Identifier
-
Mp00214:
Semistandard tableaux
—subcrystal⟶
Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000380: Integer partitions ⟶ ℤ
Values
[[1,2]] => ([(0,1)],2) => [2] => 3
[[2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1],[2]] => ([],1) => [1] => 2
[[1,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1],[3]] => ([(0,1)],2) => [2] => 3
[[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2]] => ([(0,1)],2) => [2] => 3
[[1,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[2,2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1],[2]] => ([],1) => [1] => 2
[[1,2],[2]] => ([(0,1)],2) => [2] => 3
[[1,4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[1],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[1,1],[3]] => ([(0,1)],2) => [2] => 3
[[1,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,3],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 6
[[1],[2],[3]] => ([],1) => [1] => 2
[[1,1,1,2]] => ([(0,1)],2) => [2] => 3
[[1,1,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1],[2]] => ([],1) => [1] => 2
[[1,1,2],[2]] => ([(0,1)],2) => [2] => 3
[[1,2,2],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[2,2]] => ([],1) => [1] => 2
[[1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[1],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[1,1,4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 9
[[3,4,4]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[4,4,4]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[1,1],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[2,2],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[3,4],[4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[1],[2],[4]] => ([(0,1)],2) => [2] => 3
[[1],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[1,1,1],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,3],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 6
[[1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[1,1],[2,3]] => ([(0,1)],2) => [2] => 3
[[1,1],[3,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2],[2,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
>>> Load all 1514 entries. <<<[[2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1],[2],[3]] => ([],1) => [1] => 2
[[1,2],[2],[3]] => ([(0,1)],2) => [2] => 3
[[1,3],[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,1,1,1],[2]] => ([],1) => [1] => 2
[[1,1,1,2],[2]] => ([(0,1)],2) => [2] => 3
[[1,1,2,2],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1],[2,2]] => ([],1) => [1] => 2
[[1,1,2],[2,2]] => ([(0,1)],2) => [2] => 3
[[1,6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[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] => 9
[[4,6]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[5,6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[6,6]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[1,1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[2,3,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[2,4,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[2,5,5]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[3,3,5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[3,4,5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[3,5,5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[4,4,5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[4,5,5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[5,5,5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,5],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[1,5],[3]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[2,5],[4]] => ([(0,7),(0,8),(1,10),(1,16),(2,11),(3,10),(4,12),(4,13),(5,3),(6,2),(6,16),(7,9),(8,5),(9,1),(9,6),(10,14),(11,12),(11,15),(12,17),(13,17),(14,13),(14,15),(15,17),(16,4),(16,11),(16,14)],18) => [8,6,4] => 9
[[2,5],[5]] => ([(0,8),(0,9),(1,15),(1,18),(2,13),(3,11),(3,17),(4,11),(5,12),(6,4),(7,5),(7,17),(8,10),(9,6),(10,3),(10,7),(11,14),(12,16),(12,18),(14,15),(14,16),(15,19),(16,19),(17,1),(17,12),(17,14),(18,2),(18,19),(19,13)],20) => [9,7,4] => 10
[[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] => 9
[[3,4],[5]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[3,5],[4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => [9,7,5,4,1] => 10
[[3,5],[5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => [10,8,6,4,1] => 11
[[4,4],[5]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[4,5],[5]] => ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40) => [11,9,7,5,5,3] => 12
[[1],[2],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1],[3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1],[4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[2],[3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[1,1,1,4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 9
[[1,3,4,4]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,4,4,4]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[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] => 8
[[2,2,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[2,2,4,4]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[2,3,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[2,3,4,4]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[2,4,4,4]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[3,3,3,4]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[3,3,4,4]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[3,4,4,4]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[4,4,4,4]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1,1],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[1,1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[1,2,2],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,2,4],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[1,3,4],[4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 9
[[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] => 10
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 9
[[2,3,4],[3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => [8,6,5,3,1] => 9
[[2,3,4],[4]] => ([(0,2),(0,3),(1,8),(1,10),(2,1),(3,5),(3,7),(4,26),(5,22),(6,20),(7,12),(7,22),(8,21),(9,18),(9,19),(10,21),(10,25),(11,14),(11,15),(12,9),(12,24),(12,25),(13,27),(14,27),(15,27),(16,13),(17,14),(18,16),(19,17),(20,11),(20,17),(21,4),(21,23),(22,6),(22,24),(23,16),(23,26),(24,19),(24,20),(25,18),(25,23),(26,13),(26,15)],28) => [9,7,6,4,2] => 10
[[2,4,4],[3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => [9,7,5,4,1] => 10
[[2,4,4],[4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => [10,8,5,4,1] => 11
[[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] => 10
[[3,3,4],[4]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,28),(5,24),(6,22),(7,17),(8,13),(8,24),(9,23),(10,15),(10,16),(11,20),(11,21),(12,23),(12,27),(13,11),(13,26),(13,27),(14,29),(15,29),(16,7),(16,29),(18,16),(19,14),(20,19),(21,18),(22,10),(22,18),(23,4),(23,25),(24,6),(24,26),(25,19),(25,28),(26,21),(26,22),(27,20),(27,25),(28,14),(28,15),(29,17)],30) => [10,8,6,4,2] => 11
[[3,4,4],[4]] => ([(0,1),(0,2),(1,10),(1,12),(2,9),(2,11),(3,35),(4,33),(5,42),(6,32),(7,31),(8,15),(8,34),(9,36),(10,37),(11,16),(11,36),(12,17),(12,18),(12,37),(13,21),(13,23),(14,24),(14,38),(15,22),(15,28),(16,14),(16,40),(16,41),(17,30),(17,41),(18,26),(18,30),(20,44),(21,44),(22,43),(23,4),(23,44),(24,25),(25,23),(26,34),(27,20),(27,43),(28,35),(28,43),(29,31),(30,5),(30,39),(31,19),(32,13),(32,25),(33,19),(34,3),(34,28),(35,7),(35,29),(36,6),(36,40),(37,8),(37,26),(38,22),(38,27),(39,27),(39,42),(40,24),(40,32),(41,38),(41,39),(42,20),(42,21),(43,29),(44,33)],45) => [11,9,7,7,5,3,3] => 12
[[1,1],[2,4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,2],[2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[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] => 6
[[1,3],[2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 7
[[1,3],[3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 8
[[2,3],[4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => [8,5,5,1] => 9
[[3,3],[4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => [9,5,5,1] => 10
[[1,1],[2],[4]] => ([(0,1)],2) => [2] => 3
[[1,1],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 4
[[1,2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,3],[2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [4,1] => 5
[[1,4],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,4],[2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,3],[3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => 6
[[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] => 7
[[2,2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[1],[2],[3],[4]] => ([],1) => [1] => 2
[[1,1,1,1,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,2,2,3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[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] => 9
[[2,2,3,3,3]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[2,3,3,3,3]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[3,3,3,3,3]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1,1,1],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,3],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,2,3],[3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 6
[[1,1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[1,2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,2,2,3],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[2,2,2,2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[2,2,3,3],[3]] => ([(0,10),(0,11),(1,12),(2,17),(3,13),(4,14),(5,9),(5,12),(6,5),(7,3),(8,1),(8,17),(9,4),(9,15),(10,6),(11,2),(11,8),(12,15),(13,16),(14,16),(15,13),(15,14),(17,7)],18) => [8,6,4] => 9
[[2,3,3,3],[3]] => ([(0,13),(0,14),(1,16),(2,15),(3,17),(4,19),(5,18),(6,12),(6,16),(7,6),(8,2),(8,22),(9,1),(9,22),(10,4),(11,3),(11,23),(12,5),(12,20),(13,7),(14,8),(14,9),(15,23),(16,20),(17,21),(18,21),(20,17),(20,18),(21,19),(22,11),(22,15),(23,10)],24) => [9,7,5,3] => 10
[[1,1,1],[2,3]] => ([(0,1)],2) => [2] => 3
[[1,1,1],[3,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2],[2,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,3],[2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,3],[2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,3],[3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,2,2],[2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,2,3],[2,3]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 6
[[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] => 7
[[2,2,2],[3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 8
[[1,1,1],[2],[3]] => ([],1) => [1] => 2
[[1,1,2],[2],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,3],[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2,2],[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2,3],[2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,3,3],[2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1],[2,2],[3]] => ([],1) => [1] => 2
[[1,1],[2,3],[3]] => ([(0,1)],2) => [2] => 3
[[1,2],[2,3],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,1,2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[2,2,2,2,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1,1,1,1,1],[2]] => ([],1) => [1] => 2
[[1,1,1,1,2],[2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2,2],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,2,2,2],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,1],[2,2]] => ([],1) => [1] => 2
[[1,1,1,2],[2,2]] => ([(0,1)],2) => [2] => 3
[[1,1,2,2],[2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1],[2,2,2]] => ([],1) => [1] => 2
[[1,7]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1],[7]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[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] => 9
[[4],[7]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[5],[7]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[6],[7]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1,6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[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] => 9
[[1,4,6]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,5,6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,6,6]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[1,6],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[2,3],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[2,4],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[2,5],[6]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[3,3],[6]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[3,4],[6]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[3,5],[6]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[4,4],[6]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[4,5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[5,5],[6]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1],[2],[6]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1],[3],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 9
[[3],[5],[6]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[4],[5],[6]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[1,1,1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[1,2,3,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[1,2,4,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,2,5,5]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,3,3,5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,3,4,5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,3,5,5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,4,4,5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,4,5,5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,5,5,5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1,1],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,1,5],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 9
[[1,2,5],[4]] => ([(0,7),(0,8),(1,10),(1,16),(2,11),(3,10),(4,12),(4,13),(5,3),(6,2),(6,16),(7,9),(8,5),(9,1),(9,6),(10,14),(11,12),(11,15),(12,17),(13,17),(14,13),(14,15),(15,17),(16,4),(16,11),(16,14)],18) => [8,6,4] => 9
[[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] => 9
[[1,2,5],[5]] => ([(0,8),(0,9),(1,15),(1,18),(2,13),(3,11),(3,17),(4,11),(5,12),(6,4),(7,5),(7,17),(8,10),(9,6),(10,3),(10,7),(11,14),(12,16),(12,18),(14,15),(14,16),(15,19),(16,19),(17,1),(17,12),(17,14),(18,2),(18,19),(19,13)],20) => [9,7,4] => 10
[[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] => 10
[[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] => 9
[[1,3,4],[5]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,3,5],[4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => [9,7,5,4,1] => 10
[[1,3,5],[5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => [10,8,6,4,1] => 11
[[1,4,4],[5]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[1,4,5],[5]] => ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40) => [11,9,7,5,5,3] => 12
[[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] => 8
[[2,2,3],[5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[2,2,4],[5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[2,3,3],[5]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[2,3,4],[5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[2,4,4],[5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[3,3,3],[5]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[3,3,4],[5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[3,4,4],[5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[4,4,4],[5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1],[2,5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1],[3,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[1,2],[2,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 10
[[1,1],[2],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1],[4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,2],[2],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => 5
[[1,2],[3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 6
[[1,5],[2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 7
[[1,5],[2],[4]] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => 7
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[1],[2],[3],[5]] => ([(0,1)],2) => [2] => 3
[[1],[2],[4],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1],[3],[4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[2],[3],[4],[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,1,4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 9
[[1,1,3,4,4]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,1,4,4,4]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[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] => 8
[[1,2,2,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[1,2,2,4,4]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,2,3,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,2,3,4,4]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,2,4,4,4]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,3,3,3,4]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,3,3,4,4]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,3,4,4,4]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,4,4,4,4]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1,1,1],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[1,1,1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[1,1,2,2],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,1,2,4],[2]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[1,1,3,4],[4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 9
[[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] => 10
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 9
[[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] => 9
[[1,2,3,4],[3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => [8,6,5,3,1] => 9
[[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] => 9
[[1,2,3,4],[4]] => ([(0,2),(0,3),(1,8),(1,10),(2,1),(3,5),(3,7),(4,26),(5,22),(6,20),(7,12),(7,22),(8,21),(9,18),(9,19),(10,21),(10,25),(11,14),(11,15),(12,9),(12,24),(12,25),(13,27),(14,27),(15,27),(16,13),(17,14),(18,16),(19,17),(20,11),(20,17),(21,4),(21,23),(22,6),(22,24),(23,16),(23,26),(24,19),(24,20),(25,18),(25,23),(26,13),(26,15)],28) => [9,7,6,4,2] => 10
[[1,2,4,4],[3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => [9,7,5,4,1] => 10
[[1,3,4,4],[2]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,2,4,4],[4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => [10,8,5,4,1] => 11
[[1,4,4,4],[2]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[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] => 10
[[1,3,3,4],[4]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,28),(5,24),(6,22),(7,17),(8,13),(8,24),(9,23),(10,15),(10,16),(11,20),(11,21),(12,23),(12,27),(13,11),(13,26),(13,27),(14,29),(15,29),(16,7),(16,29),(18,16),(19,14),(20,19),(21,18),(22,10),(22,18),(23,4),(23,25),(24,6),(24,26),(25,19),(25,28),(26,21),(26,22),(27,20),(27,25),(28,14),(28,15),(29,17)],30) => [10,8,6,4,2] => 11
[[1,3,4,4],[4]] => ([(0,1),(0,2),(1,10),(1,12),(2,9),(2,11),(3,35),(4,33),(5,42),(6,32),(7,31),(8,15),(8,34),(9,36),(10,37),(11,16),(11,36),(12,17),(12,18),(12,37),(13,21),(13,23),(14,24),(14,38),(15,22),(15,28),(16,14),(16,40),(16,41),(17,30),(17,41),(18,26),(18,30),(20,44),(21,44),(22,43),(23,4),(23,44),(24,25),(25,23),(26,34),(27,20),(27,43),(28,35),(28,43),(29,31),(30,5),(30,39),(31,19),(32,13),(32,25),(33,19),(34,3),(34,28),(35,7),(35,29),(36,6),(36,40),(37,8),(37,26),(38,22),(38,27),(39,27),(39,42),(40,24),(40,32),(41,38),(41,39),(42,20),(42,21),(43,29),(44,33)],45) => [11,9,7,7,5,3,3] => 12
[[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] => 8
[[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] => 9
[[2,2,3,3],[4]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[2,3,3,3],[4]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[3,3,3,3],[4]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1,1],[2,4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1],[3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,2],[2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,4],[2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,3],[2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,4],[2,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[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] => 7
[[1,1,4],[2,4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[1,1,3],[3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[1,2,2],[2,4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[1,2,3],[4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => [8,5,5,1] => 9
[[1,3,4],[2,4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 9
[[1,3,3],[4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => [9,5,5,1] => 10
[[1,1,1],[2],[4]] => ([(0,1)],2) => [2] => 3
[[1,1,1],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 4
[[1,1,2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,3],[2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [4,1] => 5
[[1,1,4],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,4],[2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,3],[3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => 6
[[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] => 7
[[1,2,2],[2],[4]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => 5
[[1,2,2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 6
[[1,2,4],[2],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[2,2,2],[3],[4]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,1],[2,2],[4]] => ([(0,1)],2) => [2] => 3
[[1,1],[2,3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[2,4],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[2,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1],[3,4],[4]] => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 6
[[1,2],[2,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2],[2,4],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,2],[2,4],[4]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,2],[3,3],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[1,3],[2,4],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[2,2],[3,3],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[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] => 8
[[2,3],[3,4],[4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[1,1],[2],[3],[4]] => ([],1) => [1] => 2
[[1,2],[2],[3],[4]] => ([(0,1)],2) => [2] => 3
[[1,3],[2],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,4],[2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1,1,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[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] => 9
[[1,2,2,3,3,3]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,2,3,3,3,3]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,3,3,3,3,3]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1,1,1,1],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,3],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[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] => 6
[[1,1,1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[1,1,2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[1,2,2,2,2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[1,2,2,3,3],[3]] => ([(0,10),(0,11),(1,12),(2,17),(3,13),(4,14),(5,9),(5,12),(6,5),(7,3),(8,1),(8,17),(9,4),(9,15),(10,6),(11,2),(11,8),(12,15),(13,16),(14,16),(15,13),(15,14),(17,7)],18) => [8,6,4] => 9
[[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] => 9
[[1,2,3,3,3],[3]] => ([(0,13),(0,14),(1,16),(2,15),(3,17),(4,19),(5,18),(6,12),(6,16),(7,6),(8,2),(8,22),(9,1),(9,22),(10,4),(11,3),(11,23),(12,5),(12,20),(13,7),(14,8),(14,9),(15,23),(16,20),(17,21),(18,21),(20,17),(20,18),(21,19),(22,11),(22,15),(23,10)],24) => [9,7,5,3] => 10
[[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] => 10
[[2,2,2,2,2],[3]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1,1,1,1],[2,3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1],[3,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2],[2,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,3],[2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,3],[2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,3],[3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,2,2],[2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,3],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 6
[[1,1,3,3],[2,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 7
[[1,1,3,3],[2,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[1,2,2,2],[2,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,2,2,2],[3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[1,1,1,1],[2],[3]] => ([],1) => [1] => 2
[[1,1,1,2],[2],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,3],[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2,2],[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2,3],[2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,3,3],[2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,2,2,2],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 8
[[1,1,1],[2,2,3]] => ([(0,1)],2) => [2] => 3
[[1,1,1],[2,3,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1],[3,3,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2],[2,2,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2],[2,3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[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] => 6
[[1,2,2],[2,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 7
[[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] => 8
[[1,1,1],[2,2],[3]] => ([],1) => [1] => 2
[[1,1,1],[2,3],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,2],[2,2],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,2],[2,3],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,3],[2,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,3],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,2],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1],[2,2],[3,3]] => ([],1) => [1] => 2
[[1,1,1,1,1,1,2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,1,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,2,2,2,2,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[2,2,2,2,2,2,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => 9
[[1,1,1,1,1,1],[2]] => ([],1) => [1] => 2
[[1,1,1,1,1,2],[2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,2,2],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,2,2,2],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,2,2,2,2,2],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,1,1,1,1],[2,2]] => ([],1) => [1] => 2
[[1,1,1,1,2],[2,2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2,2],[2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2,2,2],[2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1],[2,2,2]] => ([],1) => [1] => 2
[[1,1,1,2],[2,2,2]] => ([(0,1)],2) => [2] => 3
[[1,8]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => 9
[[1],[8]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1,1,7]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1,1],[7]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[1,7],[2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[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] => 9
[[1,4],[7]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,5],[7]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,6],[7]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1],[2],[7]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[2],[4],[7]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[2],[5],[7]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[2],[6],[7]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[3],[4],[7]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[3],[5],[7]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[3],[6],[7]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[4],[5],[7]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[4],[6],[7]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[5],[6],[7]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1,1,6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[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] => 9
[[1,1,4,6]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,1,5,6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,1,6,6]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1,1],[6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[1,1,6],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[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] => 8
[[1,2,3],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[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] => 9
[[1,2,4],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,4,6],[2]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,2,5],[6]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,5,6],[2]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,6,6],[2]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,3,3],[6]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,3,4],[6]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,3,5],[6]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,4,4],[6]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,4,5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,5,5],[6]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1],[2,6]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[1,1],[2],[6]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1],[3],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 6
[[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] => 7
[[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] => 7
[[1,6],[2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[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] => 9
[[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] => 9
[[1,3],[5],[6]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,4],[5],[6]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[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] => 8
[[2,2],[4],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[2,2],[5],[6]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[2,3],[4],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[2,3],[5],[6]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[2,4],[5],[6]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[3,3],[4],[6]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[3,3],[5],[6]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[3,4],[5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[4,4],[5],[6]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1],[2],[3],[6]] => ([(0,2),(2,1)],3) => [3] => 4
[[1],[2],[4],[6]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1],[2],[5],[6]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1],[3],[4],[6]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[1,1,1,1,5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[1,1,2,3,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[1,1,2,4,5]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,1,2,5,5]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,1,3,3,5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,1,3,4,5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,1,3,5,5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,1,4,4,5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,1,4,5,5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,1,5,5,5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1,1,1],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,1,1,5],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 9
[[1,1,2,5],[4]] => ([(0,7),(0,8),(1,10),(1,16),(2,11),(3,10),(4,12),(4,13),(5,3),(6,2),(6,16),(7,9),(8,5),(9,1),(9,6),(10,14),(11,12),(11,15),(12,17),(13,17),(14,13),(14,15),(15,17),(16,4),(16,11),(16,14)],18) => [8,6,4] => 9
[[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] => 9
[[1,1,2,5],[5]] => ([(0,8),(0,9),(1,15),(1,18),(2,13),(3,11),(3,17),(4,11),(5,12),(6,4),(7,5),(7,17),(8,10),(9,6),(10,3),(10,7),(11,14),(12,16),(12,18),(14,15),(14,16),(15,19),(16,19),(17,1),(17,12),(17,14),(18,2),(18,19),(19,13)],20) => [9,7,4] => 10
[[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] => 10
[[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] => 9
[[1,1,3,4],[5]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,1,3,5],[4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => [9,7,5,4,1] => 10
[[1,1,3,5],[5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => [10,8,6,4,1] => 11
[[1,1,4,4],[5]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[1,1,4,5],[5]] => ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40) => [11,9,7,5,5,3] => 12
[[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] => 8
[[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] => 8
[[1,2,2,3],[5]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[1,2,3,5],[2]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[1,2,2,4],[5]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,2,4,5],[2]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,2,5,5],[2]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,2,3,3],[5]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,3,3,5],[2]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,2,3,4],[5]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,3,4,5],[2]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,3,5,5],[2]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,2,4,4],[5]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,4,4,5],[2]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,4,5,5],[2]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,5,5,5],[2]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,3,3,3],[5]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,3,3,4],[5]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,3,4,4],[5]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,4,4,4],[5]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1,1],[2,5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1],[3,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 8
[[1,1,2],[2,5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,1,5],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[1,2,5],[2,4]] => ([(0,7),(0,8),(1,10),(1,16),(2,11),(3,10),(4,12),(4,13),(5,3),(6,2),(6,16),(7,9),(8,5),(9,1),(9,6),(10,14),(11,12),(11,15),(12,17),(13,17),(14,13),(14,15),(15,17),(16,4),(16,11),(16,14)],18) => [8,6,4] => 9
[[1,2,5],[2,5]] => ([(0,8),(0,9),(1,15),(1,18),(2,13),(3,11),(3,17),(4,11),(5,12),(6,4),(7,5),(7,17),(8,10),(9,6),(10,3),(10,7),(11,14),(12,16),(12,18),(14,15),(14,16),(15,19),(16,19),(17,1),(17,12),(17,14),(18,2),(18,19),(19,13)],20) => [9,7,4] => 10
[[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] => 9
[[1,3,4],[2,5]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,3,5],[2,4]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => [9,7,5,4,1] => 10
[[1,3,5],[2,5]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,23),(5,24),(6,17),(7,22),(8,13),(8,24),(9,10),(9,27),(10,26),(11,16),(11,20),(12,19),(12,27),(13,18),(13,19),(15,28),(16,4),(16,28),(17,7),(18,17),(19,25),(20,22),(20,28),(21,14),(22,21),(23,14),(24,6),(24,18),(25,15),(25,20),(26,15),(26,16),(27,11),(27,25),(27,26),(28,21),(28,23)],29) => [10,8,6,4,1] => 11
[[1,4,4],[2,5]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[1,4,5],[2,5]] => ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40) => [11,9,7,5,5,3] => 12
[[1,1,1],[2],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1],[3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1],[4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,2],[2],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => 5
[[1,1,2],[3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 6
[[1,1,5],[2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 7
[[1,1,5],[2],[4]] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => 7
[[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] => 7
[[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] => 8
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 9
[[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] => 10
[[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] => 10
[[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] => 8
[[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] => 9
[[2,2,3],[4],[5]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[2,3,3],[4],[5]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[3,3,3],[4],[5]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1],[2,2],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[2,3],[5]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1],[2,5],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1],[2,4],[5]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1],[2,5],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[1,1],[2,5],[5]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[1,1],[3,3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[1,1],[4,5],[5]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[1,2],[2,3],[5]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[1,2],[2,5],[3]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 9
[[1,1],[2],[3],[5]] => ([(0,1)],2) => [2] => 3
[[1,1],[2],[4],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[3],[4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2],[2],[3],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 4
[[1,2],[2],[4],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => 5
[[1,3],[2],[3],[5]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => 5
[[1,2],[3],[4],[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,3],[2],[4],[5]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => 6
[[1,4],[2],[3],[5]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => 6
[[1,5],[2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,5],[2],[3],[5]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 7
[[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] => 7
[[2,2],[3],[4],[5]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1],[2],[3],[4],[5]] => ([],1) => [1] => 2
[[1,1,1,1,1,4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 9
[[1,1,1,3,4,4]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,1,1,4,4,4]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[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] => 8
[[1,1,2,2,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[1,1,2,2,4,4]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,1,2,3,3,4]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,1,2,3,4,4]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,1,2,4,4,4]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,1,3,3,3,4]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,1,3,3,4,4]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,1,3,4,4,4]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,1,4,4,4,4]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,1,1,1,1],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,1,4],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1,3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1,1,4],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[1,1,1,1,4],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[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] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[1,1,1,3,4],[4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 9
[[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] => 10
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 9
[[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] => 9
[[1,1,2,3,4],[3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => [8,6,5,3,1] => 9
[[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] => 9
[[1,1,2,3,4],[4]] => ([(0,2),(0,3),(1,8),(1,10),(2,1),(3,5),(3,7),(4,26),(5,22),(6,20),(7,12),(7,22),(8,21),(9,18),(9,19),(10,21),(10,25),(11,14),(11,15),(12,9),(12,24),(12,25),(13,27),(14,27),(15,27),(16,13),(17,14),(18,16),(19,17),(20,11),(20,17),(21,4),(21,23),(22,6),(22,24),(23,16),(23,26),(24,19),(24,20),(25,18),(25,23),(26,13),(26,15)],28) => [9,7,6,4,2] => 10
[[1,1,2,4,4],[3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => [9,7,5,4,1] => 10
[[1,1,3,4,4],[2]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,1,2,4,4],[4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => [10,8,5,4,1] => 11
[[1,1,4,4,4],[2]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[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] => 10
[[1,1,3,3,4],[4]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,28),(5,24),(6,22),(7,17),(8,13),(8,24),(9,23),(10,15),(10,16),(11,20),(11,21),(12,23),(12,27),(13,11),(13,26),(13,27),(14,29),(15,29),(16,7),(16,29),(18,16),(19,14),(20,19),(21,18),(22,10),(22,18),(23,4),(23,25),(24,6),(24,26),(25,19),(25,28),(26,21),(26,22),(27,20),(27,25),(28,14),(28,15),(29,17)],30) => [10,8,6,4,2] => 11
[[1,1,3,4,4],[4]] => ([(0,1),(0,2),(1,10),(1,12),(2,9),(2,11),(3,35),(4,33),(5,42),(6,32),(7,31),(8,15),(8,34),(9,36),(10,37),(11,16),(11,36),(12,17),(12,18),(12,37),(13,21),(13,23),(14,24),(14,38),(15,22),(15,28),(16,14),(16,40),(16,41),(17,30),(17,41),(18,26),(18,30),(20,44),(21,44),(22,43),(23,4),(23,44),(24,25),(25,23),(26,34),(27,20),(27,43),(28,35),(28,43),(29,31),(30,5),(30,39),(31,19),(32,13),(32,25),(33,19),(34,3),(34,28),(35,7),(35,29),(36,6),(36,40),(37,8),(37,26),(38,22),(38,27),(39,27),(39,42),(40,24),(40,32),(41,38),(41,39),(42,20),(42,21),(43,29),(44,33)],45) => [11,9,7,7,5,3,3] => 12
[[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] => 8
[[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] => 8
[[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] => 9
[[1,2,2,3,4],[2]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[1,2,2,4,4],[2]] => ([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22) => [9,6,4,3] => 10
[[1,2,2,3,3],[4]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,2,3,3,4],[2]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,2,3,4,4],[2]] => ([(0,1),(1,3),(1,4),(2,21),(3,6),(3,22),(4,5),(4,22),(5,20),(6,7),(6,23),(7,19),(8,13),(8,18),(9,14),(9,17),(10,26),(11,26),(12,27),(13,24),(14,2),(14,25),(15,13),(15,27),(16,12),(16,25),(17,8),(17,15),(17,25),(18,10),(18,24),(19,12),(19,15),(20,14),(20,16),(21,10),(21,11),(22,9),(22,20),(22,23),(23,16),(23,17),(23,19),(24,26),(25,18),(25,21),(25,27),(27,11),(27,24)],28) => [10,7,6,4,1] => 11
[[1,2,4,4,4],[2]] => ([(0,1),(1,4),(1,5),(2,23),(3,16),(4,7),(4,24),(5,6),(5,24),(6,22),(7,8),(7,25),(8,21),(9,13),(9,20),(10,15),(10,19),(11,28),(12,29),(13,26),(14,3),(14,28),(15,2),(15,27),(17,13),(17,29),(18,12),(18,27),(19,9),(19,17),(19,27),(20,14),(20,26),(21,12),(21,17),(22,15),(22,18),(23,11),(23,14),(24,10),(24,22),(24,25),(25,18),(25,19),(25,21),(26,28),(27,20),(27,23),(27,29),(28,16),(29,11),(29,26)],30) => [11,8,6,4,1] => 12
[[1,2,3,3,3],[4]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,3,3,3,4],[2]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[1,3,3,4,4],[2]] => ([(0,1),(1,4),(1,5),(2,24),(3,21),(4,7),(4,25),(5,6),(5,25),(6,23),(7,8),(7,26),(8,22),(9,16),(9,20),(10,15),(10,19),(11,29),(12,29),(14,30),(15,2),(15,28),(16,3),(16,27),(17,16),(17,30),(18,14),(18,28),(19,9),(19,17),(19,28),(20,12),(20,27),(21,13),(22,14),(22,17),(23,15),(23,18),(24,11),(24,12),(25,10),(25,23),(25,26),(26,18),(26,19),(26,22),(27,21),(27,29),(28,20),(28,24),(28,30),(29,13),(30,11),(30,27)],31) => [11,8,6,5,1] => 12
[[1,3,4,4,4],[2]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,4,4,4,4],[2]] => ([(0,2),(2,6),(2,7),(3,25),(4,28),(5,24),(6,9),(6,29),(7,10),(7,29),(8,27),(9,8),(9,30),(10,26),(11,17),(11,23),(12,18),(12,22),(13,31),(14,34),(15,1),(16,5),(16,34),(17,3),(17,33),(18,4),(18,32),(19,15),(20,17),(20,31),(21,13),(21,32),(22,11),(22,20),(22,32),(23,16),(23,33),(24,15),(25,19),(26,18),(26,21),(27,13),(27,20),(28,14),(28,16),(29,12),(29,26),(29,30),(30,21),(30,22),(30,27),(31,14),(31,33),(32,23),(32,28),(32,31),(33,25),(33,34),(34,19),(34,24)],35) => [13,9,7,5,1] => 14
[[1,3,3,3,3],[4]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1,1,1],[2,4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1],[3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,1],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1,2],[2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,4],[2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,1,3],[2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1,4],[2,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[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] => 7
[[1,1,1,4],[2,4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[1,1,1,3],[3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[1,1,2,3],[4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => [8,5,5,1] => 9
[[1,1,3,4],[2,4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 9
[[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] => 10
[[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] => 9
[[1,1,3,3],[4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => [9,5,5,1] => 10
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 9
[[1,2,3,4],[2,3]] => ([(0,9),(0,11),(1,14),(2,12),(2,13),(3,12),(3,17),(4,18),(5,15),(5,16),(6,7),(7,4),(7,13),(8,5),(8,19),(9,6),(10,2),(10,3),(10,14),(11,1),(11,10),(12,20),(13,18),(13,20),(14,8),(14,17),(15,22),(16,22),(17,19),(18,15),(18,21),(19,16),(20,21),(21,22)],23) => [8,6,5,3,1] => 9
[[1,2,3,4],[2,4]] => ([(0,2),(0,3),(1,8),(1,10),(2,1),(3,5),(3,7),(4,26),(5,22),(6,20),(7,12),(7,22),(8,21),(9,18),(9,19),(10,21),(10,25),(11,14),(11,15),(12,9),(12,24),(12,25),(13,27),(14,27),(15,27),(16,13),(17,14),(18,16),(19,17),(20,11),(20,17),(21,4),(21,23),(22,6),(22,24),(23,16),(23,26),(24,19),(24,20),(25,18),(25,23),(26,13),(26,15)],28) => [9,7,6,4,2] => 10
[[1,2,4,4],[2,3]] => ([(0,10),(0,12),(1,15),(2,13),(2,14),(3,16),(3,18),(4,20),(5,13),(5,17),(6,21),(7,8),(8,6),(8,14),(9,3),(9,24),(10,7),(11,2),(11,5),(11,15),(12,1),(12,11),(13,22),(14,21),(14,22),(15,9),(15,17),(16,20),(16,25),(17,24),(18,25),(20,19),(21,18),(21,23),(22,23),(23,25),(24,4),(24,16),(25,19)],26) => [9,7,5,4,1] => 10
[[1,2,4,4],[2,4]] => ([(0,11),(0,13),(1,19),(2,20),(3,26),(4,17),(4,22),(5,16),(6,14),(6,21),(7,14),(7,15),(8,9),(9,1),(9,15),(10,4),(10,25),(11,8),(12,6),(12,7),(12,16),(13,5),(13,12),(14,23),(15,19),(15,23),(16,10),(16,21),(17,26),(17,27),(18,20),(19,22),(19,24),(21,25),(22,27),(23,24),(24,27),(25,3),(25,17),(26,2),(26,18),(27,18)],28) => [10,8,5,4,1] => 11
[[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] => 10
[[1,3,3,4],[2,4]] => ([(0,2),(0,3),(1,9),(1,12),(2,1),(3,5),(3,8),(4,28),(5,24),(6,22),(7,17),(8,13),(8,24),(9,23),(10,15),(10,16),(11,20),(11,21),(12,23),(12,27),(13,11),(13,26),(13,27),(14,29),(15,29),(16,7),(16,29),(18,16),(19,14),(20,19),(21,18),(22,10),(22,18),(23,4),(23,25),(24,6),(24,26),(25,19),(25,28),(26,21),(26,22),(27,20),(27,25),(28,14),(28,15),(29,17)],30) => [10,8,6,4,2] => 11
[[1,3,4,4],[2,4]] => ([(0,1),(0,2),(1,10),(1,12),(2,9),(2,11),(3,35),(4,33),(5,42),(6,32),(7,31),(8,15),(8,34),(9,36),(10,37),(11,16),(11,36),(12,17),(12,18),(12,37),(13,21),(13,23),(14,24),(14,38),(15,22),(15,28),(16,14),(16,40),(16,41),(17,30),(17,41),(18,26),(18,30),(20,44),(21,44),(22,43),(23,4),(23,44),(24,25),(25,23),(26,34),(27,20),(27,43),(28,35),(28,43),(29,31),(30,5),(30,39),(31,19),(32,13),(32,25),(33,19),(34,3),(34,28),(35,7),(35,29),(36,6),(36,40),(37,8),(37,26),(38,22),(38,27),(39,27),(39,42),(40,24),(40,32),(41,38),(41,39),(42,20),(42,21),(43,29),(44,33)],45) => [11,9,7,7,5,3,3] => 12
[[1,1,1,1],[2],[4]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 4
[[1,1,1,2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,3],[2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [4,1] => 5
[[1,1,1,4],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,4],[2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,3],[3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => 6
[[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] => 7
[[1,1,2,2],[2],[4]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => 5
[[1,1,2,2],[3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 6
[[1,2,2,2],[3],[4]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[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] => 9
[[1,3,4,4],[2],[3]] => ([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19) => [9,6,4] => 10
[[1,4,4,4],[2],[3]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[2,2,2,2],[3],[4]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1,1,1],[2,2,4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1],[2,3,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1],[2,4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 6
[[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] => 7
[[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] => 8
[[1,1,2],[2,2,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[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] => 6
[[1,1,3],[2,2,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 7
[[1,1,3],[2,3,4]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 8
[[1,2,3],[2,4,4]] => ([(0,2),(1,8),(2,5),(2,6),(2,7),(3,17),(4,16),(5,12),(5,13),(6,12),(6,14),(7,13),(7,14),(8,10),(8,11),(9,18),(10,18),(11,18),(12,1),(13,4),(13,15),(14,3),(14,15),(15,16),(15,17),(16,9),(16,10),(17,9),(17,11)],19) => [8,5,5,1] => 9
[[1,3,3],[2,4,4]] => ([(0,9),(1,10),(1,18),(2,10),(2,17),(3,17),(3,18),(5,14),(6,15),(7,12),(7,13),(8,7),(9,1),(9,2),(9,3),(10,8),(11,14),(11,15),(12,19),(13,19),(14,12),(14,16),(15,13),(15,16),(16,19),(17,5),(17,11),(18,6),(18,11),(19,4)],20) => [9,5,5,1] => 10
[[1,1,1],[2,2],[4]] => ([(0,1)],2) => [2] => 3
[[1,1,1],[2,3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1],[2,4],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1],[2,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,2],[2,2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 4
[[1,1,2],[2,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2],[2,4],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,3],[2,2],[4]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [4,1] => 5
[[1,1,4],[2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,4],[2,2],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,2],[3,3],[4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[1,1,3],[2,3],[4]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => 6
[[1,1,3],[2,4],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,4],[2,3],[3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[1,1,4],[2,4],[3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[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] => 8
[[1,1,3],[3,3],[4]] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[1,2,2],[2,3],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 6
[[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] => 7
[[1,2,2],[3,3],[4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [6,1] => 7
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 8
[[1,2,3],[3,4],[4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[1,3,4],[2,4],[3]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 8
[[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] => 9
[[1,1,1],[2],[3],[4]] => ([],1) => [1] => 2
[[1,1,2],[2],[3],[4]] => ([(0,1)],2) => [2] => 3
[[1,1,3],[2],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,4],[2],[3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,2,2],[2],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2,3],[2],[3],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[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] => 6
[[1,3,3],[2],[3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 7
[[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] => 8
[[1,1],[2,2],[3,4]] => ([(0,1)],2) => [2] => 3
[[1,1],[2,2],[4,4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[2,3],[3,4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1],[2,3],[4,4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1],[3,3],[4,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,2],[2,3],[3,4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 8
[[1,1],[2,2],[3],[4]] => ([],1) => [1] => 2
[[1,1],[2,3],[3],[4]] => ([(0,1)],2) => [2] => 3
[[1,1],[2,4],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2],[2,3],[3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,2],[2,4],[3],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,3],[2,4],[3],[4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1,1,1,1,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,1,2,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,1,1,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[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] => 8
[[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] => 9
[[1,1,2,2,3,3,3]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,1,2,3,3,3,3]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,1,3,3,3,3,3]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[1,1,1,1,1,1],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,1,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,1,3],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,1,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1,2,2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1,2,3],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[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] => 6
[[1,1,1,1,3,3],[2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1,1,3,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[1,1,1,2,2,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 9
[[1,1,2,2,2,2],[3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[1,1,2,2,3,3],[3]] => ([(0,10),(0,11),(1,12),(2,17),(3,13),(4,14),(5,9),(5,12),(6,5),(7,3),(8,1),(8,17),(9,4),(9,15),(10,6),(11,2),(11,8),(12,15),(13,16),(14,16),(15,13),(15,14),(17,7)],18) => [8,6,4] => 9
[[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] => 9
[[1,1,2,3,3,3],[3]] => ([(0,13),(0,14),(1,16),(2,15),(3,17),(4,19),(5,18),(6,12),(6,16),(7,6),(8,2),(8,22),(9,1),(9,22),(10,4),(11,3),(11,23),(12,5),(12,20),(13,7),(14,8),(14,9),(15,23),(16,20),(17,21),(18,21),(20,17),(20,18),(21,19),(22,11),(22,15),(23,10)],24) => [9,7,5,3] => 10
[[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] => 10
[[1,2,2,2,2,2],[3]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[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] => 8
[[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] => 9
[[1,2,2,3,3,3],[2]] => ([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18) => [9,6,3] => 10
[[1,2,3,3,3,3],[2]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,3,3,3,3,3],[2]] => ([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21) => [11,7,3] => 12
[[2,2,2,2,2,2],[3]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => 9
[[1,1,1,1,1],[2,3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,1],[3,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2],[2,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,3],[2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2],[3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,1,3],[2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1,3],[3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,2,2],[2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2,3],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,2,2],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 6
[[1,1,1,3,3],[2,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 7
[[1,1,1,3,3],[2,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[1,1,2,2,2],[2,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 6
[[1,1,2,2,2],[3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 8
[[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] => 8
[[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] => 9
[[1,2,2,2,2],[2,3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[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] => 8
[[1,2,2,3,3],[2,3]] => ([(0,10),(0,11),(1,12),(2,17),(3,13),(4,14),(5,9),(5,12),(6,5),(7,3),(8,1),(8,17),(9,4),(9,15),(10,6),(11,2),(11,8),(12,15),(13,16),(14,16),(15,13),(15,14),(17,7)],18) => [8,6,4] => 9
[[1,2,3,3,3],[2,3]] => ([(0,13),(0,14),(1,16),(2,15),(3,17),(4,19),(5,18),(6,12),(6,16),(7,6),(8,2),(8,22),(9,1),(9,22),(10,4),(11,3),(11,23),(12,5),(12,20),(13,7),(14,8),(14,9),(15,23),(16,20),(17,21),(18,21),(20,17),(20,18),(21,19),(22,11),(22,15),(23,10)],24) => [9,7,5,3] => 10
[[1,1,1,1,1],[2],[3]] => ([],1) => [1] => 2
[[1,1,1,1,2],[2],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,3],[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2,2],[2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2,3],[2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,3,3],[2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,2,2,2],[2],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 8
[[1,2,2,2,2],[2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 10
[[1,1,1,1],[2,2,3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1],[2,3,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1],[3,3,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2],[2,2,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,3],[2,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2],[2,3,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,1,1,3],[2,2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,1,3],[2,3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,3],[3,3,3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,1,2,2],[2,2,3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,2],[2,3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[1,2,2,2],[2,3,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[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] => 8
[[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] => 8
[[1,2,2,3],[3,3,3]] => ([(0,10),(0,11),(1,12),(2,17),(3,13),(4,14),(5,9),(5,12),(6,5),(7,3),(8,1),(8,17),(9,4),(9,15),(10,6),(11,2),(11,8),(12,15),(13,16),(14,16),(15,13),(15,14),(17,7)],18) => [8,6,4] => 9
[[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] => 9
[[2,2,2,3],[3,3,3]] => ([(0,13),(0,14),(1,16),(2,15),(3,17),(4,19),(5,18),(6,12),(6,16),(7,6),(8,2),(8,22),(9,1),(9,22),(10,4),(11,3),(11,23),(12,5),(12,20),(13,7),(14,8),(14,9),(15,23),(16,20),(17,21),(18,21),(20,17),(20,18),(21,19),(22,11),(22,15),(23,10)],24) => [9,7,5,3] => 10
[[1,1,1,1],[2,2],[3]] => ([],1) => [1] => 2
[[1,1,1,1],[2,3],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2],[2,2],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2],[2,3],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,3],[2,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,3],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,2],[2,2],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2,2],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,3],[2,2],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[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] => 6
[[1,1,3,3],[2,2],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,3,3],[2,3],[3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [6,1] => 7
[[1,2,2,2],[2,3],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[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] => 8
[[1,1,1],[2,2,2],[3]] => ([],1) => [1] => 2
[[1,1,1],[2,2,3],[3]] => ([(0,1)],2) => [2] => 3
[[1,1,1],[2,3,3],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2],[2,2,3],[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,2],[2,3,3],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 5
[[1,2,2],[2,3,3],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [5,1] => 6
[[1,1,1],[2,2],[3,3]] => ([],1) => [1] => 2
[[1,1,2],[2,2],[3,3]] => ([(0,1)],2) => [2] => 3
[[1,1,3],[2,2],[3,3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,1,1,1,2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,1,1,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,1,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,2,2,2,2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,1,2,2,2,2,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1,2,2,2,2,2,2,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => [8] => 9
[[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] => 10
[[1,1,1,1,1,1,1],[2]] => ([],1) => [1] => 2
[[1,1,1,1,1,1,2],[2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,1,2,2],[2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2,2,2],[2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2,2,2,2],[2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,2,2,2,2,2],[2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,2,2,2,2,2,2],[2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [7] => 8
[[1,1,1,1,1,1],[2,2]] => ([],1) => [1] => 2
[[1,1,1,1,1,2],[2,2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,2,2],[2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2,2,2],[2,2]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,2,2,2],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,1,1],[2,2,2]] => ([],1) => [1] => 2
[[1,1,1,1,2],[2,2,2]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2,2],[2,2,2]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1],[2,2,2,2]] => ([],1) => [1] => 2
[[1]] => ([],1) => [1] => 2
[[1,1,1,1],[2,2,2],[3,3],[4]] => ([],1) => [1] => 2
[[1,1,1,2],[2,2,2],[3,3],[4]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1],[2,2,3],[3,3],[4]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2],[2,2,3],[3,3],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,3],[2,2,3],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,2,2],[2,2,3],[3,3],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,1,1],[2,2,2],[3,4],[4]] => ([(0,1)],2) => [2] => 3
[[1,1,1,2],[2,2,2],[3,4],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 4
[[1,1,1,1],[2,2,3],[3,4],[4]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,2],[2,2,3],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,2,2],[2,2,3],[3,4],[4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[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] => 7
[[1,1,1,1],[2,2,4],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[1,1,1,1],[2,3,3],[3,4],[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 8
[[1,1,2,3],[2,3,4],[3,4],[4]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 8
[[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] => 9
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => ([],1) => [1] => 2
[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,1)],2) => [2] => 3
[[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]] => ([(0,1)],2) => [2] => 3
[[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] => 4
[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 7
[[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] => 6
[[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] => 7
[[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] => 9
[[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 8
[[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] => 9
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]] => ([(0,1)],2) => [2] => 3
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 6
[[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] => 6
[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]] => ([(0,2),(2,1)],3) => [3] => 4
[[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] => 5
[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 6
[[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] => 7
[[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] => 7
[[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 8
[[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] => 7
[[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[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] => 6
[[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] => 7
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 9
[[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => [9,7,5,4,1] => 10
[[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]] => ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40) => [11,9,7,5,5,3] => 12
[[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] => 8
[[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] => 9
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([],1) => [1] => 2
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 5
[[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] => 6
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 6
[[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] => 7
[[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] => 5
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 6
[[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] => 7
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 6
[[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] => 4
[[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] => 5
[[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] => 5
[[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] => 6
[[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] => 7
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 5
[[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] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 8
[[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] => 9
[[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] => 8
[[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] => 6
[[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] => 7
[[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] => 8
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => [9,7,5,4,1] => 10
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40) => [11,9,7,5,5,3] => 12
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 6
[[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] => 4
[[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] => 5
[[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] => 5
[[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] => 6
[[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] => 7
[[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] => 6
[[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] => 4
[[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] => 5
[[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] => 5
[[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] => 6
[[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] => 7
[[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] => 5
[[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] => 6
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 6
[[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] => 7
[[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] => 7
[[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] => 7
[[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] => 5
[[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] => 6
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 6
[[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] => 7
[[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] => 8
[[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] => 7
[[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] => 8
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19) => [8,5,4,2] => 9
[[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] => 9
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23) => [9,6,5,3] => 10
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => ([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25) => [10,7,5,3] => 11
[[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] => 8
[[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] => 6
[[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] => 7
[[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] => 8
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]] => ([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20) => [8,6,4,2] => 9
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => ([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26) => [9,7,5,4,1] => 10
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => ([(0,2),(0,3),(1,9),(1,15),(2,1),(3,7),(3,8),(4,30),(5,31),(6,23),(7,16),(7,37),(8,10),(8,37),(9,11),(9,36),(10,34),(11,35),(12,25),(12,29),(13,19),(13,22),(14,21),(14,27),(15,26),(15,36),(16,26),(16,33),(17,39),(18,38),(19,12),(19,38),(20,6),(21,4),(21,39),(22,5),(22,38),(24,23),(25,28),(26,32),(27,25),(27,39),(28,24),(29,20),(30,24),(31,20),(32,17),(32,27),(33,18),(33,19),(34,18),(34,22),(35,17),(35,21),(36,14),(36,32),(36,35),(37,13),(37,33),(37,34),(38,29),(38,31),(39,28),(39,30)],40) => [11,9,7,5,5,3] => 12
[[2]] => ([(0,1)],2) => [2] => 3
[[1,1]] => ([],1) => [1] => 2
[[3]] => ([(0,2),(2,1)],3) => [3] => 4
[[1,1,1]] => ([],1) => [1] => 2
[[4]] => ([(0,3),(2,1),(3,2)],4) => [4] => 5
[[1,1,1,1]] => ([],1) => [1] => 2
[[5]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 6
[[1,1,1,1,1]] => ([],1) => [1] => 2
[[6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,2,3],[4],[5],[6]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[1,2],[3],[4],[5],[6]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1,3,4],[2,5],[6]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[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] => 10
[[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] => 7
[[1,4,5],[2,6],[3]] => ([(0,1),(1,5),(1,6),(2,24),(3,27),(4,23),(5,8),(5,28),(6,9),(6,28),(7,26),(8,7),(8,29),(9,25),(10,16),(10,22),(11,17),(11,21),(13,30),(14,33),(15,4),(15,33),(16,2),(16,32),(17,3),(17,31),(18,16),(18,30),(19,12),(20,13),(20,31),(21,10),(21,18),(21,31),(22,15),(22,32),(23,12),(24,19),(25,17),(25,20),(26,13),(26,18),(27,14),(27,15),(28,11),(28,25),(28,29),(29,20),(29,21),(29,26),(30,14),(30,32),(31,22),(31,27),(31,30),(32,24),(32,33),(33,19),(33,23)],34) => [12,9,7,5,1] => 13
[[1,4],[2,5],[3,6]] => ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20) => [10,6,4] => 11
[[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] => 7
[[1,5,6],[2],[3],[4]] => ([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20) => [10,7,3] => 11
[[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] => 10
[[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] => 7
[[1,6],[2],[3],[4],[5]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 7
[[1],[2],[3],[4],[5],[6]] => ([],1) => [1] => 2
[[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] => 8
[[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] => 9
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Generating function
$F_{(2, 2)} = q^{2} + q^{3} + q^{4}$
$F_{(2, 3)} = q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{(3, 2)} = q^{2} + 2\ q^{3} + q^{4} + q^{5}$
$F_{(2, 4)} = q^{4} + 2\ q^{5} + 2\ q^{6} + q^{7} + q^{8}$
$F_{(3, 3)} = q^{2} + q^{3} + 3\ q^{4} + 3\ q^{5} + 3\ q^{6} + q^{7} + q^{8}$
$F_{(4, 2)} = 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{(2, 5)} = q^{5} + 2\ q^{6} + 2\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{(3, 4)} = q^{3} + 2\ q^{4} + 4\ q^{5} + 4\ q^{6} + 5\ q^{7} + 4\ q^{8} + 3\ q^{9} + q^{10} + q^{11}$
$F_{(4, 3)} = q^{2} + 3\ q^{3} + 6\ q^{4} + 5\ q^{5} + 6\ q^{6} + 4\ q^{7} + 3\ q^{8} + q^{9} + q^{10}$
$F_{(5, 2)} = 2\ q^{2} + 3\ q^{3} + 2\ q^{4} + 2\ q^{5} + q^{6} + q^{7}$
$F_{(2, 6)} = q^{6} + 2\ q^{7} + 2\ q^{8} + 2\ q^{9} + 2\ q^{10} + q^{11} + q^{12}$
$F_{(3, 5)} = q^{4} + 2\ q^{5} + 5\ q^{6} + 5\ q^{7} + 7\ q^{8} + 6\ q^{9} + 6\ q^{10} + 4\ q^{11} + 3\ q^{12} + q^{13} + q^{14}$
$F_{(4, 4)} = q^{2} + q^{3} + 4\ q^{4} + 8\ q^{5} + 11\ q^{6} + 12\ q^{7} + 13\ q^{8} + 9\ q^{9} + 8\ q^{10} + 5\ q^{11} + 3\ q^{12} + q^{13} + q^{14}$
$F_{(5, 3)} = 2\ q^{2} + 4\ q^{3} + 9\ q^{4} + 8\ q^{5} + 10\ q^{6} + 8\ q^{7} + 7\ q^{8} + 4\ q^{9} + 3\ q^{10} + q^{11} + q^{12}$
$F_{(6, 2)} = 3\ q^{2} + 3\ q^{3} + 3\ q^{4} + 2\ q^{5} + 2\ q^{6} + q^{7} + q^{8}$
$F_{(7, 2)} = 3\ q^{2} + 4\ q^{3} + 3\ q^{4} + 3\ q^{5} + 2\ q^{6} + 2\ q^{7} + q^{8} + q^{9}$
$F_{(8, 2)} = 4\ q^{2} + 4\ q^{3} + 4\ q^{4} + 3\ q^{5} + 3\ q^{6} + 2\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
Description
Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition.
Put differently, this is the smallest number $n$ such that the partition fits into the triangular partition $(n-1,n-2,\dots,1)$.
Put differently, this is the smallest number $n$ such that the partition fits into the triangular partition $(n-1,n-2,\dots,1)$.
Map
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.
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.
Map
subcrystal
Description
The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.
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