

q=10000
J0.sort()
J12.sort()
J23.sort()
J34.sort()
 
# segments incompatibles avec carac. Lipshitz
def blu(i):
    for j in range(len(i)-1):
        x=i[j][0]/q        
        y=i[j+1][0]/q
        dx=i[j][2]
        dy=i[j+1][2]
        a=pi/y^2/sqrt(3)
        if abs((dx-dy)/(x-y))>a:
            print('pb sur [%d,%d]'%(i[j][0],i[j+1][0]))

# corrige via carac. Lipshitz
def blo(i):
    corr=false
    for j in range(1,len(i)-1):
        z=min(i[j-1][2]+1/q*pi/sqrt(3)/(i[j][0]/q)^2, i[j+1][2]+1/q*pi/sqrt(3)/(i[j+1][0]/q)^2)
        z=z.n(digits=29)
        if i[j][2]>z:
            i[j][2]=z
            corr=true
    return corr

# dessin qui utilise caractère Lipshitz

def bla(i):
    g=Graphics()
    for j in range(len(i)-1):
        x=i[j][0]/q
        y=i[j+1][0]/q
        dx=i[j][2]
        dy=i[j+1][2]
        a=pi/y^2/sqrt(3)
        z=(x+y)/2+1/a*(dy-dx)
        t=dx+(z-x)*a
        g+=line([(x,dx),(z,t),(y,dy)])
    return g
    
g=points([(i[0]/1000,i[1]) for i in J0],color='black')
g=points([(i[0]/1000,i[2]) for i in J0],color='red')
g+=plot(density,0.106,0.445,color='darkgreen')
g+=plot(df,0.106,0.445)

g=points([(i[0]/10000,i[2]) for i in J34+J23+J12+J0],color='red')
g+=plot(density,0,1,color='darkgreen')
g+=plot(df,1e-5,rb1)
g+=plot(db,rb1,rb2)


# J34=[6269, 6469] -> 42 min.
# J23=[5146, 5666] -> 98 min.
# J12=[4532, 4917] -> 97 min.
J0 315 445 1000 -> 41 min
J0 250 314 1000 -> 46 min
J0 150 249 1000 -> 162 min
J0 106 149 1000 -> 12h ; Florian rejoint à 110


J0=
[[1060, 0.96034613113961475594493322205, 0.96454748634751474867243814515],
 [1070, 0.96052911107038174698402599461, 0.96429071027802581994592401316],
 [1080, 0.95961950894569070236173047306, 0.96403510810622972115879747435],
 [1090, 0.95949599395775986288015246828, 0.96378067350870733065448803245],
 [1100, 0.95959415272919745820701109551, 0.96352740020430016620878177491],
 [1110, 0.95880799890859425005373850581, 0.96320461891176956115145912918],
 [1120, 0.95813762914362676781365735224, 0.96279267552954450604119074342],
 [1130, 0.95849713867843866488271942217, 0.96233867987409926758601841357],
 [1140, 0.95814500810007363629239307556, 0.96181982740247984331460884277],
 [1150, 0.95728709112860232988140296584, 0.96141921912275862815988602961],
 [1160, 0.95684033535460566444186270019, 0.96101520923063099566263645102],
 [1170, 0.95660465260086968708463928124, 0.96064199888666146343041418732],
 [1180, 0.95574195075907775187573633957, 0.96017656327580247488384657118],
 [1190, 0.95592377507312942253037135742, 0.95956032484958520001327997306],
 [1200, 0.95591758924805403374591605825, 0.95926716493573893629331905686],
 [1210, 0.95622700994281140118857820198, 0.95903925910778065055950492024],
 [1220, 0.95558744318740940215661794355, 0.95848895689688662358207693615],
 [1230, 0.95505716377299931796329701683, 0.95782754748516718557027616043],
 [1240, 0.95484295219051795733378185105, 0.95743512613704473412923334763],
 [1250, 0.95380058945843204654124747321, 0.95709276828867573261305778942],
 [1260, 0.95317926635243777067074688603, 0.95683489018635559109071664352],
 [1270, 0.95297343310289983620009479637, 0.95620836616807280972096805272],
 [1280, 0.95311367358548337858081822560, 0.95570447652881984623718381045],
 [1290, 0.95892779708736741728358765613, 0.95892779708736741728358765613],
 [1300, 0.95380585647318916198145188901, 0.95508632261060744106373476825],
 [1310, 0.95347115231077472774501302410, 0.95476091591179557127588850562],
 [1320, 0.95286223030701810987608268988, 0.95459207551552183179666144497],
 [1330, 0.95199525732098044805695735704, 0.95414836125507385133914795006],
 [1340, 0.95111018575506556249621326060, 0.95375471659204491547967563747],
 [1350, 0.95012056239826447878726867202, 0.95337641988400367853984107569],
 [1360, 0.94982352998454266934658107857, 0.95281079322798101216562827176],
 [1370, 0.95020378442437958277366760740, 0.95254682040489679906158926315],
 [1380, 0.95059816578203704118266159639, 0.95253303947322565115030101879],
 [1390, 0.95098819991279515129178889765, 0.95254387866230771919617836829],
 [1400, 0.95137391720249742110837587461, 0.95258241511060959272327863801],
 [1410, 0.95176741313593082871591377625, 0.95266213133565214032927315202],
 [1420, 0.95136376673906986045636813287, 0.95232283365297099031465677399],
 [1430, 0.95056818825322364485685966429, 0.95183065309241821072561151596],
 [1440, 0.94980260373751934643848926498, 0.95136631448908359764971010009],
 [1450, 0.94904295112740566509046402644, 0.95088159809531791477610340735],
 [1460, 0.94828919221373153547460788104, 0.95044935013455811301241737965],
 [1470, 0.94754128904674950195641258688, 0.94998849774760041331234106110],
 [1480, 0.94754772704862433307937408244, 0.94973829017708599753433418300],
 [1490, 0.94792590771566287433103070725, 0.94981693389061949694962549984],
 [1510, 0.94880831535083565153598783581, 0.94997104550786770627013311241],
 [1520, 0.94917349658629002195908697104, 0.95005244791190046615980691058],
 [1530, 0.94958036366147102746992914035, 0.95011368838225085386994805958],
 [1540, 0.95007388744108389744269516086, 0.95025324631666219232783987536],
 [1550, 0.95006334395815117410677430598, 0.95015120845387346371069270390],
 [1560, 0.94923654746005414750698037096, 0.94964914264084576700497564161],
 [1570, 0.94842184791215755623738914437, 0.94910449566071697358182746029],
 [1580, 0.94759955151686225960361298348, 0.94861094017996117067070827034],
 [1590, 0.94680600043670515297833389923, 0.94805340356836198534296045182],
 [1600, 0.94598541617688680638309506321, 0.94762437891843920301226944503],
 [1610, 0.94521547409239303760841721669, 0.94722593909787489163676355020],
 [1620, 0.94438564539495306604521829286, 0.94673543510431235059598975567],
 [1630, 0.94364994580161110082627828888, 0.94642490646192400927105836672],
 [1640, 0.94374242179979395128697206019, 0.94646673308418083347959282037],
 [1650, 0.94409360682756326976772243142, 0.94636837180130228830421401654],
 [1660, 0.94443554071097968183323700941, 0.94634967259766711311641529392],
 [1670, 0.94479519246303156343458340416, 0.94643615350244236772425665549],
 [1680, 0.94438045844822704477650177069, 0.94606412879531232018592845634],
 [1690, 0.94353186980355874258208359606, 0.94549403664504461097806142789],
 [1700, 0.94269006267961141798394919533, 0.94510338171220598102451049272],
 [1710, 0.94185499377234849216478096423, 0.94474140493360669879052693432],
 [1720, 0.94102662006375714653927389009, 0.94425047649520787995669479642],
 [1730, 0.94020489881966118339562399342, 0.94369095300755445610008109725],
 [1740, 0.93938978758755353748455263485, 0.94319913576105074426436658541],
 [1750, 0.93878869356908456467181167682, 0.94298727442795660103058708046],
 [1760, 0.93916296553934430768606489437, 0.94310862184567778587762632014],
 [1770, 0.93961551431508127940617214335, 0.94315909125445462901637938558],
 [1780, 0.93996104290899329392061645194, 0.94312618257553848533092377693],
 [1790, 0.93965071747110373578948383511, 0.94286166112590585886010785543],
 [1800, 0.93986997706723285350705054952, 0.94260874304568731396614111873],
 [1810, 0.94020781472054948402217178227, 0.94247948047741281207834163069],
 [1820, 0.94050176543901731207597549655, 0.94237059469050221682806522949],
 [1830, 0.94083246662592912024081215350, 0.94248654459943936867460934081],
 [1840, 0.94115954661781930923325489857, 0.94261035897959699614290229874],
 [1850, 0.94100683276995056303348974325, 0.94242736376393188013622648214],
 [1860, 0.94022267288545979813108033341, 0.94180687634524162810123470990],
 [1870, 0.93935629631261496896854623628, 0.94121822319937775702669569000],
 [1880, 0.93855567951143703542271623519, 0.94067684437091125815300074464],
 [1890, 0.93779075786646870493967753646, 0.94037849833022058021470002132],
 [1900, 0.93699318519134500160561174198, 0.94014881934413585540255553497],
 [1910, 0.93624071263771146966803371470, 0.93981908009506132106736231435],
 [1920, 0.93541258296883000866728252731, 0.93953434129879775937865815649],
 [1930, 0.93582617424629765956467508659, 0.93935751660286193054361092436],
 [1940, 0.93615448991732674866028673932, 0.93910900026614874125385767911],
 [1950, 0.93653621982013246505260894992, 0.93892896730630748258761286707],
 [1960, 0.93638497337448489687972141837, 0.93875814141252156286299168642],
 [1970, 0.93561380187821352460986190636, 0.93836564220935347879759547141],
 [1980, 0.93473654569469266650827421472, 0.93808174575619907020751497839],
 [1990, 0.93450030009619511339735709044, 0.93783060409287144487677778670],
 [2000, 0.93478520441045775957178420868, 0.93753060306925894984431124613],
 [2010, 0.93502081338809761579256019104, 0.93724876664226774991561796924],
 [2020, 0.93534456206990690407820920882, 0.93741083053651363954372754961],
 [2030, 0.93573122150970200472386295587, 0.93753169794325197372586444544],
 [2040, 0.93603978971886492299603332867, 0.93781714601412013987413729410],
 [2050, 0.93638130630496396733519759437, 0.93801189624012026868626890064],
 [2060, 0.93670110683141105667459669348, 0.93829581370915504656693428842],
 [2070, 0.93665771241679229852650223620, 0.93818319870254496262163002029],
 [2080, 0.93595155105679472828938969542, 0.93765195561326430961912592466],
 [2090, 0.93525107098871484989643931840, 0.93714847754783858757576808785],
 [2100, 0.93455623671665222218507551588, 0.93661654720662912421147439090],
 [2110, 0.93390234849530162630770746546, 0.93607493123098073350973891138],
 [2120, 0.93346478725474979487586324467, 0.93553038484922856898862164599],
 [2130, 0.93296052729634182387741248021, 0.93497914730128250937468692428],
 [2140, 0.93294831702096037151505925067, 0.93535940975293474508589497418],
 [2150, 0.93342159274772729116165237429, 0.93560810689702356146568718032],
 [2160, 0.93387281814297240511990594314, 0.93590487221296314590546217005],
 [2170, 0.93416465880630317197841350208, 0.93605527766533780376079221242],
 [2180, 0.93349444833844852364990174465, 0.93550932055658575503542806473],
 [2190, 0.93282965620856495014834308677, 0.93496763151130479752026758433],
 [2200, 0.93217024870588882645705552932, 0.93443018421717949362204080899],
 [2210, 0.93151619233067672887216303934, 0.93411931563408723278030265647],
 [2220, 0.93086745379268764910563049852, 0.93391602684677499368604003394],
 [2230, 0.93047515083179610506647350121, 0.93375901323486820704289357309],
 [2240, 0.93100261803201855848044488084, 0.93367061496641945428365261250],
 [2250, 0.93147508353230390465427035451, 0.93375349956017172914357615810],
 [2260, 0.93121594685882469466520205970, 0.93336065362525300059814981068],
 [2270, 0.93123818542638547857137609753, 0.93278137522469228848365219164],
 [2280, 0.93125970881072872575856536059, 0.93229370043360537678722721466],
 [2290, 0.93129682094653354340607620543, 0.93252326002229768420193067868],
 [2300, 0.93178739877586591600078236297, 0.93275282100129708329205868722],
 [2310, 0.93219229529102654030481289738, 0.93308171212274548800280626892],
 [2320, 0.93262519181974512516575259724, 0.93342971649485828589121183541],
 [2330, 0.93276551622614556347201641984, 0.93357656341290651269559930370],
 [2340, 0.93290403234397345499928633217, 0.93384677755969280887882177922],
 [2350, 0.93313594261028398602064726219, 0.93414138861204709662899858813],
 [2360, 0.93358435400638850598653561974, 0.93436472939756487487983349638],
 [2370, 0.93330885341024139023602401721, 0.93397044466018386277283980235],
 [2380, 0.93290807935780928339397632953, 0.93354982471372671692932954102],
 [2390, 0.93229218991490170331815079408, 0.93298948545199944515360357400],
 [2400, 0.93168127524903898706298832622, 0.93243360807296571390878625607],
 [2410, 0.93160034314896911222803055352, 0.93215867901881976909095328665],
 [2420, 0.93176364900626562626229087982, 0.93252601816077429486284700033],
 [2430, 0.93208181664444234026944968719, 0.93326403234406896114450091773],
 [2440, 0.93257749960660540899937132053, 0.93352349346960650233739897885],
 [2450, 0.93214302800014037231335350953, 0.93315799086785256033493851646],
 [2460, 0.93154583152287617764386595809, 0.93264304078169346645665882534],
 [2470, 0.93095346458702765701787029684, 0.93206728152240947427031869665],
 [2480, 0.93035093509423272273295424384, 0.93151730675069244203001517235],
 [2490, 0.92976820594962794608306921873, 0.93097982722246530595811009334],
 [2510, 0.92976830902980045490124894059, 0.93091045100356706321065303200],
 [2520, 0.92910635693102927579190009055, 0.93035952821036027593493145105],
 [2530, 0.92850838928294110452554832591, 0.92994287642853301623091510919],
 [2540, 0.92785708207758932353215186595, 0.92968328518913345703822415089],
 [2550, 0.92784902951016212657719961499, 0.92954082532424842089113781185],
 [2560, 0.92810035012378577778946464605, 0.92940636752636218709255899739],
 [2570, 0.92823401282688133839826605254, 0.92911931513281742489596126688],
 [2580, 0.92830700962968659695206952165, 0.92860925922344816907383346916],
 [2590, 0.92872411034657287309812545573, 0.92895189331121263975887814013],
 [2600, 0.92896513147456194481321745116, 0.92911105959997897230095986743],
 [2610, 0.92878025115785989296313118757, 0.92894183175095512705610190096],
 [2620, 0.92845611399295435717249347363, 0.92862310798157154945187130579],
 [2630, 0.92810646481811565067232550064, 0.92827761818902476687043190395],
 [2640, 0.92760641273548660734604709433, 0.92789367518556586933442531517],
 [2650, 0.92730351323329496260328141943, 0.92761010749494277050075652369],
 [2660, 0.92740457664196196407857541999, 0.92796108725920045667834301639],
 [2670, 0.92720137271999381045617383279, 0.92789960198678778091618823964],
 [2680, 0.92675355146717153242974518434, 0.92767862408014012398638215018],
 [2690, 0.92633654845089574703109747134, 0.92726422839344135873318464292],
 [2700, 0.92678964489800730319757349207, 0.92781722911659558761243715708],
 [2710, 0.92723819383017247464096044496, 0.92791817496560080602563402863],
 [2720, 0.92770906522720308906571062835, 0.92814648810573274761992479398],
 [2730, 0.92816852353024570376760493673, 0.92852502914844892156764899482],
 [2740, 0.92866323585216603575531735260, 0.92892796519443010527794513109],
 [2750, 0.92911987689850672467173353652, 0.92935692630284472137702778127],
 [2760, 0.92962458798422764605362544899, 0.93029667458191567241954089695],
 [2770, 0.93007173369869644563578958696, 0.93021521430034781463547233216],
 [2780, 0.93056653114534904069898857415, 0.93067997715596739727317299185],
 [2790, 0.93108229815852217026161952163, 0.93110504656418457969380142458],
 [2800, 0.93152813245091903304739844316, 0.93157099584115654611338186442],
 [2810, 0.93178902325970369702190509997, 0.93182766607917744128286585692],
 [2820, 0.93105966512592253092606142673, 0.93107248735907577330550566330],
 [2830, 0.93033639241664622954175456471, 0.93036830184237384600010045688],
 [2840, 0.92961916808100064635311809980, 0.92972081248225235672322241953],
 [2850, 0.92890795528591318941380450269, 0.92903759289557030776052215515],
 [2860, 0.92820271741465409931493013573, 0.92839471237969728445449391074],
 [2870, 0.92750341806539182698543299921, 0.92772743356050013652236430062],
 [2880, 0.92685992135162498239964179447, 0.92708759147890562601901365270],
 [2890, 0.92617216260321322263138199560, 0.92644574783228506031917959263],
 [2900, 0.92549023539181929365327050618, 0.92586416371232360678078521232],
 [2910, 0.92470336171319933438184079932, 0.92523352193575247870427347152],
 [2920, 0.92402124955134323780470140264, 0.92467462510664522046255342502],
 [2930, 0.92333278061796664193394690301, 0.92404641211910643061600012516],
 [2940, 0.92267449623264707891934222062, 0.92357828361133587069531358793],
 [2950, 0.92197354149078292184782412733, 0.92331149508959220462145367492],
 [2960, 0.92132675018924525822683335718, 0.92306292532051381627411501540],
 [2970, 0.92068554215007281094074187422, 0.92291500958580663382946340789],
 [2980, 0.91993072962858313257328291002, 0.92286321208065624777105995236],
 [2990, 0.91998905114416318351544532561, 0.92295569810228705875942978309],
 [3000, 0.92016459412676199214331518306, 0.92291764738907144938195870054],
 [3010, 0.92043223278207275672713194581, 0.92180867697569379703992353825],
 [3020, 0.92055672485643347258132962452, 0.92166948714552210386585784363],
 [3030, 0.92067975409016400423212189708, 0.92145117498653428267374465577],
 [3040, 0.92047679588492492541718092980, 0.92082523544110339575041734861],
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