manifold_11_13_9_1=[[1,2,3,4,5,6,7,8,9,10,11,12],
  [1,2,3,4,5,6,7,8,9,10,11,13],
  [1,2,3,4,5,6,7,8,9,10,12,13],
  [1,2,3,4,5,6,7,8,9,11,12,13],
  [1,2,3,4,5,6,7,8,10,11,12,13],
  [1,2,3,4,5,6,7,9,10,11,12,13],
  [1,2,3,4,5,6,8,9,10,11,12,13],
  [1,2,3,4,5,7,8,9,10,11,12,13],
  [1,2,3,4,6,7,8,9,10,11,12,13],
  [1,2,3,5,6,7,8,9,10,11,12,13],
  [1,2,4,5,6,7,8,9,10,11,12,13],
  [1,3,4,5,6,7,8,9,10,11,12,13],
  [2,3,4,5,6,7,8,9,10,11,12,13]]

manifold_11_14_61_1=[[1,2,3,4,5,6,7,8,9,10,11,12],
  [1,2,3,4,5,6,7,8,9,10,11,14],
  [1,2,3,4,5,6,7,8,9,10,12,13],
  [1,2,3,4,5,6,7,8,9,10,13,14],
  [1,2,3,4,5,6,7,8,9,11,12,14],
  [1,2,3,4,5,6,7,8,9,12,13,14],
  [1,2,3,4,5,6,7,8,10,11,12,13],
  [1,2,3,4,5,6,7,8,10,11,13,14],
  [1,2,3,4,5,6,7,8,11,12,13,14],
  [1,2,3,4,5,6,7,9,10,11,12,14],
  [1,2,3,4,5,6,7,9,10,12,13,14],
  [1,2,3,4,5,6,7,10,11,12,13,14],
  [1,2,3,4,5,6,8,9,10,11,12,13],
  [1,2,3,4,5,6,8,9,10,11,13,14],
  [1,2,3,4,5,6,8,9,11,12,13,14],
  [1,2,3,4,5,6,9,10,11,12,13,14],
  [1,2,3,4,5,7,8,9,10,11,12,14],
  [1,2,3,4,5,7,8,9,10,12,13,14],
  [1,2,3,4,5,7,8,10,11,12,13,14],
  [1,2,3,4,5,8,9,10,11,12,13,14],
  [1,2,3,4,6,7,8,9,10,11,12,13],
  [1,2,3,4,6,7,8,9,10,11,13,14],
  [1,2,3,4,6,7,8,9,11,12,13,14],
  [1,2,3,4,6,7,9,10,11,12,13,14],
  [1,2,3,4,7,8,9,10,11,12,13,14],
  [1,2,3,5,6,7,8,9,10,11,12,14],
  [1,2,3,5,6,7,8,9,10,12,13,14],
  [1,2,3,5,6,7,8,10,11,12,13,14],
  [1,2,3,5,6,8,9,10,11,12,13,14],
  [1,2,3,6,7,8,9,10,11,12,13,14],
  [1,2,4,5,6,7,8,9,10,11,12,13],
  [1,2,4,5,6,7,8,9,10,11,13,14],
  [1,2,4,5,6,7,8,9,11,12,13,14],
  [1,2,4,5,6,7,9,10,11,12,13,14],
  [1,2,4,5,7,8,9,10,11,12,13,14],
  [1,2,5,6,7,8,9,10,11,12,13,14],
  [1,3,4,5,6,7,8,9,10,11,12,14],
  [1,3,4,5,6,7,8,9,10,12,13,14],
  [1,3,4,5,6,7,8,10,11,12,13,14],
  [1,3,4,5,6,8,9,10,11,12,13,14],
  [1,3,4,6,7,8,9,10,11,12,13,14],
  [1,4,5,6,7,8,9,10,11,12,13,14],
  [2,3,4,5,6,7,8,9,10,11,12,13],
  [2,3,4,5,6,7,8,9,10,11,13,14],
  [2,3,4,5,6,7,8,9,11,12,13,14],
  [2,3,4,5,6,7,9,10,11,12,13,14],
  [2,3,4,5,7,8,9,10,11,12,13,14],
  [2,3,5,6,7,8,9,10,11,12,13,14],
  [3,4,5,6,7,8,9,10,11,12,13,14]]

manifold_11_15_102_1=[[1,2,3,4,5,6,7,8,9,10,11,12],
  [1,2,3,4,5,6,7,8,9,10,11,15],
  [1,2,3,4,5,6,7,8,9,10,12,14],
  [1,2,3,4,5,6,7,8,9,10,14,15],
  [1,2,3,4,5,6,7,8,9,11,12,13],
  [1,2,3,4,5,6,7,8,9,11,13,15],
  [1,2,3,4,5,6,7,8,9,12,13,14],
  [1,2,3,4,5,6,7,8,9,13,14,15],
  [1,2,3,4,5,6,7,8,10,11,12,15],
  [1,2,3,4,5,6,7,8,10,12,14,15],
  [1,2,3,4,5,6,7,8,11,12,13,15],
  [1,2,3,4,5,6,7,8,12,13,14,15],
  [1,2,3,4,5,6,7,9,10,11,12,14],
  [1,2,3,4,5,6,7,9,10,11,14,15],
  [1,2,3,4,5,6,7,9,11,12,13,14],
  [1,2,3,4,5,6,7,9,11,13,14,15],
  [1,2,3,4,5,6,7,10,11,12,14,15],
  [1,2,3,4,5,6,7,11,12,13,14,15],
  [1,2,3,4,5,6,8,9,10,11,12,13],
  [1,2,3,4,5,6,8,9,10,11,13,15],
  [1,2,3,4,5,6,8,9,10,12,13,14],
  [1,2,3,4,5,6,8,9,10,13,14,15],
  [1,2,3,4,5,6,8,10,11,12,13,15],
  [1,2,3,4,5,6,8,10,12,13,14,15],
  [1,2,3,4,5,6,9,10,11,12,13,14],
  [1,2,3,4,5,6,9,10,11,13,14,15],
  [1,2,3,4,5,6,10,11,12,13,14,15],
  [1,2,3,4,5,7,8,9,10,11,12,15],
  [1,2,3,4,5,7,8,9,10,12,14,15],
  [1,2,3,4,5,7,8,9,11,12,13,15],
  [1,2,3,4,5,7,8,9,12,13,14,15],
  [1,2,3,4,5,7,9,10,11,12,14,15],
  [1,2,3,4,5,7,9,11,12,13,14,15],
  [1,2,3,4,5,8,9,10,11,12,13,15],
  [1,2,3,4,5,8,9,10,12,13,14,15],
  [1,2,3,4,5,9,10,11,12,13,14,15],
  [1,2,3,4,6,7,8,9,10,11,12,14],
  [1,2,3,4,6,7,8,9,10,11,14,15],
  [1,2,3,4,6,7,8,9,11,12,13,14],
  [1,2,3,4,6,7,8,9,11,13,14,15],
  [1,2,3,4,6,7,8,10,11,12,14,15],
  [1,2,3,4,6,7,8,11,12,13,14,15],
  [1,2,3,4,6,8,9,10,11,12,13,14],
  [1,2,3,4,6,8,9,10,11,13,14,15],
  [1,2,3,4,6,8,10,11,12,13,14,15],
  [1,2,3,4,7,8,9,10,11,12,14,15],
  [1,2,3,4,7,8,9,11,12,13,14,15],
  [1,2,3,4,8,9,10,11,12,13,14,15],
  [1,2,3,5,6,7,8,9,10,11,12,13],
  [1,2,3,5,6,7,8,9,10,11,13,15],
  [1,2,3,5,6,7,8,9,10,12,13,14],
  [1,2,3,5,6,7,8,9,10,13,14,15],
  [1,2,3,5,6,7,8,10,11,12,13,15],
  [1,2,3,5,6,7,8,10,12,13,14,15],
  [1,2,3,5,6,7,9,10,11,12,13,14],
  [1,2,3,5,6,7,9,10,11,13,14,15],
  [1,2,3,5,6,7,10,11,12,13,14,15],
  [1,2,3,5,7,8,9,10,11,12,13,15],
  [1,2,3,5,7,8,9,10,12,13,14,15],
  [1,2,3,5,7,9,10,11,12,13,14,15],
  [1,2,3,6,7,8,9,10,11,12,13,14],
  [1,2,3,6,7,8,9,10,11,13,14,15],
  [1,2,3,6,7,8,10,11,12,13,14,15],
  [1,2,3,7,8,9,10,11,12,13,14,15],
  [1,2,4,5,6,7,8,9,10,11,12,15],
  [1,2,4,5,6,7,8,9,10,12,14,15],
  [1,2,4,5,6,7,8,9,11,12,13,15],
  [1,2,4,5,6,7,8,9,12,13,14,15],
  [1,2,4,5,6,7,9,10,11,12,14,15],
  [1,2,4,5,6,7,9,11,12,13,14,15],
  [1,2,4,5,6,8,9,10,11,12,13,15],
  [1,2,4,5,6,8,9,10,12,13,14,15],
  [1,2,4,5,6,9,10,11,12,13,14,15],
  [1,2,4,6,7,8,9,10,11,12,14,15],
  [1,2,4,6,7,8,9,11,12,13,14,15],
  [1,2,4,6,8,9,10,11,12,13,14,15],
  [1,2,5,6,7,8,9,10,11,12,13,15],
  [1,2,5,6,7,8,9,10,12,13,14,15],
  [1,2,5,6,7,9,10,11,12,13,14,15],
  [1,2,6,7,8,9,10,11,12,13,14,15],
  [1,3,4,5,6,7,8,9,10,11,12,14],
  [1,3,4,5,6,7,8,9,10,11,14,15],
  [1,3,4,5,6,7,8,9,11,12,13,14],
  [1,3,4,5,6,7,8,9,11,13,14,15],
  [1,3,4,5,6,7,8,10,11,12,14,15],
  [1,3,4,5,6,7,8,11,12,13,14,15],
  [1,3,4,5,6,8,9,10,11,12,13,14],
  [1,3,4,5,6,8,9,10,11,13,14,15],
  [1,3,4,5,6,8,10,11,12,13,14,15],
  [1,3,4,5,7,8,9,10,11,12,14,15],
  [1,3,4,5,7,8,9,11,12,13,14,15],
  [1,3,4,5,8,9,10,11,12,13,14,15],
  [1,3,5,6,7,8,9,10,11,12,13,14],
  [1,3,5,6,7,8,9,10,11,13,14,15],
  [1,3,5,6,7,8,10,11,12,13,14,15],
  [1,3,5,7,8,9,10,11,12,13,14,15],
  [1,4,5,6,7,8,9,10,11,12,14,15],
  [1,4,5,6,7,8,9,11,12,13,14,15],
  [1,4,5,6,8,9,10,11,12,13,14,15],
  [1,5,6,7,8,9,10,11,12,13,14,15],
  [2,3,4,5,6,7,8,9,10,11,12,13],
  [2,3,4,5,6,7,8,9,10,11,13,15],
  [2,3,4,5,6,7,8,9,10,12,13,14],
  [2,3,4,5,6,7,8,9,10,13,14,15],
  [2,3,4,5,6,7,8,10,11,12,13,15],
  [2,3,4,5,6,7,8,10,12,13,14,15],
  [2,3,4,5,6,7,9,10,11,12,13,14],
  [2,3,4,5,6,7,9,10,11,13,14,15],
  [2,3,4,5,6,7,10,11,12,13,14,15],
  [2,3,4,5,7,8,9,10,11,12,13,15],
  [2,3,4,5,7,8,9,10,12,13,14,15],
  [2,3,4,5,7,9,10,11,12,13,14,15],
  [2,3,4,6,7,8,9,10,11,12,13,14],
  [2,3,4,6,7,8,9,10,11,13,14,15],
  [2,3,4,6,7,8,10,11,12,13,14,15],
  [2,3,4,7,8,9,10,11,12,13,14,15],
  [2,4,5,6,7,8,9,10,11,12,13,15],
  [2,4,5,6,7,8,9,10,12,13,14,15],
  [2,4,5,6,7,9,10,11,12,13,14,15],
  [2,4,6,7,8,9,10,11,12,13,14,15],
  [3,4,5,6,7,8,9,10,11,12,13,14],
  [3,4,5,6,7,8,9,10,11,13,14,15],
  [3,4,5,6,7,8,10,11,12,13,14,15],
  [3,4,5,7,8,9,10,11,12,13,14,15],
  [4,5,6,7,8,9,10,11,12,13,14,15]]

manifold_11_15_86_1=[[1,2,3,4,5,6,7,8,9,10,11,12],
  [1,2,3,4,5,6,7,8,9,10,11,15],
  [1,2,3,4,5,6,7,8,9,10,12,13],
  [1,2,3,4,5,6,7,8,9,10,13,14],
  [1,2,3,4,5,6,7,8,9,10,14,15],
  [1,2,3,4,5,6,7,8,9,11,12,15],
  [1,2,3,4,5,6,7,8,9,12,13,15],
  [1,2,3,4,5,6,7,8,9,13,14,15],
  [1,2,3,4,5,6,7,8,10,11,12,14],
  [1,2,3,4,5,6,7,8,10,11,14,15],
  [1,2,3,4,5,6,7,8,10,12,13,14],
  [1,2,3,4,5,6,7,8,11,12,14,15],
  [1,2,3,4,5,6,7,8,12,13,14,15],
  [1,2,3,4,5,6,7,9,10,11,12,13],
  [1,2,3,4,5,6,7,9,10,11,13,15],
  [1,2,3,4,5,6,7,9,10,13,14,15],
  [1,2,3,4,5,6,7,9,11,12,13,15],
  [1,2,3,4,5,6,7,10,11,12,13,14],
  [1,2,3,4,5,6,7,10,11,13,14,15],
  [1,2,3,4,5,6,7,11,12,13,14,15],
  [1,2,3,4,5,6,8,9,10,11,12,15],
  [1,2,3,4,5,6,8,9,10,12,13,14],
  [1,2,3,4,5,6,8,9,10,12,14,15],
  [1,2,3,4,5,6,8,9,12,13,14,15],
  [1,2,3,4,5,6,8,10,11,12,14,15],
  [1,2,3,4,5,6,9,10,11,12,13,15],
  [1,2,3,4,5,6,9,10,12,13,14,15],
  [1,2,3,4,5,6,10,11,12,13,14,15],
  [1,2,3,4,5,7,8,9,10,11,12,13],
  [1,2,3,4,5,7,8,9,10,11,13,14],
  [1,2,3,4,5,7,8,9,10,11,14,15],
  [1,2,3,4,5,7,8,9,11,12,13,15],
  [1,2,3,4,5,7,8,9,11,13,14,15],
  [1,2,3,4,5,7,8,10,11,12,13,14],
  [1,2,3,4,5,7,8,11,12,13,14,15],
  [1,2,3,4,5,7,9,10,11,13,14,15],
  [1,2,3,4,5,8,9,10,11,12,13,14],
  [1,2,3,4,5,8,9,10,11,12,14,15],
  [1,2,3,4,5,8,9,11,12,13,14,15],
  [1,2,3,4,5,9,10,11,12,13,14,15],
  [1,2,3,4,6,7,8,9,10,11,12,15],
  [1,2,3,4,6,7,8,9,10,12,13,15],
  [1,2,3,4,6,7,8,9,10,13,14,15],
  [1,2,3,4,6,7,8,10,11,12,14,15],
  [1,2,3,4,6,7,8,10,12,13,14,15],
  [1,2,3,4,6,7,9,10,11,12,13,15],
  [1,2,3,4,6,7,10,11,12,13,14,15],
  [1,2,3,4,6,8,9,10,12,13,14,15],
  [1,2,3,4,7,8,9,10,11,12,13,15],
  [1,2,3,4,7,8,9,10,11,13,14,15],
  [1,2,3,4,7,8,10,11,12,13,14,15],
  [1,2,3,4,8,9,10,11,12,13,14,15],
  [1,2,3,5,6,7,8,9,10,11,12,14],
  [1,2,3,5,6,7,8,9,10,11,14,15],
  [1,2,3,5,6,7,8,9,10,12,13,14],
  [1,2,3,5,6,7,8,9,11,12,14,15],
  [1,2,3,5,6,7,8,9,12,13,14,15],
  [1,2,3,5,6,7,9,10,11,12,13,14],
  [1,2,3,5,6,7,9,10,11,13,14,15],
  [1,2,3,5,6,7,9,11,12,13,14,15],
  [1,2,3,5,6,8,9,10,11,12,14,15],
  [1,2,3,5,6,9,10,11,12,13,14,15],
  [1,2,3,5,7,8,9,10,11,12,13,14],
  [1,2,3,5,7,8,9,11,12,13,14,15],
  [1,2,3,6,7,8,9,10,11,12,14,15],
  [1,2,3,6,7,8,9,10,12,13,14,15],
  [1,2,3,6,7,9,10,11,12,13,14,15],
  [1,2,3,7,8,9,10,11,12,13,14,15],
  [1,2,4,5,6,7,8,9,10,11,12,13],
  [1,2,4,5,6,7,8,9,10,11,13,15],
  [1,2,4,5,6,7,8,9,10,13,14,15],
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  [1,2,4,5,6,7,8,10,11,12,13,14],
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  [1,2,4,5,6,7,8,11,12,13,14,15],
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  [1,2,4,5,6,8,9,10,12,13,14,15],
  [1,2,4,5,6,8,10,11,12,13,14,15],
  [1,2,4,5,7,8,9,10,11,13,14,15],
  [1,2,4,5,8,9,10,11,12,13,14,15],
  [1,2,4,6,7,8,9,10,11,12,13,15],
  [1,2,4,6,7,8,10,11,12,13,14,15],
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  [1,2,5,6,8,9,10,11,12,13,14,15],
  [1,2,6,7,8,9,10,11,12,13,14,15],
  [1,3,4,5,6,7,8,9,10,11,12,15],
  [1,3,4,5,6,7,8,9,10,12,13,14],
  [1,3,4,5,6,7,8,9,10,12,14,15],
  [1,3,4,5,6,7,8,9,12,13,14,15],
  [1,3,4,5,6,7,8,10,11,12,14,15],
  [1,3,4,5,6,7,9,10,11,12,13,15],
  [1,3,4,5,6,7,9,10,12,13,14,15],
  [1,3,4,5,6,7,10,11,12,13,14,15],
  [1,3,4,5,7,8,9,10,11,12,13,14],
  [1,3,4,5,7,8,9,10,11,12,14,15],
  [1,3,4,5,7,8,9,11,12,13,14,15],
  [1,3,4,5,7,9,10,11,12,13,14,15],
  [1,3,4,6,7,8,9,10,12,13,14,15],
  [1,3,4,7,8,9,10,11,12,13,14,15],
  [1,3,5,6,7,8,9,10,11,12,14,15],
  [1,3,5,6,7,9,10,11,12,13,14,15],
  [1,4,5,6,7,8,9,10,11,12,13,15],
  [1,4,5,6,7,8,9,10,12,13,14,15],
  [1,4,5,6,7,8,10,11,12,13,14,15],
  [1,4,5,7,8,9,10,11,12,13,14,15],
  [1,5,6,7,8,9,10,11,12,13,14,15],
  [2,3,4,5,6,7,8,9,10,11,12,13],
  [2,3,4,5,6,7,8,9,10,11,13,14],
  [2,3,4,5,6,7,8,9,10,11,14,15],
  [2,3,4,5,6,7,8,9,11,12,13,15],
  [2,3,4,5,6,7,8,9,11,13,14,15],
  [2,3,4,5,6,7,8,10,11,12,13,14],
  [2,3,4,5,6,7,8,11,12,13,14,15],
  [2,3,4,5,6,7,9,10,11,13,14,15],
  [2,3,4,5,6,8,9,10,11,12,13,14],
  [2,3,4,5,6,8,9,10,11,12,14,15],
  [2,3,4,5,6,8,9,11,12,13,14,15],
  [2,3,4,5,6,9,10,11,12,13,14,15],
  [2,3,4,6,7,8,9,10,11,12,13,15],
  [2,3,4,6,7,8,9,10,11,13,14,15],
  [2,3,4,6,7,8,10,11,12,13,14,15],
  [2,3,4,6,8,9,10,11,12,13,14,15],
  [2,3,5,6,7,8,9,10,11,12,13,14],
  [2,3,5,6,7,8,9,11,12,13,14,15],
  [2,3,6,7,8,9,10,11,12,13,14,15],
  [2,4,5,6,7,8,9,10,11,13,14,15],
  [2,4,5,6,8,9,10,11,12,13,14,15],
  [3,4,5,6,7,8,9,10,11,12,13,14],
  [3,4,5,6,7,8,9,10,11,12,14,15],
  [3,4,5,6,7,8,9,11,12,13,14,15],
  [3,4,5,6,7,9,10,11,12,13,14,15],
  [3,4,6,7,8,9,10,11,12,13,14,15],
  [4,5,6,7,8,9,10,11,12,13,14,15]]

manifold_11_15_2_1=[[1,2,3,4,5,6,7,8,9,10,11,12],
  [1,2,3,4,5,6,7,8,9,10,11,15],
  [1,2,3,4,5,6,7,8,9,10,12,13],
  [1,2,3,4,5,6,7,8,9,10,13,14],
  [1,2,3,4,5,6,7,8,9,10,14,15],
  [1,2,3,4,5,6,7,8,9,11,12,15],
  [1,2,3,4,5,6,7,8,9,12,13,15],
  [1,2,3,4,5,6,7,8,9,13,14,15],
  [1,2,3,4,5,6,7,8,10,11,12,13],
  [1,2,3,4,5,6,7,8,10,11,13,14],
  [1,2,3,4,5,6,7,8,10,11,14,15],
  [1,2,3,4,5,6,7,8,11,12,13,14],
  [1,2,3,4,5,6,7,8,11,12,14,15],
  [1,2,3,4,5,6,7,8,12,13,14,15],
  [1,2,3,4,5,6,7,9,10,11,12,15],
  [1,2,3,4,5,6,7,9,10,12,13,15],
  [1,2,3,4,5,6,7,9,10,13,14,15],
  [1,2,3,4,5,6,7,10,11,12,13,15],
  [1,2,3,4,5,6,7,10,11,13,14,15],
  [1,2,3,4,5,6,7,11,12,13,14,15],
  [1,2,3,4,5,6,8,9,10,11,12,13],
  [1,2,3,4,5,6,8,9,10,11,13,14],
  [1,2,3,4,5,6,8,9,10,11,14,15],
  [1,2,3,4,5,6,8,9,11,12,13,14],
  [1,2,3,4,5,6,8,9,11,12,14,15],
  [1,2,3,4,5,6,8,9,12,13,14,15],
  [1,2,3,4,5,6,9,10,11,12,13,14],
  [1,2,3,4,5,6,9,10,11,12,14,15],
  [1,2,3,4,5,6,9,10,12,13,14,15],
  [1,2,3,4,5,6,10,11,12,13,14,15],
  [1,2,3,4,5,7,8,9,10,11,12,15],
  [1,2,3,4,5,7,8,9,10,12,13,15],
  [1,2,3,4,5,7,8,9,10,13,14,15],
  [1,2,3,4,5,7,8,10,11,12,13,15],
  [1,2,3,4,5,7,8,10,11,13,14,15],
  [1,2,3,4,5,7,8,11,12,13,14,15],
  [1,2,3,4,5,8,9,10,11,12,13,15],
  [1,2,3,4,5,8,9,10,11,13,14,15],
  [1,2,3,4,5,8,9,11,12,13,14,15],
  [1,2,3,4,5,9,10,11,12,13,14,15],
  [1,2,3,4,6,7,8,9,10,11,12,13],
  [1,2,3,4,6,7,8,9,10,11,13,14],
  [1,2,3,4,6,7,8,9,10,11,14,15],
  [1,2,3,4,6,7,8,9,11,12,13,14],
  [1,2,3,4,6,7,8,9,11,12,14,15],
  [1,2,3,4,6,7,8,9,12,13,14,15],
  [1,2,3,4,6,7,9,10,11,12,13,14],
  [1,2,3,4,6,7,9,10,11,12,14,15],
  [1,2,3,4,6,7,9,10,12,13,14,15],
  [1,2,3,4,6,7,10,11,12,13,14,15],
  [1,2,3,4,7,8,9,10,11,12,13,14],
  [1,2,3,4,7,8,9,10,11,12,14,15],
  [1,2,3,4,7,8,9,10,12,13,14,15],
  [1,2,3,4,7,8,10,11,12,13,14,15],
  [1,2,3,4,8,9,10,11,12,13,14,15],
  [1,2,3,5,6,7,8,9,10,11,12,15],
  [1,2,3,5,6,7,8,9,10,12,13,15],
  [1,2,3,5,6,7,8,9,10,13,14,15],
  [1,2,3,5,6,7,8,10,11,12,13,15],
  [1,2,3,5,6,7,8,10,11,13,14,15],
  [1,2,3,5,6,7,8,11,12,13,14,15],
  [1,2,3,5,6,8,9,10,11,12,13,15],
  [1,2,3,5,6,8,9,10,11,13,14,15],
  [1,2,3,5,6,8,9,11,12,13,14,15],
  [1,2,3,5,6,9,10,11,12,13,14,15],
  [1,2,3,6,7,8,9,10,11,12,13,15],
  [1,2,3,6,7,8,9,10,11,13,14,15],
  [1,2,3,6,7,8,9,11,12,13,14,15],
  [1,2,3,6,7,9,10,11,12,13,14,15],
  [1,2,3,7,8,9,10,11,12,13,14,15],
  [1,2,4,5,6,7,8,9,10,11,12,13],
  [1,2,4,5,6,7,8,9,10,11,13,14],
  [1,2,4,5,6,7,8,9,10,11,14,15],
  [1,2,4,5,6,7,8,9,11,12,13,14],
  [1,2,4,5,6,7,8,9,11,12,14,15],
  [1,2,4,5,6,7,8,9,12,13,14,15],
  [1,2,4,5,6,7,9,10,11,12,13,14],
  [1,2,4,5,6,7,9,10,11,12,14,15],
  [1,2,4,5,6,7,9,10,12,13,14,15],
  [1,2,4,5,6,7,10,11,12,13,14,15],
  [1,2,4,5,7,8,9,10,11,12,13,14],
  [1,2,4,5,7,8,9,10,11,12,14,15],
  [1,2,4,5,7,8,9,10,12,13,14,15],
  [1,2,4,5,7,8,10,11,12,13,14,15],
  [1,2,4,5,8,9,10,11,12,13,14,15],
  [1,2,5,6,7,8,9,10,11,12,13,14],
  [1,2,5,6,7,8,9,10,11,12,14,15],
  [1,2,5,6,7,8,9,10,12,13,14,15],
  [1,2,5,6,7,8,10,11,12,13,14,15],
  [1,2,5,6,8,9,10,11,12,13,14,15],
  [1,2,6,7,8,9,10,11,12,13,14,15],
  [1,3,4,5,6,7,8,9,10,11,12,15],
  [1,3,4,5,6,7,8,9,10,12,13,15],
  [1,3,4,5,6,7,8,9,10,13,14,15],
  [1,3,4,5,6,7,8,10,11,12,13,15],
  [1,3,4,5,6,7,8,10,11,13,14,15],
  [1,3,4,5,6,7,8,11,12,13,14,15],
  [1,3,4,5,6,8,9,10,11,12,13,15],
  [1,3,4,5,6,8,9,10,11,13,14,15],
  [1,3,4,5,6,8,9,11,12,13,14,15],
  [1,3,4,5,6,9,10,11,12,13,14,15],
  [1,3,4,6,7,8,9,10,11,12,13,15],
  [1,3,4,6,7,8,9,10,11,13,14,15],
  [1,3,4,6,7,8,9,11,12,13,14,15],
  [1,3,4,6,7,9,10,11,12,13,14,15],
  [1,3,4,7,8,9,10,11,12,13,14,15],
  [1,4,5,6,7,8,9,10,11,12,13,15],
  [1,4,5,6,7,8,9,10,11,13,14,15],
  [1,4,5,6,7,8,9,11,12,13,14,15],
  [1,4,5,6,7,9,10,11,12,13,14,15],
  [1,4,5,7,8,9,10,11,12,13,14,15],
  [1,5,6,7,8,9,10,11,12,13,14,15],
  [2,3,4,5,6,7,8,9,10,11,12,13],
  [2,3,4,5,6,7,8,9,10,11,13,14],
  [2,3,4,5,6,7,8,9,10,11,14,15],
  [2,3,4,5,6,7,8,9,11,12,13,14],
  [2,3,4,5,6,7,8,9,11,12,14,15],
  [2,3,4,5,6,7,8,9,12,13,14,15],
  [2,3,4,5,6,7,9,10,11,12,13,14],
  [2,3,4,5,6,7,9,10,11,12,14,15],
  [2,3,4,5,6,7,9,10,12,13,14,15],
  [2,3,4,5,6,7,10,11,12,13,14,15],
  [2,3,4,5,7,8,9,10,11,12,13,14],
  [2,3,4,5,7,8,9,10,11,12,14,15],
  [2,3,4,5,7,8,9,10,12,13,14,15],
  [2,3,4,5,7,8,10,11,12,13,14,15],
  [2,3,4,5,8,9,10,11,12,13,14,15],
  [2,3,5,6,7,8,9,10,11,12,13,14],
  [2,3,5,6,7,8,9,10,11,12,14,15],
  [2,3,5,6,7,8,9,10,12,13,14,15],
  [2,3,5,6,7,8,10,11,12,13,14,15],
  [2,3,5,6,8,9,10,11,12,13,14,15],
  [2,3,6,7,8,9,10,11,12,13,14,15],
  [3,4,5,6,7,8,9,10,11,12,13,14],
  [3,4,5,6,7,8,9,10,11,12,14,15],
  [3,4,5,6,7,8,9,10,12,13,14,15],
  [3,4,5,6,7,8,10,11,12,13,14,15],
  [3,4,5,6,8,9,10,11,12,13,14,15],
  [3,4,6,7,8,9,10,11,12,13,14,15],
  [4,5,6,7,8,9,10,11,12,13,14,15]]