text: sc1 = {
  1:[0]}
  
  sc2 = {
  1:[0,1],
  2:[0,2],
  3:[0,3],
  4:[0,4],
  5:[0,5],
  6:[0,6]}
  
  sc3 = {
  1:[0,1,2],
  2:[0,1,3],
  3:[0,1,4],
  4:[0,1,5],
  5:[0,1,6],
  6:[0,2,4],
  7:[0,2,5],
  8:[0,2,6],
  9:[0,2,7],
  10:[0,3,6],
  11:[0,3,7],
  12:[0,4,8]}
  
  sc4 = {
  1:[0,1,2,3],
  2:[0,1,2,4],
  3:[0,1,3,4],
  4:[0,1,2,5],
  5:[0,1,2,6],
  6:[0,1,2,7],
  7:[0,1,4,5],
  8:[0,1,5,6],
  9:[0,1,6,7],
  10:[0,2,3,5],
  11:[0,1,3,5],
  12:[0,2,3,6],
  13:[0,1,3,6],
  14:[0,2,3,7],
  15:[0,1,4,6],
  16:[0,1,5,7],
  17:[0,3,4,7],
  18:[0,1,4,7],
  19:[0,1,4,8],
  20:[0,1,5,8],
  21:[0,2,4,6],
  22:[0,2,4,7],
  23:[0,2,5,7],
  24:[0,2,4,8],
  25:[0,2,6,8],
  26:[0,3,5,8],
  27:[0,2,5,8],
  28:[0,3,6,9],
  29:[0,1,3,7]}
  
  sc5 = {
  1:[0,1,2,3,4],
  2:[0,1,2,3,5],
  3:[0,1,2,4,5],
  4:[0,1,2,3,6],
  5:[0,1,2,3,7],
  6:[0,1,2,5,6],
  7:[0,1,2,6,7],
  8:[0,2,3,4,6],
  9:[0,1,2,4,6],
  10:[0,1,3,4,6],
  11:[0,2,3,4,7],
  12:[0,1,3,5,6],
  13:[0,1,2,4,8],
  14:[0,1,2,5,7],
  15:[0,1,2,6,8],
  16:[0,1,3,4,7],
  17:[0,1,3,4,8],
  18:[0,1,4,5,7],
  19:[0,1,3,6,7],
  20:[0,1,5,6,8],
  21:[0,1,4,5,8],
  22:[0,1,4,7,8],
  23:[0,2,3,5,7],
  24:[0,1,3,5,7],
  25:[0,2,3,5,8],
  26:[0,2,4,5,8],
  27:[0,1,3,5,8],
  28:[0,2,3,6,8],
  29:[0,1,3,6,8],
  30:[0,1,4,6,8],
  31:[0,1,3,6,9],
  32:[0,1,4,6,9],
  33:[0,2,4,6,8],
  34:[0,2,4,6,9],
  35:[0,2,4,7,9],
  36:[0,1,2,4,7],
  37:[0,3,4,5,8],
  38:[0,1,2,5,8]}
  
  sc6 = {
  1:[0,1,2,3,4,5],
  2:[0,1,2,3,4,6],
  3:[0,1,2,3,5,6],
  4:[0,1,2,4,5,6],
  5:[0,1,2,3,6,7],
  6:[0,1,2,5,6,7],
  7:[0,1,2,6,7,8],
  8:[0,2,3,4,5,7],
  9:[0,1,2,3,5,7],
  10:[0,1,3,4,5,7],
  11:[0,1,2,4,5,7],
  12:[0,1,2,4,6,7],
  13:[0,1,3,4,6,7],
  14:[0,1,3,4,5,8],
  15:[0,1,2,4,5,8],
  16:[0,1,4,5,6,8],
  17:[0,1,2,4,7,8],
  18:[0,1,2,5,7,8],
  19:[0,1,3,4,7,8],
  20:[0,1,4,5,8,9],
  21:[0,2,3,4,6,8],
  22:[0,1,2,4,6,8],
  23:[0,2,3,5,6,8],
  24:[0,1,3,4,6,8],
  25:[0,1,3,5,6,8],
  26:[0,1,3,5,7,8],
  27:[0,1,3,4,6,9],
  28:[0,1,3,5,6,9],
  29:[0,2,3,6,7,9],
  30:[0,1,3,6,7,9],
  31:[0,1,4,5,7,9],
  32:[0,2,4,5,7,9],
  33:[0,2,3,5,7,9],
  34:[0,1,3,5,7,9],
  35:[0,2,4,6,8,10],
  36:[0,1,2,3,4,7],
  37:[0,1,2,3,4,8],
  38:[0,1,2,3,7,8],
  39:[0,2,3,4,5,8],
  40:[0,1,2,3,5,8],
  41:[0,1,2,3,6,8],
  42:[0,1,2,3,6,9],
  43:[0,1,2,5,6,8],
  44:[0,1,2,5,6,9],
  45:[0,2,3,4,6,9],
  46:[0,1,2,4,6,9],
  47:[0,1,2,4,7,9],
  48:[0,1,2,5,7,9],
  49:[0,1,3,4,7,9],
  50:[0,1,4,6,7,9]}
  
  sc7 = {
  1:[0,1,2,3,4,5,6],
  2:[0,1,2,3,4,5,7],
  3:[0,1,2,3,4,5,8],
  4:[0,1,2,3,4,6,7],
  5:[0,1,2,3,5,6,7],
  6:[0,1,2,3,4,7,8],
  7:[0,1,2,3,6,7,8],
  8:[0,2,3,4,5,6,8],
  9:[0,1,2,3,4,6,8],
  10:[0,1,2,3,4,6,9],
  11:[0,1,3,4,5,6,8],
  12:[0,1,2,3,4,7,9],
  13:[0,1,2,4,5,6,8],
  14:[0,1,2,3,5,7,8],
  15:[0,1,2,4,6,7,8],
  16:[0,1,2,3,5,6,9],
  17:[0,1,2,4,5,6,9],
  18:[0,1,4,5,6,7,9],
  19:[0,1,2,3,6,7,9],
  20:[0,1,2,5,6,7,9],
  21:[0,1,2,4,5,8,9],
  22:[0,1,2,5,6,8,9],
  23:[0,2,3,4,5,7,9],
  24:[0,1,2,3,5,7,9],
  25:[0,2,3,4,6,7,9],
  26:[0,1,3,4,5,7,9],
  27:[0,1,2,4,5,7,9],
  28:[0,1,3,5,6,7,9],
  29:[0,1,2,4,6,7,9],
  30:[0,1,2,4,6,8,9],
  31:[0,1,3,4,6,7,9],
  32:[0,1,3,4,6,8,9],
  33:[0,1,2,4,6,8,10],
  34:[0,1,3,4,6,8,10],
  35:[0,1,3,5,6,8,10],
  36:[0,1,2,3,5,6,8],
  37:[0,1,3,4,5,7,8],
  38:[0,1,2,4,5,7,8]}
  
  sc8 = {
  1:[0,1,2,3,4,5,6,7],
  2:[0,1,2,3,4,5,6,8],
  3:[0,1,2,3,4,5,6,9],
  4:[0,1,2,3,4,5,7,8],
  5:[0,1,2,3,4,6,7,8],
  6:[0,1,2,3,5,6,7,8],
  7:[0,1,2,3,4,5,8,9],
  8:[0,1,2,3,4,7,8,9],
  9:[0,1,2,3,6,7,8,9],
  10:[0,2,3,4,5,6,7,9],
  11:[0,1,2,3,4,5,7,9],
  12:[0,1,3,4,5,6,7,9],
  13:[0,1,2,3,4,6,7,9],
  14:[0,1,2,4,5,6,7,9],
  15:[0,1,2,3,4,6,8,9],
  16:[0,1,2,3,5,7,8,9],
  17:[0,1,3,4,5,6,8,9],
  18:[0,1,2,3,5,6,8,9],
  19:[0,1,2,4,5,6,8,9],
  20:[0,1,2,4,5,7,8,9],
  21:[0,1,2,3,4,6,8,10],
  22:[0,1,2,3,5,6,8,10],
  23:[0,1,2,3,5,7,8,10],
  24:[0,1,2,4,5,6,8,10],
  25:[0,1,2,4,6,7,8,10],
  26:[0,1,3,4,5,7,8,10],
  27:[0,1,2,4,5,7,8,10],
  28:[0,1,3,4,6,7,9,10],
  29:[0,1,2,3,5,6,7,9]}
  
  sc9 = {
  1:[0,1,2,3,4,5,6,7,8],
  2:[0,1,2,3,4,5,6,7,9],
  3:[0,1,2,3,4,5,6,8,9],
  4:[0,1,2,3,4,5,7,8,9],
  5:[0,1,2,3,4,6,7,8,9],
  6:[0,1,2,3,4,5,6,8,10],
  7:[0,1,2,3,4,5,7,8,10],
  8:[0,1,2,3,4,6,7,8,10],
  9:[0,1,2,3,5,6,7,8,10],
  10:[0,1,2,3,4,6,7,9,10],
  11:[0,1,2,3,5,6,7,9,10],
  12:[0,1,2,4,5,6,8,9,10]}
  
  sc10 = {
  1:[0,1,2,3,4,5,6,7,8,9],
  2:[0,1,2,3,4,5,6,7,8,10],
  3:[0,1,2,3,4,5,6,7,9,10],
  4:[0,1,2,3,4,5,6,8,9,10],
  5:[0,1,2,3,4,5,7,8,9,10],
  6:[0,1,2,3,4,6,7,8,9,10]}
  
  sc11 = {
  1:[0,1,2,3,4,5,6,7,8,9,10]}
  
  sc12 = {
  1:[0,1,2,3,4,5,6,7,8,9,10,11]}
  
  def convert(n):
      if n == 1: n = sc1
      elif n == 2: n = sc2
      elif n == 3: n = sc3
      elif n == 4: n = sc4
      elif n == 5: n = sc5
      elif n == 6: n = sc6
      elif n == 7: n = sc7
      elif n == 8: n = sc8
      elif n == 9: n = sc9
      elif n == 10: n = sc10
      elif n == 11: n = sc11
      elif n == 12: n = sc12
      return n
  