8 phat 4 dirichlet min maxes function [2, 1, 2, 1, 0, 1, 1, 0, 1] 
dist 0=[45.468948910462024783  ,45.468948910462024783  ] 
dist 1=[44.713304169690472718  ,46.227275501003648323  ] 
dist 2=[43.813970438414606991  ,46.880870045191373785  ] 
dist 3=[42.481447034108314574  ,47.218250165727492205  ] 
dist 4=[40.968836293584452718  ,47.388436713131781459  ] 
dist 5=[39.350070138705897587  ,47.413335208640602276  ] 
dist 6=[37.339309978862229821  ,47.287902323634119214  ] 
dist 7=[34.260886904887389187  ,47.201615982183134993  ] 
dist 8=[31.150946509948609179  ,47.015543518138038339  ] 
dist 9=[29.014171617670574732  ,46.924169118364101217  ] 
dist 10=[27.175111449184551822  ,44.742825709774477836  ] 
dist 11=[25.254029540226832375  ,44.363023096145066436  ] 
dist 12=[23.419844527479651608  ,43.816166364077916043  ] 
dist 13=[21.927616789132786288  ,43.632336953508044737  ] 
dist 14=[20.394594606651976901  ,39.636856273677858551  ] 
dist 15=[18.396993548273048204  ,38.900743790250345183  ] 
dist 16=[16.437856261750661761  ,35.030414311905951838  ] 
dist 17=[15.058225998793602167  ,34.470425267225243908  ] 
dist 18=[13.832469142323456706  ,28.280639765856339221  ] 
dist 19=[12.487691654174610799  ,27.477602028970224056  ] 
dist 20=[11.159933732456896578  ,25.917807016501822629  ] 
dist 21=[10.001707218587140786  ,25.518508155377418340  ] 
dist 22=[8.7379308703239869768 ,24.136546477016992698  ] 
dist 23=[6.9874860791044567851 ,23.809371818677112739  ] 
dist 24=[5.2690764808325483809 ,23.413362402429076333  ] 
dist 25=[4.1332073098814412454 ,23.267463904377873897  ] 
dist 26=[3.1978272106200831418 ,13.993594635732782767  ] 
dist 27=[2.2811687904733091421 ,13.121915069995800093  ] 
dist 28=[1.4378053326754025010 ,12.929464250553227809  ] 
dist 29=[.44860059361950720535,11.051633088356188680  ] 
dist 30=[-1.4510593474887019763 ,10.744977449488663689  ] 
dist 31=[-2.8707377557331902324 ,9.5235697449301380420 ] 
dist 32=[-4.2156285078659819059 ,7.5752995812367012450 ] 
dist 33=[-5.8165255574396494140 ,.59095184023833591044] 
dist 34=[-7.3152287087261736367 ,.58570543252483877188] 
dist 35=[-8.2518959946053671653 ,.69190143565835347344] 
dist 36=[-8.9595265361546042187 ,.85817287873842390657] 
dist 37=[-9.5433346788683783954 ,1.0929265983449709905 ] 
dist 38=[-10.011774825284174046  ,1.4207526876193982718 ] 
dist 39=[-10.258502454897509010  ,1.9585164879377215016 ] 
dist 40=[-10.391004900107080535  ,2.5054648879028779776 ] 
dist 41=[-10.419492866351343094  ,2.8700824930855808232 ] 
dist 42=[-8.9537202819797191592 ,3.1694464396492300449 ] 
dist 43=[-9.0744398289395117141 ,3.4563333116351965712 ] 
dist 44=[-9.1257260600397300653 ,3.7120062965332379602 ] 
dist 45=[-9.1366177991240619895 ,3.8869589838261982686 ] 
dist 46=[-9.1244168762972166288 ,4.0357415974516088089 ] 
dist 47=[-9.0432308303271895589 ,4.1870964915909884822 ] 
dist 48=[-9.0071751518895228852 ,4.3154274504967960946 ] 
dist 49=[-7.3141169607094926699 ,4.3723374913380551229 ] 
dist 50=[-6.1187579986519147750 ,4.3972141347691440622 ] 
dist 51=[-5.4757874656494640571 ,4.3978344923517412715 ] 
dist 52=[-5.3791590815683538530 ,4.2985378385250902359 ] 
dist 53=[-4.7668693600926124705 ,4.2663056627528121876 ] 
dist 54=[-4.3679181605220220962 ,4.2411600649355122731 ] 
dist 55=[-4.2767987053314962297 ,4.2193704471523682567 ] 
dist 56=[-4.1518675521679730410 ,3.2436401004479781387 ] 
dist 57=[-4.1112023520909471114 ,3.3439214391826078246 ] 
dist 58=[-2.0463658937522157348 ,3.8057740446664968746 ] 
dist 59=[-1.6144198170449632717 ,4.1822284699535883383 ] 
dist 60=[-1.5022514777865526976 ,4.5416674107663107166 ] 
dist 61=[-1.0933552390886151960 ,4.8638393791432712611 ] 
dist 62=[-1.0131990620942626355 ,5.0915840676790629142 ] 
dist 63=[-.87639021865591501998,5.2947141468060007905 ] 
dist 64=[-.84656701583044412015,5.5187776696814270938 ] 
dist 65=[.78958242335830534316,5.7173369671939874832 ] 
dist 66=[.55078399952983846736,5.8186445933433687646 ] 
dist 67=[.27746639329422833916,5.8699345494599905336 ] 
dist 68=[.00243586234489810884,5.8789832536769426682 ] 
dist 69=[-.24325490500450061822,5.8399431271123561080 ] 
dist 70=[-.51496206445888952294,5.8145696548056131452 ] 
dist 71=[-.89394327216085441099,5.7802978071210041028 ] 
dist 72=[-1.2667080269030602379 ,5.7596389834386078892 ] 
dist 73=[-1.5136088522933724175 ,5.1012206011663335441 ] 
dist 74=[-1.7161407970730742657 ,5.0010658698958437210 ] 
dist 75=[-1.9117207658513883566 ,4.7940750135783703046 ] 
dist 76=[-2.0884098802673720071 ,4.7328943115470978827 ] 
dist 77=[-2.2155033531938923012 ,4.4740639502709381059 ] 
dist 78=[-2.3309171391595584089 ,4.4174485235019431495 ] 
dist 79=[-2.4609679472624925391 ,4.2673535899138616303 ] 
dist 80=[-2.5786051114657969519 ,4.2315335378999663077 ] 
dist 81=[-2.6444436470235459669 ,3.1630346441037194613 ] 
dist 82=[-2.6851171159179634185 ,3.1257537454821444502 ] 
dist 83=[-2.7022493102130117238 ,3.0202846165612841807 ] 
dist 84=[-2.7080503259046508122 ,3.0012529190936185677 ] 
dist 85=[-2.8068130434263423300 ,2.7854036014655461106 ] 
dist 86=[-3.1483212602847996695 ,2.7385007905547264982 ] 
dist 87=[-3.4563031095945648625 ,2.6875871938330568772 ] 
dist 88=[-3.7997266079594200876 ,2.6669710607842273337 ] 
dist 89=[-4.1160470327268447844 ,2.1055086787633306630 ] 
dist 90=[-4.3158096414612789279 ,2.0294607179998130971 ] 
dist 91=[-4.4687533571515343605 ,1.8957815674252464134 ] 
dist 92=[-4.5981461973550648037 ,2.0951492251382227068 ] 
dist 93=[-4.7027801127577704924 ,2.2361170442835337662 ] 
dist 94=[-4.7568764503745960944 ,2.3613978856178421099 ] 
dist 95=[-4.7844551393802870532 ,2.4981516314870230525 ] 
dist 96=[-4.7843860850123755781 ,2.6192310472038836304 ] 
dist 97=[-2.8413431501162735222 ,2.6819423629546064127 ] 
dist 98=[-2.5855221079470167510 ,2.7163081645293501003 ] 
dist 99=[-2.5452837311062299042 ,2.7242313718483714035 ] 
dist 100=[-2.4829515248066449269 ,2.7013228147468440908 ] 
dist 101=[-2.4627962493634309935 ,2.6946315859213965365 ] 
dist 102=[-2.4104272879344049675 ,2.6899438071350325577 ] 
dist 103=[-2.3919260435202037968 ,2.6867819842707315628 ] 
dist 104=[-2.3805265268182123572 ,2.5853245042514185284 ] 
dist 105=[-2.3759304604160507562 ,2.5809379546226252336 ] 
dist 106=[-.81305971711141682757,2.5499880506557876847 ] 
dist 107=[-1.0501239426026029692 ,2.5429083981491582895 ] 
dist 108=[-1.3136020754964695368 ,2.4178635044722650120 ] 
dist 109=[-1.5154869388158389734 ,2.3865296588707167172 ] 
dist 110=[-1.7110139709130196712 ,2.3598697078844307673 ] 
dist 111=[-1.9491086150171510272 ,2.3467808451928446720 ] 
dist 112=[-2.1732677885348915412 ,1.8699784444738813520 ] 
dist 113=[-2.3131650857969127028 ,1.8045559910611382654 ] 
dist 114=[-2.4181736398956286185 ,1.6767847588801821709 ] 
dist 115=[-2.5030619534735393161 ,1.6481459485949531986 ] 
dist 116=[-2.5685185364422892798 ,1.8326038273120439091 ] 
dist 117=[-2.5959553827689969238 ,2.0317739716274639425 ] 
dist 118=[-2.6069956465218326782 ,2.2255568640215911239 ] 
dist 119=[-2.6070185224368791363 ,2.3885150937185967493 ] 
dist 120=[-.03582450876217940167,2.5604046598461090630 ] 
dist 121=[-.3079259987589743458 ,2.7898675392030126673 ] 
dist 122=[-.58724891843530382253,3.0080305024366512731 ] 
dist 123=[-.78391005716478307369,3.1348050721858713903 ] 
dist 124=[-.95782042669087770602,3.2191712683552814301 ] 
dist 125=[-1.1463277310715880497 ,3.2679969582589221070 ] 
dist 126=[-1.3299679340682903004 ,3.2998501972377375384 ] 
dist 127=[-1.4844528105432780457 ,3.3164397578986925174 ] 
dist 128=[-1.6473013478024321342 ,3.3250854271848758187 ] 
dist 129=[-1.8643356394504172845 ,3.3252026236142691982 ] 
dist 130=[-2.0782640497689762796 ,2.9644210802383254840 ] 
dist 131=[-2.2287163349762794006 ,2.9099108788060344968 ] 
dist 132=[-2.3616234495612563284 ,2.8194374141063785043 ] 
dist 133=[-2.5055123926949428755 ,2.7934218578396578494 ] 
dist 134=[-2.6456256786531738419 ,2.7164722347680139990 ] 
dist 135=[-2.7634633247333730578 ,2.6893649318580223386 ] 
dist 136=[-2.8876846885190104751 ,2.6711597306996930814 ] 
dist 137=[-3.0532897010402301540 ,2.6608794949049739858 ] 
dist 138=[-3.2108107007378069139 ,.65291158576057261647] 
dist 139=[-3.3027590630381241129 ,.48778872464303588707] 
dist 140=[-3.3643864310024204170 ,.11785220001840801278] 
dist 141=[-3.4008533147430518584 ,.04853108940189519009] 
dist 142=[-3.4207501697982553378 ,-.14101155680440253042] 
dist 143=[-3.4214833812166656390 ,.03918476930200188345] 
dist 144=[-3.4037286059585903220 ,.22214875931980534875] 
dist 145=[-3.3918276522215945985 ,.35979150879264030303] 
dist 146=[-3.1860363090070146508 ,.49075568018561274606] 
dist 147=[-3.1474281131011333156 ,.64705927288901500948] 
dist 148=[-3.0521834025632098184 ,.80792388606350615107] 
dist 149=[-3.0190369951620083763 ,.95710060126347692381] 
dist 150=[-2.8492763699759277317 ,1.1264814822459721112 ] 
dist 151=[-2.8096232971360719259 ,1.3680153112109812837 ] 
dist 152=[-2.7276181898666147362 ,1.6056198531341955148 ] 
dist 153=[-2.7014078610753638217 ,1.7593138612548479622 ] 
dist 154=[-2.7397058233632721358 ,1.8811669868952474678 ] 
dist 155=[-2.8064509497765901086 ,1.9916451134272589910 ] 
dist 156=[-2.8478805951645040679 ,2.0865242957055727978 ] 
dist 157=[-2.8657091728450399155 ,2.1836042499211402112 ] 
dist 158=[-2.8715666585381375493 ,2.4989210748607269212 ] 
dist 159=[-2.8669531733335248282 ,2.7166457504448540456 ] 
dist 160=[-2.8523270590760411008 ,2.9048164756891030857 ] 
dist 161=[-2.8420461002912088088 ,3.1021373817837525585 ] 
dist 162=[-2.6036693856269689376 ,3.2803944422271406584 ] 
dist 163=[-2.5636548811343196621 ,3.3924537726049431468 ] 
dist 164=[-2.4754836937873647561 ,3.4775943718894297162 ] 
dist 165=[-2.4470029690639945526 ,3.5483831809161099828 ] 
dist 166=[-2.3150310500004234600 ,3.6046123691298054727 ] 
dist 167=[-2.2860294442767567874 ,3.6316263577882559320 ] 
dist 168=[-2.2077040588308549988 ,3.6424387249437535118 ] 
dist 169=[-2.1887785316993697661 ,3.6386204859911254244 ] 
dist 170=[-.80162380230255763221,1.6576374391661891097 ] 
dist 171=[-1.0444418991166014004 ,1.6414227591382068852 ] 
dist 172=[-1.2684585195565748653 ,1.4613583629477253186 ] 
dist 173=[-1.4370972783284245065 ,1.4240544285231206992 ] 
dist 174=[-1.5976743878859875900 ,1.3830707387491178775 ] 
dist 175=[-1.7895045437300456182 ,1.3693985391032735347 ] 
dist 176=[-1.9685002797315723875 ,.95914037162799031581] 
dist 177=[-2.0778355359921956102 ,1.0152341473694120797 ] 
dist 178=[-2.1572075981995205734 ,1.1259595541588292046 ] 
dist 179=[-2.2165743387280251148 ,1.1931076436259290726 ] 
dist 180=[-2.2608824977415365605 ,1.2412843929425842470 ] 
dist 181=[-2.2801327782330996940 ,1.2762646599365820178 ] 
dist 182=[-2.2865619530825766059 ,1.3025396502585451615 ] 
dist 183=[-2.2846421117935874601 ,1.3159583789779058287 ] 
dist 184=[-.26450073735551686715,1.3225475906951806633 ] 
dist 185=[-.4127128311205332517 ,1.3219805223515362068 ] 
dist 186=[-.53998374515825706924,1.2259679417629247004 ] 
dist 187=[-.67218423241535287568,1.2110626552497982162 ] 
dist 188=[-.79764520717587610474,1.1747297164930705812 ] 
dist 189=[-.89800782748906791231,1.1619163009076263758 ] 
dist 190=[-.99934150438995971595,1.0985716668141420041 ] 
dist 191=[-1.1286796474510902524 ,1.0838003654122023865 ] 
dist 192=[-1.2536340605291563709 ,1.0525014708793160502 ] 
dist 193=[-1.3374651671054763453 ,1.0423576795984274045 ] 
dist 194=[-1.4073355366713788243 ,.89364336831828742953] 
dist 195=[-1.4765499177784506142 ,.87133159606363447233] 
dist 196=[-1.5401542238254336913 ,.81452756446910986005] 
dist 197=[-1.5876256754999438972 ,.80407243153792518937] 
dist 198=[-1.6324342457148608795 ,.70855062205820657161] 
dist 199=[-1.6854067339739378093 ,.6891282085368927181 ] 
dist 200=[-1.7325939027757231906 ,.66340039473713987448] 
dist 201=[-1.7543038165170710184 ,.65447335703653474866] 
dist 202=[-1.7642844364176605872 ,.66281593985627968054] 
dist 203=[-1.7646408716456892999 ,.81143853786601403895] 
dist 204=[-1.7359409876374267306 ,.95264131411693639065] 
dist 205=[-1.7530214021280669421 ,1.0658412009461433218 ] 
dist 206=[-1.8256092007958714014 ,1.1803555763803954756 ] 
dist 207=[-1.8704006057018746839 ,1.3268069517262977080 ] 
dist 208=[-1.9034658025687797107 ,1.4684244654122988218 ] 
dist 209=[-1.9292355764388824629 ,1.5636394399334088435 ] 
dist 210=[-1.9469813767761216014 ,1.6432183011056371160 ] 
dist 211=[-1.9500076085825659389 ,1.7224075139141651023 ] 
dist 212=[-1.9436313119273883330 ,1.7954080747120963156 ] 
dist 213=[-1.9397877883965555844 ,1.8502784726837715646 ] 
dist 214=[-1.8739480627780304374 ,1.9024494085947507528 ] 
dist 215=[-1.8554943384820541110 ,1.9646726877774168519 ] 
dist 216=[-1.8386548028846013919 ,2.0208164827596810609 ] 
dist 217=[-1.8275777790695727856 ,2.0487145511035246346 ] 
dist 218=[-1.4011120472271871644 ,2.0616892040093491229 ] 
dist 219=[-1.3502711455303156619 ,2.0632082681207059025 ] 
dist 220=[-1.2285338773273934746 ,2.0450799451848288384 ] 
dist 221=[-1.2037379371223813420 ,2.0356659516388590364 ] 
dist 222=[-1.0239857450258631287 ,2.0180419962934692367 ] 
dist 223=[-.98871543101468208473,2.0102219224176798398 ] 
dist 224=[-.92961855475909332807,1.7895239956358102582 ] 
dist 225=[-.91441974490980641574,1.7550023814718603114 ] 
dist 226=[-.62321118528187806648,1.6809851782652338766 ] 
dist 227=[-.58428407175378966872,1.6582524457656478467 ] 
dist 228=[-.49165092118072045244,1.5572454132136055369 ] 
dist 229=[-.4755840054486432414 ,1.5101292063978157126 ] 
dist 230=[-.34478742963198873018,1.3462814054109956660 ] 
dist 231=[-.3204224739597619321 ,1.2143327420463127149 ] 
dist 232=[-.28414246125590647703,.62361756641983834998] 
dist 233=[-.2741083718186214964 ,.61534318579190682075] 
dist 234=[-.35911683751315533954,.59184041067688104334] 
dist 235=[-.44938931700966823748,.58753259787243713206] 
dist 236=[-.5312287693250372851 ,.53908326912714670503] 
dist 237=[-.59041893997262060365,.52853415560959486889] 
dist 238=[-.64443131256318281669,.51692342757167220921] 
dist 239=[-.70559821060717414558,.51210551165773408568] 
dist 240=[-.76177567923027662653,.38622265815741878515] 
dist 241=[-.7958671203782863439 ,.36921270412944601399] 
dist 242=[-.82035173160686388787,.33478627671720200722] 
dist 243=[-.83817224871776797221,.32551685723346273664] 
dist 244=[-.85088363068036125416,.2905411266846896089 ] 
dist 245=[-.85496954086002467861,.27193950421773718389] 
dist 246=[-.85541747553458294872,.20860972039335612532] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 0, 0, 2, 1, 2] 
dist 0=[50.850357165739651511  ,50.850357165739651511  ] 
dist 1=[50.765655272148574625  ,50.873383674106914862  ] 
dist 2=[50.450175779403698373  ,50.872032311846616527  ] 
dist 3=[49.857718768381424008  ,50.837196707796574841  ] 
dist 4=[48.728678248097050153  ,50.795209306049519807  ] 
dist 5=[47.506368380757292613  ,50.765342492088552507  ] 
dist 6=[46.541330754636321465  ,50.738856355099284735  ] 
dist 7=[45.394422728934909092  ,50.270828633960358572  ] 
dist 8=[43.962081037309173395  ,47.111652447400717142  ] 
dist 9=[41.962774115439311148  ,46.590061008102997284  ] 
dist 10=[39.744377258773677587  ,45.671987568548721788  ] 
dist 11=[37.436822573494918844  ,45.435036238694243897  ] 
dist 12=[34.614547636563496085  ,44.655989252278948945  ] 
dist 13=[30.340013926360149551  ,44.409362379907695439  ] 
dist 14=[26.034225364555076167  ,44.204943153288524182  ] 
dist 15=[23.087043790109591564  ,43.681553383384807776  ] 
dist 16=[20.561381116321467655  ,33.278607384712626328  ] 
dist 17=[17.939259111836958355  ,31.949645532448328049  ] 
dist 18=[15.445262533575147957  ,31.615847946958948021  ] 
dist 19=[13.431277239872995971  ,31.280675655099961660  ] 
dist 20=[11.376032562541873036  ,31.180792401890740801  ] 
dist 21=[8.7169588046158912830 ,17.058250655449095657  ] 
dist 22=[6.1199856540518728059 ,15.917388463509954044  ] 
dist 23=[4.3126663384847915618 ,15.624678987204275249  ] 
dist 24=[2.7305257876614232823 ,10.742548254586286089  ] 
dist 25=[1.0328906087132943484 ,10.131832357192638130  ] 
dist 26=[-.61840810988908542604,8.8065379624979729321 ] 
dist 27=[-2.0157377612978562569 ,8.5647047277163063517 ] 
dist 28=[-3.5019080908594445311 ,7.1664341288597330436 ] 
dist 29=[-5.5087802034234383323 ,6.9454198119712025391 ] 
dist 30=[-7.4526167232504085672 ,6.4921686222053577752 ] 
dist 31=[-8.6870246020485314312 ,6.4250269134721875275 ] 
dist 32=[-9.6453823663986697705 ,-3.4459968869152817055 ] 
dist 33=[-10.485936226076130723  ,-4.7516388469689538365 ] 
dist 34=[-11.193150136956830958  ,-4.9451704135174159124 ] 
dist 35=[-11.618696852969197448  ,-5.2758635932590648026 ] 
dist 36=[-11.923014544116534248  ,-5.3291093476010579217 ] 
dist 37=[-12.146025681233687164  ,-7.7138188189886963169 ] 
dist 38=[-12.307608834654911702  ,-7.8639570475940166615 ] 
dist 39=[-12.366428846410651435  ,-8.1305847716090490969 ] 
dist 40=[-12.366374470744795573  ,-8.1734072673683231492 ] 
dist 41=[-12.348309949959691343  ,-8.1839213244543542236 ] 
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dist 158=[-.82078581989110324925,.6393504045117421199 ] 
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dist 187=[-.75944605028762609736,.75474063498762644584] 
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dist 192=[-.9265378809460545886 ,.66998558213915952168] 
dist 193=[-.94153733969881530351,.63647112176091489806] 
dist 194=[-.94906101023505526253,.62876248647838217314] 
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dist 197=[-.13409155155604650149,.1184509246571228859 ] 
dist 198=[-.16557506809953735489,.13078711197352549042] 
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dist 200=[-.21031879274888782129,.14978749304170394582] 
dist 201=[-.23536726210472691667,.1614438348552287016 ] 
dist 202=[-.26078376748266042495,.1736610106923985663 ] 
dist 203=[-.28381970160218939194,.18531463678461971195] 
dist 204=[-.30956079424093723385,.19879685316016391084] 
dist 205=[-.34577925540251675043,.21831333883270309189] 
dist 206=[-.38100979878309179116,.2374814507154167451 ] 
dist 207=[-.40280654840763272841,.24957267391645086036] 
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dist 214=[-.43301543536410427289,.38305137489986912033] 
dist 215=[-.42971084047483817055,.3956572549517173774 ] 
dist 216=[-.4224323059695692287 ,.40514581202082676905] 
dist 217=[-.41968629220632183349,.41287461884302233983] 
dist 218=[-.40550582461787961661,.41888905393117984872] 
dist 219=[-.40207610254576218001,.42153306322185808062] 
dist 220=[-.3919058368031983226 ,.42221587872741243645] 
dist 221=[-.3893724864737491502 ,.42177450116910747741] 
dist 222=[-.27994501226903192316,.41738755518786884239] 
dist 223=[-.27430740436742499265,.41565659422212541436] 
dist 224=[-.25898593280343190624,.4094188598092662326 ] 
dist 225=[-.25665354962203379495,.40729947575256702443] 
dist 226=[-.2279861062305746858 ,.3888027404331075585 ] 
dist 227=[-.22206586570657537926,.38414102065625846927] 
dist 228=[-.2161888417395263965 ,.37762269062701297169] 
dist 229=[-.21470000757270825128,.37507657849466610527] 
dist 230=[-.1476520083847868436 ,.31072262736288974276] 
dist 231=[-.1389909748816731669 ,.3015014040147757217 ] 
dist 232=[-.12183139129833179246,.28201246549434080954] 
dist 233=[-.11739277791947696718,.2763840650044186837 ] 
dist 234=[-.10170523537988110003,.25289922968135068696] 
dist 235=[-.09814753377414030646,.24809994177375760342] 
dist 236=[-.09331519311185035316,.23536333421908055263] 
dist 237=[-.09173961224047025995,.2329907898441963255 ] 
dist 238=[-.12323995114119873809,.25118325822015368451] 
dist 239=[-.1719619417253478012 ,.27067985455225409223] 
dist 240=[-.21197644065081449274,.28606219789124518729] 
dist 241=[-.25063852108407569386,.29988251060968940918] 
dist 242=[-.2855284791715812227 ,.31166457060461604743] 
dist 243=[-.31048255066664048116,.31890886320136986503] 
dist 244=[-.33296784820075491256,.32422734159721832134] 
dist 245=[-.35800099847329377414,.3283204403978146326 ] 
dist 246=[-.38074265611364401484,.3310647205925793112 ] 
dist 247=[-.39407902187598297914,.33152130218354406363] 
dist 248=[-.40309475104019333957,.33011355958097704554] 
dist 249=[-.40858605922987460219,.32959460452785851217] 
dist 250=[-.41200611196953030401,.31747599631297782709] 
dist 251=[-.41275229905122854032,.31417547028576891573] 
dist 252=[-.41202552930492657879,.31167711797936815387] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 0, 0, 0, 0, 2] 
dist 0=[53.658016902968273464  ,53.658016902968273464  ] 
dist 1=[53.256409716854799821  ,53.853482882763146788  ] 
dist 2=[52.372164686735864838  ,53.914089437490633414  ] 
dist 3=[51.376495963262896824  ,53.875326341705436601  ] 
dist 4=[50.529848315004495681  ,53.648160452634085818  ] 
dist 5=[49.627096558608248035  ,53.400838463526448098  ] 
dist 6=[48.407465916881995364  ,53.255925820519784413  ] 
dist 7=[47.072475055440117786  ,53.158177303356575837  ] 
dist 8=[45.708990419056038440  ,52.542757628296517804  ] 
dist 9=[44.059064841144299603  ,48.466043125249467063  ] 
dist 10=[41.579957798834135940  ,47.808038406354550302  ] 
dist 11=[38.998495336518378826  ,46.617933720276859404  ] 
dist 12=[36.780236661025750849  ,46.309452049551412932  ] 
dist 13=[33.516903499555055060  ,45.270758986064010040  ] 
dist 14=[28.608128185255378091  ,44.965943571314650257  ] 
dist 15=[23.682750119950517246  ,44.666650155760674935  ] 
dist 16=[20.353014035109528652  ,44.080069834319339389  ] 
dist 17=[17.545275633513544337  ,34.547447389767354842  ] 
dist 18=[14.704619050447159095  ,34.370978073317693933  ] 
dist 19=[12.049895091643874793  ,19.992019885217097496  ] 
dist 20=[9.9845804877271438601 ,19.426944387542749116  ] 
dist 21=[7.6837296566433254224 ,14.474679391784869159  ] 
dist 22=[5.0459134866410865148 ,13.598515346288724165  ] 
dist 23=[2.6277734461753672312 ,12.412073922097081165  ] 
dist 24=[.82497911730563469232,12.124654259920211441  ] 
dist 25=[-.87774620747380798724,6.1784345455356895877 ] 
dist 26=[-2.8961564183099116609 ,5.4718943229203439455 ] 
dist 27=[-4.7872210756505136783 ,3.9063672341404110653 ] 
dist 28=[-5.9813325670375401253 ,3.6722186635214188782 ] 
dist 29=[-6.8973133951584091894 ,1.9550318551346522867 ] 
dist 30=[-7.6775898376912402892 ,1.6916928349020760886 ] 
dist 31=[-8.3145682923513853429 ,1.2430469768175682997 ] 
dist 32=[-8.6583400085850950345 ,1.1649591549903235471 ] 
dist 33=[-8.8573199154728397456 ,-4.5189241709787739134 ] 
dist 34=[-8.9059920800923983890 ,-4.5850383377819207234 ] 
dist 35=[-8.3502050959948600231 ,-4.6959341960397011207 ] 
dist 36=[-8.3218045383168747714 ,-4.6536939608213019252 ] 
dist 37=[-8.5246457087204003885 ,-4.5401376317781816416 ] 
dist 38=[-8.7351386978900546495 ,-4.3044506566281275007 ] 
dist 39=[-8.8502958707778395372 ,-4.0119819201810346318 ] 
dist 40=[-8.8736227546727248045 ,-3.6713427831730744197 ] 
dist 41=[-8.6286847099493869272 ,-3.2318963695516773790 ] 
dist 42=[-8.5666412254886163306 ,-2.5447176155648925835 ] 
dist 43=[-8.5038422184771376506 ,-1.8239847047799293590 ] 
dist 44=[-8.4621138162521905162 ,-1.2503725581127035553 ] 
dist 45=[-8.3858809469187130829 ,-.67515998260069423348] 
dist 46=[-8.3443521618769995791 ,.64914756389694303999] 
dist 47=[-8.3065314096367061281 ,2.3691282610507445250 ] 
dist 48=[-8.2720697691009594687 ,3.4998271659379990349 ] 
dist 49=[-5.9358258682789357909 ,4.4163283688184538165 ] 
dist 50=[-5.3349501271714229633 ,5.2813171865094719908 ] 
dist 51=[-2.1817163453032624319 ,6.0481648651301104602 ] 
dist 52=[-2.0461365058145633054 ,6.5729526896203336532 ] 
dist 53=[-.76474413899313976741,7.0217645041026633976 ] 
dist 54=[-.53730903337623136763,7.4854318698501475908 ] 
dist 55=[-.25182947960772370804,7.8984806275794746445 ] 
dist 56=[-.20036007993273153825,8.1451842896312927208 ] 
dist 57=[1.4385381630946588539 ,8.3178373393603431955 ] 
dist 58=[1.5653164423717127329 ,8.4350477903424759877 ] 
dist 59=[1.7180864656576407041 ,8.5076347848077540243 ] 
dist 60=[1.7079206830675115421 ,8.5176256296825880718 ] 
dist 61=[1.6351731495188431735 ,8.4493934296396871253 ] 
dist 62=[1.4586319123936200322 ,8.1945862992727252697 ] 
dist 63=[1.2293398939401894353 ,5.6305926028538751722 ] 
dist 64=[.9459853818128156603 ,5.6583169146372045326 ] 
dist 65=[.5689383480589968413 ,5.6690379254398097465 ] 
dist 66=[-.0343628203478062049 ,5.6595425932603387255 ] 
dist 67=[-.64662315271393827317,3.7875685261889396338 ] 
dist 68=[-1.0594593533921967603 ,3.7837398249752929143 ] 
dist 69=[-1.4052432155065941704 ,3.6706246147889757056 ] 
dist 70=[-1.7499133425282957662 ,3.6383548552008171482 ] 
dist 71=[-2.0675270332601075223 ,3.6137942638015608482 ] 
dist 72=[-2.3053422343999231991 ,3.5977029206124279659 ] 
dist 73=[-2.5303236396285315464 ,3.0340997707422805690 ] 
dist 74=[-2.7967430357239501997 ,2.9550120586874028207 ] 
dist 75=[-3.0438675151121406875 ,2.8022315022909277261 ] 
dist 76=[-3.1918474275602473317 ,2.7613091242870749169 ] 
dist 77=[-3.2956657232030841959 ,2.6118287214457701154 ] 
dist 78=[-3.3665297166416984924 ,2.5748210925790234958 ] 
dist 79=[-3.4143563223946507126 ,2.5137764966271742873 ] 
dist 80=[-3.4262044652796027111 ,2.4958139731893735588 ] 
dist 81=[-3.4705787319292607152 ,.87579361931475207651] 
dist 82=[-3.6536183439158543294 ,.74402832480571971334] 
dist 83=[-3.8252303944790054949 ,.55472366674946186445] 
dist 84=[-4.0093356492241928776 ,.96399946324601753455] 
dist 85=[-4.1734323032585425665 ,1.3077218861217055082 ] 
dist 86=[-4.3538850587678087306 ,1.6517405268884221258 ] 
dist 87=[-4.5150201096504774686 ,1.9695098229232680612 ] 
dist 88=[-4.6019707945532940353 ,2.2084652305046330492 ] 
dist 89=[-4.6516004823733215979 ,2.4353757923482202765 ] 
dist 90=[-4.6636722803835637894 ,2.7050621729410882363 ] 
dist 91=[-4.6583317803753504338 ,2.9552428308055803667 ] 
dist 92=[-4.6458534072296723053 ,3.1042992912451008654 ] 
dist 93=[-4.6111838921747653839 ,3.2077259350439103720 ] 
dist 94=[-4.5916790841018464080 ,3.2757900306633700454 ] 
dist 95=[-2.8884827474559908756 ,3.3223484984915825288 ] 
dist 96=[-2.8475363592765433995 ,3.3399563167511070245 ] 
dist 97=[-2.7741116662513202372 ,3.3397046209860146516 ] 
dist 98=[-2.7528098492578480534 ,3.3578670771788282486 ] 
dist 99=[-1.2394326652661372049 ,3.7125384916286301928 ] 
dist 100=[-1.2259756561016011270 ,3.9671342561334896244 ] 
dist 101=[-1.0935244160386374229 ,4.1974659058966698146 ] 
dist 102=[-1.0665706298494771483 ,4.4553019769843899361 ] 
dist 103=[-1.0331206938636950954 ,4.6871217008214765318 ] 
dist 104=[-1.0206446605697577130 ,4.8136052455880448731 ] 
dist 105=[-.74736491717391109312,4.8873885195742723493 ] 
dist 106=[-.71118519508597580835,4.9088290916379187503 ] 
dist 107=[-.63505010032836921408,4.9379959993133618431 ] 
dist 108=[-.61431516808436978657,4.9597373883454607622 ] 
dist 109=[-.62511473259290906265,4.9585417541328071501 ] 
dist 110=[-.67019462333389307856,4.9476077528080006392 ] 
dist 111=[-.77942431596773250948,4.5907338258138247053 ] 
dist 112=[-1.4009456503093878580 ,4.5336284309879337822 ] 
dist 113=[-1.9217582892040682171 ,4.3609620756654943505 ] 
dist 114=[-2.4416421423888004069 ,4.1305668234328423338 ] 
dist 115=[-2.9214261449795689527 ,3.5220214622505899025 ] 
dist 116=[-3.2821692795214308388 ,3.4404239992976018405 ] 
dist 117=[-3.6249683698229724630 ,3.3209828358742702118 ] 
dist 118=[-4.0331205974929952109 ,3.2826404916839905566 ] 
dist 119=[-4.4127301731819539623 ,2.6205130675798401089 ] 
dist 120=[-4.6415918940244158097 ,2.6244269984409004210 ] 
dist 121=[-4.8039340162364295443 ,2.5745492732920276575 ] 
dist 122=[-4.9180111293988747439 ,2.5585321778118311108 ] 
dist 123=[-4.9995799501661090354 ,2.5405903953339004962 ] 
dist 124=[-5.0321586361549111356 ,2.5293452293678446968 ] 
dist 125=[-5.0378689023075123059 ,2.4984379684785868500 ] 
dist 126=[-5.0310798458509668985 ,2.4844234417514412764 ] 
dist 127=[-1.8344689130971264337 ,2.4565273643304949221 ] 
dist 128=[-1.8932674046280051669 ,2.4450983580434490921 ] 
dist 129=[-1.9481238929227900456 ,1.1130363856580857618 ] 
dist 130=[-1.9773219763250137741 ,.9971233114188860161 ] 
dist 131=[-1.9933248427350097214 ,.73013890378180504845] 
dist 132=[-1.9955080699407490799 ,.68186003527924157242] 
dist 133=[-1.9901640439535374909 ,.33717164572708844017] 
dist 134=[-1.9847449285464554685 ,.27551153127467948802] 
dist 135=[-1.9610235840919593253 ,.16898331209593354731] 
dist 136=[-1.9514986328736202244 ,.1453755621070547335 ] 
dist 137=[-1.8073224820333695463 ,-.13583192296595450777] 
dist 138=[-1.7817022954353012051 ,-.13125482334721490616] 
dist 139=[-1.7687797369486518007 ,-.11564188658623383708] 
dist 140=[-1.7864681301122505892 ,-.08090050065340587007] 
dist 141=[-1.7929528007051339844 ,-.03651651091111738123] 
dist 142=[-1.7920678597150259816 ,.02226957208549508272] 
dist 143=[-1.5374722838555259545 ,.12916461535282423932] 
dist 144=[-1.6557596843497207608 ,.50888462776935789038] 
dist 145=[-1.8169733211075133926 ,.94923022344821331015] 
dist 146=[-1.9176532981768573815 ,1.2373214722269337962 ] 
dist 147=[-1.9934222322415937777 ,1.4693239777460465032 ] 
dist 148=[-2.0551743661427515756 ,1.6857471573509722057 ] 
dist 149=[-2.1033136438688415456 ,1.8758265701298670801 ] 
dist 150=[-2.1247325220211251160 ,2.0026562572929356020 ] 
dist 151=[-2.1331622669554877110 ,2.1075530847933673312 ] 
dist 152=[-2.1316707120741513590 ,2.2100675246664541159 ] 
dist 153=[-2.0966152339239615124 ,2.3004297517727716053 ] 
dist 154=[-2.0855313646738001352 ,2.3568115068115274242 ] 
dist 155=[-2.0523149427500027354 ,2.3991376556318096457 ] 
dist 156=[-2.0382369505155266136 ,2.4333887304073153654 ] 
dist 157=[-1.9535902065837902742 ,2.4598498356739992383 ] 
dist 158=[-1.9318972652759420362 ,2.4710773430327538877 ] 
dist 159=[-1.8918170022951751466 ,2.4732962528251850509 ] 
dist 160=[-1.8791681720326640642 ,2.4689580041501788576 ] 
dist 161=[-.33172676228383142133,2.0717037063743027285 ] 
dist 162=[-.27255259707907827019,2.1867363707611634622 ] 
dist 163=[-.13670445003433523608,2.2836772724524600543 ] 
dist 164=[-.11342351100628300626,2.3412033686706959358 ] 
dist 165=[.05854050843369484209,2.3809544749436270916 ] 
dist 166=[.08860119467164816445,2.4069311284287237677 ] 
dist 167=[.13872638013321863501,2.4229638308495304178 ] 
dist 168=[.14993015885694534215,2.4234007488696210656 ] 
dist 169=[.31636894198227157545,2.4159998242951434369 ] 
dist 170=[.33822752249294313116,2.4075312756839347096 ] 
dist 171=[.37705255116825106622,2.3458776764766111082 ] 
dist 172=[.38474144495581545727,2.3274994774058734946 ] 
dist 173=[.39771639421147934013,2.2905936976963969944 ] 
dist 174=[.30191808189743714684,2.2770721952236716711 ] 
dist 175=[-.15351779345627507977,1.7455020001892209824 ] 
dist 176=[-.45985804502313332681,1.6938843993341555227 ] 
dist 177=[-.71599396083216291873,1.5600106950193348535 ] 
dist 178=[-.97099185391463995315,1.5396819419677267853 ] 
dist 179=[-1.2060902094121389027 ,1.3114671392649545591 ] 
dist 180=[-1.3827783307656511585 ,1.2660630826460174362 ] 
dist 181=[-1.5507228223698524335 ,1.2173469404221001249 ] 
dist 182=[-1.7509127133884904144 ,1.2053091009556008298 ] 
dist 183=[-1.9374604888037800351 ,.90049628154511021059] 
dist 184=[-2.0509394394044495946 ,.89931533257226626793] 
dist 185=[-2.1327495061050580401 ,.86054737949013573482] 
dist 186=[-2.1928605919881194298 ,.85267006058303721224] 
dist 187=[-2.2379065588552050599 ,.82974023878884258492] 
dist 188=[-2.2595696432172773245 ,.82409832089128080781] 
dist 189=[-2.2682728717592132257 ,.77313251094205104476] 
dist 190=[-2.2676351380644606154 ,.76140049587533434263] 
dist 191=[-.64318469065465746014,.74552560907923020395] 
dist 192=[-.78847714785323714053,.73951359216070257892] 
dist 193=[-.93252771413404333589,-.3219887042436858245 ] 
dist 194=[-1.0275789537410994149 ,-.38672763240378600586] 
dist 195=[-1.1050566061873378012 ,-.44767071963028933853] 
dist 196=[-1.1789434256244436075 ,-.45608576804171466192] 
dist 197=[-1.2449756949712029469 ,-.4537294260549141835 ] 
dist 198=[-1.2910934740957511994 ,-.43607031710367736452] 
dist 199=[-1.3315123931410368649 ,-.41200914104772265456] 
dist 200=[-1.3747914438485234770 ,-.38409234503950700645] 
dist 201=[-1.4126086024315806308 ,-.34797945392293202926] 
dist 202=[-1.4312205075676012413 ,-.2911940438172297584 ] 
dist 203=[-1.4433695454324109835 ,-.2253904338794601869 ] 
dist 204=[-1.4506895208632045772 ,-.1532721932983317890 ] 
dist 205=[-1.4516854155027220983 ,-.0626321944455409027 ] 
dist 206=[-1.4487848448914926702 ,.0771187576376614882 ] 
dist 207=[-1.4114736984588785911 ,.2180796897176084714 ] 
dist 208=[-1.4014749072912755933 ,.3135511309938003795 ] 
dist 209=[-1.2474317023646520365 ,.43734283456282170043] 
dist 210=[-1.2241601946114069719 ,.6131620551068401915 ] 
dist 211=[-1.1665595421869896496 ,.77635360792166387944] 
dist 212=[-1.1519817901957462852 ,.93788830152120757455] 
dist 213=[-1.0558242474035219500 ,1.0862317147210527984 ] 
dist 214=[-1.0352080335536482751 ,1.1967561195613933537 ] 
dist 215=[-.99821287659607250185,1.3008804614386536903 ] 
dist 216=[-.98821786373378177765,1.4236706881432757811 ] 
dist 217=[-.7870581674182019661 ,1.5374240108971248240 ] 
dist 218=[-.75870792150935294647,1.6054677866393561508 ] 
dist 219=[-.69166395335950187055,1.6531356653381998691 ] 
dist 220=[-.67713293215816167166,1.6855370047631332149 ] 
dist 221=[-.58025532720130769855,1.7081289227963085281 ] 
dist 222=[-.56118287793737970231,1.7166329338442672647 ] 
dist 223=[-.52680609262019661334,1.7172199518707293900 ] 
dist 224=[-.51822472596690619846,1.7147648019191813454 ] 
dist 225=[-.17361328108815060194,.92625898470111231721] 
dist 226=[-.13794393663428278318,.92248327371386284436] 
dist 227=[-.05424647625197372211,.88253602466158470351] 
dist 228=[-.04161039735754981759,.87228770910512638018] 
dist 229=[.06937102339081222739,.85985262372947994278] 
dist 230=[.08881962260002226153,.85412338869881632866] 
dist 231=[.1154174459751314661 ,.70483817174388693495] 
dist 232=[.12156746219876253631,.68361608721474762412] 
dist 233=[.24745864321787442347,.64000499868936315542] 
dist 234=[.26243786612196684897,.62771321163361497724] 
dist 235=[.29303489883833818365,.5783738703179341024 ] 
dist 236=[.2131538182649584428 ,.5677501849487156909 ] 
dist 237=[.10477428337878549392,.54273187798810027734] 
dist 238=[-.05508875218140748472,.53518196456394430329] 
dist 239=[-.21437508682965375518,.3972358061796517344 ] 
dist 240=[-.32045225024776892241,.39373997817931299626] 
dist 241=[-.40799784707804551014,.30882613272375427669] 
dist 242=[-.49329511380057713337,.30583089274654386997] 
dist 243=[-.57074415830568995138,.2964069055258245696 ] 
dist 244=[-.62695472797174767956,.2932361704526434643 ] 
dist 245=[-.67844108037043112343,.2902136500425886673 ] 
dist 246=[-.73702751697217489677,.2883328746534839725 ] 
dist 247=[-.79058044620816797523,.2866199740524694765 ] 
dist 248=[-.82197054835092273572,.2780303089814297526 ] 
dist 249=[-.84317295847986127634,.0577462574481006548 ] 
dist 250=[-.85605278214012329126,.0373765604285591993 ] 
dist 251=[-.86442246824206153492,.0136421874173451699 ] 
dist 252=[-.86761751963434122857,-.0118499122775541153 ] 
dist 253=[-.86763556411832988468,-.07882773534036986220] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 0, 1, 1, 1, 0, 2] 
dist 0=[41.610363673903332033  ,41.610363673903332033  ] 
dist 1=[41.291813094971677069  ,41.880960778612358557  ] 
dist 2=[40.290178831481087665  ,42.261868046375582661  ] 
dist 3=[39.224201613677948136  ,42.469470174556621316  ] 
dist 4=[38.415788109233104787  ,42.591823555544068118  ] 
dist 5=[37.638887391393798113  ,42.632310344112386860  ] 
dist 6=[36.698591950872396374  ,42.620584944546200399  ] 
dist 7=[35.721284385517144993  ,42.580882533001843790  ] 
dist 8=[34.796376382622154063  ,40.808073898724097659  ] 
dist 9=[33.729125281757823072  ,40.519983860771069223  ] 
dist 10=[32.182938295231702365  ,39.998868953690455186  ] 
dist 11=[30.593655976860141076  ,39.851217845340075140  ] 
dist 12=[29.354101010111017893  ,39.287087540948448337  ] 
dist 13=[28.127990239278535655  ,39.124724699601373983  ] 
dist 14=[26.592223049538032026  ,38.812547580986284384  ] 
dist 15=[24.966112118334893024  ,38.709041600798267949  ] 
dist 16=[23.378812237321681984  ,28.291251842385860123  ] 
dist 17=[21.507965609974743197  ,27.950735162489947302  ] 
dist 18=[18.748483896877518160  ,27.859073713086137722  ] 
dist 19=[15.992475293869106577  ,24.146716787572341983  ] 
dist 20=[14.135459639817178501  ,20.990288268143043956  ] 
dist 21=[12.572103211500993093  ,20.404570238827770228  ] 
dist 22=[10.989733325442245052  ,19.572262850040482059  ] 
dist 23=[9.5066043321790468258 ,19.330823151266788303  ] 
dist 24=[8.3398532227018122333 ,16.033875656653599935  ] 
dist 25=[6.8133583943008425193 ,15.838856035379060842  ] 
dist 26=[5.3096680688790486166 ,14.912445519598941500  ] 
dist 27=[3.6072430208280760860 ,12.660079451956785248  ] 
dist 28=[1.8970517628761406007 ,11.172895003783078123  ] 
dist 29=[.36186596092549098058,10.907129517065171448  ] 
dist 30=[-1.3479706977234914011 ,10.337327235422168118  ] 
dist 31=[-3.7568723419053932152 ,10.198648532944560267  ] 
dist 32=[-6.1067929299946108969 ,5.0049916686737486815 ] 
dist 33=[-7.5811184396879666821 ,4.4920041836231958567 ] 
dist 34=[-8.7059125226668830984 ,3.3917985471632921329 ] 
dist 35=[-9.6588257954482841751 ,3.1510890792017426475 ] 
dist 36=[-10.437273398984185885  ,1.9717842433037770782 ] 
dist 37=[-10.864944486952461041  ,1.7691044643845663781 ] 
dist 38=[-11.122444276044329383  ,1.3068587674827116591 ] 
dist 39=[-11.221286725991507778  ,1.2354313930750823833 ] 
dist 40=[-11.259909477188631564  ,.60769733771373643297] 
dist 41=[-11.276672980910870006  ,.4905309610436547519 ] 
dist 42=[-11.345630067031589091  ,.41830376830892254165] 
dist 43=[-11.544136026598373586  ,.45841836124597729052] 
dist 44=[-11.695322742613511324  ,.55331817847295208026] 
dist 45=[-11.757362065688285005  ,.7181704223790398646 ] 
dist 46=[-11.766729408976274066  ,.96422632946857725495] 
dist 47=[-11.751690251040638098  ,1.3832147360675606506 ] 
dist 48=[-6.4728110136736254830 ,1.8161719625454601267 ] 
dist 49=[-6.0653825999451789434 ,2.1180830015984407691 ] 
dist 50=[-5.5975239649710187224 ,2.3805959913037107057 ] 
dist 51=[-4.9329139269276299329 ,2.6566261026682402350 ] 
dist 52=[-3.5356873578309941502 ,2.9192705370780069598 ] 
dist 53=[-3.2799109639709698997 ,3.1285117250312303434 ] 
dist 54=[-2.9451429596142972358 ,3.3383459510534787961 ] 
dist 55=[-2.8569249631591275248 ,3.6034976401945650252 ] 
dist 56=[-.89131073803860986821,3.8576143035741920463 ] 
dist 57=[-.65144142310125191617,4.0234910638025816562 ] 
dist 58=[-.12430374948369492795,4.1565811927553067769 ] 
dist 59=[-.02641469826249905856,4.2799556432918917285 ] 
dist 60=[.55583712358741578969,4.4305585833099868679 ] 
dist 61=[.65072765838911542596,4.5761610384460746144 ] 
dist 62=[.84284036469090629032,4.6571972468029305556 ] 
dist 63=[.880434316116865602  ,4.6745162760134863588 ] 
dist 64=[1.0697242454474176755 ,4.2022592789284608692 ] 
dist 65=[.6889747636260516016 ,4.1836485292661165999 ] 
dist 66=[.09723459478866444583,4.3399905988644449984 ] 
dist 67=[-.49905792207792068383,4.6102756356745097280 ] 
dist 68=[-.8979839355192925759 ,4.8477656091825577848 ] 
dist 69=[-1.2285930317979332902 ,5.0078885762623041994 ] 
dist 70=[-1.5522393924252214496 ,5.1427263206152530986 ] 
dist 71=[-1.8464837954792807697 ,5.2792479693830733798 ] 
dist 72=[-2.0597472898537118285 ,5.3950937495762235841 ] 
dist 73=[-2.2544307577579519885 ,5.4473461503469860892 ] 
dist 74=[-2.4745091807369430414 ,5.4676083048232635410 ] 
dist 75=[-2.6759324042484406889 ,5.4650841338138029700 ] 
dist 76=[-2.7961632174116080738 ,5.3925366157057148976 ] 
dist 77=[-2.8798477590791652276 ,5.3637147177790643394 ] 
dist 78=[-2.9354291352593163545 ,5.3110969399959006200 ] 
dist 79=[-2.9723205290205654226 ,5.2900437433318192301 ] 
dist 80=[-3.0215290665669575612 ,2.0478096322144241091 ] 
dist 81=[-3.6200284168754930301 ,1.9519585715605373239 ] 
dist 82=[-4.1104485668329207432 ,1.9369031908293141828 ] 
dist 83=[-4.5823255273541178707 ,.19088767988300076099] 
dist 84=[-5.0068032824542531938 ,.14476082998561409184] 
dist 85=[-5.3080039514759033613 ,.03784913586987302102] 
dist 86=[-5.5769699964653117118 ,.02206629890237104164] 
dist 87=[-5.8727800315296626500 ,-.11408809323968000916] 
dist 88=[-6.1358897909045755424 ,-.13729084177757457979] 
dist 89=[-6.2743138477422079957 ,-.16952691778108249233] 
dist 90=[-6.3489338856303546991 ,-.17600702065062184249] 
dist 91=[-6.3647793685745407242 ,-.30935291304689316735] 
dist 92=[-6.3354443973004843912 ,-.32504831448373387703] 
dist 93=[-6.3160465301009648245 ,-.35351919370849435139] 
dist 94=[-6.2919664528593684015 ,-.35900617160228742987] 
dist 95=[-6.2670595154781210099 ,-.14544777892293875443] 
dist 96=[-5.8851944286141188685 ,.90236575770873550142] 
dist 97=[-5.8320743181950142698 ,1.7023515332405532722 ] 
dist 98=[-5.6556982092535982634 ,2.3730484911298260762 ] 
dist 99=[-5.6296850633523911058 ,3.0432678491354045731 ] 
dist 100=[-5.1926997206110971946 ,3.6624049540226995129 ] 
dist 101=[-5.0949283085384349932 ,4.1291854269019792412 ] 
dist 102=[-5.0169553192169846461 ,4.5740673112815600096 ] 
dist 103=[-4.9987351515730175320 ,5.1057853007034948324 ] 
dist 104=[-3.6776985838336304377 ,5.6015521328477957821 ] 
dist 105=[-3.5046058329728574294 ,5.9029175925052797702 ] 
dist 106=[-3.1723269368753171754 ,6.1197669125663286931 ] 
dist 107=[-3.0873373415686073099 ,6.2781471876624666079 ] 
dist 108=[-2.7976351275834362997 ,6.3934457524849246113 ] 
dist 109=[-2.7254935938308287927 ,6.4383166800806426809 ] 
dist 110=[-2.6544484161650453825 ,6.4488210839338524946 ] 
dist 111=[-2.6362713232944872618 ,6.4379188680922761099 ] 
dist 112=[-.24858177640285292116,1.1880923838105129533 ] 
dist 113=[-.31771644006891541252,1.2435581163932630935 ] 
dist 114=[-.38289943251761078786,1.2804904938111215726 ] 
dist 115=[-.45099709287734834658,1.3020979867269655950 ] 
dist 116=[-.51555551185319971244,1.3161984521585985881 ] 
dist 117=[-.56662610912422971989,1.3231356183673363768 ] 
dist 118=[-.61748149341292379094,1.3262494871097411945 ] 
dist 119=[-.68118560150840338165,1.3250492542263971004 ] 
dist 120=[-.74178304254780543436,1.1807090654793467652 ] 
dist 121=[-.78024710535293940621,1.1587311335929955453 ] 
dist 122=[-.80978275898104816993,1.1200815863643442569 ] 
dist 123=[-.83476429228249839642,1.1096866773860296761 ] 
dist 124=[-.85483812615630590224,1.0744196621730928275 ] 
dist 125=[-.86479568242110548829,1.0631915632222072268 ] 
dist 126=[-.86922154089753612708,1.0515212441914520673 ] 
dist 127=[-.86843990469402924168,1.0450581884489066239 ] 
dist 128=[.24374451016991728975,.45989883503339776477] 
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dist 130=[.02200269696019698626,.45419941782618547241] 
dist 131=[-.08149671145532572841,.22520088584048111584] 
dist 132=[-.19239249618303169692,.20796250522060149446] 
dist 133=[-.28141208451553969688,.16590968013386568773] 
dist 134=[-.3715728659227186361 ,.15986934634879908256] 
dist 135=[-.48703342752454497574,.09832285786279037769] 
dist 136=[-.59879423010100181973,.08703146242991336008] 
dist 137=[-.67418797581467845408,.07385065680319038785] 
dist 138=[-.7375009878776405136 ,.07156369910697043807] 
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dist 140=[-.85999738956182089333,-.03252955883559729933] 
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dist 143=[-1.0020185153568798344 ,-.08298775860253563369] 
dist 144=[-1.0511120711743171814 ,-.02955183023302542181] 
dist 145=[-1.0780157936383098704 ,.03797454298054829440] 
dist 146=[-1.0939156382670209764 ,.09961080527733894424] 
dist 147=[-1.0990629926728878166 ,.16936336669854658819] 
dist 148=[-1.0999194663527128045 ,.23904255548325301104] 
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dist 150=[-1.0956900084488337305 ,.3674243198995524665 ] 
dist 151=[-1.0923561082813462690 ,.4598163440067237014 ] 
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dist 155=[-.9062348732050553128 ,.7518390997384185650 ] 
dist 156=[-.8659532119519730284 ,.8226395747015158181 ] 
dist 157=[-.8558544415918123532 ,.8855972716808075982 ] 
dist 158=[-.8343359847215651687 ,.9549353998896821371 ] 
dist 159=[-.8272083618304767458 ,1.0512116013204834729 ] 
dist 160=[-.27066765883283749125,1.1444614675221788108 ] 
dist 161=[-.2781588885544505814 ,1.2017182986536699251 ] 
dist 162=[-.28899627440747965365,1.2436357233511161109 ] 
dist 163=[-.2996985066090223602 ,1.2756451516851978849 ] 
dist 164=[-.30665001190752037777,1.2990660830882848561 ] 
dist 165=[-.31220370229655101329,1.3066944256175840824 ] 
dist 166=[-.31732303477721783788,1.3083856933114795480 ] 
dist 167=[-.32178809130754038086,1.3081036895606705734 ] 
dist 168=[-.32472863709941235438,1.2593445885759161423 ] 
dist 169=[-.32712394252118156598,1.2484397158183214036 ] 
dist 170=[-.32941143815374639274,1.2224645664962774330 ] 
dist 171=[-.3312589483511968727 ,1.2126407089913210761 ] 
dist 172=[-.33189698273754914637,1.1618326197673371125 ] 
dist 173=[-.33177363886407394783,1.1495274200885514691 ] 
dist 174=[-.33097795437617403326,1.1192268640484975061 ] 
dist 175=[-.32878731061960565809,1.1081465701149598963 ] 
dist 176=[-.32752942619616386734,1.0096728878279781900 ] 
dist 177=[-.38353891791003370411,1.0114195020253112132 ] 
dist 178=[-.52363938960041366026,1.0092827370902778673 ] 
dist 179=[-.65922199958230934709,1.0067515119748518727 ] 
dist 180=[-.7816994678016604121 ,.9763778313914567658 ] 
dist 181=[-.8694775171827870052 ,.9675313905583965236 ] 
dist 182=[-.9487410001249112780 ,.9573347752109930801 ] 
dist 183=[-1.0372226036075161701 ,.9519857263261324172 ] 
dist 184=[-1.1184358741533840928 ,.8042001139782182707 ] 
dist 185=[-1.1686811362577281940 ,.7828491039067668023 ] 
dist 186=[-1.2059111050556655295 ,.7394919082197820445 ] 
dist 187=[-1.2351640597935215947 ,.7272351932583710493 ] 
dist 188=[-1.2570824969041685967 ,.6781210106654596699 ] 
dist 189=[-1.2650312893586484745 ,.6672203477859677472 ] 
dist 190=[-1.2669263789084184323 ,.6419177357952170497 ] 
dist 191=[-1.2646750816392085822 ,.6336071082945711613 ] 
dist 192=[-.25092698156549300363,.11695883238325186437] 
dist 193=[-.31490050291733544375,.12160302954385610957] 
dist 194=[-.3661591812390458419 ,.17650625624848901204] 
dist 195=[-.41356016020128303142,.24993056864606587715] 
dist 196=[-.45492721750105286753,.29743806732052339077] 
dist 197=[-.48209565908382097307,.33511712443532388163] 
dist 198=[-.5068762283422118605 ,.36930036182630830623] 
dist 199=[-.53309841710910930576,.39866903249975696116] 
dist 200=[-.54866768366583153574,.41712531093056362244] 
dist 201=[-.55943226430670863454,.43114351035362991372] 
dist 202=[-.56647282226901160046,.44279233351773712244] 
dist 203=[-.57115196531372796843,.45238384748923205194] 
dist 204=[-.57248856638524221   ,.45818828312591760169] 
dist 205=[-.57157419444097602405,.46233611885484569503] 
dist 206=[-.55865773415606083447,.46531460320834186769] 
dist 207=[-.51771479580766270251,.46731907228122514341] 
dist 208=[-.33610046510080966595,.46757889731216044331] 
dist 209=[-.31556145321884333238,.46661346271868071215] 

8 phat 4 dirichlet min maxes function [2, 2, 1, 1, 1, 1, 2, 0, 1] 
dist 0=[50.775919163069725981  ,50.775919163069725981  ] 
dist 1=[50.486078240193301837  ,50.837208910856098601  ] 
dist 2=[49.954958731219840247  ,50.796583267455293383  ] 
dist 3=[48.929571601621059367  ,50.723308658397253387  ] 
dist 4=[47.813001471449587389  ,50.606865117996909197  ] 
dist 5=[46.917632729324480283  ,50.559212050788637687  ] 
dist 6=[46.009138011017293401  ,50.513932639826450998  ] 
dist 7=[44.840264973842401332  ,50.368697638818512832  ] 
dist 8=[43.587958865757712286  ,46.384565347052540683  ] 
dist 9=[42.346212825505658470  ,45.810082910696263960  ] 
dist 10=[40.869695736389101794  ,45.127070839128853428  ] 
dist 11=[38.679534229769086500  ,44.581564015267158095  ] 
dist 12=[36.408600921843654109  ,44.046496877482065902  ] 
dist 13=[34.609423393273285446  ,43.796025806060394589  ] 
dist 14=[31.088541449723936351  ,43.654791803683992464  ] 
dist 15=[26.971574981874848806  ,43.423063948076507402  ] 
dist 16=[24.151884027912059650  ,32.640209400288561106  ] 
dist 17=[21.733400465745837261  ,32.308693500905866713  ] 
dist 18=[19.218998590748340268  ,31.989452303557132049  ] 
dist 19=[16.825031006808327167  ,31.900315798559488373  ] 
dist 20=[14.486817816634859279  ,16.838677668231774346  ] 
dist 21=[11.686670885985938581  ,15.716674499436592746  ] 
dist 22=[9.3463359330729611957 ,15.421855416653931739  ] 
dist 23=[7.0097822992697313040 ,13.195190281344224222  ] 
dist 24=[4.8440586493533732395 ,9.8259805728575781403 ] 
dist 25=[3.1860819572109773411 ,8.4659005071655923558 ] 
dist 26=[1.5759804016971357242 ,8.2345468967846932004 ] 
dist 27=[-.39870272686885502716,6.7380858690636790878 ] 
dist 28=[-2.2774304481689883584 ,6.4993999987258470015 ] 
dist 29=[-3.5043039726552984149 ,6.0484403778370093530 ] 
dist 30=[-4.4941509154987297734 ,5.9563373689802564098 ] 
dist 31=[-6.2112863000723221031 ,5.3444763193264283697 ] 
dist 32=[-8.0792452137112524812 ,-4.3543188788966617296 ] 
dist 33=[-9.2602206221703435405 ,-4.5483399792317912203 ] 
dist 34=[-10.171192881255595677  ,-4.8834275886729043978 ] 
dist 35=[-10.960024134371375919  ,-4.9363148693842519948 ] 
dist 36=[-11.616494855751893926  ,-7.7938913202282758931 ] 
dist 37=[-11.998568278420835873  ,-7.9643071806878825277 ] 
dist 38=[-12.256276722323965456  ,-8.2738229261637141840 ] 
dist 39=[-12.416017553740973250  ,-8.3255690515059065151 ] 
dist 40=[-12.516899096375873391  ,-8.3753280132278212052 ] 
dist 41=[-12.539369369372071425  ,-8.2810273266727076313 ] 
dist 42=[-12.514321304606869157  ,-7.5667281886140836972 ] 
dist 43=[-12.487591144486734734  ,-6.7162984528888568181 ] 
dist 44=[-12.272005421472109806  ,-5.7663749039100689810 ] 
dist 45=[-12.206000098985398800  ,-4.5612459548786954125 ] 
dist 46=[-11.988730659342981382  ,-2.6917798261460036608 ] 
dist 47=[-11.921920321277528927  ,-.80258352670529260416] 
dist 48=[-8.2407719371601897774 ,.48140639684899895971] 
dist 49=[-7.5402420676360556252 ,1.5690831889961252347 ] 
dist 50=[-7.4187277180358271648 ,2.6746345335145772034 ] 
dist 51=[-6.9661277300683430838 ,3.7084284598816749974 ] 
dist 52=[-6.1194298611604565246 ,4.5096768769826343452 ] 
dist 53=[-5.8334755148034464208 ,5.2949687044326158626 ] 
dist 54=[-5.7406801691350029731 ,6.2651128471933125831 ] 
dist 55=[-3.8514426126253184620 ,7.1868984223392334774 ] 
dist 56=[-3.6049037013425004717 ,7.7791383277132250023 ] 
dist 57=[-3.0703743573692190066 ,8.2441683607760082776 ] 
dist 58=[-2.9383422759858795505 ,8.6580724275344899693 ] 
dist 59=[-2.3342151133751652028 ,9.0233660044391970758 ] 
dist 60=[-2.2249549819489852527 ,9.3246346901034754494 ] 
dist 61=[-1.9610011921873084404 ,9.4675506041172299811 ] 
dist 62=[-1.9204068208338382200 ,9.5373441734327823618 ] 
dist 63=[.51219178871218260313,9.5466906659580424439 ] 
dist 64=[1.9213981853325035402 ,4.7136139626831533742 ] 
dist 65=[2.0618167326585840122 ,4.8072685050467805342 ] 
dist 66=[2.2552829446836362568 ,4.8596304683051334197 ] 
dist 67=[2.2428588067715655351 ,4.8705470357884408852 ] 
dist 68=[2.2149126901174065636 ,2.7452281193137399118 ] 
dist 69=[2.1826497831544679087 ,2.8341089259061923690 ] 
dist 70=[2.1335018824367831320 ,2.8926540057814688023 ] 
dist 71=[2.0037071794184000484 ,2.9255064265386669273 ] 
dist 72=[1.8630180316406186810 ,2.9465139117043200660 ] 
dist 73=[1.7221951848556614656 ,2.9577487425054051523 ] 
dist 74=[1.5542261767229168370 ,2.9641315521170098066 ] 
dist 75=[1.3051143613968981533 ,2.9657414838251923956 ] 
dist 76=[1.0478711899361724603 ,2.9643053082801897924 ] 
dist 77=[.84741110447062989889,2.9585172015697740825 ] 
dist 78=[.64987476090724418817,2.9485102339617210363 ] 
dist 79=[.40426718529992584209,2.9395039551169316485 ] 
dist 80=[.14601605233361879326,1.4907960128957161671 ] 
dist 81=[-.10203279089443789611,1.3670242487810691272 ] 
dist 82=[-.39062763737648958958,1.2499190770061873215 ] 
dist 83=[-.81081941242631238188,1.2394493553201953221 ] 
dist 84=[-1.2262786878388115415 ,.8725616498209028375 ] 
dist 85=[-1.4959841448072829674 ,.82825273787937926653] 
dist 86=[-1.7111488244712818482 ,.74292598473892633146] 
dist 87=[-1.9088085894935291460 ,.72149140025320457187] 
dist 88=[-2.0806329383421235062 ,.64977747132464477671] 
dist 89=[-2.1926315732915288216 ,.63244027921429877193] 
dist 90=[-2.2825416966561563742 ,.61700160602291281137] 
dist 91=[-2.3661695661445300772 ,.61510295284650860555] 
dist 92=[-2.4381838288892432952 ,.61919256750520043571] 
dist 93=[-2.4817138077250251590 ,.63147018694930065028] 
dist 94=[-2.5128624494443865485 ,.65199766983604046468] 
dist 95=[-2.5354144430264917485 ,.68904073788729381101] 
dist 96=[-2.5508048971130043488 ,.73379068165951400029] 
dist 97=[-2.5533436638155891997 ,.78509173113731596365] 
dist 98=[-2.5477336129563228956 ,.85099420894341201177] 
dist 99=[-2.5424008866821447755 ,.95403578581025522687] 
dist 100=[-1.9288711960667901616 ,1.0573494305947591313 ] 
dist 101=[-1.9398968468954734164 ,1.1243427055871735696 ] 
dist 102=[-1.9413645958603450879 ,1.1775633268042645249 ] 
dist 103=[-1.9393843028180299616 ,1.2259077300419601169 ] 
dist 104=[-1.7992990187061820392 ,1.2674229026538435563 ] 
dist 105=[-1.7749998398390050113 ,1.2933867151077931660 ] 
dist 106=[-1.7286736969871683693 ,1.3129355585779057337 ] 
dist 107=[-1.7145688683763468163 ,1.3288473289675599828 ] 
dist 108=[-1.6549915733492813353 ,1.3398597676192237941 ] 
dist 109=[-1.6394769421299540552 ,1.3410643267641168646 ] 
dist 110=[-1.6013504939596817662 ,1.3359035085252861181 ] 
dist 111=[-1.5872144825303290992 ,1.3311679905627589977 ] 
dist 112=[-.64860548300275780337,1.2873759986201994943 ] 
dist 113=[-.56452636454939162163,1.2746919292923437692 ] 
dist 114=[-.36976488261326122326,1.2574348365234726772 ] 
dist 115=[-.3365245823218763635 ,1.2498778384464769914 ] 
dist 116=[-.1692761084544167874 ,1.0456365014467146921 ] 
dist 117=[-.18719925087804713391,1.0163650018798853436 ] 
dist 118=[-.2024326784310311519 ,.95173866259214194822] 
dist 119=[-.21782981471285899752,.9323353191451177112 ] 
dist 120=[-.23202493264127101946,.84789561261292287559] 
dist 121=[-.24246865342469477565,.83058165235111209481] 
dist 122=[-.25208766236751240567,.78705697721828416755] 
dist 123=[-.26299287338651584554,.77710288522715011556] 
dist 124=[-.2726905612256609659 ,.66773325533455841476] 
dist 125=[-.27749464418376121044,.64882353368897410825] 
dist 126=[-.27960132012777301129,.64021449433481792587] 
dist 127=[-.27979088928588952791,.63743819438280282322] 
dist 128=[-.27606250756233512725,.63073199105344636689] 
dist 129=[-.27420601410524227416,.62738250036052152323] 
dist 130=[-.27023812535212663577,.62178336223832588633] 
dist 131=[-.26842578751831790812,.61942582480268594954] 
dist 132=[.18655524662293829448,.41366859055805473153] 
dist 133=[.1172904324092478792 ,.40653185374354468819] 
dist 134=[.05604028467963428759,.39603268184113083631] 
dist 135=[-.01038116623935228805,.39265601266207936331] 
dist 136=[-.07513991636833428288,.31854467499516615404] 
dist 137=[-.12975443832210982098,.30837890284360816943] 
dist 138=[-.18747128222392099748,.28609090604824368452] 
dist 139=[-.26462002713307137678,.27996248392173746856] 
dist 140=[-.34083821206941351587,.25290117520627577001] 
dist 141=[-.39484167712155613279,.24763942289700812262] 
dist 142=[-.44299536815494669578,.23491552823724978308] 
dist 143=[-.49585994699105004008,.23220594554681265489] 
dist 144=[-.5478147583160556486 ,.08657607065232208849] 
dist 145=[-.5923388701520588695 ,.07246401838849255518] 
dist 146=[-.64003082052981295998,.05422322328980345388] 
dist 147=[-.70463953343852385554,.12384392525586211318] 
dist 148=[-.7664937448436106154 ,.19514323605785090467] 
dist 149=[-.80318837762212206869,.24505686286847883684] 
dist 150=[-.82855495533286597426,.28889709492891877221] 
dist 151=[-.84517569497923491596,.33595284773814418418] 
dist 152=[-.85687660571375928266,.38151552802062606351] 
dist 153=[-.86259667052667599364,.41939631450973441555] 
dist 154=[-.86504909952984458031,.45893539293955620736] 
dist 155=[-.86387307426645667121,.51111921493123246152] 
dist 156=[-.78833041035351103046,.5623156749955294091 ] 
dist 157=[-.77608049578631183384,.5979137253475484476 ] 
dist 158=[-.75521776872779072136,.62893342590620202992] 
dist 159=[-.74917718577923593191,.66185342117296951594] 
dist 160=[-.72884731160415945949,.6935127928256608729 ] 
dist 161=[-.72215999289449672071,.71950067469155772028] 
dist 162=[-.71322838776049540539,.74633832572388350823] 
dist 163=[-.70928627783476968983,.78139142466463080781] 
dist 164=[-.22665143382906638295,.81434431683069724517] 
dist 165=[-.18587477724589937354,.83279755605179078174] 
dist 166=[-.11337088171984117315,.8441823551316877397 ] 
dist 167=[-.11063617131265047844,.8489154475069634729 ] 
dist 168=[-.06229664284013953988,.850085489500363683  ] 
dist 169=[-.05611000983207383019,.84868049925290165881] 
dist 170=[-.04165600268803034257,.84283137634982213268] 
dist 171=[-.03946453795427073822,.83901037595492466538] 
dist 172=[-.02039814345392050129,.77327874377096836779] 
dist 173=[-.01703274441440213825,.76186044289401319423] 
dist 174=[-.01874766326086884250,.73515234748168757451] 
dist 175=[-.03741082888454732066,.72615504627942094414] 
dist 176=[-.05607456785880474912,.68309842142928605418] 
dist 177=[-.06822640245439560436,.67334278765172617047] 
dist 178=[-.07791673975701868569,.65107058469201529265] 
dist 179=[-.08675855762146718050,.64361133822274326359] 
dist 180=[-.2434940407343744041 ,.6587260976016277658 ] 
dist 181=[-.35600644451606122057,.68013246205524526446] 
dist 182=[-.44740938334000897774,.69472715619832187354] 
dist 183=[-.53404576925402717377,.70388070731538163046] 
dist 184=[-.61110158198621259701,.70946338009788519634] 
dist 185=[-.66425435442414948327,.71004466351477265129] 
dist 186=[-.71013496296055173398,.70806339475401643698] 
dist 187=[-.75815648611639716886,.70547266973161876343] 
dist 188=[-.80153117049543069964,.66295452781180586559] 
dist 189=[-.82885945862194953516,.65499200307624925255] 
dist 190=[-.84969430470986419945,.63645780628182530753] 
dist 191=[-.86714464548244755661,.63003691053866981172] 
dist 192=[-.88110303731306510517,.59868387073157977577] 
dist 193=[-.88799654687293872168,.59144871694345787142] 
dist 194=[-.89103974834361058015,.5740567997660456076 ] 
dist 195=[-.89008385832485963555,.5679590261151778858 ] 
dist 196=[-.07651219134462359081,.06680204430358860182] 
dist 197=[-.09841274276833350047,.07113100271230621334] 
dist 198=[-.1221623599217039229 ,.07684290091963181772] 
dist 199=[-.1546903206753568533 ,.08594340506697337539] 
dist 200=[-.18718436303537027588,.09559784516979133299] 
dist 201=[-.2107989582806865466 ,.10352092001852646295] 
dist 202=[-.23246598372837947847,.11170006361211606764] 
dist 203=[-.25718448458176227807,.12237641103004804462] 
dist 204=[-.28201907225777952206,.13385137286664779874] 
dist 205=[-.30415017191199057405,.14521837474926017351] 
dist 206=[-.32857573484863585447,.15869220721963485076] 
dist 207=[-.3625726109364428765 ,.17857732552220897827] 
dist 208=[-.39548795220739110595,.19826467241189974561] 
dist 209=[-.41559538434779666536,.21703714815675523339] 
dist 210=[-.43020373199812179182,.24431965806351578109] 
dist 211=[-.44116203031033544115,.27199079639517497148] 
dist 212=[-.44923556200576642498,.29783033766981848464] 
dist 213=[-.45232525814129927688,.31780037521385835091] 
dist 214=[-.45318712802423355988,.33731773586620722518] 
dist 215=[-.45236944369229931303,.36134997925717495954] 
dist 216=[-.43244698060225126572,.38413679333082153514] 
dist 217=[-.42827667263810017982,.39868187107180053318] 
dist 218=[-.41952064113520958188,.40999043834934160551] 
dist 219=[-.4164780047083309318 ,.41985574853127313556] 
dist 220=[-.40158925542036902642,.42805009633071050065] 
dist 221=[-.39814761889638899186,.43268743748047090778] 
dist 222=[-.38699029802596681914,.43561142391908443562] 
dist 223=[-.38517203246557276612,.43696521064101266329] 
dist 224=[-.2329148373805283949 ,.43706198685351179407] 
dist 225=[-.22662577684116208515,.43632521023535460302] 
dist 226=[-.21005371538509945736,.43236997323313982852] 
dist 227=[-.207664912895246015  ,.43045944672006299278] 
dist 228=[-.17862000007686287036,.41460982552891435093] 
dist 229=[-.17280726801645549547,.41033366868713251995] 
dist 230=[-.16705752705269175936,.40410885521082793123] 
dist 231=[-.16595247113674469972,.40167701007433757727] 
dist 232=[-.10364944581966682125,.33848556986745601021] 
dist 233=[-.09578144311080478755,.32929582359550212594] 
dist 234=[-.08019921443891395498,.3098156482235292726 ] 
dist 235=[-.07622833096222358962,.30412490904176589614] 
dist 236=[-.06249952185882930445,.28006449148664850583] 
dist 237=[-.05940535520350855197,.27514310986915974351] 
dist 238=[-.05593654260060078481,.26167472652921577694] 
dist 239=[-.05519124807513922768,.259382129546744397  ] 
dist 240=[-.12218605783992317068,.27031768078155147216] 
dist 241=[-.17409481295396888777,.28838982695804762672] 
dist 242=[-.21668929912307360783,.3024347871010727607 ] 
dist 243=[-.25778290846244839328,.31468472462165984234] 
dist 244=[-.29482688181377532629,.32486449292269489312] 
dist 245=[-.32125290024985447758,.33064394690339276801] 
dist 246=[-.34499443782914164399,.33431582168685823512] 
dist 247=[-.37132033754251631894,.33608088912384974422] 
dist 248=[-.39525828382580723625,.33656590919667149602] 
dist 249=[-.40946574195745969761,.33619680096173453293] 
dist 250=[-.41928236057397327803,.33328421488046103376] 
dist 251=[-.4256896455722140609 ,.33215714617749487458] 
dist 252=[-.42984113552508483691,.31925236668773959957] 
dist 253=[-.43065140062565098051,.3158351886013528892 ] 
dist 254=[-.42998744913798597495,.31190954386472721467] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 0, 0, 1, 1, 1, 2] 
dist 0=[50.129341772821974240  ,50.129341772821974240  ] 
dist 1=[49.391817270200513598  ,50.509102083724631720  ] 
dist 2=[48.533575585657315503  ,50.700153004873874152  ] 
dist 3=[47.671644457122086388  ,50.728599280006112406  ] 
dist 4=[46.639756642045720735  ,50.586548531244453897  ] 
dist 5=[45.102480107908203280  ,50.489546905952639831  ] 
dist 6=[43.352431702048352692  ,50.283716609031386287  ] 
dist 7=[41.470554736881859184  ,50.183420315585114436  ] 
dist 8=[39.125804082919192159  ,49.498953483338224808  ] 
dist 9=[35.526731854438894727  ,47.300834369899951055  ] 
dist 10=[31.883069804902558629  ,46.692223627414431091  ] 
dist 11=[29.360135445416071880  ,46.484606607265184885  ] 
dist 12=[27.167182173707929798  ,46.109524353517560681  ] 
dist 13=[24.841495129141873829  ,45.386657461525040429  ] 
dist 14=[22.599169090816628357  ,41.722320498592441676  ] 
dist 15=[20.739062671391959505  ,39.269755137186120895  ] 
dist 16=[18.796075845026351038  ,36.663326445291189018  ] 
dist 17=[16.222403615009817936  ,30.221470149608475720  ] 
dist 18=[13.680509748042588393  ,29.387459896256303294  ] 
dist 19=[11.864313233303230577  ,27.755455907890456829  ] 
dist 20=[10.224718502936942589  ,27.336204696060014862  ] 
dist 21=[8.3880968603841798646 ,25.871827012748731098  ] 
dist 22=[6.5554304108162025400 ,25.532154676395852343  ] 
dist 23=[4.9313336527727811089 ,25.090672229111410482  ] 
dist 24=[3.1408888661498500102 ,24.936795097374070858  ] 
dist 25=[.64300767915075973815,12.713806531132643243  ] 
dist 26=[-1.8047806678929313703 ,11.705626681051662538  ] 
dist 27=[-3.3951677428112779443 ,11.478280664634505317  ] 
dist 28=[-4.6704946224151814178 ,10.863654303000829943  ] 
dist 29=[-5.8591510835064007071 ,10.427535999883982631  ] 
dist 30=[-6.9092689103223993896 ,9.0105571106729511333 ] 
dist 31=[-7.6310125506210409513 ,8.2428541935893429802 ] 
dist 32=[-8.2550537663050917329 ,.35099652574912518427] 
dist 33=[-8.9149508827026687873 ,-3.6441155824380126756 ] 
dist 34=[-9.5000181269036220275 ,-4.1162511128610520527 ] 
dist 35=[-10.336445227056792643  ,-5.1300136926160261869 ] 
dist 36=[-11.201293447467524977  ,-5.2957772264770641673 ] 
dist 37=[-11.733702036563931458  ,-6.3042341698520744119 ] 
dist 38=[-12.128890229709289378  ,-6.0982821485526888368 ] 
dist 39=[-12.445695021795562941  ,-5.3289286509218978407 ] 
dist 40=[-12.692629188402582443  ,-4.3199457472042561159 ] 
dist 41=[-12.808578945468150061  ,-2.7207685114999325428 ] 
dist 42=[-12.853356203482013524  ,-1.0954977716820776882 ] 
dist 43=[-12.843845731881963734  ,.01775793996286920050] 
dist 44=[-12.734667175829207937  ,.96915931565225486662] 
dist 45=[-12.687456253941089901  ,1.9485181441882008115 ] 
dist 46=[-12.488367403874460156  ,2.8711357276386159503 ] 
dist 47=[-12.437850267822595416  ,3.5961138399110794187 ] 
dist 48=[-7.8725822191208244930 ,4.3154274504967960660 ] 
dist 49=[-7.4323392385661293902 ,5.2154883341694334038 ] 
dist 50=[-6.3700382520531457117 ,6.0751448220955060683 ] 
dist 51=[-6.1971593920055858398 ,6.6331887989676872382 ] 
dist 52=[-5.5036824561100020444 ,7.0774215043571964139 ] 
dist 53=[-5.1156604719920095874 ,7.4827638007521497063 ] 
dist 54=[-5.0268285107885218406 ,7.8322630680873026771 ] 
dist 55=[-4.8771727299238005763 ,8.0535679303508728966 ] 
dist 56=[-4.8371585595085482034 ,8.2233734051562219744 ] 
dist 57=[-1.9098554406933571617 ,8.3672623798223755280 ] 
dist 58=[-1.3409490709607725776 ,8.4791996943283029568 ] 
dist 59=[-.76381873258406368511,8.5214492869542194332 ] 
dist 60=[-.68122968511206293566,8.5205953609624589633 ] 
dist 61=[.10468727441643191487,8.5075783526001754412 ] 
dist 62=[.24448235258607599693,8.3743497967125367713 ] 
dist 63=[.41541472197393311816,8.2307941316837673573 ] 
dist 64=[.44397759652348232113,3.6361096552695819100 ] 
dist 65=[1.4782936468375461841 ,4.0396741029199492987 ] 
dist 66=[1.5990230357061355433 ,4.2837252396105299284 ] 
dist 67=[1.8555276234649463393 ,4.4585657814912610391 ] 
dist 68=[1.9050680634894410385 ,4.5857165684860153400 ] 
dist 69=[2.1531430673718499779 ,4.6813213489156121910 ] 
dist 70=[2.1941737969970669364 ,4.7301222769624387168 ] 
dist 71=[2.2597894801825269888 ,4.7542175237902812230 ] 
dist 72=[2.2723907173926086922 ,4.7528748100856949129 ] 
dist 73=[1.8070695381013521542 ,3.9248593514771926697 ] 
dist 74=[1.3222895731609646990 ,3.2844189652071352894 ] 
dist 75=[.98081687014346898134,3.2829523997549507050 ] 
dist 76=[.6786924525504953995 ,3.2781574716082850760 ] 
dist 77=[.35096541082604636968,3.2689957903765265308 ] 
dist 78=[.03152019846116272859,3.2549317653616194632 ] 
dist 79=[-.23756133979438521128,3.2450076894796469869 ] 
dist 80=[-.52156715529882983312,2.3208607500909223581 ] 
dist 81=[-.90061902474847116765,2.2908701928870169972 ] 
dist 82=[-1.2746776959280687253 ,1.6830925168715965848 ] 
dist 83=[-1.5387614729991737688 ,1.6005851183856968378 ] 
dist 84=[-1.7731947243193296679 ,1.4082261446535971152 ] 
dist 85=[-2.0288918769127408984 ,1.3687666684116827366 ] 
dist 86=[-2.2791473543880795691 ,1.1048755131746946750 ] 
dist 87=[-2.4918711535952005512 ,1.0547210315113664798 ] 
dist 88=[-2.7182062040455118906 ,.96414001251360202792] 
dist 89=[-3.0714470834595557116 ,.94237519776236737917] 
dist 90=[-3.3161506461839936663 ,.63150282344999479774] 
dist 91=[-3.4973182933559425658 ,.7247522329885980792 ] 
dist 92=[-3.6313740235657169663 ,.84074795478856526678] 
dist 93=[-3.7365746737002946379 ,.96245203001591213439] 
dist 94=[-3.8154644127379668966 ,1.0785010047171797322 ] 
dist 95=[-3.8444678800087682062 ,1.2126466182955997699 ] 
dist 96=[-3.8537247255213262809 ,1.4065993205184371000 ] 
dist 97=[-3.8537392853672827221 ,1.6045582141139122392 ] 
dist 98=[-3.7414561189061469611 ,1.7547039778661257118 ] 
dist 99=[-3.7137821708453617288 ,1.8986487307991772558 ] 
dist 100=[-3.6439010197178867858 ,2.0718683157169007819 ] 
dist 101=[-3.6160419196293253606 ,2.2507866482914399301 ] 
dist 102=[-3.4674955813645359036 ,2.4174896400670443795 ] 
dist 103=[-3.4307100366154022030 ,2.6073063411179142565 ] 
dist 104=[-3.3471330363999950785 ,2.8785055917385549284 ] 
dist 105=[-3.3175942738809358873 ,3.1433977452869994249 ] 
dist 106=[-2.2622283610092018846 ,3.3080375123001544358 ] 
dist 107=[-2.2462658802161501406 ,3.4308991356796319832 ] 
dist 108=[-2.1676228540215836569 ,3.5290049277830173006 ] 
dist 109=[-2.1493295259559754215 ,3.6037646380227806612 ] 
dist 110=[-2.0932315526276398215 ,3.6334227863246245193 ] 
dist 111=[-2.0819521273125086692 ,3.6431902070954795386 ] 
dist 112=[-1.2792360326304899989 ,3.6385482045189403014 ] 
dist 113=[-1.2069711962301165030 ,3.5545554699889947485 ] 
dist 114=[-1.0317201501801930081 ,3.5313042058976236375 ] 
dist 115=[-1.0040875843975949060 ,3.4661559682533422909 ] 
dist 116=[-.74695284917941777064,3.4386119209139844715 ] 
dist 117=[-.69882598611950280687,3.2864620852007343733 ] 
dist 118=[-.63711089403210952664,3.0675840695428233783 ] 
dist 119=[-.61952596467802456597,3.0113562547728503498 ] 
dist 120=[-.22125141008655266224,2.6728136538834685711 ] 
dist 121=[-.34426189794416914939,1.9603769411508895412 ] 
dist 122=[-.44544493248350295403,1.8496382450255904834 ] 
dist 123=[-.53013177847776973798,1.9116181969348055374 ] 
dist 124=[-.61441674415786266796,1.9596277664964959981 ] 
dist 125=[-.69196403061135572413,1.9834510194641418519 ] 
dist 126=[-.74976017240289046764,1.9941580717934718110 ] 
dist 127=[-.80413901485081062101,1.9953363366200989550 ] 
dist 128=[-.86804573697009215669,1.2127635147272612929 ] 
dist 129=[-.92696120669314207679,1.0716065289478334917 ] 
dist 130=[-.9614185386963270677 ,1.0506474495076682418 ] 
dist 131=[-.98453654251706536829,1.0150411858255163620 ] 
dist 132=[-.99819473668692353572,1.0051950202508467685 ] 
dist 133=[-1.0063085675109254042 ,.97505701411233288667] 
dist 134=[-1.0072993137240699485 ,.96480495344259916071] 
dist 135=[-1.0045707866143452820 ,.95808454693112728259] 
dist 136=[-1.0013533259623057718 ,.95489414391849198923] 
dist 137=[.21791510838978928004,.93667235282816163381] 
dist 138=[.09177121335050632101,.9475057253758448084 ] 
dist 139=[-.01987369394467954803,.95086866641008180509] 
dist 140=[-.14111007365670209757,.95076543664674239208] 
dist 141=[-.25941823846953308596,.94853658028308351171] 
dist 142=[-.35937443655619531502,.94297445554718207987] 
dist 143=[-.46516553715298636197,.93964472854965903229] 
dist 144=[-.60677339131804630678,.85701195081052084064] 
dist 145=[-.74675004335115229777,.84426548590858851207] 
dist 146=[-.84603013483374963674,.80956158621727438839] 
dist 147=[-.93465060251143294529,.80274296533658600755] 
dist 148=[-1.0320695193004508120 ,.73535763271647222701] 
dist 149=[-1.1278646797313849931 ,.72079657751285481181] 
dist 150=[-1.2100045970331293656 ,.70286368861666604475] 
dist 151=[-1.2980051227602228333 ,.69572852359870361367] 
dist 152=[-1.4172047751306380699 ,.52947867332296895451] 
dist 153=[-1.5311959484704651638 ,.5067847630860070412 ] 
dist 154=[-1.5984013976716504922 ,.54189879524082897792] 
dist 155=[-1.6443147107968077796 ,.63690831896429549126] 
dist 156=[-1.6732903598160400869 ,.73733298993364534716] 
dist 157=[-1.6930228805286799541 ,.83367352018202529383] 
dist 158=[-1.7020288721297283702 ,.91237888142051748718] 
dist 159=[-1.7049231118687857832 ,.99332229944368455422] 
dist 160=[-1.7022127125366814308 ,1.0985990456613073776 ] 
dist 161=[-1.5493033564595002010 ,1.2012021461218807127 ] 
dist 162=[-1.5245503082028604597 ,1.2714721290359066198 ] 
dist 163=[-1.4805757614085891907 ,1.3315886916929970166 ] 
dist 164=[-1.4683188112368784598 ,1.3936567383580004526 ] 
dist 165=[-1.4231147590399043616 ,1.4523117254227124894 ] 
dist 166=[-1.4093670665952967949 ,1.4988029866537792935 ] 
dist 167=[-1.3860830411548174556 ,1.5453429633881622852 ] 
dist 168=[-1.3782962427649424085 ,1.6041939436524799387 ] 
dist 169=[-.8522732422921213792 ,1.6587908749704524467 ] 
dist 170=[-.805931263958965136  ,1.6883471441135952132 ] 
dist 171=[-.7931867505896037651 ,1.7052547450564736832 ] 
dist 172=[-.74448298414539261385,1.7093521046924088751 ] 
dist 173=[-.73291804524230137747,1.7070262399129972652 ] 
dist 174=[-.70984805502242835902,1.7026890688264439184 ] 
dist 175=[-.70286767360443774894,1.6874672329489602918 ] 
dist 176=[-.47194685589667024322,1.6788690948187463257 ] 
dist 177=[-.46690807008614155286,1.5441511316401426052 ] 
dist 178=[-.45546021481802214669,1.5209355068571288539 ] 
dist 179=[-.45144232446295090952,1.4652043061407890846 ] 
dist 180=[-.43163042953361697994,1.4470956212717339608 ] 
dist 181=[-.42700155859472571354,1.3552751508973249754 ] 
dist 182=[-.41503245249850161569,1.3345472950396822813 ] 
dist 183=[-.41117890857928652712,1.2910406441707369846 ] 
dist 184=[-.36710788522884985435,1.2772973180836342045 ] 
dist 185=[-.54983810618360044685,1.3304631319124347500 ] 
dist 186=[-.77754389571783314789,1.3753964581973342917 ] 
dist 187=[-.96199595254400607488,1.4063490805449912404 ] 
dist 188=[-1.1359505290090467810 ,1.4263798663135499820 ] 
dist 189=[-1.2900848697649635246 ,1.4389858374034201682 ] 
dist 190=[-1.3954042851524740633 ,1.4406784337429990227 ] 
dist 191=[-1.4852571255449262984 ,1.4372261132704159558 ] 
dist 192=[-1.5776404350041611138 ,1.4323656187910683152 ] 
dist 193=[-1.6606617279327729906 ,1.3499561962647808579 ] 
dist 194=[-1.7131366869564753237 ,1.3342591076722180732 ] 
dist 195=[-1.7533425701245985920 ,1.2975604923489799806 ] 
dist 196=[-1.7873802239909960799 ,1.2847230172820189939 ] 
dist 197=[-1.8148909711628126555 ,1.2216092173158057344 ] 
dist 198=[-1.8290384720316309700 ,1.2069554112544225514 ] 
dist 199=[-1.8361201806710140223 ,1.1718708306449288627 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 1, 0, 1, 0, 2] 
dist 0=[41.986871738950401816  ,41.986871738950401816  ] 
dist 1=[41.740166771142188897  ,42.224289527707189180  ] 
dist 2=[40.992354138511294415  ,42.541825726575630543  ] 
dist 3=[40.048998082061494998  ,42.750131253666969638  ] 
dist 4=[38.909767208330826781  ,42.917781243558836567  ] 
dist 5=[37.405809760432157567  ,43.072776018722854608  ] 
dist 6=[35.005697789309878831  ,43.247576463214591127  ] 
dist 7=[32.554822812469491558  ,43.493938527462355072  ] 
dist 8=[30.848024424976885111  ,43.723988587123181381  ] 
dist 9=[29.354717913786477495  ,43.833673441274605228  ] 
dist 10=[27.756287830760432007  ,43.875277986531125650  ] 
dist 11=[26.206356386098728673  ,43.845843953590541202  ] 
dist 12=[24.906511047474354753  ,43.741872300982015517  ] 
dist 13=[23.536006771616247008  ,43.680038405456838183  ] 
dist 14=[21.703381661727243741  ,43.344176122448033614  ] 
dist 15=[19.883801512116674400  ,42.635889887965238042  ] 
dist 16=[18.565163088923075665  ,35.355789066229706579  ] 
dist 17=[17.354751050673658048  ,34.603609003499010046  ] 
dist 18=[15.967204919611818821  ,32.725517997812561557  ] 
dist 19=[14.562520415761244941  ,32.444016984630024771  ] 
dist 20=[13.283208497792883273  ,29.463424049951845498  ] 
dist 21=[11.842526291840777795  ,28.882550760287459861  ] 
dist 22=[9.7922087592186986168 ,28.246884473422850822  ] 
dist 23=[7.7669881022705227811 ,28.097717480084860653  ] 
dist 24=[6.4264914198568933983 ,22.365725547779560375  ] 
dist 25=[5.3216472160725042682 ,21.630297736509032732  ] 
dist 26=[4.2385896996997535798 ,20.174859196285899510  ] 
dist 27=[2.1373936912953363929 ,19.800457150651587973  ] 
dist 28=[-.27655257992435889816,18.480462356656336297  ] 
dist 29=[-1.8413593997673678398 ,18.185099711509286220  ] 
dist 30=[-3.0933249484346343962 ,17.769160495590031839  ] 
dist 31=[-4.2567835736514862718 ,17.640033458533253238  ] 
dist 32=[-5.2834757484600686488 ,5.7152013486608218732 ] 
dist 33=[-5.9888484284425403620 ,4.7240118298453791823 ] 
dist 34=[-6.5991255362628332807 ,2.4459231533008036174 ] 
dist 35=[-7.2459660096088425899 ,2.0939485769487168360 ] 
dist 36=[-7.8248182383065731284 ,.86079185950745878363] 
dist 37=[-8.1633336002686906560 ,.97788778059272777278] 
dist 38=[-8.3939351131824429427 ,1.2184208296645645034 ] 
dist 39=[-8.5411708070714192104 ,1.4743186258098576633 ] 
dist 40=[-8.6355279094035733703 ,1.6528812807013047935 ] 
dist 41=[-8.6712702475060667666 ,1.8067831028858922179 ] 
dist 42=[-9.2251118998488261169 ,1.9647654803414539569 ] 
dist 43=[-9.6713445016272633854 ,2.1113690863625361525 ] 
dist 44=[-10.024456386737901828  ,2.2200776439003156130 ] 
dist 45=[-10.206248133101667593  ,2.3209171089479305462 ] 
dist 46=[-10.298181481710209897  ,2.4362683343497759496 ] 
dist 47=[-10.315271841341424370  ,2.5397378624902253459 ] 
dist 48=[-7.6730954257171645014 ,2.5932666131950979673 ] 
dist 49=[-7.5054559976830248731 ,2.6204117316642379775 ] 
dist 50=[-7.0617816154573750230 ,2.6252160865271477956 ] 
dist 51=[-6.9950928878461520062 ,2.6037648626879309439 ] 
dist 52=[-6.2149573307125578196 ,2.5896495059478491402 ] 
dist 53=[-6.0956698294071906610 ,2.9838509473716421150 ] 
dist 54=[-5.8953088010303733171 ,3.4009711949250555648 ] 
dist 55=[-5.8568590970239043119 ,3.8303575813927909400 ] 
dist 56=[-4.2159876974945503186 ,4.2358964568099598108 ] 
dist 57=[-4.0073442922520088019 ,4.5579009004982540883 ] 
dist 58=[-3.5882132042811768771 ,4.8813636794673806906 ] 
dist 59=[-3.4799338983278599606 ,5.2929015850930903516 ] 
dist 60=[-3.0950691064923998692 ,5.6809541429501839191 ] 
dist 61=[-3.0113759258126652209 ,5.9106637278725045587 ] 
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dist 63=[-2.8572482364041114701 ,6.1739452919466754448 ] 
dist 64=[.21960810718389486095,6.2432143745188654550 ] 
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dist 66=[.32043333459318659171,6.2548490697850923472 ] 
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dist 68=[-.09095329572183083695,5.8471089842268379168 ] 
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dist 72=[-1.1622431556980060917 ,5.3175716383794353344 ] 
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dist 77=[-1.8148222343521983610 ,4.3538097800912317786 ] 
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dist 80=[-3.2007925882976204640 ,3.5317447873313497170 ] 
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dist 85=[-4.9902371314434041430 ,2.4779894149298988633 ] 
dist 86=[-5.1652709950810072601 ,2.2696455320364917014 ] 
dist 87=[-5.3041374835232380799 ,2.2151494076810646801 ] 
dist 88=[-5.4093370540308786478 ,2.0201022553675462794 ] 
dist 89=[-5.4499367288255956669 ,1.9747238099953106501 ] 
dist 90=[-5.4630715303749183877 ,1.9064033673250456957 ] 
dist 91=[-5.4586219161826423098 ,1.8856985907646354560 ] 
dist 92=[-1.9267476626885127015 ,1.5439474559376543560 ] 
dist 93=[-2.0234825548620942914 ,1.6060286578257584036 ] 
dist 94=[-2.1455594653248699704 ,1.6684055410480006644 ] 
dist 95=[-2.3180160112697317151 ,1.7214690752232113019 ] 
dist 96=[-2.4793492173777838739 ,1.7463751678219938212 ] 
dist 97=[-2.5704081408635158685 ,1.7577589714777710934 ] 
dist 98=[-2.6278840456514995456 ,1.7575214683907539975 ] 
dist 99=[-2.6550757632825107786 ,1.7297094455660069915 ] 
dist 100=[-2.6695014455249356600 ,1.7178499482918516388 ] 
dist 101=[-2.6759683741509994342 ,1.7063604002206463700 ] 
dist 102=[-2.6779959061822047641 ,1.6978265821202499474 ] 
dist 103=[-2.6746382307981342027 ,1.7518172982697084451 ] 
dist 104=[-2.3521117225925283435 ,1.8078828818527878546 ] 
dist 105=[-2.3042515941661189832 ,1.8917607613539631352 ] 
dist 106=[-2.2186696231059956766 ,1.9528283585682757466 ] 
dist 107=[-2.1960289533133964240 ,1.9986152898923868400 ] 
dist 108=[-2.1185387433152853682 ,2.0309765724512122428 ] 
dist 109=[-2.0948387858403306324 ,2.0384674295722125407 ] 
dist 110=[-2.0698307566345721221 ,2.0370693283984789421 ] 
dist 111=[-2.0565109886671353623 ,2.0339713238264972757 ] 
dist 112=[-1.5793950882305764321 ,1.4143318326929951295 ] 
dist 113=[-1.6345463994911084057 ,1.3401310288887459862 ] 
dist 114=[-1.6705924958173464128 ,1.3208490038336080852 ] 
dist 115=[-1.6961186985736526387 ,1.2551269993288983934 ] 
dist 116=[-1.7092840250792670181 ,1.2367777292123243768 ] 
dist 117=[-1.7159124971303071753 ,1.2179583925513219247 ] 
dist 118=[-1.7153688561479649387 ,1.2089355419148252527 ] 
dist 119=[.02887979028273531234,1.1519615758075046642 ] 
dist 120=[-.15730912440045050157,1.4136766060214143627 ] 
dist 121=[-.3124193250977524677 ,1.5953012091302249277 ] 
dist 122=[-.46593164212682569366,1.7533144691151530947 ] 
dist 123=[-.60689342584811628527,1.9207642093364249366 ] 
dist 124=[-.71189731009624449965,2.0818075768104875297 ] 
dist 125=[-.81080666464930194437,2.2142506131474077944 ] 
dist 126=[-.92743906284874585265,2.3513617570523821864 ] 
dist 127=[-1.0358886844211685935 ,2.5310610078314854582 ] 
dist 128=[-1.1021282496938909456 ,2.7004609117254670386 ] 
dist 129=[-1.1502201434173708623 ,2.7964514470793004303 ] 
dist 130=[-1.1862120131043818284 ,2.8572591607719922749 ] 
dist 131=[-1.2135456007974260895 ,2.8861718242237811640 ] 
dist 132=[-1.2270689864850974384 ,2.9019860631555674626 ] 
dist 133=[-1.2714762353228676721 ,2.9104858238247043349 ] 
dist 134=[-1.4254840322862307724 ,2.9153012971052592192 ] 
dist 135=[-1.6309085158966602302 ,2.9163887752821927111 ] 
dist 136=[-1.8334901899686403847 ,2.5561806011428643153 ] 
dist 137=[-1.9761515719343007750 ,2.5035805463969650952 ] 
dist 138=[-2.1023803191165718626 ,2.4149857994256946380 ] 
dist 139=[-2.2393627696198088951 ,2.3905138170480799041 ] 
dist 140=[-2.3729509134866609299 ,2.3183059207408758744 ] 
dist 141=[-2.4856321550665544451 ,2.2945563480365631829 ] 
dist 142=[-2.6047114648556009669 ,2.2807860231410326357 ] 
dist 143=[-2.7638484739794379363 ,2.2770205422555042536 ] 
dist 144=[-2.9154839307743993837 ,.46304032213845136469] 
dist 145=[-3.0046152180513240510 ,.38996509814151164421] 
dist 146=[-3.0651342670118489480 ,.51573297644136971721] 
dist 147=[-3.1025365062488253183 ,.64537588927351446069] 
dist 148=[-3.1243348233012445175 ,.7659117479946116822 ] 
dist 149=[-3.1262788911965793786 ,.90302015466948631753] 
dist 150=[-3.1127653472326294369 ,1.0988318847019703237 ] 
dist 151=[-3.1025873790313079113 ,1.2916104745165471412 ] 
dist 152=[-2.9204222279661812926 ,1.4166095474086811442 ] 
dist 153=[-2.8859093759168614578 ,1.5160526099156749266 ] 
dist 154=[-2.8015081664034747308 ,1.6067973293069460472 ] 
dist 155=[-2.7714174613422046330 ,1.6851429675240776783 ] 
dist 156=[-2.6215540684329188086 ,1.7350822553528773588 ] 
dist 157=[-2.5863723218125795526 ,1.7738423710778477960 ] 
dist 158=[-2.5114649545836509164 ,1.8075553596428688015 ] 
dist 159=[-2.4869835586825535585 ,1.8333077115091311232 ] 
dist 160=[-2.4651124985208060295 ,1.8402842789479802713 ] 
dist 161=[-2.5147004701263763599 ,1.8401107230137418700 ] 
dist 162=[-2.5430093994077630424 ,1.8373142809217658242 ] 
dist 163=[-2.5497673778843777264 ,1.9202102536560066310 ] 
dist 164=[-2.5470966281472014570 ,2.2081482398058188304 ] 
dist 165=[-2.5397822752035879982 ,2.4082482266031182452 ] 
dist 166=[-2.5235994988058669033 ,2.5825502102739247931 ] 
dist 167=[-2.5145142976379875749 ,2.7674876908390243215 ] 
dist 168=[-2.2738519758397945567 ,2.9350731398982507538 ] 
dist 169=[-2.2349603763945475609 ,3.0400976711418027358 ] 
dist 170=[-2.1509052519499489564 ,3.1195164988090141102 ] 
dist 171=[-2.1245208791531040961 ,3.1848747539233661817 ] 
dist 172=[-2.0050898779755690804 ,3.2362717963829128062 ] 
dist 173=[-1.9794527878692608334 ,3.2599524976381039158 ] 
dist 174=[-1.9067556754265277397 ,3.2678880753033090018 ] 
dist 175=[-1.8928354980749485948 ,3.2649847566214245910 ] 
dist 176=[-1.7270120984344277708 ,.79999112939974992418] 
dist 177=[-1.7921278978846599114 ,.71163984248806825967] 
dist 178=[-1.8409889864996633863 ,.68806544139431286728] 
dist 179=[-1.8773969146417170205 ,.60001675392488238679] 
dist 180=[-1.8927930204696765465 ,.69177028970569538261] 
dist 181=[-1.8978180240902526691 ,.78487698042295093609] 
dist 182=[-1.8957658301237882193 ,.87213272902529775858] 
dist 183=[-.17311128897662694222,.97438204481644587424] 
dist 184=[-.29839666947611163104,1.0689590851902767948 ] 
dist 185=[-.40659875122811398902,1.1255823249087223963 ] 
dist 186=[-.51997496296029609562,1.1653222274967689375 ] 
dist 187=[-.62818021276786772837,1.1924893878110654295 ] 
dist 188=[-.71573657995325907689,1.2122474478874470572 ] 
dist 189=[-.80505374475348713516,1.2224054294827213245 ] 
dist 190=[-.92028922162302916932,1.2274914470251298998 ] 
dist 191=[-1.0322111644012612861 ,1.2269996239243806624 ] 
dist 192=[-1.1082986122323760504 ,1.0957785725592530953 ] 
dist 193=[-1.1728065772837254888 ,1.0782030902429606192 ] 
dist 194=[-1.2384959124947863192 ,1.0357542503444454395 ] 
dist 195=[-1.3000207093439005084 ,1.0229296667608670965 ] 
dist 196=[-1.3479011888444999060 ,.95331539799535454204] 
dist 197=[-1.3950206497428281164 ,.93789574224255920369] 
dist 198=[-1.4535069250769578399 ,.90677569504105017349] 
dist 199=[-1.5070163601732695490 ,.89731272355212760747] 
dist 200=[-1.5342651153891053894 ,.75086551263121690884] 
dist 201=[-1.5485102553093746944 ,.72943580306951373631] 
dist 202=[-1.5506992677784769648 ,.7226187246364332286 ] 
dist 203=[-1.5381219932756843091 ,.84110847462837253684] 
dist 204=[-1.5324656463374176254 ,.93624119113167965597] 
dist 205=[-1.5267556293297040337 ,1.0326089096144135432 ] 
dist 206=[-1.5205981461895291949 ,1.1560297325554184147 ] 
dist 207=[-1.3176142471867824556 ,1.2754633035769412263 ] 
dist 208=[-1.3141748219736435476 ,1.3559116400497418820 ] 
dist 209=[-1.4188630987697875980 ,1.4233111272856918364 ] 
dist 210=[-1.5010741262630885041 ,1.4906460157669999833 ] 
dist 211=[-1.5742568427661027757 ,1.5528902713501805630 ] 
dist 212=[-1.6361476482220967467 ,1.5999650420630314411 ] 
dist 213=[-1.6732744231094862371 ,1.6450055581101118857 ] 
dist 214=[-1.6994190568485407717 ,1.6991281251338008400 ] 
dist 215=[-1.7174626191389944557 ,1.7481570060014653333 ] 
dist 216=[-1.7285696062764557778 ,1.7728604707688910262 ] 
dist 217=[-1.7294568325237089798 ,1.7845053197941895473 ] 
dist 218=[-1.7213702284367569413 ,1.7861293231134007805 ] 
dist 219=[-1.7161134339881083196 ,1.7727275677693888442 ] 
dist 220=[-1.6596103537529485316 ,1.7651807150838071530 ] 
dist 221=[-1.6437017512392102357 ,1.7495380054973296536 ] 
dist 222=[-1.6243508457715811110 ,1.7422737018151404395 ] 
dist 223=[-1.6149427714859432900 ,1.5614950187385614354 ] 
dist 224=[-1.1972997186951530053 ,1.5327838512061504821 ] 
dist 225=[-1.1494133196894687901 ,1.4698919661484237635 ] 
dist 226=[-1.0351129640271254746 ,1.4501900601117415711 ] 
dist 227=[-1.0124201297082390582 ,1.3611514881255382485 ] 
dist 228=[-.84584675718347631109,1.3420663611706134092 ] 
dist 229=[-.81351570270083721933,1.2908054841180218163 ] 
dist 230=[-.75996202680335026407,1.2792815264100617459 ] 
dist 231=[-.74617745547935875597,.56455017704009262109] 
dist 232=[-.48536938215032100808,.55668830369550264445] 
dist 233=[-.45080552248924943731,.53354858320201085848] 
dist 234=[-.36873923622053829891,.53023326282613502629] 
dist 235=[-.44009382004007548202,.48112884009875138392] 
dist 236=[-.49273509320102012567,.47061058673916710668] 
dist 237=[-.54181874019241603094,.46165931632553983623] 
dist 238=[-.59896916156505053269,.45987329022706460452] 
dist 239=[-.65166685227100038476,.32802847808175363318] 
dist 240=[-.68297245890080085506,.31096174427853556879] 
dist 241=[-.70464166861449408953,.2780849831892997804 ] 
dist 242=[-.71886486507215827596,.26972355003883527937] 
dist 243=[-.72891801427888661158,.24137202675964991356] 
dist 244=[-.73393786057447753584,.23441536758967127695] 
dist 245=[-.73623786227318963723,.22784984879873975454] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 1, 2, 2, 1, 0, 2] 
dist 0=[42.606791317015747585  ,42.606791317015747585  ] 
dist 1=[41.930508489158461326  ,42.890927086489693256  ] 
dist 2=[40.851609287670408504  ,43.349366494027339152  ] 
dist 3=[39.101485609917550928  ,43.831302530506653991  ] 
dist 4=[37.294064905921562750  ,44.067304083889000175  ] 
dist 5=[35.986214782645104132  ,44.172308819659200872  ] 
dist 6=[34.789991705576116233  ,44.181655203345406752  ] 
dist 7=[33.428280383872580711  ,43.976320718373791359  ] 
dist 8=[32.058937539942789487  ,43.135946595749031237  ] 
dist 9=[30.832077342343268916  ,42.865575679805615200  ] 
dist 10=[29.470141097904680939  ,42.760423581917166049  ] 
dist 11=[27.560963392205501522  ,42.414507463637861395  ] 
dist 12=[25.626392425820711308  ,42.287786832792266235  ] 
dist 13=[24.162870418189826016  ,42.040403373401791755  ] 
dist 14=[22.758181265219637988  ,41.947293934364249261  ] 
dist 15=[21.058435190957889778  ,41.422578335391881249  ] 
dist 16=[19.289828607222867327  ,30.158172786636767462  ] 
dist 17=[17.609775083083411391  ,27.862546043613976565  ] 
dist 18=[15.664695355883545858  ,27.505057583424361972  ] 
dist 19=[12.836722720672198479  ,24.161642768837894008  ] 
dist 20=[10.024949675901101757  ,23.533749212586949068  ] 
dist 21=[8.1445357891953058740 ,22.750436018840410324  ] 
dist 22=[6.5770851458507708260 ,22.535422994919208616  ] 
dist 23=[5.0160331209132896716 ,19.565667795317768737  ] 
dist 24=[3.5691535483842088819 ,17.898692888628783856  ] 
dist 25=[2.4579391988047801949 ,17.605655844893598832  ] 
dist 26=[1.3740140238934235882 ,16.761018878747553687  ] 
dist 27=[.03607573874527206462,15.627044614677416932  ] 
dist 28=[-1.2437659628655160668 ,13.041887319172959578  ] 
dist 29=[-2.0955845317842284871 ,12.498145830818989973  ] 
dist 30=[-2.8017994064763217057 ,12.359627399565584515  ] 
dist 31=[-3.4998413213247760517 ,5.1396495955426428354 ] 
dist 32=[-5.4639504623806497730 ,3.5121803425526757167 ] 
dist 33=[-7.1997991008267224780 ,1.9177883438543043208 ] 
dist 34=[-8.5578424052743193441 ,1.6348730623841784015 ] 
dist 35=[-9.7665763630889105995 ,1.1218134586602802747 ] 
dist 36=[-10.795967465444724977  ,1.6652779047745873417 ] 
dist 37=[-11.437428379942003353  ,2.0557221960391169404 ] 
dist 38=[-11.922606676120714902  ,2.4062783484162140741 ] 
dist 39=[-12.327847377529421797  ,2.7910654770666469772 ] 
dist 40=[-12.656789231776571081  ,3.1659636170931665752 ] 
dist 41=[-12.837035485105116492  ,3.4772472887154698675 ] 
dist 42=[-12.945983090067661705  ,3.8001672452995963559 ] 
dist 43=[-12.989533054827292950  ,4.2215744403479281574 ] 
dist 44=[-12.990069451150902401  ,4.6295443859034407350 ] 
dist 45=[-12.963577297594063494  ,4.8989063107454007216 ] 
dist 46=[-12.845671594544933275  ,5.1172735898425175355 ] 
dist 47=[-12.775103892845921159  ,5.3218667286909258360 ] 
dist 48=[-7.3646576799198333970 ,5.5007680599408354267 ] 
dist 49=[-6.8775195623031014660 ,5.6166217469532231986 ] 
dist 50=[-5.7495612335888922974 ,5.7076610230675426244 ] 
dist 51=[-5.7022588015905711400 ,5.7874547349134159084 ] 
dist 52=[-3.7795521150477745607 ,5.8509593615207598626 ] 
dist 53=[-3.4604193082642442557 ,5.8770131217139901086 ] 
dist 54=[-3.0906659091446023126 ,5.8798668442729289609 ] 
dist 55=[-3.0038984050832935365 ,5.8635312237651969205 ] 
dist 56=[-1.4265700235349945416 ,5.8030432711863018270 ] 
dist 57=[-1.0063319191812697431 ,5.7734734948030215911 ] 
dist 58=[-.98292773513678749141,5.6601004625259128051 ] 
dist 59=[-1.0837827035797804091 ,5.6221487964828936944 ] 
dist 60=[-1.2102589759592634509 ,5.2548897988956119903 ] 
dist 61=[-1.3788973121429612488 ,5.1770130393061819537 ] 
dist 62=[-1.6478396065446293419 ,4.9583828642448178402 ] 
dist 63=[-1.9174289708594955933 ,4.6720091702912810621 ] 
dist 64=[-2.0886398329962682453 ,3.7767543190007357245 ] 
dist 65=[-2.2195511484543064426 ,4.0940310244396562747 ] 
dist 66=[-2.3284563732438161958 ,4.3303638821907841309 ] 
dist 67=[-2.4155669876881171152 ,4.5193976627641301687 ] 
dist 68=[-2.4596158536197587147 ,4.6687702393879681212 ] 
dist 69=[-2.4814823090177953525 ,4.7466523707883267204 ] 
dist 70=[-2.4843045013920891087 ,4.7874643538303101954 ] 
dist 71=[-2.3869114583260655044 ,4.7941081235158462832 ] 
dist 72=[-2.3622385442166013647 ,4.7149646269854934331 ] 
dist 73=[-2.3344745660771078384 ,4.7207505655456172710 ] 
dist 74=[-2.3186050748234704710 ,4.7214251065994392759 ] 
dist 75=[-2.2798225974420527072 ,4.5697642811521939439 ] 
dist 76=[-2.2611674761847220386 ,4.5304568949330628600 ] 
dist 77=[-2.2281363838088747599 ,4.5070233938678986669 ] 
dist 78=[-2.2150385556959227196 ,4.4993956195314973453 ] 
dist 79=[.18290162157386350871,4.3899286500990140066 ] 
dist 80=[-.1226916374274836981 ,2.2143125868515136823 ] 
dist 81=[-.4240891732904165193 ,2.2043546918160765436 ] 
dist 82=[-.78048605897190648927,2.1790716267772492963 ] 
dist 83=[-1.3056951768418981126 ,2.1680236412056599848 ] 
dist 84=[-1.8277349294528369905 ,1.9428863729040959764 ] 
dist 85=[-2.1714904529733626812 ,1.8835702880460077461 ] 
dist 86=[-2.4509186876206957061 ,1.8638612559519620314 ] 
dist 87=[-2.7161374363178565336 ,1.6596890877996890606 ] 
dist 88=[-2.9523700285243227971 ,1.6269188652753269882 ] 
dist 89=[-3.1160782561174469068 ,1.5436335755075497614 ] 
dist 90=[-3.2582767051037677829 ,1.5276581136116527043 ] 
dist 91=[-3.4086474378439879111 ,1.3869430904674279747 ] 
dist 92=[-3.5395052002416898538 ,1.3580131982878358836 ] 
dist 93=[-3.6037971724219367682 ,1.3185171320046379873 ] 
dist 94=[-3.6370918078167896038 ,1.3051136119963145186 ] 
dist 95=[-3.6441689382069694812 ,1.0144935852401316367 ] 
dist 96=[-3.5929134156802824224 ,.97405300571089928121] 
dist 97=[-3.5782984889076710500 ,.89642616292398039099] 
dist 98=[-3.5683567814051419607 ,.87658814378077746911] 
dist 99=[-3.5622503755482584778 ,.80870252934451325933] 
dist 100=[-2.9888930274080082480 ,.79197926148395076895] 
dist 101=[-2.9174423310816059116 ,.77367404351510956145] 
dist 102=[-2.8323900995415258754 ,1.0434706150519827813 ] 
dist 103=[-2.8308242302464246536 ,1.4224950427423262288 ] 
dist 104=[-2.6707622412499731729 ,1.7752380763884072901 ] 
dist 105=[-2.6418127637153959110 ,2.0456851697466789265 ] 
dist 106=[-2.5886630526539625508 ,2.3078748399126128919 ] 
dist 107=[-2.5724198801972822717 ,2.6276549782918891129 ] 
dist 108=[-2.2362883202440062092 ,2.9292115109170443142 ] 
dist 109=[-2.1707442006160561475 ,3.1186506354280134795 ] 
dist 110=[-1.9443806819130727373 ,3.2623946357826713362 ] 
dist 111=[-1.9401498939776990852 ,3.3815299304304765342 ] 
dist 112=[-.98894408683000820363,3.4758393143701777851 ] 
dist 113=[-.94967112000448014248,3.5204745450512832743 ] 
dist 114=[-.86709440173612944965,3.5402237608874526123 ] 
dist 115=[-.84416037078154886473,3.5402468243047326674 ] 
dist 116=[.26476243316791736824,1.3980105338666817282 ] 
dist 117=[.35851501337230954016,1.4351727960461188413 ] 
dist 118=[.56851329816878137963,1.4806611624316692464 ] 
dist 119=[.60296270989343058928,1.5236392430039954003 ] 
dist 120=[.84563237416339280233,1.5507794839355830884 ] 
dist 121=[.88516914518189630031,1.5715362920072598486 ] 
dist 122=[.95530328036119637964,1.5890297655522314431 ] 
dist 123=[.96860108145457310045,1.6030973530096184423 ] 
dist 124=[1.1026179821063282769 ,1.6428284234657173338 ] 
dist 125=[1.1195519492563345995 ,1.7194070009245888182 ] 
dist 126=[1.0980175836569298370 ,1.7736483749946433827 ] 
dist 127=[1.0084452091577570756 ,1.8117204312833292525 ] 
dist 128=[.91282346243710886821,1.8386954114647133988 ] 
dist 129=[.84324234787305036598,1.8486265606079177410 ] 
dist 130=[.75220824660395751139,1.8498973732584211712 ] 
dist 131=[.50319363578144857797,1.8467236628564691865 ] 
dist 132=[.24839051073274863972,1.7315373971496532556 ] 
dist 133=[.06989842894560629841,1.7125229247596456135 ] 
dist 134=[-.08706242071132457790,1.6569902913253156484 ] 
dist 135=[-.25590828253389849164,1.6458671864606440234 ] 
dist 136=[-.41969439822931761899,1.5254450600268870026 ] 
dist 137=[-.55645718815616586575,1.4986271521850777153 ] 
dist 138=[-.69977627095496516284,1.4677319035229198758 ] 
dist 139=[-.88974104586616100008,1.4541723615444978414 ] 
dist 140=[-1.0765962284368850892 ,1.1273202639663170764 ] 
dist 141=[-1.2075021622806439031 ,1.0826136362561723222 ] 
dist 142=[-1.3226489276787470785 ,.99107119419246387464] 
dist 143=[-1.4465886085954882525 ,.96604114363790468513] 
dist 144=[-1.5668837668681877823 ,.8692659172787758466 ] 
dist 145=[-1.6674822104085564960 ,.84861162346080800822] 
dist 146=[-1.7730548599192733011 ,.80482882799339539833] 
dist 147=[-1.9132137872949533429 ,.79191228198961250291] 
dist 148=[-2.0467963618534417859 ,-.28163305545364382074] 
dist 149=[-2.1261134214154703177 ,-.28861724359757775858] 
dist 150=[-2.1809759478070160020 ,-.28701704281185577127] 
dist 151=[-2.2169210344918963460 ,-.27333653259297316225] 
dist 152=[-2.2407366839293302233 ,-.25462008030929022379] 
dist 153=[-2.2471700517177505466 ,-.23291120538186613322] 
dist 154=[-2.2449496792892720300 ,-.20485412081676107793] 
dist 155=[-2.2395163088837757014 ,-.16078556588488558797] 
dist 156=[-2.0902243829801253550 ,-.10975366567366785618] 
dist 157=[-2.0633383115133066737 ,-.05389208869167392143] 
dist 158=[-2.0067017126656298598 ,.01626721233026924219] 
dist 159=[-1.9881881433251950577 ,.124385782833376249  ] 
dist 160=[-1.9015924725085836114 ,.23379221571166242131] 
dist 161=[-1.8823880894241710185 ,.30909519489193018991] 
dist 162=[-1.8217763616964942320 ,.37392522591768879481] 
dist 163=[-1.8126107193259953599 ,.44152100512001686332] 
dist 164=[-1.3421004059440805753 ,.50582410418637128262] 
dist 165=[-1.3153700096971143120 ,.55751011841327601702] 
dist 166=[-1.2464374334400602629 ,.71891393739667827177] 
dist 167=[-1.2324815634341196944 ,.93681991904156946087] 
dist 168=[-1.1117007662000130039 ,1.1336146259851524603 ] 
dist 169=[-1.0864122151510539447 ,1.2746300304108894320 ] 
dist 170=[-1.0509964020735215957 ,1.4019675790232841310 ] 
dist 171=[-1.0391020828908438962 ,1.5441525588788149539 ] 
dist 172=[-.77779196025445923319,1.6751188068292846344 ] 
dist 173=[-.7423269716070750573 ,1.7576647077937450741 ] 
dist 174=[-.66538604601247136439,1.8206480521578309866 ] 
dist 175=[-.64396964937488502323,1.8735091392121544535 ] 
dist 176=[-.55376881649547588979,1.9158888532658620727 ] 
dist 177=[-.53645238327358193799,1.9370241661930145218 ] 
dist 178=[-.62715737446129493549,1.9466646493008152204 ] 
dist 179=[-.72109588690586146442,1.9466276523590722993 ] 
dist 180=[-.80760314467113225044,1.1232545662196070715 ] 
dist 181=[-.87240613168996660825,1.1222612446950224802 ] 
dist 182=[-.93377980119264787334,1.1196642922122616618 ] 
dist 183=[-1.0065966007182701100 ,1.1161027812885661275 ] 
dist 184=[-1.0742457461018941659 ,1.0629069508969777562 ] 
dist 185=[-1.1149891132528778044 ,1.1336459642146863778 ] 
dist 186=[-1.1438600944590798918 ,1.1962124192949666175 ] 
dist 187=[-1.1641122687047177174 ,1.2641003040622009422 ] 
dist 188=[-1.1776581009854082132 ,1.3246871193135050034 ] 
dist 189=[-1.1804249907216288398 ,1.3581032409857599834 ] 
dist 190=[-1.1780062614559615815 ,1.3780580372690429212 ] 
dist 191=[-1.1761959721219127457 ,1.3848991742357511338 ] 
dist 192=[.23233088961820859973,1.3862888320692521736 ] 
dist 193=[.12163446640694627054,1.3844775521168343625 ] 
dist 194=[.02277714688363795909,1.3799720705118894230 ] 
dist 195=[-.08593618940005606960,1.3759024328882141446 ] 
dist 196=[-.19282652868798771253,1.1091955166353477322 ] 
dist 197=[-.28440581158617814891,1.0787214846574080354 ] 
dist 198=[-.38242485833921421186,1.0008608153368523251 ] 
dist 199=[-.51502656793763804495,.98747107059313662246] 
dist 200=[-.64671151240611447385,.85675202078152938901] 
dist 201=[-.74107057939895770303,.83045350932849943403] 
dist 202=[-.82627493703451016092,.79790066026275601856] 
dist 203=[-.92140970231419374071,.78587338267137829082] 
dist 204=[-1.0157925749253268255 ,.52505751068516957724] 
dist 205=[-1.0979953171813724661 ,.49070378832149936489] 
dist 206=[-1.1871268212163840161 ,.41840688807910504285] 
dist 207=[-1.3091737187055363596 ,.39878966283801335455] 
dist 208=[-1.4263443677231561478 ,.41687542722327160504] 
dist 209=[-1.4960073801795445850 ,.51215677022091519422] 
dist 210=[-1.5442951239645540196 ,.59517087256931416487] 
dist 211=[-1.5761238644209806846 ,.68327355286517944483] 
dist 212=[-1.5986354164295372542 ,.76802184557786769974] 
dist 213=[-1.6097237325081365803 ,.83764453894163012797] 
dist 214=[-1.6145818655752267267 ,.90960181414418580974] 
dist 215=[-1.6123829187192927039 ,1.0036716330099099968 ] 
dist 216=[-1.4994659944302458179 ,1.0955941985358988516 ] 
dist 217=[-1.5019106361958719224 ,1.1589792167577797325 ] 
dist 218=[-1.4996819987090242835 ,1.2136715448552041813 ] 
dist 219=[-1.4964626732235019607 ,1.2708897704380096671 ] 
dist 220=[-1.3568656921724756149 ,1.3254356383665478751 ] 
dist 221=[-1.3441412368719743772 ,1.3694594398110396382 ] 
dist 222=[-1.3279312880625512104 ,1.4142632155000905469 ] 
dist 223=[-1.3203531640596739780 ,1.4719244593170334350 ] 
dist 224=[-1.2255709964023347877 ,1.5260450611683669920 ] 
dist 225=[-1.2123822422138623477 ,1.5567131553924142109 ] 
dist 226=[-1.1816412222650425879 ,1.5761135776872070898 ] 
dist 227=[-1.1707373392623840558 ,1.5852476547702082987 ] 
dist 228=[-.4208856449556838324 ,1.5876720332233575596 ] 
dist 229=[-.35412706585973118691,1.5861035936839044365 ] 
dist 230=[-.20153181995550989354,1.5711788155083233990 ] 
dist 231=[-.17435525353706279104,1.5667517758850085285 ] 
dist 232=[.01748387933503097329,1.4748016127082206646 ] 
dist 233=[.05116652249847143907,1.4576540260315696992 ] 
dist 234=[.11024811118401146682,1.4107241415249308063 ] 
dist 235=[.1227812434082735545 ,1.3989705162122968949 ] 
dist 236=[.30511339047721741094,1.3039383329384202905 ] 
dist 237=[.26990994762345560739,1.2824826179182093725 ] 
dist 238=[.04099085652993406488,1.2504677831129743890 ] 
dist 239=[-.30025074963429519875,1.2836564089113666061 ] 
dist 240=[-.63996981618320941129,1.3572245618984253620 ] 
dist 241=[-.86281030038199272984,1.4003423687098331834 ] 
dist 242=[-1.0429677354091080510 ,1.4294590692457730457 ] 
dist 243=[-1.2122753232935138860 ,1.4471278574720639076 ] 
dist 244=[-1.3618854256720092226 ,1.4575903487413514098 ] 
dist 245=[-1.4634009602732995036 ,1.4582689421763758097 ] 
dist 246=[-1.5492461835683706402 ,1.4540225331794690322 ] 
dist 247=[-1.6362928960943164861 ,1.4488403713600944702 ] 
dist 248=[-1.7139407270194930686 ,1.3537325008673048028 ] 
dist 249=[-1.7622608897836772120 ,1.3363610292306806123 ] 
dist 250=[-1.7984065205174827961 ,1.2968896867742117410 ] 
dist 251=[-1.8274471300412310360 ,1.2834757689110585396 ] 
dist 252=[-1.8497344297069968396 ,1.2188668035678745831 ] 
dist 253=[-1.8589170979124668110 ,1.2041388309962314636 ] 
dist 254=[-1.8602653792720878926 ,1.1666835918000051022 ] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 0, 1, 1, 0, 1] 
dist 0=[46.511304038848967949  ,46.511304038848967949  ] 
dist 1=[46.190566170995373430  ,46.636145221065672858  ] 
dist 2=[45.714372440529486826  ,46.813860968553295959  ] 
dist 3=[45.113402633241723734  ,46.989713199616696527  ] 
dist 4=[44.304457738847533543  ,47.126867377700037725  ] 
dist 5=[42.997534807728183364  ,47.228350475395428486  ] 
dist 6=[41.466208035295720311  ,47.261661797993631234  ] 
dist 7=[39.403425982864917369  ,47.250799453912105794  ] 
dist 8=[36.825303893995603162  ,47.194677584449281341  ] 
dist 9=[34.233172517489579277  ,47.081717599114684128  ] 
dist 10=[30.812836763705861308  ,46.995638135560671489  ] 
dist 11=[28.422654833131150699  ,46.898029795158774740  ] 
dist 12=[26.322738273340717418  ,46.814863677243777914  ] 
dist 13=[24.061563200932001270  ,46.558534394142836000  ] 
dist 14=[21.861448797366786804  ,44.063895311720762588  ] 
dist 15=[20.005223966886397644  ,43.582228403323482557  ] 
dist 16=[18.039164634647866299  ,40.660680053822016984  ] 
dist 17=[15.399978129763477497  ,34.861777887359087242  ] 
dist 18=[12.777834943428095547  ,33.863945354434831280  ] 
dist 19=[10.879652981106376845  ,31.413191783509267253  ] 
dist 20=[9.1409580219539141252 ,31.058619072481132290  ] 
dist 21=[7.1556195528024433248 ,27.351002539395840257  ] 
dist 22=[5.1530146509260098366 ,26.649806506193185043  ] 
dist 23=[3.3449684915761669423 ,25.874315692420818162  ] 
dist 24=[1.3242109767615121030 ,25.727713337419295825  ] 
dist 25=[-1.5289410119475857365 ,19.285152617847392285  ] 
dist 26=[-4.3275359489207919500 ,18.481458762624849024  ] 
dist 27=[-6.1304363079103881794 ,16.878018059554920654  ] 
dist 28=[-7.5588070086864951626 ,16.470909800971326204  ] 
dist 29=[-8.8606828011136555324 ,15.056907087945578488  ] 
dist 30=[-9.9908253453974666110 ,14.750399538266168327  ] 
dist 31=[-10.733031126102838556  ,14.370812761047608795  ] 
dist 32=[-11.338402652847346019  ,14.274405980319860948  ] 
dist 33=[-11.922090289034582251  ,3.1456310425673810541 ] 
dist 34=[-12.419485968675033919  ,2.2381034276023920326 ] 
dist 35=[-12.680031806225361959  ,.19701524331928851836] 
dist 36=[-12.820244690553253005  ,-.13635046014212922027] 
dist 37=[-12.840724061655683464  ,-2.5650058541810675505 ] 
dist 38=[-12.798618922568123935  ,-2.9739650953468775876 ] 
dist 39=[-12.751112973806637123  ,-2.6851183741370083044 ] 
dist 40=[-12.627535940368219561  ,-1.2978799007613268969 ] 
dist 41=[-12.563339606791568395  ,-.32932075627115311294] 
dist 42=[-9.8457809650203898490 ,.51694390274588105375] 
dist 43=[-9.8015319545567911939 ,1.4163943335056600378 ] 
dist 44=[-9.5388773785625207707 ,2.2804238491564829704 ] 
dist 45=[-9.8674343195617712543 ,3.2719853252742843392 ] 
dist 46=[-10.023764650722458797  ,4.4295990658401845360 ] 
dist 47=[-10.102250138901704554  ,5.2974942208435134949 ] 
dist 48=[-10.119752605952782823  ,6.1194973082811245187 ] 
dist 49=[-6.5272259479489663167 ,7.0939883281756002913 ] 
dist 50=[-5.9983934551280397211 ,7.9989899232993822278 ] 
dist 51=[-5.8590082010129020215 ,8.5436389339751114749 ] 
dist 52=[-5.3540744420739882822 ,8.9287254837402500157 ] 
dist 53=[-5.2381327674172731659 ,9.1968207542466478176 ] 
dist 54=[-5.0521563773430220997 ,9.3943406245479753149 ] 
dist 55=[-4.9998631439940001620 ,9.4977257700070533641 ] 
dist 56=[-3.0869787943753383603 ,9.5519439020718079370 ] 
dist 57=[-2.0977385194282608832 ,9.5532315374023171481 ] 
dist 58=[-1.9686671732428955323 ,1.0029461608507175559 ] 
dist 59=[-1.6770794894078931622 ,1.3641428306619196918 ] 
dist 60=[-1.6246808092409364103 ,1.6624253962338292844 ] 
dist 61=[-1.2677373003531949277 ,1.9540117327159033154 ] 
dist 62=[-1.2049267525029552118 ,2.2199705075106044047 ] 
dist 63=[-1.0939997553757646803 ,2.4158947731960462177 ] 
dist 64=[-1.0704540200458641993 ,2.5986094651171692898 ] 
dist 65=[-.82935216821396796846,2.8118126558992281123 ] 
dist 66=[-.80672681751604909957,3.0087796436736685904 ] 
dist 67=[-.77631421428531874592,3.1266466739326957371 ] 
dist 68=[-.76651450734600991251,3.3343880363639238958 ] 
dist 69=[-.75294555638025187008,3.5279468916905728360 ] 
dist 70=[-.74950489976299129463,3.6359106824940451742 ] 
dist 71=[-.74903368116877282559,3.7026765054974570749 ] 
dist 72=[-.75144707443503991304,3.7317658812927832696 ] 
dist 73=[-.75367681190943566986,3.7451808291369676284 ] 
dist 74=[-.75252616761257278851,3.7493200040937104262 ] 
dist 75=[-.74813029857571871277,3.7479890065555008747 ] 
dist 76=[-.74373836258916764357,3.7394131872795583069 ] 
dist 77=[-.85463686098723601322,3.7271839672364301217 ] 
dist 78=[-1.1431604415820304198 ,3.7134831922878843360 ] 
dist 79=[-1.3735657486878613795 ,3.6894053606963011535 ] 
dist 80=[-1.6058081386322788429 ,3.6779173631260965704 ] 
dist 81=[-1.9016866103283837873 ,2.6518362270690297571 ] 
dist 82=[-2.1873032660083192996 ,1.9812254847861799728 ] 
dist 83=[-2.3785851926159287245 ,1.8931679973972686013 ] 
dist 84=[-2.5376779280176133670 ,1.7232933660098870379 ] 
dist 85=[-2.6947883462260451910 ,1.6796272721396474292 ] 
dist 86=[-2.8389389835058538788 ,1.5289826157035885078 ] 
dist 87=[-2.9463015047002367852 ,1.4920797785622816944 ] 
dist 88=[-3.0475175863945682245 ,1.4503223880237930007 ] 
dist 89=[-3.1671544955514972364 ,1.4351726268807744255 ] 
dist 90=[-3.2756595375486587898 ,-.4957314931808996309 ] 
dist 91=[-3.3324317911481855636 ,-.64797943483110494393] 
dist 92=[-3.3623724829730128230 ,-.74669616833802556907] 
dist 93=[-3.3669578895224895890 ,-.90350090444268004906] 
dist 94=[-3.3532874358286565677 ,-.90454249204872322883] 
dist 95=[-3.3411838743469768590 ,-.86691625118190010607] 
dist 96=[-3.3140379367025337955 ,-.7802235303235983938 ] 
dist 97=[-3.3003166030863937964 ,-.68242944313000604804] 
dist 98=[-2.9714533972342666213 ,-.60048221411772047266] 
dist 99=[-2.9185882346340639380 ,-.51454597353106458604] 
dist 100=[-2.8016808650773801382 ,-.40079110756596086412] 
dist 101=[-2.7646598799952131802 ,-.27789014365700023461] 
dist 102=[-2.5958753624065364882 ,-.15542501540286672821] 
dist 103=[-2.5594186429942296369 ,-.00978780862661462300] 
dist 104=[-2.4636734212485736156 ,.205631806840460477  ] 
dist 105=[-2.4401186452811532315 ,.4276452990017719132 ] 
dist 106=[-1.2936869673153277304 ,.77933941559585863323] 
dist 107=[-1.2850432798492684404 ,1.2007125086323744700 ] 
dist 108=[-1.2809806300069416694 ,1.5446256711947952619 ] 
dist 109=[-1.2581829747314998723 ,1.8732947905268519328 ] 
dist 110=[-1.2516028108243068381 ,2.1674619748402747949 ] 
dist 111=[-1.2290114431892714599 ,2.3736312694248087545 ] 
dist 112=[-1.2236270634758116083 ,2.5550720647690994287 ] 
dist 113=[-.03933551579567394861,2.7505170541632168936 ] 
dist 114=[.2113785612851919805 ,2.9278538431698376189 ] 
dist 115=[.25315122177358963819,3.0369979497553835029 ] 
dist 116=[.29640014810632820594,3.1172255111195535497 ] 
dist 117=[.29562672667184719824,3.1791076266677199417 ] 
dist 118=[.27588204043094288049,3.2245397518561137638 ] 
dist 119=[.22899920036079950908,3.2390868572891601064 ] 
dist 120=[.15321490708962048018,3.2395217726482097467 ] 
dist 121=[.01808365712211168119,3.2316994600971515521 ] 
dist 122=[-.12120535252589228093,2.0642084158897032413 ] 
dist 123=[-.21359080551900430233,2.0789352025946403606 ] 
dist 124=[-.28939889997389616884,2.0794589553503465818 ] 
dist 125=[-.36250913918720492291,2.0511718122780290176 ] 
dist 126=[-.42838072162110981386,2.0394114731805868681 ] 
dist 127=[-.47529209407100288305,2.0282700635212630827 ] 
dist 128=[-.51735392510268242377,2.0188528617919311102 ] 
dist 129=[-.56386812109323134091,1.6338241470291829978 ] 
dist 130=[-.60625834955597578413,1.5891552356965893964 ] 
dist 131=[-.63185629112099944818,1.4731601756800027097 ] 
dist 132=[-.77133342450327387736,1.4544560598782809491 ] 
dist 133=[-.97162989620435182358,1.2551965345096209559 ] 
dist 134=[-1.1245572431064796373 ,1.2151866361227370431 ] 
dist 135=[-1.2721985679750083430 ,1.1695798277989206118 ] 
dist 136=[-1.4513934353013782618 ,1.1555620854070594147 ] 
dist 137=[-1.6199237157760622993 ,.74650921541359578633] 
dist 138=[-1.7249911709560140663 ,.69370873818221556533] 
dist 139=[-1.8037726159306413660 ,.58479768468848981504] 
dist 140=[-1.8673665087005970900 ,.55592808200749041981] 
dist 141=[-1.9163847635847303320 ,.44829529834803005566] 
dist 142=[-1.9369785718992034487 ,.42622147024286066097] 
dist 143=[-1.9455632851804774198 ,.38466787493958189295] 
dist 144=[-1.9466400141887208781 ,.37438208371847760533] 
dist 145=[-.33636049348233629119,.1074814755299336389 ] 
dist 146=[-.45667941138113913906,.17740157313126746527] 
dist 147=[-.55560042953108831965,.22760299347214441477] 
dist 148=[-.65136033713200598798,.27301839353562489002] 
dist 149=[-.73790917774985913106,.32383439220987726531] 
dist 150=[-.80005574218426608048,.37429541020504898615] 
dist 151=[-.85631555174176560724,.41829570001613785903] 
dist 152=[-.91936368842682636949,.46604107758666031619] 
dist 153=[-.97639842613440229845,.53145663834474251599] 
dist 154=[-1.0086494021313227606 ,.59452903648536561534] 
dist 155=[-1.0289704160625657433 ,.63292041484969312293] 
dist 156=[-1.0383716206479809292 ,.66063032669253939546] 
dist 157=[-1.0430544492734527821 ,.68105788582497014344] 
dist 158=[-1.0445365977576888343 ,.69650715957687951364] 
dist 159=[-1.0439665193259897356 ,.70434119356225729627] 
dist 160=[-1.0410472530296721442 ,.70810788037662914558] 
dist 161=[-.87383026117150329753,.70793294690477197395] 
dist 162=[-.85356992219395510996,.65829242534472858701] 
dist 163=[-.80101615017671308923,.6495686182010707761 ] 
dist 164=[-.79161256165146923678,.63591989297053330184] 
dist 165=[-.70019100189625178176,.6313114591680295243 ] 
dist 166=[-.6814647759002526673 ,.6173344355072399471 ] 
dist 167=[-.65803889048620172958,.61218198276434026237] 
dist 168=[-.64932128132565925067,.60536329043869799335] 
dist 169=[-.45727895150865208092,.60214563595263763502] 
dist 170=[-.43176244984938687405,.62035187927665827673] 
dist 171=[-.37792830135435948904,.68307304562648198954] 
dist 172=[-.36319917034829965442,.749477937807652056  ] 
dist 173=[-.30543631722434277906,.81326698716338410556] 
dist 174=[-.29404081102510179546,.86554608860361122757] 
dist 175=[-.26819842657199753452,.91947604910022156899] 
dist 176=[-.26180758473385001005,.98985883070657793209] 
dist 177=[-.30166745802221723931,1.0563844916489890331 ] 
dist 178=[-.34996705961007563217,1.0949154039774659384 ] 
dist 179=[-.38019065143964766344,1.1203710442519814027 ] 
dist 180=[-.40298940003682596031,1.1346925088847427425 ] 
dist 181=[-.42164714740903987549,1.1433647399939624572 ] 
dist 182=[-.43644123044809523659,1.1462645486717676126 ] 
dist 183=[-.44381515788494240368,1.1454971434140119217 ] 
dist 184=[-.44752307078353960814,1.1431144959095140252 ] 
dist 185=[-.44794634273669222456,1.0343596892244591521 ] 
dist 186=[-.36023781065185064317,1.0168760381471108129 ] 
dist 187=[-.37518015149091433048,.98389110951752573339] 
dist 188=[-.38571402486954211619,.97435662515290416762] 
dist 189=[-.39300462639145587118,.93642592938671114557] 
dist 190=[-.39799375323772093028,.92640239002461996884] 
dist 191=[-.39933882537788736924,.90478274748524057453] 
dist 192=[-.39911106576773766644,.89732845059339687155] 
dist 193=[-.3979691156279696979 ,.51058676874137490017] 
dist 194=[-.37556562248181482644,.48509271660426257655] 
dist 195=[-.3712398971755430887 ,.42428389325468069341] 
dist 196=[-.36163025037318933541,.41312911057028741294] 
dist 197=[-.44365368991306013096,.32595880307779244722] 
dist 198=[-.51559028445548215709,.30943179915995547677] 
dist 199=[-.58255482080850960604,.2844276623259890607 ] 
dist 200=[-.66035062481396294023,.3522928250797381221 ] 
dist 201=[-.73264965488389582856,.4514534456173618095 ] 
dist 202=[-.77766837995261885116,.5493297724579748346 ] 
dist 203=[-.81137495450289158443,.6120677028606286410 ] 
dist 204=[-.83851134053331485449,.6611454217044951841 ] 
dist 205=[-.85938403064846626826,.7044854116078438816 ] 
dist 206=[-.86808359109335155266,.7408733316512372731 ] 
dist 207=[-.8716994707058527861 ,.7621960057554750885 ] 
dist 208=[-.8722743560035807205 ,.7765884482975124788 ] 
dist 209=[-.5399925551678125750 ,.7853086047920451463 ] 
dist 210=[-.5507409090732767643 ,.7907630324017573742 ] 
dist 211=[-.5564092574198830403 ,.7921175093131007350 ] 
dist 212=[-.5594453424207603944 ,.7907295904315601871 ] 
dist 213=[-.58076831309640146579,.7890640561405887737 ] 
dist 214=[-.59524671555295114294,.7776170646266803586 ] 
dist 215=[-.60347155946060582734,.7740113709745026436 ] 
dist 216=[-.60540310333685480384,.7591561774064235688 ] 
dist 217=[-.60493023067755968845,.7566165613694018869 ] 
dist 218=[-.60413165700918836993,.4457812250106724061 ] 
dist 219=[-.60289004612373046208,.41604015993449846561] 
dist 220=[-.60076010439482263611,.3458070558229716082 ] 
dist 221=[-.5981190631320194727 ,.33326527093212440312] 
dist 222=[-.59551091370832047419,.23583492698444074717] 
dist 223=[-.59135684211800093631,.21776526213444368693] 
dist 224=[-.58924555173276938227,.20181319190952372855] 
dist 225=[-.4501759577554968789 ,.19902375652338239767] 
dist 226=[-.4002300253547211868 ,.1879347140074283336 ] 
dist 227=[-.3920276798195281363 ,.18521036526197994483] 
dist 228=[-.3702790726843922821 ,.18438962425195957113] 
dist 229=[-.3663749307636347732 ,.18594645030142064528] 
dist 230=[-.32680168035865330053,.18891127385355624416] 
dist 231=[-.31855759550034745986,.19371193343893013523] 
dist 232=[-.35047200388261172524,.20078011066396835405] 
dist 233=[-.41850619978628898111,.27464151275803210054] 
dist 234=[-.4848195523721033919 ,.39065836797210929755] 
dist 235=[-.5277254348282533795 ,.46580062433547820974] 
dist 236=[-.5617462319309896991 ,.525466778907574205  ] 
dist 237=[-.5925870839536609638 ,.57969764969937368511] 
dist 238=[-.6190616046317110511 ,.6263473989666066383 ] 
dist 239=[-.6356504213387755721 ,.6557469540895214653 ] 
dist 240=[-.6481917998378193495 ,.6781682376914697821 ] 
dist 241=[-.6585074915134787026 ,.6969579315337224220 ] 
dist 242=[-.6659502577820202025 ,.7124363816526303295 ] 
dist 243=[-.6674435098903269303 ,.7216381386308237679 ] 
dist 244=[-.6659639810555537497 ,.7280114817640544445 ] 
dist 245=[-.6649049335365011103 ,.7321986144351093542 ] 
dist 246=[-.6420311575327772927 ,.7346634928901871877 ] 
dist 247=[-.6355657212805724713 ,.7341614336663153332 ] 
dist 248=[-.6303038366151445777 ,.7314433044795163415 ] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 2, 0, 0, 1] 
dist 0=[44.947045987410140729  ,44.947045987410140729  ] 
dist 1=[44.749187728936583750  ,45.114173785352108774  ] 
dist 2=[44.457290934779050818  ,45.283229354210635937  ] 
dist 3=[44.084758395895127054  ,45.440413193209866138  ] 
dist 4=[43.515601284154012419  ,45.560012780333834405  ] 
dist 5=[42.554198733017452115  ,45.674521343681399497  ] 
dist 6=[41.368293255337666697  ,45.811137408748550070  ] 
dist 7=[39.787033141115979131  ,45.928543492489086620  ] 
dist 8=[37.246451777969884621  ,45.966375586078292676  ] 
dist 9=[34.642140474507671943  ,45.952484980604838967  ] 
dist 10=[32.806271364964154240  ,45.902713707312392406  ] 
dist 11=[30.098132740620218017  ,45.733189634097403097  ] 
dist 12=[27.833120129529426351  ,45.650673382010513178  ] 
dist 13=[25.850197663021606486  ,45.233008833356619737  ] 
dist 14=[23.725506704969793261  ,44.375926355319233215  ] 
dist 15=[21.664047660588586834  ,35.970185839534529901  ] 
dist 16=[19.933494126243645877  ,35.112934541511249256  ] 
dist 17=[18.107756188508322113  ,32.981196770060529556  ] 
dist 18=[15.665718954515110482  ,32.671496560950426722  ] 
dist 19=[13.242541863854783694  ,29.340095472163517097  ] 
dist 20=[11.491939494336035196  ,28.699027768991590705  ] 
dist 21=[9.8915790450086092837 ,28.009972088437423531  ] 
dist 22=[8.0683057447449277936 ,27.874407818865606997  ] 
dist 23=[6.2308190747277236665 ,21.675003712003343542  ] 
dist 24=[4.5733012749645380692 ,20.891855663405137994  ] 
dist 25=[2.7213844913029720476 ,19.346404230332936893  ] 
dist 26=[.10646616002613382893,18.953596786777476685  ] 
dist 27=[-2.4583597084328309011 ,17.595349414338797562  ] 
dist 28=[-4.1102406522028449031 ,17.290497788804447328  ] 
dist 29=[-5.4191131693547003242 ,16.925364610016293416  ] 
dist 30=[-6.6130610973295019821 ,16.823905418561503164  ] 
dist 31=[-7.6508053499754706413 ,4.6832699168777789105 ] 
dist 32=[-8.3355089488552130678 ,3.6924869439639739012 ] 
dist 33=[-8.8978352637998913022 ,1.4299949067366569048 ] 
dist 34=[-9.4468339877733097834 ,1.0782507913014791045 ] 
dist 35=[-9.9213220272875594036 ,-1.7277296074427809225 ] 
dist 36=[-10.185858796150125147  ,-2.2075476229649762584 ] 
dist 37=[-10.350505390498760776  ,-2.9236049268602673540 ] 
dist 38=[-10.425421889914639479  ,-3.0214244266402668043 ] 
dist 39=[-10.447486161425082789  ,-2.4533922858563235578 ] 
dist 40=[-10.434248405083085971  ,-1.5012919876026387506 ] 
dist 41=[-10.336995668085809827  ,-.52031598608549605499] 
dist 42=[-10.290272556411580282  ,.16310525099511671978] 
dist 43=[-9.6883805344639543093 ,.75794586473999652984] 
dist 44=[-9.8766283542141525162 ,1.3857373075957650420 ] 
dist 45=[-9.9752573257248623132 ,1.9853939261823073561 ] 
dist 46=[-9.9927035825940934442 ,2.4680907892907119330 ] 
dist 47=[-7.0472866087146043207 ,2.9569386473213619733 ] 
dist 48=[-6.8903595787159856408 ,3.5812335304481048274 ] 
dist 49=[-6.4906225241066748324 ,4.1821977210778918371 ] 
dist 50=[-6.4209245974111486035 ,4.5779810742761639712 ] 
dist 51=[-5.7602072666943258776 ,4.8989108463272585456 ] 
dist 52=[-5.6285543331594105921 ,5.2011920625904876448 ] 
dist 53=[-5.4588620315605695431 ,5.5125305987540413552 ] 
dist 54=[-5.3994321217079165883 ,5.7813819357279973418 ] 
dist 55=[-4.1390521353591299253 ,5.9904803940029372682 ] 
dist 56=[-3.9729303194677340945 ,6.0925470214682835433 ] 
dist 57=[-3.6205715545147566742 ,6.1388414832195049554 ] 
dist 58=[-3.5243436984822665489 ,6.1423341512672868850 ] 
dist 59=[-3.1465310282440844797 ,1.5363552017810318187 ] 
dist 60=[-3.0733884590831847923 ,1.8504827037664718778 ] 
dist 61=[-2.9054852263832663121 ,2.1014553518475066102 ] 
dist 62=[-2.8681508173788496399 ,2.3330474795142957902 ] 
dist 63=[-.96785973893452578039,2.5354422321532118812 ] 
dist 64=[-.8026690505954342232 ,2.6698007949449368676 ] 
dist 65=[-.42398199490627464609,2.8055706865739850080 ] 
dist 66=[-.36031790007172631231,3.0314251047777895811 ] 
dist 67=[.12412619486938373347,3.2049902237034295391 ] 
dist 68=[.21032244300332254363,3.3532794916974094854 ] 
dist 69=[.34491955966914417411,3.4745906971162450044 ] 
dist 70=[.37816738678420322378,3.5404478970774287802 ] 
dist 71=[.92834900340592061176,3.5786804288680981927 ] 
dist 72=[.99785980323695577372,3.6849616423794273637 ] 
dist 73=[.87598867724586990552,3.7758520281227755872 ] 
dist 74=[.59972601434834081136,3.8370260683448516765 ] 
dist 75=[.34840530985614464012,3.8779648078388098765 ] 
dist 76=[.06527767558131035666,3.8880118738771869468 ] 
dist 77=[-.21682612181012619396,3.8847072486952967956 ] 
dist 78=[-.46408389218206387257,3.8744116277172518828 ] 
dist 79=[-.73337382626194081539,3.3115194942346952264 ] 
dist 80=[-1.1034598103217023896 ,3.2922899604927605270 ] 
dist 81=[-1.4734421375944044995 ,2.8017783757372888052 ] 
dist 82=[-1.7423325671928197078 ,2.7308703115734371066 ] 
dist 83=[-1.9889553012889557100 ,2.5781765713935833723 ] 
dist 84=[-2.2700578102599565168 ,2.5333081844677439320 ] 
dist 85=[-2.5522460231901587705 ,2.3418653809131421521 ] 
dist 86=[-2.8032201998019348544 ,2.3033842762607754428 ] 
dist 87=[-3.0797621781783700200 ,2.1978274161891114614 ] 
dist 88=[-3.4640558206285083519 ,2.1812565360975995098 ] 
dist 89=[-3.8375721128167663238 ,.34035509487136859743] 
dist 90=[-4.0710891254634618398 ,.32859199801610255866] 
dist 91=[-4.2471278280122791084 ,.3562491962089285128 ] 
dist 92=[-4.3911467972368246500 ,.42087150300595924591] 
dist 93=[-4.5038399167149762126 ,.51875113673797556813] 
dist 94=[-4.5548041843526320022 ,.68746009841849340143] 
dist 95=[-4.5765185500308575006 ,.86360254297407438102] 
dist 96=[-4.5739380665932046164 ,.9911579728638883904 ] 
dist 97=[-4.4979392489963279335 ,1.1074662829912048616 ] 
dist 98=[-4.4732004419483205051 ,1.2387445644440579633 ] 
dist 99=[-4.4071235710265846472 ,1.3695441278411582698 ] 
dist 100=[-4.3783158908137585048 ,1.4839556697624069639 ] 
dist 101=[-4.2173116859606890400 ,1.6082684508157260986 ] 
dist 102=[-4.1760107178588005596 ,1.7786017366529369320 ] 
dist 103=[-4.0841299561619652695 ,1.9484242518282747726 ] 
dist 104=[-4.0513585318714507617 ,2.0707067592462904794 ] 
dist 105=[-3.5099289447218586560 ,2.1816195973153716562 ] 
dist 106=[-3.4878722575800171059 ,2.3060722814064119871 ] 
dist 107=[-3.4099091363304858054 ,2.4297867145684048379 ] 
dist 108=[-3.3957153506867024903 ,2.5377628389187394882 ] 
dist 109=[-3.3253575588534770238 ,2.6549751272410181870 ] 
dist 110=[-3.3113294484866168764 ,2.9111205316087283292 ] 
dist 111=[-3.0924266507766300411 ,3.2045293877796646563 ] 
dist 112=[-3.0749344511784895210 ,3.5413805580020293856 ] 
dist 113=[-2.4003646736332937921 ,3.8518622808802855976 ] 
dist 114=[-2.3092197582612740964 ,4.0399912258280837508 ] 
dist 115=[-2.1311152113478772211 ,4.1747313618059037999 ] 
dist 116=[-2.0841379879083364364 ,4.2720615782499620587 ] 
dist 117=[-1.9147990083725982246 ,4.3424304204221673045 ] 
dist 118=[-1.8744811945027453423 ,4.3695259925588956680 ] 
dist 119=[-1.8116732224954154702 ,4.3752211817562386107 ] 
dist 120=[-1.7928341589128843849 ,4.3682514419060381859 ] 
dist 121=[-.52245339447009906424,2.8488342432545170500 ] 
dist 122=[-.51050698937449706641,2.8194917427393368736 ] 
dist 123=[.52162876925616513663,2.6513639171131470008 ] 
dist 124=[.35911867073131751547,2.6121904641013146804 ] 
dist 125=[.15547799108734348859,2.5365349887895863430 ] 
dist 126=[-.43584425821735447129,2.5899016465938640482 ] 
dist 127=[-1.1113842023520200316 ,2.7628957770354591704 ] 
dist 128=[-1.5548164486436208067 ,2.8664626048433295972 ] 
dist 129=[-1.9135637585700631256 ,2.9392003987799529496 ] 
dist 130=[-2.2510165315742414604 ,2.9890984368625404727 ] 
dist 131=[-2.5493252001848186940 ,3.0222656709260126530 ] 
dist 132=[-2.7517962547457946509 ,3.0284707217729624517 ] 
dist 133=[-2.9230184565875911880 ,3.0240403492602805814 ] 
dist 134=[-3.0965682091865393358 ,3.0169353895652426501 ] 
dist 135=[-3.2519451743414157860 ,2.8628208980172419324 ] 
dist 136=[-3.3506162365261320714 ,2.8324850035712391490 ] 
dist 137=[-3.4267167691939938830 ,2.7597106482350092022 ] 
dist 138=[-3.4919898073973600205 ,2.7335473099736436975 ] 
dist 139=[-3.5453568068118595892 ,2.6025303273105337889 ] 
dist 140=[-3.5739265330440135352 ,2.5716381424410354762 ] 
dist 141=[-3.5898146927079722618 ,2.5008548747479593704 ] 
dist 142=[-3.5925536698486442342 ,2.4764561867299598662 ] 
dist 143=[-.08441375522668757621,.85265147464127447036] 
dist 144=[-.18596293929926224962,.82868654192389799585] 
dist 145=[-.29356390568716866181,.79213192221137734894] 
dist 146=[-.43777442913149564004,.78137046469308572606] 
dist 147=[-.58043173007601266627,.55990067986763980898] 
dist 148=[-.68183099315078972979,.53009664735891686213] 
dist 149=[-.77257466120527891292,.46292115906877065493] 
dist 150=[-.87268639708222341548,.4473503274624560066 ] 
dist 151=[-.97133727122717066986,.36187370932460850688] 
dist 152=[-1.0562480027495606666 ,.34572898599910826689] 
dist 153=[-1.1474842228328069572 ,.31219894645478984584] 
dist 154=[-1.2713914016796519592 ,.30298107446256241871] 
dist 155=[-1.3911049563014570151 ,-.64164484498782827852] 
dist 156=[-1.4655970000903360115 ,-.70241203635545785537] 
dist 157=[-1.5213340668946872726 ,-.80463175045098662956] 
dist 158=[-1.5661632326280940635 ,-.74019562152274586698] 
dist 159=[-1.6006238550101447296 ,-.67040958879241189631] 
dist 160=[-1.6149617776300848896 ,-.6153537934513432678 ] 
dist 161=[-1.6204060655789331568 ,-.5604970844654660536 ] 
dist 162=[-1.6193560487537648347 ,-.49150127588248884807] 
dist 163=[-1.5854779735081439346 ,-.41861016005308692845] 
dist 164=[-1.5758709393742609272 ,-.34819919682763985816] 
dist 165=[-1.5506731922283662900 ,-.26603791169985153051] 
dist 166=[-1.5401037336244793013 ,-.14623161739297752805] 
dist 167=[-1.4821585321300090012 ,-.02334807398203841458] 
dist 168=[-1.4674827347189819396 ,.07110059688708022101] 
dist 169=[-1.4351972741814841081 ,.1629227921311367255 ] 
dist 170=[-1.4238401016561689988 ,.27532247076756981701] 
dist 171=[-1.1264125738019887631 ,.39252288199593876643] 
dist 172=[-1.1027851243815000418 ,.50351392649849597866] 
dist 173=[-1.0384256138745336966 ,.63136348156628044986] 
dist 174=[-1.0290546571928883688 ,.81587486581859910926] 
dist 175=[-.90858981975700281658,.99838043993453948434] 
dist 176=[-.88381414907842522346,1.1182222130761932948 ] 
dist 177=[-.86036393312716318308,1.2152652203457270585 ] 
dist 178=[-.85549193257269468404,1.3067445869879344202 ] 
dist 179=[-.57266508197895931414,1.3877887251967336328 ] 
dist 180=[-.53644851071502423432,1.4431683525559785567 ] 
dist 181=[-.46546378279481510563,1.4904281550332602443 ] 
dist 182=[-.44733320859698669735,1.5390538705656759341 ] 
dist 183=[-.38480348223865751667,1.5804271628809505962 ] 
dist 184=[-.37024029787789513364,1.5987311914276236757 ] 
dist 185=[-.35415271255558020394,1.6068804533668484494 ] 
dist 186=[-.35004609751568657755,1.6077078483505965479 ] 
dist 187=[.12379336333333556968,1.5760243441922045038 ] 
dist 188=[.13455875892184049269,1.5664222365129322517 ] 
dist 189=[.14468137221443235993,1.5593954017306295182 ] 
dist 190=[.07212284680397505304,1.5540329624553921428 ] 
dist 191=[-.23149040064796478222,1.3744641047292516273 ] 
dist 192=[-.43656859668120390697,1.3519306543543670231 ] 
dist 193=[-.60899537198431318984,1.2916661178696751979 ] 
dist 194=[-.78224563170889852248,1.2796314535988112186 ] 
dist 195=[-.94302538247126684138,1.1664914117010781164 ] 
dist 196=[-1.0656627600787110302 ,1.1423073089812600534 ] 
dist 197=[-1.1840025354401604861 ,1.1109494206030197753 ] 
dist 198=[-1.3276236672913538574 ,1.0957831269218745268 ] 
dist 199=[-1.4627977557540429810 ,.7010510740309735065 ] 
dist 200=[-1.5474120449621044393 ,.66174856775615276588] 
dist 201=[-1.6112957788652269439 ,.62069411347073086514] 
dist 202=[-1.6637015997291207410 ,.6873001807331954671 ] 
dist 203=[-1.7047900870701680163 ,.75259629256044541929] 
dist 204=[-1.7234884040041510476 ,.79372270750965888187] 
dist 205=[-1.7313391047239814382 ,.82506490878133387932] 
dist 206=[-1.7305119378610172974 ,.85129749151969213897] 
dist 207=[-.80908365846031818055,.87226865368062597291] 
dist 208=[-.84738878462168091775,.88260436312861507859] 
dist 209=[-.88151506333940977954,.88713568528617098511] 
dist 210=[-.91892672087874599827,.88744361325333661749] 
dist 211=[-.95212643263005286179,.87961401718464212663] 
dist 212=[-.96943605821330743435,.87631102992056117201] 
dist 213=[-.97844411392662795251,.86404428451244423748] 
dist 214=[-.9802069169889879269 ,.85967205851578454597] 
dist 215=[-.97531006372624298549,.82207025503455853177] 
dist 216=[-.97136924601418725384,.8124983793573944188 ] 
dist 217=[-.96611806235536069185,.79895620171028088173] 
dist 218=[-.96276209826424905357,.79369829279104674878] 
dist 219=[-.85188119732348834978,.55651052118649606907] 
dist 220=[-.83618628725708268265,.53030974935970414343] 
dist 221=[-.79330093233873807468,.4648684817282673106 ] 
dist 222=[-.7863513572945569188 ,.45517865343937703421] 
dist 223=[-.70477668400810848132,.35286352417065968683] 
dist 224=[-.68771642597723837437,.33332554790170465679] 
dist 225=[-.66990141595876896557,.31130430265917471605] 
dist 226=[-.66431487133039034453,.30655608999709074329] 
dist 227=[-.56842416935168089134,.12575103294908553869] 
dist 228=[-.5620217949046667314 ,.10336277207486577936] 
dist 229=[-.54994713715373813575,.05723871831211196972] 
dist 230=[-.54610553316168553698,.04533213327356407514] 
dist 231=[-.46603838041951817434,.00249134316363932357] 
dist 232=[-.45416707694008710206,-.00612620133393727718] 
dist 233=[-.42667474060416813207,-.00381919970626790546] 
dist 234=[-.41917872907710893619,.11897362975624345118] 
dist 235=[-.37969683698544425466,.24103064331313823279] 
dist 236=[-.3715107389972162402 ,.32299100230343534348] 
dist 237=[-.35439824312152238934,.39138314340222521377] 
dist 238=[-.34930788720621908982,.45926688614739783774] 
dist 239=[.26246001950103823501,.52173571348945880679] 
dist 240=[.3017768957657781121 ,.56850787632162998583] 
dist 241=[.34827674354857296495,.61280163683150860016] 
dist 242=[.34964190766749485966,.66537485262921302918] 
dist 243=[.34530239912183531642,.71426371732095141113] 
dist 244=[.33283750088086365371,.743847064651474797  ] 
dist 245=[.31201573433940721293,.76499051952747931741] 
dist 246=[.27431048353610049119,.78018180343015110792] 
dist 247=[.22857489086608860992,.79079279421228400119] 
dist 248=[.17569121972666199089,.79364905456773339357] 
dist 249=[.10737026542575669132,.79347189358923832403] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 1, 0, 1, 0, 2] 
dist 0=[46.603989105683597166  ,46.603989105683597166  ] 
dist 1=[46.183780697634345603  ,46.840373715838478353  ] 
dist 2=[45.307602587176657522  ,46.982234195562889728  ] 
dist 3=[44.224508502744774365  ,47.089009350218239815  ] 
dist 4=[42.977832562185534321  ,47.184931745433225741  ] 
dist 5=[41.368798974745472810  ,47.251964418022658117  ] 
dist 6=[38.838184412817806062  ,47.243399636225435544  ] 
dist 7=[36.252658868753143320  ,47.177175600781694506  ] 
dist 8=[34.424207425300598883  ,47.121125458154366827  ] 
dist 9=[32.794509695117551800  ,46.801052871817874184  ] 
dist 10=[31.002760371623143007  ,46.699482992324311325  ] 
dist 11=[29.236681987747948459  ,46.301391176032306372  ] 
dist 12=[27.709386856270172488  ,46.222298532103174216  ] 
dist 13=[26.058946653900799908  ,45.039527936971974237  ] 
dist 14=[23.800691243888414251  ,44.179224145717190592  ] 
dist 15=[21.536740707024666830  ,33.940013361715065134  ] 
dist 16=[19.863404569556781378  ,33.614824431554729447  ] 
dist 17=[18.295551716671348808  ,30.251894121237637042  ] 
dist 18=[16.452788438153956437  ,29.604578231732270056  ] 
dist 19=[14.564405098185941954  ,28.876862077670466196  ] 
dist 20=[12.814025103208458695  ,28.706809923241956562  ] 
dist 21=[10.821067658102871219  ,22.560986578297196187  ] 
dist 22=[7.9629822087190544590 ,21.778616227631502532  ] 
dist 23=[5.1347645743027277603 ,20.213014099828261516  ] 
dist 24=[3.2610770613661013426 ,19.809404631232448278  ] 
dist 25=[1.7185650286702618255 ,18.373849679690919859  ] 
dist 26=[.21384375228183219634,18.062645445132573481  ] 
dist 27=[-1.1606505718954165083 ,17.595411165405847729  ] 
dist 28=[-2.1827815085942316586 ,17.463879134266741750  ] 
dist 29=[-3.1480376437332149093 ,10.964451162061937286  ] 
dist 30=[-4.2953924098152025239 ,8.9540388873485204882 ] 
dist 31=[-6.4068203825155453674 ,2.6386542501271181888 ] 
dist 32=[-8.0487238789682082269 ,2.2838701585745798692 ] 
dist 33=[-9.3305850217787757157 ,-.44284426059253301834] 
dist 34=[-10.467057355162205271  ,-.91047183926353093624] 
dist 35=[-11.431901499134564061  ,-1.6391983842285170255 ] 
dist 36=[-12.027996748430454665  ,-1.8103923865572188136 ] 
dist 37=[-12.472979822941957198  ,-2.0132141961977209294 ] 
dist 38=[-12.834320529598034092  ,-1.0081659623394914297 ] 
dist 39=[-13.119802093772530727  ,.02898950598929085550] 
dist 40=[-13.261614480993353161  ,.75525372713216610865] 
dist 41=[-13.328289557659293905  ,1.3914414547841965566 ] 
dist 42=[-13.319373630124610203  ,2.0694259791112766409 ] 
dist 43=[-13.248498076617938931  ,2.7211782425225259471 ] 
dist 44=[-13.209139061184059266  ,3.2528075175869951557 ] 
dist 45=[-12.995560489564527601  ,3.7976667746764946118 ] 
dist 46=[-12.964404696045199976  ,4.5023023066985702851 ] 
dist 47=[-7.9062614362374227871 ,5.1849614870028986006 ] 
dist 48=[-7.4288110104232416073 ,5.6421541861298493611 ] 
dist 49=[-6.2785621413833661511 ,6.0213804181535888894 ] 
dist 50=[-6.0933300297692764941 ,6.3929185748871010458 ] 
dist 51=[-5.3276634768058400632 ,6.7306810356400099983 ] 
dist 52=[-5.2608090676930335625 ,6.9751089058947269571 ] 
dist 53=[-4.8668002477439728489 ,7.1976961987208172520 ] 
dist 54=[-4.8263749799835055149 ,7.4482544479854706431 ] 
dist 55=[-3.3267039624621691117 ,7.6738585908822157705 ] 
dist 56=[-3.2320275977886853316 ,7.7968485352582328863 ] 
dist 57=[-2.7802702499974304612 ,7.8679105396012953506 ] 
dist 58=[-2.6980722184283867818 ,7.8862941488727394902 ] 
dist 59=[-2.5062059613856607922 ,7.8690206664779522221 ] 
dist 60=[-2.4703245818291775986 ,7.8507530007224349286 ] 
dist 61=[-1.3608773006972162957 ,7.7257896788337355708 ] 
dist 62=[-1.2766909133806869953 ,7.4422890137333211846 ] 
dist 63=[-1.0811958631517568423 ,3.1659728078487894793 ] 
dist 64=[-1.0454423070827001011 ,3.4153412224455296826 ] 
dist 65=[-.77732012513352477938,3.5971042566435148916 ] 
dist 66=[-.72633413916264456556,3.7588707513504472320 ] 
dist 67=[-.64752907194917779424,3.9759034665167693186 ] 
dist 68=[-.62610778972046971151,4.2026201204771240803 ] 
dist 69=[-.21619897730443945426,4.4035534737781731681 ] 
dist 70=[-.16095279094286929795,4.5176023557696808870 ] 
dist 71=[-.03902728287297842341,4.5905030706887716734 ] 
dist 72=[-.00894178522800946554,4.6270005326650926694 ] 
dist 73=[.14103275815081093218,4.6435513275744152470 ] 
dist 74=[.16967668462326108909,4.6396366107524608936 ] 
dist 75=[.23275243017834719466,4.6192621987744760303 ] 
dist 76=[.25047005886786648468,4.6029968582874351897 ] 
dist 77=[.37597167249503369447,3.2790869069977220749 ] 
dist 78=[-.04861477832786968930,3.2672531455046035579 ] 
dist 79=[-.4788499597869942265 ,2.7433128315904380058 ] 
dist 80=[-.80075020233300611879,2.6824802675640909553 ] 
dist 81=[-1.1052453916612313466 ,2.5209030880419283819 ] 
dist 82=[-1.4660284692838315510 ,2.4953227328163023876 ] 
dist 83=[-1.8359034945995021570 ,2.2058239540688928503 ] 
dist 84=[-2.1767224561383508113 ,2.1469437466143319067 ] 
dist 85=[-2.5620024190229862965 ,2.0832187967252361126 ] 
dist 86=[-3.1094222733375000137 ,2.0646032355826537612 ] 
dist 87=[-3.6468674526902178494 ,.50912557457266324503] 
dist 88=[-3.9923317340805504961 ,.476543157819714163  ] 
dist 89=[-4.2638254243610863210 ,.34777526193165403132] 
dist 90=[-4.5059331925038990922 ,.32348660359265012823] 
dist 91=[-4.7110807975765798977 ,.27645541056353938533] 
dist 92=[-4.8350106427898069667 ,.56913414386895779901] 
dist 93=[-4.9234125820948074326 ,.94850205485919564976] 
dist 94=[-4.9867238276000754626 ,1.2167614713739821669 ] 
dist 95=[-5.0284345055788822145 ,1.4551074583883399765 ] 
dist 96=[-5.0331159885775820543 ,1.7150821757936527108 ] 
dist 97=[-5.0841837735216285390 ,1.9692136355475244257 ] 
dist 98=[-5.0994624065430714116 ,2.1842432704016364263 ] 
dist 99=[-5.0953598260159294624 ,2.4119394288969954218 ] 
dist 100=[-5.0309301014201990062 ,2.7166438730389794916 ] 
dist 101=[-4.7429746663931028946 ,3.0174315143590932979 ] 
dist 102=[-4.7168587285540690898 ,3.2294976064336356736 ] 
dist 103=[-3.3746299654754760088 ,3.4173321528125296554 ] 
dist 104=[-3.2253404869285791872 ,3.6213964694215323433 ] 
dist 105=[-2.8710937958010530955 ,3.8204721482476203818 ] 
dist 106=[-2.8009516174875644268 ,3.9883985385145553722 ] 
dist 107=[-2.2939579564792204552 ,4.1658221195119160173 ] 
dist 108=[-2.1965305761046913391 ,4.4028208082343142601 ] 
dist 109=[-2.0319826600126455724 ,4.6276076277362248844 ] 
dist 110=[-1.9910245311428121690 ,4.7562805195229438086 ] 
dist 111=[-1.2353950059626200746 ,4.8393037946648340736 ] 
dist 112=[-1.1358646226538050449 ,4.8818444864031327938 ] 
dist 113=[-.89462926139028864233,4.9015481838411300212 ] 
dist 114=[-.85946052246715973581,4.8974502277599606255 ] 
dist 115=[-.5608630566405292335 ,4.8730286918895017869 ] 
dist 116=[-.51743957225555661152,4.8439284530810661458 ] 
dist 117=[-.45951647440451268086,4.4744159871197972048 ] 
dist 118=[-.44236082047280885496,4.3055101216969001455 ] 
dist 119=[-.10224754661917800924,1.4481314534710454412 ] 
dist 120=[-.05977735870061554945,1.5439697747166929461 ] 
dist 121=[.03340914356244055733,1.6150326602616119395 ] 
dist 122=[.05209627593379464780,1.6710653781922637063 ] 
dist 123=[.14627650261425824473,1.7147602071018408672 ] 
dist 124=[-.06105590044542891671,1.7365530749011621514 ] 
dist 125=[-.27045548480179736146,1.7466504583767151718 ] 
dist 126=[-.4119742683305035283 ,1.7479341500637084510 ] 
dist 127=[-.53091735645819328553,1.2527074225342578290 ] 
dist 128=[-.6502045220380125224 ,1.2521882995655655447 ] 
dist 129=[-.76063048859837344538,1.2171417240133928045 ] 
dist 130=[-.8442031981881935313 ,1.2068398351024960033 ] 
dist 131=[-.92413948517700529977,1.1995737294178886626 ] 
dist 132=[-1.0200496127684411015 ,1.1945757413096740105 ] 
dist 133=[-1.1096115102575294729 ,.99188281604078239243] 
dist 134=[-1.1642074862661634026 ,.96340414821046747235] 
dist 135=[-1.2036578161529512900 ,.90899166626673696296] 
dist 136=[-1.2327629815666170917 ,.8944977130749394283 ] 
dist 137=[-1.2535645218291350210 ,.84227476689715440918] 
dist 138=[-1.2598696684834556418 ,.82896647517468184666] 
dist 139=[-1.2604588442263241930 ,.80878987468393266284] 
dist 140=[-1.2584455760399653864 ,.80218359085452168981] 
dist 141=[.00671697074053620268,.76003327769422306141] 
dist 142=[-.09443020843091471930,.75685809424150811098] 
dist 143=[-.19548869525517342143,.69420131498759784273] 
dist 144=[-.2626421403399594241 ,.6841960501777993682 ] 
dist 145=[-.3474977098385080952 ,.65744306770373099769] 
dist 146=[-.43768735642661471668,.65165208607752828424] 
dist 147=[-.53133860648940912747,.60057666162533785589] 
dist 148=[-.65437692009724474271,.58943329723077484515] 
dist 149=[-.77494503459373493352,.574203741173029663  ] 
dist 150=[-.85873512255985629716,.56874850439774446853] 
dist 151=[-.93175102874171562767,.44317819264774261346] 
dist 152=[-1.0093032583962921319 ,.42581277864560807926] 
dist 153=[-1.0839808662040696798 ,.3889255209477177575 ] 
dist 154=[-1.1455215409065910723 ,.37848487066631643378] 
dist 155=[-1.2093286279903938748 ,.33573538175815491421] 
dist 156=[-1.2930598951612450996 ,.327248228774569191  ] 
dist 157=[-1.3719640353470581855 ,.30544625013905763411] 
dist 158=[-1.4164983969197295390 ,.39982300545862936147] 
dist 159=[-1.4444636128568190328 ,.49176509750243349409] 
dist 160=[-1.4572091876785048061 ,.589341165143237829  ] 
dist 161=[-1.4635641141006263507 ,.6831959070590124453 ] 
dist 162=[-1.4660109754087070853 ,.7602820081054185504 ] 
dist 163=[-1.4660759241247059124 ,.83993402956694364407] 
dist 164=[-1.4629163626908904724 ,.94403403181149657447] 
dist 165=[-1.2945531000005958610 ,1.0457378116421844602 ] 
dist 166=[-1.2690409860045607944 ,1.1158237760237160857 ] 
dist 167=[-1.2233251024399406349 ,1.1762491690977700609 ] 
dist 168=[-1.2110658824941288094 ,1.2393848512448746466 ] 
dist 169=[-1.1680023272714741686 ,1.2995196216977029043 ] 
dist 170=[-1.1550628586258699338 ,1.3479649243912621802 ] 
dist 171=[-1.1380624056947317743 ,1.3971856621645907531 ] 
dist 172=[-1.1308369622064071287 ,1.4604177403502934019 ] 
dist 173=[-.56772111338389054404,1.5196054871662985113 ] 
dist 174=[-.5612070131166025594 ,1.5526795634070481372 ] 
dist 175=[-.41053205808079574636,1.5729982988568308307 ] 
dist 176=[-.41068683726842961316,1.5812599520051836499 ] 
dist 177=[-.40956824276101732143,1.5830437826464614965 ] 
dist 178=[-.40860008838429802305,1.5803957899069205848 ] 
dist 179=[-.40136663672674505579,1.5692125004031839978 ] 
dist 180=[-.39916579205979123803,1.5620207447106503708 ] 
dist 181=[-.39212002384407595111,1.4429358624914601872 ] 
dist 182=[-.38981672680210510915,1.4221586568436196269 ] 
dist 183=[-.35828581498709266434,1.3731754526466902771 ] 
dist 184=[-.35288677677656468942,1.3565893579116708035 ] 
dist 185=[-.33804421993294112383,1.2769137093104801262 ] 
dist 186=[-.33518933507026006085,1.2587943985436569427 ] 
dist 187=[-.30597891045057687808,1.2183191675827255620 ] 
dist 188=[-.29966410738643205113,1.2049319244486244279 ] 
dist 189=[-.43906556880945315901,1.1976842943588343450 ] 
dist 190=[-.64666127566847048606,1.2283051121521572487 ] 
dist 191=[-.81517331898253866129,1.2477432522316826087 ] 
dist 192=[-.97469281645258886613,1.2570469532046151943 ] 
dist 193=[-1.1164508516677666232 ,1.2609272229765090945 ] 
dist 194=[-1.2140492580330275171 ,1.2594754355407786332 ] 
dist 195=[-1.2981070190408684425 ,1.2535247593976447964 ] 
dist 196=[-1.3858028069252195430 ,1.2489652862059795133 ] 
dist 197=[-1.4650320893613461918 ,1.1504833397966828727 ] 
dist 198=[-1.5152870442389262255 ,1.1336368938878638693 ] 
dist 199=[-1.5539987355385009482 ,1.0961536770141733849 ] 
dist 200=[-1.5871419255324915030 ,1.0838819983861664535 ] 
dist 201=[-1.6142133608636357441 ,1.0264109311356881901 ] 
dist 202=[-1.6286838005863920673 ,1.0136480136321913282 ] 
dist 203=[-1.6367107317862460054 ,.97998694896302589869] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 2, 1, 2, 2, 1, 2] 
dist 0=[50.358726984937531399  ,50.358726984937531399  ] 
dist 1=[49.990646084440436876  ,50.544552985728707717  ] 
dist 2=[49.417225931410913690  ,50.634105832266503777  ] 
dist 3=[48.410926056042674091  ,50.617621661183112738  ] 
dist 4=[47.198459713448561228  ,50.529717375822849576  ] 
dist 5=[45.801280215232642812  ,50.463508977122467570  ] 
dist 6=[43.995467912841545722  ,49.999152953179361552  ] 
dist 7=[41.150280455604850281  ,49.863379449176257152  ] 
dist 8=[38.234498970947254314  ,49.407182494096463307  ] 
dist 9=[36.146548890830561817  ,49.283464413351705526  ] 
dist 10=[34.256639990259370434  ,47.522982260033940806  ] 
dist 11=[32.131922114487120736  ,47.147446933160714182  ] 
dist 12=[30.007510934588968710  ,46.821393177267017913  ] 
dist 13=[28.118607465381603046  ,46.626553023185787105  ] 
dist 14=[26.031478000930098756  ,41.891186393504958945  ] 
dist 15=[23.114609166807038304  ,41.042097093759828419  ] 
dist 16=[20.157481933583222808  ,36.487228589431273639  ] 
dist 17=[17.909256765788253779  ,31.137068591279198972  ] 
dist 18=[15.738172832366950196  ,26.573895840711639996  ] 
dist 19=[13.088982737331392014  ,24.270307686649481658  ] 
dist 20=[10.317187135644086575  ,22.735108982756190391  ] 
dist 21=[7.6557402636748101489 ,22.185860317366602166  ] 
dist 22=[4.5496319501491471702 ,20.510892940188045688  ] 
dist 23=[0                     ,20.175117571835179668  ] 
dist 24=[9.5590366300288895500 ,19.472368631325746862  ] 
dist 25=[5.7808573418334376758 ,19.277795555730083522  ] 
dist 26=[2.0417412864695216261 ,13.501150522423180073  ] 
dist 27=[-.42019539633623463302,13.021323934469869645  ] 
dist 28=[-2.4267679863029757357 ,12.862890616831310620  ] 
dist 29=[-4.3467098526252595544 ,10.303067052311508385  ] 
dist 30=[-6.0724059756697683520 ,9.9146315203130068084 ] 
dist 31=[-7.3030027990092824217 ,8.1274118522296171795 ] 
dist 32=[-8.4112564948160850079 ,5.0847352420954627412 ] 
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dist 36=[-12.019872256003483804  ,-1.9606663502003507513 ] 
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dist 38=[-12.784096594843189896  ,-2.2558037914804388001 ] 
dist 39=[-12.936125294634384140  ,-2.2007016015225269991 ] 
dist 40=[-12.996419593375831221  ,-2.0244445364268141560 ] 
dist 41=[-12.990244694235428399  ,-1.6405749029047539239 ] 
dist 42=[-12.151024722749133833  ,-1.2197528423279168640 ] 
dist 43=[-12.116346529476428012  ,-.8958547917214250763 ] 
dist 44=[-12.081405638439812134  ,-.5830970883570723219 ] 
dist 45=[-11.919977728145702566  ,-.2061761618641594984 ] 
dist 46=[-11.860692712919022534  ,.1814477787170759445 ] 
dist 47=[-11.666291481251606701  ,.5371943385227019530 ] 
dist 48=[-11.595948874813592230  ,.9370722336212133633 ] 
dist 49=[-6.2833848113325895341 ,1.5010814052641534544 ] 
dist 50=[-5.7986046918457428213 ,2.0700857306522720199 ] 
dist 51=[-4.7052844609515652447 ,2.4900521219230194849 ] 
dist 52=[-4.4883699592280262582 ,2.8814107434347421985 ] 
dist 53=[-3.1577282833251387470 ,3.3364412467155372860 ] 
dist 54=[-2.2854950876728142491 ,3.7984122924671355980 ] 
dist 55=[-1.9328578042280260948 ,4.3339003988542299691 ] 
dist 56=[-1.0873301489911025999 ,5.1550453390052691648 ] 
dist 57=[-1.0370542356451614689 ,5.9200333874745423629 ] 
dist 58=[.81636934672590494126,6.4034660410601971265 ] 
dist 59=[.99870922859672389448,6.7737947147873686101 ] 
dist 60=[1.3382113791355508563 ,7.0870692903407173300 ] 
dist 61=[1.4129207469595407877 ,7.3396676226291721550 ] 
dist 62=[1.6021525149254521391 ,7.4676174133537016438 ] 
dist 63=[1.6088801923109230178 ,7.5284239690234114770 ] 
dist 64=[1.5494633829944037331 ,7.5373979032561985804 ] 
dist 65=[1.3851332196112591436 ,6.1022190543856402849 ] 
dist 66=[1.1854745915303272081 ,6.3013500999214529324 ] 
dist 67=[.98497550139042642707,6.3961610740193908933 ] 
dist 68=[.74579201239776066241,6.4433885512516457432 ] 
dist 69=[.39158177708715041595,6.4523637246708165488 ] 
dist 70=[-.00941401973573582248,6.3542039276501647969 ] 
dist 71=[-.43542823438488602449,6.3255356219913243032 ] 
dist 72=[-.96155906229485879441,6.3054806469791092918 ] 
dist 73=[-1.7622823751052008696 ,6.2920213707995909763 ] 
dist 74=[-2.5643144071531503966 ,3.2106552094264348726 ] 
dist 75=[-3.0956993524611290368 ,2.8857558931346304149 ] 
dist 76=[-3.5309896856870359813 ,2.8311715310280226608 ] 
dist 77=[-3.9494381378350277922 ,2.3546490174005644823 ] 
dist 78=[-4.3254974730739418766 ,2.2648938086530751716 ] 
dist 79=[-4.5915917274288966656 ,2.1402453490094335376 ] 
dist 80=[-4.8284122772791588782 ,2.1024745717422196529 ] 
dist 81=[-5.0876485664785778443 ,1.0441851955324275674 ] 
dist 82=[-5.3176155351436604422 ,.91925211952690827561] 
dist 83=[-5.4376062151048979379 ,.68328645990663104497] 
dist 84=[-5.5015088683483197745 ,.62746342541493812548] 
dist 85=[-5.5142935371915660615 ,.46117532599581943916] 
dist 86=[-5.4820757566366417520 ,.4283595879114737028 ] 
dist 87=[-5.4621640589876934056 ,.43137671401849425048] 
dist 88=[-5.4923183939606105416 ,.4835408249823632164 ] 
dist 89=[-5.6340705376354372665 ,.55621129078585185077] 
dist 90=[-5.7121254683539038232 ,1.1784389993181457296 ] 
dist 91=[-5.7587934083928200080 ,1.9072554503531429252 ] 
dist 92=[-5.7751885784483195579 ,2.5137441761424626253 ] 
dist 93=[-5.7711161329071561711 ,3.1121982997768371559 ] 
dist 94=[-5.7610866805019646737 ,3.6599544411959665389 ] 
dist 95=[-5.6975547012081891445 ,4.0640682153031328280 ] 
dist 96=[-5.6797500747786357533 ,4.4404972752705603210 ] 
dist 97=[-5.0029944674660550835 ,4.8777336493052173407 ] 
dist 98=[-4.0137900556134192002 ,5.2787112338920988091 ] 
dist 99=[-3.8767669374106709484 ,5.5104039901332088883 ] 
dist 100=[-3.6061532444904875258 ,5.6624969430801713213 ] 
dist 101=[-3.5332529787845601398 ,5.7457407096335073315 ] 
dist 102=[-3.2617915230083039555 ,5.7979194046487238620 ] 
dist 103=[-3.1983137008631704507 ,5.8260126582108998204 ] 
dist 104=[-3.0821903607493856534 ,5.8418112993242228369 ] 
dist 105=[-3.0504526840347749060 ,5.8449172519335589714 ] 
dist 106=[-.37424088278274886525,3.7633128813618290870 ] 
dist 107=[-.24900380008442935405,3.7725252810716719669 ] 
dist 108=[.04221699813220853077,3.7681352690585818797 ] 
dist 109=[.08551423783428476200,3.6682695560053604524 ] 
dist 110=[.46018927186543851374,3.6355759975593480589 ] 
dist 111=[.15236386250161654204,3.8008355465998000121 ] 
dist 112=[-.69511359932446043541,4.0605908369191733351 ] 
dist 113=[-1.5432236352123014387 ,4.3027179226563241983 ] 
dist 114=[-2.1040338509351027260 ,4.4423336912271699103 ] 
dist 115=[-2.5620336151380681946 ,4.5339382116817176411 ] 
dist 116=[-2.9997421147651242646 ,4.5843644409040617697 ] 
dist 117=[-3.3910915528210671462 ,4.6118917194605467218 ] 
dist 118=[-3.6640281043108934841 ,4.6120483341259676053 ] 
dist 119=[-3.9025601119993321509 ,4.5977377700982157000 ] 
dist 120=[-4.1565553369474060897 ,4.5054169978187904027 ] 
dist 121=[-4.3846238740242434991 ,4.2001357145676345742 ] 
dist 122=[-4.5196640998617017162 ,1.6623446685253400099 ] 
dist 123=[-4.6124018984925617073 ,1.5171949066343981054 ] 
dist 124=[-4.6716329098195039181 ,1.4819531570664887038 ] 
dist 125=[-4.7058235759860432580 ,1.2848730817464160098 ] 
dist 126=[-4.7101727220869596935 ,1.2462280185713104834 ] 
dist 127=[-4.6807094223776592850 ,1.1673488335733535186 ] 
dist 128=[-4.6722788929015364320 ,1.1453263538113666228 ] 
dist 129=[.2876675334110603645 ,1.0193863702502945913 ] 
dist 130=[.11876488425123973653,.93205298366165028764] 
dist 131=[-.01176995326575506161,.91550394156849332195] 
dist 132=[-.1393224266118839793 ,.88009437540742017487] 
dist 133=[-.29632862511541401762,.86921444388757064357] 
dist 134=[-.46046570896430819221,.82088233463672396119] 
dist 135=[-.61649429083374041432,.81073989872990159535] 
dist 136=[-.79666104126749608189,.78096738290265133383] 
dist 137=[-1.0571770559564029023 ,.77642076076043591297] 
dist 138=[-1.3146290702804234073 ,.26048129492900744268] 
dist 139=[-1.4825653964893298869 ,.19794360995253645527] 
dist 140=[-1.6172992311552988000 ,.18331354745476167934] 
dist 141=[-1.7421907157966426062 ,.1163535844691747474 ] 
dist 142=[-1.8513925196781949069 ,.10447038797340880841] 
dist 143=[-1.9234866439486758199 ,.07813970852887776818] 
dist 144=[-1.9823083848660182547 ,.07320416825972378061] 
dist 145=[-2.0385237843023675578 ,-.18245423046551388757] 
dist 146=[-2.0848293224228815855 ,-.20616771737841710494] 
dist 147=[-2.1040853461872829486 ,-.25104848697292258275] 
dist 148=[-2.1112525157420605982 ,-.2610716494158982398 ] 
dist 149=[-2.1092872712683190167 ,-.2875822033587880371 ] 
dist 150=[-2.0666391089759811454 ,-.28926247238120660752] 
dist 151=[-2.0514667716301610274 ,-.28235458496469347262] 
dist 152=[-2.0371415439300160712 ,-.26197803664596472154] 
dist 153=[-2.0269745768473515217 ,-.23685269546080560709] 
dist 154=[-1.6339175238403372919 ,.14657415895289039265] 
dist 155=[-1.5890748571366321265 ,.40935739516556692438] 
dist 156=[-1.4738889002578012066 ,.63035181511276694131] 
dist 157=[-1.4545169147167468742 ,.85242875073654144169] 
dist 158=[-1.2597605678945706003 ,1.0584920574298946860 ] 
dist 159=[-1.2206301980941509762 ,1.2155542675973032110 ] 
dist 160=[-1.1735013843345271734 ,1.3669750083651481054 ] 
dist 161=[-1.1570917811987224236 ,1.5505157084197587494 ] 
dist 162=[-.76545023268030065682,1.7230974280358100285 ] 
dist 163=[-.71425139070013326873,1.8307657378618596989 ] 
dist 164=[-.60722845673487683638,1.9116153973899609985 ] 
dist 165=[-.57842399082615014191,1.9771265598369367036 ] 
dist 166=[-.46816625898900032882,2.0278427545039123937 ] 
dist 167=[-.44615907520666536672,2.0496250409031225890 ] 
dist 168=[-.40021029137858593911,2.0588282259290685543 ] 
dist 169=[-.38762930198173841472,2.0593234485795853137 ] 
dist 170=[.19555655000155748092,.76439972646815015204] 
dist 171=[.24051980306010035762,.79117113119285482818] 
dist 172=[.24923166508774676553,.81505973406982167273] 
dist 173=[.19383012416224507394,.83533267542196298559] 
dist 174=[.11319836451778927606,.84767127257256761951] 
dist 175=[.01204486826837760276,.87246308375717416348] 
dist 176=[-.14367207532661533756,.9052214512847092868 ] 
dist 177=[-.30050480781573079048,.93463663066554073485] 
dist 178=[-.40611298552903735475,.97418112427779016744] 
dist 179=[-.49450448627286314618,1.0180987193073787767 ] 
dist 180=[-.5826071798978699296 ,1.0499087106251196158 ] 
dist 181=[-.66386352953149186833,1.0735797054418946641 ] 
dist 182=[-.72492390215191419264,1.0905248405654546645 ] 
dist 183=[-.78293273372230910149,1.0954799957614925525 ] 
dist 184=[-.8520068706887387616 ,1.0959661846482422257 ] 
dist 185=[-.91629345538661217752,1.0950681576930690234 ] 
dist 186=[-.9551898189625240692 ,1.0498416125866329379 ] 
dist 187=[-.98296347766224295319,1.0411476170819858476 ] 
dist 188=[-1.0028470442422623446 ,1.0127967970049620067 ] 
dist 189=[-1.0166157042755185566 ,1.0079245289773887446 ] 
dist 190=[-1.0199778816676497658 ,.93801581932800091287] 
dist 191=[-1.0194184039949400863 ,.92216886527981423424] 
dist 192=[-1.0175321018259106711 ,.90774689501148275077] 
dist 193=[-.64163150026102659447,.90257073691762096094] 
dist 194=[-.74941968195581526773,.69108997408530554592] 
dist 195=[-.82381438727613221238,.66275893518328288393] 
dist 196=[-.88808667765067816342,.6073802006139186581 ] 
dist 197=[-.95546152944029094001,.59284757959597895413] 
dist 198=[-1.0197787297218390521 ,.54082549531237802275] 
dist 199=[-1.0718439829225463551 ,.52847244329861822153] 
dist 200=[-1.1249763601299015393 ,.51011159067630775688] 
dist 201=[-1.1935555309789929942 ,.50436290644786737034] 
dist 202=[-1.2580661415480274589 ,-.10042672395309024858] 
dist 203=[-1.2949547482075014274 ,-.11337556699075254732] 
dist 204=[-1.3187226752051956682 ,-.10089112898231210444] 
dist 205=[-1.3308473676174449302 ,-.05309964794540716055] 
dist 206=[-1.3369572444102710858 ,.00364095342080312637] 
dist 207=[-1.3367098643479282707 ,.07787092671592675785] 
dist 208=[-1.3324352058766580300 ,.19548734422250790783] 
dist 209=[-1.3289048678205817611 ,.31535242383024484008] 
dist 210=[-1.2144243665613486551 ,.3985602973284518076 ] 
dist 211=[-1.2478937855028723737 ,.47094116867086257975] 
dist 212=[-1.2682066887381778781 ,.54758116775983507857] 
dist 213=[-1.2817263578885694010 ,.62119650016213601022] 
dist 214=[-1.2880725907979290916 ,.68150215430171439789] 
dist 215=[-1.2903895638331671684 ,.74367787735387226603] 
dist 216=[-1.2879943726037147346 ,.82476000281019197448] 
dist 217=[-1.1628591180720825690 ,.90389816960575810477] 
dist 218=[-1.1429786399780586571 ,.95831313045896162879] 
dist 219=[-1.1082512193471369312 ,1.0051013923427883282 ] 
dist 220=[-1.0986504084455704489 ,1.0537908826082342939 ] 
dist 221=[-1.0650418112854642852 ,1.1000464947585713838 ] 
dist 222=[-1.0544146398807818182 ,1.1371181313238517596 ] 
dist 223=[-1.0396887671283114713 ,1.1746091223635055656 ] 
dist 224=[-1.0335582597320708196 ,1.2225399663151950357 ] 
dist 225=[-.62995292002557798206,1.2673525569413640554 ] 
dist 226=[-.50162636144420303944,1.2923941275431473288 ] 
dist 227=[-.4836653475112447317 ,1.3077793699465053660 ] 
dist 228=[-.44328215802573308645,1.3140387234659867930 ] 
dist 229=[-.43263652059163584105,1.3149481448818236023 ] 
dist 230=[-.37998935595346525059,1.3129469196256436056 ] 
dist 231=[-.36957320934031290224,1.3013692847922676159 ] 
dist 232=[-.34651995513468874884,1.2957737296210331850 ] 
dist 233=[-.33960906484682246608,1.2089688738819486828 ] 
dist 234=[.27154657917003303679,1.1932542222721294087 ] 
dist 235=[.25592258844981139679,1.1530764101747289977 ] 
dist 236=[.2241518455711726461 ,1.1413776037331376101 ] 
dist 237=[.18438545971436854017,1.0674644741361494295 ] 
dist 238=[.13683844171444158385,1.0507300630857353116 ] 
dist 239=[.05888857860903230438,1.0201287726900992519 ] 
dist 240=[-.19320128483687141814,1.0131924820889701183 ] 
dist 241=[-.46658111615666917085,1.0687466700736787101 ] 
dist 242=[-.6460534794024103886 ,1.1011059710887851729 ] 
dist 243=[-.79131800550115937468,1.1227099263406361648 ] 
dist 244=[-.9281226060955946431 ,1.1353227966089297885 ] 
dist 245=[-1.0492116572120564847 ,1.1424597167721602618 ] 
dist 246=[-1.1317316184912562196 ,1.1425840301714438877 ] 
dist 247=[-1.2019000541524777024 ,1.1387637081476439593 ] 
dist 248=[-1.2736753918229718530 ,1.1346720722433793335 ] 
dist 249=[-1.3379927539266259379 ,1.0572319065046221317 ] 
dist 250=[-1.3783850758855162276 ,1.0433007911375582930 ] 
dist 251=[-1.4090335227228271472 ,1.0117534570312861194 ] 
dist 252=[-1.4344482798002636927 ,1.0011138163746838732 ] 
dist 253=[-1.4545868989509054345 ,.95015264808950155988] 
dist 254=[-1.4641701982034351997 ,.9385943578748188166 ] 
dist 255=[-1.4678656857115871405 ,.90908910744576916395] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 1, 1, 1, 2] 
dist 0=[41.089220293877008330  ,41.089220293877008330  ] 
dist 1=[40.378974141629728196  ,41.583099865891744770  ] 
dist 2=[39.184910994993710315  ,41.912748273454223257  ] 
dist 3=[37.934858463968341418  ,42.144020920655248009  ] 
dist 4=[37.000880387118515318  ,42.244986176690248972  ] 
dist 5=[36.116427477018202975  ,42.270130991616707605  ] 
dist 6=[35.064094253610194545  ,42.249753594860611925  ] 
dist 7=[33.979635749019523780  ,42.097442455718480427  ] 
dist 8=[32.966737185424335834  ,41.771366825342921218  ] 
dist 9=[31.808214520958361061  ,40.226818271572370608  ] 
dist 10=[30.141805157642534970  ,40.107080191133912906  ] 
dist 11=[28.433976948330442168  ,39.645817948482567498  ] 
dist 12=[27.109877609998355237  ,39.504622966104888658  ] 
dist 13=[25.807638787552398438  ,39.231136849211851284  ] 
dist 14=[24.187000244880671810  ,39.136849684610359023  ] 
dist 15=[22.476680325109263084  ,38.733729891200090897  ] 
dist 16=[20.815941876626603265  ,38.170298196327513042  ] 
dist 17=[18.865426981514230269  ,26.522538415270331166  ] 
dist 18=[15.996925272629774364  ,26.414978614427318628  ] 
dist 19=[13.132111778078558187  ,22.779916288990717908  ] 
dist 20=[11.196304520095865562  ,22.292944771372333461  ] 
dist 21=[9.5611124993089549448 ,20.998140926956603100  ] 
dist 22=[7.8977015373792864050 ,20.812112920435996570  ] 
dist 23=[6.3339135373555475409 ,18.657264639200439834  ] 
dist 24=[5.0968580040268462935 ,18.506324992540273718  ] 
dist 25=[3.8562812489862624831 ,17.487506485529305059  ] 
dist 26=[2.2784103379490831951 ,16.896497026171223866  ] 
dist 27=[.74756140350855786011,12.218344475907661761  ] 
dist 28=[-.30513156001273243099,11.965224595344702938  ] 
dist 29=[-1.2142567333533705706 ,11.489839798756426341  ] 
dist 30=[-2.1714427707099899463 ,11.375095032695154424  ] 
dist 31=[-3.0922524041413937988 ,3.7817734876087033209 ] 
dist 32=[-3.8560988686339936193 ,3.0136667466207821833 ] 
dist 33=[-4.8488370820758534826 ,1.8207143902600975577 ] 
dist 34=[-6.4596239226796614917 ,2.0191182486288518383 ] 
dist 35=[-7.7276101316303108800 ,2.2519791218615861272 ] 
dist 36=[-8.8706745785821695421 ,2.4435924249403375670 ] 
dist 37=[-9.8553184348715206058 ,2.6388892628695089275 ] 
dist 38=[-10.490250735357836902  ,2.8870168934413627124 ] 
dist 39=[-10.995860759519505197  ,3.1474399814787866632 ] 
dist 40=[-11.464010590412379401  ,3.3920215022074878514 ] 
dist 41=[-11.856319905121378215  ,3.6703193155688721294 ] 
dist 42=[-12.058814154468608147  ,4.0653794714134759900 ] 
dist 43=[-12.164339351807386036  ,4.4623406453500890275 ] 
dist 44=[-12.175746781955727625  ,4.7483050248297064349 ] 
dist 45=[-12.126658598931681536  ,5.0065682320294348852 ] 
dist 46=[-12.085499013918065711  ,5.2931382892250671403 ] 
dist 47=[-11.955751008022698969  ,5.5746662245100168060 ] 
dist 48=[-11.888873962925792765  ,5.8128355587433352272 ] 
dist 49=[-8.3538151076641179144 ,6.0639524187300782647 ] 
dist 50=[-7.9930226041858419715 ,6.3970789586062829105 ] 
dist 51=[-7.1240143513842238154 ,6.7127136628321608010 ] 
dist 52=[-6.9702042525743170185 ,6.8940382174012837773 ] 
dist 53=[-5.7072704906154784822 ,7.0108136382411186944 ] 
dist 54=[-5.4686210018885129954 ,7.0689619915942563134 ] 
dist 55=[-5.1141253537162881581 ,7.0880909569610067491 ] 
dist 56=[-5.0141155364689768527 ,7.0801072438741793941 ] 
dist 57=[-3.1289397467463089567 ,6.9985441856466441800 ] 
dist 58=[-2.8866088301615945021 ,6.9705457024778150380 ] 
dist 59=[-2.3330234012589560109 ,6.4174129199984518976 ] 
dist 60=[-2.2317159505492656694 ,6.3132993352649436461 ] 
dist 61=[-1.5335202611583881260 ,6.0388297597956801361 ] 
dist 62=[-1.4102869067023985517 ,5.9598606480091251835 ] 
dist 63=[-1.3563624733953922899 ,5.0704661262886589927 ] 
dist 64=[-1.4491760181192675617 ,4.5062754181279784816 ] 
dist 65=[-1.5203134560453585235 ,3.4316413819164629949 ] 
dist 66=[-1.5793613324387612655 ,3.6492833090156131806 ] 
dist 67=[-1.6255989499249025052 ,3.9040632951644708177 ] 
dist 68=[-1.6457201518515553722 ,4.0693576620403434444 ] 
dist 69=[-1.6543203636982305366 ,4.1989066923485893511 ] 
dist 70=[-1.6546868888000818524 ,4.3145250927895573894 ] 
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dist 73=[-1.5460012666414918035 ,4.4703153376390112995 ] 
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dist 77=[-1.4264072863009781909 ,4.3570656573874430326 ] 
dist 78=[-1.4119293155202665759 ,4.3343729516435296332 ] 
dist 79=[-1.2713824997471730332 ,3.6744965962469885376 ] 
dist 80=[-1.6723072783453033934 ,3.6198051516492540355 ] 
dist 81=[-2.1406639272006118045 ,3.5695582568066671532 ] 
dist 82=[-2.8242082102724287604 ,3.5499023312324339532 ] 
dist 83=[-3.5006376963127765885 ,1.2147887899063257990 ] 
dist 84=[-3.9406040151685342672 ,1.1785307753233985255 ] 
dist 85=[-4.2921377581014494923 ,1.1336958096544036885 ] 
dist 86=[-4.6155140385407161690 ,1.1191571879993979667 ] 
dist 87=[-4.8965526045540309330 ,.78017821086785783417] 
dist 88=[-5.0790651207455850803 ,.73638129226474947243] 
dist 89=[-5.2246427188193575127 ,.64423229858088387347] 
dist 90=[-5.3582408980573866727 ,.61950812793449802415] 
dist 91=[-5.4653355853034512098 ,.52483720308669734098] 
dist 92=[-5.5050996723688552860 ,.50638763366174413266] 
dist 93=[-5.5160501488660575066 ,.46736443648268598579] 
dist 94=[-5.5080789478703151270 ,.45675279559103703999] 
dist 95=[-5.3738660410905307566 ,.72990832427671219232] 
dist 96=[-5.3385503487765517523 ,1.1028681806220596802 ] 
dist 97=[-5.3412198095581957394 ,1.4293084816498698861 ] 
dist 98=[-5.3391940033036079529 ,1.7778984893843562687 ] 
dist 99=[-3.9742249428642861979 ,2.1143333511369615951 ] 
dist 100=[-3.8249998957002839076 ,2.3922588317621669235 ] 
dist 101=[-3.4652150325843606992 ,2.6807663531294847889 ] 
dist 102=[-3.3939822847332315804 ,3.0594550382126076797 ] 
dist 103=[-2.8574104862183558398 ,3.4299953643174738880 ] 
dist 104=[-2.7524749147305533999 ,3.6859795086040050100 ] 
dist 105=[-2.5827033481461478888 ,3.9411485026078508728 ] 
dist 106=[-2.5374442549211885492 ,4.3756764963770370584 ] 
dist 107=[-1.6644648280920086087 ,4.7761298188801604038 ] 
dist 108=[-1.5488864763604534917 ,5.0124273372101591202 ] 
dist 109=[-1.2766400667998860159 ,5.1738833691682410157 ] 
dist 110=[-1.2284782227984101501 ,5.2755671448307447804 ] 
dist 111=[-.85445902420256033623,5.3458223845284237968 ] 
dist 112=[-.7856218100309817798 ,5.3818140153339891832 ] 
dist 113=[-.67730427598749755308,5.3996082885202152949 ] 
dist 114=[-.64957428793947787799,5.3972171940406661463 ] 
dist 115=[.00922278366951006399,.34856280845395317018] 
dist 116=[.02905229046265328025,.39923208819390009036] 
dist 117=[.07388615419907289803,.52756532339410614521] 
dist 118=[.08037929952755640562,.67087317296992854834] 
dist 119=[.13200546295026398482,.80040753886746726506] 
dist 120=[.13894318861974077658,.89344700995609275996] 
dist 121=[.13544346068914883251,.97770351167113434103] 
dist 122=[.11684693736402704059,1.0721744915482079570 ] 
dist 123=[.09002048677152124573,1.1588053863362687528 ] 
dist 124=[.03405156468209503380,1.2117595533513589216 ] 
dist 125=[-.05014438510939320650,1.2502660357010982956 ] 
dist 126=[-.180591225333302483  ,1.2792095851980168708 ] 
dist 127=[-.3120681301263510352 ,1.2999407964711688911 ] 
dist 128=[-.40037641661773846395,1.3056581054459274429 ] 
dist 129=[-.47398847065434240546,1.3061215143129850086 ] 
dist 130=[-.54680655524109034552,1.3058726312744586818 ] 
dist 131=[-.6135531467915259479 ,1.0075115904150578420 ] 
dist 132=[-.66293082333059871661,.98997741204283072872] 
dist 133=[-.70904780186285065403,.99179268860799494511] 
dist 134=[-.76277815616031387001,.99142529259590310941] 
dist 135=[-.81210940125199479793,.87731628370499872709] 
dist 136=[-.84066672574362863066,.86027336695277434755] 
dist 137=[-.85947103561525991644,.83105089325477091304] 
dist 138=[-.8698725235616932985 ,.82304781142031058367] 
dist 139=[-.87574606143713523915,.79779820989581464375] 
dist 140=[-.87647764602204410281,.78938834020957064124] 
dist 141=[-.87400008597426118424,.78279484671506660208] 
dist 142=[-.87168857085738250041,.77908216900399208624] 
dist 143=[-.65021636236072379861,.40129377711666816715] 
dist 144=[-.75719311327746330812,.38605372320068863182] 
dist 145=[-.87692242503861572635,.36224067743779010277] 
dist 146=[-1.0455773313181960552 ,.35572356467595823036] 
dist 147=[-1.2107063717697725588 ,.09714541885725718154] 
dist 148=[-1.3163592244857265780 ,.08118842416027687895] 
dist 149=[-1.3988167349955985552 ,.05623119272405913674] 
dist 150=[-1.4713358022499083092 ,.05000606112564596311] 
dist 151=[-1.5320335109809157809 ,-.05331776705559762746] 
dist 152=[-1.5672934124819486447 ,-.06647099657154477803] 
dist 153=[-1.5907230554687079184 ,-.09423505709878629797] 
dist 154=[-1.6041885617162963928 ,-.05533132298167441288] 
dist 155=[-1.6112666064239204843 ,.00099653526450132560] 
dist 156=[-1.6103309240050929917 ,.06703201814748168780] 
dist 157=[-1.6031534358841952697 ,.15289871280639800311] 
dist 158=[-1.5970572137826598622 ,.28840012573671466243] 
dist 159=[-1.5548767372019247226 ,.42625913347104153285] 
dist 160=[-1.5426028129831202515 ,.52153865622747391073] 
dist 161=[-1.5171210169779374893 ,.60397212618963387215] 
dist 162=[-1.5077358553355243341 ,.69054621165892527873] 
dist 163=[-1.4966361156317990638 ,.77326629747213118734] 
dist 164=[-1.5060541746640677462 ,.84031389669205407566] 
dist 165=[-1.5090341074733308878 ,.90879595556567132547] 
dist 166=[-1.5072178759438350955 ,.99724380861019457627] 
dist 167=[-1.3847744061937135960 ,1.0831605052919524398 ] 
dist 168=[-1.3643439347501737242 ,1.1415376847690450893 ] 
dist 169=[-1.3278707691221998404 ,1.1909855129354288071 ] 
dist 170=[-1.3174536527608113354 ,1.2412533508885464767 ] 
dist 171=[-1.2776941224830462655 ,1.2882707972632265675 ] 
dist 172=[-1.2658065740789661596 ,1.3537112323364838888 ] 
dist 173=[-1.2433455850368045660 ,1.4095546522099116351 ] 
dist 174=[-1.2358004138174379480 ,1.4517234099363373720 ] 
dist 175=[-.42825796369898832924,1.4836414155449090928 ] 
dist 176=[-.35838114568640005977,1.4985579442291629302 ] 
dist 177=[-.20008250273286506253,1.5042339506107660509 ] 
dist 178=[-.18460152985680875908,1.5040327961789320745 ] 
dist 179=[.02406975372884740266,1.4735111345134928706 ] 
dist 180=[.05815067471499284465,1.4688704127583705694 ] 
dist 181=[.12085386914849817473,1.4535865197129702320 ] 
dist 182=[.13481440174275574658,1.4455561955342395574 ] 
dist 183=[.28339249910620443704,1.3272814293870931999 ] 
dist 184=[.2684971819868818756 ,1.3069913272408237344 ] 
dist 185=[.24601161648847628306,1.2573801721968830860 ] 
dist 186=[.20725843587666797688,1.2423856576568874125 ] 
dist 187=[.16095879753648758802,1.1586438662392677745 ] 
dist 188=[.1083438921259877573 ,1.1399450046577768192 ] 
dist 189=[.04096189525962343218,1.1029627132082056234 ] 
dist 190=[-.21945649959215710314,1.0947744210498698075 ] 
dist 191=[-.52231663085529323782,1.1676215271784042565 ] 
dist 192=[-.72099558769458633273,1.2113687994351839570 ] 
dist 193=[-.8816397309880144061 ,1.2422331651789876240 ] 
dist 194=[-1.0326455607062602892 ,1.2636440628952753208 ] 
dist 195=[-1.1661087787976509028 ,1.2779876946324078096 ] 
dist 196=[-1.2567137673221073145 ,1.2807746330156431258 ] 
dist 197=[-1.3333812119900703813 ,1.2790107532818304670 ] 
dist 198=[-1.4111982784861086439 ,1.2762985730734591947 ] 
dist 199=[-1.4808243876224041623 ,1.2129424675292495637 ] 
dist 200=[-1.5247894162283093616 ,1.2003195446035384014 ] 
dist 201=[-1.5584257237721087641 ,1.1700349601793434350 ] 
dist 202=[-1.5868148697770151885 ,1.1590818176412959385 ] 
dist 203=[-1.6096953323746031106 ,1.1040075858548404328 ] 
dist 204=[-1.6213384644245382923 ,1.0909713765895994656 ] 
dist 205=[-1.6269917451809625510 ,1.0609762853371809877 ] 
dist 206=[-1.6259579941901296040 ,1.0505776483011664270 ] 
dist 207=[-.92975519874126629499,.46146941245903912272] 
dist 208=[-.96013027054205747844,.45134167970634523492] 
dist 209=[-.98838155160955938843,.43512460914389388578] 
dist 210=[-1.0211759906890588918 ,.43041809200099101873] 
dist 211=[-1.0503589804570847560 ,-.0059971822795452030 ] 
dist 212=[-1.0641913029953088927 ,-.0270479286269325953 ] 
dist 213=[-1.0706249636662731214 ,-.0754192631104748965 ] 
dist 214=[-1.0706638160158812808 ,-.0828998582881452398 ] 
dist 215=[-1.0564815496899152246 ,-.1432402657082433914 ] 
dist 216=[-1.0503782239670922065 ,-.1534632861963220788 ] 
dist 217=[-1.0444192774880256111 ,-.1689023585684458113 ] 
dist 218=[-1.0399103241556571710 ,-.1725932650895272038 ] 
dist 219=[-.9002956465068399026 ,-.22524806980824509589] 
dist 220=[-.87954412824608201916,-.23180315437249831582] 
dist 221=[-.83863197352744474406,-.23909706042127680406] 
dist 222=[-.82707499049446333619,-.20557997081438870582] 
dist 223=[-.78139341593187304707,-.16966868775568941988] 
dist 224=[-.77052859302940773032,-.14182398712770377351] 
dist 225=[-.74672242451384784081,-.07699086931466603578] 
dist 226=[-.73891513936514800305,.02276651373342073908] 
dist 227=[-.26017900290536323062,.12219731067263515051] 
dist 228=[-.25554773769467302124,.22944152176453306098] 
dist 229=[-.24646339129714951384,.33086002872989113542] 
dist 230=[-.24358873477593559336,.43024698796464017313] 
dist 231=[-.23048200475380645659,.52087422376416095625] 
dist 232=[-.22763887138034066846,.58731832578717389605] 
dist 233=[-.21957733728798894457,.64885840413801661344] 
dist 234=[-.21796476795386009981,.71990539080189004054] 
dist 235=[-.19639222978938336181,.78551969187023691995] 
dist 236=[-.19257982298833043661,.82536923274745460397] 
dist 237=[-.18344115539409284456,.85402546770561754203] 
dist 238=[-.18088220016245664011,.87494982973286191508] 
dist 239=[-.16636613410113782905,.8902754650608528209 ] 
dist 240=[-.16322497954777856279,.89657807123411877735] 
dist 241=[-.15705537991985852404,.89826376284896166005] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 2, 1, 0, 1, 2] 
dist 0=[45.022580024317554776  ,45.022580024317554776  ] 
dist 1=[44.564372615814466772  ,45.332049587687658671  ] 
dist 2=[43.781856968206294889  ,45.520324428468361026  ] 
dist 3=[42.816603172640953393  ,45.654954414327486232  ] 
dist 4=[41.628444076237664341  ,45.750021369617509432  ] 
dist 5=[40.045806942719221656  ,45.833774660944964687  ] 
dist 6=[37.504903383153040207  ,45.922964847587049264  ] 
dist 7=[34.900167538292020152  ,45.994667613836073290  ] 
dist 8=[33.062513589846444533  ,46.008619197993131518  ] 
dist 9=[31.429400601981581835  ,45.982161127436431839  ] 
dist 10=[29.641493945950567053  ,45.924517834057070974  ] 
dist 11=[27.883833992964256723  ,45.769573193203433276  ] 
dist 12=[26.371367186657168364  ,45.683453977300167914  ] 
dist 13=[24.743398526063169202  ,45.438951894549110302  ] 
dist 14=[22.524054656934268493  ,45.287795881553100935  ] 
dist 15=[20.302688698716686554  ,35.449924930343757348  ] 
dist 16=[18.666471437310618465  ,34.554100646156587820  ] 
dist 17=[17.138889664334545067  ,32.341542906137116760  ] 
dist 18=[15.351267037769494421  ,32.015281423272301747  ] 
dist 19=[13.523358978669353970  ,28.609175437146481859  ] 
dist 20=[11.834523280408348388  ,27.957222039973546884  ] 
dist 21=[9.9156358878657109929 ,27.233781517037926745  ] 
dist 22=[7.1679884198378938211 ,27.079283071575110395  ] 
dist 23=[4.4527144172859995609 ,20.930487865096371671  ] 
dist 24=[2.6630953149678813830 ,20.153261634503236696  ] 
dist 25=[1.1995218705149745795 ,18.604209485656057113  ] 
dist 26=[-.2127064649707523956 ,18.207738164634964903  ] 
dist 27=[-1.4931255860334070104 ,16.814958454055330939  ] 
dist 28=[-2.4299913208348787047 ,16.510703078854537818  ] 
dist 29=[-3.3001178224958982506 ,16.094680270737667686  ] 
dist 30=[-4.7571538161671679886 ,15.965331957103817517  ] 
dist 31=[-6.1325196935476878081 ,4.5181562643714660812 ] 
dist 32=[-7.3874497742846218623 ,3.5713225056926524351 ] 
dist 33=[-8.4780829534796411719 ,1.4217711249205119365 ] 
dist 34=[-9.1969569248534929631 ,1.0775755780037988603 ] 
dist 35=[-9.7863248813996271035 ,-1.5517643158417045958 ] 
dist 36=[-10.359737584071597150  ,-2.0003531527362521426 ] 
dist 37=[-10.855336914004337980  ,-1.9238914381055136533 ] 
dist 38=[-11.133727661595084278  ,-.8940653672745296203 ] 
dist 39=[-11.309564179847626836  ,.16338999964486570606] 
dist 40=[-11.394964186143598901  ,.89466782366289472877] 
dist 41=[-11.423479205677293717  ,1.5254945099277203919 ] 
dist 42=[-11.413340429624135423  ,2.1823873701913465736 ] 
dist 43=[-11.303898587980568816  ,2.8043840299613489045 ] 
dist 44=[-11.266580079832994531  ,3.2960743091962620107 ] 
dist 45=[-10.300060469875032058  ,3.7857657930791637560 ] 
dist 46=[-10.318701225798628338  ,4.3998539026974180575 ] 
dist 47=[-6.8652023742697197509 ,4.9852877813696057851 ] 
dist 48=[-6.6648313964114102738 ,5.3606597593896728315 ] 
dist 49=[-6.1747824980559152418 ,5.6535527924519895982 ] 
dist 50=[-6.0843219361605749340 ,5.9098658429021633463 ] 
dist 51=[-5.3402171530769676526 ,6.1224838815300926410 ] 
dist 52=[-5.1957697036280024477 ,6.2409877330159452191 ] 
dist 53=[-4.9812540639652925979 ,6.3128370771052160568 ] 
dist 54=[-4.9188137948848182753 ,6.3392010229684401412 ] 
dist 55=[-3.6905477161701665618 ,6.3411826032080616776 ] 
dist 56=[-3.5292664352183036746 ,6.3222498519427962384 ] 
dist 57=[-3.1659400892889518316 ,6.2737162157894235138 ] 
dist 58=[-3.0885539019895210761 ,6.2436506707063706995 ] 
dist 59=[-2.6356558662001793316 ,6.0510110952545471360 ] 
dist 60=[-2.5529142953697054087 ,5.8952039884805864913 ] 
dist 61=[-2.3875890680859127951 ,2.3571501730209813528 ] 
dist 62=[-2.3448469044820459567 ,2.7684970302488528860 ] 
dist 63=[-1.2336063694445971582 ,3.1024380958320654246 ] 
dist 64=[-1.1462199294200779507 ,3.4194432183883233119 ] 
dist 65=[-.95115206417097674265,3.7024359508015233658 ] 
dist 66=[-.90951580612687466742,3.9005250813946737938 ] 
dist 67=[-.66550728653555006444,4.0749699676206044734 ] 
dist 68=[-.61957640330954092801,4.2635303349994639419 ] 
dist 69=[-.53113602554250602456,4.4299556524983366705 ] 
dist 70=[-.50830081561866278358,4.5159911530158230601 ] 
dist 71=[-.20561085833094613636,4.5620081793955609748 ] 
dist 72=[-.16261679730856526905,4.5704435417658392468 ] 
dist 73=[-.05615771069023354075,4.5420635073783193057 ] 
dist 74=[-.03939694301040269283,4.5387617840657741356 ] 
dist 75=[.12847668267963178241,4.5588398518716858812 ] 
dist 76=[.16136210655627771478,4.5588852451748661485 ] 
dist 77=[-.02481902907398025172,4.5314875809677645326 ] 
dist 78=[-.54067334383715386427,4.5195026067733637261 ] 
dist 79=[-.97801582932551077081,3.6150687709144878759 ] 
dist 80=[-1.4232783717088892292 ,3.5812291025425425297 ] 
dist 81=[-1.8402266292425410204 ,3.1852181022023170674 ] 
dist 82=[-2.1645398124083232644 ,3.1032022189856493434 ] 
dist 83=[-2.4835594519438401109 ,3.0181455810021499436 ] 
dist 84=[-2.8793967097936747483 ,2.9933109373375509674 ] 
dist 85=[-3.2565123536944770527 ,2.0722061226542869405 ] 
dist 86=[-3.5007946788761718021 ,1.9518966549067977374 ] 
dist 87=[-3.6949502998294987864 ,1.7121632843451718360 ] 
dist 88=[-3.8719378181205292283 ,1.6495133880572661063 ] 
dist 89=[-4.0247699980177362692 ,1.4241042819183184641 ] 
dist 90=[-4.1224962593934535065 ,1.3736314357790219857 ] 
dist 91=[-4.1988417404373579654 ,1.2957198046187175613 ] 
dist 92=[-4.2663409032096134896 ,1.2735807011202571815 ] 
dist 93=[-4.3177402070132244100 ,-.13284947425179717168] 
dist 94=[-4.3298059355669483835 ,-.14285661014124498011] 
dist 95=[-4.3258419171916641243 ,-.68912615336464667768] 
dist 96=[-4.3131784736298011154 ,-.73635903383462696265] 
dist 97=[-4.2006689444407561624 ,-.71599226927206046433] 
dist 98=[-4.1658627854623162313 ,-.62512575117110107955] 
dist 99=[-4.1168821775366362425 ,-.51887279849698168441] 
dist 100=[-4.0954840085773397301 ,-.40134613305347892959] 
dist 101=[-3.5070685252578307382 ,-.25299533591946805271] 
dist 102=[-3.4205003242249178510 ,-.02367500169876352364] 
dist 103=[-3.2390124700567523666 ,.21681623001892796257] 
dist 104=[-3.1859884056767849223 ,.60713239409408551708] 
dist 105=[-2.9628710017321187221 ,.94588245259997743588] 
dist 106=[-2.9160125614661334022 ,1.2873807253651743130 ] 
dist 107=[-2.7908659956631261547 ,1.6049441167376105604 ] 
dist 108=[-2.7653527024607545730 ,1.8481387013270276646 ] 
dist 109=[-1.8587243736860728914 ,2.0836977019368009610 ] 
dist 110=[-1.8313932127147873560 ,2.3707783345144653280 ] 
dist 111=[-1.2419291599122815381 ,2.6415015317092214071 ] 
dist 112=[-1.1642256332204288114 ,2.8701901633405489022 ] 
dist 113=[-.99957362630544380557,3.1048344680324272828 ] 
dist 114=[-.95464526331860400441,3.3241524568288225819 ] 
dist 115=[-.77866825559392450229,3.5171115654913818838 ] 
dist 116=[-.74444257450839195337,3.6465181244397209236 ] 
dist 117=[-.6667899721841857918 ,3.7542851037328200290 ] 
dist 118=[-.64867248951801734092,3.8608459601464981285 ] 
dist 119=[.26396378985575471929,3.9489441134850980157 ] 
dist 120=[.34035029193067212707,3.9829991598013211448 ] 
dist 121=[.51003864256403853066,3.9956923497606996991 ] 
dist 122=[.46068938385446565686,3.9985096669328503651 ] 
dist 123=[.28727501864755773656,3.8854913852210586910 ] 
dist 124=[0                     ,3.7636923733920005147 ] 
dist 125=[.25579589568909857866,1.8340381710999896808 ] 
dist 126=[-.06706536911999452818,1.8351811685810771565 ] 
dist 127=[-.39309162118356926251,1.8297603334671228514 ] 
dist 128=[-.61388177497042147198,1.8250323877078361368 ] 
dist 129=[-.80001645320829566449,1.8016871024541642797 ] 
dist 130=[-.98770041432002623152,1.7949334024729778988 ] 
dist 131=[-1.1621714902967498549 ,1.7116066419791114805 ] 
dist 132=[-1.2955612682922228956 ,1.6906137485524248812 ] 
dist 133=[-1.4245002215663186279 ,1.6678167105011557001 ] 
dist 134=[-1.5812040831491327035 ,1.6561299107052759372 ] 
dist 135=[-1.7286605816977331984 ,1.5847238174991257049 ] 
dist 136=[-1.8206841425598455874 ,1.5760891277507515009 ] 
dist 137=[-1.8897861538858028746 ,1.5443483256249832324 ] 
dist 138=[-1.9457396346106555596 ,1.5381151605303891586 ] 
dist 139=[-1.9889979364184005834 ,1.4485833205710526286 ] 
dist 140=[-2.0074203121470457058 ,1.4274519898770703699 ] 
dist 141=[-2.0139249602649947972 ,1.4077866947498736244 ] 
dist 142=[-2.0116218373305541003 ,1.3990533757167424247 ] 
dist 143=[-1.0736909657821564894 ,1.1038383808625149201 ] 
dist 144=[-1.1854746096022285963 ,1.0635409661834333482 ] 
dist 145=[-1.2831746598128336582 ,.9844524882243611438 ] 
dist 146=[-1.3873746801346618451 ,.96341044860181528041] 
dist 147=[-1.4879451165973742738 ,.88647172829854050227] 
dist 148=[-1.5711549995030120624 ,.86832264584951505048] 
dist 149=[-1.6577003496277862244 ,.83746289081740374178] 
dist 150=[-1.7715902213596379687 ,.8290333201516906299 ] 
dist 151=[-1.8797673906511685454 ,-.24866618013715495238] 
dist 152=[-1.9435045169058758416 ,-.33038723880400386261] 
dist 153=[-1.9869806819076131810 ,-.40812101364622716677] 
dist 154=[-2.0142626189637089712 ,-.37631086893405343684] 
dist 155=[-2.0312510591084330530 ,-.30937268655977032544] 
dist 156=[-2.0336282521302512139 ,-.22667617272100138497] 
dist 157=[-2.0294653766159814704 ,-.11650584564088962861] 
dist 158=[-2.0230988026728299648 ,.06011875499292609416] 
dist 159=[-1.8918077814039795895 ,.24087830877716539612] 
dist 160=[-1.8678989126023404351 ,.36755777371632302894] 
dist 161=[-1.8148867118559159844 ,.47901513799273590182] 
dist 162=[-1.7970737843677033556 ,.59900423213247310261] 
dist 163=[-1.7803693078529101956 ,.71545232062407721486] 
dist 164=[-1.7809074602265623065 ,.81277391216738091844] 
dist 165=[-1.7809712741183931145 ,.91483561417789206935] 
dist 166=[-1.7804117884074394196 ,1.0502098401014050440 ] 
dist 167=[-1.5372682255041241446 ,1.1834064626965199778 ] 
dist 168=[-1.5022844966192138141 ,1.2767751553311996154 ] 
dist 169=[-1.4411373473881811131 ,1.3589578099055477279 ] 
dist 170=[-1.4252251534030035155 ,1.4474961110960240771 ] 
dist 171=[-1.3744566162726148019 ,1.5334735981847114023 ] 
dist 172=[-1.3580443820433216960 ,1.6054335579094680561 ] 
dist 173=[-1.3471860580717459089 ,1.6809997583418233048 ] 
dist 174=[-1.3429334305926809619 ,1.7813772491943839267 ] 
dist 175=[-.93384802657395669245,1.8769878851412605564 ] 
dist 176=[-.90304215043013384846,1.9335227920924662737 ] 
dist 177=[-.83761923064264415442,1.9723312517051182478 ] 
dist 178=[-.81888763143539644603,1.9971680747292565345 ] 
dist 179=[-.74129132516208700513,2.0119105919543661851 ] 
dist 180=[-.72571216073341735249,2.0138134771110735586 ] 
dist 181=[-.68477162960146992334,2.0041326055444092696 ] 
dist 182=[-.67750354663253958393,1.9997511749068025020 ] 
dist 183=[.42198744545455608479,1.8953972967093376805 ] 
dist 184=[.49799474272807585991,1.8750817518538481441 ] 
dist 185=[.58165449715491441593,1.8227451036980766984 ] 
dist 186=[.53024667844149949045,1.8054353214509637963 ] 
dist 187=[.46458692461086907406,1.7049493196648194131 ] 
dist 188=[.38444883841303423951,1.6813828293316994635 ] 
dist 189=[.21819460218770831163,1.6363117107134320356 ] 
dist 190=[-.17488453460269481565,1.6225761522476867466 ] 
dist 191=[-.58689095712861105737,1.6115595074020510179 ] 
dist 192=[-.85865062387292452921,1.6378731347873080492 ] 
dist 193=[-1.0800449619272914681 ,1.6511115005647429161 ] 
dist 194=[-1.2909661496827801900 ,1.6533662746831386333 ] 
dist 195=[-1.4793143725583156098 ,1.6435127618544056550 ] 
dist 196=[-1.6105852836801128015 ,1.6367974997472608829 ] 
dist 197=[-1.7253435366793658176 ,1.6245213830904425066 ] 
dist 198=[-1.8477640786344635936 ,1.6187418112143999544 ] 
dist 199=[-1.9586372525870074517 ,1.4439688015612916470 ] 
dist 200=[-2.0272922303959686129 ,1.4165522203991235515 ] 
dist 201=[-2.0782481041121300020 ,1.3584962643457699643 ] 
dist 202=[-2.1184572938258783095 ,1.3407613640279124846 ] 
dist 203=[-2.1487330434442415255 ,1.2624138241964478793 ] 
dist 204=[-2.1600293999803567810 ,1.2459054111475403320 ] 
dist 205=[-2.1613044245613640496 ,1.1969757704968316614 ] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 0, 0, 2, 1, 0, 2] 
dist 0=[53.415206490148474201  ,53.415206490148474201  ] 
dist 1=[52.983144168997750662  ,53.536388142546720089  ] 
dist 2=[52.230457338303872769  ,53.588140278765015154  ] 
dist 3=[50.866203105806621746  ,53.630826066119973039  ] 
dist 4=[49.347481370740030575  ,53.631630100135584922  ] 
dist 5=[47.977884432261386305  ,53.601320489982849353  ] 
dist 6=[46.452491569292069217  ,53.519440490145838676  ] 
dist 7=[44.311313372455005516  ,53.317010848457451057  ] 
dist 8=[41.931933424487046783  ,49.528126878258978823  ] 
dist 9=[39.455059816530806114  ,48.599371752477868736  ] 
dist 10=[36.425999729155164456  ,48.355176206780065337  ] 
dist 11=[31.841083221580166553  ,47.528693130923723787  ] 
dist 12=[27.231166343633194136  ,47.269828378801723978  ] 
dist 13=[24.102133546768208007  ,46.933906632183701524  ] 
dist 14=[21.450430051215100105  ,45.763571968148547402  ] 
dist 15=[18.746707700411895790  ,42.233152904104114351  ] 
dist 16=[16.206907468995791022  ,35.178370993754809226  ] 
dist 17=[14.209654299724210758  ,34.254151103750803979  ] 
dist 18=[12.220656070819995760  ,32.468529565707313336  ] 
dist 19=[9.7133269646924501111 ,32.010055142262611131  ] 
dist 20=[7.2955740456531728608 ,30.422998801693322726  ] 
dist 21=[5.6640924993593172146 ,30.039796967775805443  ] 
dist 22=[4.2891499512516082451 ,29.578755573428677790  ] 
dist 23=[2.8957659539100682646 ,29.398564526264140939  ] 
dist 24=[1.5876575351169633741 ,11.452973405871313842  ] 
dist 25=[.55283270776906720504,9.9748166419503322574 ] 
dist 26=[-.48761986302246723917,8.9594732261425091026 ] 
dist 27=[-1.8193685868515771417 ,7.3096653013207240447 ] 
dist 28=[-3.0932499139618342399 ,7.0514591989947668615 ] 
dist 29=[-3.9026256815793201975 ,6.5942194628308142653 ] 
dist 30=[-4.5347327397332265344 ,6.5132482473611844539 ] 
dist 31=[-6.3537150611197803127 ,-.39237036522967151646] 
dist 32=[-8.2107121877319377843 ,-4.0002711365243328947 ] 
dist 33=[-9.3671396786576797184 ,-4.9551416147965439494 ] 
dist 34=[-10.235532876189235303  ,-4.8317938776899305770 ] 
dist 35=[-10.942117846340182960  ,-4.4819786049065920844 ] 
dist 36=[-11.506418814121054219  ,-4.0592744438580843562 ] 
dist 37=[-11.806411632542260549  ,-3.6446755699193774454 ] 
dist 38=[-11.971260531823291406  ,-3.1588923029233937206 ] 
dist 39=[-12.001152984135471733  ,-2.4514409462425890214 ] 
dist 40=[-9.1599538466697760058 ,-1.6572925114232246360 ] 
dist 41=[-8.9925002137946264770 ,-.82517299175787050086] 
dist 42=[-8.5431640692164855168 ,.19359559702380483472] 
dist 43=[-8.4615911582942922038 ,1.7329871260572305465 ] 
dist 44=[-7.9960410673650493591 ,3.2693011787034526084 ] 
dist 45=[-8.0039163235655454973 ,4.2759050489919032974 ] 
dist 46=[-8.0018713585712815522 ,5.0873519987325821041 ] 
dist 47=[-7.1811250934059678224 ,5.8448203354893646665 ] 
dist 48=[-6.0344843230119415986 ,6.5099482210485006276 ] 
dist 49=[-5.9989900009157102982 ,6.9528873662385315440 ] 
dist 50=[-5.7743475154718124156 ,7.3182257429415464540 ] 
dist 51=[-5.3769507679500811519 ,7.6736989507641947243 ] 
dist 52=[-4.0345753051981622455 ,7.9834479374646295898 ] 
dist 53=[-3.9311015727129216442 ,8.1662435971263589507 ] 
dist 54=[-3.6946739033613838972 ,8.2912360078879354073 ] 
dist 55=[-3.6403135512877121711 ,8.3700751623804009225 ] 
dist 56=[-.596603050446976398  ,8.4128706885904407277 ] 
dist 57=[-.31805847166943126989,8.4106537044523577056 ] 
dist 58=[.27124358401283062542,8.3550698692936546607 ] 
dist 59=[.40305104718424583671,8.3192994310095473603 ] 
dist 60=[.98580050052637286934,5.0651659145530346738 ] 
dist 61=[1.0889797088650309536 ,4.7693137218666885500 ] 
dist 62=[1.2834777790063643560 ,5.0698469498443975393 ] 
dist 63=[1.3260310399617180787 ,5.4456945776381474435 ] 
dist 64=[1.4282613991337843185 ,5.7847587090932288502 ] 
dist 65=[1.4074380990875832500 ,5.9778068348819939710 ] 
dist 66=[1.3312262869510951959 ,6.1015393540006946072 ] 
dist 67=[1.1276081133364349546 ,6.1637710851783720826 ] 
dist 68=[.47838993427476574437,6.1972337843756729370 ] 
dist 69=[.02523083628018448734,6.2060440382540403685 ] 
dist 70=[-.37151475100926093115,6.1986314939424793257 ] 
dist 71=[-.79560759311504925387,6.1837226214985735490 ] 
dist 72=[-1.2055750216121239914 ,3.4443145883561477027 ] 
dist 73=[-1.5460012666414918085 ,3.3629434914033845804 ] 
dist 74=[-1.9013744451796508775 ,3.3379155523700671125 ] 
dist 75=[-2.3711383691745104215 ,3.2306098395281866410 ] 
dist 76=[-2.8274434352400804090 ,3.2033605726205723270 ] 
dist 77=[-3.1291005379425023650 ,3.1338283954942853207 ] 
dist 78=[-3.3760299323198062831 ,3.1082024598616631635 ] 
dist 79=[-3.6137685765681276886 ,1.5361926177095463992 ] 
dist 80=[-3.8282106193442180065 ,1.3961309399018447728 ] 
dist 81=[-3.9821050762385782902 ,1.0673919360830530019 ] 
dist 82=[-4.1215939203273971239 ,1.0139540015894546780 ] 
dist 83=[-4.2785192159318536651 ,.57153561492516152842] 
dist 84=[-4.4205638500323195150 ,.4920321068678959533 ] 
dist 85=[-4.5006236161292009779 ,.37629863410787988011] 
dist 86=[-4.5509143373769612341 ,.34493098630532021123] 
dist 87=[-4.5740552281214104222 ,.44060554142077325379] 
dist 88=[-4.5782182489099942712 ,1.1027996883169082380 ] 
dist 89=[-4.5738911382339294004 ,1.5454469718070504795 ] 
dist 90=[-4.5243550788842769538 ,1.9119507949166143564 ] 
dist 91=[-4.5170842145023493278 ,2.2702461381985930977 ] 
dist 92=[-4.1468183754221021096 ,2.5957166067790555791 ] 
dist 93=[-4.1397413529642005121 ,3.1716181404615196195 ] 
dist 94=[-4.1243649001462661451 ,3.6461199050660726922 ] 
dist 95=[-4.1112459216128899746 ,4.1052864685281142788 ] 
dist 96=[-3.6417515169999298904 ,4.5199548155299487131 ] 
dist 97=[-3.5695025077327202342 ,4.8168233101673540925 ] 
dist 98=[-3.4246158237682264278 ,5.0845592654440376688 ] 
dist 99=[-3.3822966661513699227 ,5.3829428353264986305 ] 
dist 100=[-3.2077771499576180499 ,5.6503572845906761971 ] 
dist 101=[-3.1671405138594394565 ,5.7944658738388264433 ] 
dist 102=[-3.0682852863723539516 ,5.8760432555850279074 ] 
dist 103=[-3.0345141088992993354 ,5.8941589505879787044 ] 
dist 104=[-.78450636055107180469,5.8882483806115972343 ] 
dist 105=[-.76363308494158855814,5.8781036054317818652 ] 
dist 106=[-.75691082333567983188,5.8659332105539311653 ] 
dist 107=[-.72584726595507871006,5.8524281727931181209 ] 
dist 108=[-.71905054497267548341,5.3326494221457347625 ] 
dist 109=[-1.3446165473204941475 ,5.2544503193519464931 ] 
dist 110=[-1.9538581624294579268 ,5.0255751292734707054 ] 
dist 111=[-2.5672954797490066108 ,4.9908063480867819859 ] 
dist 112=[-3.1369494484096816699 ,4.5077208245932305723 ] 
dist 113=[-3.5714111407345131777 ,4.4040605379051826131 ] 
dist 114=[-3.9903318752789004722 ,4.3098576744341098241 ] 
dist 115=[-4.4979457826213573579 ,4.2859347143267805868 ] 
dist 116=[-4.9747730799988246626 ,2.9327436750038559143 ] 
dist 117=[-5.2707946180203505807 ,2.7597772913405409014 ] 
dist 118=[-5.4912315349811608310 ,2.2827890775310351349 ] 
dist 119=[-5.6663284956067185813 ,2.1638292518978290196 ] 
dist 120=[-5.7989712437695565334 ,1.8229979183520947953 ] 
dist 121=[-5.8499308902986934200 ,1.7552563120789796880 ] 
dist 122=[-5.8679556378574514895 ,1.6009955446749490523 ] 
dist 123=[-5.8691346683550171515 ,1.5621614195758433736 ] 
dist 124=[.08860116538817386658,.8037526276979474577 ] 
dist 125=[.10059744737229831669,.80362443969472258681] 
dist 126=[.10333216549161584313,.80218384274605272518] 
dist 127=[.17182170375669226068,.79983471424982962962] 
dist 128=[.17926749726344858984,.79460806497636132368] 
dist 129=[.1932907028192544199 ,.79098637740170027381] 
dist 130=[.12288934756466090041,.78703648711599223194] 
dist 131=[.01197175297100948792,.78412076061134651876] 
dist 132=[-.10659482314929671432,.77578889446378056458] 
dist 133=[-.22314798053103636906,.77199454009194341235] 
dist 134=[-.36067953756315084534,.76377099069751029311] 
dist 135=[-.56300793485017319203,.76028797214567139509] 
dist 136=[-.76403095110161393002,.46605778857250398109] 
dist 137=[-.89635389413082834908,.44097457438620061895] 
dist 138=[-1.0038467278828509598 ,.43385347270418789629] 
dist 139=[-1.1057392297962557123 ,.40488647917543210075] 
dist 140=[-1.1963858540744511777 ,.3987741750136321588 ] 
dist 141=[-1.2589824629247729848 ,.38368353764777407351] 
dist 142=[-1.3131073077023958392 ,.37983898554552207045] 
dist 143=[-1.3699354717032100248 ,.2762207741510310765 ] 
dist 144=[-1.4191833816482425390 ,.27519410776806177312] 
dist 145=[-1.4430442715776056696 ,.27093412857602572337] 
dist 146=[-1.4551538908903226832 ,.27012646732376543262] 
dist 147=[-1.4574797762576548476 ,.25661988961435230231] 
dist 148=[-1.4356568262882215869 ,.25332603130739904631] 
dist 149=[-1.4292117323447705494 ,.25067501929103956867] 
dist 150=[-1.4246375456065715287 ,.24954219947035416058] 
dist 151=[-1.4214341335387087905 ,.19995670409764149345] 
dist 152=[-1.1939756515922367594 ,.19311827615410503034] 
dist 153=[-1.1663044048844903920 ,.26410190199710876808] 
dist 154=[-1.0944217117076241622 ,.4144215045439722645 ] 
dist 155=[-1.0815601511530337964 ,.56645231005600690353] 
dist 156=[-.95625129897981552231,.70811456355868742474] 
dist 157=[-.93057886188861041082,.81704093403128714052] 
dist 158=[-.8984867498548615325 ,.92295105698769716205] 
dist 159=[-.88653250401260007536,1.0525718927375574764 ] 
dist 160=[-.62316057910334637108,1.1750460737816889776 ] 
dist 161=[-.58817864798697964831,1.2524251334095522438 ] 
dist 162=[-.51435851064276554416,1.3116578262023775784 ] 
dist 163=[-.49416564421552674665,1.3616874988109991964 ] 
dist 164=[-.41501159358286186783,1.4020218480987347516 ] 
dist 165=[-.39939900425437908439,1.4225483431209710568 ] 
dist 166=[-.36410260192758797548,1.4325101363551444325 ] 
dist 167=[-.35531340125044894824,1.4336903234812133767 ] 
dist 168=[-.31709139567362739443,.12909371896823868425] 
dist 169=[-.34185094535761046988,.20688306577370506774] 
dist 170=[-.36951723918219578282,.27898553431261903993] 
dist 171=[-.39696244180234524132,.35134112061935939178] 
dist 172=[-.42083740398377857372,.41844149353672490409] 
dist 173=[-.44668567762266496459,.46956293706148702744] 
dist 174=[-.48200551700683255782,.51884492078993380273] 
dist 175=[-.51580006052227800669,.57860309125159473064] 
dist 176=[-.53555816932194320054,.63485016371964038451] 
dist 177=[-.54882209224836418186,.67011444345039883614] 
dist 178=[-.55669115788707722367,.69681812743192895627] 
dist 179=[-.56172533205293009288,.71888623837288728885] 
dist 180=[-.56367313543025073377,.73633743979227781408] 
dist 181=[-.56372749226989886775,.74460873010378685606] 
dist 182=[-.56266428478264127746,.74804123821105322194] 
dist 183=[-.51055862772779819375,.74807773330384267859] 
dist 184=[-.50209948608143327749,.73904074649568542918] 
dist 185=[-.48655719865458791596,.73607977743487721259] 
dist 186=[-.48211196849297239167,.72383116572432682178] 
dist 187=[-.46484226867121250973,.72127252423042733136] 
dist 188=[-.46001706904202991154,.68313813082468760937] 
dist 189=[-.45030122168925859475,.67394075881306862269] 
dist 190=[-.44700943918180101608,.66548778267404494487] 
dist 191=[-.41039318444056975651,.6614927661827592759 ] 
dist 192=[-.48631273453471518469,.60510412083106678628] 
dist 193=[-.53966637703073887376,.60934536599326489435] 
dist 194=[-.58677331937105646044,.60968113543658243227] 
dist 195=[-.63775306546904218085,.60792612946795143025] 
dist 196=[-.6873987030107279289 ,.60630359387035588746] 
dist 197=[-.72917949804001695903,.59945873332152292485] 
dist 198=[-.77325602374957929584,.5966871363954703697 ] 
dist 199=[-.83206805683164868285,.55536610099969767411] 
dist 200=[-.88822006863641042404,.54801950741152391185] 
dist 201=[-.92167634056447456883,.52873714580780789771] 
dist 202=[-.9449558274156308852 ,.52380279655258675296] 
dist 203=[-.96047598514801536165,.48738152482681838209] 
dist 204=[-.97078122434712492496,.4792710303571804871 ] 
dist 205=[-.9732394267393477124 ,.46612190643664468421] 
dist 206=[-.97216869914561483454,.46215131375638749727] 
dist 207=[-.96944886711705206192,.28723002908907710061] 
dist 208=[-.91113422739796117952,.26784353497565080469] 
dist 209=[-.90024722501091247368,.22525431409306090785] 
dist 210=[-.87643809851386012446,.21486256120544012129] 
dist 211=[-.86839992558224948916,.16453300532649873138] 
dist 212=[-.82986794612158647051,.15523714220084326481] 
dist 213=[-.82111870835507245607,.1339155030297282168 ] 
dist 214=[-.79617788539375919839,.12932762714158099457] 
dist 215=[-.79041472367510032322,.08688375083784566227] 
dist 216=[-.66423494336772419525,.11959863898628729448] 
dist 217=[-.66259060587194811595,.24046873035019605792] 
dist 218=[-.65436703132298922072,.33995107915554756498] 
dist 219=[-.65211231019775348248,.43644019796844815338] 
dist 220=[-.62255967411565302859,.52377157637830128321] 
dist 221=[-.61511753632582396862,.58668985016640633653] 
dist 222=[-.60746024770750930538,.64385659084195861162] 
dist 223=[-.60330380075095464345,.70822335224368215452] 
dist 224=[-.49364666675152269487,.76751325597741023575] 
dist 225=[-.4782360055930237231 ,.80440988746668411744] 
dist 226=[-.44750820425216315189,.83201381273591978986] 
dist 227=[-.43910205908135150138,.85420197382287609637] 
dist 228=[-.40697197227107267657,.87124214676279699925] 
dist 229=[-.39962781607427924991,.87829241335054055377] 
dist 230=[-.3848414310238022725 ,.88065745872662442625] 

8 phat 4 dirichlet min maxes function [1, 1, 2, 1, 0, 2, 1, 0, 1] 
dist 0=[46.161045445924511320  ,46.161045445924511320  ] 
dist 1=[45.749178577898208355  ,46.336273853036849268  ] 
dist 2=[45.084447817799265593  ,46.445750746781131359  ] 
dist 3=[43.899402686328968886  ,46.594895842391678580  ] 
dist 4=[42.469516880693857247  ,46.801069831184241855  ] 
dist 5=[40.826999171887286076  ,47.137866990465757409  ] 
dist 6=[38.710691008273772368  ,47.471239593822099773  ] 
dist 7=[35.388676542478990413  ,47.663747235164131185  ] 
dist 8=[32.012561597202746858  ,47.789111677069994517  ] 
dist 9=[29.680091999068619053  ,47.854802318468722963  ] 
dist 10=[27.660312481212344675  ,47.876733174943651074  ] 
dist 11=[25.532639391072478451  ,47.827625620657414517  ] 
dist 12=[23.491765972381423790  ,47.719397643684493053  ] 
dist 13=[21.818345300528192183  ,47.652649752499007835  ] 
dist 14=[20.088440765470113847  ,36.322044714443767756  ] 
dist 15=[17.821462802134121969  ,35.329455465066547903  ] 
dist 16=[15.594437737168752319  ,32.886713769911177147  ] 
dist 17=[14.023815607369149391  ,32.521044278217909128  ] 
dist 18=[12.626894328239930360  ,28.794618291997282362  ] 
dist 19=[11.093275329073158310  ,28.084336829241645055  ] 
dist 20=[9.5796123383592292705 ,27.271391311277795218  ] 
dist 21=[8.2618722651428173000 ,27.083894878778696574  ] 
dist 22=[6.8270907475910679300 ,20.547505276844850437  ] 
dist 23=[4.8447583934002655540 ,19.723455317838837665  ] 
dist 24=[2.9091655878801690253 ,18.136525986146119339  ] 
dist 25=[1.6609631607315016128 ,17.623036739158647196  ] 
dist 26=[.6681282006996466853 ,16.808096429486880359  ] 
dist 27=[-.2466139940368236780 ,16.281457607486960967  ] 
dist 28=[-1.0504844312048274568 ,15.627619227180830475  ] 
dist 29=[-1.6002550446779412384 ,15.104433791986850544  ] 
dist 30=[-2.8137669937447490763 ,4.1774419453788925770 ] 
dist 31=[-4.2672745802362377039 ,3.2585771943818800538 ] 
dist 32=[-5.6169897111361914209 ,1.2592979302999716597 ] 
dist 33=[-6.8060335984796564309 ,.8785284804083160676 ] 
dist 34=[-7.6175156976505973672 ,-1.2870825096881095606 ] 
dist 35=[-8.3131028966456823822 ,-1.3157859916489514161 ] 
dist 36=[-9.0392577369615620347 ,-.9487992426316907072 ] 
dist 37=[-9.6877492844118532792 ,-.5041343157213162906 ] 
dist 38=[-10.206812899063614469  ,.0803699519545676255 ] 
dist 39=[-10.885833694979627078  ,1.0054863388178936987 ] 
dist 40=[-11.369898196069136885  ,1.9395354930778896916 ] 
dist 41=[-11.717431597485673379  ,2.5597895633787482563 ] 
dist 42=[-11.977688598468980368  ,3.0670960954050303334 ] 
dist 43=[-12.112996188796755028  ,3.5506381971080638744 ] 
dist 44=[-12.183172709888680571  ,3.9798362668460074211 ] 
dist 45=[-12.182728695080996210  ,4.2703066135421359776 ] 
dist 46=[-7.3668152044510502739 ,4.5133884768426786134 ] 
dist 47=[-6.6635483077817800228 ,4.7533511716923758135 ] 
dist 48=[-6.5427547398933628765 ,4.9656222814243615501 ] 
dist 49=[-5.4730546055416650915 ,5.0982870951352434146 ] 
dist 50=[-5.2680979609061990120 ,5.1970091850184490219 ] 
dist 51=[-4.9851292076630181835 ,5.2742242043834067192 ] 
dist 52=[-4.8970994612154070731 ,5.3313538076846516232 ] 
dist 53=[-3.1737864184444273081 ,5.3501701760753333765 ] 
dist 54=[-2.9427706658084136472 ,5.3448482078301586028 ] 
dist 55=[-2.4483413831950305148 ,5.3315683163997036304 ] 
dist 56=[-2.3480007063162024923 ,4.1072486015154473741 ] 
dist 57=[-1.7600205177496155032 ,4.6763233777773686528 ] 
dist 58=[-1.6569452337554111663 ,5.1462082604942082839 ] 
dist 59=[-1.4490835220281382785 ,5.6345882522068687109 ] 
dist 60=[-1.3974612621928967767 ,6.2776867749369691792 ] 
dist 61=[.0926995428511968035 ,6.8917307427254248481 ] 
dist 62=[-.2766139748731773365 ,7.2641249772619241289 ] 
dist 63=[-.7589271878313553249 ,7.5320211487629593596 ] 
dist 64=[-1.2296251044637947534 ,7.7287189416668808868 ] 
dist 65=[-1.5526054181044405737 ,7.8727590127898594688 ] 
dist 66=[-1.8295198653733759056 ,7.9303219339829346516 ] 
dist 67=[-2.1163718609073471262 ,7.9461572164531443962 ] 
dist 68=[-2.3881427976637506744 ,7.9345129954434864080 ] 
dist 69=[-2.6048975040856098725 ,7.5208658929184565077 ] 
dist 70=[-2.8232957272715043559 ,7.4402160168025216519 ] 
dist 71=[-3.1017084610909866306 ,7.2755802525046257378 ] 
dist 72=[-3.3659332387919103736 ,7.2206451461026029183 ] 
dist 73=[-3.5276973860223095693 ,6.9619973766612362627 ] 
dist 74=[-3.6458419409239394559 ,6.9012436349386153634 ] 
dist 75=[-3.7358691230357082710 ,6.7113766032747178644 ] 
dist 76=[-3.8013287863060297371 ,6.6753425905329035391 ] 
dist 77=[-3.8213684872456970148 ,4.3812733793461047272 ] 
dist 78=[-3.8248961056250812102 ,4.2043057152507328097 ] 
dist 79=[-3.8243713284939714583 ,3.7628920617126820833 ] 
dist 80=[-3.6975592881220455875 ,3.6948360195941700889 ] 
dist 81=[-3.6684558100992019063 ,3.0037455435923063659 ] 
dist 82=[-3.8029667116985501252 ,2.8709423263216297216 ] 
dist 83=[-4.2742813431484070929 ,2.7145817100091387430 ] 
dist 84=[-4.8188653412209184942 ,2.6737561068870241638 ] 
dist 85=[-5.3241207920670989479 ,2.3267028797697422497 ] 
dist 86=[-5.6384085030163793781 ,2.6923614587040490603 ] 
dist 87=[-5.8734121257022935038 ,3.2224325187880351955 ] 
dist 88=[-6.0621006978018444260 ,3.7436850513002397692 ] 
dist 89=[-6.2068340164341752595 ,4.0741427247478355290 ] 
dist 90=[-6.2663286768651280164 ,4.3283347955444061184 ] 
dist 91=[-6.2902238119485823141 ,4.5451355681586971368 ] 
dist 92=[-6.2928366210597105010 ,4.7214533093504162556 ] 
dist 93=[-2.0185092937041171079 ,4.8140353895130650472 ] 
dist 94=[-2.3611672473893992292 ,4.8630421289650389770 ] 
dist 95=[-2.6336492407920569023 ,4.8722149932462292736 ] 
dist 96=[-2.8822679463194656951 ,4.8489689140400946022 ] 
dist 97=[-3.0970354405935608326 ,4.8302200596490507716 ] 
dist 98=[-3.2343506811976576715 ,4.7893434226991160929 ] 
dist 99=[-3.3414770416798705675 ,4.7687932905955700069 ] 
dist 100=[-3.4357050242475724162 ,4.6464657071110003599 ] 
dist 101=[-3.5139419767670353929 ,4.6137458263737827183 ] 
dist 102=[-3.5572163385053284352 ,4.5074950460395068347 ] 
dist 103=[-3.5832663062889890853 ,4.4810709101963805338 ] 
dist 104=[-3.5927220883463533107 ,3.5535804858624479651 ] 
dist 105=[-3.5908353491410446348 ,3.5049346061458141717 ] 
dist 106=[-3.5844022011507753210 ,3.3661760022135694067 ] 
dist 107=[-3.5493712937444383710 ,3.3407488268179363040 ] 
dist 108=[-3.5355726252565341716 ,3.0543872984151256537 ] 
dist 109=[-3.0391113312098354722 ,2.9922768348105514209 ] 
dist 110=[-3.2727978496991904442 ,2.9232670242878667869 ] 
dist 111=[-3.4614349896487104099 ,2.8947960615423444570 ] 
dist 112=[-3.6381113753318044925 ,2.1620150602624933650 ] 
dist 113=[-3.7937136830562039821 ,2.0636186747165405917 ] 
dist 114=[-3.9192591793013438373 ,1.8624075711089841420 ] 
dist 115=[-4.0375118535858630147 ,1.8080919802267807195 ] 
dist 116=[-4.1263273771477798881 ,1.6017146030037973805 ] 
dist 117=[-4.1626964420079875488 ,1.5577687942953629777 ] 
dist 118=[-4.1753557782137414116 ,1.5614582233238215518 ] 
dist 119=[-4.1689791861910757818 ,1.7635236669113237137 ] 
dist 120=[-1.0151206453777464204 ,1.9764496273244512665 ] 
dist 121=[-1.3696138898880365808 ,2.1804553350993241439 ] 
dist 122=[-1.6584193641814148172 ,2.3469083502163822910 ] 
dist 123=[-1.9335952148140410898 ,2.5180037068791038881 ] 
dist 124=[-2.1793623374950245296 ,2.7405530010614511912 ] 
dist 125=[-2.3507540429052627654 ,2.9516041107943950877 ] 
dist 126=[-2.5007113923677565196 ,3.0767910033992309740 ] 
dist 127=[-2.6609046144934260314 ,3.1632617561173470858 ] 
dist 128=[-2.8048494257703759521 ,3.2197238432966851375 ] 
dist 129=[-2.8899343561639629246 ,3.2584260011967984892 ] 
dist 130=[-2.9483136298929038408 ,3.2739809886534890187 ] 
dist 131=[-2.9856314624594646863 ,3.2755912177911643724 ] 
dist 132=[-3.0077556980090986386 ,3.2714316550301915906 ] 
dist 133=[-3.0105896489386440159 ,3.0191248928126385632 ] 
dist 134=[-2.9959865058863952008 ,2.9764971863336923744 ] 
dist 135=[-2.9893459227312566904 ,2.8964881819349238214 ] 
dist 136=[-2.1856677664316899609 ,2.8727013094996764514 ] 
dist 137=[-2.1051886992158668054 ,2.7752084156402861489 ] 
dist 138=[-1.9119787147171504038 ,2.7491396649206314564 ] 
dist 139=[-1.8731660729683404986 ,2.6891177256307492321 ] 
dist 140=[-1.5869230162796333386 ,2.6673888932636437782 ] 
dist 141=[-1.5308731557355678651 ,1.3767147444965190681 ] 
dist 142=[-1.4384401311698972488 ,1.2752095266510035341 ] 
dist 143=[-1.4142915414437200295 ,1.0304101448534828044 ] 
dist 144=[-.95053976065955402085,.99304546800039474158] 
dist 145=[-1.0899639701491868074 ,1.1874114660299341449 ] 
dist 146=[-1.2915334143306227185 ,1.3850327780724980805 ] 
dist 147=[-1.4797824996177964976 ,1.6039981897823823505 ] 
dist 148=[-1.6994573092723160391 ,1.8202638551130607223 ] 
dist 149=[-1.9043280142378829198 ,2.0071098668887323026 ] 
dist 150=[-2.0334671535439681735 ,2.2084427534617395728 ] 
dist 151=[-2.1320459375690812914 ,2.4825536754990266657 ] 
dist 152=[-2.2148920738905846306 ,2.7470005105866041113 ] 
dist 153=[-2.2814125558681942213 ,2.9097501946699676513 ] 
dist 154=[-2.3148035366956165917 ,3.0293859172810222298 ] 
dist 155=[-2.3309626605674263531 ,3.1216958271917722566 ] 
dist 156=[-2.3331314483953967834 ,3.1915834843503166830 ] 
dist 157=[-1.1954388473465399412 ,3.2216945774946289155 ] 
dist 158=[-1.2873511695012310255 ,3.2330879167522494307 ] 
dist 159=[-1.3581458020992734254 ,3.2297842771862793694 ] 
dist 160=[-1.4187716552202363090 ,3.0952443131005936318 ] 
dist 161=[-1.4683196793707810157 ,3.0663176345641584503 ] 
dist 162=[-1.4948833984774419715 ,3.0097569085743063659 ] 
dist 163=[-1.5097327477440459105 ,2.9904364169313012894 ] 
dist 164=[-1.5125083963989861230 ,2.8987597091355550452 ] 
dist 165=[-1.5097673038676021691 ,2.8756788840638006156 ] 
dist 166=[-1.5054394998612320064 ,2.8048760747261789227 ] 
dist 167=[-1.4933241574665479996 ,2.7878658025548255412 ] 
dist 168=[-1.4867039944751978750 ,1.6706470532383463495 ] 
dist 169=[-1.4460436342847894887 ,1.5790568309528800284 ] 
dist 170=[-1.4349554669552400361 ,1.3540419098211370802 ] 
dist 171=[-1.4070802465034730094 ,1.3198209772113006290 ] 
dist 172=[-1.4587465486408882884 ,1.5619274860501968985 ] 
dist 173=[-1.5993942704853704359 ,1.9038590929212942615 ] 
dist 174=[-1.6919176097493387208 ,2.1241213626721832249 ] 
dist 175=[-1.8722606558351111601 ,2.2977046662841023255 ] 
dist 176=[-2.0887702488974695768 ,2.4532705142223669041 ] 
dist 177=[-2.2230725275981814240 ,2.5855769771550045045 ] 
dist 178=[-2.3230378171017524038 ,2.6662979455835357295 ] 
dist 179=[-2.4024528643776875102 ,2.7247944305133306975 ] 
dist 180=[-2.4635955376123794802 ,2.7683718841863314992 ] 
dist 181=[-2.4906076896154366692 ,2.8000108905300145606 ] 
dist 182=[-2.5021771991246442608 ,2.8108428353584597491 ] 
dist 183=[-2.5016631216598540938 ,2.8095143484580907419 ] 
dist 184=[-2.0667088650048715302 ,2.8048745619072013078 ] 
dist 185=[-2.0422829405317663868 ,2.7597986467132897660 ] 
dist 186=[-2.0329558371082747029 ,2.7448141689241755741 ] 
dist 187=[-2.0025316636301133360 ,2.7010844571584721662 ] 
dist 188=[-1.9900403648564675619 ,2.6816991814596120605 ] 
dist 189=[-1.8258223510212344626 ,1.7517180728740411750 ] 
dist 190=[-1.7969194509216186204 ,1.6580079149830447709 ] 
dist 191=[-1.7261416680154414827 ,1.4322273385609337566 ] 
dist 192=[-1.7050135003876644793 ,1.3935480048180483046 ] 
dist 193=[-1.6523422999614148238 ,1.1197807358530156226 ] 
dist 194=[-1.6549258300256334692 ,1.1052864527026825454 ] 
dist 195=[-1.6519887080791898375 ,1.0753316769605494145 ] 
dist 196=[-1.6194608092883650358 ,1.0656758935906528209 ] 
dist 197=[-1.6082340111098018067 ,.91245002407663669001] 
dist 198=[-1.5908270272946773814 ,.9711341592654184169 ] 
dist 199=[-1.5835087791214662443 ,1.2962385992198236635 ] 
dist 200=[-1.5924548737864984982 ,1.6186083915055398295 ] 
dist 201=[-1.6697107608430604536 ,1.8278861536724652100 ] 
dist 202=[-1.7306616374753145825 ,1.9946374781752949598 ] 
dist 203=[-1.7853753723923398438 ,2.1472231337655483224 ] 
dist 204=[-1.8319462704914588425 ,2.2792358767043439145 ] 
dist 205=[-1.8603875046404217560 ,2.3638516522882222335 ] 
dist 206=[-1.8810132949150831846 ,2.4300544525013556455 ] 
dist 207=[-1.8963804220511293016 ,2.4885560764487122360 ] 
dist 208=[-1.9059311428781220374 ,2.5355085160042517182 ] 
dist 209=[-1.9405124895353264100 ,2.5556015382433872735 ] 
dist 210=[-2.0137792577333337031 ,2.5615888508143916981 ] 
dist 211=[-2.0758328414113891535 ,2.5592168419175536825 ] 
dist 212=[-2.1389207061450091928 ,2.5209456920377479241 ] 
dist 213=[-2.1921423243501857712 ,2.5066534517620738064 ] 
dist 214=[-2.2148056285218614124 ,2.4755251298906260330 ] 
dist 215=[-2.2241411057011460644 ,2.4624699602164367128 ] 
dist 216=[-2.2241480214490834989 ,2.3423657157946576448 ] 
dist 217=[-2.1771599928221361070 ,2.3423839690857777101 ] 
dist 218=[-2.1622071161997561933 ,2.3392343479284328350 ] 
dist 219=[-2.1507138731607104642 ,2.3122745893464050965 ] 
dist 220=[-2.1409185664618476202 ,2.3073697194274583834 ] 
dist 221=[-1.2153215938604178521 ,1.4269935273615443986 ] 
dist 222=[-1.1625752492973909524 ,1.4023376498474794696 ] 
dist 223=[-1.1483867064677368969 ,1.3935552201352581917 ] 
dist 224=[-.8900491684321031085 ,1.1721632380152582303 ] 
dist 225=[-.8538860049085485923 ,1.1400104900527320241 ] 
dist 226=[-.79962602724460407378,1.0705896694402792779 ] 
dist 227=[-.78588235432972975709,1.0500938758217816942 ] 
dist 228=[-.78251626212099683604,.96223167108769349412] 
dist 229=[-.5901260863602277871 ,.94445969532255984928] 
dist 230=[-.6401398091688277624 ,.89631713074222530146] 
dist 231=[-.8831542041944159885 ,.88813784128141557031] 
dist 232=[-1.1222761341622368826 ,1.0848321982516217409 ] 
dist 233=[-1.2806472410600551376 ,1.2743356989941984336 ] 
dist 234=[-1.4103773777764172359 ,1.4264925460906075947 ] 
dist 235=[-1.5351519809788160022 ,1.5676771050377655657 ] 
dist 236=[-1.6473668489892265294 ,1.6911666839978834754 ] 
dist 237=[-1.7269534226955033606 ,1.7726793424783224469 ] 
dist 238=[-1.7979779259175056571 ,1.8391313308697680165 ] 
dist 239=[-1.8760104773994014632 ,1.9024933075790335947 ] 
dist 240=[-1.9453372965535322769 ,1.9562980153911963489 ] 
dist 241=[-1.9816050151469499136 ,1.9845941379824981890 ] 
dist 242=[-2.0006478283777606144 ,1.9996446124717335729 ] 
dist 243=[-2.0042634180723051409 ,2.0006768822870461989 ] 
dist 244=[-1.9948933348566410273 ,1.9943476356481702593 ] 
dist 245=[-1.9868995401194437353 ,1.9883845273218732649 ] 
dist 246=[-1.9749998214433433739 ,1.9661432792361115055 ] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 1, 0, 2, 2, 0, 1] 
dist 0=[43.055211567369707644  ,43.055211567369707644  ] 
dist 1=[42.760750153933921070  ,43.186328967633655812  ] 
dist 2=[42.265271372777476976  ,43.283989225915977776  ] 
dist 3=[41.331342704763820984  ,43.444736536672699822  ] 
dist 4=[40.184198812464292065  ,43.633542020068038767  ] 
dist 5=[38.837117426889674119  ,43.843044851172688256  ] 
dist 6=[37.082051371249569702  ,44.107359849947649609  ] 
dist 7=[34.305403750372067915  ,44.514683949603815737  ] 
dist 8=[31.478464009529010614  ,44.908728790968981298  ] 
dist 9=[29.522436898959160054  ,45.120041616389262807  ] 
dist 10=[27.824554148424901241  ,45.237278136060593940  ] 
dist 11=[26.028373803020197087  ,45.256089080346864785  ] 
dist 12=[24.299685763017117734  ,45.209855738070001807  ] 
dist 13=[22.871109530719115358  ,45.163290934631744607  ] 
dist 14=[21.383557165017583481  ,44.720120163990424454  ] 
dist 15=[19.418818628881020969  ,43.446855865268342088  ] 
dist 16=[17.479596704553073604  ,36.882979682427087752  ] 
dist 17=[16.093709599082421496  ,36.126969551978302315  ] 
dist 18=[14.841345648600303249  ,34.228723081063256630  ] 
dist 19=[13.435174329507101996  ,33.944169400079159575  ] 
dist 20=[12.028124279681494714  ,30.892853527123889684  ] 
dist 21=[10.771781916197685176  ,30.294952042047477153  ] 
dist 22=[9.3769667432048777714 ,29.647723559949833646  ] 
dist 23=[7.4156969110211871127 ,29.495436176454953949  ] 
dist 24=[5.4862109013101455385 ,23.504423916329519578  ] 
dist 25=[4.2182862828883955042 ,22.734451708349218020  ] 
dist 26=[3.1829640083087871341 ,21.213849773568938716  ] 
dist 27=[1.0549665263225270185 ,20.822773986227100234  ] 
dist 28=[-.46006918808306347843,19.446430484262372510  ] 
dist 29=[-1.6690178467974109638 ,19.136322970443560242  ] 
dist 30=[-2.7872933454005988895 ,18.706429676229762786  ] 
dist 31=[-3.7707652860393388143 ,18.569902455524091457  ] 
dist 32=[-4.4409690680680675682 ,5.8746843236854542609 ] 
dist 33=[-5.0151938367967013867 ,4.8206222425138913143 ] 
dist 34=[-5.6153005163790654095 ,2.4034120647054884277 ] 
dist 35=[-6.1538932469593679780 ,2.0258474724884083913 ] 
dist 36=[-6.4822094021339987734 ,.09066866119722769370] 
dist 37=[-6.7226980961655820837 ,.30655523587639155402] 
dist 38=[-6.9098690416980207921 ,.6206065789318811911 ] 
dist 39=[-7.3248600064726154556 ,1.1475532835362455123 ] 
dist 40=[-8.6048886998935124089 ,1.6866029923570793595 ] 
dist 41=[-9.3969399758201446943 ,2.0491012664871295524 ] 
dist 42=[-9.9862058887908722116 ,2.3499178118578056790 ] 
dist 43=[-10.456140414084449873  ,2.6432125843275657231 ] 
dist 44=[-10.827188165720079988  ,2.9077408084273892414 ] 
dist 45=[-11.021377079220077991  ,3.0939333122309403002 ] 
dist 46=[-11.124038812207286512  ,3.2577151162170400898 ] 
dist 47=[-11.139730389614409027  ,3.4329373286234065342 ] 
dist 48=[-7.9871960546187920531 ,3.5873370259270628520 ] 
dist 49=[-7.7937138693385164754 ,3.6680464515733050627 ] 
dist 50=[-7.2874291721333118426 ,3.7102751127667286210 ] 
dist 51=[-7.2119729974539429829 ,3.7184505547424370947 ] 
dist 52=[-6.3422744310386626747 ,3.6926533921413148720 ] 
dist 53=[-6.1699158864174034846 ,3.6754501168264158058 ] 
dist 54=[-5.9877157959346199834 ,3.6539649679323587194 ] 
dist 55=[-5.9466646026843280810 ,3.6369144397731742169 ] 
dist 56=[-4.1781965695411957043 ,2.7284511337984040622 ] 
dist 57=[-3.9547384321009442536 ,2.6229763104379649914 ] 
dist 58=[-3.5044306366728706998 ,3.0241177763432091933 ] 
dist 59=[-3.3883306546550391400 ,3.4593124192058523378 ] 
dist 60=[-2.9761489700151638618 ,3.7318163544030950455 ] 
dist 61=[-2.8874800487624395720 ,3.9383605659025326914 ] 
dist 62=[-2.7628668843532484459 ,4.1100872440046748733 ] 
dist 63=[-2.7258319539650225051 ,4.2472571158487086363 ] 
dist 64=[.33100577325760656385,4.3157868598840338227 ] 
dist 65=[.01113294156595280561,4.3492932863635352246 ] 
dist 66=[-.29246606300335365772,4.3538039098113551179 ] 
dist 67=[-.65360173095485731263,4.3133049990772849263 ] 
dist 68=[-1.0246015804441109742 ,4.2950642734548927751 ] 
dist 69=[-1.3676289157266137302 ,4.2468025306349467514 ] 
dist 70=[-1.7563804830255151867 ,4.2242259885565209948 ] 
dist 71=[-2.3099984010508243831 ,4.0940011633819096717 ] 
dist 72=[-2.8522073008352781315 ,4.0600146354975379696 ] 
dist 73=[-3.1954202118217861571 ,4.2181599391277354456 ] 
dist 74=[-3.4591681195860135704 ,4.3657719610226862094 ] 
dist 75=[-3.6840841233593637822 ,4.4812098671907373946 ] 
dist 76=[-3.8673203758260018062 ,4.5676183817555131253 ] 
dist 77=[-3.9646501124716305497 ,4.5992740236954866464 ] 
dist 78=[-4.0194565625717526153 ,4.6095890972624192410 ] 
dist 79=[-4.0328780506512733820 ,4.6107415587549347713 ] 
dist 80=[-4.0172685762928145648 ,1.9349248551859348906 ] 
dist 81=[-4.0098985422372659558 ,1.8403104402523744535 ] 
dist 82=[-4.0015937240670976998 ,1.8602892679631724514 ] 
dist 83=[-3.9899421615115805648 ,1.9999921365512603691 ] 
dist 84=[-3.9771279906842961372 ,2.1482584249361023990 ] 
dist 85=[-3.9641815738215381769 ,2.2921471999390787307 ] 
dist 86=[-3.9487262869733983939 ,2.4603864831532870714 ] 
dist 87=[-3.9338630063120807215 ,2.7058492493619781960 ] 
dist 88=[-3.7923577755319938151 ,2.9462279126774792124 ] 
dist 89=[-3.8136700304890594268 ,3.0941742390290754943 ] 
dist 90=[-3.8181963612152006851 ,3.2027346421215640550 ] 
dist 91=[-2.1692390877064579966 ,3.2859036352404867111 ] 
dist 92=[-2.2934359997076961164 ,3.3463962475306922522 ] 
dist 93=[-2.3816359209146445164 ,3.3644457184095192010 ] 
dist 94=[-2.4884009376820727592 ,3.3674662155343576647 ] 
dist 95=[-2.6361603846190459651 ,3.3679771395146130958 ] 
dist 96=[-2.7717142100323350914 ,3.2412497315344395486 ] 
dist 97=[-2.8440157108488178301 ,3.2124084990943795574 ] 
dist 98=[-2.8844248059866688776 ,3.1412661456617133128 ] 
dist 99=[-2.8939842947844037943 ,3.1138222894518978477 ] 
dist 100=[-2.8884280664638130835 ,2.9701763131581652837 ] 
dist 101=[-2.8845526955823694006 ,2.9350588299505018641 ] 
dist 102=[-2.8797728671667339956 ,2.8543665161641030128 ] 
dist 103=[-2.8726487241779038013 ,2.8258590336815419102 ] 
dist 104=[-2.4805627834480367593 ,2.9963927597705275912 ] 
dist 105=[-2.4235435464133165276 ,3.1082021245648479053 ] 
dist 106=[-2.4885221312852003100 ,3.1855756807371184372 ] 
dist 107=[-2.8138564059406990976 ,3.2364873363364454141 ] 
dist 108=[-3.0209794524287211880 ,3.2693904066156442746 ] 
dist 109=[-3.1813147742823567880 ,3.2748470160250592176 ] 
dist 110=[-3.3198615569955111505 ,3.2692176732386757375 ] 
dist 111=[-3.4338691499401298485 ,3.2578895837946950670 ] 
dist 112=[-3.4962345228279813452 ,3.0672267344470971258 ] 
dist 113=[-3.5327026668262515428 ,3.0310518030833451013 ] 
dist 114=[-3.5433112052045166688 ,2.9468313684812109779 ] 
dist 115=[-3.5401795297636047159 ,2.9175194677521164218 ] 
dist 116=[-3.5318195924487499015 ,2.7739684245500112915 ] 
dist 117=[-3.4989606880067516964 ,2.7407941524368237439 ] 
dist 118=[-3.4354243880431618081 ,2.6602221438808220008 ] 
dist 119=[-3.1861016945842012578 ,2.6318015661956912149 ] 
dist 120=[-.20365139551583996874,1.5420895382059884931 ] 
dist 121=[-.17750058655711808799,1.7257060690460617393 ] 
dist 122=[-.17072392731312986611,1.8836995613484913870 ] 
dist 123=[.59157746560527273624,2.0483862641563850334 ] 
dist 124=[.49691647623398147584,2.2051177629574237939 ] 
dist 125=[.37429444697429375727,2.3313577027679888812 ] 
dist 126=[.20761311914150159239,2.4596908407743719660 ] 
dist 127=[-.06293986353509501780,2.6247990853985527511 ] 
dist 128=[-.34084489265427511607,2.7792619874886787176 ] 
dist 129=[-.5368793239462676157 ,2.8650930247121096895 ] 
dist 130=[-.7106355929833698952 ,2.9172905963760122244 ] 
dist 131=[-.89960996685617443807,2.9374505629303911952 ] 
dist 132=[-1.0840971591626453699 ,2.9454786142633179313 ] 
dist 133=[-1.2399442127830169925 ,2.9492260235783926064 ] 
dist 134=[-1.4048051027159889180 ,2.9505981542174953231 ] 
dist 135=[-1.6252825043683825318 ,2.9491242065920060334 ] 
dist 136=[-1.8429788451536876219 ,2.5718049759536180700 ] 
dist 137=[-1.9967399653595564784 ,2.5168425286721599260 ] 
dist 138=[-2.1332662278000498248 ,2.4208113025579433212 ] 
dist 139=[-2.2821606585655354289 ,2.3955963791697558110 ] 
dist 140=[-2.4278047221035955874 ,2.3142181499801742496 ] 
dist 141=[-2.5513582879980271740 ,2.2879563425709748115 ] 
dist 142=[-2.6825392267574810867 ,2.2681455853730869146 ] 
dist 143=[-2.8586403546396925021 ,2.2584735357403200511 ] 
dist 144=[-3.0268242692180838968 ,1.0953737564989360642 ] 
dist 145=[-3.1263976592052747125 ,1.0590349275734738868 ] 
dist 146=[-3.1948980883314027346 ,1.0455289018963789114 ] 
dist 147=[-3.2390241519880581451 ,.7301693353753504775 ] 
dist 148=[-3.2662336554864004948 ,.68838686645442813972] 
dist 149=[-3.2698094807831970734 ,.6017370629813979748 ] 
dist 150=[-3.2588815982292032301 ,.57834367980755455525] 
dist 151=[-3.2490696952964960251 ,.48871028704963775151] 
dist 152=[-3.0652464009104188190 ,.47041399652788695798] 
dist 153=[-3.0299968564856267816 ,.43217166347961929867] 
dist 154=[-2.9446656013164685378 ,.42146009444691957588] 
dist 155=[-2.9142159508599038837 ,-.11755893316749192442] 
dist 156=[-2.7624727463319233110 ,-.14631948242518952584] 
dist 157=[-2.7268300492162954808 ,-.21009557663666515354] 
dist 158=[-2.6483563431734002289 ,-.22109783988250095663] 
dist 159=[-2.6220773256783459892 ,.15304538020409874991] 
dist 160=[-2.5453250056656017788 ,.80837351381679927777] 
dist 161=[-2.5867151795671704877 ,1.2409924227151768700 ] 
dist 162=[-2.6075252157626164570 ,1.5938192628487433393 ] 
dist 163=[-2.6110353858814349963 ,1.9305773850879420227 ] 
dist 164=[-2.5955343263626489750 ,2.2316928708834883289 ] 
dist 165=[-2.5850010179546928827 ,2.4422155823889592900 ] 
dist 166=[-2.5654457895703945227 ,2.6269325536728283168 ] 
dist 167=[-2.5562212840107896808 ,2.8250161541489871180 ] 
dist 168=[-2.2830078620364283588 ,3.0050261399420592816 ] 
dist 169=[-2.2401282168011306847 ,3.1175845727577474004 ] 
dist 170=[-2.1488693993944745837 ,3.2024064850033315948 ] 
dist 171=[-2.1209057482410163154 ,3.2716819910220143249 ] 
dist 172=[-1.9969139889009776237 ,3.3257468300537081592 ] 
dist 173=[-1.9708687915749846232 ,3.3498421937584804568 ] 
dist 174=[-1.8937412729700672091 ,3.3566217935384575487 ] 
dist 175=[-1.8822772832655189607 ,3.3541531462207445727 ] 
dist 176=[-1.5004844755353685933 ,.96047141703653579327] 
dist 177=[-1.4954510517771881824 ,1.0511488883028586975 ] 
dist 178=[-1.4903226965400969497 ,1.1665756630831175754 ] 
dist 179=[-1.3121974835092920216 ,1.2779546298944009821 ] 
dist 180=[-1.2850909825193537921 ,1.3524703844543078370 ] 
dist 181=[-1.2330833627271252772 ,1.4143548438986593203 ] 
dist 182=[-1.2184278676110217721 ,1.4753007523661417356 ] 
dist 183=[-1.1613741966461025880 ,1.5310792924270858935 ] 
dist 184=[-1.1469253502020771551 ,1.5723319615867211842 ] 
dist 185=[-1.1170258854101910099 ,1.6109019630976620306 ] 
dist 186=[-1.1072730649303503357 ,1.6559693912043365420 ] 
dist 187=[-.30988892907450471425,1.6962256858432767588 ] 
dist 188=[-.24006580258726303517,1.7155863002284321567 ] 
dist 189=[-.08274757225640750712,1.7237283623193007503 ] 
dist 190=[-.05349276149025464516,1.7240939050720106725 ] 
dist 191=[.13669791664662534289,1.7065017542839255426 ] 
dist 192=[.16964233036871947007,1.6984722525320885355 ] 
dist 193=[.23121518354691630735,1.6812162874750440305 ] 
dist 194=[.24502635015114449804,1.6735398662932588077 ] 
dist 195=[.25536009798893005756,1.5004542365550929598 ] 
dist 196=[.15151746096485351485,1.4729331134845294482 ] 
dist 197=[.05900903809064623697,1.4114254773720900876 ] 
dist 198=[-.04303474311402816607,1.3919442307301220202 ] 
dist 199=[-.18494904167947157511,1.3030909683928002502 ] 
dist 200=[-.32764295066557665952,1.2838639455606158644 ] 
dist 201=[-.43280002110580617593,1.2356538161474596833 ] 
dist 202=[-.53073483634917097043,1.2221671253161558864 ] 
dist 203=[-.64459420929583565027,.55731726389751587965] 
dist 204=[-.7601599838348077401 ,.53348973203824394197] 
dist 205=[-.8649085852073646712 ,.51644329995753783313] 
dist 206=[-1.0047890991016524768 ,.51363067784363678789] 
dist 207=[-1.1545586715391238003 ,.47447809081626281299] 
dist 208=[-1.3077080459024417203 ,.46578105514781057007] 
dist 209=[-1.4109904246143270987 ,.45779646803824822938] 
dist 210=[-1.4917878400431604315 ,.45517069851879664594] 
dist 211=[-1.5631760419759714537 ,.3424338328139095608 ] 
dist 212=[-1.6231635150094645623 ,.32742633120344697188] 
dist 213=[-1.6584421571349817168 ,.29812885281815172493] 
dist 214=[-1.6824236668530108019 ,.29047736073555643264] 
dist 215=[-1.6973062998069834391 ,.26328178905924867521] 
dist 216=[-1.7054810963879405876 ,.25681679693191701491] 
dist 217=[-1.7052195145226262292 ,.2476523789238044347 ] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 0, 0, 1] 
dist 0=[47.303953924443926662  ,47.303953924443926662  ] 
dist 1=[46.397976926199616237  ,48.016558715629815809  ] 
dist 2=[45.279638748009668931  ,48.362304570585766413  ] 
dist 3=[43.786506744105680339  ,48.532883950465442260  ] 
dist 4=[41.382951385431553846  ,48.545497855402120848  ] 
dist 5=[38.898392196235907900  ,48.226996003323545551  ] 
dist 6=[37.081551674385036656  ,48.131189490249760264  ] 
dist 7=[35.398025820236916488  ,47.697508108585553324  ] 
dist 8=[33.446040347343602094  ,47.430279737886411960  ] 
dist 9=[31.460044478575862612  ,47.018674083543568189  ] 
dist 10=[29.640483048865072909  ,46.879094831117819423  ] 
dist 11=[27.585606066200421742  ,46.533990218084501078  ] 
dist 12=[24.659052275995058390  ,46.392573471222570712  ] 
dist 13=[21.668406674795985990  ,45.670711227050824166  ] 
dist 14=[19.357261248581599045  ,45.481193828073152547  ] 
dist 15=[17.089649784377101327  ,44.451521514612789454  ] 
dist 16=[14.272731342399882383  ,42.565126562122291327  ] 
dist 17=[11.300013078549846360  ,29.152815616397308748  ] 
dist 18=[8.4094887396949424062 ,27.873181675298649623  ] 
dist 19=[5.0094623123564919834 ,25.498363545093711320  ] 
dist 20=[0                     ,25.211212810442619281  ] 
dist 21=[17.403346874198630393  ,21.201251014823972371  ] 
dist 22=[15.454224101801408895  ,20.633932615028889697  ] 
dist 23=[13.632411220437772629  ,19.467652097625972030  ] 
dist 24=[11.498541515426722999  ,19.174961184923789475  ] 
dist 25=[9.3174652912725493644 ,16.968073556333103845  ] 
dist 26=[7.3070268740521338153 ,16.604707880084331816  ] 
dist 27=[5.0286608079630818923 ,15.608217682607907687  ] 
dist 28=[1.7770845049778882020 ,14.371101104912899239  ] 
dist 29=[-1.4283339281497327002 ,8.0733418430508242588 ] 
dist 30=[-3.5223222585122156165 ,7.4777548565578225798 ] 
dist 31=[-5.2111764165595168638 ,5.8624522276380258312 ] 
dist 32=[-6.7980217574502397780 ,3.8807024512484450131 ] 
dist 33=[-8.2054817026788991473 ,1.9796401334384125000 ] 
dist 34=[-9.1777155762402461003 ,1.6715705334325887443 ] 
dist 35=[-10.021528403187419404  ,1.0489886784793577708 ] 
dist 36=[-10.916076880629440784  ,.8958628660382668312 ] 
dist 37=[-11.723961361023177278  ,-.3059757703249264261 ] 
dist 38=[-12.221554051107778371  ,-.4985145131841531739 ] 
dist 39=[-12.589752507620920271  ,-.7389143645553271471 ] 
dist 40=[-12.880582176734032569  ,-.7802707317389352626 ] 
dist 41=[-13.101625324229804880  ,-.7472852923854943974 ] 
dist 42=[-13.191000791245569586  ,-.6078033542754598753 ] 
dist 43=[-13.210223694611608536  ,-.3657236775857900543 ] 
dist 44=[-13.193952481518796005  ,.0767284196963842788 ] 
dist 45=[-12.216654714548300697  ,.5426903412064123240 ] 
dist 46=[-12.179849323311288131  ,.8787383811417269394 ] 
dist 47=[-12.122566647165815985  ,1.1823636447784699883 ] 
dist 48=[-12.079989112912388194  ,1.5193467464198332280 ] 
dist 49=[-5.5487266716621374499 ,1.8507489133584594294 ] 
dist 50=[-4.9990842392204561382 ,2.1323076933726116368 ] 
dist 51=[-3.7868804783304762229 ,2.4308301718908115620 ] 
dist 52=[-3.6932705871055407857 ,2.8301338860565680330 ] 
dist 53=[-1.9322303751217461270 ,3.2236497865644557521 ] 
dist 54=[-1.6567614064147182383 ,3.4991895756117563439 ] 
dist 55=[-1.1710329360444923012 ,3.7412433578934278273 ] 
dist 56=[-.9769640898140736406 ,4.0012657223696908077 ] 
dist 57=[.07451234166781776299,4.2536690588949622564 ] 
dist 58=[.17829899866447922075,4.5567504337443834443 ] 
dist 59=[.4013997278378750079 ,4.9665519126076485975 ] 
dist 60=[.43589540331458803154,5.3171703243036931025 ] 
dist 61=[1.9571076353095073961 ,5.6033383541651927437 ] 
dist 62=[2.1021859185441463987 ,5.7560339217700204176 ] 
dist 63=[2.3419306662769939361 ,5.8408064512398497979 ] 
dist 64=[2.3918718019901853220 ,5.8563684404367224742 ] 
dist 65=[2.4357928583007182946 ,5.1797102991765239868 ] 
dist 66=[2.3725339863116239143 ,5.2732005094987579937 ] 
dist 67=[2.2365659810850194930 ,5.4418514452668633896 ] 
dist 68=[1.9665444300169442172 ,5.6176690446202574287 ] 
dist 69=[1.6608734993091905815 ,5.7698551754493643447 ] 
dist 70=[1.3825373853904404181 ,5.8441147494293654469 ] 
dist 71=[1.0711079369592591516 ,5.8779729829132237615 ] 
dist 72=[.6332055466646386431 ,5.8809547811434127212 ] 
dist 73=[.14736016768395178793,5.8255678177847123193 ] 
dist 74=[-.35552647979678996918,5.7987873321519050357 ] 
dist 75=[-.96757694236787057675,5.7497158494959531116 ] 
dist 76=[-1.8892849909873226256 ,5.7286322385586291682 ] 
dist 77=[-2.8104128037951099186 ,3.0529960684232431593 ] 
dist 78=[-3.4201750984512851908 ,2.9737018839093332328 ] 
dist 79=[-3.9191963064516705329 ,2.8879365051344061125 ] 
dist 80=[-4.3982484897717399858 ,2.8655967157327076238 ] 
dist 81=[-4.8284231801865804255 ,1.9391562910713225952 ] 
dist 82=[-5.1323366090529909601 ,1.8243503974127301642 ] 
dist 83=[-5.4023664318518898367 ,1.5939898203596833502 ] 
dist 84=[-5.6973087004424134866 ,1.5341848858394099288 ] 
dist 85=[-5.9586228967631227352 ,1.3192797695589639172 ] 
dist 86=[-6.0944163904643485495 ,1.2727068406919818218 ] 
dist 87=[-6.1676488259897965539 ,1.1972902141524842335 ] 
dist 88=[-6.1815514343378688483 ,1.1775619398123421148 ] 
dist 89=[-6.1409572222958142902 ,1.1381444603594281423 ] 
dist 90=[-6.1220510070256988725 ,1.1434180528434118823 ] 
dist 91=[-6.1025521382065612759 ,1.1697949982317284888 ] 
dist 92=[-6.0771140244115077393 ,1.2315280873558666669 ] 
dist 93=[-5.7020518081709478480 ,1.3109957815619437630 ] 
dist 94=[-5.6393163245341885131 ,1.6570168000763443198 ] 
dist 95=[-5.4424055054930528264 ,2.3144898638328644753 ] 
dist 96=[-5.4130561516039507051 ,2.9705102904814724245 ] 
dist 97=[-4.9572658453862120106 ,3.5757867146159736359 ] 
dist 98=[-4.8571578845709156654 ,4.0306992979425688592 ] 
dist 99=[-4.7727061149864194742 ,4.4628239352324200459 ] 
dist 100=[-4.7523950300383522702 ,4.9771312998921479714 ] 
dist 101=[-3.4510673472562720369 ,5.4554135372257532629 ] 
dist 102=[-3.2814898434609642499 ,5.7437300946880290673 ] 
dist 103=[-2.9523993616078676667 ,5.9482190294811254967 ] 
dist 104=[-2.8679051146227190560 ,6.0918736876318065621 ] 
dist 105=[-2.5764203519685356615 ,6.1951270851152219008 ] 
dist 106=[-2.5060405587134461391 ,6.2383444797626438116 ] 
dist 107=[-2.4286226471003326966 ,6.2471652019559623141 ] 
dist 108=[-2.4045961924571116318 ,6.2407993418887950252 ] 
dist 109=[.01067227343595335574,2.3671448475821722285 ] 
dist 110=[.10803196413149703342,2.3394443861729808589 ] 
dist 111=[-.3148667495066701795 ,2.5786955150837070187 ] 
dist 112=[-.94996996043475685613,2.9608088556755173318 ] 
dist 113=[-1.5826776325323383333 ,3.3294473227143520275 ] 
dist 114=[-1.9960073604199843670 ,3.5609573783119431764 ] 
dist 115=[-2.3279289814680851004 ,3.7367687437224888668 ] 
dist 116=[-2.6356719241853974126 ,3.8830198293159853796 ] 
dist 117=[-2.9043829998586117687 ,3.9994721168935844223 ] 
dist 118=[-3.0804904374672745513 ,4.0563146281581377380 ] 
dist 119=[-3.2224743046453339829 ,4.0826190280829122753 ] 
dist 120=[-3.3549507754694164041 ,4.0847487951438928686 ] 
dist 121=[-3.4694776631718691667 ,4.0385444208435601881 ] 
dist 122=[-3.5398153842281947156 ,4.0201624048824102780 ] 
dist 123=[-3.5911875917485821604 ,3.9285729283094091917 ] 
dist 124=[-3.6300429857207436578 ,3.7429390470854407626 ] 
dist 125=[-3.6578482668448072731 ,2.3336620849852203495 ] 
dist 126=[-3.6651319454761873788 ,2.1950604241239424480 ] 
dist 127=[-3.6587893677051818842 ,1.8400275115458787137 ] 
dist 128=[-3.6507271019759396859 ,1.4703347311652907624 ] 
dist 129=[.59912849428651252289,1.3328115441540611187 ] 
dist 130=[.45699984436952719759,1.3053127344663646008 ] 
dist 131=[.29645842202333913123,1.2440979620701978668 ] 
dist 132=[.06860882261875762657,1.2250868438483804686 ] 
dist 133=[-.1624007616455005038 ,1.1078220427756163142 ] 
dist 134=[-.33556322819044025161,1.1021156781725086632 ] 
dist 135=[-.49969850932499254529,1.0927129103537128886 ] 
dist 136=[-.69467679145172561602,1.0886772436213203640 ] 
dist 137=[-.89484081446449891746,.969371977387796707  ] 
dist 138=[-1.0796862797625393766 ,.95110987946291718054] 
dist 139=[-1.2889524597173956041 ,.91261134618746578928] 
dist 140=[-1.5866245799217117837 ,.90104522464561115984] 
dist 141=[-1.8789877831204955322 ,.85083558834835630426] 
dist 142=[-2.0670603546646420526 ,.84026495072281729144] 
dist 143=[-2.2149954297546829920 ,.81000243072915716361] 
dist 144=[-2.3471079457579883236 ,.80493482039153641409] 
dist 145=[-2.4591496203902269982 ,.35043380462868559682] 
dist 146=[-2.5269521432698850139 ,.30786383685145020652] 
dist 147=[-2.5754325777719130829 ,.2109276256633906836 ] 
dist 148=[-2.6103334130413376852 ,.1929275287271600768 ] 
dist 149=[-2.6341753204749252556 ,.07112166352956173754] 
dist 150=[-2.6385018292560934500 ,.04946405172074201337] 
dist 151=[-2.6337271724527602291 ,.01044705917925518580] 
dist 152=[-2.6259206578412265823 ,.00180214553236561900] 
dist 153=[-2.5646155286347882144 ,-.11872514854828805314] 
dist 154=[-2.5457296816811816240 ,-.13531404573447039896] 
dist 155=[-2.5072537326667293431 ,-.16629889251081672478] 
dist 156=[-2.4928012830866309321 ,-.17321359992827672029] 
dist 157=[-1.8566440824169159228 ,.10809878125706693351] 
dist 158=[-1.7927430887472122907 ,.43705257592715059954] 
dist 159=[-1.6304802665190727092 ,.71279615350137131233] 
dist 160=[-1.6051407501849368077 ,.98845800341663340764] 
dist 161=[-1.3400543375226198158 ,1.2433476394350125036 ] 
dist 162=[-1.2880681522967736577 ,1.4361594849138264510 ] 
dist 163=[-1.2283468883412273489 ,1.6206493400272533284 ] 
dist 164=[-1.2118978981421721785 ,1.8423141988313953372 ] 
dist 165=[-.70640921993451795732,2.0497781904676756178 ] 
dist 166=[-.64210711827809684262,2.1775718015683996976 ] 
dist 167=[-.50920680597087031096,2.2716201186472414296 ] 
dist 168=[-.47424606165347759873,2.3443573990754729424 ] 
dist 169=[-.34811902024002795765,2.3998158920897962220 ] 
dist 170=[-.33512277697486993589,2.4248788736349495324 ] 
dist 171=[-.30643402186205487592,2.4349038132330736886 ] 
dist 172=[-.2987898294553064458 ,2.4335895146851889486 ] 
dist 173=[-.26803480121072421032,.53438632779423295244] 
dist 174=[-.29359709358947172696,.66858437709352075634] 
dist 175=[-.32447329591871403905,.77939274340115488752] 
dist 176=[-.37066076428639359452,.88745639185315690094] 
dist 177=[-.41650132708989458048,.98565607752060795212] 
dist 178=[-.44599226840464696554,1.0570819183898213062 ] 
dist 179=[-.46914037261531020968,1.1226716387989085044 ] 
dist 180=[-.48966567999299169412,1.1975709777877830908 ] 
dist 181=[-.50691297363045550091,1.2657110008406592983 ] 
dist 182=[-.51697688421185355103,1.3043137437827206479 ] 
dist 183=[-.52368866649846751947,1.3287257176719402866 ] 
dist 184=[-.52755378565263488979,1.3402075254953666969 ] 
dist 185=[-.52924635669976940556,1.3457574801118195674 ] 
dist 186=[-.52892354593329690362,1.3464849346169988448 ] 
dist 187=[-.52446990845716493242,1.3438217549421024879 ] 
dist 188=[-.52274939324497772245,1.3404085843237889203 ] 
dist 189=[-.50063937709986029482,1.2016330191369986004 ] 
dist 190=[-.49473463793106755392,1.1821007101707888584 ] 
dist 191=[-.48848225493637705566,1.1262910667794919109 ] 
dist 192=[-.48506513204587401426,1.1182859870195501030 ] 
dist 193=[-.49869015349783415681,1.0052303826275861556 ] 
dist 194=[-.60051519120610264482,.98138388855570306292] 
dist 195=[-.7037993031580242113 ,.96036981197587734337] 
dist 196=[-.83625550505099167157,.95623136651607131279] 
dist 197=[-.96450807776294332633,.66690871400395416336] 
dist 198=[-1.0510096817678542630 ,.62965638262740053109] 
dist 199=[-1.1236011248908150714 ,.55746687897842579909] 
dist 200=[-1.1963176168355475374 ,.53909998552110440684] 
dist 201=[-1.2636627660334882903 ,.4765761928426908323 ] 
dist 202=[-1.3148097819580137315 ,.46150306436407357929] 
dist 203=[-1.3639573383102025332 ,.4468317621251135619 ] 
dist 204=[-1.4233213643947182234 ,.44405403017108296105] 
dist 205=[-1.4773262232742534565 ,.23299595052533983292] 
dist 206=[-1.5050771952822195113 ,.30226187026569930809] 
dist 207=[-1.5196909978952778016 ,.39085081641921035682] 
dist 208=[-1.5221877471560166446 ,.52910134198013109357] 
dist 209=[-1.5113350169210685334 ,.66917988765929511337] 
dist 210=[-1.5713004601185760879 ,.76506716060888046435] 
dist 211=[-1.6422045578421450975 ,.84704680233422335826] 
dist 212=[-1.6973795838090091032 ,.9316014459452333897 ] 
dist 213=[-1.7397352364077560162 ,1.0114484132117883192 ] 
dist 214=[-1.7594570115024299940 ,1.0746335629944202928 ] 
dist 215=[-1.7677470298472844688 ,1.1377841043496874645 ] 
dist 216=[-1.7674014572082181886 ,1.2174932685393232568 ] 
dist 217=[-1.6900332558255363829 ,1.2940409719278492347 ] 
dist 218=[-1.6738155131855967650 ,1.3445699636906497205 ] 
dist 219=[-1.6447922041943342412 ,1.3857704633476075132 ] 
dist 220=[-1.6353552615089760701 ,1.4250755189906538743 ] 
dist 221=[-1.5937970290344465800 ,1.4602056374032423198 ] 
dist 222=[-1.5816946939071384705 ,1.4847384433837653392 ] 
dist 223=[-1.5507987631854288270 ,1.5062349604860431139 ] 
dist 224=[-1.5385550397496611013 ,1.5292435427213210444 ] 
dist 225=[-.68467659776033185166,1.5486152302040950510 ] 
dist 226=[-.6078310582342115447 ,1.5555918472016366084 ] 
dist 227=[-.44205337441480561216,1.5555640014162538168 ] 
dist 228=[-.43473253561287701687,1.5531052575087441914 ] 
dist 229=[-.32616089245807051589,1.5279183589857052756 ] 
dist 230=[-.31083548067189062831,1.5194095501585772827 ] 
dist 231=[-.27374587677728149063,1.4962433742688994360 ] 
dist 232=[-.26730105938246611918,1.4861284438344480708 ] 
dist 233=[-.2124567682006255327 ,1.3464207749939123686 ] 
dist 234=[-.20199476598408946466,1.3232766818769824325 ] 
dist 235=[-.18716353533327994141,1.2650115918645100335 ] 
dist 236=[-.18270601487979380641,1.2503200737124653726 ] 
dist 237=[-.01853995422192251721,1.1494843536066137356 ] 
dist 238=[-.06468410665953739981,1.1276472473325158553 ] 
dist 239=[-.12372892320626053376,1.0895858215189113806 ] 
dist 240=[-.36884872408222659905,1.1622261656138204698 ] 
dist 241=[-.69409831273136055332,1.2705563381455879059 ] 
dist 242=[-.90692785802466639272,1.3381181105527127970 ] 
dist 243=[-1.0784066054905900310 ,1.3888335103643664153 ] 
dist 244=[-1.2385642609542699977 ,1.4299043723814862168 ] 
dist 245=[-1.3794028641577348175 ,1.4616882537974734170 ] 
dist 246=[-1.4737506801367109261 ,1.4753253555724996390 ] 
dist 247=[-1.5522174332742379146 ,1.4804194149812580184 ] 
dist 248=[-1.6296509095583209257 ,1.4788501859772243558 ] 
dist 249=[-1.6980875505463654162 ,1.4517542711657873813 ] 
dist 250=[-1.7406347814441531929 ,1.4435510858455792824 ] 
dist 251=[-1.7724111532307587768 ,1.4196867133396793579 ] 
dist 252=[-1.7978461400720221002 ,1.4094807456083232737 ] 
dist 253=[-1.8172898617098260156 ,1.3506871644183207578 ] 
dist 254=[-1.8251466973303396881 ,1.3356376180239484175 ] 
dist 255=[-1.8260278742249516974 ,1.3071724335041312617 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 1, 1, 2, 1, 2] 
dist 0=[51.348304141430527104  ,51.348304141430527104  ] 
dist 1=[51.000365420616838619  ,51.524635712093932877  ] 
dist 2=[50.184021991284894328  ,51.655747161848354712  ] 
dist 3=[49.215400306048279667  ,51.736422665494181619  ] 
dist 4=[48.259140394470242332  ,51.711431722573155185  ] 
dist 5=[47.126211486979155116  ,51.635976341657566415  ] 
dist 6=[45.451784883819168045  ,51.542672721885061534  ] 
dist 7=[43.551299016165537193  ,51.351968910203302303  ] 
dist 8=[41.515330080555728271  ,51.109265771725205201  ] 
dist 9=[38.983830346717033503  ,48.681278211315191939  ] 
dist 10=[35.103905604877804468  ,48.237019925769980697  ] 
dist 11=[31.178512428152681882  ,47.582891317180567190  ] 
dist 12=[28.465329855671955148  ,47.367662547861234646  ] 
dist 13=[26.112226116242438865  ,46.923574011469472690  ] 
dist 14=[23.625030838680685948  ,46.177086601944287767  ] 
dist 15=[21.232227173827129328  ,42.439761192406526147  ] 
dist 16=[19.256036675469200589  ,39.916720922099211140  ] 
dist 17=[17.199679989532460828  ,28.813258019503112581  ] 
dist 18=[14.486388637205472007  ,28.058200237175288946  ] 
dist 19=[11.811942459551229607  ,26.586316094604618629  ] 
dist 20=[9.9106079178404403808 ,26.241047368930798403  ] 
dist 21=[8.2041845124601790930 ,25.830762017688541823  ] 
dist 22=[6.3081411269092720966 ,25.692098053098929322  ] 
dist 23=[4.4253435801162582834 ,17.312031840900191180  ] 
dist 24=[2.7715356349997611614 ,17.031619535235273319  ] 
dist 25=[.96071702608970646755,12.715616089507755534  ] 
dist 26=[-1.5499729699660787156 ,12.145381135903237153  ] 
dist 27=[-4.0042408966213602726 ,11.023442002609568141  ] 
dist 28=[-5.5897244177358552012 ,10.759049681051865188  ] 
dist 29=[-6.8506948640043099001 ,9.9562843013297171407 ] 
dist 30=[-8.0081095203452439497 ,9.5053804576548091926 ] 
dist 31=[-9.0182691273775953334 ,8.2084481342961000760 ] 
dist 32=[-9.6908576478277140991 ,7.4846190017322239512 ] 
dist 33=[-10.249381753181811253  ,-5.2010555795075392746 ] 
dist 34=[-10.803981013463403232  ,-5.3669593071836496053 ] 
dist 35=[-11.283100131579543195  ,-6.3980601328905774776 ] 
dist 36=[-11.540001424230576634  ,-6.5529584399838342806 ] 
dist 37=[-12.028379642362772475  ,-6.8297206912318733672 ] 
dist 38=[-12.567675250486321869  ,-6.8761952566330171805 ] 
dist 39=[-12.965493172247551587  ,-6.9211699046605297095 ] 
dist 40=[-13.279633040040268674  ,-6.3700896803097319207 ] 
dist 41=[-13.521774021145463866  ,-5.1680181961281320918 ] 
dist 42=[-13.631863927316509880  ,-3.2805852158724664045 ] 
dist 43=[-13.668770977766804624  ,-1.3672454117821957342 ] 
dist 44=[-13.657074433505770729  ,-.06164813730742748936] 
dist 45=[-13.523820016580414471  ,1.0492539218194755936 ] 
dist 46=[-13.470180622624374313  ,2.1855254893036684345 ] 
dist 47=[-13.257734258984826085  ,3.2518320939349870016 ] 
dist 48=[-13.198806801671797405  ,4.0835012046371349152 ] 
dist 49=[-8.4014648948365644904 ,4.9031008895647412794 ] 
dist 50=[-7.9366544004161973324 ,5.9212765656487984094 ] 
dist 51=[-6.8135456630760539811 ,6.8905505247063158462 ] 
dist 52=[-6.6313491450875487656 ,7.5149478452636927640 ] 
dist 53=[-5.0017284418422166967 ,8.0067292360991798192 ] 
dist 54=[-4.6981735355697503358 ,8.4465926152203613562 ] 
dist 55=[-4.2883466240811985145 ,8.8197468842692697831 ] 
dist 56=[-4.1619027329043953523 ,9.0452108977616198826 ] 
dist 57=[-1.7582005733258923350 ,9.2057553646301838745 ] 
dist 58=[-1.4566000085067498213 ,9.3197182153582394026 ] 
dist 59=[-.78890171846264676057,9.3974195372562320511 ] 
dist 60=[-.65881410870540126011,9.4131964590725747954 ] 
dist 61=[.10684056862399212908,9.3916208235371572322 ] 
dist 62=[.23647579263160206439,9.3678853505033501739 ] 
dist 63=[.49926277569789586385,9.1784714774076429300 ] 
dist 64=[.56152424853032803316,9.0005188182652569904 ] 
dist 65=[1.2935654988880216591 ,3.7713194011114313648 ] 
dist 66=[1.1593675927912167410 ,3.8842709799315943790 ] 
dist 67=[.98313291598621132004,3.9710743186839851279 ] 
dist 68=[.76339782576342516875,4.0134583150561228820 ] 
dist 69=[.4700496444473727755 ,4.0317861840590521548 ] 
dist 70=[0                     ,4.0332722930110102436 ] 
dist 71=[2.3688526204498262590 ,4.0285637561361448548 ] 
dist 72=[2.2358581927354926879 ,4.0429626321571159850 ] 
dist 73=[2.0977951228788533257 ,4.0442684448177626259 ] 
dist 74=[1.9167547201249019896 ,4.0366584914414214997 ] 
dist 75=[1.7218463924096058408 ,3.6929742958338486740 ] 
dist 76=[1.5283811159739228831 ,3.6915936161055916218 ] 
dist 77=[1.2987278484296382979 ,3.6853929470930653682 ] 
dist 78=[.95930261606920789649,3.6738315446419330171 ] 
dist 79=[.60918842876480350977,3.6529857712232095263 ] 
dist 80=[.33683805578798135307,3.6420111961494149769 ] 
dist 81=[.06890206859973760812,1.9385969565586103288 ] 
dist 82=[-.27933710561906554639,1.7915261581736916418 ] 
dist 83=[-.6921557059419194908 ,1.6897729367696437561 ] 
dist 84=[-.99008229306077847981,1.6916202509321580773 ] 
dist 85=[-1.3366119871938924645 ,1.7020475793021988453 ] 
dist 86=[-1.9020822644252639430 ,1.7267245163648652762 ] 
dist 87=[-2.4603320871303439630 ,1.7542564878835032624 ] 
dist 88=[-2.8204476865986392043 ,1.7760773960576596823 ] 
dist 89=[-3.1050439521189393365 ,1.7977508168054276835 ] 
dist 90=[-3.3617391696325644669 ,1.8247184455119018592 ] 
dist 91=[-3.5814409496239955100 ,1.8528764359093263841 ] 
dist 92=[-3.7183223480272869830 ,1.8793097000067177021 ] 
dist 93=[-3.8210354138368553294 ,1.9094534484917338394 ] 
dist 94=[-3.9043089495994487269 ,1.9524226052678013639 ] 
dist 95=[-3.9703281068469883630 ,1.9958138203208435838 ] 
dist 96=[-4.0041424658510675617 ,2.0276471894383851730 ] 
dist 97=[-4.0209552626633958588 ,2.0570431265952210088 ] 
dist 98=[-4.0190755344467964006 ,2.0907192482410270102 ] 
dist 99=[-3.7534393314723473603 ,2.1245040785753395003 ] 
dist 100=[-3.7090413987886722477 ,2.1543391404780830236 ] 
dist 101=[-3.5365832846350674715 ,2.1869591217128942610 ] 
dist 102=[-3.2287906889262539642 ,2.2318614227487393914 ] 
dist 103=[-3.0238812904179803453 ,2.2736805189579032298 ] 
dist 104=[-3.0069629511246885809 ,2.2939951288689549452 ] 
dist 105=[-2.9436622834306801331 ,2.3024122073675284952 ] 
dist 106=[-2.9325599292419211505 ,2.3007207030445965243 ] 
dist 107=[-2.5248301351380971709 ,2.2834271450790117598 ] 
dist 108=[-2.5055114196283531730 ,2.2753021711915550067 ] 
dist 109=[-2.4186332583095508659 ,2.2402398034959797535 ] 
dist 110=[-2.3976035898007154029 ,2.2311104510827759167 ] 
dist 111=[-2.3372776090204123051 ,2.0719235473729962529 ] 
dist 112=[-2.3216741014333276636 ,2.0435970022213878924 ] 
dist 113=[-1.2875339633328148190 ,1.9627430278873199785 ] 
dist 114=[-1.1991023409799908781 ,1.9475972129388795504 ] 
dist 115=[-.98475002144568844865,1.7792783755585060551 ] 
dist 116=[-.95274547824126986462,1.7424514048795263485 ] 
dist 117=[-.64116815209154994125,1.7013646590139812199 ] 
dist 118=[-.58365449980833352403,1.6837112823377461310 ] 
dist 119=[-.51359327302827121524,1.3460679170208987926 ] 
dist 120=[-.49801943552733379814,1.5489447470339282751 ] 
dist 121=[-.02596017141043831844,1.7382390705905447186 ] 
dist 122=[.03144815762417241968,1.8545377937232081980 ] 
dist 123=[.15323797532464461182,1.9398292671416436424 ] 
dist 124=[.18069265267633684652,2.0053076080220209423 ] 
dist 125=[.30178521897037987007,2.0561031897833012424 ] 
dist 126=[.32332450589772284589,2.0827666757264111269 ] 
dist 127=[.36343775588423073064,2.0969036644802727212 ] 
dist 128=[.37197953642393908216,2.0976858204781233463 ] 
dist 129=[.59638599977250810275,1.1587191203022699892 ] 
dist 130=[.59399700961193617881,1.1613952425757120873 ] 
dist 131=[.58313063286508534288,1.1600072820571964985 ] 
dist 132=[.55788108891142044294,1.1567342640124382723 ] 
dist 133=[.52531063251415090529,1.1497348841746913034 ] 
dist 134=[.48521125340657131272,1.1458604665451765380 ] 
dist 135=[.43187940872152566462,1.1219548905424304252 ] 
dist 136=[.34647460982223024671,1.1154167413255767481 ] 
dist 137=[.25567958809864198519,1.0934525264794898652 ] 
dist 138=[.18082447013465610909,1.0882271711483893349 ] 
dist 139=[.1032189758862658062 ,1.0616785509531950184 ] 
dist 140=[-.00991855225585408920,1.0581974602470001706 ] 
dist 141=[-.12142231872436134641,1.0318108581777788939 ] 
dist 142=[-.23462945188821524246,1.0237996599915671297 ] 
dist 143=[-.3474196145725730952 ,1.0100063532915769352 ] 
dist 144=[-.5398611213356989995 ,1.0051656794198367749 ] 
dist 145=[-.7310490547971891155 ,.8289906005949796461 ] 
dist 146=[-.8559870724702790907 ,.84317782246798300138] 
dist 147=[-.9564936341914671708 ,.85318944526445645794] 
dist 148=[-1.0501359034001776231 ,.86008866069129736133] 
dist 149=[-1.1323605225787068843 ,.86442375398889232054] 
dist 150=[-1.1872815834924848219 ,.86419988552035209059] 
dist 151=[-1.2328060150707313454 ,.86140706237153855295] 
dist 152=[-1.2775161011566112060 ,.85882126903712185746] 
dist 153=[-1.3156987501385930399 ,.8400128601958448724 ] 
dist 154=[-1.3351612605412311756 ,.8346242146778815497 ] 
dist 155=[-1.3446768751245608366 ,.8183768110418999746 ] 
dist 156=[-1.3459472904884312892 ,.8127508112490175305 ] 
dist 157=[-1.3372320901629277471 ,.7724858211083129294 ] 
dist 158=[-1.3318500178694103714 ,.7625197434203964960 ] 
dist 159=[-1.3197730477398037383 ,.7461895607408830734 ] 
dist 160=[-1.3139757425219512453 ,.7408959867750305639 ] 
dist 161=[-.99752656205431236536,.6120335318812902702 ] 
dist 162=[-.9948186129994368766 ,.5937803258233993260 ] 
dist 163=[-.98213317757098387055,.5501401850116973831 ] 
dist 164=[-.97857293781126472346,.5399778753737339392 ] 
dist 165=[-.93446769648924298424,.4740563544386863479 ] 
dist 166=[-.92337787025623784362,.4606357555855597611 ] 
dist 167=[-.91151044648630300029,.4361262614138442149 ] 
dist 168=[-.9053387875313884471 ,.4297131247520649558 ] 
dist 169=[-.7433455197590816495 ,.3147811058174803474 ] 
dist 170=[-.72051891173442059682,.2988978946041667392 ] 
dist 171=[-.67477853469340708705,.2598308978850857563 ] 
dist 172=[-.66219512085564656167,.2533700384667754209 ] 
dist 173=[-.61364824990157483329,.23967698619400467175] 
dist 174=[-.60266664642781923625,.32281989938484891479] 
dist 175=[-.57987714424953699914,.39916687057330004719] 
dist 176=[-.57298485274574356586,.45607739287139040305] 
dist 177=[-.52262565542721866684,.50973714990605103009] 
dist 178=[-.60104824139433892027,.5770232937091960795 ] 
dist 179=[-.66396414521027002478,.6468588924043836681 ] 
dist 180=[-.72222808940026922007,.7149649430519816022 ] 
dist 181=[-.7730868854770479506 ,.7768562527771856998 ] 
dist 182=[-.8064408061253163035 ,.8218798973818522456 ] 
dist 183=[-.8333785500391872558 ,.8632347008243438725 ] 
dist 184=[-.8586226385300427156 ,.9104797561710339118 ] 
dist 185=[-.8796520077787650860 ,.9534845110404860841 ] 
dist 186=[-.8897640274927005759 ,.97791027512218440264] 
dist 187=[-.8938658367319714768 ,.99344454811810620937] 
dist 188=[-.8940423500137674112 ,1.0009495000758791144 ] 
dist 189=[-.8847311939306508967 ,1.0040453493807107204 ] 
dist 190=[-.8804897562239240166 ,1.0029495220430510039 ] 
dist 191=[-.8704126008672055011 ,.99763763756353302044] 
dist 192=[-.8658139569873730110 ,.99366078311540662007] 
dist 193=[-.10856454776255679056,.5083600566598231787 ] 
dist 194=[-.22086816472777093336,.51208070972526630038] 
dist 195=[-.33547540770969813651,.52796645325470306482] 
dist 196=[-.4226497588096982528 ,.54017278983658332086] 
dist 197=[-.5065308424854785753 ,.54909776621412889267] 
dist 198=[-.60799045193126852442,.55188169779105798457] 
dist 199=[-.71314090114642925852,.5523520222234611712 ] 
dist 200=[-.81175839149518392734,.55204002178219623914] 
dist 201=[-.92460710390817902948,.53523540477127067279] 
dist 202=[-1.0865771333293630929 ,.63490107748364446248] 
dist 203=[-1.2453377337896350171 ,.75167851605949105889] 
dist 204=[-1.3453729717773427933 ,.83043330438397306654] 
dist 205=[-1.4216697250293062758 ,.89649968944292572406] 
dist 206=[-1.4856535058281301466 ,.96262041129904920301] 
dist 207=[-1.5369187227900380755 ,1.0237983483538407210 ] 
dist 208=[-1.5624363665871026896 ,1.0701312641707987308 ] 
dist 209=[-1.5753668011627214145 ,1.1145122920449594848 ] 
dist 210=[-1.5768037901886429027 ,1.1678973599483026866 ] 
dist 211=[-1.5596764798441009873 ,1.2178821336855957498 ] 
dist 212=[-1.5520721227670852458 ,1.2486878631488376939 ] 
dist 213=[-1.5370547205838721389 ,1.2713737926699114541 ] 
dist 214=[-1.5304888515093388736 ,1.2889413370045974707 ] 
dist 215=[-1.4937397520589011434 ,1.3018918552872916792 ] 
dist 216=[-1.4843019818042064941 ,1.3061447737157627140 ] 
dist 217=[-1.4494166921606878774 ,1.3049240616442233783 ] 
dist 218=[-1.4443118285958054782 ,1.3028141238715717275 ] 
dist 219=[-.79514514694553592313,1.2833592279771550697 ] 
dist 220=[-.73358488219724111807,1.2764881443284320578 ] 
dist 221=[-.58928963037097937519,1.2572862330441364634 ] 
dist 222=[-.56367608065091323989,1.2487722053215156639 ] 
dist 223=[-.54340546502011158737,1.2007925247360064679 ] 
dist 224=[-.54285784533727168069,1.1884090327388394500 ] 
dist 225=[-.42113969323369985332,1.1626452986670850030 ] 
dist 226=[-.40848677074109508291,1.1537949616075438521 ] 
dist 227=[-.38035652839888372431,1.0002009282861507703 ] 
dist 228=[-.37207442632006559796,.976827500895768104  ] 
dist 229=[-.33559995946959784901,.92041654131163634052] 
dist 230=[-.32816147906606996095,.90652440052440768319] 
dist 231=[-.31041510962034983059,.81834010675137316711] 
dist 232=[-.30576322164877187025,.79995008554914077428] 
dist 233=[-.25824448308362452757,.76599986442895112707] 
dist 234=[-.36882293082997684239,.86289266234999988548] 
dist 235=[-.62494379519452111614,.979618377900768314  ] 
dist 236=[-.79277499467586489413,1.0545894238244637801 ] 
dist 237=[-.92825978783903718392,1.1134202766765588251 ] 
dist 238=[-1.0552391933834242703 ,1.1657061895858214895 ] 
dist 239=[-1.1672012822258953087 ,1.2098573731916543738 ] 
dist 240=[-1.2427300556216714854 ,1.2362103904015658598 ] 
dist 241=[-1.3061186669880779516 ,1.2546043620698505987 ] 
dist 242=[-1.3696114215934392040 ,1.2669793492178711559 ] 
dist 243=[-1.4255836369001341988 ,1.2742025838854192028 ] 
dist 244=[-1.4589468814493276880 ,1.2746199611165803965 ] 
dist 245=[-1.4821721935139701191 ,1.2671842889111625632 ] 
dist 246=[-1.4976695968394394230 ,1.2637495604967652006 ] 
dist 247=[-1.5070296355363419712 ,1.2173815984641878797 ] 
dist 248=[-1.5074775949484510893 ,1.2047238931162398000 ] 
dist 249=[-1.5007163566335388897 ,1.1915632741219513550 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 0, 0, 2, 1, 1, 2] 
dist 0=[52.167284466535583798  ,52.167284466535583798  ] 
dist 1=[51.823757768812988910  ,52.258425126372981626  ] 
dist 2=[51.189267252090463898  ,52.278709439024427741  ] 
dist 3=[49.990205219004286514  ,52.277698709137912728  ] 
dist 4=[48.645768795907965912  ,52.246222232816512482  ] 
dist 5=[47.430665812722159638  ,52.208485093269745630  ] 
dist 6=[46.074823352724142008  ,52.182620045538106116  ] 
dist 7=[44.168036167757099912  ,52.062718938497265892  ] 
dist 8=[42.046772747342857091  ,50.929652889159861527  ] 
dist 9=[39.834149584142104827  ,48.140962975753598721  ] 
dist 10=[37.124451634194206253  ,47.625183476685532498  ] 
dist 11=[33.017620929148496098  ,46.209222342880006479  ] 
dist 12=[28.882859078458678721  ,45.996559687455989668  ] 
dist 13=[26.061492049977247640  ,44.657272525863042455  ] 
dist 14=[23.653683747572188363  ,42.703027737456535535  ] 
dist 15=[21.170590731713515670  ,42.167644606711917655  ] 
dist 16=[18.819563802039039202  ,42.036553696330526284  ] 
dist 17=[16.939058534626335557  ,35.234782338171672119  ] 
dist 18=[15.036392582146665486  ,34.341655641122818708  ] 
dist 19=[12.596436667113207990  ,32.626043048366425171  ] 
dist 20=[10.223041983296144813  ,32.186541634094748976  ] 
dist 21=[8.5860339513739445813 ,30.675166106160775141  ] 
dist 22=[7.1679393100874736332 ,30.304254658231431276  ] 
dist 23=[5.6687435615595337439 ,29.880438651140885623  ] 
dist 24=[4.2226110495626535901 ,29.722021053773280832  ] 
dist 25=[2.9970094532038265905 ,11.847874980046076617  ] 
dist 26=[1.7180592816983475582 ,10.381278643202650640  ] 
dist 27=[.04669240312022116591,7.1881934551038744373 ] 
dist 28=[-1.5975275545783022388 ,6.4728491178702262077 ] 
dist 29=[-2.6460351771943122394 ,6.0443867224147271209 ] 
dist 30=[-3.4668545435978646192 ,1.3630159256489943063 ] 
dist 31=[-4.2007288535433098227 ,.30374000317341058693] 
dist 32=[-5.4691875995584489940 ,.05055650181503180248] 
dist 33=[-7.3147154584451308434 ,-4.3171020582943074498 ] 
dist 34=[-8.4712232306546493096 ,-4.7841422247220886249 ] 
dist 35=[-9.3481601265200819328 ,-4.8127960485038516988 ] 
dist 36=[-10.077074539738576976  ,-4.6974547147373936030 ] 
dist 37=[-10.663596938614043751  ,-4.3604082727134483700 ] 
dist 38=[-10.971701761260651070  ,-3.9511714730871830027 ] 
dist 39=[-11.138589328037191525  ,-3.5473586683097677470 ] 
dist 40=[-11.173751461138598897  ,-3.0724183438925071008 ] 
dist 41=[-9.6548282674556116673 ,-2.3786513444309018384 ] 
dist 42=[-9.5604837405199946586 ,-1.5988658461939180160 ] 
dist 43=[-9.2607145949158229403 ,-.78028525115739758736] 
dist 44=[-9.2149275656995553320 ,.22305702728939978181] 
dist 45=[-8.5232051051207072714 ,1.7405795968124757903 ] 
dist 46=[-8.3727853128328129957 ,3.2561916401140277476 ] 
dist 47=[-8.2386731256713294161 ,4.2520306659615985595 ] 
dist 48=[-8.2044943801460379463 ,5.0580693760269261369 ] 
dist 49=[-7.0639881407131767747 ,5.8161998100274780363 ] 
dist 50=[-7.0214111895754772028 ,6.4860121226407742082 ] 
dist 51=[-6.9743066822699027601 ,6.9395960588149878783 ] 
dist 52=[-6.7236884629714335727 ,7.3221084860496361280 ] 
dist 53=[-6.0940891580896562045 ,7.7083381921569556691 ] 
dist 54=[-4.9144681419383157007 ,8.0469059730184771900 ] 
dist 55=[-4.7899585793469698107 ,8.2391316683866818951 ] 
dist 56=[-4.7463949598568807382 ,8.3612457392730068759 ] 
dist 57=[-.32128918371222558022,8.4197354974013489279 ] 
dist 58=[.04184956038289763602,8.4381741616712671566 ] 
dist 59=[.06454951679014753861,8.4286553055520449599 ] 
dist 60=[.9930002674446600379 ,8.3495729647628090056 ] 
dist 61=[1.1680353233042316370 ,8.3154539856272145286 ] 
dist 62=[1.3559963937393721522 ,5.6434139211566088278 ] 
dist 63=[1.3868961579912512109 ,5.3790031590430069687 ] 
dist 64=[1.5726089877277556854 ,4.7509468729818730978 ] 
dist 65=[1.6008909468348400005 ,4.6314627531150781535 ] 
dist 66=[1.6487010576404219028 ,4.7945901993852963313 ] 
dist 67=[1.6565468958047755758 ,5.0123581944133637707 ] 
dist 68=[1.6522294639074977086 ,5.1886855604385071054 ] 
dist 69=[1.5822274496282187176 ,5.3254693332977780575 ] 
dist 70=[.81451699086206028712,5.3853000350144834748 ] 
dist 71=[.25577195363047769273,5.4115803065837106447 ] 
dist 72=[-.25747975900479658163,5.4143604643231262107 ] 
dist 73=[-.84367288301873435466,2.1376366194795334110 ] 
dist 74=[-1.4329528503577991530 ,2.0588669822484942638 ] 
dist 75=[-1.9586142805891115365 ,2.0353149898923195413 ] 
dist 76=[-2.5393402362993289395 ,1.3201000282706611478 ] 
dist 77=[-3.3486041329463200783 ,1.2710858874556673053 ] 
dist 78=[-4.1396481102456079094 ,1.1539639880858110435 ] 
dist 79=[-4.6476497043875336235 ,1.1323614753759380816 ] 
dist 80=[-5.0467023482167864669 ,.96271050023648258733] 
dist 81=[-5.4026844242549855954 ,.93019683872261498341] 
dist 82=[-5.7047655116267125633 ,.88039896833777049973] 
dist 83=[-5.8885869386008582851 ,.86659817058569496625] 
dist 84=[-6.0215155854738639133 ,.60187958861537126516] 
dist 85=[-6.1203976141080699016 ,.56700015119270364438] 
dist 86=[-6.1923903895834034439 ,.65761935147603678506] 
dist 87=[-6.2179458721678579882 ,.87989491728145992654] 
dist 88=[-6.2161782700685623223 ,1.1199475884891421191 ] 
dist 89=[-6.2068340164341752656 ,1.4469720046430387867 ] 
dist 90=[-6.1124465900400094359 ,1.8049550793067191383 ] 
dist 91=[-6.0808964381354103024 ,2.1686212728465700849 ] 
dist 92=[-5.9854241555442899719 ,2.6062822588221366312 ] 
dist 93=[-5.9456981834029640916 ,3.2596737797519749883 ] 
dist 94=[-3.0664413686035875955 ,3.9089619487897391882 ] 
dist 95=[-3.0753357062269143144 ,4.3302549452687961145 ] 
dist 96=[-3.0741065282985305929 ,4.6654697213931745648 ] 
dist 97=[-2.7472221469145899503 ,4.9711496780196627983 ] 
dist 98=[-2.6973957856524435704 ,5.2346825374045233715 ] 
dist 99=[-2.6119170955610695872 ,5.4016548547803241983 ] 
dist 100=[-2.5881534585376902074 ,5.5299909901980114757 ] 
dist 101=[-2.5119374658857936787 ,5.6392984564652407968 ] 
dist 102=[-2.4865848813763964018 ,5.7217258425184658623 ] 
dist 103=[-2.4642402890586187816 ,5.7427575091049332046 ] 
dist 104=[-2.4502438586179055211 ,5.7401373096629589770 ] 
dist 105=[-1.7662326465503525067 ,5.7281430351623360057 ] 
dist 106=[-2.2439356138590322571 ,5.5509517836687064681 ] 
dist 107=[-2.9615600323357636163 ,5.4976008078379834273 ] 
dist 108=[-3.6774538064194803118 ,5.4427311698929293231 ] 
dist 109=[-4.1482434297755788189 ,5.4096860057089033127 ] 
dist 110=[-4.5300130173558001124 ,5.4924258503575741020 ] 
dist 111=[-4.8905226910485987392 ,5.5344070026611639445 ] 
dist 112=[-5.2100778888839402116 ,5.5468649929843053106 ] 
dist 113=[-5.4283459119793623941 ,5.5382722968286863088 ] 
dist 114=[-5.6143497945326089123 ,5.4143521543445330860 ] 
dist 115=[-5.8050892057902056136 ,5.3723294502386835703 ] 
dist 116=[-5.9666521812928011519 ,5.3257966020663966395 ] 
dist 117=[-6.0361749481715334979 ,5.2984138899499015226 ] 
dist 118=[-6.0663333686713126249 ,4.5055871838244962316 ] 
dist 119=[-6.0707817599212012461 ,4.3898461594896002376 ] 
dist 120=[-5.9285179870652624048 ,4.1553899628214866331 ] 
dist 121=[-5.8885805952627709304 ,4.0887681229363730279 ] 
dist 122=[-5.8618377773595260818 ,3.8207569221656390130 ] 
dist 123=[-5.7226007706406660651 ,3.7606510653345499725 ] 
dist 124=[-4.7912564384275195722 ,3.6206085081200320925 ] 
dist 125=[-4.5001991980077765103 ,3.5741918822088282361 ] 
dist 126=[-1.1930376519362276978 ,3.0889268155953519492 ] 
dist 127=[-1.3611386059023019931 ,3.0910785803766371727 ] 
dist 128=[-1.5881079717766174281 ,3.0872083311994581307 ] 
dist 129=[-1.8131648333994201156 ,2.7268209047363251222 ] 
dist 130=[-1.9736344913636080117 ,2.6729187324270389731 ] 
dist 131=[-2.1176690338178439080 ,2.5777197826138700433 ] 
dist 132=[-2.2771195660766754911 ,2.5526028181795474607 ] 
dist 133=[-2.4344704747848649170 ,2.4673175625665526663 ] 
dist 134=[-2.5701275717227563164 ,2.4405388253808665023 ] 
dist 135=[-2.7160259610772093456 ,2.4126208133067096801 ] 
dist 136=[-2.9142700751894484790 ,2.3973277042403530523 ] 
dist 137=[-3.1045043023226788656 ,1.3059596499462691326 ] 
dist 138=[-3.2184259407792153552 ,1.2909855902835656040 ] 
dist 139=[-3.2983901236418152592 ,1.2829947790436277564 ] 
dist 140=[-3.3530524508033260877 ,1.1122211314731393068 ] 
dist 141=[-3.3889725700214906011 ,1.0950672333971441402 ] 
dist 142=[-3.3955634185808457580 ,1.0481885208791233123 ] 
dist 143=[-3.3883574506270018354 ,1.0394827818767406906 ] 
dist 144=[-3.3808103106603183902 ,.94855004853376424441] 
dist 145=[-3.2066975124588259222 ,.92905234113670575521] 
dist 146=[-3.1722574648088119916 ,.90627438311072675222] 
dist 147=[-3.0884110229457955472 ,.89674368376081010822] 
dist 148=[-3.0579896879124068599 ,.67399581315780834641] 
dist 149=[-2.9047146675363147377 ,.64379884540846906968] 
dist 150=[-2.8683782629154038927 ,.5819455980804409221 ] 
dist 151=[-2.7879421732597540111 ,.56513671046314731118] 
dist 152=[-2.7607367823555248278 ,.50056105913253657851] 
dist 153=[-2.6720957575161672603 ,.80773574767595192148] 
dist 154=[-2.7115368403309808808 ,1.2582471077869274585 ] 
dist 155=[-2.7304048804004510582 ,1.6260859303873788786 ] 
dist 156=[-2.7329498534444977310 ,1.9778574920105482016 ] 
dist 157=[-2.7102727814712044540 ,2.2928439659928738556 ] 
dist 158=[-2.6978943932643381615 ,2.5138181158708145841 ] 
dist 159=[-2.6762216977906557682 ,2.7084858706301210828 ] 
dist 160=[-2.6665696195676895416 ,2.9184414400823079097 ] 
dist 161=[-2.3681154278587031676 ,3.1095003074434348764 ] 
dist 162=[-2.3218184966647126101 ,3.2287240294548195946 ] 
dist 163=[-2.2238769377884936772 ,3.3182768445773458089 ] 
dist 164=[-2.1941655145825230752 ,3.3908803742482304857 ] 
dist 165=[-2.0638509297673255082 ,3.4471161415591666465 ] 
dist 166=[-2.0364317599656753477 ,3.4713239514577031012 ] 
dist 167=[-1.9562896284011253303 ,3.4771423576571553740 ] 
dist 168=[-1.9437925784587034855 ,3.4744525170465178966 ] 
dist 169=[-1.1519729739157561707 ,.28188801241861489647] 
dist 170=[-1.2199420575564738569 ,.45867478437455876106] 
dist 171=[-1.3120265825367262035 ,.60383459360418717776] 
dist 172=[-1.3999421384309008462 ,.74405200258183156935] 
dist 173=[-1.4512658445845904128 ,.87058278180130302315] 
dist 174=[-1.4856607581856641811 ,.96109835070207924649] 
dist 175=[-1.5059886259572987458 ,1.0426916247994473680 ] 
dist 176=[-1.5187493504281604574 ,1.1336013779039402074 ] 
dist 177=[-1.5229335772618466756 ,1.2166951306913842102 ] 
dist 178=[-1.5216341583388367126 ,1.2670820635939271386 ] 
dist 179=[-1.5188748386753823265 ,1.3032311659237183332 ] 
dist 180=[-1.3863953208165057122 ,1.3294763027089892944 ] 
dist 181=[-1.3645888838339629811 ,1.3477737102788882936 ] 
dist 182=[-1.3229283520561146119 ,1.3759608618960268575 ] 
dist 183=[-1.3106043155893588390 ,1.4273875052933789197 ] 
dist 184=[-1.2599579028899693622 ,1.4740749147054933970 ] 
dist 185=[-1.2469266358149375948 ,1.5079601449100568748 ] 
dist 186=[-1.2163262032349421658 ,1.5390032656296784030 ] 
dist 187=[-1.2053252386222770795 ,1.5743424818023245907 ] 
dist 188=[-.44140081838502860822,1.6054159359388811590 ] 
dist 189=[-.37306399010138725185,1.6194270348578957656 ] 
dist 190=[-.21860597360025274626,1.6241901031711808213 ] 
dist 191=[-.1892770793728020859 ,1.6234200675733906346 ] 
dist 192=[-.13394601544138773899,1.6031580817786050463 ] 
dist 193=[-.28304661578941604288,1.5950989007347496120 ] 
dist 194=[-.3926381327813826226 ,1.5762141298691156627 ] 
dist 195=[-.49441523326659880071,1.5679340341998551684 ] 
dist 196=[-.61231776019143977688,1.4109578864035571533 ] 
dist 197=[-.73175123496020248848,1.3857029568531059914 ] 
dist 198=[-.83964202507767422229,1.3271015038346834160 ] 
dist 199=[-.95988963288105704607,1.3082111896271310619 ] 
dist 200=[-1.1286608119475313570 ,1.2196555332526514354 ] 
dist 201=[-1.2937420943010690842 ,1.2001456032041500817 ] 
dist 202=[-1.3992578346494276190 ,1.1567259176607150407 ] 
dist 203=[-1.4814854564936156284 ,1.1427144350341713570 ] 
dist 204=[-1.5535859527031251283 ,.56480622191884058163] 
dist 205=[-1.6137725814631310210 ,.51508213326354066293] 
dist 206=[-1.6484328483064118400 ,.51102681447099439063] 
dist 207=[-1.6710795543872317407 ,.50954831921650410597] 
dist 208=[-1.6833013469012129240 ,.48953879016628039455] 
dist 209=[-1.6889664748543024749 ,.48422772689534263286] 
dist 210=[-1.6875410419120941179 ,.47879348903551480137] 
dist 211=[-1.6783006798479430167 ,.47572498351114063288] 
dist 212=[-1.6713109005694717994 ,.39270405709207621807] 
dist 213=[-1.6241484076849204500 ,.38090465315024158461] 
dist 214=[-1.6105932017666192292 ,.35745781452007147346] 
dist 215=[-1.5829351206714052402 ,.35100663462303573572] 
dist 216=[-1.5223341924241329576 ,.32621284960661079462] 
dist 217=[-1.0841989780189592132 ,.32048361699482086368] 
dist 218=[-1.0319158216111139909 ,.30879915279098738889] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 0, 1, 1, 1, 2] 
dist 0=[53.023821059399913166  ,53.023821059399913166  ] 
dist 1=[52.428044277130899935  ,53.296301438274206074  ] 
dist 2=[51.700788491276584758  ,53.395465143008777101  ] 
dist 3=[50.903222850899285040  ,53.385135646385168215  ] 
dist 4=[49.899594206330343064  ,53.029888977826181265  ] 
dist 5=[48.349209535500196880  ,52.878663171708086922  ] 
dist 6=[46.561082730433412311  ,52.550302627210689492  ] 
dist 7=[44.607845032431249943  ,52.406743533899814648  ] 
dist 8=[42.154232461315252758  ,51.475182249083670637  ] 
dist 9=[38.367517082610603000  ,49.116224241664381205  ] 
dist 10=[34.530245021541147544  ,48.382690769243503390  ] 
dist 11=[31.874631715332973420  ,48.132498765074444532  ] 
dist 12=[29.568851776441504210  ,47.903028492629654624  ] 
dist 13=[27.128673106349695046  ,47.021785598485817048  ] 
dist 14=[24.780173567532733392  ,42.369521877741386209  ] 
dist 15=[22.840393192646719505  ,39.352433995049901932  ] 
dist 16=[20.822236890054737076  ,35.605535536662572206  ] 
dist 17=[18.160347059338369425  ,28.583680021201609720  ] 
dist 18=[15.537778346348731328  ,27.682332467151457197  ] 
dist 19=[13.676487021686553781  ,25.874475666044812870  ] 
dist 20=[12.009440511819494144  ,25.405122583099738897  ] 
dist 21=[10.162494133775415265  ,23.720125875051912341  ] 
dist 22=[8.3314344136648272037 ,23.354187091074441557  ] 
dist 23=[6.7274673783800722118 ,22.775413856459638907  ] 
dist 24=[4.4317063506978413819 ,22.620161144895893839  ] 
dist 25=[2.5478293212385453581 ,11.546094030563589814  ] 
dist 26=[.1720829234800398410 ,7.7147239669445917527 ] 
dist 27=[-1.3771072685348215572 ,7.1688355734066983364 ] 
dist 28=[-2.6260389908692752009 ,6.7872493688498714101 ] 
dist 29=[-3.8017244284073849437 ,6.3233635970249239604 ] 
dist 30=[-4.8486264513371843762 ,4.4794580603409035796 ] 
dist 31=[-6.1113673737674497139 ,3.6345183737488286763 ] 
dist 32=[-7.6643656559918553432 ,.1163662145502837601 ] 
dist 33=[-9.1041464919739254077 ,-1.7741718366852889976 ] 
dist 34=[-9.9797326979364909293 ,-2.0541099389758091223 ] 
dist 35=[-10.612732063040028001  ,-2.3079987219846769951 ] 
dist 36=[-11.083752912385228288  ,-2.2362988793681191906 ] 
dist 37=[-11.442336266952036070  ,-2.0248832261705249435 ] 
dist 38=[-11.626092995783468531  ,-1.6303770046678601706 ] 
dist 39=[-11.717658113157478760  ,-1.0305079024541029577 ] 
dist 40=[-11.718109030884195006  ,0                     ] 
dist 41=[-10.240993915567488604  ,-3.1531300937713941899 ] 
dist 42=[-10.080641454743883693  ,-1.9914663386513390126 ] 
dist 43=[-10.008420744399345606  ,-1.1855510407672186592 ] 
dist 44=[-9.6002473306192229723 ,-.48629531405191220779] 
dist 45=[-9.4964479503183102875 ,.24987437680405376963] 
dist 46=[-9.2810113521074528124 ,.95340556534909674109] 
dist 47=[-9.2088625658396936196 ,1.5225108833581855053 ] 
dist 48=[-5.9095136722718250754 ,2.1987476051055974411 ] 
dist 49=[-5.5600136482669555662 ,3.6233387295642607581 ] 
dist 50=[-4.8526338742099705581 ,4.7835376567198637902 ] 
dist 51=[-4.6720549164740444355 ,5.8865914693827010050 ] 
dist 52=[-4.0133180276896661386 ,6.8685660709805726753 ] 
dist 53=[-2.8794903997170083018 ,7.5453939975496952984 ] 
dist 54=[-2.4979349524155775693 ,8.1280995453324176290 ] 
dist 55=[-2.4072928860565485868 ,8.7342139647284247935 ] 
dist 56=[-2.2886068619701381931 ,9.2801331664658237239 ] 
dist 57=[-2.2539462951938501170 ,9.6226057998663957319 ] 
dist 58=[1.2218581168942918756 ,9.8813507338209117630 ] 
dist 59=[1.4915216253664383671 ,10.093352672166835506  ] 
dist 60=[2.0913844707518043723 ,10.259421190837038339  ] 
dist 61=[2.1882990136443886141 ,10.335026241026569908  ] 
dist 62=[2.8655770340010502403 ,10.359522020419295188  ] 
dist 63=[2.9740819970223652806 ,10.343783552232973648  ] 
dist 64=[3.1671563734644164508 ,6.8164747109927913227 ] 
dist 65=[3.2030093206565874015 ,6.7955815369524746636 ] 
dist 66=[3.5210737250139355095 ,6.0361613859865808863 ] 
dist 67=[3.3855385048125479874 ,5.9187888462155519752 ] 
dist 68=[2.6819446436268689172 ,5.6862837749232086760 ] 
dist 69=[2.0977705598035508903 ,5.6186981856248936808 ] 
dist 70=[1.4889148975623540938 ,5.3426196742058507336 ] 
dist 71=[.6866686709874156494 ,5.2768167652372808850 ] 
dist 72=[-.0998220114580911900 ,5.1212022498081173400 ] 
dist 73=[-.6458534342914147167 ,5.0672012866917932764 ] 
dist 74=[-1.1209243270887575238 ,3.3684276876947423218 ] 
dist 75=[-1.6242306425933821600 ,3.2719476067592476635 ] 
dist 76=[-2.1082219608216081681 ,3.0401729394146130061 ] 
dist 77=[-2.6384948595524152073 ,2.9899763389985253474 ] 
dist 78=[-3.2267781713913737351 ,2.6411516688414363631 ] 
dist 79=[-3.6555640698079033096 ,2.5713149170808004013 ] 
dist 80=[-4.0501409609703028839 ,2.4494958352750455242 ] 
dist 81=[-4.5018287001503495951 ,2.4189010929836198642 ] 
dist 82=[-4.9191770101182622706 ,1.8239749082475053188 ] 
dist 83=[-5.1766541116379513092 ,1.7429309995542968511 ] 
dist 84=[-5.3666096907057130169 ,1.5490553709888476585 ] 
dist 85=[-5.5143958590026432108 ,1.5138880493422429179 ] 
dist 86=[-5.6242763348206083416 ,1.2338215748732526850 ] 
dist 87=[-5.6628860942391155391 ,1.1805790560008393722 ] 
dist 88=[-5.6744283538505130618 ,1.0995606682323434341 ] 
dist 89=[-5.6762559187575253358 ,1.0771538730810568760 ] 
dist 90=[-5.4510038987775300749 ,-.06450449346026098202] 
dist 91=[-5.4421223877361689520 ,.40454288404064193846] 
dist 92=[-5.2841952711105355921 ,.9149456249719440454 ] 
dist 93=[-5.2375546187453647756 ,1.4293192107391434852 ] 
dist 94=[-5.1940192427398788580 ,2.0454646306115642187 ] 
dist 95=[-5.1652625742487905796 ,2.9621814316076793240 ] 
dist 96=[-3.5098320972482216186 ,3.8735886841290132952 ] 
dist 97=[-3.6188706921104982449 ,4.4685545210305359216 ] 
dist 98=[-3.7105815314495924737 ,4.9461123438795852089 ] 
dist 99=[-3.7614033162261435804 ,5.3888337089564904876 ] 
dist 100=[-3.7921076746750607536 ,5.7757187178652965758 ] 
dist 101=[-3.8034884988316876852 ,6.0303848508365502651 ] 
dist 102=[-3.8016228506914319835 ,6.2372150030346550441 ] 
dist 103=[-3.7954930539750364979 ,6.4331531509072173757 ] 
dist 104=[-3.7549523214147748482 ,6.5955983249462725354 ] 
dist 105=[-3.7439150900293148600 ,6.6687214750928340062 ] 
dist 106=[-3.2696664654420911076 ,6.6975343134743356166 ] 
dist 107=[-3.7323773794237276843 ,6.6933951675618958876 ] 
dist 108=[-4.1162852528194177716 ,6.5868337462975833438 ] 
dist 109=[-4.4934988831462925139 ,6.5446128579717553688 ] 
dist 110=[-4.8379244561412964956 ,6.4760895916291758899 ] 
dist 111=[-5.0909318897019291068 ,6.3867758782513799644 ] 
dist 112=[-5.3256352012400495005 ,5.5359034011520619814 ] 
dist 113=[-5.5969792971127589741 ,5.4593083871015355159 ] 
dist 114=[-5.8453121319996897697 ,5.2313451869518194119 ] 
dist 115=[-5.9881466187684010264 ,5.1982651042667616098 ] 
dist 116=[-6.0811311892556477122 ,4.7085278346184087963 ] 
dist 117=[-6.1304512598406973583 ,4.6034949924239242297 ] 
dist 118=[-6.1509210619692521500 ,4.5127950085937374275 ] 
dist 119=[-6.1475503140820902971 ,4.4936932609306003517 ] 
dist 120=[-6.0965724586393994706 ,3.1815479426343863388 ] 
dist 121=[-6.0771572979628517277 ,3.0120617231434663803 ] 
dist 122=[-5.6951857776733151892 ,3.1805536318219309926 ] 
dist 123=[-5.6258203013836564879 ,3.3090238110209081571 ] 
dist 124=[-5.4246446337617170862 ,3.3961693464706210565 ] 
dist 125=[-5.3840802487300443309 ,3.4499189098275539620 ] 
dist 126=[-4.9508632887861087962 ,3.4854959446930856746 ] 
dist 127=[-4.6787053174236114835 ,3.5000791115206316702 ] 
dist 128=[-.94691842175507677609,3.5021071625502464923 ] 
dist 129=[-1.4391291654601209423 ,3.4963315964478306094 ] 
dist 130=[-1.8421515645148538197 ,3.1916134399937756609 ] 
dist 131=[-2.2295205446331803801 ,3.1418973525795915893 ] 
dist 132=[-2.5777561666278375894 ,3.0505047248482351338 ] 
dist 133=[-2.8245427152187206259 ,3.0242785348776074095 ] 
dist 134=[-3.0446031968699876062 ,2.9220793725861294001 ] 
dist 135=[-3.2861431967113574745 ,2.8934866154597299465 ] 
dist 136=[-3.5056270641767938003 ,2.8356726156440390800 ] 
dist 137=[-3.6376282792038287593 ,2.8160067061165785226 ] 
dist 138=[-3.7310122467034819198 ,1.3662935562619947176 ] 
dist 139=[-3.7963081175478909963 ,1.2554600573934109326 ] 
dist 140=[-3.8398378275604171929 ,.9905277334449268710 ] 
dist 141=[-3.8486787286792783987 ,.9489817381372888885 ] 
dist 142=[-3.8404275735849698671 ,.5759432087057864976 ] 
dist 143=[-3.8345544410541011886 ,.50775772838804292964] 
dist 144=[-2.8793860358441488523 ,.4167643690268746932 ] 
dist 145=[-2.7829541282832364782 ,.3915104803735663021 ] 
dist 146=[-2.5538437582430795934 ,-.12440119217479301853] 
dist 147=[-2.5035754637986948080 ,-.18765218192582059296] 
dist 148=[-2.2010208501334088045 ,-.32787996806523815971] 
dist 149=[-2.2903253417821622430 ,-.1209030425613965854 ] 
dist 150=[-2.3627542650643941528 ,.1775033639001099566 ] 
dist 151=[-2.4005318233210790323 ,.5853176203542275040 ] 
dist 152=[-2.4202219615829157699 ,.9921033086259617787 ] 
dist 153=[-2.4231082077916224159 ,1.2864080676917018584 ] 
dist 154=[-1.3773822476936402311 ,1.5550208253135576166 ] 
dist 155=[-1.4701236133388389363 ,1.8592400771294193566 ] 
dist 156=[-1.5401288884777023153 ,2.1635211156054985199 ] 
dist 157=[-1.5975469727971095062 ,2.4323869705083770763 ] 
dist 158=[-1.6425707378361531023 ,2.7271598493179727518 ] 
dist 159=[-1.6630891243890622493 ,3.1348848134283711671 ] 
dist 160=[-1.6725673534188350672 ,3.5307860140110943016 ] 
dist 161=[-1.6735109931093884611 ,3.7783544227787588389 ] 
dist 162=[-1.6423942819065010065 ,3.9649967464614228581 ] 
dist 163=[-1.6326889903842738384 ,4.1176460794537749130 ] 
dist 164=[-1.6114867957007803764 ,4.2370062611723399142 ] 
dist 165=[-1.6027970854533092111 ,4.2907406648412885100 ] 
dist 166=[-1.5557398451517281814 ,4.3157094905624496979 ] 
dist 167=[-1.5439358088003994542 ,4.3202118787869315566 ] 
dist 168=[-1.5073250603705348986 ,4.2301338936574415499 ] 
dist 169=[-1.6893655512601766794 ,4.2034552574005692380 ] 
dist 170=[-1.8725666975389961346 ,4.1478435180070281940 ] 
dist 171=[-1.9938416849664766539 ,4.1257101640819994974 ] 
dist 172=[-2.0930879085152247474 ,4.0077759798525358843 ] 
dist 173=[-2.1883442338551752707 ,3.9785492048944088930 ] 
dist 174=[-2.2738427684839762608 ,3.8800699170875567693 ] 
dist 175=[-2.3341325913665425136 ,3.8621476167802178199 ] 
dist 176=[-2.3875510442414173464 ,3.3106369315525436558 ] 
dist 177=[-2.4456152919561609225 ,3.3514258454657925489 ] 
dist 178=[-2.4967931713685547138 ,3.3782537627333531397 ] 
dist 179=[-2.5227188093146488752 ,3.3846162601149215635 ] 
dist 180=[-2.5351196012176294008 ,3.3783740599779935354 ] 
dist 181=[-2.5340349390455423318 ,3.3712637892083511554 ] 
dist 182=[-2.5208631554735642215 ,3.3128875499618591666 ] 
dist 183=[-2.6581098641910322159 ,3.2945806929579506314 ] 
dist 184=[-2.9641057877259195436 ,3.2370891064177753984 ] 
dist 185=[-3.1513120395703465480 ,3.2166356795992442748 ] 
dist 186=[-3.2875699311966328396 ,2.0302553784928388797 ] 
dist 187=[-3.3901512651029789528 ,1.9126197716475537338 ] 
dist 188=[-3.4683009017780751065 ,1.6311739575761676176 ] 
dist 189=[-3.5070153070678340373 ,1.5824345188785492119 ] 
dist 190=[-3.5242981221348692982 ,1.1795142644582690643 ] 
dist 191=[-3.5244724688337415818 ,1.1039963052606576311 ] 
dist 192=[-1.9472432582794648190 ,1.0363442651997969351 ] 
dist 193=[-1.9279860243082841965 ,1.0245886312602305819 ] 
dist 194=[-1.6550113930432410761 ,.89918824212768570302] 
dist 195=[-1.7911583353752151898 ,.87893184105583709461] 
dist 196=[-1.9105856196675418376 ,.82688326131843688176] 
dist 197=[-1.9901065304852475413 ,.81704519981752023685] 
dist 198=[-2.0557295267415595421 ,.77240570024161402275] 
dist 199=[-2.1196687406930038132 ,.80360308210407687495] 
dist 200=[-2.1733001873206471522 ,.83827317869830909151] 
dist 201=[-2.1977685790194432058 ,.97153033916161753796] 
dist 202=[-2.2081814422797902789 ,1.4338065928278538200 ] 
dist 203=[-2.2071803006833700366 ,1.7356799577446288252 ] 
dist 204=[-2.1743083846646116394 ,1.9781743906666770954 ] 
dist 205=[-2.2932203848760610847 ,2.2033884988401827631 ] 
dist 206=[-2.4162330819191904297 ,2.4005300799004498540 ] 
dist 207=[-2.4979623394177246319 ,2.5309484941184664630 ] 
dist 208=[-2.5652027355501652846 ,2.6375970765504538006 ] 
dist 209=[-2.6303705635615102670 ,2.7398398737157633731 ] 
dist 210=[-2.6834203821053166034 ,2.8279395905834204092 ] 
dist 211=[-2.7022804587028252734 ,2.8781238256878925119 ] 
dist 212=[-2.7079611856919165183 ,2.9101876974995569923 ] 
dist 213=[-2.7083893385935995196 ,2.9259452283039641475 ] 
dist 214=[-2.6302738704589404108 ,2.9300207495638917735 ] 
dist 215=[-2.6092674833782729592 ,2.9271420875147776277 ] 
dist 216=[-2.5959649961067218223 ,2.8980301271487647257 ] 
dist 217=[-2.5896767524709665255 ,2.8907643782679333531 ] 
dist 218=[-1.9898398023425020549 ,2.8138522543904256099 ] 
dist 219=[-1.9817723512055190528 ,2.8149354397564864671 ] 
dist 220=[-1.8681727484974249835 ,2.7828349550901241326 ] 
dist 221=[-1.8409688050838746177 ,2.7677761440909535921 ] 
dist 222=[-1.8151655714673697612 ,2.7473798094776357460 ] 
dist 223=[-1.8028009151437533332 ,2.7361782664798504490 ] 
dist 224=[-1.4153705119670684764 ,2.1160040119581072194 ] 
dist 225=[-1.3647054466120819388 ,2.1184993088156916785 ] 
dist 226=[-1.2441811421506403042 ,2.1110804153658843811 ] 
dist 227=[-1.2182568951148754182 ,2.1055440894067256721 ] 
dist 228=[-1.0415423156529431010 ,2.0371669999824637852 ] 
dist 229=[-1.0065940211926098785 ,2.0177267512976991968 ] 
dist 230=[-.9445421030780927727 ,1.9960162193939150760 ] 
dist 231=[-.9292267948910009729 ,1.9843907162623724853 ] 
dist 232=[-.6444089342738956691 ,1.6645194014068604748 ] 
dist 233=[-.6058781731685502617 ,1.6184366542710226257 ] 
dist 234=[-.5116351897608423133 ,1.5255349086166163961 ] 
dist 235=[-.4969332700748683170 ,1.4994562752896235424 ] 
dist 236=[-.3561677623426366281 ,1.3961193744351088994 ] 
dist 237=[-.3296949094033549072 ,1.3728683000505221873 ] 
dist 238=[-.4466085347984219822 ,1.3207515044722850415 ] 
dist 239=[-.7316692688685011827 ,1.3039675402062591930 ] 
dist 240=[-1.0132901517823746092 ,1.2084043301608024752 ] 
dist 241=[-1.2014779331102145830 ,1.3778027795596098475 ] 
dist 242=[-1.3574775175071324263 ,1.5133133226934935287 ] 
dist 243=[-1.5105896927486914661 ,1.6381777158359285268 ] 
dist 244=[-1.6503424879995138766 ,1.7467714141927385827 ] 
dist 245=[-1.7530064793725058049 ,1.8173253828855879528 ] 
dist 246=[-1.8482893853769354404 ,1.8735852190830115960 ] 
dist 247=[-1.9585756607260656326 ,1.9251126268949075621 ] 
dist 248=[-2.0596794292011010166 ,1.9674197859729761539 ] 
dist 249=[-2.1183024163267187916 ,1.9868698522302274519 ] 
dist 250=[-2.1571089764314526655 ,1.9940085606250490944 ] 
dist 251=[-2.1790968709053184307 ,1.9933688954900805863 ] 
dist 252=[-2.1906727919384266053 ,1.9683502023225479038 ] 
dist 253=[-2.1903974385949455525 ,1.9580846599274299321 ] 
dist 254=[-2.1798264811565199203 ,1.9348959123241224691 ] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 2, 2, 2, 1, 0, 1] 
dist 0=[53.157456738126324375  ,53.157456738126324375  ] 
dist 1=[52.901775743967563452  ,53.212394917812418209  ] 
dist 2=[52.499061385098749769  ,53.164886584683833417  ] 
dist 3=[51.856995327780644561  ,53.090555763757451674  ] 
dist 4=[50.915423386076216355  ,52.674838411418866609  ] 
dist 5=[49.316362424895005389  ,52.373379788457218932  ] 
dist 6=[47.578058213574797743  ,52.293160370189028641  ] 
dist 7=[46.080250242120340589  ,51.605773963969214723  ] 
dist 8=[44.467898818388118800  ,49.519954379333507661  ] 
dist 9=[42.271932601874146345  ,47.230429360269441263  ] 
dist 10=[39.861322790239757603  ,46.726159455812581250  ] 
dist 11=[37.391541039842151545  ,46.316721878331507036  ] 
dist 12=[34.398085339100227005  ,46.224697519834048762  ] 
dist 13=[29.895665695323125215  ,43.928909155025155141  ] 
dist 14=[25.375775583765749090  ,43.803117700818430279  ] 
dist 15=[22.312445403694189737  ,43.090218674428950768  ] 
dist 16=[19.720414882436039552  ,36.577598043640075944  ] 
dist 17=[17.082860374990139144  ,35.161030540138853196  ] 
dist 18=[14.607727424250764157  ,34.791884879957897334  ] 
dist 19=[12.664265026464635709  ,34.456687121316923634  ] 
dist 20=[10.731184429856574141  ,34.366576663958338111  ] 
dist 21=[8.2971238903756120849 ,14.862327757198937678  ] 
dist 22=[5.9509352548273691415 ,13.283897646349006792  ] 
dist 23=[4.3686454066085997244 ,11.334025193738591437  ] 
dist 24=[3.0361098473773613293 ,9.0656948129707401965 ] 
dist 25=[1.6873261032963701083 ,5.3154537188939525749 ] 
dist 26=[.42245597034899435337,3.9635281286806106102 ] 
dist 27=[-.57528070271361331323,3.7223172844233689538 ] 
dist 28=[-2.4039320318207697926 ,2.5319682063082299452 ] 
dist 29=[-4.4130359748048288059 ,2.4619967506859132568 ] 
dist 30=[-5.6798089934597990959 ,2.1070975183068095167 ] 
dist 31=[-6.6492285014990712658 ,1.9180482217232516441 ] 
dist 32=[-7.4707703751812692380 ,-3.9990261934730551332 ] 
dist 33=[-8.1394624439689933442 ,-4.3029485904979030528 ] 
dist 34=[-8.4982849382481214764 ,-4.8358987164280990479 ] 
dist 35=[-8.7617163138091517496 ,-4.9344822417790098500 ] 
dist 36=[-8.9410683050560594096 ,-5.0643634319550021433 ] 
dist 37=[-9.0533167010343896901 ,-4.9553231847454352362 ] 
dist 38=[-9.0772695637596915142 ,-4.7061711645906460291 ] 
dist 39=[-9.0485238091673624777 ,-4.2048095846946548392 ] 
dist 40=[-9.0417814594512290351 ,-3.6390174196588836190 ] 
dist 41=[-8.6863598732814567635 ,-3.1323844553496914464 ] 
dist 42=[-8.5926977971983363353 ,-2.5737774405545431442 ] 
dist 43=[-8.5353934869362109613 ,-1.7999653423097976236 ] 
dist 44=[-8.5142299600200169964 ,-.94797486677757044847] 
dist 45=[-7.6621312131944572632 ,-.07702723390887555632] 
dist 46=[-7.6170060248934689157 ,.97461888654177356785] 
dist 47=[-7.5633112624519219470 ,2.5481702060784096151 ] 
dist 48=[-7.5347481095321521643 ,4.1146805605866878529 ] 
dist 49=[-7.4692609743301477880 ,5.1383315445771390135 ] 
dist 50=[-7.4367300908415197664 ,5.9610032424077775517 ] 
dist 51=[-7.2046079328262887228 ,6.7253281325812546794 ] 
dist 52=[-6.6474711525332955306 ,7.3945243070171281475 ] 
dist 53=[-1.3708975574001872319 ,7.8375225135600247921 ] 
dist 54=[-.64018205678734397603,8.2003145832583794806 ] 
dist 55=[-.23950182650858930648,8.5494480175008422552 ] 
dist 56=[.04297575379398449792,8.8487574458678451066 ] 
dist 57=[.08971400693197401896,9.0126181697177640955 ] 
dist 58=[.41988949179314361142,9.1090342066318631230 ] 
dist 59=[.47483658014819796626,9.1388861541546216190 ] 
dist 60=[.56988881768512955328,9.1297294791951959097 ] 
dist 61=[.58875970848997375998,9.1097332893394275690 ] 
dist 62=[.8232160702169748293 ,9.0033297566257363387 ] 
dist 63=[.85274233167302865416,8.9416835010114992998 ] 
dist 64=[.91010245086789987866,5.9176891008656670210 ] 
dist 65=[.92191541547849322086,5.6185907289974726729 ] 
dist 66=[.9564202914943846951 ,4.9150524841681214831 ] 
dist 67=[.9589537972540798553 ,4.9476369137226466644 ] 
dist 68=[.9516155523315372637 ,4.9553825998538955132 ] 
dist 69=[.92926141079795048296,3.5510230452688217713 ] 
dist 70=[.90192326545873463996,3.2605816760032704192 ] 
dist 71=[.87465004662643046976,3.1805261931002152574 ] 
dist 72=[.75977713372404297924,1.7026505183879389699 ] 
dist 73=[.19139590186825573513,1.5152757704542102651 ] 
dist 74=[-.32376024146002970067,1.2855030608989507673 ] 
dist 75=[-.90182456293202281862,1.2479109473148598142 ] 
dist 76=[-1.4771594811111156950 ,1.2048765705924103071 ] 
dist 77=[-1.9815079029372393920 ,1.1937439013947960696 ] 
dist 78=[-2.5314412347019393252 ,.83691000386237498529] 
dist 79=[-3.2889205331718801915 ,.81624653631101996151] 
dist 80=[-4.0282686600913835876 ,.77107035664639613411] 
dist 81=[-4.5058325268295661907 ,.75739169234727086076] 
dist 82=[-4.8841928285549202941 ,.6971462874337266343 ] 
dist 83=[-5.2273813963504289933 ,.6842958013483705902 ] 
dist 84=[-5.5227490874619979500 ,.65328590932523105513] 
dist 85=[-5.7101507791407305596 ,.64409744437646694047] 
dist 86=[-5.8549158111321675583 ,.71238382998726623039] 
dist 87=[-5.9800464748224414817 ,.7830702632873345946 ] 
dist 88=[-6.0776432433728696521 ,.85737440171969251645] 
dist 89=[-6.1124598988572876108 ,.9278224305538506673 ] 
dist 90=[-6.1188758802979141441 ,.98314946250035574022] 
dist 91=[-6.1063399996599363020 ,1.0377045552506621146 ] 
dist 92=[-5.9790621954761698175 ,1.2811758948536397916 ] 
dist 93=[-5.9363898737097964082 ,1.7116725013915381390 ] 
dist 94=[-5.8711548018120556595 ,2.2316509165897735490 ] 
dist 95=[-5.8437836250027407737 ,3.0101500010712763884 ] 
dist 96=[-2.3264658302961630746 ,3.7854927766115676032 ] 
dist 97=[-2.2944712432425320433 ,4.2928849758551518853 ] 
dist 98=[-2.2816303096992573932 ,4.7015211183134512258 ] 
dist 99=[-2.2727898348716112182 ,5.0826394564393541536 ] 
dist 100=[-2.2670816392959079833 ,5.4172421446284135229 ] 
dist 101=[-.96722854961011286102,5.6401943390878228902 ] 
dist 102=[-.96473875574065701482,5.8242458942491654924 ] 
dist 103=[-.96181922847097498452,6.0035671889461190948 ] 
dist 104=[-.956544526572624417  ,6.1517865705974548374 ] 
dist 105=[-.9538479447835936145 ,6.2116784664165388468 ] 
dist 106=[-.93785158344695961084,6.2342436975109736845 ] 
dist 107=[-1.3507798502607166415 ,6.2334442280341077704 ] 
dist 108=[-1.8666886910613357042 ,6.0765878150523745680 ] 
dist 109=[-2.6490309995646912369 ,6.0284455185400185175 ] 
dist 110=[-3.4323680728988457843 ,5.9927815364461635718 ] 
dist 111=[-3.9522451472423124208 ,5.9648242103591534979 ] 
dist 112=[-4.3790887512638408046 ,5.8481904535945146993 ] 
dist 113=[-4.7910235551068200813 ,5.8456013221539590437 ] 
dist 114=[-5.1622011527659027949 ,5.7948317132964900290 ] 
dist 115=[-5.4263331642442990042 ,5.7798513565371597791 ] 
dist 116=[-5.6628107237104784386 ,5.5270039991778690668 ] 
dist 117=[-5.9235782934410377237 ,5.4612125886191737807 ] 
dist 118=[-6.1554503950764918484 ,5.4023538710021675559 ] 
dist 119=[-6.2765701047229315807 ,5.3680787691160308748 ] 
dist 120=[-6.3397762423885780376 ,4.3385074314403685426 ] 
dist 121=[-6.3520967465358998600 ,4.1950122384110035469 ] 
dist 122=[-6.3183885981533936580 ,3.9125241579685277023 ] 
dist 123=[-6.2908508963630099378 ,3.8362982502950566965 ] 
dist 124=[-6.2539932728873201374 ,3.5522009124142775118 ] 
dist 125=[-6.1733633959799796544 ,3.4852079787547054219 ] 
dist 126=[-5.4508552888461021672 ,3.3622792205492059700 ] 
dist 127=[-5.2095260171810134042 ,3.3282983676401313707 ] 
dist 128=[-1.8839816038255530316 ,2.2462045966345445434 ] 
dist 129=[-2.0145838764446550357 ,2.1796564959369276957 ] 
dist 130=[-2.1280628909273579541 ,2.1577503531242722267 ] 
dist 131=[-2.2508507860175807641 ,2.1359114940180363861 ] 
dist 132=[-2.4186226417637644612 ,2.1230657727465267805 ] 
dist 133=[-2.5798722330757062976 ,.88652317095090038726] 
dist 134=[-2.6766228536075076645 ,.86186840024166109902] 
dist 135=[-2.7447563096057170517 ,.85611129010671806604] 
dist 136=[-2.7917565021940014284 ,.83876642810918160943] 
dist 137=[-2.8228963950334078655 ,.83387035363243695284] 
dist 138=[-2.8288353785302980515 ,.79252939540451227546] 
dist 139=[-2.8232593908145664965 ,.78267968128129097434] 
dist 140=[-2.8174238958660359750 ,.7685721799130309118 ] 
dist 141=[-2.6745448535053425890 ,.76341549250492768552] 
dist 142=[-2.6460948636545887568 ,.67030199966097402617] 
dist 143=[-2.5765597538021919120 ,.66303382834080752273] 
dist 144=[-2.5512148805227976490 ,.64178540846195128628] 
dist 145=[-2.4231376485232411684 ,.63776860236868315672] 
dist 146=[-2.3927013346166504592 ,.59154853766334009268] 
dist 147=[-2.3256806339144303448 ,.58125409119957929188] 
dist 148=[-2.3030588737774692157 ,.5701987526857642832 ] 
dist 149=[-2.2568855246495503877 ,.69112629035621088594] 
dist 150=[-2.2954244586014227101 ,1.0684725269400783251 ] 
dist 151=[-2.3153516981476130237 ,1.3763773493286924740 ] 
dist 152=[-2.3187419159577719395 ,1.6704907424014149793 ] 
dist 153=[-2.3072575489100665323 ,1.9336044896174779007 ] 
dist 154=[-2.2983464429152320620 ,2.1177438236171130900 ] 
dist 155=[-2.2814733734058119202 ,2.2794893633148688272 ] 
dist 156=[-2.2732910116166681060 ,2.4531938171493528110 ] 
dist 157=[-2.0338725995346572160 ,2.6111143213494460359 ] 
dist 158=[-1.9961758447979095688 ,2.7098439354072641282 ] 
dist 159=[-1.9157136337664179586 ,2.7842139536252356821 ] 
dist 160=[-1.8909751903206207979 ,2.8448852875078000115 ] 
dist 161=[-1.7809660077327336508 ,2.8921741370163702613 ] 
dist 162=[-1.7577900332805912514 ,2.9131183019673523274 ] 
dist 163=[-1.6897373698546749611 ,2.9187942284005386592 ] 
dist 164=[-1.6791335360788680547 ,2.9166696564454972283 ] 
dist 165=[-.46991494482864233655,.23251263059064514566] 
dist 166=[-.55225119651871564428,.37457760936405879122] 
dist 167=[-.61213807233875898153,.49066902994325457204] 
dist 168=[-.66712054769569221178,.60187829537562185244] 
dist 169=[-.72987406234086778304,.70161297119036473215] 
dist 170=[-.7929060932051257287 ,.77189217090483352692] 
dist 171=[-.84899887487183240543,.83415120407780346239] 
dist 172=[-.91081285132620325503,.90186686321320459799] 
dist 173=[-.99668371298450990303,.96353265583511652556] 
dist 174=[-1.0795943773442760740 ,1.0016369227260639175 ] 
dist 175=[-1.1295891836966886314 ,1.0298349258186435453 ] 
dist 176=[-1.1650901406367935115 ,1.0519464672089545784 ] 
dist 177=[-1.1901354231898282816 ,1.0684906274655279830 ] 
dist 178=[-1.2080098583143189256 ,1.0744588989200522924 ] 
dist 179=[-1.2148826776959078260 ,1.0754119028880272598 ] 
dist 180=[-1.2159855959595506114 ,1.0733236324884997035 ] 
dist 181=[-1.2142004373332106630 ,.9620749304243602979 ] 
dist 182=[-1.1391492258674050578 ,1.0289188438498242187 ] 
dist 183=[-1.1253298264264429750 ,1.0725256554185305864 ] 
dist 184=[-1.0981361922190066638 ,1.1075237912091082276 ] 
dist 185=[-1.0894377647325412075 ,1.1399949028731760003 ] 
dist 186=[-1.0503259640746350740 ,1.1684110189581055570 ] 
dist 187=[-1.0407078361788937227 ,1.1872182468360343735 ] 
dist 188=[-1.0132895557941781677 ,1.2026143276924763022 ] 
dist 189=[-1.0058219188521641641 ,1.2174101386313694745 ] 
dist 190=[-.44454615464299501653,1.2289999856590246910 ] 
dist 191=[-.3928192220464029251 ,1.2315953814266966640 ] 
dist 192=[-.39637363696837019858,1.2298364552334680522 ] 
dist 193=[-.49313658793744899346,1.2265866834584879963 ] 
dist 194=[-.58117728986285169123,1.2002221921664430454 ] 
dist 195=[-.67981145298704337857,1.1919837757966995289 ] 
dist 196=[-.81887161739112593997,1.1745232109937752105 ] 
dist 197=[-.95514550342742586797,1.1677843025222935371 ] 
dist 198=[-1.0426556349151596798 ,1.0354876277743668789 ] 
dist 199=[-1.1113187203266286161 ,1.0148263706557436366 ] 
dist 200=[-1.1723435053790648679 ,.96696284406756741513] 
dist 201=[-1.2238853093069279019 ,.95233295528256880508] 
dist 202=[-1.2546867368687884567 ,.88138243371668129631] 
dist 203=[-1.2762370805249715534 ,.86606060374222492079] 
dist 204=[-1.2908436700377822132 ,.83254547764297592738] 
dist 205=[-1.3002062352179586879 ,.82197282778437264047] 
dist 206=[-1.3008188677945838130 ,.39008672791404143678] 
dist 207=[-1.2975418678349051903 ,.3570747735100152062 ] 
dist 208=[-1.2932499965646478824 ,.36839331845544301456] 
dist 209=[-1.2613834081083221914 ,.37583263478547820324] 
dist 210=[-1.2517936986957636037 ,.38108896391534719633] 
dist 211=[-1.2327850517669381480 ,.38369168286985570236] 
dist 212=[-1.2258314357871843499 ,.38485111458208301198] 
dist 213=[-.85243818564953043967,.38434423484003769018] 
dist 214=[-.81280068364024610415,.35031447547902116493] 
dist 215=[-.71718757082762927304,.34479894807802864832] 
dist 216=[-.70021529858474521098,.33555562028234852924] 
dist 217=[-.55968247447299537816,.33282898381914145472] 
dist 218=[-.53287202224067994507,.32396929009458498555] 
dist 219=[-.49075625261308962133,.32097905950247480691] 
dist 220=[-.42366844084126253378,.31724692224576368394] 

8 phat 4 dirichlet min maxes function [0, 2, 1, 0, 0, 2, 0, 1, 2] 
dist 0=[52.223661287543337742  ,52.223661287543337742  ] 
dist 1=[51.868115797922855078  ,52.348053344602998795  ] 
dist 2=[51.241417942461990152  ,52.390151108589157584  ] 
dist 3=[50.034401473275279143  ,52.417170163247149456  ] 
dist 4=[48.672074480885589441  ,52.426881003832148757  ] 
dist 5=[47.424981961877338035  ,52.399643589261697811  ] 
dist 6=[46.020759838673619007  ,52.339559619291676664  ] 
dist 7=[44.030669797233656860  ,52.250426604277343811  ] 
dist 8=[41.810142613469996059  ,49.007695595667467822  ] 
dist 9=[39.485444522711679168  ,48.504035144261584197  ] 
dist 10=[36.632919565720282498  ,47.648438254527755893  ] 
dist 11=[32.304107147425277350  ,47.413749118827059219  ] 
dist 12=[27.946002841113107236  ,46.694768693744037781  ] 
dist 13=[24.976376126731111376  ,46.451532266031115633  ] 
dist 14=[22.447029378002803061  ,45.444912957230749127  ] 
dist 15=[19.847219039348425979  ,43.552516891551416807  ] 
dist 16=[17.391608758373892237  ,33.500470927250168875  ] 
dist 17=[15.437981804666663581  ,31.816964226684145493  ] 
dist 18=[13.471280327091606205  ,31.375471161846709428  ] 
dist 19=[10.962993723840274365  ,29.780578587087592816  ] 
dist 20=[8.5302051704426099497 ,29.416587973459019850  ] 
dist 21=[6.8648203733032549769 ,28.819147236471663470  ] 
dist 22=[5.4356315105952073101 ,28.655800575792966772  ] 
dist 23=[3.9460026105967198355 ,16.492407828338500785  ] 
dist 24=[2.5219251683459570497 ,11.579551912385397506  ] 
dist 25=[1.3541164047188583492 ,10.754810110087246000  ] 
dist 26=[.14264370576197694378,9.3911785696298209848 ] 
dist 27=[-1.4569112065735171952 ,9.1377299732631081312 ] 
dist 28=[-2.9995573727485063482 ,7.7654497657242365143 ] 
dist 29=[-4.5081641870925026016 ,7.5443036388145293002 ] 
dist 30=[-6.2790942544516439524 ,7.0784376512190968247 ] 
dist 31=[-7.9304748188176832714 ,6.7825644209312553640 ] 
dist 32=[-8.9706093406204807078 ,-2.4271857055799751457 ] 
dist 33=[-9.7657382895093489276 ,-3.4807518847172074138 ] 
dist 34=[-10.438510475713807258  ,-3.6882798121370474535 ] 
dist 35=[-10.984438026305645053  ,-4.6326696356302933458 ] 
dist 36=[-11.272987114662225407  ,-4.7926629996187590883 ] 
dist 37=[-11.429996109041928847  ,-4.9862439981849307618 ] 
dist 38=[-11.458099078116151347  ,-4.6827345577920271498 ] 
dist 39=[-9.5339631841704716299 ,-4.0919132593233432232 ] 
dist 40=[-9.6100929342872903496 ,-3.4087395207400543418 ] 
dist 41=[-9.6897418114443675504 ,-2.6657022123318275121 ] 
dist 42=[-9.7402736716708265440 ,-1.7370775687402716138 ] 
dist 43=[-9.7668870345766696311 ,-.31288901064941799189] 
dist 44=[-9.7778798424298096867 ,1.1167679170579614811 ] 
dist 45=[-9.7657501154016169755 ,2.0673464101829049407 ] 
dist 46=[-9.7349802731714940579 ,2.8491436561627755895 ] 
dist 47=[-9.7064164651998102735 ,3.6052468560445877596 ] 
dist 48=[-5.8669788759486760621 ,4.2873857875161898038 ] 
dist 49=[-5.3824123228622498257 ,4.7740379251955021402 ] 
dist 50=[-5.2726065594773688479 ,5.2111330622514318714 ] 
dist 51=[-4.6310615093841687586 ,5.6955823173437002091 ] 
dist 52=[-4.5087942787553292766 ,6.1361154430032923372 ] 
dist 53=[-4.2653672345774247798 ,6.3978836321234675929 ] 
dist 54=[-4.2003599279318676074 ,6.5791462278983146386 ] 
dist 55=[-1.7912755489469192722 ,6.6981211026876548824 ] 
dist 56=[-1.5420457991385187188 ,6.7758730406504577926 ] 
dist 57=[-1.0248944120350504805 ,6.7926129522274846914 ] 
dist 58=[-.8909350643718365841 ,6.7814868156550715060 ] 
dist 59=[-.4022452503362199902 ,6.7590982943600385039 ] 
dist 60=[-.3069937046244602852 ,6.3998389552194761037 ] 
dist 61=[-.1351226777052298173 ,6.7347341035039234476 ] 
dist 62=[-.0970438976447990647 ,7.0691140608241770950 ] 
dist 63=[-.0065322241740494225 ,7.3621783289429752807 ] 
dist 64=[-.0213726413863599763 ,7.5320902354605621626 ] 
dist 65=[-.0837766567464292808 ,7.6449830641716374542 ] 
dist 66=[-.2267241681108048273 ,7.7103020217024701023 ] 
dist 67=[-.4100315231245165627 ,7.7405398413494079550 ] 
dist 68=[-.6336017207964273786 ,7.7402215164384205284 ] 
dist 69=[-.9293235141691777580 ,7.6753261416730821055 ] 
dist 70=[-1.4006854401627249901 ,7.6624136071856653402 ] 
dist 71=[-1.8781197791895579730 ,5.1853041584652402371 ] 
dist 72=[-2.1981169136007020522 ,4.6329623276748924096 ] 
dist 73=[-2.4641079771561758070 ,4.5484946257776863481 ] 
dist 74=[-2.7260261201996376926 ,4.3938652500187017804 ] 
dist 75=[-2.9654391459137153697 ,4.3516280512437365386 ] 
dist 76=[-3.1416361134683716670 ,4.2296948891906030909 ] 
dist 77=[-3.3054536350138872623 ,4.2016891222362122549 ] 
dist 78=[-3.4955097686156671701 ,4.1805280784289962800 ] 
dist 79=[-3.6701789922047735697 ,4.1631524102030996053 ] 
dist 80=[-3.7726019866719384822 ,1.6025081994575372247 ] 
dist 81=[-3.8420078870044235929 ,1.3912778859512239554 ] 
dist 82=[-3.8849003176622978685 ,.89363942701353823742] 
dist 83=[-3.9079238253257613212 ,.81779406364326818022] 
dist 84=[-4.0584943517898542175 ,.14709312489898125536] 
dist 85=[-4.3488404447795141177 ,.56925597542793166682] 
dist 86=[-4.7153464716436073058 ,1.4954928023845011624 ] 
dist 87=[-5.0606175680498117084 ,2.4214710902616161174 ] 
dist 88=[-5.2661947589244177800 ,3.0307706910187003820 ] 
dist 89=[-5.4093291578643728831 ,3.5248489159299762960 ] 
dist 90=[-5.5052679164151997363 ,3.9909183141041564259 ] 
dist 91=[-5.5687992860196491524 ,4.4033049522620276497 ] 
dist 92=[-5.5825126426071464551 ,4.6830981144094926960 ] 
dist 93=[-5.5753789443952154570 ,4.9192906001331992261 ] 
dist 94=[-5.5570964334244981434 ,5.1576175866338123756 ] 
dist 95=[-5.2258241517119958765 ,5.3667271471290172367 ] 
dist 96=[-5.1630056035497872936 ,5.4862982904108892040 ] 
dist 97=[-5.0187979425509548531 ,5.5630575708944878671 ] 
dist 98=[-4.9688938232848711455 ,5.6013113821965831847 ] 
dist 99=[-4.7255049850175204255 ,5.6133782976987173017 ] 
dist 100=[-4.6695058898596531215 ,5.6086081126061818873 ] 
dist 101=[-4.5278602801535664538 ,5.5511366695920231528 ] 
dist 102=[-4.4817375565173093363 ,5.5363874964138116018 ] 
dist 103=[-.98141778311855475155,3.1285561480194422223 ] 
dist 104=[-.63672277391213050357,3.1996016890124352701 ] 
dist 105=[-.59317249039858474497,3.2296568025322040580 ] 
dist 106=[-.5051266724118281696 ,3.2397769533513577912 ] 
dist 107=[-.48237957036521214098,3.2357055246339577238 ] 
dist 108=[-.47727639424199553229,3.1710721058271859260 ] 
dist 109=[-.84387583978016598958,3.1531593368777342086 ] 
dist 110=[-1.1549318165797833786 ,3.0881113492633069319 ] 
dist 111=[-1.4716044110052506390 ,3.0736677651198040564 ] 
dist 112=[-1.7677349633347360738 ,2.8916134328350823090 ] 
dist 113=[-1.9968002069315018072 ,2.8484922186291087788 ] 
dist 114=[-2.2206684675112233941 ,2.8031759904235795387 ] 
dist 115=[-2.4960575918383024981 ,2.7801397027768474267 ] 
dist 116=[-2.7566611677284780818 ,2.2079636947383811258 ] 
dist 117=[-2.9215135226511612159 ,2.1299580058064492354 ] 
dist 118=[-3.0478365991485059721 ,1.9695585333965905643 ] 
dist 119=[-3.1546501472657837452 ,1.9251291836043254578 ] 
dist 120=[-3.2407746832795289058 ,1.7505890961250766362 ] 
dist 121=[-3.2845169845057960162 ,1.7133158433111303607 ] 
dist 122=[-3.3055964392424766243 ,1.6310104523739455905 ] 
dist 123=[-3.3063831537651758816 ,1.6058218109312508767 ] 
dist 124=[.05660437822699954841,1.0691837012269991681 ] 
dist 125=[-.21362366475450174356,1.0755711193642308725 ] 
dist 126=[-.44190044984532744215,1.0769680353248668327 ] 
dist 127=[-.67297529483122608449,1.0748702686764641280 ] 
dist 128=[-.88849604669539051213,-.05000021611677562904] 
dist 129=[-1.0546796393499315666 ,-.10602265512653235298] 
dist 130=[-1.2167671510633511299 ,-.22173107277768839077] 
dist 131=[-1.4159440445382257477 ,-.24986765851408471989] 
dist 132=[-1.6047059888379860657 ,-.35143844416572288401] 
dist 133=[-1.7252163323843390627 ,-.37105634727824713003] 
dist 134=[-1.8189904068712464401 ,-.39232588423543333478] 
dist 135=[-1.9010114744119287373 ,-.39034870075771714551] 
dist 136=[-1.9693881962268525410 ,-.37164849243240630029] 
dist 137=[-2.0086936133670614029 ,-.34025072418260217045] 
dist 138=[-2.0343450374501693958 ,-.29653900324327038106] 
dist 139=[-2.0482235072146103762 ,-.22456393360219176817] 
dist 140=[-2.0539871314290649868 ,-.13987082073156165049] 
dist 141=[-2.0523730171250850680 ,-.04538775591902451144] 
dist 142=[-2.0371001061498940127 ,.07443213066627040938] 
dist 143=[-2.0292866543461127838 ,.26027012364501495503] 
dist 144=[-1.9566132658402049361 ,.44792196390748113326] 
dist 145=[-1.9368338572175109558 ,.57498328745947514838] 
dist 146=[-1.9100942825965415260 ,.68207967578896622033] 
dist 147=[-1.8987157122947324101 ,.84739002044971291297] 
dist 148=[-1.5996959589776220146 ,1.0562593404106378342 ] 
dist 149=[-1.5609214467891761564 ,1.2064347869171680771 ] 
dist 150=[-1.4793814302931388477 ,1.3425284264971827181 ] 
dist 151=[-1.4555298730272627569 ,1.4951840721622776007 ] 
dist 152=[-1.3549217857702705529 ,1.6470092958886537564 ] 
dist 153=[-1.3339225043307893551 ,1.7797919319759526268 ] 
dist 154=[-1.2773892614678298812 ,1.9242184181945772307 ] 
dist 155=[-1.2663846273073413523 ,2.1225369814362497910 ] 
dist 156=[-1.0158311522753204679 ,2.3141641687038582662 ] 
dist 157=[-1.0029953553945856501 ,2.4318773596820813284 ] 
dist 158=[-.9652954580147020671 ,2.5181332116384881410 ] 
dist 159=[-.95919417558879588801,2.5841677116644582634 ] 
dist 160=[-.3884415342138064126 ,2.6327140850906208599 ] 
dist 161=[-.33424732417079054299,2.6491474163389459696 ] 
dist 162=[-.21775575682784121048,2.6532457435140280242 ] 
dist 163=[-.19014742232615196452,2.6525440234813132872 ] 
dist 164=[-.06524184699579853866,2.5753490607012487461 ] 
dist 165=[-.04293370409622871129,2.5583094627789556097 ] 
dist 166=[.00669648302744121090,2.5152921876268882145 ] 
dist 167=[.01608201515877361321,2.4976507849791339649 ] 
dist 168=[.07132087988769569934,2.4020849473129335693 ] 
dist 169=[.07933530788201822586,2.3780988302880131407 ] 
dist 170=[.07569352321131786881,2.3222405535120556576 ] 
dist 171=[.05519009497387092779,2.3020384196677434926 ] 
dist 172=[-.36755274076939999237,2.0080954562285538753 ] 
dist 173=[-.70791374019256052868,1.9979499000383233122 ] 
dist 174=[-.9883447400861634715 ,1.9594429223949634813 ] 
dist 175=[-1.2640534133541647637 ,1.9518411487104371087 ] 
dist 176=[-1.5147694512644532578 ,1.8402059428525327132 ] 
dist 177=[-1.6973559368864139472 ,1.8137270492586597803 ] 
dist 178=[-1.8652189603268692272 ,1.7893774070184800549 ] 
dist 179=[-2.0571486071292148650 ,1.7785355095640953842 ] 
dist 180=[-2.2340112703287938567 ,1.5327962783470435633 ] 
dist 181=[-2.3417190735216957735 ,1.5417283586208146372 ] 
dist 182=[-2.4195121188273959182 ,1.5463432302112232888 ] 
dist 183=[-2.4769422411992117964 ,1.5462837369833318055 ] 
dist 184=[-2.5186379724500557440 ,1.3840527397473569807 ] 
dist 185=[-2.5336110588908976654 ,1.3635951843925417382 ] 
dist 186=[-2.5367625420320788879 ,1.3324413864936346806 ] 
dist 187=[-2.5314124977614845377 ,1.3220343958404248069 ] 
dist 188=[-1.1962306427502703804 ,1.2948119558057183164 ] 
dist 189=[-1.2525616192800387902 ,1.2843180002871632674 ] 
dist 190=[-1.3127270256500260304 ,1.2767752510082472941 ] 
dist 191=[-1.3939596974946475182 ,1.2712768255114502956 ] 
dist 192=[-1.4719458565970933754 ,.30968915563240321103] 
dist 193=[-1.5191501480926475259 ,.23198319681873745236] 
dist 194=[-1.5529049610641713569 ,.06238103496338306570] 
dist 195=[-1.5771939545598421106 ,.02636200259395643811] 
dist 196=[-1.6184040530105495452 ,-.16197379152686380604] 
dist 197=[-1.6686680493186027633 ,-.19404763336477875297] 
dist 198=[-1.7010245759474093043 ,-.26517381990449529787] 
dist 199=[-1.7174662203430810174 ,-.27707658480693200229] 
dist 200=[-1.7260695801827865054 ,-.37009777587017776908] 
dist 201=[-1.7271304687354611990 ,-.38440525504977378955] 
dist 202=[-1.7228710526887525356 ,-.38193755260499541062] 
dist 203=[-1.7189529317335588267 ,-.3559399357004940901 ] 
dist 204=[-1.4275664528003213351 ,-.31677052236269357734] 
dist 205=[-1.4064618339213963594 ,-.26171380887232512599] 
dist 206=[-1.3900378315085401625 ,-.07072976218836693187] 
dist 207=[-1.3844463120734975022 ,.2774172287627873219 ] 
dist 208=[-1.4248822620145305907 ,.62453646404502173205] 
dist 209=[-1.4547785069480178230 ,.8530722170332212811 ] 
dist 210=[-1.4720400580429096143 ,1.0389993370680203954 ] 
dist 211=[-1.4765999266199862546 ,1.2189845793332281983 ] 
dist 212=[-1.4755776057567237367 ,1.3803903899486061910 ] 
dist 213=[-1.4714348158350435610 ,1.4940779546001521121 ] 
dist 214=[-1.4625324469611970824 ,1.5947213759119065782 ] 
dist 215=[-1.4574188865888079576 ,1.7040465200324134522 ] 
dist 216=[-1.3153600404695424092 ,1.8028514584182906958 ] 
dist 217=[-1.2924170809772850240 ,1.8614925469502159497 ] 
dist 218=[-1.2433454292553496035 ,1.9020090277940785381 ] 
dist 219=[-1.2280314670297343992 ,1.9284521802999363889 ] 
dist 220=[-1.1590484433474155845 ,1.9449151034056992872 ] 
dist 221=[-1.1443159178253668074 ,1.9472906212818376810 ] 
dist 222=[-1.1010712524006650468 ,1.9408437042000579563 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 0, 1, 2, 1, 2] 
dist 0=[44.265529388604224500  ,44.265529388604224500  ] 
dist 1=[44.038026146290789206  ,44.494969785048044697  ] 
dist 2=[43.768233174875918303  ,44.707914414758662633  ] 
dist 3=[43.369812242288289881  ,44.869430998719710496  ] 
dist 4=[42.770143603528673493  ,45.023731946090948712  ] 
dist 5=[41.891903347068729114  ,45.207624335954832143  ] 
dist 6=[40.780464059806095766  ,45.365340290616806395  ] 
dist 7=[39.281824781043373878  ,45.415160318968772198  ] 
dist 8=[36.857030558412383001  ,45.394789191586661301  ] 
dist 9=[34.370218548621911108  ,45.354856689036284112  ] 
dist 10=[32.623812284409715784  ,45.094384293990047601  ] 
dist 11=[31.080071622492269980  ,45.009394440117368039  ] 
dist 12=[28.268302755528826414  ,44.636869696626009808  ] 
dist 13=[25.961723878302833971  ,44.582224215567870641  ] 
dist 14=[23.964911922384092527  ,36.342102139660015314  ] 
dist 15=[21.860908596172346407  ,35.546648025588435136  ] 
dist 16=[19.841188106788458123  ,33.583701599207368366  ] 
dist 17=[18.180750047518543694  ,33.271517257130483601  ] 
dist 18=[16.459611705147641394  ,30.222557142742747861  ] 
dist 19=[14.196954705997226524  ,29.629624761690267211  ] 
dist 20=[11.969270219993632029  ,28.920556568973977656  ] 
dist 21=[10.387564607341564350  ,28.708604942741265272  ] 
dist 22=[8.9691936546426788268 ,23.104755903760840494  ] 
dist 23=[7.3936284518950965554 ,22.375481388697897966  ] 
dist 24=[5.8273681919962374981 ,20.891516347510569074  ] 
dist 25=[4.4456880657454055392 ,20.499600375986536405  ] 
dist 26=[2.9259477604578923377 ,19.045870121521038719  ] 
dist 27=[.80710116033613368533,18.741389411273749745  ] 
dist 28=[-1.2641031574170883725 ,18.164247514056651403  ] 
dist 29=[-2.5936155672650678518 ,18.015813480393506159  ] 
dist 30=[-3.6438447662047536461 ,7.1351971003504758064 ] 
dist 31=[-4.5985825599058310668 ,6.1928041540858029678 ] 
dist 32=[-5.4281588144173581499 ,4.0497532315488531585 ] 
dist 33=[-5.9781782266112070583 ,3.6933046439356622171 ] 
dist 34=[-6.4341757973301503854 ,1.0401057922513618205 ] 
dist 35=[-6.8882960666468598756 ,.58013152795477144297] 
dist 36=[-7.2815540417488444888 ,-.16358890466959228204] 
dist 37=[-8.3395574133802901444 ,-.33376683550856018518] 
dist 38=[-9.4660911687821972248 ,-1.7639606999363352490 ] 
dist 39=[-10.170728969025529901  ,-1.5243741407228880270 ] 
dist 40=[-10.704107643132415642  ,-1.0734394761646522840 ] 
dist 41=[-11.146450401028030273  ,-.59570991447185871626] 
dist 42=[-11.498857893628209710  ,-.24902615053491064163] 
dist 43=[-11.672976998863073249  ,.06631545736673014266] 
dist 44=[-11.754481787660216087  ,.4193994998209381912 ] 
dist 45=[-11.763704193794430650  ,.76834450913232414408] 
dist 46=[-8.7173082529845248686 ,1.0673725767216126473 ] 
dist 47=[-8.4832814857701307196 ,1.7428975181587355948 ] 
dist 48=[-7.8766635546835481280 ,2.4133638854618102504 ] 
dist 49=[-7.7869270125121260657 ,2.9146251055699089863 ] 
dist 50=[-6.7655902427677418688 ,3.3881413295508484727 ] 
dist 51=[-6.5650302048794264619 ,3.9480144508990531826 ] 
dist 52=[-6.3511238022958088930 ,4.4676791196413045393 ] 
dist 53=[-6.3048646440135948446 ,4.7806895515438599473 ] 
dist 54=[-4.6626573428614303986 ,5.0024576694277198862 ] 
dist 55=[-4.6179458438567394787 ,5.1577401909439184849 ] 
dist 56=[-4.6009696843857161870 ,5.2728808876582520401 ] 
dist 57=[-3.3958111756526128106 ,5.3344641568337877586 ] 
dist 58=[-2.9292865372857867116 ,5.3687737263585951692 ] 
dist 59=[-2.8300395532243906029 ,5.3753659277599352092 ] 
dist 60=[-2.6918387753087791624 ,4.8366168672963729487 ] 
dist 61=[-2.6509530907960314780 ,4.8891522198877414114 ] 
dist 62=[.63013626320339232155,4.8972881513031944249 ] 
dist 63=[.85801578162139434995,4.8879069716373802354 ] 
dist 64=[.90620745329607063307,4.8704502638221502619 ] 
dist 65=[1.4850013782786231862 ,4.5697362825769807649 ] 
dist 66=[1.5658980463906414740 ,4.5128619789037598113 ] 
dist 67=[1.6674581641034557922 ,4.3778297234949020605 ] 
dist 68=[1.6742307420979423433 ,4.3305052422531202478 ] 
dist 69=[1.6440143811803046343 ,4.2068336360595949116 ] 
dist 70=[1.3633555223425108590 ,4.5563190282432127123 ] 
dist 71=[.69483166748466387639,4.7721405909460170736 ] 
dist 72=[-.30715139648361952272,4.9320911636909211291 ] 
dist 73=[-1.3066508114160708840 ,5.0583952077601546062 ] 
dist 74=[-1.9652657699169939939 ,5.1539351944603764717 ] 
dist 75=[-2.5009189095668787666 ,5.1909991159759150782 ] 
dist 76=[-3.0095202035021213128 ,5.2029552648994472534 ] 
dist 77=[-3.4623581583360838483 ,5.1981939731373978190 ] 
dist 78=[-3.7753840212493192583 ,4.0767073233458339424 ] 
dist 79=[-4.0462089479987073514 ,4.0527103590133903918 ] 
dist 80=[-4.3305565847287098348 ,4.0367929588399408051 ] 
dist 81=[-4.5877459129328399792 ,3.7289696001617037268 ] 
dist 82=[-4.7501485413685437430 ,3.6764288653874660845 ] 
dist 83=[-4.8743302858126905503 ,3.5562195168286228304 ] 
dist 84=[-4.9789476025630773876 ,3.5164029881347172515 ] 
dist 85=[-5.0630796349826074236 ,3.3282582948059528135 ] 
dist 86=[-5.1054879706825590148 ,3.2861011177581935395 ] 
dist 87=[-5.1254986765440129562 ,3.1841560961116744403 ] 
dist 88=[-5.1202253419275746921 ,3.1497605129744010050 ] 
dist 89=[-3.3093241032751698300 ,.9066020384423943891 ] 
dist 90=[-3.3114065286407530804 ,1.0622031475484452612 ] 
dist 91=[-3.3072699961341670669 ,1.1944259320752809177 ] 
dist 92=[-3.2439834038414542467 ,1.3293606228097554364 ] 
dist 93=[-3.3761355742461576482 ,1.4557181420884571938 ] 
dist 94=[-3.4935532057022756801 ,1.5536911060851374884 ] 
dist 95=[-3.5498701789331144809 ,1.6496047985766731914 ] 
dist 96=[-3.5776338352936792872 ,1.7677182247390897273 ] 
dist 97=[-3.5809079963422197848 ,1.8793264153178842354 ] 
dist 98=[-3.5296537805182713351 ,1.9492626093492561137 ] 
dist 99=[-3.5116840867718223350 ,2.0607761229426125720 ] 
dist 100=[-3.4967545408770203677 ,2.2630861531092773248 ] 
dist 101=[-3.4822070697611790096 ,2.5106830013749051263 ] 
dist 102=[-2.9617734666108047142 ,2.7440979570687181638 ] 
dist 103=[-2.8867515090277037310 ,2.8898094167822660958 ] 
dist 104=[-2.7436290238027605967 ,2.9991226917868545708 ] 
dist 105=[-2.7049672163067730985 ,3.0872737450618136727 ] 
dist 106=[-2.5632765902031476297 ,3.1550105822117985138 ] 
dist 107=[-2.5268474720742863989 ,3.1828489201012835260 ] 
dist 108=[-2.4665756786655474584 ,3.1912010889259210747 ] 
dist 109=[-2.4483089510510467030 ,3.1864168973592898160 ] 
dist 110=[-1.5751995502384118513 ,2.5450499129062946187 ] 
dist 111=[-1.7110706623877101931 ,2.5592834952874942670 ] 
dist 112=[-1.8723190633093400051 ,2.5628694073485612191 ] 
dist 113=[-2.0221082879948340495 ,2.5636186193515723985 ] 
dist 114=[-2.1122302469738940322 ,2.5625323487111718403 ] 
dist 115=[-2.1759589033832084922 ,2.5587506859206251468 ] 
dist 116=[-2.2203796957722520277 ,2.2184469077542175832 ] 
dist 117=[-2.2506747035578423571 ,2.1688412591709688417 ] 
dist 118=[-2.2580193828699236456 ,2.0794291430826664684 ] 
dist 119=[-2.2560747524142782350 ,2.0939596254946322701 ] 
dist 120=[-2.2492803423986299557 ,2.2760417332274772728 ] 
dist 121=[-2.1154809183460319375 ,2.4637510350986365161 ] 
dist 122=[-2.0910443767068476565 ,2.6411023275778785746 ] 
dist 123=[-1.9868541413141719017 ,2.7818383458218119016 ] 
dist 124=[.33722059600308314222,2.9229855642579938804 ] 
dist 125=[.01604687332910981223,3.1020001353521747617 ] 
dist 126=[-.31406892886994323676,3.2685136914353283043 ] 
dist 127=[-.54733577954749347383,3.3597499151976044776 ] 
dist 128=[-.75451983429286597764,3.4135365318486980379 ] 
dist 129=[-.9805164900234551528 ,3.4305089391443769406 ] 
dist 130=[-1.2015503061258284541 ,3.4341374199054194526 ] 
dist 131=[-1.3889267402266477429 ,3.4346334831041626098 ] 
dist 132=[-1.5877157690300651660 ,3.4329725982783940548 ] 
dist 133=[-1.8543172849099284492 ,3.4279687739410584291 ] 
dist 134=[-2.1179123406711859593 ,2.9860001757463816368 ] 
dist 135=[-2.3047021137891274502 ,2.9212908522505921929 ] 
dist 136=[-2.4711926095426570094 ,2.8055735394651828502 ] 
dist 137=[-2.6537518598532000130 ,2.7752084156402861334 ] 
dist 138=[-2.8329124202314837973 ,2.6721100616616187216 ] 
dist 139=[-2.9858385721630922929 ,2.6407689436959550432 ] 
dist 140=[-3.1490197502084009012 ,2.6083474440514289678 ] 
dist 141=[-3.3691290559676789312 ,2.5908030916705288171 ] 
dist 142=[-3.5799035364203151420 ,.31774002339372027688] 
dist 143=[-3.7058175064415397213 ,.13756510693967280726] 
dist 144=[-3.7938318884365390081 ,-.2615674569225824165 ] 
dist 145=[-3.8532928996320411574 ,-.3375140098021356114 ] 
dist 146=[-3.8917351611478952074 ,-.39241205238532618762] 
dist 147=[-3.8984538151108817397 ,-.21679764747869448993] 
dist 148=[-3.8881274865396840430 ,-.03586993601026227080] 
dist 149=[-3.8794597714219260051 ,.10439586694931573137] 
dist 150=[-3.6795789703971142141 ,.24189161540510266078] 
dist 151=[-3.6401892270142297444 ,.41176622009461867256] 
dist 152=[-3.5432799149190003916 ,.5897004285017545835 ] 
dist 153=[-3.5080127574435217071 ,.75937799328891668992] 
dist 154=[-3.3299710479862719632 ,.95572182718931229374] 
dist 155=[-3.2876908299535049600 ,1.2401261831839706377 ] 
dist 156=[-3.1966504028372107508 ,1.5216067254954678678 ] 
dist 157=[-3.1664026911096178197 ,1.7062787037982102717 ] 
dist 158=[-3.0507487771042161870 ,1.8556297827858406855 ] 
dist 159=[-3.0905481718065260775 ,1.9960909314118005830 ] 
dist 160=[-3.1086670959802677253 ,2.1203004832266148148 ] 
dist 161=[-3.1097656747670155774 ,2.2913186601518842116 ] 
dist 162=[-3.0761765816391928617 ,2.6532044311144603142 ] 
dist 163=[-3.0604821908151630931 ,2.9073161527346050238 ] 
dist 164=[-3.0350324620204855001 ,3.1314371309546677759 ] 
dist 165=[-3.0233751892059371409 ,3.3735820108892541544 ] 
dist 166=[-2.6693356226019869173 ,3.5939120159757529032 ] 
dist 167=[-2.6149726263393491671 ,3.7309373243468743187 ] 
dist 168=[-2.5008030158546504944 ,3.8333266734772367577 ] 
dist 169=[-2.4665186586755598754 ,3.9153761277307012027 ] 
dist 170=[-2.3180057872113330661 ,3.9781718618000377247 ] 
dist 171=[-2.2864718146890540341 ,4.0036927129538993482 ] 
dist 172=[-2.1969931585915182597 ,4.0090577222641020016 ] 
dist 173=[-2.1810500527153570487 ,4.0043534388443612138 ] 
dist 174=[-.94054321847783795008,1.9875832199528467206 ] 
dist 175=[-1.2047532581207754020 ,1.9708856404018980017 ] 
dist 176=[-1.4494179130710384714 ,1.7972910930770319789 ] 
dist 177=[-1.6351186752028550744 ,1.7600144330224867994 ] 
dist 178=[-1.8134122717728477652 ,1.7159574799611991177 ] 
dist 179=[-2.0285036834811866016 ,1.6977298224384371653 ] 
dist 180=[-2.2302640515286987936 ,1.3231566174515104874 ] 
dist 181=[-2.3553334920429669125 ,1.4619706435995127634 ] 
dist 182=[-2.4483163117861439130 ,1.5898719636078560890 ] 
dist 183=[-2.5219710976476413428 ,1.6652374477133263457 ] 
dist 184=[-2.5776562090439963279 ,1.7166506599017472630 ] 
dist 185=[-2.5988949977797194725 ,1.7489186153920712611 ] 
dist 186=[-2.6065316422116547282 ,1.7713395903206310549 ] 
dist 187=[-2.6079115548300057785 ,1.7834372322169751067 ] 
dist 188=[-.10519254423573316304,1.7903074328931518031 ] 
dist 189=[-.27700527115325153172,1.7918573234206584454 ] 
dist 190=[-.42564419357325908284,1.6015946531928376220 ] 
dist 191=[-.58179152756551640672,1.5757229940253082399 ] 
dist 192=[-.73106346796421267231,1.5109820894997834042 ] 
dist 193=[-.85225179280926728112,1.4937848220055671744 ] 
dist 194=[-.97624224814268797018,1.3820300860173631541 ] 
dist 195=[-1.1367025149560566847 ,1.3576016988614893077 ] 
dist 196=[-1.2927851857596745481 ,1.3134595061186888713 ] 
dist 197=[-1.3992977221093548195 ,1.3012551976461103725 ] 
dist 198=[-1.4900374249004928800 ,1.0547996302830163694 ] 
dist 199=[-1.5831451523643833215 ,1.0197897158975727110 ] 
dist 200=[-1.6707999200044239158 ,.9372228548303419646 ] 
dist 201=[-1.7397682470862992515 ,.91865051690811383089] 
dist 202=[-1.8083525464680843045 ,.79933123861900149586] 
dist 203=[-1.8944747067994313059 ,.77564654041307861226] 
dist 204=[-1.9737662567924707382 ,.73195391747907058803] 
dist 205=[-2.0150784386587741636 ,.72068922403824259464] 
dist 206=[-2.0375851969903597560 ,.68679101312719559301] 
dist 207=[-2.0623451574958428748 ,.84222587793128173833] 
dist 208=[-2.1622605533320696251 ,.99119154530891911165] 
dist 209=[-2.2475940035965317669 ,1.1127268554908445700 ] 
dist 210=[-2.3171544598551951151 ,1.2376037935208480622 ] 
dist 211=[-2.3540943332420072628 ,1.3999114671677354341 ] 
dist 212=[-2.3742606214091944026 ,1.5581082082249692779 ] 
dist 213=[-2.3768509599521769536 ,1.6665720352818989458 ] 
dist 214=[-2.3707567718659401635 ,1.7595143060997722861 ] 
dist 215=[-2.3641245853516832886 ,1.8557400494192332268 ] 
dist 216=[-2.3398936293753143133 ,1.9468608674042801950 ] 
dist 217=[-2.3268061990684679138 ,2.0194214387992101354 ] 
dist 218=[-2.2467560425918658952 ,2.0923785177375927309 ] 
dist 219=[-2.2249735401458756358 ,2.1850827351845883426 ] 
dist 220=[-2.1847978733371228400 ,2.2715498505228654550 ] 
dist 221=[-2.1716235127873362375 ,2.3196047101641151092 ] 
dist 222=[-1.4764402452053741478 ,2.3487823600392694599 ] 
dist 223=[-1.4016279451844923766 ,2.3598801290352783719 ] 
dist 224=[-1.2255709964023347875 ,2.3615844764408327961 ] 
dist 225=[-1.1912434768843652715 ,2.3571895894517270562 ] 
dist 226=[-.94532161147058505071,2.3408501225354504188 ] 
dist 227=[-.89869797052664224396,2.3305673942911129344 ] 
dist 228=[-.81922060997379224681,2.1473980566855088730 ] 
dist 229=[-.7999544418897522787 ,2.1158670062015537518 ] 
dist 230=[-.45451087462578518162,2.0427220113494650390 ] 
dist 231=[-.40890130506127441645,2.0182590123307195407 ] 
dist 232=[-.30085382052090763509,1.9018115633447003675 ] 
dist 233=[-.28374089906362921048,1.8529013617291394982 ] 
dist 234=[-.1352484609319865065 ,1.7068277588344028277 ] 
dist 235=[-.10842999736967538687,1.5758048673265524525 ] 
dist 236=[-.19904967016353236476,1.0010561059795284286 ] 
dist 237=[-.35741520352984641082,.98348669209844318399] 
dist 238=[-.48973999273540344556,.93541481864441877289] 
dist 239=[-.6213560297701477814 ,.9272954536003815701 ] 
dist 240=[-.74264145382551079322,.83517378587280390443] 
dist 241=[-.83372069125547900365,.81576296143735779974] 
dist 242=[-.92023276272272211181,.79477887244329163327] 
dist 243=[-1.0232837071113607773 ,.7874223769023297702 ] 
dist 244=[-1.1192972601194058654 ,.5663682497891147573 ] 
dist 245=[-1.1777121410195395073 ,.53710972812473948587] 
dist 246=[-1.2198434990724558385 ,.47799237921649519431] 
dist 247=[-1.2508439570443273535 ,.46228063085736417801] 
dist 248=[-1.2736805453483014022 ,.40404717177667906327] 
dist 249=[-1.2832167775945671868 ,.39138539114235412909] 
dist 250=[-1.2859688157475026245 ,.36819665030874948905] 

8 phat 4 dirichlet min maxes function [0, 1, 1, 1, 0, 2, 0, 0, 2] 
dist 0=[43.796260574072070412  ,43.796260574072070412  ] 
dist 1=[43.243018986329754024  ,43.988590308463982107  ] 
dist 2=[42.491455687876974789  ,44.203581184296471172  ] 
dist 3=[41.516676132603400741  ,44.463350815133049255  ] 
dist 4=[40.188502331023410211  ,44.651799293741910862  ] 
dist 5=[38.025362020371087560  ,44.791569379592300310  ] 
dist 6=[35.798138743628757162  ,44.856761304499169759  ] 
dist 7=[34.213949677359073097  ,44.879142665296301580  ] 
dist 8=[32.792487063339786813  ,44.847688830398304178  ] 
dist 9=[31.215109963031015899  ,44.793136830136454758  ] 
dist 10=[29.651663964065459588  ,44.723317321941281875  ] 
dist 11=[28.285693015894011100  ,44.627971583315111185  ] 
dist 12=[26.797626635703667888  ,44.559940430896871260  ] 
dist 13=[24.746167384948870225  ,44.288123396281887876  ] 
dist 14=[22.682085778970256085  ,44.187845991978199125  ] 
dist 15=[21.143440888185602782  ,43.552818682748043545  ] 
dist 16=[19.688579550378873417  ,41.980613128235813261  ] 
dist 17=[17.958999583789898687  ,34.348002708692412775  ] 
dist 18=[16.175413233816196270  ,33.483867854427671068  ] 
dist 19=[14.430886421900184254  ,31.345466489636327499  ] 
dist 20=[12.031335526943404152  ,31.035190718596836055  ] 
dist 21=[9.8211143907118186881 ,27.732536279171607570  ] 
dist 22=[7.0784991763304590406 ,27.100561549008033967  ] 
dist 23=[5.2574347879959736616 ,26.415025450650138485  ] 
dist 24=[3.7533533316629081889 ,26.281720852105162425  ] 
dist 25=[2.2775904463001723515 ,20.266556626324672643  ] 
dist 26=[.92357698077048264045,19.509083963259267284  ] 
dist 27=[-.95318061437106345767,18.010658112590775347  ] 
dist 28=[-3.4842965273015947579 ,17.629992428634725899  ] 
dist 29=[-5.1066360853207331072 ,16.312660330846298932  ] 
dist 30=[-6.3834016265153280928 ,16.019430981826332704  ] 
dist 31=[-7.5333757539650340225 ,15.665531931776241015  ] 
dist 32=[-8.5228707056297779097 ,15.569269261984036665  ] 
dist 33=[-9.1583865915337788218 ,4.1289682171711312932 ] 
dist 34=[-9.6613704882789650097 ,3.1955240654079378568 ] 
dist 35=[-10.121565779209852490  ,1.0688075774932367930 ] 
dist 36=[-10.509162535407261859  ,.73605051831071677681] 
dist 37=[-10.721989140517105477  ,-.630812444756759513  ] 
dist 38=[-10.850735122063830776  ,.06103196409020811929] 
dist 39=[-10.901885413082190438  ,.55324074283140515576] 
dist 40=[-10.901684776884761491  ,.99149491457049592429] 
dist 41=[-10.886101902986750460  ,1.4684372253734493548 ] 
dist 42=[-10.743427249436861820  ,1.9319757595584470665 ] 
dist 43=[-10.722572893341032325  ,2.3169100717772326574 ] 
dist 44=[-9.0220692668941469050 ,2.7170616831649968268 ] 
dist 45=[-9.3654580979234347586 ,3.2414277759003438769 ] 
dist 46=[-9.5397955840168630313 ,3.7518092775553609729 ] 
dist 47=[-9.6306985685504398321 ,4.0962142558382144340 ] 
dist 48=[-9.6446845956088368750 ,4.3844054392764635968 ] 
dist 49=[-6.5554137387555101268 ,4.6705417097794995133 ] 
dist 50=[-6.3926780369875408465 ,4.9328799988614601187 ] 
dist 51=[-5.9841639206558725514 ,5.1261250108646435488 ] 
dist 52=[-5.9128241245345538009 ,5.3054169460122240699 ] 
dist 53=[-5.2586320779582507579 ,5.5120617597668514634 ] 
dist 54=[-5.1298792979098389864 ,5.6997308603849319556 ] 
dist 55=[-4.9587128412528817559 ,5.8032999143244921510 ] 
dist 56=[-4.9015226864514250494 ,5.8647934424756033937 ] 
dist 57=[-3.7163487310371862599 ,5.8845749314151350128 ] 
dist 58=[-3.5608243497369552857 ,5.8756870398200197276 ] 
dist 59=[-3.2268237249098741581 ,5.8227644822943999910 ] 
dist 60=[-3.1395376031050059376 ,1.9538057672639586711 ] 
dist 61=[-2.7701975675237472070 ,2.2088222332268646882 ] 
dist 62=[-2.7015378849828366067 ,2.5230772115839534616 ] 
dist 63=[-2.5359823318476654315 ,2.7988727263285580863 ] 
dist 64=[-2.5082181238354180115 ,3.0177857453805419864 ] 
dist 65=[-.88487418947425784794,3.2171040467180077206 ] 
dist 66=[-.74166562440855435671,3.3893099710053852915 ] 
dist 67=[-.41533553150813785642,3.4999892954119780651 ] 
dist 68=[-.35857346545247071568,3.5872914767676516452 ] 
dist 69=[.05435184573916622244,3.6662191262914237929 ] 
dist 70=[.12802043761557232956,3.7295800132306969247 ] 
dist 71=[.24869497093885698006,3.7547252019584562622 ] 
dist 72=[.27702187830300702159,3.7608598924362552751 ] 
dist 73=[.34535254147711900226,3.7557723503121670504 ] 
dist 74=[.08410166633174047363,3.6929705511626734048 ] 
dist 75=[-.15380779279777167552,3.6710239441937119649 ] 
dist 76=[-.42031970073610660342,3.6419398279470368019 ] 
dist 77=[-.79578394633755400304,3.6743203151492379585 ] 
dist 78=[-1.1751200881490640179 ,3.6795690206535295269 ] 
dist 79=[-1.4571074392748646160 ,3.6714923804406654981 ] 
dist 80=[-1.7220473249113811268 ,3.6624225453166435068 ] 
dist 81=[-2.0333536195855161544 ,2.9720053640621758097 ] 
dist 82=[-2.3510735830308341372 ,2.7740642894514391474 ] 
dist 83=[-2.6416398057887876819 ,2.7315374557179849064 ] 
dist 84=[-2.9683529174863195808 ,2.6324749376426805365 ] 
dist 85=[-3.4304159423089436423 ,2.6000931782561560803 ] 
dist 86=[-3.8824404325825210744 ,.96065745921243173461] 
dist 87=[-4.1690805648668735765 ,.87389602048184595596] 
dist 88=[-4.3898633719285376242 ,.8478647919821540631 ] 
dist 89=[-4.5789434039519068520 ,.36461981891568219189] 
dist 90=[-4.7335043832230675850 ,.30446427491923934264] 
dist 91=[-4.8164672694362089688 ,.21523411425497340689] 
dist 92=[-4.8630099024214280261 ,.23083113126785327665] 
dist 93=[-4.8721645552264906094 ,.26737800663839417285] 
dist 94=[-4.8628089402348763393 ,.33191237736840506486] 
dist 95=[-4.8496391374196596870 ,.42921314949880405356] 
dist 96=[-4.8029459638089764384 ,.59653551231360178386] 
dist 97=[-4.7771565129255562171 ,.77113716211938778849] 
dist 98=[-4.6181821708559100708 ,.8974984297916484641 ] 
dist 99=[-4.5747568459713731059 ,1.0126483177510818760 ] 
dist 100=[-4.4891119455314582489 ,1.1425267206289216211 ] 
dist 101=[-4.4596403454739788720 ,1.2718894694147704293 ] 
dist 102=[-3.9251817552122138522 ,1.3849945674736160077 ] 
dist 103=[-3.8983324992945008584 ,1.5078529763740957284 ] 
dist 104=[-3.8048317827166587245 ,1.8178743358186307146 ] 
dist 105=[-3.7887973107250970540 ,2.3372474577424236084 ] 
dist 106=[-3.5416457015245233076 ,2.8112472028015725762 ] 
dist 107=[-3.4847764378991121635 ,3.1592817983032568424 ] 
dist 108=[-3.4353068379860028032 ,3.4820811304145066816 ] 
dist 109=[-3.4177239413474740399 ,3.8553275166418422536 ] 
dist 110=[-3.1345693876964492352 ,4.1994709425485621810 ] 
dist 111=[-3.1203915903266090792 ,4.4060794209522109609 ] 
dist 112=[-3.1098657769962821382 ,4.5517175586303639961 ] 
dist 113=[-2.2741683989551288334 ,4.6524465968630962097 ] 
dist 114=[-2.0847946688587349152 ,4.7244863079082617211 ] 
dist 115=[-2.0391824642462171635 ,4.7555834836397895038 ] 
dist 116=[-1.9747555390587107607 ,4.7626631377546701272 ] 
dist 117=[-1.9532716196525521998 ,4.7583809292147414860 ] 
dist 118=[-.61131035500821865367,3.0701246957495815956 ] 
dist 119=[-.59587130571064790579,3.0549427605067498610 ] 
dist 120=[-.51919141914081089878,3.0466998530277566160 ] 
dist 121=[-.50413925163609389155,2.8727873626383858500 ] 
dist 122=[-.47092714364891456942,2.8393732808562054718 ] 
dist 123=[-.46103093371337896024,2.7545068620898730538 ] 
dist 124=[.52030146506821270911,2.7259847961534568755 ] 
dist 125=[.54538889580699610833,2.5669961652926858277 ] 
dist 126=[.38445169861592962549,2.5297907772559174281 ] 
dist 127=[.1829912372860230459 ,2.4567862643053668723 ] 
dist 128=[-.38598015837058951692,2.4859151746780948273 ] 
dist 129=[-1.0341549864637072058 ,2.6435607384975481777 ] 
dist 130=[-1.4598030558616871855 ,2.7372557287884622821 ] 
dist 131=[-1.8043645312595628634 ,2.8022280051781450253 ] 
dist 132=[-2.1288158335726530742 ,2.8451873313614825142 ] 
dist 133=[-2.4158632620300144691 ,2.8728305829164095820 ] 
dist 134=[-2.6110945692427079784 ,2.8771392777281759154 ] 
dist 135=[-2.7766253209853502534 ,2.8713399178790487313 ] 
dist 136=[-2.9450928549136204630 ,2.8625769191454208827 ] 
dist 137=[-3.0961407810827932517 ,2.7037351598982956729 ] 
dist 138=[-3.1921279541022087969 ,2.6732296397745957228 ] 
dist 139=[-3.2662300860759595440 ,2.6011753046042685967 ] 
dist 140=[-3.3299149115020705101 ,2.5757526032959971999 ] 
dist 141=[-3.3820851298732523673 ,2.4500402779449911954 ] 
dist 142=[-3.4102224288016416967 ,2.4207167289710077249 ] 
dist 143=[-3.4261681781934303736 ,2.3518633730717624590 ] 
dist 144=[-3.4296721998836864574 ,2.3279210535281873667 ] 
dist 145=[-.19999500555374249068,.7292885084165763724 ] 
dist 146=[-.29566238909823811856,.69733654283208561113] 
dist 147=[-.42325240783141954269,.68754689866209848802] 
dist 148=[-.5491938924770769432 ,.48446028255127275811] 
dist 149=[-.63827876122163395426,.45726823367348579879] 
dist 150=[-.71756039010545645357,.39685220527521490748] 
dist 151=[-.80435877487584726006,.38220075331048362178] 
dist 152=[-.88950585215682083803,.30804446269542798806] 
dist 153=[-.96219383171637444023,.29410475839849454816] 
dist 154=[-1.0397889530992003009 ,.26334150054958011264] 
dist 155=[-1.1445290868476513947 ,.25519196408508364365] 
dist 156=[-1.2455152810223041060 ,-.55119478078491711693] 
dist 157=[-1.3081215385316027810 ,-.60405009426643877994] 
dist 158=[-1.3546931153048556470 ,-.71468623570865677431] 
dist 159=[-1.3916558205027810576 ,-.73718163473634438396] 
dist 160=[-1.4196746197631835170 ,-.72217921266150649303] 
dist 161=[-1.4305349090885422955 ,-.6513388116198021654 ] 
dist 162=[-1.4341876572850073404 ,-.59600353198070371967] 
dist 163=[-1.4334280507347928973 ,-.54138016892012501749] 
dist 164=[-1.3988750308035168747 ,-.47337767765524511842] 
dist 165=[-1.3897877764466295181 ,-.40189305100050479546] 
dist 166=[-1.3660411000214875317 ,-.33336511037857101603] 
dist 167=[-1.3562824725797464863 ,-.25379850143524132315] 
dist 168=[-1.3033558850776473460 ,-.13824002335958428606] 
dist 169=[-1.2900546304937939788 ,-.01990771446353386024] 
dist 170=[-1.2612893879014734790 ,.07073482742769580378] 
dist 171=[-1.2513257132895219527 ,.15856337785764645542] 
dist 172=[-1.0021903193780046586 ,.26566305114830859466] 
dist 173=[-.98297291668782605098,.37712139558999985625] 
dist 174=[-.9299603405447292033 ,.52302402083285751465] 
dist 175=[-.9222033285473444604 ,.6720263712519734305 ] 
dist 176=[-.8206133564226060437 ,.80809505132143881147] 
dist 177=[-.79952396772577368141,.94989233562173451654] 
dist 178=[-.77983675191845410068,1.0628540190699680291 ] 
dist 179=[-.77561400323508908888,1.1541400586777110715 ] 
dist 180=[-.53003367044131102107,1.2398802115734305990 ] 
dist 181=[-.49844408324158318302,1.3156274294971177076 ] 
dist 182=[-.43671517587619526611,1.3670159565020040000 ] 
dist 183=[-.42093327559082106434,1.4104719089068883897 ] 
dist 184=[-.36651508592183269876,1.4545483027376298151 ] 
dist 185=[-.35372082505715222698,1.4916739157140001536 ] 
dist 186=[-.33956690615411125111,1.5073784087126967256 ] 
dist 187=[-.33571255813836772158,1.5140837220781203859 ] 
dist 188=[.09602028455725858802,1.5152771596640955871 ] 
dist 189=[.10497088985325247265,1.4804427503402064050 ] 
dist 190=[.1122241663490402526 ,1.4710191297444874212 ] 
dist 191=[.10971566161789589709,1.4650016329408878889 ] 
dist 192=[.08701155130456219758,1.4620479873836741312 ] 
dist 193=[-.19780291755771887362,1.2694143168604487996 ] 
dist 194=[-.39024042260445058355,1.2459407473924138482 ] 
dist 195=[-.55210165005876644268,1.1841943628583415231 ] 
dist 196=[-.71483820298981644724,1.1721290650892353926 ] 
dist 197=[-.86592723117648311261,1.0601575555375555126 ] 
dist 198=[-.98128486876064505844,1.0365657747900225637 ] 
dist 199=[-1.0927081139064801198 ,1.0056482453852392788 ] 
dist 200=[-1.2280887032976631341 ,.97141244008481947872] 
dist 201=[-1.3555856246201722734 ,.62701786631791790062] 
dist 202=[-1.4355326957033132032 ,.59334588729808555878] 
dist 203=[-1.4960552127578723605 ,.61477406025627115424] 
dist 204=[-1.5459981182446298412 ,.67736996484602506497] 
dist 205=[-1.5853870319679408484 ,.71697178937217077486] 
dist 206=[-1.6037718303843832738 ,.74735740222872540549] 
dist 207=[-1.6116983965657782812 ,.77315749191149258447] 
dist 208=[-1.6114236871488184448 ,.79406642734421519306] 
dist 209=[-.76812630310579362067,.80492384588655376468] 
dist 210=[-.7980026642138855757 ,.81050585584225744405] 
dist 211=[-.83066290948705349871,.81091431156385024706] 
dist 212=[-.85959553077900301198,.80727626815105477709] 
dist 213=[-.87458881341174364809,.80486584359157240514] 
dist 214=[-.8822628910678939467 ,.79494672200090825474] 
dist 215=[-.88372909575744449941,.79122635523766987658] 
dist 216=[-.87880794980735053746,.75814247389046265351] 
dist 217=[-.87518821245866579222,.74959538844437180171] 
dist 218=[-.87000900809582338704,.7378107083425721839 ] 
dist 219=[-.86698065796743784958,.73305908838550744956] 
dist 220=[-.76798739169535504404,.5197571773512941883 ] 
dist 221=[-.75391163033427328886,.496076034846834534  ] 
dist 222=[-.715497267378913239  ,.43700620696675493566] 
dist 223=[-.70921419678474430674,.42807741346430005441] 
dist 224=[-.63621696715165937812,.33577015570509653517] 
dist 225=[-.62093794423132395315,.31809554676252471483] 
dist 226=[-.60482550402134185371,.29770366252490370901] 
dist 227=[-.59963561429680144616,.29282709074832923565] 
dist 228=[-.54058363186093880429,.12996918989894469085] 
dist 229=[-.51368947046742363877,.10965733714324491039] 
dist 230=[-.50717335720784307523,.06752250460273648242] 
dist 231=[-.49533552445566697821,.05654828752767234301] 
dist 232=[-.49177406098934190982,.01643284363221287378] 
dist 233=[-.41379291675599496514,.00847331738495099597] 
dist 234=[-.40240880704300684206,-.00213278753937913698] 
dist 235=[-.37626599051677710847,.10914709968852514301] 
dist 236=[-.3691783070467896968 ,.2197547626041829836 ] 
dist 237=[-.3325770409060215148 ,.2939823099132569735 ] 
dist 238=[-.32506942189205302582,.3558736347550997682 ] 
dist 239=[-.30911617745173756578,.41722690029379083767] 
dist 240=[-.30435104600993904308,.47363635715781174246] 
dist 241=[.24344376961442656404,.51578867230346738264] 
dist 242=[.27880156337606766459,.55562664349215958788] 
dist 243=[.31045138154257660527,.60279558192530441622] 
dist 244=[.30692531983417391694,.64660049704292995125] 
dist 245=[.29603701802244603651,.6730070187301233276 ] 
dist 246=[.27765437509053826597,.69175885270639881634] 
dist 247=[.24420616529049959692,.7050011895665317339 ] 
dist 248=[.2035760623893353934 ,.71417775482323877833] 
dist 249=[.15651885662865573608,.71669654890771339777] 
dist 250=[.09567496939660405887,.71645987383872963775] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 1, 1, 1, 2] 
dist 0=[52.667700861279148612  ,52.667700861279148612  ] 
dist 1=[52.464234012530892158  ,52.752025685426904684  ] 
dist 2=[51.919835898253104782  ,52.820458697252115120  ] 
dist 3=[51.019132058716181699  ,52.890782273478486386  ] 
dist 4=[49.392475957060927383  ,52.982424389927541844  ] 
dist 5=[47.658630744778550530  ,53.055486064917062639  ] 
dist 6=[46.329814264504669881  ,53.051514222323648525  ] 
dist 7=[45.038950947038245644  ,52.417624820095695209  ] 
dist 8=[43.382271431680499279  ,50.938608111046403312  ] 
dist 9=[40.896273285055388920  ,49.755697448002808505  ] 
dist 10=[38.299752648762995386  ,49.256322411087349367  ] 
dist 11=[35.118532209562891680  ,48.368963047139424204  ] 
dist 12=[30.297289178887236014  ,48.129357791854863389  ] 
dist 13=[25.449443949305284685  ,47.281479175516089442  ] 
dist 14=[22.161882869945487279  ,47.022908088683489330  ] 
dist 15=[19.379555483035125063  ,46.002911472618452569  ] 
dist 16=[16.549293708496269182  ,44.164426939367553398  ] 
dist 17=[13.895472141713758582  ,30.024200136750033814  ] 
dist 18=[11.817577831682184586  ,29.663894224471119430  ] 
dist 19=[9.7571412007209795911 ,28.987256821368911829  ] 
dist 20=[7.1725659292951966689 ,28.808482677510091682  ] 
dist 21=[4.6876427452366677110 ,18.742277258593809487  ] 
dist 22=[3.0249546716984615246 ,17.898946952943503067  ] 
dist 23=[1.6394725954623181500 ,16.745307930101850062  ] 
dist 24=[.2614102717494021976 ,16.436265793601713703  ] 
dist 25=[-1.1736433091736652657 ,10.537007319571816052  ] 
dist 26=[-2.7359415506417700644 ,9.8252582091914280762 ] 
dist 27=[-4.1749529766178694153 ,8.2227309492562567367 ] 
dist 28=[-5.8282212159480591407 ,7.9854042247288762283 ] 
dist 29=[-7.3627020335413176595 ,6.1211760623060995535 ] 
dist 30=[-8.3272874267865290219 ,5.8207339611822862612 ] 
dist 31=[-9.0624108128865782113 ,5.3598960160500835378 ] 
dist 32=[-9.6805305877313145475 ,5.2693622454136542863 ] 
dist 33=[-10.179638729596261611  ,-.1750580089320799360 ] 
dist 34=[-10.439602067430027937  ,-.2506693528320778341 ] 
dist 35=[-10.576418113770708065  ,-.20738449569959584443] 
dist 36=[-10.594916655874430399  ,0                     ] 
dist 37=[-8.1655650082558778134 ,-5.0742741035536133558 ] 
dist 38=[-8.6266960617902843173 ,-4.4937828491273411544 ] 
dist 39=[-8.9908916799437764488 ,-3.8462287666443024943 ] 
dist 40=[-9.3229923452946392238 ,-2.9398633802665112117 ] 
dist 41=[-9.5989709221402475865 ,-1.9376649854137559199 ] 
dist 42=[-9.7388423959805156406 ,-.9073055509074304373 ] 
dist 43=[-9.8081032701077489212 ,.3408598144200856864 ] 
dist 44=[-9.8142500968834470965 ,2.2127033358859249120 ] 
dist 45=[-9.7611992741622948839 ,4.0765963344433062582 ] 
dist 46=[-9.7270491966498785965 ,5.2931382892250671234 ] 
dist 47=[-9.6222160316800866783 ,6.2689145427820995367 ] 
dist 48=[-9.5696289603404237460 ,7.1718513532761272774 ] 
dist 49=[-6.8068165541924477280 ,7.9595225250456519725 ] 
dist 50=[-6.5259853677185648811 ,8.4752591447188377907 ] 
dist 51=[-5.8326857659915013522 ,8.8910714998336674281 ] 
dist 52=[-5.7231708710625741486 ,9.2799695414768897308 ] 
dist 53=[-4.6645227290398360484 ,9.6161328550718109071 ] 
dist 54=[-4.4630764154828997602 ,9.8213996026739962351 ] 
dist 55=[-4.2126378030553284126 ,9.9703505248571437336 ] 
dist 56=[-4.1412892071742561103 ,10.081494391608458187  ] 
dist 57=[-2.3765632490371508995 ,10.159459603543778711  ] 
dist 58=[-2.1539415497582531779 ,10.175792619889175838  ] 
dist 59=[-1.6816512380358785884 ,10.151850409900805585  ] 
dist 60=[-1.5640038670168589607 ,10.128054903874657663  ] 
dist 61=[-1.0797528144541265819 ,6.2523620737933544851 ] 
dist 62=[-.98976071088696136617,6.4334315241322910537 ] 
dist 63=[-.80504319018804449921,6.5695377098001333803 ] 
dist 64=[-.75832340682292315926,6.6810229309781977600 ] 
dist 65=[1.4170699257962889001 ,6.7616379599891288932 ] 
dist 66=[1.6069725367285448500 ,6.7786952537245165673 ] 
dist 67=[1.5494713402101905668 ,6.7651379345433148288 ] 
dist 68=[.7621131293450786881 ,6.7568057547227967861 ] 
dist 69=[-.0068671080459322583 ,6.5222118886962203938 ] 
dist 70=[-.5358899651582724278 ,6.4569484515560167135 ] 
dist 71=[-.9910444895977940573 ,6.4087351318303840945 ] 
dist 72=[-1.4652300745293088758 ,6.3794225967011099315 ] 
dist 73=[-1.9163704937606330714 ,5.2572436458931619105 ] 
dist 74=[-2.2796162719799932312 ,5.1011123381061868759 ] 
dist 75=[-2.6489517621058840984 ,4.7997285897221905121 ] 
dist 76=[-3.1245745915145138944 ,4.7194037005984602825 ] 
dist 77=[-3.5827357865292209865 ,4.4279674870809738631 ] 
dist 78=[-3.8823749957237224451 ,4.3557831323285923902 ] 
dist 79=[-4.1242896627316910680 ,4.2401736291728681407 ] 
dist 80=[-4.3518738539430380991 ,4.2051567314228892163 ] 
dist 81=[-4.5538385057177629003 ,2.2813674971420332774 ] 
dist 82=[-4.6934238844521801506 ,2.1833605885878296806 ] 
dist 83=[-4.8146188369993492947 ,1.9603835787580632879 ] 
dist 84=[-4.9431437422701067015 ,1.9099184782919697856 ] 
dist 85=[-5.0555199031181462575 ,1.6185979545669488096 ] 
dist 86=[-5.1122092790054310239 ,1.5630752774614150782 ] 
dist 87=[-5.1392894657925121954 ,1.4523839884117666289 ] 
dist 88=[-5.1391543326110143557 ,1.4227772385741648004 ] 
dist 89=[-5.1109130839776123695 ,1.0657592368918802348 ] 
dist 90=[-5.0945337640642492192 ,1.0131834290772038286 ] 
dist 91=[-5.0322535435189091210 ,1.4646038509575558015 ] 
dist 92=[-5.0350770442259753562 ,2.4732734116934245182 ] 
dist 93=[-5.1295059122377611783 ,3.4783281907363784255 ] 
dist 94=[-5.1786128857350316500 ,4.1389604499322225092 ] 
dist 95=[-5.2039856652179396287 ,4.6743431842844171598 ] 
dist 96=[-5.2037221623009516012 ,5.1794019778030301067 ] 
dist 97=[-2.1490380443824701725 ,5.6268384515143801197 ] 
dist 98=[-2.4225925763757407057 ,5.9321967060858017200 ] 
dist 99=[-2.6376296698957287409 ,6.1922578558291809446 ] 
dist 100=[-2.8295710520533856820 ,6.4588798855827289951 ] 
dist 101=[-2.9923831166608507300 ,6.6891326140727088090 ] 
dist 102=[-3.0911053559276625452 ,6.8040036259351328808 ] 
dist 103=[-3.1619677543529246898 ,6.8609805927278375136 ] 
dist 104=[-3.2135364707294577202 ,6.8677296832535709534 ] 
dist 105=[-3.2518020228528890259 ,6.7967089644731500167 ] 
dist 106=[-3.2695445911777084236 ,6.7604783959982625738 ] 
dist 107=[-3.2757009874762419711 ,6.7208157846570343136 ] 
dist 108=[-3.2708564613906199097 ,6.6917249112248042688 ] 
dist 109=[-3.2512220139915110895 ,5.6483251158261316979 ] 
dist 110=[-3.2407837251669740844 ,5.5487998300058101150 ] 
dist 111=[-3.1967845609728707728 ,5.2732747328998493280 ] 
dist 112=[-3.1841414325849386070 ,5.2275107663459266443 ] 
dist 113=[-2.9842968130713028135 ,4.6921739379761365768 ] 
dist 114=[-3.4870474518006355825 ,4.5794588836025783899 ] 
dist 115=[-3.9740824252263378128 ,4.4599276746694896658 ] 
dist 116=[-4.5674491517078223527 ,4.4200895937454121809 ] 
dist 117=[-5.1264597205077330004 ,3.1316802149606329390 ] 
dist 118=[-5.4763440279652991231 ,2.9624598708157568887 ] 
dist 119=[-5.7402431818433825910 ,2.6201652169411707800 ] 
dist 120=[-5.9560017471442651498 ,2.5295515008102862519 ] 
dist 121=[-6.1244064107192193557 ,2.1957426717288007536 ] 
dist 122=[-6.1992655655536676484 ,2.1233322717639639901 ] 
dist 123=[-6.2320127838051105166 ,1.9946269812272367959 ] 
dist 124=[-6.2323283750102242017 ,1.9830996305953487016 ] 
dist 125=[-.76172994268438784304,2.1400806995966986846 ] 
dist 126=[-1.2162475158208816877 ,2.2608410573371312698 ] 
dist 127=[-1.5889925401707078175 ,2.3784047259715080776 ] 
dist 128=[-1.9482326189769945969 ,2.5226289776226390426 ] 
dist 129=[-2.2718292245701662710 ,2.6558101834360307336 ] 
dist 130=[-2.5022719951914364501 ,2.7292819393430274517 ] 
dist 131=[-2.7089130353680398850 ,2.7732220188410894857 ] 
dist 132=[-2.9374894247006282125 ,2.7884844904213197263 ] 
dist 133=[-3.1458037641239926284 ,2.7929050733653125360 ] 
dist 134=[-3.2715485754448342403 ,2.7935509076226500235 ] 
dist 135=[-3.3610676879042223346 ,2.7915687992106965472 ] 
dist 136=[-3.4247427796998616135 ,2.7854870729808215214 ] 
dist 137=[-3.4681576777980749652 ,2.4479749532137322564 ] 
dist 138=[-3.4774629678220584740 ,2.3976934281119534639 ] 
dist 139=[-3.4732748317929736837 ,2.3070105035476419356 ] 
dist 140=[-3.4682110585656461987 ,2.2828406269792541476 ] 
dist 141=[-2.6336268542241301019 ,2.1983217654427317027 ] 
dist 142=[-2.5488481208488836316 ,2.1733350333598362188 ] 
dist 143=[-2.3480840867954398624 ,2.1412905907590538983 ] 
dist 144=[-2.3026382167401988383 ,2.1274912752134690312 ] 
dist 145=[-2.0094342845741031280 ,.8547725879914975711 ] 
dist 146=[-1.9509893127905651600 ,.7627618349744724006 ] 
dist 147=[-1.8433445549991149065 ,.54652757819883987754] 
dist 148=[-1.8155377946742968168 ,.51156497483233026226] 
dist 149=[-1.3453137461157833890 ,.8360103228113621001 ] 
dist 150=[-1.2808133771963667214 ,1.1060581320706727697 ] 
dist 151=[-1.1265919031701228212 ,1.3537676496444359296 ] 
dist 152=[-1.3221502675803402619 ,1.6361581808935666157 ] 
dist 153=[-1.5051967620944490776 ,1.9196515699196759200 ] 
dist 154=[-1.6185938960401566423 ,2.1717703168100946970 ] 
dist 155=[-1.7028421117891481620 ,2.4495248925010304416 ] 
dist 156=[-1.7695087339680038286 ,2.8353787107504723432 ] 
dist 157=[-1.8219250238282348532 ,3.2107244384669248264 ] 
dist 158=[-1.8492734995731691544 ,3.4465273410603519327 ] 
dist 159=[-1.8635271192913591208 ,3.6255729717487489224 ] 
dist 160=[-1.8652914156544200035 ,3.7743114862282924772 ] 
dist 161=[-1.2041122289469984599 ,3.8924216437247061020 ] 
dist 162=[-1.2599323754772418624 ,3.9491828387780712684 ] 
dist 163=[-1.2998197405120894145 ,3.9766820367742071342 ] 
dist 164=[-1.3284748053313135078 ,3.9779533749133429469 ] 
dist 165=[-1.3490337847973876268 ,3.9230876470588128633 ] 
dist 166=[-1.3565956942580895162 ,3.9024022245808384242 ] 
dist 167=[-1.3578988849058140488 ,3.8572374025574094066 ] 
dist 168=[-1.3554695434375659155 ,3.8378509696037286673 ] 
dist 169=[-1.2814662574578886923 ,3.7303302157261498667 ] 
dist 170=[-1.2672509389163167686 ,3.7028920101854845419 ] 
dist 171=[-1.2381485139024923044 ,3.6165745525275557490 ] 
dist 172=[-1.2284805521289501164 ,3.5955873325112797994 ] 
dist 173=[-1.1829831395075054758 ,2.3716896880748436649 ] 
dist 174=[-1.1724184442366793621 ,2.2641709098588369072 ] 
dist 175=[-1.2592737073799059009 ,1.9940906303198257343 ] 
dist 176=[-1.4474549471819109957 ,1.9619743630406787291 ] 
dist 177=[-1.6725841607683773782 ,2.3180591797172576768 ] 
dist 178=[-1.9482404734982884876 ,2.5451086768733747081 ] 
dist 179=[-2.2087747042454602961 ,2.7213919188204908665 ] 
dist 180=[-2.5172282959155189812 ,2.8747918478232604522 ] 
dist 181=[-2.8041711198705944820 ,3.0019658595929581894 ] 
dist 182=[-2.9788229096571044222 ,3.0735424993079771572 ] 
dist 183=[-3.1048664316059375219 ,3.1181914957464966445 ] 
dist 184=[-3.1977380945267315131 ,3.1378586110303961468 ] 
dist 185=[-3.2681181459347352054 ,3.1452386684639440488 ] 
dist 186=[-3.3043640883151980955 ,3.1408312503253661270 ] 
dist 187=[-3.3225865319860314875 ,3.1278940232328670802 ] 
dist 188=[-3.3217348730557153707 ,3.1190129693390016607 ] 
dist 189=[-2.4203408792594030084 ,3.0590184377042095862 ] 
dist 190=[-2.4176799871497705540 ,3.0417770115480205004 ] 
dist 191=[-2.3980319290738639668 ,2.9810235600767587921 ] 
dist 192=[-2.3883123571467388230 ,2.9669975794347169708 ] 
dist 193=[-2.2973211613641950436 ,1.7638194223561483964 ] 
dist 194=[-2.2758783648625802018 ,1.6474683965320537369 ] 
dist 195=[-2.2215860755608326192 ,1.3718941981936088187 ] 
dist 196=[-2.2010064851197108102 ,1.3235468338284407722 ] 
dist 197=[-2.0944193624854507814 ,.93906019398264532189] 
dist 198=[-2.0685749195864479827 ,.8677594176313773333 ] 
dist 199=[-2.0527602446888560051 ,.75873218903583815802] 
dist 200=[-2.0537926573264919873 ,.72962851543539135527] 
dist 201=[-2.0255764398507156656 ,.58362248651523427343] 
dist 202=[-2.0151303484542966850 ,.57047535559071255908] 
dist 203=[-2.0060184982993531409 ,.6031105472809977149 ] 
dist 204=[-1.9969431878054483143 ,.9340837584458316694 ] 
dist 205=[-1.6696076459865545265 ,1.2639330574564295341 ] 
dist 206=[-1.7140816915844478641 ,1.4808081759690157375 ] 
dist 207=[-1.7456749929114839130 ,1.6567020718155505275 ] 
dist 208=[-1.7679799293951672802 ,1.8229380717324315079 ] 
dist 209=[-1.8229233714431106804 ,1.9704710033724896622 ] 
dist 210=[-1.9872860451415397797 ,2.0716955412775654710 ] 
dist 211=[-2.1180517310050629591 ,2.1585055824020365316 ] 
dist 212=[-2.2373765113981262346 ,2.2484922369283224609 ] 
dist 213=[-2.3403837885526884384 ,2.3264812715156071805 ] 
dist 214=[-2.4060025884203563785 ,2.4255928438397296764 ] 
dist 215=[-2.4568805724890790739 ,2.5349075160838036249 ] 
dist 216=[-2.5010365894043658191 ,2.6409148095360139126 ] 
dist 217=[-2.5341666238706489972 ,2.7330219415758256804 ] 
dist 218=[-2.5417368041834332538 ,2.7868417648734158135 ] 
dist 219=[-2.5390477531871338381 ,2.8229715207767343865 ] 
dist 220=[-2.5369121283959512612 ,2.8444539517272957597 ] 
dist 221=[-2.4498213525689727005 ,2.8548928991371273716 ] 
dist 222=[-2.4256961468961517186 ,2.8535039257508593243 ] 
dist 223=[-2.4098041018992738590 ,2.8337646372110150163 ] 
dist 224=[-2.4009725603597459387 ,2.8234095694714584373 ] 
dist 225=[-.91619095651304503174,1.9817087081100729651 ] 
dist 226=[-.88411642710482833595,1.9630861822608775902 ] 
dist 227=[-.80487163854761272111,1.9474166100920116851 ] 
dist 228=[-.79066986828545243503,1.9359920055772175691 ] 
dist 229=[-.66673322169308542627,1.6112608713159668616 ] 
dist 230=[-.64237140770774085092,1.5649256263015884816 ] 
dist 231=[-.60864209633090674936,1.4748763789624406598 ] 
dist 232=[-.59788091712537184383,1.4504380569816551261 ] 
dist 233=[-.37765394174517745254,1.3591685939674922870 ] 
dist 234=[-.34879232311696337292,1.3369270682474964513 ] 
dist 235=[-.28537268933208970428,1.2959357028784937565 ] 
dist 236=[-.5067537166093149515 ,1.2842310956470474874 ] 
dist 237=[-.7536305248023197168 ,1.0180808065476684335 ] 
dist 238=[-.9193478523905129025 ,1.1449021993624792692 ] 
dist 239=[-1.0575392460167820337 ,1.2462821718257005314 ] 
dist 240=[-1.1945211517564492531 ,1.3395681544864453022 ] 
dist 241=[-1.3204350706941055827 ,1.4206015318513054259 ] 
dist 242=[-1.4144390945073100898 ,1.4730667654134494952 ] 
dist 243=[-1.5031873331340775579 ,1.5146932686906975606 ] 
dist 244=[-1.6081197864558864149 ,1.5524558055064947796 ] 
dist 245=[-1.7054850363386981187 ,1.5829118348332676289 ] 
dist 246=[-1.7640223375970711731 ,1.5953689557451919027 ] 
dist 247=[-1.8054027533982870509 ,1.5991315359533030639 ] 
dist 248=[-1.8342702075391416386 ,1.5969302790465500076 ] 
dist 249=[-1.8529593253644173512 ,1.5678665802781302496 ] 
dist 250=[-1.8568290553221803226 ,1.5574014661640805267 ] 
dist 251=[-1.8494780823126547736 ,1.5397739197939661165 ] 

8 phat 4 dirichlet min maxes function [0, 2, 0, 2, 2, 1, 1, 1, 2] 
dist 0=[49.106847225009424620  ,49.106847225009424620  ] 
dist 1=[48.050874842184293324  ,49.654179619576278601  ] 
dist 2=[46.859346705804938758  ,49.960971906150350540  ] 
dist 3=[45.770484380983835617  ,50.056719404528590396  ] 
dist 4=[44.546227616498687563  ,50.070128955595801896  ] 
dist 5=[42.813675871552272903  ,50.014228087496425755  ] 
dist 6=[40.881810678317919977  ,49.978439317715142383  ] 
dist 7=[38.861345695657438226  ,49.933800000785039903  ] 
dist 8=[36.383556255622916019  ,49.842030687732121797  ] 
dist 9=[32.624943714509153356  ,46.593865512696490498  ] 
dist 10=[28.841047104165495525  ,46.101957253480689889  ] 
dist 11=[26.262145891312893709  ,45.291329682168360443  ] 
dist 12=[24.064839565528831695  ,45.064889764080243346  ] 
dist 13=[21.804846117072656100  ,44.339384926783335237  ] 
dist 14=[19.668930003486393111  ,40.179414771743878189  ] 
dist 15=[17.966963832812247258  ,39.551353030997537694  ] 
dist 16=[16.250795599430675194  ,35.265787842880163337  ] 
dist 17=[14.057673730157930624  ,32.262353092385696523  ] 
dist 18=[11.927406756043963975  ,30.635836054352502961  ] 
dist 19=[10.462052029891988335  ,30.218987090234509724  ] 
dist 20=[9.1964381012098900713 ,28.782265397185577348  ] 
dist 21=[7.8637356524428886951 ,28.432172631409026127  ] 
dist 22=[6.5805009013559607104 ,28.023310643430113555  ] 
dist 23=[5.5120182152824762930 ,27.867369754001359737  ] 
dist 24=[4.3885058294107588685 ,16.097407892953377447  ] 
dist 25=[2.8843609844727116112 ,11.725216954857377549  ] 
dist 26=[1.4219008628790296386 ,11.172386318518816638  ] 
dist 27=[.46484457939234989949,10.047292451023558171  ] 
dist 28=[-.3135398726553849319 ,9.7909283061693583081 ] 
dist 29=[-1.7009015376177590817 ,8.8597017933299520718 ] 
dist 30=[-3.2341079928991875102 ,7.7082619941006069636 ] 
dist 31=[-5.0625703183142601686 ,7.4489685920235668089 ] 
dist 32=[-6.7770430528756248441 ,6.6482774900926509619 ] 
dist 33=[-7.8549330977698363431 ,-1.4367538379048749342 ] 
dist 34=[-8.6764909519433980705 ,-1.3658738619826480873 ] 
dist 35=[-9.3671149024202508208 ,-1.2243102842112399535 ] 
dist 36=[-9.9241589316999263539 ,-1.0066469931156300524 ] 
dist 37=[-10.212077849493550745  ,-.63139628810428345088] 
dist 38=[-10.370264577108948756  ,-.18599568974417337318] 
dist 39=[-10.409099919086783066  ,.31192325601423568331] 
dist 40=[-9.5038295520782396913 ,.94247436699824418203] 
dist 41=[-9.4382033863719752073 ,1.9174089450918335572 ] 
dist 42=[-9.2092708311192107391 ,2.8963586428025671704 ] 
dist 43=[-9.1721107824705884465 ,3.5430623647389184414 ] 
dist 44=[-8.5836960673895337356 ,4.0696389777334068735 ] 
dist 45=[-8.4515872886827768140 ,4.5693465010926334213 ] 
dist 46=[-8.3900580916365456701 ,5.0132239296782197289 ] 
dist 47=[-8.3001179142157057097 ,5.3170765863672048228 ] 
dist 48=[-8.2518739479441080386 ,5.5765436859639466300 ] 
dist 49=[-7.1352290823714286834 ,5.8433794465850899854 ] 
dist 50=[-5.8700818078123996227 ,6.0751448220955060874 ] 
dist 51=[-5.7526902458087537572 ,6.1946167635727374187 ] 
dist 52=[-5.3379861732384731239 ,6.2551848054774543232 ] 
dist 53=[-5.2400570719542779774 ,6.2661503375326989424 ] 
dist 54=[-5.1099419235695788390 ,6.2205862803686770765 ] 
dist 55=[-5.0647732607020608824 ,6.1892782366344407320 ] 
dist 56=[-3.5599636270511600675 ,6.1469701904173577335 ] 
dist 57=[-2.1973394003024053003 ,6.1211195340425364547 ] 
dist 58=[-2.0235825987051644355 ,4.5829182349390733965 ] 
dist 59=[-1.6410071327774686564 ,4.5768411793183672206 ] 
dist 60=[-1.5595908713469065910 ,4.8395283207932642788 ] 
dist 61=[-1.1199648499024461168 ,5.0580386467569455648 ] 
dist 62=[-1.0434979071089853065 ,5.1834685402729338961 ] 
dist 63=[-.87889217296734619576,5.2655189306688737819 ] 
dist 64=[-.84386382808610595161,5.3109865227330451528 ] 
dist 65=[.53492853762241030859,5.3316638845857798345 ] 
dist 66=[.66655832733276274231,5.3301304851009891796 ] 
dist 67=[.95413169883511453071,5.2890191667254854233 ] 
dist 68=[.88992600235783625913,5.2742954228530228078 ] 
dist 69=[.53359594280744428513,5.2577803706913051386 ] 
dist 70=[.1771970273550419966 ,5.2826508462802027520 ] 
dist 71=[-.1379842668606329598 ,5.2804945515707571995 ] 
dist 72=[-.4839942703763174977 ,4.9216536025494186690 ] 
dist 73=[-.96359281566984075958,4.0787788011138165296 ] 
dist 74=[-1.4353835762544836422 ,3.9603809732100288094 ] 
dist 75=[-1.7502370548358972931 ,3.7219318084792612373 ] 
dist 76=[-2.0112109019660339814 ,3.6562692481272104827 ] 
dist 77=[-2.2678190030384625999 ,3.4024618109183427376 ] 
dist 78=[-2.5027811644971503839 ,3.3455183101774017319 ] 
dist 79=[-2.6773071591168259226 ,3.2269244453238065667 ] 
dist 80=[-2.8414537651001832507 ,3.1911243592684379958 ] 
dist 81=[-3.0349665717219080548 ,2.3152003597895794499 ] 
dist 82=[-3.2147052317672237752 ,2.3075716926241748954 ] 
dist 83=[-3.3238381532585327897 ,2.2828055402319145040 ] 
dist 84=[-3.4024421106059275825 ,2.2716510634751393833 ] 
dist 85=[-3.4602433107928062205 ,2.2010654025536968963 ] 
dist 86=[-3.5004279084286358316 ,2.1824462307670750047 ] 
dist 87=[-3.5086677494609300110 ,2.1494509320797361793 ] 
dist 88=[-3.5049432696465055417 ,2.1390770605645945466 ] 
dist 89=[-3.7042916917492281187 ,1.8847140763595629937 ] 
dist 90=[-3.8816818871324479504 ,1.8466583152028328574 ] 
dist 91=[-4.0094003092577914506 ,1.7634618828320662869 ] 
dist 92=[-4.1030458951376482036 ,1.8499491565360698922 ] 
dist 93=[-4.1714906734408795034 ,2.1663163183141136691 ] 
dist 94=[-4.1985710173970121814 ,2.4542588994292124772 ] 
dist 95=[-4.2055474494544034228 ,2.6641492536704838727 ] 
dist 96=[-4.1995725585757943180 ,2.8572437596641638278 ] 
dist 97=[-2.8066385797114883946 ,3.0781529295362554981 ] 
dist 98=[-2.7548038408598183185 ,3.2792224417038229508 ] 
dist 99=[-2.7353451520758910942 ,3.3931235663646998786 ] 
dist 100=[-2.6920276222559114082 ,3.4651264817739773173 ] 
dist 101=[-2.6759661078522007012 ,3.4989422749972126764 ] 
dist 102=[-2.6659665442377008611 ,3.5154008025282912972 ] 
dist 103=[-2.6616020828457637603 ,3.5181022523312823451 ] 
dist 104=[-.97010627710843016836,3.5112671815973750633 ] 
dist 105=[-.85702964517806075558,3.5012424337044992859 ] 
dist 106=[-.59632701799805649259,3.3522057572373956027 ] 
dist 107=[-.83322066602384522534,3.3355856085436964441 ] 
dist 108=[-1.1542518238177831834 ,3.2726530828011347732 ] 
dist 109=[-1.4818487327742199666 ,3.2579492093576148912 ] 
dist 110=[-1.7886969987034680893 ,3.0741812066395866285 ] 
dist 111=[-2.0269143705958490938 ,3.0300988182103586293 ] 
dist 112=[-2.2605587507175285468 ,2.9833120473671684346 ] 
dist 113=[-2.5491599399030724836 ,2.9595584053454563762 ] 
dist 114=[-2.8229044195705106955 ,2.3525076409409488582 ] 
dist 115=[-2.9972503039291071943 ,2.2684262391346919819 ] 
dist 116=[-3.1322396822596329425 ,2.3953255932286809261 ] 
dist 117=[-3.2488928793198225008 ,2.5816270166376266056 ] 
dist 118=[-3.3454819775581946135 ,2.7794388204152807550 ] 
dist 119=[-3.4006964849865922401 ,3.0451792693657697219 ] 
dist 120=[-3.4317180122832338350 ,3.2985592235536027229 ] 
dist 121=[-3.4378039921206738903 ,3.4470219603989853340 ] 
dist 122=[-1.0829905804934817554 ,3.5473567007714962452 ] 
dist 123=[-1.2846088647634764042 ,3.6085618602111194474 ] 
dist 124=[-1.4811391945916446776 ,3.6500550863731033620 ] 
dist 125=[-1.6466445363313952730 ,3.6716743236447475558 ] 
dist 126=[-1.8212594492379374458 ,3.6829460235956003436 ] 
dist 127=[-2.0541618308980261914 ,3.6831041852453944311 ] 
dist 128=[-2.2838061903874761098 ,3.3031410378346934198 ] 
dist 129=[-2.4454178351789784604 ,3.2449686098106774401 ] 
dist 130=[-2.5882896976524995085 ,3.1494991506598276609 ] 
dist 131=[-2.7431263870845388850 ,3.1214206999522904307 ] 
dist 132=[-2.8939900749219252319 ,3.0394243028024288635 ] 
dist 133=[-3.0210050667741226883 ,3.0100548876460337106 ] 
dist 134=[-3.1550162132739656861 ,2.9896530257834364953 ] 
dist 135=[-3.3338169619083587399 ,2.9771060927145405084 ] 
dist 136=[-3.5039054325908496571 ,.76793840333971748409] 
dist 137=[-3.6031356258747199292 ,.58584342987621552741] 
dist 138=[-3.6695730952110573707 ,.17737089325220937111] 
dist 139=[-3.7087400657184532777 ,.10093403787595189371] 
dist 140=[-3.7298837699539037198 ,-.38588414132397517137] 
dist 141=[-3.7305604217228859145 ,-.46957378274056046592] 
dist 142=[-3.7103717285672608779 ,-.49532043288904995276] 
dist 143=[-3.6976924886199441667 ,-.36484955875922843267] 
dist 144=[-3.4743559242461670306 ,-.21622340735466852238] 
dist 145=[-3.4324160846246109039 ,-.00374850168361240415] 
dist 146=[-3.3281940199632233728 ,.21236822472424430676] 
dist 147=[-3.2925795627657585105 ,.37553724897078569549] 
dist 148=[-3.1048329485267243096 ,.53135456942612284383] 
dist 149=[-3.0610690467322122343 ,.71812533572131407562] 
dist 150=[-2.9721459352947013261 ,.91077597490837664819] 
dist 151=[-2.9440687865429523084 ,1.0900724348667965482 ] 
dist 152=[-3.0143165510869562875 ,1.2941587320664949152 ] 
dist 153=[-3.0918774095479842478 ,1.6243849850524767038 ] 
dist 154=[-3.1409766982900438694 ,2.0334994175317104707 ] 
dist 155=[-3.1642049733607167201 ,2.4210677004239880508 ] 
dist 156=[-3.1737346837435448960 ,2.7656315577683806520 ] 
dist 157=[-3.1698781336264988082 ,3.0030515204730471092 ] 
dist 158=[-3.1549768772280163541 ,3.2077108778095394363 ] 
dist 159=[-3.1436113534453310732 ,3.4214763025780309521 ] 
dist 160=[-2.8911639168306834336 ,3.6143616812012892717 ] 
dist 161=[-2.8482153959426909575 ,3.7356587901831668449 ] 
dist 162=[-2.7529755837405656981 ,3.8278648573582924720 ] 
dist 163=[-2.7219235786452510457 ,3.9046099481124560723 ] 
dist 164=[-2.5769755792156207150 ,3.9656321247438518104 ] 
dist 165=[-2.5448942900867011867 ,3.9950676321472872120 ] 
dist 166=[-2.4595053660240020088 ,4.0070299968381509514 ] 
dist 167=[-2.4375352242754823906 ,4.0026270344900625002 ] 
dist 168=[.03232626858741493083,2.5540380297693198413 ] 
dist 169=[.13573057768097836545,2.5402586035132381335 ] 
dist 170=[-.30097914098783769731,2.1182224658590272326 ] 
dist 171=[-.6447328428258236516 ,2.0734847364286020132 ] 
dist 172=[-.93244123473730494146,1.9542274442536616053 ] 
dist 173=[-1.2193666163072566471 ,1.9344557407545059310 ] 
dist 174=[-1.4842386822931617815 ,1.7173130672469959537 ] 
dist 175=[-1.6838990838348466260 ,1.6724947557860916012 ] 
dist 176=[-1.8742699727702196411 ,1.6227673116513477224 ] 
dist 177=[-2.1020534812258962515 ,1.6061406938085389605 ] 
dist 178=[-2.3147752876668326512 ,1.3852120647129811377 ] 
dist 179=[-2.4450121183324029103 ,1.4290347952123071000 ] 
dist 180=[-2.5399162624610197080 ,1.4624631691291688623 ] 
dist 181=[-2.6115718752764324354 ,1.4785093312129899404 ] 
dist 182=[-2.6652293795111197840 ,1.4849896919178417707 ] 
dist 183=[-2.6882759133688742314 ,1.4852597660116684815 ] 
dist 184=[-2.6961856921114528018 ,1.4053892183786335600 ] 
dist 185=[-2.6935611388379371773 ,1.3914967572911743172 ] 
dist 186=[-.32048193080367838099,1.3568740653005379561 ] 
dist 187=[-.49350510886593887824,1.3440691596720481993 ] 
dist 188=[-.64165599742677064309,1.2787585213448841600 ] 
dist 189=[-.79486874440337922133,1.2631234121941626647 ] 
dist 190=[-.9398518692061183164 ,1.2299071603550651814 ] 
dist 191=[-1.0551451177066242947 ,1.2189120847718390343 ] 
dist 192=[-1.1709255830973279238 ,1.0520878197332558620 ] 
dist 193=[-1.3178542431425822455 ,1.0268871254441383916 ] 
dist 194=[-1.4593966295504819446 ,.96353835332744041741] 
dist 195=[-1.5536718164928360612 ,.95083075239383043692] 
dist 196=[-1.6314997521950670534 ,.84587160719003364712] 
dist 197=[-1.7073744467155964053 ,.82435804349057058524] 
dist 198=[-1.7763065483892118621 ,.7928522005339368364 ] 
dist 199=[-1.8264154286622472401 ,.78298742428796366631] 
dist 200=[-1.8723999825765590148 ,-.18786877220458622063] 
dist 201=[-1.9248655221596485701 ,.08520282788808387080] 
dist 202=[-1.9706427685665227267 ,.36233088797940904192] 
dist 203=[-1.9929333386345179685 ,.5530230711857256828 ] 
dist 204=[-2.0741314578308586873 ,.71715455104499421265] 
dist 205=[-2.1241341007201678670 ,.88823778326982381694] 
dist 206=[-2.1609248592660487891 ,1.0509558368744562971 ] 
dist 207=[-2.1893732379100572439 ,1.1816891593761227039 ] 
dist 208=[-2.2087430810394177780 ,1.3141999680030141649 ] 
dist 209=[-2.2119640661674249973 ,1.4840153205504718886 ] 
dist 210=[-2.2039234344402813584 ,1.6483906029524520448 ] 
dist 211=[-2.1997081377408919772 ,1.7591818041558954419 ] 
dist 212=[-2.1230717938589342814 ,1.8520783710229348748 ] 
dist 213=[-2.1017783640004230725 ,1.9450082655394085558 ] 
dist 214=[-2.0830800638892215809 ,2.0309908727919963586 ] 
dist 215=[-2.0703482020863648758 ,2.0961502314691240686 ] 
dist 216=[-1.5916398329823383128 ,2.1586216793398999883 ] 
dist 217=[-1.5342179952745097405 ,2.2338733809965370834 ] 
dist 218=[-1.3969706858898697956 ,2.3021469428982730940 ] 
dist 219=[-1.3687095384207566251 ,2.3367576259983197340 ] 
dist 220=[-1.1666115380774853965 ,2.3534237886345332646 ] 
dist 221=[-1.1269179170701644744 ,2.3560428960194851032 ] 
dist 222=[-1.0594810734842089552 ,2.3388979903522255337 ] 
dist 223=[-1.0423894108122825918 ,2.3288133314138732850 ] 
dist 224=[-.7161964386809102334 ,2.3098673384216217934 ] 
dist 225=[-.67248908922979127545,2.3011793272522176135 ] 
dist 226=[-.56784475467914736525,2.0523681439651706181 ] 
dist 227=[-.55012724254279743333,2.0133157892863544243 ] 
dist 228=[-.40045948477131457246,1.9298543182996488620 ] 
dist 229=[-.37251909973569589569,1.8963884232582784470 ] 
dist 230=[-.33255132720804275399,1.5983980295020776426 ] 
dist 231=[-.32095864478249817213,1.4192558434850136604 ] 
dist 232=[.00289782756500269541,.88885292236335247209] 
dist 233=[.02793262098510538386,.88233221093481876758] 
dist 234=[-.16974499693709776751,.72718634054615735043] 
dist 235=[-.30144917125278727358,.71466068053412135485] 
dist 236=[-.41021527651548455313,.68026873322833921422] 
dist 237=[-.51631069819488742645,.67449910467155669628] 
dist 238=[-.61273262414160800471,.60821131224183621   ] 
dist 239=[-.68287661991808321459,.59422342806389187346] 
dist 240=[-.74729703124717235448,.5792870406476757651 ] 
dist 241=[-.82086749610155148454,.5741395235269722552 ] 
dist 242=[-.88853005500422472383,.41374662111348266831] 
dist 243=[-.92936240226985130118,.39252759282406104394] 
dist 244=[-.95841209407338267109,.34981455342241607023] 
dist 245=[-.97903023216419203344,.33494725073948587178] 
dist 246=[-.99373182242152792307,.21707211870378924215] 
dist 247=[-.99915919440600700634,.15357652185919070676] 
dist 248=[-.99996680795519379432,.01637738993376440006] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 2, 0, 1, 1, 2] 
dist 0=[47.620911878038129847  ,47.620911878038129847  ] 
dist 1=[47.449424782348727474  ,47.710226461994449551  ] 
dist 2=[46.993341710971411854  ,47.895131094453547933  ] 
dist 3=[46.027573429446675888  ,48.059674099893679006  ] 
dist 4=[44.837188800888269040  ,48.238673706971617535  ] 
dist 5=[43.483900662532735755  ,48.383663202084242612  ] 
dist 6=[41.748370625932224630  ,48.412438565342858724  ] 
dist 7=[39.031115150101258465  ,48.360965481440199847  ] 
dist 8=[36.261458399228897087  ,48.312651785647502236  ] 
dist 9=[34.316527794754748146  ,47.951780715448459878  ] 
dist 10=[32.597656744571613752  ,47.839858437750853751  ] 
dist 11=[30.730749168606199070  ,47.413749118827059263  ] 
dist 12=[28.904328691510326425  ,47.322661756554447433  ] 
dist 13=[27.346989461350021658  ,45.676107464362117360  ] 
dist 14=[25.682971910883200650  ,37.306020504939461270  ] 
dist 15=[23.430091523962968235  ,35.126947958734565089  ] 
dist 16=[21.182241604952302727  ,34.766959165959326541  ] 
dist 17=[19.538130594423856040  ,31.446724039427106954  ] 
dist 18=[17.899626960339535832  ,30.803825993184426783  ] 
dist 19=[15.978901255486606725  ,29.984128138947773291  ] 
dist 20=[14.002084793629235126  ,29.707557851544276166  ] 
dist 21=[11.422586724572929556  ,23.878263312535373665  ] 
dist 22=[8.8931750780007298248 ,23.113154265642811356  ] 
dist 23=[7.1161468694098201954 ,21.518163134591511857  ] 
dist 24=[5.5426856531409777344 ,21.088725480149311790  ] 
dist 25=[3.8260485650993917259 ,19.437657277030274155  ] 
dist 26=[2.1382909993152918911 ,19.109732739728336324  ] 
dist 27=[.67968909713238865687,18.398440421305505640  ] 
dist 28=[-.89912982005394539327,18.197183388198148131  ] 
dist 29=[-3.0682119713880169074 ,9.8994008921318026573 ] 
dist 30=[-5.1740789684734880657 ,6.9300692689133660959 ] 
dist 31=[-6.5004865523205644655 ,4.8466217977654450093 ] 
dist 32=[-7.5192749488595363282 ,4.4694033846737622404 ] 
dist 33=[-8.3955409048076350352 ,1.9835812172071500347 ] 
dist 34=[-9.1221793948428557680 ,1.5538821562725061965 ] 
dist 35=[-9.5430694615164978511 ,.77035593574408168532] 
dist 36=[-10.600618433367538745  ,.59961156764248301384] 
dist 37=[-11.702793151415064039  ,-1.4784425397410006821 ] 
dist 38=[-12.387418728925147740  ,-1.7688334926554879856 ] 
dist 39=[-12.900135463572348923  ,-2.2633207439709251996 ] 
dist 40=[-13.315532262157008993  ,-2.3667996277629674230 ] 
dist 41=[-13.639033977804014106  ,-2.5302805546738044740 ] 
dist 42=[-13.784674669303398872  ,-2.2720981341500512688 ] 
dist 43=[-13.839567159636433834  ,-1.9242977779029390007 ] 
dist 44=[-13.832174696934868487  ,-1.5688196681728788427 ] 
dist 45=[-9.8491741295526432790 ,-1.2456259980097177486 ] 
dist 46=[-8.4214633726143663596 ,-.88471012589421766025] 
dist 47=[-7.4986871002721306023 ,-.37848327908639923515] 
dist 48=[-7.3428987278570070727 ,.13098999477336520835] 
dist 49=[-5.9791262993387887568 ,1.0571754195991223145 ] 
dist 50=[-5.7216859753487886914 ,1.9188655242000687472 ] 
dist 51=[-5.3636033522158273270 ,2.5596781848748688775 ] 
dist 52=[-5.2550133206149938667 ,3.1619279491465805109 ] 
dist 53=[-3.1676290208972358426 ,3.8698338149763349274 ] 
dist 54=[-2.9023842557821827441 ,4.5315601435531497063 ] 
dist 55=[-2.4837783915920891579 ,4.9494550165049459405 ] 
dist 56=[-2.1933677847274260924 ,5.2691881998019911911 ] 
dist 57=[-1.4902364024809220724 ,5.5388788962379338737 ] 
dist 58=[-1.3682144685180402959 ,5.7556397009243232476 ] 
dist 59=[-1.1271110542981830954 ,5.8639337534844113602 ] 
dist 60=[-1.0689666608818544711 ,5.9173071120566486081 ] 
dist 61=[.73332361252699562307,5.9232353991651231992 ] 
dist 62=[.9175870666460387550 ,4.8543011775362330945 ] 
dist 63=[1.2549642314476744089 ,5.2345196567689508082 ] 
dist 64=[1.3279704820890239087 ,5.7144796152656118434 ] 
dist 65=[1.5024296847209434475 ,6.1355709150291455440 ] 
dist 66=[1.5000500608562411714 ,6.4175946123555880926 ] 
dist 67=[1.4286029292393415036 ,6.6527450181186551988 ] 
dist 68=[1.2450936741166943332 ,6.8866844122381594153 ] 
dist 69=[1.0250638439815312016 ,7.0850000623427166990 ] 
dist 70=[.8077707618909272015 ,7.1778814104133108951 ] 
dist 71=[.5511638019423007349 ,7.2212416743070135458 ] 
dist 72=[-.03266217839663967732,7.2216625750486515778 ] 
dist 73=[-.61764464574661254661,7.1197702564244154897 ] 
dist 74=[-1.1035613252014388156 ,7.0800340660629073071 ] 
dist 75=[-1.5818913113465395753 ,7.0441864409664986587 ] 
dist 76=[-2.1028472879753135224 ,7.0133283375709621136 ] 
dist 77=[-2.9492935564417525959 ,2.1007817596549617312 ] 
dist 78=[-3.5118861953016659482 ,1.9857493095127399116 ] 
dist 79=[-3.9747733510570820019 ,1.9467356342537304163 ] 
dist 80=[-4.4232112663168786815 ,1.1448054738999087585 ] 
dist 81=[-4.8285983539161898236 ,1.0411259185598183023 ] 
dist 82=[-5.1196445151631785452 ,.81743713504749665021] 
dist 83=[-5.3830523457621110618 ,.76243225794553322374] 
dist 84=[-5.6781449453535866698 ,.51597428352266030554] 
dist 85=[-5.9437305869945596707 ,.47149133574727674901] 
dist 86=[-6.0893577326462512628 ,.36643096808031316724] 
dist 87=[-6.1753360795129841520 ,.34944790567886887898] 
dist 88=[-6.2027991982697379000 ,-.65646058987403412031] 
dist 89=[-6.2034818483617474114 ,-.67361825675140906937] 
dist 90=[-6.1868329261283400705 ,-.70695669011178262477] 
dist 91=[-6.2859797930859317859 ,-.71198871270517040586] 
dist 92=[-6.3681743625484343601 ,.52709599613197423747] 
dist 93=[-6.4237613783225641069 ,1.7788695521280147689 ] 
dist 94=[-6.4320927871000540720 ,2.6159684807752084621 ] 
dist 95=[-6.4039498692936912084 ,3.3100154817403982848 ] 
dist 96=[-6.3897815430337206705 ,3.9907582553053361734 ] 
dist 97=[-6.1518482377198582601 ,4.6112162535832570400 ] 
dist 98=[-6.0863784914736529625 ,5.0646165537870637884 ] 
dist 99=[-6.0254629443757979747 ,5.4826724955502241378 ] 
dist 100=[-5.9866113730548079595 ,5.9620335532666754427 ] 
dist 101=[-4.9132882116344983908 ,6.3992626292306597168 ] 
dist 102=[-4.7615029574396575373 ,6.6491343333735829590 ] 
dist 103=[-4.4608618018926296711 ,6.8096701426002826791 ] 
dist 104=[-4.3786750570305910473 ,6.8902924603097546427 ] 
dist 105=[-4.0662689218297337735 ,6.9361531437579534067 ] 
dist 106=[-3.9934115110305631435 ,6.9579319304564800738 ] 
dist 107=[-3.8506089797188312285 ,6.9662069214386400603 ] 
dist 108=[-3.8087184156675326331 ,6.9581723608150742630 ] 
dist 109=[-.02849447188434382918,2.2241951112775988774 ] 
dist 110=[-.36412706408202921071,2.2446363406968795020 ] 
dist 111=[-.59343313895037720647,2.2477428149725907180 ] 
dist 112=[-.78869955540694463834,2.2381880928528386071 ] 
dist 113=[-.98848681079559489496,2.2329898117145602128 ] 
dist 114=[-1.1758267624626404930 ,2.1500926745593711699 ] 
dist 115=[-1.3214192417766943073 ,2.1272974496124537285 ] 
dist 116=[-1.4642848291934240352 ,2.1050520276173094511 ] 
dist 117=[-1.6407446191763740759 ,2.0915655772993791303 ] 
dist 118=[-1.8079549541617755858 ,1.7214328895739044744 ] 
dist 119=[-1.9139066347028838580 ,1.6691509755073469804 ] 
dist 120=[-1.9952556731074401504 ,1.5645130238785493433 ] 
dist 121=[-2.0642761061283929380 ,1.5357281700582844500 ] 
dist 122=[-2.1200713294059996415 ,1.4250648175626209787 ] 
dist 123=[-2.1486378109871966529 ,1.3997950923074242861 ] 
dist 124=[-2.1627216940658599661 ,1.3486436205408300765 ] 
dist 125=[-2.1627310049350708655 ,1.3334647810060851454 ] 
dist 126=[.09342423544004431755,.20531526920493390978] 
dist 127=[-.07744174723425777542,.20360123591976990453] 
dist 128=[-.24799105244772536228,.20516888475389620103] 
dist 129=[-.42041963635091071205,.20816721098219558477] 
dist 130=[-.58109829586989726022,.21278708273484506262] 
dist 131=[-.70474260179117873167,.22082621332090061034] 
dist 132=[-.82509724634330495313,.23044555900653315431] 
dist 133=[-.97265102821887386355,.24137197161231533014] 
dist 134=[-1.1123212524866995662 ,.25534601236840355325] 
dist 135=[-1.2012053063293850231 ,.27712824180042656475] 
dist 136=[-1.2700460440185382391 ,.29910215644515291535] 
dist 137=[-1.3296976423768318659 ,.31384117548217480406] 
dist 138=[-1.3790244251788881659 ,.3260988241479947921 ] 
dist 139=[-1.4066496558500758983 ,.33816967328617436642] 
dist 140=[-1.4331625422314921573 ,.34919174723959696345] 
dist 141=[-1.4653858239309367722 ,.35726369820375221108] 
dist 142=[-1.4916999067902569096 ,.36471762509530927261] 
dist 143=[-1.5016728050126041869 ,.37327297624964742627] 
dist 144=[-1.5042409993301266956 ,.38105311154158564616] 
dist 145=[-1.5015313280727772407 ,.3854130992271235105 ] 
dist 146=[-1.4714942840576396922 ,.38810002330084458978] 
dist 147=[-1.4611894007763628654 ,.38920299734202918719] 
dist 148=[-1.4466304647350092119 ,.4166069044504218933 ] 
dist 149=[-1.4399370916578506113 ,.5659578533362214197 ] 
dist 150=[-1.2495210108760260227 ,.7154870426663459091 ] 
dist 151=[-1.2212126457040313343 ,.8245008349312554713 ] 
dist 152=[-1.1620887765396709631 ,.9248206642537199645 ] 
dist 153=[-1.1447436849289361607 ,1.0396449424928090373 ] 
dist 154=[-1.0715669571948947254 ,1.1551551972766099337 ] 
dist 155=[-1.0560248275182161883 ,1.2582166552341800834 ] 
dist 156=[-1.0145053682153699284 ,1.3720186143579718645 ] 
dist 157=[-1.0056920925958804300 ,1.5304130822053858307 ] 
dist 158=[-.18565644478168105299,1.6842323639531460888 ] 
dist 159=[-.18020002447608866899,1.7797692462018899538 ] 
dist 160=[-.16053652637658290098,1.8510181311544145874 ] 
dist 161=[-.15751209178337288562,1.9078688427512344574 ] 
dist 162=[-.1592982937776642343 ,1.9511914651746463983 ] 
dist 163=[-.16812308070785650176,1.9684304503563301451 ] 
dist 164=[-.18081675168229634618,1.9748327886837126696 ] 
dist 165=[-.19804974781653776026,1.9748882581837502397 ] 
dist 166=[-.221935262310755617  ,1.9241036365989826041 ] 
dist 167=[-.2611898456549334795 ,1.9107934620476825394 ] 
dist 168=[-.30175971731225624095,1.8780940498493109872 ] 
dist 169=[-.33089647136192924946,1.8649081843889334412 ] 
dist 170=[-.35727707794343453624,1.7941307432444179639 ] 
dist 171=[-.38684215134000618895,1.7764876240041049200 ] 
dist 172=[-.41623859077913533612,1.7336182096960034815 ] 
dist 173=[-.44194550676226497592,1.7178066119713275712 ] 
dist 174=[-.46990689101513914129,1.4998471563150870464 ] 
dist 175=[-.5134825192725320835 ,1.4934314653823537999 ] 
dist 176=[-.7241137676642378657 ,1.4675923722377266879 ] 
dist 177=[-.9296830786303000098 ,1.4621232213807061492 ] 
dist 178=[-1.1165494835153887977 ,1.3831266807768532439 ] 
dist 179=[-1.2525082181940644705 ,1.3641137310839576168 ] 
dist 180=[-1.3773690274343379998 ,1.3462373054125846440 ] 
dist 181=[-1.5199246150838097237 ,1.3376150040270456498 ] 
dist 182=[-1.6513183723011821239 ,1.0665369366278689219 ] 
dist 183=[-1.7316157109253920065 ,1.0292794118148768778 ] 
dist 184=[-1.7899441121723323967 ,.9559022634498424360 ] 
dist 185=[-1.8336296579631652846 ,.9362589607754665192 ] 
dist 186=[-1.8654804707917563823 ,.8637190707748054005 ] 
dist 187=[-1.8765587363179442141 ,.8467228301155435390 ] 
dist 188=[-1.8789964166498479045 ,.8163593645239954141 ] 
dist 189=[-1.8763520840921542972 ,.8082645657561434522 ] 
dist 190=[-.86532216303677664995,.02398791594894837341] 
dist 191=[-.86430569470480074627,.01431225886898783882] 
dist 192=[-.85223755914629572302,-.06451577305350348539] 
dist 193=[-.84829057535624131336,-.07815290295012082744] 
dist 194=[-.88329474036731488857,-.08903558860475859805] 
dist 195=[-.94278194368817867143,-.08559487969931170665] 
dist 196=[-.99362653404771833308,-.07537266912541156370] 
dist 197=[-1.0460659180014244534 ,-.05581451736267414331] 
dist 198=[-1.0925856280470246666 ,.05735145597708048280] 
dist 199=[-1.1197954674081891440 ,.24938848301452130143] 
dist 200=[-1.1381082954968165103 ,.45057673862664268818] 
dist 201=[-1.1491054833683605418 ,.58303741272499355888] 
dist 202=[-1.1546925796804592360 ,.69068198629264959382] 
dist 203=[-1.1550377095418224513 ,.79279003020932683878] 
dist 204=[-1.1462889661311870826 ,.88367175526644527118] 
dist 205=[-1.1445771144789360470 ,.94649413252976801115] 
dist 206=[-.81492044344315030706,1.0008684354745366453 ] 
dist 207=[-.8120967910296746145 ,1.0580198450621869406 ] 
dist 208=[-.75620458896323011116,1.1090671456276549653 ] 
dist 209=[-.74612701436562277162,1.1390706764444310786 ] 
dist 210=[-.72354593314764786361,1.1594379332660644884 ] 
dist 211=[-.71595724260104396376,1.1720134452174382642 ] 
dist 212=[-.67970573522638992413,1.1789329250398483617 ] 
dist 213=[-.67150617041631293534,1.1795767003694906445 ] 
dist 214=[-.64989443380062254124,1.1722072157317770613 ] 

8 phat 4 dirichlet min maxes function [0, 2, 2, 0, 2, 0, 1, 0, 2] 
dist 0=[48.634977378524687807  ,48.634977378524687807  ] 
dist 1=[48.336783633840762195  ,48.888583051106227066  ] 
dist 2=[47.828916944832797556  ,49.149434456587351938  ] 
dist 3=[46.737804606269025745  ,49.476167943839184392  ] 
dist 4=[45.399891432354377188  ,49.763412004349189468  ] 
dist 5=[43.906342336428001289  ,49.866616991312528974  ] 
dist 6=[42.008783800134213610  ,49.860656274649552852  ] 
dist 7=[39.057087599698484262  ,49.823377973636924560  ] 
dist 8=[36.056678349182768735  ,49.443508288593276520  ] 
dist 9=[33.964446533310461966  ,49.315221998544976204  ] 
dist 10=[32.130978616297688892  ,48.933069734463646932  ] 
dist 11=[30.163902020286581586  ,48.766922640687422702  ] 
dist 12=[28.254079506487309274  ,46.764822645690677795  ] 
dist 13=[26.649091295415917081  ,46.363257457714862376  ] 
dist 14=[24.954422008475484493  ,44.418998944714625301  ] 
dist 15=[22.686006693658516205  ,36.920998195322866220  ] 
dist 16=[20.434465878672278422  ,33.551087443863475428  ] 
dist 17=[18.806994308976665292  ,32.891404229352831643  ] 
dist 18=[17.318328137641828771  ,32.094822690369552326  ] 
dist 19=[15.620987719378348776  ,31.843446875463715649  ] 
dist 20=[13.909576518464449108  ,25.553277230050681247  ] 
dist 21=[12.364318379601408580  ,24.730968737134797613  ] 
dist 22=[10.059004605436216425  ,23.047851478915874014  ] 
dist 23=[7.5138756603992883973 ,22.600536888132544819  ] 
dist 24=[5.7488475948578834209 ,20.924037361458153431  ] 
dist 25=[4.2100090622731339783 ,20.576599691347775644  ] 
dist 26=[2.5679822809429873040 ,19.893843546390618225  ] 
dist 27=[.97497203384605942603,19.712380295504767101  ] 
dist 28=[-.36860424069720854807,9.0277108079875424530 ] 
dist 29=[-1.7953334932067515102 ,8.6805361412824172939 ] 
dist 30=[-3.7216796325709120041 ,7.1663789590774926567 ] 
dist 31=[-5.5823842160432639788 ,3.7266680531710275047 ] 
dist 32=[-6.8077229923518204091 ,.87386138709786782565] 
dist 33=[-8.1485931277024482011 ,.38341573233261885587] 
dist 34=[-9.3725216750731433573 ,-.49243645777247643791] 
dist 35=[-10.762888230636692623  ,-.67622411925205843282] 
dist 36=[-12.044412703235745938  ,-3.0515304472769000978 ] 
dist 37=[-12.833579913912758871  ,-3.3769867410528002647 ] 
dist 38=[-13.416193627962922979  ,-3.4439512068624761888 ] 
dist 39=[-13.872619785210080091  ,-3.2632092975318524729 ] 
dist 40=[-14.216405280265666293  ,-3.0537055018363609802 ] 
dist 41=[-14.349015440146459261  ,-2.8813702565196872417 ] 
dist 42=[-14.397830892720614274  ,-2.7051529065780013033 ] 
dist 43=[-14.406828445173554435  ,-2.4796730156482018796 ] 
dist 44=[-9.4056231068504852373 ,-2.2412953914385466575 ] 
dist 45=[-9.2069564337382467188 ,-2.0133772709435007310 ] 
dist 46=[-9.1728448638366619260 ,-1.7500998791341324734 ] 
dist 47=[-7.1532996458460016340 ,-.62315134851076104595] 
dist 48=[-5.6790781697409643415 ,.54569539355499217148] 
dist 49=[-5.4019704743104057700 ,1.5116068733818167956 ] 
dist 50=[-5.0650275121880260164 ,2.4530901414433854203 ] 
dist 51=[-4.9817406266612446301 ,3.3067274685899442032 ] 
dist 52=[-2.7235197191018101143 ,3.9219851237995269083 ] 
dist 53=[-2.3529195401688880892 ,4.4802851749193078206 ] 
dist 54=[-2.2492613787808169163 ,5.1064931989645388759 ] 
dist 55=[-1.7524737062283837593 ,5.6846492423608037899 ] 
dist 56=[-.91206867755592496474,6.0511911626947594795 ] 
dist 57=[-.79825760791107430538,6.3327803570564084169 ] 
dist 58=[-.57792874476557914959,6.5720570467624261161 ] 
dist 59=[-.52727609485510677521,6.7661683540940360972 ] 
dist 60=[1.9213277812489923759 ,6.8676324901341493603 ] 
dist 61=[2.1381406121275840868 ,6.9212308494901262823 ] 
dist 62=[2.5482976742131468552 ,6.9245333934979076989 ] 
dist 63=[2.6387324906088439836 ,4.6382071539653114203 ] 
dist 64=[2.6563494145517129611 ,5.0217319640343186398 ] 
dist 65=[2.5826178069192849136 ,5.2969403558725184876 ] 
dist 66=[2.4707000998785201301 ,5.5464856770760949743 ] 
dist 67=[2.2730200195811826408 ,5.8275355536374400942 ] 
dist 68=[2.0197658759663095858 ,6.0823241095924467044 ] 
dist 69=[1.7377468095132556740 ,6.2269783458387926009 ] 
dist 70=[1.3804779873849712322 ,6.3192818782188645739 ] 
dist 71=[.82679977172524269645,6.3649488660131269184 ] 
dist 72=[.26776515717337218902,6.3835340003682597279 ] 
dist 73=[-.11089823348615556523,6.3780918420221388752 ] 
dist 74=[-.43022608827685167866,6.3397975375169805174 ] 
dist 75=[-1.2701087204606320433 ,6.3121537788348257276 ] 
dist 76=[-2.2648216422973574698 ,1.3458841581556479866 ] 
dist 77=[-2.9289499564230037509 ,1.2747099352930563908 ] 
dist 78=[-3.4786676575211717582 ,1.1864711677355864052 ] 
dist 79=[-4.0166642726022551801 ,1.1620717244927857105 ] 
dist 80=[-4.5065850428601798131 ,.54447209081535965467] 
dist 81=[-4.8643981428409228846 ,.46723110633420733762] 
dist 82=[-5.1943850468064578339 ,.3023836465530366286 ] 
dist 83=[-5.5732554192101531689 ,.26322001232723209751] 
dist 84=[-5.9190724413282487980 ,.09245929928582635463] 
dist 85=[-6.1171185835727856483 ,.06159899224650176402] 
dist 86=[-6.2451919038306550201 ,-.00210845953958447175] 
dist 87=[-6.3116703654821358263 ,-.01755311298984831008] 
dist 88=[-6.3459655099468779337 ,-.22888604340060066474] 
dist 89=[-6.3455283559370205776 ,-.06435913237330596884] 
dist 90=[-6.3237610315687741441 ,.17240282095621440456] 
dist 91=[-6.3222845321285417005 ,.43747863982535450998] 
dist 92=[-6.0964648984675494845 ,.93214242608003932642] 
dist 93=[-6.0499419475294472666 ,1.7088093271854829313 ] 
dist 94=[-5.8853443991020804980 ,2.3617952809428787695 ] 
dist 95=[-5.8615374046378996356 ,3.0171005494578430624 ] 
dist 96=[-5.4265253558359502239 ,3.6240709939390449892 ] 
dist 97=[-5.3278508431687103538 ,4.0841195527543106946 ] 
dist 98=[-5.2531440606136212240 ,4.5248508102815564592 ] 
dist 99=[-5.2367030388347307368 ,5.0547102332875987929 ] 
dist 100=[-3.8653899129662774650 ,5.5501243756621910051 ] 
dist 101=[-3.6856397735741283889 ,5.8533581175069414723 ] 
dist 102=[-3.3423293435868372735 ,6.0739890593840784181 ] 
dist 103=[-3.2547888413611557058 ,6.2396731890399889841 ] 
dist 104=[-2.9588258841952348936 ,6.3608758395899159749 ] 
dist 105=[-2.8839801056530358872 ,6.4039506743774298729 ] 
dist 106=[-2.8162873940713369942 ,6.4140128389547281373 ] 
dist 107=[-2.8028053639112617614 ,6.4034412581098673499 ] 
dist 108=[-.42886954498810453968,3.6985501838932395047 ] 
dist 109=[-.40115520033762476572,3.7040460441480436972 ] 
dist 110=[-.36566226595827433776,3.7038110405546160700 ] 
dist 111=[-.77117759701070803396,3.6477410776211176635 ] 
dist 112=[-1.2807593494543818686 ,3.6299687355504532259 ] 
dist 113=[-1.7034163947977731566 ,3.5644643886019201499 ] 
dist 114=[-2.1182160951874190742 ,3.5464656286705558030 ] 
dist 115=[-2.4964240286782203772 ,3.3553469407056728245 ] 
dist 116=[-2.7730116209360361835 ,3.3086866538015618460 ] 
dist 117=[-3.0282342956002722809 ,3.2523829112907395577 ] 
dist 118=[-3.3211490784722328803 ,3.2271529019417068090 ] 
dist 119=[-3.5895947260752298140 ,2.5873660629300740849 ] 
dist 120=[-3.7471424784631547008 ,2.4977777877251799215 ] 
dist 121=[-3.8536541987665655909 ,2.3121881310657525637 ] 
dist 122=[-3.9183858784205644972 ,2.1523620017650748098 ] 
dist 123=[-3.9606863258101282972 ,1.6545850704000198871 ] 
dist 124=[-3.9776592503612342096 ,.99189283224259205345] 
dist 125=[-3.9793036567236816149 ,.99242631484589110309] 
dist 126=[-3.9716162288430686545 ,.99262175896445984372] 
dist 127=[.10220368049961868217,.99241422433339962117] 
dist 128=[-.03775662684021411474,.85960902053951404279] 
dist 129=[-.15413609162839501043,.84049570345078106702] 
dist 130=[-.2689234922962063559 ,.80719918037308272848] 
dist 131=[-.37404801767836735448,.79849253580967327762] 
dist 132=[-.45185462316128002897,.77093767737756456548] 
dist 133=[-.52464602926660591482,.76197167734127521893] 
dist 134=[-.6097551610337095335 ,.7562316191197416056 ] 
dist 135=[-.68886310517766908812,.75405674509759639082] 
dist 136=[-.73769639671007374496,.29107442296424977721] 
dist 137=[-.77377414799655899004,.25892005795246069744] 
dist 138=[-.80195265594250294218,.18359649893872941053] 
dist 139=[-.82349320480243587522,.17264952418804541693] 
dist 140=[-.8330697426552655409 ,.09769266304146149488] 
dist 141=[-.83698375159376668158,.08415747345178656870] 
dist 142=[-.83630983482361863756,.06114033111754114775] 
dist 143=[-.70759306865404785608,.05587938345269317161] 
dist 144=[-.69307720254624723162,-.02907458699207456550] 
dist 145=[-.65964876885392365293,-.04030055360104678512] 
dist 146=[-.64907029056605508509,-.06379422269283624783] 
dist 147=[-.60316545683837841114,-.06926302748345980973] 
dist 148=[-.62581917088254079319,-.06460124740404077826] 
dist 149=[-.63735866217494834715,-.05203775944125147831] 
dist 150=[-.64345210710134078936,-.02499792777633717250] 
dist 151=[-.64437582702635490895,.07100411176764867001] 
dist 152=[-.46285554839642913806,.14302192746506612969] 
dist 153=[-.45138299388781119405,.21132237774243782106] 
dist 154=[-.46217030722413265453,.29248979174020201375] 
dist 155=[-.4685343273229748553 ,.37581533778803201243] 
dist 156=[-.4725317587614082749 ,.45273571773297954192] 
dist 157=[-.47386928202778293237,.53978493374805920877] 
dist 158=[-.4735183523325311882 ,.66355352785327324763] 
dist 159=[-.4726599302756005356 ,.78484995498652716715] 
dist 160=[-.43139757718001458883,.86203087097567618236] 
dist 161=[-.42463862599429592869,.92176812426664069283] 
dist 162=[-.41171415784243495044,.97342247662300157003] 
dist 163=[-.40790093148949871141,1.0160064550549602291 ] 
dist 164=[-.39228038138194699391,1.0395318285877415289 ] 
dist 165=[-.38826390884027802088,1.0536372930943286370 ] 
dist 166=[-.3789124757838677771 ,1.0586152629809625321 ] 
dist 167=[-.37556949312567667008,1.0593821747675779003 ] 
dist 168=[-.14115781247296999149,1.0568149888411565584 ] 
dist 169=[-.12031846657400910523,1.0514055995974938931 ] 
dist 170=[-.07249959428740207192,1.0479601101914590649 ] 
dist 171=[-.06410648955252464415,1.0257376904077067431 ] 
dist 172=[-.00339471592647700429,1.0195123916824354741 ] 
dist 173=[.00729488499145825342,.99800501753732574009] 
dist 174=[.02552258765948668502,.99302682491455084936] 
dist 175=[.02953398723089851218,.63657592690167164505] 
dist 176=[-.08804958961684148780,.60374896222373683075] 
dist 177=[-.19560991825378958779,.52207224641800483479] 
dist 178=[-.30280995040916037046,.51012539712446302221] 
dist 179=[-.40169723285509091211,.38401214812399805105] 
dist 180=[-.47607107888754677379,.36014597705780769661] 
dist 181=[-.54680514409896954207,.35005188001846886874] 
dist 182=[-.63116161603438155762,.35217130306447722319] 
dist 183=[-.70978499888527101075,.35242882049453885007] 
dist 184=[-.75763092639646867587,.2541930465619693797 ] 
dist 185=[-.79213812222804517305,.24586938073235087914] 
dist 186=[-.81750923188960799626,.22894077811157230593] 
dist 187=[-.8368482534709804242 ,.22425158487063756945] 
dist 188=[-.84727387583555670826,.20588488918066175434] 
dist 189=[-.85317549991866528831,.2018690069009708612 ] 
dist 190=[-.8544544142098300216 ,.19306299176320988118] 
dist 191=[-.36057452066466878057,.19033037943972180396] 
dist 192=[-.40421740159186990409,.17859223211337391183] 
dist 193=[-.43789418757885842476,.17546381001112599595] 
dist 194=[-.46683353838126989044,.17343925161813394703] 
dist 195=[-.49055420143138475586,.1732629039861542872 ] 
dist 196=[-.50339530692380650699,.1741362751176503188 ] 
dist 197=[-.51074150541557093462,.1765231314543666417 ] 
dist 198=[-.51252380102614526211,.18047017257434567643] 
dist 199=[-.5123479017741367383 ,.20240694584230525708] 
dist 200=[-.51187613005370240474,.22900886630069377313] 
dist 201=[-.51109861547788560939,.24663561715719307304] 
dist 202=[-.50970235549650417924,.26107702832882243098] 
dist 203=[-.50801709421430722556,.27496237983826444035] 
dist 204=[-.50608617016732933292,.28743879328788289278] 
dist 205=[-.50360694131758406834,.29625519972912587175] 
dist 206=[-.50175386676236082132,.30408378795127565736] 
dist 207=[-.43982852171527436074,.31261597552507405306] 
dist 208=[-.44425302469603711309,.3603954304783614575 ] 
dist 209=[-.44641732389717359982,.4099983864888375610 ] 
dist 210=[-.44615069840689042972,.4570511263208771995 ] 
dist 211=[-.44415508501532960972,.4989204891188816195 ] 
dist 212=[-.4429192623627709246 ,.5278302975977697855 ] 
dist 213=[-.4362882605507839932 ,.5528145057832201192 ] 
dist 214=[-.4351512381655689623 ,.5790124696859962087 ] 
dist 215=[-.4084146062992700981 ,.6019657169900221928 ] 
dist 216=[-.4035192545206169761 ,.6139959843614744535 ] 
dist 217=[-.3887878109842127580 ,.6203421392794209206 ] 
dist 218=[-.3863920339082430273 ,.6216405735654947727 ] 
dist 219=[-.3537352162076267337 ,.6186826455272291966 ] 
dist 220=[-.3465716255548441015 ,.6163306319026997192 ] 
dist 221=[-.3398855392175533587 ,.6132102040548979406 ] 
dist 222=[-.3377621093119291043 ,.6109553844019440586 ] 
dist 223=[-.2349117303368013068 ,.47645846001449311912] 
dist 224=[-.2223657025182823076 ,.46127676948935579146] 
dist 225=[-.1938856583338330145 ,.42259607937961418495] 
dist 226=[-.1873365203926934728 ,.41630270854590011724] 
dist 227=[-.1503704206261200756 ,.35234030924163312087] 
dist 228=[-.1433437501822412377 ,.33966733321478914945] 
dist 229=[-.1290443006481709687 ,.32460742149065099279] 
dist 230=[-.1251633754910966269 ,.31983896122995210166] 
dist 231=[-.0819431245624292361 ,.2852005070312265508 ] 
dist 232=[-.0754169605153902764 ,.3329365590223263079 ] 
dist 233=[-.0619721170303579744 ,.3631260867212516322 ] 
dist 234=[-.0583998589534803979 ,.3862741615652812539 ] 
dist 235=[-.0446933684969292798 ,.4058990744249105126 ] 
dist 236=[-.04371836862420476901,.4217823644732987987 ] 
dist 237=[-.0905900457677688190 ,.4299932180605933087 ] 
dist 238=[-.1569899394654656296 ,.4342889395610111738 ] 
dist 239=[-.2226465145502832152 ,.4350776553913216835 ] 
dist 240=[-.2665508481305124811 ,.4320721858459592557 ] 
dist 241=[-.3029746449494743849 ,.4302107817577051143 ] 
dist 242=[-.3387666354067795312 ,.4267484735739656899 ] 
dist 243=[-.3714589287582306439 ,.4251288805204659885 ] 
dist 244=[-.3955079269036821220 ,.4158506976921166752 ] 
dist 245=[-.4178581339072587003 ,.4133241863984672187 ] 
dist 246=[-.4437687442771770858 ,.4013010929845710018 ] 
dist 247=[-.4675390561852072366 ,.3741331501068152416 ] 
dist 248=[-.4813446311566066953 ,.02341199565571112806] 
dist 249=[-.4905107830079257054 ,-.00300236903747447866] 
dist 250=[-.4957589675169531077 ,-.06076583380183374558] 
dist 251=[-.4985826381697906452 ,-.07239102242824066099] 
dist 252=[-.4985586857211459565 ,-.14826233839653511766] 
dist 253=[-.4962798915147602327 ,-.08998074024474325021] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 2, 2, 2, 0, 0, 2] 
dist 0=[4.7733211320592280954 ,4.7733211320592280954 ] 
dist 1=[3.5920983521245386405 ,5.9272847100165274799 ] 
dist 2=[2.1592822909913596488 ,6.9815282441898814285 ] 
dist 3=[0                     ,7.7643153202124770478 ] 
dist 4=[4.7648453261912550346 ,8.5017551632551581581 ] 
dist 5=[6.8938987718040549069 ,9.3748750918118332068 ] 
dist 6=[7.2567684392651066548 ,10.191568881134891837  ] 
dist 7=[7.7944655564638986600 ,10.703542119301753225  ] 
dist 8=[8.5201098540391219707 ,11.092772508508548113  ] 
dist 9=[10.077459430720517887  ,11.418936319022701656  ] 
dist 10=[10.336099485283121202  ,11.682679875635355983  ] 
dist 11=[10.874850312147788861  ,11.822498551545453004  ] 
dist 12=[10.966939612767531697  ,11.900018904831498620  ] 
dist 13=[11.427194484050160754  ,11.917606462230632260  ] 
dist 14=[11.500538638530855266  ,11.849029384514420295  ] 
dist 15=[11.535411868738549167  ,11.819944477075523513  ] 
dist 16=[11.457117376004396674  ,11.785826070597547015  ] 
dist 17=[11.300013078549846360  ,11.680526848842967351  ] 
dist 18=[11.024301709035717277  ,11.599150625409112362  ] 
dist 19=[10.713585017377206289  ,11.570469886852464934  ] 
dist 20=[10.317187135644086576  ,11.502868646807825507  ] 
dist 21=[9.6991479882778892653 ,11.475682319778660284  ] 
dist 22=[9.0470879782353566237 ,11.334736579028469933  ] 
dist 23=[8.5147232887210335164 ,11.294886170170029292  ] 
dist 24=[7.9665598358781148896 ,11.227859893324960006  ] 
dist 25=[7.2512548225345806322 ,11.205490014807317862  ] 
dist 26=[6.4802886964997113694 ,11.119772535362832207  ] 
dist 27=[5.7096747943509238379 ,11.092097112701820199  ] 
dist 28=[4.7888453639108468290 ,11.033957556670045392  ] 
dist 29=[3.4176442809085915858 ,11.012276879701096753  ] 
dist 30=[2.0493768180693979829 ,10.909131078580747298  ] 
dist 31=[1.1402279304696829187 ,10.874281945537001488  ] 
dist 32=[.3898262012296137817 ,10.656567852321378082  ] 
dist 33=[-.3442393081431926462 ,1.4183245517162045879 ] 
dist 34=[-1.0151775657656598019 ,.9669693144071107372 ] 
dist 35=[-1.5134147426217967068 ,-.0294495976876173712 ] 
dist 36=[-1.9827373464141939090 ,-.1982098998365497013 ] 
dist 37=[-2.5382527653510175553 ,-1.3117213187256644344 ] 
dist 38=[-3.0573386797469368872 ,-1.4924902373451561943 ] 
dist 39=[-3.3811670881606623524 ,-1.8249731402341854736 ] 
dist 40=[-3.6257391352375686072 ,-1.8919831213027956049 ] 
dist 41=[-3.8282279566501044423 ,-2.0247072948676563115 ] 
dist 42=[-3.9901051555674819134 ,-1.8798713053290261965 ] 
dist 43=[-4.0725196907584790425 ,-1.6603564889307972745 ] 
dist 44=[-4.1470417450863661309 ,-1.3451613995596620024 ] 
dist 45=[-4.2644492575215963086 ,-.81847790728712998381] 
dist 46=[-4.3154091838517067278 ,-.2767696111706347972 ] 
dist 47=[-4.3343934229773013387 ,.09844751926097365501] 
dist 48=[-4.3296225059351718954 ,.42267340937045761635] 
dist 49=[-4.0903182867456216246 ,.7610612704187705326 ] 
dist 50=[-4.0489563066410248688 ,1.0818526835643987462 ] 
dist 51=[-3.9185714905907569033 ,1.3359278484456477333 ] 
dist 52=[-3.8963602404241551061 ,1.5893782596695498081 ] 
dist 53=[-3.6504987669511189364 ,1.9077214354271291511 ] 
dist 54=[-3.5285570929426149542 ,2.2114056667974717002 ] 
dist 55=[-3.4636331693330251553 ,2.4063847091871161658 ] 
dist 56=[-3.4414057430177476926 ,2.5588323691569527580 ] 
dist 57=[-2.6142628788957430331 ,2.6928267975754620128 ] 
dist 58=[-2.5052913387266894146 ,2.8045107665499502956 ] 
dist 59=[-2.2925385121828817800 ,2.8679413935897949934 ] 
dist 60=[-2.2289089728453760983 ,2.9080942460961732306 ] 
dist 61=[-2.2050944901038979461 ,2.9268968041608897793 ] 
dist 62=[-1.9717671287037741035 ,2.9308967725622120843 ] 
dist 63=[-1.8959114223001901736 ,2.9255425533681802534 ] 
dist 64=[-1.8754464719475169734 ,2.8725926061985148687 ] 
dist 65=[-.00700207984444220393,.66995230463458724062] 
dist 66=[.14939962137052019667,.92249849031329842895] 
dist 67=[.49856333397009360709,1.1118334090855008650 ] 
dist 68=[.55804946158750276297,1.2915032553433697610 ] 
dist 69=[.96056864206406590075,1.5054776319661920404 ] 
dist 70=[1.0268136744686273847 ,1.7051722787573903316 ] 
dist 71=[1.1475085953625318520 ,1.8278319205111274873 ] 
dist 72=[1.1718403990631960843 ,1.9178602366800270550 ] 
dist 73=[1.4023218726314285309 ,1.9872633367404559433 ] 
dist 74=[1.3525049836201825819 ,2.0404131401022177716 ] 
dist 75=[1.2697098001043130806 ,2.0655242324673504721 ] 
dist 76=[1.1469548085420686559 ,2.0761265082831974961 ] 
dist 77=[.93762177881502527764,2.0761432812772980414 ] 
dist 78=[.71932545467011264825,2.0922096019472205191 ] 
dist 79=[.56078061740889699654,2.0992957267705756925 ] 
dist 80=[.41562192171973374969,2.0989036699789795354 ] 
dist 81=[.25073485608799081705,1.9661882691115237171 ] 
dist 82=[.08570143430700296824,1.9448030413818870512 ] 
dist 83=[-.06005651054286224766,1.8856998707110016723 ] 
dist 84=[-.21970861239777477217,1.8707084052062025806 ] 
dist 85=[-.44022395048101435362,1.7498686778227161031 ] 
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dist 90=[-1.3120901002471003043 ,1.3112448889614933808 ] 
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dist 100=[-2.5482103703813168519 ,-1.0230530952855956512 ] 
dist 101=[-2.5500564167171252106 ,-1.2674088683224620405 ] 
dist 102=[-2.4930308914694263539 ,-1.3058356587408634969 ] 
dist 103=[-2.4806962816861391685 ,-1.3815730459251935409 ] 
dist 104=[-2.4785676628722249239 ,-1.3941185032830988648 ] 
dist 105=[-2.4259835853292449732 ,-1.3713829659389484568 ] 
dist 106=[-2.3601588793016832734 ,-1.2511706665963670403 ] 
dist 107=[-2.3289212693659269026 ,-1.1081032868844306679 ] 
dist 108=[-2.2983811912888949652 ,-.81855929711511968108] 
dist 109=[-2.2559617284370945140 ,-.34513219854911888371] 
dist 110=[-2.1977626651415512727 ,.12981167769320561783] 
dist 111=[-2.1363307363863704594 ,.44723817648967632451] 
dist 112=[-2.1252134202271751186 ,.71041018916114586839] 
dist 113=[-1.5647162672703805288 ,.96874844473622695151] 
dist 114=[-1.5277204032176771516 ,1.2045411685780857758 ] 
dist 115=[-1.4317182923487338264 ,1.3777019308032655504 ] 
dist 116=[-1.4149532673346484824 ,1.5383336834597986899 ] 
dist 117=[-1.2483421500401682163 ,1.7241042695761644211 ] 
dist 118=[-1.2143547374375555062 ,1.8961423484418327603 ] 
dist 119=[-1.1727971792505846522 ,2.0019483553162243103 ] 
dist 120=[-1.1570063783919280240 ,2.0796064822346808904 ] 
dist 121=[-.80887178293856758363,2.1392680768557355819 ] 
dist 122=[-.76276804566954144829,2.1839119455565748149 ] 
dist 123=[-.6661508751700643231 ,2.2016131990734068007 ] 
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dist 126=[-.51794686291423318697,2.1050590395142261163 ] 
dist 127=[-.47376922108777770797,2.1116550343607358981 ] 
dist 128=[-.46119425838095594731,2.1105584062245662504 ] 
dist 129=[.60806304275660796166,.98883226719553365665] 
dist 130=[.68363491209602775355,1.0927566686834891138 ] 
dist 131=[.85009055968265560644,1.1634511498685182709 ] 
dist 132=[.87721649881239242967,1.2234427741798798985 ] 
dist 133=[1.0576130391708328036 ,1.2846354701646969604 ] 
dist 134=[1.0855348069457406242 ,1.3387025163458113646 ] 
dist 135=[1.1377417099874480454 ,1.3702438495729608253 ] 
dist 136=[1.1476616234355407756 ,1.3913722470090780363 ] 
dist 137=[1.1272570935751723666 ,1.4038628357140849454 ] 
dist 138=[1.0594488057897065862 ,1.4098831642129679257 ] 
dist 139=[.97542583297371404441,1.4101319891573998620 ] 
dist 140=[.86332776491052968677,1.3985344077248097148 ] 
dist 141=[.68342873754581119978,1.3968179878567151069 ] 
dist 142=[.49918202614768455759,1.3885433164606180335 ] 
dist 143=[.3697249239701674433 ,1.3762888424493452558 ] 
dist 144=[.25545814384619654291,1.3744746878141781338 ] 
dist 145=[.13185703104874030475,.94609380017637108727] 
dist 146=[.01153290949218133717,.90464085838932738722] 
dist 147=[-.08965177376491104827,.80500027982502182577] 
dist 148=[-.19632494456649164702,.78651961263715529197] 
dist 149=[-.33856392617680268707,.64036545999777396709] 
dist 150=[-.47889209613744078623,.61228817084467173682] 
dist 151=[-.57793723194946434604,.56920107078595042683] 
dist 152=[-.66583738411983094612,.55725344777900409897] 
dist 153=[-.76166974941925878143,.32845875960475742871] 
dist 154=[-.85542339464644122036,.29864493089195831285] 
dist 155=[-.9350254810300048068 ,.22970310195295847201] 
dist 156=[-1.0196203298989568664 ,.21712906752212691193] 
dist 157=[-1.1333106724610926460 ,.12683357861108531282] 
dist 158=[-1.2424680285065446077 ,.11051103751288065992] 
dist 159=[-1.3089648529330638178 ,.08256213584717703694] 
dist 160=[-1.3570393103369457877 ,.07621519847808787098] 
dist 161=[-1.3926420521124004063 ,-.73848060864568281843] 
dist 162=[-1.4190151317240095511 ,-.78751196990177200553] 
dist 163=[-1.4302377895392716741 ,-.89207846203874820845] 
dist 164=[-1.4337144528283988329 ,-.90972034917673054501] 
dist 165=[-1.4323113029229472743 ,-1.0077887201545876334 ] 
dist 166=[-1.3937579165161699398 ,-1.0231267936145856424 ] 
dist 167=[-1.3964760475408288972 ,-1.0202663083134139930 ] 
dist 168=[-1.3951689614218914879 ,-.98059025660339061904] 
dist 169=[-1.3123430456553778575 ,-.91322531350620776383] 
dist 170=[-1.2969948525395597411 ,-.82976515511304198778] 
dist 171=[-1.2678116863423145130 ,-.69787373861560280378] 
dist 172=[-1.2586095088745029557 ,-.53562195277208991644] 
dist 173=[-1.2183247865218315014 ,-.28922457499885325882] 
dist 174=[-1.2077859519783173676 ,-.04201465429434789621] 
dist 175=[-1.1799379003163786735 ,.12348158681249002341] 
dist 176=[-1.1698507447636522143 ,.26102654519756695047] 
dist 177=[-.65391393128690796971,.39663810381614440486] 
dist 178=[-.61257358241036776611,.52083931922366057863] 
dist 179=[-.51208668307961108593,.61282747155892367944] 
dist 180=[-.49666116581216615394,.69895808506374896005] 
dist 181=[-.34916312786932797984,.79977295190333180278] 
dist 182=[-.32171176312906287321,.89368394408255524746] 
dist 183=[-.28744443173873186649,.95224978918999659298] 
dist 184=[-.27872847744667138916,.99621482820795342368] 
dist 185=[-.05172224744453678805,1.0318291219387651577 ] 
dist 186=[-.02376202835457811757,1.0594110172129087470 ] 
dist 187=[.03617901826439543695,1.0713059390252816174 ] 
dist 188=[.04946281854825296107,1.0766144911262712093 ] 
dist 189=[.11169515421240722743,1.0778988247170136284 ] 
dist 190=[.1225398239410980239 ,1.0285631623391358586 ] 
dist 191=[.14467954003352398613,1.0343202507117177770 ] 
dist 192=[.14963597634514471055,1.0346954793188593151 ] 
dist 193=[.26904786130630313541,.62464162211407603382] 
dist 194=[.23731119720098170736,.65481110685733694764] 
dist 195=[.20139400913008479166,.673290279941892181  ] 
dist 196=[.15549555739813440565,.68676904665856562041] 
dist 197=[.08390861778613965316,.69697374797831185773] 
dist 198=[.00853565164423961486,.70424676040794434238] 
dist 199=[-.05247891264532033198,.7060204760755709189 ] 
dist 200=[-.1147305319726991439 ,.70519742614844242219] 
dist 201=[-.1950435497841809040 ,.7033230423727000305 ] 
dist 202=[-.2809371961262448458 ,.68783079951999772689] 
dist 203=[-.3654699878963933122 ,.6842906906647085045 ] 
dist 204=[-.4653012079770124608 ,.68220050404223420608] 
dist 205=[-.6122742395088872042 ,.66948702301603615621] 
dist 206=[-.7578484031681491414 ,.70457306124373951053] 
dist 207=[-.8520950591138821656 ,.74083980196544329146] 
dist 208=[-.9269011350881339498 ,.76975785709458900954] 
dist 209=[-.9948596055332459747 ,.79624342140882320051] 
dist 210=[-1.0533109896640027807 ,.81916344301412562751] 
dist 211=[-1.0901606832911358386 ,.83384648076436821395] 
dist 212=[-1.1182889681783641539 ,.8453171364474397898 ] 
dist 213=[-1.1419212619240959044 ,.8554114905297590538 ] 
dist 214=[-1.1603892717325796259 ,.8629626746921700737 ] 
dist 215=[-1.1678992202734399175 ,.8642799870168719437 ] 
dist 216=[-1.1694572598236515112 ,.8683079719705942322 ] 
dist 217=[-1.1788597985609712153 ,.8782871311914210202 ] 
dist 218=[-1.1852746501398741964 ,.8813328273334961750 ] 
dist 219=[-1.1860180574967709100 ,.8807392834499229498 ] 
dist 220=[-1.1843579003614624937 ,.8788489436978028375 ] 
dist 221=[-1.1655721632366284926 ,.8618984715505605856 ] 
dist 222=[-1.1590528577521417572 ,.8563995509538052242 ] 
dist 223=[-1.1422639313067605662 ,.8433901428817430597 ] 
dist 224=[-1.1349992915459397515 ,.8380465001599083239 ] 
dist 225=[-.76690892588775500097,.7482560313128072291 ] 
dist 226=[-.7291588968508006351 ,.7339292741788845283 ] 
dist 227=[-.63749357526747011908,.6991034851606813394 ] 
dist 228=[-.62194128570627473889,.6896638901963934411 ] 
dist 229=[-.5607896527218552622 ,.6330824220972168622 ] 
dist 230=[-.54557961507818716548,.6208817116831848000 ] 
dist 231=[-.53329444834667722959,.5976532006021029673 ] 
dist 232=[-.529449141439698558  ,.5910232272795174441 ] 
dist 233=[-.45017696039700492769,.4759780119268447888 ] 
dist 234=[-.43847178223288975834,.4595306471912356046 ] 
dist 235=[-.41127175154389083545,.4191290416068846848 ] 
dist 236=[-.40402884603113725655,.4114974220052030798 ] 
dist 237=[-.36483095357693311926,.4356029007533415082 ] 
dist 238=[-.49468402161050780303,.5421107856822984814 ] 
dist 239=[-.58556997254542659743,.6124125702396180696 ] 
dist 240=[-.6585451194963348856 ,.6697370254509573032 ] 
dist 241=[-.72625949462437445076,.7244336028261775405 ] 
dist 242=[-.7854884949939801754 ,.7733321042144845391 ] 
dist 243=[-.8245871718875213358 ,.8075082348992741218 ] 
dist 244=[-.8564651754653746029 ,.8374870306711990511 ] 
dist 245=[-.8868665870144835137 ,.8696284563492349910 ] 
dist 246=[-.9127826524014796641 ,.8977418422961600674 ] 
dist 247=[-.9267536236824527713 ,.9116390509131997378 ] 
dist 248=[-.9346607286832592135 ,.9184473256925108812 ] 
dist 249=[-.9401623478753259061 ,.9191275824059020006 ] 
dist 250=[-.9551427238238660643 ,.9295472624896010294 ] 
dist 251=[-.9638896684012223119 ,.9354703794086292751 ] 
dist 252=[-.9664263890695689774 ,.9355312166450728443 ] 
dist 253=[-.9652204451424876148 ,.92279721605719658235] 
dist 254=[-.9632922218296905916 ,.91748526523867245908] 
dist 255=[-.9522923112776266411 ,.91242847308317262424] 

8 phat 4 dirichlet min maxes function [0, 0, 0, 1, 0, 2, 0, 1, 2] 
dist 0=[48.235660488900498174  ,48.235660488900498174  ] 
dist 1=[48.045968593416334922  ,48.455983366099063267  ] 
dist 2=[47.508082043089117440  ,48.701649900751248135  ] 
dist 3=[46.742484352662518835  ,48.866029862008910065  ] 
dist 4=[45.706164267602708804  ,48.963016904923850951  ] 
dist 5=[44.267813250516161081  ,48.945331662243012229  ] 
dist 6=[41.896006778300353806  ,48.855691036522695467  ] 
dist 7=[39.432139780968177902  ,48.776894904472180356  ] 
dist 8=[37.625969432624543247  ,48.242749470318813159  ] 
dist 9=[35.947759748317213218  ,48.065972572350850705  ] 
dist 10=[33.995076091926850805  ,47.812873202324915459  ] 
dist 11=[32.004415238936199499  ,47.702089566641194891  ] 
dist 12=[30.174313521071829104  ,47.328671130710749921  ] 
dist 13=[27.823042373097287554  ,47.189616368349688012  ] 
dist 14=[25.145220372577736368  ,46.570121835291724486  ] 
dist 15=[22.120218237560154970  ,45.368622882756383426  ] 
dist 16=[19.777139778430086032  ,34.610123442908464762  ] 
dist 17=[17.472949382368157457  ,33.530670250854753376  ] 
dist 18=[14.603110000486151816  ,30.949805603391777210  ] 
dist 19=[11.570469886852464933  ,30.528436478743272806  ] 
dist 20=[8.6153774371008235723 ,26.827650694459757562  ] 
dist 21=[5.1344983418602513879 ,26.133221244222858206  ] 
dist 22=[0                     ,25.202628861576297530  ] 
dist 23=[6.1992269010670734447 ,24.910569325227751196  ] 
dist 24=[4.2610203102017492245 ,19.224702638095977098  ] 
dist 25=[2.5302546878050344648 ,18.490968360240545155  ] 
dist 26=[.6105450421081359505 ,17.109752611324752309  ] 
dist 27=[-2.0834669429202151749 ,16.532249451248231499  ] 
dist 28=[-4.7136275854381271384 ,14.837294118972843607  ] 
dist 29=[-6.3784001905536837922 ,14.528195031379978808  ] 
dist 30=[-7.6650130844214126419 ,13.800771139850647505  ] 
dist 31=[-8.7838940539793411439 ,13.677000099674928139  ] 
dist 32=[-9.7192925499854646113 ,5.8660865581909149379 ] 
dist 33=[-10.272838472533729218  ,5.1395329568379284587 ] 
dist 34=[-10.658406175567780864  ,3.5460657734361233496 ] 
dist 35=[-10.923095801725905544  ,3.2337921081930972634 ] 
dist 36=[-11.117872834733132042  ,1.4279636021224509702 ] 
dist 37=[-11.223957950002170455  ,1.1180941428638071191 ] 
dist 38=[-11.289122057561622422  ,.4961296245717342086 ] 
dist 39=[-11.319512546750505243  ,.3446347775806051180 ] 
dist 40=[-11.827455244596155720  ,-.8653999777343995335 ] 
dist 41=[-12.325899284239485530  ,-1.0577077710109347526 ] 
dist 42=[-12.692605847932312079  ,-1.2945052746382223366 ] 
dist 43=[-12.978364821763914588  ,-1.3304697585736902056 ] 
dist 44=[-13.192400622314929441  ,-1.2906119129312437162 ] 
dist 45=[-13.272541104498439516  ,-1.1425620064956080717 ] 
dist 46=[-13.287253220733200564  ,-.8888976383569259474 ] 
dist 47=[-13.264281885743312435  ,-.1585397060208640204 ] 
dist 48=[-7.4943785427508514943 ,.7876332161149022159 ] 
dist 49=[-7.0672943411185513768 ,1.5055824828693385365 ] 
dist 50=[-6.0341690338296304774 ,2.1935265506008735846 ] 
dist 51=[-5.8742868920031910091 ,3.0198956852936275497 ] 
dist 52=[-4.3833431026055712055 ,3.7978641832317255468 ] 
dist 53=[-4.1088247982195066010 ,4.2926802467596605563 ] 
dist 54=[-3.7543668147925811714 ,4.6746687103268608069 ] 
dist 55=[-3.6615826629081491702 ,5.0025154400104452305 ] 
dist 56=[-1.5001663787273923803 ,5.2707915232226328162 ] 
dist 57=[-1.2354882703669190231 ,5.4151661297210804320 ] 
dist 58=[-.65834617553601776137,5.4969943167954529160 ] 
dist 59=[-.54448908655403719061,5.5158737011366203669 ] 
dist 60=[.08261433614832479848,4.8617025248954305429 ] 
dist 61=[.1854464353637802427 ,4.8004798281806021682 ] 
dist 62=[.40654948513973592958,4.6499955366618202697 ] 
dist 63=[.44044545896338251011,4.5980013879573242619 ] 
dist 64=[1.9444026311824062162 ,4.3391006648790333927 ] 
dist 65=[2.0876916581225236418 ,4.2800899316401935519 ] 
dist 66=[2.3250731023055440610 ,4.4077696691425073152 ] 
dist 67=[2.3743533470337905692 ,4.7277656543448021568 ] 
dist 68=[2.3487605378254500622 ,5.0104778117417313353 ] 
dist 69=[1.9294773127754978735 ,5.2038542907494941235 ] 
dist 70=[1.5139364273106821276 ,5.3697054292732315963 ] 
dist 71=[.99434506599440362746,5.5425048747359275526 ] 
dist 72=[.44685601951559797051,5.6920521414031425703 ] 
dist 73=[-.08013436375839198848,5.7650253987673381902 ] 
dist 74=[-.69385448317585573146,5.7983147745895507466 ] 
dist 75=[-1.5877092853920173356 ,5.8012560367262482552 ] 
dist 76=[-2.4708808336086062544 ,5.7469230972093008675 ] 
dist 77=[-3.0419668833189730532 ,5.7206429670817670356 ] 
dist 78=[-3.4947673297916748562 ,5.6725541129019717114 ] 
dist 79=[-3.9056423164821277212 ,5.6519010169433955764 ] 
dist 80=[-4.2590184814155719659 ,1.3009746999231323428 ] 
dist 81=[-4.4822410024526367197 ,1.2590006639410802547 ] 
dist 82=[-4.6533365648279784590 ,1.2001832342496936934 ] 
dist 83=[-4.7985966251102917239 ,1.1817914361874144500 ] 
dist 84=[-4.9198331756521349390 ,1.1638869180480049486 ] 
dist 85=[-5.0132356397671732350 ,1.1757538127531459616 ] 
dist 86=[-5.2787718952037736828 ,1.2068080830386091662 ] 
dist 87=[-5.5689762200765335446 ,1.2718599318669929993 ] 
dist 88=[-5.8262030438288330484 ,1.3535460530295258520 ] 
dist 89=[-5.9600997111637843007 ,1.4510166948733783220 ] 
dist 90=[-6.0324267596376126171 ,1.5785999709158028420 ] 
dist 91=[-6.0463728492329037376 ,1.7804904817198801231 ] 
dist 92=[-6.0080827752255883325 ,1.9831869073011713032 ] 
dist 93=[-5.9899292452717765019 ,2.1139993137571383398 ] 
dist 94=[-5.9709829026749572515 ,2.2171440387351209794 ] 
dist 95=[-5.9459702580418355121 ,2.3094315607154918018 ] 
dist 96=[-5.5840800330280513071 ,2.3876349124230279881 ] 
dist 97=[-5.5236661004400409949 ,2.4345764419455715580 ] 
dist 98=[-5.3331412636662159351 ,2.4675993915722702887 ] 
dist 99=[-5.3048064071523308364 ,2.8994953148701752452 ] 
dist 100=[-4.8612849210075274963 ,3.4912693806246262527 ] 
dist 101=[-4.7637449141407907898 ,3.9360732234665315742 ] 
dist 102=[-4.6819039195609127886 ,4.3586307929789495550 ] 
dist 103=[-4.6623638759146461272 ,4.8615983760509194115 ] 
dist 104=[-3.3905328608846333645 ,5.3293537675486341140 ] 
dist 105=[-3.2247984814775060700 ,5.6113486378103452834 ] 
dist 106=[-2.9033982115925654132 ,5.8113812583093715376 ] 
dist 107=[-2.8209167855269001204 ,5.9519558411486775960 ] 
dist 108=[-2.5366981045451568975 ,6.0530097631083346682 ] 
dist 109=[-2.4679315140954657046 ,6.0952862223016160703 ] 
dist 110=[-2.3930563671154625159 ,6.1039290121981730405 ] 
dist 111=[-2.5937646344446505519 ,6.0976754202219171382 ] 
dist 112=[-2.8624912270416220390 ,3.9121031177714655253 ] 
dist 113=[-3.0392645109574605536 ,3.9634886445609702158 ] 
dist 114=[-3.1825310043929094070 ,3.9865618952646998439 ] 
dist 115=[-3.3174851087934736859 ,3.9866961357265870491 ] 
dist 116=[-3.4345516430381404818 ,3.9311846690131342214 ] 
dist 117=[-3.5064186326487863172 ,3.9114170022824342459 ] 
dist 118=[-3.5588823370211664037 ,3.8564533294103977828 ] 
dist 119=[-3.5985271509096414138 ,3.8316724938925902152 ] 
dist 120=[-3.6268729315407387836 ,3.6909834188007346807 ] 
dist 121=[-3.6342528720879817408 ,3.6545288420263990159 ] 
dist 122=[-3.6276998066050274412 ,3.5757362667923272738 ] 
dist 123=[-3.6199640065472382728 ,3.4906099936236324027 ] 
dist 124=[1.0600761005348355464 ,1.9607627253379728150 ] 
dist 125=[1.0669474418303467129 ,1.9769363888362059407 ] 
dist 126=[1.0660393508968101506 ,1.9825194601656405157 ] 
dist 127=[1.0509869784161971748 ,1.9836581689780463760 ] 
dist 128=[1.0285454846610309218 ,1.5898566899357965827 ] 
dist 129=[.99729019886246831468,1.5491733863255631297 ] 
dist 130=[.88893866702562724004,1.4563323766946490458 ] 
dist 131=[.74230019352462464871,1.4295054209455339150 ] 
dist 132=[.59186774700563362386,1.3003183132221136381 ] 
dist 133=[.45323012211712641431,1.2735123378328980265 ] 
dist 134=[.29655271381242204796,1.2136854413627374444 ] 
dist 135=[.07409192992589334545,1.1950766413025529086 ] 
dist 136=[-.15149463065720490843,1.0006988805685821550 ] 
dist 137=[-.32065646473615439257,.97004304106904675512] 
dist 138=[-.48106254794404755383,.89867094805306359334] 
dist 139=[-.67170139528600787251,.881480268574374219  ] 
dist 140=[-.86745979390943744682,.78075378914390661997] 
dist 141=[-1.0483117423905110429 ,.76067649027760380648] 
dist 142=[-1.2531165971416242462 ,.72122317566603061452] 
dist 143=[-1.5445153139007196637 ,.71039945740173140146] 
dist 144=[-1.8307483523654009804 ,.06817234135231168249] 
dist 145=[-2.0149314470934705064 ,.04741300023462556757] 
dist 146=[-2.1598690461788057850 ,.00994292482999779462] 
dist 147=[-2.2894126696418525444 ,.00162163407163405377] 
dist 148=[-2.3993539526466347951 ,-.11352664148655466927] 
dist 149=[-2.4660294566701654316 ,-.12940450911392656226] 
dist 150=[-2.5138786684853068756 ,-.15895963263888342739] 
dist 151=[-2.5486585219238830656 ,-.16552696869913701324] 
dist 152=[-2.5726107259795086450 ,-.18239314706750541829] 
dist 153=[-2.5772293958436060864 ,-.1831659161614859509 ] 
dist 154=[-2.5728378431881342410 ,-.17811833394131283853] 
dist 155=[-2.5653013658259378047 ,-.163827594549885102  ] 
dist 156=[-2.5056552449440364894 ,-.14730249573601607791] 
dist 157=[-2.4872219040857305727 ,-.1333322312743393244 ] 
dist 158=[-2.4499206084012526963 ,-.11855292046026982621] 
dist 159=[-2.4359350771952369520 ,-.09879297993912184255] 
dist 160=[-1.8159835994567301704 ,.10583223141785477582] 
dist 161=[-1.7535549973229065862 ,.42706692014272036266] 
dist 162=[-1.5950651741677587201 ,.6963682756804110826 ] 
dist 163=[-1.5702702688931719766 ,.96563565248391003306] 
dist 164=[-1.3114147473699515558 ,1.2146420141717602641 ] 
dist 165=[-1.2606437936477369670 ,1.4030525836162383060 ] 
dist 166=[-1.2021913066429602581 ,1.5833786584860990055 ] 
dist 167=[-1.1859823684749797257 ,1.8001084371117082548 ] 
dist 168=[-.6926355759838586013 ,2.0029879365430201634 ] 
dist 169=[-.6298453733450623768 ,2.1280174805823007998 ] 
dist 170=[-.49998787730385693307,2.2201028250140504492 ] 
dist 171=[-.46580358398939754173,2.2914539628458916032 ] 
dist 172=[-.40325863737410220432,2.3458783476505187716 ] 
dist 173=[-.43231155079311694787,2.3703838522357513468 ] 
dist 174=[-.4551517645832166921 ,2.3802135079874393499 ] 
dist 175=[-.47546848081626641067,2.3788222303491347310 ] 
dist 176=[-.49258905514207945753,.76902164426501408563] 
dist 177=[-.50267179507367227068,.7935723452218295433 ] 
dist 178=[-.50951405367477190444,.80972752785880615515] 
dist 179=[-.51369815066546779313,.86344501457003249108] 
dist 180=[-.51575159272204973028,.95930559856363997312] 
dist 181=[-.51558362737351285475,1.0290279463428273136 ] 
dist 182=[-.51151701938265782927,1.0930512882377385995 ] 
dist 183=[-.5099439101619944219 ,1.1661589455039838248 ] 
dist 184=[-.48856568088109474418,1.2326675473299784852 ] 
dist 185=[-.48283802936441273587,1.2703437571694718822 ] 
dist 186=[-.47698712037828623941,1.2941668909250312614 ] 
dist 187=[-.47365873010117447982,1.3053655425411433076 ] 
dist 188=[.28802671789515945854,1.3107859720086701789 ] 
dist 189=[.19958027994367300165,1.3115379879221007478 ] 
dist 190=[.11799260541893386042,1.3090169645943785087 ] 
dist 191=[.02430105110559088113,1.3056830755040707101 ] 
dist 192=[-.07013786283340688247,1.1700321719120346929 ] 
dist 193=[-.15471007700760533739,1.1509632489084928790 ] 
dist 194=[-.24835867183551751786,1.0965220688843628589 ] 
dist 195=[-.37903600362925880554,1.0886986549450942467 ] 
dist 196=[-.5106135472237696312 ,.97854896970867373031] 
dist 197=[-.60785673731298164554,.95532358340342446877] 
dist 198=[-.69869296636442181772,.93479178623287041689] 
dist 199=[-.81057221426638532734,.93070490529477978479] 
dist 200=[-.93564544846056171736,.64934484316032938184] 
dist 201=[-1.0200591048159060820 ,.61312533413150237102] 
dist 202=[-1.1202591358941102143 ,.54285724634166406715] 
dist 203=[-1.2749216247801132192 ,.52496692041977580143] 
dist 204=[-1.4253289355292253081 ,.64526135086974633397] 
dist 205=[-1.5180949206161441787 ,.73787989825819333839] 
dist 206=[-1.5865169605922423920 ,.81707553542845455122] 
dist 207=[-1.6397296583093394982 ,.89877575922521049261] 
dist 208=[-1.6805700921081964672 ,.97593792336287076956] 
dist 209=[-1.6995949459520043697 ,1.0370162288322890402 ] 
dist 210=[-1.7075804383771858561 ,1.0980775324499378727 ] 
dist 211=[-1.7072568745696547644 ,1.1751721753119884770 ] 
dist 212=[-1.6320874944429813342 ,1.2492201003350987031 ] 
dist 213=[-1.6163705068310110255 ,1.2981179440116994632 ] 
dist 214=[-1.5882641546751221912 ,1.3380095136649363714 ] 
dist 215=[-1.5791393977393785268 ,1.3761011949195019175 ] 
dist 216=[-1.5390265367240653279 ,1.4101706984336912136 ] 
dist 217=[-1.5273277768115655778 ,1.4340044396815887255 ] 
dist 218=[-1.4975670583457483761 ,1.4549320979651866070 ] 
dist 219=[-1.4857863802407330935 ,1.4773998840363893684 ] 
dist 220=[-1.1135309290576104780 ,1.4963558781812676996 ] 
dist 221=[-1.0989840321491647200 ,1.5032630948024304178 ] 
dist 222=[-1.0708786161714623880 ,1.5033453087710506845 ] 
dist 223=[-1.0621647675378343092 ,1.5010297473637160166 ] 
dist 224=[-.62898560778287186111,1.4769572399750797366 ] 
dist 225=[-.60754954605483802431,1.4687905576334437041 ] 
dist 226=[-.55747841964653156001,1.4464501776625743088 ] 
dist 227=[-.54589326566549933676,1.4366697960396317398 ] 
dist 228=[-.47500586462426526216,1.3021868873792454233 ] 
dist 229=[-.4609653887707141887 ,1.2798808673736396154 ] 
dist 230=[-.43419600919476858601,1.2236693708821734168 ] 
dist 231=[-.42708602598774122855,1.2095161842052605538 ] 
dist 232=[-.31977400016235442687,1.1120536818345046701 ] 
dist 233=[-.30468971895258807518,1.0909411162369628590 ] 
dist 234=[-.26801428219681907856,1.1058313228076085295 ] 
dist 235=[-.35662542435590606452,1.1366200858312265233 ] 
dist 236=[-.67112819252078507134,1.2290569972455295979 ] 
dist 237=[-.87691613190982572349,1.2942070734261295260 ] 
dist 238=[-1.0427109404269817857 ,1.3430885985752812333 ] 
dist 239=[-1.1975422207375169284 ,1.3826314726513294565 ] 
dist 240=[-1.3336847656298453197 ,1.4131987589133486749 ] 
dist 241=[-1.4248651686439553043 ,1.4262452264700697323 ] 
dist 242=[-1.5006741210961704294 ,1.4310840835750223361 ] 
dist 243=[-1.5754461644067490219 ,1.4294975946637929591 ] 
dist 244=[-1.6415242013016715711 ,1.4029209695259358053 ] 
dist 245=[-1.6826226653193759220 ,1.3949221824059421288 ] 
dist 246=[-1.7133377531790036081 ,1.3717349115965734532 ] 
dist 247=[-1.7379611321072209170 ,1.3618187783431817936 ] 
dist 248=[-1.7568148866238886475 ,1.3049577808711345104 ] 
dist 249=[-1.7644953231817157012 ,1.2904097610787878463 ] 
dist 250=[-1.7654691616097915216 ,1.2628196181998873564 ] 

8 phat 4 dirichlet min maxes function [2, 1, 1, 1, 1, 2, 0, 0, 2] 
dist 0=[50.961142744394552846  ,50.961142744394552846  ] 
dist 1=[50.667174535605745642  ,51.022519464840707937  ] 
dist 2=[50.140757866428424734  ,50.980009052483384218  ] 
dist 3=[49.157983213783441974  ,50.913951462583318148  ] 
dist 4=[48.044402917605681049  ,50.812341671876090101  ] 
dist 5=[46.995513109123370642  ,50.729119789977487323  ] 
dist 6=[45.790397627007829864  ,50.473416449386092283  ] 
dist 7=[44.052626057062791760  ,50.296619801147322912  ] 
dist 8=[42.099155027639548752  ,48.841127785658520784  ] 
dist 9=[40.032352239531688111  ,46.472393462979514432  ] 
dist 10=[37.480222941404738327  ,45.918391963041893930  ] 
dist 11=[33.588033762086182050  ,45.750085368644645873  ] 
dist 12=[29.657458031803862105  ,45.676371359371331270  ] 
dist 13=[26.951918785566150159  ,45.077585434830934296  ] 
dist 14=[24.617226919915623581  ,39.767390265316657355  ] 
dist 15=[22.167857817799486580  ,39.213279419237019336  ] 
dist 16=[19.822412308738833129  ,39.095113172529779591  ] 
dist 17=[17.902694320987293755  ,32.577364431606225504  ] 
dist 18=[15.920301585046829575  ,31.731755370860818343  ] 
dist 19=[13.324200093718523737  ,30.104520044106080444  ] 
dist 20=[10.773713118558247741  ,29.690490974544678048  ] 
dist 21=[8.9733706545642918206 ,28.278982918243554981  ] 
dist 22=[7.3705100694160141827 ,27.935570832604701028  ] 
dist 23=[5.6086969351366422608 ,27.571880981626236894  ] 
dist 24=[3.8696851642648167593 ,27.465037388147480692  ] 
dist 25=[2.3575903520235524326 ,11.231414756361147570  ] 
dist 26=[.71422229400820910165,10.000121202157181824  ] 
dist 27=[-1.5499331125079570772 ,9.9192667933647302227 ] 
dist 28=[-3.7582930320407646272 ,9.6810338339962328209 ] 
dist 29=[-5.1788248240545896856 ,9.4314628367944466590 ] 
dist 30=[-6.3024232392230227542 ,1.6612887221212516643 ] 
dist 31=[-7.3240256582442719796 ,.75545222861874626468] 
dist 32=[-8.2096227597841809383 ,.5936944877364989609 ] 
dist 33=[-8.7897456506117592635 ,-4.0846268697195992750 ] 
dist 34=[-9.6206530072113225567 ,-4.6228700165957030578 ] 
dist 35=[-10.145405568622421906  ,-5.7939272629042636640 ] 
dist 36=[-10.548600730661419828  ,-5.9724070340512978554 ] 
dist 37=[-10.896746713405181959  ,-7.1817298393618744385 ] 
dist 38=[-11.179546982389230743  ,-7.3595011977827257838 ] 
dist 39=[-11.321576699590362959  ,-7.3819166646132856720 ] 
dist 40=[-11.390212565043041710  ,-6.6658368638252700649 ] 
dist 41=[-11.389606791330967804  ,-5.8382315025852260358 ] 
dist 42=[-11.327217809062205781  ,-4.7707774902894317376 ] 
dist 43=[-11.290124215177712233  ,-3.0970641087198330734 ] 
dist 44=[-11.134615950675360268  ,-1.4015239396091341721 ] 
dist 45=[-11.083358255934322719  ,-.24683172183443156962] 
dist 46=[-8.7668865630553619944 ,.73314784664590408837] 
dist 47=[-8.7188770618568010114 ,1.7313934183874691006 ] 
dist 48=[-8.7046504250454571817 ,2.6655437356044400584 ] 
dist 49=[-7.2279890114748648808 ,3.3897244771072976898 ] 
dist 50=[-7.0296037802034817143 ,4.0992391440353882674 ] 
dist 51=[-6.6572758076254940034 ,4.9748961821218715504 ] 
dist 52=[-6.5618509588113803741 ,5.8056749756942947498 ] 
dist 53=[-6.2403180916563012128 ,6.3360516371157203340 ] 
dist 54=[-6.1544671067456626805 ,6.7483320085517755656 ] 
dist 55=[-6.0768051370944190670 ,7.1076670878260291692 ] 
dist 56=[-6.0530880703564994598 ,7.4057623486678433849 ] 
dist 57=[-1.6250720563634544265 ,7.5735643075010817664 ] 
dist 58=[-1.2785229402353233828 ,7.6781442379971234566 ] 
dist 59=[-.71170078864921386633,7.7238367002469279614 ] 
dist 60=[-.35474455940279205995,7.7379109714580178662 ] 
dist 61=[.11838794746628589554,7.7162603943602910789 ] 
dist 62=[.84338323489351485015,2.0582181562300609513 ] 
dist 63=[1.0972026901791719591 ,2.4947981454901289036 ] 
dist 64=[1.1609030092367544285 ,3.0198412115742146612 ] 
dist 65=[2.1970714803777865202 ,3.5132639702811141543 ] 
dist 66=[2.3229775266952464812 ,3.8235559230101771399 ] 
dist 67=[2.5681875390450493285 ,4.0599015866872824713 ] 
dist 68=[2.6224742819994298251 ,4.2580208560852774825 ] 
dist 69=[2.6306224609742286871 ,4.4181182066861180310 ] 
dist 70=[2.5699870194153525169 ,4.5025861875845290568 ] 
dist 71=[2.4393343673148227205 ,4.5489300183132695458 ] 
dist 72=[2.2736368570986370596 ,4.5588304138996790571 ] 
dist 73=[2.0730602487792641732 ,3.2684660071457090525 ] 
dist 74=[1.8083324042578736504 ,3.2575465490177105250 ] 
dist 75=[1.3864903216053751697 ,3.2494029059868728509 ] 
dist 76=[.95560916307527221228,3.2081573110939455171 ] 
dist 77=[.65478034665815228888,3.1983620002691031759 ] 
dist 78=[.39126185553058524683,2.1534381854484305514 ] 
dist 79=[.10932591619866496126,2.0525510718901940036 ] 
dist 80=[-.16330931956140014715,1.9460215262744869000 ] 
dist 81=[-.38970573125996036404,1.7660272242876539321 ] 
dist 82=[-.62591343340133847459,1.5750432420697875698 ] 
dist 83=[-.93773696533917412844,1.5482681651056924987 ] 
dist 84=[-1.2440527882077570077 ,1.2331590808686430974 ] 
dist 85=[-1.4582768506427452690 ,1.2089214280762207220 ] 
dist 86=[-1.6464021316216523119 ,1.1004280150817263908 ] 
dist 87=[-1.8485195529384879112 ,1.1081005011954493378 ] 
dist 88=[-2.0445840877151973825 ,1.1345466712010886097 ] 
dist 89=[-2.3533967819508846638 ,1.1658359059921147891 ] 
dist 90=[-2.6414109813029494978 ,1.1928383769337568877 ] 
dist 91=[-2.8633925863793524307 ,1.2216492644085345230 ] 
dist 92=[-3.0539631231639489663 ,1.2601979953782935435 ] 
dist 93=[-3.2102805501939647868 ,1.3018356988752713453 ] 
dist 94=[-3.2954936718362456217 ,1.3429922123520048956 ] 
dist 95=[-3.3451981344345844102 ,1.3915558607656618670 ] 
dist 96=[-3.3597473667011644317 ,1.4627652549997579610 ] 
dist 97=[-3.3614484965980479414 ,1.5355984346918856371 ] 
dist 98=[-3.3598459909204920621 ,1.5906532377729197749 ] 
dist 99=[-3.3556344870219086932 ,1.6431522813835305630 ] 
dist 100=[-3.3468867289957977217 ,1.7058070861724988174 ] 
dist 101=[-3.3359671547180052104 ,1.7701432519787602945 ] 
dist 102=[-3.3230669578333328611 ,1.8293649415196790794 ] 
dist 103=[-3.3062532936787929298 ,1.8961724149544536783 ] 
dist 104=[-3.2947841001082897694 ,1.9907983204288393311 ] 
dist 105=[-2.8130583094580584709 ,2.0818793610651588955 ] 
dist 106=[-2.7371021413796749383 ,2.1345415985872221162 ] 
dist 107=[-2.7203042756634144696 ,2.1691542638588990414 ] 
dist 108=[-2.2548240665052273691 ,2.1881915291912498639 ] 
dist 109=[-2.2385163181410083044 ,2.1964418142588683277 ] 
dist 110=[-1.9035037486420278648 ,2.1957205771708553393 ] 
dist 111=[-1.8877389305532035083 ,2.1760949094079062382 ] 
dist 112=[-1.6987938697285892298 ,2.1705638427127502809 ] 
dist 113=[-1.6593027684502068335 ,2.0397140970055517683 ] 
dist 114=[-1.6189775935581163628 ,2.0149040779274799783 ] 
dist 115=[-1.6070231886742931544 ,2.0971823856354099718 ] 
dist 116=[-1.1545336095731862639 ,2.3162005797191303423 ] 
dist 117=[-1.0953267963563647558 ,2.4497399029853681493 ] 
dist 118=[-.97754047693389596775,2.5464318641918909995 ] 
dist 119=[-.94674833039948549579,2.6183259392009969595 ] 
dist 120=[-.83598919617104694137,2.6725641740759689723 ] 
dist 121=[-1.0951007143177932632 ,2.6987583901652365487 ] 
dist 122=[-1.4246778024463188980 ,2.7094596408035580743 ] 
dist 123=[-1.6903204714412110318 ,2.7091662322148178091 ] 
dist 124=[-1.9384345618916573025 ,2.4882806529007364856 ] 
dist 125=[-2.1564914756026703428 ,2.5542872989870827841 ] 
dist 126=[-2.3021412922443640787 ,2.5865027305281288814 ] 
dist 127=[-2.4227314348851986376 ,2.6005890636924671566 ] 
dist 128=[-2.5407421937897407299 ,2.6017745508102115120 ] 
dist 129=[-2.6447095414827573252 ,2.5753990602332074255 ] 
dist 130=[-2.7092370343788608708 ,2.5648639158920714528 ] 
dist 131=[-2.7572480743492202554 ,2.5293276177254513641 ] 
dist 132=[-2.7952857171807290917 ,2.5144914929687342456 ] 
dist 133=[-2.8239991839206386154 ,2.4120720371715333556 ] 
dist 134=[-2.8347891315986181861 ,2.3856005538324710732 ] 
dist 135=[-2.8345004605145691923 ,2.3408842200747261854 ] 
dist 136=[-2.8294808781263743515 ,2.3264450234841435188 ] 
dist 137=[.3280432583619788642 ,1.2903408754446162398 ] 
dist 138=[.20965281566280848511,1.2898613069757416877 ] 
dist 139=[.10989430481364840981,1.2864398369981438432 ] 
dist 140=[.00931114395556635752,1.2797544842192876367 ] 
dist 141=[-.08425607356591331259,1.2758384906714823580 ] 
dist 142=[-.1560053290832687536 ,.99581345719999389041] 
dist 143=[-.2256108590912156138 ,.96517626831825140032] 
dist 144=[-.31062266314546125313,.88832663000435505894] 
dist 145=[-.39093366108581582162,.87489283655667125741] 
dist 146=[-.44177257590513307664,.75061884992541756503] 
dist 147=[-.48083556321760898658,.72591081307141478119] 
dist 148=[-.51413178744589753173,.6937467345952139306 ] 
dist 149=[-.54130978877372309848,.68262927454382619154] 
dist 150=[-.6632072999360573118 ,.44773831824339021882] 
dist 151=[-.7517586654972513388 ,.41683811707908529967] 
dist 152=[-.82881109825141450318,.35076596863992083583] 
dist 153=[-.9104768186476513783 ,.33301720396735219686] 
dist 154=[-.98900652619020269339,.26082598669664362128] 
dist 155=[-1.0535377177646124153 ,.24715414166144094653] 
dist 156=[-1.1202736907077360868 ,.21467999583098870778] 
dist 157=[-1.2076072244726361404 ,.20862365768446234406] 
dist 158=[-1.2906323784850439542 ,-.39764777149582579101] 
dist 159=[-1.3401659987676563849 ,-.35015478069707436853] 
dist 160=[-1.3747253049316743721 ,-.27634193739006140553] 
dist 161=[-1.3979608762011372607 ,-.19874335310911939085] 
dist 162=[-1.4136067642624270599 ,-.13613386210277279654] 
dist 163=[-1.4178616758951558186 ,-.07244558249972459087] 
dist 164=[-1.4167937735360066234 ,.00946391362848299738] 
dist 165=[-1.4132559786444715016 ,.09693963984439833818] 
dist 166=[-1.3286674500270310919 ,.18285358923457719869] 
dist 167=[-1.3129733928994717331 ,.28419146452215175411] 
dist 168=[-1.2793310585245625286 ,.4332507684620578222 ] 
dist 169=[-1.2680983611808670980 ,.58180501096353856255] 
dist 170=[-1.2146948792289256151 ,.68112740868597116321] 
dist 171=[-1.2026609545243404463 ,.76353449526699357546] 
dist 172=[-1.1664199537098404667 ,.84455371462677169771] 
dist 173=[-1.1595176046262740294 ,.91860947165210312044] 
dist 174=[-.82382131878995532332,.97321595285369770008] 
dist 175=[-.80007936624484524884,1.0262474313541168918 ] 
dist 176=[-.73955304721895493954,1.0879294924646717838 ] 
dist 177=[-.729448528306313818  ,1.1446450039787101445 ] 
dist 178=[-.62860026328730751518,1.1778475978634534950 ] 
dist 179=[-.60843743600226090494,1.2002305638825360494 ] 
dist 180=[-.58412591480704714508,1.2137481080194481389 ] 
dist 181=[-.57579725764608552791,1.2213514600099845718 ] 
dist 182=[-.37585703575093892135,1.2218349255507615516 ] 
dist 183=[-.34972674470061808562,1.2159834105724292665 ] 
dist 184=[-.29526232690795425786,1.2119832049079045428 ] 
dist 185=[-.28063112226189255821,1.1803804986692028061 ] 
dist 186=[-.42531719580052685386,1.2048393427052015621 ] 
dist 187=[-.55398150908010076339,1.2142460225310437851 ] 
dist 188=[-.68363513432753624201,1.2175023778751478794 ] 
dist 189=[-.80418317516398935378,1.2174055092916614275 ] 
dist 190=[-.8964939442813771395 ,.99829850620534468255] 
dist 191=[-.98590944364841031592,.97431162835848695811] 
dist 192=[-1.0948985556133449045 ,.96636444914195631172] 
dist 193=[-1.1977038603635985001 ,.781577246972000414  ] 
dist 194=[-1.2624307957968658866 ,.75556071407406211766] 
dist 195=[-1.3117345530705719928 ,.69863755846686059552] 
dist 196=[-1.3529632380041460615 ,.68201742467878820072] 
dist 197=[-1.3859022083881449047 ,.61096042732268611407] 
dist 198=[-1.4021096151909828093 ,.57078054450165424015] 
dist 199=[-1.4091831254606747662 ,.53617955413414606409] 
dist 200=[-1.4095683595631776936 ,.5292641485233046134 ] 
dist 201=[-.34817308967099266274,.45691340951791532623] 
dist 202=[-.43129687231441395721,.51247813437789392498] 
dist 203=[-.51288112456111527767,.5680996071585294683 ] 
dist 204=[-.60907488725182084614,.63448389001164240282] 
dist 205=[-.75052917636409029252,.73301812952536768198] 
dist 206=[-.8906186769640628361 ,.83092933538773889016] 
dist 207=[-.98136362165279070867,.89482593283479011669] 
dist 208=[-1.0534562924796434774 ,.94611283342001336367] 
dist 209=[-1.1190748510851970189 ,.99368016613708423846] 
dist 210=[-1.1756107071898325988 ,1.0352765035156469640 ] 
dist 211=[-1.2114400251971273107 ,1.0627241423083079650 ] 
dist 212=[-1.2390102945015683291 ,1.0850917552212534324 ] 
dist 213=[-1.2625716727023950993 ,1.1064055632960851216 ] 
dist 214=[-1.2805924681514291076 ,1.1235085584261753606 ] 
dist 215=[-1.2860414084974330886 ,1.1290644145932573671 ] 
dist 216=[-1.2862074544771988201 ,1.1297257158815103653 ] 
dist 217=[-1.2831347929956302271 ,1.1272889791036502208 ] 
dist 218=[-1.2518959376785271883 ,1.1002673755595559692 ] 
dist 219=[-1.2419154226222268978 ,1.0915301719674023670 ] 
dist 220=[-1.2290854169847311031 ,1.0808482261712044128 ] 
dist 221=[-1.2228122249936331554 ,1.0753072100363370788 ] 
dist 222=[-.97326998288489257936,.91664221776614228308] 
dist 223=[-.97194069087716211872,.89480317445262608429] 
dist 224=[-.96976059573892331922,.83862304701151368045] 
dist 225=[-.8402568115034957339 ,.82829916169299643972] 
dist 226=[-.82124408754063891748,.73169678125031951846] 
dist 227=[-.78678925894335286279,.71189184519754228593] 
dist 228=[-.77765975220437196649,.68624937923824290521] 
dist 229=[-.74592340945034529874,.66078192805341483416] 
dist 230=[-.73664619617316393511,.38740958458996751033] 
dist 231=[-.72524488913029454183,.3523729078336221923 ] 
dist 232=[-.72016445511949406627,.23384766007614815575] 
dist 233=[-.20172512932058980838,-.03182987904090858296] 
dist 234=[-.13496116782305182693,.06965737521697364504] 
dist 235=[-.12177761966240030499,.16210056105566189551] 
dist 236=[-.09626693759078484908,.25736196086337114356] 
dist 237=[-.08997870435371806709,.34728664876750971887] 
dist 238=[.28048922530304813051,.46129105213480850317] 
dist 239=[.31308605459179137345,.54192642029136678914] 
dist 240=[.36176451940572422054,.60882342146997982481] 
dist 241=[.38993322101125362342,.67458130318859112113] 
dist 242=[.42908243076532712593,.73467470914842633873] 
dist 243=[.4384025235405151306 ,.77895601524574900696] 
dist 244=[.47820075937856695365,.82019298635491733313] 
dist 245=[.54337938921556786209,.86813201481035834132] 
dist 246=[.61081538030711029076,.91219379768737989537] 
dist 247=[.57571793528769676107,.9379506887764971745 ] 
dist 248=[.53050024504240679108,.95526447416465550694] 
dist 249=[.45957327327906126378,.96561650316608519654] 
dist 250=[.37743402026148985633,.9713378524790039592 ] 
dist 251=[.28745064468071227634,.97162786555392506749] 
dist 252=[.17436724816045501207,.96370883642953628073] 

8 phat 4 dirichlet min maxes function [2, 0, 2, 0, 2, 2, 0, 1] 
dist 0=[41.233710245310246930  ,41.233710245310246930  ] 
dist 1=[41.061764436002335977  ,41.365937686785271648  ] 
dist 2=[40.531666268618670745  ,41.737235046684260295  ] 
dist 3=[39.684921586429304773  ,42.118028376597908061  ] 
dist 4=[38.248129684755884682  ,42.288259821071871156  ] 
dist 5=[36.750960744354319511  ,42.354532163501515430  ] 
dist 6=[35.663008156489188869  ,42.343636290910639366  ] 
dist 7=[34.663090321840340692  ,41.558851325430832073  ] 
dist 8=[33.517389320824201535  ,41.391849101532340528  ] 
dist 9=[32.360698613098132268  ,41.093780564368631918  ] 
dist 10=[31.316711155910030118  ,40.996190975243048110  ] 
dist 11=[30.151166756061026997  ,40.562189707370580205  ] 
dist 12=[28.508591504394573694  ,40.436578045764951192  ] 
dist 13=[26.839250344353259458  ,40.108266230062508003  ] 
dist 14=[25.566620180121521290  ,39.977402211648799093  ] 
dist 15=[24.335138979116550729  ,30.769526900100646110  ] 
dist 16=[22.829986050518472628  ,29.925680593999969512  ] 
dist 17=[21.254983808192390457  ,27.896530968019793769  ] 
dist 18=[19.744159678784092486  ,27.566179812086024162  ] 
dist 19=[17.941073875202677313  ,24.627449542861319042  ] 
dist 20=[15.406779801109559349  ,24.509485926975588654  ] 
dist 21=[12.838694036938340902  ,23.310883856858366376  ] 
dist 22=[11.109549187104987857  ,23.073842269785503352  ] 
dist 23=[9.6545875591200978159 ,18.294394801952876374  ] 
dist 24=[8.1824391078499548110 ,17.673010612766373537  ] 
dist 25=[6.8024037089342195938 ,16.388316587016551562  ] 
dist 26=[5.6731666140626474956 ,16.014199827548908005  ] 
dist 27=[4.0492907762716882588 ,14.655400216832059334  ] 
dist 28=[2.5912598661784823470 ,14.392980774850991360  ] 
dist 29=[.96670493697418531514,13.807727940227850801  ] 
dist 30=[-1.3234230773732322348 ,13.668540128613353060  ] 
dist 31=[-3.5635342226571954494 ,6.0920082759020039793 ] 
dist 32=[-4.9883797955977192974 ,5.4028860747698241734 ] 
dist 33=[-6.0984388804953380954 ,3.8591544021695527942 ] 
dist 34=[-7.0803100419190703290 ,3.5811304427773678694 ] 
dist 35=[-7.9139137337708035632 ,1.7303714154530860897 ] 
dist 36=[-8.4314930498468407579 ,1.4090561970550166786 ] 
dist 37=[-8.8220036660962386699 ,.82967258806153918422] 
dist 38=[-9.1481803080415281210 ,.70441173263861739734] 
dist 39=[-9.4123071954848672306 ,.5575425531852243896 ] 
dist 40=[-9.5846477890876655312 ,.55926460045295270515] 
dist 41=[-9.9630585447672234130 ,.58678031396976241807] 
dist 42=[-10.282017995035847651  ,.64710326744271677979] 
dist 43=[-10.540400819838090683  ,.74159453979475789887] 
dist 44=[-10.676784780035305288  ,.90566456726398111713] 
dist 45=[-10.750873854136560237  ,1.0824155229942569609 ] 
dist 46=[-10.760417313337662635  ,1.2276652165575032858 ] 
dist 47=[-7.5677894270292592306 ,1.3769623392628705909 ] 
dist 48=[-7.3072734155321629424 ,1.5701232146143522894 ] 
dist 49=[-6.6479174156206548634 ,1.7763836344532933911 ] 
dist 50=[-6.5516857473661482385 ,1.9781096220777127991 ] 
dist 51=[-6.4531462923151079495 ,2.2152395600413689139 ] 
dist 52=[-6.4324103600524345670 ,2.5629842011823532282 ] 
dist 53=[-5.0740611416899272514 ,2.9050047121076086172 ] 
dist 54=[-5.0300362072520850978 ,3.1193320833786849713 ] 
dist 55=[-3.1219042609757193555 ,3.6878495894170516664 ] 
dist 56=[-2.8859327515998621909 ,4.1138784837911027384 ] 
dist 57=[-2.4046142217910940922 ,4.4375227532093883238 ] 
dist 58=[-2.2812747016692681743 ,4.7070563267982787496 ] 
dist 59=[-1.8442589361278917103 ,4.9228947842519435996 ] 
dist 60=[-1.7541497313601040489 ,5.0320742484980860735 ] 
dist 61=[-1.6293745804251676858 ,5.0903186043950181872 ] 
dist 62=[-1.5948583944363245922 ,5.1028602565787825469 ] 
dist 63=[.97201923723384225899,5.0202023656890543558 ] 
dist 64=[1.0216664633148371469 ,4.9988321342331529207 ] 
dist 65=[1.1542002099504903194 ,4.9105646085502364931 ] 
dist 66=[.6925223807828882116 ,4.8933903982001958323 ] 
dist 67=[.13088584303559858598,4.6265129727427110250 ] 
dist 68=[-.71430998083788881129,4.5636167880087936619 ] 
dist 69=[-1.5573489799078224240 ,4.5059420909466010343 ] 
dist 70=[-2.1103787023659872492 ,4.4816071810663850670 ] 
dist 71=[-2.5570814471761888967 ,4.1589765894038655845 ] 
dist 72=[-2.9756925110051133163 ,4.3327508811788221873 ] 
dist 73=[-3.3443520824255527781 ,4.4624472305274447876 ] 
dist 74=[-3.5916556319192521679 ,4.5665827935326685974 ] 
dist 75=[-3.7974623598946835206 ,4.6467860035449505331 ] 
dist 76=[-4.0004590491344405868 ,4.6808768414944185283 ] 
dist 77=[-4.1804449201724359794 ,4.6913673448489340098 ] 
dist 78=[-4.2943990555635026832 ,4.6871452557452869319 ] 
dist 79=[-4.3817694478792075675 ,4.0844220436403244007 ] 
dist 80=[-4.4556604392990530642 ,4.0523814356844635786 ] 
dist 81=[-4.5151922551158712611 ,3.8704799520737640264 ] 
dist 82=[-4.5452537754714173436 ,3.8256963523027747294 ] 
dist 83=[-4.5594596074486656259 ,3.7395911730652160984 ] 
dist 84=[-4.5557067921207005317 ,3.7124484100496840910 ] 
dist 85=[-2.2473617302161886280 ,1.3465600503072286075 ] 
dist 86=[-2.5570223915096373624 ,1.4591164432096369670 ] 
dist 87=[-2.8493540755201564736 ,1.5496850177264117725 ] 
dist 88=[-3.0342751842018491967 ,1.6339485054543032583 ] 
dist 89=[-3.1762996327695950375 ,1.7076706672369416543 ] 
dist 90=[-3.2973887177796084815 ,1.7561415192086653072 ] 
dist 91=[-3.3962297222119992059 ,1.7953136764102945932 ] 
dist 92=[-3.4494598219430960310 ,1.8318818987344784686 ] 
dist 93=[-3.4963140473516641400 ,1.8608342130218404468 ] 
dist 94=[-3.5435804296946907508 ,1.8696088949281395645 ] 
dist 95=[-3.5763876916035730481 ,1.8707235529476864003 ] 
dist 96=[-3.5816466114822731858 ,1.8691330317242307034 ] 
dist 97=[-3.5669620276174450782 ,1.8146813240325770570 ] 
dist 98=[-3.5595106109787591924 ,1.7984718337186138172 ] 
dist 99=[-3.4281834356211310708 ,1.9094393783612823014 ] 
dist 100=[-3.3921675891846923892 ,2.1479261499650133627 ] 
dist 101=[-3.3591145775885937369 ,2.3808010034439616624 ] 
dist 102=[-3.3377677383600780979 ,2.6669131863911411665 ] 
dist 103=[-2.7487815666639791664 ,2.9373755695943130393 ] 
dist 104=[-2.6657264126904879520 ,3.1077883341894470127 ] 
dist 105=[-2.5011773280109192154 ,3.2375480121704302220 ] 
dist 106=[-2.4563024532254855392 ,3.3457514577136796498 ] 
dist 107=[-2.2864141809255050540 ,3.4318046241609089101 ] 
dist 108=[-2.2467706934523192270 ,3.4731543017783431066 ] 
dist 109=[-2.1705677743224522345 ,3.4896602181278357404 ] 
dist 110=[-2.1487053993308588858 ,3.4901129037799006269 ] 
dist 111=[-1.5860432835839720163 ,1.9143012218637909379 ] 
dist 112=[-1.6179306066555502496 ,2.0373704217532810231 ] 
dist 113=[-1.6396214877916043985 ,2.1248864013284379055 ] 
dist 114=[-1.6501066182635233225 ,2.1871812485474588718 ] 
dist 115=[-1.6544208573794062776 ,2.2338744054282486491 ] 
dist 116=[-1.6515009546282833586 ,2.2590749108344907090 ] 
dist 117=[-1.4674635509692962694 ,2.2734795161051505610 ] 
dist 118=[-1.4407882165295321030 ,2.2770306512016844087 ] 
dist 119=[-1.3746918148361050507 ,2.0856779057894808504 ] 
dist 120=[-1.3558539521052920225 ,2.0551913873532979464 ] 
dist 121=[-1.2425939867880140944 ,2.1831325809694184954 ] 
dist 122=[-1.2023038749178744180 ,2.3368194562874536446 ] 
dist 123=[-1.1101226899347807303 ,2.4788336537217477691 ] 
dist 124=[-1.0165710583789119741 ,2.5862979656483873282 ] 
dist 125=[-.54242511133734939964,2.6892616182349378579 ] 
dist 126=[-.37867712441113995476,2.8133256820938017024 ] 
dist 127=[-.104186853089213455  ,2.9261742944363924634 ] 
dist 128=[-.32227564906775911362,2.9843593571078415614 ] 
dist 129=[-.51655223188578871216,3.0155717687796248090 ] 
dist 130=[-.72936202571085006671,3.0210879146878569473 ] 
dist 131=[-.93803578406004167993,3.0004989840351674767 ] 
dist 132=[-1.1158049301754547117 ,2.9917771112118116968 ] 
dist 133=[-1.3051613963763073949 ,2.9834005615917323603 ] 
dist 134=[-1.5601004037855626581 ,2.9733240854220539326 ] 
dist 135=[-1.8126322136759523318 ,2.5703341723428048042 ] 
dist 136=[-1.9923814622946673555 ,2.5112814425757766536 ] 
dist 137=[-2.1534294759612472161 ,2.4013611428648202188 ] 
dist 138=[-2.3313041724442741287 ,2.3718066310885137890 ] 
dist 139=[-2.5066270960970532428 ,2.2653299603117630357 ] 
dist 140=[-2.6574914568756798105 ,2.2363157488928835551 ] 
dist 141=[-2.8195187223163097253 ,2.1920722320326214439 ] 
dist 142=[-3.0394147353914435745 ,2.1768744179364338898 ] 
dist 143=[-3.2506812328968566656 ,.07370737420843092149] 
dist 144=[-3.3782567932190673796 ,-.08835206025122394760] 
dist 145=[-3.4691121819654667996 ,-.44491657063841269817] 
dist 146=[-3.5337730676676428975 ,-.51338669820066889302] 
dist 147=[-3.5778933768804340471 ,-.65934652591254086253] 
dist 148=[-3.5873495436569698513 ,-.58211544994676734337] 
dist 149=[-3.5832345989677279063 ,-.48698505646515245935] 
dist 150=[-3.5780462364065143528 ,-.34244576515759947935] 
dist 151=[-3.4135738416623858601 ,-.19180758044105291551] 
dist 152=[-3.3799125206858810746 ,-.07232422510974121118] 
dist 153=[-3.2971206188485493286 ,.04734373055550530356] 
dist 154=[-3.2665048663776604496 ,.19872587685798494552] 
dist 155=[-3.1103523198988343896 ,.35912322566247572025] 
dist 156=[-3.0729528823534107859 ,.51478834087852318795] 
dist 157=[-2.9905702496512581592 ,.69699665908555643182] 
dist 158=[-2.9626021121081930439 ,.96337254560200077361] 
dist 159=[-2.7752015044163018911 ,1.2279294086544184176 ] 
dist 160=[-2.7930826279838504855 ,1.4028769502095416578 ] 
dist 161=[-2.7975029490993621193 ,1.6358926177169408141 ] 
dist 162=[-2.7920666337615636244 ,2.0080721414558993113 ] 
dist 163=[-2.7338514748093974723 ,2.3426988115306066802 ] 
dist 164=[-2.7139608582148472775 ,2.5798678750103206829 ] 
dist 165=[-2.6881258430714528243 ,2.7913450191127002994 ] 
dist 166=[-2.6752311325802449644 ,3.0233936689048227607 ] 
dist 167=[-2.3059785350905526151 ,3.2352990739232997128 ] 
dist 168=[-2.2513023521156421346 ,3.3663540962787333533 ] 
dist 169=[-2.1389260446925167423 ,3.4634244646699218261 ] 
dist 170=[-2.1063680244205089882 ,3.5396485482264099117 ] 
dist 171=[-1.9715767942206569272 ,3.5967334957198514415 ] 
dist 172=[-1.9421493716357995102 ,3.6173922293713267705 ] 
dist 173=[-1.8675457364228757107 ,3.6211915408155836973 ] 
dist 174=[-1.8477731934831203146 ,3.6140544877674348965 ] 
dist 175=[-.36668661372014499923,1.9754499885794716452 ] 
dist 176=[-.64567726734749365418,1.9511080988569382006 ] 
dist 177=[-.88033619628508686653,1.8824938048853610355 ] 
dist 178=[-1.1162226453883644843 ,1.8682225050825387552 ] 
dist 179=[-1.3351678279194733171 ,1.7265038251105106885 ] 
dist 180=[-1.5021894879357509837 ,1.6951908006909547614 ] 
dist 181=[-1.6633570991169698008 ,1.6563565674820986235 ] 
dist 182=[-1.8589300097457587810 ,1.6407228439729619227 ] 
dist 183=[-2.0429519991349252371 ,1.6308683939183319719 ] 
dist 184=[-2.1580029096132300834 ,1.7004404024707621914 ] 
dist 185=[-2.2446893737166407741 ,1.7470902572013347433 ] 
dist 186=[-2.3154673479721904793 ,1.7747461366817833307 ] 
dist 187=[-2.3706888971848412903 ,1.7930533979680297121 ] 
dist 188=[-2.3952666433875171764 ,1.8023774134727391119 ] 
dist 189=[-2.4051474243125851667 ,1.8069203924090406852 ] 
dist 190=[-2.4034109101378800766 ,1.8061384771687398654 ] 
dist 191=[.01099162470043825291,1.5867327658716480864 ] 
dist 192=[-.14895148457970884849,1.5580809926653647826 ] 
dist 193=[-.28792799513014084926,1.4858195304468354027 ] 
dist 194=[-.43488090055970757932,1.4685523942091354661 ] 
dist 195=[-.57594873124303051015,1.3442675364956701204 ] 
dist 196=[-.69142872096946604951,1.3176687070622891621 ] 
dist 197=[-.81043865119359055229,1.2732773913397012388 ] 
dist 198=[-.9656008375324913901 ,1.2607527019334159723 ] 
dist 199=[-1.1170744474806533129 ,.99240873265754396936] 
dist 200=[-1.2213575339156842337 ,.95500816103404876318] 
dist 201=[-1.3111820556340840150 ,.86930498761037778397] 
dist 202=[-1.4049281803030383490 ,.84865346962910266666] 
dist 203=[-1.4941740925076443623 ,.73285409487500748676] 
dist 204=[-1.5660313188386856320 ,.71014998488076834599] 
dist 205=[-1.6390139953275395490 ,.66408355853773928905] 
dist 206=[-1.7434529509541951682 ,.65126966067681206254] 
dist 207=[-1.9293638648236836878 ,.32393711224059808725] 
dist 208=[-2.0458737755041964436 ,.46995399479614478604] 
dist 209=[-2.1340097917667073289 ,.5974131228567594623 ] 
dist 210=[-2.2066341020738998830 ,.73309544310977330405] 
dist 211=[-2.2638415526966790510 ,.86388812596132918017] 
dist 212=[-2.2904239280510104192 ,.9718251368131136386 ] 
dist 213=[-2.3020295201823042056 ,1.0838328812956867711 ] 
dist 214=[-2.3015033109230225856 ,1.2308784705342171615 ] 
dist 215=[-2.2681331253968425403 ,1.3748891082063030513 ] 
dist 216=[-2.2566292907004154070 ,1.4747796329204300214 ] 
dist 217=[-2.2252440486453505420 ,1.5616073342059801413 ] 
dist 218=[-2.2112408056013049046 ,1.6534636291061021184 ] 
dist 219=[-2.1320930548895263060 ,1.7416643539764548142 ] 
dist 220=[-2.1116196721455967804 ,1.8138969497108053294 ] 
dist 221=[-2.0667777641495939969 ,1.8883613302329936617 ] 
dist 222=[-2.0508477914011592514 ,1.9854727615498864884 ] 
dist 223=[-1.2970866729884031814 ,2.0772082539751303670 ] 
dist 224=[-1.2190109447705641661 ,2.1302086691331180830 ] 
dist 225=[-1.0365408889919678197 ,2.1650481398033409850 ] 
dist 226=[-1.0016253015783214222 ,2.1842741895743989755 ] 
dist 227=[-.75265013749801588703,2.1936049418437254489 ] 
dist 228=[-.70617774460104631726,2.1929478396458281500 ] 
dist 229=[-.62637485793484202594,2.1798711987071920022 ] 
dist 230=[-.60755204986341322645,2.1716467774375734252 ] 
dist 231=[-.28184750908537272165,2.0374888574875218339 ] 
dist 232=[-.23866070529283280512,2.0126141221371136791 ] 
dist 233=[-.14061031042754465411,1.9511820816200155364 ] 
dist 234=[-.12247710529316218259,1.9303612765142404193 ] 
dist 235=[-.00099671615377990736,1.7140094168820271272 ] 
dist 236=[.02033721464673485859,1.6745871063381280762 ] 
dist 237=[.05925568223708511936,1.5018625516569295444 ] 
dist 238=[-.05102775129144993848,1.2630193127362157369 ] 
dist 239=[-.33394167008777357761,1.1767271794911564739 ] 
dist 240=[-.52260474608280182842,1.1688271296990940861 ] 
dist 241=[-.67858635331908440371,1.1410582027237732575 ] 
dist 242=[-.83101828887433293006,1.1363857985446032178 ] 
dist 243=[-.96972634792525618809,1.0622189222429661539 ] 
dist 244=[-1.0709149681157943629 ,1.0451092523714419185 ] 
dist 245=[-1.1641252571943021894 ,1.0306371717197201116 ] 
dist 246=[-1.2709798365475895599 ,1.0256882817858591720 ] 
dist 247=[-1.3689339045397348826 ,.78803412645131330017] 
dist 248=[-1.4266083715530974345 ,.75619362969959928486] 
dist 249=[-1.4658902601943667558 ,.69468624004658423361] 
dist 250=[-1.4904103822537508960 ,.67866305056465988964] 
dist 251=[-1.5068517873347777400 ,.62226427893780155408] 
dist 252=[-1.5138791101407754521 ,.6084480036947706101 ] 
dist 253=[-1.5153639210737270276 ,.59022790820746957624] 

8 phat 4 dirichlet min maxes function [1, 2, 1, 0, 0, 1, 0, 0, 1] 
dist 0=[51.011916418135770090  ,51.011916418135770090  ] 
dist 1=[50.685946084502417437  ,51.097285695024152788  ] 
dist 2=[50.082534561037290116  ,51.112242638065181834  ] 
dist 3=[48.941585868653536698  ,51.103120384378480565  ] 
dist 4=[47.659842214200251880  ,51.059356013155737917  ] 
dist 5=[46.493978014491991244  ,51.010915771008201899  ] 
dist 6=[45.186801626800076857  ,50.982912478135980235  ] 
dist 7=[43.340452130702891197  ,50.866908739948163979  ] 
dist 8=[41.282429985651480544  ,49.776337580949059928  ] 
dist 9=[39.129674224728077279  ,47.188199957817202968  ] 
dist 10=[36.488762159812067059  ,46.645731759782345471  ] 
dist 11=[32.480772308028169067  ,45.753953754446323050  ] 
dist 12=[28.442370690037543975  ,45.506750194999196585  ] 
dist 13=[25.679894681007416967  ,44.857830349920076358  ] 
dist 14=[23.314754916015452737  ,44.616994508958672918  ] 
dist 15=[20.863288304762441178  ,43.113180892489164266  ] 
dist 16=[18.534326136458096225  ,39.769682784520877633  ] 
dist 17=[16.658333225478657953  ,31.969832634864758174  ] 
dist 18=[14.748168427688196695  ,30.461112108434686749  ] 
dist 19=[12.282343978850361362  ,30.110041711455004064  ] 
dist 20=[9.8761898378509679425 ,29.559839824457498954  ] 
dist 21=[8.2041845124601790859 ,29.399374828607487921  ] 
dist 22=[6.7427567203082891130 ,16.021621204335435009  ] 
dist 23=[5.1775397342892373908 ,14.874365309086247660  ] 
dist 24=[3.6558905574481112456 ,14.586002792069792269  ] 
dist 25=[2.0401084421053471062 ,9.9559980885697327410 ] 
dist 26=[-.17065557494227698124,9.3773893777480394164 ] 
dist 27=[-1.8139589404340496402 ,8.1995939078946111097 ] 
dist 28=[-3.3624801731170550855 ,7.9390130675949103381 ] 
dist 29=[-5.1948959929922570913 ,7.0130971539815724482 ] 
dist 30=[-6.9092689103223993896 ,6.8379864164889862639 ] 
dist 31=[-7.9862015274893045319 ,6.2973560719728154281 ] 
dist 32=[-8.8066992022067073361 ,5.6174551062520632951 ] 
dist 33=[-9.4962843148650107123 ,-3.3434663109561546261 ] 
dist 34=[-10.051937694210709069  ,-4.3679197089188013876 ] 
dist 35=[-10.337464618350459372  ,-4.6976358180149969903 ] 
dist 36=[-10.493364502301176580  ,-5.0463464078585295285 ] 
dist 37=[-10.530880351006679354  ,-5.1031042925904827315 ] 
dist 38=[-9.8774442206619538497 ,-5.3542443425055181137 ] 
dist 39=[-9.8029456773642431338 ,-5.3570268947145760787 ] 
dist 40=[-9.5482989142931300413 ,-5.0245902434714464394 ] 
dist 41=[-9.5058352921665636166 ,-4.3832576248090072052 ] 
dist 42=[-8.8652268412366184459 ,-3.5580706096831840763 ] 
dist 43=[-8.7221031851177529567 ,-2.2665890069230531018 ] 
dist 44=[-8.5909511979021799003 ,-.95952602302181146529] 
dist 45=[-8.5484275851575649005 ,-.07202160915099611018] 
dist 46=[-8.2239560032319905507 ,.67833174900687265631] 
dist 47=[-8.1743386066874507904 ,1.4380694913412675047 ] 
dist 48=[-8.1448943184195716528 ,2.1462412033611022495 ] 
dist 49=[-7.2511488311461274481 ,2.6908421149267612808 ] 
dist 50=[-7.1198697145934320334 ,3.2204507374354239297 ] 
dist 51=[-6.8466981971085889013 ,3.8688912244436780850 ] 
dist 52=[-6.5874971088660658448 ,4.4822573490600119670 ] 
dist 53=[-5.7810724741347975414 ,4.8718953863221230698 ] 
dist 54=[-2.2925438592335200058 ,5.2015910211065080718 ] 
dist 55=[-2.1886050466251651034 ,5.6903008481833163258 ] 
dist 56=[-1.7669855190079301436 ,6.2408352644376676069 ] 
dist 57=[-1.6874054039794294863 ,6.7420138155465533472 ] 
dist 58=[-1.5096739423681148123 ,7.0336665728519353035 ] 
dist 59=[-1.4703168133838547165 ,7.2281656850028334481 ] 
dist 60=[.64202914821509190914,7.3412804729917613217 ] 
dist 61=[.83073584282263418039,7.4120812909219028679 ] 
dist 62=[1.2615915054168694338 ,7.4376896711875907891 ] 
dist 63=[1.3249821106487005999 ,7.4353329301260386400 ] 
dist 64=[1.8509189505763481192 ,7.4185674025086899337 ] 
dist 65=[1.9383637430336547294 ,6.1164561278008753204 ] 
dist 66=[2.0644154275358051395 ,5.9681393377901212585 ] 
dist 67=[2.0890672838313192210 ,5.8068545852334657811 ] 
dist 68=[2.0089831276070488519 ,5.8268407252887546457 ] 
dist 69=[1.4862275565745270273 ,5.8240658903827300691 ] 
dist 70=[.94861059609497170284,4.6772351711100358084 ] 
dist 71=[.57511318698073789904,4.5350983660497934248 ] 
dist 72=[.25025832413007256194,4.5054714134646509122 ] 
dist 73=[-.09325882100888991786,3.5724326137664367026 ] 
dist 74=[-.42268813326491897826,3.4295679187037242053 ] 
dist 75=[-.69135251367156353336,3.3851863186470575663 ] 
dist 76=[-1.0169914744240600349 ,2.3761387398857201979 ] 
dist 77=[-1.6502679846975331160 ,2.1954031500466329599 ] 
dist 78=[-2.1733492970438768581 ,2.0581863733739240694 ] 
dist 79=[-2.6838802896826068970 ,2.0184844438196910382 ] 
dist 80=[-3.1481555234196455868 ,1.8514819923863401925 ] 
dist 81=[-3.4865433668131411242 ,1.8180394130169276911 ] 
dist 82=[-3.7980047301743365149 ,1.7253165731321062382 ] 
dist 83=[-4.1547596617677410682 ,1.7116400669793539118 ] 
dist 84=[-4.4820069542560998276 ,1.5279232938434946241 ] 
dist 85=[-4.6756544312314482851 ,1.4931171926858089190 ] 
dist 86=[-4.8087872839934796813 ,1.4246776375826658222 ] 
dist 87=[-4.8944327968864161517 ,1.4051529890869087410 ] 
dist 88=[-4.9528061189271600398 ,1.5803240983491088477 ] 
dist 89=[-4.9770403550303398439 ,1.8138080673110692566 ] 
dist 90=[-4.9809221179925265948 ,2.0315918608823253491 ] 
dist 91=[-4.9738692954466159932 ,2.1986792007241411427 ] 
dist 92=[-4.3331353723808987696 ,2.3604875084703788788 ] 
dist 93=[-4.3324915186955495612 ,2.5572017476895196397 ] 
dist 94=[-4.1320883689169224892 ,2.7417997070215040233 ] 
dist 95=[-4.1463784624834975375 ,2.8552554081923449329 ] 
dist 96=[-4.1453085399942059771 ,2.9382028616546550087 ] 
dist 97=[-3.9033846895892677874 ,3.0010537785887476522 ] 
dist 98=[-3.8089781730526408093 ,3.0460387911553857760 ] 
dist 99=[-3.7641007316831762672 ,3.0576845165580053425 ] 
dist 100=[-3.6203082220758987090 ,3.0559595039137298539 ] 
dist 101=[-3.4958084751014322309 ,3.0476085451799278566 ] 
dist 102=[-1.0505435838882758830 ,1.7664469598311736109 ] 
dist 103=[-.90439053392562085751,2.0024977401400301125 ] 
dist 104=[-.55859927195944841883,2.2940555720593051670 ] 
dist 105=[-.50779335418002126434,2.5711042549946900808 ] 
dist 106=[-.04013952867586075846,2.7492496426558107002 ] 
dist 107=[.04238274244557229046,2.8893588472198682670 ] 
dist 108=[.14932041099955722304,3.0145759207671953365 ] 
dist 109=[.17047588413169513538,3.1210344266330493359 ] 
dist 110=[.68070854994656822883,3.1862802985793026026 ] 
dist 111=[.37728961889965556195,3.2464639286404602839 ] 
dist 112=[-.12835384224260191084,3.3126324779447986211 ] 
dist 113=[-.64317522542535242045,3.3655177466147510202 ] 
dist 114=[-.99395050567642854921,3.3806376564712850216 ] 
dist 115=[-1.2917507036914385756 ,3.3812859914457901708 ] 
dist 116=[-1.5951371272904539198 ,3.3762891967242973572 ] 
dist 117=[-1.8789174955503503604 ,3.2759324779223071769 ] 
dist 118=[-2.0984660334963936873 ,3.2459235617285692890 ] 
dist 119=[-2.3130328142776766722 ,3.2186820789874978592 ] 
dist 120=[-2.5769310816209599006 ,3.2000356066157369430 ] 
dist 121=[-2.8265633934079574455 ,2.6697242686777748526 ] 
dist 122=[-2.9841900944596050905 ,2.5940389842949506006 ] 
dist 123=[-3.1046183518915390743 ,2.4441874121340198726 ] 
dist 124=[-3.2057779646027551389 ,2.4029723558005665232 ] 
dist 125=[-3.2868080167554634365 ,2.2452959675434432888 ] 
dist 126=[-3.3268907913732934462 ,2.2083328085372869942 ] 
dist 127=[-3.3446456786209254199 ,2.1349373786400594983 ] 
dist 128=[-3.3446436665780603240 ,2.1131032954624345240 ] 
dist 129=[-.03073231775417589737,1.3909610040413786023 ] 
dist 130=[-.23737010325430307795,1.3718038586917188684 ] 
dist 131=[-.44091705969442345335,1.3648145221703523775 ] 
dist 132=[-.6814294242011263308 ,1.3451983773963884175 ] 
dist 133=[-1.0356593193652450787 ,1.3365820504677932098 ] 
dist 134=[-1.3882417298245326319 ,-.54994493651085357301] 
dist 135=[-1.6221800408098048504 ,-.66834169526675957712] 
dist 136=[-1.8142897738917904426 ,-.69497092891127375892] 
dist 137=[-1.9998743413830503241 ,-.91249518536135424703] 
dist 138=[-2.1673404567544805896 ,-.93069890004409265402] 
dist 139=[-2.2871149801271906976 ,-.91568026366800050335] 
dist 140=[-2.3950546682689222543 ,-.85142263774595226678] 
dist 141=[-2.5152755251584753694 ,-.76038336820131030018] 
dist 142=[-2.6230369754131938352 ,-.63844447559256260056] 
dist 143=[-2.6812344510975562401 ,-.47041301877167332708] 
dist 144=[-2.7143648882402953864 ,-.19536224218268381614] 
dist 145=[-2.7979696559529128033 ,.08807295268703973933] 
dist 146=[-2.8599985648891280790 ,.2895790390770264306 ] 
dist 147=[-2.8940263151118231362 ,.46983106855945850623] 
dist 148=[-2.9015380502610379531 ,.66842200261513237035] 
dist 149=[-2.8914355846970829131 ,.86382253117323827336] 
dist 150=[-2.8852008048704062242 ,1.0313417777750965751 ] 
dist 151=[-2.8776995102586817300 ,1.2106878090017572901 ] 
dist 152=[-2.8670857451248763618 ,1.4533087719973355308 ] 
dist 153=[-2.4997017690599500216 ,1.6941596655637758490 ] 
dist 154=[-2.4449809448513102297 ,1.8664417705914484773 ] 
dist 155=[-2.3425511870769772479 ,2.0216684958397289832 ] 
dist 156=[-2.3146434239345917932 ,2.1944329078558676403 ] 
dist 157=[-2.2119568069628637914 ,2.3654819836394214220 ] 
dist 158=[-2.1843681597164453117 ,2.5138640047588882696 ] 
dist 159=[-2.1371817384324593533 ,2.6742384493343373202 ] 
dist 160=[-2.1228351528980060445 ,2.8931713469281354936 ] 
dist 161=[-1.3207655099298536907 ,3.1040498253351599458 ] 
dist 162=[-1.1720427760186667159 ,3.2322686760174180878 ] 
dist 163=[-1.1418682627934935045 ,3.3246417846036808388 ] 
dist 164=[-1.0704515610223160565 ,3.3924070420705569232 ] 
dist 165=[-1.0528133558403943837 ,3.4396786297459727505 ] 
dist 166=[-.02289447146000318504,3.4508438618035346536 ] 
dist 167=[.06041297697892755879,3.4484391396953203142 ] 
dist 168=[.24419094251433000607,3.4464340685208810352 ] 
dist 169=[.27900224283584555889,3.3061831447453839096 ] 
dist 170=[.48574231527657979725,3.2762562091861616776 ] 
dist 171=[.52005473411938613984,3.2004116661763841044 ] 
dist 172=[.58935461326308757889,3.1715607440997951528 ] 
dist 173=[.60448150358739709193,3.0218183442753336320 ] 
dist 174=[.68894631285134799171,2.9854464081705062216 ] 
dist 175=[.5819373992996037694 ,2.9088164239859495252 ] 
dist 176=[-.08096513984591526080,2.8833420440634308461 ] 
dist 177=[-.77361723228620290144,2.7193031466260140226 ] 
dist 178=[-1.2324158884552923665 ,2.7349158001573211402 ] 
dist 179=[-1.6083106366364643709 ,2.7379798885684363622 ] 
dist 180=[-1.9699674861501609183 ,2.7323081830364709887 ] 
dist 181=[-2.2952960819036285074 ,2.6715731003083206589 ] 
dist 182=[-2.5261489139761135479 ,2.6513707665832054012 ] 
dist 183=[-2.7322743694630952791 ,2.6259136082772435072 ] 
dist 184=[-2.9588762918603060957 ,2.6129637920639750607 ] 
dist 185=[-3.1657679116319719224 ,2.2438620952285783244 ] 
dist 186=[-3.2931999957706942676 ,2.1894450327916569436 ] 
dist 187=[-3.3869666389903387913 ,2.0780114374625936300 ] 
dist 188=[-3.4594516608137602636 ,2.0561068482687244523 ] 
dist 189=[-3.5127969277791419066 ,2.0536454301587893993 ] 
dist 190=[-3.5301495817396396738 ,1.8849056739683317947 ] 
dist 191=[-3.5322046623037247192 ,1.8128568885376319520 ] 
dist 192=[-3.5244739494100574670 ,1.7925259731784317702 ] 
dist 193=[-1.7559817030226454451 ,1.6045358658608975584 ] 
dist 194=[-1.8657201529058030236 ,1.5373926505022330029 ] 
dist 195=[-1.9576711993275573812 ,1.5171891147590449289 ] 
dist 196=[-2.0543238933743886209 ,1.4999386157758073533 ] 
dist 197=[-2.1828347809802634657 ,1.4919873628024910360 ] 
dist 198=[-2.3053583549193351224 ,.12917277843018183303] 
dist 199=[-2.3781063582492726730 ,.01983404470993581229] 
dist 200=[-2.4284132617931181098 ,-.2208520849838470625 ] 
dist 201=[-2.4613386291072443568 ,-.26786434743833444032] 
dist 202=[-2.4816257299509421244 ,-.5383875258643501939 ] 
dist 203=[-2.4846475348521158855 ,-.58366341115026343061] 
dist 204=[-2.4748780570975676893 ,-.67720725633995768242] 
dist 205=[-2.4694429589520253324 ,-.69666839895263294391] 
dist 206=[-2.3424679353531531535 ,-.82974732515967247397] 
dist 207=[-2.3176247130440899560 ,-.84859264304283733468] 
dist 208=[-2.2548920123742958177 ,-.73224452849834356174] 
dist 209=[-2.2327677230096330584 ,-.48052546449660981701] 
dist 210=[-2.1150274522850393153 ,-.30177904520258389767] 
dist 211=[-2.0871486289546072759 ,-.14203695948392375752] 
dist 212=[-2.0310562124715244356 ,.03380791752445819398] 
dist 213=[-2.0132720991893887848 ,.20681271103945514822] 
dist 214=[-1.5545659991458738460 ,.64367491411064076982] 
dist 215=[-1.5490485886101187533 ,.97404324154304606503] 
dist 216=[-1.5249095375936518829 ,1.2438963461611416240 ] 
dist 217=[-1.5196062476202203215 ,1.5021949983773883308 ] 
dist 218=[-1.4409128867171305823 ,1.7336823519591593798 ] 
dist 219=[-1.4216880887301148006 ,1.8964887286749355189 ] 
dist 220=[-1.4039237406700089075 ,2.0403672982168227341 ] 
dist 221=[-1.3950708500611353416 ,2.1962830181641052112 ] 
dist 222=[-1.1149173958393844287 ,2.3380824525488935422 ] 
dist 223=[-1.0762356316160228631 ,2.4256007248247603328 ] 
dist 224=[-1.0004052856963667538 ,2.4902213949738752928 ] 
dist 225=[-.98010836132981737504,2.5406014788361106878 ] 
dist 226=[-.90533228402737742004,2.5780418607969610772 ] 
dist 227=[-.88760344980500256181,2.5910005256581682863 ] 
dist 228=[-.85624097618882455097,2.5924518638322925341 ] 

8 phat 4 dirichlet min maxes function [1, 0, 1, 2, 2, 0, 1, 0, 2] 
dist 0=[50.957585345900116434  ,50.957585345900116434  ] 
dist 1=[50.607540660749154817  ,51.048937259805304791  ] 
dist 2=[49.985775682548519014  ,51.063610473244666717  ] 
dist 3=[48.842337138924186626  ,51.063286230031489289  ] 
dist 4=[47.561361431559007189  ,51.036142714967697136  ] 
dist 5=[46.390281655241506505  ,50.983532545045286266  ] 
dist 6=[45.072945055255121290  ,50.896540021639330221  ] 
dist 7=[43.207597704806468906  ,50.665572032925614313  ] 
dist 8=[41.126942101116867561  ,47.264149036363091383  ] 
dist 9=[38.949527794263140520  ,46.444668963066931269  ] 
dist 10=[36.278214907246648921  ,46.219548259927117721  ] 
dist 11=[32.224739423835479850  ,45.546665137837747146  ] 
dist 12=[28.143232697887502766  ,45.321794195164406100  ] 
dist 13=[25.359845806399606580  ,45.085739266604422217  ] 
dist 14=[22.986518506257687100  ,43.902016726609168972  ] 
dist 15=[20.542628153949082301  ,40.089433456725010851  ] 
dist 16=[18.231223782452057999  ,33.790207596518659747  ] 
dist 17=[16.386835759405431307  ,32.957170659798228311  ] 
dist 18=[14.524829764669690531  ,31.326313406908554914  ] 
dist 19=[12.142596052676392610  ,30.901503773189655354  ] 
dist 20=[9.8279071008899841272 ,29.387999341072486167  ] 
dist 21=[8.2354555999576719695 ,29.035079658414527188  ] 
dist 22=[6.8601381103086904620 ,28.505924144501785583  ] 
dist 23=[5.4124914557536499699 ,28.344506709765562849  ] 
dist 24=[4.0195139380406494161 ,12.524540840472079463  ] 
dist 25=[2.8621154241202511838 ,11.198993143593233567  ] 
dist 26=[1.6478082559435175856 ,9.9683303580667159442 ] 
dist 27=[.02644613678190978949,8.7565933905198325630 ] 
dist 28=[-1.5446528071063172505 ,8.5541254068230392308 ] 
dist 29=[-2.5582431681885415350 ,8.2310103734867287925 ] 
dist 30=[-3.7891722673499759892 ,7.9966022841203932690 ] 
dist 31=[-5.5714134087396762327 ,1.7962003095818808139 ] 
dist 32=[-7.2384936095047489081 ,-2.5161930988523223851 ] 
dist 33=[-8.2894614096281492708 ,-3.0365850163018372544 ] 
dist 34=[-9.0945561823895893632 ,-4.1525956929254910540 ] 
dist 35=[-9.7790537339510154436 ,-4.3435187909221877363 ] 
dist 36=[-10.336347452734920733  ,-4.2147714072140848570 ] 
dist 37=[-10.633044142306944738  ,-3.9844816256086882568 ] 
dist 38=[-10.796086868931324137  ,-3.6655544764633016990 ] 
dist 39=[-10.832506968999302467  ,-3.1450442311319458782 ] 
dist 40=[-9.8739845227681962453 ,-2.5367099452357686148 ] 
dist 41=[-9.7814226802056067240 ,-1.8669446706448823748 ] 
dist 42=[-9.4881829059597756986 ,-1.0246322703956311503 ] 
dist 43=[-9.4392907334309191312 ,.27264728879463619762] 
dist 44=[-9.3854733152881747905 ,1.5764170898459433393 ] 
dist 45=[-9.2995201591183424662 ,2.4447649959647824861 ] 
dist 46=[-9.2551095769527669039 ,3.1604083576633678692 ] 
dist 47=[-8.4209491370800193031 ,3.8548226500710247481 ] 
dist 48=[-6.5577407991306489099 ,4.4827220617415477757 ] 
dist 49=[-6.4343979820062928936 ,4.9329668437395433257 ] 
dist 50=[-6.2854614393493883719 ,5.3396713472240778952 ] 
dist 51=[-6.0058874997282389985 ,5.7939053550250894884 ] 
dist 52=[-5.2325114801669870203 ,6.2050420124178857679 ] 
dist 53=[-5.1277092201906384657 ,6.4396903129332967704 ] 
dist 54=[-4.9641749810215218653 ,6.5902508081297684110 ] 
dist 55=[-4.9176933196189914955 ,6.6655300126857683834 ] 
dist 56=[-2.3271639998470449133 ,6.7058932712607912470 ] 
dist 57=[-1.8694045503856296593 ,6.7171150283992737004 ] 
dist 58=[-1.7489740622999920614 ,6.7092996163952402191 ] 
dist 59=[-1.2936863333598682789 ,6.6899850007885427375 ] 
dist 60=[-1.2056160937988797103 ,6.0283395211701566353 ] 
dist 61=[-1.0332531254072820034 ,6.1481699189129978128 ] 
dist 62=[-.99122787895741777499,6.2402699019684499199 ] 
dist 63=[1.3525768039029962856 ,6.3042304668316100232 ] 
dist 64=[1.5544034596879702213 ,6.3148720433816819938 ] 
dist 65=[2.0066162283361519743 ,6.2990900910402236486 ] 
dist 66=[2.0757516250424469924 ,6.2824699909932642768 ] 
dist 67=[2.5838289992910026284 ,6.0858344115041546814 ] 
dist 68=[2.4304519873945041980 ,6.0294156269336900664 ] 
dist 69=[2.1804521063375760680 ,5.9623430818452050203 ] 
dist 70=[1.8354074740582738073 ,5.9285733526416163573 ] 
dist 71=[1.3816380128702685026 ,5.8317562717779229612 ] 
dist 72=[.85031679619558099995,4.8744307924278989561 ] 
dist 73=[.48179125059120481385,4.6021304940521413864 ] 
dist 74=[.16187159032257518015,4.5248203767556830038 ] 
dist 75=[-.37849894602677474308,4.2121744190651124488 ] 
dist 76=[-.97068329078577411471,4.1445312541154885554 ] 
dist 77=[-1.3678580624335924219 ,3.9829273878982767786 ] 
dist 78=[-1.6991905783030905582 ,3.9350762942131874536 ] 
dist 79=[-2.0284247187484702840 ,2.6148004755727848836 ] 
dist 80=[-2.3320951878255931825 ,2.5239315988335043694 ] 
dist 81=[-2.5613375837661305418 ,2.3199924844973704238 ] 
dist 82=[-2.8414145685673940885 ,2.2668918395050628537 ] 
dist 83=[-3.3471500133835432109 ,2.0015820047600187923 ] 
dist 84=[-3.7124879421784081361 ,1.9490235124371702537 ] 
dist 85=[-4.0454844246335881608 ,1.8342420070659780632 ] 
dist 86=[-4.4220763849800766699 ,1.8000650139982477682 ] 
dist 87=[-4.7674616986022432648 ,1.4575689149056070822 ] 
dist 88=[-4.9758595581956292636 ,1.4035798906583755020 ] 
dist 89=[-5.1241171378077412765 ,1.3611045676474889942 ] 
dist 90=[-5.2293949021552320864 ,1.5954046283197295795 ] 
dist 91=[-5.3034799626340857191 ,1.8328250027985420102 ] 
dist 92=[-5.3271829735841131073 ,2.0538566628932757871 ] 
dist 93=[-5.3284198419664490382 ,2.2227571204199107126 ] 
dist 94=[-5.3156462196377367111 ,2.3856824650150910931 ] 
dist 95=[-4.3913373199918416951 ,2.5828650569306468568 ] 
dist 96=[-4.1318041507721837832 ,2.7674661649103314041 ] 
dist 97=[-4.0844533727902208655 ,2.8801809573503356260 ] 
dist 98=[-4.0051903535590117264 ,2.9617023088343150611 ] 
dist 99=[-3.9798436234383296895 ,3.0218193287500569718 ] 
dist 100=[-3.8886753208750071227 ,3.0634346867263006960 ] 
dist 101=[-3.8586432850692126339 ,3.0721985862205578138 ] 
dist 102=[-3.8016162204227568048 ,3.0670582440827862275 ] 
dist 103=[-3.6802154186697939338 ,3.0618603801291191290 ] 
dist 104=[-1.0538195949759850940 ,3.0325097644260987599 ] 
dist 105=[-.91266970728794256971,3.0867095054042579379 ] 
dist 106=[-.57814337996476702606,3.1322572738784740625 ] 
dist 107=[-.52925672715558293173,3.1767825080104627316 ] 
dist 108=[-.59338843010679442594,3.2088098607147646078 ] 
dist 109=[-.93667186749897139916,3.2142781857531612017 ] 
dist 110=[-1.2280825194089800150 ,3.2037883586263312403 ] 
dist 111=[-1.5249511606838456088 ,3.1967104398172908478 ] 
dist 112=[-1.8026629218089258258 ,3.0846632706372779018 ] 
dist 113=[-2.0176125893882646436 ,3.0533225574985300576 ] 
dist 114=[-2.2277956673453746531 ,3.0225768209375540259 ] 
dist 115=[-2.4864835610479997283 ,3.0038594186985422593 ] 
dist 116=[-2.7313168882658145735 ,2.4866503227205550350 ] 
dist 117=[-2.8862006372779816140 ,2.4132358699142794500 ] 
dist 118=[-3.0048809626072595574 ,2.2666187163984981905 ] 
dist 119=[-3.1052099290925415742 ,2.2261961308873110158 ] 
dist 120=[-3.1860756183343954487 ,2.0704224058146537744 ] 
dist 121=[-3.2270683839980222870 ,2.0346746811173068051 ] 
dist 122=[-3.2467011105573706369 ,1.9616765602124218279 ] 
dist 123=[-3.2468560301052721000 ,1.9397341903770710104 ] 
dist 124=[.3161760309451805858 ,1.3536106286542173560 ] 
dist 125=[.02761540630320496831,1.3578082299283557732 ] 
dist 126=[-.22042932384452544139,1.3597811208605955322 ] 
dist 127=[-.47843990560958238635,1.3593469775842231101 ] 
dist 128=[-.72349194530141006329,1.3576718417517215211 ] 
dist 129=[-.91980636672654618021,1.3546840080930508420 ] 
dist 130=[-1.1182795380312799151 ,1.3502141525264743474 ] 
dist 131=[-1.3719609485373794244 ,1.3458279995529055069 ] 
dist 132=[-1.6172555962199091571 ,1.3335965314241614010 ] 
dist 133=[-1.7822492585487023761 ,1.3275732739599003177 ] 
dist 134=[-1.9202610609257330403 ,1.3129677538955650166 ] 
dist 135=[-2.0578338626302896805 ,1.3064245809459420098 ] 
dist 136=[-2.1848775214266050538 ,-.74884785719872384753] 
dist 137=[-2.2808583134812123978 ,-.63552060380125456223] 
dist 138=[-2.3726606624285016194 ,-.47917306896805120546] 
dist 139=[-2.4830382397832642980 ,-.22306322280170907562] 
dist 140=[-2.5835135842325069736 ,.04093236094687267539] 
dist 141=[-2.6357808970295778820 ,.22876357808553862602] 
dist 142=[-2.6638406154233315960 ,.39693582842042103166] 
dist 143=[-2.6692660130443035304 ,.58245425292802419309] 
dist 144=[-2.6541828839513425570 ,.76513319589639036768] 
dist 145=[-2.6464469956032657938 ,.92197323896961197662] 
dist 146=[-2.6379687519758807145 ,1.0900821741493506612 ] 
dist 147=[-2.6278624706176144186 ,1.3177540133711168691 ] 
dist 148=[-2.6190710714680001864 ,1.5438832493259185545 ] 
dist 149=[-2.6123381537562086884 ,1.7058361147279425786 ] 
dist 150=[-2.5992672605923682414 ,1.8519638673596901245 ] 
dist 151=[-2.5915016837203666695 ,2.0149177187945891171 ] 
dist 152=[-2.3784228018613082815 ,2.1764380156651694386 ] 
dist 153=[-2.3462968283051541873 ,2.3168457106663302609 ] 
dist 154=[-2.2575681434929159324 ,2.4688485273760843237 ] 
dist 155=[-2.2390302501657118889 ,2.6766660750298414413 ] 
dist 156=[-2.0618270753959666030 ,2.8769998646145541451 ] 
dist 157=[-2.0230373200904077204 ,2.9991252622861915921 ] 
dist 158=[-1.9732457324941326187 ,3.0874918895329801521 ] 
dist 159=[-1.9540909321537668043 ,3.1530444730350635122 ] 
dist 160=[-1.5073586411729786054 ,3.1992254259754520374 ] 
dist 161=[-1.4461599376717492381 ,3.2104644783863921830 ] 
dist 162=[-1.3173737104942184345 ,3.2094529864611210637 ] 
dist 163=[-1.2814134872034240723 ,3.2084355770647961000 ] 
dist 164=[-1.1371574361739692672 ,3.0836249008901207817 ] 
dist 165=[-1.1080484480006374275 ,3.0565452920527456813 ] 
dist 166=[-1.0380622704728945747 ,2.9876476262932732154 ] 
dist 167=[-1.0217838346571067645 ,2.9612388521343066091 ] 
dist 168=[-.02828096127152565670,2.8235437032343271564 ] 
dist 169=[.05382994441065864083,2.7899765677625521568 ] 
dist 170=[.23428808727162732076,2.7192364129277183503 ] 
dist 171=[-.05866532585461036673,2.6956551013061234448 ] 
dist 172=[-.70223849042747587141,2.5269665833326813867 ] 
dist 173=[-1.1287532254054569031 ,2.5372527329798184529 ] 
dist 174=[-1.4784485236679740060 ,2.5373202047180353522 ] 
dist 175=[-1.8153184392639297108 ,2.5316729749223857372 ] 
dist 176=[-2.1186328311230531611 ,2.4677167648260173636 ] 
dist 177=[-2.3343562939177334002 ,2.4476395926203294026 ] 
dist 178=[-2.5274820577971965218 ,2.4233779598993675284 ] 
dist 179=[-2.7405726392779595975 ,2.4108100537902713452 ] 
dist 180=[-2.9352794648564763888 ,2.0567380606359708933 ] 
dist 181=[-3.0550080010927631578 ,2.0049399227555916846 ] 
dist 182=[-3.1428709186658985886 ,1.8993891959236229258 ] 
dist 183=[-3.2103565313750166592 ,1.8692234671792557218 ] 
dist 184=[-3.2596604848988049646 ,1.9125320974709571737 ] 
dist 185=[-3.2749343812118508681 ,1.9503634630905025995 ] 
dist 186=[-3.2764359186394556747 ,1.9707599499670004655 ] 
dist 187=[-3.2707532929500046068 ,1.9751267370362088517 ] 
dist 188=[-.75435038642932155956,1.9578155215948010415 ] 
dist 189=[-.87184549428617969027,1.9524610941849337344 ] 
dist 190=[-.9953461891428345553 ,1.9484616145681245612 ] 
dist 191=[-1.1595439854416594155 ,1.9452623443370609252 ] 
dist 192=[-1.3213068939456715337 ,1.6598033580497034352 ] 
dist 193=[-1.4350865689053773264 ,1.6190135840610106749 ] 
dist 194=[-1.5356485097590560366 ,1.5452655431310756347 ] 
dist 195=[-1.6446394751810064895 ,1.5260744199508290399 ] 
dist 196=[-1.7508747538296023878 ,1.4612494399810319935 ] 
dist 197=[-1.8404349475534535095 ,1.4421175443442382950 ] 
dist 198=[-1.9350506559520077417 ,1.4232219841649669932 ] 
dist 199=[-2.0614712063968315236 ,1.4131250174986220805 ] 
dist 200=[-2.1822804074355873234 ,.10286292374955830537] 
dist 201=[-2.2544924966859569660 ,-.00159495676096463047] 
dist 202=[-2.3050236051354680476 ,-.23107652359166551877] 
dist 203=[-2.3392694561589841573 ,-.27616022049939023219] 
dist 204=[-2.3611122915271389130 ,-.43636680220392790123] 
dist 205=[-2.3650495905814612185 ,-.26257592176676779784] 
dist 206=[-2.3567245361372965991 ,-.10758188704330221443] 
dist 207=[-2.3529768535137783629 ,.06254925730621876519] 
dist 208=[-2.2409166873036033686 ,.22964852269440690004] 
dist 209=[-2.2184741475352124028 ,.37253857521411910225] 
dist 210=[-2.1607774557412118963 ,.52524732340593089466] 
dist 211=[-2.1405961925760566535 ,.73154963045857540888] 
dist 212=[-2.0287428033077686279 ,.93631134022478313394] 
dist 213=[-2.0021450529669762025 ,1.0828698177371078394 ] 
dist 214=[-1.9499883889930688839 ,1.2150483056215085500 ] 
dist 215=[-1.9336746678515542806 ,1.3623976818893648593 ] 
dist 216=[-1.5506300269937000136 ,1.5084572813726585346 ] 
dist 217=[-1.5472569426624170309 ,1.6354871450155396129 ] 
dist 218=[-1.5285710383095609094 ,1.7730799985731878108 ] 
dist 219=[-1.5236767702429569309 ,1.9613149628385066179 ] 
dist 220=[-1.4533389580973894904 ,2.1433474957562075608 ] 
dist 221=[-1.4355819735377374170 ,2.2561767612444201639 ] 
dist 222=[-1.4184950318888805157 ,2.3400660866954514211 ] 
dist 223=[-1.4087368850158821542 ,2.4065521554227182455 ] 
dist 224=[-1.1430361152602231334 ,2.4568638847749615230 ] 
dist 225=[-1.1058142408795446150 ,2.4761752907408041035 ] 
dist 226=[-1.0323851250553351372 ,2.4827467447376785468 ] 
dist 227=[-1.0124952839423313569 ,2.4821913354177617466 ] 
dist 228=[-.93782323153946283402,2.4176938900366222850 ] 
dist 229=[-.92033995123845677245,2.4010907773374009436 ] 
dist 230=[-.88729554969440933807,2.3328592742523840004 ] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 0, 2, 0, 2, 0, 1] 
dist 0=[47.027232729059957025  ,47.027232729059957025  ] 
dist 1=[46.731063857932937558  ,47.299625448405193218  ] 
dist 2=[45.820783167306027472  ,47.651365992740360252  ] 
dist 3=[44.694554305896554574  ,47.838418395922446232  ] 
dist 4=[43.406363744245057580  ,47.937157963587200790  ] 
dist 5=[41.749281653556765819  ,47.936218854136622722  ] 
dist 6=[39.149509104037535728  ,47.862879529778792974  ] 
dist 7=[36.497589176596982162  ,47.808651831670831351  ] 
dist 8=[34.632122089858307667  ,47.414313495437984089  ] 
dist 9=[32.980125792586496583  ,47.296639560560600065  ] 
dist 10=[31.180674230035444164  ,46.864092275717610503  ] 
dist 11=[29.417167868258894113  ,46.768843703750480939  ] 
dist 12=[27.908564291750594812  ,45.226956632655210388  ] 
dist 13=[26.292387757783277414  ,44.889005090640737428  ] 
dist 14=[24.098853302225037235  ,43.649844481085732588  ] 
dist 15=[21.907725042585954700  ,41.529441919811676050  ] 
dist 16=[20.300975466856509270  ,31.006415947684445732  ] 
dist 17=[18.808029813762176224  ,30.371254620720035064  ] 
dist 18=[17.071267545591118646  ,29.554827530398860498  ] 
dist 19=[15.300878069229308445  ,29.277074913839786295  ] 
dist 20=[13.673255512396970756  ,23.557092929756640594  ] 
dist 21=[11.830108683698833019  ,22.805747500996577986  ] 
dist 22=[9.1979757460351490059 ,21.234750944428649309  ] 
dist 23=[6.5984404457352794064 ,20.810825217807091498  ] 
dist 24=[4.8854567234527246032 ,19.174142500371181159  ] 
dist 25=[3.4846544329537471024 ,18.851196231822519892  ] 
dist 26=[2.1328162102216188002 ,18.139727732655832681  ] 
dist 27=[.90675582848476364442,17.950126796612145987  ] 
dist 28=[.00858693776018296002,10.564126252629528318  ] 
dist 29=[-1.5615636930701249552 ,10.204496794950458303  ] 
dist 30=[-3.5188839554204893910 ,8.5693951973503003855 ] 
dist 31=[-5.3851841978714677625 ,5.8012117211144050206 ] 
dist 32=[-7.0581121560360371415 ,2.2154410170050903102 ] 
dist 33=[-8.2429729350998974919 ,1.7984981770528940166 ] 
dist 34=[-9.3016455396879654849 ,1.0327097835649793115 ] 
dist 35=[-10.470575368770785877  ,.86407283204276849867] 
dist 36=[-11.541126696383015190  ,-1.1347534792831322539 ] 
dist 37=[-12.206817199322938933  ,-1.4162154451652454075 ] 
dist 38=[-12.706216621899317317  ,-1.8915911515346450781 ] 
dist 39=[-13.112428435198203393  ,-1.9923776578840858497 ] 
dist 40=[-13.430076698654646457  ,-2.1454857500551560397 ] 
dist 41=[-13.575706826908187637  ,-2.0798565217879458019 ] 
dist 42=[-13.630341560092299222  ,-1.8157678323514172042 ] 
dist 43=[-13.626054971339372254  ,-1.5083475812214485966 ] 
dist 44=[-10.491790220555573080  ,-1.0870113048739912295 ] 
dist 45=[-10.446651315532724956  ,-.77169548212319061741] 
dist 46=[-10.316253911141915055  ,-.45817281200728691603] 
dist 47=[-10.254188107570016102  ,.00284775243093451887] 
dist 48=[-5.8681191794885149162 ,.34512621012636776537] 
dist 49=[-5.6125279755887588569 ,.66592534393543716037] 
dist 50=[-5.2572192221611134081 ,1.0413775962877713239 ] 
dist 51=[-5.1494755929735720081 ,1.4236321519162668309 ] 
dist 52=[-3.0800820637501492854 ,1.8369492798913991056 ] 
dist 53=[-2.8173181205091755323 ,2.5011001353441853925 ] 
dist 54=[-2.7323521771586317778 ,3.1263341670616337080 ] 
dist 55=[-2.1152270867662736830 ,3.8628522892667059482 ] 
dist 56=[-1.4185622171762335002 ,4.5518844360974459760 ] 
dist 57=[-1.2978133410071244724 ,4.9875447518224409585 ] 
dist 58=[-1.0598760999370051536 ,5.3215125903661630573 ] 
dist 59=[-1.0027580120106174359 ,5.6044041475869848212 ] 
dist 60=[.76179522709417531374,5.8327385004418839268 ] 
dist 61=[.94239542858269870475,5.9487660941650635205 ] 
dist 62=[1.2713335387560347758 ,6.0069539238959363484 ] 
dist 63=[1.3419264003180349879 ,6.0154374774553580721 ] 
dist 64=[1.5060371101566441048 ,6.0826431108145856123 ] 
dist 65=[1.4993556231476729688 ,6.3595413957938356085 ] 
dist 66=[1.4237125163779980916 ,6.5902571515057461055 ] 
dist 67=[1.2350317856702891340 ,6.8195222552995155148 ] 
dist 68=[1.0100725650862323440 ,7.0136039981227563955 ] 
dist 69=[.7895510321456179271 ,7.1038097179543521241 ] 
dist 70=[.5303319084055275944 ,7.1456137612266262571 ] 
dist 71=[-.07025169639131164788,7.1462729621085111308 ] 
dist 72=[-.62592445653192060151,7.0405986768347736187 ] 
dist 73=[-1.0872124519565486252 ,7.0007504312527473931 ] 
dist 74=[-1.5407796145289635766 ,6.9656198922900284052 ] 
dist 75=[-2.1325681763956791306 ,6.9346463709109866750 ] 
dist 76=[-2.9801998842554005828 ,2.1137433779278951047 ] 
dist 77=[-3.5432846662511756576 ,2.0066458542433697491 ] 
dist 78=[-4.0062483785387869521 ,1.9707890307330944474 ] 
dist 79=[-4.4542119670058265353 ,1.8099027989708003023 ] 
dist 80=[-4.8588005488552199170 ,1.1320543276719813049 ] 
dist 81=[-5.1486283424408523270 ,.92224805071489172916] 
dist 82=[-5.4102698034549188121 ,.87067451716106612448] 
dist 83=[-5.7023746351724571190 ,.63369237393806736719] 
dist 84=[-5.9647051993350277458 ,.59093703657067539858] 
dist 85=[-6.1074982492073214519 ,.48788408313711939154] 
dist 86=[-6.1903961263296258773 ,.47203642268329015683] 
dist 87=[-6.2136204219290861334 ,-.57387304270883056074] 
dist 88=[-6.2106520814962081402 ,-.59069964120340234031] 
dist 89=[-6.1920977406823102345 ,-.62407162758254021669] 
dist 90=[-6.2716930365635324825 ,-.62897729297988462767] 
dist 91=[-6.3471507846710271164 ,.47679396441497533513] 
dist 92=[-6.3961115523586553382 ,1.7270807235589532692 ] 
dist 93=[-6.4023359614031581868 ,2.5634531648259491450 ] 
dist 94=[-6.3690990934430144863 ,3.2571992658893618775 ] 
dist 95=[-6.3545971313167625385 ,3.9381527440071034380 ] 
dist 96=[-6.1098829251700433850 ,4.5591429505524091327 ] 
dist 97=[-6.0433426798162592264 ,5.0135252564288956545 ] 
dist 98=[-5.9820526468558399894 ,5.4330866083638635367 ] 
dist 99=[-5.9428154619521890648 ,5.9150691490428919952 ] 
dist 100=[-4.8626867212253601974 ,6.3549915643182961492 ] 
dist 101=[-4.7102900300779357387 ,6.6066553283678865295 ] 
dist 102=[-4.4088794293634605513 ,6.7686714907914820947 ] 
dist 103=[-4.3267142303224081423 ,6.8507423724613092556 ] 
dist 104=[-4.0157250134563149452 ,6.8980322612150713865 ] 
dist 105=[-3.9430011509580562838 ,6.9212135391737991718 ] 
dist 106=[-3.8024568573304789361 ,6.9311425223094744329 ] 
dist 107=[-3.7617155483137294929 ,6.9255398707313060786 ] 
dist 108=[.09801879989478288519,2.0649246512895501872 ] 
dist 109=[.12335823196159452672,2.1162380626909161740 ] 
dist 110=[.12960797874560538718,2.1551634729731229458 ] 
dist 111=[-.04249042575095691322,2.1923088981766810384 ] 
dist 112=[-.36558644835376366021,2.2222953909995217804 ] 
dist 113=[-.5865151501765557001 ,2.2286579778404528970 ] 
dist 114=[-.77482974096491173674,2.2265477801280119732 ] 
dist 115=[-.96777312939201108698,2.2226189005245442724 ] 
dist 116=[-1.1488454603369299405 ,2.1492578900895684812 ] 
dist 117=[-1.2897872316318650123 ,2.1281416109414797094 ] 
dist 118=[-1.4282859914881547235 ,2.1086263986851017989 ] 
dist 119=[-1.5996116956674058438 ,2.0957744856274543550 ] 
dist 120=[-1.7620655665716300639 ,1.7355453082241612094 ] 
dist 121=[-1.8651583737504878663 ,1.6844530375776357628 ] 
dist 122=[-1.9444848769008548491 ,1.5828368334038832146 ] 
dist 123=[-2.0120886712941930751 ,1.5549294115834851382 ] 
dist 124=[-2.0669610622096830591 ,1.4481940101853113043 ] 
dist 125=[-2.0954769209283613456 ,1.4234378628363754130 ] 
dist 126=[-2.1101387206048509402 ,1.3743323156354594139 ] 
dist 127=[-2.1100330480753716664 ,1.3598700075419666771 ] 
dist 128=[-.05645002886212621180,.22282590619571982038] 
dist 129=[-.09001425203711618708,.19718561771829595741] 
dist 130=[-.22242159147645904548,.20565013502815924186] 
dist 131=[-.39388266267038515386,.21569794061750515645] 
dist 132=[-.55374026153780515187,.22701461169155368875] 
dist 133=[-.67688625443722333953,.24143026076557095142] 
dist 134=[-.79688288994844199635,.26384693591930921209] 
dist 135=[-.94417594704587946269,.28646414487763635879] 
dist 136=[-1.0836889967152113164 ,.30168013794263697788] 
dist 137=[-1.1726285664811570750 ,.31438981333233796231] 
dist 138=[-1.2416917923510691137 ,.32700349546281007878] 
dist 139=[-1.3039913573021525471 ,.3385911602886600541 ] 
dist 140=[-1.3698797252109337114 ,.34720567524773758465] 
dist 141=[-1.4144486025964129615 ,.35529292176139050458] 
dist 142=[-1.4520614793930077070 ,.36477610524524760835] 
dist 143=[-1.4901938115568373675 ,.37351574065267699862] 
dist 144=[-1.5223028965486282503 ,.37863527246767850831] 
dist 145=[-1.5358677093556058429 ,.38208375997882158929] 
dist 146=[-1.5407631841734830701 ,.38415377626380989417] 
dist 147=[-1.5390130653694628863 ,.38517941401763694337] 
dist 148=[-1.5122020713972162406 ,.38459058359843477406] 
dist 149=[-1.5023440095343826783 ,.38276716732113535212] 
dist 150=[-1.4892453549909607062 ,.4470279121059271554 ] 
dist 151=[-1.4826112181485503939 ,.5969110931037878350 ] 
dist 152=[-1.2890825196480369752 ,.7468952054276666006 ] 
dist 153=[-1.2602587022432077521 ,.8561105743553762766 ] 
dist 154=[-1.2007604808960219763 ,.9564844200650561724 ] 
dist 155=[-1.1834147256052665807 ,1.0711746319520184720 ] 
dist 156=[-1.1110518060591177439 ,1.1864391329279559701 ] 
dist 157=[-1.0953299183063279468 ,1.2891087536630082274 ] 
dist 158=[-1.0547897280680423591 ,1.4023358473954430632 ] 
dist 159=[-1.0446278124638326562 ,1.5597538499827856541 ] 
dist 160=[-.15129334489438258776,1.7125361845683369728 ] 
dist 161=[-.15447237930258051015,1.8072567711600677588 ] 
dist 162=[-.16500044745855997004,1.8776934256159234335 ] 
dist 163=[-.17947005332826240275,1.9335235214465949419 ] 
dist 164=[-.19838603975073953894,1.9757680832478420479 ] 
dist 165=[-.22421177555214681269,1.9919655548653660080 ] 
dist 166=[-.26626948891959083408,1.9976412170613227872 ] 
dist 167=[-.30959857556775616923,1.9978755966932701848 ] 
dist 168=[-.34050022758858548448,1.9428691414855809323 ] 
dist 169=[-.36825843744639927422,1.9289154569831122404 ] 
dist 170=[-.3990362736676428497 ,1.8947098938602888660 ] 
dist 171=[-.42944942078893336415,1.8810620621081976551 ] 
dist 172=[-.45575112356042505315,1.8082346079254511531 ] 
dist 173=[-.48411343421142025572,1.7901607450202532574 ] 
dist 174=[-.52275317488850521207,1.7464620145309041777 ] 
dist 175=[-.56124934665246421168,1.7304264511187002684 ] 
dist 176=[-.58903811441909195669,1.5210833209923672674 ] 
dist 177=[-.61433922829416420281,1.5159162442659786737 ] 
dist 178=[-.7468673294390127080 ,1.4930849027680285166 ] 
dist 179=[-.9547779017035439690 ,1.4877936132007965723 ] 
dist 180=[-1.1435823747442350076 ,1.4127296046871752417 ] 
dist 181=[-1.2806244813814084342 ,1.3943227605588198737 ] 
dist 182=[-1.4061506230688522174 ,1.3766054104665911298 ] 
dist 183=[-1.5489752760197010445 ,1.3673041697255920779 ] 
dist 184=[-1.6805224802590001264 ,1.1007029083432700163 ] 
dist 185=[-1.7610235928179113818 ,1.0637378391093708514 ] 
dist 186=[-1.8196315185332948411 ,.9906582450448673010 ] 
dist 187=[-1.8637730663321115465 ,.9709519788892444403 ] 
dist 188=[-1.8958972982567749905 ,.8973375381106420676 ] 
dist 189=[-1.9065261772432046192 ,.8802179970661838492 ] 
dist 190=[-1.9086728856142087667 ,.8483601880517531778 ] 
dist 191=[-1.9069345058400717595 ,.8395231673407403370 ] 
dist 192=[-.83947016238390663529,-.07448179724087035582] 
dist 193=[-.82315792520339009714,-.08694312692266954757] 
dist 194=[-.81945114417708189949,-.08488506435728885129] 
dist 195=[-.77992664659797372553,-.07621417966510050196] 
dist 196=[-.86617946124706045286,-.05419950781797845271] 
dist 197=[-.92519845740776044691,.05729026283459118372] 
dist 198=[-.97564891976773336606,.2454318749082204399 ] 
dist 199=[-1.0276917984740108446 ,.44486084368087023768] 
dist 200=[-1.0738964426391898792 ,.57608750455970471882] 
dist 201=[-1.1010372992714013023 ,.68264540385113314195] 
dist 202=[-1.1194483271763244495 ,.78358235101369507735] 
dist 203=[-1.1307978514187916412 ,.87332700632128868003] 
dist 204=[-1.1367591940957769731 ,.93519854026002842316] 
dist 205=[-1.1373203526242669796 ,.98857535882076810497] 
dist 206=[-1.1233198564332690245 ,1.0444034799098600999 ] 
dist 207=[-1.0723420725256683726 ,1.0942319150502362042 ] 
dist 208=[-.69766279909448675933,1.1236548578418732382 ] 
dist 209=[-.6757360096531057018 ,1.1437974632810804336 ] 
dist 210=[-.66846713240688210759,1.1565751532276670919 ] 
dist 211=[-.63409762905026877923,1.1637107671115411212 ] 
dist 212=[-.62639795519537885136,1.1646095539746973571 ] 
dist 213=[-.60563676968917681898,1.1568236603741650055 ] 

8 phat 4 dirichlet min maxes function [1, 2, 2, 2, 0, 1, 0, 1] 
dist 0=[44.138826081896149087  ,44.138826081896149087  ] 
dist 1=[43.829358103361205398  ,44.311355148867710232  ] 
dist 2=[43.117013002198067851  ,44.476637846696053138  ] 
dist 3=[42.197333583750280506  ,44.638143901031067348  ] 
dist 4=[41.059715361002394918  ,44.795417968172024783  ] 
dist 5=[39.540983532305852164  ,44.937697818177425065  ] 
dist 6=[37.099016407950395578  ,45.039195497159390572  ] 
dist 7=[34.594777349439259973  ,45.129704402240957379  ] 
dist 8=[32.827259655552559684  ,45.227845299376445774  ] 
dist 9=[31.255547340181301038  ,45.307636760448134697  ] 
dist 10=[29.533259792794781445  ,45.324907102432997033  ] 
dist 11=[27.838984195066724635  ,45.298912783471665457  ] 
dist 12=[26.378994052648533897  ,45.245272798570877996  ] 
dist 13=[24.805608291887013313  ,45.077585434830934294  ] 
dist 14=[22.658053533564932486  ,44.788181250041183113  ] 
dist 15=[20.506989453711639608  ,43.069936850748441921  ] 
dist 16=[18.919415368265750948  ,41.716060211791146966  ] 
dist 17=[17.433954801398958455  ,35.267607784293425649  ] 
dist 18=[15.690593649861961495  ,34.411160801617847516  ] 
dist 19=[13.511301687227959142  ,32.285681923421270056  ] 
dist 20=[11.788915352961531325  ,31.976444318105197305  ] 
dist 21=[10.211131414873740452  ,28.669583623111044923  ] 
dist 22=[7.6630019464573672113 ,28.034356962562119619  ] 
dist 23=[4.9903683908365534369 ,27.347855025038180522  ] 
dist 24=[3.2277658567860005023 ,27.211764724766440838  ] 
dist 25=[1.7849189140219218363 ,21.105200546205683012  ] 
dist 26=[.39023182643532250752,20.334087034261836434  ] 
dist 27=[-2.0622404810426170970 ,18.810343698523664911  ] 
dist 28=[-3.7098477529696285072 ,18.422812652037515060  ] 
dist 29=[-5.0159876269364918820 ,17.080427320479868800  ] 
dist 30=[-6.2086306957420536279 ,16.780359439947925359  ] 
dist 31=[-7.2461259591551255936 ,16.415084519284638287  ] 
dist 32=[-7.9323108904362301365 ,16.310410518395308714  ] 
dist 33=[-8.4976976723910840538 ,4.4650744698316834994 ] 
dist 34=[-9.0527529867769352167 ,3.4968951034517689137 ] 
dist 35=[-9.5343405195869805728 ,1.2877461042109621804 ] 
dist 36=[-9.8061005347378662540 ,.94310902941166481617] 
dist 37=[-9.9794758550877008119 ,-1.7915642850667990189 ] 
dist 38=[-10.067498562923709267  ,-1.2396463988662291054 ] 
dist 39=[-10.102037369122595001  ,-.36141094121649790572] 
dist 40=[-10.095025583001130512  ,.25193852205431947833] 
dist 41=[-10.003524340800396137  ,.78703981786745635119] 
dist 42=[-9.9675490870435270559 ,1.3533577528854212840 ] 
dist 43=[-8.8604336585182850344 ,1.8949372420422904142 ] 
dist 44=[-9.3048514315305692085 ,2.3314591213514608240 ] 
dist 45=[-9.6587724494038746604 ,2.7738829098265554525 ] 
dist 46=[-9.8411061155334635618 ,3.3391042306229973194 ] 
dist 47=[-9.9358666889546308292 ,3.8829441631636951108 ] 
dist 48=[-9.9532593555124125783 ,4.2400878953112478162 ] 
dist 49=[-6.9629943029797197164 ,4.5284112837523942116 ] 
dist 50=[-6.8016977818783600287 ,4.7976633819659241551 ] 
dist 51=[-6.3936570159588020187 ,5.0335946974713703657 ] 
dist 52=[-6.3219430091828761852 ,5.1889535954047653888 ] 
dist 53=[-5.6565212037139208254 ,5.3147614749147546182 ] 
dist 54=[-5.5244456056407194359 ,5.4327400336751307578 ] 
dist 55=[-5.3507465620726369221 ,5.5293448115211314026 ] 
dist 56=[-5.2914862157697686942 ,5.5698517601920357759 ] 
dist 57=[-4.0467549008266811351 ,5.5767579444601854156 ] 
dist 58=[-3.8827465351207556470 ,5.5392839150098166586 ] 
dist 59=[-3.5324096988224474457 ,1.6377942291595154986 ] 
dist 60=[-3.4376942636076052795 ,1.9520003458925675366 ] 
dist 61=[-3.0552414262004456374 ,2.2063939066591378094 ] 
dist 62=[-2.9825557883125368617 ,2.4468911772513393814 ] 
dist 63=[-2.8100200506149014553 ,2.6610717375506717877 ] 
dist 64=[-2.7773826618306423021 ,2.8103518704199926325 ] 
dist 65=[-1.0061411287231543862 ,2.9412607594952622003 ] 
dist 66=[-.85054088577654449244,3.0820809196707553064 ] 
dist 67=[-.49445075256728100283,3.2062879556607019202 ] 
dist 68=[-.43339602829695936957,3.2708432731897493576 ] 
dist 69=[.02166689523558997928,3.3056044958127083424 ] 
dist 70=[.10298275735315601224,3.3124075059365354190 ] 
dist 71=[.23279072743742984806,3.2947622296435782504 ] 
dist 72=[.26424225326994124993,3.4148721573789203907 ] 
dist 73=[.78467669827986117041,3.6259466393507610348 ] 
dist 74=[.52655864248304742538,3.7510937936712027269 ] 
dist 75=[-.02925449156255235970,3.8379396255344703090 ] 
dist 76=[-.40788066536736176204,3.8959439476579190909 ] 
dist 77=[-.72967083459718510466,3.9338903370973360749 ] 
dist 78=[-1.0585826926434115418 ,3.9406018542568256580 ] 
dist 79=[-1.3674211089616044386 ,3.9351540682416557053 ] 
dist 80=[-1.6090799449853965330 ,3.9244604970724866005 ] 
dist 81=[-1.8481654319218332460 ,2.2399197828516274155 ] 
dist 82=[-2.1467490338321899184 ,2.2146951433194770922 ] 
dist 83=[-2.4322063156476771643 ,1.6524554923417567758 ] 
dist 84=[-2.6188911742784200784 ,1.5770377377990212882 ] 
dist 85=[-2.7692929145756882324 ,1.4191808506543945301 ] 
dist 86=[-2.9098892650839947758 ,1.3759340483215338966 ] 
dist 87=[-3.0337734264171387538 ,1.2065363229609538345 ] 
dist 88=[-3.1174589027251520464 ,1.1724392004746189800 ] 
dist 89=[-3.1879524186443541067 ,1.0957711612265711860 ] 
dist 90=[-3.2591898075300588344 ,1.0749186082827235728 ] 
dist 91=[-3.3351973926935415289 ,.30951968641229835427] 
dist 92=[-3.4289832538984493042 ,.33353219388560961811] 
dist 93=[-3.4968933096801313899 ,.38024308197277996078] 
dist 94=[-3.5474421695221951533 ,.45646239431001831747] 
dist 95=[-3.5827206076656069676 ,.56880883630766569924] 
dist 96=[-3.5896598478846923889 ,.75971107424117118489] 
dist 97=[-3.5839777635077892149 ,.95821562305988879797] 
dist 98=[-3.5730468430079340342 ,1.1009120750901032042 ] 
dist 99=[-3.6548728971235326242 ,1.2299926054036136377 ] 
dist 100=[-3.7867180888359122594 ,1.3741751465284042745 ] 
dist 101=[-3.8889241594331612370 ,1.5169986544465217080 ] 
dist 102=[-3.9426095333414225196 ,1.6406676752756500324 ] 
dist 103=[-3.9711831916241456202 ,1.7739983410594370868 ] 
dist 104=[-3.9730866850923288717 ,1.9553991532704832894 ] 
dist 105=[-3.7439150900293148967 ,2.1357058160313019519 ] 
dist 106=[-3.7019260115807844174 ,2.2646770151333294197 ] 
dist 107=[-3.6441923898249408610 ,2.3807895817578598064 ] 
dist 108=[-3.6209537336609860825 ,2.5097814115277182496 ] 
dist 109=[-3.5656588425812838394 ,2.6372722798328607834 ] 
dist 110=[-3.5410989787282863812 ,2.7474029575150321952 ] 
dist 111=[-3.5207694202592910431 ,2.8659989238092447019 ] 
dist 112=[-3.5038814836499656318 ,3.0310171781576416334 ] 
dist 113=[-1.7737149951965141611 ,3.1813857885963404136 ] 
dist 114=[-1.7666184187437045962 ,3.2712137057902977041 ] 
dist 115=[-1.5680666020388680516 ,3.3312561697615065633 ] 
dist 116=[-1.5374874182196549136 ,3.3664377950048175786 ] 
dist 117=[-1.4720491838944491513 ,3.3849158163158359891 ] 
dist 118=[-1.4521395012596680650 ,3.3853623510421281681 ] 
dist 119=[-1.3643787442850539765 ,3.3643222853530681530 ] 
dist 120=[-1.3460269109213855823 ,3.3536351695438632029 ] 
dist 121=[-1.2934696299934886078 ,3.1505474028453576402 ] 
dist 122=[-1.2848093759189938261 ,3.1122692627817098111 ] 
dist 123=[.69302063066141795618,3.0145464526240257845 ] 
dist 124=[.61749785106066607865,2.9833677305833654165 ] 
dist 125=[.52233458760400004161,2.8006546139019167823 ] 
dist 126=[.35343468909985969101,2.7583814604775079762 ] 
dist 127=[.13612099077395606133,2.6777417633772611712 ] 
dist 128=[-.49414185058387681764,2.7435647542181461560 ] 
dist 129=[-1.2133950731587515126 ,2.9314629747165755326 ] 
dist 130=[-1.6853603240702750342 ,3.0443695730360887129 ] 
dist 131=[-2.0670199503048449658 ,3.1241682360355389633 ] 
dist 132=[-2.4257450871810525486 ,3.1798721649514628155 ] 
dist 133=[-2.7426751664642773867 ,3.2174376601226420456 ] 
dist 134=[-2.9574744785647693298 ,3.2249741906418891761 ] 
dist 135=[-3.1387913895119124280 ,3.2211774549727025174 ] 
dist 136=[-3.3220450470923953681 ,3.2148086713839606574 ] 
dist 137=[-3.4859220778958534828 ,3.0580854867000661829 ] 
dist 138=[-3.5898814763853336085 ,3.0267719989059222266 ] 
dist 139=[-3.6699372313394439833 ,2.9510285511808155666 ] 
dist 140=[-3.7383878096177382737 ,2.9235128366139973623 ] 
dist 141=[-3.7941943893069832784 ,2.7847776977875961430 ] 
dist 142=[-3.8237730354670734928 ,2.7518757851324157688 ] 
dist 143=[-3.8398169922926640839 ,2.6773705427228279351 ] 
dist 144=[-3.8415895310012587946 ,2.6517873583604789908 ] 
dist 145=[-.8184884070511886622 ,.68078495623138555819] 
dist 146=[-.9599804577791296782 ,.66547852093944190719] 
dist 147=[-1.1017334733033870852 ,.54588033589400059481] 
dist 148=[-1.2273815280156025606 ,.52287711222186759381] 
dist 149=[-1.3654752796904892720 ,.4871568844122761125 ] 
dist 150=[-1.5569215000024341624 ,.4773694010669510712 ] 
dist 151=[-1.7432777557492465818 ,-.53978682927058402266] 
dist 152=[-1.8610494280306063125 ,-.55567823009557445471] 
dist 153=[-1.9512941246313420694 ,-.7886212749927067009 ] 
dist 154=[-2.0277440025921639356 ,-.81755504290483404316] 
dist 155=[-2.0895991335975586821 ,-.86350296229758266861] 
dist 156=[-2.1215719952419397048 ,-.87300405448523886966] 
dist 157=[-2.1378225697652305180 ,-.87162370928899019958] 
dist 158=[-2.1400579125846705195 ,-.85072448755488412288] 
dist 159=[-2.1283501199364837558 ,-.81202516490932395978] 
dist 160=[-2.1210689288673802006 ,-.73887882748000268023] 
dist 161=[-2.0984897112132300829 ,-.65990468977160272815] 
dist 162=[-2.0870154668624774344 ,-.59793724417933782567] 
dist 163=[-2.0184234359136001404 ,-.53650157182195924747] 
dist 164=[-2.0000183825802462582 ,-.45964635519620832985] 
dist 165=[-1.9616229141309852634 ,-.37865943982520821259] 
dist 166=[-1.9480816210824588410 ,-.191492932748691764  ] 
dist 167=[-1.5285952572263973134 ,.21759354666992339998] 
dist 168=[-1.4918427989515324138 ,.49175003617301583253] 
dist 169=[-1.3937896064063870622 ,.71992481699149697222] 
dist 170=[-1.3792983146997743394 ,.94542356747122039546] 
dist 171=[-1.2026660179172486050 ,1.1522971815985506044 ] 
dist 172=[-1.1668240777437611338 ,1.3061088349094750167 ] 
dist 173=[-1.1312395651753290002 ,1.4507128647922562087 ] 
dist 174=[-1.1233700337528692132 ,1.6208240777393696181 ] 
dist 175=[-.72982027085962323587,1.7782725272697028041 ] 
dist 176=[-.67959405568496039878,1.8723187334747946519 ] 
dist 177=[-.58002361181661890071,1.9380497372710975764 ] 
dist 178=[-.55445730311184732026,1.9824455519697423931 ] 
dist 179=[-.46503341683709459243,2.0147272722309196267 ] 
dist 180=[-.44486014541216395997,2.0320912236455933498 ] 
dist 181=[-.41973323016244369727,2.0418740631703608523 ] 
dist 182=[-.41180842686936915424,2.0438878528760715538 ] 
dist 183=[.19181993139003838138,1.7099782611303259406 ] 
dist 184=[.21299699201458905217,1.7618923603905318429 ] 
dist 185=[.24905695698653694878,1.8058148102508605521 ] 
dist 186=[.25666223695387701343,1.8247631899674224532 ] 
dist 187=[.26754906601574091089,1.8327171264145730063 ] 
dist 188=[.26111495358488446731,1.8327417299308820486 ] 
dist 189=[.24463679029894440597,1.7959444943292160710 ] 
dist 190=[.21012076950606528222,1.7840486912859481385 ] 
dist 191=[.17031480222480464761,1.7747664610838062769 ] 
dist 192=[.02804932500040077632,1.7666075048670884708 ] 
dist 193=[-.32534398908014046511,1.6227937957997132678 ] 
dist 194=[-.56350969876526793762,1.6041967411695881349 ] 
dist 195=[-.76317422980721875191,1.5507353001085777657 ] 
dist 196=[-.9628487920450813976 ,1.5398312021362108291 ] 
dist 197=[-1.1475471761819876927 ,1.3971803882338654335 ] 
dist 198=[-1.2874181244167777637 ,1.3074352800248950249 ] 
dist 199=[-1.4214165418652901164 ,1.1186741644345542142 ] 
dist 200=[-1.5826681194540165605 ,1.1048196919739558005 ] 
dist 201=[-1.7337417331741359190 ,.9217207941251198801 ] 
dist 202=[-1.8271037474787698096 ,.93551418638275525352] 
dist 203=[-1.8961811042339959398 ,.94434814612710347572] 
dist 204=[-1.9502963403640962193 ,.94582929940324115847] 
dist 205=[-1.9908370950258625286 ,.94314166387550793016] 
dist 206=[-2.0057176810654229886 ,.94098587042910442497] 
dist 207=[-2.0106467736888515265 ,.89258672373990968306] 
dist 208=[-2.0114555177571640743 ,.88306586855829200575] 
dist 209=[-1.0455879725736392400 ,.8597178680471963358 ] 
dist 210=[-1.0576502427873748433 ,.85123727903686540644] 
dist 211=[-1.0645504842257402487 ,.8084735269362021053 ] 
dist 212=[-1.0649994552333268249 ,.79832570164246066083] 
dist 213=[-1.0605012313236011240 ,.77635731149105252854] 
dist 214=[-1.0566791020452520096 ,.76903056019034279064] 
dist 215=[-.99273587021720023628,.442037837550187158  ] 
dist 216=[-.98146847597809684207,.40886077793009663118] 
dist 217=[-.94858132569416200043,.32865331890772609268] 
dist 218=[-.94224297281728646761,.31641933750211525761] 
dist 219=[-.87121092938645579158,.20046747592102029845] 
dist 220=[-.85546264114822015566,.17908282949153510046] 
dist 221=[-.83793657347676139105,.15215211067193955384] 
dist 222=[-.8300659459461643571 ,.14551090397798408185] 
dist 223=[-.63772814055859565052,-.02620311731162429116] 
dist 224=[-.61150106955748048607,-.04714315711810453026] 
dist 225=[-.55826025976142083063,-.09240002580101609590] 
dist 226=[-.54995930870861904229,-.10171245106302330888] 
dist 227=[-.53478393838181211679,-.14945477713386953824] 
dist 228=[-.52956250290428967061,-.15516273301141389764] 
dist 229=[-.50418675965314967524,-.04883154303754603433] 
dist 230=[-.49835460511933513353,.10646244092564912569] 
dist 231=[-.48324054527063453177,.26099107295480366457] 
dist 232=[-.47860423407168957541,.36426656926656774371] 
dist 233=[-.42555949692263907586,.4499091604896895921 ] 
dist 234=[-.41685156708678986171,.53403591819539247437] 
dist 235=[-.39396877322888262221,.61087996310898807815] 
dist 236=[-.3897472812771516646 ,.66744517059016500831] 
dist 237=[-.3402198147163479456 ,.72006208969782708575] 
dist 238=[-.3117772521555548363 ,.78114167914966063691] 
dist 239=[-.19925408775748122686,.83722867906512617472] 
dist 240=[-.15415683038146095621,.86991187510772945331] 
dist 241=[.29571108238083208749,.89174849771009082642] 
dist 242=[.26243034730063079186,.90452907000804577811] 
dist 243=[.22065412721137946214,.91270140571578928799] 
dist 244=[.17055274567835031129,.91613961721510920062] 
dist 245=[.10469274822343509896,.91677210990101169938] 

8 phat 4 dirichlet min maxes function [0, 0, 2, 2, 0, 0, 1, 0, 1] 
dist 0=[44.941930851025860743  ,44.941930851025860743  ] 
dist 1=[44.438989239207342810  ,45.196263227757842198  ] 
dist 2=[43.655456589334887735  ,45.354289544612861435  ] 
dist 3=[42.280329137943637340  ,45.472440613108458680  ] 
dist 4=[40.828658953352398385  ,45.584430947997460217  ] 
dist 5=[39.739372821343108309  ,45.717535986076690970  ] 
dist 6=[38.703134109848651645  ,45.818189345881768419  ] 
dist 7=[37.463323543517556779  ,45.809854973088603193  ] 
dist 8=[36.182016539147718176  ,45.392805573162052278  ] 
dist 9=[34.979943906822668026  ,44.189231607438876108  ] 
dist 10=[33.601092401551553969  ,43.913398982299175807  ] 
dist 11=[31.613449000891216036  ,43.414295875689278351  ] 
dist 12=[29.575490143612928564  ,43.267543597181844459  ] 
dist 13=[27.995555913557989817  ,42.681766540834105707  ] 
dist 14=[26.006421491541039019  ,42.513675078224776353  ] 
dist 15=[23.540915268762906635  ,42.155353491845361743  ] 
dist 16=[21.384394817493816267  ,41.571580668312665955  ] 
dist 17=[19.077555765703375610  ,30.506738238162100903  ] 
dist 18=[16.842463932003966169  ,29.488570370255462338  ] 
dist 19=[14.793987703226461669  ,27.087847050427919045  ] 
dist 20=[11.409010758568779285  ,26.660269100054418860  ] 
dist 21=[9.1360283217435389833 ,23.043685896022003331  ] 
dist 22=[7.2326548997168909244 ,22.369867651914537102  ] 
dist 23=[5.3245993416823599564 ,21.594753690641152150  ] 
dist 24=[3.5497345239733868509 ,21.442804156187644309  ] 
dist 25=[2.1785613825463733706 ,15.574636754388311097  ] 
dist 26=[.3776411964690726846 ,14.847918338981365311  ] 
dist 27=[-1.3433873820130340966 ,13.378612394009725712  ] 
dist 28=[-3.2544041911623351071 ,13.004074993143441118  ] 
dist 29=[-5.9381796734320934869 ,11.685374477651487300  ] 
dist 30=[-8.5576643757585310873 ,11.410913658937622050  ] 
dist 31=[-10.211961370367841610  ,11.028260542481327000  ] 
dist 32=[-11.485611378130413196  ,10.918185160720861914  ] 
dist 33=[-12.583896824403646248  ,2.0029354582698440514 ] 
dist 34=[-13.494413346143963900  ,1.2669759417917269066 ] 
dist 35=[-14.017844098923375851  ,-.36811287139583860228] 
dist 36=[-14.362892208056133371  ,-.64671905901328457872] 
dist 37=[-14.561033463513754630  ,-.4612191875378785141 ] 
dist 38=[-14.681726712932831002  ,-.12494605566857842765] 
dist 39=[-14.717256882938272362  ,.293646418980421583  ] 
dist 40=[-14.700194556118022127  ,.73077982072743823709] 
dist 41=[-14.664340845189075424  ,1.1412893512529690448 ] 
dist 42=[-14.482390233280517483  ,1.6097038462110725288 ] 
dist 43=[-14.414200686246729163  ,2.2780803897125639914 ] 
dist 44=[-14.160170646043001754  ,2.9540991784712086894 ] 
dist 45=[-14.088702688178392126  ,3.4531173851634386001 ] 
dist 46=[-9.0698191960925734779 ,3.9173307279930235545 ] 
dist 47=[-9.1177551055473775043 ,4.4546095272289898429 ] 
dist 48=[-9.1141749018415975725 ,4.9971337557084401835 ] 
dist 49=[-7.4994705980540947284 ,5.4823531435157657203 ] 
dist 50=[-7.2474965915791617492 ,6.0182351899755257269 ] 
dist 51=[-7.1856825414800696738 ,6.7630029063917912510 ] 
dist 52=[-2.8676328294858680870 ,7.4894207584366356962 ] 
dist 53=[-2.3296725207968349728 ,7.9520918781759998285 ] 
dist 54=[-1.9128957290810566423 ,8.3099919379499715904 ] 
dist 55=[-1.6641161341496058865 ,8.6182909896558103333 ] 
dist 56=[-1.6090549478972692538 ,8.8709645340995620731 ] 
dist 57=[-.7595412618150038952 ,9.0068675981027245974 ] 
dist 58=[-.6464785763814660069 ,9.0831863782376596766 ] 
dist 59=[-.4250005125475779290 ,9.0980525354301625696 ] 
dist 60=[-.3727767082246578925 ,9.0726765757052696699 ] 
dist 61=[-.3216473300184347980 ,8.9883831545572375327 ] 
dist 62=[-.3743366970865372556 ,2.5823934357657444866 ] 
dist 63=[-.46928279096210894653,2.6620994822409173218 ] 
dist 64=[-.64538361327436998472,2.7201044780147397643 ] 
dist 65=[-.82976281445453620965,2.8618493608382458052 ] 
dist 66=[-.95775004756404058075,3.0865731133091598044 ] 
dist 67=[-1.0679543056400048335 ,3.2507126185175499010 ] 
dist 68=[-1.1815316945142667459 ,3.3764250813656224997 ] 
dist 69=[-1.2875761875432057280 ,3.4729649702568766868 ] 
dist 70=[-1.3677799527673300949 ,3.5205261926492526173 ] 
dist 71=[-1.4438219040391212418 ,3.5417139676457802020 ] 
dist 72=[-1.5332745690354312474 ,3.5439338778437544876 ] 
dist 73=[-1.6146727792532831948 ,3.3650254170070921180 ] 
dist 74=[-1.6586058148552872140 ,3.3307578169641450869 ] 
dist 75=[-1.6830806590942495974 ,3.2708757341252606886 ] 
dist 76=[-1.6871289849631332184 ,3.2520098252311049676 ] 
dist 77=[-1.6820196682384362320 ,3.1767867148353155376 ] 
dist 78=[-1.6737765328609943442 ,3.1533903815751109395 ] 
dist 79=[-1.6568329349813056913 ,3.1042710003722414108 ] 
dist 80=[-1.8312802245282583441 ,3.0862656914580384909 ] 
dist 81=[-2.1303032517530427397 ,2.0190830450939163383 ] 
dist 82=[-2.3972482313389510658 ,1.8673101653913545134 ] 
dist 83=[-2.5834859988647958405 ,1.8349406744341969088 ] 
dist 84=[-2.7466524177713733515 ,1.7615654554326245432 ] 
dist 85=[-2.9215039746379431299 ,1.7380456301810171995 ] 
dist 86=[-3.0777870212158000581 ,1.4859605249054609280 ] 
dist 87=[-3.1668108309007864659 ,1.4464795682838713618 ] 
dist 88=[-3.2238567414125205086 ,1.3450433104117564378 ] 
dist 89=[-3.2524261379959443557 ,1.3272952784256236351 ] 
dist 90=[-3.2659392658325578580 ,1.1530566823918510133 ] 
dist 91=[-3.2628623418731053055 ,1.1173519764880759823 ] 
dist 92=[-3.2506599183069979328 ,1.0740896048726402536 ] 
dist 93=[-3.2400639278718664814 ,1.0575236742333431062 ] 
dist 94=[-2.5015948550281197822 ,.68368512553530876838] 
dist 95=[-2.4235723593616656394 ,.63534794355543527293] 
dist 96=[-2.2218408760746307144 ,.52112602821364935111] 
dist 97=[-2.1923105936319643504 ,.49903117447631747259] 
dist 98=[-1.8529858882143732267 ,.3370033930996350421 ] 
dist 99=[-1.7862651291379545009 ,.3060459232702402280 ] 
dist 100=[-1.7396494146186802022 ,.2547743687550955115 ] 
dist 101=[-1.7685092633574756784 ,.2418120208332260394 ] 
dist 102=[-1.7767132679009272640 ,.0034151324332798172 ] 
dist 103=[-1.7773860541718210787 ,-.0277779164386662159 ] 
dist 104=[-1.7761624966511369284 ,-.1150827397228746250 ] 
dist 105=[-1.7028336714151560271 ,.0259918375933963166 ] 
dist 106=[-1.6874357031002336132 ,.2042429097492030431 ] 
dist 107=[-1.6484204648836172954 ,.37596334657966582507] 
dist 108=[-1.6337121702579358749 ,.58386524967951343334] 
dist 109=[-1.5578488403379336593 ,.79936521588706322392] 
dist 110=[-1.5395509627931913124 ,1.0014324061096169068 ] 
dist 111=[-1.5008547488835354750 ,1.2325971824007553524 ] 
dist 112=[-1.4880752130932607772 ,1.5642816908574243367 ] 
dist 113=[.37784133856374244862,1.8906277681805619671 ] 
dist 114=[.49810797482141200732,2.1004842228526659512 ] 
dist 115=[.7590492630947867442 ,2.2654544383508703206 ] 
dist 116=[.80991732857063733904,2.4125957013436541849 ] 
dist 117=[1.0860067952047650640 ,2.5372474822330131710 ] 
dist 118=[1.1158956476582337898 ,2.6124322097318573176 ] 
dist 119=[1.0568463481338927673 ,2.6658956269013082513 ] 
dist 120=[.97569915960036362542,2.7038328288097972385 ] 
dist 121=[.84311701418231105137,2.7299569700515032473 ] 
dist 122=[.687466726433789789  ,2.7362563998725571161 ] 
dist 123=[.51421416883106533729,2.7320727809388699932 ] 
dist 124=[.29468987845898173819,2.7252860348865782955 ] 
dist 125=[-.04570451329648579139,2.6693585505303306623 ] 
dist 126=[-.3878803350312289372 ,2.6518089626322995054 ] 
dist 127=[-.61452058618237637674,2.6085256572444026243 ] 
dist 128=[-.80018464373977772765,2.5907100983501663186 ] 
dist 129=[-.97876946525987900889,1.8613912479830089790 ] 
dist 130=[-1.1393878024161792475 ,1.7905317932734709064 ] 
dist 131=[-1.2533249644757002735 ,1.6103190249445769335 ] 
dist 132=[-1.3550330121508431976 ,1.5836911309606451647 ] 
dist 133=[-1.4668329281829413414 ,1.2905343256790195206 ] 
dist 134=[-1.5685035790746705951 ,1.2336161446999116696 ] 
dist 135=[-1.6297713346428749546 ,1.1716962206366947474 ] 
dist 136=[-1.7946123583075570018 ,1.1584010397120606128 ] 
dist 137=[-2.0049635398137512586 ,.60427032090722624552] 
dist 138=[-2.1337168259328660708 ,.53514715014947235772] 
dist 139=[-2.2274747289402943012 ,.3941966285222465741 ] 
dist 140=[-2.2981143193210937700 ,.35787874488583445225] 
dist 141=[-2.3518077963326738874 ,.22831751406816063292] 
dist 142=[-2.3779117074461951709 ,.20141515087675063683] 
dist 143=[-2.3888239752138309040 ,.16238437018051887535] 
dist 144=[-2.3889565548140843851 ,.1516197475032599518 ] 
dist 145=[-1.1164883087830397393 ,-.3186517804244720843 ] 
dist 146=[-.96328568877974007203,-.1762204032463599853 ] 
dist 147=[-.93644531411086452678,-.0527150217362406432 ] 
dist 148=[-1.0396471453463044046 ,.0807025907502011945 ] 
dist 149=[-1.1309922468463817429 ,.2627111526129415982 ] 
dist 150=[-1.1932648066264598417 ,.4440829053008078235 ] 
dist 151=[-1.2462527530723575386 ,.57496105874303940833] 
dist 152=[-1.3005303020449720263 ,.69405536144780136311] 
dist 153=[-1.3477958296416448278 ,.82838638156689193895] 
dist 154=[-1.3727878160626272650 ,.96242083696078791206] 
dist 155=[-1.3862885927740476955 ,1.0803349587447426388 ] 
dist 156=[-1.3885867269140215979 ,1.2091735528535951831 ] 
dist 157=[-1.3841443594018236681 ,1.3868290911790750614 ] 
dist 158=[-1.3792373122216800889 ,1.5589430003169792050 ] 
dist 159=[-1.3694750859528414529 ,1.6656581601532505421 ] 
dist 160=[-1.3644753992609082918 ,1.7450390395313488589 ] 
dist 161=[-1.0316537309755762112 ,1.8080202183988137154 ] 
dist 162=[-.9958964289081427053 ,1.8566860248922142377 ] 
dist 163=[-.9324381909201900379 ,1.8789112780905528086 ] 
dist 164=[-.9264058760379996679 ,1.8886739484329306959 ] 
dist 165=[-.8857877646233977409 ,1.8877892975515455551 ] 
dist 166=[-.8754557766471299863 ,1.8216147171066554729 ] 
dist 167=[-.8576394700209279794 ,1.8061349934854302613 ] 
dist 168=[-.8520763471315296705 ,1.7773441290533376420 ] 
dist 169=[-.7164420142515662100 ,1.7673789278903671115 ] 
dist 170=[-.6965948740522853202 ,1.7203617919572796649 ] 
dist 171=[-.6524552242360946908 ,1.7075477116934023610 ] 
dist 172=[-.6391313862135698569 ,1.6700795011836962830 ] 
dist 173=[-.5808368770460639093 ,1.6582999558199616459 ] 
dist 174=[-.5687771108331478073 ,1.1594648406287481048 ] 
dist 175=[-.5396039257538726077 ,1.2039177674639702614 ] 
dist 176=[-.5319224336321226624 ,1.2559888282047982895 ] 
dist 177=[-.4840173128722764091 ,1.3027816351046062249 ] 
dist 178=[-.65056052370125019532,1.3261613230699795260 ] 
dist 179=[-.77453386065984217181,1.3383712784958310450 ] 
dist 180=[-.89120950034242659075,1.3405649745220032249 ] 
dist 181=[-1.0286174935007828197 ,1.3256532002552903542 ] 
dist 182=[-1.1567684693188082422 ,1.3207398352837025459 ] 
dist 183=[-1.2364857916416427033 ,1.3168419229181449338 ] 
dist 184=[-1.2960779958592231363 ,1.3133092196567924731 ] 
dist 185=[-1.3438795708974871071 ,1.1179554512602378166 ] 
dist 186=[-1.3809581255070398803 ,1.0898541228636699999 ] 
dist 187=[-1.3977394866880247890 ,1.0381409934211457911 ] 
dist 188=[-1.4052774634192765422 ,1.0244812584038709761 ] 
dist 189=[-1.4054518701902110191 ,.97679391869211783679] 
dist 190=[-.707396506762387918  ,.9634022838279506504 ] 
dist 191=[-.77196289871218616756,.94661154349441675759] 
dist 192=[-.82119367465743961714,.93947600476656469641] 
dist 193=[-.86245660172304300823,.53213022329542905427] 
dist 194=[-.8955012173802304226 ,.5395066499792848487 ] 
dist 195=[-.91191993431123101809,.5477168766414313894 ] 
dist 196=[-.92058341057456631839,.5531068747469721354 ] 
dist 197=[-.92266401888104963091,.5562505492186465325 ] 
dist 198=[-.91021692545109660082,.5562587555471933697 ] 
dist 199=[-.90526799941552650774,.5533762625057799288 ] 
dist 200=[-.89877614799467103172,.5510822927004514337 ] 
dist 201=[-.89510961879179722196,.5322519397832439426 ] 
dist 202=[-.9008857220313730321 ,.5279726238727319661 ] 
dist 203=[-.94294532404914338286,.5133864696486171044 ] 
dist 204=[-.97593135930835359178,.5457883299998034545 ] 
dist 205=[-1.0013549876193851904 ,.7444457702341884728 ] 
dist 206=[-1.0132209127611240611 ,.9414266190557360608 ] 
dist 207=[-1.0183439760140272855 ,1.0692402888391262896 ] 
dist 208=[-1.0181674061750621280 ,1.1710026449335867391 ] 
dist 209=[-1.0204496438469557963 ,1.2639767991765605156 ] 
dist 210=[-1.0429600993548822171 ,1.3443079785137615020 ] 
dist 211=[-1.0563074288955899443 ,1.3955950772782013636 ] 
dist 212=[-1.0655055007537712798 ,1.4354870387998524469 ] 
dist 213=[-1.0714497640194315665 ,1.4703253530921146706 ] 
dist 214=[-1.0743909759789160535 ,1.4982984983692483501 ] 
dist 215=[-1.0731678634058734756 ,1.5107818718566437693 ] 
dist 216=[-1.0665810072651693790 ,1.5145934198171640860 ] 
dist 217=[-1.0618657895867369826 ,1.5137562125320114079 ] 
dist 218=[-1.0304661707707164600 ,1.4946090509338376265 ] 
dist 219=[-1.0214979251396483478 ,1.4871097026720448027 ] 
dist 220=[-1.0038504989346027282 ,1.4674889631008781062 ] 
dist 221=[-.9976126837421271615 ,1.4586624536669382305 ] 
dist 222=[-.8662043102918707486 ,.99977259089416301652] 
dist 223=[-.8463106539430427813 ,.95253718749415951927] 
dist 224=[-.7996035805341636673 ,.83752316958403362733] 
dist 225=[-.7865989097540298004 ,.81791658737279497589] 
dist 226=[-.7165925815501749600 ,.64593266316546435946] 
dist 227=[-.7017891040859690143 ,.61310514859988174532] 
dist 228=[-.6714317167230262062 ,.5678937674786838241 ] 
dist 229=[-.6623982491722529362 ,.55884053997389681019] 
dist 230=[-.5374757730007647236 ,.51471274486730148117] 
dist 231=[-.5192587415505532606 ,.50697595087751912412] 
dist 232=[-.4725213432399926225 ,.48894901026799320859] 
dist 233=[-.4653710640747748540 ,.49242233031990611871] 
dist 234=[-.3874707875453386205 ,.49479524035634665392] 
dist 235=[-.3721117797352656227 ,.49516657496128825353] 
dist 236=[-.4388130389268665970 ,.49413520599901307087] 
dist 237=[-.5817095233280836044 ,.51977929414492202923] 
dist 238=[-.7220879761131055407 ,.69730545036184623402] 
dist 239=[-.8146502966365812416 ,.8125192673207102241 ] 
dist 240=[-.8900141819400423111 ,.9042615006323339616 ] 
dist 241=[-.9617297413630764921 ,.9880822155867982984 ] 
dist 242=[-1.0257075263925807254 ,1.0604882855453939920 ] 
dist 243=[-1.0701793907068097238 ,1.1066596991072397802 ] 
dist 244=[-1.1089312993242993043 ,1.1424968880437899193 ] 
dist 245=[-1.1500733939354094111 ,1.1736450797893909947 ] 
dist 246=[-1.1858228105407260421 ,1.1992103800879672385 ] 
dist 247=[-1.2030451862799412094 ,1.2127590360291341200 ] 
dist 248=[-1.2112952010085300691 ,1.2201080746863039053 ] 
dist 249=[-1.2116527498365937673 ,1.2209233288325027084 ] 
dist 250=[-1.1962425421359676394 ,1.2174704530042356801 ] 
dist 251=[-1.1896093902304997161 ,1.2146014785588108910 ] 
dist 252=[-1.1831333267191796200 ,1.1981271571232102164 ] 

8 phat 4 dirichlet min maxes function [2, 1, 2, 0, 1, 0, 2] 
dist 0=[44.241585088039693632  ,44.241585088039693632  ] 
dist 1=[43.995472763014191701  ,44.445788082835356831  ] 
dist 2=[43.620003393187803432  ,44.653725450874955759  ] 
dist 3=[43.077130094490843926  ,44.903864819752603678  ] 
dist 4=[42.162336923012176657  ,45.276254245385562496  ] 
dist 5=[41.051893704989110153  ,45.631494373555611037  ] 
dist 6=[39.727557934034297649  ,45.813165451295475707  ] 
dist 7=[37.989357171104507011  ,45.901830422423735116  ] 
dist 8=[35.225895553361514286  ,45.886050861388974092  ] 
dist 9=[32.408281943802601302  ,45.803885153487897647  ] 
dist 10=[30.453704684196994873  ,45.747615700198614970  ] 
dist 11=[28.751692568943414555  ,45.457117760011260352  ] 
dist 12=[26.942586261914012664  ,45.397141903781575002  ] 
dist 13=[25.196218400877572074  ,37.327546177268036111  ] 
dist 14=[23.744544976609482204  ,36.555358324236093421  ] 
dist 15=[22.225450726923559132  ,34.627966793256626427  ] 
dist 16=[20.209329758989886814  ,34.331807301605261056  ] 
dist 17=[18.215146257267636837  ,31.268758937639266220  ] 
dist 18=[16.783436271515255670  ,30.669822568541687450  ] 
dist 19=[15.483134343324695511  ,29.995536902367032103  ] 
dist 20=[14.013570244737883641  ,29.818688029459851474  ] 
dist 21=[12.538025018704514390  ,23.938140563153974318  ] 
dist 22=[11.213387225510448336  ,23.178472175330931046  ] 
dist 23=[9.7373447899437312237 ,21.661268589571148832  ] 
dist 24=[7.6559775980975746443 ,21.266968196281113816  ] 
dist 25=[5.6073355716102644807 ,19.849886156914122864  ] 
dist 26=[4.2619431673420919730 ,19.539456699604939102  ] 
dist 27=[3.1648795423438125586 ,19.038878300040953622  ] 
dist 28=[.84288563810174782267,18.905738431958893762  ] 
dist 29=[-1.6551232203543894193 ,6.7918745316082861750 ] 
dist 30=[-3.2688056463884222247 ,5.7707577362029582792 ] 
dist 31=[-4.5531954265584704608 ,3.4312123025052265220 ] 
dist 32=[-5.7350350230443663481 ,3.0606154746018806638 ] 
dist 33=[-6.7695535876743655595 ,.11930006411908147963] 
dist 34=[-7.4652037347013456852 ,-.38991889380185105379] 
dist 35=[-8.0509032700360265090 ,-.66214406490170104644] 
dist 36=[-8.6462383967580365068 ,-.63484630541782427057] 
dist 37=[-9.1721516520983672142 ,-.53837495441828595746] 
dist 38=[-9.4803715918407465083 ,-.35161805545059950159] 
dist 39=[-9.9593210608277911169 ,-.06532022077389653383] 
dist 40=[-10.425827710310108470  ,.42842638719943328938] 
dist 41=[-10.792029694342158201  ,.93761440326263147332] 
dist 42=[-10.965013158943239360  ,1.2856856701648419912 ] 
dist 43=[-11.049964250899261599  ,1.5805788848666266134 ] 
dist 44=[-11.064431515018867948  ,1.8779648802483801638 ] 
dist 45=[-8.1524973916559053364 ,2.1526863334331816066 ] 
dist 46=[-7.9510308079036293968 ,2.3573176035783271067 ] 
dist 47=[-7.4316636843445071168 ,2.5491112013378352780 ] 
dist 48=[-7.3472047432930007409 ,2.7727443771940828598 ] 
dist 49=[-6.4742853267932752464 ,2.9773324217657173346 ] 
dist 50=[-6.3010378117027148243 ,3.0932103928616905350 ] 
dist 51=[-6.0959723212750995037 ,3.1661129536920296257 ] 
dist 52=[-6.0316253160317079277 ,3.1993207505671909443 ] 
dist 53=[-4.3294279593221496234 ,3.2154807438510252581 ] 
dist 54=[-4.1099919723259658773 ,3.2203173237684742150 ] 
dist 55=[-3.6528979694335863595 ,3.3558985977091205221 ] 
dist 56=[-3.5311198681307719025 ,3.8475379086440320694 ] 
dist 57=[-3.0716283042925117575 ,4.3135353070922602495 ] 
dist 58=[-2.9797919679185034989 ,4.6862968429720174202 ] 
dist 59=[-2.7973551016132114505 ,5.0632646236542024101 ] 
dist 60=[-2.7501809135796148788 ,5.5462403129103476664 ] 
dist 61=[.04091258993357687617,6.0038537392112248659 ] 
dist 62=[.28672515993599893122,6.2795735049032918098 ] 
dist 63=[.8073980727861458007 ,6.4760040715445683161 ] 
dist 64=[.91965929989815451928,6.6169037616872024055 ] 
dist 65=[1.3803140774709122086 ,6.7161177729064788203 ] 
dist 66=[1.1903405934526808636 ,6.7460132177227128442 ] 
dist 67=[1.0100808652746763693 ,6.7476594343757042818 ] 
dist 68=[.79579455653189214724,6.7339846832497048734 ] 
dist 69=[.57575406458929063965,6.4137228033577804637 ] 
dist 70=[.37247794106377979138,6.3494350940553250320 ] 
dist 71=[.14222755828419149382,6.2005374441427089595 ] 
dist 72=[-.18556646884270459387,6.1474804156757851353 ] 
dist 73=[-.51040592907553099903,5.8834952686932450595 ] 
dist 74=[-.72887275645314370779,5.8217323871490819694 ] 
dist 75=[-.91167484602814312276,5.6647630809631481570 ] 
dist 76=[-1.0941013024222501066 ,5.6120842848552654945 ] 
dist 77=[-1.2627675441964458517 ,4.0781953808553809736 ] 
dist 78=[-1.5953795939171462039 ,3.9314182192900120963 ] 
dist 79=[-2.2805506005678563812 ,3.5676139658626984911 ] 
dist 80=[-2.9460078935443829814 ,3.5062457315825039313 ] 
dist 81=[-3.5489757819890580310 ,2.9370063717292768750 ] 
dist 82=[-3.9846555284916084586 ,2.8259870076403667386 ] 
dist 83=[-4.3818707266788542760 ,2.6823656712604438531 ] 
dist 84=[-4.8312750582682027513 ,2.6333979363806089575 ] 
dist 85=[-5.2449385158834923050 ,1.6216060694803426935 ] 
dist 86=[-5.4994483259872708086 ,1.4899613040021291665 ] 
dist 87=[-5.6864888169337214552 ,1.2085283919439783843 ] 
dist 88=[-5.8307457738518218481 ,1.1355136813690896826 ] 
dist 89=[-5.9366687899018979398 ,.83144564423318805107] 
dist 90=[-5.9706372258148165225 ,.77470963739580117493] 
dist 91=[-5.9784234755720337369 ,.64325983560828538639] 
dist 92=[-5.9798275421372049341 ,.80601308687998200255] 
dist 93=[-3.8199960209996757354 ,.97425380557812795286] 
dist 94=[-3.9830404697393836488 ,1.3283935600600965644 ] 
dist 95=[-4.0922291535630701325 ,1.6404710205624928976 ] 
dist 96=[-4.1571229099042988031 ,1.9523799610254238737 ] 
dist 97=[-4.1996762951183156804 ,2.2402954878659614486 ] 
dist 98=[-4.2196252331770284097 ,2.4566055976921799718 ] 
dist 99=[-4.2270169543698060834 ,2.6618745190273279419 ] 
dist 100=[-4.2193782998999456306 ,2.9057130031354778699 ] 
dist 101=[-3.6752362581228453085 ,3.1319589019521796591 ] 
dist 102=[-3.5986390363565933310 ,3.2670058626626480804 ] 
dist 103=[-3.4787628168275676016 ,3.3610569363587540127 ] 
dist 104=[-3.4430118481448563142 ,3.4236706156357451277 ] 
dist 105=[-2.7085401765547982031 ,3.4654998760852005655 ] 
dist 106=[-2.6271666458629928530 ,3.4765993053694794586 ] 
dist 107=[-2.0891220726049115455 ,3.4729281632940397214 ] 
dist 108=[-1.9420491697989007800 ,3.4631088919579048566 ] 
dist 109=[-1.1338280112735706481 ,1.8588694814694699630 ] 
dist 110=[-1.2646247393263793609 ,1.8401460139836862264 ] 
dist 111=[-1.3924095058732391567 ,1.8209965165706665051 ] 
dist 112=[-1.5495532657240164294 ,1.8098139509649487259 ] 
dist 113=[-1.6982522533275966893 ,1.5014658176147529962 ] 
dist 114=[-1.7923290312453428867 ,1.4575564058931736062 ] 
dist 115=[-1.8644383640565069267 ,1.3694454324392343203 ] 
dist 116=[-1.9254521299605334275 ,1.3450095187478788034 ] 
dist 117=[-1.9746815102087208093 ,1.2499275148939850177 ] 
dist 118=[-1.9997519794910557860 ,1.2283245612327733300 ] 
dist 119=[-2.0119293166820846048 ,1.1827537474670072862 ] 
dist 120=[-2.0119716462130168571 ,1.1687417636696592295 ] 
dist 121=[.19940386670784908027,.96357540038347621868] 
dist 122=[.02582262360407158963,.99535373503617323238] 
dist 123=[-.12365767737990074805,1.0154117783484454773 ] 
dist 124=[-.27956859472461507058,1.0249032874247209435 ] 
dist 125=[-.42790599352261576374,1.0299359035085458164 ] 
dist 126=[-.5471529898356309379 ,1.0321922293037824732 ] 
dist 127=[-.66808374074007293913,1.0329611866679508958 ] 
dist 128=[-.82314940489581141509,1.0320358137542994363 ] 
dist 129=[-.97331462106398531506,1.0302046879069684624 ] 
dist 130=[-1.0746830656451096313 ,1.0273499175564829648 ] 
dist 131=[-1.1598635271338314619 ,1.0232617326927973327 ] 
dist 132=[-1.2454004598904673478 ,1.0198196808651004927 ] 
dist 133=[-1.3247873520384766156 ,1.0093673009260381190 ] 
dist 134=[-1.3854175944726226392 ,1.0037678954534007939 ] 
dist 135=[-1.4440350168182294176 ,.99825080439202230582] 
dist 136=[-1.5153948216413107305 ,.99418765373995245356] 
dist 137=[-1.5807215098164909422 ,.98438920604209012003] 
dist 138=[-1.6152516165115102158 ,.97940750602681539114] 
dist 139=[-1.6341129677489458964 ,.97034844208879888742] 
dist 140=[-1.6382479593555992816 ,.96666362741279856848] 
dist 141=[-1.6322764796543271668 ,.47905687713942823415] 
dist 142=[-1.6284706317375073075 ,.57403060184129970206] 
dist 143=[-1.6238237204486769375 ,.67585469067729388489] 
dist 144=[-1.6178470310112415295 ,.81379209321538486927] 
dist 145=[-1.6223247718280951828 ,.95081378865313626462] 
dist 146=[-1.7120911709979988637 ,1.0489834094830935923 ] 
dist 147=[-1.7925782619296084567 ,1.1375972730122453628 ] 
dist 148=[-1.8816077516386941944 ,1.2364711269880305641 ] 
dist 149=[-1.9610802940912506336 ,1.3345078738764703488 ] 
dist 150=[-2.0034126461518806884 ,1.4197814331097681078 ] 
dist 151=[-2.0267181621065507711 ,1.5121399739431824430 ] 
dist 152=[-2.0315492293182120530 ,1.6384654587767025180 ] 
dist 153=[-2.0263652473044563422 ,1.7602812176910773114 ] 
dist 154=[-2.0202468505939193695 ,1.8346355251153038072 ] 
dist 155=[-2.0113035222671835325 ,1.8885487593068297643 ] 
dist 156=[-2.0043392384915508711 ,1.9287541005047578765 ] 
dist 157=[-1.7937888391215486801 ,1.9571261915123599182 ] 
dist 158=[-1.7637589043382611130 ,1.9641069416181428466 ] 
dist 159=[-1.6834144961100402023 ,1.9632920803497177113 ] 
dist 160=[-1.6674658898170142072 ,1.9630234574147585043 ] 
dist 161=[-1.5168373519234327633 ,1.8900459293746767843 ] 
dist 162=[-1.4847101090167689552 ,1.8739695667706614438 ] 
dist 163=[-1.4431554327681651758 ,1.8321513454477380006 ] 
dist 164=[-1.4276633379298849512 ,1.8159077313779912400 ] 
dist 165=[-1.0750074422180949271 ,1.8097481216136997607 ] 
dist 166=[-1.0271423474505814532 ,1.9192481059094495085 ] 
dist 167=[-.92587132227717200982,2.0031454956038784064 ] 
dist 168=[-.89767210776232257908,2.0741610259376863787 ] 
dist 169=[-.78464882658160071445,2.1315441498629983361 ] 
dist 170=[-.76220040113281478243,2.1610159370639365429 ] 
dist 171=[-.93184237087979752164,2.1757124267217631414 ] 
dist 172=[-1.1391091477168469358 ,2.1768979527799729934 ] 
dist 173=[-1.3256341741506332083 ,1.5313244176216364822 ] 
dist 174=[-1.4581290738806350204 ,1.5192002148606154609 ] 
dist 175=[-1.5765744224936021438 ,1.5043971678540738534 ] 
dist 176=[-1.7070052583770826864 ,1.4967335077499257918 ] 
dist 177=[-1.8260721034850138537 ,1.2796673371491391643 ] 
dist 178=[-1.8991466637121515923 ,1.2478208762123102057 ] 
dist 179=[-1.9526040395745910157 ,1.1828691990254431757 ] 
dist 180=[-1.9933504785179389743 ,1.1642598228146910320 ] 
dist 181=[-2.0228570087796931579 ,1.0883944757868199542 ] 
dist 182=[-2.0314396907889576649 ,1.0716291491779673626 ] 
dist 183=[-2.0318060949282325517 ,1.0541703638626260374 ] 
dist 184=[-2.0285090407122714379 ,1.1125818877883094949 ] 
dist 185=[-.22098167125483712884,1.1655340222365899725 ] 
dist 186=[-.37443889643923398014,1.2038443980261953204 ] 
dist 187=[-.50287939324008357095,1.2388258241180864663 ] 
dist 188=[-.63099526815118639133,1.2784886744271701573 ] 
dist 189=[-.74929792238157116106,1.3132860599878248110 ] 
dist 190=[-.83855803700523756035,1.3288415633965256444 ] 
dist 191=[-.92375718563196487121,1.3358581206785842379 ] 
dist 192=[-1.0258461328623982955 ,1.3365587664561347327 ] 
dist 193=[-1.1212810749852905539 ,1.3112930501654844225 ] 
dist 194=[-1.1799133518819910518 ,1.3035158702876542813 ] 
dist 195=[-1.2228899602712011533 ,1.2977334056088864222 ] 
dist 196=[-1.2558177067383527035 ,1.2931540831045742390 ] 
dist 197=[-1.2802719036731011867 ,1.0925245488128828197 ] 
dist 198=[-1.2894167608300973333 ,1.0638678981702243015 ] 
dist 199=[-1.2921815951841506169 ,1.0101846507156469073 ] 
dist 200=[-1.2911625838673621638 ,.99591237496948281417] 
dist 201=[-1.2406953623024664988 ,.9450853005785356541 ] 
dist 202=[-1.2548314298772724545 ,.9314864897725450519 ] 
dist 203=[-1.3252712048148280644 ,.91202415993760724113] 
dist 204=[-1.4197944002400880423 ,.90501214925344175076] 
dist 205=[-1.5103208553461010441 ,.21777656935770919744] 
dist 206=[-1.5648034848019866986 ,.31294658256089000779] 
dist 207=[-1.6033848808938716063 ,.41447644455735984689] 
dist 208=[-1.6304240719274569932 ,.55140996458490419612] 
dist 209=[-1.6484139742591919272 ,.68721854176608513525] 
dist 210=[-1.6521068489760645853 ,.78425733045359915623] 
dist 211=[-1.6482716117511830309 ,.8716048653846533279 ] 
dist 212=[-1.6461205459333956156 ,.96872075243707485083] 
dist 213=[-1.5715827490629090703 ,1.0648381686336912552 ] 
dist 214=[-1.5563677068124252033 ,1.1481996936059829338 ] 
dist 215=[-1.5177575175239151979 ,1.2382963656265083919 ] 
dist 216=[-1.5033270207738633558 ,1.3613053586723828197 ] 
dist 217=[-1.4290788364440116022 ,1.4801428333025581956 ] 
dist 218=[-1.4111894779074543197 ,1.5535844028101396127 ] 
dist 219=[-1.3745861358615268144 ,1.6079308961319548274 ] 
dist 220=[-1.3627392722685626900 ,1.6505288443144425427 ] 
dist 221=[-1.1283133136455823764 ,1.6823781146547196126 ] 
dist 222=[-1.1253652613571900675 ,1.6938092464933991805 ] 
dist 223=[-1.1105955022351525740 ,1.6971296479550872430 ] 
dist 224=[-1.1069110954012459141 ,1.6965952729692512597 ] 
dist 225=[-1.0541972213895310517 ,1.6490640348875691099 ] 
dist 226=[-1.0410264319054135111 ,1.6372843813062872408 ] 
dist 227=[-1.0283754512847931984 ,1.6069169036969619100 ] 
dist 228=[-1.0213643722653179799 ,1.5946981311301223849 ] 
dist 229=[-.82638200192799482026,1.5291884000445836035 ] 
dist 230=[-.79915468691788467882,1.5128712697640468185 ] 
dist 231=[-.74545849305378120075,1.4773880047317665136 ] 
dist 232=[-.73094250260592270683,1.4455326446358948155 ] 
dist 233=[-.67659218619019819029,1.4650965589599199167 ] 
dist 234=[-.66386645090256055941,1.4709134865555256792 ] 
dist 235=[-.64002356759279656079,1.4707885586743168832 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 0, 0, 1] 
dist 0=[50.817608070039407952  ,50.817608070039407952  ] 
dist 1=[50.708033322942509942  ,50.830473630774155078  ] 
dist 2=[50.323447375056331262  ,50.828877576914547413  ] 
dist 3=[49.663063168328557361  ,50.816222133482777108  ] 
dist 4=[48.451759236004813990  ,50.785331498473772266  ] 
dist 5=[47.102103363706239049  ,50.754413810766359368  ] 
dist 6=[45.889015442325924477  ,50.741719097960346241  ] 
dist 7=[44.540186123810765926  ,49.945017616188423429  ] 
dist 8=[42.648192661637789121  ,48.295337163574825703  ] 
dist 9=[40.544712326557910585  ,47.004747297664624274  ] 
dist 10=[38.351027072702495912  ,46.472660443307530670  ] 
dist 11=[35.664074064049063678  ,45.571557641778700039  ] 
dist 12=[31.590137844681177405  ,45.329859990749501836  ] 
dist 13=[27.484727466137204924  ,44.628352389268651410  ] 
dist 14=[24.671983413977467426  ,44.413258823025272935  ] 
dist 15=[22.258612034095149674  ,43.380612154329119332  ] 
dist 16=[19.748391138249202751  ,41.475507046069917274  ] 
dist 17=[17.357857376339308731  ,31.416664370567692537  ] 
dist 18=[15.422445595001777398  ,31.078465278840435651  ] 
dist 19=[13.442782553358848901  ,30.739016112830463919  ] 
dist 20=[10.875201598652458222  ,30.638580245685185580  ] 
dist 21=[8.3643126135742422213 ,17.250228587318566942  ] 
dist 22=[6.6109617235630148367 ,16.502309236928050215  ] 
dist 23=[5.0696621732549098440 ,15.329359923004043531  ] 
dist 24=[3.4056675262001299050 ,15.043154546300534429  ] 
dist 25=[1.7807524665883771242 ,10.434103725860796701  ] 
dist 26=[.39526265713525472895,9.8485850444680460491 ] 
dist 27=[-1.0875794606980217995 ,8.6348263232746790313 ] 
dist 28=[-3.1021020113291188311 ,8.3699791020012177522 ] 
dist 29=[-5.0581106419580955653 ,7.3062815369527763102 ] 
dist 30=[-6.3072520446810106736 ,7.1134971382839546432 ] 
dist 31=[-7.2852720899874751902 ,6.6549193365264627909 ] 
dist 32=[-8.1576513731633340366 ,6.2180600536060749080 ] 
dist 33=[-8.9023793267342530652 ,-5.6823995485842955708 ] 
dist 34=[-9.3702978792188562383 ,-5.8760135118485580833 ] 
dist 35=[-9.7289002145356403489 ,-6.2116628402271594461 ] 
dist 36=[-10.037005141765049666  ,-6.2643020035301139961 ] 
dist 37=[-10.285891862585394312  ,-8.4237171960251354078 ] 
dist 38=[-10.468232346209528733  ,-8.5557377485279909139 ] 
dist 39=[-10.775487312100817331  ,-8.1859405876008051075 ] 
dist 40=[-11.004194119472466126  ,-7.5490570831196556109 ] 
dist 41=[-11.174610681816895179  ,-6.7902132142034995564 ] 
dist 42=[-11.248887231355099421  ,-5.9333039535373490127 ] 
dist 43=[-11.269148949617077057  ,-4.8404098031994536279 ] 
dist 44=[-11.255697926204223848  ,-3.1393107282329044735 ] 
dist 45=[-11.142529590457292619  ,-1.4192616366295466745 ] 
dist 46=[-11.099806896980682732  ,-.25062166047277831805] 
dist 47=[-10.914192837734153686  ,.73861254212337116804] 
dist 48=[-10.877680759789481238  ,1.7425615173907783842 ] 
dist 49=[-7.2245135407223535480 ,2.6800522376371032554 ] 
dist 50=[-7.1419147560512664608 ,3.4040267494266573657 ] 
dist 51=[-7.0258273378390685779 ,4.1108951476983567802 ] 
dist 52=[-6.9831000174624391013 ,4.9801396054993588729 ] 
dist 53=[-3.9425858618538247134 ,5.8036397074821317341 ] 
dist 54=[-3.6907206500060417444 ,6.3278975717003547118 ] 
dist 55=[-3.3538102248010892020 ,6.7338605405318740001 ] 
dist 56=[-3.2529548222075792942 ,7.0850916142936455989 ] 
dist 57=[-1.2741161087425722874 ,7.3746486298905263404 ] 
dist 58=[-1.0273519291715945510 ,7.5343834656890439989 ] 
dist 59=[-.48290679301081960298,7.6297284991656989779 ] 
dist 60=[-.37709850721468926727,7.6622049633154295246 ] 
dist 61=[.23951131764366646747,7.6640342755210813394 ] 
dist 62=[.34303403021680590804,7.6442731875534889786 ] 
dist 63=[.55479535462047175584,7.5929792885456315572 ] 
dist 64=[.60135422268600980202,7.4799714226070181793 ] 
dist 65=[2.0560245381050277145 ,4.9803897357440153147 ] 
dist 66=[2.1929247653506472634 ,5.0733556004658600282 ] 
dist 67=[2.4814066230562393591 ,5.1236277843246807697 ] 
dist 68=[2.4702953395132025681 ,5.1343525351175149821 ] 
dist 69=[2.3031777559169144994 ,2.8712505284073279729 ] 
dist 70=[2.1697662843307179384 ,2.9639746207816966038 ] 
dist 71=[2.0356726583763551576 ,3.0293694216948235957 ] 
dist 72=[1.8657501973970557936 ,3.0750890979383056197 ] 
dist 73=[1.6858287139892452165 ,3.1078283206585650024 ] 
dist 74=[1.5117746107808075016 ,3.1213729380308853881 ] 
dist 75=[1.3085836169193625543 ,3.1236632561824828529 ] 
dist 76=[1.0122974674723112333 ,3.1189686040673243507 ] 
dist 77=[.70848929733340546359,3.0908893904509738984 ] 
dist 78=[.4752422462201990766 ,3.0801676905857365528 ] 
dist 79=[.24872605439844286525,3.0322889309012256321 ] 
dist 80=[-.02824598282104974227,3.0236971420907482993 ] 
dist 81=[-.31698732671396637775,1.9027683491014567008 ] 
dist 82=[-.5905226997011341575 ,1.7975007973101406681 ] 
dist 83=[-.90580687232425155337,1.5399993791482361559 ] 
dist 84=[-1.3612832128567315040 ,1.5013859209045630804 ] 
dist 85=[-1.8098329551522401292 ,1.1768455049572376274 ] 
dist 86=[-2.0974696538499693315 ,1.1592297607960817472 ] 
dist 87=[-2.3228718872123778383 ,1.1429190722501199752 ] 
dist 88=[-2.5229184001339556746 ,1.1363683792601848349 ] 
dist 89=[-2.6918748391827934447 ,1.1342984010117932903 ] 
dist 90=[-2.7931400318774264304 ,1.1390339716347538118 ] 
dist 91=[-2.8644841828688515895 ,1.1494995700455055008 ] 
dist 92=[-2.9139838006854473539 ,1.1703033916569557990 ] 
dist 93=[-2.9507298518906708969 ,1.1935988851125443342 ] 
dist 94=[-2.9711453909852832359 ,1.2140194074648953435 ] 
dist 95=[-2.9836489850944155454 ,1.2361261174080995678 ] 
dist 96=[-2.9887740800650726286 ,1.2661774677408945432 ] 
dist 97=[-2.9888531611454844189 ,1.2989295478374883311 ] 
dist 98=[-2.9811925272785405885 ,1.3318272269905141281 ] 
dist 99=[-2.9666854843869999337 ,1.3710811641470426998 ] 
dist 100=[-2.9580364894777885063 ,1.4292113484681177528 ] 
dist 101=[-2.5291663015645748420 ,1.4855441606045055695 ] 
dist 102=[-2.5263911920289152330 ,1.5176295439928576257 ] 
dist 103=[-2.5187490515375233663 ,1.5380710149296209007 ] 
dist 104=[-2.5118216085994534367 ,1.5479368481837053368 ] 
dist 105=[-2.2872561042553406256 ,1.5503855418244781894 ] 
dist 106=[-2.2690268623335763922 ,1.5488834093582784440 ] 
dist 107=[-2.2080283807549880902 ,1.5306334591188000200 ] 
dist 108=[-2.1992505548316247770 ,1.5273909750618896415 ] 
dist 109=[-2.0250647788593684967 ,1.4341608249494561727 ] 
dist 110=[-2.0026649937489421422 ,1.4164931923929288419 ] 
dist 111=[-1.9500178427836948766 ,1.3648462052111342937 ] 
dist 112=[-1.9316323140245691657 ,1.3542449541163337914 ] 
dist 113=[-1.1639039925420990280 ,1.2417235005058462635 ] 
dist 114=[-1.1291561015505021472 ,1.2165592063481083506 ] 
dist 115=[-1.0834468509333995733 ,1.3188690075161475641 ] 
dist 116=[-1.0677840264291637374 ,1.5163508504718488326 ] 
dist 117=[-.97433607182306600733,1.7045647078076253699 ] 
dist 118=[-1.2216974377138580439 ,1.8339001822011919301 ] 
dist 119=[-1.4205047246317526099 ,1.9346257255336117029 ] 
dist 120=[-1.6051798175882206134 ,2.0229086009580805332 ] 
dist 121=[-1.7667411572176556854 ,2.0966522669292237481 ] 
dist 122=[-1.8732778856122841079 ,2.1393285791874667038 ] 
dist 123=[-1.9599482490540457908 ,2.1675344364913567005 ] 
dist 124=[-2.0421983398325651280 ,2.1835097793711547995 ] 
dist 125=[-2.1136088715915470494 ,2.1906863053842746639 ] 
dist 126=[-2.1570082774813242417 ,2.1895339485178937695 ] 
dist 127=[-2.1881910693784664463 ,2.1732588720777577218 ] 
dist 128=[-2.2108393026506824296 ,2.1661551289110501246 ] 
dist 129=[-2.2262437943157682519 ,2.0847792107366285674 ] 
dist 130=[-2.2285118008448099087 ,2.0628790035187613879 ] 
dist 131=[-2.2228374925760200425 ,2.0375440741311519035 ] 
dist 132=[-2.2171658833371264731 ,2.0248853111659067072 ] 
dist 133=[.38766880898284197182,.92368299286018133874] 
dist 134=[.29913040727679199883,.96664484228647390472] 
dist 135=[.22326888702302148067,1.0027913167429203378 ] 
dist 136=[.14475089697842701292,1.0391616624491961860 ] 
dist 137=[.07041930794911228426,1.0704848929820697819 ] 
dist 138=[.01126956978288406233,1.0864788877441530082 ] 
dist 139=[-.04816669048467824934,1.0943265583440688381 ] 
dist 140=[-.12364595944224179978,1.0956331520061353673 ] 
dist 141=[-.19639850144124313547,1.0885884581500655182 ] 
dist 142=[-.24495000345963585065,1.0841901824173512790 ] 
dist 143=[-.28514537522818846956,1.0761075193187167493 ] 
dist 144=[-.32453737882565272111,1.0723638182958093891 ] 
dist 145=[-.36048409979864686167,.82224870814991115266] 
dist 146=[-.38692662848957714582,.79506094593958070221] 
dist 147=[-.4115306508416209493 ,.72610676014921600931] 
dist 148=[-.44014309880173201618,.7151885727531530991 ] 
dist 149=[-.46686632753143255687,.60234742885454125469] 
dist 150=[-.48392781980580659498,.58011638703931387537] 
dist 151=[-.49723178709816593703,.55435602286935336963] 
dist 152=[-.53268212287162963399,.5468624686474703427 ] 
dist 153=[-.63647066562308933488,.32921637478635132832] 
dist 154=[-.7071220565916600575 ,.30130720597542303179] 
dist 155=[-.76713800646218287919,.24369628015961343141] 
dist 156=[-.8284610608679046897 ,.22847865615543983462] 
dist 157=[-.88604673994491371393,.171900126892257499  ] 
dist 158=[-.93114026899909042307,.16039246375745133588] 
dist 159=[-.97579232101349403198,.13875405600678196937] 
dist 160=[-1.0316160855531964686 ,.13344211726599719612] 
dist 161=[-1.0836053467468063546 ,.08582779694768972653] 
dist 162=[-1.1129470012097724842 ,.14917730916159783768] 
dist 163=[-1.1313645030354491781 ,.22446681226568772485] 
dist 164=[-1.1397350149728167990 ,.33586382739152070176] 
dist 165=[-1.1433360208911874427 ,.44708651820843101253] 
dist 166=[-1.1427090993561291151 ,.52168105986392647412] 
dist 167=[-1.1388655775580580412 ,.58382429256698709372] 
dist 168=[-1.1361448608773013620 ,.64533528482166953113] 
dist 169=[-1.0312564402283983860 ,.7018303212780102576 ] 
dist 170=[-1.0143246415972417633 ,.74394799291310004828] 
dist 171=[-.98016043504474174524,.78366012713492034015] 
dist 172=[-.96983960241341437435,.83055281725598486681] 
dist 173=[-.92551756139999961399,.87405253317521377789] 
dist 174=[-.91527766886152705745,.90021873138053642938] 
dist 175=[-.88776006000245155932,.9187411512956524973 ] 
dist 176=[-.88034456847518640548,.93172284933330761378] 
dist 177=[-.57386781885924250549,.94018470361284779994] 
dist 178=[-.55396437993912629618,.94576469035951667037] 
dist 179=[-.50503902471615634838,.94948620919174927531] 
dist 180=[-.49614564868754292477,.94905469290226033434] 
dist 181=[-.42026679667475945097,.9419143315034823687 ] 
dist 182=[-.40534809124158054516,.93863486238833466251] 
dist 183=[-.49656904551750090981,.92509694968783113616] 
dist 184=[-.59837090195158193231,.92119795257361302465] 
dist 185=[-.69254708197427643801,.87762787039122861366] 
dist 186=[-.76385868722488556318,.86675500774767928568] 
dist 187=[-.83216022480674879704,.85451193538621136397] 
dist 188=[-.91431914291587926802,.88163807084873940838] 
dist 189=[-.99125972683827012704,.90380054955576773674] 
dist 190=[-1.0387275127132440274 ,.91567399754192252896] 
dist 191=[-1.0737479898603625420 ,.92230338256294022898] 
dist 192=[-1.1009935922968779012 ,.92352875284937750269] 
dist 193=[-1.1211905459715531365 ,.56556913942494290705] 
dist 194=[-1.1280698397914406246 ,.55487212854766047456] 
dist 195=[-1.1297474847095835387 ,.53100978502842499768] 
dist 196=[-1.1291765661506960570 ,.52349751321184726256] 
dist 197=[.02928131848027401256,.15112165456041876265] 
dist 198=[-.01316090791133805573,.16352373882423537168] 
dist 199=[-.08047540590450465099,.18329968444096920856] 
dist 200=[-.1585553089404899518 ,.2183431185140382282 ] 
dist 201=[-.23421419146834579568,.2568966654406373192 ] 
dist 202=[-.29728393231685468855,.29068638643642102021] 
dist 203=[-.36329282512766536669,.3274994065743629295 ] 
dist 204=[-.45068653192759543907,.37812294012903055136] 
dist 205=[-.53661823589586635966,.433824958651201875  ] 
dist 206=[-.59679001140115356612,.49091332324501350579] 
dist 207=[-.67882439341268513744,.56002115897516070426] 
dist 208=[-.8141592497920150101 ,.66370994576422962462] 
dist 209=[-.94771210263492320002,.76719275417380041925] 
dist 210=[-1.0334204904584358705 ,.83547805580651984423] 
dist 211=[-1.1006039761138837117 ,.89113283903321285157] 
dist 212=[-1.1601944896798137339 ,.94418878225042414012] 
dist 213=[-1.2104343605556359556 ,.99158251447182027339] 
dist 214=[-1.2402847400839552965 ,1.0246309583877213950 ] 
dist 215=[-1.2609549008184106859 ,1.0535354924661813788 ] 
dist 216=[-1.2745424445672932653 ,1.0843843002166949344 ] 
dist 217=[-1.2829536875741823398 ,1.1112704262521119748 ] 
dist 218=[-1.2832204155933834314 ,1.1243539407052245549 ] 
dist 219=[-1.2792947182579050299 ,1.1298672303000213610 ] 
dist 220=[-1.2748224983382579555 ,1.1302777779797008811 ] 
dist 221=[-1.2422812381499511408 ,1.1195706495525197326 ] 
dist 222=[-1.2325807019908235113 ,1.1144913882001077928 ] 
dist 223=[-1.2134540580517496619 ,1.1026558780173757366 ] 
dist 224=[-1.2065140976250402140 ,1.0972272816860555835 ] 
dist 225=[-.84281909701322828134,.98622620802938257346] 
dist 226=[-.83351355834208356662,.96905064975559863662] 
dist 227=[-.82471808771971516241,.91861157248200078876] 
dist 228=[-.81932057443108215829,.85348073933284033004] 
dist 229=[-.5370998432025463997 ,-.17406539121512010718] 
dist 230=[-.50937393265325686179,-.06508254245333988523] 
dist 231=[-.47297515035425306877,.02874302476399172104] 
dist 232=[-.46106729399049765107,.12657667126149578906] 
dist 233=[-.22394171099138909555,.21964548762737981427] 
dist 234=[-.19365396026982764984,.29444706869149046605] 
dist 235=[-.12785372605660284379,.37028785084386171735] 
dist 236=[-.11282445029361237574,.46750546746268713385] 
dist 237=[-.03968123278167364674,.56161368629647645205] 
dist 238=[-.02692441443235458201,.62503991833070728425] 
dist 239=[.00280495794692723321,.67821379035499913434] 
dist 240=[.00727346699067849502,.73138884419618746424] 
dist 241=[.26726922729648852494,.78057145269684684213] 
dist 242=[.29209439303501200332,.81780510296325567227] 
dist 243=[.35333397731415067282,.85346135645673675713] 
dist 244=[.4141352559906166755 ,.89634568933794855752] 
dist 245=[.73660106331358577991,.93581735493654021499] 
dist 246=[.74081600046367730182,.95784831346467931563] 
dist 247=[.73116239310534701129,.97134534911309765961] 
dist 248=[.70004408131907125979,.97674519246567625894] 
dist 249=[.66096581096301252321,.97816197533648657136] 
dist 250=[.61953163354622552826,.97633034997729727019] 
dist 251=[.56838200487960803874,.97117807659573737363] 
dist 252=[.4905141283745335805 ,.9584664282714927917 ] 
dist 253=[.40130579996347289432,.74136037570132326945] 
dist 254=[.30487881049142481214,.7142057710454182046 ] 
dist 255=[.18456752194224349873,.63096341454613712315] 

8 phat 4 dirichlet min maxes function [2, 2, 2, 0, 0, 0, 2, 1, 2] 
dist 0=[51.317781279252095130  ,51.317781279252095130  ] 
dist 1=[51.225466058241602617  ,51.356795274954580237  ] 
dist 2=[50.895201672799087388  ,51.363699001818861437  ] 
dist 3=[50.293970132995448933  ,51.308562441887100529  ] 
dist 4=[49.191695414719674628  ,51.197899405861525873  ] 
dist 5=[48.000807400017781701  ,51.121379121994564620  ] 
dist 6=[47.045605356416284038  ,50.781354825854477477  ] 
dist 7=[46.075561810459879078  ,50.021266684874611271  ] 
dist 8=[44.825713300551143154  ,47.123652940326608619  ] 
dist 9=[43.485363800957463005  ,46.869487687649164621  ] 
dist 10=[42.153944709304405181  ,45.801455653642999382  ] 
dist 11=[40.098618042095339830  ,45.550891505984226522  ] 
dist 12=[37.544117195895777886  ,44.909817602561029512  ] 
dist 13=[34.917024485696015239  ,44.709162942239699676  ] 
dist 14=[31.518350196667101034  ,43.564279162923872582  ] 
dist 15=[26.921263375489147311  ,42.492137633492036793  ] 
dist 16=[22.097746970962260250  ,33.650501442445225846  ] 
dist 17=[18.833876525118439293  ,32.229804810797487371  ] 
dist 18=[16.078425703162184534  ,31.882570247641707024  ] 
dist 19=[13.285336217126301860  ,31.445460597531046385  ] 
dist 20=[10.671468722005309119  ,31.280126810911088036  ] 
dist 21=[8.6315870068447541425 ,21.048367802168879313  ] 
dist 22=[6.6143666096706401425 ,15.183015926229859001  ] 
dist 23=[4.0904855960248469518 ,14.463857287224381542  ] 
dist 24=[1.6652107420541268155 ,12.923129246454474492  ] 
dist 25=[.04157753578114461072,12.589901679079905726  ] 
dist 26=[-1.3130796192136243318 ,10.981466966493649700  ] 
dist 27=[-2.6642732180367082954 ,10.706020814153434597  ] 
dist 28=[-3.9196230785128719788 ,10.112259091909075808  ] 
dist 29=[-4.8919468291759065077 ,10.006022547671712747  ] 
dist 30=[-5.8509150983821665120 ,5.2332468312753521853 ] 
dist 31=[-7.0541044733064220012 ,4.2618793352885550878 ] 
dist 32=[-8.1924246956538233592 ,-3.0159758255322744104 ] 
dist 33=[-8.8923318200326027359 ,-4.1101818404944666603 ] 
dist 34=[-9.4130615655194867640 ,-4.2822556228438799674 ] 
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dist 39=[-10.424912782223668097  ,-4.3639159051359707101 ] 
dist 40=[-10.354780547089492592  ,-4.0802893405554745053 ] 
dist 41=[-10.322893636817996780  ,-3.7386903328892424957 ] 
dist 42=[-10.167729145391869481  ,-3.3523670845412955158 ] 
dist 43=[-10.139066654634790426  ,-2.8607935540341478966 ] 
dist 44=[-9.6238969921963647004 ,-2.0987768072143140056 ] 
dist 45=[-9.5010384215617494351 ,-1.3015018608101499204 ] 
dist 46=[-9.3986436583108361132 ,-.6689732090401974815 ] 
dist 47=[-9.3600964397383324722 ,.3835078431156651528 ] 
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dist 49=[-7.1296868068962760932 ,3.7921677002036078900 ] 
dist 50=[-6.6069481299163160959 ,4.8898759623195877444 ] 
dist 51=[-6.2321567816424453702 ,5.9282443048467234310 ] 
dist 52=[-5.0378163554978033794 ,6.8505333793346102458 ] 
dist 53=[-2.3292920125339030279 ,7.4849188421401528627 ] 
dist 54=[-2.0838990718529931620 ,8.0309697940763757712 ] 
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dist 56=[-1.4337356532164736935 ,9.1109751970719241562 ] 
dist 57=[-.87090886609441957938,9.4191897902860373937 ] 
dist 58=[-.77083341688945745507,9.6391840916861866920 ] 
dist 59=[-.54436387980932679254,9.7969628832259661162 ] 
dist 60=[-.50440901144429537914,9.9027798697386365742 ] 
dist 61=[-.23227219749883930966,9.9200146553889864243 ] 
dist 62=[-.18175206415163849763,9.8936191265866524852 ] 
dist 63=[-.17761433968904280505,9.7812901596689990922 ] 
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dist 65=[-.32687316633346930665,6.5810467612495544183 ] 
dist 66=[-.46069180903056442549,6.5971131537183986142 ] 
dist 67=[-.65053531471302715276,6.5882837842313893929 ] 
dist 68=[-.9660805964635571639 ,6.5699154345607544027 ] 
dist 69=[-1.2880334880477478905 ,4.0755404064696580792 ] 
dist 70=[-1.5034822025728605791 ,3.7927946653724449298 ] 
dist 71=[-1.6820026946451395823 ,3.7045939124396600833 ] 
dist 72=[-1.8566261753605566277 ,2.2016089877290773808 ] 
dist 73=[-2.0152891087780889148 ,1.7826125620777644054 ] 
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dist 75=[-2.2349032250806065520 ,1.2088831202310927221 ] 
dist 76=[-2.3533385809972473074 ,1.0079494913733347850 ] 
dist 77=[-2.4603521032344581905 ,.55820523700448334204] 
dist 78=[-2.5195470094828791550 ,.36435237777268853511] 
dist 79=[-2.7214555204107188177 ,.31674404761475563913] 
dist 80=[-3.4586806831150576251 ,-.20587193639234612956] 
dist 81=[-3.9403243642845203404 ,-.35916059257736063904] 
dist 82=[-4.3281560461315095275 ,-.01815262753298801744] 
dist 83=[-4.6907439696509590765 ,.40146554379253428571] 
dist 84=[-5.0105223656345443572 ,1.0380830511752270452 ] 
dist 85=[-5.2274048759961674001 ,1.6740570052796651121 ] 
dist 86=[-5.4111136881338397474 ,2.0910978939727920403 ] 
dist 87=[-5.5984443185133240133 ,2.4275826233348243846 ] 
dist 88=[-5.7576152831352767843 ,2.7420253760976244344 ] 
dist 89=[-5.8288726020484286779 ,3.0181103329950594653 ] 
dist 90=[-5.8614978628365959006 ,3.2014843477689529485 ] 
dist 91=[-5.8663151432837646492 ,3.3519408172021461416 ] 
dist 92=[-5.7521883386786096147 ,3.4966102778679979914 ] 
dist 93=[-5.7188775160312841884 ,3.6220871523294979518 ] 
dist 94=[-5.6955600748948309355 ,3.6959438491849539213 ] 
dist 95=[-5.6798474489425374999 ,3.7459917166010833742 ] 
dist 96=[-4.3226556169135574821 ,3.7764829304444877616 ] 
dist 97=[-4.1687360501670981628 ,3.7919742902523117503 ] 
dist 98=[-4.1296439029998018968 ,3.8321404624689175780 ] 
dist 99=[-4.0353360715756821570 ,4.2533938638586347165 ] 
dist 100=[-4.0004145459289905679 ,4.6311690922786407666 ] 
dist 101=[-1.2349717846947798470 ,4.8970485322599703811 ] 
dist 102=[-1.2111308666882110489 ,5.1321729990341862784 ] 
dist 103=[-1.1490703499160098555 ,5.3872035069496700629 ] 
dist 104=[-1.1376210345849217470 ,5.6120428808792609343 ] 
dist 105=[-1.0287369436451029932 ,5.7266546047190410524 ] 
dist 106=[-1.0062906553140621898 ,5.7866020847996493125 ] 
dist 107=[-.97750203322482485492,5.7960239415085555738 ] 
dist 108=[-.96701142615543087141,5.7448977801930471483 ] 
dist 109=[-.73555983306368035333,5.7213438715021592951 ] 
dist 110=[-.70457532565260949963,5.7113412691202609774 ] 
dist 111=[-.63906702351244279803,5.7091689462041432029 ] 
dist 112=[-1.1329216124364051215 ,5.5479754799246260481 ] 
dist 113=[-1.8922619063321612222 ,5.5108650269089641392 ] 
dist 114=[-2.5250411466818489554 ,5.3807107493917760126 ] 
dist 115=[-3.1509971653145915108 ,5.3238820313164858167 ] 
dist 116=[-3.7250297415848178127 ,4.9776560112558607264 ] 
dist 117=[-4.1505374012378811305 ,3.8026268833867037652 ] 
dist 118=[-4.5489433360613599500 ,3.6446425031390730382 ] 
dist 119=[-5.0147826375517538376 ,3.6002301669785862955 ] 
dist 120=[-5.4436536046679028718 ,2.6798252174706177940 ] 
dist 121=[-5.6944849277632445798 ,2.5544262981437887300 ] 
dist 122=[-5.8630042155891192960 ,2.2645324287664259261 ] 
dist 123=[-5.9632976840969677022 ,2.2017125298616035854 ] 
dist 124=[-6.0296035668125047584 ,1.8102921348769868343 ] 
dist 125=[-6.0624578472151785267 ,1.7357371124332870910 ] 
dist 126=[-6.0770857327475054359 ,1.5939676199235520136 ] 
dist 127=[-6.0706596622849706572 ,1.5578521351068099636 ] 
dist 128=[.21583046445759306718,.95501126872016030047] 
dist 129=[-.05520849483628755329,.96115101660267143673] 
dist 130=[-.28074291244907264523,.96279058057754433953] 
dist 131=[-.50349636507462403796,.96146257134467093151] 
dist 132=[-.70772579702574230027,.95955700305054175955] 
dist 133=[-.85931039102137750274,.31604905726217167423] 
dist 134=[-1.0015576231733786276 ,.27563533829394326682] 
dist 135=[-1.1685180889208381396 ,.1883669228844524161 ] 
dist 136=[-1.3240359194578338738 ,.16835604182079528784] 
dist 137=[-1.4205997856253544625 ,.07387651428065109322] 
dist 138=[-1.4926083254080201294 ,.05732368589987569699] 
dist 139=[-1.5500826142902934512 ,.02008523379569937223] 
dist 140=[-1.5945316913240238102 ,.01374207628710426241] 
dist 141=[-1.6145373234802155956 ,-.02882621016266897759] 
dist 142=[-1.6233853965351663800 ,-.03513660892170864706] 
dist 143=[-1.6232805724819308092 ,-.03289289022185744941] 
dist 144=[-1.3869700617767396752 ,-.01842696057773152823] 
dist 145=[-1.3603583786652258656 ,.00421419815290480891] 
dist 146=[-1.3011847140539180816 ,.06532343425642849337] 
dist 147=[-1.2825821571596500847 ,.14178416517956739595] 
dist 148=[-1.1983274855905889509 ,.25923050399697367631] 
dist 149=[-1.1803113052445661871 ,.3772918654232974232 ] 
dist 150=[-1.1338151159121169974 ,.4562078284135070345 ] 
dist 151=[-1.1222447582499185307 ,.52159310960055010463] 
dist 152=[-.99015607593084103757,.58564405568588411942] 
dist 153=[-.97396392262543325586,.64396320979430114554] 
dist 154=[-.9823518482932287404 ,.68646845770484930364] 
dist 155=[-.98681607745573948453,.72554430414646920309] 
dist 156=[-.98711806186372810237,.77017304493595215155] 
dist 157=[-.89822092398372338413,.83117715521644747933] 
dist 158=[-.88409154041506609539,1.0220507699295750969 ] 
dist 159=[-.86186959389053899457,1.2960082879275045366 ] 
dist 160=[-.85481236145026078116,1.5659603580878733661 ] 
dist 161=[-.83543067499428582044,1.7408445441097916937 ] 
dist 162=[-.8281528656585152157 ,1.8797957893055453326 ] 
dist 163=[-.82303358756343611135,2.0062860626348013708 ] 
dist 164=[-.81952546029716916227,2.1152799276864855944 ] 
dist 165=[-.36633487529900594631,2.1843780262556194176 ] 
dist 166=[-.33915185256699696527,2.2375812759746584553 ] 
dist 167=[-.27631834316532926695,2.2831182597612008659 ] 
dist 168=[-.26441527659788524862,2.3183176213375589311 ] 
dist 169=[-.18162943804796573103,2.3302473366593617257 ] 
dist 170=[-.16649169307080910579,2.3316691379085769127 ] 
dist 171=[-.13973455811656706733,2.3263733000536147585 ] 
dist 172=[-.13374558681314600792,2.2753797653285016876 ] 
dist 173=[-.03727698633884393336,2.2584742619820844527 ] 
dist 174=[-.02426981091243764876,2.2319221632572240204 ] 
dist 175=[.00300225307046236825,2.2211441526014311311 ] 
dist 176=[-.13853583866268677348,1.7311501317394449224 ] 
dist 177=[-.43013440193096761184,1.6793382354751180094 ] 
dist 178=[-.67484003000950604228,1.5464932176716551836 ] 
dist 179=[-.9199075597318717766 ,1.5251239751234934043 ] 
dist 180=[-1.1467763805891333104 ,1.3026310247861238184 ] 
dist 181=[-1.3188255037708569962 ,1.4277861349553709612 ] 
dist 182=[-1.4838620414443514737 ,1.5035105619918957739 ] 
dist 183=[-1.6827339445760257008 ,1.5573520494405864977 ] 
dist 184=[-1.8691472601023947691 ,1.5955117826329052372 ] 
dist 185=[-1.9844439699002531500 ,1.6234481787772618039 ] 
dist 186=[-2.0698494010042242542 ,1.6364714459576495926 ] 
dist 187=[-2.1369241798868600378 ,1.6410827277390119458 ] 
dist 188=[-2.1880696096000498073 ,1.6399756350405981068 ] 
dist 189=[-2.2098780461097269149 ,1.5235974827861953169 ] 
dist 190=[-2.2185721240360483808 ,1.5033289036868373690 ] 
dist 191=[-2.2173599032221062669 ,1.4674923247308230119 ] 
dist 192=[-1.3313601772905738981 ,1.4570322245240419367 ] 
dist 193=[-1.3775331370835369119 ,1.4162240704801538133 ] 
dist 194=[-1.4129058354109884552 ,1.4038244147967671592 ] 
dist 195=[-1.4471846650312015026 ,1.3791998243867703971 ] 
dist 196=[-1.4889914228655910688 ,1.3705615235058170461 ] 
dist 197=[-1.5270992852595853533 ,.50437573029088169953] 
dist 198=[-1.5466106293373701482 ,.42896235739299674916] 
dist 199=[-1.5562594240638656877 ,.25771554518509900254] 
dist 200=[-1.5566926704474921558 ,.22593391036829683083] 
dist 201=[-1.5484964186421165680 ,.01359068919447548409] 
dist 202=[-1.5432516134747579086 ,-.02373393077595222958] 
dist 203=[-1.5253498354068234660 ,-.09198330365642304246] 
dist 204=[-1.5161798209799056566 ,-.10714537436960386378] 
dist 205=[-1.3954787251116462598 ,-.23024436905672844557] 
dist 206=[-1.3745360589794336154 ,-.21878352797607346057] 
dist 207=[-1.3217737575317780948 ,-.19881804612134756663] 
dist 208=[-1.3072049521756709317 ,-.01582893289931145648] 
dist 209=[-1.2140560061707435306 ,.11605469711379269989] 
dist 210=[-1.1934071112949947033 ,.23012936214683437296] 
dist 211=[-1.1558010246923849323 ,.34991325187273664285] 
dist 212=[-1.1802593793040893208 ,.46437266900345668293] 
dist 213=[-1.2653704025600246738 ,.61004829721253152119] 
dist 214=[-1.3169905808528950778 ,.8224351651601198956 ] 
dist 215=[-1.3540252923992863418 ,.99374229029586831011] 
dist 216=[-1.3809032047933278173 ,1.1540583641376203464 ] 
dist 217=[-1.3995862114504367241 ,1.2952600106091387031 ] 
dist 218=[-1.4039023153389665667 ,1.3902527307616480867 ] 
dist 219=[-1.4031603994322259983 ,1.4696973607464712373 ] 
dist 220=[-1.4016489252086768702 ,1.5488229206673878522 ] 
dist 221=[-1.3411659333824142430 ,1.6191989585965644540 ] 
dist 222=[-1.3285283745670012084 ,1.6637112535349332964 ] 
dist 223=[-1.2974578708839723161 ,1.6978513436722490664 ] 
dist 224=[-1.2858717060588954574 ,1.7268170827600799836 ] 
dist 225=[-1.2264655025016565246 ,1.7502777353637158758 ] 
dist 226=[-1.2121759758688531318 ,1.7624392047016790334 ] 
dist 227=[-1.1803313145478833506 ,1.7686659293576633698 ] 
dist 228=[-1.1694039370227231776 ,1.7684326820801998320 ] 
dist 229=[-.18793527622700783634,1.4547744547523664292 ] 
dist 230=[-.14130699424718426025,1.4489071008076363296 ] 
dist 231=[-.03690736946070913081,1.4442965282603759902 ] 
dist 232=[-.01708788678001928443,1.2835296691856046220 ] 
dist 233=[.10692967480792275526,1.2586222011895773773 ] 
dist 234=[.12828564705852902275,1.2092482031146382619 ] 
dist 235=[.16940409567496135936,1.1948593716099294603 ] 
dist 236=[.17890778694273872441,1.1357959352576171680 ] 
dist 237=[.26871190522884711483,1.1217866170379403989 ] 
dist 238=[.1783301495610553844 ,1.0880547030560751579 ] 
dist 239=[.03098028963000442862,1.0762362750198124684 ] 
dist 240=[-.12214743908696074232,.7337739107465577821 ] 
dist 241=[-.29297663911140410938,.7182692064937735632 ] 
dist 242=[-.43409892252329684697,.68065545226303437044] 
dist 243=[-.57182715978153140223,.66841910970762149292] 
dist 244=[-.69703945721380911828,.60897447343324613095] 
dist 245=[-.78819040215479635628,.29353008927571616987] 
dist 246=[-.87196186683721230256,.27491119757710145995] 
dist 247=[-.9677102835662179462 ,.26886559598695376705] 
dist 248=[-1.0561515576003813779 ,.14730478769452290746] 
dist 249=[-1.1107487391329636801 ,.13161421228718570672] 
dist 250=[-1.1510750081107029481 ,.09750746692675213896] 
dist 251=[-1.1825394430871370074 ,.08945810781376538961] 
dist 252=[-1.2059451017095322470 ,.05107700467903993521] 
dist 253=[-1.2140959053248061944 ,.04425793007951903359] 
dist 254=[-1.2165360753968709557 ,.02821102797321478724] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 1, 1, 0, 2, 0, 2] 
dist 0=[53.773650666483500719  ,53.773650666483500719  ] 
dist 1=[53.463622399275948215  ,53.853938802208900482  ] 
dist 2=[52.865825463683267669  ,53.864391943931653121  ] 
dist 3=[51.717473564510566262  ,53.824589500448185394  ] 
dist 4=[50.419439760786685247  ,53.741707321571576703  ] 
dist 5=[49.223831857697811223  ,53.580097080406462998  ] 
dist 6=[47.871524338012658806  ,53.522525585948783686  ] 
dist 7=[45.947416691122824561  ,53.371261236453115785  ] 
dist 8=[43.796709011810905249  ,52.021867710989791678  ] 
dist 9=[41.539214496950321924  ,48.802738491316704758  ] 
dist 10=[38.764677772158701819  ,48.212745829616248271  ] 
dist 11=[34.548679071809139741  ,47.220662688442309666  ] 
dist 12=[30.300120504235182093  ,46.849496998103294800  ] 
dist 13=[27.395433977281961975  ,46.020371304280892555  ] 
dist 14=[24.910557996507799294  ,42.824077669373478687  ] 
dist 15=[22.338630818750905881  ,42.222570183807415161  ] 
dist 16=[19.897853891094174837  ,42.065390821886314491  ] 
dist 17=[17.629704770015501916  ,35.024151459617153141  ] 
dist 18=[15.003794404574448690  ,34.100412836104682944  ] 
dist 19=[12.940362157077395426  ,32.307227593546828629  ] 
dist 20=[10.878794510757399304  ,31.844974240583086317  ] 
dist 21=[8.3005528028220354351 ,30.231015024072455041  ] 
dist 22=[5.8077549532478182177 ,29.846280151570818707  ] 
dist 23=[4.1279214669304552133 ,29.350591558170389049  ] 
dist 24=[2.7147869183179002005 ,29.171563235083059855  ] 
dist 25=[1.2869291081101692866 ,11.489581869102705150  ] 
dist 26=[-.05077034772738200716,10.026247515498233098  ] 
dist 27=[-1.1042932049307198536 ,7.3128454330772125291 ] 
dist 28=[-2.1591408208944427836 ,6.1352229166225040043 ] 
dist 29=[-3.5033101027314987249 ,5.2244514193038566360 ] 
dist 30=[-4.7852196458842421766 ,1.1477351672347869824 ] 
dist 31=[-5.5914494597556509993 ,.05913710032227985647] 
dist 32=[-6.8039277636809597838 ,-.2150797838145501682 ] 
dist 33=[-8.6407067962069913856 ,-4.4999830301951407112 ] 
dist 34=[-9.7844826343229211403 ,-5.0275345360519566529 ] 
dist 35=[-10.643313767032116055  ,-5.9064364401346256299 ] 
dist 36=[-11.342022603646261263  ,-6.3157436871043077924 ] 
dist 37=[-11.898063720390497588  ,-5.9305607743655398899 ] 
dist 38=[-12.186962366177592378  ,-5.4192684714240135931 ] 
dist 39=[-12.336490143931770867  ,-4.9312139130796881491 ] 
dist 40=[-12.366027619020415742  ,-4.3688376361605736184 ] 
dist 41=[-9.2898440557633812743 ,-3.5602623298797141411 ] 
dist 42=[-9.1009429206686039750 ,-2.6566762309000127341 ] 
dist 43=[-8.6012231950431836074 ,-1.7147575600408196625 ] 
dist 44=[-8.5123162256157860275 ,-.56462928648798490567] 
dist 45=[-7.6251428508859086710 ,1.1703108839003283014 ] 
dist 46=[-7.4442131798634261180 ,2.9018516242328062800 ] 
dist 47=[-7.2176630403494990436 ,4.0385318922386774234 ] 
dist 48=[-7.1338072687296502670 ,4.9575514462757843446 ] 
dist 49=[-6.0313131810274241422 ,5.8203758525824665464 ] 
dist 50=[-5.7984361799211854023 ,6.5816923171824097312 ] 
dist 51=[-5.7333921430895351837 ,7.0955954892743956209 ] 
dist 52=[-5.4014092128914924002 ,7.5272057338065407686 ] 
dist 53=[-4.7258102102577481917 ,7.9601364645595144509 ] 
dist 54=[-3.7538191796109413001 ,8.3427541743500292678 ] 
dist 55=[-3.5115606325430154076 ,8.5734933092540613082 ] 
dist 56=[-3.4572715396286186947 ,8.7374888267575630525 ] 
dist 57=[-.431624480775316741  ,8.8534772618631720220 ] 
dist 58=[-.15436259911642215356,8.9294884813163182021 ] 
dist 59=[.42776618357276673825,8.9358188732174560141 ] 
dist 60=[.56085816739483732849,8.9081715065042719346 ] 
dist 61=[1.1185622793037748924 ,8.8719482166142755946 ] 
dist 62=[1.2193911357409189632 ,5.4788251662905038316 ] 
dist 63=[1.3964259407520989701 ,5.2414745541558020545 ] 
dist 64=[1.4312719231260763523 ,5.6144766759878250261 ] 
dist 65=[1.4860495811113126683 ,5.9501926263093758055 ] 
dist 66=[1.4458521786181090415 ,6.1392223098458714782 ] 
dist 67=[1.3501732070089549889 ,6.2576810180406338705 ] 
dist 68=[1.1544026697350106488 ,6.3115495194047470331 ] 
dist 69=[.90968075286442689721,6.3373594200542982237 ] 
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dist 72=[-.36505026092728615359,6.3201231163370194883 ] 
dist 73=[-.97505225883937118129,2.9092730306641588043 ] 
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dist 76=[-2.0648389836463360223 ,1.4811600837093171578 ] 
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dist 78=[-2.9018038222857684252 ,1.0713253267357313851 ] 
dist 79=[-3.2363927556086460299 ,1.0240876589970467780 ] 
dist 80=[-3.5103228958415750088 ,.63376837983263469125] 
dist 81=[-3.7741267051767655755 ,.56318659229161937897] 
dist 82=[-4.0121211959252127572 ,.46012483565745945509] 
dist 83=[-4.1829812948702855113 ,.43205825357463004398] 
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dist 86=[-4.6701514670468086477 ,-.25862017305080856871] 
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dist 89=[-4.8409082185254835282 ,1.1232920390782340092 ] 
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dist 91=[-4.8417744965404219357 ,2.0048626903637454928 ] 
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dist 95=[-4.3002680732987928727 ,3.2496706316047625011 ] 
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dist 98=[-3.6572295119133741321 ,4.6060034351844061720 ] 
dist 99=[-3.4937373890552067050 ,4.9131634682674255073 ] 
dist 100=[-3.4468353895216845337 ,5.1905798375882394411 ] 
dist 101=[-3.2575366580147258112 ,5.5003533106192326200 ] 
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dist 107=[-.64783732531378244936,6.0205449756107665239 ] 
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dist 110=[-.64167948939614572708,5.5005293897031650286 ] 
dist 111=[-1.3819857875313684934 ,5.4259090135469637607 ] 
dist 112=[-2.0055126291013433778 ,5.2035302225394450295 ] 
dist 113=[-2.6332302768641872481 ,5.1698689814992842603 ] 
dist 114=[-3.2160614704525699964 ,4.6881386551515011807 ] 
dist 115=[-3.6604058156070752653 ,4.5839982746071120640 ] 
dist 116=[-4.0886839440200898866 ,4.4913589106741531821 ] 
dist 117=[-4.6073782855074539647 ,4.4263724208381837031 ] 
dist 118=[-5.0944604312109905201 ,3.0945321380049272105 ] 
dist 119=[-5.3965442137552413301 ,2.9184518500963837081 ] 
dist 120=[-5.6211277855994881588 ,2.3158499780132052176 ] 
dist 121=[-5.7988342692632642240 ,2.2270258523135496564 ] 
dist 122=[-5.9328909180004118968 ,1.8777866467134448698 ] 
dist 123=[-5.9832249580287221033 ,1.8082626239966778620 ] 
dist 124=[-6.0005376287276522281 ,1.6504195192280426989 ] 
dist 125=[-6.0027879042136198606 ,1.6101496070877839650 ] 
dist 126=[.18519161407744603984,.81691559469078256231] 
dist 127=[.19046805673779531394,.81117629588220422252] 
dist 128=[.20622909324757149726,.80807833911112886052] 
dist 129=[.20873131273092181566,.79640542131313103002] 
dist 130=[.20748556306932282142,.79134686033008746267] 
dist 131=[.1385700006968952882 ,.78705050977086261456] 
dist 132=[.01633692721196861691,.78351383992842308994] 
dist 133=[-.11400439016847569323,.77872561733955963392] 
dist 134=[-.24167323931134971598,.77577889535993431714] 
dist 135=[-.39198185909808681525,.77304241552708936905] 
dist 136=[-.61271835116603729581,.77006803850497313747] 
dist 137=[-.83194242315017716389,.44851352102248564076] 
dist 138=[-.97621584602903434749,.4327198541678337322 ] 
dist 139=[-1.0933845260569714702 ,.42855500652644778662] 
dist 140=[-1.2043963404380839998 ,.36207976070297330034] 
dist 141=[-1.3031208745023530914 ,.36306816323948714091] 
dist 142=[-1.3712354227909313656 ,.36254103727272705751] 
dist 143=[-1.4300670950865227198 ,.36242132294427523993] 
dist 144=[-1.4917347577810870247 ,.3501174099857423443 ] 
dist 145=[-1.5451867394912712145 ,.34697740823386772331] 
dist 146=[-1.5712174298052470210 ,.34512691569519160246] 
dist 147=[-1.5844300692265863283 ,.3445362382112435726 ] 
dist 148=[-1.5867006927183093072 ,.28114898819451425844] 
dist 149=[-1.5643587416820825882 ,.2724314477842736238 ] 
dist 150=[-1.5573401255947983033 ,.25655670976213722278] 
dist 151=[-1.5520236281567071874 ,.25250870840344328735] 
dist 152=[-1.5476523991168460438 ,.23916317973168626252] 
dist 153=[-1.2754057485840486218 ,.23531443882960285021] 
dist 154=[-1.2423496257415266094 ,.2753320345922108005 ] 
dist 155=[-1.1578142648111762943 ,.43629776831727512713] 
dist 156=[-1.1426536225487908497 ,.59947876259568515987] 
dist 157=[-.99997771200597468826,.75177749506671037972] 
dist 158=[-.97108881427995634088,.86929940676802714389] 
dist 159=[-.93379887958459685485,.98396734055809394856] 
dist 160=[-.92054338373533036514,1.1248730789790012945 ] 
dist 161=[-.63430450680546079741,1.2583021780921350457 ] 
dist 162=[-.59641712156622257461,1.3431218708401907083 ] 
dist 163=[-.5155456192938014605 ,1.4089109175964517897 ] 
dist 164=[-.49329245160696126347,1.4656844709061090780 ] 
dist 165=[-.40500461916631114783,1.5122217779954285834 ] 
dist 166=[-.38803079382536266265,1.5373867654291241174 ] 
dist 167=[-.40809295236944750309,1.5517352325949220152 ] 
dist 168=[-.43852879044853019442,1.5550897481415219287 ] 
dist 169=[-.4644699431061897042 ,.16546091021769903736] 
dist 170=[-.49210707582023544896,.24915069116455611998] 
dist 171=[-.52931060686950567198,.3180407017491784042 ] 
dist 172=[-.56467305570570924707,.38487043221644181941] 
dist 173=[-.58495921748078688556,.44536765139242525564] 
dist 174=[-.59809284486416485631,.48897566580330266644] 
dist 175=[-.60490097152634094233,.53586472010233332526] 
dist 176=[-.60887359440326096845,.59146594770793015951] 
dist 177=[-.6106884379284455275 ,.64316133815248218244] 
dist 178=[-.61126527421296310439,.67446997987013651344] 
dist 179=[-.61029881460414204068,.69689245391380157067] 
dist 180=[-.54186265495069711174,.71310894735470182833] 
dist 181=[-.5313932520635254299 ,.72482533462058448983] 
dist 182=[-.51314089868030913897,.72927829076590545906] 
dist 183=[-.50820032644494379497,.73021215798049988814] 
dist 184=[-.49151797122533152458,.72899017756727774316] 
dist 185=[-.48619220289254663464,.68879195201849752156] 
dist 186=[-.48014386468672020431,.6818948722724225756 ] 
dist 187=[-.47706722165517951465,.6616096305481720498 ] 
dist 188=[-.10850345436846889723,.6573262308182655288 ] 
dist 189=[-.14444438890829261753,.66515531607529682832] 
dist 190=[-.1991987168984234884 ,.67562450976770042643] 
dist 191=[-.25720354113904613054,.68206190089164104326] 
dist 192=[-.33490846048112832803,.68542092355842724624] 
dist 193=[-.41173021471366306766,.68566364375481272913] 
dist 194=[-.46620924896860354587,.68069169936222082133] 
dist 195=[-.5148225912533353426 ,.67971989486765603764] 
dist 196=[-.5682256879087549514 ,.64935573022892643377] 
dist 197=[-.6207031470208282437 ,.64326658642698402847] 
dist 198=[-.6656211768545124395 ,.62544925929258047426] 
dist 199=[-.7136641190293137460 ,.6212723924027873301 ] 
dist 200=[-.7786185527358089675 ,.58160897541662495178] 
dist 201=[-.8410257481021530393 ,.57253006744451417428] 
dist 202=[-.8788987030062815780 ,.56078337857225651675] 
dist 203=[-.9060997204270315002 ,.55613339123336150714] 
dist 204=[-.9258980370797970167 ,.37938870897044633524] 
dist 205=[-.9400479950749019668 ,.35891920358016278964] 
dist 206=[-.9446971459624158892 ,.31341804878463497799] 
dist 207=[-.94527847619275035537,.3022597048903259024 ] 
dist 208=[-.94318734759066448345,.24616026482139310707] 
dist 209=[-.89810269954142103912,.2355581972436984765 ] 
dist 210=[-.88893928247007131074,.21207701437239635416] 
dist 211=[-.86887504609437018555,.20582009546871980936] 
dist 212=[-.86185693870723571066,.1494458708750605339 ] 
dist 213=[-.82735244865703441479,.14012713173499367014] 
dist 214=[-.8193372632612530283 ,.12294938511085083942] 
dist 215=[-.79611792058413541411,.11879998970053633956] 
dist 216=[-.79061583956594959047,.10627803550691736873] 
dist 217=[-.64337754430580516503,.10344090931008060986] 
dist 218=[-.63859312546784930864,.20354691725518757885] 
dist 219=[-.62257774308305551293,.30018427120091204419] 
dist 220=[-.61978935149974293964,.39461266959950955724] 
dist 221=[-.57907756907465032457,.4805435406901849996 ] 
dist 222=[-.56977230050264620825,.5432526566084902276 ] 
dist 223=[-.5613811071126504291 ,.60104344847836704569] 
dist 224=[-.55829309933712143696,.66733626433225010526] 
dist 225=[-.43246866233238783078,.7286191375831798476 ] 
dist 226=[-.41556606578840441784,.7664069335279952588 ] 
dist 227=[-.38258506936059252104,.7942668288362853144 ] 
dist 228=[-.373924557194994153  ,.8159118374631767817 ] 
dist 229=[-.34291743076707625521,.8320564347629262738 ] 
dist 230=[-.33551918830784974904,.8379550127804939490 ] 
dist 231=[-.32448160780285437212,.8398135638149988802 ] 

8 phat 4 dirichlet min maxes function [1, 0, 2, 0, 1, 0, 0, 2] 
dist 0=[45.215278469998708055  ,45.215278469998708055  ] 
dist 1=[44.862251764521828699  ,45.633230469747976920  ] 
dist 2=[44.490221172316355054  ,46.264101097887144665  ] 
dist 3=[43.898121241922507800  ,46.868507526323256028  ] 
dist 4=[42.666108216235393438  ,47.180789568525374225  ] 
dist 5=[41.183142179137081520  ,47.338556427270230856  ] 
dist 6=[39.588782685708532389  ,47.355553356138794898  ] 
dist 7=[37.603485892501191685  ,47.240342544035746439  ] 
dist 8=[34.558950743948236912  ,47.160677613762088405  ] 
dist 9=[31.481911049385264797  ,46.946125653593565817  ] 
dist 10=[29.366653130119771351  ,46.837296075903699978  ] 
dist 11=[27.545104076737076481  ,44.894088726486764131  ] 
dist 12=[25.640890503075461254  ,44.537361033596618395  ] 
dist 13=[23.822067168619562432  ,43.310644713684327053  ] 
dist 14=[22.341318348021585355  ,41.341653347661055742  ] 
dist 15=[20.819233217744712817  ,34.939122715332108604  ] 
dist 16=[18.834819071168863183  ,34.351440241278755707  ] 
dist 17=[16.888190479074057298  ,33.761474505373356530  ] 
dist 18=[15.516778879930232521  ,33.634673715021082974  ] 
dist 19=[14.297720379930620291  ,27.309393716141879585  ] 
dist 20=[12.959361472206868089  ,26.493170764192234728  ] 
dist 21=[11.637358367193477341  ,24.909803740604364273  ] 
dist 22=[10.483165989121638190  ,24.506244346517926990  ] 
dist 23=[9.2229070737268173471 ,23.119689044420135174  ] 
dist 24=[7.4761322229567275799 ,22.790678524996568716  ] 
dist 25=[5.7610179961250715994 ,22.417052721583899412  ] 
dist 26=[4.6271649026490718061 ,22.298780473448848420  ] 
dist 27=[3.6931785225674663277 ,13.134232872252395673  ] 
dist 28=[2.7773350796675207113 ,12.755748960978666718  ] 
dist 29=[1.8436367364430935036 ,11.512373154161330959  ] 
dist 30=[-.32454064747236952071,10.848202451029481591  ] 
dist 31=[-2.4406105821006060767 ,1.8121965553997389889 ] 
dist 32=[-3.7930128588922397840 ,1.7257032983913451601 ] 
dist 33=[-4.8539902085691195151 ,1.1597821285532204819 ] 
dist 34=[-6.2536890625134641228 ,1.0647854704429357329 ] 
dist 35=[-7.7508350953489439271 ,1.0493857875579574260 ] 
dist 36=[-8.6859229921060527721 ,1.1436647340833282191 ] 
dist 37=[-9.3915700870771132532 ,1.2961227319397264969 ] 
dist 38=[-9.9721550309964304595 ,1.5154740267329319402 ] 
dist 39=[-10.437796170818033475  ,1.8236284866500180640 ] 
dist 40=[-10.684269845071066980  ,2.3305087504164210363 ] 
dist 41=[-10.818358304220162641  ,2.8454494286208119786 ] 
dist 42=[-10.845685213990800686  ,3.1859071671410237758 ] 
dist 43=[-8.7041291131004729578 ,3.4620503510180092318 ] 
dist 44=[-8.7093692471803697706 ,3.7207043883863855670 ] 
dist 45=[-8.6855723712347109669 ,3.9468790867332862138 ] 
dist 46=[-8.6617252508836101731 ,4.0935671157760041231 ] 
dist 47=[-7.5508167540811270812 ,4.2094390005323666118 ] 
dist 48=[-7.4749274317242197628 ,4.3127457339224354467 ] 
dist 49=[-7.3214843346156742230 ,4.3948615473081515042 ] 
dist 50=[-7.2740706105659291849 ,4.4261861337249750944 ] 
dist 51=[-5.2069528665468462717 ,4.4327994406289589216 ] 
dist 52=[-4.9763235298720704590 ,4.4238943085200012940 ] 
dist 53=[-4.6052814112946487150 ,4.3255253727720161142 ] 
dist 54=[-4.3893420675448540663 ,4.2908953006552679590 ] 
dist 55=[-3.7933934396626853369 ,4.2300174737874252969 ] 
dist 56=[-3.7042733542069650638 ,4.2071828406143452762 ] 
dist 57=[-3.5838723371370157314 ,2.8683278787033716799 ] 
dist 58=[-3.5449531774915919203 ,2.7224313699956796789 ] 
dist 59=[-.02529653424048387738,3.0041775548057361019 ] 
dist 60=[.20503701271215664131,3.2814838945942944036 ] 
dist 61=[.34380260562119399799,3.5540990405925711046 ] 
dist 62=[.3725055708190806978 ,3.8931194695653915206 ] 
dist 63=[.97763817677410480621,4.2112765569231763110 ] 
dist 64=[.52021651380197767772,4.4006008402340429402 ] 
dist 65=[.06078479482875377152,4.5328377774579969438 ] 
dist 66=[-.27609285090538333218,4.6229202928080343672 ] 
dist 67=[-.58798160585052866672,4.6851699146829338797 ] 
dist 68=[-.94771761573930376388,4.7061806543131409573 ] 
dist 69=[-1.3112195711079324636 ,4.7067525459187600624 ] 
dist 70=[-1.6381920598657793224 ,4.6975077583055828631 ] 
dist 71=[-2.0015504955120472488 ,4.6062629943143165023 ] 
dist 72=[-2.5103935471650571060 ,4.6467641048664354307 ] 
dist 73=[-3.0070316821307704967 ,4.6625232798908073819 ] 
dist 74=[-3.3216737466752115487 ,4.6640019960009644607 ] 
dist 75=[-3.5638307500338116621 ,4.0457825019986282102 ] 
dist 76=[-3.7710370124989576915 ,4.0084192726520326542 ] 
dist 77=[-3.9404197603196339901 ,3.8902741765181613851 ] 
dist 78=[-4.0315517696589291586 ,3.8726573547899439622 ] 
dist 79=[-4.0830417898414877285 ,2.4692100457565303605 ] 
dist 80=[-4.0941462683079916282 ,2.3483935998895515860 ] 
dist 81=[-4.0896559717973761366 ,2.0507268744742973646 ] 
dist 82=[-4.0788780954744933648 ,2.0066584837308249247 ] 
dist 83=[-4.0615131605700954161 ,1.5625746841134825623 ] 
dist 84=[-4.0481695370111816950 ,1.7643738183612908222 ] 
dist 85=[-3.9937136816524900278 ,1.9798072864821533004 ] 
dist 86=[-3.9734793544329274894 ,2.1908950950191632582 ] 
dist 87=[-3.9121499689414396670 ,2.4393103535409622531 ] 
dist 88=[-3.8858759180696862158 ,2.8037515961195229153 ] 
dist 89=[-3.5011072180650041056 ,3.1628325874542653018 ] 
dist 90=[-3.6061239086531889842 ,3.3898523493714324798 ] 
dist 91=[-3.6859631852037476457 ,3.5636910541896928828 ] 
dist 92=[-3.7220889155468562109 ,3.7104843949418527504 ] 
dist 93=[-3.7362767365667273370 ,3.8286885342413965222 ] 
dist 94=[-3.7344633087741975702 ,3.8884016860412494065 ] 
dist 95=[-2.6879310700220638114 ,3.9167043587271413795 ] 
dist 96=[-2.7011276502707450385 ,3.9209181400093092583 ] 
dist 97=[-2.7075787154468087795 ,3.8872619504267940652 ] 
dist 98=[-2.7066745160495847405 ,3.8707793298603362895 ] 
dist 99=[-2.4037118179207110006 ,3.8231282575530360938 ] 
dist 100=[-2.3582235832371280953 ,3.7999104609249318437 ] 
dist 101=[-2.2796855896013656650 ,3.6634455864826822862 ] 
dist 102=[-2.2582415056968327266 ,3.6272333502571502749 ] 
dist 103=[-2.1893899260486529991 ,3.5478568543620099582 ] 
dist 104=[-2.1666797252817265411 ,3.5192284324125814254 ] 
dist 105=[-2.1479951366344289285 ,3.4609773419645482876 ] 
dist 106=[-2.1373072610665292635 ,3.5206810812903259176 ] 
dist 107=[-1.6565994210606182418 ,3.5504683198006765216 ] 
dist 108=[-2.0767749076271191478 ,3.5556075298027963979 ] 
dist 109=[-2.4559284544739180618 ,3.5307671199857579257 ] 
dist 110=[-2.7266970791269899358 ,3.5149751796309740897 ] 
dist 111=[-2.9701080287823524198 ,3.4900183173631385327 ] 
dist 112=[-3.2400341552835480837 ,3.4772169150180069621 ] 
dist 113=[-3.4871119011564263620 ,3.0724271668622947844 ] 
dist 114=[-3.6393128490632986524 ,3.0101246473361945808 ] 
dist 115=[-3.7512424688940168890 ,2.8795266433345752492 ] 
dist 116=[-3.8375748716292167221 ,2.8403104958103662036 ] 
dist 117=[-3.9009282566627085269 ,2.6707361246682147655 ] 
dist 118=[-3.9211386046825713856 ,2.6344942705574414870 ] 
dist 119=[-3.9236494674277914524 ,2.5326076809786615644 ] 
dist 120=[-3.9163251990655973300 ,2.5134758195296286688 ] 
dist 121=[-.17038764914443390635,2.3369592042487660683 ] 
dist 122=[-.1572443217730943956 ,2.5158661832031730287 ] 
dist 123=[-.39402036495392268746,2.6844559333634087340 ] 
dist 124=[-.57602711411631355592,2.7800652527591403671 ] 
dist 125=[-.73746804171203894693,2.8407445995033028777 ] 
dist 126=[-.91321488517173863058,2.8698545279227322570 ] 
dist 127=[-1.0848730991679013190 ,2.8858846484341880295 ] 
dist 128=[-1.2299962279639256144 ,2.8943288782678720518 ] 
dist 129=[-1.3836025680237559229 ,2.8988836949858284410 ] 
dist 130=[-1.5891321730536334915 ,2.8993657634876053759 ] 
dist 131=[-1.7920976673404312773 ,2.5456527221456400883 ] 
dist 132=[-1.9354705383240174781 ,2.4938118926606851174 ] 
dist 133=[-2.0627825373572263496 ,2.4059838261556317566 ] 
dist 134=[-2.2016339315085312232 ,2.3818537633788863868 ] 
dist 135=[-2.3374500485997213143 ,2.3092903724280484222 ] 
dist 136=[-2.4526482427956886784 ,2.2849848817617886439 ] 
dist 137=[-2.5749377588730696202 ,2.2702515674532700398 ] 
dist 138=[-2.7390705084748949711 ,2.2647144097822543812 ] 
dist 139=[-2.8957109211899943417 ,1.5241596061227590323 ] 
dist 140=[-2.9880894572917906798 ,1.5090690270534109019 ] 
dist 141=[-3.0511910484573690215 ,1.4807578263524429915 ] 
dist 142=[-3.0909451913402137632 ,1.4715854004624944604 ] 
dist 143=[-3.1148238543628614798 ,1.1559851545861875680 ] 
dist 144=[-3.1174294998465790958 ,1.1267612170709084970 ] 
dist 145=[-3.1057406931340004783 ,1.0512160101932574503 ] 
dist 146=[-3.0956028841053569845 ,1.0386503694037664872 ] 
dist 147=[-2.9147220076050043208 ,.90891223997963623952] 
dist 148=[-2.8803381427027115269 ,.88265307577115228943] 
dist 149=[-2.7971760962810221626 ,.8520254626880041712 ] 
dist 150=[-2.7676346683810680967 ,.84163474845862601736] 
dist 151=[-2.6208663849153045498 ,.57097377847533771544] 
dist 152=[-2.5864835728384312483 ,.53548872628003857311] 
dist 153=[-2.5110400627668330084 ,.46242735766090875839] 
dist 154=[-2.4858833453303070071 ,.4429034478337877301 ] 
dist 155=[-2.4438792605536800658 ,.79979727079354653859] 
dist 156=[-2.4907887514617722288 ,1.2135627027947604040 ] 
dist 157=[-2.5169173713344271169 ,1.5506352800005772324 ] 
dist 158=[-2.5216076106648487269 ,1.8717144210602393858 ] 
dist 159=[-2.5172366852551975202 ,2.1583692876725716980 ] 
dist 160=[-2.5093045473484194990 ,2.3580025848721688718 ] 
dist 161=[-2.4925852854814433876 ,2.5323430776555773793 ] 
dist 162=[-2.4836035505690395423 ,2.7180141907308942674 ] 
dist 163=[-2.2395932479573614731 ,2.8864871094571306904 ] 
dist 164=[-2.2004557600060935800 ,2.9921645362733789938 ] 
dist 165=[-2.1161285448258321492 ,3.0721877675234842597 ] 
dist 166=[-2.0898058498014848400 ,3.1382407110254802163 ] 
dist 167=[-1.9712134517640065685 ,3.1903369820261530164 ] 
dist 168=[-1.9458804193338083523 ,3.2146407057628110662 ] 
dist 169=[-1.8734744118148795217 ,3.2232637030657300387 ] 
dist 170=[-1.8602409665378145830 ,3.2205516340787557787 ] 
dist 171=[-1.1007089294635262444 ,.1550721261469042315 ] 
dist 172=[-1.1467444168162110640 ,.30751838393191544433] 
dist 173=[-1.1941861704817422650 ,.43331316570921381449] 
dist 174=[-1.2560160695362326610 ,.55585868942821650692] 
dist 175=[-1.3139397288112389472 ,.66713238775562673459] 
dist 176=[-1.3457850408214445612 ,.74792405527429273186] 
dist 177=[-1.3646477459022582688 ,.82197203239630427338] 
dist 178=[-1.3707393055892998863 ,.90632269893301610205] 
dist 179=[-1.3715475980222401364 ,.98395629742313727846] 
dist 180=[-1.3693182940502506340 ,1.0311854207922384886 ] 
dist 181=[-1.3644267781740107764 ,1.0652537593623170458 ] 
dist 182=[-1.3603703322592621661 ,1.1177901613536015145 ] 
dist 183=[-1.2142191667329933490 ,1.2148461615283975824 ] 
dist 184=[-1.1913686827681853558 ,1.2788556728568447751 ] 
dist 185=[-1.1463961485456470767 ,1.3310052242631135143 ] 
dist 186=[-1.1332720369497916233 ,1.3807074903435304647 ] 
dist 187=[-1.0794578530675125064 ,1.4251160069234931013 ] 
dist 188=[-1.0664999264780298408 ,1.4561290150928464908 ] 
dist 189=[-1.0355102516784834265 ,1.4833127296091540046 ] 
dist 190=[-1.0246145829022986003 ,1.5124319378069519011 ] 
dist 191=[-.34140584733308040432,1.5371211221703575442 ] 
dist 192=[-.28007085870418771469,1.5466169914328218065 ] 
dist 193=[-.14080186690738137567,1.5486839724686450234 ] 
dist 194=[-.11532142122461713101,1.5462311119442856137 ] 
dist 195=[-.20567142097047308216,1.5184502076029613262 ] 
dist 196=[-.29998767619404600484,1.5088002507766763672 ] 
dist 197=[-.38858018718113325818,1.4906841078427931291 ] 
dist 198=[-.49268198608718985119,1.4837438213092707478 ] 
dist 199=[-.59895395114639043301,1.3081032361511464852 ] 
dist 200=[-.69621190003222300224,1.2810845444138327254 ] 
dist 201=[-.80562806517090769123,1.2217631892450198081 ] 
dist 202=[-.96044424899646325199,1.2034724318528868155 ] 
dist 203=[-1.1124049815551002785 ,1.1219221402777755295 ] 
dist 204=[-1.2104207128225757374 ,1.1046858713191145037 ] 
dist 205=[-1.2878185705056365306 ,1.0595208420517360360 ] 
dist 206=[-1.3574597721831103541 ,1.0491744683503613507 ] 
dist 207=[-1.4168939602925843357 ,.43264129620159978262] 
dist 208=[-1.4535391517215389039 ,.42407566040607367866] 
dist 209=[-1.4805575598834113921 ,.42725808087758914294] 
dist 210=[-1.5015560384376580317 ,.42771844663264713529] 
dist 211=[-1.5163029396758489203 ,.4242981547237001468 ] 
dist 212=[-1.5187423276421477776 ,.4223423433133334882 ] 
dist 213=[-1.5156898466424476056 ,.41955944567940989413] 
dist 214=[-1.5115548644460195644 ,.41801440258203952735] 
dist 215=[-1.4677417036084611159 ,.36921451240343986197] 
dist 216=[-1.4547970623030225013 ,.36170969209786851759] 
dist 217=[-1.4387735095294805696 ,.34633998389510899127] 
dist 218=[-1.4251767465458997390 ,.34178873308090711602] 
dist 219=[-1.0684019397949381718 ,.32252297675693218434] 
dist 220=[-1.0270660458320000241 ,.3182448177077570782 ] 
dist 221=[-.92741026957777827357,.30689436961578728734] 

8 phat 4 dirichlet min maxes function [0, 1, 2, 2, 2, 0, 0, 0, 1] 
dist 0=[50.129341772821974244  ,50.129341772821974244  ] 
dist 1=[49.391817270200513602  ,50.509102083724631730  ] 
dist 2=[48.533575585657315507  ,50.700153004873874159  ] 
dist 3=[47.671644457122086394  ,50.728599280006112413  ] 
dist 4=[46.639756642045720737  ,50.586548531244453902  ] 
dist 5=[45.102480107908203282  ,50.489546905952639841  ] 
dist 6=[43.352431702048352694  ,50.283716609031386295  ] 
dist 7=[41.470554736881859182  ,50.183420315585114444  ] 
dist 8=[39.125804082919192158  ,49.498953483338224816  ] 
dist 9=[35.526731854438894724  ,47.300834369899951064  ] 
dist 10=[31.883069804902558624  ,46.692223627414431099  ] 
dist 11=[29.360135445416071874  ,46.484606607265184891  ] 
dist 12=[27.167182173707929793  ,46.109524353517560689  ] 
dist 13=[24.841495129141873819  ,45.386657461525040435  ] 
dist 14=[22.599169090816628349  ,41.722320498592441686  ] 
dist 15=[20.739062671391959495  ,39.269755137186120901  ] 
dist 16=[18.796075845026351029  ,36.663326445291189029  ] 
dist 17=[16.222403615009817924  ,30.221470149608475726  ] 
dist 18=[13.680509748042588380  ,29.387459896256303298  ] 
dist 19=[11.864313233303230567  ,27.755455907890456831  ] 
dist 20=[10.224718502936942577  ,27.336204696060014866  ] 
dist 21=[8.3880968603841798570 ,25.871827012748731104  ] 
dist 22=[6.5554304108162025291 ,25.532154676395852345  ] 
dist 23=[4.9313336527727810950 ,25.090672229111410487  ] 
dist 24=[3.1408888661498499987 ,24.936795097374070863  ] 
dist 25=[.64300767915075972655,12.713806531132643250  ] 
dist 26=[-1.8047806678929313825 ,11.705626681051662543  ] 
dist 27=[-3.3951677428112779558 ,11.478280664634505319  ] 
dist 28=[-4.6704946224151814296 ,10.863654303000829948  ] 
dist 29=[-5.8591510835064007191 ,10.427535999883982634  ] 
dist 30=[-6.9092689103223994017 ,9.0105571106729511353 ] 
dist 31=[-7.6310125506210409627 ,8.2428541935893429841 ] 
dist 32=[-8.2550537663050917442 ,.35099652574912516817] 
dist 33=[-8.9149508827026687974 ,-3.6441155824380126936 ] 
dist 34=[-9.5000181269036220367 ,-4.1162511128610520726 ] 
dist 35=[-10.336445227056792637  ,-5.1300136926160262066 ] 
dist 36=[-11.201293447467524972  ,-5.2957772264770641874 ] 
dist 37=[-11.733702036563931453  ,-6.3042341698520744339 ] 
dist 38=[-12.128890229709289372  ,-6.0982821485526888439 ] 
dist 39=[-12.445695021795562937  ,-5.3289286509218978471 ] 
dist 40=[-12.692629188402582441  ,-4.3199457472042561211 ] 
dist 41=[-12.808578945468150059  ,-2.7207685114999325472 ] 
dist 42=[-12.853356203482013522  ,-1.0954977716820776906 ] 
dist 43=[-12.843845731881963732  ,.01775793996286919873] 
dist 44=[-12.734667175829207935  ,.96915931565225486522] 
dist 45=[-12.687456253941089899  ,1.9485181441882008112 ] 
dist 46=[-12.488367403874460153  ,2.8711357276386159509 ] 
dist 47=[-12.437850267822595413  ,3.5961138399110794199 ] 
dist 48=[-7.8725822191208244990 ,4.3154274504967960669 ] 
dist 49=[-7.4323392385661293975 ,5.2154883341694334061 ] 
dist 50=[-6.3700382520531457204 ,6.0751448220955060708 ] 
dist 51=[-6.1971593920055858479 ,6.6331887989676872413 ] 
dist 52=[-5.5036824561100020315 ,7.0774215043571964174 ] 
dist 53=[-5.1156604719920095759 ,7.4827638007521497095 ] 
dist 54=[-5.0268285107885218290 ,7.8322630680873026800 ] 
dist 55=[-4.8771727299238005659 ,8.0535679303508728999 ] 
dist 56=[-4.8371585595085481928 ,8.2233734051562219769 ] 
dist 57=[-1.9098554406933571535 ,8.3672623798223755304 ] 
dist 58=[-1.3409490709607725921 ,8.4791996943283029600 ] 
dist 59=[-.76381873258406369851,8.5214492869542194354 ] 
dist 60=[-.68122968511206294936,8.5205953609624589651 ] 
dist 61=[.10468727441643190477,8.5075783526001754431 ] 
dist 62=[.24448235258607598693,8.3743497967125367731 ] 
dist 63=[.41541472197393310766,8.2307941316837673594 ] 
dist 64=[.44397759652348231073,3.6361096552695819016 ] 
dist 65=[1.4782936468375461797 ,4.0396741029199492899 ] 
dist 66=[1.5990230357061355391 ,4.2837252396105299188 ] 
dist 67=[1.8555276234649463357 ,4.4585657814912610293 ] 
dist 68=[1.9050680634894410352 ,4.5857165684860153297 ] 
dist 69=[2.1531430673718499747 ,4.6813213489156121804 ] 
dist 70=[2.1941737969970669353 ,4.7301222769624387068 ] 
dist 71=[2.2597894801825269850 ,4.7542175237902812120 ] 
dist 72=[2.2723907173926086880 ,4.7528748100856949029 ] 
dist 73=[1.8070695381013521539 ,3.9248593514771926764 ] 
dist 74=[1.3222895731609646967 ,3.2844189652071352796 ] 
dist 75=[.98081687014346897834,3.2829523997549506961 ] 
dist 76=[.6786924525504953953 ,3.2781574716082850667 ] 
dist 77=[.35096541082604636458,3.2689957903765265217 ] 
dist 78=[.03152019846116272319,3.2549317653616194543 ] 
dist 79=[-.23756133979438521728,3.2450076894796469778 ] 
dist 80=[-.52156715529882983952,2.3208607500909223614 ] 
dist 81=[-.90061902474847117465,2.2908701928870170008 ] 
dist 82=[-1.2746776959280687331 ,1.6830925168715965868 ] 
dist 83=[-1.5387614729991737772 ,1.6005851183856968390 ] 
dist 84=[-1.7731947243193296762 ,1.4082261446535971161 ] 
dist 85=[-2.0288918769127409071 ,1.3687666684116827362 ] 
dist 86=[-2.2791473543880795777 ,1.1048755131746946749 ] 
dist 87=[-2.4918711535952005600 ,1.0547210315113664806 ] 
dist 88=[-2.7182062040455118995 ,.96414001251360202832] 
dist 89=[-3.0714470834595557168 ,.94237519776236737907] 
dist 90=[-3.3161506461839936752 ,.63150282344999479884] 
dist 91=[-3.4973182933559425748 ,.7247522329885980811 ] 
dist 92=[-3.6313740235657169749 ,.84074795478856526928] 
dist 93=[-3.7365746737002946462 ,.96245203001591213849] 
dist 94=[-3.8154644127379669043 ,1.0785010047171797368 ] 
dist 95=[-3.8444678800087682143 ,1.2126466182955997753 ] 
dist 96=[-3.8537247255213262886 ,1.4065993205184371058 ] 
dist 97=[-3.8537392853672827300 ,1.6045582141139122464 ] 
dist 98=[-3.7414561189061469679 ,1.7547039778661257193 ] 
dist 99=[-3.7137821708453617350 ,1.8986487307991772639 ] 
dist 100=[-3.6439010197178867919 ,2.0718683157169007909 ] 
dist 101=[-3.6160419196293253669 ,2.2507866482914399401 ] 
dist 102=[-3.4674955813645359095 ,2.4174896400670443893 ] 
dist 103=[-3.4307100366154022086 ,2.6073063411179142665 ] 
dist 104=[-3.3471330363999950838 ,2.8785055917385549388 ] 
dist 105=[-3.3175942738809358935 ,3.1433977452869994354 ] 
dist 106=[-2.2622283610092018823 ,3.3080375123001544463 ] 
dist 107=[-2.2462658802161501384 ,3.4308991356796319935 ] 
dist 108=[-2.1676228540215836551 ,3.5290049277830173109 ] 
dist 109=[-2.1493295259559754196 ,3.6037646380227806710 ] 
dist 110=[-2.0932315526276398191 ,3.6334227863246245291 ] 
dist 111=[-2.0819521273125086668 ,3.6431902070954795484 ] 
dist 112=[-1.2792360326304899951 ,3.6385482045189403110 ] 
dist 113=[-1.2069711962301165002 ,3.5545554699889947575 ] 
dist 114=[-1.0317201501801930054 ,3.5313042058976236464 ] 
dist 115=[-1.0040875843975949040 ,3.4661559682533422994 ] 
dist 116=[-.74695284917941776959,3.4386119209139844805 ] 
dist 117=[-.69882598611950280567,3.2864620852007343818 ] 
dist 118=[-.63711089403210952651,3.0675840695428233857 ] 
dist 119=[-.61952596467802456593,3.0113562547728503578 ] 
dist 120=[-.22125141008655266425,2.6728136538834685776 ] 
dist 121=[-.34426189794416917065,1.9603769411508895465 ] 
dist 122=[-.44544493248350297454,1.8496382450255904774 ] 
dist 123=[-.53013177847776975759,1.9116181969348055319 ] 
dist 124=[-.61441674415786268758,1.9596277664964959917 ] 
dist 125=[-.69196403061135574246,1.9834510194641418454 ] 
dist 126=[-.74976017240289048501,1.9941580717934718048 ] 
dist 127=[-.80413901485081063719,1.9953363366200989484 ] 
dist 128=[-.86804573697009217287,1.2127635147272613035 ] 
dist 129=[-.92696120669314209239,1.0716065289478335035 ] 
dist 130=[-.96141853869632708269,1.0506474495076682546 ] 
dist 131=[-.98453654251706538319,1.0150411858255163743 ] 
dist 132=[-.99819473668692354971,1.0051950202508467811 ] 
dist 133=[-1.0063085675109254178 ,.97505701411233289892] 
dist 134=[-1.0072993137240699619 ,.96480495344259917279] 
dist 135=[-1.0045707866143452960 ,.95808454693112729394] 
dist 136=[-1.0013533259623057849 ,.95489414391849199967] 
dist 137=[.21791510838978929396,.93667235282816163048] 
dist 138=[.09177121335050633474,.94750572537584480574] 
dist 139=[-.01987369394467953445,.95086866641008180216] 
dist 140=[-.1411100736567020849 ,.95076543664674238946] 
dist 141=[-.25941823846953307376,.94853658028308350844] 
dist 142=[-.35937443655619530333,.94297445554718207673] 
dist 143=[-.46516553715298635108,.93964472854965902973] 
dist 144=[-.6067733913180462977 ,.8570119508105208372 ] 
dist 145=[-.7467500433511522897 ,.84426548590858850851] 
dist 146=[-.84603013483374962949,.80956158621727438431] 
dist 147=[-.93465060251143293966,.80274296533658600353] 
dist 148=[-1.0320695193004508072 ,.73535763271647222288] 
dist 149=[-1.1278646797313849902 ,.72079657751285480799] 
dist 150=[-1.2100045970331293642 ,.70286368861666604022] 
dist 151=[-1.2980051227602228343 ,.69572852359870360956] 
dist 152=[-1.4172047751306380732 ,.52947867332296894995] 
dist 153=[-1.5311959484704651699 ,.50678476308600703708] 
dist 154=[-1.5984013976716505005 ,.54189879524082899036] 
dist 155=[-1.6443147107968077898 ,.63690831896429550343] 
dist 156=[-1.6732903598160400988 ,.73733298993364535971] 
dist 157=[-1.6930228805286799677 ,.83367352018202530589] 
dist 158=[-1.7020288721297283841 ,.91237888142051749874] 
dist 159=[-1.7049231118687857976 ,.99332229944368456556] 
dist 160=[-1.7022127125366814454 ,1.0985990456613073893 ] 
dist 161=[-1.5493033564595002198 ,1.2012021461218807244 ] 
dist 162=[-1.5245503082028604790 ,1.2714721290359066317 ] 
dist 163=[-1.4805757614085892102 ,1.3315886916929970276 ] 
dist 164=[-1.4683188112368784796 ,1.3936567383580004639 ] 
dist 165=[-1.4231147590399043813 ,1.4523117254227125004 ] 
dist 166=[-1.4093670665952968148 ,1.4988029866537793039 ] 
dist 167=[-1.3860830411548174744 ,1.5453429633881622959 ] 
dist 168=[-1.3782962427649424266 ,1.6041939436524799492 ] 
dist 169=[-.85227324229212137224,1.6587908749704524572 ] 
dist 170=[-.80593126395896512946,1.6883471441135952238 ] 
dist 171=[-.793186750589603759  ,1.7052547450564736924 ] 
dist 172=[-.74448298414539260819,1.7093521046924088840 ] 
dist 173=[-.73291804524230137175,1.7070262399129972734 ] 
dist 174=[-.70984805502242835372,1.7026890688264439262 ] 
dist 175=[-.70286767360443774406,1.6874672329489602997 ] 
dist 176=[-.47194685589667023445,1.6788690948187463338 ] 
dist 177=[-.46690807008614154334,1.5441511316401426081 ] 
dist 178=[-.45546021481802213596,1.5209355068571288560 ] 
dist 179=[-.45144232446295089809,1.4652043061407890861 ] 
dist 180=[-.43163042953361696794,1.4470956212717339613 ] 
dist 181=[-.42700155859472570095,1.3552751508973249774 ] 
dist 182=[-.4150324524985016027 ,1.3345472950396822834 ] 
dist 183=[-.41117890857928651451,1.2910406441707369854 ] 
dist 184=[-.36710788522884984211,1.2772973180836342048 ] 
dist 185=[-.54983810618360042964,1.3304631319124347401 ] 
dist 186=[-.77754389571783312971,1.3753964581973342834 ] 
dist 187=[-.96199595254400605685,1.4063490805449912332 ] 
dist 188=[-1.1359505290090467632 ,1.4263798663135499763 ] 
dist 189=[-1.2900848697649635063 ,1.4389858374034201635 ] 
dist 190=[-1.3954042851524740467 ,1.4406784337429990189 ] 
dist 191=[-1.4852571255449262827 ,1.4372261132704159527 ] 
dist 192=[-1.5776404350041610991 ,1.4323656187910683123 ] 
dist 193=[-1.6606617279327729774 ,1.3499561962647808591 ] 
dist 194=[-1.7131366869564753116 ,1.3342591076722180753 ] 
dist 195=[-1.7533425701245985811 ,1.2975604923489799831 ] 
dist 196=[-1.7873802239909960681 ,1.2847230172820189976 ] 
dist 197=[-1.8148909711628126436 ,1.2216092173158057377 ] 
dist 198=[-1.8290384720316309576 ,1.2069554112544225552 ] 
dist 199=[-1.8361201806710140090 ,1.1718708306449288670 ] 

8 phat 4 dirichlet min maxes function [1, 0, 0, 0, 2, 1, 2, 0, 2] 
dist 0=[43.707109735906665005  ,43.707109735906665005  ] 
dist 1=[43.090058198726592523  ,44.080790570202709565  ] 
dist 2=[42.317497938802348711  ,44.348666146469130029  ] 
dist 3=[41.322601820159079406  ,44.542908540926761989  ] 
dist 4=[39.971078111749239178  ,44.689514832175989582  ] 
dist 5=[37.774030887489254357  ,44.766974913012364248  ] 
dist 6=[35.513745953656834316  ,44.807975887710954127  ] 
dist 7=[33.909581761145436812  ,44.808717414068541763  ] 
dist 8=[32.473881952642021209  ,44.786563142265390846  ] 
dist 9=[30.886352994559772760  ,44.736170590270582638  ] 
dist 10=[29.316148574630643311  ,44.654496836351628673  ] 
dist 11=[27.949489676584033736  ,44.590811194348987867  ] 
dist 12=[26.465055391167123353  ,44.330039305221123099  ] 
dist 13=[24.424087212200379381  ,44.233227324658847391  ] 
dist 14=[22.372965864433952904  ,43.932663761262486140  ] 
dist 15=[20.847812118005176588  ,43.574374111291478037  ] 
dist 16=[19.409441087636636148  ,34.568734999299571320  ] 
dist 17=[17.704796273289449799  ,33.716489300365471233  ] 
dist 18=[15.949720656594209243  ,31.604888493036227321  ] 
dist 19=[14.309582294183971266  ,31.297647537051134664  ] 
dist 20=[12.431148802513503558  ,28.024914069049071118  ] 
dist 21=[9.7234176644474542992 ,27.397313324174967315  ] 
dist 22=[7.0404067707242757864 ,26.716739315448177969  ] 
dist 23=[5.2606798763302429737 ,26.581913482759845796  ] 
dist 24=[3.7925380179173709623 ,20.579041731197490543  ] 
dist 25=[2.3548244965314536428 ,19.821598989864959492  ] 
dist 26=[1.0373751685124149277 ,18.323636449818772976  ] 
dist 27=[.04983772641116934420,17.942648115712688140  ] 
dist 28=[-.8907515025231556227 ,16.622139880241121076  ] 
dist 29=[-3.2610095061893778558 ,16.327766575060380937  ] 
dist 30=[-4.8690872935289750411 ,15.967396579174226142  ] 
dist 31=[-6.1344301593293329613 ,15.863766193039646078  ] 
dist 32=[-7.2738547648662040671 ,4.3175927815938781731 ] 
dist 33=[-8.2541560877689936054 ,3.3735193479907698094 ] 
dist 34=[-8.8836617953131764921 ,1.2204565510579776924 ] 
dist 35=[-9.3818088054968734100 ,.88406906795711960226] 
dist 36=[-9.8374936256498199589 ,-1.2115852686932304331 ] 
dist 37=[-10.221975711637044155  ,-.58470240381332543155] 
dist 38=[-10.435538002156007837  ,.07131217250175058843] 
dist 39=[-10.567980707179859810  ,.5377784952123042212 ] 
dist 40=[-10.627838996298467065  ,.95271494827217284593] 
dist 41=[-10.638832905533744686  ,1.4035075191088741160 ] 
dist 42=[-10.625663159095031701  ,1.8410307782711609466 ] 
dist 43=[-10.503091638231520005  ,2.2031833067870415525 ] 
dist 44=[-10.475009916028781207  ,2.5785221861546531957 ] 
dist 45=[-9.6412995741277258805 ,3.0687623838507909752 ] 
dist 46=[-9.7330168300416189615 ,3.5449774114094607135 ] 
dist 47=[-9.7497891379915338030 ,3.8644067772531003705 ] 
dist 48=[-6.7769087835308323096 ,4.1295287458495788224 ] 
dist 49=[-6.6163599078656552530 ,4.3891093037702910996 ] 
dist 50=[-6.2115797041872918542 ,4.6246217947925135068 ] 
dist 51=[-6.1402336551086808508 ,4.7937176652059149553 ] 
dist 52=[-5.4847423632746160280 ,4.9461458827689402260 ] 
dist 53=[-5.3549452883404365832 ,5.1151226799354507012 ] 
dist 54=[-5.1826058080538019726 ,5.2663754457074346513 ] 
dist 55=[-5.1245689175052169752 ,5.3480781943436455439 ] 
dist 56=[-3.9120946968476741478 ,5.3941285343483779638 ] 
dist 57=[-3.7524243697529103679 ,5.4031424738939531472 ] 
dist 58=[-3.4100957509875970956 ,5.3872813723860369854 ] 
dist 59=[-3.3190348578504548767 ,5.3714497826542845784 ] 
dist 60=[-2.9411390841939562822 ,5.2430507412972279810 ] 
dist 61=[-2.8701959907773665002 ,2.0822178815136856515 ] 
dist 62=[-2.6990999006103750449 ,2.3367612870893140492 ] 
dist 63=[-2.6694773769220907621 ,2.5393228624758005630 ] 
dist 64=[-.99414615390679294414,2.7251036933272829315 ] 
dist 65=[-.84616823398746372177,2.8868680189189693122 ] 
dist 66=[-.5079709485290057266 ,2.9934915649139028702 ] 
dist 67=[-.44935913842096922031,3.0806868712044031356 ] 
dist 68=[-.01791485019339860902,3.1648625299486051384 ] 
dist 69=[.05931460190349446749,3.2339469095041372417 ] 
dist 70=[.18424021974445367145,3.2608596315097485253 ] 
dist 71=[.2141254043229256127 ,3.3723337578437922226 ] 
dist 72=[.70755372300076807814,3.5738656818452366592 ] 
dist 73=[.77087114955592680224,3.6932372551997695513 ] 
dist 74=[.91505833075850510726,3.7759413299196563610 ] 
dist 75=[.91494439430651461133,3.8309297350014164783 ] 
dist 76=[.33252674229553996864,3.8664381676602845883 ] 
dist 77=[-.25368212801307505921,3.8723895010999541261 ] 
dist 78=[-.64931309287369357372,3.8649279337399400122 ] 
dist 79=[-.98162781271369537694,3.8553601713908476476 ] 
dist 80=[-1.3150545751402716864 ,2.3705747977399833504 ] 
dist 81=[-1.6242608739816812883 ,2.1114343090723213117 ] 
dist 82=[-1.8598843892113116063 ,2.0590566768324921742 ] 
dist 83=[-2.0871146265780480363 ,1.9783754066240658491 ] 
dist 84=[-2.3628299964151963971 ,1.9548322998144449127 ] 
dist 85=[-2.6225607126356938190 ,1.6593353787044734516 ] 
dist 86=[-2.7859766023405106080 ,1.4045336068913305487 ] 
dist 87=[-2.9104522454826103532 ,1.2570218285991192383 ] 
dist 88=[-3.0147081115530414012 ,1.2220253572432209522 ] 
dist 89=[-3.2309329068495499008 ,1.0342563110224748999 ] 
dist 90=[-3.4197921918047477396 ,.99855787521885256383] 
dist 91=[-3.5410703115359679588 ,.92329148280533927543] 
dist 92=[-3.6362682269365224842 ,.9021735188539101398 ] 
dist 93=[-3.7210063613614824661 ,.44772904315444483817] 
dist 94=[-3.7882825484645652415 ,.56230929887344359195] 
dist 95=[-3.8137609895606071339 ,.75631673642964641014] 
dist 96=[-3.8200356690457436649 ,.95784688695539852171] 
dist 97=[-3.8129437990752074434 ,1.1024594642408331546 ] 
dist 98=[-3.7347524500491079333 ,1.2330183945177696221 ] 
dist 99=[-3.7696671796722501465 ,1.3784779970447984810 ] 
dist 100=[-3.8702033856373223798 ,1.5223594111489778152 ] 
dist 101=[-3.9229131618579528697 ,1.6466315441184647361 ] 
dist 102=[-3.9508295191542914330 ,1.7803522395303788826 ] 
dist 103=[-3.9523351303644537495 ,1.9619602293595982107 ] 
dist 104=[-3.7224267965622349728 ,2.1423357407438973390 ] 
dist 105=[-3.6803795967194410644 ,2.2711444980948849686 ] 
dist 106=[-3.6220055593757198079 ,2.3868969367616902419 ] 
dist 107=[-3.5988057582567495137 ,2.5151677790062151554 ] 
dist 108=[-3.5425706773483700116 ,2.6417628012667780216 ] 
dist 109=[-3.5175565121916822842 ,2.7508350000820142386 ] 
dist 110=[-3.4966916936770469921 ,3.0236112682472559071 ] 
dist 111=[-3.4798747378151639678 ,3.2119889896085971064 ] 
dist 112=[-1.4435297662157684789 ,3.3515902485120620352 ] 
dist 113=[-1.4487689367633310629 ,3.4613222489494736546 ] 
dist 114=[-1.4482357337475030528 ,3.5449545096797793398 ] 
dist 115=[-1.4402660275079333882 ,3.5803571778230833565 ] 
dist 116=[-1.4351493927753818286 ,3.5943936077586248832 ] 
dist 117=[-1.3531254629003823648 ,3.5927239610357592960 ] 
dist 118=[-1.3377944321869270667 ,3.3566893101763789355 ] 
dist 119=[-1.3007715853229723004 ,3.3457723582805735586 ] 
dist 120=[-1.2877097573305526075 ,3.1415482491702704375 ] 
dist 121=[-1.2230775937220080117 ,3.1031576536675981182 ] 
dist 122=[-1.2079467098669980755 ,3.0051819213744801682 ] 
dist 123=[-1.1753224977819134217 ,2.9740578641248259613 ] 
dist 124=[-1.1645531695683750538 ,2.7911724950861122068 ] 
dist 125=[.35082774763872100364,2.7489120634983282764 ] 
dist 126=[.13290053044330141888,2.6684110485643948684 ] 
dist 127=[-.49625788193448285703,2.7333565675877479299 ] 
dist 128=[-1.2137107848461394660 ,2.9205413127188828074 ] 
dist 129=[-1.6844664510100950201 ,3.0330277455754247539 ] 
dist 130=[-2.0651190847237353734 ,3.1125380184627910999 ] 
dist 131=[-2.4228522195742752197 ,3.1680548737011753411 ] 
dist 132=[-2.7388773979855836569 ,3.2055010026298391298 ] 
dist 133=[-2.9530172599519954454 ,3.2130192248538887424 ] 
dist 134=[-3.1337291285967273203 ,3.2092448730680475178 ] 
dist 135=[-3.3162950198407295390 ,3.2029152557643243157 ] 
dist 136=[-3.4795346420621641657 ,3.0468676410761712658 ] 
dist 137=[-3.5830899435393624549 ,3.0156797374434951647 ] 
dist 138=[-3.6628358425660762978 ,2.9402444077888682910 ] 
dist 139=[-3.7310250376327925109 ,2.9128373202699303245 ] 
dist 140=[-3.7866221914218968504 ,2.7746385137790394596 ] 
dist 141=[-3.8160983221710743591 ,2.7418611790243594198 ] 
dist 142=[-3.8320989550435520107 ,2.6676199910133695963 ] 
dist 143=[-3.8338983277030365583 ,2.6421217129949289350 ] 
dist 144=[-.8110402490026219896 ,.7233276068743047257 ] 
dist 145=[-.96025636195718737348,.70846426310417107157] 
dist 146=[-1.1101961061131588172 ,.5826094854977956991 ] 
dist 147=[-1.2437911903561695545 ,.5583211615125443502 ] 
dist 148=[-1.3911878143506933831 ,.52365160914303658521] 
dist 149=[-1.5962343991629559563 ,.51317340331641902925] 
dist 150=[-1.7960782119864878721 ,-.53501816822041492721] 
dist 151=[-1.9227025693562715777 ,-.55089880869412028132] 
dist 152=[-2.0201108892197100169 ,-.7819538488476608177 ] 
dist 153=[-2.1033048942965627639 ,-.81084116409165853718] 
dist 154=[-2.1711288536195786104 ,-.8559165777084177968 ] 
dist 155=[-2.2071701114801895212 ,-.86536124527145953618] 
dist 156=[-2.2268820429468820601 ,-.86241409261837737043] 
dist 157=[-2.2295095650587315638 ,-.84058158855526441031] 
dist 158=[-2.2240022768727431234 ,-.80071831765937015493] 
dist 159=[-2.2175884934471333485 ,-.72578541980785013034] 
dist 160=[-2.1963317801874754679 ,-.64500679836147808328] 
dist 161=[-2.1848930117303096361 ,-.5818038395660655219 ] 
dist 162=[-2.1150213107809640196 ,-.51931019058948120283] 
dist 163=[-2.0960243161708054956 ,-.44135951492773618597] 
dist 164=[-2.0570036321515665959 ,-.35933411527777109402] 
dist 165=[-2.0432621566534506733 ,-.2063826897835596207 ] 
dist 166=[-1.6027898819186474326 ,.22007525382325753045] 
dist 167=[-1.5635148202764798688 ,.50601954625756492711] 
dist 168=[-1.4591388574307931043 ,.74416030451021975452] 
dist 169=[-1.4435733391109513419 ,.97975743665657684034] 
dist 170=[-1.2568114426287267047 ,1.1960531090455119422 ] 
dist 171=[-1.2189773565350587549 ,1.3571307389839328177 ] 
dist 172=[-1.1808377317215058428 ,1.5088200238461320674 ] 
dist 173=[-1.1720525226524560488 ,1.6876318627647214636 ] 
dist 174=[-.75999477232942482385,1.8532768942919706335 ] 
dist 175=[-.70735772266917292408,1.9523962537205805996 ] 
dist 176=[-.60262141502421719959,2.0218893386113144612 ] 
dist 177=[-.57564801205884957448,2.0692480523471568882 ] 
dist 178=[-.48069872097835025258,2.1038112173743518602 ] 
dist 179=[-.45948419407476086003,2.1222163624451028399 ] 
dist 180=[-.43163042953361697095,2.1323317179825499354 ] 
dist 181=[-.42239543546693009574,2.1337962495571199369 ] 
dist 182=[.2038806890009799445 ,1.7371459344646670714 ] 
dist 183=[.22747228164987931855,1.7885278730756656870 ] 
dist 184=[.26969613116396833919,1.8318603126770732735 ] 
dist 185=[.27844295272884448854,1.8502832343383237075 ] 
dist 186=[.29604996697832347786,1.8578182624535897379 ] 
dist 187=[.29219450180509174096,1.8576784242897718998 ] 
dist 188=[.27807191390145951947,1.8192948752728017081 ] 
dist 189=[.24622818899139247467,1.8069203924090406854 ] 
dist 190=[.20884536668172255403,1.7972894401061419192 ] 
dist 191=[.01769630476579561340,1.7888673917226368474 ] 
dist 192=[-.34217182699032200216,1.6548285228982619787 ] 
dist 193=[-.58457298788791713037,1.6374329669385372291 ] 
dist 194=[-.78764914741601409524,1.5863425927572680449 ] 
dist 195=[-.99050929444350803736,1.5758986549432073754 ] 
dist 196=[-1.1780090190215070108 ,1.4358179087437087017 ] 
dist 197=[-1.3197574390365883580 ,1.3465593615581789028 ] 
dist 198=[-1.4553185007036303863 ,1.1311532516861411259 ] 
dist 199=[-1.6181144092636930552 ,1.1171838246774906037 ] 
dist 200=[-1.7704637349443710133 ,.92369793384324982731] 
dist 201=[-1.8643158889634205232 ,.93363653906290917279] 
dist 202=[-1.9334021992036454596 ,.93913036293530801168] 
dist 203=[-1.9868719440530759937 ,.93922299744376703264] 
dist 204=[-2.0267422647227469930 ,.93530016764510792075] 
dist 205=[-2.0415322484255173045 ,.93155687396252084552] 
dist 206=[-2.0461960081178963238 ,.87169166913774197934] 
dist 207=[-2.0456366721147782502 ,.86065486990893705444] 
dist 208=[-1.0339691999657059006 ,.83482726073304562829] 
dist 209=[-1.0492966758918961715 ,.82591421725370315685] 
dist 210=[-1.0590395358159153626 ,.78250586362026165989] 
dist 211=[-1.0608173226388573570 ,.77251006481493242186] 
dist 212=[-1.0568176790410975829 ,.74905437880197154418] 
dist 213=[-1.0553163446701493104 ,.74096128027939952185] 
dist 214=[-1.0054485942588691426 ,.39647281644417255009] 
dist 215=[-.99590902094436714737,.36215800080228449518] 
dist 216=[-.9671691963542274042 ,.27986083900844479107] 
dist 217=[-.96121213213572804299,.26718416724247183393] 
dist 218=[-.89573098581005998179,.15059522235695444464] 
dist 219=[-.88089349946758852886,.12929011986543433089] 
dist 220=[-.86398917402962437857,.10157666193007112993] 
dist 221=[-.85637338657005334296,.09444570526491491924] 
dist 222=[-.67006737736314342216,-.06913834285658563207] 
dist 223=[-.64443676417956395647,-.08900944839698448260] 
dist 224=[-.59219578107280465219,-.13270504378063414336] 
dist 225=[-.57789825061023911389,-.14068563333780340424] 
dist 226=[-.52266095235331730381,-.18883228127531769241] 
dist 227=[-.51072831804313674315,-.17067075389648693666] 
dist 228=[-.48555816251785647053,-.06095026780461398009] 
dist 229=[-.47809574370627727344,.09966957076969906425] 
dist 230=[-.4476736233573679378 ,.25953697688622827784] 
dist 231=[-.44418392347983648551,.36625336159680662508] 
dist 232=[-.39902689966960959506,.45460953567639574892] 
dist 233=[-.39116725667548114489,.54117125914208614351] 
dist 234=[-.37203440983436555358,.62008802603684720596] 
dist 235=[-.36701550824663436102,.67792052226779442018] 
dist 236=[-.31573374081555964426,.73145868958607565988] 
dist 237=[-.28555000233151646935,.79322936925199130306] 
dist 238=[-.16437284843308420631,.84975056733765653186] 
dist 239=[-.11730649131321649167,.88232934235882797965] 
dist 240=[.28085904545074835983,.90364638906523916641] 
dist 241=[.25007343446640117918,.91520363658211618419] 
dist 242=[.21092244502742882324,.92229840107222843463] 
dist 243=[.16334403650926490172,.92579904518200315055] 
dist 244=[.10041967804928879188,.92734136420312799904] 

8 phat 4 dirichlet min maxes function [1, 1, 1, 1, 0, 1] 
dist 0=[18.722461785583406769  ,18.722461785583406769  ] 
dist 1=[16.892551190567447260  ,20.448459690568865679  ] 
dist 2=[15.373391213743108432  ,21.552467211598094551  ] 
dist 3=[13.783730886244908851  ,22.417725351823629694  ] 
dist 4=[11.672214939098826646  ,23.189808703503190247  ] 
dist 5=[9.3748750918118332076 ,23.848340228584129592  ] 
dist 6=[7.0427083990591957492 ,24.260017840799483689  ] 
dist 7=[4.2275117649506484766 ,24.572919024975328675  ] 
dist 8=[0                     ,24.837121128814141564  ] 
dist 9=[19.309909482626151750  ,25.050057664268870259  ] 
dist 10=[19.791049152850001990  ,25.158137946505845931  ] 
dist 11=[20.743377534784703619  ,25.212403301497295697  ] 
dist 12=[20.951566396100013106  ,25.210020421712318830  ] 
dist 13=[21.578405780458315694  ,25.173381814296512724  ] 
dist 14=[21.649168296280148358  ,25.145220372577736367  ] 
dist 15=[21.555249712803422345  ,25.008174156195682682  ] 
dist 16=[21.215035046071988599  ,24.971794754974027234  ] 
dist 17=[20.802972144270902022  ,24.476449693811262741  ] 
dist 18=[19.920177141766886270  ,24.376660191273500824  ] 
dist 19=[18.904987576631937955  ,24.093647870276133255  ] 
dist 20=[17.551454341324827743  ,24.028072532890300968  ] 
dist 21=[16.078342923581798113  ,23.431263441866779768  ] 
dist 22=[14.585286891736025630  ,23.296806243715584426  ] 
dist 23=[12.786055772175276483  ,23.115859920097511366  ] 
dist 24=[10.089548167385587707  ,23.048108922487520055  ] 
dist 25=[7.3906538082604099013 ,21.448539632917996928  ] 
dist 26=[5.5818209836607015496 ,21.218332924632372162  ] 
dist 27=[4.0717301061930762574 ,20.787664706037656410  ] 
dist 28=[2.5663381086066735960 ,20.677188190387154448  ] 
dist 29=[1.1720136190360621457 ,19.045583846513696648  ] 
dist 30=[.1055963317368111045 ,18.829251894732379235  ] 
dist 31=[-.9293386957792036772 ,17.690178759933357950  ] 
dist 32=[-2.1980386110799270630 ,15.918600630768635583  ] 
dist 33=[-3.4054113397994633398 ,.9726253331483684108 ] 
dist 34=[-4.1954142972606645635 ,.1149290174868842921 ] 
dist 35=[-4.8347987314128127921 ,-1.7706396432339834414 ] 
dist 36=[-5.4405099264047192736 ,-1.8363052962167952831 ] 
dist 37=[-5.9826460258618267751 ,-1.7638613564440856682 ] 
dist 38=[-6.3681991175282511478 ,-1.5438140752268088547 ] 
dist 39=[-6.7159871945163337184 ,-1.1760827409238807548 ] 
dist 40=[-7.1076405722307868931 ,-.51436454237989267136] 
dist 41=[-7.8179611879404834176 ,.17821863999957472572] 
dist 42=[-8.2614422054153307456 ,.66924488276979244604] 
dist 43=[-8.5571061048214782085 ,1.1043579617927038864 ] 
dist 44=[-8.7314620643350090014 ,1.5742607155623535760 ] 
dist 45=[-8.8452266815261110827 ,2.0284104722856646777 ] 
dist 46=[-8.8987498101282776820 ,2.4008411533715545903 ] 
dist 47=[-8.9194378825096953663 ,2.7835709972380880759 ] 
dist 48=[-8.9019963411762036453 ,3.2789191673900544659 ] 
dist 49=[-7.5118178385981621058 ,3.7575687105525036171 ] 
dist 50=[-7.3417703997354830624 ,4.0737378135018561188 ] 
dist 51=[-6.8861475618499997559 ,4.3306787023937689537 ] 
dist 52=[-6.8134213743491374126 ,4.5731049161694172426 ] 
dist 53=[-5.9918503814157104372 ,4.7869724124446650087 ] 
dist 54=[-5.8253087588337319910 ,4.9300004709087613617 ] 
dist 55=[-5.6417169741398388153 ,5.0481881195483849377 ] 
dist 56=[-5.5880675067010324482 ,5.1629572427191736430 ] 
dist 57=[-3.8364328562623422327 ,5.2549700588840209423 ] 
dist 58=[-3.6117404993150483078 ,5.2823551428722982124 ] 
dist 59=[-3.1492578985228166923 ,5.2791104587501817428 ] 
dist 60=[-3.0273143145478178384 ,5.2607372233775244937 ] 
dist 61=[-2.5774413938643727822 ,5.0981088141511189469 ] 
dist 62=[-2.4844698921545333347 ,5.0455380488466786677 ] 
dist 63=[-2.3192088881877555046 ,4.8148042822245272549 ] 
dist 64=[-2.2814849765666113529 ,4.3722478561393309133 ] 
dist 65=[.74338960213976514192,2.7964276346206226740 ] 
dist 66=[.99896111966396694284,3.0792525263587432435 ] 
dist 67=[1.5568463290084246010 ,3.2942606218199493505 ] 
dist 68=[1.6573666058044532735 ,3.4737460918307780343 ] 
dist 69=[2.2559602992903048153 ,3.6174095969338936804 ] 
dist 70=[2.3509481082552640973 ,3.6894210195483601318 ] 
dist 71=[2.3547044202878096526 ,3.7269852007198518182 ] 
dist 72=[2.0807413486811942220 ,3.7329481277409963577 ] 
dist 73=[1.7869707393978531372 ,3.6895590392871555165 ] 
dist 74=[1.5621668869140048923 ,3.7218740260846984891 ] 
dist 75=[1.3449896391484969916 ,3.8309207801468205461 ] 
dist 76=[1.0815848416060578502 ,3.8999167780884112495 ] 
dist 77=[.80864999850906654969,3.9465074069508851607 ] 
dist 78=[.553389974808592805  ,3.9660574987181767056 ] 
dist 79=[.26210015617200683766,3.9696537247977060623 ] 
dist 80=[-.15470146568551538844,3.9635653781984072889 ] 
dist 81=[-.57847744861153946061,3.6146559171802231549 ] 
dist 82=[-.89763280773895350084,3.5640623352031061095 ] 
dist 83=[-1.2015220591363592595 ,3.4214808044467412266 ] 
dist 84=[-1.5643909149339864717 ,3.3960922828168203063 ] 
dist 85=[-1.9378588970467500451 ,3.1084967836684078234 ] 
dist 86=[-2.2840894088042517198 ,3.0467230336876098881 ] 
dist 87=[-2.6771074559137201391 ,2.9787536047380234084 ] 
dist 88=[-3.2374039054382258118 ,2.9521482769229546260 ] 
dist 89=[-3.7869920661683065167 ,2.2316532418171581807 ] 
dist 90=[-4.1372667515865980612 ,2.1353439384810702826 ] 
dist 91=[-4.4090772853779643062 ,1.9393305493943551821 ] 
dist 92=[-4.6453963129628726660 ,1.8867019379734241910 ] 
dist 93=[-4.8412147205248508413 ,1.6884347648679414582 ] 
dist 94=[-4.9513296319080441241 ,1.6458675565588065661 ] 
dist 95=[-5.0199388350692752040 ,1.5631640731493150053 ] 
dist 96=[-5.0500560853859688010 ,1.5407925396398654202 ] 
dist 97=[-5.0598087724852118664 ,-.8095141104390764918 ] 
dist 98=[-5.0511536151037837214 ,-.98222357884044235215] 
dist 99=[-5.0229041668291886668 ,-1.3632094155502055198 ] 
dist 100=[-5.0034720555348527925 ,-1.4285987398668570553 ] 
dist 101=[-4.8754463796181042776 ,-1.8487230053793499553 ] 
dist 102=[-4.8391592706110899669 ,-1.9156526799903549687 ] 
dist 103=[-4.7465814031667006251 ,-1.6881320895671168602 ] 
dist 104=[-4.7094761824684316016 ,-.74318399721548550186] 
dist 105=[-3.9548028119809568864 ,.20669226768660267549] 
dist 106=[-3.8945225976844551268 ,.84428820118431114832] 
dist 107=[-3.7735274990389752488 ,1.3758663028009623503 ] 
dist 108=[-3.7363372960120744681 ,1.9024871528032019609 ] 
dist 109=[-3.5743137444634424808 ,2.3862428290458665038 ] 
dist 110=[-3.5362042136850724089 ,2.7466891774662970844 ] 
dist 111=[-3.4318591862714802714 ,3.0862000476076142602 ] 
dist 112=[-3.4037285345589744037 ,3.4863722519683029409 ] 
dist 113=[-2.4020476373860528003 ,3.8576182812314203559 ] 
dist 114=[-2.3472313276323151395 ,4.0816467930055808003 ] 
dist 115=[-2.2096361108276087498 ,4.2409422776492218006 ] 
dist 116=[-2.1811237418948126864 ,4.3537563447891172243 ] 
dist 117=[-1.9528850883124144712 ,4.4373442883693702557 ] 
dist 118=[-1.9058545539841004163 ,4.4799598888264848774 ] 
dist 119=[-1.8347418784413736484 ,4.5007514904138947458 ] 
dist 120=[-1.8131395618050690602 ,4.4973662000212491549 ] 
dist 121=[-1.3561765156619825264 ,3.0678881027656723840 ] 
dist 122=[-1.2941730317980568064 ,3.2284579692659878748 ] 
dist 123=[-1.1555322198978043360 ,3.3508299213401205374 ] 
dist 124=[-1.1213559813603203119 ,3.4532655783042297520 ] 
dist 125=[-.94699340041837222469,3.5351849034995222850 ] 
dist 126=[-.91370020097647354131,3.5756481829527944142 ] 
dist 127=[-.8409179862189924224 ,3.5935424744450687780 ] 
dist 128=[-.81998234859039023424,3.5941700275148716877 ] 
dist 129=[1.1934613819715315149 ,2.5405358497028226662 ] 
dist 130=[1.3234495845300331691 ,2.6085121662364564450 ] 
dist 131=[1.6080840122503825617 ,2.6550184922896935328 ] 
dist 132=[1.6549340151430097130 ,2.6844905560691917831 ] 
dist 133=[1.9569655263691698184 ,2.7008327228068272115 ] 
dist 134=[1.8990720366337080619 ,2.7029004690516475203 ] 
dist 135=[1.6931052705494770884 ,2.6842158131178876455 ] 
dist 136=[1.3604133879819571037 ,2.6814635222393131322 ] 
dist 137=[1.0189269542622179000 ,2.3970484275968515163 ] 
dist 138=[.7778462911883412195 ,2.4425596308092719047 ] 
dist 139=[.5638739870025402366 ,2.4717393925467792755 ] 
dist 140=[.3306123057859592460 ,2.4863293753946422043 ] 
dist 141=[.1024703765512346617 ,2.4904762527792261529 ] 
dist 142=[-.0910645370313408873 ,2.4887766950892865357 ] 
dist 143=[-.2965563087787937422 ,2.4634739938778123917 ] 
dist 144=[-.57244018519975634371,2.4597629828096151687 ] 
dist 145=[-.84546690323826086006,1.6654454383106669741 ] 
dist 146=[-1.0395536264552692305 ,1.5889011788169977691 ] 
dist 147=[-1.2132297513266223253 ,1.4042780681460832072 ] 
dist 148=[-1.4047693678053735050 ,1.3712385728382975145 ] 
dist 149=[-1.5934412002127577549 ,1.0995124337915147527 ] 
dist 150=[-1.7556706206912088397 ,1.0475584557672155996 ] 
dist 151=[-1.9298292452991939618 ,.97107100229099920692] 
dist 152=[-2.1661348923776566073 ,.94897277136514811386] 
dist 153=[-2.3939196821246032523 ,.52275145846899048895] 
dist 154=[-2.5340589448550084058 ,.46763246857632265551] 
dist 155=[-2.6370262887258764434 ,.34227004937613218036] 
dist 156=[-2.7163962109233405059 ,.31812155944303659375] 
dist 157=[-2.7764197411732733019 ,.16063583164463447336] 
dist 158=[-2.8021421407880359294 ,.13247866898958686118] 
dist 159=[-2.8117862658689374086 ,.08024068434501806878] 
dist 160=[-2.8087945942141337498 ,.06816400525699706207] 
dist 161=[-2.6924641112594845293 ,-1.2819662170686352137 ] 
dist 162=[-2.6674408466817539706 ,-1.3648548909008436772 ] 
dist 163=[-2.6182763764950430355 ,-1.5423451980057608644 ] 
dist 164=[-2.6014468491684155822 ,-1.5714722313809739335 ] 
dist 165=[-2.5213296640793289318 ,-1.6231952170872491757 ] 
dist 166=[-2.5013051474511842142 ,-1.3615535647583729525 ] 
dist 167=[-2.4411076944183313078 ,-1.0391273343567495412 ] 
dist 168=[-2.4386511766984903980 ,-.54887845797030338029] 
dist 169=[-2.2610290879227528207 ,-.05680027433845684436] 
dist 170=[-2.2303731612416916661 ,.27293018366311662529] 
dist 171=[-2.1731429567809898091 ,.54729907062589845908] 
dist 172=[-2.1559656408313284393 ,.81834163209519296985] 
dist 173=[-2.0849977996948364598 ,1.0669177147248246928 ] 
dist 174=[-2.0658054945364204228 ,1.2515876060629667786 ] 
dist 175=[-2.0210446988669564336 ,1.4250529925742342439 ] 
dist 176=[-2.0046301273304764334 ,1.6288949721913611578 ] 
dist 177=[-1.0569229817993813280 ,1.8187121961423883728 ] 
dist 178=[-.98311092326795467302,1.9361819733638875183 ] 
dist 179=[-.80523006363459030431,2.0232982942675349454 ] 
dist 180=[-.77743255146952686858,2.0919242172694189150 ] 
dist 181=[-.52153585161428709294,2.1447697890030997645 ] 
dist 182=[-.47426362379427154676,2.1688818545277573607 ] 
dist 183=[-.41280523621625421384,2.1792208412735467438 ] 
dist 184=[-.39596825899334700339,2.1782325482788370588 ] 
dist 185=[-.02153221052719156313,1.4283271961607425748 ] 
dist 186=[.02464468211612593076,1.5244311124817972452 ] 
dist 187=[.12549737813828681362,1.5980607512750818372 ] 
dist 188=[.14564349648897394611,1.6604083584017698551 ] 
dist 189=[.25626251444051456872,1.7108221145897551241 ] 
dist 190=[.27458999872853018626,1.7368020242130500182 ] 
dist 191=[.31399084597675513235,1.7498824177535124053 ] 
dist 192=[.2267648581401499626 ,1.7517488318427974374 ] 
dist 193=[.0959256208449040283 ,1.3836919892978491984 ] 
dist 194=[-.0113924930024189469 ,1.3917542114292934644 ] 
dist 195=[-.1221549995441289860 ,1.3932776602063039763 ] 
dist 196=[-.2667481317520191262 ,1.3906996117010332043 ] 
dist 197=[-.4222311607548061755 ,1.3635112714268155468 ] 
dist 198=[-.5764725023146485171 ,1.3542502418516206969 ] 
dist 199=[-.7595359791941629113 ,1.3379943176323098435 ] 
dist 200=[-1.0300919566063776193 ,1.3320002297574255005 ] 
dist 201=[-1.2984937037999924650 ,1.3100295371924867172 ] 
dist 202=[-1.4729572432808524666 ,1.3682640724978194720 ] 
dist 203=[-1.6122207407566630722 ,1.4138875013033630086 ] 
dist 204=[-1.7400881972295033300 ,1.4542818571614513541 ] 
dist 205=[-1.8510236613324549120 ,1.4882573807850934598 ] 
dist 206=[-1.9226875879616418297 ,1.5082543172864967867 ] 
dist 207=[-1.9793965998564458549 ,1.5218496750021169486 ] 
dist 208=[-2.0306268670135769902 ,1.5302663752722584670 ] 
dist 209=[-2.0722866963624003127 ,1.5340753755016819571 ] 
dist 210=[-2.0907859155091363532 ,1.5324451109733286295 ] 
dist 211=[-2.0970831548296463212 ,1.5217012674777817273 ] 
dist 212=[-2.0957350546896443274 ,1.5144434186829333968 ] 
dist 213=[-2.0902137601009971764 ,1.5572207262246205122 ] 
dist 214=[-2.1537929578612573566 ,1.5943389751164958272 ] 
dist 215=[-2.1995390185041653347 ,1.6261419958462143068 ] 
dist 216=[-2.2329945695970378064 ,1.6590400048104124203 ] 
dist 217=[-2.2568872273004170545 ,1.6870927202900757124 ] 
dist 218=[-2.2644534890630066496 ,1.6995514538843251250 ] 
dist 219=[-2.2626170245563572665 ,1.7029736884575666902 ] 
dist 220=[-2.2584202253924723871 ,1.7017573520430894084 ] 
dist 221=[-2.2199769544661811354 ,1.6820065003398308408 ] 
dist 222=[-2.2074347438263023703 ,1.6743134698078004890 ] 
dist 223=[-2.1719197386527856032 ,1.6500894122172731275 ] 
dist 224=[-2.1563956862479238859 ,1.6392248958200595752 ] 
dist 225=[-1.4089160926109888340 ,1.5011609157952374523 ] 
dist 226=[-1.3334008372905705284 ,1.4770832030298676033 ] 
dist 227=[-1.1514813078190026920 ,1.4180784841043399646 ] 
dist 228=[-1.1202803808343727101 ,1.4007103468581272595 ] 
dist 229=[-.89809720489415082543,1.3011855600819710681 ] 
dist 230=[-.8866677831857981746 ,1.2790969401414820204 ] 
dist 231=[-.86277786005736624095,1.2360624414924089304 ] 
dist 232=[-.85498995115991254313,1.2232825647409277217 ] 
dist 233=[-.88819098723109735069,1.0064588663584714899 ] 
dist 234=[-1.0387544012417050770 ,1.0294162111971112792 ] 
dist 235=[-1.1595453588325672796 ,1.1365508836836169101 ] 
dist 236=[-1.2714512980001253837 ,1.2398297470361325674 ] 
dist 237=[-1.3692069121995739358 ,1.3328719460528525473 ] 
dist 238=[-1.4335054292272078876 ,1.3991377329106694715 ] 
dist 239=[-1.4856688877156481398 ,1.4585616653712888667 ] 
dist 240=[-1.5349771830708481539 ,1.5242893216568677180 ] 
dist 241=[-1.5766387565797258847 ,1.5829316322983233007 ] 
dist 242=[-1.5982740595285054947 ,1.6140680488313487940 ] 
dist 243=[-1.6093974640277156603 ,1.6310592068129733903 ] 
dist 244=[-1.6100414138536154354 ,1.6341987053065909549 ] 
dist 245=[-1.6031667322137250448 ,1.6295541650514006603 ] 
dist 246=[-1.6589444959849461044 ,1.6309897113055978208 ] 
dist 247=[-1.7274957568926570975 ,1.6810704041994325027 ] 
dist 248=[-1.7934283551670715815 ,1.7319381564307318962 ] 
dist 249=[-1.8501345148746760131 ,1.7748173815472496176 ] 
dist 250=[-1.8818504587210567421 ,1.7930044743435294296 ] 
dist 251=[-1.9013612301687005167 ,1.8004578247107743745 ] 
dist 252=[-1.9093403466932120840 ,1.8004806276673298699 ] 
dist 253=[-1.9095236143450792498 ,1.7619925298221906002 ] 
dist 254=[-1.9070073175051970121 ,1.7498331059733440584 ] 
dist 255=[-1.8852444824274443245 ,1.7405522457926993021 ] 

8 phat 4 dirichlet min maxes function [2, 0, 0, 2, 1, 1, 1, 2] 
dist 0=[38.679872319808075738  ,38.679872319808075738  ] 
dist 1=[37.728297249179797205  ,39.398353622220432166  ] 
dist 2=[36.207143616095472114  ,39.988382000137643103  ] 
dist 3=[34.646402022019781313  ,40.453397244649892930  ] 
dist 4=[33.536573905088272218  ,40.672657134136585008  ] 
dist 5=[32.541569287234010708  ,40.780112560019603358  ] 
dist 6=[31.439166394432499982  ,40.798563532885302983  ] 
dist 7=[30.347664445362592540  ,40.519722927023130432  ] 
dist 8=[29.395956497705604415  ,40.330314550318865946  ] 
dist 9=[28.360594870699882513  ,40.163945955857367002  ] 
dist 10=[26.934524727878847701  ,40.091998850146828334  ] 
dist 11=[25.498967253830641323  ,39.787914110258380129  ] 
dist 12=[24.425485491312949792  ,39.688689010435611372  ] 
dist 13=[23.406342955493155633  ,39.415507847304857334  ] 
dist 14=[22.187591391168997728  ,39.299896508701842488  ] 
dist 15=[20.925254327353273543  ,38.688494421183556045  ] 
dist 16=[19.731603963026221780  ,38.096352047602861702  ] 
dist 17=[18.352030697074655258  ,28.263712834526930734  ] 
dist 18=[16.346065398114547978  ,27.989705194035994486  ] 
dist 19=[14.348940842091402210  ,25.048188914570892282  ] 
dist 20=[13.004621346350308033  ,24.484079007669258311  ] 
dist 21=[11.872201873907255090  ,23.880173154048404024  ] 
dist 22=[10.722290930958885528  ,23.766559336894264558  ] 
dist 23=[9.6397846254242727492 ,19.328387772222002095  ] 
dist 24=[8.7768442358459255077 ,19.140137503820561324  ] 
dist 25=[7.9035209557254946879 ,17.648478681810564741  ] 
dist 26=[6.7794539360419650404 ,17.004888065565751099  ] 
dist 27=[5.6784335889163088527 ,14.796136815703592457  ] 
dist 28=[4.8972475065826118873 ,14.531024754762231567  ] 
dist 29=[4.1953371549814413454 ,14.232937657053728574  ] 
dist 30=[3.4113018264646733005 ,14.163601427450044338  ] 
dist 31=[2.1267375545307582144 ,5.4843375986158419541 ] 
dist 32=[-.34815117553267011696,4.6528295378370884524 ] 
dist 33=[-2.7769924999418479089 ,4.4037710633906524006 ] 
dist 34=[-4.3301641822246227103 ,4.3427955112130821964 ] 
dist 35=[-5.5488437361668777532 ,2.4074758613614771821 ] 
dist 36=[-6.6407280559891762588 ,2.2148741385621350563 ] 
dist 37=[-7.5765583712494859626 ,1.7821823915017290524 ] 
dist 38=[-8.1716187255265562646 ,1.7059348410345570040 ] 
dist 39=[-8.6359903006510921807 ,1.1721754960335012566 ] 
dist 40=[-9.0498295296298694418 ,1.0768152552133701506 ] 
dist 41=[-9.4011832267659943658 ,.91747936749497280332] 
dist 42=[-9.6157616699860948160 ,.88084277469843213652] 
dist 43=[-9.7743167305531067216 ,.2815476226101316755 ] 
dist 44=[-9.9012571379520766780 ,.20374554870844482876] 
dist 45=[-10.000503561244498639  ,.02015848059220645947] 
dist 46=[-10.048119348241998394  ,-.00688351297700713125] 
dist 47=[-10.067861306398174886  ,-.25986825877603269356] 
dist 48=[-10.055449285855409252  ,-.30571086331181878139] 
dist 49=[-6.6975806281457684447 ,-.3622629393516743185 ] 
dist 50=[-6.4348267824124670980 ,-.37444139801464534726] 
dist 51=[-4.2065462795410407342 ,-.73003179400156844653] 
dist 52=[-4.0559561128571094046 ,-.77218868864038502001] 
dist 53=[-3.6089614920470340944 ,-.86412431090527391738] 
dist 54=[-3.5519589092519847569 ,-.88060807741231898589] 
dist 55=[-2.4168763072184305464 ,-.9427344816602951661 ] 
dist 56=[-2.2708434558070058254 ,-.12744960567135291302] 
dist 57=[-1.9512112626301264251 ,.67068345978397030656] 
dist 58=[-1.8787917535998963834 ,1.2241159444327719665 ] 
dist 59=[-1.5138999859750254754 ,1.7052073222226615304 ] 
dist 60=[-1.4493646355727799312 ,2.2146072642556364713 ] 
dist 61=[-1.3037122493633371579 ,2.7046346550100250474 ] 
dist 62=[-1.2761418979380788296 ,3.1084718001752041592 ] 
dist 63=[-1.2053966933074730217 ,3.5277104887376354336 ] 
dist 64=[-1.2039244048621919648 ,4.0794118175050842803 ] 
dist 65=[-1.1972912981483375843 ,4.6081456549389515528 ] 
dist 66=[-1.1928387146032514660 ,4.9356929603712102606 ] 
dist 67=[-.92664153061258303182,5.1798280131390142111 ] 
dist 68=[-.89798393551929257581,5.3753750977501626410 ] 
dist 69=[-.83196960371888279628,5.5268697151782703822 ] 
dist 70=[-.81523790318199298544,5.5950171388498044715 ] 
dist 71=[-.72225212308129207972,5.6262307441550524529 ] 
dist 72=[-.70329172997286054278,5.6301595307082374938 ] 
dist 73=[-.66529267693344778426,5.4827522838875609151 ] 
dist 74=[-.6544470433557351012 ,5.4448232430135183842 ] 
dist 75=[-.50423619163700503201,5.3690442672196350062 ] 
dist 76=[-.4825402725232647818 ,5.3408866325724043904 ] 
dist 77=[-.42727441885346298799,5.1981939731373978193 ] 
dist 78=[-.5363078153202597511 ,5.1626227912522228524 ] 
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dist 133=[-.25694356114186542925,1.2541313347244992976 ] 
dist 134=[-.25217005812375776067,1.2467341101755762287 ] 
dist 135=[-.20809176416829281805,1.2422724082966013608 ] 
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dist 139=[-.1064473379096396193 ,.96311191611917905586] 
dist 140=[-.09631644304623326128,.95021543417688763636] 
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dist 145=[-.16742342146153121756,.40133709727961356784] 
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dist 147=[-.3452064039700921893 ,.39812113607954310866] 
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dist 152=[-.650459698698469219  ,.36937832362325393356] 
dist 153=[-.7011695551142853577 ,.3625173423713097971 ] 
dist 154=[-.73127435379867876229,.36028549172963669674] 
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dist 156=[-.78393333406546445623,.2967335406955070589 ] 
dist 157=[-.81044863614460550893,.27883154659530403   ] 
dist 158=[-.82349876541533456034,.27345105997796413612] 
dist 159=[-.83026058532234890905,.25000154971477836522] 
dist 160=[-.83167123319485710224,.24516802456297914097] 
dist 161=[-.45167667410820193423,.23306739237537487343] 
dist 162=[-.47764730338806884824,.23100924796987006454] 
dist 163=[-.49708381547819643294,.23077911880049558809] 
dist 164=[-.51273226314154330617,.23035345660603662786] 
dist 165=[-.52477862574506896583,.2277784824536138156 ] 
dist 166=[-.52983175771377630461,.22704244243648642329] 
dist 167=[-.53192388987732513171,.21688523633395743941] 
dist 168=[-.53214702183308993854,.21428810846068394625] 
dist 169=[-.52007734183046886524,.21170726076778596224] 
dist 170=[-.516782379897149568  ,.2102390240821436446 ] 
dist 171=[-.50919489826773318918,.17105298770686495097] 
dist 172=[-.50615645802454145854,.16553569891515269589] 
dist 173=[-.48990839506038878498,.15459961759438821627] 
dist 174=[-.48586890466814991793,.15161697199472939854] 
dist 175=[-.47468623330995070158,.14029283853352137098] 
dist 176=[-.47114397033991359792,.13766788779176804569] 
dist 177=[-.41190534127547070119,.13251012714497221384] 
dist 178=[-.41080510907859835788,.13100039825975421731] 
dist 179=[-.28455519701063161785,.12480900799942609368] 
dist 180=[-.28655264213110892622,.17740829195042858953] 
dist 181=[-.28715890691413115605,.22581484508524211076] 
dist 182=[-.28708687559311167798,.26208022727766799751] 
dist 183=[-.2795053228394314537 ,.29645340118214580206] 
dist 184=[-.2772987424018467714 ,.33730557448452442028] 
dist 185=[-.27575478964469131009,.37534231092224102314] 
dist 186=[-.27470981754922434339,.39847437246200750795] 
dist 187=[-.2285805906035291704 ,.41515535606380189968] 
dist 188=[-.22205722389478227251,.42743447831120075905] 
dist 189=[-.2097999305285515449 ,.43674723479421889141] 
dist 190=[-.20655582362434334554,.44158340626882350185] 
dist 191=[-.20437263342757995345,.47740079640863832149] 
dist 192=[-.24419773697220116282,.53644662866406276643] 
dist 193=[-.29408321302485070469,.60365321488221812317] 
dist 194=[-.37081901733420124628,.69967851901900626385] 
dist 195=[-.44815661641374430529,.79359940971021684128] 
dist 196=[-.50044474277471258748,.8524041729193936577 ] 
dist 197=[-.54445527120030509639,.89681397658970061664] 
dist 198=[-.58874516313271413922,.93326320775641223353] 
dist 199=[-.62988466847148158014,.96185380184147513718] 
dist 200=[-.6613175131669538275 ,.97488812656735615343] 
dist 201=[-.69169592876972229946,.98114137948482912563] 
dist 202=[-.72862572009292478086,.9826586198450453984 ] 
dist 203=[-.76340727571845618207,.96199599043404407693] 
dist 204=[-.78520901543115113541,.95583628842173234081] 
dist 205=[-.80170168865356841511,.94398079024291035098] 
dist 206=[-.8152871626283173301 ,.93937369478963661984] 
dist 207=[-.82598130810986013565,.91545371174507605682] 
dist 208=[-.83093055838696218425,.90921731103101479583] 
dist 209=[-.8326241793142807084 ,.88805289521981299568] 
dist 210=[-.83141755609844975581,.8838386482488139077 ] 
dist 211=[-.82607578428491846975,.45995158514993463925] 
dist 212=[-.82283044592822780052,.42026956433745733163] 
dist 213=[-.81351151849599308184,.32788492469225515493] 
dist 214=[-.80895448926738575676,.31128242004941540099] 
dist 215=[-.7821325806333054866 ,.18813452482844094439] 
dist 216=[-.77500848736689123243,.16573624722192288987] 
dist 217=[-.75915136317626360195,.12872304741776345247] 
dist 218=[-.75337882458537793296,.11989666822127254992] 
dist 219=[-.66236154533665453078,-.02698306792268898884] 
dist 220=[-.64820701459751234044,-.04615811125856030449] 
dist 221=[-.61331182551272619283,-.08703667859804548141] 
dist 222=[-.60501918901897403722,-.09587232834614868847] 
dist 223=[-.54803789445137409177,-.13680524566062713858] 
dist 224=[-.53606174846192792572,-.04643940783829581807] 
dist 225=[-.51510487955251418632,.06831786613018484259] 
dist 226=[-.5766325659332634789 ,.23744097655504557749] 
dist 227=[-.64636262057413294693,.40534013296942773202] 
dist 228=[-.69081802396814793183,.51521073913198424867] 
dist 229=[-.72532271566934660244,.60374012111007452022] 
dist 230=[-.7553247928721072477 ,.68643482676137897174] 
dist 231=[-.78017577544473005362,.75916167390669731172] 
dist 232=[-.7941148143509751646 ,.80789446489274195445] 
dist 233=[-.80274461859899875554,.84843855773920480946] 
dist 234=[-.80639851712694756104,.88847188983894669234] 
dist 235=[-.80694756948183771834,.92368380248939641682] 
dist 236=[-.80574895406554992806,.94497856776027142864] 
dist 237=[-.79846202982405615535,.96017925000048061246] 
dist 238=[-.79520585606383163756,.9710612360923601343 ] 
dist 239=[-.76488579727107414182,.97834738059284667236] 
dist 240=[-.75676863860094426632,.9791921175924887439 ] 
dist 241=[-.74592192123968164876,.97687394162734665583] 

8 phat 4 dirichlet min maxes function [1, 2, 0, 1, 1, 0, 2, 0, 2] 
dist 0=[52.660646212758642351  ,52.660646212758642351  ] 
dist 1=[52.383371690164174326  ,52.721342452137944120  ] 
dist 2=[51.856169173595906479  ,52.686327363289040407  ] 
dist 3=[50.848631292703134196  ,52.580848645192212088  ] 
dist 4=[49.700810431350503580  ,52.507406478628666602  ] 
dist 5=[48.613322554056848658  ,52.289042326880420894  ] 
dist 6=[47.359141231295067699  ,52.067859493064695869  ] 
dist 7=[45.545344884447156602  ,51.883468626626273675  ] 
dist 8=[43.504504432875920795  ,50.314619815111913539  ] 
dist 9=[41.343362425352803658  ,47.395051741165306251  ] 
dist 10=[38.673852802391268545  ,47.098066518158392380  ] 
dist 11=[34.602353755697243827  ,46.963197958144734874  ] 
dist 12=[30.492792025703542128  ,46.706383824788556038  ] 
dist 13=[27.671161991213735349  ,45.958696367632569220  ] 
dist 14=[25.244362434790333037  ,40.637388953162401658  ] 
dist 15=[22.711698240903100449  ,39.971184982251372812  ] 
dist 16=[20.295127314675985858  ,39.752840374842138897  ] 
dist 17=[18.331858801404747156  ,33.319730517321365173  ] 
dist 18=[16.317834919206889533  ,32.466562344583374328  ] 
dist 19=[13.698167994328758035  ,30.763365986541305176  ] 
dist 20=[11.133099934509482484  ,30.313561799674456660  ] 
dist 21=[9.3369737284285454232 ,28.663464418569872170  ] 
dist 22=[7.3966621884853721918 ,28.297233700789457014  ] 
dist 23=[5.6573152689376289268 ,27.640971408333778752  ] 
dist 24=[4.1620891655373193826 ,27.474176296221819432  ] 
dist 25=[2.5997114917420975872 ,12.413503639195198174  ] 
dist 26=[1.1038502054309374159 ,11.126148486022471561  ] 
dist 27=[-.76174877662873246173,8.5838147786965039540 ] 
dist 28=[-2.8208617251083381429 ,7.6971246177489138041 ] 
dist 29=[-4.1360444050306980860 ,7.1787780364327075520 ] 
dist 30=[-5.1663689799943998846 ,3.3268774413366447608 ] 
dist 31=[-6.0868780442295694327 ,2.3295365013087535142 ] 
dist 32=[-7.4458958211192194374 ,2.0868456416634325370 ] 
dist 33=[-9.0351377480774366918 ,-1.7033051670444451242 ] 
dist 34=[-10.034877513440160409  ,-2.1785187468793446217 ] 
dist 35=[-10.797736037926667816  ,-3.1440603075891365693 ] 
dist 36=[-11.440804167892820956  ,-3.3584332130117455080 ] 
dist 37=[-11.960871718626417976  ,-4.1337303470562911444 ] 
dist 38=[-12.232494495192666102  ,-4.2787771375448100486 ] 
dist 39=[-12.375824662760114965  ,-4.3604604457246079045 ] 
dist 40=[-12.398955635812742772  ,-4.2584278480346102512 ] 
dist 41=[-9.7792737629930657333 ,-4.1031353736211436528 ] 
dist 42=[-9.5648296801460169321 ,-3.9410387729996764110 ] 
dist 43=[-9.0215422300464021230 ,-3.7459996246379840637 ] 
dist 44=[-8.9091792237735096306 ,-2.8324767214601394091 ] 
dist 45=[-8.5058095959296195800 ,-1.1998389712563610278 ] 
dist 46=[-7.8227909692337334439 ,.43917700484307724835] 
dist 47=[-7.5390904528288156075 ,1.5308642542377495808 ] 
dist 48=[-7.4557788653057641697 ,2.4310644506364111952 ] 
dist 49=[-5.7367068295906986515 ,3.3058609550200927191 ] 
dist 50=[-5.5062686570640629652 ,4.0980812205317450104 ] 
dist 51=[-4.9798246858036679268 ,4.6687501299005267799 ] 
dist 52=[-4.8655255152307641643 ,5.1870400349491484378 ] 
dist 53=[-4.1805734357327434045 ,5.7703081731375316848 ] 
dist 54=[-4.0524423088725239502 ,6.3050697304177168737 ] 
dist 55=[-3.8010749844242355025 ,6.6296994464595971029 ] 
dist 56=[-3.7360333142711461864 ,6.8630168637191297480 ] 
dist 57=[-1.3849176961788420906 ,7.0330525858523579339 ] 
dist 58=[-1.1408806017149618810 ,7.1538965096964948916 ] 
dist 59=[-.6447461493085804720 ,7.1908716412823663496 ] 
dist 60=[-.5193441898759778367 ,7.1933382850173436624 ] 
dist 61=[-.0819942619902508445 ,7.1762932291773761527 ] 
dist 62=[.0069747058251771015 ,6.7289065795882545377 ] 
dist 63=[.1229167111922477987 ,7.0558516066154236082 ] 
dist 64=[.1476912099966094496 ,7.3805153528925571391 ] 
dist 65=[.1386502191329035939 ,7.6632409264629890250 ] 
dist 66=[.0795979481909783380 ,7.8227140715086952610 ] 
dist 67=[-.0268269776583184359 ,7.9231036685524918600 ] 
dist 68=[-.2251063775930110995 ,7.9698351964775203711 ] 
dist 69=[-.4668640880828496148 ,7.9825113590065152783 ] 
dist 70=[-.7469095348088127976 ,7.9743625408035625188 ] 
dist 71=[-1.1085554077234515747 ,7.9019548377974580116 ] 
dist 72=[-1.6760976402587956694 ,7.8775031862280016619 ] 
dist 73=[-2.2488424226208219587 ,4.1682086998174352271 ] 
dist 74=[-2.6312915674189688420 ,4.1314980920936368659 ] 
dist 75=[-2.9477130843929708523 ,4.1150311436302479797 ] 
dist 76=[-3.2569426891073123245 ,1.8431577455189926252 ] 
dist 77=[-3.5381220592146190989 ,1.6511866419146810871 ] 
dist 78=[-3.7426093227097219958 ,1.1972601552254214695 ] 
dist 79=[-3.9303046159711756461 ,1.1263309997187500700 ] 
dist 80=[-4.1445092502117820836 ,.50595541087820882992] 
dist 81=[-4.3394791902263728013 ,.39435162179570702309] 
dist 82=[-4.4504168261533629361 ,.24154623313050008471] 
dist 83=[-4.5213463718257637963 ,.19974233901700446067] 
dist 84=[-4.5566262990691875508 ,-.59205932928765436384] 
dist 85=[-4.5689081534420067518 ,-.68794940563081888488] 
dist 86=[-4.6776897790879274594 ,-.37622891597851493703] 
dist 87=[-4.9455436359481286032 ,.30753537865651489859] 
dist 88=[-5.2736837861653984342 ,1.3478463817995243196 ] 
dist 89=[-5.5784965642968406934 ,2.3891966607431820656 ] 
dist 90=[-5.7532271985470770428 ,3.0771050129345596109 ] 
dist 91=[-5.8666273460122569986 ,3.6379947300052348877 ] 
dist 92=[-5.9265460756586335119 ,4.1723382024672922162 ] 
dist 93=[-5.9573933525856302865 ,4.6487973680970187331 ] 
dist 94=[-5.9546889417536422163 ,4.9786283160733477310 ] 
dist 95=[-5.9341176733391103199 ,5.2642133645918585854 ] 
dist 96=[-5.9147586675309693200 ,5.5640370781080870463 ] 
dist 97=[-5.4213400409056871445 ,5.8306043213388517087 ] 
dist 98=[-5.3379545234115542249 ,5.9834431097516081667 ] 
dist 99=[-5.1558925742785735551 ,6.0821541850404149636 ] 
dist 100=[-5.0971818552498586925 ,6.1326897772440078512 ] 
dist 101=[-4.8256059219241977232 ,6.1537890636770892004 ] 
dist 102=[-4.7661373551732229770 ,6.1487347180626840002 ] 
dist 103=[-4.5991557550099438601 ,6.1038005283501865218 ] 
dist 104=[-4.5635567631686847825 ,6.0753099093660331717 ] 
dist 105=[-.36883468219233183161,3.0844198272553283169 ] 
dist 106=[-.3477700725035719962 ,3.1639782342882912460 ] 
dist 107=[-.3412117761445981023 ,3.2015852745606643504 ] 
dist 108=[.21955885366655893736,3.2163260262971538071 ] 
dist 109=[.04099100616521401408,3.2165083763789717721 ] 
dist 110=[-.48394510884761834472,3.1766583878036853304 ] 
dist 111=[-.84169237919250945053,3.1628689106122403708 ] 
dist 112=[-1.1455204835911023549 ,3.1081910263566298150 ] 
dist 113=[-1.4552503853378169407 ,3.0943340405927052614 ] 
dist 114=[-1.7451174366673587492 ,2.9306416254213055804 ] 
dist 115=[-1.9696681216106945829 ,2.8907210673357957719 ] 
dist 116=[-2.1894178450412456290 ,2.8460303743771631780 ] 
dist 117=[-2.4601251224523496096 ,2.8243431591998603062 ] 
dist 118=[-2.7164527599377574461 ,2.2692526696410343596 ] 
dist 119=[-2.8788082409426975614 ,2.1919383504679579556 ] 
dist 120=[-3.0034463007700375457 ,2.0339959294848367183 ] 
dist 121=[-3.1092278953863767670 ,1.9903321582247324886 ] 
dist 122=[-3.1948099599111393804 ,1.8197269642454330702 ] 
dist 123=[-3.2388228949675700190 ,1.7827127473063099486 ] 
dist 124=[-3.2608181921623680395 ,1.7027130865004477112 ] 
dist 125=[-3.2614229363300714625 ,1.6784212486977159554 ] 
dist 126=[-.27146673641855777202,.18707622766519664617] 
dist 127=[-.36016000821183273503,.05544965481029081066] 
dist 128=[-.44521359298997910133,-.23701857145530485233] 
dist 129=[-.64499459921024383643,-.29102247491815615177] 
dist 130=[-.86281076395636724991,-.35141502927009031858] 
dist 131=[-1.0308002677621679073 ,-.33839289766960209789] 
dist 132=[-1.1946833188202683575 ,-.31707198916040497062] 
dist 133=[-1.3961148076564174246 ,-.28807497872835163443] 
dist 134=[-1.5870394241307761678 ,-.24788628447468690066] 
dist 135=[-1.7089786221564641785 ,-.18188596276427626584] 
dist 136=[-1.8039211834230323999 ,-.10428734221194286982] 
dist 137=[-1.8870657595925481608 ,-.01779716711412658010] 
dist 138=[-1.9564566649112185608 ,.09183836573088701054] 
dist 139=[-1.9964945345384108728 ,.26183417853534828133] 
dist 140=[-2.0228171223585501242 ,.43348734601177641129] 
dist 141=[-2.0374660515387416104 ,.54973955490945126889] 
dist 142=[-2.0440076590926311845 ,.64775485331891548946] 
dist 143=[-2.0487698339368460919 ,.7466068710501015305 ] 
dist 144=[-2.0487741972362796969 ,.83851697346365176643] 
dist 145=[-2.0435915682572033357 ,.90882048618059684585] 
dist 146=[-1.9947431428739263493 ,.97681409510260453276] 
dist 147=[-1.9791706334240195233 ,1.0595034892903678874 ] 
dist 148=[-1.9579672316852168553 ,1.1373469589337796644 ] 
dist 149=[-1.9482297422271227124 ,1.1859957293845555853 ] 
dist 150=[-1.6767886983048220155 ,1.2226106195076898855 ] 
dist 151=[-1.6368130661215768188 ,1.2524146973367528882 ] 
dist 152=[-1.5536276770520798797 ,1.3046538268073150123 ] 
dist 153=[-1.5294241175736479640 ,1.4587282530675076995 ] 
dist 154=[-1.4283209817432891174 ,1.6129376614019181861 ] 
dist 155=[-1.4067805844988694878 ,1.7518093973777501424 ] 
dist 156=[-1.3505836286553042317 ,1.9045951663699234726 ] 
dist 157=[-1.3377390727485211489 ,2.1165657238841155988 ] 
dist 158=[-.22092657641780668446,2.3222378540829463782 ] 
dist 159=[-.19409937906478796636,2.4498785741286029055 ] 
dist 160=[-.07788405191953073073,2.5449529078498819076 ] 
dist 161=[-.05673869297977100169,2.6206043333275307965 ] 
dist 162=[-.01099063966927528122,2.6780866449696236917 ] 
dist 163=[-.00103103549124137850,2.7006214911756375235 ] 
dist 164=[.04566002550716852021,2.7086662181623012768 ] 
dist 165=[.05159580324427392169,2.7082940743493707100 ] 
dist 166=[.04640812444177881001,2.6384234387409520267 ] 
dist 167=[.02467729697621650846,2.6202201450596274115 ] 
dist 168=[-.00606131482036729507,2.5746038330967703079 ] 
dist 169=[-.04721286410464301161,2.5561334309483777544 ] 
dist 170=[-.10392847617824626214,2.4567652328689893246 ] 
dist 171=[-.19680694237643151216,2.4319522461485939319 ] 
dist 172=[-.29263525772298953098,2.3739933438735281858 ] 
dist 173=[-.36112826060791601662,2.3530568166801264844 ] 
dist 174=[-.42279688291075535204,2.0634183994691691317 ] 
dist 175=[-.7370238876261806909 ,2.0546707707410099878 ] 
dist 176=[-1.0269334073966714451 ,2.0193320415631804282 ] 
dist 177=[-1.3096630088803268376 ,2.0118366739393454321 ] 
dist 178=[-1.5665380290352817720 ,1.9034749542908544474 ] 
dist 179=[-1.7532212305499949058 ,1.8773685542729377970 ] 
dist 180=[-1.9244583276295285995 ,1.8528528840226205055 ] 
dist 181=[-2.1196617512302714056 ,1.8410008469173399305 ] 
dist 182=[-2.2994427684040306782 ,1.4681976984082360557 ] 
dist 183=[-2.4091057079760699961 ,1.4169313141676030243 ] 
dist 184=[-2.4885240124972059327 ,1.3160298396987749396 ] 
dist 185=[-2.5475557732446096130 ,1.2890205635350346469 ] 
dist 186=[-2.5903788329820698897 ,1.2768228196232997678 ] 
dist 187=[-2.6050835811111050178 ,1.2745682595798540303 ] 
dist 188=[-2.6079856891385361797 ,1.1241843974712870464 ] 
dist 189=[-2.6036891602897830655 ,1.1130614692045817485 ] 
dist 190=[-1.4836217932747025877 ,.10026737103243008221] 
dist 191=[-1.5142631141601460690 ,.06493380467309685205] 
dist 192=[-1.5374821160778780603 ,-.1216620219371951531 ] 
dist 193=[-1.5464466067435767538 ,-.15360025400311932484] 
dist 194=[-1.5479915771886324447 ,-.2237696944952149025 ] 
dist 195=[-1.5457185030323658937 ,-.23639656184880138147] 
dist 196=[-1.5183719908123280994 ,-.33495606458379960916] 
dist 197=[-1.5157789723507049393 ,-.35147919822405688134] 
dist 198=[-1.6013532452734468478 ,-.35164459657716269351] 
dist 199=[-1.6504947208967275056 ,-.32954227284666328756] 
dist 200=[-1.6824228753914487408 ,-.29478716333981996545] 
dist 201=[-1.6992711054848652124 ,-.2444356980824440345 ] 
dist 202=[-1.7082558874089361413 ,-.05333298436079527369] 
dist 203=[-1.7087879449664267618 ,.28049137796054723555] 
dist 204=[-1.7038610715414833948 ,.6214159394969424997 ] 
dist 205=[-1.6996779823299778732 ,.84663667860100239381] 
dist 206=[-1.3904143270795433216 ,1.0305090443178112497 ] 
dist 207=[-1.3943372287397934267 ,1.2063469768443847380 ] 
dist 208=[-1.3930351746604214921 ,1.3638194227856729364 ] 
dist 209=[-1.3889731284573464347 ,1.4743658255920940464 ] 
dist 210=[-1.3804574056526496872 ,1.5718430537820706753 ] 
dist 211=[-1.3756469627862241026 ,1.6771348674261746092 ] 
dist 212=[-1.2397991073855313926 ,1.7721677121355445056 ] 
dist 213=[-1.2179289048263897816 ,1.8286856009329617321 ] 
dist 214=[-1.1712675181752968584 ,1.8678778692199833828 ] 
dist 215=[-1.1567496308344624122 ,1.8937389287250005937 ] 
dist 216=[-1.0915201985247051063 ,1.9097921989519430584 ] 
dist 217=[-1.0776267482575926049 ,1.9123072242011834804 ] 
dist 218=[-1.0365384121536049659 ,1.9048651043350980878 ] 

8 phat 4 dirichlet min maxes function [0, 0, 1, 0, 2, 2, 1, 0, 1] 
dist 0=[40.886296492532927228  ,40.886296492532927228  ] 
dist 1=[40.510727236940914346  ,41.506841007007453933  ] 
dist 2=[39.631599799013683041  ,42.189609859357030107  ] 
dist 3=[38.264229033732682130  ,42.575853824450431113  ] 
dist 4=[36.076755816599686604  ,42.819237553358614914  ] 
dist 5=[33.838676178600171917  ,42.931472212762973013  ] 
dist 6=[32.269100238135371109  ,42.986111157473946530  ] 
dist 7=[30.885156537752549401  ,42.999320868989945671  ] 
dist 8=[29.388113220469640638  ,42.850798935860329400  ] 
dist 9=[27.927933496879700979  ,42.793287033535560057  ] 
dist 10=[26.690935749439492787  ,42.733638853207207791  ] 
dist 11=[25.376358537239763985  ,42.658685899794328204  ] 
dist 12=[23.605848815095415026  ,42.566774985899791524  ] 
dist 13=[21.843219738771628100  ,42.479300798433196549  ] 
dist 14=[20.559855753443989390  ,42.369521877741386208  ] 
dist 15=[19.376169078925746841  ,42.126706643745120124  ] 
dist 16=[18.011346748899658158  ,31.601320162083562147  ] 
dist 17=[16.625649367501809914  ,30.677135094486956516  ] 
dist 18=[15.358109494954172862  ,28.427560510517329982  ] 
dist 19=[13.926505657283965620  ,28.086880768035410977  ] 
dist 20=[11.884413220333834908  ,24.738103964899151083  ] 
dist 21=[9.8668762117120908480 ,24.105430210541916777  ] 
dist 22=[8.5332620379488093942 ,23.356400203558996244  ] 
dist 23=[7.4362197403800621927 ,23.173897169691101001  ] 
dist 24=[6.3644226344579176010 ,18.586048684385297745  ] 
dist 25=[5.3814216782329406101 ,18.450803306183602430  ] 
dist 26=[4.6392672172727033823 ,16.445287013515255746  ] 
dist 27=[3.9254473154617130243 ,16.113424038561388584  ] 
dist 28=[3.0554508832632836853 ,14.600576617250190778  ] 
dist 29=[.69255048356963393627,13.371431665227729254  ] 
dist 30=[-2.0450411309495004455 ,12.876972006132619062  ] 
dist 31=[-3.8118184888209622022 ,12.764820354363944346  ] 
dist 32=[-5.2155520920533489016 ,3.8432529419465444472 ] 
dist 33=[-6.5022093548465043928 ,3.0820913939863000311 ] 
dist 34=[-7.6244551268104789321 ,2.2661000845087829767 ] 
dist 35=[-8.3712134020748252092 ,2.2599230160297297845 ] 
dist 36=[-8.9911305402168129190 ,2.3144157412374744375 ] 
dist 37=[-9.6067650446342046435 ,2.3811875141988958974 ] 
dist 38=[-10.148488807021632917  ,2.4247037152391544686 ] 
dist 39=[-10.472998646799687667  ,2.4565085371591139368 ] 
dist 40=[-10.703794553689417324  ,2.4771656733651271504 ] 
dist 41=[-10.870610357024359460  ,2.4915575284531608922 ] 
dist 42=[-10.985961464709287720  ,2.4986998074787761056 ] 
dist 43=[-11.010905375202145989  ,2.5007472601711770360 ] 
dist 44=[-10.994362673652247094  ,2.4964217553199953892 ] 
dist 45=[-10.961716416345016222  ,2.2826377958212950186 ] 
dist 46=[-10.794693795580001655  ,2.2461211486602625447 ] 
dist 47=[-10.783931307046152818  ,2.1938141320076717236 ] 
dist 48=[-7.1666633652234867883 ,2.1749953169625053558 ] 
dist 49=[-6.9334173059955186357 ,2.1260026466458371672 ] 
dist 50=[-6.3696363977718984417 ,2.1060677833887222856 ] 
dist 51=[-6.1548381604046700077 ,2.0775974932175719902 ] 
dist 52=[-5.2586788290077325774 ,2.0645613869397141163 ] 
dist 53=[-3.9950780578178368700 ,.76502589204473382041] 
dist 54=[-2.2757042769692001737 ,1.6922217184880635167 ] 
dist 55=[-2.0591040934369283317 ,2.3380712906803560156 ] 
dist 56=[-1.5594452042564120527 ,2.9024681357374498804 ] 
dist 57=[-1.4796841477039022621 ,3.5045674217974467793 ] 
dist 58=[-.89655500085903654909,4.0862986323096543370 ] 
dist 59=[-1.1028627638430772076 ,4.5694725238488448088 ] 
dist 60=[-1.3674065863071328713 ,5.0742397428813324260 ] 
dist 61=[-1.6231544293847927552 ,5.7423683720916655764 ] 
dist 62=[-1.7943602112261597912 ,6.3825081256337709138 ] 
dist 63=[-1.9365061611381794542 ,6.7755401637259871216 ] 
dist 64=[-2.0762696136972730839 ,7.0641123722301506493 ] 
dist 65=[-2.2039304572144897669 ,7.2870422548802317041 ] 
dist 66=[-2.2977778466067995132 ,7.4556293702596560362 ] 
dist 67=[-2.3849355290105432059 ,7.5271331670321138587 ] 
dist 68=[-2.4859127937161948836 ,7.5546148813452600074 ] 
dist 69=[-2.5770868189605381363 ,7.5473399501473072711 ] 
dist 70=[-2.6251110096379551286 ,7.2598946402328588120 ] 
dist 71=[-2.6508118664381090034 ,7.1963983292951678248 ] 
dist 72=[-2.6554395420264692720 ,7.0663948630166803450 ] 
dist 73=[-2.6456600217014238024 ,7.0206845999186326148 ] 
dist 74=[-2.6358741903375672519 ,6.7963015611218640620 ] 
dist 75=[-2.6184015483947516308 ,6.7430311393658457393 ] 
dist 76=[-2.6096836382698734252 ,6.5669509485352083096 ] 
dist 77=[-2.3292602348716471800 ,6.5378503458424287917 ] 
dist 78=[-2.2851497509225520520 ,4.1327555753952227522 ] 
dist 79=[-2.1927449798232092111 ,3.9331847551022383573 ] 
dist 80=[-2.1646563848877538804 ,3.4373613952734473546 ] 
dist 81=[-2.2140237521977799846 ,3.3651858009421504639 ] 
dist 82=[-2.8808467191880622808 ,2.6016351059572572108 ] 
dist 83=[-3.3775631583281303663 ,2.5544691114299369002 ] 
dist 84=[-3.8455188081091860967 ,2.8620786747770431482 ] 
dist 85=[-4.3975168124042879787 ,3.1605932781340262437 ] 
dist 86=[-4.9113160838892044232 ,3.3431458901914968153 ] 
dist 87=[-5.2267534259775620956 ,3.4758021039930718971 ] 
dist 88=[-5.4577365536548940217 ,3.5751261642136448088 ] 
dist 89=[-5.6343210410092444241 ,3.6494786231652926826 ] 
dist 90=[-5.7696147464963775845 ,3.6824516547203123168 ] 
dist 91=[-5.8357347743088150548 ,3.6937044459650601734 ] 
dist 92=[-5.8639347118395836254 ,3.6912034138020204286 ] 
dist 93=[-5.8656150113253623920 ,3.4854065315637134847 ] 
dist 94=[-1.8037191024276708252 ,3.4456411065465346246 ] 
dist 95=[-2.0716548762398370332 ,3.3721754089935232600 ] 
dist 96=[-2.2832630486060273840 ,3.3488517727018278597 ] 
dist 97=[-2.4738907982258806307 ,3.2471334173738365185 ] 
dist 98=[-2.6368760279268920481 ,3.2191344327209694683 ] 
dist 99=[-2.7381047755356669508 ,3.1471244411065085303 ] 
dist 100=[-2.8136855305028526886 ,3.1190951128898624178 ] 
dist 101=[-2.8742594019651266066 ,2.2223959021949986434 ] 
dist 102=[-2.9222986641939280905 ,2.1869951000047460187 ] 
dist 103=[-2.9478270493315297041 ,2.0919880747861225066 ] 
dist 104=[-2.9618293383239443131 ,2.0721492339182470828 ] 
dist 105=[-2.9638388261503329956 ,1.8920905178743116113 ] 
dist 106=[-2.9580208278601870279 ,1.8533502707507850543 ] 
dist 107=[-2.9508569574956708752 ,1.8010602276530527430 ] 
dist 108=[-2.9213718491223101696 ,1.7823060164842468496 ] 
dist 109=[-2.9070038453046615848 ,1.3564651127071222412 ] 
dist 110=[-2.4525497175878219897 ,1.2984682477464359153 ] 
dist 111=[-2.5580791830649293034 ,1.1738341688263232323 ] 
dist 112=[-2.6547248270993936677 ,1.1386651236025470854 ] 
dist 113=[-2.7339388342954047023 ,.99472572259478096542] 
dist 114=[-2.7767348845283364611 ,.96689811916220274889] 
dist 115=[-2.8010507409694410587 ,.89509582733650837799] 
dist 116=[-2.8064685248881009506 ,.88392358073702038761] 
dist 117=[-.88375418901428179911,.83289331148001864505] 
dist 118=[-1.1214824537008685830 ,1.1058128629793233462 ] 
dist 119=[-1.3143071049781552887 ,1.2936449016844341229 ] 
dist 120=[-1.4966098788699523055 ,1.4554076426476249742 ] 
dist 121=[-1.6584720089979912713 ,1.6242401637653527025 ] 
dist 122=[-1.7696862665918475824 ,1.7850253135186651338 ] 
dist 123=[-1.8652419807064954736 ,1.9146596483870857641 ] 
dist 124=[-1.9645871692283259302 ,2.0465261147661910240 ] 
dist 125=[-2.0528082292945022473 ,2.2162306265319385986 ] 
dist 126=[-2.1039501166017685230 ,2.3765800966728432465 ] 
dist 127=[-2.1377909829135734248 ,2.4710942946155342672 ] 
dist 128=[-2.1569357213678214663 ,2.5356502375415606544 ] 
dist 129=[-2.1661855402726878043 ,2.5763771046137321571 ] 
dist 130=[-2.1659150226974157470 ,2.6035351404859083585 ] 
dist 131=[-2.1510151844616833098 ,2.6139089081113399595 ] 
dist 132=[-2.1449374661330456912 ,2.6139995401303245147 ] 
dist 133=[-1.5382242428956103207 ,2.6101878670509350684 ] 
dist 134=[-1.4777132140311168463 ,2.4014375013023719533 ] 
dist 135=[-1.3313786295514905815 ,2.3666115031472981631 ] 
dist 136=[-1.3037891003346698746 ,2.3008252351436614573 ] 
dist 137=[-1.0851412827664329250 ,2.2813402832598740394 ] 
dist 138=[-1.0426573125800262564 ,2.2015804925492606159 ] 
dist 139=[-.97763146076997443692,2.1805431020929462764 ] 
dist 140=[-.9593134146641635831 ,2.1320035993490787636 ] 
dist 141=[-.60200323102102359216,2.1145236029413969367 ] 
dist 142=[-.55508268306299859127,1.0880278561991404881 ] 
dist 143=[-.44726968687878204335,1.0930124797732503094 ] 
dist 144=[-.42630552577353136973,1.2402545147495228336 ] 
dist 145=[-.65934461438186873843,1.3840523687580507637 ] 
dist 146=[-.87657148065453282728,1.5057357287169184434 ] 
dist 147=[-1.0371536596852236466 ,1.6346923096106264659 ] 
dist 148=[-1.1872425046000964147 ,1.8075321467134075620 ] 
dist 149=[-1.3625734310487968031 ,1.9731960097488284203 ] 
dist 150=[-1.5260906399826057247 ,2.0735024906732175931 ] 
dist 151=[-1.6290087723593395582 ,2.1452764069213003847 ] 
dist 152=[-1.7073992759919169532 ,2.1970202886142296679 ] 
dist 153=[-1.7729780605077877369 ,2.2347749283819448570 ] 
dist 154=[-1.8254078432652135628 ,2.2506939987175878774 ] 
dist 155=[-1.8512937079691682354 ,2.2548284768469162623 ] 
dist 156=[-1.8637852270833197606 ,2.2526531876858974441 ] 
dist 157=[-1.8650084351476670004 ,2.1163847550334713163 ] 
dist 158=[-.92934203703503591038,2.0912598283690020271 ] 
dist 159=[-1.0001814772182964407 ,2.0434367519401721976 ] 
dist 160=[-1.0549359039646204823 ,2.0283878393170541557 ] 
dist 161=[-1.1021666407915187076 ,1.9626112233655041857 ] 
dist 162=[-1.1410250606397241909 ,1.9454401365301157460 ] 
dist 163=[-1.1623505570707406133 ,1.9001565482267281828 ] 
dist 164=[-1.1749453680900135970 ,1.8837485871841821215 ] 
dist 165=[-1.1789439656264329498 ,1.0673689282851617645 ] 
dist 166=[-1.1785887004381342009 ,1.0029842055412090723 ] 
dist 167=[-1.1759795533769386614 ,.84654380177810719779] 
dist 168=[-1.1672067350219271048 ,.82207362168913823543] 
dist 169=[-1.1620045110442285668 ,.59210338583018521627] 
dist 170=[-1.1291617940269611387 ,.5888076724629747623 ] 
dist 171=[-1.1200596519553268130 ,.7438783627309391671 ] 
dist 172=[-1.2450672349873029960 ,.9257549933735573661 ] 
dist 173=[-1.3888891913579758089 ,1.1920792126225922606 ] 
dist 174=[-1.4791566724551803238 ,1.4553356659101360926 ] 
dist 175=[-1.5475941731726008543 ,1.6249650340037616535 ] 
dist 176=[-1.6042560318356325089 ,1.7587039865570614631 ] 
dist 177=[-1.6490899540544088294 ,1.8786671830641607177 ] 
dist 178=[-1.6703018652640457948 ,1.9807745912584043190 ] 
dist 179=[-1.6800602257570449628 ,2.0432245856767966306 ] 
dist 180=[-1.6800657061594404402 ,2.0886675984542459834 ] 
dist 181=[-1.5403128130560927040 ,2.1228762284936955164 ] 
dist 182=[-1.5644218787272749135 ,2.1479039758245797448 ] 
dist 183=[-1.5748595157320970434 ,2.1566918883630668097 ] 
dist 184=[-1.5772750925547575021 ,2.1560076931913005737 ] 
dist 185=[-1.5758701841133154444 ,2.1525856505961452725 ] 
dist 186=[-1.5569190686344112338 ,2.1185070240906552747 ] 
dist 187=[-1.5497501165083913163 ,2.1070936213600075117 ] 
dist 188=[-1.5263666817390705109 ,2.0738735104130284178 ] 
dist 189=[-1.5168497265552134513 ,2.0591277363478315259 ] 
dist 190=[-1.3915137195167663123 ,1.3495869161538988220 ] 
dist 191=[-1.3694669776441003071 ,1.2780447034822841607 ] 
dist 192=[-1.3153029202982584403 ,1.1055119319774658304 ] 
dist 193=[-1.2993029764828000193 ,1.0760332005587761674 ] 
dist 194=[-1.2073367344238152244 ,.90381109687340890689] 
dist 195=[-1.1868728758597864685 ,.8917171495520741742 ] 
dist 196=[-1.1471022711271750899 ,1.1227122708090292172 ] 
dist 197=[-1.2076909143682723602 ,1.3681288400506597417 ] 
dist 198=[-1.2793013631378269023 ,1.5265672994384930535 ] 
dist 199=[-1.3369626970376549000 ,1.6518168705319610196 ] 
dist 200=[-1.3907419079468012257 ,1.7647281490462959670 ] 
dist 201=[-1.4379685800376064781 ,1.8612241465875918683 ] 
dist 202=[-1.4694694475694727237 ,1.9209367290995939669 ] 
dist 203=[-1.4955098812993838904 ,1.9652120952666335498 ] 
dist 204=[-1.5209354067842994189 ,2.0000766866302217018 ] 
dist 205=[-1.5417209132799538421 ,2.0261749696497293595 ] 
dist 206=[-1.5492364163195835473 ,2.0354509816625881909 ] 
dist 207=[-1.5496542245811595169 ,2.0355766911574814526 ] 
dist 208=[-1.5470397601880391544 ,2.0321287512325768192 ] 
dist 209=[-1.5201398903302366993 ,1.9973431603725777180 ] 
dist 210=[-1.5110285745768035790 ,1.9856437471069478179 ] 
dist 211=[-1.5331279597115537586 ,1.9562480032627944199 ] 
dist 212=[-1.5812065878312307970 ,1.9437551976456756730 ] 
dist 213=[-1.6303776451267670910 ,1.6715584989838186513 ] 
dist 214=[-1.6720369637638625085 ,1.7249975401548694464 ] 
dist 215=[-1.6901254730794578764 ,1.7547911200814141886 ] 
dist 216=[-1.6977665686584600567 ,1.7729925702518735846 ] 
dist 217=[-1.6977115511441492995 ,1.7801524129818085154 ] 
dist 218=[-1.6638857102508930194 ,1.7800789661923051123 ] 
dist 219=[-1.6527325386414555456 ,1.7775113475788402534 ] 
dist 220=[-1.6438728094165148971 ,1.7576173048259294548 ] 
dist 221=[-1.6358121655764595444 ,1.7531125263938853281 ] 
dist 222=[-.8139246061639597281 ,.76783865540845872817] 
dist 223=[-.7424706812044648757 ,.71820501616298345399] 
dist 224=[-.7282166584537719556 ,.70400550003994898848] 
dist 225=[-.68554694406385163385,.63678773922504126617] 
dist 226=[-.64203397023293903229,.6229702325492216954 ] 
dist 227=[-.63194615712511587685,.59194470441039420357] 
dist 228=[-.7953707086165907464 ,.60550412214057387457] 
dist 229=[-.9777107813832179688 ,.85137299402350647188] 
dist 230=[-1.0978205408948681044 ,1.0176762397410114089 ] 
dist 231=[-1.1954857002032975449 ,1.1514671387898901987 ] 
dist 232=[-1.2882167336158929541 ,1.2760636270114700726 ] 
dist 233=[-1.3708095132342583509 ,1.3853650890905670199 ] 
dist 234=[-1.4279984291467843580 ,1.4580926101331662071 ] 
dist 235=[-1.4776004616841441545 ,1.5180301419588530000 ] 
dist 236=[-1.5299037605787544185 ,1.5762689489565926926 ] 
dist 237=[-1.5751499114624783407 ,1.6263817673229374230 ] 
dist 238=[-1.5965768163502721244 ,1.6538773231386973203 ] 
dist 239=[-1.6066125046188789419 ,1.6700943224216711547 ] 
dist 240=[-1.6066490341294914818 ,1.6751791898476292737 ] 
dist 241=[-1.5845070770138629932 ,1.6737184238102184196 ] 
dist 242=[-1.5753248864409158601 ,1.6704379890579232286 ] 
dist 243=[-1.5666263168112582407 ,1.6526124664816771816 ] 

8 phat 4 dirichlet min maxes function [1, 1, 0, 0, 2, 0, 1, 0, 1] 
dist 0=[46.742238252451022810  ,46.742238252451022810  ] 
dist 1=[46.569715401667554044  ,46.885219051901219120  ] 
dist 2=[46.344084736936227831  ,47.033691875567770839  ] 
dist 3=[45.909042833869576445  ,47.227955745641100341  ] 
dist 4=[44.895266746379503025  ,47.402805387702415632  ] 
dist 5=[43.656138236133766796  ,47.473775707431114432  ] 
dist 6=[42.249753594860611917  ,47.481782382560164352  ] 
dist 7=[40.447348164786291967  ,47.435021661741825153  ] 
dist 8=[37.626261342383628837  ,47.280456290879802009  ] 
dist 9=[34.749775118289678483  ,47.198444352869290970  ] 
dist 10=[32.726001127564739593  ,46.909236579017423190  ] 
dist 11=[30.933193582482619142  ,46.789010746760341861  ] 
dist 12=[28.979128602397346198  ,45.935817577743961410  ] 
dist 13=[27.063219188024744646  ,45.189844386527388172  ] 
dist 14=[25.422671829856333457  ,34.039595862979381432  ] 
dist 15=[23.663816496810375565  ,33.708700302146207638  ] 
dist 16=[21.275044249076552629  ,30.292849471045194244  ] 
dist 17=[18.888531542995558127  ,29.636505295381457873  ] 
dist 18=[17.138546542984108466  ,28.897293114113852326  ] 
dist 19=[15.512810053591934638  ,28.725782288513451602  ] 
dist 20=[13.622424211121728603  ,22.523680310930117929  ] 
dist 21=[11.696497895283190565  ,21.735245456657364456  ] 
dist 22=[9.9284848948147755843 ,20.156129089251137874  ] 
dist 23=[7.9290298258369675288 ,19.749171189516673823  ] 
dist 24=[5.0778633088766673682 ,18.301739805740780003  ] 
dist 25=[2.2632741367883748966 ,17.988843843940327773  ] 
dist 26=[.4098837539521264971 ,17.519159326210539069  ] 
dist 27=[-1.1035544847303237332 ,17.387350095182981295  ] 
dist 28=[-2.5595897035431049285 ,15.571510580393315102  ] 
dist 29=[-3.8764246070365071928 ,14.162866062338496856  ] 
dist 30=[-4.8336436279429031117 ,2.6063258624263329568 ] 
dist 31=[-6.2166488511703767758 ,2.2517634627710092358 ] 
dist 32=[-7.6403322222247976461 ,-.4550639828722050115 ] 
dist 33=[-8.9542619508237607360 ,-.91874166882559824485] 
dist 34=[-10.106349719871197440  ,-1.6469080954365221586 ] 
dist 35=[-10.883336296304507015  ,-1.8161701187456852754 ] 
dist 36=[-11.539567556720890831  ,-4.3096013535692956748 ] 
dist 37=[-12.209361808044819783  ,-4.0116078091140046966 ] 
dist 38=[-12.792940431280202152  ,-3.3261094140107519411 ] 
dist 39=[-13.104643820630610454  ,-2.4034606323266215774 ] 
dist 40=[-13.280126942238729954  ,-.91773767738543867483] 
dist 41=[-13.319091154910113280  ,.59770027665880025653] 
dist 42=[-13.304345177243820194  ,1.6390808375056803468 ] 
dist 43=[-13.265064805274933049  ,2.5318157276442495388 ] 
dist 44=[-13.201260399937569051  ,3.4541963937972529815 ] 
dist 45=[-13.156941346056781295  ,4.3243948104582476741 ] 
dist 46=[-10.307849756664902467  ,5.0089437715965405210 ] 
dist 47=[-9.9902856737495249033 ,5.6883031841762076909 ] 
dist 48=[-9.1940817515329056549 ,6.5378281655897508440 ] 
dist 49=[-9.0584122567652601879 ,7.3477495166862502791 ] 
dist 50=[-7.7870475163865596113 ,7.8690501853144827676 ] 
dist 51=[-7.5377029919483186484 ,8.2785059614629852146 ] 
dist 52=[-7.2147878424921767927 ,8.6420181482098088518 ] 
dist 53=[-7.1041582640233105116 ,8.9477231857907641056 ] 
dist 54=[-4.8063172321922622188 ,9.1264141892617733929 ] 
dist 55=[-4.5067042843365712068 ,9.2458446591508657346 ] 
dist 56=[-4.3263861494186589184 ,9.3149131564388442408 ] 
dist 57=[-3.6987082788702110226 ,9.3475584236765453185 ] 
dist 58=[-3.0072270441169257799 ,9.3365003434439632754 ] 
dist 59=[-2.8775385309875278797 ,9.2726589999164859659 ] 
dist 60=[-2.5805660966761292861 ,9.2255358844344619510 ] 
dist 61=[-2.5203983002809561880 ,8.8810719814662766070 ] 
dist 62=[-1.1118123871505475756 ,2.8124276932953503267 ] 
dist 63=[-1.0796752188457494084 ,3.2116932463912523970 ] 
dist 64=[-.85593127054526856439,3.5634486656458507665 ] 
dist 65=[-.81265980330673910017,3.8018769767004522559 ] 
dist 66=[-.74085485437673680323,4.0039215787271283289 ] 
dist 67=[-.72248608096796287661,4.2104364683370211107 ] 
dist 68=[-.36978651067103737516,4.3919478867526115576 ] 
dist 69=[-.32099960548393178999,4.4941223065442505195 ] 
dist 70=[-.21147619296815248751,4.5583878238652489294 ] 
dist 71=[-.18435897265176442542,4.5883968837346098743 ] 
dist 72=[-.04136396891289578365,4.5993310906810669451 ] 
dist 73=[-.01324667819881427797,4.5942548649231560360 ] 
dist 74=[.04567588722716419846,4.5668848794238550459 ] 
dist 75=[.06264316521796636167,4.5478058899111343449 ] 
dist 76=[.68089239756581994251,3.5862091324151267527 ] 
dist 77=[.41238427621878189876,3.4680779544011548636 ] 
dist 78=[.16872085028970278711,3.4367044226790192452 ] 
dist 79=[-.10353353220181606864,3.3669624292859671968 ] 
dist 80=[-.48621127680569356275,3.3416546715702623083 ] 
dist 81=[-.87242748820218660544,2.9427930171032771798 ] 
dist 82=[-1.1588283048129633027 ,2.8812717335177604263 ] 
dist 83=[-1.4272163567065949028 ,2.7279605366055548143 ] 
dist 84=[-1.8191760626039066405 ,2.6937239149809471817 ] 
dist 85=[-2.1231817837488181549 ,2.4408029396988420279 ] 
dist 86=[-2.3883395036151666411 ,2.3881261107050189370 ] 
dist 87=[-2.6815361564670079586 ,2.3020007235894492776 ] 
dist 88=[-3.1441827928335885033 ,2.2777726772126740508 ] 
dist 89=[-3.5967780533015737457 ,.2160767348500208848 ] 
dist 90=[-3.8843487956753769591 ,.17512081183784218754] 
dist 91=[-4.1065240264161042802 ,.16640424061374554339] 
dist 92=[-4.2980198879312965053 ,.38949567251627597937] 
dist 93=[-4.4555067132654254989 ,.61499418638502121972] 
dist 94=[-4.5419009281106230229 ,.81925839947164711799] 
dist 95=[-4.5929373062206221576 ,1.0480141037462712065 ] 
dist 96=[-4.6092661175196462542 ,1.2751021795219610419 ] 
dist 97=[-4.6072535544717380095 ,1.4727226917463569456 ] 
dist 98=[-4.5969550880940210963 ,1.6867083730147403604 ] 
dist 99=[-4.5564838544007379142 ,1.9791376853837095014 ] 
dist 100=[-4.5326379276489987185 ,2.2705727588317318075 ] 
dist 101=[-4.3824539296118747598 ,2.4805977620392422661 ] 
dist 102=[-4.3409543630805359790 ,2.6713560784845300346 ] 
dist 103=[-4.2603514229665040776 ,2.8858917338272888031 ] 
dist 104=[-4.2327020866824003126 ,3.0995135877843344600 ] 
dist 105=[-2.8018554978615581753 ,3.2866340467730458738 ] 
dist 106=[-2.6493273186529019609 ,3.4903663190657194574 ] 
dist 107=[-2.2927057930560005156 ,3.7703190949756060669 ] 
dist 108=[-2.2218950227109300614 ,4.0398932208381638717 ] 
dist 109=[-1.7320669846621991934 ,4.2021945626210702280 ] 
dist 110=[-1.6397214474365453111 ,4.3171658260889070137 ] 
dist 111=[-1.4762341904325424529 ,4.3977836678198016185 ] 
dist 112=[-1.4381795565282370958 ,4.4521374522515246635 ] 
dist 113=[-.78435172384385326051,4.4631641166101697173 ] 
dist 114=[-.69641136585602927576,4.4566360426928738306 ] 
dist 115=[-.49584089826699256455,4.4481720049995054988 ] 
dist 116=[-.45796879279886240822,4.2236381399761200360 ] 
dist 117=[-.20493210379191200042,4.1784395509729853297 ] 
dist 118=[-.15981841559818269528,4.0682429095124555496 ] 
dist 119=[-.07748907377877814131,3.9487757032963142246 ] 
dist 120=[-.05892051034250599140,3.5231578276225442123 ] 
dist 121=[.19134195634818791094,1.1769305424855788672 ] 
dist 122=[.20376185967046908349,1.1841869544138739235 ] 
dist 123=[.00143747767918533437,1.1911003295395493142 ] 
dist 124=[-.20322246812886058714,1.1933527596192935393 ] 
dist 125=[-.34204942581470590774,1.1922621057374155692 ] 
dist 126=[-.45928314156622247087,1.1808015985237958402 ] 
dist 127=[-.57775297904144132948,1.1775083163258752997 ] 
dist 128=[-.68799775405645682714,1.1255062270502858820 ] 
dist 129=[-.77240082451541154526,1.1121328735410526757 ] 
dist 130=[-.85406939990360612134,1.0996498512735069976 ] 
dist 131=[-.95339929163422463916,1.0924144275958214146 ] 
dist 132=[-1.0468458108242527448 ,.88749453666139456033] 
dist 133=[-1.1050299949184249612 ,.85890376861808400605] 
dist 134=[-1.1485436516765944535 ,.80232074505877885256] 
dist 135=[-1.1834302686654958152 ,.78700132489723161258] 
dist 136=[-1.2101073600754770886 ,.72953733317200923245] 
dist 137=[-1.2208507232592800554 ,.7161452966184190705 ] 
dist 138=[-1.2244552435290366357 ,.69109643910465667954] 
dist 139=[-1.2226381191343332969 ,.68411820386715014087] 
dist 140=[.07051097649972859528,.36082809639367382624] 
dist 141=[-.03750846246060496318,.31221437542277321592] 
dist 142=[-.13080981470973920248,.30262548712796643529] 
dist 143=[-.2285845588778173696 ,.28490689646072001691] 
dist 144=[-.32190672217773486947,.28035707548407372706] 
dist 145=[-.39743260873431322296,.20552625678170588803] 
dist 146=[-.47449286027392644696,.1952317929662690798 ] 
dist 147=[-.57394416005074084161,.16981944272428344782] 
dist 148=[-.67057128791388509298,.16595458305968801207] 
dist 149=[-.73635711798297021552,.12718491581899415354] 
dist 150=[-.79224722597383755761,.11983671230724785046] 
dist 151=[-.84936572747101540293,.11110895642216425113] 
dist 152=[-.90301579357998092584,.10896610520386646361] 
dist 153=[-.94505983323425476346,-.18198512234198710301] 
dist 154=[-.98673243863285317455,-.10859305721874330427] 
dist 155=[-1.0389044458313404693 ,.00916606016753615917] 
dist 156=[-1.0869811269433389764 ,.1296972784292983492 ] 
dist 157=[-1.1123027583571668633 ,.21415715481703013225] 
dist 158=[-1.1264575457245641114 ,.28845205035864166124] 
dist 159=[-1.1299398526808744620 ,.36840294489444174003] 
dist 160=[-1.1242999299758175393 ,.44597046956442845877] 
dist 161=[-1.1227864462111753265 ,.5107511772622121115 ] 
dist 162=[-1.1218367711771676180 ,.57864306078359435623] 
dist 163=[-1.1214152634331225532 ,.66863279753884734284] 
dist 164=[-.95831352316775148732,.75713949952539255994] 
dist 165=[-.93519506218981456681,.81911123971983165488] 
dist 166=[-.89427619463379118848,.87358258313624290052] 
dist 167=[-.88382684077830312632,.93214570027116335085] 
dist 168=[-.85007399363527365323,.98894012248907282303] 
dist 169=[-.83943209678604984362,1.0363510195031767555 ] 
dist 170=[-.83259222473148002319,1.0860277807201732035 ] 
dist 171=[-.8304394870230263284 ,1.1518700874168983251 ] 
dist 172=[-.48673039901490373111,1.2144541537227309841 ] 
dist 173=[-.43349908623667524801,1.2511227200401995741 ] 
dist 174=[-.42249397976543614208,1.2758743471743917435 ] 
dist 175=[-.40976581871524608246,1.2908795948384632688 ] 
dist 176=[-.40510423301922408318,1.2995255828463690700 ] 
dist 177=[-.28676769864389916207,1.3000961817803879381 ] 
dist 178=[-.27108610825764290524,1.2948627839834980849 ] 
dist 179=[-.23887602405943164226,1.2899889285965846139 ] 
dist 180=[-.23022678391887565914,1.2112311117323307966 ] 
dist 181=[-.19746524148185214283,1.1964787992697330471 ] 
dist 182=[-.19062174504362181994,1.1613045267666434939 ] 
dist 183=[-.17695258114088597303,1.1489822114770154145 ] 
dist 184=[-.17323459244716845859,1.0883390163257460245 ] 
dist 185=[.03827436981013799733,1.0742460985498536686 ] 
dist 186=[.04932618487593332602,1.0425007363728477172 ] 
dist 187=[-.05373858143027066849,1.0317790147568181718 ] 
dist 188=[-.31166403656846058921,.98642834888295500749] 
dist 189=[-.48195115164444267379,1.0009998702376116894 ] 
dist 190=[-.62085692433986741838,1.0079880112995567432 ] 
dist 191=[-.75349082577876261394,1.0089702457029816308 ] 
dist 192=[-.872132119305821721  ,1.0008862165676239502 ] 
dist 193=[-.9551715047296023972 ,.99639083753635388305] 
dist 194=[-1.0281338586733228137 ,.98840550064697384367] 
dist 195=[-1.1065414892834802835 ,.9848482339930285506 ] 
dist 196=[-1.1778483685858322763 ,.87570180118608971505] 
dist 197=[-1.2224607279317945254 ,.8587199348281048788 ] 
dist 198=[-1.2561125233558048726 ,.82277905096256410542] 
dist 199=[-1.2836597455684471287 ,.81185407970691472939] 
dist 200=[-1.3052107775131367476 ,.76382842285943778378] 
dist 201=[-1.3149230209437230256 ,.75372542775123194084] 
dist 202=[-1.3178329635658090584 ,.72404776586215153528] 
dist 203=[-1.3169169354534792111 ,.71950065081630654126] 
dist 204=[-.29201473803618813995,.58173629558416276039] 
dist 205=[-.33558630037589208111,.58071449255791045896] 
dist 206=[-.37035214845602636568,.57940137352003532298] 
dist 207=[-.4053740364858133097 ,.5774494326053054645 ] 
dist 208=[-.4499678735184449411 ,.57548262222240188887] 
dist 209=[-.49300195169162592213,.50710109141049067557] 
dist 210=[-.52179622600748187205,.49668709959339746694] 
dist 211=[-.54571220884225563747,.47666935806332815936] 
dist 212=[-.56926885411749215893,.47101834671674751034] 
dist 213=[-.59082955783420010104,.44895384232726282942] 
dist 214=[-.6067763910043431218 ,.44338756000428056434] 
dist 215=[-.62168666687268268721,.43176883892758640524] 
dist 216=[-.63910872407297057082,.42796230462894885144] 
dist 217=[-.6546605804297700323 ,.12209612236349614817] 
dist 218=[-.66210376503433509523,.09528327956074756559] 
dist 219=[-.66523232316496225746,.03481429500093005836] 
dist 220=[-.6653324989165642777 ,.02361512522822259114] 
dist 221=[-.65827523689055260524,-.04966221166281428642] 
dist 222=[-.65510054616058715476,-.06236090612665577595] 
dist 223=[-.64851249961855831673,-.08598039484938223413] 
dist 224=[-.64562265536669888356,-.05946383002917404911] 
dist 225=[-.57738130778359160702,-.02428858068057666251] 
dist 226=[-.56659397145724868316,.01454340482087290807] 
dist 227=[-.54269249798266041732,.06858744493194478089] 
dist 228=[-.53517834296995799427,.12294765820952891311] 
dist 229=[-.50111777526262240325,.16304216241850783886] 
dist 230=[-.49379365717384562717,.20041759520275572301] 
dist 231=[-.47493504518191282607,.24392187526464675248] 
dist 232=[-.47011175553433766471,.28810710871689379559] 
dist 233=[-.20862851984546720704,.32820153658639717967] 
dist 234=[-.20122647663724019953,.37303383788933355577] 
dist 235=[-.19567612954294950307,.43613592801203827842] 
dist 236=[-.1948677238028245289 ,.49794420053375580016] 
dist 237=[-.18081918315944921251,.53761083920409870113] 
dist 238=[-.17765225349352586346,.56870611926587655083] 
dist 239=[-.17520850492986500932,.59629206211325761558] 
dist 240=[-.1746546096896953722 ,.61955366145208203856] 
dist 241=[-.13109071962968915304,.63338344432679771534] 
dist 242=[-.12536117238296596864,.6429707046812002511 ] 
dist 243=[-.11445697144775834373,.64929356725445084362] 
dist 244=[-.11167673041189651092,.65302606112565891175] 
dist 245=[-.10228089023085971464,.65316165226308309053] 
dist 246=[-.09988841269668094888,.65000712771260261038] 
dist 247=[-.09766406505341203995,.64212661560835058568]