- FindStat

edit this statistic or download as text // json

Identifier

St000016: Standard tableaux ⟶ ℤ

Values

=>
                            Cc0007;cc-rep
                            
                            
                            

                        [[1]]=>0
[[1,2]]=>1
[[1],[2]]=>0
[[1,2,3]]=>3
[[1,3],[2]]=>1
[[1,2],[3]]=>1
[[1],[2],[3]]=>0
[[1,2,3,4]]=>6
[[1,3,4],[2]]=>3
[[1,2,4],[3]]=>3
[[1,2,3],[4]]=>3
[[1,3],[2,4]]=>3
[[1,2],[3,4]]=>3
[[1,4],[2],[3]]=>1
[[1,3],[2],[4]]=>1
[[1,2],[3],[4]]=>1
[[1],[2],[3],[4]]=>0
[[1,2,3,4,5]]=>10
[[1,3,4,5],[2]]=>6
[[1,2,4,5],[3]]=>6
[[1,2,3,5],[4]]=>6
[[1,2,3,4],[5]]=>6
[[1,3,5],[2,4]]=>5
[[1,2,5],[3,4]]=>5
[[1,3,4],[2,5]]=>5
[[1,2,4],[3,5]]=>5
[[1,2,3],[4,5]]=>5
[[1,4,5],[2],[3]]=>3
[[1,3,5],[2],[4]]=>3
[[1,2,5],[3],[4]]=>3
[[1,3,4],[2],[5]]=>3
[[1,2,4],[3],[5]]=>3
[[1,2,3],[4],[5]]=>3
[[1,4],[2,5],[3]]=>3
[[1,3],[2,5],[4]]=>3
[[1,2],[3,5],[4]]=>3
[[1,3],[2,4],[5]]=>3
[[1,2],[3,4],[5]]=>3
[[1,5],[2],[3],[4]]=>1
[[1,4],[2],[3],[5]]=>1
[[1,3],[2],[4],[5]]=>1
[[1,2],[3],[4],[5]]=>1
[[1],[2],[3],[4],[5]]=>0
[[1,2,3,4,5,6]]=>15
[[1,3,4,5,6],[2]]=>10
[[1,2,4,5,6],[3]]=>10
[[1,2,3,5,6],[4]]=>10
[[1,2,3,4,6],[5]]=>10
[[1,2,3,4,5],[6]]=>10
[[1,3,5,6],[2,4]]=>8
[[1,2,5,6],[3,4]]=>8
[[1,3,4,6],[2,5]]=>8
[[1,2,4,6],[3,5]]=>8
[[1,2,3,6],[4,5]]=>8
[[1,3,4,5],[2,6]]=>8
[[1,2,4,5],[3,6]]=>8
[[1,2,3,5],[4,6]]=>8
[[1,2,3,4],[5,6]]=>8
[[1,4,5,6],[2],[3]]=>6
[[1,3,5,6],[2],[4]]=>6
[[1,2,5,6],[3],[4]]=>6
[[1,3,4,6],[2],[5]]=>6
[[1,2,4,6],[3],[5]]=>6
[[1,2,3,6],[4],[5]]=>6
[[1,3,4,5],[2],[6]]=>6
[[1,2,4,5],[3],[6]]=>6
[[1,2,3,5],[4],[6]]=>6
[[1,2,3,4],[5],[6]]=>6
[[1,3,5],[2,4,6]]=>9
[[1,2,5],[3,4,6]]=>9
[[1,3,4],[2,5,6]]=>9
[[1,2,4],[3,5,6]]=>9
[[1,2,3],[4,5,6]]=>9
[[1,4,6],[2,5],[3]]=>5
[[1,3,6],[2,5],[4]]=>5
[[1,2,6],[3,5],[4]]=>5
[[1,3,6],[2,4],[5]]=>5
[[1,2,6],[3,4],[5]]=>5
[[1,4,5],[2,6],[3]]=>5
[[1,3,5],[2,6],[4]]=>5
[[1,2,5],[3,6],[4]]=>5
[[1,3,4],[2,6],[5]]=>5
[[1,2,4],[3,6],[5]]=>5
[[1,2,3],[4,6],[5]]=>5
[[1,3,5],[2,4],[6]]=>5
[[1,2,5],[3,4],[6]]=>5
[[1,3,4],[2,5],[6]]=>5
[[1,2,4],[3,5],[6]]=>5
[[1,2,3],[4,5],[6]]=>5
[[1,5,6],[2],[3],[4]]=>3
[[1,4,6],[2],[3],[5]]=>3
[[1,3,6],[2],[4],[5]]=>3
[[1,2,6],[3],[4],[5]]=>3
[[1,4,5],[2],[3],[6]]=>3
[[1,3,5],[2],[4],[6]]=>3
[[1,2,5],[3],[4],[6]]=>3
[[1,3,4],[2],[5],[6]]=>3
[[1,2,4],[3],[5],[6]]=>3
[[1,2,3],[4],[5],[6]]=>3
[[1,4],[2,5],[3,6]]=>5
[[1,3],[2,5],[4,6]]=>5
[[1,2],[3,5],[4,6]]=>5
[[1,3],[2,4],[5,6]]=>5
[[1,2],[3,4],[5,6]]=>5
[[1,5],[2,6],[3],[4]]=>3
[[1,4],[2,6],[3],[5]]=>3
[[1,3],[2,6],[4],[5]]=>3
[[1,2],[3,6],[4],[5]]=>3
[[1,4],[2,5],[3],[6]]=>3
[[1,3],[2,5],[4],[6]]=>3
[[1,2],[3,5],[4],[6]]=>3
[[1,3],[2,4],[5],[6]]=>3
[[1,2],[3,4],[5],[6]]=>3
[[1,6],[2],[3],[4],[5]]=>1
[[1,5],[2],[3],[4],[6]]=>1
[[1,4],[2],[3],[5],[6]]=>1
[[1,3],[2],[4],[5],[6]]=>1
[[1,2],[3],[4],[5],[6]]=>1
[[1],[2],[3],[4],[5],[6]]=>0
[[1,2,3,4,5,6,7]]=>21
[[1,3,4,5,6,7],[2]]=>15
[[1,2,4,5,6,7],[3]]=>15
[[1,2,3,5,6,7],[4]]=>15
[[1,2,3,4,6,7],[5]]=>15
[[1,2,3,4,5,7],[6]]=>15
[[1,2,3,4,5,6],[7]]=>15
[[1,3,5,6,7],[2,4]]=>12
[[1,2,5,6,7],[3,4]]=>12
[[1,3,4,6,7],[2,5]]=>12
[[1,2,4,6,7],[3,5]]=>12
[[1,2,3,6,7],[4,5]]=>12
[[1,3,4,5,7],[2,6]]=>12
[[1,2,4,5,7],[3,6]]=>12
[[1,2,3,5,7],[4,6]]=>12
[[1,2,3,4,7],[5,6]]=>12
[[1,3,4,5,6],[2,7]]=>12
[[1,2,4,5,6],[3,7]]=>12
[[1,2,3,5,6],[4,7]]=>12
[[1,2,3,4,6],[5,7]]=>12
[[1,2,3,4,5],[6,7]]=>12
[[1,4,5,6,7],[2],[3]]=>10
[[1,3,5,6,7],[2],[4]]=>10
[[1,2,5,6,7],[3],[4]]=>10
[[1,3,4,6,7],[2],[5]]=>10
[[1,2,4,6,7],[3],[5]]=>10
[[1,2,3,6,7],[4],[5]]=>10
[[1,3,4,5,7],[2],[6]]=>10
[[1,2,4,5,7],[3],[6]]=>10
[[1,2,3,5,7],[4],[6]]=>10
[[1,2,3,4,7],[5],[6]]=>10
[[1,3,4,5,6],[2],[7]]=>10
[[1,2,4,5,6],[3],[7]]=>10
[[1,2,3,5,6],[4],[7]]=>10
[[1,2,3,4,6],[5],[7]]=>10
[[1,2,3,4,5],[6],[7]]=>10
[[1,3,5,7],[2,4,6]]=>12
[[1,2,5,7],[3,4,6]]=>12
[[1,3,4,7],[2,5,6]]=>12
[[1,2,4,7],[3,5,6]]=>12
[[1,2,3,7],[4,5,6]]=>12
[[1,3,5,6],[2,4,7]]=>12
[[1,2,5,6],[3,4,7]]=>12
[[1,3,4,6],[2,5,7]]=>12
[[1,2,4,6],[3,5,7]]=>12
[[1,2,3,6],[4,5,7]]=>12
[[1,3,4,5],[2,6,7]]=>12
[[1,2,4,5],[3,6,7]]=>12
[[1,2,3,5],[4,6,7]]=>12
[[1,2,3,4],[5,6,7]]=>12
[[1,4,6,7],[2,5],[3]]=>8
[[1,3,6,7],[2,5],[4]]=>8
[[1,2,6,7],[3,5],[4]]=>8
[[1,3,6,7],[2,4],[5]]=>8
[[1,2,6,7],[3,4],[5]]=>8
[[1,4,5,7],[2,6],[3]]=>8
[[1,3,5,7],[2,6],[4]]=>8
[[1,2,5,7],[3,6],[4]]=>8
[[1,3,4,7],[2,6],[5]]=>8
[[1,2,4,7],[3,6],[5]]=>8
[[1,2,3,7],[4,6],[5]]=>8
[[1,3,5,7],[2,4],[6]]=>8
[[1,2,5,7],[3,4],[6]]=>8
[[1,3,4,7],[2,5],[6]]=>8
[[1,2,4,7],[3,5],[6]]=>8
[[1,2,3,7],[4,5],[6]]=>8
[[1,4,5,6],[2,7],[3]]=>8
[[1,3,5,6],[2,7],[4]]=>8
[[1,2,5,6],[3,7],[4]]=>8
[[1,3,4,6],[2,7],[5]]=>8
[[1,2,4,6],[3,7],[5]]=>8
[[1,2,3,6],[4,7],[5]]=>8
[[1,3,4,5],[2,7],[6]]=>8
[[1,2,4,5],[3,7],[6]]=>8
[[1,2,3,5],[4,7],[6]]=>8
[[1,2,3,4],[5,7],[6]]=>8
[[1,3,5,6],[2,4],[7]]=>8
[[1,2,5,6],[3,4],[7]]=>8
[[1,3,4,6],[2,5],[7]]=>8
[[1,2,4,6],[3,5],[7]]=>8
[[1,2,3,6],[4,5],[7]]=>8
[[1,3,4,5],[2,6],[7]]=>8
[[1,2,4,5],[3,6],[7]]=>8
[[1,2,3,5],[4,6],[7]]=>8
[[1,2,3,4],[5,6],[7]]=>8
[[1,5,6,7],[2],[3],[4]]=>6
[[1,4,6,7],[2],[3],[5]]=>6
[[1,3,6,7],[2],[4],[5]]=>6
[[1,2,6,7],[3],[4],[5]]=>6
[[1,4,5,7],[2],[3],[6]]=>6
[[1,3,5,7],[2],[4],[6]]=>6
[[1,2,5,7],[3],[4],[6]]=>6
[[1,3,4,7],[2],[5],[6]]=>6
[[1,2,4,7],[3],[5],[6]]=>6
[[1,2,3,7],[4],[5],[6]]=>6
[[1,4,5,6],[2],[3],[7]]=>6
[[1,3,5,6],[2],[4],[7]]=>6
[[1,2,5,6],[3],[4],[7]]=>6
[[1,3,4,6],[2],[5],[7]]=>6
[[1,2,4,6],[3],[5],[7]]=>6
[[1,2,3,6],[4],[5],[7]]=>6
[[1,3,4,5],[2],[6],[7]]=>6
[[1,2,4,5],[3],[6],[7]]=>6
[[1,2,3,5],[4],[6],[7]]=>6
[[1,2,3,4],[5],[6],[7]]=>6
[[1,4,6],[2,5,7],[3]]=>9
[[1,3,6],[2,5,7],[4]]=>9
[[1,2,6],[3,5,7],[4]]=>9
[[1,3,6],[2,4,7],[5]]=>9
[[1,2,6],[3,4,7],[5]]=>9
[[1,4,5],[2,6,7],[3]]=>9
[[1,3,5],[2,6,7],[4]]=>9
[[1,2,5],[3,6,7],[4]]=>9
[[1,3,4],[2,6,7],[5]]=>9
[[1,2,4],[3,6,7],[5]]=>9
[[1,2,3],[4,6,7],[5]]=>9
[[1,3,5],[2,4,7],[6]]=>9
[[1,2,5],[3,4,7],[6]]=>9
[[1,3,4],[2,5,7],[6]]=>9
[[1,2,4],[3,5,7],[6]]=>9
[[1,2,3],[4,5,7],[6]]=>9
[[1,3,5],[2,4,6],[7]]=>9
[[1,2,5],[3,4,6],[7]]=>9
[[1,3,4],[2,5,6],[7]]=>9
[[1,2,4],[3,5,6],[7]]=>9
[[1,2,3],[4,5,6],[7]]=>9
[[1,4,7],[2,5],[3,6]]=>7
[[1,3,7],[2,5],[4,6]]=>7
[[1,2,7],[3,5],[4,6]]=>7
[[1,3,7],[2,4],[5,6]]=>7
[[1,2,7],[3,4],[5,6]]=>7
[[1,4,6],[2,5],[3,7]]=>7
[[1,3,6],[2,5],[4,7]]=>7
[[1,2,6],[3,5],[4,7]]=>7
[[1,3,6],[2,4],[5,7]]=>7
[[1,2,6],[3,4],[5,7]]=>7
[[1,4,5],[2,6],[3,7]]=>7
[[1,3,5],[2,6],[4,7]]=>7
[[1,2,5],[3,6],[4,7]]=>7
[[1,3,4],[2,6],[5,7]]=>7
[[1,2,4],[3,6],[5,7]]=>7
[[1,2,3],[4,6],[5,7]]=>7
[[1,3,5],[2,4],[6,7]]=>7
[[1,2,5],[3,4],[6,7]]=>7
[[1,3,4],[2,5],[6,7]]=>7
[[1,2,4],[3,5],[6,7]]=>7
[[1,2,3],[4,5],[6,7]]=>7
[[1,5,7],[2,6],[3],[4]]=>5
[[1,4,7],[2,6],[3],[5]]=>5
[[1,3,7],[2,6],[4],[5]]=>5
[[1,2,7],[3,6],[4],[5]]=>5
[[1,4,7],[2,5],[3],[6]]=>5
[[1,3,7],[2,5],[4],[6]]=>5
[[1,2,7],[3,5],[4],[6]]=>5
[[1,3,7],[2,4],[5],[6]]=>5
[[1,2,7],[3,4],[5],[6]]=>5
[[1,5,6],[2,7],[3],[4]]=>5
[[1,4,6],[2,7],[3],[5]]=>5
[[1,3,6],[2,7],[4],[5]]=>5
[[1,2,6],[3,7],[4],[5]]=>5
[[1,4,5],[2,7],[3],[6]]=>5
[[1,3,5],[2,7],[4],[6]]=>5
[[1,2,5],[3,7],[4],[6]]=>5
[[1,3,4],[2,7],[5],[6]]=>5
[[1,2,4],[3,7],[5],[6]]=>5
[[1,2,3],[4,7],[5],[6]]=>5
[[1,4,6],[2,5],[3],[7]]=>5
[[1,3,6],[2,5],[4],[7]]=>5
[[1,2,6],[3,5],[4],[7]]=>5
[[1,3,6],[2,4],[5],[7]]=>5
[[1,2,6],[3,4],[5],[7]]=>5
[[1,4,5],[2,6],[3],[7]]=>5
[[1,3,5],[2,6],[4],[7]]=>5
[[1,2,5],[3,6],[4],[7]]=>5
[[1,3,4],[2,6],[5],[7]]=>5
[[1,2,4],[3,6],[5],[7]]=>5
[[1,2,3],[4,6],[5],[7]]=>5
[[1,3,5],[2,4],[6],[7]]=>5
[[1,2,5],[3,4],[6],[7]]=>5
[[1,3,4],[2,5],[6],[7]]=>5
[[1,2,4],[3,5],[6],[7]]=>5
[[1,2,3],[4,5],[6],[7]]=>5
[[1,6,7],[2],[3],[4],[5]]=>3
[[1,5,7],[2],[3],[4],[6]]=>3
[[1,4,7],[2],[3],[5],[6]]=>3
[[1,3,7],[2],[4],[5],[6]]=>3
[[1,2,7],[3],[4],[5],[6]]=>3
[[1,5,6],[2],[3],[4],[7]]=>3
[[1,4,6],[2],[3],[5],[7]]=>3
[[1,3,6],[2],[4],[5],[7]]=>3
[[1,2,6],[3],[4],[5],[7]]=>3
[[1,4,5],[2],[3],[6],[7]]=>3
[[1,3,5],[2],[4],[6],[7]]=>3
[[1,2,5],[3],[4],[6],[7]]=>3
[[1,3,4],[2],[5],[6],[7]]=>3
[[1,2,4],[3],[5],[6],[7]]=>3
[[1,2,3],[4],[5],[6],[7]]=>3
[[1,5],[2,6],[3,7],[4]]=>5
[[1,4],[2,6],[3,7],[5]]=>5
[[1,3],[2,6],[4,7],[5]]=>5
[[1,2],[3,6],[4,7],[5]]=>5
[[1,4],[2,5],[3,7],[6]]=>5
[[1,3],[2,5],[4,7],[6]]=>5
[[1,2],[3,5],[4,7],[6]]=>5
[[1,3],[2,4],[5,7],[6]]=>5
[[1,2],[3,4],[5,7],[6]]=>5
[[1,4],[2,5],[3,6],[7]]=>5
[[1,3],[2,5],[4,6],[7]]=>5
[[1,2],[3,5],[4,6],[7]]=>5
[[1,3],[2,4],[5,6],[7]]=>5
[[1,2],[3,4],[5,6],[7]]=>5
[[1,6],[2,7],[3],[4],[5]]=>3
[[1,5],[2,7],[3],[4],[6]]=>3
[[1,4],[2,7],[3],[5],[6]]=>3
[[1,3],[2,7],[4],[5],[6]]=>3
[[1,2],[3,7],[4],[5],[6]]=>3
[[1,5],[2,6],[3],[4],[7]]=>3
[[1,4],[2,6],[3],[5],[7]]=>3
[[1,3],[2,6],[4],[5],[7]]=>3
[[1,2],[3,6],[4],[5],[7]]=>3
[[1,4],[2,5],[3],[6],[7]]=>3
[[1,3],[2,5],[4],[6],[7]]=>3
[[1,2],[3,5],[4],[6],[7]]=>3
[[1,3],[2,4],[5],[6],[7]]=>3
[[1,2],[3,4],[5],[6],[7]]=>3
[[1,7],[2],[3],[4],[5],[6]]=>1
[[1,6],[2],[3],[4],[5],[7]]=>1
[[1,5],[2],[3],[4],[6],[7]]=>1
[[1,4],[2],[3],[5],[6],[7]]=>1
[[1,3],[2],[4],[5],[6],[7]]=>1
[[1,2],[3],[4],[5],[6],[7]]=>1
[[1],[2],[3],[4],[5],[6],[7]]=>0
[[1,2,3,4,5,6,7,8]]=>28
[[1,3,4,5,6,7,8],[2]]=>21
[[1,2,4,5,6,7,8],[3]]=>21
[[1,2,3,5,6,7,8],[4]]=>21
[[1,2,3,4,6,7,8],[5]]=>21
[[1,2,3,4,5,7,8],[6]]=>21
[[1,2,3,4,5,6,8],[7]]=>21
[[1,2,3,4,5,6,7],[8]]=>21
[[1,3,5,6,7,8],[2,4]]=>17
[[1,2,5,6,7,8],[3,4]]=>17
[[1,3,4,6,7,8],[2,5]]=>17
[[1,2,4,6,7,8],[3,5]]=>17
[[1,2,3,6,7,8],[4,5]]=>17
[[1,3,4,5,7,8],[2,6]]=>17
[[1,2,4,5,7,8],[3,6]]=>17
[[1,2,3,5,7,8],[4,6]]=>17
[[1,2,3,4,7,8],[5,6]]=>17
[[1,3,4,5,6,8],[2,7]]=>17
[[1,2,4,5,6,8],[3,7]]=>17
[[1,2,3,5,6,8],[4,7]]=>17
[[1,2,3,4,6,8],[5,7]]=>17
[[1,2,3,4,5,8],[6,7]]=>17
[[1,3,4,5,6,7],[2,8]]=>17
[[1,2,4,5,6,7],[3,8]]=>17
[[1,2,3,5,6,7],[4,8]]=>17
[[1,2,3,4,6,7],[5,8]]=>17
[[1,2,3,4,5,7],[6,8]]=>17
[[1,2,3,4,5,6],[7,8]]=>17
[[1,4,5,6,7,8],[2],[3]]=>15
[[1,3,5,6,7,8],[2],[4]]=>15
[[1,2,5,6,7,8],[3],[4]]=>15
[[1,3,4,6,7,8],[2],[5]]=>15
[[1,2,4,6,7,8],[3],[5]]=>15
[[1,2,3,6,7,8],[4],[5]]=>15
[[1,3,4,5,7,8],[2],[6]]=>15
[[1,2,4,5,7,8],[3],[6]]=>15
[[1,2,3,5,7,8],[4],[6]]=>15
[[1,2,3,4,7,8],[5],[6]]=>15
[[1,3,4,5,6,8],[2],[7]]=>15
[[1,2,4,5,6,8],[3],[7]]=>15
[[1,2,3,5,6,8],[4],[7]]=>15
[[1,2,3,4,6,8],[5],[7]]=>15
[[1,2,3,4,5,8],[6],[7]]=>15
[[1,3,4,5,6,7],[2],[8]]=>15
[[1,2,4,5,6,7],[3],[8]]=>15
[[1,2,3,5,6,7],[4],[8]]=>15
[[1,2,3,4,6,7],[5],[8]]=>15
[[1,2,3,4,5,7],[6],[8]]=>15
[[1,2,3,4,5,6],[7],[8]]=>15
[[1,3,5,7,8],[2,4,6]]=>16
[[1,2,5,7,8],[3,4,6]]=>16
[[1,3,4,7,8],[2,5,6]]=>16
[[1,2,4,7,8],[3,5,6]]=>16
[[1,2,3,7,8],[4,5,6]]=>16
[[1,3,5,6,8],[2,4,7]]=>16
[[1,2,5,6,8],[3,4,7]]=>16
[[1,3,4,6,8],[2,5,7]]=>16
[[1,2,4,6,8],[3,5,7]]=>16
[[1,2,3,6,8],[4,5,7]]=>16
[[1,3,4,5,8],[2,6,7]]=>16
[[1,2,4,5,8],[3,6,7]]=>16
[[1,2,3,5,8],[4,6,7]]=>16
[[1,2,3,4,8],[5,6,7]]=>16
[[1,3,5,6,7],[2,4,8]]=>16
[[1,2,5,6,7],[3,4,8]]=>16
[[1,3,4,6,7],[2,5,8]]=>16
[[1,2,4,6,7],[3,5,8]]=>16
[[1,2,3,6,7],[4,5,8]]=>16
[[1,3,4,5,7],[2,6,8]]=>16
[[1,2,4,5,7],[3,6,8]]=>16
[[1,2,3,5,7],[4,6,8]]=>16
[[1,2,3,4,7],[5,6,8]]=>16
[[1,3,4,5,6],[2,7,8]]=>16
[[1,2,4,5,6],[3,7,8]]=>16
[[1,2,3,5,6],[4,7,8]]=>16
[[1,2,3,4,6],[5,7,8]]=>16
[[1,2,3,4,5],[6,7,8]]=>16
[[1,4,6,7,8],[2,5],[3]]=>12
[[1,3,6,7,8],[2,5],[4]]=>12
[[1,2,6,7,8],[3,5],[4]]=>12
[[1,3,6,7,8],[2,4],[5]]=>12
[[1,2,6,7,8],[3,4],[5]]=>12
[[1,4,5,7,8],[2,6],[3]]=>12
[[1,3,5,7,8],[2,6],[4]]=>12
[[1,2,5,7,8],[3,6],[4]]=>12
[[1,3,4,7,8],[2,6],[5]]=>12
[[1,2,4,7,8],[3,6],[5]]=>12
[[1,2,3,7,8],[4,6],[5]]=>12
[[1,3,5,7,8],[2,4],[6]]=>12
[[1,2,5,7,8],[3,4],[6]]=>12
[[1,3,4,7,8],[2,5],[6]]=>12
[[1,2,4,7,8],[3,5],[6]]=>12
[[1,2,3,7,8],[4,5],[6]]=>12
[[1,4,5,6,8],[2,7],[3]]=>12
[[1,3,5,6,8],[2,7],[4]]=>12
[[1,2,5,6,8],[3,7],[4]]=>12
[[1,3,4,6,8],[2,7],[5]]=>12
[[1,2,4,6,8],[3,7],[5]]=>12
[[1,2,3,6,8],[4,7],[5]]=>12
[[1,3,4,5,8],[2,7],[6]]=>12
[[1,2,4,5,8],[3,7],[6]]=>12
[[1,2,3,5,8],[4,7],[6]]=>12
[[1,2,3,4,8],[5,7],[6]]=>12
[[1,3,5,6,8],[2,4],[7]]=>12
[[1,2,5,6,8],[3,4],[7]]=>12
[[1,3,4,6,8],[2,5],[7]]=>12
[[1,2,4,6,8],[3,5],[7]]=>12
[[1,2,3,6,8],[4,5],[7]]=>12
[[1,3,4,5,8],[2,6],[7]]=>12
[[1,2,4,5,8],[3,6],[7]]=>12
[[1,2,3,5,8],[4,6],[7]]=>12
[[1,2,3,4,8],[5,6],[7]]=>12
[[1,4,5,6,7],[2,8],[3]]=>12
[[1,3,5,6,7],[2,8],[4]]=>12
[[1,2,5,6,7],[3,8],[4]]=>12
[[1,3,4,6,7],[2,8],[5]]=>12
[[1,2,4,6,7],[3,8],[5]]=>12
[[1,2,3,6,7],[4,8],[5]]=>12
[[1,3,4,5,7],[2,8],[6]]=>12
[[1,2,4,5,7],[3,8],[6]]=>12
[[1,2,3,5,7],[4,8],[6]]=>12
[[1,2,3,4,7],[5,8],[6]]=>12
[[1,3,4,5,6],[2,8],[7]]=>12
[[1,2,4,5,6],[3,8],[7]]=>12
[[1,2,3,5,6],[4,8],[7]]=>12
[[1,2,3,4,6],[5,8],[7]]=>12
[[1,2,3,4,5],[6,8],[7]]=>12
[[1,3,5,6,7],[2,4],[8]]=>12
[[1,2,5,6,7],[3,4],[8]]=>12
[[1,3,4,6,7],[2,5],[8]]=>12
[[1,2,4,6,7],[3,5],[8]]=>12
[[1,2,3,6,7],[4,5],[8]]=>12
[[1,3,4,5,7],[2,6],[8]]=>12
[[1,2,4,5,7],[3,6],[8]]=>12
[[1,2,3,5,7],[4,6],[8]]=>12
[[1,2,3,4,7],[5,6],[8]]=>12
[[1,3,4,5,6],[2,7],[8]]=>12
[[1,2,4,5,6],[3,7],[8]]=>12
[[1,2,3,5,6],[4,7],[8]]=>12
[[1,2,3,4,6],[5,7],[8]]=>12
[[1,2,3,4,5],[6,7],[8]]=>12
[[1,5,6,7,8],[2],[3],[4]]=>10
[[1,4,6,7,8],[2],[3],[5]]=>10
[[1,3,6,7,8],[2],[4],[5]]=>10
[[1,2,6,7,8],[3],[4],[5]]=>10
[[1,4,5,7,8],[2],[3],[6]]=>10
[[1,3,5,7,8],[2],[4],[6]]=>10
[[1,2,5,7,8],[3],[4],[6]]=>10
[[1,3,4,7,8],[2],[5],[6]]=>10
[[1,2,4,7,8],[3],[5],[6]]=>10
[[1,2,3,7,8],[4],[5],[6]]=>10
[[1,4,5,6,8],[2],[3],[7]]=>10
[[1,3,5,6,8],[2],[4],[7]]=>10
[[1,2,5,6,8],[3],[4],[7]]=>10
[[1,3,4,6,8],[2],[5],[7]]=>10
[[1,2,4,6,8],[3],[5],[7]]=>10
[[1,2,3,6,8],[4],[5],[7]]=>10
[[1,3,4,5,8],[2],[6],[7]]=>10
[[1,2,4,5,8],[3],[6],[7]]=>10
[[1,2,3,5,8],[4],[6],[7]]=>10
[[1,2,3,4,8],[5],[6],[7]]=>10
[[1,4,5,6,7],[2],[3],[8]]=>10
[[1,3,5,6,7],[2],[4],[8]]=>10
[[1,2,5,6,7],[3],[4],[8]]=>10
[[1,3,4,6,7],[2],[5],[8]]=>10
[[1,2,4,6,7],[3],[5],[8]]=>10
[[1,2,3,6,7],[4],[5],[8]]=>10
[[1,3,4,5,7],[2],[6],[8]]=>10
[[1,2,4,5,7],[3],[6],[8]]=>10
[[1,2,3,5,7],[4],[6],[8]]=>10
[[1,2,3,4,7],[5],[6],[8]]=>10
[[1,3,4,5,6],[2],[7],[8]]=>10
[[1,2,4,5,6],[3],[7],[8]]=>10
[[1,2,3,5,6],[4],[7],[8]]=>10
[[1,2,3,4,6],[5],[7],[8]]=>10
[[1,2,3,4,5],[6],[7],[8]]=>10
[[1,3,5,7],[2,4,6,8]]=>18
[[1,2,5,7],[3,4,6,8]]=>18
[[1,3,4,7],[2,5,6,8]]=>18
[[1,2,4,7],[3,5,6,8]]=>18
[[1,2,3,7],[4,5,6,8]]=>18
[[1,3,5,6],[2,4,7,8]]=>18
[[1,2,5,6],[3,4,7,8]]=>18
[[1,3,4,6],[2,5,7,8]]=>18
[[1,2,4,6],[3,5,7,8]]=>18
[[1,2,3,6],[4,5,7,8]]=>18
[[1,3,4,5],[2,6,7,8]]=>18
[[1,2,4,5],[3,6,7,8]]=>18
[[1,2,3,5],[4,6,7,8]]=>18
[[1,2,3,4],[5,6,7,8]]=>18
[[1,4,6,8],[2,5,7],[3]]=>12
[[1,3,6,8],[2,5,7],[4]]=>12
[[1,2,6,8],[3,5,7],[4]]=>12
[[1,3,6,8],[2,4,7],[5]]=>12
[[1,2,6,8],[3,4,7],[5]]=>12
[[1,4,5,8],[2,6,7],[3]]=>12
[[1,3,5,8],[2,6,7],[4]]=>12
[[1,2,5,8],[3,6,7],[4]]=>12
[[1,3,4,8],[2,6,7],[5]]=>12
[[1,2,4,8],[3,6,7],[5]]=>12
[[1,2,3,8],[4,6,7],[5]]=>12
[[1,3,5,8],[2,4,7],[6]]=>12
[[1,2,5,8],[3,4,7],[6]]=>12
[[1,3,4,8],[2,5,7],[6]]=>12
[[1,2,4,8],[3,5,7],[6]]=>12
[[1,2,3,8],[4,5,7],[6]]=>12
[[1,3,5,8],[2,4,6],[7]]=>12
[[1,2,5,8],[3,4,6],[7]]=>12
[[1,3,4,8],[2,5,6],[7]]=>12
[[1,2,4,8],[3,5,6],[7]]=>12
[[1,2,3,8],[4,5,6],[7]]=>12
[[1,4,6,7],[2,5,8],[3]]=>12
[[1,3,6,7],[2,5,8],[4]]=>12
[[1,2,6,7],[3,5,8],[4]]=>12
[[1,3,6,7],[2,4,8],[5]]=>12
[[1,2,6,7],[3,4,8],[5]]=>12
[[1,4,5,7],[2,6,8],[3]]=>12
[[1,3,5,7],[2,6,8],[4]]=>12
[[1,2,5,7],[3,6,8],[4]]=>12
[[1,3,4,7],[2,6,8],[5]]=>12
[[1,2,4,7],[3,6,8],[5]]=>12
[[1,2,3,7],[4,6,8],[5]]=>12
[[1,3,5,7],[2,4,8],[6]]=>12
[[1,2,5,7],[3,4,8],[6]]=>12
[[1,3,4,7],[2,5,8],[6]]=>12
[[1,2,4,7],[3,5,8],[6]]=>12
[[1,2,3,7],[4,5,8],[6]]=>12
[[1,4,5,6],[2,7,8],[3]]=>12
[[1,3,5,6],[2,7,8],[4]]=>12
[[1,2,5,6],[3,7,8],[4]]=>12
[[1,3,4,6],[2,7,8],[5]]=>12
[[1,2,4,6],[3,7,8],[5]]=>12
[[1,2,3,6],[4,7,8],[5]]=>12
[[1,3,4,5],[2,7,8],[6]]=>12
[[1,2,4,5],[3,7,8],[6]]=>12
[[1,2,3,5],[4,7,8],[6]]=>12
[[1,2,3,4],[5,7,8],[6]]=>12
[[1,3,5,6],[2,4,8],[7]]=>12
[[1,2,5,6],[3,4,8],[7]]=>12
[[1,3,4,6],[2,5,8],[7]]=>12
[[1,2,4,6],[3,5,8],[7]]=>12
[[1,2,3,6],[4,5,8],[7]]=>12
[[1,3,4,5],[2,6,8],[7]]=>12
[[1,2,4,5],[3,6,8],[7]]=>12
[[1,2,3,5],[4,6,8],[7]]=>12
[[1,2,3,4],[5,6,8],[7]]=>12
[[1,3,5,7],[2,4,6],[8]]=>12
[[1,2,5,7],[3,4,6],[8]]=>12
[[1,3,4,7],[2,5,6],[8]]=>12
[[1,2,4,7],[3,5,6],[8]]=>12
[[1,2,3,7],[4,5,6],[8]]=>12
[[1,3,5,6],[2,4,7],[8]]=>12
[[1,2,5,6],[3,4,7],[8]]=>12
[[1,3,4,6],[2,5,7],[8]]=>12
[[1,2,4,6],[3,5,7],[8]]=>12
[[1,2,3,6],[4,5,7],[8]]=>12
[[1,3,4,5],[2,6,7],[8]]=>12
[[1,2,4,5],[3,6,7],[8]]=>12
[[1,2,3,5],[4,6,7],[8]]=>12
[[1,2,3,4],[5,6,7],[8]]=>12
[[1,4,7,8],[2,5],[3,6]]=>10
[[1,3,7,8],[2,5],[4,6]]=>10
[[1,2,7,8],[3,5],[4,6]]=>10
[[1,3,7,8],[2,4],[5,6]]=>10
[[1,2,7,8],[3,4],[5,6]]=>10
[[1,4,6,8],[2,5],[3,7]]=>10
[[1,3,6,8],[2,5],[4,7]]=>10
[[1,2,6,8],[3,5],[4,7]]=>10
[[1,3,6,8],[2,4],[5,7]]=>10
[[1,2,6,8],[3,4],[5,7]]=>10
[[1,4,5,8],[2,6],[3,7]]=>10
[[1,3,5,8],[2,6],[4,7]]=>10
[[1,2,5,8],[3,6],[4,7]]=>10
[[1,3,4,8],[2,6],[5,7]]=>10
[[1,2,4,8],[3,6],[5,7]]=>10
[[1,2,3,8],[4,6],[5,7]]=>10
[[1,3,5,8],[2,4],[6,7]]=>10
[[1,2,5,8],[3,4],[6,7]]=>10
[[1,3,4,8],[2,5],[6,7]]=>10
[[1,2,4,8],[3,5],[6,7]]=>10
[[1,2,3,8],[4,5],[6,7]]=>10
[[1,4,6,7],[2,5],[3,8]]=>10
[[1,3,6,7],[2,5],[4,8]]=>10
[[1,2,6,7],[3,5],[4,8]]=>10
[[1,3,6,7],[2,4],[5,8]]=>10
[[1,2,6,7],[3,4],[5,8]]=>10
[[1,4,5,7],[2,6],[3,8]]=>10
[[1,3,5,7],[2,6],[4,8]]=>10
[[1,2,5,7],[3,6],[4,8]]=>10
[[1,3,4,7],[2,6],[5,8]]=>10
[[1,2,4,7],[3,6],[5,8]]=>10
[[1,2,3,7],[4,6],[5,8]]=>10
[[1,3,5,7],[2,4],[6,8]]=>10
[[1,2,5,7],[3,4],[6,8]]=>10
[[1,3,4,7],[2,5],[6,8]]=>10
[[1,2,4,7],[3,5],[6,8]]=>10
[[1,2,3,7],[4,5],[6,8]]=>10
[[1,4,5,6],[2,7],[3,8]]=>10
[[1,3,5,6],[2,7],[4,8]]=>10
[[1,2,5,6],[3,7],[4,8]]=>10
[[1,3,4,6],[2,7],[5,8]]=>10
[[1,2,4,6],[3,7],[5,8]]=>10
[[1,2,3,6],[4,7],[5,8]]=>10
[[1,3,4,5],[2,7],[6,8]]=>10
[[1,2,4,5],[3,7],[6,8]]=>10
[[1,2,3,5],[4,7],[6,8]]=>10
[[1,2,3,4],[5,7],[6,8]]=>10
[[1,3,5,6],[2,4],[7,8]]=>10
[[1,2,5,6],[3,4],[7,8]]=>10
[[1,3,4,6],[2,5],[7,8]]=>10
[[1,2,4,6],[3,5],[7,8]]=>10
[[1,2,3,6],[4,5],[7,8]]=>10
[[1,3,4,5],[2,6],[7,8]]=>10
[[1,2,4,5],[3,6],[7,8]]=>10
[[1,2,3,5],[4,6],[7,8]]=>10
[[1,2,3,4],[5,6],[7,8]]=>10
[[1,5,7,8],[2,6],[3],[4]]=>8
[[1,4,7,8],[2,6],[3],[5]]=>8
[[1,3,7,8],[2,6],[4],[5]]=>8
[[1,2,7,8],[3,6],[4],[5]]=>8
[[1,4,7,8],[2,5],[3],[6]]=>8
[[1,3,7,8],[2,5],[4],[6]]=>8
[[1,2,7,8],[3,5],[4],[6]]=>8
[[1,3,7,8],[2,4],[5],[6]]=>8
[[1,2,7,8],[3,4],[5],[6]]=>8
[[1,5,6,8],[2,7],[3],[4]]=>8
[[1,4,6,8],[2,7],[3],[5]]=>8
[[1,3,6,8],[2,7],[4],[5]]=>8
[[1,2,6,8],[3,7],[4],[5]]=>8
[[1,4,5,8],[2,7],[3],[6]]=>8
[[1,3,5,8],[2,7],[4],[6]]=>8
[[1,2,5,8],[3,7],[4],[6]]=>8
[[1,3,4,8],[2,7],[5],[6]]=>8
[[1,2,4,8],[3,7],[5],[6]]=>8
[[1,2,3,8],[4,7],[5],[6]]=>8
[[1,4,6,8],[2,5],[3],[7]]=>8
[[1,3,6,8],[2,5],[4],[7]]=>8
[[1,2,6,8],[3,5],[4],[7]]=>8
[[1,3,6,8],[2,4],[5],[7]]=>8
[[1,2,6,8],[3,4],[5],[7]]=>8
[[1,4,5,8],[2,6],[3],[7]]=>8
[[1,3,5,8],[2,6],[4],[7]]=>8
[[1,2,5,8],[3,6],[4],[7]]=>8
[[1,3,4,8],[2,6],[5],[7]]=>8
[[1,2,4,8],[3,6],[5],[7]]=>8
[[1,2,3,8],[4,6],[5],[7]]=>8
[[1,3,5,8],[2,4],[6],[7]]=>8
[[1,2,5,8],[3,4],[6],[7]]=>8
[[1,3,4,8],[2,5],[6],[7]]=>8
[[1,2,4,8],[3,5],[6],[7]]=>8
[[1,2,3,8],[4,5],[6],[7]]=>8
[[1,5,6,7],[2,8],[3],[4]]=>8
[[1,4,6,7],[2,8],[3],[5]]=>8
[[1,3,6,7],[2,8],[4],[5]]=>8
[[1,2,6,7],[3,8],[4],[5]]=>8
[[1,4,5,7],[2,8],[3],[6]]=>8
[[1,3,5,7],[2,8],[4],[6]]=>8
[[1,2,5,7],[3,8],[4],[6]]=>8
[[1,3,4,7],[2,8],[5],[6]]=>8
[[1,2,4,7],[3,8],[5],[6]]=>8
[[1,2,3,7],[4,8],[5],[6]]=>8
[[1,4,5,6],[2,8],[3],[7]]=>8
[[1,3,5,6],[2,8],[4],[7]]=>8
[[1,2,5,6],[3,8],[4],[7]]=>8
[[1,3,4,6],[2,8],[5],[7]]=>8
[[1,2,4,6],[3,8],[5],[7]]=>8
[[1,2,3,6],[4,8],[5],[7]]=>8
[[1,3,4,5],[2,8],[6],[7]]=>8
[[1,2,4,5],[3,8],[6],[7]]=>8
[[1,2,3,5],[4,8],[6],[7]]=>8
[[1,2,3,4],[5,8],[6],[7]]=>8
[[1,4,6,7],[2,5],[3],[8]]=>8
[[1,3,6,7],[2,5],[4],[8]]=>8
[[1,2,6,7],[3,5],[4],[8]]=>8
[[1,3,6,7],[2,4],[5],[8]]=>8
[[1,2,6,7],[3,4],[5],[8]]=>8
[[1,4,5,7],[2,6],[3],[8]]=>8
[[1,3,5,7],[2,6],[4],[8]]=>8
[[1,2,5,7],[3,6],[4],[8]]=>8
[[1,3,4,7],[2,6],[5],[8]]=>8
[[1,2,4,7],[3,6],[5],[8]]=>8
[[1,2,3,7],[4,6],[5],[8]]=>8
[[1,3,5,7],[2,4],[6],[8]]=>8
[[1,2,5,7],[3,4],[6],[8]]=>8
[[1,3,4,7],[2,5],[6],[8]]=>8
[[1,2,4,7],[3,5],[6],[8]]=>8
[[1,2,3,7],[4,5],[6],[8]]=>8
[[1,4,5,6],[2,7],[3],[8]]=>8
[[1,3,5,6],[2,7],[4],[8]]=>8
[[1,2,5,6],[3,7],[4],[8]]=>8
[[1,3,4,6],[2,7],[5],[8]]=>8
[[1,2,4,6],[3,7],[5],[8]]=>8
[[1,2,3,6],[4,7],[5],[8]]=>8
[[1,3,4,5],[2,7],[6],[8]]=>8
[[1,2,4,5],[3,7],[6],[8]]=>8
[[1,2,3,5],[4,7],[6],[8]]=>8
[[1,2,3,4],[5,7],[6],[8]]=>8
[[1,3,5,6],[2,4],[7],[8]]=>8
[[1,2,5,6],[3,4],[7],[8]]=>8
[[1,3,4,6],[2,5],[7],[8]]=>8
[[1,2,4,6],[3,5],[7],[8]]=>8
[[1,2,3,6],[4,5],[7],[8]]=>8
[[1,3,4,5],[2,6],[7],[8]]=>8
[[1,2,4,5],[3,6],[7],[8]]=>8
[[1,2,3,5],[4,6],[7],[8]]=>8
[[1,2,3,4],[5,6],[7],[8]]=>8
[[1,6,7,8],[2],[3],[4],[5]]=>6
[[1,5,7,8],[2],[3],[4],[6]]=>6
[[1,4,7,8],[2],[3],[5],[6]]=>6
[[1,3,7,8],[2],[4],[5],[6]]=>6
[[1,2,7,8],[3],[4],[5],[6]]=>6
[[1,5,6,8],[2],[3],[4],[7]]=>6
[[1,4,6,8],[2],[3],[5],[7]]=>6
[[1,3,6,8],[2],[4],[5],[7]]=>6
[[1,2,6,8],[3],[4],[5],[7]]=>6
[[1,4,5,8],[2],[3],[6],[7]]=>6
[[1,3,5,8],[2],[4],[6],[7]]=>6
[[1,2,5,8],[3],[4],[6],[7]]=>6
[[1,3,4,8],[2],[5],[6],[7]]=>6
[[1,2,4,8],[3],[5],[6],[7]]=>6
[[1,2,3,8],[4],[5],[6],[7]]=>6
[[1,5,6,7],[2],[3],[4],[8]]=>6
[[1,4,6,7],[2],[3],[5],[8]]=>6
[[1,3,6,7],[2],[4],[5],[8]]=>6
[[1,2,6,7],[3],[4],[5],[8]]=>6
[[1,4,5,7],[2],[3],[6],[8]]=>6
[[1,3,5,7],[2],[4],[6],[8]]=>6
[[1,2,5,7],[3],[4],[6],[8]]=>6
[[1,3,4,7],[2],[5],[6],[8]]=>6
[[1,2,4,7],[3],[5],[6],[8]]=>6
[[1,2,3,7],[4],[5],[6],[8]]=>6
[[1,4,5,6],[2],[3],[7],[8]]=>6
[[1,3,5,6],[2],[4],[7],[8]]=>6
[[1,2,5,6],[3],[4],[7],[8]]=>6
[[1,3,4,6],[2],[5],[7],[8]]=>6
[[1,2,4,6],[3],[5],[7],[8]]=>6
[[1,2,3,6],[4],[5],[7],[8]]=>6
[[1,3,4,5],[2],[6],[7],[8]]=>6
[[1,2,4,5],[3],[6],[7],[8]]=>6
[[1,2,3,5],[4],[6],[7],[8]]=>6
[[1,2,3,4],[5],[6],[7],[8]]=>6
[[1,4,7],[2,5,8],[3,6]]=>11
[[1,3,7],[2,5,8],[4,6]]=>11
[[1,2,7],[3,5,8],[4,6]]=>11
[[1,3,7],[2,4,8],[5,6]]=>11
[[1,2,7],[3,4,8],[5,6]]=>11
[[1,4,6],[2,5,8],[3,7]]=>11
[[1,3,6],[2,5,8],[4,7]]=>11
[[1,2,6],[3,5,8],[4,7]]=>11
[[1,3,6],[2,4,8],[5,7]]=>11
[[1,2,6],[3,4,8],[5,7]]=>11
[[1,4,5],[2,6,8],[3,7]]=>11
[[1,3,5],[2,6,8],[4,7]]=>11
[[1,2,5],[3,6,8],[4,7]]=>11
[[1,3,4],[2,6,8],[5,7]]=>11
[[1,2,4],[3,6,8],[5,7]]=>11
[[1,2,3],[4,6,8],[5,7]]=>11
[[1,3,5],[2,4,8],[6,7]]=>11
[[1,2,5],[3,4,8],[6,7]]=>11
[[1,3,4],[2,5,8],[6,7]]=>11
[[1,2,4],[3,5,8],[6,7]]=>11
[[1,2,3],[4,5,8],[6,7]]=>11
[[1,4,6],[2,5,7],[3,8]]=>11
[[1,3,6],[2,5,7],[4,8]]=>11
[[1,2,6],[3,5,7],[4,8]]=>11
[[1,3,6],[2,4,7],[5,8]]=>11
[[1,2,6],[3,4,7],[5,8]]=>11
[[1,4,5],[2,6,7],[3,8]]=>11
[[1,3,5],[2,6,7],[4,8]]=>11
[[1,2,5],[3,6,7],[4,8]]=>11
[[1,3,4],[2,6,7],[5,8]]=>11
[[1,2,4],[3,6,7],[5,8]]=>11
[[1,2,3],[4,6,7],[5,8]]=>11
[[1,3,5],[2,4,7],[6,8]]=>11
[[1,2,5],[3,4,7],[6,8]]=>11
[[1,3,4],[2,5,7],[6,8]]=>11
[[1,2,4],[3,5,7],[6,8]]=>11
[[1,2,3],[4,5,7],[6,8]]=>11
[[1,3,5],[2,4,6],[7,8]]=>11
[[1,2,5],[3,4,6],[7,8]]=>11
[[1,3,4],[2,5,6],[7,8]]=>11
[[1,2,4],[3,5,6],[7,8]]=>11
[[1,2,3],[4,5,6],[7,8]]=>11
[[1,5,7],[2,6,8],[3],[4]]=>9
[[1,4,7],[2,6,8],[3],[5]]=>9
[[1,3,7],[2,6,8],[4],[5]]=>9
[[1,2,7],[3,6,8],[4],[5]]=>9
[[1,4,7],[2,5,8],[3],[6]]=>9
[[1,3,7],[2,5,8],[4],[6]]=>9
[[1,2,7],[3,5,8],[4],[6]]=>9
[[1,3,7],[2,4,8],[5],[6]]=>9
[[1,2,7],[3,4,8],[5],[6]]=>9
[[1,5,6],[2,7,8],[3],[4]]=>9
[[1,4,6],[2,7,8],[3],[5]]=>9
[[1,3,6],[2,7,8],[4],[5]]=>9
[[1,2,6],[3,7,8],[4],[5]]=>9
[[1,4,5],[2,7,8],[3],[6]]=>9
[[1,3,5],[2,7,8],[4],[6]]=>9
[[1,2,5],[3,7,8],[4],[6]]=>9
[[1,3,4],[2,7,8],[5],[6]]=>9
[[1,2,4],[3,7,8],[5],[6]]=>9
[[1,2,3],[4,7,8],[5],[6]]=>9
[[1,4,6],[2,5,8],[3],[7]]=>9
[[1,3,6],[2,5,8],[4],[7]]=>9
[[1,2,6],[3,5,8],[4],[7]]=>9
[[1,3,6],[2,4,8],[5],[7]]=>9
[[1,2,6],[3,4,8],[5],[7]]=>9
[[1,4,5],[2,6,8],[3],[7]]=>9
[[1,3,5],[2,6,8],[4],[7]]=>9
[[1,2,5],[3,6,8],[4],[7]]=>9
[[1,3,4],[2,6,8],[5],[7]]=>9
[[1,2,4],[3,6,8],[5],[7]]=>9
[[1,2,3],[4,6,8],[5],[7]]=>9
[[1,3,5],[2,4,8],[6],[7]]=>9
[[1,2,5],[3,4,8],[6],[7]]=>9
[[1,3,4],[2,5,8],[6],[7]]=>9
[[1,2,4],[3,5,8],[6],[7]]=>9
[[1,2,3],[4,5,8],[6],[7]]=>9
[[1,4,6],[2,5,7],[3],[8]]=>9
[[1,3,6],[2,5,7],[4],[8]]=>9
[[1,2,6],[3,5,7],[4],[8]]=>9
[[1,3,6],[2,4,7],[5],[8]]=>9
[[1,2,6],[3,4,7],[5],[8]]=>9
[[1,4,5],[2,6,7],[3],[8]]=>9
[[1,3,5],[2,6,7],[4],[8]]=>9
[[1,2,5],[3,6,7],[4],[8]]=>9
[[1,3,4],[2,6,7],[5],[8]]=>9
[[1,2,4],[3,6,7],[5],[8]]=>9
[[1,2,3],[4,6,7],[5],[8]]=>9
[[1,3,5],[2,4,7],[6],[8]]=>9
[[1,2,5],[3,4,7],[6],[8]]=>9
[[1,3,4],[2,5,7],[6],[8]]=>9
[[1,2,4],[3,5,7],[6],[8]]=>9
[[1,2,3],[4,5,7],[6],[8]]=>9
[[1,3,5],[2,4,6],[7],[8]]=>9
[[1,2,5],[3,4,6],[7],[8]]=>9
[[1,3,4],[2,5,6],[7],[8]]=>9
[[1,2,4],[3,5,6],[7],[8]]=>9
[[1,2,3],[4,5,6],[7],[8]]=>9
[[1,5,8],[2,6],[3,7],[4]]=>7
[[1,4,8],[2,6],[3,7],[5]]=>7
[[1,3,8],[2,6],[4,7],[5]]=>7
[[1,2,8],[3,6],[4,7],[5]]=>7
[[1,4,8],[2,5],[3,7],[6]]=>7
[[1,3,8],[2,5],[4,7],[6]]=>7
[[1,2,8],[3,5],[4,7],[6]]=>7
[[1,3,8],[2,4],[5,7],[6]]=>7
[[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]]=>7
[[1,2,8],[3,5],[4,6],[7]]=>7
[[1,3,8],[2,4],[5,6],[7]]=>7
[[1,2,8],[3,4],[5,6],[7]]=>7
[[1,5,7],[2,6],[3,8],[4]]=>7
[[1,4,7],[2,6],[3,8],[5]]=>7
[[1,3,7],[2,6],[4,8],[5]]=>7
[[1,2,7],[3,6],[4,8],[5]]=>7
[[1,4,7],[2,5],[3,8],[6]]=>7
[[1,3,7],[2,5],[4,8],[6]]=>7
[[1,2,7],[3,5],[4,8],[6]]=>7
[[1,3,7],[2,4],[5,8],[6]]=>7
[[1,2,7],[3,4],[5,8],[6]]=>7
[[1,5,6],[2,7],[3,8],[4]]=>7
[[1,4,6],[2,7],[3,8],[5]]=>7
[[1,3,6],[2,7],[4,8],[5]]=>7
[[1,2,6],[3,7],[4,8],[5]]=>7
[[1,4,5],[2,7],[3,8],[6]]=>7
[[1,3,5],[2,7],[4,8],[6]]=>7
[[1,2,5],[3,7],[4,8],[6]]=>7
[[1,3,4],[2,7],[5,8],[6]]=>7
[[1,2,4],[3,7],[5,8],[6]]=>7
[[1,2,3],[4,7],[5,8],[6]]=>7
[[1,4,6],[2,5],[3,8],[7]]=>7
[[1,3,6],[2,5],[4,8],[7]]=>7
[[1,2,6],[3,5],[4,8],[7]]=>7
[[1,3,6],[2,4],[5,8],[7]]=>7
[[1,2,6],[3,4],[5,8],[7]]=>7
[[1,4,5],[2,6],[3,8],[7]]=>7
[[1,3,5],[2,6],[4,8],[7]]=>7
[[1,2,5],[3,6],[4,8],[7]]=>7
[[1,3,4],[2,6],[5,8],[7]]=>7
[[1,2,4],[3,6],[5,8],[7]]=>7
[[1,2,3],[4,6],[5,8],[7]]=>7
[[1,3,5],[2,4],[6,8],[7]]=>7
[[1,2,5],[3,4],[6,8],[7]]=>7
[[1,3,4],[2,5],[6,8],[7]]=>7
[[1,2,4],[3,5],[6,8],[7]]=>7
[[1,2,3],[4,5],[6,8],[7]]=>7
[[1,4,7],[2,5],[3,6],[8]]=>7
[[1,3,7],[2,5],[4,6],[8]]=>7
[[1,2,7],[3,5],[4,6],[8]]=>7
[[1,3,7],[2,4],[5,6],[8]]=>7
[[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]]=>7
[[1,2,6],[3,5],[4,7],[8]]=>7
[[1,3,6],[2,4],[5,7],[8]]=>7
[[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]]=>7
[[1,2,5],[3,6],[4,7],[8]]=>7
[[1,3,4],[2,6],[5,7],[8]]=>7
[[1,2,4],[3,6],[5,7],[8]]=>7
[[1,2,3],[4,6],[5,7],[8]]=>7
[[1,3,5],[2,4],[6,7],[8]]=>7
[[1,2,5],[3,4],[6,7],[8]]=>7
[[1,3,4],[2,5],[6,7],[8]]=>7
[[1,2,4],[3,5],[6,7],[8]]=>7
[[1,2,3],[4,5],[6,7],[8]]=>7
[[1,6,8],[2,7],[3],[4],[5]]=>5
[[1,5,8],[2,7],[3],[4],[6]]=>5
[[1,4,8],[2,7],[3],[5],[6]]=>5
[[1,3,8],[2,7],[4],[5],[6]]=>5
[[1,2,8],[3,7],[4],[5],[6]]=>5
[[1,5,8],[2,6],[3],[4],[7]]=>5
[[1,4,8],[2,6],[3],[5],[7]]=>5
[[1,3,8],[2,6],[4],[5],[7]]=>5
[[1,2,8],[3,6],[4],[5],[7]]=>5
[[1,4,8],[2,5],[3],[6],[7]]=>5
[[1,3,8],[2,5],[4],[6],[7]]=>5
[[1,2,8],[3,5],[4],[6],[7]]=>5
[[1,3,8],[2,4],[5],[6],[7]]=>5
[[1,2,8],[3,4],[5],[6],[7]]=>5
[[1,6,7],[2,8],[3],[4],[5]]=>5
[[1,5,7],[2,8],[3],[4],[6]]=>5
[[1,4,7],[2,8],[3],[5],[6]]=>5
[[1,3,7],[2,8],[4],[5],[6]]=>5
[[1,2,7],[3,8],[4],[5],[6]]=>5
[[1,5,6],[2,8],[3],[4],[7]]=>5
[[1,4,6],[2,8],[3],[5],[7]]=>5
[[1,3,6],[2,8],[4],[5],[7]]=>5
[[1,2,6],[3,8],[4],[5],[7]]=>5
[[1,4,5],[2,8],[3],[6],[7]]=>5
[[1,3,5],[2,8],[4],[6],[7]]=>5
[[1,2,5],[3,8],[4],[6],[7]]=>5
[[1,3,4],[2,8],[5],[6],[7]]=>5
[[1,2,4],[3,8],[5],[6],[7]]=>5
[[1,2,3],[4,8],[5],[6],[7]]=>5
[[1,5,7],[2,6],[3],[4],[8]]=>5
[[1,4,7],[2,6],[3],[5],[8]]=>5
[[1,3,7],[2,6],[4],[5],[8]]=>5
[[1,2,7],[3,6],[4],[5],[8]]=>5
[[1,4,7],[2,5],[3],[6],[8]]=>5
[[1,3,7],[2,5],[4],[6],[8]]=>5
[[1,2,7],[3,5],[4],[6],[8]]=>5
[[1,3,7],[2,4],[5],[6],[8]]=>5
[[1,2,7],[3,4],[5],[6],[8]]=>5
[[1,5,6],[2,7],[3],[4],[8]]=>5
[[1,4,6],[2,7],[3],[5],[8]]=>5
[[1,3,6],[2,7],[4],[5],[8]]=>5
[[1,2,6],[3,7],[4],[5],[8]]=>5
[[1,4,5],[2,7],[3],[6],[8]]=>5
[[1,3,5],[2,7],[4],[6],[8]]=>5
[[1,2,5],[3,7],[4],[6],[8]]=>5
[[1,3,4],[2,7],[5],[6],[8]]=>5
[[1,2,4],[3,7],[5],[6],[8]]=>5
[[1,2,3],[4,7],[5],[6],[8]]=>5
[[1,4,6],[2,5],[3],[7],[8]]=>5
[[1,3,6],[2,5],[4],[7],[8]]=>5
[[1,2,6],[3,5],[4],[7],[8]]=>5
[[1,3,6],[2,4],[5],[7],[8]]=>5
[[1,2,6],[3,4],[5],[7],[8]]=>5
[[1,4,5],[2,6],[3],[7],[8]]=>5
[[1,3,5],[2,6],[4],[7],[8]]=>5
[[1,2,5],[3,6],[4],[7],[8]]=>5
[[1,3,4],[2,6],[5],[7],[8]]=>5
[[1,2,4],[3,6],[5],[7],[8]]=>5
[[1,2,3],[4,6],[5],[7],[8]]=>5
[[1,3,5],[2,4],[6],[7],[8]]=>5
[[1,2,5],[3,4],[6],[7],[8]]=>5
[[1,3,4],[2,5],[6],[7],[8]]=>5
[[1,2,4],[3,5],[6],[7],[8]]=>5
[[1,2,3],[4,5],[6],[7],[8]]=>5
[[1,7,8],[2],[3],[4],[5],[6]]=>3
[[1,6,8],[2],[3],[4],[5],[7]]=>3
[[1,5,8],[2],[3],[4],[6],[7]]=>3
[[1,4,8],[2],[3],[5],[6],[7]]=>3
[[1,3,8],[2],[4],[5],[6],[7]]=>3
[[1,2,8],[3],[4],[5],[6],[7]]=>3
[[1,6,7],[2],[3],[4],[5],[8]]=>3
[[1,5,7],[2],[3],[4],[6],[8]]=>3
[[1,4,7],[2],[3],[5],[6],[8]]=>3
[[1,3,7],[2],[4],[5],[6],[8]]=>3
[[1,2,7],[3],[4],[5],[6],[8]]=>3
[[1,5,6],[2],[3],[4],[7],[8]]=>3
[[1,4,6],[2],[3],[5],[7],[8]]=>3
[[1,3,6],[2],[4],[5],[7],[8]]=>3
[[1,2,6],[3],[4],[5],[7],[8]]=>3
[[1,4,5],[2],[3],[6],[7],[8]]=>3
[[1,3,5],[2],[4],[6],[7],[8]]=>3
[[1,2,5],[3],[4],[6],[7],[8]]=>3
[[1,3,4],[2],[5],[6],[7],[8]]=>3
[[1,2,4],[3],[5],[6],[7],[8]]=>3
[[1,2,3],[4],[5],[6],[7],[8]]=>3
[[1,5],[2,6],[3,7],[4,8]]=>7
[[1,4],[2,6],[3,7],[5,8]]=>7
[[1,3],[2,6],[4,7],[5,8]]=>7
[[1,2],[3,6],[4,7],[5,8]]=>7
[[1,4],[2,5],[3,7],[6,8]]=>7
[[1,3],[2,5],[4,7],[6,8]]=>7
[[1,2],[3,5],[4,7],[6,8]]=>7
[[1,3],[2,4],[5,7],[6,8]]=>7
[[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]]=>7
[[1,2],[3,5],[4,6],[7,8]]=>7
[[1,3],[2,4],[5,6],[7,8]]=>7
[[1,2],[3,4],[5,6],[7,8]]=>7
[[1,6],[2,7],[3,8],[4],[5]]=>5
[[1,5],[2,7],[3,8],[4],[6]]=>5
[[1,4],[2,7],[3,8],[5],[6]]=>5
[[1,3],[2,7],[4,8],[5],[6]]=>5
[[1,2],[3,7],[4,8],[5],[6]]=>5
[[1,5],[2,6],[3,8],[4],[7]]=>5
[[1,4],[2,6],[3,8],[5],[7]]=>5
[[1,3],[2,6],[4,8],[5],[7]]=>5
[[1,2],[3,6],[4,8],[5],[7]]=>5
[[1,4],[2,5],[3,8],[6],[7]]=>5
[[1,3],[2,5],[4,8],[6],[7]]=>5
[[1,2],[3,5],[4,8],[6],[7]]=>5
[[1,3],[2,4],[5,8],[6],[7]]=>5
[[1,2],[3,4],[5,8],[6],[7]]=>5
[[1,5],[2,6],[3,7],[4],[8]]=>5
[[1,4],[2,6],[3,7],[5],[8]]=>5
[[1,3],[2,6],[4,7],[5],[8]]=>5
[[1,2],[3,6],[4,7],[5],[8]]=>5
[[1,4],[2,5],[3,7],[6],[8]]=>5
[[1,3],[2,5],[4,7],[6],[8]]=>5
[[1,2],[3,5],[4,7],[6],[8]]=>5
[[1,3],[2,4],[5,7],[6],[8]]=>5
[[1,2],[3,4],[5,7],[6],[8]]=>5
[[1,4],[2,5],[3,6],[7],[8]]=>5
[[1,3],[2,5],[4,6],[7],[8]]=>5
[[1,2],[3,5],[4,6],[7],[8]]=>5
[[1,3],[2,4],[5,6],[7],[8]]=>5
[[1,2],[3,4],[5,6],[7],[8]]=>5
[[1,7],[2,8],[3],[4],[5],[6]]=>3
[[1,6],[2,8],[3],[4],[5],[7]]=>3
[[1,5],[2,8],[3],[4],[6],[7]]=>3
[[1,4],[2,8],[3],[5],[6],[7]]=>3
[[1,3],[2,8],[4],[5],[6],[7]]=>3
[[1,2],[3,8],[4],[5],[6],[7]]=>3
[[1,6],[2,7],[3],[4],[5],[8]]=>3
[[1,5],[2,7],[3],[4],[6],[8]]=>3
[[1,4],[2,7],[3],[5],[6],[8]]=>3
[[1,3],[2,7],[4],[5],[6],[8]]=>3
[[1,2],[3,7],[4],[5],[6],[8]]=>3
[[1,5],[2,6],[3],[4],[7],[8]]=>3
[[1,4],[2,6],[3],[5],[7],[8]]=>3
[[1,3],[2,6],[4],[5],[7],[8]]=>3
[[1,2],[3,6],[4],[5],[7],[8]]=>3
[[1,4],[2,5],[3],[6],[7],[8]]=>3
[[1,3],[2,5],[4],[6],[7],[8]]=>3
[[1,2],[3,5],[4],[6],[7],[8]]=>3
[[1,3],[2,4],[5],[6],[7],[8]]=>3
[[1,2],[3,4],[5],[6],[7],[8]]=>3
[[1,8],[2],[3],[4],[5],[6],[7]]=>1
[[1,7],[2],[3],[4],[5],[6],[8]]=>1
[[1,6],[2],[3],[4],[5],[7],[8]]=>1
[[1,5],[2],[3],[4],[6],[7],[8]]=>1
[[1,4],[2],[3],[5],[6],[7],[8]]=>1
[[1,3],[2],[4],[5],[6],[7],[8]]=>1
[[1,2],[3],[4],[5],[6],[7],[8]]=>1
[[1],[2],[3],[4],[5],[6],[7],[8]]=>0
                    

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Description

The number of attacking pairs of a standard tableau.
Note that this is actually a statistic on the underlying partition.
A pair of cells $(c, d)$ of a Young diagram (in English notation) is said to be attacking if one of the following conditions holds:
1. $c$ and $d$ lie in the same row with $c$ strictly to the west of $d$.
2. $c$ is in the row immediately to the south of $d$, and $c$ lies strictly east of $d$.

Code

def statistic(x):
    return len(x.shape().attacking_pairs())

Created

Sep 27, 2011 at 20:00 by Chris Berg

Updated

Oct 16, 2015 at 11:08 by Christian Stump