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Identifier
Values
=>
Cc0007;cc-rep
[[1]]=>0 [[1,2]]=>0 [[1],[2]]=>1 [[1,2,3]]=>0 [[1,3],[2]]=>2 [[1,2],[3]]=>1 [[1],[2],[3]]=>3 [[1,2,3,4]]=>0 [[1,3,4],[2]]=>3 [[1,2,4],[3]]=>2 [[1,2,3],[4]]=>1 [[1,3],[2,4]]=>4 [[1,2],[3,4]]=>2 [[1,4],[2],[3]]=>4 [[1,3],[2],[4]]=>5 [[1,2],[3],[4]]=>3 [[1],[2],[3],[4]]=>6 [[1,2,3,4,5]]=>0 [[1,3,4,5],[2]]=>4 [[1,2,4,5],[3]]=>3 [[1,2,3,5],[4]]=>2 [[1,2,3,4],[5]]=>1 [[1,3,5],[2,4]]=>6 [[1,2,5],[3,4]]=>3 [[1,3,4],[2,5]]=>5 [[1,2,4],[3,5]]=>4 [[1,2,3],[4,5]]=>2 [[1,4,5],[2],[3]]=>5 [[1,3,5],[2],[4]]=>7 [[1,2,5],[3],[4]]=>4 [[1,3,4],[2],[5]]=>6 [[1,2,4],[3],[5]]=>5 [[1,2,3],[4],[5]]=>3 [[1,4],[2,5],[3]]=>6 [[1,3],[2,5],[4]]=>8 [[1,2],[3,5],[4]]=>5 [[1,3],[2,4],[5]]=>7 [[1,2],[3,4],[5]]=>4 [[1,5],[2],[3],[4]]=>7 [[1,4],[2],[3],[5]]=>8 [[1,3],[2],[4],[5]]=>9 [[1,2],[3],[4],[5]]=>6 [[1],[2],[3],[4],[5]]=>10 [[1,2,3,4,5,6]]=>0 [[1,3,4,5,6],[2]]=>5 [[1,2,4,5,6],[3]]=>4 [[1,2,3,5,6],[4]]=>3 [[1,2,3,4,6],[5]]=>2 [[1,2,3,4,5],[6]]=>1 [[1,3,5,6],[2,4]]=>8 [[1,2,5,6],[3,4]]=>4 [[1,3,4,6],[2,5]]=>7 [[1,2,4,6],[3,5]]=>6 [[1,2,3,6],[4,5]]=>3 [[1,3,4,5],[2,6]]=>6 [[1,2,4,5],[3,6]]=>5 [[1,2,3,5],[4,6]]=>4 [[1,2,3,4],[5,6]]=>2 [[1,4,5,6],[2],[3]]=>6 [[1,3,5,6],[2],[4]]=>9 [[1,2,5,6],[3],[4]]=>5 [[1,3,4,6],[2],[5]]=>8 [[1,2,4,6],[3],[5]]=>7 [[1,2,3,6],[4],[5]]=>4 [[1,3,4,5],[2],[6]]=>7 [[1,2,4,5],[3],[6]]=>6 [[1,2,3,5],[4],[6]]=>5 [[1,2,3,4],[5],[6]]=>3 [[1,3,5],[2,4,6]]=>9 [[1,2,5],[3,4,6]]=>5 [[1,3,4],[2,5,6]]=>7 [[1,2,4],[3,5,6]]=>6 [[1,2,3],[4,5,6]]=>3 [[1,4,6],[2,5],[3]]=>8 [[1,3,6],[2,5],[4]]=>11 [[1,2,6],[3,5],[4]]=>7 [[1,3,6],[2,4],[5]]=>9 [[1,2,6],[3,4],[5]]=>5 [[1,4,5],[2,6],[3]]=>7 [[1,3,5],[2,6],[4]]=>10 [[1,2,5],[3,6],[4]]=>6 [[1,3,4],[2,6],[5]]=>9 [[1,2,4],[3,6],[5]]=>8 [[1,2,3],[4,6],[5]]=>5 [[1,3,5],[2,4],[6]]=>10 [[1,2,5],[3,4],[6]]=>6 [[1,3,4],[2,5],[6]]=>8 [[1,2,4],[3,5],[6]]=>7 [[1,2,3],[4,5],[6]]=>4 [[1,5,6],[2],[3],[4]]=>8 [[1,4,6],[2],[3],[5]]=>10 [[1,3,6],[2],[4],[5]]=>11 [[1,2,6],[3],[4],[5]]=>7 [[1,4,5],[2],[3],[6]]=>9 [[1,3,5],[2],[4],[6]]=>12 [[1,2,5],[3],[4],[6]]=>8 [[1,3,4],[2],[5],[6]]=>10 [[1,2,4],[3],[5],[6]]=>9 [[1,2,3],[4],[5],[6]]=>6 [[1,4],[2,5],[3,6]]=>9 [[1,3],[2,5],[4,6]]=>12 [[1,2],[3,5],[4,6]]=>8 [[1,3],[2,4],[5,6]]=>10 [[1,2],[3,4],[5,6]]=>6 [[1,5],[2,6],[3],[4]]=>9 [[1,4],[2,6],[3],[5]]=>11 [[1,3],[2,6],[4],[5]]=>12 [[1,2],[3,6],[4],[5]]=>8 [[1,4],[2,5],[3],[6]]=>10 [[1,3],[2,5],[4],[6]]=>13 [[1,2],[3,5],[4],[6]]=>9 [[1,3],[2,4],[5],[6]]=>11 [[1,2],[3,4],[5],[6]]=>7 [[1,6],[2],[3],[4],[5]]=>11 [[1,5],[2],[3],[4],[6]]=>12 [[1,4],[2],[3],[5],[6]]=>13 [[1,3],[2],[4],[5],[6]]=>14 [[1,2],[3],[4],[5],[6]]=>10 [[1],[2],[3],[4],[5],[6]]=>15 [[1,2,3,4,5,6,7]]=>0 [[1,3,4,5,6,7],[2]]=>6 [[1,2,4,5,6,7],[3]]=>5 [[1,2,3,5,6,7],[4]]=>4 [[1,2,3,4,6,7],[5]]=>3 [[1,2,3,4,5,7],[6]]=>2 [[1,2,3,4,5,6],[7]]=>1 [[1,3,5,6,7],[2,4]]=>10 [[1,2,5,6,7],[3,4]]=>5 [[1,3,4,6,7],[2,5]]=>9 [[1,2,4,6,7],[3,5]]=>8 [[1,2,3,6,7],[4,5]]=>4 [[1,3,4,5,7],[2,6]]=>8 [[1,2,4,5,7],[3,6]]=>7 [[1,2,3,5,7],[4,6]]=>6 [[1,2,3,4,7],[5,6]]=>3 [[1,3,4,5,6],[2,7]]=>7 [[1,2,4,5,6],[3,7]]=>6 [[1,2,3,5,6],[4,7]]=>5 [[1,2,3,4,6],[5,7]]=>4 [[1,2,3,4,5],[6,7]]=>2 [[1,4,5,6,7],[2],[3]]=>7 [[1,3,5,6,7],[2],[4]]=>11 [[1,2,5,6,7],[3],[4]]=>6 [[1,3,4,6,7],[2],[5]]=>10 [[1,2,4,6,7],[3],[5]]=>9 [[1,2,3,6,7],[4],[5]]=>5 [[1,3,4,5,7],[2],[6]]=>9 [[1,2,4,5,7],[3],[6]]=>8 [[1,2,3,5,7],[4],[6]]=>7 [[1,2,3,4,7],[5],[6]]=>4 [[1,3,4,5,6],[2],[7]]=>8 [[1,2,4,5,6],[3],[7]]=>7 [[1,2,3,5,6],[4],[7]]=>6 [[1,2,3,4,6],[5],[7]]=>5 [[1,2,3,4,5],[6],[7]]=>3 [[1,3,5,7],[2,4,6]]=>12 [[1,2,5,7],[3,4,6]]=>7 [[1,3,4,7],[2,5,6]]=>9 [[1,2,4,7],[3,5,6]]=>8 [[1,2,3,7],[4,5,6]]=>4 [[1,3,5,6],[2,4,7]]=>11 [[1,2,5,6],[3,4,7]]=>6 [[1,3,4,6],[2,5,7]]=>10 [[1,2,4,6],[3,5,7]]=>9 [[1,2,3,6],[4,5,7]]=>5 [[1,3,4,5],[2,6,7]]=>8 [[1,2,4,5],[3,6,7]]=>7 [[1,2,3,5],[4,6,7]]=>6 [[1,2,3,4],[5,6,7]]=>3 [[1,4,6,7],[2,5],[3]]=>10 [[1,3,6,7],[2,5],[4]]=>14 [[1,2,6,7],[3,5],[4]]=>9 [[1,3,6,7],[2,4],[5]]=>11 [[1,2,6,7],[3,4],[5]]=>6 [[1,4,5,7],[2,6],[3]]=>9 [[1,3,5,7],[2,6],[4]]=>13 [[1,2,5,7],[3,6],[4]]=>8 [[1,3,4,7],[2,6],[5]]=>12 [[1,2,4,7],[3,6],[5]]=>11 [[1,2,3,7],[4,6],[5]]=>7 [[1,3,5,7],[2,4],[6]]=>13 [[1,2,5,7],[3,4],[6]]=>8 [[1,3,4,7],[2,5],[6]]=>10 [[1,2,4,7],[3,5],[6]]=>9 [[1,2,3,7],[4,5],[6]]=>5 [[1,4,5,6],[2,7],[3]]=>8 [[1,3,5,6],[2,7],[4]]=>12 [[1,2,5,6],[3,7],[4]]=>7 [[1,3,4,6],[2,7],[5]]=>11 [[1,2,4,6],[3,7],[5]]=>10 [[1,2,3,6],[4,7],[5]]=>6 [[1,3,4,5],[2,7],[6]]=>10 [[1,2,4,5],[3,7],[6]]=>9 [[1,2,3,5],[4,7],[6]]=>8 [[1,2,3,4],[5,7],[6]]=>5 [[1,3,5,6],[2,4],[7]]=>12 [[1,2,5,6],[3,4],[7]]=>7 [[1,3,4,6],[2,5],[7]]=>11 [[1,2,4,6],[3,5],[7]]=>10 [[1,2,3,6],[4,5],[7]]=>6 [[1,3,4,5],[2,6],[7]]=>9 [[1,2,4,5],[3,6],[7]]=>8 [[1,2,3,5],[4,6],[7]]=>7 [[1,2,3,4],[5,6],[7]]=>4 [[1,5,6,7],[2],[3],[4]]=>9 [[1,4,6,7],[2],[3],[5]]=>12 [[1,3,6,7],[2],[4],[5]]=>13 [[1,2,6,7],[3],[4],[5]]=>8 [[1,4,5,7],[2],[3],[6]]=>11 [[1,3,5,7],[2],[4],[6]]=>15 [[1,2,5,7],[3],[4],[6]]=>10 [[1,3,4,7],[2],[5],[6]]=>12 [[1,2,4,7],[3],[5],[6]]=>11 [[1,2,3,7],[4],[5],[6]]=>7 [[1,4,5,6],[2],[3],[7]]=>10 [[1,3,5,6],[2],[4],[7]]=>14 [[1,2,5,6],[3],[4],[7]]=>9 [[1,3,4,6],[2],[5],[7]]=>13 [[1,2,4,6],[3],[5],[7]]=>12 [[1,2,3,6],[4],[5],[7]]=>8 [[1,3,4,5],[2],[6],[7]]=>11 [[1,2,4,5],[3],[6],[7]]=>10 [[1,2,3,5],[4],[6],[7]]=>9 [[1,2,3,4],[5],[6],[7]]=>6 [[1,4,6],[2,5,7],[3]]=>11 [[1,3,6],[2,5,7],[4]]=>15 [[1,2,6],[3,5,7],[4]]=>10 [[1,3,6],[2,4,7],[5]]=>12 [[1,2,6],[3,4,7],[5]]=>7 [[1,4,5],[2,6,7],[3]]=>9 [[1,3,5],[2,6,7],[4]]=>13 [[1,2,5],[3,6,7],[4]]=>8 [[1,3,4],[2,6,7],[5]]=>12 [[1,2,4],[3,6,7],[5]]=>11 [[1,2,3],[4,6,7],[5]]=>7 [[1,3,5],[2,4,7],[6]]=>14 [[1,2,5],[3,4,7],[6]]=>9 [[1,3,4],[2,5,7],[6]]=>11 [[1,2,4],[3,5,7],[6]]=>10 [[1,2,3],[4,5,7],[6]]=>6 [[1,3,5],[2,4,6],[7]]=>13 [[1,2,5],[3,4,6],[7]]=>8 [[1,3,4],[2,5,6],[7]]=>10 [[1,2,4],[3,5,6],[7]]=>9 [[1,2,3],[4,5,6],[7]]=>5 [[1,4,7],[2,5],[3,6]]=>11 [[1,3,7],[2,5],[4,6]]=>15 [[1,2,7],[3,5],[4,6]]=>10 [[1,3,7],[2,4],[5,6]]=>12 [[1,2,7],[3,4],[5,6]]=>7 [[1,4,6],[2,5],[3,7]]=>12 [[1,3,6],[2,5],[4,7]]=>16 [[1,2,6],[3,5],[4,7]]=>11 [[1,3,6],[2,4],[5,7]]=>13 [[1,2,6],[3,4],[5,7]]=>8 [[1,4,5],[2,6],[3,7]]=>10 [[1,3,5],[2,6],[4,7]]=>14 [[1,2,5],[3,6],[4,7]]=>9 [[1,3,4],[2,6],[5,7]]=>13 [[1,2,4],[3,6],[5,7]]=>12 [[1,2,3],[4,6],[5,7]]=>8 [[1,3,5],[2,4],[6,7]]=>14 [[1,2,5],[3,4],[6,7]]=>9 [[1,3,4],[2,5],[6,7]]=>11 [[1,2,4],[3,5],[6,7]]=>10 [[1,2,3],[4,5],[6,7]]=>6 [[1,5,7],[2,6],[3],[4]]=>11 [[1,4,7],[2,6],[3],[5]]=>14 [[1,3,7],[2,6],[4],[5]]=>15 [[1,2,7],[3,6],[4],[5]]=>10 [[1,4,7],[2,5],[3],[6]]=>12 [[1,3,7],[2,5],[4],[6]]=>16 [[1,2,7],[3,5],[4],[6]]=>11 [[1,3,7],[2,4],[5],[6]]=>13 [[1,2,7],[3,4],[5],[6]]=>8 [[1,5,6],[2,7],[3],[4]]=>10 [[1,4,6],[2,7],[3],[5]]=>13 [[1,3,6],[2,7],[4],[5]]=>14 [[1,2,6],[3,7],[4],[5]]=>9 [[1,4,5],[2,7],[3],[6]]=>12 [[1,3,5],[2,7],[4],[6]]=>16 [[1,2,5],[3,7],[4],[6]]=>11 [[1,3,4],[2,7],[5],[6]]=>13 [[1,2,4],[3,7],[5],[6]]=>12 [[1,2,3],[4,7],[5],[6]]=>8 [[1,4,6],[2,5],[3],[7]]=>13 [[1,3,6],[2,5],[4],[7]]=>17 [[1,2,6],[3,5],[4],[7]]=>12 [[1,3,6],[2,4],[5],[7]]=>14 [[1,2,6],[3,4],[5],[7]]=>9 [[1,4,5],[2,6],[3],[7]]=>11 [[1,3,5],[2,6],[4],[7]]=>15 [[1,2,5],[3,6],[4],[7]]=>10 [[1,3,4],[2,6],[5],[7]]=>14 [[1,2,4],[3,6],[5],[7]]=>13 [[1,2,3],[4,6],[5],[7]]=>9 [[1,3,5],[2,4],[6],[7]]=>15 [[1,2,5],[3,4],[6],[7]]=>10 [[1,3,4],[2,5],[6],[7]]=>12 [[1,2,4],[3,5],[6],[7]]=>11 [[1,2,3],[4,5],[6],[7]]=>7 [[1,6,7],[2],[3],[4],[5]]=>12 [[1,5,7],[2],[3],[4],[6]]=>14 [[1,4,7],[2],[3],[5],[6]]=>15 [[1,3,7],[2],[4],[5],[6]]=>16 [[1,2,7],[3],[4],[5],[6]]=>11 [[1,5,6],[2],[3],[4],[7]]=>13 [[1,4,6],[2],[3],[5],[7]]=>16 [[1,3,6],[2],[4],[5],[7]]=>17 [[1,2,6],[3],[4],[5],[7]]=>12 [[1,4,5],[2],[3],[6],[7]]=>14 [[1,3,5],[2],[4],[6],[7]]=>18 [[1,2,5],[3],[4],[6],[7]]=>13 [[1,3,4],[2],[5],[6],[7]]=>15 [[1,2,4],[3],[5],[6],[7]]=>14 [[1,2,3],[4],[5],[6],[7]]=>10 [[1,5],[2,6],[3,7],[4]]=>12 [[1,4],[2,6],[3,7],[5]]=>15 [[1,3],[2,6],[4,7],[5]]=>16 [[1,2],[3,6],[4,7],[5]]=>11 [[1,4],[2,5],[3,7],[6]]=>14 [[1,3],[2,5],[4,7],[6]]=>18 [[1,2],[3,5],[4,7],[6]]=>13 [[1,3],[2,4],[5,7],[6]]=>15 [[1,2],[3,4],[5,7],[6]]=>10 [[1,4],[2,5],[3,6],[7]]=>13 [[1,3],[2,5],[4,6],[7]]=>17 [[1,2],[3,5],[4,6],[7]]=>12 [[1,3],[2,4],[5,6],[7]]=>14 [[1,2],[3,4],[5,6],[7]]=>9 [[1,6],[2,7],[3],[4],[5]]=>13 [[1,5],[2,7],[3],[4],[6]]=>15 [[1,4],[2,7],[3],[5],[6]]=>16 [[1,3],[2,7],[4],[5],[6]]=>17 [[1,2],[3,7],[4],[5],[6]]=>12 [[1,5],[2,6],[3],[4],[7]]=>14 [[1,4],[2,6],[3],[5],[7]]=>17 [[1,3],[2,6],[4],[5],[7]]=>18 [[1,2],[3,6],[4],[5],[7]]=>13 [[1,4],[2,5],[3],[6],[7]]=>15 [[1,3],[2,5],[4],[6],[7]]=>19 [[1,2],[3,5],[4],[6],[7]]=>14 [[1,3],[2,4],[5],[6],[7]]=>16 [[1,2],[3,4],[5],[6],[7]]=>11 [[1,7],[2],[3],[4],[5],[6]]=>16 [[1,6],[2],[3],[4],[5],[7]]=>17 [[1,5],[2],[3],[4],[6],[7]]=>18 [[1,4],[2],[3],[5],[6],[7]]=>19 [[1,3],[2],[4],[5],[6],[7]]=>20 [[1,2],[3],[4],[5],[6],[7]]=>15 [[1],[2],[3],[4],[5],[6],[7]]=>21 [[1,2,3,4,5,6,7,8]]=>0 [[1,3,4,5,6,7,8],[2]]=>7 [[1,2,4,5,6,7,8],[3]]=>6 [[1,2,3,5,6,7,8],[4]]=>5 [[1,2,3,4,6,7,8],[5]]=>4 [[1,2,3,4,5,7,8],[6]]=>3 [[1,2,3,4,5,6,8],[7]]=>2 [[1,2,3,4,5,6,7],[8]]=>1 [[1,3,5,6,7,8],[2,4]]=>12 [[1,2,5,6,7,8],[3,4]]=>6 [[1,3,4,6,7,8],[2,5]]=>11 [[1,2,4,6,7,8],[3,5]]=>10 [[1,2,3,6,7,8],[4,5]]=>5 [[1,3,4,5,7,8],[2,6]]=>10 [[1,2,4,5,7,8],[3,6]]=>9 [[1,2,3,5,7,8],[4,6]]=>8 [[1,2,3,4,7,8],[5,6]]=>4 [[1,3,4,5,6,8],[2,7]]=>9 [[1,2,4,5,6,8],[3,7]]=>8 [[1,2,3,5,6,8],[4,7]]=>7 [[1,2,3,4,6,8],[5,7]]=>6 [[1,2,3,4,5,8],[6,7]]=>3 [[1,3,4,5,6,7],[2,8]]=>8 [[1,2,4,5,6,7],[3,8]]=>7 [[1,2,3,5,6,7],[4,8]]=>6 [[1,2,3,4,6,7],[5,8]]=>5 [[1,2,3,4,5,7],[6,8]]=>4 [[1,2,3,4,5,6],[7,8]]=>2 [[1,4,5,6,7,8],[2],[3]]=>8 [[1,3,5,6,7,8],[2],[4]]=>13 [[1,2,5,6,7,8],[3],[4]]=>7 [[1,3,4,6,7,8],[2],[5]]=>12 [[1,2,4,6,7,8],[3],[5]]=>11 [[1,2,3,6,7,8],[4],[5]]=>6 [[1,3,4,5,7,8],[2],[6]]=>11 [[1,2,4,5,7,8],[3],[6]]=>10 [[1,2,3,5,7,8],[4],[6]]=>9 [[1,2,3,4,7,8],[5],[6]]=>5 [[1,3,4,5,6,8],[2],[7]]=>10 [[1,2,4,5,6,8],[3],[7]]=>9 [[1,2,3,5,6,8],[4],[7]]=>8 [[1,2,3,4,6,8],[5],[7]]=>7 [[1,2,3,4,5,8],[6],[7]]=>4 [[1,3,4,5,6,7],[2],[8]]=>9 [[1,2,4,5,6,7],[3],[8]]=>8 [[1,2,3,5,6,7],[4],[8]]=>7 [[1,2,3,4,6,7],[5],[8]]=>6 [[1,2,3,4,5,7],[6],[8]]=>5 [[1,2,3,4,5,6],[7],[8]]=>3 [[1,3,5,7,8],[2,4,6]]=>15 [[1,2,5,7,8],[3,4,6]]=>9 [[1,3,4,7,8],[2,5,6]]=>11 [[1,2,4,7,8],[3,5,6]]=>10 [[1,2,3,7,8],[4,5,6]]=>5 [[1,3,5,6,8],[2,4,7]]=>14 [[1,2,5,6,8],[3,4,7]]=>8 [[1,3,4,6,8],[2,5,7]]=>13 [[1,2,4,6,8],[3,5,7]]=>12 [[1,2,3,6,8],[4,5,7]]=>7 [[1,3,4,5,8],[2,6,7]]=>10 [[1,2,4,5,8],[3,6,7]]=>9 [[1,2,3,5,8],[4,6,7]]=>8 [[1,2,3,4,8],[5,6,7]]=>4 [[1,3,5,6,7],[2,4,8]]=>13 [[1,2,5,6,7],[3,4,8]]=>7 [[1,3,4,6,7],[2,5,8]]=>12 [[1,2,4,6,7],[3,5,8]]=>11 [[1,2,3,6,7],[4,5,8]]=>6 [[1,3,4,5,7],[2,6,8]]=>11 [[1,2,4,5,7],[3,6,8]]=>10 [[1,2,3,5,7],[4,6,8]]=>9 [[1,2,3,4,7],[5,6,8]]=>5 [[1,3,4,5,6],[2,7,8]]=>9 [[1,2,4,5,6],[3,7,8]]=>8 [[1,2,3,5,6],[4,7,8]]=>7 [[1,2,3,4,6],[5,7,8]]=>6 [[1,2,3,4,5],[6,7,8]]=>3 [[1,4,6,7,8],[2,5],[3]]=>12 [[1,3,6,7,8],[2,5],[4]]=>17 [[1,2,6,7,8],[3,5],[4]]=>11 [[1,3,6,7,8],[2,4],[5]]=>13 [[1,2,6,7,8],[3,4],[5]]=>7 [[1,4,5,7,8],[2,6],[3]]=>11 [[1,3,5,7,8],[2,6],[4]]=>16 [[1,2,5,7,8],[3,6],[4]]=>10 [[1,3,4,7,8],[2,6],[5]]=>15 [[1,2,4,7,8],[3,6],[5]]=>14 [[1,2,3,7,8],[4,6],[5]]=>9 [[1,3,5,7,8],[2,4],[6]]=>16 [[1,2,5,7,8],[3,4],[6]]=>10 [[1,3,4,7,8],[2,5],[6]]=>12 [[1,2,4,7,8],[3,5],[6]]=>11 [[1,2,3,7,8],[4,5],[6]]=>6 [[1,4,5,6,8],[2,7],[3]]=>10 [[1,3,5,6,8],[2,7],[4]]=>15 [[1,2,5,6,8],[3,7],[4]]=>9 [[1,3,4,6,8],[2,7],[5]]=>14 [[1,2,4,6,8],[3,7],[5]]=>13 [[1,2,3,6,8],[4,7],[5]]=>8 [[1,3,4,5,8],[2,7],[6]]=>13 [[1,2,4,5,8],[3,7],[6]]=>12 [[1,2,3,5,8],[4,7],[6]]=>11 [[1,2,3,4,8],[5,7],[6]]=>7 [[1,3,5,6,8],[2,4],[7]]=>15 [[1,2,5,6,8],[3,4],[7]]=>9 [[1,3,4,6,8],[2,5],[7]]=>14 [[1,2,4,6,8],[3,5],[7]]=>13 [[1,2,3,6,8],[4,5],[7]]=>8 [[1,3,4,5,8],[2,6],[7]]=>11 [[1,2,4,5,8],[3,6],[7]]=>10 [[1,2,3,5,8],[4,6],[7]]=>9 [[1,2,3,4,8],[5,6],[7]]=>5 [[1,4,5,6,7],[2,8],[3]]=>9 [[1,3,5,6,7],[2,8],[4]]=>14 [[1,2,5,6,7],[3,8],[4]]=>8 [[1,3,4,6,7],[2,8],[5]]=>13 [[1,2,4,6,7],[3,8],[5]]=>12 [[1,2,3,6,7],[4,8],[5]]=>7 [[1,3,4,5,7],[2,8],[6]]=>12 [[1,2,4,5,7],[3,8],[6]]=>11 [[1,2,3,5,7],[4,8],[6]]=>10 [[1,2,3,4,7],[5,8],[6]]=>6 [[1,3,4,5,6],[2,8],[7]]=>11 [[1,2,4,5,6],[3,8],[7]]=>10 [[1,2,3,5,6],[4,8],[7]]=>9 [[1,2,3,4,6],[5,8],[7]]=>8 [[1,2,3,4,5],[6,8],[7]]=>5 [[1,3,5,6,7],[2,4],[8]]=>14 [[1,2,5,6,7],[3,4],[8]]=>8 [[1,3,4,6,7],[2,5],[8]]=>13 [[1,2,4,6,7],[3,5],[8]]=>12 [[1,2,3,6,7],[4,5],[8]]=>7 [[1,3,4,5,7],[2,6],[8]]=>12 [[1,2,4,5,7],[3,6],[8]]=>11 [[1,2,3,5,7],[4,6],[8]]=>10 [[1,2,3,4,7],[5,6],[8]]=>6 [[1,3,4,5,6],[2,7],[8]]=>10 [[1,2,4,5,6],[3,7],[8]]=>9 [[1,2,3,5,6],[4,7],[8]]=>8 [[1,2,3,4,6],[5,7],[8]]=>7 [[1,2,3,4,5],[6,7],[8]]=>4 [[1,5,6,7,8],[2],[3],[4]]=>10 [[1,4,6,7,8],[2],[3],[5]]=>14 [[1,3,6,7,8],[2],[4],[5]]=>15 [[1,2,6,7,8],[3],[4],[5]]=>9 [[1,4,5,7,8],[2],[3],[6]]=>13 [[1,3,5,7,8],[2],[4],[6]]=>18 [[1,2,5,7,8],[3],[4],[6]]=>12 [[1,3,4,7,8],[2],[5],[6]]=>14 [[1,2,4,7,8],[3],[5],[6]]=>13 [[1,2,3,7,8],[4],[5],[6]]=>8 [[1,4,5,6,8],[2],[3],[7]]=>12 [[1,3,5,6,8],[2],[4],[7]]=>17 [[1,2,5,6,8],[3],[4],[7]]=>11 [[1,3,4,6,8],[2],[5],[7]]=>16 [[1,2,4,6,8],[3],[5],[7]]=>15 [[1,2,3,6,8],[4],[5],[7]]=>10 [[1,3,4,5,8],[2],[6],[7]]=>13 [[1,2,4,5,8],[3],[6],[7]]=>12 [[1,2,3,5,8],[4],[6],[7]]=>11 [[1,2,3,4,8],[5],[6],[7]]=>7 [[1,4,5,6,7],[2],[3],[8]]=>11 [[1,3,5,6,7],[2],[4],[8]]=>16 [[1,2,5,6,7],[3],[4],[8]]=>10 [[1,3,4,6,7],[2],[5],[8]]=>15 [[1,2,4,6,7],[3],[5],[8]]=>14 [[1,2,3,6,7],[4],[5],[8]]=>9 [[1,3,4,5,7],[2],[6],[8]]=>14 [[1,2,4,5,7],[3],[6],[8]]=>13 [[1,2,3,5,7],[4],[6],[8]]=>12 [[1,2,3,4,7],[5],[6],[8]]=>8 [[1,3,4,5,6],[2],[7],[8]]=>12 [[1,2,4,5,6],[3],[7],[8]]=>11 [[1,2,3,5,6],[4],[7],[8]]=>10 [[1,2,3,4,6],[5],[7],[8]]=>9 [[1,2,3,4,5],[6],[7],[8]]=>6 [[1,3,5,7],[2,4,6,8]]=>16 [[1,2,5,7],[3,4,6,8]]=>10 [[1,3,4,7],[2,5,6,8]]=>12 [[1,2,4,7],[3,5,6,8]]=>11 [[1,2,3,7],[4,5,6,8]]=>6 [[1,3,5,6],[2,4,7,8]]=>14 [[1,2,5,6],[3,4,7,8]]=>8 [[1,3,4,6],[2,5,7,8]]=>13 [[1,2,4,6],[3,5,7,8]]=>12 [[1,2,3,6],[4,5,7,8]]=>7 [[1,3,4,5],[2,6,7,8]]=>10 [[1,2,4,5],[3,6,7,8]]=>9 [[1,2,3,5],[4,6,7,8]]=>8 [[1,2,3,4],[5,6,7,8]]=>4 [[1,4,6,8],[2,5,7],[3]]=>14 [[1,3,6,8],[2,5,7],[4]]=>19 [[1,2,6,8],[3,5,7],[4]]=>13 [[1,3,6,8],[2,4,7],[5]]=>15 [[1,2,6,8],[3,4,7],[5]]=>9 [[1,4,5,8],[2,6,7],[3]]=>11 [[1,3,5,8],[2,6,7],[4]]=>16 [[1,2,5,8],[3,6,7],[4]]=>10 [[1,3,4,8],[2,6,7],[5]]=>15 [[1,2,4,8],[3,6,7],[5]]=>14 [[1,2,3,8],[4,6,7],[5]]=>9 [[1,3,5,8],[2,4,7],[6]]=>18 [[1,2,5,8],[3,4,7],[6]]=>12 [[1,3,4,8],[2,5,7],[6]]=>14 [[1,2,4,8],[3,5,7],[6]]=>13 [[1,2,3,8],[4,5,7],[6]]=>8 [[1,3,5,8],[2,4,6],[7]]=>16 [[1,2,5,8],[3,4,6],[7]]=>10 [[1,3,4,8],[2,5,6],[7]]=>12 [[1,2,4,8],[3,5,6],[7]]=>11 [[1,2,3,8],[4,5,6],[7]]=>6 [[1,4,6,7],[2,5,8],[3]]=>13 [[1,3,6,7],[2,5,8],[4]]=>18 [[1,2,6,7],[3,5,8],[4]]=>12 [[1,3,6,7],[2,4,8],[5]]=>14 [[1,2,6,7],[3,4,8],[5]]=>8 [[1,4,5,7],[2,6,8],[3]]=>12 [[1,3,5,7],[2,6,8],[4]]=>17 [[1,2,5,7],[3,6,8],[4]]=>11 [[1,3,4,7],[2,6,8],[5]]=>16 [[1,2,4,7],[3,6,8],[5]]=>15 [[1,2,3,7],[4,6,8],[5]]=>10 [[1,3,5,7],[2,4,8],[6]]=>17 [[1,2,5,7],[3,4,8],[6]]=>11 [[1,3,4,7],[2,5,8],[6]]=>13 [[1,2,4,7],[3,5,8],[6]]=>12 [[1,2,3,7],[4,5,8],[6]]=>7 [[1,4,5,6],[2,7,8],[3]]=>10 [[1,3,5,6],[2,7,8],[4]]=>15 [[1,2,5,6],[3,7,8],[4]]=>9 [[1,3,4,6],[2,7,8],[5]]=>14 [[1,2,4,6],[3,7,8],[5]]=>13 [[1,2,3,6],[4,7,8],[5]]=>8 [[1,3,4,5],[2,7,8],[6]]=>13 [[1,2,4,5],[3,7,8],[6]]=>12 [[1,2,3,5],[4,7,8],[6]]=>11 [[1,2,3,4],[5,7,8],[6]]=>7 [[1,3,5,6],[2,4,8],[7]]=>16 [[1,2,5,6],[3,4,8],[7]]=>10 [[1,3,4,6],[2,5,8],[7]]=>15 [[1,2,4,6],[3,5,8],[7]]=>14 [[1,2,3,6],[4,5,8],[7]]=>9 [[1,3,4,5],[2,6,8],[7]]=>12 [[1,2,4,5],[3,6,8],[7]]=>11 [[1,2,3,5],[4,6,8],[7]]=>10 [[1,2,3,4],[5,6,8],[7]]=>6 [[1,3,5,7],[2,4,6],[8]]=>17 [[1,2,5,7],[3,4,6],[8]]=>11 [[1,3,4,7],[2,5,6],[8]]=>13 [[1,2,4,7],[3,5,6],[8]]=>12 [[1,2,3,7],[4,5,6],[8]]=>7 [[1,3,5,6],[2,4,7],[8]]=>15 [[1,2,5,6],[3,4,7],[8]]=>9 [[1,3,4,6],[2,5,7],[8]]=>14 [[1,2,4,6],[3,5,7],[8]]=>13 [[1,2,3,6],[4,5,7],[8]]=>8 [[1,3,4,5],[2,6,7],[8]]=>11 [[1,2,4,5],[3,6,7],[8]]=>10 [[1,2,3,5],[4,6,7],[8]]=>9 [[1,2,3,4],[5,6,7],[8]]=>5 [[1,4,7,8],[2,5],[3,6]]=>13 [[1,3,7,8],[2,5],[4,6]]=>18 [[1,2,7,8],[3,5],[4,6]]=>12 [[1,3,7,8],[2,4],[5,6]]=>14 [[1,2,7,8],[3,4],[5,6]]=>8 [[1,4,6,8],[2,5],[3,7]]=>15 [[1,3,6,8],[2,5],[4,7]]=>20 [[1,2,6,8],[3,5],[4,7]]=>14 [[1,3,6,8],[2,4],[5,7]]=>16 [[1,2,6,8],[3,4],[5,7]]=>10 [[1,4,5,8],[2,6],[3,7]]=>12 [[1,3,5,8],[2,6],[4,7]]=>17 [[1,2,5,8],[3,6],[4,7]]=>11 [[1,3,4,8],[2,6],[5,7]]=>16 [[1,2,4,8],[3,6],[5,7]]=>15 [[1,2,3,8],[4,6],[5,7]]=>10 [[1,3,5,8],[2,4],[6,7]]=>17 [[1,2,5,8],[3,4],[6,7]]=>11 [[1,3,4,8],[2,5],[6,7]]=>13 [[1,2,4,8],[3,5],[6,7]]=>12 [[1,2,3,8],[4,5],[6,7]]=>7 [[1,4,6,7],[2,5],[3,8]]=>14 [[1,3,6,7],[2,5],[4,8]]=>19 [[1,2,6,7],[3,5],[4,8]]=>13 [[1,3,6,7],[2,4],[5,8]]=>15 [[1,2,6,7],[3,4],[5,8]]=>9 [[1,4,5,7],[2,6],[3,8]]=>13 [[1,3,5,7],[2,6],[4,8]]=>18 [[1,2,5,7],[3,6],[4,8]]=>12 [[1,3,4,7],[2,6],[5,8]]=>17 [[1,2,4,7],[3,6],[5,8]]=>16 [[1,2,3,7],[4,6],[5,8]]=>11 [[1,3,5,7],[2,4],[6,8]]=>18 [[1,2,5,7],[3,4],[6,8]]=>12 [[1,3,4,7],[2,5],[6,8]]=>14 [[1,2,4,7],[3,5],[6,8]]=>13 [[1,2,3,7],[4,5],[6,8]]=>8 [[1,4,5,6],[2,7],[3,8]]=>11 [[1,3,5,6],[2,7],[4,8]]=>16 [[1,2,5,6],[3,7],[4,8]]=>10 [[1,3,4,6],[2,7],[5,8]]=>15 [[1,2,4,6],[3,7],[5,8]]=>14 [[1,2,3,6],[4,7],[5,8]]=>9 [[1,3,4,5],[2,7],[6,8]]=>14 [[1,2,4,5],[3,7],[6,8]]=>13 [[1,2,3,5],[4,7],[6,8]]=>12 [[1,2,3,4],[5,7],[6,8]]=>8 [[1,3,5,6],[2,4],[7,8]]=>16 [[1,2,5,6],[3,4],[7,8]]=>10 [[1,3,4,6],[2,5],[7,8]]=>15 [[1,2,4,6],[3,5],[7,8]]=>14 [[1,2,3,6],[4,5],[7,8]]=>9 [[1,3,4,5],[2,6],[7,8]]=>12 [[1,2,4,5],[3,6],[7,8]]=>11 [[1,2,3,5],[4,6],[7,8]]=>10 [[1,2,3,4],[5,6],[7,8]]=>6 [[1,5,7,8],[2,6],[3],[4]]=>13 [[1,4,7,8],[2,6],[3],[5]]=>17 [[1,3,7,8],[2,6],[4],[5]]=>18 [[1,2,7,8],[3,6],[4],[5]]=>12 [[1,4,7,8],[2,5],[3],[6]]=>14 [[1,3,7,8],[2,5],[4],[6]]=>19 [[1,2,7,8],[3,5],[4],[6]]=>13 [[1,3,7,8],[2,4],[5],[6]]=>15 [[1,2,7,8],[3,4],[5],[6]]=>9 [[1,5,6,8],[2,7],[3],[4]]=>12 [[1,4,6,8],[2,7],[3],[5]]=>16 [[1,3,6,8],[2,7],[4],[5]]=>17 [[1,2,6,8],[3,7],[4],[5]]=>11 [[1,4,5,8],[2,7],[3],[6]]=>15 [[1,3,5,8],[2,7],[4],[6]]=>20 [[1,2,5,8],[3,7],[4],[6]]=>14 [[1,3,4,8],[2,7],[5],[6]]=>16 [[1,2,4,8],[3,7],[5],[6]]=>15 [[1,2,3,8],[4,7],[5],[6]]=>10 [[1,4,6,8],[2,5],[3],[7]]=>16 [[1,3,6,8],[2,5],[4],[7]]=>21 [[1,2,6,8],[3,5],[4],[7]]=>15 [[1,3,6,8],[2,4],[5],[7]]=>17 [[1,2,6,8],[3,4],[5],[7]]=>11 [[1,4,5,8],[2,6],[3],[7]]=>13 [[1,3,5,8],[2,6],[4],[7]]=>18 [[1,2,5,8],[3,6],[4],[7]]=>12 [[1,3,4,8],[2,6],[5],[7]]=>17 [[1,2,4,8],[3,6],[5],[7]]=>16 [[1,2,3,8],[4,6],[5],[7]]=>11 [[1,3,5,8],[2,4],[6],[7]]=>18 [[1,2,5,8],[3,4],[6],[7]]=>12 [[1,3,4,8],[2,5],[6],[7]]=>14 [[1,2,4,8],[3,5],[6],[7]]=>13 [[1,2,3,8],[4,5],[6],[7]]=>8 [[1,5,6,7],[2,8],[3],[4]]=>11 [[1,4,6,7],[2,8],[3],[5]]=>15 [[1,3,6,7],[2,8],[4],[5]]=>16 [[1,2,6,7],[3,8],[4],[5]]=>10 [[1,4,5,7],[2,8],[3],[6]]=>14 [[1,3,5,7],[2,8],[4],[6]]=>19 [[1,2,5,7],[3,8],[4],[6]]=>13 [[1,3,4,7],[2,8],[5],[6]]=>15 [[1,2,4,7],[3,8],[5],[6]]=>14 [[1,2,3,7],[4,8],[5],[6]]=>9 [[1,4,5,6],[2,8],[3],[7]]=>13 [[1,3,5,6],[2,8],[4],[7]]=>18 [[1,2,5,6],[3,8],[4],[7]]=>12 [[1,3,4,6],[2,8],[5],[7]]=>17 [[1,2,4,6],[3,8],[5],[7]]=>16 [[1,2,3,6],[4,8],[5],[7]]=>11 [[1,3,4,5],[2,8],[6],[7]]=>14 [[1,2,4,5],[3,8],[6],[7]]=>13 [[1,2,3,5],[4,8],[6],[7]]=>12 [[1,2,3,4],[5,8],[6],[7]]=>8 [[1,4,6,7],[2,5],[3],[8]]=>15 [[1,3,6,7],[2,5],[4],[8]]=>20 [[1,2,6,7],[3,5],[4],[8]]=>14 [[1,3,6,7],[2,4],[5],[8]]=>16 [[1,2,6,7],[3,4],[5],[8]]=>10 [[1,4,5,7],[2,6],[3],[8]]=>14 [[1,3,5,7],[2,6],[4],[8]]=>19 [[1,2,5,7],[3,6],[4],[8]]=>13 [[1,3,4,7],[2,6],[5],[8]]=>18 [[1,2,4,7],[3,6],[5],[8]]=>17 [[1,2,3,7],[4,6],[5],[8]]=>12 [[1,3,5,7],[2,4],[6],[8]]=>19 [[1,2,5,7],[3,4],[6],[8]]=>13 [[1,3,4,7],[2,5],[6],[8]]=>15 [[1,2,4,7],[3,5],[6],[8]]=>14 [[1,2,3,7],[4,5],[6],[8]]=>9 [[1,4,5,6],[2,7],[3],[8]]=>12 [[1,3,5,6],[2,7],[4],[8]]=>17 [[1,2,5,6],[3,7],[4],[8]]=>11 [[1,3,4,6],[2,7],[5],[8]]=>16 [[1,2,4,6],[3,7],[5],[8]]=>15 [[1,2,3,6],[4,7],[5],[8]]=>10 [[1,3,4,5],[2,7],[6],[8]]=>15 [[1,2,4,5],[3,7],[6],[8]]=>14 [[1,2,3,5],[4,7],[6],[8]]=>13 [[1,2,3,4],[5,7],[6],[8]]=>9 [[1,3,5,6],[2,4],[7],[8]]=>17 [[1,2,5,6],[3,4],[7],[8]]=>11 [[1,3,4,6],[2,5],[7],[8]]=>16 [[1,2,4,6],[3,5],[7],[8]]=>15 [[1,2,3,6],[4,5],[7],[8]]=>10 [[1,3,4,5],[2,6],[7],[8]]=>13 [[1,2,4,5],[3,6],[7],[8]]=>12 [[1,2,3,5],[4,6],[7],[8]]=>11 [[1,2,3,4],[5,6],[7],[8]]=>7 [[1,6,7,8],[2],[3],[4],[5]]=>13 [[1,5,7,8],[2],[3],[4],[6]]=>16 [[1,4,7,8],[2],[3],[5],[6]]=>17 [[1,3,7,8],[2],[4],[5],[6]]=>18 [[1,2,7,8],[3],[4],[5],[6]]=>12 [[1,5,6,8],[2],[3],[4],[7]]=>15 [[1,4,6,8],[2],[3],[5],[7]]=>19 [[1,3,6,8],[2],[4],[5],[7]]=>20 [[1,2,6,8],[3],[4],[5],[7]]=>14 [[1,4,5,8],[2],[3],[6],[7]]=>16 [[1,3,5,8],[2],[4],[6],[7]]=>21 [[1,2,5,8],[3],[4],[6],[7]]=>15 [[1,3,4,8],[2],[5],[6],[7]]=>17 [[1,2,4,8],[3],[5],[6],[7]]=>16 [[1,2,3,8],[4],[5],[6],[7]]=>11 [[1,5,6,7],[2],[3],[4],[8]]=>14 [[1,4,6,7],[2],[3],[5],[8]]=>18 [[1,3,6,7],[2],[4],[5],[8]]=>19 [[1,2,6,7],[3],[4],[5],[8]]=>13 [[1,4,5,7],[2],[3],[6],[8]]=>17 [[1,3,5,7],[2],[4],[6],[8]]=>22 [[1,2,5,7],[3],[4],[6],[8]]=>16 [[1,3,4,7],[2],[5],[6],[8]]=>18 [[1,2,4,7],[3],[5],[6],[8]]=>17 [[1,2,3,7],[4],[5],[6],[8]]=>12 [[1,4,5,6],[2],[3],[7],[8]]=>15 [[1,3,5,6],[2],[4],[7],[8]]=>20 [[1,2,5,6],[3],[4],[7],[8]]=>14 [[1,3,4,6],[2],[5],[7],[8]]=>19 [[1,2,4,6],[3],[5],[7],[8]]=>18 [[1,2,3,6],[4],[5],[7],[8]]=>13 [[1,3,4,5],[2],[6],[7],[8]]=>16 [[1,2,4,5],[3],[6],[7],[8]]=>15 [[1,2,3,5],[4],[6],[7],[8]]=>14 [[1,2,3,4],[5],[6],[7],[8]]=>10 [[1,4,7],[2,5,8],[3,6]]=>14 [[1,3,7],[2,5,8],[4,6]]=>19 [[1,2,7],[3,5,8],[4,6]]=>13 [[1,3,7],[2,4,8],[5,6]]=>15 [[1,2,7],[3,4,8],[5,6]]=>9 [[1,4,6],[2,5,8],[3,7]]=>16 [[1,3,6],[2,5,8],[4,7]]=>21 [[1,2,6],[3,5,8],[4,7]]=>15 [[1,3,6],[2,4,8],[5,7]]=>17 [[1,2,6],[3,4,8],[5,7]]=>11 [[1,4,5],[2,6,8],[3,7]]=>13 [[1,3,5],[2,6,8],[4,7]]=>18 [[1,2,5],[3,6,8],[4,7]]=>12 [[1,3,4],[2,6,8],[5,7]]=>17 [[1,2,4],[3,6,8],[5,7]]=>16 [[1,2,3],[4,6,8],[5,7]]=>11 [[1,3,5],[2,4,8],[6,7]]=>18 [[1,2,5],[3,4,8],[6,7]]=>12 [[1,3,4],[2,5,8],[6,7]]=>14 [[1,2,4],[3,5,8],[6,7]]=>13 [[1,2,3],[4,5,8],[6,7]]=>8 [[1,4,6],[2,5,7],[3,8]]=>15 [[1,3,6],[2,5,7],[4,8]]=>20 [[1,2,6],[3,5,7],[4,8]]=>14 [[1,3,6],[2,4,7],[5,8]]=>16 [[1,2,6],[3,4,7],[5,8]]=>10 [[1,4,5],[2,6,7],[3,8]]=>12 [[1,3,5],[2,6,7],[4,8]]=>17 [[1,2,5],[3,6,7],[4,8]]=>11 [[1,3,4],[2,6,7],[5,8]]=>16 [[1,2,4],[3,6,7],[5,8]]=>15 [[1,2,3],[4,6,7],[5,8]]=>10 [[1,3,5],[2,4,7],[6,8]]=>19 [[1,2,5],[3,4,7],[6,8]]=>13 [[1,3,4],[2,5,7],[6,8]]=>15 [[1,2,4],[3,5,7],[6,8]]=>14 [[1,2,3],[4,5,7],[6,8]]=>9 [[1,3,5],[2,4,6],[7,8]]=>17 [[1,2,5],[3,4,6],[7,8]]=>11 [[1,3,4],[2,5,6],[7,8]]=>13 [[1,2,4],[3,5,6],[7,8]]=>12 [[1,2,3],[4,5,6],[7,8]]=>7 [[1,5,7],[2,6,8],[3],[4]]=>14 [[1,4,7],[2,6,8],[3],[5]]=>18 [[1,3,7],[2,6,8],[4],[5]]=>19 [[1,2,7],[3,6,8],[4],[5]]=>13 [[1,4,7],[2,5,8],[3],[6]]=>15 [[1,3,7],[2,5,8],[4],[6]]=>20 [[1,2,7],[3,5,8],[4],[6]]=>14 [[1,3,7],[2,4,8],[5],[6]]=>16 [[1,2,7],[3,4,8],[5],[6]]=>10 [[1,5,6],[2,7,8],[3],[4]]=>12 [[1,4,6],[2,7,8],[3],[5]]=>16 [[1,3,6],[2,7,8],[4],[5]]=>17 [[1,2,6],[3,7,8],[4],[5]]=>11 [[1,4,5],[2,7,8],[3],[6]]=>15 [[1,3,5],[2,7,8],[4],[6]]=>20 [[1,2,5],[3,7,8],[4],[6]]=>14 [[1,3,4],[2,7,8],[5],[6]]=>16 [[1,2,4],[3,7,8],[5],[6]]=>15 [[1,2,3],[4,7,8],[5],[6]]=>10 [[1,4,6],[2,5,8],[3],[7]]=>17 [[1,3,6],[2,5,8],[4],[7]]=>22 [[1,2,6],[3,5,8],[4],[7]]=>16 [[1,3,6],[2,4,8],[5],[7]]=>18 [[1,2,6],[3,4,8],[5],[7]]=>12 [[1,4,5],[2,6,8],[3],[7]]=>14 [[1,3,5],[2,6,8],[4],[7]]=>19 [[1,2,5],[3,6,8],[4],[7]]=>13 [[1,3,4],[2,6,8],[5],[7]]=>18 [[1,2,4],[3,6,8],[5],[7]]=>17 [[1,2,3],[4,6,8],[5],[7]]=>12 [[1,3,5],[2,4,8],[6],[7]]=>19 [[1,2,5],[3,4,8],[6],[7]]=>13 [[1,3,4],[2,5,8],[6],[7]]=>15 [[1,2,4],[3,5,8],[6],[7]]=>14 [[1,2,3],[4,5,8],[6],[7]]=>9 [[1,4,6],[2,5,7],[3],[8]]=>16 [[1,3,6],[2,5,7],[4],[8]]=>21 [[1,2,6],[3,5,7],[4],[8]]=>15 [[1,3,6],[2,4,7],[5],[8]]=>17 [[1,2,6],[3,4,7],[5],[8]]=>11 [[1,4,5],[2,6,7],[3],[8]]=>13 [[1,3,5],[2,6,7],[4],[8]]=>18 [[1,2,5],[3,6,7],[4],[8]]=>12 [[1,3,4],[2,6,7],[5],[8]]=>17 [[1,2,4],[3,6,7],[5],[8]]=>16 [[1,2,3],[4,6,7],[5],[8]]=>11 [[1,3,5],[2,4,7],[6],[8]]=>20 [[1,2,5],[3,4,7],[6],[8]]=>14 [[1,3,4],[2,5,7],[6],[8]]=>16 [[1,2,4],[3,5,7],[6],[8]]=>15 [[1,2,3],[4,5,7],[6],[8]]=>10 [[1,3,5],[2,4,6],[7],[8]]=>18 [[1,2,5],[3,4,6],[7],[8]]=>12 [[1,3,4],[2,5,6],[7],[8]]=>14 [[1,2,4],[3,5,6],[7],[8]]=>13 [[1,2,3],[4,5,6],[7],[8]]=>8 [[1,5,8],[2,6],[3,7],[4]]=>14 [[1,4,8],[2,6],[3,7],[5]]=>18 [[1,3,8],[2,6],[4,7],[5]]=>19 [[1,2,8],[3,6],[4,7],[5]]=>13 [[1,4,8],[2,5],[3,7],[6]]=>17 [[1,3,8],[2,5],[4,7],[6]]=>22 [[1,2,8],[3,5],[4,7],[6]]=>16 [[1,3,8],[2,4],[5,7],[6]]=>18 [[1,2,8],[3,4],[5,7],[6]]=>12 [[1,4,8],[2,5],[3,6],[7]]=>15 [[1,3,8],[2,5],[4,6],[7]]=>20 [[1,2,8],[3,5],[4,6],[7]]=>14 [[1,3,8],[2,4],[5,6],[7]]=>16 [[1,2,8],[3,4],[5,6],[7]]=>10 [[1,5,7],[2,6],[3,8],[4]]=>15 [[1,4,7],[2,6],[3,8],[5]]=>19 [[1,3,7],[2,6],[4,8],[5]]=>20 [[1,2,7],[3,6],[4,8],[5]]=>14 [[1,4,7],[2,5],[3,8],[6]]=>16 [[1,3,7],[2,5],[4,8],[6]]=>21 [[1,2,7],[3,5],[4,8],[6]]=>15 [[1,3,7],[2,4],[5,8],[6]]=>17 [[1,2,7],[3,4],[5,8],[6]]=>11 [[1,5,6],[2,7],[3,8],[4]]=>13 [[1,4,6],[2,7],[3,8],[5]]=>17 [[1,3,6],[2,7],[4,8],[5]]=>18 [[1,2,6],[3,7],[4,8],[5]]=>12 [[1,4,5],[2,7],[3,8],[6]]=>16 [[1,3,5],[2,7],[4,8],[6]]=>21 [[1,2,5],[3,7],[4,8],[6]]=>15 [[1,3,4],[2,7],[5,8],[6]]=>17 [[1,2,4],[3,7],[5,8],[6]]=>16 [[1,2,3],[4,7],[5,8],[6]]=>11 [[1,4,6],[2,5],[3,8],[7]]=>18 [[1,3,6],[2,5],[4,8],[7]]=>23 [[1,2,6],[3,5],[4,8],[7]]=>17 [[1,3,6],[2,4],[5,8],[7]]=>19 [[1,2,6],[3,4],[5,8],[7]]=>13 [[1,4,5],[2,6],[3,8],[7]]=>15 [[1,3,5],[2,6],[4,8],[7]]=>20 [[1,2,5],[3,6],[4,8],[7]]=>14 [[1,3,4],[2,6],[5,8],[7]]=>19 [[1,2,4],[3,6],[5,8],[7]]=>18 [[1,2,3],[4,6],[5,8],[7]]=>13 [[1,3,5],[2,4],[6,8],[7]]=>20 [[1,2,5],[3,4],[6,8],[7]]=>14 [[1,3,4],[2,5],[6,8],[7]]=>16 [[1,2,4],[3,5],[6,8],[7]]=>15 [[1,2,3],[4,5],[6,8],[7]]=>10 [[1,4,7],[2,5],[3,6],[8]]=>16 [[1,3,7],[2,5],[4,6],[8]]=>21 [[1,2,7],[3,5],[4,6],[8]]=>15 [[1,3,7],[2,4],[5,6],[8]]=>17 [[1,2,7],[3,4],[5,6],[8]]=>11 [[1,4,6],[2,5],[3,7],[8]]=>17 [[1,3,6],[2,5],[4,7],[8]]=>22 [[1,2,6],[3,5],[4,7],[8]]=>16 [[1,3,6],[2,4],[5,7],[8]]=>18 [[1,2,6],[3,4],[5,7],[8]]=>12 [[1,4,5],[2,6],[3,7],[8]]=>14 [[1,3,5],[2,6],[4,7],[8]]=>19 [[1,2,5],[3,6],[4,7],[8]]=>13 [[1,3,4],[2,6],[5,7],[8]]=>18 [[1,2,4],[3,6],[5,7],[8]]=>17 [[1,2,3],[4,6],[5,7],[8]]=>12 [[1,3,5],[2,4],[6,7],[8]]=>19 [[1,2,5],[3,4],[6,7],[8]]=>13 [[1,3,4],[2,5],[6,7],[8]]=>15 [[1,2,4],[3,5],[6,7],[8]]=>14 [[1,2,3],[4,5],[6,7],[8]]=>9 [[1,6,8],[2,7],[3],[4],[5]]=>15 [[1,5,8],[2,7],[3],[4],[6]]=>18 [[1,4,8],[2,7],[3],[5],[6]]=>19 [[1,3,8],[2,7],[4],[5],[6]]=>20 [[1,2,8],[3,7],[4],[5],[6]]=>14 [[1,5,8],[2,6],[3],[4],[7]]=>16 [[1,4,8],[2,6],[3],[5],[7]]=>20 [[1,3,8],[2,6],[4],[5],[7]]=>21 [[1,2,8],[3,6],[4],[5],[7]]=>15 [[1,4,8],[2,5],[3],[6],[7]]=>17 [[1,3,8],[2,5],[4],[6],[7]]=>22 [[1,2,8],[3,5],[4],[6],[7]]=>16 [[1,3,8],[2,4],[5],[6],[7]]=>18 [[1,2,8],[3,4],[5],[6],[7]]=>12 [[1,6,7],[2,8],[3],[4],[5]]=>14 [[1,5,7],[2,8],[3],[4],[6]]=>17 [[1,4,7],[2,8],[3],[5],[6]]=>18 [[1,3,7],[2,8],[4],[5],[6]]=>19 [[1,2,7],[3,8],[4],[5],[6]]=>13 [[1,5,6],[2,8],[3],[4],[7]]=>16 [[1,4,6],[2,8],[3],[5],[7]]=>20 [[1,3,6],[2,8],[4],[5],[7]]=>21 [[1,2,6],[3,8],[4],[5],[7]]=>15 [[1,4,5],[2,8],[3],[6],[7]]=>17 [[1,3,5],[2,8],[4],[6],[7]]=>22 [[1,2,5],[3,8],[4],[6],[7]]=>16 [[1,3,4],[2,8],[5],[6],[7]]=>18 [[1,2,4],[3,8],[5],[6],[7]]=>17 [[1,2,3],[4,8],[5],[6],[7]]=>12 [[1,5,7],[2,6],[3],[4],[8]]=>17 [[1,4,7],[2,6],[3],[5],[8]]=>21 [[1,3,7],[2,6],[4],[5],[8]]=>22 [[1,2,7],[3,6],[4],[5],[8]]=>16 [[1,4,7],[2,5],[3],[6],[8]]=>18 [[1,3,7],[2,5],[4],[6],[8]]=>23 [[1,2,7],[3,5],[4],[6],[8]]=>17 [[1,3,7],[2,4],[5],[6],[8]]=>19 [[1,2,7],[3,4],[5],[6],[8]]=>13 [[1,5,6],[2,7],[3],[4],[8]]=>15 [[1,4,6],[2,7],[3],[5],[8]]=>19 [[1,3,6],[2,7],[4],[5],[8]]=>20 [[1,2,6],[3,7],[4],[5],[8]]=>14 [[1,4,5],[2,7],[3],[6],[8]]=>18 [[1,3,5],[2,7],[4],[6],[8]]=>23 [[1,2,5],[3,7],[4],[6],[8]]=>17 [[1,3,4],[2,7],[5],[6],[8]]=>19 [[1,2,4],[3,7],[5],[6],[8]]=>18 [[1,2,3],[4,7],[5],[6],[8]]=>13 [[1,4,6],[2,5],[3],[7],[8]]=>19 [[1,3,6],[2,5],[4],[7],[8]]=>24 [[1,2,6],[3,5],[4],[7],[8]]=>18 [[1,3,6],[2,4],[5],[7],[8]]=>20 [[1,2,6],[3,4],[5],[7],[8]]=>14 [[1,4,5],[2,6],[3],[7],[8]]=>16 [[1,3,5],[2,6],[4],[7],[8]]=>21 [[1,2,5],[3,6],[4],[7],[8]]=>15 [[1,3,4],[2,6],[5],[7],[8]]=>20 [[1,2,4],[3,6],[5],[7],[8]]=>19 [[1,2,3],[4,6],[5],[7],[8]]=>14 [[1,3,5],[2,4],[6],[7],[8]]=>21 [[1,2,5],[3,4],[6],[7],[8]]=>15 [[1,3,4],[2,5],[6],[7],[8]]=>17 [[1,2,4],[3,5],[6],[7],[8]]=>16 [[1,2,3],[4,5],[6],[7],[8]]=>11 [[1,7,8],[2],[3],[4],[5],[6]]=>17 [[1,6,8],[2],[3],[4],[5],[7]]=>19 [[1,5,8],[2],[3],[4],[6],[7]]=>20 [[1,4,8],[2],[3],[5],[6],[7]]=>21 [[1,3,8],[2],[4],[5],[6],[7]]=>22 [[1,2,8],[3],[4],[5],[6],[7]]=>16 [[1,6,7],[2],[3],[4],[5],[8]]=>18 [[1,5,7],[2],[3],[4],[6],[8]]=>21 [[1,4,7],[2],[3],[5],[6],[8]]=>22 [[1,3,7],[2],[4],[5],[6],[8]]=>23 [[1,2,7],[3],[4],[5],[6],[8]]=>17 [[1,5,6],[2],[3],[4],[7],[8]]=>19 [[1,4,6],[2],[3],[5],[7],[8]]=>23 [[1,3,6],[2],[4],[5],[7],[8]]=>24 [[1,2,6],[3],[4],[5],[7],[8]]=>18 [[1,4,5],[2],[3],[6],[7],[8]]=>20 [[1,3,5],[2],[4],[6],[7],[8]]=>25 [[1,2,5],[3],[4],[6],[7],[8]]=>19 [[1,3,4],[2],[5],[6],[7],[8]]=>21 [[1,2,4],[3],[5],[6],[7],[8]]=>20 [[1,2,3],[4],[5],[6],[7],[8]]=>15 [[1,5],[2,6],[3,7],[4,8]]=>16 [[1,4],[2,6],[3,7],[5,8]]=>20 [[1,3],[2,6],[4,7],[5,8]]=>21 [[1,2],[3,6],[4,7],[5,8]]=>15 [[1,4],[2,5],[3,7],[6,8]]=>19 [[1,3],[2,5],[4,7],[6,8]]=>24 [[1,2],[3,5],[4,7],[6,8]]=>18 [[1,3],[2,4],[5,7],[6,8]]=>20 [[1,2],[3,4],[5,7],[6,8]]=>14 [[1,4],[2,5],[3,6],[7,8]]=>17 [[1,3],[2,5],[4,6],[7,8]]=>22 [[1,2],[3,5],[4,6],[7,8]]=>16 [[1,3],[2,4],[5,6],[7,8]]=>18 [[1,2],[3,4],[5,6],[7,8]]=>12 [[1,6],[2,7],[3,8],[4],[5]]=>16 [[1,5],[2,7],[3,8],[4],[6]]=>19 [[1,4],[2,7],[3,8],[5],[6]]=>20 [[1,3],[2,7],[4,8],[5],[6]]=>21 [[1,2],[3,7],[4,8],[5],[6]]=>15 [[1,5],[2,6],[3,8],[4],[7]]=>18 [[1,4],[2,6],[3,8],[5],[7]]=>22 [[1,3],[2,6],[4,8],[5],[7]]=>23 [[1,2],[3,6],[4,8],[5],[7]]=>17 [[1,4],[2,5],[3,8],[6],[7]]=>19 [[1,3],[2,5],[4,8],[6],[7]]=>24 [[1,2],[3,5],[4,8],[6],[7]]=>18 [[1,3],[2,4],[5,8],[6],[7]]=>20 [[1,2],[3,4],[5,8],[6],[7]]=>14 [[1,5],[2,6],[3,7],[4],[8]]=>17 [[1,4],[2,6],[3,7],[5],[8]]=>21 [[1,3],[2,6],[4,7],[5],[8]]=>22 [[1,2],[3,6],[4,7],[5],[8]]=>16 [[1,4],[2,5],[3,7],[6],[8]]=>20 [[1,3],[2,5],[4,7],[6],[8]]=>25 [[1,2],[3,5],[4,7],[6],[8]]=>19 [[1,3],[2,4],[5,7],[6],[8]]=>21 [[1,2],[3,4],[5,7],[6],[8]]=>15 [[1,4],[2,5],[3,6],[7],[8]]=>18 [[1,3],[2,5],[4,6],[7],[8]]=>23 [[1,2],[3,5],[4,6],[7],[8]]=>17 [[1,3],[2,4],[5,6],[7],[8]]=>19 [[1,2],[3,4],[5,6],[7],[8]]=>13 [[1,7],[2,8],[3],[4],[5],[6]]=>18 [[1,6],[2,8],[3],[4],[5],[7]]=>20 [[1,5],[2,8],[3],[4],[6],[7]]=>21 [[1,4],[2,8],[3],[5],[6],[7]]=>22 [[1,3],[2,8],[4],[5],[6],[7]]=>23 [[1,2],[3,8],[4],[5],[6],[7]]=>17 [[1,6],[2,7],[3],[4],[5],[8]]=>19 [[1,5],[2,7],[3],[4],[6],[8]]=>22 [[1,4],[2,7],[3],[5],[6],[8]]=>23 [[1,3],[2,7],[4],[5],[6],[8]]=>24 [[1,2],[3,7],[4],[5],[6],[8]]=>18 [[1,5],[2,6],[3],[4],[7],[8]]=>20 [[1,4],[2,6],[3],[5],[7],[8]]=>24 [[1,3],[2,6],[4],[5],[7],[8]]=>25 [[1,2],[3,6],[4],[5],[7],[8]]=>19 [[1,4],[2,5],[3],[6],[7],[8]]=>21 [[1,3],[2,5],[4],[6],[7],[8]]=>26 [[1,2],[3,5],[4],[6],[7],[8]]=>20 [[1,3],[2,4],[5],[6],[7],[8]]=>22 [[1,2],[3,4],[5],[6],[7],[8]]=>16 [[1,8],[2],[3],[4],[5],[6],[7]]=>22 [[1,7],[2],[3],[4],[5],[6],[8]]=>23 [[1,6],[2],[3],[4],[5],[7],[8]]=>24 [[1,5],[2],[3],[4],[6],[7],[8]]=>25 [[1,4],[2],[3],[5],[6],[7],[8]]=>26 [[1,3],[2],[4],[5],[6],[7],[8]]=>27 [[1,2],[3],[4],[5],[6],[7],[8]]=>21 [[1],[2],[3],[4],[5],[6],[7],[8]]=>28
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Description
The shifted natural comajor index of a standard Young tableau.
A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation.
The natural comajor index of a tableau of shape $\lambda$, size $n$ with natural descent set $D$ is then $b(\lambda)+\sum_{d\in D} n-d$, where $b(\lambda) = \sum_i (i-1)\lambda_i$.
References
[1] Hopkins, S. Two majs for standard Young tableaux? MathOverflow:385374
Code
def natural_descents(T):
    n = T.size()
    D = []
    for i in range(1, n):
        for row in T:
            if row.count(i):
                break
            if row.count(i+1):
                D.append(i)
                break
    return D

def statistic(T):
    n = T.size()
    D = natural_descents(T)
    return sum(n-d for d in D) + sum(i*p for i, p in enumerate(T.shape()))
Created
Mar 04, 2021 at 08:53 by Martin Rubey
Updated
Mar 15, 2021 at 15:39 by Martin Rubey