manifold_5_7_7_1=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,7],[1,2,3,5,6,7],[1,2,4,5,6,7],
  [1,3,4,5,6,7],[2,3,4,5,6,7]]

manifold_5_8_47_1=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,7],[1,2,3,5,6,7],[1,2,4,5,6,8],
  [1,2,4,5,7,8],[1,2,4,6,7,8],[1,2,5,6,7,8],
  [1,3,4,5,6,8],[1,3,4,5,7,8],[1,3,4,6,7,8],
  [1,3,5,6,7,8],[2,3,4,5,6,8],[2,3,4,5,7,8],
  [2,3,4,6,7,8],[2,3,5,6,7,8]]

manifold_5_9_31_1=[[1,2,3,4,6,7],[1,2,3,4,6,8],
  [1,2,3,4,7,8],[1,2,3,5,6,7],[1,2,3,5,6,8],
  [1,2,3,5,7,8],[1,2,4,5,6,7],[1,2,4,5,6,8],
  [1,2,4,5,7,8],[1,3,4,6,7,9],[1,3,4,6,8,9],
  [1,3,4,7,8,9],[1,3,5,6,7,9],[1,3,5,6,8,9],
  [1,3,5,7,8,9],[1,4,5,6,7,9],[1,4,5,6,8,9],
  [1,4,5,7,8,9],[2,3,4,6,7,9],[2,3,4,6,8,9],
  [2,3,4,7,8,9],[2,3,5,6,7,9],[2,3,5,6,8,9],
  [2,3,5,7,8,9],[2,4,5,6,7,9],[2,4,5,6,8,9],
  [2,4,5,7,8,9]]

manifold_5_9_3_1=[[1,2,3,4,5,6],[1,2,3,4,5,9],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,5,6,9],[1,2,3,6,7,9],[1,2,3,7,8,9],
  [1,2,4,5,6,7],[1,2,4,5,7,8],[1,2,4,5,8,9],
  [1,2,5,6,7,8],[1,2,5,6,8,9],[1,2,6,7,8,9],
  [1,3,4,5,6,9],[1,3,4,6,7,9],[1,3,4,7,8,9],
  [1,4,5,6,7,9],[1,4,5,7,8,9],[1,5,6,7,8,9],
  [2,3,4,5,6,7],[2,3,4,5,7,8],[2,3,4,5,8,9],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,6,7,8,9],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,6,7,8,9],
  [4,5,6,7,8,9]]

manifold_5_10_3_1=[[1,2,3,4,5,6],[1,2,3,4,5,10],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,10],[1,2,3,5,6,10],[1,2,3,6,7,10],
  [1,2,3,7,8,10],[1,2,3,8,9,10],[1,2,4,5,6,7],
  [1,2,4,5,7,8],[1,2,4,5,8,9],[1,2,4,5,9,10],
  [1,2,5,6,7,8],[1,2,5,6,8,9],[1,2,5,6,9,10],
  [1,2,6,7,8,9],[1,2,6,7,9,10],[1,2,7,8,9,10],
  [1,3,4,5,6,10],[1,3,4,6,7,10],[1,3,4,7,8,10],
  [1,3,4,8,9,10],[1,4,5,6,7,10],[1,4,5,7,8,10],
  [1,4,5,8,9,10],[1,5,6,7,8,10],[1,5,6,8,9,10],
  [1,6,7,8,9,10],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,5,6,7,8],
  [2,3,5,6,8,9],[2,3,5,6,9,10],[2,3,6,7,8,9],
  [2,3,6,7,9,10],[2,3,7,8,9,10],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,6,7,8,9],
  [3,4,6,7,9,10],[3,4,7,8,9,10],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,7,8,9,10],[5,6,7,8,9,10]]

manifold_5_11_2_1=[[1,2,3,4,5,6],[1,2,3,4,5,11],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,10],[1,2,3,4,10,11],[1,2,3,5,6,11],
  [1,2,3,6,7,11],[1,2,3,7,8,11],[1,2,3,8,9,11],
  [1,2,3,9,10,11],[1,2,4,5,6,7],[1,2,4,5,7,8],
  [1,2,4,5,8,9],[1,2,4,5,9,10],[1,2,4,5,10,11],
  [1,2,5,6,7,8],[1,2,5,6,8,9],[1,2,5,6,9,10],
  [1,2,5,6,10,11],[1,2,6,7,8,9],[1,2,6,7,9,10],
  [1,2,6,7,10,11],[1,2,7,8,9,10],[1,2,7,8,10,11],
  [1,2,8,9,10,11],[1,3,4,5,6,11],[1,3,4,6,7,11],
  [1,3,4,7,8,11],[1,3,4,8,9,11],[1,3,4,9,10,11],
  [1,4,5,6,7,11],[1,4,5,7,8,11],[1,4,5,8,9,11],
  [1,4,5,9,10,11],[1,5,6,7,8,11],[1,5,6,8,9,11],
  [1,5,6,9,10,11],[1,6,7,8,9,11],[1,6,7,9,10,11],
  [1,7,8,9,10,11],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,11],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,10],
  [2,3,5,6,10,11],[2,3,6,7,8,9],[2,3,6,7,9,10],
  [2,3,6,7,10,11],[2,3,7,8,9,10],[2,3,7,8,10,11],
  [2,3,8,9,10,11],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,10],[3,4,5,6,10,11],[3,4,6,7,8,9],
  [3,4,6,7,9,10],[3,4,6,7,10,11],[3,4,7,8,9,10],
  [3,4,7,8,10,11],[3,4,8,9,10,11],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,7,8,9,10],
  [4,5,7,8,10,11],[4,5,8,9,10,11],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,8,9,10,11],[6,7,8,9,10,11]]

manifold_5_11_2_2=[[1,2,3,4,5,6],[1,2,3,4,5,11],
  [1,2,3,4,6,7],[1,2,3,4,7,9],[1,2,3,4,9,10],
  [1,2,3,4,10,11],[1,2,3,5,6,11],[1,2,3,6,7,8],
  [1,2,3,6,8,11],[1,2,3,7,8,9],[1,2,3,8,9,11],
  [1,2,3,9,10,11],[1,2,4,5,6,7],[1,2,4,5,7,10],
  [1,2,4,5,10,11],[1,2,4,7,9,10],[1,2,5,6,7,11],
  [1,2,5,7,10,11],[1,2,6,7,8,11],[1,2,7,8,9,10],
  [1,2,7,8,10,11],[1,2,8,9,10,11],[1,3,4,5,6,11],
  [1,3,4,6,7,9],[1,3,4,6,9,11],[1,3,4,9,10,11],
  [1,3,6,7,8,9],[1,3,6,8,9,11],[1,4,5,6,7,10],
  [1,4,5,6,10,11],[1,4,6,7,9,10],[1,4,6,9,10,11],
  [1,5,6,7,10,11],[1,6,7,8,9,11],[1,6,7,9,10,11],
  [1,7,8,9,10,11],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,10],[2,3,4,5,10,11],[2,3,4,7,8,9],
  [2,3,4,8,9,10],[2,3,5,6,7,8],[2,3,5,6,8,11],
  [2,3,5,8,10,11],[2,3,8,9,10,11],[2,4,5,7,8,10],
  [2,4,7,8,9,10],[2,5,6,7,8,11],[2,5,7,8,10,11],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,11],
  [3,4,5,8,9,10],[3,4,5,9,10,11],[3,4,6,7,8,9],
  [3,5,6,8,9,11],[3,5,8,9,10,11],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,9,10,11],[4,5,7,8,9,10],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,6,8,9,10,11],
  [6,7,8,9,10,11]]

manifold_5_11_1_1=[[1,2,3,4,5,6],[1,2,3,4,5,11],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,10],
  [1,2,3,4,10,11],[1,2,3,5,6,11],[1,2,3,6,7,11],
  [1,2,3,7,8,10],[1,2,3,7,9,10],[1,2,3,7,9,11],
  [1,2,3,9,10,11],[1,2,4,5,6,10],[1,2,4,5,10,11],
  [1,2,4,6,7,8],[1,2,4,6,8,10],[1,2,5,6,10,11],
  [1,2,6,7,8,9],[1,2,6,7,9,11],[1,2,6,8,9,11],
  [1,2,6,8,10,11],[1,2,7,8,9,10],[1,2,8,9,10,11],
  [1,3,4,5,6,10],[1,3,4,5,9,10],[1,3,4,5,9,11],
  [1,3,4,6,7,8],[1,3,4,6,8,10],[1,3,4,9,10,11],
  [1,3,5,6,7,8],[1,3,5,6,7,11],[1,3,5,6,8,10],
  [1,3,5,7,8,10],[1,3,5,7,9,10],[1,3,5,7,9,11],
  [1,4,5,9,10,11],[1,5,6,7,8,11],[1,5,6,8,10,11],
  [1,5,7,8,10,11],[1,5,7,9,10,11],[1,6,7,8,9,11],
  [1,7,8,9,10,11],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,11],[2,3,4,8,9,11],
  [2,3,4,8,10,11],[2,3,5,6,7,11],[2,3,5,7,8,9],
  [2,3,5,7,9,11],[2,3,7,8,9,10],[2,3,8,9,10,11],
  [2,4,5,6,7,11],[2,4,5,6,10,11],[2,4,5,7,8,9],
  [2,4,5,7,9,11],[2,4,6,7,8,9],[2,4,6,7,9,11],
  [2,4,6,8,9,11],[2,4,6,8,10,11],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,6,8,9,10],
  [3,4,8,9,10,11],[3,5,6,8,9,10],[3,5,7,8,9,10],
  [4,5,6,7,8,9],[4,5,6,7,9,10],[4,5,6,7,10,11],
  [4,5,7,9,10,11],[4,6,7,9,10,11],[4,6,8,9,10,11],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[6,7,8,9,10,11]]

manifold_5_12_293_1=[[1,2,4,6,8,10],[1,2,4,6,8,11],
  [1,2,4,6,9,10],[1,2,4,6,9,11],[1,2,4,7,8,10],
  [1,2,4,7,8,11],[1,2,4,7,9,10],[1,2,4,7,9,11],
  [1,2,5,6,8,10],[1,2,5,6,8,11],[1,2,5,6,9,10],
  [1,2,5,6,9,11],[1,2,5,7,8,10],[1,2,5,7,8,11],
  [1,2,5,7,9,10],[1,2,5,7,9,11],[1,3,4,6,8,10],
  [1,3,4,6,8,11],[1,3,4,6,9,10],[1,3,4,6,9,11],
  [1,3,4,7,8,10],[1,3,4,7,8,11],[1,3,4,7,9,10],
  [1,3,4,7,9,11],[1,3,5,6,8,10],[1,3,5,6,8,11],
  [1,3,5,6,9,10],[1,3,5,6,9,11],[1,3,5,7,8,10],
  [1,3,5,7,8,11],[1,3,5,7,9,10],[1,3,5,7,9,11],
  [2,4,6,8,10,12],[2,4,6,8,11,12],[2,4,6,9,10,12],
  [2,4,6,9,11,12],[2,4,7,8,10,12],[2,4,7,8,11,12],
  [2,4,7,9,10,12],[2,4,7,9,11,12],[2,5,6,8,10,12],
  [2,5,6,8,11,12],[2,5,6,9,10,12],[2,5,6,9,11,12],
  [2,5,7,8,10,12],[2,5,7,8,11,12],[2,5,7,9,10,12],
  [2,5,7,9,11,12],[3,4,6,8,10,12],[3,4,6,8,11,12],
  [3,4,6,9,10,12],[3,4,6,9,11,12],[3,4,7,8,10,12],
  [3,4,7,8,11,12],[3,4,7,9,10,12],[3,4,7,9,11,12],
  [3,5,6,8,10,12],[3,5,6,8,11,12],[3,5,6,9,10,12],
  [3,5,6,9,11,12],[3,5,7,8,10,12],[3,5,7,8,11,12],
  [3,5,7,9,10,12],[3,5,7,9,11,12]]

manifold_5_12_83_1=[[1,2,3,4,5,6],[1,2,3,4,5,12],
  [1,2,3,4,6,8],[1,2,3,4,8,9],[1,2,3,4,9,11],
  [1,2,3,4,11,12],[1,2,3,5,6,7],[1,2,3,5,7,12],
  [1,2,3,6,7,8],[1,2,3,7,8,12],[1,2,3,8,9,10],
  [1,2,3,8,10,12],[1,2,3,9,10,11],[1,2,3,10,11,12],
  [1,2,4,5,6,12],[1,2,4,6,8,9],[1,2,4,6,9,11],
  [1,2,4,6,11,12],[1,2,5,6,7,12],[1,2,6,7,8,9],
  [1,2,6,7,9,11],[1,2,6,7,11,12],[1,2,7,8,9,12],
  [1,2,7,9,11,12],[1,2,8,9,10,12],[1,2,9,10,11,12],
  [1,3,4,5,6,11],[1,3,4,5,11,12],[1,3,4,6,8,11],
  [1,3,4,8,9,11],[1,3,5,6,7,8],[1,3,5,6,8,10],
  [1,3,5,6,10,11],[1,3,5,7,8,12],[1,3,5,8,10,12],
  [1,3,5,10,11,12],[1,3,6,8,10,11],[1,3,8,9,10,11],
  [1,4,5,6,11,12],[1,4,6,8,9,11],[1,5,6,7,8,12],
  [1,5,6,8,10,12],[1,5,6,10,11,12],[1,6,7,8,9,11],
  [1,6,7,8,11,12],[1,6,8,10,11,12],[1,7,8,9,11,12],
  [1,8,9,10,11,12],[2,3,4,5,6,7],[2,3,4,5,7,9],
  [2,3,4,5,9,10],[2,3,4,5,10,12],[2,3,4,6,7,8],
  [2,3,4,7,8,9],[2,3,4,9,10,11],[2,3,4,10,11,12],
  [2,3,5,7,9,10],[2,3,5,7,10,12],[2,3,7,8,9,10],
  [2,3,7,8,10,12],[2,4,5,6,7,12],[2,4,5,7,9,12],
  [2,4,5,9,10,12],[2,4,6,7,8,9],[2,4,6,7,9,11],
  [2,4,6,7,11,12],[2,4,7,9,11,12],[2,4,9,10,11,12],
  [2,5,7,9,10,12],[2,7,8,9,10,12],[3,4,5,6,7,8],
  [3,4,5,6,8,10],[3,4,5,6,10,11],[3,4,5,7,8,9],
  [3,4,5,8,9,10],[3,4,5,10,11,12],[3,4,6,8,10,11],
  [3,4,8,9,10,11],[3,5,7,8,9,10],[3,5,7,8,10,12],
  [4,5,6,7,8,9],[4,5,6,7,9,11],[4,5,6,7,11,12],
  [4,5,6,8,9,10],[4,5,6,9,10,11],[4,5,7,9,11,12],
  [4,5,9,10,11,12],[4,6,8,9,10,11],[5,6,7,8,9,10],
  [5,6,7,8,10,12],[5,6,7,9,10,11],[5,6,7,10,11,12],
  [5,7,9,10,11,12],[6,7,8,9,10,11],[6,7,8,10,11,12],
  [7,8,9,10,11,12]]

manifold_5_12_15_1=[[1,2,3,4,5,6],[1,2,3,4,5,8],
  [1,2,3,4,6,11],[1,2,3,4,8,9],[1,2,3,4,9,12],
  [1,2,3,4,11,12],[1,2,3,5,6,12],[1,2,3,5,8,10],
  [1,2,3,5,10,12],[1,2,3,6,11,12],[1,2,3,8,9,10],
  [1,2,3,9,10,12],[1,2,4,5,6,7],[1,2,4,5,7,8],
  [1,2,4,6,7,11],[1,2,4,7,8,11],[1,2,4,8,9,11],
  [1,2,4,9,11,12],[1,2,5,6,7,12],[1,2,5,7,8,10],
  [1,2,5,7,10,12],[1,2,6,7,11,12],[1,2,7,8,10,11],
  [1,2,7,10,11,12],[1,2,8,9,10,11],[1,2,9,10,11,12],
  [1,3,4,5,6,8],[1,3,4,6,8,9],[1,3,4,6,9,10],
  [1,3,4,6,10,11],[1,3,4,9,10,12],[1,3,4,10,11,12],
  [1,3,5,6,8,12],[1,3,5,8,10,12],[1,3,6,8,9,10],
  [1,3,6,8,10,11],[1,3,6,8,11,12],[1,3,8,10,11,12],
  [1,4,5,6,7,8],[1,4,6,7,8,11],[1,4,6,8,9,11],
  [1,4,6,9,10,11],[1,4,9,10,11,12],[1,5,6,7,8,12],
  [1,5,7,8,10,12],[1,6,7,8,11,12],[1,6,8,9,10,11],
  [1,7,8,10,11,12],[2,3,4,5,6,11],[2,3,4,5,7,8],
  [2,3,4,5,7,12],[2,3,4,5,11,12],[2,3,4,7,8,9],
  [2,3,4,7,9,12],[2,3,5,6,11,12],[2,3,5,7,8,10],
  [2,3,5,7,10,12],[2,3,7,8,9,10],[2,3,7,9,10,12],
  [2,4,5,6,7,9],[2,4,5,6,9,11],[2,4,5,7,9,12],
  [2,4,5,9,11,12],[2,4,6,7,9,11],[2,4,7,8,9,11],
  [2,5,6,7,9,12],[2,5,6,9,11,12],[2,6,7,9,11,12],
  [2,7,8,9,10,11],[2,7,9,10,11,12],[3,4,5,6,7,8],
  [3,4,5,6,7,10],[3,4,5,6,10,11],[3,4,5,7,10,12],
  [3,4,5,10,11,12],[3,4,6,7,8,9],[3,4,6,7,9,10],
  [3,4,7,9,10,12],[3,5,6,7,8,10],[3,5,6,8,10,11],
  [3,5,6,8,11,12],[3,5,8,10,11,12],[3,6,7,8,9,10],
  [4,5,6,7,9,10],[4,5,6,9,10,11],[4,5,7,9,10,12],
  [4,5,9,10,11,12],[4,6,7,8,9,11],[5,6,7,8,9,10],
  [5,6,7,8,9,12],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,7,8,9,10,12],[5,8,9,10,11,12],[6,7,8,9,11,12],
  [7,8,9,10,11,12]]

manifold_5_12_14_1=[[1,2,3,4,5,6],[1,2,3,4,5,12],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,11],
  [1,2,3,4,11,12],[1,2,3,5,6,12],[1,2,3,6,7,12],
  [1,2,3,7,8,10],[1,2,3,7,10,12],[1,2,3,8,10,11],
  [1,2,3,10,11,12],[1,2,4,5,6,11],[1,2,4,5,11,12],
  [1,2,4,6,7,9],[1,2,4,6,9,11],[1,2,4,7,8,9],
  [1,2,4,8,9,11],[1,2,5,6,11,12],[1,2,6,7,9,12],
  [1,2,6,9,11,12],[1,2,7,8,9,10],[1,2,7,9,10,12],
  [1,2,8,9,10,11],[1,2,9,10,11,12],[1,3,4,5,6,10],
  [1,3,4,5,10,12],[1,3,4,6,7,8],[1,3,4,6,8,11],
  [1,3,4,6,10,11],[1,3,4,10,11,12],[1,3,5,6,8,10],
  [1,3,5,6,8,12],[1,3,5,8,10,12],[1,3,6,7,8,12],
  [1,3,6,8,10,11],[1,3,7,8,10,12],[1,4,5,6,10,11],
  [1,4,5,10,11,12],[1,4,6,7,8,9],[1,4,6,8,9,11],
  [1,5,6,8,10,11],[1,5,6,8,11,12],[1,5,8,10,11,12],
  [1,6,7,8,9,12],[1,6,8,9,11,12],[1,7,8,9,10,12],
  [1,8,9,10,11,12],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,12],[2,3,4,8,9,11],
  [2,3,4,9,11,12],[2,3,5,6,7,12],[2,3,5,7,8,10],
  [2,3,5,7,10,12],[2,3,5,8,9,10],[2,3,5,9,10,12],
  [2,3,8,9,10,11],[2,3,9,10,11,12],[2,4,5,6,7,11],
  [2,4,5,7,8,9],[2,4,5,7,9,12],[2,4,5,7,11,12],
  [2,4,6,7,9,11],[2,4,7,9,11,12],[2,5,6,7,11,12],
  [2,5,7,8,9,10],[2,5,7,9,10,12],[2,6,7,9,11,12],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,10],
  [3,4,5,9,10,12],[3,4,6,8,9,11],[3,4,6,9,10,11],
  [3,4,9,10,11,12],[3,5,6,7,8,12],[3,5,6,8,9,10],
  [3,5,7,8,10,12],[3,6,8,9,10,11],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,7,9,10,12],
  [4,5,7,10,11,12],[4,6,7,9,10,11],[4,7,9,10,11,12],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,6,7,8,11,12],
  [5,7,8,10,11,12],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [7,8,9,10,11,12]]

manifold_5_12_13_1=[[1,2,3,4,5,7],[1,2,3,4,5,11],
  [1,2,3,4,6,7],[1,2,3,4,6,8],[1,2,3,4,8,9],
  [1,2,3,4,9,11],[1,2,3,5,7,12],[1,2,3,5,11,12],
  [1,2,3,6,7,8],[1,2,3,7,8,12],[1,2,3,8,9,10],
  [1,2,3,8,10,12],[1,2,3,9,10,12],[1,2,3,9,11,12],
  [1,2,4,5,6,7],[1,2,4,5,6,12],[1,2,4,5,11,12],
  [1,2,4,6,8,11],[1,2,4,6,11,12],[1,2,4,8,9,11],
  [1,2,5,6,7,12],[1,2,6,7,8,9],[1,2,6,7,9,11],
  [1,2,6,7,11,12],[1,2,6,8,9,11],[1,2,7,8,9,12],
  [1,2,7,9,11,12],[1,2,8,9,10,12],[1,3,4,5,6,7],
  [1,3,4,5,6,11],[1,3,4,6,8,10],[1,3,4,6,10,11],
  [1,3,4,8,9,11],[1,3,4,8,10,11],[1,3,5,6,7,8],
  [1,3,5,6,8,12],[1,3,5,6,10,11],[1,3,5,6,10,12],
  [1,3,5,7,8,12],[1,3,5,10,11,12],[1,3,6,8,10,12],
  [1,3,8,9,10,11],[1,3,9,10,11,12],[1,4,5,6,11,12],
  [1,4,6,8,10,11],[1,5,6,7,8,12],[1,5,6,10,11,12],
  [1,6,7,8,9,11],[1,6,7,8,11,12],[1,6,8,10,11,12],
  [1,7,8,9,10,11],[1,7,8,9,10,12],[1,7,8,10,11,12],
  [1,7,9,10,11,12],[2,3,4,5,7,9],[2,3,4,5,9,10],
  [2,3,4,5,10,12],[2,3,4,5,11,12],[2,3,4,6,7,8],
  [2,3,4,7,8,9],[2,3,4,9,10,11],[2,3,4,10,11,12],
  [2,3,5,7,8,10],[2,3,5,7,8,12],[2,3,5,7,9,10],
  [2,3,5,8,10,12],[2,3,7,8,9,10],[2,3,9,10,11,12],
  [2,4,5,6,7,12],[2,4,5,7,9,10],[2,4,5,7,10,12],
  [2,4,6,7,8,9],[2,4,6,7,9,12],[2,4,6,8,9,11],
  [2,4,6,9,11,12],[2,4,7,9,10,12],[2,4,9,10,11,12],
  [2,5,7,8,10,12],[2,6,7,9,11,12],[2,7,8,9,10,12],
  [3,4,5,6,7,9],[3,4,5,6,8,9],[3,4,5,6,8,10],
  [3,4,5,6,10,11],[3,4,5,8,9,10],[3,4,5,10,11,12],
  [3,4,6,7,8,9],[3,4,8,9,10,11],[3,5,6,7,8,9],
  [3,5,6,8,10,12],[3,5,7,8,9,10],[4,5,6,7,9,11],
  [4,5,6,7,11,12],[4,5,6,8,9,10],[4,5,6,9,10,11],
  [4,5,7,9,10,12],[4,5,7,9,11,12],[4,5,9,10,11,12],
  [4,6,7,9,11,12],[4,6,8,9,10,11],[5,6,7,8,9,11],
  [5,6,7,8,10,11],[5,6,7,8,10,12],[5,6,7,10,11,12],
  [5,6,8,9,10,11],[5,7,8,9,10,11],[5,7,9,10,11,12],
  [6,7,8,10,11,12]]

manifold_5_12_13_2=[[1,2,3,4,5,7],[1,2,3,4,5,11],
  [1,2,3,4,7,8],[1,2,3,4,8,11],[1,2,3,5,7,8],
  [1,2,3,5,8,12],[1,2,3,5,11,12],[1,2,3,8,9,11],
  [1,2,3,8,9,12],[1,2,3,9,11,12],[1,2,4,5,6,11],
  [1,2,4,5,6,12],[1,2,4,5,7,12],[1,2,4,6,7,8],
  [1,2,4,6,7,12],[1,2,4,6,8,11],[1,2,5,6,11,12],
  [1,2,5,7,8,12],[1,2,6,7,8,11],[1,2,6,7,9,11],
  [1,2,6,7,9,12],[1,2,6,9,11,12],[1,2,7,8,9,10],
  [1,2,7,8,9,11],[1,2,7,8,10,12],[1,2,7,9,10,12],
  [1,2,8,9,10,12],[1,3,4,5,6,7],[1,3,4,5,6,10],
  [1,3,4,5,10,11],[1,3,4,6,7,8],[1,3,4,6,8,10],
  [1,3,4,8,9,10],[1,3,4,8,9,11],[1,3,4,9,10,11],
  [1,3,5,6,7,12],[1,3,5,6,10,11],[1,3,5,6,11,12],
  [1,3,5,7,8,12],[1,3,6,7,8,12],[1,3,6,8,10,12],
  [1,3,6,10,11,12],[1,3,8,9,10,12],[1,3,9,10,11,12],
  [1,4,5,6,7,12],[1,4,5,6,10,11],[1,4,6,8,10,11],
  [1,4,8,9,10,11],[1,6,7,8,10,11],[1,6,7,8,10,12],
  [1,6,7,9,11,12],[1,6,7,10,11,12],[1,7,8,9,10,11],
  [1,7,9,10,11,12],[2,3,4,5,7,10],[2,3,4,5,10,11],
  [2,3,4,6,7,8],[2,3,4,6,7,9],[2,3,4,6,8,9],
  [2,3,4,7,9,10],[2,3,4,8,9,11],[2,3,4,9,10,12],
  [2,3,4,9,11,12],[2,3,4,10,11,12],[2,3,5,7,8,9],
  [2,3,5,7,9,10],[2,3,5,8,9,10],[2,3,5,8,10,12],
  [2,3,5,10,11,12],[2,3,6,7,8,9],[2,3,8,9,10,12],
  [2,4,5,6,11,12],[2,4,5,7,10,12],[2,4,5,10,11,12],
  [2,4,6,7,9,12],[2,4,6,8,9,11],[2,4,6,9,11,12],
  [2,4,7,9,10,12],[2,5,7,8,9,10],[2,5,7,8,10,12],
  [2,6,7,8,9,11],[3,4,5,6,7,9],[3,4,5,6,9,10],
  [3,4,5,7,9,10],[3,4,6,8,9,10],[3,4,9,10,11,12],
  [3,5,6,7,8,9],[3,5,6,7,8,12],[3,5,6,8,9,10],
  [3,5,6,8,10,12],[3,5,6,10,11,12],[4,5,6,7,9,12],
  [4,5,6,8,9,10],[4,5,6,8,9,11],[4,5,6,8,10,11],
  [4,5,6,9,11,12],[4,5,7,9,10,11],[4,5,7,9,11,12],
  [4,5,7,10,11,12],[4,5,8,9,10,11],[4,7,9,10,11,12],
  [5,6,7,8,9,11],[5,6,7,8,11,12],[5,6,7,9,11,12],
  [5,6,8,10,11,12],[5,7,8,9,10,11],[5,7,8,10,11,12],
  [6,7,8,10,11,12]]

manifold_5_12_12_1=[[1,2,3,4,5,6],[1,2,3,4,5,12],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,10],[1,2,3,4,10,11],[1,2,3,4,11,12],
  [1,2,3,5,6,12],[1,2,3,6,7,12],[1,2,3,7,8,12],
  [1,2,3,8,9,12],[1,2,3,9,10,12],[1,2,3,10,11,12],
  [1,2,4,5,6,7],[1,2,4,5,7,8],[1,2,4,5,8,9],
  [1,2,4,5,9,10],[1,2,4,5,10,11],[1,2,4,5,11,12],
  [1,2,5,6,7,8],[1,2,5,6,8,9],[1,2,5,6,9,10],
  [1,2,5,6,10,11],[1,2,5,6,11,12],[1,2,6,7,8,9],
  [1,2,6,7,9,10],[1,2,6,7,10,11],[1,2,6,7,11,12],
  [1,2,7,8,9,10],[1,2,7,8,10,11],[1,2,7,8,11,12],
  [1,2,8,9,10,11],[1,2,8,9,11,12],[1,2,9,10,11,12],
  [1,3,4,5,6,12],[1,3,4,6,7,12],[1,3,4,7,8,12],
  [1,3,4,8,9,12],[1,3,4,9,10,12],[1,3,4,10,11,12],
  [1,4,5,6,7,12],[1,4,5,7,8,12],[1,4,5,8,9,12],
  [1,4,5,9,10,12],[1,4,5,10,11,12],[1,5,6,7,8,12],
  [1,5,6,8,9,12],[1,5,6,9,10,12],[1,5,6,10,11,12],
  [1,6,7,8,9,12],[1,6,7,9,10,12],[1,6,7,10,11,12],
  [1,7,8,9,10,12],[1,7,8,10,11,12],[1,8,9,10,11,12],
  [2,3,4,5,6,7],[2,3,4,5,7,8],[2,3,4,5,8,9],
  [2,3,4,5,9,10],[2,3,4,5,10,11],[2,3,4,5,11,12],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,10],
  [2,3,5,6,10,11],[2,3,5,6,11,12],[2,3,6,7,8,9],
  [2,3,6,7,9,10],[2,3,6,7,10,11],[2,3,6,7,11,12],
  [2,3,7,8,9,10],[2,3,7,8,10,11],[2,3,7,8,11,12],
  [2,3,8,9,10,11],[2,3,8,9,11,12],[2,3,9,10,11,12],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,10],
  [3,4,5,6,10,11],[3,4,5,6,11,12],[3,4,6,7,8,9],
  [3,4,6,7,9,10],[3,4,6,7,10,11],[3,4,6,7,11,12],
  [3,4,7,8,9,10],[3,4,7,8,10,11],[3,4,7,8,11,12],
  [3,4,8,9,10,11],[3,4,8,9,11,12],[3,4,9,10,11,12],
  [4,5,6,7,8,9],[4,5,6,7,9,10],[4,5,6,7,10,11],
  [4,5,6,7,11,12],[4,5,7,8,9,10],[4,5,7,8,10,11],
  [4,5,7,8,11,12],[4,5,8,9,10,11],[4,5,8,9,11,12],
  [4,5,9,10,11,12],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,12],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,6,9,10,11,12],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,9,10,11,12],[7,8,9,10,11,12]]

manifold_5_12_8_1=[[1,2,3,4,5,7],[1,2,3,4,5,12],
  [1,2,3,4,7,8],[1,2,3,4,8,12],[1,2,3,5,6,9],
  [1,2,3,5,6,12],[1,2,3,5,7,9],[1,2,3,6,7,8],
  [1,2,3,6,7,9],[1,2,3,6,8,12],[1,2,4,5,7,9],
  [1,2,4,5,9,10],[1,2,4,5,10,12],[1,2,4,7,8,12],
  [1,2,4,7,9,12],[1,2,4,9,10,12],[1,2,5,6,9,10],
  [1,2,5,6,10,12],[1,2,6,7,8,12],[1,2,6,7,9,12],
  [1,2,6,9,10,12],[1,3,4,5,7,10],[1,3,4,5,10,12],
  [1,3,4,6,7,8],[1,3,4,6,7,11],[1,3,4,6,8,12],
  [1,3,4,6,11,12],[1,3,4,7,10,11],[1,3,4,10,11,12],
  [1,3,5,6,9,10],[1,3,5,6,10,12],[1,3,5,7,9,11],
  [1,3,5,7,10,11],[1,3,5,9,10,11],[1,3,6,7,9,12],
  [1,3,6,7,11,12],[1,3,6,9,10,12],[1,3,7,9,11,12],
  [1,3,9,10,11,12],[1,4,5,7,8,9],[1,4,5,7,8,10],
  [1,4,5,8,9,10],[1,4,6,7,8,11],[1,4,6,8,11,12],
  [1,4,7,8,9,12],[1,4,7,8,10,11],[1,4,8,9,10,11],
  [1,4,8,9,11,12],[1,4,9,10,11,12],[1,5,7,8,9,11],
  [1,5,7,8,10,11],[1,5,8,9,10,11],[1,6,7,8,11,12],
  [1,7,8,9,11,12],[2,3,4,5,7,8],[2,3,4,5,8,12],
  [2,3,5,6,8,9],[2,3,5,6,8,12],[2,3,5,7,8,11],
  [2,3,5,7,9,11],[2,3,5,8,9,11],[2,3,6,7,8,10],
  [2,3,6,7,9,10],[2,3,6,8,9,10],[2,3,7,8,10,11],
  [2,3,7,9,10,11],[2,3,8,9,10,11],[2,4,5,6,9,10],
  [2,4,5,6,9,11],[2,4,5,6,10,12],[2,4,5,6,11,12],
  [2,4,5,7,8,12],[2,4,5,7,9,12],[2,4,5,9,11,12],
  [2,4,6,9,10,11],[2,4,6,10,11,12],[2,4,9,10,11,12],
  [2,5,6,8,9,11],[2,5,6,8,11,12],[2,5,7,8,11,12],
  [2,5,7,9,11,12],[2,6,7,8,10,11],[2,6,7,8,11,12],
  [2,6,7,9,10,12],[2,6,7,10,11,12],[2,6,8,9,10,11],
  [2,7,9,10,11,12],[3,4,5,6,8,10],[3,4,5,6,8,12],
  [3,4,5,6,10,12],[3,4,5,7,8,10],[3,4,6,7,8,10],
  [3,4,6,7,10,11],[3,4,6,10,11,12],[3,5,6,8,9,10],
  [3,5,7,8,10,11],[3,5,8,9,10,11],[3,6,7,9,10,12],
  [3,6,7,10,11,12],[3,7,9,10,11,12],[4,5,6,8,9,10],
  [4,5,6,8,9,11],[4,5,6,8,11,12],[4,5,7,8,9,12],
  [4,5,8,9,11,12],[4,6,7,8,10,11],[4,6,8,9,10,11],
  [5,7,8,9,11,12]]

manifold_5_12_8_2=[[1,2,3,4,5,8],[1,2,3,4,5,12],
  [1,2,3,4,8,12],[1,2,3,5,6,10],[1,2,3,5,6,12],
  [1,2,3,5,7,8],[1,2,3,5,7,9],[1,2,3,5,9,10],
  [1,2,3,6,9,10],[1,2,3,6,9,12],[1,2,3,7,8,12],
  [1,2,3,7,9,12],[1,2,4,5,7,8],[1,2,4,5,7,12],
  [1,2,4,7,8,12],[1,2,5,6,10,12],[1,2,5,7,9,12],
  [1,2,5,9,10,12],[1,2,6,9,10,12],[1,3,4,5,6,10],
  [1,3,4,5,6,12],[1,3,4,5,8,10],[1,3,4,6,7,8],
  [1,3,4,6,7,11],[1,3,4,6,8,12],[1,3,4,6,10,11],
  [1,3,4,7,8,10],[1,3,4,7,10,11],[1,3,5,7,8,10],
  [1,3,5,7,9,10],[1,3,6,7,8,12],[1,3,6,7,11,12],
  [1,3,6,9,10,12],[1,3,6,10,11,12],[1,3,7,9,10,12],
  [1,3,7,10,11,12],[1,4,5,6,10,12],[1,4,5,7,8,9],
  [1,4,5,7,9,12],[1,4,5,8,9,11],[1,4,5,8,10,11],
  [1,4,5,9,10,11],[1,4,5,9,10,12],[1,4,6,7,8,12],
  [1,4,6,7,11,12],[1,4,6,10,11,12],[1,4,7,8,9,11],
  [1,4,7,8,10,11],[1,4,7,9,11,12],[1,4,9,10,11,12],
  [1,5,7,8,9,11],[1,5,7,8,10,11],[1,5,7,9,10,11],
  [1,7,9,10,11,12],[2,3,4,5,6,8],[2,3,4,5,6,12],
  [2,3,4,6,8,12],[2,3,5,6,8,10],[2,3,5,7,8,9],
  [2,3,5,8,9,10],[2,3,6,7,8,11],[2,3,6,7,8,12],
  [2,3,6,7,9,10],[2,3,6,7,9,12],[2,3,6,7,10,11],
  [2,3,6,8,10,11],[2,3,7,8,9,11],[2,3,7,9,10,11],
  [2,3,8,9,10,11],[2,4,5,6,8,11],[2,4,5,6,9,10],
  [2,4,5,6,9,11],[2,4,5,6,10,12],[2,4,5,7,8,12],
  [2,4,5,8,11,12],[2,4,5,9,10,12],[2,4,5,9,11,12],
  [2,4,6,8,11,12],[2,4,6,9,10,12],[2,4,6,9,11,12],
  [2,5,6,8,9,10],[2,5,6,8,9,11],[2,5,7,8,9,12],
  [2,5,8,9,11,12],[2,6,7,8,11,12],[2,6,7,9,10,11],
  [2,6,7,9,11,12],[2,6,8,9,10,11],[2,7,8,9,11,12],
  [3,4,5,6,8,10],[3,4,6,7,8,11],[3,4,6,8,10,11],
  [3,4,7,8,10,11],[3,5,7,8,9,11],[3,5,7,8,10,11],
  [3,5,7,9,10,11],[3,5,8,9,10,11],[3,6,7,9,10,12],
  [3,6,7,10,11,12],[4,5,6,8,10,11],[4,5,6,9,10,11],
  [4,5,7,8,9,12],[4,5,8,9,11,12],[4,6,7,8,11,12],
  [4,6,9,10,11,12],[4,7,8,9,11,12],[5,6,8,9,10,11],
  [6,7,9,10,11,12]]

manifold_5_12_8_3=[[1,2,3,4,6,8],[1,2,3,4,6,12],
  [1,2,3,4,8,12],[1,2,3,5,8,11],[1,2,3,5,8,12],
  [1,2,3,5,10,11],[1,2,3,5,10,12],[1,2,3,6,8,11],
  [1,2,3,6,10,11],[1,2,3,6,10,12],[1,2,4,5,6,10],
  [1,2,4,5,6,12],[1,2,4,5,8,11],[1,2,4,5,8,12],
  [1,2,4,5,10,11],[1,2,4,6,8,11],[1,2,4,6,10,11],
  [1,2,5,6,10,12],[1,3,4,6,7,11],[1,3,4,6,7,12],
  [1,3,4,6,8,11],[1,3,4,7,8,11],[1,3,4,7,8,12],
  [1,3,5,8,10,11],[1,3,5,8,10,12],[1,3,6,7,10,11],
  [1,3,6,7,10,12],[1,3,7,8,10,11],[1,3,7,8,10,12],
  [1,4,5,6,7,10],[1,4,5,6,7,12],[1,4,5,7,8,11],
  [1,4,5,7,8,12],[1,4,5,7,10,11],[1,4,6,7,10,11],
  [1,5,6,7,9,10],[1,5,6,7,9,12],[1,5,6,9,10,12],
  [1,5,7,8,9,10],[1,5,7,8,9,12],[1,5,7,8,10,11],
  [1,5,8,9,10,12],[1,6,7,9,10,12],[1,7,8,9,10,12],
  [2,3,4,6,8,9],[2,3,4,6,9,12],[2,3,4,7,8,9],
  [2,3,4,7,8,12],[2,3,4,7,9,12],[2,3,5,8,10,11],
  [2,3,5,8,10,12],[2,3,6,8,9,11],[2,3,6,9,10,11],
  [2,3,6,9,10,12],[2,3,7,8,9,10],[2,3,7,8,10,12],
  [2,3,7,9,10,12],[2,3,8,9,10,11],[2,4,5,6,9,11],
  [2,4,5,6,9,12],[2,4,5,6,10,11],[2,4,5,8,9,11],
  [2,4,5,8,9,12],[2,4,6,8,9,11],[2,4,7,8,9,12],
  [2,5,6,9,10,11],[2,5,6,9,10,12],[2,5,8,9,10,11],
  [2,5,8,9,10,12],[2,7,8,9,10,12],[3,4,6,7,11,12],
  [3,4,6,8,9,11],[3,4,6,9,11,12],[3,4,7,8,9,11],
  [3,4,7,9,11,12],[3,6,7,9,10,11],[3,6,7,9,10,12],
  [3,6,7,9,11,12],[3,7,8,9,10,11],[4,5,6,7,10,11],
  [4,5,6,7,11,12],[4,5,6,9,11,12],[4,5,7,8,9,11],
  [4,5,7,8,9,12],[4,5,7,9,11,12],[5,6,7,9,10,11],
  [5,6,7,9,11,12],[5,7,8,9,10,11]]

manifold_5_12_5_1=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,11],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,12],[1,2,3,4,11,12],[1,2,3,5,6,11],
  [1,2,3,5,7,8],[1,2,3,5,8,10],[1,2,3,5,10,12],
  [1,2,3,5,11,12],[1,2,3,8,9,10],[1,2,3,9,10,12],
  [1,2,4,5,6,7],[1,2,4,6,7,8],[1,2,4,6,8,11],
  [1,2,4,8,9,11],[1,2,4,9,11,12],[1,2,5,6,7,12],
  [1,2,5,6,11,12],[1,2,5,7,8,12],[1,2,5,8,10,12],
  [1,2,6,7,8,11],[1,2,6,7,11,12],[1,2,7,8,9,10],
  [1,2,7,8,9,11],[1,2,7,8,10,12],[1,2,7,9,10,11],
  [1,2,7,10,11,12],[1,2,9,10,11,12],[1,3,4,5,6,8],
  [1,3,4,5,7,8],[1,3,4,6,8,10],[1,3,4,6,10,11],
  [1,3,4,8,9,10],[1,3,4,9,10,11],[1,3,4,9,11,12],
  [1,3,5,6,8,12],[1,3,5,6,11,12],[1,3,5,8,10,12],
  [1,3,6,8,10,11],[1,3,6,8,11,12],[1,3,8,10,11,12],
  [1,3,9,10,11,12],[1,4,5,6,7,8],[1,4,6,8,9,10],
  [1,4,6,8,9,11],[1,4,6,9,10,11],[1,5,6,7,8,12],
  [1,6,7,8,11,12],[1,6,8,9,10,11],[1,7,8,9,10,11],
  [1,7,8,10,11,12],[2,3,4,5,6,11],[2,3,4,5,7,12],
  [2,3,4,5,11,12],[2,3,4,7,8,9],[2,3,4,7,9,10],
  [2,3,4,7,10,12],[2,3,4,9,10,12],[2,3,5,7,8,10],
  [2,3,5,7,10,12],[2,3,7,8,9,10],[2,4,5,6,7,9],
  [2,4,5,6,9,12],[2,4,5,6,11,12],[2,4,5,7,9,12],
  [2,4,6,7,8,11],[2,4,6,7,9,11],[2,4,6,9,11,12],
  [2,4,7,8,9,11],[2,4,7,9,10,12],[2,5,6,7,9,12],
  [2,5,7,8,10,12],[2,6,7,9,11,12],[2,7,9,10,11,12],
  [3,4,5,6,7,8],[3,4,5,6,7,9],[3,4,5,6,9,10],
  [3,4,5,6,10,11],[3,4,5,7,9,10],[3,4,5,7,10,12],
  [3,4,5,10,11,12],[3,4,6,7,8,9],[3,4,6,8,9,10],
  [3,4,9,10,11,12],[3,5,6,7,8,10],[3,5,6,7,9,10],
  [3,5,6,8,10,12],[3,5,6,10,11,12],[3,6,7,8,9,10],
  [3,6,8,10,11,12],[4,5,6,9,10,11],[4,5,6,9,11,12],
  [4,5,7,9,10,12],[4,5,9,10,11,12],[4,6,7,8,9,11],
  [5,6,7,8,9,10],[5,6,7,8,9,11],[5,6,7,8,11,12],
  [5,6,7,9,11,12],[5,6,8,9,10,11],[5,6,8,10,11,12],
  [5,7,8,9,10,12],[5,7,8,9,11,12],[5,8,9,10,11,12],
  [7,8,9,10,11,12]]

manifold_5_12_5_2=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,11],[1,2,3,4,7,10],[1,2,3,4,9,10],
  [1,2,3,4,9,12],[1,2,3,4,11,12],[1,2,3,5,6,11],
  [1,2,3,5,7,8],[1,2,3,5,8,10],[1,2,3,5,10,12],
  [1,2,3,5,11,12],[1,2,3,7,8,10],[1,2,3,9,10,12],
  [1,2,4,5,6,7],[1,2,4,6,7,8],[1,2,4,6,8,11],
  [1,2,4,7,8,9],[1,2,4,7,9,10],[1,2,4,8,9,11],
  [1,2,4,9,11,12],[1,2,5,6,7,8],[1,2,5,6,8,11],
  [1,2,5,8,10,12],[1,2,5,8,11,12],[1,2,7,8,9,11],
  [1,2,7,8,10,12],[1,2,7,8,11,12],[1,2,7,9,10,11],
  [1,2,7,10,11,12],[1,2,9,10,11,12],[1,3,4,5,6,8],
  [1,3,4,5,7,8],[1,3,4,6,8,10],[1,3,4,6,10,11],
  [1,3,4,7,8,10],[1,3,4,9,10,11],[1,3,4,9,11,12],
  [1,3,5,6,8,12],[1,3,5,6,11,12],[1,3,5,8,10,12],
  [1,3,6,8,10,11],[1,3,6,8,11,12],[1,3,8,10,11,12],
  [1,3,9,10,11,12],[1,4,5,6,7,8],[1,4,6,8,9,10],
  [1,4,6,8,9,11],[1,4,6,9,10,11],[1,4,7,8,9,10],
  [1,5,6,8,11,12],[1,6,8,9,10,11],[1,7,8,9,10,11],
  [1,7,8,10,11,12],[2,3,4,5,6,11],[2,3,4,5,7,12],
  [2,3,4,5,11,12],[2,3,4,7,10,12],[2,3,4,9,10,12],
  [2,3,5,7,8,10],[2,3,5,7,10,12],[2,4,5,6,7,9],
  [2,4,5,6,9,12],[2,4,5,6,11,12],[2,4,5,7,9,12],
  [2,4,6,7,8,11],[2,4,6,7,9,11],[2,4,6,9,11,12],
  [2,4,7,8,9,11],[2,4,7,9,10,12],[2,5,6,7,8,11],
  [2,5,6,7,9,12],[2,5,6,7,11,12],[2,5,7,8,10,12],
  [2,5,7,8,11,12],[2,6,7,9,11,12],[2,7,9,10,11,12],
  [3,4,5,6,7,8],[3,4,5,6,7,9],[3,4,5,6,9,12],
  [3,4,5,6,11,12],[3,4,5,7,9,10],[3,4,5,7,10,12],
  [3,4,5,9,10,12],[3,4,6,7,8,9],[3,4,6,8,9,10],
  [3,4,6,9,10,11],[3,4,6,9,11,12],[3,4,7,8,9,10],
  [3,5,6,7,8,10],[3,5,6,7,9,10],[3,5,6,8,10,12],
  [3,5,6,9,10,12],[3,6,7,8,9,10],[3,6,8,10,11,12],
  [3,6,9,10,11,12],[4,5,7,9,10,12],[4,6,7,8,9,11],
  [5,6,7,8,9,10],[5,6,7,8,9,11],[5,6,7,9,11,12],
  [5,6,8,9,10,11],[5,6,8,10,11,12],[5,6,9,10,11,12],
  [5,7,8,9,10,12],[5,7,8,9,11,12],[5,8,9,10,11,12],
  [7,8,9,10,11,12]]

manifold_5_12_5_3=[[1,2,3,4,5,7],[1,2,3,4,5,8],
  [1,2,3,4,6,8],[1,2,3,4,6,9],[1,2,3,4,7,12],
  [1,2,3,4,9,12],[1,2,3,5,7,12],[1,2,3,5,8,10],
  [1,2,3,5,10,11],[1,2,3,5,11,12],[1,2,3,6,8,11],
  [1,2,3,6,9,12],[1,2,3,6,11,12],[1,2,3,8,10,11],
  [1,2,4,5,7,8],[1,2,4,6,8,11],[1,2,4,6,9,12],
  [1,2,4,6,11,12],[1,2,4,7,8,11],[1,2,4,7,11,12],
  [1,2,5,7,8,10],[1,2,5,7,10,12],[1,2,5,10,11,12],
  [1,2,7,8,10,11],[1,2,7,10,11,12],[1,3,4,5,7,12],
  [1,3,4,5,8,10],[1,3,4,5,10,12],[1,3,4,6,8,10],
  [1,3,4,6,9,10],[1,3,4,9,10,12],[1,3,5,10,11,12],
  [1,3,6,8,9,10],[1,3,6,8,9,12],[1,3,6,8,11,12],
  [1,3,8,9,10,11],[1,3,8,9,11,12],[1,3,9,10,11,12],
  [1,4,5,6,7,8],[1,4,5,6,7,10],[1,4,5,6,8,10],
  [1,4,5,7,10,12],[1,4,6,7,8,11],[1,4,6,7,10,11],
  [1,4,6,9,10,11],[1,4,6,9,11,12],[1,4,7,10,11,12],
  [1,4,9,10,11,12],[1,5,6,7,8,10],[1,6,7,8,9,10],
  [1,6,7,8,9,11],[1,6,7,9,10,11],[1,6,8,9,11,12],
  [1,7,8,9,10,11],[2,3,4,5,6,9],[2,3,4,5,6,11],
  [2,3,4,5,7,9],[2,3,4,5,8,11],[2,3,4,6,8,11],
  [2,3,4,7,9,12],[2,3,5,6,7,9],[2,3,5,6,7,12],
  [2,3,5,6,11,12],[2,3,5,8,10,11],[2,3,6,7,9,12],
  [2,4,5,6,9,11],[2,4,5,7,8,9],[2,4,5,8,9,11],
  [2,4,6,9,11,12],[2,4,7,8,9,11],[2,4,7,9,10,11],
  [2,4,7,9,10,12],[2,4,7,10,11,12],[2,4,9,10,11,12],
  [2,5,6,7,9,12],[2,5,6,9,11,12],[2,5,7,8,9,12],
  [2,5,7,8,10,12],[2,5,8,9,10,11],[2,5,8,9,10,12],
  [2,5,9,10,11,12],[2,7,8,9,10,11],[2,7,8,9,10,12],
  [3,4,5,6,7,9],[3,4,5,6,7,10],[3,4,5,6,8,10],
  [3,4,5,6,8,11],[3,4,5,7,10,12],[3,4,6,7,9,10],
  [3,4,7,9,10,12],[3,5,6,7,10,12],[3,5,6,8,10,12],
  [3,5,6,8,11,12],[3,5,8,10,11,12],[3,6,7,8,9,10],
  [3,6,7,8,9,12],[3,6,7,8,10,12],[3,7,8,9,10,12],
  [3,8,9,10,11,12],[4,5,6,7,8,11],[4,5,6,7,9,11],
  [4,5,7,8,9,11],[4,6,7,9,10,11],[5,6,7,8,9,11],
  [5,6,7,8,9,12],[5,6,7,8,10,12],[5,6,8,9,11,12],
  [5,8,9,10,11,12]]

manifold_5_12_5_4=[[1,2,3,4,5,7],[1,2,3,4,5,8],
  [1,2,3,4,6,8],[1,2,3,4,6,12],[1,2,3,4,7,12],
  [1,2,3,5,7,12],[1,2,3,5,8,11],[1,2,3,5,11,12],
  [1,2,3,6,8,11],[1,2,3,6,11,12],[1,2,4,5,7,8],
  [1,2,4,6,8,11],[1,2,4,6,11,12],[1,2,4,7,8,11],
  [1,2,4,7,10,11],[1,2,4,7,10,12],[1,2,4,10,11,12],
  [1,2,5,7,8,10],[1,2,5,7,10,12],[1,2,5,8,10,11],
  [1,2,5,10,11,12],[1,2,7,8,10,11],[1,3,4,5,7,10],
  [1,3,4,5,8,10],[1,3,4,6,8,10],[1,3,4,6,9,10],
  [1,3,4,6,9,12],[1,3,4,7,10,12],[1,3,4,9,10,12],
  [1,3,5,7,10,12],[1,3,5,8,10,11],[1,3,5,10,11,12],
  [1,3,6,8,9,10],[1,3,6,8,9,11],[1,3,6,9,11,12],
  [1,3,8,9,10,11],[1,3,9,10,11,12],[1,4,5,7,8,10],
  [1,4,6,7,8,10],[1,4,6,7,8,11],[1,4,6,7,9,10],
  [1,4,6,7,9,11],[1,4,6,9,11,12],[1,4,7,9,10,11],
  [1,4,9,10,11,12],[1,6,7,8,9,10],[1,6,7,8,9,11],
  [1,7,8,9,10,11],[2,3,4,5,6,8],[2,3,4,5,6,9],
  [2,3,4,5,7,9],[2,3,4,6,9,12],[2,3,4,7,9,12],
  [2,3,5,6,8,11],[2,3,5,6,9,12],[2,3,5,6,11,12],
  [2,3,5,7,9,12],[2,4,5,6,8,11],[2,4,5,6,9,11],
  [2,4,5,7,8,11],[2,4,5,7,9,11],[2,4,6,9,11,12],
  [2,4,7,9,10,11],[2,4,7,9,10,12],[2,4,9,10,11,12],
  [2,5,6,9,11,12],[2,5,7,8,9,11],[2,5,7,8,9,12],
  [2,5,7,8,10,12],[2,5,8,9,11,12],[2,5,8,10,11,12],
  [2,7,8,9,10,11],[2,7,8,9,10,12],[2,8,9,10,11,12],
  [3,4,5,6,7,9],[3,4,5,6,7,10],[3,4,5,6,8,10],
  [3,4,6,7,9,10],[3,4,7,9,10,12],[3,5,6,7,9,12],
  [3,5,6,7,10,12],[3,5,6,8,10,12],[3,5,6,8,11,12],
  [3,5,8,10,11,12],[3,6,7,9,10,12],[3,6,8,9,10,12],
  [3,6,8,9,11,12],[3,8,9,10,11,12],[4,5,6,7,8,10],
  [4,5,6,7,8,11],[4,5,6,7,9,11],[5,6,7,8,9,11],
  [5,6,7,8,9,12],[5,6,7,8,10,12],[5,6,8,9,11,12],
  [6,7,8,9,10,12]]

manifold_5_12_3_1=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,8],[1,2,3,4,7,11],[1,2,3,4,8,12],
  [1,2,3,4,11,12],[1,2,3,5,6,10],[1,2,3,5,7,9],
  [1,2,3,5,9,12],[1,2,3,5,10,12],[1,2,3,6,8,12],
  [1,2,3,6,10,12],[1,2,3,7,9,12],[1,2,3,7,11,12],
  [1,2,4,5,6,9],[1,2,4,5,7,9],[1,2,4,6,8,11],
  [1,2,4,6,9,11],[1,2,4,7,9,11],[1,2,4,8,11,12],
  [1,2,5,6,9,10],[1,2,5,9,10,12],[1,2,6,8,10,11],
  [1,2,6,8,10,12],[1,2,6,9,10,11],[1,2,7,9,11,12],
  [1,2,8,10,11,12],[1,2,9,10,11,12],[1,3,4,5,6,11],
  [1,3,4,5,7,11],[1,3,4,6,8,11],[1,3,4,8,11,12],
  [1,3,5,6,8,10],[1,3,5,6,8,11],[1,3,5,7,9,11],
  [1,3,5,8,10,11],[1,3,5,9,10,11],[1,3,5,9,10,12],
  [1,3,6,8,10,12],[1,3,7,9,11,12],[1,3,8,10,11,12],
  [1,3,9,10,11,12],[1,4,5,6,7,9],[1,4,5,6,7,11],
  [1,4,6,7,9,11],[1,5,6,7,9,11],[1,5,6,8,9,10],
  [1,5,6,8,9,11],[1,5,8,9,10,11],[1,6,8,9,10,11],
  [2,3,4,5,6,12],[2,3,4,5,7,12],[2,3,4,6,8,12],
  [2,3,4,7,11,12],[2,3,5,6,10,12],[2,3,5,7,9,12],
  [2,4,5,6,7,9],[2,4,5,6,7,10],[2,4,5,6,10,12],
  [2,4,5,7,10,12],[2,4,6,7,9,10],[2,4,6,8,9,10],
  [2,4,6,8,9,11],[2,4,6,8,10,12],[2,4,7,9,10,12],
  [2,4,7,9,11,12],[2,4,8,9,10,11],[2,4,8,10,11,12],
  [2,4,9,10,11,12],[2,5,6,7,9,10],[2,5,7,9,10,12],
  [2,6,8,9,10,11],[3,4,5,6,7,8],[3,4,5,6,7,11],
  [3,4,5,6,8,12],[3,4,5,7,8,12],[3,4,6,7,8,11],
  [3,4,7,8,11,12],[3,5,6,7,8,11],[3,5,6,8,10,12],
  [3,5,7,8,9,10],[3,5,7,8,9,11],[3,5,7,8,10,12],
  [3,5,7,9,10,12],[3,5,8,9,10,11],[3,7,8,9,10,11],
  [3,7,8,10,11,12],[3,7,9,10,11,12],[4,5,6,7,8,12],
  [4,5,6,7,10,12],[4,6,7,8,9,10],[4,6,7,8,9,11],
  [4,6,7,8,10,12],[4,7,8,9,10,12],[4,7,8,9,11,12],
  [4,8,9,10,11,12],[5,6,7,8,9,10],[5,6,7,8,9,11],
  [5,6,7,8,10,12],[7,8,9,10,11,12]]

manifold_5_12_3_2=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,8],[1,2,3,4,7,12],[1,2,3,4,8,11],
  [1,2,3,4,11,12],[1,2,3,5,6,12],[1,2,3,5,7,9],
  [1,2,3,5,9,10],[1,2,3,5,10,12],[1,2,3,6,8,12],
  [1,2,3,7,9,12],[1,2,3,8,11,12],[1,2,3,9,10,12],
  [1,2,4,5,6,7],[1,2,4,6,7,9],[1,2,4,6,8,11],
  [1,2,4,6,9,11],[1,2,4,7,9,11],[1,2,4,7,11,12],
  [1,2,5,6,7,9],[1,2,5,6,9,10],[1,2,5,6,10,12],
  [1,2,6,8,9,10],[1,2,6,8,9,11],[1,2,6,8,10,12],
  [1,2,7,9,11,12],[1,2,8,9,10,11],[1,2,8,10,11,12],
  [1,2,9,10,11,12],[1,3,4,5,6,11],[1,3,4,5,7,11],
  [1,3,4,6,8,11],[1,3,4,7,11,12],[1,3,5,6,8,10],
  [1,3,5,6,8,11],[1,3,5,6,10,12],[1,3,5,7,9,11],
  [1,3,5,8,10,11],[1,3,5,9,10,11],[1,3,6,8,10,12],
  [1,3,7,9,11,12],[1,3,8,10,11,12],[1,3,9,10,11,12],
  [1,4,5,6,7,11],[1,4,6,7,9,11],[1,5,6,7,9,11],
  [1,5,6,8,10,11],[1,5,6,9,10,11],[1,6,8,9,10,11],
  [2,3,4,5,6,12],[2,3,4,5,7,12],[2,3,4,6,8,12],
  [2,3,4,8,11,12],[2,3,5,7,9,12],[2,3,5,9,10,12],
  [2,4,5,6,7,9],[2,4,5,6,9,10],[2,4,5,6,10,12],
  [2,4,5,7,9,10],[2,4,5,7,10,12],[2,4,6,8,9,10],
  [2,4,6,8,9,11],[2,4,6,8,10,12],[2,4,7,9,10,12],
  [2,4,7,9,11,12],[2,4,8,9,10,11],[2,4,8,10,11,12],
  [2,4,9,10,11,12],[2,5,7,9,10,12],[3,4,5,6,7,8],
  [3,4,5,6,7,12],[3,4,5,6,8,11],[3,4,5,7,8,11],
  [3,4,6,7,8,12],[3,4,7,8,11,12],[3,5,6,7,8,12],
  [3,5,6,8,10,12],[3,5,7,8,9,10],[3,5,7,8,9,11],
  [3,5,7,8,10,12],[3,5,7,9,10,12],[3,5,8,9,10,11],
  [3,7,8,9,10,12],[3,7,8,9,11,12],[3,8,9,10,11,12],
  [4,5,6,7,8,11],[4,5,6,7,9,10],[4,5,6,7,10,12],
  [4,6,7,8,9,10],[4,6,7,8,9,11],[4,6,7,8,10,12],
  [4,7,8,9,10,11],[4,7,8,10,11,12],[4,7,9,10,11,12],
  [5,6,7,8,9,10],[5,6,7,8,9,11],[5,6,7,8,10,12],
  [5,6,8,9,10,11],[7,8,9,10,11,12]]

manifold_5_12_3_3=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,9],[1,2,3,4,7,10],[1,2,3,4,9,12],
  [1,2,3,4,10,12],[1,2,3,5,6,11],[1,2,3,5,7,8],
  [1,2,3,5,8,12],[1,2,3,5,11,12],[1,2,3,6,9,12],
  [1,2,3,6,11,12],[1,2,3,7,8,12],[1,2,3,7,10,12],
  [1,2,4,5,6,8],[1,2,4,5,7,8],[1,2,4,6,8,11],
  [1,2,4,6,9,11],[1,2,4,7,8,11],[1,2,4,7,9,10],
  [1,2,4,7,9,11],[1,2,4,9,10,12],[1,2,5,6,8,11],
  [1,2,5,8,11,12],[1,2,6,9,11,12],[1,2,7,8,10,11],
  [1,2,7,8,10,12],[1,2,7,9,10,11],[1,2,8,10,11,12],
  [1,2,9,10,11,12],[1,3,4,5,6,10],[1,3,4,5,7,10],
  [1,3,4,6,8,10],[1,3,4,6,8,11],[1,3,4,6,9,11],
  [1,3,4,8,10,11],[1,3,4,9,10,11],[1,3,4,9,10,12],
  [1,3,5,6,8,10],[1,3,5,6,8,11],[1,3,5,7,8,10],
  [1,3,5,8,11,12],[1,3,6,9,11,12],[1,3,7,8,10,12],
  [1,3,8,10,11,12],[1,3,9,10,11,12],[1,4,5,6,7,8],
  [1,4,5,6,7,10],[1,4,6,7,8,10],[1,4,7,8,9,10],
  [1,4,7,8,9,11],[1,4,8,9,10,11],[1,5,6,7,8,10],
  [1,7,8,9,10,11],[2,3,4,5,6,12],[2,3,4,5,7,12],
  [2,3,4,6,9,12],[2,3,4,7,10,12],[2,3,5,6,11,12],
  [2,3,5,7,8,12],[2,4,5,6,7,8],[2,4,5,6,7,11],
  [2,4,5,6,11,12],[2,4,5,7,11,12],[2,4,6,7,8,11],
  [2,4,6,9,11,12],[2,4,7,9,10,12],[2,4,7,9,11,12],
  [2,5,6,7,8,11],[2,5,7,8,9,10],[2,5,7,8,9,11],
  [2,5,7,8,10,12],[2,5,7,9,10,12],[2,5,7,9,11,12],
  [2,5,8,9,10,11],[2,5,8,10,11,12],[2,5,9,10,11,12],
  [2,7,8,9,10,11],[3,4,5,6,7,9],[3,4,5,6,7,10],
  [3,4,5,6,9,12],[3,4,5,7,9,12],[3,4,6,7,9,10],
  [3,4,6,8,9,10],[3,4,6,8,9,11],[3,4,7,9,10,12],
  [3,4,8,9,10,11],[3,5,6,7,9,10],[3,5,6,8,10,12],
  [3,5,6,8,11,12],[3,5,6,9,10,12],[3,5,7,8,10,12],
  [3,5,7,9,10,12],[3,6,8,9,10,11],[3,6,8,10,11,12],
  [3,6,9,10,11,12],[4,5,6,7,9,12],[4,5,6,7,11,12],
  [4,6,7,8,9,10],[4,6,7,8,9,11],[4,6,7,9,11,12],
  [5,6,7,8,9,10],[5,6,7,8,9,11],[5,6,7,9,11,12],
  [5,6,8,9,10,12],[5,6,8,9,11,12],[5,8,9,10,11,12],
  [6,8,9,10,11,12]]

manifold_5_12_3_4=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,9],[1,2,3,4,7,12],[1,2,3,4,9,10],
  [1,2,3,4,10,12],[1,2,3,5,6,12],[1,2,3,5,7,8],
  [1,2,3,5,8,11],[1,2,3,5,11,12],[1,2,3,6,9,12],
  [1,2,3,7,8,12],[1,2,3,8,11,12],[1,2,3,9,10,12],
  [1,2,4,5,6,7],[1,2,4,6,7,8],[1,2,4,6,8,11],
  [1,2,4,6,9,11],[1,2,4,7,8,11],[1,2,4,7,9,10],
  [1,2,4,7,9,11],[1,2,4,7,10,12],[1,2,5,6,7,8],
  [1,2,5,6,8,11],[1,2,5,6,11,12],[1,2,6,9,11,12],
  [1,2,7,8,9,10],[1,2,7,8,9,11],[1,2,7,8,10,12],
  [1,2,8,9,10,11],[1,2,8,10,11,12],[1,2,9,10,11,12],
  [1,3,4,5,6,10],[1,3,4,5,7,10],[1,3,4,6,8,10],
  [1,3,4,6,8,11],[1,3,4,6,9,11],[1,3,4,7,10,12],
  [1,3,4,8,10,11],[1,3,4,9,10,11],[1,3,5,6,8,10],
  [1,3,5,6,8,11],[1,3,5,6,11,12],[1,3,5,7,8,10],
  [1,3,6,9,11,12],[1,3,7,8,10,12],[1,3,8,10,11,12],
  [1,3,9,10,11,12],[1,4,5,6,7,10],[1,4,6,7,8,10],
  [1,4,7,8,10,11],[1,4,7,9,10,11],[1,5,6,7,8,10],
  [1,7,8,9,10,11],[2,3,4,5,6,12],[2,3,4,5,7,12],
  [2,3,4,6,9,12],[2,3,4,9,10,12],[2,3,5,7,8,12],
  [2,3,5,8,11,12],[2,4,5,6,7,8],[2,4,5,6,8,11],
  [2,4,5,6,11,12],[2,4,5,7,8,11],[2,4,5,7,11,12],
  [2,4,6,9,11,12],[2,4,7,9,10,12],[2,4,7,9,11,12],
  [2,5,7,8,9,10],[2,5,7,8,9,11],[2,5,7,8,10,12],
  [2,5,7,9,10,12],[2,5,7,9,11,12],[2,5,8,9,10,11],
  [2,5,8,10,11,12],[2,5,9,10,11,12],[3,4,5,6,7,9],
  [3,4,5,6,7,12],[3,4,5,6,9,10],[3,4,5,7,9,10],
  [3,4,6,7,9,12],[3,4,6,8,9,10],[3,4,6,8,9,11],
  [3,4,7,9,10,12],[3,4,8,9,10,11],[3,5,6,7,9,12],
  [3,5,6,8,10,12],[3,5,6,8,11,12],[3,5,6,9,10,12],
  [3,5,7,8,10,12],[3,5,7,9,10,12],[3,6,8,9,10,12],
  [3,6,8,9,11,12],[3,8,9,10,11,12],[4,5,6,7,8,11],
  [4,5,6,7,9,10],[4,5,6,7,11,12],[4,6,7,8,9,10],
  [4,6,7,8,9,11],[4,6,7,9,11,12],[4,7,8,9,10,11],
  [5,6,7,8,9,10],[5,6,7,8,9,11],[5,6,7,9,11,12],
  [5,6,8,9,10,11],[5,6,8,10,11,12],[5,6,9,10,11,12],
  [6,8,9,10,11,12]]

manifold_5_12_3_5=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,10],[1,2,3,4,7,12],[1,2,3,4,10,12],
  [1,2,3,5,6,12],[1,2,3,5,7,11],[1,2,3,5,11,12],
  [1,2,3,6,9,10],[1,2,3,6,9,12],[1,2,3,7,8,11],
  [1,2,3,7,8,12],[1,2,3,8,11,12],[1,2,3,9,10,12],
  [1,2,4,5,6,7],[1,2,4,6,7,10],[1,2,4,7,8,10],
  [1,2,4,7,8,12],[1,2,4,8,10,12],[1,2,5,6,7,10],
  [1,2,5,6,9,10],[1,2,5,6,9,12],[1,2,5,7,8,10],
  [1,2,5,7,8,11],[1,2,5,8,9,10],[1,2,5,8,9,11],
  [1,2,5,9,11,12],[1,2,8,9,10,11],[1,2,8,10,11,12],
  [1,2,9,10,11,12],[1,3,4,5,6,9],[1,3,4,5,7,9],
  [1,3,4,6,9,10],[1,3,4,7,8,10],[1,3,4,7,8,12],
  [1,3,4,7,9,10],[1,3,4,8,10,12],[1,3,5,6,9,12],
  [1,3,5,7,9,11],[1,3,5,9,11,12],[1,3,7,8,10,11],
  [1,3,7,9,10,11],[1,3,8,10,11,12],[1,3,9,10,11,12],
  [1,4,5,6,7,10],[1,4,5,6,9,10],[1,4,5,7,9,10],
  [1,5,7,8,9,10],[1,5,7,8,9,11],[1,7,8,9,10,11],
  [2,3,4,5,6,12],[2,3,4,5,7,12],[2,3,4,6,10,12],
  [2,3,5,7,11,12],[2,3,6,9,10,12],[2,3,7,8,11,12],
  [2,4,5,6,7,8],[2,4,5,6,8,12],[2,4,5,7,8,12],
  [2,4,6,7,8,10],[2,4,6,8,10,12],[2,5,6,7,8,10],
  [2,5,6,8,10,11],[2,5,6,8,11,12],[2,5,6,9,10,11],
  [2,5,6,9,11,12],[2,5,7,8,11,12],[2,5,8,9,10,11],
  [2,6,8,10,11,12],[2,6,9,10,11,12],[3,4,5,6,7,9],
  [3,4,5,6,7,12],[3,4,6,7,9,11],[3,4,6,7,11,12],
  [3,4,6,9,10,12],[3,4,6,9,11,12],[3,4,7,8,10,11],
  [3,4,7,8,11,12],[3,4,7,9,10,11],[3,4,8,9,10,11],
  [3,4,8,9,10,12],[3,4,8,9,11,12],[3,5,6,7,9,11],
  [3,5,6,7,11,12],[3,5,6,9,11,12],[3,8,9,10,11,12],
  [4,5,6,7,8,11],[4,5,6,7,9,10],[4,5,6,7,11,12],
  [4,5,6,8,11,12],[4,5,7,8,11,12],[4,6,7,8,9,10],
  [4,6,7,8,9,11],[4,6,8,9,10,12],[4,6,8,9,11,12],
  [4,7,8,9,10,11],[5,6,7,8,9,10],[5,6,7,8,9,11],
  [5,6,8,9,10,11],[6,8,9,10,11,12]]

manifold_5_12_3_6=[[1,2,3,4,5,6],[1,2,3,4,5,7],
  [1,2,3,4,6,11],[1,2,3,4,7,12],[1,2,3,4,11,12],
  [1,2,3,5,6,12],[1,2,3,5,7,10],[1,2,3,5,10,12],
  [1,2,3,6,8,11],[1,2,3,6,8,12],[1,2,3,7,9,10],
  [1,2,3,7,9,12],[1,2,3,8,11,12],[1,2,3,9,10,12],
  [1,2,4,5,6,7],[1,2,4,6,7,11],[1,2,4,7,8,10],
  [1,2,4,7,8,11],[1,2,4,7,9,10],[1,2,4,7,9,12],
  [1,2,4,8,9,10],[1,2,4,8,9,11],[1,2,4,9,11,12],
  [1,2,5,6,7,11],[1,2,5,6,8,11],[1,2,5,6,8,12],
  [1,2,5,7,8,10],[1,2,5,7,8,11],[1,2,5,8,10,12],
  [1,2,8,9,10,11],[1,2,8,10,11,12],[1,2,9,10,11,12],
  [1,3,4,5,6,8],[1,3,4,5,7,8],[1,3,4,6,8,10],
  [1,3,4,6,9,10],[1,3,4,6,9,11],[1,3,4,7,8,10],
  [1,3,4,7,9,10],[1,3,4,7,9,12],[1,3,4,9,11,12],
  [1,3,5,6,8,12],[1,3,5,7,8,10],[1,3,5,8,10,12],
  [1,3,6,8,10,11],[1,3,6,9,10,11],[1,3,8,10,11,12],
  [1,3,9,10,11,12],[1,4,5,6,7,11],[1,4,5,6,8,11],
  [1,4,5,7,8,11],[1,4,6,8,9,10],[1,4,6,8,9,11],
  [1,6,8,9,10,11],[2,3,4,5,6,12],[2,3,4,5,7,12],
  [2,3,4,6,11,12],[2,3,5,7,10,12],[2,3,6,8,11,12],
  [2,3,7,9,10,12],[2,4,5,6,7,9],[2,4,5,6,9,12],
  [2,4,5,7,9,12],[2,4,6,7,9,11],[2,4,6,9,11,12],
  [2,4,7,8,10,11],[2,4,7,9,10,11],[2,4,8,9,10,11],
  [2,5,6,7,9,11],[2,5,6,8,11,12],[2,5,6,9,11,12],
  [2,5,7,8,10,12],[2,5,7,8,11,12],[2,5,7,9,11,12],
  [2,7,8,10,11,12],[2,7,9,10,11,12],[3,4,5,6,7,8],
  [3,4,5,6,7,12],[3,4,6,7,8,10],[3,4,6,7,10,12],
  [3,4,6,9,10,12],[3,4,6,9,11,12],[3,4,7,9,10,12],
  [3,5,6,7,8,10],[3,5,6,7,10,12],[3,5,6,8,10,11],
  [3,5,6,8,11,12],[3,5,6,9,10,11],[3,5,6,9,10,12],
  [3,5,6,9,11,12],[3,5,8,9,10,11],[3,5,8,9,10,12],
  [3,5,8,9,11,12],[3,8,9,10,11,12],[4,5,6,7,8,11],
  [4,5,6,7,9,10],[4,5,6,7,10,12],[4,5,6,9,10,12],
  [4,5,7,9,10,12],[4,6,7,8,9,10],[4,6,7,8,9,11],
  [4,7,8,9,10,11],[5,6,7,8,9,10],[5,6,7,8,9,11],
  [5,6,8,9,10,11],[5,7,8,9,10,12],[5,7,8,9,11,12],
  [7,8,9,10,11,12]]

manifold_5_12_3_7=[[1,2,3,4,5,6],[1,2,3,4,5,8],
  [1,2,3,4,6,8],[1,2,3,5,6,8],[1,2,4,5,6,11],
  [1,2,4,5,8,9],[1,2,4,5,9,10],[1,2,4,5,10,11],
  [1,2,4,6,8,9],[1,2,4,6,9,11],[1,2,4,9,10,11],
  [1,2,5,6,8,9],[1,2,5,6,9,10],[1,2,5,6,10,11],
  [1,2,6,7,9,10],[1,2,6,7,9,11],[1,2,6,7,10,11],
  [1,2,7,9,10,12],[1,2,7,9,11,12],[1,2,7,10,11,12],
  [1,2,9,10,11,12],[1,3,4,5,6,11],[1,3,4,5,8,11],
  [1,3,4,6,8,11],[1,3,5,6,8,10],[1,3,5,6,10,11],
  [1,3,5,8,10,11],[1,3,6,8,10,12],[1,3,6,8,11,12],
  [1,3,6,10,11,12],[1,3,8,10,11,12],[1,4,5,8,9,12],
  [1,4,5,8,11,12],[1,4,5,9,10,12],[1,4,5,10,11,12],
  [1,4,6,7,8,9],[1,4,6,7,8,11],[1,4,6,7,9,11],
  [1,4,7,8,9,12],[1,4,7,8,11,12],[1,4,7,9,11,12],
  [1,4,9,10,11,12],[1,5,6,8,9,12],[1,5,6,8,10,12],
  [1,5,6,9,10,12],[1,5,8,10,11,12],[1,6,7,8,9,12],
  [1,6,7,8,11,12],[1,6,7,9,10,12],[1,6,7,10,11,12],
  [2,3,4,5,6,11],[2,3,4,5,7,10],[2,3,4,5,7,12],
  [2,3,4,5,8,9],[2,3,4,5,9,12],[2,3,4,5,10,11],
  [2,3,4,6,8,11],[2,3,4,7,8,9],[2,3,4,7,8,11],
  [2,3,4,7,9,12],[2,3,4,7,10,11],[2,3,5,6,8,9],
  [2,3,5,6,9,10],[2,3,5,6,10,11],[2,3,5,7,9,10],
  [2,3,5,7,9,12],[2,3,6,7,8,9],[2,3,6,7,8,11],
  [2,3,6,7,9,10],[2,3,6,7,10,11],[2,4,5,7,10,12],
  [2,4,5,9,10,12],[2,4,6,8,9,11],[2,4,7,8,9,11],
  [2,4,7,9,11,12],[2,4,7,10,11,12],[2,4,9,10,11,12],
  [2,5,7,9,10,12],[2,6,7,8,9,11],[3,4,5,7,10,12],
  [3,4,5,8,9,12],[3,4,5,8,11,12],[3,4,5,10,11,12],
  [3,4,7,8,9,12],[3,4,7,8,11,12],[3,4,7,10,11,12],
  [3,5,6,8,9,10],[3,5,7,8,9,10],[3,5,7,8,9,12],
  [3,5,7,8,10,12],[3,5,8,10,11,12],[3,6,7,8,9,10],
  [3,6,7,8,10,12],[3,6,7,8,11,12],[3,6,7,10,11,12],
  [4,6,7,8,9,11],[5,6,7,8,9,10],[5,6,7,8,9,12],
  [5,6,7,8,10,12],[5,6,7,9,10,12]]

manifold_5_12_3_8=[[1,2,3,4,5,6],[1,2,3,4,5,9],
  [1,2,3,4,6,9],[1,2,3,5,6,9],[1,2,4,5,6,10],
  [1,2,4,5,9,11],[1,2,4,5,10,11],[1,2,4,6,9,11],
  [1,2,4,6,10,11],[1,2,5,6,9,10],[1,2,5,9,10,11],
  [1,2,6,9,10,12],[1,2,6,9,11,12],[1,2,6,10,11,12],
  [1,2,9,10,11,12],[1,3,4,5,6,10],[1,3,4,5,8,9],
  [1,3,4,5,8,10],[1,3,4,6,8,9],[1,3,4,6,8,11],
  [1,3,4,6,10,11],[1,3,4,8,10,11],[1,3,5,6,8,9],
  [1,3,5,6,8,10],[1,3,6,7,8,10],[1,3,6,7,8,11],
  [1,3,6,7,10,11],[1,3,7,8,10,12],[1,3,7,8,11,12],
  [1,3,7,10,11,12],[1,3,8,10,11,12],[1,4,5,8,9,12],
  [1,4,5,8,10,12],[1,4,5,9,11,12],[1,4,5,10,11,12],
  [1,4,6,8,9,12],[1,4,6,8,11,12],[1,4,6,9,11,12],
  [1,4,8,10,11,12],[1,5,6,7,8,9],[1,5,6,7,8,10],
  [1,5,6,7,9,10],[1,5,7,8,9,12],[1,5,7,8,10,12],
  [1,5,7,9,10,12],[1,5,9,10,11,12],[1,6,7,8,9,12],
  [1,6,7,8,11,12],[1,6,7,9,10,12],[1,6,7,10,11,12],
  [2,3,4,5,6,10],[2,3,4,5,7,11],[2,3,4,5,7,12],
  [2,3,4,5,8,9],[2,3,4,5,8,12],[2,3,4,5,10,11],
  [2,3,4,6,9,11],[2,3,4,6,10,11],[2,3,4,7,8,9],
  [2,3,4,7,8,12],[2,3,4,7,9,11],[2,3,5,6,8,9],
  [2,3,5,6,8,10],[2,3,5,7,8,10],[2,3,5,7,8,12],
  [2,3,5,7,10,11],[2,3,6,7,8,9],[2,3,6,7,8,10],
  [2,3,6,7,9,11],[2,3,6,7,10,11],[2,4,5,7,11,12],
  [2,4,5,8,9,12],[2,4,5,9,11,12],[2,4,7,8,9,12],
  [2,4,7,9,11,12],[2,5,6,8,9,10],[2,5,7,8,9,10],
  [2,5,7,8,9,12],[2,5,7,9,10,12],[2,5,7,10,11,12],
  [2,5,9,10,11,12],[2,6,7,8,9,10],[2,6,7,9,10,12],
  [2,6,7,9,11,12],[2,6,7,10,11,12],[3,4,5,7,11,12],
  [3,4,5,8,10,12],[3,4,5,10,11,12],[3,4,6,8,9,11],
  [3,4,7,8,9,11],[3,4,7,8,11,12],[3,4,8,10,11,12],
  [3,5,7,8,10,12],[3,5,7,10,11,12],[3,6,7,8,9,11],
  [4,6,7,8,9,11],[4,6,7,8,9,12],[4,6,7,8,11,12],
  [4,6,7,9,11,12],[5,6,7,8,9,10]]

manifold_5_12_3_9=[[1,2,3,4,5,6],[1,2,3,4,5,10],
  [1,2,3,4,6,10],[1,2,3,5,6,10],[1,2,4,5,6,9],
  [1,2,4,5,9,11],[1,2,4,5,10,11],[1,2,4,6,9,11],
  [1,2,4,6,10,11],[1,2,5,6,9,10],[1,2,5,9,10,12],
  [1,2,5,9,11,12],[1,2,5,10,11,12],[1,2,6,9,10,11],
  [1,2,9,10,11,12],[1,3,4,5,6,9],[1,3,4,5,8,9],
  [1,3,4,5,8,10],[1,3,4,6,8,9],[1,3,4,6,8,11],
  [1,3,4,6,10,11],[1,3,4,8,10,12],[1,3,4,8,11,12],
  [1,3,4,10,11,12],[1,3,5,6,8,9],[1,3,5,6,8,10],
  [1,3,6,7,8,10],[1,3,6,7,8,11],[1,3,6,7,10,11],
  [1,3,7,8,10,11],[1,3,8,10,11,12],[1,4,5,8,9,12],
  [1,4,5,8,10,12],[1,4,5,9,11,12],[1,4,5,10,11,12],
  [1,4,6,8,9,12],[1,4,6,8,11,12],[1,4,6,9,11,12],
  [1,5,6,8,9,10],[1,5,7,8,9,10],[1,5,7,8,9,12],
  [1,5,7,8,10,12],[1,5,7,9,10,12],[1,6,7,8,9,10],
  [1,6,7,8,9,12],[1,6,7,8,11,12],[1,6,7,9,10,12],
  [1,6,7,10,11,12],[1,6,9,10,11,12],[1,7,8,10,11,12],
  [2,3,4,5,6,9],[2,3,4,5,7,8],[2,3,4,5,7,12],
  [2,3,4,5,8,9],[2,3,4,5,10,11],[2,3,4,5,11,12],
  [2,3,4,6,9,11],[2,3,4,6,10,11],[2,3,4,7,8,9],
  [2,3,4,7,9,11],[2,3,4,7,11,12],[2,3,5,6,8,9],
  [2,3,5,6,8,10],[2,3,5,7,8,10],[2,3,5,7,10,11],
  [2,3,5,7,11,12],[2,3,6,7,8,9],[2,3,6,7,8,10],
  [2,3,6,7,9,11],[2,3,6,7,10,11],[2,4,5,7,8,12],
  [2,4,5,8,9,12],[2,4,5,9,11,12],[2,4,7,8,9,12],
  [2,4,7,9,11,12],[2,5,6,7,8,9],[2,5,6,7,8,10],
  [2,5,6,7,9,10],[2,5,7,8,9,12],[2,5,7,9,10,12],
  [2,5,7,10,11,12],[2,6,7,9,10,12],[2,6,7,9,11,12],
  [2,6,7,10,11,12],[2,6,9,10,11,12],[3,4,5,7,8,12],
  [3,4,5,8,10,12],[3,4,5,10,11,12],[3,4,6,7,8,9],
  [3,4,6,7,8,11],[3,4,6,7,9,11],[3,4,7,8,11,12],
  [3,5,7,8,10,12],[3,5,7,10,11,12],[3,7,8,10,11,12],
  [4,6,7,8,9,11],[4,6,8,9,11,12],[4,7,8,9,11,12],
  [5,6,7,8,9,10],[6,7,8,9,11,12]]

manifold_5_12_3_10=[[1,2,3,4,5,6],[1,2,3,4,5,10],
  [1,2,3,4,6,11],[1,2,3,4,10,11],[1,2,3,5,6,10],
  [1,2,3,6,10,11],[1,2,4,5,6,9],[1,2,4,5,9,12],
  [1,2,4,5,10,11],[1,2,4,5,11,12],[1,2,4,6,9,11],
  [1,2,4,9,11,12],[1,2,5,6,9,10],[1,2,5,9,10,12],
  [1,2,5,10,11,12],[1,2,6,9,10,11],[1,2,9,10,11,12],
  [1,3,4,5,6,8],[1,3,4,5,8,12],[1,3,4,5,10,12],
  [1,3,4,6,8,11],[1,3,4,8,11,12],[1,3,4,10,11,12],
  [1,3,5,6,8,10],[1,3,5,8,10,12],[1,3,6,8,10,11],
  [1,3,8,10,11,12],[1,4,5,6,8,9],[1,4,5,8,9,12],
  [1,4,5,10,11,12],[1,4,6,8,9,11],[1,4,8,9,11,12],
  [1,5,6,8,9,10],[1,5,8,9,10,12],[1,6,7,8,9,10],
  [1,6,7,8,9,12],[1,6,7,8,10,11],[1,6,7,8,11,12],
  [1,6,7,9,10,12],[1,6,7,10,11,12],[1,6,8,9,11,12],
  [1,6,9,10,11,12],[1,7,8,9,10,12],[1,7,8,10,11,12],
  [2,3,4,5,6,9],[2,3,4,5,7,8],[2,3,4,5,7,12],
  [2,3,4,5,8,9],[2,3,4,5,10,11],[2,3,4,5,11,12],
  [2,3,4,6,7,9],[2,3,4,6,7,11],[2,3,4,7,8,9],
  [2,3,4,7,11,12],[2,3,5,6,7,8],[2,3,5,6,7,10],
  [2,3,5,6,8,9],[2,3,5,7,10,12],[2,3,5,10,11,12],
  [2,3,6,7,8,9],[2,3,6,7,10,11],[2,3,7,10,11,12],
  [2,4,5,7,8,9],[2,4,5,7,9,12],[2,4,6,7,9,11],
  [2,4,7,9,11,12],[2,5,6,7,8,9],[2,5,6,7,9,10],
  [2,5,7,9,10,12],[2,6,7,9,10,11],[2,7,9,10,11,12],
  [3,4,5,6,8,9],[3,4,5,7,8,12],[3,4,5,10,11,12],
  [3,4,6,7,8,9],[3,4,6,7,8,11],[3,4,7,8,11,12],
  [3,5,6,7,8,10],[3,5,7,8,10,12],[3,6,7,8,10,11],
  [3,7,8,10,11,12],[4,5,7,8,9,12],[4,6,7,8,9,11],
  [4,7,8,9,11,12],[5,6,7,8,9,10],[5,7,8,9,10,12],
  [6,7,8,9,11,12],[6,7,9,10,11,12]]

manifold_5_12_3_11=[[1,2,3,4,5,6],[1,2,3,4,5,11],
  [1,2,3,4,6,11],[1,2,3,5,6,10],[1,2,3,5,10,11],
  [1,2,3,6,10,11],[1,2,4,5,6,9],[1,2,4,5,9,12],
  [1,2,4,5,10,11],[1,2,4,5,10,12],[1,2,4,6,9,11],
  [1,2,4,9,11,12],[1,2,4,10,11,12],[1,2,5,6,9,10],
  [1,2,5,9,10,12],[1,2,6,9,10,11],[1,2,9,10,11,12],
  [1,3,4,5,6,8],[1,3,4,5,8,12],[1,3,4,5,11,12],
  [1,3,4,6,8,11],[1,3,4,8,11,12],[1,3,5,6,8,10],
  [1,3,5,8,10,12],[1,3,5,10,11,12],[1,3,6,8,10,11],
  [1,3,8,10,11,12],[1,4,5,6,8,9],[1,4,5,8,9,12],
  [1,4,5,10,11,12],[1,4,6,8,9,11],[1,4,8,9,11,12],
  [1,5,6,8,9,10],[1,5,8,9,10,12],[1,6,7,8,9,11],
  [1,6,7,8,9,12],[1,6,7,8,11,12],[1,6,7,9,10,11],
  [1,6,7,9,10,12],[1,6,7,10,11,12],[1,6,8,9,10,12],
  [1,6,8,10,11,12],[1,7,8,9,11,12],[1,7,9,10,11,12],
  [2,3,4,5,6,8],[2,3,4,5,7,9],[2,3,4,5,7,12],
  [2,3,4,5,8,9],[2,3,4,5,10,11],[2,3,4,5,10,12],
  [2,3,4,6,7,8],[2,3,4,6,7,11],[2,3,4,7,8,9],
  [2,3,4,7,11,12],[2,3,4,10,11,12],[2,3,5,6,7,9],
  [2,3,5,6,7,10],[2,3,5,6,8,9],[2,3,5,7,10,12],
  [2,3,6,7,8,9],[2,3,6,7,10,11],[2,3,7,10,11,12],
  [2,4,5,6,8,9],[2,4,5,7,9,12],[2,4,6,7,8,9],
  [2,4,6,7,9,11],[2,4,7,9,11,12],[2,5,6,7,9,10],
  [2,5,7,9,10,12],[2,6,7,9,10,11],[2,7,9,10,11,12],
  [3,4,5,7,8,9],[3,4,5,7,8,12],[3,4,5,10,11,12],
  [3,4,6,7,8,11],[3,4,7,8,11,12],[3,5,6,7,8,9],
  [3,5,6,7,8,10],[3,5,7,8,10,12],[3,6,7,8,10,11],
  [3,7,8,10,11,12],[4,5,7,8,9,12],[4,6,7,8,9,11],
  [4,7,8,9,11,12],[5,6,7,8,9,10],[5,7,8,9,10,12],
  [6,7,8,9,10,12],[6,7,8,10,11,12]]

manifold_5_12_3_12=[[1,2,3,4,5,6],[1,2,3,4,5,11],
  [1,2,3,4,6,11],[1,2,3,5,6,11],[1,2,4,5,6,8],
  [1,2,4,5,8,9],[1,2,4,5,9,10],[1,2,4,5,10,11],
  [1,2,4,6,8,9],[1,2,4,6,9,11],[1,2,4,9,10,12],
  [1,2,4,9,11,12],[1,2,4,10,11,12],[1,2,5,6,8,9],
  [1,2,5,6,9,10],[1,2,5,6,10,11],[1,2,6,7,9,10],
  [1,2,6,7,9,11],[1,2,6,7,10,11],[1,2,7,9,10,11],
  [1,2,9,10,11,12],[1,3,4,5,6,8],[1,3,4,5,8,11],
  [1,3,4,6,8,11],[1,3,5,6,8,10],[1,3,5,6,10,11],
  [1,3,5,8,10,12],[1,3,5,8,11,12],[1,3,5,10,11,12],
  [1,3,6,8,10,11],[1,3,8,10,11,12],[1,4,5,8,9,12],
  [1,4,5,8,11,12],[1,4,5,9,10,12],[1,4,5,10,11,12],
  [1,4,6,8,9,11],[1,4,7,8,9,11],[1,4,7,8,9,12],
  [1,4,7,8,11,12],[1,4,7,9,11,12],[1,5,6,8,9,12],
  [1,5,6,8,10,12],[1,5,6,9,10,12],[1,6,7,8,9,11],
  [1,6,7,8,9,12],[1,6,7,8,11,12],[1,6,7,9,10,12],
  [1,6,7,10,11,12],[1,6,8,10,11,12],[1,7,9,10,11,12],
  [2,3,4,5,6,8],[2,3,4,5,7,9],[2,3,4,5,7,12],
  [2,3,4,5,8,9],[2,3,4,5,10,11],[2,3,4,5,10,12],
  [2,3,4,6,8,11],[2,3,4,7,8,9],[2,3,4,7,8,11],
  [2,3,4,7,10,11],[2,3,4,7,10,12],[2,3,5,6,8,9],
  [2,3,5,6,9,10],[2,3,5,6,10,11],[2,3,5,7,9,10],
  [2,3,5,7,10,12],[2,3,6,7,8,9],[2,3,6,7,8,11],
  [2,3,6,7,9,10],[2,3,6,7,10,11],[2,4,5,7,9,12],
  [2,4,5,9,10,12],[2,4,6,7,8,9],[2,4,6,7,8,11],
  [2,4,6,7,9,11],[2,4,7,9,11,12],[2,4,7,10,11,12],
  [2,5,7,9,10,12],[2,7,9,10,11,12],[3,4,5,7,9,12],
  [3,4,5,8,9,12],[3,4,5,8,11,12],[3,4,5,10,11,12],
  [3,4,7,8,9,12],[3,4,7,8,11,12],[3,4,7,10,11,12],
  [3,5,6,7,8,9],[3,5,6,7,8,10],[3,5,6,7,9,10],
  [3,5,7,8,9,12],[3,5,7,8,10,12],[3,6,7,8,10,12],
  [3,6,7,8,11,12],[3,6,7,10,11,12],[3,6,8,10,11,12],
  [4,6,7,8,9,11],[5,6,7,8,9,10],[5,6,8,9,10,12],
  [5,7,8,9,10,12],[6,7,8,9,10,12]]

manifold_5_12_1_1=[[1,2,3,4,5,6],[1,2,3,4,5,12],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,11],[1,2,3,4,11,12],[1,2,3,5,6,12],
  [1,2,3,6,7,12],[1,2,3,7,8,12],[1,2,3,8,9,11],
  [1,2,3,8,10,11],[1,2,3,8,10,12],[1,2,3,10,11,12],
  [1,2,4,5,6,11],[1,2,4,5,11,12],[1,2,4,6,7,8],
  [1,2,4,6,8,9],[1,2,4,6,9,11],[1,2,5,6,11,12],
  [1,2,6,7,8,9],[1,2,6,7,9,11],[1,2,6,7,11,12],
  [1,2,7,8,9,10],[1,2,7,8,10,12],[1,2,7,9,10,12],
  [1,2,7,9,11,12],[1,2,8,9,10,11],[1,2,9,10,11,12],
  [1,3,4,5,6,11],[1,3,4,5,10,11],[1,3,4,5,10,12],
  [1,3,4,6,7,8],[1,3,4,6,8,11],[1,3,4,8,9,11],
  [1,3,4,10,11,12],[1,3,5,6,7,8],[1,3,5,6,7,12],
  [1,3,5,6,8,10],[1,3,5,6,10,11],[1,3,5,7,8,12],
  [1,3,5,8,10,12],[1,3,6,8,10,11],[1,4,5,10,11,12],
  [1,4,6,8,9,11],[1,5,6,7,8,12],[1,5,6,8,10,12],
  [1,5,6,10,11,12],[1,6,7,8,9,12],[1,6,7,9,11,12],
  [1,6,8,9,11,12],[1,6,8,10,11,12],[1,7,8,9,10,12],
  [1,8,9,10,11,12],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,12],
  [2,3,4,9,10,12],[2,3,4,9,11,12],[2,3,5,6,7,12],
  [2,3,5,7,8,9],[2,3,5,7,9,10],[2,3,5,7,10,12],
  [2,3,7,8,9,10],[2,3,7,8,10,12],[2,3,8,9,10,11],
  [2,3,9,10,11,12],[2,4,5,6,7,12],[2,4,5,6,11,12],
  [2,4,5,7,8,9],[2,4,5,7,9,12],[2,4,5,9,10,12],
  [2,4,6,7,8,9],[2,4,6,7,9,11],[2,4,6,7,11,12],
  [2,4,7,9,11,12],[2,5,7,9,10,12],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,11],
  [3,4,6,8,9,10],[3,4,6,8,10,11],[3,4,8,9,10,11],
  [3,4,9,10,11,12],[3,5,6,8,9,10],[3,5,7,8,9,10],
  [3,5,7,8,10,12],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,7,10,11],[4,5,6,7,11,12],[4,5,7,9,10,11],
  [4,5,7,9,11,12],[4,5,9,10,11,12],[4,6,7,9,10,11],
  [4,6,8,9,10,11],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,12],[5,6,8,10,11,12],[5,7,8,10,11,12],
  [5,7,9,10,11,12],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [7,8,9,10,11,12]]

manifold_5_13_5_1=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,11],[1,2,3,4,11,12],
  [1,2,3,4,12,13],[1,2,3,5,6,13],[1,2,3,6,7,10],
  [1,2,3,6,10,13],[1,2,3,7,10,11],[1,2,3,10,11,13],
  [1,2,3,11,12,13],[1,2,4,5,6,7],[1,2,4,5,7,11],
  [1,2,4,5,8,11],[1,2,4,5,8,12],[1,2,4,5,12,13],
  [1,2,4,8,11,12],[1,2,5,6,7,11],[1,2,5,6,9,10],
  [1,2,5,6,9,13],[1,2,5,6,10,11],[1,2,5,8,11,12],
  [1,2,5,9,10,11],[1,2,5,9,11,12],[1,2,5,9,12,13],
  [1,2,6,7,10,11],[1,2,6,9,10,13],[1,2,9,10,11,12],
  [1,2,9,10,12,13],[1,2,10,11,12,13],[1,3,4,5,6,13],
  [1,3,4,6,7,10],[1,3,4,6,10,13],[1,3,4,7,10,13],
  [1,3,4,7,11,13],[1,3,4,11,12,13],[1,3,7,10,11,13],
  [1,4,5,6,7,10],[1,4,5,6,10,13],[1,4,5,7,8,10],
  [1,4,5,7,8,11],[1,4,5,8,9,10],[1,4,5,8,9,13],
  [1,4,5,8,12,13],[1,4,5,9,10,13],[1,4,7,8,10,11],
  [1,4,7,10,11,13],[1,4,8,9,10,13],[1,4,8,10,11,13],
  [1,4,8,11,12,13],[1,5,6,7,10,11],[1,5,6,9,10,13],
  [1,5,7,8,10,11],[1,5,8,9,10,11],[1,5,8,9,11,12],
  [1,5,8,9,12,13],[1,8,9,10,11,13],[1,8,9,11,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,12],[2,3,4,5,12,13],[2,3,4,7,8,11],
  [2,3,4,8,11,12],[2,3,5,6,7,8],[2,3,5,6,8,12],
  [2,3,5,6,9,12],[2,3,5,6,9,13],[2,3,5,9,12,13],
  [2,3,6,7,8,12],[2,3,6,7,10,11],[2,3,6,7,11,12],
  [2,3,6,9,12,13],[2,3,6,10,11,12],[2,3,6,10,12,13],
  [2,3,7,8,11,12],[2,3,10,11,12,13],[2,4,5,7,8,11],
  [2,5,6,7,8,11],[2,5,6,8,9,11],[2,5,6,8,9,12],
  [2,5,6,9,10,11],[2,5,8,9,11,12],[2,6,7,8,11,12],
  [2,6,8,9,11,12],[2,6,9,10,11,12],[2,6,9,10,12,13],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,13],
  [3,4,5,8,9,12],[3,4,5,9,12,13],[3,4,6,7,8,9],
  [3,4,6,7,9,13],[3,4,6,7,10,13],[3,4,7,8,9,13],
  [3,4,7,8,11,12],[3,4,7,8,12,13],[3,4,7,11,12,13],
  [3,4,8,9,12,13],[3,5,6,8,9,12],[3,6,7,8,9,12],
  [3,6,7,9,10,12],[3,6,7,9,10,13],[3,6,7,10,11,12],
  [3,6,9,10,12,13],[3,7,8,9,12,13],[3,7,9,10,12,13],
  [3,7,10,11,12,13],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,9,10,13],[4,5,7,8,9,10],[4,5,8,9,12,13],
  [4,6,7,9,10,13],[4,7,8,9,10,13],[4,7,8,10,11,13],
  [4,7,8,11,12,13],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,8,9,10,11],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,9,10,11,12],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,10,11,12,13],[8,9,10,11,12,13]]

manifold_5_13_5_2=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,10],[1,2,3,4,7,10],[1,2,3,4,7,11],
  [1,2,3,4,8,11],[1,2,3,4,8,12],[1,2,3,4,12,13],
  [1,2,3,5,6,9],[1,2,3,5,9,13],[1,2,3,6,9,13],
  [1,2,3,6,10,13],[1,2,3,7,10,13],[1,2,3,7,11,13],
  [1,2,3,8,11,12],[1,2,3,11,12,13],[1,2,4,5,6,11],
  [1,2,4,5,8,11],[1,2,4,5,8,13],[1,2,4,6,7,10],
  [1,2,4,6,7,11],[1,2,4,8,12,13],[1,2,5,6,9,10],
  [1,2,5,6,10,11],[1,2,5,8,11,12],[1,2,5,8,12,13],
  [1,2,5,9,10,12],[1,2,5,9,12,13],[1,2,5,10,11,12],
  [1,2,6,7,10,11],[1,2,6,9,10,12],[1,2,6,9,12,13],
  [1,2,6,10,12,13],[1,2,7,10,11,13],[1,2,10,11,12,13],
  [1,3,4,5,6,10],[1,3,4,5,10,13],[1,3,4,7,10,13],
  [1,3,4,7,11,12],[1,3,4,7,12,13],[1,3,4,8,11,12],
  [1,3,5,6,9,13],[1,3,5,6,10,13],[1,3,7,11,12,13],
  [1,4,5,6,7,10],[1,4,5,6,7,11],[1,4,5,7,8,9],
  [1,4,5,7,8,11],[1,4,5,7,9,10],[1,4,5,8,9,13],
  [1,4,5,9,10,13],[1,4,7,8,9,10],[1,4,7,8,10,11],
  [1,4,7,10,11,13],[1,4,7,11,12,13],[1,4,8,9,10,11],
  [1,4,8,9,11,13],[1,4,8,11,12,13],[1,4,9,10,11,13],
  [1,5,6,7,8,10],[1,5,6,7,8,11],[1,5,6,8,10,11],
  [1,5,6,9,10,13],[1,5,7,8,9,10],[1,5,8,9,10,11],
  [1,5,8,9,11,13],[1,5,8,11,12,13],[1,5,9,10,11,12],
  [1,5,9,11,12,13],[1,6,7,8,10,11],[1,6,9,10,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,11],
  [2,3,4,5,8,11],[2,3,4,5,8,12],[2,3,4,5,9,12],
  [2,3,4,5,9,13],[2,3,4,6,7,10],[2,3,4,9,12,13],
  [2,3,5,6,7,12],[2,3,5,6,9,12],[2,3,5,7,8,11],
  [2,3,5,7,8,12],[2,3,6,7,10,11],[2,3,6,7,11,12],
  [2,3,6,9,12,13],[2,3,6,10,11,13],[2,3,6,11,12,13],
  [2,3,7,8,11,12],[2,3,7,10,11,13],[2,4,5,6,7,11],
  [2,4,5,8,12,13],[2,4,5,9,12,13],[2,5,6,7,8,11],
  [2,5,6,7,8,12],[2,5,6,8,9,10],[2,5,6,8,9,12],
  [2,5,6,8,10,11],[2,5,8,9,10,11],[2,5,8,9,11,12],
  [2,5,9,10,11,12],[2,6,7,8,9,11],[2,6,7,8,9,12],
  [2,6,7,9,11,12],[2,6,8,9,10,11],[2,6,9,10,11,12],
  [2,6,10,11,12,13],[2,7,8,9,11,12],[3,4,5,6,7,8],
  [3,4,5,6,8,12],[3,4,5,6,9,12],[3,4,5,6,9,13],
  [3,4,5,6,10,13],[3,4,5,7,8,11],[3,4,6,7,8,13],
  [3,4,6,7,10,13],[3,4,6,8,9,12],[3,4,6,8,9,13],
  [3,4,7,8,11,12],[3,4,7,8,12,13],[3,4,8,9,12,13],
  [3,5,6,7,8,12],[3,6,7,8,9,12],[3,6,7,8,9,13],
  [3,6,7,9,10,11],[3,6,7,9,10,13],[3,6,7,9,11,12],
  [3,6,9,10,11,12],[3,6,9,10,12,13],[3,6,10,11,12,13],
  [3,7,8,9,10,12],[3,7,8,9,10,13],[3,7,8,10,12,13],
  [3,7,9,10,11,12],[3,7,10,11,12,13],[3,8,9,10,12,13],
  [4,5,6,7,8,9],[4,5,6,7,9,13],[4,5,6,7,10,13],
  [4,5,6,8,9,12],[4,5,7,9,10,13],[4,5,8,9,12,13],
  [4,6,7,8,9,13],[4,7,8,9,10,13],[4,7,8,10,11,12],
  [4,7,8,10,12,13],[4,7,10,11,12,13],[4,8,9,10,11,13],
  [4,8,10,11,12,13],[5,6,7,8,9,10],[5,6,7,9,10,13],
  [5,8,9,11,12,13],[6,7,8,9,10,11],[7,8,9,10,11,12],
  [8,9,10,11,12,13]]

manifold_5_13_3_1=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,11],[1,2,3,4,8,11],
  [1,2,3,4,8,12],[1,2,3,4,12,13],[1,2,3,5,6,13],
  [1,2,3,6,7,10],[1,2,3,6,10,13],[1,2,3,7,10,13],
  [1,2,3,7,11,13],[1,2,3,8,11,12],[1,2,3,11,12,13],
  [1,2,4,5,6,11],[1,2,4,5,8,11],[1,2,4,5,8,12],
  [1,2,4,5,12,13],[1,2,4,6,7,11],[1,2,5,6,9,10],
  [1,2,5,6,9,13],[1,2,5,6,10,11],[1,2,5,8,11,12],
  [1,2,5,9,10,11],[1,2,5,9,11,12],[1,2,5,9,12,13],
  [1,2,6,7,10,11],[1,2,6,9,10,12],[1,2,6,9,12,13],
  [1,2,6,10,12,13],[1,2,7,10,11,13],[1,2,9,10,11,12],
  [1,2,10,11,12,13],[1,3,4,5,6,10],[1,3,4,5,10,13],
  [1,3,4,6,7,10],[1,3,4,7,10,13],[1,3,4,7,11,13],
  [1,3,4,8,11,12],[1,3,4,11,12,13],[1,3,5,6,10,13],
  [1,4,5,6,7,10],[1,4,5,6,7,11],[1,4,5,7,8,9],
  [1,4,5,7,8,11],[1,4,5,7,9,10],[1,4,5,8,9,13],
  [1,4,5,8,12,13],[1,4,5,9,10,13],[1,4,7,8,9,10],
  [1,4,7,8,10,11],[1,4,7,10,11,13],[1,4,8,9,10,13],
  [1,4,8,10,11,13],[1,4,8,11,12,13],[1,5,6,7,10,11],
  [1,5,6,9,10,13],[1,5,7,8,9,10],[1,5,7,8,10,11],
  [1,5,8,9,10,11],[1,5,8,9,11,13],[1,5,8,11,12,13],
  [1,5,9,11,12,13],[1,6,9,10,12,13],[1,8,9,10,11,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,12],[2,3,4,5,9,12],[2,3,4,5,9,13],
  [2,3,4,7,8,11],[2,3,4,9,12,13],[2,3,5,6,7,12],
  [2,3,5,6,9,12],[2,3,5,6,9,13],[2,3,5,7,8,12],
  [2,3,6,7,10,11],[2,3,6,7,11,12],[2,3,6,9,12,13],
  [2,3,6,10,11,12],[2,3,6,10,12,13],[2,3,7,8,11,12],
  [2,3,7,10,11,13],[2,3,10,11,12,13],[2,4,5,6,7,11],
  [2,4,5,7,8,11],[2,4,5,9,12,13],[2,5,6,7,8,11],
  [2,5,6,7,8,12],[2,5,6,8,9,10],[2,5,6,8,9,12],
  [2,5,6,8,10,11],[2,5,8,9,10,11],[2,5,8,9,11,12],
  [2,6,7,8,11,12],[2,6,8,9,10,11],[2,6,8,9,11,12],
  [2,6,9,10,11,12],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,13],[3,4,5,6,10,13],[3,4,5,8,9,12],
  [3,4,6,7,8,13],[3,4,6,7,10,13],[3,4,6,8,9,13],
  [3,4,7,8,11,12],[3,4,7,8,12,13],[3,4,7,11,12,13],
  [3,4,8,9,12,13],[3,5,6,7,8,12],[3,5,6,8,9,12],
  [3,6,7,8,9,12],[3,6,7,8,9,13],[3,6,7,9,10,11],
  [3,6,7,9,10,13],[3,6,7,9,11,12],[3,6,9,10,11,12],
  [3,6,9,10,12,13],[3,7,8,9,12,13],[3,7,9,10,11,12],
  [3,7,9,10,12,13],[3,7,10,11,12,13],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,9,10,13],[4,5,8,9,12,13],
  [4,6,7,8,9,13],[4,6,7,9,10,13],[4,7,8,9,10,13],
  [4,7,8,10,11,12],[4,7,8,10,12,13],[4,7,10,11,12,13],
  [4,8,10,11,12,13],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,8,9,11,12,13],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[8,9,10,11,12,13]]

manifold_5_13_3_2=[[1,2,3,4,5,8],[1,2,3,4,5,9],
  [1,2,3,4,7,9],[1,2,3,4,7,13],[1,2,3,4,8,13],
  [1,2,3,5,6,9],[1,2,3,5,6,10],[1,2,3,5,8,10],
  [1,2,3,6,8,10],[1,2,3,6,8,13],[1,2,3,6,9,12],
  [1,2,3,6,12,13],[1,2,3,7,9,12],[1,2,3,7,12,13],
  [1,2,4,5,8,13],[1,2,4,5,9,13],[1,2,4,7,9,13],
  [1,2,5,6,9,12],[1,2,5,6,10,12],[1,2,5,7,9,12],
  [1,2,5,7,9,13],[1,2,5,7,12,13],[1,2,5,8,10,11],
  [1,2,5,8,11,13],[1,2,5,10,11,12],[1,2,5,11,12,13],
  [1,2,6,8,10,11],[1,2,6,8,11,13],[1,2,6,10,11,12],
  [1,2,6,11,12,13],[1,3,4,5,8,11],[1,3,4,5,9,11],
  [1,3,4,7,8,11],[1,3,4,7,8,12],[1,3,4,7,9,11],
  [1,3,4,7,12,13],[1,3,4,8,12,13],[1,3,5,6,9,10],
  [1,3,5,8,10,11],[1,3,5,9,10,11],[1,3,6,8,9,10],
  [1,3,6,8,9,12],[1,3,6,8,12,13],[1,3,7,8,9,11],
  [1,3,7,8,9,12],[1,3,8,9,10,11],[1,4,5,8,11,13],
  [1,4,5,9,11,13],[1,4,6,7,8,11],[1,4,6,7,8,12],
  [1,4,6,7,10,11],[1,4,6,7,10,12],[1,4,6,8,11,13],
  [1,4,6,8,12,13],[1,4,6,10,11,12],[1,4,6,11,12,13],
  [1,4,7,9,10,11],[1,4,7,9,10,13],[1,4,7,10,12,13],
  [1,4,9,10,11,13],[1,4,10,11,12,13],[1,5,6,7,9,10],
  [1,5,6,7,9,12],[1,5,6,7,10,12],[1,5,7,9,10,13],
  [1,5,7,10,12,13],[1,5,9,10,11,13],[1,5,10,11,12,13],
  [1,6,7,8,9,10],[1,6,7,8,9,12],[1,6,7,8,10,11],
  [1,7,8,9,10,11],[2,3,4,5,6,9],[2,3,4,5,6,10],
  [2,3,4,5,8,10],[2,3,4,6,7,10],[2,3,4,6,7,11],
  [2,3,4,6,9,11],[2,3,4,7,9,11],[2,3,4,7,10,13],
  [2,3,4,8,10,13],[2,3,6,7,10,13],[2,3,6,7,11,13],
  [2,3,6,8,10,13],[2,3,6,9,11,12],[2,3,6,11,12,13],
  [2,3,7,9,11,12],[2,3,7,11,12,13],[2,4,5,6,9,12],
  [2,4,5,6,10,12],[2,4,5,8,9,12],[2,4,5,8,9,13],
  [2,4,5,8,10,12],[2,4,6,7,10,11],[2,4,6,9,11,12],
  [2,4,6,10,11,12],[2,4,7,9,10,11],[2,4,7,9,10,13],
  [2,4,8,9,10,12],[2,4,8,9,10,13],[2,4,9,10,11,12],
  [2,5,7,8,9,12],[2,5,7,8,9,13],[2,5,7,8,11,12],
  [2,5,7,8,11,13],[2,5,7,11,12,13],[2,5,8,10,11,12],
  [2,6,7,8,10,11],[2,6,7,8,10,13],[2,6,7,8,11,13],
  [2,7,8,9,10,11],[2,7,8,9,10,13],[2,7,8,9,11,12],
  [2,8,9,10,11,12],[3,4,5,6,7,10],[3,4,5,6,7,11],
  [3,4,5,6,9,11],[3,4,5,7,8,11],[3,4,5,7,8,12],
  [3,4,5,7,10,12],[3,4,5,8,10,12],[3,4,7,10,12,13],
  [3,4,8,10,12,13],[3,5,6,7,10,13],[3,5,6,7,11,13],
  [3,5,6,9,10,13],[3,5,6,9,11,13],[3,5,7,8,11,12],
  [3,5,7,10,12,13],[3,5,7,11,12,13],[3,5,8,10,11,12],
  [3,5,9,10,11,13],[3,5,10,11,12,13],[3,6,8,9,10,13],
  [3,6,8,9,12,13],[3,6,9,11,12,13],[3,7,8,9,11,12],
  [3,8,9,10,11,12],[3,8,9,10,12,13],[3,9,10,11,12,13],
  [4,5,6,7,8,11],[4,5,6,7,8,12],[4,5,6,7,10,12],
  [4,5,6,8,9,12],[4,5,6,8,9,13],[4,5,6,8,11,13],
  [4,5,6,9,11,13],[4,6,8,9,12,13],[4,6,9,11,12,13],
  [4,8,9,10,12,13],[4,9,10,11,12,13],[5,6,7,8,9,12],
  [5,6,7,8,9,13],[5,6,7,8,11,13],[5,6,7,9,10,13],
  [6,7,8,9,10,13]]

manifold_5_13_2_1=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,10],[1,2,3,4,10,11],[1,2,3,4,11,12],
  [1,2,3,4,12,13],[1,2,3,5,6,13],[1,2,3,6,7,13],
  [1,2,3,7,8,13],[1,2,3,8,9,13],[1,2,3,9,10,13],
  [1,2,3,10,11,13],[1,2,3,11,12,13],[1,2,4,5,6,7],
  [1,2,4,5,7,8],[1,2,4,5,8,9],[1,2,4,5,9,10],
  [1,2,4,5,10,11],[1,2,4,5,11,12],[1,2,4,5,12,13],
  [1,2,5,6,7,8],[1,2,5,6,8,9],[1,2,5,6,9,10],
  [1,2,5,6,10,11],[1,2,5,6,11,12],[1,2,5,6,12,13],
  [1,2,6,7,8,9],[1,2,6,7,9,10],[1,2,6,7,10,11],
  [1,2,6,7,11,12],[1,2,6,7,12,13],[1,2,7,8,9,10],
  [1,2,7,8,10,11],[1,2,7,8,11,12],[1,2,7,8,12,13],
  [1,2,8,9,10,11],[1,2,8,9,11,12],[1,2,8,9,12,13],
  [1,2,9,10,11,12],[1,2,9,10,12,13],[1,2,10,11,12,13],
  [1,3,4,5,6,13],[1,3,4,6,7,13],[1,3,4,7,8,13],
  [1,3,4,8,9,13],[1,3,4,9,10,13],[1,3,4,10,11,13],
  [1,3,4,11,12,13],[1,4,5,6,7,13],[1,4,5,7,8,13],
  [1,4,5,8,9,13],[1,4,5,9,10,13],[1,4,5,10,11,13],
  [1,4,5,11,12,13],[1,5,6,7,8,13],[1,5,6,8,9,13],
  [1,5,6,9,10,13],[1,5,6,10,11,13],[1,5,6,11,12,13],
  [1,6,7,8,9,13],[1,6,7,9,10,13],[1,6,7,10,11,13],
  [1,6,7,11,12,13],[1,7,8,9,10,13],[1,7,8,10,11,13],
  [1,7,8,11,12,13],[1,8,9,10,11,13],[1,8,9,11,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,11],
  [2,3,4,5,11,12],[2,3,4,5,12,13],[2,3,5,6,7,8],
  [2,3,5,6,8,9],[2,3,5,6,9,10],[2,3,5,6,10,11],
  [2,3,5,6,11,12],[2,3,5,6,12,13],[2,3,6,7,8,9],
  [2,3,6,7,9,10],[2,3,6,7,10,11],[2,3,6,7,11,12],
  [2,3,6,7,12,13],[2,3,7,8,9,10],[2,3,7,8,10,11],
  [2,3,7,8,11,12],[2,3,7,8,12,13],[2,3,8,9,10,11],
  [2,3,8,9,11,12],[2,3,8,9,12,13],[2,3,9,10,11,12],
  [2,3,9,10,12,13],[2,3,10,11,12,13],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,11],
  [3,4,5,6,11,12],[3,4,5,6,12,13],[3,4,6,7,8,9],
  [3,4,6,7,9,10],[3,4,6,7,10,11],[3,4,6,7,11,12],
  [3,4,6,7,12,13],[3,4,7,8,9,10],[3,4,7,8,10,11],
  [3,4,7,8,11,12],[3,4,7,8,12,13],[3,4,8,9,10,11],
  [3,4,8,9,11,12],[3,4,8,9,12,13],[3,4,9,10,11,12],
  [3,4,9,10,12,13],[3,4,10,11,12,13],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,6,7,11,12],
  [4,5,6,7,12,13],[4,5,7,8,9,10],[4,5,7,8,10,11],
  [4,5,7,8,11,12],[4,5,7,8,12,13],[4,5,8,9,10,11],
  [4,5,8,9,11,12],[4,5,8,9,12,13],[4,5,9,10,11,12],
  [4,5,9,10,12,13],[4,5,10,11,12,13],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,8,11,12],[5,6,7,8,12,13],
  [5,6,8,9,10,11],[5,6,8,9,11,12],[5,6,8,9,12,13],
  [5,6,9,10,11,12],[5,6,9,10,12,13],[5,6,10,11,12,13],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[6,7,8,9,12,13],
  [6,7,9,10,11,12],[6,7,9,10,12,13],[6,7,10,11,12,13],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[7,8,10,11,12,13],
  [8,9,10,11,12,13]]

manifold_5_13_2_2=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,10],
  [1,2,3,4,10,11],[1,2,3,4,11,12],[1,2,3,4,12,13],
  [1,2,3,5,6,13],[1,2,3,6,7,13],[1,2,3,7,8,9],
  [1,2,3,7,9,13],[1,2,3,8,9,10],[1,2,3,9,10,13],
  [1,2,3,10,11,13],[1,2,3,11,12,13],[1,2,4,5,6,7],
  [1,2,4,5,7,8],[1,2,4,5,8,11],[1,2,4,5,11,12],
  [1,2,4,5,12,13],[1,2,4,8,10,11],[1,2,5,6,7,8],
  [1,2,5,6,8,12],[1,2,5,6,12,13],[1,2,5,8,11,12],
  [1,2,6,7,8,13],[1,2,6,8,12,13],[1,2,7,8,9,13],
  [1,2,8,9,10,11],[1,2,8,9,11,12],[1,2,8,9,12,13],
  [1,2,9,10,11,12],[1,2,9,10,12,13],[1,2,10,11,12,13],
  [1,3,4,5,6,13],[1,3,4,6,7,13],[1,3,4,7,8,10],
  [1,3,4,7,10,13],[1,3,4,10,11,13],[1,3,4,11,12,13],
  [1,3,7,8,9,10],[1,3,7,9,10,13],[1,4,5,6,7,13],
  [1,4,5,7,8,11],[1,4,5,7,11,13],[1,4,5,11,12,13],
  [1,4,7,8,10,11],[1,4,7,10,11,13],[1,5,6,7,8,12],
  [1,5,6,7,12,13],[1,5,7,8,11,12],[1,5,7,11,12,13],
  [1,6,7,8,12,13],[1,7,8,9,10,13],[1,7,8,10,11,13],
  [1,7,8,11,12,13],[1,8,9,10,11,13],[1,8,9,11,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,11],[2,3,4,5,11,12],
  [2,3,4,5,12,13],[2,3,4,8,9,10],[2,3,4,9,10,11],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,12],
  [2,3,5,6,12,13],[2,3,5,9,11,12],[2,3,6,7,8,9],
  [2,3,6,7,9,13],[2,3,6,9,12,13],[2,3,9,10,11,12],
  [2,3,9,10,12,13],[2,3,10,11,12,13],[2,4,5,8,9,11],
  [2,4,8,9,10,11],[2,5,6,8,9,12],[2,5,8,9,11,12],
  [2,6,7,8,9,13],[2,6,8,9,12,13],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,12],
  [3,4,5,6,12,13],[3,4,5,9,10,11],[3,4,5,10,11,12],
  [3,4,6,7,8,9],[3,4,6,7,9,10],[3,4,6,7,10,13],
  [3,4,6,10,12,13],[3,4,7,8,9,10],[3,4,10,11,12,13],
  [3,5,6,9,10,12],[3,5,9,10,11,12],[3,6,7,9,10,13],
  [3,6,9,10,12,13],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,7,10,11],[4,5,6,7,11,13],[4,5,6,10,11,12],
  [4,5,6,11,12,13],[4,5,7,8,9,10],[4,5,7,8,10,11],
  [4,5,8,9,10,11],[4,6,7,10,11,13],[4,6,10,11,12,13],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,6,7,8,11,12],
  [5,6,7,11,12,13],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,6,9,10,11,12],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,8,9,12,13],[6,7,9,10,11,12],[6,7,9,10,12,13],
  [6,7,10,11,12,13],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,10,11,12,13],[8,9,10,11,12,13]]

manifold_5_13_2_3=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,9],[1,2,3,4,9,11],
  [1,2,3,4,11,12],[1,2,3,4,12,13],[1,2,3,5,6,13],
  [1,2,3,6,7,8],[1,2,3,6,8,13],[1,2,3,7,8,9],
  [1,2,3,8,9,10],[1,2,3,8,10,13],[1,2,3,9,10,11],
  [1,2,3,10,11,13],[1,2,3,11,12,13],[1,2,4,5,6,7],
  [1,2,4,5,7,12],[1,2,4,5,12,13],[1,2,4,7,9,12],
  [1,2,4,9,11,12],[1,2,5,6,7,13],[1,2,5,7,12,13],
  [1,2,6,7,8,13],[1,2,7,8,9,13],[1,2,7,9,12,13],
  [1,2,8,9,10,13],[1,2,9,10,11,12],[1,2,9,10,12,13],
  [1,2,10,11,12,13],[1,3,4,5,6,13],[1,3,4,6,7,9],
  [1,3,4,6,9,11],[1,3,4,6,11,13],[1,3,4,11,12,13],
  [1,3,6,7,8,9],[1,3,6,8,9,11],[1,3,6,8,11,13],
  [1,3,8,9,10,11],[1,3,8,10,11,13],[1,4,5,6,7,12],
  [1,4,5,6,12,13],[1,4,6,7,9,12],[1,4,6,9,11,12],
  [1,4,6,11,12,13],[1,5,6,7,12,13],[1,6,7,8,9,12],
  [1,6,7,8,12,13],[1,6,8,9,11,12],[1,6,8,11,12,13],
  [1,7,8,9,12,13],[1,8,9,10,11,13],[1,8,9,11,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,10],[2,3,4,5,10,12],[2,3,4,5,12,13],
  [2,3,4,7,8,9],[2,3,4,8,9,10],[2,3,4,9,10,11],
  [2,3,4,10,11,12],[2,3,5,6,7,8],[2,3,5,6,8,13],
  [2,3,5,8,10,13],[2,3,5,10,12,13],[2,3,10,11,12,13],
  [2,4,5,7,8,10],[2,4,5,7,10,12],[2,4,7,8,9,10],
  [2,4,7,9,10,12],[2,4,9,10,11,12],[2,5,6,7,8,13],
  [2,5,7,8,10,13],[2,5,7,10,12,13],[2,7,8,9,10,13],
  [2,7,9,10,12,13],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,11],[3,4,5,6,11,13],[3,4,5,8,9,10],
  [3,4,5,9,10,11],[3,4,5,10,11,12],[3,4,5,11,12,13],
  [3,4,6,7,8,9],[3,5,6,8,9,11],[3,5,6,8,11,13],
  [3,5,8,9,10,11],[3,5,8,10,11,13],[3,5,10,11,12,13],
  [4,5,6,7,8,9],[4,5,6,7,9,10],[4,5,6,7,10,12],
  [4,5,6,9,10,11],[4,5,6,10,11,12],[4,5,6,11,12,13],
  [4,5,7,8,9,10],[4,6,7,9,10,12],[4,6,9,10,11,12],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,6,7,8,11,13],
  [5,6,7,10,11,12],[5,6,7,11,12,13],[5,6,8,9,10,11],
  [5,7,8,10,11,13],[5,7,10,11,12,13],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,8,11,12,13],[6,7,9,10,11,12],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[7,8,10,11,12,13],
  [8,9,10,11,12,13]]

manifold_5_13_2_4=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,11],[1,2,3,4,11,12],
  [1,2,3,4,12,13],[1,2,3,5,6,13],[1,2,3,6,7,11],
  [1,2,3,6,10,11],[1,2,3,6,10,13],[1,2,3,10,11,13],
  [1,2,3,11,12,13],[1,2,4,5,6,7],[1,2,4,5,7,10],
  [1,2,4,5,9,10],[1,2,4,5,9,12],[1,2,4,5,12,13],
  [1,2,4,7,9,10],[1,2,4,7,9,12],[1,2,4,7,11,12],
  [1,2,5,6,7,10],[1,2,5,6,10,13],[1,2,5,9,10,13],
  [1,2,5,9,12,13],[1,2,6,7,9,10],[1,2,6,7,9,12],
  [1,2,6,7,11,12],[1,2,6,9,10,11],[1,2,6,9,11,12],
  [1,2,9,10,11,12],[1,2,9,10,12,13],[1,2,10,11,12,13],
  [1,3,4,5,6,13],[1,3,4,6,7,11],[1,3,4,6,9,11],
  [1,3,4,6,9,13],[1,3,4,8,9,11],[1,3,4,8,9,13],
  [1,3,4,8,11,13],[1,3,4,11,12,13],[1,3,6,8,9,11],
  [1,3,6,8,9,13],[1,3,6,8,11,13],[1,3,6,10,11,13],
  [1,4,5,6,7,10],[1,4,5,6,9,10],[1,4,5,6,9,13],
  [1,4,5,9,12,13],[1,4,6,7,9,10],[1,4,6,7,9,12],
  [1,4,6,7,11,12],[1,4,6,9,11,12],[1,4,8,9,11,12],
  [1,4,8,9,12,13],[1,4,8,11,12,13],[1,5,6,8,9,11],
  [1,5,6,8,9,13],[1,5,6,8,11,13],[1,5,6,9,10,11],
  [1,5,6,10,11,13],[1,5,8,9,10,11],[1,5,8,9,10,13],
  [1,5,8,10,11,13],[1,8,9,10,11,13],[1,8,9,11,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,12],[2,3,4,5,12,13],[2,3,4,7,8,12],
  [2,3,4,7,11,12],[2,3,5,6,7,8],[2,3,5,6,8,11],
  [2,3,5,6,10,11],[2,3,5,6,10,13],[2,3,5,8,10,11],
  [2,3,5,8,10,13],[2,3,5,8,12,13],[2,3,6,7,8,11],
  [2,3,7,8,10,11],[2,3,7,8,10,13],[2,3,7,8,12,13],
  [2,3,7,10,11,12],[2,3,7,10,12,13],[2,3,10,11,12,13],
  [2,4,5,7,8,12],[2,4,5,7,10,12],[2,4,5,9,10,12],
  [2,4,7,9,10,12],[2,5,6,7,8,11],[2,5,6,7,10,11],
  [2,5,7,8,10,11],[2,5,7,8,10,13],[2,5,7,8,12,13],
  [2,5,7,10,12,13],[2,5,9,10,12,13],[2,6,7,9,10,12],
  [2,6,7,10,11,12],[2,6,9,10,11,12],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,13],[3,4,5,8,9,13],
  [3,4,5,8,12,13],[3,4,6,7,8,9],[3,4,6,7,9,12],
  [3,4,6,7,11,12],[3,4,6,9,11,12],[3,4,7,8,9,12],
  [3,4,8,9,11,12],[3,4,8,11,12,13],[3,5,6,8,9,13],
  [3,5,6,8,11,13],[3,5,6,10,11,13],[3,5,8,10,11,13],
  [3,6,7,8,9,12],[3,6,7,8,11,12],[3,6,8,9,11,12],
  [3,7,8,10,11,13],[3,7,8,11,12,13],[3,7,10,11,12,13],
  [4,5,6,7,8,9],[4,5,6,7,9,10],[4,5,7,8,9,10],
  [4,5,7,8,10,13],[4,5,7,8,12,13],[4,5,7,10,12,13],
  [4,5,8,9,10,13],[4,5,9,10,12,13],[4,7,8,9,10,13],
  [4,7,8,9,12,13],[4,7,9,10,12,13],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,8,9,10,11],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,9,10,11,12],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[7,8,10,11,12,13],[8,9,10,11,12,13]
]

manifold_5_13_2_5=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,9],[1,2,3,4,9,12],[1,2,3,4,12,13],
  [1,2,3,5,6,7],[1,2,3,5,7,8],[1,2,3,5,8,13],
  [1,2,3,6,7,8],[1,2,3,6,8,9],[1,2,3,8,9,11],
  [1,2,3,8,11,13],[1,2,3,9,10,11],[1,2,3,9,10,12],
  [1,2,3,10,11,12],[1,2,3,11,12,13],[1,2,4,5,6,13],
  [1,2,4,6,7,8],[1,2,4,6,7,13],[1,2,4,6,8,9],
  [1,2,4,7,8,9],[1,2,4,7,9,12],[1,2,4,7,12,13],
  [1,2,5,6,7,13],[1,2,5,7,8,13],[1,2,7,8,9,12],
  [1,2,7,8,10,12],[1,2,7,8,10,13],[1,2,7,10,12,13],
  [1,2,8,9,10,12],[1,2,8,9,10,13],[1,2,8,9,11,13],
  [1,2,9,10,11,13],[1,2,10,11,12,13],[1,3,4,5,6,11],
  [1,3,4,5,11,12],[1,3,4,5,12,13],[1,3,4,6,9,11],
  [1,3,4,9,10,11],[1,3,4,9,10,12],[1,3,4,10,11,12],
  [1,3,5,6,7,13],[1,3,5,6,11,12],[1,3,5,6,12,13],
  [1,3,5,7,8,13],[1,3,6,7,8,13],[1,3,6,8,9,11],
  [1,3,6,8,11,13],[1,3,6,11,12,13],[1,4,5,6,11,12],
  [1,4,5,6,12,13],[1,4,6,7,8,9],[1,4,6,7,9,12],
  [1,4,6,7,12,13],[1,4,6,9,11,12],[1,4,9,10,11,12],
  [1,6,7,8,9,11],[1,6,7,8,11,13],[1,6,7,9,11,13],
  [1,6,7,9,12,13],[1,6,9,11,12,13],[1,7,8,9,11,13],
  [1,7,8,9,12,13],[1,7,8,10,12,13],[1,8,9,10,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,10],
  [2,3,4,5,10,13],[2,3,4,6,7,8],[2,3,4,6,8,9],
  [2,3,4,7,8,9],[2,3,4,7,9,10],[2,3,4,9,10,12],
  [2,3,4,10,11,12],[2,3,4,10,11,13],[2,3,4,11,12,13],
  [2,3,5,7,8,9],[2,3,5,7,9,10],[2,3,5,8,9,10],
  [2,3,5,8,10,13],[2,3,8,9,10,13],[2,3,8,9,11,13],
  [2,3,9,10,11,13],[2,4,5,6,7,12],[2,4,5,6,12,13],
  [2,4,5,7,10,12],[2,4,5,10,11,12],[2,4,5,10,11,13],
  [2,4,5,11,12,13],[2,4,6,7,12,13],[2,4,7,9,10,12],
  [2,5,6,7,12,13],[2,5,7,8,9,10],[2,5,7,8,10,13],
  [2,5,7,10,12,13],[2,5,10,11,12,13],[2,7,8,9,10,12],
  [3,4,5,6,7,8],[3,4,5,6,8,11],[3,4,5,7,8,9],
  [3,4,5,7,9,10],[3,4,5,8,9,10],[3,4,5,8,10,11],
  [3,4,5,10,11,13],[3,4,5,11,12,13],[3,4,6,8,9,10],
  [3,4,6,8,10,11],[3,4,6,9,10,11],[3,5,6,7,8,13],
  [3,5,6,8,11,13],[3,5,6,11,12,13],[3,5,8,10,11,13],
  [3,6,8,9,10,11],[3,8,9,10,11,13],[4,5,6,7,8,9],
  [4,5,6,7,9,12],[4,5,6,8,9,10],[4,5,6,8,10,11],
  [4,5,6,9,10,11],[4,5,6,9,11,12],[4,5,7,9,10,11],
  [4,5,7,9,11,12],[4,5,7,10,11,12],[4,7,9,10,11,12],
  [5,6,7,8,9,10],[5,6,7,8,10,13],[5,6,7,9,10,11],
  [5,6,7,9,11,12],[5,6,7,10,11,12],[5,6,7,10,12,13],
  [5,6,8,10,11,12],[5,6,8,10,12,13],[5,6,8,11,12,13],
  [5,8,10,11,12,13],[6,7,8,9,10,11],[6,7,8,10,11,12],
  [6,7,8,10,12,13],[6,7,8,11,12,13],[6,7,9,11,12,13],
  [7,8,9,10,11,12],[7,8,9,11,12,13],[8,9,10,11,12,13]]

manifold_5_13_2_6=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,9],[1,2,3,4,9,12],[1,2,3,4,12,13],
  [1,2,3,5,6,7],[1,2,3,5,7,8],[1,2,3,5,8,13],
  [1,2,3,6,7,8],[1,2,3,6,8,11],[1,2,3,6,9,11],
  [1,2,3,8,11,13],[1,2,3,9,10,11],[1,2,3,9,10,12],
  [1,2,3,10,11,12],[1,2,3,11,12,13],[1,2,4,5,6,13],
  [1,2,4,6,7,8],[1,2,4,6,7,13],[1,2,4,6,8,9],
  [1,2,4,7,8,12],[1,2,4,7,12,13],[1,2,4,8,9,12],
  [1,2,5,6,7,13],[1,2,5,7,8,10],[1,2,5,7,10,13],
  [1,2,5,8,10,13],[1,2,6,8,9,11],[1,2,7,8,10,12],
  [1,2,7,10,12,13],[1,2,8,9,10,12],[1,2,8,9,10,13],
  [1,2,8,9,11,13],[1,2,9,10,11,13],[1,2,10,11,12,13],
  [1,3,4,5,6,11],[1,3,4,5,11,12],[1,3,4,5,12,13],
  [1,3,4,6,9,10],[1,3,4,6,10,11],[1,3,4,9,10,12],
  [1,3,4,10,11,12],[1,3,5,6,7,13],[1,3,5,6,11,12],
  [1,3,5,6,12,13],[1,3,5,7,8,13],[1,3,6,7,8,11],
  [1,3,6,7,11,13],[1,3,6,9,10,11],[1,3,6,11,12,13],
  [1,3,7,8,11,13],[1,4,5,6,9,11],[1,4,5,6,9,12],
  [1,4,5,6,12,13],[1,4,5,9,11,12],[1,4,6,7,8,9],
  [1,4,6,7,9,13],[1,4,6,9,10,11],[1,4,6,9,12,13],
  [1,4,7,8,9,12],[1,4,7,9,12,13],[1,4,9,10,11,12],
  [1,5,6,9,11,12],[1,5,7,8,10,13],[1,6,7,8,9,11],
  [1,6,7,9,11,13],[1,6,9,11,12,13],[1,7,8,9,11,13],
  [1,7,8,9,12,13],[1,7,8,10,12,13],[1,8,9,10,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,10],
  [2,3,4,5,10,13],[2,3,4,6,7,8],[2,3,4,6,8,9],
  [2,3,4,7,8,9],[2,3,4,7,9,12],[2,3,4,7,10,12],
  [2,3,4,10,11,12],[2,3,4,10,11,13],[2,3,4,11,12,13],
  [2,3,5,7,8,9],[2,3,5,7,9,10],[2,3,5,8,9,13],
  [2,3,5,9,10,13],[2,3,6,8,9,11],[2,3,7,9,10,12],
  [2,3,8,9,11,13],[2,3,9,10,11,13],[2,4,5,6,7,12],
  [2,4,5,6,12,13],[2,4,5,7,10,11],[2,4,5,7,11,12],
  [2,4,5,10,11,13],[2,4,5,11,12,13],[2,4,6,7,12,13],
  [2,4,7,8,9,12],[2,4,7,10,11,12],[2,5,6,7,10,12],
  [2,5,6,7,10,13],[2,5,6,10,12,13],[2,5,7,8,9,10],
  [2,5,7,10,11,12],[2,5,8,9,10,13],[2,5,10,11,12,13],
  [2,6,7,10,12,13],[2,7,8,9,10,12],[3,4,5,6,7,8],
  [3,4,5,6,8,11],[3,4,5,7,8,9],[3,4,5,7,9,10],
  [3,4,5,8,9,10],[3,4,5,8,10,13],[3,4,5,8,11,13],
  [3,4,5,11,12,13],[3,4,6,8,9,10],[3,4,6,8,10,11],
  [3,4,7,9,10,12],[3,4,8,10,11,13],[3,5,6,7,8,13],
  [3,5,6,8,11,12],[3,5,6,8,12,13],[3,5,8,9,10,13],
  [3,5,8,11,12,13],[3,6,7,8,11,13],[3,6,8,9,10,11],
  [3,6,8,11,12,13],[3,8,9,10,11,13],[4,5,6,7,8,9],
  [4,5,6,7,9,12],[4,5,6,8,9,10],[4,5,6,8,10,11],
  [4,5,6,9,10,11],[4,5,7,9,10,11],[4,5,7,9,11,12],
  [4,5,8,10,11,13],[4,6,7,9,12,13],[4,7,9,10,11,12],
  [5,6,7,8,9,10],[5,6,7,8,10,13],[5,6,7,9,10,11],
  [5,6,7,9,11,12],[5,6,7,10,11,12],[5,6,8,10,11,12],
  [5,6,8,10,12,13],[5,8,10,11,12,13],[6,7,8,9,10,11],
  [6,7,8,10,11,12],[6,7,8,10,12,13],[6,7,8,11,12,13],
  [6,7,9,11,12,13],[7,8,9,10,11,12],[7,8,9,11,12,13],
  [8,9,10,11,12,13]]

manifold_5_13_2_7=[[1,2,3,4,5,7],[1,2,3,4,5,12],
  [1,2,3,4,6,7],[1,2,3,4,6,13],[1,2,3,4,11,12],
  [1,2,3,4,11,13],[1,2,3,5,6,7],[1,2,3,5,6,13],
  [1,2,3,5,12,13],[1,2,3,10,11,12],[1,2,3,10,11,13],
  [1,2,3,10,12,13],[1,2,4,5,6,7],[1,2,4,5,6,13],
  [1,2,4,5,12,13],[1,2,4,11,12,13],[1,2,9,10,11,12],
  [1,2,9,10,11,13],[1,2,9,10,12,13],[1,2,9,11,12,13],
  [1,3,4,5,6,7],[1,3,4,5,6,13],[1,3,4,5,12,13],
  [1,3,4,11,12,13],[1,3,10,11,12,13],[1,8,9,10,11,12],
  [1,8,9,10,11,13],[1,8,9,10,12,13],[1,8,9,11,12,13],
  [1,8,10,11,12,13],[2,3,4,5,6,8],[2,3,4,5,6,13],
  [2,3,4,5,7,8],[2,3,4,5,12,13],[2,3,4,6,7,8],
  [2,3,4,11,12,13],[2,3,5,6,7,8],[2,3,10,11,12,13],
  [2,4,5,6,7,8],[2,9,10,11,12,13],[3,4,5,6,7,9],
  [3,4,5,6,8,9],[3,4,5,7,8,9],[3,4,6,7,8,9],
  [3,5,6,7,8,9],[4,5,6,7,8,10],[4,5,6,7,9,10],
  [4,5,6,8,9,10],[4,5,7,8,9,10],[4,6,7,8,9,10],
  [5,6,7,8,9,11],[5,6,7,8,10,11],[5,6,7,9,10,11],
  [5,6,8,9,10,11],[5,7,8,9,10,11],[6,7,8,9,10,12],
  [6,7,8,9,11,12],[6,7,8,10,11,12],[6,7,9,10,11,12],
  [6,8,9,10,11,12],[7,8,9,10,11,13],[7,8,9,10,12,13],
  [7,8,9,11,12,13],[7,8,10,11,12,13],[7,9,10,11,12,13]
]

manifold_5_13_1_1=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,11],[1,2,3,4,11,12],[1,2,3,4,12,13],
  [1,2,3,5,6,13],[1,2,3,6,7,13],[1,2,3,7,8,13],
  [1,2,3,8,9,11],[1,2,3,8,10,11],[1,2,3,8,10,13],
  [1,2,3,10,11,13],[1,2,3,11,12,13],[1,2,4,5,6,7],
  [1,2,4,5,7,12],[1,2,4,5,12,13],[1,2,4,7,8,9],
  [1,2,4,7,9,12],[1,2,4,9,11,12],[1,2,5,6,7,12],
  [1,2,5,6,12,13],[1,2,6,7,12,13],[1,2,7,8,9,10],
  [1,2,7,8,10,13],[1,2,7,9,10,13],[1,2,7,9,12,13],
  [1,2,8,9,10,11],[1,2,9,10,11,12],[1,2,9,10,12,13],
  [1,2,10,11,12,13],[1,3,4,5,6,13],[1,3,4,6,7,9],
  [1,3,4,6,9,11],[1,3,4,6,11,13],[1,3,4,7,8,9],
  [1,3,4,11,12,13],[1,3,6,7,8,9],[1,3,6,7,8,13],
  [1,3,6,8,9,11],[1,3,6,8,11,13],[1,3,8,10,11,13],
  [1,4,5,6,7,12],[1,4,5,6,11,12],[1,4,5,6,11,13],
  [1,4,5,11,12,13],[1,4,6,7,9,12],[1,4,6,9,11,12],
  [1,5,6,11,12,13],[1,6,7,8,9,13],[1,6,7,9,12,13],
  [1,6,8,9,11,12],[1,6,8,9,12,13],[1,6,8,11,12,13],
  [1,7,8,9,10,13],[1,8,9,10,11,13],[1,8,9,11,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,12],
  [2,3,4,5,12,13],[2,3,4,9,10,12],[2,3,4,9,11,12],
  [2,3,5,6,7,8],[2,3,5,6,8,13],[2,3,5,8,9,10],
  [2,3,5,8,10,13],[2,3,5,10,12,13],[2,3,6,7,8,13],
  [2,3,8,9,10,11],[2,3,9,10,11,12],[2,3,10,11,12,13],
  [2,4,5,7,8,10],[2,4,5,7,10,12],[2,4,5,8,9,10],
  [2,4,7,8,9,10],[2,4,7,9,10,12],[2,5,6,7,8,13],
  [2,5,6,7,12,13],[2,5,7,8,10,13],[2,5,7,10,12,13],
  [2,7,9,10,12,13],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,10],[3,4,5,6,10,11],[3,4,5,6,11,13],
  [3,4,5,10,11,13],[3,4,5,10,12,13],[3,4,6,7,8,9],
  [3,4,6,9,10,11],[3,4,9,10,11,12],[3,4,10,11,12,13],
  [3,5,6,8,9,11],[3,5,6,8,11,13],[3,5,6,9,10,11],
  [3,5,8,9,10,11],[3,5,8,10,11,13],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,6,7,11,12],
  [4,5,7,8,9,10],[4,5,7,10,11,12],[4,5,10,11,12,13],
  [4,6,7,9,10,12],[4,6,7,10,11,12],[4,6,9,10,11,12],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,6,7,8,11,12],
  [5,6,7,8,12,13],[5,6,8,9,10,11],[5,6,8,11,12,13],
  [5,7,8,10,11,13],[5,7,8,11,12,13],[5,7,10,11,12,13],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[6,7,8,9,12,13],
  [6,7,9,10,11,12],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,10,11,12,13],[8,9,10,11,12,13]]

manifold_5_13_1_2=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,12],[1,2,3,4,12,13],[1,2,3,5,6,13],
  [1,2,3,6,7,13],[1,2,3,7,8,13],[1,2,3,8,9,11],
  [1,2,3,8,11,13],[1,2,3,9,11,12],[1,2,3,11,12,13],
  [1,2,4,5,6,12],[1,2,4,5,12,13],[1,2,4,6,7,12],
  [1,2,4,7,8,9],[1,2,4,7,9,12],[1,2,5,6,12,13],
  [1,2,6,7,12,13],[1,2,7,8,9,10],[1,2,7,8,10,13],
  [1,2,7,9,10,12],[1,2,7,10,12,13],[1,2,8,9,10,11],
  [1,2,8,10,11,13],[1,2,9,10,11,12],[1,2,10,11,12,13],
  [1,3,4,5,6,11],[1,3,4,5,11,13],[1,3,4,6,7,8],
  [1,3,4,6,8,9],[1,3,4,6,9,11],[1,3,4,9,11,12],
  [1,3,4,11,12,13],[1,3,5,6,11,13],[1,3,6,7,8,13],
  [1,3,6,8,9,11],[1,3,6,8,11,13],[1,4,5,6,11,12],
  [1,4,5,11,12,13],[1,4,6,7,8,9],[1,4,6,7,9,12],
  [1,4,6,9,11,12],[1,5,6,11,12,13],[1,6,7,8,9,13],
  [1,6,7,9,12,13],[1,6,8,9,11,13],[1,6,9,11,12,13],
  [1,7,8,9,10,13],[1,7,9,10,12,13],[1,8,9,10,11,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,13],
  [2,3,4,9,10,12],[2,3,4,10,12,13],[2,3,5,6,7,13],
  [2,3,5,7,8,13],[2,3,5,8,9,10],[2,3,5,8,10,13],
  [2,3,8,9,10,11],[2,3,8,10,11,13],[2,3,9,10,11,12],
  [2,3,10,11,12,13],[2,4,5,6,7,12],[2,4,5,7,8,9],
  [2,4,5,7,9,10],[2,4,5,7,10,12],[2,4,5,10,12,13],
  [2,4,7,9,10,12],[2,5,6,7,12,13],[2,5,7,8,9,10],
  [2,5,7,8,10,13],[2,5,7,10,12,13],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,11],
  [3,4,5,10,11,13],[3,4,6,9,10,11],[3,4,9,10,11,12],
  [3,4,10,11,12,13],[3,5,6,7,8,13],[3,5,6,8,9,10],
  [3,5,6,8,10,11],[3,5,6,8,11,13],[3,5,8,10,11,13],
  [3,6,8,9,10,11],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,7,10,11],[4,5,6,7,11,12],[4,5,7,10,11,12],
  [4,5,10,11,12,13],[4,6,7,9,10,11],[4,6,7,9,11,12],
  [4,7,9,10,11,12],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,12],[5,6,7,8,12,13],[5,6,8,11,12,13],
  [5,7,8,10,11,12],[5,7,8,10,12,13],[5,8,10,11,12,13],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[6,7,8,9,12,13],
  [6,8,9,11,12,13],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [8,9,10,11,12,13]]

manifold_5_13_1_3=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,10],
  [1,2,3,4,10,12],[1,2,3,4,12,13],[1,2,3,5,6,13],
  [1,2,3,6,7,13],[1,2,3,7,8,9],[1,2,3,7,9,13],
  [1,2,3,8,9,10],[1,2,3,9,10,12],[1,2,3,9,11,12],
  [1,2,3,9,11,13],[1,2,3,11,12,13],[1,2,4,5,6,12],
  [1,2,4,5,12,13],[1,2,4,6,7,8],[1,2,4,6,8,12],
  [1,2,4,8,10,12],[1,2,5,6,12,13],[1,2,6,7,8,13],
  [1,2,6,8,12,13],[1,2,7,8,9,13],[1,2,8,9,10,11],
  [1,2,8,9,11,13],[1,2,8,10,11,13],[1,2,8,10,12,13],
  [1,2,9,10,11,12],[1,2,10,11,12,13],[1,3,4,5,6,12],
  [1,3,4,5,11,12],[1,3,4,5,11,13],[1,3,4,6,7,8],
  [1,3,4,6,8,10],[1,3,4,6,10,12],[1,3,4,11,12,13],
  [1,3,5,6,7,8],[1,3,5,6,7,13],[1,3,5,6,8,12],
  [1,3,5,7,8,10],[1,3,5,7,9,11],[1,3,5,7,9,12],
  [1,3,5,7,10,12],[1,3,5,7,11,13],[1,3,5,8,10,12],
  [1,3,5,9,11,12],[1,3,6,8,10,12],[1,3,7,8,9,10],
  [1,3,7,9,10,12],[1,3,7,9,11,13],[1,4,5,11,12,13],
  [1,4,6,8,10,12],[1,5,6,7,8,12],[1,5,6,7,12,13],
  [1,5,7,8,10,12],[1,5,7,9,11,12],[1,5,7,11,12,13],
  [1,6,7,8,12,13],[1,7,8,9,10,13],[1,7,8,10,12,13],
  [1,7,9,10,12,13],[1,7,9,11,12,13],[1,8,9,10,11,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,11],[2,3,4,5,11,13],
  [2,3,4,8,9,10],[2,3,4,9,10,11],[2,3,4,10,11,13],
  [2,3,4,10,12,13],[2,3,5,6,7,13],[2,3,5,7,8,9],
  [2,3,5,7,9,13],[2,3,5,9,11,13],[2,3,9,10,11,12],
  [2,3,10,11,12,13],[2,4,5,6,7,13],[2,4,5,6,12,13],
  [2,4,5,7,8,9],[2,4,5,7,9,11],[2,4,5,7,11,13],
  [2,4,6,7,8,9],[2,4,6,7,9,13],[2,4,6,8,9,11],
  [2,4,6,8,10,12],[2,4,6,8,10,13],[2,4,6,8,11,13],
  [2,4,6,9,11,13],[2,4,6,10,12,13],[2,4,7,9,11,13],
  [2,4,8,9,10,11],[2,4,8,10,11,13],[2,5,7,9,11,13],
  [2,6,7,8,9,13],[2,6,8,9,11,13],[2,6,8,10,12,13],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,10],
  [3,4,5,6,10,12],[3,4,5,9,10,11],[3,4,5,10,11,12],
  [3,4,6,8,9,10],[3,4,10,11,12,13],[3,5,6,8,9,10],
  [3,5,6,8,10,12],[3,5,7,8,9,10],[3,5,7,9,10,12],
  [3,5,7,9,11,13],[3,5,9,10,11,12],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,6,7,11,13],
  [4,5,6,10,11,12],[4,5,6,11,12,13],[4,5,7,9,10,11],
  [4,6,7,9,10,11],[4,6,7,9,11,13],[4,6,8,9,10,11],
  [4,6,8,10,11,13],[4,6,10,11,12,13],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,8,11,12],[5,6,7,11,12,13],
  [5,6,8,10,11,12],[5,7,8,10,11,12],[5,7,9,10,11,12],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[6,7,8,9,12,13],
  [6,7,9,11,12,13],[6,8,9,11,12,13],[6,8,10,11,12,13],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[8,9,10,11,12,13]]

manifold_5_13_1_4=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,11],
  [1,2,3,4,11,12],[1,2,3,4,12,13],[1,2,3,5,6,13],
  [1,2,3,6,7,13],[1,2,3,7,8,10],[1,2,3,7,10,13],
  [1,2,3,8,10,11],[1,2,3,10,11,13],[1,2,3,11,12,13],
  [1,2,4,5,6,7],[1,2,4,5,7,12],[1,2,4,5,12,13],
  [1,2,4,7,8,10],[1,2,4,7,9,10],[1,2,4,7,9,12],
  [1,2,4,8,9,10],[1,2,4,8,9,11],[1,2,4,9,11,12],
  [1,2,5,6,7,12],[1,2,5,6,12,13],[1,2,6,7,9,12],
  [1,2,6,7,9,13],[1,2,6,9,12,13],[1,2,7,9,10,13],
  [1,2,8,9,10,11],[1,2,9,10,11,12],[1,2,9,10,12,13],
  [1,2,10,11,12,13],[1,3,4,5,6,13],[1,3,4,6,7,9],
  [1,3,4,6,9,11],[1,3,4,6,11,13],[1,3,4,7,8,9],
  [1,3,4,8,9,11],[1,3,4,11,12,13],[1,3,6,7,9,13],
  [1,3,6,8,9,11],[1,3,6,8,9,13],[1,3,6,8,11,13],
  [1,3,7,8,9,13],[1,3,7,8,10,13],[1,3,8,10,11,13],
  [1,4,5,6,7,11],[1,4,5,6,11,13],[1,4,5,7,11,12],
  [1,4,5,11,12,13],[1,4,6,7,9,12],[1,4,6,7,11,12],
  [1,4,6,9,11,12],[1,4,7,8,9,10],[1,5,6,7,11,12],
  [1,5,6,8,11,12],[1,5,6,8,11,13],[1,5,6,8,12,13],
  [1,5,8,11,12,13],[1,6,8,9,11,12],[1,6,8,9,12,13],
  [1,7,8,9,10,13],[1,8,9,10,11,13],[1,8,9,11,12,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,12],[2,3,4,5,12,13],
  [2,3,4,8,9,11],[2,3,4,9,11,12],[2,3,5,6,7,8],
  [2,3,5,6,8,13],[2,3,5,8,9,11],[2,3,5,8,10,11],
  [2,3,5,8,10,13],[2,3,5,9,10,11],[2,3,5,9,10,12],
  [2,3,5,10,12,13],[2,3,6,7,8,13],[2,3,7,8,10,13],
  [2,3,9,10,11,12],[2,3,10,11,12,13],[2,4,5,7,8,10],
  [2,4,5,7,10,12],[2,4,5,8,9,10],[2,4,5,9,10,12],
  [2,4,7,9,10,12],[2,5,6,7,8,12],[2,5,6,8,12,13],
  [2,5,7,8,10,13],[2,5,7,8,12,13],[2,5,7,10,12,13],
  [2,5,8,9,10,11],[2,6,7,8,12,13],[2,6,7,9,12,13],
  [2,7,9,10,12,13],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,10],[3,4,5,6,10,13],[3,4,5,9,10,12],
  [3,4,5,10,12,13],[3,4,6,7,8,9],[3,4,6,9,10,12],
  [3,4,6,9,11,12],[3,4,6,10,11,12],[3,4,6,10,11,13],
  [3,4,10,11,12,13],[3,5,6,8,9,11],[3,5,6,8,11,13],
  [3,5,6,9,10,11],[3,5,6,10,11,13],[3,5,8,10,11,13],
  [3,6,7,8,9,13],[3,6,9,10,11,12],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,6,10,11,13],
  [4,5,7,8,9,10],[4,5,7,10,11,13],[4,5,7,10,12,13],
  [4,5,7,11,12,13],[4,6,7,9,10,12],[4,6,7,10,11,12],
  [4,7,10,11,12,13],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,12],[5,6,8,9,10,11],[5,7,8,10,11,13],
  [5,7,8,11,12,13],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,8,9,12,13],[6,7,9,10,11,12],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[7,8,10,11,12,13],[8,9,10,11,12,13]
]

manifold_5_13_1_5=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,9],[1,2,3,4,9,12],
  [1,2,3,4,12,13],[1,2,3,5,6,13],[1,2,3,6,7,8],
  [1,2,3,6,8,13],[1,2,3,7,8,9],[1,2,3,8,9,10],
  [1,2,3,8,10,11],[1,2,3,8,11,13],[1,2,3,9,10,11],
  [1,2,3,9,11,12],[1,2,3,11,12,13],[1,2,4,5,6,12],
  [1,2,4,5,12,13],[1,2,4,6,7,12],[1,2,4,7,9,12],
  [1,2,5,6,7,12],[1,2,5,6,7,13],[1,2,5,7,12,13],
  [1,2,6,7,8,13],[1,2,7,8,9,13],[1,2,7,9,10,12],
  [1,2,7,9,10,13],[1,2,7,10,12,13],[1,2,8,9,10,13],
  [1,2,8,10,11,13],[1,2,9,10,11,12],[1,2,10,11,12,13],
  [1,3,4,5,6,11],[1,3,4,5,11,13],[1,3,4,6,7,8],
  [1,3,4,6,8,9],[1,3,4,6,9,11],[1,3,4,7,8,9],
  [1,3,4,9,11,12],[1,3,4,11,12,13],[1,3,5,6,11,13],
  [1,3,6,8,9,11],[1,3,6,8,11,13],[1,3,8,9,10,11],
  [1,4,5,6,11,13],[1,4,5,6,12,13],[1,4,6,7,8,9],
  [1,4,6,7,9,12],[1,4,6,9,11,12],[1,4,6,11,12,13],
  [1,5,6,7,12,13],[1,6,7,8,9,12],[1,6,7,8,12,13],
  [1,6,8,9,11,13],[1,6,8,9,12,13],[1,6,9,11,12,13],
  [1,7,8,9,12,13],[1,7,9,10,12,13],[1,8,9,10,11,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,10],[2,3,4,5,10,13],[2,3,4,7,8,9],
  [2,3,4,8,9,10],[2,3,4,9,10,11],[2,3,4,9,11,12],
  [2,3,4,10,11,12],[2,3,4,10,12,13],[2,3,5,6,7,13],
  [2,3,5,7,8,13],[2,3,5,8,10,13],[2,3,6,7,8,13],
  [2,3,8,10,11,13],[2,3,10,11,12,13],[2,4,5,6,7,12],
  [2,4,5,7,8,9],[2,4,5,7,9,10],[2,4,5,7,10,12],
  [2,4,5,8,9,10],[2,4,5,10,12,13],[2,4,7,9,10,12],
  [2,4,9,10,11,12],[2,5,7,8,9,10],[2,5,7,8,10,13],
  [2,5,7,10,12,13],[2,7,8,9,10,13],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,11],[3,4,5,8,9,10],
  [3,4,5,9,10,11],[3,4,5,10,11,12],[3,4,5,10,12,13],
  [3,4,5,11,12,13],[3,5,6,7,8,13],[3,5,6,8,9,10],
  [3,5,6,8,10,11],[3,5,6,8,11,13],[3,5,6,9,10,11],
  [3,5,8,10,11,13],[3,5,10,11,12,13],[3,6,8,9,10,11],
  [4,5,6,7,8,9],[4,5,6,7,9,10],[4,5,6,7,10,12],
  [4,5,6,9,10,11],[4,5,6,10,11,12],[4,5,6,11,12,13],
  [4,6,7,9,10,11],[4,6,7,9,11,12],[4,6,7,10,11,12],
  [4,7,9,10,11,12],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,13],[5,6,7,10,11,12],[5,6,7,11,12,13],
  [5,7,8,10,11,12],[5,7,8,10,12,13],[5,7,8,11,12,13],
  [5,8,10,11,12,13],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,8,11,12,13],[6,8,9,11,12,13],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[8,9,10,11,12,13]]

manifold_5_13_1_6=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,12],[1,2,3,4,12,13],
  [1,2,3,5,6,13],[1,2,3,6,7,8],[1,2,3,6,8,11],
  [1,2,3,6,11,13],[1,2,3,7,8,9],[1,2,3,7,9,12],
  [1,2,3,8,9,10],[1,2,3,8,10,11],[1,2,3,9,10,11],
  [1,2,3,9,11,12],[1,2,3,11,12,13],[1,2,4,5,6,12],
  [1,2,4,5,12,13],[1,2,4,6,7,12],[1,2,5,6,7,12],
  [1,2,5,6,7,13],[1,2,5,7,10,12],[1,2,5,7,10,13],
  [1,2,5,10,12,13],[1,2,6,7,8,13],[1,2,6,8,11,13],
  [1,2,7,8,9,13],[1,2,7,9,10,12],[1,2,7,9,10,13],
  [1,2,8,9,10,13],[1,2,8,10,11,13],[1,2,9,10,11,12],
  [1,2,10,11,12,13],[1,3,4,5,6,9],[1,3,4,5,9,11],
  [1,3,4,5,11,13],[1,3,4,6,7,8],[1,3,4,6,8,9],
  [1,3,4,7,8,9],[1,3,4,7,9,12],[1,3,4,9,11,12],
  [1,3,4,11,12,13],[1,3,5,6,9,11],[1,3,5,6,11,13],
  [1,3,6,8,9,10],[1,3,6,8,10,11],[1,3,6,9,10,11],
  [1,4,5,6,9,11],[1,4,5,6,11,13],[1,4,5,6,12,13],
  [1,4,6,7,8,12],[1,4,6,8,9,12],[1,4,6,9,11,13],
  [1,4,6,9,12,13],[1,4,7,8,9,12],[1,4,9,11,12,13],
  [1,5,6,7,12,13],[1,5,7,10,12,13],[1,6,7,8,12,13],
  [1,6,8,9,10,11],[1,6,8,9,11,13],[1,6,8,9,12,13],
  [1,7,8,9,12,13],[1,7,9,10,12,13],[1,8,9,10,11,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,13],[2,3,4,7,8,9],[2,3,4,7,9,12],
  [2,3,4,8,9,10],[2,3,4,8,10,13],[2,3,4,9,10,11],
  [2,3,4,9,11,12],[2,3,4,10,11,12],[2,3,4,10,12,13],
  [2,3,5,6,7,13],[2,3,5,7,8,13],[2,3,6,7,8,13],
  [2,3,6,8,11,13],[2,3,8,10,11,13],[2,3,10,11,12,13],
  [2,4,5,6,7,10],[2,4,5,6,10,12],[2,4,5,7,8,9],
  [2,4,5,7,9,10],[2,4,5,8,9,10],[2,4,5,8,10,13],
  [2,4,5,10,12,13],[2,4,6,7,10,12],[2,4,7,9,10,11],
  [2,4,7,9,11,12],[2,4,7,10,11,12],[2,5,6,7,10,12],
  [2,5,7,8,9,13],[2,5,7,9,10,13],[2,5,8,9,10,13],
  [2,7,9,10,11,12],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,8,9,10],[3,4,5,8,10,13],[3,4,5,9,10,11],
  [3,4,5,10,11,12],[3,4,5,10,12,13],[3,4,5,11,12,13],
  [3,5,6,7,8,11],[3,5,6,7,11,13],[3,5,6,8,9,10],
  [3,5,6,8,10,11],[3,5,6,9,10,11],[3,5,7,8,11,13],
  [3,5,8,10,11,12],[3,5,8,10,12,13],[3,5,8,11,12,13],
  [3,6,7,8,11,13],[3,8,10,11,12,13],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,9,10,11],[4,5,6,10,11,12],
  [4,5,6,11,12,13],[4,6,7,8,9,12],[4,6,7,9,10,11],
  [4,6,7,9,11,12],[4,6,7,10,11,12],[4,6,9,11,12,13],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,6,7,10,11,12],
  [5,6,7,11,12,13],[5,7,8,9,10,13],[5,7,8,10,11,12],
  [5,7,8,10,12,13],[5,7,8,11,12,13],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,8,11,12,13],[6,8,9,11,12,13],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[8,9,10,11,12,13]]

manifold_5_13_1_7=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,7,12],[1,2,3,4,12,13],
  [1,2,3,5,6,13],[1,2,3,6,7,11],[1,2,3,6,11,13],
  [1,2,3,7,11,12],[1,2,3,11,12,13],[1,2,4,5,6,10],
  [1,2,4,5,9,10],[1,2,4,5,9,12],[1,2,4,5,12,13],
  [1,2,4,6,7,10],[1,2,4,7,9,10],[1,2,4,7,9,12],
  [1,2,5,6,10,13],[1,2,5,9,10,12],[1,2,5,10,12,13],
  [1,2,6,7,9,10],[1,2,6,7,9,12],[1,2,6,7,11,12],
  [1,2,6,9,10,11],[1,2,6,9,11,12],[1,2,6,10,11,13],
  [1,2,9,10,11,12],[1,2,10,11,12,13],[1,3,4,5,6,9],
  [1,3,4,5,9,13],[1,3,4,6,7,11],[1,3,4,6,9,11],
  [1,3,4,7,11,12],[1,3,4,8,9,11],[1,3,4,8,9,13],
  [1,3,4,8,11,13],[1,3,4,11,12,13],[1,3,5,6,9,13],
  [1,3,6,8,9,11],[1,3,6,8,9,13],[1,3,6,8,11,13],
  [1,4,5,6,9,10],[1,4,5,9,12,13],[1,4,6,7,9,10],
  [1,4,6,7,9,12],[1,4,6,7,11,12],[1,4,6,9,11,12],
  [1,4,8,9,11,13],[1,4,9,11,12,13],[1,5,6,8,9,10],
  [1,5,6,8,9,13],[1,5,6,8,10,11],[1,5,6,8,11,13],
  [1,5,6,10,11,13],[1,5,8,9,10,13],[1,5,8,10,11,13],
  [1,5,9,10,12,13],[1,6,8,9,10,11],[1,8,9,10,11,13],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,13],[2,3,4,7,8,12],[2,3,4,8,12,13],
  [2,3,5,6,7,11],[2,3,5,6,10,11],[2,3,5,6,10,13],
  [2,3,5,7,8,11],[2,3,5,8,10,11],[2,3,5,8,10,13],
  [2,3,6,10,11,13],[2,3,7,8,10,11],[2,3,7,8,10,13],
  [2,3,7,8,12,13],[2,3,7,10,11,12],[2,3,7,10,12,13],
  [2,3,10,11,12,13],[2,4,5,6,7,10],[2,4,5,7,8,12],
  [2,4,5,7,10,12],[2,4,5,8,12,13],[2,4,5,9,10,12],
  [2,4,7,9,10,12],[2,5,6,7,10,11],[2,5,7,8,10,11],
  [2,5,7,8,10,13],[2,5,7,8,12,13],[2,5,7,10,12,13],
  [2,6,7,9,10,11],[2,6,7,9,11,12],[2,7,9,10,11,12],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,8,9,13],
  [3,4,6,7,8,12],[3,4,6,7,11,12],[3,4,6,8,9,12],
  [3,4,6,9,11,12],[3,4,8,9,11,12],[3,4,8,11,12,13],
  [3,5,6,7,8,11],[3,5,6,8,9,13],[3,5,6,8,11,13],
  [3,5,6,10,11,13],[3,5,8,10,11,13],[3,6,7,8,11,12],
  [3,6,8,9,11,12],[3,7,8,10,11,12],[3,7,8,10,12,13],
  [3,8,10,11,12,13],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,7,8,9,13],[4,5,7,8,12,13],[4,5,7,9,10,13],
  [4,5,7,10,12,13],[4,5,9,10,12,13],[4,6,7,8,9,12],
  [4,7,8,9,12,13],[4,7,9,10,12,13],[4,8,9,11,12,13],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,7,8,9,10,13],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[8,9,10,11,12,13]]

manifold_5_13_1_8=[[1,2,3,4,5,6],[1,2,3,4,5,13],
  [1,2,3,4,6,12],[1,2,3,4,12,13],[1,2,3,5,6,8],
  [1,2,3,5,8,10],[1,2,3,5,10,11],[1,2,3,5,11,13],
  [1,2,3,6,7,8],[1,2,3,6,7,9],[1,2,3,6,9,11],
  [1,2,3,6,11,12],[1,2,3,7,8,9],[1,2,3,8,9,10],
  [1,2,3,9,10,11],[1,2,3,11,12,13],[1,2,4,5,6,9],
  [1,2,4,5,7,9],[1,2,4,5,7,13],[1,2,4,6,9,11],
  [1,2,4,6,11,12],[1,2,4,7,9,13],[1,2,4,9,10,11],
  [1,2,4,9,10,13],[1,2,4,10,11,12],[1,2,4,10,12,13],
  [1,2,5,6,7,9],[1,2,5,6,7,13],[1,2,5,6,8,13],
  [1,2,5,8,10,13],[1,2,5,10,11,13],[1,2,6,7,8,13],
  [1,2,7,8,9,13],[1,2,8,9,10,13],[1,2,10,11,12,13],
  [1,3,4,5,6,8],[1,3,4,5,8,13],[1,3,4,6,8,13],
  [1,3,4,6,12,13],[1,3,5,8,10,13],[1,3,5,10,11,13],
  [1,3,6,7,8,11],[1,3,6,7,9,11],[1,3,6,8,11,12],
  [1,3,6,8,12,13],[1,3,7,8,9,11],[1,3,8,9,10,13],
  [1,3,8,9,11,12],[1,3,8,9,12,13],[1,3,9,10,11,13],
  [1,3,9,11,12,13],[1,4,5,6,8,13],[1,4,5,6,9,12],
  [1,4,5,6,12,13],[1,4,5,7,9,12],[1,4,5,7,12,13],
  [1,4,6,9,10,11],[1,4,6,9,10,12],[1,4,6,10,11,12],
  [1,4,7,9,12,13],[1,4,9,10,12,13],[1,5,6,7,9,12],
  [1,5,6,7,12,13],[1,6,7,8,11,12],[1,6,7,8,12,13],
  [1,6,7,9,10,11],[1,6,7,9,10,12],[1,6,7,10,11,12],
  [1,7,8,9,11,12],[1,7,8,9,12,13],[1,7,9,10,11,12],
  [1,9,10,11,12,13],[2,3,4,5,6,7],[2,3,4,5,7,13],
  [2,3,4,6,7,9],[2,3,4,6,9,11],[2,3,4,6,11,12],
  [2,3,4,7,8,9],[2,3,4,7,8,10],[2,3,4,7,10,12],
  [2,3,4,7,12,13],[2,3,4,8,9,10],[2,3,4,9,10,11],
  [2,3,4,10,11,12],[2,3,5,6,7,10],[2,3,5,6,8,10],
  [2,3,5,7,10,12],[2,3,5,7,12,13],[2,3,5,10,11,12],
  [2,3,5,11,12,13],[2,3,6,7,8,10],[2,4,5,6,7,9],
  [2,4,7,8,9,12],[2,4,7,8,10,12],[2,4,7,9,12,13],
  [2,4,8,9,10,12],[2,4,9,10,12,13],[2,5,6,7,10,13],
  [2,5,6,8,10,13],[2,5,7,10,11,12],[2,5,7,10,11,13],
  [2,5,7,11,12,13],[2,6,7,8,10,13],[2,7,8,9,12,13],
  [2,7,8,10,11,12],[2,7,8,10,11,13],[2,7,8,11,12,13],
  [2,8,9,10,12,13],[2,8,10,11,12,13],[3,4,5,6,7,8],
  [3,4,5,7,8,10],[3,4,5,7,10,12],[3,4,5,7,12,13],
  [3,4,5,8,9,10],[3,4,5,8,9,11],[3,4,5,8,11,13],
  [3,4,5,9,10,11],[3,4,5,10,11,12],[3,4,5,11,12,13],
  [3,4,6,7,8,11],[3,4,6,7,9,11],[3,4,6,8,11,13],
  [3,4,6,11,12,13],[3,4,7,8,9,11],[3,5,6,7,8,10],
  [3,5,8,9,10,13],[3,5,8,9,11,13],[3,5,9,10,11,13],
  [3,6,8,11,12,13],[3,8,9,11,12,13],[4,5,6,7,8,9],
  [4,5,6,8,9,11],[4,5,6,8,11,13],[4,5,6,9,10,11],
  [4,5,6,9,10,12],[4,5,6,10,11,12],[4,5,6,11,12,13],
  [4,5,7,8,9,12],[4,5,7,8,10,12],[4,5,8,9,10,12],
  [4,6,7,8,9,11],[5,6,7,8,9,10],[5,6,7,9,10,12],
  [5,6,7,10,11,12],[5,6,7,10,11,13],[5,6,7,11,12,13],
  [5,6,8,9,10,13],[5,6,8,9,11,13],[5,6,9,10,11,13],
  [5,7,8,9,10,12],[6,7,8,9,10,11],[6,7,8,10,11,13],
  [6,7,8,11,12,13],[6,8,9,10,11,13],[7,8,9,10,11,12],
  [8,9,10,11,12,13]]

manifold_5_14_49_1=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,12],[1,2,3,4,12,13],
  [1,2,3,4,13,14],[1,2,3,5,6,14],[1,2,3,6,7,12],
  [1,2,3,6,11,12],[1,2,3,6,11,14],[1,2,3,11,12,14],
  [1,2,3,12,13,14],[1,2,4,5,6,7],[1,2,4,5,7,10],
  [1,2,4,5,10,13],[1,2,4,5,13,14],[1,2,4,7,10,13],
  [1,2,4,7,12,13],[1,2,5,6,7,10],[1,2,5,6,10,11],
  [1,2,5,6,11,14],[1,2,5,10,11,14],[1,2,5,10,13,14],
  [1,2,6,7,10,11],[1,2,6,7,11,12],[1,2,7,10,11,12],
  [1,2,7,10,12,13],[1,2,10,11,12,13],[1,2,10,11,13,14],
  [1,2,11,12,13,14],[1,3,4,5,6,14],[1,3,4,6,7,12],
  [1,3,4,6,9,12],[1,3,4,6,9,14],[1,3,4,9,12,14],
  [1,3,4,12,13,14],[1,3,6,9,12,14],[1,3,6,11,12,14],
  [1,4,5,6,7,10],[1,4,5,6,9,10],[1,4,5,6,9,14],
  [1,4,5,9,10,14],[1,4,5,10,13,14],[1,4,6,7,9,10],
  [1,4,6,7,9,12],[1,4,7,9,10,12],[1,4,7,10,12,13],
  [1,4,9,10,12,13],[1,4,9,10,13,14],[1,4,9,12,13,14],
  [1,5,6,9,10,14],[1,5,6,10,11,14],[1,6,7,9,10,12],
  [1,6,7,10,11,12],[1,6,9,10,11,12],[1,6,9,10,11,14],
  [1,6,9,11,12,14],[1,9,10,11,12,14],[1,9,10,12,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,13],[2,3,4,5,13,14],[2,3,4,7,8,13],
  [2,3,4,7,12,13],[2,3,5,6,7,8],[2,3,5,6,8,11],
  [2,3,5,6,11,14],[2,3,5,8,11,14],[2,3,5,8,13,14],
  [2,3,6,7,8,11],[2,3,6,7,11,12],[2,3,7,8,11,12],
  [2,3,7,8,12,13],[2,3,8,11,12,13],[2,3,8,11,13,14],
  [2,3,11,12,13,14],[2,4,5,7,8,13],[2,4,5,7,10,13],
  [2,5,6,7,8,11],[2,5,6,7,10,11],[2,5,7,8,10,11],
  [2,5,7,8,10,13],[2,5,8,10,11,13],[2,5,8,11,13,14],
  [2,5,10,11,13,14],[2,7,8,10,11,13],[2,7,8,11,12,13],
  [2,7,10,11,12,13],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,14],[3,4,5,8,9,14],[3,4,5,8,13,14],
  [3,4,6,7,8,9],[3,4,6,7,9,12],[3,4,7,8,9,12],
  [3,4,7,8,12,13],[3,4,8,9,12,13],[3,4,8,9,13,14],
  [3,4,9,12,13,14],[3,5,6,8,9,14],[3,5,6,8,11,14],
  [3,6,7,8,9,12],[3,6,7,8,11,12],[3,6,8,9,11,12],
  [3,6,8,9,11,14],[3,6,9,11,12,14],[3,8,9,11,12,14],
  [3,8,9,12,13,14],[3,8,11,12,13,14],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,7,8,9,10],[4,5,7,8,10,13],
  [4,5,8,9,10,13],[4,5,8,9,13,14],[4,5,9,10,13,14],
  [4,7,8,9,10,13],[4,7,8,9,12,13],[4,7,9,10,12,13],
  [5,6,7,8,9,10],[5,6,7,8,10,11],[5,6,8,9,10,11],
  [5,6,8,9,11,14],[5,6,9,10,11,14],[5,8,9,10,11,14],
  [5,8,9,10,13,14],[5,8,10,11,13,14],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,9,10,11,12],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[7,8,10,11,12,13],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,11,12,13,14],
  [9,10,11,12,13,14]]

manifold_5_14_19_1=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,12],[1,2,3,4,12,13],[1,2,3,4,13,14],
  [1,2,3,5,6,11],[1,2,3,5,11,14],[1,2,3,6,11,12],
  [1,2,3,11,12,14],[1,2,3,12,13,14],[1,2,4,5,6,7],
  [1,2,4,5,7,10],[1,2,4,5,10,14],[1,2,4,6,7,12],
  [1,2,4,7,10,13],[1,2,4,7,12,13],[1,2,4,10,13,14],
  [1,2,5,6,7,10],[1,2,5,6,10,11],[1,2,5,10,11,14],
  [1,2,6,7,10,11],[1,2,6,7,11,12],[1,2,7,10,11,13],
  [1,2,7,11,12,13],[1,2,10,11,13,14],[1,2,11,12,13,14],
  [1,3,4,5,6,14],[1,3,4,6,9,12],[1,3,4,6,9,14],
  [1,3,4,9,12,13],[1,3,4,9,13,14],[1,3,5,6,11,14],
  [1,3,6,9,12,14],[1,3,6,11,12,14],[1,3,9,12,13,14],
  [1,4,5,6,7,9],[1,4,5,6,9,14],[1,4,5,7,9,10],
  [1,4,5,9,10,14],[1,4,6,7,9,12],[1,4,7,9,10,12],
  [1,4,7,10,12,13],[1,4,9,10,12,13],[1,4,9,10,13,14],
  [1,5,6,7,9,10],[1,5,6,9,10,14],[1,5,6,10,11,14],
  [1,6,7,9,10,12],[1,6,7,10,11,12],[1,6,9,10,12,14],
  [1,6,10,11,12,14],[1,7,10,11,12,13],
  [1,9,10,12,13,14],[1,10,11,12,13,14],[2,3,4,5,6,7],
  [2,3,4,5,7,13],[2,3,4,5,13,14],[2,3,4,6,7,12],
  [2,3,4,7,12,13],[2,3,5,6,7,8],[2,3,5,6,8,11],
  [2,3,5,7,8,13],[2,3,5,8,11,14],[2,3,5,8,13,14],
  [2,3,6,7,8,11],[2,3,6,7,11,12],[2,3,7,8,11,12],
  [2,3,7,8,12,13],[2,3,8,11,12,14],[2,3,8,12,13,14],
  [2,4,5,7,10,13],[2,4,5,10,13,14],[2,5,6,7,8,10],
  [2,5,6,8,10,11],[2,5,7,8,10,13],[2,5,8,10,11,13],
  [2,5,8,11,13,14],[2,5,10,11,13,14],[2,6,7,8,10,11],
  [2,7,8,10,11,13],[2,7,8,11,12,13],[2,8,11,12,13,14],
  [3,4,5,6,7,8],[3,4,5,6,8,14],[3,4,5,7,8,13],
  [3,4,5,8,13,14],[3,4,6,7,8,9],[3,4,6,7,9,12],
  [3,4,6,8,9,14],[3,4,7,8,9,12],[3,4,7,8,12,13],
  [3,4,8,9,12,13],[3,4,8,9,13,14],[3,5,6,8,11,14],
  [3,6,7,8,9,11],[3,6,7,9,11,12],[3,6,8,9,11,14],
  [3,6,9,11,12,14],[3,7,8,9,11,12],[3,8,9,11,12,14],
  [3,8,9,12,13,14],[4,5,6,7,8,9],[4,5,6,8,9,14],
  [4,5,7,8,9,10],[4,5,7,8,10,13],[4,5,8,9,10,13],
  [4,5,8,9,13,14],[4,5,9,10,13,14],[4,7,8,9,10,12],
  [4,7,8,10,12,13],[4,8,9,10,12,13],[5,6,7,8,9,10],
  [5,6,8,9,10,11],[5,6,8,9,11,14],[5,6,9,10,11,14],
  [5,8,9,10,11,13],[5,8,9,11,13,14],[5,9,10,11,13,14],
  [6,7,8,9,10,11],[6,7,9,10,11,12],[6,9,10,11,12,14],
  [7,8,9,10,11,12],[7,8,10,11,12,13],[8,9,10,11,12,13],
  [8,9,11,12,13,14],[9,10,11,12,13,14]]

manifold_5_14_16_1=[[1,2,3,4,5,12],[1,2,3,4,5,14],
  [1,2,3,4,6,11],[1,2,3,4,6,13],[1,2,3,4,9,10],
  [1,2,3,4,9,12],[1,2,3,4,10,11],[1,2,3,4,13,14],
  [1,2,3,5,12,14],[1,2,3,6,7,10],[1,2,3,6,7,14],
  [1,2,3,6,10,11],[1,2,3,6,13,14],[1,2,3,7,10,12],
  [1,2,3,7,12,14],[1,2,3,9,10,12],[1,2,4,5,8,9],
  [1,2,4,5,8,13],[1,2,4,5,9,12],[1,2,4,5,13,14],
  [1,2,4,6,11,13],[1,2,4,8,9,11],[1,2,4,8,11,13],
  [1,2,4,9,10,11],[1,2,5,6,7,12],[1,2,5,6,7,14],
  [1,2,5,6,8,11],[1,2,5,6,8,13],[1,2,5,6,11,12],
  [1,2,5,6,13,14],[1,2,5,7,12,14],[1,2,5,8,9,12],
  [1,2,5,8,11,12],[1,2,6,7,10,11],[1,2,6,7,11,12],
  [1,2,6,8,11,13],[1,2,7,10,11,12],[1,2,8,9,11,12],
  [1,2,9,10,11,12],[1,3,4,5,12,14],[1,3,4,6,7,10],
  [1,3,4,6,7,14],[1,3,4,6,10,11],[1,3,4,6,13,14],
  [1,3,4,7,10,12],[1,3,4,7,12,14],[1,3,4,9,10,12],
  [1,4,5,8,9,12],[1,4,5,8,12,13],[1,4,5,12,13,14],
  [1,4,6,7,9,10],[1,4,6,7,9,12],[1,4,6,7,12,13],
  [1,4,6,7,13,14],[1,4,6,8,9,11],[1,4,6,8,9,13],
  [1,4,6,8,11,13],[1,4,6,9,10,11],[1,4,6,9,12,13],
  [1,4,7,9,10,12],[1,4,7,12,13,14],[1,4,8,9,12,13],
  [1,5,6,7,12,14],[1,5,6,8,11,12],[1,5,6,8,12,13],
  [1,5,6,12,13,14],[1,6,7,9,10,12],[1,6,7,10,11,12],
  [1,6,7,12,13,14],[1,6,8,9,11,12],[1,6,8,9,12,13],
  [1,6,9,10,11,12],[2,3,4,5,8,9],[2,3,4,5,8,13],
  [2,3,4,5,9,12],[2,3,4,5,13,14],[2,3,4,6,11,13],
  [2,3,4,8,9,11],[2,3,4,8,11,13],[2,3,4,9,10,11],
  [2,3,5,7,10,12],[2,3,5,7,10,14],[2,3,5,7,12,14],
  [2,3,5,8,9,10],[2,3,5,8,10,11],[2,3,5,8,11,14],
  [2,3,5,8,13,14],[2,3,5,9,10,12],[2,3,5,10,11,14],
  [2,3,6,7,10,11],[2,3,6,7,11,14],[2,3,6,11,13,14],
  [2,3,7,10,11,14],[2,3,8,9,10,11],[2,3,8,11,13,14],
  [2,5,6,7,11,12],[2,5,6,7,11,14],[2,5,6,8,11,13],
  [2,5,6,11,13,14],[2,5,7,10,11,12],[2,5,7,10,11,14],
  [2,5,8,9,10,11],[2,5,8,9,11,12],[2,5,8,11,13,14],
  [2,5,9,10,11,12],[3,4,5,8,9,14],[3,4,5,8,13,14],
  [3,4,5,9,12,14],[3,4,6,7,10,13],[3,4,6,7,13,14],
  [3,4,6,10,11,13],[3,4,7,9,10,12],[3,4,7,9,10,14],
  [3,4,7,9,12,14],[3,4,7,10,13,14],[3,4,8,9,10,11],
  [3,4,8,9,10,13],[3,4,8,9,13,14],[3,4,8,10,11,13],
  [3,4,9,10,13,14],[3,5,7,10,12,14],[3,5,8,9,10,14],
  [3,5,8,10,11,14],[3,5,9,10,12,14],[3,6,7,10,11,14],
  [3,6,7,10,13,14],[3,6,10,11,13,14],[3,7,9,10,12,14],
  [3,8,9,10,13,14],[3,8,10,11,13,14],[4,5,8,9,12,13],
  [4,5,8,9,13,14],[4,5,9,12,13,14],[4,6,7,9,10,13],
  [4,6,7,9,12,13],[4,6,8,9,11,13],[4,6,9,10,11,13],
  [4,7,9,10,13,14],[4,7,9,12,13,14],[4,8,9,10,11,13],
  [5,6,7,8,11,12],[5,6,7,8,11,14],[5,6,7,8,12,13],
  [5,6,7,8,13,14],[5,6,7,12,13,14],[5,6,8,11,13,14],
  [5,7,8,9,10,12],[5,7,8,9,10,14],[5,7,8,9,12,14],
  [5,7,8,10,11,12],[5,7,8,10,11,14],[5,7,8,12,13,14],
  [5,7,9,10,12,14],[5,8,9,10,11,12],[5,8,9,12,13,14],
  [6,7,8,9,10,11],[6,7,8,9,10,13],[6,7,8,9,11,12],
  [6,7,8,9,12,13],[6,7,8,10,11,13],[6,7,8,11,13,14],
  [6,7,9,10,11,12],[6,7,10,11,13,14],[6,8,9,10,11,13],
  [7,8,9,10,11,12],[7,8,9,10,13,14],[7,8,9,12,13,14],
  [7,8,10,11,13,14]]

manifold_5_14_7_1=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,12],[1,2,3,4,7,12],[1,2,3,4,7,13],
  [1,2,3,4,13,14],[1,2,3,5,6,11],[1,2,3,5,11,14],
  [1,2,3,6,11,14],[1,2,3,6,12,14],[1,2,3,7,12,13],
  [1,2,3,12,13,14],[1,2,4,5,6,10],[1,2,4,5,10,14],
  [1,2,4,6,7,10],[1,2,4,6,7,12],[1,2,4,7,10,13],
  [1,2,4,10,13,14],[1,2,5,6,10,11],[1,2,5,10,11,13],
  [1,2,5,10,13,14],[1,2,5,11,13,14],[1,2,6,7,10,11],
  [1,2,6,7,11,12],[1,2,6,11,12,14],[1,2,7,10,11,13],
  [1,2,7,11,12,13],[1,2,11,12,13,14],[1,3,4,5,6,9],
  [1,3,4,5,9,14],[1,3,4,6,9,12],[1,3,4,7,12,13],
  [1,3,4,9,12,13],[1,3,4,9,13,14],[1,3,5,6,9,14],
  [1,3,5,6,11,14],[1,3,6,9,12,14],[1,3,9,12,13,14],
  [1,4,5,6,7,9],[1,4,5,6,7,10],[1,4,5,7,9,10],
  [1,4,5,9,10,14],[1,4,6,7,9,12],[1,4,7,9,10,12],
  [1,4,7,10,12,13],[1,4,9,10,12,14],[1,4,9,12,13,14],
  [1,4,10,12,13,14],[1,5,6,7,9,10],[1,5,6,9,10,14],
  [1,5,6,10,11,14],[1,5,10,11,13,14],[1,6,7,9,10,11],
  [1,6,7,9,11,12],[1,6,9,10,11,12],[1,6,9,10,12,14],
  [1,6,10,11,12,14],[1,7,9,10,11,12],[1,7,10,11,12,13],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,13],
  [2,3,4,5,8,13],[2,3,4,5,8,14],[2,3,4,6,7,12],
  [2,3,4,8,13,14],[2,3,5,6,7,11],[2,3,5,7,8,11],
  [2,3,5,7,8,13],[2,3,5,8,11,14],[2,3,6,7,11,12],
  [2,3,6,11,12,14],[2,3,7,8,11,12],[2,3,7,8,12,13],
  [2,3,8,11,12,14],[2,3,8,12,13,14],[2,4,5,6,7,10],
  [2,4,5,7,10,13],[2,4,5,8,13,14],[2,4,5,10,13,14],
  [2,5,6,7,8,10],[2,5,6,7,8,11],[2,5,6,8,10,11],
  [2,5,7,8,10,13],[2,5,8,10,11,13],[2,5,8,11,13,14],
  [2,6,7,8,10,11],[2,7,8,10,11,12],[2,7,8,10,12,13],
  [2,7,10,11,12,13],[2,8,10,11,12,13],
  [2,8,11,12,13,14],[3,4,5,6,7,8],[3,4,5,6,8,14],
  [3,4,5,6,9,14],[3,4,5,7,8,13],[3,4,6,7,8,12],
  [3,4,6,8,9,12],[3,4,6,8,9,14],[3,4,7,8,12,13],
  [3,4,8,9,12,13],[3,4,8,9,13,14],[3,5,6,7,8,11],
  [3,5,6,8,11,14],[3,6,7,8,9,11],[3,6,7,8,9,12],
  [3,6,7,9,11,12],[3,6,8,9,11,14],[3,6,9,11,12,14],
  [3,7,8,9,11,12],[3,8,9,11,12,13],[3,8,9,11,13,14],
  [3,8,11,12,13,14],[3,9,11,12,13,14],[4,5,6,7,8,9],
  [4,5,6,8,9,14],[4,5,7,8,9,13],[4,5,7,9,10,13],
  [4,5,8,9,13,14],[4,5,9,10,13,14],[4,6,7,8,9,12],
  [4,7,8,9,10,12],[4,7,8,9,10,13],[4,7,8,10,12,13],
  [4,8,9,10,12,13],[4,9,10,12,13,14],[5,6,7,8,9,10],
  [5,6,8,9,10,14],[5,6,8,10,11,14],[5,7,8,9,10,13],
  [5,8,9,10,11,13],[5,8,9,10,11,14],[5,8,9,11,13,14],
  [5,9,10,11,13,14],[6,7,8,9,10,11],[6,8,9,10,11,14],
  [6,9,10,11,12,14],[7,8,9,10,11,12],[8,9,10,11,12,13],
  [9,10,11,12,13,14]]

manifold_5_14_4_1=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,12],[1,2,3,4,12,13],
  [1,2,3,4,13,14],[1,2,3,5,6,11],[1,2,3,5,11,14],
  [1,2,3,6,7,12],[1,2,3,6,11,14],[1,2,3,6,12,14],
  [1,2,3,12,13,14],[1,2,4,5,6,10],[1,2,4,5,10,13],
  [1,2,4,5,13,14],[1,2,4,6,7,10],[1,2,4,7,10,13],
  [1,2,4,7,12,13],[1,2,5,6,10,11],[1,2,5,10,11,14],
  [1,2,5,10,13,14],[1,2,6,7,10,11],[1,2,6,7,11,12],
  [1,2,6,11,12,14],[1,2,7,10,11,13],[1,2,7,11,12,13],
  [1,2,10,11,13,14],[1,2,11,12,13,14],[1,3,4,5,6,14],
  [1,3,4,6,7,12],[1,3,4,6,9,12],[1,3,4,6,9,14],
  [1,3,4,9,12,13],[1,3,4,9,13,14],[1,3,5,6,11,14],
  [1,3,6,9,12,14],[1,3,9,12,13,14],[1,4,5,6,7,9],
  [1,4,5,6,7,10],[1,4,5,6,9,14],[1,4,5,7,9,10],
  [1,4,5,9,10,14],[1,4,5,10,13,14],[1,4,6,7,9,12],
  [1,4,7,9,10,12],[1,4,7,10,12,13],[1,4,9,10,12,14],
  [1,4,9,12,13,14],[1,4,10,12,13,14],[1,5,6,7,9,10],
  [1,5,6,9,10,14],[1,5,6,10,11,14],[1,6,7,9,10,12],
  [1,6,7,10,11,12],[1,6,9,10,11,12],[1,6,9,10,11,14],
  [1,6,9,11,12,14],[1,7,10,11,12,13],[1,9,10,11,12,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,13],
  [2,3,4,5,8,13],[2,3,4,5,8,14],[2,3,4,7,12,13],
  [2,3,4,8,13,14],[2,3,5,6,7,8],[2,3,5,6,8,11],
  [2,3,5,7,8,13],[2,3,5,8,11,14],[2,3,6,7,8,11],
  [2,3,6,7,11,12],[2,3,6,11,12,14],[2,3,7,8,11,12],
  [2,3,7,8,12,13],[2,3,8,11,12,13],[2,3,8,11,13,14],
  [2,3,11,12,13,14],[2,4,5,6,7,10],[2,4,5,7,10,13],
  [2,4,5,8,13,14],[2,5,6,7,8,11],[2,5,6,7,10,11],
  [2,5,7,8,10,11],[2,5,7,8,10,13],[2,5,8,10,11,13],
  [2,5,8,11,13,14],[2,5,10,11,13,14],[2,7,8,10,11,12],
  [2,7,8,10,12,13],[2,7,10,11,12,13],[2,8,10,11,12,13],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,14],
  [3,4,5,7,8,13],[3,4,5,8,9,14],[3,4,6,7,8,12],
  [3,4,6,8,9,12],[3,4,7,8,12,13],[3,4,8,9,12,13],
  [3,4,8,9,13,14],[3,5,6,8,9,14],[3,5,6,8,11,14],
  [3,6,7,8,9,11],[3,6,7,8,9,12],[3,6,7,9,11,12],
  [3,6,8,9,11,14],[3,6,9,11,12,14],[3,7,8,9,11,12],
  [3,8,9,11,12,14],[3,8,9,12,13,14],[3,8,11,12,13,14],
  [4,5,6,7,8,9],[4,5,7,8,9,10],[4,5,7,8,10,13],
  [4,5,8,9,10,13],[4,5,8,9,13,14],[4,5,9,10,13,14],
  [4,6,7,8,9,12],[4,7,8,9,10,13],[4,7,8,9,12,13],
  [4,7,9,10,12,13],[4,9,10,12,13,14],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,8,9,10,14],[5,6,8,10,11,14],
  [5,8,9,10,11,13],[5,8,9,10,11,14],[5,8,9,11,13,14],
  [5,9,10,11,13,14],[6,7,8,9,10,11],[6,7,9,10,11,12],
  [6,8,9,10,11,14],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [8,9,10,11,12,13],[8,9,11,12,13,14],
  [9,10,11,12,13,14]]

manifold_5_14_4_2=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,12],[1,2,3,4,12,13],
  [1,2,3,4,13,14],[1,2,3,5,6,12],[1,2,3,5,12,14],
  [1,2,3,6,7,12],[1,2,3,12,13,14],[1,2,4,5,6,9],
  [1,2,4,5,9,10],[1,2,4,5,10,13],[1,2,4,5,13,14],
  [1,2,4,6,7,9],[1,2,4,7,9,10],[1,2,4,7,10,13],
  [1,2,4,7,12,13],[1,2,5,6,9,10],[1,2,5,6,10,11],
  [1,2,5,6,11,12],[1,2,5,10,11,14],[1,2,5,10,13,14],
  [1,2,5,11,12,14],[1,2,6,7,9,10],[1,2,6,7,10,11],
  [1,2,6,7,11,12],[1,2,7,8,10,11],[1,2,7,8,10,13],
  [1,2,7,8,11,12],[1,2,7,8,12,13],[1,2,8,10,11,13],
  [1,2,8,11,12,13],[1,2,10,11,13,14],[1,2,11,12,13,14],
  [1,3,4,5,6,14],[1,3,4,6,7,12],[1,3,4,6,9,12],
  [1,3,4,6,9,14],[1,3,4,9,10,12],[1,3,4,9,10,14],
  [1,3,4,10,12,13],[1,3,4,10,13,14],[1,3,5,6,12,14],
  [1,3,6,9,12,14],[1,3,9,10,12,14],[1,3,10,12,13,14],
  [1,4,5,6,9,14],[1,4,5,9,10,14],[1,4,5,10,13,14],
  [1,4,6,7,9,12],[1,4,7,9,10,12],[1,4,7,10,12,13],
  [1,5,6,9,10,14],[1,5,6,10,11,14],[1,5,6,11,12,14],
  [1,6,7,9,10,12],[1,6,7,10,11,12],[1,6,9,10,11,12],
  [1,6,9,10,11,14],[1,6,9,11,12,14],[1,7,8,10,11,12],
  [1,7,8,10,12,13],[1,8,10,11,12,13],[1,9,10,11,12,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,14],
  [2,3,4,7,12,13],[2,3,4,7,13,14],[2,3,5,6,7,8],
  [2,3,5,6,8,11],[2,3,5,6,11,12],[2,3,5,7,8,14],
  [2,3,5,8,11,14],[2,3,5,11,12,14],[2,3,6,7,8,11],
  [2,3,6,7,11,12],[2,3,7,8,11,12],[2,3,7,8,12,13],
  [2,3,7,8,13,14],[2,3,8,11,12,13],[2,3,8,11,13,14],
  [2,3,11,12,13,14],[2,4,5,6,7,9],[2,4,5,7,9,10],
  [2,4,5,7,10,13],[2,4,5,7,13,14],[2,5,6,7,8,11],
  [2,5,6,7,9,10],[2,5,6,7,10,11],[2,5,7,8,10,11],
  [2,5,7,8,10,13],[2,5,7,8,13,14],[2,5,8,10,11,13],
  [2,5,8,11,13,14],[2,5,10,11,13,14],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,14],[3,4,5,7,8,14],
  [3,4,5,8,9,14],[3,4,6,7,8,11],[3,4,6,7,11,12],
  [3,4,6,8,9,11],[3,4,6,9,11,12],[3,4,7,8,11,12],
  [3,4,7,8,12,13],[3,4,7,8,13,14],[3,4,8,9,11,12],
  [3,4,8,9,12,13],[3,4,8,9,13,14],[3,4,9,10,12,13],
  [3,4,9,10,13,14],[3,5,6,8,9,14],[3,5,6,8,11,14],
  [3,5,6,11,12,14],[3,6,8,9,11,14],[3,6,9,11,12,14],
  [3,8,9,11,12,14],[3,8,9,12,13,14],[3,8,11,12,13,14],
  [3,9,10,12,13,14],[4,5,6,7,8,9],[4,5,7,8,9,10],
  [4,5,7,8,10,13],[4,5,7,8,13,14],[4,5,8,9,10,13],
  [4,5,8,9,13,14],[4,5,9,10,13,14],[4,6,7,8,9,11],
  [4,6,7,9,11,12],[4,7,8,9,10,13],[4,7,8,9,11,12],
  [4,7,8,9,12,13],[4,7,9,10,12,13],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,8,9,10,13],[5,6,8,9,13,14],
  [5,6,8,10,11,13],[5,6,8,11,13,14],[5,6,9,10,13,14],
  [5,6,10,11,13,14],[6,7,8,9,10,11],[6,7,9,10,11,12],
  [6,8,9,10,11,13],[6,8,9,11,13,14],[6,9,10,11,13,14],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[8,9,10,11,12,13],
  [8,9,11,12,13,14],[9,10,11,12,13,14]]

manifold_5_14_4_3=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,12],[1,2,3,4,7,12],[1,2,3,4,7,13],
  [1,2,3,4,13,14],[1,2,3,5,6,12],[1,2,3,5,12,14],
  [1,2,3,7,12,13],[1,2,3,12,13,14],[1,2,4,5,6,9],
  [1,2,4,5,9,10],[1,2,4,5,10,14],[1,2,4,6,7,9],
  [1,2,4,6,7,12],[1,2,4,7,9,10],[1,2,4,7,10,13],
  [1,2,4,10,13,14],[1,2,5,6,9,10],[1,2,5,6,10,11],
  [1,2,5,6,11,12],[1,2,5,10,11,13],[1,2,5,10,13,14],
  [1,2,5,11,12,14],[1,2,5,11,13,14],[1,2,6,7,9,10],
  [1,2,6,7,10,11],[1,2,6,7,11,12],[1,2,7,8,10,11],
  [1,2,7,8,10,13],[1,2,7,8,11,12],[1,2,7,8,12,13],
  [1,2,8,10,11,13],[1,2,8,11,12,13],[1,2,11,12,13,14],
  [1,3,4,5,6,9],[1,3,4,5,9,14],[1,3,4,6,9,12],
  [1,3,4,7,12,13],[1,3,4,9,10,12],[1,3,4,9,10,14],
  [1,3,4,10,12,13],[1,3,4,10,13,14],[1,3,5,6,9,14],
  [1,3,5,6,12,14],[1,3,6,9,12,14],[1,3,9,10,12,14],
  [1,3,10,12,13,14],[1,4,5,9,10,14],[1,4,6,7,9,12],
  [1,4,7,9,10,12],[1,4,7,10,12,13],[1,5,6,9,10,14],
  [1,5,6,10,11,14],[1,5,6,11,12,14],[1,5,10,11,13,14],
  [1,6,7,9,10,11],[1,6,7,9,11,12],[1,6,9,10,11,12],
  [1,6,9,10,12,14],[1,6,10,11,12,14],[1,7,8,10,11,12],
  [1,7,8,10,12,13],[1,7,9,10,11,12],[1,8,10,11,12,13],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,14],
  [2,3,4,6,7,12],[2,3,4,7,13,14],[2,3,5,6,7,11],
  [2,3,5,6,11,12],[2,3,5,7,8,11],[2,3,5,7,8,14],
  [2,3,5,8,11,14],[2,3,5,11,12,14],[2,3,6,7,11,12],
  [2,3,7,8,11,12],[2,3,7,8,12,13],[2,3,7,8,13,14],
  [2,3,8,11,12,14],[2,3,8,12,13,14],[2,4,5,6,7,9],
  [2,4,5,7,9,10],[2,4,5,7,10,13],[2,4,5,7,13,14],
  [2,4,5,10,13,14],[2,5,6,7,8,10],[2,5,6,7,8,11],
  [2,5,6,7,9,10],[2,5,6,8,10,11],[2,5,7,8,10,13],
  [2,5,7,8,13,14],[2,5,8,10,11,13],[2,5,8,11,13,14],
  [2,6,7,8,10,11],[2,8,11,12,13,14],[3,4,5,6,7,8],
  [3,4,5,6,8,14],[3,4,5,6,9,14],[3,4,5,7,8,14],
  [3,4,6,7,8,11],[3,4,6,7,11,12],[3,4,6,8,9,11],
  [3,4,6,8,9,14],[3,4,6,9,11,12],[3,4,7,8,11,12],
  [3,4,7,8,12,13],[3,4,7,8,13,14],[3,4,8,9,11,12],
  [3,4,8,9,12,13],[3,4,8,9,13,14],[3,4,9,10,12,13],
  [3,4,9,10,13,14],[3,5,6,7,8,11],[3,5,6,8,11,14],
  [3,5,6,11,12,14],[3,6,8,9,11,14],[3,6,9,11,12,14],
  [3,8,9,11,12,13],[3,8,9,11,13,14],[3,8,11,12,13,14],
  [3,9,10,12,13,14],[3,9,11,12,13,14],[4,5,6,7,8,9],
  [4,5,6,8,9,14],[4,5,7,8,9,13],[4,5,7,8,13,14],
  [4,5,7,9,10,13],[4,5,8,9,13,14],[4,5,9,10,13,14],
  [4,6,7,8,9,11],[4,6,7,9,11,12],[4,7,8,9,10,12],
  [4,7,8,9,10,13],[4,7,8,9,11,12],[4,7,8,10,12,13],
  [4,8,9,10,12,13],[5,6,7,8,9,10],[5,6,8,9,10,13],
  [5,6,8,9,13,14],[5,6,8,10,11,13],[5,6,8,11,13,14],
  [5,6,9,10,13,14],[5,6,10,11,13,14],[5,7,8,9,10,13],
  [6,7,8,9,10,11],[6,8,9,10,11,13],[6,8,9,11,13,14],
  [6,9,10,11,12,14],[6,9,10,11,13,14],[7,8,9,10,11,12],
  [8,9,10,11,12,13],[9,10,11,12,13,14]]

manifold_5_14_4_4=[[1,2,3,4,6,11],[1,2,3,4,6,13],
  [1,2,3,4,8,11],[1,2,3,4,8,13],[1,2,3,6,9,13],
  [1,2,3,6,9,14],[1,2,3,6,11,14],[1,2,3,8,9,13],
  [1,2,3,8,9,14],[1,2,3,8,11,14],[1,2,4,6,11,13],
  [1,2,4,8,9,13],[1,2,4,8,9,14],[1,2,4,8,11,14],
  [1,2,4,9,13,14],[1,2,4,11,13,14],[1,2,6,9,13,14],
  [1,2,6,11,13,14],[1,3,4,5,6,8],[1,3,4,5,6,10],
  [1,3,4,5,8,11],[1,3,4,5,10,11],[1,3,4,6,8,13],
  [1,3,4,6,10,11],[1,3,5,6,8,10],[1,3,5,8,10,11],
  [1,3,6,8,9,13],[1,3,6,8,9,14],[1,3,6,8,10,14],
  [1,3,6,10,11,14],[1,3,8,10,11,14],[1,4,5,6,7,10],
  [1,4,5,6,7,12],[1,4,5,6,8,12],[1,4,5,7,10,14],
  [1,4,5,7,12,14],[1,4,5,8,9,12],[1,4,5,8,9,14],
  [1,4,5,8,11,14],[1,4,5,9,12,14],[1,4,5,10,11,14],
  [1,4,6,7,10,11],[1,4,6,7,11,13],[1,4,6,7,12,13],
  [1,4,6,8,12,13],[1,4,7,10,11,14],[1,4,7,11,13,14],
  [1,4,7,12,13,14],[1,4,8,9,12,13],[1,4,9,12,13,14],
  [1,5,6,7,8,10],[1,5,6,7,8,12],[1,5,7,8,9,12],
  [1,5,7,8,9,14],[1,5,7,8,10,14],[1,5,7,9,12,14],
  [1,5,8,10,11,14],[1,6,7,8,9,12],[1,6,7,8,9,14],
  [1,6,7,8,10,14],[1,6,7,9,12,14],[1,6,7,10,11,14],
  [1,6,7,11,13,14],[1,6,7,12,13,14],[1,6,8,9,12,13],
  [1,6,9,12,13,14],[2,3,4,5,8,11],[2,3,4,5,8,13],
  [2,3,4,5,10,11],[2,3,4,5,10,13],[2,3,4,6,10,11],
  [2,3,4,6,10,13],[2,3,5,8,10,11],[2,3,5,8,10,12],
  [2,3,5,8,12,13],[2,3,5,10,12,13],[2,3,6,7,9,12],
  [2,3,6,7,9,14],[2,3,6,7,10,11],[2,3,6,7,10,13],
  [2,3,6,7,11,14],[2,3,6,7,12,13],[2,3,6,9,12,13],
  [2,3,7,9,10,11],[2,3,7,9,10,12],[2,3,7,9,11,14],
  [2,3,7,10,12,13],[2,3,8,9,10,11],[2,3,8,9,10,12],
  [2,3,8,9,11,14],[2,3,8,9,12,13],[2,4,5,8,9,11],
  [2,4,5,8,9,13],[2,4,5,9,11,13],[2,4,5,10,11,13],
  [2,4,6,10,11,13],[2,4,8,9,11,14],[2,4,9,11,13,14],
  [2,5,8,9,10,11],[2,5,8,9,10,12],[2,5,8,9,12,13],
  [2,5,9,10,11,12],[2,5,9,11,12,13],[2,5,10,11,12,13],
  [2,6,7,9,12,14],[2,6,7,10,11,13],[2,6,7,11,13,14],
  [2,6,7,12,13,14],[2,6,9,12,13,14],[2,7,9,10,11,12],
  [2,7,9,11,12,14],[2,7,10,11,12,13],[2,7,11,12,13,14],
  [2,9,11,12,13,14],[3,4,5,6,8,13],[3,4,5,6,10,13],
  [3,5,6,7,8,10],[3,5,6,7,8,12],[3,5,6,7,10,13],
  [3,5,6,7,12,13],[3,5,6,8,12,13],[3,5,7,8,10,12],
  [3,5,7,10,12,13],[3,6,7,8,9,12],[3,6,7,8,9,14],
  [3,6,7,8,10,14],[3,6,7,10,11,14],[3,6,8,9,12,13],
  [3,7,8,9,10,12],[3,7,8,9,10,14],[3,7,9,10,11,14],
  [3,8,9,10,11,14],[4,5,6,7,10,13],[4,5,6,7,12,13],
  [4,5,6,8,12,13],[4,5,7,10,12,13],[4,5,7,10,12,14],
  [4,5,8,9,11,14],[4,5,8,9,12,13],[4,5,9,11,12,13],
  [4,5,9,11,12,14],[4,5,10,11,12,13],[4,5,10,11,12,14],
  [4,6,7,10,11,13],[4,7,10,11,12,13],[4,7,10,11,12,14],
  [4,7,11,12,13,14],[4,9,11,12,13,14],[5,7,8,9,10,12],
  [5,7,8,9,10,14],[5,7,9,10,12,14],[5,8,9,10,11,14],
  [5,9,10,11,12,14],[7,9,10,11,12,14]]

manifold_5_14_4_5=[[1,2,3,4,7,8],[1,2,3,4,7,12],
  [1,2,3,4,8,9],[1,2,3,4,9,10],[1,2,3,4,10,11],
  [1,2,3,4,11,12],[1,2,3,7,8,10],[1,2,3,7,10,12],
  [1,2,3,8,9,10],[1,2,3,10,11,12],[1,2,4,5,7,8],
  [1,2,4,5,7,12],[1,2,4,5,8,11],[1,2,4,5,11,12],
  [1,2,4,8,9,11],[1,2,4,9,10,11],[1,2,5,6,7,8],
  [1,2,5,6,7,14],[1,2,5,6,8,9],[1,2,5,6,9,12],
  [1,2,5,6,12,13],[1,2,5,6,13,14],[1,2,5,7,10,12],
  [1,2,5,7,10,14],[1,2,5,8,9,12],[1,2,5,8,11,12],
  [1,2,5,10,12,13],[1,2,5,10,13,14],[1,2,6,7,8,13],
  [1,2,6,7,13,14],[1,2,6,8,9,13],[1,2,6,9,12,13],
  [1,2,7,8,9,10],[1,2,7,8,9,14],[1,2,7,8,13,14],
  [1,2,7,9,10,14],[1,2,8,9,11,12],[1,2,8,9,13,14],
  [1,2,9,10,11,12],[1,2,9,10,12,13],[1,2,9,10,13,14],
  [1,3,4,7,8,14],[1,3,4,7,12,14],[1,3,4,8,9,10],
  [1,3,4,8,10,11],[1,3,4,8,11,14],[1,3,4,11,12,14],
  [1,3,5,8,10,12],[1,3,5,8,10,14],[1,3,5,8,12,14],
  [1,3,5,10,12,14],[1,3,6,8,10,11],[1,3,6,8,10,13],
  [1,3,6,8,11,12],[1,3,6,8,12,13],[1,3,6,10,11,12],
  [1,3,6,10,12,13],[1,3,7,8,10,14],[1,3,7,10,12,14],
  [1,3,8,10,12,13],[1,3,8,11,12,14],[1,4,5,7,8,12],
  [1,4,5,8,11,12],[1,4,6,8,9,11],[1,4,6,8,9,13],
  [1,4,6,8,11,13],[1,4,6,9,10,11],[1,4,6,9,10,13],
  [1,4,6,10,11,13],[1,4,7,8,11,12],[1,4,7,8,11,14],
  [1,4,7,11,12,14],[1,4,8,9,10,13],[1,4,8,10,11,13],
  [1,5,6,7,8,14],[1,5,6,8,9,12],[1,5,6,8,12,13],
  [1,5,6,8,13,14],[1,5,7,8,12,14],[1,5,7,10,12,14],
  [1,5,8,10,12,13],[1,5,8,10,13,14],[1,6,7,8,13,14],
  [1,6,8,9,11,12],[1,6,8,10,11,13],[1,6,9,10,11,12],
  [1,6,9,10,12,13],[1,7,8,9,10,14],[1,7,8,11,12,14],
  [1,8,9,10,13,14],[2,3,4,7,8,9],[2,3,4,7,9,12],
  [2,3,4,9,10,11],[2,3,4,9,11,12],[2,3,5,6,9,10],
  [2,3,5,6,9,14],[2,3,5,6,10,13],[2,3,5,6,13,14],
  [2,3,5,7,10,12],[2,3,5,7,10,14],[2,3,5,7,12,14],
  [2,3,5,9,10,12],[2,3,5,9,12,14],[2,3,5,10,13,14],
  [2,3,6,9,10,13],[2,3,6,9,13,14],[2,3,7,8,9,10],
  [2,3,7,9,10,14],[2,3,7,9,12,14],[2,3,9,10,11,12],
  [2,3,9,10,13,14],[2,4,5,7,8,11],[2,4,5,7,9,12],
  [2,4,5,7,9,14],[2,4,5,7,11,14],[2,4,5,9,11,12],
  [2,4,5,9,11,14],[2,4,6,7,9,11],[2,4,6,7,9,13],
  [2,4,6,7,11,13],[2,4,6,9,11,13],[2,4,7,8,9,13],
  [2,4,7,8,11,13],[2,4,7,9,11,14],[2,4,8,9,11,13],
  [2,5,6,7,8,11],[2,5,6,7,11,14],[2,5,6,8,9,11],
  [2,5,6,9,10,13],[2,5,6,9,11,14],[2,5,6,9,12,13],
  [2,5,7,9,12,14],[2,5,8,9,11,12],[2,5,9,10,12,13],
  [2,6,7,8,11,13],[2,6,7,9,11,14],[2,6,7,9,13,14],
  [2,6,8,9,11,13],[2,7,8,9,13,14],[3,4,5,6,9,10],
  [3,4,5,6,9,14],[3,4,5,6,10,11],[3,4,5,6,11,12],
  [3,4,5,6,12,13],[3,4,5,6,13,14],[3,4,5,9,10,12],
  [3,4,5,9,12,14],[3,4,5,10,11,12],[3,4,5,12,13,14],
  [3,4,6,7,9,10],[3,4,6,7,9,14],[3,4,6,7,10,13],
  [3,4,6,7,13,14],[3,4,6,10,11,13],[3,4,6,11,12,13],
  [3,4,7,8,9,10],[3,4,7,8,10,11],[3,4,7,8,11,14],
  [3,4,7,9,12,14],[3,4,7,10,11,14],[3,4,7,10,13,14],
  [3,4,9,10,11,12],[3,4,10,11,13,14],[3,4,11,12,13,14],
  [3,5,6,10,11,12],[3,5,6,10,12,13],[3,5,7,10,12,14],
  [3,5,8,10,12,13],[3,5,8,10,13,14],[3,5,8,12,13,14],
  [3,6,7,9,10,14],[3,6,7,10,13,14],[3,6,8,10,11,13],
  [3,6,8,11,12,13],[3,6,9,10,13,14],[3,7,8,10,11,14],
  [3,8,10,11,13,14],[3,8,11,12,13,14],[4,5,6,9,10,11],
  [4,5,6,9,11,14],[4,5,6,11,12,13],[4,5,6,11,13,14],
  [4,5,7,8,11,12],[4,5,7,9,12,14],[4,5,7,11,12,14],
  [4,5,9,10,11,12],[4,5,11,12,13,14],[4,6,7,9,10,13],
  [4,6,7,9,11,14],[4,6,7,11,13,14],[4,6,8,9,11,13],
  [4,7,8,9,10,13],[4,7,8,10,11,13],[4,7,10,11,13,14],
  [5,6,7,8,11,12],[5,6,7,8,12,13],[5,6,7,8,13,14],
  [5,6,7,11,12,14],[5,6,7,12,13,14],[5,6,8,9,11,12],
  [5,6,9,10,11,12],[5,6,9,10,12,13],[5,6,11,12,13,14],
  [5,7,8,12,13,14],[6,7,8,11,12,13],[6,7,9,10,13,14],
  [6,7,11,12,13,14],[7,8,9,10,13,14],[7,8,10,11,13,14],
  [7,8,11,12,13,14]]

manifold_5_14_3_1=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,10],[1,2,3,4,10,11],[1,2,3,4,11,12],
  [1,2,3,4,12,13],[1,2,3,4,13,14],[1,2,3,5,6,14],
  [1,2,3,6,7,14],[1,2,3,7,8,14],[1,2,3,8,9,14],
  [1,2,3,9,10,14],[1,2,3,10,11,14],[1,2,3,11,12,14],
  [1,2,3,12,13,14],[1,2,4,5,6,7],[1,2,4,5,7,8],
  [1,2,4,5,8,9],[1,2,4,5,9,10],[1,2,4,5,10,11],
  [1,2,4,5,11,12],[1,2,4,5,12,13],[1,2,4,5,13,14],
  [1,2,5,6,7,8],[1,2,5,6,8,9],[1,2,5,6,9,10],
  [1,2,5,6,10,11],[1,2,5,6,11,12],[1,2,5,6,12,13],
  [1,2,5,6,13,14],[1,2,6,7,8,9],[1,2,6,7,9,10],
  [1,2,6,7,10,11],[1,2,6,7,11,12],[1,2,6,7,12,13],
  [1,2,6,7,13,14],[1,2,7,8,9,10],[1,2,7,8,10,11],
  [1,2,7,8,11,12],[1,2,7,8,12,13],[1,2,7,8,13,14],
  [1,2,8,9,10,11],[1,2,8,9,11,12],[1,2,8,9,12,13],
  [1,2,8,9,13,14],[1,2,9,10,11,12],[1,2,9,10,12,13],
  [1,2,9,10,13,14],[1,2,10,11,12,13],[1,2,10,11,13,14],
  [1,2,11,12,13,14],[1,3,4,5,6,14],[1,3,4,6,7,14],
  [1,3,4,7,8,14],[1,3,4,8,9,14],[1,3,4,9,10,14],
  [1,3,4,10,11,14],[1,3,4,11,12,14],[1,3,4,12,13,14],
  [1,4,5,6,7,14],[1,4,5,7,8,14],[1,4,5,8,9,14],
  [1,4,5,9,10,14],[1,4,5,10,11,14],[1,4,5,11,12,14],
  [1,4,5,12,13,14],[1,5,6,7,8,14],[1,5,6,8,9,14],
  [1,5,6,9,10,14],[1,5,6,10,11,14],[1,5,6,11,12,14],
  [1,5,6,12,13,14],[1,6,7,8,9,14],[1,6,7,9,10,14],
  [1,6,7,10,11,14],[1,6,7,11,12,14],[1,6,7,12,13,14],
  [1,7,8,9,10,14],[1,7,8,10,11,14],[1,7,8,11,12,14],
  [1,7,8,12,13,14],[1,8,9,10,11,14],[1,8,9,11,12,14],
  [1,8,9,12,13,14],[1,9,10,11,12,14],[1,9,10,12,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,11],
  [2,3,4,5,11,12],[2,3,4,5,12,13],[2,3,4,5,13,14],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,10],
  [2,3,5,6,10,11],[2,3,5,6,11,12],[2,3,5,6,12,13],
  [2,3,5,6,13,14],[2,3,6,7,8,9],[2,3,6,7,9,10],
  [2,3,6,7,10,11],[2,3,6,7,11,12],[2,3,6,7,12,13],
  [2,3,6,7,13,14],[2,3,7,8,9,10],[2,3,7,8,10,11],
  [2,3,7,8,11,12],[2,3,7,8,12,13],[2,3,7,8,13,14],
  [2,3,8,9,10,11],[2,3,8,9,11,12],[2,3,8,9,12,13],
  [2,3,8,9,13,14],[2,3,9,10,11,12],[2,3,9,10,12,13],
  [2,3,9,10,13,14],[2,3,10,11,12,13],[2,3,10,11,13,14],
  [2,3,11,12,13,14],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,10],[3,4,5,6,10,11],[3,4,5,6,11,12],
  [3,4,5,6,12,13],[3,4,5,6,13,14],[3,4,6,7,8,9],
  [3,4,6,7,9,10],[3,4,6,7,10,11],[3,4,6,7,11,12],
  [3,4,6,7,12,13],[3,4,6,7,13,14],[3,4,7,8,9,10],
  [3,4,7,8,10,11],[3,4,7,8,11,12],[3,4,7,8,12,13],
  [3,4,7,8,13,14],[3,4,8,9,10,11],[3,4,8,9,11,12],
  [3,4,8,9,12,13],[3,4,8,9,13,14],[3,4,9,10,11,12],
  [3,4,9,10,12,13],[3,4,9,10,13,14],[3,4,10,11,12,13],
  [3,4,10,11,13,14],[3,4,11,12,13,14],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,6,7,11,12],
  [4,5,6,7,12,13],[4,5,6,7,13,14],[4,5,7,8,9,10],
  [4,5,7,8,10,11],[4,5,7,8,11,12],[4,5,7,8,12,13],
  [4,5,7,8,13,14],[4,5,8,9,10,11],[4,5,8,9,11,12],
  [4,5,8,9,12,13],[4,5,8,9,13,14],[4,5,9,10,11,12],
  [4,5,9,10,12,13],[4,5,9,10,13,14],[4,5,10,11,12,13],
  [4,5,10,11,13,14],[4,5,11,12,13,14],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,8,11,12],[5,6,7,8,12,13],
  [5,6,7,8,13,14],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,6,8,9,12,13],[5,6,8,9,13,14],[5,6,9,10,11,12],
  [5,6,9,10,12,13],[5,6,9,10,13,14],[5,6,10,11,12,13],
  [5,6,10,11,13,14],[5,6,11,12,13,14],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,8,9,12,13],[6,7,8,9,13,14],
  [6,7,9,10,11,12],[6,7,9,10,12,13],[6,7,9,10,13,14],
  [6,7,10,11,12,13],[6,7,10,11,13,14],
  [6,7,11,12,13,14],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,9,10,13,14],[7,8,10,11,12,13],[7,8,10,11,13,14],
  [7,8,11,12,13,14],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,11,12,13,14],
  [9,10,11,12,13,14]]

manifold_5_14_3_2=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,11],
  [1,2,3,4,11,12],[1,2,3,4,12,13],[1,2,3,4,13,14],
  [1,2,3,5,6,14],[1,2,3,6,7,14],[1,2,3,7,8,11],
  [1,2,3,7,10,11],[1,2,3,7,10,14],[1,2,3,10,11,14],
  [1,2,3,11,12,14],[1,2,3,12,13,14],[1,2,4,5,6,7],
  [1,2,4,5,7,8],[1,2,4,5,8,12],[1,2,4,5,12,13],
  [1,2,4,5,13,14],[1,2,4,8,11,12],[1,2,5,6,7,8],
  [1,2,5,6,8,12],[1,2,5,6,9,10],[1,2,5,6,9,13],
  [1,2,5,6,10,11],[1,2,5,6,11,12],[1,2,5,6,13,14],
  [1,2,5,9,10,11],[1,2,5,9,11,12],[1,2,5,9,12,13],
  [1,2,6,7,8,12],[1,2,6,7,10,11],[1,2,6,7,10,14],
  [1,2,6,7,11,12],[1,2,6,9,10,14],[1,2,6,9,13,14],
  [1,2,7,8,11,12],[1,2,9,10,11,12],[1,2,9,10,12,13],
  [1,2,9,10,13,14],[1,2,10,11,12,13],[1,2,10,11,13,14],
  [1,2,11,12,13,14],[1,3,4,5,6,14],[1,3,4,6,7,14],
  [1,3,4,7,8,11],[1,3,4,7,11,14],[1,3,4,11,12,14],
  [1,3,4,12,13,14],[1,3,7,10,11,14],[1,4,5,6,7,14],
  [1,4,5,7,8,11],[1,4,5,7,11,14],[1,4,5,8,9,11],
  [1,4,5,8,9,14],[1,4,5,8,12,14],[1,4,5,9,10,11],
  [1,4,5,9,10,14],[1,4,5,10,11,14],[1,4,5,12,13,14],
  [1,4,8,9,10,11],[1,4,8,9,10,14],[1,4,8,10,11,14],
  [1,4,8,11,12,14],[1,5,6,7,8,12],[1,5,6,7,11,12],
  [1,5,6,7,11,14],[1,5,6,9,10,14],[1,5,6,9,13,14],
  [1,5,6,10,11,14],[1,5,7,8,11,12],[1,5,8,9,11,12],
  [1,5,8,9,12,13],[1,5,8,9,13,14],[1,5,8,12,13,14],
  [1,6,7,10,11,14],[1,8,9,10,11,14],[1,8,9,11,12,14],
  [1,8,9,12,13,14],[1,9,10,11,12,14],[1,9,10,12,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,12],[2,3,4,5,12,13],
  [2,3,4,5,13,14],[2,3,4,8,9,12],[2,3,4,8,11,12],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,13],
  [2,3,5,6,13,14],[2,3,5,9,12,13],[2,3,6,7,8,9],
  [2,3,6,7,9,13],[2,3,6,7,10,11],[2,3,6,7,10,14],
  [2,3,6,7,11,12],[2,3,6,7,12,13],[2,3,6,10,11,12],
  [2,3,6,10,12,13],[2,3,6,10,13,14],[2,3,7,8,9,13],
  [2,3,7,8,11,12],[2,3,7,8,12,13],[2,3,8,9,12,13],
  [2,3,10,11,12,13],[2,3,10,11,13,14],
  [2,3,11,12,13,14],[2,4,5,8,9,12],[2,5,6,8,9,12],
  [2,5,6,9,10,12],[2,5,6,10,11,12],[2,5,9,10,11,12],
  [2,6,7,8,9,13],[2,6,7,8,12,13],[2,6,8,9,12,13],
  [2,6,9,10,12,13],[2,6,9,10,13,14],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,13],
  [3,4,5,6,13,14],[3,4,5,9,10,13],[3,4,5,9,12,13],
  [3,4,6,7,8,9],[3,4,6,7,9,10],[3,4,6,7,10,14],
  [3,4,6,10,13,14],[3,4,7,8,9,10],[3,4,7,8,10,14],
  [3,4,7,8,11,12],[3,4,7,8,12,13],[3,4,7,8,13,14],
  [3,4,7,11,12,13],[3,4,7,11,13,14],[3,4,8,9,10,14],
  [3,4,8,9,12,13],[3,4,8,9,13,14],[3,4,9,10,13,14],
  [3,4,11,12,13,14],[3,5,6,9,10,13],[3,6,7,9,10,13],
  [3,6,7,10,11,13],[3,6,7,11,12,13],[3,6,10,11,12,13],
  [3,7,8,9,10,14],[3,7,8,9,13,14],[3,7,9,10,13,14],
  [3,7,10,11,13,14],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,7,10,11],[4,5,6,7,11,14],[4,5,6,10,11,14],
  [4,5,6,10,13,14],[4,5,7,8,9,10],[4,5,7,8,10,11],
  [4,5,8,9,10,11],[4,5,8,9,12,13],[4,5,8,9,13,14],
  [4,5,8,12,13,14],[4,5,9,10,13,14],[4,6,7,10,11,14],
  [4,7,8,10,11,14],[4,7,8,11,12,14],[4,7,8,12,13,14],
  [4,7,11,12,13,14],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,12],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,6,9,10,11,12],[5,6,9,10,13,14],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,8,9,12,13],[6,7,9,10,11,12],
  [6,7,9,10,12,13],[6,7,10,11,12,13],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[7,8,9,10,13,14],[7,8,10,11,12,13],
  [7,8,10,11,13,14],[7,8,11,12,13,14],
  [8,9,10,11,12,13],[8,9,10,11,13,14],
  [8,9,11,12,13,14],[9,10,11,12,13,14]]

manifold_5_14_3_3=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,9],[1,2,3,4,9,10],
  [1,2,3,4,10,12],[1,2,3,4,12,13],[1,2,3,4,13,14],
  [1,2,3,5,6,14],[1,2,3,6,7,8],[1,2,3,6,8,14],
  [1,2,3,7,8,9],[1,2,3,8,9,14],[1,2,3,9,10,11],
  [1,2,3,9,11,14],[1,2,3,10,11,12],[1,2,3,11,12,14],
  [1,2,3,12,13,14],[1,2,4,5,6,7],[1,2,4,5,7,13],
  [1,2,4,5,13,14],[1,2,4,7,9,10],[1,2,4,7,10,13],
  [1,2,4,10,12,13],[1,2,5,6,7,14],[1,2,5,7,13,14],
  [1,2,6,7,8,14],[1,2,7,8,9,10],[1,2,7,8,10,13],
  [1,2,7,8,13,14],[1,2,8,9,10,14],[1,2,8,10,13,14],
  [1,2,9,10,11,14],[1,2,10,11,12,13],[1,2,10,11,13,14],
  [1,2,11,12,13,14],[1,3,4,5,6,14],[1,3,4,6,7,9],
  [1,3,4,6,9,12],[1,3,4,6,12,14],[1,3,4,9,10,12],
  [1,3,4,12,13,14],[1,3,6,7,8,9],[1,3,6,8,9,14],
  [1,3,6,9,12,14],[1,3,9,10,11,12],[1,3,9,11,12,14],
  [1,4,5,6,7,13],[1,4,5,6,13,14],[1,4,6,7,9,12],
  [1,4,6,7,12,13],[1,4,6,12,13,14],[1,4,7,9,10,12],
  [1,4,7,10,12,13],[1,5,6,7,13,14],[1,6,7,8,9,14],
  [1,6,7,9,12,14],[1,6,7,12,13,14],[1,7,8,9,10,13],
  [1,7,8,9,13,14],[1,7,9,10,12,13],[1,7,9,12,13,14],
  [1,8,9,10,13,14],[1,9,10,11,12,14],[1,9,10,12,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,10],[2,3,4,5,10,11],[2,3,4,5,11,13],
  [2,3,4,5,13,14],[2,3,4,7,8,9],[2,3,4,8,9,10],
  [2,3,4,10,11,12],[2,3,4,11,12,13],[2,3,5,6,7,8],
  [2,3,5,6,8,14],[2,3,5,8,10,11],[2,3,5,8,11,14],
  [2,3,5,11,13,14],[2,3,8,9,10,11],[2,3,8,9,11,14],
  [2,3,11,12,13,14],[2,4,5,7,8,10],[2,4,5,7,10,13],
  [2,4,5,10,11,13],[2,4,7,8,9,10],[2,4,10,11,12,13],
  [2,5,6,7,8,14],[2,5,7,8,10,13],[2,5,7,8,13,14],
  [2,5,8,10,11,13],[2,5,8,11,13,14],[2,8,9,10,11,14],
  [2,8,10,11,13,14],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,11],[3,4,5,6,11,12],[3,4,5,6,12,14],
  [3,4,5,8,9,10],[3,4,5,9,10,11],[3,4,5,11,12,13],
  [3,4,5,12,13,14],[3,4,6,7,8,9],[3,4,6,9,11,12],
  [3,4,9,10,11,12],[3,5,6,8,9,11],[3,5,6,8,11,14],
  [3,5,6,11,12,14],[3,5,8,9,10,11],[3,5,11,12,13,14],
  [3,6,8,9,11,14],[3,6,9,11,12,14],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,12],[4,5,6,7,12,13],
  [4,5,6,9,10,11],[4,5,6,10,11,12],[4,5,6,12,13,14],
  [4,5,7,8,9,10],[4,5,7,10,12,13],[4,5,10,11,12,13],
  [4,6,7,9,10,12],[4,6,9,10,11,12],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,8,11,13],[5,6,7,8,13,14],
  [5,6,7,10,11,12],[5,6,7,11,12,13],[5,6,8,9,10,11],
  [5,6,8,11,13,14],[5,6,11,12,13,14],[5,7,8,10,11,13],
  [5,7,10,11,12,13],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,8,9,12,14],[6,7,8,11,12,13],[6,7,8,12,13,14],
  [6,7,9,10,11,12],[6,8,9,11,12,14],[6,8,11,12,13,14],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[7,8,9,12,13,14],
  [7,8,10,11,12,13],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,11,12,13,14],
  [9,10,11,12,13,14]]

manifold_5_14_3_4=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,11],[1,2,3,4,8,11],
  [1,2,3,4,8,12],[1,2,3,4,12,13],[1,2,3,4,13,14],
  [1,2,3,5,6,14],[1,2,3,6,7,10],[1,2,3,6,10,14],
  [1,2,3,7,10,14],[1,2,3,7,11,14],[1,2,3,8,11,12],
  [1,2,3,11,12,14],[1,2,3,12,13,14],[1,2,4,5,6,7],
  [1,2,4,5,7,8],[1,2,4,5,8,12],[1,2,4,5,12,13],
  [1,2,4,5,13,14],[1,2,4,7,8,11],[1,2,5,6,7,12],
  [1,2,5,6,9,10],[1,2,5,6,9,14],[1,2,5,6,10,11],
  [1,2,5,6,11,12],[1,2,5,7,8,12],[1,2,5,9,10,12],
  [1,2,5,9,12,13],[1,2,5,9,13,14],[1,2,5,10,11,12],
  [1,2,6,7,10,11],[1,2,6,7,11,12],[1,2,6,9,10,13],
  [1,2,6,9,13,14],[1,2,6,10,13,14],[1,2,7,8,11,12],
  [1,2,7,10,11,14],[1,2,9,10,12,13],[1,2,10,11,12,13],
  [1,2,10,11,13,14],[1,2,11,12,13,14],[1,3,4,5,6,14],
  [1,3,4,6,7,14],[1,3,4,7,11,14],[1,3,4,8,11,12],
  [1,3,4,11,12,14],[1,3,4,12,13,14],[1,3,6,7,10,14],
  [1,4,5,6,7,11],[1,4,5,6,11,14],[1,4,5,7,8,11],
  [1,4,5,8,9,10],[1,4,5,8,9,14],[1,4,5,8,10,11],
  [1,4,5,8,12,13],[1,4,5,8,13,14],[1,4,5,9,10,14],
  [1,4,5,10,11,14],[1,4,6,7,11,14],[1,4,8,9,10,11],
  [1,4,8,9,11,14],[1,4,8,11,12,14],[1,4,8,12,13,14],
  [1,4,9,10,11,14],[1,5,6,7,8,11],[1,5,6,7,8,12],
  [1,5,6,8,11,12],[1,5,6,9,10,14],[1,5,6,10,11,14],
  [1,5,8,9,10,11],[1,5,8,9,11,12],[1,5,8,9,12,14],
  [1,5,8,12,13,14],[1,5,9,10,11,12],[1,5,9,12,13,14],
  [1,6,7,8,11,12],[1,6,7,10,11,14],[1,6,9,10,13,14],
  [1,8,9,11,12,14],[1,9,10,11,12,14],[1,9,10,12,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,12],[2,3,4,5,9,12],[2,3,4,5,9,13],
  [2,3,4,5,13,14],[2,3,4,7,8,11],[2,3,4,9,12,13],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,13],
  [2,3,5,6,13,14],[2,3,5,8,9,12],[2,3,6,7,8,13],
  [2,3,6,7,10,11],[2,3,6,7,11,12],[2,3,6,7,12,13],
  [2,3,6,8,9,13],[2,3,6,10,11,13],[2,3,6,10,13,14],
  [2,3,6,11,12,13],[2,3,7,8,11,12],[2,3,7,8,12,13],
  [2,3,7,10,11,14],[2,3,8,9,12,13],[2,3,10,11,13,14],
  [2,3,11,12,13,14],[2,4,5,9,12,13],[2,5,6,7,8,12],
  [2,5,6,8,9,12],[2,5,6,9,10,11],[2,5,6,9,11,12],
  [2,5,6,9,13,14],[2,5,9,10,11,12],[2,6,7,8,9,12],
  [2,6,7,8,9,13],[2,6,7,9,12,13],[2,6,9,10,11,12],
  [2,6,9,10,12,13],[2,6,10,11,12,13],[2,7,8,9,12,13],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,13],
  [3,4,5,6,10,13],[3,4,5,6,10,14],[3,4,5,8,9,12],
  [3,4,5,10,13,14],[3,4,6,7,8,9],[3,4,6,7,9,10],
  [3,4,6,7,10,14],[3,4,6,9,10,13],[3,4,7,8,9,14],
  [3,4,7,8,11,12],[3,4,7,8,12,13],[3,4,7,8,13,14],
  [3,4,7,9,10,14],[3,4,7,11,12,14],[3,4,7,12,13,14],
  [3,4,8,9,12,13],[3,4,8,9,13,14],[3,4,9,10,13,14],
  [3,5,6,10,13,14],[3,6,7,8,9,13],[3,6,7,9,10,13],
  [3,6,7,10,11,12],[3,6,7,10,12,13],[3,6,10,11,12,13],
  [3,7,8,9,10,13],[3,7,8,9,10,14],[3,7,8,10,13,14],
  [3,7,10,11,12,13],[3,7,10,11,13,14],
  [3,7,11,12,13,14],[3,8,9,10,13,14],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,14],[4,5,6,7,11,14],
  [4,5,6,9,10,13],[4,5,7,8,9,10],[4,5,7,8,10,11],
  [4,5,7,10,11,14],[4,5,8,9,12,13],[4,5,8,9,13,14],
  [4,5,9,10,13,14],[4,7,8,9,10,14],[4,7,8,10,11,14],
  [4,7,8,11,12,13],[4,7,8,11,13,14],[4,7,11,12,13,14],
  [4,8,9,10,11,14],[4,8,11,12,13,14],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,10,11,14],[5,6,8,9,10,11],
  [5,6,8,9,11,12],[5,6,9,10,13,14],[5,8,9,12,13,14],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[6,7,9,10,11,12],
  [6,7,9,10,12,13],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,10,11,12,13],[7,8,10,11,13,14],
  [8,9,10,11,12,13],[8,9,10,11,13,14],
  [8,9,11,12,13,14],[9,10,11,12,13,14]]

manifold_5_14_3_5=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,7,12],[1,2,3,4,12,13],
  [1,2,3,4,13,14],[1,2,3,5,6,14],[1,2,3,6,7,11],
  [1,2,3,6,11,14],[1,2,3,7,11,12],[1,2,3,11,12,14],
  [1,2,3,12,13,14],[1,2,4,5,6,7],[1,2,4,5,7,8],
  [1,2,4,5,8,12],[1,2,4,5,12,13],[1,2,4,5,13,14],
  [1,2,4,7,8,12],[1,2,5,6,7,11],[1,2,5,6,9,10],
  [1,2,5,6,9,12],[1,2,5,6,10,14],[1,2,5,6,11,12],
  [1,2,5,7,8,11],[1,2,5,8,11,12],[1,2,5,9,10,13],
  [1,2,5,9,12,13],[1,2,5,10,13,14],[1,2,6,9,10,12],
  [1,2,6,10,11,12],[1,2,6,10,11,14],[1,2,7,8,11,12],
  [1,2,9,10,12,13],[1,2,10,11,12,13],[1,2,10,11,13,14],
  [1,2,11,12,13,14],[1,3,4,5,6,14],[1,3,4,6,7,14],
  [1,3,4,7,11,12],[1,3,4,7,11,14],[1,3,4,11,12,14],
  [1,3,4,12,13,14],[1,3,6,7,11,14],[1,4,5,6,7,10],
  [1,4,5,6,10,14],[1,4,5,7,8,11],[1,4,5,7,10,11],
  [1,4,5,8,9,12],[1,4,5,8,9,14],[1,4,5,8,11,14],
  [1,4,5,9,12,13],[1,4,5,9,13,14],[1,4,5,10,11,14],
  [1,4,6,7,10,14],[1,4,7,8,11,12],[1,4,7,10,11,14],
  [1,4,8,9,12,14],[1,4,8,11,12,14],[1,4,9,12,13,14],
  [1,5,6,7,10,11],[1,5,6,9,10,11],[1,5,6,9,11,12],
  [1,5,8,9,11,12],[1,5,8,9,11,14],[1,5,9,10,11,14],
  [1,5,9,10,13,14],[1,6,7,10,11,14],[1,6,9,10,11,12],
  [1,8,9,11,12,14],[1,9,10,11,12,14],[1,9,10,12,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,13],[2,3,4,5,13,14],[2,3,4,7,8,12],
  [2,3,4,8,12,13],[2,3,5,6,7,8],[2,3,5,6,8,9],
  [2,3,5,6,9,13],[2,3,5,6,13,14],[2,3,5,8,9,13],
  [2,3,6,7,8,12],[2,3,6,7,10,11],[2,3,6,7,10,13],
  [2,3,6,7,12,13],[2,3,6,8,9,12],[2,3,6,9,12,13],
  [2,3,6,10,11,14],[2,3,6,10,13,14],[2,3,7,10,11,13],
  [2,3,7,11,12,13],[2,3,8,9,12,13],[2,3,10,11,13,14],
  [2,3,11,12,13,14],[2,4,5,8,12,13],[2,5,6,7,8,11],
  [2,5,6,8,9,12],[2,5,6,8,11,12],[2,5,6,9,10,13],
  [2,5,6,10,13,14],[2,5,8,9,12,13],[2,6,7,8,11,12],
  [2,6,7,10,11,12],[2,6,7,10,12,13],[2,6,9,10,12,13],
  [2,7,10,11,12,13],[3,4,5,6,7,8],[3,4,5,6,8,9],
  [3,4,5,6,9,14],[3,4,5,8,9,13],[3,4,5,9,13,14],
  [3,4,6,7,8,9],[3,4,6,7,9,10],[3,4,6,7,10,14],
  [3,4,6,9,10,14],[3,4,7,8,9,13],[3,4,7,8,11,12],
  [3,4,7,8,11,14],[3,4,7,8,13,14],[3,4,7,9,10,13],
  [3,4,7,10,13,14],[3,4,8,11,12,14],[3,4,8,12,13,14],
  [3,4,9,10,13,14],[3,5,6,9,13,14],[3,6,7,8,9,12],
  [3,6,7,9,10,13],[3,6,7,9,12,13],[3,6,7,10,11,14],
  [3,6,9,10,13,14],[3,7,8,9,12,13],[3,7,8,11,12,13],
  [3,7,8,11,13,14],[3,7,10,11,13,14],[3,8,11,12,13,14],
  [4,5,6,7,8,9],[4,5,6,7,9,10],[4,5,6,9,10,14],
  [4,5,7,8,9,10],[4,5,7,8,10,11],[4,5,8,9,10,14],
  [4,5,8,9,12,13],[4,5,8,10,11,14],[4,7,8,9,10,13],
  [4,7,8,10,11,14],[4,7,8,10,13,14],[4,8,9,10,13,14],
  [4,8,9,12,13,14],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,8,9,10,11],[5,6,8,9,11,12],[5,6,9,10,13,14],
  [5,8,9,10,11,14],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,9,10,11,12],[6,7,9,10,12,13],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[7,8,10,11,12,13],[7,8,10,11,13,14],
  [8,9,10,11,12,13],[8,9,10,11,13,14],
  [8,9,11,12,13,14],[9,10,11,12,13,14]]

manifold_5_14_3_6=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,8],[1,2,3,4,8,9],[1,2,3,4,9,10],
  [1,2,3,4,10,11],[1,2,3,4,11,13],[1,2,3,4,13,14],
  [1,2,3,5,6,7],[1,2,3,5,7,14],[1,2,3,6,7,8],
  [1,2,3,7,8,14],[1,2,3,8,9,14],[1,2,3,9,10,14],
  [1,2,3,10,11,12],[1,2,3,10,12,14],[1,2,3,11,12,13],
  [1,2,3,12,13,14],[1,2,4,5,6,14],[1,2,4,6,7,9],
  [1,2,4,6,7,13],[1,2,4,6,8,9],[1,2,4,6,13,14],
  [1,2,4,7,9,10],[1,2,4,7,10,13],[1,2,4,10,11,13],
  [1,2,5,6,7,14],[1,2,6,7,8,9],[1,2,6,7,13,14],
  [1,2,7,8,9,10],[1,2,7,8,10,13],[1,2,7,8,13,14],
  [1,2,8,9,10,11],[1,2,8,9,11,13],[1,2,8,9,13,14],
  [1,2,8,10,11,13],[1,2,9,10,11,14],[1,2,9,11,13,14],
  [1,2,10,11,12,14],[1,2,11,12,13,14],[1,3,4,5,6,13],
  [1,3,4,5,13,14],[1,3,4,6,8,9],[1,3,4,6,9,12],
  [1,3,4,6,12,13],[1,3,4,9,10,12],[1,3,4,10,11,13],
  [1,3,4,10,12,13],[1,3,5,6,7,8],[1,3,5,6,8,14],
  [1,3,5,6,12,13],[1,3,5,6,12,14],[1,3,5,7,8,14],
  [1,3,5,12,13,14],[1,3,6,8,9,14],[1,3,6,9,12,14],
  [1,3,9,10,12,14],[1,3,10,11,12,13],[1,4,5,6,13,14],
  [1,4,6,7,9,12],[1,4,6,7,12,13],[1,4,7,9,10,12],
  [1,4,7,10,12,13],[1,5,6,7,8,14],[1,5,6,12,13,14],
  [1,6,7,8,9,14],[1,6,7,9,12,14],[1,6,7,12,13,14],
  [1,7,8,9,10,14],[1,7,8,10,12,13],[1,7,8,10,12,14],
  [1,7,8,12,13,14],[1,7,9,10,12,14],[1,8,9,10,11,13],
  [1,8,9,10,13,14],[1,8,10,12,13,14],[1,9,10,11,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,9],
  [2,3,4,5,9,10],[2,3,4,5,10,11],[2,3,4,5,11,12],
  [2,3,4,5,12,14],[2,3,4,6,7,8],[2,3,4,7,8,9],
  [2,3,4,11,12,13],[2,3,4,12,13,14],[2,3,5,7,8,10],
  [2,3,5,7,8,14],[2,3,5,7,9,10],[2,3,5,8,10,11],
  [2,3,5,8,11,14],[2,3,5,11,12,14],[2,3,7,8,9,10],
  [2,3,8,9,10,11],[2,3,8,9,11,14],[2,3,9,10,11,12],
  [2,3,9,10,12,14],[2,3,9,11,12,14],[2,4,5,6,7,14],
  [2,4,5,7,9,10],[2,4,5,7,10,13],[2,4,5,7,13,14],
  [2,4,5,10,11,13],[2,4,5,11,12,14],[2,4,5,11,13,14],
  [2,4,6,7,8,9],[2,4,6,7,13,14],[2,4,11,12,13,14],
  [2,5,7,8,10,13],[2,5,7,8,13,14],[2,5,8,10,11,13],
  [2,5,8,11,13,14],[2,8,9,11,13,14],[2,9,10,11,12,14],
  [3,4,5,6,7,8],[3,4,5,6,8,10],[3,4,5,6,10,11],
  [3,4,5,6,11,12],[3,4,5,6,12,13],[3,4,5,7,8,9],
  [3,4,5,8,9,10],[3,4,5,12,13,14],[3,4,6,8,9,11],
  [3,4,6,8,10,11],[3,4,6,9,11,12],[3,4,8,9,10,11],
  [3,4,9,10,11,12],[3,4,10,11,12,13],[3,5,6,8,10,11],
  [3,5,6,8,11,14],[3,5,6,11,12,14],[3,5,7,8,9,10],
  [3,6,8,9,11,14],[3,6,9,11,12,14],[4,5,6,7,8,9],
  [4,5,6,7,9,11],[4,5,6,7,11,12],[4,5,6,7,12,13],
  [4,5,6,7,13,14],[4,5,6,8,9,10],[4,5,6,9,10,11],
  [4,5,7,9,10,12],[4,5,7,9,11,12],[4,5,7,10,12,13],
  [4,5,9,10,11,12],[4,5,10,11,12,13],[4,5,11,12,13,14],
  [4,6,7,9,11,12],[4,6,8,9,10,11],[5,6,7,8,9,10],
  [5,6,7,8,10,12],[5,6,7,8,12,13],[5,6,7,8,13,14],
  [5,6,7,9,10,11],[5,6,7,10,11,12],[5,6,8,10,11,13],
  [5,6,8,10,12,13],[5,6,8,11,13,14],[5,6,10,11,12,13],
  [5,6,11,12,13,14],[5,7,8,10,12,13],[5,7,9,10,11,12],
  [6,7,8,9,10,11],[6,7,8,9,11,13],[6,7,8,9,13,14],
  [6,7,8,10,11,12],[6,7,8,11,12,13],[6,7,9,11,12,14],
  [6,7,9,11,13,14],[6,7,11,12,13,14],[6,8,9,11,13,14],
  [6,8,10,11,12,13],[7,8,9,10,11,12],[7,8,9,10,12,14],
  [7,8,9,11,12,13],[7,8,9,12,13,14],[7,9,11,12,13,14],
  [8,9,10,11,12,13],[8,9,10,12,13,14],
  [9,10,11,12,13,14]]

manifold_5_14_3_7=[[1,2,3,4,5,6],[1,2,3,4,5,14],
  [1,2,3,4,6,9],[1,2,3,4,9,10],[1,2,3,4,10,13],
  [1,2,3,4,13,14],[1,2,3,5,6,7],[1,2,3,5,7,8],
  [1,2,3,5,8,14],[1,2,3,6,7,8],[1,2,3,6,8,9],
  [1,2,3,8,9,14],[1,2,3,9,10,12],[1,2,3,9,12,14],
  [1,2,3,10,11,12],[1,2,3,10,11,13],[1,2,3,11,12,13],
  [1,2,3,12,13,14],[1,2,4,5,6,14],[1,2,4,6,7,8],
  [1,2,4,6,7,14],[1,2,4,6,8,9],[1,2,4,7,8,9],
  [1,2,4,7,9,10],[1,2,4,7,10,13],[1,2,4,7,13,14],
  [1,2,5,6,7,14],[1,2,5,7,8,14],[1,2,7,8,9,10],
  [1,2,7,8,10,13],[1,2,7,8,13,14],[1,2,8,9,10,13],
  [1,2,8,9,11,13],[1,2,8,9,11,14],[1,2,8,11,13,14],
  [1,2,9,10,11,13],[1,2,9,10,11,14],[1,2,9,10,12,14],
  [1,2,10,11,12,14],[1,2,11,12,13,14],[1,3,4,5,6,12],
  [1,3,4,5,12,13],[1,3,4,5,13,14],[1,3,4,6,9,12],
  [1,3,4,9,10,12],[1,3,4,10,11,12],[1,3,4,10,11,13],
  [1,3,4,11,12,13],[1,3,5,6,7,14],[1,3,5,6,12,13],
  [1,3,5,6,13,14],[1,3,5,7,8,14],[1,3,6,7,8,14],
  [1,3,6,8,9,14],[1,3,6,9,12,14],[1,3,6,12,13,14],
  [1,4,5,6,12,13],[1,4,5,6,13,14],[1,4,6,7,8,9],
  [1,4,6,7,9,12],[1,4,6,7,12,13],[1,4,6,7,13,14],
  [1,4,7,9,10,12],[1,4,7,10,12,13],[1,4,10,11,12,13],
  [1,6,7,8,9,14],[1,6,7,9,12,14],[1,6,7,12,13,14],
  [1,7,8,9,10,12],[1,7,8,9,12,14],[1,7,8,10,12,14],
  [1,7,8,10,13,14],[1,7,10,12,13,14],[1,8,9,10,12,14],
  [1,8,9,10,13,14],[1,8,9,11,13,14],[1,9,10,11,13,14],
  [1,10,11,12,13,14],[2,3,4,5,6,7],[2,3,4,5,7,10],
  [2,3,4,5,10,11],[2,3,4,5,11,14],[2,3,4,6,7,8],
  [2,3,4,6,8,9],[2,3,4,7,8,9],[2,3,4,7,9,10],
  [2,3,4,10,11,13],[2,3,4,11,12,13],[2,3,4,11,12,14],
  [2,3,4,12,13,14],[2,3,5,7,8,9],[2,3,5,7,9,10],
  [2,3,5,8,9,10],[2,3,5,8,10,11],[2,3,5,8,11,14],
  [2,3,8,9,10,11],[2,3,8,9,11,14],[2,3,9,10,11,14],
  [2,3,9,10,12,14],[2,3,10,11,12,14],[2,4,5,6,7,13],
  [2,4,5,6,13,14],[2,4,5,7,10,13],[2,4,5,10,11,13],
  [2,4,5,11,12,13],[2,4,5,11,12,14],[2,4,5,12,13,14],
  [2,4,6,7,13,14],[2,5,6,7,13,14],[2,5,7,8,9,10],
  [2,5,7,8,10,13],[2,5,7,8,13,14],[2,5,8,10,11,13],
  [2,5,8,11,13,14],[2,5,11,12,13,14],[2,8,9,10,11,13],
  [3,4,5,6,7,8],[3,4,5,6,8,11],[3,4,5,6,11,12],
  [3,4,5,7,8,9],[3,4,5,7,9,10],[3,4,5,8,9,10],
  [3,4,5,8,10,11],[3,4,5,11,12,14],[3,4,5,12,13,14],
  [3,4,6,8,9,10],[3,4,6,8,10,11],[3,4,6,9,10,11],
  [3,4,6,9,11,12],[3,4,9,10,11,12],[3,5,6,7,8,14],
  [3,5,6,8,11,14],[3,5,6,11,12,14],[3,5,6,12,13,14],
  [3,6,8,9,10,11],[3,6,8,9,11,14],[3,6,9,11,12,14],
  [3,9,10,11,12,14],[4,5,6,7,8,9],[4,5,6,7,9,12],
  [4,5,6,7,12,13],[4,5,6,8,9,10],[4,5,6,8,10,11],
  [4,5,6,9,10,11],[4,5,6,9,11,12],[4,5,7,9,10,11],
  [4,5,7,9,11,12],[4,5,7,10,11,12],[4,5,7,10,12,13],
  [4,5,10,11,12,13],[4,7,9,10,11,12],[5,6,7,8,9,10],
  [5,6,7,8,10,13],[5,6,7,8,13,14],[5,6,7,9,10,11],
  [5,6,7,9,11,12],[5,6,7,10,11,12],[5,6,7,10,12,13],
  [5,6,8,10,11,12],[5,6,8,10,12,13],[5,6,8,11,12,13],
  [5,6,8,11,13,14],[5,6,11,12,13,14],[5,8,10,11,12,13],
  [6,7,8,9,10,11],[6,7,8,9,11,14],[6,7,8,10,11,12],
  [6,7,8,10,12,13],[6,7,8,11,12,13],[6,7,8,11,13,14],
  [6,7,9,11,12,13],[6,7,9,11,13,14],[6,7,9,12,13,14],
  [6,9,11,12,13,14],[7,8,9,10,11,12],[7,8,9,11,12,13],
  [7,8,9,11,13,14],[7,8,9,12,13,14],[7,8,10,12,13,14],
  [8,9,10,11,12,13],[8,9,10,12,13,14],
  [9,10,11,12,13,14]]

manifold_5_14_3_8=[[1,2,3,4,5,7],[1,2,3,4,5,13],
  [1,2,3,4,6,7],[1,2,3,4,6,14],[1,2,3,4,12,13],
  [1,2,3,4,12,14],[1,2,3,5,6,7],[1,2,3,5,6,14],
  [1,2,3,5,13,14],[1,2,3,11,12,13],[1,2,3,11,12,14],
  [1,2,3,11,13,14],[1,2,4,5,6,7],[1,2,4,5,6,14],
  [1,2,4,5,13,14],[1,2,4,12,13,14],[1,2,10,11,12,13],
  [1,2,10,11,12,14],[1,2,10,11,13,14],
  [1,2,10,12,13,14],[1,3,4,5,6,7],[1,3,4,5,6,14],
  [1,3,4,5,13,14],[1,3,4,12,13,14],[1,3,11,12,13,14],
  [1,9,10,11,12,13],[1,9,10,11,12,14],
  [1,9,10,11,13,14],[1,9,10,12,13,14],
  [1,9,11,12,13,14],[2,3,4,5,6,8],[2,3,4,5,6,14],
  [2,3,4,5,7,8],[2,3,4,5,13,14],[2,3,4,6,7,8],
  [2,3,4,12,13,14],[2,3,5,6,7,8],[2,3,11,12,13,14],
  [2,4,5,6,7,8],[2,10,11,12,13,14],[3,4,5,6,7,9],
  [3,4,5,6,8,9],[3,4,5,7,8,9],[3,4,6,7,8,9],
  [3,5,6,7,8,9],[4,5,6,7,8,10],[4,5,6,7,9,10],
  [4,5,6,8,9,10],[4,5,7,8,9,10],[4,6,7,8,9,10],
  [5,6,7,8,9,11],[5,6,7,8,10,11],[5,6,7,9,10,11],
  [5,6,8,9,10,11],[5,7,8,9,10,11],[6,7,8,9,10,12],
  [6,7,8,9,11,12],[6,7,8,10,11,12],[6,7,9,10,11,12],
  [6,8,9,10,11,12],[7,8,9,10,11,13],[7,8,9,10,12,13],
  [7,8,9,11,12,13],[7,8,10,11,12,13],[7,9,10,11,12,13],
  [8,9,10,11,12,14],[8,9,10,11,13,14],
  [8,9,10,12,13,14],[8,9,11,12,13,14],
  [8,10,11,12,13,14]]

manifold_5_14_3_9=[[1,2,3,4,6,7],[1,2,3,4,6,12],
  [1,2,3,4,7,13],[1,2,3,4,12,13],[1,2,3,5,6,7],
  [1,2,3,5,6,14],[1,2,3,5,7,11],[1,2,3,5,11,14],
  [1,2,3,6,12,14],[1,2,3,7,11,13],[1,2,3,11,12,13],
  [1,2,3,11,12,14],[1,2,4,5,6,7],[1,2,4,5,6,14],
  [1,2,4,5,7,13],[1,2,4,5,13,14],[1,2,4,6,10,12],
  [1,2,4,6,10,14],[1,2,4,10,12,13],[1,2,4,10,13,14],
  [1,2,5,7,11,13],[1,2,5,11,13,14],[1,2,6,10,12,14],
  [1,2,10,11,12,13],[1,2,10,11,12,14],
  [1,2,10,11,13,14],[1,3,4,5,6,9],[1,3,4,5,6,14],
  [1,3,4,5,9,13],[1,3,4,5,13,14],[1,3,4,6,7,9],
  [1,3,4,6,12,14],[1,3,4,7,9,13],[1,3,4,12,13,14],
  [1,3,5,6,7,11],[1,3,5,6,9,11],[1,3,5,9,11,14],
  [1,3,5,9,13,14],[1,3,6,7,9,11],[1,3,7,9,11,12],
  [1,3,7,9,12,13],[1,3,7,11,12,13],[1,3,9,11,12,14],
  [1,3,9,12,13,14],[1,4,5,6,7,9],[1,4,5,7,9,13],
  [1,4,6,10,12,14],[1,4,10,12,13,14],[1,5,6,7,9,11],
  [1,5,7,9,10,11],[1,5,7,9,10,13],[1,5,7,10,11,13],
  [1,5,9,10,11,13],[1,5,9,11,13,14],[1,7,9,10,11,12],
  [1,7,9,10,12,13],[1,7,10,11,12,13],[1,9,10,11,12,14],
  [1,9,10,11,13,14],[1,9,10,12,13,14],[2,3,4,5,7,8],
  [2,3,4,5,7,13],[2,3,4,5,8,14],[2,3,4,5,13,14],
  [2,3,4,6,7,8],[2,3,4,6,8,12],[2,3,4,8,12,14],
  [2,3,4,12,13,14],[2,3,5,6,7,8],[2,3,5,6,8,14],
  [2,3,5,7,11,13],[2,3,5,11,13,14],[2,3,6,8,12,14],
  [2,3,11,12,13,14],[2,4,5,6,7,10],[2,4,5,6,10,14],
  [2,4,5,7,8,10],[2,4,5,8,10,14],[2,4,6,7,8,12],
  [2,4,6,7,10,12],[2,4,7,8,10,12],[2,4,8,10,12,13],
  [2,4,8,10,13,14],[2,4,8,12,13,14],[2,5,6,7,8,10],
  [2,5,6,8,10,14],[2,6,7,8,10,12],[2,6,8,10,11,12],
  [2,6,8,10,11,14],[2,6,8,11,12,14],[2,6,10,11,12,14],
  [2,8,10,11,12,13],[2,8,10,11,13,14],
  [2,8,11,12,13,14],[3,4,5,6,8,9],[3,4,5,6,8,14],
  [3,4,5,7,8,9],[3,4,5,7,9,13],[3,4,6,7,8,9],
  [3,4,6,8,12,14],[3,5,6,7,8,11],[3,5,6,8,9,11],
  [3,5,7,8,9,13],[3,5,7,8,11,13],[3,5,8,9,11,13],
  [3,5,9,11,13,14],[3,6,7,8,9,11],[3,7,8,9,11,13],
  [3,7,9,11,12,13],[3,9,11,12,13,14],[4,5,6,7,9,10],
  [4,5,6,8,9,10],[4,5,6,8,10,14],[4,5,7,8,9,10],
  [4,6,7,8,9,12],[4,6,7,9,10,12],[4,6,8,9,10,14],
  [4,6,8,9,12,14],[4,6,9,10,12,14],[4,7,8,9,10,12],
  [4,8,9,10,12,14],[4,8,10,12,13,14],[5,6,7,8,10,11],
  [5,6,7,9,10,11],[5,6,8,9,10,11],[5,7,8,9,10,13],
  [5,7,8,10,11,13],[5,8,9,10,11,13],[6,7,8,9,11,12],
  [6,7,8,10,11,12],[6,7,9,10,11,12],[6,8,9,10,11,14],
  [6,8,9,11,12,14],[6,9,10,11,12,14],[7,8,9,10,12,13],
  [7,8,9,11,12,13],[7,8,10,11,12,13],[8,9,10,11,13,14],
  [8,9,10,12,13,14],[8,9,11,12,13,14]]

manifold_5_14_3_10=[[1,2,3,4,8,9],[1,2,3,4,8,10],
  [1,2,3,4,9,11],[1,2,3,4,10,11],[1,2,3,7,8,9],
  [1,2,3,7,8,14],[1,2,3,7,9,14],[1,2,3,8,10,14],
  [1,2,3,9,10,11],[1,2,3,9,10,14],[1,2,4,8,9,11],
  [1,2,4,8,10,11],[1,2,6,7,8,9],[1,2,6,7,8,14],
  [1,2,6,7,9,13],[1,2,6,7,13,14],[1,2,6,8,9,13],
  [1,2,6,8,13,14],[1,2,7,9,13,14],[1,2,8,9,10,11],
  [1,2,8,9,10,14],[1,2,8,9,13,14],[1,3,4,8,9,11],
  [1,3,4,8,10,11],[1,3,7,8,9,10],[1,3,7,8,10,14],
  [1,3,7,9,10,14],[1,3,8,9,10,11],[1,5,6,7,8,13],
  [1,5,6,7,8,14],[1,5,6,7,13,14],[1,5,6,8,12,13],
  [1,5,6,8,12,14],[1,5,6,12,13,14],[1,5,7,8,12,13],
  [1,5,7,8,12,14],[1,5,7,12,13,14],[1,6,7,8,9,13],
  [1,6,8,12,13,14],[1,7,8,9,10,14],[1,7,8,9,13,14],
  [1,7,8,12,13,14],[2,3,4,5,9,10],[2,3,4,5,9,11],
  [2,3,4,5,10,12],[2,3,4,5,11,12],[2,3,4,8,9,10],
  [2,3,4,10,11,12],[2,3,5,9,10,12],[2,3,5,9,11,12],
  [2,3,7,8,9,10],[2,3,7,8,10,14],[2,3,7,9,10,14],
  [2,3,9,10,11,12],[2,4,5,9,10,12],[2,4,5,9,11,12],
  [2,4,8,9,10,11],[2,4,9,10,11,12],[2,6,7,8,9,14],
  [2,6,7,9,13,14],[2,6,8,9,13,14],[2,7,8,9,10,14],
  [3,4,5,6,10,11],[3,4,5,6,10,12],[3,4,5,6,11,13],
  [3,4,5,6,12,13],[3,4,5,9,10,11],[3,4,5,11,12,13],
  [3,4,6,10,11,13],[3,4,6,10,12,13],[3,4,8,9,10,11],
  [3,4,10,11,12,13],[3,5,6,10,11,13],[3,5,6,10,12,13],
  [3,5,9,10,11,12],[3,5,10,11,12,13],[4,5,6,7,11,12],
  [4,5,6,7,11,13],[4,5,6,7,12,14],[4,5,6,7,13,14],
  [4,5,6,10,11,12],[4,5,6,12,13,14],[4,5,7,11,12,14],
  [4,5,7,11,13,14],[4,5,9,10,11,12],[4,5,11,12,13,14],
  [4,6,7,11,12,14],[4,6,7,11,13,14],[4,6,10,11,12,13],
  [4,6,11,12,13,14],[5,6,7,8,12,13],[5,6,7,8,12,14],
  [5,6,7,11,12,13],[5,6,10,11,12,13],[5,7,11,12,13,14],
  [6,7,8,9,13,14],[6,7,8,12,13,14],[6,7,11,12,13,14]]

manifold_5_14_3_11=[[1,2,3,4,8,9],[1,2,3,4,8,11],
  [1,2,3,4,9,10],[1,2,3,4,10,11],[1,2,3,7,8,10],
  [1,2,3,7,8,14],[1,2,3,7,10,14],[1,2,3,8,9,14],
  [1,2,3,8,10,11],[1,2,3,9,10,14],[1,2,4,8,9,11],
  [1,2,4,9,10,11],[1,2,6,7,8,9],[1,2,6,7,8,13],
  [1,2,6,7,9,14],[1,2,6,7,13,14],[1,2,6,8,9,13],
  [1,2,6,9,13,14],[1,2,7,8,9,10],[1,2,7,8,13,14],
  [1,2,7,9,10,14],[1,2,8,9,10,11],[1,2,8,9,13,14],
  [1,3,4,8,9,10],[1,3,4,8,10,11],[1,3,7,8,10,14],
  [1,3,8,9,10,14],[1,4,8,9,10,11],[1,5,6,7,8,12],
  [1,5,6,7,8,14],[1,5,6,7,12,14],[1,5,6,8,12,13],
  [1,5,6,8,13,14],[1,5,6,12,13,14],[1,5,7,8,12,14],
  [1,5,8,12,13,14],[1,6,7,8,9,14],[1,6,7,8,12,13],
  [1,6,7,12,13,14],[1,6,8,9,13,14],[1,7,8,9,10,14],
  [1,7,8,12,13,14],[2,3,4,5,9,10],[2,3,4,5,9,12],
  [2,3,4,5,10,11],[2,3,4,5,11,12],[2,3,4,8,9,11],
  [2,3,4,9,11,12],[2,3,5,9,10,12],[2,3,5,10,11,12],
  [2,3,7,8,9,10],[2,3,7,8,9,14],[2,3,7,9,10,14],
  [2,3,8,9,10,11],[2,3,9,10,11,12],[2,4,5,9,10,11],
  [2,4,5,9,11,12],[2,5,9,10,11,12],[2,6,7,8,9,13],
  [2,6,7,9,13,14],[2,7,8,9,13,14],[3,4,5,6,10,11],
  [3,4,5,6,10,13],[3,4,5,6,11,12],[3,4,5,6,12,13],
  [3,4,5,9,10,12],[3,4,5,10,12,13],[3,4,6,10,11,13],
  [3,4,6,11,12,13],[3,4,8,9,10,11],[3,4,9,10,11,12],
  [3,4,10,11,12,13],[3,5,6,10,11,12],[3,5,6,10,12,13],
  [3,6,10,11,12,13],[3,7,8,9,10,14],[4,5,6,7,11,12],
  [4,5,6,7,11,14],[4,5,6,7,12,13],[4,5,6,7,13,14],
  [4,5,6,10,11,13],[4,5,6,11,13,14],[4,5,7,11,12,14],
  [4,5,7,12,13,14],[4,5,9,10,11,12],[4,5,10,11,12,13],
  [4,5,11,12,13,14],[4,6,7,11,12,13],[4,6,7,11,13,14],
  [4,7,11,12,13,14],[5,6,7,8,12,13],[5,6,7,8,13,14],
  [5,6,7,11,12,14],[5,6,10,11,12,13],[5,6,11,12,13,14],
  [5,7,8,12,13,14],[6,7,8,9,13,14],[6,7,11,12,13,14]]

manifold_5_14_3_12=[[1,2,3,4,8,10],[1,2,3,4,8,11],
  [1,2,3,4,9,10],[1,2,3,4,9,11],[1,2,3,7,9,10],
  [1,2,3,7,9,14],[1,2,3,7,10,14],[1,2,3,8,9,11],
  [1,2,3,8,9,14],[1,2,3,8,10,14],[1,2,4,8,9,10],
  [1,2,4,8,9,11],[1,2,6,8,9,13],[1,2,6,8,9,14],
  [1,2,6,8,13,14],[1,2,6,9,13,14],[1,2,7,8,9,10],
  [1,2,7,8,9,13],[1,2,7,8,10,14],[1,2,7,8,13,14],
  [1,2,7,9,13,14],[1,3,4,8,10,11],[1,3,4,9,10,11],
  [1,3,7,8,9,10],[1,3,7,8,9,14],[1,3,7,8,10,14],
  [1,3,8,9,10,11],[1,4,8,9,10,11],[1,5,6,7,8,12],
  [1,5,6,7,8,13],[1,5,6,7,12,13],[1,5,6,8,12,13],
  [1,5,7,8,12,14],[1,5,7,8,13,14],[1,5,7,12,13,14],
  [1,5,8,12,13,14],[1,6,7,8,9,13],[1,6,7,8,9,14],
  [1,6,7,8,12,14],[1,6,7,9,13,14],[1,6,7,12,13,14],
  [1,6,8,12,13,14],[2,3,4,5,9,11],[2,3,4,5,9,12],
  [2,3,4,5,10,11],[2,3,4,5,10,12],[2,3,4,8,10,11],
  [2,3,4,9,10,12],[2,3,5,9,10,11],[2,3,5,9,10,12],
  [2,3,7,9,10,14],[2,3,8,9,10,11],[2,3,8,9,10,14],
  [2,4,5,9,11,12],[2,4,5,10,11,12],[2,4,8,9,10,11],
  [2,4,9,10,11,12],[2,5,9,10,11,12],[2,6,7,8,9,13],
  [2,6,7,8,9,14],[2,6,7,8,13,14],[2,6,7,9,13,14],
  [2,7,8,9,10,14],[3,4,5,6,10,12],[3,4,5,6,10,13],
  [3,4,5,6,11,12],[3,4,5,6,11,13],[3,4,5,9,11,12],
  [3,4,5,10,11,13],[3,4,6,10,11,12],[3,4,6,10,11,13],
  [3,4,9,10,11,12],[3,5,6,10,12,13],[3,5,6,11,12,13],
  [3,5,9,10,11,12],[3,5,10,11,12,13],[3,6,10,11,12,13],
  [3,7,8,9,10,14],[4,5,6,7,11,13],[4,5,6,7,11,14],
  [4,5,6,7,12,13],[4,5,6,7,12,14],[4,5,6,10,12,13],
  [4,5,6,11,12,14],[4,5,7,11,12,13],[4,5,7,11,12,14],
  [4,5,10,11,12,13],[4,6,7,11,13,14],[4,6,7,12,13,14],
  [4,6,10,11,12,13],[4,6,11,12,13,14],
  [4,7,11,12,13,14],[5,6,7,8,12,14],[5,6,7,8,13,14],
  [5,6,7,11,13,14],[5,6,8,12,13,14],[5,6,11,12,13,14],
  [5,7,11,12,13,14]]

manifold_5_14_3_13=[[1,2,3,5,6,7],[1,2,3,5,6,9],
  [1,2,3,5,7,13],[1,2,3,5,9,11],[1,2,3,5,11,13],
  [1,2,3,6,7,9],[1,2,3,7,9,13],[1,2,3,9,11,12],
  [1,2,3,9,12,13],[1,2,3,11,12,13],[1,2,4,5,6,12],
  [1,2,4,5,6,14],[1,2,4,5,8,9],[1,2,4,5,8,14],
  [1,2,4,5,9,11],[1,2,4,5,11,12],[1,2,4,6,12,14],
  [1,2,4,8,9,11],[1,2,4,8,10,11],[1,2,4,8,10,14],
  [1,2,4,10,11,12],[1,2,4,10,12,14],[1,2,5,6,7,13],
  [1,2,5,6,8,9],[1,2,5,6,8,14],[1,2,5,6,12,13],
  [1,2,5,11,12,13],[1,2,6,7,9,13],[1,2,6,8,9,13],
  [1,2,6,8,12,13],[1,2,6,8,12,14],[1,2,8,9,11,12],
  [1,2,8,9,12,13],[1,2,8,10,11,14],[1,2,8,11,12,14],
  [1,2,10,11,12,14],[1,3,4,5,7,9],[1,3,4,5,7,13],
  [1,3,4,5,9,11],[1,3,4,5,11,14],[1,3,4,5,13,14],
  [1,3,4,7,8,9],[1,3,4,7,8,14],[1,3,4,7,13,14],
  [1,3,4,8,9,11],[1,3,4,8,10,11],[1,3,4,8,10,14],
  [1,3,4,10,11,14],[1,3,5,6,7,9],[1,3,5,11,13,14],
  [1,3,7,8,9,11],[1,3,7,8,10,11],[1,3,7,8,10,14],
  [1,3,7,9,10,11],[1,3,7,9,10,14],[1,3,7,9,13,14],
  [1,3,9,10,11,14],[1,3,9,11,12,13],[1,3,9,11,13,14],
  [1,4,5,6,12,14],[1,4,5,7,8,9],[1,4,5,7,8,14],
  [1,4,5,7,13,14],[1,4,5,11,12,14],[1,4,10,11,12,14],
  [1,5,6,7,9,13],[1,5,6,8,9,13],[1,5,6,8,12,13],
  [1,5,6,8,12,14],[1,5,7,8,9,13],[1,5,7,8,12,13],
  [1,5,7,8,12,14],[1,5,7,11,12,13],[1,5,7,11,12,14],
  [1,5,7,11,13,14],[1,7,8,9,11,12],[1,7,8,9,12,13],
  [1,7,8,10,11,14],[1,7,8,11,12,14],[1,7,9,10,11,13],
  [1,7,9,10,13,14],[1,7,9,11,12,13],[1,7,10,11,13,14],
  [1,9,10,11,13,14],[2,3,4,6,7,8],[2,3,4,6,7,10],
  [2,3,4,6,8,14],[2,3,4,6,10,12],[2,3,4,6,12,14],
  [2,3,4,7,8,10],[2,3,4,8,10,14],[2,3,4,10,12,13],
  [2,3,4,10,13,14],[2,3,4,12,13,14],[2,3,5,6,7,13],
  [2,3,5,6,9,10],[2,3,5,6,10,12],[2,3,5,6,12,13],
  [2,3,5,9,10,12],[2,3,5,9,11,12],[2,3,5,11,12,13],
  [2,3,6,7,8,14],[2,3,6,7,9,10],[2,3,6,7,13,14],
  [2,3,6,12,13,14],[2,3,7,8,10,14],[2,3,7,9,10,14],
  [2,3,7,9,13,14],[2,3,9,10,12,13],[2,3,9,10,13,14],
  [2,4,5,6,8,10],[2,4,5,6,8,14],[2,4,5,6,10,12],
  [2,4,5,8,9,10],[2,4,5,9,10,12],[2,4,5,9,11,12],
  [2,4,6,7,8,10],[2,4,8,9,10,12],[2,4,8,9,11,12],
  [2,4,8,10,11,12],[2,4,10,12,13,14],[2,5,6,8,9,10],
  [2,6,7,8,10,14],[2,6,7,9,10,14],[2,6,7,9,13,14],
  [2,6,8,9,10,14],[2,6,8,9,13,14],[2,6,8,12,13,14],
  [2,8,9,10,12,13],[2,8,9,10,13,14],[2,8,10,11,12,14],
  [2,8,10,12,13,14],[3,4,5,7,8,9],[3,4,5,7,8,11],
  [3,4,5,7,11,13],[3,4,5,8,9,11],[3,4,5,11,13,14],
  [3,4,6,7,8,14],[3,4,6,7,10,11],[3,4,6,7,11,13],
  [3,4,6,7,13,14],[3,4,6,10,11,13],[3,4,6,10,12,13],
  [3,4,6,12,13,14],[3,4,7,8,10,11],[3,4,10,11,13,14],
  [3,5,6,7,9,11],[3,5,6,7,11,13],[3,5,6,9,10,11],
  [3,5,6,10,11,13],[3,5,6,10,12,13],[3,5,7,8,9,11],
  [3,5,9,10,11,13],[3,5,9,10,12,13],[3,5,9,11,12,13],
  [3,6,7,9,10,11],[3,9,10,11,13,14],[4,5,6,8,9,10],
  [4,5,6,8,9,12],[4,5,6,8,12,14],[4,5,6,9,10,12],
  [4,5,7,8,11,12],[4,5,7,8,12,14],[4,5,7,11,12,14],
  [4,5,7,11,13,14],[4,5,8,9,11,12],[4,6,7,8,10,12],
  [4,6,7,8,12,14],[4,6,7,10,11,12],[4,6,7,11,12,14],
  [4,6,7,11,13,14],[4,6,8,9,10,12],[4,6,10,11,12,14],
  [4,6,10,11,13,14],[4,6,10,12,13,14],[4,7,8,10,11,12],
  [5,6,7,9,10,11],[5,6,7,9,10,13],[5,6,7,10,11,13],
  [5,6,8,9,12,13],[5,6,9,10,12,13],[5,7,8,9,11,13],
  [5,7,8,11,12,13],[5,7,9,10,11,13],[5,8,9,11,12,13],
  [6,7,8,10,11,12],[6,7,8,10,11,14],[6,7,8,11,12,14],
  [6,7,9,10,13,14],[6,7,10,11,13,14],[6,8,9,10,12,14],
  [6,8,9,12,13,14],[6,8,10,11,12,14],[6,9,10,12,13,14],
  [7,8,9,11,12,13],[8,9,10,12,13,14]]

manifold_5_14_3_14=[[1,2,3,5,6,7],[1,2,3,5,6,12],
  [1,2,3,5,7,9],[1,2,3,5,9,11],[1,2,3,5,11,12],
  [1,2,3,6,7,13],[1,2,3,6,12,13],[1,2,3,7,9,13],
  [1,2,3,9,11,13],[1,2,3,11,12,13],[1,2,4,5,6,9],
  [1,2,4,5,6,14],[1,2,4,5,9,11],[1,2,4,5,11,14],
  [1,2,4,6,8,9],[1,2,4,6,8,14],[1,2,4,8,9,11],
  [1,2,4,8,10,11],[1,2,4,8,10,14],[1,2,4,10,11,14],
  [1,2,5,6,7,9],[1,2,5,6,12,14],[1,2,5,11,12,14],
  [1,2,6,7,9,13],[1,2,6,8,9,13],[1,2,6,8,12,13],
  [1,2,6,8,12,14],[1,2,8,9,11,13],[1,2,8,10,11,12],
  [1,2,8,10,12,14],[1,2,8,11,12,13],[1,2,10,11,12,14],
  [1,3,4,5,8,9],[1,3,4,5,8,14],[1,3,4,5,9,11],
  [1,3,4,5,11,13],[1,3,4,5,13,14],[1,3,4,8,9,11],
  [1,3,4,8,10,11],[1,3,4,8,10,14],[1,3,4,10,11,13],
  [1,3,4,10,13,14],[1,3,5,6,7,13],[1,3,5,6,12,13],
  [1,3,5,7,8,9],[1,3,5,7,8,14],[1,3,5,7,13,14],
  [1,3,5,11,12,13],[1,3,7,8,9,11],[1,3,7,8,10,11],
  [1,3,7,8,10,14],[1,3,7,9,10,11],[1,3,7,9,10,14],
  [1,3,7,9,13,14],[1,3,9,10,11,13],[1,3,9,10,13,14],
  [1,4,5,6,8,9],[1,4,5,6,8,14],[1,4,5,11,13,14],
  [1,4,10,11,13,14],[1,5,6,7,9,13],[1,5,6,8,9,13],
  [1,5,6,8,12,13],[1,5,6,8,12,14],[1,5,7,8,9,13],
  [1,5,7,8,12,13],[1,5,7,8,12,14],[1,5,7,11,12,13],
  [1,5,7,11,12,14],[1,5,7,11,13,14],[1,7,8,9,11,13],
  [1,7,8,10,11,12],[1,7,8,10,12,14],[1,7,8,11,12,13],
  [1,7,9,10,11,14],[1,7,9,11,13,14],[1,7,10,11,12,14],
  [1,9,10,11,13,14],[2,3,4,6,7,8],[2,3,4,6,7,13],
  [2,3,4,6,8,10],[2,3,4,6,10,12],[2,3,4,6,12,13],
  [2,3,4,7,8,14],[2,3,4,7,13,14],[2,3,4,8,10,14],
  [2,3,4,10,12,14],[2,3,4,12,13,14],[2,3,5,6,7,10],
  [2,3,5,6,10,12],[2,3,5,7,9,10],[2,3,5,9,10,12],
  [2,3,5,9,11,12],[2,3,6,7,8,10],[2,3,7,8,10,14],
  [2,3,7,9,10,14],[2,3,7,9,13,14],[2,3,9,10,12,14],
  [2,3,9,11,12,13],[2,3,9,12,13,14],[2,4,5,6,9,10],
  [2,4,5,6,10,12],[2,4,5,6,12,14],[2,4,5,9,10,12],
  [2,4,5,9,11,12],[2,4,5,11,12,14],[2,4,6,7,8,14],
  [2,4,6,7,13,14],[2,4,6,8,9,10],[2,4,6,12,13,14],
  [2,4,8,9,10,12],[2,4,8,9,11,12],[2,4,8,10,11,12],
  [2,4,10,11,12,14],[2,5,6,7,9,10],[2,6,7,8,10,14],
  [2,6,7,9,10,14],[2,6,7,9,13,14],[2,6,8,9,10,14],
  [2,6,8,9,13,14],[2,6,8,12,13,14],[2,8,9,10,12,14],
  [2,8,9,11,12,13],[2,8,9,12,13,14],[3,4,5,7,8,9],
  [3,4,5,7,8,14],[3,4,5,7,9,11],[3,4,5,7,11,13],
  [3,4,5,7,13,14],[3,4,6,7,8,11],[3,4,6,7,11,13],
  [3,4,6,8,10,11],[3,4,6,10,11,13],[3,4,6,10,12,13],
  [3,4,7,8,9,11],[3,4,10,12,13,14],[3,5,6,7,10,11],
  [3,5,6,7,11,13],[3,5,6,10,11,13],[3,5,6,10,12,13],
  [3,5,7,9,10,11],[3,5,9,10,11,13],[3,5,9,10,12,13],
  [3,5,9,11,12,13],[3,6,7,8,10,11],[3,9,10,12,13,14],
  [4,5,6,8,9,10],[4,5,6,8,10,12],[4,5,6,8,12,14],
  [4,5,7,8,9,12],[4,5,7,8,12,14],[4,5,7,9,11,12],
  [4,5,7,11,12,14],[4,5,7,11,13,14],[4,5,8,9,10,12],
  [4,6,7,8,11,12],[4,6,7,8,12,14],[4,6,7,11,12,14],
  [4,6,7,11,13,14],[4,6,8,10,11,12],[4,6,10,11,12,14],
  [4,6,10,11,13,14],[4,6,10,12,13,14],[4,7,8,9,11,12],
  [5,6,7,9,10,11],[5,6,7,9,11,13],[5,6,8,9,10,13],
  [5,6,8,10,12,13],[5,6,9,10,11,13],[5,7,8,9,12,13],
  [5,7,9,11,12,13],[5,8,9,10,12,13],[6,7,8,10,11,12],
  [6,7,8,10,12,14],[6,7,9,10,11,14],[6,7,9,11,13,14],
  [6,7,10,11,12,14],[6,8,9,10,13,14],[6,8,10,12,13,14],
  [6,9,10,11,13,14],[7,8,9,11,12,13],[8,9,10,12,13,14]
]

manifold_5_14_3_15=[[1,2,3,5,6,7],[1,2,3,5,6,13],
  [1,2,3,5,7,9],[1,2,3,5,9,11],[1,2,3,5,11,12],
  [1,2,3,5,12,13],[1,2,3,6,7,13],[1,2,3,7,9,13],
  [1,2,3,9,11,13],[1,2,3,11,12,13],[1,2,4,5,6,8],
  [1,2,4,5,6,14],[1,2,4,5,8,9],[1,2,4,5,9,11],
  [1,2,4,5,11,12],[1,2,4,5,12,14],[1,2,4,6,8,14],
  [1,2,4,8,9,11],[1,2,4,8,10,11],[1,2,4,8,10,14],
  [1,2,4,10,11,14],[1,2,4,11,12,14],[1,2,5,6,7,9],
  [1,2,5,6,8,9],[1,2,5,6,12,13],[1,2,5,6,12,14],
  [1,2,6,7,9,13],[1,2,6,8,9,13],[1,2,6,8,12,13],
  [1,2,6,8,12,14],[1,2,8,9,11,12],[1,2,8,9,12,13],
  [1,2,8,10,11,12],[1,2,8,10,12,14],[1,2,9,11,12,13],
  [1,2,10,11,12,14],[1,3,4,5,7,8],[1,3,4,5,7,14],
  [1,3,4,5,8,9],[1,3,4,5,9,11],[1,3,4,5,11,13],
  [1,3,4,5,13,14],[1,3,4,7,8,14],[1,3,4,8,9,11],
  [1,3,4,8,10,11],[1,3,4,8,10,14],[1,3,4,10,11,14],
  [1,3,4,11,13,14],[1,3,5,6,7,13],[1,3,5,7,8,9],
  [1,3,5,7,13,14],[1,3,5,11,12,13],[1,3,7,8,9,11],
  [1,3,7,8,10,11],[1,3,7,8,10,14],[1,3,7,9,10,11],
  [1,3,7,9,10,14],[1,3,7,9,13,14],[1,3,9,10,11,13],
  [1,3,9,10,13,14],[1,3,10,11,13,14],[1,4,5,6,8,14],
  [1,4,5,7,8,14],[1,4,5,11,12,14],[1,4,5,11,13,14],
  [1,5,6,7,9,13],[1,5,6,8,9,13],[1,5,6,8,12,13],
  [1,5,6,8,12,14],[1,5,7,8,9,13],[1,5,7,8,12,13],
  [1,5,7,8,12,14],[1,5,7,11,12,13],[1,5,7,11,12,14],
  [1,5,7,11,13,14],[1,7,8,9,11,13],[1,7,8,10,11,14],
  [1,7,8,11,12,13],[1,7,8,11,12,14],[1,7,9,10,11,14],
  [1,7,9,11,13,14],[1,8,9,11,12,13],[1,8,10,11,12,14],
  [1,9,10,11,13,14],[2,3,4,6,7,8],[2,3,4,6,7,14],
  [2,3,4,6,8,10],[2,3,4,6,10,12],[2,3,4,6,12,13],
  [2,3,4,6,13,14],[2,3,4,7,8,14],[2,3,4,8,10,14],
  [2,3,4,10,12,14],[2,3,4,12,13,14],[2,3,5,6,7,9],
  [2,3,5,6,9,10],[2,3,5,6,10,12],[2,3,5,6,12,13],
  [2,3,5,9,10,12],[2,3,5,9,11,12],[2,3,6,7,8,10],
  [2,3,6,7,9,10],[2,3,6,7,13,14],[2,3,7,8,10,14],
  [2,3,7,9,10,14],[2,3,7,9,13,14],[2,3,9,10,12,13],
  [2,3,9,10,13,14],[2,3,9,11,12,13],[2,3,10,12,13,14],
  [2,4,5,6,8,9],[2,4,5,6,9,10],[2,4,5,6,10,12],
  [2,4,5,6,12,14],[2,4,5,9,10,12],[2,4,5,9,11,12],
  [2,4,6,7,8,14],[2,4,6,8,9,10],[2,4,6,12,13,14],
  [2,4,8,9,10,12],[2,4,8,9,11,12],[2,4,8,10,11,12],
  [2,4,10,11,12,14],[2,6,7,8,10,14],[2,6,7,9,10,14],
  [2,6,7,9,13,14],[2,6,8,9,10,14],[2,6,8,9,13,14],
  [2,6,8,12,13,14],[2,8,9,10,12,14],[2,8,9,12,13,14],
  [2,9,10,12,13,14],[3,4,5,7,8,9],[3,4,5,7,9,11],
  [3,4,5,7,11,13],[3,4,5,7,13,14],[3,4,6,7,8,10],
  [3,4,6,7,10,11],[3,4,6,7,11,13],[3,4,6,7,13,14],
  [3,4,6,10,11,13],[3,4,6,10,12,13],[3,4,7,8,9,11],
  [3,4,7,8,10,11],[3,4,10,11,13,14],[3,4,10,12,13,14],
  [3,5,6,7,9,10],[3,5,6,7,10,11],[3,5,6,7,11,13],
  [3,5,6,10,11,13],[3,5,6,10,12,13],[3,5,7,9,10,11],
  [3,5,9,10,11,13],[3,5,9,10,12,13],[3,5,9,11,12,13],
  [4,5,6,8,9,10],[4,5,6,8,10,12],[4,5,6,8,12,14],
  [4,5,7,8,9,11],[4,5,7,8,11,12],[4,5,7,8,12,14],
  [4,5,7,11,12,14],[4,5,7,11,13,14],[4,5,8,9,10,12],
  [4,5,8,9,11,12],[4,6,7,8,10,11],[4,6,7,8,11,12],
  [4,6,7,8,12,14],[4,6,7,11,12,14],[4,6,7,11,13,14],
  [4,6,8,10,11,12],[4,6,10,11,12,14],[4,6,10,11,13,14],
  [4,6,10,12,13,14],[5,6,7,9,10,11],[5,6,7,9,11,13],
  [5,6,8,9,10,12],[5,6,8,9,12,13],[5,6,9,10,11,13],
  [5,6,9,10,12,13],[5,7,8,9,11,12],[5,7,8,9,12,13],
  [5,7,9,11,12,13],[6,7,8,10,11,12],[6,7,8,10,12,14],
  [6,7,9,10,11,13],[6,7,9,10,13,14],[6,7,10,11,12,14],
  [6,7,10,11,13,14],[6,8,9,10,12,13],[6,8,9,10,13,14],
  [6,8,10,12,13,14],[7,8,9,11,12,13],[7,8,10,11,12,14],
  [7,9,10,11,13,14],[8,9,10,12,13,14]]

manifold_5_14_3_16=[[1,2,3,7,8,9],[1,2,3,7,8,10],
  [1,2,3,7,9,10],[1,2,3,8,9,11],[1,2,3,8,10,11],
  [1,2,3,9,10,11],[1,2,4,8,9,10],[1,2,4,8,9,11],
  [1,2,4,8,10,11],[1,2,4,9,10,11],[1,2,6,7,8,13],
  [1,2,6,7,8,14],[1,2,6,7,9,13],[1,2,6,7,9,14],
  [1,2,6,8,9,13],[1,2,6,8,9,14],[1,2,7,8,9,13],
  [1,2,7,8,10,14],[1,2,7,9,10,14],[1,2,8,9,10,14],
  [1,3,4,8,9,10],[1,3,4,8,9,11],[1,3,4,8,10,11],
  [1,3,4,9,10,11],[1,3,7,8,9,14],[1,3,7,8,10,14],
  [1,3,7,9,10,14],[1,3,8,9,10,14],[1,5,6,7,12,13],
  [1,5,6,7,12,14],[1,5,6,7,13,14],[1,5,6,8,12,13],
  [1,5,6,8,12,14],[1,5,6,8,13,14],[1,5,7,8,12,13],
  [1,5,7,8,12,14],[1,5,7,8,13,14],[1,6,7,8,12,13],
  [1,6,7,8,12,14],[1,6,7,9,13,14],[1,6,8,9,13,14],
  [1,7,8,9,13,14],[2,3,4,8,9,10],[2,3,4,8,9,11],
  [2,3,4,8,10,11],[2,3,4,9,10,12],[2,3,4,9,11,12],
  [2,3,4,10,11,12],[2,3,5,9,10,11],[2,3,5,9,10,12],
  [2,3,5,9,11,12],[2,3,5,10,11,12],[2,3,7,8,9,14],
  [2,3,7,8,10,14],[2,3,7,9,10,14],[2,3,8,9,10,14],
  [2,4,5,9,10,11],[2,4,5,9,10,12],[2,4,5,9,11,12],
  [2,4,5,10,11,12],[2,6,7,8,13,14],[2,6,7,9,13,14],
  [2,6,8,9,13,14],[2,7,8,9,13,14],[3,4,5,9,10,11],
  [3,4,5,9,10,12],[3,4,5,9,11,12],[3,4,5,10,11,13],
  [3,4,5,10,12,13],[3,4,5,11,12,13],[3,4,6,10,11,12],
  [3,4,6,10,11,13],[3,4,6,10,12,13],[3,4,6,11,12,13],
  [3,5,6,10,11,12],[3,5,6,10,11,13],[3,5,6,10,12,13],
  [3,5,6,11,12,13],[4,5,6,10,11,12],[4,5,6,10,11,13],
  [4,5,6,10,12,13],[4,5,6,11,12,14],[4,5,6,11,13,14],
  [4,5,6,12,13,14],[4,5,7,11,12,13],[4,5,7,11,12,14],
  [4,5,7,11,13,14],[4,5,7,12,13,14],[4,6,7,11,12,13],
  [4,6,7,11,12,14],[4,6,7,11,13,14],[4,6,7,12,13,14],
  [5,6,7,11,12,13],[5,6,7,11,12,14],[5,6,7,11,13,14],
  [5,6,8,12,13,14],[5,7,8,12,13,14],[6,7,8,12,13,14]]

manifold_5_15_60_1=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,14],[1,2,3,4,14,15],[1,2,3,5,6,13],
  [1,2,3,5,13,15],[1,2,3,6,13,14],[1,2,3,13,14,15],
  [1,2,4,5,6,9],[1,2,4,5,9,12],[1,2,4,5,12,15],
  [1,2,4,6,9,14],[1,2,4,9,12,14],[1,2,4,12,14,15],
  [1,2,5,6,9,13],[1,2,5,9,12,13],[1,2,5,12,13,15],
  [1,2,6,9,13,14],[1,2,9,12,13,14],[1,2,12,13,14,15],
  [1,3,4,5,6,8],[1,3,4,5,8,15],[1,3,4,6,8,11],
  [1,3,4,6,11,14],[1,3,4,8,11,15],[1,3,4,11,14,15],
  [1,3,5,6,8,13],[1,3,5,8,13,15],[1,3,6,8,11,13],
  [1,3,6,11,13,14],[1,3,8,11,13,15],[1,3,11,13,14,15],
  [1,4,5,6,8,9],[1,4,5,8,9,12],[1,4,5,8,12,15],
  [1,4,6,8,9,11],[1,4,6,9,11,14],[1,4,8,9,11,12],
  [1,4,8,11,12,15],[1,4,9,11,12,14],[1,4,11,12,14,15],
  [1,5,6,8,9,13],[1,5,8,9,12,13],[1,5,8,12,13,15],
  [1,6,8,9,11,13],[1,6,9,11,13,14],[1,8,9,11,12,13],
  [1,8,11,12,13,15],[1,9,11,12,13,14],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,15],
  [2,3,4,6,7,14],[2,3,4,7,14,15],[2,3,5,6,7,10],
  [2,3,5,6,10,13],[2,3,5,7,10,15],[2,3,5,10,13,15],
  [2,3,6,7,10,14],[2,3,6,10,13,14],[2,3,7,10,14,15],
  [2,3,10,13,14,15],[2,4,5,6,7,9],[2,4,5,7,9,12],
  [2,4,5,7,12,15],[2,4,6,7,9,14],[2,4,7,9,12,14],
  [2,4,7,12,14,15],[2,5,6,7,9,10],[2,5,6,9,10,13],
  [2,5,7,9,10,12],[2,5,7,10,12,15],[2,5,9,10,12,13],
  [2,5,10,12,13,15],[2,6,7,9,10,14],[2,6,9,10,13,14],
  [2,7,9,10,12,14],[2,7,10,12,14,15],[2,9,10,12,13,14],
  [2,10,12,13,14,15],[3,4,5,6,7,8],[3,4,5,7,8,15],
  [3,4,6,7,8,11],[3,4,6,7,11,14],[3,4,7,8,11,15],
  [3,4,7,11,14,15],[3,5,6,7,8,10],[3,5,6,8,10,13],
  [3,5,7,8,10,15],[3,5,8,10,13,15],[3,6,7,8,10,11],
  [3,6,7,10,11,14],[3,6,8,10,11,13],[3,6,10,11,13,14],
  [3,7,8,10,11,15],[3,7,10,11,14,15],[3,8,10,11,13,15],
  [3,10,11,13,14,15],[4,5,6,7,8,9],[4,5,7,8,9,12],
  [4,5,7,8,12,15],[4,6,7,8,9,11],[4,6,7,9,11,14],
  [4,7,8,9,11,12],[4,7,8,11,12,15],[4,7,9,11,12,14],
  [4,7,11,12,14,15],[5,6,7,8,9,10],[5,6,8,9,10,13],
  [5,7,8,9,10,12],[5,7,8,10,12,15],[5,8,9,10,12,13],
  [5,8,10,12,13,15],[6,7,8,9,10,11],[6,7,9,10,11,14],
  [6,8,9,10,11,13],[6,9,10,11,13,14],[7,8,9,10,11,12],
  [7,8,10,11,12,15],[7,9,10,11,12,14],
  [7,10,11,12,14,15],[8,9,10,11,12,13],
  [8,10,11,12,13,15],[9,10,11,12,13,14],
  [10,11,12,13,14,15]]

manifold_5_15_7_1=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,12],
  [1,2,3,4,12,13],[1,2,3,4,13,14],[1,2,3,4,14,15],
  [1,2,3,5,6,15],[1,2,3,6,7,15],[1,2,3,7,8,12],
  [1,2,3,7,11,12],[1,2,3,7,11,15],[1,2,3,11,12,15],
  [1,2,3,12,13,15],[1,2,3,13,14,15],[1,2,4,5,6,7],
  [1,2,4,5,7,8],[1,2,4,5,8,13],[1,2,4,5,13,14],
  [1,2,4,5,14,15],[1,2,4,8,12,13],[1,2,5,6,7,8],
  [1,2,5,6,8,12],[1,2,5,6,9,12],[1,2,5,6,9,13],
  [1,2,5,6,10,13],[1,2,5,6,10,14],[1,2,5,6,14,15],
  [1,2,5,8,12,13],[1,2,5,9,12,13],[1,2,5,10,13,14],
  [1,2,6,7,8,12],[1,2,6,7,11,12],[1,2,6,7,11,15],
  [1,2,6,9,12,13],[1,2,6,10,11,12],[1,2,6,10,11,15],
  [1,2,6,10,12,13],[1,2,6,10,14,15],[1,2,10,11,12,13],
  [1,2,10,11,13,14],[1,2,10,11,14,15],
  [1,2,11,12,13,14],[1,2,11,12,14,15],
  [1,2,12,13,14,15],[1,3,4,5,6,15],[1,3,4,6,7,15],
  [1,3,4,7,8,12],[1,3,4,7,12,15],[1,3,4,12,13,15],
  [1,3,4,13,14,15],[1,3,7,11,12,15],[1,4,5,6,7,15],
  [1,4,5,7,8,11],[1,4,5,7,11,15],[1,4,5,8,9,12],
  [1,4,5,8,9,13],[1,4,5,8,11,15],[1,4,5,8,12,15],
  [1,4,5,9,12,15],[1,4,5,9,13,15],[1,4,5,13,14,15],
  [1,4,7,8,11,12],[1,4,7,11,12,15],[1,4,8,9,12,13],
  [1,4,8,11,12,15],[1,4,9,12,13,15],[1,5,6,7,8,12],
  [1,5,6,7,11,12],[1,5,6,7,11,15],[1,5,6,9,10,12],
  [1,5,6,9,10,13],[1,5,6,10,11,12],[1,5,6,10,11,15],
  [1,5,6,10,14,15],[1,5,7,8,11,12],[1,5,8,9,12,13],
  [1,5,8,11,12,15],[1,5,9,10,11,12],[1,5,9,10,11,15],
  [1,5,9,10,13,14],[1,5,9,10,14,15],[1,5,9,11,12,15],
  [1,5,9,13,14,15],[1,6,9,10,12,13],[1,9,10,11,12,15],
  [1,9,10,12,13,15],[1,9,10,13,14,15],
  [1,10,11,12,13,15],[1,10,11,13,14,15],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,13],[2,3,4,5,13,14],
  [2,3,4,5,14,15],[2,3,4,8,9,13],[2,3,4,8,12,13],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,14],
  [2,3,5,6,14,15],[2,3,5,9,13,14],[2,3,6,7,8,9],
  [2,3,6,7,9,13],[2,3,6,7,10,13],[2,3,6,7,10,14],
  [2,3,6,7,11,14],[2,3,6,7,11,15],[2,3,6,9,13,14],
  [2,3,6,10,13,14],[2,3,6,11,14,15],[2,3,7,8,9,13],
  [2,3,7,8,12,13],[2,3,7,10,13,14],[2,3,7,11,12,13],
  [2,3,7,11,13,14],[2,3,11,12,13,14],[2,3,11,12,14,15],
  [2,3,12,13,14,15],[2,4,5,8,9,13],[2,5,6,8,9,12],
  [2,5,6,9,10,13],[2,5,6,9,10,14],[2,5,8,9,12,13],
  [2,5,9,10,13,14],[2,6,7,8,9,13],[2,6,7,8,12,13],
  [2,6,7,10,11,13],[2,6,7,10,11,14],[2,6,7,11,12,13],
  [2,6,8,9,12,13],[2,6,9,10,13,14],[2,6,10,11,12,13],
  [2,6,10,11,14,15],[2,7,10,11,13,14],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,14],
  [3,4,5,6,14,15],[3,4,5,9,10,14],[3,4,5,9,13,14],
  [3,4,6,7,8,9],[3,4,6,7,9,10],[3,4,6,7,10,15],
  [3,4,6,10,14,15],[3,4,7,8,9,10],[3,4,7,8,10,14],
  [3,4,7,8,11,14],[3,4,7,8,11,15],[3,4,7,8,12,15],
  [3,4,7,10,14,15],[3,4,7,11,14,15],[3,4,8,9,10,14],
  [3,4,8,9,13,14],[3,4,8,11,14,15],[3,4,8,12,13,14],
  [3,4,8,12,14,15],[3,4,12,13,14,15],[3,5,6,9,10,14],
  [3,6,7,9,10,13],[3,6,7,10,11,14],[3,6,7,10,11,15],
  [3,6,9,10,13,14],[3,6,10,11,14,15],[3,7,8,9,10,14],
  [3,7,8,9,13,14],[3,7,8,11,12,14],[3,7,8,11,12,15],
  [3,7,8,12,13,14],[3,7,9,10,13,14],[3,7,10,11,14,15],
  [3,7,11,12,13,14],[3,8,11,12,14,15],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,6,7,11,15],
  [4,5,6,10,11,15],[4,5,6,10,14,15],[4,5,7,8,9,10],
  [4,5,7,8,10,11],[4,5,8,9,10,11],[4,5,8,9,11,15],
  [4,5,8,9,12,15],[4,5,9,10,11,15],[4,5,9,10,14,15],
  [4,5,9,13,14,15],[4,6,7,10,11,15],[4,7,8,10,11,14],
  [4,7,8,11,12,15],[4,7,10,11,14,15],[4,8,9,10,11,15],
  [4,8,9,10,14,15],[4,8,9,12,13,15],[4,8,9,13,14,15],
  [4,8,10,11,14,15],[4,8,12,13,14,15],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,8,11,12],[5,6,8,9,10,11],
  [5,6,8,9,11,12],[5,6,9,10,11,12],[5,8,9,11,12,15],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[6,7,8,9,12,13],
  [6,7,9,10,11,12],[6,7,9,10,12,13],[6,7,10,11,12,13],
  [7,8,9,10,11,12],[7,8,9,10,12,13],[7,8,9,10,13,14],
  [7,8,10,11,12,13],[7,8,10,11,13,14],
  [7,8,11,12,13,14],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,10,11,14,15],
  [8,9,11,12,13,14],[8,9,11,12,14,15],
  [8,9,12,13,14,15],[9,10,11,12,13,14],
  [9,10,11,12,14,15],[9,10,12,13,14,15],
  [10,11,12,13,14,15]]

manifold_5_15_7_2=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,7],[1,2,3,4,7,12],[1,2,3,4,8,12],
  [1,2,3,4,8,13],[1,2,3,4,13,14],[1,2,3,4,14,15],
  [1,2,3,5,6,15],[1,2,3,6,7,11],[1,2,3,6,11,15],
  [1,2,3,7,11,15],[1,2,3,7,12,15],[1,2,3,8,12,13],
  [1,2,3,12,13,15],[1,2,3,13,14,15],[1,2,4,5,6,7],
  [1,2,4,5,7,8],[1,2,4,5,8,13],[1,2,4,5,13,14],
  [1,2,4,5,14,15],[1,2,4,7,8,12],[1,2,5,6,7,12],
  [1,2,5,6,9,12],[1,2,5,6,9,13],[1,2,5,6,10,13],
  [1,2,5,6,10,15],[1,2,5,7,8,12],[1,2,5,8,12,13],
  [1,2,5,9,12,13],[1,2,5,10,13,14],[1,2,5,10,14,15],
  [1,2,6,7,11,12],[1,2,6,9,12,13],[1,2,6,10,11,13],
  [1,2,6,10,11,14],[1,2,6,10,14,15],[1,2,6,11,12,13],
  [1,2,6,11,14,15],[1,2,7,11,12,15],[1,2,10,11,13,14],
  [1,2,11,12,13,14],[1,2,11,12,14,15],
  [1,2,12,13,14,15],[1,3,4,5,6,15],[1,3,4,6,7,15],
  [1,3,4,7,12,15],[1,3,4,8,12,13],[1,3,4,12,13,15],
  [1,3,4,13,14,15],[1,3,6,7,11,15],[1,4,5,6,7,11],
  [1,4,5,6,11,15],[1,4,5,7,8,11],[1,4,5,8,9,12],
  [1,4,5,8,9,13],[1,4,5,8,11,15],[1,4,5,8,12,15],
  [1,4,5,9,12,15],[1,4,5,9,13,14],[1,4,5,9,14,15],
  [1,4,6,7,11,15],[1,4,7,8,11,12],[1,4,7,11,12,15],
  [1,4,8,9,12,13],[1,4,8,11,12,15],[1,4,9,12,13,15],
  [1,4,9,13,14,15],[1,5,6,7,8,11],[1,5,6,7,8,12],
  [1,5,6,8,11,12],[1,5,6,9,10,11],[1,5,6,9,10,13],
  [1,5,6,9,11,12],[1,5,6,10,11,15],[1,5,8,9,12,13],
  [1,5,8,11,12,15],[1,5,9,10,11,12],[1,5,9,10,12,15],
  [1,5,9,10,13,15],[1,5,9,13,14,15],[1,5,10,11,12,15],
  [1,5,10,13,14,15],[1,6,7,8,11,12],[1,6,9,10,11,12],
  [1,6,9,10,12,13],[1,6,10,11,12,13],[1,6,10,11,14,15],
  [1,9,10,12,13,15],[1,10,11,12,13,15],
  [1,10,11,13,14,15],[1,11,12,13,14,15],[2,3,4,5,6,7],
  [2,3,4,5,7,8],[2,3,4,5,8,13],[2,3,4,5,9,13],
  [2,3,4,5,9,14],[2,3,4,5,14,15],[2,3,4,7,8,12],
  [2,3,4,9,13,14],[2,3,5,6,7,8],[2,3,5,6,8,9],
  [2,3,5,6,9,14],[2,3,5,6,14,15],[2,3,5,8,9,13],
  [2,3,6,7,8,13],[2,3,6,7,10,13],[2,3,6,7,10,14],
  [2,3,6,7,11,14],[2,3,6,8,9,13],[2,3,6,9,13,14],
  [2,3,6,10,13,14],[2,3,6,11,14,15],[2,3,7,8,12,13],
  [2,3,7,10,13,14],[2,3,7,11,12,14],[2,3,7,11,12,15],
  [2,3,7,12,13,14],[2,3,11,12,14,15],[2,3,12,13,14,15],
  [2,4,5,9,13,14],[2,5,6,7,8,12],[2,5,6,8,9,12],
  [2,5,6,9,10,13],[2,5,6,9,10,14],[2,5,6,10,14,15],
  [2,5,8,9,12,13],[2,5,9,10,13,14],[2,6,7,8,9,12],
  [2,6,7,8,9,13],[2,6,7,9,12,13],[2,6,7,10,11,12],
  [2,6,7,10,11,14],[2,6,7,10,12,13],[2,6,9,10,13,14],
  [2,6,10,11,12,13],[2,7,8,9,12,13],[2,7,10,11,12,13],
  [2,7,10,11,13,14],[2,7,11,12,13,14],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,14],[3,4,5,6,10,14],
  [3,4,5,6,10,15],[3,4,5,8,9,13],[3,4,5,10,14,15],
  [3,4,6,7,8,9],[3,4,6,7,9,10],[3,4,6,7,10,15],
  [3,4,6,9,10,14],[3,4,7,8,9,14],[3,4,7,8,11,14],
  [3,4,7,8,11,15],[3,4,7,8,12,15],[3,4,7,9,10,14],
  [3,4,7,10,14,15],[3,4,7,11,14,15],[3,4,8,9,13,14],
  [3,4,8,11,14,15],[3,4,8,12,13,15],[3,4,8,13,14,15],
  [3,5,6,10,14,15],[3,6,7,8,9,13],[3,6,7,9,10,13],
  [3,6,7,10,11,14],[3,6,7,10,11,15],[3,6,9,10,13,14],
  [3,6,10,11,14,15],[3,7,8,9,10,13],[3,7,8,9,10,14],
  [3,7,8,10,13,14],[3,7,8,11,12,13],[3,7,8,11,12,15],
  [3,7,8,11,13,14],[3,7,10,11,14,15],[3,7,11,12,13,14],
  [3,8,9,10,13,14],[3,8,11,12,13,14],[3,8,11,12,14,15],
  [3,8,12,13,14,15],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,7,10,15],[4,5,6,7,11,15],[4,5,6,9,10,14],
  [4,5,7,8,9,10],[4,5,7,8,10,11],[4,5,7,10,11,15],
  [4,5,8,9,10,15],[4,5,8,9,12,15],[4,5,8,10,11,15],
  [4,5,9,10,14,15],[4,7,8,9,10,14],[4,7,8,10,11,14],
  [4,7,8,11,12,15],[4,7,10,11,14,15],[4,8,9,10,11,14],
  [4,8,9,10,11,15],[4,8,9,11,14,15],[4,8,9,12,13,14],
  [4,8,9,12,14,15],[4,8,12,13,14,15],[4,9,10,11,14,15],
  [4,9,12,13,14,15],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,10,11,15],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,8,9,10,11,15],[5,8,9,11,12,15],[5,9,10,11,12,15],
  [5,9,10,13,14,15],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,9,10,11,12],[6,7,9,10,12,13],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[7,8,10,11,12,13],[7,8,10,11,13,14],
  [8,9,10,11,12,13],[8,9,10,11,13,14],
  [8,9,11,12,13,14],[8,9,11,12,14,15],
  [9,10,11,12,13,14],[9,10,11,12,14,15],
  [9,10,12,13,14,15],[10,11,12,13,14,15]]

manifold_5_15_7_3=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,14],[1,2,3,4,14,15],[1,2,3,5,6,14],
  [1,2,3,5,13,14],[1,2,3,5,13,15],[1,2,3,13,14,15],
  [1,2,4,5,6,8],[1,2,4,5,8,9],[1,2,4,5,9,12],
  [1,2,4,5,12,13],[1,2,4,5,13,15],[1,2,4,6,8,9],
  [1,2,4,6,9,14],[1,2,4,9,12,14],[1,2,4,12,13,15],
  [1,2,4,12,14,15],[1,2,5,6,8,9],[1,2,5,6,9,13],
  [1,2,5,6,13,14],[1,2,5,9,12,13],[1,2,6,9,13,14],
  [1,2,9,10,12,13],[1,2,9,10,12,14],[1,2,9,10,13,14],
  [1,2,10,12,13,14],[1,2,12,13,14,15],[1,3,4,5,6,8],
  [1,3,4,5,7,8],[1,3,4,5,7,15],[1,3,4,6,8,11],
  [1,3,4,6,11,14],[1,3,4,7,8,15],[1,3,4,8,11,15],
  [1,3,4,11,12,14],[1,3,4,11,12,15],[1,3,4,12,14,15],
  [1,3,5,6,8,13],[1,3,5,6,13,14],[1,3,5,7,8,15],
  [1,3,5,8,13,15],[1,3,6,8,11,13],[1,3,6,11,13,14],
  [1,3,8,11,13,15],[1,3,11,12,14,15],[1,3,11,13,14,15],
  [1,4,5,7,8,15],[1,4,5,8,9,12],[1,4,5,8,12,15],
  [1,4,5,12,13,15],[1,4,6,8,9,11],[1,4,6,9,11,14],
  [1,4,8,9,11,12],[1,4,8,11,12,15],[1,4,9,11,12,14],
  [1,5,6,8,9,13],[1,5,8,9,12,13],[1,5,8,12,13,15],
  [1,6,8,9,11,13],[1,6,9,11,13,14],[1,8,9,11,12,15],
  [1,8,9,11,13,15],[1,8,9,12,13,15],[1,9,10,12,13,14],
  [1,9,11,12,13,14],[1,9,11,12,13,15],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,15],
  [2,3,4,6,7,15],[2,3,4,6,14,15],[2,3,5,6,7,9],
  [2,3,5,6,9,10],[2,3,5,6,10,13],[2,3,5,6,13,14],
  [2,3,5,7,9,10],[2,3,5,7,10,15],[2,3,5,10,13,15],
  [2,3,6,7,9,10],[2,3,6,7,10,14],[2,3,6,7,14,15],
  [2,3,6,10,13,14],[2,3,7,10,14,15],[2,3,10,11,13,14],
  [2,3,10,11,13,15],[2,3,10,11,14,15],
  [2,3,11,13,14,15],[2,4,5,6,7,9],[2,4,5,6,8,9],
  [2,4,5,7,9,12],[2,4,5,7,12,15],[2,4,5,12,13,15],
  [2,4,6,7,9,14],[2,4,6,7,14,15],[2,4,7,9,12,14],
  [2,4,7,12,14,15],[2,5,6,9,10,13],[2,5,7,9,10,12],
  [2,5,7,10,12,15],[2,5,9,10,12,13],[2,5,10,12,13,15],
  [2,6,7,9,10,14],[2,6,9,10,13,14],[2,7,9,10,12,14],
  [2,7,10,12,14,15],[2,10,11,13,14,15],
  [2,10,12,13,14,15],[3,4,5,6,7,8],[3,4,6,7,8,10],
  [3,4,6,7,10,11],[3,4,6,7,11,14],[3,4,6,7,14,15],
  [3,4,6,8,10,11],[3,4,7,8,10,11],[3,4,7,8,11,15],
  [3,4,7,11,14,15],[3,4,11,12,14,15],[3,5,6,7,8,10],
  [3,5,6,7,9,10],[3,5,6,8,10,13],[3,5,7,8,10,15],
  [3,5,8,10,13,15],[3,6,7,10,11,14],[3,6,8,10,11,13],
  [3,6,10,11,13,14],[3,7,8,10,11,15],[3,7,10,11,14,15],
  [3,8,10,11,13,15],[4,5,6,7,8,9],[4,5,7,8,9,11],
  [4,5,7,8,11,12],[4,5,7,8,12,15],[4,5,7,9,11,12],
  [4,5,8,9,11,12],[4,6,7,8,9,11],[4,6,7,8,10,11],
  [4,6,7,9,11,14],[4,7,8,11,12,15],[4,7,9,11,12,14],
  [4,7,11,12,14,15],[5,6,7,8,9,10],[5,6,8,9,10,12],
  [5,6,8,9,12,13],[5,6,8,10,12,13],[5,6,9,10,12,13],
  [5,7,8,9,10,12],[5,7,8,9,11,12],[5,7,8,10,12,15],
  [5,8,10,12,13,15],[6,7,8,9,10,11],[6,7,9,10,11,13],
  [6,7,9,10,13,14],[6,7,9,11,13,14],[6,7,10,11,13,14],
  [6,8,9,10,11,13],[6,8,9,10,12,13],[7,8,9,10,11,12],
  [7,8,10,11,12,14],[7,8,10,11,14,15],
  [7,8,10,12,14,15],[7,8,11,12,14,15],
  [7,9,10,11,12,14],[7,9,10,11,13,14],
  [8,9,10,11,12,13],[8,9,11,12,13,15],
  [8,10,11,12,13,15],[8,10,11,12,14,15],
  [9,10,11,12,13,14],[10,11,12,13,14,15]]

manifold_5_15_7_4=[[1,2,3,6,7,8],[1,2,3,6,7,11],
  [1,2,3,6,8,13],[1,2,3,6,11,13],[1,2,3,7,8,12],
  [1,2,3,7,11,12],[1,2,3,8,12,13],[1,2,3,11,12,13],
  [1,2,5,6,7,12],[1,2,5,6,7,15],[1,2,5,6,10,12],
  [1,2,5,6,10,15],[1,2,5,7,12,15],[1,2,5,10,12,15],
  [1,2,6,7,8,12],[1,2,6,7,11,15],[1,2,6,8,12,13],
  [1,2,6,10,11,12],[1,2,6,10,11,15],[1,2,6,11,12,13],
  [1,2,7,11,12,15],[1,2,10,11,12,15],[1,3,6,7,8,11],
  [1,3,6,8,11,13],[1,3,7,8,11,12],[1,3,8,11,12,13],
  [1,4,5,6,9,11],[1,4,5,6,9,14],[1,4,5,6,11,15],
  [1,4,5,6,14,15],[1,4,5,9,11,15],[1,4,5,9,14,15],
  [1,4,6,9,11,14],[1,4,6,11,14,15],[1,4,9,11,14,15],
  [1,5,6,7,11,12],[1,5,6,7,11,15],[1,5,6,9,10,11],
  [1,5,6,9,10,14],[1,5,6,10,11,12],[1,5,6,10,14,15],
  [1,5,7,11,12,15],[1,5,9,10,11,15],[1,5,9,10,14,15],
  [1,5,10,11,12,15],[1,6,7,8,11,12],[1,6,8,11,12,13],
  [1,6,9,10,11,14],[1,6,10,11,14,15],[1,9,10,11,14,15],
  [2,3,4,7,8,9],[2,3,4,7,8,12],[2,3,4,7,9,14],
  [2,3,4,7,12,14],[2,3,4,8,9,13],[2,3,4,8,12,13],
  [2,3,4,9,13,14],[2,3,4,12,13,14],[2,3,6,7,8,13],
  [2,3,6,7,11,13],[2,3,7,8,9,13],[2,3,7,9,13,14],
  [2,3,7,11,12,13],[2,3,7,12,13,14],[2,4,7,8,9,12],
  [2,4,7,9,12,14],[2,4,8,9,12,13],[2,4,9,12,13,14],
  [2,5,6,7,10,12],[2,5,6,7,10,15],[2,5,7,10,12,15],
  [2,6,7,8,12,13],[2,6,7,10,11,12],[2,6,7,10,11,15],
  [2,6,7,11,12,13],[2,7,8,9,12,13],[2,7,9,12,13,14],
  [2,7,10,11,12,15],[3,4,5,8,9,10],[3,4,5,8,9,13],
  [3,4,5,8,10,15],[3,4,5,8,13,15],[3,4,5,9,10,14],
  [3,4,5,9,13,14],[3,4,5,10,14,15],[3,4,5,13,14,15],
  [3,4,7,8,9,14],[3,4,7,8,12,14],[3,4,8,9,10,14],
  [3,4,8,10,14,15],[3,4,8,12,13,14],[3,4,8,13,14,15],
  [3,5,8,9,10,13],[3,5,8,10,13,15],[3,5,9,10,13,14],
  [3,5,10,13,14,15],[3,6,7,8,11,13],[3,7,8,9,13,14],
  [3,7,8,11,12,13],[3,7,8,12,13,14],[3,8,9,10,13,14],
  [3,8,10,13,14,15],[4,5,6,9,10,11],[4,5,6,9,10,14],
  [4,5,6,10,11,15],[4,5,6,10,14,15],[4,5,8,9,10,15],
  [4,5,8,9,13,15],[4,5,9,10,11,15],[4,5,9,13,14,15],
  [4,6,9,10,11,14],[4,6,10,11,14,15],[4,7,8,9,12,14],
  [4,8,9,10,14,15],[4,8,9,12,13,14],[4,8,9,13,14,15],
  [4,9,10,11,14,15],[5,6,7,10,11,12],[5,6,7,10,11,15],
  [5,7,10,11,12,15],[5,8,9,10,13,15],[5,9,10,13,14,15],
  [6,7,8,11,12,13],[7,8,9,12,13,14],[8,9,10,13,14,15]]

manifold_5_15_4_1=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,13],
  [1,2,3,4,13,14],[1,2,3,4,14,15],[1,2,3,5,6,15],
  [1,2,3,6,7,15],[1,2,3,7,8,12],[1,2,3,7,12,15],
  [1,2,3,8,12,13],[1,2,3,12,13,15],[1,2,3,13,14,15],
  [1,2,4,5,6,7],[1,2,4,5,7,8],[1,2,4,5,8,13],
  [1,2,4,5,13,14],[1,2,4,5,14,15],[1,2,5,6,7,12],
  [1,2,5,6,9,12],[1,2,5,6,9,13],[1,2,5,6,10,13],
  [1,2,5,6,10,14],[1,2,5,6,14,15],[1,2,5,7,8,12],
  [1,2,5,8,12,13],[1,2,5,9,12,13],[1,2,5,10,13,14],
  [1,2,6,7,11,12],[1,2,6,7,11,15],[1,2,6,9,12,13],
  [1,2,6,10,11,12],[1,2,6,10,11,14],[1,2,6,10,12,13],
  [1,2,6,11,14,15],[1,2,7,11,12,15],[1,2,10,11,12,13],
  [1,2,10,11,13,14],[1,2,11,12,13,14],
  [1,2,11,12,14,15],[1,2,12,13,14,15],[1,3,4,5,6,15],
  [1,3,4,6,7,15],[1,3,4,7,8,12],[1,3,4,7,12,15],
  [1,3,4,8,12,13],[1,3,4,12,13,15],[1,3,4,13,14,15],
  [1,4,5,6,7,11],[1,4,5,6,11,15],[1,4,5,7,8,11],
  [1,4,5,8,9,12],[1,4,5,8,9,13],[1,4,5,8,11,15],
  [1,4,5,8,12,15],[1,4,5,9,12,15],[1,4,5,9,13,15],
  [1,4,5,13,14,15],[1,4,6,7,11,15],[1,4,7,8,11,12],
  [1,4,7,11,12,15],[1,4,8,9,12,13],[1,4,8,11,12,15],
  [1,4,9,12,13,15],[1,5,6,7,11,12],[1,5,6,9,10,11],
  [1,5,6,9,10,13],[1,5,6,9,11,12],[1,5,6,10,11,15],
  [1,5,6,10,14,15],[1,5,7,8,11,12],[1,5,8,9,12,13],
  [1,5,8,11,12,15],[1,5,9,10,11,15],[1,5,9,10,13,15],
  [1,5,9,11,12,15],[1,5,10,13,14,15],[1,6,9,10,11,12],
  [1,6,9,10,12,13],[1,6,10,11,14,15],[1,9,10,11,12,15],
  [1,9,10,12,13,15],[1,10,11,12,13,15],
  [1,10,11,13,14,15],[1,11,12,13,14,15],[2,3,4,5,6,7],
  [2,3,4,5,7,8],[2,3,4,5,8,9],[2,3,4,5,9,14],
  [2,3,4,5,14,15],[2,3,4,8,9,13],[2,3,4,9,13,14],
  [2,3,5,6,7,8],[2,3,5,6,8,9],[2,3,5,6,9,14],
  [2,3,5,6,14,15],[2,3,6,7,8,13],[2,3,6,7,10,13],
  [2,3,6,7,10,14],[2,3,6,7,11,14],[2,3,6,7,11,15],
  [2,3,6,8,9,13],[2,3,6,9,13,14],[2,3,6,10,13,14],
  [2,3,6,11,14,15],[2,3,7,8,12,13],[2,3,7,10,13,14],
  [2,3,7,11,12,13],[2,3,7,11,12,15],[2,3,7,11,13,14],
  [2,3,11,12,13,14],[2,3,11,12,14,15],
  [2,3,12,13,14,15],[2,4,5,8,9,13],[2,4,5,9,13,14],
  [2,5,6,7,8,12],[2,5,6,8,9,12],[2,5,6,9,10,13],
  [2,5,6,9,10,14],[2,5,8,9,12,13],[2,5,9,10,13,14],
  [2,6,7,8,12,13],[2,6,7,10,11,12],[2,6,7,10,11,14],
  [2,6,7,10,12,13],[2,6,8,9,12,13],[2,6,9,10,13,14],
  [2,7,10,11,12,13],[2,7,10,11,13,14],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,15],
  [3,4,5,9,10,14],[3,4,5,10,14,15],[3,4,6,7,8,9],
  [3,4,6,7,9,10],[3,4,6,7,10,15],[3,4,7,8,9,14],
  [3,4,7,8,11,14],[3,4,7,8,11,15],[3,4,7,8,12,15],
  [3,4,7,9,10,14],[3,4,7,10,14,15],[3,4,7,11,14,15],
  [3,4,8,9,13,14],[3,4,8,11,14,15],[3,4,8,12,13,14],
  [3,4,8,12,14,15],[3,4,12,13,14,15],[3,5,6,9,10,14],
  [3,5,6,10,14,15],[3,6,7,8,9,13],[3,6,7,9,10,13],
  [3,6,7,10,11,14],[3,6,7,10,11,15],[3,6,9,10,13,14],
  [3,6,10,11,14,15],[3,7,8,9,13,14],[3,7,8,11,12,13],
  [3,7,8,11,12,15],[3,7,8,11,13,14],[3,7,9,10,13,14],
  [3,7,10,11,14,15],[3,8,11,12,13,14],
  [3,8,11,12,14,15],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,7,10,11],[4,5,6,10,11,15],[4,5,7,8,9,10],
  [4,5,7,8,10,11],[4,5,8,9,10,15],[4,5,8,9,12,15],
  [4,5,8,10,11,15],[4,5,9,10,14,15],[4,5,9,13,14,15],
  [4,6,7,10,11,15],[4,7,8,9,10,14],[4,7,8,10,11,14],
  [4,7,8,11,12,15],[4,7,10,11,14,15],[4,8,9,10,14,15],
  [4,8,9,12,13,14],[4,8,9,12,14,15],[4,8,10,11,14,15],
  [4,9,12,13,14,15],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,12],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,8,9,10,11,15],[5,8,9,11,12,15],[5,9,10,13,14,15],
  [6,7,8,9,10,11],[6,7,8,9,11,12],[6,7,8,9,12,13],
  [6,7,9,10,11,12],[6,7,9,10,12,13],[7,8,9,10,11,12],
  [7,8,9,10,12,13],[7,8,9,10,13,14],[7,8,10,11,12,13],
  [7,8,10,11,13,14],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,10,11,14,15],
  [8,9,11,12,13,14],[8,9,11,12,14,15],
  [9,10,11,12,13,14],[9,10,11,12,14,15],
  [9,10,12,13,14,15],[10,11,12,13,14,15]]

manifold_5_15_4_2=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,10],[1,2,3,4,8,10],[1,2,3,4,8,14],
  [1,2,3,4,14,15],[1,2,3,5,6,11],[1,2,3,5,9,11],
  [1,2,3,5,9,15],[1,2,3,6,7,10],[1,2,3,6,7,11],
  [1,2,3,7,9,11],[1,2,3,7,9,15],[1,2,3,7,10,14],
  [1,2,3,7,13,14],[1,2,3,7,13,15],[1,2,3,8,10,14],
  [1,2,3,13,14,15],[1,2,4,5,6,10],[1,2,4,5,10,15],
  [1,2,4,8,10,15],[1,2,4,8,14,15],[1,2,5,6,9,13],
  [1,2,5,6,9,15],[1,2,5,6,10,15],[1,2,5,6,11,13],
  [1,2,5,9,11,12],[1,2,5,9,12,13],[1,2,5,11,12,13],
  [1,2,6,7,10,14],[1,2,6,7,11,12],[1,2,6,7,12,14],
  [1,2,6,8,10,14],[1,2,6,8,10,15],[1,2,6,8,14,15],
  [1,2,6,9,13,15],[1,2,6,11,12,13],[1,2,6,12,13,15],
  [1,2,6,12,14,15],[1,2,7,9,11,12],[1,2,7,9,12,13],
  [1,2,7,9,13,15],[1,2,7,12,13,14],[1,2,12,13,14,15],
  [1,3,4,5,6,10],[1,3,4,5,9,12],[1,3,4,5,9,15],
  [1,3,4,5,10,12],[1,3,4,8,9,12],[1,3,4,8,9,14],
  [1,3,4,8,10,12],[1,3,4,9,14,15],[1,3,5,6,10,11],
  [1,3,5,9,11,12],[1,3,5,10,11,12],[1,3,6,7,10,11],
  [1,3,7,9,10,11],[1,3,7,9,10,14],[1,3,7,9,14,15],
  [1,3,7,13,14,15],[1,3,8,9,10,12],[1,3,8,9,10,14],
  [1,3,9,10,11,12],[1,4,5,8,9,12],[1,4,5,8,9,14],
  [1,4,5,8,12,15],[1,4,5,8,14,15],[1,4,5,9,14,15],
  [1,4,5,10,12,15],[1,4,8,10,11,12],[1,4,8,10,11,15],
  [1,4,8,11,12,15],[1,4,10,11,12,15],[1,5,6,9,13,15],
  [1,5,6,10,11,15],[1,5,6,11,13,15],[1,5,7,8,9,13],
  [1,5,7,8,9,14],[1,5,7,8,12,13],[1,5,7,8,12,14],
  [1,5,7,9,13,15],[1,5,7,9,14,15],[1,5,7,12,13,14],
  [1,5,7,13,14,15],[1,5,8,9,12,13],[1,5,8,12,14,15],
  [1,5,10,11,12,15],[1,5,11,12,13,14],
  [1,5,11,12,14,15],[1,5,11,13,14,15],[1,6,7,8,10,11],
  [1,6,7,8,10,14],[1,6,7,8,11,12],[1,6,7,8,12,14],
  [1,6,8,10,11,15],[1,6,8,11,12,15],[1,6,8,12,14,15],
  [1,6,11,12,13,15],[1,7,8,9,10,12],[1,7,8,9,10,14],
  [1,7,8,9,12,13],[1,7,8,10,11,12],[1,7,9,10,11,12],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,11],
  [2,3,4,5,9,11],[2,3,4,5,9,15],[2,3,4,6,7,12],
  [2,3,4,6,10,12],[2,3,4,7,8,11],[2,3,4,7,8,12],
  [2,3,4,8,10,12],[2,3,4,8,11,15],[2,3,4,8,14,15],
  [2,3,4,9,11,15],[2,3,5,6,7,11],[2,3,6,7,10,14],
  [2,3,6,7,12,14],[2,3,6,10,12,13],[2,3,6,10,13,14],
  [2,3,6,12,13,14],[2,3,7,8,11,15],[2,3,7,8,12,13],
  [2,3,7,8,13,15],[2,3,7,9,11,15],[2,3,7,12,13,14],
  [2,3,8,10,12,13],[2,3,8,10,13,14],[2,3,8,13,14,15],
  [2,4,5,6,7,11],[2,4,5,6,10,13],[2,4,5,6,11,13],
  [2,4,5,9,10,13],[2,4,5,9,10,15],[2,4,5,9,11,13],
  [2,4,6,7,11,12],[2,4,6,10,12,13],[2,4,6,11,12,13],
  [2,4,7,8,11,12],[2,4,8,10,11,12],[2,4,8,10,11,15],
  [2,4,9,10,11,13],[2,4,9,10,11,15],[2,4,10,11,12,13],
  [2,5,6,9,10,13],[2,5,6,9,10,15],[2,5,9,11,12,13],
  [2,6,8,9,10,14],[2,6,8,9,10,15],[2,6,8,9,13,14],
  [2,6,8,9,13,15],[2,6,8,13,14,15],[2,6,9,10,13,14],
  [2,6,12,13,14,15],[2,7,8,9,11,12],[2,7,8,9,11,15],
  [2,7,8,9,12,13],[2,7,8,9,13,15],[2,8,9,10,11,13],
  [2,8,9,10,11,15],[2,8,9,10,13,14],[2,8,9,11,12,13],
  [2,8,10,11,12,13],[3,4,5,6,7,8],[3,4,5,6,8,12],
  [3,4,5,6,10,12],[3,4,5,7,8,13],[3,4,5,7,11,13],
  [3,4,5,8,9,12],[3,4,5,8,9,13],[3,4,5,9,11,13],
  [3,4,6,7,8,12],[3,4,7,8,11,15],[3,4,7,8,13,15],
  [3,4,7,11,13,14],[3,4,7,11,14,15],[3,4,7,13,14,15],
  [3,4,8,9,13,14],[3,4,8,13,14,15],[3,4,9,11,13,14],
  [3,4,9,11,14,15],[3,5,6,7,8,12],[3,5,6,7,11,14],
  [3,5,6,7,12,14],[3,5,6,10,11,14],[3,5,6,10,12,14],
  [3,5,7,8,12,13],[3,5,7,11,13,14],[3,5,7,12,13,14],
  [3,5,8,9,12,13],[3,5,9,11,12,13],[3,5,10,11,12,14],
  [3,5,11,12,13,14],[3,6,7,10,11,14],[3,6,10,12,13,14],
  [3,7,9,10,11,15],[3,7,9,10,14,15],[3,7,10,11,14,15],
  [3,8,9,10,12,13],[3,8,9,10,13,14],[3,9,10,11,12,14],
  [3,9,10,11,14,15],[3,9,10,12,13,14],
  [3,9,11,12,13,14],[4,5,6,7,8,9],[4,5,6,7,9,13],
  [4,5,6,7,11,13],[4,5,6,8,9,14],[4,5,6,8,12,14],
  [4,5,6,9,10,13],[4,5,6,9,10,14],[4,5,6,10,12,14],
  [4,5,7,8,9,13],[4,5,8,12,14,15],[4,5,9,10,14,15],
  [4,5,10,12,14,15],[4,6,7,8,9,13],[4,6,7,8,12,15],
  [4,6,7,8,13,15],[4,6,7,11,12,15],[4,6,7,11,13,15],
  [4,6,8,9,13,14],[4,6,8,12,14,15],[4,6,8,13,14,15],
  [4,6,9,10,13,14],[4,6,10,12,13,14],[4,6,11,12,13,15],
  [4,6,12,13,14,15],[4,7,8,11,12,15],[4,7,11,13,14,15],
  [4,9,10,11,13,14],[4,9,10,11,14,15],
  [4,10,11,12,13,15],[4,10,11,13,14,15],
  [4,10,12,13,14,15],[5,6,7,8,9,10],[5,6,7,8,10,14],
  [5,6,7,8,12,14],[5,6,7,9,10,15],[5,6,7,9,13,15],
  [5,6,7,10,11,14],[5,6,7,10,11,15],[5,6,7,11,13,15],
  [5,6,8,9,10,14],[5,7,8,9,10,14],[5,7,9,10,14,15],
  [5,7,10,11,14,15],[5,7,11,13,14,15],
  [5,10,11,12,14,15],[6,7,8,9,10,11],[6,7,8,9,11,15],
  [6,7,8,9,13,15],[6,7,8,11,12,15],[6,7,9,10,11,15],
  [6,8,9,10,11,15],[7,8,9,10,11,12],[8,9,10,11,12,13],
  [9,10,11,12,13,14],[10,11,12,13,14,15]]

manifold_5_15_4_3=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,14],[1,2,3,4,14,15],[1,2,3,5,6,8],
  [1,2,3,5,8,13],[1,2,3,5,13,15],[1,2,3,6,8,13],
  [1,2,3,6,13,14],[1,2,3,13,14,15],[1,2,4,5,6,9],
  [1,2,4,5,7,12],[1,2,4,5,7,15],[1,2,4,5,9,12],
  [1,2,4,6,9,14],[1,2,4,7,12,15],[1,2,4,9,12,13],
  [1,2,4,9,13,14],[1,2,4,12,13,14],[1,2,4,12,14,15],
  [1,2,5,6,8,13],[1,2,5,6,9,13],[1,2,5,7,12,15],
  [1,2,5,9,12,13],[1,2,5,12,13,15],[1,2,6,9,13,14],
  [1,2,12,13,14,15],[1,3,4,5,6,8],[1,3,4,5,8,15],
  [1,3,4,6,8,11],[1,3,4,6,11,15],[1,3,4,6,14,15],
  [1,3,4,8,11,15],[1,3,5,8,13,15],[1,3,6,8,11,13],
  [1,3,6,11,13,14],[1,3,6,11,14,15],[1,3,8,11,12,13],
  [1,3,8,11,12,15],[1,3,8,12,13,15],[1,3,11,12,13,15],
  [1,3,11,13,14,15],[1,4,5,6,8,11],[1,4,5,6,9,11],
  [1,4,5,7,12,15],[1,4,5,8,9,11],[1,4,5,8,9,12],
  [1,4,5,8,12,15],[1,4,6,9,11,14],[1,4,6,11,14,15],
  [1,4,8,9,11,12],[1,4,8,11,12,15],[1,4,9,11,12,14],
  [1,4,9,12,13,14],[1,4,11,12,14,15],[1,5,6,8,9,11],
  [1,5,6,8,9,13],[1,5,8,9,12,13],[1,5,8,12,13,15],
  [1,6,8,9,11,13],[1,6,9,10,11,13],[1,6,9,10,11,14],
  [1,6,9,10,13,14],[1,6,10,11,13,14],[1,8,9,11,12,13],
  [1,9,10,11,13,14],[1,9,11,12,13,14],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,15],
  [2,3,4,6,7,9],[2,3,4,6,9,14],[2,3,4,7,9,14],
  [2,3,4,7,14,15],[2,3,5,6,7,10],[2,3,5,6,8,13],
  [2,3,5,6,10,13],[2,3,5,7,10,15],[2,3,5,10,13,14],
  [2,3,5,10,14,15],[2,3,5,13,14,15],[2,3,6,7,9,14],
  [2,3,6,7,10,14],[2,3,6,10,13,14],[2,3,7,10,14,15],
  [2,4,5,6,7,9],[2,4,5,7,9,12],[2,4,7,9,12,14],
  [2,4,7,12,14,15],[2,4,9,12,13,14],[2,5,6,7,9,12],
  [2,5,6,7,10,12],[2,5,6,9,10,12],[2,5,6,9,10,13],
  [2,5,7,10,12,15],[2,5,9,10,12,13],[2,5,10,12,13,15],
  [2,5,10,13,14,15],[2,6,7,9,10,12],[2,6,7,9,10,14],
  [2,6,9,10,13,14],[2,7,9,10,12,14],[2,7,10,11,12,14],
  [2,7,10,11,12,15],[2,7,10,11,14,15],
  [2,7,11,12,14,15],[2,9,10,12,13,14],
  [2,10,11,12,14,15],[2,10,12,13,14,15],[3,4,5,6,7,8],
  [3,4,5,7,8,10],[3,4,5,7,10,15],[3,4,5,8,10,15],
  [3,4,6,7,8,11],[3,4,6,7,9,14],[3,4,6,7,11,14],
  [3,4,6,11,14,15],[3,4,7,8,10,15],[3,4,7,8,11,15],
  [3,4,7,11,14,15],[3,5,6,7,8,10],[3,5,6,8,10,13],
  [3,5,8,10,13,15],[3,5,10,13,14,15],[3,6,7,8,10,13],
  [3,6,7,8,11,13],[3,6,7,10,11,13],[3,6,7,10,11,14],
  [3,6,10,11,13,14],[3,7,8,10,11,13],[3,7,8,10,11,15],
  [3,7,10,11,14,15],[3,8,10,11,13,15],
  [3,8,11,12,13,15],[3,10,11,13,14,15],[4,5,6,7,8,9],
  [4,5,6,8,9,11],[4,5,7,8,9,12],[4,5,7,8,10,15],
  [4,5,7,8,12,15],[4,6,7,8,9,11],[4,6,7,9,11,14],
  [4,7,8,9,11,14],[4,7,8,9,12,14],[4,7,8,11,12,14],
  [4,7,8,11,12,15],[4,7,11,12,14,15],[4,8,9,11,12,14],
  [5,6,7,8,9,10],[5,6,7,9,10,12],[5,6,8,9,10,13],
  [5,7,8,9,10,12],[5,7,8,10,12,15],[5,8,9,10,12,15],
  [5,8,9,10,13,15],[5,8,9,12,13,15],[5,9,10,12,13,15],
  [6,7,8,9,10,11],[6,7,8,10,11,13],[6,7,9,10,11,14],
  [6,8,9,10,11,13],[7,8,9,10,11,12],[7,8,9,11,12,14],
  [7,8,10,11,12,15],[7,9,10,11,12,14],
  [8,9,10,11,12,13],[8,9,10,12,13,15],
  [8,10,11,12,13,15],[9,10,11,12,13,14],
  [10,11,12,13,14,15]]

manifold_5_15_4_4=[[1,2,3,4,5,7],[1,2,3,4,5,8],
  [1,2,3,4,6,8],[1,2,3,4,6,15],[1,2,3,4,7,15],
  [1,2,3,5,6,8],[1,2,3,5,6,14],[1,2,3,5,7,15],
  [1,2,3,5,14,15],[1,2,3,6,14,15],[1,2,4,5,7,15],
  [1,2,4,5,8,9],[1,2,4,5,9,13],[1,2,4,5,13,15],
  [1,2,4,6,8,9],[1,2,4,6,9,14],[1,2,4,6,14,15],
  [1,2,4,9,12,13],[1,2,4,9,12,14],[1,2,4,12,13,14],
  [1,2,4,13,14,15],[1,2,5,6,8,13],[1,2,5,6,13,14],
  [1,2,5,8,9,13],[1,2,5,13,14,15],[1,2,6,8,9,13],
  [1,2,6,9,10,13],[1,2,6,9,10,14],[1,2,6,10,13,14],
  [1,2,9,10,12,13],[1,2,9,10,12,14],[1,2,10,12,13,14],
  [1,3,4,5,7,8],[1,3,4,6,8,11],[1,3,4,6,11,14],
  [1,3,4,6,14,15],[1,3,4,7,8,15],[1,3,4,8,11,12],
  [1,3,4,8,12,15],[1,3,4,11,12,14],[1,3,4,12,14,15],
  [1,3,5,6,8,13],[1,3,5,6,13,14],[1,3,5,7,8,15],
  [1,3,5,8,13,15],[1,3,5,13,14,15],[1,3,6,8,11,13],
  [1,3,6,11,13,14],[1,3,8,11,12,15],[1,3,8,11,13,15],
  [1,3,11,12,13,14],[1,3,11,12,13,15],
  [1,3,12,13,14,15],[1,4,5,7,8,12],[1,4,5,7,12,15],
  [1,4,5,8,9,11],[1,4,5,8,11,12],[1,4,5,9,11,12],
  [1,4,5,9,12,13],[1,4,5,12,13,15],[1,4,6,8,9,11],
  [1,4,6,9,11,14],[1,4,7,8,12,15],[1,4,9,11,12,14],
  [1,4,12,13,14,15],[1,5,7,8,12,15],[1,5,8,9,11,12],
  [1,5,8,9,12,15],[1,5,8,9,13,15],[1,5,9,12,13,15],
  [1,6,8,9,11,13],[1,6,9,10,13,14],[1,6,9,11,13,14],
  [1,8,9,11,12,15],[1,8,9,11,13,15],[1,9,10,11,12,13],
  [1,9,10,11,12,14],[1,9,10,11,13,14],
  [1,9,11,12,13,15],[1,10,11,12,13,14],[2,3,4,5,6,8],
  [2,3,4,5,6,9],[2,3,4,5,7,9],[2,3,4,6,7,9],
  [2,3,4,6,7,15],[2,3,5,6,9,10],[2,3,5,6,10,14],
  [2,3,5,7,9,10],[2,3,5,7,10,15],[2,3,5,10,13,14],
  [2,3,5,10,13,15],[2,3,5,13,14,15],[2,3,6,7,9,14],
  [2,3,6,7,14,15],[2,3,6,9,10,14],[2,3,7,9,10,14],
  [2,3,7,10,11,14],[2,3,7,10,11,15],[2,3,7,11,14,15],
  [2,3,10,11,13,14],[2,3,10,11,13,15],
  [2,3,11,13,14,15],[2,4,5,6,8,9],[2,4,5,7,9,12],
  [2,4,5,7,12,15],[2,4,5,9,12,13],[2,4,5,12,13,15],
  [2,4,6,7,9,14],[2,4,6,7,14,15],[2,4,7,9,12,14],
  [2,4,7,12,14,15],[2,4,12,13,14,15],[2,5,6,8,9,13],
  [2,5,6,9,10,12],[2,5,6,9,12,13],[2,5,6,10,12,13],
  [2,5,6,10,13,14],[2,5,7,9,10,12],[2,5,7,10,12,15],
  [2,5,10,12,13,15],[2,6,9,10,12,13],[2,7,9,10,12,14],
  [2,7,10,11,14,15],[2,7,10,12,14,15],
  [2,10,11,12,13,14],[2,10,11,12,13,15],
  [2,10,11,12,14,15],[2,11,12,13,14,15],[3,4,5,6,7,9],
  [3,4,5,6,7,10],[3,4,5,6,8,10],[3,4,5,7,8,10],
  [3,4,6,7,10,11],[3,4,6,7,11,15],[3,4,6,8,10,11],
  [3,4,6,11,14,15],[3,4,7,8,10,15],[3,4,7,10,11,15],
  [3,4,8,10,11,15],[3,4,8,11,12,15],[3,4,11,12,14,15],
  [3,5,6,7,9,10],[3,5,6,8,10,13],[3,5,6,10,13,14],
  [3,5,7,8,10,15],[3,5,8,10,13,15],[3,6,7,9,10,14],
  [3,6,7,10,11,13],[3,6,7,10,13,14],[3,6,7,11,13,14],
  [3,6,7,11,14,15],[3,6,8,10,11,13],[3,7,10,11,13,14],
  [3,8,10,11,13,15],[3,11,12,13,14,15],[4,5,6,7,8,10],
  [4,5,6,7,8,11],[4,5,6,7,9,11],[4,5,6,8,9,11],
  [4,5,7,8,11,12],[4,5,7,9,11,12],[4,6,7,8,10,11],
  [4,6,7,9,11,14],[4,6,7,11,14,15],[4,7,8,10,11,15],
  [4,7,8,11,12,14],[4,7,8,11,14,15],[4,7,8,12,14,15],
  [4,7,9,11,12,14],[4,8,11,12,14,15],[5,6,7,8,9,11],
  [5,6,7,8,9,12],[5,6,7,8,10,12],[5,6,7,9,10,12],
  [5,6,8,9,12,13],[5,6,8,10,12,13],[5,7,8,9,11,12],
  [5,7,8,10,12,15],[5,8,9,12,13,15],[5,8,10,12,13,15],
  [6,7,8,9,10,12],[6,7,8,9,10,13],[6,7,8,9,11,13],
  [6,7,8,10,11,13],[6,7,9,10,13,14],[6,7,9,11,13,14],
  [6,8,9,10,12,13],[7,8,9,10,11,13],[7,8,9,10,11,14],
  [7,8,9,10,12,14],[7,8,9,11,12,14],[7,8,10,11,14,15],
  [7,8,10,12,14,15],[7,9,10,11,13,14],
  [8,9,10,11,12,14],[8,9,10,11,12,15],
  [8,9,10,11,13,15],[8,9,10,12,13,15],
  [8,10,11,12,14,15],[9,10,11,12,13,15]]

manifold_5_15_4_5=[[1,2,3,4,5,7],[1,2,3,4,5,8],
  [1,2,3,4,6,8],[1,2,3,4,6,15],[1,2,3,4,7,15],
  [1,2,3,5,7,15],[1,2,3,5,8,13],[1,2,3,5,13,14],
  [1,2,3,5,14,15],[1,2,3,6,8,13],[1,2,3,6,13,14],
  [1,2,3,6,14,15],[1,2,4,5,6,8],[1,2,4,5,6,9],
  [1,2,4,5,7,12],[1,2,4,5,9,13],[1,2,4,5,12,13],
  [1,2,4,6,9,14],[1,2,4,6,14,15],[1,2,4,7,12,15],
  [1,2,4,9,13,14],[1,2,4,12,13,15],[1,2,4,13,14,15],
  [1,2,5,6,8,9],[1,2,5,7,12,15],[1,2,5,8,9,13],
  [1,2,5,12,13,15],[1,2,5,13,14,15],[1,2,6,8,9,13],
  [1,2,6,9,10,13],[1,2,6,9,10,14],[1,2,6,10,13,14],
  [1,2,9,10,13,14],[1,3,4,5,7,15],[1,3,4,5,8,15],
  [1,3,4,6,8,11],[1,3,4,6,11,15],[1,3,4,8,11,12],
  [1,3,4,8,12,15],[1,3,4,11,12,15],[1,3,5,8,13,15],
  [1,3,5,13,14,15],[1,3,6,8,11,13],[1,3,6,11,13,14],
  [1,3,6,11,14,15],[1,3,8,11,12,13],[1,3,8,12,13,15],
  [1,3,11,12,13,14],[1,3,11,12,14,15],
  [1,3,12,13,14,15],[1,4,5,6,8,11],[1,4,5,6,9,11],
  [1,4,5,7,8,12],[1,4,5,7,8,15],[1,4,5,8,11,12],
  [1,4,5,9,11,12],[1,4,5,9,12,13],[1,4,6,9,11,14],
  [1,4,6,11,14,15],[1,4,7,8,12,15],[1,4,9,11,12,14],
  [1,4,9,12,13,14],[1,4,11,12,14,15],[1,4,12,13,14,15],
  [1,5,6,8,9,11],[1,5,7,8,12,15],[1,5,8,9,11,12],
  [1,5,8,9,12,15],[1,5,8,9,13,15],[1,5,9,12,13,15],
  [1,6,8,9,11,13],[1,6,9,10,11,13],[1,6,9,10,11,14],
  [1,6,10,11,13,14],[1,8,9,11,12,13],[1,8,9,12,13,15],
  [1,9,10,11,12,13],[1,9,10,11,12,14],
  [1,9,10,12,13,14],[1,10,11,12,13,14],[2,3,4,5,6,8],
  [2,3,4,5,6,9],[2,3,4,5,7,9],[2,3,4,6,9,14],
  [2,3,4,6,14,15],[2,3,4,7,9,14],[2,3,4,7,14,15],
  [2,3,5,6,7,9],[2,3,5,6,7,10],[2,3,5,6,8,13],
  [2,3,5,6,10,14],[2,3,5,6,13,14],[2,3,5,7,10,15],
  [2,3,5,10,14,15],[2,3,6,7,9,10],[2,3,6,9,10,14],
  [2,3,7,9,10,14],[2,3,7,10,11,14],[2,3,7,10,11,15],
  [2,3,7,11,14,15],[2,3,10,11,14,15],[2,4,5,7,9,12],
  [2,4,5,9,12,13],[2,4,7,9,12,14],[2,4,7,12,14,15],
  [2,4,9,12,13,14],[2,4,12,13,14,15],[2,5,6,7,9,12],
  [2,5,6,7,10,12],[2,5,6,8,9,13],[2,5,6,9,12,13],
  [2,5,6,10,12,13],[2,5,6,10,13,14],[2,5,7,10,12,15],
  [2,5,10,12,13,15],[2,5,10,13,14,15],[2,6,7,9,10,12],
  [2,6,9,10,12,13],[2,7,9,10,12,14],[2,7,10,11,12,14],
  [2,7,10,11,12,15],[2,7,11,12,14,15],
  [2,9,10,12,13,14],[2,10,11,12,13,14],
  [2,10,11,12,13,15],[2,10,11,13,14,15],
  [2,11,12,13,14,15],[3,4,5,6,7,9],[3,4,5,6,7,10],
  [3,4,5,6,8,10],[3,4,5,7,10,15],[3,4,5,8,10,15],
  [3,4,6,7,8,10],[3,4,6,7,8,11],[3,4,6,7,9,14],
  [3,4,6,7,11,15],[3,4,6,7,14,15],[3,4,7,8,10,11],
  [3,4,7,10,11,15],[3,4,8,10,11,15],[3,4,8,11,12,15],
  [3,5,6,8,10,13],[3,5,6,10,13,14],[3,5,8,10,13,15],
  [3,5,10,13,14,15],[3,6,7,8,10,13],[3,6,7,8,11,13],
  [3,6,7,9,10,14],[3,6,7,10,13,14],[3,6,7,11,13,14],
  [3,6,7,11,14,15],[3,7,8,10,11,13],[3,7,10,11,13,14],
  [3,8,10,11,13,15],[3,8,11,12,13,15],
  [3,10,11,13,14,15],[3,11,12,13,14,15],[4,5,6,7,8,10],
  [4,5,6,7,8,11],[4,5,6,7,9,11],[4,5,7,8,9,11],
  [4,5,7,8,9,12],[4,5,7,8,10,15],[4,5,8,9,11,12],
  [4,6,7,9,11,14],[4,6,7,11,14,15],[4,7,8,9,11,14],
  [4,7,8,9,12,14],[4,7,8,10,11,15],[4,7,8,11,14,15],
  [4,7,8,12,14,15],[4,8,9,11,12,14],[4,8,11,12,14,15],
  [5,6,7,8,9,11],[5,6,7,8,9,12],[5,6,7,8,10,12],
  [5,6,8,9,10,12],[5,6,8,9,10,13],[5,6,9,10,12,13],
  [5,7,8,10,12,15],[5,8,9,10,12,15],[5,8,9,10,13,15],
  [5,9,10,12,13,15],[6,7,8,9,10,12],[6,7,8,9,10,13],
  [6,7,8,9,11,13],[6,7,9,10,11,13],[6,7,9,10,11,14],
  [6,7,10,11,13,14],[7,8,9,10,11,13],[7,8,9,10,11,14],
  [7,8,9,10,12,14],[7,8,10,11,12,14],[7,8,10,11,12,15],
  [7,8,11,12,14,15],[8,9,10,11,12,14],
  [8,9,10,11,12,15],[8,9,10,11,13,15],
  [8,9,11,12,13,15],[9,10,11,12,13,15]]

manifold_5_15_4_6=[[1,2,3,4,5,9],[1,2,3,4,5,10],
  [1,2,3,4,8,10],[1,2,3,4,8,15],[1,2,3,4,9,15],
  [1,2,3,5,6,10],[1,2,3,5,6,11],[1,2,3,5,9,11],
  [1,2,3,6,7,11],[1,2,3,6,7,14],[1,2,3,6,10,14],
  [1,2,3,7,9,11],[1,2,3,7,9,15],[1,2,3,7,14,15],
  [1,2,3,8,10,14],[1,2,3,8,14,15],[1,2,4,5,9,15],
  [1,2,4,5,10,15],[1,2,4,8,10,15],[1,2,5,6,10,15],
  [1,2,5,6,11,13],[1,2,5,6,13,15],[1,2,5,9,11,13],
  [1,2,5,9,13,15],[1,2,6,7,11,12],[1,2,6,7,12,14],
  [1,2,6,8,10,14],[1,2,6,8,10,15],[1,2,6,8,14,15],
  [1,2,6,11,12,13],[1,2,6,12,13,14],[1,2,6,13,14,15],
  [1,2,7,9,11,12],[1,2,7,9,12,13],[1,2,7,9,13,15],
  [1,2,7,12,13,14],[1,2,7,13,14,15],[1,2,9,11,12,13],
  [1,3,4,5,8,9],[1,3,4,5,8,12],[1,3,4,5,10,12],
  [1,3,4,8,9,14],[1,3,4,8,10,12],[1,3,4,8,14,15],
  [1,3,4,9,14,15],[1,3,5,6,10,11],[1,3,5,8,9,12],
  [1,3,5,9,11,12],[1,3,5,10,11,12],[1,3,6,7,10,11],
  [1,3,6,7,10,14],[1,3,7,9,10,11],[1,3,7,9,10,14],
  [1,3,7,9,14,15],[1,3,8,9,10,12],[1,3,8,9,10,14],
  [1,3,9,10,11,12],[1,4,5,8,9,14],[1,4,5,8,12,14],
  [1,4,5,9,14,15],[1,4,5,10,12,15],[1,4,5,12,14,15],
  [1,4,8,10,12,15],[1,4,8,12,14,15],[1,5,6,10,11,15],
  [1,5,6,11,13,15],[1,5,7,8,9,12],[1,5,7,8,9,14],
  [1,5,7,8,12,14],[1,5,7,9,12,13],[1,5,7,9,13,15],
  [1,5,7,9,14,15],[1,5,7,12,13,14],[1,5,7,13,14,15],
  [1,5,9,11,12,13],[1,5,10,11,12,15],[1,5,11,12,13,15],
  [1,5,12,13,14,15],[1,6,7,8,10,11],[1,6,7,8,10,14],
  [1,6,7,8,11,12],[1,6,7,8,12,14],[1,6,8,10,11,15],
  [1,6,8,11,12,15],[1,6,8,12,14,15],[1,6,11,12,13,15],
  [1,6,12,13,14,15],[1,7,8,9,10,11],[1,7,8,9,10,14],
  [1,7,8,9,11,12],[1,8,9,10,11,12],[1,8,10,11,12,15],
  [2,3,4,5,6,10],[2,3,4,5,6,11],[2,3,4,5,9,11],
  [2,3,4,6,7,11],[2,3,4,6,7,12],[2,3,4,6,10,12],
  [2,3,4,7,8,12],[2,3,4,7,8,15],[2,3,4,7,11,15],
  [2,3,4,8,10,12],[2,3,4,9,11,15],[2,3,6,7,12,14],
  [2,3,6,10,12,14],[2,3,7,8,12,13],[2,3,7,8,13,15],
  [2,3,7,9,11,15],[2,3,7,12,13,14],[2,3,7,13,14,15],
  [2,3,8,10,12,13],[2,3,8,10,13,14],[2,3,8,13,14,15],
  [2,3,10,12,13,14],[2,4,5,6,9,10],[2,4,5,6,9,13],
  [2,4,5,6,11,13],[2,4,5,9,10,15],[2,4,5,9,11,13],
  [2,4,6,7,11,12],[2,4,6,9,10,13],[2,4,6,10,12,13],
  [2,4,6,11,12,13],[2,4,7,8,11,12],[2,4,7,8,11,15],
  [2,4,8,10,11,12],[2,4,8,10,11,15],[2,4,9,10,11,13],
  [2,4,9,10,11,15],[2,4,10,11,12,13],[2,5,6,9,10,15],
  [2,5,6,9,13,15],[2,6,8,9,10,13],[2,6,8,9,10,15],
  [2,6,8,9,13,15],[2,6,8,10,13,14],[2,6,8,13,14,15],
  [2,6,10,12,13,14],[2,7,8,9,11,12],[2,7,8,9,11,15],
  [2,7,8,9,12,13],[2,7,8,9,13,15],[2,8,9,10,11,12],
  [2,8,9,10,11,15],[2,8,9,10,12,13],[2,9,10,11,12,13],
  [3,4,5,6,7,11],[3,4,5,6,7,12],[3,4,5,6,10,12],
  [3,4,5,7,8,12],[3,4,5,7,8,13],[3,4,5,7,11,13],
  [3,4,5,8,9,13],[3,4,5,9,11,13],[3,4,7,8,13,15],
  [3,4,7,11,13,15],[3,4,8,9,13,14],[3,4,8,13,14,15],
  [3,4,9,11,13,14],[3,4,9,11,14,15],[3,4,11,13,14,15],
  [3,5,6,7,10,11],[3,5,6,7,10,14],[3,5,6,7,12,14],
  [3,5,6,10,12,14],[3,5,7,8,12,13],[3,5,7,10,11,14],
  [3,5,7,11,13,14],[3,5,7,12,13,14],[3,5,8,9,12,13],
  [3,5,9,11,12,13],[3,5,10,11,12,14],[3,5,11,12,13,14],
  [3,7,9,10,11,14],[3,7,9,11,14,15],[3,7,11,13,14,15],
  [3,8,9,10,12,13],[3,8,9,10,13,14],[3,9,10,11,12,13],
  [3,9,10,11,13,14],[3,10,11,12,13,14],[4,5,6,7,8,12],
  [4,5,6,7,8,13],[4,5,6,7,11,13],[4,5,6,8,9,13],
  [4,5,6,8,9,14],[4,5,6,8,12,14],[4,5,6,9,10,14],
  [4,5,6,10,12,14],[4,5,9,10,14,15],[4,5,10,12,14,15],
  [4,6,7,8,11,12],[4,6,7,8,11,15],[4,6,7,8,13,15],
  [4,6,7,11,13,15],[4,6,8,9,13,14],[4,6,8,11,12,15],
  [4,6,8,12,14,15],[4,6,8,13,14,15],[4,6,9,10,13,14],
  [4,6,10,12,13,14],[4,6,11,12,13,15],
  [4,6,12,13,14,15],[4,8,10,11,12,15],
  [4,9,10,11,13,14],[4,9,10,11,14,15],
  [4,10,11,12,13,14],[4,10,11,12,14,15],
  [4,11,12,13,14,15],[5,6,7,8,9,13],[5,6,7,8,9,14],
  [5,6,7,8,12,14],[5,6,7,9,10,14],[5,6,7,9,10,15],
  [5,6,7,9,13,15],[5,6,7,10,11,15],[5,6,7,11,13,15],
  [5,7,8,9,12,13],[5,7,9,10,14,15],[5,7,10,11,14,15],
  [5,7,11,13,14,15],[5,10,11,12,14,15],
  [5,11,12,13,14,15],[6,7,8,9,10,14],[6,7,8,9,10,15],
  [6,7,8,9,13,15],[6,7,8,10,11,15],[6,8,9,10,13,14],
  [7,8,9,10,11,15],[7,9,10,11,14,15]]

manifold_5_15_4_7=[[1,2,3,4,5,10],[1,2,3,4,5,11],
  [1,2,3,4,9,11],[1,2,3,4,9,15],[1,2,3,4,10,15],
  [1,2,3,5,6,10],[1,2,3,5,6,11],[1,2,3,6,7,11],
  [1,2,3,6,7,14],[1,2,3,6,8,10],[1,2,3,6,8,14],
  [1,2,3,7,9,11],[1,2,3,7,9,14],[1,2,3,8,10,15],
  [1,2,3,8,14,15],[1,2,3,9,14,15],[1,2,4,5,9,11],
  [1,2,4,5,9,15],[1,2,4,5,10,15],[1,2,5,6,10,15],
  [1,2,5,6,11,13],[1,2,5,6,13,15],[1,2,5,7,9,13],
  [1,2,5,7,9,15],[1,2,5,7,13,15],[1,2,5,9,11,13],
  [1,2,6,7,11,12],[1,2,6,7,12,14],[1,2,6,8,10,15],
  [1,2,6,8,13,14],[1,2,6,8,13,15],[1,2,6,11,12,13],
  [1,2,6,12,13,14],[1,2,7,9,11,12],[1,2,7,9,12,13],
  [1,2,7,9,14,15],[1,2,7,12,13,14],[1,2,7,13,14,15],
  [1,2,8,13,14,15],[1,2,9,11,12,13],[1,3,4,5,8,9],
  [1,3,4,5,8,10],[1,3,4,5,9,11],[1,3,4,8,9,14],
  [1,3,4,8,10,15],[1,3,4,8,14,15],[1,3,4,9,14,15],
  [1,3,5,6,10,11],[1,3,5,8,9,12],[1,3,5,8,10,12],
  [1,3,5,9,11,13],[1,3,5,9,12,13],[1,3,5,10,11,12],
  [1,3,5,11,12,13],[1,3,6,7,10,11],[1,3,6,7,10,14],
  [1,3,6,8,10,14],[1,3,7,9,11,14],[1,3,7,10,11,14],
  [1,3,8,9,10,11],[1,3,8,9,10,14],[1,3,8,9,11,12],
  [1,3,8,10,11,12],[1,3,9,10,11,14],[1,3,9,11,12,13],
  [1,4,5,8,9,14],[1,4,5,8,10,12],[1,4,5,8,12,14],
  [1,4,5,9,14,15],[1,4,5,10,12,15],[1,4,5,12,14,15],
  [1,4,6,8,12,14],[1,4,6,8,12,15],[1,4,6,8,14,15],
  [1,4,6,12,14,15],[1,4,8,10,12,15],[1,5,6,10,11,15],
  [1,5,6,11,13,15],[1,5,7,9,12,13],[1,5,7,9,12,14],
  [1,5,7,9,14,15],[1,5,7,12,13,15],[1,5,7,12,14,15],
  [1,5,8,9,12,14],[1,5,10,11,12,15],[1,5,11,12,13,15],
  [1,6,7,8,9,10],[1,6,7,8,9,14],[1,6,7,8,10,11],
  [1,6,7,8,11,12],[1,6,7,8,12,14],[1,6,7,9,10,14],
  [1,6,8,9,10,14],[1,6,8,10,11,15],[1,6,8,11,12,15],
  [1,6,8,13,14,15],[1,6,11,12,13,15],[1,6,12,13,14,15],
  [1,7,8,9,10,11],[1,7,8,9,11,12],[1,7,8,9,12,14],
  [1,7,9,10,11,14],[1,7,12,13,14,15],[1,8,10,11,12,15],
  [2,3,4,5,6,11],[2,3,4,5,6,12],[2,3,4,5,10,12],
  [2,3,4,6,7,11],[2,3,4,6,7,12],[2,3,4,7,8,12],
  [2,3,4,7,8,15],[2,3,4,7,9,11],[2,3,4,7,9,15],
  [2,3,4,8,10,12],[2,3,4,8,10,15],[2,3,5,6,10,12],
  [2,3,6,7,12,14],[2,3,6,8,10,14],[2,3,6,10,12,14],
  [2,3,7,8,12,13],[2,3,7,8,13,15],[2,3,7,9,14,15],
  [2,3,7,12,13,14],[2,3,7,13,14,15],[2,3,8,10,12,13],
  [2,3,8,10,13,14],[2,3,8,13,14,15],[2,3,10,12,13,14],
  [2,4,5,6,9,10],[2,4,5,6,9,11],[2,4,5,6,10,12],
  [2,4,5,9,10,15],[2,4,6,7,11,12],[2,4,6,9,10,13],
  [2,4,6,9,11,13],[2,4,6,10,12,14],[2,4,6,10,13,14],
  [2,4,6,11,12,13],[2,4,6,12,13,14],[2,4,7,8,11,12],
  [2,4,7,8,11,15],[2,4,7,9,11,15],[2,4,8,10,12,15],
  [2,4,8,11,12,15],[2,4,9,10,11,12],[2,4,9,10,11,15],
  [2,4,9,10,12,13],[2,4,9,11,12,13],[2,4,10,11,12,15],
  [2,4,10,12,13,14],[2,5,6,9,10,15],[2,5,6,9,11,13],
  [2,5,6,9,13,15],[2,5,7,9,13,15],[2,6,8,10,13,14],
  [2,6,8,10,13,15],[2,6,9,10,13,15],[2,7,8,9,10,11],
  [2,7,8,9,10,15],[2,7,8,9,11,12],[2,7,8,9,12,13],
  [2,7,8,9,13,15],[2,7,8,10,11,15],[2,7,9,10,11,15],
  [2,8,9,10,11,12],[2,8,9,10,12,13],[2,8,9,10,13,15],
  [2,8,10,11,12,15],[3,4,5,6,7,12],[3,4,5,6,7,13],
  [3,4,5,6,11,13],[3,4,5,7,8,12],[3,4,5,7,8,13],
  [3,4,5,8,9,13],[3,4,5,8,10,12],[3,4,5,9,11,13],
  [3,4,6,7,11,13],[3,4,7,8,13,15],[3,4,7,9,11,15],
  [3,4,7,11,13,15],[3,4,8,9,13,14],[3,4,8,13,14,15],
  [3,4,9,11,13,14],[3,4,9,11,14,15],[3,4,11,13,14,15],
  [3,5,6,7,10,11],[3,5,6,7,10,12],[3,5,6,7,11,13],
  [3,5,7,8,12,13],[3,5,7,10,11,14],[3,5,7,10,12,14],
  [3,5,7,11,13,15],[3,5,7,11,14,15],[3,5,7,12,13,14],
  [3,5,7,13,14,15],[3,5,8,9,12,13],[3,5,10,11,12,13],
  [3,5,10,11,13,14],[3,5,10,12,13,14],
  [3,5,11,13,14,15],[3,6,7,10,12,14],[3,7,9,11,14,15],
  [3,8,9,10,11,12],[3,8,9,10,12,13],[3,8,9,10,13,14],
  [3,9,10,11,12,13],[3,9,10,11,13,14],[4,5,6,7,8,13],
  [4,5,6,7,8,14],[4,5,6,7,12,14],[4,5,6,8,9,13],
  [4,5,6,8,9,14],[4,5,6,9,10,14],[4,5,6,9,11,13],
  [4,5,6,10,12,14],[4,5,7,8,12,14],[4,5,9,10,14,15],
  [4,5,10,12,14,15],[4,6,7,8,11,12],[4,6,7,8,11,13],
  [4,6,7,8,12,14],[4,6,8,9,13,14],[4,6,8,11,12,15],
  [4,6,8,11,13,15],[4,6,8,13,14,15],[4,6,9,10,13,14],
  [4,6,11,12,13,14],[4,6,11,12,14,15],
  [4,6,11,13,14,15],[4,7,8,11,13,15],[4,9,10,11,12,13],
  [4,9,10,11,13,14],[4,9,10,11,14,15],
  [4,10,11,12,13,14],[4,10,11,12,14,15],[5,6,7,8,9,14],
  [5,6,7,8,9,15],[5,6,7,8,13,15],[5,6,7,9,10,14],
  [5,6,7,9,10,15],[5,6,7,10,11,15],[5,6,7,10,12,14],
  [5,6,7,11,13,15],[5,6,8,9,13,15],[5,7,8,9,12,13],
  [5,7,8,9,12,14],[5,7,8,9,13,15],[5,7,9,10,14,15],
  [5,7,10,11,14,15],[5,7,12,13,14,15],
  [5,10,11,12,13,14],[5,10,11,12,14,15],
  [5,11,12,13,14,15],[6,7,8,9,10,15],[6,7,8,10,11,15],
  [6,7,8,11,13,15],[6,8,9,10,13,14],[6,8,9,10,13,15],
  [6,11,12,13,14,15],[7,9,10,11,14,15]]

manifold_5_15_4_8=[[1,2,3,4,6,7],[1,2,3,4,6,8],
  [1,2,3,4,7,8],[1,2,3,5,6,8],[1,2,3,5,6,15],
  [1,2,3,5,7,8],[1,2,3,5,7,15],[1,2,3,6,7,15],
  [1,2,4,5,7,8],[1,2,4,5,7,15],[1,2,4,5,8,13],
  [1,2,4,5,13,14],[1,2,4,5,14,15],[1,2,4,6,7,15],
  [1,2,4,6,8,9],[1,2,4,6,9,14],[1,2,4,6,14,15],
  [1,2,4,8,9,13],[1,2,4,9,12,13],[1,2,4,9,12,14],
  [1,2,4,12,13,14],[1,2,5,6,8,13],[1,2,5,6,10,13],
  [1,2,5,6,10,14],[1,2,5,6,14,15],[1,2,5,10,13,14],
  [1,2,6,8,9,13],[1,2,6,9,10,12],[1,2,6,9,10,14],
  [1,2,6,9,12,13],[1,2,6,10,12,13],[1,2,9,10,12,14],
  [1,2,10,11,12,13],[1,2,10,11,12,14],
  [1,2,10,11,13,14],[1,2,11,12,13,14],[1,3,4,6,7,15],
  [1,3,4,6,8,11],[1,3,4,6,11,14],[1,3,4,6,14,15],
  [1,3,4,7,8,12],[1,3,4,7,12,15],[1,3,4,8,11,12],
  [1,3,4,11,12,14],[1,3,4,12,13,14],[1,3,4,12,13,15],
  [1,3,4,13,14,15],[1,3,5,6,8,13],[1,3,5,6,13,14],
  [1,3,5,6,14,15],[1,3,5,7,8,15],[1,3,5,8,13,15],
  [1,3,5,13,14,15],[1,3,6,8,11,13],[1,3,6,11,13,14],
  [1,3,7,8,12,15],[1,3,8,11,12,15],[1,3,8,11,13,15],
  [1,3,11,12,13,14],[1,3,11,12,13,15],[1,4,5,7,8,11],
  [1,4,5,7,11,12],[1,4,5,7,12,15],[1,4,5,8,9,11],
  [1,4,5,8,9,13],[1,4,5,9,11,12],[1,4,5,9,12,15],
  [1,4,5,9,13,15],[1,4,5,13,14,15],[1,4,6,8,9,11],
  [1,4,6,9,11,14],[1,4,7,8,11,12],[1,4,9,11,12,14],
  [1,4,9,12,13,15],[1,5,6,10,13,14],[1,5,7,8,11,12],
  [1,5,7,8,12,15],[1,5,8,9,11,15],[1,5,8,9,13,15],
  [1,5,8,11,12,15],[1,5,9,11,12,15],[1,6,8,9,11,13],
  [1,6,9,10,12,13],[1,6,9,10,13,14],[1,6,9,11,13,14],
  [1,8,9,11,13,15],[1,9,10,11,12,14],[1,9,10,11,12,15],
  [1,9,10,11,13,14],[1,9,10,11,13,15],
  [1,9,10,12,13,15],[1,10,11,12,13,15],[2,3,4,5,7,8],
  [2,3,4,5,7,9],[2,3,4,5,8,9],[2,3,4,6,7,9],
  [2,3,4,6,8,9],[2,3,5,6,8,9],[2,3,5,6,9,14],
  [2,3,5,6,14,15],[2,3,5,7,9,10],[2,3,5,7,10,15],
  [2,3,5,9,10,14],[2,3,5,10,13,14],[2,3,5,10,13,15],
  [2,3,5,13,14,15],[2,3,6,7,9,14],[2,3,6,7,11,14],
  [2,3,6,7,11,15],[2,3,6,11,14,15],[2,3,7,9,10,14],
  [2,3,7,10,11,13],[2,3,7,10,11,15],[2,3,7,10,13,14],
  [2,3,7,11,13,14],[2,3,10,11,13,15],[2,3,11,12,13,14],
  [2,3,11,12,13,15],[2,3,11,12,14,15],
  [2,3,12,13,14,15],[2,4,5,7,9,12],[2,4,5,7,12,15],
  [2,4,5,8,9,13],[2,4,5,9,12,13],[2,4,5,12,13,15],
  [2,4,5,13,14,15],[2,4,6,7,9,14],[2,4,6,7,14,15],
  [2,4,7,9,12,14],[2,4,7,12,14,15],[2,4,12,13,14,15],
  [2,5,6,8,9,12],[2,5,6,8,12,13],[2,5,6,9,10,12],
  [2,5,6,9,10,14],[2,5,6,10,12,13],[2,5,7,9,10,12],
  [2,5,7,10,12,15],[2,5,8,9,12,13],[2,5,10,12,13,15],
  [2,6,7,11,14,15],[2,6,8,9,12,13],[2,7,9,10,12,14],
  [2,7,10,11,13,14],[2,7,10,11,14,15],
  [2,7,10,12,14,15],[2,10,11,12,13,15],
  [2,10,11,12,14,15],[3,4,5,6,8,9],[3,4,5,6,8,10],
  [3,4,5,6,9,10],[3,4,5,7,8,10],[3,4,5,7,9,10],
  [3,4,6,7,9,10],[3,4,6,7,10,15],[3,4,6,8,10,11],
  [3,4,6,10,11,15],[3,4,6,11,14,15],[3,4,7,8,10,15],
  [3,4,7,8,12,15],[3,4,8,10,11,15],[3,4,8,11,12,14],
  [3,4,8,11,14,15],[3,4,8,12,14,15],[3,4,12,13,14,15],
  [3,5,6,8,10,13],[3,5,6,9,10,14],[3,5,6,10,13,14],
  [3,5,7,8,10,15],[3,5,8,10,13,15],[3,6,7,9,10,13],
  [3,6,7,9,13,14],[3,6,7,10,11,13],[3,6,7,10,11,15],
  [3,6,7,11,13,14],[3,6,8,10,11,13],[3,6,9,10,13,14],
  [3,7,9,10,13,14],[3,8,10,11,13,15],[3,8,11,12,14,15],
  [4,5,6,7,9,10],[4,5,6,7,9,11],[4,5,6,7,10,11],
  [4,5,6,8,9,11],[4,5,6,8,10,11],[4,5,7,8,10,11],
  [4,5,7,9,11,12],[4,5,9,12,13,15],[4,6,7,9,11,14],
  [4,6,7,10,11,15],[4,6,7,11,14,15],[4,7,8,10,11,14],
  [4,7,8,10,14,15],[4,7,8,11,12,14],[4,7,8,12,14,15],
  [4,7,9,11,12,14],[4,7,10,11,14,15],[4,8,10,11,14,15],
  [5,6,7,8,10,11],[5,6,7,8,10,12],[5,6,7,8,11,12],
  [5,6,7,9,10,12],[5,6,7,9,11,12],[5,6,8,9,11,12],
  [5,6,8,10,12,13],[5,7,8,10,12,15],[5,8,9,11,12,15],
  [5,8,9,12,13,15],[5,8,10,12,13,15],[6,7,8,9,11,12],
  [6,7,8,9,11,13],[6,7,8,9,12,13],[6,7,8,10,11,13],
  [6,7,8,10,12,13],[6,7,9,10,12,13],[6,7,9,11,13,14],
  [7,8,9,10,12,13],[7,8,9,10,12,14],[7,8,9,10,13,14],
  [7,8,9,11,12,14],[7,8,9,11,13,14],[7,8,10,11,13,14],
  [7,8,10,12,14,15],[8,9,10,11,13,14],
  [8,9,10,11,13,15],[8,9,10,11,14,15],
  [8,9,10,12,13,15],[8,9,10,12,14,15],
  [8,9,11,12,14,15],[9,10,11,12,14,15]]

manifold_5_15_3_1=[[1,2,3,4,5,7],[1,2,3,4,5,8],
  [1,2,3,4,6,8],[1,2,3,4,6,15],[1,2,3,4,7,15],
  [1,2,3,5,6,8],[1,2,3,5,6,14],[1,2,3,5,7,15],
  [1,2,3,5,14,15],[1,2,3,6,14,15],[1,2,4,5,7,15],
  [1,2,4,5,8,12],[1,2,4,5,12,13],[1,2,4,5,13,15],
  [1,2,4,6,8,9],[1,2,4,6,9,14],[1,2,4,6,14,15],
  [1,2,4,8,9,12],[1,2,4,9,12,14],[1,2,4,12,13,14],
  [1,2,4,13,14,15],[1,2,5,6,8,9],[1,2,5,6,9,14],
  [1,2,5,8,9,12],[1,2,5,9,10,12],[1,2,5,9,10,13],
  [1,2,5,9,13,14],[1,2,5,10,12,13],[1,2,5,13,14,15],
  [1,2,9,10,12,14],[1,2,9,10,13,14],[1,2,10,12,13,14],
  [1,3,4,5,7,8],[1,3,4,6,8,11],[1,3,4,6,11,14],
  [1,3,4,6,14,15],[1,3,4,7,8,11],[1,3,4,7,11,15],
  [1,3,4,11,12,14],[1,3,4,11,12,15],[1,3,4,12,14,15],
  [1,3,5,6,8,13],[1,3,5,6,13,14],[1,3,5,7,8,15],
  [1,3,5,8,13,15],[1,3,5,13,14,15],[1,3,6,8,11,13],
  [1,3,6,11,13,14],[1,3,7,8,11,15],[1,3,8,11,13,15],
  [1,3,11,12,13,14],[1,3,11,12,13,15],
  [1,3,12,13,14,15],[1,4,5,7,8,15],[1,4,5,8,12,13],
  [1,4,5,8,13,15],[1,4,6,8,9,11],[1,4,6,9,11,14],
  [1,4,7,8,11,15],[1,4,8,9,11,15],[1,4,8,9,12,15],
  [1,4,8,12,13,15],[1,4,9,11,12,14],[1,4,9,11,12,15],
  [1,4,12,13,14,15],[1,5,6,8,9,12],[1,5,6,8,12,13],
  [1,5,6,9,12,13],[1,5,6,9,13,14],[1,5,9,10,12,13],
  [1,6,8,9,11,13],[1,6,8,9,12,13],[1,6,9,11,13,14],
  [1,8,9,11,13,15],[1,8,9,12,13,15],[1,9,10,11,12,13],
  [1,9,10,11,12,14],[1,9,10,11,13,14],
  [1,9,11,12,13,15],[1,10,11,12,13,14],[2,3,4,5,6,8],
  [2,3,4,5,6,9],[2,3,4,5,7,9],[2,3,4,6,7,9],
  [2,3,4,6,7,15],[2,3,5,6,9,13],[2,3,5,6,13,14],
  [2,3,5,7,9,10],[2,3,5,7,10,15],[2,3,5,9,10,13],
  [2,3,5,10,13,15],[2,3,5,13,14,15],[2,3,6,7,9,10],
  [2,3,6,7,10,15],[2,3,6,9,10,13],[2,3,6,10,11,13],
  [2,3,6,10,11,14],[2,3,6,10,14,15],[2,3,6,11,13,14],
  [2,3,10,11,13,15],[2,3,10,11,14,15],
  [2,3,11,13,14,15],[2,4,5,6,8,9],[2,4,5,7,9,12],
  [2,4,5,7,12,15],[2,4,5,8,9,12],[2,4,5,12,13,15],
  [2,4,6,7,9,14],[2,4,6,7,14,15],[2,4,7,9,12,14],
  [2,4,7,12,14,15],[2,4,12,13,14,15],[2,5,6,9,13,14],
  [2,5,7,9,10,12],[2,5,7,10,12,15],[2,5,10,12,13,15],
  [2,6,7,9,10,13],[2,6,7,9,13,14],[2,6,7,10,13,14],
  [2,6,7,10,14,15],[2,6,10,11,13,14],[2,7,9,10,12,14],
  [2,7,9,10,13,14],[2,7,10,12,14,15],
  [2,10,11,12,13,14],[2,10,11,12,13,15],
  [2,10,11,12,14,15],[2,11,12,13,14,15],[3,4,5,6,7,9],
  [3,4,5,6,7,10],[3,4,5,6,8,10],[3,4,5,7,8,10],
  [3,4,6,7,10,14],[3,4,6,7,14,15],[3,4,6,8,10,11],
  [3,4,6,10,11,14],[3,4,7,8,10,11],[3,4,7,10,11,14],
  [3,4,7,11,12,14],[3,4,7,11,12,15],[3,4,7,12,14,15],
  [3,5,6,7,9,10],[3,5,6,8,10,13],[3,5,6,9,10,13],
  [3,5,7,8,10,15],[3,5,8,10,13,15],[3,6,7,10,14,15],
  [3,6,8,10,11,13],[3,7,8,10,11,14],[3,7,8,10,14,15],
  [3,7,8,11,14,15],[3,7,11,12,14,15],[3,8,10,11,13,15],
  [3,8,10,11,14,15],[3,11,12,13,14,15],[4,5,6,7,8,10],
  [4,5,6,7,8,11],[4,5,6,7,9,11],[4,5,6,8,9,11],
  [4,5,7,8,11,15],[4,5,7,9,11,12],[4,5,7,11,12,15],
  [4,5,8,9,11,12],[4,5,8,11,12,15],[4,5,8,12,13,15],
  [4,6,7,8,10,11],[4,6,7,9,11,14],[4,6,7,10,11,14],
  [4,7,9,11,12,14],[4,8,9,11,12,15],[5,6,7,8,9,11],
  [5,6,7,8,9,12],[5,6,7,8,10,12],[5,6,7,9,10,12],
  [5,6,8,10,12,13],[5,6,9,10,12,13],[5,7,8,9,11,12],
  [5,7,8,10,12,15],[5,7,8,11,12,15],[5,8,10,12,13,15],
  [6,7,8,9,10,12],[6,7,8,9,10,13],[6,7,8,9,11,13],
  [6,7,8,10,11,13],[6,7,9,11,13,14],[6,7,10,11,13,14],
  [6,8,9,10,12,13],[7,8,9,10,11,13],[7,8,9,10,11,14],
  [7,8,9,10,12,14],[7,8,9,11,12,14],[7,8,10,12,14,15],
  [7,8,11,12,14,15],[7,9,10,11,13,14],
  [8,9,10,11,12,14],[8,9,10,11,12,15],
  [8,9,10,11,13,15],[8,9,10,12,13,15],
  [8,10,11,12,14,15],[9,10,11,12,13,15]]

manifold_5_15_3_2=[[1,2,3,4,5,7],[1,2,3,4,5,13],
  [1,2,3,4,6,13],[1,2,3,4,6,15],[1,2,3,4,7,12],
  [1,2,3,4,12,15],[1,2,3,5,7,12],[1,2,3,5,10,13],
  [1,2,3,5,10,14],[1,2,3,5,12,15],[1,2,3,5,14,15],
  [1,2,3,6,10,11],[1,2,3,6,10,13],[1,2,3,6,11,15],
  [1,2,3,10,11,14],[1,2,3,11,14,15],[1,2,4,5,7,9],
  [1,2,4,5,9,13],[1,2,4,6,11,14],[1,2,4,6,11,15],
  [1,2,4,6,13,14],[1,2,4,7,9,12],[1,2,4,9,12,15],
  [1,2,4,9,13,15],[1,2,4,11,14,15],[1,2,4,13,14,15],
  [1,2,5,7,8,9],[1,2,5,7,8,12],[1,2,5,8,9,12],
  [1,2,5,9,10,13],[1,2,5,9,10,15],[1,2,5,9,12,15],
  [1,2,5,10,14,15],[1,2,6,10,11,14],[1,2,6,10,13,14],
  [1,2,7,8,9,12],[1,2,9,10,13,15],[1,2,10,13,14,15],
  [1,3,4,5,7,12],[1,3,4,5,12,13],[1,3,4,6,8,13],
  [1,3,4,6,8,15],[1,3,4,8,12,13],[1,3,4,8,12,15],
  [1,3,5,10,13,15],[1,3,5,10,14,15],[1,3,5,12,13,15],
  [1,3,6,8,11,13],[1,3,6,8,11,15],[1,3,6,10,11,13],
  [1,3,8,11,13,14],[1,3,8,11,14,15],[1,3,8,12,13,14],
  [1,3,8,12,14,15],[1,3,10,11,13,14],[1,3,10,13,14,15],
  [1,3,12,13,14,15],[1,4,5,6,7,8],[1,4,5,6,7,9],
  [1,4,5,6,8,13],[1,4,5,6,9,13],[1,4,5,7,8,12],
  [1,4,5,8,12,13],[1,4,6,7,8,15],[1,4,6,7,9,11],
  [1,4,6,7,11,15],[1,4,6,9,11,14],[1,4,6,9,13,14],
  [1,4,7,8,9,11],[1,4,7,8,9,12],[1,4,7,8,11,15],
  [1,4,8,9,11,14],[1,4,8,9,12,15],[1,4,8,9,14,15],
  [1,4,8,11,14,15],[1,4,9,13,14,15],[1,5,6,7,8,11],
  [1,5,6,7,9,11],[1,5,6,8,11,13],[1,5,6,9,11,12],
  [1,5,6,9,12,13],[1,5,6,11,12,13],[1,5,7,8,9,11],
  [1,5,8,9,11,12],[1,5,8,11,12,13],[1,5,9,10,13,15],
  [1,5,9,12,13,15],[1,6,7,8,11,15],[1,6,9,11,12,14],
  [1,6,9,12,13,14],[1,6,10,11,12,13],[1,6,10,11,12,14],
  [1,6,10,12,13,14],[1,8,9,11,12,14],[1,8,9,12,14,15],
  [1,8,11,12,13,14],[1,9,12,13,14,15],
  [1,10,11,12,13,14],[2,3,4,5,6,8],[2,3,4,5,6,14],
  [2,3,4,5,7,14],[2,3,4,5,8,13],[2,3,4,6,8,13],
  [2,3,4,6,11,14],[2,3,4,6,11,15],[2,3,4,7,11,12],
  [2,3,4,7,11,14],[2,3,4,11,12,15],[2,3,5,6,8,10],
  [2,3,5,6,10,14],[2,3,5,7,12,15],[2,3,5,7,14,15],
  [2,3,5,8,10,13],[2,3,6,8,9,10],[2,3,6,8,9,13],
  [2,3,6,9,10,13],[2,3,6,10,11,14],[2,3,7,11,12,15],
  [2,3,7,11,14,15],[2,3,8,9,10,13],[2,4,5,6,8,13],
  [2,4,5,6,13,14],[2,4,5,7,9,14],[2,4,5,9,13,14],
  [2,4,7,9,12,14],[2,4,7,11,12,14],[2,4,9,12,14,15],
  [2,4,9,13,14,15],[2,4,11,12,14,15],[2,5,6,7,8,9],
  [2,5,6,7,8,10],[2,5,6,7,9,14],[2,5,6,7,10,14],
  [2,5,6,8,9,13],[2,5,6,9,13,14],[2,5,7,8,10,12],
  [2,5,7,10,12,15],[2,5,7,10,14,15],[2,5,8,9,10,12],
  [2,5,8,9,10,13],[2,5,9,10,12,15],[2,6,7,8,9,12],
  [2,6,7,8,10,12],[2,6,7,9,12,14],[2,6,7,10,12,13],
  [2,6,7,10,13,14],[2,6,7,12,13,14],[2,6,8,9,10,12],
  [2,6,9,10,12,13],[2,6,9,12,13,14],[2,7,10,12,13,15],
  [2,7,10,13,14,15],[2,7,11,12,13,14],
  [2,7,11,12,13,15],[2,7,11,13,14,15],
  [2,9,10,12,13,15],[2,9,12,13,14,15],
  [2,11,12,13,14,15],[3,4,5,6,7,9],[3,4,5,6,7,15],
  [3,4,5,6,8,15],[3,4,5,6,9,14],[3,4,5,7,9,14],
  [3,4,5,7,12,15],[3,4,5,8,12,13],[3,4,5,8,12,15],
  [3,4,6,7,9,11],[3,4,6,7,11,15],[3,4,6,9,11,14],
  [3,4,7,9,10,11],[3,4,7,9,10,14],[3,4,7,10,11,14],
  [3,4,7,11,12,15],[3,4,9,10,11,14],[3,5,6,7,9,14],
  [3,5,6,7,14,15],[3,5,6,8,10,15],[3,5,6,10,14,15],
  [3,5,8,10,13,15],[3,5,8,12,13,15],[3,6,7,8,9,10],
  [3,6,7,8,9,11],[3,6,7,8,10,15],[3,6,7,8,11,15],
  [3,6,7,9,10,14],[3,6,7,10,14,15],[3,6,8,9,11,13],
  [3,6,9,10,11,13],[3,6,9,10,11,14],[3,7,8,9,10,13],
  [3,7,8,9,11,13],[3,7,8,10,13,15],[3,7,8,11,13,14],
  [3,7,8,11,14,15],[3,7,8,13,14,15],[3,7,9,10,11,13],
  [3,7,10,11,13,14],[3,7,10,13,14,15],
  [3,8,12,13,14,15],[4,5,6,7,8,10],[4,5,6,7,10,15],
  [4,5,6,8,10,15],[4,5,6,9,13,14],[4,5,7,8,10,12],
  [4,5,7,10,12,15],[4,5,8,10,11,12],[4,5,8,10,11,15],
  [4,5,8,11,12,15],[4,5,10,11,12,15],[4,6,7,8,10,15],
  [4,7,8,9,10,11],[4,7,8,9,10,12],[4,7,8,10,11,15],
  [4,7,9,10,12,14],[4,7,10,11,12,14],[4,7,10,11,12,15],
  [4,8,9,10,11,14],[4,8,9,10,12,14],[4,8,9,12,14,15],
  [4,8,10,11,12,14],[4,8,11,12,14,15],[5,6,7,8,9,11],
  [5,6,7,10,14,15],[5,6,8,9,11,13],[5,6,9,11,12,13],
  [5,8,9,10,11,12],[5,8,9,10,11,13],[5,8,10,11,13,15],
  [5,8,11,12,13,15],[5,9,10,11,12,15],
  [5,9,10,11,13,15],[5,9,11,12,13,15],[6,7,8,9,10,12],
  [6,7,9,10,12,14],[6,7,10,12,13,14],[6,9,10,11,12,13],
  [6,9,10,11,12,14],[7,8,9,10,11,13],[7,8,10,11,13,15],
  [7,8,11,13,14,15],[7,10,11,12,13,14],
  [7,10,11,12,13,15],[8,9,10,11,12,14],
  [8,11,12,13,14,15],[9,10,11,12,13,15]]

manifold_5_15_3_3=[[1,2,3,4,5,8],[1,2,3,4,5,9],
  [1,2,3,4,6,9],[1,2,3,4,6,14],[1,2,3,4,7,14],
  [1,2,3,4,7,15],[1,2,3,4,8,15],[1,2,3,5,8,15],
  [1,2,3,5,9,13],[1,2,3,5,13,15],[1,2,3,6,9,13],
  [1,2,3,6,13,15],[1,2,3,6,14,15],[1,2,3,7,14,15],
  [1,2,4,5,8,12],[1,2,4,5,9,12],[1,2,4,6,9,14],
  [1,2,4,7,14,15],[1,2,4,8,12,15],[1,2,4,9,12,14],
  [1,2,4,12,14,15],[1,2,5,8,12,15],[1,2,5,9,12,14],
  [1,2,5,9,13,14],[1,2,5,12,14,15],[1,2,5,13,14,15],
  [1,2,6,9,13,14],[1,2,6,13,14,15],[1,3,4,5,6,8],
  [1,3,4,5,6,9],[1,3,4,6,8,11],[1,3,4,6,11,14],
  [1,3,4,7,11,14],[1,3,4,7,11,15],[1,3,4,8,11,15],
  [1,3,5,6,8,13],[1,3,5,6,9,13],[1,3,5,8,13,15],
  [1,3,6,8,11,13],[1,3,6,11,13,14],[1,3,6,13,14,15],
  [1,3,7,11,14,15],[1,3,8,11,13,15],[1,3,11,13,14,15],
  [1,4,5,6,8,12],[1,4,5,6,9,12],[1,4,6,8,9,11],
  [1,4,6,8,9,12],[1,4,6,9,11,14],[1,4,7,11,14,15],
  [1,4,8,9,11,12],[1,4,8,11,12,13],[1,4,8,11,13,15],
  [1,4,8,12,13,15],[1,4,9,11,12,14],[1,4,11,12,13,14],
  [1,4,11,13,14,15],[1,4,12,13,14,15],[1,5,6,8,9,12],
  [1,5,6,8,9,13],[1,5,8,9,10,12],[1,5,8,9,10,13],
  [1,5,8,10,12,13],[1,5,8,12,13,15],[1,5,9,10,12,13],
  [1,5,9,12,13,14],[1,5,12,13,14,15],[1,6,8,9,11,13],
  [1,6,9,11,13,14],[1,8,9,10,11,12],[1,8,9,10,11,13],
  [1,8,10,11,12,13],[1,9,10,11,12,13],
  [1,9,11,12,13,14],[2,3,4,5,6,9],[2,3,4,5,6,10],
  [2,3,4,5,7,10],[2,3,4,5,7,15],[2,3,4,5,8,15],
  [2,3,4,6,10,14],[2,3,4,7,10,14],[2,3,5,6,9,13],
  [2,3,5,6,10,13],[2,3,5,7,10,15],[2,3,5,10,13,15],
  [2,3,6,10,13,15],[2,3,6,10,14,15],[2,3,7,10,14,15],
  [2,4,5,6,7,9],[2,4,5,6,7,10],[2,4,5,7,9,12],
  [2,4,5,7,12,15],[2,4,5,8,12,15],[2,4,6,7,9,14],
  [2,4,6,7,10,14],[2,4,7,9,12,14],[2,4,7,12,14,15],
  [2,5,6,7,9,13],[2,5,6,7,10,13],[2,5,7,9,10,12],
  [2,5,7,9,10,13],[2,5,7,10,12,15],[2,5,9,10,12,13],
  [2,5,9,12,13,14],[2,5,10,12,13,15],[2,5,12,13,14,15],
  [2,6,7,9,10,13],[2,6,7,9,10,14],[2,6,9,10,11,13],
  [2,6,9,10,11,14],[2,6,9,11,13,14],[2,6,10,11,13,14],
  [2,6,10,13,14,15],[2,7,9,10,12,14],[2,7,10,12,14,15],
  [2,9,10,11,12,13],[2,9,10,11,12,14],
  [2,9,11,12,13,14],[2,10,11,12,13,14],
  [2,10,12,13,14,15],[3,4,5,6,7,10],[3,4,5,6,7,11],
  [3,4,5,6,8,11],[3,4,5,7,11,15],[3,4,5,8,11,15],
  [3,4,6,7,10,14],[3,4,6,7,11,14],[3,5,6,7,8,10],
  [3,5,6,7,8,11],[3,5,6,8,10,13],[3,5,7,8,10,15],
  [3,5,7,8,11,15],[3,5,8,10,13,15],[3,6,7,8,10,14],
  [3,6,7,8,11,14],[3,6,8,10,11,13],[3,6,8,10,11,14],
  [3,6,10,11,13,14],[3,6,10,13,14,15],[3,7,8,10,11,14],
  [3,7,8,10,11,15],[3,7,10,11,12,14],[3,7,10,11,12,15],
  [3,7,10,12,14,15],[3,7,11,12,14,15],
  [3,8,10,11,13,15],[3,10,11,12,13,14],
  [3,10,11,12,13,15],[3,10,12,13,14,15],
  [3,11,12,13,14,15],[4,5,6,7,8,11],[4,5,6,7,8,12],
  [4,5,6,7,9,12],[4,5,7,8,11,15],[4,5,7,8,12,15],
  [4,6,7,8,9,11],[4,6,7,8,9,12],[4,6,7,9,11,14],
  [4,7,8,9,11,15],[4,7,8,9,12,15],[4,7,9,11,12,14],
  [4,7,9,11,12,15],[4,7,11,12,14,15],[4,8,9,11,12,15],
  [4,8,11,12,13,15],[4,11,12,13,14,15],[5,6,7,8,9,12],
  [5,6,7,8,9,13],[5,6,7,8,10,13],[5,7,8,9,10,12],
  [5,7,8,9,10,13],[5,7,8,10,12,15],[5,8,10,12,13,15],
  [6,7,8,9,10,13],[6,7,8,9,10,14],[6,7,8,9,11,14],
  [6,8,9,10,11,13],[6,8,9,10,11,14],[7,8,9,10,11,14],
  [7,8,9,10,11,15],[7,8,9,10,12,15],[7,9,10,11,12,14],
  [7,9,10,11,12,15],[8,9,10,11,12,15],
  [8,10,11,12,13,15]]

manifold_5_15_3_4=[[1,2,3,4,5,8],[1,2,3,4,5,9],
  [1,2,3,4,7,14],[1,2,3,4,7,15],[1,2,3,4,8,15],
  [1,2,3,4,9,14],[1,2,3,5,8,13],[1,2,3,5,9,13],
  [1,2,3,6,9,13],[1,2,3,6,9,14],[1,2,3,6,13,15],
  [1,2,3,6,14,15],[1,2,3,7,14,15],[1,2,3,8,13,15],
  [1,2,4,5,8,12],[1,2,4,5,9,14],[1,2,4,5,12,14],
  [1,2,4,7,12,14],[1,2,4,7,12,15],[1,2,4,8,12,15],
  [1,2,5,8,12,15],[1,2,5,8,13,15],[1,2,5,9,13,14],
  [1,2,5,12,14,15],[1,2,5,13,14,15],[1,2,6,9,11,13],
  [1,2,6,9,11,14],[1,2,6,11,13,14],[1,2,6,13,14,15],
  [1,2,7,12,14,15],[1,2,9,11,13,14],[1,3,4,5,6,9],
  [1,3,4,5,6,11],[1,3,4,5,8,11],[1,3,4,6,7,11],
  [1,3,4,6,7,14],[1,3,4,6,9,14],[1,3,4,7,11,15],
  [1,3,4,8,11,13],[1,3,4,8,13,15],[1,3,4,11,13,15],
  [1,3,5,6,8,9],[1,3,5,6,8,11],[1,3,5,8,9,13],
  [1,3,6,7,11,14],[1,3,6,8,9,13],[1,3,6,8,11,13],
  [1,3,6,11,13,15],[1,3,6,11,14,15],[1,3,7,11,14,15],
  [1,4,5,6,8,11],[1,4,5,6,8,12],[1,4,5,6,9,12],
  [1,4,5,9,12,14],[1,4,6,7,11,14],[1,4,6,8,11,12],
  [1,4,6,9,11,12],[1,4,6,9,11,14],[1,4,7,11,14,15],
  [1,4,7,12,14,15],[1,4,8,11,12,13],[1,4,8,12,13,15],
  [1,4,9,11,12,13],[1,4,9,11,13,14],[1,4,9,12,13,14],
  [1,4,11,13,14,15],[1,4,12,13,14,15],[1,5,6,8,9,12],
  [1,5,8,9,10,12],[1,5,8,9,10,13],[1,5,8,10,12,15],
  [1,5,8,10,13,15],[1,5,9,10,12,13],[1,5,9,12,13,14],
  [1,5,10,12,13,15],[1,5,12,13,14,15],[1,6,8,9,10,11],
  [1,6,8,9,10,13],[1,6,8,9,11,12],[1,6,8,10,11,13],
  [1,6,9,10,11,13],[1,6,11,13,14,15],[1,8,9,10,11,12],
  [1,8,10,11,12,13],[1,8,10,12,13,15],
  [1,9,10,11,12,13],[2,3,4,5,6,9],[2,3,4,5,6,10],
  [2,3,4,5,8,15],[2,3,4,5,10,15],[2,3,4,6,9,14],
  [2,3,4,6,10,14],[2,3,4,7,10,14],[2,3,4,7,10,15],
  [2,3,5,6,9,13],[2,3,5,6,10,15],[2,3,5,6,13,15],
  [2,3,5,8,13,15],[2,3,6,10,14,15],[2,3,7,10,12,14],
  [2,3,7,10,12,15],[2,3,7,12,14,15],[2,3,10,12,14,15],
  [2,4,5,6,7,10],[2,4,5,6,7,12],[2,4,5,6,9,12],
  [2,4,5,7,8,12],[2,4,5,7,8,15],[2,4,5,7,10,15],
  [2,4,5,9,12,14],[2,4,6,7,9,10],[2,4,6,7,9,12],
  [2,4,6,9,10,14],[2,4,7,8,12,15],[2,4,7,9,10,14],
  [2,4,7,9,12,14],[2,5,6,7,9,12],[2,5,6,7,9,13],
  [2,5,6,7,10,13],[2,5,6,10,13,15],[2,5,7,8,12,15],
  [2,5,7,9,12,13],[2,5,7,10,12,13],[2,5,7,10,12,15],
  [2,5,9,12,13,14],[2,5,10,12,13,14],[2,5,10,12,14,15],
  [2,5,10,13,14,15],[2,6,7,9,10,13],[2,6,9,10,11,13],
  [2,6,9,10,11,14],[2,6,10,11,13,14],[2,6,10,13,14,15],
  [2,7,9,10,11,12],[2,7,9,10,11,14],[2,7,9,10,12,13],
  [2,7,9,11,12,14],[2,7,10,11,12,14],[2,9,10,11,12,13],
  [2,9,11,12,13,14],[2,10,11,12,13,14],[3,4,5,6,7,10],
  [3,4,5,6,7,11],[3,4,5,7,10,15],[3,4,5,7,11,15],
  [3,4,5,8,11,15],[3,4,6,7,10,14],[3,4,8,11,13,15],
  [3,5,6,7,8,11],[3,5,6,7,8,13],[3,5,6,7,10,13],
  [3,5,6,8,9,13],[3,5,6,10,13,15],[3,5,7,8,10,11],
  [3,5,7,8,10,13],[3,5,7,10,11,15],[3,5,8,10,11,15],
  [3,5,8,10,13,15],[3,6,7,8,10,13],[3,6,7,8,10,14],
  [3,6,7,8,11,14],[3,6,8,10,13,14],[3,6,8,11,13,14],
  [3,6,10,13,14,15],[3,6,11,13,14,15],[3,7,8,10,11,14],
  [3,7,10,11,12,14],[3,7,10,11,12,15],
  [3,7,11,12,14,15],[3,8,10,11,12,13],
  [3,8,10,11,12,15],[3,8,10,11,13,14],
  [3,8,10,12,13,15],[3,8,11,12,13,15],
  [3,10,11,12,13,14],[3,10,12,13,14,15],
  [3,11,12,13,14,15],[4,5,6,7,8,11],[4,5,6,7,8,12],
  [4,5,7,8,11,15],[4,6,7,8,9,12],[4,6,7,8,9,14],
  [4,6,7,8,11,14],[4,6,7,9,10,14],[4,6,8,9,11,12],
  [4,6,8,9,11,14],[4,7,8,9,11,14],[4,7,8,9,11,15],
  [4,7,8,9,12,15],[4,7,9,11,14,15],[4,7,9,12,14,15],
  [4,8,9,11,12,15],[4,8,11,12,13,15],[4,9,11,12,13,14],
  [4,9,11,12,14,15],[4,11,12,13,14,15],[5,6,7,8,9,12],
  [5,6,7,8,9,13],[5,7,8,9,10,13],[5,7,8,9,10,15],
  [5,7,8,9,12,15],[5,7,8,10,11,15],[5,7,9,10,12,13],
  [5,7,9,10,12,15],[5,8,9,10,12,15],[5,10,12,13,14,15],
  [6,7,8,9,10,13],[6,7,8,9,10,14],[6,8,9,10,11,14],
  [6,8,10,11,13,14],[7,8,9,10,11,14],[7,8,9,10,11,15],
  [7,9,10,11,12,15],[7,9,11,12,14,15],
  [8,9,10,11,12,15]]

manifold_5_15_3_5=[[1,2,3,4,6,7],[1,2,3,4,6,8],
  [1,2,3,4,7,8],[1,2,3,5,6,8],[1,2,3,5,6,15],
  [1,2,3,5,7,8],[1,2,3,5,7,15],[1,2,3,6,7,15],
  [1,2,4,5,7,8],[1,2,4,5,7,15],[1,2,4,5,8,13],
  [1,2,4,5,13,14],[1,2,4,5,14,15],[1,2,4,6,7,15],
  [1,2,4,6,8,9],[1,2,4,6,9,14],[1,2,4,6,14,15],
  [1,2,4,8,9,12],[1,2,4,8,12,13],[1,2,4,9,12,14],
  [1,2,4,12,13,14],[1,2,5,6,8,12],[1,2,5,6,9,12],
  [1,2,5,6,9,14],[1,2,5,6,14,15],[1,2,5,8,12,13],
  [1,2,5,9,10,12],[1,2,5,9,10,14],[1,2,5,10,12,13],
  [1,2,5,10,13,14],[1,2,6,8,9,12],[1,2,9,10,12,14],
  [1,2,10,11,12,13],[1,2,10,11,12,14],
  [1,2,10,11,13,14],[1,2,11,12,13,14],[1,3,4,6,7,15],
  [1,3,4,6,8,11],[1,3,4,6,11,14],[1,3,4,6,14,15],
  [1,3,4,7,8,11],[1,3,4,7,11,12],[1,3,4,7,12,15],
  [1,3,4,11,12,14],[1,3,4,12,13,14],[1,3,4,12,13,15],
  [1,3,4,13,14,15],[1,3,5,6,8,13],[1,3,5,6,13,14],
  [1,3,5,6,14,15],[1,3,5,7,8,15],[1,3,5,8,13,15],
  [1,3,5,13,14,15],[1,3,6,8,11,13],[1,3,6,11,13,14],
  [1,3,7,8,11,15],[1,3,7,11,12,15],[1,3,8,11,13,15],
  [1,3,11,12,13,14],[1,3,11,12,13,15],[1,4,5,7,8,11],
  [1,4,5,7,11,15],[1,4,5,8,11,15],[1,4,5,8,13,15],
  [1,4,5,13,14,15],[1,4,6,8,9,11],[1,4,6,9,11,14],
  [1,4,7,11,12,15],[1,4,8,9,11,15],[1,4,8,9,12,13],
  [1,4,8,9,13,15],[1,4,9,11,12,14],[1,4,9,11,12,15],
  [1,4,9,12,13,15],[1,5,6,8,12,13],[1,5,6,9,10,12],
  [1,5,6,9,10,13],[1,5,6,9,13,14],[1,5,6,10,12,13],
  [1,5,7,8,11,15],[1,5,9,10,13,14],[1,6,8,9,11,13],
  [1,6,8,9,12,13],[1,6,9,10,12,13],[1,6,9,11,13,14],
  [1,8,9,11,13,15],[1,9,10,11,12,14],[1,9,10,11,12,15],
  [1,9,10,11,13,14],[1,9,10,11,13,15],
  [1,9,10,12,13,15],[1,10,11,12,13,15],[2,3,4,5,7,8],
  [2,3,4,5,7,9],[2,3,4,5,8,9],[2,3,4,6,7,9],
  [2,3,4,6,8,9],[2,3,5,6,8,9],[2,3,5,6,9,14],
  [2,3,5,6,14,15],[2,3,5,7,9,10],[2,3,5,7,10,15],
  [2,3,5,9,10,13],[2,3,5,9,13,14],[2,3,5,10,13,15],
  [2,3,5,13,14,15],[2,3,6,7,9,13],[2,3,6,7,10,13],
  [2,3,6,7,10,15],[2,3,6,9,13,14],[2,3,6,10,11,13],
  [2,3,6,10,11,15],[2,3,6,11,13,14],[2,3,6,11,14,15],
  [2,3,7,9,10,13],[2,3,10,11,13,15],[2,3,11,12,13,14],
  [2,3,11,12,13,15],[2,3,11,12,14,15],
  [2,3,12,13,14,15],[2,4,5,7,9,12],[2,4,5,7,12,15],
  [2,4,5,8,9,12],[2,4,5,8,12,13],[2,4,5,12,13,15],
  [2,4,5,13,14,15],[2,4,6,7,9,14],[2,4,6,7,14,15],
  [2,4,7,9,12,14],[2,4,7,12,14,15],[2,4,12,13,14,15],
  [2,5,6,8,9,12],[2,5,7,9,10,12],[2,5,7,10,12,15],
  [2,5,9,10,13,14],[2,5,10,12,13,15],[2,6,7,9,13,14],
  [2,6,7,10,11,13],[2,6,7,10,11,14],[2,6,7,10,14,15],
  [2,6,7,11,13,14],[2,6,10,11,14,15],[2,7,9,10,12,14],
  [2,7,9,10,13,14],[2,7,10,11,13,14],[2,7,10,12,14,15],
  [2,10,11,12,13,15],[2,10,11,12,14,15],[3,4,5,6,8,9],
  [3,4,5,6,8,10],[3,4,5,6,9,10],[3,4,5,7,8,10],
  [3,4,5,7,9,10],[3,4,6,7,9,10],[3,4,6,7,10,15],
  [3,4,6,8,10,11],[3,4,6,10,11,14],[3,4,6,10,14,15],
  [3,4,7,8,10,14],[3,4,7,8,11,14],[3,4,7,10,14,15],
  [3,4,7,11,12,14],[3,4,7,12,14,15],[3,4,8,10,11,14],
  [3,4,12,13,14,15],[3,5,6,8,10,13],[3,5,6,9,10,13],
  [3,5,6,9,13,14],[3,5,7,8,10,15],[3,5,8,10,13,15],
  [3,6,7,9,10,13],[3,6,8,10,11,13],[3,6,10,11,14,15],
  [3,7,8,10,14,15],[3,7,8,11,12,14],[3,7,8,11,12,15],
  [3,7,8,12,14,15],[3,8,10,11,13,15],[3,8,10,11,14,15],
  [3,8,11,12,14,15],[4,5,6,7,9,10],[4,5,6,7,9,11],
  [4,5,6,7,10,11],[4,5,6,8,9,11],[4,5,6,8,10,11],
  [4,5,7,8,10,11],[4,5,7,9,11,12],[4,5,7,11,12,15],
  [4,5,8,9,11,15],[4,5,8,9,12,15],[4,5,8,12,13,15],
  [4,5,9,11,12,15],[4,6,7,9,11,14],[4,6,7,10,11,14],
  [4,6,7,10,14,15],[4,7,8,10,11,14],[4,7,9,11,12,14],
  [4,8,9,12,13,15],[5,6,7,8,10,11],[5,6,7,8,10,12],
  [5,6,7,8,11,12],[5,6,7,9,10,12],[5,6,7,9,11,12],
  [5,6,8,9,11,12],[5,6,8,10,12,13],[5,7,8,10,12,15],
  [5,7,8,11,12,15],[5,8,9,11,12,15],[5,8,10,12,13,15],
  [6,7,8,9,11,12],[6,7,8,9,11,13],[6,7,8,9,12,13],
  [6,7,8,10,11,13],[6,7,8,10,12,13],[6,7,9,10,12,13],
  [6,7,9,11,13,14],[7,8,9,10,12,13],[7,8,9,10,12,14],
  [7,8,9,10,13,14],[7,8,9,11,12,14],[7,8,9,11,13,14],
  [7,8,10,11,13,14],[7,8,10,12,14,15],
  [8,9,10,11,13,14],[8,9,10,11,13,15],
  [8,9,10,11,14,15],[8,9,10,12,13,15],
  [8,9,10,12,14,15],[8,9,11,12,14,15],
  [9,10,11,12,14,15]]

manifold_5_15_3_6=[[1,2,3,6,8,11],[1,2,3,6,8,12],
  [1,2,3,6,11,12],[1,2,3,7,8,11],[1,2,3,7,8,12],
  [1,2,3,7,11,12],[1,2,5,7,10,12],[1,2,5,7,10,15],
  [1,2,5,7,11,12],[1,2,5,7,11,15],[1,2,5,10,11,12],
  [1,2,5,10,11,15],[1,2,6,7,8,11],[1,2,6,7,8,12],
  [1,2,6,7,10,12],[1,2,6,7,10,15],[1,2,6,7,11,15],
  [1,2,6,10,11,12],[1,2,6,10,11,15],[1,3,6,8,11,13],
  [1,3,6,8,12,13],[1,3,6,11,12,13],[1,3,7,8,11,13],
  [1,3,7,8,12,13],[1,3,7,11,12,13],[1,4,6,9,11,14],
  [1,4,6,9,11,15],[1,4,6,9,14,15],[1,4,6,10,11,14],
  [1,4,6,10,11,15],[1,4,6,10,14,15],[1,4,9,10,11,14],
  [1,4,9,10,11,15],[1,4,9,10,14,15],[1,5,6,7,10,12],
  [1,5,6,7,10,15],[1,5,6,7,11,12],[1,5,6,7,11,15],
  [1,5,6,9,11,14],[1,5,6,9,11,15],[1,5,6,9,14,15],
  [1,5,6,10,11,12],[1,5,6,10,11,14],[1,5,6,10,14,15],
  [1,5,9,10,11,14],[1,5,9,10,11,15],[1,5,9,10,14,15],
  [1,6,7,8,11,13],[1,6,7,8,12,13],[1,6,7,11,12,13],
  [2,3,4,7,9,12],[2,3,4,7,9,13],[2,3,4,7,12,13],
  [2,3,4,8,9,12],[2,3,4,8,9,13],[2,3,4,8,12,13],
  [2,3,6,8,11,13],[2,3,6,8,12,13],[2,3,6,11,12,13],
  [2,3,7,8,9,12],[2,3,7,8,9,13],[2,3,7,8,11,13],
  [2,3,7,11,12,13],[2,4,7,9,12,14],[2,4,7,9,13,14],
  [2,4,7,12,13,14],[2,4,8,9,12,14],[2,4,8,9,13,14],
  [2,4,8,12,13,14],[2,5,7,10,12,15],[2,5,7,11,12,15],
  [2,5,10,11,12,15],[2,6,7,8,11,13],[2,6,7,8,12,13],
  [2,6,7,10,12,15],[2,6,7,11,12,13],[2,6,7,11,12,15],
  [2,6,10,11,12,15],[2,7,8,9,12,14],[2,7,8,9,13,14],
  [2,7,8,12,13,14],[3,4,5,8,10,13],[3,4,5,8,10,14],
  [3,4,5,8,13,14],[3,4,5,9,10,13],[3,4,5,9,10,14],
  [3,4,5,9,13,14],[3,4,7,9,12,14],[3,4,7,9,13,14],
  [3,4,7,12,13,14],[3,4,8,9,10,13],[3,4,8,9,10,14],
  [3,4,8,9,12,14],[3,4,8,12,13,14],[3,5,8,10,13,15],
  [3,5,8,10,14,15],[3,5,8,13,14,15],[3,5,9,10,13,15],
  [3,5,9,10,14,15],[3,5,9,13,14,15],[3,7,8,9,12,14],
  [3,7,8,9,13,14],[3,7,8,12,13,14],[3,8,9,10,13,15],
  [3,8,9,10,14,15],[3,8,9,13,14,15],[4,5,6,9,11,14],
  [4,5,6,9,11,15],[4,5,6,9,14,15],[4,5,6,10,11,14],
  [4,5,6,10,11,15],[4,5,6,10,14,15],[4,5,8,10,13,15],
  [4,5,8,10,14,15],[4,5,8,13,14,15],[4,5,9,10,11,14],
  [4,5,9,10,11,15],[4,5,9,10,13,15],[4,5,9,13,14,15],
  [4,8,9,10,13,15],[4,8,9,10,14,15],[4,8,9,13,14,15],
  [5,6,7,10,12,15],[5,6,7,11,12,15],[5,6,10,11,12,15]]

manifold_5_15_2_1=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,10],[1,2,3,4,10,11],[1,2,3,4,11,12],
  [1,2,3,4,12,13],[1,2,3,4,13,14],[1,2,3,4,14,15],
  [1,2,3,5,6,15],[1,2,3,6,7,15],[1,2,3,7,8,15],
  [1,2,3,8,9,15],[1,2,3,9,10,15],[1,2,3,10,11,15],
  [1,2,3,11,12,15],[1,2,3,12,13,15],[1,2,3,13,14,15],
  [1,2,4,5,6,7],[1,2,4,5,7,8],[1,2,4,5,8,9],
  [1,2,4,5,9,10],[1,2,4,5,10,11],[1,2,4,5,11,12],
  [1,2,4,5,12,13],[1,2,4,5,13,14],[1,2,4,5,14,15],
  [1,2,5,6,7,8],[1,2,5,6,8,9],[1,2,5,6,9,10],
  [1,2,5,6,10,11],[1,2,5,6,11,12],[1,2,5,6,12,13],
  [1,2,5,6,13,14],[1,2,5,6,14,15],[1,2,6,7,8,9],
  [1,2,6,7,9,10],[1,2,6,7,10,11],[1,2,6,7,11,12],
  [1,2,6,7,12,13],[1,2,6,7,13,14],[1,2,6,7,14,15],
  [1,2,7,8,9,10],[1,2,7,8,10,11],[1,2,7,8,11,12],
  [1,2,7,8,12,13],[1,2,7,8,13,14],[1,2,7,8,14,15],
  [1,2,8,9,10,11],[1,2,8,9,11,12],[1,2,8,9,12,13],
  [1,2,8,9,13,14],[1,2,8,9,14,15],[1,2,9,10,11,12],
  [1,2,9,10,12,13],[1,2,9,10,13,14],[1,2,9,10,14,15],
  [1,2,10,11,12,13],[1,2,10,11,13,14],
  [1,2,10,11,14,15],[1,2,11,12,13,14],
  [1,2,11,12,14,15],[1,2,12,13,14,15],[1,3,4,5,6,15],
  [1,3,4,6,7,15],[1,3,4,7,8,15],[1,3,4,8,9,15],
  [1,3,4,9,10,15],[1,3,4,10,11,15],[1,3,4,11,12,15],
  [1,3,4,12,13,15],[1,3,4,13,14,15],[1,4,5,6,7,15],
  [1,4,5,7,8,15],[1,4,5,8,9,15],[1,4,5,9,10,15],
  [1,4,5,10,11,15],[1,4,5,11,12,15],[1,4,5,12,13,15],
  [1,4,5,13,14,15],[1,5,6,7,8,15],[1,5,6,8,9,15],
  [1,5,6,9,10,15],[1,5,6,10,11,15],[1,5,6,11,12,15],
  [1,5,6,12,13,15],[1,5,6,13,14,15],[1,6,7,8,9,15],
  [1,6,7,9,10,15],[1,6,7,10,11,15],[1,6,7,11,12,15],
  [1,6,7,12,13,15],[1,6,7,13,14,15],[1,7,8,9,10,15],
  [1,7,8,10,11,15],[1,7,8,11,12,15],[1,7,8,12,13,15],
  [1,7,8,13,14,15],[1,8,9,10,11,15],[1,8,9,11,12,15],
  [1,8,9,12,13,15],[1,8,9,13,14,15],[1,9,10,11,12,15],
  [1,9,10,12,13,15],[1,9,10,13,14,15],
  [1,10,11,12,13,15],[1,10,11,13,14,15],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,11],
  [2,3,4,5,11,12],[2,3,4,5,12,13],[2,3,4,5,13,14],
  [2,3,4,5,14,15],[2,3,5,6,7,8],[2,3,5,6,8,9],
  [2,3,5,6,9,10],[2,3,5,6,10,11],[2,3,5,6,11,12],
  [2,3,5,6,12,13],[2,3,5,6,13,14],[2,3,5,6,14,15],
  [2,3,6,7,8,9],[2,3,6,7,9,10],[2,3,6,7,10,11],
  [2,3,6,7,11,12],[2,3,6,7,12,13],[2,3,6,7,13,14],
  [2,3,6,7,14,15],[2,3,7,8,9,10],[2,3,7,8,10,11],
  [2,3,7,8,11,12],[2,3,7,8,12,13],[2,3,7,8,13,14],
  [2,3,7,8,14,15],[2,3,8,9,10,11],[2,3,8,9,11,12],
  [2,3,8,9,12,13],[2,3,8,9,13,14],[2,3,8,9,14,15],
  [2,3,9,10,11,12],[2,3,9,10,12,13],[2,3,9,10,13,14],
  [2,3,9,10,14,15],[2,3,10,11,12,13],[2,3,10,11,13,14],
  [2,3,10,11,14,15],[2,3,11,12,13,14],
  [2,3,11,12,14,15],[2,3,12,13,14,15],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,10],[3,4,5,6,10,11],
  [3,4,5,6,11,12],[3,4,5,6,12,13],[3,4,5,6,13,14],
  [3,4,5,6,14,15],[3,4,6,7,8,9],[3,4,6,7,9,10],
  [3,4,6,7,10,11],[3,4,6,7,11,12],[3,4,6,7,12,13],
  [3,4,6,7,13,14],[3,4,6,7,14,15],[3,4,7,8,9,10],
  [3,4,7,8,10,11],[3,4,7,8,11,12],[3,4,7,8,12,13],
  [3,4,7,8,13,14],[3,4,7,8,14,15],[3,4,8,9,10,11],
  [3,4,8,9,11,12],[3,4,8,9,12,13],[3,4,8,9,13,14],
  [3,4,8,9,14,15],[3,4,9,10,11,12],[3,4,9,10,12,13],
  [3,4,9,10,13,14],[3,4,9,10,14,15],[3,4,10,11,12,13],
  [3,4,10,11,13,14],[3,4,10,11,14,15],
  [3,4,11,12,13,14],[3,4,11,12,14,15],
  [3,4,12,13,14,15],[4,5,6,7,8,9],[4,5,6,7,9,10],
  [4,5,6,7,10,11],[4,5,6,7,11,12],[4,5,6,7,12,13],
  [4,5,6,7,13,14],[4,5,6,7,14,15],[4,5,7,8,9,10],
  [4,5,7,8,10,11],[4,5,7,8,11,12],[4,5,7,8,12,13],
  [4,5,7,8,13,14],[4,5,7,8,14,15],[4,5,8,9,10,11],
  [4,5,8,9,11,12],[4,5,8,9,12,13],[4,5,8,9,13,14],
  [4,5,8,9,14,15],[4,5,9,10,11,12],[4,5,9,10,12,13],
  [4,5,9,10,13,14],[4,5,9,10,14,15],[4,5,10,11,12,13],
  [4,5,10,11,13,14],[4,5,10,11,14,15],
  [4,5,11,12,13,14],[4,5,11,12,14,15],
  [4,5,12,13,14,15],[5,6,7,8,9,10],[5,6,7,8,10,11],
  [5,6,7,8,11,12],[5,6,7,8,12,13],[5,6,7,8,13,14],
  [5,6,7,8,14,15],[5,6,8,9,10,11],[5,6,8,9,11,12],
  [5,6,8,9,12,13],[5,6,8,9,13,14],[5,6,8,9,14,15],
  [5,6,9,10,11,12],[5,6,9,10,12,13],[5,6,9,10,13,14],
  [5,6,9,10,14,15],[5,6,10,11,12,13],[5,6,10,11,13,14],
  [5,6,10,11,14,15],[5,6,11,12,13,14],
  [5,6,11,12,14,15],[5,6,12,13,14,15],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,8,9,12,13],[6,7,8,9,13,14],
  [6,7,8,9,14,15],[6,7,9,10,11,12],[6,7,9,10,12,13],
  [6,7,9,10,13,14],[6,7,9,10,14,15],[6,7,10,11,12,13],
  [6,7,10,11,13,14],[6,7,10,11,14,15],
  [6,7,11,12,13,14],[6,7,11,12,14,15],
  [6,7,12,13,14,15],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,9,10,13,14],[7,8,9,10,14,15],[7,8,10,11,12,13],
  [7,8,10,11,13,14],[7,8,10,11,14,15],
  [7,8,11,12,13,14],[7,8,11,12,14,15],
  [7,8,12,13,14,15],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,10,11,14,15],
  [8,9,11,12,13,14],[8,9,11,12,14,15],
  [8,9,12,13,14,15],[9,10,11,12,13,14],
  [9,10,11,12,14,15],[9,10,12,13,14,15],
  [10,11,12,13,14,15]]

manifold_5_15_2_2=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,7],[1,2,3,4,7,8],[1,2,3,4,8,9],
  [1,2,3,4,9,11],[1,2,3,4,11,12],[1,2,3,4,12,13],
  [1,2,3,4,13,14],[1,2,3,4,14,15],[1,2,3,5,6,15],
  [1,2,3,6,7,15],[1,2,3,7,8,15],[1,2,3,8,9,10],
  [1,2,3,8,10,15],[1,2,3,9,10,11],[1,2,3,10,11,15],
  [1,2,3,11,12,15],[1,2,3,12,13,15],[1,2,3,13,14,15],
  [1,2,4,5,6,7],[1,2,4,5,7,8],[1,2,4,5,8,9],
  [1,2,4,5,9,12],[1,2,4,5,12,13],[1,2,4,5,13,14],
  [1,2,4,5,14,15],[1,2,4,9,11,12],[1,2,5,6,7,8],
  [1,2,5,6,8,9],[1,2,5,6,9,13],[1,2,5,6,13,14],
  [1,2,5,6,14,15],[1,2,5,9,12,13],[1,2,6,7,8,9],
  [1,2,6,7,9,14],[1,2,6,7,14,15],[1,2,6,9,13,14],
  [1,2,7,8,9,15],[1,2,7,9,14,15],[1,2,8,9,10,15],
  [1,2,9,10,11,12],[1,2,9,10,12,13],[1,2,9,10,13,14],
  [1,2,9,10,14,15],[1,2,10,11,12,13],[1,2,10,11,13,14],
  [1,2,10,11,14,15],[1,2,11,12,13,14],
  [1,2,11,12,14,15],[1,2,12,13,14,15],[1,3,4,5,6,15],
  [1,3,4,6,7,15],[1,3,4,7,8,15],[1,3,4,8,9,11],
  [1,3,4,8,11,15],[1,3,4,11,12,15],[1,3,4,12,13,15],
  [1,3,4,13,14,15],[1,3,8,9,10,11],[1,3,8,10,11,15],
  [1,4,5,6,7,15],[1,4,5,7,8,15],[1,4,5,8,9,12],
  [1,4,5,8,12,15],[1,4,5,12,13,15],[1,4,5,13,14,15],
  [1,4,8,9,11,12],[1,4,8,11,12,15],[1,5,6,7,8,15],
  [1,5,6,8,9,13],[1,5,6,8,13,15],[1,5,6,13,14,15],
  [1,5,8,9,12,13],[1,5,8,12,13,15],[1,6,7,8,9,14],
  [1,6,7,8,14,15],[1,6,8,9,13,14],[1,6,8,13,14,15],
  [1,7,8,9,14,15],[1,8,9,10,11,15],[1,8,9,11,12,15],
  [1,8,9,12,13,15],[1,8,9,13,14,15],[1,9,10,11,12,15],
  [1,9,10,12,13,15],[1,9,10,13,14,15],
  [1,10,11,12,13,15],[1,10,11,13,14,15],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,8],
  [2,3,4,5,8,9],[2,3,4,5,9,10],[2,3,4,5,10,12],
  [2,3,4,5,12,13],[2,3,4,5,13,14],[2,3,4,5,14,15],
  [2,3,4,9,10,11],[2,3,4,10,11,12],[2,3,5,6,7,8],
  [2,3,5,6,8,9],[2,3,5,6,9,10],[2,3,5,6,10,13],
  [2,3,5,6,13,14],[2,3,5,6,14,15],[2,3,5,10,12,13],
  [2,3,6,7,8,9],[2,3,6,7,9,10],[2,3,6,7,10,14],
  [2,3,6,7,14,15],[2,3,6,10,13,14],[2,3,7,8,9,10],
  [2,3,7,8,10,15],[2,3,7,10,14,15],[2,3,10,11,12,13],
  [2,3,10,11,13,14],[2,3,10,11,14,15],
  [2,3,11,12,13,14],[2,3,11,12,14,15],
  [2,3,12,13,14,15],[2,4,5,9,10,12],[2,4,9,10,11,12],
  [2,5,6,9,10,13],[2,5,9,10,12,13],[2,6,7,9,10,14],
  [2,6,9,10,13,14],[2,7,8,9,10,15],[2,7,9,10,14,15],
  [3,4,5,6,7,8],[3,4,5,6,8,9],[3,4,5,6,9,10],
  [3,4,5,6,10,11],[3,4,5,6,11,13],[3,4,5,6,13,14],
  [3,4,5,6,14,15],[3,4,5,10,11,12],[3,4,5,11,12,13],
  [3,4,6,7,8,9],[3,4,6,7,9,10],[3,4,6,7,10,11],
  [3,4,6,7,11,14],[3,4,6,7,14,15],[3,4,6,11,13,14],
  [3,4,7,8,9,10],[3,4,7,8,10,11],[3,4,7,8,11,15],
  [3,4,7,11,14,15],[3,4,8,9,10,11],[3,4,11,12,13,14],
  [3,4,11,12,14,15],[3,4,12,13,14,15],[3,5,6,10,11,13],
  [3,5,10,11,12,13],[3,6,7,10,11,14],[3,6,10,11,13,14],
  [3,7,8,10,11,15],[3,7,10,11,14,15],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,11],[4,5,6,7,11,12],
  [4,5,6,7,12,14],[4,5,6,7,14,15],[4,5,6,11,12,13],
  [4,5,6,12,13,14],[4,5,7,8,9,10],[4,5,7,8,10,11],
  [4,5,7,8,11,12],[4,5,7,8,12,15],[4,5,7,12,14,15],
  [4,5,8,9,10,11],[4,5,8,9,11,12],[4,5,9,10,11,12],
  [4,5,12,13,14,15],[4,6,7,11,12,14],[4,6,11,12,13,14],
  [4,7,8,11,12,15],[4,7,11,12,14,15],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,8,11,12],[5,6,7,8,12,13],
  [5,6,7,8,13,15],[5,6,7,12,13,14],[5,6,7,13,14,15],
  [5,6,8,9,10,11],[5,6,8,9,11,12],[5,6,8,9,12,13],
  [5,6,9,10,11,12],[5,6,9,10,12,13],[5,6,10,11,12,13],
  [5,7,8,12,13,15],[5,7,12,13,14,15],[6,7,8,9,10,11],
  [6,7,8,9,11,12],[6,7,8,9,12,13],[6,7,8,9,13,14],
  [6,7,8,13,14,15],[6,7,9,10,11,12],[6,7,9,10,12,13],
  [6,7,9,10,13,14],[6,7,10,11,12,13],[6,7,10,11,13,14],
  [6,7,11,12,13,14],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,9,10,13,14],[7,8,9,10,14,15],[7,8,10,11,12,13],
  [7,8,10,11,13,14],[7,8,10,11,14,15],
  [7,8,11,12,13,14],[7,8,11,12,14,15],
  [7,8,12,13,14,15],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,10,11,14,15],
  [8,9,11,12,13,14],[8,9,11,12,14,15],
  [8,9,12,13,14,15],[9,10,11,12,13,14],
  [9,10,11,12,14,15],[9,10,12,13,14,15],
  [10,11,12,13,14,15]]

manifold_5_15_2_3=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,7],[1,2,3,4,7,9],[1,2,3,4,9,11],
  [1,2,3,4,11,13],[1,2,3,4,13,14],[1,2,3,4,14,15],
  [1,2,3,5,6,15],[1,2,3,6,7,8],[1,2,3,6,8,15],
  [1,2,3,7,8,9],[1,2,3,8,9,10],[1,2,3,8,10,15],
  [1,2,3,9,10,11],[1,2,3,10,11,12],[1,2,3,10,12,15],
  [1,2,3,11,12,13],[1,2,3,12,13,15],[1,2,3,13,14,15],
  [1,2,4,5,6,7],[1,2,4,5,7,14],[1,2,4,5,14,15],
  [1,2,4,7,9,14],[1,2,4,9,11,14],[1,2,4,11,13,14],
  [1,2,5,6,7,15],[1,2,5,7,14,15],[1,2,6,7,8,15],
  [1,2,7,8,9,15],[1,2,7,9,14,15],[1,2,8,9,10,15],
  [1,2,9,10,11,15],[1,2,9,11,14,15],[1,2,10,11,12,15],
  [1,2,11,12,13,14],[1,2,11,12,14,15],
  [1,2,12,13,14,15],[1,3,4,5,6,15],[1,3,4,6,7,9],
  [1,3,4,6,9,11],[1,3,4,6,11,13],[1,3,4,6,13,15],
  [1,3,4,13,14,15],[1,3,6,7,8,9],[1,3,6,8,9,11],
  [1,3,6,8,11,13],[1,3,6,8,13,15],[1,3,8,9,10,11],
  [1,3,8,10,11,13],[1,3,8,10,13,15],[1,3,10,11,12,13],
  [1,3,10,12,13,15],[1,4,5,6,7,14],[1,4,5,6,14,15],
  [1,4,6,7,9,14],[1,4,6,9,11,14],[1,4,6,11,13,14],
  [1,4,6,13,14,15],[1,5,6,7,14,15],[1,6,7,8,9,14],
  [1,6,7,8,14,15],[1,6,8,9,11,14],[1,6,8,11,13,14],
  [1,6,8,13,14,15],[1,7,8,9,14,15],[1,8,9,10,11,14],
  [1,8,9,10,14,15],[1,8,10,11,13,14],[1,8,10,13,14,15],
  [1,9,10,11,14,15],[1,10,11,12,13,15],
  [1,10,11,13,14,15],[1,11,12,13,14,15],[2,3,4,5,6,7],
  [2,3,4,5,7,8],[2,3,4,5,8,10],[2,3,4,5,10,12],
  [2,3,4,5,12,14],[2,3,4,5,14,15],[2,3,4,7,8,9],
  [2,3,4,8,9,10],[2,3,4,9,10,11],[2,3,4,10,11,12],
  [2,3,4,11,12,13],[2,3,4,12,13,14],[2,3,5,6,7,8],
  [2,3,5,6,8,15],[2,3,5,8,10,15],[2,3,5,10,12,15],
  [2,3,5,12,14,15],[2,3,12,13,14,15],[2,4,5,7,8,10],
  [2,4,5,7,10,12],[2,4,5,7,12,14],[2,4,7,8,9,10],
  [2,4,7,9,10,12],[2,4,7,9,12,14],[2,4,9,10,11,12],
  [2,4,9,11,12,14],[2,4,11,12,13,14],[2,5,6,7,8,15],
  [2,5,7,8,10,15],[2,5,7,10,12,15],[2,5,7,12,14,15],
  [2,7,8,9,10,15],[2,7,9,10,12,15],[2,7,9,12,14,15],
  [2,9,10,11,12,15],[2,9,11,12,14,15],[3,4,5,6,7,8],
  [3,4,5,6,8,9],[3,4,5,6,9,11],[3,4,5,6,11,13],
  [3,4,5,6,13,15],[3,4,5,8,9,10],[3,4,5,9,10,11],
  [3,4,5,10,11,12],[3,4,5,11,12,13],[3,4,5,12,13,14],
  [3,4,5,13,14,15],[3,4,6,7,8,9],[3,5,6,8,9,11],
  [3,5,6,8,11,13],[3,5,6,8,13,15],[3,5,8,9,10,11],
  [3,5,8,10,11,13],[3,5,8,10,13,15],[3,5,10,11,12,13],
  [3,5,10,12,13,15],[3,5,12,13,14,15],[4,5,6,7,8,9],
  [4,5,6,7,9,10],[4,5,6,7,10,12],[4,5,6,7,12,14],
  [4,5,6,9,10,11],[4,5,6,10,11,12],[4,5,6,11,12,13],
  [4,5,6,12,13,14],[4,5,6,13,14,15],[4,5,7,8,9,10],
  [4,6,7,9,10,12],[4,6,7,9,12,14],[4,6,9,10,11,12],
  [4,6,9,11,12,14],[4,6,11,12,13,14],[5,6,7,8,9,10],
  [5,6,7,8,10,11],[5,6,7,8,11,13],[5,6,7,8,13,15],
  [5,6,7,10,11,12],[5,6,7,11,12,13],[5,6,7,12,13,14],
  [5,6,7,13,14,15],[5,6,8,9,10,11],[5,7,8,10,11,13],
  [5,7,8,10,13,15],[5,7,10,11,12,13],[5,7,10,12,13,15],
  [5,7,12,13,14,15],[6,7,8,9,10,11],[6,7,8,9,11,12],
  [6,7,8,9,12,14],[6,7,8,11,12,13],[6,7,8,12,13,14],
  [6,7,8,13,14,15],[6,7,9,10,11,12],[6,8,9,11,12,14],
  [6,8,11,12,13,14],[7,8,9,10,11,12],[7,8,9,10,12,13],
  [7,8,9,10,13,15],[7,8,9,12,13,14],[7,8,9,13,14,15],
  [7,8,10,11,12,13],[7,9,10,12,13,15],
  [7,9,12,13,14,15],[8,9,10,11,12,13],
  [8,9,10,11,13,14],[8,9,10,13,14,15],
  [8,9,11,12,13,14],[9,10,11,12,13,14],
  [9,10,11,12,14,15],[9,10,12,13,14,15],
  [10,11,12,13,14,15]]

manifold_5_15_2_4=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,8],[1,2,3,4,8,9],[1,2,3,4,9,11],
  [1,2,3,4,11,12],[1,2,3,4,12,14],[1,2,3,4,14,15],
  [1,2,3,5,6,7],[1,2,3,5,7,15],[1,2,3,6,7,8],
  [1,2,3,7,8,15],[1,2,3,8,9,10],[1,2,3,8,10,15],
  [1,2,3,9,10,11],[1,2,3,10,11,15],[1,2,3,11,12,13],
  [1,2,3,11,13,15],[1,2,3,12,13,14],[1,2,3,13,14,15],
  [1,2,4,5,6,15],[1,2,4,6,7,9],[1,2,4,6,7,14],
  [1,2,4,6,8,9],[1,2,4,6,14,15],[1,2,4,7,9,14],
  [1,2,4,9,11,14],[1,2,4,11,12,14],[1,2,5,6,7,15],
  [1,2,6,7,8,9],[1,2,6,7,14,15],[1,2,7,8,9,15],
  [1,2,7,9,14,15],[1,2,8,9,10,15],[1,2,9,10,11,12],
  [1,2,9,10,12,14],[1,2,9,10,14,15],[1,2,9,11,12,14],
  [1,2,10,11,12,15],[1,2,10,12,14,15],
  [1,2,11,12,13,15],[1,2,12,13,14,15],[1,3,4,5,6,14],
  [1,3,4,5,14,15],[1,3,4,6,8,9],[1,3,4,6,9,11],
  [1,3,4,6,11,13],[1,3,4,6,13,14],[1,3,4,11,12,14],
  [1,3,4,11,13,14],[1,3,5,6,7,8],[1,3,5,6,8,15],
  [1,3,5,6,13,14],[1,3,5,6,13,15],[1,3,5,7,8,15],
  [1,3,5,13,14,15],[1,3,6,8,9,11],[1,3,6,8,11,13],
  [1,3,6,8,13,15],[1,3,8,9,10,11],[1,3,8,10,11,13],
  [1,3,8,10,13,15],[1,3,10,11,13,15],[1,3,11,12,13,14],
  [1,4,5,6,14,15],[1,4,6,7,9,14],[1,4,6,9,11,14],
  [1,4,6,11,13,14],[1,5,6,7,8,15],[1,5,6,13,14,15],
  [1,6,7,8,9,14],[1,6,7,8,14,15],[1,6,8,9,11,14],
  [1,6,8,11,13,14],[1,6,8,13,14,15],[1,7,8,9,14,15],
  [1,8,9,10,11,15],[1,8,9,11,13,14],[1,8,9,11,13,15],
  [1,8,9,13,14,15],[1,8,10,11,13,15],[1,9,10,11,12,14],
  [1,9,10,11,14,15],[1,9,11,13,14,15],
  [1,10,11,12,14,15],[1,11,12,13,14,15],[2,3,4,5,6,7],
  [2,3,4,5,7,9],[2,3,4,5,9,10],[2,3,4,5,10,12],
  [2,3,4,5,12,13],[2,3,4,5,13,15],[2,3,4,6,7,8],
  [2,3,4,7,8,9],[2,3,4,9,10,11],[2,3,4,10,11,12],
  [2,3,4,12,13,14],[2,3,4,13,14,15],[2,3,5,7,8,10],
  [2,3,5,7,8,15],[2,3,5,7,9,10],[2,3,5,8,10,15],
  [2,3,5,10,12,15],[2,3,5,12,13,15],[2,3,7,8,9,10],
  [2,3,10,11,12,13],[2,3,10,11,13,15],
  [2,3,10,12,13,15],[2,4,5,6,7,15],[2,4,5,7,9,10],
  [2,4,5,7,10,12],[2,4,5,7,12,14],[2,4,5,7,14,15],
  [2,4,5,12,13,15],[2,4,5,12,14,15],[2,4,6,7,8,9],
  [2,4,6,7,14,15],[2,4,7,9,10,12],[2,4,7,9,12,14],
  [2,4,9,10,11,12],[2,4,9,11,12,14],[2,4,12,13,14,15],
  [2,5,7,8,10,15],[2,5,7,10,12,15],[2,5,7,12,14,15],
  [2,7,8,9,10,15],[2,7,9,10,12,15],[2,7,9,12,14,15],
  [2,9,10,12,14,15],[2,10,11,12,13,15],[3,4,5,6,7,8],
  [3,4,5,6,8,10],[3,4,5,6,10,11],[3,4,5,6,11,13],
  [3,4,5,6,13,14],[3,4,5,7,8,9],[3,4,5,8,9,10],
  [3,4,5,10,11,12],[3,4,5,11,12,13],[3,4,5,13,14,15],
  [3,4,6,8,9,11],[3,4,6,8,10,11],[3,4,8,9,10,11],
  [3,4,11,12,13,14],[3,5,6,8,10,11],[3,5,6,8,11,13],
  [3,5,6,8,13,15],[3,5,7,8,9,10],[3,5,8,10,11,13],
  [3,5,8,10,13,15],[3,5,10,11,12,13],[3,5,10,12,13,15],
  [4,5,6,7,8,9],[4,5,6,7,9,11],[4,5,6,7,11,12],
  [4,5,6,7,12,14],[4,5,6,7,14,15],[4,5,6,8,9,10],
  [4,5,6,9,10,11],[4,5,6,11,12,13],[4,5,6,12,13,14],
  [4,5,7,9,10,12],[4,5,7,9,11,12],[4,5,9,10,11,12],
  [4,5,12,13,14,15],[4,6,7,9,11,12],[4,6,7,9,12,14],
  [4,6,8,9,10,11],[4,6,9,11,12,14],[4,6,11,12,13,14],
  [5,6,7,8,9,10],[5,6,7,8,10,12],[5,6,7,8,12,13],
  [5,6,7,8,13,15],[5,6,7,9,10,11],[5,6,7,10,11,12],
  [5,6,7,12,13,14],[5,6,7,13,14,15],[5,6,8,10,11,13],
  [5,6,8,10,12,13],[5,6,10,11,12,13],[5,7,8,10,12,13],
  [5,7,8,10,13,15],[5,7,9,10,11,12],[5,7,10,12,13,15],
  [5,7,12,13,14,15],[6,7,8,9,10,11],[6,7,8,9,11,13],
  [6,7,8,9,13,14],[6,7,8,10,11,12],[6,7,8,11,12,13],
  [6,7,8,13,14,15],[6,7,9,11,12,14],[6,7,9,11,13,14],
  [6,7,11,12,13,14],[6,8,9,11,13,14],[6,8,10,11,12,13],
  [7,8,9,10,11,12],[7,8,9,10,12,14],[7,8,9,10,14,15],
  [7,8,9,11,12,13],[7,8,9,12,13,14],[7,8,10,12,13,15],
  [7,8,10,12,14,15],[7,8,12,13,14,15],
  [7,9,10,12,14,15],[7,9,11,12,13,14],
  [8,9,10,11,12,13],[8,9,10,11,13,15],
  [8,9,10,12,13,14],[8,9,10,13,14,15],
  [8,10,12,13,14,15],[9,10,11,12,13,14],
  [9,10,11,13,14,15],[10,11,12,13,14,15]]

manifold_5_15_2_5=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,8],[1,2,3,4,8,9],[1,2,3,4,9,11],
  [1,2,3,4,11,12],[1,2,3,4,12,14],[1,2,3,4,14,15],
  [1,2,3,5,6,7],[1,2,3,5,7,15],[1,2,3,6,7,8],
  [1,2,3,7,8,15],[1,2,3,8,9,10],[1,2,3,8,10,15],
  [1,2,3,9,10,11],[1,2,3,10,11,15],[1,2,3,11,12,13],
  [1,2,3,11,13,15],[1,2,3,12,13,14],[1,2,3,13,14,15],
  [1,2,4,5,6,15],[1,2,4,6,8,9],[1,2,4,6,9,14],
  [1,2,4,6,14,15],[1,2,4,9,11,12],[1,2,4,9,12,14],
  [1,2,5,6,7,15],[1,2,6,7,8,9],[1,2,6,7,9,14],
  [1,2,6,7,14,15],[1,2,7,8,9,15],[1,2,7,9,14,15],
  [1,2,8,9,10,15],[1,2,9,10,11,12],[1,2,9,10,12,14],
  [1,2,9,10,14,15],[1,2,10,11,12,15],[1,2,10,12,14,15],
  [1,2,11,12,13,15],[1,2,12,13,14,15],[1,3,4,5,6,14],
  [1,3,4,5,14,15],[1,3,4,6,8,11],[1,3,4,6,11,14],
  [1,3,4,8,9,11],[1,3,4,11,12,14],[1,3,5,6,7,8],
  [1,3,5,6,8,13],[1,3,5,6,13,14],[1,3,5,7,8,15],
  [1,3,5,8,13,15],[1,3,5,13,14,15],[1,3,6,8,11,13],
  [1,3,6,11,13,14],[1,3,8,9,10,11],[1,3,8,10,11,15],
  [1,3,8,11,13,15],[1,3,11,12,13,14],[1,4,5,6,14,15],
  [1,4,6,8,9,11],[1,4,6,9,11,14],[1,4,9,11,12,14],
  [1,5,6,7,8,15],[1,5,6,8,13,15],[1,5,6,13,14,15],
  [1,6,7,8,9,14],[1,6,7,8,14,15],[1,6,8,9,11,13],
  [1,6,8,9,13,14],[1,6,8,13,14,15],[1,6,9,11,13,14],
  [1,7,8,9,14,15],[1,8,9,10,11,15],[1,8,9,11,13,15],
  [1,8,9,13,14,15],[1,9,10,11,12,14],[1,9,10,11,14,15],
  [1,9,11,13,14,15],[1,10,11,12,14,15],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,9],
  [2,3,4,5,9,10],[2,3,4,5,10,12],[2,3,4,5,12,13],
  [2,3,4,5,13,15],[2,3,4,6,7,8],[2,3,4,7,8,9],
  [2,3,4,9,10,11],[2,3,4,10,11,12],[2,3,4,12,13,14],
  [2,3,4,13,14,15],[2,3,5,7,9,10],[2,3,5,7,10,15],
  [2,3,5,10,12,13],[2,3,5,10,13,15],[2,3,7,8,9,10],
  [2,3,7,8,10,15],[2,3,10,11,12,13],[2,3,10,11,13,15],
  [2,4,5,6,7,15],[2,4,5,7,9,12],[2,4,5,7,12,15],
  [2,4,5,9,10,12],[2,4,5,12,13,15],[2,4,6,7,8,9],
  [2,4,6,7,9,14],[2,4,6,7,14,15],[2,4,7,9,12,14],
  [2,4,7,12,14,15],[2,4,9,10,11,12],[2,4,12,13,14,15],
  [2,5,7,9,10,12],[2,5,7,10,12,15],[2,5,10,12,13,15],
  [2,7,8,9,10,15],[2,7,9,10,12,14],[2,7,9,10,14,15],
  [2,7,10,12,14,15],[2,10,11,12,13,15],[3,4,5,6,7,8],
  [3,4,5,6,8,10],[3,4,5,6,10,11],[3,4,5,6,11,13],
  [3,4,5,6,13,14],[3,4,5,7,8,9],[3,4,5,8,9,10],
  [3,4,5,10,11,12],[3,4,5,11,12,13],[3,4,5,13,14,15],
  [3,4,6,8,10,11],[3,4,6,11,13,14],[3,4,8,9,10,11],
  [3,4,11,12,13,14],[3,5,6,8,10,13],[3,5,6,10,11,13],
  [3,5,7,8,9,10],[3,5,7,8,10,15],[3,5,8,10,13,15],
  [3,5,10,11,12,13],[3,6,8,10,11,13],[3,8,10,11,13,15],
  [4,5,6,7,8,9],[4,5,6,7,9,11],[4,5,6,7,11,12],
  [4,5,6,7,12,14],[4,5,6,7,14,15],[4,5,6,8,9,10],
  [4,5,6,9,10,11],[4,5,6,11,12,13],[4,5,6,12,13,14],
  [4,5,7,9,11,12],[4,5,7,12,14,15],[4,5,9,10,11,12],
  [4,5,12,13,14,15],[4,6,7,9,11,14],[4,6,7,11,12,14],
  [4,6,8,9,10,11],[4,6,11,12,13,14],[4,7,9,11,12,14],
  [5,6,7,8,9,10],[5,6,7,8,10,12],[5,6,7,8,12,13],
  [5,6,7,8,13,15],[5,6,7,9,10,11],[5,6,7,10,11,12],
  [5,6,7,12,13,14],[5,6,7,13,14,15],[5,6,8,10,12,13],
  [5,6,10,11,12,13],[5,7,8,10,12,15],[5,7,8,12,13,15],
  [5,7,9,10,11,12],[5,7,12,13,14,15],[5,8,10,12,13,15],
  [6,7,8,9,10,11],[6,7,8,9,11,13],[6,7,8,9,13,14],
  [6,7,8,10,11,12],[6,7,8,11,12,13],[6,7,8,13,14,15],
  [6,7,9,11,13,14],[6,7,11,12,13,14],[6,8,10,11,12,13],
  [7,8,9,10,11,12],[7,8,9,10,12,14],[7,8,9,10,14,15],
  [7,8,9,11,12,13],[7,8,9,12,13,14],[7,8,10,12,14,15],
  [7,8,12,13,14,15],[7,9,11,12,13,14],
  [8,9,10,11,12,13],[8,9,10,11,13,15],
  [8,9,10,12,13,14],[8,9,10,13,14,15],
  [8,10,12,13,14,15],[9,10,11,12,13,14],
  [9,10,11,13,14,15],[10,11,12,13,14,15]]

manifold_5_15_2_6=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,9],[1,2,3,4,9,11],[1,2,3,4,11,14],
  [1,2,3,4,14,15],[1,2,3,5,6,7],[1,2,3,5,7,8],
  [1,2,3,5,8,15],[1,2,3,6,7,8],[1,2,3,6,8,9],
  [1,2,3,8,9,10],[1,2,3,8,10,15],[1,2,3,9,10,11],
  [1,2,3,10,11,13],[1,2,3,10,13,15],[1,2,3,11,12,13],
  [1,2,3,11,12,14],[1,2,3,12,13,14],[1,2,3,13,14,15],
  [1,2,4,5,6,15],[1,2,4,6,7,8],[1,2,4,6,7,15],
  [1,2,4,6,8,9],[1,2,4,7,8,9],[1,2,4,7,9,14],
  [1,2,4,7,14,15],[1,2,4,9,11,14],[1,2,5,6,7,15],
  [1,2,5,7,8,15],[1,2,7,8,9,15],[1,2,7,9,14,15],
  [1,2,8,9,10,15],[1,2,9,10,11,14],[1,2,9,10,12,14],
  [1,2,9,10,12,15],[1,2,9,12,14,15],[1,2,10,11,12,14],
  [1,2,10,11,12,15],[1,2,10,11,13,15],
  [1,2,11,12,13,15],[1,2,12,13,14,15],[1,3,4,5,6,13],
  [1,3,4,5,13,14],[1,3,4,5,14,15],[1,3,4,6,9,11],
  [1,3,4,6,11,13],[1,3,4,11,12,13],[1,3,4,11,12,14],
  [1,3,4,12,13,14],[1,3,5,6,7,15],[1,3,5,6,13,14],
  [1,3,5,6,14,15],[1,3,5,7,8,15],[1,3,6,7,8,15],
  [1,3,6,8,9,11],[1,3,6,8,11,13],[1,3,6,8,13,15],
  [1,3,6,13,14,15],[1,3,8,9,10,11],[1,3,8,10,11,13],
  [1,3,8,10,13,15],[1,4,5,6,13,14],[1,4,5,6,14,15],
  [1,4,6,7,8,9],[1,4,6,7,9,14],[1,4,6,7,14,15],
  [1,4,6,9,11,14],[1,4,6,11,13,14],[1,4,11,12,13,14],
  [1,6,7,8,9,14],[1,6,7,8,14,15],[1,6,8,9,11,14],
  [1,6,8,11,13,14],[1,6,8,13,14,15],[1,7,8,9,14,15],
  [1,8,9,10,11,13],[1,8,9,10,13,15],[1,8,9,11,13,15],
  [1,8,9,11,14,15],[1,8,11,13,14,15],[1,9,10,11,13,15],
  [1,9,10,11,14,15],[1,9,10,12,14,15],
  [1,10,11,12,14,15],[1,11,12,13,14,15],[2,3,4,5,6,7],
  [2,3,4,5,7,10],[2,3,4,5,10,12],[2,3,4,5,12,15],
  [2,3,4,6,7,8],[2,3,4,6,8,9],[2,3,4,7,8,9],
  [2,3,4,7,9,10],[2,3,4,9,10,11],[2,3,4,10,11,12],
  [2,3,4,11,12,14],[2,3,4,12,13,14],[2,3,4,12,13,15],
  [2,3,4,13,14,15],[2,3,5,7,8,9],[2,3,5,7,9,10],
  [2,3,5,8,9,10],[2,3,5,8,10,15],[2,3,5,10,12,15],
  [2,3,10,11,12,15],[2,3,10,11,13,15],
  [2,3,11,12,13,15],[2,4,5,6,7,14],[2,4,5,6,14,15],
  [2,4,5,7,10,12],[2,4,5,7,12,14],[2,4,5,12,13,14],
  [2,4,5,12,13,15],[2,4,5,13,14,15],[2,4,6,7,14,15],
  [2,4,7,9,10,12],[2,4,7,9,12,14],[2,4,9,10,11,12],
  [2,4,9,11,12,14],[2,5,6,7,14,15],[2,5,7,8,9,10],
  [2,5,7,8,10,15],[2,5,7,10,12,15],[2,5,7,12,14,15],
  [2,5,12,13,14,15],[2,7,8,9,10,15],[2,7,9,10,12,15],
  [2,7,9,12,14,15],[2,9,10,11,12,14],[3,4,5,6,7,8],
  [3,4,5,6,8,11],[3,4,5,6,11,13],[3,4,5,7,8,9],
  [3,4,5,7,9,10],[3,4,5,8,9,10],[3,4,5,8,10,11],
  [3,4,5,10,11,12],[3,4,5,11,12,13],[3,4,5,12,13,15],
  [3,4,5,13,14,15],[3,4,6,8,9,10],[3,4,6,8,10,11],
  [3,4,6,9,10,11],[3,5,6,7,8,15],[3,5,6,8,11,13],
  [3,5,6,8,13,15],[3,5,6,13,14,15],[3,5,8,10,11,13],
  [3,5,8,10,13,15],[3,5,10,11,12,13],[3,5,10,12,13,15],
  [3,6,8,9,10,11],[3,10,11,12,13,15],[4,5,6,7,8,9],
  [4,5,6,7,9,12],[4,5,6,7,12,14],[4,5,6,8,9,10],
  [4,5,6,8,10,11],[4,5,6,9,10,11],[4,5,6,9,11,12],
  [4,5,6,11,12,13],[4,5,6,12,13,14],[4,5,7,9,10,11],
  [4,5,7,9,11,12],[4,5,7,10,11,12],[4,6,7,9,12,14],
  [4,6,9,11,12,14],[4,6,11,12,13,14],[4,7,9,10,11,12],
  [5,6,7,8,9,10],[5,6,7,8,10,13],[5,6,7,8,13,15],
  [5,6,7,9,10,11],[5,6,7,9,11,12],[5,6,7,10,11,12],
  [5,6,7,10,12,13],[5,6,7,12,13,14],[5,6,7,13,14,15],
  [5,6,8,10,11,12],[5,6,8,10,12,13],[5,6,8,11,12,13],
  [5,7,8,10,13,15],[5,7,10,12,13,15],[5,7,12,13,14,15],
  [5,8,10,11,12,13],[6,7,8,9,10,11],[6,7,8,9,11,14],
  [6,7,8,10,11,12],[6,7,8,10,12,13],[6,7,8,11,12,13],
  [6,7,8,11,13,14],[6,7,8,13,14,15],[6,7,9,11,12,13],
  [6,7,9,11,13,14],[6,7,9,12,13,14],[6,9,11,12,13,14],
  [7,8,9,10,11,12],[7,8,9,10,12,15],[7,8,9,11,12,13],
  [7,8,9,11,13,14],[7,8,9,12,13,14],[7,8,9,12,14,15],
  [7,8,10,12,13,14],[7,8,10,12,14,15],
  [7,8,10,13,14,15],[7,10,12,13,14,15],
  [8,9,10,11,12,13],[8,9,10,12,13,14],
  [8,9,10,12,14,15],[8,9,10,13,14,15],
  [8,9,11,13,14,15],[9,10,11,12,13,14],
  [9,10,11,13,14,15],[10,11,12,13,14,15]]

manifold_5_15_2_7=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,10],[1,2,3,4,10,14],[1,2,3,4,14,15],
  [1,2,3,5,6,7],[1,2,3,5,7,8],[1,2,3,5,8,9],
  [1,2,3,5,9,15],[1,2,3,6,7,8],[1,2,3,6,8,11],
  [1,2,3,6,10,11],[1,2,3,8,9,13],[1,2,3,8,11,13],
  [1,2,3,9,13,15],[1,2,3,10,11,14],[1,2,3,11,12,13],
  [1,2,3,11,12,14],[1,2,3,12,13,14],[1,2,3,13,14,15],
  [1,2,4,5,6,15],[1,2,4,6,7,8],[1,2,4,6,7,15],
  [1,2,4,6,8,9],[1,2,4,6,9,10],[1,2,4,7,8,15],
  [1,2,4,8,9,14],[1,2,4,8,14,15],[1,2,4,9,10,14],
  [1,2,5,6,7,15],[1,2,5,7,8,9],[1,2,5,7,9,10],
  [1,2,5,7,10,15],[1,2,5,9,10,15],[1,2,6,8,9,11],
  [1,2,6,9,10,11],[1,2,7,8,9,12],[1,2,7,8,12,15],
  [1,2,7,9,10,12],[1,2,7,10,12,15],[1,2,8,9,11,13],
  [1,2,8,9,12,14],[1,2,8,12,14,15],[1,2,9,10,11,13],
  [1,2,9,10,12,14],[1,2,9,10,13,15],[1,2,10,11,12,14],
  [1,2,10,11,12,15],[1,2,10,11,13,15],
  [1,2,11,12,13,15],[1,2,12,13,14,15],[1,3,4,5,6,12],
  [1,3,4,5,12,13],[1,3,4,5,13,14],[1,3,4,5,14,15],
  [1,3,4,6,10,11],[1,3,4,6,11,12],[1,3,4,10,11,14],
  [1,3,4,11,12,14],[1,3,4,12,13,14],[1,3,5,6,7,15],
  [1,3,5,6,12,13],[1,3,5,6,13,14],[1,3,5,6,14,15],
  [1,3,5,7,8,15],[1,3,5,8,9,15],[1,3,6,7,8,13],
  [1,3,6,7,13,14],[1,3,6,7,14,15],[1,3,6,8,11,13],
  [1,3,6,11,12,13],[1,3,7,8,13,15],[1,3,7,13,14,15],
  [1,3,8,9,13,15],[1,4,5,6,11,12],[1,4,5,6,11,14],
  [1,4,5,6,14,15],[1,4,5,11,12,14],[1,4,5,12,13,14],
  [1,4,6,7,8,15],[1,4,6,8,9,15],[1,4,6,9,10,11],
  [1,4,6,9,11,14],[1,4,6,9,14,15],[1,4,8,9,14,15],
  [1,4,9,10,11,14],[1,5,6,11,12,13],[1,5,6,11,13,14],
  [1,5,7,8,9,10],[1,5,7,8,10,15],[1,5,8,9,10,15],
  [1,5,11,12,13,14],[1,6,7,8,11,13],[1,6,7,8,11,15],
  [1,6,7,11,13,14],[1,6,7,11,14,15],[1,6,8,9,11,15],
  [1,6,9,11,14,15],[1,7,8,9,10,12],[1,7,8,10,12,15],
  [1,7,8,11,13,15],[1,7,11,13,14,15],[1,8,9,10,12,15],
  [1,8,9,11,13,15],[1,8,9,12,14,15],[1,9,10,11,13,15],
  [1,9,10,11,14,15],[1,9,10,12,14,15],
  [1,10,11,12,14,15],[1,11,12,13,14,15],[2,3,4,5,6,7],
  [2,3,4,5,7,11],[2,3,4,5,11,15],[2,3,4,6,7,8],
  [2,3,4,6,8,9],[2,3,4,6,9,10],[2,3,4,7,8,9],
  [2,3,4,7,9,12],[2,3,4,7,11,12],[2,3,4,9,10,14],
  [2,3,4,9,12,14],[2,3,4,11,12,15],[2,3,4,12,13,14],
  [2,3,4,12,13,15],[2,3,4,13,14,15],[2,3,5,7,8,9],
  [2,3,5,7,9,10],[2,3,5,7,10,11],[2,3,5,9,10,15],
  [2,3,5,10,11,15],[2,3,6,8,9,10],[2,3,6,8,10,11],
  [2,3,7,9,10,12],[2,3,7,10,11,12],[2,3,8,9,10,13],
  [2,3,8,10,11,13],[2,3,9,10,12,14],[2,3,9,10,13,15],
  [2,3,10,11,12,14],[2,3,10,11,13,15],
  [2,3,11,12,13,15],[2,4,5,6,7,13],[2,4,5,6,13,14],
  [2,4,5,6,14,15],[2,4,5,7,11,12],[2,4,5,7,12,13],
  [2,4,5,11,12,15],[2,4,5,12,13,15],[2,4,5,13,14,15],
  [2,4,6,7,13,14],[2,4,6,7,14,15],[2,4,7,8,9,14],
  [2,4,7,8,14,15],[2,4,7,9,12,14],[2,4,7,12,13,14],
  [2,5,6,7,12,13],[2,5,6,7,12,15],[2,5,6,12,13,15],
  [2,5,6,13,14,15],[2,5,7,10,11,12],[2,5,7,10,12,15],
  [2,5,10,11,12,15],[2,6,7,12,13,14],[2,6,7,12,14,15],
  [2,6,8,9,10,11],[2,6,12,13,14,15],[2,7,8,9,12,14],
  [2,7,8,12,14,15],[2,8,9,10,11,13],[3,4,5,6,7,8],
  [3,4,5,6,8,12],[3,4,5,7,8,9],[3,4,5,7,9,10],
  [3,4,5,7,10,11],[3,4,5,8,9,10],[3,4,5,8,10,13],
  [3,4,5,8,12,13],[3,4,5,10,11,15],[3,4,5,10,13,15],
  [3,4,5,13,14,15],[3,4,6,8,9,10],[3,4,6,8,10,11],
  [3,4,6,8,11,12],[3,4,7,9,10,11],[3,4,7,9,11,12],
  [3,4,8,10,11,13],[3,4,8,11,12,13],[3,4,9,10,11,14],
  [3,4,9,11,12,14],[3,4,10,11,13,15],[3,4,11,12,13,15],
  [3,5,6,7,8,14],[3,5,6,7,14,15],[3,5,6,8,12,13],
  [3,5,6,8,13,14],[3,5,7,8,14,15],[3,5,8,9,10,15],
  [3,5,8,10,13,15],[3,5,8,13,14,15],[3,6,7,8,13,14],
  [3,6,8,11,12,13],[3,7,8,13,14,15],[3,7,9,10,11,12],
  [3,8,9,10,13,15],[3,9,10,11,12,14],[4,5,6,7,8,9],
  [4,5,6,7,9,13],[4,5,6,8,9,10],[4,5,6,8,10,11],
  [4,5,6,8,11,12],[4,5,6,9,10,11],[4,5,6,9,11,14],
  [4,5,6,9,13,14],[4,5,7,9,10,11],[4,5,7,9,11,12],
  [4,5,7,9,12,13],[4,5,8,10,11,12],[4,5,8,10,12,13],
  [4,5,9,11,12,14],[4,5,9,12,13,14],[4,5,10,11,12,15],
  [4,5,10,12,13,15],[4,6,7,8,9,15],[4,6,7,9,13,14],
  [4,6,7,9,14,15],[4,7,8,9,14,15],[4,7,9,12,13,14],
  [4,8,10,11,12,13],[4,10,11,12,13,15],[5,6,7,8,9,10],
  [5,6,7,8,10,14],[5,6,7,9,10,11],[5,6,7,9,11,12],
  [5,6,7,9,12,13],[5,6,7,10,11,12],[5,6,7,10,12,15],
  [5,6,7,10,14,15],[5,6,8,10,11,12],[5,6,8,10,12,13],
  [5,6,8,10,13,14],[5,6,9,11,12,13],[5,6,9,11,13,14],
  [5,6,10,12,13,15],[5,6,10,13,14,15],[5,7,8,10,14,15],
  [5,8,10,13,14,15],[5,9,11,12,13,14],[6,7,8,9,10,11],
  [6,7,8,9,11,15],[6,7,8,10,11,12],[6,7,8,10,12,13],
  [6,7,8,10,13,14],[6,7,8,11,12,13],[6,7,9,11,12,13],
  [6,7,9,11,13,14],[6,7,9,11,14,15],[6,7,10,12,13,14],
  [6,7,10,12,14,15],[6,10,12,13,14,15],
  [7,8,9,10,11,12],[7,8,9,11,12,13],[7,8,9,11,13,14],
  [7,8,9,11,14,15],[7,8,9,12,13,14],[7,8,10,12,13,14],
  [7,8,10,12,14,15],[7,8,11,13,14,15],
  [8,9,10,11,12,13],[8,9,10,12,13,14],
  [8,9,10,12,14,15],[8,9,10,13,14,15],
  [8,9,11,13,14,15],[9,10,11,12,13,14],
  [9,10,11,13,14,15],[10,11,12,13,14,15]]

manifold_5_15_2_8=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,10],[1,2,3,4,10,14],[1,2,3,4,14,15],
  [1,2,3,5,6,7],[1,2,3,5,7,9],[1,2,3,5,9,15],
  [1,2,3,6,7,8],[1,2,3,6,8,11],[1,2,3,6,10,11],
  [1,2,3,7,8,9],[1,2,3,8,9,13],[1,2,3,8,11,13],
  [1,2,3,9,13,15],[1,2,3,10,11,12],[1,2,3,10,12,14],
  [1,2,3,11,12,13],[1,2,3,12,13,14],[1,2,3,13,14,15],
  [1,2,4,5,6,15],[1,2,4,6,8,9],[1,2,4,6,8,15],
  [1,2,4,6,9,10],[1,2,4,8,9,14],[1,2,4,8,14,15],
  [1,2,4,9,10,14],[1,2,5,6,7,15],[1,2,5,7,9,10],
  [1,2,5,7,10,15],[1,2,5,9,10,15],[1,2,6,7,8,15],
  [1,2,6,8,9,11],[1,2,6,9,10,11],[1,2,7,8,9,12],
  [1,2,7,8,12,15],[1,2,7,9,10,12],[1,2,7,10,12,15],
  [1,2,8,9,11,13],[1,2,8,9,12,14],[1,2,8,12,14,15],
  [1,2,9,10,11,15],[1,2,9,10,12,14],[1,2,9,11,13,15],
  [1,2,10,11,12,15],[1,2,11,12,13,15],
  [1,2,12,13,14,15],[1,3,4,5,6,12],[1,3,4,5,12,14],
  [1,3,4,5,14,15],[1,3,4,6,10,11],[1,3,4,6,11,12],
  [1,3,4,10,11,14],[1,3,4,11,12,14],[1,3,5,6,7,14],
  [1,3,5,6,12,13],[1,3,5,6,13,14],[1,3,5,7,8,9],
  [1,3,5,7,8,15],[1,3,5,7,14,15],[1,3,5,8,9,15],
  [1,3,5,12,13,14],[1,3,6,7,8,13],[1,3,6,7,13,14],
  [1,3,6,8,11,13],[1,3,6,11,12,13],[1,3,7,8,13,15],
  [1,3,7,13,14,15],[1,3,8,9,13,15],[1,3,10,11,12,14],
  [1,4,5,6,11,12],[1,4,5,6,11,14],[1,4,5,6,14,15],
  [1,4,5,11,12,14],[1,4,6,8,9,15],[1,4,6,9,10,11],
  [1,4,6,9,11,14],[1,4,6,9,14,15],[1,4,8,9,14,15],
  [1,4,9,10,11,14],[1,5,6,7,14,15],[1,5,6,11,12,13],
  [1,5,6,11,13,14],[1,5,7,8,9,10],[1,5,7,8,10,15],
  [1,5,8,9,10,15],[1,5,11,12,13,14],[1,6,7,8,11,13],
  [1,6,7,8,11,15],[1,6,7,11,13,14],[1,6,7,11,14,15],
  [1,6,8,9,11,15],[1,6,9,11,14,15],[1,7,8,9,10,12],
  [1,7,8,10,12,15],[1,7,8,11,13,15],[1,7,11,13,14,15],
  [1,8,9,10,12,14],[1,8,9,10,14,15],[1,8,9,11,13,15],
  [1,8,10,12,14,15],[1,9,10,11,14,15],
  [1,10,11,12,14,15],[1,11,12,13,14,15],[2,3,4,5,6,7],
  [2,3,4,5,7,11],[2,3,4,5,11,15],[2,3,4,6,7,8],
  [2,3,4,6,8,10],[2,3,4,7,8,9],[2,3,4,7,9,12],
  [2,3,4,7,11,12],[2,3,4,8,9,10],[2,3,4,9,10,14],
  [2,3,4,9,12,14],[2,3,4,11,12,13],[2,3,4,11,13,15],
  [2,3,4,12,13,14],[2,3,4,13,14,15],[2,3,5,7,9,10],
  [2,3,5,7,10,11],[2,3,5,9,10,15],[2,3,5,10,11,15],
  [2,3,6,8,10,11],[2,3,7,9,10,12],[2,3,7,10,11,12],
  [2,3,8,9,10,13],[2,3,8,10,11,13],[2,3,9,10,12,14],
  [2,3,9,10,13,15],[2,3,10,11,13,15],[2,4,5,6,7,13],
  [2,4,5,6,13,15],[2,4,5,7,11,12],[2,4,5,7,12,13],
  [2,4,5,11,12,15],[2,4,5,12,13,15],[2,4,6,7,8,15],
  [2,4,6,7,13,14],[2,4,6,7,14,15],[2,4,6,8,9,10],
  [2,4,6,13,14,15],[2,4,7,8,9,14],[2,4,7,8,14,15],
  [2,4,7,9,12,14],[2,4,7,12,13,14],[2,4,11,12,13,15],
  [2,5,6,7,12,13],[2,5,6,7,12,15],[2,5,6,12,13,15],
  [2,5,7,10,11,12],[2,5,7,10,12,15],[2,5,10,11,12,15],
  [2,6,7,12,13,14],[2,6,7,12,14,15],[2,6,8,9,10,11],
  [2,6,12,13,14,15],[2,7,8,9,12,14],[2,7,8,12,14,15],
  [2,8,9,10,11,13],[2,9,10,11,13,15],[3,4,5,6,7,8],
  [3,4,5,6,8,12],[3,4,5,7,8,9],[3,4,5,7,9,11],
  [3,4,5,8,9,10],[3,4,5,8,10,13],[3,4,5,8,12,13],
  [3,4,5,9,10,11],[3,4,5,10,11,15],[3,4,5,10,13,15],
  [3,4,5,12,13,14],[3,4,5,13,14,15],[3,4,6,8,10,11],
  [3,4,6,8,11,12],[3,4,7,9,11,12],[3,4,8,10,11,13],
  [3,4,8,11,12,13],[3,4,9,10,11,14],[3,4,9,11,12,14],
  [3,4,10,11,13,15],[3,5,6,7,8,14],[3,5,6,8,12,13],
  [3,5,6,8,13,14],[3,5,7,8,14,15],[3,5,7,9,10,11],
  [3,5,8,9,10,15],[3,5,8,10,13,15],[3,5,8,13,14,15],
  [3,6,7,8,13,14],[3,6,8,11,12,13],[3,7,8,13,14,15],
  [3,7,9,10,11,12],[3,8,9,10,13,15],[3,9,10,11,12,14],
  [4,5,6,7,8,9],[4,5,6,7,9,13],[4,5,6,8,9,10],
  [4,5,6,8,10,12],[4,5,6,9,10,11],[4,5,6,9,11,14],
  [4,5,6,9,13,14],[4,5,6,10,11,12],[4,5,6,13,14,15],
  [4,5,7,9,11,12],[4,5,7,9,12,13],[4,5,8,10,12,13],
  [4,5,9,11,12,14],[4,5,9,12,13,14],[4,5,10,11,12,15],
  [4,5,10,12,13,15],[4,6,7,8,9,15],[4,6,7,9,13,14],
  [4,6,7,9,14,15],[4,6,8,10,11,12],[4,7,8,9,14,15],
  [4,7,9,12,13,14],[4,8,10,11,12,13],
  [4,10,11,12,13,15],[5,6,7,8,9,10],[5,6,7,8,10,14],
  [5,6,7,9,10,11],[5,6,7,9,11,13],[5,6,7,10,11,12],
  [5,6,7,10,12,15],[5,6,7,10,14,15],[5,6,7,11,12,13],
  [5,6,8,10,12,13],[5,6,8,10,13,14],[5,6,9,11,13,14],
  [5,6,10,12,13,15],[5,6,10,13,14,15],[5,7,8,10,14,15],
  [5,7,9,11,12,13],[5,8,10,13,14,15],[5,9,11,12,13,14],
  [6,7,8,9,10,11],[6,7,8,9,11,15],[6,7,8,10,11,12],
  [6,7,8,10,12,14],[6,7,8,11,12,13],[6,7,8,12,13,14],
  [6,7,9,11,13,14],[6,7,9,11,14,15],[6,7,10,12,14,15],
  [6,8,10,12,13,14],[6,10,12,13,14,15],
  [7,8,9,10,11,12],[7,8,9,11,12,13],[7,8,9,11,13,15],
  [7,8,9,12,13,14],[7,8,9,13,14,15],[7,8,10,12,14,15],
  [7,9,11,13,14,15],[8,9,10,11,12,13],
  [8,9,10,12,13,14],[8,9,10,13,14,15],
  [9,10,11,12,13,14],[9,10,11,13,14,15],
  [10,11,12,13,14,15]]

manifold_5_15_2_9=[[1,2,3,4,5,6],[1,2,3,4,5,15],
  [1,2,3,4,6,14],[1,2,3,4,14,15],[1,2,3,5,6,13],
  [1,2,3,5,13,15],[1,2,3,6,13,14],[1,2,3,13,14,15],
  [1,2,4,5,6,9],[1,2,4,5,9,12],[1,2,4,5,12,15],
  [1,2,4,6,7,9],[1,2,4,6,7,14],[1,2,4,7,9,14],
  [1,2,4,9,11,12],[1,2,4,9,11,14],[1,2,4,11,12,14],
  [1,2,4,12,14,15],[1,2,5,6,9,13],[1,2,5,9,12,13],
  [1,2,5,12,13,15],[1,2,6,7,9,14],[1,2,6,9,13,14],
  [1,2,9,11,12,14],[1,2,9,12,13,14],[1,2,12,13,14,15],
  [1,3,4,5,6,8],[1,3,4,5,8,15],[1,3,4,6,8,9],
  [1,3,4,6,9,11],[1,3,4,6,11,13],[1,3,4,6,13,14],
  [1,3,4,8,9,11],[1,3,4,8,11,15],[1,3,4,11,13,14],
  [1,3,4,11,14,15],[1,3,5,6,8,15],[1,3,5,6,13,15],
  [1,3,6,8,9,11],[1,3,6,8,11,13],[1,3,6,8,13,15],
  [1,3,8,10,11,13],[1,3,8,10,11,15],[1,3,8,10,13,15],
  [1,3,10,11,13,15],[1,3,11,13,14,15],[1,4,5,6,8,9],
  [1,4,5,8,9,12],[1,4,5,8,12,15],[1,4,6,7,9,14],
  [1,4,6,9,11,14],[1,4,6,11,13,14],[1,4,8,9,11,12],
  [1,4,8,11,12,15],[1,4,11,12,14,15],[1,5,6,8,9,13],
  [1,5,6,8,13,15],[1,5,8,9,12,13],[1,5,8,12,13,15],
  [1,6,8,9,11,14],[1,6,8,9,13,14],[1,6,8,11,13,14],
  [1,8,9,11,12,13],[1,8,9,11,13,14],[1,8,10,11,13,15],
  [1,8,11,12,13,15],[1,9,11,12,13,14],
  [1,11,12,13,14,15],[2,3,4,5,6,7],[2,3,4,5,7,15],
  [2,3,4,6,7,14],[2,3,4,7,14,15],[2,3,5,6,7,10],
  [2,3,5,6,10,13],[2,3,5,7,8,10],[2,3,5,7,8,15],
  [2,3,5,8,10,15],[2,3,5,10,12,13],[2,3,5,10,12,15],
  [2,3,5,12,13,15],[2,3,6,7,10,14],[2,3,6,10,13,14],
  [2,3,7,8,10,15],[2,3,7,10,14,15],[2,3,10,12,13,15],
  [2,3,10,13,14,15],[2,4,5,6,7,9],[2,4,5,7,9,10],
  [2,4,5,7,10,12],[2,4,5,7,12,14],[2,4,5,7,14,15],
  [2,4,5,9,10,12],[2,4,5,12,14,15],[2,4,7,9,10,12],
  [2,4,7,9,12,14],[2,4,9,11,12,14],[2,5,6,7,9,10],
  [2,5,6,9,10,13],[2,5,7,8,10,15],[2,5,7,10,12,15],
  [2,5,7,12,14,15],[2,5,9,10,12,13],[2,6,7,9,10,14],
  [2,6,9,10,13,14],[2,7,9,10,12,15],[2,7,9,10,14,15],
  [2,7,9,12,14,15],[2,9,10,12,13,14],[2,9,10,12,14,15],
  [2,10,12,13,14,15],[3,4,5,6,7,8],[3,4,5,7,8,15],
  [3,4,6,7,8,11],[3,4,6,7,11,14],[3,4,6,8,9,11],
  [3,4,6,11,13,14],[3,4,7,8,11,15],[3,4,7,11,14,15],
  [3,5,6,7,8,10],[3,5,6,8,10,11],[3,5,6,8,11,13],
  [3,5,6,8,13,15],[3,5,6,10,11,13],[3,5,8,10,11,13],
  [3,5,8,10,13,15],[3,5,10,12,13,15],[3,6,7,8,10,11],
  [3,6,7,10,11,14],[3,6,10,11,13,14],[3,7,8,10,11,15],
  [3,7,10,11,14,15],[3,10,11,13,14,15],[4,5,6,7,8,9],
  [4,5,7,8,9,12],[4,5,7,8,12,15],[4,5,7,9,10,12],
  [4,5,7,12,14,15],[4,6,7,8,9,11],[4,6,7,9,11,12],
  [4,6,7,9,12,14],[4,6,7,11,12,14],[4,6,9,11,12,14],
  [4,7,8,9,11,12],[4,7,8,11,12,15],[4,7,11,12,14,15],
  [5,6,7,8,9,10],[5,6,8,9,10,13],[5,6,8,10,11,13],
  [5,7,8,9,10,12],[5,7,8,10,12,13],[5,7,8,10,13,15],
  [5,7,8,12,13,15],[5,7,10,12,13,15],[5,8,9,10,12,13],
  [6,7,8,9,10,11],[6,7,9,10,11,14],[6,7,9,11,12,14],
  [6,8,9,10,11,13],[6,8,9,11,13,14],[6,9,10,11,13,14],
  [7,8,9,10,11,12],[7,8,10,11,12,15],[7,8,10,12,13,15],
  [7,9,10,11,12,14],[7,9,10,12,14,15],
  [7,10,11,12,14,15],[8,9,10,11,12,13],
  [8,10,11,12,13,15],[9,10,11,12,13,14],
  [10,11,12,13,14,15]]

manifold_5_15_2_10=[[1,2,3,4,5,7],[1,2,3,4,5,14],
  [1,2,3,4,6,7],[1,2,3,4,6,15],[1,2,3,4,13,14],
  [1,2,3,4,13,15],[1,2,3,5,6,7],[1,2,3,5,6,15],
  [1,2,3,5,14,15],[1,2,3,12,13,14],[1,2,3,12,13,15],
  [1,2,3,12,14,15],[1,2,4,5,6,7],[1,2,4,5,6,15],
  [1,2,4,5,14,15],[1,2,4,13,14,15],[1,2,11,12,13,14],
  [1,2,11,12,13,15],[1,2,11,12,14,15],
  [1,2,11,13,14,15],[1,3,4,5,6,7],[1,3,4,5,6,15],
  [1,3,4,5,14,15],[1,3,4,13,14,15],[1,3,12,13,14,15],
  [1,10,11,12,13,14],[1,10,11,12,13,15],
  [1,10,11,12,14,15],[1,10,11,13,14,15],
  [1,10,12,13,14,15],[2,3,4,5,6,8],[2,3,4,5,6,15],
  [2,3,4,5,7,8],[2,3,4,5,14,15],[2,3,4,6,7,8],
  [2,3,4,13,14,15],[2,3,5,6,7,8],[2,3,12,13,14,15],
  [2,4,5,6,7,8],[2,11,12,13,14,15],[3,4,5,6,7,9],
  [3,4,5,6,8,9],[3,4,5,7,8,9],[3,4,6,7,8,9],
  [3,5,6,7,8,9],[4,5,6,7,8,10],[4,5,6,7,9,10],
  [4,5,6,8,9,10],[4,5,7,8,9,10],[4,6,7,8,9,10],
  [5,6,7,8,9,11],[5,6,7,8,10,11],[5,6,7,9,10,11],
  [5,6,8,9,10,11],[5,7,8,9,10,11],[6,7,8,9,10,12],
  [6,7,8,9,11,12],[6,7,8,10,11,12],[6,7,9,10,11,12],
  [6,8,9,10,11,12],[7,8,9,10,11,13],[7,8,9,10,12,13],
  [7,8,9,11,12,13],[7,8,10,11,12,13],[7,9,10,11,12,13],
  [8,9,10,11,12,14],[8,9,10,11,13,14],
  [8,9,10,12,13,14],[8,9,11,12,13,14],
  [8,10,11,12,13,14],[9,10,11,12,13,15],
  [9,10,11,12,14,15],[9,10,11,13,14,15],
  [9,10,12,13,14,15],[9,11,12,13,14,15]]

manifold_5_15_2_11=[[1,2,3,4,5,8],[1,2,3,4,5,13],
  [1,2,3,4,7,8],[1,2,3,4,7,15],[1,2,3,4,12,13],
  [1,2,3,4,12,15],[1,2,3,5,6,7],[1,2,3,5,6,14],
  [1,2,3,5,7,8],[1,2,3,5,13,14],[1,2,3,6,7,15],
  [1,2,3,6,14,15],[1,2,3,11,12,14],[1,2,3,11,12,15],
  [1,2,3,11,14,15],[1,2,3,12,13,14],[1,2,4,5,6,8],
  [1,2,4,5,6,15],[1,2,4,5,13,15],[1,2,4,6,7,8],
  [1,2,4,6,7,15],[1,2,4,12,13,15],[1,2,5,6,7,8],
  [1,2,5,6,14,15],[1,2,5,13,14,15],[1,2,10,11,12,13],
  [1,2,10,11,12,14],[1,2,10,11,13,15],
  [1,2,10,11,14,15],[1,2,10,12,13,14],
  [1,2,10,13,14,15],[1,2,11,12,13,15],[1,3,4,5,7,8],
  [1,3,4,5,7,15],[1,3,4,5,13,14],[1,3,4,5,14,15],
  [1,3,4,12,13,14],[1,3,4,12,14,15],[1,3,5,6,7,15],
  [1,3,5,6,14,15],[1,3,11,12,14,15],[1,4,5,6,7,8],
  [1,4,5,6,7,15],[1,4,5,13,14,15],[1,4,12,13,14,15],
  [1,9,10,11,12,13],[1,9,10,11,12,15],
  [1,9,10,11,13,15],[1,9,10,12,13,14],
  [1,9,10,12,14,15],[1,9,10,13,14,15],
  [1,9,11,12,13,15],[1,9,12,13,14,15],
  [1,10,11,12,14,15],[2,3,4,5,6,9],[2,3,4,5,6,14],
  [2,3,4,5,8,9],[2,3,4,5,13,14],[2,3,4,6,7,8],
  [2,3,4,6,7,15],[2,3,4,6,8,9],[2,3,4,6,14,15],
  [2,3,4,12,13,15],[2,3,4,13,14,15],[2,3,5,6,7,9],
  [2,3,5,7,8,9],[2,3,6,7,8,9],[2,3,11,12,13,14],
  [2,3,11,12,13,15],[2,3,11,13,14,15],[2,4,5,6,8,9],
  [2,4,5,6,14,15],[2,4,5,13,14,15],[2,5,6,7,8,9],
  [2,10,11,12,13,14],[2,10,11,13,14,15],[3,4,5,6,7,10],
  [3,4,5,6,7,15],[3,4,5,6,9,10],[3,4,5,6,14,15],
  [3,4,5,7,8,9],[3,4,5,7,9,10],[3,4,6,7,8,10],
  [3,4,6,8,9,10],[3,4,7,8,9,10],[3,4,12,13,14,15],
  [3,5,6,7,9,10],[3,6,7,8,9,10],[3,11,12,13,14,15],
  [4,5,6,7,8,11],[4,5,6,7,10,11],[4,5,6,8,9,10],
  [4,5,6,8,10,11],[4,5,7,8,9,11],[4,5,7,9,10,11],
  [4,5,8,9,10,11],[4,6,7,8,10,11],[4,7,8,9,10,11],
  [5,6,7,8,9,12],[5,6,7,8,11,12],[5,6,7,9,10,11],
  [5,6,7,9,11,12],[5,6,8,9,10,12],[5,6,8,10,11,12],
  [5,6,9,10,11,12],[5,7,8,9,11,12],[5,8,9,10,11,12],
  [6,7,8,9,10,13],[6,7,8,9,12,13],[6,7,8,10,11,12],
  [6,7,8,10,12,13],[6,7,9,10,11,13],[6,7,9,11,12,13],
  [6,7,10,11,12,13],[6,8,9,10,12,13],[6,9,10,11,12,13],
  [7,8,9,10,11,14],[7,8,9,10,13,14],[7,8,9,11,12,13],
  [7,8,9,11,13,14],[7,8,10,11,12,14],[7,8,10,12,13,14],
  [7,8,11,12,13,14],[7,9,10,11,13,14],
  [7,10,11,12,13,14],[8,9,10,11,12,15],
  [8,9,10,11,14,15],[8,9,10,12,13,14],
  [8,9,10,12,14,15],[8,9,11,12,13,15],
  [8,9,11,13,14,15],[8,9,12,13,14,15],
  [8,10,11,12,14,15],[8,11,12,13,14,15],
  [9,10,11,13,14,15]]

manifold_5_15_2_12=[[1,2,3,4,5,10],[1,2,3,4,5,11],
  [1,2,3,4,9,11],[1,2,3,4,9,15],[1,2,3,4,10,15],
  [1,2,3,5,10,11],[1,2,3,8,9,11],[1,2,3,8,9,14],
  [1,2,3,8,10,11],[1,2,3,8,10,15],[1,2,3,8,14,15],
  [1,2,3,9,14,15],[1,2,4,5,10,11],[1,2,4,9,10,11],
  [1,2,4,9,10,15],[1,2,7,8,9,11],[1,2,7,8,9,14],
  [1,2,7,8,10,11],[1,2,7,8,10,15],[1,2,7,8,13,14],
  [1,2,7,8,13,15],[1,2,7,9,10,11],[1,2,7,9,10,15],
  [1,2,7,9,14,15],[1,2,7,13,14,15],[1,2,8,13,14,15],
  [1,3,4,5,10,11],[1,3,4,9,10,11],[1,3,4,9,10,15],
  [1,3,8,9,10,11],[1,3,8,9,10,15],[1,3,8,9,14,15],
  [1,6,7,8,9,10],[1,6,7,8,9,14],[1,6,7,8,10,15],
  [1,6,7,8,13,14],[1,6,7,8,13,15],[1,6,7,9,10,15],
  [1,6,7,9,14,15],[1,6,7,12,13,14],[1,6,7,12,13,15],
  [1,6,7,12,14,15],[1,6,8,9,10,15],[1,6,8,9,14,15],
  [1,6,8,13,14,15],[1,6,12,13,14,15],[1,7,8,9,10,11],
  [1,7,12,13,14,15],[2,3,4,5,6,11],[2,3,4,5,6,12],
  [2,3,4,5,10,12],[2,3,4,6,11,12],[2,3,4,9,10,12],
  [2,3,4,9,10,15],[2,3,4,9,11,12],[2,3,5,6,11,12],
  [2,3,5,10,11,12],[2,3,8,9,10,12],[2,3,8,9,10,15],
  [2,3,8,9,11,12],[2,3,8,9,14,15],[2,3,8,10,11,12],
  [2,4,5,6,11,12],[2,4,5,10,11,12],[2,4,9,10,11,12],
  [2,7,8,9,10,11],[2,7,8,9,10,15],[2,7,8,9,14,15],
  [2,7,8,13,14,15],[2,8,9,10,11,12],[3,4,5,6,7,12],
  [3,4,5,6,7,13],[3,4,5,6,11,13],[3,4,5,7,12,13],
  [3,4,5,10,11,13],[3,4,5,10,12,13],[3,4,6,7,12,13],
  [3,4,6,11,12,13],[3,4,9,10,11,13],[3,4,9,10,12,13],
  [3,4,9,11,12,13],[3,5,6,7,12,13],[3,5,6,11,12,13],
  [3,5,10,11,12,13],[3,8,9,10,11,12],[3,9,10,11,12,13],
  [4,5,6,7,8,13],[4,5,6,7,8,14],[4,5,6,7,12,14],
  [4,5,6,8,13,14],[4,5,6,11,12,14],[4,5,6,11,13,14],
  [4,5,7,8,13,14],[4,5,7,12,13,14],[4,5,10,11,12,14],
  [4,5,10,11,13,14],[4,5,10,12,13,14],[4,6,7,8,13,14],
  [4,6,7,12,13,14],[4,6,11,12,13,14],[4,9,10,11,12,13],
  [4,10,11,12,13,14],[5,6,7,8,9,14],[5,6,7,8,9,15],
  [5,6,7,8,13,15],[5,6,7,9,14,15],[5,6,7,12,13,15],
  [5,6,7,12,14,15],[5,6,8,9,14,15],[5,6,8,13,14,15],
  [5,6,11,12,13,15],[5,6,11,12,14,15],
  [5,6,11,13,14,15],[5,7,8,9,14,15],[5,7,8,13,14,15],
  [5,7,12,13,14,15],[5,10,11,12,13,14],
  [5,11,12,13,14,15],[6,7,8,9,10,15],
  [6,11,12,13,14,15]]

manifold_5_15_2_13=[[1,2,3,6,7,8],[1,2,3,6,7,11],
  [1,2,3,6,8,13],[1,2,3,6,11,13],[1,2,3,7,8,11],
  [1,2,3,8,11,12],[1,2,3,8,12,13],[1,2,3,11,12,13],
  [1,2,5,6,7,12],[1,2,5,6,7,15],[1,2,5,6,10,11],
  [1,2,5,6,10,15],[1,2,5,6,11,12],[1,2,5,7,12,15],
  [1,2,5,10,11,12],[1,2,5,10,12,15],[1,2,6,7,8,13],
  [1,2,6,7,10,11],[1,2,6,7,10,15],[1,2,6,7,12,13],
  [1,2,6,11,12,13],[1,2,7,8,11,12],[1,2,7,8,12,13],
  [1,2,7,10,11,15],[1,2,7,11,12,15],[1,2,10,11,12,15],
  [1,3,6,7,8,11],[1,3,6,8,11,13],[1,3,8,11,12,13],
  [1,4,5,6,9,11],[1,4,5,6,9,14],[1,4,5,6,11,15],
  [1,4,5,6,14,15],[1,4,5,9,10,11],[1,4,5,9,10,15],
  [1,4,5,9,14,15],[1,4,5,10,11,15],[1,4,6,9,11,14],
  [1,4,6,11,14,15],[1,4,9,10,11,15],[1,4,9,11,14,15],
  [1,5,6,7,12,15],[1,5,6,9,10,11],[1,5,6,9,10,15],
  [1,5,6,9,14,15],[1,5,6,11,12,15],[1,5,10,11,12,15],
  [1,6,7,8,11,12],[1,6,7,8,12,13],[1,6,7,10,11,15],
  [1,6,7,11,12,15],[1,6,8,11,12,13],[1,6,9,10,11,14],
  [1,6,9,10,14,15],[1,6,10,11,14,15],[1,9,10,11,14,15],
  [2,3,4,7,8,9],[2,3,4,7,8,12],[2,3,4,7,9,14],
  [2,3,4,7,12,14],[2,3,4,8,9,12],[2,3,4,9,12,13],
  [2,3,4,9,13,14],[2,3,4,12,13,14],[2,3,6,7,8,13],
  [2,3,6,7,11,12],[2,3,6,7,12,13],[2,3,6,11,12,13],
  [2,3,7,8,9,14],[2,3,7,8,11,12],[2,3,7,8,13,14],
  [2,3,7,12,13,14],[2,3,8,9,12,13],[2,3,8,9,13,14],
  [2,4,7,8,9,12],[2,4,7,9,12,14],[2,4,9,12,13,14],
  [2,5,6,7,10,12],[2,5,6,7,10,15],[2,5,6,10,11,12],
  [2,5,7,10,12,15],[2,6,7,10,11,12],[2,7,8,9,12,13],
  [2,7,8,9,13,14],[2,7,9,12,13,14],[2,7,10,11,12,15],
  [3,4,5,8,9,10],[3,4,5,8,9,13],[3,4,5,8,10,15],
  [3,4,5,8,13,15],[3,4,5,9,10,13],[3,4,5,10,13,14],
  [3,4,5,10,14,15],[3,4,5,13,14,15],[3,4,7,8,9,14],
  [3,4,7,8,12,13],[3,4,7,8,13,14],[3,4,7,12,13,14],
  [3,4,8,9,10,15],[3,4,8,9,12,13],[3,4,8,9,14,15],
  [3,4,8,13,14,15],[3,4,9,10,13,14],[3,4,9,10,14,15],
  [3,5,8,9,10,13],[3,5,8,10,13,15],[3,5,10,13,14,15],
  [3,6,7,8,11,13],[3,6,7,11,12,13],[3,7,8,11,12,13],
  [3,8,9,10,13,14],[3,8,9,10,14,15],[3,8,10,13,14,15],
  [4,5,6,9,10,11],[4,5,6,9,10,14],[4,5,6,10,11,14],
  [4,5,6,11,14,15],[4,5,8,9,10,15],[4,5,8,9,13,14],
  [4,5,8,9,14,15],[4,5,8,13,14,15],[4,5,9,10,13,14],
  [4,5,10,11,14,15],[4,6,9,10,11,14],[4,7,8,9,12,14],
  [4,7,8,12,13,14],[4,8,9,12,13,14],[4,9,10,11,14,15],
  [5,6,7,10,11,12],[5,6,7,10,11,15],[5,6,7,11,12,15],
  [5,6,9,10,14,15],[5,6,10,11,14,15],[5,7,10,11,12,15],
  [5,8,9,10,13,15],[5,8,9,13,14,15],[5,9,10,13,14,15],
  [6,7,8,11,12,13],[7,8,9,12,13,14],[8,9,10,13,14,15]]

manifold_5_15_2_14=[[1,2,3,6,7,8],[1,2,3,6,7,12],
  [1,2,3,6,8,11],[1,2,3,6,11,12],[1,2,3,7,8,13],
  [1,2,3,7,12,13],[1,2,3,8,11,13],[1,2,3,11,12,13],
  [1,2,5,6,7,11],[1,2,5,6,7,15],[1,2,5,6,11,15],
  [1,2,5,7,10,11],[1,2,5,7,10,15],[1,2,5,10,11,15],
  [1,2,6,7,8,11],[1,2,6,7,12,15],[1,2,6,11,12,15],
  [1,2,7,8,11,13],[1,2,7,10,11,12],[1,2,7,10,12,15],
  [1,2,7,11,12,13],[1,2,10,11,12,15],[1,3,6,7,8,13],
  [1,3,6,7,12,13],[1,3,6,8,11,13],[1,3,6,11,12,13],
  [1,4,5,6,10,11],[1,4,5,6,10,15],[1,4,5,6,11,14],
  [1,4,5,6,14,15],[1,4,5,10,11,14],[1,4,5,10,14,15],
  [1,4,6,9,10,11],[1,4,6,9,10,15],[1,4,6,9,11,14],
  [1,4,6,9,14,15],[1,4,9,10,11,14],[1,4,9,10,14,15],
  [1,5,6,7,10,11],[1,5,6,7,10,15],[1,5,6,11,14,15],
  [1,5,10,11,14,15],[1,6,7,8,11,13],[1,6,7,10,11,12],
  [1,6,7,10,12,15],[1,6,7,11,12,13],[1,6,9,10,11,15],
  [1,6,9,11,14,15],[1,6,10,11,12,15],[1,9,10,11,14,15],
  [2,3,4,7,8,9],[2,3,4,7,8,13],[2,3,4,7,9,12],
  [2,3,4,7,12,13],[2,3,4,8,9,14],[2,3,4,8,13,14],
  [2,3,4,9,12,14],[2,3,4,12,13,14],[2,3,6,7,8,12],
  [2,3,6,8,11,12],[2,3,7,8,9,12],[2,3,8,9,12,14],
  [2,3,8,11,12,13],[2,3,8,12,13,14],[2,4,7,8,9,14],
  [2,4,7,8,13,14],[2,4,7,9,12,14],[2,4,7,12,13,14],
  [2,5,6,7,11,12],[2,5,6,7,12,15],[2,5,6,11,12,15],
  [2,5,7,10,11,12],[2,5,7,10,12,15],[2,5,10,11,12,15],
  [2,6,7,8,11,12],[2,7,8,9,12,14],[2,7,8,11,12,13],
  [2,7,8,12,13,14],[3,4,5,8,9,10],[3,4,5,8,9,14],
  [3,4,5,8,10,13],[3,4,5,8,13,14],[3,4,5,9,10,15],
  [3,4,5,9,14,15],[3,4,5,10,13,15],[3,4,5,13,14,15],
  [3,4,7,8,9,13],[3,4,7,9,12,13],[3,4,8,9,10,13],
  [3,4,9,10,13,15],[3,4,9,12,13,14],[3,4,9,13,14,15],
  [3,5,8,9,10,15],[3,5,8,9,14,15],[3,5,8,10,13,15],
  [3,5,8,13,14,15],[3,6,7,8,12,13],[3,6,8,11,12,13],
  [3,7,8,9,12,13],[3,8,9,10,13,15],[3,8,9,12,13,14],
  [3,8,9,13,14,15],[4,5,6,9,10,11],[4,5,6,9,10,15],
  [4,5,6,9,11,14],[4,5,6,9,14,15],[4,5,8,9,10,14],
  [4,5,8,10,13,14],[4,5,9,10,11,14],[4,5,10,13,14,15],
  [4,7,8,9,13,14],[4,7,9,12,13,14],[4,8,9,10,13,14],
  [4,9,10,13,14,15],[5,6,7,10,11,12],[5,6,7,10,12,15],
  [5,6,9,10,11,15],[5,6,9,11,14,15],[5,6,10,11,12,15],
  [5,8,9,10,14,15],[5,8,10,13,14,15],[5,9,10,11,14,15],
  [6,7,8,11,12,13],[7,8,9,12,13,14],[8,9,10,13,14,15]]

manifold_5_15_2_15=[[1,2,3,6,7,8],[1,2,3,6,7,13],
  [1,2,3,6,8,11],[1,2,3,6,11,12],[1,2,3,6,12,13],
  [1,2,3,7,8,13],[1,2,3,8,11,13],[1,2,3,11,12,13],
  [1,2,5,6,7,10],[1,2,5,6,7,15],[1,2,5,6,10,11],
  [1,2,5,6,11,12],[1,2,5,6,12,15],[1,2,5,7,10,15],
  [1,2,5,10,11,15],[1,2,5,11,12,15],[1,2,6,7,8,11],
  [1,2,6,7,10,11],[1,2,6,7,12,13],[1,2,6,7,12,15],
  [1,2,7,8,11,12],[1,2,7,8,12,13],[1,2,7,10,11,12],
  [1,2,7,10,12,15],[1,2,8,11,12,13],[1,2,10,11,12,15],
  [1,3,6,7,8,13],[1,3,6,8,11,13],[1,3,6,11,12,13],
  [1,4,5,6,9,10],[1,4,5,6,9,15],[1,4,5,6,10,11],
  [1,4,5,6,11,14],[1,4,5,6,14,15],[1,4,5,9,10,15],
  [1,4,5,10,11,15],[1,4,5,11,14,15],[1,4,6,9,10,11],
  [1,4,6,9,11,14],[1,4,6,9,14,15],[1,4,9,10,11,14],
  [1,4,9,10,14,15],[1,4,10,11,14,15],[1,5,6,7,10,15],
  [1,5,6,9,10,15],[1,5,6,11,12,15],[1,5,6,11,14,15],
  [1,6,7,8,11,13],[1,6,7,10,11,15],[1,6,7,11,12,13],
  [1,6,7,11,12,15],[1,6,9,10,11,15],[1,6,9,11,14,15],
  [1,7,8,11,12,13],[1,7,10,11,12,15],[1,9,10,11,14,15],
  [2,3,4,7,8,9],[2,3,4,7,8,14],[2,3,4,7,9,12],
  [2,3,4,7,12,13],[2,3,4,7,13,14],[2,3,4,8,9,14],
  [2,3,4,9,12,14],[2,3,4,12,13,14],[2,3,6,7,8,11],
  [2,3,6,7,11,12],[2,3,6,7,12,13],[2,3,7,8,9,12],
  [2,3,7,8,11,12],[2,3,7,8,13,14],[2,3,8,9,12,13],
  [2,3,8,9,13,14],[2,3,8,11,12,13],[2,3,9,12,13,14],
  [2,4,7,8,9,14],[2,4,7,9,12,14],[2,4,7,12,13,14],
  [2,5,6,7,10,11],[2,5,6,7,11,12],[2,5,6,7,12,15],
  [2,5,7,10,11,12],[2,5,7,10,12,15],[2,5,10,11,12,15],
  [2,7,8,9,12,14],[2,7,8,12,13,14],[2,8,9,12,13,14],
  [3,4,5,8,9,10],[3,4,5,8,9,15],[3,4,5,8,10,13],
  [3,4,5,8,13,14],[3,4,5,8,14,15],[3,4,5,9,10,15],
  [3,4,5,10,13,15],[3,4,5,13,14,15],[3,4,7,8,9,12],
  [3,4,7,8,12,13],[3,4,7,8,13,14],[3,4,8,9,10,13],
  [3,4,8,9,12,13],[3,4,8,9,14,15],[3,4,9,10,13,14],
  [3,4,9,10,14,15],[3,4,9,12,13,14],[3,4,10,13,14,15],
  [3,5,8,9,10,15],[3,5,8,10,13,15],[3,5,8,13,14,15],
  [3,6,7,8,11,12],[3,6,7,8,12,13],[3,6,8,11,12,13],
  [3,8,9,10,13,15],[3,8,9,13,14,15],[3,9,10,13,14,15],
  [4,5,6,9,10,11],[4,5,6,9,11,14],[4,5,6,9,14,15],
  [4,5,8,9,10,13],[4,5,8,9,13,14],[4,5,8,9,14,15],
  [4,5,9,10,11,14],[4,5,9,10,13,14],[4,5,10,11,14,15],
  [4,5,10,13,14,15],[4,7,8,9,12,13],[4,7,8,9,13,14],
  [4,7,9,12,13,14],[5,6,7,10,11,12],[5,6,7,10,12,15],
  [5,6,9,10,11,14],[5,6,9,10,14,15],[5,6,10,11,12,15],
  [5,6,10,11,14,15],[5,8,9,10,13,14],[5,8,9,10,14,15],
  [5,8,10,13,14,15],[6,7,8,11,12,13],[6,7,10,11,12,15],
  [6,9,10,11,14,15],[7,8,9,12,13,14],[8,9,10,13,14,15]]

manifold_5_15_2_16=[[1,2,3,6,8,11],[1,2,3,6,8,12],
  [1,2,3,6,11,12],[1,2,3,7,8,12],[1,2,3,7,8,13],
  [1,2,3,7,11,12],[1,2,3,7,11,13],[1,2,3,8,11,13],
  [1,2,5,7,10,11],[1,2,5,7,10,15],[1,2,5,7,11,15],
  [1,2,5,10,11,15],[1,2,6,7,8,11],[1,2,6,7,8,12],
  [1,2,6,7,11,15],[1,2,6,7,12,15],[1,2,6,10,11,12],
  [1,2,6,10,11,15],[1,2,6,10,12,15],[1,2,7,8,11,13],
  [1,2,7,10,11,12],[1,2,7,10,12,15],[1,3,6,7,8,12],
  [1,3,6,7,8,13],[1,3,6,7,12,13],[1,3,6,8,11,13],
  [1,3,6,11,12,13],[1,3,7,11,12,13],[1,4,5,6,10,11],
  [1,4,5,6,10,14],[1,4,5,6,11,14],[1,4,5,10,11,14],
  [1,4,6,9,10,11],[1,4,6,9,10,15],[1,4,6,9,11,14],
  [1,4,6,9,14,15],[1,4,6,10,14,15],[1,4,9,10,11,14],
  [1,4,9,10,14,15],[1,5,6,7,10,12],[1,5,6,7,10,15],
  [1,5,6,7,11,12],[1,5,6,7,11,15],[1,5,6,10,11,12],
  [1,5,6,10,14,15],[1,5,6,11,14,15],[1,5,7,10,11,12],
  [1,5,9,10,11,14],[1,5,9,10,11,15],[1,5,9,10,14,15],
  [1,5,9,11,14,15],[1,6,7,8,11,13],[1,6,7,10,12,15],
  [1,6,7,11,12,13],[1,6,9,10,11,15],[1,6,9,11,14,15],
  [2,3,4,7,9,12],[2,3,4,7,9,13],[2,3,4,7,12,13],
  [2,3,4,8,9,13],[2,3,4,8,9,14],[2,3,4,8,12,13],
  [2,3,4,8,12,14],[2,3,4,9,12,14],[2,3,6,8,11,12],
  [2,3,7,8,9,12],[2,3,7,8,9,13],[2,3,7,11,12,13],
  [2,3,8,9,12,14],[2,3,8,11,12,13],[2,4,7,8,9,13],
  [2,4,7,8,9,14],[2,4,7,8,13,14],[2,4,7,9,12,14],
  [2,4,7,12,13,14],[2,4,8,12,13,14],[2,5,6,7,11,12],
  [2,5,6,7,11,15],[2,5,6,7,12,15],[2,5,6,11,12,15],
  [2,5,7,10,11,12],[2,5,7,10,12,15],[2,5,10,11,12,15],
  [2,6,7,8,11,13],[2,6,7,8,12,13],[2,6,7,11,12,13],
  [2,6,8,11,12,13],[2,6,10,11,12,15],[2,7,8,9,12,14],
  [2,7,8,12,13,14],[3,4,5,8,10,13],[3,4,5,8,10,14],
  [3,4,5,8,13,14],[3,4,5,9,10,14],[3,4,5,9,10,15],
  [3,4,5,9,13,14],[3,4,5,9,13,15],[3,4,5,10,13,15],
  [3,4,7,9,12,13],[3,4,8,9,10,13],[3,4,8,9,10,14],
  [3,4,8,12,13,14],[3,4,9,10,13,15],[3,4,9,12,13,14],
  [3,5,8,9,10,14],[3,5,8,9,10,15],[3,5,8,9,14,15],
  [3,5,8,10,13,15],[3,5,8,13,14,15],[3,5,9,13,14,15],
  [3,6,7,8,12,13],[3,6,8,11,12,13],[3,7,8,9,12,14],
  [3,7,8,9,13,14],[3,7,8,12,13,14],[3,7,9,12,13,14],
  [3,8,9,10,13,15],[3,8,9,13,14,15],[4,5,6,9,11,14],
  [4,5,6,9,11,15],[4,5,6,9,14,15],[4,5,6,10,11,15],
  [4,5,6,10,14,15],[4,5,8,10,13,14],[4,5,9,10,11,14],
  [4,5,9,10,11,15],[4,5,9,13,14,15],[4,5,10,13,14,15],
  [4,6,9,10,11,15],[4,7,8,9,13,14],[4,7,9,12,13,14],
  [4,8,9,10,13,15],[4,8,9,10,14,15],[4,8,9,13,14,15],
  [4,8,10,13,14,15],[5,6,7,10,12,15],[5,6,9,11,14,15],
  [5,6,10,11,12,15],[5,8,9,10,14,15],[5,8,10,13,14,15]]