Quelle  refinementseqlngs.g   Sprache: unbekannt

#############################################################################
##
#W  refinementseqlngs.g            GAP4 Package `RCWA'            Stefan Kohl
##
##  Data library of groups generated by 3 class transpositions which inter-
##  change residue classes with moduli <= 6: part containing a list of lists
##  of numbers of parts into which Z can be partitioned by applying words of
##  length 1, 2, 3, ... in the generators. For finite groups, the sequences
##  get constant at the length of a shortest respected partition of the res-
##  pective group.
##
#############################################################################

local  refinementseqlngsset, refinementseqlngspos, i;

refinementseqlngsset :=
[[3,3],[3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,
   265,351,465],
 [3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,512],
 [4,4],[4,5,5],[4,5,6,6],
 [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],
 [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],
 [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],
 [4,5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,
   32,33,35,36,38,39,41,42,44,45,47,48,50,51],
 [4,5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,
   32,33,35,36,38,39,41,42,44,45,47,48,50,51,53],
 [4,5,6,8,10,13,16,21,26,34,42,55,68,89,110,144,178,233,
   288,377,466],
 [4,5,6,8,10,13,17,22,29,38,50,66,87,115,152,201,266,352,
   466],
 [4,5,6,8,11,14,19,25,33,44,58,77,102,135,179,237,314,416]
  ,[4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,
   31,32,34,35,37,38,40,41,43,44,46,47,49,50,52],
 [4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,
   32,34,35,37,38,40,41,43,44,46,47,49,50,52,53],
 [4,5,7,9,13,17,25,33,49,65,97,129,193,257,385,513],
 [4,5,7,10,14,20,28,40,56,80,112,160,224,320,448],
 [4,6,6],
 [4,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,
   33,34,36,37,39,40,42,43,45,46,48,49,51,52],
 [4,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,
   33,34,36,37,39,40,42,43,45,46,48,49,51,52,54],
 [4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40],
 [4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,
   42,44,46,48],
 [4,6,8,12,16,22,30,40,54,72,96,128,170,226,300,398,528],
 [4,6,8,12,20,32,52,84,136,220,356,576],
 [4,6,9,13,18,25,34,46,62,83,111,148,197,262,348,462],
 [4,6,9,13,19,27,39,55,79,111,159,223,319,447],
 [4,6,10,14,22,30,46,62,94,126,190,254,382,510],
 [4,6,10,16,26,42,68,110,178,288,466],
 [4,7,11,17,25,37,53,77,109,157,221,317,445],[5,5],
 [5,6,6],[5,6,7,7],
 [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],
 [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],
 [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],
 [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],
 [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],
 [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],
 [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],
 [5,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,
   33,34,36,37,39,40,42,43,45,46,48,49],
 [5,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,
   33,34,36,37,39,40,42,43,45,46,48,49,51],
 [5,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,
   33,34,36,37,39,40,42,43,45,46,48,49,51,52],
 [5,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,
   33,34,36,37,39,40,42,43,45,46,48,49,51,52,54],
 [5,6,7,9,11,14,17,22,27,35,43,56,69,90,111,145,179,234,
   289,378,467],
 [5,6,7,9,11,14,18,23,30,39,51,67,88,116,153,202,267,353,
   467],
 [5,6,7,9,12,15,20,26,34,45,59,78,103,136,180,238,315,417]
  ,[5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,
   32,33,35,36,38,39,41,42,44,45,47,48,50],
 [5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,
   33,35,36,38,39,41,42,44,45,47,48,50,51],
 [5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,
   33,35,36,38,39,41,42,44,45,47,48,50,51,53],
 [5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,
   33,35,36,38,39,41,42,44,45,47,48,50,51,53,54],
 [5,6,8,10,14,18,26,34,50,66,98,130,194,258,386,514],
 [5,6,8,11,15,21,29,41,57,81,113,161,225,321,449],
 [5,7,7],[5,7,8,8],
 [5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,
   34,35,37,38,40,41,43,44,46,47,49,50],
 [5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,
   34,35,37,38,40,41,43,44,46,47,49,50,52],
 [5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,
   34,35,37,38,40,41,43,44,46,47,49,50,52,53],
 [5,7,9,9],
 [5,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,
   34,36,37,39,40,42,43,45,46,48,49,51,52],
 [5,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,
   34,36,37,39,40,42,43,45,46,48,49,51,52,54],
 [5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39],
 [5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,
   43,45],
 [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],
 [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],
 [5,7,9,13,15,19,21,25,27,31,33,37,39,43,45,49,51,55,57,
   61,63],
 [5,7,9,13,17,23,31,41,55,73,97,129,171,227,301,399,529],
 [5,7,9,13,21,33,53,85,137,221,357,577],
 [5,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55],
 [5,7,10,14,19,26,35,47,63,84,112,149,198,263,349,463],
 [5,7,10,14,20,28,40,56,80,112,160,224,320,448],
 [5,7,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53,55,59,
   61,65],[5,7,11,15,23,31,47,63,95,127,191,255,383,511],
 [5,7,11,17,27,43,69,111,179,289,467],
 [5,8,11,14,17,20,23,26,29,32,35,38,41,44],
 [5,8,11,14,17,20,23,26,29,32,35,38,41,44,47],
 [5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56],
 [5,8,12,18,25,35,48,65,88,118,158,211,281],
 [5,8,12,18,26,38,54,78,110,158,222,318,446],
 [5,8,13,19,27,38,52,71,96,129,173,231,308],
 [5,8,13,19,29,41,61,85,125,173,253,349,509],
 [5,8,15,26,37,52,67,86,105,128,151,178,205],
 [5,8,15,26,41,68,118,213,406],
 [5,8,15,26,44,81,148,277,519],[5,9,9],
 [5,9,11,15,17,21,23,27,29,33,35,39,41,45,47,51,53,57,59,
   63,65],[5,9,15,23,35,51,75,107,155,219,315,443],
 [5,10,16,26,38,58,82,122,170,250,346,506],[5,12,12],
 [5,12,15,18,21,24,29,36,45,58,73,93,117,146,184,231,290,
   364,458],
 [5,12,15,18,23,30,37,47,58,73,91,112,139,172,213,262,323,
   399,492],
 [5,12,15,18,23,30,37,48,61,78,101,130,169,220,287,376,493]
  ,[5,12,16,20,28,40,52,72,96,128,172,228,304,404],
 [5,12,19,30,41,56,71,90,109,132,155,182,209],
 [5,12,19,30,41,56,73,94,117,144,171,202,233],
 [5,12,19,30,43,60,77,98,119,144,169,198,227],
 [5,12,19,30,47,87,168,351,760],
 [5,12,19,33,64,134,276,580],
 [5,12,19,34,57,101,188,361,704],
 [5,12,19,34,59,100,184,369,774],
 [5,12,19,34,66,137,288,610],
 [5,12,19,35,63,118,208,375,668],
 [5,12,19,36,55,88,149,255,445],
 [5,12,19,36,63,117,207,372,664],
 [5,12,19,37,70,126,232,436],
 [5,12,22,40,68,120,216,384,720],
 [5,12,22,40,76,160,328,672],[5,12,22,44,84,152,288,536],
 [5,12,23,42,73,120,199,310,501],
 [5,12,23,42,73,120,199,325,563],
 [5,12,23,42,73,120,214,402],[5,12,23,42,73,127,229,402],
 [5,12,23,42,80,164,334,678],[5,12,23,45,87,157,290,526],
 [5,12,26,56,116,240,488],[6,6],[6,7,7],[6,7,8,8],
 [6,7,8,9,9],[6,7,8,9,10,10],
 [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],
 [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],
 [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],
 [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],
 [6,7,8,9,11,12,13,15,16,17,19,20,21,23,24,25,27,28,29,
   31,32,33,35,36,37,39,40,41,43,44,45,47,48,49,51,52,53,
   55,56,57,59,60,61,63,64,65],
 [6,7,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,
   33,35,36,38,39,41,42,44,45,47,48,50,51],
 [6,7,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,
   33,35,36,38,39,41,42,44,45,47,48,50,51,53],
 [6,7,8,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,
   41,43,45,47,49,51,53,55,57,59,61,63,65],
 [6,7,8,9,11,13,16,19,22,27,32,38,46,54,65,78,92,111,132,
   157,189,224,268,321,381,457],
 [6,7,8,9,11,13,16,20,25,31,38,47,58,72,89,110,136,168,
   208,257,318,393,486],
 [6,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,
   34,35,37,38,40,41,43,44,46,47,49,50,52],
 [6,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,
   34,35,37,38,40,41,43,44,46,47,49,50,52,53],
 [6,7,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,
   42,44,46,48,50,52,54,56,58,60,62,64,66],
 [6,7,8,10,12,15,18,23,28,36,44,57,70,91,112,146,180,235,
   290,379,468],
 [6,7,8,10,12,15,19,24,31,40,52,68,89,117,154,203,268,354,
   468],
 [6,7,8,10,12,16,20,26,32,42,52,68,84,110,136,178,220,288,
   356,466],
 [6,7,8,10,13,16,21,27,35,46,60,79,104,137,181,239,316,418 
  ],[6,7,9,9],[6,7,9,10,10],
 [6,7,9,10,11,13,14,15,17,18,19,21,22,23,25,26,27,29,30,
   31,33,34,35,37,38,39,41,42,43,45,46,47,49,50,51,53,54,
   55,57,58,59,61,62,63,65,66],
 [6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,
   34,36,37,39,40,42,43,45,46,48,49,51,52],
 [6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,
   34,36,37,39,40,42,43,45,46,48,49,51,52,54],
 [6,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,
   43,45,47,49,51,53,55,57,59,61,63,65,67],
 [6,7,9,11,13,16,20,24,29,36,44,53,65,80,97,118,145,177,
   215,263,322,392,478],
 [6,7,9,11,14,17,21,26,32,40,49,61,75,93,115,142,176,217,
   269,332,411],
 [6,7,9,11,14,18,23,29,37,47,60,76,97,123,157,199,254,322,
   411],
 [6,7,9,11,14,18,23,30,39,51,67,88,116,153,202,267,353,467 
  ],[6,7,9,11,15,19,27,35,51,67,99,131,195,259,387,515],
 [6,7,9,12,16,22,30,42,58,82,114,162,226,322,450],
 [6,7,9,13,18,26,36,52,72,104,144,208,288,416],[6,8,8],
 [6,8,9,9],[6,8,9,10,10],
 [6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
   26,27,28,29,30,31,32,33,34,35,36,37,38],
 [6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
   26,27,28,29,30,31,32,33,34,35,36,37,38,39],
 [6,8,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,
   34,36,37,39,40,42,43,45,46,48,49,51],
 [6,8,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,
   34,36,37,39,40,42,43,45,46,48,49,51,52],
 [6,8,9,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,
   42,44,46,48,50,52,54,56,58,60,62,64],
 [6,8,9,10,12,14,17,20,25,30,37,44,54,64,79,94,116,138,
   170,202,249,296,365,434],
 [6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,
   35,36,38,39,41,42,44,45,47,48,50,51,53],
 [6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,
   35,36,38,39,41,42,44,45,47,48,50,51,53,54],
 [6,8,10,10],
 [6,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,
   35,37,38,40,41,43,44,46,47,49,50,52],
 [6,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,
   35,37,38,40,41,43,44,46,47,49,50,52,53],
 [6,8,10,12,12],
 [6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40],
 [6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46],
 [6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48],
 [6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48,50,52,54],
 [6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48,50,52,54,56,58,60,62,64],
 [6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48,50,52,54,56,58,60,62,64,66],
 [6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
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   234,288,352,428],
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   123,134,146,158,171,184,198,212,227,242],
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   62,66],
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   27,28,29,30,31,32,33,34,35,36,37],
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   36,37,39,40,42,43,45,46,48,49],
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   36,37,39,40,42,43,45,46,48,49,51],[6,9,11,11],
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   36,38,39,41,42,44,45,47,48,50],
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   36,38,39,41,42,44,45,47,48,50,51],[6,9,11,13,13],
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   39,41,43,45,47,49,51,53,55,57,59,61],
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   45,47,49,51,53,55,57,59,61,63],
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   280,346,426],
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   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],
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   36,37,39,40,42,43,45,46,48,49,51],
 [8,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,
   36,37,39,40,42,43,45,46,48,49,51,52],[8,10,10],
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   44,46,48],
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   44,46,48,50,52,54,56,58,60,62,64],
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   60,62,66],
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   60,64,66],
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   56,58,62,64,66,70,72,74,78,80],
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   56,58,62,64,66,70,72,74,78,80,82],
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   62,64,68],
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   78,82,86],
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   46,48],
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   80,84,88],
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   420],[8,13,16,21,26,33,41,51,64,79,98,121,150,185,228,
   281,347,427],
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   73,77,80,84,87,91,94,98,101,105,108],
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   49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,
   85,87,89,91,93,95],
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   402],
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   95,99],
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   84,87,92,95,100,103,108,111,116,119],
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   84,87,92,95,100,103,108,111,116,119,124],
 [8,15,22,31,40,51,62,75,88,103,118,135,152],
 [8,15,22,34,46,65,84,115,146,196,246,327],
 [8,15,24,35,48,63,80,99,120,143,168,195,224],
 [8,15,24,37,56,75,102,127,162,193,236,273],
 [8,15,24,39,73,144,301,634],
 [8,15,24,40,53,77,94,126,147,187,212,260],
 [8,15,24,40,60,97,160,273,464],
 [8,15,24,40,75,134,237,429],
 [8,15,24,44,74,123,198,335,540],
 [8,15,24,44,80,135,230,385,644],
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 [8,15,29,58,126,252,532],
 [8,18,24,32,44,58,75,96,121,152,191,239,296,367,454],
 [8,18,24,32,44,58,76,100,130,170,222,290,380,498],
 [8,18,26,36,48,63,81,103,130,164,205,255,317,392],
 [8,18,26,36,48,64,84,110,144,188,246,322,422],
 [8,18,27,45,58,84,101,135,156,198,223,273],
 [8,18,32,50,72,98,128,162,200,242],
 [8,18,32,52,78,106,140,176,218,262],
 [8,18,32,52,78,108,142,180,222],
 [8,18,32,52,78,108,142,180,222,268],
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 [8,18,32,58,121,260,596],[8,18,32,58,122,276,676],
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 [8,18,32,65,152,344,791],[8,18,32,66,125,237,442],
 [8,18,32,68,168,376,875],[8,18,32,70,170,394,956],
 [8,18,32,72,176,412],[8,18,34,54,78,106,138,174,214],
 [8,18,34,54,78,106,138,174,214,258],
 [8,18,35,65,111,203,357,663],[8,18,35,65,126,245,440],
 [8,18,35,70,125,245,530],[8,18,35,71,135,255,479],
 [8,18,35,82,197,445],[8,18,36,77,143,276,511],
 [8,18,37,65,117,211,439],[8,18,37,75,173,337,757],
 [8,18,37,79,146,281,518],[8,18,38,74,140,284,614],
 [8,18,38,76,174,406],[8,18,38,82,182,365,747],
 [8,18,40,70,146,283,615],[8,18,40,77,175,357,791],
 [8,18,40,80,156,336,748],[8,18,40,80,185,367,813],
 [8,18,40,96,234,546],[8,18,43,97,225,461],
 [8,18,46,97,218,440],[8,21,43,85,147,259,417],
 [8,21,43,85,147,281,515],[8,21,43,85,169,377,765],
 [8,21,43,95,193,391,743],[8,21,45,99,231,467],
 [8,21,53,119,263,555],[9,9],[9,10,10],[9,10,11,11],
 [9,10,11,12,12],[9,10,11,12,13,13],
 [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],
 [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],
 [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],
 [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],
 [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],
 [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],
 [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],
 [9,10,11,12,13,14,15,17,18,19,20,21,23,24,25,26,27,29,
   30,31,32,33,35,36,37,38,39,41,42,43,44,45,47,48,49,50,
   51,53,54,55,56,57,59,60,61,62,63,65,66,67],
 [9,10,11,12,13,15,15],[9,10,11,12,14,14],
 [9,10,11,12,14,15,16,17,19,20,21,22,24,25,26,27,29,30,
   31,32,34,35,36,37,39,40,41,42,44,45,46,47,49,50,51,52,
   54,55,56,57,59,60,61,62,64,65,66,67,69,70],
 [9,10,11,12,14,15,16,18,19,20,22,23,24,26,27,28,30,31,
   32,34,35,36,38,39,40,42,43,44,46,47,48,50,51,52,54,55,
   56,58,59,60,62,63,64,66],
 [9,10,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,
   35,36,38,39,41,42,44,45,47,48,50,51,53],
 [9,10,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,
   35,36,38,39,41,42,44,45,47,48,50,51,53,54],
 [9,10,11,12,14,16,17,18,20,22,23,24,26,28,29,30,32,34,
   35,36,38,40,41,42,44,46,47,48,50,52,53,54,56,58,59,60,
   62,64,65,66,68,70,71,72,74,76,77,78,80,82],
 [9,10,11,12,14,16,17,19,21,22,24,26,27,29,31,32,34,36,
   37,39,41,42,44,46,47,49,51,52,54,56,57,59,61,62,64,66,
   67,69,71,72,74,76],
 [9,10,11,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,
   42,44,46,48,50,52,54,56,58,60,62,64,66],
 [9,10,11,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,
   42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,
   78,80,82,84,86,88],
 [9,10,11,12,14,16,20,22,26,28,32,34,38,40,44,46,50,52,
   56,58,62,64,68,70,74,76,80,82,86,88],
 [9,10,11,13,14,14],
 [9,10,11,13,14,15,16,17,19,20,21,22,23,25,26,27,28,29,
   31,32,33,34,35,37,38,39,40,41,43,44,45,46,47,49,50,51,
   52,53,55,56,57,58,59,61,62,63,64,65,67,68],
 [9,10,11,13,14,15,16,18,19,20,21,23,24,25,26,28,29,30,
   31,33,34,35,36,38,39,40,41,43,44,45,46,48,49,50,51,53,
   54,55,56,58,59,60,61,63,64,65,66,68,69,70],
 [9,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,
   35,37,38,40,41,43,44,46,47,49,50,52],
 [9,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,
   35,37,38,40,41,43,44,46,47,49,50,52,53],
 [9,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,
   35,37,38,40,41,43,44,46,47,49,50,52,53,55],
 [9,10,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,
   43,45,47,49,51,53,55,57,59,61,63,65,67],
 [9,10,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,
   43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,
   79,81,83,85,87,89],
 [9,10,11,13,15,18,20,23,25,28,30,33,35,38,40,43,45,48,
   50,53,55,58,60,63,65,68,70,73,75,78],
 [9,10,11,13,15,18,21,24,27,30,33,36,39,42,45,48,51,54,
   57,60,63,66,69,72,75,78,81,84,87,90],
 [9,10,11,13,15,19,21,25,27,31,33,37,39,43,45,49,51,55,
   57,61,63,67,69,73,75,79,81,85,87,91],
 [9,10,11,13,15,19,23,30,36,47,57,75,91,120,146,193,235,
   311,379,502],[9,10,12,12],[9,10,12,13,13],
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   32,33,34,35,37,38,39,40,42,43,44,45,47,48,49,50,52,53,
   54,55,57,58,59,60,62,63,64,65,67,68,69,70],
 [9,10,12,13,14,16,17,18,20,21,22,24,25,26,28,29,30,32,
   33,34,36,37,38,40,41,42,44,45,46,48,49,50,52,53,54,56,
   57,58,60,61,62,64,65],
 [9,10,12,13,14,16,17,18,20,21,22,24,25,26,28,29,30,32,
   33,34,36,37,38,40,41,42,44,45,46,48,49,50,52,53,54,56,
   57,58,60,61,62,64,65,66],
 [9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,
   36,37,39,40,42,43,45,46,48,49,51,52],
 [9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,
   36,37,39,40,42,43,45,46,48,49,51,52,54],
 [9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,
   36,37,39,40,42,43,45,46,48,49,51,52,54,55],
 [9,10,12,13,15,17,18,20,22,23,25,27,28,30,32,33,35,37,
   38,40,42,43,45,47,48,50,52,53,55,57,58,60,62,63,65,67,
   68,70,72,73,75,77,78],
 [9,10,12,14,15,17,19,20,22,24,25,27,29,30,32,34,35,37,
   39,40,42,44,45,47,49,50,52,54,55,57,59,60,62,64,65,67,
   69,70,72,74,75,77,79],
 [9,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48,50,52,54,56,58,60,62,64,66],
 [9,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48,50,52,54,56,58,60,62,64,66,68],
 [9,10,12,14,17,19,22,24,27,29,32,34,37,39,42,44,47,49,
   52,54,57,59,62,64,67,69,72,74,77,79,82],
 [9,10,12,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56,
   59,62,65,68,71,74,77,80,83,86,89,92],
 [9,10,12,14,17,20,24,29,35,42,51,62,75,91,111,135,164,
   200,244,297,362,442],
 [9,10,12,14,17,21,26,33,42,54,70,91,119,156,205,270,356,
   470],
 [9,10,12,14,18,21,26,31,38,47,57,71,86,107,131,162,200,
   246,305,375,465],
 [9,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,50,
   52,55,57,60,62,65,67,70,72,75,77,80,82],
 [9,10,12,15,18,22,27,34,42,53,66,84,105,134,168,215,270,
   346,435],
 [9,10,12,16,22,30,42,58,82,114,162,226,322,450],
 [9,11,11],[9,11,12,12],[9,11,12,13,13],
 [9,11,12,13,14,14],[9,11,12,13,14,15,15],
 [9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
   28,29,30,31,32,33,34,35,36,37,38,39,40],
 [9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
   28,29,30,31,32,33,34,35,36,37,38,39,40,41],
 [9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
   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],
 [9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
   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],
 [9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
   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],
 [9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,
   32,33,34,36,37,38,39,41,42,43,44,46,47,48,49,51,52,53,
   54,56,57,58,59,61,62,63,64,66,67,68,69,71],
 [9,11,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,
   36,37,39,40,42,43,45,46,48,49,51,52],
 [9,11,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,
   36,37,39,40,42,43,45,46,48,49,51,52,54],
 [9,11,12,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,
   43,45,47,49,51,53,55,57,59,61,63,65],
 [9,11,12,13,15,17,20,22,25,27,30,32,35,37,40,42,45,47,
   50,52,55,57,60,62,65,67,70,72,75],[9,11,12,14,15,15],
 [9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,35,
   36,38,39,41,42,44,45,47,48,50,51,53],
 [9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,35,
   36,38,39,41,42,44,45,47,48,50,51,53,54],[9,11,13,13],
 [9,11,13,14,14],[9,11,13,14,15,15],
 [9,11,13,14,15,16,16],
 [9,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
   29,30,31,32,33,34,35,36,37,38,39,40,41],
 [9,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
   29,30,31,32,33,34,35,36,37,38,39,40,41,42],
 [9,11,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,32,
   33,34,36,37,38,39,41,42,43,44,46,47,48,49,51,52,53,54,
   56,57,58,59,61,62,63,64,66,67,68,69,71,72],
 [9,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35,
   37,38,40,41,43,44,46,47,49,50,52],
 [9,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35,
   37,38,40,41,43,44,46,47,49,50,52,53],
 [9,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,34,35,
   37,38,40,41,43,44,46,47,49,50,52,53,55],
 [9,11,13,14,16,18,19,20,22,24,25,26,28,30,31,32,34,36,
   37,38,40,42,43,44,46,48,49,50,52,54,55,56,58,60,61,62,
   64,66,67,68,70,72,73,74,76,78,79,80,82,84],
 [9,11,13,14,16,18,19,21,23,24,26,28,29,31,33,34,36,38,
   39,41,43,44,46,48,49,51,53,54,56,58,59,61,63,64,66,68,
   69,71,73,74,76,78],
 [9,11,13,14,16,18,19,21,23,24,26,28,29,31,33,34,36,38,
   39,41,43,44,46,48,49,51,53,54,56,58,59,61,63,64,66,68,
   69,71,73,74,76,78,79],
 [9,11,13,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48,50,52,54,56,58,60,62,64],
 [9,11,13,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,
   44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,
   80,82,84,86,88,90],[9,11,13,15,15],
 [9,11,13,15,16,17,17],
 [9,11,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
   30,31,32,33,34,35,36,37,38,39,40,41,42],
 [9,11,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
   30,31,32,33,34,35,36,37,38,39,40,41,42,43],
 [9,11,13,15,17,17],
 [9,11,13,15,17,18,20,22,23,25,27,28,30,32,33,35,37,38,
   40,42,43,45,47,48,50,52,53,55,57,58,60,62,63,65,67,68,
   70,72,73,75,77,78],
 [9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41],
 [9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,
   45,47],
 [9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,
   45,47,49,51,53],
 [9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,
   45,47,49,51,53,55],
 [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],
 [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],
 [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],
 [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],
 [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]
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   43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,
   79,81],
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   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],
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   65,68,72,75,78,82,85,88,92,95,98,102,105,108,112,115,
   118,122,125,128],
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   118,122,125,128,132],
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   61,63,67,69,73,75,79,81,85,87,91,93,97],
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   46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,
   82,84,86,88,90,92],
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   96,104,112,121,130,139,149,159,169,180,191,202,214,226,
   238,251,264,277,291],
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   271,334,413],
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   46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,
   82,84,86,88,90,92],
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   51,53,56,58,60,63,65,67,70,72,74,77,79,81,84,86,88,91,
   93,95,98,100,102],
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   52,55,57,59,62,64,67,69,71,74,76,79,81,83,86,88,91,93]
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   47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,
   83,85,87,89],
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   62,65,68,71,74,77,80,83,86,89,92,95],
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   237,285,340,406],
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   255],
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   108,116,125,135,144,154,165,175,186,198,209,221,234,246,
   259,273,286,300,315],
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   55,57,59,61,65,67,69,71,75,77,79,81,85,87,89,91,95],
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   57,59,63,65,67],
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   63,65,69,71,75,77,81,83,87,89,93],
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   63,65,69,71,75,77,81,83,87,89,93,95],
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   63,66,69,72,75,78,81,84,87,90,93,96],
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   151,171,182,204,216,240,253,279,293,321],
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   69,71,75,79,81],
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   69,71,75,79,81,85,89,91,95],
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   79,83,87,91,95,99,103,107,111,115],
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   29,30,31,32,33,34,35,36,37,38],
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   29,30,31,32,33,34,35,36,37,38,39,40,41],
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   29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
   47,48],
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   29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
   47,48,49],
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   29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
   47,48,49,50,51],
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   29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
   47,48,49,50,51,52],
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   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],
 [9,12,13,14,16,17,18,20,21,22,24,25,26,28,29,30,32,33,
   34,36,37,38,40,41,42,44,45,46,48,49,50,52,53,54,56,57,
   58,60,61,62,64],
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   37,39,40,42,43,45,46,48,49],
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   37,39,40,42,43,45,46,48,49,51],
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   38,39,41,42,44,45,47,48,50],
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   38,39,41,42,44,45,47,48,50,51],
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   44,46,48,50,52,54,56,58,60],
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   46,48,50,52,54,56,58,60,62],
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   56,60,62,64,68,70,72,76,78,80,84,86,88,92,94,96,100,
   102,104,108,110],
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   270,332,408],
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   106,113,124,132,144,152,165,174,188,197],
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   249,299,365,438],
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   358],[9,12,14,18,22,30,36,48,58,78,94,126,152,204,246,
   330],[9,12,15,15],[9,12,15,16,16],
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   31,32,33,34,35,36,37,38,39,40],
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   31,32,33,34,35,36,37,38,39,40,41],
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   31,32,33,34,35,36,37,38,39,40,41,42,43],
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   47,49,51,53,55,57,59,61,63,65,67],
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   60,63,66,69],
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   63,66,69,72,75],
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   63,66,69,72,75,78,81],
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   63,66,69,72,75,78,81,84],
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   63,66,69,72,75,78,81,84,87],
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   63,66,69,72,75,78,81,84,87,90,93,96],
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   384,488],
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--> --------------------

--> maximum size reached

--> --------------------