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[]
[null,null,null,"Les lampadaires"]
[]
[]
[null,"Transmis par Christophe le 21 novembre 2020"]
[]
[null,"https://www.ilemaths.net/sujet-des-lampadaires-cauchemardesques-726505.html"]
[null,"https://fr.wikipedia.org/wiki/Probl%C3%A8me_de_Jos%C3%A8phe "]
[]
["Enoncé"]
[]
[null,"Le responsable de l'éclairage d'une ville a fait un cauchemar dans la nuit de la Saint-Sylvestre. Il raconte à un collègue :"]
[]
[null,"- Il y avait une route circulaire bordée de lampadaires tous allumés et numérotés 1,2,3, etc. Je devais la parcourir en partant du 1 et en allant dans l'ordre croissant, et éteindre les lampadaires "]
[null,null,"mais en respectant un ordre particulier : je devais laisser le 1 allumé, puis éteindre le 2, laisser ensuite le 3 allumé, puis éteindre le 4, etc., en laissant toujours un lampadaire allumé et un seul avant d'en éteindre un autre."]
[null,null,"Et continuer ainsi sur cette fichue route circulaire en éteignant au fur et à mesure ces maudits lampadaires jusqu'à ce qu'il n'en reste plus qu'un allumé."]
[null,"- Ah ! Et il y en avait beaucoup en tout ?"]
[null,"- Oh oui, mais j'ai oublié combien exactement. Moins de 10000 c'est sûr car je me souviens que le plus grand numéro était composé de quatre chiffres."]
[null,"- Oh là là, quel cauchemar !"]
[null,"- Oui tu peux le dire ! Je me suis réveillé en sursaut au tout dernier lampadaire resté allumé, et ça je m'en souviens très précisément, c'était le numéro 2017."]
[null,"- Ah oui, forcément, facile à retenir !"]
[]
[null,"Combien de lampadaires pouvait-il y avoir sur cette route ?"]
[null,"S'il existe plusieurs solutions donnez-les toutes."]
[]
["Trois grandes étapes"]
[]
[null,"Mettre au point un algorithme et utilisation, de recherche du n° du dernier lampadaire éteint en fonction du nombre de lampadaires"]
[null,"Vérification par la méthode des nombres binaires"]
[null,"Recherche de la fonction inverse qui donne le nombre en fonction du dernier éteint"]
[]
["Algorithme"]
[]
[null,"Mis au point sur la feuille \"Méthode\""]
[]
["Avec les nombres binaires"]
[]
[null,"Lorsque le nombre de lampadaires est exprimé en binaire, on trouve le dernier lampadaire allumé en déplaçant simplement le digit de poids le plus fort vers les unités"]
[null,"Excel permet de faire des transformations du décimal vers le binaire ou du binaire vers le décimal à condition de ne pas dépasser 9 digits."]
[null,"Pour contourner la difficulté, on va couper le nombre en deux parties : 1 - les digits supérieurs à 511 et 2 - les digits inférieurs à 512"]
[]
[null,"Quelques difficultés avec la gestion des zéros"]
[]
[null,"Les résultats de l'algorithme et de la méthode des nombres binaires sont parfaitement identiques"]
[]
["Fonction inverse"]
[]
[null,"Nombre de lampadaires en fonction du n° final"]
[null,"Les colonnes C et B de la feuille \"Et1 Et2\" sont reportées dans les colonnes B, C puis E, F de la feuille \"Inverse\""]
[null,"Les colonnes E et F sont classées par ordre de E"]
[]
[null,"On a la réponse au problème sur les lignes 5064 à 5067."]
[]
[null,"Est-ce qu'on peut trouver une formule ?"]
[]
[null,"Après plusieurs tatonnements on arrive à cette forme en fonction de nf (le n° final)"]
[null,null,"On calcule deux variable intermédiaires k1 et k2."]
[null,null,"k1 = valeur à l'arrondi supérieur entier de (log((nf + 1)/2)/log(2))"]
[null,null,"k2 = (nf - 1)/2"]
[]
[null,"Solution n° k (à partir de k = 0)",null,null,null,"Solution 0 = k2 + 2^k1"]
[null,null,null,null,null,"Solution 1 = k2 + 2^(k1 + 1)"]
[null,null,null,null,null,"Solution 2 = k2 + 2^(k1 + 2)"]
[null,null,null,null,null,"Solution k = k2 + 2^(k1 + k)"]
[]
[null,"Le problème,  nf = 2017"]
[null,null,"k1 = log(2018/2)/log(2) = 9,98",null,null,null,"Arrondi supérieur",null,null,"k1 = 10"]
[null,null,"k2 = 2016/2 = 1008"]
[null,null,null,null,null,null,"Solution 0 = 1008 + 2^10 = 1008 + 1024 = 2032"]
[null,null,null,null,null,null,"Solution 1 = 1008 + 2^11 = 1008 + 2048 = 3056"]
[null,null,null,null,null,null,"Solution 2 = 1008 + 2^12 = 1008 + 4096 = 5104"]
[null,null,null,null,null,null,"Solution 3 = 1008 + 2^13 = 1008 + 8192 = 9200"]
[null,null,null,null,null,null,"Solution 4 = 1008 + 2^14 = 1008 + 16384 = 17 392",null,null,null,null,null,"Nombre à 5 chiffres en dehors de l'énoncé"]

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[]
[null,null,"Mise au point de l'algorithme","k = dernière posiion occupée"]
[]
[null,null,"Soit par exemple un nombre de 123 lampadaires.","Positions",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122]
[null,null,"Je range les n° dans un tableau aux positions n° 0 à 122. Dernière position paire.","k = 122",1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123]
[null,null,"Premier passage, je retire les n° des positions impaires. Le dernier en position paire reste",null,1,null,3,null,5,null,7,null,9,null,11,null,13,null,15,null,17,null,19,null,21,null,23,null,25,null,27,null,29,null,31,null,33,null,35,null,37,null,39,null,41,null,43,null,45,null,47,null,49,null,51,null,53,null,55,null,57,null,59,null,61,null,63,null,65,null,67,null,69,null,71,null,73,null,75,null,77,null,79,null,81,null,83,null,85,null,87,null,89,null,91,null,93,null,95,null,97,null,99,null,101,null,103,null,105,null,107,null,109,null,111,null,113,null,115,null,117,null,119,null,121,null,123]
[null,null,"Je déplace pour regrouper. Les positions n passent en position n/2.","k = 61",1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123]
[null,null,"Deuxième passage, le premier doit être enlevé. Je retire les positions paires. Le dernier impair reste",null,null,3,null,7,null,11,null,15,null,19,null,23,null,27,null,31,null,35,null,39,null,43,null,47,null,51,null,55,null,59,null,63,null,67,null,71,null,75,null,79,null,83,null,87,null,91,null,95,null,99,null,103,null,107,null,111,null,115,null,119,null,123]
[null,null,"Décalage. La position n passe en (n - 1)/2","k = 30",3,7,11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,87,91,95,99,103,107,111,115,119,123]
[null,null,"Troisième passage, retrait des pairs (le dernier en position paire, s'en va)",null,null,7,null,15,null,23,null,31,null,39,null,47,null,55,null,63,null,71,null,79,null,87,null,95,null,103,null,111,null,119]
[null,null,"Décalage, de la position n à la position (n - 1)/2","k = 14",7,15,23,31,39,47,55,63,71,79,87,95,103,111,119]
[null,null,"Quatrième passage, retrait des impairs (le dernier pair reste)",null,7,null,23,null,39,null,55,null,71,null,87,null,103,null,119]
[null,null,"Décalage, de la position n à la position n/2","k = 7",7,23,39,55,71,87,103,119]
[null,null,"Cinquième passage, retrait des pairs (le dernier impair reste)",null,null,23,null,55,null,87,null,119]
[null,null,"Décalage, de la position n à la position (n - 1)/2","k = 3",23,55,87,119]
[null,null,"Sixième passage, retrait des pairs (le dernier impair reste)",null,null,55,null,119]
[null,null,"Décalage, de la position n à la position n/2","k = 1",55,119]
[null,null,"Septième passage, retrait des pairs (le dernier impair reste)",null,null,119]
[null,null,"Décalage, de la position n à la position n/2","k = 0",119]
[]
[]
[null,null,"Macro \"Vérif\" avec l'exemple pour n = 123 ci-dessus",122,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123]
[null,null,"ok",61,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123]
[null,null,null,30,3,7,11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,87,91,95,99,103,107,111,115,119,123]
[null,null,"Quand on retire les impairs, ce sont les pairs qui sont décalés de n à n/2",14,7,15,23,31,39,47,55,63,71,79,87,95,103,111,119]
[null,null,"et quand on retire les pairs, ce sont les impairs qui sont décalés de n à (n - 1)/2",7,7,23,39,55,71,87,103,119]
[null,null,null,3,23,55,87,119]
[null,null,null,1,55,119]
[null,null,null,0,119]
[]
[]
[null,null,"Un essai jusqu'à 1023 (une fraction de seconde)",null,1,1]
[null,null,null,null,2,1]
[null,null,null,null,3,3]
[null,null,null,null,4,1]
[null,null,null,null,5,3]
[null,null,null,null,6,5]
[null,null,null,null,7,7]
[null,null,null,null,8,1]
[null,null,null,null,9,3]
[null,null,null,null,10,5]
[null,null,null,null,11,7]
[null,null,null,null,12,9]
[null,null,null,null,13,11]
[null,null,null,null,14,13]
[null,null,null,null,15,15]
[null,null,null,null,16,1]
[null,null,null,null,17,3]
[null,null,null,null,18,5]
[null,null,null,null,19,7]
[null,null,null,null,20,9]
[null,null,null,null,21,11]
[null,null,null,null,22,13]
[null,null,null,null,23,15]
[null,null,null,null,24,17]
[null,null,null,null,25,19]
[null,null,null,null,26,21]
[null,null,null,null,27,23]
[null,null,null,null,28,25]
[null,null,null,null,29,27]
[null,null,null,null,30,29]
[null,null,null,null,31,31]
[null,null,null,null,32,1]
[null,null,null,null,33,3]
[null,null,null,null,34,5]
[null,null,null,null,35,7]
[null,null,null,null,36,9]
[null,null,null,null,37,11]
[null,null,null,null,38,13]
[null,null,null,null,39,15]
[null,null,null,null,40,17]
[null,null,null,null,41,19]
[null,null,null,null,42,21]
[null,null,null,null,43,23]
[null,null,null,null,44,25]
[null,null,null,null,45,27]
[null,null,null,null,46,29]
[null,null,null,null,47,31]
[null,null,null,null,48,33]
[null,null,null,null,49,35]
[null,null,null,null,50,37]
[null,null,null,null,51,39]
[null,null,null,null,52,41]
[null,null,null,null,53,43]
[null,null,null,null,54,45]
[null,null,null,null,55,47]
[null,null,null,null,56,49]
[null,null,null,null,57,51]
[null,null,null,null,58,53]
[null,null,null,null,59,55]
[null,null,null,null,60,57]
[null,null,null,null,61,59]
[null,null,null,null,62,61]
[null,null,null,null,63,63]
[null,null,null,null,64,1]
[null,null,null,null,65,3]
[null,null,null,null,66,5]
[null,null,null,null,67,7]
[null,null,null,null,68,9]
[null,null,null,null,69,11]
[null,null,null,null,70,13]
[null,null,null,null,71,15]
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[null,null,null,null,77,27]
[null,null,null,null,78,29]
[null,null,null,null,79,31]
[null,null,null,null,80,33]
[null,null,null,null,81,35]
[null,null,null,null,82,37]
[null,null,null,null,83,39]
[null,null,null,null,84,41]
[null,null,null,null,85,43]
[null,null,null,null,86,45]
[null,null,null,null,87,47]
[null,null,null,null,88,49]
[null,null,null,null,89,51]
[null,null,null,null,90,53]
[null,null,null,null,91,55]
[null,null,null,null,92,57]
[null,null,null,null,93,59]
[null,null,null,null,94,61]
[null,null,null,null,95,63]
[null,null,null,null,96,65]
[null,null,null,null,97,67]
[null,null,null,null,98,69]
[null,null,null,null,99,71]
[null,null,null,null,100,73]
[null,null,null,null,101,75]
[null,null,null,null,102,77]
[null,null,null,null,103,79]
[null,null,null,null,104,81]
[null,null,null,null,105,83]
[null,null,null,null,106,85]
[null,null,null,null,107,87]
[null,null,null,null,108,89]
[null,null,null,null,109,91]
[null,null,null,null,110,93]
[null,null,null,null,111,95]
[null,null,null,null,112,97]
[null,null,null,null,113,99]
[null,null,null,null,114,101]
[null,null,null,null,115,103]
[null,null,null,null,116,105]
[null,null,null,null,117,107]
[null,null,null,null,118,109]
[null,null,null,null,119,111]
[null,null,null,null,120,113]
[null,null,null,null,121,115]
[null,null,null,null,122,117]
[null,null,null,null,123,119]
[null,null,null,null,124,121]
[null,null,null,null,125,123]
[null,null,null,null,126,125]
[null,null,null,null,127,127]
[null,null,null,null,128,1]
[null,null,null,null,129,3]
[null,null,null,null,130,5]
[null,null,null,null,131,7]
[null,null,null,null,132,9]
[null,null,null,null,133,11]
[null,null,null,null,134,13]
[null,null,null,null,135,15]
[null,null,null,null,136,17]
[null,null,null,null,137,19]
[null,null,null,null,138,21]
[null,null,null,null,139,23]
[null,null,null,null,140,25]
[null,null,null,null,141,27]
[null,null,null,null,142,29]
[null,null,null,null,143,31]
[null,null,null,null,144,33]
[null,null,null,null,145,35]
[null,null,null,null,146,37]
[null,null,null,null,147,39]
[null,null,null,null,148,41]
[null,null,null,null,149,43]
[null,null,null,null,150,45]
[null,null,null,null,151,47]
[null,null,null,null,152,49]
[null,null,null,null,153,51]
[null,null,null,null,154,53]
[null,null,null,null,155,55]
[null,null,null,null,156,57]
[null,null,null,null,157,59]
[null,null,null,null,158,61]
[null,null,null,null,159,63]
[null,null,null,null,160,65]
[null,null,null,null,161,67]
[null,null,null,null,162,69]
[null,null,null,null,163,71]
[null,null,null,null,164,73]
[null,null,null,null,165,75]
[null,null,null,null,166,77]
[null,null,null,null,167,79]
[null,null,null,null,168,81]
[null,null,null,null,169,83]
[null,null,null,null,170,85]
[null,null,null,null,171,87]
[null,null,null,null,172,89]
[null,null,null,null,173,91]
[null,null,null,null,174,93]
[null,null,null,null,175,95]
[null,null,null,null,176,97]
[null,null,null,null,177,99]
[null,null,null,null,178,101]
[null,null,null,null,179,103]
[null,null,null,null,180,105]
[null,null,null,null,181,107]
[null,null,null,null,182,109]
[null,null,null,null,183,111]
[null,null,null,null,184,113]
[null,null,null,null,185,115]
[null,null,null,null,186,117]
[null,null,null,null,187,119]
[null,null,null,null,188,121]
[null,null,null,null,189,123]
[null,null,null,null,190,125]
[null,null,null,null,191,127]
[null,null,null,null,192,129]
[null,null,null,null,193,131]
[null,null,null,null,194,133]
[null,null,null,null,195,135]
[null,null,null,null,196,137]
[null,null,null,null,197,139]
[null,null,null,null,198,141]
[null,null,null,null,199,143]
[null,null,null,null,200,145]
[null,null,null,null,201,147]
[null,null,null,null,202,149]
[null,null,null,null,203,151]
[null,null,null,null,204,153]
[null,null,null,null,205,155]
[null,null,null,null,206,157]
[null,null,null,null,207,159]
[null,null,null,null,208,161]
[null,null,null,null,209,163]
[null,null,null,null,210,165]
[null,null,null,null,211,167]
[null,null,null,null,212,169]
[null,null,null,null,213,171]
[null,null,null,null,214,173]
[null,null,null,null,215,175]
[null,null,null,null,216,177]
[null,null,null,null,217,179]
[null,null,null,null,218,181]
[null,null,null,null,219,183]
[null,null,null,null,220,185]
[null,null,null,null,221,187]
[null,null,null,null,222,189]
[null,null,null,null,223,191]
[null,null,null,null,224,193]
[null,null,null,null,225,195]
[null,null,null,null,226,197]
[null,null,null,null,227,199]
[null,null,null,null,228,201]
[null,null,null,null,229,203]
[null,null,null,null,230,205]
[null,null,null,null,231,207]
[null,null,null,null,232,209]
[null,null,null,null,233,211]
[null,null,null,null,234,213]
[null,null,null,null,235,215]
[null,null,null,null,236,217]
[null,null,null,null,237,219]
[null,null,null,null,238,221]
[null,null,null,null,239,223]
[null,null,null,null,240,225]
[null,null,null,null,241,227]
[null,null,null,null,242,229]
[null,null,null,null,243,231]
[null,null,null,null,244,233]
[null,null,null,null,245,235]
[null,null,null,null,246,237]
[null,null,null,null,247,239]
[null,null,null,null,248,241]
[null,null,null,null,249,243]
[null,null,null,null,250,245]
[null,null,null,null,251,247]
[null,null,null,null,252,249]
[null,null,null,null,253,251]
[null,null,null,null,254,253]
[null,null,null,null,255,255]
[null,null,null,null,256,1]
[null,null,null,null,257,3]
[null,null,null,null,258,5]
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{"sheet":"Et1 Et2","index":2,"n_rows":16398,"n_cols":18,"rows_kept":4500,"cut":true,"hidden":false,"merged":[[3,1,3,2]],"bounds":{"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0}}
[]
[null,null,"Etape 1 : calcul direct par la macro - Etape 2 : calcul en passant par les binaires",null,null,null,null,null,null,null,null,null,"ok, les deux méthodes donnent le même résultat"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"nb de \".\"",null,{"$f":"COUNTIF($P$16:$P$16398,\".\")","v":16383}]
[null,"Avec la macro",null,null,"(moins d'une minute)",null,null,null,null,null,null,null,null,"nb de \"N\"",null,{"$f":"COUNTIF($P$16:$P$16398,\"N\")","v":0}]
[]
[null,2016,null,null,{"$f":"IF(B6>511,INT(B6/512),0)","v":3},{"$f":"B6-512*E6","v":480},{"$f":"DEC2BIN(E6)","v":"11"},{"$f":"CONCATENATE(IF(E6=0,\"\",IF(F6<2,\"00000000\",IF(F6<4,\"0000000\",IF(F6<8,\"000000\",IF(F6<16,\"00000\",IF(F6<32,\"0000\",IF(F6<64,\"000\",IF(F6<128,\"00\",IF(F6<256,\"0\",\"\"))))))))),DEC2BIN(F6))","v":"111100000"},{"$f":"CONCATENATE(IF(G6=\"0\",\"\",G6),H6)","v":"11111100000"},{"$f":"CONCATENATE(RIGHT(I6,LEN(I6)-1),LEFT(I6,1))","v":"11111000001"},{"$f":"IF(LEN(J6)>9,LEFT(J6,LEN(J6)-9),0)","v":"11"},{"$f":"RIGHT(J6,9)","v":"111000001"},{"$f":"BIN2DEC(K6)","v":3},{"$f":"BIN2DEC(L6)","v":449},{"$f":"512*M6+N6","v":1985},{"$f":"IF(C6=O6,\".\",\"N\")","v":"N"},null,"Pour alléger le fichier les formules ont été effacées. On a ces formules sur la ligne 6"]
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[]
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[null,15913,15443,null,31,41,"11111","000101001","11111000101001","11110001010011","11110","001010011",30,83,15443,"."]
[null,15914,15445,null,31,42,"11111","000101010","11111000101010","11110001010101","11110","001010101",30,85,15445,"."]
[null,15915,15447,null,31,43,"11111","000101011","11111000101011","11110001010111","11110","001010111",30,87,15447,"."]
[null,15916,15449,null,31,44,"11111","000101100","11111000101100","11110001011001","11110","001011001",30,89,15449,"."]
[null,15917,15451,null,31,45,"11111","000101101","11111000101101","11110001011011","11110","001011011",30,91,15451,"."]
[null,15918,15453,null,31,46,"11111","000101110","11111000101110","11110001011101","11110","001011101",30,93,15453,"."]
[null,15919,15455,null,31,47,"11111","000101111","11111000101111","11110001011111","11110","001011111",30,95,15455,"."]
[null,15920,15457,null,31,48,"11111","000110000","11111000110000","11110001100001","11110","001100001",30,97,15457,"."]
[null,15921,15459,null,31,49,"11111","000110001","11111000110001","11110001100011","11110","001100011",30,99,15459,"."]
[null,15922,15461,null,31,50,"11111","000110010","11111000110010","11110001100101","11110","001100101",30,101,15461,"."]
[null,15923,15463,null,31,51,"11111","000110011","11111000110011","11110001100111","11110","001100111",30,103,15463,"."]
[null,15924,15465,null,31,52,"11111","000110100","11111000110100","11110001101001","11110","001101001",30,105,15465,"."]
[null,15925,15467,null,31,53,"11111","000110101","11111000110101","11110001101011","11110","001101011",30,107,15467,"."]
[null,15926,15469,null,31,54,"11111","000110110","11111000110110","11110001101101","11110","001101101",30,109,15469,"."]
[null,15927,15471,null,31,55,"11111","000110111","11111000110111","11110001101111","11110","001101111",30,111,15471,"."]
[null,15928,15473,null,31,56,"11111","000111000","11111000111000","11110001110001","11110","001110001",30,113,15473,"."]
[null,15929,15475,null,31,57,"11111","000111001","11111000111001","11110001110011","11110","001110011",30,115,15475,"."]
[null,15930,15477,null,31,58,"11111","000111010","11111000111010","11110001110101","11110","001110101",30,117,15477,"."]
[null,15931,15479,null,31,59,"11111","000111011","11111000111011","11110001110111","11110","001110111",30,119,15479,"."]
[null,15932,15481,null,31,60,"11111","000111100","11111000111100","11110001111001","11110","001111001",30,121,15481,"."]
[null,15933,15483,null,31,61,"11111","000111101","11111000111101","11110001111011","11110","001111011",30,123,15483,"."]
[null,15934,15485,null,31,62,"11111","000111110","11111000111110","11110001111101","11110","001111101",30,125,15485,"."]
[null,15935,15487,null,31,63,"11111","000111111","11111000111111","11110001111111","11110","001111111",30,127,15487,"."]
[null,15936,15489,null,31,64,"11111","001000000","11111001000000","11110010000001","11110","010000001",30,129,15489,"."]
[null,15937,15491,null,31,65,"11111","001000001","11111001000001","11110010000011","11110","010000011",30,131,15491,"."]
[null,15938,15493,null,31,66,"11111","001000010","11111001000010","11110010000101","11110","010000101",30,133,15493,"."]
[null,15939,15495,null,31,67,"11111","001000011","11111001000011","11110010000111","11110","010000111",30,135,15495,"."]
[null,15940,15497,null,31,68,"11111","001000100","11111001000100","11110010001001","11110","010001001",30,137,15497,"."]
[null,15941,15499,null,31,69,"11111","001000101","11111001000101","11110010001011","11110","010001011",30,139,15499,"."]
[null,15942,15501,null,31,70,"11111","001000110","11111001000110","11110010001101","11110","010001101",30,141,15501,"."]
[null,15943,15503,null,31,71,"11111","001000111","11111001000111","11110010001111","11110","010001111",30,143,15503,"."]
[null,15944,15505,null,31,72,"11111","001001000","11111001001000","11110010010001","11110","010010001",30,145,15505,"."]
[null,15945,15507,null,31,73,"11111","001001001","11111001001001","11110010010011","11110","010010011",30,147,15507,"."]
[null,15946,15509,null,31,74,"11111","001001010","11111001001010","11110010010101","11110","010010101",30,149,15509,"."]
[null,15947,15511,null,31,75,"11111","001001011","11111001001011","11110010010111","11110","010010111",30,151,15511,"."]
[null,15948,15513,null,31,76,"11111","001001100","11111001001100","11110010011001","11110","010011001",30,153,15513,"."]
[null,15949,15515,null,31,77,"11111","001001101","11111001001101","11110010011011","11110","010011011",30,155,15515,"."]
[null,15950,15517,null,31,78,"11111","001001110","11111001001110","11110010011101","11110","010011101",30,157,15517,"."]
[null,15951,15519,null,31,79,"11111","001001111","11111001001111","11110010011111","11110","010011111",30,159,15519,"."]
[null,15952,15521,null,31,80,"11111","001010000","11111001010000","11110010100001","11110","010100001",30,161,15521,"."]
[null,15953,15523,null,31,81,"11111","001010001","11111001010001","11110010100011","11110","010100011",30,163,15523,"."]
[null,15954,15525,null,31,82,"11111","001010010","11111001010010","11110010100101","11110","010100101",30,165,15525,"."]
[null,15955,15527,null,31,83,"11111","001010011","11111001010011","11110010100111","11110","010100111",30,167,15527,"."]
[null,15956,15529,null,31,84,"11111","001010100","11111001010100","11110010101001","11110","010101001",30,169,15529,"."]
[null,15957,15531,null,31,85,"11111","001010101","11111001010101","11110010101011","11110","010101011",30,171,15531,"."]
[null,15958,15533,null,31,86,"11111","001010110","11111001010110","11110010101101","11110","010101101",30,173,15533,"."]
[null,15959,15535,null,31,87,"11111","001010111","11111001010111","11110010101111","11110","010101111",30,175,15535,"."]
[null,15960,15537,null,31,88,"11111","001011000","11111001011000","11110010110001","11110","010110001",30,177,15537,"."]
[null,15961,15539,null,31,89,"11111","001011001","11111001011001","11110010110011","11110","010110011",30,179,15539,"."]
[null,15962,15541,null,31,90,"11111","001011010","11111001011010","11110010110101","11110","010110101",30,181,15541,"."]
[null,15963,15543,null,31,91,"11111","001011011","11111001011011","11110010110111","11110","010110111",30,183,15543,"."]
[null,15964,15545,null,31,92,"11111","001011100","11111001011100","11110010111001","11110","010111001",30,185,15545,"."]
[null,15965,15547,null,31,93,"11111","001011101","11111001011101","11110010111011","11110","010111011",30,187,15547,"."]
[null,15966,15549,null,31,94,"11111","001011110","11111001011110","11110010111101","11110","010111101",30,189,15549,"."]
[null,15967,15551,null,31,95,"11111","001011111","11111001011111","11110010111111","11110","010111111",30,191,15551,"."]
[null,15968,15553,null,31,96,"11111","001100000","11111001100000","11110011000001","11110","011000001",30,193,15553,"."]
[null,15969,15555,null,31,97,"11111","001100001","11111001100001","11110011000011","11110","011000011",30,195,15555,"."]
[null,15970,15557,null,31,98,"11111","001100010","11111001100010","11110011000101","11110","011000101",30,197,15557,"."]
[null,15971,15559,null,31,99,"11111","001100011","11111001100011","11110011000111","11110","011000111",30,199,15559,"."]
[null,15972,15561,null,31,100,"11111","001100100","11111001100100","11110011001001","11110","011001001",30,201,15561,"."]
[null,15973,15563,null,31,101,"11111","001100101","11111001100101","11110011001011","11110","011001011",30,203,15563,"."]
[null,15974,15565,null,31,102,"11111","001100110","11111001100110","11110011001101","11110","011001101",30,205,15565,"."]
[null,15975,15567,null,31,103,"11111","001100111","11111001100111","11110011001111","11110","011001111",30,207,15567,"."]
[null,15976,15569,null,31,104,"11111","001101000","11111001101000","11110011010001","11110","011010001",30,209,15569,"."]
[null,15977,15571,null,31,105,"11111","001101001","11111001101001","11110011010011","11110","011010011",30,211,15571,"."]
[null,15978,15573,null,31,106,"11111","001101010","11111001101010","11110011010101","11110","011010101",30,213,15573,"."]
[null,15979,15575,null,31,107,"11111","001101011","11111001101011","11110011010111","11110","011010111",30,215,15575,"."]
[null,15980,15577,null,31,108,"11111","001101100","11111001101100","11110011011001","11110","011011001",30,217,15577,"."]
[null,15981,15579,null,31,109,"11111","001101101","11111001101101","11110011011011","11110","011011011",30,219,15579,"."]
[null,15982,15581,null,31,110,"11111","001101110","11111001101110","11110011011101","11110","011011101",30,221,15581,"."]
[null,15983,15583,null,31,111,"11111","001101111","11111001101111","11110011011111","11110","011011111",30,223,15583,"."]
[null,15984,15585,null,31,112,"11111","001110000","11111001110000","11110011100001","11110","011100001",30,225,15585,"."]
[null,15985,15587,null,31,113,"11111","001110001","11111001110001","11110011100011","11110","011100011",30,227,15587,"."]
[null,15986,15589,null,31,114,"11111","001110010","11111001110010","11110011100101","11110","011100101",30,229,15589,"."]
[null,15987,15591,null,31,115,"11111","001110011","11111001110011","11110011100111","11110","011100111",30,231,15591,"."]
[null,15988,15593,null,31,116,"11111","001110100","11111001110100","11110011101001","11110","011101001",30,233,15593,"."]
[null,15989,15595,null,31,117,"11111","001110101","11111001110101","11110011101011","11110","011101011",30,235,15595,"."]
[null,15990,15597,null,31,118,"11111","001110110","11111001110110","11110011101101","11110","011101101",30,237,15597,"."]
[null,15991,15599,null,31,119,"11111","001110111","11111001110111","11110011101111","11110","011101111",30,239,15599,"."]
[null,15992,15601,null,31,120,"11111","001111000","11111001111000","11110011110001","11110","011110001",30,241,15601,"."]
[null,15993,15603,null,31,121,"11111","001111001","11111001111001","11110011110011","11110","011110011",30,243,15603,"."]
[null,15994,15605,null,31,122,"11111","001111010","11111001111010","11110011110101","11110","011110101",30,245,15605,"."]
[null,15995,15607,null,31,123,"11111","001111011","11111001111011","11110011110111","11110","011110111",30,247,15607,"."]
[null,15996,15609,null,31,124,"11111","001111100","11111001111100","11110011111001","11110","011111001",30,249,15609,"."]
[null,15997,15611,null,31,125,"11111","001111101","11111001111101","11110011111011","11110","011111011",30,251,15611,"."]
[null,15998,15613,null,31,126,"11111","001111110","11111001111110","11110011111101","11110","011111101",30,253,15613,"."]
[null,15999,15615,null,31,127,"11111","001111111","11111001111111","11110011111111","11110","011111111",30,255,15615,"."]
[null,16000,15617,null,31,128,"11111","010000000","11111010000000","11110100000001","11110","100000001",30,257,15617,"."]
[null,16001,15619,null,31,129,"11111","010000001","11111010000001","11110100000011","11110","100000011",30,259,15619,"."]
[null,16002,15621,null,31,130,"11111","010000010","11111010000010","11110100000101","11110","100000101",30,261,15621,"."]
[null,16003,15623,null,31,131,"11111","010000011","11111010000011","11110100000111","11110","100000111",30,263,15623,"."]
[null,16004,15625,null,31,132,"11111","010000100","11111010000100","11110100001001","11110","100001001",30,265,15625,"."]
[null,16005,15627,null,31,133,"11111","010000101","11111010000101","11110100001011","11110","100001011",30,267,15627,"."]
[null,16006,15629,null,31,134,"11111","010000110","11111010000110","11110100001101","11110","100001101",30,269,15629,"."]
[null,16007,15631,null,31,135,"11111","010000111","11111010000111","11110100001111","11110","100001111",30,271,15631,"."]
[null,16008,15633,null,31,136,"11111","010001000","11111010001000","11110100010001","11110","100010001",30,273,15633,"."]
[null,16009,15635,null,31,137,"11111","010001001","11111010001001","11110100010011","11110","100010011",30,275,15635,"."]
[null,16010,15637,null,31,138,"11111","010001010","11111010001010","11110100010101","11110","100010101",30,277,15637,"."]
[null,16011,15639,null,31,139,"11111","010001011","11111010001011","11110100010111","11110","100010111",30,279,15639,"."]
[null,16012,15641,null,31,140,"11111","010001100","11111010001100","11110100011001","11110","100011001",30,281,15641,"."]
[null,16013,15643,null,31,141,"11111","010001101","11111010001101","11110100011011","11110","100011011",30,283,15643,"."]
[null,16014,15645,null,31,142,"11111","010001110","11111010001110","11110100011101","11110","100011101",30,285,15645,"."]
[null,16015,15647,null,31,143,"11111","010001111","11111010001111","11110100011111","11110","100011111",30,287,15647,"."]
[null,16016,15649,null,31,144,"11111","010010000","11111010010000","11110100100001","11110","100100001",30,289,15649,"."]
[null,16017,15651,null,31,145,"11111","010010001","11111010010001","11110100100011","11110","100100011",30,291,15651,"."]
[null,16018,15653,null,31,146,"11111","010010010","11111010010010","11110100100101","11110","100100101",30,293,15653,"."]
[null,16019,15655,null,31,147,"11111","010010011","11111010010011","11110100100111","11110","100100111",30,295,15655,"."]
[null,16020,15657,null,31,148,"11111","010010100","11111010010100","11110100101001","11110","100101001",30,297,15657,"."]
[null,16021,15659,null,31,149,"11111","010010101","11111010010101","11110100101011","11110","100101011",30,299,15659,"."]
[null,16022,15661,null,31,150,"11111","010010110","11111010010110","11110100101101","11110","100101101",30,301,15661,"."]
[null,16023,15663,null,31,151,"11111","010010111","11111010010111","11110100101111","11110","100101111",30,303,15663,"."]
[null,16024,15665,null,31,152,"11111","010011000","11111010011000","11110100110001","11110","100110001",30,305,15665,"."]
[null,16025,15667,null,31,153,"11111","010011001","11111010011001","11110100110011","11110","100110011",30,307,15667,"."]
[null,16026,15669,null,31,154,"11111","010011010","11111010011010","11110100110101","11110","100110101",30,309,15669,"."]
[null,16027,15671,null,31,155,"11111","010011011","11111010011011","11110100110111","11110","100110111",30,311,15671,"."]
[null,16028,15673,null,31,156,"11111","010011100","11111010011100","11110100111001","11110","100111001",30,313,15673,"."]
[null,16029,15675,null,31,157,"11111","010011101","11111010011101","11110100111011","11110","100111011",30,315,15675,"."]
[null,16030,15677,null,31,158,"11111","010011110","11111010011110","11110100111101","11110","100111101",30,317,15677,"."]
[null,16031,15679,null,31,159,"11111","010011111","11111010011111","11110100111111","11110","100111111",30,319,15679,"."]
[null,16032,15681,null,31,160,"11111","010100000","11111010100000","11110101000001","11110","101000001",30,321,15681,"."]
[null,16033,15683,null,31,161,"11111","010100001","11111010100001","11110101000011","11110","101000011",30,323,15683,"."]
[null,16034,15685,null,31,162,"11111","010100010","11111010100010","11110101000101","11110","101000101",30,325,15685,"."]
[null,16035,15687,null,31,163,"11111","010100011","11111010100011","11110101000111","11110","101000111",30,327,15687,"."]
[null,16036,15689,null,31,164,"11111","010100100","11111010100100","11110101001001","11110","101001001",30,329,15689,"."]
[null,16037,15691,null,31,165,"11111","010100101","11111010100101","11110101001011","11110","101001011",30,331,15691,"."]
[null,16038,15693,null,31,166,"11111","010100110","11111010100110","11110101001101","11110","101001101",30,333,15693,"."]
[null,16039,15695,null,31,167,"11111","010100111","11111010100111","11110101001111","11110","101001111",30,335,15695,"."]
[null,16040,15697,null,31,168,"11111","010101000","11111010101000","11110101010001","11110","101010001",30,337,15697,"."]
[null,16041,15699,null,31,169,"11111","010101001","11111010101001","11110101010011","11110","101010011",30,339,15699,"."]
[null,16042,15701,null,31,170,"11111","010101010","11111010101010","11110101010101","11110","101010101",30,341,15701,"."]
[null,16043,15703,null,31,171,"11111","010101011","11111010101011","11110101010111","11110","101010111",30,343,15703,"."]
[null,16044,15705,null,31,172,"11111","010101100","11111010101100","11110101011001","11110","101011001",30,345,15705,"."]
[null,16045,15707,null,31,173,"11111","010101101","11111010101101","11110101011011","11110","101011011",30,347,15707,"."]
[null,16046,15709,null,31,174,"11111","010101110","11111010101110","11110101011101","11110","101011101",30,349,15709,"."]
[null,16047,15711,null,31,175,"11111","010101111","11111010101111","11110101011111","11110","101011111",30,351,15711,"."]
[null,16048,15713,null,31,176,"11111","010110000","11111010110000","11110101100001","11110","101100001",30,353,15713,"."]
[null,16049,15715,null,31,177,"11111","010110001","11111010110001","11110101100011","11110","101100011",30,355,15715,"."]
[null,16050,15717,null,31,178,"11111","010110010","11111010110010","11110101100101","11110","101100101",30,357,15717,"."]
[null,16051,15719,null,31,179,"11111","010110011","11111010110011","11110101100111","11110","101100111",30,359,15719,"."]
[null,16052,15721,null,31,180,"11111","010110100","11111010110100","11110101101001","11110","101101001",30,361,15721,"."]
[null,16053,15723,null,31,181,"11111","010110101","11111010110101","11110101101011","11110","101101011",30,363,15723,"."]
[null,16054,15725,null,31,182,"11111","010110110","11111010110110","11110101101101","11110","101101101",30,365,15725,"."]
[null,16055,15727,null,31,183,"11111","010110111","11111010110111","11110101101111","11110","101101111",30,367,15727,"."]
[null,16056,15729,null,31,184,"11111","010111000","11111010111000","11110101110001","11110","101110001",30,369,15729,"."]
[null,16057,15731,null,31,185,"11111","010111001","11111010111001","11110101110011","11110","101110011",30,371,15731,"."]
[null,16058,15733,null,31,186,"11111","010111010","11111010111010","11110101110101","11110","101110101",30,373,15733,"."]
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[null,16063,15743,null,31,191,"11111","010111111","11111010111111","11110101111111","11110","101111111",30,383,15743,"."]
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[null,16066,15749,null,31,194,"11111","011000010","11111011000010","11110110000101","11110","110000101",30,389,15749,"."]
[null,16067,15751,null,31,195,"11111","011000011","11111011000011","11110110000111","11110","110000111",30,391,15751,"."]
[null,16068,15753,null,31,196,"11111","011000100","11111011000100","11110110001001","11110","110001001",30,393,15753,"."]
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[null,16230,16077,null,31,358,"11111","101100110","11111101100110","11111011001101","11111","011001101",31,205,16077,"."]
[null,16231,16079,null,31,359,"11111","101100111","11111101100111","11111011001111","11111","011001111",31,207,16079,"."]
[null,16232,16081,null,31,360,"11111","101101000","11111101101000","11111011010001","11111","011010001",31,209,16081,"."]
[null,16233,16083,null,31,361,"11111","101101001","11111101101001","11111011010011","11111","011010011",31,211,16083,"."]
[null,16234,16085,null,31,362,"11111","101101010","11111101101010","11111011010101","11111","011010101",31,213,16085,"."]
[null,16235,16087,null,31,363,"11111","101101011","11111101101011","11111011010111","11111","011010111",31,215,16087,"."]
[null,16236,16089,null,31,364,"11111","101101100","11111101101100","11111011011001","11111","011011001",31,217,16089,"."]
[null,16237,16091,null,31,365,"11111","101101101","11111101101101","11111011011011","11111","011011011",31,219,16091,"."]
[null,16238,16093,null,31,366,"11111","101101110","11111101101110","11111011011101","11111","011011101",31,221,16093,"."]
[null,16239,16095,null,31,367,"11111","101101111","11111101101111","11111011011111","11111","011011111",31,223,16095,"."]
[null,16240,16097,null,31,368,"11111","101110000","11111101110000","11111011100001","11111","011100001",31,225,16097,"."]
[null,16241,16099,null,31,369,"11111","101110001","11111101110001","11111011100011","11111","011100011",31,227,16099,"."]
[null,16242,16101,null,31,370,"11111","101110010","11111101110010","11111011100101","11111","011100101",31,229,16101,"."]
[null,16243,16103,null,31,371,"11111","101110011","11111101110011","11111011100111","11111","011100111",31,231,16103,"."]
[null,16244,16105,null,31,372,"11111","101110100","11111101110100","11111011101001","11111","011101001",31,233,16105,"."]
[null,16245,16107,null,31,373,"11111","101110101","11111101110101","11111011101011","11111","011101011",31,235,16107,"."]
[null,16246,16109,null,31,374,"11111","101110110","11111101110110","11111011101101","11111","011101101",31,237,16109,"."]
[null,16247,16111,null,31,375,"11111","101110111","11111101110111","11111011101111","11111","011101111",31,239,16111,"."]
[null,16248,16113,null,31,376,"11111","101111000","11111101111000","11111011110001","11111","011110001",31,241,16113,"."]
[null,16249,16115,null,31,377,"11111","101111001","11111101111001","11111011110011","11111","011110011",31,243,16115,"."]
[null,16250,16117,null,31,378,"11111","101111010","11111101111010","11111011110101","11111","011110101",31,245,16117,"."]
[null,16251,16119,null,31,379,"11111","101111011","11111101111011","11111011110111","11111","011110111",31,247,16119,"."]
[null,16252,16121,null,31,380,"11111","101111100","11111101111100","11111011111001","11111","011111001",31,249,16121,"."]
[null,16253,16123,null,31,381,"11111","101111101","11111101111101","11111011111011","11111","011111011",31,251,16123,"."]
[null,16254,16125,null,31,382,"11111","101111110","11111101111110","11111011111101","11111","011111101",31,253,16125,"."]
[null,16255,16127,null,31,383,"11111","101111111","11111101111111","11111011111111","11111","011111111",31,255,16127,"."]
[null,16256,16129,null,31,384,"11111","110000000","11111110000000","11111100000001","11111","100000001",31,257,16129,"."]
[null,16257,16131,null,31,385,"11111","110000001","11111110000001","11111100000011","11111","100000011",31,259,16131,"."]
[null,16258,16133,null,31,386,"11111","110000010","11111110000010","11111100000101","11111","100000101",31,261,16133,"."]
[null,16259,16135,null,31,387,"11111","110000011","11111110000011","11111100000111","11111","100000111",31,263,16135,"."]
[null,16260,16137,null,31,388,"11111","110000100","11111110000100","11111100001001","11111","100001001",31,265,16137,"."]
[null,16261,16139,null,31,389,"11111","110000101","11111110000101","11111100001011","11111","100001011",31,267,16139,"."]
[null,16262,16141,null,31,390,"11111","110000110","11111110000110","11111100001101","11111","100001101",31,269,16141,"."]
[null,16263,16143,null,31,391,"11111","110000111","11111110000111","11111100001111","11111","100001111",31,271,16143,"."]
[null,16264,16145,null,31,392,"11111","110001000","11111110001000","11111100010001","11111","100010001",31,273,16145,"."]
[null,16265,16147,null,31,393,"11111","110001001","11111110001001","11111100010011","11111","100010011",31,275,16147,"."]
[null,16266,16149,null,31,394,"11111","110001010","11111110001010","11111100010101","11111","100010101",31,277,16149,"."]
[null,16267,16151,null,31,395,"11111","110001011","11111110001011","11111100010111","11111","100010111",31,279,16151,"."]
[null,16268,16153,null,31,396,"11111","110001100","11111110001100","11111100011001","11111","100011001",31,281,16153,"."]
[null,16269,16155,null,31,397,"11111","110001101","11111110001101","11111100011011","11111","100011011",31,283,16155,"."]
[null,16270,16157,null,31,398,"11111","110001110","11111110001110","11111100011101","11111","100011101",31,285,16157,"."]
[null,16271,16159,null,31,399,"11111","110001111","11111110001111","11111100011111","11111","100011111",31,287,16159,"."]
[null,16272,16161,null,31,400,"11111","110010000","11111110010000","11111100100001","11111","100100001",31,289,16161,"."]
[null,16273,16163,null,31,401,"11111","110010001","11111110010001","11111100100011","11111","100100011",31,291,16163,"."]
[null,16274,16165,null,31,402,"11111","110010010","11111110010010","11111100100101","11111","100100101",31,293,16165,"."]
[null,16275,16167,null,31,403,"11111","110010011","11111110010011","11111100100111","11111","100100111",31,295,16167,"."]
[null,16276,16169,null,31,404,"11111","110010100","11111110010100","11111100101001","11111","100101001",31,297,16169,"."]
[null,16277,16171,null,31,405,"11111","110010101","11111110010101","11111100101011","11111","100101011",31,299,16171,"."]
[null,16278,16173,null,31,406,"11111","110010110","11111110010110","11111100101101","11111","100101101",31,301,16173,"."]
[null,16279,16175,null,31,407,"11111","110010111","11111110010111","11111100101111","11111","100101111",31,303,16175,"."]
[null,16280,16177,null,31,408,"11111","110011000","11111110011000","11111100110001","11111","100110001",31,305,16177,"."]
[null,16281,16179,null,31,409,"11111","110011001","11111110011001","11111100110011","11111","100110011",31,307,16179,"."]
[null,16282,16181,null,31,410,"11111","110011010","11111110011010","11111100110101","11111","100110101",31,309,16181,"."]
[null,16283,16183,null,31,411,"11111","110011011","11111110011011","11111100110111","11111","100110111",31,311,16183,"."]
[null,16284,16185,null,31,412,"11111","110011100","11111110011100","11111100111001","11111","100111001",31,313,16185,"."]
[null,16285,16187,null,31,413,"11111","110011101","11111110011101","11111100111011","11111","100111011",31,315,16187,"."]
[null,16286,16189,null,31,414,"11111","110011110","11111110011110","11111100111101","11111","100111101",31,317,16189,"."]
[null,16287,16191,null,31,415,"11111","110011111","11111110011111","11111100111111","11111","100111111",31,319,16191,"."]
[null,16288,16193,null,31,416,"11111","110100000","11111110100000","11111101000001","11111","101000001",31,321,16193,"."]
[null,16289,16195,null,31,417,"11111","110100001","11111110100001","11111101000011","11111","101000011",31,323,16195,"."]
[null,16290,16197,null,31,418,"11111","110100010","11111110100010","11111101000101","11111","101000101",31,325,16197,"."]
[null,16291,16199,null,31,419,"11111","110100011","11111110100011","11111101000111","11111","101000111",31,327,16199,"."]
[null,16292,16201,null,31,420,"11111","110100100","11111110100100","11111101001001","11111","101001001",31,329,16201,"."]
[null,16293,16203,null,31,421,"11111","110100101","11111110100101","11111101001011","11111","101001011",31,331,16203,"."]
[null,16294,16205,null,31,422,"11111","110100110","11111110100110","11111101001101","11111","101001101",31,333,16205,"."]
[null,16295,16207,null,31,423,"11111","110100111","11111110100111","11111101001111","11111","101001111",31,335,16207,"."]
[null,16296,16209,null,31,424,"11111","110101000","11111110101000","11111101010001","11111","101010001",31,337,16209,"."]
[null,16297,16211,null,31,425,"11111","110101001","11111110101001","11111101010011","11111","101010011",31,339,16211,"."]
[null,16298,16213,null,31,426,"11111","110101010","11111110101010","11111101010101","11111","101010101",31,341,16213,"."]
[null,16299,16215,null,31,427,"11111","110101011","11111110101011","11111101010111","11111","101010111",31,343,16215,"."]
[null,16300,16217,null,31,428,"11111","110101100","11111110101100","11111101011001","11111","101011001",31,345,16217,"."]
[null,16301,16219,null,31,429,"11111","110101101","11111110101101","11111101011011","11111","101011011",31,347,16219,"."]
[null,16302,16221,null,31,430,"11111","110101110","11111110101110","11111101011101","11111","101011101",31,349,16221,"."]
[null,16303,16223,null,31,431,"11111","110101111","11111110101111","11111101011111","11111","101011111",31,351,16223,"."]
[null,16304,16225,null,31,432,"11111","110110000","11111110110000","11111101100001","11111","101100001",31,353,16225,"."]
[null,16305,16227,null,31,433,"11111","110110001","11111110110001","11111101100011","11111","101100011",31,355,16227,"."]
[null,16306,16229,null,31,434,"11111","110110010","11111110110010","11111101100101","11111","101100101",31,357,16229,"."]
[null,16307,16231,null,31,435,"11111","110110011","11111110110011","11111101100111","11111","101100111",31,359,16231,"."]
[null,16308,16233,null,31,436,"11111","110110100","11111110110100","11111101101001","11111","101101001",31,361,16233,"."]
[null,16309,16235,null,31,437,"11111","110110101","11111110110101","11111101101011","11111","101101011",31,363,16235,"."]
[null,16310,16237,null,31,438,"11111","110110110","11111110110110","11111101101101","11111","101101101",31,365,16237,"."]
[null,16311,16239,null,31,439,"11111","110110111","11111110110111","11111101101111","11111","101101111",31,367,16239,"."]
[null,16312,16241,null,31,440,"11111","110111000","11111110111000","11111101110001","11111","101110001",31,369,16241,"."]
[null,16313,16243,null,31,441,"11111","110111001","11111110111001","11111101110011","11111","101110011",31,371,16243,"."]
[null,16314,16245,null,31,442,"11111","110111010","11111110111010","11111101110101","11111","101110101",31,373,16245,"."]
[null,16315,16247,null,31,443,"11111","110111011","11111110111011","11111101110111","11111","101110111",31,375,16247,"."]
[null,16316,16249,null,31,444,"11111","110111100","11111110111100","11111101111001","11111","101111001",31,377,16249,"."]
[null,16317,16251,null,31,445,"11111","110111101","11111110111101","11111101111011","11111","101111011",31,379,16251,"."]
[null,16318,16253,null,31,446,"11111","110111110","11111110111110","11111101111101","11111","101111101",31,381,16253,"."]
[null,16319,16255,null,31,447,"11111","110111111","11111110111111","11111101111111","11111","101111111",31,383,16255,"."]
[null,16320,16257,null,31,448,"11111","111000000","11111111000000","11111110000001","11111","110000001",31,385,16257,"."]
[null,16321,16259,null,31,449,"11111","111000001","11111111000001","11111110000011","11111","110000011",31,387,16259,"."]
[null,16322,16261,null,31,450,"11111","111000010","11111111000010","11111110000101","11111","110000101",31,389,16261,"."]
[null,16323,16263,null,31,451,"11111","111000011","11111111000011","11111110000111","11111","110000111",31,391,16263,"."]
[null,16324,16265,null,31,452,"11111","111000100","11111111000100","11111110001001","11111","110001001",31,393,16265,"."]
[null,16325,16267,null,31,453,"11111","111000101","11111111000101","11111110001011","11111","110001011",31,395,16267,"."]
[null,16326,16269,null,31,454,"11111","111000110","11111111000110","11111110001101","11111","110001101",31,397,16269,"."]
[null,16327,16271,null,31,455,"11111","111000111","11111111000111","11111110001111","11111","110001111",31,399,16271,"."]
[null,16328,16273,null,31,456,"11111","111001000","11111111001000","11111110010001","11111","110010001",31,401,16273,"."]
[null,16329,16275,null,31,457,"11111","111001001","11111111001001","11111110010011","11111","110010011",31,403,16275,"."]
[null,16330,16277,null,31,458,"11111","111001010","11111111001010","11111110010101","11111","110010101",31,405,16277,"."]
[null,16331,16279,null,31,459,"11111","111001011","11111111001011","11111110010111","11111","110010111",31,407,16279,"."]
[null,16332,16281,null,31,460,"11111","111001100","11111111001100","11111110011001","11111","110011001",31,409,16281,"."]
[null,16333,16283,null,31,461,"11111","111001101","11111111001101","11111110011011","11111","110011011",31,411,16283,"."]
[null,16334,16285,null,31,462,"11111","111001110","11111111001110","11111110011101","11111","110011101",31,413,16285,"."]
[null,16335,16287,null,31,463,"11111","111001111","11111111001111","11111110011111","11111","110011111",31,415,16287,"."]
[null,16336,16289,null,31,464,"11111","111010000","11111111010000","11111110100001","11111","110100001",31,417,16289,"."]
[null,16337,16291,null,31,465,"11111","111010001","11111111010001","11111110100011","11111","110100011",31,419,16291,"."]
[null,16338,16293,null,31,466,"11111","111010010","11111111010010","11111110100101","11111","110100101",31,421,16293,"."]
[null,16339,16295,null,31,467,"11111","111010011","11111111010011","11111110100111","11111","110100111",31,423,16295,"."]
[null,16340,16297,null,31,468,"11111","111010100","11111111010100","11111110101001","11111","110101001",31,425,16297,"."]
[null,16341,16299,null,31,469,"11111","111010101","11111111010101","11111110101011","11111","110101011",31,427,16299,"."]
[null,16342,16301,null,31,470,"11111","111010110","11111111010110","11111110101101","11111","110101101",31,429,16301,"."]
[null,16343,16303,null,31,471,"11111","111010111","11111111010111","11111110101111","11111","110101111",31,431,16303,"."]
[null,16344,16305,null,31,472,"11111","111011000","11111111011000","11111110110001","11111","110110001",31,433,16305,"."]
[null,16345,16307,null,31,473,"11111","111011001","11111111011001","11111110110011","11111","110110011",31,435,16307,"."]
[null,16346,16309,null,31,474,"11111","111011010","11111111011010","11111110110101","11111","110110101",31,437,16309,"."]
[null,16347,16311,null,31,475,"11111","111011011","11111111011011","11111110110111","11111","110110111",31,439,16311,"."]
[null,16348,16313,null,31,476,"11111","111011100","11111111011100","11111110111001","11111","110111001",31,441,16313,"."]
[null,16349,16315,null,31,477,"11111","111011101","11111111011101","11111110111011","11111","110111011",31,443,16315,"."]
[null,16350,16317,null,31,478,"11111","111011110","11111111011110","11111110111101","11111","110111101",31,445,16317,"."]
[null,16351,16319,null,31,479,"11111","111011111","11111111011111","11111110111111","11111","110111111",31,447,16319,"."]
[null,16352,16321,null,31,480,"11111","111100000","11111111100000","11111111000001","11111","111000001",31,449,16321,"."]
[null,16353,16323,null,31,481,"11111","111100001","11111111100001","11111111000011","11111","111000011",31,451,16323,"."]
[null,16354,16325,null,31,482,"11111","111100010","11111111100010","11111111000101","11111","111000101",31,453,16325,"."]
[null,16355,16327,null,31,483,"11111","111100011","11111111100011","11111111000111","11111","111000111",31,455,16327,"."]
[null,16356,16329,null,31,484,"11111","111100100","11111111100100","11111111001001","11111","111001001",31,457,16329,"."]
[null,16357,16331,null,31,485,"11111","111100101","11111111100101","11111111001011","11111","111001011",31,459,16331,"."]
[null,16358,16333,null,31,486,"11111","111100110","11111111100110","11111111001101","11111","111001101",31,461,16333,"."]
[null,16359,16335,null,31,487,"11111","111100111","11111111100111","11111111001111","11111","111001111",31,463,16335,"."]
[null,16360,16337,null,31,488,"11111","111101000","11111111101000","11111111010001","11111","111010001",31,465,16337,"."]
[null,16361,16339,null,31,489,"11111","111101001","11111111101001","11111111010011","11111","111010011",31,467,16339,"."]
[null,16362,16341,null,31,490,"11111","111101010","11111111101010","11111111010101","11111","111010101",31,469,16341,"."]
[null,16363,16343,null,31,491,"11111","111101011","11111111101011","11111111010111","11111","111010111",31,471,16343,"."]
[null,16364,16345,null,31,492,"11111","111101100","11111111101100","11111111011001","11111","111011001",31,473,16345,"."]
[null,16365,16347,null,31,493,"11111","111101101","11111111101101","11111111011011","11111","111011011",31,475,16347,"."]
[null,16366,16349,null,31,494,"11111","111101110","11111111101110","11111111011101","11111","111011101",31,477,16349,"."]
[null,16367,16351,null,31,495,"11111","111101111","11111111101111","11111111011111","11111","111011111",31,479,16351,"."]
[null,16368,16353,null,31,496,"11111","111110000","11111111110000","11111111100001","11111","111100001",31,481,16353,"."]
[null,16369,16355,null,31,497,"11111","111110001","11111111110001","11111111100011","11111","111100011",31,483,16355,"."]
[null,16370,16357,null,31,498,"11111","111110010","11111111110010","11111111100101","11111","111100101",31,485,16357,"."]
[null,16371,16359,null,31,499,"11111","111110011","11111111110011","11111111100111","11111","111100111",31,487,16359,"."]
[null,16372,16361,null,31,500,"11111","111110100","11111111110100","11111111101001","11111","111101001",31,489,16361,"."]
[null,16373,16363,null,31,501,"11111","111110101","11111111110101","11111111101011","11111","111101011",31,491,16363,"."]
[null,16374,16365,null,31,502,"11111","111110110","11111111110110","11111111101101","11111","111101101",31,493,16365,"."]
[null,16375,16367,null,31,503,"11111","111110111","11111111110111","11111111101111","11111","111101111",31,495,16367,"."]
[null,16376,16369,null,31,504,"11111","111111000","11111111111000","11111111110001","11111","111110001",31,497,16369,"."]
[null,16377,16371,null,31,505,"11111","111111001","11111111111001","11111111110011","11111","111110011",31,499,16371,"."]
[null,16378,16373,null,31,506,"11111","111111010","11111111111010","11111111110101","11111","111110101",31,501,16373,"."]
[null,16379,16375,null,31,507,"11111","111111011","11111111111011","11111111110111","11111","111110111",31,503,16375,"."]
[null,16380,16377,null,31,508,"11111","111111100","11111111111100","11111111111001","11111","111111001",31,505,16377,"."]
[null,16381,16379,null,31,509,"11111","111111101","11111111111101","11111111111011","11111","111111011",31,507,16379,"."]
[null,16382,16381,null,31,510,"11111","111111110","11111111111110","11111111111101","11111","111111101",31,509,16381,"."]
[null,16383,16383,null,31,511,"11111","111111111","11111111111111","11111111111111","11111","111111111",31,511,16383,"."]

{"sheet":"Inverse","index":3,"n_rows":16391,"n_cols":50,"rows_kept":16391,"cut":false,"hidden":false,"merged":[[4,4,4,5]]}
[]
[null,null,null,null,"Fonction inverse : nb de lampadaires qui aboutissent à un n° du dernier lampadaire à éteindre"]
[]
[]
[null,null,null,null,"Classt par N° fin"]
[]
[null,"N° fin","nb de\nlamp",null,"N° fin","nb de\nlamp",null,null,null,null,null,null,null,null,null,null,null,"nf","k",null,null,"1er",null,null,0,1,2,3,4,5]
[]
[null,1,1,null,1,1,null,"Ce sont toutes les puissances de 2, à partir de 20",null,null,null,null,null,null,null,null,null,1,{"$f":"(R9-1)/2","v":0},null,null,{"$f":"CONCATENATE(S9,\" + 2^\",S9)","v":"0 + 2^0"},null,null,{"$f":"$S9+2^($S9+Y$7)","v":1},{"$f":"$S9+2^($S9+Z$7)","v":2},4,8,16,32]
[null,1,2,null,1,2,null,null,null,null,null,null,null,null,null,null,null,3,{"$f":"(R10-1)/2","v":1},null,null,{"$f":"CONCATENATE(S10,\" + 2^\",S10)","v":"1 + 2^1"},null,null,{"$f":"$S10+2^($S10+Y$7)","v":3},5,9,17,33,65]
[null,3,3,null,1,4,null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"(R11-1)/2","v":2},null,null,{"$f":"CONCATENATE(S11,\" + 2^\",S11)","v":"2 + 2^2"},null,null,{"$f":"$S11+2^($S11+Y$7)","v":6},10,18,34,66,130]
[null,1,4,null,1,8,null,null,null,null,null,null,null,null,null,null,null,7,{"$f":"(R12-1)/2","v":3},null,null,{"$f":"CONCATENATE(S12,\" + 2^\",S12)","v":"3 + 2^3"},null,null,{"$f":"$S12+2^($S12+Y$7)","v":11},19,35,67,131,259,null,"Exception, il démarre avec k = 2 pour la puissance"]
[null,3,5,null,1,16,null,null,null,null,null,null,null,null,null,null,null,null,"k1","k2"]
[null,5,6,null,1,32,null,null,null,null,null,null,null,null,null,null,null,7,{"$f":"T14-1","v":2},{"$f":"(R14-1)/2","v":3},null,{"$f":"CONCATENATE(T14,\" + 2^\",S14)","v":"3 + 2^2"},null,null,{"$f":"$T14+2^($S14+Y$7)","v":7},{"$f":"$T14+2^($S14+Z$7)","v":11},19,35,67,131]
[null,7,7,null,1,64,null,null,null,null,null,null,null,null,null,null,null,9,{"$f":"T15-1","v":3},{"$f":"(R15-1)/2","v":4},null,{"$f":"CONCATENATE(T15,\" + 2^\",S15)","v":"4 + 2^3"},null,null,{"$f":"$T15+2^($S15+Y$7)","v":12},20,36,68,132,260]
[null,1,8,null,1,128,null,null,null,null,null,null,null,null,null,null,null,11,{"$f":"T16-1","v":4},{"$f":"(R16-1)/2","v":5},null,{"$f":"CONCATENATE(T16,\" + 2^\",S16)","v":"5 + 2^4"},null,null,{"$f":"$T16+2^($S16+Y$7)","v":21},37,69,133,261,517,null,"Là aussi on redescend la puissance"]
[null,3,9,null,1,256,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Il semble, de manière à ce que le 1er nb de lampadaires soit supérieur ou égal à nf"]
[null,5,10,null,1,512,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Chercher la première puissance x"]
[null,7,11,null,1,1024,null,null,null,null,null,null,null,null,null,null,null,1,{"$f":"ROUNDUP(LOG((R19+1)/2)/LOG(2),0)","v":0},{"$f":"(R19-1)/2","v":0},null,{"$f":"CONCATENATE(T19,\" + 2^\",S19)","v":"0 + 2^0"},null,null,{"$f":"$T19+2^($S19+Y$7)","v":1},{"$f":"$T19+2^($S19+Z$7)","v":2},4,8,16,32,null,"k2 + 2x = nf",null,null,null,"avec k2 = (nf - 1)/2"]
[null,9,12,null,1,2048,null,null,null,null,null,null,null,null,null,null,null,3,{"$f":"ROUNDUP(LOG((R20+1)/2)/LOG(2),0)","v":1},{"$f":"(R20-1)/2","v":1},null,{"$f":"CONCATENATE(T20,\" + 2^\",S20)","v":"1 + 2^1"},null,null,{"$f":"$T20+2^($S20+Y$7)","v":3},5,9,17,33,65,null,"2x = nf - (nf - 1)/2 = (nf + 1)/2"]
[null,11,13,null,1,4096,null,null,null,null,null,null,null,null,null,null,null,5,2,2,null,"2 + 2^2",null,null,6,10,18,34,66,130,null,"x log(2)= log(nf + 1)-log2",null,null,null,null,null,null,"nf",1,3,5,7,9,11,13,15,17,19,21]
[null,13,14,null,1,8192,null,null,null,null,null,null,null,null,null,null,null,7,2,3,null,"3 + 2^2",null,null,7,11,19,35,67,131,null,null,null,null,null,null,null,null,"x",{"$f":"(LOG(AN21+1)-LOG(2))/LOG(2)","v":0},{"$f":"(LOG(AO21+1)-LOG(2))/LOG(2)","v":1},1.5849625007211561,1.9999999999999996,2.3219280948873622,2.5849625007211561,2.8073549220576037,3,3.1699250014423122,3.3219280948873622,3.4594316186372969]
[null,15,15,null,3,3,null,"Ce sont les valeurs de 1 + 2n, à partir de n = 1",null,null,null,null,null,null,null,null,null,9,3,4,null,"4 + 2^3",null,null,12,20,36,68,132,260,null,"Arrondi supérieur",null,null,null,null,null,null,"k1",{"$f":"ROUNDUP(AN22,0)","v":0},{"$f":"ROUNDUP(AO22,0)","v":1},2,2,3,3,3,3,4,4,4]
[null,1,16,null,3,5,null,null,null,null,null,null,null,null,null,null,null,11,3,5,null,"5 + 2^3",null,null,13,21,37,69,133,261]
[null,3,17,null,3,9,null,null,null,null,null,null,null,null,null,null,null,13,3,6,null,"6 + 2^3",null,null,14,22,38,70,134,262]
[null,5,18,null,3,17,null,null,null,null,null,null,null,null,null,null,null,15,3,7,null,"7 + 2^3",null,null,15,23,39,71,135,263]
[null,7,19,null,3,33,null,null,null,null,null,null,null,null,null,null,null,17,4,8,null,"8 + 2^4",null,null,24,40,72,136,264,520]
[null,9,20,null,3,65,null,null,null,null,null,null,null,null,null,null,null,19,4,9,null,"9 + 2^4",null,null,25,41,73,137,265,521]
[null,11,21,null,3,129]
[null,13,22,null,3,257,null,null,null,null,null,null,null,null,null,null,null,35,5,{"$f":"(R30-1)/2","v":17},null,{"$f":"CONCATENATE(T30,\" + 2^\",S30)","v":"17 + 2^5"},null,null,49,81,145,273,529,1041]
[null,15,23,null,3,513]
[null,17,24,null,3,1025,null,null,null,null,null,null,null,null,null,null,null,101,6,{"$f":"(R32-1)/2","v":50},null,{"$f":"CONCATENATE(T32,\" + 2^\",S32)","v":"50 + 2^6"},null,null,114,178,306,562,1074,2098]
[null,19,25,null,3,2049]
[null,21,26,null,3,4097,null,null,null,null,null,null,null,null,null,null,null,223,7,{"$f":"(R34-1)/2","v":111},null,{"$f":"CONCATENATE(T34,\" + 2^\",S34)","v":"111 + 2^7"},null,null,239,367,623,1135,2159,4207]
[null,23,27,null,3,8193]
[null,25,28,null,5,6,null,"Valeurs de 2 + 2n, à partir de n = 2",null,null,null,null,null,null,null,null,null,527,9,{"$f":"(R36-1)/2","v":263},null,{"$f":"CONCATENATE(T36,\" + 2^\",S36)","v":"263 + 2^9"},null,null,775,1287,2311,4359,8455,16647]
[null,27,29,null,5,10]
[null,29,30,null,5,18,null,null,null,null,null,null,null,null,null,null,null,1051,10,{"$f":"(R38-1)/2","v":525},null,{"$f":"CONCATENATE(T38,\" + 2^\",S38)","v":"525 + 2^10"},null,null,1549,2573,4621,8717,16909,33293]
[null,31,31,null,5,34,null,"Soit nf le n° du lampadaire final, le dernier à éteindre"]
[null,1,32,null,5,66,null,"La première puissance de 2 est k avec k = (nf - 1)/2",null,null,null,null,null,null,null,null,null,1517,10,{"$f":"(R40-1)/2","v":758},null,{"$f":"CONCATENATE(T40,\" + 2^\",S40)","v":"758 + 2^10"},null,null,1782,2806,4854,8950,17142,33526]
[null,3,33,null,5,130,null,null,null,"à incrémenter"]
[null,5,34,null,5,258,null,"La quantité à ajouter est k également, qui reste constante",null,null,null,null,null,null,null,null,null,2017,10,{"$f":"(R42-1)/2","v":1008},null,{"$f":"CONCATENATE(T42,\" + 2^\",S42)","v":"1008 + 2^10"},null,null,2032,3056,5104,9200,17392,33776]
[null,7,35,null,5,514]
[null,9,36,null,5,1026]
[null,11,37,null,5,2050]
[null,13,38,null,5,4098]
[null,15,39,null,5,8194]
[null,17,40,null,7,7]
[null,19,41,null,7,11]
[null,21,42,null,7,19]
[null,23,43,null,7,35]
[null,25,44,null,7,67]
[null,27,45,null,7,131]
[null,29,46,null,7,259]
[null,31,47,null,7,515]
[null,33,48,null,7,1027]
[null,35,49,null,7,2051]
[null,37,50,null,7,4099]
[null,39,51,null,7,8195]
[null,41,52,null,9,12]
[null,43,53,null,9,20]
[null,45,54,null,9,36]
[null,47,55,null,9,68]
[null,49,56,null,9,132]
[null,51,57,null,9,260]
[null,53,58,null,9,516]
[null,55,59,null,9,1028]
[null,57,60,null,9,2052]
[null,59,61,null,9,4100]
[null,61,62,null,9,8196]
[null,63,63,null,11,13]
[null,1,64,null,11,21]
[null,3,65,null,11,37]
[null,5,66,null,11,69]
[null,7,67,null,11,133]
[null,9,68,null,11,261]
[null,11,69,null,11,517]
[null,13,70,null,11,1029]
[null,15,71,null,11,2053]
[null,17,72,null,11,4101]
[null,19,73,null,11,8197]
[null,21,74,null,13,14]
[null,23,75,null,13,22]
[null,25,76,null,13,38]
[null,27,77,null,13,70]
[null,29,78,null,13,134]
[null,31,79,null,13,262]
[null,33,80,null,13,518]
[null,35,81,null,13,1030]
[null,37,82,null,13,2054]
[null,39,83,null,13,4102]
[null,41,84,null,13,8198]
[null,43,85,null,15,15]
[null,45,86,null,15,23]
[null,47,87,null,15,39]
[null,49,88,null,15,71]
[null,51,89,null,15,135]
[null,53,90,null,15,263]
[null,55,91,null,15,519]
[null,57,92,null,15,1031]
[null,59,93,null,15,2055]
[null,61,94,null,15,4103]
[null,63,95,null,15,8199]
[null,65,96,null,17,24]
[null,67,97,null,17,40]
[null,69,98,null,17,72]
[null,71,99,null,17,136]
[null,73,100,null,17,264]
[null,75,101,null,17,520]
[null,77,102,null,17,1032]
[null,79,103,null,17,2056]
[null,81,104,null,17,4104]
[null,83,105,null,17,8200]
[null,85,106,null,19,25]
[null,87,107,null,19,41]
[null,89,108,null,19,73]
[null,91,109,null,19,137]
[null,93,110,null,19,265]
[null,95,111,null,19,521]
[null,97,112,null,19,1033]
[null,99,113,null,19,2057]
[null,101,114,null,19,4105]
[null,103,115,null,19,8201]
[null,105,116,null,21,26]
[null,107,117,null,21,42]
[null,109,118,null,21,74]
[null,111,119,null,21,138]
[null,113,120,null,21,266]
[null,115,121,null,21,522]
[null,117,122,null,21,1034]
[null,119,123,null,21,2058]
[null,121,124,null,21,4106]
[null,123,125,null,21,8202]
[null,125,126,null,23,27]
[null,127,127,null,23,43]
[null,1,128,null,23,75]
[null,3,129,null,23,139]
[null,5,130,null,23,267]
[null,7,131,null,23,523]
[null,9,132,null,23,1035]
[null,11,133,null,23,2059]
[null,13,134,null,23,4107]
[null,15,135,null,23,8203]
[null,17,136,null,25,28]
[null,19,137,null,25,44]
[null,21,138,null,25,76]
[null,23,139,null,25,140]
[null,25,140,null,25,268]
[null,27,141,null,25,524]
[null,29,142,null,25,1036]
[null,31,143,null,25,2060]
[null,33,144,null,25,4108]
[null,35,145,null,25,8204]
[null,37,146,null,27,29]
[null,39,147,null,27,45]
[null,41,148,null,27,77]
[null,43,149,null,27,141]
[null,45,150,null,27,269]
[null,47,151,null,27,525]
[null,49,152,null,27,1037]
[null,51,153,null,27,2061]
[null,53,154,null,27,4109]
[null,55,155,null,27,8205]
[null,57,156,null,29,30]
[null,59,157,null,29,46]
[null,61,158,null,29,78]
[null,63,159,null,29,142]
[null,65,160,null,29,270]
[null,67,161,null,29,526]
[null,69,162,null,29,1038]
[null,71,163,null,29,2062]
[null,73,164,null,29,4110]
[null,75,165,null,29,8206]
[null,77,166,null,31,31]
[null,79,167,null,31,47]
[null,81,168,null,31,79]
[null,83,169,null,31,143]
[null,85,170,null,31,271]
[null,87,171,null,31,527]
[null,89,172,null,31,1039]
[null,91,173,null,31,2063]
[null,93,174,null,31,4111]
[null,95,175,null,31,8207]
[null,97,176,null,33,48]
[null,99,177,null,33,80]
[null,101,178,null,33,144]
[null,103,179,null,33,272]
[null,105,180,null,33,528]
[null,107,181,null,33,1040]
[null,109,182,null,33,2064]
[null,111,183,null,33,4112]
[null,113,184,null,33,8208]
[null,115,185,null,35,49]
[null,117,186,null,35,81]
[null,119,187,null,35,145]
[null,121,188,null,35,273]
[null,123,189,null,35,529]
[null,125,190,null,35,1041]
[null,127,191,null,35,2065]
[null,129,192,null,35,4113]
[null,131,193,null,35,8209]
[null,133,194,null,37,50]
[null,135,195,null,37,82]
[null,137,196,null,37,146]
[null,139,197,null,37,274]
[null,141,198,null,37,530]
[null,143,199,null,37,1042]
[null,145,200,null,37,2066]
[null,147,201,null,37,4114]
[null,149,202,null,37,8210]
[null,151,203,null,39,51]
[null,153,204,null,39,83]
[null,155,205,null,39,147]
[null,157,206,null,39,275]
[null,159,207,null,39,531]
[null,161,208,null,39,1043]
[null,163,209,null,39,2067]
[null,165,210,null,39,4115]
[null,167,211,null,39,8211]
[null,169,212,null,41,52]
[null,171,213,null,41,84]
[null,173,214,null,41,148]
[null,175,215,null,41,276]
[null,177,216,null,41,532]
[null,179,217,null,41,1044]
[null,181,218,null,41,2068]
[null,183,219,null,41,4116]
[null,185,220,null,41,8212]
[null,187,221,null,43,53]
[null,189,222,null,43,85]
[null,191,223,null,43,149]
[null,193,224,null,43,277]
[null,195,225,null,43,533]
[null,197,226,null,43,1045]
[null,199,227,null,43,2069]
[null,201,228,null,43,4117]
[null,203,229,null,43,8213]
[null,205,230,null,45,54]
[null,207,231,null,45,86]
[null,209,232,null,45,150]
[null,211,233,null,45,278]
[null,213,234,null,45,534]
[null,215,235,null,45,1046]
[null,217,236,null,45,2070]
[null,219,237,null,45,4118]
[null,221,238,null,45,8214]
[null,223,239,null,47,55]
[null,225,240,null,47,87]
[null,227,241,null,47,151]
[null,229,242,null,47,279]
[null,231,243,null,47,535]
[null,233,244,null,47,1047]
[null,235,245,null,47,2071]
[null,237,246,null,47,4119]
[null,239,247,null,47,8215]
[null,241,248,null,49,56]
[null,243,249,null,49,88]
[null,245,250,null,49,152]
[null,247,251,null,49,280]
[null,249,252,null,49,536]
[null,251,253,null,49,1048]
[null,253,254,null,49,2072]
[null,255,255,null,49,4120]
[null,1,256,null,49,8216]
[null,3,257,null,51,57]
[null,5,258,null,51,89]
[null,7,259,null,51,153]
[null,9,260,null,51,281]
[null,11,261,null,51,537]
[null,13,262,null,51,1049]
[null,15,263,null,51,2073]
[null,17,264,null,51,4121]
[null,19,265,null,51,8217]
[null,21,266,null,53,58]
[null,23,267,null,53,90]
[null,25,268,null,53,154]
[null,27,269,null,53,282]
[null,29,270,null,53,538]
[null,31,271,null,53,1050]
[null,33,272,null,53,2074]
[null,35,273,null,53,4122]
[null,37,274,null,53,8218]
[null,39,275,null,55,59]
[null,41,276,null,55,91]
[null,43,277,null,55,155]
[null,45,278,null,55,283]
[null,47,279,null,55,539]
[null,49,280,null,55,1051]
[null,51,281,null,55,2075]
[null,53,282,null,55,4123]
[null,55,283,null,55,8219]
[null,57,284,null,57,60]
[null,59,285,null,57,92]
[null,61,286,null,57,156]
[null,63,287,null,57,284]
[null,65,288,null,57,540]
[null,67,289,null,57,1052]
[null,69,290,null,57,2076]
[null,71,291,null,57,4124]
[null,73,292,null,57,8220]
[null,75,293,null,59,61]
[null,77,294,null,59,93]
[null,79,295,null,59,157]
[null,81,296,null,59,285]
[null,83,297,null,59,541]
[null,85,298,null,59,1053]
[null,87,299,null,59,2077]
[null,89,300,null,59,4125]
[null,91,301,null,59,8221]
[null,93,302,null,61,62]
[null,95,303,null,61,94]
[null,97,304,null,61,158]
[null,99,305,null,61,286]
[null,101,306,null,61,542]
[null,103,307,null,61,1054]
[null,105,308,null,61,2078]
[null,107,309,null,61,4126]
[null,109,310,null,61,8222]
[null,111,311,null,63,63]
[null,113,312,null,63,95]
[null,115,313,null,63,159]
[null,117,314,null,63,287]
[null,119,315,null,63,543]
[null,121,316,null,63,1055]
[null,123,317,null,63,2079]
[null,125,318,null,63,4127]
[null,127,319,null,63,8223]
[null,129,320,null,65,96]
[null,131,321,null,65,160]
[null,133,322,null,65,288]
[null,135,323,null,65,544]
[null,137,324,null,65,1056]
[null,139,325,null,65,2080]
[null,141,326,null,65,4128]
[null,143,327,null,65,8224]
[null,145,328,null,67,97]
[null,147,329,null,67,161]
[null,149,330,null,67,289]
[null,151,331,null,67,545]
[null,153,332,null,67,1057]
[null,155,333,null,67,2081]
[null,157,334,null,67,4129]
[null,159,335,null,67,8225]
[null,161,336,null,69,98]
[null,163,337,null,69,162]
[null,165,338,null,69,290]
[null,167,339,null,69,546]
[null,169,340,null,69,1058]
[null,171,341,null,69,2082]
[null,173,342,null,69,4130]
[null,175,343,null,69,8226]
[null,177,344,null,71,99]
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