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Identifier
Values
=>
Cc0028;cc-rep
[[1],[]]=>2 [[2],[]]=>3 [[1,1],[]]=>3 [[2,1],[1]]=>4 [[3],[]]=>4 [[2,1],[]]=>5 [[3,1],[1]]=>6 [[2,2],[1]]=>5 [[3,2],[2]]=>6 [[1,1,1],[]]=>4 [[2,2,1],[1,1]]=>6 [[2,1,1],[1]]=>6 [[3,2,1],[2,1]]=>8 [[4],[]]=>5 [[3,1],[]]=>7 [[4,1],[1]]=>8 [[2,2],[]]=>7 [[3,2],[1]]=>8 [[4,2],[2]]=>9 [[2,1,1],[]]=>7 [[3,2,1],[1,1]]=>10 [[3,1,1],[1]]=>9 [[4,2,1],[2,1]]=>12 [[3,3],[2]]=>7 [[4,3],[3]]=>8 [[2,2,1],[1]]=>8 [[3,3,1],[2,1]]=>10 [[3,2,1],[2]]=>10 [[4,3,1],[3,1]]=>12 [[2,2,2],[1,1]]=>7 [[3,3,2],[2,2]]=>9 [[3,2,2],[2,1]]=>10 [[4,3,2],[3,2]]=>12 [[1,1,1,1],[]]=>5 [[2,2,2,1],[1,1,1]]=>8 [[2,2,1,1],[1,1]]=>9 [[3,3,2,1],[2,2,1]]=>12 [[2,1,1,1],[1]]=>8 [[3,2,2,1],[2,1,1]]=>12 [[3,2,1,1],[2,1]]=>12 [[4,3,2,1],[3,2,1]]=>16 [[5],[]]=>6 [[4,1],[]]=>9 [[5,1],[1]]=>10 [[3,2],[]]=>10 [[4,2],[1]]=>11 [[5,2],[2]]=>12 [[3,1,1],[]]=>10 [[4,2,1],[1,1]]=>14 [[4,1,1],[1]]=>12 [[5,2,1],[2,1]]=>16 [[3,3],[1]]=>10 [[4,3],[2]]=>11 [[5,3],[3]]=>12 [[2,2,1],[]]=>10 [[3,3,1],[1,1]]=>14 [[3,2,1],[1]]=>13 [[4,3,1],[2,1]]=>16 [[4,2,1],[2]]=>15 [[5,3,1],[3,1]]=>18 [[3,2,2],[1,1]]=>12 [[4,3,2],[2,2]]=>15 [[4,2,2],[2,1]]=>15 [[5,3,2],[3,2]]=>18 [[2,1,1,1],[]]=>9 [[3,2,2,1],[1,1,1]]=>14 [[3,2,1,1],[1,1]]=>15 [[4,3,2,1],[2,2,1]]=>20 [[3,1,1,1],[1]]=>12 [[4,2,2,1],[2,1,1]]=>18 [[4,2,1,1],[2,1]]=>18 [[5,3,2,1],[3,2,1]]=>24 [[4,4],[3]]=>9 [[5,4],[4]]=>10 [[3,3,1],[2]]=>12 [[4,4,1],[3,1]]=>14 [[4,3,1],[3]]=>14 [[5,4,1],[4,1]]=>16 [[2,2,2],[1]]=>10 [[3,3,2],[2,1]]=>13 [[4,4,2],[3,2]]=>15 [[3,2,2],[2]]=>14 [[4,3,2],[3,1]]=>16 [[5,4,2],[4,2]]=>18 [[2,2,1,1],[1]]=>11 [[3,3,2,1],[2,1,1]]=>16 [[3,3,1,1],[2,1]]=>15 [[4,4,2,1],[3,2,1]]=>20 [[3,2,1,1],[2]]=>14 [[4,3,2,1],[3,1,1]]=>20 [[4,3,1,1],[3,1]]=>18 [[5,4,2,1],[4,2,1]]=>24 [[3,3,3],[2,2]]=>10 [[4,4,3],[3,3]]=>12 [[4,3,3],[3,2]]=>14 [[5,4,3],[4,3]]=>16 [[2,2,2,1],[1,1]]=>11 [[3,3,3,1],[2,2,1]]=>14 [[3,3,2,1],[2,2]]=>15 [[4,4,3,1],[3,3,1]]=>18 [[3,2,2,1],[2,1]]=>16 [[4,3,3,1],[3,2,1]]=>20 [[4,3,2,1],[3,2]]=>20 [[5,4,3,1],[4,3,1]]=>24 [[2,2,2,2],[1,1,1]]=>9 [[3,3,3,2],[2,2,2]]=>12 [[3,3,2,2],[2,2,1]]=>15 [[4,4,3,2],[3,3,2]]=>18 [[3,2,2,2],[2,1,1]]=>14 [[4,3,3,2],[3,2,2]]=>18 [[4,3,2,2],[3,2,1]]=>20 [[5,4,3,2],[4,3,2]]=>24 [[1,1,1,1,1],[]]=>6 [[2,2,2,2,1],[1,1,1,1]]=>10 [[2,2,2,1,1],[1,1,1]]=>12 [[3,3,3,2,1],[2,2,2,1]]=>16 [[2,2,1,1,1],[1,1]]=>12 [[3,3,2,2,1],[2,2,1,1]]=>18 [[3,3,2,1,1],[2,2,1]]=>18 [[4,4,3,2,1],[3,3,2,1]]=>24 [[2,1,1,1,1],[1]]=>10 [[3,2,2,2,1],[2,1,1,1]]=>16 [[3,2,2,1,1],[2,1,1]]=>18 [[4,3,3,2,1],[3,2,2,1]]=>24 [[3,2,1,1,1],[2,1]]=>16 [[4,3,2,2,1],[3,2,1,1]]=>24 [[4,3,2,1,1],[3,2,1]]=>24 [[5,4,3,2,1],[4,3,2,1]]=>32 [[6],[]]=>7 [[5,1],[]]=>11 [[6,1],[1]]=>12 [[4,2],[]]=>13 [[5,2],[1]]=>14 [[6,2],[2]]=>15 [[4,1,1],[]]=>13 [[5,2,1],[1,1]]=>18 [[5,1,1],[1]]=>15 [[6,2,1],[2,1]]=>20 [[3,3],[]]=>13 [[4,3],[1]]=>14 [[5,3],[2]]=>15 [[6,3],[3]]=>16 [[3,2,1],[]]=>15 [[4,3,1],[1,1]]=>20 [[4,2,1],[1]]=>18 [[5,3,1],[2,1]]=>22 [[5,2,1],[2]]=>20 [[6,3,1],[3,1]]=>24 [[4,2,2],[1,1]]=>17 [[5,3,2],[2,2]]=>21 [[5,2,2],[2,1]]=>20 [[6,3,2],[3,2]]=>24 [[3,1,1,1],[]]=>13 [[4,2,2,1],[1,1,1]]=>20 [[4,2,1,1],[1,1]]=>21 [[5,3,2,1],[2,2,1]]=>28 [[4,1,1,1],[1]]=>16 [[5,2,2,1],[2,1,1]]=>24 [[5,2,1,1],[2,1]]=>24 [[6,3,2,1],[3,2,1]]=>32 [[4,4],[2]]=>13 [[5,4],[3]]=>14 [[6,4],[4]]=>15 [[3,3,1],[1]]=>17 [[4,4,1],[2,1]]=>20 [[4,3,1],[2]]=>19 [[5,4,1],[3,1]]=>22 [[5,3,1],[3]]=>21 [[6,4,1],[4,1]]=>24 [[2,2,2],[]]=>13 [[3,3,2],[1,1]]=>17 [[4,4,2],[2,2]]=>21 [[3,2,2],[1]]=>17 [[4,3,2],[2,1]]=>21 [[5,4,2],[3,2]]=>24 [[4,2,2],[2]]=>21 [[5,3,2],[3,1]]=>24 [[6,4,2],[4,2]]=>27 [[2,2,1,1],[]]=>13 [[3,3,2,1],[1,1,1]]=>20 [[3,3,1,1],[1,1]]=>21 [[4,4,2,1],[2,2,1]]=>28 [[3,2,1,1],[1]]=>18 [[4,3,2,1],[2,1,1]]=>26 [[4,3,1,1],[2,1]]=>24 [[5,4,2,1],[3,2,1]]=>32 [[4,2,1,1],[2]]=>21 [[5,3,2,1],[3,1,1]]=>30 [[5,3,1,1],[3,1]]=>27 [[6,4,2,1],[4,2,1]]=>36 [[4,3,3],[2,2]]=>17 [[5,4,3],[3,3]]=>20 [[5,3,3],[3,2]]=>21 [[6,4,3],[4,3]]=>24 [[3,2,2,1],[1,1]]=>19 [[4,3,3,1],[2,2,1]]=>24 [[4,3,2,1],[2,2]]=>25 [[5,4,3,1],[3,3,1]]=>30 [[4,2,2,1],[2,1]]=>24 [[5,3,3,1],[3,2,1]]=>30 [[5,3,2,1],[3,2]]=>30 [[6,4,3,1],[4,3,1]]=>36 [[3,2,2,2],[1,1,1]]=>16 [[4,3,3,2],[2,2,2]]=>21 [[4,3,2,2],[2,2,1]]=>25 [[5,4,3,2],[3,3,2]]=>30 [[4,2,2,2],[2,1,1]]=>21 [[5,3,3,2],[3,2,2]]=>27 [[5,3,2,2],[3,2,1]]=>30 [[6,4,3,2],[4,3,2]]=>36 [[2,1,1,1,1],[]]=>11 [[3,2,2,2,1],[1,1,1,1]]=>18 [[3,2,2,1,1],[1,1,1]]=>21 [[4,3,3,2,1],[2,2,2,1]]=>28 [[3,2,1,1,1],[1,1]]=>20 [[4,3,2,2,1],[2,2,1,1]]=>30 [[4,3,2,1,1],[2,2,1]]=>30 [[5,4,3,2,1],[3,3,2,1]]=>40 [[3,1,1,1,1],[1]]=>15 [[4,2,2,2,1],[2,1,1,1]]=>24 [[4,2,2,1,1],[2,1,1]]=>27 [[5,3,3,2,1],[3,2,2,1]]=>36 [[4,2,1,1,1],[2,1]]=>24 [[5,3,2,2,1],[3,2,1,1]]=>36 [[5,3,2,1,1],[3,2,1]]=>36 [[6,4,3,2,1],[4,3,2,1]]=>48 [[5,5],[4]]=>11 [[6,5],[5]]=>12 [[4,4,1],[3]]=>16 [[5,5,1],[4,1]]=>18 [[5,4,1],[4]]=>18 [[6,5,1],[5,1]]=>20 [[3,3,2],[2]]=>17 [[4,4,2],[3,1]]=>19 [[5,5,2],[4,2]]=>21 [[4,3,2],[3]]=>20 [[5,4,2],[4,1]]=>22 [[6,5,2],[5,2]]=>24 [[3,3,1,1],[2]]=>17 [[4,4,2,1],[3,1,1]]=>24 [[4,4,1,1],[3,1]]=>21 [[5,5,2,1],[4,2,1]]=>28 [[4,3,1,1],[3]]=>20 [[5,4,2,1],[4,1,1]]=>28 [[5,4,1,1],[4,1]]=>24 [[6,5,2,1],[5,2,1]]=>32 [[3,3,3],[2,1]]=>15 [[4,4,3],[3,2]]=>18 [[5,5,3],[4,3]]=>20 [[4,3,3],[3,1]]=>20 [[5,4,3],[4,2]]=>22 [[6,5,3],[5,3]]=>24 [[2,2,2,1],[1]]=>14 [[3,3,3,1],[2,1,1]]=>20 [[3,3,2,1],[2,1]]=>21 [[4,4,3,1],[3,2,1]]=>26 [[4,4,2,1],[3,2]]=>25 [[5,5,3,1],[4,3,1]]=>30 [[3,2,2,1],[2]]=>20 [[4,3,3,1],[3,1,1]]=>28 [[4,3,2,1],[3,1]]=>26 [[5,4,3,1],[4,2,1]]=>32 [[5,4,2,1],[4,2]]=>30 [[6,5,3,1],[5,3,1]]=>36 [[3,3,2,2],[2,1,1]]=>19 [[4,4,3,2],[3,2,2]]=>24 [[4,4,2,2],[3,2,1]]=>25 [[5,5,3,2],[4,3,2]]=>30 [[4,3,2,2],[3,1,1]]=>24 [[5,4,3,2],[4,2,2]]=>30 [[5,4,2,2],[4,2,1]]=>30 [[6,5,3,2],[5,3,2]]=>36 [[2,2,1,1,1],[1]]=>14 [[3,3,2,2,1],[2,1,1,1]]=>22 [[3,3,2,1,1],[2,1,1]]=>24 [[4,4,3,2,1],[3,2,2,1]]=>32 [[3,3,1,1,1],[2,1]]=>20 [[4,4,2,2,1],[3,2,1,1]]=>30 [[4,4,2,1,1],[3,2,1]]=>30 [[5,5,3,2,1],[4,3,2,1]]=>40 [[3,2,1,1,1],[2]]=>18 [[4,3,2,2,1],[3,1,1,1]]=>28 [[4,3,2,1,1],[3,1,1]]=>30 [[5,4,3,2,1],[4,2,2,1]]=>40 [[4,3,1,1,1],[3,1]]=>24 [[5,4,2,2,1],[4,2,1,1]]=>36 [[5,4,2,1,1],[4,2,1]]=>36 [[6,5,3,2,1],[5,3,2,1]]=>48 [[4,4,4],[3,3]]=>13 [[5,5,4],[4,4]]=>15 [[5,4,4],[4,3]]=>18 [[6,5,4],[5,4]]=>20 [[3,3,3,1],[2,2]]=>17 [[4,4,4,1],[3,3,1]]=>20 [[4,4,3,1],[3,3]]=>21 [[5,5,4,1],[4,4,1]]=>24 [[4,3,3,1],[3,2]]=>24 [[5,4,4,1],[4,3,1]]=>28 [[5,4,3,1],[4,3]]=>28 [[6,5,4,1],[5,4,1]]=>32 [[2,2,2,2],[1,1]]=>13 [[3,3,3,2],[2,2,1]]=>18 [[4,4,4,2],[3,3,2]]=>21 [[3,3,2,2],[2,2]]=>21 [[4,4,3,2],[3,3,1]]=>24 [[5,5,4,2],[4,4,2]]=>27 [[3,2,2,2],[2,1]]=>20 [[4,3,3,2],[3,2,1]]=>26 [[5,4,4,2],[4,3,2]]=>30 [[4,3,2,2],[3,2]]=>28 [[5,4,3,2],[4,3,1]]=>32 [[6,5,4,2],[5,4,2]]=>36 [[2,2,2,1,1],[1,1]]=>15 [[3,3,3,2,1],[2,2,1,1]]=>22 [[3,3,3,1,1],[2,2,1]]=>21 [[4,4,4,2,1],[3,3,2,1]]=>28 [[3,3,2,1,1],[2,2]]=>21 [[4,4,3,2,1],[3,3,1,1]]=>30 [[4,4,3,1,1],[3,3,1]]=>27 [[5,5,4,2,1],[4,4,2,1]]=>36 [[3,2,2,1,1],[2,1]]=>22 [[4,3,3,2,1],[3,2,1,1]]=>32 [[4,3,3,1,1],[3,2,1]]=>30 [[5,4,4,2,1],[4,3,2,1]]=>40 [[4,3,2,1,1],[3,2]]=>28 [[5,4,3,2,1],[4,3,1,1]]=>40 [[5,4,3,1,1],[4,3,1]]=>36 [[6,5,4,2,1],[5,4,2,1]]=>48 [[3,3,3,3],[2,2,2]]=>13 [[4,4,4,3],[3,3,3]]=>16 [[4,4,3,3],[3,3,2]]=>21 [[5,5,4,3],[4,4,3]]=>24 [[4,3,3,3],[3,2,2]]=>20 [[5,4,4,3],[4,3,3]]=>24 [[5,4,3,3],[4,3,2]]=>28 [[6,5,4,3],[5,4,3]]=>32 [[2,2,2,2,1],[1,1,1]]=>14 [[3,3,3,3,1],[2,2,2,1]]=>18 [[3,3,3,2,1],[2,2,2]]=>20 [[4,4,4,3,1],[3,3,3,1]]=>24 [[3,3,2,2,1],[2,2,1]]=>24 [[4,4,3,3,1],[3,3,2,1]]=>30 [[4,4,3,2,1],[3,3,2]]=>30 [[5,5,4,3,1],[4,4,3,1]]=>36 [[3,2,2,2,1],[2,1,1]]=>22 [[4,3,3,3,1],[3,2,2,1]]=>28 [[4,3,3,2,1],[3,2,2]]=>30 [[5,4,4,3,1],[4,3,3,1]]=>36 [[4,3,2,2,1],[3,2,1]]=>32 [[5,4,3,3,1],[4,3,2,1]]=>40 [[5,4,3,2,1],[4,3,2]]=>40 [[6,5,4,3,1],[5,4,3,1]]=>48 [[2,2,2,2,2],[1,1,1,1]]=>11 [[3,3,3,3,2],[2,2,2,2]]=>15 [[3,3,3,2,2],[2,2,2,1]]=>20 [[4,4,4,3,2],[3,3,3,2]]=>24 [[3,3,2,2,2],[2,2,1,1]]=>21 [[4,4,3,3,2],[3,3,2,2]]=>27 [[4,4,3,2,2],[3,3,2,1]]=>30 [[5,5,4,3,2],[4,4,3,2]]=>36 [[3,2,2,2,2],[2,1,1,1]]=>18 [[4,3,3,3,2],[3,2,2,2]]=>24 [[4,3,3,2,2],[3,2,2,1]]=>30 [[5,4,4,3,2],[4,3,3,2]]=>36 [[4,3,2,2,2],[3,2,1,1]]=>28 [[5,4,3,3,2],[4,3,2,2]]=>36 [[5,4,3,2,2],[4,3,2,1]]=>40 [[6,5,4,3,2],[5,4,3,2]]=>48 [[1,1,1,1,1,1],[]]=>7 [[2,2,2,2,2,1],[1,1,1,1,1]]=>12 [[2,2,2,2,1,1],[1,1,1,1]]=>15 [[3,3,3,3,2,1],[2,2,2,2,1]]=>20 [[2,2,2,1,1,1],[1,1,1]]=>16 [[3,3,3,2,2,1],[2,2,2,1,1]]=>24 [[3,3,3,2,1,1],[2,2,2,1]]=>24 [[4,4,4,3,2,1],[3,3,3,2,1]]=>32 [[2,2,1,1,1,1],[1,1]]=>15 [[3,3,2,2,2,1],[2,2,1,1,1]]=>24 [[3,3,2,2,1,1],[2,2,1,1]]=>27 [[4,4,3,3,2,1],[3,3,2,2,1]]=>36 [[3,3,2,1,1,1],[2,2,1]]=>24 [[4,4,3,2,2,1],[3,3,2,1,1]]=>36 [[4,4,3,2,1,1],[3,3,2,1]]=>36 [[5,5,4,3,2,1],[4,4,3,2,1]]=>48 [[2,1,1,1,1,1],[1]]=>12 [[3,2,2,2,2,1],[2,1,1,1,1]]=>20 [[3,2,2,2,1,1],[2,1,1,1]]=>24 [[4,3,3,3,2,1],[3,2,2,2,1]]=>32 [[3,2,2,1,1,1],[2,1,1]]=>24 [[4,3,3,2,2,1],[3,2,2,1,1]]=>36 [[4,3,3,2,1,1],[3,2,2,1]]=>36 [[5,4,4,3,2,1],[4,3,3,2,1]]=>48 [[3,2,1,1,1,1],[2,1]]=>20 [[4,3,2,2,2,1],[3,2,1,1,1]]=>32 [[4,3,2,2,1,1],[3,2,1,1]]=>36 [[5,4,3,3,2,1],[4,3,2,2,1]]=>48 [[4,3,2,1,1,1],[3,2,1]]=>32 [[5,4,3,2,2,1],[4,3,2,1,1]]=>48 [[5,4,3,2,1,1],[4,3,2,1]]=>48 [[6,5,4,3,2,1],[5,4,3,2,1]]=>64 [[7],[]]=>8 [[6,1],[]]=>13 [[7,1],[1]]=>14 [[5,2],[]]=>16 [[6,2],[1]]=>17 [[7,2],[2]]=>18 [[5,1,1],[]]=>16 [[6,2,1],[1,1]]=>22 [[6,1,1],[1]]=>18 [[7,2,1],[2,1]]=>24 [[4,3],[]]=>17 [[5,3],[1]]=>18 [[6,3],[2]]=>19 [[7,3],[3]]=>20 [[4,2,1],[]]=>20 [[5,3,1],[1,1]]=>26 [[5,2,1],[1]]=>23 [[6,3,1],[2,1]]=>28 [[6,2,1],[2]]=>25 [[7,3,1],[3,1]]=>30 [[5,2,2],[1,1]]=>22 [[6,3,2],[2,2]]=>27 [[6,2,2],[2,1]]=>25 [[7,3,2],[3,2]]=>30 [[4,1,1,1],[]]=>17 [[5,2,2,1],[1,1,1]]=>26 [[5,2,1,1],[1,1]]=>27 [[6,3,2,1],[2,2,1]]=>36 [[5,1,1,1],[1]]=>20 [[6,2,2,1],[2,1,1]]=>30 [[6,2,1,1],[2,1]]=>30 [[7,3,2,1],[3,2,1]]=>40 [[4,4],[1]]=>17 [[5,4],[2]]=>18 [[6,4],[3]]=>19 [[7,4],[4]]=>20 [[3,3,1],[]]=>20 [[4,4,1],[1,1]]=>26 [[4,3,1],[1]]=>24 [[5,4,1],[2,1]]=>28 [[5,3,1],[2]]=>26 [[6,4,1],[3,1]]=>30 [[6,3,1],[3]]=>28 [[7,4,1],[4,1]]=>32 [[3,2,2],[]]=>20 [[4,3,2],[1,1]]=>25 [[5,4,2],[2,2]]=>30 [[4,2,2],[1]]=>24 [[5,3,2],[2,1]]=>29 [[6,4,2],[3,2]]=>33 [[5,2,2],[2]]=>28 [[6,3,2],[3,1]]=>32 [[7,4,2],[4,2]]=>36 [[3,2,1,1],[]]=>20 [[4,3,2,1],[1,1,1]]=>30 [[4,3,1,1],[1,1]]=>30 [[5,4,2,1],[2,2,1]]=>40 [[4,2,1,1],[1]]=>25 [[5,3,2,1],[2,1,1]]=>36 [[5,3,1,1],[2,1]]=>33 [[6,4,2,1],[3,2,1]]=>44 [[5,2,1,1],[2]]=>28 [[6,3,2,1],[3,1,1]]=>40 [[6,3,1,1],[3,1]]=>36 [[7,4,2,1],[4,2,1]]=>48 [[5,3,3],[2,2]]=>24 [[6,4,3],[3,3]]=>28 [[6,3,3],[3,2]]=>28 [[7,4,3],[4,3]]=>32 [[4,2,2,1],[1,1]]=>27 [[5,3,3,1],[2,2,1]]=>34 [[5,3,2,1],[2,2]]=>35 [[6,4,3,1],[3,3,1]]=>42 [[5,2,2,1],[2,1]]=>32 [[6,3,3,1],[3,2,1]]=>40 [[6,3,2,1],[3,2]]=>40 [[7,4,3,1],[4,3,1]]=>48 [[4,2,2,2],[1,1,1]]=>23 [[5,3,3,2],[2,2,2]]=>30 [[5,3,2,2],[2,2,1]]=>35 [[6,4,3,2],[3,3,2]]=>42 [[5,2,2,2],[2,1,1]]=>28 [[6,3,3,2],[3,2,2]]=>36 [[6,3,2,2],[3,2,1]]=>40 [[7,4,3,2],[4,3,2]]=>48 [[3,1,1,1,1],[]]=>16 [[4,2,2,2,1],[1,1,1,1]]=>26 [[4,2,2,1,1],[1,1,1]]=>30 [[5,3,3,2,1],[2,2,2,1]]=>40 [[4,2,1,1,1],[1,1]]=>28 [[5,3,2,2,1],[2,2,1,1]]=>42 [[5,3,2,1,1],[2,2,1]]=>42 [[6,4,3,2,1],[3,3,2,1]]=>56 [[4,1,1,1,1],[1]]=>20 [[5,2,2,2,1],[2,1,1,1]]=>32 [[5,2,2,1,1],[2,1,1]]=>36 [[6,3,3,2,1],[3,2,2,1]]=>48 [[5,2,1,1,1],[2,1]]=>32 [[6,3,2,2,1],[3,2,1,1]]=>48 [[6,3,2,1,1],[3,2,1]]=>48 [[7,4,3,2,1],[4,3,2,1]]=>64 [[5,5],[3]]=>16 [[6,5],[4]]=>17 [[7,5],[5]]=>18 [[4,4,1],[2]]=>23 [[5,5,1],[3,1]]=>26 [[5,4,1],[3]]=>25 [[6,5,1],[4,1]]=>28 [[6,4,1],[4]]=>27 [[7,5,1],[5,1]]=>30 [[3,3,2],[1]]=>22 [[4,4,2],[2,1]]=>27 [[5,5,2],[3,2]]=>30 [[4,3,2],[2]]=>27 [[5,4,2],[3,1]]=>30 [[6,5,2],[4,2]]=>33 [[5,3,2],[3]]=>30 [[6,4,2],[4,1]]=>33 [[7,5,2],[5,2]]=>36 [[3,3,1,1],[1]]=>24 [[4,4,2,1],[2,1,1]]=>34 [[4,4,1,1],[2,1]]=>30 [[5,5,2,1],[3,2,1]]=>40 [[4,3,1,1],[2]]=>27 [[5,4,2,1],[3,1,1]]=>38 [[5,4,1,1],[3,1]]=>33 [[6,5,2,1],[4,2,1]]=>44 [[5,3,1,1],[3]]=>30 [[6,4,2,1],[4,1,1]]=>42 [[6,4,1,1],[4,1]]=>36 [[7,5,2,1],[5,2,1]]=>48 [[3,3,3],[1,1]]=>20 [[4,4,3],[2,2]]=>24 [[5,5,3],[3,3]]=>28 [[4,3,3],[2,1]]=>25 [[5,4,3],[3,2]]=>29 [[6,5,3],[4,3]]=>32 [[5,3,3],[3,1]]=>30 [[6,4,3],[4,2]]=>33 [[7,5,3],[5,3]]=>36 [[2,2,2,1],[]]=>17 [[3,3,3,1],[1,1,1]]=>26 [[3,3,2,1],[1,1]]=>27 [[4,4,3,1],[2,2,1]]=>34 [[4,4,2,1],[2,2]]=>35 [[5,5,3,1],[3,3,1]]=>42 [[3,2,2,1],[1]]=>24 [[4,3,3,1],[2,1,1]]=>34 [[4,3,2,1],[2,1]]=>34 [[5,4,3,1],[3,2,1]]=>42 [[5,4,2,1],[3,2]]=>40 [[6,5,3,1],[4,3,1]]=>48 [[4,2,2,1],[2]]=>30 [[5,3,3,1],[3,1,1]]=>42 [[5,3,2,1],[3,1]]=>39 [[6,4,3,1],[4,2,1]]=>48 [[6,4,2,1],[4,2]]=>45 [[7,5,3,1],[5,3,1]]=>54 [[3,3,2,2],[1,1,1]]=>23 [[4,4,3,2],[2,2,2]]=>30 [[4,4,2,2],[2,2,1]]=>35 [[5,5,3,2],[3,3,2]]=>42 [[4,3,2,2],[2,1,1]]=>31 [[5,4,3,2],[3,2,2]]=>39 [[5,4,2,2],[3,2,1]]=>40 [[6,5,3,2],[4,3,2]]=>48 [[5,3,2,2],[3,1,1]]=>36 [[6,4,3,2],[4,2,2]]=>45 [[6,4,2,2],[4,2,1]]=>45 [[7,5,3,2],[5,3,2]]=>54 [[2,2,1,1,1],[]]=>16 [[3,3,2,2,1],[1,1,1,1]]=>26 [[3,3,2,1,1],[1,1,1]]=>30 [[4,4,3,2,1],[2,2,2,1]]=>40 [[3,3,1,1,1],[1,1]]=>28 [[4,4,2,2,1],[2,2,1,1]]=>42 [[4,4,2,1,1],[2,2,1]]=>42 [[5,5,3,2,1],[3,3,2,1]]=>56 [[3,2,1,1,1],[1]]=>23 [[4,3,2,2,1],[2,1,1,1]]=>36 [[4,3,2,1,1],[2,1,1]]=>39 [[5,4,3,2,1],[3,2,2,1]]=>52 [[4,3,1,1,1],[2,1]]=>32 [[5,4,2,2,1],[3,2,1,1]]=>48 [[5,4,2,1,1],[3,2,1]]=>48 [[6,5,3,2,1],[4,3,2,1]]=>64 [[4,2,1,1,1],[2]]=>27 [[5,3,2,2,1],[3,1,1,1]]=>42 [[5,3,2,1,1],[3,1,1]]=>45 [[6,4,3,2,1],[4,2,2,1]]=>60 [[5,3,1,1,1],[3,1]]=>36 [[6,4,2,2,1],[4,2,1,1]]=>54 [[6,4,2,1,1],[4,2,1]]=>54 [[7,5,3,2,1],[5,3,2,1]]=>72 [[5,4,4],[3,3]]=>22 [[6,5,4],[4,4]]=>25 [[6,4,4],[4,3]]=>27 [[7,5,4],[5,4]]=>30 [[4,3,3,1],[2,2]]=>29 [[5,4,4,1],[3,3,1]]=>34 [[5,4,3,1],[3,3]]=>35 [[6,5,4,1],[4,4,1]]=>40 [[5,3,3,1],[3,2]]=>36 [[6,4,4,1],[4,3,1]]=>42 [[6,4,3,1],[4,3]]=>42 [[7,5,4,1],[5,4,1]]=>48 [[3,2,2,2],[1,1]]=>23 [[4,3,3,2],[2,2,1]]=>31 [[5,4,4,2],[3,3,2]]=>36 [[4,3,2,2],[2,2]]=>35 [[5,4,3,2],[3,3,1]]=>40 [[6,5,4,2],[4,4,2]]=>45 [[4,2,2,2],[2,1]]=>30 [[5,3,3,2],[3,2,1]]=>39 [[6,4,4,2],[4,3,2]]=>45 [[5,3,2,2],[3,2]]=>42 [[6,4,3,2],[4,3,1]]=>48 [[7,5,4,2],[5,4,2]]=>54 [[3,2,2,1,1],[1,1]]=>26 [[4,3,3,2,1],[2,2,1,1]]=>38 [[4,3,3,1,1],[2,2,1]]=>36 [[5,4,4,2,1],[3,3,2,1]]=>48 [[4,3,2,1,1],[2,2]]=>35 [[5,4,3,2,1],[3,3,1,1]]=>50 [[5,4,3,1,1],[3,3,1]]=>45 [[6,5,4,2,1],[4,4,2,1]]=>60 [[4,2,2,1,1],[2,1]]=>33 [[5,3,3,2,1],[3,2,1,1]]=>48 [[5,3,3,1,1],[3,2,1]]=>45 [[6,4,4,2,1],[4,3,2,1]]=>60 [[5,3,2,1,1],[3,2]]=>42 [[6,4,3,2,1],[4,3,1,1]]=>60 [[6,4,3,1,1],[4,3,1]]=>54 [[7,5,4,2,1],[5,4,2,1]]=>72 [[4,3,3,3],[2,2,2]]=>23 [[5,4,4,3],[3,3,3]]=>28 [[5,4,3,3],[3,3,2]]=>35 [[6,5,4,3],[4,4,3]]=>40 [[5,3,3,3],[3,2,2]]=>30 [[6,4,4,3],[4,3,3]]=>36 [[6,4,3,3],[4,3,2]]=>42 [[7,5,4,3],[5,4,3]]=>48 [[3,2,2,2,1],[1,1,1]]=>25 [[4,3,3,3,1],[2,2,2,1]]=>32 [[4,3,3,2,1],[2,2,2]]=>35 [[5,4,4,3,1],[3,3,3,1]]=>42 [[4,3,2,2,1],[2,2,1]]=>40 [[5,4,3,3,1],[3,3,2,1]]=>50 [[5,4,3,2,1],[3,3,2]]=>50 [[6,5,4,3,1],[4,4,3,1]]=>60 [[4,2,2,2,1],[2,1,1]]=>33 [[5,3,3,3,1],[3,2,2,1]]=>42 [[5,3,3,2,1],[3,2,2]]=>45 [[6,4,4,3,1],[4,3,3,1]]=>54 [[5,3,2,2,1],[3,2,1]]=>48 [[6,4,3,3,1],[4,3,2,1]]=>60 [[6,4,3,2,1],[4,3,2]]=>60 [[7,5,4,3,1],[5,4,3,1]]=>72 [[3,2,2,2,2],[1,1,1,1]]=>20 [[4,3,3,3,2],[2,2,2,2]]=>27 [[4,3,3,2,2],[2,2,2,1]]=>35 [[5,4,4,3,2],[3,3,3,2]]=>42 [[4,3,2,2,2],[2,2,1,1]]=>35 [[5,4,3,3,2],[3,3,2,2]]=>45 [[5,4,3,2,2],[3,3,2,1]]=>50 [[6,5,4,3,2],[4,4,3,2]]=>60 [[4,2,2,2,2],[2,1,1,1]]=>27 [[5,3,3,3,2],[3,2,2,2]]=>36 [[5,3,3,2,2],[3,2,2,1]]=>45 [[6,4,4,3,2],[4,3,3,2]]=>54 [[5,3,2,2,2],[3,2,1,1]]=>42 [[6,4,3,3,2],[4,3,2,2]]=>54 [[6,4,3,2,2],[4,3,2,1]]=>60 [[7,5,4,3,2],[5,4,3,2]]=>72 [[2,1,1,1,1,1],[]]=>13 [[3,2,2,2,2,1],[1,1,1,1,1]]=>22 [[3,2,2,2,1,1],[1,1,1,1]]=>27 [[4,3,3,3,2,1],[2,2,2,2,1]]=>36 [[3,2,2,1,1,1],[1,1,1]]=>28 [[4,3,3,2,2,1],[2,2,2,1,1]]=>42 [[4,3,3,2,1,1],[2,2,2,1]]=>42 [[5,4,4,3,2,1],[3,3,3,2,1]]=>56 [[3,2,1,1,1,1],[1,1]]=>25 [[4,3,2,2,2,1],[2,2,1,1,1]]=>40 [[4,3,2,2,1,1],[2,2,1,1]]=>45 [[5,4,3,3,2,1],[3,3,2,2,1]]=>60 [[4,3,2,1,1,1],[2,2,1]]=>40 [[5,4,3,2,2,1],[3,3,2,1,1]]=>60 [[5,4,3,2,1,1],[3,3,2,1]]=>60 [[6,5,4,3,2,1],[4,4,3,2,1]]=>80 [[3,1,1,1,1,1],[1]]=>18 [[4,2,2,2,2,1],[2,1,1,1,1]]=>30 [[4,2,2,2,1,1],[2,1,1,1]]=>36 [[5,3,3,3,2,1],[3,2,2,2,1]]=>48 [[4,2,2,1,1,1],[2,1,1]]=>36 [[5,3,3,2,2,1],[3,2,2,1,1]]=>54 [[5,3,3,2,1,1],[3,2,2,1]]=>54 [[6,4,4,3,2,1],[4,3,3,2,1]]=>72 [[4,2,1,1,1,1],[2,1]]=>30 [[5,3,2,2,2,1],[3,2,1,1,1]]=>48 [[5,3,2,2,1,1],[3,2,1,1]]=>54 [[6,4,3,3,2,1],[4,3,2,2,1]]=>72 [[5,3,2,1,1,1],[3,2,1]]=>48 [[6,4,3,2,2,1],[4,3,2,1,1]]=>72 [[6,4,3,2,1,1],[4,3,2,1]]=>72 [[7,5,4,3,2,1],[5,4,3,2,1]]=>96 [[6,6],[5]]=>13 [[7,6],[6]]=>14 [[5,5,1],[4]]=>20 [[6,6,1],[5,1]]=>22 [[6,5,1],[5]]=>22 [[7,6,1],[6,1]]=>24 [[4,4,2],[3]]=>23 [[5,5,2],[4,1]]=>25 [[6,6,2],[5,2]]=>27 [[5,4,2],[4]]=>26 [[6,5,2],[5,1]]=>28 [[7,6,2],[6,2]]=>30 [[4,4,1,1],[3]]=>23 [[5,5,2,1],[4,1,1]]=>32 [[5,5,1,1],[4,1]]=>27 [[6,6,2,1],[5,2,1]]=>36 [[5,4,1,1],[4]]=>26 [[6,5,2,1],[5,1,1]]=>36 [[6,5,1,1],[5,1]]=>30 [[7,6,2,1],[6,2,1]]=>40 [[3,3,3],[2]]=>20 [[4,4,3],[3,1]]=>24 [[5,5,3],[4,2]]=>26 [[6,6,3],[5,3]]=>28 [[4,3,3],[3]]=>26 [[5,4,3],[4,1]]=>28 [[6,5,3],[5,2]]=>30 [[7,6,3],[6,3]]=>32 [[3,3,2,1],[2]]=>25 [[4,4,3,1],[3,1,1]]=>34 [[4,4,2,1],[3,1]]=>31 [[5,5,3,1],[4,2,1]]=>38 [[5,5,2,1],[4,2]]=>35 [[6,6,3,1],[5,3,1]]=>42 [[4,3,2,1],[3]]=>30 [[5,4,3,1],[4,1,1]]=>40 [[5,4,2,1],[4,1]]=>36 [[6,5,3,1],[5,2,1]]=>44 [[6,5,2,1],[5,2]]=>40 [[7,6,3,1],[6,3,1]]=>48 [[4,4,2,2],[3,1,1]]=>29 [[5,5,3,2],[4,2,2]]=>36 [[5,5,2,2],[4,2,1]]=>35 [[6,6,3,2],[5,3,2]]=>42 [[5,4,2,2],[4,1,1]]=>34 [[6,5,3,2],[5,2,2]]=>42 [[6,5,2,2],[5,2,1]]=>40 [[7,6,3,2],[6,3,2]]=>48 [[3,3,1,1,1],[2]]=>22 [[4,4,2,2,1],[3,1,1,1]]=>34 [[4,4,2,1,1],[3,1,1]]=>36 [[5,5,3,2,1],[4,2,2,1]]=>48 [[4,4,1,1,1],[3,1]]=>28 [[5,5,2,2,1],[4,2,1,1]]=>42 [[5,5,2,1,1],[4,2,1]]=>42 [[6,6,3,2,1],[5,3,2,1]]=>56 [[4,3,1,1,1],[3]]=>26 [[5,4,2,2,1],[4,1,1,1]]=>40 [[5,4,2,1,1],[4,1,1]]=>42 [[6,5,3,2,1],[5,2,2,1]]=>56 [[5,4,1,1,1],[4,1]]=>32 [[6,5,2,2,1],[5,2,1,1]]=>48 [[6,5,2,1,1],[5,2,1]]=>48 [[7,6,3,2,1],[6,3,2,1]]=>64 [[4,4,4],[3,2]]=>20 [[5,5,4],[4,3]]=>23 [[6,6,4],[5,4]]=>25 [[5,4,4],[4,2]]=>26 [[6,5,4],[5,3]]=>28 [[7,6,4],[6,4]]=>30 [[3,3,3,1],[2,1]]=>25 [[4,4,4,1],[3,2,1]]=>30 [[4,4,3,1],[3,2]]=>31 [[5,5,4,1],[4,3,1]]=>36 [[5,5,3,1],[4,3]]=>35 [[6,6,4,1],[5,4,1]]=>40 [[4,3,3,1],[3,1]]=>34 [[5,4,4,1],[4,2,1]]=>40 [[5,4,3,1],[4,2]]=>38 [[6,5,4,1],[5,3,1]]=>44 [[6,5,3,1],[5,3]]=>42 [[7,6,4,1],[6,4,1]]=>48 [[2,2,2,2],[1]]=>17 [[3,3,3,2],[2,1,1]]=>24 [[4,4,4,2],[3,2,2]]=>30 [[3,3,2,2],[2,1]]=>27 [[4,4,3,2],[3,2,1]]=>34 [[5,5,4,2],[4,3,2]]=>39 [[4,4,2,2],[3,2]]=>35 [[5,5,3,2],[4,3,1]]=>40 [[6,6,4,2],[5,4,2]]=>45 [[3,2,2,2],[2]]=>26 [[4,3,3,2],[3,1,1]]=>34 [[5,4,4,2],[4,2,2]]=>42 [[4,3,2,2],[3,1]]=>34 [[5,4,3,2],[4,2,1]]=>42 [[6,5,4,2],[5,3,2]]=>48 [[5,4,2,2],[4,2]]=>42 [[6,5,3,2],[5,3,1]]=>48 [[7,6,4,2],[6,4,2]]=>54 [[2,2,2,1,1],[1]]=>18 [[3,3,3,2,1],[2,1,1,1]]=>28 [[3,3,3,1,1],[2,1,1]]=>30 [[4,4,4,2,1],[3,2,2,1]]=>40 [[3,3,2,1,1],[2,1]]=>29 [[4,4,3,2,1],[3,2,1,1]]=>42 [[4,4,3,1,1],[3,2,1]]=>39 [[5,5,4,2,1],[4,3,2,1]]=>52 [[4,4,2,1,1],[3,2]]=>35 [[5,5,3,2,1],[4,3,1,1]]=>50 [[5,5,3,1,1],[4,3,1]]=>45 [[6,6,4,2,1],[5,4,2,1]]=>60 [[3,2,2,1,1],[2]]=>26 [[4,3,3,2,1],[3,1,1,1]]=>40 [[4,3,3,1,1],[3,1,1]]=>42 [[5,4,4,2,1],[4,2,2,1]]=>56 [[4,3,2,1,1],[3,1]]=>36 [[5,4,3,2,1],[4,2,1,1]]=>52 [[5,4,3,1,1],[4,2,1]]=>48 [[6,5,4,2,1],[5,3,2,1]]=>64 [[5,4,2,1,1],[4,2]]=>42 [[6,5,3,2,1],[5,3,1,1]]=>60 [[6,5,3,1,1],[5,3,1]]=>54 [[7,6,4,2,1],[6,4,2,1]]=>72 [[4,4,3,3],[3,2,2]]=>27 [[5,5,4,3],[4,3,3]]=>32 [[5,5,3,3],[4,3,2]]=>35 [[6,6,4,3],[5,4,3]]=>40 [[5,4,3,3],[4,2,2]]=>34 [[6,5,4,3],[5,3,3]]=>40 [[6,5,3,3],[5,3,2]]=>42 [[7,6,4,3],[6,4,3]]=>48 [[3,3,2,2,1],[2,1,1]]=>30 [[4,4,3,3,1],[3,2,2,1]]=>38 [[4,4,3,2,1],[3,2,2]]=>40 [[5,5,4,3,1],[4,3,3,1]]=>48 [[4,4,2,2,1],[3,2,1]]=>40 [[5,5,3,3,1],[4,3,2,1]]=>50 [[5,5,3,2,1],[4,3,2]]=>50 [[6,6,4,3,1],[5,4,3,1]]=>60 [[4,3,2,2,1],[3,1,1]]=>38 [[5,4,3,3,1],[4,2,2,1]]=>48 [[5,4,3,2,1],[4,2,2]]=>50 [[6,5,4,3,1],[5,3,3,1]]=>60 [[5,4,2,2,1],[4,2,1]]=>48 [[6,5,3,3,1],[5,3,2,1]]=>60 [[6,5,3,2,1],[5,3,2]]=>60 [[7,6,4,3,1],[6,4,3,1]]=>72 [[3,3,2,2,2],[2,1,1,1]]=>25 [[4,4,3,3,2],[3,2,2,2]]=>33 [[4,4,3,2,2],[3,2,2,1]]=>40 [[5,5,4,3,2],[4,3,3,2]]=>48 [[4,4,2,2,2],[3,2,1,1]]=>35 [[5,5,3,3,2],[4,3,2,2]]=>45 [[5,5,3,2,2],[4,3,2,1]]=>50 [[6,6,4,3,2],[5,4,3,2]]=>60 [[4,3,2,2,2],[3,1,1,1]]=>32 [[5,4,3,3,2],[4,2,2,2]]=>42 [[5,4,3,2,2],[4,2,2,1]]=>50 [[6,5,4,3,2],[5,3,3,2]]=>60 [[5,4,2,2,2],[4,2,1,1]]=>42 [[6,5,3,3,2],[5,3,2,2]]=>54 [[6,5,3,2,2],[5,3,2,1]]=>60 [[7,6,4,3,2],[6,4,3,2]]=>72 [[2,2,1,1,1,1],[1]]=>17 [[3,3,2,2,2,1],[2,1,1,1,1]]=>28 [[3,3,2,2,1,1],[2,1,1,1]]=>33 [[4,4,3,3,2,1],[3,2,2,2,1]]=>44 [[3,3,2,1,1,1],[2,1,1]]=>32 [[4,4,3,2,2,1],[3,2,2,1,1]]=>48 [[4,4,3,2,1,1],[3,2,2,1]]=>48 [[5,5,4,3,2,1],[4,3,3,2,1]]=>64 [[3,3,1,1,1,1],[2,1]]=>25 [[4,4,2,2,2,1],[3,2,1,1,1]]=>40 [[4,4,2,2,1,1],[3,2,1,1]]=>45 [[5,5,3,3,2,1],[4,3,2,2,1]]=>60 [[4,4,2,1,1,1],[3,2,1]]=>40 [[5,5,3,2,2,1],[4,3,2,1,1]]=>60 [[5,5,3,2,1,1],[4,3,2,1]]=>60 [[6,6,4,3,2,1],[5,4,3,2,1]]=>80 [[3,2,1,1,1,1],[2]]=>22 [[4,3,2,2,2,1],[3,1,1,1,1]]=>36 [[4,3,2,2,1,1],[3,1,1,1]]=>42 [[5,4,3,3,2,1],[4,2,2,2,1]]=>56 [[4,3,2,1,1,1],[3,1,1]]=>40 [[5,4,3,2,2,1],[4,2,2,1,1]]=>60 [[5,4,3,2,1,1],[4,2,2,1]]=>60 [[6,5,4,3,2,1],[5,3,3,2,1]]=>80 [[4,3,1,1,1,1],[3,1]]=>30 [[5,4,2,2,2,1],[4,2,1,1,1]]=>48 [[5,4,2,2,1,1],[4,2,1,1]]=>54 [[6,5,3,3,2,1],[5,3,2,2,1]]=>72 [[5,4,2,1,1,1],[4,2,1]]=>48 [[6,5,3,2,2,1],[5,3,2,1,1]]=>72 [[6,5,3,2,1,1],[5,3,2,1]]=>72 [[7,6,4,3,2,1],[6,4,3,2,1]]=>96 [[5,5,5],[4,4]]=>16 [[6,6,5],[5,5]]=>18 [[6,5,5],[5,4]]=>22 [[7,6,5],[6,5]]=>24 [[4,4,4,1],[3,3]]=>23 [[5,5,5,1],[4,4,1]]=>26 [[5,5,4,1],[4,4]]=>27 [[6,6,5,1],[5,5,1]]=>30 [[5,4,4,1],[4,3]]=>32 [[6,5,5,1],[5,4,1]]=>36 [[6,5,4,1],[5,4]]=>36 [[7,6,5,1],[6,5,1]]=>40 [[3,3,3,2],[2,2]]=>24 [[4,4,4,2],[3,3,1]]=>27 [[5,5,5,2],[4,4,2]]=>30 [[4,4,3,2],[3,3]]=>30 [[5,5,4,2],[4,4,1]]=>33 [[6,6,5,2],[5,5,2]]=>36 [[4,3,3,2],[3,2]]=>34 [[5,4,4,2],[4,3,1]]=>38 [[6,5,5,2],[5,4,2]]=>42 [[5,4,3,2],[4,3]]=>40 [[6,5,4,2],[5,4,1]]=>44 [[7,6,5,2],[6,5,2]]=>48 [[3,3,3,1,1],[2,2]]=>24 [[4,4,4,2,1],[3,3,1,1]]=>34 [[4,4,4,1,1],[3,3,1]]=>30 [[5,5,5,2,1],[4,4,2,1]]=>40 [[4,4,3,1,1],[3,3]]=>30 [[5,5,4,2,1],[4,4,1,1]]=>42 [[5,5,4,1,1],[4,4,1]]=>36 [[6,6,5,2,1],[5,5,2,1]]=>48 [[4,3,3,1,1],[3,2]]=>34 [[5,4,4,2,1],[4,3,1,1]]=>48 [[5,4,4,1,1],[4,3,1]]=>42 [[6,5,5,2,1],[5,4,2,1]]=>56 [[5,4,3,1,1],[4,3]]=>40 [[6,5,4,2,1],[5,4,1,1]]=>56 [[6,5,4,1,1],[5,4,1]]=>48 [[7,6,5,2,1],[6,5,2,1]]=>64 [[3,3,3,3],[2,2,1]]=>20 [[4,4,4,3],[3,3,2]]=>25 [[5,5,5,3],[4,4,3]]=>28 [[4,4,3,3],[3,3,1]]=>30 [[5,5,4,3],[4,4,2]]=>33 [[6,6,5,3],[5,5,3]]=>36 [[4,3,3,3],[3,2,1]]=>30 [[5,4,4,3],[4,3,2]]=>36 [[6,5,5,3],[5,4,3]]=>40 [[5,4,3,3],[4,3,1]]=>40 [[6,5,4,3],[5,4,2]]=>44 [[7,6,5,3],[6,5,3]]=>48 [[2,2,2,2,1],[1,1]]=>18 [[3,3,3,3,1],[2,2,1,1]]=>26 [[3,3,3,2,1],[2,2,1]]=>29 [[4,4,4,3,1],[3,3,2,1]]=>36 [[4,4,4,2,1],[3,3,2]]=>35 [[5,5,5,3,1],[4,4,3,1]]=>42 [[3,3,2,2,1],[2,2]]=>30 [[4,4,3,3,1],[3,3,1,1]]=>42 [[4,4,3,2,1],[3,3,1]]=>39 [[5,5,4,3,1],[4,4,2,1]]=>48 [[5,5,4,2,1],[4,4,2]]=>45 [[6,6,5,3,1],[5,5,3,1]]=>54 [[3,2,2,2,1],[2,1]]=>28 [[4,3,3,3,1],[3,2,1,1]]=>40 [[4,3,3,2,1],[3,2,1]]=>42 [[5,4,4,3,1],[4,3,2,1]]=>52 [[5,4,4,2,1],[4,3,2]]=>50 [[6,5,5,3,1],[5,4,3,1]]=>60 [[4,3,2,2,1],[3,2]]=>40 [[5,4,3,3,1],[4,3,1,1]]=>56 [[5,4,3,2,1],[4,3,1]]=>52 [[6,5,4,3,1],[5,4,2,1]]=>64 [[6,5,4,2,1],[5,4,2]]=>60 [[7,6,5,3,1],[6,5,3,1]]=>72 [[3,3,3,2,2],[2,2,1,1]]=>26 [[4,4,4,3,2],[3,3,2,2]]=>33 [[4,4,4,2,2],[3,3,2,1]]=>35 [[5,5,5,3,2],[4,4,3,2]]=>42 [[4,4,3,2,2],[3,3,1,1]]=>36 [[5,5,4,3,2],[4,4,2,2]]=>45 [[5,5,4,2,2],[4,4,2,1]]=>45 [[6,6,5,3,2],[5,5,3,2]]=>54 [[4,3,3,2,2],[3,2,1,1]]=>38 [[5,4,4,3,2],[4,3,2,2]]=>48 [[5,4,4,2,2],[4,3,2,1]]=>50 [[6,5,5,3,2],[5,4,3,2]]=>60 [[5,4,3,2,2],[4,3,1,1]]=>48 [[6,5,4,3,2],[5,4,2,2]]=>60 [[6,5,4,2,2],[5,4,2,1]]=>60 [[7,6,5,3,2],[6,5,3,2]]=>72 [[2,2,2,1,1,1],[1,1]]=>19 [[3,3,3,2,2,1],[2,2,1,1,1]]=>30 [[3,3,3,2,1,1],[2,2,1,1]]=>33 [[4,4,4,3,2,1],[3,3,2,2,1]]=>44 [[3,3,3,1,1,1],[2,2,1]]=>28 [[4,4,4,2,2,1],[3,3,2,1,1]]=>42 [[4,4,4,2,1,1],[3,3,2,1]]=>42 [[5,5,5,3,2,1],[4,4,3,2,1]]=>56 [[3,3,2,1,1,1],[2,2]]=>27 [[4,4,3,2,2,1],[3,3,1,1,1]]=>42 [[4,4,3,2,1,1],[3,3,1,1]]=>45 [[5,5,4,3,2,1],[4,4,2,2,1]]=>60 [[4,4,3,1,1,1],[3,3,1]]=>36 [[5,5,4,2,2,1],[4,4,2,1,1]]=>54 [[5,5,4,2,1,1],[4,4,2,1]]=>54 [[6,6,5,3,2,1],[5,5,3,2,1]]=>72 [[3,2,2,1,1,1],[2,1]]=>28 [[4,3,3,2,2,1],[3,2,1,1,1]]=>44 [[4,3,3,2,1,1],[3,2,1,1]]=>48 [[5,4,4,3,2,1],[4,3,2,2,1]]=>64 [[4,3,3,1,1,1],[3,2,1]]=>40 [[5,4,4,2,2,1],[4,3,2,1,1]]=>60 [[5,4,4,2,1,1],[4,3,2,1]]=>60 [[6,5,5,3,2,1],[5,4,3,2,1]]=>80 [[4,3,2,1,1,1],[3,2]]=>36 [[5,4,3,2,2,1],[4,3,1,1,1]]=>56 [[5,4,3,2,1,1],[4,3,1,1]]=>60 [[6,5,4,3,2,1],[5,4,2,2,1]]=>80 [[5,4,3,1,1,1],[4,3,1]]=>48 [[6,5,4,2,2,1],[5,4,2,1,1]]=>72 [[6,5,4,2,1,1],[5,4,2,1]]=>72 [[7,6,5,3,2,1],[6,5,3,2,1]]=>96 [[4,4,4,4],[3,3,3]]=>17 [[5,5,5,4],[4,4,4]]=>20 [[5,5,4,4],[4,4,3]]=>27 [[6,6,5,4],[5,5,4]]=>30 [[5,4,4,4],[4,3,3]]=>26 [[6,5,5,4],[5,4,4]]=>30 [[6,5,4,4],[5,4,3]]=>36 [[7,6,5,4],[6,5,4]]=>40 [[3,3,3,3,1],[2,2,2]]=>22 [[4,4,4,4,1],[3,3,3,1]]=>26 [[4,4,4,3,1],[3,3,3]]=>28 [[5,5,5,4,1],[4,4,4,1]]=>32 [[4,4,3,3,1],[3,3,2]]=>36 [[5,5,4,4,1],[4,4,3,1]]=>42 [[5,5,4,3,1],[4,4,3]]=>42 [[6,6,5,4,1],[5,5,4,1]]=>48 [[4,3,3,3,1],[3,2,2]]=>34 [[5,4,4,4,1],[4,3,3,1]]=>40 [[5,4,4,3,1],[4,3,3]]=>42 [[6,5,5,4,1],[5,4,4,1]]=>48 [[5,4,3,3,1],[4,3,2]]=>48 [[6,5,4,4,1],[5,4,3,1]]=>56 [[6,5,4,3,1],[5,4,3]]=>56 [[7,6,5,4,1],[6,5,4,1]]=>64 [[2,2,2,2,2],[1,1,1]]=>16 [[3,3,3,3,2],[2,2,2,1]]=>23 [[4,4,4,4,2],[3,3,3,2]]=>27 [[3,3,3,2,2],[2,2,2]]=>28 [[4,4,4,3,2],[3,3,3,1]]=>32 [[5,5,5,4,2],[4,4,4,2]]=>36 [[3,3,2,2,2],[2,2,1]]=>30 [[4,4,3,3,2],[3,3,2,1]]=>39 [[5,5,4,4,2],[4,4,3,2]]=>45 [[4,4,3,2,2],[3,3,2]]=>42 [[5,5,4,3,2],[4,4,3,1]]=>48 [[6,6,5,4,2],[5,5,4,2]]=>54 [[3,2,2,2,2],[2,1,1]]=>26 [[4,3,3,3,2],[3,2,2,1]]=>36 [[5,4,4,4,2],[4,3,3,2]]=>42 [[4,3,3,2,2],[3,2,2]]=>42 [[5,4,4,3,2],[4,3,3,1]]=>48 [[6,5,5,4,2],[5,4,4,2]]=>54 [[4,3,2,2,2],[3,2,1]]=>40 [[5,4,3,3,2],[4,3,2,1]]=>52 [[6,5,4,4,2],[5,4,3,2]]=>60 [[5,4,3,2,2],[4,3,2]]=>56 [[6,5,4,3,2],[5,4,3,1]]=>64 [[7,6,5,4,2],[6,5,4,2]]=>72 [[2,2,2,2,1,1],[1,1,1]]=>19 [[3,3,3,3,2,1],[2,2,2,1,1]]=>28 [[3,3,3,3,1,1],[2,2,2,1]]=>27 [[4,4,4,4,2,1],[3,3,3,2,1]]=>36 [[3,3,3,2,1,1],[2,2,2]]=>28 [[4,4,4,3,2,1],[3,3,3,1,1]]=>40 [[4,4,4,3,1,1],[3,3,3,1]]=>36 [[5,5,5,4,2,1],[4,4,4,2,1]]=>48 [[3,3,2,2,1,1],[2,2,1]]=>33 [[4,4,3,3,2,1],[3,3,2,1,1]]=>48 [[4,4,3,3,1,1],[3,3,2,1]]=>45 [[5,5,4,4,2,1],[4,4,3,2,1]]=>60 [[4,4,3,2,1,1],[3,3,2]]=>42 [[5,5,4,3,2,1],[4,4,3,1,1]]=>60 [[5,5,4,3,1,1],[4,4,3,1]]=>54 [[6,6,5,4,2,1],[5,5,4,2,1]]=>72 [[3,2,2,2,1,1],[2,1,1]]=>30 [[4,3,3,3,2,1],[3,2,2,1,1]]=>44 [[4,3,3,3,1,1],[3,2,2,1]]=>42 [[5,4,4,4,2,1],[4,3,3,2,1]]=>56 [[4,3,3,2,1,1],[3,2,2]]=>42 [[5,4,4,3,2,1],[4,3,3,1,1]]=>60 [[5,4,4,3,1,1],[4,3,3,1]]=>54 [[6,5,5,4,2,1],[5,4,4,2,1]]=>72 [[4,3,2,2,1,1],[3,2,1]]=>44 [[5,4,3,3,2,1],[4,3,2,1,1]]=>64 [[5,4,3,3,1,1],[4,3,2,1]]=>60 [[6,5,4,4,2,1],[5,4,3,2,1]]=>80 [[5,4,3,2,1,1],[4,3,2]]=>56 [[6,5,4,3,2,1],[5,4,3,1,1]]=>80 [[6,5,4,3,1,1],[5,4,3,1]]=>72 [[7,6,5,4,2,1],[6,5,4,2,1]]=>96 [[3,3,3,3,3],[2,2,2,2]]=>16 [[4,4,4,4,3],[3,3,3,3]]=>20 [[4,4,4,3,3],[3,3,3,2]]=>28 [[5,5,5,4,3],[4,4,4,3]]=>32 [[4,4,3,3,3],[3,3,2,2]]=>30 [[5,5,4,4,3],[4,4,3,3]]=>36 [[5,5,4,3,3],[4,4,3,2]]=>42 [[6,6,5,4,3],[5,5,4,3]]=>48 [[4,3,3,3,3],[3,2,2,2]]=>26 [[5,4,4,4,3],[4,3,3,3]]=>32 [[5,4,4,3,3],[4,3,3,2]]=>42 [[6,5,5,4,3],[5,4,4,3]]=>48 [[5,4,3,3,3],[4,3,2,2]]=>40 [[6,5,4,4,3],[5,4,3,3]]=>48 [[6,5,4,3,3],[5,4,3,2]]=>56 [[7,6,5,4,3],[6,5,4,3]]=>64 [[2,2,2,2,2,1],[1,1,1,1]]=>17 [[3,3,3,3,3,1],[2,2,2,2,1]]=>22 [[3,3,3,3,2,1],[2,2,2,2]]=>25 [[4,4,4,4,3,1],[3,3,3,3,1]]=>30 [[3,3,3,2,2,1],[2,2,2,1]]=>32 [[4,4,4,3,3,1],[3,3,3,2,1]]=>40 [[4,4,4,3,2,1],[3,3,3,2]]=>40 [[5,5,5,4,3,1],[4,4,4,3,1]]=>48 [[3,3,2,2,2,1],[2,2,1,1]]=>33 [[4,4,3,3,3,1],[3,3,2,2,1]]=>42 [[4,4,3,3,2,1],[3,3,2,2]]=>45 [[5,5,4,4,3,1],[4,4,3,3,1]]=>54 [[4,4,3,2,2,1],[3,3,2,1]]=>48 [[5,5,4,3,3,1],[4,4,3,2,1]]=>60 [[5,5,4,3,2,1],[4,4,3,2]]=>60 [[6,6,5,4,3,1],[5,5,4,3,1]]=>72 [[3,2,2,2,2,1],[2,1,1,1]]=>28 [[4,3,3,3,3,1],[3,2,2,2,1]]=>36 [[4,3,3,3,2,1],[3,2,2,2]]=>40 [[5,4,4,4,3,1],[4,3,3,3,1]]=>48 [[4,3,3,2,2,1],[3,2,2,1]]=>48 [[5,4,4,3,3,1],[4,3,3,2,1]]=>60 [[5,4,4,3,2,1],[4,3,3,2]]=>60 [[6,5,5,4,3,1],[5,4,4,3,1]]=>72 [[4,3,2,2,2,1],[3,2,1,1]]=>44 [[5,4,3,3,3,1],[4,3,2,2,1]]=>56 [[5,4,3,3,2,1],[4,3,2,2]]=>60 [[6,5,4,4,3,1],[5,4,3,3,1]]=>72 [[5,4,3,2,2,1],[4,3,2,1]]=>64 [[6,5,4,3,3,1],[5,4,3,2,1]]=>80 [[6,5,4,3,2,1],[5,4,3,2]]=>80 [[7,6,5,4,3,1],[6,5,4,3,1]]=>96 [[2,2,2,2,2,2],[1,1,1,1,1]]=>13 [[3,3,3,3,3,2],[2,2,2,2,2]]=>18 [[3,3,3,3,2,2],[2,2,2,2,1]]=>25 [[4,4,4,4,3,2],[3,3,3,3,2]]=>30 [[3,3,3,2,2,2],[2,2,2,1,1]]=>28 [[4,4,4,3,3,2],[3,3,3,2,2]]=>36 [[4,4,4,3,2,2],[3,3,3,2,1]]=>40 [[5,5,5,4,3,2],[4,4,4,3,2]]=>48 [[3,3,2,2,2,2],[2,2,1,1,1]]=>27 [[4,4,3,3,3,2],[3,3,2,2,2]]=>36 [[4,4,3,3,2,2],[3,3,2,2,1]]=>45 [[5,5,4,4,3,2],[4,4,3,3,2]]=>54 [[4,4,3,2,2,2],[3,3,2,1,1]]=>42 [[5,5,4,3,3,2],[4,4,3,2,2]]=>54 [[5,5,4,3,2,2],[4,4,3,2,1]]=>60 [[6,6,5,4,3,2],[5,5,4,3,2]]=>72 [[3,2,2,2,2,2],[2,1,1,1,1]]=>22 [[4,3,3,3,3,2],[3,2,2,2,2]]=>30 [[4,3,3,3,2,2],[3,2,2,2,1]]=>40 [[5,4,4,4,3,2],[4,3,3,3,2]]=>48 [[4,3,3,2,2,2],[3,2,2,1,1]]=>42 [[5,4,4,3,3,2],[4,3,3,2,2]]=>54 [[5,4,4,3,2,2],[4,3,3,2,1]]=>60 [[6,5,5,4,3,2],[5,4,4,3,2]]=>72 [[4,3,2,2,2,2],[3,2,1,1,1]]=>36 [[5,4,3,3,3,2],[4,3,2,2,2]]=>48 [[5,4,3,3,2,2],[4,3,2,2,1]]=>60 [[6,5,4,4,3,2],[5,4,3,3,2]]=>72 [[5,4,3,2,2,2],[4,3,2,1,1]]=>56 [[6,5,4,3,3,2],[5,4,3,2,2]]=>72 [[6,5,4,3,2,2],[5,4,3,2,1]]=>80 [[7,6,5,4,3,2],[6,5,4,3,2]]=>96 [[1,1,1,1,1,1,1],[]]=>8 [[2,2,2,2,2,2,1],[1,1,1,1,1,1]]=>14 [[2,2,2,2,2,1,1],[1,1,1,1,1]]=>18 [[3,3,3,3,3,2,1],[2,2,2,2,2,1]]=>24 [[2,2,2,2,1,1,1],[1,1,1,1]]=>20 [[3,3,3,3,2,2,1],[2,2,2,2,1,1]]=>30 [[3,3,3,3,2,1,1],[2,2,2,2,1]]=>30 [[4,4,4,4,3,2,1],[3,3,3,3,2,1]]=>40 [[2,2,2,1,1,1,1],[1,1,1]]=>20 [[3,3,3,2,2,2,1],[2,2,2,1,1,1]]=>32 [[3,3,3,2,2,1,1],[2,2,2,1,1]]=>36 [[4,4,4,3,3,2,1],[3,3,3,2,2,1]]=>48 [[3,3,3,2,1,1,1],[2,2,2,1]]=>32 [[4,4,4,3,2,2,1],[3,3,3,2,1,1]]=>48
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Description
The total number of rook placements on a Ferrers board.
References
[1] wikipedia:Rook_polynomial
Code
def statistic(nu):
    import itertools
    rook_matrix = matrix([[0]*q + [1]*(p-q) + [0]*(nu[0][0]-p)
                          for p, q in itertools.zip_longest(*nu, fillvalue=0)])
    return sum(rook_matrix.rook_vector())
Created
Dec 22, 2020 at 14:13 by Martin Rubey
Updated
Dec 22, 2020 at 14:13 by Martin Rubey