manifold_8_10_45_1=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,10],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,8,9,10],[1,2,3,4,5,7,8,9,10], [1,2,3,4,6,7,8,9,10],[1,2,3,5,6,7,8,9,10], [1,2,4,5,6,7,8,9,10],[1,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,9,10]] manifold_8_12_294_1=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,12],[1,2,3,4,5,6,7,9,11], [1,2,3,4,5,6,7,11,12],[1,2,3,4,5,6,8,9,10], [1,2,3,4,5,6,8,10,12],[1,2,3,4,5,6,9,10,11], [1,2,3,4,5,6,10,11,12],[1,2,3,4,5,7,8,9,12], [1,2,3,4,5,7,9,11,12],[1,2,3,4,5,8,9,10,12], [1,2,3,4,5,9,10,11,12],[1,2,3,4,6,7,8,9,11], [1,2,3,4,6,7,8,11,12],[1,2,3,4,6,8,9,10,11], [1,2,3,4,6,8,10,11,12],[1,2,3,4,7,8,9,11,12], [1,2,3,4,8,9,10,11,12],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,12],[1,2,3,5,6,7,9,10,11], [1,2,3,5,6,7,10,11,12],[1,2,3,5,7,8,9,10,12], [1,2,3,5,7,9,10,11,12],[1,2,3,6,7,8,9,10,11], [1,2,3,6,7,8,10,11,12],[1,2,3,7,8,9,10,11,12], [1,2,4,5,6,7,8,9,12],[1,2,4,5,6,7,9,11,12], [1,2,4,5,6,8,9,10,12],[1,2,4,5,6,9,10,11,12], [1,2,4,6,7,8,9,11,12],[1,2,4,6,8,9,10,11,12], [1,2,5,6,7,8,9,10,12],[1,2,5,6,7,9,10,11,12], [1,2,6,7,8,9,10,11,12],[1,3,4,5,6,7,8,9,11], [1,3,4,5,6,7,8,11,12],[1,3,4,5,6,8,9,10,11], [1,3,4,5,6,8,10,11,12],[1,3,4,5,7,8,9,11,12], [1,3,4,5,8,9,10,11,12],[1,3,5,6,7,8,9,10,11], [1,3,5,6,7,8,10,11,12],[1,3,5,7,8,9,10,11,12], [1,4,5,6,7,8,9,11,12],[1,4,5,6,8,9,10,11,12], [1,5,6,7,8,9,10,11,12],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,9,10,11], [2,3,4,5,6,7,10,11,12],[2,3,4,5,7,8,9,10,12], [2,3,4,5,7,9,10,11,12],[2,3,4,6,7,8,9,10,11], [2,3,4,6,7,8,10,11,12],[2,3,4,7,8,9,10,11,12], [2,4,5,6,7,8,9,10,12],[2,4,5,6,7,9,10,11,12], [2,4,6,7,8,9,10,11,12],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,10,11,12],[3,4,5,7,8,9,10,11,12], [4,5,6,7,8,9,10,11,12]] manifold_8_14_38_1=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,12], [1,2,3,4,5,6,7,12,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,14],[1,2,3,4,5,6,9,10,14], [1,2,3,4,5,6,10,11,14],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,7,10,11,13],[1,2,3,4,5,7,11,12,13], [1,2,3,4,5,8,9,13,14],[1,2,3,4,5,9,10,13,14], [1,2,3,4,5,10,11,13,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,12],[1,2,3,4,6,7,8,12,14], [1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,10,11,12], [1,2,3,4,6,7,12,13,14],[1,2,3,4,6,8,9,12,14], [1,2,3,4,6,9,10,12,14],[1,2,3,4,6,10,11,12,14], [1,2,3,4,7,8,9,12,13],[1,2,3,4,7,8,12,13,14], [1,2,3,4,7,9,10,12,13],[1,2,3,4,7,10,11,12,13], [1,2,3,4,8,9,12,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,11], [1,2,3,5,6,7,8,11,14],[1,2,3,5,6,7,9,10,11], [1,2,3,5,6,7,11,12,13],[1,2,3,5,6,7,11,13,14], [1,2,3,5,6,8,9,11,14],[1,2,3,5,6,9,10,11,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,11,13], [1,2,3,5,7,8,11,13,14],[1,2,3,5,7,9,10,11,13], [1,2,3,5,8,9,11,13,14],[1,2,3,5,9,10,11,13,14], [1,2,3,6,7,8,9,11,12],[1,2,3,6,7,8,11,12,14], [1,2,3,6,7,9,10,11,12],[1,2,3,6,7,11,12,13,14], [1,2,3,6,8,9,11,12,14],[1,2,3,6,9,10,11,12,14], [1,2,3,7,8,9,11,12,13],[1,2,3,7,8,11,12,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,8,9,11,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,10,11,12], [1,2,4,5,6,7,10,12,13],[1,2,4,5,6,7,10,13,14], [1,2,4,5,6,8,9,10,14],[1,2,4,5,6,10,11,12,14], [1,2,4,5,6,10,12,13,14],[1,2,4,5,7,8,9,10,13], [1,2,4,5,7,8,10,13,14],[1,2,4,5,7,10,11,12,13], [1,2,4,5,8,9,10,13,14],[1,2,4,5,10,11,12,13,14], [1,2,4,6,7,8,9,10,12],[1,2,4,6,7,8,10,12,14], [1,2,4,6,7,10,12,13,14],[1,2,4,6,8,9,10,12,14], [1,2,4,7,8,9,10,12,13],[1,2,4,7,8,10,12,13,14], [1,2,4,8,9,10,12,13,14],[1,2,5,6,7,8,9,10,11], [1,2,5,6,7,8,10,11,14],[1,2,5,6,7,10,11,12,13], [1,2,5,6,7,10,11,13,14],[1,2,5,6,8,9,10,11,14], [1,2,5,6,10,11,12,13,14],[1,2,5,7,8,9,10,11,13], [1,2,5,7,8,10,11,13,14],[1,2,5,8,9,10,11,13,14], [1,2,6,7,8,9,10,11,12],[1,2,6,7,8,10,11,12,14], [1,2,6,7,10,11,12,13,14],[1,2,6,8,9,10,11,12,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,14], [1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,11,12], [1,3,4,5,6,7,9,12,13],[1,3,4,5,6,7,9,13,14], [1,3,4,5,6,9,10,11,14],[1,3,4,5,6,9,11,12,14], [1,3,4,5,6,9,12,13,14],[1,3,4,5,7,8,9,13,14], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,9,10,11,13,14],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,8,9,12,14],[1,3,4,6,7,9,10,11,12], [1,3,4,6,7,9,12,13,14],[1,3,4,6,9,10,11,12,14], [1,3,4,7,8,9,12,13,14],[1,3,4,7,9,10,11,12,13], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,9,11,14], [1,3,5,6,7,9,11,12,13],[1,3,5,6,7,9,11,13,14], [1,3,5,6,9,11,12,13,14],[1,3,5,7,8,9,11,13,14], [1,3,6,7,8,9,11,12,14],[1,3,6,7,9,11,12,13,14], [1,3,7,8,9,11,12,13,14],[1,4,5,6,7,8,9,10,14], [1,4,5,6,7,9,10,11,12],[1,4,5,6,7,9,10,12,13], [1,4,5,6,7,9,10,13,14],[1,4,5,6,9,10,11,12,14], [1,4,5,6,9,10,12,13,14],[1,4,5,7,8,9,10,13,14], [1,4,5,7,9,10,11,12,13],[1,4,5,9,10,11,12,13,14], [1,4,6,7,8,9,10,12,14],[1,4,6,7,9,10,12,13,14], [1,4,7,8,9,10,12,13,14],[1,5,6,7,8,9,10,11,14], [1,5,6,7,9,10,11,12,13],[1,5,6,7,9,10,11,13,14], [1,5,6,9,10,11,12,13,14],[1,5,7,8,9,10,11,13,14], [1,6,7,8,9,10,11,12,14],[1,6,7,9,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,11,12], [2,3,4,5,6,7,8,12,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,8,9,10,14],[2,3,4,5,6,8,10,11,14], [2,3,4,5,6,8,11,12,14],[2,3,4,5,6,8,12,13,14], [2,3,4,5,7,8,9,10,13],[2,3,4,5,7,8,10,11,13], [2,3,4,5,7,8,11,12,13],[2,3,4,5,8,9,10,13,14], [2,3,4,5,8,10,11,13,14],[2,3,4,5,8,11,12,13,14], [2,3,4,6,7,8,9,10,12],[2,3,4,6,7,8,10,11,12], [2,3,4,6,7,8,12,13,14],[2,3,4,6,8,9,10,12,14], [2,3,4,6,8,10,11,12,14],[2,3,4,7,8,9,10,12,13], [2,3,4,7,8,10,11,12,13],[2,3,4,8,9,10,12,13,14], [2,3,4,8,10,11,12,13,14],[2,3,5,6,7,8,9,10,11], [2,3,5,6,7,8,11,12,13],[2,3,5,6,7,8,11,13,14], [2,3,5,6,8,9,10,11,14],[2,3,5,6,8,11,12,13,14], [2,3,5,7,8,9,10,11,13],[2,3,5,8,9,10,11,13,14], [2,3,6,7,8,9,10,11,12],[2,3,6,7,8,11,12,13,14], [2,3,6,8,9,10,11,12,14],[2,3,7,8,9,10,11,12,13], [2,3,8,9,10,11,12,13,14],[2,4,5,6,7,8,10,11,12], [2,4,5,6,7,8,10,12,13],[2,4,5,6,7,8,10,13,14], [2,4,5,6,8,10,11,12,14],[2,4,5,6,8,10,12,13,14], [2,4,5,7,8,10,11,12,13],[2,4,5,8,10,11,12,13,14], [2,4,6,7,8,10,12,13,14],[2,5,6,7,8,10,11,12,13], [2,5,6,7,8,10,11,13,14],[2,5,6,8,10,11,12,13,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,9,13,14],[3,4,5,6,8,9,10,11,14], [3,4,5,6,8,9,11,12,14],[3,4,5,6,8,9,12,13,14], [3,4,5,7,8,9,10,11,13],[3,4,5,7,8,9,11,12,13], [3,4,5,8,9,10,11,13,14],[3,4,5,8,9,11,12,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,12,13,14], [3,4,6,8,9,10,11,12,14],[3,4,7,8,9,10,11,12,13], [3,4,8,9,10,11,12,13,14],[3,5,6,7,8,9,11,12,13], [3,5,6,7,8,9,11,13,14],[3,5,6,8,9,11,12,13,14], [3,6,7,8,9,11,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,9,10,12,13],[4,5,6,7,8,9,10,13,14], [4,5,6,8,9,10,11,12,14],[4,5,6,8,9,10,12,13,14], [4,5,7,8,9,10,11,12,13],[4,5,8,9,10,11,12,13,14], [4,6,7,8,9,10,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_1=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,12], [1,2,3,4,5,6,7,12,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,14],[1,2,3,4,5,6,9,10,14], [1,2,3,4,5,6,10,11,14],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,10], [1,2,3,4,5,7,8,10,11],[1,2,3,4,5,7,8,11,12], [1,2,3,4,5,7,8,12,13],[1,2,3,4,5,7,8,13,14], [1,2,3,4,5,8,9,10,11],[1,2,3,4,5,8,9,11,12], [1,2,3,4,5,8,9,12,13],[1,2,3,4,5,8,9,13,14], [1,2,3,4,5,9,10,11,13],[1,2,3,4,5,9,10,13,14], [1,2,3,4,5,9,11,12,13],[1,2,3,4,5,10,11,13,14], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,10], [1,2,3,4,6,7,8,10,14],[1,2,3,4,6,7,10,11,14], [1,2,3,4,6,7,11,12,14],[1,2,3,4,6,7,12,13,14], [1,2,3,4,6,8,9,10,14],[1,2,3,4,7,8,10,11,14], [1,2,3,4,7,8,11,12,14],[1,2,3,4,7,8,12,13,14], [1,2,3,4,8,9,10,11,14],[1,2,3,4,8,9,11,12,14], [1,2,3,4,8,9,12,13,14],[1,2,3,4,9,10,11,12,13], [1,2,3,4,9,10,11,12,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,13], [1,2,3,5,6,7,8,13,14],[1,2,3,5,6,7,9,10,11], [1,2,3,5,6,7,9,11,13],[1,2,3,5,6,7,11,12,13], [1,2,3,5,6,8,9,13,14],[1,2,3,5,6,9,10,11,13], [1,2,3,5,6,9,10,13,14],[1,2,3,5,6,10,11,13,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,10,11], [1,2,3,5,7,8,9,11,12],[1,2,3,5,7,8,9,12,13], [1,2,3,5,7,9,11,12,13],[1,2,3,6,7,8,9,10,14], [1,2,3,6,7,8,9,13,14],[1,2,3,6,7,9,10,11,13], [1,2,3,6,7,9,10,13,14],[1,2,3,6,7,10,11,13,14], [1,2,3,6,7,11,12,13,14],[1,2,3,7,8,9,10,11,14], [1,2,3,7,8,9,11,12,13],[1,2,3,7,8,9,11,13,14], [1,2,3,7,8,11,12,13,14],[1,2,3,7,9,10,11,13,14], [1,2,3,8,9,11,12,13,14],[1,2,3,9,10,11,12,13,14], [1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,10,11], [1,2,4,5,6,7,8,11,12],[1,2,4,5,6,7,8,12,13], [1,2,4,5,6,7,8,13,14],[1,2,4,5,6,8,9,10,14], [1,2,4,5,6,8,10,11,12],[1,2,4,5,6,8,10,12,14], [1,2,4,5,6,8,12,13,14],[1,2,4,5,6,10,11,12,14], [1,2,4,5,8,9,10,11,12],[1,2,4,5,8,9,10,12,14], [1,2,4,5,8,9,12,13,14],[1,2,4,5,9,10,11,12,13], [1,2,4,5,9,10,12,13,14],[1,2,4,5,10,11,12,13,14], [1,2,4,6,7,8,10,11,14],[1,2,4,6,7,8,11,12,14], [1,2,4,6,7,8,12,13,14],[1,2,4,6,8,10,11,12,14], [1,2,4,8,9,10,11,12,14],[1,2,5,6,7,8,9,10,11], [1,2,5,6,7,8,9,11,12],[1,2,5,6,7,8,9,12,13], [1,2,5,6,7,9,11,12,13],[1,2,5,6,8,9,10,11,12], [1,2,5,6,8,9,10,12,14],[1,2,5,6,8,9,12,13,14], [1,2,5,6,9,10,11,12,13],[1,2,5,6,9,10,12,13,14], [1,2,5,6,10,11,12,13,14],[1,2,6,7,8,9,10,11,12], [1,2,6,7,8,9,10,12,14],[1,2,6,7,8,9,12,13,14], [1,2,6,7,8,10,11,12,14],[1,2,6,7,9,10,11,12,13], [1,2,6,7,9,10,12,13,14],[1,2,6,7,10,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,11,13,14], [1,2,7,8,9,10,12,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,14], [1,3,4,5,6,7,9,10,14],[1,3,4,5,6,7,10,11,14], [1,3,4,5,6,7,11,12,13],[1,3,4,5,6,7,11,13,14], [1,3,4,5,6,11,12,13,14],[1,3,4,5,7,8,9,10,11], [1,3,4,5,7,8,9,11,13],[1,3,4,5,7,8,9,13,14], [1,3,4,5,7,8,11,12,13],[1,3,4,5,7,9,10,11,14], [1,3,4,5,7,9,11,13,14],[1,3,4,5,8,9,11,12,13], [1,3,4,5,9,10,11,13,14],[1,3,4,6,7,8,9,10,14], [1,3,4,6,7,11,12,13,14],[1,3,4,7,8,9,10,11,14], [1,3,4,7,8,9,11,13,14],[1,3,4,7,8,11,12,13,14], [1,3,4,8,9,11,12,13,14],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,13,14],[1,3,5,6,7,9,10,11,13], [1,3,5,6,7,9,10,13,14],[1,3,5,6,7,10,11,13,14], [1,3,5,7,8,9,11,12,13],[1,3,5,7,9,10,11,13,14], [1,4,5,6,7,8,9,10,14],[1,4,5,6,7,8,10,11,14], [1,4,5,6,7,8,11,12,14],[1,4,5,6,7,8,12,13,14], [1,4,5,6,7,11,12,13,14],[1,4,5,6,8,10,11,12,14], [1,4,5,7,8,9,10,11,14],[1,4,5,7,8,9,11,13,14], [1,4,5,7,8,11,12,13,14],[1,4,5,8,9,10,11,12,14], [1,4,5,8,9,11,12,13,14],[1,4,5,9,10,11,12,13,14], [1,5,6,7,8,9,10,11,14],[1,5,6,7,8,9,11,12,14], [1,5,6,7,8,9,12,13,14],[1,5,6,7,9,10,11,13,14], [1,5,6,7,9,11,12,13,14],[1,5,6,8,9,10,11,12,14], [1,5,6,9,10,11,12,13,14],[1,5,7,8,9,11,12,13,14], [1,6,7,8,9,10,11,12,14],[1,6,7,9,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,11,12], [2,3,4,5,6,7,8,12,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,8,9,10,12],[2,3,4,5,6,8,9,12,13], [2,3,4,5,6,8,9,13,14],[2,3,4,5,6,8,10,11,12], [2,3,4,5,6,9,10,12,13],[2,3,4,5,6,9,10,13,14], [2,3,4,5,6,10,11,12,13],[2,3,4,5,6,10,11,13,14], [2,3,4,5,6,11,12,13,14],[2,3,4,5,8,9,10,11,12], [2,3,4,5,9,10,11,12,13],[2,3,4,6,7,8,10,11,12], [2,3,4,6,7,8,10,12,14],[2,3,4,6,7,8,12,13,14], [2,3,4,6,7,10,11,12,14],[2,3,4,6,8,9,10,12,13], [2,3,4,6,8,9,10,13,14],[2,3,4,6,8,10,12,13,14], [2,3,4,6,10,11,12,13,14],[2,3,4,7,8,10,11,12,14], [2,3,4,8,9,10,11,12,14],[2,3,4,8,9,10,12,13,14], [2,3,5,6,7,8,9,10,11],[2,3,5,6,7,8,9,11,12], [2,3,5,6,7,8,9,12,13],[2,3,5,6,7,9,11,12,13], [2,3,5,6,8,9,10,11,12],[2,3,5,6,9,10,11,12,13], [2,3,6,7,8,9,10,11,12],[2,3,6,7,8,9,10,12,13], [2,3,6,7,8,9,10,13,14],[2,3,6,7,8,10,12,13,14], [2,3,6,7,9,10,11,12,13],[2,3,6,7,10,11,12,13,14], [2,3,7,8,9,10,11,12,13],[2,3,7,8,9,10,11,13,14], [2,3,7,8,10,11,12,13,14],[2,3,8,9,10,11,12,13,14], [2,4,5,6,8,9,10,12,14],[2,4,5,6,8,9,12,13,14], [2,4,5,6,9,10,12,13,14],[2,4,5,6,10,11,12,13,14], [2,4,6,7,8,10,11,12,14],[2,4,6,8,9,10,12,13,14], [2,6,7,8,9,10,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,9,13,14],[3,4,5,6,7,9,10,11,12], [3,4,5,6,7,9,10,12,13],[3,4,5,6,7,9,10,13,14], [3,4,5,6,7,10,11,12,13],[3,4,5,6,7,10,11,13,14], [3,4,5,6,8,9,10,11,12],[3,4,5,7,8,9,11,12,13], [3,4,5,7,9,10,11,12,13],[3,4,5,7,9,10,11,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,10,12,13], [3,4,6,7,8,9,10,13,14],[3,4,6,7,8,10,12,13,14], [3,4,6,7,10,11,12,13,14],[3,4,7,8,9,10,11,12,13], [3,4,7,8,9,10,11,13,14],[3,4,7,8,10,11,12,13,14], [3,4,8,9,10,11,12,13,14],[3,5,6,7,9,10,11,12,13], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,9,10,12,13], [4,5,6,7,8,9,10,13,14],[4,5,6,7,8,10,11,12,14], [4,5,6,7,8,10,12,13,14],[4,5,6,7,10,11,12,13,14], [4,5,6,8,9,10,12,13,14],[4,5,7,8,9,10,11,12,13], [4,5,7,8,9,10,11,13,14],[4,5,7,8,10,11,12,13,14], [4,5,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,9,11,12,13,14], [5,6,7,8,10,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_2=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,12], [1,2,3,4,5,6,7,12,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,14],[1,2,3,4,5,6,9,10,14], [1,2,3,4,5,6,10,11,14],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,7,10,11,13],[1,2,3,4,5,7,11,12,13], [1,2,3,4,5,8,9,13,14],[1,2,3,4,5,9,10,13,14], [1,2,3,4,5,10,11,13,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,12],[1,2,3,4,6,7,8,12,14], [1,2,3,4,6,7,9,10,11],[1,2,3,4,6,7,9,11,12], [1,2,3,4,6,7,12,13,14],[1,2,3,4,6,8,9,12,14], [1,2,3,4,6,9,10,11,12],[1,2,3,4,6,9,10,12,14], [1,2,3,4,6,10,11,12,14],[1,2,3,4,7,8,9,10,12], [1,2,3,4,7,8,9,10,13],[1,2,3,4,7,8,10,12,13], [1,2,3,4,7,8,12,13,14],[1,2,3,4,7,9,10,11,12], [1,2,3,4,7,10,11,12,13],[1,2,3,4,8,9,10,12,13], [1,2,3,4,8,9,12,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,11], [1,2,3,5,6,7,8,11,14],[1,2,3,5,6,7,9,10,11], [1,2,3,5,6,7,11,12,13],[1,2,3,5,6,7,11,13,14], [1,2,3,5,6,8,9,11,14],[1,2,3,5,6,9,10,11,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,11,13], [1,2,3,5,7,8,11,13,14],[1,2,3,5,7,9,10,11,13], [1,2,3,5,8,9,11,13,14],[1,2,3,5,9,10,11,13,14], [1,2,3,6,7,8,9,11,12],[1,2,3,6,7,8,11,12,14], [1,2,3,6,7,11,12,13,14],[1,2,3,6,8,9,11,12,14], [1,2,3,6,9,10,11,12,14],[1,2,3,7,8,9,10,12,13], [1,2,3,7,8,9,11,12,13],[1,2,3,7,8,11,12,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,8,9,11,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,10,11,12], [1,2,4,5,6,7,10,12,13],[1,2,4,5,6,7,10,13,14], [1,2,4,5,6,8,9,10,14],[1,2,4,5,6,10,11,12,14], [1,2,4,5,6,10,12,13,14],[1,2,4,5,7,8,9,10,14], [1,2,4,5,7,8,9,13,14],[1,2,4,5,7,9,10,13,14], [1,2,4,5,7,10,11,12,13],[1,2,4,5,10,11,12,13,14], [1,2,4,6,7,8,9,10,12],[1,2,4,6,7,8,10,12,14], [1,2,4,6,7,9,10,11,12],[1,2,4,6,7,10,12,13,14], [1,2,4,6,8,9,10,12,14],[1,2,4,7,8,9,10,13,14], [1,2,4,7,8,10,12,13,14],[1,2,4,8,9,10,12,13,14], [1,2,5,6,7,8,9,10,11],[1,2,5,6,7,8,10,11,13], [1,2,5,6,7,8,10,13,14],[1,2,5,6,7,8,11,13,14], [1,2,5,6,7,10,11,12,13],[1,2,5,6,8,9,10,11,14], [1,2,5,6,8,10,11,13,14],[1,2,5,6,10,11,12,13,14], [1,2,5,7,8,9,10,11,13],[1,2,5,7,8,9,10,13,14], [1,2,5,8,9,10,11,13,14],[1,2,6,7,8,9,10,11,12], [1,2,6,7,8,10,11,12,14],[1,2,6,7,8,10,11,13,14], [1,2,6,7,10,11,12,13,14],[1,2,6,8,9,10,11,12,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,14], [1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,11,12], [1,3,4,5,6,7,9,12,13],[1,3,4,5,6,7,9,13,14], [1,3,4,5,6,9,10,11,12],[1,3,4,5,6,9,10,12,14], [1,3,4,5,6,9,12,13,14],[1,3,4,5,6,10,11,12,14], [1,3,4,5,7,8,9,13,14],[1,3,4,5,7,9,10,11,13], [1,3,4,5,7,9,11,12,13],[1,3,4,5,9,10,11,12,14], [1,3,4,5,9,10,11,13,14],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,8,9,12,14],[1,3,4,6,7,9,12,13,14], [1,3,4,7,8,9,10,12,13],[1,3,4,7,8,9,12,13,14], [1,3,4,7,9,10,11,12,13],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,11,14],[1,3,5,6,7,9,11,12,13], [1,3,5,6,7,9,11,13,14],[1,3,5,6,9,10,11,12,14], [1,3,5,6,9,11,12,13,14],[1,3,5,7,8,9,11,13,14], [1,3,6,7,8,9,11,12,14],[1,3,6,7,9,11,12,13,14], [1,3,7,8,9,11,12,13,14],[1,4,5,6,7,8,9,10,14], [1,4,5,6,7,9,10,11,12],[1,4,5,6,7,9,10,12,13], [1,4,5,6,7,9,10,13,14],[1,4,5,6,9,10,12,13,14], [1,4,5,7,9,10,11,12,13],[1,4,5,9,10,11,12,13,14], [1,4,6,7,8,9,10,12,14],[1,4,6,7,9,10,12,13,14], [1,4,7,8,9,10,12,13,14],[1,5,6,7,8,9,10,11,14], [1,5,6,7,8,10,11,13,14],[1,5,6,7,9,10,11,12,13], [1,5,6,7,9,10,11,13,14],[1,5,6,9,10,11,12,13,14], [1,5,7,8,9,10,11,13,14],[1,6,7,8,9,10,11,12,14], [1,6,7,9,10,11,12,13,14],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,11], [2,3,4,5,6,7,8,11,12],[2,3,4,5,6,7,8,12,13], [2,3,4,5,6,7,8,13,14],[2,3,4,5,6,8,9,10,14], [2,3,4,5,6,8,10,11,14],[2,3,4,5,6,8,11,12,14], [2,3,4,5,6,8,12,13,14],[2,3,4,5,7,8,9,10,13], [2,3,4,5,7,8,10,11,13],[2,3,4,5,7,8,11,12,13], [2,3,4,5,8,9,10,13,14],[2,3,4,5,8,10,11,13,14], [2,3,4,5,8,11,12,13,14],[2,3,4,6,7,8,9,10,12], [2,3,4,6,7,8,10,11,12],[2,3,4,6,7,8,12,13,14], [2,3,4,6,7,9,10,11,12],[2,3,4,6,8,9,10,12,14], [2,3,4,6,8,10,11,12,14],[2,3,4,7,8,10,11,12,13], [2,3,4,8,9,10,12,13,14],[2,3,4,8,10,11,12,13,14], [2,3,5,6,7,8,9,10,11],[2,3,5,6,7,8,11,12,14], [2,3,5,6,7,8,12,13,14],[2,3,5,6,7,11,12,13,14], [2,3,5,6,8,9,10,11,14],[2,3,5,7,8,9,10,11,13], [2,3,5,7,8,11,12,13,14],[2,3,5,8,9,10,11,13,14], [2,3,6,7,8,9,10,11,12],[2,3,6,8,9,10,11,12,14], [2,3,7,8,9,10,11,12,13],[2,3,8,9,10,11,12,13,14], [2,4,5,6,7,8,10,11,12],[2,4,5,6,7,8,10,12,13], [2,4,5,6,7,8,10,13,14],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,7,8,9,10,13,14], [2,4,5,7,8,10,11,12,13],[2,4,5,8,10,11,12,13,14], [2,4,6,7,8,10,12,13,14],[2,5,6,7,8,10,11,12,13], [2,5,6,7,8,11,12,13,14],[2,5,6,8,10,11,12,13,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,9,13,14],[3,4,5,6,8,9,10,11,14], [3,4,5,6,8,9,11,12,13],[3,4,5,6,8,9,11,13,14], [3,4,5,6,8,11,12,13,14],[3,4,5,6,9,10,11,12,14], [3,4,5,6,9,11,12,13,14],[3,4,5,7,8,9,10,11,13], [3,4,5,7,8,9,11,12,13],[3,4,5,8,9,10,11,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,12,13,14], [3,4,6,8,9,10,11,12,14],[3,4,6,8,9,11,12,13,14], [3,4,7,8,9,10,11,12,13],[3,4,8,9,10,11,12,13,14], [3,5,6,7,8,9,11,12,13],[3,5,6,7,8,9,11,13,14], [3,5,6,7,8,11,12,13,14],[3,6,7,8,9,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,9,10,12,13], [4,5,6,7,8,9,10,13,14],[4,5,6,8,9,10,11,12,14], [4,5,6,8,9,10,12,13,14],[4,5,6,8,9,11,12,13,14], [4,5,7,8,9,10,11,12,13],[4,5,8,9,10,11,12,13,14], [4,6,7,8,9,10,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_3=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,10], [1,2,3,4,5,6,8,10,14],[1,2,3,4,5,6,10,11,14], [1,2,3,4,5,6,11,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,7,10,11,13],[1,2,3,4,5,8,9,10,11], [1,2,3,4,5,8,9,11,14],[1,2,3,4,5,8,9,13,14], [1,2,3,4,5,8,10,11,14],[1,2,3,4,5,9,10,11,13], [1,2,3,4,5,9,11,13,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,12],[1,2,3,4,6,7,8,12,13], [1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,9,10,12], [1,2,3,4,6,7,10,11,12],[1,2,3,4,6,7,11,12,13], [1,2,3,4,6,8,9,10,14],[1,2,3,4,6,8,9,12,14], [1,2,3,4,6,8,12,13,14],[1,2,3,4,6,9,10,12,14], [1,2,3,4,6,10,11,12,14],[1,2,3,4,7,8,9,12,13], [1,2,3,4,7,9,10,12,13],[1,2,3,4,7,10,11,12,13], [1,2,3,4,8,9,10,11,14],[1,2,3,4,8,9,12,13,14], [1,2,3,4,9,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,11],[1,2,3,5,6,7,8,11,14], [1,2,3,5,6,7,11,13,14],[1,2,3,5,6,8,10,11,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,10,11], [1,2,3,5,7,8,9,11,13],[1,2,3,5,7,8,11,13,14], [1,2,3,5,7,9,10,11,13],[1,2,3,5,8,9,11,13,14], [1,2,3,6,7,8,9,10,14],[1,2,3,6,7,8,9,12,13], [1,2,3,6,7,8,9,13,14],[1,2,3,6,7,8,10,11,14], [1,2,3,6,7,9,10,11,12],[1,2,3,6,7,9,10,11,14], [1,2,3,6,7,9,11,12,14],[1,2,3,6,7,9,12,13,14], [1,2,3,6,7,11,12,13,14],[1,2,3,6,8,9,12,13,14], [1,2,3,6,9,10,11,12,14],[1,2,3,7,8,9,10,11,14], [1,2,3,7,8,9,11,13,14],[1,2,3,7,9,10,11,12,13], [1,2,3,7,9,11,12,13,14],[1,2,3,9,10,11,12,13,14], [1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,10,14], [1,2,4,5,6,7,10,11,13],[1,2,4,5,6,7,10,13,14], [1,2,4,5,6,10,11,13,14],[1,2,4,5,6,11,12,13,14], [1,2,4,5,7,8,9,10,13],[1,2,4,5,7,8,10,13,14], [1,2,4,5,8,9,10,11,14],[1,2,4,5,8,9,10,13,14], [1,2,4,5,9,10,11,13,14],[1,2,4,6,7,8,9,10,12], [1,2,4,6,7,8,10,12,14],[1,2,4,6,7,8,12,13,14], [1,2,4,6,7,10,11,12,13],[1,2,4,6,7,10,12,13,14], [1,2,4,6,8,9,10,12,14],[1,2,4,6,10,11,12,13,14], [1,2,4,7,8,9,10,12,13],[1,2,4,7,8,10,12,13,14], [1,2,4,8,9,10,12,13,14],[1,2,5,6,7,8,10,11,14], [1,2,5,6,7,10,11,13,14],[1,2,5,7,8,9,10,11,13], [1,2,5,7,8,10,11,13,14],[1,2,5,8,9,10,11,13,14], [1,2,6,7,8,9,10,12,14],[1,2,6,7,8,9,12,13,14], [1,2,6,7,9,10,11,12,14],[1,2,6,7,10,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,11,12,14], [1,2,7,8,9,11,12,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,10,11], [1,3,4,5,6,7,9,11,12],[1,3,4,5,6,7,9,12,13], [1,3,4,5,6,7,11,12,13],[1,3,4,5,6,8,9,10,14], [1,3,4,5,6,8,9,13,14],[1,3,4,5,6,9,10,11,14], [1,3,4,5,6,9,11,12,14],[1,3,4,5,6,9,12,13,14], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,8,9,10,11,14],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,8,9,12,13],[1,3,4,6,7,9,10,11,12], [1,3,4,6,8,9,12,13,14],[1,3,4,6,9,10,11,12,14], [1,3,4,7,9,10,11,12,13],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,10,11],[1,3,5,6,7,8,9,11,14], [1,3,5,6,7,8,9,13,14],[1,3,5,6,7,9,11,12,13], [1,3,5,6,7,9,11,13,14],[1,3,5,6,8,9,10,11,14], [1,3,5,6,9,11,12,13,14],[1,3,5,7,8,9,11,13,14], [1,3,6,7,8,9,10,11,14],[1,3,6,7,9,11,12,13,14], [1,4,5,6,7,8,9,10,14],[1,4,5,6,7,8,9,12,13], [1,4,5,6,7,8,9,12,14],[1,4,5,6,7,8,12,13,14], [1,4,5,6,7,9,10,11,12],[1,4,5,6,7,9,10,12,14], [1,4,5,6,7,10,11,12,14],[1,4,5,6,7,10,11,13,14], [1,4,5,6,7,11,12,13,14],[1,4,5,6,8,9,12,13,14], [1,4,5,6,9,10,11,12,14],[1,4,5,7,8,9,10,13,14], [1,4,5,7,8,9,12,13,14],[1,4,5,7,9,10,11,12,13], [1,4,5,7,9,10,12,13,14],[1,4,5,7,10,11,12,13,14], [1,4,5,9,10,11,12,13,14],[1,4,6,7,8,9,10,12,14], [1,4,6,7,10,11,12,13,14],[1,4,7,8,9,10,12,13,14], [1,5,6,7,8,9,10,11,14],[1,5,6,7,8,9,12,13,14], [1,5,6,7,9,10,11,12,14],[1,5,6,7,9,11,12,13,14], [1,5,7,8,9,10,11,13,14],[1,5,7,9,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,12,13], [2,3,4,5,6,7,8,13,14],[2,3,4,5,6,7,10,11,13], [2,3,4,5,6,7,10,12,13],[2,3,4,5,6,8,10,11,12], [2,3,4,5,6,8,10,11,14],[2,3,4,5,6,8,11,12,14], [2,3,4,5,6,8,12,13,14],[2,3,4,5,6,10,11,12,13], [2,3,4,5,7,8,9,10,13],[2,3,4,5,7,8,10,12,13], [2,3,4,5,8,9,10,11,12],[2,3,4,5,8,9,10,12,13], [2,3,4,5,8,9,11,12,13],[2,3,4,5,8,9,11,13,14], [2,3,4,5,8,11,12,13,14],[2,3,4,5,9,10,11,12,13], [2,3,4,6,7,8,9,10,12],[2,3,4,6,7,10,11,12,13], [2,3,4,6,8,9,10,12,14],[2,3,4,6,8,10,11,12,14], [2,3,4,7,8,9,10,12,13],[2,3,4,8,9,10,11,12,14], [2,3,4,8,9,11,12,13,14],[2,3,4,9,10,11,12,13,14], [2,3,5,6,7,8,10,11,12],[2,3,5,6,7,8,11,12,13], [2,3,5,6,7,8,11,13,14],[2,3,5,6,7,10,11,12,13], [2,3,5,6,8,11,12,13,14],[2,3,5,7,8,9,10,11,13], [2,3,5,7,8,10,11,12,13],[2,3,5,8,9,10,11,12,13], [2,3,6,7,8,9,10,11,12],[2,3,6,7,8,9,10,11,14], [2,3,6,7,8,9,11,12,14],[2,3,6,7,8,9,12,13,14], [2,3,6,7,8,11,12,13,14],[2,3,6,8,9,10,11,12,14], [2,3,7,8,9,10,11,12,13],[2,3,7,8,9,11,12,13,14], [2,4,5,6,7,8,10,12,13],[2,4,5,6,7,8,10,13,14], [2,4,5,6,8,10,11,12,14],[2,4,5,6,8,10,12,13,14], [2,4,5,6,10,11,12,13,14],[2,4,5,8,9,10,11,12,13], [2,4,5,8,9,10,11,13,14],[2,4,5,8,10,11,12,13,14], [2,4,6,7,8,10,12,13,14],[2,4,8,9,10,11,12,13,14], [2,5,6,7,8,10,11,12,13],[2,5,6,7,8,10,11,13,14], [2,5,6,8,10,11,12,13,14],[2,6,7,8,9,10,11,12,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,10,11,12],[3,4,5,6,7,10,11,12,13], [3,4,5,6,8,9,10,11,14],[3,4,5,6,8,9,11,12,14], [3,4,5,6,8,9,12,13,14],[3,4,5,7,8,9,10,11,12], [3,4,5,7,8,9,10,12,13],[3,4,5,7,9,10,11,12,13], [3,4,5,8,9,11,12,13,14],[3,4,6,7,8,9,10,11,12], [3,4,6,8,9,10,11,12,14],[3,5,6,7,8,9,11,12,13], [3,5,6,7,8,9,11,13,14],[3,5,6,8,9,11,12,13,14], [3,5,7,8,9,10,11,12,13],[3,6,7,8,9,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,9,10,12,14], [4,5,6,7,8,10,12,13,14],[4,5,6,7,10,11,12,13,14], [4,5,6,8,9,10,11,12,14],[4,5,7,8,9,10,12,13,14], [4,5,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,9,10,12,13,14], [5,6,7,9,10,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_4=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,10], [1,2,3,4,5,6,8,10,14],[1,2,3,4,5,6,10,11,14], [1,2,3,4,5,6,11,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,7,10,11,13],[1,2,3,4,5,8,9,10,11], [1,2,3,4,5,8,9,11,14],[1,2,3,4,5,8,9,13,14], [1,2,3,4,5,8,10,11,14],[1,2,3,4,5,9,10,11,13], [1,2,3,4,5,9,11,13,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,13],[1,2,3,4,6,7,8,13,14], [1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,9,12,13], [1,2,3,4,6,7,10,11,13],[1,2,3,4,6,7,10,12,13], [1,2,3,4,6,8,9,10,14],[1,2,3,4,6,8,9,12,13], [1,2,3,4,6,8,9,12,14],[1,2,3,4,6,8,12,13,14], [1,2,3,4,6,9,10,12,14],[1,2,3,4,6,10,11,12,13], [1,2,3,4,6,10,11,12,14],[1,2,3,4,7,9,10,12,13], [1,2,3,4,8,9,10,11,14],[1,2,3,4,8,9,12,13,14], [1,2,3,4,9,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,14],[1,2,3,5,6,7,10,11,14], [1,2,3,5,6,7,11,13,14],[1,2,3,5,6,11,12,13,14], [1,2,3,5,7,8,9,10,11],[1,2,3,5,7,8,9,11,13], [1,2,3,5,7,8,10,11,14],[1,2,3,5,7,8,11,13,14], [1,2,3,5,7,9,10,11,13],[1,2,3,5,8,9,11,13,14], [1,2,3,6,7,8,9,10,14],[1,2,3,6,7,8,9,13,14], [1,2,3,6,7,9,10,12,14],[1,2,3,6,7,9,12,13,14], [1,2,3,6,7,10,11,12,13],[1,2,3,6,7,10,11,12,14], [1,2,3,6,7,11,12,13,14],[1,2,3,6,8,9,12,13,14], [1,2,3,7,8,9,10,11,14],[1,2,3,7,8,9,11,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,7,9,10,11,12,14], [1,2,3,7,9,11,12,13,14],[1,2,3,9,10,11,12,13,14], [1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,10,14], [1,2,4,5,6,7,10,11,14],[1,2,4,5,6,7,11,13,14], [1,2,4,5,6,11,12,13,14],[1,2,4,5,7,8,9,10,13], [1,2,4,5,7,8,10,13,14],[1,2,4,5,7,10,11,13,14], [1,2,4,5,8,9,10,11,13],[1,2,4,5,8,9,11,13,14], [1,2,4,5,8,10,11,13,14],[1,2,4,6,7,8,9,10,12], [1,2,4,6,7,8,9,12,13],[1,2,4,6,7,8,10,12,14], [1,2,4,6,7,8,12,13,14],[1,2,4,6,7,10,11,13,14], [1,2,4,6,7,10,12,13,14],[1,2,4,6,8,9,10,12,14], [1,2,4,6,10,11,12,13,14],[1,2,4,7,8,9,10,12,13], [1,2,4,7,8,10,12,13,14],[1,2,4,8,9,10,11,13,14], [1,2,4,8,9,10,12,13,14],[1,2,5,7,8,9,10,11,13], [1,2,5,7,8,10,11,13,14],[1,2,6,7,8,9,10,12,14], [1,2,6,7,8,9,12,13,14],[1,2,6,7,10,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,11,12,14], [1,2,7,8,9,11,12,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,10,11], [1,3,4,5,6,7,9,11,12],[1,3,4,5,6,7,9,12,13], [1,3,4,5,6,7,11,12,13],[1,3,4,5,6,8,9,10,11], [1,3,4,5,6,8,9,11,14],[1,3,4,5,6,8,9,12,13], [1,3,4,5,6,8,9,12,14],[1,3,4,5,6,8,10,11,14], [1,3,4,5,6,8,12,13,14],[1,3,4,5,6,9,11,12,14], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,8,9,12,13,14],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,9,10,11,12],[1,3,4,6,7,10,11,12,13], [1,3,4,6,8,9,10,11,14],[1,3,4,6,9,10,11,12,14], [1,3,4,7,9,10,11,12,13],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,10,11],[1,3,5,6,7,8,9,11,14], [1,3,5,6,7,8,9,13,14],[1,3,5,6,7,8,10,11,14], [1,3,5,6,7,9,11,12,13],[1,3,5,6,7,9,11,13,14], [1,3,5,6,8,9,12,13,14],[1,3,5,6,9,11,12,13,14], [1,3,5,7,8,9,11,13,14],[1,3,6,7,8,9,10,11,14], [1,3,6,7,9,10,11,12,14],[1,3,6,7,9,11,12,13,14], [1,4,5,6,7,8,9,10,14],[1,4,5,6,7,8,9,12,13], [1,4,5,6,7,8,9,12,14],[1,4,5,6,7,8,12,13,14], [1,4,5,6,7,9,10,11,14],[1,4,5,6,7,9,11,12,14], [1,4,5,6,7,11,12,13,14],[1,4,5,6,8,9,10,11,14], [1,4,5,7,8,9,10,12,13],[1,4,5,7,8,9,10,12,14], [1,4,5,7,8,10,12,13,14],[1,4,5,7,9,10,11,12,13], [1,4,5,7,9,10,11,12,14],[1,4,5,7,10,11,12,13,14], [1,4,5,8,9,10,11,13,14],[1,4,5,8,9,10,12,13,14], [1,4,5,9,10,11,12,13,14],[1,4,6,7,8,9,10,12,14], [1,4,6,7,9,10,11,12,14],[1,4,6,7,10,11,12,13,14], [1,5,6,7,8,9,10,11,14],[1,5,6,7,8,9,12,13,14], [1,5,6,7,9,11,12,13,14],[1,5,7,8,9,10,11,13,14], [1,5,7,8,9,10,12,13,14],[1,5,7,9,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,12,13], [2,3,4,5,6,7,8,13,14],[2,3,4,5,6,7,10,11,13], [2,3,4,5,6,7,10,12,13],[2,3,4,5,6,8,10,11,12], [2,3,4,5,6,8,10,11,14],[2,3,4,5,6,8,11,12,14], [2,3,4,5,6,8,12,13,14],[2,3,4,5,6,10,11,12,13], [2,3,4,5,7,8,9,10,12],[2,3,4,5,7,8,9,12,13], [2,3,4,5,7,9,10,12,13],[2,3,4,5,8,9,10,11,12], [2,3,4,5,8,9,11,12,14],[2,3,4,5,8,9,12,13,14], [2,3,4,5,9,10,11,12,13],[2,3,4,5,9,11,12,13,14], [2,3,4,6,7,8,9,10,12],[2,3,4,6,7,8,9,12,13], [2,3,4,6,8,9,10,12,14],[2,3,4,6,8,10,11,12,14], [2,3,4,8,9,10,11,12,14],[2,3,4,9,10,11,12,13,14], [2,3,5,6,7,8,10,11,13],[2,3,5,6,7,8,10,11,14], [2,3,5,6,7,8,10,12,13],[2,3,5,6,7,8,11,13,14], [2,3,5,6,8,10,11,12,13],[2,3,5,6,8,11,12,13,14], [2,3,5,7,8,9,10,11,13],[2,3,5,7,8,9,10,12,13], [2,3,5,8,9,10,11,12,13],[2,3,5,8,9,11,12,13,14], [2,3,6,7,8,9,10,11,12],[2,3,6,7,8,9,10,11,14], [2,3,6,7,8,9,11,12,13],[2,3,6,7,8,9,11,13,14], [2,3,6,7,8,10,11,12,13],[2,3,6,7,9,10,11,12,14], [2,3,6,7,9,11,12,13,14],[2,3,6,8,9,10,11,12,14], [2,3,6,8,9,11,12,13,14],[2,3,7,8,9,10,11,12,13], [2,4,5,6,7,8,10,12,13],[2,4,5,6,7,8,10,13,14], [2,4,5,6,7,10,11,13,14],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,6,10,11,12,13,14], [2,4,5,7,8,9,10,12,13],[2,4,5,8,9,10,11,12,13], [2,4,5,8,9,11,12,13,14],[2,4,5,8,10,11,12,13,14], [2,4,6,7,8,10,12,13,14],[2,4,8,9,10,11,12,13,14], [2,5,6,7,8,10,11,13,14],[2,5,6,8,10,11,12,13,14], [2,6,7,8,9,10,11,12,14],[2,6,7,8,9,11,12,13,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,10,11,12],[3,4,5,6,7,10,11,12,13], [3,4,5,6,8,9,11,12,14],[3,4,5,7,8,9,10,11,12], [3,4,5,7,9,10,11,12,13],[3,4,6,7,8,9,10,11,12], [3,4,6,8,9,10,11,12,14],[3,5,6,7,8,9,11,12,13], [3,5,6,7,8,9,11,13,14],[3,5,6,7,8,10,11,12,13], [3,5,6,8,9,11,12,13,14],[3,5,7,8,9,10,11,12,13], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,9,10,12,14], [4,5,6,7,8,10,12,13,14],[4,5,6,7,9,10,11,12,14], [4,5,6,7,10,11,12,13,14],[4,5,6,8,9,10,11,12,14], [4,5,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,9,10,12,13,14], [5,6,7,9,10,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_5=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,10], [1,2,3,4,5,6,8,10,14],[1,2,3,4,5,6,10,11,14], [1,2,3,4,5,6,11,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,7,10,11,13],[1,2,3,4,5,8,9,10,14], [1,2,3,4,5,8,9,13,14],[1,2,3,4,5,9,10,11,13], [1,2,3,4,5,9,10,11,14],[1,2,3,4,5,9,11,13,14], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,12], [1,2,3,4,6,7,8,12,13],[1,2,3,4,6,7,8,13,14], [1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,10,11,12], [1,2,3,4,6,7,11,12,13],[1,2,3,4,6,8,9,10,14], [1,2,3,4,6,8,9,12,14],[1,2,3,4,6,8,12,13,14], [1,2,3,4,6,9,10,12,14],[1,2,3,4,6,10,11,12,14], [1,2,3,4,7,8,9,12,13],[1,2,3,4,7,9,10,12,13], [1,2,3,4,7,10,11,12,13],[1,2,3,4,8,9,12,13,14], [1,2,3,4,9,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,11],[1,2,3,5,6,7,8,11,14], [1,2,3,5,6,7,11,13,14],[1,2,3,5,6,8,10,11,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,10,11], [1,2,3,5,7,8,9,11,13],[1,2,3,5,7,8,11,13,14], [1,2,3,5,7,9,10,11,13],[1,2,3,5,8,9,10,11,14], [1,2,3,5,8,9,11,13,14],[1,2,3,6,7,8,9,10,11], [1,2,3,6,7,8,9,11,14],[1,2,3,6,7,8,9,12,14], [1,2,3,6,7,8,12,13,14],[1,2,3,6,7,9,10,11,12], [1,2,3,6,7,9,11,12,14],[1,2,3,6,7,11,12,13,14], [1,2,3,6,8,9,10,11,14],[1,2,3,6,9,10,11,12,14], [1,2,3,7,8,9,11,13,14],[1,2,3,7,8,9,12,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,7,9,11,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,10,11,13], [1,2,4,5,6,7,10,13,14],[1,2,4,5,6,10,11,13,14], [1,2,4,5,6,11,12,13,14],[1,2,4,5,7,8,9,10,13], [1,2,4,5,7,8,10,13,14],[1,2,4,5,8,9,10,13,14], [1,2,4,5,9,10,11,13,14],[1,2,4,6,7,8,9,10,12], [1,2,4,6,7,8,10,12,14],[1,2,4,6,7,8,12,13,14], [1,2,4,6,7,10,11,12,13],[1,2,4,6,7,10,12,13,14], [1,2,4,6,8,9,10,12,14],[1,2,4,6,10,11,12,13,14], [1,2,4,7,8,9,10,12,13],[1,2,4,7,8,10,12,13,14], [1,2,4,8,9,10,12,13,14],[1,2,5,6,7,8,10,11,14], [1,2,5,6,7,10,11,13,14],[1,2,5,7,8,9,10,11,13], [1,2,5,7,8,10,11,13,14],[1,2,5,8,9,10,11,13,14], [1,2,6,7,8,9,10,11,14],[1,2,6,7,8,9,10,12,14], [1,2,6,7,9,10,11,12,14],[1,2,6,7,10,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,11,12,14], [1,2,7,8,9,11,12,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,10,11], [1,3,4,5,6,7,9,11,12],[1,3,4,5,6,7,9,12,13], [1,3,4,5,6,7,11,12,13],[1,3,4,5,6,8,9,10,14], [1,3,4,5,6,8,9,13,14],[1,3,4,5,6,9,10,11,14], [1,3,4,5,6,9,11,12,14],[1,3,4,5,6,9,12,13,14], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,9,11,12,13,14],[1,3,4,6,7,8,9,12,13], [1,3,4,6,7,9,10,11,12],[1,3,4,6,8,9,12,13,14], [1,3,4,6,9,10,11,12,14],[1,3,4,7,9,10,11,12,13], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,9,10,11], [1,3,5,6,7,8,9,11,14],[1,3,5,6,7,8,9,13,14], [1,3,5,6,7,9,11,12,13],[1,3,5,6,7,9,11,13,14], [1,3,5,6,8,9,10,11,14],[1,3,5,6,9,11,12,13,14], [1,3,5,7,8,9,11,13,14],[1,3,6,7,8,9,12,13,14], [1,3,6,7,9,11,12,13,14],[1,4,5,6,7,8,9,10,14], [1,4,5,6,7,8,9,13,14],[1,4,5,6,7,9,10,11,12], [1,4,5,6,7,9,10,12,14],[1,4,5,6,7,9,12,13,14], [1,4,5,6,7,10,11,12,13],[1,4,5,6,7,10,12,13,14], [1,4,5,6,9,10,11,12,14],[1,4,5,6,10,11,12,13,14], [1,4,5,7,8,9,10,13,14],[1,4,5,7,9,10,11,12,13], [1,4,5,7,9,10,12,13,14],[1,4,5,9,10,11,12,13,14], [1,4,6,7,8,9,10,12,14],[1,4,6,7,8,9,12,13,14], [1,4,7,8,9,10,12,13,14],[1,5,6,7,8,9,10,11,14], [1,5,6,7,9,10,11,12,14],[1,5,6,7,9,11,12,13,14], [1,5,6,7,10,11,12,13,14],[1,5,7,8,9,10,11,13,14], [1,5,7,9,10,11,12,13,14],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,12], [2,3,4,5,6,7,8,12,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,7,10,11,12],[2,3,4,5,6,7,11,12,13], [2,3,4,5,6,8,10,11,12],[2,3,4,5,6,8,10,11,14], [2,3,4,5,6,8,11,12,14],[2,3,4,5,6,8,12,13,14], [2,3,4,5,7,8,9,10,13],[2,3,4,5,7,8,10,12,13], [2,3,4,5,7,10,11,12,13],[2,3,4,5,8,9,10,11,13], [2,3,4,5,8,9,10,11,14],[2,3,4,5,8,9,11,13,14], [2,3,4,5,8,10,11,12,13],[2,3,4,5,8,11,12,13,14], [2,3,4,6,7,8,9,10,12],[2,3,4,6,8,9,10,12,14], [2,3,4,6,8,10,11,12,14],[2,3,4,7,8,9,10,12,13], [2,3,4,8,9,10,11,12,13],[2,3,4,8,9,10,11,12,14], [2,3,4,8,9,11,12,13,14],[2,3,4,9,10,11,12,13,14], [2,3,5,6,7,8,10,11,12],[2,3,5,6,7,8,11,12,13], [2,3,5,6,7,8,11,13,14],[2,3,5,6,8,11,12,13,14], [2,3,5,7,8,9,10,11,13],[2,3,5,7,8,10,11,12,13], [2,3,6,7,8,9,10,11,12],[2,3,6,7,8,9,11,12,14], [2,3,6,7,8,11,12,13,14],[2,3,6,8,9,10,11,12,14], [2,3,7,8,9,10,11,12,13],[2,3,7,8,9,11,12,13,14], [2,4,5,6,7,8,10,12,13],[2,4,5,6,7,8,10,13,14], [2,4,5,6,7,10,11,12,13],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,6,10,11,12,13,14], [2,4,5,8,9,10,11,13,14],[2,4,5,8,10,11,12,13,14], [2,4,6,7,8,10,12,13,14],[2,4,8,9,10,11,12,13,14], [2,5,6,7,8,10,11,12,13],[2,5,6,7,8,10,11,13,14], [2,5,6,8,10,11,12,13,14],[2,6,7,8,9,10,11,12,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,10,11,12],[3,4,5,6,8,9,10,11,14], [3,4,5,6,8,9,11,12,14],[3,4,5,6,8,9,12,13,14], [3,4,5,7,8,9,10,11,12],[3,4,5,7,8,9,10,12,13], [3,4,5,7,9,10,11,12,13],[3,4,5,8,9,10,11,12,13], [3,4,5,8,9,11,12,13,14],[3,4,6,7,8,9,10,11,12], [3,4,6,8,9,10,11,12,14],[3,5,6,7,8,9,11,12,13], [3,5,6,7,8,9,11,13,14],[3,5,6,8,9,11,12,13,14], [3,5,7,8,9,10,11,12,13],[3,6,7,8,9,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,9,10,12,14], [4,5,6,7,8,9,12,13,14],[4,5,6,7,8,10,12,13,14], [4,5,6,8,9,10,11,12,14],[4,5,7,8,9,10,12,13,14], [4,5,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,9,10,12,13,14], [5,6,7,9,10,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_6=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,10],[1,2,3,4,5,6,8,10,11], [1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,10,11,13], [1,2,3,4,5,6,11,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,8,9,10,11],[1,2,3,4,5,8,9,11,13], [1,2,3,4,5,8,11,13,14],[1,2,3,4,5,9,10,11,13], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,12], [1,2,3,4,6,7,8,12,13],[1,2,3,4,6,7,8,13,14], [1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,10,11,12], [1,2,3,4,6,7,10,11,13],[1,2,3,4,6,7,11,12,13], [1,2,3,4,6,8,9,10,14],[1,2,3,4,6,8,9,12,13], [1,2,3,4,6,8,9,13,14],[1,2,3,4,6,8,10,11,14], [1,2,3,4,6,9,10,12,14],[1,2,3,4,6,9,12,13,14], [1,2,3,4,6,10,11,12,14],[1,2,3,4,7,8,9,12,13], [1,2,3,4,7,9,10,12,13],[1,2,3,4,7,10,11,12,13], [1,2,3,4,8,9,10,11,14],[1,2,3,4,8,9,11,13,14], [1,2,3,4,9,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,11],[1,2,3,5,6,7,8,11,14], [1,2,3,5,6,7,10,11,13],[1,2,3,5,6,7,11,13,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,10,11], [1,2,3,5,7,8,9,11,13],[1,2,3,5,7,8,11,13,14], [1,2,3,5,7,9,10,11,13],[1,2,3,6,7,8,9,10,14], [1,2,3,6,7,8,9,12,13],[1,2,3,6,7,8,9,13,14], [1,2,3,6,7,8,10,11,14],[1,2,3,6,7,9,10,11,12], [1,2,3,6,7,9,10,11,14],[1,2,3,6,7,9,11,12,13], [1,2,3,6,7,9,11,13,14],[1,2,3,6,9,10,11,12,14], [1,2,3,6,9,11,12,13,14],[1,2,3,7,8,9,10,11,14], [1,2,3,7,8,9,11,13,14],[1,2,3,7,9,10,11,12,13], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,10,13,14], [1,2,4,5,6,8,10,11,14],[1,2,4,5,6,10,11,13,14], [1,2,4,5,6,11,12,13,14],[1,2,4,5,7,8,9,10,13], [1,2,4,5,7,8,10,13,14],[1,2,4,5,8,9,10,11,14], [1,2,4,5,8,9,10,13,14],[1,2,4,5,8,9,11,13,14], [1,2,4,5,9,10,11,13,14],[1,2,4,6,7,8,9,10,12], [1,2,4,6,7,8,10,12,14],[1,2,4,6,7,8,12,13,14], [1,2,4,6,7,10,11,12,14],[1,2,4,6,7,10,11,13,14], [1,2,4,6,7,11,12,13,14],[1,2,4,6,8,9,10,12,14], [1,2,4,6,8,9,12,13,14],[1,2,4,7,8,9,10,12,13], [1,2,4,7,8,10,12,13,14],[1,2,4,7,10,11,12,13,14], [1,2,4,8,9,10,12,13,14],[1,2,5,6,7,8,10,11,14], [1,2,5,6,7,10,11,13,14],[1,2,5,7,8,9,10,11,13], [1,2,5,7,8,10,11,13,14],[1,2,5,8,9,10,11,13,14], [1,2,6,7,8,9,10,12,14],[1,2,6,7,8,9,12,13,14], [1,2,6,7,9,10,11,12,14],[1,2,6,7,9,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,11,12,14], [1,2,7,8,9,11,12,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,12,13],[1,3,4,5,6,7,8,13,14], [1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,11,12], [1,3,4,5,6,7,10,11,13],[1,3,4,5,6,7,11,12,13], [1,3,4,5,6,8,9,10,14],[1,3,4,5,6,8,9,12,13], [1,3,4,5,6,8,9,13,14],[1,3,4,5,6,8,10,11,14], [1,3,4,5,6,9,10,11,14],[1,3,4,5,6,9,11,12,14], [1,3,4,5,6,9,12,13,14],[1,3,4,5,7,8,9,12,13], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,8,9,10,11,14],[1,3,4,5,8,9,11,13,14], [1,3,4,5,9,11,12,13,14],[1,3,4,6,7,9,10,11,12], [1,3,4,6,9,10,11,12,14],[1,3,4,7,9,10,11,12,13], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,9,10,14], [1,3,5,6,7,8,9,12,13],[1,3,5,6,7,8,9,13,14], [1,3,5,6,7,8,10,11,14],[1,3,5,6,7,9,10,11,14], [1,3,5,6,7,9,11,12,13],[1,3,5,6,7,9,11,13,14], [1,3,5,6,9,11,12,13,14],[1,3,5,7,8,9,10,11,14], [1,3,5,7,8,9,11,13,14],[1,4,5,6,7,8,9,10,12], [1,4,5,6,7,8,10,12,14],[1,4,5,6,7,8,12,13,14], [1,4,5,6,7,9,10,11,12],[1,4,5,6,7,10,11,12,14], [1,4,5,6,7,10,11,13,14],[1,4,5,6,7,11,12,13,14], [1,4,5,6,8,9,10,12,14],[1,4,5,6,8,9,12,13,14], [1,4,5,6,9,10,11,12,14],[1,4,5,7,8,9,10,12,14], [1,4,5,7,8,9,10,13,14],[1,4,5,7,8,9,12,13,14], [1,4,5,7,9,10,11,12,14],[1,4,5,7,9,10,11,13,14], [1,4,5,7,9,11,12,13,14],[1,4,7,8,9,10,12,13,14], [1,4,7,9,10,11,12,13,14],[1,5,6,7,8,9,10,12,14], [1,5,6,7,8,9,12,13,14],[1,5,6,7,9,10,11,12,14], [1,5,6,7,9,11,12,13,14],[1,5,7,8,9,10,11,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,8,10,11,12],[2,3,4,5,6,8,10,12,13], [2,3,4,5,6,8,11,12,14],[2,3,4,5,6,8,12,13,14], [2,3,4,5,6,10,11,12,13],[2,3,4,5,7,8,9,10,13], [2,3,4,5,8,9,10,11,12],[2,3,4,5,8,9,10,12,13], [2,3,4,5,8,9,11,12,13],[2,3,4,5,8,11,12,13,14], [2,3,4,5,9,10,11,12,13],[2,3,4,6,7,8,9,10,12], [2,3,4,6,7,8,10,12,13],[2,3,4,6,7,10,11,12,13], [2,3,4,6,8,9,10,12,14],[2,3,4,6,8,9,12,13,14], [2,3,4,6,8,10,11,12,14],[2,3,4,7,8,9,10,12,13], [2,3,4,8,9,10,11,12,14],[2,3,4,8,9,11,12,13,14], [2,3,4,9,10,11,12,13,14],[2,3,5,6,7,8,10,11,12], [2,3,5,6,7,8,10,12,13],[2,3,5,6,7,8,11,12,13], [2,3,5,6,7,8,11,13,14],[2,3,5,6,7,10,11,12,13], [2,3,5,6,8,11,12,13,14],[2,3,5,7,8,9,10,11,12], [2,3,5,7,8,9,10,12,13],[2,3,5,7,8,9,11,12,13], [2,3,5,7,9,10,11,12,13],[2,3,6,7,8,9,10,12,14], [2,3,6,7,8,9,12,13,14],[2,3,6,7,8,10,11,12,14], [2,3,6,7,8,11,12,13,14],[2,3,6,7,9,10,11,12,14], [2,3,6,7,9,11,12,13,14],[2,3,7,8,9,10,11,12,14], [2,3,7,8,9,11,12,13,14],[2,4,5,6,7,8,10,13,14], [2,4,5,6,8,10,11,12,14],[2,4,5,6,8,10,12,13,14], [2,4,5,6,10,11,12,13,14],[2,4,5,8,9,10,11,12,14], [2,4,5,8,9,10,12,13,14],[2,4,5,8,9,11,12,13,14], [2,4,5,9,10,11,12,13,14],[2,4,6,7,8,10,12,13,14], [2,4,6,7,10,11,12,13,14],[2,5,6,7,8,10,11,12,13], [2,5,6,7,8,10,11,13,14],[2,5,6,8,10,11,12,13,14], [2,5,7,8,9,10,11,12,13],[2,5,8,9,10,11,12,13,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,11,12], [3,4,5,6,7,8,10,12,13],[3,4,5,6,7,10,11,12,13], [3,4,5,6,8,9,10,11,14],[3,4,5,6,8,9,11,12,14], [3,4,5,6,8,9,12,13,14],[3,4,5,7,8,9,10,11,12], [3,4,5,7,8,9,10,12,13],[3,4,5,7,9,10,11,12,13], [3,4,5,8,9,11,12,13,14],[3,4,6,7,8,9,10,11,12], [3,4,6,8,9,10,11,12,14],[3,5,6,7,8,9,10,11,14], [3,5,6,7,8,9,11,12,13],[3,5,6,7,8,9,11,13,14], [3,5,6,8,9,11,12,13,14],[3,6,7,8,9,10,11,12,14], [3,6,7,8,9,11,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,10,12,13,14],[4,5,6,7,10,11,12,13,14], [4,5,6,8,9,10,11,12,14],[4,5,7,8,9,10,12,13,14], [4,5,7,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,9,10,12,13,14], [5,6,7,9,10,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_7=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,10],[1,2,3,4,5,6,8,10,11], [1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,10,11,13], [1,2,3,4,5,6,11,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,8,9,10,11],[1,2,3,4,5,8,9,11,13], [1,2,3,4,5,8,11,13,14],[1,2,3,4,5,9,10,11,13], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,13], [1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,9,10,12], [1,2,3,4,6,7,9,12,13],[1,2,3,4,6,7,10,12,13], [1,2,3,4,6,8,9,10,14],[1,2,3,4,6,8,9,13,14], [1,2,3,4,6,8,10,11,14],[1,2,3,4,6,9,10,12,14], [1,2,3,4,6,9,12,13,14],[1,2,3,4,6,10,11,12,13], [1,2,3,4,6,10,11,12,14],[1,2,3,4,7,9,10,12,13], [1,2,3,4,8,9,10,11,14],[1,2,3,4,8,9,11,13,14], [1,2,3,4,9,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,14],[1,2,3,5,6,7,10,11,13], [1,2,3,5,6,7,10,11,14],[1,2,3,5,6,7,11,13,14], [1,2,3,5,6,8,10,11,14],[1,2,3,5,6,11,12,13,14], [1,2,3,5,7,8,9,10,11],[1,2,3,5,7,8,9,11,13], [1,2,3,5,7,8,10,11,14],[1,2,3,5,7,8,11,13,14], [1,2,3,5,7,9,10,11,13],[1,2,3,6,7,8,9,10,14], [1,2,3,6,7,8,9,13,14],[1,2,3,6,7,9,10,12,14], [1,2,3,6,7,9,11,12,13],[1,2,3,6,7,9,11,12,14], [1,2,3,6,7,9,11,13,14],[1,2,3,6,7,10,11,12,13], [1,2,3,6,7,10,11,12,14],[1,2,3,6,9,11,12,13,14], [1,2,3,7,8,9,10,11,14],[1,2,3,7,8,9,11,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,7,9,10,11,12,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,14],[1,2,4,5,6,7,10,11,13], [1,2,4,5,6,7,10,11,14],[1,2,4,5,6,7,11,13,14], [1,2,4,5,6,8,10,11,14],[1,2,4,5,6,11,12,13,14], [1,2,4,5,7,8,9,10,13],[1,2,4,5,7,8,10,13,14], [1,2,4,5,7,10,11,13,14],[1,2,4,5,8,9,10,11,13], [1,2,4,5,8,10,11,13,14],[1,2,4,6,7,8,9,10,12], [1,2,4,6,7,8,9,12,13],[1,2,4,6,7,8,10,12,14], [1,2,4,6,7,8,12,13,14],[1,2,4,6,7,10,11,12,13], [1,2,4,6,7,10,11,12,14],[1,2,4,6,7,11,12,13,14], [1,2,4,6,8,9,10,12,14],[1,2,4,6,8,9,12,13,14], [1,2,4,7,8,9,10,12,13],[1,2,4,7,8,10,12,13,14], [1,2,4,7,10,11,12,13,14],[1,2,4,8,9,10,11,13,14], [1,2,4,8,9,10,12,13,14],[1,2,5,7,8,9,10,11,13], [1,2,5,7,8,10,11,13,14],[1,2,6,7,8,9,10,12,14], [1,2,6,7,8,9,12,13,14],[1,2,6,7,9,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,11,12,14], [1,2,7,8,9,11,12,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,12,13],[1,3,4,5,6,7,8,13,14], [1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,11,12], [1,3,4,5,6,7,10,11,13],[1,3,4,5,6,7,11,12,13], [1,3,4,5,6,8,9,10,11],[1,3,4,5,6,8,9,11,14], [1,3,4,5,6,8,9,12,14],[1,3,4,5,6,8,12,13,14], [1,3,4,5,6,9,11,12,14],[1,3,4,5,7,8,9,12,13], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,8,9,11,13,14],[1,3,4,5,8,9,12,13,14], [1,3,4,5,9,11,12,13,14],[1,3,4,6,7,8,9,12,13], [1,3,4,6,7,9,10,11,12],[1,3,4,6,7,10,11,12,13], [1,3,4,6,8,9,10,11,14],[1,3,4,6,8,9,12,13,14], [1,3,4,6,9,10,11,12,14],[1,3,4,7,9,10,11,12,13], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,9,10,14], [1,3,5,6,7,8,9,12,13],[1,3,5,6,7,8,9,13,14], [1,3,5,6,7,9,10,11,14],[1,3,5,6,7,9,11,12,13], [1,3,5,6,7,9,11,13,14],[1,3,5,6,8,9,10,11,14], [1,3,5,6,8,9,12,13,14],[1,3,5,6,9,11,12,13,14], [1,3,5,7,8,9,10,11,14],[1,3,5,7,8,9,11,13,14], [1,3,6,7,9,10,11,12,14],[1,4,5,6,7,8,9,10,12], [1,4,5,6,7,8,10,12,14],[1,4,5,6,7,8,12,13,14], [1,4,5,6,7,9,10,11,14],[1,4,5,6,7,9,10,12,14], [1,4,5,6,7,9,11,12,14],[1,4,5,6,7,11,12,13,14], [1,4,5,6,8,9,10,11,14],[1,4,5,6,8,9,10,12,14], [1,4,5,7,8,9,10,12,13],[1,4,5,7,8,10,12,13,14], [1,4,5,7,9,10,11,13,14],[1,4,5,7,9,10,12,13,14], [1,4,5,7,9,11,12,13,14],[1,4,5,8,9,10,11,13,14], [1,4,5,8,9,10,12,13,14],[1,4,6,7,9,10,11,12,14], [1,4,7,9,10,11,12,13,14],[1,5,6,7,8,9,10,12,14], [1,5,6,7,8,9,12,13,14],[1,5,6,7,9,11,12,13,14], [1,5,7,8,9,10,11,13,14],[1,5,7,8,9,10,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,8,10,11,12],[2,3,4,5,6,8,10,12,13], [2,3,4,5,6,8,11,12,14],[2,3,4,5,6,8,12,13,14], [2,3,4,5,6,10,11,12,13],[2,3,4,5,7,8,9,10,12], [2,3,4,5,7,8,9,12,13],[2,3,4,5,7,8,10,12,13], [2,3,4,5,7,9,10,12,13],[2,3,4,5,8,9,10,11,12], [2,3,4,5,8,9,11,12,14],[2,3,4,5,8,9,11,13,14], [2,3,4,5,8,9,12,13,14],[2,3,4,5,9,10,11,12,13], [2,3,4,5,9,11,12,13,14],[2,3,4,6,7,8,9,10,12], [2,3,4,6,7,8,9,12,13],[2,3,4,6,7,8,10,12,13], [2,3,4,6,8,9,10,12,14],[2,3,4,6,8,9,12,13,14], [2,3,4,6,8,10,11,12,14],[2,3,4,8,9,10,11,12,14], [2,3,4,9,10,11,12,13,14],[2,3,5,6,7,8,10,11,13], [2,3,5,6,7,8,10,11,14],[2,3,5,6,7,8,11,13,14], [2,3,5,6,8,10,11,12,13],[2,3,5,6,8,11,12,13,14], [2,3,5,7,8,9,10,11,12],[2,3,5,7,8,9,11,12,13], [2,3,5,7,8,10,11,12,13],[2,3,5,7,9,10,11,12,13], [2,3,5,8,9,11,12,13,14],[2,3,6,7,8,9,10,12,14], [2,3,6,7,8,9,11,12,13],[2,3,6,7,8,9,11,12,14], [2,3,6,7,8,9,11,13,14],[2,3,6,7,8,10,11,12,13], [2,3,6,7,8,10,11,12,14],[2,3,6,8,9,11,12,13,14], [2,3,7,8,9,10,11,12,14],[2,4,5,6,7,8,10,13,14], [2,4,5,6,7,10,11,13,14],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,6,10,11,12,13,14], [2,4,5,7,8,9,10,12,13],[2,4,5,8,9,10,11,12,14], [2,4,5,8,9,10,11,13,14],[2,4,5,8,9,10,12,13,14], [2,4,5,9,10,11,12,13,14],[2,4,6,7,8,10,12,13,14], [2,4,6,7,10,11,12,13,14],[2,5,6,7,8,10,11,13,14], [2,5,6,8,10,11,12,13,14],[2,5,7,8,9,10,11,12,13], [2,5,8,9,10,11,12,13,14],[2,6,7,8,9,11,12,13,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,11,12], [3,4,5,6,7,8,10,12,13],[3,4,5,6,7,10,11,12,13], [3,4,5,6,8,9,11,12,14],[3,4,5,7,8,9,10,11,12], [3,4,5,7,9,10,11,12,13],[3,4,6,7,8,9,10,11,12], [3,4,6,8,9,10,11,12,14],[3,5,6,7,8,9,10,11,14], [3,5,6,7,8,9,11,12,13],[3,5,6,7,8,9,11,13,14], [3,5,6,7,8,10,11,12,13],[3,5,6,8,9,11,12,13,14], [3,6,7,8,9,10,11,12,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,10,12,13,14],[4,5,6,7,9,10,11,12,14], [4,5,6,7,10,11,12,13,14],[4,5,6,8,9,10,11,12,14], [4,5,7,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,9,10,12,13,14], [5,6,7,9,10,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_8=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,11],[1,2,3,4,5,6,8,11,14], [1,2,3,4,5,6,9,10,11],[1,2,3,4,5,6,10,11,12], [1,2,3,4,5,6,10,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,11], [1,2,3,4,5,7,8,11,13],[1,2,3,4,5,7,8,13,14], [1,2,3,4,5,7,9,10,11],[1,2,3,4,5,7,10,11,13], [1,2,3,4,5,8,11,13,14],[1,2,3,4,5,10,11,12,13], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,14], [1,2,3,4,6,7,9,10,13],[1,2,3,4,6,7,9,13,14], [1,2,3,4,6,8,9,11,12],[1,2,3,4,6,8,9,12,14], [1,2,3,4,6,8,11,12,14],[1,2,3,4,6,9,10,11,12], [1,2,3,4,6,9,10,12,13],[1,2,3,4,6,9,12,13,14], [1,2,3,4,7,8,9,10,12],[1,2,3,4,7,8,9,10,13], [1,2,3,4,7,8,9,11,12],[1,2,3,4,7,8,9,13,14], [1,2,3,4,7,8,10,11,12],[1,2,3,4,7,8,10,11,13], [1,2,3,4,7,9,10,11,12],[1,2,3,4,8,9,10,12,14], [1,2,3,4,8,9,10,13,14],[1,2,3,4,8,10,11,12,14], [1,2,3,4,8,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,14], [1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,13,14], [1,2,3,5,6,8,9,11,14],[1,2,3,5,6,9,10,11,12], [1,2,3,5,6,9,10,12,13],[1,2,3,5,6,9,11,12,13], [1,2,3,5,6,9,11,13,14],[1,2,3,5,6,11,12,13,14], [1,2,3,5,7,8,9,11,13],[1,2,3,5,7,8,9,13,14], [1,2,3,5,7,9,10,11,13],[1,2,3,5,8,9,11,13,14], [1,2,3,5,9,10,11,12,13],[1,2,3,6,8,9,11,12,14], [1,2,3,6,9,11,12,13,14],[1,2,3,7,8,9,10,11,12], [1,2,3,7,8,9,10,11,13],[1,2,3,8,9,10,11,12,14], [1,2,3,8,9,10,11,13,14],[1,2,3,9,10,11,12,13,14], [1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,10,12], [1,2,4,5,6,7,8,12,14],[1,2,4,5,6,7,10,12,13], [1,2,4,5,6,7,12,13,14],[1,2,4,5,6,8,9,10,12], [1,2,4,5,6,8,9,11,12],[1,2,4,5,6,8,11,12,14], [1,2,4,5,6,9,10,11,12],[1,2,4,5,7,8,9,10,12], [1,2,4,5,7,8,9,11,12],[1,2,4,5,7,8,11,12,14], [1,2,4,5,7,8,11,13,14],[1,2,4,5,7,9,10,11,12], [1,2,4,5,7,10,11,12,13],[1,2,4,5,7,11,12,13,14], [1,2,4,6,7,8,9,10,14],[1,2,4,6,7,8,10,12,14], [1,2,4,6,7,9,10,13,14],[1,2,4,6,7,10,12,13,14], [1,2,4,6,8,9,10,12,14],[1,2,4,6,9,10,12,13,14], [1,2,4,7,8,9,10,13,14],[1,2,4,7,8,10,11,12,14], [1,2,4,7,8,10,11,13,14],[1,2,4,7,10,11,12,13,14], [1,2,5,6,7,8,9,10,14],[1,2,5,6,7,8,10,12,13], [1,2,5,6,7,8,10,13,14],[1,2,5,6,7,8,11,12,13], [1,2,5,6,7,8,11,12,14],[1,2,5,6,7,8,11,13,14], [1,2,5,6,7,9,10,13,14],[1,2,5,6,7,11,12,13,14], [1,2,5,6,8,9,10,12,13],[1,2,5,6,8,9,10,13,14], [1,2,5,6,8,9,11,12,13],[1,2,5,6,8,9,11,13,14], [1,2,5,7,8,9,10,12,13],[1,2,5,7,8,9,10,13,14], [1,2,5,7,8,9,11,12,13],[1,2,5,7,9,10,11,12,13], [1,2,6,7,8,10,12,13,14],[1,2,6,7,8,11,12,13,14], [1,2,6,8,9,10,12,13,14],[1,2,6,8,9,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,12,14],[1,3,4,5,6,7,9,10,13], [1,3,4,5,6,7,9,12,13],[1,3,4,5,6,7,12,13,14], [1,3,4,5,6,8,9,11,12],[1,3,4,5,6,8,11,12,14], [1,3,4,5,6,9,10,11,12],[1,3,4,5,6,9,10,12,13], [1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,11,12,14], [1,3,4,5,7,8,11,13,14],[1,3,4,5,7,9,10,11,13], [1,3,4,5,7,9,11,12,13],[1,3,4,5,7,11,12,13,14], [1,3,4,5,9,10,11,12,13],[1,3,4,6,7,8,9,12,14], [1,3,4,6,7,9,12,13,14],[1,3,4,7,8,9,10,12,14], [1,3,4,7,8,9,10,13,14],[1,3,4,7,8,10,11,12,14], [1,3,4,7,8,10,11,13,14],[1,3,4,7,9,10,11,12,14], [1,3,4,7,9,10,11,13,14],[1,3,4,7,9,11,12,13,14], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,9,11,12], [1,3,5,6,7,8,9,11,14],[1,3,5,6,7,8,11,12,14], [1,3,5,6,7,9,11,12,13],[1,3,5,6,7,9,11,13,14], [1,3,5,6,7,11,12,13,14],[1,3,5,7,8,9,11,13,14], [1,3,6,7,8,9,11,12,14],[1,3,6,7,9,11,12,13,14], [1,3,7,8,9,10,11,12,14],[1,3,7,8,9,10,11,13,14], [1,4,5,6,7,8,9,10,12],[1,4,5,6,7,9,10,12,13], [1,4,5,7,9,10,11,12,13],[1,4,6,7,8,9,10,12,14], [1,4,6,7,9,10,12,13,14],[1,4,7,9,10,11,12,13,14], [1,5,6,7,8,9,10,12,13],[1,5,6,7,8,9,10,13,14], [1,5,6,7,8,9,11,12,13],[1,5,6,7,8,9,11,13,14], [1,6,7,8,9,10,12,13,14],[1,6,7,8,9,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,8,9,10,11],[2,3,4,5,6,8,10,11,14], [2,3,4,5,6,8,10,13,14],[2,3,4,5,6,10,11,12,14], [2,3,4,5,6,10,12,13,14],[2,3,4,5,7,8,9,10,11], [2,3,4,5,7,8,10,11,13],[2,3,4,5,8,10,11,13,14], [2,3,4,5,10,11,12,13,14],[2,3,4,6,7,8,9,10,14], [2,3,4,6,7,8,10,13,14],[2,3,4,6,7,9,10,13,14], [2,3,4,6,8,9,10,11,12],[2,3,4,6,8,9,10,12,14], [2,3,4,6,8,10,11,12,14],[2,3,4,6,9,10,12,13,14], [2,3,4,7,8,9,10,11,12],[2,3,4,7,8,9,10,13,14], [2,3,5,6,7,8,9,10,14],[2,3,5,6,7,8,10,13,14], [2,3,5,6,7,9,10,13,14],[2,3,5,6,8,9,10,11,14], [2,3,5,6,9,10,11,12,14],[2,3,5,6,9,10,12,13,14], [2,3,5,6,9,11,12,13,14],[2,3,5,7,8,9,10,11,13], [2,3,5,7,8,9,10,13,14],[2,3,5,8,9,10,11,13,14], [2,3,5,9,10,11,12,13,14],[2,3,6,8,9,10,11,12,14], [2,4,5,6,7,8,10,12,13],[2,4,5,6,7,8,12,13,14], [2,4,5,6,8,9,10,11,12],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,7,8,9,10,11,12], [2,4,5,7,8,10,11,12,13],[2,4,5,7,8,11,12,13,14], [2,4,5,8,10,11,12,13,14],[2,4,6,7,8,10,12,13,14], [2,4,7,8,10,11,12,13,14],[2,5,6,7,8,11,12,13,14], [2,5,6,8,9,10,11,12,14],[2,5,6,8,9,10,12,13,14], [2,5,6,8,9,11,12,13,14],[2,5,7,8,9,10,11,12,13], [2,5,8,9,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,11,13], [3,4,5,6,7,8,11,12,13],[3,4,5,6,7,8,12,13,14], [3,4,5,6,7,9,10,11,13],[3,4,5,6,7,9,11,12,13], [3,4,5,6,8,10,11,13,14],[3,4,5,6,8,11,12,13,14], [3,4,5,6,9,10,11,12,14],[3,4,5,6,9,10,11,13,14], [3,4,5,6,9,10,12,13,14],[3,4,5,6,9,11,12,13,14], [3,4,5,7,8,11,12,13,14],[3,4,5,9,10,11,12,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,10,12,14], [3,4,6,7,8,10,11,12,14],[3,4,6,7,8,10,11,13,14], [3,4,6,7,8,11,12,13,14],[3,4,6,7,9,10,11,12,14], [3,4,6,7,9,10,11,13,14],[3,4,6,7,9,11,12,13,14], [3,5,6,7,8,9,10,11,14],[3,5,6,7,8,10,11,13,14], [3,5,6,7,8,11,12,13,14],[3,5,6,7,9,10,11,13,14], [3,5,7,8,9,10,11,13,14],[3,6,7,8,9,10,11,12,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,10,11,12,13], [4,5,6,7,9,10,11,12,13],[4,5,6,8,10,11,12,13,14], [4,5,6,9,10,11,12,13,14],[4,6,7,8,10,11,12,13,14], [4,6,7,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_9=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,11],[1,2,3,4,5,6,8,11,14], [1,2,3,4,5,6,9,10,12],[1,2,3,4,5,6,9,11,12], [1,2,3,4,5,6,10,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,11], [1,2,3,4,5,7,8,11,13],[1,2,3,4,5,7,8,13,14], [1,2,3,4,5,7,9,10,11],[1,2,3,4,5,7,10,11,13], [1,2,3,4,5,8,11,13,14],[1,2,3,4,5,9,10,11,12], [1,2,3,4,5,10,11,12,13],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,14],[1,2,3,4,6,7,9,10,13], [1,2,3,4,6,7,9,13,14],[1,2,3,4,6,8,9,11,12], [1,2,3,4,6,8,9,12,14],[1,2,3,4,6,8,11,12,14], [1,2,3,4,6,9,10,12,13],[1,2,3,4,6,9,12,13,14], [1,2,3,4,7,8,9,10,11],[1,2,3,4,7,8,9,10,14], [1,2,3,4,7,8,10,11,13],[1,2,3,4,7,8,10,13,14], [1,2,3,4,7,9,10,13,14],[1,2,3,4,8,9,10,11,12], [1,2,3,4,8,9,10,12,14],[1,2,3,4,8,10,11,12,14], [1,2,3,4,8,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,14], [1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,13,14], [1,2,3,5,6,8,9,11,14],[1,2,3,5,6,9,10,12,13], [1,2,3,5,6,9,11,12,13],[1,2,3,5,6,9,11,13,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,11,13], [1,2,3,5,7,8,9,13,14],[1,2,3,5,7,9,10,11,13], [1,2,3,5,8,9,11,13,14],[1,2,3,5,9,10,11,12,13], [1,2,3,6,8,9,11,12,14],[1,2,3,6,9,11,12,13,14], [1,2,3,7,8,9,10,11,13],[1,2,3,7,8,9,10,13,14], [1,2,3,8,9,10,11,12,14],[1,2,3,8,9,10,11,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,12],[1,2,4,5,6,7,8,12,14], [1,2,4,5,6,7,10,12,13],[1,2,4,5,6,7,12,13,14], [1,2,4,5,6,8,9,10,12],[1,2,4,5,6,8,9,11,12], [1,2,4,5,6,8,11,12,14],[1,2,4,5,7,8,9,10,12], [1,2,4,5,7,8,9,11,12],[1,2,4,5,7,8,11,12,14], [1,2,4,5,7,8,11,13,14],[1,2,4,5,7,9,10,11,12], [1,2,4,5,7,10,11,12,13],[1,2,4,5,7,11,12,13,14], [1,2,4,6,7,8,9,10,14],[1,2,4,6,7,8,10,12,14], [1,2,4,6,7,9,10,13,14],[1,2,4,6,7,10,12,13,14], [1,2,4,6,8,9,10,12,14],[1,2,4,6,9,10,12,13,14], [1,2,4,7,8,9,10,11,12],[1,2,4,7,8,10,11,12,14], [1,2,4,7,8,10,11,13,14],[1,2,4,7,10,11,12,13,14], [1,2,5,6,7,8,9,10,13],[1,2,5,6,7,8,9,13,14], [1,2,5,6,7,8,10,12,13],[1,2,5,6,7,8,12,13,14], [1,2,5,6,8,9,10,12,13],[1,2,5,6,8,9,11,12,13], [1,2,5,6,8,9,11,13,14],[1,2,5,6,8,11,12,13,14], [1,2,5,7,8,9,10,12,13],[1,2,5,7,8,9,11,12,13], [1,2,5,7,8,11,12,13,14],[1,2,5,7,9,10,11,12,13], [1,2,6,7,8,9,10,13,14],[1,2,6,7,8,10,12,13,14], [1,2,6,8,9,10,12,13,14],[1,2,6,8,9,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,12,14],[1,3,4,5,6,7,9,10,13], [1,3,4,5,6,7,9,12,13],[1,3,4,5,6,7,12,13,14], [1,3,4,5,6,8,9,11,12],[1,3,4,5,6,8,11,12,14], [1,3,4,5,6,9,10,12,13],[1,3,4,5,7,8,9,11,12], [1,3,4,5,7,8,11,12,14],[1,3,4,5,7,8,11,13,14], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,7,11,12,13,14],[1,3,4,5,9,10,11,12,13], [1,3,4,6,7,8,9,12,14],[1,3,4,6,7,9,12,13,14], [1,3,4,7,8,9,10,11,12],[1,3,4,7,8,9,10,12,14], [1,3,4,7,8,10,11,12,14],[1,3,4,7,8,10,11,13,14], [1,3,4,7,9,10,11,12,14],[1,3,4,7,9,10,11,13,14], [1,3,4,7,9,11,12,13,14],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,11,12],[1,3,5,6,7,8,9,11,14], [1,3,5,6,7,8,11,12,14],[1,3,5,6,7,9,11,12,13], [1,3,5,6,7,9,11,13,14],[1,3,5,6,7,11,12,13,14], [1,3,5,7,8,9,11,13,14],[1,3,6,7,8,9,11,12,14], [1,3,6,7,9,11,12,13,14],[1,3,7,8,9,10,11,12,14], [1,3,7,8,9,10,11,13,14],[1,4,5,6,7,8,9,10,12], [1,4,5,6,7,9,10,12,13],[1,4,5,7,9,10,11,12,13], [1,4,6,7,8,9,10,12,14],[1,4,6,7,9,10,12,13,14], [1,4,7,9,10,11,12,13,14],[1,5,6,7,8,9,10,12,13], [1,5,6,7,8,9,11,12,13],[1,5,6,7,8,9,11,13,14], [1,5,6,7,8,11,12,13,14],[1,6,7,8,9,10,12,13,14], [1,6,7,8,9,11,12,13,14],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,13], [2,3,4,5,6,7,8,13,14],[2,3,4,5,6,8,9,10,11], [2,3,4,5,6,8,10,11,14],[2,3,4,5,6,8,10,13,14], [2,3,4,5,6,9,10,11,12],[2,3,4,5,6,10,11,12,14], [2,3,4,5,6,10,12,13,14],[2,3,4,5,7,8,9,10,11], [2,3,4,5,7,8,10,11,13],[2,3,4,5,8,10,11,13,14], [2,3,4,5,10,11,12,13,14],[2,3,4,6,7,8,9,10,14], [2,3,4,6,7,8,10,13,14],[2,3,4,6,7,9,10,13,14], [2,3,4,6,8,9,10,11,12],[2,3,4,6,8,9,10,12,14], [2,3,4,6,8,10,11,12,14],[2,3,4,6,9,10,12,13,14], [2,3,5,6,7,8,9,10,14],[2,3,5,6,7,8,10,13,14], [2,3,5,6,7,9,10,13,14],[2,3,5,6,8,9,10,11,14], [2,3,5,6,9,10,11,12,14],[2,3,5,6,9,10,12,13,14], [2,3,5,6,9,11,12,13,14],[2,3,5,7,8,9,10,11,13], [2,3,5,7,8,9,10,13,14],[2,3,5,8,9,10,11,13,14], [2,3,5,9,10,11,12,13,14],[2,3,6,8,9,10,11,12,14], [2,4,5,6,7,8,10,12,13],[2,4,5,6,7,8,12,13,14], [2,4,5,6,8,9,10,11,12],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,7,8,9,10,11,12], [2,4,5,7,8,10,11,12,13],[2,4,5,7,8,11,12,13,14], [2,4,5,8,10,11,12,13,14],[2,4,6,7,8,10,12,13,14], [2,4,7,8,10,11,12,13,14],[2,5,6,7,8,9,10,13,14], [2,5,6,8,9,10,11,12,14],[2,5,6,8,9,10,12,13,14], [2,5,6,8,9,11,12,13,14],[2,5,7,8,9,10,11,12,13], [2,5,8,9,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,11,13], [3,4,5,6,7,8,11,12,14],[3,4,5,6,7,8,11,13,14], [3,4,5,6,7,9,10,11,13],[3,4,5,6,7,9,11,12,13], [3,4,5,6,7,11,12,13,14],[3,4,5,6,8,10,11,13,14], [3,4,5,6,9,10,11,12,13],[3,4,5,6,10,11,12,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,10,12,14], [3,4,6,7,8,10,11,12,14],[3,4,6,7,8,10,11,13,14], [3,4,6,7,9,10,11,12,14],[3,4,6,7,9,10,11,13,14], [3,4,6,7,9,11,12,13,14],[3,4,6,9,10,11,12,13,14], [3,5,6,7,8,9,10,11,14],[3,5,6,7,8,10,11,13,14], [3,5,6,7,9,10,11,13,14],[3,5,6,9,10,11,12,13,14], [3,5,7,8,9,10,11,13,14],[3,6,7,8,9,10,11,12,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,10,11,12,13], [4,5,6,7,8,11,12,13,14],[4,5,6,7,9,10,11,12,13], [4,5,6,8,10,11,12,13,14],[4,6,7,8,10,11,12,13,14], [4,6,7,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_10=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,12],[1,2,3,4,5,6,8,11,12], [1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,9,10,13], [1,2,3,4,5,6,9,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,10], [1,2,3,4,5,7,8,10,11],[1,2,3,4,5,7,8,11,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,10,11,13], [1,2,3,4,5,8,9,10,11],[1,2,3,4,5,8,9,11,12], [1,2,3,4,5,8,11,13,14],[1,2,3,4,5,9,10,11,13], [1,2,3,4,5,9,11,12,13],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,10],[1,2,3,4,6,7,8,10,14], [1,2,3,4,6,7,10,13,14],[1,2,3,4,6,8,9,10,14], [1,2,3,4,6,8,9,12,14],[1,2,3,4,6,8,11,12,14], [1,2,3,4,6,9,10,13,14],[1,2,3,4,6,9,12,13,14], [1,2,3,4,7,8,10,11,14],[1,2,3,4,7,8,11,13,14], [1,2,3,4,7,10,11,13,14],[1,2,3,4,8,9,10,11,14], [1,2,3,4,8,9,11,12,14],[1,2,3,4,9,10,11,12,13], [1,2,3,4,9,10,11,12,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,13], [1,2,3,5,6,7,8,13,14],[1,2,3,5,6,7,9,10,13], [1,2,3,5,6,8,9,11,12],[1,2,3,5,6,8,9,11,14], [1,2,3,5,6,8,9,13,14],[1,2,3,5,6,9,11,12,13], [1,2,3,5,6,9,11,13,14],[1,2,3,5,6,11,12,13,14], [1,2,3,5,7,8,9,10,11],[1,2,3,5,7,8,9,11,13], [1,2,3,5,7,9,10,11,13],[1,2,3,5,8,9,11,13,14], [1,2,3,6,7,8,9,10,14],[1,2,3,6,7,8,9,13,14], [1,2,3,6,7,9,10,13,14],[1,2,3,6,8,9,11,12,14], [1,2,3,6,9,11,12,13,14],[1,2,3,7,8,9,10,11,14], [1,2,3,7,8,9,11,13,14],[1,2,3,7,9,10,11,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,12],[1,2,4,5,6,7,8,12,13], [1,2,4,5,6,7,8,13,14],[1,2,4,5,6,7,10,12,13], [1,2,4,5,6,8,9,10,12],[1,2,4,5,6,8,11,12,14], [1,2,4,5,6,8,12,13,14],[1,2,4,5,6,9,10,12,13], [1,2,4,5,7,8,10,11,12],[1,2,4,5,7,8,11,12,13], [1,2,4,5,7,10,11,12,13],[1,2,4,5,8,9,10,11,12], [1,2,4,5,8,11,12,13,14],[1,2,4,5,9,10,11,12,13], [1,2,4,6,7,8,10,12,14],[1,2,4,6,7,8,12,13,14], [1,2,4,6,7,10,12,13,14],[1,2,4,6,8,9,10,12,14], [1,2,4,6,9,10,12,13,14],[1,2,4,7,8,10,11,12,14], [1,2,4,7,8,11,12,13,14],[1,2,4,7,10,11,12,13,14], [1,2,4,8,9,10,11,12,14],[1,2,5,6,7,8,9,10,12], [1,2,5,6,7,8,9,12,13],[1,2,5,6,7,9,10,12,13], [1,2,5,6,8,9,11,12,14],[1,2,5,6,8,9,12,13,14], [1,2,5,6,9,11,12,13,14],[1,2,5,7,8,9,10,11,12], [1,2,5,7,8,9,11,12,13],[1,2,5,7,9,10,11,12,13], [1,2,5,8,9,11,12,13,14],[1,2,6,7,8,9,10,12,14], [1,2,6,7,8,9,12,13,14],[1,2,6,7,9,10,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,11,13,14], [1,2,7,8,9,10,12,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,11,12],[1,3,4,5,6,7,8,11,14], [1,3,4,5,6,7,9,10,13],[1,3,4,5,6,7,9,12,13], [1,3,4,5,6,7,11,12,13],[1,3,4,5,6,7,11,13,14], [1,3,4,5,6,11,12,13,14],[1,3,4,5,7,8,9,10,11], [1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,11,13,14], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,6,7,8,9,10,14],[1,3,4,6,7,8,9,12,14], [1,3,4,6,7,8,11,12,14],[1,3,4,6,7,9,10,13,14], [1,3,4,6,7,9,12,13,14],[1,3,4,6,7,11,12,13,14], [1,3,4,7,8,9,10,11,14],[1,3,4,7,8,9,11,12,14], [1,3,4,7,9,10,11,13,14],[1,3,4,7,9,11,12,13,14], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,9,11,12], [1,3,5,6,7,8,9,11,14],[1,3,5,6,7,8,9,13,14], [1,3,5,6,7,9,11,12,13],[1,3,5,6,7,9,11,13,14], [1,3,5,7,8,9,11,13,14],[1,3,6,7,8,9,11,12,14], [1,3,6,7,9,11,12,13,14],[1,4,5,6,7,8,9,10,12], [1,4,5,6,7,8,11,12,14],[1,4,5,6,7,8,12,13,14], [1,4,5,6,7,9,10,12,13],[1,4,5,6,7,11,12,13,14], [1,4,5,7,8,9,10,11,12],[1,4,5,7,8,11,12,13,14], [1,4,5,7,9,10,11,12,13],[1,4,6,7,8,9,10,12,14], [1,4,6,7,9,10,12,13,14],[1,4,7,8,9,10,11,12,14], [1,4,7,9,10,11,12,13,14],[1,5,6,7,8,9,11,12,14], [1,5,6,7,8,9,12,13,14],[1,5,6,7,9,11,12,13,14], [1,5,7,8,9,11,12,13,14],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,13], [2,3,4,5,6,7,8,13,14],[2,3,4,5,6,8,9,10,12], [2,3,4,5,6,8,10,11,12],[2,3,4,5,6,8,10,11,14], [2,3,4,5,6,8,10,13,14],[2,3,4,5,6,9,10,12,13], [2,3,4,5,6,10,11,12,13],[2,3,4,5,6,10,11,13,14], [2,3,4,5,6,11,12,13,14],[2,3,4,5,7,8,10,11,13], [2,3,4,5,8,9,10,11,12],[2,3,4,5,8,10,11,13,14], [2,3,4,5,9,10,11,12,13],[2,3,4,6,7,8,10,13,14], [2,3,4,6,8,9,10,12,14],[2,3,4,6,8,10,11,12,14], [2,3,4,6,9,10,12,13,14],[2,3,4,6,10,11,12,13,14], [2,3,4,7,8,10,11,13,14],[2,3,4,8,9,10,11,12,14], [2,3,5,6,7,8,9,10,13],[2,3,5,6,8,9,10,11,12], [2,3,5,6,8,9,10,11,14],[2,3,5,6,8,9,10,13,14], [2,3,5,6,9,10,11,12,13],[2,3,5,6,9,10,11,13,14], [2,3,5,7,8,9,10,11,13],[2,3,5,8,9,10,11,13,14], [2,3,6,7,8,9,10,13,14],[2,3,6,8,9,10,11,12,14], [2,3,6,9,10,11,12,13,14],[2,3,7,8,9,10,11,13,14], [2,4,5,6,7,8,10,12,13],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,6,10,11,12,13,14], [2,4,5,7,8,10,11,12,13],[2,4,5,8,10,11,12,13,14], [2,4,6,7,8,10,12,13,14],[2,4,7,8,10,11,12,13,14], [2,5,6,7,8,9,10,12,13],[2,5,6,8,9,10,11,12,14], [2,5,6,8,9,10,12,13,14],[2,5,6,9,10,11,12,13,14], [2,5,7,8,9,10,11,12,13],[2,5,8,9,10,11,12,13,14], [2,6,7,8,9,10,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,11,14], [3,4,5,6,7,8,10,13,14],[3,4,5,6,7,9,10,11,12], [3,4,5,6,7,9,10,12,13],[3,4,5,6,7,10,11,12,13], [3,4,5,6,7,10,11,13,14],[3,4,5,6,8,9,10,11,12], [3,4,5,7,8,10,11,13,14],[3,4,5,7,9,10,11,12,13], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,10,12,14], [3,4,6,7,8,10,11,12,14],[3,4,6,7,9,10,12,13,14], [3,4,6,7,10,11,12,13,14],[3,4,7,8,9,10,11,12,14], [3,4,7,9,10,11,12,13,14],[3,5,6,7,8,9,10,11,14], [3,5,6,7,8,9,10,13,14],[3,5,6,7,9,10,11,12,13], [3,5,6,7,9,10,11,13,14],[3,5,7,8,9,10,11,13,14], [3,6,7,8,9,10,11,12,14],[3,6,7,9,10,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,10,11,12,14], [4,5,6,7,8,10,12,13,14],[4,5,6,7,10,11,12,13,14], [4,5,7,8,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,9,11,12,13,14], [5,6,7,8,10,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_11=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,12],[1,2,3,4,5,6,8,11,12], [1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,9,10,13], [1,2,3,4,5,6,9,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,11], [1,2,3,4,5,7,8,11,13],[1,2,3,4,5,7,8,13,14], [1,2,3,4,5,7,9,10,11],[1,2,3,4,5,7,10,11,13], [1,2,3,4,5,8,9,11,12],[1,2,3,4,5,8,11,13,14], [1,2,3,4,5,9,10,11,12],[1,2,3,4,5,9,10,12,13], [1,2,3,4,5,10,11,12,13],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,14],[1,2,3,4,6,7,9,10,14], [1,2,3,4,6,7,10,13,14],[1,2,3,4,6,8,9,12,14], [1,2,3,4,6,8,11,12,14],[1,2,3,4,6,9,10,13,14], [1,2,3,4,6,9,12,13,14],[1,2,3,4,7,8,9,10,11], [1,2,3,4,7,8,9,10,14],[1,2,3,4,7,8,10,11,14], [1,2,3,4,7,8,11,13,14],[1,2,3,4,7,10,11,13,14], [1,2,3,4,8,9,10,11,12],[1,2,3,4,8,9,10,12,14], [1,2,3,4,8,10,11,12,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,14], [1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,13,14], [1,2,3,5,6,8,9,11,12],[1,2,3,5,6,8,9,11,14], [1,2,3,5,6,9,11,12,13],[1,2,3,5,6,9,11,13,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,11,13], [1,2,3,5,7,8,9,13,14],[1,2,3,5,7,9,10,11,13], [1,2,3,5,8,9,11,13,14],[1,2,3,5,9,10,11,12,13], [1,2,3,6,7,9,10,13,14],[1,2,3,6,8,9,11,12,14], [1,2,3,6,9,11,12,13,14],[1,2,3,7,8,9,10,11,13], [1,2,3,7,8,9,10,13,14],[1,2,3,7,8,10,11,13,14], [1,2,3,8,9,10,11,12,14],[1,2,3,8,9,10,11,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,10], [1,2,4,5,6,7,8,10,12],[1,2,4,5,6,7,8,12,14], [1,2,4,5,6,7,10,12,13],[1,2,4,5,6,7,12,13,14], [1,2,4,5,6,8,9,10,12],[1,2,4,5,6,8,11,12,14], [1,2,4,5,6,9,10,12,13],[1,2,4,5,7,8,9,10,11], [1,2,4,5,7,8,10,11,12],[1,2,4,5,7,8,11,12,13], [1,2,4,5,7,8,12,13,14],[1,2,4,5,7,10,11,12,13], [1,2,4,5,8,9,10,11,12],[1,2,4,5,8,11,12,13,14], [1,2,4,6,7,8,9,10,14],[1,2,4,6,7,8,10,12,14], [1,2,4,6,7,10,12,13,14],[1,2,4,6,8,9,10,12,14], [1,2,4,6,9,10,12,13,14],[1,2,4,7,8,10,11,12,14], [1,2,4,7,8,11,12,13,14],[1,2,4,7,10,11,12,13,14], [1,2,5,6,7,8,9,10,12],[1,2,5,6,7,8,9,12,13], [1,2,5,6,7,8,9,13,14],[1,2,5,6,7,8,12,13,14], [1,2,5,6,7,9,10,12,13],[1,2,5,6,8,9,11,12,14], [1,2,5,6,8,9,12,13,14],[1,2,5,6,9,11,12,13,14], [1,2,5,7,8,9,10,11,12],[1,2,5,7,8,9,11,12,13], [1,2,5,7,9,10,11,12,13],[1,2,5,8,9,11,12,13,14], [1,2,6,7,8,9,10,12,13],[1,2,6,7,8,9,10,13,14], [1,2,6,7,8,10,12,13,14],[1,2,6,8,9,10,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,11,12],[1,3,4,5,6,7,8,11,14], [1,3,4,5,6,7,9,10,13],[1,3,4,5,6,7,9,12,13], [1,3,4,5,6,7,11,12,14],[1,3,4,5,6,7,12,13,14], [1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,11,13,14], [1,3,4,5,7,9,10,11,13],[1,3,4,5,7,9,11,12,13], [1,3,4,5,7,11,12,13,14],[1,3,4,5,9,10,11,12,13], [1,3,4,6,7,8,9,12,14],[1,3,4,6,7,8,11,12,14], [1,3,4,6,7,9,10,13,14],[1,3,4,6,7,9,12,13,14], [1,3,4,7,8,9,10,11,14],[1,3,4,7,8,9,11,12,14], [1,3,4,7,9,10,11,13,14],[1,3,4,7,9,11,12,13,14], [1,3,4,8,9,10,11,12,14],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,11,12],[1,3,5,6,7,8,9,11,14], [1,3,5,6,7,9,11,12,13],[1,3,5,6,7,9,11,13,14], [1,3,5,6,7,11,12,13,14],[1,3,5,7,8,9,11,13,14], [1,3,6,7,8,9,11,12,14],[1,3,6,7,9,11,12,13,14], [1,3,7,8,9,10,11,13,14],[1,4,5,6,7,8,9,10,12], [1,4,5,6,7,8,11,12,14],[1,4,5,6,7,9,10,12,13], [1,4,5,7,8,9,10,11,12],[1,4,5,7,8,11,12,13,14], [1,4,5,7,9,10,11,12,13],[1,4,6,7,8,9,10,12,14], [1,4,6,7,9,10,12,13,14],[1,4,7,8,9,10,11,12,14], [1,4,7,9,10,11,12,13,14],[1,5,6,7,8,9,11,12,13], [1,5,6,7,8,9,11,13,14],[1,5,6,7,8,11,12,13,14], [1,5,6,8,9,11,12,13,14],[1,6,7,8,9,10,12,13,14], [1,6,7,8,9,11,12,13,14],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,13], [2,3,4,5,6,7,8,13,14],[2,3,4,5,6,8,9,10,11], [2,3,4,5,6,8,9,11,12],[2,3,4,5,6,8,10,11,14], [2,3,4,5,6,8,10,13,14],[2,3,4,5,6,9,10,11,12], [2,3,4,5,6,9,10,12,13],[2,3,4,5,6,10,11,12,14], [2,3,4,5,6,10,12,13,14],[2,3,4,5,7,8,9,10,11], [2,3,4,5,7,8,10,11,13],[2,3,4,5,8,10,11,13,14], [2,3,4,5,10,11,12,13,14],[2,3,4,6,7,8,9,10,14], [2,3,4,6,7,8,10,13,14],[2,3,4,6,8,9,10,11,12], [2,3,4,6,8,9,10,12,14],[2,3,4,6,8,10,11,12,14], [2,3,4,6,9,10,12,13,14],[2,3,4,7,8,10,11,13,14], [2,3,5,6,7,8,9,10,13],[2,3,5,6,7,8,9,13,14], [2,3,5,6,8,9,10,11,14],[2,3,5,6,8,9,10,13,14], [2,3,5,6,9,10,11,12,13],[2,3,5,6,9,10,11,13,14], [2,3,5,6,10,11,12,13,14],[2,3,5,7,8,9,10,11,13], [2,3,5,8,9,10,11,13,14],[2,3,6,7,8,9,10,13,14], [2,3,6,8,9,10,11,12,14],[2,3,6,9,10,11,12,13,14], [2,4,5,6,7,8,10,12,13],[2,4,5,6,7,8,12,13,14], [2,4,5,6,8,9,10,11,12],[2,4,5,6,8,10,11,12,14], [2,4,5,6,8,10,12,13,14],[2,4,5,7,8,10,11,12,13], [2,4,5,8,10,11,12,13,14],[2,4,6,7,8,10,12,13,14], [2,4,7,8,10,11,12,13,14],[2,5,6,7,8,9,10,12,13], [2,5,6,8,9,10,11,12,14],[2,5,6,8,9,10,12,13,14], [2,5,6,9,10,11,12,13,14],[2,5,7,8,9,10,11,12,13], [2,5,8,9,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,11,14], [3,4,5,6,7,8,10,13,14],[3,4,5,6,7,9,10,11,13], [3,4,5,6,7,9,11,12,13],[3,4,5,6,7,10,11,13,14], [3,4,5,6,7,11,12,13,14],[3,4,5,6,9,10,11,12,13], [3,4,5,6,10,11,12,13,14],[3,4,5,7,8,10,11,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,10,12,14], [3,4,6,7,8,10,11,12,14],[3,4,6,7,9,10,11,12,13], [3,4,6,7,9,10,12,13,14],[3,4,6,7,10,11,12,13,14], [3,4,7,8,9,10,11,12,14],[3,4,7,9,10,11,12,13,14], [3,5,6,7,8,9,10,11,14],[3,5,6,7,8,9,10,13,14], [3,5,6,7,9,10,11,13,14],[3,5,7,8,9,10,11,13,14], [3,6,7,8,9,10,11,12,14],[3,6,7,9,10,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,10,11,12,13], [4,5,6,7,8,10,11,13,14],[4,5,6,7,8,11,12,13,14], [4,5,6,7,9,10,11,12,13],[4,5,6,8,10,11,12,13,14], [4,6,7,8,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_12=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,12],[1,2,3,4,5,6,8,11,12], [1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,9,10,13], [1,2,3,4,5,6,9,12,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,8,9,12,13],[1,2,3,4,5,8,11,12,13], [1,2,3,4,5,8,11,13,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,12],[1,2,3,4,6,7,8,11,12], [1,2,3,4,6,7,8,11,14],[1,2,3,4,6,7,9,10,12], [1,2,3,4,6,7,10,11,12],[1,2,3,4,6,7,10,11,14], [1,2,3,4,6,7,10,13,14],[1,2,3,4,6,9,10,12,14], [1,2,3,4,6,9,10,13,14],[1,2,3,4,6,9,12,13,14], [1,2,3,4,6,10,11,12,14],[1,2,3,4,7,8,9,12,13], [1,2,3,4,7,8,11,12,13],[1,2,3,4,7,8,11,13,14], [1,2,3,4,7,9,10,12,13],[1,2,3,4,7,10,11,12,13], [1,2,3,4,7,10,11,13,14],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,12], [1,2,3,5,6,7,8,11,12],[1,2,3,5,6,7,8,11,14], [1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,11,12], [1,2,3,5,6,7,9,11,13],[1,2,3,5,6,7,11,13,14], [1,2,3,5,6,9,11,12,13],[1,2,3,5,6,11,12,13,14], [1,2,3,5,7,8,9,12,13],[1,2,3,5,7,8,11,12,13], [1,2,3,5,7,8,11,13,14],[1,2,3,5,7,9,11,12,13], [1,2,3,6,7,9,10,11,12],[1,2,3,6,7,9,10,11,13], [1,2,3,6,7,10,11,13,14],[1,2,3,6,9,10,11,12,14], [1,2,3,6,9,10,11,13,14],[1,2,3,6,9,11,12,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,9,10,11,12,13,14], [1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,10,14], [1,2,4,5,6,7,10,13,14],[1,2,4,5,6,8,9,10,12], [1,2,4,5,6,8,10,12,14],[1,2,4,5,6,8,11,12,14], [1,2,4,5,6,9,10,12,14],[1,2,4,5,6,9,10,13,14], [1,2,4,5,6,9,12,13,14],[1,2,4,5,7,8,9,10,13], [1,2,4,5,7,8,10,13,14],[1,2,4,5,8,9,10,12,14], [1,2,4,5,8,9,10,13,14],[1,2,4,5,8,9,12,13,14], [1,2,4,5,8,11,12,13,14],[1,2,4,6,7,8,9,10,12], [1,2,4,6,7,8,10,11,12],[1,2,4,6,7,8,10,11,14], [1,2,4,6,8,10,11,12,14],[1,2,4,7,8,9,10,12,13], [1,2,4,7,8,10,11,12,14],[1,2,4,7,8,10,12,13,14], [1,2,4,7,8,11,12,13,14],[1,2,4,7,10,11,12,13,14], [1,2,4,8,9,10,12,13,14],[1,2,5,6,7,8,9,10,12], [1,2,5,6,7,8,10,11,12],[1,2,5,6,7,8,10,11,14], [1,2,5,6,7,9,10,11,12],[1,2,5,6,7,9,10,11,13], [1,2,5,6,7,10,11,13,14],[1,2,5,6,8,10,11,12,14], [1,2,5,6,9,10,11,12,14],[1,2,5,6,9,10,11,13,14], [1,2,5,6,9,11,12,13,14],[1,2,5,7,8,9,10,11,12], [1,2,5,7,8,9,10,11,13],[1,2,5,7,8,9,11,12,13], [1,2,5,7,8,10,11,13,14],[1,2,5,8,9,10,11,12,14], [1,2,5,8,9,10,11,13,14],[1,2,5,8,9,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,11,12],[1,3,4,5,6,7,8,11,14], [1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,11,12], [1,3,4,5,6,7,10,11,14],[1,3,4,5,6,7,10,13,14], [1,3,4,5,6,9,10,11,14],[1,3,4,5,6,9,10,13,14], [1,3,4,5,6,9,11,12,14],[1,3,4,5,6,9,12,13,14], [1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,9,11,13], [1,3,4,5,7,8,11,13,14],[1,3,4,5,7,9,10,11,14], [1,3,4,5,7,9,10,13,14],[1,3,4,5,7,9,11,13,14], [1,3,4,5,8,9,11,12,13],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,9,10,11,12],[1,3,4,6,9,10,11,12,14], [1,3,4,7,8,9,11,12,13],[1,3,4,7,9,10,11,12,13], [1,3,4,7,9,10,11,13,14],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,9,10,11,13],[1,3,5,6,7,10,11,13,14], [1,3,5,6,9,10,11,13,14],[1,3,5,6,9,11,12,13,14], [1,3,5,7,8,9,11,12,13],[1,3,5,7,9,10,11,13,14], [1,4,5,6,7,8,9,10,12],[1,4,5,6,7,8,10,11,12], [1,4,5,6,7,8,10,11,14],[1,4,5,6,7,9,10,11,12], [1,4,5,6,8,10,11,12,14],[1,4,5,6,9,10,11,12,14], [1,4,5,7,8,9,10,11,12],[1,4,5,7,8,9,10,11,14], [1,4,5,7,8,9,10,13,14],[1,4,5,7,8,9,11,13,14], [1,4,5,8,9,10,11,12,14],[1,4,5,8,9,11,12,13,14], [1,4,7,8,9,10,11,12,14],[1,4,7,8,9,10,12,13,14], [1,4,7,8,9,11,12,13,14],[1,4,7,9,10,11,12,13,14], [1,5,7,8,9,10,11,13,14],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,13], [2,3,4,5,6,7,8,13,14],[2,3,4,5,6,8,9,10,13], [2,3,4,5,6,8,9,12,13],[2,3,4,5,6,8,11,12,14], [2,3,4,5,6,8,12,13,14],[2,3,4,5,7,8,9,10,13], [2,3,4,5,8,11,12,13,14],[2,3,4,6,7,8,9,10,12], [2,3,4,6,7,8,10,12,14],[2,3,4,6,7,8,10,13,14], [2,3,4,6,7,8,11,12,14],[2,3,4,6,7,10,11,12,14], [2,3,4,6,8,9,10,12,13],[2,3,4,6,8,10,12,13,14], [2,3,4,6,9,10,12,13,14],[2,3,4,7,8,9,10,12,13], [2,3,4,7,8,10,12,13,14],[2,3,4,7,8,11,12,13,14], [2,3,4,7,10,11,12,13,14],[2,3,5,6,7,8,9,10,13], [2,3,5,6,7,8,9,12,13],[2,3,5,6,7,8,11,12,13], [2,3,5,6,7,8,11,13,14],[2,3,5,6,7,9,11,12,13], [2,3,5,6,8,11,12,13,14],[2,3,6,7,8,9,10,12,13], [2,3,6,7,8,10,12,13,14],[2,3,6,7,8,11,12,13,14], [2,3,6,7,9,10,11,12,13],[2,3,6,7,10,11,12,13,14], [2,3,6,9,10,11,12,13,14],[2,4,5,6,7,8,10,13,14], [2,4,5,6,8,9,10,12,14],[2,4,5,6,8,9,10,13,14], [2,4,5,6,8,9,12,13,14],[2,4,6,7,8,10,11,12,14], [2,4,6,8,9,10,12,13,14],[2,5,6,7,8,9,10,12,13], [2,5,6,7,8,10,11,12,13],[2,5,6,7,8,10,11,13,14], [2,5,6,7,9,10,11,12,13],[2,5,6,8,9,10,12,13,14], [2,5,6,8,10,11,12,13,14],[2,5,6,9,10,11,12,13,14], [2,5,7,8,9,10,11,12,13],[2,5,8,9,10,11,12,13,14], [2,6,7,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,11,14], [3,4,5,6,7,8,10,13,14],[3,4,5,6,8,9,10,11,14], [3,4,5,6,8,9,10,13,14],[3,4,5,6,8,9,11,12,14], [3,4,5,6,8,9,12,13,14],[3,4,5,7,8,9,10,11,14], [3,4,5,7,8,9,10,13,14],[3,4,5,7,8,9,11,13,14], [3,4,5,8,9,11,12,13,14],[3,4,6,7,8,9,10,11,12], [3,4,6,7,8,10,11,12,14],[3,4,6,8,9,10,11,12,14], [3,4,6,8,9,10,12,13,14],[3,4,7,8,9,10,11,12,14], [3,4,7,8,9,10,12,13,14],[3,4,7,8,9,11,12,13,14], [3,4,7,9,10,11,12,13,14],[3,5,6,7,8,9,10,11,14], [3,5,6,7,8,9,10,13,14],[3,5,6,7,8,9,11,12,13], [3,5,6,7,8,9,11,13,14],[3,5,6,7,9,10,11,13,14], [3,5,6,8,9,11,12,13,14],[3,6,7,8,9,10,11,12,14], [3,6,7,8,9,10,12,13,14],[3,6,7,8,9,11,12,13,14], [3,6,7,9,10,11,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,8,9,10,11,12,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_13=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,13],[1,2,3,4,5,6,8,11,12], [1,2,3,4,5,6,8,11,14],[1,2,3,4,5,6,8,12,13], [1,2,3,4,5,6,9,10,13],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,13], [1,2,3,4,5,8,11,12,13],[1,2,3,4,5,8,11,13,14], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,12], [1,2,3,4,6,7,8,11,12],[1,2,3,4,6,7,8,11,14], [1,2,3,4,6,7,9,10,12],[1,2,3,4,6,7,10,11,12], [1,2,3,4,6,7,10,11,13],[1,2,3,4,6,7,11,13,14], [1,2,3,4,6,8,9,12,13],[1,2,3,4,6,9,10,12,14], [1,2,3,4,6,9,10,13,14],[1,2,3,4,6,9,12,13,14], [1,2,3,4,6,10,11,12,14],[1,2,3,4,6,10,11,13,14], [1,2,3,4,7,8,9,12,13],[1,2,3,4,7,8,11,12,13], [1,2,3,4,7,8,11,13,14],[1,2,3,4,7,9,10,12,13], [1,2,3,4,7,10,11,12,13],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,12], [1,2,3,5,6,7,8,11,12],[1,2,3,5,6,7,8,11,14], [1,2,3,5,6,7,9,10,13],[1,2,3,5,6,7,9,11,12], [1,2,3,5,6,7,9,11,13],[1,2,3,5,6,7,11,13,14], [1,2,3,5,6,8,9,12,13],[1,2,3,5,6,9,11,12,13], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,12,13], [1,2,3,5,7,8,11,12,13],[1,2,3,5,7,8,11,13,14], [1,2,3,5,7,9,11,12,13],[1,2,3,6,7,9,10,11,12], [1,2,3,6,7,9,10,11,13],[1,2,3,6,9,10,11,12,14], [1,2,3,6,9,10,11,13,14],[1,2,3,6,9,11,12,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,9,10,11,12,13,14], [1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,10,14], [1,2,4,5,6,7,10,13,14],[1,2,4,5,6,8,9,10,12], [1,2,4,5,6,8,9,12,13],[1,2,4,5,6,8,10,12,14], [1,2,4,5,6,8,11,12,14],[1,2,4,5,6,9,10,12,14], [1,2,4,5,6,9,10,13,14],[1,2,4,5,6,9,12,13,14], [1,2,4,5,7,8,9,10,13],[1,2,4,5,7,8,10,13,14], [1,2,4,5,8,9,10,12,14],[1,2,4,5,8,9,10,13,14], [1,2,4,5,8,9,11,12,13],[1,2,4,5,8,9,11,12,14], [1,2,4,5,8,9,11,13,14],[1,2,4,5,9,11,12,13,14], [1,2,4,6,7,8,9,10,12],[1,2,4,6,7,8,10,11,12], [1,2,4,6,7,8,10,11,14],[1,2,4,6,7,10,11,13,14], [1,2,4,6,8,10,11,12,14],[1,2,4,7,8,9,10,12,13], [1,2,4,7,8,10,11,12,14],[1,2,4,7,8,10,12,13,14], [1,2,4,7,8,11,12,13,14],[1,2,4,7,10,11,12,13,14], [1,2,4,8,9,10,12,13,14],[1,2,4,8,9,11,12,13,14], [1,2,5,6,7,8,9,10,12],[1,2,5,6,7,8,10,11,12], [1,2,5,6,7,8,10,11,14],[1,2,5,6,7,9,10,11,12], [1,2,5,6,7,9,10,11,13],[1,2,5,6,7,10,11,13,14], [1,2,5,6,8,10,11,12,14],[1,2,5,6,9,10,11,12,14], [1,2,5,6,9,10,11,13,14],[1,2,5,6,9,11,12,13,14], [1,2,5,7,8,9,10,11,12],[1,2,5,7,8,9,10,11,13], [1,2,5,7,8,9,11,12,13],[1,2,5,7,8,10,11,13,14], [1,2,5,8,9,10,11,12,14],[1,2,5,8,9,10,11,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,12], [1,3,4,5,6,7,8,10,11],[1,3,4,5,6,7,8,10,14], [1,3,4,5,6,7,8,11,12],[1,3,4,5,6,7,9,10,11], [1,3,4,5,6,7,9,11,12],[1,3,4,5,6,7,10,13,14], [1,3,4,5,6,8,9,12,13],[1,3,4,5,6,8,10,11,14], [1,3,4,5,6,9,10,11,14],[1,3,4,5,6,9,10,13,14], [1,3,4,5,6,9,11,12,14],[1,3,4,5,6,9,12,13,14], [1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,9,11,13], [1,3,4,5,7,8,10,11,14],[1,3,4,5,7,8,11,13,14], [1,3,4,5,7,9,10,11,14],[1,3,4,5,7,9,10,13,14], [1,3,4,5,7,9,11,13,14],[1,3,4,5,8,9,11,12,13], [1,3,4,5,9,11,12,13,14],[1,3,4,6,7,8,10,11,14], [1,3,4,6,7,9,10,11,12],[1,3,4,6,7,10,11,13,14], [1,3,4,6,9,10,11,12,14],[1,3,4,7,8,9,11,12,13], [1,3,4,7,9,10,11,12,13],[1,3,4,7,9,10,11,13,14], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,10,11,14], [1,3,5,6,7,9,10,11,13],[1,3,5,6,7,10,11,13,14], [1,3,5,6,9,10,11,13,14],[1,3,5,6,9,11,12,13,14], [1,3,5,7,8,9,11,12,13],[1,3,5,7,9,10,11,13,14], [1,4,5,6,7,8,9,10,12],[1,4,5,6,7,8,10,11,12], [1,4,5,6,7,9,10,11,12],[1,4,5,6,8,10,11,12,14], [1,4,5,6,9,10,11,12,14],[1,4,5,7,8,9,10,12,14], [1,4,5,7,8,9,10,13,14],[1,4,5,7,8,9,11,12,14], [1,4,5,7,8,9,11,13,14],[1,4,5,7,8,10,11,12,14], [1,4,5,7,9,10,11,12,14],[1,4,7,8,9,10,12,13,14], [1,4,7,8,9,11,12,13,14],[1,4,7,9,10,11,12,13,14], [1,5,7,8,9,10,11,12,14],[1,5,7,8,9,10,11,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,8,9,10,13],[2,3,4,5,6,8,11,12,14], [2,3,4,5,6,8,12,13,14],[2,3,4,5,7,8,9,10,13], [2,3,4,5,8,11,12,13,14],[2,3,4,6,7,8,9,10,12], [2,3,4,6,7,8,10,12,14],[2,3,4,6,7,8,10,13,14], [2,3,4,6,7,8,11,12,14],[2,3,4,6,7,10,11,12,14], [2,3,4,6,7,10,11,13,14],[2,3,4,6,8,9,10,12,13], [2,3,4,6,8,10,12,13,14],[2,3,4,6,9,10,12,13,14], [2,3,4,7,8,9,10,12,13],[2,3,4,7,8,10,12,13,14], [2,3,4,7,8,11,12,13,14],[2,3,4,7,10,11,12,13,14], [2,3,5,6,7,8,9,10,12],[2,3,5,6,7,8,10,12,13], [2,3,5,6,7,8,11,12,13],[2,3,5,6,7,8,11,13,14], [2,3,5,6,7,9,10,12,13],[2,3,5,6,7,9,11,12,13], [2,3,5,6,8,9,10,12,13],[2,3,5,6,8,11,12,13,14], [2,3,5,7,8,9,10,12,13],[2,3,6,7,8,10,12,13,14], [2,3,6,7,8,11,12,13,14],[2,3,6,7,9,10,11,12,14], [2,3,6,7,9,10,11,13,14],[2,3,6,7,9,10,12,13,14], [2,3,6,7,9,11,12,13,14],[2,3,7,9,10,11,12,13,14], [2,4,5,6,7,8,10,13,14],[2,4,5,6,8,9,10,12,14], [2,4,5,6,8,9,10,13,14],[2,4,5,6,8,9,12,13,14], [2,4,5,8,9,11,12,13,14],[2,4,6,7,8,10,11,12,14], [2,4,6,8,9,10,12,13,14],[2,5,6,7,8,10,11,12,13], [2,5,6,7,8,10,11,13,14],[2,5,6,7,9,10,11,12,13], [2,5,6,8,9,10,12,13,14],[2,5,6,8,10,11,12,13,14], [2,5,6,9,10,11,12,13,14],[2,5,7,8,9,10,11,12,13], [2,5,8,9,10,11,12,13,14],[2,6,7,8,10,11,12,13,14], [2,6,7,9,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,10,13,14], [3,4,5,6,8,9,10,11,14],[3,4,5,6,8,9,10,13,14], [3,4,5,6,8,9,11,12,14],[3,4,5,6,8,9,12,13,14], [3,4,5,7,8,9,10,11,14],[3,4,5,7,8,9,10,13,14], [3,4,5,7,8,9,11,13,14],[3,4,5,8,9,11,12,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,10,11,12,14], [3,4,6,8,9,10,11,12,14],[3,4,6,8,9,10,12,13,14], [3,4,7,8,9,10,11,12,14],[3,4,7,8,9,10,12,13,14], [3,4,7,8,9,11,12,13,14],[3,4,7,9,10,11,12,13,14], [3,5,6,7,8,9,10,11,14],[3,5,6,7,8,9,10,12,13], [3,5,6,7,8,9,10,13,14],[3,5,6,7,8,9,11,12,13], [3,5,6,7,8,9,11,13,14],[3,5,6,7,9,10,11,13,14], [3,5,6,8,9,11,12,13,14],[3,6,7,8,9,10,11,12,14], [3,6,7,8,9,10,12,13,14],[3,6,7,8,9,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,5,6,8,9,10,11,12,14], [4,5,7,8,9,10,11,12,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_14=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,11], [1,2,3,4,5,6,7,11,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,10],[1,2,3,4,5,6,8,10,14], [1,2,3,4,5,6,9,10,11],[1,2,3,4,5,6,10,11,12], [1,2,3,4,5,6,10,12,14],[1,2,3,4,5,6,11,12,13], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,14], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,9,13,14], [1,2,3,4,5,8,9,10,14],[1,2,3,4,5,9,10,11,14], [1,2,3,4,5,9,11,13,14],[1,2,3,4,5,10,11,12,14], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,11], [1,2,3,4,6,7,8,11,13],[1,2,3,4,6,7,8,13,14], [1,2,3,4,6,8,9,10,11],[1,2,3,4,6,8,10,11,12], [1,2,3,4,6,8,10,12,14],[1,2,3,4,6,8,11,12,13], [1,2,3,4,6,8,12,13,14],[1,2,3,4,7,8,9,11,13], [1,2,3,4,7,8,9,13,14],[1,2,3,4,8,9,10,11,13], [1,2,3,4,8,9,10,13,14],[1,2,3,4,8,10,11,12,13], [1,2,3,4,8,10,12,13,14],[1,2,3,4,9,10,11,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,12],[1,2,3,5,6,7,8,12,14], [1,2,3,5,6,7,9,10,11],[1,2,3,5,6,7,10,11,12], [1,2,3,5,6,7,11,12,13],[1,2,3,5,6,7,12,13,14], [1,2,3,5,6,8,10,12,14],[1,2,3,5,7,8,9,10,14], [1,2,3,5,7,8,10,12,14],[1,2,3,5,7,9,10,11,12], [1,2,3,5,7,9,10,12,14],[1,2,3,5,7,9,11,12,14], [1,2,3,5,7,9,11,13,14],[1,2,3,5,7,11,12,13,14], [1,2,3,5,9,10,11,12,14],[1,2,3,6,7,8,9,10,11], [1,2,3,6,7,8,10,11,12],[1,2,3,6,7,8,11,12,13], [1,2,3,6,7,8,12,13,14],[1,2,3,7,8,9,10,11,12], [1,2,3,7,8,9,10,12,14],[1,2,3,7,8,9,11,12,13], [1,2,3,7,8,9,12,13,14],[1,2,3,7,9,11,12,13,14], [1,2,3,8,9,10,11,12,13],[1,2,3,8,9,10,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,14], [1,2,4,5,6,7,9,11,13],[1,2,4,5,6,7,9,13,14], [1,2,4,5,6,8,9,10,14],[1,2,4,5,6,9,10,11,14], [1,2,4,5,6,9,11,13,14],[1,2,4,5,6,10,11,12,14], [1,2,4,5,6,11,12,13,14],[1,2,4,6,7,8,9,11,13], [1,2,4,6,7,8,9,13,14],[1,2,4,6,8,9,10,11,13], [1,2,4,6,8,9,10,13,14],[1,2,4,6,8,10,11,12,13], [1,2,4,6,8,10,12,13,14],[1,2,4,6,9,10,11,13,14], [1,2,4,6,10,11,12,13,14],[1,2,5,6,7,8,9,10,14], [1,2,5,6,7,8,10,12,14],[1,2,5,6,7,9,10,11,14], [1,2,5,6,7,9,11,13,14],[1,2,5,6,7,10,11,12,14], [1,2,5,6,7,11,12,13,14],[1,2,5,7,9,10,11,12,14], [1,2,6,7,8,9,10,11,14],[1,2,6,7,8,9,11,13,14], [1,2,6,7,8,10,11,12,14],[1,2,6,7,8,11,12,13,14], [1,2,6,8,9,10,11,13,14],[1,2,6,8,10,11,12,13,14], [1,2,7,8,9,10,11,12,14],[1,2,7,8,9,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,11,13], [1,3,4,5,6,8,9,10,13],[1,3,4,5,6,8,10,13,14], [1,3,4,5,6,9,10,11,13],[1,3,4,5,6,10,11,12,13], [1,3,4,5,6,10,12,13,14],[1,3,4,5,7,8,9,13,14], [1,3,4,5,8,9,10,13,14],[1,3,4,5,9,10,11,13,14], [1,3,4,5,10,11,12,13,14],[1,3,4,6,7,8,9,11,13], [1,3,4,6,8,9,10,11,13],[1,3,4,6,8,10,11,12,13], [1,3,4,6,8,10,12,13,14],[1,3,5,6,7,8,9,10,11], [1,3,5,6,7,8,9,11,13],[1,3,5,6,7,8,10,11,12], [1,3,5,6,7,8,11,12,13],[1,3,5,6,7,8,12,13,14], [1,3,5,6,8,9,10,11,13],[1,3,5,6,8,10,11,12,13], [1,3,5,6,8,10,12,13,14],[1,3,5,7,8,9,10,11,13], [1,3,5,7,8,9,10,13,14],[1,3,5,7,8,10,11,12,13], [1,3,5,7,8,10,12,13,14],[1,3,5,7,9,10,11,12,13], [1,3,5,7,9,10,12,13,14],[1,3,5,7,9,11,12,13,14], [1,3,5,9,10,11,12,13,14],[1,3,7,8,9,10,11,12,13], [1,3,7,8,9,10,12,13,14],[1,4,5,6,7,8,9,13,14], [1,4,5,6,8,9,10,13,14],[1,4,5,6,9,10,11,13,14], [1,4,5,6,10,11,12,13,14],[1,5,6,7,8,9,10,11,13], [1,5,6,7,8,9,10,13,14],[1,5,6,7,8,10,11,12,13], [1,5,6,7,8,10,12,13,14],[1,5,6,7,9,10,11,13,14], [1,5,6,7,10,11,12,13,14],[1,5,7,9,10,11,12,13,14], [1,6,7,8,9,10,11,13,14],[1,6,7,8,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,12,14], [2,3,4,5,6,7,9,10,11],[2,3,4,5,6,7,10,11,12], [2,3,4,5,6,7,11,12,13],[2,3,4,5,6,7,12,13,14], [2,3,4,5,6,8,10,12,14],[2,3,4,5,7,8,9,10,14], [2,3,4,5,7,8,10,12,14],[2,3,4,5,7,9,10,11,12], [2,3,4,5,7,9,10,12,14],[2,3,4,5,7,9,11,12,14], [2,3,4,5,7,9,11,13,14],[2,3,4,5,7,11,12,13,14], [2,3,4,5,9,10,11,12,14],[2,3,4,6,7,8,9,10,11], [2,3,4,6,7,8,10,11,12],[2,3,4,6,7,8,11,12,13], [2,3,4,6,7,8,12,13,14],[2,3,4,7,8,9,10,11,12], [2,3,4,7,8,9,10,12,14],[2,3,4,7,8,9,11,12,13], [2,3,4,7,8,9,12,13,14],[2,3,4,7,9,11,12,13,14], [2,3,4,8,9,10,11,12,13],[2,3,4,8,9,10,12,13,14], [2,3,4,9,10,11,12,13,14],[2,4,5,6,7,8,9,10,14], [2,4,5,6,7,8,10,12,14],[2,4,5,6,7,9,10,11,12], [2,4,5,6,7,9,10,12,14],[2,4,5,6,7,9,11,12,14], [2,4,5,6,7,9,11,13,14],[2,4,5,6,7,11,12,13,14], [2,4,5,6,9,10,11,12,14],[2,4,6,7,8,9,10,11,12], [2,4,6,7,8,9,10,12,14],[2,4,6,7,8,9,11,12,14], [2,4,6,7,8,9,11,13,14],[2,4,6,7,8,11,12,13,14], [2,4,6,8,9,10,11,12,14],[2,4,6,8,9,10,11,13,14], [2,4,6,8,10,11,12,13,14],[2,4,7,8,9,11,12,13,14], [2,4,8,9,10,11,12,13,14],[2,5,6,7,9,10,11,12,14], [2,6,7,8,9,10,11,12,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,13],[3,4,5,6,7,8,10,11,12], [3,4,5,6,7,8,11,12,13],[3,4,5,6,7,8,12,13,14], [3,4,5,6,8,9,10,11,13],[3,4,5,6,8,10,11,12,13], [3,4,5,6,8,10,12,13,14],[3,4,5,7,8,9,10,11,12], [3,4,5,7,8,9,10,12,14],[3,4,5,7,8,9,11,12,13], [3,4,5,7,8,9,12,13,14],[3,4,5,7,9,11,12,13,14], [3,4,5,8,9,10,11,12,13],[3,4,5,8,9,10,12,13,14], [3,4,5,9,10,11,12,13,14],[3,5,7,8,9,10,11,12,13], [3,5,7,8,9,10,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,9,10,12,14],[4,5,6,7,8,9,11,12,13], [4,5,6,7,8,9,12,13,14],[4,5,6,7,9,11,12,13,14], [4,5,6,8,9,10,11,12,13],[4,5,6,8,9,10,12,13,14], [4,5,6,9,10,11,12,13,14],[4,6,7,8,9,11,12,13,14], [4,6,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,12,13,14],[5,6,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_15=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,10], [1,2,3,4,5,6,8,10,12],[1,2,3,4,5,6,8,12,14], [1,2,3,4,5,6,9,10,12],[1,2,3,4,5,6,9,11,12], [1,2,3,4,5,6,9,11,13],[1,2,3,4,5,6,11,12,13], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,10], [1,2,3,4,5,7,8,10,12],[1,2,3,4,5,7,8,12,14], [1,2,3,4,5,7,9,10,12],[1,2,3,4,5,7,9,11,12], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,11,12,14], [1,2,3,4,5,7,11,13,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,10],[1,2,3,4,6,7,8,10,13], [1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,9,10,13], [1,2,3,4,6,8,10,12,14],[1,2,3,4,6,8,10,13,14], [1,2,3,4,6,9,10,12,13],[1,2,3,4,6,9,11,12,13], [1,2,3,4,6,10,12,13,14],[1,2,3,4,7,8,10,12,14], [1,2,3,4,7,8,10,13,14],[1,2,3,4,7,9,10,12,14], [1,2,3,4,7,9,10,13,14],[1,2,3,4,7,9,11,12,14], [1,2,3,4,7,9,11,13,14],[1,2,3,4,9,10,11,12,13], [1,2,3,4,9,10,11,12,14],[1,2,3,4,9,10,11,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,13],[1,2,3,5,6,7,8,13,14], [1,2,3,5,6,7,9,10,13],[1,2,3,5,6,8,10,12,14], [1,2,3,5,6,8,10,13,14],[1,2,3,5,6,9,10,12,13], [1,2,3,5,6,9,11,12,13],[1,2,3,5,6,10,12,13,14], [1,2,3,5,7,8,10,12,14],[1,2,3,5,7,8,10,13,14], [1,2,3,5,7,9,10,12,14],[1,2,3,5,7,9,10,13,14], [1,2,3,5,7,9,11,12,14],[1,2,3,5,7,9,11,13,14], [1,2,3,5,9,10,12,13,14],[1,2,3,5,9,11,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,11], [1,2,4,5,6,7,8,11,13],[1,2,4,5,6,7,8,13,14], [1,2,4,5,6,7,9,11,13],[1,2,4,5,6,8,9,10,12], [1,2,4,5,6,8,9,11,12],[1,2,4,5,6,8,11,12,14], [1,2,4,5,6,8,11,13,14],[1,2,4,5,6,11,12,13,14], [1,2,4,5,7,8,9,10,12],[1,2,4,5,7,8,9,11,12], [1,2,4,5,7,8,11,12,14],[1,2,4,5,7,8,11,13,14], [1,2,4,6,7,8,9,10,13],[1,2,4,6,7,8,9,11,13], [1,2,4,6,8,9,10,11,12],[1,2,4,6,8,9,10,11,13], [1,2,4,6,8,10,11,12,13],[1,2,4,6,8,10,12,13,14], [1,2,4,6,8,11,12,13,14],[1,2,4,6,9,10,11,12,13], [1,2,4,7,8,9,10,11,12],[1,2,4,7,8,9,10,11,13], [1,2,4,7,8,10,11,12,14],[1,2,4,7,8,10,11,13,14], [1,2,4,7,9,10,11,12,14],[1,2,4,7,9,10,11,13,14], [1,2,4,8,10,11,12,13,14],[1,2,5,6,7,8,9,10,13], [1,2,5,6,7,8,9,11,13],[1,2,5,6,8,9,10,12,13], [1,2,5,6,8,9,11,12,13],[1,2,5,6,8,10,12,13,14], [1,2,5,6,8,11,12,13,14],[1,2,5,7,8,9,10,12,13], [1,2,5,7,8,9,11,12,13],[1,2,5,7,8,10,12,13,14], [1,2,5,7,8,11,12,13,14],[1,2,5,7,9,10,12,13,14], [1,2,5,7,9,11,12,13,14],[1,2,6,8,9,10,11,12,13], [1,2,7,8,9,10,11,12,14],[1,2,7,8,9,10,11,13,14], [1,2,7,8,9,10,12,13,14],[1,2,7,8,9,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,11], [1,3,4,5,6,7,8,11,13],[1,3,4,5,6,7,8,13,14], [1,3,4,5,6,7,9,11,13],[1,3,4,5,6,8,9,10,12], [1,3,4,5,6,8,9,11,12],[1,3,4,5,6,8,11,12,14], [1,3,4,5,6,8,11,13,14],[1,3,4,5,6,11,12,13,14], [1,3,4,5,7,8,9,10,12],[1,3,4,5,7,8,9,11,12], [1,3,4,5,7,8,11,12,14],[1,3,4,5,7,8,11,13,14], [1,3,4,6,7,8,9,10,13],[1,3,4,6,7,8,9,11,13], [1,3,4,6,8,9,10,11,12],[1,3,4,6,8,9,10,11,13], [1,3,4,6,8,10,11,12,13],[1,3,4,6,8,10,12,13,14], [1,3,4,6,8,11,12,13,14],[1,3,4,6,9,10,11,12,13], [1,3,4,7,8,9,10,11,12],[1,3,4,7,8,9,10,11,13], [1,3,4,7,8,10,11,12,14],[1,3,4,7,8,10,11,13,14], [1,3,4,7,9,10,11,12,14],[1,3,4,7,9,10,11,13,14], [1,3,4,8,10,11,12,13,14],[1,3,5,6,7,8,9,10,13], [1,3,5,6,7,8,9,11,13],[1,3,5,6,8,9,10,11,12], [1,3,5,6,8,9,10,11,13],[1,3,5,6,8,10,11,12,13], [1,3,5,6,8,10,12,13,14],[1,3,5,6,8,11,12,13,14], [1,3,5,6,9,10,11,12,13],[1,3,5,7,8,9,10,11,12], [1,3,5,7,8,9,10,11,13],[1,3,5,7,8,10,11,12,13], [1,3,5,7,8,10,12,13,14],[1,3,5,7,8,11,12,13,14], [1,3,5,7,9,10,11,12,13],[1,3,5,7,9,10,12,13,14], [1,3,5,7,9,11,12,13,14],[1,3,7,8,10,11,12,13,14], [1,3,7,9,10,11,12,13,14],[1,5,6,8,9,10,11,12,13], [1,5,7,8,9,10,11,12,13],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,14], [2,3,4,5,6,7,9,10,14],[2,3,4,5,6,7,9,13,14], [2,3,4,5,6,8,10,12,14],[2,3,4,5,6,9,10,12,14], [2,3,4,5,6,9,11,12,14],[2,3,4,5,6,9,11,13,14], [2,3,4,5,6,11,12,13,14],[2,3,4,5,7,8,10,12,14], [2,3,4,5,7,9,10,12,14],[2,3,4,5,7,9,11,12,14], [2,3,4,5,7,9,11,13,14],[2,3,4,6,7,8,10,13,14], [2,3,4,6,7,9,10,13,14],[2,3,4,6,9,10,12,13,14], [2,3,4,6,9,11,12,13,14],[2,3,4,9,10,11,12,13,14], [2,3,5,6,7,8,10,13,14],[2,3,5,6,7,9,10,13,14], [2,3,5,6,9,10,12,13,14],[2,3,5,6,9,11,12,13,14], [2,4,5,6,7,8,9,10,12],[2,4,5,6,7,8,9,11,12], [2,4,5,6,7,8,10,12,14],[2,4,5,6,7,8,11,12,14], [2,4,5,6,7,8,11,13,14],[2,4,5,6,7,9,10,12,14], [2,4,5,6,7,9,11,12,14],[2,4,5,6,7,9,11,13,14], [2,4,6,7,8,9,10,12,14],[2,4,6,7,8,9,10,13,14], [2,4,6,7,8,9,11,12,14],[2,4,6,7,8,9,11,13,14], [2,4,6,8,9,10,11,12,14],[2,4,6,8,9,10,11,13,14], [2,4,6,8,10,11,12,13,14],[2,4,6,9,10,11,12,13,14], [2,4,7,8,9,10,11,12,14],[2,4,7,8,9,10,11,13,14], [2,5,6,7,8,9,10,12,14],[2,5,6,7,8,9,10,13,14], [2,5,6,7,8,9,11,12,14],[2,5,6,7,8,9,11,13,14], [2,5,6,8,9,10,12,13,14],[2,5,6,8,9,11,12,13,14], [2,5,7,8,9,10,12,13,14],[2,5,7,8,9,11,12,13,14], [2,6,8,9,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,10,11,12],[3,4,5,6,7,8,10,12,14], [3,4,5,6,7,8,11,12,14],[3,4,5,6,7,8,11,13,14], [3,4,5,6,7,9,10,11,12],[3,4,5,6,7,9,10,12,14], [3,4,5,6,7,9,11,12,14],[3,4,5,6,7,9,11,13,14], [3,4,5,6,8,9,10,11,12],[3,4,5,7,8,9,10,11,12], [3,4,6,7,8,9,10,11,13],[3,4,6,7,8,10,11,12,14], [3,4,6,7,8,10,11,13,14],[3,4,6,7,9,10,11,12,14], [3,4,6,7,9,10,11,13,14],[3,4,6,8,10,11,12,13,14], [3,4,6,9,10,11,12,13,14],[3,5,6,7,8,9,10,11,13], [3,5,6,7,8,10,11,12,14],[3,5,6,7,8,10,11,13,14], [3,5,6,7,9,10,11,12,14],[3,5,6,7,9,10,11,13,14], [3,5,6,8,10,11,12,13,14],[3,5,6,9,10,11,12,13,14], [3,5,7,8,10,11,12,13,14],[3,5,7,9,10,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,6,7,8,9,10,11,12,14], [4,6,7,8,9,10,11,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,12,13,14],[5,6,7,8,9,11,12,13,14], [5,6,7,8,10,11,12,13,14],[5,6,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_2_16=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,10], [1,2,3,4,5,6,8,10,12],[1,2,3,4,5,6,8,12,14], [1,2,3,4,5,6,9,10,12],[1,2,3,4,5,6,9,11,12], [1,2,3,4,5,6,9,11,13],[1,2,3,4,5,6,11,12,13], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,10], [1,2,3,4,5,7,8,10,14],[1,2,3,4,5,7,9,10,12], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,9,11,14], [1,2,3,4,5,7,9,12,14],[1,2,3,4,5,7,10,12,14], [1,2,3,4,5,7,11,13,14],[1,2,3,4,5,8,10,12,14], [1,2,3,4,5,9,11,12,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,10],[1,2,3,4,6,7,8,10,13], [1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,9,10,13], [1,2,3,4,6,8,10,12,14],[1,2,3,4,6,8,10,13,14], [1,2,3,4,6,9,10,12,13],[1,2,3,4,6,9,11,12,13], [1,2,3,4,6,10,12,13,14],[1,2,3,4,7,8,10,13,14], [1,2,3,4,7,9,10,12,14],[1,2,3,4,7,9,10,13,14], [1,2,3,4,7,9,11,13,14],[1,2,3,4,9,10,11,12,13], [1,2,3,4,9,10,11,12,14],[1,2,3,4,9,10,11,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,13],[1,2,3,5,6,7,8,13,14], [1,2,3,5,6,7,9,10,13],[1,2,3,5,6,8,10,12,13], [1,2,3,5,6,8,12,13,14],[1,2,3,5,6,9,10,12,13], [1,2,3,5,6,9,11,12,13],[1,2,3,5,7,8,10,13,14], [1,2,3,5,7,9,10,12,13],[1,2,3,5,7,9,11,13,14], [1,2,3,5,7,9,12,13,14],[1,2,3,5,7,10,12,13,14], [1,2,3,5,8,10,12,13,14],[1,2,3,5,9,11,12,13,14], [1,2,3,6,8,10,12,13,14],[1,2,3,7,9,10,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,13], [1,2,4,5,6,7,8,13,14],[1,2,4,5,6,8,9,10,12], [1,2,4,5,6,8,9,11,12],[1,2,4,5,6,8,9,11,13], [1,2,4,5,6,8,11,12,14],[1,2,4,5,6,8,11,13,14], [1,2,4,5,6,11,12,13,14],[1,2,4,5,7,8,9,10,12], [1,2,4,5,7,8,9,11,12],[1,2,4,5,7,8,9,11,13], [1,2,4,5,7,8,10,12,14],[1,2,4,5,7,8,11,12,14], [1,2,4,5,7,8,11,13,14],[1,2,4,5,7,9,11,12,14], [1,2,4,6,7,8,9,10,13],[1,2,4,6,8,9,10,12,13], [1,2,4,6,8,9,11,12,13],[1,2,4,6,8,10,12,13,14], [1,2,4,6,8,11,12,13,14],[1,2,4,7,8,9,10,11,12], [1,2,4,7,8,9,10,11,13],[1,2,4,7,8,10,11,12,14], [1,2,4,7,8,10,11,13,14],[1,2,4,7,9,10,11,12,14], [1,2,4,7,9,10,11,13,14],[1,2,4,8,9,10,11,12,13], [1,2,4,8,10,11,12,13,14],[1,2,5,6,7,8,9,10,13], [1,2,5,6,8,9,10,12,13],[1,2,5,6,8,9,11,12,13], [1,2,5,6,8,11,12,13,14],[1,2,5,7,8,9,10,12,13], [1,2,5,7,8,9,11,12,13],[1,2,5,7,8,10,12,13,14], [1,2,5,7,8,11,12,13,14],[1,2,5,7,9,11,12,13,14], [1,2,7,8,9,10,11,12,14],[1,2,7,8,9,10,11,13,14], [1,2,7,8,9,10,12,13,14],[1,2,7,8,9,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,11], [1,3,4,5,6,7,8,11,13],[1,3,4,5,6,7,8,13,14], [1,3,4,5,6,7,9,11,13],[1,3,4,5,6,8,9,10,12], [1,3,4,5,6,8,9,11,12],[1,3,4,5,6,8,11,12,14], [1,3,4,5,6,8,11,13,14],[1,3,4,5,6,11,12,13,14], [1,3,4,5,7,8,9,10,12],[1,3,4,5,7,8,9,11,12], [1,3,4,5,7,8,10,12,14],[1,3,4,5,7,8,11,12,14], [1,3,4,5,7,8,11,13,14],[1,3,4,5,7,9,11,12,14], [1,3,4,6,7,8,9,10,11],[1,3,4,6,7,8,10,11,13], [1,3,4,6,7,9,10,11,13],[1,3,4,6,8,9,10,11,12], [1,3,4,6,8,10,11,12,14],[1,3,4,6,8,10,11,13,14], [1,3,4,6,9,10,11,12,13],[1,3,4,6,10,11,12,13,14], [1,3,4,7,8,9,10,11,12],[1,3,4,7,8,10,11,12,14], [1,3,4,7,8,10,11,13,14],[1,3,4,7,9,10,11,12,14], [1,3,4,7,9,10,11,13,14],[1,3,5,6,7,8,9,10,13], [1,3,5,6,7,8,9,11,13],[1,3,5,6,8,9,10,12,13], [1,3,5,6,8,9,11,12,13],[1,3,5,6,8,11,12,13,14], [1,3,5,7,8,9,10,11,12],[1,3,5,7,8,9,10,11,13], [1,3,5,7,8,10,11,12,14],[1,3,5,7,8,10,11,13,14], [1,3,5,7,9,10,11,12,13],[1,3,5,7,9,11,12,13,14], [1,3,5,7,10,11,12,13,14],[1,3,5,8,9,10,11,12,13], [1,3,5,8,10,11,12,13,14],[1,3,6,7,8,9,10,11,13], [1,3,6,8,9,10,11,12,13],[1,3,6,8,10,11,12,13,14], [1,3,7,9,10,11,12,13,14],[1,4,5,6,7,8,9,11,13], [1,4,6,7,8,9,10,11,13],[1,4,6,8,9,10,11,12,13], [1,4,6,8,10,11,12,13,14],[1,5,7,8,9,10,11,12,13], [1,5,7,8,10,11,12,13,14],[1,7,8,9,10,11,12,13,14], [2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,10,14], [2,3,4,5,6,7,9,10,12],[2,3,4,5,6,7,9,11,13], [2,3,4,5,6,7,9,11,14],[2,3,4,5,6,7,9,12,14], [2,3,4,5,6,7,10,12,14],[2,3,4,5,6,7,11,13,14], [2,3,4,5,6,8,10,12,14],[2,3,4,5,6,9,11,12,14], [2,3,4,5,6,11,12,13,14],[2,3,4,6,7,8,10,13,14], [2,3,4,6,7,9,10,12,14],[2,3,4,6,7,9,10,13,14], [2,3,4,6,7,9,11,13,14],[2,3,4,6,9,10,12,13,14], [2,3,4,6,9,11,12,13,14],[2,3,4,9,10,11,12,13,14], [2,3,5,6,7,8,10,13,14],[2,3,5,6,7,9,10,12,14], [2,3,5,6,7,9,10,13,14],[2,3,5,6,7,9,11,13,14], [2,3,5,6,8,10,12,13,14],[2,3,5,6,9,10,12,13,14], [2,3,5,6,9,11,12,13,14],[2,3,5,7,9,10,12,13,14], [2,4,5,6,7,8,9,10,12],[2,4,5,6,7,8,9,11,13], [2,4,5,6,7,8,9,11,14],[2,4,5,6,7,8,9,12,14], [2,4,5,6,7,8,10,12,14],[2,4,5,6,7,8,11,13,14], [2,4,5,6,8,9,11,12,14],[2,4,5,7,8,9,11,12,14], [2,4,6,7,8,9,10,11,13],[2,4,6,7,8,9,10,11,14], [2,4,6,7,8,9,10,12,14],[2,4,6,7,8,10,11,13,14], [2,4,6,7,9,10,11,13,14],[2,4,6,8,9,10,11,12,13], [2,4,6,8,9,10,11,12,14],[2,4,6,8,10,11,12,13,14], [2,4,6,9,10,11,12,13,14],[2,4,7,8,9,10,11,12,14], [2,5,6,7,8,9,10,12,14],[2,5,6,7,8,9,10,13,14], [2,5,6,7,8,9,11,13,14],[2,5,6,8,9,10,12,13,14], [2,5,6,8,9,11,12,13,14],[2,5,7,8,9,10,12,13,14], [2,5,7,8,9,11,12,13,14],[2,6,7,8,9,10,11,13,14], [2,6,8,9,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,10,11,12],[3,4,5,6,7,8,10,12,14], [3,4,5,6,7,8,11,12,14],[3,4,5,6,7,8,11,13,14], [3,4,5,6,7,9,10,11,12],[3,4,5,6,7,9,11,12,14], [3,4,5,6,8,9,10,11,12],[3,4,5,7,8,9,10,11,12], [3,4,6,7,8,10,11,12,14],[3,4,6,7,8,10,11,13,14], [3,4,6,7,9,10,11,12,14],[3,4,6,7,9,10,11,13,14], [3,4,6,9,10,11,12,13,14],[3,5,6,7,8,9,10,11,13], [3,5,6,7,8,10,11,12,14],[3,5,6,7,8,10,11,13,14], [3,5,6,7,9,10,11,12,14],[3,5,6,7,9,10,11,13,14], [3,5,6,8,9,10,11,12,13],[3,5,6,8,10,11,12,13,14], [3,5,6,9,10,11,12,13,14],[3,5,7,9,10,11,12,13,14], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,9,11,12,14], [4,6,7,8,9,10,11,12,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,12,13,14],[5,6,7,8,9,11,12,13,14], [5,6,7,8,10,11,12,13,14],[5,6,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_1_1=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,12], [1,2,3,4,5,6,7,12,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,14],[1,2,3,4,5,6,9,10,14], [1,2,3,4,5,6,10,11,14],[1,2,3,4,5,6,11,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,10], [1,2,3,4,5,7,8,10,11],[1,2,3,4,5,7,8,11,12], [1,2,3,4,5,7,8,12,13],[1,2,3,4,5,7,8,13,14], [1,2,3,4,5,8,9,10,11],[1,2,3,4,5,8,9,11,12], [1,2,3,4,5,8,9,12,13],[1,2,3,4,5,8,9,13,14], [1,2,3,4,5,9,10,11,13],[1,2,3,4,5,9,10,13,14], [1,2,3,4,5,9,11,12,13],[1,2,3,4,5,10,11,13,14], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,14], [1,2,3,4,6,7,9,10,14],[1,2,3,4,6,7,10,11,14], [1,2,3,4,6,7,11,12,14],[1,2,3,4,6,7,12,13,14], [1,2,3,4,7,8,9,10,14],[1,2,3,4,7,8,10,11,14], [1,2,3,4,7,8,11,12,14],[1,2,3,4,7,8,12,13,14], [1,2,3,4,8,9,10,11,12],[1,2,3,4,8,9,10,12,14], [1,2,3,4,8,9,12,13,14],[1,2,3,4,8,10,11,12,14], [1,2,3,4,9,10,11,12,13],[1,2,3,4,9,10,12,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,13], [1,2,3,5,6,7,8,13,14],[1,2,3,5,6,7,9,10,11], [1,2,3,5,6,7,9,11,13],[1,2,3,5,6,7,11,12,13], [1,2,3,5,6,8,9,13,14],[1,2,3,5,6,9,10,11,13], [1,2,3,5,6,9,10,13,14],[1,2,3,5,6,10,11,13,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,10,11], [1,2,3,5,7,8,9,11,12],[1,2,3,5,7,8,9,12,13], [1,2,3,5,7,9,11,12,13],[1,2,3,6,7,8,9,13,14], [1,2,3,6,7,9,10,11,13],[1,2,3,6,7,9,10,13,14], [1,2,3,6,7,10,11,13,14],[1,2,3,6,7,11,12,13,14], [1,2,3,7,8,9,10,11,14],[1,2,3,7,8,9,11,12,13], [1,2,3,7,8,9,11,13,14],[1,2,3,7,8,11,12,13,14], [1,2,3,7,9,10,11,13,14],[1,2,3,8,9,10,11,12,14], [1,2,3,8,9,11,12,13,14],[1,2,3,9,10,11,12,13,14], [1,2,4,5,6,7,8,9,10],[1,2,4,5,6,7,8,10,11], [1,2,4,5,6,7,8,11,12],[1,2,4,5,6,7,8,12,14], [1,2,4,5,6,7,12,13,14],[1,2,4,5,6,8,9,10,14], [1,2,4,5,6,8,10,11,12],[1,2,4,5,6,8,10,12,14], [1,2,4,5,6,10,11,12,14],[1,2,4,5,7,8,12,13,14], [1,2,4,5,8,9,10,11,12],[1,2,4,5,8,9,10,12,14], [1,2,4,5,8,9,12,13,14],[1,2,4,5,9,10,11,12,13], [1,2,4,5,9,10,12,13,14],[1,2,4,5,10,11,12,13,14], [1,2,4,6,7,8,9,10,14],[1,2,4,6,7,8,10,11,14], [1,2,4,6,7,8,11,12,14],[1,2,4,6,8,10,11,12,14], [1,2,5,6,7,8,9,10,11],[1,2,5,6,7,8,9,11,12], [1,2,5,6,7,8,9,12,13],[1,2,5,6,7,8,12,13,14], [1,2,5,6,7,9,11,12,13],[1,2,5,6,8,9,10,11,12], [1,2,5,6,8,9,10,12,14],[1,2,5,6,8,9,12,13,14], [1,2,5,6,9,10,11,12,13],[1,2,5,6,9,10,12,13,14], [1,2,5,6,10,11,12,13,14],[1,2,6,7,8,9,10,11,12], [1,2,6,7,8,9,10,12,13],[1,2,6,7,8,9,10,13,14], [1,2,6,7,8,10,11,12,14],[1,2,6,7,8,10,12,13,14], [1,2,6,7,9,10,11,12,13],[1,2,6,7,10,11,12,13,14], [1,2,6,8,9,10,12,13,14],[1,2,7,8,9,10,11,12,13], [1,2,7,8,9,10,11,13,14],[1,2,7,8,10,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,14], [1,3,4,5,6,7,9,10,14],[1,3,4,5,6,7,10,11,14], [1,3,4,5,6,7,11,12,13],[1,3,4,5,6,7,11,13,14], [1,3,4,5,6,11,12,13,14],[1,3,4,5,7,8,9,10,11], [1,3,4,5,7,8,9,11,13],[1,3,4,5,7,8,9,13,14], [1,3,4,5,7,8,11,12,13],[1,3,4,5,7,9,10,11,14], [1,3,4,5,7,9,11,13,14],[1,3,4,5,8,9,11,12,13], [1,3,4,5,9,10,11,13,14],[1,3,4,6,7,11,12,13,14], [1,3,4,7,8,9,10,11,14],[1,3,4,7,8,9,11,13,14], [1,3,4,7,8,11,12,13,14],[1,3,4,8,9,10,11,12,14], [1,3,4,8,9,11,12,13,14],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,13,14],[1,3,5,6,7,9,10,11,13], [1,3,5,6,7,9,10,13,14],[1,3,5,6,7,10,11,13,14], [1,3,5,7,8,9,11,12,13],[1,3,5,7,9,10,11,13,14], [1,4,5,6,7,8,9,10,14],[1,4,5,6,7,8,10,11,14], [1,4,5,6,7,8,11,12,14],[1,4,5,6,7,11,12,13,14], [1,4,5,6,8,10,11,12,14],[1,4,5,7,8,9,10,11,14], [1,4,5,7,8,9,11,13,14],[1,4,5,7,8,11,12,13,14], [1,4,5,8,9,10,11,12,14],[1,4,5,8,9,11,12,13,14], [1,4,5,9,10,11,12,13,14],[1,5,6,7,8,9,10,11,14], [1,5,6,7,8,9,11,12,14],[1,5,6,7,8,9,12,13,14], [1,5,6,7,9,10,11,13,14],[1,5,6,7,9,11,12,13,14], [1,5,6,8,9,10,11,12,14],[1,5,6,9,10,11,12,13,14], [1,5,7,8,9,11,12,13,14],[1,6,7,8,9,10,11,12,14], [1,6,7,8,9,10,12,13,14],[1,6,7,9,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,11,12], [2,3,4,5,6,7,8,12,13],[2,3,4,5,6,7,8,13,14], [2,3,4,5,6,8,9,10,11],[2,3,4,5,6,8,9,11,12], [2,3,4,5,6,8,9,12,13],[2,3,4,5,6,8,9,13,14], [2,3,4,5,6,9,10,11,12],[2,3,4,5,6,9,10,12,13], [2,3,4,5,6,9,10,13,14],[2,3,4,5,6,10,11,12,14], [2,3,4,5,6,10,12,13,14],[2,3,4,5,9,10,11,12,13], [2,3,4,5,10,11,12,13,14],[2,3,4,6,7,8,9,10,14], [2,3,4,6,7,8,10,11,12],[2,3,4,6,7,8,10,12,14], [2,3,4,6,7,8,12,13,14],[2,3,4,6,7,10,11,12,14], [2,3,4,6,8,9,10,11,12],[2,3,4,6,8,9,10,12,13], [2,3,4,6,8,9,10,13,14],[2,3,4,6,8,10,12,13,14], [2,3,4,7,8,10,11,12,14],[2,3,4,8,9,10,12,13,14], [2,3,5,6,7,8,9,10,11],[2,3,5,6,7,8,9,11,12], [2,3,5,6,7,8,9,12,13],[2,3,5,6,7,9,11,12,13], [2,3,5,6,9,10,11,12,13],[2,3,5,6,10,11,12,13,14], [2,3,6,7,8,9,10,11,12],[2,3,6,7,8,9,10,12,13], [2,3,6,7,8,9,10,13,14],[2,3,6,7,8,10,12,13,14], [2,3,6,7,9,10,11,12,13],[2,3,6,7,10,11,12,13,14], [2,3,7,8,9,10,11,12,13],[2,3,7,8,9,10,11,13,14], [2,3,7,8,10,11,12,13,14],[2,3,8,9,10,11,12,13,14], [2,4,5,6,7,8,12,13,14],[2,4,5,6,8,9,10,11,12], [2,4,5,6,8,9,10,12,14],[2,4,5,6,8,9,12,13,14], [2,4,5,6,9,10,12,13,14],[2,4,6,7,8,10,11,12,14], [2,4,6,8,9,10,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,9,13,14],[3,4,5,6,7,9,10,11,12], [3,4,5,6,7,9,10,12,13],[3,4,5,6,7,9,10,13,14], [3,4,5,6,7,10,11,12,13],[3,4,5,6,7,10,11,13,14], [3,4,5,6,10,11,12,13,14],[3,4,5,7,8,9,11,12,13], [3,4,5,7,9,10,11,12,13],[3,4,5,7,9,10,11,13,14], [3,4,6,7,8,9,10,11,12],[3,4,6,7,8,9,10,12,13], [3,4,6,7,8,9,10,13,14],[3,4,6,7,8,10,12,13,14], [3,4,6,7,10,11,12,13,14],[3,4,7,8,9,10,11,12,13], [3,4,7,8,9,10,11,13,14],[3,4,7,8,10,11,12,13,14], [3,4,8,9,10,11,12,13,14],[3,5,6,7,9,10,11,12,13], [4,5,6,7,8,9,10,11,12],[4,5,6,7,8,9,10,12,13], [4,5,6,7,8,9,10,13,14],[4,5,6,7,8,10,11,12,13], [4,5,6,7,8,10,11,13,14],[4,5,6,7,8,11,12,13,14], [4,5,6,8,9,10,12,13,14],[4,5,6,8,10,11,12,13,14], [4,5,7,8,9,10,11,12,13],[4,5,7,8,9,10,11,13,14], [4,5,8,9,10,11,12,13,14],[4,6,7,8,10,11,12,13,14], [5,6,7,8,9,10,11,12,13],[5,6,7,8,9,10,11,13,14], [5,6,7,8,9,11,12,13,14],[5,6,8,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_1_2=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,14], [1,2,3,4,5,6,9,10,14],[1,2,3,4,5,6,10,11,12], [1,2,3,4,5,6,10,12,14],[1,2,3,4,5,6,11,12,13], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,11], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,8,9,13,14], [1,2,3,4,5,9,10,11,14],[1,2,3,4,5,9,11,13,14], [1,2,3,4,5,10,11,12,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,11],[1,2,3,4,6,7,8,11,13], [1,2,3,4,6,7,8,12,13],[1,2,3,4,6,7,8,12,14], [1,2,3,4,6,7,9,10,11],[1,2,3,4,6,7,12,13,14], [1,2,3,4,6,8,9,10,11],[1,2,3,4,6,8,9,10,14], [1,2,3,4,6,8,10,11,13],[1,2,3,4,6,8,10,12,13], [1,2,3,4,6,8,10,12,14],[1,2,3,4,6,10,11,12,13], [1,2,3,4,7,8,9,11,13],[1,2,3,4,7,8,12,13,14], [1,2,3,4,8,9,10,11,13],[1,2,3,4,8,9,10,13,14], [1,2,3,4,8,10,12,13,14],[1,2,3,4,9,10,11,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,14],[1,2,3,5,6,7,10,11,12], [1,2,3,5,6,7,10,12,14],[1,2,3,5,6,7,11,12,14], [1,2,3,5,6,7,11,13,14],[1,2,3,5,6,8,9,10,14], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,10,14], [1,2,3,5,7,8,9,13,14],[1,2,3,5,7,9,10,11,12], [1,2,3,5,7,9,10,12,14],[1,2,3,5,7,9,11,12,14], [1,2,3,5,7,9,11,13,14],[1,2,3,5,9,10,11,12,14], [1,2,3,6,7,8,9,10,11],[1,2,3,6,7,8,10,11,12], [1,2,3,6,7,8,10,12,14],[1,2,3,6,7,8,11,12,13], [1,2,3,6,7,11,12,13,14],[1,2,3,6,8,10,11,12,13], [1,2,3,7,8,9,10,11,13],[1,2,3,7,8,9,10,12,13], [1,2,3,7,8,9,10,12,14],[1,2,3,7,8,9,12,13,14], [1,2,3,7,8,10,11,12,13],[1,2,3,7,9,10,11,12,13], [1,2,3,7,9,11,12,13,14],[1,2,3,8,9,10,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,14], [1,2,4,5,6,7,9,10,11],[1,2,4,5,6,7,9,11,13], [1,2,4,5,6,7,9,13,14],[1,2,4,5,6,9,10,11,14], [1,2,4,5,6,9,11,13,14],[1,2,4,5,6,10,11,12,13], [1,2,4,5,6,10,11,13,14],[1,2,4,5,6,10,12,13,14], [1,2,4,5,7,8,9,13,14],[1,2,4,5,10,11,12,13,14], [1,2,4,6,7,8,9,11,13],[1,2,4,6,7,8,9,13,14], [1,2,4,6,7,8,12,13,14],[1,2,4,6,8,9,10,11,14], [1,2,4,6,8,9,11,13,14],[1,2,4,6,8,10,11,13,14], [1,2,4,6,8,10,12,13,14],[1,2,4,8,9,10,11,13,14], [1,2,5,6,7,8,9,10,14],[1,2,5,6,7,9,10,11,14], [1,2,5,6,7,9,11,13,14],[1,2,5,6,7,10,11,12,14], [1,2,5,6,10,11,12,13,14],[1,2,5,7,9,10,11,12,14], [1,2,6,7,8,9,10,11,12],[1,2,6,7,8,9,10,12,14], [1,2,6,7,8,9,11,12,14],[1,2,6,7,8,9,11,13,14], [1,2,6,7,8,11,12,13,14],[1,2,6,7,9,10,11,12,14], [1,2,6,8,9,10,11,12,14],[1,2,6,8,10,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,10,11], [1,3,4,5,6,7,9,11,13],[1,3,4,5,6,8,9,10,13], [1,3,4,5,6,8,9,10,14],[1,3,4,5,6,8,10,12,13], [1,3,4,5,6,8,10,12,14],[1,3,4,5,6,8,12,13,14], [1,3,4,5,6,9,10,11,13],[1,3,4,5,6,10,11,12,13], [1,3,4,5,8,9,10,13,14],[1,3,4,5,8,10,12,13,14], [1,3,4,5,9,10,11,12,13],[1,3,4,5,9,10,11,12,14], [1,3,4,5,9,10,12,13,14],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,8,9,11,13],[1,3,4,6,7,8,12,13,14], [1,3,4,6,8,9,10,11,13],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,10,11],[1,3,5,6,7,8,9,11,13], [1,3,5,6,7,8,10,11,12],[1,3,5,6,7,8,10,12,14], [1,3,5,6,7,8,11,12,13],[1,3,5,6,7,8,12,13,14], [1,3,5,6,7,11,12,13,14],[1,3,5,6,8,9,10,11,13], [1,3,5,6,8,10,11,12,13],[1,3,5,7,8,9,10,11,13], [1,3,5,7,8,9,10,13,14],[1,3,5,7,8,10,11,12,13], [1,3,5,7,8,10,12,13,14],[1,3,5,7,9,10,11,12,13], [1,3,5,7,9,10,12,13,14],[1,3,5,7,9,11,12,13,14], [1,3,7,8,9,10,12,13,14],[1,4,5,6,7,8,9,13,14], [1,4,5,6,8,9,10,13,14],[1,4,5,6,8,10,12,13,14], [1,4,5,6,9,10,11,13,14],[1,4,5,9,10,11,12,13,14], [1,4,6,8,9,10,11,13,14],[1,5,6,7,8,9,10,11,14], [1,5,6,7,8,9,11,13,14],[1,5,6,7,8,10,11,12,13], [1,5,6,7,8,10,11,13,14],[1,5,6,7,8,10,12,13,14], [1,5,6,7,10,11,12,13,14],[1,5,6,8,9,10,11,13,14], [1,5,7,8,9,10,11,13,14],[1,5,7,9,10,11,12,13,14], [1,6,7,8,9,10,11,12,14],[1,6,7,8,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,11,12], [2,3,4,5,6,7,8,12,14],[2,3,4,5,6,7,11,12,13], [2,3,4,5,6,7,12,13,14],[2,3,4,5,6,8,9,10,14], [2,3,4,5,6,8,10,11,12],[2,3,4,5,6,8,10,12,14], [2,3,4,5,7,8,9,10,12],[2,3,4,5,7,8,9,12,14], [2,3,4,5,7,8,9,13,14],[2,3,4,5,7,8,10,11,12], [2,3,4,5,7,9,10,11,12],[2,3,4,5,7,9,11,12,14], [2,3,4,5,7,9,11,13,14],[2,3,4,5,7,11,12,13,14], [2,3,4,5,8,9,10,12,14],[2,3,4,5,9,10,11,12,14], [2,3,4,6,7,8,9,10,11],[2,3,4,6,7,8,11,12,13], [2,3,4,6,8,10,11,12,13],[2,3,4,7,8,9,10,11,12], [2,3,4,7,8,9,11,12,13],[2,3,4,7,8,9,12,13,14], [2,3,4,7,9,11,12,13,14],[2,3,4,8,9,10,11,12,14], [2,3,4,8,9,10,11,13,14],[2,3,4,8,9,11,12,13,14], [2,3,4,8,10,11,12,13,14],[2,3,5,6,7,8,10,11,12], [2,3,5,6,7,8,10,12,14],[2,3,5,6,7,11,12,13,14], [2,3,5,7,8,9,10,12,14],[2,3,7,8,9,10,11,12,13], [2,3,8,9,10,11,12,13,14],[2,4,5,6,7,8,9,10,14], [2,4,5,6,7,8,10,11,12],[2,4,5,6,7,8,10,12,14], [2,4,5,6,7,9,10,11,14],[2,4,5,6,7,9,11,13,14], [2,4,5,6,7,10,11,12,14],[2,4,5,6,7,11,12,13,14], [2,4,5,6,10,11,12,13,14],[2,4,5,7,8,9,10,12,14], [2,4,5,7,9,10,11,12,14],[2,4,6,7,8,9,10,11,12], [2,4,6,7,8,9,10,12,14],[2,4,6,7,8,9,11,12,13], [2,4,6,7,8,9,12,13,14],[2,4,6,7,9,10,11,12,14], [2,4,6,7,9,11,12,13,14],[2,4,6,8,9,10,11,12,14], [2,4,6,8,9,11,12,13,14],[2,4,6,8,10,11,12,13,14], [2,6,7,8,9,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,12,13,14],[3,4,5,6,7,9,11,12,13], [3,4,5,6,8,9,10,11,13],[3,4,5,6,8,9,11,12,13], [3,4,5,6,8,10,11,12,13],[3,4,5,7,8,9,10,11,12], [3,4,5,7,8,9,12,13,14],[3,4,5,7,9,11,12,13,14], [3,4,5,8,9,10,11,12,13],[3,4,5,8,9,10,12,13,14], [3,4,6,7,8,9,11,12,13],[3,4,8,9,10,11,12,13,14], [3,5,6,7,8,9,11,12,13],[3,5,7,8,9,10,11,12,13], [3,5,7,8,9,10,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,9,10,12,13],[4,5,6,7,8,9,10,13,14], [4,5,6,7,8,10,12,13,14],[4,5,6,7,9,10,11,12,14], [4,5,6,7,9,10,12,13,14],[4,5,6,7,9,11,12,13,14], [4,5,6,8,9,10,11,12,13],[4,5,6,9,10,11,12,13,14], [4,5,7,8,9,10,12,13,14],[4,6,7,8,9,10,12,13,14], [4,6,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_1_3=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,14], [1,2,3,4,5,6,9,10,14],[1,2,3,4,5,6,10,11,12], [1,2,3,4,5,6,10,12,14],[1,2,3,4,5,6,11,12,13], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,11], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,8,9,13,14], [1,2,3,4,5,9,10,11,14],[1,2,3,4,5,9,11,13,14], [1,2,3,4,5,10,11,12,14],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,13],[1,2,3,4,6,7,8,12,13], [1,2,3,4,6,7,8,12,14],[1,2,3,4,6,7,9,10,11], [1,2,3,4,6,7,9,11,13],[1,2,3,4,6,7,12,13,14], [1,2,3,4,6,8,9,10,11],[1,2,3,4,6,8,9,10,14], [1,2,3,4,6,8,9,11,13],[1,2,3,4,6,8,10,11,12], [1,2,3,4,6,8,10,12,14],[1,2,3,4,6,8,11,12,13], [1,2,3,4,7,8,12,13,14],[1,2,3,4,8,9,10,11,13], [1,2,3,4,8,9,10,13,14],[1,2,3,4,8,10,11,12,13], [1,2,3,4,8,10,12,13,14],[1,2,3,4,9,10,11,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,12],[1,2,3,5,6,7,8,12,14], [1,2,3,5,6,7,10,11,12],[1,2,3,5,6,7,11,12,14], [1,2,3,5,6,7,11,13,14],[1,2,3,5,6,8,9,10,14], [1,2,3,5,6,8,10,12,14],[1,2,3,5,6,11,12,13,14], [1,2,3,5,7,8,9,10,14],[1,2,3,5,7,8,9,13,14], [1,2,3,5,7,8,10,12,14],[1,2,3,5,7,9,10,11,14], [1,2,3,5,7,9,11,13,14],[1,2,3,5,7,10,11,12,14], [1,2,3,6,7,8,9,10,11],[1,2,3,6,7,8,9,11,13], [1,2,3,6,7,8,10,11,12],[1,2,3,6,7,8,11,12,13], [1,2,3,6,7,11,12,13,14],[1,2,3,7,8,9,10,11,13], [1,2,3,7,8,9,10,12,13],[1,2,3,7,8,9,10,12,14], [1,2,3,7,8,9,12,13,14],[1,2,3,7,8,10,11,12,13], [1,2,3,7,9,10,11,12,13],[1,2,3,7,9,10,11,12,14], [1,2,3,7,9,11,12,13,14],[1,2,3,8,9,10,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,14], [1,2,4,5,6,7,9,10,11],[1,2,4,5,6,7,9,11,14], [1,2,4,5,6,7,11,13,14],[1,2,4,5,6,9,10,11,14], [1,2,4,5,6,10,11,12,13],[1,2,4,5,6,10,11,13,14], [1,2,4,5,6,10,12,13,14],[1,2,4,5,7,8,9,13,14], [1,2,4,5,7,9,11,13,14],[1,2,4,5,10,11,12,13,14], [1,2,4,6,7,8,9,13,14],[1,2,4,6,7,8,12,13,14], [1,2,4,6,7,9,11,13,14],[1,2,4,6,8,9,10,11,13], [1,2,4,6,8,9,10,13,14],[1,2,4,6,8,10,11,12,13], [1,2,4,6,8,10,12,13,14],[1,2,4,6,9,10,11,13,14], [1,2,5,6,7,8,9,10,14],[1,2,5,6,7,8,10,12,14], [1,2,5,6,7,9,10,11,14],[1,2,5,6,7,10,11,12,14], [1,2,5,6,10,11,12,13,14],[1,2,6,7,8,9,10,11,12], [1,2,6,7,8,9,10,12,14],[1,2,6,7,8,9,11,12,14], [1,2,6,7,8,9,11,13,14],[1,2,6,7,8,11,12,13,14], [1,2,6,7,9,10,11,12,14],[1,2,6,8,9,10,11,12,14], [1,2,6,8,9,10,11,13,14],[1,2,6,8,10,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,10,11], [1,3,4,5,6,7,9,11,13],[1,3,4,5,6,8,9,10,11], [1,3,4,5,6,8,9,10,14],[1,3,4,5,6,8,9,11,13], [1,3,4,5,6,8,10,11,13],[1,3,4,5,6,8,10,13,14], [1,3,4,5,6,10,11,12,13],[1,3,4,5,6,10,12,13,14], [1,3,4,5,8,9,10,11,13],[1,3,4,5,8,9,10,13,14], [1,3,4,5,9,10,11,12,13],[1,3,4,5,9,10,11,12,14], [1,3,4,5,9,10,12,13,14],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,8,12,13,14],[1,3,4,6,8,10,11,12,13], [1,3,4,6,8,10,12,13,14],[1,3,4,9,10,11,12,13,14], [1,3,5,6,7,8,9,10,11],[1,3,5,6,7,8,9,11,13], [1,3,5,6,7,8,10,11,13],[1,3,5,6,7,8,10,12,13], [1,3,5,6,7,8,12,13,14],[1,3,5,6,7,10,11,12,13], [1,3,5,6,7,11,12,13,14],[1,3,5,6,8,10,12,13,14], [1,3,5,7,8,9,10,11,13],[1,3,5,7,8,9,10,12,13], [1,3,5,7,8,9,10,12,14],[1,3,5,7,8,9,12,13,14], [1,3,5,7,9,10,11,12,13],[1,3,5,7,9,10,11,12,14], [1,3,5,7,9,11,12,13,14],[1,3,5,8,9,10,12,13,14], [1,3,6,7,8,10,11,12,13],[1,4,5,6,7,8,9,13,14], [1,4,5,6,7,9,11,13,14],[1,4,5,6,8,9,10,11,13], [1,4,5,6,8,9,10,13,14],[1,4,5,6,9,10,11,13,14], [1,4,5,9,10,11,12,13,14],[1,5,6,7,8,9,10,11,14], [1,5,6,7,8,9,11,13,14],[1,5,6,7,8,10,11,13,14], [1,5,6,7,8,10,12,13,14],[1,5,6,7,10,11,12,13,14], [1,5,6,8,9,10,11,13,14],[1,5,7,8,9,10,11,13,14], [1,5,7,8,9,10,12,13,14],[1,5,7,9,10,11,12,13,14], [1,6,7,8,9,10,11,12,14],[1,6,7,8,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,11,12], [2,3,4,5,6,7,8,12,14],[2,3,4,5,6,7,11,12,13], [2,3,4,5,6,7,12,13,14],[2,3,4,5,6,8,9,10,14], [2,3,4,5,6,8,10,11,12],[2,3,4,5,6,8,10,12,14], [2,3,4,5,7,8,9,10,14],[2,3,4,5,7,8,9,13,14], [2,3,4,5,7,8,10,11,12],[2,3,4,5,7,8,10,12,14], [2,3,4,5,7,9,10,11,12],[2,3,4,5,7,9,10,12,14], [2,3,4,5,7,9,11,12,13],[2,3,4,5,7,9,12,13,14], [2,3,4,5,9,10,11,12,14],[2,3,4,5,9,11,12,13,14], [2,3,4,6,7,8,9,10,11],[2,3,4,6,7,8,9,11,13], [2,3,4,6,7,8,11,12,13],[2,3,4,7,8,9,10,11,12], [2,3,4,7,8,9,10,12,14],[2,3,4,7,8,9,11,12,13], [2,3,4,7,8,9,12,13,14],[2,3,4,8,9,10,11,12,14], [2,3,4,8,9,10,11,13,14],[2,3,4,8,9,11,12,13,14], [2,3,4,8,10,11,12,13,14],[2,3,5,6,7,8,10,11,12], [2,3,5,6,7,11,12,13,14],[2,3,5,7,9,10,11,12,14], [2,3,5,7,9,11,12,13,14],[2,3,7,8,9,10,11,12,13], [2,3,8,9,10,11,12,13,14],[2,4,5,6,7,8,9,10,14], [2,4,5,6,7,8,10,11,12],[2,4,5,6,7,8,10,12,14], [2,4,5,6,7,9,10,11,12],[2,4,5,6,7,9,10,12,14], [2,4,5,6,7,9,11,12,14],[2,4,5,6,7,11,12,13,14], [2,4,5,6,9,10,11,12,14],[2,4,5,6,10,11,12,13,14], [2,4,5,7,9,11,12,13,14],[2,4,6,7,8,9,10,11,12], [2,4,6,7,8,9,10,12,14],[2,4,6,7,8,9,11,12,14], [2,4,6,7,8,9,11,13,14],[2,4,6,7,8,11,12,13,14], [2,4,6,8,9,10,11,12,14],[2,4,6,8,9,10,11,13,14], [2,4,6,8,10,11,12,13,14],[2,4,7,8,9,11,12,13,14], [2,5,6,7,9,10,11,12,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,8,12,13,14],[3,4,5,6,7,9,11,12,13], [3,4,5,6,8,9,11,12,13],[3,4,5,6,8,10,11,12,13], [3,4,5,6,8,10,12,13,14],[3,4,5,7,8,9,10,11,12], [3,4,5,7,8,9,10,12,14],[3,4,5,7,8,9,12,13,14], [3,4,5,8,9,10,11,12,13],[3,4,5,8,9,10,12,13,14], [3,4,6,7,8,9,11,12,13],[3,4,8,9,10,11,12,13,14], [3,5,6,7,8,9,11,12,13],[3,5,6,7,8,10,11,12,13], [3,5,7,8,9,10,11,12,13],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,9,10,12,13],[4,5,6,7,8,9,10,13,14], [4,5,6,7,8,10,12,13,14],[4,5,6,7,9,10,12,13,14], [4,5,6,7,9,11,12,13,14],[4,5,6,8,9,10,11,12,13], [4,5,6,9,10,11,12,13,14],[4,5,7,8,9,10,12,13,14], [4,6,7,8,9,10,12,13,14],[4,6,7,8,9,11,12,13,14], [4,6,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_1_4=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,10], [1,2,3,4,5,6,7,10,11],[1,2,3,4,5,6,7,11,13], [1,2,3,4,5,6,7,13,14],[1,2,3,4,5,6,8,9,14], [1,2,3,4,5,6,9,10,14],[1,2,3,4,5,6,10,11,13], [1,2,3,4,5,6,10,12,13],[1,2,3,4,5,6,10,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,13], [1,2,3,4,5,7,8,13,14],[1,2,3,4,5,7,9,10,11], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,8,9,13,14], [1,2,3,4,5,9,10,11,12],[1,2,3,4,5,9,10,12,14], [1,2,3,4,5,9,11,12,14],[1,2,3,4,5,9,11,13,14], [1,2,3,4,5,10,11,12,13],[1,2,3,4,5,11,12,13,14], [1,2,3,4,6,7,8,9,10],[1,2,3,4,6,7,8,10,11], [1,2,3,4,6,7,8,11,13],[1,2,3,4,6,7,8,12,13], [1,2,3,4,6,7,8,12,14],[1,2,3,4,6,7,12,13,14], [1,2,3,4,6,8,9,10,14],[1,2,3,4,6,8,10,11,13], [1,2,3,4,6,8,10,12,13],[1,2,3,4,6,8,10,12,14], [1,2,3,4,7,8,9,10,11],[1,2,3,4,7,8,9,11,13], [1,2,3,4,7,8,12,13,14],[1,2,3,4,8,9,10,11,14], [1,2,3,4,8,9,11,13,14],[1,2,3,4,8,10,11,13,14], [1,2,3,4,8,10,12,13,14],[1,2,3,4,9,10,11,12,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,14], [1,2,3,5,6,7,9,10,14],[1,2,3,5,6,7,10,11,12], [1,2,3,5,6,7,10,12,14],[1,2,3,5,6,7,11,12,14], [1,2,3,5,6,7,11,13,14],[1,2,3,5,6,10,11,12,13], [1,2,3,5,6,11,12,13,14],[1,2,3,5,7,8,9,13,14], [1,2,3,5,7,9,10,11,12],[1,2,3,5,7,9,10,12,14], [1,2,3,5,7,9,11,12,14],[1,2,3,5,7,9,11,13,14], [1,2,3,6,7,8,9,10,14],[1,2,3,6,7,8,10,11,12], [1,2,3,6,7,8,10,12,14],[1,2,3,6,7,8,11,12,13], [1,2,3,6,7,11,12,13,14],[1,2,3,6,8,10,11,12,13], [1,2,3,7,8,9,10,11,13],[1,2,3,7,8,9,10,13,14], [1,2,3,7,8,10,11,12,13],[1,2,3,7,8,10,12,13,14], [1,2,3,7,9,10,11,12,13],[1,2,3,7,9,10,12,13,14], [1,2,3,7,9,11,12,13,14],[1,2,3,8,9,10,11,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,13], [1,2,4,5,6,7,8,13,14],[1,2,4,5,6,7,9,10,11], [1,2,4,5,6,7,9,11,13],[1,2,4,5,6,8,9,13,14], [1,2,4,5,6,9,10,11,14],[1,2,4,5,6,9,11,13,14], [1,2,4,5,6,10,11,13,14],[1,2,4,5,6,10,12,13,14], [1,2,4,5,9,10,11,12,14],[1,2,4,5,10,11,12,13,14], [1,2,4,6,7,8,9,10,11],[1,2,4,6,7,8,9,11,13], [1,2,4,6,7,8,12,13,14],[1,2,4,6,8,9,10,11,14], [1,2,4,6,8,9,11,13,14],[1,2,4,6,8,10,11,13,14], [1,2,4,6,8,10,12,13,14],[1,2,5,6,7,8,9,13,14], [1,2,5,6,7,9,10,11,14],[1,2,5,6,7,9,11,13,14], [1,2,5,6,7,10,11,12,14],[1,2,5,6,10,11,12,13,14], [1,2,5,7,9,10,11,12,14],[1,2,6,7,8,9,10,11,12], [1,2,6,7,8,9,10,12,14],[1,2,6,7,8,9,11,12,13], [1,2,6,7,8,9,12,13,14],[1,2,6,7,9,10,11,12,14], [1,2,6,7,9,11,12,13,14],[1,2,6,8,9,10,11,12,14], [1,2,6,8,9,11,12,13,14],[1,2,6,8,10,11,12,13,14], [1,2,7,8,9,10,11,12,13],[1,2,7,8,9,10,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,12,13],[1,3,4,5,6,7,8,12,14], [1,3,4,5,6,7,9,10,11],[1,3,4,5,6,7,9,11,13], [1,3,4,5,6,7,12,13,14],[1,3,4,5,6,8,9,10,13], [1,3,4,5,6,8,9,10,14],[1,3,4,5,6,8,10,12,13], [1,3,4,5,6,8,10,12,14],[1,3,4,5,6,9,10,11,13], [1,3,4,5,7,8,12,13,14],[1,3,4,5,8,9,10,13,14], [1,3,4,5,8,10,12,13,14],[1,3,4,5,9,10,11,12,13], [1,3,4,5,9,10,12,13,14],[1,3,4,5,9,11,12,13,14], [1,3,4,6,7,8,9,10,11],[1,3,4,6,7,8,9,11,13], [1,3,4,6,8,9,10,11,13],[1,3,4,8,9,10,11,13,14], [1,3,4,9,10,11,12,13,14],[1,3,5,6,7,8,9,10,11], [1,3,5,6,7,8,9,10,14],[1,3,5,6,7,8,9,11,13], [1,3,5,6,7,8,10,11,12],[1,3,5,6,7,8,10,12,14], [1,3,5,6,7,8,11,12,13],[1,3,5,6,7,11,12,13,14], [1,3,5,6,8,9,10,11,13],[1,3,5,6,8,10,11,12,13], [1,3,5,7,8,9,10,11,13],[1,3,5,7,8,9,10,13,14], [1,3,5,7,8,10,11,12,13],[1,3,5,7,8,10,12,13,14], [1,3,5,7,9,10,11,12,13],[1,3,5,7,9,10,12,13,14], [1,3,5,7,9,11,12,13,14],[1,4,5,6,7,8,12,13,14], [1,4,5,6,8,9,10,13,14],[1,4,5,6,8,10,12,13,14], [1,4,5,6,9,10,11,13,14],[1,4,5,9,10,11,12,13,14], [1,4,6,8,9,10,11,13,14],[1,5,6,7,8,9,10,11,14], [1,5,6,7,8,9,11,13,14],[1,5,6,7,8,10,11,12,14], [1,5,6,7,8,11,12,13,14],[1,5,6,8,9,10,11,13,14], [1,5,6,8,10,11,12,13,14],[1,5,7,8,9,10,11,13,14], [1,5,7,8,10,11,12,13,14],[1,5,7,9,10,11,12,13,14], [1,6,7,8,9,10,11,12,14],[1,6,7,8,9,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,11],[2,3,4,5,6,7,8,11,12], [2,3,4,5,6,7,8,12,14],[2,3,4,5,6,7,11,12,14], [2,3,4,5,6,7,11,13,14],[2,3,4,5,6,8,9,10,14], [2,3,4,5,6,8,10,11,12],[2,3,4,5,6,8,10,12,14], [2,3,4,5,6,10,11,12,13],[2,3,4,5,6,11,12,13,14], [2,3,4,5,7,8,9,10,11],[2,3,4,5,7,8,9,11,12], [2,3,4,5,7,8,9,12,14],[2,3,4,5,7,8,9,13,14], [2,3,4,5,7,9,11,12,14],[2,3,4,5,7,9,11,13,14], [2,3,4,5,8,9,10,11,12],[2,3,4,5,8,9,10,12,14], [2,3,4,6,7,8,11,12,13],[2,3,4,6,7,11,12,13,14], [2,3,4,6,8,10,11,12,13],[2,3,4,7,8,9,11,12,13], [2,3,4,7,8,9,12,13,14],[2,3,4,7,9,11,12,13,14], [2,3,4,8,9,10,11,12,14],[2,3,4,8,9,11,12,13,14], [2,3,4,8,10,11,12,13,14],[2,3,5,6,7,8,9,10,14], [2,3,5,6,7,8,10,11,12],[2,3,5,6,7,8,10,12,14], [2,3,5,7,8,9,10,11,12],[2,3,5,7,8,9,10,12,14], [2,3,7,8,9,10,11,12,13],[2,3,7,8,9,10,12,13,14], [2,3,8,9,10,11,12,13,14],[2,4,5,6,7,8,9,10,14], [2,4,5,6,7,8,9,13,14],[2,4,5,6,7,8,10,11,12], [2,4,5,6,7,8,10,12,14],[2,4,5,6,7,9,10,11,14], [2,4,5,6,7,9,11,13,14],[2,4,5,6,7,10,11,12,14], [2,4,5,6,10,11,12,13,14],[2,4,5,7,8,9,10,11,12], [2,4,5,7,8,9,10,12,14],[2,4,5,7,9,10,11,12,14], [2,4,6,7,8,9,10,11,12],[2,4,6,7,8,9,10,12,14], [2,4,6,7,8,9,11,12,13],[2,4,6,7,8,9,12,13,14], [2,4,6,7,9,10,11,12,14],[2,4,6,7,9,11,12,13,14], [2,4,6,8,9,10,11,12,14],[2,4,6,8,9,11,12,13,14], [2,4,6,8,10,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,12],[3,4,5,6,7,8,9,12,13], [3,4,5,6,7,9,11,12,13],[3,4,5,6,7,11,12,13,14], [3,4,5,6,8,9,10,11,12],[3,4,5,6,8,9,10,12,13], [3,4,5,6,9,10,11,12,13],[3,4,5,7,8,9,12,13,14], [3,4,5,7,9,11,12,13,14],[3,4,5,8,9,10,12,13,14], [3,4,6,7,8,9,11,12,13],[3,4,6,8,9,10,11,12,13], [3,4,8,9,10,11,12,13,14],[3,5,6,7,8,9,11,12,13], [3,5,6,8,9,10,11,12,13],[3,5,7,8,9,10,11,12,13], [3,5,7,8,9,10,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,9,10,12,13],[4,5,6,7,8,9,10,13,14], [4,5,6,7,8,10,12,13,14],[4,5,6,7,9,10,11,12,13], [4,5,6,7,9,10,11,13,14],[4,5,6,7,10,11,12,13,14], [4,5,7,8,9,10,12,13,14],[4,5,7,9,10,11,12,13,14], [4,6,7,8,9,10,12,13,14],[4,6,7,9,10,11,12,13,14], [4,6,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,11,13,14],[5,6,7,8,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_1_5=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,11], [1,2,3,4,5,6,7,11,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,10],[1,2,3,4,5,6,8,10,14], [1,2,3,4,5,6,9,10,11],[1,2,3,4,5,6,10,11,12], [1,2,3,4,5,6,10,12,14],[1,2,3,4,5,6,11,12,13], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,14], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,9,13,14], [1,2,3,4,5,8,9,10,14],[1,2,3,4,5,9,10,11,14], [1,2,3,4,5,9,11,13,14],[1,2,3,4,5,10,11,12,14], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,11], [1,2,3,4,6,7,8,11,13],[1,2,3,4,6,7,8,13,14], [1,2,3,4,6,8,9,10,11],[1,2,3,4,6,8,10,11,13], [1,2,3,4,6,8,10,12,13],[1,2,3,4,6,8,10,12,14], [1,2,3,4,6,8,12,13,14],[1,2,3,4,6,10,11,12,13], [1,2,3,4,7,8,9,11,13],[1,2,3,4,7,8,9,13,14], [1,2,3,4,8,9,10,11,13],[1,2,3,4,8,9,10,13,14], [1,2,3,4,8,10,12,13,14],[1,2,3,4,9,10,11,13,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,10], [1,2,3,5,6,7,8,10,14],[1,2,3,5,6,7,9,10,11], [1,2,3,5,6,7,10,11,12],[1,2,3,5,6,7,10,12,14], [1,2,3,5,6,7,11,12,13],[1,2,3,5,6,7,12,13,14], [1,2,3,5,7,8,9,10,14],[1,2,3,5,7,9,10,11,12], [1,2,3,5,7,9,10,12,14],[1,2,3,5,7,9,11,12,14], [1,2,3,5,7,9,11,13,14],[1,2,3,5,7,11,12,13,14], [1,2,3,5,9,10,11,12,14],[1,2,3,6,7,8,9,10,11], [1,2,3,6,7,8,10,11,12],[1,2,3,6,7,8,10,12,14], [1,2,3,6,7,8,11,12,13],[1,2,3,6,7,8,12,13,14], [1,2,3,6,8,10,11,12,13],[1,2,3,7,8,9,10,11,12], [1,2,3,7,8,9,10,12,14],[1,2,3,7,8,9,11,12,13], [1,2,3,7,8,9,12,13,14],[1,2,3,7,9,11,12,13,14], [1,2,3,8,9,10,11,12,13],[1,2,3,8,9,10,12,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,14], [1,2,4,5,6,7,9,11,13],[1,2,4,5,6,7,9,13,14], [1,2,4,5,6,8,9,10,14],[1,2,4,5,6,9,10,11,14], [1,2,4,5,6,9,11,13,14],[1,2,4,5,6,10,11,12,14], [1,2,4,5,6,11,12,13,14],[1,2,4,6,7,8,9,11,13], [1,2,4,6,7,8,9,13,14],[1,2,4,6,8,9,10,11,14], [1,2,4,6,8,9,11,13,14],[1,2,4,6,8,10,11,13,14], [1,2,4,6,8,10,12,13,14],[1,2,4,6,10,11,12,13,14], [1,2,4,8,9,10,11,13,14],[1,2,5,6,7,8,9,10,14], [1,2,5,6,7,9,10,11,14],[1,2,5,6,7,9,11,13,14], [1,2,5,6,7,10,11,12,14],[1,2,5,6,7,11,12,13,14], [1,2,5,7,9,10,11,12,14],[1,2,6,7,8,9,10,11,14], [1,2,6,7,8,9,11,13,14],[1,2,6,7,8,10,11,12,14], [1,2,6,7,8,11,12,13,14],[1,2,6,8,10,11,12,13,14], [1,2,7,8,9,10,11,12,14],[1,2,7,8,9,11,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,13,14],[1,3,4,5,6,7,9,11,13], [1,3,4,5,6,8,9,10,13],[1,3,4,5,6,8,10,12,13], [1,3,4,5,6,8,10,12,14],[1,3,4,5,6,8,12,13,14], [1,3,4,5,6,9,10,11,13],[1,3,4,5,6,10,11,12,13], [1,3,4,5,7,8,9,13,14],[1,3,4,5,8,9,10,13,14], [1,3,4,5,8,10,12,13,14],[1,3,4,5,9,10,11,13,14], [1,3,4,5,10,11,12,13,14],[1,3,4,6,7,8,9,11,13], [1,3,4,6,8,9,10,11,13],[1,3,5,6,7,8,9,10,11], [1,3,5,6,7,8,9,11,13],[1,3,5,6,7,8,10,11,12], [1,3,5,6,7,8,10,12,14],[1,3,5,6,7,8,11,12,13], [1,3,5,6,7,8,12,13,14],[1,3,5,6,8,9,10,11,13], [1,3,5,6,8,10,11,12,13],[1,3,5,7,8,9,10,11,13], [1,3,5,7,8,9,10,13,14],[1,3,5,7,8,10,11,12,13], [1,3,5,7,8,10,12,13,14],[1,3,5,7,9,10,11,12,13], [1,3,5,7,9,10,12,13,14],[1,3,5,7,9,11,12,13,14], [1,3,5,9,10,11,12,13,14],[1,3,7,8,9,10,11,12,13], [1,3,7,8,9,10,12,13,14],[1,4,5,6,7,8,9,13,14], [1,4,5,6,8,9,10,13,14],[1,4,5,6,8,10,12,13,14], [1,4,5,6,9,10,11,13,14],[1,4,5,6,10,11,12,13,14], [1,4,6,8,9,10,11,13,14],[1,5,6,7,8,9,10,11,13], [1,5,6,7,8,9,10,13,14],[1,5,6,7,8,10,11,12,13], [1,5,6,7,8,10,12,13,14],[1,5,6,7,9,10,11,13,14], [1,5,6,7,10,11,12,13,14],[1,5,7,9,10,11,12,13,14], [1,6,7,8,9,10,11,13,14],[1,6,7,8,10,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,12,14], [2,3,4,5,6,7,9,10,11],[2,3,4,5,6,7,10,11,12], [2,3,4,5,6,7,11,12,13],[2,3,4,5,6,7,12,13,14], [2,3,4,5,6,8,10,12,14],[2,3,4,5,7,8,9,10,12], [2,3,4,5,7,8,9,12,14],[2,3,4,5,7,9,10,11,12], [2,3,4,5,7,9,11,12,14],[2,3,4,5,7,9,11,13,14], [2,3,4,5,7,11,12,13,14],[2,3,4,5,8,9,10,12,14], [2,3,4,5,9,10,11,12,14],[2,3,4,6,7,8,9,10,11], [2,3,4,6,7,8,10,11,12],[2,3,4,6,7,8,11,12,13], [2,3,4,6,7,8,12,13,14],[2,3,4,6,8,10,11,12,13], [2,3,4,7,8,9,10,11,12],[2,3,4,7,8,9,11,12,13], [2,3,4,7,8,9,12,13,14],[2,3,4,7,9,11,12,13,14], [2,3,4,8,9,10,11,12,13],[2,3,4,8,9,10,12,13,14], [2,3,4,9,10,11,12,13,14],[2,3,5,6,7,8,10,12,14], [2,3,5,7,8,9,10,12,14],[2,4,5,6,7,8,9,10,14], [2,4,5,6,7,8,10,12,14],[2,4,5,6,7,9,10,11,14], [2,4,5,6,7,9,11,13,14],[2,4,5,6,7,10,11,12,14], [2,4,5,6,7,11,12,13,14],[2,4,5,7,8,9,10,12,14], [2,4,5,7,9,10,11,12,14],[2,4,6,7,8,9,10,11,12], [2,4,6,7,8,9,10,12,14],[2,4,6,7,8,9,11,12,13], [2,4,6,7,8,9,12,13,14],[2,4,6,7,9,10,11,12,14], [2,4,6,7,9,11,12,13,14],[2,4,6,8,9,10,11,12,14], [2,4,6,8,9,11,12,13,14],[2,4,6,8,10,11,12,13,14], [2,4,8,9,10,11,12,13,14],[2,6,7,8,9,10,11,12,14], [2,6,7,8,9,11,12,13,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,13],[3,4,5,6,7,8,10,11,12], [3,4,5,6,7,8,11,12,13],[3,4,5,6,7,8,12,13,14], [3,4,5,6,8,9,10,11,13],[3,4,5,6,8,10,11,12,13], [3,4,5,7,8,9,10,11,12],[3,4,5,7,8,9,11,12,13], [3,4,5,7,8,9,12,13,14],[3,4,5,7,9,11,12,13,14], [3,4,5,8,9,10,11,12,13],[3,4,5,8,9,10,12,13,14], [3,4,5,9,10,11,12,13,14],[3,5,7,8,9,10,11,12,13], [3,5,7,8,9,10,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,9,10,12,14],[4,5,6,7,8,9,11,12,13], [4,5,6,7,8,9,12,13,14],[4,5,6,7,9,10,11,12,14], [4,5,6,7,9,11,12,13,14],[4,5,6,8,9,10,11,12,13], [4,5,6,8,9,10,12,13,14],[4,5,6,9,10,11,12,13,14], [4,6,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,12,13,14],[5,6,7,9,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_14_1_6=[[1,2,3,4,5,6,7,8,9], [1,2,3,4,5,6,7,8,14],[1,2,3,4,5,6,7,9,11], [1,2,3,4,5,6,7,11,13],[1,2,3,4,5,6,7,13,14], [1,2,3,4,5,6,8,9,10],[1,2,3,4,5,6,8,10,14], [1,2,3,4,5,6,9,10,11],[1,2,3,4,5,6,10,11,13], [1,2,3,4,5,6,10,12,13],[1,2,3,4,5,6,10,12,14], [1,2,3,4,5,6,12,13,14],[1,2,3,4,5,7,8,9,14], [1,2,3,4,5,7,9,11,13],[1,2,3,4,5,7,9,13,14], [1,2,3,4,5,8,9,10,14],[1,2,3,4,5,9,10,11,12], [1,2,3,4,5,9,10,12,14],[1,2,3,4,5,9,11,12,14], [1,2,3,4,5,9,11,13,14],[1,2,3,4,5,10,11,12,13], [1,2,3,4,5,11,12,13,14],[1,2,3,4,6,7,8,9,10], [1,2,3,4,6,7,8,10,11],[1,2,3,4,6,7,8,11,13], [1,2,3,4,6,7,8,13,14],[1,2,3,4,6,7,9,10,11], [1,2,3,4,6,8,10,11,13],[1,2,3,4,6,8,10,12,13], [1,2,3,4,6,8,10,12,14],[1,2,3,4,6,8,12,13,14], [1,2,3,4,7,8,9,10,11],[1,2,3,4,7,8,9,11,13], [1,2,3,4,7,8,9,13,14],[1,2,3,4,8,9,10,11,14], [1,2,3,4,8,9,11,13,14],[1,2,3,4,8,10,11,13,14], [1,2,3,4,8,10,12,13,14],[1,2,3,4,9,10,11,12,14], [1,2,3,4,10,11,12,13,14],[1,2,3,5,6,7,8,9,14], [1,2,3,5,6,7,9,10,11],[1,2,3,5,6,7,9,10,14], [1,2,3,5,6,7,10,11,12],[1,2,3,5,6,7,10,12,14], [1,2,3,5,6,7,11,12,13],[1,2,3,5,6,7,12,13,14], [1,2,3,5,6,8,9,10,14],[1,2,3,5,6,10,11,12,13], [1,2,3,5,7,9,10,11,12],[1,2,3,5,7,9,10,12,14], [1,2,3,5,7,9,11,12,14],[1,2,3,5,7,9,11,13,14], [1,2,3,5,7,11,12,13,14],[1,2,3,6,7,8,9,10,14], [1,2,3,6,7,8,10,11,12],[1,2,3,6,7,8,10,12,14], [1,2,3,6,7,8,11,12,13],[1,2,3,6,7,8,12,13,14], [1,2,3,6,8,10,11,12,13],[1,2,3,7,8,9,10,11,12], [1,2,3,7,8,9,10,12,13],[1,2,3,7,8,9,10,13,14], [1,2,3,7,8,9,11,12,13],[1,2,3,7,8,10,12,13,14], [1,2,3,7,9,10,12,13,14],[1,2,3,7,9,11,12,13,14], [1,2,3,8,9,10,11,12,13],[1,2,3,8,9,10,11,13,14], [1,2,3,9,10,11,12,13,14],[1,2,4,5,6,7,8,9,13], [1,2,4,5,6,7,8,13,14],[1,2,4,5,6,7,9,11,13], [1,2,4,5,6,8,9,10,14],[1,2,4,5,6,8,9,13,14], [1,2,4,5,6,9,10,11,14],[1,2,4,5,6,9,11,13,14], [1,2,4,5,6,10,11,12,13],[1,2,4,5,6,10,11,12,14], [1,2,4,5,6,11,12,13,14],[1,2,4,5,7,8,9,13,14], [1,2,4,5,9,10,11,12,14],[1,2,4,6,7,8,9,10,11], [1,2,4,6,7,8,9,11,13],[1,2,4,6,8,9,10,11,14], [1,2,4,6,8,9,11,13,14],[1,2,4,6,8,10,11,13,14], [1,2,4,6,8,10,12,13,14],[1,2,4,6,10,11,12,13,14], [1,2,5,6,7,8,9,13,14],[1,2,5,6,7,9,10,11,14], [1,2,5,6,7,9,11,13,14],[1,2,5,6,7,10,11,12,14], [1,2,5,6,7,11,12,13,14],[1,2,5,7,9,10,11,12,14], [1,2,6,7,8,9,10,11,14],[1,2,6,7,8,9,11,12,13], [1,2,6,7,8,9,11,12,14],[1,2,6,7,8,9,12,13,14], [1,2,6,7,8,10,11,12,14],[1,2,6,7,9,11,12,13,14], [1,2,6,8,9,11,12,13,14],[1,2,6,8,10,11,12,13,14], [1,2,7,8,9,10,11,12,14],[1,2,7,8,9,10,12,13,14], [1,2,8,9,10,11,12,13,14],[1,3,4,5,6,7,8,9,13], [1,3,4,5,6,7,8,12,13],[1,3,4,5,6,7,8,12,14], [1,3,4,5,6,7,9,11,13],[1,3,4,5,6,7,12,13,14], [1,3,4,5,6,8,9,10,13],[1,3,4,5,6,8,10,12,13], [1,3,4,5,6,8,10,12,14],[1,3,4,5,6,9,10,11,13], [1,3,4,5,7,8,9,13,14],[1,3,4,5,7,8,12,13,14], [1,3,4,5,8,9,10,13,14],[1,3,4,5,8,10,12,13,14], [1,3,4,5,9,10,11,12,14],[1,3,4,5,9,10,11,13,14], [1,3,4,5,10,11,12,13,14],[1,3,4,6,7,8,9,10,11], [1,3,4,6,7,8,9,11,13],[1,3,4,6,7,8,12,13,14], [1,3,4,6,8,9,10,11,13],[1,3,4,8,9,10,11,13,14], [1,3,5,6,7,8,9,10,11],[1,3,5,6,7,8,9,10,14], [1,3,5,6,7,8,9,11,13],[1,3,5,6,7,8,10,11,12], [1,3,5,6,7,8,10,12,14],[1,3,5,6,7,8,11,12,13], [1,3,5,6,8,9,10,11,13],[1,3,5,6,8,10,11,12,13], [1,3,5,7,8,9,10,11,13],[1,3,5,7,8,9,10,13,14], [1,3,5,7,8,10,11,12,13],[1,3,5,7,8,10,12,13,14], [1,3,5,7,9,10,11,12,13],[1,3,5,7,9,10,12,13,14], [1,3,5,7,9,11,12,13,14],[1,3,5,9,10,11,12,13,14], [1,3,7,8,9,10,11,12,13],[1,4,5,6,7,8,12,13,14], [1,4,5,6,8,9,10,13,14],[1,4,5,6,8,10,12,13,14], [1,4,5,6,9,10,11,13,14],[1,4,5,6,10,11,12,13,14], [1,4,6,8,9,10,11,13,14],[1,5,6,7,8,9,10,11,13], [1,5,6,7,8,9,10,13,14],[1,5,6,7,8,10,11,12,14], [1,5,6,7,8,10,11,13,14],[1,5,6,7,8,11,12,13,14], [1,5,6,7,9,10,11,13,14],[1,5,6,8,10,11,12,13,14], [1,5,7,8,10,11,12,13,14],[1,5,7,9,10,11,12,13,14], [1,6,7,8,9,10,11,13,14],[1,6,7,8,9,11,12,13,14], [1,7,8,9,10,11,12,13,14],[2,3,4,5,6,7,8,9,10], [2,3,4,5,6,7,8,10,12],[2,3,4,5,6,7,8,12,14], [2,3,4,5,6,7,9,10,11],[2,3,4,5,6,7,10,11,12], [2,3,4,5,6,7,11,12,14],[2,3,4,5,6,7,11,13,14], [2,3,4,5,6,8,10,12,14],[2,3,4,5,6,10,11,12,13], [2,3,4,5,6,11,12,13,14],[2,3,4,5,7,8,9,10,11], [2,3,4,5,7,8,9,11,12],[2,3,4,5,7,8,9,12,14], [2,3,4,5,7,8,10,11,12],[2,3,4,5,7,9,11,12,14], [2,3,4,5,7,9,11,13,14],[2,3,4,5,8,9,10,11,12], [2,3,4,5,8,9,10,12,14],[2,3,4,6,7,8,10,11,12], [2,3,4,6,7,8,11,12,13],[2,3,4,6,7,8,12,13,14], [2,3,4,6,7,11,12,13,14],[2,3,4,6,8,10,11,12,13], [2,3,4,7,8,9,11,12,13],[2,3,4,7,8,9,12,13,14], [2,3,4,7,9,11,12,13,14],[2,3,4,8,9,10,11,12,13], [2,3,4,8,9,10,11,13,14],[2,3,4,8,9,10,12,13,14], [2,3,4,9,10,11,12,13,14],[2,3,5,6,7,8,9,10,14], [2,3,5,6,7,8,10,12,14],[2,3,5,6,7,11,12,13,14], [2,3,5,7,8,9,10,11,12],[2,3,5,7,8,9,10,12,14], [2,3,7,8,9,10,12,13,14],[2,4,5,6,7,8,9,10,14], [2,4,5,6,7,8,9,13,14],[2,4,5,6,7,8,10,12,14], [2,4,5,6,7,9,10,11,14],[2,4,5,6,7,9,11,13,14], [2,4,5,6,7,10,11,12,14],[2,4,5,7,8,9,10,11,12], [2,4,5,7,8,9,10,12,14],[2,4,5,7,9,10,11,12,14], [2,4,6,7,8,9,10,11,12],[2,4,6,7,8,9,10,12,14], [2,4,6,7,8,9,11,12,13],[2,4,6,7,8,9,12,13,14], [2,4,6,7,9,10,11,12,14],[2,4,6,7,9,11,12,13,14], [2,4,6,8,9,10,11,12,14],[2,4,6,8,9,11,12,13,14], [2,4,6,8,10,11,12,13,14],[2,4,8,9,10,11,12,13,14], [2,6,7,8,9,10,11,12,14],[3,4,5,6,7,8,9,10,11], [3,4,5,6,7,8,9,11,13],[3,4,5,6,7,8,10,11,12], [3,4,5,6,7,8,11,12,13],[3,4,5,6,7,11,12,13,14], [3,4,5,6,8,9,10,11,12],[3,4,5,6,8,9,10,12,13], [3,4,5,6,8,9,11,12,13],[3,4,5,6,9,10,11,12,13], [3,4,5,7,8,9,11,12,13],[3,4,5,7,8,9,12,13,14], [3,4,5,7,9,11,12,13,14],[3,4,5,8,9,10,12,13,14], [3,4,5,9,10,11,12,13,14],[3,4,6,8,9,10,11,12,13], [3,5,6,8,9,10,11,12,13],[3,5,7,8,9,10,11,12,13], [3,5,7,8,9,10,12,13,14],[4,5,6,7,8,9,10,11,12], [4,5,6,7,8,9,10,12,14],[4,5,6,7,8,9,11,12,13], [4,5,6,7,8,9,12,13,14],[4,5,6,7,9,10,11,12,13], [4,5,6,7,9,10,11,13,14],[4,5,6,7,9,10,12,13,14], [4,5,6,7,10,11,12,13,14],[4,5,6,8,9,10,12,13,14], [4,5,7,9,10,11,12,13,14],[4,6,7,9,10,11,12,13,14], [4,6,8,9,10,11,12,13,14],[5,6,7,8,9,10,11,12,13], [5,6,7,8,9,10,12,13,14],[5,6,7,8,10,11,12,13,14], [6,7,8,9,10,11,12,13,14]] manifold_8_15_5_1=[[1,2,3,4,5,6,7,8,12], [1,2,3,4,5,6,7,8,13],[1,2,3,4,5,6,7,12,14], [1,2,3,4,5,6,7,13,15],[1,2,3,4,5,6,7,14,15], [1,2,3,4,5,6,8,9,12],[1,2,3,4,5,6,8,9,13], [1,2,3,4,5,6,9,12,14],[1,2,3,4,5,6,9,13,15], [1,2,3,4,5,6,9,14,15],[1,2,3,4,5,7,8,10,11], [1,2,3,4,5,7,8,10,12],[1,2,3,4,5,7,8,11,13], 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