Identifier
- St000507: Standard tableaux ⟶ ℤ
Values
=>
Cc0007;cc-rep
[]=>0
[[1]]=>1
[[1,2]]=>2
[[1],[2]]=>1
[[1,2,3]]=>3
[[1,3],[2]]=>2
[[1,2],[3]]=>2
[[1],[2],[3]]=>1
[[1,2,3,4]]=>4
[[1,3,4],[2]]=>3
[[1,2,4],[3]]=>3
[[1,2,3],[4]]=>3
[[1,3],[2,4]]=>2
[[1,2],[3,4]]=>3
[[1,4],[2],[3]]=>2
[[1,3],[2],[4]]=>2
[[1,2],[3],[4]]=>2
[[1],[2],[3],[4]]=>1
[[1,2,3,4,5]]=>5
[[1,3,4,5],[2]]=>4
[[1,2,4,5],[3]]=>4
[[1,2,3,5],[4]]=>4
[[1,2,3,4],[5]]=>4
[[1,3,5],[2,4]]=>3
[[1,2,5],[3,4]]=>4
[[1,3,4],[2,5]]=>3
[[1,2,4],[3,5]]=>3
[[1,2,3],[4,5]]=>4
[[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]]=>2
[[1,3],[2,5],[4]]=>3
[[1,2],[3,5],[4]]=>3
[[1,3],[2,4],[5]]=>2
[[1,2],[3,4],[5]]=>3
[[1,5],[2],[3],[4]]=>2
[[1,4],[2],[3],[5]]=>2
[[1,3],[2],[4],[5]]=>2
[[1,2],[3],[4],[5]]=>2
[[1],[2],[3],[4],[5]]=>1
[[1,2,3,4,5,6]]=>6
[[1,3,4,5,6],[2]]=>5
[[1,2,4,5,6],[3]]=>5
[[1,2,3,5,6],[4]]=>5
[[1,2,3,4,6],[5]]=>5
[[1,2,3,4,5],[6]]=>5
[[1,3,5,6],[2,4]]=>4
[[1,2,5,6],[3,4]]=>5
[[1,3,4,6],[2,5]]=>4
[[1,2,4,6],[3,5]]=>4
[[1,2,3,6],[4,5]]=>5
[[1,3,4,5],[2,6]]=>4
[[1,2,4,5],[3,6]]=>4
[[1,2,3,5],[4,6]]=>4
[[1,2,3,4],[5,6]]=>5
[[1,4,5,6],[2],[3]]=>4
[[1,3,5,6],[2],[4]]=>4
[[1,2,5,6],[3],[4]]=>4
[[1,3,4,6],[2],[5]]=>4
[[1,2,4,6],[3],[5]]=>4
[[1,2,3,6],[4],[5]]=>4
[[1,3,4,5],[2],[6]]=>4
[[1,2,4,5],[3],[6]]=>4
[[1,2,3,5],[4],[6]]=>4
[[1,2,3,4],[5],[6]]=>4
[[1,3,5],[2,4,6]]=>3
[[1,2,5],[3,4,6]]=>4
[[1,3,4],[2,5,6]]=>4
[[1,2,4],[3,5,6]]=>4
[[1,2,3],[4,5,6]]=>5
[[1,4,6],[2,5],[3]]=>3
[[1,3,6],[2,5],[4]]=>4
[[1,2,6],[3,5],[4]]=>4
[[1,3,6],[2,4],[5]]=>3
[[1,2,6],[3,4],[5]]=>4
[[1,4,5],[2,6],[3]]=>3
[[1,3,5],[2,6],[4]]=>3
[[1,2,5],[3,6],[4]]=>3
[[1,3,4],[2,6],[5]]=>4
[[1,2,4],[3,6],[5]]=>4
[[1,2,3],[4,6],[5]]=>4
[[1,3,5],[2,4],[6]]=>3
[[1,2,5],[3,4],[6]]=>4
[[1,3,4],[2,5],[6]]=>3
[[1,2,4],[3,5],[6]]=>3
[[1,2,3],[4,5],[6]]=>4
[[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]]=>2
[[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]]=>4
[[1,5],[2,6],[3],[4]]=>2
[[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]]=>2
[[1,3],[2,5],[4],[6]]=>3
[[1,2],[3,5],[4],[6]]=>3
[[1,3],[2,4],[5],[6]]=>2
[[1,2],[3,4],[5],[6]]=>3
[[1,6],[2],[3],[4],[5]]=>2
[[1,5],[2],[3],[4],[6]]=>2
[[1,4],[2],[3],[5],[6]]=>2
[[1,3],[2],[4],[5],[6]]=>2
[[1,2],[3],[4],[5],[6]]=>2
[[1],[2],[3],[4],[5],[6]]=>1
[[1,2,3,4,5,6,7]]=>7
[[1,3,4,5,6,7],[2]]=>6
[[1,2,4,5,6,7],[3]]=>6
[[1,2,3,5,6,7],[4]]=>6
[[1,2,3,4,6,7],[5]]=>6
[[1,2,3,4,5,7],[6]]=>6
[[1,2,3,4,5,6],[7]]=>6
[[1,3,5,6,7],[2,4]]=>5
[[1,2,5,6,7],[3,4]]=>6
[[1,3,4,6,7],[2,5]]=>5
[[1,2,4,6,7],[3,5]]=>5
[[1,2,3,6,7],[4,5]]=>6
[[1,3,4,5,7],[2,6]]=>5
[[1,2,4,5,7],[3,6]]=>5
[[1,2,3,5,7],[4,6]]=>5
[[1,2,3,4,7],[5,6]]=>6
[[1,3,4,5,6],[2,7]]=>5
[[1,2,4,5,6],[3,7]]=>5
[[1,2,3,5,6],[4,7]]=>5
[[1,2,3,4,6],[5,7]]=>5
[[1,2,3,4,5],[6,7]]=>6
[[1,4,5,6,7],[2],[3]]=>5
[[1,3,5,6,7],[2],[4]]=>5
[[1,2,5,6,7],[3],[4]]=>5
[[1,3,4,6,7],[2],[5]]=>5
[[1,2,4,6,7],[3],[5]]=>5
[[1,2,3,6,7],[4],[5]]=>5
[[1,3,4,5,7],[2],[6]]=>5
[[1,2,4,5,7],[3],[6]]=>5
[[1,2,3,5,7],[4],[6]]=>5
[[1,2,3,4,7],[5],[6]]=>5
[[1,3,4,5,6],[2],[7]]=>5
[[1,2,4,5,6],[3],[7]]=>5
[[1,2,3,5,6],[4],[7]]=>5
[[1,2,3,4,6],[5],[7]]=>5
[[1,2,3,4,5],[6],[7]]=>5
[[1,3,5,7],[2,4,6]]=>4
[[1,2,5,7],[3,4,6]]=>5
[[1,3,4,7],[2,5,6]]=>5
[[1,2,4,7],[3,5,6]]=>5
[[1,2,3,7],[4,5,6]]=>6
[[1,3,5,6],[2,4,7]]=>4
[[1,2,5,6],[3,4,7]]=>5
[[1,3,4,6],[2,5,7]]=>4
[[1,2,4,6],[3,5,7]]=>4
[[1,2,3,6],[4,5,7]]=>5
[[1,3,4,5],[2,6,7]]=>5
[[1,2,4,5],[3,6,7]]=>5
[[1,2,3,5],[4,6,7]]=>5
[[1,2,3,4],[5,6,7]]=>6
[[1,4,6,7],[2,5],[3]]=>4
[[1,3,6,7],[2,5],[4]]=>5
[[1,2,6,7],[3,5],[4]]=>5
[[1,3,6,7],[2,4],[5]]=>4
[[1,2,6,7],[3,4],[5]]=>5
[[1,4,5,7],[2,6],[3]]=>4
[[1,3,5,7],[2,6],[4]]=>4
[[1,2,5,7],[3,6],[4]]=>4
[[1,3,4,7],[2,6],[5]]=>5
[[1,2,4,7],[3,6],[5]]=>5
[[1,2,3,7],[4,6],[5]]=>5
[[1,3,5,7],[2,4],[6]]=>4
[[1,2,5,7],[3,4],[6]]=>5
[[1,3,4,7],[2,5],[6]]=>4
[[1,2,4,7],[3,5],[6]]=>4
[[1,2,3,7],[4,5],[6]]=>5
[[1,4,5,6],[2,7],[3]]=>4
[[1,3,5,6],[2,7],[4]]=>4
[[1,2,5,6],[3,7],[4]]=>4
[[1,3,4,6],[2,7],[5]]=>4
[[1,2,4,6],[3,7],[5]]=>4
[[1,2,3,6],[4,7],[5]]=>4
[[1,3,4,5],[2,7],[6]]=>5
[[1,2,4,5],[3,7],[6]]=>5
[[1,2,3,5],[4,7],[6]]=>5
[[1,2,3,4],[5,7],[6]]=>5
[[1,3,5,6],[2,4],[7]]=>4
[[1,2,5,6],[3,4],[7]]=>5
[[1,3,4,6],[2,5],[7]]=>4
[[1,2,4,6],[3,5],[7]]=>4
[[1,2,3,6],[4,5],[7]]=>5
[[1,3,4,5],[2,6],[7]]=>4
[[1,2,4,5],[3,6],[7]]=>4
[[1,2,3,5],[4,6],[7]]=>4
[[1,2,3,4],[5,6],[7]]=>5
[[1,5,6,7],[2],[3],[4]]=>4
[[1,4,6,7],[2],[3],[5]]=>4
[[1,3,6,7],[2],[4],[5]]=>4
[[1,2,6,7],[3],[4],[5]]=>4
[[1,4,5,7],[2],[3],[6]]=>4
[[1,3,5,7],[2],[4],[6]]=>4
[[1,2,5,7],[3],[4],[6]]=>4
[[1,3,4,7],[2],[5],[6]]=>4
[[1,2,4,7],[3],[5],[6]]=>4
[[1,2,3,7],[4],[5],[6]]=>4
[[1,4,5,6],[2],[3],[7]]=>4
[[1,3,5,6],[2],[4],[7]]=>4
[[1,2,5,6],[3],[4],[7]]=>4
[[1,3,4,6],[2],[5],[7]]=>4
[[1,2,4,6],[3],[5],[7]]=>4
[[1,2,3,6],[4],[5],[7]]=>4
[[1,3,4,5],[2],[6],[7]]=>4
[[1,2,4,5],[3],[6],[7]]=>4
[[1,2,3,5],[4],[6],[7]]=>4
[[1,2,3,4],[5],[6],[7]]=>4
[[1,4,6],[2,5,7],[3]]=>3
[[1,3,6],[2,5,7],[4]]=>4
[[1,2,6],[3,5,7],[4]]=>4
[[1,3,6],[2,4,7],[5]]=>3
[[1,2,6],[3,4,7],[5]]=>4
[[1,4,5],[2,6,7],[3]]=>4
[[1,3,5],[2,6,7],[4]]=>4
[[1,2,5],[3,6,7],[4]]=>4
[[1,3,4],[2,6,7],[5]]=>5
[[1,2,4],[3,6,7],[5]]=>5
[[1,2,3],[4,6,7],[5]]=>5
[[1,3,5],[2,4,7],[6]]=>4
[[1,2,5],[3,4,7],[6]]=>5
[[1,3,4],[2,5,7],[6]]=>4
[[1,2,4],[3,5,7],[6]]=>4
[[1,2,3],[4,5,7],[6]]=>5
[[1,3,5],[2,4,6],[7]]=>3
[[1,2,5],[3,4,6],[7]]=>4
[[1,3,4],[2,5,6],[7]]=>4
[[1,2,4],[3,5,6],[7]]=>4
[[1,2,3],[4,5,6],[7]]=>5
[[1,4,7],[2,5],[3,6]]=>3
[[1,3,7],[2,5],[4,6]]=>4
[[1,2,7],[3,5],[4,6]]=>4
[[1,3,7],[2,4],[5,6]]=>4
[[1,2,7],[3,4],[5,6]]=>5
[[1,4,6],[2,5],[3,7]]=>3
[[1,3,6],[2,5],[4,7]]=>4
[[1,2,6],[3,5],[4,7]]=>4
[[1,3,6],[2,4],[5,7]]=>3
[[1,2,6],[3,4],[5,7]]=>4
[[1,4,5],[2,6],[3,7]]=>3
[[1,3,5],[2,6],[4,7]]=>3
[[1,2,5],[3,6],[4,7]]=>3
[[1,3,4],[2,6],[5,7]]=>4
[[1,2,4],[3,6],[5,7]]=>4
[[1,2,3],[4,6],[5,7]]=>4
[[1,3,5],[2,4],[6,7]]=>4
[[1,2,5],[3,4],[6,7]]=>5
[[1,3,4],[2,5],[6,7]]=>4
[[1,2,4],[3,5],[6,7]]=>4
[[1,2,3],[4,5],[6,7]]=>5
[[1,5,7],[2,6],[3],[4]]=>3
[[1,4,7],[2,6],[3],[5]]=>4
[[1,3,7],[2,6],[4],[5]]=>4
[[1,2,7],[3,6],[4],[5]]=>4
[[1,4,7],[2,5],[3],[6]]=>3
[[1,3,7],[2,5],[4],[6]]=>4
[[1,2,7],[3,5],[4],[6]]=>4
[[1,3,7],[2,4],[5],[6]]=>3
[[1,2,7],[3,4],[5],[6]]=>4
[[1,5,6],[2,7],[3],[4]]=>3
[[1,4,6],[2,7],[3],[5]]=>3
[[1,3,6],[2,7],[4],[5]]=>3
[[1,2,6],[3,7],[4],[5]]=>3
[[1,4,5],[2,7],[3],[6]]=>4
[[1,3,5],[2,7],[4],[6]]=>4
[[1,2,5],[3,7],[4],[6]]=>4
[[1,3,4],[2,7],[5],[6]]=>4
[[1,2,4],[3,7],[5],[6]]=>4
[[1,2,3],[4,7],[5],[6]]=>4
[[1,4,6],[2,5],[3],[7]]=>3
[[1,3,6],[2,5],[4],[7]]=>4
[[1,2,6],[3,5],[4],[7]]=>4
[[1,3,6],[2,4],[5],[7]]=>3
[[1,2,6],[3,4],[5],[7]]=>4
[[1,4,5],[2,6],[3],[7]]=>3
[[1,3,5],[2,6],[4],[7]]=>3
[[1,2,5],[3,6],[4],[7]]=>3
[[1,3,4],[2,6],[5],[7]]=>4
[[1,2,4],[3,6],[5],[7]]=>4
[[1,2,3],[4,6],[5],[7]]=>4
[[1,3,5],[2,4],[6],[7]]=>3
[[1,2,5],[3,4],[6],[7]]=>4
[[1,3,4],[2,5],[6],[7]]=>3
[[1,2,4],[3,5],[6],[7]]=>3
[[1,2,3],[4,5],[6],[7]]=>4
[[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]]=>2
[[1,4],[2,6],[3,7],[5]]=>3
[[1,3],[2,6],[4,7],[5]]=>3
[[1,2],[3,6],[4,7],[5]]=>3
[[1,4],[2,5],[3,7],[6]]=>3
[[1,3],[2,5],[4,7],[6]]=>4
[[1,2],[3,5],[4,7],[6]]=>4
[[1,3],[2,4],[5,7],[6]]=>3
[[1,2],[3,4],[5,7],[6]]=>4
[[1,4],[2,5],[3,6],[7]]=>2
[[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]]=>4
[[1,6],[2,7],[3],[4],[5]]=>2
[[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]]=>2
[[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]]=>2
[[1,3],[2,5],[4],[6],[7]]=>3
[[1,2],[3,5],[4],[6],[7]]=>3
[[1,3],[2,4],[5],[6],[7]]=>2
[[1,2],[3,4],[5],[6],[7]]=>3
[[1,7],[2],[3],[4],[5],[6]]=>2
[[1,6],[2],[3],[4],[5],[7]]=>2
[[1,5],[2],[3],[4],[6],[7]]=>2
[[1,4],[2],[3],[5],[6],[7]]=>2
[[1,3],[2],[4],[5],[6],[7]]=>2
[[1,2],[3],[4],[5],[6],[7]]=>2
[[1],[2],[3],[4],[5],[6],[7]]=>1
[[1,2,3,4,5,6,7,8]]=>8
[[1,3,4,5,6,7,8],[2]]=>7
[[1,2,4,5,6,7,8],[3]]=>7
[[1,2,3,5,6,7,8],[4]]=>7
[[1,2,3,4,6,7,8],[5]]=>7
[[1,2,3,4,5,7,8],[6]]=>7
[[1,2,3,4,5,6,8],[7]]=>7
[[1,2,3,4,5,6,7],[8]]=>7
[[1,3,5,6,7,8],[2,4]]=>6
[[1,2,5,6,7,8],[3,4]]=>7
[[1,3,4,6,7,8],[2,5]]=>6
[[1,2,4,6,7,8],[3,5]]=>6
[[1,2,3,6,7,8],[4,5]]=>7
[[1,3,4,5,7,8],[2,6]]=>6
[[1,2,4,5,7,8],[3,6]]=>6
[[1,2,3,5,7,8],[4,6]]=>6
[[1,2,3,4,7,8],[5,6]]=>7
[[1,3,4,5,6,8],[2,7]]=>6
[[1,2,4,5,6,8],[3,7]]=>6
[[1,2,3,5,6,8],[4,7]]=>6
[[1,2,3,4,6,8],[5,7]]=>6
[[1,2,3,4,5,8],[6,7]]=>7
[[1,3,4,5,6,7],[2,8]]=>6
[[1,2,4,5,6,7],[3,8]]=>6
[[1,2,3,5,6,7],[4,8]]=>6
[[1,2,3,4,6,7],[5,8]]=>6
[[1,2,3,4,5,7],[6,8]]=>6
[[1,2,3,4,5,6],[7,8]]=>7
[[1,4,5,6,7,8],[2],[3]]=>6
[[1,3,5,6,7,8],[2],[4]]=>6
[[1,2,5,6,7,8],[3],[4]]=>6
[[1,3,4,6,7,8],[2],[5]]=>6
[[1,2,4,6,7,8],[3],[5]]=>6
[[1,2,3,6,7,8],[4],[5]]=>6
[[1,3,4,5,7,8],[2],[6]]=>6
[[1,2,4,5,7,8],[3],[6]]=>6
[[1,2,3,5,7,8],[4],[6]]=>6
[[1,2,3,4,7,8],[5],[6]]=>6
[[1,3,4,5,6,8],[2],[7]]=>6
[[1,2,4,5,6,8],[3],[7]]=>6
[[1,2,3,5,6,8],[4],[7]]=>6
[[1,2,3,4,6,8],[5],[7]]=>6
[[1,2,3,4,5,8],[6],[7]]=>6
[[1,3,4,5,6,7],[2],[8]]=>6
[[1,2,4,5,6,7],[3],[8]]=>6
[[1,2,3,5,6,7],[4],[8]]=>6
[[1,2,3,4,6,7],[5],[8]]=>6
[[1,2,3,4,5,7],[6],[8]]=>6
[[1,2,3,4,5,6],[7],[8]]=>6
[[1,3,5,7,8],[2,4,6]]=>5
[[1,2,5,7,8],[3,4,6]]=>6
[[1,3,4,7,8],[2,5,6]]=>6
[[1,2,4,7,8],[3,5,6]]=>6
[[1,2,3,7,8],[4,5,6]]=>7
[[1,3,5,6,8],[2,4,7]]=>5
[[1,2,5,6,8],[3,4,7]]=>6
[[1,3,4,6,8],[2,5,7]]=>5
[[1,2,4,6,8],[3,5,7]]=>5
[[1,2,3,6,8],[4,5,7]]=>6
[[1,3,4,5,8],[2,6,7]]=>6
[[1,2,4,5,8],[3,6,7]]=>6
[[1,2,3,5,8],[4,6,7]]=>6
[[1,2,3,4,8],[5,6,7]]=>7
[[1,3,5,6,7],[2,4,8]]=>5
[[1,2,5,6,7],[3,4,8]]=>6
[[1,3,4,6,7],[2,5,8]]=>5
[[1,2,4,6,7],[3,5,8]]=>5
[[1,2,3,6,7],[4,5,8]]=>6
[[1,3,4,5,7],[2,6,8]]=>5
[[1,2,4,5,7],[3,6,8]]=>5
[[1,2,3,5,7],[4,6,8]]=>5
[[1,2,3,4,7],[5,6,8]]=>6
[[1,3,4,5,6],[2,7,8]]=>6
[[1,2,4,5,6],[3,7,8]]=>6
[[1,2,3,5,6],[4,7,8]]=>6
[[1,2,3,4,6],[5,7,8]]=>6
[[1,2,3,4,5],[6,7,8]]=>7
[[1,4,6,7,8],[2,5],[3]]=>5
[[1,3,6,7,8],[2,5],[4]]=>6
[[1,2,6,7,8],[3,5],[4]]=>6
[[1,3,6,7,8],[2,4],[5]]=>5
[[1,2,6,7,8],[3,4],[5]]=>6
[[1,4,5,7,8],[2,6],[3]]=>5
[[1,3,5,7,8],[2,6],[4]]=>5
[[1,2,5,7,8],[3,6],[4]]=>5
[[1,3,4,7,8],[2,6],[5]]=>6
[[1,2,4,7,8],[3,6],[5]]=>6
[[1,2,3,7,8],[4,6],[5]]=>6
[[1,3,5,7,8],[2,4],[6]]=>5
[[1,2,5,7,8],[3,4],[6]]=>6
[[1,3,4,7,8],[2,5],[6]]=>5
[[1,2,4,7,8],[3,5],[6]]=>5
[[1,2,3,7,8],[4,5],[6]]=>6
[[1,4,5,6,8],[2,7],[3]]=>5
[[1,3,5,6,8],[2,7],[4]]=>5
[[1,2,5,6,8],[3,7],[4]]=>5
[[1,3,4,6,8],[2,7],[5]]=>5
[[1,2,4,6,8],[3,7],[5]]=>5
[[1,2,3,6,8],[4,7],[5]]=>5
[[1,3,4,5,8],[2,7],[6]]=>6
[[1,2,4,5,8],[3,7],[6]]=>6
[[1,2,3,5,8],[4,7],[6]]=>6
[[1,2,3,4,8],[5,7],[6]]=>6
[[1,3,5,6,8],[2,4],[7]]=>5
[[1,2,5,6,8],[3,4],[7]]=>6
[[1,3,4,6,8],[2,5],[7]]=>5
[[1,2,4,6,8],[3,5],[7]]=>5
[[1,2,3,6,8],[4,5],[7]]=>6
[[1,3,4,5,8],[2,6],[7]]=>5
[[1,2,4,5,8],[3,6],[7]]=>5
[[1,2,3,5,8],[4,6],[7]]=>5
[[1,2,3,4,8],[5,6],[7]]=>6
[[1,4,5,6,7],[2,8],[3]]=>5
[[1,3,5,6,7],[2,8],[4]]=>5
[[1,2,5,6,7],[3,8],[4]]=>5
[[1,3,4,6,7],[2,8],[5]]=>5
[[1,2,4,6,7],[3,8],[5]]=>5
[[1,2,3,6,7],[4,8],[5]]=>5
[[1,3,4,5,7],[2,8],[6]]=>5
[[1,2,4,5,7],[3,8],[6]]=>5
[[1,2,3,5,7],[4,8],[6]]=>5
[[1,2,3,4,7],[5,8],[6]]=>5
[[1,3,4,5,6],[2,8],[7]]=>6
[[1,2,4,5,6],[3,8],[7]]=>6
[[1,2,3,5,6],[4,8],[7]]=>6
[[1,2,3,4,6],[5,8],[7]]=>6
[[1,2,3,4,5],[6,8],[7]]=>6
[[1,3,5,6,7],[2,4],[8]]=>5
[[1,2,5,6,7],[3,4],[8]]=>6
[[1,3,4,6,7],[2,5],[8]]=>5
[[1,2,4,6,7],[3,5],[8]]=>5
[[1,2,3,6,7],[4,5],[8]]=>6
[[1,3,4,5,7],[2,6],[8]]=>5
[[1,2,4,5,7],[3,6],[8]]=>5
[[1,2,3,5,7],[4,6],[8]]=>5
[[1,2,3,4,7],[5,6],[8]]=>6
[[1,3,4,5,6],[2,7],[8]]=>5
[[1,2,4,5,6],[3,7],[8]]=>5
[[1,2,3,5,6],[4,7],[8]]=>5
[[1,2,3,4,6],[5,7],[8]]=>5
[[1,2,3,4,5],[6,7],[8]]=>6
[[1,5,6,7,8],[2],[3],[4]]=>5
[[1,4,6,7,8],[2],[3],[5]]=>5
[[1,3,6,7,8],[2],[4],[5]]=>5
[[1,2,6,7,8],[3],[4],[5]]=>5
[[1,4,5,7,8],[2],[3],[6]]=>5
[[1,3,5,7,8],[2],[4],[6]]=>5
[[1,2,5,7,8],[3],[4],[6]]=>5
[[1,3,4,7,8],[2],[5],[6]]=>5
[[1,2,4,7,8],[3],[5],[6]]=>5
[[1,2,3,7,8],[4],[5],[6]]=>5
[[1,4,5,6,8],[2],[3],[7]]=>5
[[1,3,5,6,8],[2],[4],[7]]=>5
[[1,2,5,6,8],[3],[4],[7]]=>5
[[1,3,4,6,8],[2],[5],[7]]=>5
[[1,2,4,6,8],[3],[5],[7]]=>5
[[1,2,3,6,8],[4],[5],[7]]=>5
[[1,3,4,5,8],[2],[6],[7]]=>5
[[1,2,4,5,8],[3],[6],[7]]=>5
[[1,2,3,5,8],[4],[6],[7]]=>5
[[1,2,3,4,8],[5],[6],[7]]=>5
[[1,4,5,6,7],[2],[3],[8]]=>5
[[1,3,5,6,7],[2],[4],[8]]=>5
[[1,2,5,6,7],[3],[4],[8]]=>5
[[1,3,4,6,7],[2],[5],[8]]=>5
[[1,2,4,6,7],[3],[5],[8]]=>5
[[1,2,3,6,7],[4],[5],[8]]=>5
[[1,3,4,5,7],[2],[6],[8]]=>5
[[1,2,4,5,7],[3],[6],[8]]=>5
[[1,2,3,5,7],[4],[6],[8]]=>5
[[1,2,3,4,7],[5],[6],[8]]=>5
[[1,3,4,5,6],[2],[7],[8]]=>5
[[1,2,4,5,6],[3],[7],[8]]=>5
[[1,2,3,5,6],[4],[7],[8]]=>5
[[1,2,3,4,6],[5],[7],[8]]=>5
[[1,2,3,4,5],[6],[7],[8]]=>5
[[1,3,5,7],[2,4,6,8]]=>4
[[1,2,5,7],[3,4,6,8]]=>5
[[1,3,4,7],[2,5,6,8]]=>5
[[1,2,4,7],[3,5,6,8]]=>5
[[1,2,3,7],[4,5,6,8]]=>6
[[1,3,5,6],[2,4,7,8]]=>5
[[1,2,5,6],[3,4,7,8]]=>6
[[1,3,4,6],[2,5,7,8]]=>5
[[1,2,4,6],[3,5,7,8]]=>5
[[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]]=>7
[[1,4,6,8],[2,5,7],[3]]=>4
[[1,3,6,8],[2,5,7],[4]]=>5
[[1,2,6,8],[3,5,7],[4]]=>5
[[1,3,6,8],[2,4,7],[5]]=>4
[[1,2,6,8],[3,4,7],[5]]=>5
[[1,4,5,8],[2,6,7],[3]]=>5
[[1,3,5,8],[2,6,7],[4]]=>5
[[1,2,5,8],[3,6,7],[4]]=>5
[[1,3,4,8],[2,6,7],[5]]=>6
[[1,2,4,8],[3,6,7],[5]]=>6
[[1,2,3,8],[4,6,7],[5]]=>6
[[1,3,5,8],[2,4,7],[6]]=>5
[[1,2,5,8],[3,4,7],[6]]=>6
[[1,3,4,8],[2,5,7],[6]]=>5
[[1,2,4,8],[3,5,7],[6]]=>5
[[1,2,3,8],[4,5,7],[6]]=>6
[[1,3,5,8],[2,4,6],[7]]=>4
[[1,2,5,8],[3,4,6],[7]]=>5
[[1,3,4,8],[2,5,6],[7]]=>5
[[1,2,4,8],[3,5,6],[7]]=>5
[[1,2,3,8],[4,5,6],[7]]=>6
[[1,4,6,7],[2,5,8],[3]]=>4
[[1,3,6,7],[2,5,8],[4]]=>5
[[1,2,6,7],[3,5,8],[4]]=>5
[[1,3,6,7],[2,4,8],[5]]=>4
[[1,2,6,7],[3,4,8],[5]]=>5
[[1,4,5,7],[2,6,8],[3]]=>4
[[1,3,5,7],[2,6,8],[4]]=>4
[[1,2,5,7],[3,6,8],[4]]=>4
[[1,3,4,7],[2,6,8],[5]]=>5
[[1,2,4,7],[3,6,8],[5]]=>5
[[1,2,3,7],[4,6,8],[5]]=>5
[[1,3,5,7],[2,4,8],[6]]=>4
[[1,2,5,7],[3,4,8],[6]]=>5
[[1,3,4,7],[2,5,8],[6]]=>4
[[1,2,4,7],[3,5,8],[6]]=>4
[[1,2,3,7],[4,5,8],[6]]=>5
[[1,4,5,6],[2,7,8],[3]]=>5
[[1,3,5,6],[2,7,8],[4]]=>5
[[1,2,5,6],[3,7,8],[4]]=>5
[[1,3,4,6],[2,7,8],[5]]=>5
[[1,2,4,6],[3,7,8],[5]]=>5
[[1,2,3,6],[4,7,8],[5]]=>5
[[1,3,4,5],[2,7,8],[6]]=>6
[[1,2,4,5],[3,7,8],[6]]=>6
[[1,2,3,5],[4,7,8],[6]]=>6
[[1,2,3,4],[5,7,8],[6]]=>6
[[1,3,5,6],[2,4,8],[7]]=>5
[[1,2,5,6],[3,4,8],[7]]=>6
[[1,3,4,6],[2,5,8],[7]]=>5
[[1,2,4,6],[3,5,8],[7]]=>5
[[1,2,3,6],[4,5,8],[7]]=>6
[[1,3,4,5],[2,6,8],[7]]=>5
[[1,2,4,5],[3,6,8],[7]]=>5
[[1,2,3,5],[4,6,8],[7]]=>5
[[1,2,3,4],[5,6,8],[7]]=>6
[[1,3,5,7],[2,4,6],[8]]=>4
[[1,2,5,7],[3,4,6],[8]]=>5
[[1,3,4,7],[2,5,6],[8]]=>5
[[1,2,4,7],[3,5,6],[8]]=>5
[[1,2,3,7],[4,5,6],[8]]=>6
[[1,3,5,6],[2,4,7],[8]]=>4
[[1,2,5,6],[3,4,7],[8]]=>5
[[1,3,4,6],[2,5,7],[8]]=>4
[[1,2,4,6],[3,5,7],[8]]=>4
[[1,2,3,6],[4,5,7],[8]]=>5
[[1,3,4,5],[2,6,7],[8]]=>5
[[1,2,4,5],[3,6,7],[8]]=>5
[[1,2,3,5],[4,6,7],[8]]=>5
[[1,2,3,4],[5,6,7],[8]]=>6
[[1,4,7,8],[2,5],[3,6]]=>4
[[1,3,7,8],[2,5],[4,6]]=>5
[[1,2,7,8],[3,5],[4,6]]=>5
[[1,3,7,8],[2,4],[5,6]]=>5
[[1,2,7,8],[3,4],[5,6]]=>6
[[1,4,6,8],[2,5],[3,7]]=>4
[[1,3,6,8],[2,5],[4,7]]=>5
[[1,2,6,8],[3,5],[4,7]]=>5
[[1,3,6,8],[2,4],[5,7]]=>4
[[1,2,6,8],[3,4],[5,7]]=>5
[[1,4,5,8],[2,6],[3,7]]=>4
[[1,3,5,8],[2,6],[4,7]]=>4
[[1,2,5,8],[3,6],[4,7]]=>4
[[1,3,4,8],[2,6],[5,7]]=>5
[[1,2,4,8],[3,6],[5,7]]=>5
[[1,2,3,8],[4,6],[5,7]]=>5
[[1,3,5,8],[2,4],[6,7]]=>5
[[1,2,5,8],[3,4],[6,7]]=>6
[[1,3,4,8],[2,5],[6,7]]=>5
[[1,2,4,8],[3,5],[6,7]]=>5
[[1,2,3,8],[4,5],[6,7]]=>6
[[1,4,6,7],[2,5],[3,8]]=>4
[[1,3,6,7],[2,5],[4,8]]=>5
[[1,2,6,7],[3,5],[4,8]]=>5
[[1,3,6,7],[2,4],[5,8]]=>4
[[1,2,6,7],[3,4],[5,8]]=>5
[[1,4,5,7],[2,6],[3,8]]=>4
[[1,3,5,7],[2,6],[4,8]]=>4
[[1,2,5,7],[3,6],[4,8]]=>4
[[1,3,4,7],[2,6],[5,8]]=>5
[[1,2,4,7],[3,6],[5,8]]=>5
[[1,2,3,7],[4,6],[5,8]]=>5
[[1,3,5,7],[2,4],[6,8]]=>4
[[1,2,5,7],[3,4],[6,8]]=>5
[[1,3,4,7],[2,5],[6,8]]=>4
[[1,2,4,7],[3,5],[6,8]]=>4
[[1,2,3,7],[4,5],[6,8]]=>5
[[1,4,5,6],[2,7],[3,8]]=>4
[[1,3,5,6],[2,7],[4,8]]=>4
[[1,2,5,6],[3,7],[4,8]]=>4
[[1,3,4,6],[2,7],[5,8]]=>4
[[1,2,4,6],[3,7],[5,8]]=>4
[[1,2,3,6],[4,7],[5,8]]=>4
[[1,3,4,5],[2,7],[6,8]]=>5
[[1,2,4,5],[3,7],[6,8]]=>5
[[1,2,3,5],[4,7],[6,8]]=>5
[[1,2,3,4],[5,7],[6,8]]=>5
[[1,3,5,6],[2,4],[7,8]]=>5
[[1,2,5,6],[3,4],[7,8]]=>6
[[1,3,4,6],[2,5],[7,8]]=>5
[[1,2,4,6],[3,5],[7,8]]=>5
[[1,2,3,6],[4,5],[7,8]]=>6
[[1,3,4,5],[2,6],[7,8]]=>5
[[1,2,4,5],[3,6],[7,8]]=>5
[[1,2,3,5],[4,6],[7,8]]=>5
[[1,2,3,4],[5,6],[7,8]]=>6
[[1,5,7,8],[2,6],[3],[4]]=>4
[[1,4,7,8],[2,6],[3],[5]]=>5
[[1,3,7,8],[2,6],[4],[5]]=>5
[[1,2,7,8],[3,6],[4],[5]]=>5
[[1,4,7,8],[2,5],[3],[6]]=>4
[[1,3,7,8],[2,5],[4],[6]]=>5
[[1,2,7,8],[3,5],[4],[6]]=>5
[[1,3,7,8],[2,4],[5],[6]]=>4
[[1,2,7,8],[3,4],[5],[6]]=>5
[[1,5,6,8],[2,7],[3],[4]]=>4
[[1,4,6,8],[2,7],[3],[5]]=>4
[[1,3,6,8],[2,7],[4],[5]]=>4
[[1,2,6,8],[3,7],[4],[5]]=>4
[[1,4,5,8],[2,7],[3],[6]]=>5
[[1,3,5,8],[2,7],[4],[6]]=>5
[[1,2,5,8],[3,7],[4],[6]]=>5
[[1,3,4,8],[2,7],[5],[6]]=>5
[[1,2,4,8],[3,7],[5],[6]]=>5
[[1,2,3,8],[4,7],[5],[6]]=>5
[[1,4,6,8],[2,5],[3],[7]]=>4
[[1,3,6,8],[2,5],[4],[7]]=>5
[[1,2,6,8],[3,5],[4],[7]]=>5
[[1,3,6,8],[2,4],[5],[7]]=>4
[[1,2,6,8],[3,4],[5],[7]]=>5
[[1,4,5,8],[2,6],[3],[7]]=>4
[[1,3,5,8],[2,6],[4],[7]]=>4
[[1,2,5,8],[3,6],[4],[7]]=>4
[[1,3,4,8],[2,6],[5],[7]]=>5
[[1,2,4,8],[3,6],[5],[7]]=>5
[[1,2,3,8],[4,6],[5],[7]]=>5
[[1,3,5,8],[2,4],[6],[7]]=>4
[[1,2,5,8],[3,4],[6],[7]]=>5
[[1,3,4,8],[2,5],[6],[7]]=>4
[[1,2,4,8],[3,5],[6],[7]]=>4
[[1,2,3,8],[4,5],[6],[7]]=>5
[[1,5,6,7],[2,8],[3],[4]]=>4
[[1,4,6,7],[2,8],[3],[5]]=>4
[[1,3,6,7],[2,8],[4],[5]]=>4
[[1,2,6,7],[3,8],[4],[5]]=>4
[[1,4,5,7],[2,8],[3],[6]]=>4
[[1,3,5,7],[2,8],[4],[6]]=>4
[[1,2,5,7],[3,8],[4],[6]]=>4
[[1,3,4,7],[2,8],[5],[6]]=>4
[[1,2,4,7],[3,8],[5],[6]]=>4
[[1,2,3,7],[4,8],[5],[6]]=>4
[[1,4,5,6],[2,8],[3],[7]]=>5
[[1,3,5,6],[2,8],[4],[7]]=>5
[[1,2,5,6],[3,8],[4],[7]]=>5
[[1,3,4,6],[2,8],[5],[7]]=>5
[[1,2,4,6],[3,8],[5],[7]]=>5
[[1,2,3,6],[4,8],[5],[7]]=>5
[[1,3,4,5],[2,8],[6],[7]]=>5
[[1,2,4,5],[3,8],[6],[7]]=>5
[[1,2,3,5],[4,8],[6],[7]]=>5
[[1,2,3,4],[5,8],[6],[7]]=>5
[[1,4,6,7],[2,5],[3],[8]]=>4
[[1,3,6,7],[2,5],[4],[8]]=>5
[[1,2,6,7],[3,5],[4],[8]]=>5
[[1,3,6,7],[2,4],[5],[8]]=>4
[[1,2,6,7],[3,4],[5],[8]]=>5
[[1,4,5,7],[2,6],[3],[8]]=>4
[[1,3,5,7],[2,6],[4],[8]]=>4
[[1,2,5,7],[3,6],[4],[8]]=>4
[[1,3,4,7],[2,6],[5],[8]]=>5
[[1,2,4,7],[3,6],[5],[8]]=>5
[[1,2,3,7],[4,6],[5],[8]]=>5
[[1,3,5,7],[2,4],[6],[8]]=>4
[[1,2,5,7],[3,4],[6],[8]]=>5
[[1,3,4,7],[2,5],[6],[8]]=>4
[[1,2,4,7],[3,5],[6],[8]]=>4
[[1,2,3,7],[4,5],[6],[8]]=>5
[[1,4,5,6],[2,7],[3],[8]]=>4
[[1,3,5,6],[2,7],[4],[8]]=>4
[[1,2,5,6],[3,7],[4],[8]]=>4
[[1,3,4,6],[2,7],[5],[8]]=>4
[[1,2,4,6],[3,7],[5],[8]]=>4
[[1,2,3,6],[4,7],[5],[8]]=>4
[[1,3,4,5],[2,7],[6],[8]]=>5
[[1,2,4,5],[3,7],[6],[8]]=>5
[[1,2,3,5],[4,7],[6],[8]]=>5
[[1,2,3,4],[5,7],[6],[8]]=>5
[[1,3,5,6],[2,4],[7],[8]]=>4
[[1,2,5,6],[3,4],[7],[8]]=>5
[[1,3,4,6],[2,5],[7],[8]]=>4
[[1,2,4,6],[3,5],[7],[8]]=>4
[[1,2,3,6],[4,5],[7],[8]]=>5
[[1,3,4,5],[2,6],[7],[8]]=>4
[[1,2,4,5],[3,6],[7],[8]]=>4
[[1,2,3,5],[4,6],[7],[8]]=>4
[[1,2,3,4],[5,6],[7],[8]]=>5
[[1,6,7,8],[2],[3],[4],[5]]=>4
[[1,5,7,8],[2],[3],[4],[6]]=>4
[[1,4,7,8],[2],[3],[5],[6]]=>4
[[1,3,7,8],[2],[4],[5],[6]]=>4
[[1,2,7,8],[3],[4],[5],[6]]=>4
[[1,5,6,8],[2],[3],[4],[7]]=>4
[[1,4,6,8],[2],[3],[5],[7]]=>4
[[1,3,6,8],[2],[4],[5],[7]]=>4
[[1,2,6,8],[3],[4],[5],[7]]=>4
[[1,4,5,8],[2],[3],[6],[7]]=>4
[[1,3,5,8],[2],[4],[6],[7]]=>4
[[1,2,5,8],[3],[4],[6],[7]]=>4
[[1,3,4,8],[2],[5],[6],[7]]=>4
[[1,2,4,8],[3],[5],[6],[7]]=>4
[[1,2,3,8],[4],[5],[6],[7]]=>4
[[1,5,6,7],[2],[3],[4],[8]]=>4
[[1,4,6,7],[2],[3],[5],[8]]=>4
[[1,3,6,7],[2],[4],[5],[8]]=>4
[[1,2,6,7],[3],[4],[5],[8]]=>4
[[1,4,5,7],[2],[3],[6],[8]]=>4
[[1,3,5,7],[2],[4],[6],[8]]=>4
[[1,2,5,7],[3],[4],[6],[8]]=>4
[[1,3,4,7],[2],[5],[6],[8]]=>4
[[1,2,4,7],[3],[5],[6],[8]]=>4
[[1,2,3,7],[4],[5],[6],[8]]=>4
[[1,4,5,6],[2],[3],[7],[8]]=>4
[[1,3,5,6],[2],[4],[7],[8]]=>4
[[1,2,5,6],[3],[4],[7],[8]]=>4
[[1,3,4,6],[2],[5],[7],[8]]=>4
[[1,2,4,6],[3],[5],[7],[8]]=>4
[[1,2,3,6],[4],[5],[7],[8]]=>4
[[1,3,4,5],[2],[6],[7],[8]]=>4
[[1,2,4,5],[3],[6],[7],[8]]=>4
[[1,2,3,5],[4],[6],[7],[8]]=>4
[[1,2,3,4],[5],[6],[7],[8]]=>4
[[1,4,7],[2,5,8],[3,6]]=>3
[[1,3,7],[2,5,8],[4,6]]=>4
[[1,2,7],[3,5,8],[4,6]]=>4
[[1,3,7],[2,4,8],[5,6]]=>4
[[1,2,7],[3,4,8],[5,6]]=>5
[[1,4,6],[2,5,8],[3,7]]=>4
[[1,3,6],[2,5,8],[4,7]]=>5
[[1,2,6],[3,5,8],[4,7]]=>5
[[1,3,6],[2,4,8],[5,7]]=>4
[[1,2,6],[3,4,8],[5,7]]=>5
[[1,4,5],[2,6,8],[3,7]]=>4
[[1,3,5],[2,6,8],[4,7]]=>4
[[1,2,5],[3,6,8],[4,7]]=>4
[[1,3,4],[2,6,8],[5,7]]=>5
[[1,2,4],[3,6,8],[5,7]]=>5
[[1,2,3],[4,6,8],[5,7]]=>5
[[1,3,5],[2,4,8],[6,7]]=>5
[[1,2,5],[3,4,8],[6,7]]=>6
[[1,3,4],[2,5,8],[6,7]]=>5
[[1,2,4],[3,5,8],[6,7]]=>5
[[1,2,3],[4,5,8],[6,7]]=>6
[[1,4,6],[2,5,7],[3,8]]=>3
[[1,3,6],[2,5,7],[4,8]]=>4
[[1,2,6],[3,5,7],[4,8]]=>4
[[1,3,6],[2,4,7],[5,8]]=>3
[[1,2,6],[3,4,7],[5,8]]=>4
[[1,4,5],[2,6,7],[3,8]]=>4
[[1,3,5],[2,6,7],[4,8]]=>4
[[1,2,5],[3,6,7],[4,8]]=>4
[[1,3,4],[2,6,7],[5,8]]=>5
[[1,2,4],[3,6,7],[5,8]]=>5
[[1,2,3],[4,6,7],[5,8]]=>5
[[1,3,5],[2,4,7],[6,8]]=>4
[[1,2,5],[3,4,7],[6,8]]=>5
[[1,3,4],[2,5,7],[6,8]]=>4
[[1,2,4],[3,5,7],[6,8]]=>4
[[1,2,3],[4,5,7],[6,8]]=>5
[[1,3,5],[2,4,6],[7,8]]=>4
[[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]]=>6
[[1,5,7],[2,6,8],[3],[4]]=>3
[[1,4,7],[2,6,8],[3],[5]]=>4
[[1,3,7],[2,6,8],[4],[5]]=>4
[[1,2,7],[3,6,8],[4],[5]]=>4
[[1,4,7],[2,5,8],[3],[6]]=>3
[[1,3,7],[2,5,8],[4],[6]]=>4
[[1,2,7],[3,5,8],[4],[6]]=>4
[[1,3,7],[2,4,8],[5],[6]]=>3
[[1,2,7],[3,4,8],[5],[6]]=>4
[[1,5,6],[2,7,8],[3],[4]]=>4
[[1,4,6],[2,7,8],[3],[5]]=>4
[[1,3,6],[2,7,8],[4],[5]]=>4
[[1,2,6],[3,7,8],[4],[5]]=>4
[[1,4,5],[2,7,8],[3],[6]]=>5
[[1,3,5],[2,7,8],[4],[6]]=>5
[[1,2,5],[3,7,8],[4],[6]]=>5
[[1,3,4],[2,7,8],[5],[6]]=>5
[[1,2,4],[3,7,8],[5],[6]]=>5
[[1,2,3],[4,7,8],[5],[6]]=>5
[[1,4,6],[2,5,8],[3],[7]]=>4
[[1,3,6],[2,5,8],[4],[7]]=>5
[[1,2,6],[3,5,8],[4],[7]]=>5
[[1,3,6],[2,4,8],[5],[7]]=>4
[[1,2,6],[3,4,8],[5],[7]]=>5
[[1,4,5],[2,6,8],[3],[7]]=>4
[[1,3,5],[2,6,8],[4],[7]]=>4
[[1,2,5],[3,6,8],[4],[7]]=>4
[[1,3,4],[2,6,8],[5],[7]]=>5
[[1,2,4],[3,6,8],[5],[7]]=>5
[[1,2,3],[4,6,8],[5],[7]]=>5
[[1,3,5],[2,4,8],[6],[7]]=>4
[[1,2,5],[3,4,8],[6],[7]]=>5
[[1,3,4],[2,5,8],[6],[7]]=>4
[[1,2,4],[3,5,8],[6],[7]]=>4
[[1,2,3],[4,5,8],[6],[7]]=>5
[[1,4,6],[2,5,7],[3],[8]]=>3
[[1,3,6],[2,5,7],[4],[8]]=>4
[[1,2,6],[3,5,7],[4],[8]]=>4
[[1,3,6],[2,4,7],[5],[8]]=>3
[[1,2,6],[3,4,7],[5],[8]]=>4
[[1,4,5],[2,6,7],[3],[8]]=>4
[[1,3,5],[2,6,7],[4],[8]]=>4
[[1,2,5],[3,6,7],[4],[8]]=>4
[[1,3,4],[2,6,7],[5],[8]]=>5
[[1,2,4],[3,6,7],[5],[8]]=>5
[[1,2,3],[4,6,7],[5],[8]]=>5
[[1,3,5],[2,4,7],[6],[8]]=>4
[[1,2,5],[3,4,7],[6],[8]]=>5
[[1,3,4],[2,5,7],[6],[8]]=>4
[[1,2,4],[3,5,7],[6],[8]]=>4
[[1,2,3],[4,5,7],[6],[8]]=>5
[[1,3,5],[2,4,6],[7],[8]]=>3
[[1,2,5],[3,4,6],[7],[8]]=>4
[[1,3,4],[2,5,6],[7],[8]]=>4
[[1,2,4],[3,5,6],[7],[8]]=>4
[[1,2,3],[4,5,6],[7],[8]]=>5
[[1,5,8],[2,6],[3,7],[4]]=>3
[[1,4,8],[2,6],[3,7],[5]]=>4
[[1,3,8],[2,6],[4,7],[5]]=>4
[[1,2,8],[3,6],[4,7],[5]]=>4
[[1,4,8],[2,5],[3,7],[6]]=>4
[[1,3,8],[2,5],[4,7],[6]]=>5
[[1,2,8],[3,5],[4,7],[6]]=>5
[[1,3,8],[2,4],[5,7],[6]]=>4
[[1,2,8],[3,4],[5,7],[6]]=>5
[[1,4,8],[2,5],[3,6],[7]]=>3
[[1,3,8],[2,5],[4,6],[7]]=>4
[[1,2,8],[3,5],[4,6],[7]]=>4
[[1,3,8],[2,4],[5,6],[7]]=>4
[[1,2,8],[3,4],[5,6],[7]]=>5
[[1,5,7],[2,6],[3,8],[4]]=>3
[[1,4,7],[2,6],[3,8],[5]]=>4
[[1,3,7],[2,6],[4,8],[5]]=>4
[[1,2,7],[3,6],[4,8],[5]]=>4
[[1,4,7],[2,5],[3,8],[6]]=>3
[[1,3,7],[2,5],[4,8],[6]]=>4
[[1,2,7],[3,5],[4,8],[6]]=>4
[[1,3,7],[2,4],[5,8],[6]]=>3
[[1,2,7],[3,4],[5,8],[6]]=>4
[[1,5,6],[2,7],[3,8],[4]]=>3
[[1,4,6],[2,7],[3,8],[5]]=>3
[[1,3,6],[2,7],[4,8],[5]]=>3
[[1,2,6],[3,7],[4,8],[5]]=>3
[[1,4,5],[2,7],[3,8],[6]]=>4
[[1,3,5],[2,7],[4,8],[6]]=>4
[[1,2,5],[3,7],[4,8],[6]]=>4
[[1,3,4],[2,7],[5,8],[6]]=>4
[[1,2,4],[3,7],[5,8],[6]]=>4
[[1,2,3],[4,7],[5,8],[6]]=>4
[[1,4,6],[2,5],[3,8],[7]]=>4
[[1,3,6],[2,5],[4,8],[7]]=>5
[[1,2,6],[3,5],[4,8],[7]]=>5
[[1,3,6],[2,4],[5,8],[7]]=>4
[[1,2,6],[3,4],[5,8],[7]]=>5
[[1,4,5],[2,6],[3,8],[7]]=>4
[[1,3,5],[2,6],[4,8],[7]]=>4
[[1,2,5],[3,6],[4,8],[7]]=>4
[[1,3,4],[2,6],[5,8],[7]]=>5
[[1,2,4],[3,6],[5,8],[7]]=>5
[[1,2,3],[4,6],[5,8],[7]]=>5
[[1,3,5],[2,4],[6,8],[7]]=>4
[[1,2,5],[3,4],[6,8],[7]]=>5
[[1,3,4],[2,5],[6,8],[7]]=>4
[[1,2,4],[3,5],[6,8],[7]]=>4
[[1,2,3],[4,5],[6,8],[7]]=>5
[[1,4,7],[2,5],[3,6],[8]]=>3
[[1,3,7],[2,5],[4,6],[8]]=>4
[[1,2,7],[3,5],[4,6],[8]]=>4
[[1,3,7],[2,4],[5,6],[8]]=>4
[[1,2,7],[3,4],[5,6],[8]]=>5
[[1,4,6],[2,5],[3,7],[8]]=>3
[[1,3,6],[2,5],[4,7],[8]]=>4
[[1,2,6],[3,5],[4,7],[8]]=>4
[[1,3,6],[2,4],[5,7],[8]]=>3
[[1,2,6],[3,4],[5,7],[8]]=>4
[[1,4,5],[2,6],[3,7],[8]]=>3
[[1,3,5],[2,6],[4,7],[8]]=>3
[[1,2,5],[3,6],[4,7],[8]]=>3
[[1,3,4],[2,6],[5,7],[8]]=>4
[[1,2,4],[3,6],[5,7],[8]]=>4
[[1,2,3],[4,6],[5,7],[8]]=>4
[[1,3,5],[2,4],[6,7],[8]]=>4
[[1,2,5],[3,4],[6,7],[8]]=>5
[[1,3,4],[2,5],[6,7],[8]]=>4
[[1,2,4],[3,5],[6,7],[8]]=>4
[[1,2,3],[4,5],[6,7],[8]]=>5
[[1,6,8],[2,7],[3],[4],[5]]=>3
[[1,5,8],[2,7],[3],[4],[6]]=>4
[[1,4,8],[2,7],[3],[5],[6]]=>4
[[1,3,8],[2,7],[4],[5],[6]]=>4
[[1,2,8],[3,7],[4],[5],[6]]=>4
[[1,5,8],[2,6],[3],[4],[7]]=>3
[[1,4,8],[2,6],[3],[5],[7]]=>4
[[1,3,8],[2,6],[4],[5],[7]]=>4
[[1,2,8],[3,6],[4],[5],[7]]=>4
[[1,4,8],[2,5],[3],[6],[7]]=>3
[[1,3,8],[2,5],[4],[6],[7]]=>4
[[1,2,8],[3,5],[4],[6],[7]]=>4
[[1,3,8],[2,4],[5],[6],[7]]=>3
[[1,2,8],[3,4],[5],[6],[7]]=>4
[[1,6,7],[2,8],[3],[4],[5]]=>3
[[1,5,7],[2,8],[3],[4],[6]]=>3
[[1,4,7],[2,8],[3],[5],[6]]=>3
[[1,3,7],[2,8],[4],[5],[6]]=>3
[[1,2,7],[3,8],[4],[5],[6]]=>3
[[1,5,6],[2,8],[3],[4],[7]]=>4
[[1,4,6],[2,8],[3],[5],[7]]=>4
[[1,3,6],[2,8],[4],[5],[7]]=>4
[[1,2,6],[3,8],[4],[5],[7]]=>4
[[1,4,5],[2,8],[3],[6],[7]]=>4
[[1,3,5],[2,8],[4],[6],[7]]=>4
[[1,2,5],[3,8],[4],[6],[7]]=>4
[[1,3,4],[2,8],[5],[6],[7]]=>4
[[1,2,4],[3,8],[5],[6],[7]]=>4
[[1,2,3],[4,8],[5],[6],[7]]=>4
[[1,5,7],[2,6],[3],[4],[8]]=>3
[[1,4,7],[2,6],[3],[5],[8]]=>4
[[1,3,7],[2,6],[4],[5],[8]]=>4
[[1,2,7],[3,6],[4],[5],[8]]=>4
[[1,4,7],[2,5],[3],[6],[8]]=>3
[[1,3,7],[2,5],[4],[6],[8]]=>4
[[1,2,7],[3,5],[4],[6],[8]]=>4
[[1,3,7],[2,4],[5],[6],[8]]=>3
[[1,2,7],[3,4],[5],[6],[8]]=>4
[[1,5,6],[2,7],[3],[4],[8]]=>3
[[1,4,6],[2,7],[3],[5],[8]]=>3
[[1,3,6],[2,7],[4],[5],[8]]=>3
[[1,2,6],[3,7],[4],[5],[8]]=>3
[[1,4,5],[2,7],[3],[6],[8]]=>4
[[1,3,5],[2,7],[4],[6],[8]]=>4
[[1,2,5],[3,7],[4],[6],[8]]=>4
[[1,3,4],[2,7],[5],[6],[8]]=>4
[[1,2,4],[3,7],[5],[6],[8]]=>4
[[1,2,3],[4,7],[5],[6],[8]]=>4
[[1,4,6],[2,5],[3],[7],[8]]=>3
[[1,3,6],[2,5],[4],[7],[8]]=>4
[[1,2,6],[3,5],[4],[7],[8]]=>4
[[1,3,6],[2,4],[5],[7],[8]]=>3
[[1,2,6],[3,4],[5],[7],[8]]=>4
[[1,4,5],[2,6],[3],[7],[8]]=>3
[[1,3,5],[2,6],[4],[7],[8]]=>3
[[1,2,5],[3,6],[4],[7],[8]]=>3
[[1,3,4],[2,6],[5],[7],[8]]=>4
[[1,2,4],[3,6],[5],[7],[8]]=>4
[[1,2,3],[4,6],[5],[7],[8]]=>4
[[1,3,5],[2,4],[6],[7],[8]]=>3
[[1,2,5],[3,4],[6],[7],[8]]=>4
[[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]]=>4
[[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]]=>2
[[1,4],[2,6],[3,7],[5,8]]=>3
[[1,3],[2,6],[4,7],[5,8]]=>3
[[1,2],[3,6],[4,7],[5,8]]=>3
[[1,4],[2,5],[3,7],[6,8]]=>3
[[1,3],[2,5],[4,7],[6,8]]=>4
[[1,2],[3,5],[4,7],[6,8]]=>4
[[1,3],[2,4],[5,7],[6,8]]=>3
[[1,2],[3,4],[5,7],[6,8]]=>4
[[1,4],[2,5],[3,6],[7,8]]=>3
[[1,3],[2,5],[4,6],[7,8]]=>4
[[1,2],[3,5],[4,6],[7,8]]=>4
[[1,3],[2,4],[5,6],[7,8]]=>4
[[1,2],[3,4],[5,6],[7,8]]=>5
[[1,6],[2,7],[3,8],[4],[5]]=>2
[[1,5],[2,7],[3,8],[4],[6]]=>3
[[1,4],[2,7],[3,8],[5],[6]]=>3
[[1,3],[2,7],[4,8],[5],[6]]=>3
[[1,2],[3,7],[4,8],[5],[6]]=>3
[[1,5],[2,6],[3,8],[4],[7]]=>3
[[1,4],[2,6],[3,8],[5],[7]]=>4
[[1,3],[2,6],[4,8],[5],[7]]=>4
[[1,2],[3,6],[4,8],[5],[7]]=>4
[[1,4],[2,5],[3,8],[6],[7]]=>3
[[1,3],[2,5],[4,8],[6],[7]]=>4
[[1,2],[3,5],[4,8],[6],[7]]=>4
[[1,3],[2,4],[5,8],[6],[7]]=>3
[[1,2],[3,4],[5,8],[6],[7]]=>4
[[1,5],[2,6],[3,7],[4],[8]]=>2
[[1,4],[2,6],[3,7],[5],[8]]=>3
[[1,3],[2,6],[4,7],[5],[8]]=>3
[[1,2],[3,6],[4,7],[5],[8]]=>3
[[1,4],[2,5],[3,7],[6],[8]]=>3
[[1,3],[2,5],[4,7],[6],[8]]=>4
[[1,2],[3,5],[4,7],[6],[8]]=>4
[[1,3],[2,4],[5,7],[6],[8]]=>3
[[1,2],[3,4],[5,7],[6],[8]]=>4
[[1,4],[2,5],[3,6],[7],[8]]=>2
[[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]]=>4
[[1,7],[2,8],[3],[4],[5],[6]]=>2
[[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]]=>2
[[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]]=>2
[[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]]=>2
[[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]]=>2
[[1,2],[3,4],[5],[6],[7],[8]]=>3
[[1,8],[2],[3],[4],[5],[6],[7]]=>2
[[1,7],[2],[3],[4],[5],[6],[8]]=>2
[[1,6],[2],[3],[4],[5],[7],[8]]=>2
[[1,5],[2],[3],[4],[6],[7],[8]]=>2
[[1,4],[2],[3],[5],[6],[7],[8]]=>2
[[1,3],[2],[4],[5],[6],[7],[8]]=>2
[[1,2],[3],[4],[5],[6],[7],[8]]=>2
[[1],[2],[3],[4],[5],[6],[7],[8]]=>1
[[1,2,3,4,5,6,7,8,9]]=>9
[[1,2,3,4,5,6,7,8],[9]]=>8
[[1,2,3,4,5,6,7],[8,9]]=>8
[[1,2,3,4,5,6,7],[8],[9]]=>7
[[1,2,3,4,5,6],[7,8,9]]=>8
[[1,2,3,4,5,6],[7,8],[9]]=>7
[[1,2,3,4,5,6],[7],[8],[9]]=>6
[[1,2,3,4,5],[6,7,8,9]]=>8
[[1,2,3,4,5],[6,7,8],[9]]=>7
[[1,2,3,4,5],[6,7],[8,9]]=>7
[[1,2,3,4,5],[6,7],[8],[9]]=>6
[[1,2,3,4,5],[6],[7],[8],[9]]=>5
[[1,2,3,4],[5,6,7,8],[9]]=>7
[[1,2,3,4],[5,6,7],[8,9]]=>7
[[1,2,3,4],[5,6,7],[8],[9]]=>6
[[1,2,3,4],[5,6],[7,8],[9]]=>6
[[1,2,3,4],[5,6],[7],[8],[9]]=>5
[[1,2,3,4],[5],[6],[7],[8],[9]]=>4
[[1,2,3],[4,5,6],[7,8,9]]=>7
[[1,2,3],[4,5,6],[7,8],[9]]=>6
[[1,2,3],[4,5,6],[7],[8],[9]]=>5
[[1,2,3],[4,5],[6,7],[8,9]]=>6
[[1,2,3],[4,5],[6,7],[8],[9]]=>5
[[1,2,3],[4,5],[6],[7],[8],[9]]=>4
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>3
[[1,2],[3,4],[5,6],[7,8],[9]]=>5
[[1,2],[3,4],[5,6],[7],[8],[9]]=>4
[[1,2],[3,4],[5],[6],[7],[8],[9]]=>3
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>2
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>1
[[1,3,4,5,6,7,8,9],[2]]=>8
[[1,2,5,6,7,8,9],[3,4]]=>8
[[1,4,5,6,7,8,9],[2],[3]]=>7
[[1,2,3,7,8,9],[4,5,6]]=>8
[[1,3,6,7,8,9],[2,5],[4]]=>7
[[1,5,6,7,8,9],[2],[3],[4]]=>6
[[1,2,3,4,9],[5,6,7,8]]=>8
[[1,3,4,8,9],[2,6,7],[5]]=>7
[[1,2,7,8,9],[3,4],[5,6]]=>7
[[1,4,7,8,9],[2,6],[3],[5]]=>6
[[1,6,7,8,9],[2],[3],[4],[5]]=>5
[[1,3,4,5],[2,7,8,9],[6]]=>7
[[1,2,5,9],[3,4,8],[6,7]]=>7
[[1,4,5,9],[2,7,8],[3],[6]]=>6
[[1,3,8,9],[2,5],[4,7],[6]]=>6
[[1,5,8,9],[2,7],[3],[4],[6]]=>5
[[1,7,8,9],[2],[3],[4],[5],[6]]=>4
[[1,3,6],[2,5,9],[4,8],[7]]=>6
[[1,5,6],[2,8,9],[3],[4],[7]]=>5
[[1,2,9],[3,4],[5,6],[7,8]]=>6
[[1,4,9],[2,6],[3,8],[5],[7]]=>5
[[1,6,9],[2,8],[3],[4],[5],[7]]=>4
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>3
[[1,3],[2,5],[4,7],[6,9],[8]]=>5
[[1,5],[2,7],[3,9],[4],[6],[8]]=>4
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>3
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>2
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>2
[[1,7],[2,8],[3,9],[4],[5],[6]]=>2
[[1,7,9],[2,8],[3],[4],[5],[6]]=>3
[[1,6],[2,7],[3,8],[4,9],[5]]=>2
[[1,6,9],[2,7],[3,8],[4],[5]]=>3
[[1,6,8],[2,7,9],[3],[4],[5]]=>3
[[1,6,8,9],[2,7],[3],[4],[5]]=>4
[[1,5,9],[2,6],[3,7],[4,8]]=>3
[[1,5,8],[2,6,9],[3,7],[4]]=>3
[[1,5,8,9],[2,6],[3,7],[4]]=>4
[[1,5,7,9],[2,6,8],[3],[4]]=>4
[[1,5,7,8,9],[2,6],[3],[4]]=>5
[[1,4,7],[2,5,8],[3,6,9]]=>3
[[1,4,7,9],[2,5,8],[3,6]]=>4
[[1,4,7,8,9],[2,5],[3,6]]=>5
[[1,4,6,8],[2,5,7,9],[3]]=>4
[[1,4,6,8,9],[2,5,7],[3]]=>5
[[1,4,6,7,8,9],[2,5],[3]]=>6
[[1,3,5,7,9],[2,4,6,8]]=>5
[[1,3,5,7,8,9],[2,4,6]]=>6
[[1,3,5,6,7,8,9],[2,4]]=>7
[[1,3],[2,4],[5],[6],[7],[8],[9]]=>2
[[1,4],[2,5],[3,6],[7],[8],[9]]=>2
[[1,2,4],[3,5],[6],[7],[8],[9]]=>3
[[1,5],[2,6],[3,7],[4,8],[9]]=>2
[[1,2,5],[3,6],[4,7],[8],[9]]=>3
[[1,3,5],[2,4,6],[7],[8],[9]]=>3
[[1,2,3,5],[4,6],[7],[8],[9]]=>4
[[1,2,6],[3,7],[4,8],[5,9]]=>3
[[1,3,6],[2,4,7],[5,8],[9]]=>3
[[1,2,3,6],[4,7],[5,8],[9]]=>4
[[1,2,4,6],[3,5,7],[8],[9]]=>4
[[1,2,3,4,6],[5,7],[8],[9]]=>5
[[1,2,4,7],[3,5,8],[6,9]]=>4
[[1,2,3,4,7],[5,8],[6,9]]=>5
[[1,3,5,7],[2,4,6,8],[9]]=>4
[[1,2,3,5,7],[4,6,8],[9]]=>5
[[1,2,3,4,5,7],[6,8],[9]]=>6
[[1,2,4,6,8],[3,5,7,9]]=>5
[[1,2,3,4,6,8],[5,7,9]]=>6
[[1,2,3,4,5,6,8],[7,9]]=>7
[[1,2,3,4,9],[5,6],[7,8]]=>7
[[1,2,9],[3],[4],[5],[6],[7],[8]]=>3
[[1,2,4,5,6,7,8,9],[3]]=>8
[[1,2,5,6,7,8,9],[3],[4]]=>7
[[1,2,6,7,8,9],[3],[4],[5]]=>6
[[1,2,7,8,9],[3],[4],[5],[6]]=>5
[[1,2,8,9],[3],[4],[5],[6],[7]]=>4
[[1,2,3,4,7,8,9],[5,6]]=>8
[[1,2,4,5,8,9],[3,7],[6]]=>7
[[1,2,4,5,6,7],[3,9],[8]]=>7
[[1,2,5,6,9],[3,8],[4],[7]]=>6
[[1,2,3,4,7,8],[5,6],[9]]=>7
[[1,2,5,6,7,8],[3],[4],[9]]=>6
[[1,2,4,5],[3,7],[6,9],[8]]=>6
[[1,2,6,7],[3,9],[4],[5],[8]]=>5
[[1,2,5,6],[3,8],[4],[7],[9]]=>5
[[1,2,7,8],[3],[4],[5],[6],[9]]=>4
[[1,3,5,7,9],[2,4,6,8,10]]=>5
[[1,3,5,7,8],[2,4,6,9,10]]=>6
[[1,3,5,6,9],[2,4,7,8,10]]=>6
[[1,3,5,6,8],[2,4,7,9,10]]=>6
[[1,3,5,6,7],[2,4,8,9,10]]=>7
[[1,3,4,7,9],[2,5,6,8,10]]=>6
[[1,3,4,7,8],[2,5,6,9,10]]=>7
[[1,3,4,6,9],[2,5,7,8,10]]=>6
[[1,3,4,6,8],[2,5,7,9,10]]=>6
[[1,3,4,6,7],[2,5,8,9,10]]=>7
[[1,3,4,5,9],[2,6,7,8,10]]=>7
[[1,3,4,5,8],[2,6,7,9,10]]=>7
[[1,3,4,5,7],[2,6,8,9,10]]=>7
[[1,3,4,5,6],[2,7,8,9,10]]=>8
[[1,2,5,7,9],[3,4,6,8,10]]=>6
[[1,2,5,7,8],[3,4,6,9,10]]=>7
[[1,2,5,6,9],[3,4,7,8,10]]=>7
[[1,2,5,6,8],[3,4,7,9,10]]=>7
[[1,2,5,6,7],[3,4,8,9,10]]=>8
[[1,2,4,7,9],[3,5,6,8,10]]=>6
[[1,2,4,7,8],[3,5,6,9,10]]=>7
[[1,2,4,6,9],[3,5,7,8,10]]=>6
[[1,2,4,6,8],[3,5,7,9,10]]=>6
[[1,2,4,6,7],[3,5,8,9,10]]=>7
[[1,2,4,5,9],[3,6,7,8,10]]=>7
[[1,2,4,5,8],[3,6,7,9,10]]=>7
[[1,2,4,5,7],[3,6,8,9,10]]=>7
[[1,2,4,5,6],[3,7,8,9,10]]=>8
[[1,2,3,7,9],[4,5,6,8,10]]=>7
[[1,2,3,7,8],[4,5,6,9,10]]=>8
[[1,2,3,6,9],[4,5,7,8,10]]=>7
[[1,2,3,6,8],[4,5,7,9,10]]=>7
[[1,2,3,6,7],[4,5,8,9,10]]=>8
[[1,2,3,5,9],[4,6,7,8,10]]=>7
[[1,2,3,5,8],[4,6,7,9,10]]=>7
[[1,2,3,5,7],[4,6,8,9,10]]=>7
[[1,2,3,5,6],[4,7,8,9,10]]=>8
[[1,2,3,4,9],[5,6,7,8,10]]=>8
[[1,2,3,4,8],[5,6,7,9,10]]=>8
[[1,2,3,4,7],[5,6,8,9,10]]=>8
[[1,2,3,4,6],[5,7,8,9,10]]=>8
[[1,2,3,4,5],[6,7,8,9,10]]=>9
[[1,2,3,4,5,6,7,8,9,10]]=>10
[[1,2,3,4,5,6,7,8,9],[10]]=>9
[[1,2,3,4,5,6,7,8],[9,10]]=>9
[[1,2,3,4,5,6,7,8],[9],[10]]=>8
[[1,2,3,4,5,6,7],[8,9,10]]=>9
[[1,2,3,4,5,6,7],[8,9],[10]]=>8
[[1,2,3,4,5,6,7],[8],[9],[10]]=>7
[[1,2,3,4,5,6],[7,8,9,10]]=>9
[[1,2,3,4,5,6],[7,8,9],[10]]=>8
[[1,2,3,4,5,6],[7,8],[9,10]]=>8
[[1,2,3,4,5,6],[7,8],[9],[10]]=>7
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>6
[[1,2,3,4,5],[6,7,8,9],[10]]=>8
[[1,2,3,4,5],[6,7,8],[9,10]]=>8
[[1,2,3,4,5],[6,7,8],[9],[10]]=>7
[[1,2,3,4,5],[6,7],[8,9],[10]]=>7
[[1,2,3,4,5],[6,7],[8],[9],[10]]=>6
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>5
[[1,2,3,4],[5,6,7,8],[9,10]]=>8
[[1,2,3,4],[5,6,7,8],[9],[10]]=>7
[[1,2,3,4],[5,6,7],[8,9,10]]=>8
[[1,2,3,4],[5,6,7],[8,9],[10]]=>7
[[1,2,3,4],[5,6,7],[8],[9],[10]]=>6
[[1,2,3,4],[5,6],[7,8],[9,10]]=>7
[[1,2,3,4],[5,6],[7,8],[9],[10]]=>6
[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>5
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>4
[[1,2,3],[4,5,6],[7,8,9],[10]]=>7
[[1,2,3],[4,5,6],[7,8],[9,10]]=>7
[[1,2,3],[4,5,6],[7,8],[9],[10]]=>6
[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>5
[[1,2,3],[4,5],[6,7],[8,9],[10]]=>6
[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>5
[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>4
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>3
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>6
[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>5
[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>4
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>3
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>2
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>1
[[1,3,4,5,6,7,8,9,10],[2]]=>9
[[1,2,5,6,7,8,9,10],[3,4]]=>9
[[1,4,5,6,7,8,9,10],[2],[3]]=>8
[[1,2,3,7,8,9,10],[4,5,6]]=>9
[[1,3,6,7,8,9,10],[2,5],[4]]=>8
[[1,5,6,7,8,9,10],[2],[3],[4]]=>7
[[1,2,3,4,9,10],[5,6,7,8]]=>9
[[1,3,4,8,9,10],[2,6,7],[5]]=>8
[[1,2,7,8,9,10],[3,4],[5,6]]=>8
[[1,4,7,8,9,10],[2,6],[3],[5]]=>7
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>6
[[1,3,4,5,10],[2,7,8,9],[6]]=>8
[[1,2,5,9,10],[3,4,8],[6,7]]=>8
[[1,4,5,9,10],[2,7,8],[3],[6]]=>7
[[1,3,8,9,10],[2,5],[4,7],[6]]=>7
[[1,5,8,9,10],[2,7],[3],[4],[6]]=>6
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>5
[[1,2,5,6],[3,4,9,10],[7,8]]=>8
[[1,4,5,6],[2,8,9,10],[3],[7]]=>7
[[1,2,3,10],[4,5,6],[7,8,9]]=>8
[[1,3,6,10],[2,5,9],[4,8],[7]]=>7
[[1,5,6,10],[2,8,9],[3],[4],[7]]=>6
[[1,2,9,10],[3,4],[5,6],[7,8]]=>7
[[1,4,9,10],[2,6],[3,8],[5],[7]]=>6
[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>5
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>4
[[1,3,4],[2,6,7],[5,9,10],[8]]=>7
[[1,2,7],[3,4,10],[5,6],[8,9]]=>7
[[1,4,7],[2,6,10],[3,9],[5],[8]]=>6
[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>5
[[1,3,10],[2,5],[4,7],[6,9],[8]]=>6
[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>5
[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>4
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>3
[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>5
[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>4
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>3
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>2
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>2
[[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>2
[[1,8,10],[2,9],[3],[4],[5],[6],[7]]=>3
[[1,7],[2,8],[3,9],[4,10],[5],[6]]=>2
[[1,7,10],[2,8],[3,9],[4],[5],[6]]=>3
[[1,7,9],[2,8,10],[3],[4],[5],[6]]=>3
[[1,7,9,10],[2,8],[3],[4],[5],[6]]=>4
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>2
[[1,6,10],[2,7],[3,8],[4,9],[5]]=>3
[[1,6,9],[2,7,10],[3,8],[4],[5]]=>3
[[1,6,9,10],[2,7],[3,8],[4],[5]]=>4
[[1,6,8,10],[2,7,9],[3],[4],[5]]=>4
[[1,6,8,9,10],[2,7],[3],[4],[5]]=>5
[[1,5,9],[2,6,10],[3,7],[4,8]]=>3
[[1,5,9,10],[2,6],[3,7],[4,8]]=>4
[[1,5,8],[2,6,9],[3,7,10],[4]]=>3
[[1,5,8,10],[2,6,9],[3,7],[4]]=>4
[[1,5,8,9,10],[2,6],[3,7],[4]]=>5
[[1,5,7,9],[2,6,8,10],[3],[4]]=>4
[[1,5,7,9,10],[2,6,8],[3],[4]]=>5
[[1,5,7,8,9,10],[2,6],[3],[4]]=>6
[[1,4,7,10],[2,5,8],[3,6,9]]=>4
[[1,4,7,9],[2,5,8,10],[3,6]]=>4
[[1,4,7,9,10],[2,5,8],[3,6]]=>5
[[1,4,7,8,9,10],[2,5],[3,6]]=>6
[[1,4,6,8,10],[2,5,7,9],[3]]=>5
[[1,4,6,8,9,10],[2,5,7],[3]]=>6
[[1,4,6,7,8,9,10],[2,5],[3]]=>7
[[1,3,5,7,9,10],[2,4,6,8]]=>6
[[1,3,5,7,8,9,10],[2,4,6]]=>7
[[1,3,5,6,7,8,9,10],[2,4]]=>8
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>2
[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>2
[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>3
[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>2
[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>3
[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>3
[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>4
[[1,2,6],[3,7],[4,8],[5,9],[10]]=>3
[[1,3,6],[2,4,7],[5,8],[9],[10]]=>3
[[1,2,3,6],[4,7],[5,8],[9],[10]]=>4
[[1,2,4,6],[3,5,7],[8],[9],[10]]=>4
[[1,2,3,4,6],[5,7],[8],[9],[10]]=>5
[[1,3,7],[2,4,8],[5,9],[6,10]]=>3
[[1,2,3,7],[4,8],[5,9],[6,10]]=>4
[[1,4,7],[2,5,8],[3,6,9],[10]]=>3
[[1,2,4,7],[3,5,8],[6,9],[10]]=>4
[[1,2,3,4,7],[5,8],[6,9],[10]]=>5
[[1,3,5,7],[2,4,6,8],[9],[10]]=>4
[[1,2,3,5,7],[4,6,8],[9],[10]]=>5
[[1,2,3,4,5,7],[6,8],[9],[10]]=>6
[[1,2,5,8],[3,6,9],[4,7,10]]=>4
[[1,3,5,8],[2,4,6,9],[7,10]]=>4
[[1,2,3,5,8],[4,6,9],[7,10]]=>5
[[1,2,3,4,5,8],[6,9],[7,10]]=>6
[[1,2,4,6,8],[3,5,7,9],[10]]=>5
[[1,2,3,4,6,8],[5,7,9],[10]]=>6
[[1,2,3,4,5,6,8],[7,9],[10]]=>7
[[1,2,3,5,7,9],[4,6,8,10]]=>6
[[1,2,3,4,5,7,9],[6,8,10]]=>7
[[1,2,3,4,5,6,7,9],[8,10]]=>8
[[1,2],[3,4],[5,6],[7,9],[8,10]]=>5
[[1,2],[3,4],[5,7],[6,8],[9,10]]=>5
[[1,2],[3,4],[5,7],[6,9],[8,10]]=>5
[[1,2],[3,4],[5,8],[6,9],[7,10]]=>4
[[1,2],[3,5],[4,6],[7,8],[9,10]]=>5
[[1,2],[3,5],[4,6],[7,9],[8,10]]=>4
[[1,2],[3,5],[4,7],[6,8],[9,10]]=>5
[[1,2],[3,5],[4,7],[6,9],[8,10]]=>5
[[1,2],[3,5],[4,8],[6,9],[7,10]]=>4
[[1,2],[3,6],[4,7],[5,8],[9,10]]=>4
[[1,2],[3,6],[4,7],[5,9],[8,10]]=>4
[[1,2],[3,6],[4,8],[5,9],[7,10]]=>4
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>3
[[1,3],[2,4],[5,6],[7,8],[9,10]]=>5
[[1,3],[2,4],[5,6],[7,9],[8,10]]=>4
[[1,3],[2,4],[5,7],[6,8],[9,10]]=>4
[[1,3],[2,4],[5,7],[6,9],[8,10]]=>4
[[1,3],[2,4],[5,8],[6,9],[7,10]]=>3
[[1,3],[2,5],[4,6],[7,8],[9,10]]=>5
[[1,3],[2,5],[4,6],[7,9],[8,10]]=>4
[[1,3],[2,5],[4,7],[6,8],[9,10]]=>5
[[1,3],[2,5],[4,7],[6,9],[8,10]]=>5
[[1,3],[2,5],[4,8],[6,9],[7,10]]=>4
[[1,3],[2,6],[4,7],[5,8],[9,10]]=>4
[[1,3],[2,6],[4,7],[5,9],[8,10]]=>4
[[1,3],[2,6],[4,8],[5,9],[7,10]]=>4
[[1,3],[2,7],[4,8],[5,9],[6,10]]=>3
[[1,4],[2,5],[3,6],[7,8],[9,10]]=>4
[[1,4],[2,5],[3,6],[7,9],[8,10]]=>3
[[1,4],[2,5],[3,7],[6,8],[9,10]]=>4
[[1,4],[2,5],[3,7],[6,9],[8,10]]=>4
[[1,4],[2,5],[3,8],[6,9],[7,10]]=>3
[[1,4],[2,6],[3,7],[5,8],[9,10]]=>4
[[1,4],[2,6],[3,7],[5,9],[8,10]]=>4
[[1,4],[2,6],[3,8],[5,9],[7,10]]=>4
[[1,4],[2,7],[3,8],[5,9],[6,10]]=>3
[[1,5],[2,6],[3,7],[4,8],[9,10]]=>3
[[1,5],[2,6],[3,7],[4,9],[8,10]]=>3
[[1,5],[2,6],[3,8],[4,9],[7,10]]=>3
[[1,5],[2,7],[3,8],[4,9],[6,10]]=>3
[[1,2,3,4,5,6,7,8,10],[9]]=>9
[[1,2,3,4,5,6,10],[7,8,9]]=>9
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>3
[[1,2,4,5,6,7,8,9,10],[3]]=>9
[[1,2,4,6,8,10],[3,5,7,9]]=>6
[[1,2,4,6,8,9,10],[3,5,7]]=>7
[[1,2,4,6,7,8,10],[3,5,9]]=>7
[[1,2,4,6,7,9,10],[3,5,8]]=>7
[[1,2,4,6,7,8,9,10],[3,5]]=>8
[[1,2,4,5,6,8,10],[3,7,9]]=>7
[[1,2,4,5,6,9,10],[3,7,8]]=>8
[[1,2,4,5,7,8,10],[3,6,9]]=>7
[[1,2,4,5,7,9,10],[3,6,8]]=>7
[[1,2,4,5,7,8,9,10],[3,6]]=>8
[[1,2,4,5,6,7,8,10],[3,9]]=>8
[[1,2,4,5,6,7,9,10],[3,8]]=>8
[[1,2,4,5,6,8,9,10],[3,7]]=>8
[[1,2,3,4,6,8,10],[5,7,9]]=>7
[[1,2,3,4,6,9,10],[5,7,8]]=>8
[[1,2,3,4,7,8,10],[5,6,9]]=>8
[[1,2,3,4,7,9,10],[5,6,8]]=>8
[[1,2,3,4,7,8,9,10],[5,6]]=>9
[[1,2,3,5,6,8,10],[4,7,9]]=>7
[[1,2,3,5,6,9,10],[4,7,8]]=>8
[[1,2,3,5,7,8,10],[4,6,9]]=>7
[[1,2,3,5,7,9,10],[4,6,8]]=>7
[[1,2,3,5,7,8,9,10],[4,6]]=>8
[[1,2,3,5,6,7,8,10],[4,9]]=>8
[[1,2,3,5,6,7,9,10],[4,8]]=>8
[[1,2,3,5,6,8,9,10],[4,7]]=>8
[[1,2,3,5,6,7,8,9,10],[4]]=>9
[[1,2,3,4,5,6,8,10],[7,9]]=>8
[[1,2,3,4,5,6,9,10],[7,8]]=>9
[[1,2,3,4,5,7,8,10],[6,9]]=>8
[[1,2,3,4,5,7,9,10],[6,8]]=>8
[[1,2,3,4,5,8,9,10],[6,7]]=>9
[[1,2,3,4,6,7,8,10],[5,9]]=>8
[[1,2,3,4,6,7,9,10],[5,8]]=>8
[[1,2,3,4,6,8,9,10],[5,7]]=>8
[[1,2,3,4,6,7,8,9,10],[5]]=>9
[[1,2,3,4,5,6,7,9,10],[8]]=>9
[[1,2,3,4,5,6,8,9,10],[7]]=>9
[[1,2,3,4,5,7,8,9,10],[6]]=>9
[[1,2,5,6,7,8,9,10],[3],[4]]=>8
[[1,2,6,7,8,9,10],[3],[4],[5]]=>7
[[1,2,7,8,9,10],[3],[4],[5],[6]]=>6
[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>5
[[1,2,9,10],[3],[4],[5],[6],[7],[8]]=>4
[[1,2,4,5,8,9,10],[3,7],[6]]=>8
[[1,2,4,5,6,7],[3,9,10],[8]]=>8
[[1,2,3,4,9,10],[5,6],[7,8]]=>8
[[1,2,5,6,9,10],[3,8],[4],[7]]=>7
[[1,2,4,5,6,7,8,9],[3],[10]]=>8
[[1,2,3,4,7,8],[5,6],[9,10]]=>8
[[1,2,5,6,7,8],[3,10],[4],[9]]=>7
[[1,2,4,5,10],[3,7],[6,9],[8]]=>7
[[1,2,6,7,10],[3,9],[4],[5],[8]]=>6
[[1,2,4,5,8,9],[3,7],[6],[10]]=>7
[[1,2,6,7,8,9],[3],[4],[5],[10]]=>6
[[1,2,5,6],[3,8],[4,10],[7],[9]]=>6
[[1,2,7,8],[3,10],[4],[5],[6],[9]]=>5
[[1,2,4,5],[3,7],[6,9],[8],[10]]=>6
[[1,2,6,7],[3,9],[4],[5],[8],[10]]=>5
[[1,2,8,9],[3],[4],[5],[6],[7],[10]]=>4
[[1,2,3,4,5],[6,7,8,9],[10,11]]=>9
[[1,2,3,4,5],[6,7,8,9],[10],[11]]=>8
[[1,2,3,4,5],[6,7,8],[9,10,11]]=>9
[[1,2,3,4,5],[6,7,8],[9,10],[11]]=>8
[[1,2,3,4,5],[6,7,8],[9],[10],[11]]=>7
[[1,2,3,4,5],[6,7],[8,9],[10,11]]=>8
[[1,2,3,4,5],[6,7],[8,9],[10],[11]]=>7
[[1,2,3,4],[5,6,7,8],[9,10,11]]=>9
[[1,2,3,4],[5,6,7,8],[9,10],[11]]=>8
[[1,2,3,4],[5,6,7,8],[9],[10],[11]]=>7
[[1,2,3,4],[5,6,7],[8,9,10],[11]]=>8
[[1,2,3,4],[5,6,7],[8,9],[10,11]]=>8
[[1,2,3,4],[5,6,7],[8,9],[10],[11]]=>7
[[1,2,3,4],[5,6],[7,8],[9,10],[11]]=>7
[[1,2,3],[4,5,6],[7,8,9],[10,11]]=>8
[[1,2,3],[4,5,6],[7,8,9],[10],[11]]=>7
[[1,2,3],[4,5,6],[7,8],[9,10],[11]]=>7
[[1,2,5,6,11],[3,4,9,10],[7,8]]=>9
[[1,4,5,6,11],[2,8,9,10],[3],[7]]=>8
[[1,2,3,10,11],[4,5,6],[7,8,9]]=>9
[[1,3,6,10,11],[2,5,9],[4,8],[7]]=>8
[[1,5,6,10,11],[2,8,9],[3],[4],[7]]=>7
[[1,2,9,10,11],[3,4],[5,6],[7,8]]=>8
[[1,4,9,10,11],[2,6],[3,8],[5],[7]]=>7
[[1,2,3,7],[4,5,6,11],[8,9,10]]=>9
[[1,3,6,7],[2,5,10,11],[4,9],[8]]=>8
[[1,5,6,7],[2,9,10,11],[3],[4],[8]]=>7
[[1,3,4,11],[2,6,7],[5,9,10],[8]]=>8
[[1,2,7,11],[3,4,10],[5,6],[8,9]]=>8
[[1,4,7,11],[2,6,10],[3,9],[5],[8]]=>7
[[1,3,10,11],[2,5],[4,7],[6,9],[8]]=>7
[[1,2,5],[3,4,8],[6,7,11],[9,10]]=>8
[[1,4,5],[2,7,8],[3,10,11],[6],[9]]=>7
[[1,3,8],[2,5,11],[4,7],[6,10],[9]]=>7
[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>6
[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>7
[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>7
[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>7
[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>8
[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>7
[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>8
[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>7
[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>7
[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>8
[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>8
[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>8
[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>8
[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>9
[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>7
[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>8
[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>8
[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>8
[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>9
[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>7
[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>8
[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>7
[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>7
[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>8
[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>8
[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>8
[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>8
[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>9
[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>8
[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>9
[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>8
[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>8
[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>9
[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>8
[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>8
[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>8
[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>9
[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>9
[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>9
[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>9
[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>9
[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>10
[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>7
[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>8
[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>8
[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>8
[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>9
[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>8
[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>9
[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>8
[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>8
[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>9
[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>9
[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>9
[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>9
[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>10
[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>7
[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>8
[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>8
[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>8
[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>9
[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>7
[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>8
[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>7
[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>7
[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>8
[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>8
[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>8
[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>8
[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>9
[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>8
[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>9
[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>8
[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>8
[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>9
[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>8
[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>8
[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>8
[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>9
[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>9
[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>9
[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>9
[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>9
[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>10
[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>8
[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>9
[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>9
[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>9
[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>10
[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>8
[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>9
[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>8
[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>8
[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>9
[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>9
[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>9
[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>9
[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>10
[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>8
[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>9
[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>8
[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>8
[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>9
[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>8
[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>8
[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>8
[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>9
[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>9
[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>9
[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>9
[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>9
[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>10
[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>9
[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>10
[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>9
[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>9
[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>10
[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>9
[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>9
[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>9
[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>10
[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>9
[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>9
[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>9
[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>9
[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>10
[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>10
[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>10
[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>10
[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>10
[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>10
[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>11
[[1,2,3,4,5,6,7,8,9,10,11,12]]=>12
[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>10
[[1,2,3,4,5],[6,7,8,9],[10,11,12]]=>10
[[1,2,3,4,5],[6,7,8,9],[10,11],[12]]=>9
[[1,2,3,4,5],[6,7,8,9],[10],[11],[12]]=>8
[[1,2,3,4,5],[6,7,8],[9,10,11],[12]]=>9
[[1,2,3,4,5],[6,7,8],[9,10],[11,12]]=>9
[[1,2,3,4,5],[6,7,8],[9,10],[11],[12]]=>8
[[1,2,3,4,5],[6,7],[8,9],[10,11],[12]]=>8
[[1,2,3,4],[5,6,7,8],[9,10,11],[12]]=>9
[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>9
[[1,2,3,4],[5,6,7,8],[9,10],[11],[12]]=>8
[[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>9
[[1,2,3,4],[5,6,7],[8,9,10],[11],[12]]=>8
[[1,2,3,4],[5,6,7],[8,9],[10,11],[12]]=>8
[[1,2,3],[4,5,6],[7,8,9],[10,11],[12]]=>8
[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]]=>7
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>7
[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>10
[[1,2,3,7,12],[4,5,6,11],[8,9,10]]=>10
[[1,3,6,7,12],[2,5,10,11],[4,9],[8]]=>9
[[1,5,6,7,12],[2,9,10,11],[3],[4],[8]]=>8
[[1,3,4,11,12],[2,6,7],[5,9,10],[8]]=>9
[[1,2,7,11,12],[3,4,10],[5,6],[8,9]]=>9
[[1,4,7,11,12],[2,6,10],[3,9],[5],[8]]=>8
[[1,3,10,11,12],[2,5],[4,7],[6,9],[8]]=>8
[[1,3,4,8],[2,6,7,12],[5,10,11],[9]]=>9
[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>9
[[1,4,7,8],[2,6,11,12],[3,10],[5],[9]]=>8
[[1,2,5,12],[3,4,8],[6,7,11],[9,10]]=>9
[[1,4,5,12],[2,7,8],[3,10,11],[6],[9]]=>8
[[1,3,8,12],[2,5,11],[4,7],[6,10],[9]]=>8
[[1,3,6],[2,5,9],[4,8,12],[7,11],[10]]=>8
[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>7
[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>6
[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>6
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>6
[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>5
[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>6
[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>5
[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>6
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>6
[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>5
[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>5
[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>5
[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>5
[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>4
[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>6
[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>5
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>5
[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>5
[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>4
[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>6
[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>5
[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>6
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>6
[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>5
[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>5
[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>5
[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>5
[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>4
[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>5
[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>4
[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>5
[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>5
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>4
[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>5
[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>5
[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>5
[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>4
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>4
[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>4
[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>4
[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>4
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>3
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>6
[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>5
[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>5
[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>5
[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>4
[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>5
[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>4
[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>5
[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>5
[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>4
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>4
[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>4
[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>4
[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>3
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>6
[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>5
[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>5
[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>5
[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>4
[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>6
[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>5
[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>6
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>6
[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>5
[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>5
[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>5
[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>5
[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>4
[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>5
[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>4
[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>5
[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>5
[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>4
[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>5
[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>5
[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>5
[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>4
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>4
[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>4
[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>4
[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>4
[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>3
[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>5
[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>4
[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>4
[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>4
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>3
[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>5
[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>4
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>5
[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>5
[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>4
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>4
[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>4
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>4
[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>3
[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>5
[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>4
[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>5
[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>5
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>4
[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>5
[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>5
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>5
[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>4
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>4
[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>4
[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>4
[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>4
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>3
[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>4
[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>3
[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>4
[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>4
[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>3
[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>4
[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>4
[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>4
[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>3
[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>4
[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>4
[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>4
[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>4
[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>3
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>3
[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>3
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>3
[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>3
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>3
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>2
[[1,2,4,6,8,10,12],[3,5,7,9,11]]=>7
[[1,2,4,6,8,10,11,12],[3,5,7,9]]=>8
[[1,2,4,6,8,9,10,12],[3,5,7,11]]=>8
[[1,2,4,6,8,9,11,12],[3,5,7,10]]=>8
[[1,2,4,6,8,9,10,11,12],[3,5,7]]=>9
[[1,2,4,6,7,8,10,12],[3,5,9,11]]=>8
[[1,2,4,6,7,8,11,12],[3,5,9,10]]=>9
[[1,2,4,6,7,9,10,12],[3,5,8,11]]=>8
[[1,2,4,6,7,9,11,12],[3,5,8,10]]=>8
[[1,2,4,6,7,9,10,11,12],[3,5,8]]=>9
[[1,2,4,6,7,8,9,10,12],[3,5,11]]=>9
[[1,2,4,6,7,8,9,11,12],[3,5,10]]=>9
[[1,2,4,6,7,8,10,11,12],[3,5,9]]=>9
[[1,2,4,6,7,8,9,10,11,12],[3,5]]=>10
[[1,2,4,5,6,8,10,12],[3,7,9,11]]=>8
[[1,2,4,5,6,8,11,12],[3,7,9,10]]=>9
[[1,2,4,5,6,9,10,12],[3,7,8,11]]=>9
[[1,2,4,5,6,9,11,12],[3,7,8,10]]=>9
[[1,2,4,5,6,9,10,11,12],[3,7,8]]=>10
[[1,2,4,5,7,8,10,12],[3,6,9,11]]=>8
[[1,2,4,5,7,8,11,12],[3,6,9,10]]=>9
[[1,2,4,5,7,9,10,12],[3,6,8,11]]=>8
[[1,2,4,5,7,9,11,12],[3,6,8,10]]=>8
[[1,2,4,5,7,9,10,11,12],[3,6,8]]=>9
[[1,2,4,5,7,8,9,10,12],[3,6,11]]=>9
[[1,2,4,5,7,8,9,11,12],[3,6,10]]=>9
[[1,2,4,5,7,8,10,11,12],[3,6,9]]=>9
[[1,2,4,5,7,8,9,10,11,12],[3,6]]=>10
[[1,2,4,5,6,7,8,10,12],[3,9,11]]=>9
[[1,2,4,5,6,7,8,11,12],[3,9,10]]=>10
[[1,2,4,5,6,7,9,10,12],[3,8,11]]=>9
[[1,2,4,5,6,7,9,11,12],[3,8,10]]=>9
[[1,2,4,5,6,7,10,11,12],[3,8,9]]=>10
[[1,2,4,5,6,8,9,10,12],[3,7,11]]=>9
[[1,2,4,5,6,8,9,11,12],[3,7,10]]=>9
[[1,2,4,5,6,8,10,11,12],[3,7,9]]=>9
[[1,2,4,5,6,8,9,10,11,12],[3,7]]=>10
[[1,2,4,5,6,7,8,9,10,12],[3,11]]=>10
[[1,2,4,5,6,7,8,9,11,12],[3,10]]=>10
[[1,2,4,5,6,7,8,10,11,12],[3,9]]=>10
[[1,2,4,5,6,7,9,10,11,12],[3,8]]=>10
[[1,2,4,5,6,7,8,9,10,11,12],[3]]=>11
[[1,2,3,4,6,8,10,12],[5,7,9,11]]=>8
[[1,2,3,4,6,8,11,12],[5,7,9,10]]=>9
[[1,2,3,4,6,9,10,12],[5,7,8,11]]=>9
[[1,2,3,4,6,9,11,12],[5,7,8,10]]=>9
[[1,2,3,4,6,9,10,11,12],[5,7,8]]=>10
[[1,2,3,4,7,8,10,12],[5,6,9,11]]=>9
[[1,2,3,4,7,8,11,12],[5,6,9,10]]=>10
[[1,2,3,4,7,9,10,12],[5,6,8,11]]=>9
[[1,2,3,4,7,9,11,12],[5,6,8,10]]=>9
[[1,2,3,4,7,9,10,11,12],[5,6,8]]=>10
[[1,2,3,4,7,8,9,10,12],[5,6,11]]=>10
[[1,2,3,4,7,8,9,11,12],[5,6,10]]=>10
[[1,2,3,4,7,8,10,11,12],[5,6,9]]=>10
[[1,2,3,4,7,8,9,10,11,12],[5,6]]=>11
[[1,2,3,5,6,8,10,12],[4,7,9,11]]=>8
[[1,2,3,5,6,8,11,12],[4,7,9,10]]=>9
[[1,2,3,5,6,9,10,12],[4,7,8,11]]=>9
[[1,2,3,5,6,9,11,12],[4,7,8,10]]=>9
[[1,2,3,5,6,9,10,11,12],[4,7,8]]=>10
[[1,2,3,5,7,8,10,12],[4,6,9,11]]=>8
[[1,2,3,5,7,8,11,12],[4,6,9,10]]=>9
[[1,2,3,5,7,9,10,12],[4,6,8,11]]=>8
[[1,2,3,5,7,9,11,12],[4,6,8,10]]=>8
[[1,2,3,5,7,9,10,11,12],[4,6,8]]=>9
[[1,2,3,5,7,8,9,10,12],[4,6,11]]=>9
[[1,2,3,5,7,8,9,11,12],[4,6,10]]=>9
[[1,2,3,5,7,8,10,11,12],[4,6,9]]=>9
[[1,2,3,5,7,8,9,10,11,12],[4,6]]=>10
[[1,2,3,5,6,7,8,10,12],[4,9,11]]=>9
[[1,2,3,5,6,7,8,11,12],[4,9,10]]=>10
[[1,2,3,5,6,7,9,10,12],[4,8,11]]=>9
[[1,2,3,5,6,7,9,11,12],[4,8,10]]=>9
[[1,2,3,5,6,7,10,11,12],[4,8,9]]=>10
[[1,2,3,5,6,8,9,10,12],[4,7,11]]=>9
[[1,2,3,5,6,8,9,11,12],[4,7,10]]=>9
[[1,2,3,5,6,8,10,11,12],[4,7,9]]=>9
[[1,2,3,5,6,8,9,10,11,12],[4,7]]=>10
[[1,2,3,5,6,7,8,9,10,12],[4,11]]=>10
[[1,2,3,5,6,7,8,9,11,12],[4,10]]=>10
[[1,2,3,5,6,7,8,10,11,12],[4,9]]=>10
[[1,2,3,5,6,7,9,10,11,12],[4,8]]=>10
[[1,2,3,5,6,7,8,9,10,11,12],[4]]=>11
[[1,2,3,4,5,6,8,10,12],[7,9,11]]=>9
[[1,2,3,4,5,6,8,11,12],[7,9,10]]=>10
[[1,2,3,4,5,6,9,10,12],[7,8,11]]=>10
[[1,2,3,4,5,6,9,11,12],[7,8,10]]=>10
[[1,2,3,4,5,6,10,11,12],[7,8,9]]=>11
[[1,2,3,4,5,7,8,10,12],[6,9,11]]=>9
[[1,2,3,4,5,7,8,11,12],[6,9,10]]=>10
[[1,2,3,4,5,7,9,10,12],[6,8,11]]=>9
[[1,2,3,4,5,7,9,11,12],[6,8,10]]=>9
[[1,2,3,4,5,7,10,11,12],[6,8,9]]=>10
[[1,2,3,4,5,8,9,10,12],[6,7,11]]=>10
[[1,2,3,4,5,8,9,11,12],[6,7,10]]=>10
[[1,2,3,4,5,8,10,11,12],[6,7,9]]=>10
[[1,2,3,4,5,8,9,10,11,12],[6,7]]=>11
[[1,2,3,4,6,7,8,10,12],[5,9,11]]=>9
[[1,2,3,4,6,7,8,11,12],[5,9,10]]=>10
[[1,2,3,4,6,7,9,10,12],[5,8,11]]=>9
[[1,2,3,4,6,7,9,11,12],[5,8,10]]=>9
[[1,2,3,4,6,7,10,11,12],[5,8,9]]=>10
[[1,2,3,4,6,8,9,10,12],[5,7,11]]=>9
[[1,2,3,4,6,8,9,11,12],[5,7,10]]=>9
[[1,2,3,4,6,8,10,11,12],[5,7,9]]=>9
[[1,2,3,4,6,8,9,10,11,12],[5,7]]=>10
[[1,2,3,4,6,7,8,9,10,12],[5,11]]=>10
[[1,2,3,4,6,7,8,9,11,12],[5,10]]=>10
[[1,2,3,4,6,7,8,10,11,12],[5,9]]=>10
[[1,2,3,4,6,7,9,10,11,12],[5,8]]=>10
[[1,2,3,4,6,7,8,9,10,11,12],[5]]=>11
[[1,2,3,4,5,6,7,8,10,12],[9,11]]=>10
[[1,2,3,4,5,6,7,8,11,12],[9,10]]=>11
[[1,2,3,4,5,6,7,9,10,12],[8,11]]=>10
[[1,2,3,4,5,6,7,9,11,12],[8,10]]=>10
[[1,2,3,4,5,6,7,10,11,12],[8,9]]=>11
[[1,2,3,4,5,6,8,9,10,12],[7,11]]=>10
[[1,2,3,4,5,6,8,9,11,12],[7,10]]=>10
[[1,2,3,4,5,6,8,10,11,12],[7,9]]=>10
[[1,2,3,4,5,6,9,10,11,12],[7,8]]=>11
[[1,2,3,4,5,7,8,9,10,12],[6,11]]=>10
[[1,2,3,4,5,7,8,9,11,12],[6,10]]=>10
[[1,2,3,4,5,7,8,10,11,12],[6,9]]=>10
[[1,2,3,4,5,7,9,10,11,12],[6,8]]=>10
[[1,2,3,4,5,7,8,9,10,11,12],[6]]=>11
[[1,2,3,4,5,6,7,8,9,10,12],[11]]=>11
[[1,2,3,4,5,6,7,8,9,11,12],[10]]=>11
[[1,2,3,4,5,6,7,8,10,11,12],[9]]=>11
[[1,2,3,4,5,6,7,9,10,11,12],[8]]=>11
[[1,2,3,4,5,6,8,9,10,11,12],[7]]=>11
[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]]=>10
[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]]=>10
[[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]]=>9
[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]]=>10
[[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]]=>9
[[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]=>9
[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]]=>10
[[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]]=>9
[[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]]=>9
[[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]]=>9
[[1,3,4,8,13],[2,6,7,12],[5,10,11],[9]]=>10
[[1,2,7,8,13],[3,4,11,12],[5,6],[9,10]]=>10
[[1,4,7,8,13],[2,6,11,12],[3,10],[5],[9]]=>9
[[1,2,5,12,13],[3,4,8],[6,7,11],[9,10]]=>10
[[1,4,5,12,13],[2,7,8],[3,10,11],[6],[9]]=>9
[[1,3,8,12,13],[2,5,11],[4,7],[6,10],[9]]=>9
[[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]]=>10
[[1,4,5,9],[2,7,8,13],[3,11,12],[6],[10]]=>9
[[1,3,8,9],[2,5,12,13],[4,7],[6,11],[10]]=>9
[[1,3,6,13],[2,5,9],[4,8,12],[7,11],[10]]=>9
[[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]]=>11
[[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]]=>10
[[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]]=>11
[[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]]=>11
[[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]]=>10
[[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]]=>10
[[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]]=>11
[[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]]=>11
[[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]]=>11
[[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]]=>11
[[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]]=>11
[[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]]=>12
[[1,2,5,6,7,8,9],[3,4,10,11,12,13,14]]=>12
[[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]]=>11
[[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]]=>10
[[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]]=>11
[[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]]=>11
[[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]]=>10
[[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]]=>10
[[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]]=>11
[[1,2,3,4,5,11,12],[6,7,8,9,10,13,14]]=>12
[[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]]=>11
[[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]]=>11
[[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]]=>11
[[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]]=>11
[[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]]=>12
[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]]=>11
[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]]=>10
[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]]=>10
[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]]=>10
[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]]=>10
[[1,2,5,9,14],[3,4,8,13],[6,7,12],[10,11]]=>11
[[1,4,5,9,14],[2,7,8,13],[3,11,12],[6],[10]]=>10
[[1,3,8,9,14],[2,5,12,13],[4,7],[6,11],[10]]=>10
[[1,3,6,13,14],[2,5,9],[4,8,12],[7,11],[10]]=>10
[[1,3,6,10],[2,5,9,14],[4,8,13],[7,12],[11]]=>10
[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]]=>11
[[1,3,6,10,15],[2,5,9,14],[4,8,13],[7,12],[11]]=>11
[[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]]=>13
[[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]]=>12
[[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]]=>13
[[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]]=>13
[[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]]=>13
[[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]]=>13
[[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]]=>14
[[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]]=>13
[[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]]=>12
[[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]]=>13
[[1,2,3,4,5,6,10,15],[7,8,9,11,12,13,14,16]]=>13
[[1,2,3,4,5,6,9,15],[7,8,10,11,12,13,14,16]]=>13
[[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]]=>13
[[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]]=>14
[[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]]=>16
[[1,3,4,5,6,7,8,9,10],[2,11,12,13,14,15,16,17,18]]=>16
[[1,2,3,4,5,6,7,9,17],[8,10,11,12,13,14,15,16,18]]=>15
[[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]]=>15
[[1,2,3,4,5,6,7,10,17],[8,9,11,12,13,14,15,16,18]]=>15
[[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]]=>15
[[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]]=>15
[[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]]=>15
[[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]]=>18
[[1,3,4,5,6,7,8,9,10,11],[2,12,13,14,15,16,17,18,19,20]]=>18
[[1,2,3,4,5,6,7,8,10,19],[9,11,12,13,14,15,16,17,18,20]]=>17
[[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]]=>17
[[1,2,3,4,5,6,7,8,9,10,21],[11,12,13,14,15,16,17,18,19,20,22]]=>20
[[1,3,4,5,6,7,8,9,10,11,12],[2,13,14,15,16,17,18,19,20,21,22]]=>20
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Description
The number of ascents of a standard tableau.
Entry $i$ of a standard Young tableau is an ascent if $i+1$ appears to the right or above $i$ in the tableau (with respect to the English notation for tableaux).
Entry $i$ of a standard Young tableau is an ascent if $i+1$ appears to the right or above $i$ in the tableau (with respect to the English notation for tableaux).
References
[1] Sagan, B. E. The Symmetric Group DOI:10.1007/978-1-4757-6804-6
[2] The number of descents of a standard tableau. The number of descents of a standard tableau. St000157
[2] The number of descents of a standard tableau. The number of descents of a standard tableau. St000157
Code
def statistic(t): return t.size() - t.standard_number_of_descents()
Created
May 25, 2016 at 17:00 by Franco Saliola
Updated
Apr 14, 2018 at 17:27 by Martin Rubey
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