manifold_7_9_34_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,9], [1,2,3,4,5,6,8,9],[1,2,3,4,5,7,8,9], [1,2,3,4,6,7,8,9],[1,2,3,5,6,7,8,9], [1,2,4,5,6,7,8,9],[1,3,4,5,6,7,8,9], [2,3,4,5,6,7,8,9]] manifold_7_10_43_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,10], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,7,8,10],[1,2,3,4,5,8,9,10], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,10], [1,2,3,4,7,8,9,10],[1,2,3,5,6,7,8,10], [1,2,3,5,6,8,9,10],[1,2,3,6,7,8,9,10], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,7,8,9,10],[1,2,5,6,7,8,9,10], [1,3,4,5,6,7,8,10],[1,3,4,5,6,8,9,10], [1,3,4,6,7,8,9,10],[1,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,7,8,9,10],[2,3,5,6,7,8,9,10], [3,4,5,6,7,8,9,10]] manifold_7_11_2_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,11], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,7,8,11], [1,2,3,4,5,8,9,11],[1,2,3,4,5,9,10,11], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,10], [1,2,3,4,6,7,10,11],[1,2,3,4,7,8,9,10], [1,2,3,4,7,8,10,11],[1,2,3,4,8,9,10,11], [1,2,3,5,6,7,8,11],[1,2,3,5,6,8,9,11], [1,2,3,5,6,9,10,11],[1,2,3,6,7,8,9,11], [1,2,3,6,7,9,10,11],[1,2,3,7,8,9,10,11], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,11],[1,2,4,5,7,8,9,10], [1,2,4,5,7,8,10,11],[1,2,4,5,8,9,10,11], [1,2,5,6,7,8,9,10],[1,2,5,6,7,8,10,11], [1,2,5,6,8,9,10,11],[1,2,6,7,8,9,10,11], [1,3,4,5,6,7,8,11],[1,3,4,5,6,8,9,11], [1,3,4,5,6,9,10,11],[1,3,4,6,7,8,9,11], [1,3,4,6,7,9,10,11],[1,3,4,7,8,9,10,11], [1,4,5,6,7,8,9,11],[1,4,5,6,7,9,10,11], [1,4,5,7,8,9,10,11],[1,5,6,7,8,9,10,11], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,7,8,9,10], [2,3,4,5,7,8,10,11],[2,3,4,5,8,9,10,11], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,11], [2,3,5,6,8,9,10,11],[2,3,6,7,8,9,10,11], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,8,9,10,11],[3,4,6,7,8,9,10,11], [4,5,6,7,8,9,10,11]] manifold_7_12_289_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,12], [1,2,3,4,5,6,8,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,7,8,10],[1,2,3,4,5,7,10,12], [1,2,3,4,5,8,10,11],[1,2,3,4,5,10,11,12], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,12], [1,2,3,4,6,8,9,11],[1,2,3,4,6,9,11,12], [1,2,3,4,7,8,9,10],[1,2,3,4,7,9,10,12], [1,2,3,4,8,9,10,11],[1,2,3,4,9,10,11,12], [1,2,3,5,6,7,8,12],[1,2,3,5,6,8,11,12], [1,2,3,5,7,8,10,12],[1,2,3,5,8,10,11,12], [1,2,3,6,7,8,9,12],[1,2,3,6,8,9,11,12], [1,2,3,7,8,9,10,12],[1,2,3,8,9,10,11,12], [1,2,4,5,6,7,8,11],[1,2,4,5,6,7,11,12], [1,2,4,5,7,8,10,11],[1,2,4,5,7,10,11,12], [1,2,4,6,7,8,9,11],[1,2,4,6,7,9,11,12], [1,2,4,7,8,9,10,11],[1,2,4,7,9,10,11,12], [1,2,5,6,7,8,11,12],[1,2,5,7,8,10,11,12], [1,2,6,7,8,9,11,12],[1,2,7,8,9,10,11,12], [1,3,4,5,6,7,8,10],[1,3,4,5,6,7,10,12], [1,3,4,5,6,8,10,11],[1,3,4,5,6,10,11,12], [1,3,4,6,7,8,9,10],[1,3,4,6,7,9,10,12], [1,3,4,6,8,9,10,11],[1,3,4,6,9,10,11,12], [1,3,5,6,7,8,10,12],[1,3,5,6,8,10,11,12], [1,3,6,7,8,9,10,12],[1,3,6,8,9,10,11,12], [1,4,5,6,7,8,10,11],[1,4,5,6,7,10,11,12], [1,4,6,7,8,9,10,11],[1,4,6,7,9,10,11,12], [1,5,6,7,8,10,11,12],[1,6,7,8,9,10,11,12], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,12], [2,3,4,5,6,8,9,11],[2,3,4,5,6,9,11,12], [2,3,4,5,7,8,9,10],[2,3,4,5,7,9,10,12], [2,3,4,5,8,9,10,11],[2,3,4,5,9,10,11,12], [2,3,5,6,7,8,9,12],[2,3,5,6,8,9,11,12], [2,3,5,7,8,9,10,12],[2,3,5,8,9,10,11,12], [2,4,5,6,7,8,9,11],[2,4,5,6,7,9,11,12], [2,4,5,7,8,9,10,11],[2,4,5,7,9,10,11,12], [2,5,6,7,8,9,11,12],[2,5,7,8,9,10,11,12], [3,4,5,6,7,8,9,10],[3,4,5,6,7,9,10,12], [3,4,5,6,8,9,10,11],[3,4,5,6,9,10,11,12], [3,5,6,7,8,9,10,12],[3,5,6,8,9,10,11,12], [4,5,6,7,8,9,10,11],[4,5,6,7,9,10,11,12], [5,6,7,8,9,10,11,12]] manifold_7_12_193_1=[[1,2,3,4,5,6,8,10],[1,2,3,4,5,6,8,11], [1,2,3,4,5,6,9,10],[1,2,3,4,5,6,9,11], [1,2,3,4,5,7,8,10],[1,2,3,4,5,7,8,11], [1,2,3,4,5,7,9,10],[1,2,3,4,5,7,9,11], [1,2,3,4,6,8,10,12],[1,2,3,4,6,8,11,12], [1,2,3,4,6,9,10,12],[1,2,3,4,6,9,11,12], [1,2,3,4,7,8,10,12],[1,2,3,4,7,8,11,12], [1,2,3,4,7,9,10,12],[1,2,3,4,7,9,11,12], [1,2,3,5,6,8,10,12],[1,2,3,5,6,8,11,12], [1,2,3,5,6,9,10,12],[1,2,3,5,6,9,11,12], [1,2,3,5,7,8,10,12],[1,2,3,5,7,8,11,12], [1,2,3,5,7,9,10,12],[1,2,3,5,7,9,11,12], [1,2,4,5,6,7,8,10],[1,2,4,5,6,7,8,11], [1,2,4,5,6,7,9,10],[1,2,4,5,6,7,9,11], [1,2,4,6,7,8,9,10],[1,2,4,6,7,8,9,11], [1,2,4,6,8,9,10,11],[1,2,4,6,8,10,11,12], [1,2,4,6,9,10,11,12],[1,2,4,7,8,9,10,11], [1,2,4,7,8,10,11,12],[1,2,4,7,9,10,11,12], [1,2,5,6,7,8,9,10],[1,2,5,6,7,8,9,11], [1,2,5,6,8,9,10,11],[1,2,5,6,8,10,11,12], [1,2,5,6,9,10,11,12],[1,2,5,7,8,9,10,11], [1,2,5,7,8,10,11,12],[1,2,5,7,9,10,11,12], [1,3,4,5,6,7,8,10],[1,3,4,5,6,7,8,11], [1,3,4,5,6,7,9,10],[1,3,4,5,6,7,9,11], [1,3,4,6,7,8,9,10],[1,3,4,6,7,8,9,11], [1,3,4,6,8,9,10,11],[1,3,4,6,8,10,11,12], [1,3,4,6,9,10,11,12],[1,3,4,7,8,9,10,11], [1,3,4,7,8,10,11,12],[1,3,4,7,9,10,11,12], [1,3,5,6,7,8,9,10],[1,3,5,6,7,8,9,11], [1,3,5,6,8,9,10,11],[1,3,5,6,8,10,11,12], [1,3,5,6,9,10,11,12],[1,3,5,7,8,9,10,11], [1,3,5,7,8,10,11,12],[1,3,5,7,9,10,11,12], [2,3,4,5,6,8,10,12],[2,3,4,5,6,8,11,12], [2,3,4,5,6,9,10,12],[2,3,4,5,6,9,11,12], [2,3,4,5,7,8,10,12],[2,3,4,5,7,8,11,12], [2,3,4,5,7,9,10,12],[2,3,4,5,7,9,11,12], [2,4,5,6,7,8,10,12],[2,4,5,6,7,8,11,12], [2,4,5,6,7,9,10,12],[2,4,5,6,7,9,11,12], [2,4,6,7,8,9,10,12],[2,4,6,7,8,9,11,12], [2,4,6,8,9,10,11,12],[2,4,7,8,9,10,11,12], [2,5,6,7,8,9,10,12],[2,5,6,7,8,9,11,12], [2,5,6,8,9,10,11,12],[2,5,7,8,9,10,11,12], [3,4,5,6,7,8,10,12],[3,4,5,6,7,8,11,12], [3,4,5,6,7,9,10,12],[3,4,5,6,7,9,11,12], [3,4,6,7,8,9,10,12],[3,4,6,7,8,9,11,12], [3,4,6,8,9,10,11,12],[3,4,7,8,9,10,11,12], [3,5,6,7,8,9,10,12],[3,5,6,7,8,9,11,12], [3,5,6,8,9,10,11,12],[3,5,7,8,9,10,11,12]] manifold_7_12_12_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,12], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,7,8,12],[1,2,3,4,5,8,9,12], [1,2,3,4,5,9,10,12],[1,2,3,4,5,10,11,12], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,10], [1,2,3,4,6,7,10,11],[1,2,3,4,6,7,11,12], [1,2,3,4,7,8,9,10],[1,2,3,4,7,8,10,11], [1,2,3,4,7,8,11,12],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,12],[1,2,3,4,9,10,11,12], [1,2,3,5,6,7,8,12],[1,2,3,5,6,8,9,12], [1,2,3,5,6,9,10,12],[1,2,3,5,6,10,11,12], [1,2,3,6,7,8,9,12],[1,2,3,6,7,9,10,12], [1,2,3,6,7,10,11,12],[1,2,3,7,8,9,10,12], [1,2,3,7,8,10,11,12],[1,2,3,8,9,10,11,12], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,11],[1,2,4,5,6,7,11,12], [1,2,4,5,7,8,9,10],[1,2,4,5,7,8,10,11], [1,2,4,5,7,8,11,12],[1,2,4,5,8,9,10,11], [1,2,4,5,8,9,11,12],[1,2,4,5,9,10,11,12], [1,2,5,6,7,8,9,10],[1,2,5,6,7,8,10,11], [1,2,5,6,7,8,11,12],[1,2,5,6,8,9,10,11], [1,2,5,6,8,9,11,12],[1,2,5,6,9,10,11,12], [1,2,6,7,8,9,10,11],[1,2,6,7,8,9,11,12], [1,2,6,7,9,10,11,12],[1,2,7,8,9,10,11,12], [1,3,4,5,6,7,8,12],[1,3,4,5,6,8,9,12], [1,3,4,5,6,9,10,12],[1,3,4,5,6,10,11,12], [1,3,4,6,7,8,9,12],[1,3,4,6,7,9,10,12], [1,3,4,6,7,10,11,12],[1,3,4,7,8,9,10,12], [1,3,4,7,8,10,11,12],[1,3,4,8,9,10,11,12], [1,4,5,6,7,8,9,12],[1,4,5,6,7,9,10,12], [1,4,5,6,7,10,11,12],[1,4,5,7,8,9,10,12], [1,4,5,7,8,10,11,12],[1,4,5,8,9,10,11,12], [1,5,6,7,8,9,10,12],[1,5,6,7,8,10,11,12], [1,5,6,8,9,10,11,12],[1,6,7,8,9,10,11,12], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,7,8,9,10],[2,3,4,5,7,8,10,11], [2,3,4,5,7,8,11,12],[2,3,4,5,8,9,10,11], [2,3,4,5,8,9,11,12],[2,3,4,5,9,10,11,12], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,11], [2,3,5,6,7,8,11,12],[2,3,5,6,8,9,10,11], [2,3,5,6,8,9,11,12],[2,3,5,6,9,10,11,12], [2,3,6,7,8,9,10,11],[2,3,6,7,8,9,11,12], [2,3,6,7,9,10,11,12],[2,3,7,8,9,10,11,12], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,8,9,10,11], [3,4,5,6,8,9,11,12],[3,4,5,6,9,10,11,12], [3,4,6,7,8,9,10,11],[3,4,6,7,8,9,11,12], [3,4,6,7,9,10,11,12],[3,4,7,8,9,10,11,12], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,9,10,11,12],[4,5,7,8,9,10,11,12], [5,6,7,8,9,10,11,12]] manifold_7_12_8_1=[[1,2,3,4,5,6,7,11],[1,2,3,4,5,6,7,12], [1,2,3,4,5,6,9,11],[1,2,3,4,5,6,9,12], [1,2,3,4,5,7,11,12],[1,2,3,4,5,9,11,12], [1,2,3,4,6,7,9,10],[1,2,3,4,6,7,9,11], [1,2,3,4,6,7,10,12],[1,2,3,4,6,9,10,12], [1,2,3,4,7,9,10,11],[1,2,3,4,7,10,11,12], [1,2,3,4,8,9,10,11],[1,2,3,4,8,9,10,12], [1,2,3,4,8,9,11,12],[1,2,3,4,8,10,11,12], [1,2,3,5,6,7,11,12],[1,2,3,5,6,9,11,12], [1,2,3,6,7,9,10,11],[1,2,3,6,7,10,11,12], [1,2,3,6,9,10,11,12],[1,2,3,8,9,10,11,12], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,8,12], [1,2,4,5,6,7,9,11],[1,2,4,5,6,8,9,12], [1,2,4,5,7,8,9,11],[1,2,4,5,7,8,11,12], [1,2,4,5,8,9,11,12],[1,2,4,6,7,8,9,10], [1,2,4,6,7,8,10,12],[1,2,4,6,8,9,10,12], [1,2,4,7,8,9,10,11],[1,2,4,7,8,10,11,12], [1,2,5,6,7,8,9,11],[1,2,5,6,7,8,10,11], [1,2,5,6,7,8,10,12],[1,2,5,6,7,10,11,12], [1,2,5,6,8,9,11,12],[1,2,5,6,8,10,11,12], [1,2,5,7,8,10,11,12],[1,2,6,7,8,9,10,11], [1,2,6,8,9,10,11,12],[1,3,4,5,6,7,8,9], [1,3,4,5,6,7,8,12],[1,3,4,5,6,7,9,11], [1,3,4,5,6,8,9,12],[1,3,4,5,7,8,9,11], [1,3,4,5,7,8,11,12],[1,3,4,5,8,9,11,12], [1,3,4,6,7,8,9,10],[1,3,4,6,7,8,10,12], [1,3,4,6,8,9,10,12],[1,3,4,7,8,9,10,11], [1,3,4,7,8,10,11,12],[1,3,5,6,7,8,9,11], [1,3,5,6,7,8,11,12],[1,3,5,6,8,9,11,12], [1,3,6,7,8,9,10,11],[1,3,6,7,8,10,11,12], [1,3,6,8,9,10,11,12],[1,5,6,7,8,10,11,12], [2,3,4,5,6,7,9,10],[2,3,4,5,6,7,9,11], [2,3,4,5,6,7,10,12],[2,3,4,5,6,9,10,12], [2,3,4,5,7,9,10,11],[2,3,4,5,7,10,11,12], [2,3,4,5,9,10,11,12],[2,3,4,8,9,10,11,12], [2,3,5,6,7,9,10,11],[2,3,5,6,7,10,11,12], [2,3,5,6,9,10,11,12],[2,4,5,6,7,8,9,10], [2,4,5,6,7,8,10,12],[2,4,5,6,8,9,10,12], [2,4,5,7,8,9,10,11],[2,4,5,7,8,10,11,12], [2,4,5,8,9,10,11,12],[2,5,6,7,8,9,10,11], [2,5,6,8,9,10,11,12],[3,4,5,6,7,8,9,12], [3,4,5,6,7,9,10,12],[3,4,5,7,8,9,10,11], [3,4,5,7,8,9,10,12],[3,4,5,7,8,10,11,12], [3,4,5,8,9,10,11,12],[3,4,6,7,8,9,10,12], [3,5,6,7,8,9,10,11],[3,5,6,7,8,9,10,12], [3,5,6,7,8,10,11,12],[3,5,6,8,9,10,11,12], [4,5,6,7,8,9,10,12]] manifold_7_13_4_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,13], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,7,8,13], [1,2,3,4,5,8,9,13],[1,2,3,4,5,9,10,13], [1,2,3,4,5,10,11,13],[1,2,3,4,5,11,12,13], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,11], [1,2,3,4,6,7,11,12],[1,2,3,4,6,7,12,13], [1,2,3,4,6,9,10,11],[1,2,3,4,7,8,9,12], [1,2,3,4,7,8,12,13],[1,2,3,4,7,9,11,12], [1,2,3,4,8,9,12,13],[1,2,3,4,9,10,11,12], [1,2,3,4,9,10,12,13],[1,2,3,4,10,11,12,13], [1,2,3,5,6,7,8,13],[1,2,3,5,6,8,9,10], [1,2,3,5,6,8,10,13],[1,2,3,5,6,10,11,13], [1,2,3,5,6,11,12,13],[1,2,3,5,8,9,10,13], [1,2,3,6,7,8,9,11],[1,2,3,6,7,8,11,13], [1,2,3,6,7,11,12,13],[1,2,3,6,8,9,10,11], [1,2,3,6,8,10,11,13],[1,2,3,7,8,9,11,12], [1,2,3,7,8,11,12,13],[1,2,3,8,9,10,11,13], [1,2,3,8,9,11,12,13],[1,2,3,9,10,11,12,13], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,12],[1,2,4,5,6,7,12,13], [1,2,4,5,6,10,11,12],[1,2,4,5,7,8,9,13], [1,2,4,5,7,9,10,12],[1,2,4,5,7,9,12,13], [1,2,4,5,9,10,12,13],[1,2,4,5,10,11,12,13], [1,2,4,6,7,9,10,12],[1,2,4,6,7,9,11,12], [1,2,4,6,9,10,11,12],[1,2,4,7,8,9,12,13], [1,2,5,6,7,8,9,10],[1,2,5,6,7,8,10,13], [1,2,5,6,7,10,12,13],[1,2,5,6,10,11,12,13], [1,2,5,7,8,9,10,13],[1,2,5,7,9,10,12,13], [1,2,6,7,8,9,10,11],[1,2,6,7,8,10,11,13], [1,2,6,7,9,10,11,12],[1,2,6,7,10,11,12,13], [1,2,7,8,9,10,11,12],[1,2,7,8,9,10,12,13], [1,2,7,8,10,11,12,13],[1,2,8,9,10,11,12,13], [1,3,4,5,6,7,8,13],[1,3,4,5,6,8,9,13], [1,3,4,5,6,9,10,11],[1,3,4,5,6,9,11,13], [1,3,4,5,6,11,12,13],[1,3,4,5,9,10,11,13], [1,3,4,6,7,8,9,12],[1,3,4,6,7,8,12,13], [1,3,4,6,7,9,11,12],[1,3,4,6,8,9,11,12], [1,3,4,6,8,9,11,13],[1,3,4,6,8,11,12,13], [1,3,4,8,9,11,12,13],[1,3,4,9,10,11,12,13], [1,3,5,6,8,9,10,11],[1,3,5,6,8,9,11,13], [1,3,5,6,8,10,11,13],[1,3,5,8,9,10,11,13], [1,3,6,7,8,9,11,12],[1,3,6,7,8,11,12,13], [1,4,5,6,7,8,9,13],[1,4,5,6,7,9,10,12], [1,4,5,6,7,9,12,13],[1,4,5,6,9,10,11,12], [1,4,5,6,9,11,12,13],[1,4,5,9,10,11,12,13], [1,4,6,7,8,9,12,13],[1,4,6,8,9,11,12,13], [1,5,6,7,8,9,10,13],[1,5,6,7,9,10,12,13], [1,5,6,8,9,10,11,13],[1,5,6,9,10,11,12,13], [1,6,7,8,9,10,11,13],[1,6,7,8,9,11,12,13], [1,6,7,9,10,11,12,13],[1,7,8,9,10,11,12,13], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,7,8,9,10], [2,3,4,5,7,8,10,12],[2,3,4,5,7,8,12,13], [2,3,4,5,7,10,11,12],[2,3,4,5,8,9,10,13], [2,3,4,5,8,10,12,13],[2,3,4,5,10,11,12,13], [2,3,4,6,7,9,10,11],[2,3,4,7,8,9,10,12], [2,3,4,7,9,10,11,12],[2,3,4,8,9,10,12,13], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,11], [2,3,5,6,7,8,11,13],[2,3,5,6,7,11,12,13], [2,3,5,6,8,10,11,13],[2,3,5,7,8,10,11,13], [2,3,5,7,8,10,12,13],[2,3,5,7,10,11,12,13], [2,3,6,7,8,9,10,11],[2,3,7,8,9,10,11,12], [2,3,7,8,10,11,12,13],[2,3,8,9,10,11,12,13], [2,4,5,6,7,10,11,12],[2,4,5,7,8,9,10,13], [2,4,5,7,8,10,12,13],[2,4,5,7,9,10,12,13], [2,4,6,7,9,10,11,12],[2,4,7,8,9,10,12,13], [2,5,6,7,8,10,11,13],[2,5,6,7,10,11,12,13], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,13], [3,4,5,6,8,9,10,11],[3,4,5,6,8,9,11,13], [3,4,5,6,8,11,12,13],[3,4,5,7,8,10,11,12], [3,4,5,8,9,10,11,13],[3,4,5,8,10,11,12,13], [3,4,6,7,8,9,10,11],[3,4,6,7,8,9,11,12], [3,4,7,8,9,10,11,12],[3,4,8,9,10,11,12,13], [3,5,6,7,8,11,12,13],[3,5,7,8,10,11,12,13], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,8,9,12,13],[4,5,6,7,9,10,11,12], [4,5,6,8,9,11,12,13],[4,5,7,8,9,10,11,12], [4,5,7,8,9,10,12,13],[4,5,8,9,10,11,12,13], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,10,11,12,13],[5,6,8,9,10,11,12,13], [6,7,8,9,10,11,12,13]] manifold_7_13_4_2=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,13], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,11], [1,2,3,4,5,6,11,12],[1,2,3,4,5,6,12,13], [1,2,3,4,5,7,8,13],[1,2,3,4,5,8,9,10], [1,2,3,4,5,8,10,13],[1,2,3,4,5,9,10,11], [1,2,3,4,5,10,11,13],[1,2,3,4,5,11,12,13], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,11], [1,2,3,4,6,7,11,12],[1,2,3,4,6,7,12,13], [1,2,3,4,7,8,9,13],[1,2,3,4,7,9,11,12], [1,2,3,4,7,9,12,13],[1,2,3,4,8,9,10,13], [1,2,3,4,9,10,11,12],[1,2,3,4,9,10,12,13], [1,2,3,4,10,11,12,13],[1,2,3,5,6,7,8,13], [1,2,3,5,6,8,9,10],[1,2,3,5,6,8,10,13], [1,2,3,5,6,9,10,11],[1,2,3,5,6,10,11,13], [1,2,3,5,6,11,12,13],[1,2,3,6,7,8,9,10], [1,2,3,6,7,8,10,11],[1,2,3,6,7,8,11,12], [1,2,3,6,7,8,12,13],[1,2,3,6,7,9,10,11], [1,2,3,6,8,10,11,13],[1,2,3,6,8,11,12,13], [1,2,3,7,8,9,10,11],[1,2,3,7,8,9,11,12], [1,2,3,7,8,9,12,13],[1,2,3,8,9,10,11,13], [1,2,3,8,9,11,12,13],[1,2,3,9,10,11,12,13], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,12],[1,2,4,5,6,7,12,13], [1,2,4,5,6,9,10,11],[1,2,4,5,6,10,11,12], [1,2,4,5,7,8,9,13],[1,2,4,5,7,9,10,12], [1,2,4,5,7,9,12,13],[1,2,4,5,8,9,10,13], [1,2,4,5,9,10,12,13],[1,2,4,5,10,11,12,13], [1,2,4,6,7,9,10,12],[1,2,4,6,7,9,11,12], [1,2,4,6,9,10,11,12],[1,2,5,6,7,8,9,13], [1,2,5,6,7,9,10,13],[1,2,5,6,7,10,11,12], [1,2,5,6,7,10,11,13],[1,2,5,6,7,11,12,13], [1,2,5,6,8,9,10,13],[1,2,5,7,9,10,12,13], [1,2,5,7,10,11,12,13],[1,2,6,7,8,9,10,13], [1,2,6,7,8,10,11,13],[1,2,6,7,8,11,12,13], [1,2,6,7,9,10,11,12],[1,2,7,8,9,10,11,12], [1,2,7,8,9,10,12,13],[1,2,7,8,10,11,12,13], [1,2,8,9,10,11,12,13],[1,3,4,5,6,7,8,13], [1,3,4,5,6,8,9,13],[1,3,4,5,6,9,11,13], [1,3,4,5,6,11,12,13],[1,3,4,5,8,9,10,13], [1,3,4,5,9,10,11,13],[1,3,4,6,7,8,9,12], [1,3,4,6,7,8,12,13],[1,3,4,6,7,9,11,12], [1,3,4,6,8,9,11,12],[1,3,4,6,8,9,11,13], [1,3,4,6,8,11,12,13],[1,3,4,7,8,9,12,13], [1,3,4,8,9,11,12,13],[1,3,4,9,10,11,12,13], [1,3,5,6,8,9,10,11],[1,3,5,6,8,9,11,13], [1,3,5,6,8,10,11,13],[1,3,5,8,9,10,11,13], [1,3,6,7,8,9,10,11],[1,3,6,7,8,9,11,12], [1,4,5,6,7,8,9,12],[1,4,5,6,7,8,12,13], [1,4,5,6,7,9,10,12],[1,4,5,6,8,9,12,13], [1,4,5,6,9,10,11,13],[1,4,5,6,9,10,12,13], [1,4,5,6,10,11,12,13],[1,4,5,7,8,9,12,13], [1,4,6,8,9,11,12,13],[1,4,6,9,10,11,12,13], [1,5,6,7,8,9,12,13],[1,5,6,7,9,10,12,13], [1,5,6,7,10,11,12,13],[1,5,6,8,9,10,11,13], [1,6,7,8,9,10,11,13],[1,6,7,8,9,11,12,13], [1,6,7,9,10,11,12,13],[1,7,8,9,10,11,12,13], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,12],[2,3,4,5,6,7,12,13], [2,3,4,5,6,9,10,11],[2,3,4,5,6,10,11,12], [2,3,4,5,7,8,9,10],[2,3,4,5,7,8,10,12], [2,3,4,5,7,8,12,13],[2,3,4,5,8,10,12,13], [2,3,4,5,10,11,12,13],[2,3,4,6,7,9,10,11], [2,3,4,6,7,10,11,12],[2,3,4,7,8,9,10,11], [2,3,4,7,8,9,11,12],[2,3,4,7,8,9,12,13], [2,3,4,7,8,10,11,12],[2,3,4,8,9,10,11,12], [2,3,4,8,9,10,12,13],[2,3,5,6,7,8,9,10], [2,3,5,6,7,8,10,11],[2,3,5,6,7,8,11,13], [2,3,5,6,7,10,11,12],[2,3,5,6,7,11,12,13], [2,3,5,6,8,10,11,13],[2,3,5,7,8,10,11,13], [2,3,5,7,8,10,12,13],[2,3,5,7,10,11,12,13], [2,3,6,7,8,11,12,13],[2,3,7,8,10,11,12,13], [2,3,8,9,10,11,12,13],[2,4,5,7,8,9,10,13], [2,4,5,7,8,10,12,13],[2,4,5,7,9,10,12,13], [2,4,6,7,9,10,11,12],[2,4,7,8,9,10,11,12], [2,4,7,8,9,10,12,13],[2,5,6,7,8,9,10,13], [2,5,6,7,8,10,11,13],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,13], [3,4,5,6,7,10,11,12],[3,4,5,6,7,11,12,13], [3,4,5,6,8,9,10,11],[3,4,5,6,8,9,11,13], [3,4,5,7,8,10,11,12],[3,4,5,7,8,11,12,13], [3,4,5,8,9,10,11,12],[3,4,5,8,9,10,12,13], [3,4,5,8,9,11,12,13],[3,4,5,9,10,11,12,13], [3,4,6,7,8,9,10,11],[3,4,6,7,8,9,11,12], [3,4,6,7,8,11,12,13],[3,5,7,8,10,11,12,13], [3,5,8,9,10,11,12,13],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,11,12,13], [4,5,6,7,9,10,11,12],[4,5,6,8,9,11,12,13], [4,5,6,9,10,11,12,13],[4,5,7,8,9,10,11,12], [4,5,7,8,9,10,12,13],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,10,11,12,13], [5,6,8,9,10,11,12,13],[6,7,8,9,10,11,12,13]] manifold_7_13_2_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,13], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,7,8,13], [1,2,3,4,5,8,9,13],[1,2,3,4,5,9,10,13], [1,2,3,4,5,10,11,13],[1,2,3,4,5,11,12,13], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,10], [1,2,3,4,6,7,10,11],[1,2,3,4,6,7,11,12], [1,2,3,4,6,7,12,13],[1,2,3,4,7,8,9,10], [1,2,3,4,7,8,10,11],[1,2,3,4,7,8,11,12], [1,2,3,4,7,8,12,13],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,12],[1,2,3,4,8,9,12,13], [1,2,3,4,9,10,11,12],[1,2,3,4,9,10,12,13], [1,2,3,4,10,11,12,13],[1,2,3,5,6,7,8,13], [1,2,3,5,6,8,9,13],[1,2,3,5,6,9,10,13], [1,2,3,5,6,10,11,13],[1,2,3,5,6,11,12,13], [1,2,3,6,7,8,9,13],[1,2,3,6,7,9,10,13], [1,2,3,6,7,10,11,13],[1,2,3,6,7,11,12,13], [1,2,3,7,8,9,10,13],[1,2,3,7,8,10,11,13], [1,2,3,7,8,11,12,13],[1,2,3,8,9,10,11,13], [1,2,3,8,9,11,12,13],[1,2,3,9,10,11,12,13], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,11],[1,2,4,5,6,7,11,12], [1,2,4,5,6,7,12,13],[1,2,4,5,7,8,9,10], [1,2,4,5,7,8,10,11],[1,2,4,5,7,8,11,12], [1,2,4,5,7,8,12,13],[1,2,4,5,8,9,10,11], [1,2,4,5,8,9,11,12],[1,2,4,5,8,9,12,13], [1,2,4,5,9,10,11,12],[1,2,4,5,9,10,12,13], [1,2,4,5,10,11,12,13],[1,2,5,6,7,8,9,10], [1,2,5,6,7,8,10,11],[1,2,5,6,7,8,11,12], [1,2,5,6,7,8,12,13],[1,2,5,6,8,9,10,11], [1,2,5,6,8,9,11,12],[1,2,5,6,8,9,12,13], [1,2,5,6,9,10,11,12],[1,2,5,6,9,10,12,13], [1,2,5,6,10,11,12,13],[1,2,6,7,8,9,10,11], [1,2,6,7,8,9,11,12],[1,2,6,7,8,9,12,13], [1,2,6,7,9,10,11,12],[1,2,6,7,9,10,12,13], [1,2,6,7,10,11,12,13],[1,2,7,8,9,10,11,12], [1,2,7,8,9,10,12,13],[1,2,7,8,10,11,12,13], [1,2,8,9,10,11,12,13],[1,3,4,5,6,7,8,13], [1,3,4,5,6,8,9,13],[1,3,4,5,6,9,10,13], [1,3,4,5,6,10,11,13],[1,3,4,5,6,11,12,13], [1,3,4,6,7,8,9,13],[1,3,4,6,7,9,10,13], [1,3,4,6,7,10,11,13],[1,3,4,6,7,11,12,13], [1,3,4,7,8,9,10,13],[1,3,4,7,8,10,11,13], [1,3,4,7,8,11,12,13],[1,3,4,8,9,10,11,13], [1,3,4,8,9,11,12,13],[1,3,4,9,10,11,12,13], [1,4,5,6,7,8,9,13],[1,4,5,6,7,9,10,13], [1,4,5,6,7,10,11,13],[1,4,5,6,7,11,12,13], [1,4,5,7,8,9,10,13],[1,4,5,7,8,10,11,13], [1,4,5,7,8,11,12,13],[1,4,5,8,9,10,11,13], [1,4,5,8,9,11,12,13],[1,4,5,9,10,11,12,13], [1,5,6,7,8,9,10,13],[1,5,6,7,8,10,11,13], [1,5,6,7,8,11,12,13],[1,5,6,8,9,10,11,13], [1,5,6,8,9,11,12,13],[1,5,6,9,10,11,12,13], [1,6,7,8,9,10,11,13],[1,6,7,8,9,11,12,13], [1,6,7,9,10,11,12,13],[1,7,8,9,10,11,12,13], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,7,8,9,10], [2,3,4,5,7,8,10,11],[2,3,4,5,7,8,11,12], [2,3,4,5,7,8,12,13],[2,3,4,5,8,9,10,11], [2,3,4,5,8,9,11,12],[2,3,4,5,8,9,12,13], [2,3,4,5,9,10,11,12],[2,3,4,5,9,10,12,13], [2,3,4,5,10,11,12,13],[2,3,5,6,7,8,9,10], [2,3,5,6,7,8,10,11],[2,3,5,6,7,8,11,12], [2,3,5,6,7,8,12,13],[2,3,5,6,8,9,10,11], [2,3,5,6,8,9,11,12],[2,3,5,6,8,9,12,13], [2,3,5,6,9,10,11,12],[2,3,5,6,9,10,12,13], [2,3,5,6,10,11,12,13],[2,3,6,7,8,9,10,11], [2,3,6,7,8,9,11,12],[2,3,6,7,8,9,12,13], [2,3,6,7,9,10,11,12],[2,3,6,7,9,10,12,13], [2,3,6,7,10,11,12,13],[2,3,7,8,9,10,11,12], [2,3,7,8,9,10,12,13],[2,3,7,8,10,11,12,13], [2,3,8,9,10,11,12,13],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,12], [3,4,5,6,7,8,12,13],[3,4,5,6,8,9,10,11], [3,4,5,6,8,9,11,12],[3,4,5,6,8,9,12,13], [3,4,5,6,9,10,11,12],[3,4,5,6,9,10,12,13], [3,4,5,6,10,11,12,13],[3,4,6,7,8,9,10,11], [3,4,6,7,8,9,11,12],[3,4,6,7,8,9,12,13], [3,4,6,7,9,10,11,12],[3,4,6,7,9,10,12,13], [3,4,6,7,10,11,12,13],[3,4,7,8,9,10,11,12], [3,4,7,8,9,10,12,13],[3,4,7,8,10,11,12,13], [3,4,8,9,10,11,12,13],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,9,10,11,12],[4,5,6,7,9,10,12,13], [4,5,6,7,10,11,12,13],[4,5,7,8,9,10,11,12], [4,5,7,8,9,10,12,13],[4,5,7,8,10,11,12,13], [4,5,8,9,10,11,12,13],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,10,11,12,13], [5,6,8,9,10,11,12,13],[6,7,8,9,10,11,12,13]] manifold_7_13_2_2=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,13], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,7,8,13], [1,2,3,4,5,8,9,13],[1,2,3,4,5,9,10,13], [1,2,3,4,5,10,11,13],[1,2,3,4,5,11,12,13], [1,2,3,4,6,7,8,12],[1,2,3,4,6,7,12,13], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,12], [1,2,3,4,6,10,11,12],[1,2,3,4,7,8,12,13], [1,2,3,4,8,9,10,12],[1,2,3,4,8,9,12,13], [1,2,3,4,9,10,12,13],[1,2,3,4,10,11,12,13], [1,2,3,5,6,7,8,10],[1,2,3,5,6,7,10,11], [1,2,3,5,6,7,11,13],[1,2,3,5,6,8,9,10], [1,2,3,5,6,11,12,13],[1,2,3,5,7,8,9,10], [1,2,3,5,7,8,9,13],[1,2,3,5,7,9,10,11], [1,2,3,5,7,9,11,13],[1,2,3,5,9,10,11,13], [1,2,3,6,7,8,10,12],[1,2,3,6,7,10,11,12], [1,2,3,6,7,11,12,13],[1,2,3,7,8,9,10,12], [1,2,3,7,8,9,11,12],[1,2,3,7,8,9,11,13], [1,2,3,7,8,11,12,13],[1,2,3,7,9,10,11,12], [1,2,3,8,9,11,12,13],[1,2,3,9,10,11,12,13], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,13], [1,2,4,5,6,9,10,13],[1,2,4,5,6,10,11,12], [1,2,4,5,6,10,12,13],[1,2,4,5,7,8,9,13], [1,2,4,5,10,11,12,13],[1,2,4,6,7,8,9,13], [1,2,4,6,7,8,12,13],[1,2,4,6,8,9,10,13], [1,2,4,6,8,10,12,13],[1,2,4,8,9,10,12,13], [1,2,5,6,7,8,9,10],[1,2,5,6,7,9,10,11], [1,2,5,6,7,9,11,13],[1,2,5,6,9,10,11,13], [1,2,5,6,10,11,12,13],[1,2,6,7,8,9,10,11], [1,2,6,7,8,9,11,13],[1,2,6,7,8,10,11,13], [1,2,6,7,8,10,12,13],[1,2,6,7,10,11,12,13], [1,2,6,8,9,10,11,13],[1,2,7,8,9,10,11,12], [1,2,7,8,10,11,12,13],[1,2,8,9,10,11,12,13], [1,3,4,5,6,7,8,13],[1,3,4,5,6,8,9,10], [1,3,4,5,6,8,10,12],[1,3,4,5,6,8,12,13], [1,3,4,5,6,10,11,12],[1,3,4,5,8,9,10,12], [1,3,4,5,8,9,12,13],[1,3,4,5,9,10,11,12], [1,3,4,5,9,10,11,13],[1,3,4,5,9,11,12,13], [1,3,4,6,7,8,12,13],[1,3,4,9,10,11,12,13], [1,3,5,6,7,8,10,12],[1,3,5,6,7,8,12,13], [1,3,5,6,7,10,11,12],[1,3,5,6,7,11,12,13], [1,3,5,7,8,9,10,12],[1,3,5,7,8,9,12,13], [1,3,5,7,9,10,11,12],[1,3,5,7,9,11,12,13], [1,3,7,8,9,11,12,13],[1,4,5,6,7,8,9,13], [1,4,5,6,8,9,10,13],[1,4,5,6,8,10,12,13], [1,4,5,8,9,10,12,13],[1,4,5,9,10,11,12,13], [1,5,6,7,8,9,10,13],[1,5,6,7,8,10,12,13], [1,5,6,7,9,10,11,12],[1,5,6,7,9,10,12,13], [1,5,6,7,9,11,12,13],[1,5,6,9,10,11,12,13], [1,5,7,8,9,10,12,13],[1,6,7,8,9,10,11,13], [1,6,7,9,10,11,12,13],[1,7,8,9,10,11,12,13], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,7,8,9,13], [2,3,4,5,7,9,10,11],[2,3,4,5,7,9,11,13], [2,3,4,5,7,11,12,13],[2,3,4,5,9,10,11,13], [2,3,4,6,7,8,9,11],[2,3,4,6,7,8,11,12], [2,3,4,6,7,9,10,11],[2,3,4,6,8,9,10,11], [2,3,4,6,8,10,11,12],[2,3,4,7,8,9,11,13], [2,3,4,7,8,11,12,13],[2,3,4,8,9,10,11,13], [2,3,4,8,9,10,12,13],[2,3,4,8,10,11,12,13], [2,3,5,6,7,8,9,10],[2,3,5,6,7,11,12,13], [2,3,6,7,8,9,10,11],[2,3,6,7,8,10,11,12], [2,3,7,8,9,10,11,12],[2,3,8,9,10,11,12,13], [2,4,5,6,7,9,10,11],[2,4,5,6,7,9,11,13], [2,4,5,6,7,11,12,13],[2,4,5,6,9,10,11,13], [2,4,5,6,10,11,12,13],[2,4,6,7,8,9,11,13], [2,4,6,7,8,11,12,13],[2,4,6,8,9,10,11,13], [2,4,6,8,10,11,12,13],[2,6,7,8,10,11,12,13], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,13], [3,4,5,6,8,10,11,12],[3,4,5,7,8,9,10,12], [3,4,5,7,8,9,12,13],[3,4,5,7,8,10,11,12], [3,4,5,7,9,10,11,12],[3,4,5,7,9,11,12,13], [3,4,6,7,8,9,10,11],[3,4,7,8,9,10,11,12], [3,4,7,8,9,11,12,13],[3,4,8,9,10,11,12,13], [3,5,6,7,8,10,11,12],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,9,11,12,13],[4,5,6,8,9,10,11,13], [4,5,6,8,9,11,12,13],[4,5,6,8,10,11,12,13], [4,5,7,8,9,10,11,12],[4,5,8,9,10,11,12,13], [4,6,7,8,9,11,12,13],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,8,9,10,11,12,13], [6,7,8,9,10,11,12,13]] manifold_7_13_2_3=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,13], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,11], [1,2,3,4,5,6,11,12],[1,2,3,4,5,6,12,13], [1,2,3,4,5,7,8,13],[1,2,3,4,5,8,9,11], [1,2,3,4,5,8,10,11],[1,2,3,4,5,8,10,13], [1,2,3,4,5,10,11,13],[1,2,3,4,5,11,12,13], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,12], [1,2,3,4,6,7,12,13],[1,2,3,4,6,9,11,12], [1,2,3,4,7,8,9,10],[1,2,3,4,7,8,10,13], [1,2,3,4,7,9,10,13],[1,2,3,4,7,9,12,13], [1,2,3,4,8,9,10,11],[1,2,3,4,9,10,11,12], [1,2,3,4,9,10,12,13],[1,2,3,4,10,11,12,13], [1,2,3,5,6,7,8,13],[1,2,3,5,6,8,9,11], [1,2,3,5,6,8,11,13],[1,2,3,5,6,11,12,13], [1,2,3,5,8,10,11,13],[1,2,3,6,7,8,9,13], [1,2,3,6,7,9,12,13],[1,2,3,6,8,9,11,12], [1,2,3,6,8,9,12,13],[1,2,3,6,8,11,12,13], [1,2,3,7,8,9,10,13],[1,2,3,8,9,10,11,13], [1,2,3,8,9,11,12,13],[1,2,3,9,10,11,12,13], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,12], [1,2,4,5,6,7,12,13],[1,2,4,5,6,9,11,12], [1,2,4,5,7,8,9,12],[1,2,4,5,7,8,10,11], [1,2,4,5,7,8,10,13],[1,2,4,5,7,8,11,12], [1,2,4,5,7,10,11,12],[1,2,4,5,7,10,12,13], [1,2,4,5,8,9,11,12],[1,2,4,5,10,11,12,13], [1,2,4,7,8,9,10,11],[1,2,4,7,8,9,11,12], [1,2,4,7,9,10,11,12],[1,2,4,7,9,10,12,13], [1,2,5,6,7,8,9,12],[1,2,5,6,7,8,12,13], [1,2,5,6,8,9,11,12],[1,2,5,6,8,11,12,13], [1,2,5,7,8,10,11,13],[1,2,5,7,8,11,12,13], [1,2,5,7,10,11,12,13],[1,2,6,7,8,9,12,13], [1,2,7,8,9,10,11,12],[1,2,7,8,9,10,12,13], [1,2,7,8,10,11,12,13],[1,2,8,9,10,11,12,13], [1,3,4,5,6,7,8,13],[1,3,4,5,6,8,9,11], [1,3,4,5,6,8,11,13],[1,3,4,5,6,11,12,13], [1,3,4,5,8,10,11,13],[1,3,4,6,7,8,9,11], [1,3,4,6,7,8,11,13],[1,3,4,6,7,9,10,11], [1,3,4,6,7,9,10,13],[1,3,4,6,7,9,12,13], [1,3,4,6,7,10,11,13],[1,3,4,6,9,10,11,13], [1,3,4,6,9,11,12,13],[1,3,4,7,8,9,10,11], [1,3,4,7,8,10,11,13],[1,3,4,9,10,11,12,13], [1,3,6,7,8,9,10,11],[1,3,6,7,8,9,10,13], [1,3,6,7,8,10,11,13],[1,3,6,8,9,10,11,13], [1,3,6,8,9,11,12,13],[1,4,5,6,7,8,9,12], [1,4,5,6,7,8,11,12],[1,4,5,6,7,8,11,13], [1,4,5,6,7,11,12,13],[1,4,5,6,8,9,11,12], [1,4,5,7,8,10,11,13],[1,4,5,7,10,11,12,13], [1,4,6,7,8,9,11,12],[1,4,6,7,9,10,11,12], [1,4,6,7,9,10,12,13],[1,4,6,7,10,11,12,13], [1,4,6,9,10,11,12,13],[1,5,6,7,8,11,12,13], [1,6,7,8,9,10,11,13],[1,6,7,8,9,11,12,13], [1,6,7,9,10,11,12,13],[1,7,8,9,10,11,12,13], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,12],[2,3,4,5,6,7,12,13], [2,3,4,5,6,9,10,12],[2,3,4,5,6,9,11,12], [2,3,4,5,7,8,9,10],[2,3,4,5,7,8,10,13], [2,3,4,5,7,10,12,13],[2,3,4,5,8,9,10,11], [2,3,4,5,9,10,11,12],[2,3,4,5,10,11,12,13], [2,3,4,6,7,9,10,12],[2,3,4,7,9,10,12,13], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,13], [2,3,5,6,7,10,12,13],[2,3,5,6,8,9,10,13], [2,3,5,6,8,9,11,12],[2,3,5,6,8,9,12,13], [2,3,5,6,8,11,12,13],[2,3,5,6,9,10,12,13], [2,3,5,8,9,10,11,12],[2,3,5,8,9,10,12,13], [2,3,5,8,10,11,12,13],[2,3,6,7,8,9,10,13], [2,3,6,7,9,10,12,13],[2,3,8,9,10,11,12,13], [2,4,5,6,7,9,10,12],[2,4,5,7,8,9,10,12], [2,4,5,7,8,10,11,12],[2,4,5,8,9,10,11,12], [2,4,7,8,9,10,11,12],[2,5,6,7,8,9,10,13], [2,5,6,7,8,9,12,13],[2,5,6,7,9,10,12,13], [2,5,7,8,9,10,12,13],[2,5,7,8,10,11,12,13], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,13],[3,4,5,6,7,10,11,13], [3,4,5,6,7,10,12,13],[3,4,5,6,8,9,10,11], [3,4,5,6,9,10,11,12],[3,4,5,6,10,11,12,13], [3,4,5,7,8,10,11,13],[3,4,6,7,8,9,10,11], [3,4,6,7,9,10,12,13],[3,4,6,9,10,11,12,13], [3,5,6,7,8,10,11,13],[3,5,6,8,9,10,11,13], [3,5,6,8,9,11,12,13],[3,5,6,9,10,11,12,13], [3,5,8,9,10,11,12,13],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,9,10,11,12], [4,5,6,7,10,11,12,13],[4,5,7,8,9,10,11,12], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,10,11,12,13],[5,6,8,9,10,11,12,13], [6,7,8,9,10,11,12,13]] manifold_7_13_1_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,13], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,12],[1,2,3,4,5,6,12,13], [1,2,3,4,5,7,8,13],[1,2,3,4,5,8,9,13], [1,2,3,4,5,9,10,11],[1,2,3,4,5,9,11,13], [1,2,3,4,5,10,11,12],[1,2,3,4,5,11,12,13], [1,2,3,4,6,7,8,12],[1,2,3,4,6,7,12,13], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,12], [1,2,3,4,7,8,12,13],[1,2,3,4,8,9,10,13], [1,2,3,4,8,10,12,13],[1,2,3,4,9,10,11,13], [1,2,3,4,10,11,12,13],[1,2,3,5,6,7,8,9], [1,2,3,5,6,7,9,10],[1,2,3,5,6,7,10,11], [1,2,3,5,6,7,11,13],[1,2,3,5,6,10,11,12], [1,2,3,5,6,11,12,13],[1,2,3,5,7,8,9,13], [1,2,3,5,7,9,10,11],[1,2,3,5,7,9,11,13], [1,2,3,6,7,8,9,10],[1,2,3,6,7,8,10,12], [1,2,3,6,7,10,11,12],[1,2,3,6,7,11,12,13], [1,2,3,7,8,9,10,12],[1,2,3,7,8,9,12,13], [1,2,3,7,9,10,11,12],[1,2,3,7,9,11,12,13], [1,2,3,8,9,10,12,13],[1,2,3,9,10,11,12,13], [1,2,4,5,6,7,8,13],[1,2,4,5,6,8,9,13], [1,2,4,5,6,9,10,13],[1,2,4,5,6,10,12,13], [1,2,4,5,9,10,11,13],[1,2,4,5,10,11,12,13], [1,2,4,6,7,8,12,13],[1,2,4,6,8,9,10,13], [1,2,4,6,8,10,12,13],[1,2,5,6,7,8,9,13], [1,2,5,6,7,9,10,11],[1,2,5,6,7,9,11,13], [1,2,5,6,9,10,11,13],[1,2,5,6,10,11,12,13], [1,2,6,7,8,9,10,11],[1,2,6,7,8,9,11,13], [1,2,6,7,8,10,11,12],[1,2,6,7,8,11,12,13], [1,2,6,8,9,10,11,13],[1,2,6,8,10,11,12,13], [1,2,7,8,9,10,11,12],[1,2,7,8,9,11,12,13], [1,2,8,9,10,11,12,13],[1,3,4,5,6,7,8,12], [1,3,4,5,6,7,12,13],[1,3,4,5,6,8,9,10], [1,3,4,5,6,8,10,12],[1,3,4,5,7,8,12,13], [1,3,4,5,8,9,10,12],[1,3,4,5,8,9,12,13], [1,3,4,5,9,10,11,12],[1,3,4,5,9,11,12,13], [1,3,4,8,9,10,12,13],[1,3,4,9,10,11,12,13], [1,3,5,6,7,8,9,10],[1,3,5,6,7,8,10,12], [1,3,5,6,7,10,11,12],[1,3,5,6,7,11,12,13], [1,3,5,7,8,9,10,12],[1,3,5,7,8,9,12,13], [1,3,5,7,9,10,11,12],[1,3,5,7,9,11,12,13], [1,4,5,6,7,8,12,13],[1,4,5,6,8,9,10,13], [1,4,5,6,8,10,12,13],[1,4,5,8,9,10,12,13], [1,4,5,9,10,11,12,13],[1,5,6,7,8,9,10,13], [1,5,6,7,8,10,12,13],[1,5,6,7,9,10,11,13], [1,5,6,7,10,11,12,13],[1,5,7,8,9,10,12,13], [1,5,7,9,10,11,12,13],[1,6,7,8,9,10,11,13], [1,6,7,8,10,11,12,13],[1,7,8,9,10,11,12,13], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,13], [2,3,4,5,6,10,11,12],[2,3,4,5,6,11,12,13], [2,3,4,5,7,8,9,13],[2,3,4,5,7,9,10,11], [2,3,4,5,7,9,11,13],[2,3,4,6,7,8,9,10], [2,3,4,6,7,8,10,11],[2,3,4,6,7,8,11,12], [2,3,4,6,7,11,12,13],[2,3,4,6,8,10,11,12], [2,3,4,7,8,9,10,11],[2,3,4,7,8,9,11,13], [2,3,4,7,8,11,12,13],[2,3,4,8,9,10,11,13], [2,3,4,8,10,11,12,13],[2,3,6,7,8,10,11,12], [2,3,7,8,9,10,11,12],[2,3,7,8,9,11,12,13], [2,3,8,9,10,11,12,13],[2,4,5,6,7,8,9,13], [2,4,5,6,7,9,10,11],[2,4,5,6,7,9,11,13], [2,4,5,6,9,10,11,13],[2,4,5,6,10,11,12,13], [2,4,6,7,8,9,10,11],[2,4,6,7,8,9,11,13], [2,4,6,7,8,11,12,13],[2,4,6,8,9,10,11,13], [2,4,6,8,10,11,12,13],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,12], [3,4,5,6,7,11,12,13],[3,4,5,6,8,10,11,12], [3,4,5,7,8,9,10,11],[3,4,5,7,8,9,11,12], [3,4,5,7,8,9,12,13],[3,4,5,7,9,11,12,13], [3,4,5,8,9,10,11,12],[3,4,7,8,9,11,12,13], [3,4,8,9,10,11,12,13],[3,5,6,7,8,10,11,12], [3,5,7,8,9,10,11,12],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,9,11,12,13],[4,5,6,8,9,10,11,12], [4,5,6,8,9,10,12,13],[4,5,6,9,10,11,12,13], [4,6,7,8,9,11,12,13],[4,6,8,9,10,11,12,13], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,9,10,11,12,13],[6,7,8,9,10,11,12,13]] manifold_7_14_20_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,14], [1,2,3,4,5,6,8,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,7,8,10],[1,2,3,4,5,7,10,12], [1,2,3,4,5,7,12,14],[1,2,3,4,5,8,10,13], [1,2,3,4,5,10,12,13],[1,2,3,4,5,12,13,14], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,14], [1,2,3,4,6,8,9,11],[1,2,3,4,6,8,11,13], [1,2,3,4,6,9,11,14],[1,2,3,4,6,11,13,14], [1,2,3,4,7,8,9,10],[1,2,3,4,7,9,10,12], [1,2,3,4,7,9,12,14],[1,2,3,4,8,9,10,11], [1,2,3,4,8,10,11,13],[1,2,3,4,9,10,11,12], [1,2,3,4,9,11,12,14],[1,2,3,4,10,11,12,13], [1,2,3,4,11,12,13,14],[1,2,3,5,6,7,8,14], [1,2,3,5,6,8,13,14],[1,2,3,5,7,8,10,14], [1,2,3,5,7,10,12,14],[1,2,3,5,8,10,13,14], [1,2,3,5,10,12,13,14],[1,2,3,6,7,8,9,14], [1,2,3,6,8,9,11,14],[1,2,3,6,8,11,13,14], [1,2,3,7,8,9,10,14],[1,2,3,7,9,10,12,14], [1,2,3,8,9,10,11,14],[1,2,3,8,10,11,13,14], [1,2,3,9,10,11,12,14],[1,2,3,10,11,12,13,14], [1,2,4,5,6,7,8,13],[1,2,4,5,6,7,13,14], [1,2,4,5,7,8,10,13],[1,2,4,5,7,10,12,13], [1,2,4,5,7,12,13,14],[1,2,4,6,7,8,9,13], [1,2,4,6,7,9,13,14],[1,2,4,6,8,9,11,13], [1,2,4,6,9,11,13,14],[1,2,4,7,8,9,10,13], [1,2,4,7,9,10,12,13],[1,2,4,7,9,12,13,14], [1,2,4,8,9,10,11,13],[1,2,4,9,10,11,12,13], [1,2,4,9,11,12,13,14],[1,2,5,6,7,8,13,14], [1,2,5,7,8,10,13,14],[1,2,5,7,10,12,13,14], [1,2,6,7,8,9,13,14],[1,2,6,8,9,11,13,14], [1,2,7,8,9,10,13,14],[1,2,7,9,10,12,13,14], [1,2,8,9,10,11,13,14],[1,2,9,10,11,12,13,14], [1,3,4,5,6,7,8,10],[1,3,4,5,6,7,10,12], [1,3,4,5,6,7,12,14],[1,3,4,5,6,8,10,13], [1,3,4,5,6,10,12,13],[1,3,4,5,6,12,13,14], [1,3,4,6,7,8,9,10],[1,3,4,6,7,9,10,12], [1,3,4,6,7,9,12,14],[1,3,4,6,8,9,10,11], [1,3,4,6,8,10,11,13],[1,3,4,6,9,10,11,12], [1,3,4,6,9,11,12,14],[1,3,4,6,10,11,12,13], [1,3,4,6,11,12,13,14],[1,3,5,6,7,8,10,12], [1,3,5,6,7,8,12,14],[1,3,5,6,8,10,12,13], [1,3,5,6,8,12,13,14],[1,3,5,7,8,10,12,14], [1,3,5,8,10,12,13,14],[1,3,6,7,8,9,10,12], [1,3,6,7,8,9,12,14],[1,3,6,8,9,10,11,12], [1,3,6,8,9,11,12,14],[1,3,6,8,10,11,12,13], [1,3,6,8,11,12,13,14],[1,3,7,8,9,10,12,14], [1,3,8,9,10,11,12,14],[1,3,8,10,11,12,13,14], [1,4,5,6,7,8,10,13],[1,4,5,6,7,10,12,13], [1,4,5,6,7,12,13,14],[1,4,6,7,8,9,10,13], [1,4,6,7,9,10,12,13],[1,4,6,7,9,12,13,14], [1,4,6,8,9,10,11,13],[1,4,6,9,10,11,12,13], [1,4,6,9,11,12,13,14],[1,5,6,7,8,10,12,13], [1,5,6,7,8,12,13,14],[1,5,7,8,10,12,13,14], [1,6,7,8,9,10,12,13],[1,6,7,8,9,12,13,14], [1,6,8,9,10,11,12,13],[1,6,8,9,11,12,13,14], [1,7,8,9,10,12,13,14],[1,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,14], [2,3,4,5,6,8,9,11],[2,3,4,5,6,8,11,13], [2,3,4,5,6,9,11,14],[2,3,4,5,6,11,13,14], [2,3,4,5,7,8,9,10],[2,3,4,5,7,9,10,12], [2,3,4,5,7,9,12,14],[2,3,4,5,8,9,10,11], [2,3,4,5,8,10,11,13],[2,3,4,5,9,10,11,12], [2,3,4,5,9,11,12,14],[2,3,4,5,10,11,12,13], [2,3,4,5,11,12,13,14],[2,3,5,6,7,8,9,14], [2,3,5,6,8,9,11,14],[2,3,5,6,8,11,13,14], [2,3,5,7,8,9,10,14],[2,3,5,7,9,10,12,14], [2,3,5,8,9,10,11,14],[2,3,5,8,10,11,13,14], [2,3,5,9,10,11,12,14],[2,3,5,10,11,12,13,14], [2,4,5,6,7,8,9,11],[2,4,5,6,7,8,11,13], [2,4,5,6,7,9,11,14],[2,4,5,6,7,11,13,14], [2,4,5,7,8,9,10,11],[2,4,5,7,8,10,11,13], [2,4,5,7,9,10,11,12],[2,4,5,7,9,11,12,14], [2,4,5,7,10,11,12,13],[2,4,5,7,11,12,13,14], [2,4,6,7,8,9,11,13],[2,4,6,7,9,11,13,14], [2,4,7,8,9,10,11,13],[2,4,7,9,10,11,12,13], [2,4,7,9,11,12,13,14],[2,5,6,7,8,9,11,14], [2,5,6,7,8,11,13,14],[2,5,7,8,9,10,11,14], [2,5,7,8,10,11,13,14],[2,5,7,9,10,11,12,14], [2,5,7,10,11,12,13,14],[2,6,7,8,9,11,13,14], [2,7,8,9,10,11,13,14],[2,7,9,10,11,12,13,14], [3,4,5,6,7,8,9,10],[3,4,5,6,7,9,10,12], [3,4,5,6,7,9,12,14],[3,4,5,6,8,9,10,11], [3,4,5,6,8,10,11,13],[3,4,5,6,9,10,11,12], [3,4,5,6,9,11,12,14],[3,4,5,6,10,11,12,13], [3,4,5,6,11,12,13,14],[3,5,6,7,8,9,10,12], [3,5,6,7,8,9,12,14],[3,5,6,8,9,10,11,12], [3,5,6,8,9,11,12,14],[3,5,6,8,10,11,12,13], [3,5,6,8,11,12,13,14],[3,5,7,8,9,10,12,14], [3,5,8,9,10,11,12,14],[3,5,8,10,11,12,13,14], [4,5,6,7,8,9,10,11],[4,5,6,7,8,10,11,13], [4,5,6,7,9,10,11,12],[4,5,6,7,9,11,12,14], [4,5,6,7,10,11,12,13],[4,5,6,7,11,12,13,14], [4,6,7,8,9,10,11,13],[4,6,7,9,10,11,12,13], [4,6,7,9,11,12,13,14],[5,6,7,8,9,10,11,12], [5,6,7,8,9,11,12,14],[5,6,7,8,10,11,12,13], [5,6,7,8,11,12,13,14],[5,7,8,9,10,11,12,14], [5,7,8,10,11,12,13,14],[6,7,8,9,10,11,12,13], [6,7,8,9,11,12,13,14],[7,8,9,10,11,12,13,14]] manifold_7_14_3_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,14], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,7,8,14],[1,2,3,4,5,8,9,14], [1,2,3,4,5,9,10,14],[1,2,3,4,5,10,11,14], [1,2,3,4,5,11,12,14],[1,2,3,4,5,12,13,14], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,10], [1,2,3,4,6,7,10,11],[1,2,3,4,6,7,11,12], [1,2,3,4,6,7,12,13],[1,2,3,4,6,7,13,14], [1,2,3,4,7,8,9,10],[1,2,3,4,7,8,10,11], [1,2,3,4,7,8,11,12],[1,2,3,4,7,8,12,13], [1,2,3,4,7,8,13,14],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,12],[1,2,3,4,8,9,12,13], [1,2,3,4,8,9,13,14],[1,2,3,4,9,10,11,12], [1,2,3,4,9,10,12,13],[1,2,3,4,9,10,13,14], [1,2,3,4,10,11,12,13],[1,2,3,4,10,11,13,14], [1,2,3,4,11,12,13,14],[1,2,3,5,6,7,8,14], [1,2,3,5,6,8,9,14],[1,2,3,5,6,9,10,14], [1,2,3,5,6,10,11,14],[1,2,3,5,6,11,12,14], [1,2,3,5,6,12,13,14],[1,2,3,6,7,8,9,14], [1,2,3,6,7,9,10,14],[1,2,3,6,7,10,11,14], [1,2,3,6,7,11,12,14],[1,2,3,6,7,12,13,14], [1,2,3,7,8,9,10,14],[1,2,3,7,8,10,11,14], [1,2,3,7,8,11,12,14],[1,2,3,7,8,12,13,14], [1,2,3,8,9,10,11,14],[1,2,3,8,9,11,12,14], [1,2,3,8,9,12,13,14],[1,2,3,9,10,11,12,14], [1,2,3,9,10,12,13,14],[1,2,3,10,11,12,13,14], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,11],[1,2,4,5,6,7,11,12], [1,2,4,5,6,7,12,13],[1,2,4,5,6,7,13,14], [1,2,4,5,7,8,9,10],[1,2,4,5,7,8,10,11], [1,2,4,5,7,8,11,12],[1,2,4,5,7,8,12,13], [1,2,4,5,7,8,13,14],[1,2,4,5,8,9,10,11], [1,2,4,5,8,9,11,12],[1,2,4,5,8,9,12,13], [1,2,4,5,8,9,13,14],[1,2,4,5,9,10,11,12], [1,2,4,5,9,10,12,13],[1,2,4,5,9,10,13,14], [1,2,4,5,10,11,12,13],[1,2,4,5,10,11,13,14], [1,2,4,5,11,12,13,14],[1,2,5,6,7,8,9,10], [1,2,5,6,7,8,10,11],[1,2,5,6,7,8,11,12], [1,2,5,6,7,8,12,13],[1,2,5,6,7,8,13,14], [1,2,5,6,8,9,10,11],[1,2,5,6,8,9,11,12], [1,2,5,6,8,9,12,13],[1,2,5,6,8,9,13,14], [1,2,5,6,9,10,11,12],[1,2,5,6,9,10,12,13], [1,2,5,6,9,10,13,14],[1,2,5,6,10,11,12,13], [1,2,5,6,10,11,13,14],[1,2,5,6,11,12,13,14], [1,2,6,7,8,9,10,11],[1,2,6,7,8,9,11,12], [1,2,6,7,8,9,12,13],[1,2,6,7,8,9,13,14], [1,2,6,7,9,10,11,12],[1,2,6,7,9,10,12,13], [1,2,6,7,9,10,13,14],[1,2,6,7,10,11,12,13], [1,2,6,7,10,11,13,14],[1,2,6,7,11,12,13,14], [1,2,7,8,9,10,11,12],[1,2,7,8,9,10,12,13], [1,2,7,8,9,10,13,14],[1,2,7,8,10,11,12,13], [1,2,7,8,10,11,13,14],[1,2,7,8,11,12,13,14], [1,2,8,9,10,11,12,13],[1,2,8,9,10,11,13,14], [1,2,8,9,11,12,13,14],[1,2,9,10,11,12,13,14], [1,3,4,5,6,7,8,14],[1,3,4,5,6,8,9,14], [1,3,4,5,6,9,10,14],[1,3,4,5,6,10,11,14], [1,3,4,5,6,11,12,14],[1,3,4,5,6,12,13,14], [1,3,4,6,7,8,9,14],[1,3,4,6,7,9,10,14], [1,3,4,6,7,10,11,14],[1,3,4,6,7,11,12,14], [1,3,4,6,7,12,13,14],[1,3,4,7,8,9,10,14], [1,3,4,7,8,10,11,14],[1,3,4,7,8,11,12,14], [1,3,4,7,8,12,13,14],[1,3,4,8,9,10,11,14], [1,3,4,8,9,11,12,14],[1,3,4,8,9,12,13,14], [1,3,4,9,10,11,12,14],[1,3,4,9,10,12,13,14], [1,3,4,10,11,12,13,14],[1,4,5,6,7,8,9,14], [1,4,5,6,7,9,10,14],[1,4,5,6,7,10,11,14], [1,4,5,6,7,11,12,14],[1,4,5,6,7,12,13,14], [1,4,5,7,8,9,10,14],[1,4,5,7,8,10,11,14], [1,4,5,7,8,11,12,14],[1,4,5,7,8,12,13,14], [1,4,5,8,9,10,11,14],[1,4,5,8,9,11,12,14], [1,4,5,8,9,12,13,14],[1,4,5,9,10,11,12,14], [1,4,5,9,10,12,13,14],[1,4,5,10,11,12,13,14], [1,5,6,7,8,9,10,14],[1,5,6,7,8,10,11,14], [1,5,6,7,8,11,12,14],[1,5,6,7,8,12,13,14], [1,5,6,8,9,10,11,14],[1,5,6,8,9,11,12,14], [1,5,6,8,9,12,13,14],[1,5,6,9,10,11,12,14], [1,5,6,9,10,12,13,14],[1,5,6,10,11,12,13,14], [1,6,7,8,9,10,11,14],[1,6,7,8,9,11,12,14], [1,6,7,8,9,12,13,14],[1,6,7,9,10,11,12,14], [1,6,7,9,10,12,13,14],[1,6,7,10,11,12,13,14], [1,7,8,9,10,11,12,14],[1,7,8,9,10,12,13,14], [1,7,8,10,11,12,13,14],[1,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,6,7,13,14], [2,3,4,5,7,8,9,10],[2,3,4,5,7,8,10,11], [2,3,4,5,7,8,11,12],[2,3,4,5,7,8,12,13], [2,3,4,5,7,8,13,14],[2,3,4,5,8,9,10,11], [2,3,4,5,8,9,11,12],[2,3,4,5,8,9,12,13], [2,3,4,5,8,9,13,14],[2,3,4,5,9,10,11,12], [2,3,4,5,9,10,12,13],[2,3,4,5,9,10,13,14], [2,3,4,5,10,11,12,13],[2,3,4,5,10,11,13,14], [2,3,4,5,11,12,13,14],[2,3,5,6,7,8,9,10], [2,3,5,6,7,8,10,11],[2,3,5,6,7,8,11,12], [2,3,5,6,7,8,12,13],[2,3,5,6,7,8,13,14], [2,3,5,6,8,9,10,11],[2,3,5,6,8,9,11,12], [2,3,5,6,8,9,12,13],[2,3,5,6,8,9,13,14], [2,3,5,6,9,10,11,12],[2,3,5,6,9,10,12,13], [2,3,5,6,9,10,13,14],[2,3,5,6,10,11,12,13], [2,3,5,6,10,11,13,14],[2,3,5,6,11,12,13,14], [2,3,6,7,8,9,10,11],[2,3,6,7,8,9,11,12], [2,3,6,7,8,9,12,13],[2,3,6,7,8,9,13,14], [2,3,6,7,9,10,11,12],[2,3,6,7,9,10,12,13], [2,3,6,7,9,10,13,14],[2,3,6,7,10,11,12,13], [2,3,6,7,10,11,13,14],[2,3,6,7,11,12,13,14], [2,3,7,8,9,10,11,12],[2,3,7,8,9,10,12,13], [2,3,7,8,9,10,13,14],[2,3,7,8,10,11,12,13], [2,3,7,8,10,11,13,14],[2,3,7,8,11,12,13,14], [2,3,8,9,10,11,12,13],[2,3,8,9,10,11,13,14], [2,3,8,9,11,12,13,14],[2,3,9,10,11,12,13,14], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,13], [3,4,5,6,7,8,13,14],[3,4,5,6,8,9,10,11], [3,4,5,6,8,9,11,12],[3,4,5,6,8,9,12,13], [3,4,5,6,8,9,13,14],[3,4,5,6,9,10,11,12], [3,4,5,6,9,10,12,13],[3,4,5,6,9,10,13,14], [3,4,5,6,10,11,12,13],[3,4,5,6,10,11,13,14], [3,4,5,6,11,12,13,14],[3,4,6,7,8,9,10,11], [3,4,6,7,8,9,11,12],[3,4,6,7,8,9,12,13], [3,4,6,7,8,9,13,14],[3,4,6,7,9,10,11,12], [3,4,6,7,9,10,12,13],[3,4,6,7,9,10,13,14], [3,4,6,7,10,11,12,13],[3,4,6,7,10,11,13,14], [3,4,6,7,11,12,13,14],[3,4,7,8,9,10,11,12], [3,4,7,8,9,10,12,13],[3,4,7,8,9,10,13,14], [3,4,7,8,10,11,12,13],[3,4,7,8,10,11,13,14], [3,4,7,8,11,12,13,14],[3,4,8,9,10,11,12,13], [3,4,8,9,10,11,13,14],[3,4,8,9,11,12,13,14], [3,4,9,10,11,12,13,14],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,8,9,13,14],[4,5,6,7,9,10,11,12], [4,5,6,7,9,10,12,13],[4,5,6,7,9,10,13,14], [4,5,6,7,10,11,12,13],[4,5,6,7,10,11,13,14], [4,5,6,7,11,12,13,14],[4,5,7,8,9,10,11,12], [4,5,7,8,9,10,12,13],[4,5,7,8,9,10,13,14], [4,5,7,8,10,11,12,13],[4,5,7,8,10,11,13,14], [4,5,7,8,11,12,13,14],[4,5,8,9,10,11,12,13], [4,5,8,9,10,11,13,14],[4,5,8,9,11,12,13,14], [4,5,9,10,11,12,13,14],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,9,10,13,14], [5,6,7,8,10,11,12,13],[5,6,7,8,10,11,13,14], [5,6,7,8,11,12,13,14],[5,6,8,9,10,11,12,13], [5,6,8,9,10,11,13,14],[5,6,8,9,11,12,13,14], [5,6,9,10,11,12,13,14],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,11,12,13,14], [6,7,9,10,11,12,13,14],[7,8,9,10,11,12,13,14]] manifold_7_14_3_2=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,14], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,7,8,14],[1,2,3,4,5,8,9,14], [1,2,3,4,5,9,10,14],[1,2,3,4,5,10,11,14], [1,2,3,4,5,11,12,14],[1,2,3,4,5,12,13,14], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,10], [1,2,3,4,6,7,10,12],[1,2,3,4,6,7,12,13], [1,2,3,4,6,7,13,14],[1,2,3,4,6,10,11,12], [1,2,3,4,7,8,9,13],[1,2,3,4,7,8,13,14], [1,2,3,4,7,9,10,12],[1,2,3,4,7,9,12,13], [1,2,3,4,8,9,13,14],[1,2,3,4,9,10,12,13], [1,2,3,4,9,10,13,14],[1,2,3,4,10,11,12,13], [1,2,3,4,10,11,13,14],[1,2,3,4,11,12,13,14], [1,2,3,5,6,7,8,14],[1,2,3,5,6,8,9,14], [1,2,3,5,6,9,10,11],[1,2,3,5,6,9,11,14], [1,2,3,5,6,11,12,14],[1,2,3,5,6,12,13,14], [1,2,3,5,9,10,11,14],[1,2,3,6,7,8,9,11], [1,2,3,6,7,8,11,12],[1,2,3,6,7,8,12,14], [1,2,3,6,7,9,10,11],[1,2,3,6,7,10,11,12], [1,2,3,6,7,12,13,14],[1,2,3,6,8,9,11,14], [1,2,3,6,8,11,12,14],[1,2,3,7,8,9,11,12], [1,2,3,7,8,9,12,13],[1,2,3,7,8,12,13,14], [1,2,3,7,9,10,11,12],[1,2,3,8,9,11,12,14], [1,2,3,8,9,12,13,14],[1,2,3,9,10,11,12,14], [1,2,3,9,10,12,13,14],[1,2,3,10,11,12,13,14], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,12],[1,2,4,5,6,7,12,13], [1,2,4,5,6,7,13,14],[1,2,4,5,6,10,11,12], [1,2,4,5,7,8,9,10],[1,2,4,5,7,8,10,13], [1,2,4,5,7,8,13,14],[1,2,4,5,7,10,12,13], [1,2,4,5,8,9,10,14],[1,2,4,5,8,10,13,14], [1,2,4,5,10,11,12,13],[1,2,4,5,10,11,13,14], [1,2,4,5,11,12,13,14],[1,2,4,7,8,9,10,13], [1,2,4,7,9,10,12,13],[1,2,4,8,9,10,13,14], [1,2,5,6,7,8,9,10],[1,2,5,6,7,8,10,14], [1,2,5,6,7,10,11,12],[1,2,5,6,7,10,11,14], [1,2,5,6,7,11,12,13],[1,2,5,6,7,11,13,14], [1,2,5,6,8,9,10,14],[1,2,5,6,9,10,11,14], [1,2,5,6,11,12,13,14],[1,2,5,7,8,10,13,14], [1,2,5,7,10,11,12,13],[1,2,5,7,10,11,13,14], [1,2,6,7,8,9,10,11],[1,2,6,7,8,10,11,14], [1,2,6,7,8,11,12,14],[1,2,6,7,11,12,13,14], [1,2,6,8,9,10,11,14],[1,2,7,8,9,10,11,12], [1,2,7,8,9,10,12,13],[1,2,7,8,10,11,12,13], [1,2,7,8,10,11,13,14],[1,2,7,8,11,12,13,14], [1,2,8,9,10,11,12,13],[1,2,8,9,10,11,13,14], [1,2,8,9,11,12,13,14],[1,2,9,10,11,12,13,14], [1,3,4,5,6,7,8,14],[1,3,4,5,6,8,9,14], [1,3,4,5,6,9,10,11],[1,3,4,5,6,9,11,14], [1,3,4,5,6,11,12,14],[1,3,4,5,6,12,13,14], [1,3,4,5,9,10,11,14],[1,3,4,6,7,8,9,14], [1,3,4,6,7,9,10,12],[1,3,4,6,7,9,12,14], [1,3,4,6,7,12,13,14],[1,3,4,6,9,10,11,12], [1,3,4,6,9,11,12,14],[1,3,4,7,8,9,13,14], [1,3,4,7,9,12,13,14],[1,3,4,9,10,11,12,14], [1,3,4,9,10,12,13,14],[1,3,4,10,11,12,13,14], [1,3,6,7,8,9,11,12],[1,3,6,7,8,9,12,14], [1,3,6,7,9,10,11,12],[1,3,6,8,9,11,12,14], [1,3,7,8,9,12,13,14],[1,4,5,6,7,8,9,14], [1,4,5,6,7,9,10,13],[1,4,5,6,7,9,13,14], [1,4,5,6,7,10,12,13],[1,4,5,6,9,10,11,14], [1,4,5,6,9,10,13,14],[1,4,5,6,10,11,12,14], [1,4,5,6,10,12,13,14],[1,4,5,7,8,9,10,13], [1,4,5,7,8,9,13,14],[1,4,5,8,9,10,13,14], [1,4,5,10,11,12,13,14],[1,4,6,7,9,10,12,13], [1,4,6,7,9,12,13,14],[1,4,6,9,10,11,12,14], [1,4,6,9,10,12,13,14],[1,5,6,7,8,9,10,14], [1,5,6,7,9,10,13,14],[1,5,6,7,10,11,12,13], [1,5,6,7,10,11,13,14],[1,5,6,10,11,12,13,14], [1,5,7,8,9,10,13,14],[1,6,7,8,9,10,11,14], [1,6,7,8,9,11,12,14],[1,6,7,9,10,11,12,14], [1,6,7,9,10,12,13,14],[1,6,7,10,11,12,13,14], [1,7,8,9,10,11,12,14],[1,7,8,9,10,12,13,14], [1,7,8,10,11,12,13,14],[1,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,6,7,13,14], [2,3,4,5,7,8,9,10],[2,3,4,5,7,8,10,11], [2,3,4,5,7,8,11,13],[2,3,4,5,7,8,13,14], [2,3,4,5,7,11,12,13],[2,3,4,5,8,9,10,14], [2,3,4,5,8,10,11,13],[2,3,4,5,8,10,13,14], [2,3,4,5,10,11,13,14],[2,3,4,5,11,12,13,14], [2,3,4,6,7,10,11,12],[2,3,4,7,8,9,10,12], [2,3,4,7,8,9,12,13],[2,3,4,7,8,10,11,12], [2,3,4,7,8,11,12,13],[2,3,4,8,9,10,12,13], [2,3,4,8,9,10,13,14],[2,3,4,8,10,11,12,13], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,11], [2,3,5,6,7,8,11,13],[2,3,5,6,7,8,13,14], [2,3,5,6,7,11,12,13],[2,3,5,6,8,9,10,11], [2,3,5,6,8,9,11,14],[2,3,5,6,8,11,13,14], [2,3,5,6,11,12,13,14],[2,3,5,8,9,10,11,14], [2,3,5,8,10,11,13,14],[2,3,6,7,8,9,10,11], [2,3,6,7,8,11,12,13],[2,3,6,7,8,12,13,14], [2,3,6,8,11,12,13,14],[2,3,7,8,9,10,11,12], [2,3,8,9,10,11,12,13],[2,3,8,9,10,11,13,14], [2,3,8,9,11,12,13,14],[2,3,9,10,11,12,13,14], [2,4,5,6,7,10,11,12],[2,4,5,7,8,10,11,13], [2,4,5,7,10,11,12,13],[2,4,7,8,9,10,12,13], [2,4,7,8,10,11,12,13],[2,5,6,7,8,10,11,14], [2,5,6,7,8,11,13,14],[2,5,6,8,9,10,11,14], [2,5,7,8,10,11,13,14],[2,6,7,8,11,12,13,14], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,13], [3,4,5,6,7,8,13,14],[3,4,5,6,8,9,10,11], [3,4,5,6,8,9,11,12],[3,4,5,6,8,9,12,14], [3,4,5,6,8,12,13,14],[3,4,5,6,9,11,12,14], [3,4,5,7,8,11,12,13],[3,4,5,8,9,10,11,13], [3,4,5,8,9,10,13,14],[3,4,5,8,9,11,12,13], [3,4,5,8,9,12,13,14],[3,4,5,9,10,11,13,14], [3,4,5,9,11,12,13,14],[3,4,6,7,8,9,10,11], [3,4,6,7,8,9,11,12],[3,4,6,7,8,9,12,14], [3,4,6,7,8,12,13,14],[3,4,6,7,9,10,11,12], [3,4,7,8,9,10,11,12],[3,4,7,8,9,12,13,14], [3,4,8,9,10,11,12,13],[3,4,9,10,11,12,13,14], [3,5,6,7,8,11,12,13],[3,5,6,8,9,11,12,14], [3,5,6,8,11,12,13,14],[3,5,8,9,10,11,13,14], [3,5,8,9,11,12,13,14],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,8,9,13,14],[4,5,6,7,9,10,11,12], [4,5,6,7,9,10,12,13],[4,5,6,8,9,12,13,14], [4,5,6,9,10,11,12,14],[4,5,6,9,10,12,13,14], [4,5,7,8,9,10,11,12],[4,5,7,8,9,10,12,13], [4,5,7,8,10,11,12,13],[4,5,8,9,10,11,12,13], [4,5,9,10,11,12,13,14],[4,6,7,8,9,12,13,14], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,10,13,14],[5,6,7,8,10,11,12,13], [5,6,7,8,10,11,13,14],[5,6,8,9,10,11,12,13], [5,6,8,9,10,11,13,14],[5,6,8,9,11,12,13,14], [5,6,9,10,11,12,13,14],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,11,12,13,14], [6,7,9,10,11,12,13,14],[7,8,9,10,11,12,13,14]] manifold_7_14_3_3=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,14], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,7,8,14],[1,2,3,4,5,8,9,14], [1,2,3,4,5,9,10,14],[1,2,3,4,5,10,11,14], [1,2,3,4,5,11,12,14],[1,2,3,4,5,12,13,14], [1,2,3,4,6,7,8,13],[1,2,3,4,6,7,13,14], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,11], [1,2,3,4,6,8,11,13],[1,2,3,4,6,11,12,13], [1,2,3,4,7,8,13,14],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,13],[1,2,3,4,8,9,13,14], [1,2,3,4,9,10,11,13],[1,2,3,4,9,10,13,14], [1,2,3,4,10,11,13,14],[1,2,3,4,11,12,13,14], [1,2,3,5,6,7,8,10],[1,2,3,5,6,7,10,12], [1,2,3,5,6,7,12,14],[1,2,3,5,6,8,9,10], [1,2,3,5,6,10,11,12],[1,2,3,5,6,12,13,14], [1,2,3,5,7,8,9,10],[1,2,3,5,7,8,9,14], [1,2,3,5,7,9,10,14],[1,2,3,5,7,10,12,14], [1,2,3,5,10,11,12,14],[1,2,3,6,7,8,10,11], [1,2,3,6,7,8,11,12],[1,2,3,6,7,8,12,13], [1,2,3,6,7,10,11,12],[1,2,3,6,7,12,13,14], [1,2,3,6,8,11,12,13],[1,2,3,7,8,9,10,14], [1,2,3,7,8,10,11,12],[1,2,3,7,8,10,12,14], [1,2,3,7,8,12,13,14],[1,2,3,8,9,10,11,13], [1,2,3,8,9,10,12,13],[1,2,3,8,9,10,12,14], [1,2,3,8,9,12,13,14],[1,2,3,8,10,11,12,13], [1,2,3,9,10,12,13,14],[1,2,3,10,11,12,13,14], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,14], [1,2,4,5,6,9,10,11],[1,2,4,5,6,9,11,14], [1,2,4,5,6,11,12,13],[1,2,4,5,6,11,13,14], [1,2,4,5,7,8,9,14],[1,2,4,5,9,10,11,14], [1,2,4,5,11,12,13,14],[1,2,4,6,7,8,9,14], [1,2,4,6,7,8,13,14],[1,2,4,6,8,9,10,11], [1,2,4,6,8,9,11,13],[1,2,4,6,8,9,13,14], [1,2,4,6,9,11,13,14],[1,2,4,9,10,11,13,14], [1,2,5,6,7,8,9,10],[1,2,5,6,7,9,10,14], [1,2,5,6,7,10,11,12],[1,2,5,6,7,10,11,14], [1,2,5,6,7,11,12,14],[1,2,5,6,9,10,11,14], [1,2,5,6,11,12,13,14],[1,2,5,7,10,11,12,14], [1,2,6,7,8,9,10,11],[1,2,6,7,8,9,11,13], [1,2,6,7,8,9,13,14],[1,2,6,7,8,11,12,13], [1,2,6,7,9,10,11,14],[1,2,6,7,9,11,13,14], [1,2,6,7,11,12,13,14],[1,2,7,8,9,10,11,12], [1,2,7,8,9,10,12,14],[1,2,7,8,9,11,12,14], [1,2,7,8,9,11,13,14],[1,2,7,8,11,12,13,14], [1,2,7,9,10,11,12,14],[1,2,8,9,10,11,12,13], [1,2,8,9,11,12,13,14],[1,2,9,10,11,12,13,14], [1,3,4,5,6,7,8,14],[1,3,4,5,6,8,9,10], [1,3,4,5,6,8,10,13],[1,3,4,5,6,8,13,14], [1,3,4,5,6,10,11,13],[1,3,4,5,6,11,12,13], [1,3,4,5,8,9,10,14],[1,3,4,5,8,10,13,14], [1,3,4,5,10,11,12,13],[1,3,4,5,10,11,12,14], [1,3,4,5,10,12,13,14],[1,3,4,6,7,8,13,14], [1,3,4,6,8,10,11,13],[1,3,4,8,9,10,11,13], [1,3,4,8,9,10,13,14],[1,3,4,10,11,12,13,14], [1,3,5,6,7,8,10,12],[1,3,5,6,7,8,12,13], [1,3,5,6,7,8,13,14],[1,3,5,6,7,12,13,14], [1,3,5,6,8,10,12,13],[1,3,5,6,10,11,12,13], [1,3,5,7,8,9,10,14],[1,3,5,7,8,10,12,14], [1,3,5,7,8,12,13,14],[1,3,5,8,10,12,13,14], [1,3,6,7,8,10,11,12],[1,3,6,8,10,11,12,13], [1,3,8,9,10,12,13,14],[1,4,5,6,7,8,9,14], [1,4,5,6,8,9,10,13],[1,4,5,6,8,9,13,14], [1,4,5,6,9,10,11,14],[1,4,5,6,9,10,13,14], [1,4,5,6,10,11,13,14],[1,4,5,8,9,10,13,14], [1,4,5,10,11,12,13,14],[1,4,6,8,9,10,11,13], [1,4,6,9,10,11,13,14],[1,5,6,7,8,9,10,14], [1,5,6,7,8,10,12,14],[1,5,6,7,8,12,13,14], [1,5,6,7,10,11,12,14],[1,5,6,8,9,10,13,14], [1,5,6,8,10,12,13,14],[1,5,6,10,11,12,13,14], [1,6,7,8,9,10,11,14],[1,6,7,8,9,11,13,14], [1,6,7,8,10,11,12,13],[1,6,7,8,10,11,13,14], [1,6,7,8,10,12,13,14],[1,6,7,10,11,12,13,14], [1,6,8,9,10,11,13,14],[1,7,8,9,10,11,12,14], [1,7,8,10,11,12,13,14],[1,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,6,7,13,14], [2,3,4,5,7,8,9,14],[2,3,4,5,7,9,10,11], [2,3,4,5,7,9,11,12],[2,3,4,5,7,9,12,14], [2,3,4,5,7,12,13,14],[2,3,4,5,9,10,11,12], [2,3,4,5,9,10,12,14],[2,3,4,5,10,11,12,14], [2,3,4,6,7,8,9,11],[2,3,4,6,7,8,11,13], [2,3,4,6,7,9,10,11],[2,3,4,6,7,11,12,13], [2,3,4,6,8,9,10,11],[2,3,4,7,8,9,11,12], [2,3,4,7,8,9,12,13],[2,3,4,7,8,9,13,14], [2,3,4,7,8,11,12,13],[2,3,4,7,9,12,13,14], [2,3,4,8,9,11,12,13],[2,3,4,9,10,11,12,14], [2,3,4,9,10,11,13,14],[2,3,4,9,11,12,13,14], [2,3,5,6,7,8,9,10],[2,3,5,6,7,10,11,12], [2,3,5,6,7,12,13,14],[2,3,5,7,9,10,11,12], [2,3,5,7,9,10,12,14],[2,3,6,7,8,9,10,11], [2,3,6,7,8,11,12,13],[2,3,7,8,9,10,11,12], [2,3,7,8,9,10,12,14],[2,3,7,8,9,12,13,14], [2,3,8,9,10,11,12,13],[2,3,9,10,11,12,13,14], [2,4,5,6,7,9,10,11],[2,4,5,6,7,9,11,14], [2,4,5,6,7,11,12,14],[2,4,5,6,7,12,13,14], [2,4,5,6,11,12,13,14],[2,4,5,7,9,11,12,14], [2,4,5,9,10,11,12,14],[2,4,6,7,8,9,11,13], [2,4,6,7,8,9,13,14],[2,4,6,7,9,11,13,14], [2,4,6,7,11,12,13,14],[2,4,7,8,9,11,12,13], [2,4,7,9,11,12,13,14],[2,5,6,7,9,10,11,14], [2,5,7,9,10,11,12,14],[2,7,8,9,11,12,13,14], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,13], [3,4,5,6,7,8,13,14],[3,4,5,6,8,10,11,12], [3,4,5,6,8,10,12,13],[3,4,5,6,10,11,12,13], [3,4,5,7,8,9,10,12],[3,4,5,7,8,9,12,14], [3,4,5,7,8,10,11,12],[3,4,5,7,8,12,13,14], [3,4,5,7,9,10,11,12],[3,4,5,8,9,10,12,13], [3,4,5,8,9,10,13,14],[3,4,5,8,9,12,13,14], [3,4,5,9,10,12,13,14],[3,4,6,7,8,9,10,11], [3,4,6,7,8,11,12,13],[3,4,6,8,10,11,12,13], [3,4,7,8,9,10,11,12],[3,4,7,8,9,12,13,14], [3,4,8,9,10,11,12,13],[3,4,9,10,11,12,13,14], [3,5,6,7,8,10,11,12],[3,5,7,8,9,10,12,14], [3,5,8,9,10,12,13,14],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,8,9,13,14],[4,5,6,7,9,11,12,13], [4,5,6,7,9,11,13,14],[4,5,6,7,11,12,13,14], [4,5,6,8,9,10,11,13],[4,5,6,8,9,11,12,13], [4,5,6,8,10,11,12,13],[4,5,6,9,10,11,13,14], [4,5,7,8,9,10,11,12],[4,5,7,8,9,12,13,14], [4,5,7,9,11,12,13,14],[4,5,8,9,10,11,12,13], [4,5,9,10,11,12,13,14],[4,6,7,8,9,11,12,13], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,10,13,14],[5,6,7,8,10,12,13,14], [5,6,7,9,10,11,12,14],[5,6,7,9,10,12,13,14], [5,6,7,9,11,12,13,14],[5,6,8,9,10,11,12,13], [5,6,9,10,11,12,13,14],[5,7,8,9,10,12,13,14], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,14], [6,7,9,10,11,12,13,14],[7,8,9,10,11,12,13,14]] manifold_7_14_3_4=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,14], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,7,8,14],[1,2,3,4,5,8,9,14], [1,2,3,4,5,9,10,14],[1,2,3,4,5,10,11,14], [1,2,3,4,5,11,12,14],[1,2,3,4,5,12,13,14], [1,2,3,4,6,7,8,13],[1,2,3,4,6,7,13,14], [1,2,3,4,6,8,9,11],[1,2,3,4,6,8,11,13], [1,2,3,4,6,9,10,11],[1,2,3,4,6,11,12,13], [1,2,3,4,7,8,13,14],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,10,13],[1,2,3,4,8,9,13,14], [1,2,3,4,8,10,11,13],[1,2,3,4,9,10,13,14], [1,2,3,4,10,11,13,14],[1,2,3,4,11,12,13,14], [1,2,3,5,6,7,8,10],[1,2,3,5,6,7,10,12], [1,2,3,5,6,7,12,14],[1,2,3,5,6,8,9,10], [1,2,3,5,6,10,11,12],[1,2,3,5,6,12,13,14], [1,2,3,5,7,8,10,14],[1,2,3,5,7,10,12,14], [1,2,3,5,8,9,10,14],[1,2,3,5,10,11,12,14], [1,2,3,6,7,8,10,11],[1,2,3,6,7,8,11,12], [1,2,3,6,7,8,12,13],[1,2,3,6,7,10,11,12], [1,2,3,6,7,12,13,14],[1,2,3,6,8,9,10,11], [1,2,3,6,8,11,12,13],[1,2,3,7,8,9,10,12], [1,2,3,7,8,9,10,14],[1,2,3,7,8,9,12,14], [1,2,3,7,8,10,11,12],[1,2,3,7,8,12,13,14], [1,2,3,7,9,10,12,14],[1,2,3,8,9,10,12,13], [1,2,3,8,9,12,13,14],[1,2,3,8,10,11,12,13], [1,2,3,9,10,12,13,14],[1,2,3,10,11,12,13,14], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,14], [1,2,4,5,6,9,10,11],[1,2,4,5,6,9,11,14], [1,2,4,5,6,11,12,13],[1,2,4,5,6,11,13,14], [1,2,4,5,7,8,9,14],[1,2,4,5,9,10,11,14], [1,2,4,5,11,12,13,14],[1,2,4,6,7,8,9,13], [1,2,4,6,7,9,13,14],[1,2,4,6,8,9,11,13], [1,2,4,6,9,11,13,14],[1,2,4,7,8,9,13,14], [1,2,4,8,9,10,11,13],[1,2,4,9,10,11,13,14], [1,2,5,6,7,8,9,10],[1,2,5,6,7,9,10,14], [1,2,5,6,7,10,11,12],[1,2,5,6,7,10,11,14], [1,2,5,6,7,11,12,14],[1,2,5,6,9,10,11,14], [1,2,5,6,11,12,13,14],[1,2,5,7,8,9,10,14], [1,2,5,7,10,11,12,14],[1,2,6,7,8,9,10,11], [1,2,6,7,8,9,11,14],[1,2,6,7,8,9,13,14], [1,2,6,7,8,11,12,13],[1,2,6,7,8,11,13,14], [1,2,6,7,9,10,11,14],[1,2,6,7,11,12,13,14], [1,2,6,8,9,11,13,14],[1,2,7,8,9,10,11,12], [1,2,7,8,9,11,12,14],[1,2,7,8,11,12,13,14], [1,2,7,9,10,11,12,14],[1,2,8,9,10,11,12,13], [1,2,8,9,11,12,13,14],[1,2,9,10,11,12,13,14], [1,3,4,5,6,7,8,14],[1,3,4,5,6,8,9,10], [1,3,4,5,6,8,10,13],[1,3,4,5,6,8,13,14], [1,3,4,5,6,10,11,12],[1,3,4,5,6,10,12,13], [1,3,4,5,8,9,10,14],[1,3,4,5,8,10,13,14], [1,3,4,5,10,11,12,14],[1,3,4,5,10,12,13,14], [1,3,4,6,7,8,13,14],[1,3,4,6,8,9,10,11], [1,3,4,6,8,10,11,13],[1,3,4,6,10,11,12,13], [1,3,4,8,9,10,13,14],[1,3,4,10,11,12,13,14], [1,3,5,6,7,8,10,12],[1,3,5,6,7,8,12,14], [1,3,5,6,8,10,12,13],[1,3,5,6,8,12,13,14], [1,3,5,7,8,10,12,14],[1,3,5,8,10,12,13,14], [1,3,6,7,8,10,11,12],[1,3,6,7,8,12,13,14], [1,3,6,8,10,11,12,13],[1,3,7,8,9,10,12,14], [1,3,8,9,10,12,13,14],[1,4,5,6,7,8,9,14], [1,4,5,6,8,9,10,13],[1,4,5,6,8,9,13,14], [1,4,5,6,9,10,11,14],[1,4,5,6,9,10,13,14], [1,4,5,6,10,11,12,13],[1,4,5,6,10,11,13,14], [1,4,5,8,9,10,13,14],[1,4,5,10,11,12,13,14], [1,4,6,7,8,9,13,14],[1,4,6,8,9,10,11,13], [1,4,6,9,10,11,13,14],[1,5,6,7,8,9,10,14], [1,5,6,7,8,10,12,13],[1,5,6,7,8,10,13,14], [1,5,6,7,8,12,13,14],[1,5,6,7,10,11,12,14], [1,5,6,7,10,12,13,14],[1,5,6,8,9,10,13,14], [1,5,6,10,11,12,13,14],[1,5,7,8,10,12,13,14], [1,6,7,8,9,10,11,14],[1,6,7,8,10,11,12,13], [1,6,7,8,10,11,13,14],[1,6,7,10,11,12,13,14], [1,6,8,9,10,11,13,14],[1,7,8,9,10,11,12,14], [1,7,8,10,11,12,13,14],[1,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,6,7,13,14], [2,3,4,5,7,8,9,14],[2,3,4,5,7,9,10,12], [2,3,4,5,7,9,12,14],[2,3,4,5,7,10,11,12], [2,3,4,5,7,12,13,14],[2,3,4,5,9,10,11,12], [2,3,4,5,9,10,11,14],[2,3,4,5,9,11,12,14], [2,3,4,6,7,8,9,11],[2,3,4,6,7,8,11,13], [2,3,4,6,7,9,10,11],[2,3,4,6,7,11,12,13], [2,3,4,7,8,9,11,12],[2,3,4,7,8,9,12,13], [2,3,4,7,8,9,13,14],[2,3,4,7,8,11,12,13], [2,3,4,7,9,10,11,12],[2,3,4,7,9,12,13,14], [2,3,4,8,9,10,11,13],[2,3,4,8,9,11,12,13], [2,3,4,9,10,11,13,14],[2,3,4,9,11,12,13,14], [2,3,5,6,7,8,9,10],[2,3,5,6,7,10,11,12], [2,3,5,6,7,12,13,14],[2,3,5,7,8,9,10,14], [2,3,5,7,9,10,12,14],[2,3,5,9,10,11,12,14], [2,3,6,7,8,9,10,11],[2,3,6,7,8,11,12,13], [2,3,7,8,9,10,11,12],[2,3,7,8,9,12,13,14], [2,3,8,9,10,11,12,13],[2,3,9,10,11,12,13,14], [2,4,5,6,7,9,10,11],[2,4,5,6,7,9,11,14], [2,4,5,6,7,11,12,13],[2,4,5,6,7,11,13,14], [2,4,5,7,9,10,11,12],[2,4,5,7,9,11,12,14], [2,4,5,7,11,12,13,14],[2,4,6,7,8,9,11,13], [2,4,6,7,9,11,13,14],[2,4,7,8,9,11,12,13], [2,4,7,9,11,12,13,14],[2,5,6,7,9,10,11,14], [2,5,6,7,11,12,13,14],[2,5,7,9,10,11,12,14], [2,6,7,8,9,11,13,14],[2,7,8,9,11,12,13,14], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,13], [3,4,5,6,7,8,13,14],[3,4,5,6,8,10,11,13], [3,4,5,6,8,11,12,13],[3,4,5,6,10,11,12,13], [3,4,5,7,8,9,10,12],[3,4,5,7,8,9,12,14], [3,4,5,7,8,10,11,12],[3,4,5,7,8,12,13,14], [3,4,5,8,9,10,12,13],[3,4,5,8,9,10,13,14], [3,4,5,8,9,12,13,14],[3,4,5,8,10,11,12,13], [3,4,5,9,10,11,12,14],[3,4,5,9,10,12,13,14], [3,4,6,7,8,9,10,11],[3,4,6,7,8,11,12,13], [3,4,7,8,9,10,11,12],[3,4,7,8,9,12,13,14], [3,4,8,9,10,11,12,13],[3,4,9,10,11,12,13,14], [3,5,6,7,8,10,11,12],[3,5,6,7,8,12,13,14], [3,5,6,8,10,11,12,13],[3,5,7,8,9,10,12,14], [3,5,8,9,10,12,13,14],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,8,9,13,14],[4,5,6,7,9,11,12,14], [4,5,6,7,9,12,13,14],[4,5,6,7,11,12,13,14], [4,5,6,8,9,10,11,13],[4,5,6,8,9,11,12,13], [4,5,6,9,10,11,13,14],[4,5,6,9,11,12,13,14], [4,5,7,8,9,10,11,12],[4,5,7,8,9,12,13,14], [4,5,8,9,10,11,12,13],[4,5,9,10,11,12,13,14], [4,6,7,8,9,11,12,13],[4,6,7,9,11,12,13,14], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,10,13,14],[5,6,7,9,10,11,12,14], [5,6,7,9,10,12,13,14],[5,6,8,9,10,11,12,13], [5,6,9,10,11,12,13,14],[5,7,8,9,10,12,13,14], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,14], [6,7,9,10,11,12,13,14],[7,8,9,10,11,12,13,14]] manifold_7_14_3_5=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,14], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,7,8,14],[1,2,3,4,5,8,9,11], [1,2,3,4,5,8,11,14],[1,2,3,4,5,9,11,12], [1,2,3,4,5,11,12,14],[1,2,3,4,5,12,13,14], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,13], [1,2,3,4,6,7,13,14],[1,2,3,4,6,9,10,12], [1,2,3,4,6,9,10,13],[1,2,3,4,6,10,12,13], [1,2,3,4,7,8,9,10],[1,2,3,4,7,8,10,14], [1,2,3,4,7,9,10,13],[1,2,3,4,7,10,13,14], [1,2,3,4,8,9,10,11],[1,2,3,4,8,10,11,14], [1,2,3,4,9,10,11,12],[1,2,3,4,10,11,12,13], [1,2,3,4,10,11,13,14],[1,2,3,4,11,12,13,14], [1,2,3,5,6,7,8,14],[1,2,3,5,6,8,9,12], [1,2,3,5,6,8,12,14],[1,2,3,5,6,12,13,14], [1,2,3,5,8,9,11,14],[1,2,3,5,8,9,12,14], [1,2,3,5,9,11,12,14],[1,2,3,6,7,8,9,14], [1,2,3,6,7,9,13,14],[1,2,3,6,8,9,12,14], [1,2,3,6,9,10,12,13],[1,2,3,6,9,12,13,14], [1,2,3,7,8,9,10,14],[1,2,3,7,9,10,13,14], [1,2,3,8,9,10,11,14],[1,2,3,9,10,11,12,14], [1,2,3,9,10,12,13,14],[1,2,3,10,11,12,13,14], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,13], [1,2,4,5,6,7,13,14],[1,2,4,5,6,9,12,13], [1,2,4,5,7,8,9,12],[1,2,4,5,7,8,10,12], [1,2,4,5,7,8,10,13],[1,2,4,5,7,8,11,13], [1,2,4,5,7,8,11,14],[1,2,4,5,7,9,12,13], [1,2,4,5,7,10,12,13],[1,2,4,5,7,11,13,14], [1,2,4,5,8,9,11,12],[1,2,4,5,8,10,12,13], [1,2,4,5,8,11,12,13],[1,2,4,5,11,12,13,14], [1,2,4,6,9,10,12,13],[1,2,4,7,8,9,10,12], [1,2,4,7,8,10,13,14],[1,2,4,7,8,11,13,14], [1,2,4,7,9,10,12,13],[1,2,4,8,9,10,11,12], [1,2,4,8,10,11,12,13],[1,2,4,8,10,11,13,14], [1,2,5,6,7,8,9,13],[1,2,5,6,7,8,13,14], [1,2,5,6,8,9,12,13],[1,2,5,6,8,12,13,14], [1,2,5,7,8,9,10,12],[1,2,5,7,8,9,10,13], [1,2,5,7,8,11,13,14],[1,2,5,7,9,10,12,13], [1,2,5,8,9,10,12,13],[1,2,5,8,9,11,12,14], [1,2,5,8,11,12,13,14],[1,2,6,7,8,9,13,14], [1,2,6,8,9,12,13,14],[1,2,7,8,9,10,13,14], [1,2,8,9,10,11,12,13],[1,2,8,9,10,11,13,14], [1,2,8,9,11,12,13,14],[1,2,9,10,11,12,13,14], [1,3,4,5,6,7,8,14],[1,3,4,5,6,8,9,11], [1,3,4,5,6,8,11,12],[1,3,4,5,6,8,12,14], [1,3,4,5,6,9,11,12],[1,3,4,5,6,12,13,14], [1,3,4,5,8,11,12,14],[1,3,4,6,7,8,9,11], [1,3,4,6,7,8,11,14],[1,3,4,6,7,9,10,12], [1,3,4,6,7,9,10,13],[1,3,4,6,7,9,11,14], [1,3,4,6,7,9,12,14],[1,3,4,6,7,10,12,14], [1,3,4,6,7,10,13,14],[1,3,4,6,8,11,12,14], [1,3,4,6,9,11,12,14],[1,3,4,6,10,12,13,14], [1,3,4,7,8,9,10,11],[1,3,4,7,8,10,11,14], [1,3,4,7,9,10,11,12],[1,3,4,7,9,11,12,14], [1,3,4,7,10,11,12,14],[1,3,4,10,11,12,13,14], [1,3,5,6,8,9,11,12],[1,3,5,8,9,11,12,14], [1,3,6,7,8,9,11,14],[1,3,6,7,9,10,12,13], [1,3,6,7,9,12,13,14],[1,3,6,7,10,12,13,14], [1,3,6,8,9,11,12,14],[1,3,7,8,9,10,11,14], [1,3,7,9,10,11,12,14],[1,3,7,9,10,12,13,14], [1,4,5,6,7,8,9,12],[1,4,5,6,7,8,12,14], [1,4,5,6,7,9,12,13],[1,4,5,6,7,12,13,14], [1,4,5,6,8,9,11,12],[1,4,5,7,8,10,11,12], [1,4,5,7,8,10,11,13],[1,4,5,7,8,11,12,14], [1,4,5,7,10,11,12,13],[1,4,5,7,11,12,13,14], [1,4,5,8,10,11,12,13],[1,4,6,7,8,9,11,14], [1,4,6,7,8,9,12,14],[1,4,6,7,9,10,12,13], [1,4,6,7,10,12,13,14],[1,4,6,8,9,11,12,14], [1,4,7,8,9,10,11,12],[1,4,7,8,9,11,12,14], [1,4,7,8,10,11,13,14],[1,4,7,10,11,12,13,14], [1,5,6,7,8,9,12,13],[1,5,6,7,8,12,13,14], [1,5,7,8,9,10,12,13],[1,5,7,8,10,11,12,13], [1,5,7,8,11,12,13,14],[1,6,7,8,9,12,13,14], [1,7,8,9,10,11,12,14],[1,7,8,9,10,12,13,14], [1,7,8,10,11,12,13,14],[1,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,13],[2,3,4,5,6,7,13,14], [2,3,4,5,6,9,10,12],[2,3,4,5,6,10,12,13], [2,3,4,5,7,8,9,10],[2,3,4,5,7,8,10,14], [2,3,4,5,7,10,11,13],[2,3,4,5,7,10,11,14], [2,3,4,5,7,11,13,14],[2,3,4,5,8,9,10,11], [2,3,4,5,8,10,11,14],[2,3,4,5,9,10,11,12], [2,3,4,5,10,11,12,13],[2,3,4,5,11,12,13,14], [2,3,4,6,7,9,10,13],[2,3,4,7,10,11,13,14], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,14], [2,3,5,6,7,10,13,14],[2,3,5,6,8,9,10,13], [2,3,5,6,8,9,11,13],[2,3,5,6,8,9,11,14], [2,3,5,6,8,9,12,14],[2,3,5,6,8,10,13,14], [2,3,5,6,8,11,13,14],[2,3,5,6,9,10,12,13], [2,3,5,6,9,11,13,14],[2,3,5,6,9,12,13,14], [2,3,5,7,10,11,13,14],[2,3,5,8,9,10,11,13], [2,3,5,8,10,11,13,14],[2,3,5,9,10,11,12,13], [2,3,5,9,11,12,13,14],[2,3,6,7,8,9,10,14], [2,3,6,7,9,10,13,14],[2,3,6,8,9,10,11,13], [2,3,6,8,9,10,11,14],[2,3,6,8,10,11,13,14], [2,3,6,9,10,11,13,14],[2,3,9,10,11,12,13,14], [2,4,5,6,7,9,10,12],[2,4,5,6,7,9,12,13], [2,4,5,6,7,10,12,13],[2,4,5,7,8,9,10,12], [2,4,5,7,8,10,11,13],[2,4,5,7,8,10,11,14], [2,4,5,8,9,10,11,12],[2,4,5,8,10,11,12,13], [2,4,6,7,9,10,12,13],[2,4,7,8,10,11,13,14], [2,5,6,7,8,9,10,13],[2,5,6,7,8,10,13,14], [2,5,6,7,9,10,12,13],[2,5,6,8,9,11,12,13], [2,5,6,8,9,11,12,14],[2,5,6,8,11,12,13,14], [2,5,6,9,11,12,13,14],[2,5,7,8,10,11,13,14], [2,5,8,9,10,11,12,13],[2,6,7,8,9,10,13,14], [2,6,8,9,10,11,13,14],[2,6,8,9,11,12,13,14], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,14],[3,4,5,6,7,10,11,13], [3,4,5,6,7,11,13,14],[3,4,5,6,8,9,10,11], [3,4,5,6,8,11,12,14],[3,4,5,6,9,10,11,12], [3,4,5,6,10,11,12,13],[3,4,5,6,11,12,13,14], [3,4,5,7,8,10,11,14],[3,4,6,7,8,9,10,11], [3,4,6,7,9,10,11,14],[3,4,6,7,9,10,12,14], [3,4,6,7,10,11,13,14],[3,4,6,9,10,11,12,14], [3,4,6,10,11,12,13,14],[3,4,7,9,10,11,12,14], [3,5,6,7,8,10,11,13],[3,5,6,7,8,10,13,14], [3,5,6,7,8,11,13,14],[3,5,6,8,9,10,11,13], [3,5,6,8,9,11,12,14],[3,5,6,9,10,11,12,13], [3,5,6,9,11,12,13,14],[3,5,7,8,10,11,13,14], [3,6,7,8,9,10,11,14],[3,6,7,8,10,11,13,14], [3,6,7,9,10,12,13,14],[3,6,9,10,11,12,13,14], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,8,11,12,14],[4,5,6,7,9,10,11,12], [4,5,6,7,10,11,12,13],[4,5,6,7,11,12,13,14], [4,5,7,8,9,10,11,12],[4,6,7,8,9,11,12,14], [4,6,7,9,10,11,12,14],[4,6,7,10,11,12,13,14], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,10,11,12,13],[5,6,7,8,11,12,13,14], [5,6,8,9,10,11,12,13],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,11,12,13,14], [6,7,9,10,11,12,13,14],[7,8,9,10,11,12,13,14]] manifold_7_15_29_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,10],[1,2,3,4,5,6,10,12], [1,2,3,4,5,6,12,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,9],[1,2,3,4,5,7,9,15], [1,2,3,4,5,8,9,10],[1,2,3,4,5,9,10,12], [1,2,3,4,5,9,11,12],[1,2,3,4,5,9,11,15], [1,2,3,4,5,11,12,13],[1,2,3,4,5,11,13,15], [1,2,3,4,5,12,13,14],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,15],[1,2,3,4,6,8,10,14], [1,2,3,4,6,8,14,15],[1,2,3,4,6,10,12,14], [1,2,3,4,7,8,9,15],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,15],[1,2,3,4,8,10,11,15], [1,2,3,4,8,10,14,15],[1,2,3,4,9,10,11,12], [1,2,3,4,10,11,12,15],[1,2,3,4,10,12,14,15], [1,2,3,4,11,12,13,15],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,9],[1,2,3,5,6,7,9,14], [1,2,3,5,6,7,14,15],[1,2,3,5,6,8,9,10], [1,2,3,5,6,9,10,14],[1,2,3,5,6,10,12,14], [1,2,3,5,7,9,13,14],[1,2,3,5,7,9,13,15], [1,2,3,5,7,13,14,15],[1,2,3,5,9,10,12,13], [1,2,3,5,9,10,13,14],[1,2,3,5,9,11,12,13], [1,2,3,5,9,11,13,15],[1,2,3,5,10,12,13,14], [1,2,3,6,7,8,9,10],[1,2,3,6,7,8,10,14], [1,2,3,6,7,8,14,15],[1,2,3,6,7,9,10,14], [1,2,3,7,8,9,10,15],[1,2,3,7,8,10,14,15], [1,2,3,7,9,10,14,15],[1,2,3,7,9,13,14,15], [1,2,3,8,9,10,11,15],[1,2,3,9,10,11,12,13], [1,2,3,9,10,11,13,14],[1,2,3,9,10,11,14,15], [1,2,3,9,11,13,14,15],[1,2,3,10,11,12,13,14], [1,2,3,10,11,12,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,15],[1,2,4,5,6,8,10,12], [1,2,4,5,6,8,12,13],[1,2,4,5,6,8,13,15], [1,2,4,5,6,12,13,14],[1,2,4,5,6,13,14,15], [1,2,4,5,7,8,9,15],[1,2,4,5,8,9,10,12], [1,2,4,5,8,9,12,13],[1,2,4,5,8,9,13,15], [1,2,4,5,9,11,12,13],[1,2,4,5,9,11,13,15], [1,2,4,6,8,10,12,14],[1,2,4,6,8,12,13,15], [1,2,4,6,8,12,14,15],[1,2,4,6,12,13,14,15], [1,2,4,8,9,10,11,12],[1,2,4,8,9,11,12,15], [1,2,4,8,9,12,13,15],[1,2,4,8,10,11,12,15], [1,2,4,8,10,12,14,15],[1,2,4,9,11,12,13,15], [1,2,5,6,7,8,9,15],[1,2,5,6,7,9,13,14], [1,2,5,6,7,9,13,15],[1,2,5,6,7,13,14,15], [1,2,5,6,8,9,10,12],[1,2,5,6,8,9,12,13], [1,2,5,6,8,9,13,15],[1,2,5,6,9,10,12,13], [1,2,5,6,9,10,13,14],[1,2,5,6,10,12,13,14], [1,2,6,7,8,9,10,14],[1,2,6,7,8,9,14,15], [1,2,6,7,9,13,14,15],[1,2,6,8,9,10,12,13], [1,2,6,8,9,10,13,14],[1,2,6,8,9,13,14,15], [1,2,6,8,10,12,13,14],[1,2,6,8,12,13,14,15], [1,2,7,8,9,10,14,15],[1,2,8,9,10,11,12,15], [1,2,8,9,10,12,13,15],[1,2,8,9,10,13,14,15], [1,2,8,10,12,13,14,15],[1,2,9,10,11,12,13,15], [1,2,9,10,11,13,14,15],[1,2,10,11,12,13,14,15], [1,3,4,5,6,7,8,14],[1,3,4,5,6,7,14,15], [1,3,4,5,6,8,10,12],[1,3,4,5,6,8,12,14], [1,3,4,5,7,8,9,11],[1,3,4,5,7,8,11,12], [1,3,4,5,7,8,12,14],[1,3,4,5,7,9,11,15], [1,3,4,5,7,11,12,15],[1,3,4,5,7,12,14,15], [1,3,4,5,8,9,10,12],[1,3,4,5,8,9,11,12], [1,3,4,5,11,12,13,15],[1,3,4,5,12,13,14,15], [1,3,4,6,7,8,14,15],[1,3,4,6,8,10,12,14], [1,3,4,7,8,9,11,15],[1,3,4,7,8,11,12,15], [1,3,4,7,8,12,14,15],[1,3,4,8,9,10,11,12], [1,3,4,8,10,11,12,15],[1,3,4,8,10,12,14,15], [1,3,5,6,7,8,9,10],[1,3,5,6,7,8,10,14], [1,3,5,6,7,9,10,14],[1,3,5,6,8,10,12,14], [1,3,5,7,8,9,10,12],[1,3,5,7,8,9,11,12], [1,3,5,7,8,10,12,14],[1,3,5,7,9,10,12,14], [1,3,5,7,9,11,12,14],[1,3,5,7,9,11,13,14], [1,3,5,7,9,11,13,15],[1,3,5,7,11,12,14,15], [1,3,5,7,11,13,14,15],[1,3,5,9,10,12,13,14], [1,3,5,9,11,12,13,14],[1,3,5,11,12,13,14,15], [1,3,7,8,9,10,11,12],[1,3,7,8,9,10,11,15], [1,3,7,8,10,11,12,14],[1,3,7,8,10,11,14,15], [1,3,7,8,11,12,14,15],[1,3,7,9,10,11,12,14], [1,3,7,9,10,11,14,15],[1,3,7,9,11,13,14,15], [1,3,8,10,11,12,14,15],[1,3,9,10,11,12,13,14], [1,4,5,6,7,8,14,15],[1,4,5,6,8,12,13,15], [1,4,5,6,8,12,14,15],[1,4,5,6,12,13,14,15], [1,4,5,7,8,9,11,15],[1,4,5,7,8,11,12,15], [1,4,5,7,8,12,14,15],[1,4,5,8,9,11,12,15], [1,4,5,8,9,12,13,15],[1,4,5,9,11,12,13,15], [1,5,6,7,8,9,10,14],[1,5,6,7,8,9,13,14], [1,5,6,7,8,9,13,15],[1,5,6,7,8,13,14,15], [1,5,6,8,9,10,12,14],[1,5,6,8,9,12,13,14], [1,5,6,8,12,13,14,15],[1,5,6,9,10,12,13,14], [1,5,7,8,9,10,12,14],[1,5,7,8,9,11,12,15], [1,5,7,8,9,12,13,14],[1,5,7,8,9,12,13,15], [1,5,7,8,12,13,14,15],[1,5,7,9,11,12,13,14], [1,5,7,9,11,12,13,15],[1,5,7,11,12,13,14,15], [1,6,7,8,9,13,14,15],[1,6,8,9,10,12,13,14], [1,7,8,9,10,11,12,14],[1,7,8,9,10,11,14,15], [1,7,8,9,11,12,14,15],[1,7,8,9,12,13,14,15], [1,7,9,11,12,13,14,15],[1,8,9,10,11,12,14,15], [1,8,9,10,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,11], [2,3,4,5,6,7,11,13],[2,3,4,5,6,7,13,15], [2,3,4,5,6,8,9,10],[2,3,4,5,6,9,10,11], [2,3,4,5,6,10,11,13],[2,3,4,5,6,10,12,13], [2,3,4,5,6,12,13,14],[2,3,4,5,6,13,14,15], [2,3,4,5,7,9,11,15],[2,3,4,5,7,11,13,15], [2,3,4,5,9,10,11,12],[2,3,4,5,10,11,12,13], [2,3,4,6,7,8,9,10],[2,3,4,6,7,8,10,15], [2,3,4,6,7,9,10,11],[2,3,4,6,7,10,11,15], [2,3,4,6,7,11,13,15],[2,3,4,6,8,10,14,15], [2,3,4,6,10,11,13,14],[2,3,4,6,10,11,14,15], [2,3,4,6,10,12,13,14],[2,3,4,6,11,13,14,15], [2,3,4,7,8,9,10,11],[2,3,4,7,8,9,11,15], [2,3,4,7,8,10,11,15],[2,3,4,10,11,12,13,14], [2,3,4,10,11,12,14,15],[2,3,4,11,12,13,14,15], [2,3,5,6,7,9,11,13],[2,3,5,6,7,9,13,14], [2,3,5,6,7,13,14,15],[2,3,5,6,9,10,11,13], [2,3,5,6,9,10,13,14],[2,3,5,6,10,12,13,14], [2,3,5,7,9,11,13,15],[2,3,5,9,10,11,12,13], [2,3,6,7,8,10,14,15],[2,3,6,7,9,10,11,13], [2,3,6,7,9,10,13,14],[2,3,6,7,10,11,13,14], [2,3,6,7,10,11,14,15],[2,3,6,7,11,13,14,15], [2,3,7,8,9,10,11,15],[2,3,7,9,10,11,13,14], [2,3,7,9,10,11,14,15],[2,3,7,9,11,13,14,15], [2,4,5,6,7,8,9,15],[2,4,5,6,7,9,11,13], [2,4,5,6,7,9,13,15],[2,4,5,6,8,9,10,12], [2,4,5,6,8,9,12,13],[2,4,5,6,8,9,13,15], [2,4,5,6,9,10,11,13],[2,4,5,6,9,10,12,13], [2,4,5,7,9,11,13,15],[2,4,5,9,10,11,12,13], [2,4,6,7,8,9,10,11],[2,4,6,7,8,9,11,15], [2,4,6,7,8,10,11,15],[2,4,6,7,9,11,13,15], [2,4,6,8,9,10,11,13],[2,4,6,8,9,10,12,13], [2,4,6,8,9,11,13,15],[2,4,6,8,10,11,13,15], [2,4,6,8,10,12,13,15],[2,4,6,8,10,12,14,15], [2,4,6,10,11,13,14,15],[2,4,6,10,12,13,14,15], [2,4,8,9,10,11,12,13],[2,4,8,9,11,12,13,15], [2,4,8,10,11,12,13,15],[2,4,10,11,12,13,14,15], [2,6,7,8,9,10,11,15],[2,6,7,8,9,10,14,15], [2,6,7,9,10,11,13,15],[2,6,7,9,10,13,14,15], [2,6,7,10,11,13,14,15],[2,6,8,9,10,11,13,15], [2,6,8,9,10,13,14,15],[2,6,8,10,12,13,14,15], [2,7,9,10,11,13,14,15],[2,8,9,10,11,12,13,15], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,12], [3,4,5,6,7,8,12,14],[3,4,5,6,7,9,10,11], [3,4,5,6,7,10,11,12],[3,4,5,6,7,11,12,14], [3,4,5,6,7,11,13,14],[3,4,5,6,7,13,14,15], [3,4,5,6,10,11,12,13],[3,4,5,6,11,12,13,14], [3,4,5,7,8,9,10,11],[3,4,5,7,8,10,11,12], [3,4,5,7,11,12,14,15],[3,4,5,7,11,13,14,15], [3,4,5,8,9,10,11,12],[3,4,5,11,12,13,14,15], [3,4,6,7,8,10,12,14],[3,4,6,7,8,10,14,15], [3,4,6,7,10,11,12,14],[3,4,6,7,10,11,14,15], [3,4,6,7,11,13,14,15],[3,4,6,10,11,12,13,14], [3,4,7,8,10,11,12,14],[3,4,7,8,10,11,14,15], [3,4,7,8,11,12,14,15],[3,4,8,10,11,12,14,15], [3,5,6,7,8,10,12,14],[3,5,6,7,9,10,11,13], [3,5,6,7,9,10,13,14],[3,5,6,7,10,11,12,14], [3,5,6,7,10,11,13,14],[3,5,6,10,11,12,13,14], [3,5,7,8,9,10,11,12],[3,5,7,9,10,11,12,14], [3,5,7,9,10,11,13,14],[3,5,9,10,11,12,13,14], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,13], [4,5,6,7,8,9,13,15],[4,5,6,7,8,10,11,12], [4,5,6,7,8,11,12,13],[4,5,6,7,8,12,13,15], [4,5,6,7,8,12,14,15],[4,5,6,7,11,12,13,14], [4,5,6,7,12,13,14,15],[4,5,6,8,9,10,11,12], [4,5,6,8,9,11,12,13],[4,5,6,9,10,11,12,13], [4,5,7,8,9,11,13,15],[4,5,7,8,11,12,13,15], [4,5,7,11,12,13,14,15],[4,5,8,9,11,12,13,15], [4,6,7,8,9,11,13,15],[4,6,7,8,10,11,12,14], [4,6,7,8,10,11,14,15],[4,6,7,8,11,12,13,15], [4,6,7,8,11,12,14,15],[4,6,7,11,12,13,14,15], [4,6,8,9,10,11,12,13],[4,6,8,10,11,12,13,15], [4,6,8,10,11,12,14,15],[4,6,10,11,12,13,14,15], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,14], [5,6,7,8,9,11,12,13],[5,6,7,8,9,12,13,14], [5,6,7,8,12,13,14,15],[5,6,7,9,10,11,12,13], [5,6,7,9,10,12,13,14],[5,6,7,10,11,12,13,14], [5,7,8,9,11,12,13,15],[5,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,15], [6,7,8,9,10,12,13,14],[6,7,8,9,10,13,14,15], [6,7,8,10,11,12,13,14],[6,7,8,10,11,13,14,15], [6,7,8,11,12,13,14,15],[6,8,10,11,12,13,14,15], [7,8,9,10,11,12,13,14],[7,8,9,10,11,13,14,15], [7,8,9,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_8_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,15],[1,2,3,4,5,8,9,15], [1,2,3,4,5,9,10,12],[1,2,3,4,5,9,12,13], [1,2,3,4,5,9,13,15],[1,2,3,4,5,10,12,14], [1,2,3,4,5,12,13,14],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,14],[1,2,3,4,6,7,14,15], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,14], [1,2,3,4,7,8,14,15],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,15],[1,2,3,4,8,10,11,12], [1,2,3,4,8,10,12,14],[1,2,3,4,8,11,12,15], [1,2,3,4,8,12,14,15],[1,2,3,4,9,10,11,12], [1,2,3,4,9,11,12,13],[1,2,3,4,9,11,13,15], [1,2,3,4,11,12,13,15],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,9],[1,2,3,5,6,7,9,13], [1,2,3,5,6,7,13,15],[1,2,3,5,6,9,10,14], [1,2,3,5,6,9,13,14],[1,2,3,5,6,13,14,15], [1,2,3,5,7,8,9,15],[1,2,3,5,7,9,13,15], [1,2,3,5,9,10,12,14],[1,2,3,5,9,12,13,14], [1,2,3,6,7,8,9,14],[1,2,3,6,7,9,13,14], [1,2,3,6,7,13,14,15],[1,2,3,6,8,9,10,14], [1,2,3,7,8,9,10,14],[1,2,3,7,8,9,10,15], [1,2,3,7,8,10,14,15],[1,2,3,7,9,10,11,14], [1,2,3,7,9,10,11,15],[1,2,3,7,9,11,13,14], [1,2,3,7,9,11,13,15],[1,2,3,7,10,11,14,15], [1,2,3,7,11,13,14,15],[1,2,3,8,9,10,11,15], [1,2,3,8,10,11,12,15],[1,2,3,8,10,12,14,15], [1,2,3,9,10,11,12,14],[1,2,3,9,11,12,13,14], [1,2,3,10,11,12,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,15],[1,2,4,5,6,8,9,12], [1,2,4,5,6,8,12,15],[1,2,4,5,6,9,10,12], [1,2,4,5,6,10,12,14],[1,2,4,5,6,12,14,15], [1,2,4,5,8,9,12,13],[1,2,4,5,8,9,13,15], [1,2,4,5,8,12,13,15],[1,2,4,5,12,13,14,15], [1,2,4,6,7,8,14,15],[1,2,4,6,8,9,10,12], [1,2,4,6,8,10,12,14],[1,2,4,6,8,12,14,15], [1,2,4,8,9,10,11,12],[1,2,4,8,9,11,12,13], [1,2,4,8,9,11,13,15],[1,2,4,8,11,12,13,15], [1,2,5,6,7,8,9,13],[1,2,5,6,7,8,13,15], [1,2,5,6,8,9,12,13],[1,2,5,6,8,12,13,15], [1,2,5,6,9,10,12,13],[1,2,5,6,9,10,13,14], [1,2,5,6,10,12,13,14],[1,2,5,6,12,13,14,15], [1,2,5,7,8,9,13,15],[1,2,5,9,10,12,13,14], [1,2,6,7,8,9,13,15],[1,2,6,7,8,9,14,15], [1,2,6,7,9,13,14,15],[1,2,6,8,9,10,12,13], [1,2,6,8,9,10,13,15],[1,2,6,8,9,10,14,15], [1,2,6,8,10,12,13,15],[1,2,6,8,10,12,14,15], [1,2,6,9,10,13,14,15],[1,2,6,10,12,13,14,15], [1,2,7,8,9,10,14,15],[1,2,7,9,10,11,14,15], [1,2,7,9,11,13,14,15],[1,2,8,9,10,11,12,13], [1,2,8,9,10,11,13,15],[1,2,8,10,11,12,13,15], [1,2,9,10,11,12,13,14],[1,2,9,10,11,13,14,15], [1,2,10,11,12,13,14,15],[1,3,4,5,6,7,8,12], [1,3,4,5,6,7,12,14],[1,3,4,5,6,7,14,15], [1,3,4,5,6,8,9,10],[1,3,4,5,6,8,10,12], [1,3,4,5,6,10,12,14],[1,3,4,5,7,8,11,12], [1,3,4,5,7,8,11,15],[1,3,4,5,7,11,12,14], [1,3,4,5,7,11,14,15],[1,3,4,5,8,9,10,11], [1,3,4,5,8,9,11,15],[1,3,4,5,8,10,11,12], [1,3,4,5,9,10,11,12],[1,3,4,5,9,11,12,13], [1,3,4,5,9,11,13,15],[1,3,4,5,11,12,13,14], [1,3,4,5,11,13,14,15],[1,3,4,6,7,8,12,14], [1,3,4,6,8,10,12,14],[1,3,4,7,8,11,12,15], [1,3,4,7,8,12,14,15],[1,3,4,7,11,12,14,15], [1,3,4,11,12,13,14,15],[1,3,5,6,7,8,9,14], [1,3,5,6,7,8,12,14],[1,3,5,6,7,9,13,14], [1,3,5,6,7,13,14,15],[1,3,5,6,8,9,10,14], [1,3,5,6,8,10,12,14],[1,3,5,7,8,9,10,11], [1,3,5,7,8,9,10,14],[1,3,5,7,8,9,11,15], [1,3,5,7,8,10,11,12],[1,3,5,7,8,10,12,14], [1,3,5,7,9,10,11,12],[1,3,5,7,9,10,12,14], [1,3,5,7,9,11,12,14],[1,3,5,7,9,11,13,14], [1,3,5,7,9,11,13,15],[1,3,5,7,11,13,14,15], [1,3,5,9,11,12,13,14],[1,3,7,8,9,10,11,15], [1,3,7,8,10,11,12,15],[1,3,7,8,10,12,14,15], [1,3,7,9,10,11,12,14],[1,3,7,10,11,12,14,15], [1,4,5,6,7,8,12,15],[1,4,5,6,7,12,14,15], [1,4,5,6,8,9,10,12],[1,4,5,7,8,11,12,15], [1,4,5,7,11,12,14,15],[1,4,5,8,9,10,11,12], [1,4,5,8,9,11,12,15],[1,4,5,8,9,12,13,15], [1,4,5,9,11,12,13,15],[1,4,5,11,12,13,14,15], [1,4,6,7,8,12,14,15],[1,4,8,9,11,12,13,15], [1,5,6,7,8,9,13,14],[1,5,6,7,8,12,14,15], [1,5,6,7,8,13,14,15],[1,5,6,8,9,10,12,13], [1,5,6,8,9,10,13,14],[1,5,6,8,10,12,13,14], [1,5,6,8,12,13,14,15],[1,5,7,8,9,10,11,12], [1,5,7,8,9,10,12,14],[1,5,7,8,9,11,12,15], [1,5,7,8,9,12,14,15],[1,5,7,8,9,13,14,15], [1,5,7,9,11,12,14,15],[1,5,7,9,11,13,14,15], [1,5,8,9,10,12,13,14],[1,5,8,9,12,13,14,15], [1,5,9,11,12,13,14,15],[1,6,7,8,9,13,14,15], [1,6,8,9,10,13,14,15],[1,6,8,10,12,13,14,15], [1,7,8,9,10,11,12,15],[1,7,8,9,10,12,14,15], [1,7,9,10,11,12,14,15],[1,8,9,10,11,12,13,15], [1,8,9,10,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,15], [2,3,4,5,6,10,11,13],[2,3,4,5,6,10,13,14], [2,3,4,5,6,11,13,15],[2,3,4,5,6,13,14,15], [2,3,4,5,7,8,9,15],[2,3,4,5,7,9,10,11], [2,3,4,5,7,9,11,15],[2,3,4,5,9,10,11,12], [2,3,4,5,9,11,12,13],[2,3,4,5,9,11,13,15], [2,3,4,5,10,11,12,13],[2,3,4,5,10,12,13,14], [2,3,4,6,7,8,9,10],[2,3,4,6,7,8,10,14], [2,3,4,6,7,10,11,15],[2,3,4,6,7,10,14,15], [2,3,4,6,10,11,13,15],[2,3,4,6,10,13,14,15], [2,3,4,7,8,9,10,15],[2,3,4,7,8,10,14,15], [2,3,4,7,9,10,11,15],[2,3,4,8,9,10,11,15], [2,3,4,8,10,11,12,15],[2,3,4,8,10,12,14,15], [2,3,4,10,11,12,13,15],[2,3,4,10,12,13,14,15], [2,3,5,6,7,9,10,13],[2,3,5,6,7,10,11,13], [2,3,5,6,7,11,13,15],[2,3,5,6,9,10,13,14], [2,3,5,7,9,10,11,13],[2,3,5,7,9,11,13,15], [2,3,5,9,10,11,12,13],[2,3,5,9,10,12,13,14], [2,3,6,7,8,9,10,14],[2,3,6,7,9,10,13,14], [2,3,6,7,10,11,13,14],[2,3,6,7,10,11,14,15], [2,3,6,7,11,13,14,15],[2,3,6,10,11,13,14,15], [2,3,7,9,10,11,13,14],[2,3,9,10,11,12,13,14], [2,3,10,11,12,13,14,15],[2,4,5,6,7,8,9,13], [2,4,5,6,7,8,13,15],[2,4,5,6,7,9,10,11], [2,4,5,6,7,9,11,13],[2,4,5,6,7,11,13,15], [2,4,5,6,8,9,12,13],[2,4,5,6,8,12,13,15], [2,4,5,6,9,10,11,12],[2,4,5,6,9,11,12,13], [2,4,5,6,10,11,12,13],[2,4,5,6,10,12,13,14], [2,4,5,6,12,13,14,15],[2,4,5,7,8,9,13,15], [2,4,5,7,9,11,13,15],[2,4,6,7,8,9,10,15], [2,4,6,7,8,9,13,15],[2,4,6,7,8,10,14,15], [2,4,6,7,9,10,11,15],[2,4,6,7,9,11,13,15], [2,4,6,8,9,10,11,12],[2,4,6,8,9,10,11,15], [2,4,6,8,9,11,12,13],[2,4,6,8,9,11,13,15], [2,4,6,8,10,11,12,13],[2,4,6,8,10,11,13,15], [2,4,6,8,10,12,13,15],[2,4,6,8,10,12,14,15], [2,4,6,10,12,13,14,15],[2,4,8,10,11,12,13,15], [2,5,6,7,9,10,11,13],[2,5,6,9,10,11,12,13], [2,6,7,8,9,10,14,15],[2,6,7,9,10,11,13,14], [2,6,7,9,10,11,14,15],[2,6,7,9,11,13,14,15], [2,6,8,9,10,11,12,13],[2,6,8,9,10,11,13,15], [2,6,9,10,11,13,14,15],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,12], [3,4,5,6,7,11,12,14],[3,4,5,6,7,11,14,15], [3,4,5,6,8,10,11,12],[3,4,5,6,10,11,12,13], [3,4,5,6,10,12,13,14],[3,4,5,6,11,12,13,14], [3,4,5,6,11,13,14,15],[3,4,5,7,8,9,10,11], [3,4,5,7,8,9,11,15],[3,4,6,7,8,10,11,14], [3,4,6,7,8,11,12,14],[3,4,6,7,10,11,14,15], [3,4,6,8,10,11,12,14],[3,4,6,10,11,12,13,14], [3,4,6,10,11,13,14,15],[3,4,7,8,9,10,11,15], [3,4,7,8,10,11,14,15],[3,4,7,8,11,12,14,15], [3,4,8,10,11,12,14,15],[3,4,10,11,12,13,14,15], [3,5,6,7,8,9,10,14],[3,5,6,7,8,10,11,12], [3,5,6,7,8,10,12,14],[3,5,6,7,9,10,13,14], [3,5,6,7,10,11,12,13],[3,5,6,7,10,12,13,14], [3,5,6,7,11,12,13,14],[3,5,6,7,11,13,14,15], [3,5,7,9,10,11,12,13],[3,5,7,9,10,12,13,14], [3,5,7,9,11,12,13,14],[3,6,7,8,10,11,12,14], [3,6,7,10,11,12,13,14],[3,7,8,10,11,12,14,15], [3,7,9,10,11,12,13,14],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,8,12,13,15],[4,5,6,7,9,11,12,13], [4,5,6,7,11,12,13,14],[4,5,6,7,11,13,14,15], [4,5,6,7,12,13,14,15],[4,5,6,8,9,10,11,12], [4,5,7,8,9,11,12,15],[4,5,7,8,9,12,13,15], [4,5,7,9,11,12,13,15],[4,5,7,11,12,13,14,15], [4,6,7,8,9,10,11,15],[4,6,7,8,9,11,12,13], [4,6,7,8,9,11,13,15],[4,6,7,8,10,11,14,15], [4,6,7,8,11,12,13,14],[4,6,7,8,11,13,14,15], [4,6,7,8,12,13,14,15],[4,6,8,10,11,12,13,14], [4,6,8,10,11,13,14,15],[4,6,8,10,12,13,14,15], [4,7,8,9,11,12,13,15],[4,7,8,11,12,13,14,15], [4,8,10,11,12,13,14,15],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,9,10,13,14], [5,6,7,8,10,12,13,14],[5,6,7,8,12,13,14,15], [5,6,7,9,10,11,12,13],[5,7,8,9,10,12,13,14], [5,7,8,9,12,13,14,15],[5,7,9,11,12,13,14,15], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,14], [6,7,8,9,10,11,14,15],[6,7,8,9,11,13,14,15], [6,7,8,10,11,12,13,14],[6,8,9,10,11,13,14,15], [7,8,9,10,11,12,13,14],[7,8,9,10,11,12,14,15], [7,8,9,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_6_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,12], [1,2,3,4,5,6,12,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,15],[1,2,3,4,5,8,9,11], [1,2,3,4,5,8,11,15],[1,2,3,4,5,9,11,12], [1,2,3,4,5,11,12,13],[1,2,3,4,5,11,13,15], [1,2,3,4,5,12,13,14],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,10],[1,2,3,4,6,7,10,14], [1,2,3,4,6,7,14,15],[1,2,3,4,6,8,9,12], [1,2,3,4,6,8,10,12],[1,2,3,4,6,10,12,14], [1,2,3,4,7,8,10,15],[1,2,3,4,7,10,14,15], [1,2,3,4,8,9,10,11],[1,2,3,4,8,9,10,12], [1,2,3,4,8,10,11,15],[1,2,3,4,9,10,11,12], [1,2,3,4,10,11,12,15],[1,2,3,4,10,12,14,15], [1,2,3,4,11,12,13,15],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,9],[1,2,3,5,6,7,9,15], [1,2,3,5,6,9,10,12],[1,2,3,5,6,9,10,14], [1,2,3,5,6,9,13,14],[1,2,3,5,6,9,13,15], [1,2,3,5,6,10,12,14],[1,2,3,5,6,13,14,15], [1,2,3,5,7,8,9,11],[1,2,3,5,7,8,11,15], [1,2,3,5,7,9,11,15],[1,2,3,5,9,10,11,12], [1,2,3,5,9,10,11,14],[1,2,3,5,9,11,13,14], [1,2,3,5,9,11,13,15],[1,2,3,5,10,11,12,14], [1,2,3,5,11,12,13,14],[1,2,3,6,7,8,9,10], [1,2,3,6,7,9,10,14],[1,2,3,6,7,9,14,15], [1,2,3,6,8,9,10,12],[1,2,3,6,9,13,14,15], [1,2,3,7,8,9,10,15],[1,2,3,7,8,9,11,15], [1,2,3,7,9,10,14,15],[1,2,3,8,9,10,11,15], [1,2,3,9,10,11,14,15],[1,2,3,9,11,13,14,15], [1,2,3,10,11,12,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,15],[1,2,4,5,6,8,9,12], [1,2,4,5,6,8,12,14],[1,2,4,5,6,8,14,15], [1,2,4,5,8,9,11,15],[1,2,4,5,8,9,12,13], [1,2,4,5,8,9,13,15],[1,2,4,5,8,12,13,15], [1,2,4,5,8,12,14,15],[1,2,4,5,9,11,12,13], [1,2,4,5,9,11,13,15],[1,2,4,5,12,13,14,15], [1,2,4,6,7,8,10,15],[1,2,4,6,7,10,14,15], [1,2,4,6,8,10,12,14],[1,2,4,6,8,10,14,15], [1,2,4,8,9,10,11,15],[1,2,4,8,9,10,12,13], [1,2,4,8,9,10,13,15],[1,2,4,8,10,12,13,15], [1,2,4,8,10,12,14,15],[1,2,4,9,10,11,12,13], [1,2,4,9,10,11,13,15],[1,2,4,10,11,12,13,15], [1,2,5,6,7,8,9,15],[1,2,5,6,8,9,12,13], [1,2,5,6,8,9,13,15],[1,2,5,6,8,12,13,14], [1,2,5,6,8,13,14,15],[1,2,5,6,9,10,12,13], [1,2,5,6,9,10,13,14],[1,2,5,6,10,12,13,14], [1,2,5,7,8,9,11,15],[1,2,5,8,12,13,14,15], [1,2,5,9,10,11,12,14],[1,2,5,9,10,12,13,14], [1,2,5,9,11,12,13,14],[1,2,6,7,8,9,10,14], [1,2,6,7,8,9,14,15],[1,2,6,7,8,10,14,15], [1,2,6,8,9,10,12,13],[1,2,6,8,9,10,13,14], [1,2,6,8,9,13,14,15],[1,2,6,8,10,12,13,14], [1,2,7,8,9,10,14,15],[1,2,8,9,10,13,14,15], [1,2,8,10,12,13,14,15],[1,2,9,10,11,12,13,14], [1,2,9,10,11,13,14,15],[1,2,10,11,12,13,14,15], [1,3,4,5,6,7,8,14],[1,3,4,5,6,7,14,15], [1,3,4,5,6,8,9,12],[1,3,4,5,6,8,12,14], [1,3,4,5,7,8,11,12],[1,3,4,5,7,8,11,15], [1,3,4,5,7,8,12,14],[1,3,4,5,7,11,12,13], [1,3,4,5,7,11,13,15],[1,3,4,5,7,12,13,14], [1,3,4,5,7,13,14,15],[1,3,4,5,8,9,11,12], [1,3,4,6,7,8,10,14],[1,3,4,6,8,10,12,14], [1,3,4,7,8,10,14,15],[1,3,4,7,8,11,12,15], [1,3,4,7,8,12,14,15],[1,3,4,7,11,12,13,14], [1,3,4,7,11,12,14,15],[1,3,4,7,11,13,14,15], [1,3,4,8,9,10,11,12],[1,3,4,8,10,11,12,15], [1,3,4,8,10,12,14,15],[1,3,4,11,12,13,14,15], [1,3,5,6,7,8,9,10],[1,3,5,6,7,8,10,14], [1,3,5,6,7,9,10,14],[1,3,5,6,7,9,14,15], [1,3,5,6,8,9,10,12],[1,3,5,6,8,10,12,14], [1,3,5,6,9,13,14,15],[1,3,5,7,8,9,10,12], [1,3,5,7,8,9,11,12],[1,3,5,7,8,10,12,14], [1,3,5,7,9,10,12,14],[1,3,5,7,9,11,12,14], [1,3,5,7,9,11,13,14],[1,3,5,7,9,11,13,15], [1,3,5,7,9,13,14,15],[1,3,5,7,11,12,13,14], [1,3,5,9,10,11,12,14],[1,3,7,8,9,10,12,14], [1,3,7,8,9,10,14,15],[1,3,7,8,9,11,12,15], [1,3,7,8,9,12,14,15],[1,3,7,9,11,12,14,15], [1,3,7,9,11,13,14,15],[1,3,8,9,10,11,12,15], [1,3,8,9,10,12,14,15],[1,3,9,10,11,12,14,15], [1,4,5,6,7,8,14,15],[1,4,5,7,8,11,12,15], [1,4,5,7,8,12,14,15],[1,4,5,7,11,12,13,15], [1,4,5,7,12,13,14,15],[1,4,5,8,9,11,12,15], [1,4,5,8,9,12,13,15],[1,4,5,9,11,12,13,15], [1,4,6,7,8,10,14,15],[1,4,7,11,12,13,14,15], [1,4,8,9,10,11,12,13],[1,4,8,9,10,11,13,15], [1,4,8,9,11,12,13,15],[1,4,8,10,11,12,13,15], [1,5,6,7,8,9,10,13],[1,5,6,7,8,9,13,15], [1,5,6,7,8,10,12,13],[1,5,6,7,8,10,12,14], [1,5,6,7,8,12,13,14],[1,5,6,7,8,13,14,15], [1,5,6,7,9,10,13,14],[1,5,6,7,9,13,14,15], [1,5,6,7,10,12,13,14],[1,5,6,8,9,10,12,13], [1,5,7,8,9,10,12,13],[1,5,7,8,9,11,12,15], [1,5,7,8,9,12,13,15],[1,5,7,8,12,13,14,15], [1,5,7,9,10,12,13,14],[1,5,7,9,11,12,13,14], [1,5,7,9,11,12,13,15],[1,6,7,8,9,10,13,14], [1,6,7,8,9,13,14,15],[1,6,7,8,10,12,13,14], [1,7,8,9,10,12,13,14],[1,7,8,9,12,13,14,15], [1,7,9,11,12,13,14,15],[1,8,9,10,11,12,13,15], [1,8,9,10,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,13],[2,3,4,5,6,7,13,15], [2,3,4,5,6,9,10,12],[2,3,4,5,6,10,12,13], [2,3,4,5,6,12,13,14],[2,3,4,5,6,13,14,15], [2,3,4,5,7,8,9,11],[2,3,4,5,7,8,11,15], [2,3,4,5,7,9,10,13],[2,3,4,5,7,9,11,13], [2,3,4,5,7,11,13,15],[2,3,4,5,9,10,11,12], [2,3,4,5,9,10,11,13],[2,3,4,5,10,11,12,13], [2,3,4,6,7,8,9,10],[2,3,4,6,7,10,11,13], [2,3,4,6,7,10,11,15],[2,3,4,6,7,10,14,15], [2,3,4,6,7,11,13,15],[2,3,4,6,8,9,10,12], [2,3,4,6,10,11,12,13],[2,3,4,6,10,11,12,15], [2,3,4,6,10,12,14,15],[2,3,4,6,11,12,13,15], [2,3,4,6,12,13,14,15],[2,3,4,7,8,9,10,11], [2,3,4,7,8,10,11,15],[2,3,4,7,9,10,11,13], [2,3,5,6,7,9,10,13],[2,3,5,6,7,9,13,15], [2,3,5,6,9,10,13,14],[2,3,5,6,10,12,13,14], [2,3,5,7,9,11,13,15],[2,3,5,9,10,11,13,14], [2,3,5,10,11,12,13,14],[2,3,6,7,9,10,13,14], [2,3,6,7,9,13,14,15],[2,3,6,7,10,11,13,14], [2,3,6,7,10,11,14,15],[2,3,6,7,11,13,14,15], [2,3,6,10,11,12,13,15],[2,3,6,10,11,13,14,15], [2,3,6,10,12,13,14,15],[2,3,7,8,9,10,11,15], [2,3,7,9,10,11,13,14],[2,3,7,9,10,11,14,15], [2,3,7,9,11,13,14,15],[2,3,10,11,12,13,14,15], [2,4,5,6,7,8,9,15],[2,4,5,6,7,9,10,13], [2,4,5,6,7,9,13,15],[2,4,5,6,8,9,12,13], [2,4,5,6,8,9,13,15],[2,4,5,6,8,12,13,14], [2,4,5,6,8,13,14,15],[2,4,5,6,9,10,12,13], [2,4,5,7,8,9,11,15],[2,4,5,7,9,11,13,15], [2,4,5,8,12,13,14,15],[2,4,5,9,10,11,12,13], [2,4,6,7,8,9,10,11],[2,4,6,7,8,9,11,15], [2,4,6,7,8,10,11,15],[2,4,6,7,9,10,11,13], [2,4,6,7,9,11,13,15],[2,4,6,8,9,10,11,13], [2,4,6,8,9,10,12,13],[2,4,6,8,9,11,13,15], [2,4,6,8,10,11,13,15],[2,4,6,8,10,12,13,15], [2,4,6,8,10,12,14,15],[2,4,6,8,12,13,14,15], [2,4,6,10,11,12,13,15],[2,4,8,9,10,11,13,15], [2,5,9,10,11,12,13,14],[2,6,7,8,9,10,11,14], [2,6,7,8,9,11,13,14],[2,6,7,8,9,11,13,15], [2,6,7,8,9,13,14,15],[2,6,7,8,10,11,14,15], [2,6,7,8,11,13,14,15],[2,6,7,9,10,11,13,14], [2,6,8,9,10,11,13,14],[2,6,8,10,11,13,14,15], [2,6,8,10,12,13,14,15],[2,7,8,9,10,11,14,15], [2,7,8,9,11,13,14,15],[2,8,9,10,11,13,14,15], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,14],[3,4,5,6,7,10,11,13], [3,4,5,6,7,11,13,14],[3,4,5,6,7,13,14,15], [3,4,5,6,8,9,10,12],[3,4,5,6,8,10,11,14], [3,4,5,6,8,10,12,14],[3,4,5,6,10,11,12,13], [3,4,5,6,10,11,12,14],[3,4,5,6,11,12,13,14], [3,4,5,7,8,9,10,11],[3,4,5,7,8,11,12,14], [3,4,5,7,9,10,11,13],[3,4,5,7,11,12,13,14], [3,4,5,8,9,10,11,12],[3,4,5,8,10,11,12,14], [3,4,6,7,8,10,11,14],[3,4,6,7,10,11,14,15], [3,4,6,7,11,13,14,15],[3,4,6,10,11,12,14,15], [3,4,6,11,12,13,14,15],[3,4,7,8,10,11,14,15], [3,4,7,8,11,12,14,15],[3,4,8,10,11,12,14,15], [3,5,6,7,8,10,11,14],[3,5,6,7,9,10,13,14], [3,5,6,7,9,13,14,15],[3,5,6,7,10,11,13,14], [3,5,6,10,11,12,13,14],[3,5,7,8,9,10,11,12], [3,5,7,8,10,11,12,14],[3,5,7,9,10,11,12,14], [3,5,7,9,10,11,13,14],[3,6,10,11,12,13,14,15], [3,7,8,9,10,11,12,15],[3,7,8,9,10,12,14,15], [3,7,8,10,11,12,14,15],[3,7,9,10,11,12,14,15], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,8,9,12,15],[4,5,6,7,8,11,12,14], [4,5,6,7,8,12,14,15],[4,5,6,7,9,10,11,13], [4,5,6,7,9,11,12,15],[4,5,6,7,9,11,13,15], [4,5,6,7,11,12,13,14],[4,5,6,7,11,12,13,15], [4,5,6,7,12,13,14,15],[4,5,6,8,9,10,11,12], [4,5,6,8,9,12,13,15],[4,5,6,8,10,11,12,14], [4,5,6,8,12,13,14,15],[4,5,6,9,10,11,12,13], [4,5,6,9,11,12,13,15],[4,5,7,8,9,11,12,15], [4,6,7,8,9,11,12,15],[4,6,7,8,10,11,14,15], [4,6,7,8,11,12,14,15],[4,6,7,11,12,13,14,15], [4,6,8,9,10,11,12,13],[4,6,8,9,11,12,13,15], [4,6,8,10,11,12,13,15],[4,6,8,10,11,12,14,15], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,12,13,15],[5,6,7,8,10,11,12,14], [5,6,7,8,12,13,14,15],[5,6,7,9,10,11,12,13], [5,6,7,9,11,12,13,15],[5,6,7,10,11,12,13,14], [5,7,9,10,11,12,13,14],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,11,12,13,15], [6,7,8,10,11,12,13,14],[6,7,8,11,12,13,14,15], [6,8,10,11,12,13,14,15],[7,8,9,10,11,12,13,14], [7,8,9,10,11,12,14,15],[7,8,9,11,12,13,14,15], [8,9,10,11,12,13,14,15]] manifold_7_15_6_2=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,10],[1,2,3,4,5,6,10,14], [1,2,3,4,5,6,14,15],[1,2,3,4,5,7,8,9], [1,2,3,4,5,7,9,15],[1,2,3,4,5,8,9,10], [1,2,3,4,5,9,10,12],[1,2,3,4,5,9,12,13], [1,2,3,4,5,9,13,15],[1,2,3,4,5,10,12,13], [1,2,3,4,5,10,13,14],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,15],[1,2,3,4,6,8,10,14], [1,2,3,4,6,8,14,15],[1,2,3,4,7,8,9,15], [1,2,3,4,8,9,10,11],[1,2,3,4,8,9,11,15], [1,2,3,4,8,10,11,14],[1,2,3,4,8,11,12,14], [1,2,3,4,8,11,12,15],[1,2,3,4,8,12,14,15], [1,2,3,4,9,10,11,12],[1,2,3,4,9,11,12,15], [1,2,3,4,9,12,13,15],[1,2,3,4,10,11,12,14], [1,2,3,4,10,12,13,14],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,14],[1,2,3,5,6,7,14,15], [1,2,3,5,6,8,10,14],[1,2,3,5,7,8,9,10], [1,2,3,5,7,8,10,14],[1,2,3,5,7,9,10,14], [1,2,3,5,7,9,13,14],[1,2,3,5,7,9,13,15], [1,2,3,5,7,13,14,15],[1,2,3,5,9,10,12,13], [1,2,3,5,9,10,13,14],[1,2,3,6,7,8,14,15], [1,2,3,7,8,9,10,15],[1,2,3,7,8,10,14,15], [1,2,3,7,9,10,13,14],[1,2,3,7,9,10,13,15], [1,2,3,7,10,11,13,14],[1,2,3,7,10,11,13,15], [1,2,3,7,10,11,14,15],[1,2,3,7,11,13,14,15], [1,2,3,8,9,10,11,15],[1,2,3,8,10,11,14,15], [1,2,3,8,11,12,14,15],[1,2,3,9,10,11,12,13], [1,2,3,9,10,11,13,15],[1,2,3,9,11,12,13,15], [1,2,3,10,11,12,13,14],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,13],[1,2,4,5,6,7,13,15], [1,2,4,5,6,8,10,12],[1,2,4,5,6,8,12,13], [1,2,4,5,6,10,12,13],[1,2,4,5,6,10,13,14], [1,2,4,5,6,13,14,15],[1,2,4,5,7,8,9,13], [1,2,4,5,7,9,13,15],[1,2,4,5,8,9,10,12], [1,2,4,5,8,9,12,13],[1,2,4,6,7,8,9,13], [1,2,4,6,7,8,9,15],[1,2,4,6,7,9,13,15], [1,2,4,6,8,9,13,15],[1,2,4,6,8,10,12,14], [1,2,4,6,8,12,13,15],[1,2,4,6,8,12,14,15], [1,2,4,6,10,12,13,14],[1,2,4,6,12,13,14,15], [1,2,4,8,9,10,11,12],[1,2,4,8,9,11,12,15], [1,2,4,8,9,12,13,15],[1,2,4,8,10,11,12,14], [1,2,5,6,7,8,9,13],[1,2,5,6,7,8,9,14], [1,2,5,6,7,9,13,14],[1,2,5,6,7,13,14,15], [1,2,5,6,8,9,10,12],[1,2,5,6,8,9,10,14], [1,2,5,6,8,9,12,13],[1,2,5,6,9,10,12,13], [1,2,5,6,9,10,13,14],[1,2,5,7,8,9,10,14], [1,2,6,7,8,9,14,15],[1,2,6,7,9,13,14,15], [1,2,6,8,9,10,12,14],[1,2,6,8,9,12,13,15], [1,2,6,8,9,12,14,15],[1,2,6,9,10,12,13,15], [1,2,6,9,10,12,14,15],[1,2,6,9,10,13,14,15], [1,2,6,10,12,13,14,15],[1,2,7,8,9,10,14,15], [1,2,7,9,10,13,14,15],[1,2,7,10,11,13,14,15], [1,2,8,9,10,11,12,15],[1,2,8,9,10,12,14,15], [1,2,8,10,11,12,14,15],[1,2,9,10,11,12,13,15], [1,2,10,11,12,13,14,15],[1,3,4,5,6,7,8,12], [1,3,4,5,6,7,12,15],[1,3,4,5,6,8,10,12], [1,3,4,5,6,10,12,13],[1,3,4,5,6,10,13,14], [1,3,4,5,6,12,13,14],[1,3,4,5,6,12,14,15], [1,3,4,5,7,8,9,10],[1,3,4,5,7,8,10,12], [1,3,4,5,7,9,10,12],[1,3,4,5,7,9,11,12], [1,3,4,5,7,9,11,15],[1,3,4,5,7,11,12,15], [1,3,4,5,9,11,12,15],[1,3,4,5,9,12,13,15], [1,3,4,5,12,13,14,15],[1,3,4,6,7,8,12,15], [1,3,4,6,8,10,12,14],[1,3,4,6,8,12,14,15], [1,3,4,6,10,12,13,14],[1,3,4,7,8,9,10,11], [1,3,4,7,8,9,11,15],[1,3,4,7,8,10,11,12], [1,3,4,7,8,11,12,15],[1,3,4,7,9,10,11,12], [1,3,4,8,10,11,12,14],[1,3,5,6,7,8,12,15], [1,3,5,6,7,8,14,15],[1,3,5,6,8,10,12,14], [1,3,5,6,8,12,14,15],[1,3,5,6,10,12,13,14], [1,3,5,7,8,10,12,14],[1,3,5,7,8,12,14,15], [1,3,5,7,9,10,12,14],[1,3,5,7,9,11,12,14], [1,3,5,7,9,11,13,14],[1,3,5,7,9,11,13,15], [1,3,5,7,11,12,14,15],[1,3,5,7,11,13,14,15], [1,3,5,9,10,12,13,14],[1,3,5,9,11,12,13,14], [1,3,5,9,11,12,13,15],[1,3,5,11,12,13,14,15], [1,3,7,8,9,10,11,15],[1,3,7,8,10,11,12,14], [1,3,7,8,10,11,14,15],[1,3,7,8,11,12,14,15], [1,3,7,9,10,11,12,14],[1,3,7,9,10,11,13,14], [1,3,7,9,10,11,13,15],[1,3,9,10,11,12,13,14], [1,4,5,6,7,8,12,15],[1,4,5,6,7,8,13,15], [1,4,5,6,8,12,13,15],[1,4,5,6,12,13,14,15], [1,4,5,7,8,9,10,11],[1,4,5,7,8,9,11,15], [1,4,5,7,8,9,13,15],[1,4,5,7,8,10,11,12], [1,4,5,7,8,11,12,15],[1,4,5,7,9,10,11,12], [1,4,5,8,9,10,11,12],[1,4,5,8,9,11,12,15], [1,4,5,8,9,12,13,15],[1,4,6,7,8,9,13,15], [1,5,6,7,8,9,13,14],[1,5,6,7,8,13,14,15], [1,5,6,8,9,10,12,14],[1,5,6,8,9,12,13,14], [1,5,6,8,12,13,14,15],[1,5,6,9,10,12,13,14], [1,5,7,8,9,10,11,12],[1,5,7,8,9,10,12,14], [1,5,7,8,9,11,12,14],[1,5,7,8,9,11,13,14], [1,5,7,8,9,11,13,15],[1,5,7,8,11,12,14,15], [1,5,7,8,11,13,14,15],[1,5,8,9,11,12,14,15], [1,5,8,9,11,13,14,15],[1,5,8,9,12,13,14,15], [1,5,9,11,12,13,14,15],[1,6,7,8,9,13,14,15], [1,6,8,9,12,13,14,15],[1,6,9,10,12,13,14,15], [1,7,8,9,10,11,12,14],[1,7,8,9,10,11,14,15], [1,7,8,9,11,13,14,15],[1,7,9,10,11,13,14,15], [1,8,9,10,11,12,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,11], [2,3,4,5,6,7,11,15],[2,3,4,5,6,8,9,10], [2,3,4,5,6,9,10,11],[2,3,4,5,6,10,11,13], [2,3,4,5,6,10,13,14],[2,3,4,5,6,11,13,14], [2,3,4,5,6,11,14,15],[2,3,4,5,7,9,11,15], [2,3,4,5,9,10,11,12],[2,3,4,5,9,11,12,15], [2,3,4,5,9,12,13,15],[2,3,4,5,10,11,12,13], [2,3,4,5,11,12,13,15],[2,3,4,5,11,13,14,15], [2,3,4,6,7,8,9,15],[2,3,4,6,7,9,11,15], [2,3,4,6,8,9,10,11],[2,3,4,6,8,9,11,15], [2,3,4,6,8,10,11,15],[2,3,4,6,8,10,14,15], [2,3,4,6,10,11,13,14],[2,3,4,6,10,11,14,15], [2,3,4,8,10,11,14,15],[2,3,4,8,11,12,14,15], [2,3,4,10,11,12,13,14],[2,3,4,11,12,13,14,15], [2,3,5,6,7,8,9,14],[2,3,5,6,7,9,11,13], [2,3,5,6,7,9,13,14],[2,3,5,6,7,11,13,14], [2,3,5,6,7,11,14,15],[2,3,5,6,8,9,10,14], [2,3,5,6,9,10,11,13],[2,3,5,6,9,10,13,14], [2,3,5,7,8,9,10,14],[2,3,5,7,9,11,13,15], [2,3,5,7,11,13,14,15],[2,3,5,9,10,11,12,13], [2,3,5,9,11,12,13,15],[2,3,6,7,8,9,10,14], [2,3,6,7,8,9,10,15],[2,3,6,7,8,10,14,15], [2,3,6,7,9,10,11,13],[2,3,6,7,9,10,11,15], [2,3,6,7,9,10,13,14],[2,3,6,7,10,11,13,14], [2,3,6,7,10,11,14,15],[2,3,6,8,9,10,11,15], [2,3,7,9,10,11,13,15],[2,4,5,6,7,8,9,13], [2,4,5,6,7,9,11,13],[2,4,5,6,7,11,13,14], [2,4,5,6,7,11,14,15],[2,4,5,6,7,13,14,15], [2,4,5,6,8,9,10,11],[2,4,5,6,8,9,11,13], [2,4,5,6,8,10,11,13],[2,4,5,6,8,10,12,13], [2,4,5,7,9,11,13,15],[2,4,5,7,11,13,14,15], [2,4,5,8,9,10,11,12],[2,4,5,8,9,11,12,13], [2,4,5,8,10,11,12,13],[2,4,5,9,11,12,13,15], [2,4,6,7,9,11,13,15],[2,4,6,7,11,13,14,15], [2,4,6,8,9,11,13,15],[2,4,6,8,10,11,13,15], [2,4,6,8,10,12,13,15],[2,4,6,8,10,12,14,15], [2,4,6,10,11,13,14,15],[2,4,6,10,12,13,14,15], [2,4,8,9,11,12,13,15],[2,4,8,10,11,12,13,15], [2,4,8,10,11,12,14,15],[2,4,10,11,12,13,14,15], [2,5,6,8,9,10,11,12],[2,5,6,8,9,11,12,13], [2,5,6,8,10,11,12,13],[2,5,6,9,10,11,12,13], [2,6,7,8,9,10,14,15],[2,6,7,9,10,11,13,15], [2,6,7,9,10,13,14,15],[2,6,7,10,11,13,14,15], [2,6,8,9,10,11,12,13],[2,6,8,9,10,11,13,15], [2,6,8,9,10,12,13,15],[2,6,8,9,10,12,14,15], [2,8,9,10,11,12,13,15],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,12],[3,4,5,6,7,9,10,11], [3,4,5,6,7,10,11,12],[3,4,5,6,7,11,12,14], [3,4,5,6,7,11,14,15],[3,4,5,6,7,12,14,15], [3,4,5,6,10,11,12,13],[3,4,5,6,11,12,13,14], [3,4,5,7,9,10,11,12],[3,4,5,7,11,12,14,15], [3,4,5,11,12,13,14,15],[3,4,6,7,8,9,10,15], [3,4,6,7,8,10,12,14],[3,4,6,7,8,10,14,15], [3,4,6,7,8,12,14,15],[3,4,6,7,9,10,11,15], [3,4,6,7,10,11,12,14],[3,4,6,7,10,11,14,15], [3,4,6,8,9,10,11,15],[3,4,6,10,11,12,13,14], [3,4,7,8,9,10,11,15],[3,4,7,8,10,11,12,14], [3,4,7,8,10,11,14,15],[3,4,7,8,11,12,14,15], [3,5,6,7,8,9,10,14],[3,5,6,7,8,10,12,14], [3,5,6,7,8,12,14,15],[3,5,6,7,9,10,11,12], [3,5,6,7,9,10,12,14],[3,5,6,7,9,11,12,14], [3,5,6,7,9,11,13,14],[3,5,6,9,10,11,12,13], [3,5,6,9,10,12,13,14],[3,5,6,9,11,12,13,14], [3,6,7,9,10,11,12,13],[3,6,7,9,10,12,13,14], [3,6,7,9,11,12,13,14],[3,6,7,10,11,12,13,14], [3,7,9,10,11,12,13,14],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,13],[4,5,6,7,8,10,11,12], [4,5,6,7,8,11,12,13],[4,5,6,7,8,12,13,15], [4,5,6,7,11,12,13,14],[4,5,6,7,12,13,14,15], [4,5,6,8,10,11,12,13],[4,5,7,8,9,11,13,15], [4,5,7,8,11,12,13,15],[4,5,7,11,12,13,14,15], [4,5,8,9,11,12,13,15],[4,6,7,8,9,10,11,15], [4,6,7,8,9,11,13,15],[4,6,7,8,10,11,12,13], [4,6,7,8,10,11,13,15],[4,6,7,8,10,12,13,15], [4,6,7,8,10,12,14,15],[4,6,7,10,11,12,13,14], [4,6,7,10,11,13,14,15],[4,6,7,10,12,13,14,15], [4,7,8,10,11,12,13,14],[4,7,8,10,11,13,14,15], [4,7,8,10,12,13,14,15],[4,7,8,11,12,13,14,15], [4,8,10,11,12,13,14,15],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,14],[5,6,7,8,9,11,12,13], [5,6,7,8,9,12,13,14],[5,6,7,8,12,13,14,15], [5,6,7,9,11,12,13,14],[5,7,8,9,11,12,13,14], [5,7,8,11,12,13,14,15],[5,8,9,11,12,13,14,15], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,15], [6,7,8,9,10,12,13,14],[6,7,8,9,10,13,14,15], [6,7,8,10,12,13,14,15],[6,8,9,10,12,13,14,15], [7,8,9,10,11,12,13,14],[7,8,9,10,11,13,14,15], [8,9,10,11,12,13,14,15]] manifold_7_15_3_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,12],[1,2,3,4,5,6,12,14], [1,2,3,4,5,6,14,15],[1,2,3,4,5,7,8,15], [1,2,3,4,5,8,9,15],[1,2,3,4,5,9,10,12], [1,2,3,4,5,9,11,12],[1,2,3,4,5,9,11,15], [1,2,3,4,5,11,12,13],[1,2,3,4,5,11,13,15], [1,2,3,4,5,12,13,14],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,14],[1,2,3,4,6,7,14,15], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,14], [1,2,3,4,6,10,12,14],[1,2,3,4,7,8,14,15], [1,2,3,4,8,9,10,11],[1,2,3,4,8,9,11,15], [1,2,3,4,8,10,11,15],[1,2,3,4,8,10,14,15], [1,2,3,4,9,10,11,12],[1,2,3,4,10,11,12,15], [1,2,3,4,10,12,14,15],[1,2,3,4,11,12,13,15], [1,2,3,4,12,13,14,15],[1,2,3,5,6,7,8,9], [1,2,3,5,6,7,9,13],[1,2,3,5,6,7,13,15], [1,2,3,5,6,9,10,14],[1,2,3,5,6,9,13,14], [1,2,3,5,6,10,12,14],[1,2,3,5,6,13,14,15], [1,2,3,5,7,8,9,15],[1,2,3,5,7,9,13,15], [1,2,3,5,9,10,12,14],[1,2,3,5,9,11,12,13], [1,2,3,5,9,11,13,15],[1,2,3,5,9,12,13,14], [1,2,3,6,7,8,9,10],[1,2,3,6,7,8,10,14], [1,2,3,6,7,9,10,14],[1,2,3,6,7,9,13,14], [1,2,3,6,7,13,14,15],[1,2,3,7,8,9,10,15], [1,2,3,7,8,10,14,15],[1,2,3,7,9,10,14,15], [1,2,3,7,9,13,14,15],[1,2,3,8,9,10,11,15], [1,2,3,9,10,11,12,14],[1,2,3,9,10,11,14,15], [1,2,3,9,11,12,13,14],[1,2,3,9,11,13,14,15], [1,2,3,10,11,12,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,15],[1,2,4,5,6,8,9,12], [1,2,4,5,6,8,12,15],[1,2,4,5,6,9,10,12], [1,2,4,5,6,12,14,15],[1,2,4,5,8,9,12,13], [1,2,4,5,8,9,13,15],[1,2,4,5,8,12,13,15], [1,2,4,5,9,11,12,13],[1,2,4,5,9,11,13,15], [1,2,4,5,12,13,14,15],[1,2,4,6,7,8,14,15], [1,2,4,6,8,9,10,12],[1,2,4,6,8,10,12,14], [1,2,4,6,8,12,14,15],[1,2,4,8,9,10,11,12], [1,2,4,8,9,11,12,13],[1,2,4,8,9,11,13,15], [1,2,4,8,10,11,12,15],[1,2,4,8,10,12,14,15], [1,2,4,8,11,12,13,15],[1,2,5,6,7,8,9,15], [1,2,5,6,7,9,13,15],[1,2,5,6,8,9,12,13], [1,2,5,6,8,9,13,15],[1,2,5,6,8,12,13,15], [1,2,5,6,9,10,12,13],[1,2,5,6,9,10,13,14], [1,2,5,6,10,12,13,14],[1,2,5,6,12,13,14,15], [1,2,5,9,10,12,13,14],[1,2,6,7,8,9,10,14], [1,2,6,7,8,9,14,15],[1,2,6,7,9,13,14,15], [1,2,6,8,9,10,12,13],[1,2,6,8,9,10,13,14], [1,2,6,8,9,13,14,15],[1,2,6,8,10,12,13,14], [1,2,6,8,12,13,14,15],[1,2,7,8,9,10,14,15], [1,2,8,9,10,11,12,13],[1,2,8,9,10,11,13,15], [1,2,8,9,10,13,14,15],[1,2,8,10,11,12,13,15], [1,2,8,10,12,13,14,15],[1,2,9,10,11,12,13,14], [1,2,9,10,11,13,14,15],[1,2,10,11,12,13,14,15], [1,3,4,5,6,7,8,14],[1,3,4,5,6,7,14,15], [1,3,4,5,6,8,9,10],[1,3,4,5,6,8,10,12], [1,3,4,5,6,8,12,14],[1,3,4,5,7,8,11,12], [1,3,4,5,7,8,11,15],[1,3,4,5,7,8,12,14], [1,3,4,5,7,11,12,14],[1,3,4,5,7,11,14,15], [1,3,4,5,8,9,10,12],[1,3,4,5,8,9,11,12], [1,3,4,5,8,9,11,15],[1,3,4,5,11,12,13,14], [1,3,4,5,11,13,14,15],[1,3,4,6,8,10,12,14], [1,3,4,7,8,11,12,15],[1,3,4,7,8,12,14,15], [1,3,4,7,11,12,14,15],[1,3,4,8,9,10,11,12], [1,3,4,8,10,11,12,15],[1,3,4,8,10,12,14,15], [1,3,4,11,12,13,14,15],[1,3,5,6,7,8,9,10], [1,3,5,6,7,8,10,14],[1,3,5,6,7,9,10,14], [1,3,5,6,7,9,13,14],[1,3,5,6,7,13,14,15], [1,3,5,6,8,10,12,14],[1,3,5,7,8,9,10,12], [1,3,5,7,8,9,11,12],[1,3,5,7,8,9,11,15], [1,3,5,7,8,10,12,14],[1,3,5,7,9,10,12,14], [1,3,5,7,9,11,12,14],[1,3,5,7,9,11,13,14], [1,3,5,7,9,11,13,15],[1,3,5,7,11,13,14,15], [1,3,5,9,11,12,13,14],[1,3,7,8,9,10,11,12], [1,3,7,8,9,10,11,15],[1,3,7,8,10,11,12,15], [1,3,7,8,10,12,14,15],[1,3,7,9,10,11,12,14], [1,3,7,9,10,11,14,15],[1,3,7,9,11,13,14,15], [1,3,7,10,11,12,14,15],[1,4,5,6,7,8,14,15], [1,4,5,6,8,9,10,12],[1,4,5,6,8,12,14,15], [1,4,5,7,8,11,12,15],[1,4,5,7,8,12,14,15], [1,4,5,7,11,12,14,15],[1,4,5,8,9,11,12,15], [1,4,5,8,9,12,13,15],[1,4,5,9,11,12,13,15], [1,4,5,11,12,13,14,15],[1,4,8,9,11,12,13,15], [1,5,6,7,8,9,10,14],[1,5,6,7,8,9,13,14], [1,5,6,7,8,9,13,15],[1,5,6,7,8,13,14,15], [1,5,6,8,9,10,12,13],[1,5,6,8,9,10,13,14], [1,5,6,8,10,12,13,14],[1,5,6,8,12,13,14,15], [1,5,7,8,9,10,12,14],[1,5,7,8,9,11,12,15], [1,5,7,8,9,12,13,14],[1,5,7,8,9,12,13,15], [1,5,7,8,12,13,14,15],[1,5,7,9,11,12,13,14], [1,5,7,9,11,12,13,15],[1,5,7,11,12,13,14,15], [1,5,8,9,10,12,13,14],[1,6,7,8,9,13,14,15], [1,7,8,9,10,11,12,15],[1,7,8,9,10,12,14,15], [1,7,8,9,12,13,14,15],[1,7,9,10,11,12,14,15], [1,7,9,11,12,13,14,15],[1,8,9,10,11,12,13,15], [1,8,9,10,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,13], [2,3,4,5,6,7,13,15],[2,3,4,5,6,10,11,13], [2,3,4,5,6,10,12,13],[2,3,4,5,6,12,13,14], [2,3,4,5,6,13,14,15],[2,3,4,5,7,8,9,15], [2,3,4,5,7,9,10,11],[2,3,4,5,7,9,11,15], [2,3,4,5,7,11,13,15],[2,3,4,5,9,10,11,12], [2,3,4,5,10,11,12,13],[2,3,4,6,7,8,9,10], [2,3,4,6,7,8,10,14],[2,3,4,6,7,10,11,15], [2,3,4,6,7,10,14,15],[2,3,4,6,7,11,13,15], [2,3,4,6,10,11,13,15],[2,3,4,6,10,12,13,14], [2,3,4,6,10,13,14,15],[2,3,4,7,8,9,10,11], [2,3,4,7,8,9,11,15],[2,3,4,7,8,10,11,15], [2,3,4,7,8,10,14,15],[2,3,4,10,11,12,13,15], [2,3,4,10,12,13,14,15],[2,3,5,6,7,9,10,13], [2,3,5,6,7,10,11,13],[2,3,5,6,9,10,13,14], [2,3,5,6,10,12,13,14],[2,3,5,7,9,10,11,13], [2,3,5,7,9,11,13,15],[2,3,5,9,10,11,12,13], [2,3,5,9,10,12,13,14],[2,3,6,7,9,10,13,14], [2,3,6,7,10,11,13,14],[2,3,6,7,10,11,14,15], [2,3,6,7,11,13,14,15],[2,3,6,10,11,13,14,15], [2,3,7,8,9,10,11,15],[2,3,7,9,10,11,13,14], [2,3,7,9,10,11,14,15],[2,3,7,9,11,13,14,15], [2,3,9,10,11,12,13,14],[2,3,10,11,12,13,14,15], [2,4,5,6,7,8,9,15],[2,4,5,6,7,9,10,11], [2,4,5,6,7,9,11,13],[2,4,5,6,7,9,13,15], [2,4,5,6,8,9,12,13],[2,4,5,6,8,9,13,15], [2,4,5,6,8,12,13,15],[2,4,5,6,9,10,11,13], [2,4,5,6,9,10,12,13],[2,4,5,6,12,13,14,15], [2,4,5,7,9,11,13,15],[2,4,5,9,10,11,12,13], [2,4,6,7,8,9,10,11],[2,4,6,7,8,9,11,15], [2,4,6,7,8,10,11,15],[2,4,6,7,8,10,14,15], [2,4,6,7,9,11,13,15],[2,4,6,8,9,10,11,13], [2,4,6,8,9,10,12,13],[2,4,6,8,9,11,13,15], [2,4,6,8,10,11,13,15],[2,4,6,8,10,12,13,15], [2,4,6,8,10,12,14,15],[2,4,6,10,12,13,14,15], [2,4,8,9,10,11,12,13],[2,4,8,10,11,12,13,15], [2,5,6,7,9,10,11,13],[2,6,7,8,9,10,11,15], [2,6,7,8,9,10,14,15],[2,6,7,9,10,11,13,14], [2,6,7,9,10,11,14,15],[2,6,7,9,11,13,14,15], [2,6,8,9,10,11,13,15],[2,6,8,9,10,13,14,15], [2,6,8,10,12,13,14,15],[2,6,9,10,11,13,14,15], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,14], [3,4,5,6,7,11,12,14],[3,4,5,6,7,11,13,14], [3,4,5,6,7,13,14,15],[3,4,5,6,8,10,11,12], [3,4,5,6,10,11,12,13],[3,4,5,6,11,12,13,14], [3,4,5,7,8,9,10,11],[3,4,5,7,8,9,11,15], [3,4,5,7,11,13,14,15],[3,4,5,8,9,10,11,12], [3,4,6,7,8,10,11,14],[3,4,6,7,8,11,12,14], [3,4,6,7,10,11,14,15],[3,4,6,7,11,13,14,15], [3,4,6,8,10,11,12,14],[3,4,6,10,11,12,13,14], [3,4,6,10,11,13,14,15],[3,4,7,8,10,11,14,15], [3,4,7,8,11,12,14,15],[3,4,8,10,11,12,14,15], [3,4,10,11,12,13,14,15],[3,5,6,7,8,10,11,12], [3,5,6,7,8,10,12,14],[3,5,6,7,9,10,13,14], [3,5,6,7,10,11,12,14],[3,5,6,7,10,11,13,14], [3,5,6,10,11,12,13,14],[3,5,7,8,9,10,11,12], [3,5,7,9,10,11,12,14],[3,5,7,9,10,11,13,14], [3,5,9,10,11,12,13,14],[3,6,7,8,10,11,12,14], [3,7,8,10,11,12,14,15],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,8,9,13,15],[4,5,6,7,8,12,13,15], [4,5,6,7,8,12,14,15],[4,5,6,7,9,11,12,13], [4,5,6,7,11,12,13,14],[4,5,6,7,12,13,14,15], [4,5,6,8,9,10,11,12],[4,5,6,9,10,11,12,13], [4,5,7,8,9,11,12,15],[4,5,7,8,9,12,13,15], [4,5,7,9,11,12,13,15],[4,5,7,11,12,13,14,15], [4,6,7,8,9,11,12,13],[4,6,7,8,9,11,13,15], [4,6,7,8,10,11,14,15],[4,6,7,8,11,12,13,15], [4,6,7,8,11,12,14,15],[4,6,7,11,12,13,14,15], [4,6,8,9,10,11,12,13],[4,6,8,10,11,12,13,15], [4,6,8,10,11,12,14,15],[4,6,10,11,12,13,14,15], [4,7,8,9,11,12,13,15],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,9,10,13,14], [5,6,7,8,10,12,13,14],[5,6,7,8,12,13,14,15], [5,6,7,9,10,11,12,13],[5,6,7,10,11,12,13,14], [5,7,8,9,10,12,13,14],[5,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,14], [6,7,8,9,10,11,14,15],[6,7,8,9,11,13,14,15], [6,7,8,10,11,12,13,14],[6,7,8,11,12,13,14,15], [6,8,9,10,11,13,14,15],[6,8,10,11,12,13,14,15], [7,8,9,10,11,12,13,14],[7,8,9,10,11,12,14,15], [7,8,9,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_3_2=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,12], [1,2,3,4,5,6,12,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,15],[1,2,3,4,5,8,9,11], [1,2,3,4,5,8,11,15],[1,2,3,4,5,9,11,12], [1,2,3,4,5,11,12,13],[1,2,3,4,5,11,13,15], [1,2,3,4,5,12,13,14],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,10],[1,2,3,4,6,7,10,14], [1,2,3,4,6,7,14,15],[1,2,3,4,6,8,9,10], [1,2,3,4,6,9,10,12],[1,2,3,4,6,10,12,14], [1,2,3,4,7,8,10,15],[1,2,3,4,7,10,14,15], [1,2,3,4,8,9,10,11],[1,2,3,4,8,10,11,15], [1,2,3,4,9,10,11,12],[1,2,3,4,10,11,12,15], [1,2,3,4,10,12,14,15],[1,2,3,4,11,12,13,15], [1,2,3,4,12,13,14,15],[1,2,3,5,6,7,8,9], [1,2,3,5,6,7,9,15],[1,2,3,5,6,9,10,12], [1,2,3,5,6,9,10,14],[1,2,3,5,6,9,13,14], [1,2,3,5,6,9,13,15],[1,2,3,5,6,10,12,14], [1,2,3,5,6,13,14,15],[1,2,3,5,7,8,9,15], [1,2,3,5,8,9,11,15],[1,2,3,5,9,10,12,14], [1,2,3,5,9,11,12,14],[1,2,3,5,9,11,13,14], [1,2,3,5,9,11,13,15],[1,2,3,5,11,12,13,14], [1,2,3,6,7,8,9,10],[1,2,3,6,7,9,10,14], [1,2,3,6,7,9,14,15],[1,2,3,6,9,13,14,15], [1,2,3,7,8,9,10,15],[1,2,3,7,9,10,14,15], [1,2,3,8,9,10,11,15],[1,2,3,9,10,11,12,14], [1,2,3,9,10,11,14,15],[1,2,3,9,11,13,14,15], [1,2,3,10,11,12,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,15],[1,2,4,5,6,8,9,12], [1,2,4,5,6,8,12,14],[1,2,4,5,6,8,14,15], [1,2,4,5,8,9,11,15],[1,2,4,5,8,9,12,13], [1,2,4,5,8,9,13,15],[1,2,4,5,8,12,13,15], [1,2,4,5,8,12,14,15],[1,2,4,5,9,11,12,13], [1,2,4,5,9,11,13,15],[1,2,4,5,12,13,14,15], [1,2,4,6,7,8,10,14],[1,2,4,6,7,8,14,15], [1,2,4,6,8,9,10,12],[1,2,4,6,8,10,12,14], [1,2,4,7,8,10,14,15],[1,2,4,8,9,10,11,13], [1,2,4,8,9,10,12,13],[1,2,4,8,9,11,13,15], [1,2,4,8,10,11,13,15],[1,2,4,8,10,12,13,15], [1,2,4,8,10,12,14,15],[1,2,4,9,10,11,12,13], [1,2,4,10,11,12,13,15],[1,2,5,6,7,8,9,15], [1,2,5,6,8,9,12,13],[1,2,5,6,8,9,13,15], [1,2,5,6,8,12,13,14],[1,2,5,6,8,13,14,15], [1,2,5,6,9,10,12,13],[1,2,5,6,9,10,13,14], [1,2,5,6,10,12,13,14],[1,2,5,8,12,13,14,15], [1,2,5,9,10,12,13,14],[1,2,5,9,11,12,13,14], [1,2,6,7,8,9,10,14],[1,2,6,7,8,9,14,15], [1,2,6,8,9,10,12,13],[1,2,6,8,9,10,13,14], [1,2,6,8,9,13,14,15],[1,2,6,8,10,12,13,14], [1,2,7,8,9,10,14,15],[1,2,8,9,10,11,13,15], [1,2,8,9,10,13,14,15],[1,2,8,10,12,13,14,15], [1,2,9,10,11,12,13,14],[1,2,9,10,11,13,14,15], [1,2,10,11,12,13,14,15],[1,3,4,5,6,7,8,14], [1,3,4,5,6,7,14,15],[1,3,4,5,6,8,9,12], [1,3,4,5,6,8,12,14],[1,3,4,5,7,8,11,12], [1,3,4,5,7,8,11,15],[1,3,4,5,7,8,12,14], [1,3,4,5,7,11,12,14],[1,3,4,5,7,11,13,14], [1,3,4,5,7,11,13,15],[1,3,4,5,7,13,14,15], [1,3,4,5,8,9,11,12],[1,3,4,5,11,12,13,14], [1,3,4,6,7,8,10,14],[1,3,4,6,8,9,10,12], [1,3,4,6,8,10,12,14],[1,3,4,7,8,10,14,15], [1,3,4,7,8,11,12,15],[1,3,4,7,8,12,14,15], [1,3,4,7,11,12,14,15],[1,3,4,7,11,13,14,15], [1,3,4,8,9,10,11,12],[1,3,4,8,10,11,12,15], [1,3,4,8,10,12,14,15],[1,3,4,11,12,13,14,15], [1,3,5,6,7,8,9,10],[1,3,5,6,7,8,10,14], [1,3,5,6,7,9,10,14],[1,3,5,6,7,9,13,14], [1,3,5,6,7,9,13,15],[1,3,5,6,7,13,14,15], [1,3,5,6,8,9,10,12],[1,3,5,6,8,10,12,14], [1,3,5,7,8,9,10,12],[1,3,5,7,8,9,11,12], [1,3,5,7,8,9,11,15],[1,3,5,7,8,10,12,14], [1,3,5,7,9,10,12,14],[1,3,5,7,9,11,12,14], [1,3,5,7,9,11,13,14],[1,3,5,7,9,11,13,15], [1,3,6,7,9,13,14,15],[1,3,7,8,9,10,12,15], [1,3,7,8,9,11,12,15],[1,3,7,8,10,12,14,15], [1,3,7,9,10,12,14,15],[1,3,7,9,11,12,14,15], [1,3,7,9,11,13,14,15],[1,3,8,9,10,11,12,15], [1,3,9,10,11,12,14,15],[1,4,5,6,7,8,14,15], [1,4,5,7,8,11,12,15],[1,4,5,7,8,12,14,15], [1,4,5,7,11,12,13,14],[1,4,5,7,11,12,13,15], [1,4,5,7,12,13,14,15],[1,4,5,8,9,11,12,15], [1,4,5,8,9,12,13,15],[1,4,5,9,11,12,13,15], [1,4,7,11,12,13,14,15],[1,4,8,9,10,11,12,13], [1,4,8,9,11,12,13,15],[1,4,8,10,11,12,13,15], [1,5,6,7,8,9,10,13],[1,5,6,7,8,9,13,15], [1,5,6,7,8,10,13,14],[1,5,6,7,8,13,14,15], [1,5,6,7,9,10,13,14],[1,5,6,8,9,10,12,13], [1,5,6,8,10,12,13,14],[1,5,7,8,9,10,12,13], [1,5,7,8,9,11,12,15],[1,5,7,8,9,12,13,15], [1,5,7,8,10,12,13,14],[1,5,7,8,12,13,14,15], [1,5,7,9,10,12,13,14],[1,5,7,9,11,12,13,14], [1,5,7,9,11,12,13,15],[1,6,7,8,9,10,13,14], [1,6,7,8,9,13,14,15],[1,7,8,9,10,12,13,14], [1,7,8,9,10,12,14,15],[1,7,8,9,12,13,14,15], [1,7,9,11,12,13,14,15],[1,8,9,10,11,12,13,15], [1,8,9,10,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,13],[2,3,4,5,6,7,13,15], [2,3,4,5,6,9,10,12],[2,3,4,5,6,10,12,13], [2,3,4,5,6,12,13,14],[2,3,4,5,6,13,14,15], [2,3,4,5,7,8,9,11],[2,3,4,5,7,8,11,15], [2,3,4,5,7,9,10,11],[2,3,4,5,7,10,11,13], [2,3,4,5,7,11,13,15],[2,3,4,5,9,10,11,12], [2,3,4,5,10,11,12,13],[2,3,4,6,7,8,9,10], [2,3,4,6,7,10,11,13],[2,3,4,6,7,10,11,15], [2,3,4,6,7,10,14,15],[2,3,4,6,7,11,13,15], [2,3,4,6,10,11,13,15],[2,3,4,6,10,12,13,15], [2,3,4,6,10,12,14,15],[2,3,4,6,12,13,14,15], [2,3,4,7,8,9,10,11],[2,3,4,7,8,10,11,15], [2,3,4,10,11,12,13,15],[2,3,5,6,7,9,10,13], [2,3,5,6,7,9,13,15],[2,3,5,6,9,10,13,14], [2,3,5,6,10,12,13,14],[2,3,5,7,8,9,11,15], [2,3,5,7,9,10,11,13],[2,3,5,7,9,11,13,15], [2,3,5,9,10,11,12,14],[2,3,5,9,10,11,13,14], [2,3,5,10,11,12,13,14],[2,3,6,7,9,10,13,14], [2,3,6,7,9,13,14,15],[2,3,6,7,10,11,13,14], [2,3,6,7,10,11,14,15],[2,3,6,7,11,13,14,15], [2,3,6,10,11,13,14,15],[2,3,6,10,12,13,14,15], [2,3,7,8,9,10,11,15],[2,3,7,9,10,11,13,14], [2,3,7,9,10,11,14,15],[2,3,7,9,11,13,14,15], [2,3,10,11,12,13,14,15],[2,4,5,6,7,8,9,15], [2,4,5,6,7,9,10,13],[2,4,5,6,7,9,13,15], [2,4,5,6,8,9,12,13],[2,4,5,6,8,9,13,15], [2,4,5,6,8,12,13,15],[2,4,5,6,8,12,14,15], [2,4,5,6,9,10,12,13],[2,4,5,6,12,13,14,15], [2,4,5,7,8,9,11,15],[2,4,5,7,9,10,11,13], [2,4,5,7,9,11,13,15],[2,4,5,9,10,11,12,13], [2,4,6,7,8,9,10,11],[2,4,6,7,8,9,11,15], [2,4,6,7,8,10,11,15],[2,4,6,7,8,10,14,15], [2,4,6,7,9,10,11,13],[2,4,6,7,9,11,13,15], [2,4,6,8,9,10,11,13],[2,4,6,8,9,10,12,13], [2,4,6,8,9,11,13,15],[2,4,6,8,10,11,13,15], [2,4,6,8,10,12,13,15],[2,4,6,8,10,12,14,15], [2,5,6,8,12,13,14,15],[2,5,9,10,11,12,13,14], [2,6,7,8,9,10,11,14],[2,6,7,8,9,11,14,15], [2,6,7,8,10,11,14,15],[2,6,7,9,10,11,13,14], [2,6,7,9,11,13,14,15],[2,6,8,9,10,11,13,14], [2,6,8,9,11,13,14,15],[2,6,8,10,11,13,14,15], [2,6,8,10,12,13,14,15],[2,7,8,9,10,11,14,15], [2,8,9,10,11,13,14,15],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,14], [3,4,5,6,7,10,11,13],[3,4,5,6,7,11,13,14], [3,4,5,6,7,13,14,15],[3,4,5,6,8,9,10,12], [3,4,5,6,8,10,11,12],[3,4,5,6,8,11,12,14], [3,4,5,6,10,11,12,13],[3,4,5,6,11,12,13,14], [3,4,5,7,8,9,10,11],[3,4,5,7,8,11,12,14], [3,4,5,8,9,10,11,12],[3,4,6,7,8,10,11,14], [3,4,6,7,10,11,14,15],[3,4,6,7,11,13,14,15], [3,4,6,8,10,11,12,14],[3,4,6,10,11,12,13,15], [3,4,6,10,11,12,14,15],[3,4,6,11,12,13,14,15], [3,4,7,8,10,11,14,15],[3,4,7,8,11,12,14,15], [3,4,8,10,11,12,14,15],[3,5,6,7,8,10,11,14], [3,5,6,7,9,10,13,14],[3,5,6,7,10,11,13,14], [3,5,6,8,10,11,12,14],[3,5,6,10,11,12,13,14], [3,5,7,8,9,10,11,12],[3,5,7,8,10,11,12,14], [3,5,7,9,10,11,12,14],[3,5,7,9,10,11,13,14], [3,6,10,11,12,13,14,15],[3,7,8,9,10,11,12,15], [3,7,8,10,11,12,14,15],[3,7,9,10,11,12,14,15], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,8,9,12,15],[4,5,6,7,8,11,12,14], [4,5,6,7,8,12,14,15],[4,5,6,7,9,10,11,13], [4,5,6,7,9,11,12,13],[4,5,6,7,9,12,13,15], [4,5,6,7,11,12,13,14],[4,5,6,7,12,13,14,15], [4,5,6,8,9,10,11,12],[4,5,6,8,9,12,13,15], [4,5,6,9,10,11,12,13],[4,5,7,8,9,11,12,15], [4,5,7,9,11,12,13,15],[4,6,7,8,9,11,12,15], [4,6,7,8,10,11,14,15],[4,6,7,8,11,12,14,15], [4,6,7,9,11,12,13,15],[4,6,7,11,12,13,14,15], [4,6,8,9,10,11,12,13],[4,6,8,9,11,12,13,15], [4,6,8,10,11,12,13,15],[4,6,8,10,11,12,14,15], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,12,13,15],[5,6,7,8,10,11,12,14], [5,6,7,8,10,12,13,14],[5,6,7,8,12,13,14,15], [5,6,7,9,10,11,12,13],[5,6,7,10,11,12,13,14], [5,7,9,10,11,12,13,14],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,11,12,13,15], [6,7,8,9,11,13,14,15],[6,7,8,10,11,12,13,14], [6,7,8,11,12,13,14,15],[6,8,10,11,12,13,14,15], [7,8,9,10,11,12,13,14],[7,8,9,10,11,12,14,15], [7,8,9,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_2_1=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,6,14,15],[1,2,3,4,5,7,8,15], [1,2,3,4,5,8,9,15],[1,2,3,4,5,9,10,15], [1,2,3,4,5,10,11,15],[1,2,3,4,5,11,12,15], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,10], [1,2,3,4,6,7,10,11],[1,2,3,4,6,7,11,12], [1,2,3,4,6,7,12,13],[1,2,3,4,6,7,13,14], 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[1,2,5,6,9,10,14,15],[1,2,5,6,10,11,12,13], [1,2,5,6,10,11,13,14],[1,2,5,6,10,11,14,15], [1,2,5,6,11,12,13,14],[1,2,5,6,11,12,14,15], [1,2,5,6,12,13,14,15],[1,2,6,7,8,9,10,11], [1,2,6,7,8,9,11,12],[1,2,6,7,8,9,12,13], [1,2,6,7,8,9,13,14],[1,2,6,7,8,9,14,15], [1,2,6,7,9,10,11,12],[1,2,6,7,9,10,12,13], [1,2,6,7,9,10,13,14],[1,2,6,7,9,10,14,15], [1,2,6,7,10,11,12,13],[1,2,6,7,10,11,13,14], [1,2,6,7,10,11,14,15],[1,2,6,7,11,12,13,14], [1,2,6,7,11,12,14,15],[1,2,6,7,12,13,14,15], [1,2,7,8,9,10,11,12],[1,2,7,8,9,10,12,13], [1,2,7,8,9,10,13,14],[1,2,7,8,9,10,14,15], [1,2,7,8,10,11,12,13],[1,2,7,8,10,11,13,14], [1,2,7,8,10,11,14,15],[1,2,7,8,11,12,13,14], [1,2,7,8,11,12,14,15],[1,2,7,8,12,13,14,15], [1,2,8,9,10,11,12,13],[1,2,8,9,10,11,13,14], [1,2,8,9,10,11,14,15],[1,2,8,9,11,12,13,14], [1,2,8,9,11,12,14,15],[1,2,8,9,12,13,14,15], [1,2,9,10,11,12,13,14],[1,2,9,10,11,12,14,15], [1,2,9,10,12,13,14,15],[1,2,10,11,12,13,14,15], [1,3,4,5,6,7,8,15],[1,3,4,5,6,8,9,15], 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[3,4,5,6,9,10,14,15],[3,4,5,6,10,11,12,13], [3,4,5,6,10,11,13,14],[3,4,5,6,10,11,14,15], [3,4,5,6,11,12,13,14],[3,4,5,6,11,12,14,15], [3,4,5,6,12,13,14,15],[3,4,6,7,8,9,10,11], [3,4,6,7,8,9,11,12],[3,4,6,7,8,9,12,13], [3,4,6,7,8,9,13,14],[3,4,6,7,8,9,14,15], [3,4,6,7,9,10,11,12],[3,4,6,7,9,10,12,13], [3,4,6,7,9,10,13,14],[3,4,6,7,9,10,14,15], [3,4,6,7,10,11,12,13],[3,4,6,7,10,11,13,14], [3,4,6,7,10,11,14,15],[3,4,6,7,11,12,13,14], [3,4,6,7,11,12,14,15],[3,4,6,7,12,13,14,15], [3,4,7,8,9,10,11,12],[3,4,7,8,9,10,12,13], [3,4,7,8,9,10,13,14],[3,4,7,8,9,10,14,15], [3,4,7,8,10,11,12,13],[3,4,7,8,10,11,13,14], [3,4,7,8,10,11,14,15],[3,4,7,8,11,12,13,14], [3,4,7,8,11,12,14,15],[3,4,7,8,12,13,14,15], [3,4,8,9,10,11,12,13],[3,4,8,9,10,11,13,14], [3,4,8,9,10,11,14,15],[3,4,8,9,11,12,13,14], [3,4,8,9,11,12,14,15],[3,4,8,9,12,13,14,15], [3,4,9,10,11,12,13,14],[3,4,9,10,11,12,14,15], [3,4,9,10,12,13,14,15],[3,4,10,11,12,13,14,15], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,8,9,12,13],[4,5,6,7,8,9,13,14], [4,5,6,7,8,9,14,15],[4,5,6,7,9,10,11,12], [4,5,6,7,9,10,12,13],[4,5,6,7,9,10,13,14], [4,5,6,7,9,10,14,15],[4,5,6,7,10,11,12,13], [4,5,6,7,10,11,13,14],[4,5,6,7,10,11,14,15], [4,5,6,7,11,12,13,14],[4,5,6,7,11,12,14,15], [4,5,6,7,12,13,14,15],[4,5,7,8,9,10,11,12], [4,5,7,8,9,10,12,13],[4,5,7,8,9,10,13,14], [4,5,7,8,9,10,14,15],[4,5,7,8,10,11,12,13], [4,5,7,8,10,11,13,14],[4,5,7,8,10,11,14,15], [4,5,7,8,11,12,13,14],[4,5,7,8,11,12,14,15], [4,5,7,8,12,13,14,15],[4,5,8,9,10,11,12,13], [4,5,8,9,10,11,13,14],[4,5,8,9,10,11,14,15], [4,5,8,9,11,12,13,14],[4,5,8,9,11,12,14,15], [4,5,8,9,12,13,14,15],[4,5,9,10,11,12,13,14], [4,5,9,10,11,12,14,15],[4,5,9,10,12,13,14,15], [4,5,10,11,12,13,14,15],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,9,10,13,14], [5,6,7,8,9,10,14,15],[5,6,7,8,10,11,12,13], [5,6,7,8,10,11,13,14],[5,6,7,8,10,11,14,15], [5,6,7,8,11,12,13,14],[5,6,7,8,11,12,14,15], [5,6,7,8,12,13,14,15],[5,6,8,9,10,11,12,13], [5,6,8,9,10,11,13,14],[5,6,8,9,10,11,14,15], [5,6,8,9,11,12,13,14],[5,6,8,9,11,12,14,15], [5,6,8,9,12,13,14,15],[5,6,9,10,11,12,13,14], [5,6,9,10,11,12,14,15],[5,6,9,10,12,13,14,15], [5,6,10,11,12,13,14,15],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,10,11,14,15], [6,7,8,9,11,12,13,14],[6,7,8,9,11,12,14,15], [6,7,8,9,12,13,14,15],[6,7,9,10,11,12,13,14], [6,7,9,10,11,12,14,15],[6,7,9,10,12,13,14,15], [6,7,10,11,12,13,14,15],[7,8,9,10,11,12,13,14], [7,8,9,10,11,12,14,15],[7,8,9,10,12,13,14,15], [7,8,10,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_2_2=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,11],[1,2,3,4,5,6,11,12], [1,2,3,4,5,6,12,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,6,14,15],[1,2,3,4,5,7,8,15], [1,2,3,4,5,8,9,15],[1,2,3,4,5,9,10,15], [1,2,3,4,5,10,11,15],[1,2,3,4,5,11,12,15], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,14],[1,2,3,4,6,7,14,15], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,12], [1,2,3,4,6,8,12,14],[1,2,3,4,6,10,11,12], [1,2,3,4,6,12,13,14],[1,2,3,4,7,8,14,15], [1,2,3,4,8,9,10,14],[1,2,3,4,8,9,14,15], [1,2,3,4,8,10,12,14],[1,2,3,4,9,10,14,15], [1,2,3,4,10,11,12,14],[1,2,3,4,10,11,14,15], [1,2,3,4,11,12,14,15],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,10],[1,2,3,5,6,7,10,11], [1,2,3,5,6,7,11,12],[1,2,3,5,6,7,12,13], [1,2,3,5,6,7,13,15],[1,2,3,5,6,8,9,10], [1,2,3,5,6,13,14,15],[1,2,3,5,7,8,9,10], [1,2,3,5,7,8,9,15],[1,2,3,5,7,9,10,11], [1,2,3,5,7,9,11,15],[1,2,3,5,7,11,12,13], [1,2,3,5,7,11,13,15],[1,2,3,5,9,10,11,15], [1,2,3,5,11,12,13,15],[1,2,3,6,7,8,10,12], [1,2,3,6,7,8,12,14],[1,2,3,6,7,10,11,12], [1,2,3,6,7,12,13,14],[1,2,3,6,7,13,14,15], [1,2,3,7,8,9,10,12],[1,2,3,7,8,9,12,13], [1,2,3,7,8,9,13,15],[1,2,3,7,8,12,13,14], [1,2,3,7,8,13,14,15],[1,2,3,7,9,10,11,12], [1,2,3,7,9,11,12,13],[1,2,3,7,9,11,13,15], [1,2,3,8,9,10,12,14],[1,2,3,8,9,12,13,14], [1,2,3,8,9,13,14,15],[1,2,3,9,10,11,12,14], [1,2,3,9,10,11,13,14],[1,2,3,9,10,11,13,15], [1,2,3,9,10,13,14,15],[1,2,3,9,11,12,13,14], [1,2,3,10,11,13,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,15], [1,2,4,5,6,9,10,15],[1,2,4,5,6,10,11,15], [1,2,4,5,6,11,12,15],[1,2,4,5,6,12,13,14], [1,2,4,5,6,12,14,15],[1,2,4,5,7,8,9,15], [1,2,4,5,12,13,14,15],[1,2,4,6,7,8,9,15], [1,2,4,6,7,8,14,15],[1,2,4,6,8,9,10,15], [1,2,4,6,8,10,12,14],[1,2,4,6,8,10,14,15], [1,2,4,6,10,11,12,15],[1,2,4,6,10,12,14,15], [1,2,4,8,9,10,14,15],[1,2,4,10,11,12,14,15], [1,2,5,6,7,8,9,10],[1,2,5,6,7,9,10,11], [1,2,5,6,7,9,11,15],[1,2,5,6,7,11,12,13], [1,2,5,6,7,11,13,15],[1,2,5,6,9,10,11,15], [1,2,5,6,11,12,13,15],[1,2,5,6,12,13,14,15], [1,2,6,7,8,9,10,11],[1,2,6,7,8,9,11,15], [1,2,6,7,8,10,11,12],[1,2,6,7,8,11,12,15], [1,2,6,7,8,12,14,15],[1,2,6,7,11,12,13,15], [1,2,6,7,12,13,14,15],[1,2,6,8,9,10,11,15], [1,2,6,8,10,11,12,15],[1,2,6,8,10,12,14,15], [1,2,7,8,9,10,11,12],[1,2,7,8,9,11,12,13], [1,2,7,8,9,11,13,15],[1,2,7,8,11,12,13,15], [1,2,7,8,12,13,14,15],[1,2,8,9,10,11,12,13], [1,2,8,9,10,11,13,15],[1,2,8,9,10,12,13,15], [1,2,8,9,10,12,14,15],[1,2,8,9,12,13,14,15], [1,2,8,10,11,12,13,15],[1,2,9,10,11,12,13,14], [1,2,9,10,12,13,14,15],[1,2,10,11,12,13,14,15], [1,3,4,5,6,7,8,15],[1,3,4,5,6,8,9,10], [1,3,4,5,6,8,10,14],[1,3,4,5,6,8,14,15], [1,3,4,5,6,10,11,12],[1,3,4,5,6,10,12,14], [1,3,4,5,6,12,13,14],[1,3,4,5,8,9,10,14], [1,3,4,5,8,9,14,15],[1,3,4,5,9,10,14,15], [1,3,4,5,10,11,12,14],[1,3,4,5,10,11,14,15], [1,3,4,5,11,12,13,14],[1,3,4,5,11,12,13,15], [1,3,4,5,11,13,14,15],[1,3,4,6,7,8,14,15], [1,3,4,6,8,10,12,14],[1,3,4,11,12,13,14,15], [1,3,5,6,7,8,10,12],[1,3,5,6,7,8,12,14], [1,3,5,6,7,8,14,15],[1,3,5,6,7,10,11,12], [1,3,5,6,7,12,13,14],[1,3,5,6,7,13,14,15], [1,3,5,6,8,10,12,14],[1,3,5,7,8,9,10,14], [1,3,5,7,8,9,14,15],[1,3,5,7,8,10,12,14], [1,3,5,7,9,10,11,12],[1,3,5,7,9,10,12,14], [1,3,5,7,9,11,12,14],[1,3,5,7,9,11,13,14], [1,3,5,7,9,11,13,15],[1,3,5,7,9,13,14,15], [1,3,5,7,11,12,13,14],[1,3,5,9,10,11,12,14], [1,3,5,9,10,11,14,15],[1,3,5,9,11,13,14,15], [1,3,7,8,9,10,12,14],[1,3,7,8,9,12,13,14], [1,3,7,8,9,13,14,15],[1,3,7,9,11,12,13,14], [1,3,9,10,11,13,14,15],[1,4,5,6,7,8,9,15], [1,4,5,6,8,9,10,15],[1,4,5,6,8,10,14,15], [1,4,5,6,10,11,12,15],[1,4,5,6,10,12,14,15], [1,4,5,8,9,10,14,15],[1,4,5,10,11,12,14,15], [1,4,5,11,12,13,14,15],[1,5,6,7,8,9,10,15], [1,5,6,7,8,10,12,14],[1,5,6,7,8,10,14,15], [1,5,6,7,9,10,11,15],[1,5,6,7,10,11,12,14], [1,5,6,7,10,11,14,15],[1,5,6,7,11,12,13,14], [1,5,6,7,11,13,14,15],[1,5,6,10,11,12,14,15], [1,5,6,11,12,13,14,15],[1,5,7,8,9,10,14,15], [1,5,7,9,10,11,12,14],[1,5,7,9,10,11,14,15], [1,5,7,9,11,13,14,15],[1,6,7,8,9,10,11,15], [1,6,7,8,10,11,12,15],[1,6,7,8,10,12,14,15], [1,6,7,10,11,12,14,15],[1,6,7,11,12,13,14,15], [1,7,8,9,10,11,12,15],[1,7,8,9,10,12,14,15], [1,7,8,9,11,12,13,14],[1,7,8,9,11,12,14,15], [1,7,8,9,11,13,14,15],[1,7,8,11,12,13,14,15], [1,7,9,10,11,12,14,15],[1,8,9,10,11,12,13,15], [1,8,9,11,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,12], [2,3,4,5,6,7,12,13],[2,3,4,5,6,7,13,14], [2,3,4,5,6,7,14,15],[2,3,4,5,7,8,9,15], [2,3,4,5,7,9,10,11],[2,3,4,5,7,9,11,13], [2,3,4,5,7,9,13,15],[2,3,4,5,7,11,12,13], [2,3,4,5,7,13,14,15],[2,3,4,5,9,10,11,15], [2,3,4,5,9,11,13,15],[2,3,4,5,11,12,13,15], [2,3,4,6,7,8,9,11],[2,3,4,6,7,8,11,12], [2,3,4,6,7,8,12,13],[2,3,4,6,7,8,13,14], [2,3,4,6,7,9,10,11],[2,3,4,6,8,9,10,11], [2,3,4,6,8,10,11,12],[2,3,4,6,8,12,13,14], [2,3,4,7,8,9,11,13],[2,3,4,7,8,9,13,15], [2,3,4,7,8,11,12,13],[2,3,4,7,8,13,14,15], [2,3,4,8,9,10,11,13],[2,3,4,8,9,10,13,14], [2,3,4,8,9,13,14,15],[2,3,4,8,10,11,12,13], [2,3,4,8,10,12,13,14],[2,3,4,9,10,11,13,15], [2,3,4,9,10,13,14,15],[2,3,4,10,11,12,13,15], [2,3,4,10,11,12,14,15],[2,3,4,10,12,13,14,15], [2,3,5,6,7,8,9,10],[2,3,5,6,7,13,14,15], [2,3,5,7,9,11,13,15],[2,3,6,7,8,9,10,11], [2,3,6,7,8,10,11,12],[2,3,6,7,8,12,13,14], [2,3,7,8,9,10,11,12],[2,3,7,8,9,11,12,13], [2,3,8,9,10,11,12,13],[2,3,8,9,10,12,13,14], [2,3,9,10,11,12,13,14],[2,3,10,11,12,13,14,15], [2,4,5,6,7,9,10,11],[2,4,5,6,7,9,11,15], [2,4,5,6,7,11,12,13],[2,4,5,6,7,11,13,15], [2,4,5,6,7,13,14,15],[2,4,5,6,9,10,11,15], [2,4,5,6,11,12,13,15],[2,4,5,6,12,13,14,15], [2,4,5,7,9,11,13,15],[2,4,6,7,8,9,11,13], [2,4,6,7,8,9,13,15],[2,4,6,7,8,11,12,13], [2,4,6,7,8,13,14,15],[2,4,6,7,9,11,13,15], [2,4,6,8,9,10,11,15],[2,4,6,8,9,11,13,15], [2,4,6,8,10,11,12,13],[2,4,6,8,10,11,13,15], [2,4,6,8,10,12,13,15],[2,4,6,8,10,12,14,15], [2,4,6,8,12,13,14,15],[2,4,6,10,11,12,13,15], [2,4,8,9,10,11,13,15],[2,4,8,9,10,13,14,15], [2,4,8,10,12,13,14,15],[2,6,7,8,9,11,13,15], [2,6,7,8,11,12,13,15],[2,6,7,8,12,13,14,15], [2,6,8,10,11,12,13,15],[2,8,9,10,12,13,14,15], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,12],[3,4,5,6,7,8,12,13], [3,4,5,6,7,8,13,14],[3,4,5,6,7,8,14,15], [3,4,5,6,8,10,11,12],[3,4,5,6,8,10,12,14], [3,4,5,6,8,12,13,14],[3,4,5,7,8,9,10,12], [3,4,5,7,8,9,12,13],[3,4,5,7,8,9,13,14], [3,4,5,7,8,9,14,15],[3,4,5,7,8,10,11,12], [3,4,5,7,9,10,11,12],[3,4,5,7,9,11,12,13], [3,4,5,7,9,13,14,15],[3,4,5,8,9,10,12,14], [3,4,5,8,9,12,13,14],[3,4,5,9,10,11,12,14], [3,4,5,9,10,11,14,15],[3,4,5,9,11,12,13,14], [3,4,5,9,11,13,14,15],[3,4,6,7,8,9,10,11], [3,4,7,8,9,10,11,12],[3,4,7,8,9,11,12,13], [3,4,7,8,9,13,14,15],[3,4,8,9,10,11,12,13], [3,4,8,9,10,12,13,14],[3,4,9,10,11,12,13,14], [3,4,9,10,11,13,14,15],[3,4,10,11,12,13,14,15], [3,5,6,7,8,10,11,12],[3,5,6,7,8,12,13,14], [3,5,7,8,9,10,12,14],[3,5,7,8,9,12,13,14], [3,5,7,9,11,12,13,14],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,13], [4,5,6,7,8,9,13,14],[4,5,6,7,8,9,14,15], [4,5,6,7,9,11,12,13],[4,5,6,7,9,11,13,15], [4,5,6,7,9,13,14,15],[4,5,6,8,9,10,11,13], [4,5,6,8,9,10,13,14],[4,5,6,8,9,10,14,15], [4,5,6,8,9,11,12,13],[4,5,6,8,10,11,12,13], [4,5,6,8,10,12,13,14],[4,5,6,9,10,11,13,15], [4,5,6,9,10,13,14,15],[4,5,6,10,11,12,13,15], [4,5,6,10,12,13,14,15],[4,5,7,8,9,10,11,12], [4,5,8,9,10,11,12,13],[4,5,8,9,10,12,13,14], [4,5,9,10,11,12,13,14],[4,5,9,10,11,13,14,15], [4,5,10,11,12,13,14,15],[4,6,7,8,9,11,12,13], [4,6,7,8,9,13,14,15],[4,6,8,9,10,11,13,15], [4,6,8,9,10,13,14,15],[4,6,8,10,12,13,14,15], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,10,13,14],[5,6,7,8,9,10,14,15], [5,6,7,8,10,12,13,14],[5,6,7,9,10,11,12,14], [5,6,7,9,10,11,14,15],[5,6,7,9,10,12,13,14], [5,6,7,9,11,12,13,14],[5,6,7,9,11,13,14,15], [5,6,8,9,10,11,12,13],[5,6,9,10,11,12,13,14], [5,6,9,10,11,13,14,15],[5,6,10,11,12,13,14,15], [5,7,8,9,10,12,13,14],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,10,11,14,15], [6,7,8,9,11,13,14,15],[6,7,8,10,11,12,13,15], [6,7,8,10,11,13,14,15],[6,7,8,10,12,13,14,15], [6,7,9,10,11,12,13,14],[6,7,10,11,12,13,14,15], [6,8,9,10,11,13,14,15],[7,8,9,10,11,12,13,14], [7,8,9,10,11,12,14,15],[7,8,10,11,12,13,14,15], [8,9,10,11,12,13,14,15]] manifold_7_15_2_3=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,12],[1,2,3,4,5,6,12,13], [1,2,3,4,5,6,13,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,15],[1,2,3,4,5,8,9,15], [1,2,3,4,5,9,10,11],[1,2,3,4,5,9,11,15], [1,2,3,4,5,10,11,12],[1,2,3,4,5,11,12,15], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,12],[1,2,3,4,6,7,12,13], [1,2,3,4,6,7,13,14],[1,2,3,4,6,7,14,15], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,12], [1,2,3,4,7,8,12,13],[1,2,3,4,7,8,13,14], [1,2,3,4,7,8,14,15],[1,2,3,4,8,9,10,15], [1,2,3,4,8,10,12,14],[1,2,3,4,8,10,14,15], [1,2,3,4,8,12,13,14],[1,2,3,4,9,10,11,15], [1,2,3,4,10,11,12,14],[1,2,3,4,10,11,14,15], [1,2,3,4,11,12,14,15],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,12],[1,2,3,5,6,7,11,12], [1,2,3,5,6,7,11,15],[1,2,3,5,6,8,9,10], [1,2,3,5,6,8,10,12],[1,2,3,5,6,11,12,15], [1,2,3,5,6,12,13,15],[1,2,3,5,6,13,14,15], [1,2,3,5,7,8,9,10],[1,2,3,5,7,8,9,15], [1,2,3,5,7,8,10,11],[1,2,3,5,7,8,11,12], [1,2,3,5,7,9,10,11],[1,2,3,5,7,9,11,15], [1,2,3,5,8,10,11,12],[1,2,3,6,7,11,12,15], [1,2,3,6,7,12,13,15],[1,2,3,6,7,13,14,15], [1,2,3,7,8,9,10,11],[1,2,3,7,8,9,11,14], [1,2,3,7,8,9,14,15],[1,2,3,7,8,11,12,14], [1,2,3,7,8,12,13,14],[1,2,3,7,9,11,13,14], [1,2,3,7,9,11,13,15],[1,2,3,7,9,13,14,15], [1,2,3,7,11,12,13,14],[1,2,3,7,11,12,13,15], [1,2,3,8,9,10,11,12],[1,2,3,8,9,10,12,14], [1,2,3,8,9,10,14,15],[1,2,3,8,9,11,12,14], [1,2,3,9,10,11,12,14],[1,2,3,9,10,11,13,14], [1,2,3,9,10,11,13,15],[1,2,3,9,10,13,14,15], [1,2,3,10,11,13,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,10], [1,2,4,5,6,7,10,11],[1,2,4,5,6,7,11,15], [1,2,4,5,6,10,11,15],[1,2,4,5,6,10,12,14], [1,2,4,5,6,10,14,15],[1,2,4,5,6,12,13,14], [1,2,4,5,7,8,9,15],[1,2,4,5,7,9,10,11], [1,2,4,5,7,9,11,15],[1,2,4,5,10,11,12,14], [1,2,4,5,10,11,14,15],[1,2,4,5,11,12,14,15], [1,2,4,5,12,13,14,15],[1,2,4,6,7,8,9,15], [1,2,4,6,7,8,12,13],[1,2,4,6,7,8,13,14], [1,2,4,6,7,8,14,15],[1,2,4,6,7,9,10,15], [1,2,4,6,7,10,11,15],[1,2,4,6,8,9,10,15], [1,2,4,6,8,10,12,14],[1,2,4,6,8,10,14,15], [1,2,4,6,8,12,13,14],[1,2,4,7,9,10,11,15], [1,2,5,6,7,8,9,10],[1,2,5,6,7,8,10,11], [1,2,5,6,7,8,11,12],[1,2,5,6,8,10,11,12], [1,2,5,6,10,11,12,14],[1,2,5,6,10,11,14,15], [1,2,5,6,11,12,14,15],[1,2,5,6,12,13,14,15], [1,2,6,7,8,9,10,15],[1,2,6,7,8,10,11,12], [1,2,6,7,8,10,12,13],[1,2,6,7,8,10,13,15], [1,2,6,7,8,13,14,15],[1,2,6,7,10,11,12,13], [1,2,6,7,10,11,13,15],[1,2,6,7,11,12,13,15], [1,2,6,8,10,12,13,15],[1,2,6,8,10,12,14,15], [1,2,6,8,12,13,14,15],[1,2,6,10,11,12,13,15], [1,2,6,10,11,12,14,15],[1,2,7,8,9,10,11,15], [1,2,7,8,9,11,13,14],[1,2,7,8,9,11,13,15], [1,2,7,8,9,13,14,15],[1,2,7,8,10,11,12,13], [1,2,7,8,10,11,13,15],[1,2,7,8,11,12,13,14], [1,2,8,9,10,11,12,13],[1,2,8,9,10,11,13,15], [1,2,8,9,10,12,13,15],[1,2,8,9,10,12,14,15], [1,2,8,9,11,12,13,14],[1,2,8,9,12,13,14,15], [1,2,9,10,11,12,13,14],[1,2,9,10,12,13,14,15], [1,2,10,11,12,13,14,15],[1,3,4,5,6,7,8,15], [1,3,4,5,6,8,9,15],[1,3,4,5,6,9,10,15], [1,3,4,5,6,10,12,14],[1,3,4,5,6,10,14,15], [1,3,4,5,6,12,13,14],[1,3,4,5,9,10,11,13], [1,3,4,5,9,10,13,14],[1,3,4,5,9,10,14,15], [1,3,4,5,9,11,13,15],[1,3,4,5,9,13,14,15], [1,3,4,5,10,11,12,14],[1,3,4,5,10,11,13,14], [1,3,4,5,11,12,13,14],[1,3,4,5,11,12,13,15], [1,3,4,6,7,8,12,14],[1,3,4,6,7,8,14,15], [1,3,4,6,7,12,13,14],[1,3,4,6,8,9,10,15], [1,3,4,6,8,10,12,14],[1,3,4,6,8,10,14,15], [1,3,4,7,8,12,13,14],[1,3,4,9,10,11,13,15], [1,3,4,9,10,13,14,15],[1,3,4,10,11,13,14,15], [1,3,4,11,12,13,14,15],[1,3,5,6,7,8,12,14], [1,3,5,6,7,8,14,15],[1,3,5,6,7,11,12,15], [1,3,5,6,7,12,13,14],[1,3,5,6,7,12,13,15], [1,3,5,6,7,13,14,15],[1,3,5,6,8,9,10,14], [1,3,5,6,8,9,14,15],[1,3,5,6,8,10,12,14], [1,3,5,6,9,10,14,15],[1,3,5,7,8,9,10,14], [1,3,5,7,8,9,14,15],[1,3,5,7,8,10,11,12], [1,3,5,7,8,10,12,14],[1,3,5,7,9,10,11,12], [1,3,5,7,9,10,12,14],[1,3,5,7,9,11,12,14], [1,3,5,7,9,11,13,14],[1,3,5,7,9,11,13,15], [1,3,5,7,9,13,14,15],[1,3,5,7,11,12,13,14], [1,3,5,7,11,12,13,15],[1,3,5,9,10,11,12,14], [1,3,5,9,10,11,13,14],[1,3,6,8,9,10,14,15], [1,3,7,8,9,10,11,12],[1,3,7,8,9,10,12,14], [1,3,7,8,9,11,12,14],[1,4,5,6,7,8,9,15], [1,4,5,6,7,9,10,15],[1,4,5,6,7,10,11,15], [1,4,5,7,9,10,11,15],[1,4,5,9,10,11,13,15], [1,4,5,9,10,13,14,15],[1,4,5,10,11,13,14,15], [1,4,5,11,12,13,14,15],[1,4,6,7,8,12,13,14], [1,5,6,7,8,9,10,14],[1,5,6,7,8,9,14,15], [1,5,6,7,8,10,11,12],[1,5,6,7,8,10,12,14], [1,5,6,7,9,10,11,12],[1,5,6,7,9,10,11,15], [1,5,6,7,9,10,12,14],[1,5,6,7,9,11,12,15], [1,5,6,7,9,12,14,15],[1,5,6,7,12,13,14,15], [1,5,6,9,10,11,12,15],[1,5,6,9,10,12,14,15], [1,5,6,10,11,12,14,15],[1,5,7,9,11,12,14,15], [1,5,7,9,11,13,14,15],[1,5,7,11,12,13,14,15], [1,5,9,10,11,12,14,15],[1,5,9,10,11,13,14,15], [1,6,7,8,9,10,14,15],[1,6,7,8,10,12,13,15], [1,6,7,8,10,12,14,15],[1,6,7,8,12,13,14,15], [1,6,7,9,10,11,12,15],[1,6,7,9,10,12,14,15], [1,6,7,10,11,12,13,15],[1,7,8,9,10,11,12,15], [1,7,8,9,10,12,14,15],[1,7,8,9,11,12,14,15], [1,7,8,9,11,13,14,15],[1,7,8,10,11,12,13,15], [1,7,8,11,12,13,14,15],[1,8,9,10,11,12,13,15], [1,8,9,11,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,13], [2,3,4,5,6,7,13,14],[2,3,4,5,6,7,14,15], [2,3,4,5,6,10,11,12],[2,3,4,5,6,11,12,13], [2,3,4,5,7,8,9,13],[2,3,4,5,7,8,13,14], [2,3,4,5,7,8,14,15],[2,3,4,5,7,9,10,11], [2,3,4,5,7,9,11,13],[2,3,4,5,8,9,13,14], [2,3,4,5,8,9,14,15],[2,3,4,5,9,11,13,15], [2,3,4,5,9,13,14,15],[2,3,4,5,11,12,13,15], [2,3,4,6,7,8,9,13],[2,3,4,6,7,8,12,13], [2,3,4,6,7,9,10,11],[2,3,4,6,7,9,11,13], [2,3,4,6,8,9,10,11],[2,3,4,6,8,9,11,12], [2,3,4,6,8,9,12,13],[2,3,4,6,8,10,11,12], [2,3,4,6,9,11,12,13],[2,3,4,8,9,10,11,12], [2,3,4,8,9,10,12,15],[2,3,4,8,9,12,13,15], [2,3,4,8,9,13,14,15],[2,3,4,8,10,12,14,15], [2,3,4,8,12,13,14,15],[2,3,4,9,10,11,12,13], [2,3,4,9,10,11,13,15],[2,3,4,9,10,12,13,15], [2,3,4,10,11,12,13,15],[2,3,4,10,11,12,14,15], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,11], [2,3,5,6,7,8,11,12],[2,3,5,6,7,11,13,15], [2,3,5,6,7,13,14,15],[2,3,5,6,8,10,11,12], [2,3,5,6,11,12,13,15],[2,3,5,7,8,9,13,14], [2,3,5,7,8,9,14,15],[2,3,5,7,9,11,13,15], [2,3,5,7,9,13,14,15],[2,3,6,7,8,9,10,11], [2,3,6,7,8,9,11,12],[2,3,6,7,8,9,12,13], [2,3,6,7,9,11,12,13],[2,3,6,7,11,12,13,15], [2,3,7,8,9,11,12,13],[2,3,7,8,9,11,13,14], [2,3,7,8,11,12,13,14],[2,3,8,9,10,12,14,15], [2,3,8,9,11,12,13,14],[2,3,8,9,12,13,14,15], [2,3,9,10,11,12,13,14],[2,3,9,10,12,13,14,15], [2,3,10,11,12,13,14,15],[2,4,5,6,7,11,13,15], [2,4,5,6,7,13,14,15],[2,4,5,6,10,11,12,14], [2,4,5,6,10,11,14,15],[2,4,5,6,11,12,13,15], [2,4,5,6,11,12,14,15],[2,4,5,6,12,13,14,15], [2,4,5,7,8,9,13,15],[2,4,5,7,8,13,14,15], [2,4,5,7,9,11,13,15],[2,4,5,8,9,13,14,15], [2,4,6,7,8,9,13,15],[2,4,6,7,8,13,14,15], [2,4,6,7,9,10,11,15],[2,4,6,7,9,11,13,15], [2,4,6,8,9,10,11,15],[2,4,6,8,9,11,12,13], [2,4,6,8,9,11,13,15],[2,4,6,8,10,11,12,13], [2,4,6,8,10,11,13,15],[2,4,6,8,10,12,13,15], [2,4,6,8,10,12,14,15],[2,4,6,8,12,13,14,15], [2,4,6,10,11,12,13,15],[2,4,6,10,11,12,14,15], [2,4,8,9,10,11,12,13],[2,4,8,9,10,11,13,15], [2,4,8,9,10,12,13,15],[2,5,7,8,9,13,14,15], [2,6,7,8,9,10,11,15],[2,6,7,8,9,11,12,13], [2,6,7,8,9,11,13,15],[2,6,7,8,10,11,12,13], [2,6,7,8,10,11,13,15],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,12], [3,4,5,6,7,8,12,14],[3,4,5,6,7,8,14,15], [3,4,5,6,7,11,12,13],[3,4,5,6,7,12,13,14], [3,4,5,6,8,9,10,14],[3,4,5,6,8,9,14,15], [3,4,5,6,8,10,11,12],[3,4,5,6,8,10,12,14], [3,4,5,6,9,10,14,15],[3,4,5,7,8,9,10,14], [3,4,5,7,8,9,13,14],[3,4,5,7,8,10,11,12], [3,4,5,7,8,10,12,14],[3,4,5,7,9,10,11,12], [3,4,5,7,9,10,12,13],[3,4,5,7,9,10,13,14], [3,4,5,7,9,11,12,13],[3,4,5,7,10,12,13,14], [3,4,5,9,10,11,12,13],[3,4,5,10,11,12,13,14], [3,4,6,7,8,9,10,11],[3,4,6,7,8,9,11,12], [3,4,6,7,8,9,12,13],[3,4,6,7,9,11,12,13], [3,4,6,8,9,10,14,15],[3,4,7,8,9,10,11,12], [3,4,7,8,9,10,12,13],[3,4,7,8,9,10,13,14], [3,4,7,8,10,12,13,14],[3,4,8,9,10,12,13,14], [3,4,8,9,10,12,14,15],[3,4,8,9,12,13,14,15], [3,4,9,10,12,13,14,15],[3,4,10,11,12,13,14,15], [3,5,6,7,11,12,13,15],[3,5,7,9,10,12,13,14], [3,5,7,9,11,12,13,14],[3,5,9,10,11,12,13,14], [3,7,8,9,10,12,13,14],[3,7,8,9,11,12,13,14], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,8,9,12,13],[4,5,6,7,8,9,13,15], [4,5,6,7,8,12,13,14],[4,5,6,7,8,13,14,15], [4,5,6,7,9,10,11,15],[4,5,6,7,9,11,12,13], [4,5,6,7,9,11,13,15],[4,5,6,8,9,10,11,15], [4,5,6,8,9,10,14,15],[4,5,6,8,9,11,12,13], [4,5,6,8,9,11,13,15],[4,5,6,8,10,11,12,13], [4,5,6,8,10,11,13,14],[4,5,6,8,10,11,14,15], [4,5,6,8,10,12,13,14],[4,5,6,8,11,13,14,15], [4,5,6,10,11,12,13,14],[4,5,6,11,12,13,14,15], [4,5,7,8,9,10,11,12],[4,5,7,8,9,10,12,13], [4,5,7,8,9,10,13,14],[4,5,7,8,10,12,13,14], [4,5,8,9,10,11,12,13],[4,5,8,9,10,11,13,14], [4,5,8,9,10,11,14,15],[4,5,8,9,11,13,14,15], [4,5,9,10,11,13,14,15],[4,6,8,10,11,13,14,15], [4,6,8,10,12,13,14,15],[4,6,10,11,12,13,14,15], [4,8,9,10,11,13,14,15],[4,8,9,10,12,13,14,15], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,10,13,14],[5,6,7,8,9,13,14,15], [5,6,7,8,10,12,13,14],[5,6,7,9,10,12,13,14], [5,6,7,9,11,12,13,14],[5,6,7,9,11,12,14,15], [5,6,7,9,11,13,14,15],[5,6,7,11,12,13,14,15], [5,6,8,9,10,11,12,13],[5,6,8,9,10,11,13,14], [5,6,8,9,10,11,14,15],[5,6,8,9,11,13,14,15], [5,6,9,10,11,12,13,14],[5,6,9,10,11,12,14,15], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,14], [6,7,8,9,10,11,14,15],[6,7,8,9,11,13,14,15], [6,7,8,10,11,13,14,15],[6,7,8,10,12,13,14,15], [6,7,9,10,11,12,13,14],[6,7,9,10,11,12,14,15], [6,7,10,11,12,13,14,15],[7,8,9,10,11,12,13,14], [7,8,9,10,11,12,14,15],[7,8,10,11,12,13,14,15], [8,9,10,11,12,13,14,15]] manifold_7_15_2_4=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,10], [1,2,3,4,5,6,10,12],[1,2,3,4,5,6,12,13], [1,2,3,4,5,6,13,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,15],[1,2,3,4,5,8,9,15], [1,2,3,4,5,9,10,11],[1,2,3,4,5,9,11,15], [1,2,3,4,5,10,11,12],[1,2,3,4,5,11,12,15], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,14],[1,2,3,4,6,7,14,15], [1,2,3,4,6,8,9,10],[1,2,3,4,6,8,10,12], [1,2,3,4,6,8,12,14],[1,2,3,4,6,12,13,14], [1,2,3,4,7,8,14,15],[1,2,3,4,8,9,10,15], [1,2,3,4,8,10,12,14],[1,2,3,4,8,10,14,15], [1,2,3,4,9,10,11,15],[1,2,3,4,10,11,12,14], [1,2,3,4,10,11,14,15],[1,2,3,4,11,12,14,15], [1,2,3,4,12,13,14,15],[1,2,3,5,6,7,8,10], [1,2,3,5,6,7,10,11],[1,2,3,5,6,7,11,12], [1,2,3,5,6,7,12,13],[1,2,3,5,6,7,13,15], [1,2,3,5,6,8,9,10],[1,2,3,5,6,10,11,12], [1,2,3,5,6,13,14,15],[1,2,3,5,7,8,9,10], [1,2,3,5,7,8,9,15],[1,2,3,5,7,9,10,11], [1,2,3,5,7,9,11,15],[1,2,3,5,7,11,12,13], [1,2,3,5,7,11,13,15],[1,2,3,5,11,12,13,15], [1,2,3,6,7,8,10,12],[1,2,3,6,7,8,12,14], [1,2,3,6,7,10,11,12],[1,2,3,6,7,12,13,14], [1,2,3,6,7,13,14,15],[1,2,3,7,8,9,10,11], [1,2,3,7,8,9,11,12],[1,2,3,7,8,9,12,13], [1,2,3,7,8,9,13,14],[1,2,3,7,8,9,14,15], [1,2,3,7,8,10,11,12],[1,2,3,7,8,12,13,14], [1,2,3,7,9,11,12,13],[1,2,3,7,9,11,13,15], [1,2,3,7,9,13,14,15],[1,2,3,8,9,10,11,12], [1,2,3,8,9,10,12,14],[1,2,3,8,9,10,14,15], [1,2,3,8,9,12,13,14],[1,2,3,9,10,11,12,14], [1,2,3,9,10,11,13,14],[1,2,3,9,10,11,13,15], [1,2,3,9,10,13,14,15],[1,2,3,9,11,12,13,14], [1,2,3,10,11,13,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,15], [1,2,4,5,6,9,10,15],[1,2,4,5,6,10,11,12], [1,2,4,5,6,10,11,15],[1,2,4,5,6,11,12,15], [1,2,4,5,6,12,13,14],[1,2,4,5,6,12,14,15], [1,2,4,5,7,8,9,15],[1,2,4,5,9,10,11,15], [1,2,4,5,12,13,14,15],[1,2,4,6,7,8,9,15], [1,2,4,6,7,8,14,15],[1,2,4,6,8,9,10,15], [1,2,4,6,8,10,12,14],[1,2,4,6,8,10,14,15], [1,2,4,6,10,11,12,15],[1,2,4,6,10,12,14,15], [1,2,4,10,11,12,14,15],[1,2,5,6,7,8,9,10], [1,2,5,6,7,9,10,11],[1,2,5,6,7,9,11,15], [1,2,5,6,7,11,12,13],[1,2,5,6,7,11,13,15], [1,2,5,6,9,10,11,15],[1,2,5,6,11,12,13,15], [1,2,5,6,12,13,14,15],[1,2,6,7,8,9,10,15], [1,2,6,7,8,10,11,12],[1,2,6,7,8,10,11,15], [1,2,6,7,8,11,12,15],[1,2,6,7,8,12,13,14], [1,2,6,7,8,12,13,15],[1,2,6,7,8,13,14,15], [1,2,6,7,9,10,11,15],[1,2,6,7,11,12,13,15], [1,2,6,8,10,11,12,15],[1,2,6,8,10,12,14,15], [1,2,6,8,12,13,14,15],[1,2,7,8,9,10,11,15], [1,2,7,8,9,11,12,13],[1,2,7,8,9,11,13,15], [1,2,7,8,9,13,14,15],[1,2,7,8,11,12,13,15], [1,2,8,9,10,11,12,13],[1,2,8,9,10,11,13,15], [1,2,8,9,10,12,13,15],[1,2,8,9,10,12,14,15], [1,2,8,9,12,13,14,15],[1,2,8,10,11,12,13,15], [1,2,9,10,11,12,13,14],[1,2,9,10,12,13,14,15], [1,2,10,11,12,13,14,15],[1,3,4,5,6,7,8,15], [1,3,4,5,6,8,9,10],[1,3,4,5,6,8,10,14], [1,3,4,5,6,8,14,15],[1,3,4,5,6,10,12,14], [1,3,4,5,6,12,13,14],[1,3,4,5,8,9,10,14], [1,3,4,5,8,9,14,15],[1,3,4,5,9,10,11,15], [1,3,4,5,9,10,14,15],[1,3,4,5,10,11,12,14], [1,3,4,5,10,11,14,15],[1,3,4,5,11,12,13,14], [1,3,4,5,11,12,13,15],[1,3,4,5,11,13,14,15], [1,3,4,6,7,8,14,15],[1,3,4,6,8,10,12,14], [1,3,4,8,9,10,14,15],[1,3,4,11,12,13,14,15], [1,3,5,6,7,8,10,12],[1,3,5,6,7,8,12,14], [1,3,5,6,7,8,14,15],[1,3,5,6,7,10,11,12], [1,3,5,6,7,12,13,14],[1,3,5,6,7,13,14,15], [1,3,5,6,8,10,12,14],[1,3,5,7,8,9,10,14], [1,3,5,7,8,9,14,15],[1,3,5,7,8,10,12,14], [1,3,5,7,9,10,11,12],[1,3,5,7,9,10,12,14], [1,3,5,7,9,11,12,14],[1,3,5,7,9,11,13,14], [1,3,5,7,9,11,13,15],[1,3,5,7,9,13,14,15], [1,3,5,7,11,12,13,14],[1,3,5,9,10,11,12,14], [1,3,5,9,10,11,14,15],[1,3,5,9,11,13,14,15], [1,3,7,8,9,10,11,12],[1,3,7,8,9,10,12,14], [1,3,7,8,9,12,13,14],[1,3,7,9,11,12,13,14], [1,3,9,10,11,13,14,15],[1,4,5,6,7,8,9,15], [1,4,5,6,8,9,10,15],[1,4,5,6,8,10,14,15], [1,4,5,6,10,11,12,15],[1,4,5,6,10,12,14,15], [1,4,5,8,9,10,14,15],[1,4,5,10,11,12,14,15], [1,4,5,11,12,13,14,15],[1,5,6,7,8,9,10,14], [1,5,6,7,8,9,14,15],[1,5,6,7,8,10,12,14], [1,5,6,7,9,10,11,15],[1,5,6,7,9,10,14,15], [1,5,6,7,10,11,12,14],[1,5,6,7,10,11,14,15], [1,5,6,7,11,12,13,15],[1,5,6,7,11,12,14,15], [1,5,6,7,12,13,14,15],[1,5,6,8,9,10,14,15], [1,5,6,10,11,12,14,15],[1,5,7,9,10,11,12,14], [1,5,7,9,10,11,14,15],[1,5,7,9,11,13,14,15], [1,5,7,11,12,13,14,15],[1,6,7,8,9,10,14,15], [1,6,7,8,10,11,12,15],[1,6,7,8,10,12,14,15], [1,6,7,8,12,13,14,15],[1,6,7,10,11,12,14,15], [1,7,8,9,10,11,12,15],[1,7,8,9,10,12,14,15], [1,7,8,9,11,12,13,14],[1,7,8,9,11,12,14,15], [1,7,8,9,11,13,14,15],[1,7,8,11,12,13,14,15], [1,7,9,10,11,12,14,15],[1,8,9,10,11,12,13,15], [1,8,9,11,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,11],[2,3,4,5,6,7,11,13], [2,3,4,5,6,7,13,14],[2,3,4,5,6,7,14,15], [2,3,4,5,6,10,11,12],[2,3,4,5,6,11,12,13], [2,3,4,5,7,8,9,15],[2,3,4,5,7,9,10,11], [2,3,4,5,7,9,11,13],[2,3,4,5,7,9,13,15], [2,3,4,5,7,13,14,15],[2,3,4,5,9,11,13,15], [2,3,4,5,11,12,13,15],[2,3,4,6,7,8,9,11], [2,3,4,6,7,8,11,12],[2,3,4,6,7,8,12,13], [2,3,4,6,7,8,13,14],[2,3,4,6,7,9,10,11], [2,3,4,6,7,11,12,13],[2,3,4,6,8,9,10,11], [2,3,4,6,8,10,11,12],[2,3,4,6,8,12,13,14], [2,3,4,7,8,9,11,13],[2,3,4,7,8,9,13,15], [2,3,4,7,8,11,12,13],[2,3,4,7,8,13,14,15], [2,3,4,8,9,10,11,12],[2,3,4,8,9,10,12,13], [2,3,4,8,9,10,13,14],[2,3,4,8,9,10,14,15], [2,3,4,8,9,11,12,13],[2,3,4,8,9,13,14,15], [2,3,4,8,10,12,13,14],[2,3,4,9,10,11,12,13], [2,3,4,9,10,11,13,15],[2,3,4,9,10,13,14,15], [2,3,4,10,11,12,13,15],[2,3,4,10,11,12,14,15], [2,3,4,10,12,13,14,15],[2,3,5,6,7,8,9,10], [2,3,5,6,7,11,12,13],[2,3,5,6,7,13,14,15], [2,3,5,7,9,11,13,15],[2,3,6,7,8,9,10,11], [2,3,6,7,8,10,11,12],[2,3,6,7,8,12,13,14], [2,3,7,8,9,11,12,13],[2,3,7,8,9,13,14,15], [2,3,8,9,10,12,13,14],[2,3,9,10,11,12,13,14], [2,3,10,11,12,13,14,15],[2,4,5,6,7,9,10,11], [2,4,5,6,7,9,11,15],[2,4,5,6,7,11,13,15], [2,4,5,6,7,13,14,15],[2,4,5,6,9,10,11,15], [2,4,5,6,11,12,13,15],[2,4,5,6,12,13,14,15], [2,4,5,7,9,11,13,15],[2,4,6,7,8,9,11,13], [2,4,6,7,8,9,13,15],[2,4,6,7,8,11,12,13], [2,4,6,7,8,13,14,15],[2,4,6,7,9,11,13,15], [2,4,6,8,9,10,11,15],[2,4,6,8,9,11,13,15], [2,4,6,8,10,11,12,13],[2,4,6,8,10,11,13,15], [2,4,6,8,10,12,13,15],[2,4,6,8,10,12,14,15], [2,4,6,8,12,13,14,15],[2,4,6,10,11,12,13,15], [2,4,8,9,10,11,12,13],[2,4,8,9,10,11,13,15], [2,4,8,9,10,13,14,15],[2,4,8,10,12,13,14,15], [2,6,7,8,9,10,11,15],[2,6,7,8,9,11,13,15], [2,6,7,8,11,12,13,15],[2,6,8,10,11,12,13,15], [2,8,9,10,12,13,14,15],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,12], [3,4,5,6,7,8,12,14],[3,4,5,6,7,8,14,15], [3,4,5,6,7,11,12,13],[3,4,5,6,7,12,13,14], [3,4,5,6,8,10,11,12],[3,4,5,6,8,10,12,14], [3,4,5,7,8,9,10,12],[3,4,5,7,8,9,12,13], [3,4,5,7,8,9,13,14],[3,4,5,7,8,9,14,15], [3,4,5,7,8,10,11,12],[3,4,5,7,8,12,13,14], [3,4,5,7,9,10,11,12],[3,4,5,7,9,11,12,13], [3,4,5,7,9,13,14,15],[3,4,5,8,9,10,12,14], [3,4,5,8,9,12,13,14],[3,4,5,9,10,11,12,13], [3,4,5,9,10,11,13,14],[3,4,5,9,10,11,14,15], [3,4,5,9,10,12,13,14],[3,4,5,9,11,13,14,15], [3,4,5,10,11,12,13,14],[3,4,6,7,8,9,10,11], [3,4,6,7,8,12,13,14],[3,4,7,8,9,10,11,12], [3,4,7,8,9,11,12,13],[3,4,7,8,9,13,14,15], [3,4,8,9,10,12,13,14],[3,4,9,10,11,13,14,15], [3,4,10,11,12,13,14,15],[3,5,6,7,8,10,11,12], [3,5,7,8,9,10,12,14],[3,5,7,8,9,12,13,14], [3,5,7,9,11,12,13,14],[3,5,9,10,11,12,13,14], [4,5,6,7,8,9,10,11],[4,5,6,7,8,9,11,12], [4,5,6,7,8,9,12,13],[4,5,6,7,8,9,13,15], [4,5,6,7,8,12,13,14],[4,5,6,7,8,13,14,15], [4,5,6,7,9,11,12,13],[4,5,6,7,9,11,13,15], [4,5,6,8,9,10,11,13],[4,5,6,8,9,10,13,14], [4,5,6,8,9,10,14,15],[4,5,6,8,9,11,12,13], [4,5,6,8,9,13,14,15],[4,5,6,8,10,11,12,13], [4,5,6,8,10,12,13,14],[4,5,6,9,10,11,13,15], [4,5,6,9,10,13,14,15],[4,5,6,10,11,12,13,14], [4,5,6,10,11,12,14,15],[4,5,6,10,11,13,14,15], [4,5,6,11,12,13,14,15],[4,5,7,8,9,10,11,12], [4,5,7,8,9,13,14,15],[4,5,8,9,10,11,12,13], [4,5,8,9,10,12,13,14],[4,5,9,10,11,13,14,15], [4,6,7,8,9,11,12,13],[4,6,8,9,10,11,13,15], [4,6,8,9,10,13,14,15],[4,6,8,10,12,13,14,15], [4,6,10,11,12,13,14,15],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,9,10,13,14], [5,6,7,8,9,13,14,15],[5,6,7,8,10,12,13,14], [5,6,7,9,10,11,12,14],[5,6,7,9,10,11,14,15], [5,6,7,9,10,12,13,14],[5,6,7,9,11,12,13,14], [5,6,7,9,11,13,14,15],[5,6,7,11,12,13,14,15], [5,6,8,9,10,11,12,13],[5,6,9,10,11,12,13,14], [5,6,9,10,11,13,14,15],[5,7,8,9,10,12,13,14], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,14], [6,7,8,9,10,11,14,15],[6,7,8,9,11,13,14,15], [6,7,8,10,11,12,13,15],[6,7,8,10,11,13,14,15], [6,7,8,10,12,13,14,15],[6,7,9,10,11,12,13,14], [6,7,10,11,12,13,14,15],[6,8,9,10,11,13,14,15], [7,8,9,10,11,12,13,14],[7,8,9,10,11,12,14,15], [7,8,10,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_2_5=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,11], [1,2,3,4,5,6,11,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,6,14,15],[1,2,3,4,5,7,8,15], [1,2,3,4,5,8,9,10],[1,2,3,4,5,8,10,15], [1,2,3,4,5,9,10,12],[1,2,3,4,5,9,11,12], [1,2,3,4,5,10,12,15],[1,2,3,4,5,11,12,13], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,14], [1,2,3,4,6,7,14,15],[1,2,3,4,6,9,11,14], [1,2,3,4,6,11,13,14],[1,2,3,4,7,8,9,15], [1,2,3,4,7,9,14,15],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,15],[1,2,3,4,8,10,11,15], [1,2,3,4,9,10,11,12],[1,2,3,4,9,11,14,15], [1,2,3,4,10,11,12,15],[1,2,3,4,11,12,13,14], [1,2,3,4,11,12,14,15],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,15],[1,2,3,5,6,8,9,10], [1,2,3,5,6,8,10,13],[1,2,3,5,6,8,13,15], [1,2,3,5,6,9,10,13],[1,2,3,5,6,9,11,13], [1,2,3,5,6,13,14,15],[1,2,3,5,8,10,13,15], [1,2,3,5,9,10,12,13],[1,2,3,5,9,11,12,13], [1,2,3,5,10,12,13,15],[1,2,3,6,7,8,9,10], [1,2,3,6,7,8,10,14],[1,2,3,6,7,8,14,15], [1,2,3,6,7,9,10,14],[1,2,3,6,8,10,13,14], [1,2,3,6,8,13,14,15],[1,2,3,6,9,10,13,14], [1,2,3,6,9,11,13,14],[1,2,3,7,8,9,10,15], [1,2,3,7,8,10,14,15],[1,2,3,7,9,10,14,15], [1,2,3,8,9,10,11,15],[1,2,3,8,10,13,14,15], [1,2,3,9,10,11,12,13],[1,2,3,9,10,11,13,14], [1,2,3,9,10,11,14,15],[1,2,3,10,11,12,13,15], [1,2,3,10,11,13,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,14], [1,2,4,5,6,7,14,15],[1,2,4,5,6,9,11,13], [1,2,4,5,6,9,12,13],[1,2,4,5,6,9,12,14], [1,2,4,5,6,12,13,14],[1,2,4,5,7,8,9,15], [1,2,4,5,7,9,12,14],[1,2,4,5,7,9,12,15], [1,2,4,5,7,12,14,15],[1,2,4,5,8,9,10,12], [1,2,4,5,8,9,12,15],[1,2,4,5,8,10,12,15], [1,2,4,5,9,11,12,13],[1,2,4,5,12,13,14,15], [1,2,4,6,9,11,13,14],[1,2,4,6,9,12,13,14], [1,2,4,7,9,12,14,15],[1,2,4,8,9,10,11,12], [1,2,4,8,9,11,12,15],[1,2,4,8,10,11,12,15], [1,2,4,9,11,12,13,14],[1,2,4,9,11,12,14,15], [1,2,5,6,7,8,9,15],[1,2,5,6,7,9,13,14], [1,2,5,6,7,9,13,15],[1,2,5,6,7,13,14,15], [1,2,5,6,8,9,10,13],[1,2,5,6,8,9,13,15], [1,2,5,6,9,12,13,14],[1,2,5,7,9,12,13,14], [1,2,5,7,9,12,13,15],[1,2,5,7,12,13,14,15], [1,2,5,8,9,10,12,13],[1,2,5,8,9,12,13,15], [1,2,5,8,10,12,13,15],[1,2,6,7,8,9,10,14], [1,2,6,7,8,9,14,15],[1,2,6,7,9,13,14,15], [1,2,6,8,9,10,13,14],[1,2,6,8,9,13,14,15], [1,2,7,8,9,10,14,15],[1,2,7,9,12,13,14,15], [1,2,8,9,10,11,12,15],[1,2,8,9,10,12,13,15], [1,2,8,9,10,13,14,15],[1,2,9,10,11,12,13,14], [1,2,9,10,11,12,14,15],[1,2,9,10,12,13,14,15], [1,2,10,11,12,13,14,15],[1,3,4,5,6,7,8,15], [1,3,4,5,6,8,9,11],[1,3,4,5,6,8,11,13], [1,3,4,5,6,8,13,15],[1,3,4,5,6,13,14,15], [1,3,4,5,8,9,10,12],[1,3,4,5,8,9,11,12], [1,3,4,5,8,10,12,15],[1,3,4,5,8,11,12,15], [1,3,4,5,8,11,13,15],[1,3,4,5,11,12,13,15], [1,3,4,6,7,8,9,11],[1,3,4,6,7,8,11,14], [1,3,4,6,7,8,14,15],[1,3,4,6,7,9,11,14], [1,3,4,6,8,11,13,15],[1,3,4,6,8,11,14,15], [1,3,4,6,11,13,14,15],[1,3,4,7,8,9,11,15], [1,3,4,7,8,11,14,15],[1,3,4,7,9,11,14,15], [1,3,4,8,9,10,11,12],[1,3,4,8,10,11,12,15], [1,3,4,11,12,13,14,15],[1,3,5,6,8,9,10,13], [1,3,5,6,8,9,11,13],[1,3,5,8,9,10,12,13], [1,3,5,8,9,11,12,13],[1,3,5,8,10,12,13,15], [1,3,5,8,11,12,13,15],[1,3,6,7,8,9,10,11], [1,3,6,7,8,10,11,14],[1,3,6,7,9,10,11,14], [1,3,6,8,9,10,11,13],[1,3,6,8,10,11,13,14], [1,3,6,8,11,13,14,15],[1,3,6,9,10,11,13,14], [1,3,7,8,9,10,11,15],[1,3,7,8,10,11,14,15], [1,3,7,9,10,11,14,15],[1,3,8,9,10,11,12,13], [1,3,8,10,11,12,13,15],[1,3,8,10,11,13,14,15], [1,4,5,6,7,8,9,14],[1,4,5,6,7,8,14,15], [1,4,5,6,8,9,11,13],[1,4,5,6,8,9,12,13], [1,4,5,6,8,9,12,14],[1,4,5,6,8,12,13,15], [1,4,5,6,8,12,14,15],[1,4,5,6,12,13,14,15], [1,4,5,7,8,9,12,14],[1,4,5,7,8,9,12,15], [1,4,5,7,8,12,14,15],[1,4,5,8,9,11,12,13], [1,4,5,8,11,12,13,15],[1,4,6,7,8,9,11,14], [1,4,6,8,9,11,12,13],[1,4,6,8,9,11,12,14], [1,4,6,8,11,12,13,15],[1,4,6,8,11,12,14,15], [1,4,6,9,11,12,13,14],[1,4,6,11,12,13,14,15], [1,4,7,8,9,11,12,14],[1,4,7,8,9,11,12,15], [1,4,7,8,11,12,14,15],[1,4,7,9,11,12,14,15], [1,5,6,7,8,9,13,14],[1,5,6,7,8,9,13,15], [1,5,6,7,8,13,14,15],[1,5,6,8,9,12,13,14], [1,5,6,8,12,13,14,15],[1,5,7,8,9,12,13,14], [1,5,7,8,9,12,13,15],[1,5,7,8,12,13,14,15], [1,6,7,8,9,10,11,14],[1,6,7,8,9,13,14,15], [1,6,8,9,10,11,13,14],[1,6,8,9,11,12,13,14], [1,6,8,11,12,13,14,15],[1,7,8,9,10,11,14,15], [1,7,8,9,11,12,14,15],[1,7,8,9,12,13,14,15], [1,8,9,10,11,12,13,15],[1,8,9,10,11,13,14,15], [1,8,9,11,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,12],[2,3,4,5,6,7,12,14], [2,3,4,5,6,7,14,15],[2,3,4,5,6,9,10,11], [2,3,4,5,6,10,11,13],[2,3,4,5,6,10,12,13], [2,3,4,5,6,12,13,14],[2,3,4,5,7,8,9,10], [2,3,4,5,7,8,10,15],[2,3,4,5,7,10,12,15], [2,3,4,5,7,12,14,15],[2,3,4,5,9,10,11,12], [2,3,4,5,10,11,12,13],[2,3,4,5,12,13,14,15], [2,3,4,6,7,9,10,11],[2,3,4,6,7,9,11,14], [2,3,4,6,7,10,11,14],[2,3,4,6,7,10,12,14], [2,3,4,6,10,11,13,14],[2,3,4,6,10,12,13,14], [2,3,4,7,8,9,10,11],[2,3,4,7,8,9,11,15], [2,3,4,7,8,10,11,15],[2,3,4,7,9,11,14,15], [2,3,4,7,10,11,14,15],[2,3,4,7,10,12,14,15], [2,3,4,10,11,12,13,14],[2,3,4,10,11,12,14,15], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,15], [2,3,5,6,7,10,12,14],[2,3,5,6,7,10,13,14], [2,3,5,6,7,10,13,15],[2,3,5,6,7,13,14,15], [2,3,5,6,8,10,13,15],[2,3,5,6,9,10,11,13], [2,3,5,6,10,12,13,14],[2,3,5,7,10,12,14,15], [2,3,5,7,10,13,14,15],[2,3,5,9,10,11,12,13], [2,3,5,10,12,13,14,15],[2,3,6,7,8,10,14,15], [2,3,6,7,9,10,11,14],[2,3,6,7,10,13,14,15], [2,3,6,8,10,13,14,15],[2,3,6,9,10,11,13,14], [2,3,7,8,9,10,11,15],[2,3,7,9,10,11,14,15], [2,3,10,11,12,13,14,15],[2,4,5,6,7,9,10,12], [2,4,5,6,7,9,12,14],[2,4,5,6,9,10,11,13], [2,4,5,6,9,10,12,13],[2,4,5,7,8,9,10,12], [2,4,5,7,8,9,12,15],[2,4,5,7,8,10,12,15], [2,4,5,9,10,11,12,13],[2,4,6,7,9,10,11,14], [2,4,6,7,9,10,12,14],[2,4,6,9,10,11,13,14], [2,4,6,9,10,12,13,14],[2,4,7,8,9,10,11,12], [2,4,7,8,9,11,12,15],[2,4,7,8,10,11,12,15], [2,4,7,9,10,11,12,14],[2,4,7,9,11,12,14,15], [2,4,7,10,11,12,14,15],[2,4,9,10,11,12,13,14], [2,5,6,7,8,9,10,15],[2,5,6,7,9,10,12,14], [2,5,6,7,9,10,13,14],[2,5,6,7,9,10,13,15], [2,5,6,8,9,10,13,15],[2,5,6,9,10,12,13,14], [2,5,7,8,9,10,12,15],[2,5,7,9,10,12,13,14], [2,5,7,9,10,12,13,15],[2,5,7,10,12,13,14,15], [2,5,8,9,10,12,13,15],[2,6,7,8,9,10,14,15], [2,6,7,9,10,13,14,15],[2,6,8,9,10,13,14,15], [2,7,8,9,10,11,12,15],[2,7,9,10,11,12,14,15], [2,7,9,10,12,13,14,15],[3,4,5,6,7,8,9,10], [3,4,5,6,7,8,10,11],[3,4,5,6,7,8,11,13], [3,4,5,6,7,8,13,15],[3,4,5,6,7,10,11,12], [3,4,5,6,7,11,12,14],[3,4,5,6,7,11,13,14], [3,4,5,6,7,13,14,15],[3,4,5,6,8,9,10,11], [3,4,5,6,10,11,12,13],[3,4,5,6,11,12,13,14], [3,4,5,7,8,10,11,12],[3,4,5,7,8,10,12,15], [3,4,5,7,8,11,12,15],[3,4,5,7,8,11,13,15], [3,4,5,7,11,12,14,15],[3,4,5,7,11,13,14,15], [3,4,5,8,9,10,11,12],[3,4,5,11,12,13,14,15], [3,4,6,7,8,9,10,11],[3,4,6,7,8,11,13,15], [3,4,6,7,8,11,14,15],[3,4,6,7,10,11,12,14], [3,4,6,7,11,13,14,15],[3,4,6,10,11,12,13,14], [3,4,7,8,10,11,12,15],[3,4,7,10,11,12,14,15], [3,5,6,7,8,10,11,13],[3,5,6,7,8,10,13,15], [3,5,6,7,10,11,12,14],[3,5,6,7,10,11,13,14], [3,5,6,8,9,10,11,13],[3,5,6,10,11,12,13,14], [3,5,7,8,10,11,12,15],[3,5,7,8,10,11,13,15], [3,5,7,10,11,12,14,15],[3,5,7,10,11,13,14,15], [3,5,8,9,10,11,12,13],[3,5,8,10,11,12,13,15], [3,5,10,11,12,13,14,15],[3,6,7,8,10,11,13,15], [3,6,7,8,10,11,14,15],[3,6,7,10,11,13,14,15], [3,6,8,10,11,13,14,15],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,14], [4,5,6,7,8,11,12,13],[4,5,6,7,8,12,13,15], [4,5,6,7,8,12,14,15],[4,5,6,7,9,10,11,12], [4,5,6,7,11,12,13,14],[4,5,6,7,12,13,14,15], [4,5,6,8,9,11,12,13],[4,5,6,9,10,11,12,13], [4,5,7,8,9,10,11,12],[4,5,7,8,11,12,13,15], [4,5,7,11,12,13,14,15],[4,6,7,8,9,11,12,14], [4,6,7,8,11,12,13,15],[4,6,7,8,11,12,14,15], [4,6,7,9,10,11,12,14],[4,6,7,11,12,13,14,15], [4,6,9,10,11,12,13,14],[5,6,7,8,9,10,11,12], [5,6,7,8,9,10,12,13],[5,6,7,8,9,10,13,15], [5,6,7,8,9,12,13,14],[5,6,7,8,10,11,12,13], [5,6,7,8,12,13,14,15],[5,6,7,9,10,12,13,14], [5,6,7,10,11,12,13,14],[5,6,8,9,10,11,12,13], [5,7,8,9,10,12,13,15],[5,7,8,10,11,12,13,15], [5,7,10,11,12,13,14,15],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,10,13,14,15], [6,7,8,9,11,12,13,14],[6,7,8,10,11,13,14,15], [6,7,8,11,12,13,14,15],[6,7,9,10,11,12,13,14], [7,8,9,10,11,12,13,14],[7,8,9,10,11,12,14,15], [7,8,9,10,12,13,14,15],[7,8,10,11,12,13,14,15], [8,9,10,11,12,13,14,15]] manifold_7_15_2_6=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,11], [1,2,3,4,5,6,11,13],[1,2,3,4,5,6,13,14], [1,2,3,4,5,6,14,15],[1,2,3,4,5,7,8,15], [1,2,3,4,5,8,9,10],[1,2,3,4,5,8,10,15], [1,2,3,4,5,9,10,12],[1,2,3,4,5,9,11,12], [1,2,3,4,5,10,12,15],[1,2,3,4,5,11,12,13], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,14], [1,2,3,4,6,7,14,15],[1,2,3,4,6,9,11,14], [1,2,3,4,6,11,13,14],[1,2,3,4,7,8,9,15], [1,2,3,4,7,9,14,15],[1,2,3,4,8,9,10,11], [1,2,3,4,8,9,11,15],[1,2,3,4,8,10,11,15], [1,2,3,4,9,10,11,12],[1,2,3,4,9,11,14,15], [1,2,3,4,10,11,12,15],[1,2,3,4,11,12,13,14], [1,2,3,4,11,12,14,15],[1,2,3,4,12,13,14,15], [1,2,3,5,6,7,8,15],[1,2,3,5,6,8,9,13], [1,2,3,5,6,8,13,15],[1,2,3,5,6,9,11,13], [1,2,3,5,6,13,14,15],[1,2,3,5,8,9,10,13], [1,2,3,5,8,10,13,15],[1,2,3,5,9,10,12,13], [1,2,3,5,9,11,12,13],[1,2,3,5,10,12,13,15], [1,2,3,6,7,8,9,10],[1,2,3,6,7,8,10,14], [1,2,3,6,7,8,14,15],[1,2,3,6,7,9,10,14], [1,2,3,6,8,9,10,13],[1,2,3,6,8,10,13,14], [1,2,3,6,8,13,14,15],[1,2,3,6,9,10,11,13], [1,2,3,6,9,10,11,14],[1,2,3,6,10,11,13,14], [1,2,3,7,8,9,10,15],[1,2,3,7,8,10,14,15], [1,2,3,7,9,10,14,15],[1,2,3,8,9,10,11,15], [1,2,3,8,10,13,14,15],[1,2,3,9,10,11,12,13], [1,2,3,9,10,11,14,15],[1,2,3,10,11,12,13,15], [1,2,3,10,11,13,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,14], [1,2,4,5,6,7,14,15],[1,2,4,5,6,9,11,13], [1,2,4,5,6,9,13,14],[1,2,4,5,7,8,9,12], [1,2,4,5,7,8,12,15],[1,2,4,5,7,9,12,14], [1,2,4,5,7,12,14,15],[1,2,4,5,8,9,10,12], [1,2,4,5,8,10,12,15],[1,2,4,5,9,11,12,13], [1,2,4,5,9,12,13,14],[1,2,4,5,12,13,14,15], [1,2,4,6,9,11,13,14],[1,2,4,7,8,9,12,15], [1,2,4,7,9,12,14,15],[1,2,4,8,9,10,11,12], [1,2,4,8,9,11,12,15],[1,2,4,8,10,11,12,15], [1,2,4,9,11,12,13,14],[1,2,4,9,11,12,14,15], [1,2,5,6,7,8,9,15],[1,2,5,6,7,9,13,14], [1,2,5,6,7,9,13,15],[1,2,5,6,7,13,14,15], [1,2,5,6,8,9,13,15],[1,2,5,7,8,9,12,15], [1,2,5,7,9,12,13,14],[1,2,5,7,9,12,13,15], [1,2,5,7,12,13,14,15],[1,2,5,8,9,10,12,15], [1,2,5,8,9,10,13,15],[1,2,5,9,10,12,13,15], [1,2,6,7,8,9,10,14],[1,2,6,7,8,9,14,15], [1,2,6,7,9,13,14,15],[1,2,6,8,9,10,13,14], [1,2,6,8,9,13,14,15],[1,2,6,9,10,11,13,14], [1,2,7,8,9,10,14,15],[1,2,7,9,12,13,14,15], [1,2,8,9,10,11,12,15],[1,2,8,9,10,13,14,15], [1,2,9,10,11,12,13,14],[1,2,9,10,11,12,14,15], [1,2,9,10,12,13,14,15],[1,2,10,11,12,13,14,15], [1,3,4,5,6,7,8,15],[1,3,4,5,6,8,9,11], [1,3,4,5,6,8,11,13],[1,3,4,5,6,8,13,15], [1,3,4,5,6,13,14,15],[1,3,4,5,8,9,10,12], [1,3,4,5,8,9,11,12],[1,3,4,5,8,10,12,15], [1,3,4,5,8,11,12,13],[1,3,4,5,8,12,13,15], [1,3,4,6,7,8,9,11],[1,3,4,6,7,8,11,15], [1,3,4,6,7,9,11,14],[1,3,4,6,7,11,14,15], [1,3,4,6,8,11,13,15],[1,3,4,6,11,13,14,15], [1,3,4,7,8,9,11,15],[1,3,4,7,9,11,14,15], [1,3,4,8,9,10,11,12],[1,3,4,8,10,11,12,15], [1,3,4,8,11,12,13,15],[1,3,4,11,12,13,14,15], [1,3,5,6,8,9,11,13],[1,3,5,8,9,10,12,13], [1,3,5,8,9,11,12,13],[1,3,5,8,10,12,13,15], [1,3,6,7,8,9,10,11],[1,3,6,7,8,10,11,14], [1,3,6,7,8,11,14,15],[1,3,6,7,9,10,11,14], [1,3,6,8,9,10,11,13],[1,3,6,8,10,11,13,14], [1,3,6,8,11,13,14,15],[1,3,7,8,9,10,11,15], [1,3,7,8,10,11,14,15],[1,3,7,9,10,11,14,15], [1,3,8,9,10,11,12,13],[1,3,8,10,11,12,13,15], [1,3,8,10,11,13,14,15],[1,4,5,6,7,8,9,14], [1,4,5,6,7,8,14,15],[1,4,5,6,8,9,11,12], [1,4,5,6,8,9,12,14],[1,4,5,6,8,11,12,13], [1,4,5,6,8,12,13,15],[1,4,5,6,8,12,14,15], [1,4,5,6,9,11,12,13],[1,4,5,6,9,12,13,14], [1,4,5,6,12,13,14,15],[1,4,5,7,8,9,12,14], [1,4,5,7,8,12,14,15],[1,4,6,7,8,9,11,14], [1,4,6,7,8,11,14,15],[1,4,6,8,9,11,12,14], [1,4,6,8,11,12,13,15],[1,4,6,8,11,12,14,15], [1,4,6,9,11,12,13,14],[1,4,6,11,12,13,14,15], [1,4,7,8,9,11,14,15],[1,4,7,8,9,12,14,15], [1,4,8,9,11,12,14,15],[1,5,6,7,8,9,13,14], [1,5,6,7,8,9,13,15],[1,5,6,7,8,13,14,15], [1,5,6,8,9,11,12,13],[1,5,6,8,9,12,13,14], [1,5,6,8,12,13,14,15],[1,5,7,8,9,12,13,14], [1,5,7,8,9,12,13,15],[1,5,7,8,12,13,14,15], [1,5,8,9,10,12,13,15],[1,6,7,8,9,10,11,14], [1,6,7,8,9,13,14,15],[1,6,8,9,10,11,13,14], [1,6,8,9,11,12,13,14],[1,6,8,11,12,13,14,15], [1,7,8,9,10,11,14,15],[1,7,8,9,12,13,14,15], [1,8,9,10,11,12,13,15],[1,8,9,10,11,13,14,15], [1,8,9,11,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,12],[2,3,4,5,6,7,12,14], [2,3,4,5,6,7,14,15],[2,3,4,5,6,9,10,11], [2,3,4,5,6,10,11,13],[2,3,4,5,6,10,12,13], [2,3,4,5,6,12,13,14],[2,3,4,5,7,8,9,10], [2,3,4,5,7,8,10,15],[2,3,4,5,7,10,12,15], [2,3,4,5,7,12,14,15],[2,3,4,5,9,10,11,12], [2,3,4,5,10,11,12,13],[2,3,4,5,12,13,14,15], [2,3,4,6,7,9,10,14],[2,3,4,6,7,10,12,14], [2,3,4,6,9,10,11,14],[2,3,4,6,10,11,13,14], [2,3,4,6,10,12,13,14],[2,3,4,7,8,9,10,11], [2,3,4,7,8,9,11,15],[2,3,4,7,8,10,11,15], [2,3,4,7,9,10,11,14],[2,3,4,7,9,11,14,15], [2,3,4,7,10,11,12,14],[2,3,4,7,10,11,12,15], [2,3,4,7,11,12,14,15],[2,3,4,10,11,12,13,14], [2,3,5,6,7,8,9,10],[2,3,5,6,7,8,10,15], [2,3,5,6,7,10,12,14],[2,3,5,6,7,10,14,15], [2,3,5,6,8,9,10,13],[2,3,5,6,8,10,13,15], [2,3,5,6,9,10,11,13],[2,3,5,6,10,12,13,14], [2,3,5,6,10,13,14,15],[2,3,5,7,10,12,14,15], [2,3,5,9,10,11,12,13],[2,3,5,10,12,13,14,15], [2,3,6,7,8,10,14,15],[2,3,6,8,10,13,14,15], [2,3,7,8,9,10,11,15],[2,3,7,9,10,11,14,15], [2,3,7,10,11,12,14,15],[2,3,10,11,12,13,14,15], [2,4,5,6,7,9,10,12],[2,4,5,6,7,9,12,14], [2,4,5,6,9,10,11,13],[2,4,5,6,9,10,12,13], [2,4,5,6,9,12,13,14],[2,4,5,7,8,9,10,12], [2,4,5,7,8,10,12,15],[2,4,5,9,10,11,12,13], [2,4,6,7,9,10,12,14],[2,4,6,9,10,11,13,14], [2,4,6,9,10,12,13,14],[2,4,7,8,9,10,11,12], [2,4,7,8,9,11,12,15],[2,4,7,8,10,11,12,15], [2,4,7,9,10,11,12,14],[2,4,7,9,11,12,14,15], [2,4,9,10,11,12,13,14],[2,5,6,7,8,9,10,15], [2,5,6,7,9,10,12,13],[2,5,6,7,9,10,13,15], [2,5,6,7,9,12,13,14],[2,5,6,7,10,12,13,14], [2,5,6,7,10,13,14,15],[2,5,6,8,9,10,13,15], [2,5,7,8,9,10,12,15],[2,5,7,9,10,12,13,15], [2,5,7,10,12,13,14,15],[2,6,7,8,9,10,14,15], [2,6,7,9,10,12,13,14],[2,6,7,9,10,13,14,15], [2,6,8,9,10,13,14,15],[2,7,8,9,10,11,12,15], [2,7,9,10,11,12,14,15],[2,7,9,10,12,13,14,15], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,13],[3,4,5,6,7,8,13,15], [3,4,5,6,7,10,11,12],[3,4,5,6,7,11,12,14], [3,4,5,6,7,11,13,14],[3,4,5,6,7,13,14,15], [3,4,5,6,8,9,10,11],[3,4,5,6,10,11,12,13], [3,4,5,6,11,12,13,14],[3,4,5,7,8,10,11,15], [3,4,5,7,8,11,13,15],[3,4,5,7,10,11,12,15], [3,4,5,7,11,12,14,15],[3,4,5,7,11,13,14,15], [3,4,5,8,9,10,11,12],[3,4,5,8,10,11,12,15], [3,4,5,8,11,12,13,15],[3,4,5,11,12,13,14,15], [3,4,6,7,8,9,10,11],[3,4,6,7,8,11,13,15], [3,4,6,7,9,10,11,14],[3,4,6,7,10,11,12,14], [3,4,6,7,11,13,14,15],[3,4,6,10,11,12,13,14], [3,5,6,7,8,10,11,13],[3,5,6,7,8,10,13,15], [3,5,6,7,10,11,12,14],[3,5,6,7,10,11,13,14], [3,5,6,7,10,13,14,15],[3,5,6,8,9,10,11,13], [3,5,6,10,11,12,13,14],[3,5,7,8,10,11,13,15], [3,5,7,10,11,12,14,15],[3,5,7,10,11,13,14,15], [3,5,8,9,10,11,12,13],[3,5,8,10,11,12,13,15], [3,5,10,11,12,13,14,15],[3,6,7,8,10,11,13,14], [3,6,7,8,10,13,14,15],[3,6,7,8,11,13,14,15], [3,7,8,10,11,13,14,15],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,9,12,14], [4,5,6,7,8,11,12,13],[4,5,6,7,8,12,13,15], [4,5,6,7,8,12,14,15],[4,5,6,7,9,10,11,12], [4,5,6,7,11,12,13,14],[4,5,6,7,12,13,14,15], [4,5,6,9,10,11,12,13],[4,5,7,8,9,10,11,12], [4,5,7,8,10,11,12,15],[4,5,7,8,11,12,13,15], [4,5,7,11,12,13,14,15],[4,6,7,8,9,11,12,14], [4,6,7,8,11,12,13,15],[4,6,7,8,11,12,14,15], [4,6,7,9,10,11,12,14],[4,6,7,11,12,13,14,15], [4,6,9,10,11,12,13,14],[4,7,8,9,11,12,14,15], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,10,13,15],[5,6,7,8,9,12,13,14], [5,6,7,8,10,11,12,13],[5,6,7,8,12,13,14,15], [5,6,7,10,11,12,13,14],[5,6,8,9,10,11,12,13], [5,7,8,9,10,12,13,15],[5,7,8,10,11,12,13,15], [5,7,10,11,12,13,14,15],[6,7,8,9,10,11,12,13], [6,7,8,9,10,11,13,14],[6,7,8,9,10,13,14,15], [6,7,8,9,11,12,13,14],[6,7,8,11,12,13,14,15], [6,7,9,10,11,12,13,14],[7,8,9,10,11,12,13,14], [7,8,9,10,11,12,14,15],[7,8,9,10,12,13,14,15], [7,8,10,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_2_7=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,13], [1,2,3,4,5,6,13,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,15],[1,2,3,4,5,8,9,10], [1,2,3,4,5,8,10,12],[1,2,3,4,5,8,12,15], [1,2,3,4,5,9,10,12],[1,2,3,4,5,9,11,12], [1,2,3,4,5,9,11,13],[1,2,3,4,5,11,12,13], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,14], [1,2,3,4,6,7,14,15],[1,2,3,4,6,9,11,13], [1,2,3,4,6,9,11,14],[1,2,3,4,6,11,13,14], [1,2,3,4,7,8,9,15],[1,2,3,4,7,9,11,14], [1,2,3,4,7,9,11,15],[1,2,3,4,7,11,14,15], [1,2,3,4,8,9,10,11],[1,2,3,4,8,9,11,15], [1,2,3,4,8,10,11,15],[1,2,3,4,8,10,12,15], [1,2,3,4,9,10,11,12],[1,2,3,4,10,11,12,15], [1,2,3,4,11,12,13,14],[1,2,3,4,11,12,14,15], [1,2,3,4,12,13,14,15],[1,2,3,5,6,7,8,15], [1,2,3,5,6,8,9,10],[1,2,3,5,6,8,10,13], [1,2,3,5,6,8,13,15],[1,2,3,5,6,9,10,13], [1,2,3,5,6,13,14,15],[1,2,3,5,8,10,12,15], [1,2,3,5,8,10,13,15],[1,2,3,5,9,10,12,13], [1,2,3,5,9,11,12,13],[1,2,3,5,10,12,13,15], [1,2,3,6,7,8,9,10],[1,2,3,6,7,8,10,14], [1,2,3,6,7,8,14,15],[1,2,3,6,7,9,10,14], [1,2,3,6,8,10,13,15],[1,2,3,6,8,10,14,15], [1,2,3,6,9,10,13,14],[1,2,3,6,9,11,13,14], [1,2,3,6,10,13,14,15],[1,2,3,7,8,9,10,15], [1,2,3,7,8,10,14,15],[1,2,3,7,9,10,14,15], [1,2,3,7,9,11,14,15],[1,2,3,8,9,10,11,15], [1,2,3,9,10,11,12,13],[1,2,3,9,10,11,13,14], [1,2,3,9,10,11,14,15],[1,2,3,10,11,12,13,15], [1,2,3,10,11,13,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,14], [1,2,4,5,6,7,14,15],[1,2,4,5,6,9,12,13], [1,2,4,5,6,9,12,14],[1,2,4,5,6,12,13,14], [1,2,4,5,7,8,9,15],[1,2,4,5,7,9,12,14], [1,2,4,5,7,9,12,15],[1,2,4,5,7,12,14,15], [1,2,4,5,8,9,10,12],[1,2,4,5,8,9,12,15], [1,2,4,5,9,11,12,13],[1,2,4,5,12,13,14,15], [1,2,4,6,9,11,13,14],[1,2,4,6,9,12,13,14], [1,2,4,7,9,11,14,15],[1,2,4,7,9,12,14,15], [1,2,4,8,9,10,11,12],[1,2,4,8,9,11,12,15], [1,2,4,8,10,11,12,15],[1,2,4,9,11,12,13,14], [1,2,4,9,11,12,14,15],[1,2,5,6,7,8,9,15], [1,2,5,6,7,9,13,14],[1,2,5,6,7,9,13,15], [1,2,5,6,7,13,14,15],[1,2,5,6,8,9,10,13], [1,2,5,6,8,9,13,15],[1,2,5,6,9,12,13,14], [1,2,5,7,9,12,14,15],[1,2,5,7,9,13,14,15], [1,2,5,8,9,10,12,13],[1,2,5,8,9,12,13,15], [1,2,5,8,10,12,13,15],[1,2,5,9,12,13,14,15], [1,2,6,7,8,9,10,14],[1,2,6,7,8,9,14,15], [1,2,6,7,9,13,14,15],[1,2,6,8,9,10,13,14], [1,2,6,8,9,13,14,15],[1,2,6,8,10,13,14,15], [1,2,7,8,9,10,14,15],[1,2,8,9,10,11,12,15], [1,2,8,9,10,12,13,15],[1,2,8,9,10,13,14,15], [1,2,9,10,11,12,13,14],[1,2,9,10,11,12,14,15], [1,2,9,10,12,13,14,15],[1,2,10,11,12,13,14,15], [1,3,4,5,6,7,8,15],[1,3,4,5,6,8,9,11], [1,3,4,5,6,8,11,13],[1,3,4,5,6,8,13,15], [1,3,4,5,6,9,11,13],[1,3,4,5,6,13,14,15], [1,3,4,5,8,9,10,12],[1,3,4,5,8,9,11,12], [1,3,4,5,8,11,12,15],[1,3,4,5,8,11,13,15], [1,3,4,5,11,12,13,15],[1,3,4,6,7,8,9,11], [1,3,4,6,7,8,11,14],[1,3,4,6,7,8,14,15], [1,3,4,6,7,9,11,14],[1,3,4,6,8,11,13,15], [1,3,4,6,8,11,14,15],[1,3,4,6,11,13,14,15], [1,3,4,7,8,9,11,15],[1,3,4,7,8,11,14,15], [1,3,4,8,9,10,11,12],[1,3,4,8,10,11,12,15], [1,3,4,11,12,13,14,15],[1,3,5,6,8,9,10,13], [1,3,5,6,8,9,11,13],[1,3,5,8,9,10,11,12], [1,3,5,8,9,10,11,13],[1,3,5,8,10,11,12,13], [1,3,5,8,10,12,13,15],[1,3,5,8,11,12,13,15], [1,3,5,9,10,11,12,13],[1,3,6,7,8,9,10,14], [1,3,6,7,8,9,11,14],[1,3,6,8,9,10,11,13], [1,3,6,8,9,10,11,14],[1,3,6,8,10,11,13,14], [1,3,6,8,10,13,14,15],[1,3,6,8,11,13,14,15], [1,3,6,9,10,11,13,14],[1,3,7,8,9,10,11,14], [1,3,7,8,9,10,11,15],[1,3,7,8,10,11,14,15], [1,3,7,9,10,11,14,15],[1,3,8,10,11,12,13,15], [1,3,8,10,11,13,14,15],[1,4,5,6,7,8,9,12], [1,4,5,6,7,8,12,14],[1,4,5,6,7,8,14,15], [1,4,5,6,7,9,12,14],[1,4,5,6,8,9,11,13], [1,4,5,6,8,9,12,13],[1,4,5,6,8,12,13,15], [1,4,5,6,8,12,14,15],[1,4,5,6,12,13,14,15], [1,4,5,7,8,9,12,15],[1,4,5,7,8,12,14,15], [1,4,5,8,9,11,12,13],[1,4,5,8,11,12,13,15], [1,4,6,7,8,9,11,14],[1,4,6,7,8,9,12,14], [1,4,6,8,9,11,12,13],[1,4,6,8,9,11,12,14], [1,4,6,8,11,12,13,14],[1,4,6,8,11,13,14,15], [1,4,6,8,12,13,14,15],[1,4,6,9,11,12,13,14], [1,4,7,8,9,11,12,14],[1,4,7,8,9,11,12,15], [1,4,7,8,11,12,14,15],[1,4,7,9,11,12,14,15], [1,4,8,11,12,13,14,15],[1,5,6,7,8,9,12,14], [1,5,6,7,8,9,13,14],[1,5,6,7,8,9,13,15], [1,5,6,7,8,13,14,15],[1,5,6,8,9,12,13,14], [1,5,6,8,12,13,14,15],[1,5,7,8,9,12,13,14], [1,5,7,8,9,12,13,15],[1,5,7,8,12,13,14,15], [1,5,7,9,12,13,14,15],[1,5,8,9,10,11,12,13], [1,6,7,8,9,13,14,15],[1,6,8,9,10,11,13,14], [1,6,8,9,11,12,13,14],[1,7,8,9,10,11,14,15], [1,7,8,9,11,12,14,15],[1,7,8,9,12,13,14,15], [1,8,9,10,11,12,13,15],[1,8,9,10,11,13,14,15], [1,8,9,11,12,13,14,15],[1,9,10,11,12,13,14,15], [2,3,4,5,6,7,8,9],[2,3,4,5,6,7,9,10], [2,3,4,5,6,7,10,14],[2,3,4,5,6,7,14,15], [2,3,4,5,6,9,10,11],[2,3,4,5,6,9,11,13], [2,3,4,5,6,10,11,13],[2,3,4,5,6,10,12,13], [2,3,4,5,6,10,12,14],[2,3,4,5,6,12,13,14], [2,3,4,5,7,8,9,10],[2,3,4,5,7,8,10,15], [2,3,4,5,7,10,12,14],[2,3,4,5,7,10,12,15], [2,3,4,5,7,12,14,15],[2,3,4,5,8,10,12,15], [2,3,4,5,9,10,11,12],[2,3,4,5,10,11,12,13], [2,3,4,5,12,13,14,15],[2,3,4,6,7,9,10,11], [2,3,4,6,7,9,11,14],[2,3,4,6,7,10,11,14], [2,3,4,6,10,11,13,14],[2,3,4,6,10,12,13,14], [2,3,4,7,8,9,10,11],[2,3,4,7,8,9,11,15], [2,3,4,7,8,10,11,15],[2,3,4,7,10,11,14,15], [2,3,4,7,10,12,14,15],[2,3,4,10,11,12,13,14], [2,3,4,10,11,12,14,15],[2,3,5,6,7,8,9,10], [2,3,5,6,7,8,10,15],[2,3,5,6,7,10,13,14], [2,3,5,6,7,10,13,15],[2,3,5,6,7,13,14,15], [2,3,5,6,8,10,13,15],[2,3,5,6,9,10,11,13], [2,3,5,6,10,12,13,14],[2,3,5,7,10,12,14,15], [2,3,5,7,10,13,14,15],[2,3,5,9,10,11,12,13], [2,3,5,10,12,13,14,15],[2,3,6,7,8,10,14,15], [2,3,6,7,9,10,11,14],[2,3,6,7,10,13,14,15], [2,3,6,9,10,11,13,14],[2,3,7,8,9,10,11,15], [2,3,7,9,10,11,14,15],[2,3,10,11,12,13,14,15], [2,4,5,6,7,9,10,12],[2,4,5,6,7,9,12,14], [2,4,5,6,7,10,12,14],[2,4,5,6,9,10,11,13], [2,4,5,6,9,10,12,13],[2,4,5,7,8,9,10,12], [2,4,5,7,8,9,12,15],[2,4,5,7,8,10,12,15], [2,4,5,9,10,11,12,13],[2,4,6,7,9,10,11,14], [2,4,6,7,9,10,12,14],[2,4,6,9,10,11,12,13], [2,4,6,9,10,11,12,14],[2,4,6,9,11,12,13,14], [2,4,6,10,11,12,13,14],[2,4,7,8,9,10,11,15], [2,4,7,8,9,10,12,15],[2,4,7,9,10,11,12,14], [2,4,7,9,10,11,12,15],[2,4,7,9,11,12,14,15], [2,4,7,10,11,12,14,15],[2,4,8,9,10,11,12,15], [2,5,6,7,8,9,10,13],[2,5,6,7,8,9,13,15], [2,5,6,7,8,10,13,15],[2,5,6,7,9,10,12,14], [2,5,6,7,9,10,13,14],[2,5,6,9,10,12,13,14], [2,5,7,8,9,10,12,15],[2,5,7,8,9,10,13,15], [2,5,7,9,10,12,13,14],[2,5,7,9,10,12,13,15], [2,5,7,9,12,13,14,15],[2,5,7,10,12,13,14,15], [2,5,8,9,10,12,13,15],[2,6,7,8,9,10,13,15], [2,6,7,8,9,10,14,15],[2,6,7,9,10,13,14,15], [2,6,8,9,10,13,14,15],[2,6,9,10,11,12,13,14], [2,7,9,10,11,12,14,15],[2,7,9,10,12,13,14,15], [3,4,5,6,7,8,9,10],[3,4,5,6,7,8,10,11], [3,4,5,6,7,8,11,15],[3,4,5,6,7,10,11,12], [3,4,5,6,7,10,12,14],[3,4,5,6,7,11,12,14], [3,4,5,6,7,11,13,14],[3,4,5,6,7,11,13,15], [3,4,5,6,7,13,14,15],[3,4,5,6,8,9,10,11], [3,4,5,6,8,11,13,15],[3,4,5,6,10,11,12,13], [3,4,5,6,11,12,13,14],[3,4,5,7,8,10,11,12], [3,4,5,7,8,10,12,15],[3,4,5,7,8,11,12,15], [3,4,5,7,11,12,14,15],[3,4,5,7,11,13,14,15], [3,4,5,8,9,10,11,12],[3,4,5,11,12,13,14,15], [3,4,6,7,8,9,10,11],[3,4,6,7,8,11,14,15], [3,4,6,7,10,11,12,14],[3,4,6,7,11,13,14,15], [3,4,6,10,11,12,13,14],[3,4,7,8,10,11,12,15], [3,4,7,10,11,12,14,15],[3,5,6,7,8,10,11,13], [3,5,6,7,8,10,13,15],[3,5,6,7,8,11,13,15], [3,5,6,7,10,11,12,14],[3,5,6,7,10,11,13,14], [3,5,6,8,9,10,11,13],[3,5,6,10,11,12,13,14], [3,5,7,8,10,11,12,15],[3,5,7,8,10,11,13,15], [3,5,7,10,11,12,13,14],[3,5,7,10,11,12,13,15], [3,5,7,10,12,13,14,15],[3,5,7,11,12,13,14,15], [3,5,8,10,11,12,13,15],[3,6,7,8,9,10,11,14], [3,6,7,8,10,11,13,15],[3,6,7,8,10,11,14,15], [3,6,7,10,11,13,14,15],[3,6,8,10,11,13,14,15], [3,7,10,11,12,13,14,15],[4,5,6,7,8,9,10,11], [4,5,6,7,8,9,11,12],[4,5,6,7,8,11,12,13], [4,5,6,7,8,11,13,15],[4,5,6,7,8,12,13,15], [4,5,6,7,8,12,14,15],[4,5,6,7,9,10,11,12], [4,5,6,7,11,12,13,14],[4,5,6,7,12,13,14,15], [4,5,6,8,9,11,12,13],[4,5,6,9,10,11,12,13], [4,5,7,8,9,10,11,12],[4,5,7,8,11,12,13,15], [4,5,7,11,12,13,14,15],[4,6,7,8,9,11,12,14], [4,6,7,8,11,12,13,15],[4,6,7,8,11,12,14,15], [4,6,7,9,10,11,12,14],[4,6,7,11,12,13,14,15], [4,6,8,11,12,13,14,15],[4,7,8,9,10,11,12,15], [5,6,7,8,9,10,11,12],[5,6,7,8,9,10,12,13], [5,6,7,8,9,12,13,14],[5,6,7,8,10,11,12,13], [5,6,7,8,12,13,14,15],[5,6,7,9,10,12,13,14], [5,6,7,10,11,12,13,14],[5,6,8,9,10,11,12,13], [5,7,8,9,10,12,13,15],[5,7,8,10,11,12,13,15], [6,7,8,9,10,11,12,13],[6,7,8,9,10,11,13,14], [6,7,8,9,10,13,14,15],[6,7,8,9,11,12,13,14], [6,7,8,10,11,13,14,15],[6,7,8,11,12,13,14,15], [6,7,9,10,11,12,13,14],[7,8,9,10,11,12,13,14], [7,8,9,10,11,12,14,15],[7,8,9,10,12,13,14,15], [7,8,10,11,12,13,14,15],[8,9,10,11,12,13,14,15]] manifold_7_15_2_8=[[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,15], [1,2,3,4,5,6,8,9],[1,2,3,4,5,6,9,13], [1,2,3,4,5,6,13,14],[1,2,3,4,5,6,14,15], [1,2,3,4,5,7,8,15],[1,2,3,4,5,8,9,10], [1,2,3,4,5,8,10,12],[1,2,3,4,5,8,12,15], [1,2,3,4,5,9,10,12],[1,2,3,4,5,9,11,12], [1,2,3,4,5,9,11,13],[1,2,3,4,5,11,12,13], [1,2,3,4,5,12,13,15],[1,2,3,4,5,13,14,15], [1,2,3,4,6,7,8,9],[1,2,3,4,6,7,9,14], [1,2,3,4,6,7,14,15],[1,2,3,4,6,9,11,13], [1,2,3,4,6,9,11,14],[1,2,3,4,6,11,13,14], [1,2,3,4,7,8,9,15],[1,2,3,4,7,9,11,14], [1,2,3,4,7,9,11,15],[1,2,3,4,7,11,14,15], [1,2,3,4,8,9,10,11],[1,2,3,4,8,9,11,15], [1,2,3,4,8,10,11,15],[1,2,3,4,8,10,12,15], [1,2,3,4,9,10,11,12],[1,2,3,4,10,11,12,15], [1,2,3,4,11,12,13,14],[1,2,3,4,11,12,14,15], [1,2,3,4,12,13,14,15],[1,2,3,5,6,7,8,15], [1,2,3,5,6,8,9,13],[1,2,3,5,6,8,13,15], [1,2,3,5,6,13,14,15],[1,2,3,5,8,9,10,13], [1,2,3,5,8,10,12,15],[1,2,3,5,8,10,13,15], [1,2,3,5,9,10,12,13],[1,2,3,5,9,11,12,13], [1,2,3,5,10,12,13,15],[1,2,3,6,7,8,9,10], [1,2,3,6,7,8,10,14],[1,2,3,6,7,8,14,15], [1,2,3,6,7,9,10,14],[1,2,3,6,8,9,10,13], [1,2,3,6,8,10,13,15],[1,2,3,6,8,10,14,15], [1,2,3,6,9,10,11,13],[1,2,3,6,9,10,11,14], [1,2,3,6,10,11,13,14],[1,2,3,6,10,13,14,15], [1,2,3,7,8,9,10,15],[1,2,3,7,8,10,14,15], [1,2,3,7,9,10,14,15],[1,2,3,7,9,11,14,15], [1,2,3,8,9,10,11,15],[1,2,3,9,10,11,12,13], [1,2,3,9,10,11,14,15],[1,2,3,10,11,12,13,15], [1,2,3,10,11,13,14,15],[1,2,3,11,12,13,14,15], [1,2,4,5,6,7,8,9],[1,2,4,5,6,7,9,14], [1,2,4,5,6,7,14,15],[1,2,4,5,6,9,13,14], [1,2,4,5,7,8,9,12],[1,2,4,5,7,8,12,15], [1,2,4,5,7,9,12,14],[1,2,4,5,7,12,14,15], [1,2,4,5,8,9,10,12],[1,2,4,5,9,11,12,13], [1,2,4,5,9,12,13,14],[1,2,4,5,12,13,14,15], [1,2,4,6,9,11,13,14],[1,2,4,7,8,9,12,15], [1,2,4,7,9,11,14,15],[1,2,4,7,9,12,14,15], [1,2,4,8,9,10,11,12],[1,2,4,8,9,11,12,15], [1,2,4,8,10,11,12,15],[1,2,4,9,11,12,13,14], [1,2,4,9,11,12,14,15],[1,2,5,6,7,8,9,15], [1,2,5,6,7,9,13,14],[1,2,5,6,7,9,13,15], [1,2,5,6,7,13,14,15],[1,2,5,6,8,9,13,15], [1,2,5,7,8,9,12,15],[1,2,5,7,9,12,14,15], [1,2,5,7,9,13,14,15],[1,2,5,8,9,10,12,15], [1,2,5,8,9,10,13,15],[1,2,5,9,10,12,13,15], [1,2,5,9,12,13,14,15],[1,2,6,7,8,9,10,14], [1,2,6,7,8,9,14,15],[1,2,6,7,9,13,14,15], [1,2,6,8,9,10,13,14],[1,2,6,8,9,13,14,15], [1,2,6,8,10,13,14,15],[1,2,6,9,10,11,13,14], [1,2,7,8,9,10,14,15],[1,2,8,9,10,11,12,15], [1,2,8,9,10,13,14,15],[1,2,9,10,11,12,13,14], [1,2,9,10,11,12,14,15],[1,2,9,10,12,13,14,15], [1,2,10,11,12,13,14,15],[1,3,4,5,6,7,8,15], [1,3,4,5,6,8,9,11],[1,3,4,5,6,8,11,13], [1,3,4,5,6,8,13,15],[1,3,4,5,6,9,11,13], [1,3,4,5,6,13,14,15],[1,3,4,5,8,9,10,12], [1,3,4,5,8,9,11,12],[1,3,4,5,8,11,12,13], [1,3,4,5,8,12,13,15],[1,3,4,6,7,8,9,11], [1,3,4,6,7,8,11,15],[1,3,4,6,7,9,11,14], [1,3,4,6,7,11,14,15],[1,3,4,6,8,11,13,15], [1,3,4,6,11,13,14,15],[1,3,4,7,8,9,11,15], [1,3,4,8,9,10,11,12],[1,3,4,8,10,11,12,15], [1,3,4,8,11,12,13,15],[1,3,4,11,12,13,14,15], [1,3,5,6,8,9,11,13],[1,3,5,8,9,10,11,12], [1,3,5,8,9,10,11,13],[1,3,5,8,10,11,12,13], [1,3,5,8,10,12,13,15],[1,3,5,9,10,11,12,13], [1,3,6,7,8,9,10,14],[1,3,6,7,8,9,11,14], [1,3,6,7,8,11,14,15],[1,3,6,8,9,10,11,13], [1,3,6,8,9,10,11,14],[1,3,6,8,10,11,13,14], [1,3,6,8,10,13,14,15],[1,3,6,8,11,13,14,15], [1,3,7,8,9,10,11,14],[1,3,7,8,9,10,11,15], [1,3,7,8,10,11,14,15],[1,3,7,9,10,11,14,15], [1,3,8,10,11,12,13,15],[1,3,8,10,11,13,14,15], [1,4,5,6,7,8,9,12],[1,4,5,6,7,8,12,14], [1,4,5,6,7,8,14,15],[1,4,5,6,7,9,12,14], [1,4,5,6,8,9,11,12],[1,4,5,6,8,11,12,13], [1,4,5,6,8,12,13,15],[1,4,5,6,8,12,14,15], [1,4,5,6,9,11,12,13],[1,4,5,6,9,12,13,14], [1,4,5,6,12,13,14,15],[1,4,5,7,8,12,14,15], [1,4,6,7,8,9,11,14],[1,4,6,7,8,9,12,14], [1,4,6,7,8,11,14,15],[1,4,6,8,9,11,12,14], [1,4,6,8,11,12,13,14],[1,4,6,8,11,13,14,15], [1,4,6,8,12,13,14,15],[1,4,6,9,11,12,13,14], [1,4,7,8,9,11,14,15],[1,4,7,8,9,12,14,15], [1,4,8,9,11,12,14,15],[1,4,8,11,12,13,14,15], [1,5,6,7,8,9,12,14],[1,5,6,7,8,9,13,14], [1,5,6,7,8,9,13,15],[1,5,6,7,8,13,14,15], 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