- FindStat

Identifier

Mp00189: Skew partitions —rotate⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000069: Posets ⟶ ℤ

Values

[[1],[]] => [[1],[]] => ([],1) => 1

[[2],[]] => [[2],[]] => ([(0,1)],2) => 1

[[1,1],[]] => [[1,1],[]] => ([(0,1)],2) => 1

[[2,1],[1]] => [[2,1],[1]] => ([],2) => 2

[[3],[]] => [[3],[]] => ([(0,2),(2,1)],3) => 1

[[2,1],[]] => [[2,2],[1]] => ([(0,2),(1,2)],3) => 1

[[3,1],[1]] => [[3,2],[2]] => ([(1,2)],3) => 2

[[2,2],[1]] => [[2,1],[]] => ([(0,1),(0,2)],3) => 2

[[3,2],[2]] => [[3,1],[1]] => ([(1,2)],3) => 2

[[1,1,1],[]] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 1

[[2,2,1],[1,1]] => [[2,1,1],[1]] => ([(1,2)],3) => 2

[[2,1,1],[1]] => [[2,2,1],[1,1]] => ([(1,2)],3) => 2

[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => ([],3) => 3

[[4],[]] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 1

[[3,1],[]] => [[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => 1

[[4,1],[1]] => [[4,3],[3]] => ([(1,2),(2,3)],4) => 2

[[2,2],[]] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1

[[3,2],[1]] => [[3,2],[1]] => ([(0,3),(1,2),(1,3)],4) => 2

[[4,2],[2]] => [[4,2],[2]] => ([(0,3),(1,2)],4) => 2

[[2,1,1],[]] => [[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => 1

[[3,2,1],[1,1]] => [[3,2,2],[2,1]] => ([(1,3),(2,3)],4) => 2

[[3,1,1],[1]] => [[3,3,2],[2,2]] => ([(0,3),(1,2)],4) => 2

[[4,2,1],[2,1]] => [[4,3,2],[3,2]] => ([(2,3)],4) => 3

[[3,3],[2]] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 2

[[4,3],[3]] => [[4,1],[1]] => ([(1,2),(2,3)],4) => 2

[[2,2,1],[1]] => [[2,2,1],[1]] => ([(0,3),(1,2),(1,3)],4) => 2

[[3,3,1],[2,1]] => [[3,2,1],[2]] => ([(1,2),(1,3)],4) => 3

[[3,2,1],[2]] => [[3,3,1],[2,1]] => ([(1,3),(2,3)],4) => 2

[[4,3,1],[3,1]] => [[4,3,1],[3,1]] => ([(2,3)],4) => 3

[[2,2,2],[1,1]] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 2

[[3,3,2],[2,2]] => [[3,1,1],[1]] => ([(0,3),(1,2)],4) => 2

[[3,2,2],[2,1]] => [[3,2,1],[1,1]] => ([(1,2),(1,3)],4) => 3

[[4,3,2],[3,2]] => [[4,2,1],[2,1]] => ([(2,3)],4) => 3

[[1,1,1,1],[]] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 1

[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] => ([(1,2),(2,3)],4) => 2

[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] => ([(0,3),(1,2)],4) => 2

[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] => ([(2,3)],4) => 3

[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] => ([(1,2),(2,3)],4) => 2

[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] => ([(2,3)],4) => 3

[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] => ([(2,3)],4) => 3

[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => ([],4) => 4

[[5],[]] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[[4,1],[]] => [[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 1

[[5,1],[1]] => [[5,4],[4]] => ([(1,4),(3,2),(4,3)],5) => 2

[[3,2],[]] => [[3,3],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1

[[4,2],[1]] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 2

[[5,2],[2]] => [[5,3],[3]] => ([(0,3),(1,4),(4,2)],5) => 2

[[3,1,1],[]] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 1

[[4,2,1],[1,1]] => [[4,3,3],[3,2]] => ([(1,4),(2,3),(3,4)],5) => 2

[[4,1,1],[1]] => [[4,4,3],[3,3]] => ([(0,3),(1,4),(4,2)],5) => 2

[[5,2,1],[2,1]] => [[5,4,3],[4,3]] => ([(2,3),(3,4)],5) => 3

[[3,3],[1]] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 2

[[4,3],[2]] => [[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 2

[[5,3],[3]] => [[5,2],[2]] => ([(0,3),(1,4),(4,2)],5) => 2

[[2,2,1],[]] => [[2,2,2],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1

[[3,3,1],[1,1]] => [[3,2,2],[2]] => ([(1,2),(1,3),(2,4),(3,4)],5) => 2

[[3,2,1],[1]] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2

[[4,3,1],[2,1]] => [[4,3,2],[3,1]] => ([(1,4),(2,3),(2,4)],5) => 3

[[4,2,1],[2]] => [[4,4,2],[3,2]] => ([(0,4),(1,4),(2,3)],5) => 2

[[5,3,1],[3,1]] => [[5,4,2],[4,2]] => ([(1,4),(2,3)],5) => 3

[[3,2,2],[1,1]] => [[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2

[[4,3,2],[2,2]] => [[4,2,2],[2,1]] => ([(0,4),(1,4),(2,3)],5) => 2

[[4,2,2],[2,1]] => [[4,3,2],[2,2]] => ([(0,4),(1,2),(1,3)],5) => 3

[[5,3,2],[3,2]] => [[5,3,2],[3,2]] => ([(1,4),(2,3)],5) => 3

[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 1

[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] => ([(1,4),(2,3),(3,4)],5) => 2

[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] => ([(0,4),(1,4),(2,3)],5) => 2

[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] => ([(2,4),(3,4)],5) => 3

[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] => ([(0,3),(1,4),(4,2)],5) => 2

[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] => ([(1,4),(2,3)],5) => 3

[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] => ([(1,4),(2,3)],5) => 3

[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] => ([(3,4)],5) => 4

[[4,4],[3]] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 2

[[5,4],[4]] => [[5,1],[1]] => ([(1,4),(3,2),(4,3)],5) => 2

[[3,3,1],[2]] => [[3,3,1],[2]] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2

[[4,4,1],[3,1]] => [[4,3,1],[3]] => ([(1,3),(1,4),(4,2)],5) => 3

[[4,3,1],[3]] => [[4,4,1],[3,1]] => ([(1,4),(2,3),(3,4)],5) => 2

[[5,4,1],[4,1]] => [[5,4,1],[4,1]] => ([(2,3),(3,4)],5) => 3

[[2,2,2],[1]] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 2

[[3,3,2],[2,1]] => [[3,2,1],[1]] => ([(0,3),(0,4),(1,2),(1,4)],5) => 3

[[4,4,2],[3,2]] => [[4,2,1],[2]] => ([(0,4),(1,2),(1,3)],5) => 3

[[3,2,2],[2]] => [[3,3,1],[1,1]] => ([(1,2),(1,3),(2,4),(3,4)],5) => 2

[[4,3,2],[3,1]] => [[4,3,1],[2,1]] => ([(1,4),(2,3),(2,4)],5) => 3

[[5,4,2],[4,2]] => [[5,3,1],[3,1]] => ([(1,4),(2,3)],5) => 3

[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] => ([(0,3),(1,2),(1,4),(3,4)],5) => 2

[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] => ([(1,4),(2,3),(2,4)],5) => 3

[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] => ([(0,4),(1,2),(1,3)],5) => 3

[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] => ([(2,3),(2,4)],5) => 4

[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] => ([(1,4),(2,3),(3,4)],5) => 2

[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] => ([(2,4),(3,4)],5) => 3

[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] => ([(1,4),(2,3)],5) => 3

[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] => ([(3,4)],5) => 4

[[3,3,3],[2,2]] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 2

[[4,4,3],[3,3]] => [[4,1,1],[1]] => ([(0,3),(1,4),(4,2)],5) => 2

[[4,3,3],[3,2]] => [[4,2,1],[1,1]] => ([(1,3),(1,4),(4,2)],5) => 3

[[5,4,3],[4,3]] => [[5,2,1],[2,1]] => ([(2,3),(3,4)],5) => 3

[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => 2

[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] => ([(1,3),(1,4),(4,2)],5) => 3

[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] => ([(0,4),(1,4),(2,3)],5) => 2

[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] => ([(1,4),(2,3)],5) => 3

[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] => ([(1,4),(2,3),(2,4)],5) => 3

>>> Load all 1054 entries. <<<

[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] => ([(2,3),(2,4)],5) => 4

[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] => ([(2,4),(3,4)],5) => 3

[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] => ([(3,4)],5) => 4

[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 2

[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] => ([(0,3),(1,4),(4,2)],5) => 2

[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] => ([(0,4),(1,2),(1,3)],5) => 3

[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] => ([(1,4),(2,3)],5) => 3

[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] => ([(1,3),(1,4),(4,2)],5) => 3

[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] => ([(1,4),(2,3)],5) => 3

[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] => ([(2,3),(2,4)],5) => 4

[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] => ([(3,4)],5) => 4

[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] => ([(1,4),(3,2),(4,3)],5) => 2

[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(4,2)],5) => 2

[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] => ([(2,3),(3,4)],5) => 3

[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] => ([(0,3),(1,4),(4,2)],5) => 2

[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] => ([(1,4),(2,3)],5) => 3

[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] => ([(1,4),(2,3)],5) => 3

[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] => ([(3,4)],5) => 4

[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] => ([(1,4),(3,2),(4,3)],5) => 2

[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] => ([(2,3),(3,4)],5) => 3

[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] => ([(1,4),(2,3)],5) => 3

[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => ([(3,4)],5) => 4

[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] => ([(2,3),(3,4)],5) => 3

[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] => ([(3,4)],5) => 4

[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] => ([(3,4)],5) => 4

[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => ([],5) => 5

[[6],[]] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[[5,1],[]] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1

[[6,1],[1]] => [[6,5],[5]] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2

[[4,2],[]] => [[4,4],[2]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 1

[[5,2],[1]] => [[5,4],[3]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 2

[[6,2],[2]] => [[6,4],[4]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[4,1,1],[]] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 1

[[5,2,1],[1,1]] => [[5,4,4],[4,3]] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2

[[5,1,1],[1]] => [[5,5,4],[4,4]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[6,2,1],[2,1]] => [[6,5,4],[5,4]] => ([(2,3),(3,5),(5,4)],6) => 3

[[3,3],[]] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[[4,3],[1]] => [[4,3],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 2

[[5,3],[2]] => [[5,3],[2]] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 2

[[6,3],[3]] => [[6,3],[3]] => ([(0,5),(1,4),(4,2),(5,3)],6) => 2

[[3,2,1],[]] => [[3,3,3],[2,1]] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 1

[[4,3,1],[1,1]] => [[4,3,3],[3,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2

[[4,2,1],[1]] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 2

[[5,3,1],[2,1]] => [[5,4,3],[4,2]] => ([(1,4),(2,3),(2,5),(4,5)],6) => 3

[[5,2,1],[2]] => [[5,5,3],[4,3]] => ([(0,5),(1,5),(2,3),(3,4)],6) => 2

[[6,3,1],[3,1]] => [[6,5,3],[5,3]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,2,2],[1,1]] => [[4,3,3],[2,2]] => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 2

[[5,3,2],[2,2]] => [[5,3,3],[3,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[5,2,2],[2,1]] => [[5,4,3],[3,3]] => ([(0,5),(1,3),(1,4),(5,2)],6) => 3

[[6,3,2],[3,2]] => [[6,4,3],[4,3]] => ([(1,3),(2,4),(4,5)],6) => 3

[[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 1

[[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2

[[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]] => ([(2,5),(3,4),(4,5)],6) => 3

[[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]] => ([(0,5),(1,4),(4,2),(5,3)],6) => 2

[[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]] => ([(1,3),(2,4),(4,5)],6) => 3

[[5,2,1,1],[2,1]] => [[5,5,4,3],[4,4,3]] => ([(1,3),(2,4),(4,5)],6) => 3

[[6,3,2,1],[3,2,1]] => [[6,5,4,3],[5,4,3]] => ([(3,4),(4,5)],6) => 4

[[4,4],[2]] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 2

[[5,4],[3]] => [[5,2],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 2

[[6,4],[4]] => [[6,2],[2]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[3,3,1],[1]] => [[3,3,2],[2]] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 2

[[4,4,1],[2,1]] => [[4,3,2],[3]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 3

[[4,3,1],[2]] => [[4,4,2],[3,1]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2

[[5,4,1],[3,1]] => [[5,4,2],[4,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => 3

[[5,3,1],[3]] => [[5,5,2],[4,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[6,4,1],[4,1]] => [[6,5,2],[5,2]] => ([(1,3),(2,4),(4,5)],6) => 3

[[2,2,2],[]] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[[3,3,2],[1,1]] => [[3,2,2],[1]] => ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 2

[[4,4,2],[2,2]] => [[4,2,2],[2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 2

[[3,2,2],[1]] => [[3,3,2],[1,1]] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 2

[[4,3,2],[2,1]] => [[4,3,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 3

[[5,4,2],[3,2]] => [[5,3,2],[3,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[4,2,2],[2]] => [[4,4,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 2

[[5,3,2],[3,1]] => [[5,4,2],[3,2]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[6,4,2],[4,2]] => [[6,4,2],[4,2]] => ([(0,5),(1,4),(2,3)],6) => 3

[[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 1

[[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2

[[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 2

[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] => ([(2,3),(2,4),(3,5),(4,5)],6) => 3

[[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 2

[[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5)],6) => 3

[[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[5,4,2,1],[3,2,1]] => [[5,4,3,2],[4,3,1]] => ([(2,5),(3,4),(3,5)],6) => 4

[[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[5,3,2,1],[3,1,1]] => [[5,4,4,2],[4,3,2]] => ([(1,5),(2,5),(3,4)],6) => 3

[[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]] => ([(0,5),(1,4),(2,3)],6) => 3

[[6,4,2,1],[4,2,1]] => [[6,5,4,2],[5,4,2]] => ([(2,5),(3,4)],6) => 4

[[4,3,3],[2,2]] => [[4,2,2],[1,1]] => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 2

[[5,4,3],[3,3]] => [[5,2,2],[2,1]] => ([(0,5),(1,5),(2,3),(3,4)],6) => 2

[[5,3,3],[3,2]] => [[5,3,2],[2,2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[6,4,3],[4,3]] => [[6,3,2],[3,2]] => ([(1,3),(2,4),(4,5)],6) => 3

[[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2

[[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]] => ([(1,5),(2,3),(2,4),(4,5)],6) => 3

[[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]] => ([(0,5),(1,5),(2,4),(3,4)],6) => 2

[[5,4,3,1],[3,3,1]] => [[5,4,2,2],[4,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[5,3,3,1],[3,2,1]] => [[5,4,3,2],[4,2,2]] => ([(1,5),(2,3),(2,4)],6) => 4

[[5,3,2,1],[3,2]] => [[5,5,3,2],[4,3,2]] => ([(1,5),(2,5),(3,4)],6) => 3

[[6,4,3,1],[4,3,1]] => [[6,5,3,2],[5,3,2]] => ([(2,5),(3,4)],6) => 4

[[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]] => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 2

[[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]] => ([(0,5),(1,5),(2,3),(2,4)],6) => 3

[[5,4,3,2],[3,3,2]] => [[5,3,2,2],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]] => ([(0,5),(1,4),(2,3)],6) => 3

[[5,3,2,2],[3,2,1]] => [[5,4,3,2],[3,3,2]] => ([(1,5),(2,3),(2,4)],6) => 4

[[6,4,3,2],[4,3,2]] => [[6,4,3,2],[4,3,2]] => ([(2,5),(3,4)],6) => 4

[[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1

[[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2

[[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]] => ([(2,5),(3,4),(4,5)],6) => 3

[[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]] => ([(0,5),(1,5),(2,3),(3,4)],6) => 2

[[4,3,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[4,3,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]] => ([(3,5),(4,5)],6) => 4

[[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]] => ([(0,5),(1,4),(2,3)],6) => 3

[[5,3,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,2]] => ([(2,5),(3,4)],6) => 4

[[4,2,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,2]] => ([(1,3),(2,4),(4,5)],6) => 3

[[5,3,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,2]] => ([(2,5),(3,4)],6) => 4

[[5,3,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,2]] => ([(2,5),(3,4)],6) => 4

[[6,4,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,2]] => ([(4,5)],6) => 5

[[5,5],[4]] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 2

[[6,5],[5]] => [[6,1],[1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2

[[4,4,1],[3]] => [[4,4,1],[3]] => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 2

[[5,5,1],[4,1]] => [[5,4,1],[4]] => ([(1,3),(1,5),(4,2),(5,4)],6) => 3

[[5,4,1],[4]] => [[5,5,1],[4,1]] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2

[[6,5,1],[5,1]] => [[6,5,1],[5,1]] => ([(2,3),(3,5),(5,4)],6) => 3

[[3,3,2],[2]] => [[3,3,1],[1]] => ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 2

[[4,4,2],[3,1]] => [[4,3,1],[2]] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 3

[[5,5,2],[4,2]] => [[5,3,1],[3]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[4,3,2],[3]] => [[4,4,1],[2,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2

[[5,4,2],[4,1]] => [[5,4,1],[3,1]] => ([(1,4),(2,3),(2,5),(4,5)],6) => 3

[[6,5,2],[5,2]] => [[6,4,1],[4,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[3,3,1,1],[2]] => [[3,3,3,1],[2,2]] => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 2

[[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]] => ([(1,5),(2,3),(2,4),(4,5)],6) => 3

[[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]] => ([(2,3),(2,4),(4,5)],6) => 4

[[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2

[[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]] => ([(2,5),(3,4),(4,5)],6) => 3

[[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[6,5,2,1],[5,2,1]] => [[6,5,4,1],[5,4,1]] => ([(3,4),(4,5)],6) => 4

[[3,3,3],[2,1]] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 3

[[4,4,3],[3,2]] => [[4,2,1],[1]] => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 3

[[5,5,3],[4,3]] => [[5,2,1],[2]] => ([(0,5),(1,3),(1,4),(5,2)],6) => 3

[[4,3,3],[3,1]] => [[4,3,1],[1,1]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 3

[[5,4,3],[4,2]] => [[5,3,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => 3

[[6,5,3],[5,3]] => [[6,3,1],[3,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[2,2,2,1],[1]] => [[2,2,2,1],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 2

[[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 3

[[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 3

[[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]] => ([(1,4),(1,5),(2,3),(2,5)],6) => 4

[[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]] => ([(0,5),(1,5),(2,3),(2,4)],6) => 3

[[5,5,3,1],[4,3,1]] => [[5,4,2,1],[4,2]] => ([(1,5),(2,3),(2,4)],6) => 4

[[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2

[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] => ([(2,3),(2,4),(3,5),(4,5)],6) => 3

[[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5)],6) => 3

[[5,4,3,1],[4,2,1]] => [[5,4,3,1],[4,2,1]] => ([(2,5),(3,4),(3,5)],6) => 4

[[5,4,2,1],[4,2]] => [[5,5,3,1],[4,3,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[6,5,3,1],[5,3,1]] => [[6,5,3,1],[5,3,1]] => ([(2,5),(3,4)],6) => 4

[[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 3

[[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]] => ([(0,4),(0,5),(1,2),(1,3)],6) => 4

[[5,5,3,2],[4,3,2]] => [[5,3,2,1],[3,2]] => ([(1,5),(2,3),(2,4)],6) => 4

[[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]] => ([(1,5),(2,3),(2,4),(4,5)],6) => 3

[[5,4,3,2],[4,2,2]] => [[5,3,3,1],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[5,4,2,2],[4,2,1]] => [[5,4,3,1],[3,3,1]] => ([(1,5),(2,3),(2,4)],6) => 4

[[6,5,3,2],[5,3,2]] => [[6,4,3,1],[4,3,1]] => ([(2,5),(3,4)],6) => 4

[[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 2

[[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]] => ([(1,4),(2,3),(2,5),(4,5)],6) => 3

[[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[4,4,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1]] => ([(2,5),(3,4),(3,5)],6) => 4

[[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]] => ([(0,5),(1,3),(1,4),(5,2)],6) => 3

[[4,4,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2]] => ([(1,5),(2,3),(2,4)],6) => 4

[[4,4,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2]] => ([(1,5),(2,3),(2,4)],6) => 4

[[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2]] => ([(3,4),(3,5)],6) => 5

[[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2

[[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]] => ([(2,5),(3,4),(4,5)],6) => 3

[[4,3,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2,1]] => ([(3,5),(4,5)],6) => 4

[[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[5,4,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3,1]] => ([(2,5),(3,4)],6) => 4

[[5,4,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3,1]] => ([(2,5),(3,4)],6) => 4

[[6,5,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]] => ([(4,5)],6) => 5

[[4,4,4],[3,3]] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 2

[[5,5,4],[4,4]] => [[5,1,1],[1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[5,4,4],[4,3]] => [[5,2,1],[1,1]] => ([(1,3),(1,5),(4,2),(5,4)],6) => 3

[[6,5,4],[5,4]] => [[6,2,1],[2,1]] => ([(2,3),(3,5),(5,4)],6) => 3

[[3,3,3,1],[2,2]] => [[3,3,1,1],[2]] => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 2

[[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]] => ([(1,4),(1,5),(4,3),(5,2)],6) => 3

[[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]] => ([(1,5),(2,3),(2,4),(4,5)],6) => 3

[[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]] => ([(2,3),(2,4),(4,5)],6) => 4

[[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]] => ([(2,5),(3,4),(4,5)],6) => 3

[[6,5,4,1],[5,4,1]] => [[6,5,2,1],[5,2,1]] => ([(3,4),(4,5)],6) => 4

[[2,2,2,2],[1,1]] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 2

[[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]] => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 3

[[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 2

[[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]] => ([(0,5),(1,4),(2,3)],6) => 3

[[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 3

[[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]] => ([(1,4),(1,5),(2,3),(2,5)],6) => 4

[[5,4,4,2],[4,3,2]] => [[5,3,2,1],[3,1,1]] => ([(1,5),(2,3),(2,4)],6) => 4

[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] => ([(2,3),(2,4),(3,5),(4,5)],6) => 3

[[5,4,3,2],[4,3,1]] => [[5,4,2,1],[3,2,1]] => ([(2,5),(3,4),(3,5)],6) => 4

[[6,5,4,2],[5,4,2]] => [[6,4,2,1],[4,2,1]] => ([(2,5),(3,4)],6) => 4

[[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 2

[[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => 3

[[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]] => ([(2,3),(2,4),(4,5)],6) => 4

[[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2

[[4,4,3,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]] => ([(0,5),(1,4),(2,3)],6) => 3

[[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3,1]] => ([(2,5),(3,4)],6) => 4

[[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]] => ([(1,4),(2,3),(2,5),(4,5)],6) => 3

[[4,3,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1,1]] => ([(2,5),(3,4),(3,5)],6) => 4

[[4,3,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1,1]] => ([(1,5),(2,3),(2,4)],6) => 4

[[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1,1]] => ([(3,4),(3,5)],6) => 5

[[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]] => ([(2,5),(3,4),(4,5)],6) => 3

[[5,4,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2,1]] => ([(3,5),(4,5)],6) => 4

[[5,4,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2,1]] => ([(2,5),(3,4)],6) => 4

[[6,5,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2,1]] => ([(4,5)],6) => 5

[[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 2

[[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]] => ([(0,5),(1,4),(4,2),(5,3)],6) => 2

[[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]] => ([(1,4),(1,5),(4,3),(5,2)],6) => 3

[[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]] => ([(2,3),(2,4),(4,5)],6) => 4

[[6,5,4,3],[5,4,3]] => [[6,3,2,1],[3,2,1]] => ([(3,4),(4,5)],6) => 4

[[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 2

[[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]] => ([(1,3),(1,5),(4,2),(5,4)],6) => 3

[[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]] => ([(0,5),(1,5),(2,3),(3,4)],6) => 2

[[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => 3

[[4,4,3,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1,1]] => ([(1,5),(2,3),(2,4)],6) => 4

[[4,4,3,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[5,5,4,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2,1]] => ([(2,5),(3,4)],6) => 4

[[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => 3

[[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]] => ([(2,3),(2,4),(4,5)],6) => 4

[[4,3,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1,1]] => ([(1,5),(2,5),(3,4)],6) => 3

[[5,4,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1,1]] => ([(2,5),(3,4)],6) => 4

[[4,3,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2,1]] => ([(2,5),(3,4),(3,5)],6) => 4

[[5,4,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2,1]] => ([(3,4),(3,5)],6) => 5

[[5,4,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2,1]] => ([(3,5),(4,5)],6) => 4

[[6,5,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2,1]] => ([(4,5)],6) => 5

[[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 2

[[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]] => ([(0,5),(1,3),(1,4),(5,2)],6) => 3

[[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]] => ([(0,4),(1,3),(1,5),(5,2)],6) => 3

[[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]] => ([(0,5),(1,4),(2,3)],6) => 3

[[4,4,3,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2,1]] => ([(1,5),(2,3),(2,4)],6) => 4

[[5,5,4,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2,1]] => ([(2,5),(3,4)],6) => 4

[[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]] => ([(1,3),(1,5),(4,2),(5,4)],6) => 3

[[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,3,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1,1]] => ([(1,5),(2,3),(2,4)],6) => 4

[[5,4,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1,1]] => ([(2,5),(3,4)],6) => 4

[[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]] => ([(2,3),(2,4),(4,5)],6) => 4

[[5,4,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2,1]] => ([(2,5),(3,4)],6) => 4

[[5,4,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2,1]] => ([(3,4),(3,5)],6) => 5

[[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]] => ([(4,5)],6) => 5

[[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2

[[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]] => ([(2,3),(3,5),(5,4)],6) => 3

[[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]] => ([(0,5),(1,4),(4,2),(5,3)],6) => 2

[[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,4,4,3,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2,1]] => ([(3,4),(4,5)],6) => 4

[[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2

[[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[3,3,2,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1,1]] => ([(0,5),(1,4),(2,3)],6) => 3

[[4,4,3,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1,1]] => ([(2,5),(3,4)],6) => 4

[[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,4,3,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2,1]] => ([(2,5),(3,4)],6) => 4

[[4,4,3,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2,1]] => ([(2,5),(3,4)],6) => 4

[[5,5,4,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]] => ([(4,5)],6) => 5

[[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2

[[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] => ([(2,3),(3,5),(5,4)],6) => 3

[[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,3,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1,1]] => ([(3,4),(4,5)],6) => 4

[[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]] => ([(1,3),(2,4),(4,5)],6) => 3

[[4,3,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1,1]] => ([(2,5),(3,4)],6) => 4

[[4,3,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1,1]] => ([(2,5),(3,4)],6) => 4

[[5,4,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1,1]] => ([(4,5)],6) => 5

[[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]] => ([(2,3),(3,5),(5,4)],6) => 3

[[4,3,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2,1]] => ([(3,4),(4,5)],6) => 4

[[4,3,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2,1]] => ([(2,5),(3,4)],6) => 4

[[5,4,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2,1]] => ([(4,5)],6) => 5

[[4,3,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2,1]] => ([(3,4),(4,5)],6) => 4

[[5,4,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2,1]] => ([(4,5)],6) => 5

[[5,4,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2,1]] => ([(4,5)],6) => 5

[[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]] => ([],6) => 6

[[7],[]] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[[6,1],[]] => [[6,6],[5]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 1

[[7,1],[1]] => [[7,6],[6]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => 2

[[5,2],[]] => [[5,5],[3]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 1

[[6,2],[1]] => [[6,5],[4]] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => 2

[[5,1,1],[]] => [[5,5,5],[4,4]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 1

[[6,2,1],[1,1]] => [[6,5,5],[5,4]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 2

[[7,2,1],[2,1]] => [[7,6,5],[6,5]] => ([(2,6),(4,5),(5,3),(6,4)],7) => 3

[[4,3],[]] => [[4,4],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => 1

[[5,3],[1]] => [[5,4],[2]] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => 2

[[6,3],[2]] => [[6,4],[3]] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => 2

[[4,2,1],[]] => [[4,4,4],[3,2]] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 1

[[5,3,1],[1,1]] => [[5,4,4],[4,2]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 2

[[5,2,1],[1]] => [[5,5,4],[4,3]] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 2

[[6,2,1],[2]] => [[6,6,4],[5,4]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 2

[[7,3,1],[3,1]] => [[7,6,4],[6,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[5,2,2],[1,1]] => [[5,4,4],[3,3]] => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7) => 2

[[6,3,2],[2,2]] => [[6,4,4],[4,3]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[7,3,2],[3,2]] => [[7,5,4],[5,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 1

[[5,2,2,1],[1,1,1]] => [[5,4,4,4],[4,3,3]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 2

[[5,2,1,1],[1,1]] => [[5,5,4,4],[4,4,3]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[6,2,2,1],[2,1,1]] => [[6,5,5,4],[5,4,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[6,2,1,1],[2,1]] => [[6,6,5,4],[5,5,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[7,3,2,1],[3,2,1]] => [[7,6,5,4],[6,5,4]] => ([(3,4),(4,6),(6,5)],7) => 4

[[4,4],[1]] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 2

[[5,4],[2]] => [[5,3],[1]] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => 2

[[6,4],[3]] => [[6,3],[2]] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => 2

[[3,3,1],[]] => [[3,3,3],[2]] => ([(0,2),(0,3),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 1

[[4,3,1],[1]] => [[4,4,3],[3,1]] => ([(0,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => 2

[[5,4,1],[2,1]] => [[5,4,3],[4,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 3

[[5,3,1],[2]] => [[5,5,3],[4,2]] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => 2

[[7,4,1],[4,1]] => [[7,6,3],[6,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[3,2,2],[]] => [[3,3,3],[1,1]] => ([(0,2),(0,3),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 1

[[4,3,2],[1,1]] => [[4,3,3],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(4,6),(5,6)],7) => 2

[[4,2,2],[1]] => [[4,4,3],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6)],7) => 2

[[5,3,2],[2,1]] => [[5,4,3],[3,2]] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7) => 3

[[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 1

[[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2

[[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3

[[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]] => ([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7) => 2

[[5,3,2,1],[2,1,1]] => [[5,4,4,3],[4,3,2]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 3

[[6,3,2,1],[3,1,1]] => [[6,5,5,3],[5,4,3]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[7,4,2,1],[4,2,1]] => [[7,6,5,3],[6,5,3]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,3,3],[2,2]] => [[5,3,3],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7) => 2

[[7,4,3],[4,3]] => [[7,4,3],[4,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => 2

[[5,3,2,1],[2,2]] => [[5,5,3,3],[4,3,2]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 2

[[6,4,3,1],[3,3,1]] => [[6,5,3,3],[5,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[6,3,2,1],[3,2]] => [[6,6,4,3],[5,4,3]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[7,4,3,1],[4,3,1]] => [[7,6,4,3],[6,4,3]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]] => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7) => 2

[[6,4,3,2],[3,3,2]] => [[6,4,3,3],[4,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[7,4,3,2],[4,3,2]] => [[7,5,4,3],[5,4,3]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 1

[[4,2,2,2,1],[1,1,1,1]] => [[4,3,3,3,3],[3,2,2,2]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 2

[[5,3,3,2,1],[2,2,2,1]] => [[5,4,3,3,3],[4,3,2,2]] => ([(2,5),(3,4),(4,6),(5,6)],7) => 3

[[5,3,2,2,1],[2,2,1,1]] => [[5,4,4,3,3],[4,3,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[5,3,2,1,1],[2,2,1]] => [[5,5,4,3,3],[4,4,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[5,2,2,2,1],[2,1,1,1]] => [[5,4,4,4,3],[4,3,3,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[6,3,3,2,1],[3,2,2,1]] => [[6,5,4,4,3],[5,4,3,3]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,2,1,1,1],[2,1]] => [[5,5,5,4,3],[4,4,4,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[6,3,2,2,1],[3,2,1,1]] => [[6,5,5,4,3],[5,4,4,3]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,3,2,1,1],[3,2,1]] => [[6,6,5,4,3],[5,5,4,3]] => ([(2,4),(3,5),(5,6)],7) => 4

[[7,4,3,2,1],[4,3,2,1]] => [[7,6,5,4,3],[6,5,4,3]] => ([(4,5),(5,6)],7) => 5

[[5,5],[3]] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 2

[[6,5],[4]] => [[6,2],[1]] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => 2

[[4,4,1],[2]] => [[4,4,2],[3]] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 2

[[5,5,1],[3,1]] => [[5,4,2],[4]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => 3

[[5,4,1],[3]] => [[5,5,2],[4,1]] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 2

[[6,5,1],[4,1]] => [[6,5,2],[5,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 3

[[6,4,1],[4]] => [[6,6,2],[5,2]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[7,5,1],[5,1]] => [[7,6,2],[6,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[3,3,2],[1]] => [[3,3,2],[1]] => ([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(6,4),(6,5)],7) => 2

[[4,4,2],[2,1]] => [[4,3,2],[2]] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(3,6)],7) => 3

[[4,3,2],[2]] => [[4,4,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7) => 2

[[5,4,2],[3,1]] => [[5,4,2],[3,1]] => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7) => 3

[[3,3,1,1],[1]] => [[3,3,3,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6)],7) => 2

[[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4

[[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => 2

[[6,5,2,1],[4,2,1]] => [[6,5,4,2],[5,4,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => 4

[[6,4,2,1],[4,1,1]] => [[6,5,5,2],[5,4,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[7,5,2,1],[5,2,1]] => [[7,6,5,2],[6,5,2]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,3,3],[1,1]] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 2

[[4,4,3],[2,2]] => [[4,2,2],[1]] => ([(0,3),(0,6),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 2

[[4,3,3],[2,1]] => [[4,3,2],[1,1]] => ([(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5)],7) => 3

[[5,4,3],[3,2]] => [[5,3,2],[2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 3

[[2,2,2,1],[]] => [[2,2,2,2],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => 1

[[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7) => 2

[[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]] => ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => 2

[[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]] => ([(0,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => 2

[[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]] => ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => 3

[[5,4,2,1],[3,2]] => [[5,5,3,2],[4,3,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 3

[[6,5,3,1],[4,3,1]] => [[6,5,3,2],[5,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,3,2,1],[3,1]] => [[5,5,4,2],[4,3,2]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 3

[[6,4,3,1],[4,2,1]] => [[6,5,4,2],[5,3,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,4,2,1],[4,2]] => [[6,6,4,2],[5,4,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[7,5,3,1],[5,3,1]] => [[7,6,4,2],[6,4,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]] => ([(0,4),(0,6),(1,2),(1,3),(3,6),(4,5),(6,5)],7) => 2

[[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 3

[[5,4,3,2],[3,2,2]] => [[5,3,3,2],[3,2,1]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 3

[[6,5,3,2],[4,3,2]] => [[6,4,3,2],[4,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,4,3,2],[4,2,2]] => [[6,4,4,2],[4,3,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[7,5,3,2],[5,3,2]] => [[7,5,4,2],[5,4,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 1

[[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 2

[[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3

[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] => ([(3,4),(3,5),(4,6),(5,6)],7) => 4

[[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 2

[[4,3,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,1]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 3

[[4,3,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,1]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 3

[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]] => ([(2,6),(3,5),(4,5),(4,6)],7) => 4

[[5,4,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,4,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,5,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[4,2,1,1,1],[2]] => [[4,4,4,4,2],[3,3,3,2]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[5,3,2,2,1],[3,1,1,1]] => [[5,4,4,4,2],[4,3,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[5,3,2,1,1],[3,1,1]] => [[5,5,4,4,2],[4,4,3,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[6,4,3,2,1],[4,2,2,1]] => [[6,5,4,4,2],[5,4,3,2]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,4,2,2,1],[4,2,1,1]] => [[6,5,5,4,2],[5,4,4,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,4,2,1,1],[4,2,1]] => [[6,6,5,4,2],[5,5,4,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[7,5,3,2,1],[5,3,2,1]] => [[7,6,5,4,2],[6,5,4,2]] => ([(3,6),(4,5)],7) => 5

[[5,4,4],[3,3]] => [[5,2,2],[1,1]] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7) => 2

[[6,5,4],[4,4]] => [[6,2,2],[2,1]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 2

[[6,4,4],[4,3]] => [[6,3,2],[2,2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[7,5,4],[5,4]] => [[7,3,2],[3,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2

[[5,4,3,1],[3,3]] => [[5,5,2,2],[4,2,1]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 2

[[6,5,4,1],[4,4,1]] => [[6,5,2,2],[5,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[6,4,3,1],[4,3]] => [[6,6,3,2],[5,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[7,5,4,1],[5,4,1]] => [[7,6,3,2],[6,3,2]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 2

[[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]] => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7) => 3

[[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]] => ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => 2

[[5,4,3,2],[3,3,1]] => [[5,4,2,2],[3,2,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 3

[[6,5,4,2],[4,4,2]] => [[6,4,2,2],[4,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[6,4,3,2],[4,3,1]] => [[6,5,3,2],[4,3,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[7,5,4,2],[5,4,2]] => [[7,5,3,2],[5,3,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => 2

[[4,3,2,1,1],[2,2]] => [[4,4,4,2,2],[3,3,2,1]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 2

[[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]] => ([(1,6),(2,6),(3,5),(4,5)],7) => 3

[[5,4,3,1,1],[3,3,1]] => [[5,5,4,2,2],[4,4,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[6,5,4,2,1],[4,4,2,1]] => [[6,5,4,2,2],[5,4,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,3,3,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,2,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,4,4,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,2,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,3,2,1,1],[3,2]] => [[5,5,5,3,2],[4,4,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[6,4,3,2,1],[4,3,1,1]] => [[6,5,5,3,2],[5,4,3,2]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,4,3,1,1],[4,3,1]] => [[6,6,5,3,2],[5,5,3,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[7,5,4,2,1],[5,4,2,1]] => [[7,6,5,3,2],[6,5,3,2]] => ([(3,6),(4,5)],7) => 5

[[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]] => ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 2

[[5,4,3,3],[3,3,2]] => [[5,3,2,2],[2,2,1]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 3

[[6,5,4,3],[4,4,3]] => [[6,3,2,2],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[7,5,4,3],[5,4,3]] => [[7,4,3,2],[4,3,2]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 2

[[4,3,3,2,1],[2,2,2]] => [[4,4,2,2,2],[3,2,1,1]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 2

[[5,4,4,3,1],[3,3,3,1]] => [[5,4,2,2,2],[4,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[4,3,2,2,1],[2,2,1]] => [[4,4,3,2,2],[3,2,2,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 3

[[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => 4

[[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]] => ([(1,6),(2,6),(3,5),(4,5)],7) => 3

[[6,5,4,3,1],[4,4,3,1]] => [[6,5,3,2,2],[5,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,3,3,2,1],[3,2,2]] => [[5,5,3,3,2],[4,3,2,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[6,4,4,3,1],[4,3,3,1]] => [[6,5,3,3,2],[5,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,3,2,2,1],[3,2,1]] => [[5,5,4,3,2],[4,3,3,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,4,3,3,1],[4,3,2,1]] => [[6,5,4,3,2],[5,3,3,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,4,3,2,1],[4,3,2]] => [[6,6,4,3,2],[5,4,3,2]] => ([(2,6),(3,6),(4,5)],7) => 4

[[7,5,4,3,1],[5,4,3,1]] => [[7,6,4,3,2],[6,4,3,2]] => ([(3,6),(4,5)],7) => 5

[[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]] => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7) => 2

[[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[5,4,4,3,2],[3,3,3,2]] => [[5,3,2,2,2],[3,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[4,3,2,2,2],[2,2,1,1]] => [[4,3,3,2,2],[2,2,2,1]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 3

[[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => 4

[[6,5,4,3,2],[4,4,3,2]] => [[6,4,3,2,2],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[6,4,4,3,2],[4,3,3,2]] => [[6,4,3,3,2],[4,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,4,3,3,2],[4,3,2,2]] => [[6,4,4,3,2],[4,3,3,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,4,3,2,2],[4,3,2,1]] => [[6,5,4,3,2],[4,4,3,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[7,5,4,3,2],[5,4,3,2]] => [[7,5,4,3,2],[5,4,3,2]] => ([(3,6),(4,5)],7) => 5

[[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 1

[[3,2,2,2,2,1],[1,1,1,1,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 2

[[3,2,2,2,1,1],[1,1,1,1]] => [[3,3,2,2,2,2],[2,2,1,1,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[4,3,3,2,2,1],[2,2,2,1,1]] => [[4,3,3,2,2,2],[3,2,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[4,3,3,2,1,1],[2,2,2,1]] => [[4,4,3,2,2,2],[3,3,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[3,2,1,1,1,1],[1,1]] => [[3,3,3,3,2,2],[2,2,2,2,1]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 2

[[4,3,2,2,2,1],[2,2,1,1,1]] => [[4,3,3,3,2,2],[3,2,2,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[4,3,2,2,1,1],[2,2,1,1]] => [[4,4,3,3,2,2],[3,3,2,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[5,4,3,3,2,1],[3,3,2,2,1]] => [[5,4,3,3,2,2],[4,3,2,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[4,3,2,1,1,1],[2,2,1]] => [[4,4,4,3,2,2],[3,3,3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[5,4,3,2,2,1],[3,3,2,1,1]] => [[5,4,4,3,2,2],[4,3,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,4,3,2,1,1],[3,3,2,1]] => [[5,5,4,3,2,2],[4,4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2,2],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => 5

[[4,2,2,2,2,1],[2,1,1,1,1]] => [[4,3,3,3,3,2],[3,2,2,2,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[5,3,3,3,2,1],[3,2,2,2,1]] => [[5,4,3,3,3,2],[4,3,2,2,2]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,3,3,2,2,1],[3,2,2,1,1]] => [[5,4,4,3,3,2],[4,3,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,3,3,2,1,1],[3,2,2,1]] => [[5,5,4,3,3,2],[4,4,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,3,2],[5,4,3,2,2]] => ([(3,6),(4,5)],7) => 5

[[4,2,1,1,1,1],[2,1]] => [[4,4,4,4,3,2],[3,3,3,3,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[5,3,2,2,2,1],[3,2,1,1,1]] => [[5,4,4,4,3,2],[4,3,3,3,2]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,3,2,2,1,1],[3,2,1,1]] => [[5,5,4,4,3,2],[4,4,3,3,2]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,4,3,2],[5,4,3,3,2]] => ([(3,6),(4,5)],7) => 5

[[5,3,2,1,1,1],[3,2,1]] => [[5,5,5,4,3,2],[4,4,4,3,2]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,5,4,3,2],[5,4,4,3,2]] => ([(3,6),(4,5)],7) => 5

[[6,4,3,2,1,1],[4,3,2,1]] => [[6,6,5,4,3,2],[5,5,4,3,2]] => ([(3,6),(4,5)],7) => 5

[[7,5,4,3,2,1],[5,4,3,2,1]] => [[7,6,5,4,3,2],[6,5,4,3,2]] => ([(5,6)],7) => 6

[[6,6],[5]] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 2

[[7,6],[6]] => [[7,1],[1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => 2

[[5,5,1],[4]] => [[5,5,1],[4]] => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7) => 2

[[6,5,1],[5]] => [[6,6,1],[5,1]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 2

[[7,6,1],[6,1]] => [[7,6,1],[6,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => 3

[[4,4,2],[3]] => [[4,4,1],[2]] => ([(0,4),(0,6),(1,2),(1,3),(3,6),(4,5),(6,5)],7) => 2

[[5,5,2],[4,1]] => [[5,4,1],[3]] => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7) => 3

[[6,6,2],[5,2]] => [[6,4,1],[4]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[5,4,2],[4]] => [[5,5,1],[3,1]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 2

[[7,6,2],[6,2]] => [[7,5,1],[5,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,4,1,1],[3]] => [[4,4,4,1],[3,3]] => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7) => 2

[[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[5,4,1,1],[4]] => [[5,5,5,1],[4,4,1]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 2

[[6,5,1,1],[5,1]] => [[6,6,5,1],[5,5,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[7,6,2,1],[6,2,1]] => [[7,6,5,1],[6,5,1]] => ([(3,4),(4,6),(6,5)],7) => 4

[[3,3,3],[2]] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 2

[[4,4,3],[3,1]] => [[4,3,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => 3

[[5,5,3],[4,2]] => [[5,3,1],[2]] => ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7) => 3

[[5,4,3],[4,1]] => [[5,4,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 3

[[7,6,3],[6,3]] => [[7,4,1],[4,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[3,3,2,1],[2]] => [[3,3,3,1],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(4,6),(5,6)],7) => 2

[[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 3

[[5,5,2,1],[4,2]] => [[5,5,3,1],[4,3]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 3

[[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2

[[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3

[[5,4,2,1],[4,1]] => [[5,5,4,1],[4,3,1]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 3

[[6,5,2,1],[5,2]] => [[6,6,4,1],[5,4,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[7,6,3,1],[6,3,1]] => [[7,6,4,1],[6,4,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]] => ([(0,3),(0,5),(1,2),(1,4),(4,6),(5,6)],7) => 3

[[6,5,3,2],[5,2,2]] => [[6,4,4,1],[4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[7,6,3,2],[6,3,2]] => [[7,5,4,1],[5,4,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]] => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7) => 2

[[6,6,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3]] => ([(3,4),(3,5),(5,6)],7) => 5

[[4,3,1,1,1],[3]] => [[4,4,4,4,1],[3,3,3,1]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 2

[[5,4,2,2,1],[4,1,1,1]] => [[5,4,4,4,1],[4,3,3,1]] => ([(2,5),(3,4),(4,6),(5,6)],7) => 3

[[5,4,2,1,1],[4,1,1]] => [[5,5,4,4,1],[4,4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[5,4,1,1,1],[4,1]] => [[5,5,5,4,1],[4,4,4,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[6,5,2,2,1],[5,2,1,1]] => [[6,5,5,4,1],[5,4,4,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,5,2,1,1],[5,2,1]] => [[6,6,5,4,1],[5,5,4,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[7,6,3,2,1],[6,3,2,1]] => [[7,6,5,4,1],[6,5,4,1]] => ([(4,5),(5,6)],7) => 5

[[4,4,4],[3,2]] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 3

[[5,5,4],[4,3]] => [[5,2,1],[1]] => ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7) => 3

[[5,4,4],[4,2]] => [[5,3,1],[1,1]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => 3

[[6,5,4],[5,3]] => [[6,3,1],[2,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 3

[[7,6,4],[6,4]] => [[7,3,1],[3,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[3,3,3,1],[2,1]] => [[3,3,2,1],[2]] => ([(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5)],7) => 3

[[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]] => ([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => 4

[[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]] => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7) => 3

[[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4

[[6,5,4,1],[5,3,1]] => [[6,5,3,1],[5,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => 4

[[6,5,3,1],[5,3]] => [[6,6,3,1],[5,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[7,6,4,1],[6,4,1]] => [[7,6,3,1],[6,3,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[2,2,2,2],[1]] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 2

[[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => 3

[[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(3,6)],7) => 3

[[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5)],7) => 4

[[6,5,4,2],[5,3,2]] => [[6,4,3,1],[4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,5,3,2],[5,3,1]] => [[6,5,3,1],[4,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[7,6,4,2],[6,4,2]] => [[7,5,3,1],[5,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => 2

[[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 3

[[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4

[[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7) => 3

[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]] => ([(2,5),(2,6),(3,4),(3,6)],7) => 5

[[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]] => ([(1,6),(2,6),(3,4),(3,5)],7) => 4

[[6,6,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 2

[[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3

[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] => ([(3,4),(3,5),(4,6),(5,6)],7) => 4

[[4,3,2,1,1],[3,1]] => [[4,4,4,3,1],[3,3,2,1]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 3

[[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]] => ([(2,6),(3,5),(4,5),(4,6)],7) => 4

[[5,4,3,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,5,4,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,2,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[5,4,2,1,1],[4,2]] => [[5,5,5,3,1],[4,4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[6,5,3,2,1],[5,3,1,1]] => [[6,5,5,3,1],[5,4,3,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,3,1,1],[5,3,1]] => [[6,6,5,3,1],[5,5,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[7,6,4,2,1],[6,4,2,1]] => [[7,6,5,3,1],[6,5,3,1]] => ([(3,6),(4,5)],7) => 5

[[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7) => 3

[[6,5,4,3],[5,3,3]] => [[6,3,3,1],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[7,6,4,3],[6,4,3]] => [[7,4,3,1],[4,3,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]] => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7) => 3

[[4,4,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 3

[[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]] => ([(1,5),(1,6),(2,3),(2,4)],7) => 5

[[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]] => ([(1,6),(2,6),(3,4),(3,5)],7) => 4

[[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]] => ([(1,6),(2,6),(3,5),(4,5)],7) => 3

[[6,5,4,3,1],[5,3,3,1]] => [[6,5,3,3,1],[5,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,4,2,2,1],[4,2,1]] => [[5,5,4,3,1],[4,3,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,5,3,3,1],[5,3,2,1]] => [[6,5,4,3,1],[5,3,3,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,5,3,2,1],[5,3,2]] => [[6,6,4,3,1],[5,4,3,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[7,6,4,3,1],[6,4,3,1]] => [[7,6,4,3,1],[6,4,3,1]] => ([(3,6),(4,5)],7) => 5

[[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]] => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7) => 3

[[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]] => ([(1,5),(1,6),(2,3),(2,4)],7) => 5

[[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,4,3,3,2],[4,2,2,2]] => [[5,3,3,3,1],[3,2,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => 4

[[6,5,4,3,2],[5,3,3,2]] => [[6,4,3,3,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,3,3,2],[5,3,2,2]] => [[6,4,4,3,1],[4,3,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,5,3,2,2],[5,3,2,1]] => [[6,5,4,3,1],[4,4,3,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[7,6,4,3,2],[6,4,3,2]] => [[7,5,4,3,1],[5,4,3,1]] => ([(3,6),(4,5)],7) => 5

[[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => 2

[[4,4,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[4,4,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,5,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[5,5,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,5,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,5,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]] => ([(4,5),(4,6)],7) => 6

[[3,2,1,1,1,1],[2]] => [[3,3,3,3,3,1],[2,2,2,2,1]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 2

[[4,3,2,2,1,1],[3,1,1,1]] => [[4,4,3,3,3,1],[3,3,2,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[4,3,2,1,1,1],[3,1,1]] => [[4,4,4,3,3,1],[3,3,3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[5,4,3,2,2,1],[4,2,2,1,1]] => [[5,4,4,3,3,1],[4,3,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,4,3,2,1,1],[4,2,2,1]] => [[5,5,4,3,3,1],[4,4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,4,3,2,1],[5,3,3,2,1]] => [[6,5,4,3,3,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => 5

[[4,3,1,1,1,1],[3,1]] => [[4,4,4,4,3,1],[3,3,3,3,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[5,4,2,2,2,1],[4,2,1,1,1]] => [[5,4,4,4,3,1],[4,3,3,3,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,2,2,1,1],[4,2,1,1]] => [[5,5,4,4,3,1],[4,4,3,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,5,3,3,2,1],[5,3,2,2,1]] => [[6,5,4,4,3,1],[5,4,3,3,1]] => ([(3,6),(4,5)],7) => 5

[[5,4,2,1,1,1],[4,2,1]] => [[5,5,5,4,3,1],[4,4,4,3,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,5,3,2,2,1],[5,3,2,1,1]] => [[6,5,5,4,3,1],[5,4,4,3,1]] => ([(3,6),(4,5)],7) => 5

[[6,5,3,2,1,1],[5,3,2,1]] => [[6,6,5,4,3,1],[5,5,4,3,1]] => ([(3,6),(4,5)],7) => 5

[[7,6,4,3,2,1],[6,4,3,2,1]] => [[7,6,5,4,3,1],[6,5,4,3,1]] => ([(5,6)],7) => 6

[[5,5,5],[4,4]] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 2

[[7,6,5],[6,5]] => [[7,2,1],[2,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => 3

[[4,4,4,1],[3,3]] => [[4,4,1,1],[3]] => ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 2

[[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 3

[[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[6,6,5,1],[5,5,1]] => [[6,5,1,1],[5,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[7,6,5,1],[6,5,1]] => [[7,6,2,1],[6,2,1]] => ([(3,4),(4,6),(6,5)],7) => 4

[[3,3,3,2],[2,2]] => [[3,3,1,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 2

[[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7) => 3

[[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3

[[7,6,5,2],[6,5,2]] => [[7,5,2,1],[5,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7) => 2

[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]] => ([(2,5),(2,6),(5,4),(6,3)],7) => 4

[[5,5,4,2,1],[4,4,1,1]] => [[5,4,4,1,1],[4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[6,6,5,2,1],[5,5,2,1]] => [[6,5,4,1,1],[5,4,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,5,5,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,1,1]] => ([(3,4),(3,5),(5,6)],7) => 5

[[5,4,3,1,1],[4,3]] => [[5,5,5,2,1],[4,4,2,1]] => ([(2,5),(3,4),(4,6),(5,6)],7) => 3

[[6,5,4,1,1],[5,4,1]] => [[6,6,5,2,1],[5,5,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[7,6,5,2,1],[6,5,2,1]] => [[7,6,5,2,1],[6,5,2,1]] => ([(4,5),(5,6)],7) => 5

[[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => 3

[[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]] => ([(0,5),(0,6),(1,4),(1,6),(4,2),(5,3)],7) => 3

[[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]] => ([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => 4

[[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4

[[6,5,4,3],[5,4,2]] => [[6,4,2,1],[3,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => 4

[[7,6,5,3],[6,5,3]] => [[7,4,2,1],[4,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => 2

[[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => 3

[[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 3

[[4,4,4,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 3

[[4,4,3,2,1],[3,3,1]] => [[4,4,3,1,1],[3,2,1]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 3

[[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[6,6,5,3,1],[5,5,3,1]] => [[6,5,3,1,1],[5,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 3

[[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4

[[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]] => ([(2,5),(2,6),(3,4),(3,6)],7) => 5

[[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => 4

[[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3

[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] => ([(3,4),(3,5),(4,6),(5,6)],7) => 4

[[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]] => ([(2,6),(3,5),(4,5),(4,6)],7) => 4

[[6,5,4,3,1],[5,4,2,1]] => [[6,5,4,2,1],[5,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[6,5,4,2,1],[5,4,2]] => [[6,6,4,2,1],[5,4,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[7,6,5,3,1],[6,5,3,1]] => [[7,6,4,2,1],[6,4,2,1]] => ([(3,6),(4,5)],7) => 5

[[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]] => ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7) => 3

[[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[6,6,5,3,2],[5,5,3,2]] => [[6,4,3,1,1],[4,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]] => ([(1,5),(1,6),(2,3),(2,4)],7) => 5

[[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,5,4,3,2],[5,4,2,2]] => [[6,4,4,2,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,4,2,2],[5,4,2,1]] => [[6,5,4,2,1],[4,4,2,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[7,6,5,3,2],[6,5,3,2]] => [[7,5,4,2,1],[5,4,2,1]] => ([(3,6),(4,5)],7) => 5

[[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => 2

[[4,4,4,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => 4

[[5,5,5,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]] => ([(3,4),(3,5),(5,6)],7) => 5

[[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 2

[[4,4,3,2,2,1],[3,3,1,1,1]] => [[4,3,3,3,1,1],[3,2,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[4,4,3,2,1,1],[3,3,1,1]] => [[4,4,3,3,1,1],[3,3,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[5,5,4,3,2,1],[4,4,2,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,5,4,2,2,1],[4,4,2,1,1]] => [[5,4,4,3,1,1],[4,3,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,5,4,2,1,1],[4,4,2,1]] => [[5,5,4,3,1,1],[4,4,3,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,6,5,3,2,1],[5,5,3,2,1]] => [[6,5,4,3,1,1],[5,4,3,1]] => ([(3,6),(4,5)],7) => 5

[[4,3,3,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,4,4,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,1,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[5,4,4,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,4,4,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]] => ([(4,5),(4,6)],7) => 6

[[5,4,3,2,1,1],[4,3,1,1]] => [[5,5,4,4,2,1],[4,4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,4,3,2,1],[5,4,2,2,1]] => [[6,5,4,4,2,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => 5

[[5,4,3,1,1,1],[4,3,1]] => [[5,5,5,4,2,1],[4,4,4,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,5,4,2,2,1],[5,4,2,1,1]] => [[6,5,5,4,2,1],[5,4,4,2,1]] => ([(3,6),(4,5)],7) => 5

[[6,5,4,2,1,1],[5,4,2,1]] => [[6,6,5,4,2,1],[5,5,4,2,1]] => ([(3,6),(4,5)],7) => 5

[[7,6,5,3,2,1],[6,5,3,2,1]] => [[7,6,5,4,2,1],[6,5,4,2,1]] => ([(5,6)],7) => 6

[[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 2

[[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 3

[[6,5,5,4],[5,4,4]] => [[6,2,2,1],[2,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[7,6,5,4],[6,5,4]] => [[7,3,2,1],[3,2,1]] => ([(3,4),(4,6),(6,5)],7) => 4

[[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7) => 2

[[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 3

[[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[5,5,4,3,1],[4,4,3]] => [[5,5,2,1,1],[4,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[6,6,5,4,1],[5,5,4,1]] => [[6,5,2,1,1],[5,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]] => ([(2,5),(2,6),(5,4),(6,3)],7) => 4

[[5,4,4,3,1],[4,3,3]] => [[5,5,2,2,1],[4,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[6,5,5,4,1],[5,4,4,1]] => [[6,5,2,2,1],[5,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]] => ([(3,4),(3,5),(5,6)],7) => 5

[[7,6,5,4,1],[6,5,4,1]] => [[7,6,3,2,1],[6,3,2,1]] => ([(4,5),(5,6)],7) => 5

[[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 2

[[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]] => ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7) => 3

[[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,6,5,4,2],[5,5,4,2]] => [[6,4,2,1,1],[4,2,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => 3

[[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[6,5,5,4,2],[5,4,4,2]] => [[6,4,2,2,1],[4,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4

[[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]] => ([(2,5),(2,6),(3,4),(3,6)],7) => 5

[[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] => ([(3,4),(3,5),(4,6),(5,6)],7) => 4

[[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[7,6,5,4,2],[6,5,4,2]] => [[7,5,3,2,1],[5,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => 2

[[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 3

[[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[4,4,4,3,2,1],[3,3,3,1,1]] => [[4,3,3,1,1,1],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[5,5,5,4,2,1],[4,4,4,2,1]] => [[5,4,3,1,1,1],[4,3,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,4,3,3,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,5,4,4,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[4,4,3,2,1,1],[3,3,2]] => [[4,4,4,2,1,1],[3,3,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[5,5,4,3,2,1],[4,4,3,1,1]] => [[5,4,4,2,1,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,5,4,3,1,1],[4,4,3,1]] => [[5,5,4,2,1,1],[4,4,2,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,6,5,4,2,1],[5,5,4,2,1]] => [[6,5,4,2,1,1],[5,4,2,1]] => ([(3,6),(4,5)],7) => 5

[[4,3,3,3,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,1,1,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => 4

[[5,4,4,4,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]] => ([(3,4),(3,5),(5,6)],7) => 5

[[4,3,3,2,1,1],[3,2,2]] => [[4,4,4,2,2,1],[3,3,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => 3

[[5,4,4,3,2,1],[4,3,3,1,1]] => [[5,4,4,2,2,1],[4,3,2,1,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[5,4,4,3,1,1],[4,3,3,1]] => [[5,5,4,2,2,1],[4,4,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[6,5,5,4,2,1],[5,4,4,2,1]] => [[6,5,4,2,2,1],[5,4,2,1,1]] => ([(3,6),(4,5)],7) => 5

[[5,4,3,3,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,2,2,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[5,4,3,3,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]] => ([(4,5),(4,6)],7) => 6

[[6,5,4,3,2,1],[5,4,3,1,1]] => [[6,5,5,3,2,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => 5

[[6,5,4,3,1,1],[5,4,3,1]] => [[6,6,5,3,2,1],[5,5,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[7,6,5,4,2,1],[6,5,4,2,1]] => [[7,6,5,3,2,1],[6,5,3,2,1]] => ([(5,6)],7) => 6

[[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 2

[[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[6,6,5,4,3],[5,5,4,3]] => [[6,3,2,1,1],[3,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 3

[[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[6,5,5,4,3],[5,4,4,3]] => [[6,3,2,2,1],[3,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]] => ([(2,5),(2,6),(5,4),(6,3)],7) => 4

[[6,5,4,4,3],[5,4,3,3]] => [[6,3,3,2,1],[3,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] => ([(3,4),(3,5),(5,6)],7) => 5

[[7,6,5,4,3],[6,5,4,3]] => [[7,4,3,2,1],[4,3,2,1]] => ([(4,5),(5,6)],7) => 5

[[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => 2

[[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 2

[[4,4,4,4,3,1],[3,3,3,3,1]] => [[4,3,1,1,1,1],[3,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,4,4,3,2,1],[3,3,3,2]] => [[4,4,2,1,1,1],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[5,5,5,4,3,1],[4,4,4,3,1]] => [[5,4,2,1,1,1],[4,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,4,3,3,2,1],[3,3,2,2]] => [[4,4,2,2,1,1],[3,2,1,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3

[[5,5,4,4,3,1],[4,4,3,3,1]] => [[5,4,2,2,1,1],[4,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[4,4,3,2,2,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,2,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,5,4,3,3,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,5,4,3,2,1],[4,4,3,2]] => [[5,5,3,2,1,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,6,5,4,3,1],[5,5,4,3,1]] => [[6,5,3,2,1,1],[5,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 3

[[4,3,3,3,2,1],[3,2,2,2]] => [[4,4,2,2,2,1],[3,2,1,1,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3

[[5,4,4,4,3,1],[4,3,3,3,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,3,3,2,2,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => 4

[[5,4,4,3,3,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[5,4,4,3,2,1],[4,3,3,2]] => [[5,5,3,2,2,1],[4,3,2,1,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,5,4,3,1],[5,4,4,3,1]] => [[6,5,3,2,2,1],[5,3,2,1,1]] => ([(3,6),(4,5)],7) => 5

[[4,3,2,2,2,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,2,2,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => 4

[[5,4,3,3,3,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,2,2,2,1]] => ([(3,4),(3,5),(5,6)],7) => 5

[[5,4,3,3,2,1],[4,3,2,2]] => [[5,5,3,3,2,1],[4,3,2,2,1]] => ([(2,6),(3,6),(4,5)],7) => 4

[[6,5,4,4,3,1],[5,4,3,3,1]] => [[6,5,3,3,2,1],[5,3,2,2,1]] => ([(3,6),(4,5)],7) => 5

[[5,4,3,2,2,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,3,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => 5

[[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]] => ([(4,5),(4,6)],7) => 6

[[6,5,4,3,2,1],[5,4,3,2]] => [[6,6,4,3,2,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => 5

[[7,6,5,4,3,1],[6,5,4,3,1]] => [[7,6,4,3,2,1],[6,4,3,2,1]] => ([(5,6)],7) => 6

[[2,2,2,2,2,2],[1,1,1,1,1]] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 2

[[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[5,5,5,4,3,2],[4,4,4,3,2]] => [[5,3,2,1,1,1],[3,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => 3

[[5,5,4,4,3,2],[4,4,3,3,2]] => [[5,3,2,2,1,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,5,4,3,3,2],[4,4,3,2,2]] => [[5,3,3,2,1,1],[3,2,2,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,5,4,3,2,2],[4,4,3,2,1]] => [[5,4,3,2,1,1],[3,3,2,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,4,3,2,1,1],[4,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[4,3,3,3,3,2],[3,2,2,2,2]] => [[4,2,2,2,2,1],[2,1,1,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[5,4,4,4,3,2],[4,3,3,3,2]] => [[5,3,2,2,2,1],[3,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,4,3,3,2],[4,3,3,2,2]] => [[5,3,3,2,2,1],[3,2,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,4,4,3,2,2],[4,3,3,2,1]] => [[5,4,3,2,2,1],[3,3,2,1,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,5,5,4,3,2],[5,4,4,3,2]] => [[6,4,3,2,2,1],[4,3,2,1,1]] => ([(3,6),(4,5)],7) => 5

[[5,4,3,3,3,2],[4,3,2,2,2]] => [[5,3,3,3,2,1],[3,2,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,3,3,2,2],[4,3,2,2,1]] => [[5,4,3,3,2,1],[3,3,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => 5

[[6,5,4,4,3,2],[5,4,3,3,2]] => [[6,4,3,3,2,1],[4,3,2,2,1]] => ([(3,6),(4,5)],7) => 5

[[5,4,3,2,2,2],[4,3,2,1,1]] => [[5,4,4,3,2,1],[3,3,3,2,1]] => ([(3,4),(3,5),(5,6)],7) => 5

[[6,5,4,3,3,2],[5,4,3,2,2]] => [[6,4,4,3,2,1],[4,3,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,5,4,3,2,1],[4,4,3,2,1]] => ([(4,5),(4,6)],7) => 6

[[7,6,5,4,3,2],[6,5,4,3,2]] => [[7,5,4,3,2,1],[5,4,3,2,1]] => ([(5,6)],7) => 6

[[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [[2,1,1,1,1,1,1],[1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => 2

[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[3,2,1,1,1,1,1],[2,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => 3

[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [[3,2,2,1,1,1,1],[2,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [[3,3,2,1,1,1,1],[2,2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [[4,3,2,1,1,1,1],[3,2,1]] => ([(3,4),(4,6),(6,5)],7) => 4

[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [[3,2,2,2,1,1,1],[2,1,1,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [[4,3,2,2,1,1,1],[3,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[3,3,3,2,1,1,1],[2,2,2,1]] => [[3,3,3,2,1,1,1],[2,2,2,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [[4,3,3,2,1,1,1],[3,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [[4,4,3,2,1,1,1],[3,3,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [[5,4,3,2,1,1,1],[4,3,2,1]] => ([(4,5),(5,6)],7) => 5

[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [[3,2,2,2,2,1,1],[2,1,1,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [[4,3,2,2,2,1,1],[3,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [[4,3,3,2,2,1,1],[3,2,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [[4,4,3,2,2,1,1],[3,3,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [[5,4,3,2,2,1,1],[4,3,2,1,1]] => ([(3,6),(4,5)],7) => 5

[[3,3,2,1,1,1,1],[2,2,1]] => [[3,3,3,3,2,1,1],[2,2,2,2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [[4,3,3,3,2,1,1],[3,2,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [[4,4,3,3,2,1,1],[3,3,2,2,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [[5,4,3,3,2,1,1],[4,3,2,2,1]] => ([(3,6),(4,5)],7) => 5

[[4,4,3,2,1,1,1],[3,3,2,1]] => [[4,4,4,3,2,1,1],[3,3,3,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [[5,4,4,3,2,1,1],[4,3,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [[5,5,4,3,2,1,1],[4,4,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [[6,5,4,3,2,1,1],[5,4,3,2,1]] => ([(5,6)],7) => 6

[[2,1,1,1,1,1,1],[1]] => [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => 2

[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => 3

[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => ([(3,4),(4,6),(6,5)],7) => 4

[[3,2,2,2,1,1,1],[2,1,1,1]] => [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => 3

[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => ([(4,5),(5,6)],7) => 5

[[3,2,2,1,1,1,1],[2,1,1]] => [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => 3

[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => 4

[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => ([(3,6),(4,5)],7) => 5

[[4,3,3,2,1,1,1],[3,2,2,1]] => [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => ([(3,6),(4,5)],7) => 5

[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => ([(3,6),(4,5)],7) => 5

[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => ([(5,6)],7) => 6

[[3,2,1,1,1,1,1],[2,1]] => [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => 3

[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => ([(3,4),(4,6),(6,5)],7) => 4

[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => ([(4,5),(5,6)],7) => 5

[[4,3,2,2,1,1,1],[3,2,1,1]] => [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => 4

[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => ([(3,6),(4,5)],7) => 5

[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => ([(3,6),(4,5)],7) => 5

[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => ([(5,6)],7) => 6

[[4,3,2,1,1,1,1],[3,2,1]] => [[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => ([(3,4),(4,6),(6,5)],7) => 4

[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => ([(4,5),(5,6)],7) => 5

[[5,4,3,2,2,1,1],[4,3,2,1,1]] => [[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => ([(3,6),(4,5)],7) => 5

[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => ([(5,6)],7) => 6

[[5,4,3,2,1,1,1],[4,3,2,1]] => [[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => ([(4,5),(5,6)],7) => 5

[[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => ([(5,6)],7) => 6

[[6,5,4,3,2,1,1],[5,4,3,2,1]] => [[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => ([(5,6)],7) => 6

[[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => [[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => ([],7) => 7

[[8],[]] => [[8],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[[5,3],[]] => [[5,5],[2]] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => 1

[[4,4],[]] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[[4,3,1],[]] => [[4,4,4],[3,1]] => ([(0,7),(1,6),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8) => 1

[[4,2,2],[]] => [[4,4,4],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => 1

[[3,3,2],[]] => [[3,3,3],[1]] => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8) => 1

[[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => 1

[[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => ([(0,7),(1,6),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8) => 1

[[2,2,2,2],[]] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => 1

[[1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[[9],[]] => [[9],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[[5,4],[]] => [[5,5],[1]] => ([(0,8),(1,4),(1,8),(2,3),(2,7),(3,5),(4,2),(4,6),(6,7),(7,5),(8,6)],9) => 1

[[4,4,1],[]] => [[4,4,4],[3]] => ([(0,2),(0,3),(1,7),(2,8),(3,4),(3,8),(4,6),(4,7),(6,5),(7,5),(8,6)],9) => 1

[[4,3,2],[]] => [[4,4,4],[2,1]] => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,6),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => 1

[[3,3,3],[]] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,6),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => 1

[[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => ([(0,2),(0,3),(1,7),(2,8),(3,4),(3,8),(4,6),(4,7),(6,5),(7,5),(8,6)],9) => 1

[[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => ([(0,8),(1,4),(1,8),(2,3),(2,7),(3,5),(4,2),(4,6),(6,7),(7,5),(8,6)],9) => 1

[[1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[[10],[]] => [[10],[]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[[5,5],[]] => [[5,5],[]] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[[4,4,2],[]] => [[4,4,4],[2]] => ([(0,3),(0,4),(1,2),(1,9),(2,8),(3,7),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => 1

[[4,3,3],[]] => [[4,4,4],[1,1]] => ([(0,3),(0,4),(1,7),(2,8),(3,2),(3,9),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => 1

[[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10) => 1

[[3,3,3,1],[]] => [[3,3,3,3],[2]] => ([(0,3),(0,4),(1,7),(2,8),(3,2),(3,9),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => 1

[[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => ([(0,3),(0,4),(1,2),(1,9),(2,8),(3,7),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => 1

[[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[[1,1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1,1],[]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[[4,4,3],[]] => [[4,4,4],[1]] => ([(0,3),(0,10),(1,4),(1,10),(2,7),(3,8),(4,2),(4,9),(6,5),(7,5),(8,6),(9,6),(9,7),(10,8),(10,9)],11) => 1

[[3,3,3,2],[]] => [[3,3,3,3],[1]] => ([(0,3),(0,10),(1,4),(1,10),(2,7),(3,8),(4,2),(4,9),(6,5),(7,5),(8,6),(9,6),(9,7),(10,8),(10,9)],11) => 1

[[6,6],[]] => [[6,6],[]] => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => 1

[[4,4,4],[]] => [[4,4,4],[]] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[[3,3,3,3],[]] => [[3,3,3,3],[]] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => 1

[[5,5,5],[]] => [[5,5,5],[]] => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => 1

[[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15) => 1

[[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => 1

[[4,4,4,4],[]] => [[4,4,4,4],[]] => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16) => 1

[[3,3,3],[1]] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => 2

[[3,3,3,1],[1,1]] => [[3,3,2,2],[2]] => ([(0,7),(1,3),(1,4),(2,6),(3,5),(3,7),(4,2),(4,5),(5,6)],8) => 2

[[4,4,1],[1]] => [[4,4,3],[3]] => ([(0,7),(1,3),(1,4),(2,6),(2,7),(3,5),(4,2),(4,5),(5,6)],8) => 2

[[3,3,2,1],[1]] => [[3,3,3,2],[2,1]] => ([(0,6),(1,3),(1,7),(2,6),(2,7),(3,5),(6,4),(7,4),(7,5)],8) => 2

[[2,2,2,2,1],[1]] => [[2,2,2,2,1],[1]] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => 2

[[3,3,3,1],[2]] => [[3,3,3,1],[2]] => ([(0,7),(1,3),(1,4),(3,5),(3,7),(4,2),(4,5),(5,6),(7,6)],8) => 2

[[3,3,3,1],[1]] => [[3,3,3,2],[2]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,8),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => 2

[[3,3,3,2],[1,1,1]] => [[3,2,2,2],[1]] => ([(0,3),(0,7),(1,4),(1,7),(2,6),(4,2),(4,5),(5,6),(7,5)],8) => 2

[[4,4,2],[1,1]] => [[4,3,3],[2]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(5,6),(7,6)],8) => 2

[[4,4,4],[2,2]] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 2

[[5,5],[2]] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 2

[[4,4,3],[2,1]] => [[4,3,2],[1]] => ([(0,3),(0,7),(1,4),(1,7),(3,5),(4,2),(4,6),(7,5),(7,6)],8) => 3

[[3,3,3,3],[2,1,1]] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 3

[[4,3,3],[1,1]] => [[4,3,3],[1,1]] => ([(0,7),(1,3),(1,4),(3,5),(3,7),(4,2),(4,5),(5,6),(7,6)],8) => 2

[[3,3,3,3],[1,1,1]] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 2

[[4,4,3],[1,1]] => [[4,3,3],[1]] => ([(0,3),(0,8),(1,4),(1,8),(3,6),(4,2),(4,7),(6,5),(7,5),(8,6),(8,7)],9) => 2

[[4,4,4],[3,1]] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 3

[[5,4],[1]] => [[5,4],[1]] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => 2

[[4,4,4],[2,1]] => [[4,3,2],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 3

[[5,5],[1]] => [[5,4],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 2

[[4,4,4],[1,1]] => [[4,3,3],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10) => 2

[[3,3,2,2],[1,1]] => [[3,3,2,2],[1,1]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(4,6),(7,6)],8) => 2

[[4,4,2],[2]] => [[4,4,2],[2]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(4,6),(7,6)],8) => 2

[[3,3,3,2],[2,1]] => [[3,3,2,1],[1]] => ([(0,3),(0,7),(1,4),(1,7),(3,5),(4,2),(4,6),(7,5),(7,6)],8) => 3

[[4,3,2],[1]] => [[4,4,3],[2,1]] => ([(0,6),(1,3),(1,7),(2,6),(2,7),(3,5),(6,4),(7,4),(7,5)],8) => 2

[[3,3,3,2],[1,1]] => [[3,3,2,2],[1]] => ([(0,3),(0,8),(1,4),(1,8),(2,5),(3,6),(4,2),(4,7),(7,5),(8,6),(8,7)],9) => 2

[[4,4,2],[1]] => [[4,4,3],[2]] => ([(0,3),(0,4),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => 2

[[2,2,2,2,2],[1,1]] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 2

[[3,2,2,2],[1]] => [[3,3,3,2],[1,1,1]] => ([(0,7),(1,3),(1,4),(2,6),(2,7),(3,5),(4,2),(4,5),(5,6)],8) => 2

[[3,3,2,2],[2]] => [[3,3,3,1],[1,1]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(5,6),(7,6)],8) => 2

[[3,3,2,2],[1]] => [[3,3,3,2],[1,1]] => ([(0,3),(0,4),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => 2

[[2,2,2,2,2],[1]] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => 2

[[3,3,3,2],[2]] => [[3,3,3,1],[1]] => ([(0,3),(0,8),(1,4),(1,8),(3,6),(4,2),(4,7),(6,5),(7,5),(8,6),(8,7)],9) => 2

[[3,3,3,2],[1]] => [[3,3,3,2],[1]] => ([(0,3),(0,9),(1,4),(1,9),(2,5),(3,2),(3,8),(4,7),(7,6),(8,5),(8,6),(9,7),(9,8)],10) => 2

[[3,3,3,3],[2,2]] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => 2

[[4,3,3],[2]] => [[4,4,2],[1,1]] => ([(0,7),(1,3),(1,4),(2,6),(3,5),(3,7),(4,2),(4,5),(5,6)],8) => 2

[[4,4,3],[3]] => [[4,4,1],[1]] => ([(0,3),(0,7),(1,4),(1,7),(2,6),(4,2),(4,5),(5,6),(7,5)],8) => 2

[[4,4,3],[2]] => [[4,4,2],[1]] => ([(0,3),(0,8),(1,4),(1,8),(2,5),(3,6),(4,2),(4,7),(7,5),(8,6),(8,7)],9) => 2

[[3,3,3,3],[2,1]] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => 3

[[4,3,3],[1]] => [[4,4,3],[1,1]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,8),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => 2

[[3,3,3,3],[1,1]] => [[3,3,2,2],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10) => 2

[[4,4,3],[1]] => [[4,4,3],[1]] => ([(0,3),(0,9),(1,4),(1,9),(2,5),(3,2),(3,8),(4,7),(7,6),(8,5),(8,6),(9,7),(9,8)],10) => 2

[[4,4,4],[3]] => [[4,4,1],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => 2

[[4,4,4],[2]] => [[4,4,2],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10) => 2

[[4,4,4],[1]] => [[4,4,3],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(8,10),(9,7),(9,10)],11) => 2

[[3,3,3,3],[2]] => [[3,3,3,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10) => 2

[[3,3,3,3],[1]] => [[3,3,3,2],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(8,10),(9,7),(9,10)],11) => 2

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Description

The number of maximal elements of a poset.

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rotate

Description

The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.

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cell poset

Description

The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.