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Identifier
Values
=>
Cc0007;cc-rep
[[1]]=>1 [[1,2]]=>2 [[1],[2]]=>1 [[1,2,3]]=>3 [[1,3],[2]]=>2 [[1,2],[3]]=>2 [[1],[2],[3]]=>1 [[1,2,3,4]]=>4 [[1,3,4],[2]]=>3 [[1,2,4],[3]]=>3 [[1,2,3],[4]]=>3 [[1,3],[2,4]]=>2 [[1,2],[3,4]]=>1 [[1,4],[2],[3]]=>2 [[1,3],[2],[4]]=>1 [[1,2],[3],[4]]=>2 [[1],[2],[3],[4]]=>1 [[1,2,3,4,5]]=>5 [[1,3,4,5],[2]]=>4 [[1,2,4,5],[3]]=>4 [[1,2,3,5],[4]]=>4 [[1,2,3,4],[5]]=>4 [[1,3,5],[2,4]]=>3 [[1,2,5],[3,4]]=>2 [[1,3,4],[2,5]]=>3 [[1,2,4],[3,5]]=>3 [[1,2,3],[4,5]]=>2 [[1,4,5],[2],[3]]=>3 [[1,3,5],[2],[4]]=>2 [[1,2,5],[3],[4]]=>3 [[1,3,4],[2],[5]]=>1 [[1,2,4],[3],[5]]=>2 [[1,2,3],[4],[5]]=>3 [[1,4],[2,5],[3]]=>2 [[1,3],[2,5],[4]]=>1 [[1,2],[3,5],[4]]=>1 [[1,3],[2,4],[5]]=>2 [[1,2],[3,4],[5]]=>1 [[1,5],[2],[3],[4]]=>2 [[1,4],[2],[3],[5]]=>1 [[1,3],[2],[4],[5]]=>1 [[1,2],[3],[4],[5]]=>2 [[1],[2],[3],[4],[5]]=>1 [[1,2,3,4,5,6]]=>6 [[1,3,4,5,6],[2]]=>5 [[1,2,4,5,6],[3]]=>5 [[1,2,3,5,6],[4]]=>5 [[1,2,3,4,6],[5]]=>5 [[1,2,3,4,5],[6]]=>5 [[1,3,5,6],[2,4]]=>4 [[1,2,5,6],[3,4]]=>3 [[1,3,4,6],[2,5]]=>4 [[1,2,4,6],[3,5]]=>4 [[1,2,3,6],[4,5]]=>3 [[1,3,4,5],[2,6]]=>4 [[1,2,4,5],[3,6]]=>4 [[1,2,3,5],[4,6]]=>4 [[1,2,3,4],[5,6]]=>3 [[1,4,5,6],[2],[3]]=>4 [[1,3,5,6],[2],[4]]=>3 [[1,2,5,6],[3],[4]]=>4 [[1,3,4,6],[2],[5]]=>2 [[1,2,4,6],[3],[5]]=>3 [[1,2,3,6],[4],[5]]=>4 [[1,3,4,5],[2],[6]]=>1 [[1,2,4,5],[3],[6]]=>2 [[1,2,3,5],[4],[6]]=>3 [[1,2,3,4],[5],[6]]=>4 [[1,3,5],[2,4,6]]=>3 [[1,2,5],[3,4,6]]=>2 [[1,3,4],[2,5,6]]=>2 [[1,2,4],[3,5,6]]=>1 [[1,2,3],[4,5,6]]=>1 [[1,4,6],[2,5],[3]]=>3 [[1,3,6],[2,5],[4]]=>2 [[1,2,6],[3,5],[4]]=>2 [[1,3,6],[2,4],[5]]=>3 [[1,2,6],[3,4],[5]]=>2 [[1,4,5],[2,6],[3]]=>3 [[1,3,5],[2,6],[4]]=>2 [[1,2,5],[3,6],[4]]=>3 [[1,3,4],[2,6],[5]]=>1 [[1,2,4],[3,6],[5]]=>2 [[1,2,3],[4,6],[5]]=>2 [[1,3,5],[2,4],[6]]=>2 [[1,2,5],[3,4],[6]]=>1 [[1,3,4],[2,5],[6]]=>3 [[1,2,4],[3,5],[6]]=>3 [[1,2,3],[4,5],[6]]=>2 [[1,5,6],[2],[3],[4]]=>3 [[1,4,6],[2],[3],[5]]=>2 [[1,3,6],[2],[4],[5]]=>2 [[1,2,6],[3],[4],[5]]=>3 [[1,4,5],[2],[3],[6]]=>1 [[1,3,5],[2],[4],[6]]=>1 [[1,2,5],[3],[4],[6]]=>2 [[1,3,4],[2],[5],[6]]=>1 [[1,2,4],[3],[5],[6]]=>2 [[1,2,3],[4],[5],[6]]=>3 [[1,4],[2,5],[3,6]]=>2 [[1,3],[2,5],[4,6]]=>1 [[1,2],[3,5],[4,6]]=>1 [[1,3],[2,4],[5,6]]=>1 [[1,2],[3,4],[5,6]]=>1 [[1,5],[2,6],[3],[4]]=>2 [[1,4],[2,6],[3],[5]]=>1 [[1,3],[2,6],[4],[5]]=>1 [[1,2],[3,6],[4],[5]]=>1 [[1,4],[2,5],[3],[6]]=>1 [[1,3],[2,5],[4],[6]]=>1 [[1,2],[3,5],[4],[6]]=>1 [[1,3],[2,4],[5],[6]]=>2 [[1,2],[3,4],[5],[6]]=>1 [[1,6],[2],[3],[4],[5]]=>2 [[1,5],[2],[3],[4],[6]]=>1 [[1,4],[2],[3],[5],[6]]=>1 [[1,3],[2],[4],[5],[6]]=>1 [[1,2],[3],[4],[5],[6]]=>2 [[1],[2],[3],[4],[5],[6]]=>1 [[1,2,3,4,5,6,7]]=>7 [[1,3,4,5,6,7],[2]]=>6 [[1,2,4,5,6,7],[3]]=>6 [[1,2,3,5,6,7],[4]]=>6 [[1,2,3,4,6,7],[5]]=>6 [[1,2,3,4,5,7],[6]]=>6 [[1,2,3,4,5,6],[7]]=>6 [[1,3,5,6,7],[2,4]]=>5 [[1,2,5,6,7],[3,4]]=>4 [[1,3,4,6,7],[2,5]]=>5 [[1,2,4,6,7],[3,5]]=>5 [[1,2,3,6,7],[4,5]]=>4 [[1,3,4,5,7],[2,6]]=>5 [[1,2,4,5,7],[3,6]]=>5 [[1,2,3,5,7],[4,6]]=>5 [[1,2,3,4,7],[5,6]]=>4 [[1,3,4,5,6],[2,7]]=>5 [[1,2,4,5,6],[3,7]]=>5 [[1,2,3,5,6],[4,7]]=>5 [[1,2,3,4,6],[5,7]]=>5 [[1,2,3,4,5],[6,7]]=>4 [[1,4,5,6,7],[2],[3]]=>5 [[1,3,5,6,7],[2],[4]]=>4 [[1,2,5,6,7],[3],[4]]=>5 [[1,3,4,6,7],[2],[5]]=>3 [[1,2,4,6,7],[3],[5]]=>4 [[1,2,3,6,7],[4],[5]]=>5 [[1,3,4,5,7],[2],[6]]=>2 [[1,2,4,5,7],[3],[6]]=>3 [[1,2,3,5,7],[4],[6]]=>4 [[1,2,3,4,7],[5],[6]]=>5 [[1,3,4,5,6],[2],[7]]=>1 [[1,2,4,5,6],[3],[7]]=>2 [[1,2,3,5,6],[4],[7]]=>3 [[1,2,3,4,6],[5],[7]]=>4 [[1,2,3,4,5],[6],[7]]=>5 [[1,3,5,7],[2,4,6]]=>4 [[1,2,5,7],[3,4,6]]=>3 [[1,3,4,7],[2,5,6]]=>3 [[1,2,4,7],[3,5,6]]=>2 [[1,2,3,7],[4,5,6]]=>2 [[1,3,5,6],[2,4,7]]=>4 [[1,2,5,6],[3,4,7]]=>3 [[1,3,4,6],[2,5,7]]=>4 [[1,2,4,6],[3,5,7]]=>4 [[1,2,3,6],[4,5,7]]=>3 [[1,3,4,5],[2,6,7]]=>3 [[1,2,4,5],[3,6,7]]=>3 [[1,2,3,5],[4,6,7]]=>2 [[1,2,3,4],[5,6,7]]=>2 [[1,4,6,7],[2,5],[3]]=>4 [[1,3,6,7],[2,5],[4]]=>3 [[1,2,6,7],[3,5],[4]]=>3 [[1,3,6,7],[2,4],[5]]=>4 [[1,2,6,7],[3,4],[5]]=>3 [[1,4,5,7],[2,6],[3]]=>4 [[1,3,5,7],[2,6],[4]]=>3 [[1,2,5,7],[3,6],[4]]=>4 [[1,3,4,7],[2,6],[5]]=>2 [[1,2,4,7],[3,6],[5]]=>3 [[1,2,3,7],[4,6],[5]]=>3 [[1,3,5,7],[2,4],[6]]=>3 [[1,2,5,7],[3,4],[6]]=>2 [[1,3,4,7],[2,5],[6]]=>4 [[1,2,4,7],[3,5],[6]]=>4 [[1,2,3,7],[4,5],[6]]=>3 [[1,4,5,6],[2,7],[3]]=>4 [[1,3,5,6],[2,7],[4]]=>3 [[1,2,5,6],[3,7],[4]]=>4 [[1,3,4,6],[2,7],[5]]=>2 [[1,2,4,6],[3,7],[5]]=>3 [[1,2,3,6],[4,7],[5]]=>4 [[1,3,4,5],[2,7],[6]]=>1 [[1,2,4,5],[3,7],[6]]=>2 [[1,2,3,5],[4,7],[6]]=>3 [[1,2,3,4],[5,7],[6]]=>3 [[1,3,5,6],[2,4],[7]]=>2 [[1,2,5,6],[3,4],[7]]=>1 [[1,3,4,6],[2,5],[7]]=>3 [[1,2,4,6],[3,5],[7]]=>3 [[1,2,3,6],[4,5],[7]]=>2 [[1,3,4,5],[2,6],[7]]=>4 [[1,2,4,5],[3,6],[7]]=>4 [[1,2,3,5],[4,6],[7]]=>4 [[1,2,3,4],[5,6],[7]]=>3 [[1,5,6,7],[2],[3],[4]]=>4 [[1,4,6,7],[2],[3],[5]]=>3 [[1,3,6,7],[2],[4],[5]]=>3 [[1,2,6,7],[3],[4],[5]]=>4 [[1,4,5,7],[2],[3],[6]]=>2 [[1,3,5,7],[2],[4],[6]]=>2 [[1,2,5,7],[3],[4],[6]]=>3 [[1,3,4,7],[2],[5],[6]]=>2 [[1,2,4,7],[3],[5],[6]]=>3 [[1,2,3,7],[4],[5],[6]]=>4 [[1,4,5,6],[2],[3],[7]]=>1 [[1,3,5,6],[2],[4],[7]]=>1 [[1,2,5,6],[3],[4],[7]]=>2 [[1,3,4,6],[2],[5],[7]]=>1 [[1,2,4,6],[3],[5],[7]]=>2 [[1,2,3,6],[4],[5],[7]]=>3 [[1,3,4,5],[2],[6],[7]]=>1 [[1,2,4,5],[3],[6],[7]]=>2 [[1,2,3,5],[4],[6],[7]]=>3 [[1,2,3,4],[5],[6],[7]]=>4 [[1,4,6],[2,5,7],[3]]=>3 [[1,3,6],[2,5,7],[4]]=>2 [[1,2,6],[3,5,7],[4]]=>2 [[1,3,6],[2,4,7],[5]]=>3 [[1,2,6],[3,4,7],[5]]=>2 [[1,4,5],[2,6,7],[3]]=>2 [[1,3,5],[2,6,7],[4]]=>1 [[1,2,5],[3,6,7],[4]]=>1 [[1,3,4],[2,6,7],[5]]=>1 [[1,2,4],[3,6,7],[5]]=>1 [[1,2,3],[4,6,7],[5]]=>1 [[1,3,5],[2,4,7],[6]]=>2 [[1,2,5],[3,4,7],[6]]=>1 [[1,3,4],[2,5,7],[6]]=>2 [[1,2,4],[3,5,7],[6]]=>1 [[1,2,3],[4,5,7],[6]]=>1 [[1,3,5],[2,4,6],[7]]=>3 [[1,2,5],[3,4,6],[7]]=>2 [[1,3,4],[2,5,6],[7]]=>2 [[1,2,4],[3,5,6],[7]]=>1 [[1,2,3],[4,5,6],[7]]=>1 [[1,4,7],[2,5],[3,6]]=>3 [[1,3,7],[2,5],[4,6]]=>2 [[1,2,7],[3,5],[4,6]]=>2 [[1,3,7],[2,4],[5,6]]=>2 [[1,2,7],[3,4],[5,6]]=>2 [[1,4,6],[2,5],[3,7]]=>2 [[1,3,6],[2,5],[4,7]]=>1 [[1,2,6],[3,5],[4,7]]=>1 [[1,3,6],[2,4],[5,7]]=>1 [[1,2,6],[3,4],[5,7]]=>1 [[1,4,5],[2,6],[3,7]]=>3 [[1,3,5],[2,6],[4,7]]=>2 [[1,2,5],[3,6],[4,7]]=>3 [[1,3,4],[2,6],[5,7]]=>1 [[1,2,4],[3,6],[5,7]]=>2 [[1,2,3],[4,6],[5,7]]=>2 [[1,3,5],[2,4],[6,7]]=>1 [[1,2,5],[3,4],[6,7]]=>1 [[1,3,4],[2,5],[6,7]]=>1 [[1,2,4],[3,5],[6,7]]=>2 [[1,2,3],[4,5],[6,7]]=>2 [[1,5,7],[2,6],[3],[4]]=>3 [[1,4,7],[2,6],[3],[5]]=>2 [[1,3,7],[2,6],[4],[5]]=>2 [[1,2,7],[3,6],[4],[5]]=>2 [[1,4,7],[2,5],[3],[6]]=>2 [[1,3,7],[2,5],[4],[6]]=>2 [[1,2,7],[3,5],[4],[6]]=>2 [[1,3,7],[2,4],[5],[6]]=>3 [[1,2,7],[3,4],[5],[6]]=>2 [[1,5,6],[2,7],[3],[4]]=>3 [[1,4,6],[2,7],[3],[5]]=>2 [[1,3,6],[2,7],[4],[5]]=>2 [[1,2,6],[3,7],[4],[5]]=>3 [[1,4,5],[2,7],[3],[6]]=>1 [[1,3,5],[2,7],[4],[6]]=>1 [[1,2,5],[3,7],[4],[6]]=>2 [[1,3,4],[2,7],[5],[6]]=>1 [[1,2,4],[3,7],[5],[6]]=>2 [[1,2,3],[4,7],[5],[6]]=>2 [[1,4,6],[2,5],[3],[7]]=>1 [[1,3,6],[2,5],[4],[7]]=>1 [[1,2,6],[3,5],[4],[7]]=>1 [[1,3,6],[2,4],[5],[7]]=>2 [[1,2,6],[3,4],[5],[7]]=>1 [[1,4,5],[2,6],[3],[7]]=>1 [[1,3,5],[2,6],[4],[7]]=>1 [[1,2,5],[3,6],[4],[7]]=>2 [[1,3,4],[2,6],[5],[7]]=>1 [[1,2,4],[3,6],[5],[7]]=>2 [[1,2,3],[4,6],[5],[7]]=>2 [[1,3,5],[2,4],[6],[7]]=>2 [[1,2,5],[3,4],[6],[7]]=>1 [[1,3,4],[2,5],[6],[7]]=>3 [[1,2,4],[3,5],[6],[7]]=>3 [[1,2,3],[4,5],[6],[7]]=>2 [[1,6,7],[2],[3],[4],[5]]=>3 [[1,5,7],[2],[3],[4],[6]]=>2 [[1,4,7],[2],[3],[5],[6]]=>2 [[1,3,7],[2],[4],[5],[6]]=>2 [[1,2,7],[3],[4],[5],[6]]=>3 [[1,5,6],[2],[3],[4],[7]]=>1 [[1,4,6],[2],[3],[5],[7]]=>1 [[1,3,6],[2],[4],[5],[7]]=>1 [[1,2,6],[3],[4],[5],[7]]=>2 [[1,4,5],[2],[3],[6],[7]]=>1 [[1,3,5],[2],[4],[6],[7]]=>1 [[1,2,5],[3],[4],[6],[7]]=>2 [[1,3,4],[2],[5],[6],[7]]=>1 [[1,2,4],[3],[5],[6],[7]]=>2 [[1,2,3],[4],[5],[6],[7]]=>3 [[1,5],[2,6],[3,7],[4]]=>2 [[1,4],[2,6],[3,7],[5]]=>1 [[1,3],[2,6],[4,7],[5]]=>1 [[1,2],[3,6],[4,7],[5]]=>1 [[1,4],[2,5],[3,7],[6]]=>1 [[1,3],[2,5],[4,7],[6]]=>1 [[1,2],[3,5],[4,7],[6]]=>1 [[1,3],[2,4],[5,7],[6]]=>1 [[1,2],[3,4],[5,7],[6]]=>1 [[1,4],[2,5],[3,6],[7]]=>2 [[1,3],[2,5],[4,6],[7]]=>1 [[1,2],[3,5],[4,6],[7]]=>1 [[1,3],[2,4],[5,6],[7]]=>1 [[1,2],[3,4],[5,6],[7]]=>1 [[1,6],[2,7],[3],[4],[5]]=>2 [[1,5],[2,7],[3],[4],[6]]=>1 [[1,4],[2,7],[3],[5],[6]]=>1 [[1,3],[2,7],[4],[5],[6]]=>1 [[1,2],[3,7],[4],[5],[6]]=>1 [[1,5],[2,6],[3],[4],[7]]=>1 [[1,4],[2,6],[3],[5],[7]]=>1 [[1,3],[2,6],[4],[5],[7]]=>1 [[1,2],[3,6],[4],[5],[7]]=>1 [[1,4],[2,5],[3],[6],[7]]=>1 [[1,3],[2,5],[4],[6],[7]]=>1 [[1,2],[3,5],[4],[6],[7]]=>1 [[1,3],[2,4],[5],[6],[7]]=>2 [[1,2],[3,4],[5],[6],[7]]=>1 [[1,7],[2],[3],[4],[5],[6]]=>2 [[1,6],[2],[3],[4],[5],[7]]=>1 [[1,5],[2],[3],[4],[6],[7]]=>1 [[1,4],[2],[3],[5],[6],[7]]=>1 [[1,3],[2],[4],[5],[6],[7]]=>1 [[1,2],[3],[4],[5],[6],[7]]=>2 [[1],[2],[3],[4],[5],[6],[7]]=>1 [[1,2,3,4,5,6,7,8]]=>8 [[1,3,4,5,6,7,8],[2]]=>7 [[1,2,4,5,6,7,8],[3]]=>7 [[1,2,3,5,6,7,8],[4]]=>7 [[1,2,3,4,6,7,8],[5]]=>7 [[1,2,3,4,5,7,8],[6]]=>7 [[1,2,3,4,5,6,8],[7]]=>7 [[1,2,3,4,5,6,7],[8]]=>7 [[1,3,5,6,7,8],[2,4]]=>6 [[1,2,5,6,7,8],[3,4]]=>5 [[1,3,4,6,7,8],[2,5]]=>6 [[1,2,4,6,7,8],[3,5]]=>6 [[1,2,3,6,7,8],[4,5]]=>5 [[1,3,4,5,7,8],[2,6]]=>6 [[1,2,4,5,7,8],[3,6]]=>6 [[1,2,3,5,7,8],[4,6]]=>6 [[1,2,3,4,7,8],[5,6]]=>5 [[1,3,4,5,6,8],[2,7]]=>6 [[1,2,4,5,6,8],[3,7]]=>6 [[1,2,3,5,6,8],[4,7]]=>6 [[1,2,3,4,6,8],[5,7]]=>6 [[1,2,3,4,5,8],[6,7]]=>5 [[1,3,4,5,6,7],[2,8]]=>6 [[1,2,4,5,6,7],[3,8]]=>6 [[1,2,3,5,6,7],[4,8]]=>6 [[1,2,3,4,6,7],[5,8]]=>6 [[1,2,3,4,5,7],[6,8]]=>6 [[1,2,3,4,5,6],[7,8]]=>5 [[1,4,5,6,7,8],[2],[3]]=>6 [[1,3,5,6,7,8],[2],[4]]=>5 [[1,2,5,6,7,8],[3],[4]]=>6 [[1,3,4,6,7,8],[2],[5]]=>4 [[1,2,4,6,7,8],[3],[5]]=>5 [[1,2,3,6,7,8],[4],[5]]=>6 [[1,3,4,5,7,8],[2],[6]]=>3 [[1,2,4,5,7,8],[3],[6]]=>4 [[1,2,3,5,7,8],[4],[6]]=>5 [[1,2,3,4,7,8],[5],[6]]=>6 [[1,3,4,5,6,8],[2],[7]]=>2 [[1,2,4,5,6,8],[3],[7]]=>3 [[1,2,3,5,6,8],[4],[7]]=>4 [[1,2,3,4,6,8],[5],[7]]=>5 [[1,2,3,4,5,8],[6],[7]]=>6 [[1,3,4,5,6,7],[2],[8]]=>1 [[1,2,4,5,6,7],[3],[8]]=>2 [[1,2,3,5,6,7],[4],[8]]=>3 [[1,2,3,4,6,7],[5],[8]]=>4 [[1,2,3,4,5,7],[6],[8]]=>5 [[1,2,3,4,5,6],[7],[8]]=>6 [[1,3,5,7,8],[2,4,6]]=>5 [[1,2,5,7,8],[3,4,6]]=>4 [[1,3,4,7,8],[2,5,6]]=>4 [[1,2,4,7,8],[3,5,6]]=>3 [[1,2,3,7,8],[4,5,6]]=>3 [[1,3,5,6,8],[2,4,7]]=>5 [[1,2,5,6,8],[3,4,7]]=>4 [[1,3,4,6,8],[2,5,7]]=>5 [[1,2,4,6,8],[3,5,7]]=>5 [[1,2,3,6,8],[4,5,7]]=>4 [[1,3,4,5,8],[2,6,7]]=>4 [[1,2,4,5,8],[3,6,7]]=>4 [[1,2,3,5,8],[4,6,7]]=>3 [[1,2,3,4,8],[5,6,7]]=>3 [[1,3,5,6,7],[2,4,8]]=>5 [[1,2,5,6,7],[3,4,8]]=>4 [[1,3,4,6,7],[2,5,8]]=>5 [[1,2,4,6,7],[3,5,8]]=>5 [[1,2,3,6,7],[4,5,8]]=>4 [[1,3,4,5,7],[2,6,8]]=>5 [[1,2,4,5,7],[3,6,8]]=>5 [[1,2,3,5,7],[4,6,8]]=>5 [[1,2,3,4,7],[5,6,8]]=>4 [[1,3,4,5,6],[2,7,8]]=>4 [[1,2,4,5,6],[3,7,8]]=>4 [[1,2,3,5,6],[4,7,8]]=>4 [[1,2,3,4,6],[5,7,8]]=>3 [[1,2,3,4,5],[6,7,8]]=>3 [[1,4,6,7,8],[2,5],[3]]=>5 [[1,3,6,7,8],[2,5],[4]]=>4 [[1,2,6,7,8],[3,5],[4]]=>4 [[1,3,6,7,8],[2,4],[5]]=>5 [[1,2,6,7,8],[3,4],[5]]=>4 [[1,4,5,7,8],[2,6],[3]]=>5 [[1,3,5,7,8],[2,6],[4]]=>4 [[1,2,5,7,8],[3,6],[4]]=>5 [[1,3,4,7,8],[2,6],[5]]=>3 [[1,2,4,7,8],[3,6],[5]]=>4 [[1,2,3,7,8],[4,6],[5]]=>4 [[1,3,5,7,8],[2,4],[6]]=>4 [[1,2,5,7,8],[3,4],[6]]=>3 [[1,3,4,7,8],[2,5],[6]]=>5 [[1,2,4,7,8],[3,5],[6]]=>5 [[1,2,3,7,8],[4,5],[6]]=>4 [[1,4,5,6,8],[2,7],[3]]=>5 [[1,3,5,6,8],[2,7],[4]]=>4 [[1,2,5,6,8],[3,7],[4]]=>5 [[1,3,4,6,8],[2,7],[5]]=>3 [[1,2,4,6,8],[3,7],[5]]=>4 [[1,2,3,6,8],[4,7],[5]]=>5 [[1,3,4,5,8],[2,7],[6]]=>2 [[1,2,4,5,8],[3,7],[6]]=>3 [[1,2,3,5,8],[4,7],[6]]=>4 [[1,2,3,4,8],[5,7],[6]]=>4 [[1,3,5,6,8],[2,4],[7]]=>3 [[1,2,5,6,8],[3,4],[7]]=>2 [[1,3,4,6,8],[2,5],[7]]=>4 [[1,2,4,6,8],[3,5],[7]]=>4 [[1,2,3,6,8],[4,5],[7]]=>3 [[1,3,4,5,8],[2,6],[7]]=>5 [[1,2,4,5,8],[3,6],[7]]=>5 [[1,2,3,5,8],[4,6],[7]]=>5 [[1,2,3,4,8],[5,6],[7]]=>4 [[1,4,5,6,7],[2,8],[3]]=>5 [[1,3,5,6,7],[2,8],[4]]=>4 [[1,2,5,6,7],[3,8],[4]]=>5 [[1,3,4,6,7],[2,8],[5]]=>3 [[1,2,4,6,7],[3,8],[5]]=>4 [[1,2,3,6,7],[4,8],[5]]=>5 [[1,3,4,5,7],[2,8],[6]]=>2 [[1,2,4,5,7],[3,8],[6]]=>3 [[1,2,3,5,7],[4,8],[6]]=>4 [[1,2,3,4,7],[5,8],[6]]=>5 [[1,3,4,5,6],[2,8],[7]]=>1 [[1,2,4,5,6],[3,8],[7]]=>2 [[1,2,3,5,6],[4,8],[7]]=>3 [[1,2,3,4,6],[5,8],[7]]=>4 [[1,2,3,4,5],[6,8],[7]]=>4 [[1,3,5,6,7],[2,4],[8]]=>2 [[1,2,5,6,7],[3,4],[8]]=>1 [[1,3,4,6,7],[2,5],[8]]=>3 [[1,2,4,6,7],[3,5],[8]]=>3 [[1,2,3,6,7],[4,5],[8]]=>2 [[1,3,4,5,7],[2,6],[8]]=>4 [[1,2,4,5,7],[3,6],[8]]=>4 [[1,2,3,5,7],[4,6],[8]]=>4 [[1,2,3,4,7],[5,6],[8]]=>3 [[1,3,4,5,6],[2,7],[8]]=>5 [[1,2,4,5,6],[3,7],[8]]=>5 [[1,2,3,5,6],[4,7],[8]]=>5 [[1,2,3,4,6],[5,7],[8]]=>5 [[1,2,3,4,5],[6,7],[8]]=>4 [[1,5,6,7,8],[2],[3],[4]]=>5 [[1,4,6,7,8],[2],[3],[5]]=>4 [[1,3,6,7,8],[2],[4],[5]]=>4 [[1,2,6,7,8],[3],[4],[5]]=>5 [[1,4,5,7,8],[2],[3],[6]]=>3 [[1,3,5,7,8],[2],[4],[6]]=>3 [[1,2,5,7,8],[3],[4],[6]]=>4 [[1,3,4,7,8],[2],[5],[6]]=>3 [[1,2,4,7,8],[3],[5],[6]]=>4 [[1,2,3,7,8],[4],[5],[6]]=>5 [[1,4,5,6,8],[2],[3],[7]]=>2 [[1,3,5,6,8],[2],[4],[7]]=>2 [[1,2,5,6,8],[3],[4],[7]]=>3 [[1,3,4,6,8],[2],[5],[7]]=>2 [[1,2,4,6,8],[3],[5],[7]]=>3 [[1,2,3,6,8],[4],[5],[7]]=>4 [[1,3,4,5,8],[2],[6],[7]]=>2 [[1,2,4,5,8],[3],[6],[7]]=>3 [[1,2,3,5,8],[4],[6],[7]]=>4 [[1,2,3,4,8],[5],[6],[7]]=>5 [[1,4,5,6,7],[2],[3],[8]]=>1 [[1,3,5,6,7],[2],[4],[8]]=>1 [[1,2,5,6,7],[3],[4],[8]]=>2 [[1,3,4,6,7],[2],[5],[8]]=>1 [[1,2,4,6,7],[3],[5],[8]]=>2 [[1,2,3,6,7],[4],[5],[8]]=>3 [[1,3,4,5,7],[2],[6],[8]]=>1 [[1,2,4,5,7],[3],[6],[8]]=>2 [[1,2,3,5,7],[4],[6],[8]]=>3 [[1,2,3,4,7],[5],[6],[8]]=>4 [[1,3,4,5,6],[2],[7],[8]]=>1 [[1,2,4,5,6],[3],[7],[8]]=>2 [[1,2,3,5,6],[4],[7],[8]]=>3 [[1,2,3,4,6],[5],[7],[8]]=>4 [[1,2,3,4,5],[6],[7],[8]]=>5 [[1,3,5,7],[2,4,6,8]]=>4 [[1,2,5,7],[3,4,6,8]]=>3 [[1,3,4,7],[2,5,6,8]]=>3 [[1,2,4,7],[3,5,6,8]]=>2 [[1,2,3,7],[4,5,6,8]]=>2 [[1,3,5,6],[2,4,7,8]]=>3 [[1,2,5,6],[3,4,7,8]]=>2 [[1,3,4,6],[2,5,7,8]]=>2 [[1,2,4,6],[3,5,7,8]]=>1 [[1,2,3,6],[4,5,7,8]]=>1 [[1,3,4,5],[2,6,7,8]]=>2 [[1,2,4,5],[3,6,7,8]]=>1 [[1,2,3,5],[4,6,7,8]]=>1 [[1,2,3,4],[5,6,7,8]]=>1 [[1,4,6,8],[2,5,7],[3]]=>4 [[1,3,6,8],[2,5,7],[4]]=>3 [[1,2,6,8],[3,5,7],[4]]=>3 [[1,3,6,8],[2,4,7],[5]]=>4 [[1,2,6,8],[3,4,7],[5]]=>3 [[1,4,5,8],[2,6,7],[3]]=>3 [[1,3,5,8],[2,6,7],[4]]=>2 [[1,2,5,8],[3,6,7],[4]]=>2 [[1,3,4,8],[2,6,7],[5]]=>2 [[1,2,4,8],[3,6,7],[5]]=>2 [[1,2,3,8],[4,6,7],[5]]=>2 [[1,3,5,8],[2,4,7],[6]]=>3 [[1,2,5,8],[3,4,7],[6]]=>2 [[1,3,4,8],[2,5,7],[6]]=>3 [[1,2,4,8],[3,5,7],[6]]=>2 [[1,2,3,8],[4,5,7],[6]]=>2 [[1,3,5,8],[2,4,6],[7]]=>4 [[1,2,5,8],[3,4,6],[7]]=>3 [[1,3,4,8],[2,5,6],[7]]=>3 [[1,2,4,8],[3,5,6],[7]]=>2 [[1,2,3,8],[4,5,6],[7]]=>2 [[1,4,6,7],[2,5,8],[3]]=>4 [[1,3,6,7],[2,5,8],[4]]=>3 [[1,2,6,7],[3,5,8],[4]]=>3 [[1,3,6,7],[2,4,8],[5]]=>4 [[1,2,6,7],[3,4,8],[5]]=>3 [[1,4,5,7],[2,6,8],[3]]=>4 [[1,3,5,7],[2,6,8],[4]]=>3 [[1,2,5,7],[3,6,8],[4]]=>4 [[1,3,4,7],[2,6,8],[5]]=>2 [[1,2,4,7],[3,6,8],[5]]=>3 [[1,2,3,7],[4,6,8],[5]]=>3 [[1,3,5,7],[2,4,8],[6]]=>3 [[1,2,5,7],[3,4,8],[6]]=>2 [[1,3,4,7],[2,5,8],[6]]=>4 [[1,2,4,7],[3,5,8],[6]]=>4 [[1,2,3,7],[4,5,8],[6]]=>3 [[1,4,5,6],[2,7,8],[3]]=>3 [[1,3,5,6],[2,7,8],[4]]=>2 [[1,2,5,6],[3,7,8],[4]]=>3 [[1,3,4,6],[2,7,8],[5]]=>1 [[1,2,4,6],[3,7,8],[5]]=>2 [[1,2,3,6],[4,7,8],[5]]=>2 [[1,3,4,5],[2,7,8],[6]]=>1 [[1,2,4,5],[3,7,8],[6]]=>2 [[1,2,3,5],[4,7,8],[6]]=>2 [[1,2,3,4],[5,7,8],[6]]=>2 [[1,3,5,6],[2,4,8],[7]]=>2 [[1,2,5,6],[3,4,8],[7]]=>1 [[1,3,4,6],[2,5,8],[7]]=>3 [[1,2,4,6],[3,5,8],[7]]=>3 [[1,2,3,6],[4,5,8],[7]]=>2 [[1,3,4,5],[2,6,8],[7]]=>3 [[1,2,4,5],[3,6,8],[7]]=>3 [[1,2,3,5],[4,6,8],[7]]=>2 [[1,2,3,4],[5,6,8],[7]]=>2 [[1,3,5,7],[2,4,6],[8]]=>3 [[1,2,5,7],[3,4,6],[8]]=>2 [[1,3,4,7],[2,5,6],[8]]=>2 [[1,2,4,7],[3,5,6],[8]]=>1 [[1,2,3,7],[4,5,6],[8]]=>1 [[1,3,5,6],[2,4,7],[8]]=>4 [[1,2,5,6],[3,4,7],[8]]=>3 [[1,3,4,6],[2,5,7],[8]]=>4 [[1,2,4,6],[3,5,7],[8]]=>4 [[1,2,3,6],[4,5,7],[8]]=>3 [[1,3,4,5],[2,6,7],[8]]=>3 [[1,2,4,5],[3,6,7],[8]]=>3 [[1,2,3,5],[4,6,7],[8]]=>2 [[1,2,3,4],[5,6,7],[8]]=>2 [[1,4,7,8],[2,5],[3,6]]=>4 [[1,3,7,8],[2,5],[4,6]]=>3 [[1,2,7,8],[3,5],[4,6]]=>3 [[1,3,7,8],[2,4],[5,6]]=>3 [[1,2,7,8],[3,4],[5,6]]=>3 [[1,4,6,8],[2,5],[3,7]]=>3 [[1,3,6,8],[2,5],[4,7]]=>2 [[1,2,6,8],[3,5],[4,7]]=>2 [[1,3,6,8],[2,4],[5,7]]=>2 [[1,2,6,8],[3,4],[5,7]]=>2 [[1,4,5,8],[2,6],[3,7]]=>4 [[1,3,5,8],[2,6],[4,7]]=>3 [[1,2,5,8],[3,6],[4,7]]=>4 [[1,3,4,8],[2,6],[5,7]]=>2 [[1,2,4,8],[3,6],[5,7]]=>3 [[1,2,3,8],[4,6],[5,7]]=>3 [[1,3,5,8],[2,4],[6,7]]=>2 [[1,2,5,8],[3,4],[6,7]]=>2 [[1,3,4,8],[2,5],[6,7]]=>2 [[1,2,4,8],[3,5],[6,7]]=>3 [[1,2,3,8],[4,5],[6,7]]=>3 [[1,4,6,7],[2,5],[3,8]]=>2 [[1,3,6,7],[2,5],[4,8]]=>1 [[1,2,6,7],[3,5],[4,8]]=>1 [[1,3,6,7],[2,4],[5,8]]=>1 [[1,2,6,7],[3,4],[5,8]]=>1 [[1,4,5,7],[2,6],[3,8]]=>3 [[1,3,5,7],[2,6],[4,8]]=>2 [[1,2,5,7],[3,6],[4,8]]=>3 [[1,3,4,7],[2,6],[5,8]]=>1 [[1,2,4,7],[3,6],[5,8]]=>2 [[1,2,3,7],[4,6],[5,8]]=>2 [[1,3,5,7],[2,4],[6,8]]=>1 [[1,2,5,7],[3,4],[6,8]]=>1 [[1,3,4,7],[2,5],[6,8]]=>1 [[1,2,4,7],[3,5],[6,8]]=>2 [[1,2,3,7],[4,5],[6,8]]=>2 [[1,4,5,6],[2,7],[3,8]]=>4 [[1,3,5,6],[2,7],[4,8]]=>3 [[1,2,5,6],[3,7],[4,8]]=>4 [[1,3,4,6],[2,7],[5,8]]=>2 [[1,2,4,6],[3,7],[5,8]]=>3 [[1,2,3,6],[4,7],[5,8]]=>4 [[1,3,4,5],[2,7],[6,8]]=>1 [[1,2,4,5],[3,7],[6,8]]=>2 [[1,2,3,5],[4,7],[6,8]]=>3 [[1,2,3,4],[5,7],[6,8]]=>3 [[1,3,5,6],[2,4],[7,8]]=>1 [[1,2,5,6],[3,4],[7,8]]=>1 [[1,3,4,6],[2,5],[7,8]]=>1 [[1,2,4,6],[3,5],[7,8]]=>2 [[1,2,3,6],[4,5],[7,8]]=>2 [[1,3,4,5],[2,6],[7,8]]=>1 [[1,2,4,5],[3,6],[7,8]]=>2 [[1,2,3,5],[4,6],[7,8]]=>3 [[1,2,3,4],[5,6],[7,8]]=>3 [[1,5,7,8],[2,6],[3],[4]]=>4 [[1,4,7,8],[2,6],[3],[5]]=>3 [[1,3,7,8],[2,6],[4],[5]]=>3 [[1,2,7,8],[3,6],[4],[5]]=>3 [[1,4,7,8],[2,5],[3],[6]]=>3 [[1,3,7,8],[2,5],[4],[6]]=>3 [[1,2,7,8],[3,5],[4],[6]]=>3 [[1,3,7,8],[2,4],[5],[6]]=>4 [[1,2,7,8],[3,4],[5],[6]]=>3 [[1,5,6,8],[2,7],[3],[4]]=>4 [[1,4,6,8],[2,7],[3],[5]]=>3 [[1,3,6,8],[2,7],[4],[5]]=>3 [[1,2,6,8],[3,7],[4],[5]]=>4 [[1,4,5,8],[2,7],[3],[6]]=>2 [[1,3,5,8],[2,7],[4],[6]]=>2 [[1,2,5,8],[3,7],[4],[6]]=>3 [[1,3,4,8],[2,7],[5],[6]]=>2 [[1,2,4,8],[3,7],[5],[6]]=>3 [[1,2,3,8],[4,7],[5],[6]]=>3 [[1,4,6,8],[2,5],[3],[7]]=>2 [[1,3,6,8],[2,5],[4],[7]]=>2 [[1,2,6,8],[3,5],[4],[7]]=>2 [[1,3,6,8],[2,4],[5],[7]]=>3 [[1,2,6,8],[3,4],[5],[7]]=>2 [[1,4,5,8],[2,6],[3],[7]]=>2 [[1,3,5,8],[2,6],[4],[7]]=>2 [[1,2,5,8],[3,6],[4],[7]]=>3 [[1,3,4,8],[2,6],[5],[7]]=>2 [[1,2,4,8],[3,6],[5],[7]]=>3 [[1,2,3,8],[4,6],[5],[7]]=>3 [[1,3,5,8],[2,4],[6],[7]]=>3 [[1,2,5,8],[3,4],[6],[7]]=>2 [[1,3,4,8],[2,5],[6],[7]]=>4 [[1,2,4,8],[3,5],[6],[7]]=>4 [[1,2,3,8],[4,5],[6],[7]]=>3 [[1,5,6,7],[2,8],[3],[4]]=>4 [[1,4,6,7],[2,8],[3],[5]]=>3 [[1,3,6,7],[2,8],[4],[5]]=>3 [[1,2,6,7],[3,8],[4],[5]]=>4 [[1,4,5,7],[2,8],[3],[6]]=>2 [[1,3,5,7],[2,8],[4],[6]]=>2 [[1,2,5,7],[3,8],[4],[6]]=>3 [[1,3,4,7],[2,8],[5],[6]]=>2 [[1,2,4,7],[3,8],[5],[6]]=>3 [[1,2,3,7],[4,8],[5],[6]]=>4 [[1,4,5,6],[2,8],[3],[7]]=>1 [[1,3,5,6],[2,8],[4],[7]]=>1 [[1,2,5,6],[3,8],[4],[7]]=>2 [[1,3,4,6],[2,8],[5],[7]]=>1 [[1,2,4,6],[3,8],[5],[7]]=>2 [[1,2,3,6],[4,8],[5],[7]]=>3 [[1,3,4,5],[2,8],[6],[7]]=>1 [[1,2,4,5],[3,8],[6],[7]]=>2 [[1,2,3,5],[4,8],[6],[7]]=>3 [[1,2,3,4],[5,8],[6],[7]]=>3 [[1,4,6,7],[2,5],[3],[8]]=>1 [[1,3,6,7],[2,5],[4],[8]]=>1 [[1,2,6,7],[3,5],[4],[8]]=>1 [[1,3,6,7],[2,4],[5],[8]]=>2 [[1,2,6,7],[3,4],[5],[8]]=>1 [[1,4,5,7],[2,6],[3],[8]]=>1 [[1,3,5,7],[2,6],[4],[8]]=>1 [[1,2,5,7],[3,6],[4],[8]]=>2 [[1,3,4,7],[2,6],[5],[8]]=>1 [[1,2,4,7],[3,6],[5],[8]]=>2 [[1,2,3,7],[4,6],[5],[8]]=>2 [[1,3,5,7],[2,4],[6],[8]]=>2 [[1,2,5,7],[3,4],[6],[8]]=>1 [[1,3,4,7],[2,5],[6],[8]]=>3 [[1,2,4,7],[3,5],[6],[8]]=>3 [[1,2,3,7],[4,5],[6],[8]]=>2 [[1,4,5,6],[2,7],[3],[8]]=>1 [[1,3,5,6],[2,7],[4],[8]]=>1 [[1,2,5,6],[3,7],[4],[8]]=>2 [[1,3,4,6],[2,7],[5],[8]]=>1 [[1,2,4,6],[3,7],[5],[8]]=>2 [[1,2,3,6],[4,7],[5],[8]]=>3 [[1,3,4,5],[2,7],[6],[8]]=>1 [[1,2,4,5],[3,7],[6],[8]]=>2 [[1,2,3,5],[4,7],[6],[8]]=>3 [[1,2,3,4],[5,7],[6],[8]]=>3 [[1,3,5,6],[2,4],[7],[8]]=>2 [[1,2,5,6],[3,4],[7],[8]]=>1 [[1,3,4,6],[2,5],[7],[8]]=>3 [[1,2,4,6],[3,5],[7],[8]]=>3 [[1,2,3,6],[4,5],[7],[8]]=>2 [[1,3,4,5],[2,6],[7],[8]]=>4 [[1,2,4,5],[3,6],[7],[8]]=>4 [[1,2,3,5],[4,6],[7],[8]]=>4 [[1,2,3,4],[5,6],[7],[8]]=>3 [[1,6,7,8],[2],[3],[4],[5]]=>4 [[1,5,7,8],[2],[3],[4],[6]]=>3 [[1,4,7,8],[2],[3],[5],[6]]=>3 [[1,3,7,8],[2],[4],[5],[6]]=>3 [[1,2,7,8],[3],[4],[5],[6]]=>4 [[1,5,6,8],[2],[3],[4],[7]]=>2 [[1,4,6,8],[2],[3],[5],[7]]=>2 [[1,3,6,8],[2],[4],[5],[7]]=>2 [[1,2,6,8],[3],[4],[5],[7]]=>3 [[1,4,5,8],[2],[3],[6],[7]]=>2 [[1,3,5,8],[2],[4],[6],[7]]=>2 [[1,2,5,8],[3],[4],[6],[7]]=>3 [[1,3,4,8],[2],[5],[6],[7]]=>2 [[1,2,4,8],[3],[5],[6],[7]]=>3 [[1,2,3,8],[4],[5],[6],[7]]=>4 [[1,5,6,7],[2],[3],[4],[8]]=>1 [[1,4,6,7],[2],[3],[5],[8]]=>1 [[1,3,6,7],[2],[4],[5],[8]]=>1 [[1,2,6,7],[3],[4],[5],[8]]=>2 [[1,4,5,7],[2],[3],[6],[8]]=>1 [[1,3,5,7],[2],[4],[6],[8]]=>1 [[1,2,5,7],[3],[4],[6],[8]]=>2 [[1,3,4,7],[2],[5],[6],[8]]=>1 [[1,2,4,7],[3],[5],[6],[8]]=>2 [[1,2,3,7],[4],[5],[6],[8]]=>3 [[1,4,5,6],[2],[3],[7],[8]]=>1 [[1,3,5,6],[2],[4],[7],[8]]=>1 [[1,2,5,6],[3],[4],[7],[8]]=>2 [[1,3,4,6],[2],[5],[7],[8]]=>1 [[1,2,4,6],[3],[5],[7],[8]]=>2 [[1,2,3,6],[4],[5],[7],[8]]=>3 [[1,3,4,5],[2],[6],[7],[8]]=>1 [[1,2,4,5],[3],[6],[7],[8]]=>2 [[1,2,3,5],[4],[6],[7],[8]]=>3 [[1,2,3,4],[5],[6],[7],[8]]=>4 [[1,4,7],[2,5,8],[3,6]]=>3 [[1,3,7],[2,5,8],[4,6]]=>2 [[1,2,7],[3,5,8],[4,6]]=>2 [[1,3,7],[2,4,8],[5,6]]=>2 [[1,2,7],[3,4,8],[5,6]]=>2 [[1,4,6],[2,5,8],[3,7]]=>2 [[1,3,6],[2,5,8],[4,7]]=>1 [[1,2,6],[3,5,8],[4,7]]=>1 [[1,3,6],[2,4,8],[5,7]]=>1 [[1,2,6],[3,4,8],[5,7]]=>1 [[1,4,5],[2,6,8],[3,7]]=>2 [[1,3,5],[2,6,8],[4,7]]=>1 [[1,2,5],[3,6,8],[4,7]]=>1 [[1,3,4],[2,6,8],[5,7]]=>1 [[1,2,4],[3,6,8],[5,7]]=>1 [[1,2,3],[4,6,8],[5,7]]=>1 [[1,3,5],[2,4,8],[6,7]]=>1 [[1,2,5],[3,4,8],[6,7]]=>1 [[1,3,4],[2,5,8],[6,7]]=>1 [[1,2,4],[3,5,8],[6,7]]=>1 [[1,2,3],[4,5,8],[6,7]]=>1 [[1,4,6],[2,5,7],[3,8]]=>3 [[1,3,6],[2,5,7],[4,8]]=>2 [[1,2,6],[3,5,7],[4,8]]=>2 [[1,3,6],[2,4,7],[5,8]]=>3 [[1,2,6],[3,4,7],[5,8]]=>2 [[1,4,5],[2,6,7],[3,8]]=>2 [[1,3,5],[2,6,7],[4,8]]=>1 [[1,2,5],[3,6,7],[4,8]]=>1 [[1,3,4],[2,6,7],[5,8]]=>1 [[1,2,4],[3,6,7],[5,8]]=>1 [[1,2,3],[4,6,7],[5,8]]=>1 [[1,3,5],[2,4,7],[6,8]]=>2 [[1,2,5],[3,4,7],[6,8]]=>1 [[1,3,4],[2,5,7],[6,8]]=>2 [[1,2,4],[3,5,7],[6,8]]=>1 [[1,2,3],[4,5,7],[6,8]]=>1 [[1,3,5],[2,4,6],[7,8]]=>2 [[1,2,5],[3,4,6],[7,8]]=>1 [[1,3,4],[2,5,6],[7,8]]=>2 [[1,2,4],[3,5,6],[7,8]]=>1 [[1,2,3],[4,5,6],[7,8]]=>1 [[1,5,7],[2,6,8],[3],[4]]=>3 [[1,4,7],[2,6,8],[3],[5]]=>2 [[1,3,7],[2,6,8],[4],[5]]=>2 [[1,2,7],[3,6,8],[4],[5]]=>2 [[1,4,7],[2,5,8],[3],[6]]=>2 [[1,3,7],[2,5,8],[4],[6]]=>2 [[1,2,7],[3,5,8],[4],[6]]=>2 [[1,3,7],[2,4,8],[5],[6]]=>3 [[1,2,7],[3,4,8],[5],[6]]=>2 [[1,5,6],[2,7,8],[3],[4]]=>2 [[1,4,6],[2,7,8],[3],[5]]=>1 [[1,3,6],[2,7,8],[4],[5]]=>1 [[1,2,6],[3,7,8],[4],[5]]=>1 [[1,4,5],[2,7,8],[3],[6]]=>1 [[1,3,5],[2,7,8],[4],[6]]=>1 [[1,2,5],[3,7,8],[4],[6]]=>1 [[1,3,4],[2,7,8],[5],[6]]=>1 [[1,2,4],[3,7,8],[5],[6]]=>1 [[1,2,3],[4,7,8],[5],[6]]=>1 [[1,4,6],[2,5,8],[3],[7]]=>1 [[1,3,6],[2,5,8],[4],[7]]=>1 [[1,2,6],[3,5,8],[4],[7]]=>1 [[1,3,6],[2,4,8],[5],[7]]=>2 [[1,2,6],[3,4,8],[5],[7]]=>1 [[1,4,5],[2,6,8],[3],[7]]=>1 [[1,3,5],[2,6,8],[4],[7]]=>1 [[1,2,5],[3,6,8],[4],[7]]=>1 [[1,3,4],[2,6,8],[5],[7]]=>1 [[1,2,4],[3,6,8],[5],[7]]=>1 [[1,2,3],[4,6,8],[5],[7]]=>1 [[1,3,5],[2,4,8],[6],[7]]=>2 [[1,2,5],[3,4,8],[6],[7]]=>1 [[1,3,4],[2,5,8],[6],[7]]=>2 [[1,2,4],[3,5,8],[6],[7]]=>1 [[1,2,3],[4,5,8],[6],[7]]=>1 [[1,4,6],[2,5,7],[3],[8]]=>1 [[1,3,6],[2,5,7],[4],[8]]=>1 [[1,2,6],[3,5,7],[4],[8]]=>1 [[1,3,6],[2,4,7],[5],[8]]=>2 [[1,2,6],[3,4,7],[5],[8]]=>1 [[1,4,5],[2,6,7],[3],[8]]=>1 [[1,3,5],[2,6,7],[4],[8]]=>1 [[1,2,5],[3,6,7],[4],[8]]=>1 [[1,3,4],[2,6,7],[5],[8]]=>1 [[1,2,4],[3,6,7],[5],[8]]=>1 [[1,2,3],[4,6,7],[5],[8]]=>1 [[1,3,5],[2,4,7],[6],[8]]=>2 [[1,2,5],[3,4,7],[6],[8]]=>1 [[1,3,4],[2,5,7],[6],[8]]=>2 [[1,2,4],[3,5,7],[6],[8]]=>1 [[1,2,3],[4,5,7],[6],[8]]=>1 [[1,3,5],[2,4,6],[7],[8]]=>3 [[1,2,5],[3,4,6],[7],[8]]=>2 [[1,3,4],[2,5,6],[7],[8]]=>2 [[1,2,4],[3,5,6],[7],[8]]=>1 [[1,2,3],[4,5,6],[7],[8]]=>1 [[1,5,8],[2,6],[3,7],[4]]=>3 [[1,4,8],[2,6],[3,7],[5]]=>2 [[1,3,8],[2,6],[4,7],[5]]=>2 [[1,2,8],[3,6],[4,7],[5]]=>2 [[1,4,8],[2,5],[3,7],[6]]=>2 [[1,3,8],[2,5],[4,7],[6]]=>2 [[1,2,8],[3,5],[4,7],[6]]=>2 [[1,3,8],[2,4],[5,7],[6]]=>2 [[1,2,8],[3,4],[5,7],[6]]=>2 [[1,4,8],[2,5],[3,6],[7]]=>3 [[1,3,8],[2,5],[4,6],[7]]=>2 [[1,2,8],[3,5],[4,6],[7]]=>2 [[1,3,8],[2,4],[5,6],[7]]=>2 [[1,2,8],[3,4],[5,6],[7]]=>2 [[1,5,7],[2,6],[3,8],[4]]=>2 [[1,4,7],[2,6],[3,8],[5]]=>1 [[1,3,7],[2,6],[4,8],[5]]=>1 [[1,2,7],[3,6],[4,8],[5]]=>1 [[1,4,7],[2,5],[3,8],[6]]=>1 [[1,3,7],[2,5],[4,8],[6]]=>1 [[1,2,7],[3,5],[4,8],[6]]=>1 [[1,3,7],[2,4],[5,8],[6]]=>1 [[1,2,7],[3,4],[5,8],[6]]=>1 [[1,5,6],[2,7],[3,8],[4]]=>3 [[1,4,6],[2,7],[3,8],[5]]=>2 [[1,3,6],[2,7],[4,8],[5]]=>2 [[1,2,6],[3,7],[4,8],[5]]=>3 [[1,4,5],[2,7],[3,8],[6]]=>1 [[1,3,5],[2,7],[4,8],[6]]=>1 [[1,2,5],[3,7],[4,8],[6]]=>2 [[1,3,4],[2,7],[5,8],[6]]=>1 [[1,2,4],[3,7],[5,8],[6]]=>2 [[1,2,3],[4,7],[5,8],[6]]=>2 [[1,4,6],[2,5],[3,8],[7]]=>1 [[1,3,6],[2,5],[4,8],[7]]=>1 [[1,2,6],[3,5],[4,8],[7]]=>1 [[1,3,6],[2,4],[5,8],[7]]=>1 [[1,2,6],[3,4],[5,8],[7]]=>1 [[1,4,5],[2,6],[3,8],[7]]=>1 [[1,3,5],[2,6],[4,8],[7]]=>1 [[1,2,5],[3,6],[4,8],[7]]=>2 [[1,3,4],[2,6],[5,8],[7]]=>1 [[1,2,4],[3,6],[5,8],[7]]=>2 [[1,2,3],[4,6],[5,8],[7]]=>2 [[1,3,5],[2,4],[6,8],[7]]=>1 [[1,2,5],[3,4],[6,8],[7]]=>1 [[1,3,4],[2,5],[6,8],[7]]=>1 [[1,2,4],[3,5],[6,8],[7]]=>2 [[1,2,3],[4,5],[6,8],[7]]=>2 [[1,4,7],[2,5],[3,6],[8]]=>2 [[1,3,7],[2,5],[4,6],[8]]=>1 [[1,2,7],[3,5],[4,6],[8]]=>1 [[1,3,7],[2,4],[5,6],[8]]=>1 [[1,2,7],[3,4],[5,6],[8]]=>1 [[1,4,6],[2,5],[3,7],[8]]=>2 [[1,3,6],[2,5],[4,7],[8]]=>1 [[1,2,6],[3,5],[4,7],[8]]=>1 [[1,3,6],[2,4],[5,7],[8]]=>1 [[1,2,6],[3,4],[5,7],[8]]=>1 [[1,4,5],[2,6],[3,7],[8]]=>3 [[1,3,5],[2,6],[4,7],[8]]=>2 [[1,2,5],[3,6],[4,7],[8]]=>3 [[1,3,4],[2,6],[5,7],[8]]=>1 [[1,2,4],[3,6],[5,7],[8]]=>2 [[1,2,3],[4,6],[5,7],[8]]=>2 [[1,3,5],[2,4],[6,7],[8]]=>1 [[1,2,5],[3,4],[6,7],[8]]=>1 [[1,3,4],[2,5],[6,7],[8]]=>1 [[1,2,4],[3,5],[6,7],[8]]=>2 [[1,2,3],[4,5],[6,7],[8]]=>2 [[1,6,8],[2,7],[3],[4],[5]]=>3 [[1,5,8],[2,7],[3],[4],[6]]=>2 [[1,4,8],[2,7],[3],[5],[6]]=>2 [[1,3,8],[2,7],[4],[5],[6]]=>2 [[1,2,8],[3,7],[4],[5],[6]]=>2 [[1,5,8],[2,6],[3],[4],[7]]=>2 [[1,4,8],[2,6],[3],[5],[7]]=>2 [[1,3,8],[2,6],[4],[5],[7]]=>2 [[1,2,8],[3,6],[4],[5],[7]]=>2 [[1,4,8],[2,5],[3],[6],[7]]=>2 [[1,3,8],[2,5],[4],[6],[7]]=>2 [[1,2,8],[3,5],[4],[6],[7]]=>2 [[1,3,8],[2,4],[5],[6],[7]]=>3 [[1,2,8],[3,4],[5],[6],[7]]=>2 [[1,6,7],[2,8],[3],[4],[5]]=>3 [[1,5,7],[2,8],[3],[4],[6]]=>2 [[1,4,7],[2,8],[3],[5],[6]]=>2 [[1,3,7],[2,8],[4],[5],[6]]=>2 [[1,2,7],[3,8],[4],[5],[6]]=>3 [[1,5,6],[2,8],[3],[4],[7]]=>1 [[1,4,6],[2,8],[3],[5],[7]]=>1 [[1,3,6],[2,8],[4],[5],[7]]=>1 [[1,2,6],[3,8],[4],[5],[7]]=>2 [[1,4,5],[2,8],[3],[6],[7]]=>1 [[1,3,5],[2,8],[4],[6],[7]]=>1 [[1,2,5],[3,8],[4],[6],[7]]=>2 [[1,3,4],[2,8],[5],[6],[7]]=>1 [[1,2,4],[3,8],[5],[6],[7]]=>2 [[1,2,3],[4,8],[5],[6],[7]]=>2 [[1,5,7],[2,6],[3],[4],[8]]=>1 [[1,4,7],[2,6],[3],[5],[8]]=>1 [[1,3,7],[2,6],[4],[5],[8]]=>1 [[1,2,7],[3,6],[4],[5],[8]]=>1 [[1,4,7],[2,5],[3],[6],[8]]=>1 [[1,3,7],[2,5],[4],[6],[8]]=>1 [[1,2,7],[3,5],[4],[6],[8]]=>1 [[1,3,7],[2,4],[5],[6],[8]]=>2 [[1,2,7],[3,4],[5],[6],[8]]=>1 [[1,5,6],[2,7],[3],[4],[8]]=>1 [[1,4,6],[2,7],[3],[5],[8]]=>1 [[1,3,6],[2,7],[4],[5],[8]]=>1 [[1,2,6],[3,7],[4],[5],[8]]=>2 [[1,4,5],[2,7],[3],[6],[8]]=>1 [[1,3,5],[2,7],[4],[6],[8]]=>1 [[1,2,5],[3,7],[4],[6],[8]]=>2 [[1,3,4],[2,7],[5],[6],[8]]=>1 [[1,2,4],[3,7],[5],[6],[8]]=>2 [[1,2,3],[4,7],[5],[6],[8]]=>2 [[1,4,6],[2,5],[3],[7],[8]]=>1 [[1,3,6],[2,5],[4],[7],[8]]=>1 [[1,2,6],[3,5],[4],[7],[8]]=>1 [[1,3,6],[2,4],[5],[7],[8]]=>2 [[1,2,6],[3,4],[5],[7],[8]]=>1 [[1,4,5],[2,6],[3],[7],[8]]=>1 [[1,3,5],[2,6],[4],[7],[8]]=>1 [[1,2,5],[3,6],[4],[7],[8]]=>2 [[1,3,4],[2,6],[5],[7],[8]]=>1 [[1,2,4],[3,6],[5],[7],[8]]=>2 [[1,2,3],[4,6],[5],[7],[8]]=>2 [[1,3,5],[2,4],[6],[7],[8]]=>2 [[1,2,5],[3,4],[6],[7],[8]]=>1 [[1,3,4],[2,5],[6],[7],[8]]=>3 [[1,2,4],[3,5],[6],[7],[8]]=>3 [[1,2,3],[4,5],[6],[7],[8]]=>2 [[1,7,8],[2],[3],[4],[5],[6]]=>3 [[1,6,8],[2],[3],[4],[5],[7]]=>2 [[1,5,8],[2],[3],[4],[6],[7]]=>2 [[1,4,8],[2],[3],[5],[6],[7]]=>2 [[1,3,8],[2],[4],[5],[6],[7]]=>2 [[1,2,8],[3],[4],[5],[6],[7]]=>3 [[1,6,7],[2],[3],[4],[5],[8]]=>1 [[1,5,7],[2],[3],[4],[6],[8]]=>1 [[1,4,7],[2],[3],[5],[6],[8]]=>1 [[1,3,7],[2],[4],[5],[6],[8]]=>1 [[1,2,7],[3],[4],[5],[6],[8]]=>2 [[1,5,6],[2],[3],[4],[7],[8]]=>1 [[1,4,6],[2],[3],[5],[7],[8]]=>1 [[1,3,6],[2],[4],[5],[7],[8]]=>1 [[1,2,6],[3],[4],[5],[7],[8]]=>2 [[1,4,5],[2],[3],[6],[7],[8]]=>1 [[1,3,5],[2],[4],[6],[7],[8]]=>1 [[1,2,5],[3],[4],[6],[7],[8]]=>2 [[1,3,4],[2],[5],[6],[7],[8]]=>1 [[1,2,4],[3],[5],[6],[7],[8]]=>2 [[1,2,3],[4],[5],[6],[7],[8]]=>3 [[1,5],[2,6],[3,7],[4,8]]=>2 [[1,4],[2,6],[3,7],[5,8]]=>1 [[1,3],[2,6],[4,7],[5,8]]=>1 [[1,2],[3,6],[4,7],[5,8]]=>1 [[1,4],[2,5],[3,7],[6,8]]=>1 [[1,3],[2,5],[4,7],[6,8]]=>1 [[1,2],[3,5],[4,7],[6,8]]=>1 [[1,3],[2,4],[5,7],[6,8]]=>1 [[1,2],[3,4],[5,7],[6,8]]=>1 [[1,4],[2,5],[3,6],[7,8]]=>1 [[1,3],[2,5],[4,6],[7,8]]=>1 [[1,2],[3,5],[4,6],[7,8]]=>1 [[1,3],[2,4],[5,6],[7,8]]=>1 [[1,2],[3,4],[5,6],[7,8]]=>1 [[1,6],[2,7],[3,8],[4],[5]]=>2 [[1,5],[2,7],[3,8],[4],[6]]=>1 [[1,4],[2,7],[3,8],[5],[6]]=>1 [[1,3],[2,7],[4,8],[5],[6]]=>1 [[1,2],[3,7],[4,8],[5],[6]]=>1 [[1,5],[2,6],[3,8],[4],[7]]=>1 [[1,4],[2,6],[3,8],[5],[7]]=>1 [[1,3],[2,6],[4,8],[5],[7]]=>1 [[1,2],[3,6],[4,8],[5],[7]]=>1 [[1,4],[2,5],[3,8],[6],[7]]=>1 [[1,3],[2,5],[4,8],[6],[7]]=>1 [[1,2],[3,5],[4,8],[6],[7]]=>1 [[1,3],[2,4],[5,8],[6],[7]]=>1 [[1,2],[3,4],[5,8],[6],[7]]=>1 [[1,5],[2,6],[3,7],[4],[8]]=>1 [[1,4],[2,6],[3,7],[5],[8]]=>1 [[1,3],[2,6],[4,7],[5],[8]]=>1 [[1,2],[3,6],[4,7],[5],[8]]=>1 [[1,4],[2,5],[3,7],[6],[8]]=>1 [[1,3],[2,5],[4,7],[6],[8]]=>1 [[1,2],[3,5],[4,7],[6],[8]]=>1 [[1,3],[2,4],[5,7],[6],[8]]=>1 [[1,2],[3,4],[5,7],[6],[8]]=>1 [[1,4],[2,5],[3,6],[7],[8]]=>2 [[1,3],[2,5],[4,6],[7],[8]]=>1 [[1,2],[3,5],[4,6],[7],[8]]=>1 [[1,3],[2,4],[5,6],[7],[8]]=>1 [[1,2],[3,4],[5,6],[7],[8]]=>1 [[1,7],[2,8],[3],[4],[5],[6]]=>2 [[1,6],[2,8],[3],[4],[5],[7]]=>1 [[1,5],[2,8],[3],[4],[6],[7]]=>1 [[1,4],[2,8],[3],[5],[6],[7]]=>1 [[1,3],[2,8],[4],[5],[6],[7]]=>1 [[1,2],[3,8],[4],[5],[6],[7]]=>1 [[1,6],[2,7],[3],[4],[5],[8]]=>1 [[1,5],[2,7],[3],[4],[6],[8]]=>1 [[1,4],[2,7],[3],[5],[6],[8]]=>1 [[1,3],[2,7],[4],[5],[6],[8]]=>1 [[1,2],[3,7],[4],[5],[6],[8]]=>1 [[1,5],[2,6],[3],[4],[7],[8]]=>1 [[1,4],[2,6],[3],[5],[7],[8]]=>1 [[1,3],[2,6],[4],[5],[7],[8]]=>1 [[1,2],[3,6],[4],[5],[7],[8]]=>1 [[1,4],[2,5],[3],[6],[7],[8]]=>1 [[1,3],[2,5],[4],[6],[7],[8]]=>1 [[1,2],[3,5],[4],[6],[7],[8]]=>1 [[1,3],[2,4],[5],[6],[7],[8]]=>2 [[1,2],[3,4],[5],[6],[7],[8]]=>1 [[1,8],[2],[3],[4],[5],[6],[7]]=>2 [[1,7],[2],[3],[4],[5],[6],[8]]=>1 [[1,6],[2],[3],[4],[5],[7],[8]]=>1 [[1,5],[2],[3],[4],[6],[7],[8]]=>1 [[1,4],[2],[3],[5],[6],[7],[8]]=>1 [[1,3],[2],[4],[5],[6],[7],[8]]=>1 [[1,2],[3],[4],[5],[6],[7],[8]]=>2 [[1],[2],[3],[4],[5],[6],[7],[8]]=>1
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Description
The number of factors of a standard tableaux under concatenation.
The concatenation of two standard Young tableaux $T_1$ and $T_2$ is obtained by adding the largest entry of $T_1$ to each entry of $T_2$, and then appending the rows of the result to $T_1$, see [1, dfn 2.10].
This statistic returns the maximal number of standard tableaux such that their concatenation is the given tableau.
References
[1] Jagenteufel, J. A Sundaram type bijection for $\mathrm {SO}(2k+1)$: vacillating tableaux and pairs consisting of a standard Young tableau and an orthogonal Littlewood-Richardson tableau arXiv:1902.03843
Code
def factor(T):
    """
    Return smallest i such that the entries i+1,...,n form a SYT.
    """
    n = T.size()
    for i in range(1, n):
        rows = [tuple([e-i for e in row if e > i]) for row in T]
        while not rows[-1]:
            rows = rows[:-1]
        try:
            StandardTableau(rows)
            return (T.restrict(i), StandardTableau(rows))
        except ValueError:
            pass
    return (T, StandardTableau([]))

@cached_function
def statistic(T):
    A, B = factor(T)
    if B.size() > 0:
        return 1 + statistic(B)
    return 1
Created
Aug 11, 2019 at 09:18 by Martin Rubey
Updated
Aug 11, 2019 at 09:18 by Martin Rubey