- FindStat

Identifier

Mp00214: Semistandard tableaux —subcrystal⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St001392: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

[[5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

[[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) => [6,3] => 5

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3,1] => 5

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

[[2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

[[3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

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

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

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

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

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

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

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

[[2,3,3],[3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

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

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

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

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

>>> Load all 1247 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[3,6]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

[[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) => [6,3] => 5

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

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

[[5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

[[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) => [6,3] => 5

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

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

[[1,5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

[[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) => [6,3,1] => 5

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

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

[[2,4],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[3,3],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

[[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) => [6,3] => 5

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3,1] => 5

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

[[1,2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

[[2,2,4],[4]] => ([(0,7),(0,8),(1,16),(2,10),(2,16),(3,11),(4,12),(5,6),(6,4),(6,10),(7,9),(8,5),(9,1),(9,2),(10,12),(10,13),(11,15),(12,14),(13,11),(13,14),(14,15),(16,3),(16,13)],17) => [8,6,3] => 7

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

[[3,3,3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[2,4],[3],[4]] => ([(0,9),(0,10),(1,12),(2,11),(3,11),(3,12),(4,7),(5,8),(6,3),(7,2),(8,1),(9,4),(9,14),(10,5),(10,14),(11,13),(12,13),(14,6)],15) => [7,5,3] => 6

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

[[1,3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

[[2,2,2,3,3]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

[[1,2,3,3],[3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[2,2,3],[3,3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[3],[7]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

[[1,3,6]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

[[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) => [6,3] => 5

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

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

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

[[1,5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3,1] => 5

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

[[2],[5],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[3],[4],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

[[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) => [6,3] => 5

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

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

[[1,1,5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

[[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) => [6,3,1] => 5

[[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) => [6,3] => 5

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

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

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

[[1,2,4],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

[[1,5,5],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

[[1,3,3],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

[[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) => [6,3] => 5

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

[[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) => [5,3] => 4

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

[[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) => [6,3] => 5

[[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) => [6,3] => 5

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

[[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) => [6,4] => 5

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

[[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) => [6,3] => 5

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

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

[[3,3],[4],[5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3,1] => 5

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

[[1,1,2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,1,3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

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

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

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

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

[[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) => [6,3] => 5

[[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) => [6,3,1] => 5

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

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

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

[[1,2,2,4],[4]] => ([(0,7),(0,8),(1,16),(2,10),(2,16),(3,11),(4,12),(5,6),(6,4),(6,10),(7,9),(8,5),(9,1),(9,2),(10,12),(10,13),(11,15),(12,14),(13,11),(13,14),(14,15),(16,3),(16,13)],17) => [8,6,3] => 7

[[1,2,4,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

[[1,3,3,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,3,3,3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

[[2,2,2,3],[4]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [5,3] => 4

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

[[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) => [6,3] => 5

[[1,2,4],[3],[4]] => ([(0,9),(0,10),(1,12),(2,11),(3,11),(3,12),(4,7),(5,8),(6,3),(7,2),(8,1),(9,4),(9,14),(10,5),(10,14),(11,13),(12,13),(14,6)],15) => [7,5,3] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

[[1,1,3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

[[1,2,2,2,3,3]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

[[1,1,2,3,3],[3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

[[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) => [6,3] => 5

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

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

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

[[1,3,3,3,3],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,2,2,3],[3,3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

[[1,2,3,3],[2,3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,3],[7]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

[[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) => [6,3] => 5

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

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

[[1],[6],[7]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

[[1,1,3,6]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

[[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) => [6,3] => 5

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

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

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

[[1,1,5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

[[1,3,6],[2]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

[[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) => [6,3] => 5

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

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

[[1,1],[6,6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

[[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) => [6,3] => 5

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

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

[[1,5],[2,6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

[[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) => [6,3] => 5

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

[[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) => [5,3] => 4

[[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) => [6,3,1] => 5

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

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

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

[[1,2],[5],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,3],[4],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

[[3],[4],[5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

[[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) => [6,3] => 5

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

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

[[1,1,1,5,5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

[[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) => [6,3,1] => 5

[[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) => [6,3] => 5

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

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

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

[[1,1,2,4],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

[[1,1,5,5],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

[[1,1,3,3],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

[[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) => [6,3] => 5

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

[[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) => [6,3,1] => 5

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

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

[[1,2,4],[2,5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,3,3],[2,5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

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

[[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) => [5,3] => 4

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

[[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) => [6,3] => 5

[[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) => [6,3] => 5

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

[[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) => [6,4] => 5

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

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

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

[[1,5,5],[2],[3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

[[1,3,3],[4],[5]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

[[2,2,2],[4],[5]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

[[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) => [6,3] => 5

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3,1] => 5

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

[[1,1,1,2,4,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,1,1,3,3,4]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

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

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

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

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

[[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) => [6,3] => 5

[[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) => [6,3,1] => 5

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

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

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

[[1,1,2,2,4],[4]] => ([(0,7),(0,8),(1,16),(2,10),(2,16),(3,11),(4,12),(5,6),(6,4),(6,10),(7,9),(8,5),(9,1),(9,2),(10,12),(10,13),(11,15),(12,14),(13,11),(13,14),(14,15),(16,3),(16,13)],17) => [8,6,3] => 7

[[1,1,2,4,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

[[1,1,3,3,4],[2]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,1,3,3,3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

[[1,2,2,2,3],[4]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,2] => 5

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

[[1,2,2,4],[2,4]] => ([(0,7),(0,8),(1,16),(2,10),(2,16),(3,11),(4,12),(5,6),(6,4),(6,10),(7,9),(8,5),(9,1),(9,2),(10,12),(10,13),(11,15),(12,14),(13,11),(13,14),(14,15),(16,3),(16,13)],17) => [8,6,3] => 7

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

[[1,3,3,3],[2,4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

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

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

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

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

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

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

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

[[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) => [5,3] => 4

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

[[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) => [6,3] => 5

[[1,1,2,4],[3],[4]] => ([(0,9),(0,10),(1,12),(2,11),(3,11),(3,12),(4,7),(5,8),(6,3),(7,2),(8,1),(9,4),(9,14),(10,5),(10,14),(11,13),(12,13),(14,6)],15) => [7,5,3] => 6

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

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

[[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) => [5,3] => 4

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

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

[[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) => [6,3,1] => 5

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

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

[[1,2,4,4],[2],[3]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,3,3,4],[2],[3]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

[[1,1,4],[3,4],[4]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

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

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

[[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) => [6,3,1] => 5

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

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

[[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) => [6,3] => 5

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

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

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

[[1,2,4],[2,3],[4]] => ([(0,9),(0,10),(1,12),(2,11),(3,11),(3,12),(4,7),(5,8),(6,3),(7,2),(8,1),(9,4),(9,14),(10,5),(10,14),(11,13),(12,13),(14,6)],15) => [7,5,3] => 6

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

[[1,2,4],[2,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

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

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

[[1,3,3],[3,4],[4]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => [9,4,3] => 8

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

[[2,2,2],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

[[2,2,3],[3,3],[4]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

[[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) => [6,3] => 5

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

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

[[1,1,1,3,3,3,3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

[[1,1,2,2,2,3,3]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

[[1,1,1,2,3,3],[3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

[[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) => [6,3] => 5

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

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

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

[[1,1,3,3,3,3],[2]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

[[1,2,2,2,3,3],[2]] => ([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15) => [8,5,2] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

[[1,1,2,2,3],[3,3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

[[1,1,2,3,3],[2,3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

[[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) => [6,3] => 5

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

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

[[1,3,3,3,3],[2],[3]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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) => [6,3] => 5

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

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

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

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

[[1,2,2,3],[2,3,3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

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

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

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

[[1,1,1,2],[2,2],[3]] => ([(0,1)],2) => [2] => 1

[[1,1,1,2],[2,3],[3]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,3],[2,2],[3]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,3],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,2,2],[2,2],[3]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,2,2],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,2,3],[2,2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 3

[[1,1,2,3],[2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,3,3],[2,2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 4

[[1,1,3,3],[2,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 5

[[1,2,2,2],[2,3],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 4

[[1,2,2,3],[2,3],[3]] => ([(0,6),(0,7),(1,9),(2,8),(3,5),(4,2),(5,1),(5,8),(6,3),(7,4),(8,9)],10) => [6,4] => 5

[[1,2,3,3],[2,3],[3]] => ([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15) => [7,5,3] => 6

[[1,1,1],[2,2,2],[3]] => ([],1) => [1] => 0

[[1,1,1],[2,2,3],[3]] => ([(0,1)],2) => [2] => 1

[[1,1,1],[2,3,3],[3]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,2],[2,2,3],[3]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,2],[2,3,3],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 3

[[1,2,2],[2,3,3],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 4

[[1,1,1],[2,2],[3,3]] => ([],1) => [1] => 0

[[1,1,2],[2,2],[3,3]] => ([(0,1)],2) => [2] => 1

[[1,1,3],[2,2],[3,3]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,1,1,1,1,2]] => ([(0,1)],2) => [2] => 1

[[1,1,1,1,1,1,2,2]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 4

[[1,1,1,2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 5

[[1,1,2,2,2,2,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 6

[[1,2,2,2,2,2,2,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => 7

[[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) => [9] => 8

[[1,1,1,1,1,1,1],[2]] => ([],1) => [1] => 0

[[1,1,1,1,1,1,2],[2]] => ([(0,1)],2) => [2] => 1

[[1,1,1,1,1,2,2],[2]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,2,2,2,2],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 4

[[1,1,2,2,2,2,2],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 5

[[1,2,2,2,2,2,2],[2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 6

[[1,1,1,1,1,1],[2,2]] => ([],1) => [1] => 0

[[1,1,1,1,1,2],[2,2]] => ([(0,1)],2) => [2] => 1

[[1,1,1,1,2,2],[2,2]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,2,2,2],[2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,2,2,2,2],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 4

[[1,1,1,1,1],[2,2,2]] => ([],1) => [1] => 0

[[1,1,1,1,2],[2,2,2]] => ([(0,1)],2) => [2] => 1

[[1,1,1,2,2],[2,2,2]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,1],[2,2,2,2]] => ([],1) => [1] => 0

[[1]] => ([],1) => [1] => 0

[[1,1,1,1],[2,2,2],[3,3],[4]] => ([],1) => [1] => 0

[[1,1,1,2],[2,2,2],[3,3],[4]] => ([(0,1)],2) => [2] => 1

[[1,1,1,1],[2,2,3],[3,3],[4]] => ([(0,1)],2) => [2] => 1

[[1,1,1,2],[2,2,3],[3,3],[4]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,3],[2,2,3],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,2,2],[2,2,3],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,2,3],[2,2,3],[3,3],[4]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1],[2,2,2],[3,4],[4]] => ([(0,1)],2) => [2] => 1

[[1,1,1,2],[2,2,2],[3,4],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 2

[[1,1,1,1],[2,2,3],[3,4],[4]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,2],[2,2,3],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,3],[2,2,3],[3,4],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => 4

[[1,1,2,2],[2,2,3],[3,4],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 4

[[1,1,2,3],[2,2,3],[3,4],[4]] => ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10) => [6,4] => 5

[[1,1,1,1],[2,2,4],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[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) => [5,2] => 4

[[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) => [6,3] => 5

[[1,1,1,4],[2,2,4],[3,4],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[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) => [6,3,1] => 5

[[1,1,2,3],[2,2,4],[3,4],[4]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => [7,4,3] => 6

[[1,1,2,4],[2,2,4],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

[[1,1,1,1],[2,3,3],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,2],[2,3,3],[3,4],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 4

[[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) => [6,1] => 5

[[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) => [6,1] => 5

[[1,1,2,3],[2,3,3],[3,4],[4]] => ([(0,3),(0,8),(1,10),(2,9),(3,11),(4,2),(5,4),(6,7),(7,1),(7,9),(8,5),(8,11),(9,10),(11,6)],12) => [7,5] => 6

[[1,1,1,1],[2,3,4],[3,4],[4]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,2],[2,3,4],[3,4],[4]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => [6,4,1] => 5

[[1,1,1,3],[2,3,4],[3,4],[4]] => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10) => [7,3] => 6

[[1,1,1,4],[2,3,4],[3,4],[4]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

[[1,1,2,2],[2,3,4],[3,4],[4]] => ([(0,6),(0,7),(1,9),(2,12),(3,9),(3,12),(4,10),(5,1),(6,5),(7,8),(8,2),(8,3),(9,11),(11,10),(12,4),(12,11)],13) => [7,5,1] => 6

[[1,1,3,3],[2,3,4],[3,4],[4]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => [9,4,3] => 8

[[1,2,2,2],[2,3,3],[3,4],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[1,2,2,3],[2,3,3],[3,4],[4]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

[[1,2,2,2],[2,3,4],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => ([],1) => [1] => 0

[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]] => ([(0,1)],2) => [2] => 1

[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,1)],2) => [2] => 1

[[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]] => ([(0,1)],2) => [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) => [3,1] => 2

[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[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) => [5,1] => 4

[[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10) => [6,4] => 5

[[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[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) => [5,2] => 4

[[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) => [6,3] => 5

[[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[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) => [6,3,1] => 5

[[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

[[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[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) => [6,1] => 5

[[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => [6,4,1] => 5

[[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

[[1,1,1,3,3],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => [9,4,3] => 8

[[1,1,2,2,2],[2,2,3,3],[3,3,4],[4,4],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

[[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]] => ([(0,1)],2) => [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) => [3,1] => 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) => [3,1] => 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) => [4,2] => 3

[[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) => [5,3] => 4

[[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) => [5,3] => 4

[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]] => ([(0,2),(2,1)],3) => [3] => 2

[[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) => [4,2] => 3

[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 4

[[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) => [6,2] => 5

[[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) => [5,1] => 4

[[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) => [6,4] => 5

[[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]] => ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10) => [6,4] => 5

[[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[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) => [5,3] => 4

[[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) => [5,2] => 4

[[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) => [6,3,1] => 5

[[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) => [6,3] => 5

[[1,1,1,1,2],[2,2,2,4],[3,3,5],[4,5],[5]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => [7,4,3] => 6

[[1,1,1,1,3],[2,2,2,4],[3,3,5],[4,5],[5]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[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) => [6,3,1] => 5

[[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

[[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[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) => [5,3] => 4

[[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) => [6,1] => 5

[[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => [6,4,1] => 5

[[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14) => [7,5,2] => 6

[[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

[[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]] => ([(0,8),(2,11),(2,12),(3,10),(4,9),(5,4),(5,14),(6,3),(6,14),(7,1),(8,5),(8,6),(9,11),(9,13),(10,12),(10,13),(11,15),(12,15),(13,15),(14,2),(14,9),(14,10),(15,7)],16) => [9,4,3] => 8

[[1,1,1,1,1],[2,3,3,3],[3,4,4],[4,5],[5]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

[[1,1,1,1,1],[2,3,3,3],[3,4,5],[4,5],[5]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([],1) => [1] => 0

[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,1)],2) => [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) => [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) => [3] => 2

[[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) => [4] => 3

[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,1)],2) => [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) => [3,1] => 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) => [3] => 2

[[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) => [4] => 3

[[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) => [5,1] => 4

[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10) => [6,4] => 5

[[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) => [4] => 3

[[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) => [5,2] => 4

[[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) => [6,3] => 5

[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => [6,4,1] => 5

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1)],2) => [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) => [3,1] => 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) => [3,1] => 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) => [4,2] => 3

[[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) => [5,3] => 4

[[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) => [3] => 2

[[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) => [4,2] => 3

[[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) => [4] => 3

[[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) => [5] => 4

[[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) => [6,2] => 5

[[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) => [5,1] => 4

[[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) => [6,4] => 5

[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10) => [6,4] => 5

[[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) => [4] => 3

[[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) => [5,3] => 4

[[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) => [5,2] => 4

[[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) => [6,3,1] => 5

[[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) => [6,3] => 5

[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => [7,4,3] => 6

[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => [6,4,1] => 5

[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14) => [7,5,2] => 6

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1)],2) => [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) => [3,1] => 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) => [3,1] => 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) => [4,2] => 3

[[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) => [5,3] => 4

[[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) => [3,1] => 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) => [4,2,2] => 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) => [4,2] => 3

[[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) => [5,3] => 4

[[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) => [6,4,2] => 5

[[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) => [5,3] => 4

[[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) => [6,4,3,1] => 5

[[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) => [3] => 2

[[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) => [4,2] => 3

[[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) => [4,2] => 3

[[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) => [5,3,1] => 4

[[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) => [6,4,2] => 5

[[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) => [4] => 3

[[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) => [5,3] => 4

[[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) => [5] => 4

[[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) => [6] => 5

[[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) => [6,2] => 5

[[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) => [5,1] => 4

[[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) => [6,4,2] => 5

[[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) => [6,4] => 5

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]] => ([(0,3),(0,7),(1,8),(2,8),(3,9),(4,5),(5,1),(6,2),(7,4),(7,9),(9,6)],10) => [6,4] => 5

[[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) => [4] => 3

[[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) => [5,3] => 4

[[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) => [5,3] => 4

[[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) => [6,4,2] => 5

[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(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) => [7,5,3,1] => 6

[[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) => [5,2] => 4

[[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) => [6,4,3,1] => 5

[[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) => [6,3,1] => 5

[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13) => [7,4,2] => 6

[[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) => [6,3] => 5

[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14) => [7,4,3] => 6

[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16) => [8,5,3] => 7

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 4

[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]] => ([(0,5),(0,6),(1,8),(2,9),(3,8),(3,9),(4,1),(5,4),(6,7),(7,2),(7,3),(8,10),(9,10)],11) => [6,4,1] => 5

[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14) => [7,5,2] => 6

[[2]] => ([(0,1)],2) => [2] => 1

[[1,1]] => ([],1) => [1] => 0

[[3]] => ([(0,2),(2,1)],3) => [3] => 2

[[1,1,1]] => ([],1) => [1] => 0

[[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 3

[[1,1,1,1]] => ([],1) => [1] => 0

[[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 4

[[1,1,1,1,1]] => ([],1) => [1] => 0

[[6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 5

[[1,2],[3],[4],[5],[6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 5

[[1,3],[2,4],[5],[6]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

[[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) => [6,3] => 5

[[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) => [6,3,1] => 5

[[1,5],[2,6],[3],[4]] => ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15) => [9,5,1] => 8

[[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) => [6,3] => 5

[[1,6],[2],[3],[4],[5]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 5

[[1],[2],[3],[4],[5],[6]] => ([],1) => [1] => 0

[[1,1,1,1,2,2,2],[3,3],[4]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => [7,1] => 6

[[1,1,1,1,2,2,3],[3,3],[4]] => ([(0,5),(0,10),(1,16),(2,15),(3,14),(4,13),(5,12),(6,2),(6,13),(7,4),(7,14),(8,1),(9,6),(10,11),(10,12),(11,3),(11,7),(12,9),(13,15),(14,8),(15,16)],17) => [8,6,3] => 7

[[1,1,1,1,2,2,2],[3,4],[4]] => ([(0,7),(0,8),(1,12),(2,11),(3,10),(4,10),(4,11),(5,3),(6,1),(6,13),(7,9),(8,5),(9,2),(9,4),(10,14),(11,6),(11,14),(13,12),(14,13)],15) => [8,6,1] => 7

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Description

The largest nonnegative integer which is not a part and is smaller than the largest part of the partition.

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Greene-Kleitman invariant

Description

The Greene-Kleitman invariant of a poset.
This is the partition $(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$, where $c_k$ is the maximum cardinality of a union of $k$ chains of the poset. Equivalently, this is the conjugate of the partition $(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$, where $a_k$ is the maximum cardinality of a union of $k$ antichains of the poset.

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subcrystal

Description

The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.