e-05,8.15995302290122000000e-06] 
dist 188=[-6.96169071797753600000e-05,6.09630660324450000000e-06] 
dist 189=[-2.33891142000089700000e-05,5.68661720858770000000e-06] 
dist 190=[-2.18765134831110600000e-05,-8.47195395760590000000e-06] 
dist 191=[-1.77954410884509100000e-05,-1.01286252798894000000e-05] 
dist 192=[-1.72084758267589100000e-05,-1.29136885691555500000e-05] 
dist 193=[-1.75574948194749000000e-05,-9.21536056475858000000e-06] 
dist 194=[-1.94572195481160000000e-05,-6.02734802216499000000e-06] 
dist 195=[-2.04539916852978000000e-05,-2.64197136584914000000e-06] 
dist 196=[-2.09706566251780000000e-05,1.84216803268214000000e-06] 
dist 197=[-2.10666069015157000000e-05,6.18652611073856000000e-06] 
dist 198=[-1.27794146898952000000e-05,9.01598520946511000000e-06] 
dist 199=[-1.20392853154594000000e-05,1.12447033457185000000e-05] 
dist 200=[-1.01504488196659500000e-05,1.31990098090551000000e-05] 
dist 201=[-9.77210382973184000000e-06,1.47999824091980100000e-05] 
dist 202=[-6.67959328404000000000e-06,1.56229208642650200000e-05] 
dist 203=[-6.07377898721355000000e-06,1.60519499032079000000e-05] 
dist 204=[-5.09932019108530000000e-06,1.61171769236625200000e-05] 
dist 205=[-4.83738987931250000000e-06,1.06483485196184100000e-05] 
dist 206=[3.19491090662100000000e-08,1.01269262283205000000e-05] 
dist 207=[6.74303413415980000000e-07,8.76526705066396000000e-06] 
dist 208=[1.57885874344087000000e-06,8.47348412349766000000e-06] 
dist 209=[1.77026473011720000000e-06,9.09041886211140000000e-06] 
dist 210=[1.44028751135148000000e-06,1.00257210593571000000e-05] 
dist 211=[-1.34572226225090000000e-07,1.05106539002160000000e-05] 
dist 212=[-2.29134340714510000000e-06,1.07551411807533000000e-05] 
dist 213=[-4.39536757560030000000e-06,1.07985579870810000000e-05] 
dist 214=[-5.76044378218818000000e-06,2.13256703396454000000e-06] 
dist 215=[-6.82959191788723000000e-06,1.94251690452694000000e-06] 
dist 216=[-7.75632038666235000000e-06,1.47534785372983000000e-06] 
dist 217=[-8.50750866636074000000e-06,1.38974962033706000000e-06] 
dist 218=[-8.87828903513786000000e-06,7.00881466667630000000e-07] 
dist 219=[-9.05711298420453000000e-06,5.74086504467900000000e-07] 
dist 220=[-9.07066597017554000000e-06,3.65650810109740000000e-07] 
dist 221=[-2.08456351645322700000e-06,3.14882036553820000000e-07] 
dist 222=[-1.95285268997345100000e-06,-5.13665654288060000000e-07] 
dist 223=[-1.59863213247763000000e-06,-6.23706684783570000000e-07] 
dist 224=[-1.66577853932727000000e-06,-6.68955691602630000000e-07] 
dist 225=[-1.82360784937644000000e-06,-3.34874507561910000000e-07] 
dist 226=[-1.94469110448123000000e-06,-4.15387080517900000000e-08] 
dist 227=[-2.00840812255621000000e-06,2.74471092433930000000e-07] 
dist 228=[-2.04170745251711000000e-06,6.98803053721250000000e-07] 
dist 229=[-2.04171467067932000000e-06,1.10899260234363000000e-06] 
dist 230=[-1.51981646630291850000e-06,1.36876005076026000000e-06] 
dist 231=[-1.45053765140170700000e-06,1.56505536400766000000e-06] 
dist 232=[-1.28461456039487000000e-06,1.72274671115085000000e-06] 
dist 233=[-1.23376343821915000000e-06,1.84410793362554000000e-06] 
dist 234=[-9.78413474769610000000e-07,1.89585424740406000000e-06] 
dist 235=[-9.24887939972200000000e-07,1.91585389472395000000e-06] 
dist 236=[-8.04729344764690000000e-07,1.91092307240988000000e-06] 
dist 237=[-7.67822821175970000000e-07,1.69980865603155000000e-06] 
dist 238=[-3.88818821392250000000e-07,1.65782288910625000000e-06] 
dist 239=[-3.27486826102320000000e-07,1.54177713326352000000e-06] 
dist 240=[-2.14864078009900000000e-07,1.50491193797155000000e-06] 
dist 241=[-1.88551194963410000000e-07,1.26508543830007000000e-06] 
dist 242=[-1.16683562331230000000e-07,1.21064568521033000000e-06] 
dist 243=[-1.08165997895410000000e-07,1.10809335135472000000e-06] 
dist 244=[-1.75208879596300000000e-07,9.51235461695090000000e-07] 
dist 245=[-3.45320232336714000000e-07,5.27163894532830000000e-07] 
dist 246=[-4.54840826363744000000e-07,-3.94922043285820000000e-08] 
dist 247=[-5.39652238108403000000e-07,-9.32728905169130000000e-08] 
dist 248=[-6.11468777072280000000e-07,-1.05919725479177000000e-07] 
dist 249=[-6.68427730839717000000e-07,-1.14668339192426700000e-07] 
dist 250=[-6.94134375897380000000e-07,-9.88536841208696000000e-08] 
dist 251=[-7.06186664796720000000e-07,-6.54734443927002200000e-08] 

8 phat 4 dirichlet min maxes function [2, 1, 0, 2, 0, 0, 0, 1] 
dist 0=[73.759985906428686363  ,73.759985906428686363  ] 
dist 1=[71.595188930700761649  ,75.102781811215184797  ] 
dist 2=[67.743419746285157957  ,75.674322095719864367  ] 
dist 3=[63.659500655062012125  ,75.959752422168835725  ] 
dist 4=[60.568408433313173106  ,76.160721158557335996  ] 
dist 5=[57.614365150095209015  ,76.435105502892409159  ] 
dist 6=[54.077658249262027860  ,76.621969873860355014  ] 
dist 7=[50.440477398083941141  ,76.666994916679474367  ] 
dist 8=[47.085693926363019737  ,75.780277631322272847  ] 
dist 9=[43.298204470552757295  ,69.151623216960631671  ] 
dist 10=[37.934583944114766934  ,68.027840429531802785  ] 
dist 11=[32.519793583064968581  ,66.001499852475199514  ] 
dist 12=[28.528147564693714588  ,65.454573369867083583  ] 
dist 13=[24.818306296105190643  ,63.516476924419831542  ] 
dist 14=[20.527891013408145545  ,62.939573907005788369  ] 
dist 15=[16.197341898326168133  ,62.169960124416738746  ] 
dist 16=[12.240949325543646231  ,61.169798788227214265  ] 
dist 17=[6.8860680254807703045 ,25.963341096333906524  ] 
dist 18=[1.718820967849963852  ,25.722871968534109610  ] 
dist 19=[-3.679199197034226441  ,14.760161289280972061  ] 
dist 20=[-7.451786982636453036  ,13.734422079639812449  ] 
dist 21=[-10.456392863851628229  ,4.564842799692064597  ] 
dist 22=[-13.197977149338910024  ,4.0052691610417902612 ] 
dist 23=[-15.562989975793427612  ,.902955941975731098  ] 
dist 24=[-17.138566512503771111  ,.546454111003824435  ] 
dist 25=[-18.437374309651879825  ,-1.8809784370727575217 ] 
dist 26=[-19.404538451300033291  ,-2.0332095602372788584 ] 
dist 27=[-20.084024277924072333  ,-5.7511609987392784516 ] 
dist 28=[-20.248749496588040133  ,-6.1760517265956032281 ] 
dist 29=[-20.202565635483176250  ,-6.8630688806982536734 ] 
dist 30=[-19.265396923807306993  ,-6.9949111739271605668 ] 
dist 31=[-15.978033222735152308  ,-6.9727097593407350491 ] 
dist 32=[-16.011833720999812938  ,-6.6759547718520861635 ] 
dist 33=[-8.5666376222709981052 ,-5.7609525416835059225 ] 
dist 34=[-8.6002037147571878896 ,-3.897160564457243104  ] 
dist 35=[-6.2324753228086769040 ,-2.129892410657223958  ] 
dist 36=[-5.9568685276438527877 ,-.749177922594732132  ] 
dist 37=[-3.6565610099348645987 ,.603547062133377372  ] 
dist 38=[-3.2310767751933098618 ,2.260270967760217067  ] 
dist 39=[-2.5710172606997584027 ,3.828007026738478279  ] 
dist 40=[-2.3982418429224178820 ,4.826426104618301637  ] 
dist 41=[-.87577340274710802924,5.594077708016755612  ] 
dist 42=[-.78827407283573746788,6.242162612982618327  ] 
dist 43=[.64921212451279638898,6.760322222434292187  ] 
dist 44=[.83338563993592121056,7.010170756385896404  ] 
dist 45=[1.1783141464746432097 ,7.128566916891302140  ] 
dist 46=[1.2518090571798894663 ,7.133034784339046022  ] 
dist 47=[1.4203579168673361438 ,6.291195484767600120  ] 
dist 48=[1.0568063164671131107 ,6.317476104878873372  ] 
dist 49=[.4817719820015514904 ,3.2662088417108910345 ] 
dist 50=[.0583943267134174579 ,3.2670161874323153953 ] 
dist 51=[-.3300530675625680787 ,2.1032517196021796105 ] 
dist 52=[-.766363073086938704  ,1.9059551165043310085 ] 
dist 53=[-1.194539193505594192  ,1.5815971862142922313 ] 
dist 54=[-1.550780712645576805  ,1.4989293613158591913 ] 
dist 55=[-2.239401238046921121  ,.29669227580672642375] 
dist 56=[-2.694354129557783564  ,.27724856305887569484] 
dist 57=[-3.040417123179027273  ,.09705622878889446003] 
dist 58=[-3.324556891339021959  ,.08377856384819914585] 
dist 59=[-3.544770259916089690  ,-.30932922505521948207] 
dist 60=[-3.636284533228751504  ,-.35518159052239671175] 
dist 61=[-3.673031834578138227  ,-.44237625832501775558] 
dist 62=[-3.675008733505005252  ,-.46048901416659915336] 
dist 63=[-1.0523052245735891800 ,-.49943454871993712504] 
dist 64=[-1.0592851459341676414 ,-.49129236630592046888] 
dist 65=[-.6548697239987096952 ,-.41878957449859280563] 
dist 66=[-.65702464687390705193,-.3079760578502665101 ] 
dist 67=[-.46488371616763544004,-.2003796919105963747 ] 
dist 68=[-.44729189405393478065,-.1127229586116031411 ] 
dist 69=[-.30697647068986269385,-.0237289848720081848 ] 
dist 70=[-.29746367802185466667,.0892344092472870255 ] 
dist 71=[-.21700103540774174222,.1975377660839418729 ] 
dist 72=[-.2043021652914411079 ,.2679905536347191834 ] 
dist 73=[-.15030457730350679742,.3236189552576451548 ] 
dist 74=[-.14416947591339319489,.3728943789843633959 ] 
dist 75=[.03281274320678104768,.4138257635837897238 ] 
dist 76=[.05382028620456452434,.4362275634833386863 ] 
dist 77=[.09607727392462219059,.4491670195207929525 ] 
dist 78=[.10316858108592126945,.4524161843721902554 ] 
dist 79=[.12156782758884575211,.43925545226346834669] 
dist 80=[.12170896145047620159,.44231486074611020302] 
dist 81=[.11513175569202551567,.24507176410654281932] 
dist 82=[.09779177037488822930,.24589768538284576212] 
dist 83=[.07859576529705403639,.12430241950853839489] 
dist 84=[.06361960506802276620,.11154197664144704791] 
dist 85=[.03016742274607745083,.09228710233500074988] 
dist 86=[-.02256043791003058010,.08685605677700477662] 
dist 87=[-.07390122223672104275,.04717687762402092900] 
dist 88=[-.1073996003488701495 ,.04290295581948352615] 
dist 89=[-.1339253993827132929 ,.03491356154030546979] 
dist 90=[-.1575105889628832766 ,.03294518088340481418] 
dist 91=[-.1771334821865545197 ,.00373589892461853343] 
dist 92=[-.1878858516939724562 ,-.00040814374468766252] 
dist 93=[-.1941013464322302329 ,-.00797051383189788826] 
dist 94=[-.1956625873600528958 ,-.00960600254501063547] 
dist 95=[-.09523950420961574835,-.01332933433763585077] 
dist 96=[-.09567731393826495872,-.01302834791852530313] 
dist 97=[-.09093326654495634575,-.01101455650240966537] 
dist 98=[-.08847112828228593715,-.00617329583625108828] 
dist 99=[-.05233326328759378660,-.00086630478197583149] 
dist 100=[-.05122275503515714175,.00300211908534589258] 
dist 101=[-.03671695514785309968,.00651361878545498933] 
dist 102=[-.03378785298712242769,.01040177121963347280] 
dist 103=[-.03071966680135235552,.01566496601714136613] 
dist 104=[-.03002556153414831136,.02190830679673061970] 
dist 105=[-.01182745318811912758,.02681081956972852008] 
dist 106=[-.01112137943651473429,.03109634774884712523] 
dist 107=[.00191173740636422714,.03460734764403044341] 
dist 108=[.00359031902544094863,.03642686631540911715] 
dist 109=[.00692958382645242703,.03736970404118944711] 
dist 110=[.00688067810469331334,.03753247714187462145] 
dist 111=[.00444652182162240458,.03738123624954029892] 
dist 112=[0                     ,.03736339449580075469] 
dist 113=[.00981843156485062838,.0256313243207832926 ] 
dist 114=[.00847913151320321234,.0258355702326013206 ] 
dist 115=[.00695236717213740079,.01327796969436918434] 
dist 116=[.00555687682323648935,.01208076992560214949] 
dist 117=[.00244732182816587041,.01068985025411824625] 
dist 118=[-.00175011353555281353,.01031036769110300261] 
dist 119=[-.00582876438167342000,.00257906188153520484] 
dist 120=[-.00846582140563885376,.00215882180033850365] 
dist 121=[-.01052482465267439728,.00165199179045831367] 
dist 122=[-.01230297685035007507,.00154740610326147698] 
dist 123=[-.01374580847360703312,-.00190618626239009660] 
dist 124=[-.01447021981606840776,-.00231145386427472099] 
dist 125=[-.01485371092884748721,-.00312053311745079564] 
dist 126=[-.01493963950149145605,-.00330176692189489472] 
dist 127=[-.00493368482648790504,-.00378894968594709038] 
dist 128=[-.0048901517231615168 ,-.00379755107349722809] 
dist 129=[-.0050136319085949026 ,-.00347002848734634368] 
dist 130=[-.0050345142068376777 ,-.00266109046431813173] 
dist 131=[-.00325463032507574730,-.00185967919440945231] 
dist 132=[-.00309250762781620736,-.00118339578422881155] 
dist 133=[-.00264879073030512308,-.00047696221290162128] 
dist 134=[-.00257838844808718394,.00044461153638345735] 
dist 135=[-.00176752219355077952,.00133506429447674804] 
dist 136=[-.00160708925111703445,.00191770958396300741] 
dist 137=[-.00142019697835844329,.00238030533363850848] 
dist 138=[-.00136900057791067240,.00279301134764809290] 
dist 139=[.00016783310580530206,.00313683161472225563] 
dist 140=[.00035103239873821811,.00332528126635216420] 
dist 141=[.00068448459572193075,.00343408057087420101] 
dist 142=[.00075100059619069379,.00346090373161575242] 
dist 143=[.00094213116216745644,.00207734845251978939] 
dist 144=[.00096024096128715662,.00196044924597709144] 
dist 145=[.00092280483141592821,.0020087951228110873 ] 
dist 146=[.00080047784598640135,.0020197896643609605 ] 
dist 147=[.00066151563898174031,.00108636939148906547] 
dist 148=[.00055786759627287033,.00098585746744055968] 
dist 149=[.00030588365564665145,.00083510421976404231] 
dist 150=[-.00013389756982011671,.00079119621739210501] 
dist 151=[-.00056382201097169266,.00025262047867368000] 
dist 152=[-.00084539179101996979,.00021240323179612022] 
dist 153=[-.00106913880153647018,.00016636227262690570] 
dist 154=[-.00126897346322903072,.00015838427996378099] 
dist 155=[-.00143552292872405664,-.0001859356666031991 ] 
dist 156=[-.00152681664176329877,-.0002257180361862684 ] 
dist 157=[-.00157950127890083523,-.0003062749242180705 ] 
dist 158=[-.00159240739948927259,-.0003233261283008769 ] 
dist 159=[-.00044193386083990515,-.00037585973517167643] 
dist 160=[-.0004566268258909600 ,-.00036788211436607054] 
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dist 162=[-.0004744545789948764 ,-.00023560309750547410] 
dist 163=[-.00028366299877287207,-.00016444696376285321] 
dist 164=[-.00026747419896827556,-.00010343621448843323] 
dist 165=[-.00022555189111012615,-3.88911344370116100000e-05] 
dist 166=[-.00021753434009059778,4.63410235080260600000e-05] 
dist 167=[-.00014730688193328071,.00012872040484410374] 
dist 168=[-.00013354851778360169,.00018191835731297840] 
dist 169=[-.00011276851027968587,.00022334215872113552] 
dist 170=[-.00010677308546925166,.00025887127652082232] 
dist 171=[7.28029646886920800000e-06,.00028748526727025802] 
dist 172=[2.20193304153939960000e-05,.00030139358535174300] 
dist 173=[5.11131894434481600000e-05,.00030850407173502395] 
dist 174=[5.79361995278807300000e-05,.00031006597021412224] 
dist 175=[7.81679140294517900000e-05,.00021976777625060803] 
dist 176=[8.07269084548797300000e-05,.0002120366562766329 ] 
dist 177=[7.79109617415474700000e-05,.0002191005300854560 ] 
dist 178=[6.70759357322578260000e-05,.0002206847673354760 ] 
dist 179=[4.54911436517171210000e-05,.00012951363771592685] 
dist 180=[2.11450505454875650000e-05,.00011929122748166629] 
dist 181=[-5.19004646166827000000e-06,.00010706329924031996] 
dist 182=[-4.07083745135761000000e-05,.00010301876537429491] 
dist 183=[-7.51498783691818300000e-05,2.47495838923004100000e-05] 
dist 184=[-9.72020408681552650000e-05,2.11870287269879900000e-05] 
dist 185=[-.00011415600411177872,1.71621935820033000000e-05] 
dist 186=[-.00012831301541632853,1.64424057821086100000e-05] 
dist 187=[-.00013947074724743586,-8.93027407521242000000e-06] 
dist 188=[-.00014449029388613969,-1.16882122181466000000e-05] 
dist 189=[-.00014678827016927381,-1.49369728821060461300e-05] 
dist 190=[-.00014711672712837570,0                     ] 
dist 191=[-4.88672482655888000000e-05,-1.73894437544310430000e-05] 
dist 192=[-5.06246675533368000000e-05,-1.57915336929382300000e-05] 
dist 193=[-5.15140132756503000000e-05,-1.26605144841490800000e-05] 
dist 194=[-5.15242615957870000000e-05,-6.67387463160056000000e-06] 
dist 195=[-4.22063045455381000000e-05,-2.95477781655700000000e-07] 
dist 196=[-4.08024083361951000000e-05,4.39455457464380000000e-06] 
dist 197=[-3.69634968094852000000e-05,8.68683355074700000000e-06] 
dist 198=[-3.60233064872042000000e-05,1.71832666608239000000e-05] 
dist 199=[-2.85873407967519000000e-05,2.58836143890814000000e-05] 
dist 200=[-2.69962863531108000000e-05,3.12880054282464000000e-05] 
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dist 203=[-8.08433410353245000000e-06,4.04598635873320000000e-05] 
dist 204=[-6.01304914014519000000e-06,4.14891116140685000000e-05] 
dist 205=[-1.36526086880945000000e-06,4.18236070159718000000e-05] 
dist 206=[-4.05519046894020000000e-07,4.17822519820190000000e-05] 
dist 207=[3.82896762693715590000e-06,3.43242722581446100000e-05] 
dist 208=[3.23592543509242490000e-06,3.30885295443759400000e-05] 
dist 209=[2.11499735040286613000e-06,3.02343249256959800000e-05] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 0, 0, 0, 2] 
dist 0=[73.730938170706890669  ,73.730938170706890669  ] 
dist 1=[71.571788250913490526  ,75.069098255749749542  ] 
dist 2=[67.728426482925349477  ,75.636252309239995944  ] 
dist 3=[63.653182716241595036  ,75.918240284002261380  ] 
dist 4=[60.568803525922274773  ,76.118328481699902008  ] 
dist 5=[57.621237589737589153  ,76.403898695734239128  ] 
dist 6=[54.092270623379740765  ,76.589565857005784081  ] 
dist 7=[50.462935796274287745  ,76.632546938303481119  ] 
dist 8=[47.115053039505973569  ,75.751123739699914537  ] 
dist 9=[43.335013293774081351  ,69.144907727877050558  ] 
dist 10=[37.981424425010623907  ,68.024429989849132288  ] 
dist 11=[32.576359362733452171  ,66.002421336546591478  ] 
dist 12=[28.590944209683976368  ,65.456016826807886930  ] 
dist 13=[24.885898554090342545  ,63.515562586104801952  ] 
dist 14=[20.599497009173589123  ,62.939301508954645104  ] 
dist 15=[16.272097220417755533  ,62.160558540350904984  ] 
dist 16=[12.224359757197641922  ,61.169370860733444791  ] 
dist 17=[6.872272053889473440  ,25.967161518655333598  ] 
dist 18=[1.706732683281674904  ,25.719574171134312857  ] 
dist 19=[-3.6057974851840934391 ,14.848343308062879838  ] 
dist 20=[-7.3811537255189346440 ,13.830351547652361509  ] 
dist 21=[-10.389680668577256098  ,4.6308759366165973344 ] 
dist 22=[-13.137731610650804474  ,3.9022570287165163521 ] 
dist 23=[-15.510266192942103897  ,.9801450682785936667 ] 
dist 24=[-17.160628869888073148  ,.6461442239154873202 ] 
dist 25=[-18.458387774551838988  ,-1.9613581259635328002 ] 
dist 26=[-19.421647933205031378  ,-2.1363353067441083660 ] 
dist 27=[-20.096194954762647200  ,-5.6759924399771032132 ] 
dist 28=[-20.259930562602045909  ,-6.0877539804584984622 ] 
dist 29=[-20.216767005828957337  ,-6.7169607875229157475 ] 
dist 30=[-19.293058094654152143  ,-6.8193483672099521477 ] 
dist 31=[-15.884493473699341215  ,-6.7428566523308648445 ] 
dist 32=[-15.970990441481205216  ,-6.4088956562104163075 ] 
dist 33=[-8.6559329412684216025 ,-5.8280641998891430194 ] 
dist 34=[-8.6592593828990704120 ,-3.9969852459244686224 ] 
dist 35=[-6.0057368266536704120 ,-2.2399913843610867464 ] 
dist 36=[-5.7364325966789890648 ,-.8686098689027786218 ] 
dist 37=[-3.4442580836162996138 ,.4737993851844441893 ] 
dist 38=[-3.0219728279734782345 ,2.1163353856290007903 ] 
dist 39=[-2.3798431391861415786 ,3.6718626886744555608 ] 
dist 40=[-2.2087799790511642869 ,4.6678413717294932280 ] 
dist 41=[-1.0687612025742056361 ,5.4397672620910870250 ] 
dist 42=[-.9795422211561566824 ,6.1023648316650574694 ] 
dist 43=[.4857762513492758157 ,6.6403088020365422259 ] 
dist 44=[.6766106739189761292 ,6.9154100466181481551 ] 
dist 45=[.9399683867079593349 ,7.0495843699931574112 ] 
dist 46=[.9561544488865482932 ,7.0716567434185883610 ] 
dist 47=[.9090355814670080075 ,5.8694272598476949949 ] 
dist 48=[.7723443848858823381 ,5.9124117885827945851 ] 
dist 49=[.5461270060141269366 ,3.6731699297767207009 ] 
dist 50=[.14243481818370621177,3.6771828292208122473 ] 
dist 51=[-.2825429595016897405 ,1.9292578126205854904 ] 
dist 52=[-.5936153642094645427 ,1.7347139040216406109 ] 
dist 53=[-.8775848466806597401 ,1.4257696725595521813 ] 
dist 54=[-1.1948361002076085318 ,1.3446070115555638507 ] 
dist 55=[-1.7919619182328718047 ,.3293588384294828972 ] 
dist 56=[-2.2519953485103340335 ,.3060855662318305433 ] 
dist 57=[-2.6068119798711363183 ,.0700166173822221160 ] 
dist 58=[-2.9068317253061745945 ,.0590855888378136996 ] 
dist 59=[-3.1459766865456335952 ,-.3085367223928587218 ] 
dist 60=[-3.2583717942922482516 ,-.3509687215479890634 ] 
dist 61=[-3.3118480998123725014 ,-.4317310718574607593 ] 
dist 62=[-3.3162821526770215486 ,-.4484362188013978762 ] 
dist 63=[-1.1222191459776117753 ,-.4839891922656009482 ] 
dist 64=[-1.1249756656143990720 ,-.4760138328172010983 ] 
dist 65=[-.73199482161339646356,-.4483470228100113236 ] 
dist 66=[-.69452530032338839904,-.3396970721083605084 ] 
dist 67=[-.5940673324783533022 ,-.2238370574932540497 ] 
dist 68=[-.5773408339073637789 ,-.1290950353458654525 ] 
dist 69=[-.3998446174531666057 ,-.0326100818350269202 ] 
dist 70=[-.3649260861953656031 ,.0902347643618238485 ] 
dist 71=[-.3212409768205463257 ,.2081131499103803614 ] 
dist 72=[-.3073675195121556651 ,.2848389044956905638 ] 
dist 73=[-.1048710487886778916 ,.3454535431103574959 ] 
dist 74=[-.0977409641067832532 ,.3991842180409469117 ] 
dist 75=[.0318570193139941229 ,.4438300398274442771 ] 
dist 76=[.0482754512345407780 ,.4682702372483427310 ] 
dist 77=[.0795203660902944511 ,.4823891675894579029 ] 
dist 78=[.08624523052103523425,.4859347180266223456 ] 
dist 79=[.05583932086378081821,.49137227521084669941] 
dist 80=[0                     ,.49189851052227680756] 
dist 81=[.10120951718464324053,.2475061342954368544 ] 
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dist 83=[.06978967666121161050,.13589070259211670165] 
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dist 85=[.03409919361944522607,.10143614102840496643] 
dist 86=[-.0230318996264873666 ,.09556834267588096775] 
dist 87=[-.0786853226109232033 ,.0457080406900287814 ] 
dist 88=[-.1150132478697888721 ,.0423977437000212036 ] 
dist 89=[-.1437913799200433654 ,.0346486615259883707 ] 
dist 90=[-.1693928124378515915 ,.0326569538680342473 ] 
dist 91=[-.1906980209290091542 ,.0114085467711150976 ] 
dist 92=[-.2023741473604274202 ,.0080925696925002348 ] 
dist 93=[-.2091243598795784597 ,.0024848389486414781 ] 
dist 94=[-.2108199891348835162 ,.0011913376082880953 ] 
dist 95=[-.1014287471593389251 ,-.0010552388073566982 ] 
dist 96=[-.1018703356665833571 ,-.0005161866909839479 ] 
dist 97=[-.09156697206963928406,.0014183208086626409 ] 
dist 98=[-.08779635908495120516,.0057277854683724294 ] 
dist 99=[-.03795909409155268955,.0103699770615421487 ] 
dist 100=[-.03642835107779944836,.0136297947945540622 ] 
dist 101=[-.0322377126990019307 ,.0164644336120658918 ] 
dist 102=[-.0314490977706682164 ,.0194161114812351265 ] 
dist 103=[-.0236000415082373950 ,.0221799939898818862 ] 
dist 104=[-.0219938511722595378 ,.0242682528238876957 ] 
dist 105=[-.0198590115821952568 ,.0286209172070636348 ] 
dist 106=[-.0191163712179412906 ,.0332669781302082376 ] 
dist 107=[-.0034394486132469814 ,.0370745201200976346 ] 
dist 108=[-.0014791901837701120 ,.0390487766475097051 ] 
dist 109=[.0030829284457543772 ,.0400740532272152378 ] 
dist 110=[.0037855692561006662 ,.0402515003619141340 ] 
dist 111=[.0094181265651960066 ,.0322531450542312623 ] 
dist 112=[.0103245817423030212 ,.03151800464841989513] 
dist 113=[.01054081627368291444,.02586592137584725848] 
dist 114=[.00905722879179658689,.02421138798600641471] 
dist 115=[.00741827037840729537,.01438645485191477811] 
dist 116=[.00609457911362515422,.01309863462778834085] 
dist 117=[.00274139830253474786,.01160603628533411662] 
dist 118=[-.00179114940816775364,.01119777296976723347] 
dist 119=[-.00619724867969943890,.0026924150191269646 ] 
dist 120=[-.0090474648606853773 ,.0022362104214912035 ] 
dist 121=[-.0112741897847135573 ,.0017074410770235471 ] 
dist 122=[-.0131990427291094763 ,.0016167084008674370 ] 
dist 123=[-.0147614527372750203 ,-.0022015345989631257 ] 
dist 124=[-.0155456857099107962 ,-.0026425820155929261 ] 
dist 125=[-.0159612610862651069 ,-.0035296827151567434 ] 
dist 126=[-.0160564193285534381 ,-.0037199403312035278 ] 
dist 127=[-.00531871954937521212,-.0042749962953959799 ] 
dist 128=[-.0051755478745737464 ,-.0042911427458552868 ] 
dist 129=[-.0053372201669914614 ,-.00375741667600887838] 
dist 130=[-.0053778325251331984 ,-.00289123462027975897] 
dist 131=[-.00314342549763621066,-.00203193043342047846] 
dist 132=[-.00295620408598786329,-.00130511683771276122] 
dist 133=[-.00247455805631351851,-.00054452775034373179] 
dist 134=[-.00238380958397454492,.00044937474423216785] 
dist 135=[-.00158958654057642254,.00141015700906559707] 
dist 136=[-.00143519187564342871,.00203900995383912761] 
dist 137=[-.00120224710755193651,.00253843463135061881] 
dist 138=[-.00113553365786032961,.00298416229928135824] 
dist 139=[.00012049885227657970,.00335555075577368727] 
dist 140=[.00028250702340223687,.00355913502310838667] 
dist 141=[.00060799447921730821,.00367668249037000722] 
dist 142=[.00068476171796420004,.00370566707850278312] 
dist 143=[.00091418911371897308,.00223480895378019318] 
dist 144=[.00094457429592899424,.0023391097454428973 ] 
dist 145=[.00091536863400122379,.0024182709936960881 ] 
dist 146=[.00079777149798840014,.0024381588857951321 ] 
dist 147=[.00066191693075406732,.00117572130369592668] 
dist 148=[.00056004450776383679,.00106789815294106199] 
dist 149=[.00033630378366526666,.00090632276667814344] 
dist 150=[-.00013726281737801159,.00085912938980071748] 
dist 151=[-.00060034208858789308,.00026187545614009269] 
dist 152=[-.00090370511857549096,.00022255417435577336] 
dist 153=[-.00114482951759525840,.00017580948311693369] 
dist 154=[-.00136025374201444779,.00016601266976658827] 
dist 155=[-.00153982094369051576,-.00016705267581261582] 
dist 156=[-.00163826157455932302,-.00020616354792125568] 
dist 157=[-.00169507647489260712,-.00028505171999930851] 
dist 158=[-.00170899999637566405,-.00030236097633563990] 
dist 159=[-.00047546821880125169,-.00035303660365011131] 
dist 160=[-.0004562396768152704 ,-.00035558260798937762] 
dist 161=[-.0004683397162700423 ,-.00033124030493097763] 
dist 162=[-.0004703667305242913 ,-.00025509755307549656] 
dist 163=[-.0003110164230283134 ,-.00017889222908852697] 
dist 164=[-.0002962973754778478 ,-.00011342622912485037] 
dist 165=[-.0002555032065976403 ,-4.40663005768757800000e-05] 
dist 166=[-.0002489910431766020 ,4.76464428588908900000e-05] 
dist 167=[-.00017274409872000285,.00013632199174904364] 
dist 168=[-.00015753882168633130,.00019360157912751755] 
dist 169=[-.00013998835706696364,.00023821635065180571] 
dist 170=[-.00013509333075513108,.00027649882975674117] 
dist 171=[1.33592416627109800000e-05,.00030734601954261521] 
dist 172=[3.10742471608282500000e-05,.00032237628776077039] 
dist 173=[6.22226269321398000000e-05,.00033007283443132532] 
dist 174=[6.87431559647108000000e-05,.00033173608159498031] 
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dist 176=[9.00027790051126800000e-05,.00022601361585306427] 
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dist 179=[4.95574198389098080000e-05,.00013943098984353682] 
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dist 181=[-4.83716133264039200000e-06,.00011537741313840716] 
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dist 239=[3.53100240401817500000e-07,2.96788608456182490000e-06] 
dist 240=[3.00226506681535000000e-07,2.86430554450344700000e-06] 
dist 241=[1.97037741091099640000e-07,2.62812161224614000000e-06]