- FindStat

Identifier

Mp00214: Semistandard tableaux —subcrystal⟶ Posets
St000527: Posets ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

[[2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

[[3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

[[1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

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

[[2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

[[1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[2],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

[[1,2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

[[1,3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

>>> Load all 809 entries. <<<

[[1,5],[3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2

[[2,2],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

[[2],[4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

[[1,1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

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

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

[[1,2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,3,4],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[2,2,2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

[[1,2,3,3],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,2],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

[[1],[4],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[2],[3],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

[[1,1,2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

[[1,1,3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,5],[3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2

[[1,2,2],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

[[1,2,5],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

[[1,1],[4,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

[[1,3],[2,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

[[1,3],[2],[5]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => 2

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

[[1,2],[4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,4],[2],[5]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 2

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

[[1,3],[3],[5]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => 2

[[2,2],[3],[5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

[[1,1,1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

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

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

[[1,1,2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,3,4],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,2,2,2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

[[1,2,2,4],[2]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

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

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

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

[[1,1,4],[3,3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2

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

[[1,2,3],[2,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

[[1,2,3],[2],[4]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => 2

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

[[1,2,4],[2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

[[1,3,3],[2],[4]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 2

[[1,3,4],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

[[1,3],[2,4],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

[[1,1,1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

[[1,1,2,3,3],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

[[1,2,2,2,3],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,2,3,3],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

[[1,2,2],[3,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[2,2,2,2,2,2,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

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

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

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

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

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

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

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

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

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

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

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

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

[[1,8]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[[1],[8]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

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

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

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

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

[[1],[3],[7]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

[[1,1,2],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

[[1,1],[3,6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

[[1,2],[2,6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

[[1,1],[4],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,2],[2],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

[[1,2],[3],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

[[1,3],[2],[6]] => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => 3

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

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

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

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

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

[[1],[3],[5],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[2],[3],[4],[6]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

[[1,1,1,2,5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

[[1,1,1,3],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,1,5],[3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2

[[1,1,2,2],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

[[1,1,2,5],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

[[1,1,1],[4,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

[[1,1,3],[2,5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,5],[2,3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2

[[1,2,2],[2,5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

[[1,1,3],[2],[5]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => 2

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

[[1,1,2],[4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,4],[2],[5]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 2

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

[[1,1,3],[3],[5]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => 2

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

[[1,2,2],[3],[5]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

[[1,2,3],[2],[5]] => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13) => 3

[[1,2,5],[2],[3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

[[1,1],[3,4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

[[1,2],[2,4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,2],[2,5],[4]] => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11) => 3

[[1,2],[3,3],[5]] => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11) => 3

[[1,3],[2,5],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

[[1,4],[2],[4],[5]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2

[[1,3],[3],[4],[5]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2

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

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

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

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

[[1,1,1,1,3,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,1,2,2,4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

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

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

[[1,1,1,2,3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,1,3,4],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,2,2,2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

[[1,1,2,2,4],[2]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

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

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

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

[[1,1,1,4],[3,3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2

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

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

[[1,1,2,3],[2,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,3,4],[2,2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,2,2,2],[2,4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

[[1,1,2,3],[2],[4]] => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => 2

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

[[1,1,2,4],[2],[4]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

[[1,1,3,3],[2],[4]] => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) => 2

[[1,1,3,4],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,2,2,2],[2],[4]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

[[1,2,2,3],[2],[4]] => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) => 3

[[1,2,2,4],[2],[3]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

[[1,1,1],[3,4,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1,3],[2,4],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

[[1,2,2],[2,4],[4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

[[1,2,3],[2,4],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

[[1,3,4],[2],[3],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

[[1,2],[3,3],[4,4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

[[1,1,1,1,2,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,1,2,2,2,3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

[[1,1,1,2,3,3],[2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

[[1,1,2,2,2,3],[2]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

[[2,2,2,2,2,2],[3]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1,2,3,3],[2,2]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

[[1,1,2,3,3],[2],[3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

[[1,2,2,2,3],[2],[3]] => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1,2,2],[3,3,3]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,2,2,2,2,2,2,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[[2,2,2,2,2,2,2,2]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1,1,3],[2,2,4],[3,4],[4]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,2,2],[2,2,4],[3,4],[4]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

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

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

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

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

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

[[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

[[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

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

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

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

[[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,5],[5]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2

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

[[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,5],[5]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => 2

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

[[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

[[1,1,1,1,2],[2,2,2,3],[3,3,5],[4,5],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

[[1,1,1,1,1],[2,2,2,4],[3,3,5],[4,5],[5]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

[[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

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

[[1,1,1,1,2],[2,2,2,2],[3,4,4],[4,5],[5]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

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

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

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

[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2

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

[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => 2

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

[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 3

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

[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12) => 3

[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14) => 4

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

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

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

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

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

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

[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

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

[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2

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

[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]] => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12) => 3

[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) => 2

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

[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

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

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

[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]] => ([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14) => 4

[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) => 3

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) => 2

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

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

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

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

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

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

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

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

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

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

[[1,3],[2],[4],[5],[6]] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 2

[[1,4],[2],[3],[5],[6]] => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => 3

[[1,5],[2],[3],[4],[6]] => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => 2

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

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

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$F_{(2, 2)} = 3\ q$

$F_{(2, 3)} = 3\ q + 2\ q^{2}$

$F_{(3, 2)} = 5\ q$

$F_{(4, 2)} = 8\ q$

$F_{(5, 2)} = 11\ q$

$F_{(6, 2)} = 15\ q$

$F_{(7, 2)} = 19\ q$

$F_{(8, 2)} = 24\ q$

Description

The width of the poset.
This is the size of the poset's longest antichain, also called Dilworth number.

Map

subcrystal

Description

The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.