###################################################### ###################################################### ### ### ### 25 combinatorially distinct vertex-minimal ### ### triangulations of ### ### S^3 x S^2 ### ### ### ### with f-vector f=(12,66,220,390,336,112) ### ### ### ###################################################### ###################################################### S3xS2_12^a=[[1,2,3,4,6,10],[1,2,3,4,6,11],[1,2,3,4,7,8], [1,2,3,4,7,11],[1,2,3,4,8,10],[1,2,3,5,7,11], [1,2,3,5,7,12],[1,2,3,5,9,11],[1,2,3,5,9,12], [1,2,3,6,10,11],[1,2,3,7,8,12],[1,2,3,8,10,12], [1,2,3,9,10,11],[1,2,3,9,10,12],[1,2,4,6,7,8], [1,2,4,6,7,11],[1,2,4,6,8,9],[1,2,4,6,9,10], [1,2,4,8,9,10],[1,2,5,7,11,12],[1,2,5,9,11,12], [1,2,6,7,8,12],[1,2,6,7,11,12],[1,2,6,8,9,12], [1,2,6,9,10,11],[1,2,6,9,11,12],[1,2,8,9,10,12], [1,3,4,6,7,8],[1,3,4,6,7,11],[1,3,4,6,8,10], [1,3,5,7,9,11],[1,3,5,7,9,12],[1,3,6,7,8,12], [1,3,6,7,11,12],[1,3,6,8,10,12],[1,3,6,10,11,12], [1,3,7,9,10,11],[1,3,7,9,10,12],[1,3,7,10,11,12], [1,4,5,6,8,9],[1,4,5,6,8,10],[1,4,5,6,9,10], [1,4,5,8,9,12],[1,4,5,8,10,12],[1,4,5,9,10,12], [1,4,8,9,10,12],[1,5,6,8,9,11],[1,5,6,8,10,11], [1,5,6,9,10,11],[1,5,7,9,10,11],[1,5,7,9,10,12], [1,5,7,10,11,12],[1,5,8,9,11,12],[1,5,8,10,11,12], [1,6,8,9,11,12],[1,6,8,10,11,12],[2,3,4,5,6,10], [2,3,4,5,6,12],[2,3,4,5,8,10],[2,3,4,5,8,11], [2,3,4,5,11,12],[2,3,4,6,11,12],[2,3,4,7,8,11], [2,3,5,6,7,8],[2,3,5,6,7,12],[2,3,5,6,8,10], [2,3,5,7,8,11],[2,3,5,9,11,12],[2,3,6,7,8,12], [2,3,6,8,10,12],[2,3,6,10,11,12],[2,3,9,10,11,12], [2,4,5,6,7,10],[2,4,5,6,7,12],[2,4,5,7,8,10], [2,4,5,7,8,11],[2,4,5,7,11,12],[2,4,6,7,8,9], [2,4,6,7,9,10],[2,4,6,7,11,12],[2,4,7,8,9,10], [2,5,6,7,8,10],[2,6,7,8,9,10],[2,6,8,9,10,12], [2,6,9,10,11,12],[3,4,5,6,7,9],[3,4,5,6,7,12], [3,4,5,6,8,9],[3,4,5,6,8,10],[3,4,5,7,9,12], [3,4,5,8,9,11],[3,4,5,9,11,12],[3,4,6,7,8,9], [3,4,6,7,11,12],[3,4,7,8,9,11],[3,4,7,9,11,12], [3,5,6,7,8,9],[3,5,7,8,9,11],[3,7,9,10,11,12], [4,5,6,7,9,10],[4,5,7,8,10,11],[4,5,7,9,10,12], [4,5,7,10,11,12],[4,5,8,9,11,12],[4,5,8,10,11,12], [4,7,8,9,10,11],[4,7,9,10,11,12],[4,8,9,10,11,12], [5,6,7,8,9,10],[5,6,8,9,10,11],[5,7,8,9,10,11], [6,8,9,10,11,12]] S3xS2_12^b=[[1,2,3,6,7,8],[1,2,3,6,7,12],[1,2,3,6,8,12], [1,2,3,7,8,12],[1,2,4,5,8,10],[1,2,4,5,8,11], [1,2,4,5,9,11],[1,2,4,5,9,12],[1,2,4,5,10,12], [1,2,4,8,10,11],[1,2,4,9,10,11],[1,2,4,9,10,12], [1,2,5,7,8,9],[1,2,5,7,8,11],[1,2,5,7,9,11], [1,2,5,8,9,12],[1,2,5,8,10,12],[1,2,6,7,8,9], [1,2,6,7,9,12],[1,2,6,8,9,12],[1,2,7,8,10,11], [1,2,7,8,10,12],[1,2,7,9,10,11],[1,2,7,9,10,12], [1,3,4,5,6,10],[1,3,4,5,6,12],[1,3,4,5,10,12], [1,3,4,6,7,9],[1,3,4,6,7,12],[1,3,4,6,9,11], [1,3,4,6,10,11],[1,3,4,7,9,10],[1,3,4,7,10,12], [1,3,4,9,10,11],[1,3,5,6,10,11],[1,3,5,6,11,12], [1,3,5,8,9,10],[1,3,5,8,9,12],[1,3,5,8,10,12], [1,3,5,9,10,11],[1,3,5,9,11,12],[1,3,6,7,8,9], [1,3,6,8,9,12],[1,3,6,9,11,12],[1,3,7,8,9,10], [1,3,7,8,10,12],[1,4,5,6,10,11],[1,4,5,6,11,12], [1,4,5,8,10,11],[1,4,5,9,11,12],[1,4,6,7,9,12], [1,4,6,9,11,12],[1,4,7,9,10,12],[1,5,7,8,9,10], [1,5,7,8,10,11],[1,5,7,9,10,11],[2,3,4,5,6,7], [2,3,4,5,6,10],[2,3,4,5,7,11],[2,3,4,5,9,10], [2,3,4,5,9,11],[2,3,4,6,7,8],[2,3,4,6,8,11], [2,3,4,6,10,11],[2,3,4,7,8,11],[2,3,4,9,10,11], [2,3,5,6,7,11],[2,3,5,6,10,11],[2,3,5,9,10,11], [2,3,6,7,11,12],[2,3,6,8,11,12],[2,3,7,8,11,12], [2,4,5,6,7,8],[2,4,5,6,8,10],[2,4,5,7,8,11], [2,4,5,9,10,12],[2,4,6,8,10,11],[2,5,6,7,8,9], [2,5,6,7,9,10],[2,5,6,7,10,11],[2,5,6,8,9,10], [2,5,7,9,10,11],[2,5,8,9,10,12],[2,6,7,9,10,12], [2,6,7,10,11,12],[2,6,8,9,10,12],[2,6,8,10,11,12], [2,7,8,10,11,12],[3,4,5,6,7,12],[3,4,5,7,11,12], [3,4,5,9,10,12],[3,4,5,9,11,12],[3,4,6,7,8,9], [3,4,6,8,9,11],[3,4,7,8,9,12],[3,4,7,8,11,12], [3,4,7,9,10,12],[3,4,8,9,11,12],[3,5,6,7,11,12], [3,5,8,9,10,12],[3,6,8,9,11,12],[3,7,8,9,10,12], [4,5,6,7,8,11],[4,5,6,7,11,12],[4,5,6,8,10,11], [4,6,7,8,9,12],[4,6,7,8,11,12],[4,6,8,9,11,12], [5,6,7,8,9,10],[5,6,7,8,10,11],[6,7,8,9,10,12], [6,7,8,10,11,12]] S3xS2_12^c=[[1,2,3,4,6,8],[1,2,3,4,6,12],[1,2,3,4,7,11], [1,2,3,4,7,12],[1,2,3,4,8,11],[1,2,3,6,8,12], [1,2,3,7,8,11],[1,2,3,7,8,12],[1,2,4,5,6,8], [1,2,4,5,6,12],[1,2,4,5,8,12],[1,2,4,7,8,11], [1,2,4,7,8,12],[1,2,5,6,8,9],[1,2,5,6,9,10], [1,2,5,6,10,12],[1,2,5,8,9,12],[1,2,5,9,10,12], [1,2,6,8,9,12],[1,2,6,9,10,12],[1,3,4,5,6,8], [1,3,4,5,6,12],[1,3,4,5,7,9],[1,3,4,5,7,12], [1,3,4,5,8,9],[1,3,4,7,9,11],[1,3,4,8,9,10], [1,3,4,8,10,11],[1,3,4,9,10,11],[1,3,5,6,8,9], [1,3,5,6,9,11],[1,3,5,6,11,12],[1,3,5,7,9,11], [1,3,5,7,10,11],[1,3,5,7,10,12],[1,3,5,10,11,12], [1,3,6,8,9,12],[1,3,6,9,11,12],[1,3,7,8,10,11], [1,3,7,8,10,12],[1,3,8,9,10,12],[1,3,9,10,11,12], [1,4,5,7,8,10],[1,4,5,7,8,12],[1,4,5,7,9,10], [1,4,5,8,9,10],[1,4,7,8,10,11],[1,4,7,9,10,11], [1,5,6,7,9,10],[1,5,6,7,9,11],[1,5,6,7,10,11], [1,5,6,10,11,12],[1,5,7,8,10,12],[1,5,8,9,10,12], [1,6,7,9,10,11],[1,6,9,10,11,12],[2,3,4,6,7,10], [2,3,4,6,7,12],[2,3,4,6,8,10],[2,3,4,7,9,10], [2,3,4,7,9,11],[2,3,4,8,10,11],[2,3,4,9,10,11], [2,3,5,7,9,10],[2,3,5,7,9,11],[2,3,5,7,10,11], [2,3,5,9,10,11],[2,3,6,7,8,10],[2,3,6,7,8,12], [2,3,7,8,10,11],[2,4,5,6,8,11],[2,4,5,6,11,12], [2,4,5,8,11,12],[2,4,6,7,9,10],[2,4,6,7,9,12], [2,4,6,8,10,11],[2,4,6,9,10,12],[2,4,6,10,11,12], [2,4,7,8,11,12],[2,4,7,9,11,12],[2,4,9,10,11,12], [2,5,6,7,9,10],[2,5,6,7,9,11],[2,5,6,7,10,11], [2,5,6,8,9,11],[2,5,6,10,11,12],[2,5,8,9,11,12], [2,5,9,10,11,12],[2,6,7,8,9,11],[2,6,7,8,9,12], [2,6,7,8,10,11],[2,7,8,9,11,12],[3,4,5,6,8,12], [3,4,5,7,8,10],[3,4,5,7,8,12],[3,4,5,7,9,10], [3,4,5,8,9,10],[3,4,6,7,8,10],[3,4,6,7,8,12], [3,5,6,8,9,12],[3,5,6,9,11,12],[3,5,7,8,10,12], [3,5,8,9,10,12],[3,5,9,10,11,12],[4,5,6,8,11,12], [4,6,7,8,10,11],[4,6,7,8,11,12],[4,6,7,9,10,11], [4,6,7,9,11,12],[4,6,9,10,11,12],[5,6,8,9,11,12], [6,7,8,9,11,12]] S3xS2_12^d=[[1,2,3,4,6,7],[1,2,3,4,6,10],[1,2,3,4,7,11], [1,2,3,4,9,11],[1,2,3,4,9,12],[1,2,3,4,10,12], [1,2,3,5,7,9],[1,2,3,5,7,11],[1,2,3,5,9,11], [1,2,3,6,7,12],[1,2,3,6,10,12],[1,2,3,7,9,12], [1,2,4,6,7,8],[1,2,4,6,8,10],[1,2,4,7,8,12], [1,2,4,7,11,12],[1,2,4,8,10,12],[1,2,4,9,11,12], [1,2,5,7,9,11],[1,2,6,7,8,10],[1,2,6,7,10,12], [1,2,7,8,10,12],[1,2,7,9,11,12],[1,3,4,5,6,7], [1,3,4,5,6,10],[1,3,4,5,7,11],[1,3,4,5,10,11], [1,3,4,9,10,11],[1,3,4,9,10,12],[1,3,5,6,7,12], [1,3,5,6,8,11],[1,3,5,6,8,12],[1,3,5,6,10,11], [1,3,5,7,9,12],[1,3,5,8,9,11],[1,3,5,8,9,12], [1,3,6,8,10,11],[1,3,6,8,10,12],[1,3,8,9,10,11], [1,3,8,9,10,12],[1,4,5,6,7,12],[1,4,5,6,8,10], [1,4,5,6,8,12],[1,4,5,7,9,11],[1,4,5,7,9,12], [1,4,5,8,10,12],[1,4,5,9,10,11],[1,4,5,9,10,12], [1,4,6,7,8,12],[1,4,7,9,11,12],[1,5,6,8,9,10], [1,5,6,8,9,11],[1,5,6,9,10,11],[1,5,8,9,10,12], [1,6,7,8,10,12],[1,6,8,9,10,11],[2,3,4,6,7,9], [2,3,4,6,9,12],[2,3,4,6,10,12],[2,3,4,7,8,9], [2,3,4,7,8,11],[2,3,4,8,9,11],[2,3,5,7,8,9], [2,3,5,7,8,11],[2,3,5,8,9,11],[2,3,6,7,9,12], [2,4,5,6,8,10],[2,4,5,6,8,12],[2,4,5,6,10,12], [2,4,5,8,10,12],[2,4,6,7,8,9],[2,4,6,8,9,11], [2,4,6,8,11,12],[2,4,6,9,11,12],[2,4,7,8,11,12], [2,5,6,8,9,10],[2,5,6,8,9,11],[2,5,6,8,11,12], [2,5,6,9,10,11],[2,5,6,10,11,12],[2,5,7,8,9,10], [2,5,7,8,10,11],[2,5,7,9,10,11],[2,5,8,10,11,12], [2,6,7,8,9,10],[2,6,7,9,10,11],[2,6,7,9,11,12], [2,6,7,10,11,12],[2,7,8,10,11,12],[3,4,5,6,7,12], [3,4,5,6,10,12],[3,4,5,7,9,10],[3,4,5,7,9,12], [3,4,5,7,10,11],[3,4,5,9,10,12],[3,4,6,7,9,12], [3,4,7,8,9,11],[3,4,7,9,10,11],[3,5,6,8,11,12], [3,5,6,10,11,12],[3,5,7,8,9,10],[3,5,7,8,10,11], [3,5,8,9,10,12],[3,5,8,10,11,12],[3,6,8,10,11,12], [3,7,8,9,10,11],[4,5,7,9,10,11],[4,6,7,8,9,11], [4,6,7,8,11,12],[4,6,7,9,11,12],[6,7,8,9,10,11], [6,7,8,10,11,12]] S3xS2_12^e=[[1,2,3,4,8,10],[1,2,3,4,8,12],[1,2,3,4,10,12], [1,2,3,5,6,7],[1,2,3,5,6,12],[1,2,3,5,7,11], [1,2,3,5,9,10],[1,2,3,5,9,11],[1,2,3,5,10,12], [1,2,3,6,7,8],[1,2,3,6,8,12],[1,2,3,7,8,10], [1,2,3,7,10,11],[1,2,3,9,10,11],[1,2,4,8,10,11], [1,2,4,8,11,12],[1,2,4,9,10,11],[1,2,4,9,10,12], [1,2,4,9,11,12],[1,2,5,6,7,8],[1,2,5,6,8,12], [1,2,5,7,8,12],[1,2,5,7,9,11],[1,2,5,7,9,12], [1,2,5,9,10,12],[1,2,7,8,10,11],[1,2,7,8,11,12], [1,2,7,9,11,12],[1,3,4,8,10,12],[1,3,5,6,7,11], [1,3,5,6,8,9],[1,3,5,6,8,12],[1,3,5,6,9,11], [1,3,5,8,9,10],[1,3,5,8,10,12],[1,3,6,7,8,9], [1,3,6,7,9,10],[1,3,6,7,10,11],[1,3,6,9,10,11], [1,3,7,8,9,10],[1,4,5,6,7,9],[1,4,5,6,7,11], [1,4,5,6,9,11],[1,4,5,7,9,11],[1,4,6,7,9,10], [1,4,6,7,10,11],[1,4,6,9,10,11],[1,4,7,9,10,12], [1,4,7,9,11,12],[1,4,7,10,11,12],[1,4,8,10,11,12], [1,5,6,7,8,9],[1,5,7,8,9,10],[1,5,7,8,10,12], [1,5,7,9,10,12],[1,7,8,10,11,12],[2,3,4,5,6,7], [2,3,4,5,6,12],[2,3,4,5,7,8],[2,3,4,5,8,10], [2,3,4,5,10,12],[2,3,4,6,7,8],[2,3,4,6,8,12], [2,3,5,7,8,10],[2,3,5,7,9,10],[2,3,5,7,9,11], [2,3,7,9,10,11],[2,4,5,6,7,8],[2,4,5,6,8,10], [2,4,5,6,10,12],[2,4,6,8,9,11],[2,4,6,8,9,12], [2,4,6,8,10,11],[2,4,6,9,10,11],[2,4,6,9,10,12], [2,4,8,9,11,12],[2,5,6,8,10,12],[2,5,7,8,10,12], [2,5,7,9,10,12],[2,6,8,9,11,12],[2,6,8,10,11,12], [2,6,9,10,11,12],[2,7,8,10,11,12],[2,7,9,10,11,12], [3,4,5,6,7,11],[3,4,5,6,11,12],[3,4,5,7,8,9], [3,4,5,7,9,11],[3,4,5,8,9,11],[3,4,5,8,10,12], [3,4,5,8,11,12],[3,4,6,7,8,9],[3,4,6,7,9,12], [3,4,6,7,11,12],[3,4,6,8,9,12],[3,4,7,9,11,12], [3,4,8,9,11,12],[3,5,6,8,9,11],[3,5,6,8,11,12], [3,5,7,8,9,10],[3,6,7,9,10,11],[3,6,7,9,11,12], [3,6,8,9,11,12],[4,5,6,7,8,9],[4,5,6,8,9,11], [4,5,6,8,10,11],[4,5,6,10,11,12],[4,5,8,10,11,12], [4,6,7,9,10,12],[4,6,7,10,11,12],[5,6,8,10,11,12], [6,7,9,10,11,12]] S3xS2_12^1=[[1,2,3,5,8,10],[1,2,3,5,8,11], [1,2,3,5,10,11],[1,2,3,6,7,10],[1,2,3,6,7,11], [1,2,3,6,10,11],[1,2,3,7,8,10],[1,2,3,7,8,11], [1,2,4,6,7,9],[1,2,4,6,7,11],[1,2,4,6,9,12], [1,2,4,6,11,12],[1,2,4,7,9,12],[1,2,4,7,11,12], [1,2,5,8,10,11],[1,2,6,7,9,12],[1,2,6,7,10,12], [1,2,6,10,11,12],[1,2,7,8,10,11],[1,2,7,10,11,12], [1,3,4,5,9,10],[1,3,4,5,9,12],[1,3,4,5,10,12], [1,3,4,6,8,9],[1,3,4,6,8,11],[1,3,4,6,9,12], [1,3,4,6,11,12],[1,3,4,8,9,11],[1,3,4,9,10,11], [1,3,4,10,11,12],[1,3,5,8,9,11],[1,3,5,8,9,12], [1,3,5,8,10,12],[1,3,5,9,10,11],[1,3,6,7,8,11], [1,3,6,7,8,12],[1,3,6,7,10,12],[1,3,6,8,9,12], [1,3,6,10,11,12],[1,3,7,8,10,12],[1,4,5,6,7,8], [1,4,5,6,7,9],[1,4,5,6,8,9],[1,4,5,7,8,12], [1,4,5,7,9,12],[1,4,5,8,9,10],[1,4,5,8,10,12], [1,4,6,7,8,11],[1,4,7,8,11,12],[1,4,8,9,10,11], [1,4,8,10,11,12],[1,5,6,7,8,12],[1,5,6,7,9,12], [1,5,6,8,9,12],[1,5,8,9,10,11],[1,7,8,10,11,12], [2,3,4,5,7,9],[2,3,4,5,7,10],[2,3,4,5,8,10], [2,3,4,5,8,12],[2,3,4,5,9,12],[2,3,4,7,9,10], [2,3,4,8,9,10],[2,3,4,8,9,12],[2,3,5,6,7,10], [2,3,5,6,7,11],[2,3,5,6,10,11],[2,3,5,7,9,11], [2,3,5,8,9,11],[2,3,5,8,9,12],[2,3,7,8,9,10], [2,3,7,8,9,11],[2,4,5,6,7,10],[2,4,5,6,7,11], [2,4,5,6,8,10],[2,4,5,6,8,12],[2,4,5,6,11,12], [2,4,5,7,9,12],[2,4,5,7,11,12],[2,4,6,7,9,10], [2,4,6,8,9,10],[2,4,6,8,9,12],[2,5,6,8,9,10], [2,5,6,8,9,12],[2,5,6,9,10,11],[2,5,6,9,11,12], [2,5,7,9,11,12],[2,5,8,9,10,11],[2,6,7,9,10,12], [2,6,9,10,11,12],[2,7,8,9,10,11],[2,7,9,10,11,12], [3,4,5,7,9,10],[3,4,5,8,10,12],[3,4,6,8,9,12], [3,4,6,8,11,12],[3,4,8,9,10,11],[3,4,8,10,11,12], [3,5,6,7,10,11],[3,5,7,9,10,11],[3,6,7,8,11,12], [3,6,7,10,11,12],[3,7,8,9,10,11],[3,7,8,10,11,12], [4,5,6,7,8,12],[4,5,6,7,9,10],[4,5,6,7,11,12], [4,5,6,8,9,10],[4,6,7,8,11,12],[5,6,7,9,10,11], [5,6,7,9,11,12],[6,7,9,10,11,12]] S3xS2_12^2=[[1,2,3,4,5,6],[1,2,3,4,5,8],[1,2,3,4,6,11], [1,2,3,4,7,8],[1,2,3,4,7,11],[1,2,3,5,6,9], [1,2,3,5,8,12],[1,2,3,5,9,12],[1,2,3,6,7,11], [1,2,3,6,7,12],[1,2,3,6,9,12],[1,2,3,7,8,12], [1,2,4,5,6,10],[1,2,4,5,8,10],[1,2,4,6,9,10], [1,2,4,6,9,11],[1,2,4,7,8,10],[1,2,4,7,9,10], [1,2,4,7,9,12],[1,2,4,7,11,12],[1,2,4,9,11,12], [1,2,5,6,9,10],[1,2,5,7,8,10],[1,2,5,7,8,12], [1,2,5,7,9,10],[1,2,5,7,9,12],[1,2,6,7,11,12], [1,2,6,9,11,12],[1,3,4,5,6,11],[1,3,4,5,8,12], [1,3,4,5,9,11],[1,3,4,5,9,12],[1,3,4,7,8,12], [1,3,4,7,11,12],[1,3,4,9,11,12],[1,3,5,6,9,10], [1,3,5,6,10,11],[1,3,5,9,10,11],[1,3,6,7,11,12], [1,3,6,9,10,12],[1,3,6,10,11,12],[1,3,9,10,11,12], [1,4,5,6,8,10],[1,4,5,6,8,11],[1,4,5,7,8,9], [1,4,5,7,8,12],[1,4,5,7,9,12],[1,4,5,8,9,11], [1,4,6,8,9,10],[1,4,6,8,9,11],[1,4,7,8,9,10], [1,5,6,8,10,11],[1,5,7,8,9,10],[1,5,8,9,10,11], [1,6,8,9,10,11],[1,6,9,10,11,12],[2,3,4,5,6,9], [2,3,4,5,8,12],[2,3,4,5,9,12],[2,3,4,6,9,11], [2,3,4,7,8,10],[2,3,4,7,10,11],[2,3,4,8,10,12], [2,3,4,9,11,12],[2,3,4,10,11,12],[2,3,6,7,8,11], [2,3,6,7,8,12],[2,3,6,8,9,11],[2,3,6,8,9,12], [2,3,7,8,10,11],[2,3,8,9,11,12],[2,3,8,10,11,12], [2,4,5,6,9,10],[2,4,5,7,9,10],[2,4,5,7,9,12], [2,4,5,7,10,12],[2,4,5,8,10,12],[2,4,7,10,11,12], [2,5,7,8,10,11],[2,5,7,8,11,12],[2,5,7,10,11,12], [2,5,8,10,11,12],[2,6,7,8,11,12],[2,6,8,9,11,12], [3,4,5,6,9,11],[3,4,7,8,10,12],[3,4,7,10,11,12], [3,5,6,7,9,10],[3,5,6,7,9,11],[3,5,6,7,10,11], [3,5,7,9,10,11],[3,6,7,8,9,10],[3,6,7,8,9,11], [3,6,7,8,10,12],[3,6,7,10,11,12],[3,6,8,9,10,12], [3,7,8,9,10,11],[3,8,9,10,11,12],[4,5,6,7,8,9], [4,5,6,7,8,12],[4,5,6,7,9,10],[4,5,6,7,10,12], [4,5,6,8,9,11],[4,5,6,8,10,12],[4,6,7,8,9,10], [4,6,7,8,10,12],[5,6,7,8,9,11],[5,6,7,8,11,12], [5,6,7,10,11,12],[5,6,8,10,11,12],[5,7,8,9,10,11], [6,8,9,10,11,12]] S3xS2_12^3=[[1,2,3,4,5,11],[1,2,3,4,5,12],[1,2,3,4,6,7], [1,2,3,4,6,9],[1,2,3,4,7,12],[1,2,3,4,8,9], [1,2,3,4,8,11],[1,2,3,5,10,11],[1,2,3,5,10,12], [1,2,3,6,7,9],[1,2,3,7,9,11],[1,2,3,7,10,11], [1,2,3,7,10,12],[1,2,3,8,9,11],[1,2,4,5,8,11], [1,2,4,5,8,12],[1,2,4,6,7,8],[1,2,4,6,8,9], [1,2,4,7,8,12],[1,2,5,8,11,12],[1,2,5,10,11,12], [1,2,6,7,8,9],[1,2,7,8,9,12],[1,2,7,9,11,12], [1,2,7,10,11,12],[1,2,8,9,11,12],[1,3,4,5,8,11], [1,3,4,5,8,12],[1,3,4,6,7,12],[1,3,4,6,9,12], [1,3,4,8,9,12],[1,3,5,6,7,10],[1,3,5,6,7,11], [1,3,5,6,10,12],[1,3,5,6,11,12],[1,3,5,7,10,11], [1,3,5,8,11,12],[1,3,6,7,9,11],[1,3,6,7,10,12], [1,3,6,9,11,12],[1,3,8,9,11,12],[1,4,6,7,8,10], [1,4,6,7,10,12],[1,4,6,8,9,10],[1,4,6,9,10,12], [1,4,7,8,9,10],[1,4,7,8,9,12],[1,4,7,9,10,12], [1,5,6,7,9,10],[1,5,6,7,9,11],[1,5,6,9,10,11], [1,5,6,10,11,12],[1,5,7,9,10,11],[1,6,7,8,9,10], [1,6,9,10,11,12],[1,7,9,10,11,12],[2,3,4,5,9,10], [2,3,4,5,9,12],[2,3,4,5,10,11],[2,3,4,6,7,9], [2,3,4,7,9,12],[2,3,4,8,9,10],[2,3,4,8,10,11], [2,3,5,8,9,10],[2,3,5,8,9,12],[2,3,5,8,10,12], [2,3,7,9,11,12],[2,3,7,10,11,12],[2,3,8,9,11,12], [2,3,8,10,11,12],[2,4,5,6,7,8],[2,4,5,6,7,9], [2,4,5,6,8,11],[2,4,5,6,9,10],[2,4,5,6,10,11], [2,4,5,7,8,12],[2,4,5,7,9,12],[2,4,6,8,9,10], [2,4,6,8,10,11],[2,5,6,7,8,9],[2,5,6,8,9,10], [2,5,6,8,10,12],[2,5,6,8,11,12],[2,5,6,10,11,12], [2,5,7,8,9,12],[2,6,8,10,11,12],[3,4,5,8,9,10], [3,4,5,8,9,12],[3,4,5,8,10,11],[3,4,6,7,9,12], [3,5,6,7,8,10],[3,5,6,7,8,11],[3,5,6,8,10,12], [3,5,6,8,11,12],[3,5,7,8,10,11],[3,6,7,8,10,11], [3,6,7,9,11,12],[3,6,7,10,11,12],[3,6,8,10,11,12], [4,5,6,7,8,11],[4,5,6,7,9,11],[4,5,6,9,10,11], [4,5,7,8,9,10],[4,5,7,8,9,12],[4,5,7,8,10,11], [4,5,7,9,10,11],[4,6,7,8,10,11],[4,6,7,9,11,12], [4,6,7,10,11,12],[4,6,9,10,11,12],[4,7,9,10,11,12], [5,6,7,8,9,10]] S3xS2_12^4=[[1,2,3,4,5,7],[1,2,3,4,5,10],[1,2,3,4,7,8], [1,2,3,4,8,12],[1,2,3,4,9,10],[1,2,3,4,9,12], [1,2,3,5,7,11],[1,2,3,5,10,11],[1,2,3,7,8,12], [1,2,3,7,11,12],[1,2,3,9,10,12],[1,2,3,10,11,12], [1,2,4,5,7,10],[1,2,4,7,8,9],[1,2,4,7,9,10], [1,2,4,8,9,12],[1,2,5,6,7,10],[1,2,5,6,7,11], [1,2,5,6,10,11],[1,2,6,7,10,11],[1,2,7,8,9,12], [1,2,7,9,10,12],[1,2,7,10,11,12],[1,3,4,5,7,10], [1,3,4,6,8,9],[1,3,4,6,8,12],[1,3,4,6,9,12], [1,3,4,7,8,9],[1,3,4,7,9,10],[1,3,5,6,7,9], [1,3,5,6,7,11],[1,3,5,6,9,11],[1,3,5,7,9,10], [1,3,5,9,10,12],[1,3,5,9,11,12],[1,3,5,10,11,12], [1,3,6,7,8,9],[1,3,6,7,8,12],[1,3,6,7,11,12], [1,3,6,9,11,12],[1,4,6,8,9,11],[1,4,6,8,11,12], [1,4,6,9,11,12],[1,4,8,9,11,12],[1,5,6,7,8,9], [1,5,6,7,8,12],[1,5,6,7,10,12],[1,5,6,8,9,11], [1,5,6,8,10,11],[1,5,6,8,10,12],[1,5,7,8,9,12], [1,5,7,9,10,12],[1,5,8,9,11,12],[1,5,8,10,11,12], [1,6,7,10,11,12],[1,6,8,10,11,12],[2,3,4,5,7,11], [2,3,4,5,8,10],[2,3,4,5,8,11],[2,3,4,6,8,10], [2,3,4,6,8,12],[2,3,4,6,9,10],[2,3,4,6,9,12], [2,3,4,7,8,11],[2,3,5,8,10,11],[2,3,6,8,9,10], [2,3,6,8,9,12],[2,3,7,8,9,10],[2,3,7,8,9,12], [2,3,7,8,10,11],[2,3,7,9,10,12],[2,3,7,10,11,12], [2,4,5,6,7,10],[2,4,5,6,7,11],[2,4,5,6,8,10], [2,4,5,6,8,12],[2,4,5,6,9,11],[2,4,5,6,9,12], [2,4,5,8,9,11],[2,4,5,8,9,12],[2,4,6,7,10,11], [2,4,6,9,10,11],[2,4,7,8,9,11],[2,4,7,9,10,11], [2,5,6,8,9,11],[2,5,6,8,9,12],[2,5,6,8,10,11], [2,6,8,9,10,11],[2,7,8,9,10,11],[3,4,5,7,10,11], [3,4,5,8,10,11],[3,4,6,8,9,10],[3,4,7,8,9,10], [3,4,7,8,10,11],[3,5,6,7,9,12],[3,5,6,7,11,12], [3,5,6,9,11,12],[3,5,7,9,10,12],[3,5,7,10,11,12], [3,6,7,8,9,12],[4,5,6,7,10,12],[4,5,6,7,11,12], [4,5,6,8,10,12],[4,5,6,9,11,12],[4,5,7,10,11,12], [4,5,8,9,11,12],[4,5,8,10,11,12],[4,6,7,10,11,12], [4,6,8,9,10,11],[4,6,8,10,11,12],[4,7,8,9,10,11], [5,6,7,8,9,12]] S3xS2_12^5=[[1,2,3,4,5,7],[1,2,3,4,5,9],[1,2,3,4,7,10], [1,2,3,4,9,10],[1,2,3,5,6,7],[1,2,3,5,6,12], [1,2,3,5,9,12],[1,2,3,6,7,10],[1,2,3,6,8,10], [1,2,3,6,8,11],[1,2,3,6,11,12],[1,2,3,8,9,10], [1,2,3,8,9,12],[1,2,3,8,11,12],[1,2,4,5,7,11], [1,2,4,5,8,9],[1,2,4,5,8,11],[1,2,4,6,8,10], [1,2,4,6,8,11],[1,2,4,6,10,12],[1,2,4,6,11,12], [1,2,4,7,10,12],[1,2,4,7,11,12],[1,2,4,8,9,10], [1,2,5,6,7,12],[1,2,5,7,8,11],[1,2,5,7,8,12], [1,2,5,8,9,12],[1,2,6,7,10,12],[1,2,7,8,11,12], [1,3,4,5,7,11],[1,3,4,5,8,10],[1,3,4,5,8,11], [1,3,4,5,9,10],[1,3,4,6,7,10],[1,3,4,6,7,11], [1,3,4,6,8,10],[1,3,4,6,8,11],[1,3,5,6,7,11], [1,3,5,6,11,12],[1,3,5,8,10,11],[1,3,5,9,10,11], [1,3,5,9,11,12],[1,3,8,9,10,11],[1,3,8,9,11,12], [1,4,5,8,9,10],[1,4,6,7,10,12],[1,4,6,7,11,12], [1,5,6,7,9,11],[1,5,6,7,9,12],[1,5,6,9,11,12], [1,5,7,8,9,11],[1,5,7,8,9,12],[1,5,8,9,10,11], [1,6,7,9,11,12],[1,7,8,9,11,12],[2,3,4,5,7,11], [2,3,4,5,8,9],[2,3,4,5,8,11],[2,3,4,6,7,9], [2,3,4,6,7,11],[2,3,4,6,8,9],[2,3,4,6,8,11], [2,3,4,7,9,10],[2,3,5,6,7,11],[2,3,5,6,11,12], [2,3,5,8,9,12],[2,3,5,8,11,12],[2,3,6,7,9,10], [2,3,6,8,9,10],[2,4,6,7,9,11],[2,4,6,8,9,10], [2,4,6,9,10,11],[2,4,6,10,11,12],[2,4,7,9,10,11], [2,4,7,10,11,12],[2,5,6,7,10,11],[2,5,6,7,10,12], [2,5,6,10,11,12],[2,5,7,8,11,12],[2,5,7,10,11,12], [2,6,7,9,10,11],[3,4,5,8,9,12],[3,4,5,8,10,12], [3,4,5,9,10,12],[3,4,6,7,8,9],[3,4,6,7,8,10], [3,4,7,8,9,12],[3,4,7,8,10,12],[3,4,7,9,10,12], [3,5,8,10,11,12],[3,5,9,10,11,12],[3,6,7,8,9,10], [3,7,8,9,10,12],[3,8,9,10,11,12],[4,5,6,8,9,10], [4,5,6,8,9,12],[4,5,6,8,10,12],[4,5,6,9,10,12], [4,6,7,8,9,12],[4,6,7,8,10,12],[4,6,7,9,11,12], [4,6,9,10,11,12],[4,7,9,10,11,12],[5,6,7,8,9,10], [5,6,7,8,9,12],[5,6,7,8,10,12],[5,6,7,9,10,11], [5,6,9,10,11,12],[5,7,8,9,10,11],[5,7,8,10,11,12], [7,8,9,10,11,12]] S3xS2_12^6=[[1,2,3,4,7,10],[1,2,3,4,7,11],[1,2,3,4,8,10], [1,2,3,4,8,11],[1,2,3,5,7,11],[1,2,3,5,7,12], [1,2,3,5,11,12],[1,2,3,6,8,9],[1,2,3,6,8,10], [1,2,3,6,9,12],[1,2,3,6,10,12],[1,2,3,7,10,12], [1,2,3,8,9,11],[1,2,3,9,11,12],[1,2,4,6,9,10], [1,2,4,6,9,12],[1,2,4,6,10,12],[1,2,4,7,10,12], [1,2,4,7,11,12],[1,2,4,8,10,11],[1,2,4,9,10,11], [1,2,4,9,11,12],[1,2,5,7,11,12],[1,2,6,8,9,10], [1,2,8,9,10,11],[1,3,4,6,7,8],[1,3,4,6,7,11], [1,3,4,6,8,9],[1,3,4,6,9,12],[1,3,4,6,11,12], [1,3,4,7,8,10],[1,3,4,8,9,11],[1,3,4,9,11,12], [1,3,5,6,7,10],[1,3,5,6,7,11],[1,3,5,6,10,12], [1,3,5,6,11,12],[1,3,5,7,10,12],[1,3,6,7,8,10], [1,4,5,6,8,9],[1,4,5,6,8,12],[1,4,5,6,9,10], [1,4,5,6,10,12],[1,4,5,8,9,10],[1,4,5,8,10,12], [1,4,6,7,8,12],[1,4,6,7,11,12],[1,4,7,8,10,12], [1,4,8,9,10,11],[1,5,6,7,8,9],[1,5,6,7,8,12], [1,5,6,7,9,10],[1,5,6,7,11,12],[1,5,7,8,9,10], [1,5,7,8,10,12],[1,6,7,8,9,10],[2,3,4,5,7,9], [2,3,4,5,7,11],[2,3,4,5,8,9],[2,3,4,5,8,11], [2,3,4,6,8,9],[2,3,4,6,8,10],[2,3,4,6,9,12], [2,3,4,6,10,12],[2,3,4,7,9,12],[2,3,4,7,10,12], [2,3,5,7,9,12],[2,3,5,8,9,12],[2,3,5,8,11,12], [2,3,8,9,11,12],[2,4,5,6,8,9],[2,4,5,6,8,10], [2,4,5,6,9,10],[2,4,5,7,9,11],[2,4,5,8,10,11], [2,4,5,9,10,11],[2,4,7,9,11,12],[2,5,6,7,8,9], [2,5,6,7,8,11],[2,5,6,7,9,11],[2,5,6,8,10,11], [2,5,6,9,10,11],[2,5,7,8,9,12],[2,5,7,8,11,12], [2,6,7,8,9,11],[2,6,8,9,10,11],[2,7,8,9,11,12], [3,4,5,7,9,11],[3,4,5,8,9,11],[3,4,6,7,8,10], [3,4,6,7,10,12],[3,4,6,7,11,12],[3,4,7,9,11,12], [3,5,6,7,10,11],[3,5,6,10,11,12],[3,5,7,9,10,11], [3,5,7,9,10,12],[3,5,8,9,11,12],[3,5,9,10,11,12], [3,6,7,10,11,12],[3,7,9,10,11,12],[4,5,6,8,10,12], [4,5,8,9,10,11],[4,6,7,8,10,12],[5,6,7,8,11,12], [5,6,7,9,10,11],[5,6,8,10,11,12],[5,7,8,9,10,12], [5,8,9,10,11,12],[6,7,8,9,10,11],[6,7,8,10,11,12], [7,8,9,10,11,12]] S3xS2_12^7=[[1,2,3,6,7,8],[1,2,3,6,7,10],[1,2,3,6,8,11], [1,2,3,6,10,11],[1,2,3,7,8,10],[1,2,3,8,10,11], [1,2,4,5,8,9],[1,2,4,5,8,10],[1,2,4,5,9,12], [1,2,4,5,10,12],[1,2,4,6,7,8],[1,2,4,6,7,10], [1,2,4,6,8,11],[1,2,4,6,10,11],[1,2,4,7,8,9], [1,2,4,7,9,12],[1,2,4,7,10,12],[1,2,4,8,10,11], [1,2,5,7,8,10],[1,2,5,7,8,12],[1,2,5,7,10,12], [1,2,5,8,9,12],[1,2,7,8,9,12],[1,3,4,5,7,9], [1,3,4,5,7,12],[1,3,4,5,9,12],[1,3,4,7,9,12], [1,3,5,6,9,11],[1,3,5,6,9,12],[1,3,5,6,11,12], [1,3,5,7,9,11],[1,3,5,7,11,12],[1,3,6,7,8,9], [1,3,6,7,9,10],[1,3,6,8,9,12],[1,3,6,8,11,12], [1,3,6,9,10,11],[1,3,7,8,9,12],[1,3,7,8,10,11], [1,3,7,8,11,12],[1,3,7,9,10,11],[1,4,5,7,9,10], [1,4,5,7,10,12],[1,4,5,8,9,10],[1,4,6,7,8,9], [1,4,6,7,9,10],[1,4,6,8,9,10],[1,4,6,8,10,11], [1,5,6,9,11,12],[1,5,7,8,10,11],[1,5,7,8,11,12], [1,5,7,9,10,11],[1,5,8,9,10,11],[1,5,8,9,11,12], [1,6,8,9,10,11],[1,6,8,9,11,12],[2,3,4,5,6,8], [2,3,4,5,6,11],[2,3,4,5,8,10],[2,3,4,5,9,11], [2,3,4,5,9,12],[2,3,4,5,10,12],[2,3,4,6,8,11], [2,3,4,8,10,11],[2,3,4,9,11,12],[2,3,4,10,11,12], [2,3,5,6,8,10],[2,3,5,6,9,11],[2,3,5,6,9,12], [2,3,5,6,10,12],[2,3,6,7,8,10],[2,3,6,9,10,11], [2,3,6,9,10,12],[2,3,9,10,11,12],[2,4,5,6,7,8], [2,4,5,6,7,11],[2,4,5,7,8,9],[2,4,5,7,9,11], [2,4,6,7,10,12],[2,4,6,7,11,12],[2,4,6,10,11,12], [2,4,7,9,11,12],[2,5,6,7,8,10],[2,5,6,7,10,12], [2,5,6,7,11,12],[2,5,6,9,11,12],[2,5,7,8,9,12], [2,5,7,9,11,12],[2,6,9,10,11,12],[3,4,5,6,8,10], [3,4,5,6,10,12],[3,4,5,6,11,12],[3,4,5,7,9,11], [3,4,5,7,11,12],[3,4,6,8,10,12],[3,4,6,8,11,12], [3,4,7,9,11,12],[3,4,8,10,11,12],[3,6,7,8,9,10], [3,6,8,9,10,12],[3,7,8,9,10,11],[3,7,8,9,11,12], [3,8,9,10,11,12],[4,5,6,7,8,10],[4,5,6,7,10,12], [4,5,6,7,11,12],[4,5,7,8,9,10],[4,6,7,8,9,10], [4,6,8,10,11,12],[5,7,8,9,10,11],[5,7,8,9,11,12], [6,8,9,10,11,12]] S3xS2_12^8=[[1,2,3,4,5,8],[1,2,3,4,5,11],[1,2,3,4,8,10], [1,2,3,4,10,11],[1,2,3,5,6,9],[1,2,3,5,6,12], [1,2,3,5,8,9],[1,2,3,5,11,12],[1,2,3,6,7,9], [1,2,3,6,7,11],[1,2,3,6,11,12],[1,2,3,7,8,9], [1,2,3,7,8,10],[1,2,3,7,10,11],[1,2,4,5,8,10], [1,2,4,5,10,11],[1,2,5,6,8,9],[1,2,5,6,8,10], [1,2,5,6,10,12],[1,2,5,7,10,11],[1,2,5,7,10,12], [1,2,5,7,11,12],[1,2,6,7,9,12],[1,2,6,7,11,12], [1,2,6,8,9,12],[1,2,6,8,10,12],[1,2,7,8,9,12], [1,2,7,8,10,12],[1,3,4,5,8,10],[1,3,4,5,10,12], [1,3,4,5,11,12],[1,3,4,10,11,12],[1,3,5,6,8,9], [1,3,5,6,8,10],[1,3,5,6,10,12],[1,3,6,7,8,9], [1,3,6,7,8,10],[1,3,6,7,10,11],[1,3,6,10,11,12], [1,4,5,7,10,11],[1,4,5,7,10,12],[1,4,5,7,11,12], [1,4,6,7,9,11],[1,4,6,7,9,12],[1,4,6,7,11,12], [1,4,6,9,11,12],[1,4,7,9,10,11],[1,4,7,9,10,12], [1,4,9,10,11,12],[1,6,7,8,9,11],[1,6,7,8,10,11], [1,6,8,9,11,12],[1,6,8,10,11,12],[1,7,8,9,10,11], [1,7,8,9,10,12],[1,8,9,10,11,12],[2,3,4,5,8,11], [2,3,4,6,7,8],[2,3,4,6,7,9],[2,3,4,6,8,10], [2,3,4,6,9,10],[2,3,4,7,8,9],[2,3,4,8,9,11], [2,3,4,9,10,11],[2,3,5,6,9,10],[2,3,5,6,10,12], [2,3,5,8,9,11],[2,3,5,9,10,11],[2,3,5,10,11,12], [2,3,6,7,8,10],[2,3,6,7,10,11],[2,3,6,10,11,12], [2,4,5,6,8,9],[2,4,5,6,8,10],[2,4,5,6,9,10], [2,4,5,8,9,11],[2,4,5,9,10,11],[2,4,6,7,8,12], [2,4,6,7,9,12],[2,4,6,8,9,12],[2,4,7,8,9,12], [2,5,7,10,11,12],[2,6,7,8,10,12],[2,6,7,10,11,12], [3,4,5,6,7,8],[3,4,5,6,7,9],[3,4,5,6,8,10], [3,4,5,6,9,10],[3,4,5,7,8,12],[3,4,5,7,9,12], [3,4,5,8,11,12],[3,4,5,9,10,12],[3,4,7,8,9,12], [3,4,8,9,11,12],[3,4,9,10,11,12],[3,5,6,7,8,9], [3,5,7,8,9,12],[3,5,8,9,11,12],[3,5,9,10,11,12], [4,5,6,7,8,11],[4,5,6,7,9,11],[4,5,6,8,9,11], [4,5,7,8,11,12],[4,5,7,9,10,11],[4,5,7,9,10,12], [4,6,7,8,11,12],[4,6,8,9,11,12],[5,6,7,8,9,11], [5,7,8,9,11,12],[5,7,9,10,11,12],[6,7,8,10,11,12], [7,8,9,10,11,12]] S3xS2_12^9=[[1,2,3,4,5,8],[1,2,3,4,5,10],[1,2,3,4,8,11], [1,2,3,4,10,12],[1,2,3,4,11,12],[1,2,3,5,8,10], [1,2,3,6,8,9],[1,2,3,6,8,11],[1,2,3,6,9,11], [1,2,3,7,8,9],[1,2,3,7,8,12],[1,2,3,7,9,11], [1,2,3,7,11,12],[1,2,3,8,10,12],[1,2,4,5,8,12], [1,2,4,5,10,12],[1,2,4,8,11,12],[1,2,5,8,10,12], [1,2,6,7,8,9],[1,2,6,7,8,12],[1,2,6,7,9,11], [1,2,6,7,11,12],[1,2,6,8,11,12],[1,3,4,5,7,10], [1,3,4,5,7,12],[1,3,4,5,8,11],[1,3,4,5,11,12], [1,3,4,7,10,12],[1,3,5,7,8,10],[1,3,5,7,8,11], [1,3,5,7,11,12],[1,3,6,8,9,11],[1,3,7,8,9,11], [1,3,7,8,10,12],[1,4,5,6,7,9],[1,4,5,6,7,12], [1,4,5,6,9,12],[1,4,5,7,9,10],[1,4,5,8,11,12], [1,4,5,9,10,12],[1,4,6,7,9,10],[1,4,6,7,10,12], [1,4,6,9,10,12],[1,5,6,7,9,11],[1,5,6,7,11,12], [1,5,6,9,10,11],[1,5,6,9,10,12],[1,5,6,10,11,12], [1,5,7,8,10,11],[1,5,7,9,10,11],[1,5,8,10,11,12], [1,6,7,8,9,10],[1,6,7,8,10,12],[1,6,8,9,10,11], [1,6,8,10,11,12],[1,7,8,9,10,11],[2,3,4,5,6,8], [2,3,4,5,6,10],[2,3,4,6,8,11],[2,3,4,6,10,11], [2,3,4,9,10,11],[2,3,4,9,10,12],[2,3,4,9,11,12], [2,3,5,6,8,9],[2,3,5,6,9,10],[2,3,5,8,9,12], [2,3,5,8,10,12],[2,3,5,9,10,12],[2,3,6,9,10,11], [2,3,7,8,9,12],[2,3,7,9,11,12],[2,4,5,6,7,9], [2,4,5,6,7,10],[2,4,5,6,8,9],[2,4,5,7,9,10], [2,4,5,8,9,12],[2,4,5,9,10,12],[2,4,6,7,8,9], [2,4,6,7,8,11],[2,4,6,7,10,11],[2,4,7,8,9,11], [2,4,7,9,10,11],[2,4,8,9,11,12],[2,5,6,7,9,11], [2,5,6,7,10,11],[2,5,6,9,10,11],[2,5,7,9,10,11], [2,6,7,8,11,12],[2,7,8,9,11,12],[3,4,5,6,7,10], [3,4,5,6,7,12],[3,4,5,6,8,9],[3,4,5,6,9,12], [3,4,5,8,9,12],[3,4,5,8,11,12],[3,4,6,7,10,12], [3,4,6,8,9,11],[3,4,6,9,10,11],[3,4,6,9,10,12], [3,4,8,9,11,12],[3,5,6,7,10,12],[3,5,6,9,10,12], [3,5,7,8,10,12],[3,5,7,8,11,12],[3,7,8,9,11,12], [4,6,7,8,9,10],[4,6,7,8,10,11],[4,6,8,9,10,11], [4,7,8,9,10,11],[5,6,7,10,11,12],[5,7,8,10,11,12], [6,7,8,10,11,12]] S3xS2_12^10=[[1,2,3,5,6,10],[1,2,3,5,6,11], [1,2,3,5,10,12],[1,2,3,5,11,12],[1,2,3,6,7,8], [1,2,3,6,7,9],[1,2,3,6,8,11],[1,2,3,6,9,10], [1,2,3,7,8,9],[1,2,3,8,9,11],[1,2,3,9,10,11], [1,2,3,10,11,12],[1,2,4,5,7,10],[1,2,4,5,7,11], [1,2,4,5,10,12],[1,2,4,5,11,12],[1,2,4,7,10,11], [1,2,4,10,11,12],[1,2,5,6,7,10],[1,2,5,6,7,11], [1,2,6,7,8,11],[1,2,6,7,9,10],[1,2,7,8,9,11], [1,2,7,9,10,11],[1,3,4,6,7,8],[1,3,4,6,7,9], [1,3,4,6,8,9],[1,3,4,7,8,9],[1,3,5,6,10,11], [1,3,5,10,11,12],[1,3,6,8,9,11],[1,3,6,9,10,11], [1,4,5,7,8,9],[1,4,5,7,8,10],[1,4,5,7,9,12], [1,4,5,7,11,12],[1,4,5,8,9,12],[1,4,5,8,10,12], [1,4,6,7,8,12],[1,4,6,7,9,12],[1,4,6,8,9,12], [1,4,7,8,10,11],[1,4,7,8,11,12],[1,4,8,10,11,12], [1,5,6,7,10,12],[1,5,6,7,11,12],[1,5,6,10,11,12], [1,5,7,8,9,10],[1,5,7,9,10,12],[1,5,8,9,10,12], [1,6,7,8,11,12],[1,6,7,9,10,12],[1,6,8,9,11,12], [1,6,9,10,11,12],[1,7,8,9,10,11],[1,8,9,10,11,12], [2,3,4,5,9,11],[2,3,4,5,9,12],[2,3,4,5,11,12], [2,3,4,6,8,10],[2,3,4,6,8,12],[2,3,4,6,9,10], [2,3,4,6,9,12],[2,3,4,8,10,12],[2,3,4,9,10,11], [2,3,4,10,11,12],[2,3,5,6,8,10],[2,3,5,6,8,11], [2,3,5,8,9,11],[2,3,5,8,9,12],[2,3,5,8,10,12], [2,3,6,7,8,12],[2,3,6,7,9,12],[2,3,7,8,9,12], [2,4,5,6,8,9],[2,4,5,6,8,10],[2,4,5,6,9,11], [2,4,5,6,10,11],[2,4,5,7,10,11],[2,4,5,8,9,12], [2,4,5,8,10,12],[2,4,6,8,9,12],[2,4,6,9,10,11], [2,5,6,7,10,11],[2,5,6,8,9,11],[2,6,7,8,9,11], [2,6,7,8,9,12],[2,6,7,9,10,11],[3,4,5,6,8,9], [3,4,5,6,8,10],[3,4,5,6,9,11],[3,4,5,6,10,11], [3,4,5,7,8,9],[3,4,5,7,8,10],[3,4,5,7,9,12], [3,4,5,7,10,11],[3,4,5,7,11,12],[3,4,6,7,8,12], [3,4,6,7,9,12],[3,4,6,9,10,11],[3,4,7,8,10,12], [3,4,7,10,11,12],[3,5,6,8,9,11],[3,5,7,8,9,12], [3,5,7,8,10,12],[3,5,7,10,11,12],[4,7,8,10,11,12], [5,6,7,10,11,12],[5,7,8,9,10,12],[6,7,8,9,11,12], [6,7,9,10,11,12],[7,8,9,10,11,12]] S3xS2_12^11=[[1,2,3,4,5,8],[1,2,3,4,5,10],[1,2,3,4,6,10], [1,2,3,4,6,12],[1,2,3,4,8,12],[1,2,3,5,8,9], [1,2,3,5,9,10],[1,2,3,6,9,10],[1,2,3,6,9,12], [1,2,3,8,9,12],[1,2,4,5,8,9],[1,2,4,5,9,10], [1,2,4,6,7,10],[1,2,4,6,7,12],[1,2,4,7,8,9], [1,2,4,7,8,11],[1,2,4,7,9,10],[1,2,4,7,11,12], [1,2,4,8,11,12],[1,2,6,7,10,11],[1,2,6,7,11,12], [1,2,6,9,10,12],[1,2,6,10,11,12],[1,2,7,8,9,10], [1,2,7,8,10,11],[1,2,8,9,10,12],[1,2,8,10,11,12], [1,3,4,5,6,7],[1,3,4,5,6,8],[1,3,4,5,7,10], [1,3,4,6,7,10],[1,3,4,6,8,9],[1,3,4,6,9,12], [1,3,4,8,9,12],[1,3,5,6,7,11],[1,3,5,6,8,9], [1,3,5,6,9,11],[1,3,5,7,10,11],[1,3,5,9,10,11], [1,3,6,7,10,11],[1,3,6,9,10,11],[1,4,5,6,7,9], [1,4,5,6,8,9],[1,4,5,7,9,10],[1,4,6,7,9,12], [1,4,7,8,9,12],[1,4,7,8,11,12],[1,5,6,7,9,12], [1,5,6,7,11,12],[1,5,6,9,10,11],[1,5,6,9,10,12], [1,5,6,10,11,12],[1,5,7,9,10,12],[1,5,7,10,11,12], [1,7,8,9,10,12],[1,7,8,10,11,12],[2,3,4,5,8,12], [2,3,4,5,9,10],[2,3,4,5,9,11],[2,3,4,5,11,12], [2,3,4,6,9,10],[2,3,4,6,9,12],[2,3,4,9,11,12], [2,3,5,7,8,11],[2,3,5,7,8,12],[2,3,5,7,11,12], [2,3,5,8,9,11],[2,3,7,8,9,11],[2,3,7,8,9,12], [2,3,7,9,11,12],[2,4,5,8,9,11],[2,4,5,8,11,12], [2,4,6,7,9,10],[2,4,6,7,9,12],[2,4,7,8,9,11], [2,4,7,9,11,12],[2,5,6,7,8,11],[2,5,6,7,8,12], [2,5,6,7,11,12],[2,5,6,8,11,12],[2,6,7,8,10,11], [2,6,7,8,10,12],[2,6,7,9,10,12],[2,6,8,10,11,12], [2,7,8,9,10,12],[3,4,5,6,7,10],[3,4,5,6,8,10], [3,4,5,8,10,12],[3,4,5,9,10,11],[3,4,5,10,11,12], [3,4,6,8,9,11],[3,4,6,8,10,11],[3,4,6,9,10,11], [3,4,8,9,11,12],[3,4,8,10,11,12],[3,5,6,7,8,10], [3,5,6,7,8,11],[3,5,6,8,9,11],[3,5,7,8,10,12], [3,5,7,10,11,12],[3,6,7,8,10,11],[3,7,8,9,11,12], [3,7,8,10,11,12],[4,5,6,7,9,10],[4,5,6,8,9,11], [4,5,6,8,10,11],[4,5,6,9,10,11],[4,5,8,10,11,12], [4,7,8,9,11,12],[5,6,7,8,10,12],[5,6,7,9,10,12], [5,6,8,10,11,12]] S3xS2_12^12=[[1,2,3,5,8,10],[1,2,3,5,8,11], [1,2,3,5,10,12],[1,2,3,5,11,12],[1,2,3,6,7,8], [1,2,3,6,7,9],[1,2,3,6,8,12],[1,2,3,6,9,12], [1,2,3,7,8,11],[1,2,3,7,9,11],[1,2,3,8,10,12], [1,2,3,9,11,12],[1,2,4,6,7,9],[1,2,4,6,7,11], [1,2,4,6,9,11],[1,2,4,7,9,11],[1,2,5,6,8,10], [1,2,5,6,8,11],[1,2,5,6,10,12],[1,2,5,6,11,12], [1,2,6,7,8,11],[1,2,6,8,10,12],[1,2,6,9,11,12], [1,3,4,5,8,10],[1,3,4,5,8,12],[1,3,4,5,10,12], [1,3,4,8,10,12],[1,3,5,6,7,9],[1,3,5,6,7,12], [1,3,5,6,9,11],[1,3,5,6,11,12],[1,3,5,7,8,11], [1,3,5,7,8,12],[1,3,5,7,9,11],[1,3,6,7,8,12], [1,3,6,9,11,12],[1,4,5,7,8,9],[1,4,5,7,8,12], [1,4,5,7,9,10],[1,4,5,7,10,12],[1,4,5,8,9,10], [1,4,6,7,9,10],[1,4,6,7,10,11],[1,4,6,9,10,11], [1,4,7,8,9,11],[1,4,7,8,10,11],[1,4,7,8,10,12], [1,4,8,9,10,11],[1,5,6,7,9,10],[1,5,6,7,10,12], [1,5,6,8,9,10],[1,5,6,8,9,11],[1,5,7,8,9,11], [1,6,7,8,10,11],[1,6,7,8,10,12],[1,6,8,9,10,11], [2,3,4,5,6,8],[2,3,4,5,6,11],[2,3,4,5,8,10], [2,3,4,5,10,11],[2,3,4,6,7,9],[2,3,4,6,7,11], [2,3,4,6,8,12],[2,3,4,6,9,12],[2,3,4,7,9,10], [2,3,4,7,10,11],[2,3,4,8,9,10],[2,3,4,8,9,12], [2,3,5,6,8,11],[2,3,5,10,11,12],[2,3,6,7,8,11], [2,3,7,9,10,11],[2,3,8,9,10,12],[2,3,9,10,11,12], [2,4,5,6,8,12],[2,4,5,6,11,12],[2,4,5,7,9,10], [2,4,5,7,9,12],[2,4,5,7,10,12],[2,4,5,8,9,10], [2,4,5,8,9,12],[2,4,5,10,11,12],[2,4,6,9,11,12], [2,4,7,9,11,12],[2,4,7,10,11,12],[2,5,6,8,10,12], [2,5,7,9,10,12],[2,5,8,9,10,12],[2,7,9,10,11,12], [3,4,5,6,8,12],[3,4,5,6,11,12],[3,4,5,10,11,12], [3,4,6,7,9,10],[3,4,6,7,10,11],[3,4,6,9,10,11], [3,4,6,9,11,12],[3,4,8,9,10,12],[3,4,9,10,11,12], [3,5,6,7,8,11],[3,5,6,7,8,12],[3,5,6,7,9,11], [3,6,7,9,10,11],[4,5,7,8,9,12],[4,7,8,9,11,12], [4,7,8,10,11,12],[4,8,9,10,11,12],[5,6,7,8,9,10], [5,6,7,8,9,11],[5,6,7,8,10,12],[5,7,8,9,10,12], [6,7,8,9,10,11],[7,8,9,10,11,12]] S3xS2_12^13=[[1,2,3,4,6,9],[1,2,3,4,6,10],[1,2,3,4,7,9], [1,2,3,4,7,11],[1,2,3,4,10,11],[1,2,3,6,7,9], [1,2,3,6,7,11],[1,2,3,6,8,10],[1,2,3,6,8,11], [1,2,3,8,10,12],[1,2,3,8,11,12],[1,2,3,10,11,12], [1,2,4,5,6,7],[1,2,4,5,6,9],[1,2,4,5,7,9], [1,2,4,6,7,11],[1,2,4,6,10,11],[1,2,5,6,7,9], [1,2,6,8,10,11],[1,2,8,10,11,12],[1,3,4,6,9,10], [1,3,4,7,9,10],[1,3,4,7,10,11],[1,3,5,6,7,8], [1,3,5,6,7,11],[1,3,5,6,8,11],[1,3,5,7,8,12], [1,3,5,7,10,11],[1,3,5,7,10,12],[1,3,5,8,11,12], [1,3,5,10,11,12],[1,3,6,7,8,9],[1,3,6,8,9,10], [1,3,7,8,9,10],[1,3,7,8,10,12],[1,4,5,6,7,12], [1,4,5,6,9,12],[1,4,5,7,8,9],[1,4,5,7,8,12], [1,4,5,8,9,12],[1,4,6,7,10,11],[1,4,6,7,10,12], [1,4,6,9,10,12],[1,4,7,8,9,12],[1,4,7,9,10,12], [1,5,6,7,8,9],[1,5,6,7,10,11],[1,5,6,7,10,12], [1,5,6,8,9,10],[1,5,6,8,10,11],[1,5,6,9,10,12], [1,5,8,9,10,11],[1,5,8,9,11,12],[1,5,9,10,11,12], [1,7,8,9,10,12],[1,8,9,10,11,12],[2,3,4,5,8,10], [2,3,4,5,8,12],[2,3,4,5,9,11],[2,3,4,5,9,12], [2,3,4,5,10,11],[2,3,4,6,8,10],[2,3,4,6,8,12], [2,3,4,6,9,12],[2,3,4,7,9,11],[2,3,5,8,10,12], [2,3,5,9,11,12],[2,3,5,10,11,12],[2,3,6,7,9,11], [2,3,6,8,11,12],[2,3,6,9,11,12],[2,4,5,6,7,12], [2,4,5,6,9,12],[2,4,5,7,8,9],[2,4,5,7,8,12], [2,4,5,8,9,11],[2,4,5,8,10,11],[2,4,6,7,11,12], [2,4,6,8,10,11],[2,4,6,8,11,12],[2,4,7,8,9,11], [2,4,7,8,11,12],[2,5,6,7,9,12],[2,5,7,8,9,10], [2,5,7,8,10,12],[2,5,7,9,10,12],[2,5,8,9,10,11], [2,5,9,10,11,12],[2,6,7,9,11,12],[2,7,8,9,10,12], [2,7,8,9,11,12],[2,8,9,10,11,12],[3,4,5,8,10,11], [3,4,5,8,11,12],[3,4,5,9,11,12],[3,4,6,7,9,10], [3,4,6,7,9,11],[3,4,6,7,10,11],[3,4,6,8,10,11], [3,4,6,8,11,12],[3,4,6,9,11,12],[3,5,6,7,8,10], [3,5,6,7,10,11],[3,5,6,8,10,11],[3,5,7,8,10,12], [3,6,7,8,9,10],[4,5,8,9,11,12],[4,6,7,9,10,12], [4,6,7,9,11,12],[4,7,8,9,11,12],[5,6,7,8,9,10], [5,6,7,9,10,12]] S3xS2_12^14=[[1,2,3,4,5,9],[1,2,3,4,5,12],[1,2,3,4,9,12], [1,2,3,5,7,8],[1,2,3,5,7,12],[1,2,3,5,8,9], [1,2,3,7,8,10],[1,2,3,7,9,10],[1,2,3,7,9,12], [1,2,3,8,9,10],[1,2,4,5,9,11],[1,2,4,5,10,11], [1,2,4,5,10,12],[1,2,4,6,10,11],[1,2,4,6,10,12], [1,2,4,6,11,12],[1,2,4,9,11,12],[1,2,5,7,8,10], [1,2,5,7,10,12],[1,2,5,8,9,10],[1,2,5,9,10,11], [1,2,6,10,11,12],[1,2,7,9,10,12],[1,2,9,10,11,12], [1,3,4,5,9,12],[1,3,5,6,7,8],[1,3,5,6,7,9], [1,3,5,6,8,9],[1,3,5,7,9,12],[1,3,6,7,8,11], [1,3,6,7,9,10],[1,3,6,7,10,11],[1,3,6,8,9,11], [1,3,6,9,10,11],[1,3,7,8,10,11],[1,3,8,9,10,11], [1,4,5,8,10,11],[1,4,5,8,10,12],[1,4,5,8,11,12], [1,4,5,9,11,12],[1,4,6,7,8,10],[1,4,6,7,8,11], [1,4,6,7,10,11],[1,4,6,8,10,12],[1,4,6,8,11,12], [1,4,7,8,10,11],[1,5,6,7,8,9],[1,5,7,8,9,12], [1,5,7,8,10,12],[1,5,8,9,10,11],[1,5,8,9,11,12], [1,6,7,8,9,12],[1,6,7,8,10,12],[1,6,7,9,10,12], [1,6,8,9,11,12],[1,6,9,10,11,12],[2,3,4,5,6,9], [2,3,4,5,6,12],[2,3,4,6,8,9],[2,3,4,6,8,12], [2,3,4,7,8,9],[2,3,4,7,8,11],[2,3,4,7,9,12], [2,3,4,7,11,12],[2,3,4,8,11,12],[2,3,5,6,7,8], [2,3,5,6,7,11],[2,3,5,6,8,9],[2,3,5,6,11,12], [2,3,5,7,11,12],[2,3,6,7,8,11],[2,3,6,8,11,12], [2,3,7,8,9,10],[2,4,5,6,7,9],[2,4,5,6,7,11], [2,4,5,6,10,11],[2,4,5,6,10,12],[2,4,5,7,9,11], [2,4,6,7,8,9],[2,4,6,7,8,11],[2,4,6,8,11,12], [2,4,7,9,11,12],[2,5,6,7,8,9],[2,5,6,10,11,12], [2,5,7,8,9,10],[2,5,7,9,10,12],[2,5,7,9,11,12], [2,5,9,10,11,12],[3,4,5,6,7,9],[3,4,5,6,7,11], [3,4,5,6,10,11],[3,4,5,6,10,12],[3,4,5,7,9,12], [3,4,5,7,11,12],[3,4,5,10,11,12],[3,4,6,7,9,10], [3,4,6,7,10,11],[3,4,6,8,9,10],[3,4,6,8,10,12], [3,4,7,8,9,10],[3,4,7,8,10,11],[3,4,8,10,11,12], [3,5,6,10,11,12],[3,6,8,9,10,11],[3,6,8,10,11,12], [4,5,7,9,11,12],[4,5,8,10,11,12],[4,6,7,8,9,10], [5,7,8,9,10,12],[5,8,9,10,11,12],[6,7,8,9,10,12], [6,8,9,10,11,12]] S3xS2_12^15=[[1,2,3,4,5,6],[1,2,3,4,5,12],[1,2,3,4,6,10], [1,2,3,4,10,12],[1,2,3,5,6,10],[1,2,3,5,10,12], [1,2,4,5,6,9],[1,2,4,5,9,12],[1,2,4,6,9,10], [1,2,4,9,10,12],[1,2,5,6,7,10],[1,2,5,6,7,11], [1,2,5,6,9,12],[1,2,5,6,11,12],[1,2,5,7,10,11], [1,2,5,10,11,12],[1,2,6,7,9,10],[1,2,6,7,9,11], [1,2,6,9,11,12],[1,2,7,8,9,10],[1,2,7,8,9,11], [1,2,7,8,10,11],[1,2,8,9,10,11],[1,2,9,10,11,12], [1,3,4,5,6,8],[1,3,4,5,8,11],[1,3,4,5,11,12], [1,3,4,6,8,12],[1,3,4,6,10,12],[1,3,4,7,8,11], [1,3,4,7,8,12],[1,3,4,7,11,12],[1,3,5,6,7,8], [1,3,5,6,7,10],[1,3,5,7,8,10],[1,3,5,8,10,11], [1,3,5,10,11,12],[1,3,6,7,8,12],[1,3,6,7,9,10], [1,3,6,7,9,11],[1,3,6,7,11,12],[1,3,6,9,10,11], [1,3,6,10,11,12],[1,3,7,8,9,10],[1,3,7,8,9,11], [1,3,8,9,10,11],[1,4,5,6,8,12],[1,4,5,6,9,12], [1,4,5,7,8,11],[1,4,5,7,8,12],[1,4,5,7,11,12], [1,4,6,9,10,12],[1,5,6,7,8,12],[1,5,6,7,11,12], [1,5,7,8,10,11],[1,6,9,10,11,12],[2,3,4,5,6,8], [2,3,4,5,8,9],[2,3,4,5,9,12],[2,3,4,6,8,12], [2,3,4,6,10,12],[2,3,4,7,8,11],[2,3,4,7,8,12], [2,3,4,7,9,11],[2,3,4,7,9,12],[2,3,4,8,9,11], [2,3,5,6,8,12],[2,3,5,6,10,12],[2,3,5,8,9,12], [2,3,7,8,9,11],[2,3,7,8,9,12],[2,4,5,6,8,9], [2,4,6,7,9,10],[2,4,6,7,9,11],[2,4,6,7,10,11], [2,4,6,8,9,11],[2,4,6,8,10,11],[2,4,6,8,10,12], [2,4,7,8,10,11],[2,4,7,8,10,12],[2,4,7,9,10,12], [2,5,6,7,10,11],[2,5,6,8,9,12],[2,5,6,10,11,12], [2,6,8,9,11,12],[2,6,8,10,11,12],[2,7,8,9,10,12], [2,8,9,10,11,12],[3,4,5,7,9,11],[3,4,5,7,9,12], [3,4,5,7,11,12],[3,4,5,8,9,11],[3,5,6,7,8,12], [3,5,6,7,10,11],[3,5,6,7,11,12],[3,5,6,10,11,12], [3,5,7,8,9,10],[3,5,7,8,9,12],[3,5,7,9,10,11], [3,5,8,9,10,11],[3,6,7,9,10,11],[4,5,6,8,9,12], [4,5,7,8,9,10],[4,5,7,8,9,12],[4,5,7,8,10,11], [4,5,7,9,10,11],[4,5,8,9,10,11],[4,6,7,9,10,11], [4,6,8,9,10,11],[4,6,8,9,10,12],[4,7,8,9,10,12], [6,8,9,10,11,12]] S3xS2_12^16=[[1,2,3,4,6,8],[1,2,3,4,6,12],[1,2,3,4,8,10], [1,2,3,4,10,12],[1,2,3,6,8,12],[1,2,3,8,10,12], [1,2,4,6,8,11],[1,2,4,6,11,12],[1,2,4,8,10,11], [1,2,4,10,11,12],[1,2,5,6,7,9],[1,2,5,6,7,11], [1,2,5,6,8,9],[1,2,5,6,8,11],[1,2,5,7,9,11], [1,2,5,8,9,11],[1,2,6,7,9,12],[1,2,6,7,11,12], [1,2,6,8,9,12],[1,2,7,9,11,12],[1,2,8,9,11,12], [1,2,8,10,11,12],[1,3,4,5,7,8],[1,3,4,5,7,9], [1,3,4,5,8,9],[1,3,4,6,8,9],[1,3,4,6,9,10], [1,3,4,6,10,12],[1,3,4,7,8,10],[1,3,4,7,9,10], [1,3,5,6,7,10],[1,3,5,6,7,11],[1,3,5,6,10,12], [1,3,5,6,11,12],[1,3,5,7,8,10],[1,3,5,7,9,11], [1,3,5,8,9,12],[1,3,5,8,10,12],[1,3,5,9,11,12], [1,3,6,7,9,10],[1,3,6,7,9,11],[1,3,6,8,9,12], [1,3,6,9,11,12],[1,4,5,6,8,9],[1,4,5,6,8,11], [1,4,5,6,9,10],[1,4,5,6,10,12],[1,4,5,6,11,12], [1,4,5,7,8,10],[1,4,5,7,9,10],[1,4,5,8,10,12], [1,4,5,8,11,12],[1,4,8,10,11,12],[1,5,6,7,9,10], [1,5,8,9,11,12],[1,6,7,9,11,12],[2,3,4,5,7,9], [2,3,4,5,7,12],[2,3,4,5,9,10],[2,3,4,5,10,12], [2,3,4,6,8,12],[2,3,4,7,8,11],[2,3,4,7,8,12], [2,3,4,7,9,11],[2,3,4,8,10,11],[2,3,4,9,10,11], [2,3,5,7,9,11],[2,3,5,7,10,11],[2,3,5,7,10,12], [2,3,5,9,10,11],[2,3,7,8,10,11],[2,3,7,8,10,12], [2,4,5,7,9,10],[2,4,5,7,10,12],[2,4,6,7,8,11], [2,4,6,7,8,12],[2,4,6,7,11,12],[2,4,7,9,10,12], [2,4,7,9,11,12],[2,4,9,10,11,12],[2,5,6,7,9,10], [2,5,6,7,10,11],[2,5,6,8,9,11],[2,5,6,9,10,11], [2,6,7,8,9,10],[2,6,7,8,9,12],[2,6,7,8,10,11], [2,6,8,9,10,11],[2,7,8,9,10,12],[2,8,9,10,11,12], [3,4,5,6,8,9],[3,4,5,6,8,12],[3,4,5,6,9,10], [3,4,5,6,10,12],[3,4,5,7,8,12],[3,4,7,8,10,11], [3,4,7,9,10,11],[3,5,6,7,10,11],[3,5,6,8,9,12], [3,5,6,9,10,11],[3,5,6,9,11,12],[3,5,7,8,10,12], [3,6,7,9,10,11],[4,5,6,8,11,12],[4,5,7,8,10,12], [4,6,7,8,11,12],[4,7,8,10,11,12],[4,7,9,10,11,12], [5,6,8,9,11,12],[6,7,8,9,10,11],[6,7,8,9,11,12], [7,8,9,10,11,12]] S3xS2_12^17=[[1,2,3,4,7,9],[1,2,3,4,7,10],[1,2,3,4,9,12], [1,2,3,4,10,12],[1,2,3,5,6,7],[1,2,3,5,6,12], [1,2,3,5,7,9],[1,2,3,5,8,9],[1,2,3,5,8,12], [1,2,3,6,7,10],[1,2,3,6,10,11],[1,2,3,6,11,12], [1,2,3,8,9,12],[1,2,3,10,11,12],[1,2,4,7,9,10], [1,2,4,9,10,12],[1,2,5,6,7,10],[1,2,5,6,8,10], [1,2,5,6,8,11],[1,2,5,6,11,12],[1,2,5,7,9,10], [1,2,5,8,9,10],[1,2,5,8,11,12],[1,2,6,8,10,11], [1,2,8,9,10,12],[1,2,8,10,11,12],[1,3,4,5,7,8], [1,3,4,5,7,9],[1,3,4,5,8,10],[1,3,4,5,9,10], [1,3,4,7,8,10],[1,3,4,9,10,12],[1,3,5,6,7,12], [1,3,5,7,8,12],[1,3,5,8,9,10],[1,3,6,7,8,10], [1,3,6,7,8,12],[1,3,6,8,10,11],[1,3,6,8,11,12], [1,3,8,9,10,12],[1,3,8,10,11,12],[1,4,5,6,8,10], [1,4,5,6,8,11],[1,4,5,6,9,10],[1,4,5,6,9,11], [1,4,5,7,8,11],[1,4,5,7,9,11],[1,4,6,7,8,10], [1,4,6,7,8,11],[1,4,6,7,9,10],[1,4,6,7,9,11], [1,5,6,7,9,10],[1,5,6,7,9,11],[1,5,6,7,11,12], [1,5,7,8,11,12],[1,6,7,8,11,12],[2,3,4,6,9,11], [2,3,4,6,9,12],[2,3,4,6,11,12],[2,3,4,7,9,11], [2,3,4,7,10,11],[2,3,4,10,11,12],[2,3,5,6,7,10], [2,3,5,6,8,10],[2,3,5,6,8,12],[2,3,5,7,9,10], [2,3,5,8,9,10],[2,3,6,8,9,11],[2,3,6,8,9,12], [2,3,6,8,10,11],[2,3,7,9,10,11],[2,3,8,9,10,11], [2,4,5,6,8,11],[2,4,5,6,8,12],[2,4,5,6,11,12], [2,4,5,8,11,12],[2,4,6,8,9,11],[2,4,6,8,9,12], [2,4,7,8,9,11],[2,4,7,8,9,12],[2,4,7,8,11,12], [2,4,7,9,10,12],[2,4,7,10,11,12],[2,7,8,9,11,12], [2,7,9,10,11,12],[2,8,9,10,11,12],[3,4,5,7,8,10], [3,4,5,7,9,11],[3,4,5,7,10,11],[3,4,5,9,10,11], [3,4,6,9,11,12],[3,4,9,10,11,12],[3,5,6,7,8,10], [3,5,6,7,8,12],[3,5,7,9,10,11],[3,6,8,9,11,12], [3,8,9,10,11,12],[4,5,6,7,8,10],[4,5,6,7,8,12], [4,5,6,7,10,12],[4,5,6,9,10,12],[4,5,6,9,11,12], [4,5,7,8,11,12],[4,5,7,10,11,12],[4,5,9,10,11,12], [4,6,7,8,9,11],[4,6,7,8,9,12],[4,6,7,9,10,12], [5,6,7,9,10,12],[5,6,7,9,11,12],[5,7,9,10,11,12], [6,7,8,9,11,12]] S3xS2_12^18=[[1,2,3,6,8,10],[1,2,3,6,8,11], [1,2,3,6,10,11],[1,2,3,7,8,10],[1,2,3,7,8,11], [1,2,3,7,10,11],[1,2,4,5,6,9],[1,2,4,5,6,11], [1,2,4,5,9,12],[1,2,4,5,11,12],[1,2,4,6,8,9], [1,2,4,6,8,11],[1,2,4,8,9,12],[1,2,4,8,10,11], [1,2,4,8,10,12],[1,2,4,10,11,12],[1,2,5,6,8,9], [1,2,5,6,8,10],[1,2,5,6,10,12],[1,2,5,6,11,12], [1,2,5,8,9,10],[1,2,5,9,10,12],[1,2,6,10,11,12], [1,2,7,8,10,11],[1,2,8,9,10,12],[1,3,4,5,6,7], [1,3,4,5,6,9],[1,3,4,5,7,12],[1,3,4,5,9,12], [1,3,4,6,7,9],[1,3,4,7,9,12],[1,3,5,6,7,10], [1,3,5,6,8,9],[1,3,5,6,8,10],[1,3,5,7,8,9], [1,3,5,7,8,10],[1,3,5,7,9,12],[1,3,6,7,9,10], [1,3,6,8,9,11],[1,3,6,9,10,11],[1,3,7,8,9,11], [1,3,7,9,10,11],[1,4,5,6,7,12],[1,4,5,6,11,12], [1,4,6,7,9,12],[1,4,6,8,9,12],[1,4,6,8,11,12], [1,4,8,10,11,12],[1,5,6,7,10,12],[1,5,7,8,9,10], [1,5,7,9,10,12],[1,6,7,9,10,12],[1,6,8,9,11,12], [1,6,9,10,11,12],[1,7,8,9,10,11],[1,8,9,10,11,12], [2,3,4,5,9,11],[2,3,4,5,9,12],[2,3,4,5,11,12], [2,3,4,7,8,10],[2,3,4,7,8,12],[2,3,4,7,9,11], [2,3,4,7,9,12],[2,3,4,7,10,11],[2,3,4,8,10,12], [2,3,4,10,11,12],[2,3,5,7,9,11],[2,3,5,7,9,12], [2,3,5,7,11,12],[2,3,6,8,10,12],[2,3,6,8,11,12], [2,3,6,10,11,12],[2,3,7,8,11,12],[2,4,5,6,7,9], [2,4,5,6,7,11],[2,4,5,7,9,11],[2,4,6,7,8,11], [2,4,6,7,8,12],[2,4,6,7,9,12],[2,4,6,8,9,12], [2,4,7,8,10,11],[2,5,6,7,9,12],[2,5,6,7,11,12], [2,5,6,8,9,10],[2,5,6,9,10,12],[2,6,7,8,11,12], [2,6,8,9,10,12],[3,4,5,6,7,10],[3,4,5,6,9,10], [3,4,5,7,8,10],[3,4,5,7,8,12],[3,4,5,8,10,11], [3,4,5,8,11,12],[3,4,5,9,10,11],[3,4,6,7,9,10], [3,4,7,9,10,11],[3,4,8,10,11,12],[3,5,6,8,9,10], [3,5,7,8,9,11],[3,5,7,8,11,12],[3,5,8,9,10,11], [3,6,8,9,10,11],[3,6,8,10,11,12],[4,5,6,7,9,10], [4,5,6,7,11,12],[4,5,7,8,10,11],[4,5,7,8,11,12], [4,5,7,9,10,11],[4,6,7,8,11,12],[5,6,7,9,10,12], [5,7,8,9,10,11],[6,8,9,10,11,12]] S3xS2_12^19=[[1,2,3,4,6,7],[1,2,3,4,6,11],[1,2,3,4,7,9], [1,2,3,4,9,12],[1,2,3,4,11,12],[1,2,3,5,6,8], [1,2,3,5,6,11],[1,2,3,5,8,10],[1,2,3,5,10,11], [1,2,3,6,7,8],[1,2,3,7,8,10],[1,2,3,7,9,10], [1,2,3,9,10,12],[1,2,3,10,11,12],[1,2,4,6,7,10], [1,2,4,6,10,11],[1,2,4,7,9,10],[1,2,4,9,10,11], [1,2,4,9,11,12],[1,2,5,6,7,8],[1,2,5,6,7,10], [1,2,5,6,10,11],[1,2,5,7,8,10],[1,2,9,10,11,12], [1,3,4,6,7,10],[1,3,4,6,10,12],[1,3,4,6,11,12], [1,3,4,7,9,10],[1,3,4,9,10,12],[1,3,5,6,8,11], [1,3,5,7,8,10],[1,3,5,7,8,11],[1,3,5,7,10,11], [1,3,6,7,8,11],[1,3,6,7,10,12],[1,3,6,7,11,12], [1,3,7,10,11,12],[1,4,5,8,9,11],[1,4,5,8,9,12], [1,4,5,8,11,12],[1,4,5,9,11,12],[1,4,6,8,9,11], [1,4,6,8,9,12],[1,4,6,8,11,12],[1,4,6,9,10,11], [1,4,6,9,10,12],[1,5,6,7,8,12],[1,5,6,7,10,12], [1,5,6,8,9,11],[1,5,6,8,9,12],[1,5,6,9,10,11], [1,5,6,9,10,12],[1,5,7,8,11,12],[1,5,7,10,11,12], [1,5,9,10,11,12],[1,6,7,8,11,12],[2,3,4,5,6,7], [2,3,4,5,6,10],[2,3,4,5,7,9],[2,3,4,5,8,10], [2,3,4,5,8,12],[2,3,4,5,9,12],[2,3,4,6,10,11], [2,3,4,8,10,12],[2,3,4,10,11,12],[2,3,5,6,7,9], [2,3,5,6,8,9],[2,3,5,6,10,11],[2,3,5,8,9,12], [2,3,6,7,8,9],[2,3,7,8,9,10],[2,3,8,9,10,12], [2,4,5,6,7,10],[2,4,5,7,8,10],[2,4,5,7,8,12], [2,4,5,7,9,12],[2,4,7,8,9,10],[2,4,7,8,9,11], [2,4,7,8,11,12],[2,4,7,9,11,12],[2,4,8,9,10,11], [2,4,8,10,11,12],[2,5,6,7,8,12],[2,5,6,7,9,12], [2,5,6,8,9,12],[2,6,7,8,9,12],[2,7,8,9,11,12], [2,8,9,10,11,12],[3,4,5,6,7,10],[3,4,5,7,8,9], [3,4,5,7,8,10],[3,4,5,8,9,12],[3,4,6,10,11,12], [3,4,7,8,9,10],[3,4,8,9,10,12],[3,5,6,7,9,11], [3,5,6,7,10,11],[3,5,6,8,9,11],[3,5,7,8,9,11], [3,6,7,8,9,11],[3,6,7,10,11,12],[4,5,7,8,9,11], [4,5,7,8,11,12],[4,5,7,9,11,12],[4,6,8,9,10,11], [4,6,8,9,10,12],[4,6,8,10,11,12],[5,6,7,9,11,12], [5,6,7,10,11,12],[5,6,9,10,11,12],[6,7,8,9,11,12], [6,8,9,10,11,12]] S3xS2_12^20=[[1,2,3,4,5,10],[1,2,3,4,5,12],[1,2,3,4,6,7], [1,2,3,4,6,10],[1,2,3,4,7,11],[1,2,3,4,11,12], [1,2,3,5,10,12],[1,2,3,6,7,9],[1,2,3,6,9,11], [1,2,3,6,10,12],[1,2,3,6,11,12],[1,2,3,7,9,11], [1,2,4,5,10,11],[1,2,4,5,11,12],[1,2,4,6,7,10], [1,2,4,7,10,11],[1,2,5,8,9,11],[1,2,5,8,9,12], [1,2,5,8,10,11],[1,2,5,8,10,12],[1,2,5,9,11,12], [1,2,6,7,9,10],[1,2,6,9,10,12],[1,2,6,9,11,12], [1,2,7,8,9,10],[1,2,7,8,9,11],[1,2,7,8,10,11], [1,2,8,9,10,12],[1,3,4,5,6,7],[1,3,4,5,6,8], [1,3,4,5,7,12],[1,3,4,5,8,10],[1,3,4,6,8,10], [1,3,4,7,11,12],[1,3,5,6,7,12],[1,3,5,6,8,12], [1,3,5,8,10,12],[1,3,6,7,9,11],[1,3,6,7,11,12], [1,3,6,8,10,12],[1,4,5,6,7,12],[1,4,5,6,8,12], [1,4,5,8,9,10],[1,4,5,8,9,12],[1,4,5,9,10,11], [1,4,5,9,11,12],[1,4,6,7,10,11],[1,4,6,7,11,12], [1,4,6,8,10,12],[1,4,6,10,11,12],[1,4,8,9,10,12], [1,4,9,10,11,12],[1,5,8,9,10,11],[1,6,7,9,10,11], [1,6,9,10,11,12],[1,7,8,9,10,11],[2,3,4,5,10,12], [2,3,4,6,7,9],[2,3,4,6,8,9],[2,3,4,6,8,11], [2,3,4,6,10,12],[2,3,4,6,11,12],[2,3,4,7,8,9], [2,3,4,7,8,11],[2,3,6,8,9,11],[2,3,7,8,9,11], [2,4,5,10,11,12],[2,4,6,7,8,9],[2,4,6,7,8,11], [2,4,6,7,10,11],[2,4,6,10,11,12],[2,5,6,7,8,9], [2,5,6,7,8,11],[2,5,6,7,9,10],[2,5,6,7,10,11], [2,5,6,8,9,11],[2,5,6,9,10,11],[2,5,7,8,9,12], [2,5,7,8,10,11],[2,5,7,8,10,12],[2,5,7,9,10,12], [2,5,9,10,11,12],[2,6,9,10,11,12],[2,7,8,9,10,12], [3,4,5,6,7,9],[3,4,5,6,8,9],[3,4,5,7,9,12], [3,4,5,8,9,10],[3,4,5,9,10,12],[3,4,6,8,10,12], [3,4,6,8,11,12],[3,4,7,8,9,12],[3,4,7,8,11,12], [3,4,8,9,10,12],[3,5,6,7,8,11],[3,5,6,7,8,12], [3,5,6,7,9,11],[3,5,6,8,9,11],[3,5,7,8,10,11], [3,5,7,8,10,12],[3,5,7,9,10,11],[3,5,7,9,10,12], [3,5,8,9,10,11],[3,6,7,8,11,12],[3,7,8,9,10,11], [3,7,8,9,10,12],[4,5,6,7,8,9],[4,5,6,7,8,12], [4,5,7,8,9,12],[4,5,9,10,11,12],[4,6,7,8,11,12], [5,6,7,9,10,11]]