manifold_9_11_8_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,11],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,9,10,11],[1,2,3,4,5,6,8,9,10,11],
  [1,2,3,4,5,7,8,9,10,11],[1,2,3,4,6,7,8,9,10,11],
  [1,2,3,5,6,7,8,9,10,11],[1,2,4,5,6,7,8,9,10,11],
  [1,3,4,5,6,7,8,9,10,11],[2,3,4,5,6,7,8,9,10,11]]

manifold_9_12_299_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,12],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,8,11,12],[1,2,3,4,5,6,7,9,10,12],
  [1,2,3,4,5,6,7,10,11,12],[1,2,3,4,5,6,8,9,10,11],
  [1,2,3,4,5,6,8,9,11,12],[1,2,3,4,5,6,9,10,11,12],
  [1,2,3,4,5,7,8,9,10,12],[1,2,3,4,5,7,8,10,11,12],
  [1,2,3,4,5,8,9,10,11,12],[1,2,3,4,6,7,8,9,10,11],
  [1,2,3,4,6,7,8,9,11,12],[1,2,3,4,6,7,9,10,11,12],
  [1,2,3,4,7,8,9,10,11,12],[1,2,3,5,6,7,8,9,10,12],
  [1,2,3,5,6,7,8,10,11,12],[1,2,3,5,6,8,9,10,11,12],
  [1,2,3,6,7,8,9,10,11,12],[1,2,4,5,6,7,8,9,10,11],
  [1,2,4,5,6,7,8,9,11,12],[1,2,4,5,6,7,9,10,11,12],
  [1,2,4,5,7,8,9,10,11,12],[1,2,5,6,7,8,9,10,11,12],
  [1,3,4,5,6,7,8,9,10,12],[1,3,4,5,6,7,8,10,11,12],
  [1,3,4,5,6,8,9,10,11,12],[1,3,4,6,7,8,9,10,11,12],
  [1,4,5,6,7,8,9,10,11,12],[2,3,4,5,6,7,8,9,10,11],
  [2,3,4,5,6,7,8,9,11,12],[2,3,4,5,6,7,9,10,11,12],
  [2,3,4,5,7,8,9,10,11,12],[2,3,5,6,7,8,9,10,11,12],
  [3,4,5,6,7,8,9,10,11,12]]

manifold_9_13_2_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,13],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,8,11,12],[1,2,3,4,5,6,7,8,12,13],
  [1,2,3,4,5,6,7,9,10,13],[1,2,3,4,5,6,7,10,11,13],
  [1,2,3,4,5,6,7,11,12,13],[1,2,3,4,5,6,8,9,10,11],
  [1,2,3,4,5,6,8,9,11,12],[1,2,3,4,5,6,8,9,12,13],
  [1,2,3,4,5,6,9,10,11,12],[1,2,3,4,5,6,9,10,12,13],
  [1,2,3,4,5,6,10,11,12,13],[1,2,3,4,5,7,8,9,10,13],
  [1,2,3,4,5,7,8,10,11,13],[1,2,3,4,5,7,8,11,12,13],
  [1,2,3,4,5,8,9,10,11,13],[1,2,3,4,5,8,9,11,12,13],
  [1,2,3,4,5,9,10,11,12,13],[1,2,3,4,6,7,8,9,10,11],
  [1,2,3,4,6,7,8,9,11,12],[1,2,3,4,6,7,8,9,12,13],
  [1,2,3,4,6,7,9,10,11,12],[1,2,3,4,6,7,9,10,12,13],
  [1,2,3,4,6,7,10,11,12,13],[1,2,3,4,7,8,9,10,11,12],
  [1,2,3,4,7,8,9,10,12,13],[1,2,3,4,7,8,10,11,12,13],
  [1,2,3,4,8,9,10,11,12,13],[1,2,3,5,6,7,8,9,10,13],
  [1,2,3,5,6,7,8,10,11,13],[1,2,3,5,6,7,8,11,12,13],
  [1,2,3,5,6,8,9,10,11,13],[1,2,3,5,6,8,9,11,12,13],
  [1,2,3,5,6,9,10,11,12,13],[1,2,3,6,7,8,9,10,11,13],
  [1,2,3,6,7,8,9,11,12,13],[1,2,3,6,7,9,10,11,12,13],
  [1,2,3,7,8,9,10,11,12,13],[1,2,4,5,6,7,8,9,10,11],
  [1,2,4,5,6,7,8,9,11,12],[1,2,4,5,6,7,8,9,12,13],
  [1,2,4,5,6,7,9,10,11,12],[1,2,4,5,6,7,9,10,12,13],
  [1,2,4,5,6,7,10,11,12,13],[1,2,4,5,7,8,9,10,11,12],
  [1,2,4,5,7,8,9,10,12,13],[1,2,4,5,7,8,10,11,12,13],
  [1,2,4,5,8,9,10,11,12,13],[1,2,5,6,7,8,9,10,11,12],
  [1,2,5,6,7,8,9,10,12,13],[1,2,5,6,7,8,10,11,12,13],
  [1,2,5,6,8,9,10,11,12,13],[1,2,6,7,8,9,10,11,12,13],
  [1,3,4,5,6,7,8,9,10,13],[1,3,4,5,6,7,8,10,11,13],
  [1,3,4,5,6,7,8,11,12,13],[1,3,4,5,6,8,9,10,11,13],
  [1,3,4,5,6,8,9,11,12,13],[1,3,4,5,6,9,10,11,12,13],
  [1,3,4,6,7,8,9,10,11,13],[1,3,4,6,7,8,9,11,12,13],
  [1,3,4,6,7,9,10,11,12,13],[1,3,4,7,8,9,10,11,12,13],
  [1,4,5,6,7,8,9,10,11,13],[1,4,5,6,7,8,9,11,12,13],
  [1,4,5,6,7,9,10,11,12,13],[1,4,5,7,8,9,10,11,12,13],
  [1,5,6,7,8,9,10,11,12,13],[2,3,4,5,6,7,8,9,10,11],
  [2,3,4,5,6,7,8,9,11,12],[2,3,4,5,6,7,8,9,12,13],
  [2,3,4,5,6,7,9,10,11,12],[2,3,4,5,6,7,9,10,12,13],
  [2,3,4,5,6,7,10,11,12,13],[2,3,4,5,7,8,9,10,11,12],
  [2,3,4,5,7,8,9,10,12,13],[2,3,4,5,7,8,10,11,12,13],
  [2,3,4,5,8,9,10,11,12,13],[2,3,5,6,7,8,9,10,11,12],
  [2,3,5,6,7,8,9,10,12,13],[2,3,5,6,7,8,10,11,12,13],
  [2,3,5,6,8,9,10,11,12,13],[2,3,6,7,8,9,10,11,12,13],
  [3,4,5,6,7,8,9,10,11,12],[3,4,5,6,7,8,9,10,12,13],
  [3,4,5,6,7,8,10,11,12,13],[3,4,5,6,8,9,10,11,12,13],
  [3,4,6,7,8,9,10,11,12,13],[4,5,6,7,8,9,10,11,12,13]]

manifold_9_14_3_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,14],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,8,11,12],[1,2,3,4,5,6,7,8,12,13],
  [1,2,3,4,5,6,7,8,13,14],[1,2,3,4,5,6,7,9,10,14],
  [1,2,3,4,5,6,7,10,11,14],[1,2,3,4,5,6,7,11,12,14],
  [1,2,3,4,5,6,7,12,13,14],[1,2,3,4,5,6,8,9,10,11],
  [1,2,3,4,5,6,8,9,11,12],[1,2,3,4,5,6,8,9,12,13],
  [1,2,3,4,5,6,8,9,13,14],[1,2,3,4,5,6,9,10,11,12],
  [1,2,3,4,5,6,9,10,12,13],[1,2,3,4,5,6,9,10,13,14],
  [1,2,3,4,5,6,10,11,12,13],[1,2,3,4,5,6,10,11,13,14],
  [1,2,3,4,5,6,11,12,13,14],[1,2,3,4,5,7,8,9,10,14],
  [1,2,3,4,5,7,8,10,11,14],[1,2,3,4,5,7,8,11,12,14],
  [1,2,3,4,5,7,8,12,13,14],[1,2,3,4,5,8,9,10,11,14],
  [1,2,3,4,5,8,9,11,12,14],[1,2,3,4,5,8,9,12,13,14],
  [1,2,3,4,5,9,10,11,12,14],[1,2,3,4,5,9,10,12,13,14],
  [1,2,3,4,5,10,11,12,13,14],[1,2,3,4,6,7,8,9,10,11],
  [1,2,3,4,6,7,8,9,11,12],[1,2,3,4,6,7,8,9,12,13],
  [1,2,3,4,6,7,8,9,13,14],[1,2,3,4,6,7,9,10,11,12],
  [1,2,3,4,6,7,9,10,12,13],[1,2,3,4,6,7,9,10,13,14],
  [1,2,3,4,6,7,10,11,12,13],[1,2,3,4,6,7,10,11,13,14],
  [1,2,3,4,6,7,11,12,13,14],[1,2,3,4,7,8,9,10,11,12],
  [1,2,3,4,7,8,9,10,12,13],[1,2,3,4,7,8,9,10,13,14],
  [1,2,3,4,7,8,10,11,12,13],[1,2,3,4,7,8,10,11,13,14],
  [1,2,3,4,7,8,11,12,13,14],[1,2,3,4,8,9,10,11,12,13],
  [1,2,3,4,8,9,10,11,13,14],[1,2,3,4,8,9,11,12,13,14],
  [1,2,3,4,9,10,11,12,13,14],[1,2,3,5,6,7,8,9,10,14],
  [1,2,3,5,6,7,8,10,11,14],[1,2,3,5,6,7,8,11,12,14],
  [1,2,3,5,6,7,8,12,13,14],[1,2,3,5,6,8,9,10,11,14],
  [1,2,3,5,6,8,9,11,12,14],[1,2,3,5,6,8,9,12,13,14],
  [1,2,3,5,6,9,10,11,12,14],[1,2,3,5,6,9,10,12,13,14],
  [1,2,3,5,6,10,11,12,13,14],[1,2,3,6,7,8,9,10,11,14],
  [1,2,3,6,7,8,9,11,12,14],[1,2,3,6,7,8,9,12,13,14],
  [1,2,3,6,7,9,10,11,12,14],[1,2,3,6,7,9,10,12,13,14],
  [1,2,3,6,7,10,11,12,13,14],[1,2,3,7,8,9,10,11,12,14],
  [1,2,3,7,8,9,10,12,13,14],[1,2,3,7,8,10,11,12,13,14],
  [1,2,3,8,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10,11],
  [1,2,4,5,6,7,8,9,11,12],[1,2,4,5,6,7,8,9,12,13],
  [1,2,4,5,6,7,8,9,13,14],[1,2,4,5,6,7,9,10,11,12],
  [1,2,4,5,6,7,9,10,12,13],[1,2,4,5,6,7,9,10,13,14],
  [1,2,4,5,6,7,10,11,12,13],[1,2,4,5,6,7,10,11,13,14],
  [1,2,4,5,6,7,11,12,13,14],[1,2,4,5,7,8,9,10,11,12],
  [1,2,4,5,7,8,9,10,12,13],[1,2,4,5,7,8,9,10,13,14],
  [1,2,4,5,7,8,10,11,12,13],[1,2,4,5,7,8,10,11,13,14],
  [1,2,4,5,7,8,11,12,13,14],[1,2,4,5,8,9,10,11,12,13],
  [1,2,4,5,8,9,10,11,13,14],[1,2,4,5,8,9,11,12,13,14],
  [1,2,4,5,9,10,11,12,13,14],[1,2,5,6,7,8,9,10,11,12],
  [1,2,5,6,7,8,9,10,12,13],[1,2,5,6,7,8,9,10,13,14],
  [1,2,5,6,7,8,10,11,12,13],[1,2,5,6,7,8,10,11,13,14],
  [1,2,5,6,7,8,11,12,13,14],[1,2,5,6,8,9,10,11,12,13],
  [1,2,5,6,8,9,10,11,13,14],[1,2,5,6,8,9,11,12,13,14],
  [1,2,5,6,9,10,11,12,13,14],[1,2,6,7,8,9,10,11,12,13],
  [1,2,6,7,8,9,10,11,13,14],[1,2,6,7,8,9,11,12,13,14],
  [1,2,6,7,9,10,11,12,13,14],[1,2,7,8,9,10,11,12,13,14],
  [1,3,4,5,6,7,8,9,10,14],[1,3,4,5,6,7,8,10,11,14],
  [1,3,4,5,6,7,8,11,12,14],[1,3,4,5,6,7,8,12,13,14],
  [1,3,4,5,6,8,9,10,11,14],[1,3,4,5,6,8,9,11,12,14],
  [1,3,4,5,6,8,9,12,13,14],[1,3,4,5,6,9,10,11,12,14],
  [1,3,4,5,6,9,10,12,13,14],[1,3,4,5,6,10,11,12,13,14],
  [1,3,4,6,7,8,9,10,11,14],[1,3,4,6,7,8,9,11,12,14],
  [1,3,4,6,7,8,9,12,13,14],[1,3,4,6,7,9,10,11,12,14],
  [1,3,4,6,7,9,10,12,13,14],[1,3,4,6,7,10,11,12,13,14],
  [1,3,4,7,8,9,10,11,12,14],[1,3,4,7,8,9,10,12,13,14],
  [1,3,4,7,8,10,11,12,13,14],[1,3,4,8,9,10,11,12,13,14],
  [1,4,5,6,7,8,9,10,11,14],[1,4,5,6,7,8,9,11,12,14],
  [1,4,5,6,7,8,9,12,13,14],
  [1,4,5,6,7,9,10,11,12,14],[1,4,5,6,7,9,10,12,13,14],
  [1,4,5,6,7,10,11,12,13,14],[1,4,5,7,8,9,10,11,12,14],
  [1,4,5,7,8,9,10,12,13,14],[1,4,5,7,8,10,11,12,13,14],
  [1,4,5,8,9,10,11,12,13,14],[1,5,6,7,8,9,10,11,12,14],
  [1,5,6,7,8,9,10,12,13,14],[1,5,6,7,8,10,11,12,13,14],
  [1,5,6,8,9,10,11,12,13,14],[1,6,7,8,9,10,11,12,13,14],
  [2,3,4,5,6,7,8,9,10,11],[2,3,4,5,6,7,8,9,11,12],
  [2,3,4,5,6,7,8,9,12,13],[2,3,4,5,6,7,8,9,13,14],
  [2,3,4,5,6,7,9,10,11,12],[2,3,4,5,6,7,9,10,12,13],
  [2,3,4,5,6,7,9,10,13,14],[2,3,4,5,6,7,10,11,12,13],
  [2,3,4,5,6,7,10,11,13,14],[2,3,4,5,6,7,11,12,13,14],
  [2,3,4,5,7,8,9,10,11,12],[2,3,4,5,7,8,9,10,12,13],
  [2,3,4,5,7,8,9,10,13,14],[2,3,4,5,7,8,10,11,12,13],
  [2,3,4,5,7,8,10,11,13,14],[2,3,4,5,7,8,11,12,13,14],
  [2,3,4,5,8,9,10,11,12,13],[2,3,4,5,8,9,10,11,13,14],
  [2,3,4,5,8,9,11,12,13,14],[2,3,4,5,9,10,11,12,13,14],
  [2,3,5,6,7,8,9,10,11,12],[2,3,5,6,7,8,9,10,12,13],
  [2,3,5,6,7,8,9,10,13,14],[2,3,5,6,7,8,10,11,12,13],
  [2,3,5,6,7,8,10,11,13,14],[2,3,5,6,7,8,11,12,13,14],
  [2,3,5,6,8,9,10,11,12,13],[2,3,5,6,8,9,10,11,13,14],
  [2,3,5,6,8,9,11,12,13,14],[2,3,5,6,9,10,11,12,13,14],
  [2,3,6,7,8,9,10,11,12,13],[2,3,6,7,8,9,10,11,13,14],
  [2,3,6,7,8,9,11,12,13,14],[2,3,6,7,9,10,11,12,13,14],
  [2,3,7,8,9,10,11,12,13,14],[3,4,5,6,7,8,9,10,11,12],
  [3,4,5,6,7,8,9,10,12,13],[3,4,5,6,7,8,9,10,13,14],
  [3,4,5,6,7,8,10,11,12,13],[3,4,5,6,7,8,10,11,13,14],
  [3,4,5,6,7,8,11,12,13,14],[3,4,5,6,8,9,10,11,12,13],
  [3,4,5,6,8,9,10,11,13,14],[3,4,5,6,8,9,11,12,13,14],
  [3,4,5,6,9,10,11,12,13,14],[3,4,6,7,8,9,10,11,12,13],
  [3,4,6,7,8,9,10,11,13,14],[3,4,6,7,8,9,11,12,13,14],
  [3,4,6,7,9,10,11,12,13,14],[3,4,7,8,9,10,11,12,13,14],
  [4,5,6,7,8,9,10,11,12,13],
  [4,5,6,7,8,9,10,11,13,14],[4,5,6,7,8,9,11,12,13,14],
  [4,5,6,7,9,10,11,12,13,14],[4,5,7,8,9,10,11,12,13,14],
  [5,6,7,8,9,10,11,12,13,14]]

manifold_9_15_93_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,15],[1,2,3,4,5,6,7,8,10,14],
  [1,2,3,4,5,6,7,8,14,15],[1,2,3,4,5,6,7,9,10,13],
  [1,2,3,4,5,6,7,9,13,15],[1,2,3,4,5,6,7,10,13,14],
  [1,2,3,4,5,6,7,13,14,15],[1,2,3,4,5,6,8,9,10,12],
  [1,2,3,4,5,6,8,9,12,15],[1,2,3,4,5,6,8,10,12,14],
  [1,2,3,4,5,6,8,12,14,15],[1,2,3,4,5,6,9,10,12,13],
  [1,2,3,4,5,6,9,12,13,15],[1,2,3,4,5,6,10,12,13,14],
  [1,2,3,4,5,6,12,13,14,15],[1,2,3,4,5,7,8,9,10,11],
  [1,2,3,4,5,7,8,9,11,15],[1,2,3,4,5,7,8,10,11,14],
  [1,2,3,4,5,7,8,11,14,15],[1,2,3,4,5,7,9,10,11,13],
  [1,2,3,4,5,7,9,11,13,15],[1,2,3,4,5,7,10,11,13,14],
  [1,2,3,4,5,7,11,13,14,15],[1,2,3,4,5,8,9,10,11,12],
  [1,2,3,4,5,8,9,11,12,15],[1,2,3,4,5,8,10,11,12,14],
  [1,2,3,4,5,8,11,12,14,15],[1,2,3,4,5,9,10,11,12,13],
  [1,2,3,4,5,9,11,12,13,15],[1,2,3,4,5,10,11,12,13,14],
  [1,2,3,4,5,11,12,13,14,15],[1,2,3,4,6,7,8,9,10,15],
  [1,2,3,4,6,7,8,10,14,15],[1,2,3,4,6,7,9,10,13,15],
  [1,2,3,4,6,7,10,13,14,15],[1,2,3,4,6,8,9,10,12,15],
  [1,2,3,4,6,8,10,12,14,15],[1,2,3,4,6,9,10,12,13,15],
  [1,2,3,4,6,10,12,13,14,15],[1,2,3,4,7,8,9,10,11,15],
  [1,2,3,4,7,8,10,11,14,15],[1,2,3,4,7,9,10,11,13,15],
  [1,2,3,4,7,10,11,13,14,15],[1,2,3,4,8,9,10,11,12,15],
  [1,2,3,4,8,10,11,12,14,15],[1,2,3,4,9,10,11,12,13,15],
  [1,2,3,4,10,11,12,13,14,15],
  [1,2,3,5,6,7,8,9,10,14],[1,2,3,5,6,7,8,9,14,15],
  [1,2,3,5,6,7,9,10,13,14],[1,2,3,5,6,7,9,13,14,15],
  [1,2,3,5,6,8,9,10,12,14],[1,2,3,5,6,8,9,12,14,15],
  [1,2,3,5,6,9,10,12,13,14],[1,2,3,5,6,9,12,13,14,15],
  [1,2,3,5,7,8,9,10,11,14],[1,2,3,5,7,8,9,11,14,15],
  [1,2,3,5,7,9,10,11,13,14],[1,2,3,5,7,9,11,13,14,15],
  [1,2,3,5,8,9,10,11,12,14],[1,2,3,5,8,9,11,12,14,15],
  [1,2,3,5,9,10,11,12,13,14],[1,2,3,5,9,11,12,13,14,15],
  [1,2,3,6,7,8,9,10,14,15],
  [1,2,3,6,7,9,10,13,14,15],[1,2,3,6,8,9,10,12,14,15],
  [1,2,3,6,9,10,12,13,14,15],[1,2,3,7,8,9,10,11,14,15],
  [1,2,3,7,9,10,11,13,14,15],[1,2,3,8,9,10,11,12,14,15],
  [1,2,3,9,10,11,12,13,14,15],
  [1,2,4,5,6,7,8,9,10,13],[1,2,4,5,6,7,8,9,13,15],
  [1,2,4,5,6,7,8,10,13,14],[1,2,4,5,6,7,8,13,14,15],
  [1,2,4,5,6,8,9,10,12,13],[1,2,4,5,6,8,9,12,13,15],
  [1,2,4,5,6,8,10,12,13,14],[1,2,4,5,6,8,12,13,14,15],
  [1,2,4,5,7,8,9,10,11,13],[1,2,4,5,7,8,9,11,13,15],
  [1,2,4,5,7,8,10,11,13,14],[1,2,4,5,7,8,11,13,14,15],
  [1,2,4,5,8,9,10,11,12,13],[1,2,4,5,8,9,11,12,13,15],
  [1,2,4,5,8,10,11,12,13,14],[1,2,4,5,8,11,12,13,14,15],
  [1,2,4,6,7,8,9,10,13,15],
  [1,2,4,6,7,8,10,13,14,15],[1,2,4,6,8,9,10,12,13,15],
  [1,2,4,6,8,10,12,13,14,15],[1,2,4,7,8,9,10,11,13,15],
  [1,2,4,7,8,10,11,13,14,15],[1,2,4,8,9,10,11,12,13,15],
  [1,2,4,8,10,11,12,13,14,15],
  [1,2,5,6,7,8,9,10,13,14],[1,2,5,6,7,8,9,13,14,15],
  [1,2,5,6,8,9,10,12,13,14],[1,2,5,6,8,9,12,13,14,15],
  [1,2,5,7,8,9,10,11,13,14],[1,2,5,7,8,9,11,13,14,15],
  [1,2,5,8,9,10,11,12,13,14],[1,2,5,8,9,11,12,13,14,15],
  [1,2,6,7,8,9,10,13,14,15],
  [1,2,6,8,9,10,12,13,14,15],[1,2,7,8,9,10,11,13,14,15],
  [1,2,8,9,10,11,12,13,14,15],
  [1,3,4,5,6,7,8,9,10,12],[1,3,4,5,6,7,8,9,12,15],
  [1,3,4,5,6,7,8,10,12,14],[1,3,4,5,6,7,8,12,14,15],
  [1,3,4,5,6,7,9,10,12,13],[1,3,4,5,6,7,9,12,13,15],
  [1,3,4,5,6,7,10,12,13,14],[1,3,4,5,6,7,12,13,14,15],
  [1,3,4,5,7,8,9,10,11,12],[1,3,4,5,7,8,9,11,12,15],
  [1,3,4,5,7,8,10,11,12,14],[1,3,4,5,7,8,11,12,14,15],
  [1,3,4,5,7,9,10,11,12,13],[1,3,4,5,7,9,11,12,13,15],
  [1,3,4,5,7,10,11,12,13,14],[1,3,4,5,7,11,12,13,14,15],
  [1,3,4,6,7,8,9,10,12,15],
  [1,3,4,6,7,8,10,12,14,15],[1,3,4,6,7,9,10,12,13,15],
  [1,3,4,6,7,10,12,13,14,15],[1,3,4,7,8,9,10,11,12,15],
  [1,3,4,7,8,10,11,12,14,15],[1,3,4,7,9,10,11,12,13,15],
  [1,3,4,7,10,11,12,13,14,15],
  [1,3,5,6,7,8,9,10,12,14],[1,3,5,6,7,8,9,12,14,15],
  [1,3,5,6,7,9,10,12,13,14],[1,3,5,6,7,9,12,13,14,15],
  [1,3,5,7,8,9,10,11,12,14],[1,3,5,7,8,9,11,12,14,15],
  [1,3,5,7,9,10,11,12,13,14],[1,3,5,7,9,11,12,13,14,15],
  [1,3,6,7,8,9,10,12,14,15],
  [1,3,6,7,9,10,12,13,14,15],[1,3,7,8,9,10,11,12,14,15],
  [1,3,7,9,10,11,12,13,14,15],
  [1,4,5,6,7,8,9,10,12,13],[1,4,5,6,7,8,9,12,13,15],
  [1,4,5,6,7,8,10,12,13,14],[1,4,5,6,7,8,12,13,14,15],
  [1,4,5,7,8,9,10,11,12,13],[1,4,5,7,8,9,11,12,13,15],
  [1,4,5,7,8,10,11,12,13,14],[1,4,5,7,8,11,12,13,14,15],
  [1,4,6,7,8,9,10,12,13,15],
  [1,4,6,7,8,10,12,13,14,15],[1,4,7,8,9,10,11,12,13,15],
  [1,4,7,8,10,11,12,13,14,15],
  [1,5,6,7,8,9,10,12,13,14],[1,5,6,7,8,9,12,13,14,15],
  [1,5,7,8,9,10,11,12,13,14],[1,5,7,8,9,11,12,13,14,15],
  [1,6,7,8,9,10,12,13,14,15],
  [1,7,8,9,10,11,12,13,14,15],[2,3,4,5,6,7,8,9,10,11],
  [2,3,4,5,6,7,8,9,11,15],[2,3,4,5,6,7,8,10,11,14],
  [2,3,4,5,6,7,8,11,14,15],[2,3,4,5,6,7,9,10,11,13],
  [2,3,4,5,6,7,9,11,13,15],[2,3,4,5,6,7,10,11,13,14],
  [2,3,4,5,6,7,11,13,14,15],[2,3,4,5,6,8,9,10,11,12],
  [2,3,4,5,6,8,9,11,12,15],[2,3,4,5,6,8,10,11,12,14],
  [2,3,4,5,6,8,11,12,14,15],[2,3,4,5,6,9,10,11,12,13],
  [2,3,4,5,6,9,11,12,13,15],[2,3,4,5,6,10,11,12,13,14],
  [2,3,4,5,6,11,12,13,14,15],[2,3,4,6,7,8,9,10,11,15],
  [2,3,4,6,7,8,10,11,14,15],[2,3,4,6,7,9,10,11,13,15],
  [2,3,4,6,7,10,11,13,14,15],[2,3,4,6,8,9,10,11,12,15],
  [2,3,4,6,8,10,11,12,14,15],[2,3,4,6,9,10,11,12,13,15],
  [2,3,4,6,10,11,12,13,14,15],
  [2,3,5,6,7,8,9,10,11,14],[2,3,5,6,7,8,9,11,14,15],
  [2,3,5,6,7,9,10,11,13,14],[2,3,5,6,7,9,11,13,14,15],
  [2,3,5,6,8,9,10,11,12,14],[2,3,5,6,8,9,11,12,14,15],
  [2,3,5,6,9,10,11,12,13,14],[2,3,5,6,9,11,12,13,14,15],
  [2,3,6,7,8,9,10,11,14,15],
  [2,3,6,7,9,10,11,13,14,15],[2,3,6,8,9,10,11,12,14,15],
  [2,3,6,9,10,11,12,13,14,15],
  [2,4,5,6,7,8,9,10,11,13],[2,4,5,6,7,8,9,11,13,15],
  [2,4,5,6,7,8,10,11,13,14],[2,4,5,6,7,8,11,13,14,15],
  [2,4,5,6,8,9,10,11,12,13],[2,4,5,6,8,9,11,12,13,15],
  [2,4,5,6,8,10,11,12,13,14],[2,4,5,6,8,11,12,13,14,15],
  [2,4,6,7,8,9,10,11,13,15],
  [2,4,6,7,8,10,11,13,14,15],[2,4,6,8,9,10,11,12,13,15],
  [2,4,6,8,10,11,12,13,14,15],
  [2,5,6,7,8,9,10,11,13,14],[2,5,6,7,8,9,11,13,14,15],
  [2,5,6,8,9,10,11,12,13,14],[2,5,6,8,9,11,12,13,14,15],
  [2,6,7,8,9,10,11,13,14,15],
  [2,6,8,9,10,11,12,13,14,15],[3,4,5,6,7,8,9,10,11,12],
  [3,4,5,6,7,8,9,11,12,15],[3,4,5,6,7,8,10,11,12,14],
  [3,4,5,6,7,8,11,12,14,15],[3,4,5,6,7,9,10,11,12,13],
  [3,4,5,6,7,9,11,12,13,15],[3,4,5,6,7,10,11,12,13,14],
  [3,4,5,6,7,11,12,13,14,15],[3,4,6,7,8,9,10,11,12,15],
  [3,4,6,7,8,10,11,12,14,15],[3,4,6,7,9,10,11,12,13,15],
  [3,4,6,7,10,11,12,13,14,15],
  [3,5,6,7,8,9,10,11,12,14],[3,5,6,7,8,9,11,12,14,15],
  [3,5,6,7,9,10,11,12,13,14],[3,5,6,7,9,11,12,13,14,15],
  [3,6,7,8,9,10,11,12,14,15],
  [3,6,7,9,10,11,12,13,14,15],[4,5,6,7,8,9,10,11,12,13],
  [4,5,6,7,8,9,11,12,13,15],
  [4,5,6,7,8,10,11,12,13,14],[4,5,6,7,8,11,12,13,14,15],
  [4,6,7,8,9,10,11,12,13,15],
  [4,6,7,8,10,11,12,13,14,15],
  [5,6,7,8,9,10,11,12,13,14],[5,6,7,8,9,11,12,13,14,15],
  [6,7,8,9,10,11,12,13,14,15]]

manifold_9_15_7_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,15],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,8,11,12],[1,2,3,4,5,6,7,8,12,13],
  [1,2,3,4,5,6,7,8,13,14],[1,2,3,4,5,6,7,8,14,15],
  [1,2,3,4,5,6,7,9,10,15],[1,2,3,4,5,6,7,10,11,15],
  [1,2,3,4,5,6,7,11,12,15],[1,2,3,4,5,6,7,12,13,15],
  [1,2,3,4,5,6,7,13,14,15],[1,2,3,4,5,6,8,9,10,14],
  [1,2,3,4,5,6,8,9,14,15],[1,2,3,4,5,6,8,10,11,12],
  [1,2,3,4,5,6,8,10,12,14],[1,2,3,4,5,6,8,12,13,14],
  [1,2,3,4,5,6,9,10,14,15],[1,2,3,4,5,6,10,11,12,14],
  [1,2,3,4,5,6,10,11,14,15],[1,2,3,4,5,6,11,12,14,15],
  [1,2,3,4,5,6,12,13,14,15],[1,2,3,4,5,7,8,9,10,11],
  [1,2,3,4,5,7,8,9,11,12],[1,2,3,4,5,7,8,9,12,13],
  [1,2,3,4,5,7,8,9,13,15],[1,2,3,4,5,7,8,13,14,15],
  [1,2,3,4,5,7,9,10,11,15],[1,2,3,4,5,7,9,11,12,13],
  [1,2,3,4,5,7,9,11,13,15],[1,2,3,4,5,7,11,12,13,15],
  [1,2,3,4,5,8,9,10,11,12],[1,2,3,4,5,8,9,10,12,14],
  [1,2,3,4,5,8,9,12,13,14],[1,2,3,4,5,8,9,13,14,15],
  [1,2,3,4,5,9,10,11,12,13],[1,2,3,4,5,9,10,11,13,15],
  [1,2,3,4,5,9,10,12,13,14],[1,2,3,4,5,9,10,13,14,15],
  [1,2,3,4,5,10,11,12,13,14],[1,2,3,4,5,10,11,13,14,15],
  [1,2,3,4,5,11,12,13,14,15],
  [1,2,3,4,6,7,8,9,10,15],[1,2,3,4,6,7,8,10,11,15],
  [1,2,3,4,6,7,8,11,12,15],[1,2,3,4,6,7,8,12,13,14],
  [1,2,3,4,6,7,8,12,14,15],[1,2,3,4,6,7,12,13,14,15],
  [1,2,3,4,6,8,9,10,14,15],[1,2,3,4,6,8,10,11,12,15],
  [1,2,3,4,6,8,10,12,14,15],[1,2,3,4,6,10,11,12,14,15],
  [1,2,3,4,7,8,9,10,11,15],[1,2,3,4,7,8,9,11,12,13],
  [1,2,3,4,7,8,9,11,13,15],[1,2,3,4,7,8,11,12,13,15],
  [1,2,3,4,7,8,12,13,14,15],[1,2,3,4,8,9,10,11,12,15],
  [1,2,3,4,8,9,10,12,14,15],[1,2,3,4,8,9,11,12,13,15],
  [1,2,3,4,8,9,12,13,14,15],[1,2,3,4,9,10,11,12,13,15],
  [1,2,3,4,9,10,12,13,14,15],
  [1,2,3,4,10,11,12,13,14,15],[1,2,3,5,6,7,8,9,10,12],
  [1,2,3,5,6,7,8,9,12,13],[1,2,3,5,6,7,8,9,13,14],
  [1,2,3,5,6,7,8,9,14,15],[1,2,3,5,6,7,8,10,11,12],
  [1,2,3,5,6,7,9,10,12,13],[1,2,3,5,6,7,9,10,13,14],
  [1,2,3,5,6,7,9,10,14,15],[1,2,3,5,6,7,10,11,12,13],
  [1,2,3,5,6,7,10,11,13,14],[1,2,3,5,6,7,10,11,14,15],
  [1,2,3,5,6,7,11,12,13,15],[1,2,3,5,6,7,11,13,14,15],
  [1,2,3,5,6,8,9,10,12,14],[1,2,3,5,6,8,9,12,13,14],
  [1,2,3,5,6,9,10,12,13,14],[1,2,3,5,6,10,11,12,13,14],
  [1,2,3,5,6,11,12,13,14,15],[1,2,3,5,7,8,9,10,11,12],
  [1,2,3,5,7,8,9,13,14,15],[1,2,3,5,7,9,10,11,12,13],
  [1,2,3,5,7,9,10,11,13,14],[1,2,3,5,7,9,10,11,14,15],
  [1,2,3,5,7,9,11,13,14,15],[1,2,3,5,9,10,11,13,14,15],
  [1,2,3,6,7,8,9,10,12,14],[1,2,3,6,7,8,9,10,14,15],
  [1,2,3,6,7,8,9,12,13,14],[1,2,3,6,7,8,10,11,12,15],
  [1,2,3,6,7,8,10,12,14,15],[1,2,3,6,7,9,10,12,13,14],
  [1,2,3,6,7,10,11,12,13,14],[1,2,3,6,7,10,11,12,14,15],
  [1,2,3,6,7,11,12,13,14,15],
  [1,2,3,7,8,9,10,11,12,14],[1,2,3,7,8,9,10,11,14,15],
  [1,2,3,7,8,9,11,12,13,14],[1,2,3,7,8,9,11,13,14,15],
  [1,2,3,7,8,10,11,12,14,15],[1,2,3,7,8,11,12,13,14,15],
  [1,2,3,7,9,10,11,12,13,14],
  [1,2,3,8,9,10,11,12,14,15],[1,2,3,8,9,11,12,13,14,15],
  [1,2,3,9,10,11,12,13,14,15],
  [1,2,4,5,6,7,8,9,10,11],[1,2,4,5,6,7,8,9,11,15],
  [1,2,4,5,6,7,8,11,12,15],[1,2,4,5,6,7,8,12,13,15],
  [1,2,4,5,6,7,8,13,14,15],[1,2,4,5,6,7,9,10,11,15],
  [1,2,4,5,6,8,9,10,11,12],[1,2,4,5,6,8,9,10,12,13],
  [1,2,4,5,6,8,9,10,13,14],[1,2,4,5,6,8,9,11,12,15],
  [1,2,4,5,6,8,9,12,13,15],[1,2,4,5,6,8,9,13,14,15],
  [1,2,4,5,6,8,10,12,13,14],[1,2,4,5,6,9,10,11,12,15],
  [1,2,4,5,6,9,10,12,13,15],[1,2,4,5,6,9,10,13,14,15],
  [1,2,4,5,6,10,11,12,14,15],[1,2,4,5,6,10,12,13,14,15],
  [1,2,4,5,7,8,9,11,12,13],[1,2,4,5,7,8,9,11,13,15],
  [1,2,4,5,7,8,11,12,13,15],
  [1,2,4,5,8,9,10,12,13,14],[1,2,4,5,8,9,11,12,13,15],
  [1,2,4,5,9,10,11,12,13,15],
  [1,2,4,5,10,11,12,13,14,15],[1,2,4,6,7,8,9,10,11,15],
  [1,2,4,6,7,8,12,13,14,15],[1,2,4,6,8,9,10,11,12,15],
  [1,2,4,6,8,9,10,12,13,15],[1,2,4,6,8,9,10,13,14,15],
  [1,2,4,6,8,10,12,13,14,15],[1,2,4,8,9,10,12,13,14,15],
  [1,2,5,6,7,8,9,10,11,12],[1,2,5,6,7,8,9,11,12,13],
  [1,2,5,6,7,8,9,11,13,15],[1,2,5,6,7,8,9,13,14,15],
  [1,2,5,6,7,8,11,12,13,15],
  [1,2,5,6,7,9,10,11,12,13],[1,2,5,6,7,9,10,11,13,14],
  [1,2,5,6,7,9,10,11,14,15],[1,2,5,6,7,9,11,13,14,15],
  [1,2,5,6,8,9,10,12,13,14],[1,2,5,6,8,9,11,12,13,15],
  [1,2,5,6,9,10,11,12,13,15],[1,2,5,6,9,10,11,13,14,15],
  [1,2,5,6,10,11,12,13,14,15],
  [1,2,6,7,8,9,10,11,12,13],[1,2,6,7,8,9,10,11,13,15],
  [1,2,6,7,8,9,10,12,13,14],[1,2,6,7,8,9,10,13,14,15],
  [1,2,6,7,8,10,11,12,13,15],[1,2,6,7,8,10,12,13,14,15],
  [1,2,6,7,9,10,11,13,14,15],
  [1,2,6,7,10,11,12,13,14,15],
  [1,2,6,8,9,10,11,12,13,15],[1,2,7,8,9,10,11,12,13,14],
  [1,2,7,8,9,10,11,13,14,15],
  [1,2,7,8,10,11,12,13,14,15],
  [1,2,8,9,10,11,12,13,14,15],[1,3,4,5,6,7,8,9,10,15],
  [1,3,4,5,6,7,8,10,11,12],[1,3,4,5,6,7,8,10,12,14],
  [1,3,4,5,6,7,8,10,14,15],[1,3,4,5,6,7,8,12,13,14],
  [1,3,4,5,6,7,10,11,12,14],[1,3,4,5,6,7,10,11,14,15],
  [1,3,4,5,6,7,11,12,14,15],[1,3,4,5,6,7,12,13,14,15],
  [1,3,4,5,6,8,9,10,14,15],[1,3,4,5,7,8,9,10,11,15],
  [1,3,4,5,7,8,9,11,12,15],[1,3,4,5,7,8,9,12,13,15],
  [1,3,4,5,7,8,10,11,12,14],[1,3,4,5,7,8,10,11,14,15],
  [1,3,4,5,7,8,11,12,14,15],[1,3,4,5,7,8,12,13,14,15],
  [1,3,4,5,7,9,11,12,13,15],[1,3,4,5,8,9,10,11,12,14],
  [1,3,4,5,8,9,10,11,14,15],[1,3,4,5,8,9,11,12,14,15],
  [1,3,4,5,8,9,12,13,14,15],[1,3,4,5,9,10,11,12,13,14],
  [1,3,4,5,9,10,11,13,14,15],[1,3,4,5,9,11,12,13,14,15],
  [1,3,4,6,7,8,10,11,12,15],
  [1,3,4,6,7,8,10,12,14,15],[1,3,4,6,7,10,11,12,14,15],
  [1,3,4,7,8,9,11,12,13,15],[1,3,4,7,8,10,11,12,14,15],
  [1,3,4,8,9,10,11,12,14,15],
  [1,3,4,9,10,11,12,13,14,15],[1,3,5,6,7,8,9,10,12,14],
  [1,3,5,6,7,8,9,10,14,15],[1,3,5,6,7,8,9,12,13,14],
  [1,3,5,6,7,9,10,12,13,14],[1,3,5,6,7,10,11,12,13,14],
  [1,3,5,6,7,11,12,13,14,15],[1,3,5,7,8,9,10,11,12,14],
  [1,3,5,7,8,9,10,11,14,15],[1,3,5,7,8,9,11,12,14,15],
  [1,3,5,7,8,9,12,13,14,15],[1,3,5,7,9,10,11,12,13,14],
  [1,3,5,7,9,11,12,13,14,15],[1,3,7,8,9,11,12,13,14,15],
  [1,4,5,6,7,8,9,10,11,15],
  [1,4,5,6,7,8,10,11,12,15],[1,4,5,6,7,8,10,12,14,15],
  [1,4,5,6,7,8,12,13,14,15],[1,4,5,6,7,10,11,12,14,15],
  [1,4,5,6,8,9,10,11,12,15],[1,4,5,6,8,9,10,12,13,15],
  [1,4,5,6,8,9,10,13,14,15],[1,4,5,6,8,10,12,13,14,15],
  [1,4,5,7,8,9,11,12,13,15],[1,4,5,7,8,10,11,12,14,15],
  [1,4,5,8,9,10,11,12,14,15],[1,4,5,8,9,10,12,13,14,15],
  [1,4,5,9,10,11,12,13,14,15],
  [1,5,6,7,8,9,10,11,12,15],[1,5,6,7,8,9,10,12,14,15],
  [1,5,6,7,8,9,11,12,13,15],[1,5,6,7,8,9,12,13,14,15],
  [1,5,6,7,9,10,11,12,13,14],[1,5,6,7,9,10,11,12,14,15],
  [1,5,6,7,9,11,12,13,14,15],
  [1,5,6,8,9,10,12,13,14,15],
  [1,5,6,9,10,11,12,13,14,15],
  [1,5,7,8,9,10,11,12,14,15],[1,6,7,8,9,10,11,12,13,15],
  [1,6,7,8,9,10,12,13,14,15],
  [1,6,7,9,10,11,12,13,14,15],
  [1,7,8,9,10,11,12,13,14,15],[2,3,4,5,6,7,8,9,10,11],
  [2,3,4,5,6,7,8,9,11,12],[2,3,4,5,6,7,8,9,12,13],
  [2,3,4,5,6,7,8,9,13,14],[2,3,4,5,6,7,8,9,14,15],
  [2,3,4,5,6,7,9,10,11,15],[2,3,4,5,6,7,9,11,12,13],
  [2,3,4,5,6,7,9,11,13,15],[2,3,4,5,6,7,9,13,14,15],
  [2,3,4,5,6,7,11,12,13,15],[2,3,4,5,6,8,9,10,11,12],
  [2,3,4,5,6,8,9,10,12,13],[2,3,4,5,6,8,9,10,13,14],
  [2,3,4,5,6,8,10,12,13,14],[2,3,4,5,6,9,10,11,12,13],
  [2,3,4,5,6,9,10,11,13,15],[2,3,4,5,6,9,10,13,14,15],
  [2,3,4,5,6,10,11,12,13,14],[2,3,4,5,6,10,11,13,14,15],
  [2,3,4,5,6,11,12,13,14,15],
  [2,3,4,5,7,8,9,13,14,15],[2,3,4,5,8,9,10,12,13,14],
  [2,3,4,6,7,8,9,10,11,13],[2,3,4,6,7,8,9,10,13,14],
  [2,3,4,6,7,8,9,10,14,15],[2,3,4,6,7,8,9,11,12,13],
  [2,3,4,6,7,8,10,11,13,14],[2,3,4,6,7,8,10,11,14,15],
  [2,3,4,6,7,8,11,12,13,14],[2,3,4,6,7,8,11,12,14,15],
  [2,3,4,6,7,9,10,11,13,15],[2,3,4,6,7,9,10,13,14,15],
  [2,3,4,6,7,10,11,13,14,15],[2,3,4,6,7,11,12,13,14,15],
  [2,3,4,6,8,9,10,11,12,13],
  [2,3,4,6,8,10,11,12,13,14],[2,3,4,6,8,10,11,12,14,15],
  [2,3,4,7,8,9,10,11,13,15],
  [2,3,4,7,8,9,10,13,14,15],[2,3,4,7,8,10,11,13,14,15],
  [2,3,4,7,8,11,12,13,14,15],[2,3,4,8,9,10,11,12,13,15],
  [2,3,4,8,9,10,12,13,14,15],
  [2,3,4,8,10,11,12,13,14,15],[2,3,5,6,7,8,9,10,11,12],
  [2,3,5,6,7,9,10,11,12,13],[2,3,5,6,7,9,10,11,13,14],
  [2,3,5,6,7,9,10,11,14,15],[2,3,5,6,7,9,11,13,14,15],
  [2,3,5,6,8,9,10,12,13,14],[2,3,5,6,9,10,11,13,14,15],
  [2,3,6,7,8,9,10,11,12,13],[2,3,6,7,8,9,10,12,13,14],
  [2,3,6,7,8,10,11,12,13,14],[2,3,6,7,8,10,11,12,14,15],
  [2,3,6,7,9,10,11,13,14,15],
  [2,3,7,8,9,10,11,12,13,14],[2,3,7,8,9,10,11,13,14,15],
  [2,3,8,9,10,11,12,13,14,15],
  [2,4,5,6,7,8,9,11,12,13],[2,4,5,6,7,8,9,11,13,15],
  [2,4,5,6,7,8,9,13,14,15],[2,4,5,6,7,8,11,12,13,15],
  [2,4,5,6,8,9,11,12,13,15],[2,4,5,6,9,10,11,12,13,15],
  [2,4,5,6,10,11,12,13,14,15],[2,4,6,7,8,9,10,11,13,15],
  [2,4,6,7,8,9,10,13,14,15],
  [2,4,6,7,8,10,11,13,14,15],[2,4,6,7,8,11,12,13,14,15],
  [2,4,6,8,9,10,11,12,13,15],
  [2,4,6,8,10,11,12,13,14,15],
  [2,6,7,8,10,11,12,13,14,15],[3,4,5,6,7,8,9,10,11,12],
  [3,4,5,6,7,8,9,10,12,13],[3,4,5,6,7,8,9,10,13,14],
  [3,4,5,6,7,8,9,10,14,15],[3,4,5,6,7,8,10,12,13,14],
  [3,4,5,6,7,9,10,11,12,13],[3,4,5,6,7,9,10,11,13,14],
  [3,4,5,6,7,9,10,11,14,15],[3,4,5,6,7,9,11,13,14,15],
  [3,4,5,6,7,10,11,12,13,14],[3,4,5,6,7,11,12,13,14,15],
  [3,4,5,6,9,10,11,13,14,15],
  [3,4,5,7,8,9,10,11,12,14],[3,4,5,7,8,9,10,11,14,15],
  [3,4,5,7,8,9,10,12,13,14],[3,4,5,7,8,9,11,12,14,15],
  [3,4,5,7,8,9,12,13,14,15],[3,4,5,7,9,10,11,12,13,14],
  [3,4,5,7,9,11,12,13,14,15],[3,4,6,7,8,9,10,11,12,13],
  [3,4,6,7,8,10,11,12,13,14],[3,4,6,7,8,10,11,12,14,15],
  [3,4,6,7,9,10,11,13,14,15],
  [3,4,7,8,9,10,11,12,13,14],[3,4,7,8,9,10,11,13,14,15],
  [3,4,7,8,9,11,12,13,14,15],
  [3,4,8,9,10,11,12,13,14,15],[3,5,6,7,8,9,10,12,13,14],
  [4,5,6,7,8,9,10,11,12,13],
  [4,5,6,7,8,9,10,11,13,14],[4,5,6,7,8,9,10,11,14,15],
  [4,5,6,7,8,9,11,13,14,15],[4,5,6,7,8,10,11,12,13,14],
  [4,5,6,7,8,10,11,12,14,15],[4,5,6,7,8,11,12,13,14,15],
  [4,5,6,8,9,10,11,12,13,15],
  [4,5,6,8,9,10,11,13,14,15],
  [4,5,6,8,10,11,12,13,14,15],
  [4,5,7,8,9,10,11,12,13,14],[4,5,7,8,9,11,12,13,14,15],
  [4,5,8,9,10,11,12,13,14,15],
  [4,6,7,8,9,10,11,13,14,15],[5,6,7,8,9,10,11,12,13,14],
  [5,6,7,8,9,10,11,12,14,15],
  [5,6,7,8,9,11,12,13,14,15],
  [5,6,8,9,10,11,12,13,14,15],
  [6,7,8,9,10,11,12,13,14,15]]

manifold_9_15_4_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,15],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,8,11,12],[1,2,3,4,5,6,7,8,12,14],
  [1,2,3,4,5,6,7,8,14,15],[1,2,3,4,5,6,7,9,10,15],
  [1,2,3,4,5,6,7,10,11,15],[1,2,3,4,5,6,7,11,12,13],
  [1,2,3,4,5,6,7,11,13,15],[1,2,3,4,5,6,7,12,13,14],
  [1,2,3,4,5,6,7,13,14,15],[1,2,3,4,5,6,8,9,10,14],
  [1,2,3,4,5,6,8,9,14,15],[1,2,3,4,5,6,8,10,11,12],
  [1,2,3,4,5,6,8,10,12,14],[1,2,3,4,5,6,9,10,14,15],
  [1,2,3,4,5,6,10,11,12,15],[1,2,3,4,5,6,10,12,14,15],
  [1,2,3,4,5,6,11,12,13,15],[1,2,3,4,5,6,12,13,14,15],
  [1,2,3,4,5,7,8,9,10,11],[1,2,3,4,5,7,8,9,11,12],
  [1,2,3,4,5,7,8,9,12,13],[1,2,3,4,5,7,8,9,13,15],
  [1,2,3,4,5,7,8,12,13,14],[1,2,3,4,5,7,8,13,14,15],
  [1,2,3,4,5,7,9,10,11,15],[1,2,3,4,5,7,9,11,12,13],
  [1,2,3,4,5,7,9,11,13,15],[1,2,3,4,5,8,9,10,11,12],
  [1,2,3,4,5,8,9,10,12,13],[1,2,3,4,5,8,9,10,13,14],
  [1,2,3,4,5,8,9,13,14,15],[1,2,3,4,5,8,10,12,13,14],
  [1,2,3,4,5,9,10,11,12,13],[1,2,3,4,5,9,10,11,13,14],
  [1,2,3,4,5,9,10,11,14,15],[1,2,3,4,5,9,11,13,14,15],
  [1,2,3,4,5,10,11,12,13,14],[1,2,3,4,5,10,11,12,14,15],
  [1,2,3,4,5,11,12,13,14,15],
  [1,2,3,4,6,7,8,9,10,15],[1,2,3,4,6,7,8,10,11,15],
  [1,2,3,4,6,7,8,11,12,15],[1,2,3,4,6,7,8,12,14,15],
  [1,2,3,4,6,7,11,12,13,15],[1,2,3,4,6,7,12,13,14,15],
  [1,2,3,4,6,8,9,10,14,15],[1,2,3,4,6,8,10,11,12,15],
  [1,2,3,4,6,8,10,12,14,15],[1,2,3,4,7,8,9,10,11,15],
  [1,2,3,4,7,8,9,11,12,15],[1,2,3,4,7,8,9,12,13,15],
  [1,2,3,4,7,8,12,13,14,15],[1,2,3,4,7,9,11,12,13,15],
  [1,2,3,4,8,9,10,11,12,15],[1,2,3,4,8,9,10,12,13,15],
  [1,2,3,4,8,9,10,13,14,15],[1,2,3,4,8,10,12,13,14,15],
  [1,2,3,4,9,10,11,12,13,15],[1,2,3,4,9,10,11,13,14,15],
  [1,2,3,4,10,11,12,13,14,15],
  [1,2,3,5,6,7,8,9,10,11],[1,2,3,5,6,7,8,9,11,12],
  [1,2,3,5,6,7,8,9,12,14],[1,2,3,5,6,7,8,9,14,15],
  [1,2,3,5,6,7,9,10,11,13],[1,2,3,5,6,7,9,10,13,14],
  [1,2,3,5,6,7,9,10,14,15],[1,2,3,5,6,7,9,11,12,13],
  [1,2,3,5,6,7,9,12,13,14],[1,2,3,5,6,7,10,11,13,14],
  [1,2,3,5,6,7,10,11,14,15],[1,2,3,5,6,7,11,13,14,15],
  [1,2,3,5,6,8,9,10,11,12],[1,2,3,5,6,8,9,10,12,14],
  [1,2,3,5,6,9,10,11,12,13],[1,2,3,5,6,9,10,12,13,14],
  [1,2,3,5,6,10,11,12,13,14],[1,2,3,5,6,10,11,12,14,15],
  [1,2,3,5,6,11,12,13,14,15],
  [1,2,3,5,7,8,9,12,13,14],[1,2,3,5,7,8,9,13,14,15],
  [1,2,3,5,7,9,10,11,13,14],[1,2,3,5,7,9,10,11,14,15],
  [1,2,3,5,7,9,11,13,14,15],[1,2,3,5,8,9,10,12,13,14],
  [1,2,3,6,7,8,9,10,11,12],[1,2,3,6,7,8,9,10,12,14],
  [1,2,3,6,7,8,9,10,14,15],[1,2,3,6,7,8,10,11,12,14],
  [1,2,3,6,7,8,10,11,14,15],[1,2,3,6,7,8,11,12,14,15],
  [1,2,3,6,7,9,10,11,12,13],[1,2,3,6,7,9,10,12,13,14],
  [1,2,3,6,7,10,11,12,13,14],[1,2,3,6,7,11,12,13,14,15],
  [1,2,3,6,8,10,11,12,14,15],
  [1,2,3,7,8,9,10,11,12,14],[1,2,3,7,8,9,10,11,14,15],
  [1,2,3,7,8,9,11,12,14,15],[1,2,3,7,8,9,12,13,14,15],
  [1,2,3,7,9,10,11,12,13,14],[1,2,3,7,9,11,12,13,14,15],
  [1,2,3,8,9,10,11,12,14,15],
  [1,2,3,8,9,10,12,13,14,15],
  [1,2,3,9,10,11,12,13,14,15],[1,2,4,5,6,7,8,9,10,15],
  [1,2,4,5,6,7,8,10,11,15],[1,2,4,5,6,7,8,11,12,13],
  [1,2,4,5,6,7,8,11,13,15],[1,2,4,5,6,7,8,12,13,14],
  [1,2,4,5,6,7,8,13,14,15],[1,2,4,5,6,8,9,10,12,13],
  [1,2,4,5,6,8,9,10,12,15],[1,2,4,5,6,8,9,10,13,14],
  [1,2,4,5,6,8,9,12,13,15],[1,2,4,5,6,8,9,13,14,15],
  [1,2,4,5,6,8,10,11,12,15],[1,2,4,5,6,8,10,12,13,14],
  [1,2,4,5,6,8,11,12,13,15],[1,2,4,5,6,9,10,12,13,15],
  [1,2,4,5,6,9,10,13,14,15],[1,2,4,5,6,10,12,13,14,15],
  [1,2,4,5,7,8,9,10,11,15],[1,2,4,5,7,8,9,11,12,13],
  [1,2,4,5,7,8,9,11,13,15],[1,2,4,5,8,9,10,11,12,15],
  [1,2,4,5,8,9,11,12,13,15],[1,2,4,5,9,10,11,12,13,15],
  [1,2,4,5,9,10,11,13,14,15],
  [1,2,4,5,10,11,12,13,14,15],[1,2,4,6,7,8,11,12,13,15],
  [1,2,4,6,7,8,12,13,14,15],
  [1,2,4,6,8,9,10,12,13,15],[1,2,4,6,8,9,10,13,14,15],
  [1,2,4,6,8,10,12,13,14,15],[1,2,4,7,8,9,11,12,13,15],
  [1,2,5,6,7,8,9,10,11,15],[1,2,5,6,7,8,9,11,12,13],
  [1,2,5,6,7,8,9,11,13,15],[1,2,5,6,7,8,9,12,13,14],
  [1,2,5,6,7,8,9,13,14,15],[1,2,5,6,7,9,10,11,13,15],
  [1,2,5,6,7,9,10,13,14,15],[1,2,5,6,7,10,11,13,14,15],
  [1,2,5,6,8,9,10,11,12,15],[1,2,5,6,8,9,10,12,13,14],
  [1,2,5,6,8,9,11,12,13,15],[1,2,5,6,9,10,11,12,13,15],
  [1,2,5,6,10,11,12,13,14,15],
  [1,2,5,7,9,10,11,13,14,15],[1,2,6,7,8,9,10,11,12,13],
  [1,2,6,7,8,9,10,11,13,15],[1,2,6,7,8,9,10,12,13,14],
  [1,2,6,7,8,9,10,13,14,15],[1,2,6,7,8,10,11,12,13,14],
  [1,2,6,7,8,10,11,13,14,15],[1,2,6,7,8,11,12,13,14,15],
  [1,2,6,8,9,10,11,12,13,15],
  [1,2,6,8,10,11,12,13,14,15],
  [1,2,7,8,9,10,11,12,13,14],[1,2,7,8,9,10,11,13,14,15],
  [1,2,7,8,9,11,12,13,14,15],
  [1,2,8,9,10,11,12,13,14,15],[1,3,4,5,6,7,8,9,10,14],
  [1,3,4,5,6,7,8,9,14,15],[1,3,4,5,6,7,8,10,11,12],
  [1,3,4,5,6,7,8,10,12,14],[1,3,4,5,6,7,9,10,14,15],
  [1,3,4,5,6,7,10,11,12,15],[1,3,4,5,6,7,10,12,14,15],
  [1,3,4,5,6,7,11,12,13,15],[1,3,4,5,6,7,12,13,14,15],
  [1,3,4,5,7,8,9,10,11,14],[1,3,4,5,7,8,9,11,12,15],
  [1,3,4,5,7,8,9,11,14,15],[1,3,4,5,7,8,9,12,13,15],
  [1,3,4,5,7,8,10,11,12,14],[1,3,4,5,7,8,11,12,14,15],
  [1,3,4,5,7,8,12,13,14,15],[1,3,4,5,7,9,10,11,14,15],
  [1,3,4,5,7,9,11,12,13,15],[1,3,4,5,7,10,11,12,14,15],
  [1,3,4,5,8,9,10,11,12,14],[1,3,4,5,8,9,10,12,13,14],
  [1,3,4,5,8,9,11,12,14,15],[1,3,4,5,8,9,12,13,14,15],
  [1,3,4,5,9,10,11,12,13,14],[1,3,4,5,9,11,12,13,14,15],
  [1,3,4,6,7,8,9,10,14,15],
  [1,3,4,6,7,8,10,11,12,15],[1,3,4,6,7,8,10,12,14,15],
  [1,3,4,7,8,9,10,11,14,15],[1,3,4,7,8,10,11,12,14,15],
  [1,3,4,8,9,10,11,12,14,15],[1,3,4,8,9,10,12,13,14,15],
  [1,3,4,9,10,11,12,13,14,15],
  [1,3,5,6,7,8,9,10,11,12],[1,3,5,6,7,8,9,10,12,14],
  [1,3,5,6,7,9,10,11,12,13],[1,3,5,6,7,9,10,12,13,14],
  [1,3,5,6,7,10,11,12,13,14],[1,3,5,6,7,10,11,12,14,15],
  [1,3,5,6,7,11,12,13,14,15],
  [1,3,5,7,8,9,10,11,12,14],[1,3,5,7,8,9,11,12,14,15],
  [1,3,5,7,8,9,12,13,14,15],[1,3,5,7,9,10,11,12,13,14],
  [1,3,5,7,9,11,12,13,14,15],[1,3,6,7,8,10,11,12,14,15],
  [1,4,5,6,7,8,9,10,14,15],
  [1,4,5,6,7,8,10,11,12,15],[1,4,5,6,7,8,10,12,14,15],
  [1,4,5,6,7,8,11,12,13,15],[1,4,5,6,7,8,12,13,14,15],
  [1,4,5,6,8,9,10,12,13,14],[1,4,5,6,8,9,10,12,14,15],
  [1,4,5,6,8,9,12,13,14,15],[1,4,5,6,9,10,12,13,14,15],
  [1,4,5,7,8,9,10,11,14,15],[1,4,5,7,8,9,11,12,13,15],
  [1,4,5,7,8,10,11,12,14,15],[1,4,5,8,9,10,11,12,14,15],
  [1,4,5,9,10,11,12,13,14,15],
  [1,4,6,8,9,10,12,13,14,15],[1,5,6,7,8,9,10,11,12,15],
  [1,5,6,7,8,9,10,12,14,15],[1,5,6,7,8,9,11,12,13,15],
  [1,5,6,7,8,9,12,13,14,15],[1,5,6,7,9,10,11,12,13,15],
  [1,5,6,7,9,10,12,13,14,15],
  [1,5,6,7,10,11,12,13,14,15],
  [1,5,7,8,9,10,11,12,14,15],
  [1,5,7,9,10,11,12,13,14,15],
  [1,6,7,8,9,10,11,12,13,15],[1,6,7,8,9,10,12,13,14,15],
  [1,6,7,8,10,11,12,13,14,15],
  [1,7,8,9,10,11,12,13,14,15],[2,3,4,5,6,7,8,9,10,11],
  [2,3,4,5,6,7,8,9,11,12],[2,3,4,5,6,7,8,9,12,13],
  [2,3,4,5,6,7,8,9,13,15],[2,3,4,5,6,7,8,12,13,14],
  [2,3,4,5,6,7,8,13,14,15],[2,3,4,5,6,7,9,10,11,15],
  [2,3,4,5,6,7,9,11,12,13],[2,3,4,5,6,7,9,11,13,15],
  [2,3,4,5,6,8,9,10,11,12],[2,3,4,5,6,8,9,10,12,13],
  [2,3,4,5,6,8,9,10,13,14],[2,3,4,5,6,8,9,13,14,15],
  [2,3,4,5,6,8,10,12,13,14],[2,3,4,5,6,9,10,11,12,13],
  [2,3,4,5,6,9,10,11,13,14],[2,3,4,5,6,9,10,11,14,15],
  [2,3,4,5,6,9,11,13,14,15],[2,3,4,5,6,10,11,12,13,14],
  [2,3,4,5,6,10,11,12,14,15],[2,3,4,5,6,11,12,13,14,15],
  [2,3,4,6,7,8,9,10,11,12],[2,3,4,6,7,8,9,10,12,13],
  [2,3,4,6,7,8,9,10,13,15],
  [2,3,4,6,7,8,10,11,12,14],[2,3,4,6,7,8,10,11,14,15],
  [2,3,4,6,7,8,10,12,13,14],[2,3,4,6,7,8,10,13,14,15],
  [2,3,4,6,7,8,11,12,14,15],[2,3,4,6,7,9,10,11,12,13],
  [2,3,4,6,7,9,10,11,13,15],[2,3,4,6,7,10,11,12,13,14],
  [2,3,4,6,7,10,11,13,14,15],[2,3,4,6,7,11,12,13,14,15],
  [2,3,4,6,8,9,10,13,14,15],
  [2,3,4,6,8,10,11,12,14,15],[2,3,4,6,9,10,11,13,14,15],
  [2,3,4,7,8,9,10,11,12,13],
  [2,3,4,7,8,9,10,11,13,15],[2,3,4,7,8,9,11,12,13,15],
  [2,3,4,7,8,10,11,12,13,14],[2,3,4,7,8,10,11,13,14,15],
  [2,3,4,7,8,11,12,13,14,15],
  [2,3,4,8,9,10,11,12,13,15],
  [2,3,4,8,10,11,12,13,14,15],[2,3,5,6,7,8,9,12,13,14],
  [2,3,5,6,7,8,9,13,14,15],[2,3,5,6,7,9,10,11,13,14],
  [2,3,5,6,7,9,10,11,14,15],[2,3,5,6,7,9,11,13,14,15],
  [2,3,5,6,8,9,10,12,13,14],[2,3,6,7,8,9,10,12,13,14],
  [2,3,6,7,8,9,10,13,14,15],[2,3,6,7,9,10,11,13,14,15],
  [2,3,7,8,9,10,11,12,13,14],[2,3,7,8,9,10,11,13,14,15],
  [2,3,7,8,9,11,12,13,14,15],
  [2,3,8,9,10,11,12,13,14,15],[2,4,5,6,7,8,9,10,11,15],
  [2,4,5,6,7,8,9,11,12,13],[2,4,5,6,7,8,9,11,13,15],
  [2,4,5,6,8,9,10,11,12,15],[2,4,5,6,8,9,11,12,13,15],
  [2,4,5,6,9,10,11,12,13,15],[2,4,5,6,9,10,11,13,14,15],
  [2,4,5,6,10,11,12,13,14,15],
  [2,4,6,7,8,9,10,11,12,13],[2,4,6,7,8,9,10,11,13,15],
  [2,4,6,7,8,10,11,12,13,14],[2,4,6,7,8,10,11,13,14,15],
  [2,4,6,7,8,11,12,13,14,15],
  [2,4,6,8,9,10,11,12,13,15],
  [2,4,6,8,10,11,12,13,14,15],
  [2,5,6,7,9,10,11,13,14,15],[3,4,5,6,7,8,9,10,11,12],
  [3,4,5,6,7,8,9,10,12,13],[3,4,5,6,7,8,9,10,13,14],
  [3,4,5,6,7,8,9,13,14,15],[3,4,5,6,7,8,10,12,13,14],
  [3,4,5,6,7,9,10,11,12,13],[3,4,5,6,7,9,10,11,13,14],
  [3,4,5,6,7,9,10,11,14,15],[3,4,5,6,7,9,11,13,14,15],
  [3,4,5,6,7,10,11,12,13,14],[3,4,5,6,7,10,11,12,14,15],
  [3,4,5,6,7,11,12,13,14,15],
  [3,4,5,7,8,9,10,11,12,13],[3,4,5,7,8,9,10,11,13,14],
  [3,4,5,7,8,9,11,12,13,15],[3,4,5,7,8,9,11,13,14,15],
  [3,4,5,7,8,10,11,12,13,14],[3,4,5,7,8,11,12,13,14,15],
  [3,4,5,8,9,10,11,12,13,14],
  [3,4,5,8,9,11,12,13,14,15],[3,4,6,7,8,9,10,13,14,15],
  [3,4,6,7,8,10,11,12,14,15],[3,4,6,7,9,10,11,13,14,15],
  [3,4,7,8,9,10,11,13,14,15],
  [3,4,8,9,10,11,12,13,14,15],[3,5,6,7,8,9,10,12,13,14],
  [3,5,7,8,9,10,11,12,13,14],
  [3,5,7,8,9,11,12,13,14,15],[4,5,6,7,8,9,10,11,12,13],
  [4,5,6,7,8,9,10,11,13,14],[4,5,6,7,8,9,10,11,14,15],
  [4,5,6,7,8,9,11,13,14,15],[4,5,6,7,8,10,11,12,13,14],
  [4,5,6,7,8,10,11,12,14,15],[4,5,6,7,8,11,12,13,14,15],
  [4,5,6,8,9,10,11,12,13,14],
  [4,5,6,8,9,10,11,12,14,15],[4,5,6,8,9,11,12,13,14,15],
  [4,5,6,9,10,11,12,13,14,15],
  [4,6,7,8,9,10,11,13,14,15],
  [4,6,8,9,10,11,12,13,14,15],
  [5,6,7,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,14,15],
  [5,6,7,8,9,11,12,13,14,15],
  [5,6,7,9,10,11,12,13,14,15],
  [6,7,8,9,10,11,12,13,14,15]]

manifold_9_15_2_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,15],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,8,11,12],[1,2,3,4,5,6,7,8,12,13],
  [1,2,3,4,5,6,7,8,13,14],[1,2,3,4,5,6,7,8,14,15],
  [1,2,3,4,5,6,7,9,10,15],[1,2,3,4,5,6,7,10,11,15],
  [1,2,3,4,5,6,7,11,12,15],[1,2,3,4,5,6,7,12,13,15],
  [1,2,3,4,5,6,7,13,14,15],[1,2,3,4,5,6,8,9,10,11],
  [1,2,3,4,5,6,8,9,11,12],[1,2,3,4,5,6,8,9,12,13],
  [1,2,3,4,5,6,8,9,13,14],[1,2,3,4,5,6,8,9,14,15],
  [1,2,3,4,5,6,9,10,11,12],[1,2,3,4,5,6,9,10,12,13],
  [1,2,3,4,5,6,9,10,13,14],[1,2,3,4,5,6,9,10,14,15],
  [1,2,3,4,5,6,10,11,12,13],[1,2,3,4,5,6,10,11,13,14],
  [1,2,3,4,5,6,10,11,14,15],[1,2,3,4,5,6,11,12,13,14],
  [1,2,3,4,5,6,11,12,14,15],[1,2,3,4,5,6,12,13,14,15],
  [1,2,3,4,5,7,8,9,10,15],[1,2,3,4,5,7,8,10,11,15],
  [1,2,3,4,5,7,8,11,12,15],[1,2,3,4,5,7,8,12,13,15],
  [1,2,3,4,5,7,8,13,14,15],[1,2,3,4,5,8,9,10,11,15],
  [1,2,3,4,5,8,9,11,12,15],[1,2,3,4,5,8,9,12,13,15],
  [1,2,3,4,5,8,9,13,14,15],[1,2,3,4,5,9,10,11,12,15],
  [1,2,3,4,5,9,10,12,13,15],[1,2,3,4,5,9,10,13,14,15],
  [1,2,3,4,5,10,11,12,13,15],[1,2,3,4,5,10,11,13,14,15],
  [1,2,3,4,5,11,12,13,14,15],
  [1,2,3,4,6,7,8,9,10,11],[1,2,3,4,6,7,8,9,11,12],
  [1,2,3,4,6,7,8,9,12,13],[1,2,3,4,6,7,8,9,13,14],
  [1,2,3,4,6,7,8,9,14,15],[1,2,3,4,6,7,9,10,11,12],
  [1,2,3,4,6,7,9,10,12,13],[1,2,3,4,6,7,9,10,13,14],
  [1,2,3,4,6,7,9,10,14,15],[1,2,3,4,6,7,10,11,12,13],
  [1,2,3,4,6,7,10,11,13,14],[1,2,3,4,6,7,10,11,14,15],
  [1,2,3,4,6,7,11,12,13,14],[1,2,3,4,6,7,11,12,14,15],
  [1,2,3,4,6,7,12,13,14,15],[1,2,3,4,7,8,9,10,11,12],
  [1,2,3,4,7,8,9,10,12,13],[1,2,3,4,7,8,9,10,13,14],
  [1,2,3,4,7,8,9,10,14,15],[1,2,3,4,7,8,10,11,12,13],
  [1,2,3,4,7,8,10,11,13,14],[1,2,3,4,7,8,10,11,14,15],
  [1,2,3,4,7,8,11,12,13,14],[1,2,3,4,7,8,11,12,14,15],
  [1,2,3,4,7,8,12,13,14,15],[1,2,3,4,8,9,10,11,12,13],
  [1,2,3,4,8,9,10,11,13,14],[1,2,3,4,8,9,10,11,14,15],
  [1,2,3,4,8,9,11,12,13,14],[1,2,3,4,8,9,11,12,14,15],
  [1,2,3,4,8,9,12,13,14,15],[1,2,3,4,9,10,11,12,13,14],
  [1,2,3,4,9,10,11,12,14,15],[1,2,3,4,9,10,12,13,14,15],
  [1,2,3,4,10,11,12,13,14,15],
  [1,2,3,5,6,7,8,9,10,15],[1,2,3,5,6,7,8,10,11,15],
  [1,2,3,5,6,7,8,11,12,15],[1,2,3,5,6,7,8,12,13,15],
  [1,2,3,5,6,7,8,13,14,15],[1,2,3,5,6,8,9,10,11,15],
  [1,2,3,5,6,8,9,11,12,15],[1,2,3,5,6,8,9,12,13,15],
  [1,2,3,5,6,8,9,13,14,15],[1,2,3,5,6,9,10,11,12,15],
  [1,2,3,5,6,9,10,12,13,15],[1,2,3,5,6,9,10,13,14,15],
  [1,2,3,5,6,10,11,12,13,15],[1,2,3,5,6,10,11,13,14,15],
  [1,2,3,5,6,11,12,13,14,15],
  [1,2,3,6,7,8,9,10,11,15],[1,2,3,6,7,8,9,11,12,15],
  [1,2,3,6,7,8,9,12,13,15],[1,2,3,6,7,8,9,13,14,15],
  [1,2,3,6,7,9,10,11,12,15],[1,2,3,6,7,9,10,12,13,15],
  [1,2,3,6,7,9,10,13,14,15],[1,2,3,6,7,10,11,12,13,15],
  [1,2,3,6,7,10,11,13,14,15],[1,2,3,6,7,11,12,13,14,15],
  [1,2,3,7,8,9,10,11,12,15],
  [1,2,3,7,8,9,10,12,13,15],[1,2,3,7,8,9,10,13,14,15],
  [1,2,3,7,8,10,11,12,13,15],[1,2,3,7,8,10,11,13,14,15],
  [1,2,3,7,8,11,12,13,14,15],
  [1,2,3,8,9,10,11,12,13,15],[1,2,3,8,9,10,11,13,14,15],
  [1,2,3,8,9,11,12,13,14,15],
  [1,2,3,9,10,11,12,13,14,15],[1,2,4,5,6,7,8,9,10,11],
  [1,2,4,5,6,7,8,9,11,12],[1,2,4,5,6,7,8,9,12,13],
  [1,2,4,5,6,7,8,9,13,14],[1,2,4,5,6,7,8,9,14,15],
  [1,2,4,5,6,7,9,10,11,12],[1,2,4,5,6,7,9,10,12,13],
  [1,2,4,5,6,7,9,10,13,14],[1,2,4,5,6,7,9,10,14,15],
  [1,2,4,5,6,7,10,11,12,13],[1,2,4,5,6,7,10,11,13,14],
  [1,2,4,5,6,7,10,11,14,15],[1,2,4,5,6,7,11,12,13,14],
  [1,2,4,5,6,7,11,12,14,15],[1,2,4,5,6,7,12,13,14,15],
  [1,2,4,5,7,8,9,10,11,12],[1,2,4,5,7,8,9,10,12,13],
  [1,2,4,5,7,8,9,10,13,14],[1,2,4,5,7,8,9,10,14,15],
  [1,2,4,5,7,8,10,11,12,13],[1,2,4,5,7,8,10,11,13,14],
  [1,2,4,5,7,8,10,11,14,15],[1,2,4,5,7,8,11,12,13,14],
  [1,2,4,5,7,8,11,12,14,15],[1,2,4,5,7,8,12,13,14,15],
  [1,2,4,5,8,9,10,11,12,13],[1,2,4,5,8,9,10,11,13,14],
  [1,2,4,5,8,9,10,11,14,15],[1,2,4,5,8,9,11,12,13,14],
  [1,2,4,5,8,9,11,12,14,15],[1,2,4,5,8,9,12,13,14,15],
  [1,2,4,5,9,10,11,12,13,14],[1,2,4,5,9,10,11,12,14,15],
  [1,2,4,5,9,10,12,13,14,15],
  [1,2,4,5,10,11,12,13,14,15],[1,2,5,6,7,8,9,10,11,12],
  [1,2,5,6,7,8,9,10,12,13],[1,2,5,6,7,8,9,10,13,14],
  [1,2,5,6,7,8,9,10,14,15],[1,2,5,6,7,8,10,11,12,13],
  [1,2,5,6,7,8,10,11,13,14],[1,2,5,6,7,8,10,11,14,15],
  [1,2,5,6,7,8,11,12,13,14],[1,2,5,6,7,8,11,12,14,15],
  [1,2,5,6,7,8,12,13,14,15],[1,2,5,6,8,9,10,11,12,13],
  [1,2,5,6,8,9,10,11,13,14],[1,2,5,6,8,9,10,11,14,15],
  [1,2,5,6,8,9,11,12,13,14],[1,2,5,6,8,9,11,12,14,15],
  [1,2,5,6,8,9,12,13,14,15],[1,2,5,6,9,10,11,12,13,14],
  [1,2,5,6,9,10,11,12,14,15],[1,2,5,6,9,10,12,13,14,15],
  [1,2,5,6,10,11,12,13,14,15],
  [1,2,6,7,8,9,10,11,12,13],[1,2,6,7,8,9,10,11,13,14],
  [1,2,6,7,8,9,10,11,14,15],[1,2,6,7,8,9,11,12,13,14],
  [1,2,6,7,8,9,11,12,14,15],[1,2,6,7,8,9,12,13,14,15],
  [1,2,6,7,9,10,11,12,13,14],[1,2,6,7,9,10,11,12,14,15],
  [1,2,6,7,9,10,12,13,14,15],
  [1,2,6,7,10,11,12,13,14,15],
  [1,2,7,8,9,10,11,12,13,14],[1,2,7,8,9,10,11,12,14,15],
  [1,2,7,8,9,10,12,13,14,15],
  [1,2,7,8,10,11,12,13,14,15],
  [1,2,8,9,10,11,12,13,14,15],[1,3,4,5,6,7,8,9,10,15],
  [1,3,4,5,6,7,8,10,11,15],[1,3,4,5,6,7,8,11,12,15],
  [1,3,4,5,6,7,8,12,13,15],[1,3,4,5,6,7,8,13,14,15],
  [1,3,4,5,6,8,9,10,11,15],[1,3,4,5,6,8,9,11,12,15],
  [1,3,4,5,6,8,9,12,13,15],[1,3,4,5,6,8,9,13,14,15],
  [1,3,4,5,6,9,10,11,12,15],[1,3,4,5,6,9,10,12,13,15],
  [1,3,4,5,6,9,10,13,14,15],[1,3,4,5,6,10,11,12,13,15],
  [1,3,4,5,6,10,11,13,14,15],[1,3,4,5,6,11,12,13,14,15],
  [1,3,4,6,7,8,9,10,11,15],[1,3,4,6,7,8,9,11,12,15],
  [1,3,4,6,7,8,9,12,13,15],[1,3,4,6,7,8,9,13,14,15],
  [1,3,4,6,7,9,10,11,12,15],
  [1,3,4,6,7,9,10,12,13,15],[1,3,4,6,7,9,10,13,14,15],
  [1,3,4,6,7,10,11,12,13,15],[1,3,4,6,7,10,11,13,14,15],
  [1,3,4,6,7,11,12,13,14,15],
  [1,3,4,7,8,9,10,11,12,15],[1,3,4,7,8,9,10,12,13,15],
  [1,3,4,7,8,9,10,13,14,15],[1,3,4,7,8,10,11,12,13,15],
  [1,3,4,7,8,10,11,13,14,15],[1,3,4,7,8,11,12,13,14,15],
  [1,3,4,8,9,10,11,12,13,15],
  [1,3,4,8,9,10,11,13,14,15],[1,3,4,8,9,11,12,13,14,15],
  [1,3,4,9,10,11,12,13,14,15],
  [1,4,5,6,7,8,9,10,11,15],[1,4,5,6,7,8,9,11,12,15],
  [1,4,5,6,7,8,9,12,13,15],[1,4,5,6,7,8,9,13,14,15],
  [1,4,5,6,7,9,10,11,12,15],[1,4,5,6,7,9,10,12,13,15],
  [1,4,5,6,7,9,10,13,14,15],[1,4,5,6,7,10,11,12,13,15],
  [1,4,5,6,7,10,11,13,14,15],[1,4,5,6,7,11,12,13,14,15],
  [1,4,5,7,8,9,10,11,12,15],
  [1,4,5,7,8,9,10,12,13,15],[1,4,5,7,8,9,10,13,14,15],
  [1,4,5,7,8,10,11,12,13,15],[1,4,5,7,8,10,11,13,14,15],
  [1,4,5,7,8,11,12,13,14,15],
  [1,4,5,8,9,10,11,12,13,15],[1,4,5,8,9,10,11,13,14,15],
  [1,4,5,8,9,11,12,13,14,15],
  [1,4,5,9,10,11,12,13,14,15],[1,5,6,7,8,9,10,11,12,15],
  [1,5,6,7,8,9,10,12,13,15],
  [1,5,6,7,8,9,10,13,14,15],[1,5,6,7,8,10,11,12,13,15],
  [1,5,6,7,8,10,11,13,14,15],[1,5,6,7,8,11,12,13,14,15],
  [1,5,6,8,9,10,11,12,13,15],
  [1,5,6,8,9,10,11,13,14,15],[1,5,6,8,9,11,12,13,14,15],
  [1,5,6,9,10,11,12,13,14,15],
  [1,6,7,8,9,10,11,12,13,15],[1,6,7,8,9,10,11,13,14,15],
  [1,6,7,8,9,11,12,13,14,15],
  [1,6,7,9,10,11,12,13,14,15],
  [1,7,8,9,10,11,12,13,14,15],[2,3,4,5,6,7,8,9,10,11],
  [2,3,4,5,6,7,8,9,11,12],[2,3,4,5,6,7,8,9,12,13],
  [2,3,4,5,6,7,8,9,13,14],[2,3,4,5,6,7,8,9,14,15],
  [2,3,4,5,6,7,9,10,11,12],[2,3,4,5,6,7,9,10,12,13],
  [2,3,4,5,6,7,9,10,13,14],[2,3,4,5,6,7,9,10,14,15],
  [2,3,4,5,6,7,10,11,12,13],[2,3,4,5,6,7,10,11,13,14],
  [2,3,4,5,6,7,10,11,14,15],[2,3,4,5,6,7,11,12,13,14],
  [2,3,4,5,6,7,11,12,14,15],[2,3,4,5,6,7,12,13,14,15],
  [2,3,4,5,7,8,9,10,11,12],[2,3,4,5,7,8,9,10,12,13],
  [2,3,4,5,7,8,9,10,13,14],[2,3,4,5,7,8,9,10,14,15],
  [2,3,4,5,7,8,10,11,12,13],[2,3,4,5,7,8,10,11,13,14],
  [2,3,4,5,7,8,10,11,14,15],[2,3,4,5,7,8,11,12,13,14],
  [2,3,4,5,7,8,11,12,14,15],[2,3,4,5,7,8,12,13,14,15],
  [2,3,4,5,8,9,10,11,12,13],[2,3,4,5,8,9,10,11,13,14],
  [2,3,4,5,8,9,10,11,14,15],[2,3,4,5,8,9,11,12,13,14],
  [2,3,4,5,8,9,11,12,14,15],[2,3,4,5,8,9,12,13,14,15],
  [2,3,4,5,9,10,11,12,13,14],[2,3,4,5,9,10,11,12,14,15],
  [2,3,4,5,9,10,12,13,14,15],
  [2,3,4,5,10,11,12,13,14,15],[2,3,5,6,7,8,9,10,11,12],
  [2,3,5,6,7,8,9,10,12,13],[2,3,5,6,7,8,9,10,13,14],
  [2,3,5,6,7,8,9,10,14,15],[2,3,5,6,7,8,10,11,12,13],
  [2,3,5,6,7,8,10,11,13,14],[2,3,5,6,7,8,10,11,14,15],
  [2,3,5,6,7,8,11,12,13,14],[2,3,5,6,7,8,11,12,14,15],
  [2,3,5,6,7,8,12,13,14,15],[2,3,5,6,8,9,10,11,12,13],
  [2,3,5,6,8,9,10,11,13,14],[2,3,5,6,8,9,10,11,14,15],
  [2,3,5,6,8,9,11,12,13,14],[2,3,5,6,8,9,11,12,14,15],
  [2,3,5,6,8,9,12,13,14,15],[2,3,5,6,9,10,11,12,13,14],
  [2,3,5,6,9,10,11,12,14,15],[2,3,5,6,9,10,12,13,14,15],
  [2,3,5,6,10,11,12,13,14,15],
  [2,3,6,7,8,9,10,11,12,13],[2,3,6,7,8,9,10,11,13,14],
  [2,3,6,7,8,9,10,11,14,15],[2,3,6,7,8,9,11,12,13,14],
  [2,3,6,7,8,9,11,12,14,15],[2,3,6,7,8,9,12,13,14,15],
  [2,3,6,7,9,10,11,12,13,14],[2,3,6,7,9,10,11,12,14,15],
  [2,3,6,7,9,10,12,13,14,15],
  [2,3,6,7,10,11,12,13,14,15],
  [2,3,7,8,9,10,11,12,13,14],[2,3,7,8,9,10,11,12,14,15],
  [2,3,7,8,9,10,12,13,14,15],
  [2,3,7,8,10,11,12,13,14,15],
  [2,3,8,9,10,11,12,13,14,15],[3,4,5,6,7,8,9,10,11,12],
  [3,4,5,6,7,8,9,10,12,13],[3,4,5,6,7,8,9,10,13,14],
  [3,4,5,6,7,8,9,10,14,15],[3,4,5,6,7,8,10,11,12,13],
  [3,4,5,6,7,8,10,11,13,14],[3,4,5,6,7,8,10,11,14,15],
  [3,4,5,6,7,8,11,12,13,14],[3,4,5,6,7,8,11,12,14,15],
  [3,4,5,6,7,8,12,13,14,15],[3,4,5,6,8,9,10,11,12,13],
  [3,4,5,6,8,9,10,11,13,14],[3,4,5,6,8,9,10,11,14,15],
  [3,4,5,6,8,9,11,12,13,14],[3,4,5,6,8,9,11,12,14,15],
  [3,4,5,6,8,9,12,13,14,15],[3,4,5,6,9,10,11,12,13,14],
  [3,4,5,6,9,10,11,12,14,15],[3,4,5,6,9,10,12,13,14,15],
  [3,4,5,6,10,11,12,13,14,15],
  [3,4,6,7,8,9,10,11,12,13],[3,4,6,7,8,9,10,11,13,14],
  [3,4,6,7,8,9,10,11,14,15],[3,4,6,7,8,9,11,12,13,14],
  [3,4,6,7,8,9,11,12,14,15],[3,4,6,7,8,9,12,13,14,15],
  [3,4,6,7,9,10,11,12,13,14],[3,4,6,7,9,10,11,12,14,15],
  [3,4,6,7,9,10,12,13,14,15],
  [3,4,6,7,10,11,12,13,14,15],
  [3,4,7,8,9,10,11,12,13,14],[3,4,7,8,9,10,11,12,14,15],
  [3,4,7,8,9,10,12,13,14,15],
  [3,4,7,8,10,11,12,13,14,15],
  [3,4,8,9,10,11,12,13,14,15],[4,5,6,7,8,9,10,11,12,13],
  [4,5,6,7,8,9,10,11,13,14],
  [4,5,6,7,8,9,10,11,14,15],[4,5,6,7,8,9,11,12,13,14],
  [4,5,6,7,8,9,11,12,14,15],[4,5,6,7,8,9,12,13,14,15],
  [4,5,6,7,9,10,11,12,13,14],[4,5,6,7,9,10,11,12,14,15],
  [4,5,6,7,9,10,12,13,14,15],
  [4,5,6,7,10,11,12,13,14,15],
  [4,5,7,8,9,10,11,12,13,14],[4,5,7,8,9,10,11,12,14,15],
  [4,5,7,8,9,10,12,13,14,15],
  [4,5,7,8,10,11,12,13,14,15],
  [4,5,8,9,10,11,12,13,14,15],
  [5,6,7,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,14,15],
  [5,6,7,8,9,10,12,13,14,15],
  [5,6,7,8,10,11,12,13,14,15],
  [5,6,8,9,10,11,12,13,14,15],
  [6,7,8,9,10,11,12,13,14,15]]

manifold_9_15_1_1=[[1,2,3,4,5,6,7,8,9,10],
  [1,2,3,4,5,6,7,8,9,15],[1,2,3,4,5,6,7,8,10,11],
  [1,2,3,4,5,6,7,8,11,12],[1,2,3,4,5,6,7,8,12,13],
  [1,2,3,4,5,6,7,8,13,14],[1,2,3,4,5,6,7,8,14,15],
  [1,2,3,4,5,6,7,9,10,15],[1,2,3,4,5,6,7,10,11,15],
  [1,2,3,4,5,6,7,11,12,15],[1,2,3,4,5,6,7,12,13,15],
  [1,2,3,4,5,6,7,13,14,15],[1,2,3,4,5,6,8,9,10,14],
  [1,2,3,4,5,6,8,9,14,15],[1,2,3,4,5,6,8,10,11,12],
  [1,2,3,4,5,6,8,10,12,14],[1,2,3,4,5,6,8,12,13,14],
  [1,2,3,4,5,6,9,10,14,15],[1,2,3,4,5,6,10,11,12,14],
  [1,2,3,4,5,6,10,11,14,15],[1,2,3,4,5,6,11,12,14,15],
  [1,2,3,4,5,6,12,13,14,15],[1,2,3,4,5,7,8,9,10,11],
  [1,2,3,4,5,7,8,9,11,12],[1,2,3,4,5,7,8,9,12,13],
  [1,2,3,4,5,7,8,9,13,15],[1,2,3,4,5,7,8,13,14,15],
  [1,2,3,4,5,7,9,10,11,15],[1,2,3,4,5,7,9,11,12,13],
  [1,2,3,4,5,7,9,11,13,15],[1,2,3,4,5,7,11,12,13,15],
  [1,2,3,4,5,8,9,10,11,12],[1,2,3,4,5,8,9,10,12,13],
  [1,2,3,4,5,8,9,10,13,14],[1,2,3,4,5,8,9,13,14,15],
  [1,2,3,4,5,8,10,12,13,14],[1,2,3,4,5,9,10,11,12,13],
  [1,2,3,4,5,9,10,11,13,15],[1,2,3,4,5,9,10,13,14,15],
  [1,2,3,4,5,10,11,12,13,14],[1,2,3,4,5,10,11,13,14,15],
  [1,2,3,4,5,11,12,13,14,15],
  [1,2,3,4,6,7,8,9,10,15],[1,2,3,4,6,7,8,10,11,15],
  [1,2,3,4,6,7,8,11,12,15],[1,2,3,4,6,7,8,12,13,14],
  [1,2,3,4,6,7,8,12,14,15],[1,2,3,4,6,7,12,13,14,15],
  [1,2,3,4,6,8,9,10,14,15],[1,2,3,4,6,8,10,11,12,15],
  [1,2,3,4,6,8,10,12,14,15],[1,2,3,4,6,10,11,12,14,15],
  [1,2,3,4,7,8,9,10,11,15],[1,2,3,4,7,8,9,11,12,15],
  [1,2,3,4,7,8,9,12,13,15],[1,2,3,4,7,8,12,13,14,15],
  [1,2,3,4,7,9,11,12,13,15],[1,2,3,4,8,9,10,11,12,15],
  [1,2,3,4,8,9,10,12,13,14],[1,2,3,4,8,9,10,12,14,15],
  [1,2,3,4,8,9,12,13,14,15],[1,2,3,4,9,10,11,12,13,15],
  [1,2,3,4,9,10,12,13,14,15],
  [1,2,3,4,10,11,12,13,14,15],[1,2,3,5,6,7,8,9,10,12],
  [1,2,3,5,6,7,8,9,12,14],[1,2,3,5,6,7,8,9,14,15],
  [1,2,3,5,6,7,8,10,11,12],[1,2,3,5,6,7,8,12,13,14],
  [1,2,3,5,6,7,9,10,11,12],[1,2,3,5,6,7,9,10,11,13],
  [1,2,3,5,6,7,9,10,13,14],[1,2,3,5,6,7,9,10,14,15],
  [1,2,3,5,6,7,9,11,12,13],[1,2,3,5,6,7,9,12,13,14],
  [1,2,3,5,6,7,10,11,13,14],[1,2,3,5,6,7,10,11,14,15],
  [1,2,3,5,6,7,11,12,13,15],[1,2,3,5,6,7,11,13,14,15],
  [1,2,3,5,6,8,9,10,12,14],[1,2,3,5,6,9,10,11,12,13],
  [1,2,3,5,6,9,10,12,13,14],[1,2,3,5,6,10,11,12,13,14],
  [1,2,3,5,6,11,12,13,14,15],[1,2,3,5,7,8,9,10,11,12],
  [1,2,3,5,7,8,9,12,13,14],[1,2,3,5,7,8,9,13,14,15],
  [1,2,3,5,7,9,10,11,13,14],[1,2,3,5,7,9,10,11,14,15],
  [1,2,3,5,7,9,11,13,14,15],[1,2,3,5,8,9,10,12,13,14],
  [1,2,3,5,9,10,11,13,14,15],[1,2,3,6,7,8,9,10,12,14],
  [1,2,3,6,7,8,9,10,14,15],[1,2,3,6,7,8,10,11,12,14],
  [1,2,3,6,7,8,10,11,14,15],[1,2,3,6,7,8,11,12,14,15],
  [1,2,3,6,7,9,10,11,12,13],[1,2,3,6,7,9,10,12,13,14],
  [1,2,3,6,7,10,11,12,13,14],[1,2,3,6,7,11,12,13,14,15],
  [1,2,3,6,8,10,11,12,14,15],
  [1,2,3,7,8,9,10,11,12,14],[1,2,3,7,8,9,10,11,14,15],
  [1,2,3,7,8,9,11,12,13,14],[1,2,3,7,8,9,11,12,13,15],
  [1,2,3,7,8,9,11,13,14,15],[1,2,3,7,8,11,12,13,14,15],
  [1,2,3,7,9,10,11,12,13,14],[1,2,3,8,9,10,11,12,14,15],
  [1,2,3,8,9,11,12,13,14,15],
  [1,2,3,9,10,11,12,13,14,15],[1,2,4,5,6,7,8,9,10,11],
  [1,2,4,5,6,7,8,9,11,15],[1,2,4,5,6,7,8,11,12,13],
  [1,2,4,5,6,7,8,11,13,15],[1,2,4,5,6,7,8,13,14,15],
  [1,2,4,5,6,7,9,10,11,15],[1,2,4,5,6,7,11,12,13,15],
  [1,2,4,5,6,8,9,10,11,15],[1,2,4,5,6,8,9,10,12,13],
  [1,2,4,5,6,8,9,10,12,15],[1,2,4,5,6,8,9,10,13,14],
  [1,2,4,5,6,8,9,12,13,15],[1,2,4,5,6,8,9,13,14,15],
  [1,2,4,5,6,8,10,11,12,15],[1,2,4,5,6,8,10,12,13,14],
  [1,2,4,5,6,8,11,12,13,15],[1,2,4,5,6,9,10,12,13,15],
  [1,2,4,5,6,9,10,13,14,15],[1,2,4,5,6,10,11,12,14,15],
  [1,2,4,5,6,10,12,13,14,15],[1,2,4,5,7,8,9,11,12,13],
  [1,2,4,5,7,8,9,11,13,15],[1,2,4,5,8,9,10,11,12,15],
  [1,2,4,5,8,9,11,12,13,15],[1,2,4,5,9,10,11,12,13,15],
  [1,2,4,5,10,11,12,13,14,15],[1,2,4,6,7,8,9,10,11,15],
  [1,2,4,6,7,8,11,12,13,15],[1,2,4,6,7,8,12,13,14,15],
  [1,2,4,6,8,9,10,12,13,15],[1,2,4,6,8,9,10,13,14,15],
  [1,2,4,6,8,10,12,13,14,15],[1,2,4,7,8,9,11,12,13,15],
  [1,2,4,8,9,10,12,13,14,15],[1,2,5,6,7,8,9,10,11,12],
  [1,2,5,6,7,8,9,11,12,13],[1,2,5,6,7,8,9,11,13,15],
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  [1,2,5,6,8,9,10,12,13,14],[1,2,5,6,8,9,11,12,13,15],
  [1,2,5,6,9,10,11,12,13,15],
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  [1,3,4,5,9,11,12,13,14,15],
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  [1,3,4,7,8,9,10,11,14,15],[1,3,4,7,8,10,11,12,14,15],
  [1,3,4,8,9,10,11,12,14,15],
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  [1,3,5,6,7,9,10,12,13,14],[1,3,5,6,7,10,11,12,13,14],
  [1,3,5,6,7,10,11,12,14,15],[1,3,5,6,7,11,12,13,14,15],
  [1,3,5,7,8,9,10,11,12,14],
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  [1,3,5,7,9,10,11,12,13,14],[1,3,5,7,9,11,12,13,14,15],
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  [1,4,5,7,8,10,11,12,14,15],[1,4,5,8,9,10,11,12,14,15],
  [1,4,5,9,10,11,12,13,14,15],
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  [1,5,6,7,9,11,12,13,14,15],
  [1,5,6,9,10,11,12,13,14,15],
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  [1,6,7,8,9,10,12,13,14,15],
  [1,6,7,9,10,11,12,13,14,15],
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  [2,3,4,5,6,7,11,12,13,15],[2,3,4,5,6,8,9,10,11,12],
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  [2,3,4,5,6,8,10,12,13,14],[2,3,4,5,6,9,10,11,12,13],
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  [2,3,4,6,7,10,11,12,13,14],[2,3,4,6,7,10,11,13,14,15],
  [2,3,4,6,7,11,12,13,14,15],
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  [2,3,4,6,8,10,11,12,14,15],[2,3,4,6,9,10,11,13,14,15],
  [2,3,4,7,8,9,10,11,13,15],
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  [2,3,4,7,8,10,11,13,14,15],[2,3,4,7,8,11,12,13,14,15],
  [2,3,4,8,9,10,11,12,13,15],
  [2,3,4,8,9,10,12,13,14,15],
  [2,3,4,8,10,11,12,13,14,15],[2,3,5,6,7,8,9,10,11,12],
  [2,3,5,6,7,8,9,12,13,14],[2,3,5,6,7,9,10,11,13,14],
  [2,3,5,6,7,9,10,11,14,15],[2,3,5,6,7,9,11,13,14,15],
  [2,3,5,6,8,9,10,12,13,14],[2,3,6,7,8,9,10,11,12,13],
  [2,3,6,7,8,9,10,12,13,14],[2,3,6,7,8,9,10,13,14,15],
  [2,3,6,7,9,10,11,13,14,15],[2,3,7,8,9,10,11,12,13,14],
  [2,3,7,8,9,10,11,13,14,15],
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  [2,4,5,6,7,8,9,11,13,15],[2,4,5,6,7,8,9,13,14,15],
  [2,4,5,6,8,9,10,11,12,15],[2,4,5,6,8,9,11,12,13,15],
  [2,4,5,6,9,10,11,12,13,15],[2,4,5,6,9,10,11,13,14,15],
  [2,4,5,6,10,11,12,13,14,15],
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  [2,4,6,7,8,10,11,13,14,15],[2,4,6,7,8,11,12,13,14,15],
  [2,4,6,8,9,10,11,12,13,15],
  [2,4,6,8,10,11,12,13,14,15],
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  [3,4,5,6,7,9,10,11,14,15],[3,4,5,6,7,9,11,13,14,15],
  [3,4,5,6,7,10,11,12,13,14],[3,4,5,6,7,10,11,12,14,15],
  [3,4,5,6,7,11,12,13,14,15],
  [3,4,5,7,8,9,10,11,12,14],[3,4,5,7,8,9,10,12,13,14],
  [3,4,5,7,8,9,11,12,13,14],[3,4,5,7,8,9,11,12,13,15],
  [3,4,5,7,8,9,11,13,14,15],[3,4,5,7,8,11,12,13,14,15],
  [3,4,5,7,9,10,11,12,13,14],[3,4,5,8,9,11,12,13,14,15],
  [3,4,6,7,8,9,10,11,12,13],
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  [3,4,6,7,9,10,11,13,14,15],[3,4,7,8,9,10,11,12,13,14],
  [3,4,7,8,9,10,11,13,14,15],
  [3,4,8,9,10,11,12,13,14,15],[3,5,6,7,8,9,10,12,13,14],
  [3,5,7,8,9,11,12,13,14,15],
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  [4,5,6,7,8,9,10,11,14,15],[4,5,6,7,8,9,11,13,14,15],
  [4,5,6,7,8,10,11,12,13,14],[4,5,6,7,8,10,11,12,14,15],
  [4,5,6,7,8,11,12,13,14,15],
  [4,5,6,8,9,10,11,12,13,15],[4,5,6,8,9,10,11,13,14,15],
  [4,5,6,8,9,10,12,13,14,15],
  [4,5,6,8,10,11,12,13,14,15],
  [4,5,7,8,9,10,11,12,13,14],
  [4,5,8,9,10,11,12,13,14,15],
  [4,6,7,8,9,10,11,13,14,15],[5,6,7,8,9,10,11,12,13,14],
  [5,6,7,8,9,10,11,12,14,15],
  [5,6,7,8,9,11,12,13,14,15],
  [5,6,8,9,10,11,12,13,14,15],
  [6,7,8,9,10,11,12,13,14,15]]