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Identifier
Values
=>
Cc0007;cc-rep
[[1,2]]=>4 [[1],[2]]=>0 [[1,2,3]]=>9 [[1,3],[2]]=>0 [[1,2],[3]]=>4 [[1],[2],[3]]=>1 [[1,2,3,4]]=>16 [[1,3,4],[2]]=>0 [[1,2,4],[3]]=>6 [[1,2,3],[4]]=>10 [[1,3],[2,4]]=>0 [[1,2],[3,4]]=>4 [[1,4],[2],[3]]=>2 [[1,3],[2],[4]]=>0 [[1,2],[3],[4]]=>6 [[1],[2],[3],[4]]=>0 [[1,2,3,4,5]]=>25 [[1,3,4,5],[2]]=>0 [[1,2,4,5],[3]]=>8 [[1,2,3,5],[4]]=>14 [[1,2,3,4],[5]]=>18 [[1,3,5],[2,4]]=>0 [[1,2,5],[3,4]]=>5 [[1,3,4],[2,5]]=>0 [[1,2,4],[3,5]]=>7 [[1,2,3],[4,5]]=>11 [[1,4,5],[2],[3]]=>3 [[1,3,5],[2],[4]]=>0 [[1,2,5],[3],[4]]=>9 [[1,3,4],[2],[5]]=>0 [[1,2,4],[3],[5]]=>7 [[1,2,3],[4],[5]]=>13 [[1,4],[2,5],[3]]=>3 [[1,3],[2,5],[4]]=>0 [[1,2],[3,5],[4]]=>7 [[1,3],[2,4],[5]]=>0 [[1,2],[3,4],[5]]=>5 [[1,5],[2],[3],[4]]=>0 [[1,4],[2],[3],[5]]=>2 [[1,3],[2],[4],[5]]=>0 [[1,2],[3],[4],[5]]=>6 [[1],[2],[3],[4],[5]]=>1 [[1,2,3,4,5,6]]=>36 [[1,3,4,5,6],[2]]=>0 [[1,2,4,5,6],[3]]=>10 [[1,2,3,5,6],[4]]=>18 [[1,2,3,4,6],[5]]=>24 [[1,2,3,4,5],[6]]=>28 [[1,3,5,6],[2,4]]=>0 [[1,2,5,6],[3,4]]=>6 [[1,3,4,6],[2,5]]=>0 [[1,2,4,6],[3,5]]=>9 [[1,2,3,6],[4,5]]=>14 [[1,3,4,5],[2,6]]=>0 [[1,2,4,5],[3,6]]=>9 [[1,2,3,5],[4,6]]=>16 [[1,2,3,4],[5,6]]=>20 [[1,4,5,6],[2],[3]]=>4 [[1,3,5,6],[2],[4]]=>0 [[1,2,5,6],[3],[4]]=>12 [[1,3,4,6],[2],[5]]=>0 [[1,2,4,6],[3],[5]]=>9 [[1,2,3,6],[4],[5]]=>18 [[1,3,4,5],[2],[6]]=>0 [[1,2,4,5],[3],[6]]=>9 [[1,2,3,5],[4],[6]]=>16 [[1,2,3,4],[5],[6]]=>22 [[1,3,5],[2,4,6]]=>0 [[1,2,5],[3,4,6]]=>7 [[1,3,4],[2,5,6]]=>0 [[1,2,4],[3,5,6]]=>7 [[1,2,3],[4,5,6]]=>12 [[1,4,6],[2,5],[3]]=>4 [[1,3,6],[2,5],[4]]=>0 [[1,2,6],[3,5],[4]]=>9 [[1,3,6],[2,4],[5]]=>0 [[1,2,6],[3,4],[5]]=>6 [[1,4,5],[2,6],[3]]=>4 [[1,3,5],[2,6],[4]]=>0 [[1,2,5],[3,6],[4]]=>11 [[1,3,4],[2,6],[5]]=>0 [[1,2,4],[3,6],[5]]=>8 [[1,2,3],[4,6],[5]]=>15 [[1,3,5],[2,4],[6]]=>0 [[1,2,5],[3,4],[6]]=>6 [[1,3,4],[2,5],[6]]=>0 [[1,2,4],[3,5],[6]]=>8 [[1,2,3],[4,5],[6]]=>13 [[1,5,6],[2],[3],[4]]=>0 [[1,4,6],[2],[3],[5]]=>3 [[1,3,6],[2],[4],[5]]=>0 [[1,2,6],[3],[4],[5]]=>8 [[1,4,5],[2],[3],[6]]=>3 [[1,3,5],[2],[4],[6]]=>0 [[1,2,5],[3],[4],[6]]=>10 [[1,3,4],[2],[5],[6]]=>0 [[1,2,4],[3],[5],[6]]=>8 [[1,2,3],[4],[5],[6]]=>14 [[1,4],[2,5],[3,6]]=>5 [[1,3],[2,5],[4,6]]=>0 [[1,2],[3,5],[4,6]]=>8 [[1,3],[2,4],[5,6]]=>0 [[1,2],[3,4],[5,6]]=>5 [[1,5],[2,6],[3],[4]]=>0 [[1,4],[2,6],[3],[5]]=>3 [[1,3],[2,6],[4],[5]]=>0 [[1,2],[3,6],[4],[5]]=>6 [[1,4],[2,5],[3],[6]]=>3 [[1,3],[2,5],[4],[6]]=>0 [[1,2],[3,5],[4],[6]]=>8 [[1,3],[2,4],[5],[6]]=>0 [[1,2],[3,4],[5],[6]]=>6 [[1,6],[2],[3],[4],[5]]=>2 [[1,5],[2],[3],[4],[6]]=>0 [[1,4],[2],[3],[5],[6]]=>2 [[1,3],[2],[4],[5],[6]]=>0 [[1,2],[3],[4],[5],[6]]=>8 [[1],[2],[3],[4],[5],[6]]=>0 [[1,2,3,4,5,6,7]]=>49 [[1,3,4,5,6,7],[2]]=>0 [[1,2,4,5,6,7],[3]]=>12 [[1,2,3,5,6,7],[4]]=>22 [[1,2,3,4,6,7],[5]]=>30 [[1,2,3,4,5,7],[6]]=>36 [[1,2,3,4,5,6],[7]]=>40 [[1,3,5,6,7],[2,4]]=>0 [[1,2,5,6,7],[3,4]]=>7 [[1,3,4,6,7],[2,5]]=>0 [[1,2,4,6,7],[3,5]]=>11 [[1,2,3,6,7],[4,5]]=>17 [[1,3,4,5,7],[2,6]]=>0 [[1,2,4,5,7],[3,6]]=>11 [[1,2,3,5,7],[4,6]]=>20 [[1,2,3,4,7],[5,6]]=>25 [[1,3,4,5,6],[2,7]]=>0 [[1,2,4,5,6],[3,7]]=>11 [[1,2,3,5,6],[4,7]]=>20 [[1,2,3,4,6],[5,7]]=>27 [[1,2,3,4,5],[6,7]]=>31 [[1,4,5,6,7],[2],[3]]=>5 [[1,3,5,6,7],[2],[4]]=>0 [[1,2,5,6,7],[3],[4]]=>15 [[1,3,4,6,7],[2],[5]]=>0 [[1,2,4,6,7],[3],[5]]=>11 [[1,2,3,6,7],[4],[5]]=>23 [[1,3,4,5,7],[2],[6]]=>0 [[1,2,4,5,7],[3],[6]]=>11 [[1,2,3,5,7],[4],[6]]=>20 [[1,2,3,4,7],[5],[6]]=>29 [[1,3,4,5,6],[2],[7]]=>0 [[1,2,4,5,6],[3],[7]]=>11 [[1,2,3,5,6],[4],[7]]=>20 [[1,2,3,4,6],[5],[7]]=>27 [[1,2,3,4,5],[6],[7]]=>33 [[1,3,5,7],[2,4,6]]=>0 [[1,2,5,7],[3,4,6]]=>8 [[1,3,4,7],[2,5,6]]=>0 [[1,2,4,7],[3,5,6]]=>8 [[1,2,3,7],[4,5,6]]=>14 [[1,3,5,6],[2,4,7]]=>0 [[1,2,5,6],[3,4,7]]=>8 [[1,3,4,6],[2,5,7]]=>0 [[1,2,4,6],[3,5,7]]=>10 [[1,2,3,6],[4,5,7]]=>17 [[1,3,4,5],[2,6,7]]=>0 [[1,2,4,5],[3,6,7]]=>10 [[1,2,3,5],[4,6,7]]=>17 [[1,2,3,4],[5,6,7]]=>22 [[1,4,6,7],[2,5],[3]]=>5 [[1,3,6,7],[2,5],[4]]=>0 [[1,2,6,7],[3,5],[4]]=>11 [[1,3,6,7],[2,4],[5]]=>0 [[1,2,6,7],[3,4],[5]]=>7 [[1,4,5,7],[2,6],[3]]=>5 [[1,3,5,7],[2,6],[4]]=>0 [[1,2,5,7],[3,6],[4]]=>14 [[1,3,4,7],[2,6],[5]]=>0 [[1,2,4,7],[3,6],[5]]=>10 [[1,2,3,7],[4,6],[5]]=>19 [[1,3,5,7],[2,4],[6]]=>0 [[1,2,5,7],[3,4],[6]]=>7 [[1,3,4,7],[2,5],[6]]=>0 [[1,2,4,7],[3,5],[6]]=>10 [[1,2,3,7],[4,5],[6]]=>16 [[1,4,5,6],[2,7],[3]]=>5 [[1,3,5,6],[2,7],[4]]=>0 [[1,2,5,6],[3,7],[4]]=>14 [[1,3,4,6],[2,7],[5]]=>0 [[1,2,4,6],[3,7],[5]]=>10 [[1,2,3,6],[4,7],[5]]=>21 [[1,3,4,5],[2,7],[6]]=>0 [[1,2,4,5],[3,7],[6]]=>10 [[1,2,3,5],[4,7],[6]]=>18 [[1,2,3,4],[5,7],[6]]=>25 [[1,3,5,6],[2,4],[7]]=>0 [[1,2,5,6],[3,4],[7]]=>7 [[1,3,4,6],[2,5],[7]]=>0 [[1,2,4,6],[3,5],[7]]=>10 [[1,2,3,6],[4,5],[7]]=>16 [[1,3,4,5],[2,6],[7]]=>0 [[1,2,4,5],[3,6],[7]]=>10 [[1,2,3,5],[4,6],[7]]=>18 [[1,2,3,4],[5,6],[7]]=>23 [[1,5,6,7],[2],[3],[4]]=>0 [[1,4,6,7],[2],[3],[5]]=>4 [[1,3,6,7],[2],[4],[5]]=>0 [[1,2,6,7],[3],[4],[5]]=>10 [[1,4,5,7],[2],[3],[6]]=>4 [[1,3,5,7],[2],[4],[6]]=>0 [[1,2,5,7],[3],[4],[6]]=>13 [[1,3,4,7],[2],[5],[6]]=>0 [[1,2,4,7],[3],[5],[6]]=>10 [[1,2,3,7],[4],[5],[6]]=>18 [[1,4,5,6],[2],[3],[7]]=>4 [[1,3,5,6],[2],[4],[7]]=>0 [[1,2,5,6],[3],[4],[7]]=>13 [[1,3,4,6],[2],[5],[7]]=>0 [[1,2,4,6],[3],[5],[7]]=>10 [[1,2,3,6],[4],[5],[7]]=>20 [[1,3,4,5],[2],[6],[7]]=>0 [[1,2,4,5],[3],[6],[7]]=>10 [[1,2,3,5],[4],[6],[7]]=>18 [[1,2,3,4],[5],[6],[7]]=>24 [[1,4,6],[2,5,7],[3]]=>5 [[1,3,6],[2,5,7],[4]]=>0 [[1,2,6],[3,5,7],[4]]=>12 [[1,3,6],[2,4,7],[5]]=>0 [[1,2,6],[3,4,7],[5]]=>8 [[1,4,5],[2,6,7],[3]]=>5 [[1,3,5],[2,6,7],[4]]=>0 [[1,2,5],[3,6,7],[4]]=>12 [[1,3,4],[2,6,7],[5]]=>0 [[1,2,4],[3,6,7],[5]]=>8 [[1,2,3],[4,6,7],[5]]=>17 [[1,3,5],[2,4,7],[6]]=>0 [[1,2,5],[3,4,7],[6]]=>8 [[1,3,4],[2,5,7],[6]]=>0 [[1,2,4],[3,5,7],[6]]=>8 [[1,2,3],[4,5,7],[6]]=>14 [[1,3,5],[2,4,6],[7]]=>0 [[1,2,5],[3,4,6],[7]]=>8 [[1,3,4],[2,5,6],[7]]=>0 [[1,2,4],[3,5,6],[7]]=>8 [[1,2,3],[4,5,6],[7]]=>14 [[1,4,7],[2,5],[3,6]]=>6 [[1,3,7],[2,5],[4,6]]=>0 [[1,2,7],[3,5],[4,6]]=>10 [[1,3,7],[2,4],[5,6]]=>0 [[1,2,7],[3,4],[5,6]]=>6 [[1,4,6],[2,5],[3,7]]=>6 [[1,3,6],[2,5],[4,7]]=>0 [[1,2,6],[3,5],[4,7]]=>10 [[1,3,6],[2,4],[5,7]]=>0 [[1,2,6],[3,4],[5,7]]=>6 [[1,4,5],[2,6],[3,7]]=>6 [[1,3,5],[2,6],[4,7]]=>0 [[1,2,5],[3,6],[4,7]]=>14 [[1,3,4],[2,6],[5,7]]=>0 [[1,2,4],[3,6],[5,7]]=>9 [[1,2,3],[4,6],[5,7]]=>17 [[1,3,5],[2,4],[6,7]]=>0 [[1,2,5],[3,4],[6,7]]=>6 [[1,3,4],[2,5],[6,7]]=>0 [[1,2,4],[3,5],[6,7]]=>9 [[1,2,3],[4,5],[6,7]]=>14 [[1,5,7],[2,6],[3],[4]]=>0 [[1,4,7],[2,6],[3],[5]]=>4 [[1,3,7],[2,6],[4],[5]]=>0 [[1,2,7],[3,6],[4],[5]]=>7 [[1,4,7],[2,5],[3],[6]]=>4 [[1,3,7],[2,5],[4],[6]]=>0 [[1,2,7],[3,5],[4],[6]]=>10 [[1,3,7],[2,4],[5],[6]]=>0 [[1,2,7],[3,4],[5],[6]]=>7 [[1,5,6],[2,7],[3],[4]]=>0 [[1,4,6],[2,7],[3],[5]]=>4 [[1,3,6],[2,7],[4],[5]]=>0 [[1,2,6],[3,7],[4],[5]]=>9 [[1,4,5],[2,7],[3],[6]]=>4 [[1,3,5],[2,7],[4],[6]]=>0 [[1,2,5],[3,7],[4],[6]]=>12 [[1,3,4],[2,7],[5],[6]]=>0 [[1,2,4],[3,7],[5],[6]]=>9 [[1,2,3],[4,7],[5],[6]]=>15 [[1,4,6],[2,5],[3],[7]]=>4 [[1,3,6],[2,5],[4],[7]]=>0 [[1,2,6],[3,5],[4],[7]]=>10 [[1,3,6],[2,4],[5],[7]]=>0 [[1,2,6],[3,4],[5],[7]]=>7 [[1,4,5],[2,6],[3],[7]]=>4 [[1,3,5],[2,6],[4],[7]]=>0 [[1,2,5],[3,6],[4],[7]]=>12 [[1,3,4],[2,6],[5],[7]]=>0 [[1,2,4],[3,6],[5],[7]]=>9 [[1,2,3],[4,6],[5],[7]]=>17 [[1,3,5],[2,4],[6],[7]]=>0 [[1,2,5],[3,4],[6],[7]]=>7 [[1,3,4],[2,5],[6],[7]]=>0 [[1,2,4],[3,5],[6],[7]]=>9 [[1,2,3],[4,5],[6],[7]]=>15 [[1,6,7],[2],[3],[4],[5]]=>3 [[1,5,7],[2],[3],[4],[6]]=>0 [[1,4,7],[2],[3],[5],[6]]=>3 [[1,3,7],[2],[4],[5],[6]]=>0 [[1,2,7],[3],[4],[5],[6]]=>11 [[1,5,6],[2],[3],[4],[7]]=>0 [[1,4,6],[2],[3],[5],[7]]=>3 [[1,3,6],[2],[4],[5],[7]]=>0 [[1,2,6],[3],[4],[5],[7]]=>9 [[1,4,5],[2],[3],[6],[7]]=>3 [[1,3,5],[2],[4],[6],[7]]=>0 [[1,2,5],[3],[4],[6],[7]]=>11 [[1,3,4],[2],[5],[6],[7]]=>0 [[1,2,4],[3],[5],[6],[7]]=>9 [[1,2,3],[4],[5],[6],[7]]=>17 [[1,5],[2,6],[3,7],[4]]=>0 [[1,4],[2,6],[3,7],[5]]=>4 [[1,3],[2,6],[4,7],[5]]=>0 [[1,2],[3,6],[4,7],[5]]=>6 [[1,4],[2,5],[3,7],[6]]=>4 [[1,3],[2,5],[4,7],[6]]=>0 [[1,2],[3,5],[4,7],[6]]=>9 [[1,3],[2,4],[5,7],[6]]=>0 [[1,2],[3,4],[5,7],[6]]=>6 [[1,4],[2,5],[3,6],[7]]=>6 [[1,3],[2,5],[4,6],[7]]=>0 [[1,2],[3,5],[4,6],[7]]=>9 [[1,3],[2,4],[5,6],[7]]=>0 [[1,2],[3,4],[5,6],[7]]=>6 [[1,6],[2,7],[3],[4],[5]]=>3 [[1,5],[2,7],[3],[4],[6]]=>0 [[1,4],[2,7],[3],[5],[6]]=>3 [[1,3],[2,7],[4],[5],[6]]=>0 [[1,2],[3,7],[4],[5],[6]]=>9 [[1,5],[2,6],[3],[4],[7]]=>0 [[1,4],[2,6],[3],[5],[7]]=>3 [[1,3],[2,6],[4],[5],[7]]=>0 [[1,2],[3,6],[4],[5],[7]]=>7 [[1,4],[2,5],[3],[6],[7]]=>3 [[1,3],[2,5],[4],[6],[7]]=>0 [[1,2],[3,5],[4],[6],[7]]=>9 [[1,3],[2,4],[5],[6],[7]]=>0 [[1,2],[3,4],[5],[6],[7]]=>7 [[1,7],[2],[3],[4],[5],[6]]=>0 [[1,6],[2],[3],[4],[5],[7]]=>2 [[1,5],[2],[3],[4],[6],[7]]=>0 [[1,4],[2],[3],[5],[6],[7]]=>2 [[1,3],[2],[4],[5],[6],[7]]=>0 [[1,2],[3],[4],[5],[6],[7]]=>8 [[1],[2],[3],[4],[5],[6],[7]]=>1 [[1,2,3,4,5,6,7,8]]=>64 [[1,3,4,5,6,7,8],[2]]=>0 [[1,2,4,5,6,7,8],[3]]=>14 [[1,2,3,5,6,7,8],[4]]=>26 [[1,2,3,4,6,7,8],[5]]=>36 [[1,2,3,4,5,7,8],[6]]=>44 [[1,2,3,4,5,6,8],[7]]=>50 [[1,2,3,4,5,6,7],[8]]=>54 [[1,3,5,6,7,8],[2,4]]=>0 [[1,2,5,6,7,8],[3,4]]=>8 [[1,3,4,6,7,8],[2,5]]=>0 [[1,2,4,6,7,8],[3,5]]=>13 [[1,2,3,6,7,8],[4,5]]=>20 [[1,3,4,5,7,8],[2,6]]=>0 [[1,2,4,5,7,8],[3,6]]=>13 [[1,2,3,5,7,8],[4,6]]=>24 [[1,2,3,4,7,8],[5,6]]=>30 [[1,3,4,5,6,8],[2,7]]=>0 [[1,2,4,5,6,8],[3,7]]=>13 [[1,2,3,5,6,8],[4,7]]=>24 [[1,2,3,4,6,8],[5,7]]=>33 [[1,2,3,4,5,8],[6,7]]=>38 [[1,3,4,5,6,7],[2,8]]=>0 [[1,2,4,5,6,7],[3,8]]=>13 [[1,2,3,5,6,7],[4,8]]=>24 [[1,2,3,4,6,7],[5,8]]=>33 [[1,2,3,4,5,7],[6,8]]=>40 [[1,2,3,4,5,6],[7,8]]=>44 [[1,4,5,6,7,8],[2],[3]]=>6 [[1,3,5,6,7,8],[2],[4]]=>0 [[1,2,5,6,7,8],[3],[4]]=>18 [[1,3,4,6,7,8],[2],[5]]=>0 [[1,2,4,6,7,8],[3],[5]]=>13 [[1,2,3,6,7,8],[4],[5]]=>28 [[1,3,4,5,7,8],[2],[6]]=>0 [[1,2,4,5,7,8],[3],[6]]=>13 [[1,2,3,5,7,8],[4],[6]]=>24 [[1,2,3,4,7,8],[5],[6]]=>36 [[1,3,4,5,6,8],[2],[7]]=>0 [[1,2,4,5,6,8],[3],[7]]=>13 [[1,2,3,5,6,8],[4],[7]]=>24 [[1,2,3,4,6,8],[5],[7]]=>33 [[1,2,3,4,5,8],[6],[7]]=>42 [[1,3,4,5,6,7],[2],[8]]=>0 [[1,2,4,5,6,7],[3],[8]]=>13 [[1,2,3,5,6,7],[4],[8]]=>24 [[1,2,3,4,6,7],[5],[8]]=>33 [[1,2,3,4,5,7],[6],[8]]=>40 [[1,2,3,4,5,6],[7],[8]]=>46 [[1,3,5,7,8],[2,4,6]]=>0 [[1,2,5,7,8],[3,4,6]]=>9 [[1,3,4,7,8],[2,5,6]]=>0 [[1,2,4,7,8],[3,5,6]]=>9 [[1,2,3,7,8],[4,5,6]]=>16 [[1,3,5,6,8],[2,4,7]]=>0 [[1,2,5,6,8],[3,4,7]]=>9 [[1,3,4,6,8],[2,5,7]]=>0 [[1,2,4,6,8],[3,5,7]]=>12 [[1,2,3,6,8],[4,5,7]]=>20 [[1,3,4,5,8],[2,6,7]]=>0 [[1,2,4,5,8],[3,6,7]]=>12 [[1,2,3,5,8],[4,6,7]]=>20 [[1,2,3,4,8],[5,6,7]]=>26 [[1,3,5,6,7],[2,4,8]]=>0 [[1,2,5,6,7],[3,4,8]]=>9 [[1,3,4,6,7],[2,5,8]]=>0 [[1,2,4,6,7],[3,5,8]]=>12 [[1,2,3,6,7],[4,5,8]]=>20 [[1,3,4,5,7],[2,6,8]]=>0 [[1,2,4,5,7],[3,6,8]]=>12 [[1,2,3,5,7],[4,6,8]]=>22 [[1,2,3,4,7],[5,6,8]]=>29 [[1,3,4,5,6],[2,7,8]]=>0 [[1,2,4,5,6],[3,7,8]]=>12 [[1,2,3,5,6],[4,7,8]]=>22 [[1,2,3,4,6],[5,7,8]]=>29 [[1,2,3,4,5],[6,7,8]]=>34 [[1,4,6,7,8],[2,5],[3]]=>6 [[1,3,6,7,8],[2,5],[4]]=>0 [[1,2,6,7,8],[3,5],[4]]=>13 [[1,3,6,7,8],[2,4],[5]]=>0 [[1,2,6,7,8],[3,4],[5]]=>8 [[1,4,5,7,8],[2,6],[3]]=>6 [[1,3,5,7,8],[2,6],[4]]=>0 [[1,2,5,7,8],[3,6],[4]]=>17 [[1,3,4,7,8],[2,6],[5]]=>0 [[1,2,4,7,8],[3,6],[5]]=>12 [[1,2,3,7,8],[4,6],[5]]=>23 [[1,3,5,7,8],[2,4],[6]]=>0 [[1,2,5,7,8],[3,4],[6]]=>8 [[1,3,4,7,8],[2,5],[6]]=>0 [[1,2,4,7,8],[3,5],[6]]=>12 [[1,2,3,7,8],[4,5],[6]]=>19 [[1,4,5,6,8],[2,7],[3]]=>6 [[1,3,5,6,8],[2,7],[4]]=>0 [[1,2,5,6,8],[3,7],[4]]=>17 [[1,3,4,6,8],[2,7],[5]]=>0 [[1,2,4,6,8],[3,7],[5]]=>12 [[1,2,3,6,8],[4,7],[5]]=>26 [[1,3,4,5,8],[2,7],[6]]=>0 [[1,2,4,5,8],[3,7],[6]]=>12 [[1,2,3,5,8],[4,7],[6]]=>22 [[1,2,3,4,8],[5,7],[6]]=>31 [[1,3,5,6,8],[2,4],[7]]=>0 [[1,2,5,6,8],[3,4],[7]]=>8 [[1,3,4,6,8],[2,5],[7]]=>0 [[1,2,4,6,8],[3,5],[7]]=>12 [[1,2,3,6,8],[4,5],[7]]=>19 [[1,3,4,5,8],[2,6],[7]]=>0 [[1,2,4,5,8],[3,6],[7]]=>12 [[1,2,3,5,8],[4,6],[7]]=>22 [[1,2,3,4,8],[5,6],[7]]=>28 [[1,4,5,6,7],[2,8],[3]]=>6 [[1,3,5,6,7],[2,8],[4]]=>0 [[1,2,5,6,7],[3,8],[4]]=>17 [[1,3,4,6,7],[2,8],[5]]=>0 [[1,2,4,6,7],[3,8],[5]]=>12 [[1,2,3,6,7],[4,8],[5]]=>26 [[1,3,4,5,7],[2,8],[6]]=>0 [[1,2,4,5,7],[3,8],[6]]=>12 [[1,2,3,5,7],[4,8],[6]]=>22 [[1,2,3,4,7],[5,8],[6]]=>33 [[1,3,4,5,6],[2,8],[7]]=>0 [[1,2,4,5,6],[3,8],[7]]=>12 [[1,2,3,5,6],[4,8],[7]]=>22 [[1,2,3,4,6],[5,8],[7]]=>30 [[1,2,3,4,5],[6,8],[7]]=>37 [[1,3,5,6,7],[2,4],[8]]=>0 [[1,2,5,6,7],[3,4],[8]]=>8 [[1,3,4,6,7],[2,5],[8]]=>0 [[1,2,4,6,7],[3,5],[8]]=>12 [[1,2,3,6,7],[4,5],[8]]=>19 [[1,3,4,5,7],[2,6],[8]]=>0 [[1,2,4,5,7],[3,6],[8]]=>12 [[1,2,3,5,7],[4,6],[8]]=>22 [[1,2,3,4,7],[5,6],[8]]=>28 [[1,3,4,5,6],[2,7],[8]]=>0 [[1,2,4,5,6],[3,7],[8]]=>12 [[1,2,3,5,6],[4,7],[8]]=>22 [[1,2,3,4,6],[5,7],[8]]=>30 [[1,2,3,4,5],[6,7],[8]]=>35 [[1,5,6,7,8],[2],[3],[4]]=>0 [[1,4,6,7,8],[2],[3],[5]]=>5 [[1,3,6,7,8],[2],[4],[5]]=>0 [[1,2,6,7,8],[3],[4],[5]]=>12 [[1,4,5,7,8],[2],[3],[6]]=>5 [[1,3,5,7,8],[2],[4],[6]]=>0 [[1,2,5,7,8],[3],[4],[6]]=>16 [[1,3,4,7,8],[2],[5],[6]]=>0 [[1,2,4,7,8],[3],[5],[6]]=>12 [[1,2,3,7,8],[4],[5],[6]]=>22 [[1,4,5,6,8],[2],[3],[7]]=>5 [[1,3,5,6,8],[2],[4],[7]]=>0 [[1,2,5,6,8],[3],[4],[7]]=>16 [[1,3,4,6,8],[2],[5],[7]]=>0 [[1,2,4,6,8],[3],[5],[7]]=>12 [[1,2,3,6,8],[4],[5],[7]]=>25 [[1,3,4,5,8],[2],[6],[7]]=>0 [[1,2,4,5,8],[3],[6],[7]]=>12 [[1,2,3,5,8],[4],[6],[7]]=>22 [[1,2,3,4,8],[5],[6],[7]]=>30 [[1,4,5,6,7],[2],[3],[8]]=>5 [[1,3,5,6,7],[2],[4],[8]]=>0 [[1,2,5,6,7],[3],[4],[8]]=>16 [[1,3,4,6,7],[2],[5],[8]]=>0 [[1,2,4,6,7],[3],[5],[8]]=>12 [[1,2,3,6,7],[4],[5],[8]]=>25 [[1,3,4,5,7],[2],[6],[8]]=>0 [[1,2,4,5,7],[3],[6],[8]]=>12 [[1,2,3,5,7],[4],[6],[8]]=>22 [[1,2,3,4,7],[5],[6],[8]]=>32 [[1,3,4,5,6],[2],[7],[8]]=>0 [[1,2,4,5,6],[3],[7],[8]]=>12 [[1,2,3,5,6],[4],[7],[8]]=>22 [[1,2,3,4,6],[5],[7],[8]]=>30 [[1,2,3,4,5],[6],[7],[8]]=>36 [[1,3,5,7],[2,4,6,8]]=>0 [[1,2,5,7],[3,4,6,8]]=>10 [[1,3,4,7],[2,5,6,8]]=>0 [[1,2,4,7],[3,5,6,8]]=>10 [[1,2,3,7],[4,5,6,8]]=>18 [[1,3,5,6],[2,4,7,8]]=>0 [[1,2,5,6],[3,4,7,8]]=>10 [[1,3,4,6],[2,5,7,8]]=>0 [[1,2,4,6],[3,5,7,8]]=>10 [[1,2,3,6],[4,5,7,8]]=>18 [[1,3,4,5],[2,6,7,8]]=>0 [[1,2,4,5],[3,6,7,8]]=>10 [[1,2,3,5],[4,6,7,8]]=>18 [[1,2,3,4],[5,6,7,8]]=>24 [[1,4,6,8],[2,5,7],[3]]=>6 [[1,3,6,8],[2,5,7],[4]]=>0 [[1,2,6,8],[3,5,7],[4]]=>14 [[1,3,6,8],[2,4,7],[5]]=>0 [[1,2,6,8],[3,4,7],[5]]=>9 [[1,4,5,8],[2,6,7],[3]]=>6 [[1,3,5,8],[2,6,7],[4]]=>0 [[1,2,5,8],[3,6,7],[4]]=>14 [[1,3,4,8],[2,6,7],[5]]=>0 [[1,2,4,8],[3,6,7],[5]]=>9 [[1,2,3,8],[4,6,7],[5]]=>20 [[1,3,5,8],[2,4,7],[6]]=>0 [[1,2,5,8],[3,4,7],[6]]=>9 [[1,3,4,8],[2,5,7],[6]]=>0 [[1,2,4,8],[3,5,7],[6]]=>9 [[1,2,3,8],[4,5,7],[6]]=>16 [[1,3,5,8],[2,4,6],[7]]=>0 [[1,2,5,8],[3,4,6],[7]]=>9 [[1,3,4,8],[2,5,6],[7]]=>0 [[1,2,4,8],[3,5,6],[7]]=>9 [[1,2,3,8],[4,5,6],[7]]=>16 [[1,4,6,7],[2,5,8],[3]]=>6 [[1,3,6,7],[2,5,8],[4]]=>0 [[1,2,6,7],[3,5,8],[4]]=>14 [[1,3,6,7],[2,4,8],[5]]=>0 [[1,2,6,7],[3,4,8],[5]]=>9 [[1,4,5,7],[2,6,8],[3]]=>6 [[1,3,5,7],[2,6,8],[4]]=>0 [[1,2,5,7],[3,6,8],[4]]=>16 [[1,3,4,7],[2,6,8],[5]]=>0 [[1,2,4,7],[3,6,8],[5]]=>11 [[1,2,3,7],[4,6,8],[5]]=>23 [[1,3,5,7],[2,4,8],[6]]=>0 [[1,2,5,7],[3,4,8],[6]]=>9 [[1,3,4,7],[2,5,8],[6]]=>0 [[1,2,4,7],[3,5,8],[6]]=>11 [[1,2,3,7],[4,5,8],[6]]=>19 [[1,4,5,6],[2,7,8],[3]]=>6 [[1,3,5,6],[2,7,8],[4]]=>0 [[1,2,5,6],[3,7,8],[4]]=>16 [[1,3,4,6],[2,7,8],[5]]=>0 [[1,2,4,6],[3,7,8],[5]]=>11 [[1,2,3,6],[4,7,8],[5]]=>23 [[1,3,4,5],[2,7,8],[6]]=>0 [[1,2,4,5],[3,7,8],[6]]=>11 [[1,2,3,5],[4,7,8],[6]]=>19 [[1,2,3,4],[5,7,8],[6]]=>28 [[1,3,5,6],[2,4,8],[7]]=>0 [[1,2,5,6],[3,4,8],[7]]=>9 [[1,3,4,6],[2,5,8],[7]]=>0 [[1,2,4,6],[3,5,8],[7]]=>11 [[1,2,3,6],[4,5,8],[7]]=>19 [[1,3,4,5],[2,6,8],[7]]=>0 [[1,2,4,5],[3,6,8],[7]]=>11 [[1,2,3,5],[4,6,8],[7]]=>19 [[1,2,3,4],[5,6,8],[7]]=>25 [[1,3,5,7],[2,4,6],[8]]=>0 [[1,2,5,7],[3,4,6],[8]]=>9 [[1,3,4,7],[2,5,6],[8]]=>0 [[1,2,4,7],[3,5,6],[8]]=>9 [[1,2,3,7],[4,5,6],[8]]=>16 [[1,3,5,6],[2,4,7],[8]]=>0 [[1,2,5,6],[3,4,7],[8]]=>9 [[1,3,4,6],[2,5,7],[8]]=>0 [[1,2,4,6],[3,5,7],[8]]=>11 [[1,2,3,6],[4,5,7],[8]]=>19 [[1,3,4,5],[2,6,7],[8]]=>0 [[1,2,4,5],[3,6,7],[8]]=>11 [[1,2,3,5],[4,6,7],[8]]=>19 [[1,2,3,4],[5,6,7],[8]]=>25 [[1,4,7,8],[2,5],[3,6]]=>7 [[1,3,7,8],[2,5],[4,6]]=>0 [[1,2,7,8],[3,5],[4,6]]=>12 [[1,3,7,8],[2,4],[5,6]]=>0 [[1,2,7,8],[3,4],[5,6]]=>7 [[1,4,6,8],[2,5],[3,7]]=>7 [[1,3,6,8],[2,5],[4,7]]=>0 [[1,2,6,8],[3,5],[4,7]]=>12 [[1,3,6,8],[2,4],[5,7]]=>0 [[1,2,6,8],[3,4],[5,7]]=>7 [[1,4,5,8],[2,6],[3,7]]=>7 [[1,3,5,8],[2,6],[4,7]]=>0 [[1,2,5,8],[3,6],[4,7]]=>17 [[1,3,4,8],[2,6],[5,7]]=>0 [[1,2,4,8],[3,6],[5,7]]=>11 [[1,2,3,8],[4,6],[5,7]]=>21 [[1,3,5,8],[2,4],[6,7]]=>0 [[1,2,5,8],[3,4],[6,7]]=>7 [[1,3,4,8],[2,5],[6,7]]=>0 [[1,2,4,8],[3,5],[6,7]]=>11 [[1,2,3,8],[4,5],[6,7]]=>17 [[1,4,6,7],[2,5],[3,8]]=>7 [[1,3,6,7],[2,5],[4,8]]=>0 [[1,2,6,7],[3,5],[4,8]]=>12 [[1,3,6,7],[2,4],[5,8]]=>0 [[1,2,6,7],[3,4],[5,8]]=>7 [[1,4,5,7],[2,6],[3,8]]=>7 [[1,3,5,7],[2,6],[4,8]]=>0 [[1,2,5,7],[3,6],[4,8]]=>17 [[1,3,4,7],[2,6],[5,8]]=>0 [[1,2,4,7],[3,6],[5,8]]=>11 [[1,2,3,7],[4,6],[5,8]]=>21 [[1,3,5,7],[2,4],[6,8]]=>0 [[1,2,5,7],[3,4],[6,8]]=>7 [[1,3,4,7],[2,5],[6,8]]=>0 [[1,2,4,7],[3,5],[6,8]]=>11 [[1,2,3,7],[4,5],[6,8]]=>17 [[1,4,5,6],[2,7],[3,8]]=>7 [[1,3,5,6],[2,7],[4,8]]=>0 [[1,2,5,6],[3,7],[4,8]]=>17 [[1,3,4,6],[2,7],[5,8]]=>0 [[1,2,4,6],[3,7],[5,8]]=>11 [[1,2,3,6],[4,7],[5,8]]=>25 [[1,3,4,5],[2,7],[6,8]]=>0 [[1,2,4,5],[3,7],[6,8]]=>11 [[1,2,3,5],[4,7],[6,8]]=>20 [[1,2,3,4],[5,7],[6,8]]=>28 [[1,3,5,6],[2,4],[7,8]]=>0 [[1,2,5,6],[3,4],[7,8]]=>7 [[1,3,4,6],[2,5],[7,8]]=>0 [[1,2,4,6],[3,5],[7,8]]=>11 [[1,2,3,6],[4,5],[7,8]]=>17 [[1,3,4,5],[2,6],[7,8]]=>0 [[1,2,4,5],[3,6],[7,8]]=>11 [[1,2,3,5],[4,6],[7,8]]=>20 [[1,2,3,4],[5,6],[7,8]]=>25 [[1,5,7,8],[2,6],[3],[4]]=>0 [[1,4,7,8],[2,6],[3],[5]]=>5 [[1,3,7,8],[2,6],[4],[5]]=>0 [[1,2,7,8],[3,6],[4],[5]]=>8 [[1,4,7,8],[2,5],[3],[6]]=>5 [[1,3,7,8],[2,5],[4],[6]]=>0 [[1,2,7,8],[3,5],[4],[6]]=>12 [[1,3,7,8],[2,4],[5],[6]]=>0 [[1,2,7,8],[3,4],[5],[6]]=>8 [[1,5,6,8],[2,7],[3],[4]]=>0 [[1,4,6,8],[2,7],[3],[5]]=>5 [[1,3,6,8],[2,7],[4],[5]]=>0 [[1,2,6,8],[3,7],[4],[5]]=>11 [[1,4,5,8],[2,7],[3],[6]]=>5 [[1,3,5,8],[2,7],[4],[6]]=>0 [[1,2,5,8],[3,7],[4],[6]]=>15 [[1,3,4,8],[2,7],[5],[6]]=>0 [[1,2,4,8],[3,7],[5],[6]]=>11 [[1,2,3,8],[4,7],[5],[6]]=>18 [[1,4,6,8],[2,5],[3],[7]]=>5 [[1,3,6,8],[2,5],[4],[7]]=>0 [[1,2,6,8],[3,5],[4],[7]]=>12 [[1,3,6,8],[2,4],[5],[7]]=>0 [[1,2,6,8],[3,4],[5],[7]]=>8 [[1,4,5,8],[2,6],[3],[7]]=>5 [[1,3,5,8],[2,6],[4],[7]]=>0 [[1,2,5,8],[3,6],[4],[7]]=>15 [[1,3,4,8],[2,6],[5],[7]]=>0 [[1,2,4,8],[3,6],[5],[7]]=>11 [[1,2,3,8],[4,6],[5],[7]]=>21 [[1,3,5,8],[2,4],[6],[7]]=>0 [[1,2,5,8],[3,4],[6],[7]]=>8 [[1,3,4,8],[2,5],[6],[7]]=>0 [[1,2,4,8],[3,5],[6],[7]]=>11 [[1,2,3,8],[4,5],[6],[7]]=>18 [[1,5,6,7],[2,8],[3],[4]]=>0 [[1,4,6,7],[2,8],[3],[5]]=>5 [[1,3,6,7],[2,8],[4],[5]]=>0 [[1,2,6,7],[3,8],[4],[5]]=>11 [[1,4,5,7],[2,8],[3],[6]]=>5 [[1,3,5,7],[2,8],[4],[6]]=>0 [[1,2,5,7],[3,8],[4],[6]]=>15 [[1,3,4,7],[2,8],[5],[6]]=>0 [[1,2,4,7],[3,8],[5],[6]]=>11 [[1,2,3,7],[4,8],[5],[6]]=>20 [[1,4,5,6],[2,8],[3],[7]]=>5 [[1,3,5,6],[2,8],[4],[7]]=>0 [[1,2,5,6],[3,8],[4],[7]]=>15 [[1,3,4,6],[2,8],[5],[7]]=>0 [[1,2,4,6],[3,8],[5],[7]]=>11 [[1,2,3,6],[4,8],[5],[7]]=>23 [[1,3,4,5],[2,8],[6],[7]]=>0 [[1,2,4,5],[3,8],[6],[7]]=>11 [[1,2,3,5],[4,8],[6],[7]]=>20 [[1,2,3,4],[5,8],[6],[7]]=>26 [[1,4,6,7],[2,5],[3],[8]]=>5 [[1,3,6,7],[2,5],[4],[8]]=>0 [[1,2,6,7],[3,5],[4],[8]]=>12 [[1,3,6,7],[2,4],[5],[8]]=>0 [[1,2,6,7],[3,4],[5],[8]]=>8 [[1,4,5,7],[2,6],[3],[8]]=>5 [[1,3,5,7],[2,6],[4],[8]]=>0 [[1,2,5,7],[3,6],[4],[8]]=>15 [[1,3,4,7],[2,6],[5],[8]]=>0 [[1,2,4,7],[3,6],[5],[8]]=>11 [[1,2,3,7],[4,6],[5],[8]]=>21 [[1,3,5,7],[2,4],[6],[8]]=>0 [[1,2,5,7],[3,4],[6],[8]]=>8 [[1,3,4,7],[2,5],[6],[8]]=>0 [[1,2,4,7],[3,5],[6],[8]]=>11 [[1,2,3,7],[4,5],[6],[8]]=>18 [[1,4,5,6],[2,7],[3],[8]]=>5 [[1,3,5,6],[2,7],[4],[8]]=>0 [[1,2,5,6],[3,7],[4],[8]]=>15 [[1,3,4,6],[2,7],[5],[8]]=>0 [[1,2,4,6],[3,7],[5],[8]]=>11 [[1,2,3,6],[4,7],[5],[8]]=>23 [[1,3,4,5],[2,7],[6],[8]]=>0 [[1,2,4,5],[3,7],[6],[8]]=>11 [[1,2,3,5],[4,7],[6],[8]]=>20 [[1,2,3,4],[5,7],[6],[8]]=>28 [[1,3,5,6],[2,4],[7],[8]]=>0 [[1,2,5,6],[3,4],[7],[8]]=>8 [[1,3,4,6],[2,5],[7],[8]]=>0 [[1,2,4,6],[3,5],[7],[8]]=>11 [[1,2,3,6],[4,5],[7],[8]]=>18 [[1,3,4,5],[2,6],[7],[8]]=>0 [[1,2,4,5],[3,6],[7],[8]]=>11 [[1,2,3,5],[4,6],[7],[8]]=>20 [[1,2,3,4],[5,6],[7],[8]]=>26 [[1,6,7,8],[2],[3],[4],[5]]=>4 [[1,5,7,8],[2],[3],[4],[6]]=>0 [[1,4,7,8],[2],[3],[5],[6]]=>4 [[1,3,7,8],[2],[4],[5],[6]]=>0 [[1,2,7,8],[3],[4],[5],[6]]=>14 [[1,5,6,8],[2],[3],[4],[7]]=>0 [[1,4,6,8],[2],[3],[5],[7]]=>4 [[1,3,6,8],[2],[4],[5],[7]]=>0 [[1,2,6,8],[3],[4],[5],[7]]=>11 [[1,4,5,8],[2],[3],[6],[7]]=>4 [[1,3,5,8],[2],[4],[6],[7]]=>0 [[1,2,5,8],[3],[4],[6],[7]]=>14 [[1,3,4,8],[2],[5],[6],[7]]=>0 [[1,2,4,8],[3],[5],[6],[7]]=>11 [[1,2,3,8],[4],[5],[6],[7]]=>22 [[1,5,6,7],[2],[3],[4],[8]]=>0 [[1,4,6,7],[2],[3],[5],[8]]=>4 [[1,3,6,7],[2],[4],[5],[8]]=>0 [[1,2,6,7],[3],[4],[5],[8]]=>11 [[1,4,5,7],[2],[3],[6],[8]]=>4 [[1,3,5,7],[2],[4],[6],[8]]=>0 [[1,2,5,7],[3],[4],[6],[8]]=>14 [[1,3,4,7],[2],[5],[6],[8]]=>0 [[1,2,4,7],[3],[5],[6],[8]]=>11 [[1,2,3,7],[4],[5],[6],[8]]=>20 [[1,4,5,6],[2],[3],[7],[8]]=>4 [[1,3,5,6],[2],[4],[7],[8]]=>0 [[1,2,5,6],[3],[4],[7],[8]]=>14 [[1,3,4,6],[2],[5],[7],[8]]=>0 [[1,2,4,6],[3],[5],[7],[8]]=>11 [[1,2,3,6],[4],[5],[7],[8]]=>22 [[1,3,4,5],[2],[6],[7],[8]]=>0 [[1,2,4,5],[3],[6],[7],[8]]=>11 [[1,2,3,5],[4],[6],[7],[8]]=>20 [[1,2,3,4],[5],[6],[7],[8]]=>28 [[1,4,7],[2,5,8],[3,6]]=>7 [[1,3,7],[2,5,8],[4,6]]=>0 [[1,2,7],[3,5,8],[4,6]]=>12 [[1,3,7],[2,4,8],[5,6]]=>0 [[1,2,7],[3,4,8],[5,6]]=>7 [[1,4,6],[2,5,8],[3,7]]=>7 [[1,3,6],[2,5,8],[4,7]]=>0 [[1,2,6],[3,5,8],[4,7]]=>12 [[1,3,6],[2,4,8],[5,7]]=>0 [[1,2,6],[3,4,8],[5,7]]=>7 [[1,4,5],[2,6,8],[3,7]]=>7 [[1,3,5],[2,6,8],[4,7]]=>0 [[1,2,5],[3,6,8],[4,7]]=>15 [[1,3,4],[2,6,8],[5,7]]=>0 [[1,2,4],[3,6,8],[5,7]]=>9 [[1,2,3],[4,6,8],[5,7]]=>19 [[1,3,5],[2,4,8],[6,7]]=>0 [[1,2,5],[3,4,8],[6,7]]=>7 [[1,3,4],[2,5,8],[6,7]]=>0 [[1,2,4],[3,5,8],[6,7]]=>9 [[1,2,3],[4,5,8],[6,7]]=>15 [[1,4,6],[2,5,7],[3,8]]=>7 [[1,3,6],[2,5,7],[4,8]]=>0 [[1,2,6],[3,5,7],[4,8]]=>15 [[1,3,6],[2,4,7],[5,8]]=>0 [[1,2,6],[3,4,7],[5,8]]=>9 [[1,4,5],[2,6,7],[3,8]]=>7 [[1,3,5],[2,6,7],[4,8]]=>0 [[1,2,5],[3,6,7],[4,8]]=>15 [[1,3,4],[2,6,7],[5,8]]=>0 [[1,2,4],[3,6,7],[5,8]]=>9 [[1,2,3],[4,6,7],[5,8]]=>19 [[1,3,5],[2,4,7],[6,8]]=>0 [[1,2,5],[3,4,7],[6,8]]=>9 [[1,3,4],[2,5,7],[6,8]]=>0 [[1,2,4],[3,5,7],[6,8]]=>9 [[1,2,3],[4,5,7],[6,8]]=>15 [[1,3,5],[2,4,6],[7,8]]=>0 [[1,2,5],[3,4,6],[7,8]]=>9 [[1,3,4],[2,5,6],[7,8]]=>0 [[1,2,4],[3,5,6],[7,8]]=>9 [[1,2,3],[4,5,6],[7,8]]=>15 [[1,5,7],[2,6,8],[3],[4]]=>0 [[1,4,7],[2,6,8],[3],[5]]=>5 [[1,3,7],[2,6,8],[4],[5]]=>0 [[1,2,7],[3,6,8],[4],[5]]=>9 [[1,4,7],[2,5,8],[3],[6]]=>5 [[1,3,7],[2,5,8],[4],[6]]=>0 [[1,2,7],[3,5,8],[4],[6]]=>13 [[1,3,7],[2,4,8],[5],[6]]=>0 [[1,2,7],[3,4,8],[5],[6]]=>9 [[1,5,6],[2,7,8],[3],[4]]=>0 [[1,4,6],[2,7,8],[3],[5]]=>5 [[1,3,6],[2,7,8],[4],[5]]=>0 [[1,2,6],[3,7,8],[4],[5]]=>9 [[1,4,5],[2,7,8],[3],[6]]=>5 [[1,3,5],[2,7,8],[4],[6]]=>0 [[1,2,5],[3,7,8],[4],[6]]=>13 [[1,3,4],[2,7,8],[5],[6]]=>0 [[1,2,4],[3,7,8],[5],[6]]=>9 [[1,2,3],[4,7,8],[5],[6]]=>16 [[1,4,6],[2,5,8],[3],[7]]=>5 [[1,3,6],[2,5,8],[4],[7]]=>0 [[1,2,6],[3,5,8],[4],[7]]=>13 [[1,3,6],[2,4,8],[5],[7]]=>0 [[1,2,6],[3,4,8],[5],[7]]=>9 [[1,4,5],[2,6,8],[3],[7]]=>5 [[1,3,5],[2,6,8],[4],[7]]=>0 [[1,2,5],[3,6,8],[4],[7]]=>13 [[1,3,4],[2,6,8],[5],[7]]=>0 [[1,2,4],[3,6,8],[5],[7]]=>9 [[1,2,3],[4,6,8],[5],[7]]=>19 [[1,3,5],[2,4,8],[6],[7]]=>0 [[1,2,5],[3,4,8],[6],[7]]=>9 [[1,3,4],[2,5,8],[6],[7]]=>0 [[1,2,4],[3,5,8],[6],[7]]=>9 [[1,2,3],[4,5,8],[6],[7]]=>16 [[1,4,6],[2,5,7],[3],[8]]=>5 [[1,3,6],[2,5,7],[4],[8]]=>0 [[1,2,6],[3,5,7],[4],[8]]=>13 [[1,3,6],[2,4,7],[5],[8]]=>0 [[1,2,6],[3,4,7],[5],[8]]=>9 [[1,4,5],[2,6,7],[3],[8]]=>5 [[1,3,5],[2,6,7],[4],[8]]=>0 [[1,2,5],[3,6,7],[4],[8]]=>13 [[1,3,4],[2,6,7],[5],[8]]=>0 [[1,2,4],[3,6,7],[5],[8]]=>9 [[1,2,3],[4,6,7],[5],[8]]=>19 [[1,3,5],[2,4,7],[6],[8]]=>0 [[1,2,5],[3,4,7],[6],[8]]=>9 [[1,3,4],[2,5,7],[6],[8]]=>0 [[1,2,4],[3,5,7],[6],[8]]=>9 [[1,2,3],[4,5,7],[6],[8]]=>16 [[1,3,5],[2,4,6],[7],[8]]=>0 [[1,2,5],[3,4,6],[7],[8]]=>9 [[1,3,4],[2,5,6],[7],[8]]=>0 [[1,2,4],[3,5,6],[7],[8]]=>9 [[1,2,3],[4,5,6],[7],[8]]=>16 [[1,5,8],[2,6],[3,7],[4]]=>0 [[1,4,8],[2,6],[3,7],[5]]=>5 [[1,3,8],[2,6],[4,7],[5]]=>0 [[1,2,8],[3,6],[4,7],[5]]=>7 [[1,4,8],[2,5],[3,7],[6]]=>5 [[1,3,8],[2,5],[4,7],[6]]=>0 [[1,2,8],[3,5],[4,7],[6]]=>11 [[1,3,8],[2,4],[5,7],[6]]=>0 [[1,2,8],[3,4],[5,7],[6]]=>7 [[1,4,8],[2,5],[3,6],[7]]=>7 [[1,3,8],[2,5],[4,6],[7]]=>0 [[1,2,8],[3,5],[4,6],[7]]=>11 [[1,3,8],[2,4],[5,6],[7]]=>0 [[1,2,8],[3,4],[5,6],[7]]=>7 [[1,5,7],[2,6],[3,8],[4]]=>0 [[1,4,7],[2,6],[3,8],[5]]=>5 [[1,3,7],[2,6],[4,8],[5]]=>0 [[1,2,7],[3,6],[4,8],[5]]=>7 [[1,4,7],[2,5],[3,8],[6]]=>5 [[1,3,7],[2,5],[4,8],[6]]=>0 [[1,2,7],[3,5],[4,8],[6]]=>11 [[1,3,7],[2,4],[5,8],[6]]=>0 [[1,2,7],[3,4],[5,8],[6]]=>7 [[1,5,6],[2,7],[3,8],[4]]=>0 [[1,4,6],[2,7],[3,8],[5]]=>5 [[1,3,6],[2,7],[4,8],[5]]=>0 [[1,2,6],[3,7],[4,8],[5]]=>10 [[1,4,5],[2,7],[3,8],[6]]=>5 [[1,3,5],[2,7],[4,8],[6]]=>0 [[1,2,5],[3,7],[4,8],[6]]=>14 [[1,3,4],[2,7],[5,8],[6]]=>0 [[1,2,4],[3,7],[5,8],[6]]=>10 [[1,2,3],[4,7],[5,8],[6]]=>16 [[1,4,6],[2,5],[3,8],[7]]=>5 [[1,3,6],[2,5],[4,8],[7]]=>0 [[1,2,6],[3,5],[4,8],[7]]=>11 [[1,3,6],[2,4],[5,8],[7]]=>0 [[1,2,6],[3,4],[5,8],[7]]=>7 [[1,4,5],[2,6],[3,8],[7]]=>5 [[1,3,5],[2,6],[4,8],[7]]=>0 [[1,2,5],[3,6],[4,8],[7]]=>14 [[1,3,4],[2,6],[5,8],[7]]=>0 [[1,2,4],[3,6],[5,8],[7]]=>10 [[1,2,3],[4,6],[5,8],[7]]=>19 [[1,3,5],[2,4],[6,8],[7]]=>0 [[1,2,5],[3,4],[6,8],[7]]=>7 [[1,3,4],[2,5],[6,8],[7]]=>0 [[1,2,4],[3,5],[6,8],[7]]=>10 [[1,2,3],[4,5],[6,8],[7]]=>16 [[1,4,7],[2,5],[3,6],[8]]=>7 [[1,3,7],[2,5],[4,6],[8]]=>0 [[1,2,7],[3,5],[4,6],[8]]=>11 [[1,3,7],[2,4],[5,6],[8]]=>0 [[1,2,7],[3,4],[5,6],[8]]=>7 [[1,4,6],[2,5],[3,7],[8]]=>7 [[1,3,6],[2,5],[4,7],[8]]=>0 [[1,2,6],[3,5],[4,7],[8]]=>11 [[1,3,6],[2,4],[5,7],[8]]=>0 [[1,2,6],[3,4],[5,7],[8]]=>7 [[1,4,5],[2,6],[3,7],[8]]=>7 [[1,3,5],[2,6],[4,7],[8]]=>0 [[1,2,5],[3,6],[4,7],[8]]=>16 [[1,3,4],[2,6],[5,7],[8]]=>0 [[1,2,4],[3,6],[5,7],[8]]=>10 [[1,2,3],[4,6],[5,7],[8]]=>19 [[1,3,5],[2,4],[6,7],[8]]=>0 [[1,2,5],[3,4],[6,7],[8]]=>7 [[1,3,4],[2,5],[6,7],[8]]=>0 [[1,2,4],[3,5],[6,7],[8]]=>10 [[1,2,3],[4,5],[6,7],[8]]=>16 [[1,6,8],[2,7],[3],[4],[5]]=>4 [[1,5,8],[2,7],[3],[4],[6]]=>0 [[1,4,8],[2,7],[3],[5],[6]]=>4 [[1,3,8],[2,7],[4],[5],[6]]=>0 [[1,2,8],[3,7],[4],[5],[6]]=>11 [[1,5,8],[2,6],[3],[4],[7]]=>0 [[1,4,8],[2,6],[3],[5],[7]]=>4 [[1,3,8],[2,6],[4],[5],[7]]=>0 [[1,2,8],[3,6],[4],[5],[7]]=>8 [[1,4,8],[2,5],[3],[6],[7]]=>4 [[1,3,8],[2,5],[4],[6],[7]]=>0 [[1,2,8],[3,5],[4],[6],[7]]=>11 [[1,3,8],[2,4],[5],[6],[7]]=>0 [[1,2,8],[3,4],[5],[6],[7]]=>8 [[1,6,7],[2,8],[3],[4],[5]]=>4 [[1,5,7],[2,8],[3],[4],[6]]=>0 [[1,4,7],[2,8],[3],[5],[6]]=>4 [[1,3,7],[2,8],[4],[5],[6]]=>0 [[1,2,7],[3,8],[4],[5],[6]]=>13 [[1,5,6],[2,8],[3],[4],[7]]=>0 [[1,4,6],[2,8],[3],[5],[7]]=>4 [[1,3,6],[2,8],[4],[5],[7]]=>0 [[1,2,6],[3,8],[4],[5],[7]]=>10 [[1,4,5],[2,8],[3],[6],[7]]=>4 [[1,3,5],[2,8],[4],[6],[7]]=>0 [[1,2,5],[3,8],[4],[6],[7]]=>13 [[1,3,4],[2,8],[5],[6],[7]]=>0 [[1,2,4],[3,8],[5],[6],[7]]=>10 [[1,2,3],[4,8],[5],[6],[7]]=>19 [[1,5,7],[2,6],[3],[4],[8]]=>0 [[1,4,7],[2,6],[3],[5],[8]]=>4 [[1,3,7],[2,6],[4],[5],[8]]=>0 [[1,2,7],[3,6],[4],[5],[8]]=>8 [[1,4,7],[2,5],[3],[6],[8]]=>4 [[1,3,7],[2,5],[4],[6],[8]]=>0 [[1,2,7],[3,5],[4],[6],[8]]=>11 [[1,3,7],[2,4],[5],[6],[8]]=>0 [[1,2,7],[3,4],[5],[6],[8]]=>8 [[1,5,6],[2,7],[3],[4],[8]]=>0 [[1,4,6],[2,7],[3],[5],[8]]=>4 [[1,3,6],[2,7],[4],[5],[8]]=>0 [[1,2,6],[3,7],[4],[5],[8]]=>10 [[1,4,5],[2,7],[3],[6],[8]]=>4 [[1,3,5],[2,7],[4],[6],[8]]=>0 [[1,2,5],[3,7],[4],[6],[8]]=>13 [[1,3,4],[2,7],[5],[6],[8]]=>0 [[1,2,4],[3,7],[5],[6],[8]]=>10 [[1,2,3],[4,7],[5],[6],[8]]=>17 [[1,4,6],[2,5],[3],[7],[8]]=>4 [[1,3,6],[2,5],[4],[7],[8]]=>0 [[1,2,6],[3,5],[4],[7],[8]]=>11 [[1,3,6],[2,4],[5],[7],[8]]=>0 [[1,2,6],[3,4],[5],[7],[8]]=>8 [[1,4,5],[2,6],[3],[7],[8]]=>4 [[1,3,5],[2,6],[4],[7],[8]]=>0 [[1,2,5],[3,6],[4],[7],[8]]=>13 [[1,3,4],[2,6],[5],[7],[8]]=>0 [[1,2,4],[3,6],[5],[7],[8]]=>10 [[1,2,3],[4,6],[5],[7],[8]]=>19 [[1,3,5],[2,4],[6],[7],[8]]=>0 [[1,2,5],[3,4],[6],[7],[8]]=>8 [[1,3,4],[2,5],[6],[7],[8]]=>0 [[1,2,4],[3,5],[6],[7],[8]]=>10 [[1,2,3],[4,5],[6],[7],[8]]=>17 [[1,7,8],[2],[3],[4],[5],[6]]=>0 [[1,6,8],[2],[3],[4],[5],[7]]=>3 [[1,5,8],[2],[3],[4],[6],[7]]=>0 [[1,4,8],[2],[3],[5],[6],[7]]=>3 [[1,3,8],[2],[4],[5],[6],[7]]=>0 [[1,2,8],[3],[4],[5],[6],[7]]=>10 [[1,6,7],[2],[3],[4],[5],[8]]=>3 [[1,5,7],[2],[3],[4],[6],[8]]=>0 [[1,4,7],[2],[3],[5],[6],[8]]=>3 [[1,3,7],[2],[4],[5],[6],[8]]=>0 [[1,2,7],[3],[4],[5],[6],[8]]=>12 [[1,5,6],[2],[3],[4],[7],[8]]=>0 [[1,4,6],[2],[3],[5],[7],[8]]=>3 [[1,3,6],[2],[4],[5],[7],[8]]=>0 [[1,2,6],[3],[4],[5],[7],[8]]=>10 [[1,4,5],[2],[3],[6],[7],[8]]=>3 [[1,3,5],[2],[4],[6],[7],[8]]=>0 [[1,2,5],[3],[4],[6],[7],[8]]=>12 [[1,3,4],[2],[5],[6],[7],[8]]=>0 [[1,2,4],[3],[5],[6],[7],[8]]=>10 [[1,2,3],[4],[5],[6],[7],[8]]=>18 [[1,5],[2,6],[3,7],[4,8]]=>0 [[1,4],[2,6],[3,7],[5,8]]=>6 [[1,3],[2,6],[4,7],[5,8]]=>0 [[1,2],[3,6],[4,7],[5,8]]=>6 [[1,4],[2,5],[3,7],[6,8]]=>6 [[1,3],[2,5],[4,7],[6,8]]=>0 [[1,2],[3,5],[4,7],[6,8]]=>10 [[1,3],[2,4],[5,7],[6,8]]=>0 [[1,2],[3,4],[5,7],[6,8]]=>6 [[1,4],[2,5],[3,6],[7,8]]=>6 [[1,3],[2,5],[4,6],[7,8]]=>0 [[1,2],[3,5],[4,6],[7,8]]=>10 [[1,3],[2,4],[5,6],[7,8]]=>0 [[1,2],[3,4],[5,6],[7,8]]=>6 [[1,6],[2,7],[3,8],[4],[5]]=>4 [[1,5],[2,7],[3,8],[4],[6]]=>0 [[1,4],[2,7],[3,8],[5],[6]]=>4 [[1,3],[2,7],[4,8],[5],[6]]=>0 [[1,2],[3,7],[4,8],[5],[6]]=>10 [[1,5],[2,6],[3,8],[4],[7]]=>0 [[1,4],[2,6],[3,8],[5],[7]]=>4 [[1,3],[2,6],[4,8],[5],[7]]=>0 [[1,2],[3,6],[4,8],[5],[7]]=>7 [[1,4],[2,5],[3,8],[6],[7]]=>4 [[1,3],[2,5],[4,8],[6],[7]]=>0 [[1,2],[3,5],[4,8],[6],[7]]=>10 [[1,3],[2,4],[5,8],[6],[7]]=>0 [[1,2],[3,4],[5,8],[6],[7]]=>7 [[1,5],[2,6],[3,7],[4],[8]]=>0 [[1,4],[2,6],[3,7],[5],[8]]=>4 [[1,3],[2,6],[4,7],[5],[8]]=>0 [[1,2],[3,6],[4,7],[5],[8]]=>7 [[1,4],[2,5],[3,7],[6],[8]]=>4 [[1,3],[2,5],[4,7],[6],[8]]=>0 [[1,2],[3,5],[4,7],[6],[8]]=>10 [[1,3],[2,4],[5,7],[6],[8]]=>0 [[1,2],[3,4],[5,7],[6],[8]]=>7 [[1,4],[2,5],[3,6],[7],[8]]=>7 [[1,3],[2,5],[4,6],[7],[8]]=>0 [[1,2],[3,5],[4,6],[7],[8]]=>10 [[1,3],[2,4],[5,6],[7],[8]]=>0 [[1,2],[3,4],[5,6],[7],[8]]=>7 [[1,7],[2,8],[3],[4],[5],[6]]=>0 [[1,6],[2,8],[3],[4],[5],[7]]=>3 [[1,5],[2,8],[3],[4],[6],[7]]=>0 [[1,4],[2,8],[3],[5],[6],[7]]=>3 [[1,3],[2,8],[4],[5],[6],[7]]=>0 [[1,2],[3,8],[4],[5],[6],[7]]=>8 [[1,6],[2,7],[3],[4],[5],[8]]=>3 [[1,5],[2,7],[3],[4],[6],[8]]=>0 [[1,4],[2,7],[3],[5],[6],[8]]=>3 [[1,3],[2,7],[4],[5],[6],[8]]=>0 [[1,2],[3,7],[4],[5],[6],[8]]=>10 [[1,5],[2,6],[3],[4],[7],[8]]=>0 [[1,4],[2,6],[3],[5],[7],[8]]=>3 [[1,3],[2,6],[4],[5],[7],[8]]=>0 [[1,2],[3,6],[4],[5],[7],[8]]=>8 [[1,4],[2,5],[3],[6],[7],[8]]=>3 [[1,3],[2,5],[4],[6],[7],[8]]=>0 [[1,2],[3,5],[4],[6],[7],[8]]=>10 [[1,3],[2,4],[5],[6],[7],[8]]=>0 [[1,2],[3,4],[5],[6],[7],[8]]=>8 [[1,8],[2],[3],[4],[5],[6],[7]]=>2 [[1,7],[2],[3],[4],[5],[6],[8]]=>0 [[1,6],[2],[3],[4],[5],[7],[8]]=>2 [[1,5],[2],[3],[4],[6],[7],[8]]=>0 [[1,4],[2],[3],[5],[6],[7],[8]]=>2 [[1,3],[2],[4],[5],[6],[7],[8]]=>0 [[1,2],[3],[4],[5],[6],[7],[8]]=>10 [[1],[2],[3],[4],[5],[6],[7],[8]]=>0 [[1,2,3,4,5,6,7,8,9]]=>81 [[1,2,3,4,5,6,7,8],[9]]=>70 [[1,2,3,4,5,6,7],[8,9]]=>59 [[1,2,3,4,5,6,7],[8],[9]]=>61 [[1,3,4,5,6,7,8,9],[2]]=>0 [[1,2,5,6,7,8,9],[3,4]]=>9 [[1,4,5,6,7,8,9],[2],[3]]=>7 [[1,2,3,7,8,9],[4,5,6]]=>18 [[1,3,5,7,8,9],[2,4,6]]=>0 [[1,3,5,6,7,8,9],[2,4]]=>0 [[1,2,3,4,5,6,7,9],[8]]=>66 [[1,2,3,4,5,6,9],[7,8]]=>53 [[1,2,3,4,5,6,9],[7],[8]]=>57 [[1,3,4,5,6,7,8],[2,9]]=>0 [[1,3,4,5,6,7,8],[2],[9]]=>0 [[1,2,3,4,5,6,8],[7,9]]=>55 [[1,2,4,5,6,7,8,9],[3]]=>16 [[1,2,3,4,7,8,9],[5,6]]=>35 [[1,2,5,6,7,8,9],[3],[4]]=>21 [[1,2,3,6,7,8,9],[4,5]]=>23 [[1,2,3,4,8,9],[5,6,7]]=>30 [[1,2,3,4,5,6,8,9],[7]]=>60 [[1,3,5,6,7,8,9],[2],[4]]=>0 [[1,2,4,5,6,7,8],[3],[9]]=>15 [[1,2,3,4,5,7,9],[6,8]]=>48 [[1,2,4,6,7,8,9],[3,5]]=>15 [[1,3,4,5,6,7,9],[2,8]]=>0 [[1,2,4,5,6,7,8],[3,9]]=>15 [[1,2,4,6,8,9],[3,5,7]]=>14 [[1,2,3,4,5,8,9],[6],[7]]=>51 [[1,2,3,4,5,8,9],[6,7]]=>45 [[1,2,3,5,7,9],[4,6,8]]=>26 [[1,3,4,5,7,9],[2,6,8]]=>0 [[1,2,3,6,7,8,9],[4],[5]]=>33 [[1,2,3,5,6,7,8,9],[4]]=>30 [[1,2,3,5,6,7,8],[4],[9]]=>28 [[1,2,3,4,6,7,8],[5],[9]]=>39 [[1,3,4,5,7,8,9],[2],[6]]=>0 [[1,2,3,4,5,7,8],[6],[9]]=>48 [[1,3,4,5,6,8,9],[2],[7]]=>0 [[1,3,4,6,7,8,9],[2],[5]]=>0 [[1,2,3,4,6,7,9],[5],[8]]=>39 [[1,2,4,5,7,8,9],[3],[6]]=>15 [[1,3,4,5,7,8,9],[2,6]]=>0 [[1,3,4,6,7,8,9],[2,5]]=>0 [[1,3,4,5,6,7,9],[2],[8]]=>0 [[1,2,3,4,5,6,8],[7],[9]]=>55 [[1,2,3,4,5,7,8],[6,9]]=>48 [[1,2,4,5,6,7,9],[3,8]]=>15 [[1,2,3,5,6,7,8],[4,9]]=>28 [[1,2,4,6,7,8,9],[3],[5]]=>15 [[1,2,3,4,5,7,9],[6],[8]]=>48 [[1,2,4,5,6,7,9],[3],[8]]=>15 [[1,2,3,4,6,7,9],[5,8]]=>39 [[1,3,4,5,6,8,9],[2,7]]=>0 [[1,2,5,6,7,9],[3,4,8]]=>10 [[1,3,4,7,8,9],[2,5,6]]=>0 [[1,2,3,4,5,7,8,9],[6]]=>52 [[1,2,3,4,6,8,9],[5,7]]=>39 [[1,2,3,5,7,8,9],[4,6]]=>28 [[1,2,4,7,8,9],[3,5,6]]=>10 [[1,2,4,5,7,9],[3,6,8]]=>14 [[1,3,5,6,7,9],[2,4,8]]=>0 [[1,2,3,5,6,8,9],[4],[7]]=>28 [[1,2,3,4,6,7,8,9],[5]]=>42 [[1,3,4,5,8,9],[2,6,7]]=>0 [[1,2,4,5,7,8,9],[3,6]]=>15 [[1,3,5,6,8,9],[2,4,7]]=>0 [[1,2,3,4,7,8,9],[5],[6]]=>43 [[1,2,3,5,6,8,9],[4,7]]=>28 [[1,2,3,5,7,8,9],[4],[6]]=>28 [[1,2,5,7,8,9],[3,4,6]]=>10 [[1,2,3,4,6,8,9],[5],[7]]=>39 [[1,2,4,5,6,8,9],[3,7]]=>15 [[1,2,3,6,7,9],[4,5,8]]=>23 [[1,2,3,5,6,7,9],[4],[8]]=>28 [[1,2,3,5,6,7,9],[4,8]]=>28 [[1,2,3,4,6,7,8],[5,9]]=>39 [[1,2,4,5,6,8,9],[3],[7]]=>15 [[1,2,5,6,8,9],[3,4,7]]=>10 [[1,3,4,6,8,9],[2,5,7]]=>0 [[1,2,3,6,8,9],[4,5,7]]=>23 [[1,2,4,5,8,9],[3,6,7]]=>14 [[1,2,3,5,8,9],[4,6,7]]=>23 [[1,3,4,6,7,9],[2,5,8]]=>0 [[1,2,4,6,7,9],[3,5,8]]=>14
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Description
Eigenvalues of the random-to-random operator acting on a simple module.
The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module [1].
References
[1] Dieker, A. B., Saliola, F. Spectral analysis of random-to-random Markov chains arXiv:1509.08580
[2] Eigenvalues of the random-to-random operator acting on the regular representation Eigenvalues of the random-to-random operator acting on the regular representation. St000500
[3] The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000046
Code
def diagonal_index_of_partition(la):
    return sum((j - i) for (i, j) in la.cells())

def binomial_shifted_diagonal_index_of_partition(partition):
    return binomial(partition.size() + 1, 2) + diagonal_index_of_partition(partition)

def is_desarrangement_tableau(t):
    if t.size() == 0:
        return True
    descents = t.standard_descents()
    ascents = [i for i in t.entries() if i not in descents]
    return min(ascents) % 2 == 0

def r2r_statistic_on_standard_tableaux(t):
    # remove 1 and rectify until we get a desarrangement tableau
    s = copy(t)
    while not is_desarrangement_tableau(s):
        s = SkewTableau([[(i-1 if i > 1 else None) for i in row] for row in s])
        s = StandardTableau(s.rectify())
    return binomial_shifted_diagonal_index_of_partition(t.shape()) \
           - binomial_shifted_diagonal_index_of_partition(s.shape())

def statistic(t):
    return r2r_statistic_on_standard_tableaux(t)
Created
May 25, 2016 at 18:06 by Franco Saliola
Updated
Dec 30, 2016 at 10:33 by Christian Stump